Finite Group Databasebeta

← C2×#22601990 #32905616

Subgroups — C2×#22601990 #32905616

Order 18176.

11254 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556176C211yesmaximal, characteristic, complemented
2C23×Q8×D71C211yesmaximal, characteristic, complemented
3#22601990C2132yesmaximal, direct product factor
4C2×#17986664C213yesmaximal, complemented
5C2×Q8×C22⋊D71C211yesmaximal, characteristic, complemented
6C2×#17986662C213yesmaximal, complemented
7C2×#17986661C211yesmaximal, characteristic, complemented
8C2×#17986660C211yesmaximal, characteristic, complemented
9C2×#17986659C213yesmaximal, complemented
10C2×#17986658C213yesmaximal, complemented
11C2×#17986574C213yesmaximal, complemented
12C2×#17986572C213yesmaximal, complemented
13C2×#17986512C213yesmaximal, complemented
14C2×#17986508C213yesmaximal, complemented
15C2×#17986475C211yesmaximal, characteristic, complemented
16C2×D4×Q8×C71C211yesmaximal, characteristic, complemented
17C2×#14556176—216no—
18C2×#14556176C22116yescomplemented
19C22×#11765866C2213yes—
20C22×#11765866C2211yescharacteristic, complemented
21C22×#11765865C2213yes—
22C22×#11765865C2213yescomplemented
23C23×Dic142C2213yes—
24C22×Q8×D71—216no—
25C22×Q8×D71C2213yes—
26C22×Q8×D71C2211yescharacteristic
27C22×Q8×D71C2213yes—
28C22×Q8×D71C2211yescharacteristic
29C22×Q8×D71C22116yescomplemented
30C22×Q8×D71C2213yescomplemented
31C23×C4×D71C2213yes—
32#17986664C22148yescomplemented
33Q8×C22⋊D71C22116yescomplemented
34#17986662C22148yescomplemented
35#17986661C22116yescomplemented
36#17986660C22116yescomplemented
37#17986659C22148yescomplemented
38#17986658C22148yescomplemented
39#17986574C22148yescomplemented
40#17986572C22148yescomplemented
41C2×#14556127C2216yescomplemented
42C2×#14556126C2213yescomplemented
43C2×#14556117C2213yescomplemented
44C2×#14556116C2213yescomplemented
45C2×#14556114C2216yescomplemented
46#17986512C22148yescomplemented
47#17986508C22148yescomplemented
48C2×#14556113C2213yes—
49C2×#14556113C2216yes—
50C2×#14556110C2213yes—
51C2×#14556108C2213yescomplemented
52C2×#14556107C2213yescomplemented
53C2×#14556106C2213yes—
54C2×#14556106C2216yescomplemented
55C2×#14556106C2216yescomplemented
56C2×#14556105C2213yes—
57C2×#14556104C2213yes—
58C2×#14556104C2213yescomplemented
59C2×#14556103C2213yes—
60C2×#14556102C2213yes—
61C2×#14556101C2213yes—
62C2×#14556100C2213yes—
63C2×#14556098C2213yes—
64C2×#14556096C2211yescharacteristic
65#17986475C22116yescomplemented
66C2×Q8×Dic71C2211yescharacteristic, complemented
67C2×C4×Dic142C2213yescomplemented
68C2×#14556093C2213yescomplemented
69C2×C4×D284C2213yes—
70C2×#14556090C2216yes—
71C2×C4×C22⋊D71C2213yes—
72C2×C4×C22⋊D71C2213yes—
73C2×(C22⋊D71)⋊C4C2216yes—
74C2×#14556086C2213yes—
75C2×#14556085C2213yes—
76C23×Q8×C71C2211yescharacteristic
77C23×Q8×C71C2211yescharacteristic, complemented
78D4×Q8×C71C22116yescomplemented
79C2×C4⋊Q8×C71C2213yescomplemented
80C2×C22⋊Q8×C71C2213yes—
81C2×C22⋊Q8×C71C2213yescomplemented
82C2×C4×Q8×C71C2211yescharacteristic, complemented
83C2×C4×D4×C71C2213yes—
84C24×D71C2311yescharacteristic
85#14556176—2128no—
86C2×#11765866—224no—
87C2×#11765866—28no—
88C2×#11765866C23124yes—
89C2×#11765866C2318yescomplemented
90C2×#11765865—224no—
91C2×#11765865—224no—
92C2×#11765865C23124yes—
93C2×#11765865C23124yescomplemented
94C22×Dic142—224no—
95C22×Dic142C2316yes—
96C22×Dic142C2313yes—
97C22×Dic142C23124yes—
98C22×Dic142C2313yes—
99C22×Dic142C2313yes—
100C2×Q8×D71—224no—
101C2×Q8×D71—224no—
102C2×Q8×D71—2128no—
103C2×Q8×D71—224no—
104C2×Q8×D71—28no—
105C2×Q8×D71D4116yescomplemented
106C2×Q8×D71C23124yes—
107C2×Q8×D71C23124yes—
108C2×Q8×D71C2318yes—
109C2×Q8×D71C2318yes—
110C2×Q8×D71C23124yescomplemented
111C22×D284C2313yes—
112C22×D284C2313yes—
113C22×D284C2313yes—
114C22×C22⋊D71C2311yescharacteristic
115C22×C22⋊D71C2313yes—
116C22×C22⋊D71C2313yes—
117C22×C22⋊D71C2311yescharacteristic
118C23×Dic71C2313yes—
119C22×C4×D71—224no—
120C22×C4×D71C2313yes—
121C22×C4×D71C2313yes—
122C22×C4×D71C2313yes—
123C22×C4×D71C23124yes—
124C22×C4×D71C2313yes—
125C22×C4×D71C2316yes—
126C22×C4×D71C2313yes—
127#14556127C23148yescomplemented
128#14556126C23124yescomplemented
129#14556117C23124yescomplemented
130#14556116C23124yescomplemented
131#14556114C23148yescomplemented
132#14556113C23148yes—
133#14556113C23124yes—
134#14556110C23124yes—
135#14556108C23124yescomplemented
136#14556107C23124yescomplemented
137#14556106C23124yes—
138#14556106C23148yescomplemented
139#14556106C23148yescomplemented
140#14556105C23124yes—
141#14556104C23124yes—
142#14556104C23124yescomplemented
143#14556103C23124yes—
144#14556102C23124yes—
145#14556101C23124yes—
146#14556100C23124yes—
147#14556098C23124yes—
148#14556096C2318yes—
149Q8×Dic71C2318yescomplemented
150C4×Dic142C23124yescomplemented
151#14556093C23124yescomplemented
152C4×D284C23124yes—
153#14556090C23148yes—
154C4×C22⋊D71C23124yes—
155C4×C22⋊D71C23124yes—
156(C22⋊D71)⋊C4C23148yes—
157#14556086C23124yes—
158#14556085C23124yes—
159C2×C4⋊Dic71C2313yes—
160C2×C4⋊Dic71C2313yes—
161C2×Dic71⋊C4C2313yes—
162C2×Dic71⋊C4C2313yes—
163C2×Dic71⋊C4C2316yes—
164C2×Dic71⋊C4C2313yes—
165C2×Dic71⋊C4C2313yes—
166C2×C22⋊Dic71C2311yescharacteristic
167C2×C22⋊Dic71C2313yes—
168C2×(C2×D71)⋊C4C2311yescharacteristic
169C2×(C2×D71)⋊C4C2313yes—
170C2×(C2×D71)⋊C4C2316yes—
171C2×(C2×D71)⋊C4C2313yes—
172C2×(C2×D71)⋊C4C2313yes—
173C2×(C2×D71)⋊C4C2316yes—
174C2×(C2×D71)⋊C4C2311yescharacteristic
175C2×(C2×D71)⋊C4C2313yes—
176C2×C4×Dic71C2313yes—
177C2×C4×Dic71C2316yes—
178C22×Q8×C71—28no—
179C22×Q8×C71—28no—
180C22×Q8×C71C2313yes—
181C22×Q8×C71C2318yes—
182C22×Q8×C71C2313yes—
183C22×Q8×C71C2311yescharacteristic
184C22×Q8×C71C2318yescomplemented
185C22×D4×C71C2311yescharacteristic
186C23×C4×C71C2313yes—
187C23×C4×C71C2313yes—
188C4⋊Q8×C71C23124yescomplemented
189C22⋊Q8×C71C23124yes—
190C22⋊Q8×C71C23124yescomplemented
191C4×Q8×C71C2318yescomplemented
192C4×D4×C71C23124yes—
193C2×C4⋊C4×C71C2313yes—
194C2×C4⋊C4×C71C2313yes—
195C2×C4⋊C4×C71C2316yes—
196C2×C22⋊C4×C71C2313yes—
197C2×C22⋊C4×C71C2313yes—
198C2×C42×C71C2313yes—
199C23×D71—24no—
200C23×D71—24no—
201C23×D71—24no—
202C23×D71C2414yes—
203C23×D71C2413yes—
204C23×D71C2411yescharacteristic
205C23×D71C2411yescharacteristic
206#11765866—232no—
207#11765866—296no—
208#11765865—296no—
209#11765865—296no—
210C2×Dic142—212no—
211C2×Dic142—224no—
212C2×Dic142—212no—
213C2×Dic142—296no—
214C2×Dic142C2×D4124yes—
215C2×Dic142C24124yes—
216C2×Dic142C24112yes—
217C2×Dic142C24112yes—
218C2×Dic142C24112yes—
219Q8×D71—232no—
220Q8×D71—296no—
221Q8×D71—296no—
222Q8×D71—296no—
223Q8×D71C2×D4164yescomplemented
224C2×D284—212no—
225C2×D284—212no—
226C2×D284—212no—
227C2×D284C24112yes—
228C2×D284C24112yes—
229C2×D284C24112yes—
230C2×C22⋊D71—212no—
231C2×C22⋊D71—24no—
232C2×C22⋊D71—24no—
233C2×C22⋊D71—212no—
234C2×C22⋊D71C2414yes—
235C2×C22⋊D71C24112yes—
236C2×C22⋊D71C24112yes—
237C2×C22⋊D71C2414yes—
238C22×Dic71—212no—
239C22×Dic71C2411yescharacteristic
240C22×Dic71C2413yes—
241C22×Dic71C24112yes—
242C22×Dic71C2411yescharacteristic
243C22×Dic71C2413yes—
244C22×Dic71C2413yes—
245C2×C4×D71—212no—
246C2×C4×D71—212no—
247C2×C4×D71—212no—
248C2×C4×D71—212no—
249C2×C4×D71—224no—
250C2×C4×D71—296no—
251C2×C4×D71C2×D4124yes—
252C2×C4×D71C24112yes—
253C2×C4×D71C24112yes—
254C2×C4×D71C24112yes—
255C2×C4×D71C24112yes—
256C2×C4×D71C24124yes—
257C2×C4×D71C24112yes—
258C4⋊Dic71C24112yes—
259C4⋊Dic71C24112yes—
260Dic71⋊C4C24112yes—
261Dic71⋊C4C24112yes—
262Dic71⋊C4C24124yes—
263Dic71⋊C4C24112yes—
264Dic71⋊C4C24112yes—
265C22⋊Dic71C2414yes—
266C22⋊Dic71C24112yes—
267(C2×D71)⋊C4C2414yes—
268(C2×D71)⋊C4C24112yes—
269(C2×D71)⋊C4C24124yes—
270(C2×D71)⋊C4C24112yes—
271(C2×D71)⋊C4C24112yes—
272(C2×D71)⋊C4C24124yes—
273(C2×D71)⋊C4C2414yes—
274(C2×D71)⋊C4C24112yes—
275C4×Dic71C24112yes—
276C4×Dic71C24124yes—
277C24×C71C2411yescharacteristic
278C24×C71C2411yescharacteristic
279C2×Q8×C71—232no—
280C2×Q8×C71—232no—
281C2×Q8×C71—212no—
282C2×Q8×C71—212no—
283C2×Q8×C71C2×D418yes—
284C2×Q8×C71C24112yes—
285C2×Q8×C71C24112yes—
286C2×Q8×C71C2414yes—
287C2×D4×C71—24no—
288C2×D4×C71C2414yes—
289C22×C4×C71—212no—
290C22×C4×C71—212no—
291C22×C4×C71C2413yes—
292C22×C4×C71C2413yes—
293C22×C4×C71C24112yes—
294C22×C4×C71C2413yes—
295C22×C4×C71C24112yes—
296C22×C4×C71C2411yescharacteristic
297C22×C4×C71C2413yes—
298C4⋊C4×C71C24112yes—
299C4⋊C4×C71C24112yes—
300C4⋊C4×C71C24124yes—
301C22⋊C4×C71C24112yes—
302C22⋊C4×C71C24112yes—
303C42×C71C24112yes—
304C23×C71—22no—
305C23×C71—22no—
306C23×C71—22no—
307C23×C71—22no—
308C23×C71—22no—
309C23×C712−1+414yescomplemented
310C23×C71C2512yes—
311C23×C71C2512yes—
312C23×C71C2511yescharacteristic
313C22×D71—232no—
314C22×D71—22no—
315C22×D71—22no—
316C22×D71—22no—
317C22×D71—22no—
318C22×D71—28no—
319C22×D71—28no—
320C22×D71—28no—
321C22×D71—26no—
322C22×D71—26no—
323C22×D71—26no—
324C22×D71C22×D414yes—
325C22×D712−1+414yescomplemented
326C22×D71C2516yes—
327C22×D71C2512yes—
328C22×D71C2512yes—
329Q8×C71—224no—
330Q8×C71—224no—
331Q8×C71C22×D4116yes—
332D4×C71—28no—
333C2×C4×C71—26no—
334C2×C4×C71—26no—
335C2×C4×C71—22no—
336C2×C4×C71—26no—
337C2×C4×C71—224no—
338C2×C4×C71—224no—
339C2×C4×C71C22×D4112yes—
340C2×C4×C71C2512yes—
341C2×C4×C71C2516yes—
342C2×C4×C71C2516yes—
343C2×C4×C71C2516yes—
344C2×C4×C71C2516yes—
345C22⋊D71—224no—
346C22⋊D71—28no—
347C22⋊D71—28no—
348C22⋊D71—224no—
349C2×Dic71—22no—
350C2×Dic71—26no—
351C2×Dic71—22no—
352C2×Dic71—26no—
353C2×Dic71—224no—
354C2×Dic71C22×D4112yes—
355C2×Dic71C2512yes—
356C2×Dic71C2516yes—
357C2×Dic71C2516yes—
358C2×Dic71C2512yes—
359C2×Dic71C2516yes—
360D284—224no—
361D284—224no—
362D284—224no—
363C4×D71—224no—
364C4×D71—224no—
365C4×D71—224no—
366C4×D71—224no—
367C4×D71—248no—
368C4×D71C22×D4148yes—
369Dic142—224no—
370Dic142—248no—
371Dic142—224no—
372Dic142C22×D4148yes—
373C22×C71—22no—
374C22×C71—22no—
375C22×C71—28no—
376C22×C71—22no—
377C22×C71—22no—
378C22×C71—22no—
379C22×C71—44no—
380C22×C71C23×D412yes—
381C22×C71C2×2−1+412yes—
382C22×C71C2×2−1+412yes—
383C22×C71C2×2−1+414yescomplemented
384C22×C71C2611yescharacteristic
385C2×D71—232no—
386C2×D71—22no—
387C2×D71—22no—
388C2×D71—22no—
389C2×D71—22no—
390C2×D71—28no—
391C2×D71—28no—
392C2×D71—26no—
393C2×D71—26no—
394C2×D71—26no—
395C2×D71—412no—
396C2×D71C23×D414yes—
397C2×D71C2×2−1+414yescomplemented
398C4×C71—26no—
399C4×C71—26no—
400C4×C71—26no—
401C4×C71—22no—
402C4×C71C23×D4112yes—
403Dic71—26no—
404Dic71—22no—
405Dic71—22no—
406Dic71—26no—
407Dic71C23×D4112yes—
408C2×#3486—711nomaximal, Sylow
409C2×C71—24no—
410C2×C71—42no—
411C2×C71#348614yescomplemented
412C2×C71C24×D411yescharacteristic
413C2×C71C22×2−1+411yescharacteristic
414C2×C71C22×2−1+411yescharacteristic
415D71—24no—
416D71—24no—
417D71—46no—
418C22×2−1+4—711no—
419C24×Q8—711no—
420#3486—7132no—
421C2×D4×Q8—711no—
422C2×D4×Q8—713no—
423C2×D4×Q8—713no—
424C2×D4×Q8D7111yescharacteristic, complemented
425C2×#548—711no—
426C2×#548—713no—
427C2×#548—711no—
428C2×#548—713no—
429C2×#536—713no—
430C2×#536—713no—
431C2×#525—713no—
432C2×#525—713no—
433C2×#519—711no—
434C71C2×#348611yescharacteristic, complemented, Sylow
435C2×2−1+4—7116no—
436C2×2−1+4—14216no—
437C22×#41—713no—
438C22×#41—711no—
439C22×#41—713no—
440C22×#41—713no—
441C23×Q8—711no—
442C23×Q8—713no—
443C23×Q8—713no—
444C23×Q8—711no—
445C23×Q8—7116no—
446C23×Q8—713no—
447C23×Q8—713no—
448C23×Q8—14216no—
449C23×Q8C2×D7111yescharacteristic
450C23×Q8C2×D7111yescharacteristic, complemented
451C24×C4—713no—
452D4×Q8—7116no—
453D4×Q8—7148no—
454D4×Q8—7148no—
455D4×Q8C2×D71116yescomplemented
456#548—7116no—
457#548—7148no—
458#548—7116no—
459#548—7148no—
460#536—7148no—
461#536—7148no—
462C2×C4⋊Q8—713no—
463C2×C4⋊Q8—716no—
464C2×C4⋊Q8C2×D7113yescomplemented
465C2×#124—713no—
466C2×#124—716no—
467C2×#124—713no—
468#525—7148no—
469#525—7148no—
470C2×#123—716no—
471C2×#123—713no—
472C2×#123—713no—
473C2×C22⋊Q8—713no—
474C2×C22⋊Q8—713no—
475C2×C22⋊Q8—713no—
476C2×C22⋊Q8—713no—
477C2×C22⋊Q8—716no—
478C2×C22⋊Q8—716no—
479C2×C22⋊Q8—713no—
480C2×C22⋊Q8—713no—
481C2×C22⋊Q8C2×D7113yes—
482C2×C22⋊Q8C2×D7113yescomplemented
483C2×#121—713no—
484C2×#121—713no—
485C2×#121—713no—
486C2×#121—713no—
487C2×#120—711no—
488C2×#120—713no—
489#519—7116no—
490C2×C4×Q8—711no—
491C2×C4×Q8—713no—
492C2×C4×Q8—713no—
493C2×C4×Q8C2×D7111yescharacteristic, complemented
494C2×C4×D4—713no—
495C2×C4×D4—713no—
496C2×C4×D4—716no—
497C2×C4×D4—716no—
498C2×C4×D4—713no—
499C2×C4×D4C2×D7113yes—
500C2×#117—713no—
501C2×#117—713no—
502C25—711no—
5032−1+4—142128no—
504C2×#41—7124no—
505C2×#41—718no—
506C2×#41—7124no—
507C2×#41—7124no—
508C2×#41—14224no—
509C2×#41—14224no—
510C2×#41—14224no—
511C2×#41—1428no—
512C22×Q8—28no—
513C22×Q8—28no—
514C22×Q8—7116no—
515C22×Q8—718no—
516C22×Q8—7124no—
517C22×Q8—7124no—
518C22×Q8—718no—
519C22×Q8—7124no—
520C22×Q8—713no—
521C22×Q8—716no—
522C22×Q8—713no—
523C22×Q8—713no—
524C22×Q8—7124no—
525C22×Q8—14224no—
526C22×Q8—14224no—
527C22×Q8—142128no—
528C22×Q8—14224no—
529C22×Q8—14224no—
530C22×Q8—1428no—
531C22×Q8C22×D7113yes—
532C22×Q8C22×D7113yes—
533C22×Q8C22×D7118yes—
534C22×Q8C22×D7111yescharacteristic
535C22×Q8C22×D7118yescomplemented
536C22×D4—711no—
537C22×D4—713no—
538C22×D4—711no—
539C22×D4—713no—
540C22×D4—713no—
541C22×D4—713no—
542C22×D4—713no—
543C22×D4C22×D7111yescharacteristic
544C23×C4—713no—
545C23×C4—713no—
546C23×C4—713no—
547C23×C4—713no—
548C23×C4—716no—
549C23×C4—713no—
550C23×C4—713no—
551C23×C4—7124no—
552C23×C4—14224no—
553C23×C4C22×D7113yes—
554C23×C4C22×D7113yes—
555C4⋊Q8—7124no—
556C4⋊Q8—7148no—
557C4⋊Q8C22×D71124yescomplemented
558#124—7124no—
559#124—7148no—
560#124—7124no—
561#123—7148no—
562#123—7124no—
563#123—7124no—
564C22⋊Q8—7124no—
565C22⋊Q8—7124no—
566C22⋊Q8—7124no—
567C22⋊Q8—7124no—
568C22⋊Q8—7148no—
569C22⋊Q8—7148no—
570C22⋊Q8—7124no—
571C22⋊Q8—7124no—
572C22⋊Q8C22×D71124yes—
573C22⋊Q8C22×D71124yescomplemented
574#121—7124no—
575#121—7124no—
576#121—7124no—
577#121—7124no—
578#120—718no—
579#120—7124no—
580C4×Q8—718no—
581C4×Q8—7124no—
582C4×Q8—7124no—
583C4×Q8C22×D7118yescomplemented
584C4×D4—7124no—
585C4×D4—7124no—
586C4×D4—7148no—
587C4×D4—7148no—
588C4×D4—7124no—
589C4×D4C22×D71124yes—
590#117—7124no—
591#117—7124no—
592C2×C4⋊C4—713no—
593C2×C4⋊C4—713no—
594C2×C4⋊C4—713no—
595C2×C4⋊C4—713no—
596C2×C4⋊C4—716no—
597C2×C4⋊C4—713no—
598C2×C4⋊C4—713no—
599C2×C4⋊C4C22×D7113yes—
600C2×C4⋊C4C22×D7116yes—
601C2×C4⋊C4C22×D7113yes—
602C2×C22⋊C4—711no—
603C2×C22⋊C4—713no—
604C2×C22⋊C4—713no—
605C2×C22⋊C4—711no—
606C2×C22⋊C4—713no—
607C2×C22⋊C4—711no—
608C2×C22⋊C4—713no—
609C2×C22⋊C4—716no—
610C2×C22⋊C4—716no—
611C2×C22⋊C4—713no—
612C2×C22⋊C4C22×D7113yes—
613C2×C22⋊C4C22×D7113yes—
614C2×C42—716no—
615C2×C42—713no—
616C2×C42C22×D7113yes—
617C24—711no—
618C24—711no—
619C24—714no—
620C24—713no—
621C24—1424no—
622C24—1424no—
623C24—1424no—
624C24C23×D7111yescharacteristic
625C24C23×D7111yescharacteristic
626#41—14296no—
627#41—14296no—
628#41—14296no—
629#41—14232no—
630C2×Q8—232no—
631C2×Q8—232no—
632C2×Q8—212no—
633C2×Q8—212no—
634C2×Q8—7164no—
635C2×Q8—7124no—
636C2×Q8—7112no—
637C2×Q8—7124no—
638C2×Q8—7112no—
639C2×Q8—7112no—
640C2×Q8—14224no—
641C2×Q8—14212no—
642C2×Q8—14296no—
643C2×Q8—14296no—
644C2×Q8—14296no—
645C2×Q8—14296no—
646C2×Q8—14232no—
647C2×Q8—14212no—
648C2×Q8D4×D7118yes—
649C2×Q8C23×D71112yes—
650C2×Q8C23×D71112yes—
651C2×Q8C23×D7114yes—
652C2×D4—24no—
653C2×D4—714no—
654C2×D4—7112no—
655C2×D4—714no—
656C2×D4—7112no—
657C2×D4—7112no—
658C2×D4—7112no—
659C2×D4—7112no—
660C2×D4—14212no—
661C2×D4—14212no—
662C2×D4—14212no—
663C2×D4—1424no—
664C2×D4—1424no—
665C2×D4—14212no—
666C2×D4—14212no—
667C2×D4C23×D7114yes—
668C22×C4—212no—
669C22×C4—212no—
670C22×C4—713no—
671C22×C4—7124no—
672C22×C4—7112no—
673C22×C4—7112no—
674C22×C4—711no—
675C22×C4—713no—
676C22×C4—713no—
677C22×C4—711no—
678C22×C4—7112no—
679C22×C4—7112no—
680C22×C4—7124no—
681C22×C4—7112no—
682C22×C4—7112no—
683C22×C4—14212no—
684C22×C4—14296no—
685C22×C4—14224no—
686C22×C4—14212no—
687C22×C4—14212no—
688C22×C4—14212no—
689C22×C4—14212no—
690C22×C4C23×D71112yes—
691C22×C4C23×D71112yes—
692C22×C4C23×D7113yes—
693C22×C4C23×D7111yescharacteristic
694C22×C4C23×D7113yes—
695C22×C4C23×D7113yes—
696C22×C4C23×D7113yes—
697C4⋊C4—7112no—
698C4⋊C4—7112no—
699C4⋊C4—7124no—
700C4⋊C4—7112no—
701C4⋊C4—7112no—
702C4⋊C4—7112no—
703C4⋊C4—7112no—
704C4⋊C4C23×D71112yes—
705C4⋊C4C23×D71124yes—
706C4⋊C4C23×D71112yes—
707C22⋊C4—714no—
708C22⋊C4—7112no—
709C22⋊C4—7112no—
710C22⋊C4—714no—
711C22⋊C4—7112no—
712C22⋊C4—714no—
713C22⋊C4—7112no—
714C22⋊C4—7124no—
715C22⋊C4—7124no—
716C22⋊C4—7112no—
717C22⋊C4C23×D71112yes—
718C22⋊C4C23×D71112yes—
719C42—7124no—
720C42—7112no—
721C42C23×D71112yes—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—714no—
728C23—714no—
729C23—712no—
730C23—712no—
731C23—716no—
732C23—1428no—
733C23—1428no—
734C23—14232no—
735C23—1426no—
736C23—1426no—
737C23—1426no—
738C23—1422no—
739C23—1422no—
740C23—1422no—
741C23—1422no—
742C23—1428no—
743C23#1455617614yescomplemented
744C23C24×D7112yes—
745C23C24×D7112yes—
746C23C24×D7111yescharacteristic
747Q8—224no—
748Q8—224no—
749Q8—7148no—
750Q8—14248no—
751Q8—14224no—
752Q8—14224no—
753Q8C2×D4×D71116yes—
754D4—28no—
755D4—14224no—
756D4—14224no—
757D4—14224no—
758D4—1428no—
759D4—1428no—
760D4—14224no—
761D4—14224no—
762C2×C4—26no—
763C2×C4—26no—
764C2×C4—26no—
765C2×C4—22no—
766C2×C4—224no—
767C2×C4—224no—
768C2×C4—7112no—
769C2×C4—716no—
770C2×C4—7148no—
771C2×C4—712no—
772C2×C4—716no—
773C2×C4—716no—
774C2×C4—712no—
775C2×C4—14224no—
776C2×C4—14248no—
777C2×C4—14224no—
778C2×C4—14224no—
779C2×C4—1422no—
780C2×C4—1426no—
781C2×C4—1422no—
782C2×C4—1426no—
783C2×C4—14224no—
784C2×C4—14224no—
785C2×C4C2×D4×D71112yes—
786C2×C4C24×D7116yes—
787C2×C4C24×D7112yes—
788C2×C4C24×D7116yes—
789C2×C4C24×D7116yes—
790C2×C4C24×D7116yes—
791C22—28no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—44no—
798C22—28412no—
799C22—714no—
800C22—714no—
801C22—14232no—
802C22—1426no—
803C22—1426no—
804C22—1426no—
805C22—1428no—
806C22—1428no—
807C22—1422no—
808C22—1422no—
809C22—1422no—
810C22—1422no—
811C22C22×D4×D7112yes—
812C222−1+4×D7112yes—
813C22C2×#1455617612yes—
814C22C2×#1455617614yescomplemented
815C22C25×D7111yescharacteristic
816C4—26no—
817C4—26no—
818C4—26no—
819C4—22no—
820C4—7112no—
821C4—1422no—
822C4—1426no—
823C4—1422no—
824C4—1426no—
825C4C22×D4×D71112yes—
826C2—24no—
827C2—42no—
828C2—2846no—
829C2—1424no—
830C2—1424no—
831C2#2260199014yesdirect product factor
832C2C23×D4×D7111yescharacteristic
833C2C2×2−1+4×D7111yescharacteristic
834C2C22×#1455617611yescharacteristic
subgroupG/H
centerC23C24×D71
commutator, cosocleC22×C71C26
FrattiniC22C25×D71
FittingC2×D4×Q8×C71C2
socleC23×C71C25
hypercenterC2×D4×Q8D71
hypocenterC71C2×#3486
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. C22×#14556176C2semidirect
2. C23×Q8×D71C2semidirect
3. #22601990C2direct (N × H)
4. C2×#17986664C2semidirect
5. C2×Q8×C22⋊D71C2semidirect
6. C2×#17986662C2semidirect
7. C2×#17986661C2semidirect
8. C2×#17986660C2semidirect
9. C2×#17986659C2semidirect
10. C2×#17986658C2semidirect
11. C2×#17986574C2semidirect
12. C2×#17986572C2semidirect
13. C2×#17986512C2semidirect
14. C2×#17986508C2semidirect
15. C2×#17986475C2semidirect
16. C2×D4×Q8×C71C2semidirect
18. C2×#14556176C22semidirect
20. C22×#11765866C22semidirect
22. C22×#11765865C22semidirect
29. C22×Q8×D71C22semidirect
30. C22×Q8×D71C22semidirect
32. #17986664C22semidirect
33. Q8×C22⋊D71C22semidirect
34. #17986662C22semidirect
35. #17986661C22semidirect
36. #17986660C22semidirect
37. #17986659C22semidirect
38. #17986658C22semidirect
39. #17986574C22semidirect
40. #17986572C22semidirect
41. C2×#14556127C22semidirect
42. C2×#14556126C22semidirect
43. C2×#14556117C22semidirect
44. C2×#14556116C22semidirect
45. C2×#14556114C22semidirect
46. #17986512C22semidirect
47. #17986508C22semidirect
51. C2×#14556108C22semidirect
52. C2×#14556107C22semidirect
54. C2×#14556106C22semidirect
55. C2×#14556106C22semidirect
58. C2×#14556104C22semidirect
65. #17986475C22semidirect
66. C2×Q8×Dic71C22semidirect
67. C2×C4×Dic142C22semidirect
68. C2×#14556093C22semidirect
77. C23×Q8×C71C22semidirect
78. D4×Q8×C71C22semidirect
79. C2×C4⋊Q8×C71C22semidirect
81. C2×C22⋊Q8×C71C22semidirect
82. C2×C4×Q8×C71C22semidirect
89. C2×#11765866C23semidirect
93. C2×#11765865C23semidirect
105. C2×Q8×D71D4semidirect
110. C2×Q8×D71C23semidirect
127. #14556127C23semidirect
128. #14556126C23semidirect
129. #14556117C23semidirect
130. #14556116C23semidirect
131. #14556114C23semidirect
135. #14556108C23semidirect
136. #14556107C23semidirect
138. #14556106C23semidirect
139. #14556106C23semidirect
142. #14556104C23semidirect
149. Q8×Dic71C23semidirect
150. C4×Dic142C23semidirect
151. #14556093C23semidirect
184. C22×Q8×C71C23semidirect
188. C4⋊Q8×C71C23semidirect
190. C22⋊Q8×C71C23semidirect
191. C4×Q8×C71C23semidirect
223. Q8×D71C2×D4semidirect
309. C23×C712−1+4semidirect
325. C22×D712−1+4semidirect
383. C22×C71C2×2−1+4semidirect
397. C2×D71C2×2−1+4semidirect
411. C2×C71#3486semidirect
424. C2×D4×Q8D71semidirect
434. C71C2×#3486semidirect
450. C23×Q8C2×D71semidirect
455. D4×Q8C2×D71semidirect
464. C2×C4⋊Q8C2×D71semidirect
482. C2×C22⋊Q8C2×D71semidirect
493. C2×C4×Q8C2×D71semidirect
535. C22×Q8C22×D71semidirect
557. C4⋊Q8C22×D71semidirect
573. C22⋊Q8C22×D71semidirect
583. C4×Q8C22×D71semidirect
743. C23#14556176semidirect
814. C22C2×#14556176semidirect
831. C2#22601990direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561762
C23×Q8×D712
#226019902
C2×#179866642
C2×Q8×C22⋊D712
C2×#179866622
C2×#179866612
C2×#179866602
C2×#179866592
C2×#179866582
C2×#179865742
C2×#179865722
C2×#179865122
C2×#179865082
C2×#179864752
C2×D4×Q8×C712
C2×#348671