Finite Group Databasebeta

← C2×#22592589 #32165063

Subgroups — C2×#22592589 #32165063

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
2C22×C22⋊C4×D71C211yesmaximal, characteristic
3#22592589C2116yesmaximal, direct product factor
4C2×#17985928C211yesmaximal, characteristic, complemented
5C2×#17985925C211yesmaximal, characteristic, complemented
6C2×#17985924C211yesmaximal, characteristic, complemented
7C2×#17985893C211yesmaximal, characteristic, complemented
8C2×#17985889C211yesmaximal, characteristic, complemented
9C2×#17985887C211yesmaximal, characteristic, complemented
10C2×#17985870C211yesmaximal, characteristic, complemented
11C2×#17985870C211yesmaximal, characteristic, complemented
12C2×#17985856C211yesmaximal, characteristic, complemented
13C2×#17985854C211yesmaximal, characteristic
14C2×#17985854C211yesmaximal, characteristic
15C2×#17985846C211yesmaximal, characteristic, complemented
16C2×#396×C71C211yesmaximal, characteristic, complemented
17C25×D71C2211yescharacteristic
18C23×C4×D71C2211yescharacteristic
19C23×C4×D71C2211yescharacteristic
20C2×#14556123—28no—
21C2×#14556123C2218yescomplemented
22C22×C4⋊Dic71C2211yescharacteristic, complemented
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
41C22×C4×Dic71C2211yescharacteristic, complemented
42#17985928C2218yescomplemented
43#17985925C2218yescomplemented
44#17985924C2218yescomplemented
45#17985893C2218yescomplemented
46#17985889C2218yescomplemented
47#17985887C2218yescomplemented
48#17985870C2218yescomplemented
49#17985870C2218yescomplemented
50#17985856C2218yescomplemented
51#17985854C2218yes—
52#17985854C2218yes—
53#17985846C2218yescomplemented
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×C4⋊C4×C71C2211yescharacteristic, complemented
63C22×C4⋊C4×C71C2211yescharacteristic, complemented
64C22×C22⋊C4×C71C2211yescharacteristic
65C22×C22⋊C4×C71C2211yescharacteristic
66C22×C22⋊C4×C71C2211yescharacteristic
67#396×C71C2218yescomplemented
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
79C23×Dic71C2311yescharacteristic
80C23×Dic71C2311yescharacteristic
81C23×Dic71C2311yescharacteristic
82C23×Dic71C2311yescharacteristic
83C23×Dic71C2311yescharacteristic
84C23×Dic71C2311yescharacteristic
85C22×C4×D71—24no—
86C22×C4×D71—24no—
87C22×C4×D71—24no—
88C22×C4×D71—24no—
89C22×C4×D71—42no—
90C22×C4×D71—42no—
91C22×C4×D71C2314yes—
92C22×C4×D71C2314yes—
93#14556123—232no—
94C2×C4⋊Dic71—24no—
95C2×C4⋊Dic71C2314yescomplemented
96C2×Dic71⋊C4—24no—
97C2×Dic71⋊C4—42no—
98C2×Dic71⋊C4C2314yescomplemented
99C2×Dic71⋊C4C2314yescomplemented
100C2×C22⋊Dic71—24no—
101C2×C22⋊Dic71—24no—
102C2×C22⋊Dic71—24no—
103C2×C22⋊Dic71C2314yes—
104C2×C22⋊Dic71C2314yes—
105C2×C22⋊Dic71C2314yes—
106C2×(C2×D71)⋊C4—24no—
107C2×(C2×D71)⋊C4—24no—
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—42no—
114C2×(C2×D71)⋊C4—42no—
115C2×(C2×D71)⋊C4D418yes—
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—
126C22⋊C4×D71—232no—
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
137C71⋊#95C2314yescomplemented
138C25×C71C2311yescharacteristic
139C23×C4×C71C2311yescharacteristic
140C23×C4×C71C2311yescharacteristic
141C23×C4×C71C2311yescharacteristic
142C23×C4×C71C2311yescharacteristic
143C23×C4×C71C2311yescharacteristic
144C23×C4×C71C2311yescharacteristic
145C2×C4⋊C4×C71—24no—
146C2×C4⋊C4×C71—42no—
147C2×C4⋊C4×C71—42no—
148C2×C4⋊C4×C71C2314yescomplemented
149C2×C4⋊C4×C71C2314yescomplemented
150C2×C4⋊C4×C71C2314yescomplemented
151C2×C22⋊C4×C71—24no—
152C2×C22⋊C4×C71—42no—
153C2×C22⋊C4×C71—42no—
154C2×C22⋊C4×C71C2314yes—
155C2×C22⋊C4×C71C2314yes—
156C2×C22⋊C4×C71C2314yes—
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—
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×Dic71—22no—
201C22×Dic71—22no—
202C22×Dic71—22no—
203C22×Dic71—22no—
204C22×Dic71—22no—
205C22×Dic71C2×D414yes—
206C22×Dic71C2412yes—
207C22×Dic71C2412yes—
208C22×Dic71C2412yes—
209C22×Dic71C2412yes—
210C22×Dic71C2412yes—
211C22×Dic71C2412yes—
212C2×C4×D71—28no—
213C2×C4×D71—28no—
214C2×C4×D71—28no—
215C2×C4×D71—28no—
216C2×C4×D71—44no—
217C2×C4×D71—44no—
218C2×C4×D71—416no—
219C2×C4×D71—416no—
220C4⋊Dic71—28no—
221Dic71⋊C4—28no—
222Dic71⋊C4—44no—
223C22⋊Dic71—28no—
224C22⋊Dic71—28no—
225C22⋊Dic71—28no—
226(C2×D71)⋊C4—28no—
227(C2×D71)⋊C4—28no—
228(C2×D71)⋊C4—28no—
229(C2×D71)⋊C4—28no—
230(C2×D71)⋊C4—28no—
231(C2×D71)⋊C4—28no—
232(C2×D71)⋊C4—28no—
233(C2×D71)⋊C4—44no—
234(C2×D71)⋊C4—44no—
235(C2×D71)⋊C4C2×D4116yes—
236C4×Dic71—28no—
237C4×Dic71—44no—
238C24×C71—22no—
239C24×C71—22no—
240C24×C71—22no—
241C24×C71—22no—
242C24×C71—22no—
243C24×C71—22no—
244C24×C71#4114yes—
245C24×C71C2412yes—
246C24×C71C2411yescharacteristic
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×C71—22no—
260C22×C4×C71—22no—
261C22×C4×C71—22no—
262C22×C4×C71—22no—
263C22×C4×C71—22no—
264C22×C4×C71C2×D414yes—
265C22×C4×C71C2412yes—
266C22×C4×C71C2412yes—
267C22×C4×C71C2412yes—
268C22×C4×C71C2412yes—
269C22×C4×C71C2412yes—
270C22×C4×C71C2412yes—
271C4⋊C4×C71—28no—
272C4⋊C4×C71—44no—
273C4⋊C4×C71—44no—
274C22⋊C4×C71—28no—
275C22⋊C4×C71—44no—
276C22⋊C4×C71—44no—
277C23×C71—28no—
278C23×C71—28no—
279C23×C71—28no—
280C23×C71—22no—
281C23×C71—22no—
282C23×C71—22no—
283C23×C71—22no—
284C23×C71—22no—
285C23×C71—22no—
286C23×C71—44no—
287C23×C71—44no—
288C23×C71—44no—
289C23×C71—44no—
290C23×C71C22×D412yes—
291C23×C71C2×#4112yes—
292C23×C71C2×#4112yes—
293C23×C71C2×#4112yes—
294C23×C71C2×#4114yes—
295C23×C71C2×#4112yes—
296C23×C71H(5,𝔽2)12yes—
297C23×C71H(5,𝔽2)12yes—
298C23×C71C2511yescharacteristic
299C22×D71—28no—
300C22×D71—28no—
301C22×D71—28no—
302C22×D71—28no—
303C22×D71—28no—
304C22×D71—28no—
305C22×D71—22no—
306C22×D71—22no—
307C22×D71—22no—
308C22×D71—22no—
309C22×D71—232no—
310C22×D71—28no—
311C22×D71—28no—
312C22×D71—28no—
313C22×D71—22no—
314C22×D71—22no—
315C22×D71—22no—
316C22×D71—22no—
317C22×D71—22no—
318C22×D71—22no—
319C22×D71—416no—
320C22×D71—416no—
321C22×D71—416no—
322C22×D71—416no—
323C22×D71—416no—
324C22×D71—4128no—
325C22×D71—44no—
326C22×D71—44no—
327C22×D71—44no—
328C22×D71—44no—
329C22×D71—416no—
330C22×D71#126116yescomplemented
331C22×D71C22×D414yes—
332C22×D71C2×#4114yes—
333C22×D71C2×#4114yes—
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—44no—
354C2×C4×C71—44no—
355C2×C4×C71—44no—
356C2×C4×C71—44no—
357C2×C4×C71—44no—
358C2×C4×C71C22×D414yes—
359C2×Dic71—28no—
360C2×Dic71—22no—
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—44no—
378C2×Dic71—44no—
379C2×Dic71—44no—
380C2×Dic71—44no—
381C2×Dic71—44no—
382C2×Dic71C22×D414yes—
383C4×D71—416no—
384C4×D71—416no—
385C22×C71—24no—
386C22×C71—24no—
387C22×C71—24no—
388C22×C71—42no—
389C22×C71—42no—
390C22×C71—42no—
391C22×C71—42no—
392C22×C71—416no—
393C22×C71#52514yes—
394C22×C71C2×#12614yes—
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—232no—
414C2×D71—24no—
415C2×D71—24no—
416C2×D71—24no—
417C2×D71—464no—
418C2×D71—42no—
419C2×D71—42no—
420C2×D71—42no—
421C2×D71—42no—
422C2×D71—416no—
423C2×D71C2×#12618yescomplemented
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—44no—
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—28no—
447D71—44no—
448C22×#126—711no—
449C23×C22⋊C4—711no—
450#2480—7116no—
451C2×#397—711no—
452C2×#397—711no—
453C2×#397—711no—
454C2×#396D7111yescharacteristic, complemented
455C2×#388—711no—
456C2×#388—711no—
457C2×#388—711no—
458C2×#385—711no—
459C2×#385—711no—
460C2×#380—711no—
461C2×#379—711no—
462C2×#379—711no—
463C2×C4×C22⋊C4—711no—
464C71C2×#248011yescharacteristic, complemented, Sylow
465C26—711no—
466C24×C4—711no—
467C24×C4—711no—
468C2×#126—718no—
469C2×#126—1428no—
470C22×C4⋊C4—711no—
471C22×C4⋊C4—711no—
472C22×C4⋊C4—711no—
473C22×C4⋊C4C2×D7111yescharacteristic, complemented
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—1428no—
491C22×C22⋊C4C2×D7111yescharacteristic
492C22×C22⋊C4C2×D7111yescharacteristic
493C22×C22⋊C4C2×D7111yescharacteristic
494C22×C42—711no—
495C22×C42—711no—
496#397—718no—
497#397—718no—
498#397—718no—
499#396C2×D7118yescomplemented
500#388—718no—
501#388—718no—
502#388—718no—
503#385—718no—
504#385—718no—
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×#95—711no—
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—2842no—
529C23×C4—2842no—
530C23×C4—714no—
531C23×C4—714no—
532C23×C4—711no—
533C23×C4—711no—
534C23×C4—711no—
535C23×C4—711no—
536C23×C4—711no—
537C23×C4—711no—
538C23×C4—1424no—
539C23×C4—1424no—
540C23×C4—1424no—
541C23×C4—1424no—
542C23×C4C22×D7111yescharacteristic
543C23×C4C22×D7111yescharacteristic
544C23×C4C22×D7111yescharacteristic
545C23×C4C22×D7111yescharacteristic
546C23×C4C22×D7111yescharacteristic
547C23×C4C22×D7111yescharacteristic
548#126—14232no—
549C2×C4⋊C4—24no—
550C2×C4⋊C4—42no—
551C2×C4⋊C4—42no—
552C2×C4⋊C4—2842no—
553C2×C4⋊C4—714no—
554C2×C4⋊C4—714no—
555C2×C4⋊C4—714no—
556C2×C4⋊C4—1424no—
557C2×C4⋊C4—1424no—
558C2×C4⋊C4C22×D7114yescomplemented
559C2×C4⋊C4C22×D7114yescomplemented
560C2×C4⋊C4C22×D7114yescomplemented
561C2×C22⋊C4—24no—
562C2×C22⋊C4—42no—
563C2×C22⋊C4—42no—
564C2×C22⋊C4—2842no—
565C2×C22⋊C4—2842no—
566C2×C22⋊C4—714no—
567C2×C22⋊C4—714no—
568C2×C22⋊C4—718no—
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—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#95—714no—
605#95C22×D7114yescomplemented
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—28416no—
613C24—28416no—
614C24—2844no—
615C24—2844no—
616C24—28416no—
617C24—28416no—
618C24—28416no—
619C24—28416no—
620C24—714no—
621C24—714no—
622C24—714no—
623C24—712no—
624C24—714no—
625C24—712no—
626C24—1428no—
627C24—1428no—
628C24—1428no—
629C24—1428no—
630C24—14232no—
631C24—1422no—
632C24—1422no—
633C24—1422no—
634C24—1428no—
635C24—1422no—
636C24—1422no—
637C24—1422no—
638C24—1422no—
639C24—1422no—
640C24—1422no—
641C24—1422no—
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—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—28416no—
663C22×C4—2844no—
664C22×C4—2844no—
665C22×C4—28416no—
666C22×C4—714no—
667C22×C4—712no—
668C22×C4—712no—
669C22×C4—712no—
670C22×C4—712no—
671C22×C4—712no—
672C22×C4—712no—
673C22×C4—1428no—
674C22×C4—1428no—
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—1422no—
687C22×C4—1422no—
688C22×C4—1422no—
689C22×C4—1422no—
690C22×C4—1422no—
691C22×C4—1428no—
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—44no—
704C4⋊C4—2844no—
705C4⋊C4—1428no—
706C4⋊C4—1428no—
707C22⋊C4—28no—
708C22⋊C4—44no—
709C22⋊C4—44no—
710C22⋊C4—2844no—
711C22⋊C4—2844no—
712C22⋊C4—7116no—
713C22⋊C4—1428no—
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—22no—
730C23—22no—
731C23—28no—
732C23—28no—
733C23—28no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—28416no—
739C23—28416no—
740C23—28416no—
741C23—284128no—
742C23—28416no—
743C23—28416no—
744C23—28416no—
745C23—2844no—
746C23—2844no—
747C23—2844no—
748C23—2844no—
749C23—714no—
750C23—714no—
751C23—714no—
752C23—7116no—
753C23—714no—
754C23—14232no—
755C23—1422no—
756C23—1422no—
757C23—1422no—
758C23—1422no—
759C23—1422no—
760C23—1422no—
761C23—1428no—
762C23—1428no—
763C23—1428no—
764C23—1422no—
765C23—1422no—
766C23—1422no—
767C23—1422no—
768C23—1428no—
769C23—1428no—
770C23—1428no—
771C23—1428no—
772C23—1428no—
773C23—1428no—
774C23C2×D4×D7112yes—
775C23#41×D7112yes—
776C23#41×D7112yes—
777C23#41×D7112yes—
778C23C2×#1176586614yes—
779C23C2×#1176586612yes—
780C23#1455617312yes—
781C23#1455617312yes—
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—44no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4—44no—
805C2×C4—44no—
806C2×C4—28416no—
807C2×C4—28416no—
808C2×C4—2844no—
809C2×C4—2844no—
810C2×C4—2844no—
811C2×C4—2844no—
812C2×C4—2844no—
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—24no—
836C22—42no—
837C22—42no—
838C22—416no—
839C22—42no—
840C22—42no—
841C22—28464no—
842C22—28416no—
843C22—2842no—
844C22—2842no—
845C22—2842no—
846C22—2842no—
847C22—718no—
848C22—1424no—
849C22—1424no—
850C22—1424no—
851C22—1424no—
852C22—1424no—
853C22—14232no—
854C22—1424no—
855C22—1424no—
856C22—1424no—
857C22—1424no—
858C22#1798651214yes—
859C22#126×D7114yes—
860C22#1798658114yes—
861C22#1798663814yes—
862C22#1798664614yes—
863C22#1798667614yes—
864C22#1798667614yes—
865C22C22×D4×D7111yescharacteristic
866C22C2×#41×D7111yescharacteristic
867C22C2×#41×D7111yescharacteristic
868C22C2×#41×D7111yescharacteristic
869C22C22×#1176586611yescharacteristic
870C22C2×#1455617311yescharacteristic
871C22C2×#1455617311yescharacteristic
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—44no—
885C2—2844no—
886C2—1428no—
887C2#2259258918yesdirect product factor
888C2C2×#1798651211yescharacteristic
889C2C2×#126×D7111yescharacteristic
890C2C2×#1798658111yescharacteristic
891C2C2×#1798663811yescharacteristic
892C2C2×#1798664611yescharacteristic
893C2C2×#1798667611yescharacteristic
894C2C2×#1798667611yescharacteristic
subgroupG/H
centerC24C23×D71
commutator, cosocleC23×C71C25
FrattiniC23C24×D71
FittingC2×#396×C71C2
socleC24×C71C24
prime radicalC25×D71C22
hypercenterC2×#396D71
hypocenterC71C2×#2480
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C22×#14556123C2semidirect
3. #22592589C2direct (N × H)
4. C2×#17985928C2semidirect
5. C2×#17985925C2semidirect
6. C2×#17985924C2semidirect
7. C2×#17985893C2semidirect
8. C2×#17985889C2semidirect
9. C2×#17985887C2semidirect
10. C2×#17985870C2semidirect
11. C2×#17985870C2semidirect
12. C2×#17985856C2semidirect
15. C2×#17985846C2semidirect
16. C2×#396×C71C2semidirect
21. C2×#14556123C22semidirect
22. C22×C4⋊Dic71C22semidirect
23. C22×Dic71⋊C4C22semidirect
24. C22×Dic71⋊C4C22semidirect
40. C22×C4×Dic71C22semidirect
41. C22×C4×Dic71C22semidirect
42. #17985928C22semidirect
43. #17985925C22semidirect
44. #17985924C22semidirect
45. #17985893C22semidirect
46. #17985889C22semidirect
47. #17985887C22semidirect
48. #17985870C22semidirect
49. #17985870C22semidirect
50. #17985856C22semidirect
53. #17985846C22semidirect
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
62. C22×C4⋊C4×C71C22semidirect
63. C22×C4⋊C4×C71C22semidirect
67. #396×C71C22semidirect
68. C2×#95×C71C22semidirect
95. C2×C4⋊Dic71C23semidirect
98. C2×Dic71⋊C4C23semidirect
99. 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
137. C71⋊#95C23semidirect
148. C2×C4⋊C4×C71C23semidirect
149. C2×C4⋊C4×C71C23semidirect
150. C2×C4⋊C4×C71C23semidirect
157. #95×C71C23semidirect
330. C22×D71#126semidirect
423. C2×D71C2×#126semidirect
438. C2×C71#2480semidirect
454. C2×#396D71semidirect
464. C71C2×#2480semidirect
473. C22×C4⋊C4C2×D71semidirect
474. C22×C4⋊C4C2×D71semidirect
475. C22×C4⋊C4C2×D71semidirect
499. #396C2×D71semidirect
516. C2×#95C2×D71semidirect
558. C2×C4⋊C4C22×D71semidirect
559. C2×C4⋊C4C22×D71semidirect
560. C2×C4⋊C4C22×D71semidirect
605. #95C22×D71semidirect
887. C2#22592589direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561232
C22×C22⋊C4×D712
#225925892
C2×#179859282
C2×#179859252
C2×#179859242
C2×#179858932
C2×#179858892
C2×#179858872
C2×#179858702
C2×#179858562
C2×#179858542
C2×#179858462
C2×#396×C712
C2×#248071