Finite Group Databasebeta

← C2×#21444993 #29655769

Subgroups — C2×#21444993 #29655769

Order 15616.

946 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840482C211yesmaximal, characteristic
2C2×#16840113C211yesmaximal, characteristic, complemented
3C2×#16840058C211yesmaximal, characteristic, complemented
4C2×#16840052C211yesmaximal, characteristic
5#21444993C218yesmaximal, direct product factor
6C2×#16839507C211yesmaximal, characteristic, complemented
7C2×#16839494C211yesmaximal, characteristic, complemented
8C2×C61×D4⋊C8C211yesmaximal, characteristic
9#16840482—22no—
10#16840482—22no—
11#16840482—22no—
12#16840482C2214yes—
13C2×#14519777C2211yescharacteristic
14C2×#14519777C2211yescharacteristic
15C2×#14519770—22no—
16C2×#14519764—21no—
17C2×#14519756—21no—
18C2×C4×Dic122C2211yescharacteristic
19C2×#14519742—21no—
20C2×#14519736—21no—
21#16840113—22no—
22#16840113C2214yescomplemented
23#16840058—22no—
24#16840058C2214yescomplemented
25#16840052—22no—
26#16840052C2214yes—
27C2×#14519711—21no—
28C2×#14519708—21no—
29C2×C4⋊#92418C2211yescharacteristic
30C2×#14519702—22no—
31C2×#14519702—21no—
32C2×#14519698—21no—
33#16839507C2214yescomplemented
34#16839494C2214yescomplemented
35C2×C4×D4×C61C2211yescharacteristic
36C2×C4⋊C8×C61C2211yescharacteristic
37C2×C4×C8×C61C2211yescharacteristic
38C61×D4⋊C8C2214yes—
39C22×Dic122—21no—
40C22×Dic122—21no—
41C22×Dic122D411yescharacteristic
42C22×#92418—21no—
43#14519777—21no—
44#14519777—21no—
45#14519777—21no—
46#14519777—21no—
47#14519777—21no—
48#14519777D412yes—
49#14519777C2312yes—
50#14519777C2312yes—
51#14519770—28no—
52#14519770—28no—
53#14519764—24no—
54#14519764—24no—
55#14519756—24no—
56#14519756—24no—
57C4×Dic122—21no—
58C4×Dic122—21no—
59C4×Dic122D412yes—
60C4×Dic122C2312yes—
61#14519742—24no—
62#14519742—24no—
63#14519736—24no—
64#14519736—24no—
65C2×C4⋊Dic61—21no—
66C2×C4⋊Dic61—21no—
67C2×C4⋊Dic61—21no—
68C2×C4⋊Dic61D411yescharacteristic
69C2×C4⋊Dic61D412yes—
70C2×#11758196—22no—
71C2×#11758196—21no—
72C2×C22⋊Dic61—22no—
73C2×C22⋊Dic61—22no—
74C2×C4×Dic61—22no—
75C2×C4×Dic61—21no—
76#14519711—24no—
77#14519708—24no—
78C4⋊#92418—21no—
79C4⋊#92418C2312yes—
80#14519702—24no—
81#14519702—28no—
82#14519698—24no—
83C22×D4×C61D411yescharacteristic
84C23×C4×C61—21no—
85C22×C8×C61—21no—
86C22×C8×C61—21no—
87C4×D4×C61—21no—
88C4×D4×C61—21no—
89C4×D4×C61D412yes—
90C4×D4×C61C2312yes—
91C2×C4⋊C4×C61D411yescharacteristic
92C2×C22⋊C4×C61—21no—
93C2×C42×C61C2311yescharacteristic
94C4⋊C8×C61—21no—
95C4⋊C8×C61C2312yes—
96C4×C8×C61—21no—
97C4×C8×C61C2312yes—
98C24×C61—21no—
99C2×D4×C61—21no—
100C2×D4×C61—22no—
101C2×D4×C61—22no—
102C2×D4×C61C2×D412yes—
103C22×C4×C61—21no—
104C22×C4×C61—22no—
105C22×C4×C61—22no—
106C22×C4×C61—42no—
107C22×C4×C61—42no—
108C22×C4×C61C2×D411yescharacteristic
109C22×C4×C61C2×D411yescharacteristic
110C22×C4×C61C2×D411yescharacteristic
111C22×Dic61—22no—
112C22×Dic61—21no—
113C22×Dic61—21no—
114C22×Dic61—41no—
115C2×Dic122—22no—
116C2×Dic122—22no—
117C2×Dic122—22no—
118C2×Dic122—21no—
119C2×Dic122—22no—
120C2×Dic122—22no—
121C2×Dic122—42no—
122C2×Dic122—42no—
123C2×Dic122—44no—
124C2×Dic122—41no—
125C2×Dic122C2×D412yes—
126C2×C8×C61—22no—
127C2×C8×C61—22no—
128C2×C8×C61—42no—
129C2×C8×C61—42no—
130C4⋊C4×C61—21no—
131C4⋊C4×C61C2×D412yes—
132C22⋊C4×C61—22no—
133C22⋊C4×C61—22no—
134C42×C61C2×D411yescharacteristic
135C42×C61C2×D411yescharacteristic
136C42×C61C2×D411yescharacteristic
137C42×C61C2411yescharacteristic
138C22⋊Dic61—28no—
139C22⋊Dic61—28no—
140C4⋊Dic61—22no—
141C4⋊Dic61—21no—
142C4⋊Dic61—22no—
143C4⋊Dic61—22no—
144C4⋊Dic61—22no—
145C4⋊Dic61—22no—
146C4⋊Dic61—41no—
147C4⋊Dic61—41no—
148C4⋊Dic61C2×D414yes—
149C4⋊Dic61C2×D412yes—
150#11758196—28no—
151#11758196—22no—
152#11758196—22no—
153C4×Dic61—28no—
154C4×Dic61—22no—
155C4×Dic61—22no—
156C2×#92418—22no—
157C2×#92418—42no—
158C23×C61—22no—
159C23×C61—42no—
160C23×C61—42no—
161C23×C61—42no—
162C23×C61#12011yescharacteristic
163D4×C61—22no—
164D4×C61—22no—
165D4×C61—42no—
166C2×C4×C61—22no—
167C2×C4×C61—22no—
168C2×C4×C61—42no—
169C2×C4×C61—42no—
170C2×C4×C61—42no—
171C2×C4×C61—44no—
172C2×C4×C61#12011yescharacteristic
173C2×C4×C61#12011yescharacteristic
174C2×C4×C61#12011yescharacteristic
175C2×C4×C61#13512yes—
176C2×C4×C61#13512yes—
177C2×C4×C61#13712yes—
178C2×C4×C61#13712yes—
179C2×C4×C61C22×D411yescharacteristic
180C2×C4×C61C22×D411yescharacteristic
181C2×C4×C61C22×D411yescharacteristic
182C2×Dic61—22no—
183C2×Dic61—22no—
184C2×Dic61—24no—
185C2×Dic61—42no—
186C2×Dic61—44no—
187C2×Dic61—42no—
188C2×Dic61—42no—
189C2×Dic61—82no—
190Dic122—22no—
191Dic122—22no—
192Dic122—42no—
193Dic122—42no—
194Dic122—42no—
195Dic122—44no—
196Dic122—44no—
197Dic122—82no—
198C8×C61—42no—
199C8×C61—42no—
200#92418—42no—
201C2×#1638—611nomaximal, Sylow
202C22×C61—42no—
203C22×C61—42no—
204C22×C61—42no—
205C22×C61—84no—
206C22×C61#45212yes—
207C22×C61#45212yes—
208C22×C61#45412yes—
209C22×C61C2×#12011yescharacteristic
210C4×C61—21no—
211C4×C61—21no—
212C4×C61—42no—
213C4×C61#45212yes—
214C4×C61#45212yes—
215C4×C61C2×#13511yescharacteristic
216C4×C61C2×#13511yescharacteristic
217C4×C61C2×#13711yescharacteristic
218C4×C61C2×#13711yescharacteristic
219Dic61—42no—
220Dic61—44no—
221Dic61—42no—
222Dic61—82no—
223C2×#556—611no—
224C2×#487—611no—
225C2×#477—611no—
226C2×#476—611no—
227#1638—618no—
228C2×#332—611no—
229C2×Q8⋊C8—611no—
230C2×D4⋊C8D6111yescharacteristic
231C2×C61—82no—
232C2×C61#163814yescomplemented
233C2×C61C2×#45211yescharacteristic
234C2×C61C2×#45211yescharacteristic
235C2×C61C2×#45411yescharacteristic
236#556—614no—
237#556—1222no—
238#556—1222no—
239#556—1222no—
240C2×C4⋊Q8—611no—
241C2×C4⋊Q8—611no—
242C2×#126—1222no—
243C2×#124—1221no—
244C2×C22⋊Q8—1221no—
245C2×C4×Q8—611no—
246C2×C4×Q8—1221no—
247C2×C4×D4C2×D6111yescharacteristic
248C2×#117—1221no—
249#487—614no—
250#487—1222no—
251#477—614no—
252#477—1222no—
253#476—614no—
254#476—1222no—
255C2×#107—1221no—
256C2×#106—1221no—
257C2×C4⋊C8—611no—
258C2×C4⋊C8C2×D6111yescharacteristic
259C2×#103—1222no—
260C2×#103—1221no—
261C2×#102—1221no—
262C2×C4×C8C2×D6111yescharacteristic
263#332—614no—
264Q8⋊C8—614no—
265D4⋊C8C2×D6114yes—
266C61C2×#163811yescharacteristic, complemented, Sylow
267C22×Q8—611no—
268C22×Q8—1221no—
269C22×Q8—1221no—
270C22×D4D24411yescharacteristic
271C23×C4—21no—
272C22×C8—21no—
273C22×C8—21no—
274C22×C8—1221no—
275C4⋊Q8—612no—
276C4⋊Q8—612no—
277C4⋊Q8—612no—
278C4⋊Q8—1221no—
279C4⋊Q8—1221no—
280C4⋊Q8—1221no—
281C4⋊Q8—1221no—
282C4⋊Q8—1221no—
283#126—1228no—
284#126—1228no—
285#124—1224no—
286#124—1224no—
287C22⋊Q8—1224no—
288C22⋊Q8—1224no—
289C4×Q8—612no—
290C4×Q8—612no—
291C4×Q8—1224no—
292C4×Q8—1224no—
293C4×Q8—1221no—
294C4×Q8—1221no—
295C4×D4—21no—
296C4×D4—21no—
297C4×D4D24412yes—
298C4×D4C22×D6112yes—
299#117—1224no—
300#117—1224no—
301C2×C4⋊C4—611no—
302C2×C4⋊C4—612no—
303C2×C4⋊C4—1222no—
304C2×C4⋊C4—1221no—
305C2×C4⋊C4—1221no—
306C2×C4⋊C4—1221no—
307C2×C4⋊C4—1221no—
308C2×C4⋊C4D24411yescharacteristic
309C2×C22⋊C4—21no—
310C2×C22⋊C4—1222no—
311C2×C22⋊C4—1222no—
312C2×C42—1222no—
313C2×C42—1221no—
314C2×C42C22×D6111yescharacteristic
315#107—1224no—
316#106—1224no—
317C4⋊C8—21no—
318C4⋊C8—612no—
319C4⋊C8—1221no—
320C4⋊C8C22×D6112yes—
321#103—1228no—
322#103—1224no—
323#102—1224no—
324C4×C8—21no—
325C4×C8C22×D6112yes—
326C24—21no—
327C2×Q8—612no—
328C2×Q8—1222no—
329C2×Q8—1221no—
330C2×Q8—1222no—
331C2×Q8—1222no—
332C2×Q8—1222no—
333C2×Q8—1222no—
334C2×Q8—2444no—
335C2×Q8—2442no—
336C2×Q8—2441no—
337C2×Q8—2442no—
338C2×D4—22no—
339C2×D4—21no—
340C2×D4—22no—
341C2×D4C2×D24412yes—
342C22×C4—21no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—42no—
346C22×C4—42no—
347C22×C4—1221no—
348C22×C4—1222no—
349C22×C4—1221no—
350C22×C4—2441no—
351C22×C4C2×D24411yescharacteristic
352C22×C4D4×D6111yescharacteristic
353C22×C4D4×D6111yescharacteristic
354C2×C8—22no—
355C2×C8—22no—
356C2×C8—42no—
357C2×C8—42no—
358C2×C8—1222no—
359C2×C8—2442no—
360C4⋊C4—21no—
361C4⋊C4—614no—
362C4⋊C4—612no—
363C4⋊C4—1228no—
364C4⋊C4—1222no—
365C4⋊C4—1222no—
366C4⋊C4—1221no—
367C4⋊C4—1222no—
368C4⋊C4—1222no—
369C4⋊C4—1222no—
370C4⋊C4—1222no—
371C4⋊C4—1222no—
372C4⋊C4—2441no—
373C4⋊C4—2441no—
374C4⋊C4C2×D24412yes—
375C22⋊C4—22no—
376C22⋊C4—22no—
377C22⋊C4—1228no—
378C22⋊C4—1228no—
379C42—1228no—
380C42—1222no—
381C42—1222no—
382C42C2×D24411yescharacteristic
383C42D4×D6111yescharacteristic
384C42D4×D6111yescharacteristic
385C42C23×D6111yescharacteristic
386C23—22no—
387C23—42no—
388C23—42no—
389C23—42no—
390C23#1451974711yescharacteristic
391Q8—1222no—
392Q8—1222no—
393Q8—4882no—
394Q8—2444no—
395Q8—2442no—
396Q8—2442no—
397Q8—2442no—
398Q8—2444no—
399D4—22no—
400D4—22no—
401D4—42no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—44no—
408C2×C4—1222no—
409C2×C4—1224no—
410C2×C4—1222no—
411C2×C4—4882no—
412C2×C4—2442no—
413C2×C4—2442no—
414C2×C4—2442no—
415C2×C4—2444no—
416C2×C4#1451974711yescharacteristic
417C2×C4#1451974711yescharacteristic
418C2×C4#1451974711yescharacteristic
419C2×C4#1451979612yes—
420C2×C4#1451979912yes—
421C2×C4#1451980612yes—
422C2×C4#1451981012yes—
423C2×C4C2×D4×D6111yescharacteristic
424C2×C4C2×D4×D6111yescharacteristic
425C2×C4C22×D24411yescharacteristic
426C8—42no—
427C8—42no—
428C8—2442no—
429C22—42no—
430C22—42no—
431C22—42no—
432C22—84no—
433C22#1683992512yes—
434C22#1683992612yes—
435C22#1683993612yes—
436C22C2×#1451974711yescharacteristic
437C4—21no—
438C4—21no—
439C4—42no—
440C4—4882no—
441C4—2442no—
442C4—2442no—
443C4—2444no—
444C4#1683992512yes—
445C4#1683992612yes—
446C4C2×#1451979611yescharacteristic
447C4C2×#1451979911yescharacteristic
448C4C2×#1451980611yescharacteristic
449C4C2×#1451981011yescharacteristic
450C2—82no—
451C2#2144499314yesdirect product factor
452C2C2×#1683992511yescharacteristic
453C2C2×#1683992611yescharacteristic
454C2C2×#1683993611yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×D4⋊C8C2
socleC23×C61#120
prime radicalC22×D4×C61D4
hypercenterC2×D4⋊C8D61
hypocenterC61C2×#1638
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×D4⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#16840113C2semidirect
3. C2×#16840058C2semidirect
5. #21444993C2direct (N × H)
6. C2×#16839507C2semidirect
7. C2×#16839494C2semidirect
22. #16840113C22semidirect
24. #16840058C22semidirect
33. #16839507C22semidirect
34. #16839494C22semidirect
232. C2×C61#1638semidirect
266. C61C2×#1638semidirect
451. C2#21444993direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404822
C2×#168401132
C2×#168400582
C2×#168400522
#214449932
C2×#168395072
C2×#168394942
C2×C61×D4⋊C82
C2×#163861