Finite Group Databasebeta

← C2×#22592462 #32165025

Subgroups — C2×#22592462 #32165025

Order 18176.

4946 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556104C211yesmaximal, characteristic, complemented
2C22×#14556096C211yesmaximal, characteristic
3C22×C22⋊C4×D71C211yesmaximal, characteristic, complemented
4#22592462C2116yesmaximal, direct product factor
5C2×#17985927C211yesmaximal, characteristic, complemented
6C2×#17985915C211yesmaximal, characteristic, complemented
7C2×#17985913C211yesmaximal, characteristic, complemented
8C2×#17985910C211yesmaximal, characteristic, complemented
9C2×#17985899C211yesmaximal, characteristic, complemented
10C2×#17985892C211yesmaximal, characteristic, complemented
11C2×#17985890C211yesmaximal, characteristic, complemented
12C2×#17985875C211yesmaximal, characteristic, complemented
13C2×#17985875C211yesmaximal, characteristic, complemented
14C2×#17985854C211yesmaximal, characteristic, complemented
15C2×C4×(C2×D71)⋊C4C211yesmaximal, characteristic, complemented
16C22×#124×C71C211yesmaximal, characteristic, complemented
17C25×D71C2211yescharacteristic
18C23×C22⋊D71C2211yescharacteristic
19C23×C22⋊D71C2211yescharacteristic
20C23×C4×D71C2211yescharacteristic
21C23×C4×D71C2211yescharacteristic
22C2×#14556104—28no—
23C2×#14556104C2218yescomplemented
24C2×#14556096—28no—
25C2×#14556096C2218yes—
26C22×C4⋊Dic71C2211yescharacteristic, complemented
27C22×Dic71⋊C4C2211yescharacteristic, complemented
28C22×Dic71⋊C4C2211yescharacteristic, complemented
29C22×C22⋊Dic71C2211yescharacteristic
30C22×C22⋊Dic71C2211yescharacteristic
31C22×C22⋊Dic71C2211yescharacteristic
32C22×C22⋊Dic71C2211yescharacteristic, complemented
33C22×C22⋊Dic71C2211yescharacteristic, complemented
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×(C2×D71)⋊C4C2211yescharacteristic
42C2×C22⋊C4×D71—28no—
43C2×C22⋊C4×D71C2218yescomplemented
44C22×C4×Dic71C2211yescharacteristic, complemented
45#17985927C2218yescomplemented
46#17985915C2218yescomplemented
47#17985913C2218yescomplemented
48#17985910C2218yescomplemented
49#17985899C2218yescomplemented
50#17985892C2218yescomplemented
51#17985890C2218yescomplemented
52#17985875C2218yescomplemented
53#17985875C2218yescomplemented
54#17985854C2218yescomplemented
55C4×(C2×D71)⋊C4C2218yescomplemented
56C2×C71⋊#95C2211yescharacteristic, complemented
57C2×C71⋊#95C2211yescharacteristic, complemented
58C2×C71⋊#95C2211yescharacteristic, complemented
59C2×C71⋊#95C2211yescharacteristic, complemented
60C2×C71⋊#95C2211yescharacteristic, complemented
61C2×C71⋊#95C2211yescharacteristic, complemented
62C23×Q8×C71C2211yescharacteristic, complemented
63C23×D4×C71C2211yescharacteristic
64C2×#124×C71—28no—
65C2×#124×C71C2218yescomplemented
66C22×C22⋊C4×C71C2211yescharacteristic
67C22×C22⋊C4×C71C2211yescharacteristic
68C22×C22⋊C4×C71C2211yescharacteristic, complemented
69C22×C22⋊C4×C71C2211yescharacteristic, complemented
70C22×C42×C71C2211yescharacteristic, complemented
71C24×D71—24no—
72C24×D71—24no—
73C24×D71—24no—
74C24×D71—24no—
75C24×D71—24no—
76C24×D71—42no—
77C24×D71—42no—
78C24×D71C2311yescharacteristic
79C24×D71C2314yes—
80C24×D71C2311yescharacteristic
81C22×C22⋊D71—24no—
82C22×C22⋊D71—24no—
83C22×C22⋊D71—24no—
84C22×C22⋊D71—24no—
85C22×C22⋊D71—24no—
86C22×C22⋊D71—42no—
87C22×C22⋊D71C2314yes—
88C22×C22⋊D71C2314yes—
89C23×Dic71C2311yescharacteristic
90C23×Dic71C2311yescharacteristic
91C23×Dic71C2311yescharacteristic
92C23×Dic71C2311yescharacteristic
93C23×Dic71C2311yescharacteristic
94C23×Dic71C2311yescharacteristic
95C22×C4×D71—24no—
96C22×C4×D71—24no—
97C22×C4×D71—24no—
98C22×C4×D71—24no—
99C22×C4×D71—42no—
100C22×C4×D71—42no—
101C22×C4×D71C2314yes—
102C22×C4×D71C2314yes—
103#14556104—232no—
104#14556096—232no—
105C2×C4⋊Dic71—24no—
106C2×C4⋊Dic71C2314yescomplemented
107C2×Dic71⋊C4—24no—
108C2×Dic71⋊C4—24no—
109C2×Dic71⋊C4C2314yescomplemented
110C2×Dic71⋊C4C2314yescomplemented
111C2×C22⋊Dic71—24no—
112C2×C22⋊Dic71—24no—
113C2×C22⋊Dic71—42no—
114C2×C22⋊Dic71—42no—
115C2×C22⋊Dic71—42no—
116C2×C22⋊Dic71C2314yes—
117C2×C22⋊Dic71C2314yes—
118C2×C22⋊Dic71C2314yes—
119C2×C22⋊Dic71C2314yescomplemented
120C2×C22⋊Dic71C2314yescomplemented
121C2×(C2×D71)⋊C4—24no—
122C2×(C2×D71)⋊C4—24no—
123C2×(C2×D71)⋊C4—24no—
124C2×(C2×D71)⋊C4—24no—
125C2×(C2×D71)⋊C4—24no—
126C2×(C2×D71)⋊C4—24no—
127C2×(C2×D71)⋊C4—42no—
128C2×(C2×D71)⋊C4D418yes—
129C2×(C2×D71)⋊C4C2314yes—
130C2×(C2×D71)⋊C4C2314yes—
131C2×(C2×D71)⋊C4C2314yes—
132C2×(C2×D71)⋊C4C2314yes—
133C2×(C2×D71)⋊C4C2314yes—
134C2×(C2×D71)⋊C4C2314yes—
135C2×(C2×D71)⋊C4C2314yes—
136C2×(C2×D71)⋊C4C2314yes—
137C22⋊C4×D71—232no—
138C2×C4×Dic71—42no—
139C2×C4×Dic71C2314yescomplemented
140C71⋊#95C2314yescomplemented
141C71⋊#95C2314yescomplemented
142C71⋊#95C2314yescomplemented
143C71⋊#95C2314yescomplemented
144C71⋊#95C2314yescomplemented
145C71⋊#95C2314yescomplemented
146C25×C71C2311yescharacteristic
147C25×C71C2311yescharacteristic
148C22×Q8×C71—24no—
149C22×Q8×C71—24no—
150C22×Q8×C71—42no—
151C22×Q8×C71C2314yescomplemented
152C22×D4×C71—24no—
153C22×D4×C71—24no—
154C22×D4×C71—42no—
155C22×D4×C71C2314yes—
156C23×C4×C71C2311yescharacteristic
157C23×C4×C71C2311yescharacteristic
158C23×C4×C71C2311yescharacteristic
159C23×C4×C71C2311yescharacteristic
160C23×C4×C71C2311yescharacteristic
161#124×C71—232no—
162C2×C22⋊C4×C71—24no—
163C2×C22⋊C4×C71—24no—
164C2×C22⋊C4×C71—24no—
165C2×C22⋊C4×C71D418yescomplemented
166C2×C22⋊C4×C71C2314yes—
167C2×C22⋊C4×C71C2314yes—
168C2×C22⋊C4×C71C2314yescomplemented
169C2×C22⋊C4×C71C2314yescomplemented
170C2×C42×C71—24no—
171C2×C42×C71C2314yescomplemented
172C23×D71—22no—
173C23×D71—22no—
174C23×D71—22no—
175C23×D71—22no—
176C23×D71—232no—
177C23×D71—22no—
178C23×D71—28no—
179C23×D71—22no—
180C23×D71—22no—
181C23×D71—22no—
182C23×D71—22no—
183C23×D71—22no—
184C23×D71—28no—
185C23×D71—28no—
186C23×D71—28no—
187C23×D71—28no—
188C23×D71—44no—
189C23×D71—44no—
190C23×D71—416no—
191C23×D71—416no—
192C23×D71—416no—
193C23×D71—416no—
194C23×D71—416no—
195C23×D71—416no—
196C23×D71C2×D414yes—
197C23×D71#4114yes—
198C23×D71#4114yes—
199C23×D71#4114yes—
200C23×D71C2412yes—
201C23×D71C2412yes—
202C2×C22⋊D71—28no—
203C2×C22⋊D71—28no—
204C2×C22⋊D71—28no—
205C2×C22⋊D71—28no—
206C2×C22⋊D71—28no—
207C2×C22⋊D71—44no—
208C2×C22⋊D71—416no—
209C2×C22⋊D71—416no—
210C22×Dic71—22no—
211C22×Dic71—22no—
212C22×Dic71—22no—
213C22×Dic71—22no—
214C22×Dic71—22no—
215C22×Dic71—22no—
216C22×Dic71—22no—
217C22×Dic71—22no—
218C22×Dic71—22no—
219C22×Dic71—22no—
220C22×Dic71—22no—
221C22×Dic71—22no—
222C22×Dic71—22no—
223C22×Dic71—22no—
224C22×Dic71—22no—
225C22×Dic71—22no—
226C22×Dic71—22no—
227C22×Dic71C2×D414yes—
228C22×Dic71C2412yes—
229C22×Dic71C2412yes—
230C22×Dic71C2412yes—
231C22×Dic71C2412yes—
232C22×Dic71C2412yes—
233C22×Dic71C2412yes—
234C2×C4×D71—28no—
235C2×C4×D71—28no—
236C2×C4×D71—28no—
237C2×C4×D71—28no—
238C2×C4×D71—44no—
239C2×C4×D71—44no—
240C2×C4×D71—416no—
241C2×C4×D71—416no—
242C4⋊Dic71—28no—
243Dic71⋊C4—28no—
244Dic71⋊C4—28no—
245C22⋊Dic71—28no—
246C22⋊Dic71—28no—
247C22⋊Dic71—44no—
248C22⋊Dic71—44no—
249C22⋊Dic71—44no—
250(C2×D71)⋊C4—28no—
251(C2×D71)⋊C4—28no—
252(C2×D71)⋊C4—28no—
253(C2×D71)⋊C4—28no—
254(C2×D71)⋊C4—28no—
255(C2×D71)⋊C4—28no—
256(C2×D71)⋊C4—44no—
257(C2×D71)⋊C4C2×D4116yes—
258C4×Dic71—44no—
259C24×C71—22no—
260C24×C71—22no—
261C24×C71—22no—
262C24×C71—22no—
263C24×C71—22no—
264C24×C71—22no—
265C24×C71—22no—
266C24×C71—22no—
267C24×C71—22no—
268C24×C71—22no—
269C24×C71—22no—
270C24×C71—22no—
271C24×C71—22no—
272C24×C71C2×D414yes—
273C24×C71C2412yes—
274C24×C71C2412yes—
275C24×C71C2411yescharacteristic
276C2×Q8×C71—28no—
277C2×Q8×C71—28no—
278C2×Q8×C71—44no—
279C2×Q8×C71—416no—
280C2×D4×C71—28no—
281C2×D4×C71—28no—
282C2×D4×C71—44no—
283C2×D4×C71—416no—
284C22×C4×C71—22no—
285C22×C4×C71—22no—
286C22×C4×C71—22no—
287C22×C4×C71—22no—
288C22×C4×C71—22no—
289C22×C4×C71—22no—
290C22×C4×C71—22no—
291C22×C4×C71—22no—
292C22×C4×C71—22no—
293C22×C4×C71—22no—
294C22×C4×C71—22no—
295C22×C4×C71—22no—
296C22×C4×C71C2×D414yes—
297C22×C4×C71C2×D414yes—
298C22×C4×C71C2×D414yes—
299C22×C4×C71C2412yes—
300C22×C4×C71C2412yes—
301C22×C4×C71C2412yes—
302C22×C4×C71C2412yes—
303C22×C4×C71C2412yes—
304C22⋊C4×C71—28no—
305C22⋊C4×C71—28no—
306C22⋊C4×C71—28no—
307C22⋊C4×C71C2×D4116yescomplemented
308C42×C71—28no—
309C23×C71—28no—
310C23×C71—28no—
311C23×C71—28no—
312C23×C71—22no—
313C23×C71—22no—
314C23×C71—22no—
315C23×C71—22no—
316C23×C71—22no—
317C23×C71—22no—
318C23×C71—22no—
319C23×C71—22no—
320C23×C71—22no—
321C23×C71—22no—
322C23×C71—22no—
323C23×C71—22no—
324C23×C71—22no—
325C23×C71—44no—
326C23×C71—44no—
327C23×C71—44no—
328C23×C71—44no—
329C23×C71—44no—
330C23×C71—44no—
331C23×C71—44no—
332C23×C71—44no—
333C23×C71—44no—
334C23×C71—44no—
335C23×C71—44no—
336C23×C71C22×D412yes—
337C23×C71C22×D414yes—
338C23×C71C22×D412yes—
339C23×C71C2×#4112yes—
340C23×C71C2×#4112yes—
341C23×C71C2×#4112yes—
342C23×C71H(5,𝔽2)12yes—
343C23×C71H(5,𝔽2)12yes—
344C23×C71C2511yescharacteristic
345C22×D71—28no—
346C22×D71—28no—
347C22×D71—28no—
348C22×D71—28no—
349C22×D71—28no—
350C22×D71—28no—
351C22×D71—22no—
352C22×D71—22no—
353C22×D71—22no—
354C22×D71—22no—
355C22×D71—232no—
356C22×D71—28no—
357C22×D71—28no—
358C22×D71—28no—
359C22×D71—22no—
360C22×D71—22no—
361C22×D71—22no—
362C22×D71—22no—
363C22×D71—22no—
364C22×D71—22no—
365C22×D71—416no—
366C22×D71—416no—
367C22×D71—416no—
368C22×D71—416no—
369C22×D71—416no—
370C22×D71—4128no—
371C22×D71—44no—
372C22×D71—44no—
373C22×D71—44no—
374C22×D71—44no—
375C22×D71—416no—
376C22×D71#124116yescomplemented
377C22×D71C22×D414yes—
378C22×D71C2×#4114yes—
379C22×D71C2×#4114yes—
380C22×D71C2×#4114yes—
381Q8×C71—416no—
382D4×C71—416no—
383C2×C4×C71—28no—
384C2×C4×C71—28no—
385C2×C4×C71—28no—
386C2×C4×C71—22no—
387C2×C4×C71—22no—
388C2×C4×C71—22no—
389C2×C4×C71—22no—
390C2×C4×C71—22no—
391C2×C4×C71—22no—
392C2×C4×C71—22no—
393C2×C4×C71—22no—
394C2×C4×C71—22no—
395C2×C4×C71—22no—
396C2×C4×C71—22no—
397C2×C4×C71—22no—
398C2×C4×C71—44no—
399C2×C4×C71—44no—
400C2×C4×C71C22×D414yes—
401C2×C4×C71C22×D414yes—
402C2×C4×C71C22×D414yes—
403C22⋊D71—416no—
404C22⋊D71—416no—
405C2×Dic71—28no—
406C2×Dic71—22no—
407C2×Dic71—22no—
408C2×Dic71—22no—
409C2×Dic71—22no—
410C2×Dic71—22no—
411C2×Dic71—22no—
412C2×Dic71—22no—
413C2×Dic71—22no—
414C2×Dic71—22no—
415C2×Dic71—22no—
416C2×Dic71—22no—
417C2×Dic71—22no—
418C2×Dic71—22no—
419C2×Dic71—22no—
420C2×Dic71—22no—
421C2×Dic71—22no—
422C2×Dic71—22no—
423C2×Dic71—44no—
424C2×Dic71—44no—
425C2×Dic71—44no—
426C2×Dic71—44no—
427C2×Dic71—44no—
428C2×Dic71C22×D414yes—
429C4×D71—416no—
430C4×D71—416no—
431C22×C71—24no—
432C22×C71—24no—
433C22×C71—24no—
434C22×C71—42no—
435C22×C71—42no—
436C22×C71—42no—
437C22×C71—42no—
438C22×C71—416no—
439C22×C71—42no—
440C22×C71—42no—
441C22×C71—42no—
442C22×C71—42no—
443C22×C71—42no—
444C22×C71—42no—
445C22×C71—42no—
446C22×C71—88no—
447C22×C71#52514yes—
448C22×C71C2×#12414yes—
449C22×C71#53814yes—
450C22×C71D4214yes—
451C22×C71#54614yes—
452C22×C71#54614yes—
453C22×C71#55114yes—
454C22×C71C23×D411yescharacteristic
455C22×C71C23×D411yescharacteristic
456C22×C71C22×#4111yescharacteristic
457C22×C71C22×#4111yescharacteristic
458C22×C71C22×#4111yescharacteristic
459C22×C71C2×H(5,𝔽2)11yescharacteristic
460C22×C71C2×H(5,𝔽2)11yescharacteristic
461C2×D71—24no—
462C2×D71—24no—
463C2×D71—24no—
464C2×D71—24no—
465C2×D71—24no—
466C2×D71—24no—
467C2×D71—232no—
468C2×D71—24no—
469C2×D71—24no—
470C2×D71—24no—
471C2×D71—464no—
472C2×D71—42no—
473C2×D71—42no—
474C2×D71—42no—
475C2×D71—42no—
476C2×D71—416no—
477C2×D71C2×#12418yescomplemented
478C4×C71—24no—
479C4×C71—24no—
480C4×C71—24no—
481C4×C71—42no—
482C4×C71—42no—
483Dic71—24no—
484Dic71—42no—
485Dic71—42no—
486Dic71—42no—
487Dic71—42no—
488Dic71—42no—
489C2×#2472—711nomaximal, Sylow
490C2×C71—44no—
491C2×C71—82no—
492C2×C71#247218yescomplemented
493C2×C71C2×#52511yescharacteristic
494C2×C71C22×#12411yescharacteristic
495C2×C71C2×#53811yescharacteristic
496C2×C71C2×D4211yescharacteristic
497C2×C71C2×#54611yescharacteristic
498C2×C71C2×#54611yescharacteristic
499C2×C71C2×#55111yescharacteristic
500D71—28no—
501D71—44no—
502C22×#124D7111yescharacteristic, complemented
503C22×C22⋊Q8—711no—
504C22×#120—711no—
505C23×C22⋊C4—711no—
506#2472—7116no—
507C2×#397—711no—
508C2×#394—711no—
509C2×#394—711no—
510C2×#393—711no—
511C2×#390—711no—
512C2×#388—711no—
513C2×#388—711no—
514C2×#386—711no—
515C2×#386—711no—
516C2×#379—711no—
517C2×C4×C22⋊C4—711no—
518C71C2×#247211yescharacteristic, complemented, Sylow
519C26—711no—
520C23×Q8C2×D7111yescharacteristic, complemented
521C23×D4—711no—
522C23×D4—711no—
523C23×D4C2×D7111yescharacteristic
524C24×C4—711no—
525C24×C4—711no—
526C2×#124—28no—
527C2×#124C2×D7118yescomplemented
528C2×C22⋊Q8—718no—
529C2×C22⋊Q8—1428no—
530C2×#120—718no—
531C2×#120—1428no—
532C22×C4⋊C4—711no—
533C22×C4⋊C4—711no—
534C22×C4⋊C4—711no—
535C22×C22⋊C4—711no—
536C22×C22⋊C4—711no—
537C22×C22⋊C4—711no—
538C22×C22⋊C4—711no—
539C22×C22⋊C4—711no—
540C22×C22⋊C4—711no—
541C22×C22⋊C4—711no—
542C22×C22⋊C4—711no—
543C22×C22⋊C4—711no—
544C22×C22⋊C4—711no—
545C22×C22⋊C4—711no—
546C22×C22⋊C4—711no—
547C22×C22⋊C4—711no—
548C22×C22⋊C4—718no—
549C22×C22⋊C4—1428no—
550C22×C22⋊C4C2×D7111yescharacteristic
551C22×C22⋊C4C2×D7111yescharacteristic
552C22×C22⋊C4C2×D7111yescharacteristic, complemented
553C22×C22⋊C4C2×D7111yescharacteristic, complemented
554C22×C42—711no—
555C22×C42C2×D7111yescharacteristic, complemented
556#397—718no—
557#394—718no—
558#394—718no—
559#393—718no—
560#390—718no—
561#388—718no—
562#388—718no—
563#386—718no—
564#386—718no—
565#379—718no—
566C4×C22⋊C4—718no—
567C2×#95—711no—
568C2×#95—711no—
569C2×#95—711no—
570C2×#95—711no—
571C2×#95—711no—
572C2×#95—711no—
573C25—2842no—
574C25—2842no—
575C25—714no—
576C25—711no—
577C25—711no—
578C25—1424no—
579C25—1424no—
580C25—1424no—
581C25—1424no—
582C25—1424no—
583C25C22×D7111yescharacteristic
584C25C22×D7111yescharacteristic
585C22×Q8—24no—
586C22×Q8—24no—
587C22×Q8—42no—
588C22×Q8C22×D7114yescomplemented
589C22×D4—24no—
590C22×D4—24no—
591C22×D4—42no—
592C22×D4—2842no—
593C22×D4—714no—
594C22×D4—714no—
595C22×D4—1424no—
596C22×D4—1424no—
597C22×D4—1424no—
598C22×D4—1424no—
599C22×D4—1424no—
600C22×D4C22×D7114yes—
601C23×C4—2842no—
602C23×C4—2842no—
603C23×C4—714no—
604C23×C4—714no—
605C23×C4—711no—
606C23×C4—711no—
607C23×C4—711no—
608C23×C4—711no—
609C23×C4—711no—
610C23×C4—711no—
611C23×C4—1424no—
612C23×C4—1424no—
613C23×C4—1424no—
614C23×C4—1424no—
615C23×C4C22×D7111yescharacteristic
616C23×C4C22×D7111yescharacteristic
617C23×C4C22×D7111yescharacteristic
618C23×C4C22×D7111yescharacteristic
619C23×C4C22×D7111yescharacteristic
620#124—232no—
621C22⋊Q8—14232no—
622#120—14232no—
623C2×C4⋊C4—714no—
624C2×C4⋊C4—714no—
625C2×C4⋊C4—714no—
626C2×C4⋊C4—1424no—
627C2×C4⋊C4—1424no—
628C2×C4⋊C4—1424no—
629C2×C22⋊C4—24no—
630C2×C22⋊C4—24no—
631C2×C22⋊C4—24no—
632C2×C22⋊C4—2842no—
633C2×C22⋊C4—2842no—
634C2×C22⋊C4—2842no—
635C2×C22⋊C4—2842no—
636C2×C22⋊C4—714no—
637C2×C22⋊C4—714no—
638C2×C22⋊C4—714no—
639C2×C22⋊C4—714no—
640C2×C22⋊C4—718no—
641C2×C22⋊C4—714no—
642C2×C22⋊C4—714no—
643C2×C22⋊C4—714no—
644C2×C22⋊C4—714no—
645C2×C22⋊C4—714no—
646C2×C22⋊C4—714no—
647C2×C22⋊C4—714no—
648C2×C22⋊C4—714no—
649C2×C22⋊C4—714no—
650C2×C22⋊C4—1424no—
651C2×C22⋊C4—1424no—
652C2×C22⋊C4—1424no—
653C2×C22⋊C4—1424no—
654C2×C22⋊C4—1424no—
655C2×C22⋊C4—1424no—
656C2×C22⋊C4—1424no—
657C2×C22⋊C4—1424no—
658C2×C22⋊C4—14232no—
659C2×C22⋊C4C22⋊D7118yescomplemented
660C2×C22⋊C4C22×D7114yes—
661C2×C22⋊C4C22×D7114yes—
662C2×C22⋊C4C22×D7114yescomplemented
663C2×C22⋊C4C22×D7114yescomplemented
664C2×C42—24no—
665C2×C42—2842no—
666C2×C42—714no—
667C2×C42C22×D7114yescomplemented
668#95—714no—
669#95—714no—
670#95—714no—
671#95—714no—
672#95—714no—
673#95—714no—
674C24—22no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—22no—
679C24—22no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—22no—
684C24—22no—
685C24—22no—
686C24—22no—
687C24—28416no—
688C24—28416no—
689C24—2844no—
690C24—2844no—
691C24—28416no—
692C24—28416no—
693C24—28416no—
694C24—28416no—
695C24—714no—
696C24—714no—
697C24—714no—
698C24—712no—
699C24—714no—
700C24—712no—
701C24—1428no—
702C24—1428no—
703C24—1428no—
704C24—1428no—
705C24—14232no—
706C24—1422no—
707C24—1428no—
708C24—1422no—
709C24—1422no—
710C24—1422no—
711C24—1422no—
712C24—1422no—
713C24—1422no—
714C24—1422no—
715C24—1422no—
716C24—1422no—
717C24C2×C22⋊D7114yes—
718C24C23×D7112yes—
719C24C23×D7112yes—
720C24C23×D7111yescharacteristic
721C2×Q8—28no—
722C2×Q8—28no—
723C2×Q8—44no—
724C2×Q8—416no—
725C2×D4—28no—
726C2×D4—28no—
727C2×D4—44no—
728C2×D4—416no—
729C2×D4—28416no—
730C2×D4—2844no—
731C2×D4—28416no—
732C2×D4—1428no—
733C2×D4—1428no—
734C2×D4—1428no—
735C2×D4—1428no—
736C2×D4—1428no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—28416no—
750C22×C4—28416no—
751C22×C4—2844no—
752C22×C4—2844no—
753C22×C4—714no—
754C22×C4—712no—
755C22×C4—712no—
756C22×C4—712no—
757C22×C4—712no—
758C22×C4—712no—
759C22×C4—712no—
760C22×C4—1428no—
761C22×C4—1428no—
762C22×C4—1422no—
763C22×C4—1422no—
764C22×C4—1422no—
765C22×C4—1422no—
766C22×C4—1422no—
767C22×C4—1422no—
768C22×C4—1422no—
769C22×C4—1422no—
770C22×C4—1422no—
771C22×C4—1422no—
772C22×C4—1422no—
773C22×C4—1422no—
774C22×C4—1422no—
775C22×C4—1422no—
776C22×C4—1422no—
777C22×C4—1428no—
778C22×C4—1428no—
779C22×C4—1422no—
780C22×C4—1422no—
781C22×C4D4×D7114yes—
782C22×C4C2×C22⋊D7114yes—
783C22×C4C2×C22⋊D7114yes—
784C22×C4C23×D7112yes—
785C22×C4C23×D7112yes—
786C22×C4C23×D7112yes—
787C22×C4C23×D7112yes—
788C22×C4C23×D7112yes—
789C4⋊C4—1428no—
790C4⋊C4—1428no—
791C4⋊C4—1428no—
792C22⋊C4—28no—
793C22⋊C4—28no—
794C22⋊C4—28no—
795C22⋊C4—2844no—
796C22⋊C4—2844no—
797C22⋊C4—2844no—
798C22⋊C4—2844no—
799C22⋊C4—7116no—
800C22⋊C4—1428no—
801C22⋊C4—1428no—
802C22⋊C4—1428no—
803C22⋊C4—1428no—
804C22⋊C4—1428no—
805C22⋊C4—1428no—
806C22⋊C4—1428no—
807C22⋊C4—1428no—
808C22⋊C4C2×C22⋊D71116yescomplemented
809C42—28no—
810C42—2844no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—28no—
818C23—28no—
819C23—28no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—44no—
828C23—44no—
829C23—44no—
830C23—44no—
831C23—44no—
832C23—44no—
833C23—44no—
834C23—44no—
835C23—44no—
836C23—44no—
837C23—44no—
838C23—28416no—
839C23—28416no—
840C23—28416no—
841C23—28416no—
842C23—284128no—
843C23—28416no—
844C23—28416no—
845C23—2844no—
846C23—2844no—
847C23—2844no—
848C23—2844no—
849C23—714no—
850C23—714no—
851C23—714no—
852C23—7116no—
853C23—714no—
854C23—14232no—
855C23—1422no—
856C23—1422no—
857C23—1422no—
858C23—1422no—
859C23—1422no—
860C23—1422no—
861C23—1428no—
862C23—1428no—
863C23—1428no—
864C23—1422no—
865C23—1422no—
866C23—1422no—
867C23—1422no—
868C23—1428no—
869C23—1428no—
870C23—1428no—
871C23—1428no—
872C23—1428no—
873C23—1428no—
874C23C2×D4×D7112yes—
875C23C22×C22⋊D7114yes—
876C23C22×C22⋊D7112yes—
877C23#41×D7112yes—
878C23#41×D7112yes—
879C23#41×D7112yes—
880C23#1455617312yes—
881C23#1455617412yes—
882C23C24×D7111yescharacteristic
883Q8—416no—
884D4—416no—
885D4—28416no—
886D4—28416no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—28no—
894C2×C4—28no—
895C2×C4—28no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—44no—
903C2×C4—44no—
904C2×C4—28416no—
905C2×C4—28416no—
906C2×C4—2844no—
907C2×C4—2844no—
908C2×C4—2844no—
909C2×C4—2844no—
910C2×C4—2844no—
911C2×C4—714no—
912C2×C4—1422no—
913C2×C4—1422no—
914C2×C4—1422no—
915C2×C4—1422no—
916C2×C4—1422no—
917C2×C4—1422no—
918C2×C4—1422no—
919C2×C4—1422no—
920C2×C4—1422no—
921C2×C4—1422no—
922C2×C4—1422no—
923C2×C4—1422no—
924C2×C4—1422no—
925C2×C4—1422no—
926C2×C4—1422no—
927C2×C4—1422no—
928C2×C4—1422no—
929C2×C4—1428no—
930C2×C4C2×D4×D7114yes—
931C2×C4C22×C22⋊D7114yes—
932C2×C4C22×C22⋊D7114yes—
933C22—24no—
934C22—24no—
935C22—24no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22—416no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—88no—
949C22—28464no—
950C22—2842no—
951C22—2842no—
952C22—2842no—
953C22—2842no—
954C22—28416no—
955C22—718no—
956C22—1424no—
957C22—1424no—
958C22—1424no—
959C22—1424no—
960C22—1424no—
961C22—1424no—
962C22—1424no—
963C22—1424no—
964C22—1424no—
965C22—14232no—
966C22#1798650614yes—
967C22#124×D7114yes—
968C22#1798658314yes—
969C22D4×C22⋊D7114yes—
970C22#1798663714yes—
971C22#1798664214yes—
972C22#1798667914yes—
973C22C22×D4×D7111yescharacteristic
974C22C23×C22⋊D7111yescharacteristic
975C22C2×#41×D7111yescharacteristic
976C22C2×#41×D7111yescharacteristic
977C22C2×#41×D7111yescharacteristic
978C22C2×#1455617311yescharacteristic
979C22C2×#1455617411yescharacteristic
980C4—24no—
981C4—24no—
982C4—24no—
983C4—42no—
984C4—42no—
985C4—2842no—
986C4—2842no—
987C4—2842no—
988C4—2842no—
989C4—2842no—
990C4—1424no—
991C2—44no—
992C2—82no—
993C2—2844no—
994C2—1428no—
995C2#2259246218yesdirect product factor
996C2C2×#1798650611yescharacteristic
997C2C2×#124×D7111yescharacteristic
998C2C2×#1798658311yescharacteristic
999C2C2×D4×C22⋊D7111yescharacteristic
1000C2C2×#1798663711yescharacteristic
1001C2C2×#1798664211yescharacteristic
1002C2C2×#1798667911yescharacteristic
subgroupG/H
centerC24C23×D71
commutator, cosocleC23×C71C25
FrattiniC23C24×D71
FittingC22×#124×C71C2
socleC24×C71C24
prime radicalC22×#14556096C2
hypercenterC22×#124D71
hypocenterC71C2×#2472
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C22×#124

Complements

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

NH ≅ G/Ntype
1. C22×#14556104C2semidirect
3. C22×C22⋊C4×D71C2semidirect
4. #22592462C2direct (N × H)
5. C2×#17985927C2semidirect
6. C2×#17985915C2semidirect
7. C2×#17985913C2semidirect
8. C2×#17985910C2semidirect
9. C2×#17985899C2semidirect
10. C2×#17985892C2semidirect
11. C2×#17985890C2semidirect
12. C2×#17985875C2semidirect
13. C2×#17985875C2semidirect
14. C2×#17985854C2semidirect
15. C2×C4×(C2×D71)⋊C4C2semidirect
16. C22×#124×C71C2semidirect
23. C2×#14556104C22semidirect
26. C22×C4⋊Dic71C22semidirect
27. C22×Dic71⋊C4C22semidirect
28. C22×Dic71⋊C4C22semidirect
32. C22×C22⋊Dic71C22semidirect
33. C22×C22⋊Dic71C22semidirect
43. C2×C22⋊C4×D71C22semidirect
44. C22×C4×Dic71C22semidirect
45. #17985927C22semidirect
46. #17985915C22semidirect
47. #17985913C22semidirect
48. #17985910C22semidirect
49. #17985899C22semidirect
50. #17985892C22semidirect
51. #17985890C22semidirect
52. #17985875C22semidirect
53. #17985875C22semidirect
54. #17985854C22semidirect
55. C4×(C2×D71)⋊C4C22semidirect
56. C2×C71⋊#95C22semidirect
57. C2×C71⋊#95C22semidirect
58. C2×C71⋊#95C22semidirect
59. C2×C71⋊#95C22semidirect
60. C2×C71⋊#95C22semidirect
61. C2×C71⋊#95C22semidirect
62. C23×Q8×C71C22semidirect
65. C2×#124×C71C22semidirect
68. C22×C22⋊C4×C71C22semidirect
69. C22×C22⋊C4×C71C22semidirect
70. C22×C42×C71C22semidirect
106. C2×C4⋊Dic71C23semidirect
109. C2×Dic71⋊C4C23semidirect
110. C2×Dic71⋊C4C23semidirect
119. C2×C22⋊Dic71C23semidirect
120. C2×C22⋊Dic71C23semidirect
139. C2×C4×Dic71C23semidirect
140. C71⋊#95C23semidirect
141. C71⋊#95C23semidirect
142. C71⋊#95C23semidirect
143. C71⋊#95C23semidirect
144. C71⋊#95C23semidirect
145. C71⋊#95C23semidirect
151. C22×Q8×C71C23semidirect
165. C2×C22⋊C4×C71D4semidirect
168. C2×C22⋊C4×C71C23semidirect
169. C2×C22⋊C4×C71C23semidirect
171. C2×C42×C71C23semidirect
307. C22⋊C4×C71C2×D4semidirect
376. C22×D71#124semidirect
477. C2×D71C2×#124semidirect
492. C2×C71#2472semidirect
502. C22×#124D71semidirect
518. C71C2×#2472semidirect
520. C23×Q8C2×D71semidirect
527. C2×#124C2×D71semidirect
552. C22×C22⋊C4C2×D71semidirect
553. C22×C22⋊C4C2×D71semidirect
555. C22×C42C2×D71semidirect
588. C22×Q8C22×D71semidirect
659. C2×C22⋊C4C22⋊D71semidirect
662. C2×C22⋊C4C22×D71semidirect
663. C2×C22⋊C4C22×D71semidirect
667. C2×C42C22×D71semidirect
808. C22⋊C4C2×C22⋊D71semidirect
995. C2#22592462direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561042
C22×#145560962
C22×C22⋊C4×D712
#225924622
C2×#179859272
C2×#179859152
C2×#179859132
C2×#179859102
C2×#179858992
C2×#179858922
C2×#179858902
C2×#179858752
C2×#179858542
C2×C4×(C2×D71)⋊C42
C22×#124×C712
C2×#247271