Finite Group Databasebeta

← C2×#22600346 #32874154

Subgroups — C2×#22600346 #32874154

Order 18176.

2242 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
1C2×#17986695C211yesmaximal, characteristic, complemented
2#22600346C2116yesmaximal, direct product factor
3C2×#17986363C211yesmaximal, characteristic, complemented
4C2×#17986320C211yesmaximal, characteristic, complemented
5C2×#17986310C211yesmaximal, characteristic, complemented
6C2×#17986306C211yesmaximal, characteristic, complemented
7C2×#17986250C211yesmaximal, characteristic, complemented
8C2×#17986233C211yesmaximal, characteristic, complemented
9C2×#17986191C211yesmaximal, characteristic, complemented
10C2×#17986144C211yesmaximal, characteristic, complemented
11C2×#17986144C211yesmaximal, characteristic, complemented
12C2×#17986097C211yesmaximal, characteristic, complemented
13C2×#17986071C211yesmaximal, characteristic, complemented
14C2×#17986000C211yesmaximal, characteristic, complemented
15C2×#17985995C211yesmaximal, characteristic, complemented
16C2×#550×C71C211yesmaximal, characteristic, complemented
17C22×#11765852C2211yescharacteristic
18C22×#11765850C2211yescharacteristic
19C22×#11765850C2211yescharacteristic
20C22×#11765849C2211yescharacteristic
21C23×C71⋊C8C2211yescharacteristic
22#17986695—24no—
23#17986695C2218yescomplemented
24C2×#14556123—21no—
25C2×#14556120C2211yescharacteristic
26C2×#14556110—21no—
27C2×#14556102C2211yescharacteristic
28C2×#14556102C2211yescharacteristic
29C2×#14556100—21no—
30C2×C4×D284C2211yescharacteristic
31C2×(C22⋊D71)⋊C4—21no—
32C2×#14556087C2211yescharacteristic
33C22×C4⋊Dic71C2211yescharacteristic
34#17986363C2218yescomplemented
35#17986320C2218yescomplemented
36#17986310C2218yescomplemented
37#17986306C2218yescomplemented
38#17986250C2218yescomplemented
39#17986233C2218yescomplemented
40#17986191C2218yescomplemented
41#17986144C2218yescomplemented
42#17986144C2218yescomplemented
43#17986097C2218yescomplemented
44#17986071C2218yescomplemented
45C2×#14556061C2211yescharacteristic
46C2×#14556061C2211yescharacteristic
47C2×#14556059C2211yescharacteristic
48C2×C4⋊(C71⋊C8)C2211yescharacteristic
49#17986000C2218yescomplemented
50#17985995C2218yescomplemented
51C2×#14556052C2211yescharacteristic
52C2×#14556052C2211yescharacteristic
53C2×#14556052C2211yescharacteristic
54C2×#14556049C2211yescharacteristic
55C2×#14556049C2211yescharacteristic
56C2×#14556049C2211yescharacteristic
57C2×#14556049C2211yescharacteristic
58C2×#14556049C2211yescharacteristic
59C2×#14556049C2211yescharacteristic
60C2×#14556048C2211yescharacteristic
61C2×C22⋊(C71⋊C8)C2211yescharacteristic
62C2×C22⋊(C71⋊C8)C2211yescharacteristic
63C2×#14556039C2211yescharacteristic
64C22×#41×C71C2211yescharacteristic
65C22×#41×C71C2211yescharacteristic
66#550×C71—24no—
67#550×C71C2218yescomplemented
68C2×#127×C71—21no—
69C2×#127×C71C2211yescharacteristic
70C2×#121×C71—21no—
71C2×#121×C71—21no—
72C2×#121×C71C2211yescharacteristic
73C2×#121×C71C2211yescharacteristic
74C2×C4×Q8×C71C2211yescharacteristic
75C2×C4×D4×C71—21no—
76C2×C4×D4×C71C2211yescharacteristic
77C22×D284C2311yescharacteristic
78C22×C22⋊D71—21no—
79C22×C22⋊D71—21no—
80C23×Dic71—21no—
81C22×C4×D71—21no—
82C2×#11765852—24no—
83C2×#11765852C2314yes—
84C2×#11765850—42no—
85C2×#11765850—42no—
86C2×#11765850C2314yes—
87C2×#11765850C2314yes—
88C2×#11765849—42no—
89C2×#11765849C2314yes—
90C22×C71⋊C8—42no—
91C22×C71⋊C8C2311yescharacteristic
92C22×C71⋊C8C2311yescharacteristic
93C22×C71⋊C8C2311yescharacteristic
94C22×C71⋊C8C2311yescharacteristic
95C22×C71⋊C8C2314yes—
96#14556123—28no—
97#14556120—22no—
98#14556120C2314yes—
99#14556110—28no—
100#14556102—22no—
101#14556102—22no—
102#14556102C2314yes—
103#14556102C2314yes—
104#14556100—28no—
105C4×D284—22no—
106C4×D284C2314yes—
107(C22⋊D71)⋊C4—28no—
108#14556087—22no—
109#14556087C2314yes—
110C2×C4⋊Dic71—22no—
111C2×C4⋊Dic71—21no—
112C2×C4⋊Dic71C2314yes—
113C2×C4⋊Dic71C2311yescharacteristic
114C2×C4⋊Dic71C2311yescharacteristic
115C2×C4⋊Dic71C2311yescharacteristic
116C2×Dic71⋊C4—21no—
117C2×Dic71⋊C4—21no—
118C2×C22⋊Dic71—21no—
119C2×(C2×D71)⋊C4—21no—
120C2×(C2×D71)⋊C4—21no—
121C2×(C2×D71)⋊C4—21no—
122C2×C4×Dic71—21no—
123#14556061C2314yes—
124#14556061C2314yes—
125#14556059C2314yes—
126C4⋊(C71⋊C8)C2314yes—
127#14556052C2314yes—
128#14556052C2314yes—
129#14556052C2314yes—
130#14556049C2314yes—
131#14556049C2314yes—
132#14556049C2314yes—
133#14556049C2314yes—
134#14556049C2314yes—
135#14556049C2314yes—
136#14556048C2314yes—
137C22⋊(C71⋊C8)C2314yes—
138C22⋊(C71⋊C8)C2314yes—
139#14556039C2314yes—
140C2×#41×C71—22no—
141C2×#41×C71—22no—
142C2×#41×C71—24no—
143C2×#41×C71—24no—
144C2×#41×C71—42no—
145C2×#41×C71—42no—
146C2×#41×C71C2314yes—
147C2×#41×C71C2314yes—
148C22×Q8×C71C2311yescharacteristic
149C22×D4×C71—21no—
150C22×D4×C71—21no—
151C22×D4×C71—21no—
152C22×D4×C71—21no—
153C22×D4×C71—21no—
154C22×D4×C71—21no—
155C22×D4×C71D411yescharacteristic
156C22×D4×C71C2311yescharacteristic
157C22×D4×C71C2311yescharacteristic
158C23×C4×C71—21no—
159C23×C4×C71—21no—
160C23×C4×C71C2311yescharacteristic
161C23×C4×C71C2311yescharacteristic
162#127×C71—28no—
163#127×C71—22no—
164#127×C71C2314yes—
165#121×C71—22no—
166#121×C71—22no—
167#121×C71—28no—
168#121×C71—28no—
169#121×C71C2314yes—
170#121×C71C2314yes—
171C4×Q8×C71—22no—
172C4×Q8×C71C2314yes—
173C4×D4×C71—28no—
174C4×D4×C71D414yes—
175C4×D4×C71C2314yes—
176C2×C4⋊C4×C71—21no—
177C2×C4⋊C4×C71D411yescharacteristic
178C2×C4⋊C4×C71C2311yescharacteristic
179C2×C22⋊C4×C71—21no—
180C2×C22⋊C4×C71—21no—
181C2×C22⋊C4×C71D411yescharacteristic
182C2×C22⋊C4×C71D411yescharacteristic
183C2×C42×C71—21no—
184C2×C42×C71C2311yescharacteristic
185C23×D71—21no—
186C2×D284—22no—
187C2×D284—22no—
188C2×D284—21no—
189C2×D284C2412yes—
190C2×C22⋊D71—24no—
191C2×C22⋊D71—24no—
192C2×C22⋊D71—44no—
193C2×C22⋊D71—82no—
194C22×Dic71—21no—
195C22×Dic71—21no—
196C22×Dic71—21no—
197C22×Dic71—24no—
198C22×Dic71—82no—
199C2×C4×D71—24no—
200C2×C4×D71—82no—
201#11765852—28no—
202#11765850—44no—
203#11765850—44no—
204#11765849—44no—
205C2×C71⋊C8—22no—
206C2×C71⋊C8—22no—
207C2×C71⋊C8—22no—
208C2×C71⋊C8—22no—
209C2×C71⋊C8—44no—
210C2×C71⋊C8C2412yes—
211C2×C71⋊C8C2412yes—
212C2×C71⋊C8C2412yes—
213C2×C71⋊C8C2412yes—
214C4⋊Dic71—21no—
215C4⋊Dic71—21no—
216C4⋊Dic71—24no—
217C4⋊Dic71—21no—
218C4⋊Dic71C2412yes—
219C4⋊Dic71C2412yes—
220C4⋊Dic71C2412yes—
221Dic71⋊C4—24no—
222Dic71⋊C4—24no—
223C22⋊Dic71—24no—
224(C2×D71)⋊C4—24no—
225(C2×D71)⋊C4—24no—
226(C2×D71)⋊C4—24no—
227C4×Dic71—24no—
228C24×C71—21no—
229C24×C71—21no—
230C24×C71C2×D411yescharacteristic
231C24×C71C2×D411yescharacteristic
232#41×C71—28no—
233#41×C71—28no—
234#41×C71—44no—
235#41×C71—44no—
236#41×C71—48no—
237#41×C71—48no—
238C2×Q8×C71—21no—
239C2×Q8×C71—22no—
240C2×Q8×C71#4114yes—
241C2×Q8×C71C2412yes—
242C2×D4×C71—24no—
243C2×D4×C71—24no—
244C2×D4×C71—24no—
245C2×D4×C71—24no—
246C2×D4×C71—24no—
247C2×D4×C71—21no—
248C2×D4×C71—21no—
249C2×D4×C71—24no—
250C2×D4×C71—22no—
251C2×D4×C71—22no—
252C2×D4×C71—22no—
253C2×D4×C71—22no—
254C2×D4×C71—42no—
255C2×D4×C71—44no—
256C2×D4×C71—44no—
257C2×D4×C71—44no—
258C2×D4×C71—82no—
259C2×D4×C71—82no—
260C2×D4×C71—82no—
261C2×D4×C71C2×D414yes—
262C2×D4×C71C2412yes—
263C2×D4×C71C2412yes—
264C22×C4×C71—21no—
265C22×C4×C71—22no—
266C22×C4×C71—22no—
267C22×C4×C71—22no—
268C22×C4×C71—22no—
269C22×C4×C71—21no—
270C22×C4×C71—24no—
271C22×C4×C71—24no—
272C22×C4×C71—44no—
273C22×C4×C71—44no—
274C22×C4×C71C2×D411yescharacteristic
275C22×C4×C71C2×D411yescharacteristic
276C22×C4×C71C2×D411yescharacteristic
277C22×C4×C71C2×D411yescharacteristic
278C22×C4×C71C2×D412yes—
279C22×C4×C71C2×D412yes—
280C22×C4×C71C2412yes—
281C22×C4×C71C2412yes—
282C22×C4×C71C2411yescharacteristic
283C4⋊C4×C71—24no—
284C4⋊C4×C71—21no—
285C4⋊C4×C71C2×D414yes—
286C4⋊C4×C71C2412yes—
287C22⋊C4×C71—24no—
288C22⋊C4×C71—24no—
289C22⋊C4×C71C2×D414yes—
290C22⋊C4×C71C2×D414yes—
291C42×C71—24no—
292C42×C71C2×D412yes—
293C42×C71C2412yes—
294C23×C71—22no—
295C23×C71—22no—
296C23×C71—22no—
297C23×C71—22no—
298C23×C71—22no—
299C23×C71—22no—
300C23×C71—22no—
301C23×C71—22no—
302C23×C71—42no—
303C23×C71—42no—
304C23×C71—42no—
305C23×C71—42no—
306C23×C71—42no—
307C23×C71—42no—
308C23×C71C22×D412yes—
309C23×C71C22×D412yes—
310C23×C71C22×D411yescharacteristic
311C22×D71—22no—
312C22×D71—42no—
313C22×D71—42no—
314C22×D71—42no—
315Q8×C71—24no—
316Q8×C71—22no—
317Q8×C71C2×#4114yes—
318D4×C71—22no—
319D4×C71—22no—
320D4×C71—22no—
321D4×C71—22no—
322D4×C71—44no—
323D4×C71—48no—
324D4×C71—48no—
325D4×C71—48no—
326D4×C71—42no—
327D4×C71—42no—
328D4×C71—84no—
329D4×C71—84no—
330D4×C71—84no—
331C2×C4×C71—22no—
332C2×C4×C71—22no—
333C2×C4×C71—24no—
334C2×C4×C71—22no—
335C2×C4×C71—22no—
336C2×C4×C71—22no—
337C2×C4×C71—24no—
338C2×C4×C71—24no—
339C2×C4×C71—22no—
340C2×C4×C71—22no—
341C2×C4×C71—22no—
342C2×C4×C71—22no—
343C2×C4×C71—22no—
344C2×C4×C71—48no—
345C2×C4×C71—48no—
346C2×C4×C71—42no—
347C2×C4×C71C22×D412yes—
348C2×C4×C71C22×D412yes—
349C2×C4×C71C22×D412yes—
350C2×C4×C71C22×D412yes—
351C2×C4×C71C22×D411yescharacteristic
352C2×C4×C71C2×#4112yes—
353C2×C4×C71H(5,𝔽2)12yes—
354C2×C4×C71C2511yescharacteristic
355C22⋊D71—48no—
356C22⋊D71—84no—
357C2×Dic71—22no—
358C2×Dic71—22no—
359C2×Dic71—22no—
360C2×Dic71—42no—
361C2×Dic71—42no—
362C2×Dic71—42no—
363C2×Dic71—84no—
364D284—22no—
365D284—22no—
366D284—42no—
367C4×D71—84no—
368C71⋊C8—22no—
369C71⋊C8—22no—
370C71⋊C8—22no—
371C71⋊C8—22no—
372C22×C71—22no—
373C22×C71—22no—
374C22×C71—22no—
375C22×C71—22no—
376C22×C71—22no—
377C22×C71—22no—
378C22×C71—44no—
379C22×C71—44no—
380C22×C71—42no—
381C22×C71—42no—
382C22×C71—42no—
383C22×C71—42no—
384C22×C71—42no—
385C22×C71—42no—
386C22×C71—84no—
387C22×C71—84no—
388C22×C71#54612yes—
389C22×C71#57512yes—
390C22×C71#57612yes—
391C22×C71C23×D411yescharacteristic
392C2×D71—42no—
393C2×D71—42no—
394C2×D71—42no—
395C2×D71—84no—
396C4×C71—22no—
397C4×C71—22no—
398C4×C71—24no—
399C4×C71—22no—
400C4×C71—22no—
401C4×C71—42no—
402C4×C71#54612yes—
403C4×C71C22×#4111yescharacteristic
404C4×C71C2×H(5,𝔽2)11yescharacteristic
405Dic71—42no—
406Dic71—42no—
407Dic71—42no—
408C2×#3309—711nomaximal, Sylow
409C2×C71—42no—
410C2×C71—42no—
411C2×C71—82no—
412C2×C71—82no—
413C2×C71#330914yescomplemented
414C2×C71C2×#54611yescharacteristic
415C2×C71C2×#57511yescharacteristic
416C2×C71C2×#57611yescharacteristic
417D71—82no—
418C2×#553—711no—
419C2×#550D7111yescharacteristic, complemented
420#3309—7116no—
421C2×#490—711no—
422C2×#482—711no—
423C2×#480—711no—
424C2×#479—711no—
425C2×#469—711no—
426C2×#466—711no—
427C2×#459—711no—
428C2×#449—711no—
429C2×#449—711no—
430C2×#440—711no—
431C2×#435—711no—
432C2×#417—711no—
433C2×#416—711no—
434C71C2×#330911yescharacteristic, complemented, Sylow
435C22×#41C2×D7111yescharacteristic
436C22×#41C2×D7111yescharacteristic
437C22×SD16—711no—
438C22×D8—711no—
439C22×D8—711no—
440C22×M16—711no—
441C23×C8—711no—
442#553—718no—
443#553—1424no—
444#550—24no—
445#550C2×D7118yescomplemented
446C2×#127—21no—
447C2×#127C2×D7111yescharacteristic
448C2×#126—1421no—
449C2×#125—711no—
450C2×#123—1421no—
451C2×#121—21no—
452C2×#121—21no—
453C2×#121—711no—
454C2×#121—711no—
455C2×#121—1421no—
456C2×#121C2×D7111yescharacteristic
457C2×#121C2×D7111yescharacteristic
458C2×C4×Q8C2×D7111yescharacteristic
459C2×C4×D4—21no—
460C2×C4×D4—711no—
461C2×C4×D4—1421no—
462C2×C4×D4C2×D7111yescharacteristic
463C2×#117—711no—
464C22×C4⋊C4—711no—
465#490—718no—
466#482—718no—
467#480—718no—
468#479—718no—
469#469—718no—
470#466—718no—
471#459—718no—
472#449—718no—
473#449—718no—
474#440—718no—
475#435—718no—
476C2×#107—711no—
477C2×#107—711no—
478C2×#106—711no—
479C2×C4⋊C8—711no—
480#417—718no—
481#416—718no—
482C2×#103—711no—
483C2×#103—711no—
484C2×#103—711no—
485C2×#102—711no—
486C2×#102—711no—
487C2×#102—711no—
488C2×#102—711no—
489C2×#102—711no—
490C2×#102—711no—
491C2×#102—711no—
492C2×C22⋊C8—711no—
493C2×C22⋊C8—711no—
494C2×#97—711no—
495C2×#41—22no—
496C2×#41—22no—
497C2×#41—24no—
498C2×#41—24no—
499C2×#41—42no—
500C2×#41—42no—
501C2×#41C22×D7114yes—
502C2×#41C22×D7114yes—
503C22×Q8C22×D7111yescharacteristic
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—711no—
511C22×D4—1421no—
512C22×D4—1421no—
513C22×D4C22⋊D7111yescharacteristic
514C22×D4C22×D7111yescharacteristic
515C22×D4C22×D7111yescharacteristic
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—1421no—
519C23×C4—1421no—
520C23×C4C22×D7111yescharacteristic
521C23×C4C22×D7111yescharacteristic
522C2×SD16—714no—
523C2×SD16—1424no—
524C2×D8—2842no—
525C2×D8—2842no—
526C2×D8—714no—
527C2×D8—714no—
528C2×M16—2842no—
529C2×M16—714no—
530C22×C8—2842no—
531C22×C8—714no—
532C22×C8—711no—
533C22×C8—711no—
534C22×C8—711no—
535C22×C8—711no—
536#127—28no—
537#127—22no—
538#127C22×D7114yes—
539#126—1428no—
540#125—714no—
541#125—1422no—
542#123—1428no—
543#121—22no—
544#121—22no—
545#121—28no—
546#121—28no—
547#121—714no—
548#121—714no—
549#121—1428no—
550#121—1422no—
551#121—1422no—
552#121C22×D7114yes—
553#121C22×D7114yes—
554C4×Q8—22no—
555C4×Q8C22×D7114yes—
556C4×D4—28no—
557C4×D4—714no—
558C4×D4—1428no—
559C4×D4—1422no—
560C4×D4C22⋊D7114yes—
561C4×D4C22×D7114yes—
562#117—714no—
563#117—1422no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—711no—
566C2×C4⋊C4—711no—
567C2×C4⋊C4—714no—
568C2×C4⋊C4—711no—
569C2×C4⋊C4—1421no—
570C2×C4⋊C4—1422no—
571C2×C4⋊C4—1421no—
572C2×C4⋊C4—1421no—
573C2×C4⋊C4C22⋊D7111yescharacteristic
574C2×C4⋊C4C22×D7111yescharacteristic
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4—1421no—
578C2×C22⋊C4—1421no—
579C2×C22⋊C4—1421no—
580C2×C22⋊C4—1421no—
581C2×C22⋊C4C22⋊D7111yescharacteristic
582C2×C22⋊C4C22⋊D7111yescharacteristic
583C2×C42—21no—
584C2×C42—1421no—
585C2×C42C22×D7111yescharacteristic
586#107—714no—
587#107—714no—
588#106—714no—
589C4⋊C8—714no—
590#103—714no—
591#103—714no—
592#103—714no—
593#102—714no—
594#102—714no—
595#102—714no—
596#102—714no—
597#102—714no—
598#102—714no—
599#102—714no—
600C22⋊C8—714no—
601C22⋊C8—714no—
602#97—714no—
603C24—21no—
604C24—21no—
605C24—1421no—
606C24C2×C22⋊D7111yescharacteristic
607C24C2×C22⋊D7111yescharacteristic
608#41—28no—
609#41—28no—
610#41—44no—
611#41—44no—
612#41—48no—
613#41—48no—
614C2×Q8—21no—
615C2×Q8—22no—
616C2×Q8#1176586414yes—
617C2×Q8C23×D7112yes—
618C2×D4—24no—
619C2×D4—24no—
620C2×D4—24no—
621C2×D4—24no—
622C2×D4—24no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—24no—
626C2×D4—22no—
627C2×D4—22no—
628C2×D4—22no—
629C2×D4—22no—
630C2×D4—42no—
631C2×D4—44no—
632C2×D4—44no—
633C2×D4—44no—
634C2×D4—82no—
635C2×D4—82no—
636C2×D4—82no—
637C2×D4—2844no—
638C2×D4—5682no—
639C2×D4—712no—
640C2×D4—1424no—
641C2×D4—1424no—
642C2×D4—1421no—
643C2×D4—1422no—
644C2×D4—1422no—
645C2×D4C2×C22⋊D7114yes—
646C2×D4C23×D7112yes—
647C2×D4C23×D7112yes—
648C22×C4—21no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—21no—
654C22×C4—24no—
655C22×C4—24no—
656C22×C4—44no—
657C22×C4—44no—
658C22×C4—5682no—
659C22×C4—5682no—
660C22×C4—1421no—
661C22×C4—1421no—
662C22×C4—1421no—
663C22×C4—1424no—
664C22×C4—1424no—
665C22×C4C2×C22⋊D7112yes—
666C22×C4C2×C22⋊D7112yes—
667C22×C4C2×C22⋊D7111yescharacteristic
668C22×C4C2×C22⋊D7111yescharacteristic
669C22×C4C2×C22⋊D7111yescharacteristic
670C22×C4C2×C22⋊D7111yescharacteristic
671C22×C4C23×D7112yes—
672C22×C4C23×D7112yes—
673C22×C4C23×D7111yescharacteristic
674SD16—1428no—
675D8—2844no—
676D8—2844no—
677M16—2844no—
678C2×C8—2844no—
679C2×C8—712no—
680C2×C8—712no—
681C2×C8—712no—
682C2×C8—712no—
683C2×C8—1422no—
684C2×C8—1422no—
685C2×C8—1422no—
686C2×C8—1422no—
687C4⋊C4—24no—
688C4⋊C4—21no—
689C4⋊C4—712no—
690C4⋊C4—712no—
691C4⋊C4—712no—
692C4⋊C4—1424no—
693C4⋊C4—1424no—
694C4⋊C4—1421no—
695C4⋊C4—1421no—
696C4⋊C4—1424no—
697C4⋊C4—1421no—
698C4⋊C4C2×C22⋊D7114yes—
699C4⋊C4C23×D7112yes—
700C22⋊C4—24no—
701C22⋊C4—24no—
702C22⋊C4—1424no—
703C22⋊C4—1424no—
704C22⋊C4—1424no—
705C22⋊C4—1424no—
706C22⋊C4C2×C22⋊D7114yes—
707C22⋊C4C2×C22⋊D7114yes—
708C42—24no—
709C42—1424no—
710C42C2×C22⋊D7112yes—
711C42C23×D7112yes—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—2842no—
727C23—2842no—
728C23—2842no—
729C23—1422no—
730C23C22×C22⋊D7112yes—
731C23C22×C22⋊D7112yes—
732C23C22×C22⋊D7111yescharacteristic
733Q8—22no—
734Q8—24no—
735Q8C2×#1176586414yes—
736D4—22no—
737D4—22no—
738D4—22no—
739D4—22no—
740D4—44no—
741D4—48no—
742D4—48no—
743D4—48no—
744D4—42no—
745D4—42no—
746D4—84no—
747D4—84no—
748D4—84no—
749D4—2848no—
750D4—2842no—
751D4—5684no—
752D4—1422no—
753D4—1422no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—24no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—22no—
767C2×C4—48no—
768C2×C4—48no—
769C2×C4—42no—
770C2×C4—2842no—
771C2×C4—2842no—
772C2×C4—2842no—
773C2×C4—5684no—
774C2×C4—5684no—
775C2×C4—1422no—
776C2×C4—1422no—
777C2×C4—1422no—
778C2×C4C22×C22⋊D7112yes—
779C2×C4C22×C22⋊D7112yes—
780C2×C4C22×C22⋊D7112yes—
781C2×C4C22×C22⋊D7112yes—
782C2×C4C22×C22⋊D7111yescharacteristic
783C2×C4C2×#1176586412yes—
784C2×C4#1455617312yes—
785C2×C4C24×D7111yescharacteristic
786C8—1422no—
787C8—1422no—
788C8—1422no—
789C8—1422no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—44no—
797C22—44no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—42no—
803C22—42no—
804C22—84no—
805C22—84no—
806C22—2842no—
807C22—2842no—
808C22—2842no—
809C22—5684no—
810C22#1798664312yes—
811C22#1798679712yes—
812C22#1798680212yes—
813C22C23×C22⋊D7111yescharacteristic
814C4—22no—
815C4—22no—
816C4—24no—
817C4—22no—
818C4—22no—
819C4—42no—
820C4—2842no—
821C4—2842no—
822C4—2842no—
823C4#1798664312yes—
824C4C22×#1176586411yescharacteristic
825C4C2×#1455617311yescharacteristic
826C2—42no—
827C2—42no—
828C2—82no—
829C2—82no—
830C2—5682no—
831C2#2260034614yesdirect product factor
832C2C2×#1798664311yescharacteristic
833C2C2×#1798679711yescharacteristic
834C2C2×#1798680211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#550×C71C2
socleC23×C71C22×D4
hypercenterC2×#550D71
hypocenterC71C2×#3309
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C2×#17986695C2semidirect
2. #22600346C2direct (N × H)
3. C2×#17986363C2semidirect
4. C2×#17986320C2semidirect
5. C2×#17986310C2semidirect
6. C2×#17986306C2semidirect
7. C2×#17986250C2semidirect
8. C2×#17986233C2semidirect
9. C2×#17986191C2semidirect
10. C2×#17986144C2semidirect
11. C2×#17986144C2semidirect
12. C2×#17986097C2semidirect
13. C2×#17986071C2semidirect
14. C2×#17986000C2semidirect
15. C2×#17985995C2semidirect
16. C2×#550×C71C2semidirect
23. #17986695C22semidirect
34. #17986363C22semidirect
35. #17986320C22semidirect
36. #17986310C22semidirect
37. #17986306C22semidirect
38. #17986250C22semidirect
39. #17986233C22semidirect
40. #17986191C22semidirect
41. #17986144C22semidirect
42. #17986144C22semidirect
43. #17986097C22semidirect
44. #17986071C22semidirect
49. #17986000C22semidirect
50. #17985995C22semidirect
67. #550×C71C22semidirect
413. C2×C71#3309semidirect
419. C2×#550D71semidirect
434. C71C2×#3309semidirect
445. #550C2×D71semidirect
831. C2#22600346direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179866952
#226003462
C2×#179863632
C2×#179863202
C2×#179863102
C2×#179863062
C2×#179862502
C2×#179862332
C2×#179861912
C2×#179861442
C2×#179860972
C2×#179860712
C2×#179860002
C2×#179859952
C2×#550×C712
C2×#330971