Finite Group Databasebeta

← C2×#22592578 #32166016

Subgroups — C2×#22592578 #32166016

Order 18176.

2898 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556123C211yesmaximal, characteristic, complemented
2C22×#14556085C211yesmaximal, characteristic, complemented
3#22592578C2116yesmaximal, direct product factor
4C2×#17985934C211yesmaximal, characteristic, complemented
5C2×#17985934C211yesmaximal, characteristic, complemented
6C2×#17985932C211yesmaximal, characteristic, complemented
7C2×#17985916C211yesmaximal, characteristic
8C2×#17985900C211yesmaximal, characteristic
9C2×#17985890C211yesmaximal, characteristic, complemented
10C2×#17985889C211yesmaximal, characteristic, complemented
11C2×#17985888C211yesmaximal, characteristic, complemented
12C2×#17985880C211yesmaximal, characteristic, complemented
13C2×#17985877C211yesmaximal, characteristic
14C2×#17985873C211yesmaximal, characteristic, complemented
15C2×#17985850C211yesmaximal, characteristic, complemented
16C2×#389×C71C211yesmaximal, characteristic, complemented
17C23×D284C2211yescharacteristic
18C23×C4×D71C2211yescharacteristic
19C2×#14556123—28no—
20C2×#14556123C2218yescomplemented
21C2×#14556085—28no—
22C2×#14556085C2218yescomplemented
23C22×C4⋊Dic71C2211yescharacteristic
24C22×Dic71⋊C4C2211yescharacteristic
25C22×Dic71⋊C4C2211yescharacteristic
26C22×Dic71⋊C4C2211yescharacteristic
27C22×Dic71⋊C4C2211yescharacteristic
28C22×Dic71⋊C4C2211yescharacteristic
29C22×(C2×D71)⋊C4C2211yescharacteristic
30C22×(C2×D71)⋊C4C2211yescharacteristic
31C22×(C2×D71)⋊C4C2211yescharacteristic
32C22×(C2×D71)⋊C4C2211yescharacteristic
33C22×(C2×D71)⋊C4C2211yescharacteristic
34C22×(C2×D71)⋊C4C2211yescharacteristic
35C22×(C2×D71)⋊C4C2211yescharacteristic
36C22×(C2×D71)⋊C4C2211yescharacteristic
37C22×(C2×D71)⋊C4C2211yescharacteristic
38C22×(C2×D71)⋊C4C2211yescharacteristic
39C22×(C2×D71)⋊C4C2211yescharacteristic
40C22×C4×Dic71C2211yescharacteristic
41C22×C4×Dic71C2211yescharacteristic
42C22×C4×Dic71C2211yescharacteristic
43#17985934C2218yescomplemented
44#17985934C2218yescomplemented
45#17985932C2218yescomplemented
46#17985916C2218yes—
47#17985900C2218yes—
48#17985890C2218yescomplemented
49#17985889C2218yescomplemented
50#17985888C2218yescomplemented
51#17985880C2218yescomplemented
52#17985877C2218yes—
53#17985873C2218yescomplemented
54#17985850C2218yescomplemented
55C2×C71⋊#95C2211yescharacteristic
56C2×C71⋊#95C2211yescharacteristic
57C2×C71⋊#95C2211yescharacteristic
58C2×C71⋊#95C2211yescharacteristic
59C2×C71⋊#95C2211yescharacteristic
60C2×C71⋊#95C2211yescharacteristic
61C22×C4⋊C4×C71C2211yescharacteristic
62C22×C4⋊C4×C71C2211yescharacteristic
63C22×C4⋊C4×C71C2211yescharacteristic
64C22×C4⋊C4×C71C2211yescharacteristic
65C22×C42×C71C2211yescharacteristic
66#389×C71C2218yescomplemented
67C2×#95×C71C2211yescharacteristic
68C2×#95×C71C2211yescharacteristic
69C24×D71C2311yescharacteristic
70C24×D71C2311yescharacteristic
71C22×D284—24no—
72C22×D284—24no—
73C22×D284—42no—
74C22×D284C2314yes—
75C23×Dic71C2311yescharacteristic
76C23×Dic71C2311yescharacteristic
77C23×Dic71C2311yescharacteristic
78C23×Dic71C2311yescharacteristic
79C23×Dic71C2311yescharacteristic
80C23×Dic71C2311yescharacteristic
81C22×C4×D71—24no—
82C22×C4×D71—24no—
83C22×C4×D71—24no—
84C22×C4×D71C2314yes—
85#14556123—232no—
86#14556085—232no—
87C2×C4⋊Dic71—24no—
88C2×C4⋊Dic71C2314yes—
89C2×Dic71⋊C4—24no—
90C2×Dic71⋊C4—24no—
91C2×Dic71⋊C4—24no—
92C2×Dic71⋊C4—42no—
93C2×Dic71⋊C4D418yescomplemented
94C2×Dic71⋊C4C2314yes—
95C2×Dic71⋊C4C2314yes—
96C2×Dic71⋊C4C2314yes—
97C2×Dic71⋊C4C2314yes—
98C2×Dic71⋊C4C2314yes—
99C2×(C2×D71)⋊C4—24no—
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)⋊C4—24no—
107C2×(C2×D71)⋊C4—24no—
108C2×(C2×D71)⋊C4—42no—
109C2×(C2×D71)⋊C4—42no—
110C2×(C2×D71)⋊C4C2314yes—
111C2×(C2×D71)⋊C4C2314yes—
112C2×(C2×D71)⋊C4C2314yes—
113C2×(C2×D71)⋊C4C2314yes—
114C2×(C2×D71)⋊C4C2314yes—
115C2×(C2×D71)⋊C4C2314yes—
116C2×(C2×D71)⋊C4C2314yes—
117C2×(C2×D71)⋊C4C2314yes—
118C2×(C2×D71)⋊C4C2314yes—
119C2×(C2×D71)⋊C4C2314yes—
120C2×(C2×D71)⋊C4C2314yes—
121C2×C4×Dic71—24no—
122C2×C4×Dic71—24no—
123C2×C4×Dic71—24no—
124C2×C4×Dic71C2314yes—
125C2×C4×Dic71C2314yes—
126C2×C4×Dic71C2314yes—
127C71⋊#95C2314yes—
128C71⋊#95C2314yes—
129C71⋊#95C2314yes—
130C71⋊#95C2314yes—
131C71⋊#95C2314yes—
132C71⋊#95C2314yes—
133C23×C4×C71C2311yescharacteristic
134C23×C4×C71C2311yescharacteristic
135C23×C4×C71C2311yescharacteristic
136C23×C4×C71C2311yescharacteristic
137C23×C4×C71C2311yescharacteristic
138C23×C4×C71C2311yescharacteristic
139C23×C4×C71C2311yescharacteristic
140C2×C4⋊C4×C71—24no—
141C2×C4⋊C4×C71—24no—
142C2×C4⋊C4×C71—42no—
143C2×C4⋊C4×C71—42no—
144C2×C4⋊C4×C71C2314yes—
145C2×C4⋊C4×C71C2314yes—
146C2×C4⋊C4×C71C2314yes—
147C2×C4⋊C4×C71C2314yes—
148C2×C42×C71—24no—
149C2×C42×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×D71—22no—
160C23×D71—22no—
161C23×D71—22no—
162C23×D71—22no—
163C23×D71—22no—
164C23×D71—22no—
165C23×D71#4114yes—
166C23×D71C2412yes—
167C23×D71C2412yes—
168C2×D284—28no—
169C2×D284—28no—
170C2×D284—44no—
171C2×D284—416no—
172C22×Dic71—22no—
173C22×Dic71—22no—
174C22×Dic71—22no—
175C22×Dic71—22no—
176C22×Dic71—22no—
177C22×Dic71—22no—
178C22×Dic71—22no—
179C22×Dic71—22no—
180C22×Dic71—22no—
181C22×Dic71—22no—
182C22×Dic71—22no—
183C22×Dic71—22no—
184C22×Dic71—22no—
185C22×Dic71—22no—
186C22×Dic71—22no—
187C22×Dic71C2×D414yes—
188C22×Dic71C2×D414yes—
189C22×Dic71#4114yes—
190C22×Dic71C2412yes—
191C22×Dic71C2412yes—
192C22×Dic71C2412yes—
193C22×Dic71C2412yes—
194C22×Dic71C2412yes—
195C22×Dic71C2412yes—
196C2×C4×D71—232no—
197C2×C4×D71—28no—
198C2×C4×D71—28no—
199C2×C4×D71—28no—
200C4⋊Dic71—28no—
201Dic71⋊C4—28no—
202Dic71⋊C4—28no—
203Dic71⋊C4—28no—
204Dic71⋊C4—44no—
205Dic71⋊C4C2×D4116yescomplemented
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—
211(C2×D71)⋊C4—28no—
212(C2×D71)⋊C4—28no—
213(C2×D71)⋊C4—28no—
214(C2×D71)⋊C4—28no—
215(C2×D71)⋊C4—44no—
216(C2×D71)⋊C4—44no—
217C4×Dic71—28no—
218C4×Dic71—28no—
219C4×Dic71—28no—
220C24×C71C2411yescharacteristic
221C22×C4×C71—22no—
222C22×C4×C71—22no—
223C22×C4×C71—22no—
224C22×C4×C71—22no—
225C22×C4×C71—22no—
226C22×C4×C71—22no—
227C22×C4×C71—22no—
228C22×C4×C71—22no—
229C22×C4×C71—22no—
230C22×C4×C71—22no—
231C22×C4×C71—22no—
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×C71C2×D414yes—
240C22×C4×C71#4114yes—
241C22×C4×C71#4114yes—
242C22×C4×C71C2412yes—
243C22×C4×C71C2412yes—
244C22×C4×C71C2412yes—
245C22×C4×C71C2412yes—
246C22×C4×C71C2412yes—
247C22×C4×C71C2412yes—
248C22×C4×C71C2412yes—
249C4⋊C4×C71—28no—
250C4⋊C4×C71—28no—
251C4⋊C4×C71—44no—
252C4⋊C4×C71—44no—
253C42×C71—28no—
254C23×C71C22×D412yes—
255C23×C71C2×#4112yes—
256C23×C71C2×#4112yes—
257C23×C71C2×#4112yes—
258C23×C71C2×#4112yes—
259C23×C71H(5,𝔽2)12yes—
260C23×C712−1+412yes—
261C23×C71C2511yescharacteristic
262C22×D71—28no—
263C22×D71—28no—
264C22×D71—28no—
265C22×D71—22no—
266C22×D71—22no—
267C22×D71—22no—
268C22×D71—22no—
269C22×D71—22no—
270C22×D71—22no—
271C22×D71—22no—
272C22×D71—22no—
273C22×D71—22no—
274C22×D71—22no—
275C22×D71—22no—
276C22×D71—22no—
277C22×D71—22no—
278C22×D71—44no—
279C22×D71—44no—
280C22×D71—44no—
281C22×D71—44no—
282C22×D71—44no—
283C22×D71—44no—
284C22×D71—44no—
285C22×D71—44no—
286C22×D71—44no—
287C22×D71—44no—
288C22×D71—44no—
289C22×D71C2×#4114yes—
290C2×C4×C71—28no—
291C2×C4×C71—28no—
292C2×C4×C71—28no—
293C2×C4×C71—22no—
294C2×C4×C71—22no—
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—
317C2×C4×C71C2×#4114yes—
318C2×Dic71—28no—
319C2×Dic71—28no—
320C2×Dic71—28no—
321C2×Dic71—22no—
322C2×Dic71—22no—
323C2×Dic71—22no—
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—44no—
337C2×Dic71—44no—
338C2×Dic71—44no—
339C2×Dic71C22×D414yes—
340C2×Dic71C22×D414yes—
341C2×Dic71C2×#4114yes—
342D284—416no—
343C4×D71—232no—
344C22×C71#52514yes—
345C22×C71#52914yes—
346C22×C71#54214yes—
347C22×C71#54714yes—
348C22×C71#55014yes—
349C22×C71#55114yes—
350C22×C71#55214yes—
351C22×C71C23×D411yescharacteristic
352C22×C71C22×#4111yescharacteristic
353C22×C71C22×#4111yescharacteristic
354C22×C71C22×#4111yescharacteristic
355C22×C71C22×#4111yescharacteristic
356C22×C71C2×H(5,𝔽2)11yescharacteristic
357C22×C71C2×2−1+411yescharacteristic
358C2×D71—24no—
359C2×D71—24no—
360C2×D71—24no—
361C2×D71—42no—
362C2×D71—42no—
363C2×D71—42no—
364C2×D71—42no—
365C2×D71—416no—
366C2×D71—42no—
367C2×D71—42no—
368C2×D71—42no—
369C2×D71—42no—
370C2×D71—42no—
371C2×D71—42no—
372C2×D71—42no—
373C2×D71—88no—
374C4×C71—24no—
375C4×C71—24no—
376C4×C71—24no—
377C4×C71—42no—
378C4×C71—42no—
379C4×C71—42no—
380C4×C71—42no—
381Dic71—24no—
382Dic71—24no—
383Dic71—24no—
384Dic71—42no—
385Dic71—42no—
386Dic71—42no—
387C2×#2479—711nomaximal, Sylow
388C2×C71#247918yescomplemented
389C2×C71C2×#52511yescharacteristic
390C2×C71C2×#52911yescharacteristic
391C2×C71C2×#54211yescharacteristic
392C2×C71C2×#54711yescharacteristic
393C2×C71C2×#55011yescharacteristic
394C2×C71C2×#55111yescharacteristic
395C2×C71C2×#55211yescharacteristic
396D71—44no—
397D71—82no—
398C22×#126—711no—
399C22×#117—711no—
400#2479—7116no—
401C2×#399—711no—
402C2×#399—711no—
403C2×#398—711no—
404C2×#394—711no—
405C2×#390—711no—
406C2×#389D7111yescharacteristic, complemented
407C2×#388—711no—
408C2×#388—711no—
409C2×#388—711no—
410C2×#387—711no—
411C2×#386—711no—
412C2×#385—711no—
413C2×C4×C4⋊C4—711no—
414C71C2×#247911yescharacteristic, complemented, Sylow
415C23×D4—711no—
416C24×C4—711no—
417C2×#126—718no—
418C2×#126—1428no—
419C2×#117—718no—
420C2×#117—1428no—
421C22×C4⋊C4—711no—
422C22×C4⋊C4—711no—
423C22×C4⋊C4—711no—
424C22×C4⋊C4—711no—
425C22×C4⋊C4—711no—
426C22×C4⋊C4—711no—
427C22×C4⋊C4C2×D7111yescharacteristic
428C22×C4⋊C4C2×D7111yescharacteristic
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⋊C4—711no—
439C22×C22⋊C4—711no—
440C22×C22⋊C4—711no—
441C22×C22⋊C4—711no—
442C22×C42—711no—
443C22×C42—711no—
444C22×C42—711no—
445C22×C42C2×D7111yescharacteristic
446#399—718no—
447#399—718no—
448#398—718no—
449#394—718no—
450#390—718no—
451#389C2×D7118yescomplemented
452#388—718no—
453#388—718no—
454#388—718no—
455#387—718no—
456#386—718no—
457#385—718no—
458C4×C4⋊C4—718no—
459C2×#95—711no—
460C2×#95—711no—
461C2×#95—711no—
462C2×#95—711no—
463C2×#95—711no—
464C2×#95—711no—
465C2×#95C2×D7111yescharacteristic
466C2×#95C2×D7111yescharacteristic
467C25—711no—
468C25—711no—
469C22×D4—2842no—
470C22×D4—714no—
471C22×D4—1424no—
472C22×D4—1424no—
473C23×C4—711no—
474C23×C4—711no—
475C23×C4—711no—
476C23×C4—711no—
477C23×C4—711no—
478C23×C4—711no—
479C23×C4—714no—
480C23×C4—1424no—
481C23×C4—1424no—
482C23×C4—1424no—
483C23×C4C22×D7111yescharacteristic
484C23×C4C22×D7111yescharacteristic
485C23×C4C22×D7111yescharacteristic
486C23×C4C22×D7111yescharacteristic
487C23×C4C22×D7111yescharacteristic
488C23×C4C22×D7111yescharacteristic
489C23×C4C22×D7111yescharacteristic
490#126—14232no—
491#117—14232no—
492C2×C4⋊C4—24no—
493C2×C4⋊C4—24no—
494C2×C4⋊C4—42no—
495C2×C4⋊C4—42no—
496C2×C4⋊C4—2842no—
497C2×C4⋊C4—714no—
498C2×C4⋊C4—718no—
499C2×C4⋊C4—714no—
500C2×C4⋊C4—714no—
501C2×C4⋊C4—714no—
502C2×C4⋊C4—714no—
503C2×C4⋊C4—714no—
504C2×C4⋊C4—1424no—
505C2×C4⋊C4—1424no—
506C2×C4⋊C4—1424no—
507C2×C4⋊C4—1424no—
508C2×C4⋊C4C22×D7114yes—
509C2×C4⋊C4C22×D7114yes—
510C2×C4⋊C4C22×D7114yes—
511C2×C4⋊C4C22×D7114yes—
512C2×C22⋊C4—2842no—
513C2×C22⋊C4—2842no—
514C2×C22⋊C4—714no—
515C2×C22⋊C4—714no—
516C2×C22⋊C4—714no—
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—714no—
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⋊C4—1424no—
532C2×C22⋊C4—1424no—
533C2×C22⋊C4—1424no—
534C2×C42—24no—
535C2×C42—714no—
536C2×C42—714no—
537C2×C42—714no—
538C2×C42—1424no—
539C2×C42—1424no—
540C2×C42—1424no—
541C2×C42C22×D7114yes—
542#95—714no—
543#95—714no—
544#95—714no—
545#95—714no—
546#95—714no—
547#95—714no—
548#95C22×D7114yes—
549#95C22×D7114yes—
550C24—714no—
551C24—712no—
552C24—712no—
553C24—1422no—
554C24—1422no—
555C24—1422no—
556C24—1422no—
557C24—1422no—
558C24—1422no—
559C24—1422no—
560C24—1422no—
561C24—1422no—
562C24—1422no—
563C24—1422no—
564C24—1422no—
565C24—1422no—
566C24C23×D7111yescharacteristic
567C2×D4—28416no—
568C2×D4—2844no—
569C2×D4—1428no—
570C2×D4—1428no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—714no—
590C22×C4—714no—
591C22×C4—714no—
592C22×C4—712no—
593C22×C4—712no—
594C22×C4—712no—
595C22×C4—712no—
596C22×C4—712no—
597C22×C4—712no—
598C22×C4—1428no—
599C22×C4—1428no—
600C22×C4—14232no—
601C22×C4—1422no—
602C22×C4—1422no—
603C22×C4—1422no—
604C22×C4—1422no—
605C22×C4—1422no—
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—1422no—
616C22×C4—1428no—
617C22×C4D4×D7114yes—
618C22×C4#1176586514yes—
619C22×C4#1176586614yes—
620C22×C4C23×D7112yes—
621C22×C4C23×D7112yes—
622C22×C4C23×D7112yes—
623C22×C4C23×D7112yes—
624C22×C4C23×D7112yes—
625C22×C4C23×D7112yes—
626C22×C4C23×D7112yes—
627C4⋊C4—28no—
628C4⋊C4—28no—
629C4⋊C4—44no—
630C4⋊C4—44no—
631C4⋊C4—2844no—
632C4⋊C4—7116no—
633C4⋊C4—1428no—
634C4⋊C4—1428no—
635C4⋊C4—1428no—
636C4⋊C4—1428no—
637C22⋊C4—2844no—
638C22⋊C4—2844no—
639C22⋊C4—1428no—
640C22⋊C4—1428no—
641C22⋊C4—1428no—
642C22⋊C4—1428no—
643C22⋊C4—1428no—
644C22⋊C4—1428no—
645C22⋊C4—1428no—
646C22⋊C4—1428no—
647C22⋊C4—1428no—
648C42—28no—
649C42—1428no—
650C42—1428no—
651C42—1428no—
652C23—2844no—
653C23—2844no—
654C23—2844no—
655C23—2844no—
656C23—2844no—
657C23—2844no—
658C23—2844no—
659C23—2844no—
660C23—2844no—
661C23—2844no—
662C23—2844no—
663C23—714no—
664C23—1422no—
665C23—1422no—
666C23—1422no—
667C23—1422no—
668C23—1422no—
669C23—1422no—
670C23—1422no—
671C23—1422no—
672C23—1422no—
673C23—1422no—
674C23—1422no—
675C23—1422no—
676C23—1422no—
677C23—1428no—
678C23—1428no—
679C23—1428no—
680C23C2×D4×D7112yes—
681C23#41×D7112yes—
682C23#41×D7112yes—
683C23C2×#1176586512yes—
684C23C2×#1176586612yes—
685C23#1455617312yes—
686C23#1455617612yes—
687C23C24×D7111yescharacteristic
688D4—28416no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—28no—
696C2×C4—28no—
697C2×C4—28no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
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—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—2844no—
715C2×C4—2844no—
716C2×C4—2844no—
717C2×C4—714no—
718C2×C4—714no—
719C2×C4—714no—
720C2×C4—14232no—
721C2×C4—1422no—
722C2×C4—1422no—
723C2×C4—1422no—
724C2×C4—1422no—
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—1422no—
735C2×C4—1422no—
736C2×C4—1428no—
737C2×C4—1428no—
738C2×C4—1428no—
739C2×C4C2×D4×D7114yes—
740C2×C4C2×#1176586514yes—
741C2×C4C2×#1176586614yes—
742C22—28416no—
743C22—2842no—
744C22—2842no—
745C22—2842no—
746C22—2842no—
747C22—2842no—
748C22—2842no—
749C22—2842no—
750C22—2842no—
751C22—2842no—
752C22—2842no—
753C22—2842no—
754C22—5688no—
755C22—1424no—
756C22—1424no—
757C22—1424no—
758C22#1798651214yes—
759C22#1798653614yes—
760C22#1798662314yes—
761C22#1798665014yes—
762C22#1798666714yes—
763C22#1798667814yes—
764C22#1798668114yes—
765C22C22×D4×D7111yescharacteristic
766C22C2×#41×D7111yescharacteristic
767C22C2×#41×D7111yescharacteristic
768C22C22×#1176586511yescharacteristic
769C22C22×#1176586611yescharacteristic
770C22C2×#1455617311yescharacteristic
771C22C2×#1455617611yescharacteristic
772C4—24no—
773C4—24no—
774C4—24no—
775C4—42no—
776C4—42no—
777C4—42no—
778C4—42no—
779C4—2842no—
780C4—2842no—
781C4—2842no—
782C4—1424no—
783C4—1424no—
784C4—1424no—
785C2—2844no—
786C2—5682no—
787C2#2259257818yesdirect product factor
788C2C2×#1798651211yescharacteristic
789C2C2×#1798653611yescharacteristic
790C2C2×#1798662311yescharacteristic
791C2C2×#1798665011yescharacteristic
792C2C2×#1798666711yescharacteristic
793C2C2×#1798667811yescharacteristic
794C2C2×#1798668111yescharacteristic
subgroupG/H
centerC24C23×D71
commutator, cosocleC23×C71C25
FrattiniC23C24×D71
FittingC2×#389×C71C2
socleC24×C71C24
prime radicalC23×D284C22
hypercenterC2×#389D71
hypocenterC71C2×#2479
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
1. C22×#14556123C2semidirect
2. C22×#14556085C2semidirect
3. #22592578C2direct (N × H)
4. C2×#17985934C2semidirect
5. C2×#17985934C2semidirect
6. C2×#17985932C2semidirect
9. C2×#17985890C2semidirect
10. C2×#17985889C2semidirect
11. C2×#17985888C2semidirect
12. C2×#17985880C2semidirect
14. C2×#17985873C2semidirect
15. C2×#17985850C2semidirect
16. C2×#389×C71C2semidirect
20. C2×#14556123C22semidirect
22. C2×#14556085C22semidirect
43. #17985934C22semidirect
44. #17985934C22semidirect
45. #17985932C22semidirect
48. #17985890C22semidirect
49. #17985889C22semidirect
50. #17985888C22semidirect
51. #17985880C22semidirect
53. #17985873C22semidirect
54. #17985850C22semidirect
66. #389×C71C22semidirect
93. C2×Dic71⋊C4D4semidirect
205. Dic71⋊C4C2×D4semidirect
388. C2×C71#2479semidirect
406. C2×#389D71semidirect
414. C71C2×#2479semidirect
451. #389C2×D71semidirect
787. C2#22592578direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561232
C22×#145560852
#225925782
C2×#179859342
C2×#179859322
C2×#179859162
C2×#179859002
C2×#179858902
C2×#179858892
C2×#179858882
C2×#179858802
C2×#179858772
C2×#179858732
C2×#179858502
C2×#389×C712
C2×#247971