Finite Group Databasebeta

← C2×#22592003 #32164874

Subgroups — C2×#22592003 #32164874

Order 18176.

4926 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556104C211yesmaximal, characteristic, complemented
2C23×(C2×D71)⋊C4C211yesmaximal, characteristic
3C22×C22⋊C4×D71C211yesmaximal, characteristic
4#22592003C2116yesmaximal, direct product factor
5C2×#17985934C211yesmaximal, characteristic, complemented
6C2×#17985921C211yesmaximal, characteristic, complemented
7C2×#17985921C211yesmaximal, characteristic, complemented
8C2×#17985910C211yesmaximal, characteristic, complemented
9C2×#17985874C211yesmaximal, characteristic, complemented
10C2×#17985872C211yesmaximal, characteristic, complemented
11C2×#17985870C211yesmaximal, characteristic, complemented
12C2×#17985870C211yesmaximal, characteristic, complemented
13C2×#17985857C211yesmaximal, characteristic, complemented
14C2×#17985856C211yesmaximal, characteristic, complemented
15C2×#17985854C211yesmaximal, characteristic
16C22×C22⋊Q8×C71C211yesmaximal, characteristic, complemented
17C25×D71C2211yescharacteristic
18C24×Dic71C2211yescharacteristic
19C23×C4×D71C2211yescharacteristic
20C23×C4×D71C2211yescharacteristic
21C2×#14556104—28no—
22C2×#14556104C2218yescomplemented
23C22×C4⋊Dic71C2211yescharacteristic, complemented
24C22×C4⋊Dic71C2211yescharacteristic, complemented
25C22×Dic71⋊C4C2211yescharacteristic, complemented
26C22×Dic71⋊C4C2211yescharacteristic, complemented
27C22×Dic71⋊C4C2211yescharacteristic, complemented
28C22×Dic71⋊C4C2211yescharacteristic, complemented
29C22×C22⋊Dic71C2211yescharacteristic
30C22×C22⋊Dic71C2211yescharacteristic
31C22×(C2×D71)⋊C4—28no—
32C22×(C2×D71)⋊C4C2218yes—
33C22×(C2×D71)⋊C4C2211yescharacteristic
34C22×(C2×D71)⋊C4C2211yescharacteristic
35C22×(C2×D71)⋊C4C2211yescharacteristic
36C22×(C2×D71)⋊C4C2211yescharacteristic
37C22×(C2×D71)⋊C4C2211yescharacteristic
38C22×(C2×D71)⋊C4C2211yescharacteristic
39C22×(C2×D71)⋊C4C2211yescharacteristic
40C22×(C2×D71)⋊C4C2211yescharacteristic
41C22×(C2×D71)⋊C4C2211yescharacteristic
42C22×(C2×D71)⋊C4C2211yescharacteristic
43C2×C22⋊C4×D71—28no—
44C2×C22⋊C4×D71C2218yes—
45#17985934C2218yescomplemented
46#17985921C2218yescomplemented
47#17985921C2218yescomplemented
48#17985910C2218yescomplemented
49#17985874C2218yescomplemented
50#17985872C2218yescomplemented
51#17985870C2218yescomplemented
52#17985870C2218yescomplemented
53#17985857C2218yescomplemented
54#17985856C2218yescomplemented
55#17985854C2218yes—
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—42no—
76C24×D71—42no—
77C24×D71Q818yescomplemented
78C24×D71C2311yescharacteristic
79C24×D71C2314yes—
80C24×D71C2311yescharacteristic
81C23×Dic71—24no—
82C23×Dic71—24no—
83C23×Dic71—42no—
84C23×Dic71C2311yescharacteristic
85C23×Dic71C2311yescharacteristic
86C23×Dic71C2311yescharacteristic
87C23×Dic71C2311yescharacteristic
88C23×Dic71C2311yescharacteristic
89C23×Dic71C2314yes—
90C23×Dic71C2311yescharacteristic
91C22×C4×D71—24no—
92C22×C4×D71—24no—
93C22×C4×D71—24no—
94C22×C4×D71—24no—
95C22×C4×D71—42no—
96C22×C4×D71—42no—
97C22×C4×D71C2314yes—
98C22×C4×D71C2314yes—
99#14556104—232no—
100C2×C4⋊Dic71—24no—
101C2×C4⋊Dic71—42no—
102C2×C4⋊Dic71C2314yescomplemented
103C2×C4⋊Dic71C2314yescomplemented
104C2×Dic71⋊C4—24no—
105C2×Dic71⋊C4—24no—
106C2×Dic71⋊C4—42no—
107C2×Dic71⋊C4—42no—
108C2×Dic71⋊C4C2314yescomplemented
109C2×Dic71⋊C4C2314yescomplemented
110C2×Dic71⋊C4C2314yescomplemented
111C2×Dic71⋊C4C2314yescomplemented
112C2×C22⋊Dic71—24no—
113C2×C22⋊Dic71—24no—
114C2×C22⋊Dic71C2314yes—
115C2×C22⋊Dic71C2314yes—
116C2×(C2×D71)⋊C4—24no—
117C2×(C2×D71)⋊C4—24no—
118C2×(C2×D71)⋊C4—24no—
119C2×(C2×D71)⋊C4—24no—
120C2×(C2×D71)⋊C4—232no—
121C2×(C2×D71)⋊C4—24no—
122C2×(C2×D71)⋊C4—24no—
123C2×(C2×D71)⋊C4—24no—
124C2×(C2×D71)⋊C4—42no—
125C2×(C2×D71)⋊C4—42no—
126C2×(C2×D71)⋊C4D418yes—
127C2×(C2×D71)⋊C4C2314yes—
128C2×(C2×D71)⋊C4C2314yes—
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—
138C71⋊#95C2314yescomplemented
139C71⋊#95C2314yescomplemented
140C71⋊#95C2314yescomplemented
141C71⋊#95C2314yescomplemented
142C71⋊#95C2314yescomplemented
143C71⋊#95C2314yescomplemented
144C25×C71C2311yescharacteristic
145C22×Q8×C71—24no—
146C22×Q8×C71—24no—
147C22×Q8×C71—42no—
148C22×Q8×C71C2314yescomplemented
149C23×C4×C71—24no—
150C23×C4×C71—24no—
151C23×C4×C71—42no—
152C23×C4×C71C2311yescharacteristic
153C23×C4×C71C2311yescharacteristic
154C23×C4×C71C2311yescharacteristic
155C23×C4×C71C2314yes—
156C23×C4×C71C2311yescharacteristic
157C23×C4×C71C2311yescharacteristic
158C23×C4×C71C2311yescharacteristic
159C22⋊Q8×C71—232no—
160C2×C4⋊C4×C71—24no—
161C2×C4⋊C4×C71—24no—
162C2×C4⋊C4×C71—24no—
163C2×C4⋊C4×C71C2314yescomplemented
164C2×C4⋊C4×C71C2314yescomplemented
165C2×C4⋊C4×C71C2314yescomplemented
166C2×C22⋊C4×C71—24no—
167C2×C22⋊C4×C71D418yes—
168C2×C22⋊C4×C71C2314yes—
169C2×C22⋊C4×C71C2314yes—
170C23×D71—22no—
171C23×D71—22no—
172C23×D71—22no—
173C23×D71—22no—
174C23×D71—232no—
175C23×D71—28no—
176C23×D71—22no—
177C23×D71—22no—
178C23×D71—22no—
179C23×D71—28no—
180C23×D71—22no—
181C23×D71—22no—
182C23×D71—22no—
183C23×D71—232no—
184C23×D71—28no—
185C23×D71—28no—
186C23×D71—416no—
187C23×D71—44no—
188C23×D71—44no—
189C23×D71—416no—
190C23×D71—416no—
191C23×D71—416no—
192C23×D71—416no—
193C23×D71C2×D414yes—
194C23×D71C2×Q814yes—
195C23×D71C2×Q814yes—
196C23×D71C2×Q8116yescomplemented
197C23×D71#4114yes—
198C23×D71C2412yes—
199C23×D71C2412yes—
200C22×Dic71—22no—
201C22×Dic71—22no—
202C22×Dic71—22no—
203C22×Dic71—22no—
204C22×Dic71—22no—
205C22×Dic71—22no—
206C22×Dic71—22no—
207C22×Dic71—22no—
208C22×Dic71—28no—
209C22×Dic71—22no—
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—28no—
219C22×Dic71—44no—
220C22×Dic71—416no—
221C22×Dic71C2×D414yes—
222C22×Dic71C2412yes—
223C22×Dic71C2412yes—
224C22×Dic71C2412yes—
225C22×Dic71C2412yes—
226C22×Dic71C2412yes—
227C22×Dic71C2412yes—
228C2×C4×D71—28no—
229C2×C4×D71—28no—
230C2×C4×D71—28no—
231C2×C4×D71—28no—
232C2×C4×D71—44no—
233C2×C4×D71—44no—
234C2×C4×D71—416no—
235C2×C4×D71—416no—
236C4⋊Dic71—28no—
237C4⋊Dic71—44no—
238Dic71⋊C4—28no—
239Dic71⋊C4—28no—
240Dic71⋊C4—44no—
241Dic71⋊C4—44no—
242C22⋊Dic71—28no—
243C22⋊Dic71—28no—
244(C2×D71)⋊C4—28no—
245(C2×D71)⋊C4—28no—
246(C2×D71)⋊C4—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—44no—
252(C2×D71)⋊C4—44no—
253(C2×D71)⋊C4C2×D4116yes—
254C24×C71—22no—
255C24×C71—22no—
256C24×C71—22no—
257C24×C71—22no—
258C24×C71C2×D414yes—
259C24×C71C2×Q814yes—
260C24×C71#4114yes—
261C24×C71C2412yes—
262C24×C71C2411yescharacteristic
263C2×Q8×C71—28no—
264C2×Q8×C71—28no—
265C2×Q8×C71—44no—
266C2×Q8×C71—416no—
267C22×C4×C71—22no—
268C22×C4×C71—22no—
269C22×C4×C71—22no—
270C22×C4×C71—22no—
271C22×C4×C71—22no—
272C22×C4×C71—22no—
273C22×C4×C71—22no—
274C22×C4×C71—22no—
275C22×C4×C71—22no—
276C22×C4×C71—28no—
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—28no—
284C22×C4×C71—44no—
285C22×C4×C71—416no—
286C22×C4×C71C2×D414yes—
287C22×C4×C71C2×D414yes—
288C22×C4×C71C2×D414yes—
289C22×C4×C71C2412yes—
290C22×C4×C71C2412yes—
291C22×C4×C71C2412yes—
292C22×C4×C71C2412yes—
293C22×C4×C71C2412yes—
294C22×C4×C71C2412yes—
295C4⋊C4×C71—28no—
296C4⋊C4×C71—28no—
297C4⋊C4×C71—28no—
298C22⋊C4×C71—28no—
299C22⋊C4×C71C2×D4116yes—
300C23×C71—28no—
301C23×C71—28no—
302C23×C71—28no—
303C23×C71—28no—
304C23×C71—28no—
305C23×C71—28no—
306C23×C71—22no—
307C23×C71—22no—
308C23×C71—22no—
309C23×C71—22no—
310C23×C71C22⋊Q8116yescomplemented
311C23×C71C22×D412yes—
312C23×C71C22×D414yes—
313C23×C71C22×D412yes—
314C23×C71C22×Q814yes—
315C23×C71C22×Q812yes—
316C23×C71C2×#4112yes—
317C23×C71C2×#4114yes—
318C23×C71C2×#4112yes—
319C23×C71H(5,𝔽2)12yes—
320C23×C71H(5,𝔽2)12yes—
321C23×C71C2511yescharacteristic
322C22×D71—28no—
323C22×D71—28no—
324C22×D71—28no—
325C22×D71—28no—
326C22×D71—28no—
327C22×D71—28no—
328C22×D71—22no—
329C22×D71—22no—
330C22×D71—22no—
331C22×D71—22no—
332C22×D71—28no—
333C22×D71—28no—
334C22×D71—232no—
335C22×D71—28no—
336C22×D71—22no—
337C22×D71—22no—
338C22×D71—22no—
339C22×D71—22no—
340C22×D71—22no—
341C22×D71—22no—
342C22×D71—232no—
343C22×D71—416no—
344C22×D71—4128no—
345C22×D71—416no—
346C22×D71—416no—
347C22×D71—416no—
348C22×D71—416no—
349C22×D71—44no—
350C22×D71—44no—
351C22×D71—44no—
352C22×D71—44no—
353C22×D71C22⋊Q8116yescomplemented
354C22×D71C22×D414yes—
355C22×D71C22×Q814yes—
356C22×D71C22×Q814yes—
357C22×D71C2×#4114yes—
358Q8×C71—416no—
359C2×C4×C71—28no—
360C2×C4×C71—28no—
361C2×C4×C71—28no—
362C2×C4×C71—22no—
363C2×C4×C71—22no—
364C2×C4×C71—22no—
365C2×C4×C71—22no—
366C2×C4×C71—22no—
367C2×C4×C71—22no—
368C2×C4×C71—22no—
369C2×C4×C71—22no—
370C2×C4×C71—22no—
371C2×C4×C71—22no—
372C2×C4×C71—22no—
373C2×C4×C71—22no—
374C2×C4×C71—22no—
375C2×C4×C71—22no—
376C2×C4×C71—22no—
377C2×C4×C71—416no—
378C2×C4×C71—44no—
379C2×C4×C71—44no—
380C2×C4×C71—44no—
381C2×C4×C71C22×D414yes—
382C2×C4×C71C22×D414yes—
383C2×C4×C71C22×D414yes—
384C2×Dic71—28no—
385C2×Dic71—22no—
386C2×Dic71—22no—
387C2×Dic71—22no—
388C2×Dic71—22no—
389C2×Dic71—22no—
390C2×Dic71—22no—
391C2×Dic71—22no—
392C2×Dic71—22no—
393C2×Dic71—22no—
394C2×Dic71—22no—
395C2×Dic71—22no—
396C2×Dic71—22no—
397C2×Dic71—22no—
398C2×Dic71—22no—
399C2×Dic71—22no—
400C2×Dic71—22no—
401C2×Dic71—22no—
402C2×Dic71—416no—
403C2×Dic71—44no—
404C2×Dic71—44no—
405C2×Dic71—44no—
406C2×Dic71—44no—
407C2×Dic71—44no—
408C2×Dic71C22×D414yes—
409C4×D71—416no—
410C4×D71—416no—
411C22×C71—24no—
412C22×C71—24no—
413C22×C71—232no—
414C22×C71—24no—
415C22×C71—24no—
416C22×C71—24no—
417C22×C71—24no—
418C22×C71C2×C22⋊Q814yes—
419C22×C71C2×C22⋊Q814yes—
420C22×C71C2×C22⋊Q818yescomplemented
421C22×C71#54314yes—
422C22×C71D4214yes—
423C22×C71#54614yes—
424C22×C71#54614yes—
425C22×C71#55114yes—
426C22×C71C23×D411yescharacteristic
427C22×C71C23×D411yescharacteristic
428C22×C71C23×Q811yescharacteristic
429C22×C71C22×#4111yescharacteristic
430C22×C71C22×#4111yescharacteristic
431C22×C71C2×H(5,𝔽2)11yescharacteristic
432C22×C71C2×H(5,𝔽2)11yescharacteristic
433C2×D71—24no—
434C2×D71—24no—
435C2×D71—232no—
436C2×D71—24no—
437C2×D71—24no—
438C2×D71—24no—
439C2×D71—24no—
440C2×D71—24no—
441C2×D71—24no—
442C2×D71—24no—
443C2×D71—464no—
444C2×D71—416no—
445C2×D71—42no—
446C2×D71—42no—
447C2×D71—42no—
448C2×D71—42no—
449C2×D71C2×C22⋊Q818yescomplemented
450C4×C71—24no—
451C4×C71—24no—
452C4×C71—24no—
453C4×C71—42no—
454C4×C71—42no—
455C4×C71—42no—
456Dic71—24no—
457Dic71—42no—
458Dic71—42no—
459Dic71—42no—
460Dic71—42no—
461Dic71—42no—
462C2×#2437—711nomaximal, Sylow
463C2×C71—28no—
464C2×C71#243718yescomplemented
465C2×C71C22×C22⋊Q811yescharacteristic
466C2×C71C22×C22⋊Q811yescharacteristic
467C2×C71C2×#54311yescharacteristic
468C2×C71C2×D4211yescharacteristic
469C2×C71C2×#54611yescharacteristic
470C2×C71C2×#54611yescharacteristic
471C2×C71C2×#55111yescharacteristic
472D71—28no—
473D71—44no—
474C22×C22⋊Q8—711no—
475C22×C22⋊Q8D7111yescharacteristic, complemented
476C23×C22⋊C4—711no—
477C23×C22⋊C4—711no—
478#2437—7116no—
479C2×#399—711no—
480C2×#396—711no—
481C2×#396—711no—
482C2×#393—711no—
483C2×#385—711no—
484C2×#385—711no—
485C2×#385—711no—
486C2×#385—711no—
487C2×#380—711no—
488C2×#380—711no—
489C2×#379—711no—
490C71C2×#243711yescharacteristic, complemented, Sylow
491C26—711no—
492C23×Q8C2×D7111yescharacteristic, complemented
493C24×C4—711no—
494C24×C4—711no—
495C24×C4—711no—
496C24×C4C2×D7111yescharacteristic
497C2×C22⋊Q8—28no—
498C2×C22⋊Q8—718no—
499C2×C22⋊Q8—1428no—
500C2×C22⋊Q8C2×D7118yescomplemented
501C22×C4⋊C4—711no—
502C22×C4⋊C4—711no—
503C22×C4⋊C4—711no—
504C22×C4⋊C4—711no—
505C22×C4⋊C4—711no—
506C22×C4⋊C4—711no—
507C22×C4⋊C4C2×D7111yescharacteristic, complemented
508C22×C4⋊C4C2×D7111yescharacteristic, complemented
509C22×C4⋊C4C2×D7111yescharacteristic, complemented
510C22×C22⋊C4—711no—
511C22×C22⋊C4—711no—
512C22×C22⋊C4—711no—
513C22×C22⋊C4—711no—
514C22×C22⋊C4—711no—
515C22×C22⋊C4—711no—
516C22×C22⋊C4—711no—
517C22×C22⋊C4—711no—
518C22×C22⋊C4—711no—
519C22×C22⋊C4—718no—
520C22×C22⋊C4—711no—
521C22×C22⋊C4—711no—
522C22×C22⋊C4—711no—
523C22×C22⋊C4—718no—
524C22×C22⋊C4—1428no—
525C22×C22⋊C4—1428no—
526C22×C22⋊C4C2×D7111yescharacteristic
527C22×C22⋊C4C2×D7111yescharacteristic
528#399—718no—
529#396—718no—
530#396—718no—
531#393—718no—
532#385—718no—
533#385—718no—
534#385—718no—
535#385—718no—
536#380—718no—
537#380—718no—
538#379—718no—
539C2×#95—711no—
540C2×#95—711no—
541C2×#95—711no—
542C2×#95—711no—
543C2×#95—711no—
544C2×#95—711no—
545C25—2842no—
546C25—2842no—
547C25—718no—
548C25—714no—
549C25—711no—
550C25—711no—
551C25—1424no—
552C25—1424no—
553C25—1424no—
554C25—1424no—
555C25C22×D7111yescharacteristic
556C22×Q8—24no—
557C22×Q8—24no—
558C22×Q8—42no—
559C22×Q8C22×D7114yescomplemented
560C23×C4—24no—
561C23×C4—24no—
562C23×C4—42no—
563C23×C4—2842no—
564C23×C4—2842no—
565C23×C4—2842no—
566C23×C4—714no—
567C23×C4—714no—
568C23×C4—714no—
569C23×C4—711no—
570C23×C4—711no—
571C23×C4—711no—
572C23×C4—711no—
573C23×C4—711no—
574C23×C4—711no—
575C23×C4—1424no—
576C23×C4—1424no—
577C23×C4—1424no—
578C23×C4—1424no—
579C23×C4—1424no—
580C23×C4—1424no—
581C23×C4C22×D7111yescharacteristic
582C23×C4C22×D7111yescharacteristic
583C23×C4C22×D7111yescharacteristic
584C23×C4C22×D7114yes—
585C23×C4C22×D7111yescharacteristic
586C23×C4C22×D7111yescharacteristic
587C23×C4C22×D7111yescharacteristic
588C22⋊Q8—232no—
589C22⋊Q8—14232no—
590C2×C4⋊C4—24no—
591C2×C4⋊C4—24no—
592C2×C4⋊C4—24no—
593C2×C4⋊C4—2842no—
594C2×C4⋊C4—2842no—
595C2×C4⋊C4—2842no—
596C2×C4⋊C4—714no—
597C2×C4⋊C4—714no—
598C2×C4⋊C4—714no—
599C2×C4⋊C4—714no—
600C2×C4⋊C4—714no—
601C2×C4⋊C4—714no—
602C2×C4⋊C4—1424no—
603C2×C4⋊C4—1424no—
604C2×C4⋊C4—1424no—
605C2×C4⋊C4C22×D7114yescomplemented
606C2×C4⋊C4C22×D7114yescomplemented
607C2×C4⋊C4C22×D7114yescomplemented
608C2×C22⋊C4—24no—
609C2×C22⋊C4—2842no—
610C2×C22⋊C4—2842no—
611C2×C22⋊C4—714no—
612C2×C22⋊C4—714no—
613C2×C22⋊C4—718no—
614C2×C22⋊C4—714no—
615C2×C22⋊C4—714no—
616C2×C22⋊C4—714no—
617C2×C22⋊C4—714no—
618C2×C22⋊C4—714no—
619C2×C22⋊C4—714no—
620C2×C22⋊C4—714no—
621C2×C22⋊C4—714no—
622C2×C22⋊C4—714no—
623C2×C22⋊C4—714no—
624C2×C22⋊C4—14232no—
625C2×C22⋊C4—1424no—
626C2×C22⋊C4—1424no—
627C2×C22⋊C4—1424no—
628C2×C22⋊C4—1424no—
629C2×C22⋊C4—1424no—
630C2×C22⋊C4—1424no—
631C2×C22⋊C4—1424no—
632C2×C22⋊C4—1424no—
633C2×C22⋊C4—1424no—
634C2×C22⋊C4—14232no—
635C2×C22⋊C4C22⋊D7118yes—
636C2×C22⋊C4C22×D7114yes—
637C2×C22⋊C4C22×D7114yes—
638#95—714no—
639#95—714no—
640#95—714no—
641#95—714no—
642#95—714no—
643#95—714no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—28416no—
649C24—28416no—
650C24—28416no—
651C24—28416no—
652C24—2844no—
653C24—2844no—
654C24—28416no—
655C24—7116no—
656C24—714no—
657C24—714no—
658C24—714no—
659C24—712no—
660C24—714no—
661C24—712no—
662C24—1428no—
663C24—1428no—
664C24—14232no—
665C24—1422no—
666C24—1428no—
667C24—1422no—
668C24—1422no—
669C24—1428no—
670C24—1422no—
671C24—1422no—
672C24—1422no—
673C24—14232no—
674C24—1422no—
675C24—1422no—
676C24—1422no—
677C24—1422no—
678C24C2×C22⋊D7114yes—
679C24Q8×D7114yes—
680C24#1176586614yes—
681C24C23×D7112yes—
682C24C23×D7111yescharacteristic
683C2×Q8—28no—
684C2×Q8—28no—
685C2×Q8—44no—
686C2×Q8—416no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—28no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—28no—
704C22×C4—44no—
705C22×C4—416no—
706C22×C4—28416no—
707C22×C4—28416no—
708C22×C4—2844no—
709C22×C4—2844no—
710C22×C4—28416no—
711C22×C4—2844no—
712C22×C4—714no—
713C22×C4—712no—
714C22×C4—712no—
715C22×C4—712no—
716C22×C4—712no—
717C22×C4—712no—
718C22×C4—712no—
719C22×C4—1428no—
720C22×C4—1428no—
721C22×C4—1428no—
722C22×C4—1422no—
723C22×C4—1422no—
724C22×C4—1422no—
725C22×C4—1422no—
726C22×C4—1422no—
727C22×C4—1422no—
728C22×C4—1422no—
729C22×C4—1422no—
730C22×C4—1422no—
731C22×C4—1422no—
732C22×C4—1428no—
733C22×C4—1422no—
734C22×C4—1422no—
735C22×C4—1422no—
736C22×C4—1422no—
737C22×C4—1422no—
738C22×C4—1428no—
739C22×C4—1428no—
740C22×C4—1422no—
741C22×C4—1422no—
742C22×C4D4×D7114yes—
743C22×C4C2×C22⋊D7114yes—
744C22×C4C2×C22⋊D7114yes—
745C22×C4C23×D7112yes—
746C22×C4C23×D7112yes—
747C22×C4C23×D7112yes—
748C22×C4C23×D7112yes—
749C22×C4C23×D7112yes—
750C22×C4C23×D7112yes—
751C4⋊C4—28no—
752C4⋊C4—28no—
753C4⋊C4—28no—
754C4⋊C4—2844no—
755C4⋊C4—2844no—
756C4⋊C4—2844no—
757C4⋊C4—1428no—
758C4⋊C4—1428no—
759C4⋊C4—1428no—
760C22⋊C4—28no—
761C22⋊C4—2844no—
762C22⋊C4—2844no—
763C22⋊C4—7116no—
764C22⋊C4—1428no—
765C22⋊C4—1428no—
766C22⋊C4—1428no—
767C22⋊C4—1428no—
768C22⋊C4—1428no—
769C22⋊C4—1428no—
770C22⋊C4—1428no—
771C22⋊C4—1428no—
772C22⋊C4—1428no—
773C22⋊C4C2×C22⋊D71116yes—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—28no—
779C23—28no—
780C23—28no—
781C23—28no—
782C23—28no—
783C23—28no—
784C23—284128no—
785C23—28416no—
786C23—28416no—
787C23—28416no—
788C23—28416no—
789C23—28416no—
790C23—2844no—
791C23—2844no—
792C23—2844no—
793C23—2844no—
794C23—714no—
795C23—714no—
796C23—714no—
797C23—7116no—
798C23—714no—
799C23—14232no—
800C23—1422no—
801C23—1422no—
802C23—1422no—
803C23—1422no—
804C23—1422no—
805C23—1422no—
806C23—1428no—
807C23—1428no—
808C23—1428no—
809C23—14232no—
810C23—1422no—
811C23—1422no—
812C23—1422no—
813C23—1422no—
814C23—1428no—
815C23—1428no—
816C23—1428no—
817C23—1428no—
818C23—1428no—
819C23—1428no—
820C23#14556104116yescomplemented
821C23C2×D4×D7112yes—
822C23C22×C22⋊D7114yes—
823C23C22×C22⋊D7112yes—
824C23C2×Q8×D7114yes—
825C23C2×Q8×D7112yes—
826C23#41×D7112yes—
827C23C2×#1176586614yes—
828C23C2×#1176586612yes—
829C23#1455617312yes—
830C23#1455617412yes—
831C23C24×D7111yescharacteristic
832Q8—416no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—28no—
840C2×C4—28no—
841C2×C4—28no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—416no—
852C2×C4—44no—
853C2×C4—44no—
854C2×C4—44no—
855C2×C4—28416no—
856C2×C4—28416no—
857C2×C4—2844no—
858C2×C4—2844no—
859C2×C4—2844no—
860C2×C4—2844no—
861C2×C4—2844no—
862C2×C4—28416no—
863C2×C4—714no—
864C2×C4—1422no—
865C2×C4—1422no—
866C2×C4—1422no—
867C2×C4—1422no—
868C2×C4—1422no—
869C2×C4—1422no—
870C2×C4—1422no—
871C2×C4—1422no—
872C2×C4—1422no—
873C2×C4—1422no—
874C2×C4—1422no—
875C2×C4—1422no—
876C2×C4—1422no—
877C2×C4—1422no—
878C2×C4—1422no—
879C2×C4—1422no—
880C2×C4—1422no—
881C2×C4—1428no—
882C2×C4C2×D4×D7114yes—
883C2×C4C22×C22⋊D7114yes—
884C2×C4C22×C22⋊D7114yes—
885C22—232no—
886C22—24no—
887C22—24no—
888C22—24no—
889C22—24no—
890C22—24no—
891C22—24no—
892C22—28464no—
893C22—28416no—
894C22—2842no—
895C22—2842no—
896C22—2842no—
897C22—2842no—
898C22—718no—
899C22—1424no—
900C22—1424no—
901C22—1424no—
902C22—14232no—
903C22—1424no—
904C22—1424no—
905C22—1424no—
906C22—1424no—
907C22—1424no—
908C22—1424no—
909C22C22⋊Q8×D7114yes—
910C22C2×#1455610414yes—
911C22C2×#1455610418yescomplemented
912C22#1798662414yes—
913C22D4×C22⋊D7114yes—
914C22#1798663714yes—
915C22#1798664014yes—
916C22#1798667614yes—
917C22C22×D4×D7111yescharacteristic
918C22C23×C22⋊D7111yescharacteristic
919C22C22×Q8×D7111yescharacteristic
920C22C2×#41×D7111yescharacteristic
921C22C22×#1176586611yescharacteristic
922C22C2×#1455617311yescharacteristic
923C22C2×#1455617411yescharacteristic
924C4—24no—
925C4—24no—
926C4—24no—
927C4—42no—
928C4—42no—
929C4—42no—
930C4—2842no—
931C4—2842no—
932C4—2842no—
933C4—2842no—
934C4—2842no—
935C4—1424no—
936C2—28no—
937C2—2844no—
938C2—1428no—
939C2#2259200318yesdirect product factor
940C2C2×C22⋊Q8×D7111yescharacteristic
941C2C22×#1455610411yescharacteristic
942C2C2×#1798662411yescharacteristic
943C2C2×D4×C22⋊D7111yescharacteristic
944C2C2×#1798663711yescharacteristic
945C2C2×#1798664011yescharacteristic
946C2C2×#1798667611yescharacteristic
subgroupG/H
centerC24C23×D71
commutator, cosocleC23×C71C25
FrattiniC23C24×D71
FittingC22×C22⋊Q8×C71C2
socleC24×C71C24
prime radicalC25×D71C22
hypercenterC22×C22⋊Q8D71
hypocenterC71C2×#2437
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×#14556104C2semidirect
4. #22592003C2direct (N × H)
5. C2×#17985934C2semidirect
6. C2×#17985921C2semidirect
7. C2×#17985921C2semidirect
8. C2×#17985910C2semidirect
9. C2×#17985874C2semidirect
10. C2×#17985872C2semidirect
11. C2×#17985870C2semidirect
12. C2×#17985870C2semidirect
13. C2×#17985857C2semidirect
14. C2×#17985856C2semidirect
16. C22×C22⋊Q8×C71C2semidirect
22. C2×#14556104C22semidirect
23. C22×C4⋊Dic71C22semidirect
24. C22×C4⋊Dic71C22semidirect
25. C22×Dic71⋊C4C22semidirect
26. C22×Dic71⋊C4C22semidirect
27. C22×Dic71⋊C4C22semidirect
28. C22×Dic71⋊C4C22semidirect
45. #17985934C22semidirect
46. #17985921C22semidirect
47. #17985921C22semidirect
48. #17985910C22semidirect
49. #17985874C22semidirect
50. #17985872C22semidirect
51. #17985870C22semidirect
52. #17985870C22semidirect
53. #17985857C22semidirect
54. #17985856C22semidirect
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
77. C24×D71Q8semidirect
102. C2×C4⋊Dic71C23semidirect
103. C2×C4⋊Dic71C23semidirect
108. C2×Dic71⋊C4C23semidirect
109. C2×Dic71⋊C4C23semidirect
110. C2×Dic71⋊C4C23semidirect
111. C2×Dic71⋊C4C23semidirect
138. C71⋊#95C23semidirect
139. C71⋊#95C23semidirect
140. C71⋊#95C23semidirect
141. C71⋊#95C23semidirect
142. C71⋊#95C23semidirect
143. C71⋊#95C23semidirect
148. C22×Q8×C71C23semidirect
163. C2×C4⋊C4×C71C23semidirect
164. C2×C4⋊C4×C71C23semidirect
165. C2×C4⋊C4×C71C23semidirect
196. C23×D71C2×Q8semidirect
310. C23×C71C22⋊Q8semidirect
353. C22×D71C22⋊Q8semidirect
420. C22×C71C2×C22⋊Q8semidirect
449. C2×D71C2×C22⋊Q8semidirect
464. C2×C71#2437semidirect
475. C22×C22⋊Q8D71semidirect
490. C71C2×#2437semidirect
492. C23×Q8C2×D71semidirect
500. C2×C22⋊Q8C2×D71semidirect
507. C22×C4⋊C4C2×D71semidirect
508. C22×C4⋊C4C2×D71semidirect
509. C22×C4⋊C4C2×D71semidirect
559. C22×Q8C22×D71semidirect
605. C2×C4⋊C4C22×D71semidirect
606. C2×C4⋊C4C22×D71semidirect
607. C2×C4⋊C4C22×D71semidirect
820. C23#14556104semidirect
911. C22C2×#14556104semidirect
939. C2#22592003direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561042
C23×(C2×D71)⋊C42
C22×C22⋊C4×D712
#225920032
C2×#179859342
C2×#179859212
C2×#179859102
C2×#179858742
C2×#179858722
C2×#179858702
C2×#179858572
C2×#179858562
C2×#179858542
C22×C22⋊Q8×C712
C2×#243771