Finite Group Databasebeta

← C2×#22591391 #32157036

Subgroups — C2×#22591391 #32157036

Order 18176.

4262 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556101C211yesmaximal, characteristic
2C22×C4×D284C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D71C211yesmaximal, characteristic, complemented
4#22591391C2116yesmaximal, direct product factor
5C2×#17985892C211yesmaximal, characteristic, complemented
6C2×#17985890C211yesmaximal, characteristic, complemented
7C2×#17985886C211yesmaximal, characteristic, complemented
8C2×#17985883C211yesmaximal, characteristic, complemented
9C2×#17985878C211yesmaximal, characteristic, complemented
10C2×#17985877C211yesmaximal, characteristic, complemented
11C2×#17985875C211yesmaximal, characteristic, complemented
12C2×#17985875C211yesmaximal, characteristic, complemented
13C2×C4×(C2×D71)⋊C4C211yesmaximal, characteristic, complemented
14C2×#17985846C211yesmaximal, characteristic, complemented
15C2×#95×D71C211yesmaximal, characteristic, complemented
16C2×C4×C22⋊C4×C71C211yesmaximal, characteristic, complemented
17C23×D284C2211yescharacteristic
18C23×C22⋊D71C2211yescharacteristic
19C23×C22⋊D71C2211yescharacteristic
20C23×C4×D71C2211yescharacteristic
21C23×C4×D71C2211yescharacteristic
22C23×C4×D71C2211yescharacteristic
23C23×C4×D71C2211yescharacteristic
24C2×#14556101C4116yescomplemented
25C2×#14556101C2218yes—
26C2×C4×D284—28no—
27C2×C4×D284C2218yescomplemented
28C2×C4×C22⋊D71—28no—
29C2×C4×C22⋊D71C2218yescomplemented
30C22×C4⋊Dic71C2211yescharacteristic
31C22×Dic71⋊C4C2211yescharacteristic
32C22×Dic71⋊C4C2211yescharacteristic
33C22×C22⋊Dic71C2211yescharacteristic
34C22×C22⋊Dic71C2211yescharacteristic
35C22×(C2×D71)⋊C4C2211yescharacteristic
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
43#17985892C2218yescomplemented
44#17985890C2218yescomplemented
45#17985886C2218yescomplemented
46#17985883C2218yescomplemented
47#17985878C2218yescomplemented
48#17985877C2218yescomplemented
49#17985875C2218yescomplemented
50#17985875C2218yescomplemented
51C4×(C2×D71)⋊C4C2218yescomplemented
52#17985846C2218yescomplemented
53C2×C71⋊#95C2211yescharacteristic
54C2×C71⋊#95C2211yescharacteristic
55C2×C71⋊#95C2211yescharacteristic
56C2×C71⋊#95C2211yescharacteristic
57C2×C71⋊#95C2211yescharacteristic
58C2×C71⋊#95C2211yescharacteristic
59C2×C71⋊#95C2211yescharacteristic
60C2×C71⋊#95C2211yescharacteristic
61#95×D71C2218yescomplemented
62C24×C4×C71C2211yescharacteristic
63C22×C22⋊C4×C71C2211yescharacteristic
64C22×C22⋊C4×C71C2211yescharacteristic
65C22×C42×C71C2211yescharacteristic
66C22×C42×C71C2211yescharacteristic
67C4×C22⋊C4×C71C2218yescomplemented
68C2×#95×C71C2211yescharacteristic
69C2×#95×C71C2211yescharacteristic
70C24×D71C2311yescharacteristic
71C24×D71C2311yescharacteristic
72C22×D284—24no—
73C22×D284—24no—
74C22×D284C2×C418yescomplemented
75C22×D284C2314yes—
76C22×C22⋊D71—24no—
77C22×C22⋊D71—24no—
78C22×C22⋊D71—42no—
79C22×C22⋊D71—42no—
80C22×C22⋊D71C2×C418yescomplemented
81C22×C22⋊D71C2×C418yescomplemented
82C22×C22⋊D71C2314yes—
83C22×C22⋊D71C2314yes—
84C23×Dic71C2311yescharacteristic
85C23×Dic71C2311yescharacteristic
86C23×Dic71C2311yescharacteristic
87C23×Dic71C2311yescharacteristic
88C23×Dic71C2311yescharacteristic
89C23×Dic71C2311yescharacteristic
90C22×C4×D71—24no—
91C22×C4×D71—24no—
92C22×C4×D71—24no—
93C22×C4×D71—24no—
94C22×C4×D71—24no—
95C22×C4×D71—24no—
96C22×C4×D71—42no—
97C22×C4×D71—42no—
98C22×C4×D71—42no—
99C22×C4×D71—42no—
100C22×C4×D71—42no—
101C22×C4×D71C2×C418yescomplemented
102C22×C4×D71C2314yes—
103C22×C4×D71C2314yes—
104C22×C4×D71C2314yes—
105C22×C4×D71C2314yes—
106#14556101C2×C4164yescomplemented
107C4×D284—232no—
108C4×C22⋊D71—232no—
109C2×C4⋊Dic71—24no—
110C2×C4⋊Dic71C2314yes—
111C2×Dic71⋊C4—24no—
112C2×Dic71⋊C4C2×C418yescomplemented
113C2×Dic71⋊C4C2314yes—
114C2×Dic71⋊C4C2314yes—
115C2×C22⋊Dic71—24no—
116C2×C22⋊Dic71—42no—
117C2×C22⋊Dic71C2314yes—
118C2×C22⋊Dic71C2314yes—
119C2×(C2×D71)⋊C4—24no—
120C2×(C2×D71)⋊C4—24no—
121C2×(C2×D71)⋊C4—24no—
122C2×(C2×D71)⋊C4—42no—
123C2×(C2×D71)⋊C4C2×C418yescomplemented
124C2×(C2×D71)⋊C4D418yescomplemented
125C2×(C2×D71)⋊C4C2314yes—
126C2×(C2×D71)⋊C4C2314yes—
127C2×(C2×D71)⋊C4C2314yes—
128C2×(C2×D71)⋊C4C2314yes—
129C2×(C2×D71)⋊C4C2314yes—
130C2×(C2×D71)⋊C4C2314yes—
131C2×C4×Dic71—24no—
132C2×C4×Dic71—42no—
133C2×C4×Dic71C2314yes—
134C2×C4×Dic71C2314yes—
135C71⋊#95C2314yes—
136C71⋊#95C2314yes—
137C71⋊#95C2314yes—
138C71⋊#95C2314yes—
139C71⋊#95C2314yes—
140C71⋊#95C2314yes—
141C71⋊#95C2314yes—
142C71⋊#95C2314yes—
143C25×C71C2311yescharacteristic
144C23×C4×C71—24no—
145C23×C4×C71—24no—
146C23×C4×C71—42no—
147C23×C4×C71C2311yescharacteristic
148C23×C4×C71C2314yes—
149C23×C4×C71C2311yescharacteristic
150C23×C4×C71C2311yescharacteristic
151C23×C4×C71C2311yescharacteristic
152C23×C4×C71C2311yescharacteristic
153C23×C4×C71C2311yescharacteristic
154C2×C22⋊C4×C71—24no—
155C2×C22⋊C4×C71C2×C418yescomplemented
156C2×C22⋊C4×C71C2314yes—
157C2×C22⋊C4×C71C2314yes—
158C2×C42×C71—24no—
159C2×C42×C71—42no—
160C2×C42×C71C2314yes—
161C2×C42×C71C2314yes—
162#95×C71C2314yes—
163#95×C71C2314yes—
164C23×D71—22no—
165C23×D71—22no—
166C23×D71—22no—
167C23×D71—22no—
168C23×D71—22no—
169C23×D71—22no—
170C23×D71—22no—
171C23×D71—22no—
172C23×D71—22no—
173C23×D71—22no—
174C23×D71C22×C414yes—
175C23×D71C22×C414yes—
176C23×D71C2×D414yes—
177C23×D71#4114yes—
178C23×D71C2412yes—
179C23×D71C2412yes—
180C2×D284—232no—
181C2×D284—28no—
182C2×D284—28no—
183C2×D284C22×C4116yescomplemented
184C2×C22⋊D71—232no—
185C2×C22⋊D71—28no—
186C2×C22⋊D71—28no—
187C2×C22⋊D71—416no—
188C2×C22⋊D71—44no—
189C2×C22⋊D71—44no—
190C2×C22⋊D71C22×C4116yescomplemented
191C2×C22⋊D71C22×C4116yescomplemented
192C22×Dic71—22no—
193C22×Dic71—22no—
194C22×Dic71—22no—
195C22×Dic71—22no—
196C22×Dic71—22no—
197C22×Dic71—22no—
198C22×Dic71—22no—
199C22×Dic71—22no—
200C22×Dic71—22no—
201C22×Dic71—22no—
202C22×Dic71—22no—
203C22×Dic71—22no—
204C22×Dic71—22no—
205C22×Dic71—22no—
206C22×Dic71—22no—
207C22×Dic71C22×C414yes—
208C22×Dic71C22×C414yes—
209C22×Dic71C2×D414yes—
210C22×Dic71C2412yes—
211C22×Dic71C2412yes—
212C22×Dic71C2412yes—
213C22×Dic71C2412yes—
214C22×Dic71C2412yes—
215C22×Dic71C2412yes—
216C2×C4×D71—28no—
217C2×C4×D71—28no—
218C2×C4×D71—28no—
219C2×C4×D71—28no—
220C2×C4×D71—28no—
221C2×C4×D71—28no—
222C2×C4×D71—416no—
223C2×C4×D71—44no—
224C2×C4×D71—44no—
225C2×C4×D71—44no—
226C2×C4×D71—44no—
227C2×C4×D71—44no—
228C2×C4×D71—416no—
229C2×C4×D71—416no—
230C2×C4×D71—416no—
231C2×C4×D71C22×C4116yescomplemented
232C4⋊Dic71—28no—
233Dic71⋊C4—28no—
234Dic71⋊C4C22×C4116yescomplemented
235C22⋊Dic71—28no—
236C22⋊Dic71—44no—
237(C2×D71)⋊C4—28no—
238(C2×D71)⋊C4—28no—
239(C2×D71)⋊C4—28no—
240(C2×D71)⋊C4—44no—
241(C2×D71)⋊C4C22×C4116yescomplemented
242(C2×D71)⋊C4C2×D4116yescomplemented
243C4×Dic71—28no—
244C4×Dic71—44no—
245C24×C71—22no—
246C24×C71—22no—
247C24×C71—22no—
248C24×C71—22no—
249C24×C71—22no—
250C24×C71—22no—
251C24×C71C22×C414yes—
252C24×C71C2412yes—
253C24×C71C2411yescharacteristic
254C22×C4×C71—22no—
255C22×C4×C71—22no—
256C22×C4×C71—22no—
257C22×C4×C71—22no—
258C22×C4×C71—22no—
259C22×C4×C71—22no—
260C22×C4×C71—22no—
261C22×C4×C71—22no—
262C22×C4×C71—22no—
263C22×C4×C71—22no—
264C22×C4×C71—22no—
265C22×C4×C71—22no—
266C22×C4×C71—22no—
267C22×C4×C71—28no—
268C22×C4×C71—28no—
269C22×C4×C71—44no—
270C22×C4×C71—416no—
271C22×C4×C71C22×C414yes—
272C22×C4×C71C22×C414yes—
273C22×C4×C71C2×D414yes—
274C22×C4×C71#4114yes—
275C22×C4×C71#4114yes—
276C22×C4×C71C2412yes—
277C22×C4×C71C2412yes—
278C22×C4×C71C2412yes—
279C22×C4×C71C2412yes—
280C22×C4×C71C2412yes—
281C22×C4×C71C2412yes—
282C22⋊C4×C71—28no—
283C22⋊C4×C71C22×C4116yescomplemented
284C42×C71—28no—
285C42×C71—44no—
286C23×C71—28no—
287C23×C71—28no—
288C23×C71—28no—
289C23×C71—22no—
290C23×C71—22no—
291C23×C71—22no—
292C23×C71—22no—
293C23×C71—22no—
294C23×C71—22no—
295C23×C71—44no—
296C23×C71—44no—
297C23×C71—44no—
298C23×C71—44no—
299C23×C71C23×C414yes—
300C23×C71C23×C412yes—
301C23×C71C22×D412yes—
302C23×C71C2×#4112yes—
303C23×C71C2×#4112yes—
304C23×C71C2×#4112yes—
305C23×C71H(5,𝔽2)12yes—
306C23×C71H(5,𝔽2)12yes—
307C23×C71C2511yescharacteristic
308C22×D71—28no—
309C22×D71—28no—
310C22×D71—28no—
311C22×D71—28no—
312C22×D71—28no—
313C22×D71—28no—
314C22×D71—22no—
315C22×D71—22no—
316C22×D71—22no—
317C22×D71—22no—
318C22×D71—28no—
319C22×D71—28no—
320C22×D71—28no—
321C22×D71—22no—
322C22×D71—22no—
323C22×D71—22no—
324C22×D71—22no—
325C22×D71—22no—
326C22×D71—22no—
327C22×D71—44no—
328C22×D71—44no—
329C22×D71—44no—
330C22×D71—44no—
331C22×D71C4×D4116yes—
332C22×D71C23×C414yes—
333C22×D71C23×C414yes—
334C22×D71C22×D414yes—
335C22×D71C2×#4114yes—
336C2×C4×C71—28no—
337C2×C4×C71—28no—
338C2×C4×C71—28no—
339C2×C4×C71—28no—
340C2×C4×C71—28no—
341C2×C4×C71—22no—
342C2×C4×C71—22no—
343C2×C4×C71—22no—
344C2×C4×C71—22no—
345C2×C4×C71—22no—
346C2×C4×C71—22no—
347C2×C4×C71—22no—
348C2×C4×C71—22no—
349C2×C4×C71—22no—
350C2×C4×C71—22no—
351C2×C4×C71—22no—
352C2×C4×C71—22no—
353C2×C4×C71—22no—
354C2×C4×C71—416no—
355C2×C4×C71—44no—
356C2×C4×C71C23×C414yes—
357C2×C4×C71C23×C414yes—
358C2×C4×C71C22×D414yes—
359C2×C4×C71C2×#4114yes—
360C2×C4×C71C2×#4114yes—
361C22⋊D71—232no—
362C22⋊D71—416no—
363C2×Dic71—28no—
364C2×Dic71—28no—
365C2×Dic71—28no—
366C2×Dic71—22no—
367C2×Dic71—22no—
368C2×Dic71—22no—
369C2×Dic71—22no—
370C2×Dic71—22no—
371C2×Dic71—22no—
372C2×Dic71—22no—
373C2×Dic71—22no—
374C2×Dic71—22no—
375C2×Dic71—22no—
376C2×Dic71—22no—
377C2×Dic71—22no—
378C2×Dic71—22no—
379C2×Dic71—22no—
380C2×Dic71—22no—
381C2×Dic71—44no—
382C2×Dic71—44no—
383C2×Dic71—44no—
384C2×Dic71C23×C414yes—
385C2×Dic71C23×C414yes—
386C2×Dic71C22×D414yes—
387D284—232no—
388C4×D71—416no—
389C4×D71—416no—
390C4×D71—416no—
391C4×D71—416no—
392C22×C71—24no—
393C22×C71—24no—
394C22×C71—24no—
395C22×C71—416no—
396C22×C71—42no—
397C22×C71—42no—
398C22×C71—42no—
399C22×C71—42no—
400C22×C71C2×C4×D414yes—
401C22×C71C4×#4114yes—
402C22×C71#51814yes—
403C22×C71#54614yes—
404C22×C71#54614yes—
405C22×C71#55314yes—
406C22×C71#55314yes—
407C22×C71C24×C411yescharacteristic
408C22×C71C23×D411yescharacteristic
409C22×C71C22×#4111yescharacteristic
410C22×C71C22×#4111yescharacteristic
411C22×C71C22×#4111yescharacteristic
412C22×C71C2×H(5,𝔽2)11yescharacteristic
413C22×C71C2×H(5,𝔽2)11yescharacteristic
414C2×D71—232no—
415C2×D71—24no—
416C2×D71—24no—
417C2×D71—24no—
418C2×D71—24no—
419C2×D71—24no—
420C2×D71—24no—
421C2×D71—24no—
422C2×D71—24no—
423C2×D71—24no—
424C2×D71—416no—
425C2×D71—42no—
426C2×D71—42no—
427C2×D71—42no—
428C2×D71—42no—
429C2×D71C2×C4×D418yes—
430C4×C71—24no—
431C4×C71—24no—
432C4×C71—24no—
433C4×C71—24no—
434C4×C71—24no—
435C4×C71—42no—
436Dic71—24no—
437Dic71—24no—
438Dic71—24no—
439Dic71—42no—
440Dic71—42no—
441Dic71—42no—
442C2×#2364—711nomaximal, Sylow
443C2×C71—44no—
444C2×C71#236418yescomplemented
445C2×C71C22×C4×D411yescharacteristic
446C2×C71C2×C4×#4111yescharacteristic
447C2×C71C2×#51811yescharacteristic
448C2×C71C2×#54611yescharacteristic
449C2×C71C2×#54611yescharacteristic
450C2×C71C2×#55311yescharacteristic
451C2×C71C2×#55311yescharacteristic
452D71—28no—
453D71—44no—
454C22×#121—711no—
455C22×C4×D4—711no—
456C22×C4×D4—711no—
457#2364—7116no—
458C2×#388—711no—
459C2×#388—711no—
460C2×#387—711no—
461C2×#387—711no—
462C2×#386—711no—
463C2×#386—711no—
464C2×#386—711no—
465C2×#386—711no—
466C2×C4×C22⋊C4—711no—
467C2×C4×C22⋊C4—711no—
468C2×C4×C22⋊C4D7111yescharacteristic, complemented
469C22×#95—711no—
470C71C2×#236411yescharacteristic, complemented, Sylow
471C23×D4—711no—
472C23×D4—711no—
473C23×D4—711no—
474C24×C4—711no—
475C24×C4—711no—
476C24×C4—711no—
477C24×C4—711no—
478C24×C4C2×D7111yescharacteristic
479C2×#121—7116no—
480C2×#121—718no—
481C2×C4×D4—718no—
482C2×C4×D4—718no—
483C2×C4×D4—1428no—
484C2×C4×D4—1428no—
485C22×C4⋊C4—711no—
486C22×C4⋊C4—711no—
487C22×C4⋊C4—711no—
488C22×C22⋊C4—711no—
489C22×C22⋊C4—711no—
490C22×C22⋊C4—711no—
491C22×C22⋊C4—711no—
492C22×C22⋊C4—711no—
493C22×C22⋊C4—711no—
494C22×C22⋊C4—711no—
495C22×C22⋊C4—711no—
496C22×C22⋊C4C2×D7111yescharacteristic
497C22×C22⋊C4C2×D7111yescharacteristic
498C22×C42—711no—
499C22×C42—711no—
500C22×C42C2×D7111yescharacteristic
501C22×C42C2×D7111yescharacteristic
502#388—718no—
503#388—718no—
504#387—718no—
505#387—718no—
506#386—718no—
507#386—718no—
508#386—718no—
509#386—718no—
510C4×C22⋊C4—718no—
511C4×C22⋊C4—718no—
512C4×C22⋊C4C2×D7118yescomplemented
513C2×#95—711no—
514C2×#95—711no—
515C2×#95—711no—
516C2×#95—711no—
517C2×#95—711no—
518C2×#95—711no—
519C2×#95—711no—
520C2×#95—711no—
521C2×#95—718no—
522C2×#95C2×D7111yescharacteristic
523C2×#95C2×D7111yescharacteristic
524C25—711no—
525C25—711no—
526C25C22×D7111yescharacteristic
527C22×D4—2842no—
528C22×D4—2842no—
529C22×D4—718no—
530C22×D4—714no—
531C22×D4—718no—
532C22×D4—714no—
533C22×D4—718no—
534C22×D4—714no—
535C22×D4—1424no—
536C22×D4—1424no—
537C22×D4—1424no—
538C22×D4—1424no—
539C23×C4—24no—
540C23×C4—24no—
541C23×C4—42no—
542C23×C4—2842no—
543C23×C4—2842no—
544C23×C4—2842no—
545C23×C4—2842no—
546C23×C4—2842no—
547C23×C4—718no—
548C23×C4—714no—
549C23×C4—714no—
550C23×C4—714no—
551C23×C4—714no—
552C23×C4—711no—
553C23×C4—711no—
554C23×C4—711no—
555C23×C4—711no—
556C23×C4—711no—
557C23×C4—711no—
558C23×C4—1424no—
559C23×C4—1424no—
560C23×C4—1424no—
561C23×C4—1424no—
562C23×C4—1424no—
563C23×C4—1424no—
564C23×C4C22×D7111yescharacteristic
565C23×C4C22×D7114yes—
566C23×C4C22×D7111yescharacteristic
567C23×C4C22×D7111yescharacteristic
568C23×C4C22×D7111yescharacteristic
569C23×C4C22×D7111yescharacteristic
570C23×C4C22×D7111yescharacteristic
571#121—7164no—
572C4×D4—14232no—
573C4×D4—14232no—
574C2×C4⋊C4—718no—
575C2×C4⋊C4—714no—
576C2×C4⋊C4—714no—
577C2×C4⋊C4—714no—
578C2×C4⋊C4—1424no—
579C2×C4⋊C4—1424no—
580C2×C22⋊C4—24no—
581C2×C22⋊C4—2842no—
582C2×C22⋊C4—2842no—
583C2×C22⋊C4—714no—
584C2×C22⋊C4—714no—
585C2×C22⋊C4—718no—
586C2×C22⋊C4—718no—
587C2×C22⋊C4—714no—
588C2×C22⋊C4—714no—
589C2×C22⋊C4—714no—
590C2×C22⋊C4—714no—
591C2×C22⋊C4—714no—
592C2×C22⋊C4—714no—
593C2×C22⋊C4—1424no—
594C2×C22⋊C4—1424no—
595C2×C22⋊C4—1424no—
596C2×C22⋊C4—1424no—
597C2×C22⋊C4C4×D7118yescomplemented
598C2×C22⋊C4C22×D7114yes—
599C2×C22⋊C4C22×D7114yes—
600C2×C42—24no—
601C2×C42—42no—
602C2×C42—2842no—
603C2×C42—714no—
604C2×C42—714no—
605C2×C42—1424no—
606C2×C42C22×D7114yes—
607C2×C42C22×D7114yes—
608#95—714no—
609#95—714no—
610#95—714no—
611#95—714no—
612#95—714no—
613#95—714no—
614#95—714no—
615#95—714no—
616#95C22×D7114yes—
617#95C22×D7114yes—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—714no—
625C24—714no—
626C24—714no—
627C24—712no—
628C24—714no—
629C24—712no—
630C24—1422no—
631C24—1422no—
632C24—1422no—
633C24—1422no—
634C24—1422no—
635C24—1422no—
636C24—1422no—
637C24—1422no—
638C24—1422no—
639C24—1422no—
640C24C2×C4×D7114yes—
641C24C23×D7112yes—
642C24C23×D7111yescharacteristic
643C2×D4—2844no—
644C2×D4—2844no—
645C2×D4—28416no—
646C2×D4—7116no—
647C2×D4—7116no—
648C2×D4—7116no—
649C2×D4—1428no—
650C2×D4—1428no—
651C2×D4—14232no—
652C2×D4—1428no—
653C2×D4—1428no—
654C2×D4—14232no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—28no—
669C22×C4—28no—
670C22×C4—44no—
671C22×C4—416no—
672C22×C4—28416no—
673C22×C4—28416no—
674C22×C4—28416no—
675C22×C4—2844no—
676C22×C4—2844no—
677C22×C4—2844no—
678C22×C4—2844no—
679C22×C4—2844no—
680C22×C4—28416no—
681C22×C4—7116no—
682C22×C4—714no—
683C22×C4—714no—
684C22×C4—714no—
685C22×C4—712no—
686C22×C4—712no—
687C22×C4—712no—
688C22×C4—712no—
689C22×C4—712no—
690C22×C4—712no—
691C22×C4—1428no—
692C22×C4—1428no—
693C22×C4—1428no—
694C22×C4—1422no—
695C22×C4—1422no—
696C22×C4—1422no—
697C22×C4—1422no—
698C22×C4—1422no—
699C22×C4—1422no—
700C22×C4—1422no—
701C22×C4—1422no—
702C22×C4—1422no—
703C22×C4—1428no—
704C22×C4—1428no—
705C22×C4—1428no—
706C22×C4—1422no—
707C22×C4—1422no—
708C22×C4—1422no—
709C22×C4—1422no—
710C22×C4—1422no—
711C22×C4—1422no—
712C22×C4C2×C4×D7114yes—
713C22×C4C2×C4×D7114yes—
714C22×C4D4×D7114yes—
715C22×C4#1176586514yes—
716C22×C4#1176586514yes—
717C22×C4C23×D7112yes—
718C22×C4C23×D7112yes—
719C22×C4C23×D7112yes—
720C22×C4C23×D7112yes—
721C22×C4C23×D7112yes—
722C22×C4C23×D7112yes—
723C4⋊C4—7116no—
724C4⋊C4—1428no—
725C4⋊C4—1428no—
726C22⋊C4—28no—
727C22⋊C4—2844no—
728C22⋊C4—2844no—
729C22⋊C4—7116no—
730C22⋊C4—7116no—
731C22⋊C4—1428no—
732C22⋊C4—1428no—
733C22⋊C4—1428no—
734C22⋊C4—1428no—
735C22⋊C4C2×C4×D71116yescomplemented
736C42—28no—
737C42—44no—
738C42—2844no—
739C42—1428no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—28no—
747C23—28no—
748C23—28no—
749C23—44no—
750C23—44no—
751C23—44no—
752C23—44no—
753C23—2844no—
754C23—2844no—
755C23—2844no—
756C23—2844no—
757C23—714no—
758C23—714no—
759C23—714no—
760C23—7116no—
761C23—714no—
762C23—1422no—
763C23—1422no—
764C23—1422no—
765C23—1422no—
766C23—1422no—
767C23—1422no—
768C23—1428no—
769C23—1428no—
770C23—1428no—
771C23—1422no—
772C23—1422no—
773C23—1422no—
774C23—1422no—
775C23—1428no—
776C23—1428no—
777C23—1428no—
778C23—1428no—
779C23—1428no—
780C23—1428no—
781C23C22×C4×D7114yes—
782C23C22×C4×D7112yes—
783C23C2×D4×D7112yes—
784C23#41×D7112yes—
785C23C2×#1176586512yes—
786C23C2×#1176586512yes—
787C23#1455617312yes—
788C23#1455617412yes—
789C23C24×D7111yescharacteristic
790D4—28416no—
791D4—14232no—
792D4—14232no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—28no—
804C2×C4—28no—
805C2×C4—28no—
806C2×C4—28no—
807C2×C4—28no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—416no—
812C2×C4—44no—
813C2×C4—28416no—
814C2×C4—28416no—
815C2×C4—28416no—
816C2×C4—28416no—
817C2×C4—2844no—
818C2×C4—2844no—
819C2×C4—2844no—
820C2×C4—714no—
821C2×C4—714no—
822C2×C4—714no—
823C2×C4—1422no—
824C2×C4—1422no—
825C2×C4—1422no—
826C2×C4—1422no—
827C2×C4—1422no—
828C2×C4—1422no—
829C2×C4—1422no—
830C2×C4—1422no—
831C2×C4—1422no—
832C2×C4—1422no—
833C2×C4—1422no—
834C2×C4—1422no—
835C2×C4—1422no—
836C2×C4—1422no—
837C2×C4—1422no—
838C2×C4—1428no—
839C2×C4—1428no—
840C2×C4—1428no—
841C2×C4C22×C4×D7114yes—
842C2×C4C22×C4×D7114yes—
843C2×C4C2×D4×D7114yes—
844C2×C4C2×#1176586514yes—
845C2×C4C2×#1176586514yes—
846C22—24no—
847C22—24no—
848C22—24no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—416no—
854C22—2842no—
855C22—2842no—
856C22—2842no—
857C22—2842no—
858C22—28416no—
859C22—718no—
860C22—1424no—
861C22—1424no—
862C22—1424no—
863C22—1424no—
864C22—1424no—
865C22—1424no—
866C22—1424no—
867C22—1424no—
868C22—1424no—
869C22—14232no—
870C22C4×D4×D7114yes—
871C22C4×#1176586514yes—
872C22#1798647114yes—
873C22#1798663914yes—
874C22#1798664514yes—
875C22#1798669314yes—
876C22#1798669914yes—
877C22C23×C4×D7111yescharacteristic
878C22C22×D4×D7111yescharacteristic
879C22C2×#41×D7111yescharacteristic
880C22C22×#1176586511yescharacteristic
881C22C22×#1176586511yescharacteristic
882C22C2×#1455617311yescharacteristic
883C22C2×#1455617411yescharacteristic
884C4—24no—
885C4—24no—
886C4—24no—
887C4—24no—
888C4—24no—
889C4—42no—
890C4—2842no—
891C4—2842no—
892C4—2842no—
893C4—1424no—
894C4—1424no—
895C4—1424no—
896C2—44no—
897C2—2844no—
898C2—1428no—
899C2#2259139118yesdirect product factor
900C2C2×C4×D4×D7111yescharacteristic
901C2C2×C4×#1176586511yescharacteristic
902C2C2×#1798647111yescharacteristic
903C2C2×#1798663911yescharacteristic
904C2C2×#1798664511yescharacteristic
905C2C2×#1798669311yescharacteristic
906C2C2×#1798669911yescharacteristic
subgroupG/H
centerC24C23×D71
commutatorC22×C71C24×C4
FrattiniC23C24×D71
FittingC2×C4×C22⋊C4×C71C2
socleC24×C71C24
prime radicalC22×#14556101C2
cosocleC23×C71C25
hypercenterC2×C4×C22⋊C4D71
hypocenterC71C2×#2364
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C4×D284C2semidirect
3. C22×C4×C22⋊D71C2semidirect
4. #22591391C2direct (N × H)
5. C2×#17985892C2semidirect
6. C2×#17985890C2semidirect
7. C2×#17985886C2semidirect
8. C2×#17985883C2semidirect
9. C2×#17985878C2semidirect
10. C2×#17985877C2semidirect
11. C2×#17985875C2semidirect
12. C2×#17985875C2semidirect
13. C2×C4×(C2×D71)⋊C4C2semidirect
14. C2×#17985846C2semidirect
15. C2×#95×D71C2semidirect
16. C2×C4×C22⋊C4×C71C2semidirect
24. C2×#14556101C4semidirect
27. C2×C4×D284C22semidirect
29. C2×C4×C22⋊D71C22semidirect
43. #17985892C22semidirect
44. #17985890C22semidirect
45. #17985886C22semidirect
46. #17985883C22semidirect
47. #17985878C22semidirect
48. #17985877C22semidirect
49. #17985875C22semidirect
50. #17985875C22semidirect
51. C4×(C2×D71)⋊C4C22semidirect
52. #17985846C22semidirect
61. #95×D71C22semidirect
67. C4×C22⋊C4×C71C22semidirect
74. C22×D284C2×C4semidirect
80. C22×C22⋊D71C2×C4semidirect
81. C22×C22⋊D71C2×C4semidirect
101. C22×C4×D71C2×C4semidirect
106. #14556101C2×C4semidirect
112. C2×Dic71⋊C4C2×C4semidirect
123. C2×(C2×D71)⋊C4C2×C4semidirect
124. C2×(C2×D71)⋊C4D4semidirect
155. C2×C22⋊C4×C71C2×C4semidirect
183. C2×D284C22×C4semidirect
190. C2×C22⋊D71C22×C4semidirect
191. C2×C22⋊D71C22×C4semidirect
231. C2×C4×D71C22×C4semidirect
234. Dic71⋊C4C22×C4semidirect
241. (C2×D71)⋊C4C22×C4semidirect
242. (C2×D71)⋊C4C2×D4semidirect
283. C22⋊C4×C71C22×C4semidirect
444. C2×C71#2364semidirect
468. C2×C4×C22⋊C4D71semidirect
470. C71C2×#2364semidirect
512. C4×C22⋊C4C2×D71semidirect
597. C2×C22⋊C4C4×D71semidirect
735. C22⋊C4C2×C4×D71semidirect
899. C2#22591391direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561012
C22×C4×D2842
C22×C4×C22⋊D712
#225913912
C2×#179858922
C2×#179858902
C2×#179858862
C2×#179858832
C2×#179858782
C2×#179858772
C2×#179858752
C2×C4×(C2×D71)⋊C42
C2×#179858462
C2×#95×D712
C2×C4×C22⋊C4×C712
C2×#236471