Finite Group Databasebeta

← C2×#22599002 #32867314

Subgroups — C2×#22599002 #32867314

Order 18176.

1906 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986611C211yesmaximal, characteristic, complemented
2#22599002C2116yesmaximal, direct product factor
3C2×#17986405C211yesmaximal, characteristic, complemented
4C2×#17986394C211yesmaximal, characteristic, complemented
5C2×#17986353C211yesmaximal, characteristic, complemented
6C2×#17986351C211yesmaximal, characteristic, complemented
7C2×#17986255C211yesmaximal, characteristic, complemented
8C2×#17986243C211yesmaximal, characteristic
9C2×#17986238C211yesmaximal, characteristic, complemented
10C2×#17986226C211yesmaximal, characteristic
11C2×#17986104C211yesmaximal, characteristic, complemented
12C2×#17986099C211yesmaximal, characteristic, complemented
13C2×C4×#11765855C211yesmaximal, characteristic, complemented
14C2×C4×#11765853C211yesmaximal, characteristic, complemented
15C2×#17985955C211yesmaximal, characteristic, complemented
16C2×#542×C71C211yesmaximal, characteristic
17C22×#11765855C2211yescharacteristic
18C22×#11765855C2211yescharacteristic
19C22×#11765853C2211yescharacteristic
20C22×#11765853C2211yescharacteristic
21C22×#11765849C2211yescharacteristic
22C23×C71⋊C8C2211yescharacteristic
23#17986611—24no—
24#17986611C2218yescomplemented
25C2×#14556128C2211yescharacteristic
26C2×#14556121—21no—
27C2×#14556121—21no—
28C2×#14556120C2211yescharacteristic
29C2×#14556118—21no—
30C2×#14556118—21no—
31C2×#14556107C2211yescharacteristic
32C2×#14556107C2211yescharacteristic
33C2×C4×Dic142C2211yescharacteristic
34C2×C4×Dic142C2211yescharacteristic
35#17986405C2218yescomplemented
36#17986394C2218yescomplemented
37#17986353C2218yescomplemented
38#17986351C2218yescomplemented
39#17986255C2218yescomplemented
40#17986243C2218yes—
41#17986238C2218yescomplemented
42#17986226C2218yes—
43#17986104C2218yescomplemented
44#17986099C2218yescomplemented
45C4×#11765855C2218yescomplemented
46C4×#11765853C2218yescomplemented
47C2×#14556061C2211yescharacteristic
48C2×#14556061C2211yescharacteristic
49C2×#14556059C2211yescharacteristic
50C2×#14556059C2211yescharacteristic
51C2×#14556052C2211yescharacteristic
52C2×#14556052C2211yescharacteristic
53C2×#14556051C2211yescharacteristic
54C2×#14556051C2211yescharacteristic
55C2×#14556051C2211yescharacteristic
56C2×#14556051C2211yescharacteristic
57C2×#14556049C2211yescharacteristic
58C2×#14556049C2211yescharacteristic
59#17985955C2218yescomplemented
60C2×#14556039C2211yescharacteristic
61C2×#14556039C2211yescharacteristic
62C2×C4×C71⋊C8C2211yescharacteristic
63C2×C4×C71⋊C8C2211yescharacteristic
64#542×C71—24no—
65#542×C71C2218yes—
66C2×C4⋊Q8×C71C2211yescharacteristic
67C2×#126×C71—21no—
68C2×#124×C71—21no—
69C2×#124×C71C2211yescharacteristic
70C2×#123×C71—21no—
71C2×C22⋊Q8×C71—21no—
72C2×C22⋊Q8×C71C2211yescharacteristic
73C2×#121×C71C2211yescharacteristic
74C2×C4×Q8×C71C2211yescharacteristic
75C2×C4×D4×C71C2211yescharacteristic
76C2×#117×C71C2211yescharacteristic
77C22×Dic142C2311yescharacteristic
78C22×Dic142C2311yescharacteristic
79C2×#11765855—24no—
80C2×#11765855—24no—
81C2×#11765855C2314yes—
82C2×#11765855C2314yes—
83C2×#11765853—24no—
84C2×#11765853—24no—
85C2×#11765853C2314yes—
86C2×#11765853C2314yes—
87C2×#11765849—24no—
88C2×#11765849C2314yes—
89C22×C71⋊C8—24no—
90C22×C71⋊C8C2311yescharacteristic
91C22×C71⋊C8C2311yescharacteristic
92C22×C71⋊C8C2314yes—
93C22×C71⋊C8C2311yescharacteristic
94C22×C71⋊C8C2311yescharacteristic
95#14556128—22no—
96#14556128C2314yes—
97#14556121—28no—
98#14556121—28no—
99#14556120—22no—
100#14556120C2314yes—
101#14556118—28no—
102#14556118—28no—
103#14556107—22no—
104#14556107—22no—
105#14556107C2314yes—
106#14556107C2314yes—
107C4×Dic142—22no—
108C4×Dic142—22no—
109C4×Dic142C2314yes—
110C4×Dic142C2314yes—
111C2×C4⋊Dic71—21no—
112C2×C4⋊Dic71—21no—
113C2×C4⋊Dic71C2311yescharacteristic
114C2×C4⋊Dic71C2311yescharacteristic
115C2×Dic71⋊C4—21no—
116C2×Dic71⋊C4—21no—
117C2×Dic71⋊C4—21no—
118C2×Dic71⋊C4—21no—
119C2×Dic71⋊C4—21no—
120C2×Dic71⋊C4—21no—
121C2×C22⋊Dic71—21no—
122C2×C22⋊Dic71—21no—
123C2×C4×Dic71—21no—
124C2×C4×Dic71—21no—
125#14556061C2314yes—
126#14556061C2314yes—
127#14556059C2314yes—
128#14556059C2314yes—
129#14556052C2314yes—
130#14556052C2314yes—
131#14556051C2314yes—
132#14556051C2314yes—
133#14556051C2314yes—
134#14556051C2314yes—
135#14556049C2314yes—
136#14556049C2314yes—
137#14556039C2314yes—
138#14556039C2314yes—
139C4×C71⋊C8C2314yes—
140C4×C71⋊C8C2314yes—
141C22×Q8×C71—21no—
142C22×Q8×C71C2311yescharacteristic
143C22×D4×C71—21no—
144C22×D4×C71C2311yescharacteristic
145C23×C4×C71—21no—
146C23×C4×C71C2311yescharacteristic
147C4⋊Q8×C71—22no—
148C4⋊Q8×C71C2314yes—
149#126×C71—28no—
150#124×C71—28no—
151#124×C71—22no—
152#124×C71C2314yes—
153#123×C71—28no—
154C22⋊Q8×C71—22no—
155C22⋊Q8×C71—28no—
156C22⋊Q8×C71C2314yes—
157#121×C71—22no—
158#121×C71C2314yes—
159C4×Q8×C71—22no—
160C4×Q8×C71C2314yes—
161C4×D4×C71—22no—
162C4×D4×C71C2314yes—
163#117×C71D414yes—
164#117×C71C2314yes—
165C2×C4⋊C4×C71—21no—
166C2×C4⋊C4×C71—21no—
167C2×C4⋊C4×C71—21no—
168C2×C4⋊C4×C71D411yescharacteristic
169C2×C4⋊C4×C71D411yescharacteristic
170C2×C4⋊C4×C71C2311yescharacteristic
171C2×C4⋊C4×C71C2311yescharacteristic
172C2×C22⋊C4×C71—21no—
173C2×C22⋊C4×C71—21no—
174C2×C22⋊C4×C71—21no—
175C2×C22⋊C4×C71—21no—
176C2×C22⋊C4×C71—21no—
177C2×C22⋊C4×C71D411yescharacteristic
178C2×C22⋊C4×C71D411yescharacteristic
179C2×C42×C71—21no—
180C2×C42×C71C2311yescharacteristic
181C2×C42×C71C2311yescharacteristic
182C2×Dic142—22no—
183C2×Dic142—22no—
184C2×Dic142—22no—
185C2×Dic142—22no—
186C2×Dic142—21no—
187C2×Dic142—21no—
188C2×Dic142C2412yes—
189C2×Dic142C2412yes—
190C22×Dic71—21no—
191C22×Dic71—21no—
192C22×Dic71—21no—
193C22×Dic71—21no—
194#11765855—28no—
195#11765855—28no—
196#11765853—28no—
197#11765853—28no—
198#11765849—28no—
199C2×C71⋊C8—22no—
200C2×C71⋊C8—22no—
201C2×C71⋊C8—28no—
202C2×C71⋊C8#4114yes—
203C2×C71⋊C8#4114yes—
204C2×C71⋊C8C2412yes—
205C2×C71⋊C8C2412yes—
206C2×C71⋊C8C2412yes—
207C2×C71⋊C8C2412yes—
208C4⋊Dic71—24no—
209C4⋊Dic71—24no—
210C4⋊Dic71—21no—
211C4⋊Dic71—21no—
212C4⋊Dic71C2412yes—
213C4⋊Dic71C2412yes—
214Dic71⋊C4—24no—
215Dic71⋊C4—24no—
216Dic71⋊C4—24no—
217Dic71⋊C4—24no—
218Dic71⋊C4—24no—
219Dic71⋊C4—24no—
220C22⋊Dic71—24no—
221C22⋊Dic71—24no—
222C4×Dic71—24no—
223C4×Dic71—24no—
224C24×C71—21no—
225C24×C71C2×D411yescharacteristic
226C2×Q8×C71—21no—
227C2×Q8×C71—24no—
228C2×Q8×C71—22no—
229C2×Q8×C71—22no—
230C2×Q8×C71—82no—
231C2×Q8×C71C2412yes—
232C2×D4×C71—24no—
233C2×D4×C71—21no—
234C2×D4×C71—22no—
235C2×D4×C71—22no—
236C2×D4×C71—82no—
237C2×D4×C71C2412yes—
238C22×C4×C71—22no—
239C22×C4×C71—22no—
240C22×C4×C71—21no—
241C22×C4×C71—21no—
242C22×C4×C71—21no—
243C22×C4×C71—24no—
244C22×C4×C71—82no—
245C22×C4×C71C2×D411yescharacteristic
246C22×C4×C71C2×D411yescharacteristic
247C22×C4×C71C2×D411yescharacteristic
248C22×C4×C71C2×D411yescharacteristic
249C22×C4×C71C2×D411yescharacteristic
250C22×C4×C71C2×D412yes—
251C22×C4×C71C2412yes—
252C22×C4×C71C2411yescharacteristic
253C4⋊C4×C71—24no—
254C4⋊C4×C71—24no—
255C4⋊C4×C71—24no—
256C4⋊C4×C71—21no—
257C4⋊C4×C71—21no—
258C4⋊C4×C71C2×D414yes—
259C4⋊C4×C71C2×D414yes—
260C4⋊C4×C71C2412yes—
261C4⋊C4×C71C2412yes—
262C22⋊C4×C71—24no—
263C22⋊C4×C71—24no—
264C22⋊C4×C71—24no—
265C22⋊C4×C71—24no—
266C22⋊C4×C71—24no—
267C22⋊C4×C71C2×D414yes—
268C22⋊C4×C71C2×D414yes—
269C42×C71—24no—
270C42×C71C2×D412yes—
271C42×C71C2×D412yes—
272C42×C71C2412yes—
273C42×C71C2412yes—
274C23×C71—22no—
275C23×C71—22no—
276C23×C71—22no—
277C23×C71—22no—
278C23×C71—42no—
279C23×C71—42no—
280C23×C71—42no—
281C23×C71C22×D412yes—
282C23×C71C22×D411yescharacteristic
283Q8×C71—22no—
284Q8×C71—22no—
285Q8×C71—42no—
286Q8×C71—84no—
287D4×C71—22no—
288D4×C71—22no—
289D4×C71—42no—
290D4×C71—84no—
291C2×C4×C71—22no—
292C2×C4×C71—22no—
293C2×C4×C71—22no—
294C2×C4×C71—22no—
295C2×C4×C71—22no—
296C2×C4×C71—24no—
297C2×C4×C71—22no—
298C2×C4×C71—22no—
299C2×C4×C71—22no—
300C2×C4×C71—22no—
301C2×C4×C71—22no—
302C2×C4×C71—42no—
303C2×C4×C71—42no—
304C2×C4×C71—42no—
305C2×C4×C71—84no—
306C2×C4×C71C22×D412yes—
307C2×C4×C71C22×D412yes—
308C2×C4×C71C22×D412yes—
309C2×C4×C71C22×D412yes—
310C2×C4×C71C22×D412yes—
311C2×C4×C71C22×D411yescharacteristic
312C2×C4×C71C2×#4112yes—
313C2×C4×C71C2×#4112yes—
314C2×C4×C71C2511yescharacteristic
315C2×Dic71—22no—
316C2×Dic71—22no—
317C2×Dic71—22no—
318C2×Dic71—22no—
319C2×Dic71—42no—
320C2×Dic71—42no—
321C2×Dic71—42no—
322C2×Dic71—42no—
323Dic142—22no—
324Dic142—22no—
325Dic142—22no—
326Dic142—22no—
327Dic142—42no—
328Dic142—42no—
329C71⋊C8—22no—
330C71⋊C8—22no—
331C71⋊C8C2×#4114yes—
332C71⋊C8C2×#4114yes—
333C22×C71—22no—
334C22×C71—22no—
335C22×C71—22no—
336C22×C71—44no—
337C22×C71—42no—
338C22×C71—42no—
339C22×C71—42no—
340C22×C71—84no—
341C22×C71#53212yes—
342C22×C71#57712yes—
343C22×C71#57812yes—
344C22×C71C23×D411yescharacteristic
345C4×C71—22no—
346C4×C71—22no—
347C4×C71—22no—
348C4×C71—22no—
349C4×C71—22no—
350C4×C71—42no—
351C4×C71—42no—
352C4×C71—42no—
353C4×C71#53212yes—
354C4×C71C22×#4111yescharacteristic
355C4×C71C22×#4111yescharacteristic
356Dic71—42no—
357Dic71—42no—
358Dic71—42no—
359Dic71—42no—
360C2×#3178—711nomaximal, Sylow
361C2×C71—42no—
362C2×C71—82no—
363C2×C71#317814yescomplemented
364C2×C71C2×#53211yescharacteristic
365C2×C71C2×#57711yescharacteristic
366C2×C71C2×#57811yescharacteristic
367C2×#542D7111yescharacteristic
368C2×#541—711no—
369#3178—7116no—
370C2×#501—711no—
371C2×#497—711no—
372C2×#488—711no—
373C2×#487—711no—
374C2×#470—711no—
375C2×#468—711no—
376C2×#467—711no—
377C2×#465—711no—
378C2×#441—711no—
379C2×#440—711no—
380C2×C4×Q16—711no—
381C2×C4×SD16—711no—
382C2×#405—711no—
383C71C2×#317811yescharacteristic, complemented, Sylow
384C22×Q16—711no—
385C22×Q16—711no—
386C22×SD16—711no—
387C22×SD16—711no—
388C22×M16—711no—
389C23×C8—711no—
390#542—24no—
391#542C2×D7118yes—
392#541—718no—
393#541—1424no—
394C2×C4⋊Q8—711no—
395C2×C4⋊Q8C2×D7111yescharacteristic
396C2×#126—21no—
397C2×#126—1421no—
398C2×#126—1421no—
399C2×#125—711no—
400C2×#125—1421no—
401C2×#125—1421no—
402C2×#124—21no—
403C2×#124C2×D7111yescharacteristic
404C2×#123—21no—
405C2×C22⋊Q8—21no—
406C2×C22⋊Q8—711no—
407C2×C22⋊Q8—711no—
408C2×C22⋊Q8C2×D7111yescharacteristic
409C2×#121C2×D7111yescharacteristic
410C2×C4×Q8—711no—
411C2×C4×Q8—711no—
412C2×C4×Q8C2×D7111yescharacteristic
413C2×C4×D4C2×D7111yescharacteristic
414C2×#117C2×D7111yescharacteristic
415#501—718no—
416#497—718no—
417#488—718no—
418#487—718no—
419#470—718no—
420#468—718no—
421#467—718no—
422#465—718no—
423#441—718no—
424#440—718no—
425C4×Q16—718no—
426C4×SD16—718no—
427C2×#107—711no—
428C2×#107—711no—
429C2×#106—711no—
430C2×#106—711no—
431C2×#103—711no—
432C2×#103—711no—
433C2×#103—711no—
434C2×#103—711no—
435C2×#103—711no—
436C2×#103—711no—
437C2×#102—711no—
438C2×#102—711no—
439#405—718no—
440C2×#97—711no—
441C2×#97—711no—
442C2×C4×C8—711no—
443C2×C4×C8—711no—
444C22×Q8—21no—
445C22×Q8—711no—
446C22×Q8—711no—
447C22×Q8C22×D7111yescharacteristic
448C22×D4—21no—
449C22×D4C22×D7111yescharacteristic
450C23×C4—21no—
451C23×C4C22×D7111yescharacteristic
452C2×Q16—714no—
453C2×Q16—714no—
454C2×Q16—1424no—
455C2×Q16—1424no—
456C2×SD16—714no—
457C2×SD16—714no—
458C2×SD16—1424no—
459C2×SD16—1424no—
460C2×M16—714no—
461C2×M16—1424no—
462C22×C8—711no—
463C22×C8—711no—
464C22×C8—711no—
465C22×C8—714no—
466C22×C8—711no—
467C22×C8—1424no—
468C4⋊Q8—22no—
469C4⋊Q8—714no—
470C4⋊Q8—1422no—
471C4⋊Q8C22×D7114yes—
472#126—28no—
473#126—1428no—
474#126—1428no—
475#125—714no—
476#125—1428no—
477#125—1428no—
478#125—1422no—
479#124—28no—
480#124—22no—
481#124C22×D7114yes—
482#123—28no—
483C22⋊Q8—22no—
484C22⋊Q8—28no—
485C22⋊Q8—714no—
486C22⋊Q8—714no—
487C22⋊Q8—1422no—
488C22⋊Q8—1422no—
489C22⋊Q8C22×D7114yes—
490#121—22no—
491#121C22×D7114yes—
492C4×Q8—22no—
493C4×Q8—714no—
494C4×Q8—714no—
495C4×Q8—1422no—
496C4×Q8—1422no—
497C4×Q8C22×D7114yes—
498C4×D4—22no—
499C4×D4C22×D7114yes—
500#117C22⋊D7114yes—
501#117C22×D7114yes—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—711no—
506C2×C4⋊C4—711no—
507C2×C4⋊C4—1421no—
508C2×C4⋊C4—1421no—
509C2×C4⋊C4—1421no—
510C2×C4⋊C4—1421no—
511C2×C4⋊C4—1421no—
512C2×C4⋊C4—1421no—
513C2×C4⋊C4—1421no—
514C2×C4⋊C4—1421no—
515C2×C4⋊C4C22⋊D7111yescharacteristic
516C2×C4⋊C4C22⋊D7111yescharacteristic
517C2×C4⋊C4C22×D7111yescharacteristic
518C2×C4⋊C4C22×D7111yescharacteristic
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—1421no—
525C2×C22⋊C4—1421no—
526C2×C22⋊C4C22⋊D7111yescharacteristic
527C2×C22⋊C4C22⋊D7111yescharacteristic
528C2×C42—21no—
529C2×C42—1421no—
530C2×C42—1421no—
531C2×C42C22×D7111yescharacteristic
532C2×C42C22×D7111yescharacteristic
533#107—714no—
534#107—714no—
535#106—714no—
536#106—714no—
537#103—714no—
538#103—714no—
539#103—714no—
540#103—714no—
541#103—714no—
542#103—714no—
543#102—714no—
544#102—714no—
545#97—714no—
546#97—714no—
547C4×C8—714no—
548C4×C8—714no—
549C24—21no—
550C24C2×C22⋊D7111yescharacteristic
551C2×Q8—21no—
552C2×Q8—24no—
553C2×Q8—22no—
554C2×Q8—22no—
555C2×Q8—82no—
556C2×Q8—712no—
557C2×Q8—712no—
558C2×Q8—1422no—
559C2×Q8—1422no—
560C2×Q8—1422no—
561C2×Q8—1422no—
562C2×Q8—1421no—
563C2×Q8—1421no—
564C2×Q8C23×D7112yes—
565C2×D4—24no—
566C2×D4—21no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—82no—
570C2×D4C23×D7112yes—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—24no—
577C22×C4—82no—
578C22×C4—1421no—
579C22×C4—1421no—
580C22×C4—1421no—
581C22×C4—1421no—
582C22×C4C2×C22⋊D7112yes—
583C22×C4C2×C22⋊D7111yescharacteristic
584C22×C4C2×C22⋊D7111yescharacteristic
585C22×C4C2×C22⋊D7111yescharacteristic
586C22×C4C2×C22⋊D7111yescharacteristic
587C22×C4C2×C22⋊D7111yescharacteristic
588C22×C4C23×D7112yes—
589C22×C4C23×D7111yescharacteristic
590Q16—1428no—
591Q16—1428no—
592SD16—1428no—
593SD16—1428no—
594M16—1428no—
595C2×C8—714no—
596C2×C8—714no—
597C2×C8—712no—
598C2×C8—712no—
599C2×C8—712no—
600C2×C8—712no—
601C2×C8—1428no—
602C2×C8—1422no—
603C2×C8—1422no—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—712no—
610C4⋊C4—712no—
611C4⋊C4—1424no—
612C4⋊C4—1424no—
613C4⋊C4—1424no—
614C4⋊C4—1424no—
615C4⋊C4—1424no—
616C4⋊C4—1424no—
617C4⋊C4—1421no—
618C4⋊C4—1421no—
619C4⋊C4—1424no—
620C4⋊C4—1424no—
621C4⋊C4C2×C22⋊D7114yes—
622C4⋊C4C2×C22⋊D7114yes—
623C4⋊C4C23×D7112yes—
624C4⋊C4C23×D7112yes—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—24no—
628C22⋊C4—24no—
629C22⋊C4—24no—
630C22⋊C4—1424no—
631C22⋊C4—1424no—
632C22⋊C4C2×C22⋊D7114yes—
633C22⋊C4C2×C22⋊D7114yes—
634C42—24no—
635C42—1424no—
636C42—1424no—
637C42C2×C22⋊D7112yes—
638C42C2×C22⋊D7112yes—
639C42C23×D7112yes—
640C42C23×D7112yes—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23C22×C22⋊D7112yes—
649C23C22×C22⋊D7111yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—42no—
653Q8—84no—
654Q8—2842no—
655Q8—2842no—
656Q8—1422no—
657Q8—1422no—
658Q8—1422no—
659Q8—1422no—
660D4—22no—
661D4—22no—
662D4—42no—
663D4—84no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—84no—
679C2×C4—2842no—
680C2×C4—2842no—
681C2×C4—2842no—
682C2×C4—2842no—
683C2×C4—1422no—
684C2×C4—1422no—
685C2×C4—1422no—
686C2×C4—1422no—
687C2×C4C22×C22⋊D7112yes—
688C2×C4C22×C22⋊D7112yes—
689C2×C4C22×C22⋊D7112yes—
690C2×C4C22×C22⋊D7112yes—
691C2×C4C22×C22⋊D7112yes—
692C2×C4C22×C22⋊D7111yescharacteristic
693C2×C4#41×D7112yes—
694C2×C4#41×D7112yes—
695C2×C4C24×D7111yescharacteristic
696C8—714no—
697C8—714no—
698C8—1422no—
699C8—1422no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—44no—
704C22—42no—
705C22—42no—
706C22—42no—
707C22—84no—
708C22#1798654512yes—
709C22#1798681012yes—
710C22#1798681412yes—
711C22C23×C22⋊D7111yescharacteristic
712C4—22no—
713C4—22no—
714C4—22no—
715C4—22no—
716C4—22no—
717C4—42no—
718C4—42no—
719C4—42no—
720C4—2842no—
721C4—2842no—
722C4—2842no—
723C4—2842no—
724C4#1798654512yes—
725C4C2×#41×D7111yescharacteristic
726C4C2×#41×D7111yescharacteristic
727C2—42no—
728C2—82no—
729C2#2259900214yesdirect product factor
730C2C2×#1798654511yescharacteristic
731C2C2×#1798681011yescharacteristic
732C2C2×#1798681411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#542×C71C2
socleC23×C71C22×D4
prime radicalC2×#121×C71C22
hypercenterC2×#542D71
hypocenterC71C2×#3178
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#17986611C2semidirect
2. #22599002C2direct (N × H)
3. C2×#17986405C2semidirect
4. C2×#17986394C2semidirect
5. C2×#17986353C2semidirect
6. C2×#17986351C2semidirect
7. C2×#17986255C2semidirect
9. C2×#17986238C2semidirect
11. C2×#17986104C2semidirect
12. C2×#17986099C2semidirect
13. C2×C4×#11765855C2semidirect
14. C2×C4×#11765853C2semidirect
15. C2×#17985955C2semidirect
24. #17986611C22semidirect
35. #17986405C22semidirect
36. #17986394C22semidirect
37. #17986353C22semidirect
38. #17986351C22semidirect
39. #17986255C22semidirect
41. #17986238C22semidirect
43. #17986104C22semidirect
44. #17986099C22semidirect
45. C4×#11765855C22semidirect
46. C4×#11765853C22semidirect
59. #17985955C22semidirect
363. C2×C71#3178semidirect
383. C71C2×#3178semidirect
729. C2#22599002direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179866112
#225990022
C2×#179864052
C2×#179863942
C2×#179863532
C2×#179863512
C2×#179862552
C2×#179862432
C2×#179862382
C2×#179862262
C2×#179861042
C2×#179860992
C2×C4×#117658552
C2×C4×#117658532
C2×#179859552
C2×#542×C712
C2×#317871