Finite Group Databasebeta

← C2×#22591049 #32156237

Subgroups — C2×#22591049 #32156237

Order 18176.

3566 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556114C211yesmaximal, characteristic
2C22×C4×Dic142C211yesmaximal, characteristic, complemented
3C22×(C22⋊D71)⋊C4C211yesmaximal, characteristic
4#22591049C2116yesmaximal, direct product factor
5C2×#17985903C211yesmaximal, characteristic, complemented
6C2×#17985899C211yesmaximal, characteristic
7C2×#17985891C211yesmaximal, characteristic, complemented
8C2×#17985890C211yesmaximal, characteristic, complemented
9C2×#17985887C211yesmaximal, characteristic, complemented
10C2×#17985874C211yesmaximal, characteristic, complemented
11C2×#17985873C211yesmaximal, characteristic, complemented
12C2×#17985871C211yesmaximal, characteristic, complemented
13C2×#17985870C211yesmaximal, characteristic, complemented
14C2×#17985868C211yesmaximal, characteristic, complemented
15C2×#17985844C211yesmaximal, characteristic, complemented
16C2×#388×C71C211yesmaximal, characteristic, complemented
17C23×Dic142C2211yescharacteristic
18C23×C22⋊D71C2211yescharacteristic
19C24×Dic71C2211yescharacteristic
20C23×C4×D71C2211yescharacteristic
21C2×#14556114C4116yescomplemented
22C2×#14556114C2218yes—
23C2×C4×Dic142—28no—
24C2×C4×Dic142C2218yescomplemented
25C2×(C22⋊D71)⋊C4—28no—
26C2×(C22⋊D71)⋊C4C2218yes—
27C22×C4⋊Dic71C2211yescharacteristic
28C22×C4⋊Dic71C2211yescharacteristic
29C22×Dic71⋊C4C2211yescharacteristic
30C22×Dic71⋊C4C2211yescharacteristic
31C22×Dic71⋊C4C2211yescharacteristic
32C22×Dic71⋊C4C2211yescharacteristic
33C22×Dic71⋊C4C2211yescharacteristic
34C22×C22⋊Dic71C2211yescharacteristic
35C22×C22⋊Dic71C2211yescharacteristic
36C22×(C2×D71)⋊C4C2211yescharacteristic
37C22×(C2×D71)⋊C4C2211yescharacteristic
38C22×(C2×D71)⋊C4C2211yescharacteristic
39C22×(C2×D71)⋊C4C2211yescharacteristic
40C22×(C2×D71)⋊C4C2211yescharacteristic
41C22×C4×Dic71C2211yescharacteristic
42C22×C4×Dic71C2211yescharacteristic
43C22×C4×Dic71C2211yescharacteristic
44C22×C4×Dic71C2211yescharacteristic
45#17985903C2218yescomplemented
46#17985899C2218yes—
47#17985891C2218yescomplemented
48#17985890C2218yescomplemented
49#17985887C2218yescomplemented
50#17985874C2218yescomplemented
51#17985873C2218yescomplemented
52#17985871C2218yescomplemented
53#17985870C2218yescomplemented
54#17985868C2218yescomplemented
55#17985844C2218yescomplemented
56C2×C71⋊#95C2211yescharacteristic
57C2×C71⋊#95C2211yescharacteristic
58C2×C71⋊#95C2211yescharacteristic
59C2×C71⋊#95C2211yescharacteristic
60C2×C71⋊#95C2211yescharacteristic
61C2×C71⋊#95C2211yescharacteristic
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×Dic142—24no—
72C22×Dic142—24no—
73C22×Dic142C2×C418yescomplemented
74C22×Dic142C2314yes—
75C22×C22⋊D71—24no—
76C22×C22⋊D71—24no—
77C22×C22⋊D71C2×C418yes—
78C22×C22⋊D71C2314yes—
79C23×Dic71—24no—
80C23×Dic71—42no—
81C23×Dic71—42no—
82C23×Dic71C2311yescharacteristic
83C23×Dic71C2311yescharacteristic
84C23×Dic71C2311yescharacteristic
85C23×Dic71C2311yescharacteristic
86C23×Dic71C2311yescharacteristic
87C23×Dic71C2311yescharacteristic
88C23×Dic71C2314yes—
89C23×Dic71C2311yescharacteristic
90C22×C4×D71—24no—
91C22×C4×D71—42no—
92C22×C4×D71—42no—
93C22×C4×D71C2314yes—
94#14556114C2×C4164yescomplemented
95C4×Dic142—232no—
96(C22⋊D71)⋊C4—232no—
97C2×C4⋊Dic71—24no—
98C2×C4⋊Dic71—42no—
99C2×C4⋊Dic71C2314yes—
100C2×C4⋊Dic71C2314yes—
101C2×Dic71⋊C4—24no—
102C2×Dic71⋊C4—24no—
103C2×Dic71⋊C4—24no—
104C2×Dic71⋊C4—42no—
105C2×Dic71⋊C4—42no—
106C2×Dic71⋊C4C2314yes—
107C2×Dic71⋊C4C2314yes—
108C2×Dic71⋊C4C2314yes—
109C2×Dic71⋊C4C2314yes—
110C2×Dic71⋊C4C2314yes—
111C2×C22⋊Dic71—42no—
112C2×C22⋊Dic71C2×C418yescomplemented
113C2×C22⋊Dic71C2314yes—
114C2×C22⋊Dic71C2314yes—
115C2×(C2×D71)⋊C4—24no—
116C2×(C2×D71)⋊C4—42no—
117C2×(C2×D71)⋊C4—42no—
118C2×(C2×D71)⋊C4C2×C418yescomplemented
119C2×(C2×D71)⋊C4C2×C418yescomplemented
120C2×(C2×D71)⋊C4C2314yes—
121C2×(C2×D71)⋊C4C2314yes—
122C2×(C2×D71)⋊C4C2314yes—
123C2×(C2×D71)⋊C4C2314yes—
124C2×(C2×D71)⋊C4C2314yes—
125C2×C4×Dic71—24no—
126C2×C4×Dic71—24no—
127C2×C4×Dic71C2×C418yescomplemented
128C2×C4×Dic71D418yes—
129C2×C4×Dic71C2314yes—
130C2×C4×Dic71C2314yes—
131C2×C4×Dic71C2314yes—
132C2×C4×Dic71C2314yes—
133C71⋊#95C2314yes—
134C71⋊#95C2314yes—
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—42no—
147C2×C4⋊C4×C71C2314yes—
148C2×C22⋊C4×C71—24no—
149C2×C22⋊C4×C71—42no—
150C2×C22⋊C4×C71C2×C418yescomplemented
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×Dic142—232no—
167C2×Dic142—28no—
168C2×Dic142—28no—
169C2×Dic142C22×C4116yescomplemented
170C2×C22⋊D71—232no—
171C2×C22⋊D71—28no—
172C2×C22⋊D71—28no—
173C2×C22⋊D71C22×C4116yes—
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×Dic71—22no—
188C22×Dic71—22no—
189C22×Dic71—28no—
190C22×Dic71—44no—
191C22×Dic71—44no—
192C22×Dic71—416no—
193C22×Dic71C22×C414yes—
194C22×Dic71C22×C414yes—
195C22×Dic71C22×C414yes—
196C22×Dic71C2×D414yes—
197C22×Dic71C2×D414yes—
198C22×Dic71#4114yes—
199C22×Dic71C2412yes—
200C22×Dic71C2412yes—
201C22×Dic71C2412yes—
202C22×Dic71C2412yes—
203C22×Dic71C2412yes—
204C22×Dic71C2412yes—
205C22×Dic71C2412yes—
206C2×C4×D71—28no—
207C2×C4×D71—44no—
208C2×C4×D71—44no—
209C2×C4×D71—416no—
210C4⋊Dic71—28no—
211C4⋊Dic71—44no—
212Dic71⋊C4—28no—
213Dic71⋊C4—28no—
214Dic71⋊C4—28no—
215Dic71⋊C4—44no—
216Dic71⋊C4—44no—
217C22⋊Dic71—44no—
218C22⋊Dic71C22×C4116yescomplemented
219(C2×D71)⋊C4—28no—
220(C2×D71)⋊C4—44no—
221(C2×D71)⋊C4—44no—
222(C2×D71)⋊C4C22×C4116yescomplemented
223(C2×D71)⋊C4C22×C4116yescomplemented
224C4×Dic71—28no—
225C4×Dic71—28no—
226C4×Dic71C22×C4116yescomplemented
227C4×Dic71C2×D4116yes—
228C24×C71—22no—
229C24×C71—22no—
230C24×C71—22no—
231C24×C71—22no—
232C24×C71—22no—
233C24×C71—22no—
234C24×C71C22×C414yes—
235C24×C71C2412yes—
236C24×C71C2411yescharacteristic
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×C71—22no—
251C22×C4×C71—22no—
252C22×C4×C71C22×C414yes—
253C22×C4×C71C22×C414yes—
254C22×C4×C71C2×D414yes—
255C22×C4×C71C2412yes—
256C22×C4×C71C2412yes—
257C22×C4×C71C2412yes—
258C22×C4×C71C2412yes—
259C22×C4×C71C2412yes—
260C22×C4×C71C2412yes—
261C4⋊C4×C71—44no—
262C22⋊C4×C71—28no—
263C22⋊C4×C71—44no—
264C22⋊C4×C71C22×C4116yescomplemented
265C42×C71—28no—
266C23×C71—28no—
267C23×C71—28no—
268C23×C71—28no—
269C23×C71—22no—
270C23×C71—22no—
271C23×C71—22no—
272C23×C71—22no—
273C23×C71—22no—
274C23×C71—22no—
275C23×C71—44no—
276C23×C71—44no—
277C23×C71—44no—
278C23×C71—44no—
279C23×C71C23×C414yes—
280C23×C71C23×C412yes—
281C23×C71C22×D412yes—
282C23×C71C2×#4112yes—
283C23×C71H(5,𝔽2)12yes—
284C23×C71H(5,𝔽2)12yes—
285C23×C712−1+412yes—
286C23×C712−1+412yes—
287C23×C71C2511yescharacteristic
288C22×D71—28no—
289C22×D71—28no—
290C22×D71—28no—
291C22×D71—22no—
292C22×D71—22no—
293C22×D71—22no—
294C22×D71—22no—
295C22×D71—22no—
296C22×D71—22no—
297C22×D71—44no—
298C22×D71—44no—
299C22×D71—44no—
300C22×D71—44no—
301C22×D71C23×C414yes—
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—22no—
320C2×C4×C71—44no—
321C2×C4×C71—44no—
322C2×C4×C71—44no—
323C2×C4×C71C23×C414yes—
324C2×C4×C71C23×C414yes—
325C2×C4×C71C22×D414yes—
326C22⋊D71—232no—
327C2×Dic71—28no—
328C2×Dic71—28no—
329C2×Dic71—28no—
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—22no—
342C2×Dic71—22no—
343C2×Dic71—22no—
344C2×Dic71—22no—
345C2×Dic71—416no—
346C2×Dic71—44no—
347C2×Dic71—44no—
348C2×Dic71—44no—
349C2×Dic71C4×D4116yes—
350C2×Dic71C23×C414yes—
351C2×Dic71C23×C414yes—
352C2×Dic71C23×C414yes—
353C2×Dic71C22×D414yes—
354C2×Dic71C22×D414yes—
355C2×Dic71C2×#4114yes—
356C4×D71—416no—
357Dic142—232no—
358C22×C71—24no—
359C22×C71—24no—
360C22×C71—24no—
361C22×C71—416no—
362C22×C71—42no—
363C22×C71—42no—
364C22×C71—42no—
365C22×C71—42no—
366C22×C71C2×C4×D414yes—
367C22×C71#52014yes—
368C22×C71#52014yes—
369C22×C71#53514yes—
370C22×C71#53614yes—
371C22×C71#54214yes—
372C22×C71#54214yes—
373C22×C71C24×C411yescharacteristic
374C22×C71C23×D411yescharacteristic
375C22×C71C22×#4111yescharacteristic
376C22×C71C2×H(5,𝔽2)11yescharacteristic
377C22×C71C2×H(5,𝔽2)11yescharacteristic
378C22×C71C2×2−1+411yescharacteristic
379C22×C71C2×2−1+411yescharacteristic
380C2×D71—24no—
381C2×D71—24no—
382C2×D71—24no—
383C2×D71—416no—
384C2×D71—42no—
385C2×D71—42no—
386C2×D71—42no—
387C2×D71—42no—
388C4×C71—24no—
389C4×C71—24no—
390C4×C71—24no—
391C4×C71—42no—
392C4×C71—42no—
393C4×C71—42no—
394Dic71—24no—
395Dic71—24no—
396Dic71—24no—
397Dic71—42no—
398Dic71—42no—
399Dic71—42no—
400Dic71C2×C4×D418yes—
401C2×#2326—711nomaximal, Sylow
402C2×C71—44no—
403C2×C71#232618yescomplemented
404C2×C71C22×C4×D411yescharacteristic
405C2×C71C2×#52011yescharacteristic
406C2×C71C2×#52011yescharacteristic
407C2×C71C2×#53511yescharacteristic
408C2×C71C2×#53611yescharacteristic
409C2×C71C2×#54211yescharacteristic
410C2×C71C2×#54211yescharacteristic
411D71—44no—
412C22×#124—711no—
413C22×C4×Q8—711no—
414C22×C4×D4—711no—
415#2326—7116no—
416C2×#391—711no—
417C2×#390—711no—
418C2×#388—711no—
419C2×#388—711no—
420C2×#388—711no—
421C2×#388D7111yescharacteristic, complemented
422C2×#385—711no—
423C2×#385—711no—
424C2×#385—711no—
425C2×#385—711no—
426C2×#384—711no—
427C2×#376—711no—
428C71C2×#232611yescharacteristic, complemented, Sylow
429C23×Q8—711no—
430C23×D4—711no—
431C24×C4—711no—
432C24×C4—711no—
433C2×#124—7116no—
434C2×#124—718no—
435C2×C4×Q8—718no—
436C2×C4×Q8—1428no—
437C2×C4×D4—718no—
438C2×C4×D4—1428no—
439C22×C4⋊C4—711no—
440C22×C4⋊C4—711no—
441C22×C4⋊C4—711no—
442C22×C4⋊C4—711no—
443C22×C4⋊C4—711no—
444C22×C4⋊C4—711no—
445C22×C4⋊C4—711no—
446C22×C4⋊C4C2×D7111yescharacteristic
447C22×C22⋊C4—711no—
448C22×C22⋊C4—711no—
449C22×C22⋊C4—711no—
450C22×C22⋊C4—711no—
451C22×C22⋊C4—711no—
452C22×C22⋊C4—711no—
453C22×C22⋊C4—711no—
454C22×C22⋊C4C2×D7111yescharacteristic
455C22×C22⋊C4C2×D7111yescharacteristic
456C22×C22⋊C4C2×D7111yescharacteristic
457C22×C42—711no—
458C22×C42—711no—
459C22×C42—711no—
460C22×C42—711no—
461C22×C42C2×D7111yescharacteristic
462#391—718no—
463#390—718no—
464#388—718no—
465#388—718no—
466#388—718no—
467#388C2×D7118yescomplemented
468#385—718no—
469#385—718no—
470#385—718no—
471#385—718no—
472#384—718no—
473#376—718no—
474C2×#95—711no—
475C2×#95—711no—
476C2×#95—711no—
477C2×#95—711no—
478C2×#95—711no—
479C2×#95—711no—
480C2×#95C2×D7111yescharacteristic
481C2×#95C2×D7111yescharacteristic
482C25—711no—
483C25C22×D7111yescharacteristic
484C22×Q8—718no—
485C22×Q8—714no—
486C22×Q8—1424no—
487C22×Q8—1424no—
488C22×D4—718no—
489C22×D4—714no—
490C22×D4—1424no—
491C22×D4—1424no—
492C23×C4—2842no—
493C23×C4—2842no—
494C23×C4—2842no—
495C23×C4—2842no—
496C23×C4—714no—
497C23×C4—714no—
498C23×C4—711no—
499C23×C4—711no—
500C23×C4—711no—
501C23×C4—711no—
502C23×C4—711no—
503C23×C4—711no—
504C23×C4—711no—
505C23×C4—1424no—
506C23×C4—1424no—
507C23×C4C22×D7111yescharacteristic
508C23×C4C22×D7111yescharacteristic
509C23×C4C22×D7111yescharacteristic
510C23×C4C22×D7111yescharacteristic
511C23×C4C22×D7111yescharacteristic
512C23×C4C22×D7111yescharacteristic
513#124—7164no—
514C4×Q8—14232no—
515C4×D4—14232no—
516C2×C4⋊C4—42no—
517C2×C4⋊C4—2842no—
518C2×C4⋊C4—2842no—
519C2×C4⋊C4—2842no—
520C2×C4⋊C4—714no—
521C2×C4⋊C4—714no—
522C2×C4⋊C4—714no—
523C2×C4⋊C4—714no—
524C2×C4⋊C4—714no—
525C2×C4⋊C4—714no—
526C2×C4⋊C4—714no—
527C2×C4⋊C4—1424no—
528C2×C4⋊C4—1424no—
529C2×C4⋊C4—1424no—
530C2×C4⋊C4—1424no—
531C2×C4⋊C4C22×D7114yes—
532C2×C22⋊C4—24no—
533C2×C22⋊C4—42no—
534C2×C22⋊C4—2842no—
535C2×C22⋊C4—2842no—
536C2×C22⋊C4—2842no—
537C2×C22⋊C4—714no—
538C2×C22⋊C4—714no—
539C2×C22⋊C4—714no—
540C2×C22⋊C4—718no—
541C2×C22⋊C4—714no—
542C2×C22⋊C4—718no—
543C2×C22⋊C4—718no—
544C2×C22⋊C4—714no—
545C2×C22⋊C4—714no—
546C2×C22⋊C4—714no—
547C2×C22⋊C4—1424no—
548C2×C22⋊C4C4×D7118yescomplemented
549C2×C22⋊C4C22×D7114yes—
550C2×C22⋊C4C22×D7114yes—
551C2×C22⋊C4C22×D7114yes—
552C2×C42—24no—
553C2×C42—718no—
554C2×C42—718no—
555C2×C42—714no—
556C2×C42—714no—
557C2×C42—714no—
558C2×C42—714no—
559C2×C42—1424no—
560C2×C42—1424no—
561C2×C42C22×D7114yes—
562#95—714no—
563#95—714no—
564#95—714no—
565#95—714no—
566#95—714no—
567#95—714no—
568#95C22×D7114yes—
569#95C22×D7114yes—
570C24—22no—
571C24—22no—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—714no—
577C24—712no—
578C24—1422no—
579C24—1422no—
580C24—1422no—
581C24—1422no—
582C24—1422no—
583C24—1422no—
584C24C2×C4×D7114yes—
585C24C23×D7112yes—
586C24C23×D7111yescharacteristic
587C2×Q8—7116no—
588C2×Q8—1428no—
589C2×Q8—1428no—
590C2×Q8—14232no—
591C2×D4—7116no—
592C2×D4—1428no—
593C2×D4—1428no—
594C2×D4—14232no—
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—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—2844no—
611C22×C4—2844no—
612C22×C4—28416no—
613C22×C4—28416no—
614C22×C4—2844no—
615C22×C4—2844no—
616C22×C4—714no—
617C22×C4—714no—
618C22×C4—714no—
619C22×C4—712no—
620C22×C4—714no—
621C22×C4—714no—
622C22×C4—714no—
623C22×C4—712no—
624C22×C4—712no—
625C22×C4—712no—
626C22×C4—712no—
627C22×C4—712no—
628C22×C4—712no—
629C22×C4—1428no—
630C22×C4—1428no—
631C22×C4—1422no—
632C22×C4—1422no—
633C22×C4—1422no—
634C22×C4—1422no—
635C22×C4—1422no—
636C22×C4—1422no—
637C22×C4—1422no—
638C22×C4—1422no—
639C22×C4—1422no—
640C22×C4—1422no—
641C22×C4—1422no—
642C22×C4—1422no—
643C22×C4—1422no—
644C22×C4—1422no—
645C22×C4—1422no—
646C22×C4C2×C4×D7114yes—
647C22×C4C2×C4×D7114yes—
648C22×C4D4×D7114yes—
649C22×C4C23×D7112yes—
650C22×C4C23×D7112yes—
651C22×C4C23×D7112yes—
652C22×C4C23×D7112yes—
653C22×C4C23×D7112yes—
654C22×C4C23×D7112yes—
655C4⋊C4—44no—
656C4⋊C4—2844no—
657C4⋊C4—2844no—
658C4⋊C4—2844no—
659C4⋊C4—1428no—
660C4⋊C4—1428no—
661C4⋊C4—1428no—
662C4⋊C4—1428no—
663C22⋊C4—28no—
664C22⋊C4—44no—
665C22⋊C4—2844no—
666C22⋊C4—2844no—
667C22⋊C4—2844no—
668C22⋊C4—7116no—
669C22⋊C4—7116no—
670C22⋊C4—7116no—
671C22⋊C4—1428no—
672C22⋊C4C2×C4×D71116yescomplemented
673C42—28no—
674C42—7116no—
675C42—7116no—
676C42—1428no—
677C42—1428no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—28no—
685C23—28no—
686C23—28no—
687C23—44no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—2844no—
692C23—2844no—
693C23—2844no—
694C23—2844no—
695C23—714no—
696C23—1422no—
697C23—1422no—
698C23—1422no—
699C23—1422no—
700C23—1422no—
701C23—1422no—
702C23—1428no—
703C23—1428no—
704C23—1428no—
705C23C22×C4×D7114yes—
706C23C22×C4×D7112yes—
707C23C2×D4×D7112yes—
708C23#41×D7112yes—
709C23#1455617312yes—
710C23#1455617412yes—
711C23#1455617512yes—
712C23#1455617512yes—
713C23C24×D7111yescharacteristic
714Q8—14232no—
715D4—14232no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—28no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—28no—
724C2×C4—28no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—28416no—
738C2×C4—2844no—
739C2×C4—2844no—
740C2×C4—2844no—
741C2×C4—28416no—
742C2×C4—714no—
743C2×C4—714no—
744C2×C4—714no—
745C2×C4—7116no—
746C2×C4—714no—
747C2×C4—714no—
748C2×C4—714no—
749C2×C4—1422no—
750C2×C4—1422no—
751C2×C4—1422no—
752C2×C4—1422no—
753C2×C4—1422no—
754C2×C4—1422no—
755C2×C4—1422no—
756C2×C4—1422no—
757C2×C4—1422no—
758C2×C4—1422no—
759C2×C4—1428no—
760C2×C4—1422no—
761C2×C4—1422no—
762C2×C4—1422no—
763C2×C4—1422no—
764C2×C4—1422no—
765C2×C4—1428no—
766C2×C4—1428no—
767C2×C4C22×C4×D7114yes—
768C2×C4C22×C4×D7114yes—
769C2×C4C2×D4×D7114yes—
770C22—24no—
771C22—24no—
772C22—24no—
773C22—416no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—28416no—
779C22—2842no—
780C22—2842no—
781C22—2842no—
782C22—2842no—
783C22—1424no—
784C22—1424no—
785C22—1424no—
786C22C4×D4×D7114yes—
787C22#1798647814yes—
788C22#1798647914yes—
789C22#1798656514yes—
790C22#1798657114yes—
791C22#1798661314yes—
792C22#1798661514yes—
793C22C23×C4×D7111yescharacteristic
794C22C22×D4×D7111yescharacteristic
795C22C2×#41×D7111yescharacteristic
796C22C2×#1455617311yescharacteristic
797C22C2×#1455617411yescharacteristic
798C22C2×#1455617511yescharacteristic
799C22C2×#1455617511yescharacteristic
800C4—24no—
801C4—24no—
802C4—24no—
803C4—42no—
804C4—42no—
805C4—42no—
806C4—2842no—
807C4—2842no—
808C4—2842no—
809C4—718no—
810C4—1424no—
811C4—1424no—
812C4—1424no—
813C2—44no—
814C2—2844no—
815C2#2259104918yesdirect product factor
816C2C2×C4×D4×D7111yescharacteristic
817C2C2×#1798647811yescharacteristic
818C2C2×#1798647911yescharacteristic
819C2C2×#1798656511yescharacteristic
820C2C2×#1798657111yescharacteristic
821C2C2×#1798661311yescharacteristic
822C2C2×#1798661511yescharacteristic
subgroupG/H
centerC24C23×D71
commutatorC22×C71C24×C4
FrattiniC23C24×D71
FittingC2×#388×C71C2
socleC24×C71C24
prime radicalC23×C22⋊D71C22
cosocleC23×C71C25
hypercenterC2×#388D71
hypocenterC71C2×#2326
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic142C2semidirect
4. #22591049C2direct (N × H)
5. C2×#17985903C2semidirect
7. C2×#17985891C2semidirect
8. C2×#17985890C2semidirect
9. C2×#17985887C2semidirect
10. C2×#17985874C2semidirect
11. C2×#17985873C2semidirect
12. C2×#17985871C2semidirect
13. C2×#17985870C2semidirect
14. C2×#17985868C2semidirect
15. C2×#17985844C2semidirect
16. C2×#388×C71C2semidirect
21. C2×#14556114C4semidirect
24. C2×C4×Dic142C22semidirect
45. #17985903C22semidirect
47. #17985891C22semidirect
48. #17985890C22semidirect
49. #17985887C22semidirect
50. #17985874C22semidirect
51. #17985873C22semidirect
52. #17985871C22semidirect
53. #17985870C22semidirect
54. #17985868C22semidirect
55. #17985844C22semidirect
67. #388×C71C22semidirect
73. C22×Dic142C2×C4semidirect
94. #14556114C2×C4semidirect
112. C2×C22⋊Dic71C2×C4semidirect
118. C2×(C2×D71)⋊C4C2×C4semidirect
119. C2×(C2×D71)⋊C4C2×C4semidirect
127. C2×C4×Dic71C2×C4semidirect
150. C2×C22⋊C4×C71C2×C4semidirect
169. C2×Dic142C22×C4semidirect
218. C22⋊Dic71C22×C4semidirect
222. (C2×D71)⋊C4C22×C4semidirect
223. (C2×D71)⋊C4C22×C4semidirect
226. C4×Dic71C22×C4semidirect
264. C22⋊C4×C71C22×C4semidirect
403. C2×C71#2326semidirect
421. C2×#388D71semidirect
428. C71C2×#2326semidirect
467. #388C2×D71semidirect
548. C2×C22⋊C4C4×D71semidirect
672. C22⋊C4C2×C4×D71semidirect
815. C2#22591049direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561142
C22×C4×Dic1422
C22×(C22⋊D71)⋊C42
#225910492
C2×#179859032
C2×#179858992
C2×#179858912
C2×#179858902
C2×#179858872
C2×#179858742
C2×#179858732
C2×#179858712
C2×#179858702
C2×#179858682
C2×#179858442
C2×#388×C712
C2×#232671