Finite Group Databasebeta

← C2×#22590800 #32155809

Subgroups — C2×#22590800 #32155809

Order 18176.

3790 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C22⋊D71)⋊C4C211yesmaximal, characteristic
2C22×#14556086C211yesmaximal, characteristic, complemented
3C22×#14556084C211yesmaximal, characteristic, complemented
4#22590800C2116yesmaximal, direct product factor
5C2×#17985899C211yesmaximal, characteristic
6C2×#17985899C211yesmaximal, characteristic
7C2×#17985896C211yesmaximal, characteristic, complemented
8C2×#17985894C211yesmaximal, characteristic, complemented
9C2×#17985892C211yesmaximal, characteristic, complemented
10C2×#17985890C211yesmaximal, characteristic, complemented
11C2×#17985888C211yesmaximal, characteristic, complemented
12C2×#17985850C211yesmaximal, characteristic, complemented
13C2×C22⋊C4×Dic71C211yesmaximal, characteristic, complemented
14C2×#17985846C211yesmaximal, characteristic, complemented
15C2×C42×Dic71C211yesmaximal, characteristic, complemented
16C2×#388×C71C211yesmaximal, characteristic, complemented
17C23×C22⋊D71C2211yescharacteristic
18C24×Dic71C2211yescharacteristic
19C23×C4×D71C2211yescharacteristic
20C2×(C22⋊D71)⋊C4C4116yescomplemented
21C2×(C22⋊D71)⋊C4C2218yes—
22C2×#14556086—28no—
23C2×#14556086C2218yescomplemented
24C2×#14556084—28no—
25C2×#14556084C2218yescomplemented
26C22×C4⋊Dic71C2211yescharacteristic
27C22×Dic71⋊C4C2211yescharacteristic
28C22×Dic71⋊C4C2211yescharacteristic
29C22×Dic71⋊C4C2211yescharacteristic
30C22×Dic71⋊C4C2211yescharacteristic
31C22×Dic71⋊C4C2211yescharacteristic
32C22×C22⋊Dic71C2211yescharacteristic
33C22×C22⋊Dic71C2211yescharacteristic
34C22×(C2×D71)⋊C4C2211yescharacteristic
35C22×(C2×D71)⋊C4C2211yescharacteristic
36C22×(C2×D71)⋊C4C2211yescharacteristic
37C22×(C2×D71)⋊C4C2211yescharacteristic
38C22×(C2×D71)⋊C4C2211yescharacteristic
39C22×C4×Dic71C2211yescharacteristic
40C22×C4×Dic71C2211yescharacteristic
41C22×C4×Dic71C2211yescharacteristic
42C22×C4×Dic71C2211yescharacteristic
43C22×C4×Dic71C2211yescharacteristic
44C22×C4×Dic71C2211yescharacteristic
45C22×C4×Dic71C2211yescharacteristic
46C22×C4×Dic71C2211yescharacteristic
47#17985899C2218yes—
48#17985899C2218yes—
49#17985896C2218yescomplemented
50#17985894C2218yescomplemented
51#17985892C2218yescomplemented
52#17985890C2218yescomplemented
53#17985888C2218yescomplemented
54#17985850C2218yescomplemented
55C22⋊C4×Dic71C2218yescomplemented
56#17985846C2218yescomplemented
57C2×C71⋊#95C2211yescharacteristic
58C2×C71⋊#95C2211yescharacteristic
59C2×C71⋊#95C2211yescharacteristic
60C2×C71⋊#95C2211yescharacteristic
61C42×Dic71C2218yescomplemented
62C22×C4⋊C4×C71C2211yescharacteristic
63C22×C22⋊C4×C71C2211yescharacteristic
64C22×C22⋊C4×C71C2211yescharacteristic
65C22×C22⋊C4×C71C2211yescharacteristic
66C22×C42×C71C2211yescharacteristic
67#388×C71C2218yescomplemented
68C2×#95×C71C2211yescharacteristic
69C2×#95×C71C2211yescharacteristic
70C24×D71C2311yescharacteristic
71C22×C22⋊D71—24no—
72C22×C22⋊D71—24no—
73C22×C22⋊D71C2×C418yes—
74C22×C22⋊D71C2314yes—
75C23×Dic71—24no—
76C23×Dic71—24no—
77C23×Dic71C2×C418yes—
78C23×Dic71C2311yescharacteristic
79C23×Dic71C2311yescharacteristic
80C23×Dic71C2311yescharacteristic
81C23×Dic71C2314yes—
82C23×Dic71C2311yescharacteristic
83C23×Dic71C2311yescharacteristic
84C23×Dic71C2311yescharacteristic
85C23×Dic71C2311yescharacteristic
86C22×C4×D71—24no—
87C22×C4×D71—24no—
88C22×C4×D71C2×C418yes—
89C22×C4×D71C2314yes—
90(C22⋊D71)⋊C4C2×C4164yescomplemented
91#14556086—232no—
92#14556084—232no—
93C2×C4⋊Dic71—24no—
94C2×C4⋊Dic71C2314yes—
95C2×Dic71⋊C4—24no—
96C2×Dic71⋊C4—24no—
97C2×Dic71⋊C4—24no—
98C2×Dic71⋊C4—24no—
99C2×Dic71⋊C4C2×C418yes—
100C2×Dic71⋊C4C2314yes—
101C2×Dic71⋊C4C2314yes—
102C2×Dic71⋊C4C2314yes—
103C2×Dic71⋊C4C2314yes—
104C2×Dic71⋊C4C2314yes—
105C2×C22⋊Dic71—24no—
106C2×C22⋊Dic71—24no—
107C2×C22⋊Dic71C2314yes—
108C2×C22⋊Dic71C2314yes—
109C2×(C2×D71)⋊C4—24no—
110C2×(C2×D71)⋊C4—24no—
111C2×(C2×D71)⋊C4—24no—
112C2×(C2×D71)⋊C4—24no—
113C2×(C2×D71)⋊C4C2×C418yes—
114C2×(C2×D71)⋊C4C2314yes—
115C2×(C2×D71)⋊C4C2314yes—
116C2×(C2×D71)⋊C4C2314yes—
117C2×(C2×D71)⋊C4C2314yes—
118C2×(C2×D71)⋊C4C2314yes—
119C2×C4×Dic71—24no—
120C2×C4×Dic71—24no—
121C2×C4×Dic71—24no—
122C2×C4×Dic71—24no—
123C2×C4×Dic71—24no—
124C2×C4×Dic71—24no—
125C2×C4×Dic71C2×C418yes—
126C2×C4×Dic71D418yescomplemented
127C2×C4×Dic71C2314yes—
128C2×C4×Dic71C2314yes—
129C2×C4×Dic71C2314yes—
130C2×C4×Dic71C2314yes—
131C2×C4×Dic71C2314yes—
132C2×C4×Dic71C2314yes—
133C2×C4×Dic71C2314yes—
134C2×C4×Dic71C2314yes—
135C71⋊#95C2314yes—
136C71⋊#95C2314yes—
137C71⋊#95C2314yes—
138C71⋊#95C2314yes—
139C25×C71C2311yescharacteristic
140C23×C4×C71C2311yescharacteristic
141C23×C4×C71C2311yescharacteristic
142C23×C4×C71C2311yescharacteristic
143C23×C4×C71C2311yescharacteristic
144C23×C4×C71C2311yescharacteristic
145C23×C4×C71C2311yescharacteristic
146C2×C4⋊C4×C71—24no—
147C2×C4⋊C4×C71C2314yes—
148C2×C22⋊C4×C71—24no—
149C2×C22⋊C4×C71—24no—
150C2×C22⋊C4×C71C2×C418yes—
151C2×C22⋊C4×C71C2314yes—
152C2×C22⋊C4×C71C2314yes—
153C2×C22⋊C4×C71C2314yes—
154C2×C42×C71—24no—
155C2×C42×C71C2314yes—
156#95×C71C2314yes—
157#95×C71C2314yes—
158C23×D71—22no—
159C23×D71—22no—
160C23×D71—22no—
161C23×D71—22no—
162C23×D71—22no—
163C23×D71—22no—
164C23×D71C22×C414yes—
165C23×D71C2412yes—
166C2×C22⋊D71—232no—
167C2×C22⋊D71—28no—
168C2×C22⋊D71—28no—
169C2×C22⋊D71C22×C4116yes—
170C22×Dic71—22no—
171C22×Dic71—22no—
172C22×Dic71—22no—
173C22×Dic71—22no—
174C22×Dic71—22no—
175C22×Dic71—22no—
176C22×Dic71—232no—
177C22×Dic71—28no—
178C22×Dic71—28no—
179C22×Dic71—22no—
180C22×Dic71—22no—
181C22×Dic71—22no—
182C22×Dic71—22no—
183C22×Dic71—22no—
184C22×Dic71—22no—
185C22×Dic71C22×C414yes—
186C22×Dic71C22×C4116yes—
187C22×Dic71C22×C414yes—
188C22×Dic71C22×C414yes—
189C22×Dic71C2×D414yes—
190C22×Dic71C2×D414yes—
191C22×Dic71#4114yes—
192C22×Dic71#4114yes—
193C22×Dic71#4114yes—
194C22×Dic71#4114yes—
195C22×Dic71C2412yes—
196C22×Dic71C2412yes—
197C22×Dic71C2412yes—
198C22×Dic71C2412yes—
199C22×Dic71C2412yes—
200C22×Dic71C2412yes—
201C22×Dic71C2412yes—
202C2×C4×D71—232no—
203C2×C4×D71—28no—
204C2×C4×D71—28no—
205C2×C4×D71C22×C4116yes—
206C4⋊Dic71—28no—
207Dic71⋊C4—28no—
208Dic71⋊C4—28no—
209Dic71⋊C4—28no—
210Dic71⋊C4—28no—
211Dic71⋊C4C22×C4116yes—
212C22⋊Dic71—28no—
213C22⋊Dic71—28no—
214(C2×D71)⋊C4—28no—
215(C2×D71)⋊C4—28no—
216(C2×D71)⋊C4—28no—
217(C2×D71)⋊C4—28no—
218(C2×D71)⋊C4C22×C4116yes—
219C4×Dic71—28no—
220C4×Dic71—28no—
221C4×Dic71—28no—
222C4×Dic71—28no—
223C4×Dic71—28no—
224C4×Dic71—28no—
225C4×Dic71C22×C4116yes—
226C4×Dic71C2×D4116yescomplemented
227C24×C71—22no—
228C24×C71—22no—
229C24×C71—22no—
230C24×C71—22no—
231C24×C71—22no—
232C24×C71—22no—
233C24×C71C22×C414yes—
234C24×C71C2412yes—
235C24×C71C2411yescharacteristic
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×C71—22no—
245C22×C4×C71—22no—
246C22×C4×C71—22no—
247C22×C4×C71—22no—
248C22×C4×C71—22no—
249C22×C4×C71—22no—
250C22×C4×C71C22×C414yes—
251C22×C4×C71C22×C414yes—
252C22×C4×C71C2×D414yes—
253C22×C4×C71#4114yes—
254C22×C4×C71C2412yes—
255C22×C4×C71C2412yes—
256C22×C4×C71C2412yes—
257C22×C4×C71C2412yes—
258C22×C4×C71C2412yes—
259C22×C4×C71C2412yes—
260C4⋊C4×C71—28no—
261C22⋊C4×C71—28no—
262C22⋊C4×C71—28no—
263C22⋊C4×C71C22×C4116yes—
264C42×C71—28no—
265C23×C71—28no—
266C23×C71—28no—
267C23×C71—28no—
268C23×C71—22no—
269C23×C71—22no—
270C23×C71—22no—
271C23×C71—22no—
272C23×C71—22no—
273C23×C71—22no—
274C23×C71—44no—
275C23×C71—44no—
276C23×C71—44no—
277C23×C71—44no—
278C23×C71C23×C414yes—
279C23×C71C23×C412yes—
280C23×C71C22×D412yes—
281C23×C71C2×#4112yes—
282C23×C71C2×#4112yes—
283C23×C71C2×#4112yes—
284C23×C71C2×#4112yes—
285C23×C71C2×#4112yes—
286C23×C71C2511yescharacteristic
287C22×D71—28no—
288C22×D71—28no—
289C22×D71—28no—
290C22×D71—22no—
291C22×D71—22no—
292C22×D71—22no—
293C22×D71—22no—
294C22×D71—22no—
295C22×D71—22no—
296C22×D71—44no—
297C22×D71—44no—
298C22×D71—44no—
299C22×D71—44no—
300C22×D71C23×C414yes—
301C2×C4×C71—28no—
302C2×C4×C71—28no—
303C2×C4×C71—28no—
304C2×C4×C71—28no—
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—22no—
312C2×C4×C71—22no—
313C2×C4×C71—22no—
314C2×C4×C71—22no—
315C2×C4×C71—22no—
316C2×C4×C71—22no—
317C2×C4×C71—22no—
318C2×C4×C71—22no—
319C2×C4×C71—44no—
320C2×C4×C71—44no—
321C2×C4×C71C23×C414yes—
322C2×C4×C71C23×C414yes—
323C2×C4×C71C22×D414yes—
324C2×C4×C71C2×#4114yes—
325C22⋊D71—232no—
326C2×Dic71—28no—
327C2×Dic71—28no—
328C2×Dic71—28no—
329C2×Dic71—22no—
330C2×Dic71—22no—
331C2×Dic71—22no—
332C2×Dic71—22no—
333C2×Dic71—22no—
334C2×Dic71—22no—
335C2×Dic71—232no—
336C2×Dic71—22no—
337C2×Dic71—22no—
338C2×Dic71—22no—
339C2×Dic71—22no—
340C2×Dic71—22no—
341C2×Dic71—22no—
342C2×Dic71—44no—
343C2×Dic71—44no—
344C2×Dic71#117116yescomplemented
345C2×Dic71C4×D4116yes—
346C2×Dic71C23×C414yes—
347C2×Dic71C23×C414yes—
348C2×Dic71C23×C414yes—
349C2×Dic71C22×D414yes—
350C2×Dic71C22×D414yes—
351C2×Dic71C2×#4114yes—
352C2×Dic71C2×#4114yes—
353C2×Dic71C2×#4114yes—
354C2×Dic71C2×#4114yes—
355C4×D71—232no—
356C22×C71—24no—
357C22×C71—24no—
358C22×C71—24no—
359C22×C71—42no—
360C22×C71—42no—
361C22×C71—42no—
362C22×C71—42no—
363C22×C71—416no—
364C22×C71C2×#11714yes—
365C22×C71C2×C4×D414yes—
366C22×C71C4×#4114yes—
367C22×C71#52914yes—
368C22×C71#52914yes—
369C22×C71#53214yes—
370C22×C71#53214yes—
371C22×C71C24×C411yescharacteristic
372C22×C71C23×D411yescharacteristic
373C22×C71C22×#4111yescharacteristic
374C22×C71C22×#4111yescharacteristic
375C22×C71C22×#4111yescharacteristic
376C22×C71C22×#4111yescharacteristic
377C22×C71C22×#4111yescharacteristic
378C2×D71—24no—
379C2×D71—24no—
380C2×D71—24no—
381C2×D71—42no—
382C2×D71—42no—
383C2×D71—42no—
384C2×D71—42no—
385C2×D71—416no—
386C4×C71—24no—
387C4×C71—24no—
388C4×C71—24no—
389C4×C71—24no—
390C4×C71—42no—
391C4×C71—42no—
392Dic71—24no—
393Dic71—24no—
394Dic71—24no—
395Dic71—42no—
396Dic71—42no—
397Dic71C2×#11718yescomplemented
398Dic71C2×C4×D418yes—
399C2×#2293—711nomaximal, Sylow
400C2×C71—44no—
401C2×C71#229318yescomplemented
402C2×C71C22×#11711yescharacteristic
403C2×C71C22×C4×D411yescharacteristic
404C2×C71C2×C4×#4111yescharacteristic
405C2×C71C2×#52911yescharacteristic
406C2×C71C2×#52911yescharacteristic
407C2×C71C2×#53211yescharacteristic
408C2×C71C2×#53211yescharacteristic
409D71—44no—
410C22×C4×D4—711no—
411C22×#117—711no—
412C22×#117—711no—
413#2293—7116no—
414C2×#390—711no—
415C2×#390—711no—
416C2×#389—711no—
417C2×#389—711no—
418C2×#388—711no—
419C2×#388—711no—
420C2×#388—711no—
421C2×#388D7111yescharacteristic, complemented
422C2×C4×C4⋊C4—711no—
423C2×C4×C22⋊C4—711no—
424C2×C4×C22⋊C4—711no—
425C2×C43—711no—
426C71C2×#229311yescharacteristic, complemented, Sylow
427C23×D4—711no—
428C24×C4—711no—
429C24×C4—711no—
430C2×C4×D4—7116no—
431C2×C4×D4—718no—
432C2×#117—718no—
433C2×#117—718no—
434C2×#117—1428no—
435C2×#117—1428no—
436C22×C4⋊C4—711no—
437C22×C4⋊C4—711no—
438C22×C4⋊C4—711no—
439C22×C4⋊C4—711no—
440C22×C4⋊C4—711no—
441C22×C4⋊C4—711no—
442C22×C4⋊C4C2×D7111yescharacteristic
443C22×C22⋊C4—711no—
444C22×C22⋊C4—711no—
445C22×C22⋊C4—711no—
446C22×C22⋊C4—711no—
447C22×C22⋊C4—711no—
448C22×C22⋊C4—711no—
449C22×C22⋊C4—711no—
450C22×C22⋊C4C2×D7111yescharacteristic
451C22×C22⋊C4C2×D7111yescharacteristic
452C22×C22⋊C4C2×D7111yescharacteristic
453C22×C42—711no—
454C22×C42—711no—
455C22×C42—711no—
456C22×C42—711no—
457C22×C42—711no—
458C22×C42—711no—
459C22×C42—711no—
460C22×C42—711no—
461C22×C42C2×D7111yescharacteristic
462#390—718no—
463#390—718no—
464#389—718no—
465#389—718no—
466#388—718no—
467#388—718no—
468#388—718no—
469#388C2×D7118yescomplemented
470C4×C4⋊C4—718no—
471C4×C22⋊C4—718no—
472C4×C22⋊C4—718no—
473C2×#95—711no—
474C2×#95—711no—
475C2×#95—711no—
476C2×#95—711no—
477C2×#95C2×D7111yescharacteristic
478C2×#95C2×D7111yescharacteristic
479C43—718no—
480C25—711no—
481C25C22×D7111yescharacteristic
482C22×D4—718no—
483C22×D4—714no—
484C22×D4—1424no—
485C22×D4—1424no—
486C23×C4—711no—
487C23×C4—711no—
488C23×C4—718no—
489C23×C4—714no—
490C23×C4—711no—
491C23×C4—711no—
492C23×C4—711no—
493C23×C4—718no—
494C23×C4—714no—
495C23×C4—711no—
496C23×C4—711no—
497C23×C4—1424no—
498C23×C4—1424no—
499C23×C4—1424no—
500C23×C4—1424no—
501C23×C4C22×D7111yescharacteristic
502C23×C4C22×D7111yescharacteristic
503C23×C4C22×D7111yescharacteristic
504C23×C4C22×D7111yescharacteristic
505C23×C4C22×D7111yescharacteristic
506C23×C4C22×D7111yescharacteristic
507C4×D4—7164no—
508#117—14232no—
509#117—14232no—
510C2×C4⋊C4—24no—
511C2×C4⋊C4—718no—
512C2×C4⋊C4—714no—
513C2×C4⋊C4—714no—
514C2×C4⋊C4—714no—
515C2×C4⋊C4—714no—
516C2×C4⋊C4—714no—
517C2×C4⋊C4—714no—
518C2×C4⋊C4—1424no—
519C2×C4⋊C4—1424no—
520C2×C4⋊C4—1424no—
521C2×C4⋊C4—1424no—
522C2×C4⋊C4—1424no—
523C2×C4⋊C4C22×D7114yes—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—24no—
526C2×C22⋊C4—718no—
527C2×C22⋊C4—714no—
528C2×C22⋊C4—714no—
529C2×C22⋊C4—714no—
530C2×C22⋊C4—714no—
531C2×C22⋊C4—714no—
532C2×C22⋊C4—714no—
533C2×C22⋊C4—714no—
534C2×C22⋊C4—1424no—
535C2×C22⋊C4—1424no—
536C2×C22⋊C4—1424no—
537C2×C22⋊C4—1424no—
538C2×C22⋊C4—1424no—
539C2×C22⋊C4—1424no—
540C2×C22⋊C4C4×D7118yes—
541C2×C22⋊C4C22×D7114yes—
542C2×C22⋊C4C22×D7114yes—
543C2×C22⋊C4C22×D7114yes—
544C2×C42—24no—
545C2×C42—718no—
546C2×C42—718no—
547C2×C42—714no—
548C2×C42—714no—
549C2×C42—714no—
550C2×C42—714no—
551C2×C42—714no—
552C2×C42—714no—
553C2×C42—714no—
554C2×C42—714no—
555C2×C42—1424no—
556C2×C42—1424no—
557C2×C42—1424no—
558C2×C42—1424no—
559C2×C42—1424no—
560C2×C42—1424no—
561C2×C42C22×D7114yes—
562#95—714no—
563#95—714no—
564#95—714no—
565#95—714no—
566#95C22×D7114yes—
567#95C22×D7114yes—
568C24—22no—
569C24—22no—
570C24—22no—
571C24—22no—
572C24—22no—
573C24—22no—
574C24—714no—
575C24—712no—
576C24—1422no—
577C24—1422no—
578C24—1422no—
579C24—1422no—
580C24—1422no—
581C24—1422no—
582C24C2×C4×D7114yes—
583C24C23×D7112yes—
584C24C23×D7111yescharacteristic
585C2×D4—7116no—
586C2×D4—1428no—
587C2×D4—1428no—
588C2×D4—14232no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—714no—
604C22×C4—714no—
605C22×C4—714no—
606C22×C4—714no—
607C22×C4—714no—
608C22×C4—714no—
609C22×C4—712no—
610C22×C4—712no—
611C22×C4—714no—
612C22×C4—7116no—
613C22×C4—714no—
614C22×C4—714no—
615C22×C4—712no—
616C22×C4—712no—
617C22×C4—712no—
618C22×C4—7116no—
619C22×C4—712no—
620C22×C4—712no—
621C22×C4—1428no—
622C22×C4—1428no—
623C22×C4—14232no—
624C22×C4—1422no—
625C22×C4—1422no—
626C22×C4—1422no—
627C22×C4—1422no—
628C22×C4—1422no—
629C22×C4—1422no—
630C22×C4—1428no—
631C22×C4—1428no—
632C22×C4—14232no—
633C22×C4—1422no—
634C22×C4—1422no—
635C22×C4—1422no—
636C22×C4—1422no—
637C22×C4—1422no—
638C22×C4—1422no—
639C22×C4C2×C4×D7114yes—
640C22×C4C2×C4×D7114yes—
641C22×C4D4×D7114yes—
642C22×C4#1176586414yes—
643C22×C4C23×D7112yes—
644C22×C4C23×D7112yes—
645C22×C4C23×D7112yes—
646C22×C4C23×D7112yes—
647C22×C4C23×D7112yes—
648C22×C4C23×D7112yes—
649C4⋊C4—28no—
650C4⋊C4—7116no—
651C4⋊C4—1428no—
652C4⋊C4—1428no—
653C4⋊C4—1428no—
654C4⋊C4—1428no—
655C4⋊C4—1428no—
656C22⋊C4—28no—
657C22⋊C4—28no—
658C22⋊C4—7116no—
659C22⋊C4—1428no—
660C22⋊C4—1428no—
661C22⋊C4—1428no—
662C22⋊C4—1428no—
663C22⋊C4—1428no—
664C22⋊C4—1428no—
665C22⋊C4C2×C4×D71116yes—
666C42—28no—
667C42—7116no—
668C42—7116no—
669C42—1428no—
670C42—1428no—
671C42—1428no—
672C42—1428no—
673C42—1428no—
674C42—1428no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—28no—
682C23—28no—
683C23—28no—
684C23—44no—
685C23—44no—
686C23—44no—
687C23—44no—
688C23—2844no—
689C23—2844no—
690C23—2844no—
691C23—2844no—
692C23—714no—
693C23—1422no—
694C23—1422no—
695C23—1422no—
696C23—1422no—
697C23—1422no—
698C23—1422no—
699C23—1428no—
700C23—1428no—
701C23—1428no—
702C23C22×C4×D7114yes—
703C23C22×C4×D7112yes—
704C23C2×D4×D7112yes—
705C23#41×D7112yes—
706C23#41×D7112yes—
707C23#41×D7112yes—
708C23#41×D7112yes—
709C23C2×#1176586412yes—
710C23C24×D7111yescharacteristic
711D4—14232no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—28no—
721C2×C4—28no—
722C2×C4—28no—
723C2×C4—28no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—2844no—
733C2×C4—2844no—
734C2×C4—714no—
735C2×C4—714no—
736C2×C4—714no—
737C2×C4—714no—
738C2×C4—714no—
739C2×C4—714no—
740C2×C4—7116no—
741C2×C4—7116no—
742C2×C4—714no—
743C2×C4—714no—
744C2×C4—714no—
745C2×C4—14232no—
746C2×C4—1422no—
747C2×C4—1422no—
748C2×C4—1422no—
749C2×C4—1422no—
750C2×C4—1422no—
751C2×C4—1422no—
752C2×C4—14232no—
753C2×C4—1422no—
754C2×C4—1422no—
755C2×C4—1422no—
756C2×C4—1422no—
757C2×C4—1422no—
758C2×C4—1422no—
759C2×C4—1428no—
760C2×C4—1428no—
761C2×C4—1428no—
762C2×C4C22×C4×D7114yes—
763C2×C4C22×C4×D7114yes—
764C2×C4C2×D4×D7114yes—
765C2×C4C2×#1176586414yes—
766C22—24no—
767C22—24no—
768C22—24no—
769C22—416no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—28416no—
775C22—2842no—
776C22—2842no—
777C22—2842no—
778C22—2842no—
779C22—1424no—
780C22—1424no—
781C22—1424no—
782C22#117×D7114yes—
783C22C4×D4×D7114yes—
784C22C4×#1176586414yes—
785C22#1798652614yes—
786C22#1798653214yes—
787C22#1798654414yes—
788C22#1798654814yes—
789C22C23×C4×D7111yescharacteristic
790C22C22×D4×D7111yescharacteristic
791C22C2×#41×D7111yescharacteristic
792C22C2×#41×D7111yescharacteristic
793C22C2×#41×D7111yescharacteristic
794C22C2×#41×D7111yescharacteristic
795C22C22×#1176586411yescharacteristic
796C4—24no—
797C4—24no—
798C4—24no—
799C4—24no—
800C4—42no—
801C4—42no—
802C4—2842no—
803C4—2842no—
804C4—718no—
805C4—718no—
806C4—1424no—
807C4—1424no—
808C4—1424no—
809C2—44no—
810C2—2844no—
811C2#2259080018yesdirect product factor
812C2C2×#117×D7111yescharacteristic
813C2C2×C4×D4×D7111yescharacteristic
814C2C2×C4×#1176586411yescharacteristic
815C2C2×#1798652611yescharacteristic
816C2C2×#1798653211yescharacteristic
817C2C2×#1798654411yescharacteristic
818C2C2×#1798654811yescharacteristic
subgroupG/H
centerC24C23×D71
commutatorC22×C71C24×C4
FrattiniC23C24×D71
FittingC2×#388×C71C2
socleC24×C71C24
prime radicalC23×C22⋊D71C22
cosocleC23×C71C25
hypercenterC2×#388D71
hypocenterC71C2×#2293
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C22×#14556086C2semidirect
3. C22×#14556084C2semidirect
4. #22590800C2direct (N × H)
7. C2×#17985896C2semidirect
8. C2×#17985894C2semidirect
9. C2×#17985892C2semidirect
10. C2×#17985890C2semidirect
11. C2×#17985888C2semidirect
12. C2×#17985850C2semidirect
13. C2×C22⋊C4×Dic71C2semidirect
14. C2×#17985846C2semidirect
15. C2×C42×Dic71C2semidirect
16. C2×#388×C71C2semidirect
20. C2×(C22⋊D71)⋊C4C4semidirect
23. C2×#14556086C22semidirect
25. C2×#14556084C22semidirect
49. #17985896C22semidirect
50. #17985894C22semidirect
51. #17985892C22semidirect
52. #17985890C22semidirect
53. #17985888C22semidirect
54. #17985850C22semidirect
55. C22⋊C4×Dic71C22semidirect
56. #17985846C22semidirect
61. C42×Dic71C22semidirect
67. #388×C71C22semidirect
90. (C22⋊D71)⋊C4C2×C4semidirect
126. C2×C4×Dic71D4semidirect
226. C4×Dic71C2×D4semidirect
344. C2×Dic71#117semidirect
397. Dic71C2×#117semidirect
401. C2×C71#2293semidirect
421. C2×#388D71semidirect
426. C71C2×#2293semidirect
469. #388C2×D71semidirect
811. C2#22590800direct (N × H)

Maximal subgroups

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

subgroupindex
C22×(C22⋊D71)⋊C42
C22×#145560862
C22×#145560842
#225908002
C2×#179858992
C2×#179858962
C2×#179858942
C2×#179858922
C2×#179858902
C2×#179858882
C2×#179858502
C2×C22⋊C4×Dic712
C2×#179858462
C2×C42×Dic712
C2×#388×C712
C2×#229371