Finite Group Databasebeta

← C2×#19138265 #25265239

Subgroups — C2×#19138265 #25265239

Order 11008.

3006 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063302C211yesmaximal, characteristic
2#19138265C2116yesmaximal, direct product factor
3C2×#14582838C211yesmaximal, characteristic, complemented
4C2×#14582832C211yesmaximal, characteristic, complemented
5C2×#14582832C211yesmaximal, characteristic, complemented
6C2×#14582819C211yesmaximal, characteristic, complemented
7C2×#14582805C211yesmaximal, characteristic, complemented
8C2×#14582797C211yesmaximal, characteristic, complemented
9C2×#14582783C211yesmaximal, characteristic, complemented
10C2×#14582783C211yesmaximal, characteristic, complemented
11C2×#14582774C211yesmaximal, characteristic
12C2×#14582771C211yesmaximal, characteristic
13C2×#14582762C211yesmaximal, characteristic
14C2×#14582757C211yesmaximal, characteristic
15C22×C43⋊#95C211yesmaximal, characteristic
16C22×#117×C43C211yesmaximal, characteristic
17C23×Dic86C2211yescharacteristic
18C24×Dic43C2211yescharacteristic
19C24×Dic43C2211yescharacteristic
20C2×#13063302—28no—
21C2×#13063302C2218yes—
22C22×C4⋊Dic43C2211yescharacteristic
23C22×C4⋊Dic43C2211yescharacteristic
24C22×C4⋊Dic43C2211yescharacteristic
25C22×Dic43⋊C4C2211yescharacteristic
26C22×Dic43⋊C4C2211yescharacteristic
27C22×Dic43⋊C4C2211yescharacteristic
28C22×Dic43⋊C4C2211yescharacteristic
29C22×Dic43⋊C4C2211yescharacteristic
30C22×Dic43⋊C4C2211yescharacteristic
31C22×C22⋊Dic43C2211yescharacteristic
32C22×C22⋊Dic43C2211yescharacteristic
33#14582838C2218yescomplemented
34#14582832C2218yescomplemented
35#14582832C2218yescomplemented
36#14582819C2218yescomplemented
37#14582805C2218yescomplemented
38#14582797C2218yescomplemented
39#14582783C2218yescomplemented
40#14582783C2218yescomplemented
41#14582774C2218yes—
42#14582771C2218yes—
43#14582762C2218yes—
44#14582757C2218yes—
45C2×C43⋊#95C2211yescharacteristic
46C2×C43⋊#95C2211yescharacteristic
47C2×C43⋊#95C2211yescharacteristic
48C2×C43⋊#95C2211yescharacteristic
49C2×C43⋊#95C2211yescharacteristic
50C2×C43⋊#95C2211yescharacteristic
51C2×C43⋊#95C2211yescharacteristic
52C2×C43⋊#95C2211yescharacteristic
53C2×C43⋊#95C2211yescharacteristic
54C2×C43⋊#95C2211yescharacteristic
55C2×C43⋊#95C2211yescharacteristic
56C2×C43⋊#95C2211yescharacteristic
57C2×C43⋊#95C2211yescharacteristic
58C2×C43⋊#95C2218yes—
59C2×C43⋊#95C2211yescharacteristic
60C24×C4×C43C2211yescharacteristic
61C2×#117×C43—28no—
62C2×#117×C43C2218yes—
63C22×C4⋊C4×C43C2211yescharacteristic
64C22×C4⋊C4×C43C2211yescharacteristic
65C22×C22⋊C4×C43C2211yescharacteristic
66C22×C22⋊C4×C43C2211yescharacteristic
67C22×C42×C43C2211yescharacteristic
68C22×C42×C43C2211yescharacteristic
69C22×Dic86—24no—
70C22×Dic86—24no—
71C22×Dic86—42no—
72C22×Dic86C2314yes—
73C23×Dic43—24no—
74C23×Dic43—24no—
75C23×Dic43—24no—
76C23×Dic43—24no—
77C23×Dic43—42no—
78C23×Dic43—42no—
79C23×Dic43C2311yescharacteristic
80C23×Dic43C2311yescharacteristic
81C23×Dic43C2311yescharacteristic
82C23×Dic43C2311yescharacteristic
83C23×Dic43C2311yescharacteristic
84C23×Dic43C2311yescharacteristic
85C23×Dic43C2314yes—
86C23×Dic43C2314yes—
87C23×Dic43C2311yescharacteristic
88C23×Dic43C2311yescharacteristic
89#13063302—232no—
90C2×C4⋊Dic43—24no—
91C2×C4⋊Dic43—24no—
92C2×C4⋊Dic43—42no—
93C2×C4⋊Dic43C2314yes—
94C2×C4⋊Dic43C2314yes—
95C2×C4⋊Dic43C2314yes—
96C2×Dic43⋊C4—24no—
97C2×Dic43⋊C4—24no—
98C2×Dic43⋊C4—24no—
99C2×Dic43⋊C4—24no—
100C2×Dic43⋊C4—42no—
101C2×Dic43⋊C4—42no—
102C2×Dic43⋊C4C2314yes—
103C2×Dic43⋊C4C2314yes—
104C2×Dic43⋊C4C2314yes—
105C2×Dic43⋊C4C2314yes—
106C2×Dic43⋊C4C2314yes—
107C2×Dic43⋊C4C2314yes—
108C2×C22⋊Dic43—24no—
109C2×C22⋊Dic43—24no—
110C2×C22⋊Dic43C2314yes—
111C2×C22⋊Dic43C2314yes—
112C43⋊#95C2314yes—
113C43⋊#95C2314yes—
114C43⋊#95C2314yes—
115C43⋊#95C2314yes—
116C43⋊#95C2314yes—
117C43⋊#95C2314yes—
118C43⋊#95C2314yes—
119C43⋊#95C2314yes—
120C43⋊#95C2314yes—
121C43⋊#95C2314yes—
122C43⋊#95C2314yes—
123C43⋊#95C2314yes—
124C43⋊#95C2314yes—
125C43⋊#95C2314yes—
126C25×C43C2311yescharacteristic
127C23×C4×C43—24no—
128C23×C4×C43—24no—
129C23×C4×C43Q818yescomplemented
130C23×C4×C43C2311yescharacteristic
131C23×C4×C43C2311yescharacteristic
132C23×C4×C43C2311yescharacteristic
133C23×C4×C43C2311yescharacteristic
134C23×C4×C43C2311yescharacteristic
135C23×C4×C43C2311yescharacteristic
136C23×C4×C43C2314yes—
137#117×C43—232no—
138C2×C4⋊C4×C43—24no—
139C2×C4⋊C4×C43—24no—
140C2×C4⋊C4×C43C2314yes—
141C2×C4⋊C4×C43C2314yes—
142C2×C22⋊C4×C43—24no—
143C2×C22⋊C4×C43D418yes—
144C2×C22⋊C4×C43C2314yes—
145C2×C22⋊C4×C43C2314yes—
146C2×C42×C43—24no—
147C2×C42×C43—24no—
148C2×C42×C43C2314yes—
149C2×C42×C43C2314yes—
150C24×C43—22no—
151C24×C43—22no—
152C24×C43—22no—
153C24×C43—22no—
154C24×C43C2×D414yes—
155C24×C43C2×Q814yes—
156C24×C43#4114yes—
157C24×C43C2412yes—
158C24×C43C2411yescharacteristic
159C22×C4×C43—232no—
160C22×C4×C43—22no—
161C22×C4×C43—22no—
162C22×C4×C43—28no—
163C22×C4×C43—22no—
164C22×C4×C43—22no—
165C22×C4×C43—28no—
166C22×C4×C43—22no—
167C22×C4×C43—22no—
168C22×C4×C43—22no—
169C22×C4×C43—22no—
170C22×C4×C43—22no—
171C22×C4×C43—22no—
172C22×C4×C43—22no—
173C22×C4×C43—22no—
174C22×C4×C43—22no—
175C22×C4×C43—22no—
176C22×C4×C43C2×D414yes—
177C22×C4×C43C2×D414yes—
178C22×C4×C43C2×Q814yes—
179C22×C4×C43C2×Q814yes—
180C22×C4×C43C2×Q8116yescomplemented
181C22×C4×C43C2412yes—
182C22×C4×C43C2412yes—
183C22×C4×C43C2412yes—
184C22×C4×C43C2412yes—
185C22×C4×C43C2412yes—
186C22×C4×C43C2412yes—
187C22×Dic43—28no—
188C22×Dic43—28no—
189C22×Dic43—22no—
190C22×Dic43—22no—
191C22×Dic43—22no—
192C22×Dic43—22no—
193C22×Dic43—28no—
194C22×Dic43—22no—
195C22×Dic43—22no—
196C22×Dic43—22no—
197C22×Dic43—22no—
198C22×Dic43—22no—
199C22×Dic43—22no—
200C22×Dic43—22no—
201C22×Dic43—22no—
202C22×Dic43—28no—
203C22×Dic43—22no—
204C22×Dic43—22no—
205C22×Dic43—22no—
206C22×Dic43—22no—
207C22×Dic43—22no—
208C22×Dic43—22no—
209C22×Dic43—22no—
210C22×Dic43—22no—
211C22×Dic43—22no—
212C22×Dic43—22no—
213C22×Dic43—44no—
214C22×Dic43—44no—
215C22×Dic43—416no—
216C22×Dic43—416no—
217C22×Dic43#4114yes—
218C22×Dic43#4114yes—
219C22×Dic43C2412yes—
220C22×Dic43C2412yes—
221C22×Dic43C2412yes—
222C22×Dic43C2412yes—
223C22×Dic43C2412yes—
224C22×Dic43C2412yes—
225C22×Dic43C2412yes—
226C22×Dic43C2412yes—
227C2×Dic86—28no—
228C2×Dic86—28no—
229C2×Dic86—44no—
230C2×Dic86—416no—
231C4⋊C4×C43—28no—
232C4⋊C4×C43—28no—
233C22⋊C4×C43—28no—
234C22⋊C4×C43C2×D4116yes—
235C42×C43—28no—
236C42×C43—28no—
237C22⋊Dic43—28no—
238C22⋊Dic43—28no—
239C4⋊Dic43—28no—
240C4⋊Dic43—28no—
241C4⋊Dic43—44no—
242Dic43⋊C4—28no—
243Dic43⋊C4—28no—
244Dic43⋊C4—28no—
245Dic43⋊C4—28no—
246Dic43⋊C4—44no—
247Dic43⋊C4—44no—
248C23×C43—28no—
249C23×C43—28no—
250C23×C43—28no—
251C23×C43—28no—
252C23×C43—28no—
253C23×C43—28no—
254C23×C43—22no—
255C23×C43—22no—
256C23×C43—22no—
257C23×C43—22no—
258C23×C43C22⋊Q8116yes—
259C23×C43C22×D414yes—
260C23×C43C22×D412yes—
261C23×C43C22×Q814yes—
262C23×C43C22×Q812yes—
263C23×C43C2×#4112yes—
264C23×C43C2×#4112yes—
265C23×C43C2×#4114yes—
266C23×C43C2×#4112yes—
267C23×C43H(5,𝔽2)12yes—
268C23×C432−1+412yes—
269C23×C43C2511yescharacteristic
270C2×C4×C43—28no—
271C2×C4×C43—28no—
272C2×C4×C43—232no—
273C2×C4×C43—28no—
274C2×C4×C43—28no—
275C2×C4×C43—22no—
276C2×C4×C43—22no—
277C2×C4×C43—22no—
278C2×C4×C43—22no—
279C2×C4×C43—22no—
280C2×C4×C43—22no—
281C2×C4×C43—22no—
282C2×C4×C43—22no—
283C2×C4×C43—22no—
284C2×C4×C43—22no—
285C2×C4×C43—22no—
286C2×C4×C43—22no—
287C2×C4×C43—22no—
288C2×C4×C43—22no—
289C2×C4×C43—44no—
290C2×C4×C43—44no—
291C2×C4×C43C22×D414yes—
292C2×C4×C43C22×D414yes—
293C2×C4×C43C22×Q814yes—
294C2×C4×C43C22×Q814yes—
295C2×Dic43—28no—
296C2×Dic43—28no—
297C2×Dic43—22no—
298C2×Dic43—22no—
299C2×Dic43—22no—
300C2×Dic43—22no—
301C2×Dic43—22no—
302C2×Dic43—22no—
303C2×Dic43—22no—
304C2×Dic43—22no—
305C2×Dic43—22no—
306C2×Dic43—22no—
307C2×Dic43—22no—
308C2×Dic43—22no—
309C2×Dic43—22no—
310C2×Dic43—22no—
311C2×Dic43—22no—
312C2×Dic43—22no—
313C2×Dic43—22no—
314C2×Dic43—22no—
315C2×Dic43—22no—
316C2×Dic43—22no—
317C2×Dic43—22no—
318C2×Dic43—22no—
319C2×Dic43—416no—
320C2×Dic43—416no—
321C2×Dic43—44no—
322C2×Dic43—44no—
323C2×Dic43—44no—
324C2×Dic43—44no—
325C2×Dic43—44no—
326C2×Dic43—44no—
327C2×Dic43C2×#4114yes—
328C2×Dic43C2×#4114yes—
329Dic86—416no—
330C2×#2438—431nomaximal, Sylow
331C22×C43—24no—
332C22×C43—24no—
333C22×C43—232no—
334C22×C43—24no—
335C22×C43—24no—
336C22×C43—24no—
337C22×C43—24no—
338C22×C43C2×C22⋊Q818yes—
339C22×C43C2×C22⋊Q814yes—
340C22×C43#53314yes—
341C22×C43#54414yes—
342C22×C43#54614yes—
343C22×C43#54714yes—
344C22×C43#55114yes—
345C22×C43#55214yes—
346C22×C43C23×D411yescharacteristic
347C22×C43C23×Q811yescharacteristic
348C22×C43C22×#4111yescharacteristic
349C22×C43C22×#4111yescharacteristic
350C22×C43C22×#4111yescharacteristic
351C22×C43C2×H(5,𝔽2)11yescharacteristic
352C22×C43C2×2−1+411yescharacteristic
353C4×C43—24no—
354C4×C43—24no—
355C4×C43—24no—
356C4×C43—24no—
357C4×C43—42no—
358C4×C43—42no—
359Dic43—24no—
360Dic43—24no—
361Dic43—42no—
362Dic43—42no—
363Dic43—42no—
364Dic43—42no—
365Dic43—42no—
366Dic43—42no—
367C22×C22⋊Q8—431no—
368C22×#117D4311yescharacteristic
369#2438—4316no—
370C2×#400—431no—
371C2×#398—431no—
372C2×#398—431no—
373C2×#395—431no—
374C2×#391—431no—
375C2×#389—431no—
376C2×#387—431no—
377C2×#387—431no—
378C2×#385—431no—
379C2×#385—431no—
380C2×#381—431no—
381C2×#380—431no—
382C22×#95—431no—
383C2×C43—28no—
384C2×C43#243818yescomplemented
385C2×C43C22×C22⋊Q811yescharacteristic
386C2×C43C2×#53311yescharacteristic
387C2×C43C2×#54411yescharacteristic
388C2×C43C2×#54611yescharacteristic
389C2×C43C2×#54711yescharacteristic
390C2×C43C2×#55111yescharacteristic
391C2×C43C2×#55211yescharacteristic
392C23×Q8—431no—
393C24×C4—431no—
394C24×C4—431no—
395C24×C4C2×D4311yescharacteristic
396C2×C22⋊Q8—438no—
397C2×C22⋊Q8—868no—
398C2×#117—28no—
399C2×#117C2×D4318yes—
400C22×C4⋊C4—431no—
401C22×C4⋊C4—431no—
402C22×C4⋊C4—431no—
403C22×C4⋊C4—431no—
404C22×C4⋊C4—431no—
405C22×C4⋊C4—431no—
406C22×C4⋊C4—431no—
407C22×C4⋊C4—431no—
408C22×C4⋊C4—431no—
409C22×C4⋊C4C2×D4311yescharacteristic
410C22×C4⋊C4C2×D4311yescharacteristic
411C22×C22⋊C4—431no—
412C22×C22⋊C4—431no—
413C22×C22⋊C4C2×D4311yescharacteristic
414C22×C22⋊C4C2×D4311yescharacteristic
415C22×C42C2×D4311yescharacteristic
416C22×C42C2×D4311yescharacteristic
417#400—438no—
418#398—438no—
419#398—438no—
420#395—438no—
421#391—438no—
422#389—438no—
423#387—438no—
424#387—438no—
425#385—438no—
426#385—438no—
427#381—438no—
428#380—438no—
429C2×#95—431no—
430C2×#95—431no—
431C2×#95—431no—
432C2×#95—431no—
433C2×#95—431no—
434C2×#95—431no—
435C2×#95—431no—
436C2×#95—431no—
437C2×#95—431no—
438C2×#95—431no—
439C2×#95—438no—
440C2×#95—431no—
441C2×#95—431no—
442C2×#95—431no—
443C2×#95—431no—
444C43C2×#243811yescharacteristic, complemented, Sylow
445C25C22×D4311yescharacteristic
446C22×Q8—434no—
447C22×Q8—864no—
448C22×Q8—864no—
449C22×Q8—1722no—
450C23×C4—24no—
451C23×C4—24no—
452C23×C4—431no—
453C23×C4—431no—
454C23×C4—431no—
455C23×C4—431no—
456C23×C4—431no—
457C23×C4—431no—
458C23×C4—431no—
459C23×C4—431no—
460C23×C4—434no—
461C23×C4—434no—
462C23×C4—864no—
463C23×C4—864no—
464C23×C4—864no—
465C23×C4—864no—
466C23×C4—1722no—
467C23×C4—1722no—
468C23×C4Dic8618yescomplemented
469C23×C4C22×D4311yescharacteristic
470C23×C4C22×D4311yescharacteristic
471C23×C4C22×D4311yescharacteristic
472C23×C4C22×D4311yescharacteristic
473C23×C4C22×D4314yes—
474C23×C4C22×D4311yescharacteristic
475C23×C4C22×D4311yescharacteristic
476C22⋊Q8—8632no—
477#117—232no—
478C2×C4⋊C4—24no—
479C2×C4⋊C4—24no—
480C2×C4⋊C4—434no—
481C2×C4⋊C4—434no—
482C2×C4⋊C4—434no—
483C2×C4⋊C4—434no—
484C2×C4⋊C4—434no—
485C2×C4⋊C4—434no—
486C2×C4⋊C4—434no—
487C2×C4⋊C4—434no—
488C2×C4⋊C4—434no—
489C2×C4⋊C4—864no—
490C2×C4⋊C4—864no—
491C2×C4⋊C4—864no—
492C2×C4⋊C4—864no—
493C2×C4⋊C4—864no—
494C2×C4⋊C4—864no—
495C2×C4⋊C4—1722no—
496C2×C4⋊C4—1722no—
497C2×C4⋊C4—1722no—
498C2×C4⋊C4C22×D4314yes—
499C2×C4⋊C4C22×D4314yes—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—434no—
502C2×C22⋊C4—434no—
503C2×C22⋊C4—864no—
504C2×C22⋊C4—864no—
505C2×C22⋊C4C22⋊D4318yes—
506C2×C22⋊C4C22×D4314yes—
507C2×C22⋊C4C22×D4314yes—
508C2×C42—24no—
509C2×C42—24no—
510C2×C42C22×D4314yes—
511C2×C42C22×D4314yes—
512#95—434no—
513#95—434no—
514#95—434no—
515#95—434no—
516#95—434no—
517#95—434no—
518#95—434no—
519#95—434no—
520#95—434no—
521#95—434no—
522#95—434no—
523#95—434no—
524#95—434no—
525#95—434no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24C2×Dic8614yes—
531C24#1062189814yes—
532C24C2×C22⋊D4314yes—
533C24C23×D4312yes—
534C24C23×D4311yescharacteristic
535C2×Q8—868no—
536C2×Q8—868no—
537C2×Q8—1724no—
538C2×Q8—17216no—
539C22×C4—232no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—28no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—28no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—434no—
557C22×C4—434no—
558C22×C4—432no—
559C22×C4—432no—
560C22×C4—432no—
561C22×C4—432no—
562C22×C4—432no—
563C22×C4—432no—
564C22×C4—432no—
565C22×C4—432no—
566C22×C4—868no—
567C22×C4—868no—
568C22×C4—862no—
569C22×C4—862no—
570C22×C4—862no—
571C22×C4—862no—
572C22×C4—862no—
573C22×C4—862no—
574C22×C4—862no—
575C22×C4—868no—
576C22×C4—862no—
577C22×C4—862no—
578C22×C4—862no—
579C22×C4—862no—
580C22×C4—862no—
581C22×C4—862no—
582C22×C4—862no—
583C22×C4—862no—
584C22×C4—868no—
585C22×C4—862no—
586C22×C4—862no—
587C22×C4—862no—
588C22×C4—862no—
589C22×C4—862no—
590C22×C4—862no—
591C22×C4—862no—
592C22×C4—1724no—
593C22×C4—1724no—
594C22×C4—17216no—
595C22×C4—17216no—
596C22×C4C2×Dic8614yes—
597C22×C4C2×Dic8614yes—
598C22×C4C2×Dic86116yescomplemented
599C22×C4C2×C22⋊D4314yes—
600C22×C4C2×C22⋊D4314yes—
601C22×C4C23×D4312yes—
602C22×C4C23×D4312yes—
603C22×C4C23×D4312yes—
604C22×C4C23×D4312yes—
605C22×C4C23×D4312yes—
606C22×C4C23×D4312yes—
607C4⋊C4—28no—
608C4⋊C4—28no—
609C4⋊C4—868no—
610C4⋊C4—868no—
611C4⋊C4—868no—
612C4⋊C4—868no—
613C4⋊C4—868no—
614C4⋊C4—868no—
615C4⋊C4—1724no—
616C4⋊C4—1724no—
617C4⋊C4—1724no—
618C22⋊C4—28no—
619C22⋊C4—868no—
620C22⋊C4—868no—
621C22⋊C4C2×C22⋊D43116yes—
622C42—28no—
623C42—28no—
624C23—28no—
625C23—28no—
626C23—28no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—28no—
632C23—28no—
633C23—28no—
634C23#13063304116yes—
635C23C22×C22⋊D4314yes—
636C23C22×C22⋊D4312yes—
637C23C22×Dic8614yes—
638C23C22×Dic8612yes—
639C23#41×D4312yes—
640C23#41×D4312yes—
641C23C2×#1062189814yes—
642C23C2×#1062189812yes—
643C23#1306337112yes—
644C23#1306337212yes—
645C23C24×D4311yescharacteristic
646Q8—17216no—
647C2×C4—28no—
648C2×C4—28no—
649C2×C4—232no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—28no—
659C2×C4—28no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—44no—
667C2×C4—44no—
668C2×C4—434no—
669C2×C4—434no—
670C2×C4—868no—
671C2×C4—862no—
672C2×C4—862no—
673C2×C4—862no—
674C2×C4—862no—
675C2×C4—868no—
676C2×C4—862no—
677C2×C4—862no—
678C2×C4—862no—
679C2×C4—862no—
680C2×C4—862no—
681C2×C4—862no—
682C2×C4—862no—
683C2×C4—862no—
684C2×C4—862no—
685C2×C4—862no—
686C2×C4—862no—
687C2×C4—862no—
688C2×C4—862no—
689C2×C4—862no—
690C2×C4—862no—
691C2×C4—862no—
692C2×C4—862no—
693C2×C4—862no—
694C2×C4—17216no—
695C2×C4—17216no—
696C2×C4—1724no—
697C2×C4—1724no—
698C2×C4—1724no—
699C2×C4—1724no—
700C2×C4—1724no—
701C2×C4—1724no—
702C2×C4C22×C22⋊D4314yes—
703C2×C4C22×C22⋊D4314yes—
704C2×C4C22×Dic8614yes—
705C2×C4C22×Dic8614yes—
706C22—24no—
707C22—24no—
708C22—24no—
709C22—24no—
710C22—24no—
711C22—232no—
712C22—24no—
713C22C2×#1306330418yes—
714C22C2×#1306330414yes—
715C22#1458345214yes—
716C22#1458352714yes—
717C22#1458353714yes—
718C22#1458354814yes—
719C22#1458357314yes—
720C22#1458358214yes—
721C22C23×C22⋊D4311yescharacteristic
722C22C23×Dic8611yescharacteristic
723C22C2×#41×D4311yescharacteristic
724C22C2×#41×D4311yescharacteristic
725C22C22×#1062189811yescharacteristic
726C22C2×#1306337111yescharacteristic
727C22C2×#1306337211yescharacteristic
728C4—24no—
729C4—24no—
730C4—24no—
731C4—24no—
732C4—42no—
733C4—42no—
734C4—864no—
735C4—864no—
736C4—1722no—
737C4—1722no—
738C4—1722no—
739C4—1722no—
740C4—1722no—
741C4—1722no—
742C2—28no—
743C2#1913826518yesdirect product factor
744C2C22×#1306330411yescharacteristic
745C2C2×#1458345211yescharacteristic
746C2C2×#1458352711yescharacteristic
747C2C2×#1458353711yescharacteristic
748C2C2×#1458354811yescharacteristic
749C2C2×#1458357311yescharacteristic
750C2C2×#1458358211yescharacteristic
subgroupG/H
centerC24C23×D43
commutator, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC22×#117×C43C2
socleC24×C43C24
prime radicalC25×C43C23
hypercenterC22×#117D43
hypocenterC43C2×#2438
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22×#117

Complements

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

NH ≅ G/Ntype
2. #19138265C2direct (N × H)
3. C2×#14582838C2semidirect
4. C2×#14582832C2semidirect
5. C2×#14582832C2semidirect
6. C2×#14582819C2semidirect
7. C2×#14582805C2semidirect
8. C2×#14582797C2semidirect
9. C2×#14582783C2semidirect
10. C2×#14582783C2semidirect
33. #14582838C22semidirect
34. #14582832C22semidirect
35. #14582832C22semidirect
36. #14582819C22semidirect
37. #14582805C22semidirect
38. #14582797C22semidirect
39. #14582783C22semidirect
40. #14582783C22semidirect
129. C23×C4×C43Q8semidirect
180. C22×C4×C43C2×Q8semidirect
384. C2×C43#2438semidirect
444. C43C2×#2438semidirect
468. C23×C4Dic86semidirect
598. C22×C4C2×Dic86semidirect
743. C2#19138265direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633022
#191382652
C2×#145828382
C2×#145828322
C2×#145828192
C2×#145828052
C2×#145827972
C2×#145827832
C2×#145827742
C2×#145827712
C2×#145827622
C2×#145827572
C22×C43⋊#952
C22×#117×C432
C2×#243843