Finite Group Databasebeta

← #25304807

Subgroups — #25304807

Order 11008.

1494 conjugacy classes of subgroups.

The subgroup lattice has 1318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142945C211yesmaximal, characteristic, complemented
2#19142935C211yesmaximal, characteristic, complemented
3#19142475C211yesmaximal, characteristic, complemented
4#19142472C211yesmaximal, characteristic, complemented
5#19142410C211yesmaximal, characteristic, complemented
6#19142378C211yesmaximal, characteristic, complemented
7#19142331C211yesmaximal, characteristic, complemented
8#19142258C211yesmaximal, characteristic
9#19142229C211yesmaximal, characteristic
10#19142101C211yesmaximal, characteristic, complemented
11#19141959C211yesmaximal, characteristic, complemented
12#19141906C211yesmaximal, characteristic, complemented
13#19141706C211yesmaximal, characteristic
14#19141419C211yesmaximal, characteristic, complemented
15#19141383C211yesmaximal, characteristic, complemented
16#19141223C211yesmaximal, characteristic
17#19141065C211yesmaximal, characteristic, complemented
18#19140514C211yesmaximal, characteristic
19#19140514C211yesmaximal, characteristic
20#19140057C211yesmaximal, characteristic, complemented
21#19140052C211yesmaximal, characteristic, complemented
22#19140026C211yesmaximal, characteristic, complemented
23#19140017C211yesmaximal, characteristic, complemented
24#19139467C211yesmaximal, characteristic, complemented
25#19139401C211yesmaximal, characteristic, complemented
26#19138812C211yesmaximal, characteristic, complemented
27#19138764C211yesmaximal, characteristic, complemented
28#19137352C211yesmaximal, characteristic, complemented
29#19137345C211yesmaximal, characteristic, complemented
30#19137031C211yesmaximal, characteristic
31C43×#2747C211yesmaximal, characteristic, complemented
32C2×#13063324C2211yescharacteristic
33C2×#13063320C2211yescharacteristic
34C2×#13063315C2211yescharacteristic
35C2×#13063304C2211yescharacteristic
36C2×#13063302C2211yescharacteristic
37C2×#13063302C2211yescharacteristic
38C2×(C22⋊D43)⋊C4C2211yescharacteristic
39C2×#13063283C2211yescharacteristic
40C22×C4×Dic43C2211yescharacteristic
41C43⋊#401C2211yescharacteristic
42#14582841C2211yescharacteristic
43#14582841C2211yescharacteristic
44#14582840C2211yescharacteristic
45#14582840C2211yescharacteristic
46#14582839C2211yescharacteristic
47#14582839C2211yescharacteristic
48#14582839C2211yescharacteristic
49#14582838C2211yescharacteristic
50#14582837C2211yescharacteristic
51#14582837C2211yescharacteristic
52#14582834C2211yescharacteristic
53#14582833C2211yescharacteristic
54#14582833C2211yescharacteristic
55#14582833C2211yescharacteristic
56#14582832C2211yescharacteristic
57#14582831C2211yescharacteristic
58#14582831C2211yescharacteristic
59#14582831C2211yescharacteristic
60#14582831C2211yescharacteristic
61#14582831C2211yescharacteristic
62#14582830C2211yescharacteristic
63#14582828C2211yescharacteristic
64#14582828C2211yescharacteristic
65#14582828C2211yescharacteristic
66#14582827C2211yescharacteristic
67#14582827C2211yescharacteristic
68#14582826C2211yescharacteristic
69#14582826C2211yescharacteristic
70#14582821C2211yescharacteristic
71#14582821C2211yescharacteristic
72#14582821C2211yescharacteristic
73#14582819C2211yescharacteristic
74#14582819C2211yescharacteristic
75#14582819C2211yescharacteristic
76#14582815C2211yescharacteristic
77#14582815C2211yescharacteristic
78#14582814C2211yescharacteristic
79#14582814C2211yescharacteristic
80#14582812C2211yescharacteristic
81#14582812C2211yescharacteristic
82#14582812C2211yescharacteristic
83#14582805C2211yescharacteristic
84#14582804C2211yescharacteristic
85#14582804C2211yescharacteristic
86#14582804C2211yescharacteristic
87#14582803C2211yescharacteristic
88#14582803C2211yescharacteristic
89#14582803C2211yescharacteristic
90#14582803C2211yescharacteristic
91#14582803C2211yescharacteristic
92#14582803C2211yescharacteristic
93#14582798C2211yescharacteristic
94#14582798C2211yescharacteristic
95#14582798C2211yescharacteristic
96#14582798C2211yescharacteristic
97#14582797C2211yescharacteristic
98#14582796C2211yescharacteristic
99#14582796C2211yescharacteristic
100#14582795C2211yescharacteristic
101#14582795C2211yescharacteristic
102#14582794C2211yescharacteristic
103#14582793C2211yescharacteristic
104#14582793C2211yescharacteristic
105#14582792C2211yescharacteristic
106#14582792C2211yescharacteristic
107#14582791C2211yescharacteristic
108#14582791C2211yescharacteristic
109#14582791C2211yescharacteristic
110#14582791C2211yescharacteristic
111#14582790C2211yescharacteristic
112#14582790C2211yescharacteristic
113#14582789C2211yescharacteristic
114#14582789C2211yescharacteristic
115#14582788C2211yescharacteristic
116#14582787C2211yescharacteristic
117#14582787C2211yescharacteristic
118#14582786C2211yescharacteristic
119#14582786C2211yescharacteristic
120#14582786C2211yescharacteristic
121#14582786C2211yescharacteristic
122#14582786C2211yescharacteristic
123#14582786C2211yescharacteristic
124#14582786C2211yescharacteristic
125#14582785C2211yescharacteristic
126#14582785C2211yescharacteristic
127#14582785C2211yescharacteristic
128#14582785C2211yescharacteristic
129#14582784C2211yescharacteristic
130#14582784C2211yescharacteristic
131#14582784C2211yescharacteristic
132#14582784C2211yescharacteristic
133#14582784C2211yescharacteristic
134#14582784C2211yescharacteristic
135#14582784C2211yescharacteristic
136#14582783C2211yescharacteristic
137#14582782C2211yescharacteristic
138#14582782C2211yescharacteristic
139#14582782C2211yescharacteristic
140#14582782C2211yescharacteristic
141#14582782C2211yescharacteristic
142#14582782C2211yescharacteristic
143#14582781C2211yescharacteristic
144#14582780C2211yescharacteristic
145#14582780C2211yescharacteristic
146#14582780C2211yescharacteristic
147#14582778C2211yescharacteristic
148#14582776C2211yescharacteristic
149#14582774C2211yescharacteristic
150#14582774C2211yescharacteristic
151#14582774C2211yescharacteristic
152#14582773C2211yescharacteristic
153#14582773C2211yescharacteristic
154#14582770C2211yescharacteristic
155#14582770C2211yescharacteristic
156#14582768C2211yescharacteristic
157#14582766C2211yescharacteristic
158#14582765C2211yescharacteristic
159#14582760C2211yescharacteristic
160#14582760C2211yescharacteristic
161#14582759C2211yescharacteristic
162#14582757C2211yescharacteristic
163#14582757C2211yescharacteristic
164C4⋊C4×Dic43C2211yescharacteristic
165C4⋊C4×Dic43C2211yescharacteristic
166C4×Dic43⋊C4C2211yescharacteristic
167C4×C4⋊Dic43C2211yescharacteristic
168#14582750C2211yescharacteristic
169C22⋊C4×Dic43C2211yescharacteristic
170#14582746C2211yescharacteristic
171#14582744C2211yescharacteristic
172C43×#400C2211yescharacteristic
173C43×#400C2211yescharacteristic
174C43×#398C2211yescharacteristic
175C43×#398C2211yescharacteristic
176C43×#397C2211yescharacteristic
177C43×#397C2211yescharacteristic
178C43×#388C2211yescharacteristic
179C43×#388C2211yescharacteristic
180C43×#387C2211yescharacteristic
181C43×#387C2211yescharacteristic
182C43×#387C2211yescharacteristic
183C43×#387C2211yescharacteristic
184C43×#385C2211yescharacteristic
185C43×#380C2211yescharacteristic
186C43×#380C2211yescharacteristic
187C22×Dic86C2311yescharacteristic
188C22×Dic86C2311yescharacteristic
189C22×Dic86C2311yescharacteristic
190C22×C22⋊D43C2311yescharacteristic
191C23×Dic43C2311yescharacteristic
192C23×Dic43C2311yescharacteristic
193C22×C4×D43C2311yescharacteristic
194#13063324—42no—
195#13063320—42no—
196#13063315—42no—
197#13063304—42no—
198#13063302—24no—
199#13063302—24no—
200(C22⋊D43)⋊C4—24no—
201#13063283—42no—
202C2×C4⋊Dic43C2311yescharacteristic
203C2×C4⋊Dic43C2311yescharacteristic
204C2×C4⋊Dic43C2311yescharacteristic
205C2×C4⋊Dic43C2311yescharacteristic
206C2×C4⋊Dic43C2311yescharacteristic
207C2×C4⋊Dic43C2311yescharacteristic
208C2×C4⋊Dic43C2311yescharacteristic
209C2×C4⋊Dic43C2311yescharacteristic
210C2×C4⋊Dic43C2311yescharacteristic
211C2×C4⋊Dic43C2311yescharacteristic
212C2×C4⋊Dic43C2311yescharacteristic
213C2×C4⋊Dic43C2311yescharacteristic
214C2×C4⋊Dic43C2311yescharacteristic
215C2×C4⋊Dic43C2311yescharacteristic
216C2×C4⋊Dic43C2311yescharacteristic
217C2×Dic43⋊C4C2311yescharacteristic
218C2×Dic43⋊C4C2311yescharacteristic
219C2×Dic43⋊C4C2311yescharacteristic
220C2×Dic43⋊C4C2311yescharacteristic
221C2×Dic43⋊C4C2311yescharacteristic
222C2×Dic43⋊C4C2311yescharacteristic
223C2×Dic43⋊C4C2311yescharacteristic
224C2×Dic43⋊C4C2311yescharacteristic
225C2×Dic43⋊C4C2311yescharacteristic
226C2×Dic43⋊C4C2311yescharacteristic
227C2×Dic43⋊C4C2311yescharacteristic
228C2×Dic43⋊C4C2311yescharacteristic
229C2×Dic43⋊C4C2311yescharacteristic
230C2×Dic43⋊C4C2311yescharacteristic
231C2×Dic43⋊C4C2311yescharacteristic
232C2×Dic43⋊C4C2311yescharacteristic
233C2×Dic43⋊C4C2311yescharacteristic
234C2×Dic43⋊C4C2311yescharacteristic
235C2×Dic43⋊C4C2311yescharacteristic
236C2×C22⋊Dic43C2311yescharacteristic
237C2×C22⋊Dic43C2311yescharacteristic
238C2×C22⋊Dic43C2311yescharacteristic
239C2×C22⋊Dic43C2311yescharacteristic
240C2×C22⋊Dic43C2311yescharacteristic
241C2×(C2×D43)⋊C4C2311yescharacteristic
242C2×(C2×D43)⋊C4C2311yescharacteristic
243C2×(C2×D43)⋊C4C2311yescharacteristic
244C2×(C2×D43)⋊C4C2311yescharacteristic
245C2×(C2×D43)⋊C4C2311yescharacteristic
246C2×(C2×D43)⋊C4C2311yescharacteristic
247C2×(C2×D43)⋊C4C2311yescharacteristic
248C2×(C2×D43)⋊C4C2311yescharacteristic
249C2×(C2×D43)⋊C4C2311yescharacteristic
250C2×(C2×D43)⋊C4C2311yescharacteristic
251C2×(C2×D43)⋊C4C2311yescharacteristic
252C2×(C2×D43)⋊C4C2311yescharacteristic
253C2×(C2×D43)⋊C4C2311yescharacteristic
254C2×C4×Dic43—42no—
255C2×C4×Dic43C2311yescharacteristic
256C2×C4×Dic43C2311yescharacteristic
257C2×C4×Dic43C2311yescharacteristic
258C2×C4×Dic43C2311yescharacteristic
259C2×C4×Dic43C2311yescharacteristic
260C2×C4×Dic43C2311yescharacteristic
261C2×C4×Dic43C2311yescharacteristic
262C2×C4×Dic43C2311yescharacteristic
263C2×C4×Dic43C2311yescharacteristic
264C2×C4×Dic43C2311yescharacteristic
265C2×C4×Dic43C2311yescharacteristic
266C2×C4×Dic43C2311yescharacteristic
267C2×C4×Dic43C2311yescharacteristic
268C43⋊#95C2311yescharacteristic
269C43⋊#95C2311yescharacteristic
270C43⋊#95C2311yescharacteristic
271C43⋊#95C2311yescharacteristic
272C43⋊#95C2311yescharacteristic
273C43⋊#95C2311yescharacteristic
274C43⋊#95C2311yescharacteristic
275C43⋊#95C2311yescharacteristic
276C43⋊#95C2311yescharacteristic
277C43⋊#95C2311yescharacteristic
278C43⋊#95C2311yescharacteristic
279C43⋊#95C2311yescharacteristic
280C43⋊#95C2311yescharacteristic
281C43⋊#95C2311yescharacteristic
282C43⋊#95C2311yescharacteristic
283C43⋊#95C2311yescharacteristic
284C43⋊#95C2311yescharacteristic
285C43⋊#95C2311yescharacteristic
286C43⋊#95C2311yescharacteristic
287C43⋊#95C2311yescharacteristic
288C43⋊#95C2311yescharacteristic
289C43⋊#95C2311yescharacteristic
290C43⋊#95C2311yescharacteristic
291C43⋊#95C2311yescharacteristic
292C43⋊#95C2311yescharacteristic
293C43⋊#95C2311yescharacteristic
294C43⋊#95C2311yescharacteristic
295C43⋊#95C2311yescharacteristic
296C43⋊#95C2311yescharacteristic
297C43⋊#95C2311yescharacteristic
298C43⋊#95C2311yescharacteristic
299C43⋊#95C2311yescharacteristic
300C43⋊#95C2311yescharacteristic
301C43⋊#95C2311yescharacteristic
302C43⋊#95C2311yescharacteristic
303C43⋊#95C2311yescharacteristic
304C43⋊#95C2311yescharacteristic
305C43⋊#95C2311yescharacteristic
306C43⋊#95C2311yescharacteristic
307C43⋊#95C2311yescharacteristic
308C43⋊#95C2311yescharacteristic
309C43⋊#95C2311yescharacteristic
310C43⋊#95C2311yescharacteristic
311C43⋊#95C2311yescharacteristic
312C43⋊#95C2311yescharacteristic
313C43⋊#95C2311yescharacteristic
314C43⋊#95C2311yescharacteristic
315C43⋊#95C2311yescharacteristic
316C23×C4×C43C2311yescharacteristic
317C2×C4⋊C4×C43C2311yescharacteristic
318C2×C4⋊C4×C43C2311yescharacteristic
319C2×C4⋊C4×C43C2311yescharacteristic
320C2×C4⋊C4×C43C2311yescharacteristic
321C2×C4⋊C4×C43C2311yescharacteristic
322C2×C4⋊C4×C43C2311yescharacteristic
323C2×C4⋊C4×C43C2311yescharacteristic
324C2×C4⋊C4×C43C2311yescharacteristic
325C2×C4⋊C4×C43C2311yescharacteristic
326C2×C4⋊C4×C43C2311yescharacteristic
327C2×C22⋊C4×C43C2311yescharacteristic
328C2×C22⋊C4×C43C2311yescharacteristic
329C2×C22⋊C4×C43C2311yescharacteristic
330C2×C22⋊C4×C43C2311yescharacteristic
331C2×C22⋊C4×C43C2311yescharacteristic
332C2×C22⋊C4×C43C2311yescharacteristic
333C2×C42×C43C2311yescharacteristic
334C2×C42×C43C2311yescharacteristic
335#95×C43C2311yescharacteristic
336#95×C43C2311yescharacteristic
337#95×C43C2311yescharacteristic
338#95×C43C2311yescharacteristic
339#95×C43C2311yescharacteristic
340#95×C43C2311yescharacteristic
341#95×C43C2311yescharacteristic
342#95×C43C2311yescharacteristic
343#95×C43C2311yescharacteristic
344#95×C43C2311yescharacteristic
345#95×C43C2311yescharacteristic
346#95×C43C2311yescharacteristic
347#95×C43C2311yescharacteristic
348#95×C43C2311yescharacteristic
349#95×C43C2311yescharacteristic
350#95×C43C2311yescharacteristic
351C24×C43C2411yescharacteristic
352C23×D43C2411yescharacteristic
353C22×C4×C43—22no—
354C22×C4×C43—22no—
355C22×C4×C43—41no—
356C22×C4×C43C2411yescharacteristic
357C22×C4×C43C2411yescharacteristic
358C22×C4×C43C2411yescharacteristic
359C22×C4×C43C2411yescharacteristic
360C22×C4×C43C2411yescharacteristic
361C22×C4×C43C2411yescharacteristic
362C22×C4×C43C2411yescharacteristic
363C22×C4×C43C2411yescharacteristic
364C22×C4×C43C2411yescharacteristic
365C22×C4×C43C2411yescharacteristic
366C22×C4×C43C2411yescharacteristic
367C22×C4×C43C2411yescharacteristic
368C22×C4×C43C2411yescharacteristic
369C22×C4×C43C2411yescharacteristic
370C2×C22⋊D43—22no—
371C2×C22⋊D43—41no—
372C2×C22⋊D43—41no—
373C22×Dic43—22no—
374C22×Dic43—41no—
375C22×Dic43—41no—
376C22×Dic43—41no—
377C22×Dic43—41no—
378C22×Dic43#4114yes—
379C22×Dic43C2411yescharacteristic
380C22×Dic43C2411yescharacteristic
381C22×Dic43C2411yescharacteristic
382C22×Dic43C2411yescharacteristic
383C22×Dic43C2411yescharacteristic
384C22×Dic43C2411yescharacteristic
385C22×Dic43C2411yescharacteristic
386C22×Dic43C2411yescharacteristic
387C22×Dic43C2411yescharacteristic
388C22×Dic43C2411yescharacteristic
389C22×Dic43C2411yescharacteristic
390C22×Dic43C2411yescharacteristic
391C22×Dic43C2411yescharacteristic
392C22×Dic43C2411yescharacteristic
393C22×Dic43C2411yescharacteristic
394C2×C4×D43—22no—
395C2×C4×D43—41no—
396C2×C4×D43—41no—
397C2×Dic86—22no—
398C2×Dic86—22no—
399C2×Dic86—22no—
400C2×Dic86—41no—
401C2×Dic86—41no—
402C2×Dic86—41no—
403C2×Dic86—41no—
404C2×Dic86—41no—
405C2×Dic86—41no—
406C4⋊C4×C43—22no—
407C4⋊C4×C43—22no—
408C4⋊C4×C43—22no—
409C4⋊C4×C43—22no—
410C4⋊C4×C43—41no—
411C4⋊C4×C43—41no—
412C4⋊C4×C43—41no—
413C4⋊C4×C43—41no—
414C4⋊C4×C43—41no—
415C4⋊C4×C43—41no—
416C22⋊C4×C43—22no—
417C22⋊C4×C43—22no—
418C22⋊C4×C43—22no—
419C22⋊C4×C43—41no—
420C22⋊C4×C43—41no—
421C22⋊C4×C43—41no—
422C42×C43—41no—
423C42×C43—41no—
424C22⋊Dic43—22no—
425C22⋊Dic43—22no—
426C22⋊Dic43—41no—
427C22⋊Dic43—41no—
428C22⋊Dic43—41no—
429(C2×D43)⋊C4—22no—
430(C2×D43)⋊C4—22no—
431(C2×D43)⋊C4—22no—
432(C2×D43)⋊C4—22no—
433(C2×D43)⋊C4—41no—
434(C2×D43)⋊C4—41no—
435(C2×D43)⋊C4—41no—
436(C2×D43)⋊C4—41no—
437(C2×D43)⋊C4—41no—
438(C2×D43)⋊C4—41no—
439(C2×D43)⋊C4—41no—
440(C2×D43)⋊C4—41no—
441(C2×D43)⋊C4—41no—
442C4⋊Dic43—22no—
443C4⋊Dic43—22no—
444C4⋊Dic43—22no—
445C4⋊Dic43—22no—
446C4⋊Dic43—22no—
447C4⋊Dic43—22no—
448C4⋊Dic43—41no—
449C4⋊Dic43—41no—
450C4⋊Dic43—41no—
451C4⋊Dic43—41no—
452C4⋊Dic43—41no—
453C4⋊Dic43—41no—
454C4⋊Dic43—41no—
455C4⋊Dic43—41no—
456C4⋊Dic43—41no—
457Dic43⋊C4—22no—
458Dic43⋊C4—22no—
459Dic43⋊C4—22no—
460Dic43⋊C4—22no—
461Dic43⋊C4—22no—
462Dic43⋊C4—22no—
463Dic43⋊C4—22no—
464Dic43⋊C4—41no—
465Dic43⋊C4—41no—
466Dic43⋊C4—41no—
467Dic43⋊C4—41no—
468Dic43⋊C4—41no—
469Dic43⋊C4—41no—
470Dic43⋊C4—41no—
471Dic43⋊C4—41no—
472Dic43⋊C4—41no—
473Dic43⋊C4—41no—
474Dic43⋊C4—41no—
475Dic43⋊C4—41no—
476C4×Dic43—22no—
477C4×Dic43—22no—
478C4×Dic43—22no—
479C4×Dic43—41no—
480C4×Dic43—41no—
481C4×Dic43—41no—
482C4×Dic43—41no—
483C4×Dic43—41no—
484C4×Dic43—41no—
485C4×Dic43—41no—
486C4×Dic43—41no—
487C4×Dic43—41no—
488C4×Dic43—41no—
489C23×C43—21no—
490C23×C43—21no—
491C23×C43—21no—
492C23×C43—21no—
493C23×C43—21no—
494C23×C43—21no—
495C23×C43C2×#4112yes—
496C23×C43C2511yescharacteristic
497C22×D43—21no—
498C22×D43—21no—
499C22×D43—21no—
500C22×D43—21no—
501C22×D43—21no—
502C22×D43—21no—
503C22×D43—21no—
504C2×C4×C43—21no—
505C2×C4×C43—21no—
506C2×C4×C43—21no—
507C2×C4×C43—21no—
508C2×C4×C43—21no—
509C2×C4×C43—21no—
510C2×C4×C43—21no—
511C2×C4×C43—21no—
512C2×C4×C43—21no—
513C2×C4×C43—21no—
514C2×C4×C43—21no—
515C2×C4×C43—21no—
516C2×C4×C43—21no—
517C2×C4×C43—21no—
518C2×C4×C43—21no—
519C2×C4×C43—21no—
520C2×C4×C43—21no—
521C2×C4×C43—21no—
522C2×C4×C43—21no—
523C2×C4×C43—21no—
524C2×C4×C43—21no—
525C2×C4×C43—21no—
526C2×C4×C43—21no—
527C2×C4×C43—21no—
528C2×C4×C43—21no—
529C2×C4×C43—21no—
530C2×C4×C43—21no—
531C2×C4×C43—21no—
532C2×C4×C43—21no—
533C2×C4×C43—21no—
534C2×C4×C43—21no—
535C2×C4×C43—21no—
536C2×C4×C43—21no—
537C2×C4×C43—21no—
538C2×C4×C43—21no—
539C2×C4×C43—21no—
540C2×C4×C43—21no—
541C2×C4×C43—21no—
542C2×C4×C43—21no—
543C2×C4×C43—21no—
544C2×C4×C43—44no—
545C2×C4×C43H(5,𝔽2)12yes—
546C2×C4×C432−1+412yes—
547C22⋊D43—44no—
548C2×Dic43—21no—
549C2×Dic43—21no—
550C2×Dic43—21no—
551C2×Dic43—21no—
552C2×Dic43—21no—
553C2×Dic43—21no—
554C2×Dic43—21no—
555C2×Dic43—21no—
556C2×Dic43—21no—
557C2×Dic43—21no—
558C2×Dic43—21no—
559C2×Dic43—21no—
560C2×Dic43—21no—
561C2×Dic43—21no—
562C2×Dic43—21no—
563C2×Dic43—21no—
564C2×Dic43—21no—
565C2×Dic43—21no—
566C2×Dic43—21no—
567C2×Dic43—21no—
568C2×Dic43—21no—
569C2×Dic43—21no—
570C2×Dic43—21no—
571C2×Dic43—21no—
572C2×Dic43—21no—
573C2×Dic43—21no—
574C2×Dic43—21no—
575C2×Dic43—21no—
576C2×Dic43—21no—
577C2×Dic43—21no—
578C2×Dic43—21no—
579C2×Dic43—21no—
580C2×Dic43—21no—
581C2×Dic43—21no—
582C2×Dic43—21no—
583C2×Dic43—21no—
584C2×Dic43—21no—
585C2×Dic43—21no—
586C2×Dic43—21no—
587C2×Dic43—21no—
588C2×Dic43—21no—
589C2×Dic43—21no—
590C2×Dic43—44no—
591C2×Dic43—44no—
592C2×Dic43C2×#4112yes—
593C2×Dic43C2×#4112yes—
594C2×Dic432−1+412yes—
595C4×D43—44no—
596Dic86—82no—
597Dic86—82no—
598Dic86—82no—
599#36772—431nomaximal, Sylow
600C22×C43—22no—
601C22×C43—22no—
602C22×C43—22no—
603C22×C43—41no—
604C22×C43—41no—
605C22×C43—41no—
606C22×C43—41no—
607C22×C43C22×#4111yescharacteristic
608C22×C43C2×H(5,𝔽2)11yescharacteristic
609C22×C43C2×2−1+411yescharacteristic
610C22×C43C2×2−1+411yescharacteristic
611C22×C43#58511yescharacteristic
612C22×C43#58511yescharacteristic
613C22×C43#58511yescharacteristic
614C2×D43—41no—
615C2×D43—41no—
616C2×D43—41no—
617C2×D43—41no—
618C2×D43—41no—
619C2×D43—41no—
620C2×D43—41no—
621C4×C43—22no—
622C4×C43—22no—
623C4×C43—41no—
624C4×C43—41no—
625C4×C43—41no—
626C4×C43—41no—
627C4×C43—41no—
628C4×C43—41no—
629C4×C43—41no—
630C4×C43—41no—
631C4×C43—41no—
632C4×C43—41no—
633C4×C43—41no—
634C4×C43—41no—
635Dic43—22no—
636Dic43—22no—
637Dic43—22no—
638Dic43—41no—
639Dic43—41no—
640Dic43—41no—
641Dic43—41no—
642Dic43—41no—
643Dic43—41no—
644Dic43—41no—
645Dic43—41no—
646Dic43—41no—
647Dic43—41no—
648Dic43—41no—
649Dic43—41no—
650#2857—431no—
651#2855—431no—
652#2799—431no—
653#2798—431no—
654#2793—431no—
655#2791—431no—
656#2787—431no—
657#2781—431no—
658#2779—431no—
659#2770—431no—
660#2759—431no—
661#2755—431no—
662#2747D4311yescharacteristic, complemented
663#2741—431no—
664#2716—431no—
665#2713—431no—
666#2702—431no—
667#2690—431no—
668#2638—431no—
669#2638—431no—
670#2590—431no—
671#2589—431no—
672#2588—431no—
673#2587—431no—
674#2533—431no—
675#2528—431no—
676#2478—431no—
677#2475—431no—
678#2332—431no—
679#2332—431no—
680#2290—431no—
681C2×C43—42no—
682C2×C43#345511yescharacteristic
683C2×C43#350511yescharacteristic
684C2×C43#350911yescharacteristic
685C2×C43#353511yescharacteristic
686C2×C43#354111yescharacteristic
687C2×C43#355711yescharacteristic
688C2×C43#356511yescharacteristic
689D43—81no—
690C2×C4⋊Q8—431no—
691C2×#126—431no—
692C2×#125—431no—
693C2×C22⋊Q8—431no—
694C2×C22⋊Q8—431no—
695C2×C22⋊Q8—431no—
696C2×C4×D4—431no—
697C2×#117—431no—
698C22×C42—431no—
699#401—431no—
700#400—431no—
701#400—431no—
702#400—431no—
703#400—431no—
704#400—431no—
705#400—431no—
706#400—431no—
707#400—431no—
708#400—431no—
709#400—431no—
710#400C2×D4311yescharacteristic
711#400C2×D4311yescharacteristic
712#399—431no—
713#398—431no—
714#398—431no—
715#398—431no—
716#398—431no—
717#398—431no—
718#398—431no—
719#398—431no—
720#398—431no—
721#398—431no—
722#398—431no—
723#398C2×D4311yescharacteristic
724#398C2×D4311yescharacteristic
725#397—431no—
726#397—431no—
727#397—431no—
728#397—431no—
729#397—431no—
730#397—431no—
731#397—431no—
732#397C2×D4311yescharacteristic
733#397C2×D4311yescharacteristic
734#396—431no—
735#396—431no—
736#396—431no—
737#395—431no—
738#395—431no—
739#395—431no—
740#394—431no—
741#394—431no—
742#394—431no—
743#394—431no—
744#393—431no—
745#393—431no—
746#393—431no—
747#391—431no—
748#391—431no—
749#391—431no—
750#391—431no—
751#391—431no—
752#391—431no—
753#391—431no—
754#391—431no—
755#391—431no—
756#391—431no—
757#389—431no—
758#389—431no—
759#389—431no—
760#389—431no—
761#389—431no—
762#389—431no—
763#389—431no—
764#389—431no—
765#389—431no—
766#389—431no—
767#388—431no—
768#388—431no—
769#388—431no—
770#388—431no—
771#388—431no—
772#388—431no—
773#388—431no—
774#388—431no—
775#388—431no—
776#388—431no—
777#388—431no—
778#388—431no—
779#388—431no—
780#388—431no—
781#388—431no—
782#388C2×D4311yescharacteristic
783#388C2×D4311yescharacteristic
784#387—431no—
785#387—431no—
786#387—431no—
787#387—431no—
788#387—431no—
789#387—431no—
790#387—431no—
791#387—431no—
792#387—431no—
793#387—431no—
794#387—431no—
795#387—431no—
796#387—431no—
797#387—431no—
798#387—431no—
799#387—431no—
800#387—431no—
801#387—431no—
802#387—431no—
803#387—431no—
804#387—431no—
805#387—431no—
806#387—431no—
807#387—431no—
808#387—431no—
809#387—431no—
810#387—431no—
811#387—431no—
812#387—431no—
813#387C2×D4311yescharacteristic
814#387C2×D4311yescharacteristic
815#387C2×D4311yescharacteristic
816#387C2×D4311yescharacteristic
817#386—431no—
818#386—431no—
819#385—431no—
820#385—431no—
821#385—431no—
822#385—431no—
823#385—431no—
824#385—431no—
825#385—431no—
826#385C2×D4311yescharacteristic
827#384—431no—
828#383—431no—
829#382—431no—
830#381—431no—
831#381—431no—
832#380—431no—
833#380—431no—
834#380—431no—
835#380C2×D4311yescharacteristic
836#380C2×D4311yescharacteristic
837C4×C4⋊C4—431no—
838C4×C4⋊C4—431no—
839C4×C4⋊C4—431no—
840C4×C4⋊C4—431no—
841C4×C4⋊C4—431no—
842C4×C22⋊C4—431no—
843C4×C22⋊C4—431no—
844#376—431no—
845C43#3677211yescharacteristic, complemented, Sylow
846C22×Q8—431no—
847C22×Q8—431no—
848C22×Q8—431no—
849C22×D4—431no—
850C23×C4—431no—
851C23×C4—431no—
852C23×C4—431no—
853C23×C4C22×D4311yescharacteristic
854C4⋊Q8—1722no—
855#126—1722no—
856#125—1722no—
857C22⋊Q8—864no—
858C22⋊Q8—864no—
859C22⋊Q8—1722no—
860C4×D4—864no—
861#117—1722no—
862C2×C4⋊C4—431no—
863C2×C4⋊C4—431no—
864C2×C4⋊C4—431no—
865C2×C4⋊C4—431no—
866C2×C4⋊C4—431no—
867C2×C4⋊C4—431no—
868C2×C4⋊C4—431no—
869C2×C4⋊C4—431no—
870C2×C4⋊C4—431no—
871C2×C4⋊C4—431no—
872C2×C4⋊C4—431no—
873C2×C4⋊C4—431no—
874C2×C4⋊C4—431no—
875C2×C4⋊C4—431no—
876C2×C4⋊C4—431no—
877C2×C4⋊C4—431no—
878C2×C4⋊C4—431no—
879C2×C4⋊C4—431no—
880C2×C4⋊C4—431no—
881C2×C4⋊C4—431no—
882C2×C4⋊C4—431no—
883C2×C4⋊C4—431no—
884C2×C4⋊C4—431no—
885C2×C4⋊C4—431no—
886C2×C4⋊C4—431no—
887C2×C4⋊C4—431no—
888C2×C4⋊C4—431no—
889C2×C4⋊C4—431no—
890C2×C4⋊C4—431no—
891C2×C4⋊C4—431no—
892C2×C4⋊C4—431no—
893C2×C4⋊C4—431no—
894C2×C4⋊C4—431no—
895C2×C4⋊C4—431no—
896C2×C4⋊C4C22×D4311yescharacteristic
897C2×C4⋊C4C22×D4311yescharacteristic
898C2×C4⋊C4C22×D4311yescharacteristic
899C2×C4⋊C4C22×D4311yescharacteristic
900C2×C4⋊C4C22×D4311yescharacteristic
901C2×C4⋊C4C22×D4311yescharacteristic
902C2×C4⋊C4C22×D4311yescharacteristic
903C2×C4⋊C4C22×D4311yescharacteristic
904C2×C4⋊C4C22×D4311yescharacteristic
905C2×C4⋊C4C22×D4311yescharacteristic
906C2×C22⋊C4—431no—
907C2×C22⋊C4—431no—
908C2×C22⋊C4—431no—
909C2×C22⋊C4—431no—
910C2×C22⋊C4—431no—
911C2×C22⋊C4—431no—
912C2×C22⋊C4—431no—
913C2×C22⋊C4—431no—
914C2×C22⋊C4—431no—
915C2×C22⋊C4—431no—
916C2×C22⋊C4—431no—
917C2×C22⋊C4—431no—
918C2×C22⋊C4—431no—
919C2×C22⋊C4—431no—
920C2×C22⋊C4—431no—
921C2×C22⋊C4—431no—
922C2×C22⋊C4—431no—
923C2×C22⋊C4—431no—
924C2×C22⋊C4C22×D4311yescharacteristic
925C2×C22⋊C4C22×D4311yescharacteristic
926C2×C22⋊C4C22×D4311yescharacteristic
927C2×C22⋊C4C22×D4311yescharacteristic
928C2×C22⋊C4C22×D4311yescharacteristic
929C2×C22⋊C4C22×D4311yescharacteristic
930C2×C42—431no—
931C2×C42—431no—
932C2×C42—431no—
933C2×C42—431no—
934C2×C42—431no—
935C2×C42—431no—
936C2×C42—431no—
937C2×C42—431no—
938C2×C42—431no—
939C2×C42—431no—
940C2×C42—431no—
941C2×C42—431no—
942C2×C42—431no—
943C2×C42—1722no—
944C2×C42C22×D4311yescharacteristic
945C2×C42C22×D4311yescharacteristic
946#95—431no—
947#95—431no—
948#95—431no—
949#95—431no—
950#95—431no—
951#95—431no—
952#95—431no—
953#95—431no—
954#95—431no—
955#95—431no—
956#95—431no—
957#95—431no—
958#95—431no—
959#95—431no—
960#95—431no—
961#95—431no—
962#95—431no—
963#95—431no—
964#95—431no—
965#95—431no—
966#95—431no—
967#95—431no—
968#95—431no—
969#95—431no—
970#95—431no—
971#95—431no—
972#95—431no—
973#95—431no—
974#95—431no—
975#95—431no—
976#95—431no—
977#95—431no—
978#95—431no—
979#95—431no—
980#95—431no—
981#95—431no—
982#95—431no—
983#95—431no—
984#95—431no—
985#95—431no—
986#95—431no—
987#95—431no—
988#95—431no—
989#95—431no—
990#95—431no—
991#95—431no—
992#95—431no—
993#95—431no—
994#95C22×D4311yescharacteristic
995#95C22×D4311yescharacteristic
996#95C22×D4311yescharacteristic
997#95C22×D4311yescharacteristic
998#95C22×D4311yescharacteristic
999#95C22×D4311yescharacteristic
1000#95C22×D4311yescharacteristic
1001#95C22×D4311yescharacteristic
1002#95C22×D4311yescharacteristic
1003#95C22×D4311yescharacteristic
1004#95C22×D4311yescharacteristic
1005#95C22×D4311yescharacteristic
1006#95C22×D4311yescharacteristic
1007#95C22×D4311yescharacteristic
1008#95C22×D4311yescharacteristic
1009#95C22×D4311yescharacteristic
1010C24—431no—
1011C24C23×D4311yescharacteristic
1012C2×Q8—862no—
1013C2×Q8—862no—
1014C2×Q8—862no—
1015C2×Q8—1721no—
1016C2×Q8—1721no—
1017C2×Q8—1721no—
1018C2×Q8—1721no—
1019C2×Q8—1721no—
1020C2×Q8—1721no—
1021C2×D4—862no—
1022C2×D4—1721no—
1023C2×D4—1721no—
1024C22×C4—22no—
1025C22×C4—22no—
1026C22×C4—41no—
1027C22×C4—431no—
1028C22×C4—431no—
1029C22×C4—431no—
1030C22×C4—434no—
1031C22×C4—431no—
1032C22×C4—431no—
1033C22×C4—431no—
1034C22×C4—431no—
1035C22×C4—431no—
1036C22×C4—431no—
1037C22×C4—431no—
1038C22×C4—431no—
1039C22×C4—431no—
1040C22×C4—431no—
1041C22×C4—431no—
1042C22×C4—431no—
1043C22×C4—862no—
1044C22×C4—862no—
1045C22×C4—1721no—
1046C22×C4—1721no—
1047C22×C4—1721no—
1048C22×C4—1721no—
1049C22×C4—1721no—
1050C22×C4—1721no—
1051C22×C4C23×D4311yescharacteristic
1052C22×C4C23×D4311yescharacteristic
1053C22×C4C23×D4311yescharacteristic
1054C22×C4C23×D4311yescharacteristic
1055C22×C4C23×D4311yescharacteristic
1056C22×C4C23×D4311yescharacteristic
1057C22×C4C23×D4311yescharacteristic
1058C22×C4C23×D4311yescharacteristic
1059C22×C4C23×D4311yescharacteristic
1060C22×C4C23×D4311yescharacteristic
1061C22×C4C23×D4311yescharacteristic
1062C22×C4C23×D4311yescharacteristic
1063C22×C4C23×D4311yescharacteristic
1064C22×C4C23×D4311yescharacteristic
1065C4⋊C4—22no—
1066C4⋊C4—22no—
1067C4⋊C4—22no—
1068C4⋊C4—22no—
1069C4⋊C4—41no—
1070C4⋊C4—41no—
1071C4⋊C4—41no—
1072C4⋊C4—41no—
1073C4⋊C4—41no—
1074C4⋊C4—41no—
1075C4⋊C4—862no—
1076C4⋊C4—862no—
1077C4⋊C4—862no—
1078C4⋊C4—862no—
1079C4⋊C4—862no—
1080C4⋊C4—862no—
1081C4⋊C4—862no—
1082C4⋊C4—862no—
1083C4⋊C4—862no—
1084C4⋊C4—862no—
1085C4⋊C4—862no—
1086C4⋊C4—862no—
1087C4⋊C4—862no—
1088C4⋊C4—1721no—
1089C4⋊C4—1721no—
1090C4⋊C4—1721no—
1091C4⋊C4—1721no—
1092C4⋊C4—1721no—
1093C4⋊C4—1721no—
1094C4⋊C4—1721no—
1095C4⋊C4—1721no—
1096C4⋊C4—1721no—
1097C4⋊C4—1721no—
1098C4⋊C4—1721no—
1099C4⋊C4—1721no—
1100C4⋊C4—1721no—
1101C4⋊C4—1721no—
1102C4⋊C4—1721no—
1103C4⋊C4—1721no—
1104C4⋊C4—1721no—
1105C4⋊C4—1721no—
1106C4⋊C4—1721no—
1107C4⋊C4—1721no—
1108C4⋊C4—1721no—
1109C22⋊C4—22no—
1110C22⋊C4—22no—
1111C22⋊C4—22no—
1112C22⋊C4—41no—
1113C22⋊C4—41no—
1114C22⋊C4—41no—
1115C22⋊C4—862no—
1116C22⋊C4—862no—
1117C22⋊C4—862no—
1118C22⋊C4—862no—
1119C22⋊C4—862no—
1120C22⋊C4—862no—
1121C22⋊C4—1721no—
1122C22⋊C4—1721no—
1123C22⋊C4—1721no—
1124C22⋊C4—1721no—
1125C22⋊C4—1721no—
1126C22⋊C4—1721no—
1127C22⋊C4—1721no—
1128C22⋊C4—1721no—
1129C22⋊C4—1721no—
1130C22⋊C4—1721no—
1131C22⋊C4—1721no—
1132C22⋊C4—1721no—
1133C42—41no—
1134C42—41no—
1135C42—862no—
1136C42—862no—
1137C42—862no—
1138C42—1721no—
1139C42—1721no—
1140C42—1721no—
1141C42—1721no—
1142C42—1721no—
1143C42—1721no—
1144C42—1721no—
1145C42—1721no—
1146C42—1721no—
1147C42—1721no—
1148C23—21no—
1149C23—21no—
1150C23—21no—
1151C23—21no—
1152C23—21no—
1153C23—21no—
1154C23—861no—
1155C23—861no—
1156C23—861no—
1157C23—861no—
1158C23—861no—
1159C23—861no—
1160C23—861no—
1161C23#41×D4312yes—
1162C23C24×D4311yescharacteristic
1163Q8—3442no—
1164Q8—3442no—
1165Q8—3442no—
1166D4—1724no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—44no—
1208C2×C4—432no—
1209C2×C4—432no—
1210C2×C4—432no—
1211C2×C4—861no—
1212C2×C4—861no—
1213C2×C4—861no—
1214C2×C4—861no—
1215C2×C4—861no—
1216C2×C4—861no—
1217C2×C4—861no—
1218C2×C4—861no—
1219C2×C4—861no—
1220C2×C4—861no—
1221C2×C4—861no—
1222C2×C4—861no—
1223C2×C4—861no—
1224C2×C4—861no—
1225C2×C4—861no—
1226C2×C4—861no—
1227C2×C4—861no—
1228C2×C4—861no—
1229C2×C4—861no—
1230C2×C4—861no—
1231C2×C4—861no—
1232C2×C4—861no—
1233C2×C4—861no—
1234C2×C4—861no—
1235C2×C4—861no—
1236C2×C4—861no—
1237C2×C4—861no—
1238C2×C4—861no—
1239C2×C4—861no—
1240C2×C4—861no—
1241C2×C4—861no—
1242C2×C4—861no—
1243C2×C4—861no—
1244C2×C4—861no—
1245C2×C4—861no—
1246C2×C4—861no—
1247C2×C4—861no—
1248C2×C4—861no—
1249C2×C4—861no—
1250C2×C4—861no—
1251C2×C4—861no—
1252C2×C4—861no—
1253C2×C4—1724no—
1254C2×C4—1724no—
1255C2×C4—1724no—
1256C2×C4#1306337112yes—
1257C2×C4#1306337212yes—
1258C22—22no—
1259C22—22no—
1260C22—22no—
1261C22—41no—
1262C22—41no—
1263C22—41no—
1264C22—41no—
1265C22—1721no—
1266C22—1721no—
1267C22—1721no—
1268C22—1721no—
1269C22—1721no—
1270C22—1721no—
1271C22—1721no—
1272C22C2×#41×D4311yescharacteristic
1273C22C2×#1306337111yescharacteristic
1274C222−1+4×D4311yescharacteristic
1275C22C2×#1306337211yescharacteristic
1276C22#1458373411yescharacteristic
1277C22#1458373411yescharacteristic
1278C22#1458373611yescharacteristic
1279C4—22no—
1280C4—22no—
1281C4—41no—
1282C4—41no—
1283C4—41no—
1284C4—41no—
1285C4—41no—
1286C4—41no—
1287C4—41no—
1288C4—41no—
1289C4—41no—
1290C4—41no—
1291C4—41no—
1292C4—41no—
1293C4—862no—
1294C4—862no—
1295C4—862no—
1296C4—1721no—
1297C4—1721no—
1298C4—1721no—
1299C4—1721no—
1300C4—1721no—
1301C4—1721no—
1302C4—1721no—
1303C4—1721no—
1304C4—1721no—
1305C4—1721no—
1306C4—1721no—
1307C4—1721no—
1308C2—42no—
1309C2—3441no—
1310C2#1914798111yescharacteristic
1311C2#1914842411yescharacteristic
1312C2#1914847311yescharacteristic
1313C2#1914880011yescharacteristic
1314C2#1914889411yescharacteristic
1315C2#1914909411yescharacteristic
1316C2#1914922911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D43
commutator, socle, cosocleC23×C43C25
FittingC43×#2747C2
prime radicalC22×C22⋊D43C23
hypercenter#2747D43
hypocenterC43#36772
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2747

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #19142945C2semidirect
2. #19142935C2semidirect
3. #19142475C2semidirect
4. #19142472C2semidirect
5. #19142410C2semidirect
6. #19142378C2semidirect
7. #19142331C2semidirect
10. #19142101C2semidirect
11. #19141959C2semidirect
12. #19141906C2semidirect
14. #19141419C2semidirect
15. #19141383C2semidirect
17. #19141065C2semidirect
20. #19140057C2semidirect
21. #19140052C2semidirect
22. #19140026C2semidirect
23. #19140017C2semidirect
24. #19139467C2semidirect
25. #19139401C2semidirect
26. #19138812C2semidirect
27. #19138764C2semidirect
28. #19137352C2semidirect
29. #19137345C2semidirect
31. C43×#2747C2semidirect
662. #2747D43semidirect
845. C43#36772semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#191429452
#191429352
#191424752
#191424722
#191424102
#191423782
#191423312
#191422582
#191422292
#191421012
#191419592
#191419062
#191417062
#191414192
#191413832
#191412232
#191410652
#191405142
#191400572
#191400522
#191400262
#191400172
#191394672
#191394012
#191388122
#191387642
#191373522
#191373452
#191370312
C43×#27472
#3677243