Finite Group Databasebeta

← C2×#22601997 #32905695

Subgroups — C2×#22601997 #32905695

Order 18176.

11510 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556176C211yesmaximal, characteristic, complemented
2C22×#41×D71C211yesmaximal, characteristic, complemented
3#22601997C2132yesmaximal, direct product factor
4C2×#17986671C211yesmaximal, characteristic, complemented
5C2×#17986670C213yesmaximal, complemented
6C2×#17986668C211yesmaximal, characteristic, complemented
7C2×#17986667C213yesmaximal, complemented
8C2×#17986660C211yesmaximal, characteristic, complemented
9C2×#17986659C213yesmaximal, complemented
10C2×#17986657C213yesmaximal, complemented
11C2×#17986567C213yesmaximal, complemented
12C2×#17986565C213yesmaximal, complemented
13C2×#17986512C213yesmaximal, complemented
14C2×#17986508C213yesmaximal, complemented
15C2×#17986475C211yesmaximal, characteristic, complemented
16C2×#548×C71C211yesmaximal, characteristic, complemented
17C2×#14556176—216no—
18C2×#14556176C22116yescomplemented
19C22×#11765866C2211yescharacteristic
20C22×#11765866C2213yes—
21C22×#11765866C2211yescharacteristic, complemented
22C22×#11765865C2213yes—
23C22×#11765865C2213yes—
24C22×#11765865C2213yescomplemented
25C22×#11765864C2213yes—
26C2×#41×D71—216no—
27C2×#41×D71C22116yescomplemented
28C22×Q8×D71C2211yescharacteristic
29C22×Q8×D71C2213yescomplemented
30C22×D4×D71C2213yes—
31C23×C4×D71C2213yes—
32#17986671C22116yescomplemented
33#17986670C22148yescomplemented
34#17986668C22116yescomplemented
35#17986667C22148yescomplemented
36#17986660C22116yescomplemented
37#17986659C22148yescomplemented
38#17986657C22148yescomplemented
39#17986567C22148yescomplemented
40#17986565C22148yescomplemented
41C2×#14556125C2213yescomplemented
42C2×#14556124C2213yescomplemented
43C2×#14556124C2216yescomplemented
44C2×#14556117C2213yescomplemented
45C2×#14556114C2216yescomplemented
46#17986512C22148yescomplemented
47#17986508C22148yescomplemented
48C2×#14556113C2213yes—
49C2×#14556110C2211yescharacteristic
50C2×#14556106C2213yescomplemented
51C2×#14556105C2213yescomplemented
52C2×#14556104C2213yescomplemented
53C2×#14556103C2213yescomplemented
54C2×#14556103C2213yescomplemented
55C2×#14556102C2213yescomplemented
56C2×#14556102C2213yescomplemented
57C2×#14556101C2216yescomplemented
58C2×#14556101C2216yescomplemented
59C2×#14556101C2213yescomplemented
60C2×#14556100C2213yescomplemented
61C2×#14556099C2213yescomplemented
62C2×#14556098C2213yes—
63C2×#14556098C2216yes—
64C2×#14556096C2213yes—
65#17986475C22116yescomplemented
66C2×Q8×Dic71C2211yescharacteristic, complemented
67C2×C4×Dic142C2213yescomplemented
68C2×#14556093C2213yescomplemented
69C2×C4×D284C2213yescomplemented
70C2×#14556090C2216yescomplemented
71C2×C4×C22⋊D71C2213yescomplemented
72C2×C4×C22⋊D71C2213yescomplemented
73C2×(C22⋊D71)⋊C4C2216yescomplemented
74C2×#14556086C2213yes—
75C2×#14556085C2213yes—
76C22×#41×C71C2211yescharacteristic
77C23×Q8×C71C2211yescharacteristic, complemented
78#548×C71C22116yescomplemented
79C2×#124×C71C2213yescomplemented
80C2×C22⋊Q8×C71C2213yescomplemented
81C2×#121×C71C2213yescomplemented
82C2×C4×Q8×C71C2211yescharacteristic, complemented
83C2×C4×D4×C71C2213yescomplemented
84C24×D71C2313yes—
85#14556176—2128no—
86C2×#11765866—224no—
87C2×#11765866—28no—
88C2×#11765866—28no—
89C2×#11765866C23124yes—
90C2×#11765866C2318yes—
91C2×#11765866C2318yescomplemented
92C2×#11765865—224no—
93C2×#11765865—224no—
94C2×#11765865—224no—
95C2×#11765865C23124yes—
96C2×#11765865C23124yes—
97C2×#11765865C23124yescomplemented
98C2×#11765864—224no—
99C2×#11765864C23124yes—
100#41×D71—2128no—
101C22×Dic142C2313yes—
102C22×Dic142C2313yes—
103C2×Q8×D71—224no—
104C2×Q8×D71D4116yescomplemented
105C2×Q8×D71C2318yes—
106C2×Q8×D71C23124yescomplemented
107C22×D284C2313yes—
108C22×D284C2313yes—
109C22×D284C2313yes—
110C22×D284C2316yes—
111C22×D284C2313yes—
112C22×C22⋊D71C2316yes—
113C22×C22⋊D71C2311yescharacteristic
114C22×C22⋊D71C2313yes—
115C22×C22⋊D71C2316yes—
116C22×C22⋊D71C2313yes—
117C22×C22⋊D71C2313yes—
118C2×D4×D71—224no—
119C2×D4×D71C23124yes—
120C23×Dic71C2313yes—
121C22×C4×D71—224no—
122C22×C4×D71C2311yescharacteristic
123C22×C4×D71C23124yes—
124C22×C4×D71C2313yes—
125C22×C4×D71C2313yes—
126C22×C4×D71C2313yes—
127C22×C4×D71C2316yes—
128C22×C4×D71C2313yes—
129#14556125C23124yescomplemented
130#14556124C23148yescomplemented
131#14556124C23124yescomplemented
132#14556117C23124yescomplemented
133#14556114C23148yescomplemented
134#14556113C23124yes—
135#14556110C2318yes—
136#14556106C23124yescomplemented
137#14556105C23124yescomplemented
138#14556104C23124yescomplemented
139#14556103C23124yescomplemented
140#14556103C23124yescomplemented
141#14556102C23124yescomplemented
142#14556102C23124yescomplemented
143#14556101C23148yescomplemented
144#14556101C23148yescomplemented
145#14556101C23124yescomplemented
146#14556100C23124yescomplemented
147#14556099C23124yescomplemented
148#14556098C23148yes—
149#14556098C23124yes—
150#14556096C23124yes—
151Q8×Dic71C2318yescomplemented
152C4×Dic142C23124yescomplemented
153#14556093C23124yescomplemented
154C4×D284C23124yescomplemented
155#14556090C23148yescomplemented
156C4×C22⋊D71C23124yescomplemented
157C4×C22⋊D71C23124yescomplemented
158(C22⋊D71)⋊C4C23148yescomplemented
159#14556086C23124yes—
160#14556085C23124yes—
161C2×C4⋊Dic71C2313yes—
162C2×C4⋊Dic71C2311yescharacteristic
163C2×Dic71⋊C4C2313yes—
164C2×Dic71⋊C4C2313yes—
165C2×Dic71⋊C4C2313yes—
166C2×Dic71⋊C4C2311yescharacteristic
167C2×C22⋊Dic71C2311yescharacteristic
168C2×C22⋊Dic71C2313yes—
169C2×(C2×D71)⋊C4C2311yescharacteristic
170C2×(C2×D71)⋊C4C2313yes—
171C2×(C2×D71)⋊C4C2313yes—
172C2×(C2×D71)⋊C4C2313yes—
173C2×(C2×D71)⋊C4C2313yes—
174C2×(C2×D71)⋊C4C2316yes—
175C2×(C2×D71)⋊C4C2313yes—
176C2×C4×Dic71C2313yes—
177C2×C4×Dic71C2316yes—
178C2×#41×C71—28no—
179C2×#41×C71C2318yes—
180C22×Q8×C71—28no—
181C22×Q8×C71C2313yes—
182C22×Q8×C71C2311yescharacteristic
183C22×Q8×C71C2318yescomplemented
184C22×D4×C71C2313yes—
185C22×D4×C71C2313yes—
186C23×C4×C71C2313yes—
187C23×C4×C71C2313yes—
188#124×C71C23124yescomplemented
189C22⋊Q8×C71C23124yescomplemented
190#121×C71C23124yescomplemented
191C4×Q8×C71C2318yescomplemented
192C4×D4×C71C23124yescomplemented
193C2×C4⋊C4×C71C2313yes—
194C2×C4⋊C4×C71C2313yes—
195C2×C22⋊C4×C71C2311yescharacteristic
196C2×C22⋊C4×C71C2313yes—
197C2×C22⋊C4×C71C2316yes—
198C2×C42×C71C2313yes—
199C23×D71—212no—
200C23×D71—46no—
201C23×D71—46no—
202C23×D71C2413yes—
203C23×D71C2413yes—
204C23×D71C2411yescharacteristic
205C23×D71C24112yes—
206#11765866—232no—
207#11765866—232no—
208#11765866—296no—
209#11765865—296no—
210#11765865—296no—
211#11765865—296no—
212#11765864—296no—
213C2×Dic142—212no—
214C2×Dic142C2×D4124yes—
215C2×Dic142C24112yes—
216C2×Dic142C24112yes—
217Q8×D71—296no—
218Q8×D71C2×D4164yescomplemented
219C2×D284—212no—
220C2×D284—212no—
221C2×D284—212no—
222C2×D284—412no—
223C2×D284—46no—
224C2×D284C24112yes—
225C2×D284C24112yes—
226C2×D284C24112yes—
227C2×D284C24124yes—
228C2×D284C24112yes—
229C2×C22⋊D71—24no—
230C2×C22⋊D71—224no—
231C2×C22⋊D71—212no—
232C2×C22⋊D71—412no—
233C2×C22⋊D71—46no—
234C2×C22⋊D71—46no—
235C2×C22⋊D71C24124yes—
236C2×C22⋊D71C2414yes—
237C2×C22⋊D71C24112yes—
238C2×C22⋊D71C24124yes—
239C2×C22⋊D71C24112yes—
240C2×C22⋊D71C24112yes—
241D4×D71—296no—
242C22×Dic71—212no—
243C22×Dic71C2411yescharacteristic
244C22×Dic71C2411yescharacteristic
245C22×Dic71C24112yes—
246C22×Dic71C2411yescharacteristic
247C22×Dic71C2413yes—
248C22×Dic71C2413yes—
249C2×C4×D71—24no—
250C2×C4×D71—212no—
251C2×C4×D71—212no—
252C2×C4×D71—212no—
253C2×C4×D71—224no—
254C2×C4×D71—296no—
255C2×C4×D71C2×D4124yes—
256C2×C4×D71C2414yes—
257C2×C4×D71C24112yes—
258C2×C4×D71C24112yes—
259C2×C4×D71C24112yes—
260C2×C4×D71C24124yes—
261C2×C4×D71C24112yes—
262C4⋊Dic71C24112yes—
263C4⋊Dic71C2414yes—
264Dic71⋊C4C24112yes—
265Dic71⋊C4C24112yes—
266Dic71⋊C4C24112yes—
267Dic71⋊C4C2414yes—
268C22⋊Dic71C2414yes—
269C22⋊Dic71C24112yes—
270(C2×D71)⋊C4C2414yes—
271(C2×D71)⋊C4C24112yes—
272(C2×D71)⋊C4C24112yes—
273(C2×D71)⋊C4C24112yes—
274(C2×D71)⋊C4C24112yes—
275(C2×D71)⋊C4C24124yes—
276(C2×D71)⋊C4C24112yes—
277C4×Dic71C24112yes—
278C4×Dic71C24124yes—
279C24×C71C2413yes—
280C24×C71C2411yescharacteristic
281#41×C71—232no—
282C2×Q8×C71—232no—
283C2×Q8×C71—212no—
284C2×Q8×C71C2×D418yes—
285C2×Q8×C71C24112yes—
286C2×Q8×C71C2414yes—
287C2×D4×C71—212no—
288C2×D4×C71—46no—
289C2×D4×C71C24112yes—
290C2×D4×C71C24112yes—
291C22×C4×C71—212no—
292C22×C4×C71—212no—
293C22×C4×C71C2411yescharacteristic
294C22×C4×C71C2413yes—
295C22×C4×C71C24112yes—
296C22×C4×C71C2411yescharacteristic
297C22×C4×C71C2413yes—
298C22×C4×C71C24112yes—
299C22×C4×C71C2413yes—
300C4⋊C4×C71C24112yes—
301C4⋊C4×C71C24112yes—
302C22⋊C4×C71C2414yes—
303C22⋊C4×C71C24112yes—
304C22⋊C4×C71C24124yes—
305C42×C71C24112yes—
306C23×C71—22no—
307C23×C71—26no—
308C23×C71—22no—
309C23×C71—26no—
310C23×C71—22no—
311C23×C71—26no—
312C23×C71C2516yes—
313C23×C71C2512yes—
314C23×C71C2511yescharacteristic
315C22×D71—22no—
316C22×D71—22no—
317C22×D71—26no—
318C22×D71—26no—
319C22×D71—26no—
320C22×D71—26no—
321C22×D71—26no—
322C22×D71—26no—
323C22×D71—224no—
324C22×D71—412no—
325C22×D71—412no—
326C22×D71—448no—
327C22×D71C22×D414yes—
328C22×D71C2516yes—
329C22×D71C2516yes—
330C22×D71C2512yes—
331Q8×C71—224no—
332Q8×C71C22×D4116yes—
333D4×C71—224no—
334D4×C71—412no—
335C2×C4×C71—22no—
336C2×C4×C71—26no—
337C2×C4×C71—26no—
338C2×C4×C71—22no—
339C2×C4×C71—224no—
340C2×C4×C71—224no—
341C2×C4×C71C22×D4112yes—
342C2×C4×C71C2512yes—
343C2×C4×C71C2516yes—
344C2×C4×C71C2516yes—
345C2×C4×C71C2512yes—
346C2×C4×C71C2516yes—
347C22⋊D71—28no—
348C22⋊D71—248no—
349C22⋊D71—224no—
350C22⋊D71—412no—
351C22⋊D71—424no—
352C22⋊D71—412no—
353C2×Dic71—22no—
354C2×Dic71—22no—
355C2×Dic71—22no—
356C2×Dic71—26no—
357C2×Dic71—224no—
358C2×Dic71C22×D4112yes—
359C2×Dic71C2512yes—
360C2×Dic71C2516yes—
361C2×Dic71C2512yes—
362C2×Dic71C2512yes—
363C2×Dic71C2516yes—
364D284—224no—
365D284—224no—
366D284—224no—
367D284—412no—
368D284—424no—
369C4×D71—28no—
370C4×D71—224no—
371C4×D71—224no—
372C4×D71—224no—
373C4×D71—248no—
374C4×D71C22×D4148yes—
375Dic142—224no—
376Dic142C22×D4148yes—
377C22×C71—26no—
378C22×C71—22no—
379C22×C71—22no—
380C22×C71—26no—
381C22×C71—26no—
382C22×C71—22no—
383C22×C71—412no—
384C22×C71—44no—
385C22×C71C23×D412yes—
386C22×C71#58512yes—
387C22×C71#58512yes—
388C22×C71C2611yescharacteristic
389C2×D71—22no—
390C2×D71—22no—
391C2×D71—28no—
392C2×D71—26no—
393C2×D71—26no—
394C2×D71—26no—
395C2×D71—26no—
396C2×D71—26no—
397C2×D71—26no—
398C2×D71—448no—
399C2×D71—412no—
400C2×D71—412no—
401C2×D71C23×D414yes—
402C4×C71—26no—
403C4×C71—22no—
404C4×C71—22no—
405C4×C71—26no—
406C4×C71C23×D4112yes—
407Dic71—22no—
408Dic71—22no—
409Dic71—22no—
410Dic71—26no—
411Dic71C23×D4112yes—
412C2×#3487—711nomaximal, Sylow
413C2×C71—46no—
414C2×C71—42no—
415C2×C71#348714yescomplemented
416C2×C71C24×D411yescharacteristic
417C2×C71C2×#58511yescharacteristic
418C2×C71C2×#58511yescharacteristic
419D71—24no—
420D71—46no—
421D71—46no—
422C22×2−1+4—711no—
423C23×#41—711no—
424#3487—7132no—
425C2×#550—711no—
426C2×#550—713no—
427C2×#550—711no—
428C2×#550—713no—
429C2×#548—711no—
430C2×#548—713no—
431C2×#548—713no—
432C2×#548D7111yescharacteristic, complemented
433C2×#535—713no—
434C2×#535—713no—
435C2×#525—713no—
436C2×#525—713no—
437C2×#519—711no—
438C71C2×#348711yescharacteristic, complemented, Sylow
439C2×2−1+4—7116no—
440C2×2−1+4—14216no—
441C22×#41—7116no—
442C22×#41—711no—
443C22×#41—713no—
444C22×#41—711no—
445C22×#41—713no—
446C22×#41—713no—
447C22×#41—713no—
448C22×#41—713no—
449C22×#41—14216no—
450C22×#41C2×D7111yescharacteristic
451C23×Q8—711no—
452C23×Q8—713no—
453C23×Q8C2×D7111yescharacteristic, complemented
454C23×D4—713no—
455C24×C4—713no—
456#550—7116no—
457#550—7148no—
458#550—7116no—
459#550—7148no—
460#548—7116no—
461#548—7148no—
462#548—7148no—
463#548C2×D71116yescomplemented
464#535—7148no—
465#535—7148no—
466C2×#127—713no—
467C2×#127—716no—
468C2×#127—713no—
469C2×#124—713no—
470C2×#124—716no—
471C2×#124C2×D7113yescomplemented
472#525—7148no—
473#525—7148no—
474C2×#123—713no—
475C2×#123—711no—
476C2×C22⋊Q8—713no—
477C2×C22⋊Q8—713no—
478C2×C22⋊Q8—713no—
479C2×C22⋊Q8C2×D7113yescomplemented
480C2×#121—713no—
481C2×#121—713no—
482C2×#121—713no—
483C2×#121—713no—
484C2×#121—713no—
485C2×#121—713no—
486C2×#121—713no—
487C2×#121—716no—
488C2×#121—716no—
489C2×#121C2×D7113yescomplemented
490C2×#120—713no—
491C2×#120—716no—
492C2×#120—713no—
493#519—7116no—
494C2×C4×Q8—711no—
495C2×C4×Q8—713no—
496C2×C4×Q8—713no—
497C2×C4×Q8C2×D7111yescharacteristic, complemented
498C2×C4×D4—713no—
499C2×C4×D4—713no—
500C2×C4×D4—716no—
501C2×C4×D4—716no—
502C2×C4×D4—713no—
503C2×C4×D4C2×D7113yescomplemented
504C2×#117—713no—
505C2×#117—713no—
506C25—713no—
5072−1+4—142128no—
508C2×#41—28no—
509C2×#41—7124no—
510C2×#41—718no—
511C2×#41—718no—
512C2×#41—7124no—
513C2×#41—7124no—
514C2×#41—7124no—
515C2×#41—7124no—
516C2×#41—14224no—
517C2×#41—14224no—
518C2×#41—14224no—
519C2×#41—14224no—
520C2×#41—14224no—
521C2×#41—142128no—
522C2×#41—1428no—
523C2×#41—1428no—
524C2×#41C22×D7118yes—
525C22×Q8—28no—
526C22×Q8—7116no—
527C22×Q8—718no—
528C22×Q8—7124no—
529C22×Q8—713no—
530C22×Q8—713no—
531C22×Q8—14224no—
532C22×Q8C22×D7113yes—
533C22×Q8C22×D7111yescharacteristic
534C22×Q8C22×D7118yescomplemented
535C22×D4—713no—
536C22×D4—713no—
537C22×D4—716no—
538C22×D4—711no—
539C22×D4—716no—
540C22×D4—713no—
541C22×D4—7124no—
542C22×D4—716no—
543C22×D4—713no—
544C22×D4—713no—
545C22×D4—713no—
546C22×D4—713no—
547C22×D4—14224no—
548C22×D4C22×D7113yes—
549C22×D4C22×D7113yes—
550C23×C4—713no—
551C23×C4—713no—
552C23×C4—716no—
553C23×C4—713no—
554C23×C4—713no—
555C23×C4—713no—
556C23×C4—711no—
557C23×C4—7124no—
558C23×C4—14224no—
559C23×C4C22×D7113yes—
560C23×C4C22×D7113yes—
561#127—7124no—
562#127—7148no—
563#127—7124no—
564#124—7124no—
565#124—7148no—
566#124C22×D71124yescomplemented
567#123—7124no—
568#123—718no—
569C22⋊Q8—7124no—
570C22⋊Q8—7124no—
571C22⋊Q8—7124no—
572C22⋊Q8C22×D71124yescomplemented
573#121—7124no—
574#121—7124no—
575#121—7124no—
576#121—7124no—
577#121—7124no—
578#121—7124no—
579#121—7124no—
580#121—7148no—
581#121—7148no—
582#121C22×D71124yescomplemented
583#120—7124no—
584#120—7148no—
585#120—7124no—
586C4×Q8—718no—
587C4×Q8—7124no—
588C4×Q8—7124no—
589C4×Q8C22×D7118yescomplemented
590C4×D4—7124no—
591C4×D4—7124no—
592C4×D4—7148no—
593C4×D4—7148no—
594C4×D4—7124no—
595C4×D4C22×D71124yescomplemented
596#117—7124no—
597#117—7124no—
598C2×C4⋊C4—713no—
599C2×C4⋊C4—713no—
600C2×C4⋊C4—713no—
601C2×C4⋊C4—711no—
602C2×C4⋊C4—713no—
603C2×C4⋊C4—711no—
604C2×C4⋊C4C22×D7113yes—
605C2×C4⋊C4C22×D7113yes—
606C2×C22⋊C4—711no—
607C2×C22⋊C4—713no—
608C2×C22⋊C4—713no—
609C2×C22⋊C4—711no—
610C2×C22⋊C4—713no—
611C2×C22⋊C4—713no—
612C2×C22⋊C4—713no—
613C2×C22⋊C4—716no—
614C2×C22⋊C4—713no—
615C2×C22⋊C4C22×D7116yes—
616C2×C22⋊C4C22×D7111yescharacteristic
617C2×C22⋊C4C22×D7113yes—
618C2×C42—716no—
619C2×C42—713no—
620C2×C42C22×D7113yes—
621C24—2846no—
622C24—2846no—
623C24—7112no—
624C24—711no—
625C24—713no—
626C24—713no—
627C24—14212no—
628C24C23×D7113yes—
629C24C23×D7111yescharacteristic
630#41—232no—
631#41—14296no—
632#41—14296no—
633#41—14296no—
634#41—14296no—
635#41—14296no—
636#41—14232no—
637#41—14232no—
638C2×Q8—232no—
639C2×Q8—212no—
640C2×Q8—7164no—
641C2×Q8—7124no—
642C2×Q8—7112no—
643C2×Q8—7112no—
644C2×Q8—14212no—
645C2×Q8—14296no—
646C2×Q8D4×D7118yes—
647C2×Q8C23×D71112yes—
648C2×Q8C23×D7114yes—
649C2×D4—212no—
650C2×D4—46no—
651C2×D4—28412no—
652C2×D4—2846no—
653C2×D4—2846no—
654C2×D4—2846no—
655C2×D4—28412no—
656C2×D4—7112no—
657C2×D4—7124no—
658C2×D4—7112no—
659C2×D4—714no—
660C2×D4—7124no—
661C2×D4—7112no—
662C2×D4—7124no—
663C2×D4—7112no—
664C2×D4—7112no—
665C2×D4—7112no—
666C2×D4—7112no—
667C2×D4—14212no—
668C2×D4—14296no—
669C2×D4—14224no—
670C2×D4—14212no—
671C2×D4—1424no—
672C2×D4—14212no—
673C2×D4—14212no—
674C2×D4C23×D71112yes—
675C2×D4C23×D71112yes—
676C22×C4—212no—
677C22×C4—212no—
678C22×C4—713no—
679C22×C4—7124no—
680C22×C4—7112no—
681C22×C4—7112no—
682C22×C4—711no—
683C22×C4—713no—
684C22×C4—711no—
685C22×C4—711no—
686C22×C4—7124no—
687C22×C4—7112no—
688C22×C4—7112no—
689C22×C4—7112no—
690C22×C4—714no—
691C22×C4—14212no—
692C22×C4—14296no—
693C22×C4—14224no—
694C22×C4—1424no—
695C22×C4—14212no—
696C22×C4—14212no—
697C22×C4—14212no—
698C22×C4C23×D71112yes—
699C22×C4C23×D71112yes—
700C22×C4C23×D7113yes—
701C22×C4C23×D7111yescharacteristic
702C22×C4C23×D7113yes—
703C22×C4C23×D7111yescharacteristic
704C22×C4C23×D7113yes—
705C4⋊C4—7112no—
706C4⋊C4—7112no—
707C4⋊C4—714no—
708C4⋊C4—7112no—
709C4⋊C4—7112no—
710C4⋊C4—714no—
711C4⋊C4C23×D71112yes—
712C4⋊C4C23×D71112yes—
713C22⋊C4—714no—
714C22⋊C4—7112no—
715C22⋊C4—7112no—
716C22⋊C4—714no—
717C22⋊C4—7112no—
718C22⋊C4—7112no—
719C22⋊C4—7112no—
720C22⋊C4—7124no—
721C22⋊C4—7112no—
722C22⋊C4C23×D71124yes—
723C22⋊C4C23×D7114yes—
724C22⋊C4C23×D71112yes—
725C42—7124no—
726C42—7112no—
727C42C23×D71112yes—
728C23—22no—
729C23—26no—
730C23—22no—
731C23—26no—
732C23—22no—
733C23—26no—
734C23—28412no—
735C23—28412no—
736C23—28448no—
737C23—714no—
738C23—712no—
739C23—716no—
740C23—716no—
741C23—14224no—
742C23—1426no—
743C23—1426no—
744C23—1426no—
745C23—1426no—
746C23—1426no—
747C23—1426no—
748C23—1422no—
749C23—1422no—
750C23C24×D7116yes—
751C23C24×D7112yes—
752C23C24×D7111yescharacteristic
753Q8—224no—
754Q8—7148no—
755Q8—14224no—
756Q8C2×D4×D71116yes—
757D4—224no—
758D4—412no—
759D4—28424no—
760D4—28412no—
761D4—28412no—
762D4—28412no—
763D4—28424no—
764D4—14224no—
765D4—14248no—
766D4—14224no—
767D4—1428no—
768D4—14224no—
769D4—14224no—
770C2×C4—22no—
771C2×C4—26no—
772C2×C4—26no—
773C2×C4—22no—
774C2×C4—224no—
775C2×C4—224no—
776C2×C4—7112no—
777C2×C4—716no—
778C2×C4—7148no—
779C2×C4—712no—
780C2×C4—716no—
781C2×C4—712no—
782C2×C4—712no—
783C2×C4—14224no—
784C2×C4—14248no—
785C2×C4—1428no—
786C2×C4—14224no—
787C2×C4—1422no—
788C2×C4—1422no—
789C2×C4—1422no—
790C2×C4—1426no—
791C2×C4—14224no—
792C2×C4—14224no—
793C2×C4C2×D4×D71112yes—
794C2×C4C24×D7116yes—
795C2×C4C24×D7112yes—
796C2×C4C24×D7116yes—
797C2×C4C24×D7112yes—
798C2×C4C24×D7116yes—
799C22—22no—
800C22—26no—
801C22—22no—
802C22—26no—
803C22—22no—
804C22—26no—
805C22—412no—
806C22—44no—
807C22—28448no—
808C22—28412no—
809C22—28412no—
810C22—714no—
811C22—1426no—
812C22—1426no—
813C22—1426no—
814C22—1426no—
815C22—1426no—
816C22—1426no—
817C22—1428no—
818C22—1422no—
819C22—1422no—
820C22C22×D4×D7112yes—
821C22#1798683512yes—
822C22#1798683612yes—
823C22C25×D7111yescharacteristic
824C4—22no—
825C4—26no—
826C4—26no—
827C4—22no—
828C4—7112no—
829C4—1422no—
830C4—1422no—
831C4—1422no—
832C4—1426no—
833C4C22×D4×D71112yes—
834C2—46no—
835C2—42no—
836C2—2846no—
837C2—2846no—
838C2—1424no—
839C2#2260199714yesdirect product factor
840C2C23×D4×D7111yescharacteristic
841C2C2×#1798683511yescharacteristic
842C2C2×#1798683611yescharacteristic
subgroupG/H
centerC23C24×D71
commutator, cosocleC22×C71C26
FrattiniC22C25×D71
FittingC2×#548×C71C2
socleC23×C71C25
hypercenterC2×#548D71
hypocenterC71C2×#3487
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×#41×D71C2semidirect
3. #22601997C2direct (N × H)
4. C2×#17986671C2semidirect
5. C2×#17986670C2semidirect
6. C2×#17986668C2semidirect
7. C2×#17986667C2semidirect
8. C2×#17986660C2semidirect
9. C2×#17986659C2semidirect
10. C2×#17986657C2semidirect
11. C2×#17986567C2semidirect
12. C2×#17986565C2semidirect
13. C2×#17986512C2semidirect
14. C2×#17986508C2semidirect
15. C2×#17986475C2semidirect
16. C2×#548×C71C2semidirect
18. C2×#14556176C22semidirect
21. C22×#11765866C22semidirect
24. C22×#11765865C22semidirect
27. C2×#41×D71C22semidirect
29. C22×Q8×D71C22semidirect
32. #17986671C22semidirect
33. #17986670C22semidirect
34. #17986668C22semidirect
35. #17986667C22semidirect
36. #17986660C22semidirect
37. #17986659C22semidirect
38. #17986657C22semidirect
39. #17986567C22semidirect
40. #17986565C22semidirect
41. C2×#14556125C22semidirect
42. C2×#14556124C22semidirect
43. C2×#14556124C22semidirect
44. C2×#14556117C22semidirect
45. C2×#14556114C22semidirect
46. #17986512C22semidirect
47. #17986508C22semidirect
50. C2×#14556106C22semidirect
51. C2×#14556105C22semidirect
52. C2×#14556104C22semidirect
53. C2×#14556103C22semidirect
54. C2×#14556103C22semidirect
55. C2×#14556102C22semidirect
56. C2×#14556102C22semidirect
57. C2×#14556101C22semidirect
58. C2×#14556101C22semidirect
59. C2×#14556101C22semidirect
60. C2×#14556100C22semidirect
61. C2×#14556099C22semidirect
65. #17986475C22semidirect
66. C2×Q8×Dic71C22semidirect
67. C2×C4×Dic142C22semidirect
68. C2×#14556093C22semidirect
69. C2×C4×D284C22semidirect
70. C2×#14556090C22semidirect
71. C2×C4×C22⋊D71C22semidirect
72. C2×C4×C22⋊D71C22semidirect
73. C2×(C22⋊D71)⋊C4C22semidirect
77. C23×Q8×C71C22semidirect
78. #548×C71C22semidirect
79. C2×#124×C71C22semidirect
80. C2×C22⋊Q8×C71C22semidirect
81. C2×#121×C71C22semidirect
82. C2×C4×Q8×C71C22semidirect
83. C2×C4×D4×C71C22semidirect
91. C2×#11765866C23semidirect
97. C2×#11765865C23semidirect
104. C2×Q8×D71D4semidirect
106. C2×Q8×D71C23semidirect
129. #14556125C23semidirect
130. #14556124C23semidirect
131. #14556124C23semidirect
132. #14556117C23semidirect
133. #14556114C23semidirect
136. #14556106C23semidirect
137. #14556105C23semidirect
138. #14556104C23semidirect
139. #14556103C23semidirect
140. #14556103C23semidirect
141. #14556102C23semidirect
142. #14556102C23semidirect
143. #14556101C23semidirect
144. #14556101C23semidirect
145. #14556101C23semidirect
146. #14556100C23semidirect
147. #14556099C23semidirect
151. Q8×Dic71C23semidirect
152. C4×Dic142C23semidirect
153. #14556093C23semidirect
154. C4×D284C23semidirect
155. #14556090C23semidirect
156. C4×C22⋊D71C23semidirect
157. C4×C22⋊D71C23semidirect
158. (C22⋊D71)⋊C4C23semidirect
183. C22×Q8×C71C23semidirect
188. #124×C71C23semidirect
189. C22⋊Q8×C71C23semidirect
190. #121×C71C23semidirect
191. C4×Q8×C71C23semidirect
192. C4×D4×C71C23semidirect
218. Q8×D71C2×D4semidirect
415. C2×C71#3487semidirect
432. C2×#548D71semidirect
438. C71C2×#3487semidirect
453. C23×Q8C2×D71semidirect
463. #548C2×D71semidirect
471. C2×#124C2×D71semidirect
479. C2×C22⋊Q8C2×D71semidirect
489. C2×#121C2×D71semidirect
497. C2×C4×Q8C2×D71semidirect
503. C2×C4×D4C2×D71semidirect
534. C22×Q8C22×D71semidirect
566. #124C22×D71semidirect
572. C22⋊Q8C22×D71semidirect
582. #121C22×D71semidirect
589. C4×Q8C22×D71semidirect
595. C4×D4C22×D71semidirect
839. C2#22601997direct (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×#41×D712
#226019972
C2×#179866712
C2×#179866702
C2×#179866682
C2×#179866672
C2×#179866602
C2×#179866592
C2×#179866572
C2×#179865672
C2×#179865652
C2×#179865122
C2×#179865082
C2×#179864752
C2×#548×C712
C2×#348771