Finite Group Databasebeta

← C2×#22598617 #32865783

Subgroups — C2×#22598617 #32865783

Order 18176.

2134 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986620C211yesmaximal, characteristic, complemented
2#22598617C2116yesmaximal, direct product factor
3C2×#17986317C211yesmaximal, characteristic, complemented
4C2×#17986329C211yesmaximal, characteristic, complemented
5C2×#17986284C211yesmaximal, characteristic, complemented
6C2×#17986289C211yesmaximal, characteristic, complemented
7C2×#17986221C211yesmaximal, characteristic, complemented
8C2×#17986214C211yesmaximal, characteristic, complemented
9C2×#17986161C211yesmaximal, characteristic, complemented
10C2×#17986144C211yesmaximal, characteristic
11C2×#17986109C211yesmaximal, characteristic, complemented
12C2×#17986104C211yesmaximal, characteristic, complemented
13C2×C4×#11765852C211yesmaximal, characteristic, complemented
14C2×C4×#11765853C211yesmaximal, characteristic, complemented
15C2×#17986060C211yesmaximal, characteristic, complemented
16C2×#520×C71C211yesmaximal, characteristic, complemented
17C22×#11765855C2211yescharacteristic
18C22×#11765853C2211yescharacteristic
19C22×#11765852C2211yescharacteristic
20C22×#11765850C2211yescharacteristic
21#17986620—24no—
22#17986620C2218yescomplemented
23C2×#14556128C2211yescharacteristic
24C2×#14556123—21no—
25C2×#14556116C2211yescharacteristic
26C2×#14556114—21no—
27C2×#14556110—21no—
28C2×#14556107C2211yescharacteristic
29C2×#14556106—21no—
30C2×#14556102C2211yescharacteristic
31C2×C4×Dic142C2211yescharacteristic
32C2×C4×D284C2211yescharacteristic
33#17986329C2218yescomplemented
34#17986317C2218yescomplemented
35#17986289C2218yescomplemented
36#17986284C2218yescomplemented
37#17986221C2218yescomplemented
38#17986214C2218yescomplemented
39#17986161C2218yescomplemented
40#17986144C2218yes—
41#17986109C2218yescomplemented
42#17986104C2218yescomplemented
43C4×#11765852C2218yescomplemented
44C4×#11765853C2218yescomplemented
45#17986060C2218yescomplemented
46C2×#14556059C2211yescharacteristic
47C2×#14556059C2211yescharacteristic
48C2×#14556059C2211yescharacteristic
49C2×#14556059C2211yescharacteristic
50C2×C4⋊(C71⋊C8)C2211yescharacteristic
51C2×C4⋊(C71⋊C8)C2211yescharacteristic
52C2×#14556052C2211yescharacteristic
53C2×#14556052C2211yescharacteristic
54C2×#14556051C2211yescharacteristic
55C2×#14556051C2211yescharacteristic
56C2×#14556049C2211yescharacteristic
57C2×#14556049C2211yescharacteristic
58C2×#14556048C2211yescharacteristic
59C2×#14556048C2211yescharacteristic
60C2×C22⋊(C71⋊C8)C2211yescharacteristic
61C2×C22⋊(C71⋊C8)C2211yescharacteristic
62C2×#14556039C2211yescharacteristic
63C2×C4×C71⋊C8C2211yescharacteristic
64C22×#41×C71C2211yescharacteristic
65#520×C71—24no—
66#520×C71C2218yescomplemented
67C2×C4×Q8×C71C2211yescharacteristic
68C2×C4×Q8×C71C2211yescharacteristic
69C2×C4×D4×C71—21no—
70C2×C4×D4×C71—21no—
71C2×C4×D4×C71C2211yescharacteristic
72C2×C4×D4×C71C2211yescharacteristic
73C2×#117×C71—21no—
74C2×#117×C71C2211yescharacteristic
75C22×C4⋊C4×C71—21no—
76C22×C4⋊C4×C71C2211yescharacteristic
77C22×Dic142—21no—
78C22×Dic142C2311yescharacteristic
79C22×D284C2311yescharacteristic
80C22×C22⋊D71—21no—
81C22×C4×D71—21no—
82C2×#11765855—24no—
83C2×#11765855C2314yes—
84C2×#11765853—24no—
85C2×#11765853C2314yes—
86C2×#11765852—24no—
87C2×#11765852C2314yes—
88C2×#11765850—24no—
89C2×#11765850C2314yes—
90C22×C71⋊C8C2311yescharacteristic
91C22×C71⋊C8C2311yescharacteristic
92C22×C71⋊C8C2311yescharacteristic
93C22×C71⋊C8C2311yescharacteristic
94#14556128—22no—
95#14556128C2314yes—
96#14556123—28no—
97#14556116—22no—
98#14556116C2314yes—
99#14556114—28no—
100#14556110—28no—
101#14556107—22no—
102#14556107C2314yes—
103#14556106—28no—
104#14556102—22no—
105#14556102C2314yes—
106C4×Dic142—22no—
107C4×Dic142C2314yes—
108C4×D284—22no—
109C4×D284C2314yes—
110C2×C4⋊Dic71—21no—
111C2×C4⋊Dic71C2311yescharacteristic
112C2×C4⋊Dic71C2311yescharacteristic
113C2×Dic71⋊C4—21no—
114C2×Dic71⋊C4—21no—
115C2×C22⋊Dic71—21no—
116C2×(C2×D71)⋊C4—21no—
117C2×(C2×D71)⋊C4—21no—
118C2×(C2×D71)⋊C4—21no—
119C2×(C2×D71)⋊C4—21no—
120C2×C4×Dic71—21no—
121#14556059C2314yes—
122#14556059C2314yes—
123#14556059C2314yes—
124#14556059C2314yes—
125C4⋊(C71⋊C8)C2314yes—
126C4⋊(C71⋊C8)C2314yes—
127#14556052C2314yes—
128#14556052C2314yes—
129#14556051C2314yes—
130#14556051C2314yes—
131#14556049C2314yes—
132#14556049C2314yes—
133#14556048C2314yes—
134#14556048C2314yes—
135C22⋊(C71⋊C8)C2314yes—
136C22⋊(C71⋊C8)C2314yes—
137#14556039C2314yes—
138C4×C71⋊C8C2314yes—
139C2×#41×C71—24no—
140C2×#41×C71—24no—
141C2×#41×C71—22no—
142C2×#41×C71C2314yes—
143C22×Q8×C71C2311yescharacteristic
144C22×D4×C71—21no—
145C22×D4×C71C2311yescharacteristic
146C23×C4×C71—21no—
147C23×C4×C71—21no—
148C23×C4×C71—21no—
149C23×C4×C71—21no—
150C23×C4×C71C2311yescharacteristic
151C4×Q8×C71—22no—
152C4×Q8×C71—22no—
153C4×Q8×C71C2314yes—
154C4×Q8×C71C2314yes—
155C4×D4×C71—28no—
156C4×D4×C71—28no—
157C4×D4×C71—22no—
158C4×D4×C71—22no—
159C4×D4×C71C2314yes—
160C4×D4×C71C2314yes—
161#117×C71—28no—
162#117×C71D414yes—
163#117×C71C2314yes—
164C2×C4⋊C4×C71—21no—
165C2×C4⋊C4×C71—21no—
166C2×C4⋊C4×C71—21no—
167C2×C4⋊C4×C71—22no—
168C2×C4⋊C4×C71—28no—
169C2×C4⋊C4×C71D411yescharacteristic
170C2×C4⋊C4×C71D411yescharacteristic
171C2×C4⋊C4×C71C2314yes—
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—28no—
201#11765853—28no—
202#11765852—28no—
203#11765850—28no—
204C2×C71⋊C8—22no—
205C2×C71⋊C8—22no—
206C2×C71⋊C8—22no—
207C2×C71⋊C8—22no—
208C2×C71⋊C8C2412yes—
209C2×C71⋊C8C2412yes—
210C2×C71⋊C8C2412yes—
211C2×C71⋊C8C2412yes—
212C4⋊Dic71—24no—
213C4⋊Dic71—21no—
214C4⋊Dic71—21no—
215C4⋊Dic71C2412yes—
216C4⋊Dic71C2412yes—
217Dic71⋊C4—24no—
218Dic71⋊C4—24no—
219C22⋊Dic71—24no—
220(C2×D71)⋊C4—24no—
221(C2×D71)⋊C4—24no—
222(C2×D71)⋊C4—24no—
223(C2×D71)⋊C4—24no—
224C4×Dic71—24no—
225C24×C71—21no—
226C24×C71C2×D411yescharacteristic
227#41×C71—216no—
228#41×C71—28no—
229#41×C71—28no—
230C2×Q8×C71—21no—
231C2×Q8×C71—22no—
232C2×Q8×C71#4114yes—
233C2×Q8×C71C2412yes—
234C2×D4×C71—28no—
235C2×D4×C71—24no—
236C2×D4×C71—21no—
237C2×D4×C71—22no—
238C2×D4×C71#4114yes—
239C2×D4×C71C2412yes—
240C22×C4×C71—28no—
241C22×C4×C71—21no—
242C22×C4×C71—24no—
243C22×C4×C71—22no—
244C22×C4×C71—22no—
245C22×C4×C71—21no—
246C22×C4×C71—21no—
247C22×C4×C71—24no—
248C22×C4×C71—24no—
249C22×C4×C71—24no—
250C22×C4×C71—82no—
251C22×C4×C71—82no—
252C22×C4×C71—82no—
253C22×C4×C71C2×D411yescharacteristic
254C22×C4×C71C2×D411yescharacteristic
255C22×C4×C71C2×D411yescharacteristic
256C22×C4×C71C2×D411yescharacteristic
257C22×C4×C71C2×D411yescharacteristic
258C22×C4×C71C2×D412yes—
259C22×C4×C71C2412yes—
260C22×C4×C71C2411yescharacteristic
261C4⋊C4×C71—24no—
262C4⋊C4×C71—24no—
263C4⋊C4×C71—24no—
264C4⋊C4×C71—21no—
265C4⋊C4×C71—21no—
266C4⋊C4×C71C2×D414yes—
267C4⋊C4×C71C2×D414yes—
268C4⋊C4×C71C2412yes—
269C4⋊C4×C71C2412yes—
270C22⋊C4×C71—24no—
271C22⋊C4×C71—24no—
272C22⋊C4×C71C2×D414yes—
273C22⋊C4×C71C2×D414yes—
274C42×C71—24no—
275C42×C71—24no—
276C42×C71C2×D412yes—
277C42×C71C2×D412yes—
278C42×C71C2412yes—
279C42×C71C2412yes—
280C23×C71—22no—
281C23×C71—24no—
282C23×C71—22no—
283C23×C71—22no—
284C23×C71—22no—
285C23×C71—42no—
286C23×C71—42no—
287C23×C71C22×D412yes—
288C23×C71C22×D411yescharacteristic
289C22×D71—22no—
290C22×D71—42no—
291C22×D71—42no—
292C22×D71—42no—
293Q8×C71—24no—
294Q8×C71—22no—
295Q8×C71C2×#4114yes—
296D4×C71—216no—
297D4×C71—24no—
298D4×C71—22no—
299D4×C71C2×#4114yes—
300C2×C4×C71—216no—
301C2×C4×C71—22no—
302C2×C4×C71—24no—
303C2×C4×C71—22no—
304C2×C4×C71—22no—
305C2×C4×C71—22no—
306C2×C4×C71—22no—
307C2×C4×C71—22no—
308C2×C4×C71—24no—
309C2×C4×C71—22no—
310C2×C4×C71—22no—
311C2×C4×C71—22no—
312C2×C4×C71—22no—
313C2×C4×C71—42no—
314C2×C4×C71—42no—
315C2×C4×C71—84no—
316C2×C4×C71—84no—
317C2×C4×C71—84no—
318C2×C4×C71C22×D412yes—
319C2×C4×C71C22×D412yes—
320C2×C4×C71C22×D412yes—
321C2×C4×C71C22×D412yes—
322C2×C4×C71C22×D412yes—
323C2×C4×C71C22×D411yescharacteristic
324C2×C4×C71C2×#4112yes—
325C2×C4×C71C2×#4112yes—
326C2×C4×C71C2511yescharacteristic
327C22⋊D71—84no—
328C2×Dic71—22no—
329C2×Dic71—22no—
330C2×Dic71—22no—
331C2×Dic71—42no—
332C2×Dic71—42no—
333C2×Dic71—42no—
334D284—22no—
335D284—22no—
336D284—42no—
337C4×D71—84no—
338Dic142—22no—
339Dic142—22no—
340Dic142—42no—
341Dic142—84no—
342C71⋊C8—22no—
343C71⋊C8—22no—
344C71⋊C8—22no—
345C71⋊C8—22no—
346C22×C71—22no—
347C22×C71—24no—
348C22×C71—22no—
349C22×C71—22no—
350C22×C71—44no—
351C22×C71—48no—
352C22×C71—42no—
353C22×C71—42no—
354C22×C71#52512yes—
355C22×C71#57712yes—
356C22×C71#57712yes—
357C22×C71C23×D411yescharacteristic
358C2×D71—42no—
359C2×D71—42no—
360C2×D71—42no—
361C2×D71—84no—
362C4×C71—22no—
363C4×C71—24no—
364C4×C71—22no—
365C4×C71—22no—
366C4×C71—22no—
367C4×C71—22no—
368C4×C71—42no—
369C4×C71—42no—
370C4×C71#52512yes—
371C4×C71C22×#4111yescharacteristic
372C4×C71C22×#4111yescharacteristic
373Dic71—42no—
374Dic71—42no—
375Dic71—42no—
376C2×#3125—711nomaximal, Sylow
377C2×C71—42no—
378C2×C71—44no—
379C2×C71#312514yescomplemented
380C2×C71C2×#52511yescharacteristic
381C2×C71C2×#57711yescharacteristic
382C2×C71C2×#57711yescharacteristic
383D71—82no—
384C2×#542—711no—
385C2×#520D7111yescharacteristic, complemented
386#3125—7116no—
387C2×#481—711no—
388C2×#483—711no—
389C2×#475—711no—
390C2×#476—711no—
391C2×#464—711no—
392C2×#463—711no—
393C2×#452—711no—
394C2×#449—711no—
395C2×#442—711no—
396C2×#441—711no—
397C2×C4×SD16—711no—
398C2×C4×SD16—711no—
399C2×#433—711no—
400C71C2×#312511yescharacteristic, complemented, Sylow
401C22×#41C2×D7111yescharacteristic
402C22×Q16—711no—
403C22×SD16—711no—
404C22×SD16—711no—
405C22×D8—711no—
406#542—718no—
407#542—1424no—
408C2×C4⋊Q8—711no—
409C2×#126—1421no—
410C2×#124—711no—
411C2×#124—1421no—
412C2×#123—1421no—
413C2×C22⋊Q8—711no—
414C2×C22⋊Q8—1421no—
415C2×#121—711no—
416#520—24no—
417#520C2×D7118yescomplemented
418C2×C4×Q8—711no—
419C2×C4×Q8C2×D7111yescharacteristic
420C2×C4×Q8C2×D7111yescharacteristic
421C2×C4×D4—21no—
422C2×C4×D4—21no—
423C2×C4×D4—711no—
424C2×C4×D4C2×D7111yescharacteristic
425C2×C4×D4C2×D7111yescharacteristic
426C2×#117—21no—
427C2×#117C2×D7111yescharacteristic
428C22×C4⋊C4—21no—
429C22×C4⋊C4C2×D7111yescharacteristic
430#483—718no—
431#481—718no—
432#476—718no—
433#475—718no—
434#464—718no—
435#463—718no—
436#452—718no—
437#449—718no—
438#442—718no—
439#441—718no—
440C4×SD16—718no—
441C4×SD16—718no—
442#433—718no—
443C2×#106—711no—
444C2×#106—711no—
445C2×#106—711no—
446C2×#106—711no—
447C2×C4⋊C8—711no—
448C2×C4⋊C8—711no—
449C2×#103—711no—
450C2×#103—711no—
451C2×#103—711no—
452C2×#103—711no—
453C2×#102—711no—
454C2×#102—711no—
455C2×#102—711no—
456C2×#102—711no—
457C2×C22⋊C8—711no—
458C2×C22⋊C8—711no—
459C2×#97—711no—
460C2×C4×C8—711no—
461C2×#41—24no—
462C2×#41—24no—
463C2×#41—22no—
464C2×#41C22×D7114yes—
465C22×Q8—711no—
466C22×Q8—1421no—
467C22×Q8C22×D7111yescharacteristic
468C22×D4—21no—
469C22×D4—711no—
470C22×D4—1421no—
471C22×D4C22×D7111yescharacteristic
472C23×C4—21no—
473C23×C4—21no—
474C23×C4—21no—
475C23×C4—21no—
476C23×C4—1421no—
477C23×C4C22×D7111yescharacteristic
478C2×Q16—714no—
479C2×Q16—1424no—
480C2×SD16—714no—
481C2×SD16—714no—
482C2×SD16—1424no—
483C2×SD16—1424no—
484C2×D8—714no—
485C2×D8—1424no—
486C22×C8—711no—
487C22×C8—711no—
488C22×C8—711no—
489C22×C8—711no—
490C4⋊Q8—714no—
491C4⋊Q8—1422no—
492#126—1428no—
493#124—714no—
494#124—1428no—
495#124—1422no—
496#123—1428no—
497C22⋊Q8—714no—
498C22⋊Q8—1422no—
499C22⋊Q8—1428no—
500#121—714no—
501#121—1422no—
502C4×Q8—22no—
503C4×Q8—22no—
504C4×Q8—714no—
505C4×Q8—1422no—
506C4×Q8C22×D7114yes—
507C4×Q8C22×D7114yes—
508C4×D4—28no—
509C4×D4—28no—
510C4×D4—22no—
511C4×D4—22no—
512C4×D4—714no—
513C4×D4—1422no—
514C4×D4C22×D7114yes—
515C4×D4C22×D7114yes—
516#117—28no—
517#117C22⋊D7114yes—
518#117C22×D7114yes—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—22no—
523C2×C4⋊C4—28no—
524C2×C4⋊C4—711no—
525C2×C4⋊C4—711no—
526C2×C4⋊C4—1421no—
527C2×C4⋊C4—1421no—
528C2×C4⋊C4—1421no—
529C2×C4⋊C4C22⋊D7111yescharacteristic
530C2×C4⋊C4C22⋊D7111yescharacteristic
531C2×C4⋊C4C22×D7111yescharacteristic
532C2×C4⋊C4C22×D7111yescharacteristic
533C2×C4⋊C4C22×D7114yes—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—1421no—
537C2×C22⋊C4—1421no—
538C2×C22⋊C4—1421no—
539C2×C22⋊C4—1421no—
540C2×C22⋊C4—1421no—
541C2×C22⋊C4C22⋊D7111yescharacteristic
542C2×C22⋊C4C22⋊D7111yescharacteristic
543C2×C42—21no—
544C2×C42—21no—
545C2×C42—1421no—
546C2×C42C22×D7111yescharacteristic
547C2×C42C22×D7111yescharacteristic
548#106—714no—
549#106—714no—
550#106—714no—
551#106—714no—
552C4⋊C8—714no—
553C4⋊C8—714no—
554#103—714no—
555#103—714no—
556#103—714no—
557#103—714no—
558#102—714no—
559#102—714no—
560#102—714no—
561#102—714no—
562C22⋊C8—714no—
563C22⋊C8—714no—
564#97—714no—
565C4×C8—714no—
566C24—21no—
567C24—1421no—
568C24C2×C22⋊D7111yescharacteristic
569#41—216no—
570#41—28no—
571#41—28no—
572C2×Q8—21no—
573C2×Q8—22no—
574C2×Q8—5682no—
575C2×Q8—712no—
576C2×Q8—1422no—
577C2×Q8—1422no—
578C2×Q8—1421no—
579C2×Q8—1424no—
580C2×Q8#1176586514yes—
581C2×Q8C23×D7112yes—
582C2×D4—28no—
583C2×D4—24no—
584C2×D4—21no—
585C2×D4—22no—
586C2×D4—5682no—
587C2×D4—712no—
588C2×D4—1424no—
589C2×D4—1421no—
590C2×D4—1422no—
591C2×D4—1422no—
592C2×D4#1176586514yes—
593C2×D4C23×D7112yes—
594C22×C4—28no—
595C22×C4—21no—
596C22×C4—24no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—24no—
602C22×C4—24no—
603C22×C4—24no—
604C22×C4—82no—
605C22×C4—82no—
606C22×C4—82no—
607C22×C4—5682no—
608C22×C4—1421no—
609C22×C4—1421no—
610C22×C4—1421no—
611C22×C4—1424no—
612C22×C4C2×C22⋊D7112yes—
613C22×C4C2×C22⋊D7111yescharacteristic
614C22×C4C2×C22⋊D7111yescharacteristic
615C22×C4C2×C22⋊D7111yescharacteristic
616C22×C4C2×C22⋊D7111yescharacteristic
617C22×C4C2×C22⋊D7111yescharacteristic
618C22×C4C23×D7112yes—
619C22×C4C23×D7111yescharacteristic
620Q16—1428no—
621SD16—1428no—
622SD16—1428no—
623D8—1428no—
624C2×C8—712no—
625C2×C8—712no—
626C2×C8—712no—
627C2×C8—712no—
628C2×C8—1422no—
629C2×C8—1422no—
630C2×C8—1422no—
631C2×C8—1422no—
632C4⋊C4—24no—
633C4⋊C4—24no—
634C4⋊C4—24no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—712no—
638C4⋊C4—712no—
639C4⋊C4—1424no—
640C4⋊C4—1424no—
641C4⋊C4—1421no—
642C4⋊C4—1421no—
643C4⋊C4—1424no—
644C4⋊C4C2×C22⋊D7114yes—
645C4⋊C4C2×C22⋊D7114yes—
646C4⋊C4C23×D7112yes—
647C4⋊C4C23×D7112yes—
648C22⋊C4—24no—
649C22⋊C4—24no—
650C22⋊C4—1424no—
651C22⋊C4—1424no—
652C22⋊C4—1424no—
653C22⋊C4—1424no—
654C22⋊C4—1424no—
655C22⋊C4C2×C22⋊D7114yes—
656C22⋊C4C2×C22⋊D7114yes—
657C42—24no—
658C42—24no—
659C42—1424no—
660C42C2×C22⋊D7112yes—
661C42C2×C22⋊D7112yes—
662C42C23×D7112yes—
663C42C23×D7112yes—
664C23—22no—
665C23—22no—
666C23—24no—
667C23—22no—
668C23—22no—
669C23—42no—
670C23—42no—
671C23—2842no—
672C23—2842no—
673C23—2842no—
674C23—1422no—
675C23C22×C22⋊D7112yes—
676C23C22×C22⋊D7111yescharacteristic
677Q8—22no—
678Q8—24no—
679Q8—2842no—
680Q8—5684no—
681Q8—1422no—
682Q8—1422no—
683Q8C2×#1176586514yes—
684D4—216no—
685D4—22no—
686D4—24no—
687D4—2842no—
688D4—5684no—
689D4—1422no—
690D4—1422no—
691D4C2×#1176586514yes—
692C2×C4—216no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—84no—
708C2×C4—84no—
709C2×C4—84no—
710C2×C4—2842no—
711C2×C4—2842no—
712C2×C4—2842no—
713C2×C4—5684no—
714C2×C4—1422no—
715C2×C4—1422no—
716C2×C4—1422no—
717C2×C4C22×C22⋊D7112yes—
718C2×C4C22×C22⋊D7112yes—
719C2×C4C22×C22⋊D7112yes—
720C2×C4C22×C22⋊D7112yes—
721C2×C4C22×C22⋊D7112yes—
722C2×C4C22×C22⋊D7111yescharacteristic
723C2×C4C2×#1176586512yes—
724C2×C4C2×#1176586512yes—
725C2×C4C24×D7111yescharacteristic
726C8—1422no—
727C8—1422no—
728C8—1422no—
729C8—1422no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—24no—
734C22—42no—
735C22—42no—
736C22—44no—
737C22—48no—
738C22—2842no—
739C22—2842no—
740C22—2842no—
741C22—5684no—
742C22#1798651012yes—
743C22#1798680712yes—
744C22#1798681012yes—
745C22C23×C22⋊D7111yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—22no—
750C4—22no—
751C4—24no—
752C4—42no—
753C4—42no—
754C4—2842no—
755C4—2842no—
756C4—2842no—
757C4#1798651012yes—
758C4C22×#1176586511yescharacteristic
759C4C22×#1176586511yescharacteristic
760C2—42no—
761C2—44no—
762C2—5682no—
763C2#2259861714yesdirect product factor
764C2C2×#1798651011yescharacteristic
765C2C2×#1798680711yescharacteristic
766C2C2×#1798681011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#520×C71C2
socleC23×C71C22×D4
prime radicalC2×#17986144C2
hypercenterC2×#520D71
hypocenterC71C2×#3125
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. C2×#17986620C2semidirect
2. #22598617C2direct (N × H)
3. C2×#17986317C2semidirect
4. C2×#17986329C2semidirect
5. C2×#17986284C2semidirect
6. C2×#17986289C2semidirect
7. C2×#17986221C2semidirect
8. C2×#17986214C2semidirect
9. C2×#17986161C2semidirect
11. C2×#17986109C2semidirect
12. C2×#17986104C2semidirect
13. C2×C4×#11765852C2semidirect
14. C2×C4×#11765853C2semidirect
15. C2×#17986060C2semidirect
16. C2×#520×C71C2semidirect
22. #17986620C22semidirect
33. #17986329C22semidirect
34. #17986317C22semidirect
35. #17986289C22semidirect
36. #17986284C22semidirect
37. #17986221C22semidirect
38. #17986214C22semidirect
39. #17986161C22semidirect
41. #17986109C22semidirect
42. #17986104C22semidirect
43. C4×#11765852C22semidirect
44. C4×#11765853C22semidirect
45. #17986060C22semidirect
66. #520×C71C22semidirect
379. C2×C71#3125semidirect
385. C2×#520D71semidirect
400. C71C2×#3125semidirect
417. #520C2×D71semidirect
763. C2#22598617direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179866202
#225986172
C2×#179863172
C2×#179863292
C2×#179862842
C2×#179862892
C2×#179862212
C2×#179862142
C2×#179861612
C2×#179861442
C2×#179861092
C2×#179861042
C2×C4×#117658522
C2×C4×#117658532
C2×#179860602
C2×#520×C712
C2×#312571