Finite Group Databasebeta

← C2×#22596657 #32203331

Subgroups — C2×#22596657 #32203331

Order 18176.

3354 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556123C211yesmaximal, characteristic, complemented
2C23×C4×Dic71C211yesmaximal, characteristic, complemented
3#22596657C2116yesmaximal, direct product factor
4C2×#17985891C211yesmaximal, characteristic, complemented
5C2×#17985889C211yesmaximal, characteristic, complemented
6C2×#17985888C211yesmaximal, characteristic, complemented
7C2×#17985885C211yesmaximal, characteristic, complemented
8C2×#17985882C211yesmaximal, characteristic, complemented
9C2×#17985880C211yesmaximal, characteristic, complemented
10C2×#17985878C211yesmaximal, characteristic
11C2×#17985876C211yesmaximal, characteristic
12C2×#17985876C211yesmaximal, characteristic
13C2×#17985874C211yesmaximal, characteristic, complemented
14C2×#17985871C211yesmaximal, characteristic, complemented
15C2×#17985866C211yesmaximal, characteristic, complemented
16C2×#385×C71C211yesmaximal, characteristic, complemented
17C23×C22⋊D71C2211yescharacteristic
18C24×Dic71C2211yescharacteristic
19C24×Dic71C2211yescharacteristic
20C2×#14556123—28no—
21C2×#14556123C2218yescomplemented
22C22×C4⋊Dic71C2211yescharacteristic
23C22×C4⋊Dic71C2211yescharacteristic
24C22×Dic71⋊C4C2211yescharacteristic
25C22×Dic71⋊C4C2211yescharacteristic
26C22×C22⋊Dic71C2211yescharacteristic
27C22×(C2×D71)⋊C4C2211yescharacteristic
28C22×(C2×D71)⋊C4C2211yescharacteristic
29C22×(C2×D71)⋊C4C2211yescharacteristic
30C22×(C2×D71)⋊C4C2211yescharacteristic
31C22×(C2×D71)⋊C4C2211yescharacteristic
32C22×(C2×D71)⋊C4C2211yescharacteristic
33C22×C4×Dic71—28no—
34C22×C4×Dic71C2211yescharacteristic
35C22×C4×Dic71C2211yescharacteristic
36C22×C4×Dic71C2211yescharacteristic
37C22×C4×Dic71C2211yescharacteristic
38C22×C4×Dic71C2218yescomplemented
39#17985891C2218yescomplemented
40#17985889C2218yescomplemented
41#17985888C2218yescomplemented
42#17985885C2218yescomplemented
43#17985882C2218yescomplemented
44#17985880C2218yescomplemented
45#17985878C2218yes—
46#17985876C2218yes—
47#17985876C2218yes—
48#17985874C2218yescomplemented
49#17985871C2218yescomplemented
50#17985866C2218yescomplemented
51C2×C71⋊#95C2211yescharacteristic
52C2×C71⋊#95C2211yescharacteristic
53C2×C71⋊#95C2211yescharacteristic
54C2×C71⋊#95C2211yescharacteristic
55C2×C71⋊#95C2211yescharacteristic
56C2×C71⋊#95C2211yescharacteristic
57C2×C71⋊#95C2211yescharacteristic
58C2×C71⋊#95C2211yescharacteristic
59C2×C71⋊#95C2211yescharacteristic
60C2×C71⋊#95C2211yescharacteristic
61C24×C4×C71C2211yescharacteristic
62C22×C4⋊C4×C71C2211yescharacteristic
63C22×C4⋊C4×C71C2211yescharacteristic
64C22×C22⋊C4×C71C2211yescharacteristic
65C22×C22⋊C4×C71C2211yescharacteristic
66#385×C71C2218yescomplemented
67C2×#95×C71C2211yescharacteristic
68C2×#95×C71C2211yescharacteristic
69C24×D71C2311yescharacteristic
70C22×C22⋊D71—24no—
71C22×C22⋊D71—24no—
72C22×C22⋊D71—24no—
73C22×C22⋊D71C2314yes—
74C23×Dic71—24no—
75C23×Dic71—24no—
76C23×Dic71—24no—
77C23×Dic71—24no—
78C23×Dic71—24no—
79C23×Dic71—24no—
80C23×Dic71C2314yes—
81C23×Dic71C2314yes—
82C23×Dic71C2311yescharacteristic
83C23×Dic71C2311yescharacteristic
84C23×Dic71C2311yescharacteristic
85C23×Dic71C2311yescharacteristic
86C23×Dic71C2311yescharacteristic
87C23×Dic71C2311yescharacteristic
88C23×Dic71C2311yescharacteristic
89#14556123—232no—
90C2×C4⋊Dic71—24no—
91C2×C4⋊Dic71—24no—
92C2×C4⋊Dic71C2314yes—
93C2×C4⋊Dic71C2314yes—
94C2×Dic71⋊C4—24no—
95C2×Dic71⋊C4—24no—
96C2×Dic71⋊C4C2314yes—
97C2×Dic71⋊C4C2314yes—
98C2×C22⋊Dic71—24no—
99C2×C22⋊Dic71C2314yes—
100C2×(C2×D71)⋊C4—24no—
101C2×(C2×D71)⋊C4—24no—
102C2×(C2×D71)⋊C4—24no—
103C2×(C2×D71)⋊C4—24no—
104C2×(C2×D71)⋊C4—24no—
105C2×(C2×D71)⋊C4—24no—
106C2×(C2×D71)⋊C4C2314yes—
107C2×(C2×D71)⋊C4C2314yes—
108C2×(C2×D71)⋊C4C2314yes—
109C2×(C2×D71)⋊C4C2314yes—
110C2×(C2×D71)⋊C4C2314yes—
111C2×(C2×D71)⋊C4C2314yes—
112C2×C4×Dic71—24no—
113C2×C4×Dic71—24no—
114C2×C4×Dic71—232no—
115C2×C4×Dic71—24no—
116C2×C4×Dic71D418yescomplemented
117C2×C4×Dic71C2314yes—
118C2×C4×Dic71C2314yes—
119C2×C4×Dic71C2314yes—
120C2×C4×Dic71C2314yes—
121C71⋊#95C2314yes—
122C71⋊#95C2314yes—
123C71⋊#95C2314yes—
124C71⋊#95C2314yes—
125C71⋊#95C2314yes—
126C71⋊#95C2314yes—
127C71⋊#95C2314yes—
128C71⋊#95C2314yes—
129C71⋊#95C2314yes—
130C71⋊#95C2314yes—
131C25×C71C2311yescharacteristic
132C23×C4×C71—24no—
133C23×C4×C71—24no—
134C23×C4×C71—24no—
135C23×C4×C71C2311yescharacteristic
136C23×C4×C71C2311yescharacteristic
137C23×C4×C71C2311yescharacteristic
138C23×C4×C71C2311yescharacteristic
139C23×C4×C71C2314yes—
140C23×C4×C71C2311yescharacteristic
141C23×C4×C71C2311yescharacteristic
142C2×C4⋊C4×C71—24no—
143C2×C4⋊C4×C71—24no—
144C2×C4⋊C4×C71C2314yes—
145C2×C4⋊C4×C71C2314yes—
146C2×C22⋊C4×C71—24no—
147C2×C22⋊C4×C71—24no—
148C2×C22⋊C4×C71C2314yes—
149C2×C22⋊C4×C71C2314yes—
150#95×C71C2314yes—
151#95×C71C2314yes—
152C23×D71—22no—
153C23×D71—22no—
154C23×D71—22no—
155C23×D71—22no—
156C23×D71—22no—
157C23×D71—22no—
158C23×D71—22no—
159C23×D71C2412yes—
160C2×C22⋊D71—28no—
161C2×C22⋊D71—28no—
162C2×C22⋊D71—28no—
163C2×C22⋊D71—416no—
164C22×Dic71—232no—
165C22×Dic71—232no—
166C22×Dic71—22no—
167C22×Dic71—22no—
168C22×Dic71—22no—
169C22×Dic71—22no—
170C22×Dic71—28no—
171C22×Dic71—22no—
172C22×Dic71—22no—
173C22×Dic71—28no—
174C22×Dic71—22no—
175C22×Dic71—22no—
176C22×Dic71—28no—
177C22×Dic71—28no—
178C22×Dic71—28no—
179C22×Dic71—28no—
180C22×Dic71—22no—
181C22×Dic71—22no—
182C22×Dic71—22no—
183C22×Dic71—22no—
184C22×Dic71—22no—
185C22×Dic71—22no—
186C22×Dic71—22no—
187C22×Dic71—22no—
188C22×Dic71—22no—
189C22×Dic71C2×D414yes—
190C22×Dic71C2×D414yes—
191C22×Dic71#4114yes—
192C22×Dic71#4114yes—
193C22×Dic71C2412yes—
194C22×Dic71C2412yes—
195C22×Dic71C2412yes—
196C22×Dic71C2412yes—
197C22×Dic71C2412yes—
198C22×Dic71C2412yes—
199C22×Dic71C2412yes—
200C4⋊Dic71—28no—
201C4⋊Dic71—28no—
202Dic71⋊C4—28no—
203Dic71⋊C4—28no—
204C22⋊Dic71—28no—
205(C2×D71)⋊C4—28no—
206(C2×D71)⋊C4—28no—
207(C2×D71)⋊C4—28no—
208(C2×D71)⋊C4—28no—
209(C2×D71)⋊C4—28no—
210(C2×D71)⋊C4—28no—
211C4×Dic71—28no—
212C4×Dic71—28no—
213C4×Dic71—28no—
214C4×Dic71C2×D4116yescomplemented
215C24×C71—22no—
216C24×C71—22no—
217C24×C71—22no—
218C24×C71—22no—
219C24×C71#4114yes—
220C24×C71#4114yes—
221C24×C71#4114yes—
222C24×C71C2412yes—
223C24×C71C2411yescharacteristic
224C22×C4×C71—232no—
225C22×C4×C71—22no—
226C22×C4×C71—28no—
227C22×C4×C71—22no—
228C22×C4×C71—22no—
229C22×C4×C71—22no—
230C22×C4×C71—28no—
231C22×C4×C71—28no—
232C22×C4×C71—22no—
233C22×C4×C71—22no—
234C22×C4×C71—22no—
235C22×C4×C71—22no—
236C22×C4×C71—22no—
237C22×C4×C71—22no—
238C22×C4×C71—22no—
239C22×C4×C71—22no—
240C22×C4×C71—22no—
241C22×C4×C71—22no—
242C22×C4×C71—22no—
243C22×C4×C71—22no—
244C22×C4×C71C2×D414yes—
245C22×C4×C71#4114yes—
246C22×C4×C71C2412yes—
247C22×C4×C71C2412yes—
248C22×C4×C71C2412yes—
249C22×C4×C71C2412yes—
250C22×C4×C71C2412yes—
251C22×C4×C71C2412yes—
252C4⋊C4×C71—28no—
253C4⋊C4×C71—28no—
254C22⋊C4×C71—28no—
255C22⋊C4×C71—28no—
256C23×C71—28no—
257C23×C71—28no—
258C23×C71—28no—
259C23×C71—28no—
260C23×C71—28no—
261C23×C71—28no—
262C23×C71—22no—
263C23×C71—22no—
264C23×C71—22no—
265C23×C71—22no—
266C23×C71#126116yescomplemented
267C23×C71C22×D412yes—
268C23×C71C2×#4112yes—
269C23×C71C2×#4112yes—
270C23×C71C2×#4114yes—
271C23×C71C2×#4112yes—
272C23×C71C2×#4112yes—
273C23×C71C2×#4114yes—
274C23×C71C2×#4112yes—
275C23×C71C2×#4114yes—
276C23×C71C2×#4112yes—
277C23×C71C2511yescharacteristic
278C22×D71—22no—
279C22×D71—22no—
280C22×D71—22no—
281C22×D71—22no—
282C22×D71—22no—
283C22×D71—22no—
284C22×D71—22no—
285C22×D71—44no—
286C22×D71—44no—
287C22×D71—44no—
288C22×D71—44no—
289C22×D71—44no—
290C22×D71—44no—
291C22×D71—44no—
292C2×C4×C71—232no—
293C2×C4×C71—28no—
294C2×C4×C71—28no—
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—22no—
302C2×C4×C71—22no—
303C2×C4×C71—22no—
304C2×C4×C71—22no—
305C2×C4×C71—22no—
306C2×C4×C71—22no—
307C2×C4×C71—22no—
308C2×C4×C71—22no—
309C2×C4×C71—22no—
310C2×C4×C71—22no—
311C2×C4×C71—44no—
312C2×C4×C71—44no—
313C2×C4×C71—44no—
314C2×C4×C71—44no—
315C2×C4×C71C22×D414yes—
316C2×C4×C71C2×#4114yes—
317C22⋊D71—416no—
318C2×Dic71—232no—
319C2×Dic71—232no—
320C2×Dic71—28no—
321C2×Dic71—28no—
322C2×Dic71—28no—
323C2×Dic71—28no—
324C2×Dic71—22no—
325C2×Dic71—22no—
326C2×Dic71—22no—
327C2×Dic71—22no—
328C2×Dic71—22no—
329C2×Dic71—22no—
330C2×Dic71—22no—
331C2×Dic71—22no—
332C2×Dic71—22no—
333C2×Dic71—22no—
334C2×Dic71—22no—
335C2×Dic71—22no—
336C2×Dic71—22no—
337C2×Dic71—22no—
338C2×Dic71—22no—
339C2×Dic71—22no—
340C2×Dic71—22no—
341C2×Dic71—44no—
342C2×Dic71—44no—
343C2×Dic71—44no—
344C2×Dic71C22×D414yes—
345C2×Dic71C22×D414yes—
346C2×Dic71C2×#4114yes—
347C2×Dic71C2×#4114yes—
348C22×C71—232no—
349C22×C71—24no—
350C22×C71—24no—
351C22×C71—24no—
352C22×C71—24no—
353C22×C71—24no—
354C22×C71—24no—
355C22×C71#52514yes—
356C22×C71#52514yes—
357C22×C71#52514yes—
358C22×C71C2×#12614yes—
359C22×C71C2×#12618yescomplemented
360C22×C71#52914yes—
361C22×C71#52914yes—
362C22×C71#52914yes—
363C22×C71C23×D411yescharacteristic
364C22×C71C22×#4111yescharacteristic
365C22×C71C22×#4111yescharacteristic
366C22×C71C22×#4111yescharacteristic
367C22×C71C22×#4111yescharacteristic
368C22×C71C22×#4111yescharacteristic
369C22×C71C22×#4111yescharacteristic
370C2×D71—42no—
371C2×D71—42no—
372C2×D71—42no—
373C2×D71—42no—
374C2×D71—42no—
375C2×D71—42no—
376C2×D71—42no—
377C2×D71—88no—
378C4×C71—24no—
379C4×C71—24no—
380C4×C71—42no—
381C4×C71—42no—
382C4×C71—42no—
383C4×C71—42no—
384Dic71—24no—
385Dic71—24no—
386Dic71—24no—
387Dic71—24no—
388Dic71—42no—
389Dic71—42no—
390Dic71—42no—
391C2×#2852—711nomaximal, Sylow
392C2×C71—28no—
393C2×C71#285218yescomplemented
394C2×C71C2×#52511yescharacteristic
395C2×C71C2×#52511yescharacteristic
396C2×C71C2×#52511yescharacteristic
397C2×C71C22×#12611yescharacteristic
398C2×C71C2×#52911yescharacteristic
399C2×C71C2×#52911yescharacteristic
400C2×C71C2×#52911yescharacteristic
401D71—82no—
402C22×#126—711no—
403C23×C42—711no—
404#2852—7116no—
405C2×#388—711no—
406C2×#388—711no—
407C2×#388—711no—
408C2×#387—711no—
409C2×#387—711no—
410C2×#387—711no—
411C2×#386—711no—
412C2×#386—711no—
413C2×#386—711no—
414C2×#385—711no—
415C2×#385—711no—
416C2×#385D7111yescharacteristic, complemented
417C2×#383—711no—
418C71C2×#285211yescharacteristic, complemented, Sylow
419C23×D4—711no—
420C24×C4—711no—
421C24×C4—711no—
422C24×C4C2×D7111yescharacteristic
423C2×#126—718no—
424C2×#126—1428no—
425C22×C4⋊C4—711no—
426C22×C4⋊C4—711no—
427C22×C4⋊C4—711no—
428C22×C4⋊C4—711no—
429C22×C4⋊C4C2×D7111yescharacteristic
430C22×C4⋊C4C2×D7111yescharacteristic
431C22×C22⋊C4—711no—
432C22×C22⋊C4—711no—
433C22×C22⋊C4—711no—
434C22×C22⋊C4—711no—
435C22×C22⋊C4—711no—
436C22×C22⋊C4—711no—
437C22×C22⋊C4—711no—
438C22×C22⋊C4C2×D7111yescharacteristic
439C22×C22⋊C4C2×D7111yescharacteristic
440C22×C42—711no—
441C22×C42—718no—
442C22×C42—711no—
443C22×C42—711no—
444C22×C42—711no—
445C22×C42—1428no—
446#388—718no—
447#388—718no—
448#388—718no—
449#387—718no—
450#387—718no—
451#387—718no—
452#386—718no—
453#386—718no—
454#386—718no—
455#385—718no—
456#385—718no—
457#385C2×D7118yescomplemented
458#383—718no—
459C2×#95—711no—
460C2×#95—711no—
461C2×#95—711no—
462C2×#95—711no—
463C2×#95—711no—
464C2×#95—711no—
465C2×#95—711no—
466C2×#95—711no—
467C2×#95—711no—
468C2×#95—711no—
469C2×#95C2×D7111yescharacteristic
470C2×#95C2×D7111yescharacteristic
471C25—711no—
472C25C22×D7111yescharacteristic
473C22×D4—714no—
474C22×D4—1424no—
475C22×D4—1424no—
476C22×D4—1424no—
477C23×C4—24no—
478C23×C4—24no—
479C23×C4—24no—
480C23×C4—711no—
481C23×C4—711no—
482C23×C4—711no—
483C23×C4—711no—
484C23×C4—714no—
485C23×C4—714no—
486C23×C4—711no—
487C23×C4—711no—
488C23×C4—711no—
489C23×C4—1424no—
490C23×C4—1424no—
491C23×C4—1424no—
492C23×C4—1424no—
493C23×C4—1424no—
494C23×C4—1424no—
495C23×C4C22×D7114yes—
496C23×C4C22×D7111yescharacteristic
497C23×C4C22×D7111yescharacteristic
498C23×C4C22×D7111yescharacteristic
499C23×C4C22×D7111yescharacteristic
500C23×C4C22×D7111yescharacteristic
501C23×C4C22×D7111yescharacteristic
502#126—14232no—
503C2×C4⋊C4—24no—
504C2×C4⋊C4—24no—
505C2×C4⋊C4—714no—
506C2×C4⋊C4—714no—
507C2×C4⋊C4—714no—
508C2×C4⋊C4—714no—
509C2×C4⋊C4—1424no—
510C2×C4⋊C4—1424no—
511C2×C4⋊C4—1424no—
512C2×C4⋊C4—1424no—
513C2×C4⋊C4C22×D7114yes—
514C2×C4⋊C4C22×D7114yes—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—714no—
518C2×C22⋊C4—714no—
519C2×C22⋊C4—714no—
520C2×C22⋊C4—714no—
521C2×C22⋊C4—714no—
522C2×C22⋊C4—714no—
523C2×C22⋊C4—714no—
524C2×C22⋊C4—1424no—
525C2×C22⋊C4—1424no—
526C2×C22⋊C4—1424no—
527C2×C22⋊C4—1424no—
528C2×C22⋊C4—1424no—
529C2×C22⋊C4—1424no—
530C2×C22⋊C4—1424no—
531C2×C22⋊C4C22×D7114yes—
532C2×C22⋊C4C22×D7114yes—
533C2×C42—718no—
534C2×C42—714no—
535C2×C42—714no—
536C2×C42—714no—
537C2×C42—714no—
538C2×C42—14232no—
539C2×C42—1424no—
540C2×C42—1424no—
541C2×C42—1424no—
542#95—714no—
543#95—714no—
544#95—714no—
545#95—714no—
546#95—714no—
547#95—714no—
548#95—714no—
549#95—714no—
550#95—714no—
551#95—714no—
552#95C22×D7114yes—
553#95C22×D7114yes—
554C24—22no—
555C24—22no—
556C24—22no—
557C24—22no—
558C24—712no—
559C24—1422no—
560C24—1422no—
561C24—1422no—
562C24—1422no—
563C24—1422no—
564C24—1422no—
565C24—1422no—
566C24#1176586414yes—
567C24#1176586514yes—
568C24#1176586614yes—
569C24C23×D7112yes—
570C24C23×D7111yescharacteristic
571C2×D4—28416no—
572C2×D4—1428no—
573C2×D4—1428no—
574C2×D4—1428no—
575C22×C4—232no—
576C22×C4—22no—
577C22×C4—28no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—28no—
582C22×C4—28no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—714no—
596C22×C4—714no—
597C22×C4—714no—
598C22×C4—714no—
599C22×C4—712no—
600C22×C4—712no—
601C22×C4—712no—
602C22×C4—712no—
603C22×C4—712no—
604C22×C4—712no—
605C22×C4—712no—
606C22×C4—1422no—
607C22×C4—1422no—
608C22×C4—1422no—
609C22×C4—1422no—
610C22×C4—1422no—
611C22×C4—1422no—
612C22×C4—1422no—
613C22×C4—1422no—
614C22×C4—1422no—
615C22×C4—1428no—
616C22×C4—1428no—
617C22×C4—1428no—
618C22×C4—1428no—
619C22×C4—14232no—
620C22×C4—14232no—
621C22×C4—1422no—
622C22×C4—1422no—
623C22×C4—1422no—
624C22×C4—1422no—
625C22×C4—1428no—
626C22×C4—1422no—
627C22×C4—1422no—
628C22×C4—1428no—
629C22×C4—1422no—
630C22×C4—1422no—
631C22×C4D4×D7114yes—
632C22×C4#1176586414yes—
633C22×C4C23×D7112yes—
634C22×C4C23×D7112yes—
635C22×C4C23×D7112yes—
636C22×C4C23×D7112yes—
637C22×C4C23×D7112yes—
638C22×C4C23×D7112yes—
639C4⋊C4—28no—
640C4⋊C4—28no—
641C4⋊C4—1428no—
642C4⋊C4—1428no—
643C4⋊C4—1428no—
644C4⋊C4—1428no—
645C22⋊C4—28no—
646C22⋊C4—28no—
647C22⋊C4—1428no—
648C22⋊C4—1428no—
649C22⋊C4—1428no—
650C22⋊C4—1428no—
651C22⋊C4—1428no—
652C22⋊C4—1428no—
653C22⋊C4—1428no—
654C42—7116no—
655C42—1428no—
656C42—1428no—
657C42—1428no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—28no—
663C23—28no—
664C23—28no—
665C23—28no—
666C23—28no—
667C23—28no—
668C23—2844no—
669C23—2844no—
670C23—2844no—
671C23—2844no—
672C23—2844no—
673C23—2844no—
674C23—2844no—
675C23—1422no—
676C23—1422no—
677C23—1422no—
678C23—1422no—
679C23—1422no—
680C23—1422no—
681C23—1422no—
682C23#14556123116yescomplemented
683C23C2×D4×D7112yes—
684C23#41×D7112yes—
685C23#41×D7112yes—
686C23C2×#1176586414yes—
687C23C2×#1176586412yes—
688C23C2×#1176586412yes—
689C23C2×#1176586514yes—
690C23C2×#1176586512yes—
691C23C2×#1176586614yes—
692C23C2×#1176586612yes—
693C23C24×D7111yescharacteristic
694D4—28416no—
695C2×C4—232no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—28no—
701C2×C4—28no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—2844no—
719C2×C4—2844no—
720C2×C4—2844no—
721C2×C4—714no—
722C2×C4—714no—
723C2×C4—714no—
724C2×C4—714no—
725C2×C4—1422no—
726C2×C4—1422no—
727C2×C4—1422no—
728C2×C4—1422no—
729C2×C4—1422no—
730C2×C4—1422no—
731C2×C4—1422no—
732C2×C4—1422no—
733C2×C4—1422no—
734C2×C4—14232no—
735C2×C4—14232no—
736C2×C4—1422no—
737C2×C4—1422no—
738C2×C4—1422no—
739C2×C4—1422no—
740C2×C4—1422no—
741C2×C4—1422no—
742C2×C4—1422no—
743C2×C4—1422no—
744C2×C4—1428no—
745C2×C4—1428no—
746C2×C4—1428no—
747C2×C4—1428no—
748C2×C4C2×D4×D7114yes—
749C2×C4C2×#1176586414yes—
750C22—232no—
751C22—24no—
752C22—24no—
753C22—24no—
754C22—24no—
755C22—24no—
756C22—24no—
757C22—2842no—
758C22—2842no—
759C22—2842no—
760C22—2842no—
761C22—2842no—
762C22—2842no—
763C22—2842no—
764C22—5688no—
765C22#1798650514yes—
766C22#1798650814yes—
767C22#1798651214yes—
768C22C2×#1455612314yes—
769C22C2×#1455612318yescomplemented
770C22#1798652614yes—
771C22#1798652914yes—
772C22#1798653514yes—
773C22C22×D4×D7111yescharacteristic
774C22C2×#41×D7111yescharacteristic
775C22C2×#41×D7111yescharacteristic
776C22C22×#1176586411yescharacteristic
777C22C22×#1176586411yescharacteristic
778C22C22×#1176586511yescharacteristic
779C22C22×#1176586611yescharacteristic
780C4—24no—
781C4—24no—
782C4—42no—
783C4—42no—
784C4—42no—
785C4—42no—
786C4—2842no—
787C4—2842no—
788C4—2842no—
789C4—1424no—
790C4—1424no—
791C4—1424no—
792C4—1424no—
793C2—28no—
794C2—5682no—
795C2#2259665718yesdirect product factor
796C2C2×#1798650511yescharacteristic
797C2C2×#1798650811yescharacteristic
798C2C2×#1798651211yescharacteristic
799C2C22×#1455612311yescharacteristic
800C2C2×#1798652611yescharacteristic
801C2C2×#1798652911yescharacteristic
802C2C2×#1798653511yescharacteristic
subgroupG/H
centerC24C23×D71
commutator, cosocleC23×C71C25
FrattiniC23C24×D71
FittingC2×#385×C71C2
socleC24×C71C24
prime radicalC23×C22⋊D71C22
hypercenterC2×#385D71
hypocenterC71C2×#2852
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C22×#14556123C2semidirect
2. C23×C4×Dic71C2semidirect
3. #22596657C2direct (N × H)
4. C2×#17985891C2semidirect
5. C2×#17985889C2semidirect
6. C2×#17985888C2semidirect
7. C2×#17985885C2semidirect
8. C2×#17985882C2semidirect
9. C2×#17985880C2semidirect
13. C2×#17985874C2semidirect
14. C2×#17985871C2semidirect
15. C2×#17985866C2semidirect
16. C2×#385×C71C2semidirect
21. C2×#14556123C22semidirect
38. C22×C4×Dic71C22semidirect
39. #17985891C22semidirect
40. #17985889C22semidirect
41. #17985888C22semidirect
42. #17985885C22semidirect
43. #17985882C22semidirect
44. #17985880C22semidirect
48. #17985874C22semidirect
49. #17985871C22semidirect
50. #17985866C22semidirect
66. #385×C71C22semidirect
116. C2×C4×Dic71D4semidirect
214. C4×Dic71C2×D4semidirect
266. C23×C71#126semidirect
359. C22×C71C2×#126semidirect
393. C2×C71#2852semidirect
416. C2×#385D71semidirect
418. C71C2×#2852semidirect
457. #385C2×D71semidirect
682. C23#14556123semidirect
769. C22C2×#14556123semidirect
795. C2#22596657direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561232
C23×C4×Dic712
#225966572
C2×#179858912
C2×#179858892
C2×#179858882
C2×#179858852
C2×#179858822
C2×#179858802
C2×#179858782
C2×#179858762
C2×#179858742
C2×#179858712
C2×#179858662
C2×#385×C712
C2×#285271