Finite Group Databasebeta

← #25112184

Subgroups — #25112184

Order 11008.

1458 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583558C211yesmaximal, characteristic
2C2×#14582909C211yesmaximal, characteristic, complemented
3C2×#14582896C211yesmaximal, characteristic, complemented
4#19137544C211yesmaximal, characteristic, complemented
5#19135525C211yesmaximal, characteristic, complemented
6#19135411C211yesmaximal, characteristic, complemented
7#19135033C211yesmaximal, characteristic, complemented
8#19135018C211yesmaximal, characteristic, complemented
9#19134915C211yesmaximal, characteristic, complemented
10#19134905C211yesmaximal, characteristic, complemented
11#19134601C211yesmaximal, characteristic, complemented
12#19134536C211yesmaximal, characteristic, complemented
13#19134531C211yesmaximal, characteristic, complemented
14#19134426C211yesmaximal, characteristic, complemented
15C2×C43×#435C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C23×Dic86C2211yescharacteristic
18#14583558—24no—
19#14583558C418yescomplemented
20C2×#13063313C2211yescharacteristic
21C2×#13063311—21no—
22C2×#13063304C2211yescharacteristic
23C2×#13063303—21no—
24C2×#13063299C2211yescharacteristic
25C2×#13063297—21no—
26C2×C4×Dic86C2211yescharacteristic
27C2×(C22⋊D43)⋊C4—21no—
28C2×#13063284C2211yescharacteristic
29C2×#13063284C2211yescharacteristic
30#14582909—24no—
31#14582896—24no—
32C2×#13063250C2211yescharacteristic
33C2×#13063250C2211yescharacteristic
34C2×#13063250C2211yescharacteristic
35C2×#13063250C2211yescharacteristic
36C2×#13063250C2211yescharacteristic
37C2×#13063250C2211yescharacteristic
38C2×#13063250C2211yescharacteristic
39C2×#13063250C2211yescharacteristic
40C2×#13063247C2211yescharacteristic
41C2×#13063247C2211yescharacteristic
42C2×#13063247C2211yescharacteristic
43C2×#13063247C2211yescharacteristic
44#14582802—21no—
45#14582792—21no—
46#14582792—21no—
47#14582769C2211yescharacteristic
48#14582759C2211yescharacteristic
49#14582759C2211yescharacteristic
50C4⋊C4×Dic43—21no—
51C4×C4⋊Dic43C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582662C2211yescharacteristic
54#14582662C2211yescharacteristic
55#14582662C2211yescharacteristic
56C22×M16×C43C2211yescharacteristic
57C23×C8×C43C2211yescharacteristic
58C2×C4×D4×C43C2211yescharacteristic
59C43×#435—24no—
60C2×C4⋊C8×C43C2211yescharacteristic
61C2×C22⋊C8×C43C2211yescharacteristic
62C2×C22⋊C8×C43C2211yescharacteristic
63C2×#97×C43C2211yescharacteristic
64C2×#10621898—22no—
65C2×#10621898—22no—
66C2×#10621898—22no—
67C2×#10621898—41no—
68C2×#10621898—41no—
69C2×#10621898C2×C414yes—
70C22×Dic86—22no—
71C22×Dic86—22no—
72C22×Dic86—22no—
73C22×Dic86—21no—
74C22×Dic86—41no—
75C22×Dic86—41no—
76C22×Dic86C2×C414yes—
77C22×Dic86C2311yescharacteristic
78C22×Dic86C2311yescharacteristic
79C22×D172C2311yescharacteristic
80C22×C22⋊D43—21no—
81C22×C22⋊D43—21no—
82C23×Dic43—21no—
83C22×C4×D43—21no—
84#13063313—22no—
85#13063313C2×C414yes—
86#13063311—28no—
87#13063304—22no—
88#13063304C2×C414yes—
89#13063303—28no—
90#13063299—22no—
91#13063299C2×C414yes—
92#13063297—28no—
93C4×Dic86—22no—
94C4×Dic86C2×C414yes—
95(C22⋊D43)⋊C4—28no—
96#13063284—22no—
97#13063284—22no—
98#13063284—41no—
99#13063284—41no—
100C2×C4⋊Dic43—21no—
101C2×C4⋊Dic43—21no—
102C2×C4⋊Dic43C2311yescharacteristic
103C2×C4⋊Dic43C2311yescharacteristic
104C2×C4⋊Dic43C2311yescharacteristic
105C2×C4⋊Dic43C2311yescharacteristic
106C2×C4⋊Dic43C2311yescharacteristic
107C2×Dic43⋊C4—21no—
108C2×Dic43⋊C4—21no—
109C2×C22⋊Dic43—21no—
110C2×C22⋊Dic43—21no—
111C2×C22⋊Dic43—21no—
112C2×C22⋊Dic43—21no—
113C2×C22⋊Dic43—21no—
114C2×(C2×D43)⋊C4—21no—
115C2×(C2×D43)⋊C4—21no—
116C2×(C2×D43)⋊C4—21no—
117C2×C4×Dic43—21no—
118C2×C4×Dic43—21no—
119C2×C4×Dic43—21no—
120C2×C4×Dic43—21no—
121#13063250—22no—
122#13063250—22no—
123#13063250—22no—
124#13063250—22no—
125#13063250—22no—
126#13063250—41no—
127#13063250—41no—
128#13063250D414yescomplemented
129#13063247—22no—
130#13063247—22no—
131#13063247—41no—
132#13063247—41no—
133C43⋊#95—21no—
134C43⋊#95—21no—
135C43⋊#95—21no—
136C22×D4×C43D411yescharacteristic
137C23×C4×C43C2311yescharacteristic
138C23×C4×C43C2311yescharacteristic
139C2×M16×C43—22no—
140C2×M16×C43—22no—
141C2×M16×C43—41no—
142C22×C8×C43—22no—
143C22×C8×C43—22no—
144C22×C8×C43—41no—
145C22×C8×C43C2311yescharacteristic
146C22×C8×C43C2311yescharacteristic
147C22×C8×C43C2311yescharacteristic
148C22×C8×C43C2311yescharacteristic
149C4×D4×C43C2×C414yes—
150C4×D4×C43D414yes—
151C2×C4⋊C4×C43D411yescharacteristic
152C2×C22⋊C4×C43D411yescharacteristic
153C2×C22⋊C4×C43D411yescharacteristic
154C2×C42×C43C2311yescharacteristic
155C4⋊C8×C43—22no—
156C22⋊C8×C43—22no—
157C22⋊C8×C43—22no—
158#97×C43—22no—
159C24×C43C2×D411yescharacteristic
160C24×C43C2×D411yescharacteristic
161C23×D43—21no—
162C2×D4×C43—41no—
163C2×D4×C43—41no—
164C2×D4×C43C22⋊C414yes—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43C22×C412yes—
174C22×C4×C43C22×C412yes—
175C22×C4×C43C2×D412yes—
176C22×C4×C43C2×D412yes—
177C22×C4×C43C2×D411yescharacteristic
178C22×C4×C43C2×D411yescharacteristic
179C22×C4×C43C2×D411yescharacteristic
180C22×C4×C43C2×D411yescharacteristic
181C22×C4×C43C2411yescharacteristic
182C2×C22⋊D43—24no—
183C2×C22⋊D43—24no—
184C2×C22⋊D43—42no—
185C2×C22⋊D43—42no—
186C2×C22⋊D43—42no—
187C2×C22⋊D43—42no—
188C22×Dic43—24no—
189C22×Dic43—21no—
190C22×Dic43—21no—
191C22×Dic43—21no—
192C22×Dic43—21no—
193C22×Dic43—21no—
194C22×Dic43—21no—
195C22×Dic43—21no—
196C22×Dic43—42no—
197C22×Dic43—42no—
198#10621898—28no—
199#10621898—44no—
200#10621898—44no—
201#10621898—44no—
202C2×D172—21no—
203C2×D172—21no—
204C2×D172—21no—
205C2×D172—21no—
206C2×D172—21no—
207C2×D172C22×C412yes—
208C2×C4×D43—24no—
209C2×C4×D43—42no—
210C2×C4×D43—42no—
211C2×Dic86—21no—
212C2×Dic86—21no—
213C2×Dic86—21no—
214C2×Dic86—21no—
215C2×Dic86—21no—
216C2×Dic86—21no—
217C2×Dic86—21no—
218C2×Dic86—28no—
219C2×Dic86—24no—
220C2×Dic86—21no—
221C2×Dic86—44no—
222C2×Dic86—44no—
223C2×Dic86—44no—
224C2×Dic86—42no—
225C2×Dic86—42no—
226C2×Dic86C22×C412yes—
227C2×Dic86C22×C412yes—
228C2×Dic86C2×D412yes—
229C2×Dic86#4112yes—
230M16×C43—44no—
231C2×C8×C43—21no—
232C2×C8×C43—21no—
233C2×C8×C43—21no—
234C2×C8×C43—21no—
235C2×C8×C43—21no—
236C2×C8×C43—21no—
237C2×C8×C43—21no—
238C2×C8×C43—21no—
239C2×C8×C43—21no—
240C2×C8×C43—21no—
241C2×C8×C43—21no—
242C2×C8×C43—44no—
243C2×C8×C43C2×D412yes—
244C4⋊C4×C43C22⋊C414yes—
245C22⋊C4×C43C22⋊C414yes—
246C22⋊C4×C43C22⋊C414yes—
247C42×C43C22×C412yes—
248C42×C43C2×D412yes—
249C22⋊Dic43—24no—
250C22⋊Dic43—42no—
251C22⋊Dic43—42no—
252C22⋊Dic43—81no—
253C22⋊Dic43—81no—
254(C2×D43)⋊C4—24no—
255(C2×D43)⋊C4—24no—
256(C2×D43)⋊C4—24no—
257C4⋊Dic43—21no—
258C4⋊Dic43—21no—
259C4⋊Dic43—21no—
260C4⋊Dic43—21no—
261C4⋊Dic43—21no—
262C4⋊Dic43—21no—
263C4⋊Dic43—21no—
264C4⋊Dic43—21no—
265C4⋊Dic43—42no—
266C4⋊Dic43—81no—
267C4⋊Dic43C22×C412yes—
268C4⋊Dic43C2×D412yes—
269Dic43⋊C4—24no—
270Dic43⋊C4—24no—
271C4×Dic43—24no—
272C4×Dic43—42no—
273C4×Dic43—42no—
274C4×Dic43—42no—
275C23×C43—21no—
276C23×C43—21no—
277C23×C43—21no—
278C23×C43—21no—
279C23×C43—21no—
280C23×C43—21no—
281C23×C43—21no—
282C23×C43—21no—
283C23×C43—21no—
284C23×C43—21no—
285C23×C43—21no—
286C23×C43—21no—
287C23×C43C2×C22⋊C412yes—
288C23×C43C2×C22⋊C412yes—
289C23×C43C22×D411yescharacteristic
290C22×D43—22no—
291C22×D43—41no—
292C22×D43—41no—
293C22×D43—41no—
294C22×D43—41no—
295C22×D43—41no—
296C22×D43—41no—
297D4×C43—44no—
298C2×C4×C43—21no—
299C2×C4×C43—21no—
300C2×C4×C43—21no—
301C2×C4×C43—21no—
302C2×C4×C43—21no—
303C2×C4×C43—21no—
304C2×C4×C43—21no—
305C2×C4×C43—21no—
306C2×C4×C43—22no—
307C2×C4×C43—22no—
308C2×C4×C43—22no—
309C2×C4×C43—22no—
310C2×C4×C43—22no—
311C2×C4×C43—22no—
312C2×C4×C43—22no—
313C2×C4×C43—22no—
314C2×C4×C43C2×C22⋊C412yes—
315C2×C4×C43C2×C22⋊C412yes—
316C2×C4×C43C2×C22⋊C412yes—
317C2×C4×C43C2×C22⋊C412yes—
318C2×C4×C43C23×C411yescharacteristic
319C2×C4×C43C22×D411yescharacteristic
320C2×C4×C43C22×D411yescharacteristic
321C2×C4×C43C2×#4111yescharacteristic
322C2×C4×C43H(5,𝔽2)11yescharacteristic
323C2×C4×C43H(5,𝔽2)11yescharacteristic
324C22⋊D43—48no—
325C22⋊D43—48no—
326C2×Dic43—22no—
327C2×Dic43—22no—
328C2×Dic43—22no—
329C2×Dic43—22no—
330C2×Dic43—22no—
331C2×Dic43—22no—
332C2×Dic43—48no—
333C2×Dic43—41no—
334C2×Dic43—41no—
335C2×Dic43—41no—
336C2×Dic43—41no—
337C2×Dic43—41no—
338C2×Dic43—41no—
339C2×Dic43—41no—
340C2×Dic43—41no—
341C2×Dic43—41no—
342C2×Dic43—41no—
343C2×Dic43—41no—
344C2×Dic43—41no—
345C2×Dic43—41no—
346C2×Dic43—41no—
347C2×Dic43—41no—
348D172—22no—
349D172—22no—
350D172—41no—
351D172—41no—
352C4×D43—48no—
353Dic86—22no—
354Dic86—22no—
355Dic86—22no—
356Dic86—22no—
357Dic86—22no—
358Dic86—48no—
359Dic86—41no—
360Dic86—41no—
361Dic86C4×D414yes—
362C8×C43—22no—
363C8×C43—41no—
364C8×C43—41no—
365C8×C43—41no—
366#22426—431nomaximal, Sylow
367C22×C43—22no—
368C22×C43—22no—
369C22×C43—22no—
370C22×C43—22no—
371C22×C43—22no—
372C22×C43—22no—
373C22×C43—41no—
374C22×C43—41no—
375C22×C43—41no—
376C22×C43—41no—
377C22×C43—41no—
378C22×C43—41no—
379C22×C43—41no—
380C22×C43—41no—
381C22×C43C22×C22⋊C411yescharacteristic
382C22×C43D4211yescharacteristic
383C22×C43#54611yescharacteristic
384C22×C43#57511yescharacteristic
385C22×C43#57511yescharacteristic
386C22×C43#57711yescharacteristic
387C22×C43#57811yescharacteristic
388C2×D43—42no—
389C2×D43—42no—
390C2×D43—42no—
391C2×D43—81no—
392C2×D43—81no—
393C2×D43—81no—
394C2×D43—81no—
395C4×C43—22no—
396C4×C43—22no—
397C4×C43—22no—
398C4×C43—22no—
399C4×C43C2×C4×D411yescharacteristic
400C4×C43#51811yescharacteristic
401C4×C43D4211yescharacteristic
402C4×C43#54611yescharacteristic
403Dic43—24no—
404Dic43—42no—
405Dic43—42no—
406Dic43—42no—
407Dic43—81no—
408Dic43—81no—
409Dic43—81no—
410C2×#548—431no—
411C2×#435D4311yescharacteristic, complemented
412C2×#419—431no—
413C2×#416—431no—
414#2354—431no—
415#1983—431no—
416#1959—431no—
417#1895—431no—
418#1892—431no—
419#1875—431no—
420#1873—431no—
421#1803—431no—
422#1788—431no—
423#1787—431no—
424#1763—431no—
425C2×C43—42no—
426C2×C43—42no—
427C2×C43D4×C22⋊C411yescharacteristic
428C2×C43#289611yescharacteristic
429C2×C43#289811yescharacteristic
430C2×C43#326911yescharacteristic
431C2×C43#327111yescharacteristic
432C2×C43#331311yescharacteristic
433C2×C43#332111yescharacteristic
434D43—82no—
435C22×#41—431no—
436C23×Q8—431no—
437C22×M16C2×D4311yescharacteristic
438C23×C8C2×D4311yescharacteristic
439#548—438no—
440#548—864no—
441C2×#124—431no—
442C2×#124—861no—
443C2×C22⋊Q8—431no—
444C2×C22⋊Q8—861no—
445C2×#121—431no—
446C2×#121—861no—
447C2×C4×Q8—431no—
448C2×C4×D4—861no—
449C2×C4×D4C2×D4311yescharacteristic
450C2×#117—431no—
451C2×#117—431no—
452#435—24no—
453C2×C4⋊C8C2×D4311yescharacteristic
454#419—864no—
455#416—864no—
456C2×#103—431no—
457C2×#103—431no—
458C2×#103—431no—
459C2×#103—431no—
460C2×#103—431no—
461C2×#103—431no—
462C2×#103—431no—
463C2×#103—431no—
464C2×#102—431no—
465C2×#102—431no—
466C2×#102—431no—
467C2×#102—431no—
468C2×C22⋊C8C2×D4311yescharacteristic
469C2×C22⋊C8C2×D4311yescharacteristic
470C2×#97C2×D4311yescharacteristic
471#390—861no—
472#388—861no—
473#388—861no—
474#384—431no—
475#380—431no—
476#380—431no—
477C4×C4⋊C4—431no—
478C4×C4⋊C4—861no—
479#340—431no—
480#340—431no—
481#340—431no—
482#340—431no—
483C43#2242611yescharacteristic, complemented, Sylow
484C2×#41—434no—
485C2×#41—862no—
486C2×#41—862no—
487C2×#41—862no—
488C2×#41—1721no—
489C2×#41—1721no—
490C22×Q8—434no—
491C22×Q8—431no—
492C22×Q8—431no—
493C22×Q8—862no—
494C22×Q8—862no—
495C22×Q8—861no—
496C22×Q8—862no—
497C22×Q8—1721no—
498C22×Q8—1721no—
499C22×D4—431no—
500C22×D4—861no—
501C22×D4—861no—
502C22×D4D17211yescharacteristic
503C23×C4—861no—
504C23×C4—861no—
505C23×C4C22×D4311yescharacteristic
506C23×C4C22×D4311yescharacteristic
507C2×M16—22no—
508C2×M16—22no—
509C2×M16—41no—
510C22×C8—22no—
511C22×C8—22no—
512C22×C8—41no—
513C22×C8C22×D4311yescharacteristic
514C22×C8C22×D4311yescharacteristic
515C22×C8C22×D4311yescharacteristic
516C22×C8C22×D4311yescharacteristic
517#124—434no—
518#124—868no—
519#124—862no—
520C22⋊Q8—434no—
521C22⋊Q8—862no—
522C22⋊Q8—868no—
523#121—434no—
524#121—868no—
525#121—862no—
526C4×Q8—434no—
527C4×Q8—862no—
528C4×D4—868no—
529C4×D4C4×D4314yes—
530C4×D4C22⋊D4314yes—
531#117—862no—
532#117—862no—
533#117—1721no—
534#117—1721no—
535C2×C4⋊C4—431no—
536C2×C4⋊C4—431no—
537C2×C4⋊C4—431no—
538C2×C4⋊C4—431no—
539C2×C4⋊C4—431no—
540C2×C4⋊C4—861no—
541C2×C4⋊C4—861no—
542C2×C4⋊C4—861no—
543C2×C4⋊C4—861no—
544C2×C4⋊C4D17211yescharacteristic
545C2×C22⋊C4—861no—
546C2×C22⋊C4—861no—
547C2×C22⋊C4—861no—
548C2×C22⋊C4—861no—
549C2×C22⋊C4—861no—
550C2×C22⋊C4—861no—
551C2×C22⋊C4—861no—
552C2×C22⋊C4—861no—
553C2×C22⋊C4D17211yescharacteristic
554C2×C22⋊C4D17211yescharacteristic
555C2×C42—861no—
556C2×C42—861no—
557C2×C42—861no—
558C2×C42—861no—
559C2×C42C22×D4311yescharacteristic
560C4⋊C8—22no—
561#103—434no—
562#103—862no—
563#103—862no—
564#103—862no—
565#103—862no—
566#103—862no—
567#103—1721no—
568#103—1721no—
569#102—862no—
570#102—862no—
571#102—1721no—
572#102—1721no—
573C22⋊C8—22no—
574C22⋊C8—22no—
575#97—22no—
576#95—861no—
577#95—861no—
578#95—861no—
579C24—861no—
580C24C2×D17211yescharacteristic
581C24C2×D17211yescharacteristic
582#41—868no—
583#41—1724no—
584#41—1724no—
585#41—1724no—
586C2×Q8—432no—
587C2×Q8—432no—
588C2×Q8—432no—
589C2×Q8—432no—
590C2×Q8—868no—
591C2×Q8—864no—
592C2×Q8—861no—
593C2×Q8—861no—
594C2×Q8—861no—
595C2×Q8—861no—
596C2×Q8—861no—
597C2×Q8—861no—
598C2×Q8—861no—
599C2×Q8—861no—
600C2×Q8—1722no—
601C2×Q8—1722no—
602C2×Q8—1724no—
603C2×Q8—1724no—
604C2×Q8—1724no—
605C2×D4—41no—
606C2×D4—41no—
607C2×D4—432no—
608C2×D4—864no—
609C2×D4—864no—
610C2×D4—861no—
611C2×D4—861no—
612C2×D4—861no—
613C2×D4—861no—
614C2×D4—861no—
615C2×D4—1722no—
616C2×D4—1722no—
617C2×D4—1722no—
618C2×D4—1722no—
619C2×D4(C2×D43)⋊C414yes—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—861no—
629C22×C4—864no—
630C22×C4—861no—
631C22×C4—861no—
632C22×C4—861no—
633C22×C4—864no—
634C22×C4—861no—
635C22×C4—861no—
636C22×C4—861no—
637C22×C4—1722no—
638C22×C4—1722no—
639C22×C4—1722no—
640C22×C4—1722no—
641C22×C4C2×C4×D4312yes—
642C22×C4C2×C4×D4312yes—
643C22×C4C2×D17211yescharacteristic
644C22×C4C2×D17211yescharacteristic
645C22×C4C2×D17211yescharacteristic
646C22×C4C2×D17211yescharacteristic
647C22×C4C2×C22⋊D4312yes—
648C22×C4C2×C22⋊D4312yes—
649C22×C4C23×D4311yescharacteristic
650M16—44no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—44no—
663C2×C8D4×D4312yes—
664C4⋊C4—432no—
665C4⋊C4—432no—
666C4⋊C4—864no—
667C4⋊C4—864no—
668C4⋊C4—861no—
669C4⋊C4—861no—
670C4⋊C4—861no—
671C4⋊C4—861no—
672C4⋊C4—861no—
673C4⋊C4—861no—
674C4⋊C4—861no—
675C4⋊C4—861no—
676C4⋊C4—3441no—
677C4⋊C4—1722no—
678C4⋊C4(C2×D43)⋊C414yes—
679C22⋊C4—864no—
680C22⋊C4—864no—
681C22⋊C4—864no—
682C22⋊C4—864no—
683C22⋊C4—3441no—
684C22⋊C4—3441no—
685C22⋊C4—1722no—
686C22⋊C4—1722no—
687C22⋊C4(C2×D43)⋊C414yes—
688C22⋊C4(C2×D43)⋊C414yes—
689C42—864no—
690C42—1722no—
691C42—1722no—
692C42—1722no—
693C42C2×C4×D4312yes—
694C42C2×C22⋊D4312yes—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—862no—
708C23—1721no—
709C23—1721no—
710C23—1721no—
711C23—1721no—
712C23—1721no—
713C23—1721no—
714C23C2×(C2×D43)⋊C412yes—
715C23C2×(C2×D43)⋊C412yes—
716C23C22×D17211yescharacteristic
717Q8—434no—
718Q8—862no—
719Q8—862no—
720Q8—862no—
721Q8—862no—
722Q8—862no—
723Q8—1728no—
724Q8—1721no—
725Q8—1721no—
726D4—44no—
727D4—862no—
728D4—862no—
729D4—1728no—
730D4—1728no—
731D4—1721no—
732D4—1721no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—862no—
750C2×C4—862no—
751C2×C4—862no—
752C2×C4—862no—
753C2×C4—862no—
754C2×C4—862no—
755C2×C4—1728no—
756C2×C4—1728no—
757C2×C4—1721no—
758C2×C4—1721no—
759C2×C4—1721no—
760C2×C4—1721no—
761C2×C4—1721no—
762C2×C4—1721no—
763C2×C4—1721no—
764C2×C4—1721no—
765C2×C4—1721no—
766C2×C4—1721no—
767C2×C4—1721no—
768C2×C4—1721no—
769C2×C4—1721no—
770C2×C4—1721no—
771C2×C4—1721no—
772C2×C4C2×(C2×D43)⋊C412yes—
773C2×C4C2×(C2×D43)⋊C412yes—
774C2×C4C2×(C2×D43)⋊C412yes—
775C2×C4C2×(C2×D43)⋊C412yes—
776C2×C4C22×C4×D4311yescharacteristic
777C2×C4C2×D4×D4311yescharacteristic
778C2×C4C22×C22⋊D4311yescharacteristic
779C2×C4#41×D4311yescharacteristic
780C2×C4#1306337011yescharacteristic
781C2×C4#1306337111yescharacteristic
782C8—22no—
783C8—41no—
784C8—41no—
785C8—41no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—3441no—
801C22—3441no—
802C22—3441no—
803C22—3441no—
804C22—1722no—
805C22—1722no—
806C22—1722no—
807C22C22×(C2×D43)⋊C411yescharacteristic
808C22D4×D17211yescharacteristic
809C22#1458354411yescharacteristic
810C22#1458369911yescharacteristic
811C22#1458369911yescharacteristic
812C22#1458371111yescharacteristic
813C22#1458371611yescharacteristic
814C4—22no—
815C4—22no—
816C4—22no—
817C4—22no—
818C4—864no—
819C4—3441no—
820C4—3441no—
821C4—3441no—
822C4—1722no—
823C4—1722no—
824C4—1722no—
825C4C4×D4×D4311yescharacteristic
826C4#1458337111yescharacteristic
827C4D4×C22⋊D4311yescharacteristic
828C4#1458353711yescharacteristic
829C2—42no—
830C2—42no—
831C2—3442no—
832C2D4×(C2×D43)⋊C411yescharacteristic
833C2#1914311511yescharacteristic
834C2#1914312911yescharacteristic
835C2#1914615511yescharacteristic
836C2#1914618511yescharacteristic
837C2#1914666311yescharacteristic
838C2#1914678311yescharacteristic
subgroupG/H
centerC23C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#435C2
socleC23×C43C22×D4
prime radicalC2×#14583558C2
cosocleC22×C4×C43C24
hypercenterC2×#435D43
hypocenterC43#22426
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. C2×#14582909C2semidirect
3. C2×#14582896C2semidirect
4. #19137544C2semidirect
5. #19135525C2semidirect
6. #19135411C2semidirect
7. #19135033C2semidirect
8. #19135018C2semidirect
9. #19134915C2semidirect
10. #19134905C2semidirect
11. #19134601C2semidirect
12. #19134536C2semidirect
13. #19134531C2semidirect
14. #19134426C2semidirect
15. C2×C43×#435C2semidirect
19. #14583558C4semidirect
128. #13063250D4semidirect
411. C2×#435D43semidirect
483. C43#22426semidirect

Maximal subgroups

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

subgroupindex
C2×#145835582
C2×#145829092
C2×#145828962
#191375442
#191355252
#191354112
#191350332
#191350182
#191349152
#191349052
#191346012
#191345362
#191345312
#191344262
C2×C43×#4352
#2242643