Finite Group Databasebeta

← C2×#22602416 #32905660

Subgroups — C2×#22602416 #32905660

Order 18176.

7758 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22602416C2132yesmaximal, direct product factor
2C2×#17986731C213yesmaximal, complemented
3C2×Q8×Dic142C211yesmaximal, characteristic, complemented
4C2×#17986707C213yesmaximal, complemented
5C2×#17986668C211yesmaximal, characteristic, complemented
6C2×#17986660C211yesmaximal, characteristic, complemented
7C2×#17986653C213yesmaximal, complemented
8C2×#17986649C213yesmaximal, complemented
9C2×#17986622C213yesmaximal, complemented
10C2×#17986618C213yesmaximal, complemented
11C2×#17986544C213yesmaximal, complemented
12C2×#17986529C213yesmaximal, complemented
13C2×#17986482C211yesmaximal, characteristic, complemented
14C2×#17986481C211yesmaximal, characteristic, complemented
15C22×Q8×Dic71C211yesmaximal, characteristic, complemented
16C2×#548×C71C211yesmaximal, characteristic, complemented
17C22×#11765866C2211yescharacteristic
18C22×#11765864C2216yes—
19#17986731C22148yescomplemented
20Q8×Dic142C22116yescomplemented
21#17986707C22148yescomplemented
22#17986668C22116yescomplemented
23#17986660C22116yescomplemented
24#17986653C22148yescomplemented
25#17986649C22148yescomplemented
26#17986622C22148yescomplemented
27#17986618C22148yescomplemented
28#17986544C22148yescomplemented
29C2×#14556128C2213yes—
30C2×#14556127C2213yes—
31C2×#14556127C2213yes—
32C2×#14556124C2213yes—
33#17986529C22148yescomplemented
34C2×#14556123C2213yes—
35C2×#14556121C2213yes—
36C2×#14556118C2213yes—
37C2×#14556117C2213yes—
38C2×#14556114C2213yes—
39C2×#14556114C2216yes—
40C2×#14556112C2213yes—
41C2×#14556112C2216yes—
42C2×#14556110C2216yes—
43C2×#14556109C2213yes—
44C2×#14556108C2216yes—
45C2×#14556105C2216yes—
46C2×#14556105C2211yescharacteristic
47C2×#14556104C2213yes—
48C2×#14556102C2213yes—
49C2×#14556102C2213yes—
50C2×#14556100C2213yes—
51C2×#14556099C2213yes—
52#17986482C22116yescomplemented
53#17986481C22116yescomplemented
54C2×Q8×Dic71C2211yescharacteristic
55C2×Q8×Dic71C2211yescharacteristic
56C2×Q8×Dic71C2213yes—
57C2×Q8×Dic71C2213yes—
58C2×Q8×Dic71C2211yescharacteristic
59C2×Q8×Dic71C22116yescomplemented
60C2×C4×Dic142C2213yes—
61C2×C4×D284C2213yes—
62C2×D4×Dic71C2213yes—
63C2×D4×Dic71C2213yes—
64C2×#14556090C2213yes—
65C2×C4×C22⋊D71C2213yes—
66C2×C4×C22⋊D71C2213yes—
67C2×(C22⋊D71)⋊C4C2216yes—
68C2×#14556087C2213yes—
69C2×#14556085C2213yes—
70C22×C4⋊Dic71C2213yes—
71C22×C4⋊Dic71C2213yes—
72C2×C4⋊C4×D71C2213yes—
73C22×C4×Dic71C2213yes—
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—424no—
85C2×#11765864C23148yes—
86C22×Dic142C2311yescharacteristic
87C22×Dic142C2316yes—
88C22×D284C2313yes—
89C22×C22⋊D71C2313yes—
90C22×C22⋊D71C2313yes—
91C22×C22⋊D71C2316yes—
92C23×Dic71C2313yes—
93C23×Dic71C2311yescharacteristic
94C23×Dic71C2316yes—
95C22×C4×D71C2313yes—
96C22×C4×D71C2316yes—
97#14556128C23124yes—
98#14556127C23124yes—
99#14556127C23124yes—
100#14556124C23124yes—
101#14556123C23124yes—
102#14556121C23124yes—
103#14556118C23124yes—
104#14556117C23124yes—
105#14556114C23148yes—
106#14556114C23124yes—
107#14556112C23148yes—
108#14556112C23124yes—
109#14556110C23148yes—
110#14556109C23124yes—
111#14556108C23148yes—
112#14556105C23148yes—
113#14556105C2318yes—
114#14556104C23124yes—
115#14556102C23124yes—
116#14556102C23124yes—
117#14556100C23124yes—
118#14556099C23124yes—
119Q8×Dic71C23124yes—
120Q8×Dic71C2318yes—
121Q8×Dic71C2318yes—
122Q8×Dic71C23124yes—
123Q8×Dic71C2318yes—
124C4×Dic142C23124yes—
125C4×D284C23124yes—
126D4×Dic71C23124yes—
127D4×Dic71C23124yes—
128#14556090C23124yes—
129C4×C22⋊D71C23124yes—
130C4×C22⋊D71C23124yes—
131(C22⋊D71)⋊C4C23148yes—
132#14556087C23124yes—
133#14556085C23124yes—
134C2×C4⋊Dic71C23124yes—
135C2×C4⋊Dic71C23124yes—
136C2×C4⋊Dic71C2313yes—
137C2×C4⋊Dic71C2313yes—
138C2×C4⋊Dic71C2313yes—
139C2×C4⋊Dic71C2313yes—
140C2×C4⋊Dic71C2316yes—
141C2×C4⋊Dic71C2311yescharacteristic
142C2×C4⋊Dic71C2313yes—
143C2×Dic71⋊C4C2313yes—
144C2×Dic71⋊C4C2311yescharacteristic
145C2×Dic71⋊C4C2313yes—
146C2×Dic71⋊C4C2311yescharacteristic
147C2×Dic71⋊C4C2313yes—
148C2×Dic71⋊C4C2313yes—
149C4⋊C4×D71C23124yes—
150C2×C22⋊Dic71C2313yes—
151C2×C22⋊Dic71C2313yes—
152C2×C22⋊Dic71C2311yescharacteristic
153C2×C22⋊Dic71C2313yes—
154C2×(C2×D71)⋊C4C2313yes—
155C2×(C2×D71)⋊C4C2313yes—
156C2×(C2×D71)⋊C4C2316yes—
157C2×(C2×D71)⋊C4C2313yes—
158C2×(C2×D71)⋊C4C2313yes—
159C2×C4×Dic71C2313yes—
160C2×C4×Dic71C2313yes—
161C2×C4×Dic71C2313yes—
162C2×C4×Dic71C2313yes—
163C2×C4×Dic71C23124yes—
164C2×C4×Dic71C2313yes—
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—496no—
189C2×Dic142—24no—
190C2×Dic142—412no—
191C2×Dic142C2414yes—
192C2×Dic142C24124yes—
193C2×D284—212no—
194C2×D284C24112yes—
195C2×C22⋊D71—212no—
196C2×C22⋊D71—212no—
197C2×C22⋊D71—412no—
198C2×C22⋊D71C24112yes—
199C2×C22⋊D71C24112yes—
200C2×C22⋊D71C24124yes—
201C22×Dic71—212no—
202C22×Dic71—24no—
203C22×Dic71—412no—
204C22×Dic71C2411yescharacteristic
205C22×Dic71C2413yes—
206C22×Dic71C2413yes—
207C22×Dic71C2413yes—
208C22×Dic71C24112yes—
209C22×Dic71C2411yescharacteristic
210C22×Dic71C2414yes—
211C22×Dic71C2411yescharacteristic
212C22×Dic71C24124yes—
213C22×Dic71C2411yescharacteristic
214C2×C4×D71—212no—
215C2×C4×D71—412no—
216C2×C4×D71C24112yes—
217C2×C4×D71C24124yes—
218C4⋊Dic71C24112yes—
219C4⋊Dic71C24112yes—
220C4⋊Dic71C24112yes—
221C4⋊Dic71C24112yes—
222C4⋊Dic71C24124yes—
223C4⋊Dic71C2414yes—
224C4⋊Dic71C24112yes—
225Dic71⋊C4C24112yes—
226Dic71⋊C4C2414yes—
227Dic71⋊C4C24112yes—
228Dic71⋊C4C2414yes—
229Dic71⋊C4C24112yes—
230Dic71⋊C4C24112yes—
231C22⋊Dic71C24112yes—
232C22⋊Dic71C24112yes—
233C22⋊Dic71C2414yes—
234C22⋊Dic71C24112yes—
235(C2×D71)⋊C4C24112yes—
236(C2×D71)⋊C4C24112yes—
237(C2×D71)⋊C4C24124yes—
238(C2×D71)⋊C4C24112yes—
239(C2×D71)⋊C4C24112yes—
240C4×Dic71C24112yes—
241C4×Dic71C24112yes—
242C4×Dic71C24112yes—
243C4×Dic71C24112yes—
244C4×Dic71C24112yes—
245C24×C71C2413yes—
246C24×C71C2411yescharacteristic
247#41×C71—232no—
248C2×Q8×C71—232no—
249C2×Q8×C71—212no—
250C2×Q8×C71#4118yescomplemented
251C2×Q8×C71C24112yes—
252C2×Q8×C71C2414yes—
253C2×D4×C71—212no—
254C2×D4×C71—212no—
255C2×D4×C71C24112yes—
256C2×D4×C71C24112yes—
257C22×C4×C71—212no—
258C22×C4×C71—212no—
259C22×C4×C71C2413yes—
260C22×C4×C71C2411yescharacteristic
261C22×C4×C71C2413yes—
262C22×C4×C71C2411yescharacteristic
263C22×C4×C71C24112yes—
264C22×C4×C71C24112yes—
265C22×C4×C71C2413yes—
266C4⋊C4×C71C24112yes—
267C4⋊C4×C71C24112yes—
268C22⋊C4×C71C2414yes—
269C22⋊C4×C71C24112yes—
270C22⋊C4×C71C24124yes—
271C42×C71C24112yes—
272C23×C71—22no—
273C23×C71—22no—
274C23×C71—26no—
275C23×C71—26no—
276C23×C71—26no—
277C23×C71H(5,𝔽2)14yes—
278C23×C71C2516yes—
279C23×C71C2512yes—
280C23×C71C2511yescharacteristic
281C22×D71—26no—
282C22×D71—26no—
283C22×D71—26no—
284C22×D71C2516yes—
285Q8×C71—224no—
286Q8×C71C2×#41116yescomplemented
287D4×C71—224no—
288D4×C71—224no—
289C2×C4×C71—22no—
290C2×C4×C71—26no—
291C2×C4×C71—26no—
292C2×C4×C71—22no—
293C2×C4×C71—224no—
294C2×C4×C71—224no—
295C2×C4×C71C2×#41112yes—
296C2×C4×C71C2512yes—
297C2×C4×C71C2516yes—
298C2×C4×C71C2516yes—
299C2×C4×C71C2512yes—
300C2×C4×C71C2516yes—
301C22⋊D71—224no—
302C22⋊D71—224no—
303C22⋊D71—424no—
304C2×Dic71—22no—
305C2×Dic71—26no—
306C2×Dic71—26no—
307C2×Dic71—224no—
308C2×Dic71—26no—
309C2×Dic71—22no—
310C2×Dic71—22no—
311C2×Dic71—28no—
312C2×Dic71—424no—
313C2×Dic712−1+414yes—
314C2×Dic71C2512yes—
315C2×Dic71C2512yes—
316C2×Dic71C2516yes—
317C2×Dic71C2516yes—
318C2×Dic71C2516yes—
319C2×Dic71C2512yes—
320C2×Dic71C2512yes—
321D284—224no—
322C4×D71—224no—
323C4×D71—424no—
324Dic142—28no—
325Dic142—424no—
326C22×C71—22no—
327C22×C71—22no—
328C22×C71—28no—
329C22×C71—26no—
330C22×C71—26no—
331C22×C71—26no—
332C22×C71—412no—
333C22×C71C22×#4112yes—
334C22×C71C2×H(5,𝔽2)14yes—
335C22×C71C2×H(5,𝔽2)12yes—
336C22×C71C2×2−1+412yes—
337C22×C71C2611yescharacteristic
338C2×D71—26no—
339C2×D71—26no—
340C2×D71—26no—
341C2×D71—412no—
342C4×C71—22no—
343C4×C71—26no—
344C4×C71—26no—
345C4×C71—22no—
346C4×C71C22×#41112yes—
347Dic71—22no—
348Dic71—26no—
349Dic71—26no—
350Dic71—26no—
351Dic71—22no—
352Dic71—22no—
353Dic71C2×2−1+414yes—
354C2×#3522—711nomaximal, Sylow
355C2×C71—24no—
356C2×C71—46no—
357C2×C71#352214yescomplemented
358C2×C71C23×#4111yescharacteristic
359C2×C71C22×H(5,𝔽2)11yescharacteristic
360C2×C71C22×2−1+411yescharacteristic
361D71—46no—
362#3522—7132no—
363C2×#559—713no—
364C2×Q82—711no—
365C2×#554—713no—
366C2×#550—711no—
367C2×#548—711no—
368C2×#548D7111yescharacteristic, complemented
369C2×#547—713no—
370C2×#547—713no—
371C2×#542—713no—
372C2×#542—713no—
373C2×#532—713no—
374C2×#529—713no—
375C2×#520—711no—
376C2×#520—711no—
377C22×C4×Q8—711no—
378C71C2×#352211yescharacteristic, complemented, Sylow
379C22×#41—711no—
380C22×#41—716no—
381C22×#41C2×D7111yescharacteristic
382C23×Q8C2×D7111yescharacteristic
383#559—7148no—
384Q82—7116no—
385#554—7148no—
386#550—7116no—
387#548—7116no—
388#548C2×D71116yescomplemented
389#547—7148no—
390#547—7148no—
391#542—7148no—
392#542—7148no—
393#532—7148no—
394C2×C4⋊Q8—713no—
395C2×C4⋊Q8—713no—
396C2×C4⋊Q8—713no—
397C2×#127—713no—
398#529—7148no—
399C2×#126—713no—
400C2×#126—713no—
401C2×#125—713no—
402C2×#124—713no—
403C2×#124—713no—
404C2×#124—716no—
405C2×#124C2×D7113yes—
406C2×#123—713no—
407C2×#123—713no—
408C2×#123—716no—
409C2×#123—716no—
410C2×C22⋊Q8—713no—
411C2×C22⋊Q8—716no—
412C2×C22⋊Q8—711no—
413C2×C22⋊Q8—716no—
414C2×C22⋊Q8C2×D7113yes—
415C2×#121—713no—
416C2×#121—713no—
417C2×#121—713no—
418C2×#121—713no—
419C2×#121C2×D7113yes—
420#520—7116no—
421#520—7116no—
422C2×C4×Q8—711no—
423C2×C4×Q8—713no—
424C2×C4×Q8—711no—
425C2×C4×Q8—713no—
426C2×C4×Q8—7116no—
427C2×C4×Q8—711no—
428C2×C4×Q8—713no—
429C2×C4×Q8C2×D7111yescharacteristic
430C2×C4×D4—713no—
431C2×C4×D4—713no—
432C2×C4×D4—713no—
433C2×C4×D4—713no—
434C2×C4×D4—713no—
435C2×C4×D4—716no—
436C2×C4×D4—713no—
437C2×C4×D4C2×D7113yes—
438C2×#117—713no—
439C2×#117—713no—
440C22×C4⋊C4—713no—
441C22×C4⋊C4—713no—
442C22×C4⋊C4—713no—
443C22×C42—713no—
444C2×#41—28no—
445C2×#41—28424no—
446C2×#41—718no—
447C2×#41—7148no—
448C2×#41—1428no—
449C2×#41C22×D7118yes—
450C22×Q8—28no—
451C22×Q8—716no—
452C22×Q8—711no—
453C22×Q8C22×D7113yes—
454C22×Q8C22×D7118yes—
455C22×Q8C22×D7111yescharacteristic
456C22×D4—716no—
457C22×D4—713no—
458C22×D4—713no—
459C22×D4—713no—
460C22×D4C22×D7113yes—
461C22×D4C22×D7113yes—
462C23×C4—716no—
463C23×C4—716no—
464C23×C4—713no—
465C23×C4—711no—
466C23×C4—713no—
467C23×C4C22×D7113yes—
468C23×C4C22×D7113yes—
469C4⋊Q8—7124no—
470C4⋊Q8—7124no—
471C4⋊Q8—7124no—
472#127—7124no—
473#126—7124no—
474#126—7124no—
475#125—7124no—
476#124—7124no—
477#124—7124no—
478#124—7148no—
479#124C22×D71124yes—
480#123—7124no—
481#123—7124no—
482#123—7148no—
483#123—7148no—
484C22⋊Q8—7124no—
485C22⋊Q8—7148no—
486C22⋊Q8—718no—
487C22⋊Q8—7148no—
488C22⋊Q8C22×D71124yes—
489#121—7124no—
490#121—7124no—
491#121—7124no—
492#121—7124no—
493#121C22×D71124yes—
494C4×Q8—718no—
495C4×Q8—7124no—
496C4×Q8—718no—
497C4×Q8—7124no—
498C4×Q8—718no—
499C4×Q8—7124no—
500C4×Q8C22×D7118yes—
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—
511C2×C4⋊C4—713no—
512C2×C4⋊C4—713no—
513C2×C4⋊C4—713no—
514C2×C4⋊C4—713no—
515C2×C4⋊C4—713no—
516C2×C4⋊C4—716no—
517C2×C4⋊C4—7124no—
518C2×C4⋊C4—7124no—
519C2×C4⋊C4—711no—
520C2×C4⋊C4—711no—
521C2×C4⋊C4—711no—
522C2×C4⋊C4—713no—
523C2×C4⋊C4—713no—
524C2×C4⋊C4—713no—
525C2×C4⋊C4—713no—
526C2×C4⋊C4—7124no—
527C2×C4⋊C4C22×D7113yes—
528C2×C4⋊C4C22×D7113yes—
529C2×C22⋊C4—713no—
530C2×C22⋊C4—713no—
531C2×C22⋊C4—711no—
532C2×C22⋊C4—713no—
533C2×C22⋊C4—713no—
534C2×C22⋊C4—713no—
535C2×C22⋊C4—713no—
536C2×C22⋊C4—716no—
537C2×C22⋊C4—713no—
538C2×C22⋊C4C22×D7116yes—
539C2×C22⋊C4C22×D7111yescharacteristic
540C2×C22⋊C4C22×D7113yes—
541C2×C42—713no—
542C2×C42—713no—
543C2×C42—713no—
544C2×C42—713no—
545C2×C42—713no—
546C2×C42—7124no—
547C2×C42C22×D7113yes—
548C24—713no—
549C24C23×D7113yes—
550C24C23×D7111yescharacteristic
551#41—232no—
552#41—28496no—
553#41—14232no—
554C2×Q8—232no—
555C2×Q8—212no—
556C2×Q8—28412no—
557C2×Q8—7124no—
558C2×Q8—714no—
559C2×Q8—1424no—
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—28412no—
578C22×C4—28412no—
579C22×C4—7124no—
580C22×C4—7124no—
581C22×C4—711no—
582C22×C4—714no—
583C22×C4—7112no—
584C22×C4—711no—
585C22×C4—711no—
586C22×C4—713no—
587C22×C4—713no—
588C22×C4—713no—
589C22×C4—711no—
590C22×C4—7112no—
591C22×C4—1424no—
592C22×C4—14212no—
593C22×C4—14212no—
594C22×C4C23×D71112yes—
595C22×C4C23×D71112yes—
596C22×C4C23×D7113yes—
597C22×C4C23×D7111yescharacteristic
598C22×C4C23×D7113yes—
599C22×C4C23×D7111yescharacteristic
600C22×C4C23×D7113yes—
601C4⋊C4—7112no—
602C4⋊C4—714no—
603C4⋊C4—714no—
604C4⋊C4—7112no—
605C4⋊C4—7112no—
606C4⋊C4—7112no—
607C4⋊C4—7112no—
608C4⋊C4—7112no—
609C4⋊C4—7112no—
610C4⋊C4—7112no—
611C4⋊C4—7124no—
612C4⋊C4—714no—
613C4⋊C4—7112no—
614C4⋊C4C23×D71112yes—
615C4⋊C4C23×D71112yes—
616C22⋊C4—7112no—
617C22⋊C4—7112no—
618C22⋊C4—714no—
619C22⋊C4—7112no—
620C22⋊C4—7112no—
621C22⋊C4—7112no—
622C22⋊C4—7112no—
623C22⋊C4—7124no—
624C22⋊C4—7112no—
625C22⋊C4C23×D71124yes—
626C22⋊C4C23×D7114yes—
627C22⋊C4C23×D71112yes—
628C42—7112no—
629C42—7112no—
630C42—7112no—
631C42—7112no—
632C42—7112no—
633C42C23×D71112yes—
634C23—22no—
635C23—22no—
636C23—26no—
637C23—26no—
638C23—26no—
639C23—716no—
640C23—1426no—
641C23—1426no—
642C23—1426no—
643C23#1455617414yes—
644C23C24×D7116yes—
645C23C24×D7112yes—
646C23C24×D7111yescharacteristic
647Q8—224no—
648Q8—28424no—
649Q8—1428no—
650Q8C2×#11765864116yescomplemented
651D4—224no—
652D4—224no—
653D4—28424no—
654D4—14224no—
655D4—14224no—
656D4—14224no—
657C2×C4—22no—
658C2×C4—26no—
659C2×C4—26no—
660C2×C4—22no—
661C2×C4—224no—
662C2×C4—224no—
663C2×C4—28424no—
664C2×C4—28424no—
665C2×C4—714no—
666C2×C4—712no—
667C2×C4—712no—
668C2×C4—712no—
669C2×C4—716no—
670C2×C4—716no—
671C2×C4—716no—
672C2×C4—712no—
673C2×C4—1428no—
674C2×C4—1422no—
675C2×C4—1426no—
676C2×C4—1426no—
677C2×C4—1426no—
678C2×C4—14224no—
679C2×C4—1422no—
680C2×C4—1422no—
681C2×C4—14224no—
682C2×C4C2×#11765864112yes—
683C2×C4C24×D7116yes—
684C2×C4C24×D7112yes—
685C2×C4C24×D7116yes—
686C2×C4C24×D7112yes—
687C2×C4C24×D7116yes—
688C22—22no—
689C22—22no—
690C22—28no—
691C22—26no—
692C22—26no—
693C22—26no—
694C22—412no—
695C22—28412no—
696C22—1426no—
697C22—1426no—
698C22—1426no—
699C22C22×#1176586412yes—
700C22C2×#1455617414yes—
701C22C2×#1455617412yes—
702C222−1+4×D7112yes—
703C22C25×D7111yescharacteristic
704C4—22no—
705C4—26no—
706C4—26no—
707C4—22no—
708C4—714no—
709C4—1422no—
710C4—1426no—
711C4—1426no—
712C4—1426no—
713C4—1422no—
714C4—1422no—
715C4C22×#11765864112yes—
716C2—24no—
717C2—46no—
718C2—2846no—
719C2#2260241614yesdirect product factor
720C2C23×#1176586411yescharacteristic
721C2C22×#1455617411yescharacteristic
722C2C2×2−1+4×D7111yescharacteristic
subgroupG/H
centerC23C24×D71
commutator, cosocleC22×C71C26
FrattiniC22C25×D71
FittingC2×#548×C71C2
socleC23×C71C25
hypercenterC2×#548D71
hypocenterC71C2×#3522
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. #22602416C2direct (N × H)
2. C2×#17986731C2semidirect
3. C2×Q8×Dic142C2semidirect
4. C2×#17986707C2semidirect
5. C2×#17986668C2semidirect
6. C2×#17986660C2semidirect
7. C2×#17986653C2semidirect
8. C2×#17986649C2semidirect
9. C2×#17986622C2semidirect
10. C2×#17986618C2semidirect
11. C2×#17986544C2semidirect
12. C2×#17986529C2semidirect
13. C2×#17986482C2semidirect
14. C2×#17986481C2semidirect
15. C22×Q8×Dic71C2semidirect
16. C2×#548×C71C2semidirect
19. #17986731C22semidirect
20. Q8×Dic142C22semidirect
21. #17986707C22semidirect
22. #17986668C22semidirect
23. #17986660C22semidirect
24. #17986653C22semidirect
25. #17986649C22semidirect
26. #17986622C22semidirect
27. #17986618C22semidirect
28. #17986544C22semidirect
33. #17986529C22semidirect
52. #17986482C22semidirect
53. #17986481C22semidirect
59. C2×Q8×Dic71C22semidirect
76. #548×C71C22semidirect
250. C2×Q8×C71#41semidirect
286. Q8×C71C2×#41semidirect
357. C2×C71#3522semidirect
368. C2×#548D71semidirect
378. C71C2×#3522semidirect
388. #548C2×D71semidirect
560. C2×Q8#11765864semidirect
650. Q8C2×#11765864semidirect
719. C2#22602416direct (N × H)

Maximal subgroups

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

subgroupindex
#226024162
C2×#179867312
C2×Q8×Dic1422
C2×#179867072
C2×#179866682
C2×#179866602
C2×#179866532
C2×#179866492
C2×#179866222
C2×#179866182
C2×#179865442
C2×#179865292
C2×#179864822
C2×#179864812
C22×Q8×Dic712
C2×#548×C712
C2×#352271