Finite Group Databasebeta

← C2×#22599760 #32870372

Subgroups — C2×#22599760 #32870372

Order 18176.

1818 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×#17986620C211yesmaximal, characteristic
2#22599760C2116yesmaximal, direct product factor
3C2×#17986303C211yesmaximal, characteristic, complemented
4C2×#17986294C211yesmaximal, characteristic, complemented
5C2×#17986284C211yesmaximal, characteristic, complemented
6C2×#17986296C211yesmaximal, characteristic, complemented
7C2×#17986255C211yesmaximal, characteristic, complemented
8C2×#17986247C211yesmaximal, characteristic
9C2×#17986238C211yesmaximal, characteristic, complemented
10C2×#17986230C211yesmaximal, characteristic
11C2×#17986221C211yesmaximal, characteristic, complemented
12C2×#17986221C211yesmaximal, characteristic, complemented
13C2×#17986206C211yesmaximal, characteristic, complemented
14C2×#17986201C211yesmaximal, characteristic, complemented
15C2×#17986026C211yesmaximal, characteristic, complemented
16C2×#541×C71C211yesmaximal, characteristic, complemented
17C22×#11765855C2211yescharacteristic
18C22×#11765855C2211yescharacteristic
19C22×#11765852C2211yescharacteristic
20C22×#11765852C2211yescharacteristic
21C22×#11765849C2211yescharacteristic
22C23×C71⋊C8C2211yescharacteristic
23#17986620—24no—
24#17986620C2218yes—
25C2×#14556128C2211yescharacteristic
26C2×#14556123—21no—
27C2×#14556116C2211yescharacteristic
28C2×#14556114—21no—
29C2×#14556110—21no—
30C2×#14556107C2211yescharacteristic
31C2×#14556106—21no—
32C2×#14556102C2211yescharacteristic
33C2×C4×Dic142C2211yescharacteristic
34C2×C4×D284C2211yescharacteristic
35#17986303C2218yescomplemented
36#17986296C2218yescomplemented
37#17986294C2218yescomplemented
38#17986284C2218yescomplemented
39#17986255C2218yescomplemented
40#17986247C2218yes—
41#17986238C2218yescomplemented
42#17986230C2218yes—
43#17986221C2218yescomplemented
44#17986221C2218yescomplemented
45#17986206C2218yescomplemented
46#17986201C2218yescomplemented
47C2×#14556061C2211yescharacteristic
48C2×#14556061C2211yescharacteristic
49C2×#14556059C2211yescharacteristic
50C2×#14556059C2211yescharacteristic
51#17986026C2218yescomplemented
52C2×C4⋊(C71⋊C8)C2211yescharacteristic
53C2×C4⋊(C71⋊C8)C2211yescharacteristic
54C2×C4⋊(C71⋊C8)C2211yescharacteristic
55C2×C4⋊(C71⋊C8)C2211yescharacteristic
56C2×#14556052C2211yescharacteristic
57C2×#14556052C2211yescharacteristic
58C2×#14556052C2211yescharacteristic
59C2×#14556052C2211yescharacteristic
60C2×#14556051C2211yescharacteristic
61C2×#14556051C2211yescharacteristic
62C2×#14556048C2211yescharacteristic
63C2×#14556048C2211yescharacteristic
64#541×C71—24no—
65#541×C71C2218yescomplemented
66C2×C4⋊Q8×C71C2211yescharacteristic
67C2×#126×C71—21no—
68C2×#126×C71—21no—
69C2×#125×C71—21no—
70C2×#125×C71—21no—
71C2×#125×C71C2211yescharacteristic
72C2×C22⋊Q8×C71C2211yescharacteristic
73C2×C22⋊Q8×C71C2211yescharacteristic
74C2×C4×Q8×C71C2211yescharacteristic
75C2×C4×Q8×C71C2211yescharacteristic
76C2×#117×C71C2211yescharacteristic
77C22×Dic142—21no—
78C22×Dic142C2311yescharacteristic
79C22×D284C2311yescharacteristic
80C22×C22⋊D71—21no—
81C22×C4×D71—21no—
82C2×#11765855—42no—
83C2×#11765855—42no—
84C2×#11765855C2314yes—
85C2×#11765855C2314yes—
86C2×#11765852—42no—
87C2×#11765852—42no—
88C2×#11765852C2314yes—
89C2×#11765852C2314yes—
90C2×#11765849—42no—
91C2×#11765849C2314yes—
92C22×C71⋊C8—42no—
93C22×C71⋊C8C2311yescharacteristic
94C22×C71⋊C8C2311yescharacteristic
95C22×C71⋊C8C2311yescharacteristic
96C22×C71⋊C8C2311yescharacteristic
97C22×C71⋊C8C2314yes—
98#14556128—22no—
99#14556128C2314yes—
100#14556123—28no—
101#14556116—22no—
102#14556116C2314yes—
103#14556114—28no—
104#14556110—28no—
105#14556107—22no—
106#14556107C2314yes—
107#14556106—28no—
108#14556102—22no—
109#14556102C2314yes—
110C4×Dic142—22no—
111C4×Dic142C2314yes—
112C4×D284—22no—
113C4×D284C2314yes—
114C2×C4⋊Dic71—21no—
115C2×C4⋊Dic71C2311yescharacteristic
116C2×C4⋊Dic71C2311yescharacteristic
117C2×Dic71⋊C4—21no—
118C2×Dic71⋊C4—21no—
119C2×C22⋊Dic71—21no—
120C2×(C2×D71)⋊C4—21no—
121C2×(C2×D71)⋊C4—21no—
122C2×(C2×D71)⋊C4—21no—
123C2×(C2×D71)⋊C4—21no—
124C2×C4×Dic71—21no—
125#14556061C2314yes—
126#14556061C2314yes—
127#14556059C2314yes—
128#14556059C2314yes—
129C4⋊(C71⋊C8)C2314yes—
130C4⋊(C71⋊C8)C2314yes—
131C4⋊(C71⋊C8)C2314yes—
132C4⋊(C71⋊C8)C2314yes—
133#14556052C2314yes—
134#14556052C2314yes—
135#14556052C2314yes—
136#14556052C2314yes—
137#14556051C2314yes—
138#14556051C2314yes—
139#14556048C2314yes—
140#14556048C2314yes—
141C22×Q8×C71C2311yescharacteristic
142C22×Q8×C71C2311yescharacteristic
143C23×C4×C71C2311yescharacteristic
144C4⋊Q8×C71—22no—
145C4⋊Q8×C71C2314yes—
146#126×C71—28no—
147#126×C71—28no—
148#125×C71—28no—
149#125×C71—28no—
150#125×C71—22no—
151#125×C71C2314yes—
152C22⋊Q8×C71—22no—
153C22⋊Q8×C71—22no—
154C22⋊Q8×C71C2314yes—
155C22⋊Q8×C71C2314yes—
156C4×Q8×C71—22no—
157C4×Q8×C71—22no—
158C4×Q8×C71C2314yes—
159C4×Q8×C71C2314yes—
160#117×C71D414yes—
161#117×C71C2314yes—
162C2×C4⋊C4×C71—21no—
163C2×C4⋊C4×C71—21no—
164C2×C4⋊C4×C71—21no—
165C2×C4⋊C4×C71—21no—
166C2×C4⋊C4×C71—21no—
167C2×C4⋊C4×C71—21no—
168C2×C4⋊C4×C71—21no—
169C2×C4⋊C4×C71—21no—
170C2×C4⋊C4×C71D411yescharacteristic
171C2×C4⋊C4×C71D411yescharacteristic
172C2×C4⋊C4×C71C2311yescharacteristic
173C2×C4⋊C4×C71C2311yescharacteristic
174C2×C22⋊C4×C71—21no—
175C2×C22⋊C4×C71—21no—
176C2×C22⋊C4×C71D411yescharacteristic
177C2×C22⋊C4×C71D411yescharacteristic
178C2×C42×C71—21no—
179C2×C42×C71—21no—
180C2×C42×C71C2311yescharacteristic
181C2×C42×C71C2311yescharacteristic
182C23×D71—21no—
183C2×Dic142—22no—
184C2×Dic142—22no—
185C2×Dic142—21no—
186C2×Dic142—24no—
187C2×Dic142—82no—
188C2×Dic142C2412yes—
189C2×D284—22no—
190C2×D284—22no—
191C2×D284—21no—
192C2×D284C2412yes—
193C2×C22⋊D71—24no—
194C2×C22⋊D71—82no—
195C22×Dic71—21no—
196C22×Dic71—21no—
197C22×Dic71—21no—
198C2×C4×D71—24no—
199C2×C4×D71—82no—
200#11765855—44no—
201#11765855—44no—
202#11765852—44no—
203#11765852—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—24no—
215C4⋊Dic71—21no—
216C4⋊Dic71—21no—
217C4⋊Dic71C2412yes—
218C4⋊Dic71C2412yes—
219Dic71⋊C4—24no—
220Dic71⋊C4—24no—
221C22⋊Dic71—24no—
222(C2×D71)⋊C4—24no—
223(C2×D71)⋊C4—24no—
224(C2×D71)⋊C4—24no—
225(C2×D71)⋊C4—24no—
226C4×Dic71—24no—
227C24×C71C2×D411yescharacteristic
228C2×Q8×C71—21no—
229C2×Q8×C71—21no—
230C2×Q8×C71—22no—
231C2×Q8×C71—22no—
232C2×Q8×C71—22no—
233C2×Q8×C71—22no—
234C2×Q8×C71C2412yes—
235C2×Q8×C71C2412yes—
236C22×C4×C71—22no—
237C22×C4×C71—22no—
238C22×C4×C71—21no—
239C22×C4×C71—21no—
240C22×C4×C71—21no—
241C22×C4×C71—21no—
242C22×C4×C71C2×D411yescharacteristic
243C22×C4×C71C2×D411yescharacteristic
244C22×C4×C71C2×D411yescharacteristic
245C22×C4×C71C2×D411yescharacteristic
246C22×C4×C71C2×D411yescharacteristic
247C22×C4×C71C2×D412yes—
248C22×C4×C71C2412yes—
249C22×C4×C71C2411yescharacteristic
250C4⋊C4×C71—24no—
251C4⋊C4×C71—24no—
252C4⋊C4×C71—24no—
253C4⋊C4×C71—24no—
254C4⋊C4×C71—24no—
255C4⋊C4×C71—24no—
256C4⋊C4×C71—24no—
257C4⋊C4×C71—24no—
258C4⋊C4×C71—21no—
259C4⋊C4×C71—21no—
260C4⋊C4×C71C2×D414yes—
261C4⋊C4×C71C2×D414yes—
262C4⋊C4×C71C2412yes—
263C4⋊C4×C71C2412yes—
264C22⋊C4×C71—24no—
265C22⋊C4×C71—24no—
266C22⋊C4×C71C2×D414yes—
267C22⋊C4×C71C2×D414yes—
268C42×C71—24no—
269C42×C71—24no—
270C42×C71C2×D412yes—
271C42×C71C2×D412yes—
272C42×C71C2412yes—
273C42×C71C2412yes—
274C23×C71—22no—
275C23×C71—22no—
276C23×C71—22no—
277C23×C71C22×D412yes—
278C23×C71C22×D411yescharacteristic
279C22×D71—22no—
280C22×D71—42no—
281C22×D71—42no—
282C22×D71—42no—
283Q8×C71—22no—
284Q8×C71—22no—
285Q8×C71—22no—
286Q8×C71—22no—
287Q8×C71—42no—
288Q8×C71—42no—
289C2×C4×C71—22no—
290C2×C4×C71—22no—
291C2×C4×C71—22no—
292C2×C4×C71—22no—
293C2×C4×C71—22no—
294C2×C4×C71—24no—
295C2×C4×C71—22no—
296C2×C4×C71—22no—
297C2×C4×C71—22no—
298C2×C4×C71—22no—
299C2×C4×C71—22no—
300C2×C4×C71—22no—
301C2×C4×C71—42no—
302C2×C4×C71—42no—
303C2×C4×C71—42no—
304C2×C4×C71—42no—
305C2×C4×C71C22×D412yes—
306C2×C4×C71C22×D412yes—
307C2×C4×C71C22×D412yes—
308C2×C4×C71C22×D412yes—
309C2×C4×C71C22×D412yes—
310C2×C4×C71C22×D411yescharacteristic
311C2×C4×C71H(5,𝔽2)12yes—
312C2×C4×C712−1+412yes—
313C2×C4×C71C2511yescharacteristic
314C22⋊D71—84no—
315C2×Dic71—22no—
316C2×Dic71—22no—
317C2×Dic71—22no—
318C2×Dic71—42no—
319C2×Dic71—42no—
320C2×Dic71—42no—
321D284—22no—
322D284—22no—
323D284—42no—
324C4×D71—84no—
325Dic142—22no—
326Dic142—22no—
327Dic142—42no—
328Dic142—84no—
329C71⋊C8—22no—
330C71⋊C8—22no—
331C71⋊C8—22no—
332C71⋊C8—22no—
333C22×C71—22no—
334C22×C71—22no—
335C22×C71—22no—
336C22×C71—44no—
337C22×C71#53712yes—
338C22×C71#57712yes—
339C22×C71#57812yes—
340C22×C71C23×D411yescharacteristic
341C2×D71—42no—
342C2×D71—42no—
343C2×D71—42no—
344C2×D71—84no—
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—42no—
354C4×C71#53712yes—
355C4×C71C2×H(5,𝔽2)11yescharacteristic
356C4×C71C2×2−1+411yescharacteristic
357Dic71—42no—
358Dic71—42no—
359Dic71—42no—
360C2×#3258—711nomaximal, Sylow
361C2×C71—42no—
362C2×C71#325814yescomplemented
363C2×C71C2×#53711yescharacteristic
364C2×C71C2×#57711yescharacteristic
365C2×C71C2×#57811yescharacteristic
366D71—82no—
367C2×#542—711no—
368C2×#541D7111yescharacteristic, complemented
369#3258—7116no—
370C2×#479—711no—
371C2×#477—711no—
372C2×#475—711no—
373C2×#478—711no—
374C2×#470—711no—
375C2×#468—711no—
376C2×#467—711no—
377C2×#465—711no—
378C2×#464—711no—
379C2×#464—711no—
380C2×#462—711no—
381C2×#461—711no—
382C2×#424—711no—
383C71C2×#325811yescharacteristic, complemented, Sylow
384C22×Q16—711no—
385C22×Q16—711no—
386C22×SD16—711no—
387C22×SD16—711no—
388C22×M16—711no—
389C23×C8—711no—
390#542—718no—
391#542—1424no—
392#541—24no—
393#541C2×D7118yescomplemented
394C2×C4⋊Q8—711no—
395C2×C4⋊Q8C2×D7111yescharacteristic
396C2×#126—21no—
397C2×#126—21no—
398C2×#126—1421no—
399C2×#125—21no—
400C2×#125—21no—
401C2×#125C2×D7111yescharacteristic
402C2×#124—711no—
403C2×#124—1421no—
404C2×#123—1421no—
405C2×C22⋊Q8—711no—
406C2×C22⋊Q8—1421no—
407C2×C22⋊Q8C2×D7111yescharacteristic
408C2×C22⋊Q8C2×D7111yescharacteristic
409C2×#121—711no—
410C2×C4×Q8—711no—
411C2×C4×Q8C2×D7111yescharacteristic
412C2×C4×Q8C2×D7111yescharacteristic
413C2×C4×D4—711no—
414C2×#117C2×D7111yescharacteristic
415#479—718no—
416#478—718no—
417#477—718no—
418#475—718no—
419#470—718no—
420#468—718no—
421#467—718no—
422#465—718no—
423#464—718no—
424#464—718no—
425#462—718no—
426#461—718no—
427C2×#107—711no—
428C2×#107—711no—
429C2×#106—711no—
430C2×#106—711no—
431#424—718no—
432C2×C4⋊C8—711no—
433C2×C4⋊C8—711no—
434C2×C4⋊C8—711no—
435C2×C4⋊C8—711no—
436C2×#103—711no—
437C2×#103—711no—
438C2×#103—711no—
439C2×#103—711no—
440C2×#103—711no—
441C2×#103—711no—
442C2×#102—711no—
443C2×#102—711no—
444C22×Q8—711no—
445C22×Q8—1421no—
446C22×Q8C22×D7111yescharacteristic
447C22×Q8C22×D7111yescharacteristic
448C22×D4—711no—
449C22×D4—1421no—
450C23×C4—1421no—
451C23×C4C22×D7111yescharacteristic
452C2×Q16—2842no—
453C2×Q16—2842no—
454C2×Q16—714no—
455C2×Q16—714no—
456C2×SD16—2842no—
457C2×SD16—2842no—
458C2×SD16—714no—
459C2×SD16—714no—
460C2×M16—2842no—
461C2×M16—714no—
462C22×C8—2842no—
463C22×C8—714no—
464C22×C8—711no—
465C22×C8—711no—
466C22×C8—711no—
467C22×C8—711no—
468C4⋊Q8—22no—
469C4⋊Q8—714no—
470C4⋊Q8—1422no—
471C4⋊Q8C22×D7114yes—
472#126—28no—
473#126—28no—
474#126—1428no—
475#125—28no—
476#125—28no—
477#125—22no—
478#125C22×D7114yes—
479#124—714no—
480#124—1428no—
481#124—1422no—
482#123—1428no—
483C22⋊Q8—22no—
484C22⋊Q8—22no—
485C22⋊Q8—714no—
486C22⋊Q8—1422no—
487C22⋊Q8—1428no—
488C22⋊Q8C22×D7114yes—
489C22⋊Q8C22×D7114yes—
490#121—714no—
491#121—1422no—
492C4×Q8—22no—
493C4×Q8—22no—
494C4×Q8—714no—
495C4×Q8—1422no—
496C4×Q8C22×D7114yes—
497C4×Q8C22×D7114yes—
498C4×D4—714no—
499C4×D4—1422no—
500#117C22⋊D7114yes—
501#117C22×D7114yes—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—711no—
511C2×C4⋊C4—711no—
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—1421no—
522C2×C22⋊C4—1421no—
523C2×C22⋊C4—1421no—
524C2×C22⋊C4—1421no—
525C2×C22⋊C4—1421no—
526C2×C22⋊C4C22⋊D7111yescharacteristic
527C2×C22⋊C4C22⋊D7111yescharacteristic
528C2×C42—21no—
529C2×C42—21no—
530C2×C42—1421no—
531C2×C42C22×D7111yescharacteristic
532C2×C42C22×D7111yescharacteristic
533#107—714no—
534#107—714no—
535#106—714no—
536#106—714no—
537C4⋊C8—714no—
538C4⋊C8—714no—
539C4⋊C8—714no—
540C4⋊C8—714no—
541#103—714no—
542#103—714no—
543#103—714no—
544#103—714no—
545#103—714no—
546#103—714no—
547#102—714no—
548#102—714no—
549C24—1421no—
550C24C2×C22⋊D7111yescharacteristic
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—22no—
554C2×Q8—22no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—5682no—
558C2×Q8—712no—
559C2×Q8—1422no—
560C2×Q8—1422no—
561C2×Q8—1421no—
562C2×Q8—1424no—
563C2×Q8C23×D7112yes—
564C2×Q8C23×D7112yes—
565C2×D4—5682no—
566C2×D4—712no—
567C2×D4—1424no—
568C2×D4—1421no—
569C2×D4—1422no—
570C2×D4—1422no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—5682no—
578C22×C4—1421no—
579C22×C4—1421no—
580C22×C4—1421no—
581C22×C4—1424no—
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—2844no—
591Q16—2844no—
592SD16—2844no—
593SD16—2844no—
594M16—2844no—
595C2×C8—2844no—
596C2×C8—712no—
597C2×C8—712no—
598C2×C8—712no—
599C2×C8—712no—
600C2×C8—1422no—
601C2×C8—1422no—
602C2×C8—1422no—
603C2×C8—1422no—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—24no—
609C4⋊C4—24no—
610C4⋊C4—24no—
611C4⋊C4—24no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—712no—
615C4⋊C4—712no—
616C4⋊C4—1424no—
617C4⋊C4—1424no—
618C4⋊C4—1421no—
619C4⋊C4—1421no—
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—1424no—
628C22⋊C4—1424no—
629C22⋊C4—1424no—
630C22⋊C4—1424no—
631C22⋊C4—1424no—
632C22⋊C4C2×C22⋊D7114yes—
633C22⋊C4C2×C22⋊D7114yes—
634C42—24no—
635C42—24no—
636C42—1424no—
637C42C2×C22⋊D7112yes—
638C42C2×C22⋊D7112yes—
639C42C23×D7112yes—
640C42C23×D7112yes—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—2842no—
645C23—2842no—
646C23—2842no—
647C23—1422no—
648C23C22×C22⋊D7112yes—
649C23C22×C22⋊D7111yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—22no—
653Q8—22no—
654Q8—42no—
655Q8—42no—
656Q8—2842no—
657Q8—5684no—
658Q8—1422no—
659Q8—1422no—
660D4—2842no—
661D4—5684no—
662D4—1422no—
663D4—1422no—
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—22no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—2842no—
681C2×C4—2842no—
682C2×C4—2842no—
683C2×C4—5684no—
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#1455617412yes—
694C2×C4#1455617512yes—
695C2×C4C24×D7111yescharacteristic
696C8—1422no—
697C8—1422no—
698C8—1422no—
699C8—1422no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—44no—
704C22—2842no—
705C22—2842no—
706C22—2842no—
707C22—5684no—
708C22#1798657712yes—
709C22#1798680712yes—
710C22#1798681412yes—
711C22C23×C22⋊D7111yescharacteristic
712C4—22no—
713C4—22no—
714C4—22no—
715C4—22no—
716C4—22no—
717C4—42no—
718C4—42no—
719C4—42no—
720C4—42no—
721C4—2842no—
722C4—2842no—
723C4—2842no—
724C4#1798657712yes—
725C4C2×#1455617411yescharacteristic
726C4C2×#1455617511yescharacteristic
727C2—42no—
728C2—5682no—
729C2#2259976014yesdirect product factor
730C2C2×#1798657711yescharacteristic
731C2C2×#1798680711yescharacteristic
732C2C2×#1798681411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#541×C71C2
socleC23×C71C22×D4
prime radicalC2×#14556102C22
hypercenterC2×#541D71
hypocenterC71C2×#3258
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#541

Complements

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

NH ≅ G/Ntype
2. #22599760C2direct (N × H)
3. C2×#17986303C2semidirect
4. C2×#17986294C2semidirect
5. C2×#17986284C2semidirect
6. C2×#17986296C2semidirect
7. C2×#17986255C2semidirect
9. C2×#17986238C2semidirect
11. C2×#17986221C2semidirect
12. C2×#17986221C2semidirect
13. C2×#17986206C2semidirect
14. C2×#17986201C2semidirect
15. C2×#17986026C2semidirect
16. C2×#541×C71C2semidirect
35. #17986303C22semidirect
36. #17986296C22semidirect
37. #17986294C22semidirect
38. #17986284C22semidirect
39. #17986255C22semidirect
41. #17986238C22semidirect
43. #17986221C22semidirect
44. #17986221C22semidirect
45. #17986206C22semidirect
46. #17986201C22semidirect
51. #17986026C22semidirect
65. #541×C71C22semidirect
362. C2×C71#3258semidirect
368. C2×#541D71semidirect
383. C71C2×#3258semidirect
393. #541C2×D71semidirect
729. C2#22599760direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179866202
#225997602
C2×#179863032
C2×#179862942
C2×#179862842
C2×#179862962
C2×#179862552
C2×#179862472
C2×#179862382
C2×#179862302
C2×#179862212
C2×#179862062
C2×#179862012
C2×#179860262
C2×#541×C712
C2×#325871