Finite Group Databasebeta

← #25113338

Subgroups — #25113338

Order 11008.

1108 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583429C211yesmaximal, characteristic
2C2×#14583029C211yesmaximal, characteristic, complemented
3C2×#14583028C211yesmaximal, characteristic, complemented
4#19135394C211yesmaximal, characteristic, complemented
5#19135391C211yesmaximal, characteristic, complemented
6#19135391C211yesmaximal, characteristic, complemented
7#19135391C211yesmaximal, characteristic, complemented
8#19135387C211yesmaximal, characteristic, complemented
9#19134577C211yesmaximal, characteristic, complemented
10#19134576C211yesmaximal, characteristic, complemented
11#19134573C211yesmaximal, characteristic, complemented
12#19134363C211yesmaximal, characteristic, complemented
13#19134362C211yesmaximal, characteristic, complemented
14#19134359C211yesmaximal, characteristic, complemented
15C43×#1954C211yesmaximal, characteristic, complemented
16#14583429—24no—
17#14583429—24no—
18C2×#13063320C411yescharacteristic
19C2×#13063318C411yescharacteristic
20C2×#13063315C411yescharacteristic
21C2×#13063311C411yescharacteristic
22C2×#13063309C411yescharacteristic
23C2×#13063306C411yescharacteristic
24C2×#13063302C411yescharacteristic
25C2×#13063297C411yescharacteristic
26C2×C4×Dic86C2211yescharacteristic
27C2×C4×C22⋊D43C2211yescharacteristic
28C2×C4×C22⋊D43C2211yescharacteristic
29C2×#13063284C2211yescharacteristic
30C2×#13063282C2211yescharacteristic
31C22×C4×Dic43C2211yescharacteristic
32#14583029—24no—
33#14583028—24no—
34C2×C4⋊(C43⋊C8)C2211yescharacteristic
35C2×Dic43⋊C8C2211yescharacteristic
36C2×Dic43⋊C8C2211yescharacteristic
37C2×Dic43⋊C8C2211yescharacteristic
38C2×Dic43⋊C8C2211yescharacteristic
39C2×C22⋊(C43⋊C8)C2211yescharacteristic
40C2×C22⋊(C43⋊C8)C2211yescharacteristic
41C2×C22⋊(C43⋊C8)C2211yescharacteristic
42C2×C22⋊(C43⋊C8)C2211yescharacteristic
43C2×(C2×D43)⋊C8C2211yescharacteristic
44C2×(C2×D43)⋊C8C2211yescharacteristic
45C2×(C2×D43)⋊C8C2211yescharacteristic
46C2×(C2×D43)⋊C8C2211yescharacteristic
47C2×#13063236C2211yescharacteristic
48C2×#13063235C2211yescharacteristic
49C2×#13063235C2211yescharacteristic
50C2×#13063235C2211yescharacteristic
51C2×C8×Dic43C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54#14582653C2211yescharacteristic
55#14582653C2211yescharacteristic
56C2×C4×D4×C43C2211yescharacteristic
57C2×C4⋊C8×C43C2211yescharacteristic
58C2×C22⋊C8×C43C2211yescharacteristic
59C2×C22⋊C8×C43C2211yescharacteristic
60C2×C22⋊C8×C43C2211yescharacteristic
61C2×C22⋊C8×C43C2211yescharacteristic
62C2×C4×C8×C43C2211yescharacteristic
63C22×Dic86C2×C411yescharacteristic
64C22×C22⋊D43C2×C411yescharacteristic
65C22×C22⋊D43C2×C411yescharacteristic
66C23×Dic43C2×C411yescharacteristic
67C23×Dic43C2×C411yescharacteristic
68C22×C4×D43C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73#13063320—24no—
74#13063318—24no—
75#13063315—24no—
76#13063311—24no—
77#13063309—24no—
78#13063306—24no—
79#13063302—24no—
80#13063297—24no—
81C4×Dic86D414yes—
82C4×Dic86D414yes—
83C4×C22⋊D43—22no—
84C4×C22⋊D43—22no—
85C4×C22⋊D43—22no—
86C4×C22⋊D43—22no—
87#13063284—22no—
88#13063284—22no—
89#13063282—22no—
90#13063282—22no—
91C2×C4⋊Dic43C2×C411yescharacteristic
92C2×C4⋊Dic43C2×C411yescharacteristic
93C2×C4⋊Dic43C2×C411yescharacteristic
94C2×Dic43⋊C4C2×C411yescharacteristic
95C2×Dic43⋊C4C2×C411yescharacteristic
96C2×Dic43⋊C4C2×C411yescharacteristic
97C2×Dic43⋊C4C2×C411yescharacteristic
98C2×Dic43⋊C4C2×C411yescharacteristic
99C2×Dic43⋊C4C2×C411yescharacteristic
100C2×C22⋊Dic43C2×C411yescharacteristic
101C2×C22⋊Dic43C2×C411yescharacteristic
102C2×C22⋊Dic43C2×C411yescharacteristic
103C2×C22⋊Dic43C2×C411yescharacteristic
104C2×(C2×D43)⋊C4C2×C411yescharacteristic
105C2×(C2×D43)⋊C4C2×C411yescharacteristic
106C2×(C2×D43)⋊C4C2×C411yescharacteristic
107C2×(C2×D43)⋊C4C2×C411yescharacteristic
108C2×C4×Dic43—22no—
109C2×C4×Dic43—22no—
110C2×C4×Dic43C2×C411yescharacteristic
111C2×C4×Dic43C2×C411yescharacteristic
112C2×C4×Dic43C2311yescharacteristic
113C2×C4×Dic43C2311yescharacteristic
114C2×C4×Dic43C2311yescharacteristic
115C4⋊(C43⋊C8)—22no—
116Dic43⋊C8—22no—
117Dic43⋊C8—22no—
118Dic43⋊C8—22no—
119Dic43⋊C8—22no—
120C22⋊(C43⋊C8)—22no—
121C22⋊(C43⋊C8)—22no—
122C22⋊(C43⋊C8)—41no—
123C22⋊(C43⋊C8)—41no—
124(C2×D43)⋊C8—22no—
125(C2×D43)⋊C8—22no—
126(C2×D43)⋊C8—41no—
127(C2×D43)⋊C8—41no—
128#13063236—22no—
129#13063235—22no—
130#13063235—22no—
131#13063235—22no—
132C8×Dic43—22no—
133C22×D4×C43C2×C411yescharacteristic
134C23×C4×C43C2311yescharacteristic
135C23×C4×C43C2311yescharacteristic
136C22×C8×C43C2311yescharacteristic
137C22×C8×C43C2311yescharacteristic
138C22×C8×C43C2311yescharacteristic
139C22×C8×C43C2311yescharacteristic
140C4×D4×C43—22no—
141C4×D4×C43—22no—
142C2×C4⋊C4×C43C2×C411yescharacteristic
143C2×C22⋊C4×C43C2×C411yescharacteristic
144C2×C22⋊C4×C43C2×C411yescharacteristic
145C2×C42×C43C2311yescharacteristic
146C4⋊C8×C43—22no—
147C22⋊C8×C43—22no—
148C22⋊C8×C43—22no—
149C22⋊C8×C43—41no—
150C22⋊C8×C43—41no—
151C4×C8×C43—22no—
152C24×C43C22×C411yescharacteristic
153C24×C43C22×C411yescharacteristic
154C23×D43C22×C411yescharacteristic
155C2×D4×C43—22no—
156C2×D4×C43—22no—
157C2×D4×C43—41no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43C22×C411yescharacteristic
171C22×C4×C43C22×C411yescharacteristic
172C22×C4×C43C22×C411yescharacteristic
173C22×C4×C43C22×C411yescharacteristic
174C22×C4×C43C2411yescharacteristic
175C2×C22⋊D43—22no—
176C2×C22⋊D43—22no—
177C2×C22⋊D43—22no—
178C2×C22⋊D43—41no—
179C2×C22⋊D43—41no—
180C2×C22⋊D43—41no—
181C22×Dic43—22no—
182C22×Dic43—22no—
183C22×Dic43—22no—
184C22×Dic43—41no—
185C22×Dic43—41no—
186C22×Dic43—41no—
187C22×Dic43C22×C411yescharacteristic
188C22×Dic43C22×C411yescharacteristic
189C22×Dic43C22×C411yescharacteristic
190C22×Dic43C22×C411yescharacteristic
191C22×Dic43C22×C411yescharacteristic
192C22×Dic43C22×C411yescharacteristic
193C22×Dic43C22×C411yescharacteristic
194C2×C4×D43—21no—
195C2×C4×D43—21no—
196C2×C4×D43—21no—
197C2×C4×D43—21no—
198C2×C4×D43—21no—
199C2×C4×D43—21no—
200C2×Dic86—41no—
201C2×Dic86—41no—
202C2×Dic86C22⋊C414yes—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43—21no—
209C2×C8×C43—21no—
210C2×C8×C43—21no—
211C2×C8×C43—21no—
212C2×C8×C43—21no—
213C2×C8×C43—21no—
214C2×C8×C43#4112yes—
215C4⋊C4×C43—22no—
216C22⋊C4×C43—22no—
217C22⋊C4×C43—22no—
218C42×C43C2×D412yes—
219C42×C43C2×D412yes—
220C22⋊Dic43—22no—
221C22⋊Dic43—22no—
222C22⋊Dic43—22no—
223C22⋊Dic43—22no—
224(C2×D43)⋊C4—22no—
225(C2×D43)⋊C4—22no—
226(C2×D43)⋊C4—22no—
227(C2×D43)⋊C4—22no—
228C4⋊Dic43—22no—
229C4⋊Dic43—22no—
230C4⋊Dic43C22⋊C414yes—
231Dic43⋊C4—22no—
232Dic43⋊C4—22no—
233Dic43⋊C4—22no—
234Dic43⋊C4—22no—
235Dic43⋊C4C22⋊C414yes—
236Dic43⋊C4C22⋊C414yes—
237C4×Dic43—21no—
238C4×Dic43—21no—
239C4×Dic43—22no—
240C4×Dic43—22no—
241C4×Dic43C2×D412yes—
242C4×Dic43C2×D412yes—
243C4×Dic43C2×D412yes—
244C4×Dic43C2×D412yes—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8—21no—
248C2×C43⋊C8—21no—
249C2×C43⋊C8—21no—
250C2×C43⋊C8—21no—
251C2×C43⋊C8—21no—
252C2×C43⋊C8—21no—
253C2×C43⋊C8—21no—
254C2×C43⋊C8—21no—
255C2×C43⋊C8—21no—
256C2×C43⋊C8#4112yes—
257C23×C43—21no—
258C23×C43—21no—
259C23×C43—21no—
260C23×C43—21no—
261C23×C43—21no—
262C23×C43—21no—
263C23×C43—21no—
264C23×C43—21no—
265C23×C43—21no—
266C23×C43—21no—
267C23×C43—21no—
268C23×C43—21no—
269C23×C43—21no—
270C23×C43#13112yes—
271C23×C43C23×C411yescharacteristic
272C22×D43—21no—
273C22×D43—21no—
274C22×D43—21no—
275C22×D43—21no—
276C22×D43—21no—
277C22×D43—21no—
278C22×D43—21no—
279D4×C43—44no—
280C2×C4×C43—21no—
281C2×C4×C43—21no—
282C2×C4×C43—21no—
283C2×C4×C43—21no—
284C2×C4×C43—21no—
285C2×C4×C43—21no—
286C2×C4×C43—21no—
287C2×C4×C43—21no—
288C2×C4×C43—21no—
289C2×C4×C43—21no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
292C2×C4×C43—41no—
293C2×C4×C43—41no—
294C2×C4×C43—41no—
295C2×C4×C43—41no—
296C2×C4×C43—41no—
297C2×C4×C43—41no—
298C2×C4×C43C2×C22⋊C412yes—
299C2×C4×C43C2×C22⋊C412yes—
300C2×C4×C43C22×D411yescharacteristic
301C2×C4×C43C22×D411yescharacteristic
302C2×C4×C43C2×#4111yescharacteristic
303C2×C4×C43C2×#4111yescharacteristic
304C2×C4×C43H(5,𝔽2)11yescharacteristic
305C2×C4×C432−1+411yescharacteristic
306C22⋊D43—44no—
307C22⋊D43—44no—
308C2×Dic43—21no—
309C2×Dic43—21no—
310C2×Dic43—21no—
311C2×Dic43—21no—
312C2×Dic43—21no—
313C2×Dic43—21no—
314C2×Dic43—21no—
315C2×Dic43—21no—
316C2×Dic43—21no—
317C2×Dic43—21no—
318C2×Dic43—21no—
319C2×Dic43—21no—
320C2×Dic43—21no—
321C2×Dic43—21no—
322C2×Dic43—21no—
323C2×Dic43—21no—
324C2×Dic43—21no—
325C2×Dic43—44no—
326C2×Dic43—44no—
327C2×Dic43C2×C22⋊C412yes—
328C2×Dic43C2×C22⋊C412yes—
329C2×Dic43C2×C22⋊C412yes—
330C2×Dic43C2×C22⋊C412yes—
331C4×D43—41no—
332C4×D43—41no—
333C4×D43—41no—
334C4×D43—41no—
335Dic86—44no—
336C8×C43—22no—
337C8×C43—41no—
338C8×C43—41no—
339C8×C43—41no—
340C43⋊C8—22no—
341C43⋊C8—41no—
342C43⋊C8—41no—
343C43⋊C8—41no—
344#22533—431nomaximal, Sylow
345C22×C43—22no—
346C22×C43—22no—
347C22×C43—22no—
348C22×C43—41no—
349C22×C43—41no—
350C22×C43—41no—
351C22×C43—41no—
352C22×C43—41no—
353C22×C43—41no—
354C22×C43—41no—
355C22×C43—41no—
356C22×C43—41no—
357C22×C43—41no—
358C22×C43—41no—
359C22×C43C22×C22⋊C411yescharacteristic
360C22×C43C4×#4111yescharacteristic
361C22×C43#52011yescharacteristic
362C22×C43C2×#13111yescharacteristic
363C22×C43#56811yescharacteristic
364C22×C43#56811yescharacteristic
365C22×C43#56811yescharacteristic
366C2×D43—41no—
367C2×D43—41no—
368C2×D43—41no—
369C2×D43—41no—
370C2×D43—41no—
371C2×D43—41no—
372C2×D43—41no—
373C4×C43—22no—
374C4×C43—22no—
375C4×C43—41no—
376C4×C43—41no—
377C4×C43#54811yescharacteristic
378C4×C43#54811yescharacteristic
379C4×C43#55011yescharacteristic
380C4×C43#55011yescharacteristic
381Dic43—22no—
382Dic43—22no—
383Dic43—22no—
384Dic43—22no—
385Dic43—41no—
386Dic43—41no—
387Dic43—41no—
388C2×#529—431no—
389C2×#446—431no—
390C2×#446—431no—
391#1955—431no—
392#1955—431no—
393#1955—431no—
394#1955—431no—
395#1954—431no—
396#1954D4311yescharacteristic, complemented
397#1798—431no—
398#1798—431no—
399#1797—431no—
400#1750—431no—
401#1750—431no—
402#1749—431no—
403C2×C43—42no—
404C2×C43—81no—
405C2×C43#234111yescharacteristic
406C2×C43#287911yescharacteristic
407C2×C43#288011yescharacteristic
408C2×C43#296711yescharacteristic
409C2×C43#296811yescharacteristic
410C2×C43#299211yescharacteristic
411C2×C43#299511yescharacteristic
412D43—81no—
413#529—864no—
414#529—864no—
415C2×#126—431no—
416C2×#126—431no—
417C2×#125—431no—
418C2×#124—431no—
419C2×#123—431no—
420C2×#123—431no—
421C2×C22⋊Q8—431no—
422C2×#121—431no—
423C2×C4×Q8—431no—
424C2×C4×D4—431no—
425C2×C4×D4—431no—
426C2×C4×D4C2×D4311yescharacteristic
427C2×#117—431no—
428C2×#117—431no—
429C22×C42—431no—
430#446—864no—
431#446—864no—
432C2×C4⋊C8—431no—
433C2×C4⋊C8—431no—
434C2×C4⋊C8—431no—
435C2×C4⋊C8—431no—
436C2×C4⋊C8—431no—
437C2×C4⋊C8C2×D4311yescharacteristic
438C2×C22⋊C8—431no—
439C2×C22⋊C8—431no—
440C2×C22⋊C8—431no—
441C2×C22⋊C8—431no—
442C2×C22⋊C8—431no—
443C2×C22⋊C8—431no—
444C2×C22⋊C8—431no—
445C2×C22⋊C8—431no—
446C2×C22⋊C8C2×D4311yescharacteristic
447C2×C22⋊C8C2×D4311yescharacteristic
448C2×C22⋊C8C2×D4311yescharacteristic
449C2×C22⋊C8C2×D4311yescharacteristic
450C2×#97—431no—
451C2×#97—431no—
452C2×#97—431no—
453C2×#97—431no—
454C2×C4×C8—431no—
455C2×C4×C8C2×D4311yescharacteristic
456#336—431no—
457#336—431no—
458#336—431no—
459#336—431no—
460C43#2253311yescharacteristic, complemented, Sylow
461C22×Q8—431no—
462C22×D4—431no—
463C22×D4—431no—
464C22×D4C4×D4311yescharacteristic
465C23×C4—431no—
466C23×C4—431no—
467C23×C4—431no—
468C23×C4C22×D4311yescharacteristic
469C23×C4C22×D4311yescharacteristic
470C22×C8—431no—
471C22×C8—431no—
472C22×C8—431no—
473C22×C8—431no—
474C22×C8C22×D4311yescharacteristic
475C22×C8C22×D4311yescharacteristic
476C22×C8C22×D4311yescharacteristic
477C22×C8C22×D4311yescharacteristic
478#126—864no—
479#126—864no—
480#125—864no—
481#124—864no—
482#123—864no—
483#123—864no—
484C22⋊Q8—864no—
485#121—864no—
486C4×Q8—434no—
487C4×Q8—434no—
488C4×D4—22no—
489C4×D4—22no—
490C4×D4—862no—
491C4×D4—862no—
492C4×D4—862no—
493C4×D4—862no—
494#117—862no—
495#117—862no—
496#117—862no—
497#117—862no—
498C2×C4⋊C4—431no—
499C2×C4⋊C4—431no—
500C2×C4⋊C4—431no—
501C2×C4⋊C4—431no—
502C2×C4⋊C4—431no—
503C2×C4⋊C4—431no—
504C2×C4⋊C4—431no—
505C2×C4⋊C4—431no—
506C2×C4⋊C4—431no—
507C2×C4⋊C4C4×D4311yescharacteristic
508C2×C22⋊C4—431no—
509C2×C22⋊C4—431no—
510C2×C22⋊C4—431no—
511C2×C22⋊C4—431no—
512C2×C22⋊C4—431no—
513C2×C22⋊C4—431no—
514C2×C22⋊C4—431no—
515C2×C22⋊C4—431no—
516C2×C22⋊C4C4×D4311yescharacteristic
517C2×C22⋊C4C4×D4311yescharacteristic
518C2×C42—431no—
519C2×C42—431no—
520C2×C42—431no—
521C2×C42—431no—
522C2×C42—431no—
523C2×C42—862no—
524C2×C42—862no—
525C2×C42C22×D4311yescharacteristic
526C4⋊C8—22no—
527C4⋊C8—862no—
528C4⋊C8—862no—
529C4⋊C8—862no—
530C4⋊C8—862no—
531C4⋊C8—862no—
532C22⋊C8—22no—
533C22⋊C8—22no—
534C22⋊C8—41no—
535C22⋊C8—41no—
536C22⋊C8—862no—
537C22⋊C8—862no—
538C22⋊C8—862no—
539C22⋊C8—862no—
540C22⋊C8—1721no—
541C22⋊C8—1721no—
542C22⋊C8—1721no—
543C22⋊C8—1721no—
544#97—862no—
545#97—862no—
546#97—862no—
547#97—862no—
548C4×C8—22no—
549C4×C8—862no—
550C24—431no—
551C24C2×C4×D4311yescharacteristic
552C24C2×C4×D4311yescharacteristic
553C2×Q8—434no—
554C2×Q8—1721no—
555C2×Q8—1721no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—41no—
559C2×D4—862no—
560C2×D4—862no—
561C2×D4—862no—
562C2×D4—1721no—
563C2×D4—1721no—
564C2×D4—1721no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—431no—
578C22×C4—431no—
579C22×C4—431no—
580C22×C4—431no—
581C22×C4—431no—
582C22×C4—431no—
583C22×C4—431no—
584C22×C4—862no—
585C22×C4—862no—
586C22×C4—862no—
587C22×C4—861no—
588C22×C4—861no—
589C22×C4—861no—
590C22×C4—861no—
591C22×C4—861no—
592C22×C4—861no—
593C22×C4—1721no—
594C22×C4—1721no—
595C22×C4—1721no—
596C22×C4C2×C4×D4311yescharacteristic
597C22×C4C2×C4×D4311yescharacteristic
598C22×C4C2×C4×D4311yescharacteristic
599C22×C4C2×C4×D4311yescharacteristic
600C22×C4C23×D4311yescharacteristic
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—432no—
613C2×C8—861no—
614C2×C8—861no—
615C2×C8—861no—
616C2×C8—861no—
617C2×C8—861no—
618C2×C8—861no—
619C2×C8—861no—
620C2×C8—861no—
621C2×C8—861no—
622C2×C8—861no—
623C2×C8—861no—
624C2×C8#1062190012yes—
625C4⋊C4—22no—
626C4⋊C4—434no—
627C4⋊C4—434no—
628C4⋊C4—434no—
629C4⋊C4—862no—
630C4⋊C4—862no—
631C4⋊C4—862no—
632C4⋊C4—862no—
633C4⋊C4—862no—
634C4⋊C4—862no—
635C22⋊C4—22no—
636C22⋊C4—22no—
637C22⋊C4—862no—
638C22⋊C4—862no—
639C22⋊C4—862no—
640C22⋊C4—862no—
641C22⋊C4—862no—
642C22⋊C4—862no—
643C22⋊C4—862no—
644C22⋊C4—862no—
645C42—432no—
646C42—432no—
647C42—432no—
648C42—432no—
649C42—862no—
650C42—862no—
651C42—861no—
652C42—861no—
653C42D4×D4312yes—
654C42D4×D4312yes—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—861no—
669C23—861no—
670C23—861no—
671C23—861no—
672C23—861no—
673C23—861no—
674C23—861no—
675C23#1306333112yes—
676C23C22×C4×D4311yescharacteristic
677Q8—1724no—
678D4—44no—
679D4—1724no—
680D4—1724no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—432no—
700C2×C4—432no—
701C2×C4—432no—
702C2×C4—432no—
703C2×C4—861no—
704C2×C4—861no—
705C2×C4—861no—
706C2×C4—861no—
707C2×C4—861no—
708C2×C4—861no—
709C2×C4—861no—
710C2×C4—861no—
711C2×C4—861no—
712C2×C4—861no—
713C2×C4—861no—
714C2×C4—861no—
715C2×C4—861no—
716C2×C4—861no—
717C2×C4—861no—
718C2×C4—861no—
719C2×C4—861no—
720C2×C4—1724no—
721C2×C4—1724no—
722C2×C4—1721no—
723C2×C4—1721no—
724C2×C4—1721no—
725C2×C4—1721no—
726C2×C4C22⋊C4×D4312yes—
727C2×C4C22⋊C4×D4312yes—
728C2×C4C2×D4×D4311yescharacteristic
729C2×C4C2×D4×D4311yescharacteristic
730C2×C4#41×D4311yescharacteristic
731C2×C4C2×#1062190011yescharacteristic
732C2×C4#1306337011yescharacteristic
733C2×C4#1306337211yescharacteristic
734C8—22no—
735C8—41no—
736C8—41no—
737C8—41no—
738C8—862no—
739C8—1721no—
740C8—1721no—
741C8—1721no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—1721no—
757C22—1721no—
758C22—1721no—
759C22—1721no—
760C22—1721no—
761C22—1721no—
762C22—1721no—
763C22C2×C22⋊C4×D4311yescharacteristic
764C22C4×#1062190011yescharacteristic
765C22#1458337811yescharacteristic
766C22C2×#1306333111yescharacteristic
767C22#1458366411yescharacteristic
768C22#1458366411yescharacteristic
769C22#1458366511yescharacteristic
770C4—22no—
771C4—22no—
772C4—41no—
773C4—41no—
774C4—862no—
775C4—862no—
776C4—862no—
777C4—862no—
778C4—1721no—
779C4—1721no—
780C4—1721no—
781C4#1458355511yescharacteristic
782C4#1458355711yescharacteristic
783C4#1458356711yescharacteristic
784C4#1458356911yescharacteristic
785C2—42no—
786C2—81no—
787C2—3441no—
788C2#1913743411yescharacteristic
789C2#1914303711yescharacteristic
790C2#1914304111yescharacteristic
791C2#1914358111yescharacteristic
792C2#1914358311yescharacteristic
793C2#1914372811yescharacteristic
794C2#1914375911yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D43
commutator, socleC23×C43C23×C4
FittingC43×#1954C2
prime radicalC2×#13063297C4
cosocleC22×C4×C43C24
hypercenter#1954D43
hypocenterC43#22533
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ #1954

Complements

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

NH ≅ G/Ntype
2. C2×#14583029C2semidirect
3. C2×#14583028C2semidirect
4. #19135394C2semidirect
5. #19135391C2semidirect
6. #19135391C2semidirect
7. #19135391C2semidirect
8. #19135387C2semidirect
9. #19134577C2semidirect
10. #19134576C2semidirect
11. #19134573C2semidirect
12. #19134363C2semidirect
13. #19134362C2semidirect
14. #19134359C2semidirect
15. C43×#1954C2semidirect
396. #1954D43semidirect
460. C43#22533semidirect

Maximal subgroups

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

subgroupindex
C2×#145834292
C2×#145830292
C2×#145830282
#191353942
#191353912
#191353872
#191345772
#191345762
#191345732
#191343632
#191343622
#191343592
C43×#19542
#2253343