Finite Group Databasebeta

← C2×#22591010 #32156181

Subgroups — C2×#22591010 #32156181

Order 18176.

3718 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556110C211yesmaximal, characteristic
2C22×(C22⋊D71)⋊C4C211yesmaximal, characteristic
3C22×C4⋊C4×D71C211yesmaximal, characteristic, complemented
4#22591010C2116yesmaximal, direct product factor
5C2×#17985897C211yesmaximal, characteristic, complemented
6C2×#17985894C211yesmaximal, characteristic, complemented
7C2×#17985893C211yesmaximal, characteristic, complemented
8C2×#17985886C211yesmaximal, characteristic, complemented
9C2×#17985882C211yesmaximal, characteristic, complemented
10C2×#17985875C211yesmaximal, characteristic
11C2×#17985874C211yesmaximal, characteristic, complemented
12C2×#17985873C211yesmaximal, characteristic, complemented
13C2×#17985871C211yesmaximal, characteristic, complemented
14C2×#17985861C211yesmaximal, characteristic, complemented
15C2×C4×(C2×D71)⋊C4C211yesmaximal, characteristic, complemented
16C2×#388×C71C211yesmaximal, characteristic, complemented
17C23×C22⋊D71C2211yescharacteristic
18C24×Dic71C2211yescharacteristic
19C23×C4×D71C2211yescharacteristic
20C23×C4×D71C2211yescharacteristic
21C23×C4×D71C2211yescharacteristic
22C2×#14556110C4116yescomplemented
23C2×#14556110C2218yes—
24C2×(C22⋊D71)⋊C4—28no—
25C2×(C22⋊D71)⋊C4C2218yes—
26C22×C4⋊Dic71C2211yescharacteristic
27C22×C4⋊Dic71C2211yescharacteristic
28C22×C4⋊Dic71C2211yescharacteristic
29C22×Dic71⋊C4C2211yescharacteristic
30C22×Dic71⋊C4C2211yescharacteristic
31C22×Dic71⋊C4C2211yescharacteristic
32C22×Dic71⋊C4C2211yescharacteristic
33C22×Dic71⋊C4C2211yescharacteristic
34C2×C4⋊C4×D71—28no—
35C2×C4⋊C4×D71C2218yescomplemented
36C22×C22⋊Dic71C2211yescharacteristic
37C22×C22⋊Dic71C2211yescharacteristic
38C22×(C2×D71)⋊C4C2211yescharacteristic
39C22×(C2×D71)⋊C4C2211yescharacteristic
40C22×(C2×D71)⋊C4C2211yescharacteristic
41C22×C4×Dic71C2211yescharacteristic
42C22×C4×Dic71C2211yescharacteristic
43#17985897C2218yescomplemented
44#17985894C2218yescomplemented
45#17985893C2218yescomplemented
46#17985886C2218yescomplemented
47#17985882C2218yescomplemented
48#17985875C2218yes—
49#17985874C2218yescomplemented
50#17985873C2218yescomplemented
51#17985871C2218yescomplemented
52#17985861C2218yescomplemented
53C4×(C2×D71)⋊C4C2218yescomplemented
54C2×C71⋊#95C2211yescharacteristic
55C2×C71⋊#95C2211yescharacteristic
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×C22⋊D71—24no—
72C22×C22⋊D71—24no—
73C22×C22⋊D71C2×C418yes—
74C22×C22⋊D71C2314yes—
75C23×Dic71—24no—
76C23×Dic71—42no—
77C23×Dic71—42no—
78C23×Dic71C2311yescharacteristic
79C23×Dic71C2311yescharacteristic
80C23×Dic71C2311yescharacteristic
81C23×Dic71C2311yescharacteristic
82C23×Dic71C2311yescharacteristic
83C23×Dic71C2311yescharacteristic
84C23×Dic71C2311yescharacteristic
85C23×Dic71C2314yes—
86C22×C4×D71—24no—
87C22×C4×D71—24no—
88C22×C4×D71—24no—
89C22×C4×D71—42no—
90C22×C4×D71—42no—
91C22×C4×D71—42no—
92C22×C4×D71—42no—
93C22×C4×D71C2×C418yescomplemented
94C22×C4×D71D418yes—
95C22×C4×D71C2314yes—
96C22×C4×D71C2314yes—
97C22×C4×D71C2314yes—
98#14556110C2×C4164yescomplemented
99(C22⋊D71)⋊C4—232no—
100C2×C4⋊Dic71—24no—
101C2×C4⋊Dic71—42no—
102C2×C4⋊Dic71C2×C418yescomplemented
103C2×C4⋊Dic71C2314yes—
104C2×C4⋊Dic71C2314yes—
105C2×C4⋊Dic71C2314yes—
106C2×Dic71⋊C4—24no—
107C2×Dic71⋊C4—24no—
108C2×Dic71⋊C4—24no—
109C2×Dic71⋊C4—42no—
110C2×Dic71⋊C4C2×C418yescomplemented
111C2×Dic71⋊C4C2314yes—
112C2×Dic71⋊C4C2314yes—
113C2×Dic71⋊C4C2314yes—
114C2×Dic71⋊C4C2314yes—
115C2×Dic71⋊C4C2314yes—
116C4⋊C4×D71—232no—
117C2×C22⋊Dic71—42no—
118C2×C22⋊Dic71C2×C418yescomplemented
119C2×C22⋊Dic71C2314yes—
120C2×C22⋊Dic71C2314yes—
121C2×(C2×D71)⋊C4—24no—
122C2×(C2×D71)⋊C4—24no—
123C2×(C2×D71)⋊C4C2×C418yescomplemented
124C2×(C2×D71)⋊C4C2314yes—
125C2×(C2×D71)⋊C4C2314yes—
126C2×(C2×D71)⋊C4C2314yes—
127C2×C4×Dic71—24no—
128C2×C4×Dic71—42no—
129C2×C4×Dic71C2314yes—
130C2×C4×Dic71C2314yes—
131C71⋊#95C2314yes—
132C71⋊#95C2314yes—
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—24no—
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—42no—
155C2×C42×C71C2314yes—
156#95×C71C2314yes—
157#95×C71C2314yes—
158C23×D71—22no—
159C23×D71—22no—
160C23×D71—22no—
161C23×D71—22no—
162C23×D71C22×C414yes—
163C23×D71C2×D414yes—
164C23×D71#4114yes—
165C23×D71C2412yes—
166C2×C22⋊D71—232no—
167C2×C22⋊D71—28no—
168C2×C22⋊D71—28no—
169C2×C22⋊D71C22×C4116yes—
170C22×Dic71—22no—
171C22×Dic71—22no—
172C22×Dic71—22no—
173C22×Dic71—22no—
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—28no—
188C22×Dic71—44no—
189C22×Dic71—44no—
190C22×Dic71—416no—
191C22×Dic71C22×C414yes—
192C22×Dic71C22×C414yes—
193C22×Dic71C22×C414yes—
194C22×Dic71C2×D414yes—
195C22×Dic71C2412yes—
196C22×Dic71C2412yes—
197C22×Dic71C2412yes—
198C22×Dic71C2412yes—
199C22×Dic71C2412yes—
200C22×Dic71C2412yes—
201C22×Dic71C2412yes—
202C2×C4×D71—232no—
203C2×C4×D71—28no—
204C2×C4×D71—28no—
205C2×C4×D71—28no—
206C2×C4×D71—416no—
207C2×C4×D71—44no—
208C2×C4×D71—44no—
209C2×C4×D71—44no—
210C2×C4×D71—44no—
211C2×C4×D71—416no—
212C2×C4×D71C22×C4116yescomplemented
213C2×C4×D71C2×D4116yes—
214C4⋊Dic71—28no—
215C4⋊Dic71—44no—
216C4⋊Dic71C22×C4116yescomplemented
217Dic71⋊C4—28no—
218Dic71⋊C4—28no—
219Dic71⋊C4—28no—
220Dic71⋊C4—44no—
221Dic71⋊C4C22×C4116yescomplemented
222C22⋊Dic71—44no—
223C22⋊Dic71C22×C4116yescomplemented
224(C2×D71)⋊C4—28no—
225(C2×D71)⋊C4—28no—
226(C2×D71)⋊C4C22×C4116yescomplemented
227C4×Dic71—28no—
228C4×Dic71—44no—
229C24×C71—22no—
230C24×C71—22no—
231C24×C71—22no—
232C24×C71—22no—
233C24×C71—22no—
234C24×C71—22no—
235C24×C71C22×C414yes—
236C24×C71C2412yes—
237C24×C71C2411yescharacteristic
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×C71—22no—
253C22×C4×C71C22×C414yes—
254C22×C4×C71C22×C414yes—
255C22×C4×C71C2×D414yes—
256C22×C4×C71C2412yes—
257C22×C4×C71C2412yes—
258C22×C4×C71C2412yes—
259C22×C4×C71C2412yes—
260C22×C4×C71C2412yes—
261C22×C4×C71C2412yes—
262C4⋊C4×C71—28no—
263C22⋊C4×C71—28no—
264C22⋊C4×C71—44no—
265C22⋊C4×C71C22×C4116yescomplemented
266C42×C71—44no—
267C23×C71—28no—
268C23×C71—28no—
269C23×C71—28no—
270C23×C71—22no—
271C23×C71—22no—
272C23×C71—22no—
273C23×C71—22no—
274C23×C71—22no—
275C23×C71—22no—
276C23×C71—44no—
277C23×C71—44no—
278C23×C71—44no—
279C23×C71—44no—
280C23×C71C23×C414yes—
281C23×C71C23×C412yes—
282C23×C71C22×D412yes—
283C23×C71C2×#4112yes—
284C23×C71H(5,𝔽2)12yes—
285C23×C71H(5,𝔽2)12yes—
286C23×C712−1+412yes—
287C23×C712−1+412yes—
288C23×C71C2511yescharacteristic
289C22×D71—28no—
290C22×D71—28no—
291C22×D71—28no—
292C22×D71—28no—
293C22×D71—28no—
294C22×D71—28no—
295C22×D71—22no—
296C22×D71—22no—
297C22×D71—22no—
298C22×D71—22no—
299C22×D71C4×D4116yes—
300C22×D71C23×C414yes—
301C22×D71C22×D414yes—
302C22×D71C2×#4114yes—
303C2×C4×C71—28no—
304C2×C4×C71—28no—
305C2×C4×C71—28no—
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—22no—
321C2×C4×C71—44no—
322C2×C4×C71—44no—
323C2×C4×C71—44no—
324C2×C4×C71C23×C414yes—
325C2×C4×C71C23×C414yes—
326C2×C4×C71C22×D414yes—
327C22⋊D71—232no—
328C2×Dic71—28no—
329C2×Dic71—28no—
330C2×Dic71—28no—
331C2×Dic71—28no—
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—22no—
346C2×Dic71—22no—
347C2×Dic71—22no—
348C2×Dic71—22no—
349C2×Dic71—416no—
350C2×Dic71—44no—
351C2×Dic71—44no—
352C2×Dic71—44no—
353C2×Dic71C23×C414yes—
354C2×Dic71C23×C414yes—
355C2×Dic71C23×C414yes—
356C2×Dic71C22×D414yes—
357C4×D71—232no—
358C4×D71—416no—
359C4×D71—416no—
360C22×C71—24no—
361C22×C71—24no—
362C22×C71—24no—
363C22×C71—416no—
364C22×C71—42no—
365C22×C71—42no—
366C22×C71—42no—
367C22×C71—42no—
368C22×C71C2×C4×D414yes—
369C22×C71#52014yes—
370C22×C71#52014yes—
371C22×C71#53414yes—
372C22×C71#53614yes—
373C22×C71#53914yes—
374C22×C71#53914yes—
375C22×C71C24×C411yescharacteristic
376C22×C71C23×D411yescharacteristic
377C22×C71C22×#4111yescharacteristic
378C22×C71C2×H(5,𝔽2)11yescharacteristic
379C22×C71C2×H(5,𝔽2)11yescharacteristic
380C22×C71C2×2−1+411yescharacteristic
381C22×C71C2×2−1+411yescharacteristic
382C2×D71—232no—
383C2×D71—24no—
384C2×D71—24no—
385C2×D71—24no—
386C2×D71—24no—
387C2×D71—24no—
388C2×D71—24no—
389C2×D71C2×C4×D418yes—
390C4×C71—24no—
391C4×C71—24no—
392C4×C71—24no—
393C4×C71—42no—
394C4×C71—42no—
395C4×C71—42no—
396Dic71—24no—
397Dic71—24no—
398Dic71—24no—
399Dic71—24no—
400Dic71—42no—
401Dic71—42no—
402Dic71—42no—
403C2×#2322—711nomaximal, Sylow
404C2×C71—44no—
405C2×C71#232218yescomplemented
406C2×C71C22×C4×D411yescharacteristic
407C2×C71C2×#52011yescharacteristic
408C2×C71C2×#52011yescharacteristic
409C2×C71C2×#53411yescharacteristic
410C2×C71C2×#53611yescharacteristic
411C2×C71C2×#53911yescharacteristic
412C2×C71C2×#53911yescharacteristic
413D71—28no—
414C22×#123—711no—
415C22×C4×D4—711no—
416C23×C4⋊C4—711no—
417#2322—7116no—
418C2×#389—711no—
419C2×#389—711no—
420C2×#388—711no—
421C2×#388D7111yescharacteristic, complemented
422C2×#387—711no—
423C2×#387—711no—
424C2×#386—711no—
425C2×#385—711no—
426C2×#385—711no—
427C2×#385—711no—
428C2×#381—711no—
429C2×C4×C22⋊C4—711no—
430C71C2×#232211yescharacteristic, complemented, Sylow
431C23×D4—711no—
432C24×C4—711no—
433C24×C4—711no—
434C24×C4—711no—
435C24×C4—711no—
436C2×#123—7116no—
437C2×#123—718no—
438C2×C4×D4—718no—
439C2×C4×D4—1428no—
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⋊C4—711no—
447C22×C4⋊C4—711no—
448C22×C4⋊C4—718no—
449C22×C4⋊C4—1428no—
450C22×C4⋊C4C2×D7111yescharacteristic
451C22×C22⋊C4—711no—
452C22×C22⋊C4—711no—
453C22×C22⋊C4—711no—
454C22×C22⋊C4—711no—
455C22×C22⋊C4—711no—
456C22×C22⋊C4C2×D7111yescharacteristic
457C22×C22⋊C4C2×D7111yescharacteristic
458C22×C22⋊C4C2×D7111yescharacteristic
459C22×C42—711no—
460C22×C42—711no—
461C22×C42C2×D7111yescharacteristic
462#389—718no—
463#389—718no—
464#388—718no—
465#388C2×D7118yescomplemented
466#387—718no—
467#387—718no—
468#386—718no—
469#385—718no—
470#385—718no—
471#385—718no—
472#381—718no—
473C4×C22⋊C4—718no—
474C2×#95—711no—
475C2×#95—711no—
476C2×#95—711no—
477C2×#95—711no—
478C2×#95—711no—
479C2×#95—711no—
480C2×#95—711no—
481C2×#95—711no—
482C2×#95C2×D7111yescharacteristic
483C2×#95C2×D7111yescharacteristic
484C25—711no—
485C25C22×D7111yescharacteristic
486C22×D4—718no—
487C22×D4—714no—
488C22×D4—1424no—
489C22×D4—1424no—
490C23×C4—2842no—
491C23×C4—2842no—
492C23×C4—2842no—
493C23×C4—2842no—
494C23×C4—2842no—
495C23×C4—2842no—
496C23×C4—718no—
497C23×C4—714no—
498C23×C4—714no—
499C23×C4—714no—
500C23×C4—711no—
501C23×C4—711no—
502C23×C4—711no—
503C23×C4—711no—
504C23×C4—718no—
505C23×C4—714no—
506C23×C4—711no—
507C23×C4—711no—
508C23×C4—711no—
509C23×C4—1424no—
510C23×C4—1424no—
511C23×C4—1424no—
512C23×C4—1424no—
513C23×C4C22×D7111yescharacteristic
514C23×C4C22×D7111yescharacteristic
515C23×C4C22×D7111yescharacteristic
516C23×C4C22×D7111yescharacteristic
517C23×C4C22×D7111yescharacteristic
518C23×C4C22×D7111yescharacteristic
519#123—7164no—
520C4×D4—14232no—
521C2×C4⋊C4—24no—
522C2×C4⋊C4—2842no—
523C2×C4⋊C4—2842no—
524C2×C4⋊C4—714no—
525C2×C4⋊C4—714no—
526C2×C4⋊C4—718no—
527C2×C4⋊C4—718no—
528C2×C4⋊C4—714no—
529C2×C4⋊C4—714no—
530C2×C4⋊C4—714no—
531C2×C4⋊C4—714no—
532C2×C4⋊C4—714no—
533C2×C4⋊C4—714no—
534C2×C4⋊C4—14232no—
535C2×C4⋊C4—1424no—
536C2×C4⋊C4—1424no—
537C2×C4⋊C4—1424no—
538C2×C4⋊C4—1424no—
539C2×C4⋊C4C22×D7114yes—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—42no—
542C2×C22⋊C4—2842no—
543C2×C22⋊C4—714no—
544C2×C22⋊C4—718no—
545C2×C22⋊C4—714no—
546C2×C22⋊C4—718no—
547C2×C22⋊C4—714no—
548C2×C22⋊C4—714no—
549C2×C22⋊C4—714no—
550C2×C22⋊C4—1424no—
551C2×C22⋊C4—1424no—
552C2×C22⋊C4C4×D7118yescomplemented
553C2×C22⋊C4C22×D7114yes—
554C2×C22⋊C4C22×D7114yes—
555C2×C22⋊C4C22×D7114yes—
556C2×C42—42no—
557C2×C42—2842no—
558C2×C42—714no—
559C2×C42—714no—
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#95—714no—
569#95—714no—
570#95C22×D7114yes—
571#95C22×D7114yes—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—714no—
579C24—714no—
580C24—714no—
581C24—712no—
582C24—1422no—
583C24—1422no—
584C24—1422no—
585C24—1422no—
586C24C2×C4×D7114yes—
587C24C23×D7112yes—
588C24C23×D7111yescharacteristic
589C2×D4—7116no—
590C2×D4—1428no—
591C2×D4—1428no—
592C2×D4—14232no—
593C22×C4—22no—
594C22×C4—22no—
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—2844no—
609C22×C4—2844no—
610C22×C4—28416no—
611C22×C4—2844no—
612C22×C4—2844no—
613C22×C4—28416no—
614C22×C4—28416no—
615C22×C4—2844no—
616C22×C4—2844no—
617C22×C4—7116no—
618C22×C4—714no—
619C22×C4—714no—
620C22×C4—714no—
621C22×C4—714no—
622C22×C4—712no—
623C22×C4—712no—
624C22×C4—712no—
625C22×C4—712no—
626C22×C4—7116no—
627C22×C4—712no—
628C22×C4—712no—
629C22×C4—712no—
630C22×C4—1428no—
631C22×C4—1428no—
632C22×C4—1428no—
633C22×C4—14232no—
634C22×C4—1428no—
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×C4—1422no—
647C22×C4—1422no—
648C22×C4—1422no—
649C22×C4—1422no—
650C22×C4—1422no—
651C22×C4—1422no—
652C22×C4C2×C4×D7114yes—
653C22×C4C2×C4×D7114yes—
654C22×C4D4×D7114yes—
655C22×C4C23×D7112yes—
656C22×C4C23×D7112yes—
657C22×C4C23×D7112yes—
658C22×C4C23×D7112yes—
659C22×C4C23×D7112yes—
660C22×C4C23×D7112yes—
661C4⋊C4—28no—
662C4⋊C4—2844no—
663C4⋊C4—2844no—
664C4⋊C4—7116no—
665C4⋊C4—7116no—
666C4⋊C4—1428no—
667C4⋊C4—1428no—
668C4⋊C4—1428no—
669C4⋊C4—1428no—
670C22⋊C4—28no—
671C22⋊C4—44no—
672C22⋊C4—2844no—
673C22⋊C4—7116no—
674C22⋊C4—7116no—
675C22⋊C4—1428no—
676C22⋊C4—1428no—
677C22⋊C4C2×C4×D71116yescomplemented
678C42—44no—
679C42—2844no—
680C42—1428no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—28no—
688C23—28no—
689C23—28no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—714no—
695C23—714no—
696C23—714no—
697C23—7116no—
698C23—1428no—
699C23—1422no—
700C23—1422no—
701C23—1422no—
702C23—1422no—
703C23—1428no—
704C23—1428no—
705C23—1428no—
706C23—1428no—
707C23—1428no—
708C23C22×C4×D7114yes—
709C23C22×C4×D7112yes—
710C23C2×D4×D7112yes—
711C23#41×D7112yes—
712C23#1455617312yes—
713C23#1455617412yes—
714C23#1455617512yes—
715C23#1455617512yes—
716C23C24×D7111yescharacteristic
717D4—14232no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—28no—
725C2×C4—28no—
726C2×C4—28no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—28416no—
740C2×C4—28416no—
741C2×C4—2844no—
742C2×C4—2844no—
743C2×C4—2844no—
744C2×C4—28416no—
745C2×C4—714no—
746C2×C4—714no—
747C2×C4—714no—
748C2×C4—714no—
749C2×C4—14232no—
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—1422no—
760C2×C4—1422no—
761C2×C4—1422no—
762C2×C4—1422no—
763C2×C4—1422no—
764C2×C4—1422no—
765C2×C4—1422no—
766C2×C4—1422no—
767C2×C4—1428no—
768C2×C4—1428no—
769C2×C4—1428no—
770C2×C4—1428no—
771C2×C4C22×C4×D7114yes—
772C2×C4C22×C4×D7114yes—
773C2×C4C2×D4×D7114yes—
774C22—24no—
775C22—24no—
776C22—24no—
777C22—416no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—718no—
783C22—14232no—
784C22—1424no—
785C22—1424no—
786C22—1424no—
787C22—1424no—
788C22—1424no—
789C22—1424no—
790C22C4×D4×D7114yes—
791C22#1798647814yes—
792C22#1798647914yes—
793C22#1798655714yes—
794C22#1798656914yes—
795C22#1798659014yes—
796C22#1798659214yes—
797C22C23×C4×D7111yescharacteristic
798C22C22×D4×D7111yescharacteristic
799C22C2×#41×D7111yescharacteristic
800C22C2×#1455617311yescharacteristic
801C22C2×#1455617411yescharacteristic
802C22C2×#1455617511yescharacteristic
803C22C2×#1455617511yescharacteristic
804C4—24no—
805C4—24no—
806C4—24no—
807C4—42no—
808C4—42no—
809C4—42no—
810C4—2842no—
811C4—2842no—
812C4—2842no—
813C4—1424no—
814C4—1424no—
815C4—1424no—
816C4—1424no—
817C2—44no—
818C2—1428no—
819C2#2259101018yesdirect product factor
820C2C2×C4×D4×D7111yescharacteristic
821C2C2×#1798647811yescharacteristic
822C2C2×#1798647911yescharacteristic
823C2C2×#1798655711yescharacteristic
824C2C2×#1798656911yescharacteristic
825C2C2×#1798659011yescharacteristic
826C2C2×#1798659211yescharacteristic
subgroupG/H
centerC24C23×D71
commutatorC22×C71C24×C4
FrattiniC23C24×D71
FittingC2×#388×C71C2
socleC24×C71C24
prime radicalC23×C22⋊D71C22
cosocleC23×C71C25
hypercenterC2×#388D71
hypocenterC71C2×#2322
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
3. C22×C4⋊C4×D71C2semidirect
4. #22591010C2direct (N × H)
5. C2×#17985897C2semidirect
6. C2×#17985894C2semidirect
7. C2×#17985893C2semidirect
8. C2×#17985886C2semidirect
9. C2×#17985882C2semidirect
11. C2×#17985874C2semidirect
12. C2×#17985873C2semidirect
13. C2×#17985871C2semidirect
14. C2×#17985861C2semidirect
15. C2×C4×(C2×D71)⋊C4C2semidirect
16. C2×#388×C71C2semidirect
22. C2×#14556110C4semidirect
35. C2×C4⋊C4×D71C22semidirect
43. #17985897C22semidirect
44. #17985894C22semidirect
45. #17985893C22semidirect
46. #17985886C22semidirect
47. #17985882C22semidirect
49. #17985874C22semidirect
50. #17985873C22semidirect
51. #17985871C22semidirect
52. #17985861C22semidirect
53. C4×(C2×D71)⋊C4C22semidirect
67. #388×C71C22semidirect
93. C22×C4×D71C2×C4semidirect
98. #14556110C2×C4semidirect
102. C2×C4⋊Dic71C2×C4semidirect
110. C2×Dic71⋊C4C2×C4semidirect
118. C2×C22⋊Dic71C2×C4semidirect
123. C2×(C2×D71)⋊C4C2×C4semidirect
150. C2×C22⋊C4×C71C2×C4semidirect
212. C2×C4×D71C22×C4semidirect
216. C4⋊Dic71C22×C4semidirect
221. Dic71⋊C4C22×C4semidirect
223. C22⋊Dic71C22×C4semidirect
226. (C2×D71)⋊C4C22×C4semidirect
265. C22⋊C4×C71C22×C4semidirect
405. C2×C71#2322semidirect
421. C2×#388D71semidirect
430. C71C2×#2322semidirect
465. #388C2×D71semidirect
552. C2×C22⋊C4C4×D71semidirect
677. C22⋊C4C2×C4×D71semidirect
819. C2#22591010direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561102
C22×(C22⋊D71)⋊C42
C22×C4⋊C4×D712
#225910102
C2×#179858972
C2×#179858942
C2×#179858932
C2×#179858862
C2×#179858822
C2×#179858752
C2×#179858742
C2×#179858732
C2×#179858712
C2×#179858612
C2×C4×(C2×D71)⋊C42
C2×#388×C712
C2×#232271