Finite Group Databasebeta

← C2×#22602340 #32905705

Subgroups — C2×#22602340 #32905705

Order 18176.

7854 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#22602340C2132yesmaximal, direct product factor
2C2×#17986725C211yesmaximal, characteristic, complemented
3C2×#17986699C213yesmaximal, complemented
4C2×#17986697C213yesmaximal, complemented
5C2×#17986671C211yesmaximal, characteristic, complemented
6C2×#17986670C213yesmaximal, complemented
7C2×#17986668C211yesmaximal, characteristic, complemented
8C2×#17986668C211yesmaximal, characteristic, complemented
9C2×#17986650C213yesmaximal, complemented
10C2×#17986604C213yesmaximal, complemented
11C2×#17986600C213yesmaximal, complemented
12C2×#17986546C213yesmaximal, complemented
13C2×#17986527C213yesmaximal, complemented
14C2×#17986481C211yesmaximal, characteristic, complemented
15C2×C4×#11765866C211yesmaximal, characteristic, complemented
16C2×#520×C71C211yesmaximal, characteristic, complemented
17C22×#11765866C2211yescharacteristic
18C22×#11765866C2211yescharacteristic
19C22×#11765865C2216yes—
20#17986725C22116yescomplemented
21#17986699C22148yescomplemented
22#17986697C22148yescomplemented
23#17986671C22116yescomplemented
24#17986670C22148yescomplemented
25#17986668C22116yescomplemented
26#17986668C22116yescomplemented
27#17986650C22148yescomplemented
28#17986604C22148yescomplemented
29#17986600C22148yescomplemented
30#17986546C22148yescomplemented
31C2×#14556127C2213yes—
32C2×#14556125C2213yes—
33C2×#14556124C2213yes—
34C2×#14556124C2213yes—
35#17986527C22148yescomplemented
36C2×#14556123C2213yes—
37C2×#14556121C2213yes—
38C2×#14556120C2213yes—
39C2×#14556119C2213yes—
40C2×#14556118C2211yescharacteristic
41C2×#14556114C2213yes—
42C2×#14556113C2216yes—
43C2×#14556113C2213yes—
44C2×#14556111C2216yes—
45C2×#14556110C2213yes—
46C2×#14556106C2213yes—
47C2×#14556103C2213yes—
48C2×#14556103C2213yes—
49C2×#14556102C2213yes—
50C2×#14556102C2213yes—
51C2×#14556102C2216yes—
52C2×#14556101C2213yes—
53C2×#14556101C2216yes—
54C2×#14556101C2216yes—
55C2×#14556099C2213yes—
56C2×#14556099C2213yes—
57#17986481C22116yescomplemented
58C4×#11765866C22116yescomplemented
59C2×Q8×Dic71C2211yescharacteristic
60C2×Q8×Dic71C2211yescharacteristic
61C2×C4×Dic142C2213yes—
62C2×C4×D284C2213yes—
63C2×C4×D284C2213yes—
64C2×C4×D284C2213yes—
65C2×#14556090C2213yes—
66C2×#14556090C2213yes—
67C2×C4×C22⋊D71C2213yes—
68C2×C4×C22⋊D71C2213yes—
69C2×C4×C22⋊D71C2216yes—
70C2×#14556086C2213yes—
71C2×#14556085C2213yes—
72C2×C4⋊C4×D71C2213yes—
73C2×C42×D71C2213yes—
74C22×#41×C71C2211yescharacteristic
75#520×C71C22116yescomplemented
76C2×C4×Q8×C71C2211yescharacteristic
77C2×C4×Q8×C71C2211yescharacteristic
78C2×C4×D4×C71C2213yes—
79C2×C4×D4×C71C2213yes—
80C2×#117×C71C2213yes—
81C22×C4⋊C4×C71C2213yes—
82C2×#11765866—28no—
83C2×#11765866—28no—
84C2×#11765866C2318yes—
85C2×#11765866C2318yes—
86C2×#11765865—424no—
87C2×#11765865C23148yes—
88C22×Dic142C2313yes—
89C22×D284C2313yes—
90C22×D284C2313yes—
91C22×D284C2316yes—
92C22×D284C2313yes—
93C22×C22⋊D71C2313yes—
94C22×C22⋊D71C2316yes—
95C22×C22⋊D71C2316yes—
96C22×C22⋊D71C2313yes—
97C22×C4×D71C2313yes—
98C22×C4×D71C2313yes—
99C22×C4×D71C2313yes—
100C22×C4×D71C2316yes—
101C22×C4×D71C2313yes—
102#14556127C23124yes—
103#14556125C23124yes—
104#14556124C23124yes—
105#14556124C23124yes—
106#14556123C23124yes—
107#14556121C23124yes—
108#14556120C23124yes—
109#14556119C23124yes—
110#14556118C2318yes—
111#14556114C23124yes—
112#14556113C23124yes—
113#14556113C23148yes—
114#14556111C23148yes—
115#14556110C23124yes—
116#14556106C23124yes—
117#14556103C23124yes—
118#14556103C23124yes—
119#14556102C23148yes—
120#14556102C23124yes—
121#14556102C23124yes—
122#14556101C23148yes—
123#14556101C23148yes—
124#14556101C23124yes—
125#14556099C23124yes—
126#14556099C23124yes—
127Q8×Dic71C2318yes—
128Q8×Dic71C2318yes—
129C4×Dic142C23124yes—
130C4×D284C23124yes—
131C4×D284C23124yes—
132C4×D284C23124yes—
133#14556090C23124yes—
134#14556090C23124yes—
135C4×C22⋊D71C23124yes—
136C4×C22⋊D71C23124yes—
137C4×C22⋊D71C23148yes—
138#14556086C23124yes—
139#14556085C23124yes—
140C2×C4⋊Dic71C2313yes—
141C2×C4⋊Dic71C2313yes—
142C2×C4⋊Dic71C2311yescharacteristic
143C2×C4⋊Dic71C2313yes—
144C2×Dic71⋊C4C2313yes—
145C2×Dic71⋊C4C2311yescharacteristic
146C2×Dic71⋊C4C2311yescharacteristic
147C2×Dic71⋊C4C2311yescharacteristic
148C2×Dic71⋊C4C2316yes—
149C2×Dic71⋊C4C2311yescharacteristic
150C2×Dic71⋊C4C2313yes—
151C4⋊C4×D71C23124yes—
152C2×C22⋊Dic71C2313yes—
153C2×C22⋊Dic71C2313yes—
154C2×(C2×D71)⋊C4C2313yes—
155C2×(C2×D71)⋊C4C2313yes—
156C2×(C2×D71)⋊C4C2316yes—
157C2×(C2×D71)⋊C4C2313yes—
158C2×(C2×D71)⋊C4C2313yes—
159C2×(C2×D71)⋊C4C2313yes—
160C2×(C2×D71)⋊C4C2313yes—
161C2×C4×Dic71C2311yescharacteristic
162C2×C4×Dic71C2313yes—
163C2×C4×Dic71C2313yes—
164C2×C4×Dic71C2313yes—
165C42×D71C23124yes—
166C2×#41×C71—28no—
167C2×#41×C71C2318yes—
168C22×Q8×C71C2311yescharacteristic
169C22×D4×C71C2313yes—
170C23×C4×C71C2313yes—
171C23×C4×C71C2316yes—
172C4×Q8×C71C2318yes—
173C4×Q8×C71C2318yes—
174C4×D4×C71C23124yes—
175C4×D4×C71C23124yes—
176#117×C71C23124yes—
177C2×C4⋊C4×C71C23124yes—
178C2×C4⋊C4×C71C2313yes—
179C2×C4⋊C4×C71C2313yes—
180C2×C4⋊C4×C71C2313yes—
181C2×C4⋊C4×C71C2311yescharacteristic
182C2×C22⋊C4×C71C2313yes—
183C2×C22⋊C4×C71C2313yes—
184C2×C42×C71C2313yes—
185C2×C42×C71C2313yes—
186C23×D71C2413yes—
187C23×D71C2413yes—
188#11765866—232no—
189#11765866—232no—
190#11765865—496no—
191C2×Dic142—212no—
192C2×Dic142C24112yes—
193C2×D284—212no—
194C2×D284—212no—
195C2×D284—46no—
196C2×D284—412no—
197C2×D284C24112yes—
198C2×D284C24112yes—
199C2×D284C24124yes—
200C2×D284C24112yes—
201C2×C22⋊D71—212no—
202C2×C22⋊D71—412no—
203C2×C22⋊D71—46no—
204C2×C22⋊D71—412no—
205C2×C22⋊D71C24112yes—
206C2×C22⋊D71C24124yes—
207C2×C22⋊D71C24124yes—
208C2×C22⋊D71C24112yes—
209C22×Dic71C2411yescharacteristic
210C22×Dic71C2411yescharacteristic
211C22×Dic71C2413yes—
212C22×Dic71C2413yes—
213C22×Dic71C2411yescharacteristic
214C22×Dic71C2411yescharacteristic
215C2×C4×D71—212no—
216C2×C4×D71—212no—
217C2×C4×D71—212no—
218C2×C4×D71—46no—
219C2×C4×D71—412no—
220C2×C4×D71C24112yes—
221C2×C4×D71C24112yes—
222C2×C4×D71C24112yes—
223C2×C4×D71C24124yes—
224C2×C4×D71C24112yes—
225C4⋊Dic71C24112yes—
226C4⋊Dic71C24112yes—
227C4⋊Dic71C2414yes—
228C4⋊Dic71C24112yes—
229Dic71⋊C4C24112yes—
230Dic71⋊C4C2414yes—
231Dic71⋊C4C2414yes—
232Dic71⋊C4C2414yes—
233Dic71⋊C4C24124yes—
234Dic71⋊C4C2414yes—
235Dic71⋊C4C24112yes—
236C22⋊Dic71C24112yes—
237C22⋊Dic71C24112yes—
238(C2×D71)⋊C4C24112yes—
239(C2×D71)⋊C4C24112yes—
240(C2×D71)⋊C4C24124yes—
241(C2×D71)⋊C4C24112yes—
242(C2×D71)⋊C4C24112yes—
243(C2×D71)⋊C4C24112yes—
244(C2×D71)⋊C4C24112yes—
245C4×Dic71C2414yes—
246C4×Dic71C24112yes—
247C4×Dic71C24112yes—
248C4×Dic71C24112yes—
249C24×C71C2413yes—
250#41×C71—232no—
251C2×Q8×C71#4118yescomplemented
252C2×Q8×C71C2414yes—
253C2×D4×C71—212no—
254C2×D4×C71C24112yes—
255C22×C4×C71—212no—
256C22×C4×C71—412no—
257C22×C4×C71C2411yescharacteristic
258C22×C4×C71C2413yes—
259C22×C4×C71C2411yescharacteristic
260C22×C4×C71C2413yes—
261C22×C4×C71C2411yescharacteristic
262C22×C4×C71C24112yes—
263C22×C4×C71C24124yes—
264C22×C4×C71C2413yes—
265C4⋊C4×C71C24112yes—
266C4⋊C4×C71C24112yes—
267C4⋊C4×C71C24112yes—
268C4⋊C4×C71C2414yes—
269C22⋊C4×C71C24112yes—
270C22⋊C4×C71C24112yes—
271C42×C71C24112yes—
272C42×C71C24112yes—
273C23×C71—26no—
274C23×C71—26no—
275C23×C71—26no—
276C23×C71C2516yes—
277C23×C71C2511yescharacteristic
278C22×D71—26no—
279C22×D71—26no—
280C22×D71—26no—
281C22×D71—26no—
282C22×D71—26no—
283C22×D71—26no—
284C22×D71C2516yes—
285C22×D71C2516yes—
286Q8×C71C2×#41116yescomplemented
287D4×C71—224no—
288C2×C4×C71—22no—
289C2×C4×C71—26no—
290C2×C4×C71—26no—
291C2×C4×C71—22no—
292C2×C4×C71—22no—
293C2×C4×C71—224no—
294C2×C4×C71—424no—
295C2×C4×C71C2×#41112yes—
296C2×C4×C71C2512yes—
297C2×C4×C71C2512yes—
298C2×C4×C71C2516yes—
299C2×C4×C71C2516yes—
300C2×C4×C71C2512yes—
301C2×C4×C71C2516yes—
302C22⋊D71—224no—
303C22⋊D71—424no—
304C22⋊D71—412no—
305C22⋊D71—424no—
306C2×Dic71—22no—
307C2×Dic71—22no—
308C2×Dic71—26no—
309C2×Dic71—26no—
310C2×Dic71—22no—
311C2×Dic71H(5,𝔽2)14yes—
312C2×Dic71C2512yes—
313C2×Dic71C2512yes—
314C2×Dic71C2516yes—
315C2×Dic71C2516yes—
316C2×Dic71C2512yes—
317C2×Dic71C2512yes—
318D284—224no—
319D284—224no—
320D284—412no—
321D284—424no—
322C4×D71—224no—
323C4×D71—224no—
324C4×D71—224no—
325C4×D71—412no—
326C4×D71—424no—
327Dic142—224no—
328C22×C71—26no—
329C22×C71—26no—
330C22×C71—26no—
331C22×C71—412no—
332C22×C71C22×#4112yes—
333C22×C71C2×H(5,𝔽2)12yes—
334C22×C71#58512yes—
335C22×C71C2611yescharacteristic
336C2×D71—26no—
337C2×D71—26no—
338C2×D71—26no—
339C2×D71—26no—
340C2×D71—26no—
341C2×D71—26no—
342C2×D71—412no—
343C2×D71—412no—
344C4×C71—22no—
345C4×C71—26no—
346C4×C71—26no—
347C4×C71—22no—
348C4×C71—22no—
349C4×C71C22×#41112yes—
350Dic71—22no—
351Dic71—22no—
352Dic71—26no—
353Dic71—26no—
354Dic71—22no—
355Dic71C2×H(5,𝔽2)14yes—
356C2×#3517—711nomaximal, Sylow
357C2×C71—46no—
358C2×C71#351714yescomplemented
359C2×C71C23×#4111yescharacteristic
360C2×C71C22×H(5,𝔽2)11yescharacteristic
361C2×C71C2×#58511yescharacteristic
362D71—46no—
363D71—46no—
364#3517—7132no—
365C2×#557—711no—
366C2×#553—713no—
367C2×#553—713no—
368C2×#550—711no—
369C2×#550—711no—
370C2×#550—711no—
371C2×#550—713no—
372C2×#547—713no—
373C2×#540—713no—
374C2×#540—713no—
375C2×#532—713no—
376C2×#529—713no—
377C2×#520—711no—
378C2×#520D7111yescharacteristic, complemented
379C2×C4×#41—711no—
380C71C2×#351711yescharacteristic, complemented, Sylow
381C22×#41—711no—
382C22×#41—711no—
383C22×#41—716no—
384C22×#41C2×D7111yescharacteristic
385#557—7116no—
386#553—7148no—
387#553—7148no—
388#550—7116no—
389#550—7116no—
390#550—7116no—
391#550—7148no—
392#547—7148no—
393#540—7148no—
394#540—7148no—
395#532—7148no—
396C2×C4⋊Q8—713no—
397C2×#127—713no—
398C2×#127—713no—
399C2×#127—713no—
400#529—7148no—
401C2×#126—713no—
402C2×#126—713no—
403C2×#125—711no—
404C2×#125—713no—
405C2×#125—713no—
406C2×#124—713no—
407C2×#123—716no—
408C2×#123—713no—
409C2×#123—716no—
410C2×#123—713no—
411C2×C22⋊Q8—713no—
412C2×#121—713no—
413C2×#121—713no—
414C2×#121—713no—
415C2×#121—716no—
416C2×#121—713no—
417C2×#121—713no—
418C2×#121—713no—
419C2×#121—713no—
420C2×#121—716no—
421C2×#121—716no—
422#520—7116no—
423#520C2×D71116yescomplemented
424C4×#41—7116no—
425C2×C4×Q8—711no—
426C2×C4×Q8—711no—
427C2×C4×Q8—713no—
428C2×C4×Q8C2×D7111yescharacteristic
429C2×C4×Q8C2×D7111yescharacteristic
430C2×C4×D4—713no—
431C2×C4×D4—713no—
432C2×C4×D4—716no—
433C2×C4×D4—713no—
434C2×C4×D4—713no—
435C2×C4×D4—713no—
436C2×C4×D4—713no—
437C2×C4×D4—713no—
438C2×C4×D4C2×D7113yes—
439C2×C4×D4C2×D7113yes—
440C2×#117—713no—
441C2×#117—713no—
442C2×#117C2×D7113yes—
443C22×C4⋊C4—713no—
444C22×C4⋊C4C2×D7113yes—
445C22×C42—713no—
446C2×#41—28no—
447C2×#41—28424no—
448C2×#41—718no—
449C2×#41—718no—
450C2×#41—7148no—
451C2×#41—1428no—
452C2×#41—1428no—
453C2×#41C22×D7118yes—
454C22×Q8—713no—
455C22×Q8C22×D7111yescharacteristic
456C22×D4—716no—
457C22×D4—713no—
458C22×D4—716no—
459C22×D4—713no—
460C22×D4—713no—
461C22×D4—716no—
462C22×D4—713no—
463C22×D4—713no—
464C22×D4C22×D7113yes—
465C23×C4—716no—
466C23×C4—713no—
467C23×C4—713no—
468C23×C4—713no—
469C23×C4—713no—
470C23×C4C22×D7113yes—
471C23×C4C22×D7116yes—
472C4⋊Q8—7124no—
473#127—7124no—
474#127—7124no—
475#127—7124no—
476#126—7124no—
477#126—7124no—
478#125—718no—
479#125—7124no—
480#125—7124no—
481#124—7124no—
482#123—7148no—
483#123—7124no—
484#123—7148no—
485#123—7124no—
486C22⋊Q8—7124no—
487#121—7124no—
488#121—7124no—
489#121—7124no—
490#121—7148no—
491#121—7124no—
492#121—7124no—
493#121—7124no—
494#121—7124no—
495#121—7148no—
496#121—7148no—
497C4×Q8—718no—
498C4×Q8—718no—
499C4×Q8—7124no—
500C4×Q8C22×D7118yes—
501C4×Q8C22×D7118yes—
502C4×D4—7124no—
503C4×D4—7124no—
504C4×D4—7148no—
505C4×D4—7124no—
506C4×D4—7124no—
507C4×D4—7124no—
508C4×D4—7124no—
509C4×D4—7124no—
510C4×D4C22×D71124yes—
511C4×D4C22×D71124yes—
512#117—7124no—
513#117—7124no—
514#117C22×D71124yes—
515C2×C4⋊C4—713no—
516C2×C4⋊C4—713no—
517C2×C4⋊C4—711no—
518C2×C4⋊C4—713no—
519C2×C4⋊C4—711no—
520C2×C4⋊C4—711no—
521C2×C4⋊C4—711no—
522C2×C4⋊C4—716no—
523C2×C4⋊C4—711no—
524C2×C4⋊C4—713no—
525C2×C4⋊C4—713no—
526C2×C4⋊C4—7124no—
527C2×C4⋊C4C22×D7113yes—
528C2×C4⋊C4C22×D7113yes—
529C2×C4⋊C4C22×D7113yes—
530C2×C4⋊C4C22×D71124yes—
531C2×C4⋊C4C22×D7111yescharacteristic
532C2×C22⋊C4—713no—
533C2×C22⋊C4—713no—
534C2×C22⋊C4—713no—
535C2×C22⋊C4—716no—
536C2×C22⋊C4—713no—
537C2×C22⋊C4—713no—
538C2×C22⋊C4—713no—
539C2×C22⋊C4—713no—
540C2×C22⋊C4—713no—
541C2×C22⋊C4C22×D7113yes—
542C2×C22⋊C4C22×D7113yes—
543C2×C42—713no—
544C2×C42—713no—
545C2×C42—713no—
546C2×C42—711no—
547C2×C42—7124no—
548C2×C42C22×D7113yes—
549C2×C42C22×D7113yes—
550C24—713no—
551C24—713no—
552C24C23×D7113yes—
553#41—232no—
554#41—28496no—
555#41—14232no—
556#41—14232no—
557C2×Q8—7112no—
558C2×Q8—14212no—
559C2×Q8#1176586518yescomplemented
560C2×Q8C23×D7114yes—
561C2×D4—212no—
562C2×D4—2846no—
563C2×D4—28412no—
564C2×D4—28412no—
565C2×D4—2846no—
566C2×D4—28412no—
567C2×D4—7124no—
568C2×D4—7112no—
569C2×D4—7124no—
570C2×D4—7112no—
571C2×D4—7112no—
572C2×D4—7124no—
573C2×D4—7112no—
574C2×D4—7112no—
575C2×D4—14212no—
576C2×D4—14212no—
577C2×D4—14212no—
578C2×D4C23×D71112yes—
579C22×C4—212no—
580C22×C4—412no—
581C22×C4—2846no—
582C22×C4—28412no—
583C22×C4—7112no—
584C22×C4—7124no—
585C22×C4—711no—
586C22×C4—711no—
587C22×C4—711no—
588C22×C4—713no—
589C22×C4—713no—
590C22×C4—711no—
591C22×C4—7112no—
592C22×C4—7112no—
593C22×C4—7112no—
594C22×C4—14212no—
595C22×C4—14212no—
596C22×C4—14212no—
597C22×C4C23×D71112yes—
598C22×C4C23×D7111yescharacteristic
599C22×C4C23×D7113yes—
600C22×C4C23×D7111yescharacteristic
601C22×C4C23×D7113yes—
602C22×C4C23×D7111yescharacteristic
603C22×C4C23×D71124yes—
604C22×C4C23×D7113yes—
605C4⋊C4—7112no—
606C4⋊C4—714no—
607C4⋊C4—714no—
608C4⋊C4—714no—
609C4⋊C4—7124no—
610C4⋊C4—714no—
611C4⋊C4—7112no—
612C4⋊C4—7112no—
613C4⋊C4—7112no—
614C4⋊C4—714no—
615C4⋊C4—7112no—
616C4⋊C4C23×D71112yes—
617C4⋊C4C23×D71112yes—
618C4⋊C4C23×D71112yes—
619C4⋊C4C23×D7114yes—
620C22⋊C4—7112no—
621C22⋊C4—7112no—
622C22⋊C4—7112no—
623C22⋊C4—7124no—
624C22⋊C4—7112no—
625C22⋊C4—7112no—
626C22⋊C4—7112no—
627C22⋊C4—7112no—
628C22⋊C4—7112no—
629C22⋊C4C23×D71112yes—
630C22⋊C4C23×D71112yes—
631C42—714no—
632C42—7112no—
633C42—7112no—
634C42—7112no—
635C42C23×D71112yes—
636C42C23×D71112yes—
637C23—26no—
638C23—26no—
639C23—26no—
640C23—716no—
641C23—716no—
642C23—1426no—
643C23—1426no—
644C23—1426no—
645C23—1426no—
646C23—1426no—
647C23—1426no—
648C23C24×D7116yes—
649C23C24×D7111yescharacteristic
650Q8—14224no—
651Q8C2×#11765865116yescomplemented
652D4—224no—
653D4—28424no—
654D4—28412no—
655D4—28424no—
656D4—28424no—
657D4—28412no—
658D4—14224no—
659D4—14224no—
660D4—14224no—
661C2×C4—22no—
662C2×C4—26no—
663C2×C4—26no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—224no—
667C2×C4—424no—
668C2×C4—28424no—
669C2×C4—28412no—
670C2×C4—714no—
671C2×C4—712no—
672C2×C4—712no—
673C2×C4—712no—
674C2×C4—716no—
675C2×C4—716no—
676C2×C4—712no—
677C2×C4—14224no—
678C2×C4—1422no—
679C2×C4—1422no—
680C2×C4—1426no—
681C2×C4—1426no—
682C2×C4—1422no—
683C2×C4—14224no—
684C2×C4—14224no—
685C2×C4C2×#11765865112yes—
686C2×C4C24×D7112yes—
687C2×C4C24×D7116yes—
688C2×C4C24×D7112yes—
689C2×C4C24×D7116yes—
690C2×C4C24×D7112yes—
691C2×C4C24×D7116yes—
692C22—26no—
693C22—26no—
694C22—26no—
695C22—412no—
696C22—28412no—
697C22—28412no—
698C22—1426no—
699C22—1426no—
700C22—1426no—
701C22—1426no—
702C22—1426no—
703C22—1426no—
704C22C22×#1176586512yes—
705C22H(5,𝔽2)×D7112yes—
706C22#1798683612yes—
707C22C25×D7111yescharacteristic
708C4—22no—
709C4—26no—
710C4—26no—
711C4—22no—
712C4—22no—
713C4—714no—
714C4—1422no—
715C4—1422no—
716C4—1426no—
717C4—1426no—
718C4—1422no—
719C4C22×#11765865112yes—
720C2—46no—
721C2—2846no—
722C2—2846no—
723C2#2260234014yesdirect product factor
724C2C23×#1176586511yescharacteristic
725C2C2×H(5,𝔽2)×D7111yescharacteristic
726C2C2×#1798683611yescharacteristic
subgroupG/H
centerC23C24×D71
commutator, cosocleC22×C71C26
FrattiniC22C25×D71
FittingC2×#520×C71C2
socleC23×C71C25
hypercenterC2×#520D71
hypocenterC71C2×#3517
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. #22602340C2direct (N × H)
2. C2×#17986725C2semidirect
3. C2×#17986699C2semidirect
4. C2×#17986697C2semidirect
5. C2×#17986671C2semidirect
6. C2×#17986670C2semidirect
7. C2×#17986668C2semidirect
8. C2×#17986668C2semidirect
9. C2×#17986650C2semidirect
10. C2×#17986604C2semidirect
11. C2×#17986600C2semidirect
12. C2×#17986546C2semidirect
13. C2×#17986527C2semidirect
14. C2×#17986481C2semidirect
15. C2×C4×#11765866C2semidirect
16. C2×#520×C71C2semidirect
20. #17986725C22semidirect
21. #17986699C22semidirect
22. #17986697C22semidirect
23. #17986671C22semidirect
24. #17986670C22semidirect
25. #17986668C22semidirect
26. #17986668C22semidirect
27. #17986650C22semidirect
28. #17986604C22semidirect
29. #17986600C22semidirect
30. #17986546C22semidirect
35. #17986527C22semidirect
57. #17986481C22semidirect
58. C4×#11765866C22semidirect
75. #520×C71C22semidirect
251. C2×Q8×C71#41semidirect
286. Q8×C71C2×#41semidirect
358. C2×C71#3517semidirect
378. C2×#520D71semidirect
380. C71C2×#3517semidirect
423. #520C2×D71semidirect
559. C2×Q8#11765865semidirect
651. Q8C2×#11765865semidirect
723. C2#22602340direct (N × H)

Maximal subgroups

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

subgroupindex
#226023402
C2×#179867252
C2×#179866992
C2×#179866972
C2×#179866712
C2×#179866702
C2×#179866682
C2×#179866502
C2×#179866042
C2×#179866002
C2×#179865462
C2×#179865272
C2×#179864812
C2×C4×#117658662
C2×#520×C712
C2×#351771