Finite Group Databasebeta

← C2×#22597967 #32864607

Subgroups — C2×#22597967 #32864607

Order 18176.

2898 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556160C211yesmaximal, characteristic, complemented
2C23×#11765848C211yesmaximal, characteristic, complemented
3C2×#17986512C211yesmaximal, characteristic
4C2×C22⋊Q8×D71C211yesmaximal, characteristic, complemented
5#22597967C2116yesmaximal, direct product factor
6C2×#17986256C211yesmaximal, characteristic, complemented
7C2×#17986254C211yesmaximal, characteristic, complemented
8C2×#17986248C211yesmaximal, characteristic, complemented
9C2×#17986246C211yesmaximal, characteristic, complemented
10C2×#17986238C211yesmaximal, characteristic, complemented
11C2×#17986230C211yesmaximal, characteristic, complemented
12C2×#17986228C211yesmaximal, characteristic, complemented
13C2×#17986040C211yesmaximal, characteristic, complemented
14C2×#17985999C211yesmaximal, characteristic, complemented
15C2×#17986006C211yesmaximal, characteristic, complemented
16C2×#467×C71C211yesmaximal, characteristic, complemented
17C22×#11765866C2211yescharacteristic
18C22×Q8×D71C2211yescharacteristic
19C23×C4×D71C2211yescharacteristic
20C2×#14556160—28no—
21C2×#14556160C2218yescomplemented
22C22×#11765855C2211yescharacteristic, complemented
23C22×#11765854C2211yescharacteristic, complemented
24C22×#11765852C2211yescharacteristic, complemented
25C22×#11765848—28no—
26C22×#11765848C2211yescharacteristic
27C22×#11765848C2211yescharacteristic
28C22×#11765848C2211yescharacteristic
29C22×#11765848C2211yescharacteristic
30C22×#11765848C2218yescomplemented
31C23×C71⋊C8C2211yescharacteristic
32#17986512—24no—
33#17986512C2218yes—
34C2×#14556113—21no—
35C2×#14556108C2211yescharacteristic
36C2×#14556107C2211yescharacteristic
37C2×#14556106—21no—
38C2×#14556105—21no—
39C2×#14556104C2211yescharacteristic
40C2×#14556104C2211yescharacteristic
41C22⋊Q8×D71—24no—
42C22⋊Q8×D71C2218yescomplemented
43C2×#14556103C2211yescharacteristic
44C2×#14556102C2211yescharacteristic
45C2×#14556098—21no—
46C2×#14556090—21no—
47C2×(C22⋊D71)⋊C4—21no—
48C2×#14556086C2211yescharacteristic
49C2×C4⋊C4×D71—21no—
50C2×C4⋊C4×D71C2211yescharacteristic
51C2×C22⋊C4×D71—21no—
52#17986256C2218yescomplemented
53#17986254C2218yescomplemented
54#17986248C2218yescomplemented
55#17986246C2218yescomplemented
56#17986238C2218yescomplemented
57#17986230C2218yescomplemented
58#17986228C2218yescomplemented
59#17986040C2218yescomplemented
60C2×#14556061C2211yescharacteristic, complemented
61C2×#14556060C2211yescharacteristic, complemented
62C2×#14556059C2211yescharacteristic, complemented
63#17986006C2218yescomplemented
64#17985999C2218yescomplemented
65C2×#14556053C2211yescharacteristic, complemented
66C2×#14556052C2211yescharacteristic, complemented
67C2×#14556052C2211yescharacteristic, complemented
68C2×#14556051C2211yescharacteristic, complemented
69C2×#14556050C2211yescharacteristic, complemented
70C2×#14556048C2211yescharacteristic, complemented
71C22×Q16×C71C2211yescharacteristic, complemented
72C23×C8×C71C2211yescharacteristic
73C2×C22⋊Q8×C71C2211yescharacteristic
74C2×C22⋊Q8×C71C2211yescharacteristic
75#467×C71C2218yescomplemented
76C2×#107×C71C2211yescharacteristic, complemented
77C2×#103×C71C2211yescharacteristic, complemented
78C2×#103×C71C2211yescharacteristic, complemented
79C24×D71D411yescharacteristic
80C2×#11765866—22no—
81C2×#11765866—24no—
82C2×#11765866—24no—
83C2×#11765866C2314yes—
84C22×Dic142—21no—
85C22×Dic142C2311yescharacteristic
86C2×Q8×D71—22no—
87C2×Q8×D71—24no—
88C2×Q8×D71—24no—
89C2×Q8×D71C2314yes—
90C22×D284—21no—
91C22×D284—21no—
92C22×D284C2311yescharacteristic
93C22×C22⋊D71—21no—
94C23×Dic71D411yescharacteristic
95C22×C4×D71—24no—
96C22×C4×D71—24no—
97C22×C4×D71—21no—
98C22×C4×D71—21no—
99C22×C4×D71—21no—
100C22×C4×D71D411yescharacteristic
101C22×C4×D71D411yescharacteristic
102C22×C4×D71D414yes—
103C22×C4×D71C2311yescharacteristic
104C22×C4×D71C2314yes—
105C22×C4×D71C2311yescharacteristic
106#14556160—232no—
107C2×#11765855—24no—
108C2×#11765855C2314yescomplemented
109C2×#11765854—24no—
110C2×#11765854C2314yescomplemented
111C2×#11765852—24no—
112C2×#11765852C2314yescomplemented
113C2×#11765848—24no—
114C2×#11765848—232no—
115C2×#11765848—24no—
116C2×#11765848—24no—
117C2×#11765848D418yescomplemented
118C2×#11765848C2314yes—
119C2×#11765848C2314yes—
120C2×#11765848C2314yes—
121C2×#11765848C2314yes—
122C22×C71⋊C8—24no—
123C22×C71⋊C8C2314yes—
124C22×C71⋊C8C2311yescharacteristic
125C22×C71⋊C8C2311yescharacteristic
126#14556113—28no—
127#14556108—22no—
128#14556108C2314yes—
129#14556107—22no—
130#14556107C2314yes—
131#14556106—28no—
132#14556105—28no—
133#14556104—22no—
134#14556104—22no—
135#14556104C2314yes—
136#14556104C2314yes—
137#14556103—22no—
138#14556103C2314yes—
139#14556102—22no—
140#14556102C2314yes—
141#14556098—28no—
142#14556090—28no—
143(C22⋊D71)⋊C4—28no—
144#14556086—22no—
145#14556086C2314yes—
146C2×C4⋊Dic71—21no—
147C2×C4⋊Dic71C2311yescharacteristic
148C2×C4⋊Dic71C2311yescharacteristic
149C2×Dic71⋊C4—21no—
150C2×Dic71⋊C4—21no—
151C2×Dic71⋊C4—21no—
152C2×Dic71⋊C4—21no—
153C4⋊C4×D71—28no—
154C4⋊C4×D71—22no—
155C4⋊C4×D71C2314yes—
156C2×C22⋊Dic71—21no—
157C2×(C2×D71)⋊C4—21no—
158C2×(C2×D71)⋊C4—21no—
159C2×(C2×D71)⋊C4—21no—
160C2×(C2×D71)⋊C4—21no—
161C2×(C2×D71)⋊C4—21no—
162C2×(C2×D71)⋊C4—21no—
163C22⋊C4×D71—28no—
164C2×C4×Dic71—21no—
165#14556061C2314yescomplemented
166#14556060C2314yescomplemented
167#14556059C2314yescomplemented
168#14556053C2314yescomplemented
169#14556052C2314yescomplemented
170#14556052C2314yescomplemented
171#14556051C2314yescomplemented
172#14556050C2314yescomplemented
173#14556048C2314yescomplemented
174C22×Q8×C71C2311yescharacteristic
175C22×Q8×C71C2311yescharacteristic
176C23×C4×C71C2311yescharacteristic
177C2×Q16×C71—24no—
178C2×Q16×C71C2314yescomplemented
179C22×C8×C71—24no—
180C22×C8×C71C2311yescharacteristic
181C22×C8×C71C2314yes—
182C22×C8×C71C2311yescharacteristic
183C22⋊Q8×C71—22no—
184C22⋊Q8×C71—22no—
185C22⋊Q8×C71C2314yes—
186C22⋊Q8×C71C2314yes—
187C2×C4⋊C4×C71—21no—
188C2×C4⋊C4×C71—21no—
189C2×C4⋊C4×C71C2311yescharacteristic
190C2×C4⋊C4×C71C2311yescharacteristic
191C2×C22⋊C4×C71—21no—
192C2×C22⋊C4×C71—21no—
193#107×C71C2314yescomplemented
194#103×C71C2314yescomplemented
195#103×C71C2314yescomplemented
196C23×D71—24no—
197C23×D71—24no—
198C23×D71—21no—
199C23×D71—42no—
200C23×D71C2×D411yescharacteristic
201C23×D71C2×D414yes—
202C23×D71C2×D411yescharacteristic
203#11765866—28no—
204#11765866—28no—
205#11765866—48no—
206C2×Dic142—22no—
207C2×Dic142—22no—
208C2×Dic142—21no—
209C2×Dic142—24no—
210C2×Dic142—44no—
211C2×Dic142C2412yes—
212Q8×D71—28no—
213Q8×D71—28no—
214Q8×D71—48no—
215C2×D284—22no—
216C2×D284—22no—
217C2×D284—24no—
218C2×D284—24no—
219C2×D284—21no—
220C2×D284—44no—
221C2×D284—44no—
222C2×D284C2412yes—
223C2×C22⋊D71—24no—
224C2×C22⋊D71—44no—
225C22×Dic71—24no—
226C22×Dic71—21no—
227C22×Dic71—21no—
228C22×Dic71—21no—
229C22×Dic71C2×D411yescharacteristic
230C22×Dic71C2×D414yes—
231C22×Dic71C2×D411yescharacteristic
232C2×C4×D71—24no—
233C2×C4×D71—22no—
234C2×C4×D71—22no—
235C2×C4×D71—24no—
236C2×C4×D71—216no—
237C2×C4×D71—28no—
238C2×C4×D71—28no—
239C2×C4×D71—24no—
240C2×C4×D71—24no—
241C2×C4×D71—24no—
242C2×C4×D71—44no—
243C2×C4×D71—44no—
244C2×C4×D71—44no—
245C2×C4×D71C2×D414yes—
246C2×C4×D71C2×D414yes—
247C2×C4×D71C2×D412yes—
248C2×C4×D71C2×D412yes—
249C2×C4×D71C2×D414yes—
250C2×C4×D71#4114yes—
251C2×C4×D71C2412yes—
252C2×C4×D71C2412yes—
253#11765855—28no—
254#11765854—28no—
255#11765852—28no—
256#11765848—28no—
257#11765848—28no—
258#11765848—28no—
259#11765848C2×D4116yescomplemented
260C2×C71⋊C8—22no—
261C2×C71⋊C8—28no—
262C2×C71⋊C8C2×D414yes—
263C2×C71⋊C8C2412yes—
264C2×C71⋊C8C2412yes—
265C4⋊Dic71—21no—
266C4⋊Dic71—21no—
267C4⋊Dic71—24no—
268C4⋊Dic71C2412yes—
269C4⋊Dic71C2412yes—
270Dic71⋊C4—24no—
271Dic71⋊C4—24no—
272Dic71⋊C4—24no—
273Dic71⋊C4—24no—
274C22⋊Dic71—24no—
275(C2×D71)⋊C4—24no—
276(C2×D71)⋊C4—24no—
277(C2×D71)⋊C4—24no—
278(C2×D71)⋊C4—24no—
279(C2×D71)⋊C4—24no—
280(C2×D71)⋊C4—24no—
281C4×Dic71—24no—
282C24×C71C2×D411yescharacteristic
283C2×Q8×C71—21no—
284C2×Q8×C71—21no—
285C2×Q8×C71—22no—
286C2×Q8×C71—22no—
287C2×Q8×C71—22no—
288C2×Q8×C71—22no—
289C2×Q8×C71C2412yes—
290C2×Q8×C71C2412yes—
291C22×C4×C71—22no—
292C22×C4×C71—22no—
293C22×C4×C71—21no—
294C22×C4×C71—21no—
295C22×C4×C71—21no—
296C22×C4×C71—21no—
297C22×C4×C71C2×D411yescharacteristic
298C22×C4×C71C2×D412yes—
299C22×C4×C71C2412yes—
300C22×C4×C71C2411yescharacteristic
301Q16×C71—28no—
302C2×C8×C71—22no—
303C2×C8×C71—28no—
304C2×C8×C71C2×D414yes—
305C2×C8×C71C2412yes—
306C2×C8×C71C2412yes—
307C4⋊C4×C71—24no—
308C4⋊C4×C71—24no—
309C4⋊C4×C71—21no—
310C4⋊C4×C71—21no—
311C4⋊C4×C71C2412yes—
312C4⋊C4×C71C2412yes—
313C22⋊C4×C71—24no—
314C22⋊C4×C71—24no—
315C23×C71—22no—
316C23×C71—22no—
317C23×C71#13714yescomplemented
318C23×C71C22×D412yes—
319C23×C71C22×D411yescharacteristic
320C22×D71—22no—
321C22×D71—22no—
322C22×D71—22no—
323C22×D71—22no—
324C22×D71—28no—
325C22×D71—22no—
326C22×D71—28no—
327C22×D71—22no—
328C22×D71—44no—
329C22×D71—416no—
330C22×D71—42no—
331C22×D71—42no—
332C22×D71—42no—
333C22×D71#12114yes—
334C22×D71C22×D412yes—
335C22×D71C22×D412yes—
336Q8×C71—22no—
337Q8×C71—22no—
338Q8×C71—22no—
339Q8×C71—22no—
340Q8×C71—42no—
341Q8×C71—42no—
342C2×C4×C71—22no—
343C2×C4×C71—24no—
344C2×C4×C71—22no—
345C2×C4×C71—22no—
346C2×C4×C71—22no—
347C2×C4×C71—22no—
348C2×C4×C71—22no—
349C2×C4×C71—22no—
350C2×C4×C71—42no—
351C2×C4×C71—42no—
352C2×C4×C71—42no—
353C2×C4×C71—42no—
354C2×C4×C71C22×D412yes—
355C2×C4×C71C22×D411yescharacteristic
356C2×C4×C71C22×D412yes—
357C2×C4×C71C2×#4112yes—
358C2×C4×C71C2511yescharacteristic
359C22⋊D71—48no—
360C2×Dic71—22no—
361C2×Dic71—28no—
362C2×Dic71—22no—
363C2×Dic71—22no—
364C2×Dic71—22no—
365C2×Dic71—42no—
366C2×Dic71—42no—
367C2×Dic71—42no—
368C2×Dic71#12114yes—
369C2×Dic71C22×D412yes—
370C2×Dic71C22×D412yes—
371D284—22no—
372D284—22no—
373D284—48no—
374D284—48no—
375D284—42no—
376C4×D71—28no—
377C4×D71—24no—
378C4×D71—22no—
379C4×D71—22no—
380C4×D71—28no—
381C4×D71—48no—
382C4×D71—48no—
383C4×D71—48no—
384C4×D71#12118yes—
385C4×D71C22×D414yes—
386C4×D71C2×#4114yes—
387Dic142—22no—
388Dic142—22no—
389Dic142—42no—
390Dic142—48no—
391C8×C71—22no—
392C8×C71C22×D414yes—
393C71⋊C8—22no—
394C71⋊C8C22×D414yes—
395C22×C71—22no—
396C22×C71—28no—
397C22×C71—22no—
398C22×C71C2×#12112yes—
399C22×C71C2×#13712yes—
400C22×C71C2×#13714yescomplemented
401C22×C71#57512yes—
402C22×C71C23×D411yescharacteristic
403C2×D71—28no—
404C2×D71—22no—
405C2×D71—22no—
406C2×D71—22no—
407C2×D71—22no—
408C2×D71—22no—
409C2×D71—416no—
410C2×D71—44no—
411C2×D71—42no—
412C2×D71—42no—
413C2×D71—42no—
414C2×D71—84no—
415C2×D71C2×#12114yes—
416C4×C71—22no—
417C4×C71—42no—
418C4×C71—42no—
419C4×C71—42no—
420C4×C71—42no—
421C4×C71C2×#12112yes—
422C4×C71C23×D411yescharacteristic
423C4×C71C22×#4111yescharacteristic
424Dic71—22no—
425Dic71—42no—
426Dic71—42no—
427Dic71—42no—
428Dic71C2×#12114yes—
429C2×#3056—711nomaximal, Sylow
430C2×C71—24no—
431C2×C71#305614yescomplemented
432C2×C71C22×#12111yescharacteristic
433C2×C71C22×#13711yescharacteristic
434C2×C71C2×#57511yescharacteristic
435D71—24no—
436D71—42no—
437D71—82no—
438C22×#137—711no—
439C23×M16—711no—
440C2×#525—711no—
441C22×C22⋊Q8—711no—
442#3056—7116no—
443C2×#470—711no—
444C2×#470—711no—
445C2×#468—711no—
446C2×#468—711no—
447C2×#467—711no—
448C2×#467D7111yescharacteristic, complemented
449C2×#465—711no—
450C2×#465—711no—
451C2×#428—711no—
452C2×#417—711no—
453C2×#419—711no—
454C71C2×#305611yescharacteristic, complemented, Sylow
455C22×#41—711no—
456C23×Q8—711no—
457C24×C4—711no—
458C2×#137—718no—
459C2×#137—1428no—
460C22×Q16—711no—
461C22×Q16C2×D7111yescharacteristic, complemented
462C22×SD16—711no—
463C22×SD16—711no—
464C22×M16—711no—
465C22×M16—711no—
466C22×M16—711no—
467C22×M16—711no—
468C22×M16—718no—
469C22×M16—1428no—
470C23×C8—711no—
471C23×C8C2×D7111yescharacteristic
472#525—718no—
473#525—1424no—
474C2×#123—1421no—
475C2×C22⋊Q8—711no—
476C2×C22⋊Q8—711no—
477C2×C22⋊Q8—711no—
478C2×C22⋊Q8—718no—
479C2×C22⋊Q8—711no—
480C2×C22⋊Q8—1421no—
481C2×C22⋊Q8—1421no—
482C2×C22⋊Q8—1424no—
483C2×C22⋊Q8C2×D7111yescharacteristic
484C2×C22⋊Q8C2×D7111yescharacteristic
485C2×#121—711no—
486C2×#121—711no—
487C2×#120—1421no—
488C2×C4×D4—1421no—
489C2×C4×D4—1421no—
490C2×#117—711no—
491C22×C4⋊C4—711no—
492C22×C4⋊C4—1421no—
493C22×C22⋊C4—1421no—
494#470—718no—
495#470—718no—
496#468—718no—
497#468—718no—
498#467—718no—
499#467C2×D7118yescomplemented
500#465—718no—
501#465—718no—
502#428—718no—
503C2×#107—711no—
504C2×#107C2×D7111yescharacteristic, complemented
505C2×#106—711no—
506C2×#106—711no—
507#419—718no—
508#417—718no—
509C2×#103—711no—
510C2×#103—711no—
511C2×#103—711no—
512C2×#103—711no—
513C2×#103C2×D7111yescharacteristic, complemented
514C2×#103C2×D7111yescharacteristic, complemented
515C2×#102—711no—
516C2×#102—711no—
517C25—711no—
518C2×#41—714no—
519C2×#41—1424no—
520C2×#41—1424no—
521C2×#41—1422no—
522C22×Q8—714no—
523C22×Q8—711no—
524C22×Q8—1421no—
525C22×Q8—1424no—
526C22×Q8—1424no—
527C22×Q8—1422no—
528C22×Q8C22×D7111yescharacteristic
529C22×Q8C22×D7111yescharacteristic
530C22×D4—711no—
531C22×D4—1421no—
532C22×D4—1421no—
533C22×D4—1421no—
534C23×C4—711no—
535C23×C4—711no—
536C23×C4—711no—
537C23×C4—711no—
538C23×C4—714no—
539C23×C4—711no—
540C23×C4—714no—
541C23×C4—1421no—
542C23×C4—1421no—
543C23×C4—1421no—
544C23×C4—1424no—
545C23×C4—1424no—
546C23×C4C22×D7111yescharacteristic
547#137—14232no—
548C2×Q16—24no—
549C2×Q16—714no—
550C2×Q16—1424no—
551C2×Q16C22×D7114yescomplemented
552C2×SD16—714no—
553C2×SD16—714no—
554C2×SD16—1424no—
555C2×SD16—1424no—
556C2×M16—718no—
557C2×M16—714no—
558C2×M16—714no—
559C2×M16—714no—
560C2×M16—714no—
561C2×M16—1424no—
562C2×M16—14232no—
563C2×M16—1424no—
564C2×M16—1424no—
565C22×C8—24no—
566C22×C8—711no—
567C22×C8—711no—
568C22×C8—714no—
569C22×C8—1424no—
570C22×C8C22×D7111yescharacteristic
571C22×C8C22×D7114yes—
572C22×C8C22×D7111yescharacteristic
573#123—1428no—
574C22⋊Q8—22no—
575C22⋊Q8—22no—
576C22⋊Q8—714no—
577C22⋊Q8—714no—
578C22⋊Q8—714no—
579C22⋊Q8—714no—
580C22⋊Q8—1428no—
581C22⋊Q8—1428no—
582C22⋊Q8—1422no—
583C22⋊Q8—1422no—
584C22⋊Q8—1422no—
585C22⋊Q8—1422no—
586C22⋊Q8C22×D7114yes—
587C22⋊Q8C22×D7114yes—
588#121—714no—
589#121—714no—
590#121—1422no—
591#121—1422no—
592#120—1428no—
593C4×D4—1428no—
594C4×D4—1428no—
595#117—714no—
596#117—1422no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—711no—
600C2×C4⋊C4—711no—
601C2×C4⋊C4—714no—
602C2×C4⋊C4—1422no—
603C2×C4⋊C4—1428no—
604C2×C4⋊C4—1421no—
605C2×C4⋊C4—1421no—
606C2×C4⋊C4—1421no—
607C2×C4⋊C4—1421no—
608C2×C4⋊C4—1421no—
609C2×C4⋊C4C22×D7111yescharacteristic
610C2×C4⋊C4C22×D7111yescharacteristic
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—1428no—
614C2×C22⋊C4—1421no—
615C2×C22⋊C4—1421no—
616C2×C22⋊C4—1421no—
617C2×C22⋊C4—1421no—
618C2×C22⋊C4—1421no—
619C2×C22⋊C4—1421no—
620C2×C22⋊C4—1421no—
621C2×C42—1421no—
622#107—714no—
623#107C22×D7114yescomplemented
624#106—714no—
625#106—714no—
626#103—714no—
627#103—714no—
628#103—714no—
629#103—714no—
630#103C22×D7114yescomplemented
631#103C22×D7114yescomplemented
632#102—714no—
633#102—714no—
634C24—2842no—
635C24—714no—
636C24—711no—
637C24—711no—
638C24—1424no—
639C24—1421no—
640C24—1424no—
641C24D4×D7111yescharacteristic
642#41—2848no—
643#41—1428no—
644#41—1428no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—22no—
648C2×Q8—22no—
649C2×Q8—22no—
650C2×Q8—22no—
651C2×Q8—2844no—
652C2×Q8—2848no—
653C2×Q8—712no—
654C2×Q8—1424no—
655C2×Q8—1428no—
656C2×Q8—1428no—
657C2×Q8—1422no—
658C2×Q8—1422no—
659C2×Q8—1421no—
660C2×Q8C23×D7112yes—
661C2×Q8C23×D7112yes—
662C2×D4—2844no—
663C2×D4—2844no—
664C2×D4—2844no—
665C2×D4—712no—
666C2×D4—1424no—
667C2×D4—1424no—
668C2×D4—1424no—
669C2×D4—1421no—
670C2×D4—1422no—
671C2×D4—1422no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—2844no—
679C22×C4—2844no—
680C22×C4—2844no—
681C22×C4—711no—
682C22×C4—712no—
683C22×C4—714no—
684C22×C4—714no—
685C22×C4—712no—
686C22×C4—714no—
687C22×C4—711no—
688C22×C4—714no—
689C22×C4—714no—
690C22×C4—712no—
691C22×C4—712no—
692C22×C4—1424no—
693C22×C4—1424no—
694C22×C4—1424no—
695C22×C4—1428no—
696C22×C4—1424no—
697C22×C4—1428no—
698C22×C4—14216no—
699C22×C4—1424no—
700C22×C4—1421no—
701C22×C4—1421no—
702C22×C4—1421no—
703C22×C4—1424no—
704C22×C4—1422no—
705C22×C4—1422no—
706C22×C4D4×D7112yes—
707C22×C4D4×D7111yescharacteristic
708C22×C4C23×D7112yes—
709C22×C4C23×D7111yescharacteristic
710Q16—28no—
711Q16—1428no—
712SD16—1428no—
713SD16—1428no—
714M16—7116no—
715M16—1428no—
716M16—1428no—
717M16—1428no—
718C2×C8—22no—
719C2×C8—28no—
720C2×C8—714no—
721C2×C8—712no—
722C2×C8—712no—
723C2×C8—1428no—
724C2×C8—1422no—
725C2×C8D4×D7114yes—
726C2×C8C23×D7112yes—
727C2×C8C23×D7112yes—
728C4⋊C4—24no—
729C4⋊C4—24no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—712no—
733C4⋊C4—712no—
734C4⋊C4—1424no—
735C4⋊C4—1424no—
736C4⋊C4—1424no—
737C4⋊C4—1424no—
738C4⋊C4—1424no—
739C4⋊C4—1421no—
740C4⋊C4—1421no—
741C4⋊C4C23×D7112yes—
742C4⋊C4C23×D7112yes—
743C22⋊C4—24no—
744C22⋊C4—24no—
745C22⋊C4—1424no—
746C22⋊C4—1424no—
747C22⋊C4—1424no—
748C22⋊C4—1424no—
749C22⋊C4—1424no—
750C22⋊C4—1424no—
751C22⋊C4—1424no—
752C42—1424no—
753C23—22no—
754C23—22no—
755C23—28416no—
756C23—2844no—
757C23—2842no—
758C23—2842no—
759C23—2842no—
760C23—712no—
761C23—714no—
762C23—712no—
763C23—1428no—
764C23—1422no—
765C23—1422no—
766C23—1422no—
767C23—1428no—
768C23—1422no—
769C23—1422no—
770C23—1422no—
771C23#1455616014yescomplemented
772C23C2×D4×D7112yes—
773C23C2×D4×D7111yescharacteristic
774Q8—22no—
775Q8—22no—
776Q8—22no—
777Q8—22no—
778Q8—42no—
779Q8—42no—
780Q8—2848no—
781Q8—2842no—
782Q8—1422no—
783Q8—1422no—
784D4—2848no—
785D4—2848no—
786D4—2848no—
787D4—2842no—
788D4—1422no—
789D4—1422no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—24no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—2848no—
803C2×C4—2848no—
804C2×C4—2848no—
805C2×C4—2842no—
806C2×C4—2842no—
807C2×C4—2842no—
808C2×C4—712no—
809C2×C4—714no—
810C2×C4—714no—
811C2×C4—714no—
812C2×C4—718no—
813C2×C4—712no—
814C2×C4—1428no—
815C2×C4—1428no—
816C2×C4—1422no—
817C2×C4—1422no—
818C2×C4—1422no—
819C2×C4—1428no—
820C2×C4—1422no—
821C2×C4—1422no—
822C2×C4—1422no—
823C2×C4—1424no—
824C2×C4C2×D4×D7112yes—
825C2×C4C2×D4×D7112yes—
826C2×C4C2×D4×D7111yescharacteristic
827C2×C4#41×D7112yes—
828C2×C4C24×D7111yescharacteristic
829C8—22no—
830C8—714no—
831C8—1422no—
832C8C2×D4×D7114yes—
833C22—22no—
834C22—28no—
835C22—22no—
836C22—28416no—
837C22—2844no—
838C22—2842no—
839C22—2842no—
840C22—2842no—
841C22—5684no—
842C22—714no—
843C22—1422no—
844C22—1422no—
845C22—1422no—
846C22—1422no—
847C22—1422no—
848C22—1428no—
849C22#121×D7112yes—
850C22C2×#1455616012yes—
851C22C2×#1455616014yescomplemented
852C22#1798679612yes—
853C22C22×D4×D7111yescharacteristic
854C4—22no—
855C4—42no—
856C4—42no—
857C4—42no—
858C4—42no—
859C4—2842no—
860C4—2842no—
861C4—2842no—
862C4—714no—
863C4—1422no—
864C4#121×D7112yes—
865C4C22×D4×D7111yescharacteristic
866C4C2×#41×D7111yescharacteristic
867C2—24no—
868C2—2842no—
869C2—5682no—
870C2—1424no—
871C2#2259796714yesdirect product factor
872C2C2×#121×D7111yescharacteristic
873C2C22×#1455616011yescharacteristic
874C2C2×#1798679611yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#467×C71C2
socleC23×C71C22×D4
prime radicalC2×#17986512C2
hypercenterC2×#467D71
hypocenterC71C2×#3056
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#467

Complements

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

NH ≅ G/Ntype
1. C22×#14556160C2semidirect
2. C23×#11765848C2semidirect
4. C2×C22⋊Q8×D71C2semidirect
5. #22597967C2direct (N × H)
6. C2×#17986256C2semidirect
7. C2×#17986254C2semidirect
8. C2×#17986248C2semidirect
9. C2×#17986246C2semidirect
10. C2×#17986238C2semidirect
11. C2×#17986230C2semidirect
12. C2×#17986228C2semidirect
13. C2×#17986040C2semidirect
14. C2×#17985999C2semidirect
15. C2×#17986006C2semidirect
16. C2×#467×C71C2semidirect
21. C2×#14556160C22semidirect
22. C22×#11765855C22semidirect
23. C22×#11765854C22semidirect
24. C22×#11765852C22semidirect
30. C22×#11765848C22semidirect
42. C22⋊Q8×D71C22semidirect
52. #17986256C22semidirect
53. #17986254C22semidirect
54. #17986248C22semidirect
55. #17986246C22semidirect
56. #17986238C22semidirect
57. #17986230C22semidirect
58. #17986228C22semidirect
59. #17986040C22semidirect
60. C2×#14556061C22semidirect
61. C2×#14556060C22semidirect
62. C2×#14556059C22semidirect
63. #17986006C22semidirect
64. #17985999C22semidirect
65. C2×#14556053C22semidirect
66. C2×#14556052C22semidirect
67. C2×#14556052C22semidirect
68. C2×#14556051C22semidirect
69. C2×#14556050C22semidirect
70. C2×#14556048C22semidirect
71. C22×Q16×C71C22semidirect
75. #467×C71C22semidirect
76. C2×#107×C71C22semidirect
77. C2×#103×C71C22semidirect
78. C2×#103×C71C22semidirect
108. C2×#11765855C23semidirect
110. C2×#11765854C23semidirect
112. C2×#11765852C23semidirect
117. C2×#11765848D4semidirect
165. #14556061C23semidirect
166. #14556060C23semidirect
167. #14556059C23semidirect
168. #14556053C23semidirect
169. #14556052C23semidirect
170. #14556052C23semidirect
171. #14556051C23semidirect
172. #14556050C23semidirect
173. #14556048C23semidirect
178. C2×Q16×C71C23semidirect
193. #107×C71C23semidirect
194. #103×C71C23semidirect
195. #103×C71C23semidirect
259. #11765848C2×D4semidirect
317. C23×C71#137semidirect
400. C22×C71C2×#137semidirect
431. C2×C71#3056semidirect
448. C2×#467D71semidirect
454. C71C2×#3056semidirect
461. C22×Q16C2×D71semidirect
499. #467C2×D71semidirect
504. C2×#107C2×D71semidirect
513. C2×#103C2×D71semidirect
514. C2×#103C2×D71semidirect
551. C2×Q16C22×D71semidirect
623. #107C22×D71semidirect
630. #103C22×D71semidirect
631. #103C22×D71semidirect
771. C23#14556160semidirect
851. C22C2×#14556160semidirect
871. C2#22597967direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561602
C23×#117658482
C2×#179865122
C2×C22⋊Q8×D712
#225979672
C2×#179862562
C2×#179862542
C2×#179862482
C2×#179862462
C2×#179862382
C2×#179862302
C2×#179862282
C2×#179860402
C2×#179859992
C2×#179860062
C2×#467×C712
C2×#305671