Finite Group Databasebeta

← C2×#22591496 #32160048

Subgroups — C2×#22591496 #32160048

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×#14556101C211yesmaximal, characteristic
2#22591496C2116yesmaximal, direct product factor
3C2×#17985900C211yesmaximal, characteristic, complemented
4C2×#17985899C211yesmaximal, characteristic, complemented
5C2×#17985892C211yesmaximal, characteristic, complemented
6C2×#17985889C211yesmaximal, characteristic, complemented
7C2×#17985881C211yesmaximal, characteristic, complemented
8C2×#17985880C211yesmaximal, characteristic, complemented
9C2×#17985878C211yesmaximal, characteristic, complemented
10C2×#17985878C211yesmaximal, characteristic, complemented
11C2×#17985877C211yesmaximal, characteristic, complemented
12C2×#17985875C211yesmaximal, characteristic, complemented
13C2×#17985873C211yesmaximal, characteristic, complemented
14C2×#17985861C211yesmaximal, characteristic, complemented
15C2×#17985856C211yesmaximal, characteristic, complemented
16C2×#385×C71C211yesmaximal, characteristic, complemented
17C23×D284C2211yescharacteristic
18C23×C22⋊D71C2211yescharacteristic
19C23×C22⋊D71C2211yescharacteristic
20C23×C4×D71C2211yescharacteristic
21C23×C4×D71C2211yescharacteristic
22C2×#14556101C4116yescomplemented
23C2×#14556101C2218yes—
24C22×C4⋊Dic71C2211yescharacteristic
25C22×Dic71⋊C4C2211yescharacteristic
26C22×Dic71⋊C4C2211yescharacteristic
27C22×C22⋊Dic71C2211yescharacteristic
28C22×C22⋊Dic71C2211yescharacteristic
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×C4×Dic71C2211yescharacteristic
38C22×C4×Dic71C2211yescharacteristic
39#17985900C2218yescomplemented
40#17985899C2218yescomplemented
41#17985892C2218yescomplemented
42#17985889C2218yescomplemented
43#17985881C2218yescomplemented
44#17985880C2218yescomplemented
45#17985878C2218yescomplemented
46#17985878C2218yescomplemented
47#17985877C2218yescomplemented
48#17985875C2218yescomplemented
49#17985873C2218yescomplemented
50#17985861C2218yescomplemented
51#17985856C2218yescomplemented
52C2×C71⋊#95C2211yescharacteristic
53C2×C71⋊#95C2211yescharacteristic
54C2×C71⋊#95C2211yescharacteristic
55C2×C71⋊#95C2211yescharacteristic
56C2×C71⋊#95C2211yescharacteristic
57C2×C71⋊#95C2211yescharacteristic
58C2×C71⋊#95C2211yescharacteristic
59C2×C71⋊#95C2211yescharacteristic
60C24×C4×C71C2211yescharacteristic
61C22×C4⋊C4×C71C2211yescharacteristic
62C22×C4⋊C4×C71C2211yescharacteristic
63C22×C22⋊C4×C71C2211yescharacteristic
64C22×C22⋊C4×C71C2211yescharacteristic
65#385×C71C2218yescomplemented
66C2×#95×C71C2211yescharacteristic
67C2×#95×C71C2211yescharacteristic
68C24×D71C2311yescharacteristic
69C24×D71C2311yescharacteristic
70C22×D284—42no—
71C22×D284—42no—
72C22×D284C2×C418yescomplemented
73C22×D284C2314yes—
74C22×C22⋊D71—42no—
75C22×C22⋊D71—42no—
76C22×C22⋊D71—42no—
77C22×C22⋊D71—42no—
78C22×C22⋊D71C2×C418yes—
79C22×C22⋊D71C2×C418yescomplemented
80C22×C22⋊D71C2314yes—
81C22×C22⋊D71C2314yes—
82C23×Dic71C2311yescharacteristic
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×D71C2×C418yescomplemented
94C22×C4×D71C2314yes—
95C22×C4×D71C2314yes—
96#14556101C2×C4164yescomplemented
97C2×C4⋊Dic71—42no—
98C2×C4⋊Dic71C2314yes—
99C2×Dic71⋊C4—42no—
100C2×Dic71⋊C4C2×C418yescomplemented
101C2×Dic71⋊C4C2314yes—
102C2×Dic71⋊C4C2314yes—
103C2×C22⋊Dic71—42no—
104C2×C22⋊Dic71—42no—
105C2×C22⋊Dic71C2314yes—
106C2×C22⋊Dic71C2314yes—
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)⋊C4C2×C418yescomplemented
115C2×(C2×D71)⋊C4C2314yes—
116C2×(C2×D71)⋊C4C2314yes—
117C2×(C2×D71)⋊C4C2314yes—
118C2×(C2×D71)⋊C4C2314yes—
119C2×(C2×D71)⋊C4C2314yes—
120C2×(C2×D71)⋊C4C2314yes—
121C2×(C2×D71)⋊C4C2314yes—
122C2×(C2×D71)⋊C4C2314yes—
123C2×C4×Dic71—42no—
124C2×C4×Dic71—42no—
125C2×C4×Dic71C2314yes—
126C2×C4×Dic71C2314yes—
127C71⋊#95C2314yes—
128C71⋊#95C2314yes—
129C71⋊#95C2314yes—
130C71⋊#95C2314yes—
131C71⋊#95C2314yes—
132C71⋊#95C2314yes—
133C71⋊#95C2314yes—
134C71⋊#95C2314yes—
135C25×C71C2311yescharacteristic
136C23×C4×C71—42no—
137C23×C4×C71—42no—
138C23×C4×C71—42no—
139C23×C4×C71C2311yescharacteristic
140C23×C4×C71C2311yescharacteristic
141C23×C4×C71C2311yescharacteristic
142C23×C4×C71C2311yescharacteristic
143C23×C4×C71C2311yescharacteristic
144C23×C4×C71C2311yescharacteristic
145C23×C4×C71C2314yes—
146C2×C4⋊C4×C71—42no—
147C2×C4⋊C4×C71—42no—
148C2×C4⋊C4×C71C2314yes—
149C2×C4⋊C4×C71C2314yes—
150C2×C22⋊C4×C71—42no—
151C2×C22⋊C4×C71C2×C418yescomplemented
152C2×C22⋊C4×C71C2314yes—
153C2×C22⋊C4×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×D71C22×C414yes—
169C23×D71C22×C414yes—
170C23×D71C2412yes—
171C23×D71C2412yes—
172C2×D284—416no—
173C2×D284—44no—
174C2×D284—44no—
175C2×D284C22×C4116yescomplemented
176C2×C22⋊D71—416no—
177C2×C22⋊D71—416no—
178C2×C22⋊D71—44no—
179C2×C22⋊D71—44no—
180C2×C22⋊D71—44no—
181C2×C22⋊D71—44no—
182C2×C22⋊D71C22×C4116yes—
183C2×C22⋊D71C22×C4116yescomplemented
184C22×Dic71—22no—
185C22×Dic71—22no—
186C22×Dic71—22no—
187C22×Dic71—22no—
188C22×Dic71—22no—
189C22×Dic71—22no—
190C22×Dic71—22no—
191C22×Dic71—22no—
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×Dic71C22×C414yes—
201C22×Dic71C22×C414yes—
202C22×Dic71C2412yes—
203C22×Dic71C2412yes—
204C22×Dic71C2412yes—
205C22×Dic71C2412yes—
206C22×Dic71C2412yes—
207C22×Dic71C2412yes—
208C2×C4×D71—416no—
209C2×C4×D71—44no—
210C2×C4×D71—44no—
211C2×C4×D71—44no—
212C2×C4×D71—44no—
213C2×C4×D71—44no—
214C2×C4×D71—416no—
215C2×C4×D71C22×C4116yescomplemented
216C4⋊Dic71—44no—
217Dic71⋊C4—44no—
218Dic71⋊C4C22×C4116yescomplemented
219C22⋊Dic71—44no—
220C22⋊Dic71—44no—
221(C2×D71)⋊C4—44no—
222(C2×D71)⋊C4—44no—
223(C2×D71)⋊C4—44no—
224(C2×D71)⋊C4—44no—
225(C2×D71)⋊C4—44no—
226(C2×D71)⋊C4—44no—
227(C2×D71)⋊C4—44no—
228(C2×D71)⋊C4C22×C4116yescomplemented
229C4×Dic71—44no—
230C4×Dic71—44no—
231C24×C71—22no—
232C24×C71—22no—
233C24×C71—22no—
234C24×C71—22no—
235C24×C71—22no—
236C24×C71—22no—
237C24×C71C22×C414yes—
238C24×C71C2412yes—
239C24×C71C2411yescharacteristic
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×C71—22no—
253C22×C4×C71—22no—
254C22×C4×C71—22no—
255C22×C4×C71—22no—
256C22×C4×C71—44no—
257C22×C4×C71—44no—
258C22×C4×C71—44no—
259C22×C4×C71—416no—
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—
268C4⋊C4×C71—44no—
269C4⋊C4×C71—44no—
270C22⋊C4×C71—44no—
271C22⋊C4×C71C22×C4116yescomplemented
272C23×C71—28no—
273C23×C71—28no—
274C23×C71—28no—
275C23×C71—22no—
276C23×C71—22no—
277C23×C71—22no—
278C23×C71—22no—
279C23×C71—22no—
280C23×C71—22no—
281C23×C71—44no—
282C23×C71—44no—
283C23×C71—44no—
284C23×C71—44no—
285C23×C71C23×C414yes—
286C23×C71C23×C412yes—
287C23×C71H(5,𝔽2)12yes—
288C23×C71H(5,𝔽2)12yes—
289C23×C71H(5,𝔽2)12yes—
290C23×C71H(5,𝔽2)12yes—
291C23×C71H(5,𝔽2)12yes—
292C23×C712−1+412yes—
293C23×C71C2511yescharacteristic
294C22×D71—28no—
295C22×D71—28no—
296C22×D71—28no—
297C22×D71—28no—
298C22×D71—28no—
299C22×D71—28no—
300C22×D71—22no—
301C22×D71—22no—
302C22×D71—22no—
303C22×D71—22no—
304C22×D71—22no—
305C22×D71—22no—
306C22×D71—22no—
307C22×D71—22no—
308C22×D71—22no—
309C22×D71—22no—
310C22×D71—22no—
311C22×D71—22no—
312C22×D71—44no—
313C22×D71—44no—
314C22×D71—44no—
315C22×D71—44no—
316C22×D71—44no—
317C22×D71—44no—
318C22×D71—44no—
319C22×D71—44no—
320C22×D71C23×C414yes—
321C22×D71C23×C414yes—
322C2×C4×C71—28no—
323C2×C4×C71—28no—
324C2×C4×C71—22no—
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—416no—
341C2×C4×C71—44no—
342C2×C4×C71—44no—
343C2×C4×C71—44no—
344C2×C4×C71—44no—
345C2×C4×C71C23×C414yes—
346C2×C4×C71C23×C414yes—
347C22⋊D71—416no—
348C22⋊D71—416no—
349C2×Dic71—28no—
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—22no—
366C2×Dic71—22no—
367C2×Dic71—44no—
368C2×Dic71—44no—
369C2×Dic71—44no—
370C2×Dic71—44no—
371C2×Dic71C23×C414yes—
372C2×Dic71C23×C414yes—
373D284—416no—
374C4×D71—416no—
375C4×D71—416no—
376C22×C71—24no—
377C22×C71—24no—
378C22×C71—24no—
379C22×C71—416no—
380C22×C71—42no—
381C22×C71—42no—
382C22×C71—42no—
383C22×C71—42no—
384C22×C71#51814yes—
385C22×C71#51814yes—
386C22×C71#52014yes—
387C22×C71#56014yes—
388C22×C71#56014yes—
389C22×C71#56214yes—
390C22×C71#56214yes—
391C22×C71C24×C411yescharacteristic
392C22×C71C2×H(5,𝔽2)11yescharacteristic
393C22×C71C2×H(5,𝔽2)11yescharacteristic
394C22×C71C2×H(5,𝔽2)11yescharacteristic
395C22×C71C2×H(5,𝔽2)11yescharacteristic
396C22×C71C2×H(5,𝔽2)11yescharacteristic
397C22×C71C2×2−1+411yescharacteristic
398C2×D71—24no—
399C2×D71—24no—
400C2×D71—24no—
401C2×D71—24no—
402C2×D71—24no—
403C2×D71—24no—
404C2×D71—416no—
405C2×D71—416no—
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—42no—
417C4×C71—42no—
418C4×C71—42no—
419C4×C71—42no—
420Dic71—24no—
421Dic71—24no—
422Dic71—42no—
423Dic71—42no—
424Dic71—42no—
425Dic71—42no—
426C2×#2377—711nomaximal, Sylow
427C2×C71—44no—
428C2×C71#237718yescomplemented
429C2×C71C2×#51811yescharacteristic
430C2×C71C2×#51811yescharacteristic
431C2×C71C2×#52011yescharacteristic
432C2×C71C2×#56011yescharacteristic
433C2×C71C2×#56011yescharacteristic
434C2×C71C2×#56211yescharacteristic
435C2×C71C2×#56211yescharacteristic
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×#387—711no—
446C2×#386—711no—
447C2×#386—711no—
448C2×#386—711no—
449C2×#386—711no—
450C2×#385—711no—
451C2×#385D7111yescharacteristic, complemented
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×C4C2×D7111yescharacteristic
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⋊C4C2×D7111yescharacteristic
479C22×C22⋊C4C2×D7111yescharacteristic
480C22×C42—711no—
481C22×C42—711no—
482#390—718no—
483#390—718no—
484#388—718no—
485#388—718no—
486#387—718no—
487#387—718no—
488#386—718no—
489#386—718no—
490#386—718no—
491#386—718no—
492#385—718no—
493#385C2×D7118yescomplemented
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×#95—711no—
503C2×#95—711no—
504C2×#95C2×D7111yescharacteristic
505C2×#95C2×D7111yescharacteristic
506C25—711no—
507C25—711no—
508C25C22×D7111yescharacteristic
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—714no—
518C22×D4—714no—
519C22×D4—718no—
520C22×D4—714no—
521C23×C4—42no—
522C23×C4—42no—
523C23×C4—42no—
524C23×C4—2842no—
525C23×C4—2842no—
526C23×C4—2842no—
527C23×C4—2842no—
528C23×C4—2842no—
529C23×C4—714no—
530C23×C4—718no—
531C23×C4—714no—
532C23×C4—711no—
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×D7114yes—
545#121—7164no—
546C2×C4⋊C4—42no—
547C2×C4⋊C4—42no—
548C2×C4⋊C4—2842no—
549C2×C4⋊C4—2842no—
550C2×C4⋊C4—714no—
551C2×C4⋊C4—714no—
552C2×C4⋊C4—718no—
553C2×C4⋊C4—714no—
554C2×C4⋊C4C22×D7114yes—
555C2×C4⋊C4C22×D7114yes—
556C2×C22⋊C4—42no—
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—718no—
576C2×C22⋊C4—714no—
577C2×C22⋊C4C4×D7118yescomplemented
578C2×C22⋊C4C22×D7114yes—
579C2×C22⋊C4C22×D7114yes—
580C2×C42—2842no—
581C2×C42—2842no—
582C2×C42—714no—
583C2×C42—714no—
584#95—714no—
585#95—714no—
586#95—714no—
587#95—714no—
588#95—714no—
589#95—714no—
590#95—714no—
591#95—714no—
592#95C22×D7114yes—
593#95C22×D7114yes—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—714no—
601C24—714no—
602C24—712no—
603C24—712no—
604C24—1422no—
605C24—1422no—
606C24—1422no—
607C24—1422no—
608C24—1422no—
609C24—1422no—
610C24—1422no—
611C24—1422no—
612C24—1422no—
613C24—1422no—
614C24—1422no—
615C24—1422no—
616C24C2×C4×D7114yes—
617C24C23×D7112yes—
618C24C23×D7111yescharacteristic
619C2×D4—2844no—
620C2×D4—2844no—
621C2×D4—28416no—
622C2×D4—2844no—
623C2×D4—2844no—
624C2×D4—2844no—
625C2×D4—2844no—
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—44no—
648C22×C4—44no—
649C22×C4—44no—
650C22×C4—416no—
651C22×C4—2844no—
652C22×C4—2844no—
653C22×C4—28416no—
654C22×C4—2844no—
655C22×C4—2844no—
656C22×C4—2844no—
657C22×C4—28416no—
658C22×C4—7116no—
659C22×C4—714no—
660C22×C4—714no—
661C22×C4—712no—
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×C4—1422no—
682C22×C4—1422no—
683C22×C4C2×C4×D7114yes—
684C22×C4C2×C4×D7114yes—
685C22×C4C23×D7112yes—
686C22×C4C23×D7112yes—
687C22×C4C23×D7112yes—
688C22×C4C23×D7112yes—
689C22×C4C23×D7112yes—
690C22×C4C23×D7112yes—
691C4⋊C4—44no—
692C4⋊C4—44no—
693C4⋊C4—2844no—
694C4⋊C4—2844no—
695C4⋊C4—7116no—
696C22⋊C4—44no—
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⋊C4C2×C4×D71116yescomplemented
708C42—2844no—
709C42—2844no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—28no—
717C23—28no—
718C23—28no—
719C23—44no—
720C23—44no—
721C23—44no—
722C23—44no—
723C23—2844no—
724C23—2844no—
725C23—2844no—
726C23—2844no—
727C23—2844no—
728C23—2844no—
729C23—2844no—
730C23—2844no—
731C23—714no—
732C23—714no—
733C23—1422no—
734C23—1422no—
735C23—1422no—
736C23—1422no—
737C23—1422no—
738C23—1422no—
739C23—1422no—
740C23—1422no—
741C23—1422no—
742C23—1422no—
743C23—1422no—
744C23—1422no—
745C23—1428no—
746C23—1428no—
747C23—1428no—
748C23—1428no—
749C23—1428no—
750C23—1428no—
751C23C22×C4×D7114yes—
752C23C22×C4×D7112yes—
753C23#1455617312yes—
754C23#1455617312yes—
755C23#1455617312yes—
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—28no—
768C2×C4—28no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
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—416no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—28416no—
787C2×C4—28416no—
788C2×C4—2844no—
789C2×C4—2844no—
790C2×C4—2844no—
791C2×C4—2844no—
792C2×C4—714no—
793C2×C4—714no—
794C2×C4—1422no—
795C2×C4—1422no—
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×C4—1428no—
812C2×C4C22×C4×D7114yes—
813C2×C4C22×C4×D7114yes—
814C22—24no—
815C22—24no—
816C22—24no—
817C22—416no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—28416no—
823C22—28416no—
824C22—2842no—
825C22—2842no—
826C22—2842no—
827C22—2842no—
828C22—2842no—
829C22—2842no—
830C22—2842no—
831C22—2842no—
832C22—1424no—
833C22—1424no—
834C22—1424no—
835C22—1424no—
836C22—1424no—
837C22—1424no—
838C22#1798647114yes—
839C22#1798647114yes—
840C22#1798648014yes—
841C22#1798673814yes—
842C22#1798673914yes—
843C22#1798674514yes—
844C22#1798674514yes—
845C22C23×C4×D7111yescharacteristic
846C22C2×#1455617311yescharacteristic
847C22C2×#1455617311yescharacteristic
848C22C2×#1455617311yescharacteristic
849C22C2×#1455617411yescharacteristic
850C22C2×#1455617411yescharacteristic
851C22C2×#1455617611yescharacteristic
852C4—24no—
853C4—24no—
854C4—42no—
855C4—42no—
856C4—42no—
857C4—42no—
858C4—2842no—
859C4—2842no—
860C4—2842no—
861C4—2842no—
862C4—1424no—
863C4—1424no—
864C2—44no—
865C2—2844no—
866C2—2844no—
867C2#2259149618yesdirect product factor
868C2C2×#1798647111yescharacteristic
869C2C2×#1798647111yescharacteristic
870C2C2×#1798648011yescharacteristic
871C2C2×#1798673811yescharacteristic
872C2C2×#1798673911yescharacteristic
873C2C2×#1798674511yescharacteristic
874C2C2×#1798674511yescharacteristic
subgroupG/H
centerC24C23×D71
commutatorC22×C71C24×C4
FrattiniC23C24×D71
FittingC2×#385×C71C2
socleC24×C71C24
prime radicalC22×#14556101C2
cosocleC23×C71C25
hypercenterC2×#385D71
hypocenterC71C2×#2377
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. #22591496C2direct (N × H)
3. C2×#17985900C2semidirect
4. C2×#17985899C2semidirect
5. C2×#17985892C2semidirect
6. C2×#17985889C2semidirect
7. C2×#17985881C2semidirect
8. C2×#17985880C2semidirect
9. C2×#17985878C2semidirect
10. C2×#17985878C2semidirect
11. C2×#17985877C2semidirect
12. C2×#17985875C2semidirect
13. C2×#17985873C2semidirect
14. C2×#17985861C2semidirect
15. C2×#17985856C2semidirect
16. C2×#385×C71C2semidirect
22. C2×#14556101C4semidirect
39. #17985900C22semidirect
40. #17985899C22semidirect
41. #17985892C22semidirect
42. #17985889C22semidirect
43. #17985881C22semidirect
44. #17985880C22semidirect
45. #17985878C22semidirect
46. #17985878C22semidirect
47. #17985877C22semidirect
48. #17985875C22semidirect
49. #17985873C22semidirect
50. #17985861C22semidirect
51. #17985856C22semidirect
65. #385×C71C22semidirect
72. C22×D284C2×C4semidirect
79. C22×C22⋊D71C2×C4semidirect
93. C22×C4×D71C2×C4semidirect
96. #14556101C2×C4semidirect
100. C2×Dic71⋊C4C2×C4semidirect
114. C2×(C2×D71)⋊C4C2×C4semidirect
151. C2×C22⋊C4×C71C2×C4semidirect
175. C2×D284C22×C4semidirect
183. C2×C22⋊D71C22×C4semidirect
215. C2×C4×D71C22×C4semidirect
218. Dic71⋊C4C22×C4semidirect
228. (C2×D71)⋊C4C22×C4semidirect
271. C22⋊C4×C71C22×C4semidirect
428. C2×C71#2377semidirect
451. C2×#385D71semidirect
454. C71C2×#2377semidirect
493. #385C2×D71semidirect
577. C2×C22⋊C4C4×D71semidirect
707. C22⋊C4C2×C4×D71semidirect
867. C2#22591496direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561012
#225914962
C2×#179859002
C2×#179858992
C2×#179858922
C2×#179858892
C2×#179858812
C2×#179858802
C2×#179858782
C2×#179858772
C2×#179858752
C2×#179858732
C2×#179858612
C2×#179858562
C2×#385×C712
C2×#237771