Finite Group Databasebeta

← C2×#22591687 #32165766

Subgroups — C2×#22591687 #32165766

Order 18176.

5998 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#11765866C211yesmaximal, characteristic, complemented
2C22×#14556102C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D71C211yesmaximal, characteristic, complemented
4#22591687C2116yesmaximal, direct product factor
5C2×#17985916C212yesmaximal, complemented
6C2×#17985908C212yesmaximal, complemented
7C2×#17985906C211yesmaximal, characteristic, complemented
8C2×#17985900C211yesmaximal, characteristic, complemented
9C2×#17985875C212yesmaximal, complemented
10C2×#17985870C212yesmaximal, complemented
11C2×#17985856C211yesmaximal, characteristic, complemented
12C22×C22⋊Q8×C71C211yesmaximal, characteristic, complemented
13C22×#11765866—28no—
14C22×#11765866—28no—
15C22×#11765866—28no—
16C22×#11765866C2218yescomplemented
17C23×D284C2212yes—
18C23×D284C2211yescharacteristic
19C23×C22⋊D71C2211yescharacteristic
20C23×C22⋊D71C2212yes—
21C23×C4×D71C2212yes—
22C23×C4×D71C2211yescharacteristic
23C2×#14556102—28no—
24C2×#14556102C2218yescomplemented
25C2×C4×C22⋊D71—28no—
26C2×C4×C22⋊D71C2218yescomplemented
27C22×C4⋊Dic71C2211yescharacteristic
28C22×Dic71⋊C4C2211yescharacteristic
29C22×C22⋊Dic71C2211yescharacteristic
30C22×(C2×D71)⋊C4C2212yes—
31C22×(C2×D71)⋊C4C2212yes—
32C22×(C2×D71)⋊C4C2211yescharacteristic
33C22×(C2×D71)⋊C4C2212yes—
34C22×(C2×D71)⋊C4C2212yes—
35C22×C4×Dic71C2211yescharacteristic
36#17985916C22116yescomplemented
37#17985908C22116yescomplemented
38#17985906C2218yescomplemented
39#17985900C2218yescomplemented
40#17985875C22116yescomplemented
41#17985870C22116yescomplemented
42#17985856C2218yescomplemented
43C2×C71⋊#95C2212yes—
44C2×C71⋊#95C2212yes—
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×D71C2311yescharacteristic
54C24×D71C2312yes—
55C2×#11765866—2128no—
56C2×#11765866—232no—
57C2×#11765866—232no—
58C2×#11765866—232no—
59C22×D284—28no—
60C22×D284—28no—
61C22×D284—24no—
62C22×D284—28no—
63C22×D284—24no—
64C22×D284D418yescomplemented
65C22×D284C2318yes—
66C22×D284C2314yes—
67C22×C22⋊D71—24no—
68C22×C22⋊D71—28no—
69C22×C22⋊D71—24no—
70C22×C22⋊D71—24no—
71C22×C22⋊D71—28no—
72C22×C22⋊D71—44no—
73C22×C22⋊D71C2314yes—
74C22×C22⋊D71C2318yes—
75C23×Dic71C2312yes—
76C23×Dic71C2311yescharacteristic
77C23×Dic71C2311yescharacteristic
78C23×Dic71C2311yescharacteristic
79C22×C4×D71—28no—
80C22×C4×D71—28no—
81C22×C4×D71—24no—
82C22×C4×D71—28no—
83C22×C4×D71—24no—
84C22×C4×D71D418yescomplemented
85C22×C4×D71C2318yes—
86C22×C4×D71C2314yes—
87#14556102—232no—
88C4×C22⋊D71—232no—
89C2×C4⋊Dic71—24no—
90C2×C4⋊Dic71C2314yes—
91C2×Dic71⋊C4—24no—
92C2×Dic71⋊C4C2314yes—
93C2×C22⋊Dic71—24no—
94C2×C22⋊Dic71C2314yes—
95C2×(C2×D71)⋊C4—24no—
96C2×(C2×D71)⋊C4—28no—
97C2×(C2×D71)⋊C4—28no—
98C2×(C2×D71)⋊C4—44no—
99C2×(C2×D71)⋊C4—44no—
100C2×(C2×D71)⋊C4C2318yes—
101C2×(C2×D71)⋊C4C2318yes—
102C2×(C2×D71)⋊C4C2314yes—
103C2×(C2×D71)⋊C4C2318yes—
104C2×(C2×D71)⋊C4C2318yes—
105C2×C4×Dic71—24no—
106C2×C4×Dic71C2314yes—
107C71⋊#95C2318yes—
108C71⋊#95C2318yes—
109C71⋊#95C2318yes—
110C25×C71C2311yescharacteristic
111C22×Q8×C71—24no—
112C22×Q8×C71—24no—
113C22×Q8×C71D418yescomplemented
114C22×Q8×C71C2314yes—
115C23×C4×C71—24no—
116C23×C4×C71—24no—
117C23×C4×C71—24no—
118C23×C4×C71C2312yes—
119C23×C4×C71C2311yescharacteristic
120C23×C4×C71C2314yes—
121C23×C4×C71C2312yes—
122C23×C4×C71C2311yescharacteristic
123C22⋊Q8×C71—232no—
124C2×C4⋊C4×C71—24no—
125C2×C4⋊C4×C71—28no—
126C2×C4⋊C4×C71C2314yes—
127C2×C4⋊C4×C71C2318yes—
128C2×C22⋊C4×C71—28no—
129C2×C22⋊C4×C71C2318yes—
130C23×D71—24no—
131C23×D71—22no—
132C23×D71—24no—
133C23×D71—22no—
134C23×D71—22no—
135C23×D71—22no—
136C23×D71—24no—
137C23×D71—24no—
138C23×D71—24no—
139C23×D71—22no—
140C23×D71—22no—
141C23×D71—24no—
142C23×D71C2×D418yes—
143C23×D71C2×D414yes—
144C23×D71C2414yes—
145C23×D71C2412yes—
146#11765866—2256no—
147C2×D284—264no—
148C2×D284—216no—
149C2×D284—216no—
150C2×D284—232no—
151C2×D284—28no—
152C2×D284—216no—
153C2×D284—28no—
154C2×D284C2×D4116yescomplemented
155C2×C22⋊D71—232no—
156C2×C22⋊D71—28no—
157C2×C22⋊D71—28no—
158C2×C22⋊D71—216no—
159C2×C22⋊D71—216no—
160C2×C22⋊D71—28no—
161C2×C22⋊D71—48no—
162C2×C22⋊D71—432no—
163C22×Dic71—22no—
164C22×Dic71—22no—
165C22×Dic71—22no—
166C22×Dic71—22no—
167C22×Dic71—24no—
168C22×Dic71—22no—
169C22×Dic71—24no—
170C22×Dic71—24no—
171C22×Dic71—22no—
172C22×Dic71—22no—
173C22×Dic71C2×D414yes—
174C22×Dic71#4114yescomplemented
175C22×Dic71C2414yes—
176C22×Dic71C2412yes—
177C22×Dic71C2412yes—
178C22×Dic71C2412yes—
179C2×C4×D71—264no—
180C2×C4×D71—216no—
181C2×C4×D71—232no—
182C2×C4×D71—28no—
183C2×C4×D71—216no—
184C2×C4×D71—28no—
185C2×C4×D71—216no—
186C2×C4×D71C2×D4116yescomplemented
187C4⋊Dic71—28no—
188Dic71⋊C4—28no—
189C22⋊Dic71—28no—
190(C2×D71)⋊C4—28no—
191(C2×D71)⋊C4—216no—
192(C2×D71)⋊C4—216no—
193(C2×D71)⋊C4—48no—
194(C2×D71)⋊C4—48no—
195C4×Dic71—28no—
196C24×C71—22no—
197C24×C71—22no—
198C24×C71—22no—
199C24×C71—22no—
200C24×C71—22no—
201C24×C71—22no—
202C24×C71#4114yescomplemented
203C24×C71C2412yes—
204C24×C71C2411yescharacteristic
205C2×Q8×C71—232no—
206C2×Q8×C71—28no—
207C2×Q8×C71—28no—
208C2×Q8×C71C2×D4116yescomplemented
209C22×C4×C71—24no—
210C22×C4×C71—24no—
211C22×C4×C71—24no—
212C22×C4×C71—22no—
213C22×C4×C71—22no—
214C22×C4×C71—22no—
215C22×C4×C71—24no—
216C22×C4×C71—24no—
217C22×C4×C71—28no—
218C22×C4×C71—28no—
219C22×C4×C71—28no—
220C22×C4×C71—416no—
221C22×C4×C71C2×D414yes—
222C22×C4×C71C2×D414yes—
223C22×C4×C71C2×D418yes—
224C22×C4×C71C2×D414yes—
225C22×C4×C71C2414yes—
226C22×C4×C71C2412yes—
227C22×C4×C71C2414yes—
228C22×C4×C71C2412yes—
229C4⋊C4×C71—28no—
230C4⋊C4×C71—216no—
231C22⋊C4×C71—216no—
232C23×C71—28no—
233C23×C71—28no—
234C23×C71—28no—
235C23×C71—22no—
236C23×C71—22no—
237C23×C71—22no—
238C23×C71—22no—
239C23×C71—22no—
240C23×C71—22no—
241C23×C71—44no—
242C23×C71—44no—
243C23×C71—44no—
244C23×C71—44no—
245C23×C71C22×D412yes—
246C23×C71C22×D412yes—
247C23×C71C22×D412yes—
248C23×C71C2×#4112yes—
249C23×C71C2×#4112yes—
250C23×C71C2×#4114yescomplemented
251C23×C71H(5,𝔽2)12yes—
252C23×C712−1+412yes—
253C23×C71C2511yescharacteristic
254C22×D71—216no—
255C22×D71—28no—
256C22×D71—28no—
257C22×D71—28no—
258C22×D71—216no—
259C22×D71—216no—
260C22×D71—24no—
261C22×D71—22no—
262C22×D71—24no—
263C22×D71—22no—
264C22×D71—24no—
265C22×D71—22no—
266C22×D71—22no—
267C22×D71—24no—
268C22×D71—22no—
269C22×D71—24no—
270C22×D71—22no—
271C22×D71—24no—
272C22×D71—48no—
273C22×D71—48no—
274C22×D71—44no—
275C22×D71—44no—
276C22×D71—44no—
277C22×D71—48no—
278C22×D71—44no—
279C22×D71—48no—
280C22×D71C22×D418yes—
281C22×D71C22×D414yes—
282Q8×C71—232no—
283C2×C4×C71—216no—
284C2×C4×C71—24no—
285C2×C4×C71—24no—
286C2×C4×C71—24no—
287C2×C4×C71—22no—
288C2×C4×C71—22no—
289C2×C4×C71—22no—
290C2×C4×C71—24no—
291C2×C4×C71—24no—
292C2×C4×C71—44no—
293C2×C4×C71—48no—
294C2×C4×C71—416no—
295C2×C4×C71#120116yes—
296C2×C4×C71C22×D414yes—
297C2×C4×C71C22×D414yes—
298C2×C4×C71C22×D418yes—
299C2×C4×C71C22×D414yes—
300C22⋊D71—232no—
301C22⋊D71—432no—
302C2×Dic71—28no—
303C2×Dic71—28no—
304C2×Dic71—22no—
305C2×Dic71—22no—
306C2×Dic71—22no—
307C2×Dic71—22no—
308C2×Dic71—22no—
309C2×Dic71—24no—
310C2×Dic71—24no—
311C2×Dic71—22no—
312C2×Dic71—24no—
313C2×Dic71—22no—
314C2×Dic71—44no—
315C2×Dic71—48no—
316C2×Dic71C22×D414yes—
317C2×Dic71C2×#4114yescomplemented
318D284—264no—
319D284—232no—
320C4×D71—264no—
321C4×D71—232no—
322C22×C71—24no—
323C22×C71—24no—
324C22×C71—24no—
325C22×C71—416no—
326C22×C71—42no—
327C22×C71—42no—
328C22×C71—42no—
329C22×C71—42no—
330C22×C71C2×#12014yes—
331C22×C71#52514yes—
332C22×C71#53714yes—
333C22×C71#54614yes—
334C22×C71#54714yes—
335C22×C71#54814yes—
336C22×C71#55014yes—
337C22×C71C23×D411yescharacteristic
338C22×C71C23×D411yescharacteristic
339C22×C71C23×D411yescharacteristic
340C22×C71C22×#4111yescharacteristic
341C22×C71C22×#4111yescharacteristic
342C22×C71C2×H(5,𝔽2)11yescharacteristic
343C22×C71C2×2−1+411yescharacteristic
344C2×D71—28no—
345C2×D71—24no—
346C2×D71—24no—
347C2×D71—24no—
348C2×D71—28no—
349C2×D71—28no—
350C2×D71—416no—
351C2×D71—432no—
352C2×D71—44no—
353C2×D71—44no—
354C2×D71—42no—
355C2×D71—42no—
356C2×D71—42no—
357C2×D71—44no—
358C2×D71—44no—
359C2×D71—42no—
360C4×C71—28no—
361C4×C71—42no—
362C4×C71—44no—
363C4×C71C2×#12018yes—
364Dic71—24no—
365Dic71—24no—
366Dic71—42no—
367Dic71—44no—
368C2×#2407—711nomaximal, Sylow
369C2×C71—44no—
370C2×C71#240718yescomplemented
371C2×C71C22×#12011yescharacteristic
372C2×C71C2×#52511yescharacteristic
373C2×C71C2×#53711yescharacteristic
374C2×C71C2×#54611yescharacteristic
375C2×C71C2×#54711yescharacteristic
376C2×C71C2×#54811yescharacteristic
377C2×C71C2×#55011yescharacteristic
378D71—44no—
379D71—48no—
380C23×#41—711no—
381C22×C22⋊Q8D7111yescharacteristic, complemented
382C22×#121—711no—
383C22×C4×D4—711no—
384#2407—7116no—
385C2×#394—712no—
386C2×#392—712no—
387C2×#391—711no—
388C2×#390—711no—
389C2×#386—712no—
390C2×#385—712no—
391C2×#380—711no—
392C71C2×#240711yescharacteristic, complemented, Sylow
393C22×#41—718no—
394C22×#41—1428no—
395C22×#41—1428no—
396C22×#41—1428no—
397C23×Q8C2×D7111yescharacteristic
398C23×D4—712no—
399C23×D4—711no—
400C23×D4—711no—
401C23×D4—712no—
402C24×C4—711no—
403C24×C4—712no—
404C24×C4C2×D7111yescharacteristic
405C2×C22⋊Q8—28no—
406C2×C22⋊Q8C2×D7118yescomplemented
407C2×#121—718no—
408C2×#121—1428no—
409C2×C4×D4—718no—
410C2×C4×D4—1428no—
411C22×C4⋊C4—711no—
412C22×C4⋊C4—711no—
413C22×C4⋊C4C2×D7112yes—
414C22×C4⋊C4C2×D7111yescharacteristic
415C22×C22⋊C4—712no—
416C22×C22⋊C4—712no—
417C22×C22⋊C4—711no—
418C22×C22⋊C4—712no—
419C22×C22⋊C4—711no—
420C22×C22⋊C4—712no—
421C22×C22⋊C4C2×D7112yes—
422C22×C42—711no—
423#394—7116no—
424#392—7116no—
425#391—718no—
426#390—718no—
427#386—7116no—
428#385—7116no—
429#380—718no—
430C2×#95—712no—
431C2×#95—712no—
432C2×#95—712no—
433C25—711no—
434C25—712no—
435C25C22×D7111yescharacteristic
436C2×#41—14232no—
437C2×#41—14232no—
438C2×#41—142128no—
439C2×#41—14232no—
440C22×Q8—24no—
441C22×Q8—24no—
442C22×Q8C22⋊D7118yescomplemented
443C22×Q8C22×D7114yes—
444C22×D4—2844no—
445C22×D4—718no—
446C22×D4—714no—
447C22×D4—718no—
448C22×D4—714no—
449C22×D4—718no—
450C22×D4—1428no—
451C22×D4—1428no—
452C22×D4—1424no—
453C22×D4—1428no—
454C22×D4—1428no—
455C22×D4—1424no—
456C22×D4—1424no—
457C22×D4—1424no—
458C22×D4—1428no—
459C22×D4—1424no—
460C23×C4—24no—
461C23×C4—24no—
462C23×C4—24no—
463C23×C4—711no—
464C23×C4—711no—
465C23×C4—718no—
466C23×C4—714no—
467C23×C4—711no—
468C23×C4—712no—
469C23×C4—718no—
470C23×C4—1428no—
471C23×C4—1428no—
472C23×C4—1424no—
473C23×C4—1428no—
474C23×C4—1424no—
475C23×C4C22×D7114yes—
476C23×C4C22×D7112yes—
477C23×C4C22×D7111yescharacteristic
478C23×C4C22×D7112yes—
479C23×C4C22×D7111yescharacteristic
480C22⋊Q8—232no—
481#121—14232no—
482C4×D4—14232no—
483C2×C4⋊C4—24no—
484C2×C4⋊C4—28no—
485C2×C4⋊C4—714no—
486C2×C4⋊C4—714no—
487C2×C4⋊C4—1424no—
488C2×C4⋊C4—1424no—
489C2×C4⋊C4C22×D7114yes—
490C2×C4⋊C4C22×D7118yes—
491C2×C22⋊C4—28no—
492C2×C22⋊C4—2844no—
493C2×C22⋊C4—2844no—
494C2×C22⋊C4—718no—
495C2×C22⋊C4—718no—
496C2×C22⋊C4—714no—
497C2×C22⋊C4—714no—
498C2×C22⋊C4—718no—
499C2×C22⋊C4—718no—
500C2×C22⋊C4—1428no—
501C2×C22⋊C4—1424no—
502C2×C22⋊C4—1428no—
503C2×C22⋊C4—1424no—
504C2×C22⋊C4C22×D7118yes—
505C2×C42—714no—
506C2×C42—1424no—
507#95—718no—
508#95—718no—
509#95—718no—
510C24—22no—
511C24—22no—
512C24—22no—
513C24—22no—
514C24—22no—
515C24—22no—
516C24—714no—
517C24—718no—
518C24—712no—
519C24—714no—
520C24—1424no—
521C24—1422no—
522C24—1424no—
523C24—1422no—
524C24—1424no—
525C24—1422no—
526C24—1422no—
527C24—1424no—
528C24—1422no—
529C24—1424no—
530C24—1424no—
531C24—1422no—
532C24#1176586614yescomplemented
533C24C23×D7112yes—
534C24C23×D7111yescharacteristic
535#41—142256no—
536C2×Q8—28no—
537C2×Q8—28no—
538C2×Q8—232no—
539C2×Q8C2×C22⋊D71116yescomplemented
540C2×D4—28432no—
541C2×D4—2848no—
542C2×D4—7116no—
543C2×D4—14216no—
544C2×D4—14216no—
545C2×D4—14264no—
546C2×D4—1428no—
547C2×D4—14216no—
548C2×D4—14216no—
549C2×D4—1428no—
550C2×D4—14232no—
551C2×D4—1428no—
552C2×D4—1428no—
553C2×D4—14216no—
554C2×D4—1428no—
555C2×D4—14232no—
556C22×C4—24no—
557C22×C4—24no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—24no—
561C22×C4—22no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—28no—
565C22×C4—28no—
566C22×C4—28no—
567C22×C4—416no—
568C22×C4—714no—
569C22×C4—714no—
570C22×C4—712no—
571C22×C4—712no—
572C22×C4—7116no—
573C22×C4—714no—
574C22×C4—712no—
575C22×C4—14216no—
576C22×C4—14216no—
577C22×C4—14264no—
578C22×C4—1422no—
579C22×C4—1424no—
580C22×C4—1424no—
581C22×C4—1422no—
582C22×C4—1424no—
583C22×C4—1422no—
584C22×C4—1422no—
585C22×C4—1422no—
586C22×C4—1422no—
587C22×C4—1422no—
588C22×C4—1428no—
589C22×C4—14216no—
590C22×C4—1428no—
591C22×C4—14232no—
592C22×C4D4×D7114yes—
593C22×C4D4×D7114yes—
594C22×C4C2×C22⋊D7118yes—
595C22×C4C2×C22⋊D7114yes—
596C22×C4C23×D7114yes—
597C22×C4C23×D7112yes—
598C22×C4C23×D7114yes—
599C22×C4C23×D7112yes—
600C4⋊C4—28no—
601C4⋊C4—216no—
602C4⋊C4—1428no—
603C4⋊C4—1428no—
604C22⋊C4—216no—
605C22⋊C4—2848no—
606C22⋊C4—2848no—
607C22⋊C4—14216no—
608C22⋊C4—1428no—
609C22⋊C4—14216no—
610C22⋊C4—1428no—
611C42—1428no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—28no—
619C23—28no—
620C23—28no—
621C23—44no—
622C23—44no—
623C23—44no—
624C23—44no—
625C23—2848no—
626C23—2844no—
627C23—2844no—
628C23—2848no—
629C23—2844no—
630C23—2848no—
631C23—2844no—
632C23—2848no—
633C23—714no—
634C23—718no—
635C23—1422no—
636C23—1424no—
637C23—1424no—
638C23—1422no—
639C23—1424no—
640C23—1422no—
641C23—1422no—
642C23—1424no—
643C23—1422no—
644C23—1424no—
645C23—1422no—
646C23—1424no—
647C23—1428no—
648C23—14216no—
649C23—14216no—
650C23—14216no—
651C23—1428no—
652C23—1428no—
653C23C2×D4×D7112yes—
654C23C2×D4×D7112yes—
655C23C22×C22⋊D7112yes—
656C23#41×D7112yes—
657C23C2×#1176586612yes—
658C23C2×#1176586614yescomplemented
659C23#1455617412yes—
660C23#1455617612yes—
661C23C24×D7111yescharacteristic
662Q8—232no—
663D4—28432no—
664D4—14264no—
665D4—14232no—
666D4—14232no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—216no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—48no—
677C2×C4—44no—
678C2×C4—416no—
679C2×C4—2844no—
680C2×C4—2848no—
681C2×C4—714no—
682C2×C4—714no—
683C2×C4—14264no—
684C2×C4—1422no—
685C2×C4—1424no—
686C2×C4—1424no—
687C2×C4—1422no—
688C2×C4—1424no—
689C2×C4—1422no—
690C2×C4—1422no—
691C2×C4—1422no—
692C2×C4—1422no—
693C2×C4—1422no—
694C2×C4—1428no—
695C2×C4—1428no—
696C2×C4—14232no—
697C2×C4#14556096116yes—
698C2×C4C2×D4×D7114yes—
699C2×C4C2×D4×D7114yes—
700C2×C4C22×C22⋊D7118yes—
701C2×C4C22×C22⋊D7114yes—
702C22—24no—
703C22—24no—
704C22—24no—
705C22—42no—
706C22—42no—
707C22—42no—
708C22—42no—
709C22—416no—
710C22—2842no—
711C22—2842no—
712C22—2842no—
713C22—2844no—
714C22—2844no—
715C22—2842no—
716C22—2844no—
717C22—2844no—
718C22—28432no—
719C22—28416no—
720C22—1428no—
721C22—1428no—
722C22—1428no—
723C22—1424no—
724C22—1424no—
725C22—1424no—
726C22C2×#1455609614yes—
727C22#1798651214yes—
728C22#1798657914yes—
729C22#1798664014yes—
730C22#1798665114yes—
731C22#1798666014yes—
732C22#1798666814yes—
733C22C22×D4×D7111yescharacteristic
734C22C22×D4×D7111yescharacteristic
735C22C23×C22⋊D7111yescharacteristic
736C22C2×#41×D7111yescharacteristic
737C22C22×#1176586611yescharacteristic
738C22C2×#1455617411yescharacteristic
739C22C2×#1455617611yescharacteristic
740C4—28no—
741C4—42no—
742C4—44no—
743C4—2844no—
744C4—2842no—
745C4—1424no—
746C4—1424no—
747C4C2×#1455609618yes—
748C2—44no—
749C2—2844no—
750C2—2848no—
751C2#2259168718yesdirect product factor
752C2C22×#1455609611yescharacteristic
753C2C2×#1798651211yescharacteristic
754C2C2×#1798657911yescharacteristic
755C2C2×#1798664011yescharacteristic
756C2C2×#1798665111yescharacteristic
757C2C2×#1798666011yescharacteristic
758C2C2×#1798666811yescharacteristic
subgroupG/H
centerC24C23×D71
commutator, cosocleC23×C71C25
FrattiniC23C24×D71
FittingC22×C22⋊Q8×C71C2
socleC24×C71C24
hypercenterC22×C22⋊Q8D71
hypocenterC71C2×#2407
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C23×#11765866C2semidirect
2. C22×#14556102C2semidirect
3. C22×C4×C22⋊D71C2semidirect
4. #22591687C2direct (N × H)
5. C2×#17985916C2semidirect
6. C2×#17985908C2semidirect
7. C2×#17985906C2semidirect
8. C2×#17985900C2semidirect
9. C2×#17985875C2semidirect
10. C2×#17985870C2semidirect
11. C2×#17985856C2semidirect
12. C22×C22⋊Q8×C71C2semidirect
16. C22×#11765866C22semidirect
24. C2×#14556102C22semidirect
26. C2×C4×C22⋊D71C22semidirect
36. #17985916C22semidirect
37. #17985908C22semidirect
38. #17985906C22semidirect
39. #17985900C22semidirect
40. #17985875C22semidirect
41. #17985870C22semidirect
42. #17985856C22semidirect
49. C2×C22⋊Q8×C71C22semidirect
64. C22×D284D4semidirect
84. C22×C4×D71D4semidirect
113. C22×Q8×C71D4semidirect
154. C2×D284C2×D4semidirect
174. C22×Dic71#41semidirect
186. C2×C4×D71C2×D4semidirect
202. C24×C71#41semidirect
208. C2×Q8×C71C2×D4semidirect
250. C23×C71C2×#41semidirect
317. C2×Dic71C2×#41semidirect
370. C2×C71#2407semidirect
381. C22×C22⋊Q8D71semidirect
392. C71C2×#2407semidirect
406. C2×C22⋊Q8C2×D71semidirect
442. C22×Q8C22⋊D71semidirect
532. C24#11765866semidirect
539. C2×Q8C2×C22⋊D71semidirect
658. C23C2×#11765866semidirect
751. C2#22591687direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#117658662
C22×#145561022
C22×C4×C22⋊D712
#225916872
C2×#179859162
C2×#179859082
C2×#179859062
C2×#179859002
C2×#179858752
C2×#179858702
C2×#179858562
C22×C22⋊Q8×C712
C2×#240771