Finite Group Databasebeta

← C2×#22592588 #32165066

Subgroups — C2×#22592588 #32165066

Order 18176.

4102 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556123C211yesmaximal, characteristic, complemented
2C23×(C2×D71)⋊C4C211yesmaximal, characteristic
3#22592588C2116yesmaximal, direct product factor
4C2×#17985928C211yesmaximal, characteristic, complemented
5C2×#17985926C211yesmaximal, characteristic, complemented
6C2×#17985925C211yesmaximal, characteristic, complemented
7C2×#17985921C211yesmaximal, characteristic, complemented
8C2×#17985891C211yesmaximal, characteristic, complemented
9C2×#17985889C211yesmaximal, characteristic, complemented
10C2×#17985888C211yesmaximal, characteristic, complemented
11C2×#17985874C211yesmaximal, characteristic, complemented
12C2×#17985857C211yesmaximal, characteristic, complemented
13C2×#17985854C211yesmaximal, characteristic
14C2×#17985854C211yesmaximal, characteristic
15C2×C4×C22⋊Dic71C211yesmaximal, characteristic, complemented
16C2×#385×C71C211yesmaximal, characteristic, complemented
17C25×D71C2211yescharacteristic
18C24×Dic71C2211yescharacteristic
19C2×#14556123—28no—
20C2×#14556123C2218yescomplemented
21C22×C4⋊Dic71C2211yescharacteristic, complemented
22C22×C4⋊Dic71C2211yescharacteristic, complemented
23C22×Dic71⋊C4C2211yescharacteristic, complemented
24C22×Dic71⋊C4C2211yescharacteristic, complemented
25C22×C22⋊Dic71C2211yescharacteristic
26C22×C22⋊Dic71C2211yescharacteristic
27C22×(C2×D71)⋊C4—28no—
28C22×(C2×D71)⋊C4C2211yescharacteristic
29C22×(C2×D71)⋊C4C2211yescharacteristic
30C22×(C2×D71)⋊C4C2218yes—
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×(C2×D71)⋊C4C2211yescharacteristic
41C22×C4×Dic71C2211yescharacteristic, complemented
42C22×C4×Dic71C2211yescharacteristic, complemented
43#17985928C2218yescomplemented
44#17985926C2218yescomplemented
45#17985925C2218yescomplemented
46#17985921C2218yescomplemented
47#17985891C2218yescomplemented
48#17985889C2218yescomplemented
49#17985888C2218yescomplemented
50#17985874C2218yescomplemented
51#17985857C2218yescomplemented
52#17985854C2218yes—
53#17985854C2218yes—
54C4×C22⋊Dic71C2218yescomplemented
55C2×C71⋊#95C2211yescharacteristic, complemented
56C2×C71⋊#95C2211yescharacteristic, complemented
57C2×C71⋊#95C2211yescharacteristic, complemented
58C2×C71⋊#95C2211yescharacteristic, complemented
59C2×C71⋊#95C2211yescharacteristic, complemented
60C2×C71⋊#95C2211yescharacteristic, complemented
61C24×C4×C71C2211yescharacteristic
62C22×C4⋊C4×C71C2211yescharacteristic, complemented
63C22×C4⋊C4×C71C2211yescharacteristic, complemented
64C22×C22⋊C4×C71C2211yescharacteristic
65C22×C22⋊C4×C71C2211yescharacteristic
66#385×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×D71C2311yescharacteristic
78C24×D71C2314yes—
79C23×Dic71—24no—
80C23×Dic71—24no—
81C23×Dic71—42no—
82C23×Dic71C2311yescharacteristic
83C23×Dic71C2311yescharacteristic
84C23×Dic71C2311yescharacteristic
85C23×Dic71C2311yescharacteristic
86C23×Dic71C2311yescharacteristic
87C23×Dic71C2314yes—
88C23×Dic71C2311yescharacteristic
89#14556123—232no—
90C2×C4⋊Dic71—24no—
91C2×C4⋊Dic71—42no—
92C2×C4⋊Dic71C2314yescomplemented
93C2×C4⋊Dic71C2314yescomplemented
94C2×Dic71⋊C4—24no—
95C2×Dic71⋊C4—42no—
96C2×Dic71⋊C4C2314yescomplemented
97C2×Dic71⋊C4C2314yescomplemented
98C2×C22⋊Dic71—24no—
99C2×C22⋊Dic71—24no—
100C2×C22⋊Dic71C2314yes—
101C2×C22⋊Dic71C2314yes—
102C2×(C2×D71)⋊C4—24no—
103C2×(C2×D71)⋊C4—24no—
104C2×(C2×D71)⋊C4—24no—
105C2×(C2×D71)⋊C4—24no—
106C2×(C2×D71)⋊C4—24no—
107C2×(C2×D71)⋊C4—24no—
108C2×(C2×D71)⋊C4—232no—
109C2×(C2×D71)⋊C4—24no—
110C2×(C2×D71)⋊C4—42no—
111C2×(C2×D71)⋊C4—42no—
112C2×(C2×D71)⋊C4—42no—
113C2×(C2×D71)⋊C4—42no—
114C2×(C2×D71)⋊C4D418yes—
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×(C2×D71)⋊C4C2314yes—
124C2×(C2×D71)⋊C4C2314yes—
125C2×(C2×D71)⋊C4C2314yes—
126C2×(C2×D71)⋊C4C2314yes—
127C2×C4×Dic71—24no—
128C2×C4×Dic71—42no—
129C2×C4×Dic71C2314yescomplemented
130C2×C4×Dic71C2314yescomplemented
131C71⋊#95C2314yescomplemented
132C71⋊#95C2314yescomplemented
133C71⋊#95C2314yescomplemented
134C71⋊#95C2314yescomplemented
135C71⋊#95C2314yescomplemented
136C71⋊#95C2314yescomplemented
137C25×C71C2311yescharacteristic
138C23×C4×C71—24no—
139C23×C4×C71—24no—
140C23×C4×C71—42no—
141C23×C4×C71C2311yescharacteristic
142C23×C4×C71C2311yescharacteristic
143C23×C4×C71C2311yescharacteristic
144C23×C4×C71C2311yescharacteristic
145C23×C4×C71C2311yescharacteristic
146C23×C4×C71C2314yes—
147C23×C4×C71C2311yescharacteristic
148C2×C4⋊C4×C71—24no—
149C2×C4⋊C4×C71—42no—
150C2×C4⋊C4×C71C2314yescomplemented
151C2×C4⋊C4×C71C2314yescomplemented
152C2×C22⋊C4×C71—24no—
153C2×C22⋊C4×C71—24no—
154C2×C22⋊C4×C71C2314yes—
155C2×C22⋊C4×C71C2314yes—
156#95×C71C2314yescomplemented
157#95×C71C2314yescomplemented
158C23×D71—232no—
159C23×D71—22no—
160C23×D71—22no—
161C23×D71—22no—
162C23×D71—22no—
163C23×D71—28no—
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—28no—
173C23×D71—28no—
174C23×D71—28no—
175C23×D71—28no—
176C23×D71—44no—
177C23×D71—44no—
178C23×D71—416no—
179C23×D71—416no—
180C23×D71—416no—
181C23×D71—416no—
182C23×D71—416no—
183C23×D71—416no—
184C23×D71C2×D414yes—
185C23×D71#4114yes—
186C23×D71C2412yes—
187C23×D71C2412yes—
188C22×Dic71—22no—
189C22×Dic71—22no—
190C22×Dic71—22no—
191C22×Dic71—22no—
192C22×Dic71—22no—
193C22×Dic71—28no—
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—28no—
207C22×Dic71—44no—
208C22×Dic71—416no—
209C22×Dic71C2×D414yes—
210C22×Dic71C2412yes—
211C22×Dic71C2412yes—
212C22×Dic71C2412yes—
213C22×Dic71C2412yes—
214C22×Dic71C2412yes—
215C22×Dic71C2412yes—
216C4⋊Dic71—28no—
217C4⋊Dic71—44no—
218Dic71⋊C4—28no—
219Dic71⋊C4—44no—
220C22⋊Dic71—28no—
221C22⋊Dic71—28no—
222(C2×D71)⋊C4—28no—
223(C2×D71)⋊C4—28no—
224(C2×D71)⋊C4—28no—
225(C2×D71)⋊C4—28no—
226(C2×D71)⋊C4—28no—
227(C2×D71)⋊C4—28no—
228(C2×D71)⋊C4—28no—
229(C2×D71)⋊C4—44no—
230(C2×D71)⋊C4—44no—
231(C2×D71)⋊C4—44no—
232(C2×D71)⋊C4—44no—
233(C2×D71)⋊C4C2×D4116yes—
234C4×Dic71—28no—
235C4×Dic71—44no—
236C24×C71—22no—
237C24×C71—22no—
238C24×C71—22no—
239C24×C71—22no—
240C24×C71#4114yes—
241C24×C71#4114yes—
242C24×C71#4114yes—
243C24×C71C2412yes—
244C24×C71C2411yescharacteristic
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—28no—
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—28no—
264C22×C4×C71—44no—
265C22×C4×C71—416no—
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—
274C4⋊C4×C71—44no—
275C22⋊C4×C71—28no—
276C22⋊C4×C71—28no—
277C23×C71—28no—
278C23×C71—28no—
279C23×C71—28no—
280C23×C71—28no—
281C23×C71—28no—
282C23×C71—28no—
283C23×C71—22no—
284C23×C71—22no—
285C23×C71—22no—
286C23×C71—22no—
287C23×C71#126116yescomplemented
288C23×C71C22×D412yes—
289C23×C71C2×#4112yes—
290C23×C71C2×#4114yes—
291C23×C71C2×#4112yes—
292C23×C71C2×#4114yes—
293C23×C71C2×#4112yes—
294C23×C71C2×#4114yes—
295C23×C71C2×#4112yes—
296C23×C71H(5,𝔽2)12yes—
297C23×C71H(5,𝔽2)12yes—
298C23×C71C2511yescharacteristic
299C22×D71—232no—
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—22no—
311C22×D71—22no—
312C22×D71—22no—
313C22×D71—22no—
314C22×D71—22no—
315C22×D71—22no—
316C22×D71—22no—
317C22×D71—22no—
318C22×D71—416no—
319C22×D71—416no—
320C22×D71—416no—
321C22×D71—416no—
322C22×D71—416no—
323C22×D71—4128no—
324C22×D71—44no—
325C22×D71—44no—
326C22×D71—416no—
327C22×D71—44no—
328C22×D71—44no—
329C22×D71—44no—
330C22×D71—44no—
331C22×D71—44no—
332C22×D71—44no—
333C22×D71C22×D414yes—
334C22×D71C2×#4114yes—
335C2×C4×C71—28no—
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—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—416no—
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—416no—
379C2×Dic71—44no—
380C2×Dic71—44no—
381C2×Dic71—44no—
382C2×Dic71—44no—
383C2×Dic71—44no—
384C2×Dic71C22×D414yes—
385C22×C71—24no—
386C22×C71—24no—
387C22×C71—24no—
388C22×C71—24no—
389C22×C71—24no—
390C22×C71—24no—
391C22×C71—232no—
392C22×C71#52514yes—
393C22×C71C2×#12614yes—
394C22×C71C2×#12618yescomplemented
395C22×C71#53814yes—
396C22×C71#54614yes—
397C22×C71#54614yes—
398C22×C71#55114yes—
399C22×C71#55114yes—
400C22×C71C23×D411yescharacteristic
401C22×C71C22×#4111yescharacteristic
402C22×C71C22×#4111yescharacteristic
403C22×C71C22×#4111yescharacteristic
404C22×C71C22×#4111yescharacteristic
405C22×C71C2×H(5,𝔽2)11yescharacteristic
406C22×C71C2×H(5,𝔽2)11yescharacteristic
407C2×D71—24no—
408C2×D71—24no—
409C2×D71—24no—
410C2×D71—24no—
411C2×D71—24no—
412C2×D71—24no—
413C2×D71—464no—
414C2×D71—42no—
415C2×D71—42no—
416C2×D71—42no—
417C2×D71—42no—
418C2×D71—42no—
419C2×D71—42no—
420C2×D71—42no—
421C2×D71—42no—
422C2×D71—416no—
423C2×D71—416no—
424C4×C71—24no—
425C4×C71—42no—
426C4×C71—42no—
427C4×C71—42no—
428C4×C71—42no—
429C4×C71—42no—
430Dic71—24no—
431Dic71—42no—
432Dic71—42no—
433Dic71—42no—
434Dic71—42no—
435Dic71—42no—
436C2×#2480—711nomaximal, Sylow
437C2×C71—28no—
438C2×C71#248018yescomplemented
439C2×C71C2×#52511yescharacteristic
440C2×C71C22×#12611yescharacteristic
441C2×C71C2×#53811yescharacteristic
442C2×C71C2×#54611yescharacteristic
443C2×C71C2×#54611yescharacteristic
444C2×C71C2×#55111yescharacteristic
445C2×C71C2×#55111yescharacteristic
446D71—44no—
447D71—44no—
448C22×#126—711no—
449C23×C22⋊C4—711no—
450#2480—7116no—
451C2×#397—711no—
452C2×#397—711no—
453C2×#397—711no—
454C2×#396—711no—
455C2×#388—711no—
456C2×#388—711no—
457C2×#388—711no—
458C2×#385—711no—
459C2×#385D7111yescharacteristic, complemented
460C2×#380—711no—
461C2×#379—711no—
462C2×#379—711no—
463C2×C4×C22⋊C4—711no—
464C71C2×#248011yescharacteristic, complemented, Sylow
465C26—711no—
466C24×C4—711no—
467C24×C4C2×D7111yescharacteristic
468C2×#126—718no—
469C2×#126—1428no—
470C22×C4⋊C4—711no—
471C22×C4⋊C4—711no—
472C22×C4⋊C4—711no—
473C22×C4⋊C4—711no—
474C22×C4⋊C4C2×D7111yescharacteristic, complemented
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—711no—
491C22×C22⋊C4—1428no—
492C22×C22⋊C4C2×D7111yescharacteristic
493C22×C22⋊C4C2×D7111yescharacteristic
494C22×C42—711no—
495C22×C42—711no—
496#397—718no—
497#397—718no—
498#397—718no—
499#396—718no—
500#388—718no—
501#388—718no—
502#388—718no—
503#385—718no—
504#385C2×D7118yescomplemented
505#380—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×#95C2×D7111yescharacteristic, complemented
516C2×#95C2×D7111yescharacteristic, complemented
517C25—2842no—
518C25—2842no—
519C25—714no—
520C25—711no—
521C25—711no—
522C25—1424no—
523C25—1424no—
524C25—1424no—
525C25—1424no—
526C25—1424no—
527C25C22×D7111yescharacteristic
528C23×C4—24no—
529C23×C4—24no—
530C23×C4—42no—
531C23×C4—2842no—
532C23×C4—714no—
533C23×C4—711no—
534C23×C4—711no—
535C23×C4—711no—
536C23×C4—711no—
537C23×C4—711no—
538C23×C4—711no—
539C23×C4—1424no—
540C23×C4—1424no—
541C23×C4C22×D7111yescharacteristic
542C23×C4C22×D7111yescharacteristic
543C23×C4C22×D7111yescharacteristic
544C23×C4C22×D7111yescharacteristic
545C23×C4C22×D7111yescharacteristic
546C23×C4C22×D7114yes—
547C23×C4C22×D7111yescharacteristic
548#126—14232no—
549C2×C4⋊C4—24no—
550C2×C4⋊C4—42no—
551C2×C4⋊C4—2842no—
552C2×C4⋊C4—2842no—
553C2×C4⋊C4—714no—
554C2×C4⋊C4—714no—
555C2×C4⋊C4—714no—
556C2×C4⋊C4—714no—
557C2×C4⋊C4—1424no—
558C2×C4⋊C4—1424no—
559C2×C4⋊C4C22×D7114yescomplemented
560C2×C4⋊C4C22×D7114yescomplemented
561C2×C22⋊C4—24no—
562C2×C22⋊C4—24no—
563C2×C22⋊C4—2842no—
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—718no—
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—714no—
581C2×C22⋊C4—714no—
582C2×C22⋊C4—14232no—
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⋊C4—1424no—
592C2×C22⋊C4C22×D7114yes—
593C2×C22⋊C4C22×D7114yes—
594C2×C42—2842no—
595C2×C42—714no—
596C2×C42—714no—
597C2×C42—1424no—
598#95—714no—
599#95—714no—
600#95—714no—
601#95—714no—
602#95—714no—
603#95—714no—
604#95C22×D7114yescomplemented
605#95C22×D7114yescomplemented
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—28416no—
611C24—28416no—
612C24—28416no—
613C24—28416no—
614C24—28416no—
615C24—2844no—
616C24—2844no—
617C24—28416no—
618C24—714no—
619C24—714no—
620C24—712no—
621C24—712no—
622C24—1428no—
623C24—1428no—
624C24—14232no—
625C24—1428no—
626C24—1428no—
627C24—1422no—
628C24—1422no—
629C24—1422no—
630C24—1422no—
631C24—1428no—
632C24—1422no—
633C24—1422no—
634C24—1422no—
635C24—1422no—
636C24—1422no—
637C24—1422no—
638C24—1422no—
639C24—1422no—
640C24#1176586414yes—
641C24#1176586514yes—
642C24#1176586614yes—
643C24C23×D7112yes—
644C24C23×D7111yescharacteristic
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—28no—
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—28no—
664C22×C4—44no—
665C22×C4—416no—
666C22×C4—28416no—
667C22×C4—2844no—
668C22×C4—714no—
669C22×C4—712no—
670C22×C4—712no—
671C22×C4—712no—
672C22×C4—712no—
673C22×C4—712no—
674C22×C4—712no—
675C22×C4—1428no—
676C22×C4—1422no—
677C22×C4—1422no—
678C22×C4—1422no—
679C22×C4—1422no—
680C22×C4—1422no—
681C22×C4—1422no—
682C22×C4—1422no—
683C22×C4—1422no—
684C22×C4—1422no—
685C22×C4—1422no—
686C22×C4—1428no—
687C22×C4—1422no—
688C22×C4—1422no—
689C22×C4—1422no—
690C22×C4—1422no—
691C22×C4—1422no—
692C22×C4—1422no—
693C22×C4—1422no—
694C22×C4D4×D7114yes—
695C22×C4C23×D7112yes—
696C22×C4C23×D7112yes—
697C22×C4C23×D7112yes—
698C22×C4C23×D7112yes—
699C22×C4C23×D7112yes—
700C22×C4C23×D7112yes—
701C4⋊C4—28no—
702C4⋊C4—44no—
703C4⋊C4—2844no—
704C4⋊C4—2844no—
705C4⋊C4—1428no—
706C4⋊C4—1428no—
707C22⋊C4—28no—
708C22⋊C4—28no—
709C22⋊C4—2844no—
710C22⋊C4—2844no—
711C22⋊C4—2844no—
712C22⋊C4—2844no—
713C22⋊C4—7116no—
714C22⋊C4—1428no—
715C22⋊C4—1428no—
716C22⋊C4—1428no—
717C22⋊C4—1428no—
718C22⋊C4—1428no—
719C22⋊C4—1428no—
720C22⋊C4—1428no—
721C22⋊C4—1428no—
722C22⋊C4—1428no—
723C42—2844no—
724C42—1428no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—28no—
730C23—28no—
731C23—28no—
732C23—28no—
733C23—28no—
734C23—28no—
735C23—284128no—
736C23—28416no—
737C23—28416no—
738C23—28416no—
739C23—28416no—
740C23—28416no—
741C23—2844no—
742C23—2844no—
743C23—2844no—
744C23—2844no—
745C23—2844no—
746C23—2844no—
747C23—2844no—
748C23—2844no—
749C23—28416no—
750C23—714no—
751C23—714no—
752C23—14232no—
753C23—1422no—
754C23—1422no—
755C23—1422no—
756C23—1422no—
757C23—1422no—
758C23—1422no—
759C23—1422no—
760C23—1422no—
761C23—1422no—
762C23—1422no—
763C23—1422no—
764C23—1422no—
765C23—1428no—
766C23—1428no—
767C23—1428no—
768C23—1428no—
769C23—1428no—
770C23—1428no—
771C23#14556123116yescomplemented
772C23C2×D4×D7112yes—
773C23#41×D7112yes—
774C23C2×#1176586414yes—
775C23C2×#1176586412yes—
776C23C2×#1176586514yes—
777C23C2×#1176586512yes—
778C23C2×#1176586614yes—
779C23C2×#1176586612yes—
780C23#1455617312yes—
781C23#1455617412yes—
782C23C24×D7111yescharacteristic
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—28no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
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—416no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4—44no—
805C2×C4—44no—
806C2×C4—44no—
807C2×C4—2844no—
808C2×C4—2844no—
809C2×C4—2844no—
810C2×C4—2844no—
811C2×C4—2844no—
812C2×C4—28416no—
813C2×C4—714no—
814C2×C4—1422no—
815C2×C4—1422no—
816C2×C4—1422no—
817C2×C4—1422no—
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—1428no—
832C2×C4C2×D4×D7114yes—
833C22—24no—
834C22—24no—
835C22—232no—
836C22—24no—
837C22—24no—
838C22—24no—
839C22—24no—
840C22—28464no—
841C22—2842no—
842C22—2842no—
843C22—28416no—
844C22—28416no—
845C22—2842no—
846C22—2842no—
847C22—2842no—
848C22—2842no—
849C22—2842no—
850C22—2842no—
851C22—1424no—
852C22—1424no—
853C22—1424no—
854C22—1424no—
855C22—1424no—
856C22—1424no—
857C22#1798650814yes—
858C22C2×#1455612314yes—
859C22C2×#1455612318yescomplemented
860C22#1798658214yes—
861C22#1798663614yes—
862C22#1798664014yes—
863C22#1798667214yes—
864C22#1798667614yes—
865C22C22×D4×D7111yescharacteristic
866C22C2×#41×D7111yescharacteristic
867C22C22×#1176586411yescharacteristic
868C22C22×#1176586511yescharacteristic
869C22C22×#1176586611yescharacteristic
870C22C2×#1455617311yescharacteristic
871C22C2×#1455617411yescharacteristic
872C4—24no—
873C4—42no—
874C4—42no—
875C4—42no—
876C4—42no—
877C4—42no—
878C4—2842no—
879C4—2842no—
880C4—2842no—
881C4—2842no—
882C4—2842no—
883C4—1424no—
884C2—28no—
885C2—2844no—
886C2—2844no—
887C2#2259258818yesdirect product factor
888C2C2×#1798650811yescharacteristic
889C2C22×#1455612311yescharacteristic
890C2C2×#1798658211yescharacteristic
891C2C2×#1798663611yescharacteristic
892C2C2×#1798664011yescharacteristic
893C2C2×#1798667211yescharacteristic
894C2C2×#1798667611yescharacteristic
subgroupG/H
centerC24C23×D71
commutator, cosocleC23×C71C25
FrattiniC23C24×D71
FittingC2×#385×C71C2
socleC24×C71C24
prime radicalC25×D71C22
hypercenterC2×#385D71
hypocenterC71C2×#2480
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C22×#14556123C2semidirect
3. #22592588C2direct (N × H)
4. C2×#17985928C2semidirect
5. C2×#17985926C2semidirect
6. C2×#17985925C2semidirect
7. C2×#17985921C2semidirect
8. C2×#17985891C2semidirect
9. C2×#17985889C2semidirect
10. C2×#17985888C2semidirect
11. C2×#17985874C2semidirect
12. C2×#17985857C2semidirect
15. C2×C4×C22⋊Dic71C2semidirect
16. C2×#385×C71C2semidirect
20. C2×#14556123C22semidirect
21. C22×C4⋊Dic71C22semidirect
22. C22×C4⋊Dic71C22semidirect
23. C22×Dic71⋊C4C22semidirect
24. C22×Dic71⋊C4C22semidirect
41. C22×C4×Dic71C22semidirect
42. C22×C4×Dic71C22semidirect
43. #17985928C22semidirect
44. #17985926C22semidirect
45. #17985925C22semidirect
46. #17985921C22semidirect
47. #17985891C22semidirect
48. #17985889C22semidirect
49. #17985888C22semidirect
50. #17985874C22semidirect
51. #17985857C22semidirect
54. C4×C22⋊Dic71C22semidirect
55. C2×C71⋊#95C22semidirect
56. C2×C71⋊#95C22semidirect
57. C2×C71⋊#95C22semidirect
58. C2×C71⋊#95C22semidirect
59. C2×C71⋊#95C22semidirect
60. C2×C71⋊#95C22semidirect
62. C22×C4⋊C4×C71C22semidirect
63. C22×C4⋊C4×C71C22semidirect
66. #385×C71C22semidirect
67. C2×#95×C71C22semidirect
68. C2×#95×C71C22semidirect
92. C2×C4⋊Dic71C23semidirect
93. C2×C4⋊Dic71C23semidirect
96. C2×Dic71⋊C4C23semidirect
97. C2×Dic71⋊C4C23semidirect
129. C2×C4×Dic71C23semidirect
130. C2×C4×Dic71C23semidirect
131. C71⋊#95C23semidirect
132. C71⋊#95C23semidirect
133. C71⋊#95C23semidirect
134. C71⋊#95C23semidirect
135. C71⋊#95C23semidirect
136. C71⋊#95C23semidirect
150. C2×C4⋊C4×C71C23semidirect
151. C2×C4⋊C4×C71C23semidirect
156. #95×C71C23semidirect
157. #95×C71C23semidirect
287. C23×C71#126semidirect
394. C22×C71C2×#126semidirect
438. C2×C71#2480semidirect
459. C2×#385D71semidirect
464. C71C2×#2480semidirect
474. C22×C4⋊C4C2×D71semidirect
475. C22×C4⋊C4C2×D71semidirect
504. #385C2×D71semidirect
515. C2×#95C2×D71semidirect
516. C2×#95C2×D71semidirect
559. C2×C4⋊C4C22×D71semidirect
560. C2×C4⋊C4C22×D71semidirect
604. #95C22×D71semidirect
605. #95C22×D71semidirect
771. C23#14556123semidirect
859. C22C2×#14556123semidirect
887. C2#22592588direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561232
C23×(C2×D71)⋊C42
#225925882
C2×#179859282
C2×#179859262
C2×#179859252
C2×#179859212
C2×#179858912
C2×#179858892
C2×#179858882
C2×#179858742
C2×#179858572
C2×#179858542
C2×C4×C22⋊Dic712
C2×#385×C712
C2×#248071