Finite Group Databasebeta

← C2×#22601930 #32904506

Subgroups — C2×#22601930 #32904506

Order 18176.

7802 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22601930C2132yesmaximal, direct product factor
2C2×#17986731C213yesmaximal, complemented
3C2×#17986725C211yesmaximal, characteristic, complemented
4C2×#17986720C213yesmaximal, complemented
5C2×#17986701C213yesmaximal, complemented
6C2×#17986695C213yesmaximal, complemented
7C2×#17986668C211yesmaximal, characteristic, complemented
8C2×#17986660C211yesmaximal, characteristic, complemented
9C2×#17986544C213yesmaximal, complemented
10C2×#17986535C213yesmaximal, complemented
11C2×#17986528C213yesmaximal, complemented
12C2×#41×Dic71C211yesmaximal, characteristic, complemented
13C2×C4×#11765866C211yesmaximal, characteristic, complemented
14C2×C4×#11765864C213yesmaximal, complemented
15C22×Q8×Dic71C211yesmaximal, characteristic, complemented
16C2×#548×C71C211yesmaximal, characteristic, complemented
17C22×#11765866C2211yescharacteristic
18C22×#11765864C2213yes—
19#17986731C22148yescomplemented
20#17986725C22116yescomplemented
21#17986720C22148yescomplemented
22#17986701C22148yescomplemented
23#17986695C22148yescomplemented
24#17986668C22116yescomplemented
25#17986660C22116yescomplemented
26#17986544C22148yescomplemented
27C2×#14556127C2213yes—
28C2×#14556124C2213yes—
29#17986535C22148yescomplemented
30#17986528C22148yescomplemented
31C2×#14556123C2216yes—
32C2×#14556121C2216yes—
33C2×#14556120C2213yes—
34C2×#14556119C2213yes—
35C2×#14556117C2213yes—
36C2×#14556114C2216yes—
37C2×#14556112C2216yes—
38C2×#14556110C2216yes—
39C2×#14556104C2213yes—
40C2×#14556102C2213yes—
41C2×#14556102C2213yes—
42C2×#14556100C2216yes—
43C2×#14556099C2213yes—
44#41×Dic71C22116yescomplemented
45C4×#11765866C22116yescomplemented
46C4×#11765864C22148yescomplemented
47C2×Q8×Dic71C2211yescharacteristic
48C2×Q8×Dic71C2211yescharacteristic
49C2×Q8×Dic71C2213yes—
50C2×Q8×Dic71C2213yes—
51C2×Q8×Dic71C2211yescharacteristic
52C2×Q8×Dic71C22116yescomplemented
53C2×C4×Dic142C2213yes—
54C2×#14556093C2213yes—
55C2×C4×D284C2213yes—
56C2×D4×Dic71C2213yes—
57C2×D4×Dic71C2213yes—
58C2×D4×Dic71C2213yes—
59C2×#14556090C2213yes—
60C2×C4×C22⋊D71C2213yes—
61C2×C4×C22⋊D71C2213yes—
62C2×(C22⋊D71)⋊C4C2213yes—
63C2×(C22⋊D71)⋊C4C2213yes—
64C2×(C22⋊D71)⋊C4C2216yes—
65C2×#14556087C2213yes—
66C2×#14556086C2213yes—
67C2×#14556086C2213yes—
68C2×#14556084C2211yescharacteristic
69C2×#14556084C2213yes—
70C22×C4⋊Dic71C2213yes—
71C22×C4×Dic71C2213yes—
72C22×C4×Dic71C2213yes—
73C2×C42×D71C2213yes—
74C22×#41×C71C2211yescharacteristic
75C23×Q8×C71C2211yescharacteristic
76#548×C71C22116yescomplemented
77C2×#124×C71C2213yes—
78C2×C22⋊Q8×C71C2213yes—
79C2×#121×C71C2213yes—
80C2×C4×Q8×C71C2211yescharacteristic
81C2×C4×D4×C71C2213yes—
82C2×#11765866—28no—
83C2×#11765866C2318yes—
84C2×#11765864—224no—
85C2×#11765864C23124yes—
86C22×Dic142C2313yes—
87C22×D284C2313yes—
88C22×C22⋊D71C2313yes—
89C22×C22⋊D71C2313yes—
90C22×C22⋊D71C2316yes—
91C23×Dic71C2313yes—
92C23×Dic71C2313yes—
93C23×Dic71C2313yes—
94C23×Dic71C2311yescharacteristic
95C22×C4×D71C2313yes—
96C22×C4×D71C2313yes—
97C22×C4×D71C2313yes—
98#14556127C23124yes—
99#14556124C23124yes—
100#14556123C23148yes—
101#14556121C23148yes—
102#14556120C23124yes—
103#14556119C23124yes—
104#14556117C23124yes—
105#14556114C23148yes—
106#14556112C23148yes—
107#14556110C23148yes—
108#14556104C23124yes—
109#14556102C23124yes—
110#14556102C23124yes—
111#14556100C23148yes—
112#14556099C23124yes—
113Q8×Dic71C2318yes—
114Q8×Dic71C2318yes—
115Q8×Dic71C23124yes—
116Q8×Dic71C2318yes—
117Q8×Dic71C23124yes—
118C4×Dic142C23124yes—
119#14556093C23124yes—
120C4×D284C23124yes—
121D4×Dic71C23124yes—
122D4×Dic71C23124yes—
123D4×Dic71C23124yes—
124#14556090C23124yes—
125C4×C22⋊D71C23124yes—
126C4×C22⋊D71C23124yes—
127(C22⋊D71)⋊C4C23124yes—
128(C22⋊D71)⋊C4C23124yes—
129(C22⋊D71)⋊C4C23148yes—
130#14556087C23124yes—
131#14556086C23124yes—
132#14556086C23124yes—
133#14556084C2318yes—
134#14556084C23124yes—
135C2×C4⋊Dic71C23124yes—
136C2×C4⋊Dic71C2313yes—
137C2×C4⋊Dic71C2313yes—
138C2×C4⋊Dic71C2316yes—
139C2×C4⋊Dic71C2313yes—
140C2×C4⋊Dic71C2313yes—
141C2×Dic71⋊C4C2311yescharacteristic
142C2×Dic71⋊C4C2313yes—
143C2×Dic71⋊C4C2311yescharacteristic
144C2×Dic71⋊C4C2313yes—
145C2×Dic71⋊C4C2316yes—
146C2×C22⋊Dic71C2311yescharacteristic
147C2×C22⋊Dic71C2313yes—
148C2×C22⋊Dic71C2316yes—
149C2×(C2×D71)⋊C4C2313yes—
150C2×(C2×D71)⋊C4C2313yes—
151C2×(C2×D71)⋊C4C2316yes—
152C2×(C2×D71)⋊C4C2316yes—
153C2×C4×Dic71C2311yescharacteristic
154C2×C4×Dic71C2313yes—
155C2×C4×Dic71C2313yes—
156C2×C4×Dic71C2311yescharacteristic
157C2×C4×Dic71C2313yes—
158C2×C4×Dic71C2313yes—
159C2×C4×Dic71C2313yes—
160C2×C4×Dic71C2313yes—
161C2×C4×Dic71C2313yes—
162C2×C4×Dic71C23124yes—
163C2×C4×Dic71C23124yes—
164C42×D71C23124yes—
165C2×#41×C71—28no—
166C2×#41×C71C2318yes—
167C22×Q8×C71—28no—
168C22×Q8×C71C2318yes—
169C22×Q8×C71C2313yes—
170C22×Q8×C71C2311yescharacteristic
171C22×D4×C71C2313yes—
172C22×D4×C71C2313yes—
173C23×C4×C71C2313yes—
174C23×C4×C71C2313yes—
175#124×C71C23124yes—
176C22⋊Q8×C71C23124yes—
177#121×C71C23124yes—
178C4×Q8×C71C2318yes—
179C4×D4×C71C23124yes—
180C2×C4⋊C4×C71C2313yes—
181C2×C4⋊C4×C71C2313yes—
182C2×C22⋊C4×C71C2311yescharacteristic
183C2×C22⋊C4×C71C2313yes—
184C2×C22⋊C4×C71C2316yes—
185C2×C42×C71C2313yes—
186C23×D71C2413yes—
187#11765866—232no—
188#11765864—296no—
189C2×Dic142—212no—
190C2×Dic142C24112yes—
191C2×D284—212no—
192C2×D284C24112yes—
193C2×C22⋊D71—212no—
194C2×C22⋊D71—212no—
195C2×C22⋊D71—412no—
196C2×C22⋊D71C24112yes—
197C2×C22⋊D71C24112yes—
198C2×C22⋊D71C24124yes—
199C22×Dic71—212no—
200C22×Dic71—46no—
201C22×Dic71—46no—
202C22×Dic71#4118yescomplemented
203C22×Dic71C2411yescharacteristic
204C22×Dic71C2413yes—
205C22×Dic71C2411yescharacteristic
206C22×Dic71C2413yes—
207C22×Dic71C2413yes—
208C22×Dic71C24112yes—
209C22×Dic71C24112yes—
210C22×Dic71C24112yes—
211C22×Dic71C2411yescharacteristic
212C22×Dic71C2411yescharacteristic
213C22×Dic71C2414yes—
214C2×C4×D71—212no—
215C2×C4×D71—212no—
216C2×C4×D71—46no—
217C2×C4×D71C24112yes—
218C2×C4×D71C24112yes—
219C2×C4×D71C24112yes—
220C4⋊Dic71C24112yes—
221C4⋊Dic71C24112yes—
222C4⋊Dic71C24124yes—
223C4⋊Dic71C24112yes—
224C4⋊Dic71C24112yes—
225Dic71⋊C4C2414yes—
226Dic71⋊C4C24112yes—
227Dic71⋊C4C2414yes—
228Dic71⋊C4C24112yes—
229Dic71⋊C4C24124yes—
230C22⋊Dic71C2414yes—
231C22⋊Dic71C24112yes—
232C22⋊Dic71C24124yes—
233(C2×D71)⋊C4C24112yes—
234(C2×D71)⋊C4C24112yes—
235(C2×D71)⋊C4C24124yes—
236(C2×D71)⋊C4C24124yes—
237C4×Dic71C2414yes—
238C4×Dic71C24112yes—
239C4×Dic71C24112yes—
240C4×Dic71C2414yes—
241C4×Dic71C24112yes—
242C4×Dic71C24112yes—
243C4×Dic71C24112yes—
244C4×Dic71C24112yes—
245C4×Dic71C24112yes—
246C24×C71C2413yes—
247C24×C71C2411yescharacteristic
248#41×C71—232no—
249C2×Q8×C71—232no—
250C2×Q8×C71—212no—
251C2×Q8×C71#4118yescomplemented
252C2×Q8×C71C24112yes—
253C2×Q8×C71C2414yes—
254C2×D4×C71—212no—
255C2×D4×C71—212no—
256C2×D4×C71C24112yes—
257C2×D4×C71C24112yes—
258C22×C4×C71—212no—
259C22×C4×C71—212no—
260C22×C4×C71C2411yescharacteristic
261C22×C4×C71C2413yes—
262C22×C4×C71C2413yes—
263C22×C4×C71C2411yescharacteristic
264C22×C4×C71C24112yes—
265C22×C4×C71C24112yes—
266C22×C4×C71C2413yes—
267C4⋊C4×C71C24112yes—
268C4⋊C4×C71C24112yes—
269C22⋊C4×C71C2414yes—
270C22⋊C4×C71C24112yes—
271C22⋊C4×C71C24124yes—
272C42×C71C24112yes—
273C23×C71—22no—
274C23×C71—22no—
275C23×C71—26no—
276C23×C71—26no—
277C23×C71—26no—
278C23×C71C2×#4114yes—
279C23×C71C2516yes—
280C23×C71C2512yes—
281C23×C71C2511yescharacteristic
282C22×D71—26no—
283C22×D71—26no—
284C22×D71—26no—
285C22×D71C2516yes—
286Q8×C71—224no—
287Q8×C71C2×#41116yescomplemented
288D4×C71—224no—
289D4×C71—224no—
290C2×C4×C71—22no—
291C2×C4×C71—26no—
292C2×C4×C71—26no—
293C2×C4×C71—22no—
294C2×C4×C71—224no—
295C2×C4×C71—224no—
296C2×C4×C71C2×#41112yes—
297C2×C4×C71C2512yes—
298C2×C4×C71C2516yes—
299C2×C4×C71C2516yes—
300C2×C4×C71C2512yes—
301C2×C4×C71C2516yes—
302C22⋊D71—224no—
303C22⋊D71—224no—
304C22⋊D71—424no—
305C2×Dic71—22no—
306C2×Dic71—26no—
307C2×Dic71—26no—
308C2×Dic71—22no—
309C2×Dic71—26no—
310C2×Dic71—224no—
311C2×Dic71—412no—
312C2×Dic71—412no—
313C2×Dic71C2×#4114yes—
314C2×Dic71C2×#4114yes—
315C2×Dic71C2×#41116yescomplemented
316C2×Dic71C2512yes—
317C2×Dic71C2516yes—
318C2×Dic71C2512yes—
319C2×Dic71C2516yes—
320C2×Dic71C2516yes—
321C2×Dic71C2512yes—
322C2×Dic71C2512yes—
323D284—224no—
324C4×D71—224no—
325C4×D71—224no—
326C4×D71—412no—
327Dic142—224no—
328C22×C71—22no—
329C22×C71—22no—
330C22×C71—28no—
331C22×C71—26no—
332C22×C71—26no—
333C22×C71—26no—
334C22×C71—412no—
335C22×C71C22×#4114yes—
336C22×C71C22×#4112yes—
337C22×C71C22×#4112yes—
338C22×C71#58512yes—
339C22×C71C2611yescharacteristic
340C2×D71—26no—
341C2×D71—26no—
342C2×D71—26no—
343C2×D71—412no—
344C4×C71—26no—
345C4×C71—22no—
346C4×C71—26no—
347C4×C71—22no—
348C4×C71C22×#41112yes—
349Dic71—26no—
350Dic71—22no—
351Dic71—26no—
352Dic71—22no—
353Dic71—26no—
354Dic71C22×#4114yes—
355Dic71C22×#4114yes—
356C2×#3480—711nomaximal, Sylow
357C2×C71—24no—
358C2×C71—46no—
359C2×C71#348014yescomplemented
360C2×C71C23×#4111yescharacteristic
361C2×C71C23×#4111yescharacteristic
362C2×C71C2×#58511yescharacteristic
363D71—46no—
364#3480—7132no—
365C2×#559—713no—
366C2×#557—711no—
367C2×#556—713no—
368C2×#553—713no—
369C2×#553—713no—
370C2×#550—711no—
371C2×#548—711no—
372C2×#548D7111yescharacteristic, complemented
373C2×#532—713no—
374C2×#529—713no—
375C2×#529—713no—
376C2×C4×#41—711no—
377C2×C4×#41—711no—
378C2×C4×#41—713no—
379C22×C4×Q8—711no—
380C71C2×#348011yescharacteristic, complemented, Sylow
381C22×#41—711no—
382C22×#41—713no—
383C22×#41C2×D7111yescharacteristic
384C23×Q8C2×D7111yescharacteristic
385#559—7148no—
386#557—7116no—
387#556—7148no—
388#553—7148no—
389#553—7148no—
390#550—7116no—
391#548—7116no—
392#548C2×D71116yescomplemented
393#532—7148no—
394C2×C4⋊Q8—713no—
395C2×#127—713no—
396#529—7148no—
397#529—7148no—
398C2×#126—716no—
399C2×#126—716no—
400C2×#125—713no—
401C2×#125—713no—
402C2×#124—713no—
403C2×#124—716no—
404C2×#124C2×D7113yes—
405C2×#123—716no—
406C2×#123—716no—
407C2×C22⋊Q8—713no—
408C2×C22⋊Q8C2×D7113yes—
409C2×#121—713no—
410C2×#121—716no—
411C2×#121—713no—
412C2×#121—713no—
413C2×#121C2×D7113yes—
414C4×#41—7116no—
415C4×#41—7116no—
416C4×#41—7148no—
417C2×C4×Q8—711no—
418C2×C4×Q8—713no—
419C2×C4×Q8—711no—
420C2×C4×Q8—713no—
421C2×C4×Q8—7116no—
422C2×C4×Q8—711no—
423C2×C4×Q8—713no—
424C2×C4×Q8—713no—
425C2×C4×Q8C2×D7111yescharacteristic
426C2×C4×D4—713no—
427C2×C4×D4—713no—
428C2×C4×D4—713no—
429C2×C4×D4—713no—
430C2×C4×D4—713no—
431C2×C4×D4—713no—
432C2×C4×D4—713no—
433C2×C4×D4—713no—
434C2×C4×D4—716no—
435C2×C4×D4—713no—
436C2×C4×D4C2×D7113yes—
437C2×#117—713no—
438C2×#117—713no—
439C2×#117—713no—
440C2×#117—711no—
441C2×#117—713no—
442C22×C4⋊C4—713no—
443C22×C42—713no—
444C22×C42—713no—
445C22×C42—713no—
446C2×#41—28no—
447C2×#41—718no—
448C2×#41—7124no—
449C2×#41—14224no—
450C2×#41—1428no—
451C2×#41C22×D7118yes—
452C22×Q8—28no—
453C22×Q8—713no—
454C22×Q8C22×D7113yes—
455C22×Q8C22×D7118yes—
456C22×Q8C22×D7111yescharacteristic
457C22×D4—716no—
458C22×D4—713no—
459C22×D4—713no—
460C22×D4—713no—
461C22×D4C22×D7113yes—
462C22×D4C22×D7113yes—
463C23×C4—713no—
464C23×C4—713no—
465C23×C4—713no—
466C23×C4—711no—
467C23×C4—713no—
468C23×C4—713no—
469C23×C4—713no—
470C23×C4C22×D7113yes—
471C23×C4C22×D7113yes—
472C4⋊Q8—7124no—
473#127—7124no—
474#126—7148no—
475#126—7148no—
476#125—7124no—
477#125—7124no—
478#124—7124no—
479#124—7148no—
480#124C22×D71124yes—
481#123—7148no—
482#123—7148no—
483C22⋊Q8—7124no—
484C22⋊Q8C22×D71124yes—
485#121—7124no—
486#121—7148no—
487#121—7124no—
488#121—7124no—
489#121C22×D71124yes—
490C4×Q8—718no—
491C4×Q8—7124no—
492C4×Q8—718no—
493C4×Q8—7124no—
494C4×Q8—718no—
495C4×Q8—7124no—
496C4×Q8—7124no—
497C4×Q8C22×D7118yes—
498C4×D4—7124no—
499C4×D4—7124no—
500C4×D4—7124no—
501C4×D4—7124no—
502C4×D4—7124no—
503C4×D4—7124no—
504C4×D4—7124no—
505C4×D4—7124no—
506C4×D4—7148no—
507C4×D4—7124no—
508C4×D4C22×D71124yes—
509#117—7124no—
510#117—7124no—
511#117—7124no—
512#117—718no—
513#117—7124no—
514C2×C4⋊C4—713no—
515C2×C4⋊C4—713no—
516C2×C4⋊C4—716no—
517C2×C4⋊C4—7124no—
518C2×C4⋊C4—711no—
519C2×C4⋊C4—711no—
520C2×C4⋊C4—713no—
521C2×C4⋊C4—713no—
522C2×C4⋊C4—713no—
523C2×C4⋊C4—713no—
524C2×C4⋊C4—716no—
525C2×C4⋊C4C22×D7113yes—
526C2×C4⋊C4C22×D7113yes—
527C2×C22⋊C4—711no—
528C2×C22⋊C4—713no—
529C2×C22⋊C4—716no—
530C2×C22⋊C4—713no—
531C2×C22⋊C4—716no—
532C2×C22⋊C4—713no—
533C2×C22⋊C4—716no—
534C2×C22⋊C4C22×D7111yescharacteristic
535C2×C22⋊C4C22×D7113yes—
536C2×C22⋊C4C22×D7116yes—
537C2×C42—711no—
538C2×C42—711no—
539C2×C42—713no—
540C2×C42—713no—
541C2×C42—713no—
542C2×C42—713no—
543C2×C42—713no—
544C2×C42—713no—
545C2×C42—713no—
546C2×C42—7124no—
547C2×C42—7124no—
548C2×C42—7124no—
549C2×C42C22×D7113yes—
550C24—713no—
551C24C23×D7113yes—
552C24C23×D7111yescharacteristic
553#41—232no—
554#41—14296no—
555#41—14232no—
556C2×Q8—232no—
557C2×Q8—212no—
558C2×Q8—7112no—
559C2×Q8—14212no—
560C2×Q8#1176586418yescomplemented
561C2×Q8C23×D71112yes—
562C2×Q8C23×D7114yes—
563C2×D4—212no—
564C2×D4—212no—
565C2×D4—28412no—
566C2×D4—7124no—
567C2×D4—7112no—
568C2×D4—7112no—
569C2×D4—7112no—
570C2×D4—14212no—
571C2×D4—14212no—
572C2×D4—14212no—
573C2×D4C23×D71112yes—
574C2×D4C23×D71112yes—
575C22×C4—212no—
576C22×C4—212no—
577C22×C4—2846no—
578C22×C4—2846no—
579C22×C4—2846no—
580C22×C4—7112no—
581C22×C4—7112no—
582C22×C4—7112no—
583C22×C4—718no—
584C22×C4—714no—
585C22×C4—711no—
586C22×C4—711no—
587C22×C4—7112no—
588C22×C4—711no—
589C22×C4—713no—
590C22×C4—711no—
591C22×C4—713no—
592C22×C4—713no—
593C22×C4—7112no—
594C22×C4—7112no—
595C22×C4—14212no—
596C22×C4—14212no—
597C22×C4—14212no—
598C22×C4C23×D71112yes—
599C22×C4C23×D71112yes—
600C22×C4C23×D7111yescharacteristic
601C22×C4C23×D7113yes—
602C22×C4C23×D7111yescharacteristic
603C22×C4C23×D7113yes—
604C22×C4C23×D7113yes—
605C4⋊C4—714no—
606C4⋊C4—714no—
607C4⋊C4—7112no—
608C4⋊C4—7112no—
609C4⋊C4—7124no—
610C4⋊C4—7112no—
611C4⋊C4—7112no—
612C4⋊C4—7124no—
613C4⋊C4—7112no—
614C4⋊C4—7112no—
615C4⋊C4C23×D71112yes—
616C4⋊C4C23×D71112yes—
617C22⋊C4—714no—
618C22⋊C4—7112no—
619C22⋊C4—7124no—
620C22⋊C4—7112no—
621C22⋊C4—7124no—
622C22⋊C4—7112no—
623C22⋊C4—7124no—
624C22⋊C4C23×D7114yes—
625C22⋊C4C23×D71112yes—
626C22⋊C4C23×D71124yes—
627C42—714no—
628C42—714no—
629C42—7112no—
630C42—7112no—
631C42—7112no—
632C42—7112no—
633C42—7112no—
634C42—7112no—
635C42—7112no—
636C42C23×D71112yes—
637C23—22no—
638C23—22no—
639C23—26no—
640C23—26no—
641C23—26no—
642C23—716no—
643C23—1426no—
644C23—1426no—
645C23—1426no—
646C23#41×D7114yes—
647C23C24×D7116yes—
648C23C24×D7112yes—
649C23C24×D7111yescharacteristic
650Q8—224no—
651Q8—14224no—
652Q8C2×#11765864116yescomplemented
653D4—224no—
654D4—224no—
655D4—28424no—
656D4—14224no—
657D4—14224no—
658D4—14224no—
659C2×C4—26no—
660C2×C4—22no—
661C2×C4—26no—
662C2×C4—22no—
663C2×C4—224no—
664C2×C4—224no—
665C2×C4—28412no—
666C2×C4—28412no—
667C2×C4—28412no—
668C2×C4—714no—
669C2×C4—714no—
670C2×C4—7116no—
671C2×C4—712no—
672C2×C4—712no—
673C2×C4—712no—
674C2×C4—712no—
675C2×C4—716no—
676C2×C4—716no—
677C2×C4—716no—
678C2×C4—14224no—
679C2×C4—14224no—
680C2×C4—1426no—
681C2×C4—1422no—
682C2×C4—1426no—
683C2×C4—1422no—
684C2×C4—1426no—
685C2×C4—14224no—
686C2×C4C2×#11765864112yes—
687C2×C4C24×D7112yes—
688C2×C4C24×D7116yes—
689C2×C4C24×D7112yes—
690C2×C4C24×D7116yes—
691C2×C4C24×D7116yes—
692C22—22no—
693C22—22no—
694C22—28no—
695C22—26no—
696C22—26no—
697C22—26no—
698C22—412no—
699C22—28412no—
700C22—1426no—
701C22—1426no—
702C22—1426no—
703C22C2×#41×D7114yes—
704C22C2×#41×D7112yes—
705C22C22×#1176586412yes—
706C22#1798683612yes—
707C22C25×D7111yescharacteristic
708C4—26no—
709C4—22no—
710C4—26no—
711C4—22no—
712C4—714no—
713C4—714no—
714C4—1426no—
715C4—1422no—
716C4—1426no—
717C4—1422no—
718C4—1426no—
719C4C22×#11765864112yes—
720C2—24no—
721C2—46no—
722C2—2846no—
723C2#2260193014yesdirect product factor
724C2C22×#41×D7111yescharacteristic
725C2C23×#1176586411yescharacteristic
726C2C2×#1798683611yescharacteristic
subgroupG/H
centerC23C24×D71
commutator, cosocleC22×C71C26
FrattiniC22C25×D71
FittingC2×#548×C71C2
socleC23×C71C25
hypercenterC2×#548D71
hypocenterC71C2×#3480
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. #22601930C2direct (N × H)
2. C2×#17986731C2semidirect
3. C2×#17986725C2semidirect
4. C2×#17986720C2semidirect
5. C2×#17986701C2semidirect
6. C2×#17986695C2semidirect
7. C2×#17986668C2semidirect
8. C2×#17986660C2semidirect
9. C2×#17986544C2semidirect
10. C2×#17986535C2semidirect
11. C2×#17986528C2semidirect
12. C2×#41×Dic71C2semidirect
13. C2×C4×#11765866C2semidirect
14. C2×C4×#11765864C2semidirect
15. C22×Q8×Dic71C2semidirect
16. C2×#548×C71C2semidirect
19. #17986731C22semidirect
20. #17986725C22semidirect
21. #17986720C22semidirect
22. #17986701C22semidirect
23. #17986695C22semidirect
24. #17986668C22semidirect
25. #17986660C22semidirect
26. #17986544C22semidirect
29. #17986535C22semidirect
30. #17986528C22semidirect
44. #41×Dic71C22semidirect
45. C4×#11765866C22semidirect
46. C4×#11765864C22semidirect
52. C2×Q8×Dic71C22semidirect
76. #548×C71C22semidirect
202. C22×Dic71#41semidirect
251. C2×Q8×C71#41semidirect
287. Q8×C71C2×#41semidirect
315. C2×Dic71C2×#41semidirect
359. C2×C71#3480semidirect
372. C2×#548D71semidirect
380. C71C2×#3480semidirect
392. #548C2×D71semidirect
560. C2×Q8#11765864semidirect
652. Q8C2×#11765864semidirect
723. C2#22601930direct (N × H)

Maximal subgroups

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

subgroupindex
#226019302
C2×#179867312
C2×#179867252
C2×#179867202
C2×#179867012
C2×#179866952
C2×#179866682
C2×#179866602
C2×#179865442
C2×#179865352
C2×#179865282
C2×#41×Dic712
C2×C4×#117658662
C2×C4×#117658642
C22×Q8×Dic712
C2×#548×C712
C2×#348071