Finite Group Databasebeta

← C2×#22602017 #32905852

Subgroups — C2×#22602017 #32905852

Order 18176.

11438 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556176C211yesmaximal, characteristic, complemented
2C23×#11765866C211yesmaximal, characteristic, complemented
3#22602017C2132yesmaximal, direct product factor
4C2×Q8×C22⋊D71C211yesmaximal, characteristic, complemented
5C2×#17986661C211yesmaximal, characteristic, complemented
6C2×#17986660C211yesmaximal, characteristic, complemented
7C2×#17986652C213yesmaximal, complemented
8C2×#17986651C213yesmaximal, complemented
9C2×#17986645C213yesmaximal, complemented
10C2×#17986640C213yesmaximal, complemented
11C2×#17986579C213yesmaximal, complemented
12C2×#17986574C213yesmaximal, complemented
13C2×#17986508C213yesmaximal, complemented
14C2×C22⋊Q8×D71C213yesmaximal, complemented
15C2×#17986481C211yesmaximal, characteristic, complemented
16C2×D4×Q8×C71C211yesmaximal, characteristic, complemented
17C2×#14556176—216no—
18C2×#14556176C22116yescomplemented
19C22×#11765866—216no—
20C22×#11765866C2213yes—
21C22×#11765866C2211yescharacteristic
22C22×#11765866C2213yes—
23C22×#11765866C2211yescharacteristic
24C22×#11765866C22116yescomplemented
25C22×#11765866C2213yescomplemented
26C22×#11765865C2213yescomplemented
27C22×#11765865C2213yescomplemented
28C22×Q8×D71C2211yescharacteristic, complemented
29C22×Q8×D71C2213yescomplemented
30C23×D284C2213yes—
31C23×C4×D71C2213yes—
32Q8×C22⋊D71C22116yescomplemented
33#17986661C22116yescomplemented
34#17986660C22116yescomplemented
35#17986652C22148yescomplemented
36#17986651C22148yescomplemented
37#17986645C22148yescomplemented
38#17986640C22148yescomplemented
39#17986579C22148yescomplemented
40#17986574C22148yescomplemented
41C2×#14556126C2213yescomplemented
42C2×#14556117C2213yescomplemented
43C2×#14556116C2213yescomplemented
44#17986508C22148yescomplemented
45C2×#14556113C2216yescomplemented
46C2×#14556113C2216yescomplemented
47C2×#14556113C2213yescomplemented
48C2×#14556110C2213yescomplemented
49C2×#14556108C2213yescomplemented
50C2×#14556107C2213yes—
51C2×#14556106C2216yescomplemented
52C2×#14556106C2213yescomplemented
53C2×#14556105C2213yes—
54C2×#14556104C2213yescomplemented
55C2×#14556104C2213yescomplemented
56C22⋊Q8×D71C22148yescomplemented
57C2×#14556103C2216yescomplemented
58C2×#14556103C2213yescomplemented
59C2×#14556102C2213yescomplemented
60C2×#14556101C2216yescomplemented
61C2×#14556101C2213yescomplemented
62C2×#14556100C2211yescharacteristic
63C2×#14556098C2213yes—
64C2×#14556096C2213yes—
65#17986481C22116yescomplemented
66C2×Q8×Dic71C2211yescharacteristic, complemented
67C2×C4×D284C2213yescomplemented
68C2×C4×D284C2213yescomplemented
69C2×#14556090C2213yescomplemented
70C2×C4×C22⋊D71C2213yes—
71C2×C4×C22⋊D71C2213yescomplemented
72C2×#14556085C2213yescomplemented
73C2×C4⋊C4×D71C2213yescomplemented
74C2×C4⋊C4×D71C2216yescomplemented
75C2×C22⋊C4×D71C2216yes—
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×D71C2313yes—
85#14556176—2128no—
86C2×#11765866—2128no—
87C2×#11765866—224no—
88C2×#11765866—224no—
89C2×#11765866—224no—
90C2×#11765866—28no—
91C2×#11765866D4116yescomplemented
92C2×#11765866C23124yes—
93C2×#11765866C23124yes—
94C2×#11765866C2318yes—
95C2×#11765866C2318yes—
96C2×#11765866C23124yescomplemented
97C2×#11765865—224no—
98C2×#11765865—224no—
99C2×#11765865C23124yescomplemented
100C2×#11765865C23124yescomplemented
101C22×Dic142C2313yes—
102C22×Dic142C2313yes—
103C2×Q8×D71—224no—
104C2×Q8×D71—28no—
105C2×Q8×D71C23124yescomplemented
106C2×Q8×D71C2318yescomplemented
107C22×D284—224no—
108C22×D284C2316yes—
109C22×D284C2313yes—
110C22×D284C23124yes—
111C22×D284C2313yes—
112C22×D284C2313yes—
113C22×D284C2313yes—
114C22×C22⋊D71C2313yes—
115C22×C22⋊D71C2311yescharacteristic
116C22×C22⋊D71C2311yescharacteristic
117C22×C22⋊D71C2313yes—
118C23×Dic71C2311yescharacteristic
119C22×C4×D71—224no—
120C22×C4×D71C2313yes—
121C22×C4×D71C2313yes—
122C22×C4×D71C2313yes—
123C22×C4×D71C23124yes—
124C22×C4×D71C2316yes—
125C22×C4×D71C2313yes—
126C22×C4×D71C2316yes—
127C22×C4×D71C2313yes—
128#14556126C23124yescomplemented
129#14556117C23124yescomplemented
130#14556116C23124yescomplemented
131#14556113C23148yescomplemented
132#14556113C23148yescomplemented
133#14556113C23124yescomplemented
134#14556110C23124yescomplemented
135#14556108C23124yescomplemented
136#14556107C23124yes—
137#14556106C23124yescomplemented
138#14556106C23148yescomplemented
139#14556105C23124yes—
140#14556104C23124yescomplemented
141#14556104C23124yescomplemented
142#14556103C23148yescomplemented
143#14556103C23124yescomplemented
144#14556102C23124yescomplemented
145#14556101C23124yescomplemented
146#14556101C23148yescomplemented
147#14556100C2318yes—
148#14556098C23124yes—
149#14556096C23124yes—
150Q8×Dic71C2318yescomplemented
151C4×D284C23124yescomplemented
152C4×D284C23124yescomplemented
153#14556090C23124yescomplemented
154C4×C22⋊D71C23124yes—
155C4×C22⋊D71C23124yescomplemented
156#14556085C23124yescomplemented
157C2×C4⋊Dic71C2313yes—
158C2×C4⋊Dic71C2313yes—
159C2×Dic71⋊C4C2313yes—
160C2×Dic71⋊C4C2313yes—
161C2×Dic71⋊C4C2316yes—
162C2×Dic71⋊C4C2311yescharacteristic
163C2×Dic71⋊C4C2313yes—
164C4⋊C4×D71C23124yescomplemented
165C4⋊C4×D71C23148yescomplemented
166C2×C22⋊Dic71C2313yes—
167C2×C22⋊Dic71C2311yescharacteristic
168C2×(C2×D71)⋊C4C2316yes—
169C2×(C2×D71)⋊C4C2316yes—
170C2×(C2×D71)⋊C4C2313yes—
171C2×(C2×D71)⋊C4C2313yes—
172C2×(C2×D71)⋊C4C2313yes—
173C2×(C2×D71)⋊C4C2313yes—
174C2×(C2×D71)⋊C4C2311yescharacteristic
175C2×(C2×D71)⋊C4C2313yes—
176C22⋊C4×D71C23148yes—
177C2×C4×Dic71C2313yes—
178C22×Q8×C71—28no—
179C22×Q8×C71—28no—
180C22×Q8×C71C2313yes—
181C22×Q8×C71C2313yes—
182C22×Q8×C71C2318yes—
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—212no—
200C23×D71—212no—
201C23×D71—46no—
202C23×D71C2411yescharacteristic
203C23×D71C2413yes—
204C23×D71C24112yes—
205C23×D71C2413yes—
206#11765866—232no—
207#11765866—296no—
208#11765866—296no—
209#11765866—296no—
210#11765866C2×D4164yescomplemented
211#11765865—296no—
212#11765865—296no—
213C2×Dic142—212no—
214C2×Dic142—212no—
215C2×Dic142C24112yes—
216C2×Dic142C24112yes—
217Q8×D71—232no—
218Q8×D71—296no—
219C2×D284—224no—
220C2×D284—212no—
221C2×D284—212no—
222C2×D284—296no—
223C2×D284—46no—
224C2×D284C2×D4124yes—
225C2×D284C24124yes—
226C2×D284C24112yes—
227C2×D284C24112yes—
228C2×D284C24112yes—
229C2×D284C24112yes—
230C2×C22⋊D71—24no—
231C2×C22⋊D71—212no—
232C2×C22⋊D71—24no—
233C2×C22⋊D71—46no—
234C2×C22⋊D71C24112yes—
235C2×C22⋊D71C2414yes—
236C2×C22⋊D71C2414yes—
237C2×C22⋊D71C24112yes—
238C22×Dic71—24no—
239C22×Dic71C2411yescharacteristic
240C22×Dic71C2414yes—
241C22×Dic71C2413yes—
242C22×Dic71C2413yes—
243C22×Dic71C2411yescharacteristic
244C22×Dic71C2411yescharacteristic
245C2×C4×D71—212no—
246C2×C4×D71—224no—
247C2×C4×D71—212no—
248C2×C4×D71—212no—
249C2×C4×D71—212no—
250C2×C4×D71—296no—
251C2×C4×D71—412no—
252C2×C4×D71C2×D4124yes—
253C2×C4×D71C24112yes—
254C2×C4×D71C24112yes—
255C2×C4×D71C24112yes—
256C2×C4×D71C24124yes—
257C2×C4×D71C24112yes—
258C2×C4×D71C24124yes—
259C2×C4×D71C24112yes—
260C4⋊Dic71C24112yes—
261C4⋊Dic71C24112yes—
262Dic71⋊C4C24112yes—
263Dic71⋊C4C24112yes—
264Dic71⋊C4C24124yes—
265Dic71⋊C4C2414yes—
266Dic71⋊C4C24112yes—
267C22⋊Dic71C24112yes—
268C22⋊Dic71C2414yes—
269(C2×D71)⋊C4C24124yes—
270(C2×D71)⋊C4C24124yes—
271(C2×D71)⋊C4C24112yes—
272(C2×D71)⋊C4C24112yes—
273(C2×D71)⋊C4C24112yes—
274(C2×D71)⋊C4C24112yes—
275(C2×D71)⋊C4C2414yes—
276(C2×D71)⋊C4C24112yes—
277C4×Dic71C24112yes—
278C24×C71C2411yescharacteristic
279C24×C71C2411yescharacteristic
280C2×Q8×C71—232no—
281C2×Q8×C71—232no—
282C2×Q8×C71—212no—
283C2×Q8×C71—212no—
284C2×Q8×C71C2×D418yes—
285C2×Q8×C71C24112yes—
286C2×Q8×C71C24112yes—
287C2×Q8×C71C2414yes—
288C2×D4×C71—24no—
289C2×D4×C71C2414yes—
290C22×C4×C71—212no—
291C22×C4×C71—212no—
292C22×C4×C71C2413yes—
293C22×C4×C71C24112yes—
294C22×C4×C71C2413yes—
295C22×C4×C71C2413yes—
296C22×C4×C71C24112yes—
297C22×C4×C71C2411yescharacteristic
298C22×C4×C71C2413yes—
299C4⋊C4×C71C24112yes—
300C4⋊C4×C71C24112yes—
301C4⋊C4×C71C24124yes—
302C22⋊C4×C71C24112yes—
303C22⋊C4×C71C24112yes—
304C42×C71C24112yes—
305C23×C71—22no—
306C23×C71—22no—
307C23×C71—22no—
308C23×C71—22no—
309C23×C71—22no—
310C23×C712−1+414yescomplemented
311C23×C71C2512yes—
312C23×C71C2512yes—
313C23×C71C2511yescharacteristic
314C22×D71—26no—
315C22×D71—26no—
316C22×D71—22no—
317C22×D71—26no—
318C22×D71—22no—
319C22×D71—26no—
320C22×D71—224no—
321C22×D71—26no—
322C22×D71—22no—
323C22×D71—224no—
324C22×D71—412no—
325C22×D71—448no—
326C22×D71C22×D4112yes—
327C22×D71C2516yes—
328C22×D71C2512yes—
329C22×D71C2516yes—
330Q8×C71—224no—
331Q8×C71—224no—
332Q8×C71C22×D4116yes—
333D4×C71—28no—
334C2×C4×C71—26no—
335C2×C4×C71—26no—
336C2×C4×C71—22no—
337C2×C4×C71—26no—
338C2×C4×C71—224no—
339C2×C4×C71—224no—
340C2×C4×C71C22×D4112yes—
341C2×C4×C71C2512yes—
342C2×C4×C71C2516yes—
343C2×C4×C71C2516yes—
344C2×C4×C71C2516yes—
345C2×C4×C71C2516yes—
346C22⋊D71—28no—
347C22⋊D71—224no—
348C22⋊D71—28no—
349C22⋊D71—412no—
350C2×Dic71—22no—
351C2×Dic71—26no—
352C2×Dic71—22no—
353C2×Dic71—26no—
354C2×Dic71—28no—
355C2×Dic71C22×D414yes—
356C2×Dic71C2512yes—
357C2×Dic71C2516yes—
358C2×Dic71C2516yes—
359C2×Dic71C2512yes—
360C2×Dic71C2512yes—
361D284—248no—
362D284—224no—
363D284—224no—
364D284—412no—
365D284C22×D4148yes—
366C4×D71—224no—
367C4×D71—248no—
368C4×D71—224no—
369C4×D71—224no—
370C4×D71—224no—
371C4×D71—424no—
372C4×D71C22×D4148yes—
373Dic142—224no—
374Dic142—224no—
375C22×C71—22no—
376C22×C71—22no—
377C22×C71—28no—
378C22×C71—22no—
379C22×C71—22no—
380C22×C71—22no—
381C22×C71—44no—
382C22×C71C23×D412yes—
383C22×C71C2×2−1+412yes—
384C22×C71C2×2−1+414yescomplemented
385C22×C71#58512yes—
386C22×C71C2611yescharacteristic
387C2×D71—26no—
388C2×D71—26no—
389C2×D71—224no—
390C2×D71—22no—
391C2×D71—26no—
392C2×D71—22no—
393C2×D71—26no—
394C2×D71—22no—
395C2×D71—26no—
396C2×D71—448no—
397C2×D71—44no—
398C2×D71—412no—
399C2×D71C23×D4112yes—
400C4×C71—26no—
401C4×C71—26no—
402C4×C71—22no—
403C4×C71—26no—
404C4×C71C23×D4112yes—
405Dic71—26no—
406Dic71—22no—
407Dic71—22no—
408Dic71—26no—
409Dic71C23×D414yes—
410C2×#3489—711nomaximal, Sylow
411C2×C71—24no—
412C2×C71—42no—
413C2×C71#348914yescomplemented
414C2×C71C24×D411yescharacteristic
415C2×C71C22×2−1+411yescharacteristic
416C2×C71C2×#58511yescharacteristic
417D71—212no—
418D71—42no—
419D71—46no—
420C22×2−1+4—711no—
421C23×#41—711no—
422#3489—7132no—
423C2×D4×Q8—711no—
424C2×D4×Q8D7111yescharacteristic, complemented
425C2×#548—711no—
426C2×#548—711no—
427C2×#547—713no—
428C2×#547—713no—
429C2×#546—713no—
430C2×#546—713no—
431C2×#537—713no—
432C2×#536—713no—
433C2×#525—713no—
434C22×C22⋊Q8—713no—
435C2×#520—711no—
436C71C2×#348911yescharacteristic, complemented, Sylow
437C2×2−1+4—7116no—
438C2×2−1+4—14216no—
439C22×#41—711no—
440C22×#41—713no—
441C22×#41—713no—
442C22×#41—711no—
443C22×#41—7116no—
444C22×#41—713no—
445C22×#41—713no—
446C22×#41—713no—
447C22×#41—14216no—
448C23×Q8—713no—
449C23×Q8—711no—
450C23×Q8C2×D7111yescharacteristic
451C23×Q8C2×D7111yescharacteristic, complemented
452C23×D4—713no—
453C24×C4—713no—
454D4×Q8—7116no—
455D4×Q8C2×D71116yescomplemented
456#548—7116no—
457#548—7116no—
458#547—7148no—
459#547—7148no—
460#546—7148no—
461#546—7148no—
462#537—7148no—
463#536—7148no—
464C2×C4⋊Q8—713no—
465C2×C4⋊Q8C2×D7113yescomplemented
466C2×#124—713no—
467C2×#124—713no—
468#525—7148no—
469C2×#123—713no—
470C2×#123—716no—
471C2×#123—716no—
472C2×#123—713no—
473C2×C22⋊Q8—713no—
474C2×C22⋊Q8—713no—
475C2×C22⋊Q8—713no—
476C2×C22⋊Q8—7148no—
477C2×C22⋊Q8—716no—
478C2×C22⋊Q8—713no—
479C2×C22⋊Q8—713no—
480C2×C22⋊Q8—713no—
481C2×C22⋊Q8C2×D7113yes—
482C2×C22⋊Q8C2×D7113yescomplemented
483C2×#121—711no—
484C2×#121—713no—
485C2×#121—716no—
486C2×#121—713no—
487C2×#121—713no—
488C2×#121—716no—
489C2×#120—713no—
490C2×#120—713no—
491#520—7116no—
492C2×C4×Q8—711no—
493C2×C4×Q8C2×D7111yescharacteristic, complemented
494C2×C4×D4—713no—
495C2×C4×D4—713no—
496C2×C4×D4—713no—
497C2×C4×D4—713no—
498C2×C4×D4—713no—
499C2×C4×D4C2×D7113yes—
500C2×#117—713no—
501C22×C4⋊C4—713no—
502C22×C4⋊C4—716no—
503C22×C22⋊C4—716no—
504C25—713no—
5052−1+4—142128no—
506C2×#41—7116no—
507C2×#41—718no—
508C2×#41—7124no—
509C2×#41—7124no—
510C2×#41—718no—
511C2×#41—7124no—
512C2×#41—7124no—
513C2×#41—7124no—
514C2×#41—14224no—
515C2×#41—14224no—
516C2×#41—14224no—
517C2×#41—14224no—
518C2×#41—14224no—
519C2×#41—142128no—
520C2×#41—1428no—
521C22×Q8—28no—
522C22×Q8—28no—
523C22×Q8—7124no—
524C22×Q8—718no—
525C22×Q8—713no—
526C22×Q8—713no—
527C22×Q8—14224no—
528C22×Q8—1428no—
529C22×Q8C22×D7113yes—
530C22×Q8C22×D7113yes—
531C22×Q8C22×D7118yes—
532C22×Q8C22×D7111yescharacteristic
533C22×Q8C22×D7118yescomplemented
534C22×D4—713no—
535C22×D4—711no—
536C22×D4—713no—
537C22×D4—711no—
538C22×D4—713no—
539C22×D4—713no—
540C22×D4—713no—
541C22×D4—716no—
542C22×D4—713no—
543C22×D4—7124no—
544C22×D4—14224no—
545C22×D4C22×D7111yescharacteristic
546C23×C4—716no—
547C23×C4—713no—
548C23×C4—711no—
549C23×C4—716no—
550C23×C4—713no—
551C23×C4—713no—
552C23×C4—713no—
553C23×C4—713no—
554C23×C4—7124no—
555C23×C4—14224no—
556C23×C4C22×D7113yes—
557C23×C4C22×D7113yes—
558C4⋊Q8—7124no—
559C4⋊Q8C22×D71124yescomplemented
560#124—7124no—
561#124—7124no—
562#123—7124no—
563#123—7148no—
564#123—7148no—
565#123—7124no—
566C22⋊Q8—7124no—
567C22⋊Q8—7124no—
568C22⋊Q8—7124no—
569C22⋊Q8—7148no—
570C22⋊Q8—7124no—
571C22⋊Q8—7124no—
572C22⋊Q8—7124no—
573C22⋊Q8C22×D71124yes—
574C22⋊Q8C22×D71124yescomplemented
575#121—718no—
576#121—7124no—
577#121—7148no—
578#121—7124no—
579#121—7124no—
580#121—7148no—
581#120—7124no—
582#120—7124no—
583C4×Q8—718no—
584C4×Q8C22×D7118yescomplemented
585C4×D4—7124no—
586C4×D4—7124no—
587C4×D4—7124no—
588C4×D4—7124no—
589C4×D4—7124no—
590C4×D4C22×D71124yes—
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—711no—
598C2×C4⋊C4—713no—
599C2×C4⋊C4—7124no—
600C2×C4⋊C4—7148no—
601C2×C4⋊C4C22×D7113yes—
602C2×C4⋊C4C22×D7116yes—
603C2×C4⋊C4C22×D7113yes—
604C2×C22⋊C4—713no—
605C2×C22⋊C4—711no—
606C2×C22⋊C4—716no—
607C2×C22⋊C4—716no—
608C2×C22⋊C4—713no—
609C2×C22⋊C4—713no—
610C2×C22⋊C4—711no—
611C2×C22⋊C4—713no—
612C2×C22⋊C4—713no—
613C2×C22⋊C4—713no—
614C2×C22⋊C4—7148no—
615C2×C22⋊C4C22×D7113yes—
616C2×C22⋊C4C22×D7113yes—
617C2×C42—713no—
618C2×C42C22×D7113yes—
619C24—2846no—
620C24—7112no—
621C24—713no—
622C24—713no—
623C24—711no—
624C24—14212no—
625C24—14212no—
626C24C23×D7111yescharacteristic
627C24C23×D7111yescharacteristic
628#41—7164no—
629#41—14296no—
630#41—14296no—
631#41—14296no—
632#41—14296no—
633#41—14296no—
634#41—14232no—
635C2×Q8—232no—
636C2×Q8—232no—
637C2×Q8—212no—
638C2×Q8—212no—
639C2×Q8—7112no—
640C2×Q8—7112no—
641C2×Q8—14212no—
642C2×Q8—14296no—
643C2×Q8—14232no—
644C2×Q8—14212no—
645C2×Q8D4×D7118yes—
646C2×Q8C23×D71112yes—
647C2×Q8C23×D71112yes—
648C2×Q8C23×D7114yes—
649C2×D4—24no—
650C2×D4—2846no—
651C2×D4—2846no—
652C2×D4—7112no—
653C2×D4—714no—
654C2×D4—7112no—
655C2×D4—714no—
656C2×D4—7124no—
657C2×D4—7112no—
658C2×D4—7112no—
659C2×D4—7112no—
660C2×D4—7124no—
661C2×D4—7112no—
662C2×D4—14296no—
663C2×D4—14224no—
664C2×D4—14212no—
665C2×D4—1424no—
666C2×D4—14212no—
667C2×D4—1424no—
668C2×D4—14212no—
669C2×D4C23×D7114yes—
670C22×C4—212no—
671C22×C4—212no—
672C22×C4—28412no—
673C22×C4—7124no—
674C22×C4—711no—
675C22×C4—7124no—
676C22×C4—7112no—
677C22×C4—714no—
678C22×C4—711no—
679C22×C4—713no—
680C22×C4—713no—
681C22×C4—711no—
682C22×C4—7124no—
683C22×C4—7112no—
684C22×C4—7112no—
685C22×C4—7112no—
686C22×C4—7112no—
687C22×C4—14212no—
688C22×C4—14296no—
689C22×C4—14212no—
690C22×C4—14224no—
691C22×C4—1424no—
692C22×C4—14212no—
693C22×C4—14212no—
694C22×C4C23×D71112yes—
695C22×C4C23×D71112yes—
696C22×C4C23×D7111yescharacteristic
697C22×C4C23×D7113yes—
698C22×C4C23×D7113yes—
699C22×C4C23×D7113yes—
700C22×C4C23×D7113yes—
701C4⋊C4—7112no—
702C4⋊C4—7112no—
703C4⋊C4—7124no—
704C4⋊C4—714no—
705C4⋊C4—7112no—
706C4⋊C4—7112no—
707C4⋊C4—7112no—
708C4⋊C4C23×D71112yes—
709C4⋊C4C23×D71124yes—
710C4⋊C4C23×D71112yes—
711C22⋊C4—7112no—
712C22⋊C4—714no—
713C22⋊C4—7124no—
714C22⋊C4—7124no—
715C22⋊C4—7112no—
716C22⋊C4—7112no—
717C22⋊C4—714no—
718C22⋊C4—7112no—
719C22⋊C4—7112no—
720C22⋊C4—7112no—
721C22⋊C4C23×D71112yes—
722C22⋊C4C23×D71112yes—
723C42—7112no—
724C42C23×D71112yes—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—28448no—
731C23—28412no—
732C23—7112no—
733C23—716no—
734C23—716no—
735C23—712no—
736C23—14224no—
737C23—1422no—
738C23—1426no—
739C23—1422no—
740C23—1426no—
741C23—14224no—
742C23—1422no—
743C23—1426no—
744C23—1426no—
745C23—1426no—
746C23#1455617614yescomplemented
747C23C24×D7112yes—
748C23C24×D7112yes—
749C23C24×D7111yescharacteristic
750Q8—224no—
751Q8—224no—
752Q8—14224no—
753Q8—14224no—
754Q8C2×D4×D71116yes—
755D4—28no—
756D4—28412no—
757D4—28412no—
758D4—7148no—
759D4—14248no—
760D4—14224no—
761D4—1428no—
762D4—14224no—
763D4—1428no—
764D4—14224no—
765C2×C4—26no—
766C2×C4—26no—
767C2×C4—22no—
768C2×C4—26no—
769C2×C4—224no—
770C2×C4—224no—
771C2×C4—28424no—
772C2×C4—714no—
773C2×C4—712no—
774C2×C4—7148no—
775C2×C4—712no—
776C2×C4—716no—
777C2×C4—716no—
778C2×C4—712no—
779C2×C4—14224no—
780C2×C4—14224no—
781C2×C4—14248no—
782C2×C4—1428no—
783C2×C4—1422no—
784C2×C4—1426no—
785C2×C4—1422no—
786C2×C4—1426no—
787C2×C4—14224no—
788C2×C4—14224no—
789C2×C4C2×D4×D71112yes—
790C2×C4C24×D7112yes—
791C2×C4C24×D7116yes—
792C2×C4C24×D7116yes—
793C2×C4C24×D7116yes—
794C2×C4C24×D7116yes—
795C22—28no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—44no—
802C22—28448no—
803C22—28412no—
804C22—2844no—
805C22—7112no—
806C22—1422no—
807C22—1426no—
808C22—1422no—
809C22—1426no—
810C22—1422no—
811C22—1426no—
812C22—14224no—
813C22—1426no—
814C22—1426no—
815C22C22×D4×D7112yes—
816C22C2×#1455617612yes—
817C22C2×#1455617614yescomplemented
818C22#1798683612yes—
819C22C25×D7111yescharacteristic
820C4—26no—
821C4—26no—
822C4—22no—
823C4—26no—
824C4—714no—
825C4—1422no—
826C4—1426no—
827C4—1422no—
828C4—1426no—
829C4C22×D4×D71112yes—
830C2—24no—
831C2—42no—
832C2—2846no—
833C2—2842no—
834C2—14212no—
835C2#2260201714yesdirect product factor
836C2C23×D4×D7111yescharacteristic
837C2C22×#1455617611yescharacteristic
838C2C2×#1798683611yescharacteristic
subgroupG/H
centerC23C24×D71
commutator, cosocleC22×C71C26
FrattiniC22C25×D71
FittingC2×D4×Q8×C71C2
socleC23×C71C25
hypercenterC2×D4×Q8D71
hypocenterC71C2×#3489
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×#11765866C2semidirect
3. #22602017C2direct (N × H)
4. C2×Q8×C22⋊D71C2semidirect
5. C2×#17986661C2semidirect
6. C2×#17986660C2semidirect
7. C2×#17986652C2semidirect
8. C2×#17986651C2semidirect
9. C2×#17986645C2semidirect
10. C2×#17986640C2semidirect
11. C2×#17986579C2semidirect
12. C2×#17986574C2semidirect
13. C2×#17986508C2semidirect
14. C2×C22⋊Q8×D71C2semidirect
15. C2×#17986481C2semidirect
16. C2×D4×Q8×C71C2semidirect
18. C2×#14556176C22semidirect
24. C22×#11765866C22semidirect
25. C22×#11765866C22semidirect
26. C22×#11765865C22semidirect
27. C22×#11765865C22semidirect
28. C22×Q8×D71C22semidirect
29. C22×Q8×D71C22semidirect
32. Q8×C22⋊D71C22semidirect
33. #17986661C22semidirect
34. #17986660C22semidirect
35. #17986652C22semidirect
36. #17986651C22semidirect
37. #17986645C22semidirect
38. #17986640C22semidirect
39. #17986579C22semidirect
40. #17986574C22semidirect
41. C2×#14556126C22semidirect
42. C2×#14556117C22semidirect
43. C2×#14556116C22semidirect
44. #17986508C22semidirect
45. C2×#14556113C22semidirect
46. C2×#14556113C22semidirect
47. C2×#14556113C22semidirect
48. C2×#14556110C22semidirect
49. C2×#14556108C22semidirect
51. C2×#14556106C22semidirect
52. C2×#14556106C22semidirect
54. C2×#14556104C22semidirect
55. C2×#14556104C22semidirect
56. C22⋊Q8×D71C22semidirect
57. C2×#14556103C22semidirect
58. C2×#14556103C22semidirect
59. C2×#14556102C22semidirect
60. C2×#14556101C22semidirect
61. C2×#14556101C22semidirect
65. #17986481C22semidirect
66. C2×Q8×Dic71C22semidirect
67. C2×C4×D284C22semidirect
68. C2×C4×D284C22semidirect
69. C2×#14556090C22semidirect
71. C2×C4×C22⋊D71C22semidirect
72. C2×#14556085C22semidirect
73. C2×C4⋊C4×D71C22semidirect
74. C2×C4⋊C4×D71C22semidirect
77. C23×Q8×C71C22semidirect
78. D4×Q8×C71C22semidirect
79. C2×C4⋊Q8×C71C22semidirect
81. C2×C22⋊Q8×C71C22semidirect
82. C2×C4×Q8×C71C22semidirect
91. C2×#11765866D4semidirect
96. C2×#11765866C23semidirect
99. C2×#11765865C23semidirect
100. C2×#11765865C23semidirect
105. C2×Q8×D71C23semidirect
106. C2×Q8×D71C23semidirect
128. #14556126C23semidirect
129. #14556117C23semidirect
130. #14556116C23semidirect
131. #14556113C23semidirect
132. #14556113C23semidirect
133. #14556113C23semidirect
134. #14556110C23semidirect
135. #14556108C23semidirect
137. #14556106C23semidirect
138. #14556106C23semidirect
140. #14556104C23semidirect
141. #14556104C23semidirect
142. #14556103C23semidirect
143. #14556103C23semidirect
144. #14556102C23semidirect
145. #14556101C23semidirect
146. #14556101C23semidirect
150. Q8×Dic71C23semidirect
151. C4×D284C23semidirect
152. C4×D284C23semidirect
153. #14556090C23semidirect
155. C4×C22⋊D71C23semidirect
156. #14556085C23semidirect
164. C4⋊C4×D71C23semidirect
165. C4⋊C4×D71C23semidirect
184. C22×Q8×C71C23semidirect
188. C4⋊Q8×C71C23semidirect
190. C22⋊Q8×C71C23semidirect
191. C4×Q8×C71C23semidirect
210. #11765866C2×D4semidirect
310. C23×C712−1+4semidirect
384. C22×C71C2×2−1+4semidirect
413. C2×C71#3489semidirect
424. C2×D4×Q8D71semidirect
436. C71C2×#3489semidirect
451. C23×Q8C2×D71semidirect
455. D4×Q8C2×D71semidirect
465. C2×C4⋊Q8C2×D71semidirect
482. C2×C22⋊Q8C2×D71semidirect
493. C2×C4×Q8C2×D71semidirect
533. C22×Q8C22×D71semidirect
559. C4⋊Q8C22×D71semidirect
574. C22⋊Q8C22×D71semidirect
584. C4×Q8C22×D71semidirect
746. C23#14556176semidirect
817. C22C2×#14556176semidirect
835. C2#22602017direct (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×#117658662
#226020172
C2×Q8×C22⋊D712
C2×#179866612
C2×#179866602
C2×#179866522
C2×#179866512
C2×#179866452
C2×#179866402
C2×#179865792
C2×#179865742
C2×#179865082
C2×C22⋊Q8×D712
C2×#179864812
C2×D4×Q8×C712
C2×#348971