Finite Group Databasebeta

← C2×#22591028 #32156201

Subgroups — C2×#22591028 #32156201

Order 18176.

3934 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556101C211yesmaximal, characteristic
2C22×(C22⋊D71)⋊C4C211yesmaximal, characteristic, complemented
3C22×#14556086C211yesmaximal, characteristic, complemented
4#22591028C2116yesmaximal, direct product factor
5C2×#17985901C211yesmaximal, characteristic, complemented
6C2×#17985899C211yesmaximal, characteristic, complemented
7C2×#17985899C211yesmaximal, characteristic, complemented
8C2×#17985896C211yesmaximal, characteristic, complemented
9C2×#17985889C211yesmaximal, characteristic, complemented
10C2×#17985877C211yesmaximal, characteristic, complemented
11C2×#17985876C211yesmaximal, characteristic, complemented
12C2×#17985874C211yesmaximal, characteristic, complemented
13C2×#17985873C211yesmaximal, characteristic, complemented
14C2×#17985858C211yesmaximal, characteristic, complemented
15C2×C4×Dic71⋊C4C211yesmaximal, characteristic, complemented
16C2×#388×C71C211yesmaximal, characteristic, complemented
17C23×D284C2211yescharacteristic
18C23×C22⋊D71C2211yescharacteristic
19C23×C22⋊D71C2211yescharacteristic
20C24×Dic71C2211yescharacteristic
21C23×C4×D71C2211yescharacteristic
22C23×C4×D71C2211yescharacteristic
23C2×#14556101C4116yescomplemented
24C2×#14556101C2218yes—
25C2×(C22⋊D71)⋊C4—28no—
26C2×(C22⋊D71)⋊C4C2218yescomplemented
27C2×#14556086—28no—
28C2×#14556086C2218yescomplemented
29C22×C4⋊Dic71C2211yescharacteristic
30C22×C4⋊Dic71C2211yescharacteristic
31C22×Dic71⋊C4C2211yescharacteristic
32C22×Dic71⋊C4C2211yescharacteristic
33C22×Dic71⋊C4C2211yescharacteristic
34C22×Dic71⋊C4C2211yescharacteristic
35C22×C22⋊Dic71C2211yescharacteristic
36C22×(C2×D71)⋊C4C2211yescharacteristic
37C22×(C2×D71)⋊C4C2211yescharacteristic
38C22×(C2×D71)⋊C4C2211yescharacteristic
39C22×(C2×D71)⋊C4C2211yescharacteristic
40C22×(C2×D71)⋊C4C2211yescharacteristic
41C22×(C2×D71)⋊C4C2211yescharacteristic
42C22×(C2×D71)⋊C4C2211yescharacteristic
43C22×(C2×D71)⋊C4C2211yescharacteristic
44C22×C4×Dic71C2211yescharacteristic
45C22×C4×Dic71C2211yescharacteristic
46C22×C4×Dic71C2211yescharacteristic
47#17985901C2218yescomplemented
48#17985899C2218yescomplemented
49#17985899C2218yescomplemented
50#17985896C2218yescomplemented
51#17985889C2218yescomplemented
52#17985877C2218yescomplemented
53#17985876C2218yescomplemented
54#17985874C2218yescomplemented
55#17985873C2218yescomplemented
56#17985858C2218yescomplemented
57C4×Dic71⋊C4C2218yescomplemented
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
71C24×D71C2311yescharacteristic
72C22×D284—42no—
73C22×D284—42no—
74C22×D284C2×C418yescomplemented
75C22×D284C2314yes—
76C22×C22⋊D71—24no—
77C22×C22⋊D71—24no—
78C22×C22⋊D71—42no—
79C22×C22⋊D71—42no—
80C22×C22⋊D71C2×C418yes—
81C22×C22⋊D71C2×C418yescomplemented
82C22×C22⋊D71C2314yes—
83C22×C22⋊D71C2314yes—
84C23×Dic71—24no—
85C23×Dic71—42no—
86C23×Dic71—42no—
87C23×Dic71C2311yescharacteristic
88C23×Dic71C2311yescharacteristic
89C23×Dic71C2311yescharacteristic
90C23×Dic71C2311yescharacteristic
91C23×Dic71C2311yescharacteristic
92C23×Dic71C2314yes—
93C23×Dic71C2311yescharacteristic
94C22×C4×D71—24no—
95C22×C4×D71—24no—
96C22×C4×D71—24no—
97C22×C4×D71—42no—
98C22×C4×D71—42no—
99C22×C4×D71C2×C418yescomplemented
100C22×C4×D71C2314yes—
101C22×C4×D71C2314yes—
102#14556101C2×C4164yescomplemented
103(C22⋊D71)⋊C4—232no—
104#14556086—232no—
105C2×C4⋊Dic71—24no—
106C2×C4⋊Dic71—42no—
107C2×C4⋊Dic71C2314yes—
108C2×C4⋊Dic71C2314yes—
109C2×Dic71⋊C4—24no—
110C2×Dic71⋊C4—24no—
111C2×Dic71⋊C4—42no—
112C2×Dic71⋊C4C2×C418yescomplemented
113C2×Dic71⋊C4C2314yes—
114C2×Dic71⋊C4C2314yes—
115C2×Dic71⋊C4C2314yes—
116C2×Dic71⋊C4C2314yes—
117C2×C22⋊Dic71—42no—
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)⋊C4—42no—
124C2×(C2×D71)⋊C4—42no—
125C2×(C2×D71)⋊C4—42no—
126C2×(C2×D71)⋊C4C2×C418yescomplemented
127C2×(C2×D71)⋊C4C2314yes—
128C2×(C2×D71)⋊C4C2314yes—
129C2×(C2×D71)⋊C4C2314yes—
130C2×(C2×D71)⋊C4C2314yes—
131C2×(C2×D71)⋊C4C2314yes—
132C2×(C2×D71)⋊C4C2314yes—
133C2×(C2×D71)⋊C4C2314yes—
134C2×(C2×D71)⋊C4C2314yes—
135C2×C4×Dic71—24no—
136C2×C4×Dic71—42no—
137C2×C4×Dic71D418yescomplemented
138C2×C4×Dic71C2314yes—
139C2×C4×Dic71C2314yes—
140C2×C4×Dic71C2314yes—
141C71⋊#95C2314yes—
142C71⋊#95C2314yes—
143C71⋊#95C2314yes—
144C71⋊#95C2314yes—
145C25×C71C2311yescharacteristic
146C23×C4×C71C2311yescharacteristic
147C23×C4×C71C2311yescharacteristic
148C23×C4×C71C2311yescharacteristic
149C23×C4×C71C2311yescharacteristic
150C23×C4×C71C2311yescharacteristic
151C23×C4×C71C2311yescharacteristic
152C2×C4⋊C4×C71—24no—
153C2×C4⋊C4×C71C2314yes—
154C2×C22⋊C4×C71—24no—
155C2×C22⋊C4×C71—42no—
156C2×C22⋊C4×C71C2×C418yescomplemented
157C2×C22⋊C4×C71C2314yes—
158C2×C22⋊C4×C71C2314yes—
159C2×C22⋊C4×C71C2314yes—
160C2×C42×C71—42no—
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×D71—22no—
175C23×D71—22no—
176C23×D71C22×C414yes—
177C23×D71C22×C414yes—
178C23×D71C2412yes—
179C23×D71C2412yes—
180C2×D284—416no—
181C2×D284—44no—
182C2×D284—44no—
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×C4116yes—
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—28no—
206C22×Dic71—44no—
207C22×Dic71—44no—
208C22×Dic71—416no—
209C22×Dic71C22×C414yes—
210C22×Dic71C22×C414yes—
211C22×Dic71C2×D414yes—
212C22×Dic71C2×D414yes—
213C22×Dic71#4114yes—
214C22×Dic71C2412yes—
215C22×Dic71C2412yes—
216C22×Dic71C2412yes—
217C22×Dic71C2412yes—
218C22×Dic71C2412yes—
219C22×Dic71C2412yes—
220C2×C4×D71—232no—
221C2×C4×D71—28no—
222C2×C4×D71—28no—
223C2×C4×D71—28no—
224C2×C4×D71—44no—
225C2×C4×D71—44no—
226C2×C4×D71—416no—
227C2×C4×D71C22×C4116yescomplemented
228C4⋊Dic71—28no—
229C4⋊Dic71—44no—
230Dic71⋊C4—28no—
231Dic71⋊C4—28no—
232Dic71⋊C4—44no—
233Dic71⋊C4C22×C4116yescomplemented
234C22⋊Dic71—44no—
235(C2×D71)⋊C4—28no—
236(C2×D71)⋊C4—28no—
237(C2×D71)⋊C4—28no—
238(C2×D71)⋊C4—44no—
239(C2×D71)⋊C4—44no—
240(C2×D71)⋊C4—44no—
241(C2×D71)⋊C4—44no—
242(C2×D71)⋊C4C22×C4116yescomplemented
243C4×Dic71—28no—
244C4×Dic71—44no—
245C4×Dic71C2×D4116yescomplemented
246C24×C71—22no—
247C24×C71—22no—
248C24×C71—22no—
249C24×C71—22no—
250C24×C71—22no—
251C24×C71—22no—
252C24×C71C22×C414yes—
253C24×C71C2412yes—
254C24×C71C2411yescharacteristic
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—22no—
268C22×C4×C71—22no—
269C22×C4×C71—22no—
270C22×C4×C71C22×C414yes—
271C22×C4×C71C22×C414yes—
272C22×C4×C71C2×D414yes—
273C22×C4×C71C2412yes—
274C22×C4×C71C2412yes—
275C22×C4×C71C2412yes—
276C22×C4×C71C2412yes—
277C22×C4×C71C2412yes—
278C22×C4×C71C2412yes—
279C4⋊C4×C71—28no—
280C22⋊C4×C71—28no—
281C22⋊C4×C71—44no—
282C22⋊C4×C71C22×C4116yescomplemented
283C42×C71—44no—
284C23×C71—28no—
285C23×C71—28no—
286C23×C71—28no—
287C23×C71—22no—
288C23×C71—22no—
289C23×C71—22no—
290C23×C71—22no—
291C23×C71—22no—
292C23×C71—22no—
293C23×C71—44no—
294C23×C71—44no—
295C23×C71—44no—
296C23×C71—44no—
297C23×C71C23×C414yes—
298C23×C71C23×C412yes—
299C23×C71C22×D412yes—
300C23×C71C2×#4112yes—
301C23×C71H(5,𝔽2)12yes—
302C23×C71H(5,𝔽2)12yes—
303C23×C71H(5,𝔽2)12yes—
304C23×C712−1+412yes—
305C23×C71C2511yescharacteristic
306C22×D71—28no—
307C22×D71—28no—
308C22×D71—28no—
309C22×D71—28no—
310C22×D71—28no—
311C22×D71—28no—
312C22×D71—22no—
313C22×D71—22no—
314C22×D71—22no—
315C22×D71—22no—
316C22×D71—22no—
317C22×D71—22no—
318C22×D71—22no—
319C22×D71—22no—
320C22×D71—22no—
321C22×D71—22no—
322C22×D71—22no—
323C22×D71—22no—
324C22×D71—44no—
325C22×D71—44no—
326C22×D71—44no—
327C22×D71—44no—
328C22×D71—44no—
329C22×D71—44no—
330C22×D71—44no—
331C22×D71—44no—
332C22×D71C23×C414yes—
333C22×D71C23×C414yes—
334C2×C4×C71—28no—
335C2×C4×C71—28no—
336C2×C4×C71—28no—
337C2×C4×C71—22no—
338C2×C4×C71—22no—
339C2×C4×C71—22no—
340C2×C4×C71—22no—
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—44no—
353C2×C4×C71—44no—
354C2×C4×C71—44no—
355C2×C4×C71C23×C414yes—
356C2×C4×C71C23×C414yes—
357C2×C4×C71C22×D414yes—
358C22⋊D71—232no—
359C22⋊D71—416no—
360C2×Dic71—28no—
361C2×Dic71—28no—
362C2×Dic71—22no—
363C2×Dic71—22no—
364C2×Dic71—22no—
365C2×Dic71—22no—
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—416no—
376C2×Dic71—44no—
377C2×Dic71—44no—
378C2×Dic71—44no—
379C2×Dic71C4×D4116yes—
380C2×Dic71C23×C414yes—
381C2×Dic71C23×C414yes—
382C2×Dic71C22×D414yes—
383C2×Dic71C22×D414yes—
384C2×Dic71C2×#4114yes—
385D284—416no—
386C4×D71—232no—
387C4×D71—416no—
388C22×C71—24no—
389C22×C71—24no—
390C22×C71—24no—
391C22×C71—416no—
392C22×C71—42no—
393C22×C71—42no—
394C22×C71—42no—
395C22×C71—42no—
396C22×C71C2×C4×D414yes—
397C22×C71#51814yes—
398C22×C71#52014yes—
399C22×C71#53514yes—
400C22×C71#53714yes—
401C22×C71#54014yes—
402C22×C71#54214yes—
403C22×C71C24×C411yescharacteristic
404C22×C71C23×D411yescharacteristic
405C22×C71C22×#4111yescharacteristic
406C22×C71C2×H(5,𝔽2)11yescharacteristic
407C22×C71C2×H(5,𝔽2)11yescharacteristic
408C22×C71C2×H(5,𝔽2)11yescharacteristic
409C22×C71C2×2−1+411yescharacteristic
410C2×D71—24no—
411C2×D71—24no—
412C2×D71—24no—
413C2×D71—24no—
414C2×D71—24no—
415C2×D71—24no—
416C2×D71—416no—
417C2×D71—416no—
418C2×D71—42no—
419C2×D71—42no—
420C2×D71—42no—
421C2×D71—42no—
422C2×D71—42no—
423C2×D71—42no—
424C2×D71—42no—
425C2×D71—42no—
426C4×C71—24no—
427C4×C71—24no—
428C4×C71—24no—
429C4×C71—42no—
430C4×C71—42no—
431C4×C71—42no—
432Dic71—24no—
433Dic71—24no—
434Dic71—42no—
435Dic71—42no—
436Dic71—42no—
437Dic71C2×C4×D418yes—
438C2×#2324—711nomaximal, Sylow
439C2×C71—44no—
440C2×C71#232418yescomplemented
441C2×C71C22×C4×D411yescharacteristic
442C2×C71C2×#51811yescharacteristic
443C2×C71C2×#52011yescharacteristic
444C2×C71C2×#53511yescharacteristic
445C2×C71C2×#53711yescharacteristic
446C2×C71C2×#54011yescharacteristic
447C2×C71C2×#54211yescharacteristic
448D71—44no—
449D71—44no—
450C22×#121—711no—
451C22×C4×D4—711no—
452C22×#117—711no—
453#2324—7116no—
454C2×#390—711no—
455C2×#390—711no—
456C2×#390—711no—
457C2×#389—711no—
458C2×#388—711no—
459C2×#388D7111yescharacteristic, complemented
460C2×#386—711no—
461C2×#386—711no—
462C2×#385—711no—
463C2×#385—711no—
464C2×#380—711no—
465C2×C4×C4⋊C4—711no—
466C71C2×#232411yescharacteristic, complemented, Sylow
467C23×D4—711no—
468C23×D4—711no—
469C23×D4—711no—
470C24×C4—711no—
471C24×C4—711no—
472C24×C4—711no—
473C2×#121—7116no—
474C2×#121—718no—
475C2×C4×D4—718no—
476C2×C4×D4—1428no—
477C2×#117—718no—
478C2×#117—1428no—
479C22×C4⋊C4—711no—
480C22×C4⋊C4—711no—
481C22×C4⋊C4—711no—
482C22×C4⋊C4—711no—
483C22×C4⋊C4—711no—
484C22×C4⋊C4—711no—
485C22×C4⋊C4C2×D7111yescharacteristic
486C22×C22⋊C4—711no—
487C22×C22⋊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⋊C4C2×D7111yescharacteristic
496C22×C22⋊C4C2×D7111yescharacteristic
497C22×C22⋊C4C2×D7111yescharacteristic
498C22×C42—711no—
499C22×C42—711no—
500C22×C42—711no—
501C22×C42C2×D7111yescharacteristic
502#390—718no—
503#390—718no—
504#390—718no—
505#389—718no—
506#388—718no—
507#388C2×D7118yescomplemented
508#386—718no—
509#386—718no—
510#385—718no—
511#385—718no—
512#380—718no—
513C4×C4⋊C4—718no—
514C2×#95—711no—
515C2×#95—711no—
516C2×#95—711no—
517C2×#95—711no—
518C2×#95C2×D7111yescharacteristic
519C2×#95C2×D7111yescharacteristic
520C25—711no—
521C25—711no—
522C25C22×D7111yescharacteristic
523C22×D4—2842no—
524C22×D4—2842no—
525C22×D4—2842no—
526C22×D4—2842no—
527C22×D4—718no—
528C22×D4—714no—
529C22×D4—718no—
530C22×D4—714no—
531C22×D4—718no—
532C22×D4—714no—
533C22×D4—1424no—
534C22×D4—1424no—
535C23×C4—2842no—
536C23×C4—2842no—
537C23×C4—2842no—
538C23×C4—2842no—
539C23×C4—714no—
540C23×C4—714no—
541C23×C4—711no—
542C23×C4—711no—
543C23×C4—711no—
544C23×C4—718no—
545C23×C4—714no—
546C23×C4—711no—
547C23×C4—711no—
548C23×C4—711no—
549C23×C4—1424no—
550C23×C4—1424no—
551C23×C4—1424no—
552C23×C4—1424no—
553C23×C4C22×D7111yescharacteristic
554C23×C4C22×D7111yescharacteristic
555C23×C4C22×D7111yescharacteristic
556C23×C4C22×D7111yescharacteristic
557C23×C4C22×D7111yescharacteristic
558C23×C4C22×D7111yescharacteristic
559#121—7164no—
560C4×D4—14232no—
561#117—14232no—
562C2×C4⋊C4—24no—
563C2×C4⋊C4—2842no—
564C2×C4⋊C4—2842no—
565C2×C4⋊C4—714no—
566C2×C4⋊C4—714no—
567C2×C4⋊C4—718no—
568C2×C4⋊C4—714no—
569C2×C4⋊C4—714no—
570C2×C4⋊C4—714no—
571C2×C4⋊C4—714no—
572C2×C4⋊C4—1424no—
573C2×C4⋊C4—1424no—
574C2×C4⋊C4—1424no—
575C2×C4⋊C4C22×D7114yes—
576C2×C22⋊C4—24no—
577C2×C22⋊C4—42no—
578C2×C22⋊C4—2842no—
579C2×C22⋊C4—2842no—
580C2×C22⋊C4—2842no—
581C2×C22⋊C4—2842no—
582C2×C22⋊C4—2842no—
583C2×C22⋊C4—714no—
584C2×C22⋊C4—714no—
585C2×C22⋊C4—714no—
586C2×C22⋊C4—714no—
587C2×C22⋊C4—714no—
588C2×C22⋊C4—718no—
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⋊C4C4×D7118yescomplemented
597C2×C22⋊C4C22×D7114yes—
598C2×C22⋊C4C22×D7114yes—
599C2×C22⋊C4C22×D7114yes—
600C2×C42—42no—
601C2×C42—2842no—
602C2×C42—714no—
603C2×C42—718no—
604C2×C42—714no—
605C2×C42—714no—
606C2×C42—1424no—
607C2×C42C22×D7114yes—
608#95—714no—
609#95—714no—
610#95—714no—
611#95—714no—
612#95C22×D7114yes—
613#95C22×D7114yes—
614C24—22no—
615C24—22no—
616C24—22no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—714no—
621C24—714no—
622C24—712no—
623C24—712no—
624C24—1422no—
625C24—1422no—
626C24—1422no—
627C24—1422no—
628C24—1422no—
629C24—1422no—
630C24—1422no—
631C24—1422no—
632C24—1422no—
633C24—1422no—
634C24—1422no—
635C24—1422no—
636C24C2×C4×D7114yes—
637C24C23×D7112yes—
638C24C23×D7111yescharacteristic
639C2×D4—2844no—
640C2×D4—2844no—
641C2×D4—28416no—
642C2×D4—2844no—
643C2×D4—2844no—
644C2×D4—28416no—
645C2×D4—7116no—
646C2×D4—7116no—
647C2×D4—7116no—
648C2×D4—1428no—
649C2×D4—1428no—
650C2×D4—14232no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
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—2844no—
667C22×C4—2844no—
668C22×C4—28416no—
669C22×C4—28416no—
670C22×C4—2844no—
671C22×C4—2844no—
672C22×C4—714no—
673C22×C4—714no—
674C22×C4—714no—
675C22×C4—712no—
676C22×C4—714no—
677C22×C4—714no—
678C22×C4—712no—
679C22×C4—712no—
680C22×C4—7116no—
681C22×C4—712no—
682C22×C4—712no—
683C22×C4—712no—
684C22×C4—1428no—
685C22×C4—1428no—
686C22×C4—1428no—
687C22×C4—14232no—
688C22×C4—1428no—
689C22×C4—1422no—
690C22×C4—1422no—
691C22×C4—1422no—
692C22×C4—1422no—
693C22×C4—1422no—
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×C4C2×C4×D7114yes—
703C22×C4C2×C4×D7114yes—
704C22×C4D4×D7114yes—
705C22×C4C23×D7112yes—
706C22×C4C23×D7112yes—
707C22×C4C23×D7112yes—
708C22×C4C23×D7112yes—
709C22×C4C23×D7112yes—
710C22×C4C23×D7112yes—
711C4⋊C4—28no—
712C4⋊C4—2844no—
713C4⋊C4—2844no—
714C4⋊C4—7116no—
715C4⋊C4—1428no—
716C4⋊C4—1428no—
717C4⋊C4—1428no—
718C22⋊C4—28no—
719C22⋊C4—44no—
720C22⋊C4—2844no—
721C22⋊C4—2844no—
722C22⋊C4—2844no—
723C22⋊C4—2844no—
724C22⋊C4—2844no—
725C22⋊C4—7116no—
726C22⋊C4—1428no—
727C22⋊C4—1428no—
728C22⋊C4—1428no—
729C22⋊C4C2×C4×D71116yescomplemented
730C42—44no—
731C42—2844no—
732C42—7116no—
733C42—1428no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—28no—
741C23—28no—
742C23—28no—
743C23—44no—
744C23—44no—
745C23—44no—
746C23—44no—
747C23—2844no—
748C23—2844no—
749C23—2844no—
750C23—2844no—
751C23—2844no—
752C23—2844no—
753C23—2844no—
754C23—2844no—
755C23—714no—
756C23—714no—
757C23—1422no—
758C23—1422no—
759C23—1422no—
760C23—1422no—
761C23—1422no—
762C23—1422no—
763C23—1422no—
764C23—1422no—
765C23—1422no—
766C23—1422no—
767C23—1422no—
768C23—1422no—
769C23—1428no—
770C23—1428no—
771C23—1428no—
772C23—1428no—
773C23—1428no—
774C23—1428no—
775C23C22×C4×D7114yes—
776C23C22×C4×D7112yes—
777C23C2×D4×D7112yes—
778C23#41×D7112yes—
779C23#1455617312yes—
780C23#1455617412yes—
781C23#1455617412yes—
782C23#1455617512yes—
783C23C24×D7111yescharacteristic
784D4—28416no—
785D4—28416no—
786D4—14232no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—28no—
793C2×C4—22no—
794C2×C4—28no—
795C2×C4—28no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—44no—
806C2×C4—44no—
807C2×C4—44no—
808C2×C4—28416no—
809C2×C4—2844no—
810C2×C4—2844no—
811C2×C4—2844no—
812C2×C4—28416no—
813C2×C4—714no—
814C2×C4—714no—
815C2×C4—714no—
816C2×C4—7116no—
817C2×C4—714no—
818C2×C4—714no—
819C2×C4—14232no—
820C2×C4—1422no—
821C2×C4—1422no—
822C2×C4—1422no—
823C2×C4—1422no—
824C2×C4—1422no—
825C2×C4—1422no—
826C2×C4—1422no—
827C2×C4—1422no—
828C2×C4—1422no—
829C2×C4—1428no—
830C2×C4—1422no—
831C2×C4—1422no—
832C2×C4—1422no—
833C2×C4—1422no—
834C2×C4—1428no—
835C2×C4C22×C4×D7114yes—
836C2×C4C22×C4×D7114yes—
837C2×C4C2×D4×D7114yes—
838C22—24no—
839C22—24no—
840C22—24no—
841C22—416no—
842C22—42no—
843C22—42no—
844C22—42no—
845C22—42no—
846C22—28416no—
847C22—28416no—
848C22—2842no—
849C22—2842no—
850C22—2842no—
851C22—2842no—
852C22—2842no—
853C22—2842no—
854C22—2842no—
855C22—2842no—
856C22—1424no—
857C22—1424no—
858C22—1424no—
859C22—1424no—
860C22—1424no—
861C22—1424no—
862C22C4×D4×D7114yes—
863C22#1798647114yes—
864C22#1798647914yes—
865C22#1798656714yes—
866C22#1798657614yes—
867C22#1798660114yes—
868C22#1798661514yes—
869C22C23×C4×D7111yescharacteristic
870C22C22×D4×D7111yescharacteristic
871C22C2×#41×D7111yescharacteristic
872C22C2×#1455617311yescharacteristic
873C22C2×#1455617411yescharacteristic
874C22C2×#1455617411yescharacteristic
875C22C2×#1455617511yescharacteristic
876C4—24no—
877C4—24no—
878C4—24no—
879C4—42no—
880C4—42no—
881C4—42no—
882C4—2842no—
883C4—2842no—
884C4—2842no—
885C4—718no—
886C4—1424no—
887C4—1424no—
888C2—44no—
889C2—2844no—
890C2—2844no—
891C2#2259102818yesdirect product factor
892C2C2×C4×D4×D7111yescharacteristic
893C2C2×#1798647111yescharacteristic
894C2C2×#1798647911yescharacteristic
895C2C2×#1798656711yescharacteristic
896C2C2×#1798657611yescharacteristic
897C2C2×#1798660111yescharacteristic
898C2C2×#1798661511yescharacteristic
subgroupG/H
centerC24C23×D71
commutatorC22×C71C24×C4
FrattiniC23C24×D71
FittingC2×#388×C71C2
socleC24×C71C24
prime radicalC22×#14556101C2
cosocleC23×C71C25
hypercenterC2×#388D71
hypocenterC71C2×#2324
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C22×(C22⋊D71)⋊C4C2semidirect
3. C22×#14556086C2semidirect
4. #22591028C2direct (N × H)
5. C2×#17985901C2semidirect
6. C2×#17985899C2semidirect
7. C2×#17985899C2semidirect
8. C2×#17985896C2semidirect
9. C2×#17985889C2semidirect
10. C2×#17985877C2semidirect
11. C2×#17985876C2semidirect
12. C2×#17985874C2semidirect
13. C2×#17985873C2semidirect
14. C2×#17985858C2semidirect
15. C2×C4×Dic71⋊C4C2semidirect
16. C2×#388×C71C2semidirect
23. C2×#14556101C4semidirect
26. C2×(C22⋊D71)⋊C4C22semidirect
28. C2×#14556086C22semidirect
47. #17985901C22semidirect
48. #17985899C22semidirect
49. #17985899C22semidirect
50. #17985896C22semidirect
51. #17985889C22semidirect
52. #17985877C22semidirect
53. #17985876C22semidirect
54. #17985874C22semidirect
55. #17985873C22semidirect
56. #17985858C22semidirect
57. C4×Dic71⋊C4C22semidirect
67. #388×C71C22semidirect
74. C22×D284C2×C4semidirect
81. C22×C22⋊D71C2×C4semidirect
99. C22×C4×D71C2×C4semidirect
102. #14556101C2×C4semidirect
112. C2×Dic71⋊C4C2×C4semidirect
126. C2×(C2×D71)⋊C4C2×C4semidirect
137. C2×C4×Dic71D4semidirect
156. C2×C22⋊C4×C71C2×C4semidirect
183. C2×D284C22×C4semidirect
191. C2×C22⋊D71C22×C4semidirect
227. C2×C4×D71C22×C4semidirect
233. Dic71⋊C4C22×C4semidirect
242. (C2×D71)⋊C4C22×C4semidirect
245. C4×Dic71C2×D4semidirect
282. C22⋊C4×C71C22×C4semidirect
440. C2×C71#2324semidirect
459. C2×#388D71semidirect
466. C71C2×#2324semidirect
507. #388C2×D71semidirect
596. C2×C22⋊C4C4×D71semidirect
729. C22⋊C4C2×C4×D71semidirect
891. C2#22591028direct (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×(C22⋊D71)⋊C42
C22×#145560862
#225910282
C2×#179859012
C2×#179858992
C2×#179858962
C2×#179858892
C2×#179858772
C2×#179858762
C2×#179858742
C2×#179858732
C2×#179858582
C2×C4×Dic71⋊C42
C2×#388×C712
C2×#232471