Finite Group Databasebeta

← C2×#22591851 #32165321

Subgroups — C2×#22591851 #32165321

Order 18176.

3830 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556110C211yesmaximal, characteristic, complemented
2C22×#14556100C211yesmaximal, characteristic
3C22×C4×C22⋊D71C211yesmaximal, characteristic, complemented
4#22591851C2116yesmaximal, direct product factor
5C2×#17985925C211yesmaximal, characteristic, complemented
6C2×#17985924C211yesmaximal, characteristic, complemented
7C2×#17985914C211yesmaximal, characteristic, complemented
8C2×#17985913C211yesmaximal, characteristic, complemented
9C2×#17985899C211yesmaximal, characteristic, complemented
10C2×#17985894C211yesmaximal, characteristic, complemented
11C2×#17985872C211yesmaximal, characteristic, complemented
12C2×#17985870C211yesmaximal, characteristic, complemented
13C2×#17985868C211yesmaximal, characteristic, complemented
14C2×#17985857C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×Dic71C211yesmaximal, characteristic, complemented
16C22×#123×C71C211yesmaximal, characteristic, complemented
17C23×C22⋊D71C2211yescharacteristic
18C23×C22⋊D71C2211yescharacteristic
19C24×Dic71C2211yescharacteristic
20C23×C4×D71C2211yescharacteristic
21C2×#14556110—28no—
22C2×#14556110C2218yescomplemented
23C2×#14556100—28no—
24C2×#14556100C2218yes—
25C2×C4×C22⋊D71—28no—
26C2×C4×C22⋊D71C2218yescomplemented
27C22×C4⋊Dic71C2211yescharacteristic
28C22×Dic71⋊C4C2211yescharacteristic
29C22×Dic71⋊C4C2211yescharacteristic
30C22×Dic71⋊C4C2211yescharacteristic
31C22×Dic71⋊C4C2211yescharacteristic
32C22×Dic71⋊C4C2211yescharacteristic
33C22×Dic71⋊C4C2211yescharacteristic
34C22×C22⋊Dic71C2211yescharacteristic
35C22×C22⋊Dic71C2211yescharacteristic
36C22×C22⋊Dic71C2211yescharacteristic
37C22×C22⋊Dic71C2211yescharacteristic
38C22×C22⋊Dic71C2211yescharacteristic
39C22×(C2×D71)⋊C4C2211yescharacteristic
40C22×(C2×D71)⋊C4C2211yescharacteristic
41C22×(C2×D71)⋊C4C2211yescharacteristic
42C22×(C2×D71)⋊C4C2211yescharacteristic
43C22×C4×Dic71C2211yescharacteristic
44C22×C4×Dic71C2211yescharacteristic
45#17985925C2218yescomplemented
46#17985924C2218yescomplemented
47#17985914C2218yescomplemented
48#17985913C2218yescomplemented
49#17985899C2218yescomplemented
50#17985894C2218yescomplemented
51#17985872C2218yescomplemented
52#17985870C2218yescomplemented
53#17985868C2218yescomplemented
54#17985857C2218yescomplemented
55C22⋊C4×Dic71C2218yescomplemented
56C2×C71⋊#95C2211yescharacteristic
57C2×C71⋊#95C2211yescharacteristic
58C2×C71⋊#95C2211yescharacteristic
59C2×C71⋊#95C2211yescharacteristic
60C2×C71⋊#95C2211yescharacteristic
61C2×C71⋊#95C2211yescharacteristic
62C23×D4×C71C2211yescharacteristic
63C24×C4×C71C2211yescharacteristic
64C2×#123×C71—28no—
65C2×#123×C71C2218yescomplemented
66C22×C4⋊C4×C71C2211yescharacteristic
67C22×C4⋊C4×C71C2211yescharacteristic
68C22×C22⋊C4×C71C2211yescharacteristic
69C22×C22⋊C4×C71C2211yescharacteristic
70C22×C22⋊C4×C71C2211yescharacteristic
71C24×D71C2311yescharacteristic
72C22×C22⋊D71—24no—
73C22×C22⋊D71—24no—
74C22×C22⋊D71—24no—
75C22×C22⋊D71—24no—
76C22×C22⋊D71—42no—
77C22×C22⋊D71D418yes—
78C22×C22⋊D71C2314yes—
79C22×C22⋊D71C2314yes—
80C23×Dic71—24no—
81C23×Dic71—24no—
82C23×Dic71—24no—
83C23×Dic71C2311yescharacteristic
84C23×Dic71C2311yescharacteristic
85C23×Dic71C2314yes—
86C23×Dic71C2311yescharacteristic
87C23×Dic71C2311yescharacteristic
88C23×Dic71C2311yescharacteristic
89C23×Dic71C2311yescharacteristic
90C23×Dic71C2311yescharacteristic
91C22×C4×D71—24no—
92C22×C4×D71—24no—
93C22×C4×D71—42no—
94C22×C4×D71C2314yes—
95#14556110—232no—
96#14556100—232no—
97C4×C22⋊D71—232no—
98C2×C4⋊Dic71—24no—
99C2×C4⋊Dic71C2314yes—
100C2×Dic71⋊C4—24no—
101C2×Dic71⋊C4—24no—
102C2×Dic71⋊C4—24no—
103C2×Dic71⋊C4—24no—
104C2×Dic71⋊C4—42no—
105C2×Dic71⋊C4—42no—
106C2×Dic71⋊C4C2314yes—
107C2×Dic71⋊C4C2314yes—
108C2×Dic71⋊C4C2314yes—
109C2×Dic71⋊C4C2314yes—
110C2×Dic71⋊C4C2314yes—
111C2×Dic71⋊C4C2314yes—
112C2×C22⋊Dic71—24no—
113C2×C22⋊Dic71—24no—
114C2×C22⋊Dic71—24no—
115C2×C22⋊Dic71—24no—
116C2×C22⋊Dic71—24no—
117C2×C22⋊Dic71C2314yes—
118C2×C22⋊Dic71C2314yes—
119C2×C22⋊Dic71C2314yes—
120C2×C22⋊Dic71C2314yes—
121C2×C22⋊Dic71C2314yes—
122C2×(C2×D71)⋊C4—24no—
123C2×(C2×D71)⋊C4—24no—
124C2×(C2×D71)⋊C4—24no—
125C2×(C2×D71)⋊C4—24no—
126C2×(C2×D71)⋊C4C2314yes—
127C2×(C2×D71)⋊C4C2314yes—
128C2×(C2×D71)⋊C4C2314yes—
129C2×(C2×D71)⋊C4C2314yes—
130C2×C4×Dic71—24no—
131C2×C4×Dic71—24no—
132C2×C4×Dic71C2314yes—
133C2×C4×Dic71C2314yes—
134C71⋊#95C2314yes—
135C71⋊#95C2314yes—
136C71⋊#95C2314yes—
137C71⋊#95C2314yes—
138C71⋊#95C2314yes—
139C71⋊#95C2314yes—
140C25×C71C2311yescharacteristic
141C25×C71C2311yescharacteristic
142C22×D4×C71—24no—
143C22×D4×C71—24no—
144C22×D4×C71—42no—
145C22×D4×C71C2314yes—
146C23×C4×C71—24no—
147C23×C4×C71—24no—
148C23×C4×C71—42no—
149C23×C4×C71C2311yescharacteristic
150C23×C4×C71C2311yescharacteristic
151C23×C4×C71C2311yescharacteristic
152C23×C4×C71C2314yes—
153C23×C4×C71C2311yescharacteristic
154C23×C4×C71C2311yescharacteristic
155#123×C71—232no—
156C2×C4⋊C4×C71—24no—
157C2×C4⋊C4×C71—24no—
158C2×C4⋊C4×C71C2314yes—
159C2×C4⋊C4×C71C2314yes—
160C2×C22⋊C4×C71—24no—
161C2×C22⋊C4×C71—24no—
162C2×C22⋊C4×C71D418yescomplemented
163C2×C22⋊C4×C71C2314yes—
164C2×C22⋊C4×C71C2314yes—
165C2×C22⋊C4×C71C2314yes—
166C23×D71—22no—
167C23×D71—22no—
168C23×D71—22no—
169C23×D71—22no—
170C23×D71—22no—
171C23×D71—22no—
172C23×D71C2×D414yes—
173C23×D71C2412yes—
174C2×C22⋊D71—28no—
175C2×C22⋊D71—28no—
176C2×C22⋊D71—232no—
177C2×C22⋊D71—28no—
178C2×C22⋊D71—28no—
179C2×C22⋊D71—44no—
180C2×C22⋊D71—416no—
181C2×C22⋊D71C2×D4116yes—
182C22×Dic71—22no—
183C22×Dic71—22no—
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—28no—
200C22×Dic71—28no—
201C22×Dic71—28no—
202C22×Dic71—416no—
203C22×Dic71C2×D414yes—
204C22×Dic71#4114yes—
205C22×Dic71#4114yes—
206C22×Dic71#4114yes—
207C22×Dic71C2412yes—
208C22×Dic71C2412yes—
209C22×Dic71C2412yes—
210C22×Dic71C2412yes—
211C22×Dic71C2412yes—
212C22×Dic71C2412yes—
213C22×Dic71C2412yes—
214C2×C4×D71—28no—
215C2×C4×D71—28no—
216C2×C4×D71—44no—
217C2×C4×D71—416no—
218C4⋊Dic71—28no—
219Dic71⋊C4—28no—
220Dic71⋊C4—28no—
221Dic71⋊C4—28no—
222Dic71⋊C4—28no—
223Dic71⋊C4—44no—
224Dic71⋊C4—44no—
225C22⋊Dic71—28no—
226C22⋊Dic71—28no—
227C22⋊Dic71—28no—
228C22⋊Dic71—28no—
229C22⋊Dic71—28no—
230(C2×D71)⋊C4—28no—
231(C2×D71)⋊C4—28no—
232(C2×D71)⋊C4—28no—
233(C2×D71)⋊C4—28no—
234C4×Dic71—28no—
235C4×Dic71—28no—
236C24×C71—22no—
237C24×C71—22no—
238C24×C71—22no—
239C24×C71—22no—
240C24×C71—22no—
241C24×C71—22no—
242C24×C71—22no—
243C24×C71—22no—
244C24×C71—22no—
245C24×C71—22no—
246C24×C71—22no—
247C24×C71—22no—
248C24×C71C2×D414yes—
249C24×C71C2×D414yes—
250C24×C71C2412yes—
251C24×C71C2412yes—
252C24×C71C2411yescharacteristic
253C2×D4×C71—28no—
254C2×D4×C71—28no—
255C2×D4×C71—44no—
256C2×D4×C71—416no—
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—28no—
266C22×C4×C71—22no—
267C22×C4×C71—22no—
268C22×C4×C71—22no—
269C22×C4×C71—22no—
270C22×C4×C71—22no—
271C22×C4×C71—28no—
272C22×C4×C71—44no—
273C22×C4×C71—416no—
274C22×C4×C71C2×D414yes—
275C22×C4×C71C2×D414yes—
276C22×C4×C71C2412yes—
277C22×C4×C71C2412yes—
278C22×C4×C71C2412yes—
279C22×C4×C71C2412yes—
280C22×C4×C71C2412yes—
281C4⋊C4×C71—28no—
282C4⋊C4×C71—28no—
283C22⋊C4×C71—28no—
284C22⋊C4×C71—28no—
285C22⋊C4×C71C2×D4116yescomplemented
286C23×C71—28no—
287C23×C71—28no—
288C23×C71—28no—
289C23×C71—28no—
290C23×C71—28no—
291C23×C71—28no—
292C23×C71—22no—
293C23×C71—22no—
294C23×C71—22no—
295C23×C71—22no—
296C23×C71—22no—
297C23×C71—22no—
298C23×C71—22no—
299C23×C71—22no—
300C23×C71—22no—
301C23×C71—22no—
302C23×C71—22no—
303C23×C71—22no—
304C23×C71—44no—
305C23×C71—44no—
306C23×C71—44no—
307C23×C71—44no—
308C23×C71—44no—
309C23×C71—44no—
310C23×C71—44no—
311C23×C71—44no—
312C23×C71C22×D414yes—
313C23×C71C22×D412yes—
314C23×C71C22×D414yes—
315C23×C71C22×D412yes—
316C23×C71C2×#4112yes—
317C23×C71C2×#4112yes—
318C23×C71C2×#4112yes—
319C23×C71H(5,𝔽2)12yes—
320C23×C712−1+412yes—
321C23×C71C2511yescharacteristic
322C22×D71—28no—
323C22×D71—28no—
324C22×D71—28no—
325C22×D71—22no—
326C22×D71—22no—
327C22×D71—22no—
328C22×D71—22no—
329C22×D71—22no—
330C22×D71—22no—
331C22×D71—44no—
332C22×D71—44no—
333C22×D71—44no—
334C22×D71—44no—
335C22×D71C22×D414yes—
336D4×C71—416no—
337C2×C4×C71—28no—
338C2×C4×C71—28no—
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—416no—
353C2×C4×C71—44no—
354C2×C4×C71—44no—
355C2×C4×C71—44no—
356C2×C4×C71C22×D414yes—
357C2×C4×C71C22×D414yes—
358C22⋊D71—232no—
359C22⋊D71—416no—
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×Dic71—416no—
384C2×Dic71#123116yescomplemented
385C2×Dic71C22×D414yes—
386C2×Dic71C2×#4114yes—
387C2×Dic71C2×#4114yes—
388C2×Dic71C2×#4114yes—
389C4×D71—416no—
390C22×C71—24no—
391C22×C71—24no—
392C22×C71—24no—
393C22×C71—24no—
394C22×C71—24no—
395C22×C71—24no—
396C22×C71—42no—
397C22×C71—42no—
398C22×C71—416no—
399C22×C71—416no—
400C22×C71—42no—
401C22×C71—42no—
402C22×C71—42no—
403C22×C71—42no—
404C22×C71—42no—
405C22×C71—42no—
406C22×C71C2×#12314yes—
407C22×C71#53214yes—
408C22×C71#54214yes—
409C22×C71D4214yes—
410C22×C71#54714yes—
411C22×C71#54714yes—
412C22×C71#55314yes—
413C22×C71C23×D411yescharacteristic
414C22×C71C23×D411yescharacteristic
415C22×C71C22×#4111yescharacteristic
416C22×C71C22×#4111yescharacteristic
417C22×C71C22×#4111yescharacteristic
418C22×C71C2×H(5,𝔽2)11yescharacteristic
419C22×C71C2×2−1+411yescharacteristic
420C2×D71—24no—
421C2×D71—24no—
422C2×D71—24no—
423C2×D71—42no—
424C2×D71—416no—
425C2×D71—42no—
426C2×D71—42no—
427C2×D71—42no—
428C4×C71—24no—
429C4×C71—24no—
430C4×C71—42no—
431C4×C71—42no—
432C4×C71—42no—
433Dic71—24no—
434Dic71—42no—
435Dic71—42no—
436Dic71—42no—
437Dic71—42no—
438Dic71—42no—
439Dic71C2×#12318yescomplemented
440C2×#2422—711nomaximal, Sylow
441C2×C71—44no—
442C2×C71—44no—
443C2×C71#242218yescomplemented
444C2×C71C22×#12311yescharacteristic
445C2×C71C2×#53211yescharacteristic
446C2×C71C2×#54211yescharacteristic
447C2×C71C2×D4211yescharacteristic
448C2×C71C2×#54711yescharacteristic
449C2×C71C2×#54711yescharacteristic
450C2×C71C2×#55311yescharacteristic
451D71—44no—
452C22×#123—711no—
453C22×#123D7111yescharacteristic, complemented
454C22×#121—711no—
455C22×C4×D4—711no—
456#2422—7116no—
457C2×#397—711no—
458C2×#397—711no—
459C2×#394—711no—
460C2×#394—711no—
461C2×#390—711no—
462C2×#389—711no—
463C2×#385—711no—
464C2×#385—711no—
465C2×#384—711no—
466C2×#380—711no—
467C2×C4×C22⋊C4—711no—
468C71C2×#242211yescharacteristic, complemented, Sylow
469C23×D4—711no—
470C23×D4—711no—
471C23×D4C2×D7111yescharacteristic
472C24×C4—711no—
473C24×C4—711no—
474C24×C4C2×D7111yescharacteristic
475C2×#123—28no—
476C2×#123—718no—
477C2×#123—1428no—
478C2×#123C2×D7118yescomplemented
479C2×#121—718no—
480C2×#121—1428no—
481C2×C4×D4—718no—
482C2×C4×D4—1428no—
483C22×C4⋊C4—711no—
484C22×C4⋊C4—711no—
485C22×C4⋊C4—711no—
486C22×C4⋊C4—711no—
487C22×C4⋊C4—711no—
488C22×C4⋊C4—711no—
489C22×C4⋊C4—711no—
490C22×C4⋊C4C2×D7111yescharacteristic
491C22×C4⋊C4C2×D7111yescharacteristic
492C22×C22⋊C4—711no—
493C22×C22⋊C4—711no—
494C22×C22⋊C4—711no—
495C22×C22⋊C4—711no—
496C22×C22⋊C4—711no—
497C22×C22⋊C4—711no—
498C22×C22⋊C4—711no—
499C22×C22⋊C4—711no—
500C22×C22⋊C4—711no—
501C22×C22⋊C4C2×D7111yescharacteristic
502C22×C22⋊C4C2×D7111yescharacteristic
503C22×C22⋊C4C2×D7111yescharacteristic
504C22×C42—711no—
505C22×C42—711no—
506#397—718no—
507#397—718no—
508#394—718no—
509#394—718no—
510#390—718no—
511#389—718no—
512#385—718no—
513#385—718no—
514#384—718no—
515#380—718no—
516C4×C22⋊C4—718no—
517C2×#95—711no—
518C2×#95—711no—
519C2×#95—711no—
520C2×#95—711no—
521C2×#95—711no—
522C2×#95—711no—
523C25—711no—
524C25C22×D7111yescharacteristic
525C25C22×D7111yescharacteristic
526C22×D4—24no—
527C22×D4—24no—
528C22×D4—42no—
529C22×D4—2842no—
530C22×D4—714no—
531C22×D4—718no—
532C22×D4—714no—
533C22×D4—1424no—
534C22×D4—1424no—
535C22×D4—1424no—
536C22×D4—1424no—
537C22×D4C22×D7114yes—
538C23×C4—24no—
539C23×C4—24no—
540C23×C4—42no—
541C23×C4—2842no—
542C23×C4—714no—
543C23×C4—711no—
544C23×C4—711no—
545C23×C4—714no—
546C23×C4—711no—
547C23×C4—711no—
548C23×C4—711no—
549C23×C4—711no—
550C23×C4—711no—
551C23×C4—1424no—
552C23×C4—1424no—
553C23×C4—1424no—
554C23×C4—1424no—
555C23×C4—1424no—
556C23×C4C22×D7111yescharacteristic
557C23×C4C22×D7111yescharacteristic
558C23×C4C22×D7111yescharacteristic
559C23×C4C22×D7114yes—
560C23×C4C22×D7111yescharacteristic
561C23×C4C22×D7111yescharacteristic
562#123—232no—
563#123—14232no—
564#121—14232no—
565C4×D4—14232no—
566C2×C4⋊C4—24no—
567C2×C4⋊C4—24no—
568C2×C4⋊C4—2842no—
569C2×C4⋊C4—2842no—
570C2×C4⋊C4—714no—
571C2×C4⋊C4—714no—
572C2×C4⋊C4—714no—
573C2×C4⋊C4—714no—
574C2×C4⋊C4—714no—
575C2×C4⋊C4—714no—
576C2×C4⋊C4—714no—
577C2×C4⋊C4—1424no—
578C2×C4⋊C4—1424no—
579C2×C4⋊C4—1424no—
580C2×C4⋊C4—1424no—
581C2×C4⋊C4—1424no—
582C2×C4⋊C4C22×D7114yes—
583C2×C4⋊C4C22×D7114yes—
584C2×C22⋊C4—24no—
585C2×C22⋊C4—24no—
586C2×C22⋊C4—714no—
587C2×C22⋊C4—714no—
588C2×C22⋊C4—714no—
589C2×C22⋊C4—714no—
590C2×C22⋊C4—714no—
591C2×C22⋊C4—714no—
592C2×C22⋊C4—714no—
593C2×C22⋊C4—714no—
594C2×C22⋊C4—714no—
595C2×C22⋊C4—1424no—
596C2×C22⋊C4—1424no—
597C2×C22⋊C4—1424no—
598C2×C22⋊C4—1424no—
599C2×C22⋊C4—1424no—
600C2×C22⋊C4—1424no—
601C2×C22⋊C4—1424no—
602C2×C22⋊C4—1424no—
603C2×C22⋊C4—1424no—
604C2×C22⋊C4C22⋊D7118yescomplemented
605C2×C22⋊C4C22×D7114yes—
606C2×C22⋊C4C22×D7114yes—
607C2×C22⋊C4C22×D7114yes—
608C2×C42—714no—
609C2×C42—714no—
610C2×C42—1424no—
611C2×C42—1424no—
612#95—714no—
613#95—714no—
614#95—714no—
615#95—714no—
616#95—714no—
617#95—714no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—22no—
627C24—22no—
628C24—22no—
629C24—22no—
630C24—714no—
631C24—712no—
632C24—1422no—
633C24—1422no—
634C24—1422no—
635C24—1422no—
636C24—1422no—
637C24—1422no—
638C24D4×D7114yes—
639C24C2×C22⋊D7114yes—
640C24C23×D7112yes—
641C24C23×D7112yes—
642C24C23×D7111yescharacteristic
643C2×D4—28no—
644C2×D4—28no—
645C2×D4—44no—
646C2×D4—416no—
647C2×D4—28416no—
648C2×D4—2844no—
649C2×D4—7116no—
650C2×D4—1428no—
651C2×D4—1428no—
652C2×D4—14232no—
653C2×D4—1428no—
654C2×D4—1428no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—28no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—28no—
670C22×C4—44no—
671C22×C4—416no—
672C22×C4—28416no—
673C22×C4—2844no—
674C22×C4—28416no—
675C22×C4—714no—
676C22×C4—714no—
677C22×C4—714no—
678C22×C4—712no—
679C22×C4—714no—
680C22×C4—712no—
681C22×C4—712no—
682C22×C4—712no—
683C22×C4—712no—
684C22×C4—712no—
685C22×C4—712no—
686C22×C4—1428no—
687C22×C4—1428no—
688C22×C4—1428no—
689C22×C4—1428no—
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×C4—1422no—
701C22×C4—1422no—
702C22×C4—1422no—
703C22×C4—1422no—
704C22×C4—1422no—
705C22×C4—1428no—
706C22×C4—1422no—
707C22×C4—1422no—
708C22×C4C2×C22⋊D7114yes—
709C22×C4C2×C22⋊D7114yes—
710C22×C4C23×D7112yes—
711C22×C4C23×D7112yes—
712C22×C4C23×D7112yes—
713C22×C4C23×D7112yes—
714C22×C4C23×D7112yes—
715C4⋊C4—28no—
716C4⋊C4—28no—
717C4⋊C4—2844no—
718C4⋊C4—2844no—
719C4⋊C4—1428no—
720C4⋊C4—1428no—
721C4⋊C4—1428no—
722C4⋊C4—1428no—
723C4⋊C4—1428no—
724C22⋊C4—28no—
725C22⋊C4—28no—
726C22⋊C4—1428no—
727C22⋊C4—1428no—
728C22⋊C4—1428no—
729C22⋊C4—1428no—
730C22⋊C4—1428no—
731C22⋊C4—1428no—
732C22⋊C4—1428no—
733C22⋊C4—1428no—
734C22⋊C4—1428no—
735C22⋊C4C2×C22⋊D71116yescomplemented
736C42—1428no—
737C42—1428no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—28no—
751C23—28no—
752C23—28no—
753C23—28no—
754C23—28no—
755C23—28no—
756C23—44no—
757C23—44no—
758C23—44no—
759C23—44no—
760C23—44no—
761C23—44no—
762C23—44no—
763C23—44no—
764C23—2844no—
765C23—2844no—
766C23—2844no—
767C23—2844no—
768C23—714no—
769C23—1422no—
770C23—1422no—
771C23—1422no—
772C23—1422no—
773C23—1422no—
774C23—1422no—
775C23—1428no—
776C23—1428no—
777C23—1428no—
778C23C2×D4×D7114yes—
779C23C2×D4×D7112yes—
780C23C22×C22⋊D7114yes—
781C23C22×C22⋊D7112yes—
782C23#41×D7112yes—
783C23#41×D7112yes—
784C23#41×D7112yes—
785C23#1455617312yes—
786C23#1455617512yes—
787C23C24×D7111yescharacteristic
788D4—416no—
789D4—28416no—
790D4—14232no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—28no—
796C2×C4—28no—
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—22no—
806C2×C4—416no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—44no—
810C2×C4—28416no—
811C2×C4—2844no—
812C2×C4—2844no—
813C2×C4—2844no—
814C2×C4—2844no—
815C2×C4—2844no—
816C2×C4—28416no—
817C2×C4—714no—
818C2×C4—714no—
819C2×C4—714no—
820C2×C4—7116no—
821C2×C4—714no—
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—1422no—
836C2×C4—1422no—
837C2×C4—1422no—
838C2×C4—1422no—
839C2×C4—1428no—
840C2×C4C22×C22⋊D7114yes—
841C2×C4C22×C22⋊D7114yes—
842C22—24no—
843C22—24no—
844C22—24no—
845C22—24no—
846C22—24no—
847C22—24no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—416no—
852C22—416no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—2842no—
859C22—28416no—
860C22—2842no—
861C22—2842no—
862C22—2842no—
863C22—1424no—
864C22—1424no—
865C22—1424no—
866C22#123×D7114yes—
867C22#1798654514yes—
868C22#1798661714yes—
869C22D4×C22⋊D7114yes—
870C22#1798664714yes—
871C22#1798664814yes—
872C22#1798669414yes—
873C22C22×D4×D7111yescharacteristic
874C22C23×C22⋊D7111yescharacteristic
875C22C2×#41×D7111yescharacteristic
876C22C2×#41×D7111yescharacteristic
877C22C2×#41×D7111yescharacteristic
878C22C2×#1455617311yescharacteristic
879C22C2×#1455617511yescharacteristic
880C4—24no—
881C4—24no—
882C4—42no—
883C4—42no—
884C4—42no—
885C4—2842no—
886C4—2842no—
887C4—2842no—
888C4—2842no—
889C4—2842no—
890C4—718no—
891C4—1424no—
892C2—44no—
893C2—44no—
894C2—2844no—
895C2#2259185118yesdirect product factor
896C2C2×#123×D7111yescharacteristic
897C2C2×#1798654511yescharacteristic
898C2C2×#1798661711yescharacteristic
899C2C2×D4×C22⋊D7111yescharacteristic
900C2C2×#1798664711yescharacteristic
901C2C2×#1798664811yescharacteristic
902C2C2×#1798669411yescharacteristic
subgroupG/H
centerC24C23×D71
commutator, cosocleC23×C71C25
FrattiniC23C24×D71
FittingC22×#123×C71C2
socleC24×C71C24
prime radicalC22×#14556100C2
hypercenterC22×#123D71
hypocenterC71C2×#2422
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. C22×#14556110C2semidirect
3. C22×C4×C22⋊D71C2semidirect
4. #22591851C2direct (N × H)
5. C2×#17985925C2semidirect
6. C2×#17985924C2semidirect
7. C2×#17985914C2semidirect
8. C2×#17985913C2semidirect
9. C2×#17985899C2semidirect
10. C2×#17985894C2semidirect
11. C2×#17985872C2semidirect
12. C2×#17985870C2semidirect
13. C2×#17985868C2semidirect
14. C2×#17985857C2semidirect
15. C2×C22⋊C4×Dic71C2semidirect
16. C22×#123×C71C2semidirect
22. C2×#14556110C22semidirect
26. C2×C4×C22⋊D71C22semidirect
45. #17985925C22semidirect
46. #17985924C22semidirect
47. #17985914C22semidirect
48. #17985913C22semidirect
49. #17985899C22semidirect
50. #17985894C22semidirect
51. #17985872C22semidirect
52. #17985870C22semidirect
53. #17985868C22semidirect
54. #17985857C22semidirect
55. C22⋊C4×Dic71C22semidirect
65. C2×#123×C71C22semidirect
162. C2×C22⋊C4×C71D4semidirect
285. C22⋊C4×C71C2×D4semidirect
384. C2×Dic71#123semidirect
439. Dic71C2×#123semidirect
443. C2×C71#2422semidirect
453. C22×#123D71semidirect
468. C71C2×#2422semidirect
478. C2×#123C2×D71semidirect
604. C2×C22⋊C4C22⋊D71semidirect
735. C22⋊C4C2×C22⋊D71semidirect
895. C2#22591851direct (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×#145561002
C22×C4×C22⋊D712
#225918512
C2×#179859252
C2×#179859242
C2×#179859142
C2×#179859132
C2×#179858992
C2×#179858942
C2×#179858722
C2×#179858702
C2×#179858682
C2×#179858572
C2×C22⋊C4×Dic712
C22×#123×C712
C2×#242271