Finite Group Databasebeta

← C2×#22593496 #32167825

Subgroups — C2×#22593496 #32167825

Order 18176.

4166 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×#14556106C211yesmaximal, characteristic, complemented
2C22×C22⋊C4×D71C211yesmaximal, characteristic
3#22593496C2116yesmaximal, direct product factor
4C2×#17985928C211yesmaximal, characteristic, complemented
5C2×#17985927C211yesmaximal, characteristic, complemented
6C2×#17985912C211yesmaximal, characteristic, complemented
7C2×#17985911C211yesmaximal, characteristic, complemented
8C2×#17985893C211yesmaximal, characteristic, complemented
9C2×#17985890C211yesmaximal, characteristic, complemented
10C2×#17985889C211yesmaximal, characteristic, complemented
11C2×#17985861C211yesmaximal, characteristic, complemented
12C2×#17985861C211yesmaximal, characteristic, complemented
13C2×#17985854C211yesmaximal, characteristic
14C2×#17985854C211yesmaximal, characteristic
15C2×C4×(C2×D71)⋊C4C211yesmaximal, characteristic, complemented
16C2×#388×C71C211yesmaximal, characteristic, complemented
17C25×D71C2211yescharacteristic
18C23×Dic142C2211yescharacteristic, complemented
19C23×C4×D71C2211yescharacteristic
20C23×C4×D71C2211yescharacteristic
21C2×#14556106—28no—
22C2×#14556106C2218yescomplemented
23C22×Dic71⋊C4C2211yescharacteristic, complemented
24C22×Dic71⋊C4C2211yescharacteristic, complemented
25C22×C22⋊Dic71C2211yescharacteristic
26C22×C22⋊Dic71C2211yescharacteristic
27C22×C22⋊Dic71C2211yescharacteristic
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
38C2×C22⋊C4×D71—28no—
39C2×C22⋊C4×D71C2218yes—
40C22×C4×Dic71C2211yescharacteristic, complemented
41#17985928C2218yescomplemented
42#17985927C2218yescomplemented
43#17985912C2218yescomplemented
44#17985911C2218yescomplemented
45#17985893C2218yescomplemented
46#17985890C2218yescomplemented
47#17985889C2218yescomplemented
48#17985861C2218yescomplemented
49#17985861C2218yescomplemented
50#17985854C2218yes—
51#17985854C2218yes—
52C4×(C2×D71)⋊C4C2218yescomplemented
53C2×C71⋊#95C2211yescharacteristic, complemented
54C2×C71⋊#95C2211yescharacteristic, complemented
55C2×C71⋊#95C2211yescharacteristic, complemented
56C2×C71⋊#95C2211yescharacteristic, complemented
57C2×C71⋊#95C2211yescharacteristic, complemented
58C2×C71⋊#95C2211yescharacteristic, complemented
59C2×C71⋊#95C2211yescharacteristic, complemented
60C2×C71⋊#95C2211yescharacteristic, complemented
61C22×C4⋊C4×C71C2211yescharacteristic, complemented
62C22×C22⋊C4×C71C2211yescharacteristic
63C22×C22⋊C4×C71C2211yescharacteristic
64C22×C22⋊C4×C71C2211yescharacteristic
65C22×C42×C71C2211yescharacteristic, complemented
66#388×C71C2218yescomplemented
67C2×#95×C71C2211yescharacteristic, complemented
68C2×#95×C71C2211yescharacteristic, complemented
69C24×D71—24no—
70C24×D71—24no—
71C24×D71—24no—
72C24×D71—24no—
73C24×D71—24no—
74C24×D71—42no—
75C24×D71—42no—
76C24×D71C2311yescharacteristic
77C24×D71C2314yes—
78C24×D71C2311yescharacteristic
79C22×Dic142—24no—
80C22×Dic142—42no—
81C22×Dic142—42no—
82C22×Dic142C2314yescomplemented
83C23×Dic71C2311yescharacteristic
84C23×Dic71C2311yescharacteristic
85C23×Dic71C2311yescharacteristic
86C23×Dic71C2311yescharacteristic
87C23×Dic71C2311yescharacteristic
88C23×Dic71C2311yescharacteristic
89C22×C4×D71—24no—
90C22×C4×D71—24no—
91C22×C4×D71—24no—
92C22×C4×D71—42no—
93C22×C4×D71—42no—
94C22×C4×D71D418yes—
95C22×C4×D71C2314yes—
96C22×C4×D71C2314yes—
97#14556106—232no—
98C2×Dic71⋊C4—24no—
99C2×Dic71⋊C4—24no—
100C2×Dic71⋊C4C2314yescomplemented
101C2×Dic71⋊C4C2314yescomplemented
102C2×C22⋊Dic71—24no—
103C2×C22⋊Dic71—24no—
104C2×C22⋊Dic71—42no—
105C2×C22⋊Dic71C2314yes—
106C2×C22⋊Dic71C2314yes—
107C2×C22⋊Dic71C2314yes—
108C2×(C2×D71)⋊C4—24no—
109C2×(C2×D71)⋊C4—24no—
110C2×(C2×D71)⋊C4—24no—
111C2×(C2×D71)⋊C4—24no—
112C2×(C2×D71)⋊C4—24no—
113C2×(C2×D71)⋊C4—24no—
114C2×(C2×D71)⋊C4—24no—
115C2×(C2×D71)⋊C4—24no—
116C2×(C2×D71)⋊C4—42no—
117C2×(C2×D71)⋊C4—42no—
118C2×(C2×D71)⋊C4C2314yes—
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—
128C22⋊C4×D71—232no—
129C2×C4×Dic71—42no—
130C2×C4×Dic71C2314yescomplemented
131C71⋊#95C2314yescomplemented
132C71⋊#95C2314yescomplemented
133C71⋊#95C2314yescomplemented
134C71⋊#95C2314yescomplemented
135C71⋊#95C2314yescomplemented
136C71⋊#95C2314yescomplemented
137C71⋊#95C2314yescomplemented
138C71⋊#95C2314yescomplemented
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×C71C2314yescomplemented
148C2×C22⋊C4×C71—24no—
149C2×C22⋊C4×C71—24no—
150C2×C22⋊C4×C71—42no—
151C2×C22⋊C4×C71C2314yes—
152C2×C22⋊C4×C71C2314yes—
153C2×C22⋊C4×C71C2314yes—
154C2×C42×C71—42no—
155C2×C42×C71C2314yescomplemented
156#95×C71C2314yescomplemented
157#95×C71C2314yescomplemented
158C23×D71—22no—
159C23×D71—22no—
160C23×D71—22no—
161C23×D71—22no—
162C23×D71—232no—
163C23×D71—22no—
164C23×D71—22no—
165C23×D71—22no—
166C23×D71—28no—
167C23×D71—22no—
168C23×D71—22no—
169C23×D71—22no—
170C23×D71—28no—
171C23×D71—28no—
172C23×D71—28no—
173C23×D71—28no—
174C23×D71—44no—
175C23×D71—44no—
176C23×D71—416no—
177C23×D71—416no—
178C23×D71—416no—
179C23×D71—416no—
180C23×D71—416no—
181C23×D71—416no—
182C23×D71C2×D414yes—
183C23×D71#4114yes—
184C23×D71#4114yes—
185C23×D71#4114yes—
186C23×D71C2412yes—
187C23×D71C2412yes—
188C2×Dic142—28no—
189C2×Dic142—44no—
190C2×Dic142—44no—
191C2×Dic142—416no—
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×Dic71—22no—
208C22×Dic71—22no—
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—416no—
220C2×C4×D71—44no—
221C2×C4×D71—44no—
222C2×C4×D71—416no—
223C2×C4×D71C2×D4116yes—
224Dic71⋊C4—28no—
225Dic71⋊C4—28no—
226C22⋊Dic71—28no—
227C22⋊Dic71—28no—
228C22⋊Dic71—44no—
229(C2×D71)⋊C4—28no—
230(C2×D71)⋊C4—28no—
231(C2×D71)⋊C4—28no—
232(C2×D71)⋊C4—28no—
233(C2×D71)⋊C4—28no—
234(C2×D71)⋊C4—28no—
235(C2×D71)⋊C4—28no—
236(C2×D71)⋊C4—28no—
237(C2×D71)⋊C4—44no—
238(C2×D71)⋊C4—44no—
239C4×Dic71—44no—
240C24×C71—22no—
241C24×C71—22no—
242C24×C71—22no—
243C24×C71—22no—
244C24×C71—22no—
245C24×C71—22no—
246C24×C71#4114yes—
247C24×C71C2412yes—
248C24×C71C2411yescharacteristic
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×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×C71C2×D414yes—
267C22×C4×C71C2412yes—
268C22×C4×C71C2412yes—
269C22×C4×C71C2412yes—
270C22×C4×C71C2412yes—
271C22×C4×C71C2412yes—
272C22×C4×C71C2412yes—
273C4⋊C4×C71—28no—
274C22⋊C4×C71—28no—
275C22⋊C4×C71—28no—
276C22⋊C4×C71—44no—
277C42×C71—44no—
278C23×C71—28no—
279C23×C71—28no—
280C23×C71—28no—
281C23×C71—22no—
282C23×C71—22no—
283C23×C71—22no—
284C23×C71—22no—
285C23×C71—22no—
286C23×C71—22no—
287C23×C71—44no—
288C23×C71—44no—
289C23×C71—44no—
290C23×C71—44no—
291C23×C71C22×D412yes—
292C23×C71C2×#4112yes—
293C23×C71C2×#4112yes—
294C23×C71C2×#4112yes—
295C23×C71C2×#4114yes—
296C23×C71C2×#4112yes—
297C23×C71H(5,𝔽2)12yes—
298C23×C71H(5,𝔽2)12yes—
299C23×C71C2511yescharacteristic
300C22×D71—28no—
301C22×D71—28no—
302C22×D71—28no—
303C22×D71—28no—
304C22×D71—28no—
305C22×D71—28no—
306C22×D71—22no—
307C22×D71—22no—
308C22×D71—22no—
309C22×D71—22no—
310C22×D71—232no—
311C22×D71—28no—
312C22×D71—28no—
313C22×D71—28no—
314C22×D71—22no—
315C22×D71—22no—
316C22×D71—22no—
317C22×D71—22no—
318C22×D71—22no—
319C22×D71—22no—
320C22×D71—416no—
321C22×D71—416no—
322C22×D71—416no—
323C22×D71—416no—
324C22×D71—4128no—
325C22×D71—416no—
326C22×D71—44no—
327C22×D71—44no—
328C22×D71—44no—
329C22×D71—44no—
330C22×D71—416no—
331C22×D71#124116yes—
332C22×D71C22×D414yes—
333C22×D71C2×#4114yes—
334C22×D71C2×#4114yes—
335C22×D71C2×#4114yes—
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—22no—
353C2×C4×C71—22no—
354C2×C4×C71—44no—
355C2×C4×C71—44no—
356C2×C4×C71—44no—
357C2×C4×C71—44no—
358C2×C4×C71—44no—
359C2×C4×C71C22×D414yes—
360C2×Dic71—28no—
361C2×Dic71—22no—
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—22no—
376C2×Dic71—22no—
377C2×Dic71—22no—
378C2×Dic71—44no—
379C2×Dic71—44no—
380C2×Dic71—44no—
381C2×Dic71—44no—
382C2×Dic71—44no—
383C2×Dic71C22×D414yes—
384C4×D71—416no—
385C4×D71—416no—
386Dic142—416no—
387C22×C71—24no—
388C22×C71—24no—
389C22×C71—24no—
390C22×C71—416no—
391C22×C71—42no—
392C22×C71—42no—
393C22×C71—42no—
394C22×C71—42no—
395C22×C71#52514yes—
396C22×C71C2×#12414yes—
397C22×C71#53414yes—
398C22×C71#55114yes—
399C22×C71#55114yes—
400C22×C71#55114yes—
401C22×C71#55114yes—
402C22×C71C23×D411yescharacteristic
403C22×C71C22×#4111yescharacteristic
404C22×C71C22×#4111yescharacteristic
405C22×C71C22×#4111yescharacteristic
406C22×C71C22×#4111yescharacteristic
407C22×C71C2×H(5,𝔽2)11yescharacteristic
408C22×C71C2×H(5,𝔽2)11yescharacteristic
409C2×D71—232no—
410C2×D71—24no—
411C2×D71—24no—
412C2×D71—24no—
413C2×D71—24no—
414C2×D71—24no—
415C2×D71—24no—
416C2×D71—24no—
417C2×D71—24no—
418C2×D71—24no—
419C2×D71—464no—
420C2×D71—416no—
421C2×D71—42no—
422C2×D71—42no—
423C2×D71—42no—
424C2×D71—42no—
425C2×D71C2×#12418yes—
426C4×C71—24no—
427C4×C71—42no—
428C4×C71—42no—
429C4×C71—42no—
430C4×C71—42no—
431C4×C71—42no—
432Dic71—24no—
433Dic71—42no—
434Dic71—42no—
435Dic71—42no—
436Dic71—42no—
437Dic71—42no—
438C2×#2561—711nomaximal, Sylow
439C2×C71—44no—
440C2×C71#256118yescomplemented
441C2×C71C2×#52511yescharacteristic
442C2×C71C22×#12411yescharacteristic
443C2×C71C2×#53411yescharacteristic
444C2×C71C2×#55111yescharacteristic
445C2×C71C2×#55111yescharacteristic
446C2×C71C2×#55111yescharacteristic
447C2×C71C2×#55111yescharacteristic
448D71—28no—
449D71—44no—
450C22×C22⋊Q8—711no—
451C23×C22⋊C4—711no—
452#2561—7116no—
453C2×#397—711no—
454C2×#397—711no—
455C2×#393—711no—
456C2×#393—711no—
457C2×#388—711no—
458C2×#388—711no—
459C2×#388—711no—
460C2×#388D7111yescharacteristic, complemented
461C2×#381—711no—
462C2×#381—711no—
463C2×#379—711no—
464C2×#379—711no—
465C2×C4×C22⋊C4—711no—
466C71C2×#256111yescharacteristic, complemented, Sylow
467C26—711no—
468C23×Q8—711no—
469C24×C4—711no—
470C24×C4—711no—
471C2×C22⋊Q8—718no—
472C2×C22⋊Q8—1428no—
473C22×C4⋊C4—711no—
474C22×C4⋊C4—711no—
475C22×C4⋊C4C2×D7111yescharacteristic, complemented
476C22×C22⋊C4—711no—
477C22×C22⋊C4—711no—
478C22×C22⋊C4—711no—
479C22×C22⋊C4—711no—
480C22×C22⋊C4—711no—
481C22×C22⋊C4—711no—
482C22×C22⋊C4—711no—
483C22×C22⋊C4—711no—
484C22×C22⋊C4—711no—
485C22×C22⋊C4—711no—
486C22×C22⋊C4—711no—
487C22×C22⋊C4—711no—
488C22×C22⋊C4—711no—
489C22×C22⋊C4—718no—
490C22×C22⋊C4—1428no—
491C22×C22⋊C4C2×D7111yescharacteristic
492C22×C22⋊C4C2×D7111yescharacteristic
493C22×C22⋊C4C2×D7111yescharacteristic
494C22×C42—711no—
495C22×C42C2×D7111yescharacteristic, complemented
496#397—718no—
497#397—718no—
498#393—718no—
499#393—718no—
500#388—718no—
501#388—718no—
502#388—718no—
503#388C2×D7118yescomplemented
504#381—718no—
505#381—718no—
506#379—718no—
507#379—718no—
508C4×C22⋊C4—718no—
509C2×#95—711no—
510C2×#95—711no—
511C2×#95—711no—
512C2×#95—711no—
513C2×#95—711no—
514C2×#95—711no—
515C2×#95—711no—
516C2×#95—711no—
517C2×#95C2×D7111yescharacteristic, complemented
518C2×#95C2×D7111yescharacteristic, complemented
519C25—2842no—
520C25—2842no—
521C25—714no—
522C25—711no—
523C25—711no—
524C25—1424no—
525C25—1424no—
526C25—1424no—
527C25—1424no—
528C25—1424no—
529C25C22×D7111yescharacteristic
530C22×Q8—2842no—
531C22×Q8—2842no—
532C22×Q8—714no—
533C22×Q8—1424no—
534C23×C4—2842no—
535C23×C4—2842no—
536C23×C4—718no—
537C23×C4—714no—
538C23×C4—711no—
539C23×C4—711no—
540C23×C4—711no—
541C23×C4—711no—
542C23×C4—711no—
543C23×C4—711no—
544C23×C4—714no—
545C23×C4—1424no—
546C23×C4—1424no—
547C23×C4—1424no—
548C23×C4C22×D7111yescharacteristic
549C23×C4C22×D7111yescharacteristic
550C23×C4C22×D7111yescharacteristic
551C23×C4C22×D7111yescharacteristic
552C23×C4C22×D7111yescharacteristic
553C23×C4C22×D7111yescharacteristic
554C22⋊Q8—14232no—
555C2×C4⋊C4—24no—
556C2×C4⋊C4—714no—
557C2×C4⋊C4—714no—
558C2×C4⋊C4—1424no—
559C2×C4⋊C4—1424no—
560C2×C4⋊C4C22×D7114yescomplemented
561C2×C22⋊C4—24no—
562C2×C22⋊C4—24no—
563C2×C22⋊C4—42no—
564C2×C22⋊C4—2842no—
565C2×C22⋊C4—2842no—
566C2×C22⋊C4—2842no—
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—714no—
577C2×C22⋊C4—714no—
578C2×C22⋊C4—714no—
579C2×C22⋊C4—714no—
580C2×C22⋊C4—14232no—
581C2×C22⋊C4—1424no—
582C2×C22⋊C4—1424no—
583C2×C22⋊C4—1424no—
584C2×C22⋊C4—1424no—
585C2×C22⋊C4—1424no—
586C2×C22⋊C4—1424no—
587C2×C22⋊C4—1424no—
588C2×C22⋊C4—1424no—
589C2×C22⋊C4—1424no—
590C2×C22⋊C4—1424no—
591C2×C22⋊C4C22×D7114yes—
592C2×C22⋊C4C22×D7114yes—
593C2×C22⋊C4C22×D7114yes—
594C2×C42—42no—
595C2×C42—2842no—
596C2×C42—714no—
597C2×C42C22×D7114yescomplemented
598#95—714no—
599#95—714no—
600#95—714no—
601#95—714no—
602#95—714no—
603#95—714no—
604#95—714no—
605#95—714no—
606#95C22×D7114yescomplemented
607#95C22×D7114yescomplemented
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—28416no—
615C24—28416no—
616C24—2844no—
617C24—2844no—
618C24—28416no—
619C24—28416no—
620C24—28416no—
621C24—28416no—
622C24—714no—
623C24—714no—
624C24—714no—
625C24—712no—
626C24—714no—
627C24—712no—
628C24—1428no—
629C24—1428no—
630C24—1428no—
631C24—1428no—
632C24—14232no—
633C24—1422no—
634C24—1422no—
635C24—1422no—
636C24—1428no—
637C24—1422no—
638C24—1422no—
639C24—1422no—
640C24—1422no—
641C24—1422no—
642C24—1422no—
643C24—1422no—
644C24#1176586514yes—
645C24C23×D7112yes—
646C24C23×D7111yescharacteristic
647C2×Q8—2844no—
648C2×Q8—2844no—
649C2×Q8—28416no—
650C2×Q8—1428no—
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—22no—
667C22×C4—22no—
668C22×C4—2844no—
669C22×C4—2844no—
670C22×C4—28416no—
671C22×C4—28416no—
672C22×C4—7116no—
673C22×C4—714no—
674C22×C4—712no—
675C22×C4—712no—
676C22×C4—712no—
677C22×C4—712no—
678C22×C4—712no—
679C22×C4—712no—
680C22×C4—1428no—
681C22×C4—1428no—
682C22×C4—1428no—
683C22×C4—1422no—
684C22×C4—1422no—
685C22×C4—1422no—
686C22×C4—1422no—
687C22×C4—1422no—
688C22×C4—1422no—
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×C4D4×D7114yes—
701C22×C4C23×D7112yes—
702C22×C4C23×D7112yes—
703C22×C4C23×D7112yes—
704C22×C4C23×D7112yes—
705C22×C4C23×D7112yes—
706C22×C4C23×D7112yes—
707C4⋊C4—28no—
708C4⋊C4—1428no—
709C4⋊C4—1428no—
710C22⋊C4—28no—
711C22⋊C4—28no—
712C22⋊C4—44no—
713C22⋊C4—2844no—
714C22⋊C4—2844no—
715C22⋊C4—2844no—
716C22⋊C4—1428no—
717C22⋊C4—1428no—
718C22⋊C4—1428no—
719C22⋊C4—1428no—
720C22⋊C4—1428no—
721C22⋊C4—1428no—
722C22⋊C4—1428no—
723C22⋊C4—1428no—
724C22⋊C4—1428no—
725C22⋊C4—1428no—
726C42—44no—
727C42—2844no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—28no—
735C23—28no—
736C23—28no—
737C23—44no—
738C23—44no—
739C23—44no—
740C23—44no—
741C23—28416no—
742C23—28416no—
743C23—28416no—
744C23—28416no—
745C23—284128no—
746C23—28416no—
747C23—28416no—
748C23—2844no—
749C23—2844no—
750C23—2844no—
751C23—2844no—
752C23—714no—
753C23—714no—
754C23—714no—
755C23—7116no—
756C23—714no—
757C23—14232no—
758C23—1422no—
759C23—1422no—
760C23—1422no—
761C23—1422no—
762C23—1422no—
763C23—1422no—
764C23—1428no—
765C23—1428no—
766C23—1428no—
767C23—1422no—
768C23—1422no—
769C23—1422no—
770C23—1422no—
771C23—1428no—
772C23—1428no—
773C23—1428no—
774C23—1428no—
775C23—1428no—
776C23—1428no—
777C23C2×D4×D7112yes—
778C23#41×D7112yes—
779C23#41×D7112yes—
780C23#41×D7112yes—
781C23C2×#1176586514yes—
782C23C2×#1176586512yes—
783C23#1455617312yes—
784C23#1455617412yes—
785C23C24×D7111yescharacteristic
786Q8—28416no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—28no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
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—22no—
804C2×C4—22no—
805C2×C4—44no—
806C2×C4—44no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—44no—
810C2×C4—28416no—
811C2×C4—28416no—
812C2×C4—2844no—
813C2×C4—2844no—
814C2×C4—2844no—
815C2×C4—2844no—
816C2×C4—2844no—
817C2×C4—714no—
818C2×C4—1422no—
819C2×C4—1422no—
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—1422no—
830C2×C4—1422no—
831C2×C4—1422no—
832C2×C4—1422no—
833C2×C4—1422no—
834C2×C4—1422no—
835C2×C4—1428no—
836C2×C4C2×D4×D7114yes—
837C22—24no—
838C22—24no—
839C22—24no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—42no—
844C22—416no—
845C22—28464no—
846C22—2842no—
847C22—2842no—
848C22—2842no—
849C22—2842no—
850C22—28416no—
851C22—718no—
852C22—1424no—
853C22—1424no—
854C22—1424no—
855C22—1424no—
856C22—1424no—
857C22—1424no—
858C22—1424no—
859C22—1424no—
860C22—1424no—
861C22—14232no—
862C22#1798650814yes—
863C22#124×D7114yes—
864C22#1798655714yes—
865C22#1798667314yes—
866C22#1798667414yes—
867C22#1798667714yes—
868C22#1798667814yes—
869C22C22×D4×D7111yescharacteristic
870C22C2×#41×D7111yescharacteristic
871C22C2×#41×D7111yescharacteristic
872C22C2×#41×D7111yescharacteristic
873C22C22×#1176586511yescharacteristic
874C22C2×#1455617311yescharacteristic
875C22C2×#1455617411yescharacteristic
876C4—24no—
877C4—42no—
878C4—42no—
879C4—42no—
880C4—42no—
881C4—42no—
882C4—2842no—
883C4—2842no—
884C4—2842no—
885C4—2842no—
886C4—2842no—
887C4—1424no—
888C2—44no—
889C2—2844no—
890C2—1428no—
891C2#2259349618yesdirect product factor
892C2C2×#1798650811yescharacteristic
893C2C2×#124×D7111yescharacteristic
894C2C2×#1798655711yescharacteristic
895C2C2×#1798667311yescharacteristic
896C2C2×#1798667411yescharacteristic
897C2C2×#1798667711yescharacteristic
898C2C2×#1798667811yescharacteristic
subgroupG/H
centerC24C23×D71
commutator, cosocleC23×C71C25
FrattiniC23C24×D71
FittingC2×#388×C71C2
socleC24×C71C24
prime radicalC25×D71C22
hypercenterC2×#388D71
hypocenterC71C2×#2561
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×#14556106C2semidirect
3. #22593496C2direct (N × H)
4. C2×#17985928C2semidirect
5. C2×#17985927C2semidirect
6. C2×#17985912C2semidirect
7. C2×#17985911C2semidirect
8. C2×#17985893C2semidirect
9. C2×#17985890C2semidirect
10. C2×#17985889C2semidirect
11. C2×#17985861C2semidirect
12. C2×#17985861C2semidirect
15. C2×C4×(C2×D71)⋊C4C2semidirect
16. C2×#388×C71C2semidirect
18. C23×Dic142C22semidirect
22. C2×#14556106C22semidirect
23. C22×Dic71⋊C4C22semidirect
24. C22×Dic71⋊C4C22semidirect
40. C22×C4×Dic71C22semidirect
41. #17985928C22semidirect
42. #17985927C22semidirect
43. #17985912C22semidirect
44. #17985911C22semidirect
45. #17985893C22semidirect
46. #17985890C22semidirect
47. #17985889C22semidirect
48. #17985861C22semidirect
49. #17985861C22semidirect
52. C4×(C2×D71)⋊C4C22semidirect
53. C2×C71⋊#95C22semidirect
54. C2×C71⋊#95C22semidirect
55. C2×C71⋊#95C22semidirect
56. C2×C71⋊#95C22semidirect
57. C2×C71⋊#95C22semidirect
58. C2×C71⋊#95C22semidirect
59. C2×C71⋊#95C22semidirect
60. C2×C71⋊#95C22semidirect
61. C22×C4⋊C4×C71C22semidirect
65. C22×C42×C71C22semidirect
66. #388×C71C22semidirect
67. C2×#95×C71C22semidirect
68. C2×#95×C71C22semidirect
82. C22×Dic142C23semidirect
100. C2×Dic71⋊C4C23semidirect
101. C2×Dic71⋊C4C23semidirect
130. C2×C4×Dic71C23semidirect
131. C71⋊#95C23semidirect
132. C71⋊#95C23semidirect
133. C71⋊#95C23semidirect
134. C71⋊#95C23semidirect
135. C71⋊#95C23semidirect
136. C71⋊#95C23semidirect
137. C71⋊#95C23semidirect
138. C71⋊#95C23semidirect
147. C2×C4⋊C4×C71C23semidirect
155. C2×C42×C71C23semidirect
156. #95×C71C23semidirect
157. #95×C71C23semidirect
440. C2×C71#2561semidirect
460. C2×#388D71semidirect
466. C71C2×#2561semidirect
475. C22×C4⋊C4C2×D71semidirect
495. C22×C42C2×D71semidirect
503. #388C2×D71semidirect
517. C2×#95C2×D71semidirect
518. C2×#95C2×D71semidirect
560. C2×C4⋊C4C22×D71semidirect
597. C2×C42C22×D71semidirect
606. #95C22×D71semidirect
607. #95C22×D71semidirect
891. C2#22593496direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561062
C22×C22⋊C4×D712
#225934962
C2×#179859282
C2×#179859272
C2×#179859122
C2×#179859112
C2×#179858932
C2×#179858902
C2×#179858892
C2×#179858612
C2×#179858542
C2×C4×(C2×D71)⋊C42
C2×#388×C712
C2×#256171