Finite Group Databasebeta

← C2×#22592473 #32165036

Subgroups — C2×#22592473 #32165036

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×#14556117C211yesmaximal, characteristic, complemented
2C22×#14556098C211yesmaximal, characteristic
3C23×(C2×D71)⋊C4C211yesmaximal, characteristic, complemented
4#22592473C2116yesmaximal, direct product factor
5C2×#17985925C211yesmaximal, characteristic, complemented
6C2×#17985916C211yesmaximal, characteristic, complemented
7C2×#17985916C211yesmaximal, characteristic, complemented
8C2×#17985910C211yesmaximal, characteristic, complemented
9C2×#17985900C211yesmaximal, characteristic, complemented
10C2×#17985889C211yesmaximal, characteristic, complemented
11C2×#17985889C211yesmaximal, characteristic, complemented
12C2×#17985878C211yesmaximal, characteristic, complemented
13C2×#17985876C211yesmaximal, characteristic, complemented
14C2×#17985854C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×Dic71C211yesmaximal, characteristic, complemented
16C22×C22⋊Q8×C71C211yesmaximal, characteristic, complemented
17C25×D71C2211yescharacteristic
18C23×D284C2211yescharacteristic
19C23×D284C2211yescharacteristic
20C23×C22⋊D71C2211yescharacteristic
21C24×Dic71C2211yescharacteristic
22C2×#14556117—28no—
23C2×#14556117C2218yescomplemented
24C2×#14556098—28no—
25C2×#14556098C2218yes—
26C22×C22⋊Dic71C2211yescharacteristic
27C22×(C2×D71)⋊C4—28no—
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
38C22×(C2×D71)⋊C4C2218yescomplemented
39C22×(C2×D71)⋊C4C2211yescharacteristic, complemented
40C22×(C2×D71)⋊C4C2211yescharacteristic, complemented
41C22×(C2×D71)⋊C4C2211yescharacteristic, complemented
42C22×(C2×D71)⋊C4C2211yescharacteristic, complemented
43C22×C4×Dic71C2211yescharacteristic, complemented
44C22×C4×Dic71C2211yescharacteristic, complemented
45#17985925C2218yescomplemented
46#17985916C2218yescomplemented
47#17985916C2218yescomplemented
48#17985910C2218yescomplemented
49#17985900C2218yescomplemented
50#17985889C2218yescomplemented
51#17985889C2218yescomplemented
52#17985878C2218yescomplemented
53#17985876C2218yescomplemented
54#17985854C2218yescomplemented
55C22⋊C4×Dic71C2218yescomplemented
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
63C24×C4×C71C2211yescharacteristic
64C2×C22⋊Q8×C71—28no—
65C2×C22⋊Q8×C71C2218yescomplemented
66C22×C4⋊C4×C71C2211yescharacteristic, complemented
67C22×C4⋊C4×C71C2211yescharacteristic, complemented
68C22×C4⋊C4×C71C2211yescharacteristic, complemented
69C22×C22⋊C4×C71C2211yescharacteristic
70C22×C22⋊C4×C71C2211yescharacteristic
71C24×D71—24no—
72C24×D71—24no—
73C24×D71—24no—
74C24×D71—24no—
75C24×D71—24no—
76C24×D71—42no—
77C24×D71—42no—
78C24×D71C2311yescharacteristic
79C24×D71C2311yescharacteristic
80C24×D71C2311yescharacteristic
81C24×D71C2314yes—
82C22×D284—24no—
83C22×D284—24no—
84C22×D284—24no—
85C22×D284—24no—
86C22×D284—42no—
87C22×D284—42no—
88C22×D284C2314yes—
89C22×D284C2314yes—
90C22×C22⋊D71—24no—
91C22×C22⋊D71—24no—
92C22×C22⋊D71—24no—
93C22×C22⋊D71C2314yes—
94C23×Dic71—24no—
95C23×Dic71—24no—
96C23×Dic71—42no—
97C23×Dic71C2311yescharacteristic
98C23×Dic71C2311yescharacteristic
99C23×Dic71C2311yescharacteristic
100C23×Dic71C2311yescharacteristic
101C23×Dic71C2314yes—
102C23×Dic71C2311yescharacteristic
103#14556117—232no—
104#14556098—232no—
105C2×C22⋊Dic71—24no—
106C2×C22⋊Dic71C2314yes—
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—232no—
113C2×(C2×D71)⋊C4—24no—
114C2×(C2×D71)⋊C4—24no—
115C2×(C2×D71)⋊C4—24no—
116C2×(C2×D71)⋊C4—24no—
117C2×(C2×D71)⋊C4—42no—
118C2×(C2×D71)⋊C4—42no—
119C2×(C2×D71)⋊C4—42no—
120C2×(C2×D71)⋊C4—42no—
121C2×(C2×D71)⋊C4D418yescomplemented
122C2×(C2×D71)⋊C4C2314yes—
123C2×(C2×D71)⋊C4C2314yes—
124C2×(C2×D71)⋊C4C2314yes—
125C2×(C2×D71)⋊C4C2314yes—
126C2×(C2×D71)⋊C4C2314yes—
127C2×(C2×D71)⋊C4C2314yes—
128C2×(C2×D71)⋊C4C2314yes—
129C2×(C2×D71)⋊C4C2314yes—
130C2×(C2×D71)⋊C4C2314yes—
131C2×(C2×D71)⋊C4C2314yes—
132C2×(C2×D71)⋊C4C2314yescomplemented
133C2×(C2×D71)⋊C4C2314yescomplemented
134C2×(C2×D71)⋊C4C2314yescomplemented
135C2×(C2×D71)⋊C4C2314yescomplemented
136C2×C4×Dic71—24no—
137C2×C4×Dic71—42no—
138C2×C4×Dic71C2314yescomplemented
139C2×C4×Dic71C2314yescomplemented
140C71⋊#95C2314yescomplemented
141C71⋊#95C2314yescomplemented
142C71⋊#95C2314yescomplemented
143C71⋊#95C2314yescomplemented
144C71⋊#95C2314yescomplemented
145C71⋊#95C2314yescomplemented
146C25×C71C2311yescharacteristic
147C22×Q8×C71—24no—
148C22×Q8×C71—24no—
149C22×Q8×C71—42no—
150C22×Q8×C71C2314yescomplemented
151C23×C4×C71—24no—
152C23×C4×C71—24no—
153C23×C4×C71—42no—
154C23×C4×C71C2311yescharacteristic
155C23×C4×C71C2311yescharacteristic
156C23×C4×C71C2311yescharacteristic
157C23×C4×C71C2314yes—
158C23×C4×C71C2311yescharacteristic
159C23×C4×C71C2311yescharacteristic
160C23×C4×C71C2311yescharacteristic
161C22⋊Q8×C71—232no—
162C2×C4⋊C4×C71—24no—
163C2×C4⋊C4×C71—24no—
164C2×C4⋊C4×C71—24no—
165C2×C4⋊C4×C71C2314yescomplemented
166C2×C4⋊C4×C71C2314yescomplemented
167C2×C4⋊C4×C71C2314yescomplemented
168C2×C22⋊C4×C71—24no—
169C2×C22⋊C4×C71D418yes—
170C2×C22⋊C4×C71C2314yes—
171C2×C22⋊C4×C71C2314yes—
172C23×D71—232no—
173C23×D71—22no—
174C23×D71—22no—
175C23×D71—22no—
176C23×D71—22no—
177C23×D71—28no—
178C23×D71—22no—
179C23×D71—22no—
180C23×D71—22no—
181C23×D71—22no—
182C23×D71—22no—
183C23×D71—22no—
184C23×D71—22no—
185C23×D71—22no—
186C23×D71—28no—
187C23×D71—28no—
188C23×D71—22no—
189C23×D71—22no—
190C23×D71—28no—
191C23×D71—22no—
192C23×D71—22no—
193C23×D71—22no—
194C23×D71—28no—
195C23×D71—22no—
196C23×D71—22no—
197C23×D71—44no—
198C23×D71—44no—
199C23×D71—416no—
200C23×D71—416no—
201C23×D71—416no—
202C23×D71—416no—
203C23×D71—416no—
204C23×D71—416no—
205C23×D71C2×D414yes—
206C23×D71#4114yes—
207C23×D71C2412yes—
208C23×D71C2412yes—
209C23×D71C2412yes—
210C2×D284—28no—
211C2×D284—28no—
212C2×D284—28no—
213C2×D284—28no—
214C2×D284—44no—
215C2×D284—44no—
216C2×D284—416no—
217C2×D284—416no—
218C2×C22⋊D71—28no—
219C2×C22⋊D71—28no—
220C2×C22⋊D71—28no—
221C2×C22⋊D71—416no—
222C22×Dic71—22no—
223C22×Dic71—22no—
224C22×Dic71—22no—
225C22×Dic71—22no—
226C22×Dic71—22no—
227C22×Dic71—28no—
228C22×Dic71—22no—
229C22×Dic71—22no—
230C22×Dic71—22no—
231C22×Dic71—22no—
232C22×Dic71—22no—
233C22×Dic71—22no—
234C22×Dic71—22no—
235C22×Dic71—22no—
236C22×Dic71—22no—
237C22×Dic71—28no—
238C22×Dic71—44no—
239C22×Dic71—416no—
240C22×Dic71C2×D414yes—
241C22×Dic71C2412yes—
242C22×Dic71C2412yes—
243C22×Dic71C2412yes—
244C22×Dic71C2412yes—
245C22×Dic71C2412yes—
246C22⋊Dic71—28no—
247(C2×D71)⋊C4—28no—
248(C2×D71)⋊C4—28no—
249(C2×D71)⋊C4—28no—
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)⋊C4—44no—
258(C2×D71)⋊C4—44no—
259(C2×D71)⋊C4—44no—
260(C2×D71)⋊C4C2×D4116yescomplemented
261C4×Dic71—28no—
262C4×Dic71—44no—
263C24×C71—22no—
264C24×C71—22no—
265C24×C71—22no—
266C24×C71—22no—
267C24×C71C2×D414yes—
268C24×C71#4114yes—
269C24×C71#4114yes—
270C24×C71C2412yes—
271C24×C71C2411yescharacteristic
272C2×Q8×C71—28no—
273C2×Q8×C71—28no—
274C2×Q8×C71—44no—
275C2×Q8×C71—416no—
276C22×C4×C71—22no—
277C22×C4×C71—22no—
278C22×C4×C71—22no—
279C22×C4×C71—22no—
280C22×C4×C71—22no—
281C22×C4×C71—22no—
282C22×C4×C71—22no—
283C22×C4×C71—22no—
284C22×C4×C71—22no—
285C22×C4×C71—28no—
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—28no—
293C22×C4×C71—44no—
294C22×C4×C71—416no—
295C22×C4×C71C2×D414yes—
296C22×C4×C71C2×D414yes—
297C22×C4×C71C2×D414yes—
298C22×C4×C71C2412yes—
299C22×C4×C71C2412yes—
300C22×C4×C71C2412yes—
301C22×C4×C71C2412yes—
302C22×C4×C71C2412yes—
303C22×C4×C71C2412yes—
304C4⋊C4×C71—28no—
305C4⋊C4×C71—28no—
306C4⋊C4×C71—28no—
307C22⋊C4×C71—28no—
308C22⋊C4×C71C2×D4116yes—
309C23×C71—28no—
310C23×C71—28no—
311C23×C71—28no—
312C23×C71—28no—
313C23×C71—28no—
314C23×C71—28no—
315C23×C71—22no—
316C23×C71—22no—
317C23×C71—22no—
318C23×C71—22no—
319C23×C71#124116yescomplemented
320C23×C71C22×D412yes—
321C23×C71C22×D414yes—
322C23×C71C22×D412yes—
323C23×C71C2×#4112yes—
324C23×C71C2×#4114yes—
325C23×C71C2×#4114yes—
326C23×C71C2×#4112yes—
327C23×C71C2×#4112yes—
328C23×C71H(5,𝔽2)12yes—
329C23×C71H(5,𝔽2)12yes—
330C23×C71C2511yescharacteristic
331C22×D71—232no—
332C22×D71—28no—
333C22×D71—28no—
334C22×D71—28no—
335C22×D71—28no—
336C22×D71—28no—
337C22×D71—28no—
338C22×D71—22no—
339C22×D71—22no—
340C22×D71—22no—
341C22×D71—22no—
342C22×D71—22no—
343C22×D71—22no—
344C22×D71—22no—
345C22×D71—22no—
346C22×D71—22no—
347C22×D71—22no—
348C22×D71—22no—
349C22×D71—22no—
350C22×D71—22no—
351C22×D71—22no—
352C22×D71—22no—
353C22×D71—22no—
354C22×D71—22no—
355C22×D71—22no—
356C22×D71—22no—
357C22×D71—416no—
358C22×D71—416no—
359C22×D71—416no—
360C22×D71—416no—
361C22×D71—416no—
362C22×D71—4128no—
363C22×D71—44no—
364C22×D71—44no—
365C22×D71—416no—
366C22×D71—44no—
367C22×D71—44no—
368C22×D71—44no—
369C22×D71—44no—
370C22×D71—44no—
371C22×D71—44no—
372C22×D71—44no—
373C22×D71—44no—
374C22×D71—44no—
375C22×D71—44no—
376C22×D71—44no—
377C22×D71—44no—
378C22×D71—44no—
379C22×D71C22×D414yes—
380C22×D71C2×#4114yes—
381Q8×C71—416no—
382C2×C4×C71—28no—
383C2×C4×C71—28no—
384C2×C4×C71—28no—
385C2×C4×C71—22no—
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—22no—
399C2×C4×C71—22no—
400C2×C4×C71—416no—
401C2×C4×C71—44no—
402C2×C4×C71—44no—
403C2×C4×C71—44no—
404C2×C4×C71C22×D414yes—
405C2×C4×C71C22×D414yes—
406C2×C4×C71C22×D414yes—
407C22⋊D71—416no—
408C2×Dic71—28no—
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—416no—
424C2×Dic71—44no—
425C2×Dic71—44no—
426C2×Dic71—44no—
427C2×Dic71—44no—
428C2×Dic71C22×D414yes—
429D284—416no—
430D284—416no—
431C22×C71—24no—
432C22×C71—24no—
433C22×C71—24no—
434C22×C71—24no—
435C22×C71—24no—
436C22×C71—24no—
437C22×C71—232no—
438C22×C71#52514yes—
439C22×C71C2×#12414yes—
440C22×C71C2×#12418yescomplemented
441C22×C71#53814yes—
442C22×C71D4214yes—
443C22×C71#54614yes—
444C22×C71#54614yes—
445C22×C71#55114yes—
446C22×C71C23×D411yescharacteristic
447C22×C71C23×D411yescharacteristic
448C22×C71C22×#4111yescharacteristic
449C22×C71C22×#4111yescharacteristic
450C22×C71C22×#4111yescharacteristic
451C22×C71C2×H(5,𝔽2)11yescharacteristic
452C22×C71C2×H(5,𝔽2)11yescharacteristic
453C2×D71—24no—
454C2×D71—24no—
455C2×D71—24no—
456C2×D71—24no—
457C2×D71—24no—
458C2×D71—24no—
459C2×D71—464no—
460C2×D71—42no—
461C2×D71—42no—
462C2×D71—42no—
463C2×D71—42no—
464C2×D71—42no—
465C2×D71—42no—
466C2×D71—42no—
467C2×D71—42no—
468C2×D71—416no—
469C2×D71—416no—
470C2×D71—42no—
471C2×D71—42no—
472C2×D71—42no—
473C2×D71—42no—
474C2×D71—42no—
475C2×D71—42no—
476C2×D71—42no—
477C2×D71—88no—
478C4×C71—24no—
479C4×C71—24no—
480C4×C71—24no—
481C4×C71—42no—
482C4×C71—42no—
483C4×C71—42no—
484Dic71—24no—
485Dic71—42no—
486Dic71—42no—
487Dic71—42no—
488Dic71—42no—
489C2×#2472—711nomaximal, Sylow
490C2×C71—28no—
491C2×C71#247218yescomplemented
492C2×C71C2×#52511yescharacteristic
493C2×C71C22×#12411yescharacteristic
494C2×C71C2×#53811yescharacteristic
495C2×C71C2×D4211yescharacteristic
496C2×C71C2×#54611yescharacteristic
497C2×C71C2×#54611yescharacteristic
498C2×C71C2×#55111yescharacteristic
499D71—44no—
500D71—44no—
501D71—82no—
502C22×#124—711no—
503C22×C22⋊Q8D7111yescharacteristic, complemented
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×D4—711no—
524C24×C4—711no—
525C24×C4C2×D7111yescharacteristic
526C2×#124—718no—
527C2×#124—1428no—
528C2×C22⋊Q8—28no—
529C2×C22⋊Q8C2×D7118yescomplemented
530C2×#120—718no—
531C2×#120—1428no—
532C22×C4⋊C4C2×D7111yescharacteristic, complemented
533C22×C4⋊C4C2×D7111yescharacteristic, complemented
534C22×C4⋊C4C2×D7111yescharacteristic, complemented
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—711no—
549C22×C22⋊C4—718no—
550C22×C22⋊C4—711no—
551C22×C22⋊C4—1428no—
552C22×C22⋊C4C2×D7111yescharacteristic
553C22×C22⋊C4C2×D7111yescharacteristic
554C22×C42—711no—
555C22×C42—711no—
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—711no—
579C25—1424no—
580C25—1424no—
581C25—1424no—
582C25—1424no—
583C25—1424no—
584C25C22×D7111yescharacteristic
585C22×Q8—24no—
586C22×Q8—24no—
587C22×Q8—42no—
588C22×Q8C22×D7114yescomplemented
589C22×D4—2842no—
590C22×D4—2842no—
591C22×D4—714no—
592C22×D4—714no—
593C22×D4—714no—
594C22×D4—1424no—
595C22×D4—1424no—
596C22×D4—1424no—
597C22×D4—1424no—
598C22×D4—1424no—
599C22×D4—1424no—
600C22×D4—1424no—
601C23×C4—24no—
602C23×C4—24no—
603C23×C4—42no—
604C23×C4—2842no—
605C23×C4—714no—
606C23×C4—711no—
607C23×C4—711no—
608C23×C4—711no—
609C23×C4—711no—
610C23×C4—711no—
611C23×C4—1424no—
612C23×C4—1424no—
613C23×C4C22×D7111yescharacteristic
614C23×C4C22×D7111yescharacteristic
615C23×C4C22×D7111yescharacteristic
616C23×C4C22×D7114yes—
617C23×C4C22×D7111yescharacteristic
618C23×C4C22×D7111yescharacteristic
619C23×C4C22×D7111yescharacteristic
620#124—14232no—
621C22⋊Q8—232no—
622#120—14232no—
623C2×C4⋊C4—24no—
624C2×C4⋊C4—24no—
625C2×C4⋊C4—24no—
626C2×C4⋊C4C22×D7114yescomplemented
627C2×C4⋊C4C22×D7114yescomplemented
628C2×C4⋊C4C22×D7114yescomplemented
629C2×C22⋊C4—24no—
630C2×C22⋊C4—2842no—
631C2×C22⋊C4—2842no—
632C2×C22⋊C4—2842no—
633C2×C22⋊C4—2842no—
634C2×C22⋊C4—714no—
635C2×C22⋊C4—714no—
636C2×C22⋊C4—714no—
637C2×C22⋊C4—714no—
638C2×C22⋊C4—718no—
639C2×C22⋊C4—714no—
640C2×C22⋊C4—714no—
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—14232no—
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—1424no—
659C2×C22⋊C4—1424no—
660C2×C22⋊C4—1424no—
661C2×C22⋊C4C22⋊D7118yes—
662C2×C22⋊C4C22×D7114yes—
663C2×C22⋊C4C22×D7114yes—
664C2×C42—2842no—
665C2×C42—714no—
666C2×C42—714no—
667C2×C42—1424no—
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—28416no—
679C24—28416no—
680C24—28416no—
681C24—28416no—
682C24—28416no—
683C24—2844no—
684C24—2844no—
685C24—28416no—
686C24—714no—
687C24—714no—
688C24—712no—
689C24—712no—
690C24—712no—
691C24—1428no—
692C24—1428no—
693C24—14232no—
694C24—1422no—
695C24—1428no—
696C24—1422no—
697C24—1422no—
698C24—1422no—
699C24—1422no—
700C24—1428no—
701C24—1422no—
702C24—1422no—
703C24—1422no—
704C24—1422no—
705C24—1422no—
706C24—1422no—
707C24—1428no—
708C24—1422no—
709C24—1422no—
710C24—1422no—
711C24—1422no—
712C24—1422no—
713C24—1422no—
714C24—1422no—
715C24—1422no—
716C24C2×C22⋊D7114yes—
717C24#1176586614yes—
718C24#1176586614yes—
719C24C23×D7112yes—
720C24C23×D7111yescharacteristic
721C2×Q8—28no—
722C2×Q8—28no—
723C2×Q8—44no—
724C2×Q8—416no—
725C2×D4—28416no—
726C2×D4—28416no—
727C2×D4—2844no—
728C2×D4—2844no—
729C2×D4—28416no—
730C2×D4—1428no—
731C2×D4—1428no—
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—28no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—28no—
754C22×C4—44no—
755C22×C4—416no—
756C22×C4—28416no—
757C22×C4—2844no—
758C22×C4—714no—
759C22×C4—712no—
760C22×C4—712no—
761C22×C4—712no—
762C22×C4—712no—
763C22×C4—712no—
764C22×C4—1428no—
765C22×C4—1422no—
766C22×C4—1422no—
767C22×C4—1422no—
768C22×C4—1422no—
769C22×C4—1422no—
770C22×C4—1422no—
771C22×C4—1422no—
772C22×C4—1428no—
773C22×C4—1422no—
774C22×C4—1422no—
775C22×C4—1422no—
776C22×C4—1422no—
777C22×C4—1422no—
778C22×C4—1422no—
779C22×C4—1422no—
780C22×C4D4×D7114yes—
781C22×C4C2×C22⋊D7114yes—
782C22×C4C2×C22⋊D7114yes—
783C22×C4C23×D7112yes—
784C22×C4C23×D7112yes—
785C22×C4C23×D7112yes—
786C22×C4C23×D7112yes—
787C22×C4C23×D7112yes—
788C22×C4C23×D7112yes—
789C4⋊C4—28no—
790C4⋊C4—28no—
791C4⋊C4—28no—
792C22⋊C4—28no—
793C22⋊C4—2844no—
794C22⋊C4—2844no—
795C22⋊C4—2844no—
796C22⋊C4—2844no—
797C22⋊C4—7116no—
798C22⋊C4—1428no—
799C22⋊C4—1428no—
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⋊D71116yes—
809C42—2844no—
810C42—1428no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—28no—
816C23—28no—
817C23—28no—
818C23—28no—
819C23—28no—
820C23—28no—
821C23—28416no—
822C23—284128no—
823C23—28416no—
824C23—28416no—
825C23—28416no—
826C23—28416no—
827C23—2844no—
828C23—2844no—
829C23—2844no—
830C23—2844no—
831C23—2844no—
832C23—2844no—
833C23—2844no—
834C23—2844no—
835C23—28416no—
836C23—2844no—
837C23—2844no—
838C23—2844no—
839C23—2844no—
840C23—2844no—
841C23—2844no—
842C23—2844no—
843C23—714no—
844C23—714no—
845C23—14232no—
846C23—1422no—
847C23—1422no—
848C23—1422no—
849C23—1422no—
850C23—1422no—
851C23—1422no—
852C23—1422no—
853C23—1422no—
854C23—1422no—
855C23—1422no—
856C23—1422no—
857C23—1422no—
858C23—1422no—
859C23—1422no—
860C23—1422no—
861C23—1422no—
862C23—1422no—
863C23—1422no—
864C23—1422no—
865C23—1428no—
866C23—1428no—
867C23—1428no—
868C23—1428no—
869C23—1428no—
870C23—1428no—
871C23#14556117116yescomplemented
872C23C2×D4×D7112yes—
873C23C22×C22⋊D7114yes—
874C23C22×C22⋊D7112yes—
875C23#41×D7112yes—
876C23C2×#1176586614yes—
877C23C2×#1176586614yes—
878C23C2×#1176586612yes—
879C23C2×#1176586612yes—
880C23#1455617312yes—
881C23#1455617412yes—
882C23C24×D7111yescharacteristic
883Q8—416no—
884D4—28416no—
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—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—416no—
906C2×C4—44no—
907C2×C4—44no—
908C2×C4—44no—
909C2×C4—2844no—
910C2×C4—2844no—
911C2×C4—2844no—
912C2×C4—2844no—
913C2×C4—28416no—
914C2×C4—714no—
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—24no—
937C22—24no—
938C22—24no—
939C22—232no—
940C22—28464no—
941C22—2842no—
942C22—2842no—
943C22—2842no—
944C22—2842no—
945C22—2842no—
946C22—2842no—
947C22—2842no—
948C22—2842no—
949C22—28416no—
950C22—28416no—
951C22—2842no—
952C22—2842no—
953C22—2842no—
954C22—2842no—
955C22—2842no—
956C22—2842no—
957C22—2842no—
958C22—5688no—
959C22—1424no—
960C22—1424no—
961C22—1424no—
962C22—1424no—
963C22—1424no—
964C22—1424no—
965C22#1798651214yes—
966C22C2×#1455611714yes—
967C22C2×#1455611718yescomplemented
968C22#1798658914yes—
969C22D4×C22⋊D7114yes—
970C22#1798663714yes—
971C22#1798664014yes—
972C22#1798667614yes—
973C22C22×D4×D7111yescharacteristic
974C22C23×C22⋊D7111yescharacteristic
975C22C2×#41×D7111yescharacteristic
976C22C22×#1176586611yescharacteristic
977C22C22×#1176586611yescharacteristic
978C22C2×#1455617311yescharacteristic
979C22C2×#1455617411yescharacteristic
980C4—24no—
981C4—24no—
982C4—24no—
983C4—42no—
984C4—42no—
985C4—42no—
986C4—2842no—
987C4—2842no—
988C4—2842no—
989C4—2842no—
990C4—1424no—
991C2—28no—
992C2—2844no—
993C2—2844no—
994C2—5682no—
995C2#2259247318yesdirect product factor
996C2C2×#1798651211yescharacteristic
997C2C22×#1455611711yescharacteristic
998C2C2×#1798658911yescharacteristic
999C2C2×D4×C22⋊D7111yescharacteristic
1000C2C2×#1798663711yescharacteristic
1001C2C2×#1798664011yescharacteristic
1002C2C2×#1798667611yescharacteristic
subgroupG/H
centerC24C23×D71
commutator, cosocleC23×C71C25
FrattiniC23C24×D71
FittingC22×C22⋊Q8×C71C2
socleC24×C71C24
prime radicalC22×#14556098C2
hypercenterC22×C22⋊Q8D71
hypocenterC71C2×#2472
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×#14556117C2semidirect
3. C23×(C2×D71)⋊C4C2semidirect
4. #22592473C2direct (N × H)
5. C2×#17985925C2semidirect
6. C2×#17985916C2semidirect
7. C2×#17985916C2semidirect
8. C2×#17985910C2semidirect
9. C2×#17985900C2semidirect
10. C2×#17985889C2semidirect
11. C2×#17985889C2semidirect
12. C2×#17985878C2semidirect
13. C2×#17985876C2semidirect
14. C2×#17985854C2semidirect
15. C2×C22⋊C4×Dic71C2semidirect
16. C22×C22⋊Q8×C71C2semidirect
23. C2×#14556117C22semidirect
38. C22×(C2×D71)⋊C4C22semidirect
39. C22×(C2×D71)⋊C4C22semidirect
40. C22×(C2×D71)⋊C4C22semidirect
41. C22×(C2×D71)⋊C4C22semidirect
42. C22×(C2×D71)⋊C4C22semidirect
43. C22×C4×Dic71C22semidirect
44. C22×C4×Dic71C22semidirect
45. #17985925C22semidirect
46. #17985916C22semidirect
47. #17985916C22semidirect
48. #17985910C22semidirect
49. #17985900C22semidirect
50. #17985889C22semidirect
51. #17985889C22semidirect
52. #17985878C22semidirect
53. #17985876C22semidirect
54. #17985854C22semidirect
55. C22⋊C4×Dic71C22semidirect
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×C22⋊Q8×C71C22semidirect
66. C22×C4⋊C4×C71C22semidirect
67. C22×C4⋊C4×C71C22semidirect
68. C22×C4⋊C4×C71C22semidirect
121. C2×(C2×D71)⋊C4D4semidirect
132. C2×(C2×D71)⋊C4C23semidirect
133. C2×(C2×D71)⋊C4C23semidirect
134. C2×(C2×D71)⋊C4C23semidirect
135. C2×(C2×D71)⋊C4C23semidirect
138. C2×C4×Dic71C23semidirect
139. C2×C4×Dic71C23semidirect
140. C71⋊#95C23semidirect
141. C71⋊#95C23semidirect
142. C71⋊#95C23semidirect
143. C71⋊#95C23semidirect
144. C71⋊#95C23semidirect
145. C71⋊#95C23semidirect
150. C22×Q8×C71C23semidirect
165. C2×C4⋊C4×C71C23semidirect
166. C2×C4⋊C4×C71C23semidirect
167. C2×C4⋊C4×C71C23semidirect
260. (C2×D71)⋊C4C2×D4semidirect
319. C23×C71#124semidirect
440. C22×C71C2×#124semidirect
491. C2×C71#2472semidirect
503. C22×C22⋊Q8D71semidirect
518. C71C2×#2472semidirect
520. C23×Q8C2×D71semidirect
529. C2×C22⋊Q8C2×D71semidirect
532. C22×C4⋊C4C2×D71semidirect
533. C22×C4⋊C4C2×D71semidirect
534. C22×C4⋊C4C2×D71semidirect
588. C22×Q8C22×D71semidirect
626. C2×C4⋊C4C22×D71semidirect
627. C2×C4⋊C4C22×D71semidirect
628. C2×C4⋊C4C22×D71semidirect
871. C23#14556117semidirect
967. C22C2×#14556117semidirect
995. C2#22592473direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561172
C22×#145560982
C23×(C2×D71)⋊C42
#225924732
C2×#179859252
C2×#179859162
C2×#179859102
C2×#179859002
C2×#179858892
C2×#179858782
C2×#179858762
C2×#179858542
C2×C22⋊C4×Dic712
C22×C22⋊Q8×C712
C2×#247271