Finite Group Databasebeta

← C2×#22591495 #32160047

Subgroups — C2×#22591495 #32160047

Order 18176.

3302 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556103C211yesmaximal, characteristic
2#22591495C2116yesmaximal, direct product factor
3C2×#17985901C211yesmaximal, characteristic, complemented
4C2×#17985900C211yesmaximal, characteristic, complemented
5C2×#17985890C211yesmaximal, characteristic, complemented
6C2×#17985888C211yesmaximal, characteristic, complemented
7C2×#17985885C211yesmaximal, characteristic, complemented
8C2×#17985877C211yesmaximal, characteristic, complemented
9C2×#17985877C211yesmaximal, characteristic, complemented
10C2×#17985877C211yesmaximal, characteristic, complemented
11C2×#17985877C211yesmaximal, characteristic, complemented
12C2×#17985873C211yesmaximal, characteristic, complemented
13C2×#17985870C211yesmaximal, characteristic, complemented
14C2×#17985861C211yesmaximal, characteristic, complemented
15C2×#17985858C211yesmaximal, characteristic, complemented
16C2×#387×C71C211yesmaximal, characteristic, complemented
17C23×D284C2211yescharacteristic
18C23×D284C2211yescharacteristic
19C23×D284C2211yescharacteristic
20C23×C4×D71C2211yescharacteristic
21C23×C4×D71C2211yescharacteristic
22C23×C4×D71C2211yescharacteristic
23C2×#14556103C4116yescomplemented
24C2×#14556103C2218yes—
25C22×C4⋊Dic71C2211yescharacteristic
26C22×Dic71⋊C4C2211yescharacteristic
27C22×Dic71⋊C4C2211yescharacteristic
28C22×(C2×D71)⋊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
41#17985901C2218yescomplemented
42#17985900C2218yescomplemented
43#17985890C2218yescomplemented
44#17985888C2218yescomplemented
45#17985885C2218yescomplemented
46#17985877C2218yescomplemented
47#17985877C2218yescomplemented
48#17985877C2218yescomplemented
49#17985877C2218yescomplemented
50#17985873C2218yescomplemented
51#17985870C2218yescomplemented
52#17985861C2218yescomplemented
53#17985858C2218yescomplemented
54C2×C71⋊#95C2211yescharacteristic
55C2×C71⋊#95C2211yescharacteristic
56C2×C71⋊#95C2211yescharacteristic
57C2×C71⋊#95C2211yescharacteristic
58C2×C71⋊#95C2211yescharacteristic
59C2×C71⋊#95C2211yescharacteristic
60C22×C4⋊C4×C71C2211yescharacteristic
61C22×C4⋊C4×C71C2211yescharacteristic
62C22×C42×C71C2211yescharacteristic
63#387×C71C2218yescomplemented
64C2×#95×C71C2211yescharacteristic
65C2×#95×C71C2211yescharacteristic
66C2×#95×C71C2211yescharacteristic
67C2×#95×C71C2211yescharacteristic
68C24×D71C2311yescharacteristic
69C24×D71C2311yescharacteristic
70C24×D71C2311yescharacteristic
71C22×D284—42no—
72C22×D284—42no—
73C22×D284—42no—
74C22×D284—42no—
75C22×D284—42no—
76C22×D284—42no—
77C22×D284C2×C418yes—
78C22×D284C2×C418yescomplemented
79C22×D284C2×C418yescomplemented
80C22×D284C2314yes—
81C22×D284C2314yes—
82C22×D284C2314yes—
83C23×Dic71C2311yescharacteristic
84C23×Dic71C2311yescharacteristic
85C23×Dic71C2311yescharacteristic
86C23×Dic71C2311yescharacteristic
87C23×Dic71C2311yescharacteristic
88C22×C4×D71—42no—
89C22×C4×D71—42no—
90C22×C4×D71—42no—
91C22×C4×D71—42no—
92C22×C4×D71—42no—
93C22×C4×D71—42no—
94C22×C4×D71—42no—
95C22×C4×D71—42no—
96C22×C4×D71C2×C418yescomplemented
97C22×C4×D71C2314yes—
98C22×C4×D71C2314yes—
99C22×C4×D71C2314yes—
100#14556103C2×C4164yescomplemented
101C2×C4⋊Dic71—42no—
102C2×C4⋊Dic71C2314yes—
103C2×Dic71⋊C4—42no—
104C2×Dic71⋊C4—42no—
105C2×Dic71⋊C4C2314yes—
106C2×Dic71⋊C4C2314yes—
107C2×(C2×D71)⋊C4—42no—
108C2×(C2×D71)⋊C4—42no—
109C2×(C2×D71)⋊C4—42no—
110C2×(C2×D71)⋊C4—42no—
111C2×(C2×D71)⋊C4—42no—
112C2×(C2×D71)⋊C4—42no—
113C2×(C2×D71)⋊C4—42no—
114C2×(C2×D71)⋊C4—42no—
115C2×(C2×D71)⋊C4—42no—
116C2×(C2×D71)⋊C4—42no—
117C2×(C2×D71)⋊C4C2×C418yescomplemented
118C2×(C2×D71)⋊C4C2×C418yescomplemented
119C2×(C2×D71)⋊C4C2314yes—
120C2×(C2×D71)⋊C4C2314yes—
121C2×(C2×D71)⋊C4C2314yes—
122C2×(C2×D71)⋊C4C2314yes—
123C2×(C2×D71)⋊C4C2314yes—
124C2×(C2×D71)⋊C4C2314yes—
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—42no—
132C2×C4×Dic71C2314yes—
133C71⋊#95C2314yes—
134C71⋊#95C2314yes—
135C71⋊#95C2314yes—
136C71⋊#95C2314yes—
137C71⋊#95C2314yes—
138C71⋊#95C2314yes—
139C23×C4×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×C71C2×C418yescomplemented
148C2×C4⋊C4×C71C2314yes—
149C2×C4⋊C4×C71C2314yes—
150C2×C42×C71—42no—
151C2×C42×C71C2314yes—
152#95×C71C2314yes—
153#95×C71C2314yes—
154#95×C71C2314yes—
155#95×C71C2314yes—
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—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×D71C22×C414yes—
177C23×D71C2412yes—
178C23×D71C2412yes—
179C23×D71C2412yes—
180C2×D284—416no—
181C2×D284—416no—
182C2×D284—416no—
183C2×D284—44no—
184C2×D284—44no—
185C2×D284—44no—
186C2×D284—44no—
187C2×D284—44no—
188C2×D284—44no—
189C2×D284C22×C4116yes—
190C2×D284C22×C4116yescomplemented
191C2×D284C22×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×Dic71C22×C414yes—
207C22×Dic71C2412yes—
208C22×Dic71C2412yes—
209C22×Dic71C2412yes—
210C22×Dic71C2412yes—
211C22×Dic71C2412yes—
212C2×C4×D71—416no—
213C2×C4×D71—44no—
214C2×C4×D71—44no—
215C2×C4×D71—44no—
216C2×C4×D71—44no—
217C2×C4×D71—44no—
218C2×C4×D71—44no—
219C2×C4×D71—44no—
220C2×C4×D71—44no—
221C2×C4×D71—416no—
222C2×C4×D71—416no—
223C2×C4×D71C22×C4116yescomplemented
224C4⋊Dic71—44no—
225Dic71⋊C4—44no—
226Dic71⋊C4—44no—
227(C2×D71)⋊C4—44no—
228(C2×D71)⋊C4—44no—
229(C2×D71)⋊C4—44no—
230(C2×D71)⋊C4—44no—
231(C2×D71)⋊C4—44no—
232(C2×D71)⋊C4—44no—
233(C2×D71)⋊C4—44no—
234(C2×D71)⋊C4—44no—
235(C2×D71)⋊C4—44no—
236(C2×D71)⋊C4—44no—
237(C2×D71)⋊C4C22×C4116yescomplemented
238(C2×D71)⋊C4C22×C4116yescomplemented
239C4×Dic71—44no—
240C24×C71C2411yescharacteristic
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×C71—22no—
253C22×C4×C71—22no—
254C22×C4×C71—22no—
255C22×C4×C71—22no—
256C22×C4×C71—22no—
257C22×C4×C71—22no—
258C22×C4×C71—22no—
259C22×C4×C71C22×C414yes—
260C22×C4×C71C22×C414yes—
261C22×C4×C71C22×C414yes—
262C22×C4×C71C2412yes—
263C22×C4×C71C2412yes—
264C22×C4×C71C2412yes—
265C22×C4×C71C2412yes—
266C22×C4×C71C2412yes—
267C22×C4×C71C2412yes—
268C22×C4×C71C2412yes—
269C4⋊C4×C71—44no—
270C4⋊C4×C71C22×C4116yescomplemented
271C42×C71—44no—
272C23×C71C23×C412yes—
273C23×C71H(5,𝔽2)12yes—
274C23×C71H(5,𝔽2)12yes—
275C23×C71H(5,𝔽2)12yes—
276C23×C71H(5,𝔽2)12yes—
277C23×C71H(5,𝔽2)12yes—
278C23×C712−1+412yes—
279C23×C71C2511yescharacteristic
280C22×D71—28no—
281C22×D71—28no—
282C22×D71—28no—
283C22×D71—28no—
284C22×D71—28no—
285C22×D71—28no—
286C22×D71—28no—
287C22×D71—28no—
288C22×D71—28no—
289C22×D71—22no—
290C22×D71—22no—
291C22×D71—22no—
292C22×D71—22no—
293C22×D71—22no—
294C22×D71—22no—
295C22×D71—22no—
296C22×D71—22no—
297C22×D71—22no—
298C22×D71—22no—
299C22×D71—22no—
300C22×D71—22no—
301C22×D71—22no—
302C22×D71—22no—
303C22×D71—22no—
304C22×D71—22no—
305C22×D71—22no—
306C22×D71—22no—
307C22×D71—44no—
308C22×D71—44no—
309C22×D71—44no—
310C22×D71—44no—
311C22×D71—44no—
312C22×D71—44no—
313C22×D71—44no—
314C22×D71—44no—
315C22×D71—44no—
316C22×D71—44no—
317C22×D71—44no—
318C22×D71—44no—
319C22×D71C23×C414yes—
320C22×D71C23×C414yes—
321C22×D71C23×C414yes—
322C2×C4×C71—28no—
323C2×C4×C71—28no—
324C2×C4×C71—28no—
325C2×C4×C71—22no—
326C2×C4×C71—22no—
327C2×C4×C71—22no—
328C2×C4×C71—22no—
329C2×C4×C71—22no—
330C2×C4×C71—22no—
331C2×C4×C71—22no—
332C2×C4×C71—22no—
333C2×C4×C71—22no—
334C2×C4×C71—22no—
335C2×C4×C71—22no—
336C2×C4×C71—22no—
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—44no—
344C2×C4×C71—44no—
345C2×C4×C71—44no—
346C2×C4×C71—44no—
347C2×C4×C71C23×C414yes—
348C2×C4×C71C23×C414yes—
349C2×C4×C71C23×C414yes—
350C2×Dic71—28no—
351C2×Dic71—22no—
352C2×Dic71—22no—
353C2×Dic71—22no—
354C2×Dic71—22no—
355C2×Dic71—22no—
356C2×Dic71—22no—
357C2×Dic71—22no—
358C2×Dic71—22no—
359C2×Dic71—22no—
360C2×Dic71—22no—
361C2×Dic71—22no—
362C2×Dic71—22no—
363C2×Dic71—22no—
364C2×Dic71—22no—
365C2×Dic71—44no—
366C2×Dic71—44no—
367C2×Dic71—44no—
368C2×Dic71—44no—
369C2×Dic71C23×C414yes—
370D284—416no—
371D284—416no—
372D284—416no—
373C4×D71—416no—
374C4×D71—416no—
375C4×D71—416no—
376C22×C71#51814yes—
377C22×C71#51814yes—
378C22×C71#52014yes—
379C22×C71#56014yes—
380C22×C71#56014yes—
381C22×C71#56214yes—
382C22×C71#56214yes—
383C22×C71C24×C411yescharacteristic
384C22×C71C2×H(5,𝔽2)11yescharacteristic
385C22×C71C2×H(5,𝔽2)11yescharacteristic
386C22×C71C2×H(5,𝔽2)11yescharacteristic
387C22×C71C2×H(5,𝔽2)11yescharacteristic
388C22×C71C2×H(5,𝔽2)11yescharacteristic
389C22×C71C2×2−1+411yescharacteristic
390C2×D71—24no—
391C2×D71—24no—
392C2×D71—24no—
393C2×D71—24no—
394C2×D71—24no—
395C2×D71—24no—
396C2×D71—24no—
397C2×D71—24no—
398C2×D71—24no—
399C2×D71—416no—
400C2×D71—416no—
401C2×D71—416no—
402C2×D71—42no—
403C2×D71—42no—
404C2×D71—42no—
405C2×D71—42no—
406C2×D71—42no—
407C2×D71—42no—
408C2×D71—42no—
409C2×D71—42no—
410C2×D71—42no—
411C2×D71—42no—
412C2×D71—42no—
413C2×D71—42no—
414C4×C71—24no—
415C4×C71—24no—
416C4×C71—24no—
417C4×C71—42no—
418C4×C71—42no—
419C4×C71—42no—
420C4×C71—42no—
421Dic71—24no—
422Dic71—42no—
423Dic71—42no—
424Dic71—42no—
425Dic71—42no—
426C2×#2377—711nomaximal, Sylow
427C2×C71#237718yescomplemented
428C2×C71C2×#51811yescharacteristic
429C2×C71C2×#51811yescharacteristic
430C2×C71C2×#52011yescharacteristic
431C2×C71C2×#56011yescharacteristic
432C2×C71C2×#56011yescharacteristic
433C2×C71C2×#56211yescharacteristic
434C2×C71C2×#56211yescharacteristic
435D71—44no—
436D71—44no—
437D71—44no—
438C22×#121—711no—
439#2377—7116no—
440C2×#390—711no—
441C2×#390—711no—
442C2×#388—711no—
443C2×#388—711no—
444C2×#387—711no—
445C2×#387D7111yescharacteristic, complemented
446C2×#386—711no—
447C2×#386—711no—
448C2×#386—711no—
449C2×#386—711no—
450C2×#385—711no—
451C2×#385—711no—
452C2×#381—711no—
453C2×#380—711no—
454C71C2×#237711yescharacteristic, complemented, Sylow
455C23×D4—711no—
456C23×D4—711no—
457C23×D4—711no—
458C24×C4—711no—
459C24×C4—711no—
460C24×C4—711no—
461C2×#121—7116no—
462C2×#121—718no—
463C22×C4⋊C4—711no—
464C22×C4⋊C4—711no—
465C22×C4⋊C4—711no—
466C22×C4⋊C4C2×D7111yescharacteristic
467C22×C4⋊C4C2×D7111yescharacteristic
468C22×C22⋊C4—711no—
469C22×C22⋊C4—711no—
470C22×C22⋊C4—711no—
471C22×C22⋊C4—711no—
472C22×C22⋊C4—711no—
473C22×C22⋊C4—711no—
474C22×C22⋊C4—711no—
475C22×C22⋊C4—711no—
476C22×C22⋊C4—711no—
477C22×C22⋊C4—711no—
478C22×C22⋊C4—711no—
479C22×C22⋊C4—711no—
480C22×C42—711no—
481C22×C42C2×D7111yescharacteristic
482#390—718no—
483#390—718no—
484#388—718no—
485#388—718no—
486#387—718no—
487#387C2×D7118yescomplemented
488#386—718no—
489#386—718no—
490#386—718no—
491#386—718no—
492#385—718no—
493#385—718no—
494#381—718no—
495#380—718no—
496C2×#95—711no—
497C2×#95—711no—
498C2×#95—711no—
499C2×#95—711no—
500C2×#95—711no—
501C2×#95—711no—
502C2×#95C2×D7111yescharacteristic
503C2×#95C2×D7111yescharacteristic
504C2×#95C2×D7111yescharacteristic
505C2×#95C2×D7111yescharacteristic
506C25—711no—
507C25—711no—
508C25—711no—
509C22×D4—2842no—
510C22×D4—2842no—
511C22×D4—2842no—
512C22×D4—2842no—
513C22×D4—2842no—
514C22×D4—2842no—
515C22×D4—718no—
516C22×D4—718no—
517C22×D4—718no—
518C22×D4—714no—
519C22×D4—714no—
520C22×D4—714no—
521C23×C4—2842no—
522C23×C4—2842no—
523C23×C4—2842no—
524C23×C4—2842no—
525C23×C4—2842no—
526C23×C4—2842no—
527C23×C4—2842no—
528C23×C4—2842no—
529C23×C4—714no—
530C23×C4—714no—
531C23×C4—718no—
532C23×C4—714no—
533C23×C4—711no—
534C23×C4—711no—
535C23×C4—711no—
536C23×C4—711no—
537C23×C4—711no—
538C23×C4C22×D7111yescharacteristic
539C23×C4C22×D7111yescharacteristic
540C23×C4C22×D7111yescharacteristic
541C23×C4C22×D7111yescharacteristic
542C23×C4C22×D7111yescharacteristic
543C23×C4C22×D7111yescharacteristic
544C23×C4C22×D7111yescharacteristic
545#121—7164no—
546C2×C4⋊C4—42no—
547C2×C4⋊C4—2842no—
548C2×C4⋊C4—2842no—
549C2×C4⋊C4—2842no—
550C2×C4⋊C4—714no—
551C2×C4⋊C4—714no—
552C2×C4⋊C4—714no—
553C2×C4⋊C4C4×D7118yescomplemented
554C2×C4⋊C4C22×D7114yes—
555C2×C4⋊C4C22×D7114yes—
556C2×C22⋊C4—2842no—
557C2×C22⋊C4—2842no—
558C2×C22⋊C4—2842no—
559C2×C22⋊C4—2842no—
560C2×C22⋊C4—2842no—
561C2×C22⋊C4—2842no—
562C2×C22⋊C4—2842no—
563C2×C22⋊C4—2842no—
564C2×C22⋊C4—2842no—
565C2×C22⋊C4—2842no—
566C2×C22⋊C4—714no—
567C2×C22⋊C4—714no—
568C2×C22⋊C4—714no—
569C2×C22⋊C4—714no—
570C2×C22⋊C4—714no—
571C2×C22⋊C4—714no—
572C2×C22⋊C4—714no—
573C2×C22⋊C4—714no—
574C2×C22⋊C4—714no—
575C2×C22⋊C4—714no—
576C2×C22⋊C4—718no—
577C2×C22⋊C4—718no—
578C2×C22⋊C4—714no—
579C2×C22⋊C4—714no—
580C2×C42—42no—
581C2×C42—2842no—
582C2×C42—714no—
583C2×C42C22×D7114yes—
584#95—714no—
585#95—714no—
586#95—714no—
587#95—714no—
588#95—714no—
589#95—714no—
590#95C22×D7114yes—
591#95C22×D7114yes—
592#95C22×D7114yes—
593#95C22×D7114yes—
594C24—714no—
595C24—714no—
596C24—714no—
597C24—712no—
598C24—712no—
599C24—712no—
600C24—1422no—
601C24—1422no—
602C24—1422no—
603C24—1422no—
604C24—1422no—
605C24—1422no—
606C24—1422no—
607C24—1422no—
608C24—1422no—
609C24—1422no—
610C24—1422no—
611C24—1422no—
612C24—1422no—
613C24—1422no—
614C24—1422no—
615C24—1422no—
616C24—1422no—
617C24—1422no—
618C24C23×D7111yescharacteristic
619C2×D4—2844no—
620C2×D4—2844no—
621C2×D4—2844no—
622C2×D4—2844no—
623C2×D4—2844no—
624C2×D4—2844no—
625C2×D4—28416no—
626C2×D4—28416no—
627C2×D4—28416no—
628C2×D4—7116no—
629C2×D4—7116no—
630C2×D4—7116no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—2844no—
650C22×C4—2844no—
651C22×C4—28416no—
652C22×C4—2844no—
653C22×C4—2844no—
654C22×C4—2844no—
655C22×C4—2844no—
656C22×C4—2844no—
657C22×C4—2844no—
658C22×C4—28416no—
659C22×C4—28416no—
660C22×C4—7116no—
661C22×C4—714no—
662C22×C4—712no—
663C22×C4—712no—
664C22×C4—712no—
665C22×C4—712no—
666C22×C4—712no—
667C22×C4—1422no—
668C22×C4—1422no—
669C22×C4—1422no—
670C22×C4—1422no—
671C22×C4—1422no—
672C22×C4—1422no—
673C22×C4—1422no—
674C22×C4—1422no—
675C22×C4—1422no—
676C22×C4—1422no—
677C22×C4—1422no—
678C22×C4—1422no—
679C22×C4—1422no—
680C22×C4—1422no—
681C22×C4C2×C4×D7114yes—
682C22×C4C2×C4×D7114yes—
683C22×C4C2×C4×D7114yes—
684C22×C4C23×D7112yes—
685C22×C4C23×D7112yes—
686C22×C4C23×D7112yes—
687C22×C4C23×D7112yes—
688C22×C4C23×D7112yes—
689C22×C4C23×D7112yes—
690C22×C4C23×D7112yes—
691C4⋊C4—44no—
692C4⋊C4—2844no—
693C4⋊C4—2844no—
694C4⋊C4—2844no—
695C4⋊C4C2×C4×D71116yescomplemented
696C22⋊C4—2844no—
697C22⋊C4—2844no—
698C22⋊C4—2844no—
699C22⋊C4—2844no—
700C22⋊C4—2844no—
701C22⋊C4—2844no—
702C22⋊C4—2844no—
703C22⋊C4—2844no—
704C22⋊C4—2844no—
705C22⋊C4—2844no—
706C22⋊C4—7116no—
707C22⋊C4—7116no—
708C42—44no—
709C42—2844no—
710C23—2844no—
711C23—2844no—
712C23—2844no—
713C23—2844no—
714C23—2844no—
715C23—2844no—
716C23—2844no—
717C23—2844no—
718C23—2844no—
719C23—2844no—
720C23—2844no—
721C23—2844no—
722C23—714no—
723C23—714no—
724C23—714no—
725C23—1422no—
726C23—1422no—
727C23—1422no—
728C23—1422no—
729C23—1422no—
730C23—1422no—
731C23—1422no—
732C23—1422no—
733C23—1422no—
734C23—1422no—
735C23—1422no—
736C23—1422no—
737C23—1422no—
738C23—1422no—
739C23—1422no—
740C23—1422no—
741C23—1422no—
742C23—1422no—
743C23—1428no—
744C23—1428no—
745C23—1428no—
746C23—1428no—
747C23—1428no—
748C23—1428no—
749C23—1428no—
750C23—1428no—
751C23—1428no—
752C23C22×C4×D7112yes—
753C23#1455617312yes—
754C23#1455617412yes—
755C23#1455617412yes—
756C23#1455617412yes—
757C23#1455617412yes—
758C23#1455617612yes—
759C23C24×D7111yescharacteristic
760D4—28416no—
761D4—28416no—
762D4—28416no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—28no—
770C2×C4—28no—
771C2×C4—28no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—28416no—
789C2×C4—28416no—
790C2×C4—28416no—
791C2×C4—2844no—
792C2×C4—2844no—
793C2×C4—2844no—
794C2×C4—2844no—
795C2×C4—714no—
796C2×C4—1422no—
797C2×C4—1422no—
798C2×C4—1422no—
799C2×C4—1422no—
800C2×C4—1422no—
801C2×C4—1422no—
802C2×C4—1422no—
803C2×C4—1422no—
804C2×C4—1422no—
805C2×C4—1422no—
806C2×C4—1422no—
807C2×C4—1422no—
808C2×C4—1422no—
809C2×C4—1422no—
810C2×C4—1428no—
811C2×C4C22×C4×D7114yes—
812C2×C4C22×C4×D7114yes—
813C2×C4C22×C4×D7114yes—
814C22—28416no—
815C22—28416no—
816C22—28416no—
817C22—2842no—
818C22—2842no—
819C22—2842no—
820C22—2842no—
821C22—2842no—
822C22—2842no—
823C22—2842no—
824C22—2842no—
825C22—2842no—
826C22—2842no—
827C22—2842no—
828C22—2842no—
829C22—1424no—
830C22—1424no—
831C22—1424no—
832C22—1424no—
833C22—1424no—
834C22—1424no—
835C22—1424no—
836C22—1424no—
837C22—1424no—
838C22#1798647114yes—
839C22#1798647314yes—
840C22#1798648114yes—
841C22#1798673914yes—
842C22#1798674014yes—
843C22#1798674514yes—
844C22#1798674714yes—
845C22C23×C4×D7111yescharacteristic
846C22C2×#1455617311yescharacteristic
847C22C2×#1455617411yescharacteristic
848C22C2×#1455617411yescharacteristic
849C22C2×#1455617411yescharacteristic
850C22C2×#1455617411yescharacteristic
851C22C2×#1455617611yescharacteristic
852C4—24no—
853C4—24no—
854C4—24no—
855C4—42no—
856C4—42no—
857C4—42no—
858C4—42no—
859C4—2842no—
860C4—2842no—
861C4—2842no—
862C4—2842no—
863C4—1424no—
864C2—2844no—
865C2—2844no—
866C2—2844no—
867C2#2259149518yesdirect product factor
868C2C2×#1798647111yescharacteristic
869C2C2×#1798647311yescharacteristic
870C2C2×#1798648111yescharacteristic
871C2C2×#1798673911yescharacteristic
872C2C2×#1798674011yescharacteristic
873C2C2×#1798674511yescharacteristic
874C2C2×#1798674711yescharacteristic
subgroupG/H
centerC24C23×D71
commutatorC22×C71C24×C4
FrattiniC23C24×D71
FittingC2×#387×C71C2
socleC24×C71C24
prime radicalC22×#14556103C2
cosocleC23×C71C25
hypercenterC2×#387D71
hypocenterC71C2×#2377
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. #22591495C2direct (N × H)
3. C2×#17985901C2semidirect
4. C2×#17985900C2semidirect
5. C2×#17985890C2semidirect
6. C2×#17985888C2semidirect
7. C2×#17985885C2semidirect
8. C2×#17985877C2semidirect
9. C2×#17985877C2semidirect
10. C2×#17985877C2semidirect
11. C2×#17985877C2semidirect
12. C2×#17985873C2semidirect
13. C2×#17985870C2semidirect
14. C2×#17985861C2semidirect
15. C2×#17985858C2semidirect
16. C2×#387×C71C2semidirect
23. C2×#14556103C4semidirect
41. #17985901C22semidirect
42. #17985900C22semidirect
43. #17985890C22semidirect
44. #17985888C22semidirect
45. #17985885C22semidirect
46. #17985877C22semidirect
47. #17985877C22semidirect
48. #17985877C22semidirect
49. #17985877C22semidirect
50. #17985873C22semidirect
51. #17985870C22semidirect
52. #17985861C22semidirect
53. #17985858C22semidirect
63. #387×C71C22semidirect
78. C22×D284C2×C4semidirect
79. C22×D284C2×C4semidirect
96. C22×C4×D71C2×C4semidirect
100. #14556103C2×C4semidirect
117. C2×(C2×D71)⋊C4C2×C4semidirect
118. C2×(C2×D71)⋊C4C2×C4semidirect
147. C2×C4⋊C4×C71C2×C4semidirect
190. C2×D284C22×C4semidirect
191. C2×D284C22×C4semidirect
223. C2×C4×D71C22×C4semidirect
237. (C2×D71)⋊C4C22×C4semidirect
238. (C2×D71)⋊C4C22×C4semidirect
270. C4⋊C4×C71C22×C4semidirect
427. C2×C71#2377semidirect
445. C2×#387D71semidirect
454. C71C2×#2377semidirect
487. #387C2×D71semidirect
553. C2×C4⋊C4C4×D71semidirect
695. C4⋊C4C2×C4×D71semidirect
867. C2#22591495direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561032
#225914952
C2×#179859012
C2×#179859002
C2×#179858902
C2×#179858882
C2×#179858852
C2×#179858772
C2×#179858732
C2×#179858702
C2×#179858612
C2×#179858582
C2×#387×C712
C2×#237771