Finite Group Databasebeta

← C2×#21444918 #29655745

Subgroups — C2×#21444918 #29655745

Order 15616.

1030 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840491C211yesmaximal, characteristic, complemented
2C2×#16840109C211yesmaximal, characteristic
3C2×#16839963C211yesmaximal, characteristic
4C2×#16839962C211yesmaximal, characteristic
5#21444918C218yesmaximal, direct product factor
6C2×#16839509C211yesmaximal, characteristic, complemented
7C2×#16839494C211yesmaximal, characteristic, complemented
8C2×C61×Q8⋊C8C211yesmaximal, characteristic, complemented
9C22×#11758190—21no—
10C22×#11758201—21no—
11#16840491—22no—
12#16840491—22no—
13#16840491—22no—
14#16840491C2214yescomplemented
15C2×#14519777—21no—
16C2×#14519777C2211yescharacteristic
17C2×#14519774C2211yescharacteristic
18C2×#14519768—22no—
19C2×#14519768—21no—
20C2×Q8×Dic61—21no—
21C2×C4×Dic122—21no—
22C2×C4×Dic122C2211yescharacteristic
23#16840109—22no—
24#16840109C2214yes—
25#16839963—22no—
26#16839963C2214yes—
27#16839962—22no—
28#16839962C2214yes—
29C2×C4⋊#92418C2211yescharacteristic
30C2×#14519699—21no—
31C2×#14519699—22no—
32C2×#14519697—21no—
33#16839509C2214yescomplemented
34#16839494C2214yescomplemented
35C2×C4×Q8×C61C2211yescharacteristic
36C2×C4⋊C8×C61C2211yescharacteristic
37C2×C4×C8×C61C2211yescharacteristic
38C61×Q8⋊C8C2214yescomplemented
39C22×Dic122—21no—
40C22×Dic122D411yescharacteristic
41C22×D244—21no—
42C22×D244—21no—
43C22×D244—21no—
44C2×#11758190—24no—
45C2×#11758190—44no—
46C2×#11758201—24no—
47C2×#11758201—44no—
48C22×#92418—21no—
49#14519777—24no—
50#14519777—24no—
51#14519777—21no—
52#14519777—21no—
53#14519777D412yes—
54#14519777C2312yes—
55#14519774—21no—
56#14519774—21no—
57#14519774—21no—
58#14519774C2312yes—
59#14519768—28no—
60#14519768—24no—
61#14519768—24no—
62#14519768—28no—
63Q8×Dic61—24no—
64Q8×Dic61—24no—
65C4×Dic122—24no—
66C4×Dic122—21no—
67C4×Dic122—21no—
68C4×Dic122—24no—
69C4×Dic122D412yes—
70C4×Dic122C2312yes—
71C2×C4⋊Dic61—22no—
72C2×C4⋊Dic61—22no—
73C2×C4⋊Dic61—21no—
74C2×C4⋊Dic61D411yescharacteristic
75C2×C4⋊Dic61D412yes—
76C2×#11758196—22no—
77C2×#11758196—21no—
78C2×C4×Dic61—22no—
79C2×C4×Dic61—21no—
80C4⋊#92418—21no—
81C4⋊#92418C2312yes—
82#14519699—24no—
83#14519699—28no—
84#14519697—24no—
85C22×Q8×C61D411yescharacteristic
86C22×C8×C61—21no—
87C22×C8×C61—21no—
88C4×Q8×C61—21no—
89C4×Q8×C61—21no—
90C4×Q8×C61D412yes—
91C4×Q8×C61C2312yes—
92C2×C4⋊C4×C61—21no—
93C2×C4⋊C4×C61D411yescharacteristic
94C2×C42×C61—21no—
95C2×C42×C61C2311yescharacteristic
96C4⋊C8×C61—21no—
97C4⋊C8×C61C2312yes—
98C4×C8×C61—21no—
99C4×C8×C61C2312yes—
100C23×D61—41no—
101C2×Q8×C61—21no—
102C2×Q8×C61—22no—
103C2×Q8×C61SD1614yescomplemented
104C2×Q8×C61C2×D412yes—
105C22×C4×C61—21no—
106C22×C4×C61—21no—
107C22×C4×C61C2×D411yescharacteristic
108C22×C4×C61C2×D411yescharacteristic
109C22×C4×C61C2×D411yescharacteristic
110C22×Dic61—22no—
111C22×Dic61—21no—
112C22×Dic61—21no—
113C2×D244—22no—
114C2×D244—22no—
115C2×D244—22no—
116C2×D244—44no—
117C2×D244—42no—
118C2×D244—42no—
119C2×D244—42no—
120C2×D244—42no—
121C2×D244—41no—
122C2×D244—41no—
123C2×D244—41no—
124C2×Dic122—22no—
125C2×Dic122—22no—
126C2×Dic122—22no—
127C2×Dic122—21no—
128C2×Dic122—22no—
129C2×Dic122—42no—
130C2×Dic122—42no—
131C2×Dic122C2×D412yes—
132C2×C8×C61—22no—
133C2×C8×C61—22no—
134C2×C8×C61—42no—
135C2×C8×C61—42no—
136C4⋊C4×C61—22no—
137C4⋊C4×C61—21no—
138C4⋊C4×C61—22no—
139C4⋊C4×C61C2×D412yes—
140C42×C61—22no—
141C42×C61—22no—
142C42×C61C2×D411yescharacteristic
143C42×C61C2×D411yescharacteristic
144C42×C61C2×D411yescharacteristic
145C42×C61C2411yescharacteristic
146#11758201—48no—
147C4⋊Dic61—28no—
148C4⋊Dic61—28no—
149C4⋊Dic61—22no—
150C4⋊Dic61—21no—
151C4⋊Dic61—22no—
152C4⋊Dic61—22no—
153C4⋊Dic61C2×D412yes—
154C4⋊Dic61C2×D414yes—
155#11758196—28no—
156#11758196—22no—
157#11758196—22no—
158C4×Dic61—28no—
159C4×Dic61—22no—
160C4×Dic61—22no—
161C2×#92418—22no—
162C2×#92418—42no—
163#11758190—48no—
164C23×C61#12011yescharacteristic
165C22×D61—42no—
166C22×D61—82no—
167C22×D61—82no—
168C22×D61—82no—
169Q8×C61—22no—
170Q8×C61—24no—
171Q8×C61C2×SD1614yescomplemented
172C2×C4×C61—22no—
173C2×C4×C61—24no—
174C2×C4×C61—22no—
175C2×C4×C61—22no—
176C2×C4×C61—42no—
177C2×C4×C61#12011yescharacteristic
178C2×C4×C61#12011yescharacteristic
179C2×C4×C61#12011yescharacteristic
180C2×C4×C61C2×SD1612yes—
181C2×C4×C61#13512yes—
182C2×C4×C61AGL(1,ℤ/8)12yes—
183C2×C4×C61#13712yes—
184C2×C4×C61C22×D411yescharacteristic
185C2×C4×C61C22×D411yescharacteristic
186C2×C4×C61C22×D411yescharacteristic
187C2×Dic61—22no—
188C2×Dic61—22no—
189C2×Dic61—24no—
190C2×Dic61—42no—
191C2×Dic61—44no—
192C2×Dic61—42no—
193D244—44no—
194D244—42no—
195D244—42no—
196D244—42no—
197D244—42no—
198D244—82no—
199D244—82no—
200D244—82no—
201Dic122—22no—
202Dic122—22no—
203Dic122—42no—
204Dic122—42no—
205Dic122—42no—
206Dic122—44no—
207C8×C61—42no—
208C8×C61—42no—
209#92418—42no—
210C2×#1626—611nomaximal, Sylow
211C22×C61#44812yes—
212C22×C61#44912yes—
213C22×C61#45412yes—
214C22×C61C2×#12011yescharacteristic
215C2×D61—82no—
216C2×D61—82no—
217C2×D61—82no—
218C2×D61—164no—
219C4×C61—24no—
220C4×C61—21no—
221C4×C61—21no—
222C4×C61—42no—
223C4×C61#44812yes—
224C4×C61#44912yes—
225C4×C61C22×SD1611yescharacteristic
226C4×C61C2×#13511yescharacteristic
227C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
228C4×C61C2×#13711yescharacteristic
229Dic61—42no—
230Dic61—44no—
231Dic61—42no—
232C2×#557—611no—
233C2×#486—611no—
234C2×#460—611no—
235C2×#460—611no—
236#1626—618no—
237C2×#332—611no—
238C2×Q8⋊C8—611no—
239C2×Q8⋊C8D6111yescharacteristic, complemented
240C2×C61#162614yescomplemented
241C2×C61C2×#44811yescharacteristic
242C2×C61C2×#44911yescharacteristic
243C2×C61C2×#45411yescharacteristic
244D61—162no—
245C22×SD16—1221no—
246C22×SD16—1221no—
247#557—614no—
248#557—1222no—
249#557—1222no—
250#557—1222no—
251C2×C4⋊Q8—611no—
252C2×C4⋊Q8—1221no—
253C2×#127—611no—
254C2×#125—1222no—
255C2×#125—1221no—
256C2×C4×Q8—611no—
257C2×C4×Q8—1221no—
258C2×C4×Q8—1221no—
259C2×C4×Q8C2×D6111yescharacteristic
260#486—614no—
261#486—1222no—
262#460—614no—
263#460—614no—
264#460—1222no—
265#460—1222no—
266C2×C4⋊C8—611no—
267C2×C4⋊C8C2×D6111yescharacteristic
268C2×#102—1222no—
269C2×#102—1221no—
270C2×#102—1221no—
271C2×C4×C8C2×D6111yescharacteristic
272#332—614no—
273Q8⋊C8—614no—
274Q8⋊C8C2×D6114yescomplemented
275C61C2×#162611yescharacteristic, complemented, Sylow
276C22×Q8—611no—
277C22×Q8—1221no—
278C22×Q8D24411yescharacteristic
279C22×D4—1221no—
280C22×D4—1221no—
281C22×D4—1221no—
282C2×SD16—1224no—
283C2×SD16—1224no—
284C2×SD16—2444no—
285C2×SD16—2444no—
286C22×C8—21no—
287C22×C8—21no—
288C22×C8—1221no—
289C4⋊Q8—612no—
290C4⋊Q8—612no—
291C4⋊Q8—1224no—
292C4⋊Q8—1224no—
293C4⋊Q8—1221no—
294C4⋊Q8—1221no—
295#127—612no—
296#127—1221no—
297#127—1221no—
298#127—1221no—
299#125—1228no—
300#125—1228no—
301#125—1224no—
302#125—1224no—
303C4×Q8—21no—
304C4×Q8—21no—
305C4×Q8—612no—
306C4×Q8—612no—
307C4×Q8—1224no—
308C4×Q8—1224no—
309C4×Q8—1224no—
310C4×Q8—1224no—
311C4×Q8—1221no—
312C4×Q8—1221no—
313C4×Q8D24412yes—
314C4×Q8C22×D6112yes—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—611no—
317C2×C4⋊C4—612no—
318C2×C4⋊C4—1222no—
319C2×C4⋊C4—1222no—
320C2×C4⋊C4—1222no—
321C2×C4⋊C4—1221no—
322C2×C4⋊C4—1221no—
323C2×C4⋊C4D24411yescharacteristic
324C2×C42—21no—
325C2×C42—1222no—
326C2×C42—1221no—
327C2×C42C22×D6111yescharacteristic
328C4⋊C8—21no—
329C4⋊C8—612no—
330C4⋊C8—1221no—
331C4⋊C8C22×D6112yes—
332#102—1224no—
333#102—1228no—
334#102—1224no—
335C4×C8—21no—
336C4×C8C22×D6112yes—
337C24—2441no—
338C2×Q8—22no—
339C2×Q8—21no—
340C2×Q8—612no—
341C2×Q8—1222no—
342C2×Q8—1222no—
343C2×Q8—1221no—
344C2×Q8—1222no—
345C2×Q8—1222no—
346C2×Q8—2442no—
347C2×Q8—2442no—
348C2×Q8#1175819014yescomplemented
349C2×Q8C2×D24412yes—
350C2×D4—1222no—
351C2×D4—1222no—
352C2×D4—1222no—
353C2×D4—2444no—
354C2×D4—2442no—
355C2×D4—2441no—
356C2×D4—2441no—
357C2×D4—2441no—
358C2×D4—2442no—
359C2×D4—2442no—
360C2×D4—2442no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—1221no—
364C22×C4—1222no—
365C22×C4—1221no—
366C22×C4C2×D24411yescharacteristic
367C22×C4D4×D6111yescharacteristic
368C22×C4D4×D6111yescharacteristic
369SD16—2448no—
370SD16—2448no—
371C2×C8—22no—
372C2×C8—22no—
373C2×C8—42no—
374C2×C8—42no—
375C2×C8—1222no—
376C2×C8—2442no—
377C4⋊C4—22no—
378C4⋊C4—22no—
379C4⋊C4—21no—
380C4⋊C4—612no—
381C4⋊C4—614no—
382C4⋊C4—1228no—
383C4⋊C4—1228no—
384C4⋊C4—1228no—
385C4⋊C4—1222no—
386C4⋊C4—1222no—
387C4⋊C4—1221no—
388C4⋊C4—1222no—
389C4⋊C4—1222no—
390C4⋊C4—1222no—
391C4⋊C4C2×D24412yes—
392C42—22no—
393C42—22no—
394C42—1228no—
395C42—1222no—
396C42—1222no—
397C42C2×D24411yescharacteristic
398C42D4×D6111yescharacteristic
399C42D4×D6111yescharacteristic
400C42C23×D6111yescharacteristic
401C23—4882no—
402C23—4882no—
403C23—4882no—
404C23—2442no—
405C23#1451974711yescharacteristic
406Q8—22no—
407Q8—24no—
408Q8—1222no—
409Q8—1222no—
410Q8—2442no—
411Q8—2442no—
412Q8—2442no—
413Q8—2444no—
414Q8C2×#1175819014yescomplemented
415D4—4882no—
416D4—4882no—
417D4—4882no—
418D4—2444no—
419D4—2442no—
420D4—2442no—
421D4—2442no—
422D4—2442no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—24no—
426C2×C4—22no—
427C2×C4—42no—
428C2×C4—1222no—
429C2×C4—1224no—
430C2×C4—1222no—
431C2×C4—2442no—
432C2×C4—2442no—
433C2×C4—2444no—
434C2×C4#1451974711yescharacteristic
435C2×C4#1451974711yescharacteristic
436C2×C4#1451974711yescharacteristic
437C2×C4C2×#1175819012yes—
438C2×C4#1451980012yes—
439C2×C4#1451980412yes—
440C2×C4#1451981012yes—
441C2×C4C2×D4×D6111yescharacteristic
442C2×C4C2×D4×D6111yescharacteristic
443C2×C4C22×D24411yescharacteristic
444C8—42no—
445C8—42no—
446C8—2442no—
447C22—9764no—
448C22—4882no—
449C22—4882no—
450C22—4882no—
451C22#1683990312yes—
452C22#1683991012yes—
453C22#1683993612yes—
454C22C2×#1451974711yescharacteristic
455C4—21no—
456C4—21no—
457C4—24no—
458C4—42no—
459C4—2442no—
460C4—2442no—
461C4—2444no—
462C4#1683990312yes—
463C4#1683991012yes—
464C4C22×#1175819011yescharacteristic
465C4C2×#1451980011yescharacteristic
466C4C2×#1451980411yescharacteristic
467C4C2×#1451981011yescharacteristic
468C2—9762no—
469C2#2144491814yesdirect product factor
470C2C2×#1683990311yescharacteristic
471C2C2×#1683991011yescharacteristic
472C2C2×#1683993611yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×Q8⋊C8C2
socleC23×C61#120
prime radicalC2×#14519774C22
hypercenterC2×Q8⋊C8D61
hypocenterC61C2×#1626
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#16840491C2semidirect
5. #21444918C2direct (N × H)
6. C2×#16839509C2semidirect
7. C2×#16839494C2semidirect
8. C2×C61×Q8⋊C8C2semidirect
14. #16840491C22semidirect
33. #16839509C22semidirect
34. #16839494C22semidirect
38. C61×Q8⋊C8C22semidirect
103. C2×Q8×C61SD16semidirect
171. Q8×C61C2×SD16semidirect
239. C2×Q8⋊C8D61semidirect
240. C2×C61#1626semidirect
274. Q8⋊C8C2×D61semidirect
275. C61C2×#1626semidirect
348. C2×Q8#11758190semidirect
414. Q8C2×#11758190semidirect
469. C2#21444918direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404912
C2×#168401092
C2×#168399632
C2×#168399622
#214449182
C2×#168395092
C2×#168394942
C2×C61×Q8⋊C82
C2×#162661