Finite Group Databasebeta

← #25303314

Subgroups — #25303314

Order 11008.

1356 conjugacy classes of subgroups.

The subgroup lattice has 1238 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142845C211yesmaximal, characteristic, complemented
2#19142840C211yesmaximal, characteristic, complemented
3#19142837C211yesmaximal, characteristic, complemented
4#19142834C211yesmaximal, characteristic, complemented
5#19142796C211yesmaximal, characteristic
6#19142795C211yesmaximal, characteristic
7#19142789C211yesmaximal, characteristic
8#19142788C211yesmaximal, characteristic
9#19142774C211yesmaximal, characteristic, complemented
10#19142772C211yesmaximal, characteristic, complemented
11#19142771C211yesmaximal, characteristic, complemented
12#19142768C211yesmaximal, characteristic, complemented
13#19142754C211yesmaximal, characteristic
14#19142751C211yesmaximal, characteristic
15#19142744C211yesmaximal, characteristic
16#19137901C211yesmaximal, characteristic, complemented
17#19137901C211yesmaximal, characteristic, complemented
18#19137901C211yesmaximal, characteristic, complemented
19#19137899C211yesmaximal, characteristic, complemented
20#19137899C211yesmaximal, characteristic, complemented
21#19137897C211yesmaximal, characteristic
22#19137892C211yesmaximal, characteristic
23#19137892C211yesmaximal, characteristic
24#19137892C211yesmaximal, characteristic
25#19137885C211yesmaximal, characteristic, complemented
26#19137870C211yesmaximal, characteristic
27#19137862C211yesmaximal, characteristic
28#19137089C211yesmaximal, characteristic
29#19137070C211yesmaximal, characteristic, complemented
30#19137068C211yesmaximal, characteristic, complemented
31C43×#2831C211yesmaximal, characteristic
32C2×Q8×Dic43C2211yescharacteristic
33C2×#13063290C2211yescharacteristic
34C2×#13063281C2211yescharacteristic
35C43⋊#401C2211yescharacteristic
36C43⋊#401C2211yescharacteristic
37C43⋊#401C2211yescharacteristic
38C43⋊#401C2211yescharacteristic
39#14582841C2211yescharacteristic
40#14582841C2211yescharacteristic
41#14582841C2211yescharacteristic
42#14582841C2211yescharacteristic
43#14582841C2211yescharacteristic
44#14582841C2211yescharacteristic
45#14582841C2211yescharacteristic
46#14582841C2211yescharacteristic
47#14582840C2211yescharacteristic
48#14582840C2211yescharacteristic
49#14582840C2211yescharacteristic
50#14582840C2211yescharacteristic
51#14582840C2211yescharacteristic
52#14582840C2211yescharacteristic
53#14582840C2211yescharacteristic
54#14582840C2211yescharacteristic
55#14582840C2211yescharacteristic
56#14582840C2211yescharacteristic
57#14582839C2211yescharacteristic
58#14582839C2211yescharacteristic
59#14582839C2211yescharacteristic
60#14582838C2211yescharacteristic
61#14582838C2211yescharacteristic
62#14582838C2211yescharacteristic
63#14582838C2211yescharacteristic
64#14582838C2211yescharacteristic
65#14582837C2211yescharacteristic
66#14582837C2211yescharacteristic
67#14582837C2211yescharacteristic
68#14582837C2211yescharacteristic
69#14582837C2211yescharacteristic
70#14582835C2211yescharacteristic
71#14582835C2211yescharacteristic
72#14582833C2211yescharacteristic
73#14582833C2211yescharacteristic
74#14582833C2211yescharacteristic
75#14582833C2211yescharacteristic
76#14582833C2211yescharacteristic
77#14582833C2211yescharacteristic
78#14582833C2211yescharacteristic
79#14582833C2211yescharacteristic
80#14582832C2211yescharacteristic
81#14582832C2211yescharacteristic
82#14582832C2211yescharacteristic
83#14582832C2211yescharacteristic
84#14582832C2211yescharacteristic
85#14582832C2211yescharacteristic
86#14582832C2211yescharacteristic
87#14582832C2211yescharacteristic
88#14582831C2211yescharacteristic
89#14582831C2211yescharacteristic
90#14582831C2211yescharacteristic
91#14582830C2211yescharacteristic
92#14582830C2211yescharacteristic
93#14582830C2211yescharacteristic
94#14582829C2211yescharacteristic
95#14582829C2211yescharacteristic
96#14582829C2211yescharacteristic
97#14582829C2211yescharacteristic
98#14582827C2211yescharacteristic
99#14582827C2211yescharacteristic
100#14582827C2211yescharacteristic
101#14582827C2211yescharacteristic
102#14582827C2211yescharacteristic
103#14582827C2211yescharacteristic
104#14582824C2211yescharacteristic
105#14582824C2211yescharacteristic
106#14582824C2211yescharacteristic
107#14582822C2211yescharacteristic
108#14582822C2211yescharacteristic
109#14582822C2211yescharacteristic
110#14582822C2211yescharacteristic
111#14582822C2211yescharacteristic
112#14582822C2211yescharacteristic
113#14582820C2211yescharacteristic
114#14582820C2211yescharacteristic
115#14582819C2211yescharacteristic
116#14582818C2211yescharacteristic
117#14582818C2211yescharacteristic
118#14582811C2211yescharacteristic
119#14582806C2211yescharacteristic
120#14582803C2211yescharacteristic
121#14582803C2211yescharacteristic
122#14582797C2211yescharacteristic
123#14582796C2211yescharacteristic
124#14582795C2211yescharacteristic
125#14582794C2211yescharacteristic
126#14582793C2211yescharacteristic
127#14582792C2211yescharacteristic
128#14582787C2211yescharacteristic
129#14582786C2211yescharacteristic
130#14582785C2211yescharacteristic
131#14582784C2211yescharacteristic
132#14582784C2211yescharacteristic
133#14582783C2211yescharacteristic
134#14582783C2211yescharacteristic
135#14582782C2211yescharacteristic
136#14582782C2211yescharacteristic
137#14582781C2211yescharacteristic
138#14582781C2211yescharacteristic
139#14582780C2211yescharacteristic
140C4⋊C4×Dic43C2211yescharacteristic
141C4⋊C4×Dic43C2211yescharacteristic
142C4⋊C4×Dic43C2211yescharacteristic
143C4⋊C4×Dic43C2211yescharacteristic
144C4⋊C4×Dic43C2211yescharacteristic
145C4⋊C4×Dic43C2211yescharacteristic
146C4⋊C4×Dic43C2211yescharacteristic
147C4⋊C4×Dic43C2211yescharacteristic
148C4⋊C4×Dic43C2211yescharacteristic
149#14582750C2211yescharacteristic
150#14582750C2211yescharacteristic
151#14582750C2211yescharacteristic
152#14582750C2211yescharacteristic
153#14582750C2211yescharacteristic
154#14582750C2211yescharacteristic
155#14582750C2211yescharacteristic
156#14582750C2211yescharacteristic
157#14582750C2211yescharacteristic
158#14582750C2211yescharacteristic
159#14582750C2211yescharacteristic
160C22⋊C4×Dic43C2211yescharacteristic
161C22⋊C4×Dic43C2211yescharacteristic
162C22⋊C4×Dic43C2211yescharacteristic
163C22⋊C4×Dic43C2211yescharacteristic
164C22⋊C4×Dic43C2211yescharacteristic
165C22⋊C4×Dic43C2211yescharacteristic
166#14582744C2211yescharacteristic
167#14582744C2211yescharacteristic
168#14582744C2211yescharacteristic
169#14582744C2211yescharacteristic
170#14582744C2211yescharacteristic
171C42×Dic43C2211yescharacteristic
172C43×#400C2211yescharacteristic
173C43×#400C2211yescharacteristic
174C43×#400C2211yescharacteristic
175C43×#398C2211yescharacteristic
176C43×#398C2211yescharacteristic
177C43×#397C2211yescharacteristic
178C43×#397C2211yescharacteristic
179C43×#397C2211yescharacteristic
180C43×#396C2211yescharacteristic
181C43×#396C2211yescharacteristic
182C43×#395C2211yescharacteristic
183C43×#393C2211yescharacteristic
184C43×#391C2211yescharacteristic
185C43×#388C2211yescharacteristic
186C43×#387C2211yescharacteristic
187C22×Dic86C2311yescharacteristic
188C23×Dic43C2311yescharacteristic
189Q8×Dic43—24no—
190#13063290—24no—
191#13063281—24no—
192C2×C4⋊Dic43C2311yescharacteristic
193C2×C4⋊Dic43C2311yescharacteristic
194C2×C4⋊Dic43C2311yescharacteristic
195C2×C4⋊Dic43C2311yescharacteristic
196C2×C4⋊Dic43C2311yescharacteristic
197C2×C4⋊Dic43C2311yescharacteristic
198C2×C4⋊Dic43C2311yescharacteristic
199C2×C4⋊Dic43C2311yescharacteristic
200C2×C4⋊Dic43C2311yescharacteristic
201C2×C4⋊Dic43C2311yescharacteristic
202C2×C4⋊Dic43C2311yescharacteristic
203C2×C4⋊Dic43C2311yescharacteristic
204C2×Dic43⋊C4C2311yescharacteristic
205C2×Dic43⋊C4C2311yescharacteristic
206C2×Dic43⋊C4C2311yescharacteristic
207C2×Dic43⋊C4C2311yescharacteristic
208C2×Dic43⋊C4C2311yescharacteristic
209C2×Dic43⋊C4C2311yescharacteristic
210C2×Dic43⋊C4C2311yescharacteristic
211C2×Dic43⋊C4C2311yescharacteristic
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×C22⋊Dic43C2311yescharacteristic
231C2×C22⋊Dic43C2311yescharacteristic
232C2×C22⋊Dic43C2311yescharacteristic
233C2×C22⋊Dic43C2311yescharacteristic
234C2×C22⋊Dic43C2311yescharacteristic
235C2×C22⋊Dic43C2311yescharacteristic
236C2×C22⋊Dic43C2311yescharacteristic
237C2×C4×Dic43C2311yescharacteristic
238C2×C4×Dic43C2311yescharacteristic
239C2×C4×Dic43C2311yescharacteristic
240C2×C4×Dic43C2311yescharacteristic
241C2×C4×Dic43C2311yescharacteristic
242C2×C4×Dic43C2311yescharacteristic
243C2×C4×Dic43C2311yescharacteristic
244C2×C4×Dic43C2311yescharacteristic
245C2×C4×Dic43C2311yescharacteristic
246C2×C4×Dic43C2311yescharacteristic
247C2×C4×Dic43C2311yescharacteristic
248C2×C4×Dic43C2311yescharacteristic
249C2×C4×Dic43C2311yescharacteristic
250C2×C4×Dic43C2311yescharacteristic
251C2×C4×Dic43C2311yescharacteristic
252C2×C4×Dic43C2311yescharacteristic
253C2×C4×Dic43C2311yescharacteristic
254C43⋊#95C2311yescharacteristic
255C43⋊#95C2311yescharacteristic
256C43⋊#95C2311yescharacteristic
257C43⋊#95C2311yescharacteristic
258C43⋊#95C2311yescharacteristic
259C43⋊#95C2311yescharacteristic
260C43⋊#95C2311yescharacteristic
261C43⋊#95C2311yescharacteristic
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
310C22×Q8×C43C2311yescharacteristic
311C2×C4⋊C4×C43C2311yescharacteristic
312C2×C4⋊C4×C43C2311yescharacteristic
313C2×C4⋊C4×C43C2311yescharacteristic
314C2×C4⋊C4×C43C2311yescharacteristic
315C2×C4⋊C4×C43C2311yescharacteristic
316C2×C4⋊C4×C43C2311yescharacteristic
317C2×C4⋊C4×C43C2311yescharacteristic
318C2×C4⋊C4×C43C2311yescharacteristic
319C2×C4⋊C4×C43C2311yescharacteristic
320C2×C4⋊C4×C43C2311yescharacteristic
321C2×C22⋊C4×C43C2311yescharacteristic
322C2×C22⋊C4×C43C2311yescharacteristic
323C2×C22⋊C4×C43C2311yescharacteristic
324C2×C22⋊C4×C43C2311yescharacteristic
325C2×C22⋊C4×C43C2311yescharacteristic
326C2×C22⋊C4×C43C2311yescharacteristic
327C2×C22⋊C4×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
345C24×C43C2411yescharacteristic
346C2×Q8×C43—22no—
347C2×Q8×C43—41no—
348C2×Q8×C43—41no—
349C22×C4×C43C2411yescharacteristic
350C22×C4×C43C2411yescharacteristic
351C22×C4×C43C2411yescharacteristic
352C22×C4×C43C2411yescharacteristic
353C22×C4×C43C2411yescharacteristic
354C22×C4×C43C2411yescharacteristic
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×Dic43—22no—
364C22×Dic43—22no—
365C22×Dic43—22no—
366C22×Dic43C2411yescharacteristic
367C22×Dic43C2411yescharacteristic
368C22×Dic43C2411yescharacteristic
369C22×Dic43C2411yescharacteristic
370C22×Dic43C2411yescharacteristic
371C22×Dic43C2411yescharacteristic
372C22×Dic43C2411yescharacteristic
373C22×Dic43C2411yescharacteristic
374C22×Dic43C2411yescharacteristic
375C22×Dic43C2411yescharacteristic
376C22×Dic43C2411yescharacteristic
377C22×Dic43C2411yescharacteristic
378C22×Dic43C2411yescharacteristic
379C22×Dic43C2411yescharacteristic
380C22×Dic43C2411yescharacteristic
381C22×Dic43C2411yescharacteristic
382C2×Dic86—22no—
383C2×Dic86—41no—
384C2×Dic86—41no—
385C4⋊C4×C43—22no—
386C4⋊C4×C43—41no—
387C4⋊C4×C43—41no—
388C4⋊C4×C43—41no—
389C4⋊C4×C43—41no—
390C4⋊C4×C43—41no—
391C4⋊C4×C43—41no—
392C4⋊C4×C43—41no—
393C4⋊C4×C43—41no—
394C4⋊C4×C43—41no—
395C22⋊C4×C43—22no—
396C22⋊C4×C43—41no—
397C22⋊C4×C43—41no—
398C22⋊C4×C43—41no—
399C22⋊C4×C43—41no—
400C22⋊C4×C43—41no—
401C22⋊C4×C43—41no—
402C42×C43—41no—
403C22⋊Dic43—22no—
404C22⋊Dic43—41no—
405C22⋊Dic43—41no—
406C22⋊Dic43—41no—
407C22⋊Dic43—41no—
408C22⋊Dic43—41no—
409C22⋊Dic43—41no—
410C4⋊Dic43—22no—
411C4⋊Dic43—22no—
412C4⋊Dic43—22no—
413C4⋊Dic43—41no—
414C4⋊Dic43—41no—
415C4⋊Dic43—41no—
416C4⋊Dic43—41no—
417C4⋊Dic43—41no—
418C4⋊Dic43—41no—
419C4⋊Dic43—41no—
420C4⋊Dic43—41no—
421C4⋊Dic43—41no—
422Dic43⋊C4—22no—
423Dic43⋊C4—22no—
424Dic43⋊C4—22no—
425Dic43⋊C4—22no—
426Dic43⋊C4—41no—
427Dic43⋊C4—41no—
428Dic43⋊C4—41no—
429Dic43⋊C4—41no—
430Dic43⋊C4—41no—
431Dic43⋊C4—41no—
432Dic43⋊C4—41no—
433Dic43⋊C4—41no—
434Dic43⋊C4—41no—
435Dic43⋊C4—41no—
436Dic43⋊C4—41no—
437Dic43⋊C4—41no—
438Dic43⋊C4—41no—
439Dic43⋊C4—41no—
440Dic43⋊C4—41no—
441Dic43⋊C4—41no—
442Dic43⋊C4—41no—
443Dic43⋊C4—41no—
444Dic43⋊C4—41no—
445Dic43⋊C4—41no—
446Dic43⋊C4—41no—
447Dic43⋊C4—41no—
448C4×Dic43—22no—
449C4×Dic43—22no—
450C4×Dic43—22no—
451C4×Dic43—22no—
452C4×Dic43—22no—
453C4×Dic43—22no—
454C4×Dic43—22no—
455C4×Dic43—22no—
456C4×Dic43—22no—
457C4×Dic43—22no—
458C4×Dic43—22no—
459C4×Dic43—22no—
460C4×Dic43—22no—
461C4×Dic43—41no—
462C4×Dic43—41no—
463C4×Dic43—41no—
464C4×Dic43#4114yes—
465C23×C43—21no—
466C23×C43—21no—
467C23×C43—21no—
468C23×C43—21no—
469C23×C43—21no—
470C23×C43—21no—
471C23×C43—21no—
472C23×C43C2511yescharacteristic
473Q8×C43—44no—
474C2×C4×C43—21no—
475C2×C4×C43—21no—
476C2×C4×C43—21no—
477C2×C4×C43—21no—
478C2×C4×C43—21no—
479C2×C4×C43—21no—
480C2×C4×C43—21no—
481C2×C4×C43—21no—
482C2×C4×C43—21no—
483C2×C4×C43—21no—
484C2×C4×C43—21no—
485C2×C4×C43—21no—
486C2×C4×C43—21no—
487C2×C4×C43—21no—
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×C43C2×#4112yes—
516C2×Dic43—21no—
517C2×Dic43—21no—
518C2×Dic43—21no—
519C2×Dic43—21no—
520C2×Dic43—21no—
521C2×Dic43—21no—
522C2×Dic43—21no—
523C2×Dic43—21no—
524C2×Dic43—21no—
525C2×Dic43—21no—
526C2×Dic43—21no—
527C2×Dic43—21no—
528C2×Dic43—21no—
529C2×Dic43—21no—
530C2×Dic43—21no—
531C2×Dic43—21no—
532C2×Dic43—21no—
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—44no—
561C2×Dic43C2×#4112yes—
562C2×Dic43C2×#4112yes—
563C2×Dic432−1+412yes—
564C2×Dic432−1+412yes—
565Dic86—44no—
566#36700—431nomaximal, Sylow
567C22×C43—41no—
568C22×C43—41no—
569C22×C43—41no—
570C22×C43—41no—
571C22×C43—41no—
572C22×C43—41no—
573C22×C43—41no—
574C22×C43C22×#4111yescharacteristic
575C22×C43C2×2−1+411yescharacteristic
576C22×C43C2×2−1+411yescharacteristic
577C22×C43#58511yescharacteristic
578C22×C43#58511yescharacteristic
579C22×C43#58511yescharacteristic
580C22×C43#58511yescharacteristic
581C4×C43—22no—
582C4×C43—41no—
583C4×C43—41no—
584C4×C43—41no—
585C4×C43—41no—
586C4×C43—41no—
587C4×C43—41no—
588C4×C43—41no—
589C4×C43—41no—
590C4×C43—41no—
591C4×C43—41no—
592C4×C43—41no—
593C4×C43—41no—
594C4×C43—41no—
595Dic43—22no—
596Dic43—41no—
597Dic43—41no—
598Dic43—41no—
599Dic43—41no—
600Dic43—41no—
601Dic43—41no—
602Dic43—41no—
603Dic43—41no—
604Dic43—41no—
605Dic43—41no—
606Dic43—41no—
607Dic43—41no—
608Dic43—41no—
609Dic43—41no—
610Dic43#54114yes—
611#2839—431no—
612#2839—431no—
613#2839—431no—
614#2839—431no—
615#2836—431no—
616#2836—431no—
617#2836—431no—
618#2836—431no—
619#2833—431no—
620#2833—431no—
621#2833—431no—
622#2833—431no—
623#2831—431no—
624#2831—431no—
625#2831—431no—
626#2831D4311yescharacteristic
627#2402—431no—
628#2402—431no—
629#2402—431no—
630#2402—431no—
631#2402—431no—
632#2401—431no—
633#2401—431no—
634#2401—431no—
635#2401—431no—
636#2399—431no—
637#2396—431no—
638#2396—431no—
639#2298—431no—
640#2295—431no—
641#2295—431no—
642C2×C43—81no—
643C2×C43C2×#54111yescharacteristic
644C2×C43#345511yescharacteristic
645C2×C43#345511yescharacteristic
646C2×C43#353111yescharacteristic
647C2×C43#353111yescharacteristic
648C2×C43#353111yescharacteristic
649C2×C43#353111yescharacteristic
650C2×C4×Q8—431no—
651C2×C4×Q8—431no—
652C2×#117—431no—
653#401—431no—
654#401—431no—
655#401—431no—
656#401—431no—
657#400—431no—
658#400—431no—
659#400—431no—
660#400—431no—
661#400—431no—
662#400—431no—
663#400—431no—
664#400—431no—
665#400—431no—
666#400—431no—
667#400—431no—
668#400—431no—
669#400—431no—
670#400—431no—
671#400—431no—
672#400—431no—
673#400—431no—
674#400—431no—
675#400—431no—
676#400—431no—
677#400—431no—
678#400—431no—
679#400—431no—
680#400—431no—
681#400—431no—
682#400—431no—
683#400—431no—
684#400—431no—
685#400—431no—
686#400—431no—
687#400—431no—
688#400C2×D4311yescharacteristic
689#400C2×D4311yescharacteristic
690#400C2×D4311yescharacteristic
691#399—431no—
692#399—431no—
693#398—431no—
694#398—431no—
695#398—431no—
696#398—431no—
697#398—431no—
698#398—431no—
699#398—431no—
700#398—431no—
701#398—431no—
702#398—431no—
703#398—431no—
704#398—431no—
705#398—431no—
706#398—431no—
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#398C2×D4311yescharacteristic
720#398C2×D4311yescharacteristic
721#397—431no—
722#397—431no—
723#397—431no—
724#397—431no—
725#397—431no—
726#397—431no—
727#397—431no—
728#397—431no—
729#397—431no—
730#397C2×D4311yescharacteristic
731#397C2×D4311yescharacteristic
732#397C2×D4311yescharacteristic
733#396—431no—
734#396—431no—
735#396—431no—
736#396—431no—
737#396—431no—
738#396—431no—
739#396C2×D4311yescharacteristic
740#396C2×D4311yescharacteristic
741#395—431no—
742#395—431no—
743#395—431no—
744#395—431no—
745#395—431no—
746#395C2×D4311yescharacteristic
747#393—431no—
748#393C2×D4311yescharacteristic
749#391—431no—
750#391—431no—
751#391—431no—
752#391C2×D4311yescharacteristic
753#389—431no—
754#389—431no—
755#389—431no—
756#389—431no—
757#388—431no—
758#388—431no—
759#388—431no—
760#388C2×D4311yescharacteristic
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#387C2×D4311yescharacteristic
773C4×C4⋊C4—431no—
774C4×C4⋊C4—431no—
775C4×C4⋊C4—431no—
776C4×C4⋊C4—431no—
777C4×C4⋊C4—431no—
778C4×C4⋊C4—431no—
779C4×C4⋊C4—431no—
780C4×C4⋊C4—431no—
781C4×C4⋊C4—431no—
782C4×C4⋊C4—431no—
783C4×C4⋊C4—431no—
784C4×C4⋊C4—431no—
785C4×C4⋊C4—431no—
786C4×C4⋊C4—431no—
787C4×C4⋊C4—431no—
788C4×C4⋊C4—431no—
789C4×C4⋊C4—431no—
790C4×C4⋊C4—431no—
791C4×C4⋊C4—431no—
792C4×C4⋊C4—431no—
793C4×C22⋊C4—431no—
794C4×C22⋊C4—431no—
795C4×C22⋊C4—431no—
796C4×C22⋊C4—431no—
797C4×C22⋊C4—431no—
798C4×C22⋊C4—431no—
799#376—431no—
800#376—431no—
801#376—431no—
802#376—431no—
803#376—431no—
804C43—431no—
805C43#3670011yescharacteristic, complemented, Sylow
806C22×Q8—431no—
807C22×Q8C22×D4311yescharacteristic
808C23×C4—431no—
809C4×Q8—864no—
810C4×Q8—864no—
811#117—864no—
812C2×C4⋊C4—431no—
813C2×C4⋊C4—431no—
814C2×C4⋊C4—431no—
815C2×C4⋊C4—431no—
816C2×C4⋊C4—431no—
817C2×C4⋊C4—431no—
818C2×C4⋊C4—431no—
819C2×C4⋊C4—431no—
820C2×C4⋊C4—431no—
821C2×C4⋊C4—431no—
822C2×C4⋊C4—431no—
823C2×C4⋊C4—431no—
824C2×C4⋊C4—431no—
825C2×C4⋊C4—431no—
826C2×C4⋊C4—431no—
827C2×C4⋊C4—431no—
828C2×C4⋊C4—431no—
829C2×C4⋊C4—431no—
830C2×C4⋊C4—431no—
831C2×C4⋊C4—431no—
832C2×C4⋊C4—431no—
833C2×C4⋊C4—431no—
834C2×C4⋊C4—431no—
835C2×C4⋊C4—431no—
836C2×C4⋊C4—431no—
837C2×C4⋊C4—431no—
838C2×C4⋊C4—431no—
839C2×C4⋊C4—431no—
840C2×C4⋊C4—431no—
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⋊C4C22×D4311yescharacteristic
851C2×C4⋊C4C22×D4311yescharacteristic
852C2×C4⋊C4C22×D4311yescharacteristic
853C2×C4⋊C4C22×D4311yescharacteristic
854C2×C4⋊C4C22×D4311yescharacteristic
855C2×C4⋊C4C22×D4311yescharacteristic
856C2×C4⋊C4C22×D4311yescharacteristic
857C2×C4⋊C4C22×D4311yescharacteristic
858C2×C4⋊C4C22×D4311yescharacteristic
859C2×C4⋊C4C22×D4311yescharacteristic
860C2×C22⋊C4—431no—
861C2×C22⋊C4—431no—
862C2×C22⋊C4—431no—
863C2×C22⋊C4—431no—
864C2×C22⋊C4—431no—
865C2×C22⋊C4—431no—
866C2×C22⋊C4—431no—
867C2×C22⋊C4C22×D4311yescharacteristic
868C2×C22⋊C4C22×D4311yescharacteristic
869C2×C22⋊C4C22×D4311yescharacteristic
870C2×C22⋊C4C22×D4311yescharacteristic
871C2×C22⋊C4C22×D4311yescharacteristic
872C2×C22⋊C4C22×D4311yescharacteristic
873C2×C22⋊C4C22×D4311yescharacteristic
874C2×C42—431no—
875C2×C42—431no—
876C2×C42—431no—
877C2×C42—431no—
878C2×C42—431no—
879C2×C42—431no—
880C2×C42—431no—
881C2×C42—431no—
882C2×C42—431no—
883C2×C42—431no—
884C2×C42—431no—
885C2×C42—431no—
886C2×C42—431no—
887C2×C42—431no—
888C2×C42—431no—
889C2×C42—431no—
890C2×C42—431no—
891C2×C42C22×D4311yescharacteristic
892#95—431no—
893#95—431no—
894#95—431no—
895#95—431no—
896#95—431no—
897#95—431no—
898#95—431no—
899#95—431no—
900#95—431no—
901#95—431no—
902#95—431no—
903#95—431no—
904#95—431no—
905#95—431no—
906#95—431no—
907#95—431no—
908#95—431no—
909#95—431no—
910#95—431no—
911#95—431no—
912#95—431no—
913#95—431no—
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#95C22×D4311yescharacteristic
949#95C22×D4311yescharacteristic
950#95C22×D4311yescharacteristic
951#95C22×D4311yescharacteristic
952#95C22×D4311yescharacteristic
953#95C22×D4311yescharacteristic
954#95C22×D4311yescharacteristic
955#95C22×D4311yescharacteristic
956#95C22×D4311yescharacteristic
957#95C22×D4311yescharacteristic
958#95C22×D4311yescharacteristic
959#95C22×D4311yescharacteristic
960#95C22×D4311yescharacteristic
961#95C22×D4311yescharacteristic
962#95C22×D4311yescharacteristic
963#95C22×D4311yescharacteristic
964C24C23×D4311yescharacteristic
965C2×Q8—22no—
966C2×Q8—41no—
967C2×Q8—41no—
968C2×Q8—862no—
969C2×Q8—1721no—
970C2×Q8—1721no—
971C22×C4—431no—
972C22×C4—431no—
973C22×C4—431no—
974C22×C4—431no—
975C22×C4—431no—
976C22×C4—431no—
977C22×C4—431no—
978C22×C4—431no—
979C22×C4—431no—
980C22×C4—431no—
981C22×C4—431no—
982C22×C4—431no—
983C22×C4—431no—
984C22×C4—431no—
985C22×C4—431no—
986C22×C4—431no—
987C22×C4—862no—
988C22×C4—862no—
989C22×C4—862no—
990C22×C4C23×D4311yescharacteristic
991C22×C4C23×D4311yescharacteristic
992C22×C4C23×D4311yescharacteristic
993C22×C4C23×D4311yescharacteristic
994C22×C4C23×D4311yescharacteristic
995C22×C4C23×D4311yescharacteristic
996C22×C4C23×D4311yescharacteristic
997C22×C4C23×D4311yescharacteristic
998C22×C4C23×D4311yescharacteristic
999C22×C4C23×D4311yescharacteristic
1000C22×C4C23×D4311yescharacteristic
1001C22×C4C23×D4311yescharacteristic
1002C22×C4C23×D4311yescharacteristic
1003C22×C4C23×D4311yescharacteristic
1004C4⋊C4—22no—
1005C4⋊C4—41no—
1006C4⋊C4—41no—
1007C4⋊C4—41no—
1008C4⋊C4—41no—
1009C4⋊C4—41no—
1010C4⋊C4—41no—
1011C4⋊C4—41no—
1012C4⋊C4—41no—
1013C4⋊C4—41no—
1014C4⋊C4—862no—
1015C4⋊C4—862no—
1016C4⋊C4—862no—
1017C4⋊C4—862no—
1018C4⋊C4—862no—
1019C4⋊C4—862no—
1020C4⋊C4—862no—
1021C4⋊C4—1721no—
1022C4⋊C4—1721no—
1023C4⋊C4—1721no—
1024C4⋊C4—1721no—
1025C4⋊C4—1721no—
1026C4⋊C4—1721no—
1027C4⋊C4—1721no—
1028C4⋊C4—1721no—
1029C4⋊C4—1721no—
1030C4⋊C4—1721no—
1031C4⋊C4—1721no—
1032C4⋊C4—1721no—
1033C4⋊C4—1721no—
1034C4⋊C4—1721no—
1035C4⋊C4—1721no—
1036C4⋊C4—1721no—
1037C4⋊C4—1721no—
1038C4⋊C4—1721no—
1039C4⋊C4—1721no—
1040C4⋊C4—1721no—
1041C4⋊C4—1721no—
1042C4⋊C4—1721no—
1043C4⋊C4—1721no—
1044C4⋊C4—1721no—
1045C4⋊C4—1721no—
1046C4⋊C4—1721no—
1047C4⋊C4—1721no—
1048C4⋊C4—1721no—
1049C4⋊C4—1721no—
1050C4⋊C4—1721no—
1051C4⋊C4—1721no—
1052C22⋊C4—22no—
1053C22⋊C4—41no—
1054C22⋊C4—41no—
1055C22⋊C4—41no—
1056C22⋊C4—41no—
1057C22⋊C4—41no—
1058C22⋊C4—41no—
1059C22⋊C4—862no—
1060C22⋊C4—1721no—
1061C22⋊C4—1721no—
1062C22⋊C4—1721no—
1063C22⋊C4—1721no—
1064C22⋊C4—1721no—
1065C22⋊C4—1721no—
1066C42—41no—
1067C42—434no—
1068C42—862no—
1069C42—862no—
1070C42—862no—
1071C42—862no—
1072C42—862no—
1073C42—862no—
1074C42—862no—
1075C42—862no—
1076C42—862no—
1077C42—862no—
1078C42—862no—
1079C42—862no—
1080C42—862no—
1081C42—1721no—
1082C42—1721no—
1083C42—1721no—
1084C23—21no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—21no—
1089C23—21no—
1090C23—21no—
1091C23C24×D4311yescharacteristic
1092Q8—44no—
1093Q8—1724no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—432no—
1136C2×C4—432no—
1137C2×C4—432no—
1138C2×C4—432no—
1139C2×C4—861no—
1140C2×C4—861no—
1141C2×C4—861no—
1142C2×C4—861no—
1143C2×C4—861no—
1144C2×C4—861no—
1145C2×C4—861no—
1146C2×C4—861no—
1147C2×C4—861no—
1148C2×C4—861no—
1149C2×C4—861no—
1150C2×C4—861no—
1151C2×C4—861no—
1152C2×C4—861no—
1153C2×C4—861no—
1154C2×C4—861no—
1155C2×C4—861no—
1156C2×C4—861no—
1157C2×C4—861no—
1158C2×C4—861no—
1159C2×C4—861no—
1160C2×C4—861no—
1161C2×C4—861no—
1162C2×C4—861no—
1163C2×C4—861no—
1164C2×C4—861no—
1165C2×C4—861no—
1166C2×C4—861no—
1167C2×C4—861no—
1168C2×C4—861no—
1169C2×C4—861no—
1170C2×C4—861no—
1171C2×C4—861no—
1172C2×C4—861no—
1173C2×C4—861no—
1174C2×C4—861no—
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—1724no—
1184C2×C4#41×D4312yes—
1185C22—41no—
1186C22—41no—
1187C22—41no—
1188C22—41no—
1189C22—41no—
1190C22—41no—
1191C22—41no—
1192C22C2×#41×D4311yescharacteristic
1193C222−1+4×D4311yescharacteristic
1194C222−1+4×D4311yescharacteristic
1195C22#1458373411yescharacteristic
1196C22#1458373411yescharacteristic
1197C22#1458373411yescharacteristic
1198C22#1458373611yescharacteristic
1199C4—22no—
1200C4—41no—
1201C4—41no—
1202C4—41no—
1203C4—41no—
1204C4—41no—
1205C4—41no—
1206C4—41no—
1207C4—41no—
1208C4—41no—
1209C4—41no—
1210C4—41no—
1211C4—41no—
1212C4—41no—
1213C4—434no—
1214C4—862no—
1215C4—1721no—
1216C4—1721no—
1217C4—1721no—
1218C4—1721no—
1219C4—1721no—
1220C4—1721no—
1221C4—1721no—
1222C4—1721no—
1223C4—1721no—
1224C4—1721no—
1225C4—1721no—
1226C4—1721no—
1227C4—1721no—
1228C4—1721no—
1229C2—81no—
1230C2#541×D4311yescharacteristic
1231C2#1914797711yescharacteristic
1232C2#1914798211yescharacteristic
1233C2#1914873911yescharacteristic
1234C2#1914873911yescharacteristic
1235C2#1914874111yescharacteristic
1236C2#1914874111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D43
commutator, socle, cosocleC23×C43C25
FittingC43×#2831C2
prime radicalC24×C43C24
hypercenter#2831D43
hypocenterC43#36700
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2831

Complements

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

NH ≅ G/Ntype
1. #19142845C2semidirect
2. #19142840C2semidirect
3. #19142837C2semidirect
4. #19142834C2semidirect
9. #19142774C2semidirect
10. #19142772C2semidirect
11. #19142771C2semidirect
12. #19142768C2semidirect
16. #19137901C2semidirect
17. #19137901C2semidirect
18. #19137901C2semidirect
19. #19137899C2semidirect
20. #19137899C2semidirect
25. #19137885C2semidirect
29. #19137070C2semidirect
30. #19137068C2semidirect
805. C43#36700semidirect

Maximal subgroups

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

subgroupindex
#191428452
#191428402
#191428372
#191428342
#191427962
#191427952
#191427892
#191427882
#191427742
#191427722
#191427712
#191427682
#191427542
#191427512
#191427442
#191379012
#191378992
#191378972
#191378922
#191378852
#191378702
#191378622
#191370892
#191370702
#191370682
C43×#28312
#3670043