Finite Group Databasebeta

← #25304547

Subgroups — #25304547

Order 11008.

1482 conjugacy classes of subgroups.

The subgroup lattice has 1278 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142944C211yesmaximal, characteristic
2#19142902C211yesmaximal, characteristic
3#19142518C211yesmaximal, characteristic, complemented
4#19142509C211yesmaximal, characteristic, complemented
5#19142416C211yesmaximal, characteristic, complemented
6#19142412C211yesmaximal, characteristic, complemented
7#19142351C211yesmaximal, characteristic, complemented
8#19142350C211yesmaximal, characteristic, complemented
9#19142182C211yesmaximal, characteristic, complemented
10#19142179C211yesmaximal, characteristic, complemented
11#19142048C211yesmaximal, characteristic, complemented
12#19142040C211yesmaximal, characteristic, complemented
13#19141941C211yesmaximal, characteristic, complemented
14#19141467C211yesmaximal, characteristic, complemented
15#19141459C211yesmaximal, characteristic, complemented
16#19141371C211yesmaximal, characteristic, complemented
17#19141369C211yesmaximal, characteristic, complemented
18#19140409C211yesmaximal, characteristic
19#19140407C211yesmaximal, characteristic
20#19139103C211yesmaximal, characteristic
21#19139099C211yesmaximal, characteristic
22#19138983C211yesmaximal, characteristic
23#19138983C211yesmaximal, characteristic
24#19138977C211yesmaximal, characteristic
25#19138977C211yesmaximal, characteristic
26#19138742C211yesmaximal, characteristic
27#19138731C211yesmaximal, characteristic
28#19137327C211yesmaximal, characteristic
29#19137324C211yesmaximal, characteristic
30#387×D43C211yesmaximal, characteristic
31C43×#2758C211yesmaximal, characteristic, complemented
32C2×#13063323C2211yescharacteristic
33C2×#13063316C2211yescharacteristic
34C2×#13063315C2211yescharacteristic
35C2×#13063315C2211yescharacteristic
36C2×#13063305C2211yescharacteristic
37C2×#13063301C2211yescharacteristic
38C2×C4⋊C4×D43C2211yescharacteristic
39C2×C4⋊C4×D43C2211yescharacteristic
40C2×C42×D43C2211yescharacteristic
41C43⋊#401C2211yescharacteristic
42C43⋊#401C2211yescharacteristic
43C43⋊#401C2211yescharacteristic
44C43⋊#401C2211yescharacteristic
45#14582841C2211yescharacteristic
46#14582841C2211yescharacteristic
47#14582841C2211yescharacteristic
48#14582841C2211yescharacteristic
49#14582841C2211yescharacteristic
50#14582841C2211yescharacteristic
51#14582840C2211yescharacteristic
52#14582840C2211yescharacteristic
53#14582840C2211yescharacteristic
54#14582840C2211yescharacteristic
55#14582840C2211yescharacteristic
56#14582840C2211yescharacteristic
57#14582839C2211yescharacteristic
58#14582839C2211yescharacteristic
59#14582839C2211yescharacteristic
60#14582838C2211yescharacteristic
61#14582837C2211yescharacteristic
62#14582837C2211yescharacteristic
63#14582837C2211yescharacteristic
64#14582833C2211yescharacteristic
65#14582833C2211yescharacteristic
66#14582833C2211yescharacteristic
67#14582833C2211yescharacteristic
68#14582833C2211yescharacteristic
69#14582833C2211yescharacteristic
70#14582833C2211yescharacteristic
71#14582833C2211yescharacteristic
72#14582832C2211yescharacteristic
73#14582832C2211yescharacteristic
74#14582831C2211yescharacteristic
75#14582831C2211yescharacteristic
76#14582830C2211yescharacteristic
77#14582830C2211yescharacteristic
78#14582830C2211yescharacteristic
79#14582830C2211yescharacteristic
80#14582820C2211yescharacteristic
81#14582819C2211yescharacteristic
82#14582818C2211yescharacteristic
83#14582806C2211yescharacteristic
84#14582805C2211yescharacteristic
85#14582803C2211yescharacteristic
86#14582803C2211yescharacteristic
87#14582797C2211yescharacteristic
88#14582797C2211yescharacteristic
89#14582796C2211yescharacteristic
90#14582796C2211yescharacteristic
91#14582796C2211yescharacteristic
92#14582796C2211yescharacteristic
93#14582796C2211yescharacteristic
94#14582796C2211yescharacteristic
95#14582796C2211yescharacteristic
96#14582795C2211yescharacteristic
97#14582794C2211yescharacteristic
98#14582794C2211yescharacteristic
99#14582794C2211yescharacteristic
100#14582786C2211yescharacteristic
101#14582786C2211yescharacteristic
102#14582786C2211yescharacteristic
103#14582785C2211yescharacteristic
104#14582785C2211yescharacteristic
105#14582784C2211yescharacteristic
106#14582784C2211yescharacteristic
107#14582784C2211yescharacteristic
108#14582784C2211yescharacteristic
109#14582784C2211yescharacteristic
110#14582783C2211yescharacteristic
111#14582783C2211yescharacteristic
112#14582783C2211yescharacteristic
113#14582783C2211yescharacteristic
114#14582783C2211yescharacteristic
115#14582783C2211yescharacteristic
116#14582782C2211yescharacteristic
117#14582782C2211yescharacteristic
118#14582782C2211yescharacteristic
119#14582782C2211yescharacteristic
120#14582782C2211yescharacteristic
121#14582782C2211yescharacteristic
122#14582782C2211yescharacteristic
123#14582781C2211yescharacteristic
124#14582781C2211yescharacteristic
125#14582781C2211yescharacteristic
126#14582781C2211yescharacteristic
127#14582781C2211yescharacteristic
128#14582781C2211yescharacteristic
129#14582781C2211yescharacteristic
130#14582781C2211yescharacteristic
131#14582780C2211yescharacteristic
132#14582780C2211yescharacteristic
133#14582780C2211yescharacteristic
134#14582780C2211yescharacteristic
135#14582780C2211yescharacteristic
136#14582773C2211yescharacteristic
137#14582773C2211yescharacteristic
138#14582773C2211yescharacteristic
139#14582773C2211yescharacteristic
140#14582773C2211yescharacteristic
141#14582773C2211yescharacteristic
142#14582770C2211yescharacteristic
143#14582770C2211yescharacteristic
144#14582770C2211yescharacteristic
145#14582770C2211yescharacteristic
146#14582770C2211yescharacteristic
147#14582770C2211yescharacteristic
148#14582768C2211yescharacteristic
149#14582766C2211yescharacteristic
150#14582766C2211yescharacteristic
151#14582764C2211yescharacteristic
152#14582763C2211yescharacteristic
153#14582763C2211yescharacteristic
154#14582761C2211yescharacteristic
155#14582761C2211yescharacteristic
156#14582761C2211yescharacteristic
157#14582761C2211yescharacteristic
158#14582758C2211yescharacteristic
159#14582758C2211yescharacteristic
160#14582758C2211yescharacteristic
161#14582758C2211yescharacteristic
162#14582758C2211yescharacteristic
163#14582758C2211yescharacteristic
164C4×(C2×D43)⋊C4C2211yescharacteristic
165C4×(C2×D43)⋊C4C2211yescharacteristic
166#14582746C2211yescharacteristic
167#14582746C2211yescharacteristic
168#95×D43C2211yescharacteristic
169#95×D43C2211yescharacteristic
170#95×D43C2211yescharacteristic
171#95×D43C2211yescharacteristic
172C43×#400C2211yescharacteristic
173C43×#400C2211yescharacteristic
174C43×#400C2211yescharacteristic
175C43×#400C2211yescharacteristic
176C43×#400C2211yescharacteristic
177C43×#395C2211yescharacteristic
178C43×#391C2211yescharacteristic
179C43×#391C2211yescharacteristic
180C43×#389C2211yescharacteristic
181C43×#387C2211yescharacteristic
182C43×#387C2211yescharacteristic
183C43×#387C2211yescharacteristic
184C43×#387C2211yescharacteristic
185C43×#383C2211yescharacteristic
186C43×#383C2211yescharacteristic
187C22×Dic86C2311yescharacteristic
188C22×C4×D43C2311yescharacteristic
189C22×C4×D43C2311yescharacteristic
190C22×C4×D43C2311yescharacteristic
191C22×C4×D43C2311yescharacteristic
192C22×C4×D43C2311yescharacteristic
193C22×C4×D43C2311yescharacteristic
194C22×C4×D43C2311yescharacteristic
195#13063323—42no—
196#13063316—42no—
197#13063315—42no—
198#13063315—42no—
199#13063305—24no—
200#13063301—24no—
201C2×C4⋊Dic43C2311yescharacteristic
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×Dic43⋊C4C2311yescharacteristic
213C2×Dic43⋊C4C2311yescharacteristic
214C2×Dic43⋊C4C2311yescharacteristic
215C2×Dic43⋊C4C2311yescharacteristic
216C2×Dic43⋊C4C2311yescharacteristic
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×Dic43⋊C4C2311yescharacteristic
237C2×Dic43⋊C4C2311yescharacteristic
238C2×Dic43⋊C4C2311yescharacteristic
239C2×Dic43⋊C4C2311yescharacteristic
240C2×Dic43⋊C4C2311yescharacteristic
241C2×Dic43⋊C4C2311yescharacteristic
242C4⋊C4×D43—24no—
243C4⋊C4×D43—42no—
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×C4×Dic43C2311yescharacteristic
253C2×C4×Dic43C2311yescharacteristic
254C2×C4×Dic43C2311yescharacteristic
255C2×C4×Dic43C2311yescharacteristic
256C2×C4×Dic43C2311yescharacteristic
257C2×C4×Dic43C2311yescharacteristic
258C2×C4×Dic43C2311yescharacteristic
259C2×C4×Dic43C2311yescharacteristic
260C2×C4×Dic43C2311yescharacteristic
261C42×D43—42no—
262C43⋊#95C2311yescharacteristic
263C43⋊#95C2311yescharacteristic
264C43⋊#95C2311yescharacteristic
265C43⋊#95C2311yescharacteristic
266C43⋊#95C2311yescharacteristic
267C43⋊#95C2311yescharacteristic
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
316C22×Q8×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×C42×C43C2311yescharacteristic
327C2×C42×C43C2311yescharacteristic
328C2×C42×C43C2311yescharacteristic
329#95×C43C2311yescharacteristic
330#95×C43C2311yescharacteristic
331#95×C43C2311yescharacteristic
332#95×C43C2311yescharacteristic
333#95×C43C2311yescharacteristic
334#95×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
351C23×D43C2411yescharacteristic
352C2×Q8×C43—22no—
353C2×Q8×C43—41no—
354C2×Q8×C43—41no—
355C22×C4×C43C2411yescharacteristic
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
370C22×Dic43C2411yescharacteristic
371C22×Dic43C2411yescharacteristic
372C22×Dic43C2411yescharacteristic
373C22×Dic43C2411yescharacteristic
374C22×Dic43C2411yescharacteristic
375C22×Dic43C2411yescharacteristic
376C22×Dic43C2411yescharacteristic
377C22×Dic43C2411yescharacteristic
378C22×Dic43C2411yescharacteristic
379C22×Dic43C2411yescharacteristic
380C22×Dic43C2411yescharacteristic
381C22×Dic43C2411yescharacteristic
382C22×Dic43C2411yescharacteristic
383C22×Dic43C2411yescharacteristic
384C22×Dic43C2411yescharacteristic
385C2×C4×D43—22no—
386C2×C4×D43—22no—
387C2×C4×D43—22no—
388C2×C4×D43—22no—
389C2×C4×D43—22no—
390C2×C4×D43—22no—
391C2×C4×D43—22no—
392C2×C4×D43—22no—
393C2×C4×D43—22no—
394C2×C4×D43—22no—
395C2×C4×D43—41no—
396C2×C4×D43—41no—
397C2×C4×D43—41no—
398C2×C4×D43—41no—
399C2×C4×D43—41no—
400C2×C4×D43—41no—
401C2×C4×D43—41no—
402C2×C4×D43—41no—
403C2×C4×D43—41no—
404C2×C4×D43—41no—
405C2×C4×D43#4114yes—
406C2×Dic86—22no—
407C2×Dic86—41no—
408C2×Dic86—41no—
409C4⋊C4×C43—22no—
410C4⋊C4×C43—22no—
411C4⋊C4×C43—41no—
412C4⋊C4×C43—41no—
413C4⋊C4×C43—41no—
414C4⋊C4×C43—41no—
415C4⋊C4×C43—41no—
416C4⋊C4×C43—41no—
417C4⋊C4×C43—41no—
418C42×C43—41no—
419C42×C43—41no—
420C42×C43—41no—
421(C2×D43)⋊C4—22no—
422(C2×D43)⋊C4—22no—
423(C2×D43)⋊C4—22no—
424(C2×D43)⋊C4—22no—
425(C2×D43)⋊C4—22no—
426(C2×D43)⋊C4—22no—
427(C2×D43)⋊C4—22no—
428(C2×D43)⋊C4—22no—
429C4⋊Dic43—22no—
430C4⋊Dic43—22no—
431C4⋊Dic43—22no—
432C4⋊Dic43—22no—
433C4⋊Dic43—22no—
434C4⋊Dic43—22no—
435C4⋊Dic43—22no—
436C4⋊Dic43—41no—
437C4⋊Dic43—41no—
438C4⋊Dic43—41no—
439C4⋊Dic43—41no—
440Dic43⋊C4—22no—
441Dic43⋊C4—22no—
442Dic43⋊C4—22no—
443Dic43⋊C4—22no—
444Dic43⋊C4—22no—
445Dic43⋊C4—22no—
446Dic43⋊C4—22no—
447Dic43⋊C4—22no—
448Dic43⋊C4—22no—
449Dic43⋊C4—22no—
450Dic43⋊C4—22no—
451Dic43⋊C4—41no—
452Dic43⋊C4—41no—
453Dic43⋊C4—41no—
454Dic43⋊C4—41no—
455Dic43⋊C4—41no—
456Dic43⋊C4—41no—
457Dic43⋊C4—41no—
458Dic43⋊C4—41no—
459Dic43⋊C4—41no—
460Dic43⋊C4—41no—
461Dic43⋊C4—41no—
462Dic43⋊C4—41no—
463Dic43⋊C4—41no—
464Dic43⋊C4—41no—
465Dic43⋊C4—41no—
466Dic43⋊C4—41no—
467Dic43⋊C4—41no—
468Dic43⋊C4—41no—
469Dic43⋊C4—41no—
470C4×Dic43—22no—
471C4×Dic43—22no—
472C4×Dic43—41no—
473C4×Dic43—41no—
474C4×Dic43—41no—
475C4×Dic43—41no—
476C4×Dic43—41no—
477C4×Dic43—41no—
478C4×Dic43—41no—
479C23×C43C2511yescharacteristic
480C22×D43—21no—
481C22×D43—21no—
482C22×D43—21no—
483C22×D43—21no—
484C22×D43C2×#4112yes—
485C22×D432−1+412yes—
486C22×D432−1+412yes—
487Q8×C43—82no—
488C2×C4×C43—21no—
489C2×C4×C43—21no—
490C2×C4×C43—21no—
491C2×C4×C43—21no—
492C2×C4×C43—21no—
493C2×C4×C43—21no—
494C2×C4×C43—21no—
495C2×C4×C43—21no—
496C2×C4×C43—21no—
497C2×C4×C43—21no—
498C2×C4×C43—21no—
499C2×C4×C43—21no—
500C2×C4×C43—21no—
501C2×C4×C43—21no—
502C2×C4×C43—21no—
503C2×C4×C43—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×C43C2×#4112yes—
533C2×Dic43—21no—
534C2×Dic43—21no—
535C2×Dic43—21no—
536C2×Dic43—21no—
537C2×Dic43—21no—
538C2×Dic43—21no—
539C2×Dic43—21no—
540C2×Dic43—21no—
541C2×Dic43—21no—
542C2×Dic43—21no—
543C2×Dic43—21no—
544C2×Dic43—21no—
545C2×Dic43—21no—
546C2×Dic43—21no—
547C2×Dic43—21no—
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×Dic43C2×#4112yes—
576C2×Dic43H(5,𝔽2)12yes—
577C2×Dic432−1+412yes—
578C4×D43—44no—
579C4×D43—44no—
580C4×D43—44no—
581C4×D43—44no—
582C4×D43—44no—
583C4×D43—82no—
584C4×D43—82no—
585Dic86—82no—
586#36762—431nomaximal, Sylow
587C22×C43C22×#4111yescharacteristic
588C22×C43C2×H(5,𝔽2)11yescharacteristic
589C22×C43C2×2−1+411yescharacteristic
590C22×C43C2×2−1+411yescharacteristic
591C22×C43C2×2−1+411yescharacteristic
592C22×C43#58511yescharacteristic
593C22×C43#58511yescharacteristic
594C2×D43—22no—
595C2×D43—22no—
596C2×D43—22no—
597C2×D43—22no—
598C2×D43—22no—
599C2×D43—22no—
600C2×D43#54114yes—
601C4×C43—22no—
602C4×C43—41no—
603C4×C43—41no—
604C4×C43—41no—
605C4×C43—41no—
606C4×C43—41no—
607C4×C43—41no—
608C4×C43—41no—
609C4×C43—41no—
610C4×C43—41no—
611C4×C43—41no—
612C4×C43—41no—
613C4×C43—41no—
614C4×C43—41no—
615C4×C43—41no—
616Dic43—22no—
617Dic43—22no—
618Dic43—22no—
619Dic43—41no—
620Dic43—41no—
621Dic43—41no—
622Dic43—41no—
623Dic43—41no—
624Dic43—41no—
625Dic43—41no—
626Dic43—41no—
627Dic43—41no—
628Dic43—41no—
629Dic43—41no—
630Dic43—41no—
631#2857—431no—
632#2851—431no—
633#2802—431no—
634#2802—431no—
635#2794—431no—
636#2794—431no—
637#2789—431no—
638#2789—431no—
639#2776—431no—
640#2776—431no—
641#2766—431no—
642#2766—431no—
643#2758—431no—
644#2758D4311yescharacteristic, complemented
645#2719—431no—
646#2719—431no—
647#2713—431no—
648#2713—431no—
649#2627—431no—
650#2627—431no—
651#2505—431no—
652#2505—431no—
653#2493—431no—
654#2493—431no—
655#2493—431no—
656#2493—431no—
657#2473—431no—
658#2473—431no—
659#2329—431no—
660#2329—431no—
661C2×#387—431no—
662C2×C43C2×#54111yescharacteristic
663C2×C43#350511yescharacteristic
664C2×C43#350711yescharacteristic
665C2×C43#353511yescharacteristic
666C2×C43#353811yescharacteristic
667C2×C43#356311yescharacteristic
668C2×C43#356411yescharacteristic
669D43—24no—
670C2×C4⋊Q8—431no—
671C2×#125—431no—
672C2×#125—431no—
673C2×#125—431no—
674C2×C22⋊Q8—431no—
675C2×C22⋊Q8—431no—
676C22×C4⋊C4—431no—
677C22×C4⋊C4—431no—
678C22×C42—431no—
679#401—431no—
680#401—431no—
681#401—431no—
682#401—431no—
683#400—431no—
684#400—431no—
685#400—431no—
686#400—431no—
687#400—431no—
688#400—431no—
689#400—431no—
690#400—431no—
691#400—431no—
692#400—431no—
693#400—431no—
694#400—431no—
695#400—431no—
696#400—431no—
697#400—431no—
698#400—431no—
699#400—431no—
700#400—431no—
701#400—431no—
702#400C2×D4311yescharacteristic
703#400C2×D4311yescharacteristic
704#400C2×D4311yescharacteristic
705#400C2×D4311yescharacteristic
706#400C2×D4311yescharacteristic
707#398—431no—
708#398—431no—
709#398—431no—
710#398—431no—
711#398—431no—
712#398—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#395—431no—
724#395—431no—
725#395—431no—
726#395C2×D4311yescharacteristic
727#391—431no—
728#391—431no—
729#391—431no—
730#391—431no—
731#391C2×D4311yescharacteristic
732#391C2×D4311yescharacteristic
733#389—431no—
734#389—431no—
735#389—431no—
736#389—431no—
737#389—431no—
738#389—431no—
739#389—431no—
740#389—431no—
741#389—431no—
742#389—431no—
743#389—431no—
744#389—431no—
745#389—431no—
746#389C2×D4311yescharacteristic
747#387—431no—
748#387—431no—
749#387—431no—
750#387—431no—
751#387—431no—
752#387—431no—
753#387—431no—
754#387—431no—
755#387—431no—
756#387—431no—
757#387—431no—
758#387—431no—
759#387—431no—
760#387—431no—
761#387—431no—
762#387—431no—
763#387—431no—
764#387—431no—
765#387—431no—
766#387—431no—
767#387—431no—
768#387—431no—
769#387—431no—
770#387—431no—
771#387—431no—
772#387—431no—
773#387—431no—
774#387—431no—
775#387—431no—
776#387—431no—
777#387—431no—
778#387—431no—
779#387—431no—
780#387—431no—
781#387—431no—
782#387—431no—
783#387C2×D4311yescharacteristic
784#387C2×D4311yescharacteristic
785#387C2×D4311yescharacteristic
786#387C2×D4311yescharacteristic
787#385—431no—
788#385—431no—
789#385—431no—
790#385—431no—
791#385—431no—
792#385—431no—
793#385—431no—
794#385—431no—
795#385—431no—
796#385—431no—
797#385—431no—
798#385—431no—
799#384—431no—
800#383—431no—
801#383—431no—
802#383C2×D4311yescharacteristic
803#383C2×D4311yescharacteristic
804#382—431no—
805#382—431no—
806#382—431no—
807#381—431no—
808#381—431no—
809#381—431no—
810#381—431no—
811#380—431no—
812#380—431no—
813#380—431no—
814#380—431no—
815#380—431no—
816#380—431no—
817C4×C22⋊C4—431no—
818C4×C22⋊C4—431no—
819C4×C22⋊C4—431no—
820C4×C22⋊C4—431no—
821C2×#95—431no—
822C2×#95—431no—
823C2×#95—431no—
824C2×#95—431no—
825C43#3676211yescharacteristic, complemented, Sylow
826C22×Q8—431no—
827C22×Q8C22×D4311yescharacteristic
828C23×C4—431no—
829C23×C4—431no—
830C23×C4—431no—
831C23×C4—431no—
832C23×C4—431no—
833C23×C4—431no—
834C23×C4—431no—
835C4⋊Q8—1722no—
836#125—1722no—
837#125—1722no—
838#125—1722no—
839C22⋊Q8—864no—
840C22⋊Q8—864no—
841C2×C4⋊C4—431no—
842C2×C4⋊C4—431no—
843C2×C4⋊C4—431no—
844C2×C4⋊C4—431no—
845C2×C4⋊C4—431no—
846C2×C4⋊C4—431no—
847C2×C4⋊C4—431no—
848C2×C4⋊C4—431no—
849C2×C4⋊C4—431no—
850C2×C4⋊C4—431no—
851C2×C4⋊C4—431no—
852C2×C4⋊C4—431no—
853C2×C4⋊C4—431no—
854C2×C4⋊C4—431no—
855C2×C4⋊C4—431no—
856C2×C4⋊C4—431no—
857C2×C4⋊C4—431no—
858C2×C4⋊C4—431no—
859C2×C4⋊C4—431no—
860C2×C4⋊C4—431no—
861C2×C4⋊C4—431no—
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—864no—
883C2×C4⋊C4—1722no—
884C2×C4⋊C4C22×D4311yescharacteristic
885C2×C4⋊C4C22×D4311yescharacteristic
886C2×C4⋊C4C22×D4311yescharacteristic
887C2×C4⋊C4C22×D4311yescharacteristic
888C2×C4⋊C4C22×D4311yescharacteristic
889C2×C4⋊C4C22×D4311yescharacteristic
890C2×C4⋊C4C22×D4311yescharacteristic
891C2×C4⋊C4C22×D4311yescharacteristic
892C2×C4⋊C4C22×D4311yescharacteristic
893C2×C22⋊C4—431no—
894C2×C22⋊C4—431no—
895C2×C22⋊C4—431no—
896C2×C22⋊C4—431no—
897C2×C22⋊C4—431no—
898C2×C22⋊C4—431no—
899C2×C22⋊C4—431no—
900C2×C22⋊C4—431no—
901C2×C42—431no—
902C2×C42—431no—
903C2×C42—431no—
904C2×C42—431no—
905C2×C42—431no—
906C2×C42—431no—
907C2×C42—431no—
908C2×C42—431no—
909C2×C42—431no—
910C2×C42—1722no—
911C2×C42C22×D4311yescharacteristic
912C2×C42C22×D4311yescharacteristic
913C2×C42C22×D4311yescharacteristic
914#95—431no—
915#95—431no—
916#95—431no—
917#95—431no—
918#95—431no—
919#95—431no—
920#95—431no—
921#95—431no—
922#95—431no—
923#95—431no—
924#95—431no—
925#95—431no—
926#95—431no—
927#95—431no—
928#95—431no—
929#95—431no—
930#95—431no—
931#95—431no—
932#95—431no—
933#95—431no—
934#95—431no—
935#95—431no—
936#95—431no—
937#95—431no—
938#95—431no—
939#95—431no—
940#95—431no—
941#95—431no—
942#95—431no—
943#95—431no—
944#95—431no—
945#95—431no—
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#95C22×D4311yescharacteristic
969#95C22×D4311yescharacteristic
970#95C22×D4311yescharacteristic
971#95C22×D4311yescharacteristic
972#95C22×D4311yescharacteristic
973#95C22×D4311yescharacteristic
974#95C22×D4311yescharacteristic
975#95C22×D4311yescharacteristic
976#95C22×D4311yescharacteristic
977#95C22×D4311yescharacteristic
978#95C22×D4311yescharacteristic
979#95C22×D4311yescharacteristic
980#95C22×D4311yescharacteristic
981#95C22×D4311yescharacteristic
982#95C22×D4311yescharacteristic
983#95C22×D4311yescharacteristic
984#95C22×D4311yescharacteristic
985#95C22×D4311yescharacteristic
986#95C22×D4311yescharacteristic
987#95C22×D4311yescharacteristic
988#95C22×D4311yescharacteristic
989#95C22×D4311yescharacteristic
990C24—431no—
991C2×Q8—22no—
992C2×Q8—41no—
993C2×Q8—41no—
994C2×Q8—862no—
995C2×Q8—1721no—
996C2×Q8—1721no—
997C22×C4—431no—
998C22×C4—431no—
999C22×C4—431no—
1000C22×C4—434no—
1001C22×C4—431no—
1002C22×C4—431no—
1003C22×C4—431no—
1004C22×C4—431no—
1005C22×C4—431no—
1006C22×C4—431no—
1007C22×C4—431no—
1008C22×C4—431no—
1009C22×C4—431no—
1010C22×C4—431no—
1011C22×C4—431no—
1012C22×C4—431no—
1013C22×C4—862no—
1014C22×C4—862no—
1015C22×C4—862no—
1016C22×C4—862no—
1017C22×C4—862no—
1018C22×C4—862no—
1019C22×C4—862no—
1020C22×C4—862no—
1021C22×C4—862no—
1022C22×C4—862no—
1023C22×C4—1721no—
1024C22×C4—1721no—
1025C22×C4—1721no—
1026C22×C4—1721no—
1027C22×C4—1721no—
1028C22×C4—1721no—
1029C22×C4—1721no—
1030C22×C4—1721no—
1031C22×C4—1721no—
1032C22×C4—1721no—
1033C22×C4C23×D4311yescharacteristic
1034C22×C4C23×D4311yescharacteristic
1035C22×C4C23×D4311yescharacteristic
1036C22×C4C23×D4311yescharacteristic
1037C22×C4C23×D4311yescharacteristic
1038C22×C4C23×D4311yescharacteristic
1039C22×C4C23×D4311yescharacteristic
1040C22×C4C23×D4311yescharacteristic
1041C22×C4C23×D4311yescharacteristic
1042C22×C4C23×D4311yescharacteristic
1043C22×C4C23×D4311yescharacteristic
1044C22×C4C23×D4311yescharacteristic
1045C22×C4C23×D4311yescharacteristic
1046C22×C4C23×D4311yescharacteristic
1047C22×C4C23×D4311yescharacteristic
1048C4⋊C4—22no—
1049C4⋊C4—22no—
1050C4⋊C4—41no—
1051C4⋊C4—41no—
1052C4⋊C4—41no—
1053C4⋊C4—41no—
1054C4⋊C4—41no—
1055C4⋊C4—41no—
1056C4⋊C4—41no—
1057C4⋊C4—862no—
1058C4⋊C4—862no—
1059C4⋊C4—862no—
1060C4⋊C4—862no—
1061C4⋊C4—862no—
1062C4⋊C4—862no—
1063C4⋊C4—862no—
1064C4⋊C4—862no—
1065C4⋊C4—862no—
1066C4⋊C4—862no—
1067C4⋊C4—862no—
1068C4⋊C4—862no—
1069C4⋊C4—862no—
1070C4⋊C4—862no—
1071C4⋊C4—862no—
1072C4⋊C4—862no—
1073C4⋊C4—862no—
1074C4⋊C4—862no—
1075C4⋊C4—1721no—
1076C4⋊C4—1721no—
1077C4⋊C4—1721no—
1078C4⋊C4—1721no—
1079C4⋊C4—1721no—
1080C4⋊C4—1721no—
1081C4⋊C4—1721no—
1082C4⋊C4—1721no—
1083C4⋊C4—1721no—
1084C4⋊C4—1721no—
1085C4⋊C4—1721no—
1086C4⋊C4—1721no—
1087C4⋊C4—1721no—
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—
1098C22⋊C4—862no—
1099C22⋊C4—862no—
1100C22⋊C4—862no—
1101C22⋊C4—862no—
1102C22⋊C4—862no—
1103C22⋊C4—862no—
1104C22⋊C4—862no—
1105C22⋊C4—862no—
1106C42—41no—
1107C42—41no—
1108C42—41no—
1109C42—862no—
1110C42—862no—
1111C42—1721no—
1112C42—1721no—
1113C42—1721no—
1114C42—1721no—
1115C42—1721no—
1116C42—1721no—
1117C42—1721no—
1118C23—432no—
1119C23—432no—
1120C23—432no—
1121C23—861no—
1122C23—861no—
1123C23—861no—
1124C23—861no—
1125C23C24×D4311yescharacteristic
1126Q8—82no—
1127Q8—3442no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—432no—
1173C2×C4—432no—
1174C2×C4—432no—
1175C2×C4—861no—
1176C2×C4—861no—
1177C2×C4—861no—
1178C2×C4—861no—
1179C2×C4—861no—
1180C2×C4—861no—
1181C2×C4—861no—
1182C2×C4—861no—
1183C2×C4—861no—
1184C2×C4—861no—
1185C2×C4—861no—
1186C2×C4—861no—
1187C2×C4—861no—
1188C2×C4—861no—
1189C2×C4—861no—
1190C2×C4—861no—
1191C2×C4—861no—
1192C2×C4—861no—
1193C2×C4—861no—
1194C2×C4—861no—
1195C2×C4—861no—
1196C2×C4—861no—
1197C2×C4—861no—
1198C2×C4—861no—
1199C2×C4—861no—
1200C2×C4—861no—
1201C2×C4—861no—
1202C2×C4—861no—
1203C2×C4—861no—
1204C2×C4—861no—
1205C2×C4—861no—
1206C2×C4—861no—
1207C2×C4—861no—
1208C2×C4—861no—
1209C2×C4—861no—
1210C2×C4—861no—
1211C2×C4—861no—
1212C2×C4—861no—
1213C2×C4—861no—
1214C2×C4—861no—
1215C2×C4—861no—
1216C2×C4—861no—
1217C2×C4—3442no—
1218C2×C4—3442no—
1219C2×C4—1724no—
1220C2×C4—1724no—
1221C2×C4—1724no—
1222C2×C4—1724no—
1223C2×C4—1724no—
1224C2×C4#41×D4312yes—
1225C22—434no—
1226C22—862no—
1227C22—862no—
1228C22—862no—
1229C22—862no—
1230C22—862no—
1231C22—862no—
1232C22C2×#41×D4311yescharacteristic
1233C22H(5,𝔽2)×D4311yescharacteristic
1234C222−1+4×D4311yescharacteristic
1235C222−1+4×D4311yescharacteristic
1236C222−1+4×D4311yescharacteristic
1237C22#1458373511yescharacteristic
1238C22#1458373511yescharacteristic
1239C4—22no—
1240C4—41no—
1241C4—41no—
1242C4—41no—
1243C4—41no—
1244C4—41no—
1245C4—41no—
1246C4—41no—
1247C4—41no—
1248C4—41no—
1249C4—41no—
1250C4—41no—
1251C4—41no—
1252C4—41no—
1253C4—41no—
1254C4—862no—
1255C4—862no—
1256C4—862no—
1257C4—1721no—
1258C4—1721no—
1259C4—1721no—
1260C4—1721no—
1261C4—1721no—
1262C4—1721no—
1263C4—1721no—
1264C4—1721no—
1265C4—1721no—
1266C4—1721no—
1267C4—1721no—
1268C4—1721no—
1269C2—864no—
1270C2#541×D4311yescharacteristic
1271C2#1914842611yescharacteristic
1272C2#1914845611yescharacteristic
1273C2#1914879711yescharacteristic
1274C2#1914883911yescharacteristic
1275C2#1914919311yescharacteristic
1276C2#1914920611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D43
commutator, socle, cosocleC23×C43C25
FittingC43×#2758C2
prime radicalC23×D43C24
hypercenter#2758D43
hypocenterC43#36762
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2758

Complements

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

NH ≅ G/Ntype
3. #19142518C2semidirect
4. #19142509C2semidirect
5. #19142416C2semidirect
6. #19142412C2semidirect
7. #19142351C2semidirect
8. #19142350C2semidirect
9. #19142182C2semidirect
10. #19142179C2semidirect
11. #19142048C2semidirect
12. #19142040C2semidirect
13. #19141941C2semidirect
14. #19141467C2semidirect
15. #19141459C2semidirect
16. #19141371C2semidirect
17. #19141369C2semidirect
31. C43×#2758C2semidirect
644. #2758D43semidirect
825. C43#36762semidirect

Maximal subgroups

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

subgroupindex
#191429442
#191429022
#191425182
#191425092
#191424162
#191424122
#191423512
#191423502
#191421822
#191421792
#191420482
#191420402
#191419412
#191414672
#191414592
#191413712
#191413692
#191404092
#191404072
#191391032
#191390992
#191389832
#191389772
#191387422
#191387312
#191373272
#191373242
#387×D432
C43×#27582
#3676243