Finite Group Databasebeta

← C2×#22602108 #32905626

Subgroups — C2×#22602108 #32905626

Order 18176.

11210 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
2C22×#14556175C211yesmaximal, characteristic, complemented
3#22602108C2132yesmaximal, direct product factor
4C2×#17986668C211yesmaximal, characteristic, complemented
5C2×#17986667C213yesmaximal, complemented
6C2×Q8×C22⋊D71C211yesmaximal, characteristic, complemented
7C2×#17986662C213yesmaximal, complemented
8C2×#17986661C211yesmaximal, characteristic, complemented
9C2×#17986658C213yesmaximal, complemented
10C2×#17986657C213yesmaximal, complemented
11C2×#17986579C213yesmaximal, complemented
12C2×#17986578C213yesmaximal, complemented
13C2×#17986548C213yesmaximal, complemented
14C2×#17986546C213yesmaximal, complemented
15C2×C4×Q8×D71C211yesmaximal, characteristic, complemented
16C2×#548×C71C211yesmaximal, characteristic, complemented
17C2×#14556176—216no—
18C2×#14556176C22116yescomplemented
19C2×#14556175—216no—
20C2×#14556175C22116yescomplemented
21C22×#11765866C2211yescharacteristic
22C22×#11765866C2213yes—
23C22×#11765865C2213yes—
24C22×#11765865C2213yes—
25C22×#11765865C2213yes—
26C22×#11765864C2213yes—
27C22×#11765864C2213yes—
28C23×Dic142C2213yes—
29C22×Q8×D71C2213yes—
30C22×Q8×D71C2211yescharacteristic
31C22×Q8×D71C2211yescharacteristic
32#17986668C22116yescomplemented
33#17986667C22148yescomplemented
34Q8×C22⋊D71C22116yescomplemented
35#17986662C22148yescomplemented
36#17986661C22116yescomplemented
37#17986658C22148yescomplemented
38#17986657C22148yescomplemented
39#17986579C22148yescomplemented
40#17986578C22148yescomplemented
41#17986548C22148yescomplemented
42#17986546C22148yescomplemented
43C2×#14556127C2213yes—
44C2×#14556126C2213yes—
45C2×#14556124C2213yes—
46C2×#14556124C2213yes—
47C2×#14556116C2213yes—
48C2×#14556114C2213yes—
49C2×#14556114C2213yes—
50C2×#14556108C2213yes—
51C2×#14556107C2213yes—
52C2×#14556106C2216yes—
53C2×#14556105C2216yes—
54C2×#14556104C2213yes—
55C2×#14556103C2213yes—
56C2×#14556103C2213yes—
57C2×#14556102C2213yes—
58C2×#14556101C2216yes—
59C2×#14556101C2211yescharacteristic
60C2×#14556101C2213yes—
61C2×#14556101C2216yes—
62C2×#14556100C2216yes—
63C2×#14556099C2213yes—
64C2×#14556099C2213yes—
65C2×Q8×Dic71C2211yescharacteristic
66C2×C4×Dic142C2213yes—
67C2×#14556093C2213yes—
68C4×Q8×D71C22116yescomplemented
69C2×C4×D284C2213yes—
70C2×C4×C22⋊D71C2213yes—
71C2×C4×C22⋊D71C2213yes—
72C2×(C22⋊D71)⋊C4C2216yes—
73C2×(C22⋊D71)⋊C4C2216yes—
74C2×C4⋊C4×D71C2213yes—
75C2×C42×D71C2213yes—
76C22×#41×C71C2211yescharacteristic
77C23×Q8×C71C2211yescharacteristic
78#548×C71C22116yescomplemented
79C2×#124×C71C2213yes—
80C2×C22⋊Q8×C71C2213yes—
81C2×#121×C71C2213yes—
82C2×C4×Q8×C71C2211yescharacteristic
83C2×C4×D4×C71C2213yes—
84#14556176—2128no—
85#14556175—2128no—
86C2×#11765866—224no—
87C2×#11765866—28no—
88C2×#11765866C23124yes—
89C2×#11765866C2318yes—
90C2×#11765865—224no—
91C2×#11765865—224no—
92C2×#11765865—224no—
93C2×#11765865C23124yes—
94C2×#11765865C23124yes—
95C2×#11765865C23124yes—
96C2×#11765864—224no—
97C2×#11765864—224no—
98C2×#11765864C23124yes—
99C2×#11765864C23124yes—
100C22×Dic142—224no—
101C22×Dic142C2313yes—
102C22×Dic142C2313yes—
103C22×Dic142C2313yes—
104C22×Dic142C23124yes—
105C22×Dic142C2313yes—
106C2×Q8×D71—224no—
107C2×Q8×D71—28no—
108C2×Q8×D71D4116yescomplemented
109C2×Q8×D71C2318yes—
110C2×Q8×D71C23124yes—
111C2×Q8×D71C2318yes—
112C22×D284C2311yescharacteristic
113C22×D284C2313yes—
114C22×D284C2313yes—
115C22×D284C2313yes—
116C22×C22⋊D71C2313yes—
117C22×C22⋊D71C2313yes—
118C22×C22⋊D71C2311yescharacteristic
119C22×C22⋊D71C2313yes—
120C22×C22⋊D71C2313yes—
121C22×C22⋊D71C2311yescharacteristic
122C22×C22⋊D71C2316yes—
123C23×Dic71C2316yes—
124C22×C4×D71C2313yes—
125C22×C4×D71C2316yes—
126C22×C4×D71C2313yes—
127C22×C4×D71C2311yescharacteristic
128C22×C4×D71C2313yes—
129C22×C4×D71C2313yes—
130#14556127C23124yes—
131#14556126C23124yes—
132#14556124C23124yes—
133#14556124C23124yes—
134#14556116C23124yes—
135#14556114C23124yes—
136#14556114C23124yes—
137#14556108C23124yes—
138#14556107C23124yes—
139#14556106C23148yes—
140#14556105C23148yes—
141#14556104C23124yes—
142#14556103C23124yes—
143#14556103C23124yes—
144#14556102C23124yes—
145#14556101C23148yes—
146#14556101C23148yes—
147#14556101C2318yes—
148#14556101C23124yes—
149#14556100C23148yes—
150#14556099C23124yes—
151#14556099C23124yes—
152Q8×Dic71C2318yes—
153C4×Dic142C23124yes—
154#14556093C23124yes—
155C4×D284C23124yes—
156C4×C22⋊D71C23124yes—
157C4×C22⋊D71C23124yes—
158(C22⋊D71)⋊C4C23148yes—
159(C22⋊D71)⋊C4C23148yes—
160C2×C4⋊Dic71C2313yes—
161C2×C4⋊Dic71C2313yes—
162C2×Dic71⋊C4C2316yes—
163C2×Dic71⋊C4C2313yes—
164C2×Dic71⋊C4C2316yes—
165C2×Dic71⋊C4C2311yescharacteristic
166C4⋊C4×D71C23124yes—
167C2×C22⋊Dic71C2313yes—
168C2×C22⋊Dic71C2313yes—
169C2×(C2×D71)⋊C4C2313yes—
170C2×(C2×D71)⋊C4C2316yes—
171C2×(C2×D71)⋊C4C2313yes—
172C2×(C2×D71)⋊C4C2313yes—
173C2×(C2×D71)⋊C4C2311yescharacteristic
174C2×C4×Dic71C2313yes—
175C2×C4×Dic71C2313yes—
176C2×C4×Dic71C2313yes—
177C42×D71C23124yes—
178C2×#41×C71—28no—
179C2×#41×C71C2318yes—
180C22×Q8×C71—28no—
181C22×Q8×C71C2313yes—
182C22×Q8×C71C2318yes—
183C22×Q8×C71C2311yescharacteristic
184C22×D4×C71C2313yes—
185C22×D4×C71C2313yes—
186C23×C4×C71C2313yes—
187C23×C4×C71C2313yes—
188#124×C71C23124yes—
189C22⋊Q8×C71C23124yes—
190#121×C71C23124yes—
191C4×Q8×C71C2318yes—
192C4×D4×C71C23124yes—
193C2×C4⋊C4×C71C2313yes—
194C2×C4⋊C4×C71C2313yes—
195C2×C22⋊C4×C71C2311yescharacteristic
196C2×C22⋊C4×C71C2313yes—
197C2×C22⋊C4×C71C2316yes—
198C2×C42×C71C2313yes—
199C23×D71C2411yescharacteristic
200C23×D71C2413yes—
201C23×D71C2411yescharacteristic
202#11765866—232no—
203#11765866—296no—
204#11765865—296no—
205#11765865—296no—
206#11765865—296no—
207#11765864—296no—
208#11765864—296no—
209C2×Dic142—212no—
210C2×Dic142—212no—
211C2×Dic142—212no—
212C2×Dic142—296no—
213C2×Dic142C2×D4124yes—
214C2×Dic142C24112yes—
215C2×Dic142C24112yes—
216C2×Dic142C24112yes—
217C2×Dic142C24112yes—
218Q8×D71—232no—
219Q8×D71—296no—
220Q8×D71C2×D4164yescomplemented
221C2×D284—24no—
222C2×D284—212no—
223C2×D284—212no—
224C2×D284—46no—
225C2×D284C2414yes—
226C2×D284C24112yes—
227C2×D284C24112yes—
228C2×D284C24112yes—
229C2×C22⋊D71—212no—
230C2×C22⋊D71—24no—
231C2×C22⋊D71—212no—
232C2×C22⋊D71—212no—
233C2×C22⋊D71—212no—
234C2×C22⋊D71—24no—
235C2×C22⋊D71—412no—
236C2×C22⋊D71C24112yes—
237C2×C22⋊D71C24112yes—
238C2×C22⋊D71C2414yes—
239C2×C22⋊D71C24112yes—
240C2×C22⋊D71C24112yes—
241C2×C22⋊D71C2414yes—
242C2×C22⋊D71C24124yes—
243C22×Dic71—224no—
244C22×Dic71C2411yescharacteristic
245C22×Dic71C2413yes—
246C22×Dic71C2413yes—
247C22×Dic71C24124yes—
248C22×Dic71C2413yes—
249C22×Dic71C2411yescharacteristic
250C2×C4×D71—212no—
251C2×C4×D71—212no—
252C2×C4×D71—224no—
253C2×C4×D71—24no—
254C2×C4×D71—46no—
255C2×C4×D71C2×D4124yes—
256C2×C4×D71C24112yes—
257C2×C4×D71C24124yes—
258C2×C4×D71C24112yes—
259C2×C4×D71C2414yes—
260C2×C4×D71C24112yes—
261C2×C4×D71C24112yes—
262C4⋊Dic71C24112yes—
263C4⋊Dic71C24112yes—
264Dic71⋊C4C24124yes—
265Dic71⋊C4C24112yes—
266Dic71⋊C4C24124yes—
267Dic71⋊C4C2414yes—
268C22⋊Dic71C24112yes—
269C22⋊Dic71C24112yes—
270(C2×D71)⋊C4C24112yes—
271(C2×D71)⋊C4C24124yes—
272(C2×D71)⋊C4C24112yes—
273(C2×D71)⋊C4C24112yes—
274(C2×D71)⋊C4C2414yes—
275C4×Dic71C24112yes—
276C4×Dic71C24112yes—
277C4×Dic71C24112yes—
278C24×C71C2413yes—
279C24×C71C2411yescharacteristic
280#41×C71—232no—
281C2×Q8×C71—232no—
282C2×Q8×C71—212no—
283C2×Q8×C71C2×D418yes—
284C2×Q8×C71C24112yes—
285C2×Q8×C71C2414yes—
286C2×D4×C71—212no—
287C2×D4×C71—46no—
288C2×D4×C71C24112yes—
289C2×D4×C71C24112yes—
290C22×C4×C71—212no—
291C22×C4×C71—212no—
292C22×C4×C71C2413yes—
293C22×C4×C71C2413yes—
294C22×C4×C71C2411yescharacteristic
295C22×C4×C71C2411yescharacteristic
296C22×C4×C71C24112yes—
297C22×C4×C71C24112yes—
298C22×C4×C71C2413yes—
299C4⋊C4×C71C24112yes—
300C4⋊C4×C71C24112yes—
301C22⋊C4×C71C2414yes—
302C22⋊C4×C71C24112yes—
303C22⋊C4×C71C24124yes—
304C42×C71C24112yes—
305C23×C71—22no—
306C23×C71—26no—
307C23×C71—26no—
308C23×C71—22no—
309C23×C71—22no—
310C23×C71—26no—
311C23×C71C2516yes—
312C23×C71C2512yes—
313C23×C71C2511yescharacteristic
314C22×D71—22no—
315C22×D71—22no—
316C22×D71—22no—
317C22×D71—26no—
318C22×D71—22no—
319C22×D71—26no—
320C22×D71—26no—
321C22×D71—22no—
322C22×D71C22×D414yes—
323C22×D71C2516yes—
324C22×D71C2512yes—
325C22×D71C2512yes—
326Q8×C71—224no—
327Q8×C71C22×D4116yes—
328D4×C71—224no—
329D4×C71—412no—
330C2×C4×C71—22no—
331C2×C4×C71—26no—
332C2×C4×C71—22no—
333C2×C4×C71—26no—
334C2×C4×C71—224no—
335C2×C4×C71—224no—
336C2×C4×C71C22×D4112yes—
337C2×C4×C71C2512yes—
338C2×C4×C71C2516yes—
339C2×C4×C71C2516yes—
340C2×C4×C71C2512yes—
341C2×C4×C71C2516yes—
342C22⋊D71—224no—
343C22⋊D71—28no—
344C22⋊D71—224no—
345C22⋊D71—224no—
346C22⋊D71—224no—
347C22⋊D71—28no—
348C22⋊D71—424no—
349C2×Dic71—22no—
350C2×Dic71—26no—
351C2×Dic71—26no—
352C2×Dic71—248no—
353C2×Dic71C22×D4112yes—
354C2×Dic712−1+414yescomplemented
355C2×Dic71C2516yes—
356C2×Dic71C2516yes—
357C2×Dic71C2512yes—
358C2×Dic71C2516yes—
359C2×Dic71C2512yes—
360D284—28no—
361D284—224no—
362D284—224no—
363D284—412no—
364C4×D71—224no—
365C4×D71—224no—
366C4×D71—248no—
367C4×D71—28no—
368C4×D71—412no—
369C4×D71C22×D4148yes—
370Dic142—224no—
371Dic142—224no—
372Dic142—224no—
373Dic142C22×D4148yes—
374C22×C71—26no—
375C22×C71—22no—
376C22×C71—26no—
377C22×C71—22no—
378C22×C71—26no—
379C22×C71—22no—
380C22×C71—44no—
381C22×C71—412no—
382C22×C71C23×D412yes—
383C22×C71C2×2−1+412yes—
384C22×C71#58512yes—
385C22×C71C2611yescharacteristic
386C2×D71—22no—
387C2×D71—22no—
388C2×D71—28no—
389C2×D71—26no—
390C2×D71—22no—
391C2×D71—26no—
392C2×D71—22no—
393C2×D71—22no—
394C2×D71—26no—
395C2×D71—44no—
396C2×D71—412no—
397C2×D71C23×D414yes—
398C4×C71—22no—
399C4×C71—26no—
400C4×C71—22no—
401C4×C71—26no—
402C4×C71C23×D4112yes—
403Dic71—22no—
404Dic71—26no—
405Dic71—26no—
406Dic71C23×D4112yes—
407Dic71C2×2−1+414yescomplemented
408C2×#3497—711nomaximal, Sylow
409C2×C71—46no—
410C2×C71—42no—
411C2×C71#349714yescomplemented
412C2×C71C24×D411yescharacteristic
413C2×C71C22×2−1+411yescharacteristic
414C2×C71C2×#58511yescharacteristic
415D71—24no—
416D71—46no—
417D71—42no—
418C22×2−1+4—711no—
419C22×2−1+4—711no—
420#3497—7132no—
421C2×#550—711no—
422C2×#550—713no—
423C2×D4×Q8—711no—
424C2×D4×Q8—713no—
425C2×#548—713no—
426C2×#548—711no—
427C2×#548—713no—
428C2×#548D7111yescharacteristic, complemented
429C2×#537—713no—
430C2×#537—713no—
431C2×#532—713no—
432C2×#532—713no—
433C22×C4×Q8—711no—
434C71C2×#349711yescharacteristic, complemented, Sylow
435C2×2−1+4—7116no—
436C2×2−1+4—7116no—
437C2×2−1+4—14216no—
438C2×2−1+4—14216no—
439C22×#41—713no—
440C22×#41—711no—
441C22×#41—713no—
442C22×#41—713no—
443C22×#41—713no—
444C22×#41—713no—
445C22×#41—713no—
446C22×#41C2×D7111yescharacteristic
447C23×Q8—711no—
448C23×Q8—713no—
449C23×Q8—711no—
450C23×Q8—713no—
451C23×Q8C2×D7111yescharacteristic
452#550—7116no—
453#550—7148no—
454D4×Q8—7116no—
455D4×Q8—7148no—
456#548—7148no—
457#548—7116no—
458#548—7148no—
459#548C2×D71116yescomplemented
460#537—7148no—
461#537—7148no—
462#532—7148no—
463#532—7148no—
464C2×C4⋊Q8—713no—
465C2×C4⋊Q8—713no—
466C2×#127—713no—
467C2×#127—713no—
468C2×#124—713no—
469C2×#124—713no—
470C2×#124—713no—
471C2×#124C2×D7113yes—
472C2×C22⋊Q8—713no—
473C2×C22⋊Q8—713no—
474C2×C22⋊Q8—716no—
475C2×C22⋊Q8—713no—
476C2×C22⋊Q8—716no—
477C2×C22⋊Q8C2×D7113yes—
478C2×#121—713no—
479C2×#121—713no—
480C2×#121—716no—
481C2×#121—713no—
482C2×#121—713no—
483C2×#121—713no—
484C2×#121—713no—
485C2×#121—711no—
486C2×#121—716no—
487C2×#121—716no—
488C2×#121C2×D7113yes—
489C2×C4×Q8—711no—
490C2×C4×Q8—7116no—
491C2×C4×Q8—713no—
492C2×C4×Q8—713no—
493C2×C4×Q8C2×D7111yescharacteristic
494C2×C4×D4—713no—
495C2×C4×D4—713no—
496C2×C4×D4—716no—
497C2×C4×D4—716no—
498C2×C4×D4—713no—
499C2×C4×D4C2×D7113yes—
500C22×C4⋊C4—713no—
501C22×C42—713no—
5022−1+4—142128no—
5032−1+4—142128no—
504C2×#41—28no—
505C2×#41—7124no—
506C2×#41—718no—
507C2×#41—7124no—
508C2×#41—7124no—
509C2×#41—7124no—
510C2×#41—7124no—
511C2×#41—7124no—
512C2×#41—14224no—
513C2×#41—14224no—
514C2×#41—14224no—
515C2×#41—14224no—
516C2×#41—14224no—
517C2×#41—14224no—
518C2×#41—1428no—
519C2×#41C22×D7118yes—
520C22×Q8—28no—
521C22×Q8—7116no—
522C22×Q8—718no—
523C22×Q8—7124no—
524C22×Q8—718no—
525C22×Q8—713no—
526C22×Q8—713no—
527C22×Q8—713no—
528C22×Q8—713no—
529C22×Q8—7124no—
530C22×Q8—14224no—
531C22×Q8—14224no—
532C22×Q8—1428no—
533C22×Q8C22×D7113yes—
534C22×Q8C22×D7118yes—
535C22×Q8C22×D7111yescharacteristic
536C22×D4—716no—
537C22×D4—711no—
538C22×D4—713no—
539C22×D4—711no—
540C22×D4—713no—
541C22×D4—713no—
542C22×D4—713no—
543C22×D4—713no—
544C22×D4—711no—
545C22×D4—713no—
546C22×D4—713no—
547C22×D4C22×D7113yes—
548C22×D4C22×D7113yes—
549C23×C4—713no—
550C23×C4—713no—
551C23×C4—716no—
552C23×C4—716no—
553C23×C4—713no—
554C23×C4—713no—
555C23×C4—711no—
556C23×C4C22×D7113yes—
557C23×C4C22×D7113yes—
558C4⋊Q8—7124no—
559C4⋊Q8—7124no—
560#127—7124no—
561#127—7124no—
562#124—7124no—
563#124—7124no—
564#124—7124no—
565#124C22×D71124yes—
566C22⋊Q8—7124no—
567C22⋊Q8—7124no—
568C22⋊Q8—7148no—
569C22⋊Q8—7124no—
570C22⋊Q8—7148no—
571C22⋊Q8C22×D71124yes—
572#121—7124no—
573#121—7124no—
574#121—7148no—
575#121—7124no—
576#121—7124no—
577#121—7124no—
578#121—7124no—
579#121—718no—
580#121—7148no—
581#121—7148no—
582#121C22×D71124yes—
583C4×Q8—718no—
584C4×Q8—7124no—
585C4×Q8—7124no—
586C4×Q8C22×D7118yes—
587C4×D4—7124no—
588C4×D4—7124no—
589C4×D4—7148no—
590C4×D4—7148no—
591C4×D4—7124no—
592C4×D4C22×D71124yes—
593C2×C4⋊C4—716no—
594C2×C4⋊C4—713no—
595C2×C4⋊C4—711no—
596C2×C4⋊C4—713no—
597C2×C4⋊C4—716no—
598C2×C4⋊C4—713no—
599C2×C4⋊C4—7124no—
600C2×C4⋊C4C22×D7113yes—
601C2×C4⋊C4C22×D7113yes—
602C2×C22⋊C4—713no—
603C2×C22⋊C4—713no—
604C2×C22⋊C4—713no—
605C2×C22⋊C4—711no—
606C2×C22⋊C4—713no—
607C2×C22⋊C4—713no—
608C2×C22⋊C4—716no—
609C2×C22⋊C4C22×D7113yes—
610C2×C22⋊C4C22×D7116yes—
611C2×C22⋊C4C22×D7111yescharacteristic
612C2×C42—713no—
613C2×C42—713no—
614C2×C42—713no—
615C2×C42—7124no—
616C2×C42C22×D7113yes—
617C24—711no—
618C24—713no—
619C24—711no—
620C24C23×D7111yescharacteristic
621C24C23×D7113yes—
622#41—232no—
623#41—14296no—
624#41—14296no—
625#41—14296no—
626#41—14296no—
627#41—14296no—
628#41—14296no—
629#41—14232no—
630C2×Q8—232no—
631C2×Q8—212no—
632C2×Q8—7164no—
633C2×Q8—7124no—
634C2×Q8—7112no—
635C2×Q8—7112no—
636C2×Q8—7112no—
637C2×Q8—7112no—
638C2×Q8—14212no—
639C2×Q8—14212no—
640C2×Q8—14296no—
641C2×Q8—14296no—
642C2×Q8—14232no—
643C2×Q8—14212no—
644C2×Q8D4×D7118yes—
645C2×Q8C23×D71112yes—
646C2×Q8C23×D7114yes—
647C2×D4—212no—
648C2×D4—46no—
649C2×D4—2846no—
650C2×D4—28412no—
651C2×D4—7124no—
652C2×D4—714no—
653C2×D4—7112no—
654C2×D4—714no—
655C2×D4—7112no—
656C2×D4—7112no—
657C2×D4—7112no—
658C2×D4—7112no—
659C2×D4—714no—
660C2×D4—7112no—
661C2×D4—7112no—
662C2×D4—1424no—
663C2×D4—14212no—
664C2×D4—1424no—
665C2×D4—14212no—
666C2×D4—14212no—
667C2×D4—14212no—
668C2×D4—1424no—
669C2×D4—14212no—
670C2×D4—14212no—
671C2×D4C23×D71112yes—
672C2×D4C23×D71112yes—
673C22×C4—212no—
674C22×C4—212no—
675C22×C4—2846no—
676C22×C4—7112no—
677C22×C4—711no—
678C22×C4—713no—
679C22×C4—7124no—
680C22×C4—7112no—
681C22×C4—7124no—
682C22×C4—713no—
683C22×C4—711no—
684C22×C4—713no—
685C22×C4—714no—
686C22×C4—7124no—
687C22×C4—7112no—
688C22×C4—7112no—
689C22×C4—1424no—
690C22×C4—14224no—
691C22×C4—14224no—
692C22×C4—14212no—
693C22×C4—14212no—
694C22×C4C23×D71112yes—
695C22×C4C23×D71112yes—
696C22×C4C23×D7111yescharacteristic
697C22×C4C23×D7113yes—
698C22×C4C23×D7111yescharacteristic
699C22×C4C23×D7113yes—
700C22×C4C23×D7113yes—
701C4⋊C4—7124no—
702C4⋊C4—714no—
703C4⋊C4—7112no—
704C4⋊C4—7124no—
705C4⋊C4—7112no—
706C4⋊C4—7112no—
707C4⋊C4C23×D71112yes—
708C4⋊C4C23×D71112yes—
709C22⋊C4—7112no—
710C22⋊C4—7112no—
711C22⋊C4—7112no—
712C22⋊C4—714no—
713C22⋊C4—7112no—
714C22⋊C4—7112no—
715C22⋊C4—7124no—
716C22⋊C4C23×D71112yes—
717C22⋊C4C23×D71124yes—
718C22⋊C4C23×D7114yes—
719C42—7112no—
720C42—7112no—
721C42—7112no—
722C42C23×D71112yes—
723C23—22no—
724C23—26no—
725C23—22no—
726C23—26no—
727C23—22no—
728C23—26no—
729C23—714no—
730C23—712no—
731C23—716no—
732C23—712no—
733C23—1426no—
734C23—1422no—
735C23—1426no—
736C23—1422no—
737C23—1422no—
738C23—1426no—
739C23—1422no—
740C23—1422no—
741C23C24×D7112yes—
742C23C24×D7116yes—
743C23C24×D7111yescharacteristic
744Q8—224no—
745Q8—7148no—
746Q8—14224no—
747Q8—14224no—
748Q8—14224no—
749Q8C2×D4×D71116yes—
750D4—224no—
751D4—412no—
752D4—28412no—
753D4—28424no—
754D4—1428no—
755D4—14224no—
756D4—14224no—
757D4—14224no—
758D4—1428no—
759D4—14224no—
760D4—1428no—
761D4—14224no—
762D4—14224no—
763C2×C4—22no—
764C2×C4—26no—
765C2×C4—22no—
766C2×C4—26no—
767C2×C4—224no—
768C2×C4—224no—
769C2×C4—28412no—
770C2×C4—7112no—
771C2×C4—714no—
772C2×C4—712no—
773C2×C4—716no—
774C2×C4—7148no—
775C2×C4—716no—
776C2×C4—712no—
777C2×C4—716no—
778C2×C4—14248no—
779C2×C4—1428no—
780C2×C4—14248no—
781C2×C4—1426no—
782C2×C4—1422no—
783C2×C4—1426no—
784C2×C4—14224no—
785C2×C4—14224no—
786C2×C4C2×D4×D71112yes—
787C2×C4C24×D7112yes—
788C2×C4C24×D7116yes—
789C2×C4C24×D7112yes—
790C2×C4C24×D7116yes—
791C2×C4C24×D7116yes—
792C22—22no—
793C22—26no—
794C22—22no—
795C22—26no—
796C22—22no—
797C22—26no—
798C22—44no—
799C22—412no—
800C22—28412no—
801C22—2844no—
802C22—714no—
803C22—1426no—
804C22—1422no—
805C22—1426no—
806C22—1422no—
807C22—1422no—
808C22—1426no—
809C22—1428no—
810C22—1422no—
811C22—1422no—
812C22C22×D4×D7112yes—
813C222−1+4×D7112yes—
814C22#1798683512yes—
815C22C25×D7111yescharacteristic
816C4—22no—
817C4—26no—
818C4—22no—
819C4—26no—
820C4—7112no—
821C4—714no—
822C4—1426no—
823C4—1422no—
824C4—1426no—
825C4C22×D4×D71112yes—
826C2—42no—
827C2—46no—
828C2—2846no—
829C2—2842no—
830C2—1424no—
831C2#2260210814yesdirect product factor
832C2C23×D4×D7111yescharacteristic
833C2C2×2−1+4×D7111yescharacteristic
834C2C2×#1798683511yescharacteristic
subgroupG/H
centerC23C24×D71
commutator, cosocleC22×C71C26
FrattiniC22C25×D71
FittingC2×#548×C71C2
socleC23×C71C25
hypercenterC2×#548D71
hypocenterC71C2×#3497
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C22×#14556176C2semidirect
2. C22×#14556175C2semidirect
3. #22602108C2direct (N × H)
4. C2×#17986668C2semidirect
5. C2×#17986667C2semidirect
6. C2×Q8×C22⋊D71C2semidirect
7. C2×#17986662C2semidirect
8. C2×#17986661C2semidirect
9. C2×#17986658C2semidirect
10. C2×#17986657C2semidirect
11. C2×#17986579C2semidirect
12. C2×#17986578C2semidirect
13. C2×#17986548C2semidirect
14. C2×#17986546C2semidirect
15. C2×C4×Q8×D71C2semidirect
16. C2×#548×C71C2semidirect
18. C2×#14556176C22semidirect
20. C2×#14556175C22semidirect
32. #17986668C22semidirect
33. #17986667C22semidirect
34. Q8×C22⋊D71C22semidirect
35. #17986662C22semidirect
36. #17986661C22semidirect
37. #17986658C22semidirect
38. #17986657C22semidirect
39. #17986579C22semidirect
40. #17986578C22semidirect
41. #17986548C22semidirect
42. #17986546C22semidirect
68. C4×Q8×D71C22semidirect
78. #548×C71C22semidirect
108. C2×Q8×D71D4semidirect
220. Q8×D71C2×D4semidirect
354. C2×Dic712−1+4semidirect
407. Dic71C2×2−1+4semidirect
411. C2×C71#3497semidirect
428. C2×#548D71semidirect
434. C71C2×#3497semidirect
459. #548C2×D71semidirect
831. C2#22602108direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561762
C22×#145561752
#226021082
C2×#179866682
C2×#179866672
C2×Q8×C22⋊D712
C2×#179866622
C2×#179866612
C2×#179866582
C2×#179866572
C2×#179865792
C2×#179865782
C2×#179865482
C2×#179865462
C2×C4×Q8×D712
C2×#548×C712
C2×#349771