Finite Group Databasebeta

← C2×#22593278 #32168623

Subgroups — C2×#22593278 #32168623

Order 18176.

4566 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×#14556117C211yesmaximal, characteristic, complemented
2C22×#14556104C211yesmaximal, characteristic, complemented
3C22×#14556103C211yesmaximal, characteristic, complemented
4C22×#14556102C211yesmaximal, characteristic, complemented
5C22×C4×C22⋊D71C211yesmaximal, characteristic, complemented
6#22593278C2116yesmaximal, direct product factor
7C2×#17985934C212yesmaximal, complemented
8C2×#17985908C212yesmaximal, complemented
9C2×#17985900C212yesmaximal, complemented
10C2×#17985899C212yesmaximal, complemented
11C2×C4⋊C4×Dic71C211yesmaximal, characteristic, complemented
12C22×C22⋊Q8×C71C211yesmaximal, characteristic, complemented
13C23×D284C2211yescharacteristic
14C23×D284C2212yes—
15C23×C22⋊D71C2211yescharacteristic
16C23×C22⋊D71C2212yes—
17C23×C4×D71C2211yescharacteristic
18C2×#14556117—28no—
19C2×#14556117C2218yescomplemented
20C2×#14556104—28no—
21C2×#14556104C2218yescomplemented
22C2×#14556103—28no—
23C2×#14556103C2218yescomplemented
24C2×#14556102—28no—
25C2×#14556102C2218yescomplemented
26C2×C4×C22⋊D71—28no—
27C2×C4×C22⋊D71C2218yescomplemented
28C22×C4⋊Dic71C2211yescharacteristic
29C22×Dic71⋊C4C2211yescharacteristic
30C22×Dic71⋊C4C2212yes—
31C22×C22⋊Dic71C2211yescharacteristic
32C22×(C2×D71)⋊C4C2211yescharacteristic
33C22×(C2×D71)⋊C4C2212yes—
34C22×(C2×D71)⋊C4C2212yes—
35C22×(C2×D71)⋊C4C2212yes—
36C22×(C2×D71)⋊C4C2212yes—
37C22×(C2×D71)⋊C4C2212yes—
38C22×C4×Dic71C2212yes—
39C22×C4×Dic71C2211yescharacteristic
40#17985934C22116yescomplemented
41#17985908C22116yescomplemented
42#17985900C22116yescomplemented
43#17985899C22116yescomplemented
44C4⋊C4×Dic71C2218yescomplemented
45C2×C71⋊#95C2212yes—
46C23×Q8×C71C2211yescharacteristic
47C24×C4×C71C2211yescharacteristic
48C2×C22⋊Q8×C71—28no—
49C2×C22⋊Q8×C71C2218yescomplemented
50C22×C4⋊C4×C71C2212yes—
51C22×C4⋊C4×C71C2211yescharacteristic
52C22×C22⋊C4×C71C2212yes—
53C24×D71C2312yes—
54C24×D71C2311yescharacteristic
55C22×D284—28no—
56C22×D284—24no—
57C22×D284—28no—
58C22×D284—24no—
59C22×D284—24no—
60C22×D284—44no—
61C22×D284C2314yes—
62C22×D284C2318yes—
63C22×C22⋊D71—24no—
64C22×C22⋊D71—24no—
65C22×C22⋊D71—28no—
66C22×C22⋊D71—24no—
67C22×C22⋊D71—28no—
68C22×C22⋊D71—44no—
69C22×C22⋊D71C2314yes—
70C22×C22⋊D71C2318yes—
71C23×Dic71C2311yescharacteristic
72C23×Dic71C2311yescharacteristic
73C23×Dic71C2312yes—
74C23×Dic71C2311yescharacteristic
75C22×C4×D71—24no—
76C22×C4×D71—24no—
77C22×C4×D71—24no—
78C22×C4×D71C2314yes—
79#14556117—232no—
80#14556104—232no—
81#14556103—232no—
82#14556102—232no—
83C4×C22⋊D71—232no—
84C2×C4⋊Dic71D418yescomplemented
85C2×C4⋊Dic71C2314yes—
86C2×Dic71⋊C4—24no—
87C2×Dic71⋊C4—28no—
88C2×Dic71⋊C4C2318yes—
89C2×Dic71⋊C4C2314yes—
90C2×C22⋊Dic71—24no—
91C2×C22⋊Dic71C2314yes—
92C2×(C2×D71)⋊C4—24no—
93C2×(C2×D71)⋊C4—28no—
94C2×(C2×D71)⋊C4—28no—
95C2×(C2×D71)⋊C4—28no—
96C2×(C2×D71)⋊C4—28no—
97C2×(C2×D71)⋊C4—28no—
98C2×(C2×D71)⋊C4C2318yes—
99C2×(C2×D71)⋊C4C2318yes—
100C2×(C2×D71)⋊C4C2314yes—
101C2×(C2×D71)⋊C4C2318yes—
102C2×(C2×D71)⋊C4C2318yes—
103C2×(C2×D71)⋊C4C2318yes—
104C2×C4×Dic71—44no—
105C2×C4×Dic71D418yescomplemented
106C2×C4×Dic71C2318yes—
107C2×C4×Dic71C2314yes—
108C71⋊#95C2318yes—
109C25×C71C2311yescharacteristic
110C22×Q8×C71—24no—
111C22×Q8×C71—24no—
112C22×Q8×C71—24no—
113C22×Q8×C71C2314yes—
114C23×C4×C71—24no—
115C23×C4×C71—24no—
116C23×C4×C71—24no—
117C23×C4×C71C2312yes—
118C23×C4×C71C2311yescharacteristic
119C23×C4×C71C2314yes—
120C23×C4×C71C2312yes—
121C23×C4×C71C2311yescharacteristic
122C22⋊Q8×C71—232no—
123C2×C4⋊C4×C71—28no—
124C2×C4⋊C4×C71D418yescomplemented
125C2×C4⋊C4×C71C2318yes—
126C2×C4⋊C4×C71C2314yes—
127C2×C22⋊C4×C71—28no—
128C2×C22⋊C4×C71C2318yes—
129C23×D71—22no—
130C23×D71—22no—
131C23×D71—22no—
132C23×D71—22no—
133C23×D71—22no—
134C23×D71—22no—
135C23×D71—24no—
136C23×D71—24no—
137C23×D71—24no—
138C23×D71—24no—
139C23×D71—24no—
140C23×D71—24no—
141C23×D71—24no—
142C23×D71#4114yes—
143C23×D71C2414yes—
144C23×D71C2412yes—
145C2×D284—216no—
146C2×D284—28no—
147C2×D284—216no—
148C2×D284—28no—
149C2×D284—28no—
150C2×D284—48no—
151C2×D284—432no—
152C2×D284—416no—
153C2×C22⋊D71—232no—
154C2×C22⋊D71—28no—
155C2×C22⋊D71—28no—
156C2×C22⋊D71—216no—
157C2×C22⋊D71—28no—
158C2×C22⋊D71—216no—
159C2×C22⋊D71—48no—
160C2×C22⋊D71—432no—
161C22×Dic71—22no—
162C22×Dic71—22no—
163C22×Dic71—24no—
164C22×Dic71—24no—
165C22×Dic71—22no—
166C22×Dic71—22no—
167C22×Dic71—22no—
168C22×Dic71—22no—
169C22×Dic71—22no—
170C22×Dic71C2×D414yes—
171C22×Dic71C2×D418yes—
172C22×Dic71C2×D414yes—
173C22×Dic71C2412yes—
174C22×Dic71C2412yes—
175C22×Dic71C2414yes—
176C22×Dic71C2412yes—
177C2×C4×D71—28no—
178C2×C4×D71—28no—
179C2×C4×D71—28no—
180C2×C4×D71—416no—
181C4⋊Dic71C2×D4116yescomplemented
182Dic71⋊C4—28no—
183Dic71⋊C4—216no—
184C22⋊Dic71—28no—
185(C2×D71)⋊C4—216no—
186(C2×D71)⋊C4—28no—
187(C2×D71)⋊C4—216no—
188(C2×D71)⋊C4—216no—
189(C2×D71)⋊C4—216no—
190(C2×D71)⋊C4—216no—
191C4×Dic71—48no—
192C4×Dic71C2×D4116yescomplemented
193C24×C71—22no—
194C24×C71—22no—
195C24×C71—22no—
196C24×C71—22no—
197C24×C71—22no—
198C24×C71—22no—
199C24×C71#4114yes—
200C24×C71C2412yes—
201C24×C71C2411yescharacteristic
202C2×Q8×C71—28no—
203C2×Q8×C71—28no—
204C2×Q8×C71—28no—
205C2×Q8×C71—416no—
206C22×C4×C71—24no—
207C22×C4×C71—24no—
208C22×C4×C71—24no—
209C22×C4×C71—22no—
210C22×C4×C71—22no—
211C22×C4×C71—22no—
212C22×C4×C71—24no—
213C22×C4×C71—24no—
214C22×C4×C71—28no—
215C22×C4×C71—28no—
216C22×C4×C71—28no—
217C22×C4×C71—416no—
218C22×C4×C71C2×D414yes—
219C22×C4×C71C2×D414yes—
220C22×C4×C71C2×D418yes—
221C22×C4×C71C2×D414yes—
222C22×C4×C71C2414yes—
223C22×C4×C71C2412yes—
224C22×C4×C71C2414yes—
225C22×C4×C71C2412yes—
226C4⋊C4×C71—216no—
227C4⋊C4×C71C2×D4116yescomplemented
228C22⋊C4×C71—216no—
229C23×C71—28no—
230C23×C71—28no—
231C23×C71—28no—
232C23×C71—22no—
233C23×C71—22no—
234C23×C71—22no—
235C23×C71—22no—
236C23×C71—22no—
237C23×C71—22no—
238C23×C71—44no—
239C23×C71—44no—
240C23×C71—44no—
241C23×C71—44no—
242C23×C71C22×D412yes—
243C23×C71C22×D412yes—
244C23×C71C22×D412yes—
245C23×C71C2×#4112yes—
246C23×C71C2×#4114yes—
247C23×C71C2×#4112yes—
248C23×C71H(5,𝔽2)12yes—
249C23×C712−1+412yes—
250C23×C71C2511yescharacteristic
251C22×D71—28no—
252C22×D71—28no—
253C22×D71—28no—
254C22×D71—22no—
255C22×D71—22no—
256C22×D71—22no—
257C22×D71—22no—
258C22×D71—22no—
259C22×D71—22no—
260C22×D71—24no—
261C22×D71—24no—
262C22×D71—24no—
263C22×D71—24no—
264C22×D71—24no—
265C22×D71—24no—
266C22×D71—24no—
267C22×D71—44no—
268C22×D71—44no—
269C22×D71—44no—
270C22×D71—44no—
271C22×D71—48no—
272C22×D71—48no—
273C22×D71—48no—
274C22×D71—48no—
275C22×D71—48no—
276C22×D71—48no—
277C22×D71—48no—
278C22×D71C2×#4114yes—
279Q8×C71—416no—
280C2×C4×C71—216no—
281C2×C4×C71—24no—
282C2×C4×C71—24no—
283C2×C4×C71—24no—
284C2×C4×C71—22no—
285C2×C4×C71—22no—
286C2×C4×C71—22no—
287C2×C4×C71—24no—
288C2×C4×C71—24no—
289C2×C4×C71—44no—
290C2×C4×C71—48no—
291C2×C4×C71—416no—
292C2×C4×C71#127116yes—
293C2×C4×C71C22×D414yes—
294C2×C4×C71C22×D414yes—
295C2×C4×C71C22×D418yes—
296C2×C4×C71C22×D414yes—
297C22⋊D71—232no—
298C22⋊D71—432no—
299C2×Dic71—28no—
300C2×Dic71—28no—
301C2×Dic71—216no—
302C2×Dic71—22no—
303C2×Dic71—22no—
304C2×Dic71—24no—
305C2×Dic71—22no—
306C2×Dic71—24no—
307C2×Dic71—22no—
308C2×Dic71—22no—
309C2×Dic71—22no—
310C2×Dic71—22no—
311C2×Dic71—44no—
312C2×Dic71C22×D414yes—
313C2×Dic71C22×D414yes—
314C2×Dic71C22×D418yes—
315D284—432no—
316D284—416no—
317C4×D71—416no—
318C22×C71—24no—
319C22×C71—24no—
320C22×C71—24no—
321C22×C71—42no—
322C22×C71—42no—
323C22×C71—42no—
324C22×C71—42no—
325C22×C71—416no—
326C22×C71#52514yes—
327C22×C71C2×#12714yes—
328C22×C71#53714yes—
329C22×C71#54614yes—
330C22×C71#54614yes—
331C22×C71#54814yes—
332C22×C71#54814yes—
333C22×C71C23×D411yescharacteristic
334C22×C71C23×D411yescharacteristic
335C22×C71C23×D411yescharacteristic
336C22×C71C22×#4111yescharacteristic
337C22×C71C22×#4111yescharacteristic
338C22×C71C2×H(5,𝔽2)11yescharacteristic
339C22×C71C2×2−1+411yescharacteristic
340C2×D71—24no—
341C2×D71—24no—
342C2×D71—24no—
343C2×D71—42no—
344C2×D71—42no—
345C2×D71—42no—
346C2×D71—42no—
347C2×D71—416no—
348C2×D71—44no—
349C2×D71—44no—
350C2×D71—44no—
351C2×D71—44no—
352C2×D71—44no—
353C2×D71—44no—
354C2×D71—44no—
355C2×D71—816no—
356C4×C71—28no—
357C4×C71—42no—
358C4×C71—44no—
359C4×C71C2×#12718yes—
360Dic71—24no—
361Dic71—24no—
362Dic71—28no—
363Dic71—42no—
364C2×#2540—711nomaximal, Sylow
365C2×C71—44no—
366C2×C71#254018yescomplemented
367C2×C71C2×#52511yescharacteristic
368C2×C71C22×#12711yescharacteristic
369C2×C71C2×#53711yescharacteristic
370C2×C71C2×#54611yescharacteristic
371C2×C71C2×#54611yescharacteristic
372C2×C71C2×#54811yescharacteristic
373C2×C71C2×#54811yescharacteristic
374D71—44no—
375D71—84no—
376C22×#124—711no—
377C22×C22⋊Q8—711no—
378C22×C22⋊Q8D7111yescharacteristic, complemented
379C22×#121—711no—
380C22×#121—711no—
381C22×C4×D4—711no—
382#2540—7116no—
383C2×#399—712no—
384C2×#392—712no—
385C2×#390—712no—
386C2×#390—712no—
387C2×C4×C4⋊C4—711no—
388C71C2×#254011yescharacteristic, complemented, Sylow
389C23×Q8C2×D7111yescharacteristic
390C23×D4—712no—
391C23×D4—711no—
392C23×D4—712no—
393C23×D4—711no—
394C24×C4—711no—
395C24×C4C2×D7111yescharacteristic
396C2×#124—718no—
397C2×#124—1428no—
398C2×C22⋊Q8—28no—
399C2×C22⋊Q8—718no—
400C2×C22⋊Q8—1428no—
401C2×C22⋊Q8C2×D7118yescomplemented
402C2×#121—718no—
403C2×#121—718no—
404C2×#121—1428no—
405C2×#121—1428no—
406C2×C4×D4—718no—
407C2×C4×D4—1428no—
408C22×C4⋊C4—711no—
409C22×C4⋊C4—711no—
410C22×C4⋊C4—712no—
411C22×C4⋊C4C2×D7112yes—
412C22×C4⋊C4C2×D7111yescharacteristic
413C22×C22⋊C4—711no—
414C22×C22⋊C4—712no—
415C22×C22⋊C4—712no—
416C22×C22⋊C4—712no—
417C22×C22⋊C4—712no—
418C22×C22⋊C4—711no—
419C22×C22⋊C4—712no—
420C22×C22⋊C4C2×D7112yes—
421C22×C42—712no—
422C22×C42—711no—
423#399—7116no—
424#392—7116no—
425#390—7116no—
426#390—7116no—
427C4×C4⋊C4—718no—
428C2×#95—712no—
429C25—711no—
430C25—712no—
431C25C22×D7111yescharacteristic
432C22×Q8—24no—
433C22×Q8—24no—
434C22×Q8—24no—
435C22×Q8C22×D7114yes—
436C22×D4—2844no—
437C22×D4—2844no—
438C22×D4—718no—
439C22×D4—714no—
440C22×D4—718no—
441C22×D4—714no—
442C22×D4—1428no—
443C22×D4—1428no—
444C22×D4—1424no—
445C22×D4—1428no—
446C22×D4—1424no—
447C22×D4—1424no—
448C22×D4—1424no—
449C22×D4—1424no—
450C22×D4—1428no—
451C22×D4—1424no—
452C23×C4—24no—
453C23×C4—24no—
454C23×C4—24no—
455C23×C4—711no—
456C23×C4—712no—
457C23×C4—711no—
458C23×C4—711no—
459C23×C4—714no—
460C23×C4—1424no—
461C23×C4—1424no—
462C23×C4—1424no—
463C23×C4C22×D7114yes—
464C23×C4C22×D7112yes—
465C23×C4C22×D7111yescharacteristic
466C23×C4C22×D7112yes—
467C23×C4C22×D7111yescharacteristic
468#124—14232no—
469C22⋊Q8—232no—
470C22⋊Q8—14232no—
471#121—14232no—
472#121—14232no—
473C4×D4—14232no—
474C2×C4⋊C4—28no—
475C2×C4⋊C4—718no—
476C2×C4⋊C4—714no—
477C2×C4⋊C4—714no—
478C2×C4⋊C4—718no—
479C2×C4⋊C4—1424no—
480C2×C4⋊C4—1428no—
481C2×C4⋊C4C22⋊D7118yescomplemented
482C2×C4⋊C4C22×D7118yes—
483C2×C4⋊C4C22×D7114yes—
484C2×C22⋊C4—28no—
485C2×C22⋊C4—714no—
486C2×C22⋊C4—714no—
487C2×C22⋊C4—718no—
488C2×C22⋊C4—718no—
489C2×C22⋊C4—718no—
490C2×C22⋊C4—718no—
491C2×C22⋊C4—718no—
492C2×C22⋊C4—1424no—
493C2×C22⋊C4—1428no—
494C2×C22⋊C4—1428no—
495C2×C22⋊C4—1428no—
496C2×C22⋊C4—1428no—
497C2×C22⋊C4—1424no—
498C2×C22⋊C4—1428no—
499C2×C22⋊C4C22×D7118yes—
500C2×C42—2844no—
501C2×C42—718no—
502C2×C42—718no—
503C2×C42—714no—
504#95—718no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24—22no—
509C24—22no—
510C24—22no—
511C24—714no—
512C24—712no—
513C24—714no—
514C24—1424no—
515C24—1424no—
516C24—1424no—
517C24—1424no—
518C24—1424no—
519C24—1424no—
520C24—1424no—
521C24—1422no—
522C24—1422no—
523C24—1422no—
524C24—1422no—
525C24—1422no—
526C24—1422no—
527C24#1176586614yes—
528C24C23×D7112yes—
529C24C23×D7111yescharacteristic
530C2×Q8—28no—
531C2×Q8—28no—
532C2×Q8—28no—
533C2×Q8—416no—
534C2×D4—28432no—
535C2×D4—2848no—
536C2×D4—28432no—
537C2×D4—2848no—
538C2×D4—28416no—
539C2×D4—14216no—
540C2×D4—14216no—
541C2×D4—1428no—
542C2×D4—14216no—
543C2×D4—1428no—
544C2×D4—14232no—
545C2×D4—1428no—
546C2×D4—1428no—
547C2×D4—1428no—
548C2×D4—14216no—
549C2×D4—1428no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—22no—
553C22×C4—24no—
554C22×C4—22no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—22no—
558C22×C4—28no—
559C22×C4—28no—
560C22×C4—28no—
561C22×C4—416no—
562C22×C4—28416no—
563C22×C4—714no—
564C22×C4—714no—
565C22×C4—718no—
566C22×C4—712no—
567C22×C4—714no—
568C22×C4—712no—
569C22×C4—712no—
570C22×C4—1422no—
571C22×C4—1422no—
572C22×C4—1422no—
573C22×C4—1428no—
574C22×C4—1428no—
575C22×C4—1428no—
576C22×C4—1422no—
577C22×C4—1424no—
578C22×C4—1422no—
579C22×C4—1422no—
580C22×C4—1424no—
581C22×C4—1422no—
582C22×C4D4×D7114yes—
583C22×C4D4×D7114yes—
584C22×C4C2×C22⋊D7118yes—
585C22×C4C2×C22⋊D7114yes—
586C22×C4C23×D7114yes—
587C22×C4C23×D7112yes—
588C22×C4C23×D7114yes—
589C22×C4C23×D7112yes—
590C4⋊C4—216no—
591C4⋊C4—7116no—
592C4⋊C4—1428no—
593C4⋊C4—14216no—
594C4⋊C4C2×C22⋊D71116yescomplemented
595C22⋊C4—216no—
596C22⋊C4—1428no—
597C22⋊C4—14216no—
598C22⋊C4—14216no—
599C22⋊C4—14216no—
600C22⋊C4—14216no—
601C22⋊C4—1428no—
602C22⋊C4—14216no—
603C42—2848no—
604C42—7116no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—28no—
612C23—28no—
613C23—28no—
614C23—44no—
615C23—44no—
616C23—44no—
617C23—44no—
618C23—2844no—
619C23—2844no—
620C23—2844no—
621C23—2844no—
622C23—2848no—
623C23—2848no—
624C23—2848no—
625C23—2848no—
626C23—2848no—
627C23—2848no—
628C23—2848no—
629C23—714no—
630C23—1424no—
631C23—1424no—
632C23—1424no—
633C23—1424no—
634C23—1424no—
635C23—1424no—
636C23—1424no—
637C23—1422no—
638C23—1422no—
639C23—1422no—
640C23—1422no—
641C23—1422no—
642C23—1422no—
643C23—1428no—
644C23—1428no—
645C23—1428no—
646C23C2×D4×D7112yes—
647C23C2×D4×D7112yes—
648C23C22×C22⋊D7112yes—
649C23#41×D7112yes—
650C23C2×#1176586614yes—
651C23C2×#1176586612yes—
652C23#1455617412yes—
653C23#1455617612yes—
654C23C24×D7111yescharacteristic
655Q8—416no—
656D4—28432no—
657D4—28432no—
658D4—28416no—
659D4—14232no—
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—216no—
663C2×C4—22no—
664C2×C4—24no—
665C2×C4—22no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—22no—
669C2×C4—44no—
670C2×C4—48no—
671C2×C4—416no—
672C2×C4—2844no—
673C2×C4—28416no—
674C2×C4—714no—
675C2×C4—714no—
676C2×C4—718no—
677C2×C4—1422no—
678C2×C4—1422no—
679C2×C4—1422no—
680C2×C4—1422no—
681C2×C4—1424no—
682C2×C4—1422no—
683C2×C4—1422no—
684C2×C4—1424no—
685C2×C4—1422no—
686C2×C4—1428no—
687C2×C4—14216no—
688C2×C4—1428no—
689C2×C4#14556124116yes—
690C2×C4C2×D4×D7114yes—
691C2×C4C2×D4×D7114yes—
692C2×C4C22×C22⋊D7118yes—
693C2×C4C22×C22⋊D7114yes—
694C22—24no—
695C22—24no—
696C22—24no—
697C22—42no—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—416no—
702C22—2842no—
703C22—2842no—
704C22—2842no—
705C22—2842no—
706C22—28416no—
707C22—2844no—
708C22—2844no—
709C22—2844no—
710C22—2844no—
711C22—2844no—
712C22—2844no—
713C22—2844no—
714C22—56816no—
715C22—1424no—
716C22—1424no—
717C22—1424no—
718C22#1798651214yes—
719C22C2×#1455612414yes—
720C22#1798657914yes—
721C22#1798663714yes—
722C22#1798664014yes—
723C22#1798665914yes—
724C22#1798666014yes—
725C22C22×D4×D7111yescharacteristic
726C22C22×D4×D7111yescharacteristic
727C22C23×C22⋊D7111yescharacteristic
728C22C2×#41×D7111yescharacteristic
729C22C22×#1176586611yescharacteristic
730C22C2×#1455617411yescharacteristic
731C22C2×#1455617611yescharacteristic
732C4—28no—
733C4—42no—
734C4—44no—
735C4—2842no—
736C4—1428no—
737C4—1424no—
738C4—1424no—
739C4C2×#1455612418yes—
740C2—44no—
741C2—2844no—
742C2—5684no—
743C2#2259327818yesdirect product factor
744C2C2×#1798651211yescharacteristic
745C2C22×#1455612411yescharacteristic
746C2C2×#1798657911yescharacteristic
747C2C2×#1798663711yescharacteristic
748C2C2×#1798664011yescharacteristic
749C2C2×#1798665911yescharacteristic
750C2C2×#1798666011yescharacteristic
subgroupG/H
centerC24C23×D71
commutator, cosocleC23×C71C25
FrattiniC23C24×D71
FittingC22×C22⋊Q8×C71C2
socleC24×C71C24
hypercenterC22×C22⋊Q8D71
hypocenterC71C2×#2540
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×#14556117C2semidirect
2. C22×#14556104C2semidirect
3. C22×#14556103C2semidirect
4. C22×#14556102C2semidirect
5. C22×C4×C22⋊D71C2semidirect
6. #22593278C2direct (N × H)
7. C2×#17985934C2semidirect
8. C2×#17985908C2semidirect
9. C2×#17985900C2semidirect
10. C2×#17985899C2semidirect
11. C2×C4⋊C4×Dic71C2semidirect
12. C22×C22⋊Q8×C71C2semidirect
19. C2×#14556117C22semidirect
21. C2×#14556104C22semidirect
23. C2×#14556103C22semidirect
25. C2×#14556102C22semidirect
27. C2×C4×C22⋊D71C22semidirect
40. #17985934C22semidirect
41. #17985908C22semidirect
42. #17985900C22semidirect
43. #17985899C22semidirect
44. C4⋊C4×Dic71C22semidirect
49. C2×C22⋊Q8×C71C22semidirect
84. C2×C4⋊Dic71D4semidirect
105. C2×C4×Dic71D4semidirect
124. C2×C4⋊C4×C71D4semidirect
181. C4⋊Dic71C2×D4semidirect
192. C4×Dic71C2×D4semidirect
227. C4⋊C4×C71C2×D4semidirect
366. C2×C71#2540semidirect
378. C22×C22⋊Q8D71semidirect
388. C71C2×#2540semidirect
401. C2×C22⋊Q8C2×D71semidirect
481. C2×C4⋊C4C22⋊D71semidirect
594. C4⋊C4C2×C22⋊D71semidirect
743. C2#22593278direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561172
C22×#145561042
C22×#145561032
C22×#145561022
C22×C4×C22⋊D712
#225932782
C2×#179859342
C2×#179859082
C2×#179859002
C2×#179858992
C2×C4⋊C4×Dic712
C22×C22⋊Q8×C712
C2×#254071