Finite Group Databasebeta

← C2×#21461177 #30610598

Subgroups — C2×#21461177 #30610598

Order 15616.

1066 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840780C211yesmaximal, characteristic, complemented
2C2×#16840766C211yesmaximal, characteristic, complemented
3#21461177C218yesmaximal, direct product factor
4C2×#16840612C212yesmaximal, complemented
5C2×#16840610C212yesmaximal, complemented
6C2×#16840297C211yesmaximal, characteristic
7C22×#11758213—21no—
8#16840780—22no—
9#16840780C2214yescomplemented
10#16840766—22no—
11#16840766C2214yescomplemented
12C2×#14519844—21no—
13C2×C4⋊#92420—21no—
14C2×C4⋊#92420C2212yes—
15C2×#14519834—21no—
16C2×C4×#92420C2212yes—
17#16840612C2218yescomplemented
18#16840610C2218yescomplemented
19#16840297—22no—
20#16840297—22no—
21#16840297C414yes—
22#16840297C2214yes—
23C2×#14519772—21no—
24C2×#14519765C411yescharacteristic
25C2×#14519762—21no—
26C2×#14519757C411yescharacteristic
27C2×#14519752C411yescharacteristic
28C2×#14519742C2211yescharacteristic
29C2×#14519739—21no—
30C2×#14519739C2211yescharacteristic
31C2×#14519735—21no—
32C2×C42×D61C2211yescharacteristic
33C2×#125×C61C411yescharacteristic
34C2×#11758213—24no—
35C2×#11758213—44no—
36C22×#92420—22no—
37C22×#92420—22no—
38#14519844—24no—
39C4⋊#92420—24no—
40C4⋊#92420—22no—
41C4⋊#92420C2314yes—
42#14519834—24no—
43C4×#92420—22no—
44C4×#92420C2314yes—
45C22×Dic122C2×C411yescharacteristic
46C22×D244—21no—
47C22×D244C2×C411yescharacteristic
48C22×C4×D61—21no—
49C22×C4×D61C2×C411yescharacteristic
50C22×C4×D61D411yescharacteristic
51C22×C4×D61D411yescharacteristic
52#14519772—24no—
53#14519772—24no—
54#14519765—22no—
55#14519765C2×C414yes—
56#14519762—24no—
57#14519762—24no—
58#14519757—22no—
59#14519757C2×C414yes—
60#14519752—22no—
61#14519752C2×C414yes—
62#14519742—21no—
63#14519742—21no—
64#14519742C2×C412yes—
65#14519742C2312yes—
66#14519739—24no—
67#14519739—24no—
68#14519739—21no—
69#14519739—21no—
70#14519739C2×C412yes—
71#14519739C2312yes—
72#14519735—24no—
73#14519735—24no—
74C2×C4⋊Dic61—21no—
75C2×#11758196—21no—
76C2×#11758198—21no—
77C2×#11758198—21no—
78C2×#11758198—21no—
79C2×#11758198—21no—
80C2×#11758198—21no—
81C2×C4×Dic61—21no—
82C2×C4×Dic61D411yescharacteristic
83C2×C4×Dic61D411yescharacteristic
84C2×C4×Dic61C2311yescharacteristic
85C42×D61C2×C412yes—
86C42×D61D412yes—
87C42×D61D412yes—
88C42×D61C2312yes—
89#125×C61—22no—
90#125×C61C2×C414yes—
91C2×C4⋊C4×C61—21no—
92C2×C4⋊C4×C61—21no—
93C2×C4⋊C4×C61C2×C411yescharacteristic
94C2×C4⋊C4×C61C2×C411yescharacteristic
95C2×C42×C61C2×C411yescharacteristic
96C23×D61—21no—
97C23×D61C22⋊C411yescharacteristic
98C22×C4×C61—21no—
99C22×C4×C61—21no—
100C22×C4×C61C22⋊C411yescharacteristic
101C22×C4×C61C22⋊C411yescharacteristic
102C22×C4×C61C22×C411yescharacteristic
103C22×Dic61—21no—
104C22×Dic61C22⋊C411yescharacteristic
105C22×Dic61C2×D411yescharacteristic
106C22×Dic61C2×D411yescharacteristic
107C2×D244—24no—
108C2×D244—24no—
109C2×D244—21no—
110C2×D244—44no—
111C2×D244C22×C412yes—
112C2×C4×D61—24no—
113C2×C4×D61—22no—
114C2×C4×D61—22no—
115C2×C4×D61—22no—
116C2×C4×D61—22no—
117C2×C4×D61—42no—
118C2×C4×D61—42no—
119C2×C4×D61—42no—
120C2×C4×D61C22⋊C412yes—
121C2×C4×D61C22⋊C412yes—
122C2×C4×D61C22⋊C412yes—
123C2×C4×D61C22×C412yes—
124C2×C4×D61C2×D412yes—
125C2×C4×D61C2×D412yes—
126C2×Dic122—24no—
127C2×Dic122—21no—
128C2×Dic122C22×C412yes—
129C2×#92420—24no—
130C2×#92420—24no—
131C2×#92420—44no—
132C2×#92420—44no—
133#11758213—48no—
134C4⋊C4×C61—24no—
135C4⋊C4×C61—24no—
136C4⋊C4×C61—21no—
137C4⋊C4×C61—21no—
138C4⋊C4×C61C22×C412yes—
139C4⋊C4×C61C22×C412yes—
140C42×C61C22⋊C412yes—
141C42×C61C22×C412yes—
142#11758198—24no—
143#11758198—24no—
144#11758198—24no—
145#11758198—24no—
146#11758198—22no—
147#11758198—22no—
148C4⋊Dic61—24no—
149#11758196—22no—
150#11758196—22no—
151C4×Dic61—22no—
152C4×Dic61—22no—
153C4×Dic61C22⋊C412yes—
154C4×Dic61C22⋊C412yes—
155C4×Dic61C22×C411yescharacteristic
156C4×Dic61C2×D411yescharacteristic
157C4×Dic61C2×D411yescharacteristic
158C4×Dic61C2×D412yes—
159C4×Dic61C2×D412yes—
160C4×Dic61C2411yescharacteristic
161C23×C61C2×C22⋊C411yescharacteristic
162C22×D61—22no—
163C22×D61—22no—
164C22×D61—22no—
165C22×D61—22no—
166C22×D61—42no—
167C22×D61—42no—
168C22×D61—42no—
169C22×D61C2×C22⋊C412yes—
170C2×C4×C61—22no—
171C2×C4×C61—22no—
172C2×C4×C61—22no—
173C2×C4×C61—22no—
174C2×C4×C61—42no—
175C2×C4×C61—42no—
176C2×C4×C61C2×C22⋊C412yes—
177C2×C4×C61C2×C22⋊C412yes—
178C2×C4×C61C2×C22⋊C411yescharacteristic
179C2×C4×C61#13114yes—
180C2×C4×C61C23×C411yescharacteristic
181C2×Dic61—22no—
182C2×Dic61—22no—
183C2×Dic61—22no—
184C2×Dic61—42no—
185C2×Dic61C2×C22⋊C411yescharacteristic
186C2×Dic61C2×C22⋊C412yes—
187C2×Dic61C2×C22⋊C411yescharacteristic
188C2×Dic61AGL(1,ℤ/8)12yes—
189C2×Dic61#13712yes—
190C2×Dic61C22×D411yescharacteristic
191C2×Dic61C22×D411yescharacteristic
192D244—24no—
193D244—48no—
194D244—42no—
195C4×D61—24no—
196C4×D61—24no—
197C4×D61—22no—
198C4×D61—22no—
199C4×D61—24no—
200C4×D61—42no—
201C4×D61—42no—
202C4×D61—42no—
203C4×D61—42no—
204C4×D61—44no—
205Dic122—24no—
206Dic122—42no—
207#92420—44no—
208#92420—44no—
209C2×#1495—611nomaximal, Sylow
210C22×C61#40812yes—
211C22×C61#41712yes—
212C22×C61#42112yes—
213C22×C61C22×C22⋊C411yescharacteristic
214C2×D61—22no—
215C2×D61—22no—
216C2×D61—22no—
217C2×D61—44no—
218C2×D61—42no—
219C2×D61—42no—
220C2×D61—42no—
221C2×D61—84no—
222C4×C61—22no—
223C4×C61—22no—
224C4×C61—42no—
225C4×C61—42no—
226C4×C61#40812yes—
227C4×C61C2×#13112yes—
228Dic61—22no—
229Dic61—21no—
230Dic61—21no—
231Dic61—42no—
232Dic61#41712yes—
233Dic61C2×AGL(1,ℤ/8)11yescharacteristic
234Dic61C2×#13711yescharacteristic
235C2×#529—611no—
236C2×#431—611no—
237C2×#423—611no—
238#1495—618no—
239C2×Q8⋊C8—612no—
240C2×D4⋊C8—612no—
241C2×C61#149514yescomplemented
242C2×C61C2×#40811yescharacteristic
243C2×C61C2×#41711yescharacteristic
244C2×C61C2×#42111yescharacteristic
245D61—42no—
246D61—82no—
247C22×M16—1221no—
248#529—614no—
249#529—614no—
250#529—1222no—
251#529—1222no—
252C2×#126—1221no—
253C2×#125#692311yescharacteristic
254C2×#124—611no—
255C2×#123—1221no—
256C2×C22⋊Q8—611no—
257C2×#121—611no—
258C2×C4×Q8—611no—
259C2×C4×D4—611no—
260C2×C4×D4—1221no—
261C2×#117—1221no—
262C22×C42—611no—
263#431—614no—
264#431—1222no—
265#423—614no—
266#423—1222no—
267C2×C4⋊C8—612no—
268C2×C4⋊C8—1221no—
269C2×C4⋊C8—1221no—
270C2×C22⋊C8—1221no—
271C2×C4×C8—612no—
272Q8⋊C8—618no—
273D4⋊C8—618no—
274C61C2×#149511yescharacteristic, complemented, Sylow
275C22×Q8—611no—
276C22×D4—611no—
277C22×D4—1221no—
278C23×C4—611no—
279C23×C4—611no—
280C23×C4—611no—
281C23×C4—1221no—
282C2×M16—1224no—
283C2×M16—2444no—
284C22×C8—1222no—
285C22×C8—1222no—
286#126—1224no—
287#126—1224no—
288#125—22no—
289#125C2×#692314yes—
290#124—614no—
291#124—1222no—
292#123—1224no—
293#123—1224no—
294C22⋊Q8—614no—
295C22⋊Q8—1222no—
296#121—614no—
297#121—1222no—
298C4×Q8—612no—
299C4×Q8—612no—
300C4×Q8—1221no—
301C4×Q8—1221no—
302C4×D4—612no—
303C4×D4—612no—
304C4×D4—1221no—
305C4×D4—1221no—
306C4×D4—1224no—
307C4×D4—1224no—
308#117—1224no—
309#117—1224no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—1221no—
313C2×C4⋊C4—1221no—
314C2×C4⋊C4C2×#692311yescharacteristic
315C2×C4⋊C4C2×#692311yescharacteristic
316C2×C22⋊C4—1221no—
317C2×C22⋊C4—1221no—
318C2×C22⋊C4—1221no—
319C2×C22⋊C4—1221no—
320C2×C22⋊C4—1221no—
321C2×C42—611no—
322C2×C42—611no—
323C2×C42—611no—
324C2×C42—612no—
325C2×C42—612no—
326C2×C42—612no—
327C2×C42—612no—
328C2×C42—1221no—
329C2×C42C2×#692311yescharacteristic
330C4⋊C8—614no—
331C4⋊C8—1222no—
332C4⋊C8—1224no—
333C4⋊C8—1224no—
334C22⋊C8—1224no—
335C4×C8—614no—
336C4×C8—1222no—
337C24—611no—
338C24—1221no—
339C2×Q8—612no—
340C2×Q8—1221no—
341C2×Q8—1224no—
342C2×D4—612no—
343C2×D4—1224no—
344C2×D4—1221no—
345C2×D4—1224no—
346C2×D4—2444no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—611no—
350C22×C4—611no—
351C22×C4—611no—
352C22×C4—612no—
353C22×C4—612no—
354C22×C4—612no—
355C22×C4—612no—
356C22×C4—612no—
357C22×C4—612no—
358C22×C4—1222no—
359C22×C4—1222no—
360C22×C4—1222no—
361C22×C4—1222no—
362C22×C4—1224no—
363C22×C4—1221no—
364C22×C4—2442no—
365C22×C4—2442no—
366C22×C4—2442no—
367C22×C4C22⋊#692311yescharacteristic
368C22×C4C22⋊#692311yescharacteristic
369C22×C4C22×#692311yescharacteristic
370M16—2448no—
371C2×C8—1224no—
372C2×C8—1224no—
373C2×C8—2444no—
374C2×C8—2444no—
375C4⋊C4—24no—
376C4⋊C4—24no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—1222no—
380C4⋊C4—1222no—
381C4⋊C4—1224no—
382C4⋊C4C22×#692312yes—
383C4⋊C4C22×#692312yes—
384C22⋊C4—1224no—
385C22⋊C4—1222no—
386C22⋊C4—1222no—
387C22⋊C4—1224no—
388C22⋊C4—1224no—
389C22⋊C4—1224no—
390C42—611no—
391C42—612no—
392C42—611no—
393C42—612no—
394C42—612no—
395C42—612no—
396C42—611no—
397C42—611no—
398C42—1222no—
399C42—1222no—
400C42C22⋊#692312yes—
401C42C22×#692312yes—
402C23—612no—
403C23—1222no—
404C23—1222no—
405C23—1222no—
406C23—1222no—
407C23—2442no—
408C23—2442no—
409C23—2442no—
410C23C2×C22⋊#692311yescharacteristic
411Q8—1224no—
412Q8—2442no—
413D4—1224no—
414D4—2448no—
415D4—2442no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—612no—
423C2×C4—612no—
424C2×C4—611no—
425C2×C4—611no—
426C2×C4—612no—
427C2×C4—611no—
428C2×C4—611no—
429C2×C4—1222no—
430C2×C4—1222no—
431C2×C4—1224no—
432C2×C4—1222no—
433C2×C4—1222no—
434C2×C4—1224no—
435C2×C4—1224no—
436C2×C4—1222no—
437C2×C4—2442no—
438C2×C4—2442no—
439C2×C4—2442no—
440C2×C4—2442no—
441C2×C4—2444no—
442C2×C4—2442no—
443C2×C4C2×C22⋊#692312yes—
444C2×C4C2×C22⋊#692312yes—
445C2×C4C2×C22⋊#692311yescharacteristic
446C2×C4#1451986514yes—
447C2×C4C23×#692311yescharacteristic
448C8—2444no—
449C8—2444no—
450C22—1222no—
451C22—1222no—
452C22—1222no—
453C22—4884no—
454C22—2442no—
455C22—2442no—
456C22—2442no—
457C22—2444no—
458C22#1684073712yes—
459C22#1684075312yes—
460C22#1684075912yes—
461C22C22×C22⋊#692311yescharacteristic
462C4—22no—
463C4—22no—
464C4—42no—
465C4—42no—
466C4—611no—
467C4—611no—
468C4—612no—
469C4—1222no—
470C4—1221no—
471C4—1221no—
472C4—2442no—
473C4#1684073712yes—
474C4C2×#1451986512yes—
475C2—4882no—
476C2—2442no—
477C2#2146117714yesdirect product factor
478C2C2×#1684073711yescharacteristic
479C2C2×#1684075311yescharacteristic
480C2C2×#1684075911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×#125×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519752C4
cosocleC4×Dic61C24
hypercenterC2×#125#6923
hypocenterC61C2×#1495
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
1. C2×#16840780C2semidirect
2. C2×#16840766C2semidirect
3. #21461177C2direct (N × H)
4. C2×#16840612C2semidirect
5. C2×#16840610C2semidirect
9. #16840780C22semidirect
11. #16840766C22semidirect
17. #16840612C22semidirect
18. #16840610C22semidirect
241. C2×C61#1495semidirect
274. C61C2×#1495semidirect
477. C2#21461177direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168407802
C2×#168407662
#214611772
C2×#168406122
C2×#168406102
C2×#168402972
C2×#149561