Finite Group Databasebeta

← C2×#21456352 #30549640

Subgroups — C2×#21456352 #30549640

Order 15616.

1854 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840389C212yesmaximal
2#21456352C2116yesmaximal, direct product factor
3C2×#16840170C212yesmaximal, complemented
4C2×#16840168C212yesmaximal, complemented
5C2×#16840166C211yesmaximal, characteristic, complemented
6C2×#16840164C211yesmaximal, characteristic, complemented
7C2×#16840163C211yesmaximal, characteristic, complemented
8C2×#16839803C212yesmaximal
9C2×#16839799C211yesmaximal, characteristic
10C2×#107×D61C211yesmaximal, characteristic
11C2×#16839716C211yesmaximal, characteristic
12C2×C61×#500C211yesmaximal, characteristic, complemented
13C22×#11758189C2211yescharacteristic
14C22×C8×D61C2211yescharacteristic
15#16840389—28no—
16#16840389C22116yes—
17C2×#14519776C2212yes—
18C2×#14519775—22no—
19C2×#14519769C2212yes—
20C2×#14519768C2212yes—
21C2×#14519767—22no—
22C2×#14519755—22no—
23C2×#14519753—22no—
24C2×#14519735C2212yes—
25C2×#14519734C2211yescharacteristic
26C2×C4⋊C4×D61C2212yes—
27#16840170C22116yescomplemented
28#16840168C22116yescomplemented
29#16840166C2218yescomplemented
30#16840164C2218yescomplemented
31#16840163C2218yescomplemented
32#16839803C22116yes—
33#16839799C2218yes—
34C2×#14519711C2211yescharacteristic
35C2×#14519711C2211yescharacteristic
36C2×#14519710C2212yes—
37C2×#14519710C2212yes—
38#107×D61C2218yes—
39C2×#14519709C2212yes—
40C2×#14519708C2212yes—
41C2×#14519708C2212yes—
42#16839716C2218yes—
43C2×#14519688C2211yescharacteristic
44C2×#14519687C2211yescharacteristic
45C2×C8×Dic61C2211yescharacteristic
46C2×C4⋊Q8×C61C2212yes—
47C61×#500C2218yescomplemented
48C2×#107×C61C2211yescharacteristic
49C2×#107×C61C2211yescharacteristic
50C2×#107×C61C2212yes—
51C2×C4×C8×C61C2211yescharacteristic
52C22×Dic122—22no—
53C22×C4×D61—22no—
54C22×C4×D61C2311yescharacteristic
55C2×#11758189Q818yescomplemented
56C2×#11758189C2314yes—
57C22×#92418C2311yescharacteristic
58C22×#92418C2311yescharacteristic
59C2×C8×D61Q818yescomplemented
60C2×C8×D61C2314yes—
61#14519776—24no—
62#14519776C2318yes—
63#14519775—216no—
64#14519769—24no—
65#14519769C2318yes—
66#14519768—24no—
67#14519768C2318yes—
68#14519767—216no—
69#14519755—216no—
70#14519753—216no—
71#14519735—24no—
72#14519735C2318yes—
73#14519734D414yes—
74#14519734C2314yes—
75C2×C4⋊Dic61—22no—
76C2×C4⋊Dic61C2312yes—
77C2×C4⋊Dic61C2312yes—
78C2×#11758196—22no—
79C2×#11758196—22no—
80C2×#11758196—22no—
81C2×#11758196—22no—
82C2×#11758196—22no—
83C2×#11758196D411yescharacteristic
84C2×#11758196D411yescharacteristic
85C4⋊C4×D61—24no—
86C4⋊C4×D61C2318yes—
87C2×#11758198—22no—
88C2×#11758198D411yescharacteristic
89C2×#11758198D411yescharacteristic
90C2×C4×Dic61—22no—
91C2×C4×Dic61C2311yescharacteristic
92#14519711C2314yes—
93#14519711C2314yes—
94#14519710C2318yes—
95#14519710C2318yes—
96#14519709C2318yes—
97#14519708C2318yes—
98#14519708C2318yes—
99#14519688C2314yes—
100#14519687C2314yes—
101C8×Dic61C2314yes—
102C22×Q8×C61—22no—
103C22×C8×C61C2311yescharacteristic
104C22×C8×C61C2311yescharacteristic
105C4⋊Q8×C61—24no—
106C4⋊Q8×C61C2318yes—
107C2×C4⋊C4×C61—22no—
108C2×C4⋊C4×C61C2312yes—
109C2×C4⋊C4×C61C2312yes—
110C2×C42×C61C2311yescharacteristic
111#107×C61C2314yes—
112#107×C61C2314yes—
113#107×C61C2318yes—
114C4×C8×C61C2314yes—
115C23×D61C2×D411yescharacteristic
116C2×Q8×C61—28no—
117C2×Q8×C61—84no—
118C22×C4×C61—22no—
119C22×C4×C61—22no—
120C22×C4×C61C2×D411yescharacteristic
121C22×C4×C61C2×D411yescharacteristic
122C22×C4×C61C2411yescharacteristic
123C22×Dic61—22no—
124C22×Dic61—22no—
125C22×Dic61C2×D411yescharacteristic
126C22×Dic61C2×D411yescharacteristic
127C22×Dic61C2×D411yescharacteristic
128C2×C4×D61—28no—
129C2×C4×D61—84no—
130C2×C4×D61C2×D412yes—
131C2×C4×D61C2×Q814yes—
132C2×C4×D61C2×Q814yes—
133C2×C4×D61C2412yes—
134C2×Dic122—28no—
135C2×Dic122—84no—
136C2×C8×C61C2×Q814yes—
137C2×C8×C61C2×Q814yes—
138C2×C8×C61C2412yes—
139C2×C8×C61C2412yes—
140C4⋊C4×C61—28no—
141C4⋊C4×C61—22no—
142C4⋊C4×C61—22no—
143C4⋊C4×C61C2414yes—
144C4⋊C4×C61C2414yes—
145C42×C61C2×D412yes—
146C42×C61C2412yes—
147#11758198—28no—
148#11758198C2×D414yes—
149#11758198C2×D414yes—
150C4⋊Dic61—22no—
151C4⋊Dic61—22no—
152C4⋊Dic61—28no—
153C4⋊Dic61C2414yes—
154C4⋊Dic61C2414yes—
155#11758196—28no—
156#11758196—28no—
157#11758196—28no—
158#11758196—28no—
159#11758196—28no—
160#11758196C2×D414yes—
161#11758196C2×D414yes—
162C4×Dic61—28no—
163C4×Dic61C2×D412yes—
164C4×Dic61C2412yes—
165C2×#92418C2×Q814yes—
166C2×#92418C2×Q814yes—
167C2×#92418C2412yes—
168C2×#92418C2412yes—
169#11758189C2×Q8116yescomplemented
170C8×D61C2×Q8116yescomplemented
171C23×C61C22×D411yescharacteristic
172C22×D61—22no—
173C22×D61—22no—
174C22×D61C4⋊Q814yes—
175C22×D61C22×D412yes—
176Q8×C61—88no—
177C2×C4×C61—22no—
178C2×C4×C61—22no—
179C2×C4×C61—24no—
180C2×C4×C61—24no—
181C2×C4×C61—44no—
182C2×C4×C61—44no—
183C2×C4×C61C22×D412yes—
184C2×C4×C61C22×D412yes—
185C2×C4×C61C22×D411yescharacteristic
186C2×C4×C61C22×Q812yes—
187C2×C4×C61C22×Q812yes—
188C2×C4×C61C2511yescharacteristic
189C2×Dic61—22no—
190C2×Dic61—22no—
191C2×Dic61—24no—
192C2×Dic61—24no—
193C2×Dic61—44no—
194C2×Dic61—44no—
195C2×Dic61C4⋊Q814yes—
196C2×Dic61C22×D412yes—
197C2×Dic61C22×D412yes—
198C2×Dic61C22×D412yes—
199C4×D61—88no—
200C4×D61C4⋊Q818yes—
201C4×D61C22×Q814yes—
202C4×D61C22×Q814yes—
203Dic122—88no—
204C8×C61C22×Q814yes—
205C8×C61C22×Q814yes—
206#92418C22×Q814yes—
207#92418C22×Q814yes—
208C2×#3164—611nomaximal, Sylow
209C22×C61C2×C4⋊Q812yes—
210C22×C61#57612yes—
211C22×C61#57812yes—
212C22×C61C23×D411yescharacteristic
213C2×D61—28no—
214C2×D61—22no—
215C2×D61—22no—
216C2×D61C2×C4⋊Q814yes—
217C4×C61—22no—
218C4×C61—22no—
219C4×C61—44no—
220C4×C61—44no—
221C4×C61C2×C4⋊Q812yes—
222C4×C61C23×Q811yescharacteristic
223C4×C61C23×Q811yescharacteristic
224Dic61—22no—
225Dic61—22no—
226Dic61—44no—
227Dic61—44no—
228Dic61C2×C4⋊Q814yes—
229C2×#544—612no—
230#3164—6116no—
231C2×#501—612no—
232C2×#501—612no—
233C2×#500—611no—
234C2×#500D6111yescharacteristic, complemented
235C2×#499—611no—
236C2×#499—611no—
237C2×#428—612no—
238C2×#427—611no—
239C22×#107—611no—
240C2×#405—611no—
241C2×C61#316414yescomplemented
242C2×C61C22×C4⋊Q811yescharacteristic
243C2×C61C2×#57611yescharacteristic
244C2×C61C2×#57811yescharacteristic
245D61—24no—
246C22×M16—611no—
247C23×C8—611no—
248#544—6116no—
249#544—1228no—
250C2×C4⋊Q8—612no—
251C2×C4⋊Q8—1222no—
252C2×C4⋊Q8C2×D6112yes—
253C2×#125—612no—
254C2×#125—612no—
255C2×#125—1222no—
256C2×C22⋊Q8—1222no—
257C2×C22⋊Q8—1222no—
258C2×#117—611no—
259C2×#117—612no—
260C22×C4⋊C4—612no—
261#501—6116no—
262#501—6116no—
263#500—618no—
264#500C2×D6118yescomplemented
265#499—618no—
266#499—618no—
267#428—6116no—
268#427—618no—
269C2×#107—611no—
270C2×#107—611no—
271C2×#107—612no—
272C2×#107—612no—
273C2×#107—618no—
274C2×#107C2×D6111yescharacteristic
275C2×#107C2×D6111yescharacteristic
276C2×#107C2×D6112yes—
277C2×#106—612no—
278C2×#106—612no—
279C2×#106—612no—
280#405—618no—
281C2×#97—611no—
282C2×#97—611no—
283C2×C4×C8—611no—
284C2×C4×C8C2×D6111yescharacteristic
285C61C2×#316411yescharacteristic, complemented, Sylow
286C22×Q8—22no—
287C22×Q8—1222no—
288C23×C4—611no—
289C23×C4—1222no—
290C2×M16—618no—
291C2×M16—614no—
292C22×C8—611no—
293C22×C8—611no—
294C22×C8—618no—
295C22×C8—614no—
296C22×C8C22×D6111yescharacteristic
297C22×C8C22×D6111yescharacteristic
298C4⋊Q8—24no—
299C4⋊Q8—618no—
300C4⋊Q8—1224no—
301C4⋊Q8—12216no—
302C4⋊Q8C22×D6118yes—
303#125—618no—
304#125—618no—
305#125—1224no—
306#125—12216no—
307#125—1224no—
308C22⋊Q8—12216no—
309C22⋊Q8—12216no—
310#117—614no—
311#117—614no—
312#117—618no—
313#117—1224no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—611no—
316C2×C4⋊C4—611no—
317C2×C4⋊C4—612no—
318C2×C4⋊C4—612no—
319C2×C4⋊C4—618no—
320C2×C4⋊C4—1224no—
321C2×C4⋊C4—1222no—
322C2×C4⋊C4—1222no—
323C2×C4⋊C4—1222no—
324C2×C4⋊C4—1222no—
325C2×C4⋊C4—1222no—
326C2×C4⋊C4—1222no—
327C2×C4⋊C4C22×D6112yes—
328C2×C4⋊C4C22×D6112yes—
329C2×C22⋊C4—611no—
330C2×C22⋊C4—611no—
331C2×C22⋊C4—1222no—
332C2×C42—611no—
333C2×C42—1222no—
334C2×C42C22×D6111yescharacteristic
335#107—614no—
336#107—614no—
337#107—618no—
338#107—618no—
339#107C22×D6114yes—
340#107C22×D6114yes—
341#107C22×D6118yes—
342#106—618no—
343#106—618no—
344#106—618no—
345#97—614no—
346#97—614no—
347C4×C8—614no—
348C4×C8C22×D6114yes—
349C24—611no—
350C2×Q8—28no—
351C2×Q8—84no—
352C2×Q8—1228no—
353C2×Q8—4884no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—611no—
357C22×C4—612no—
358C22×C4—614no—
359C22×C4—614no—
360C22×C4—612no—
361C22×C4—611no—
362C22×C4—611no—
363C22×C4—1228no—
364C22×C4—1222no—
365C22×C4—1222no—
366C22×C4—4884no—
367C22×C4D4×D6111yescharacteristic
368C22×C4D4×D6111yescharacteristic
369C22×C4C23×D6111yescharacteristic
370M16—6116no—
371C2×C8—614no—
372C2×C8—614no—
373C2×C8—612no—
374C2×C8—612no—
375C2×C8—6116no—
376C2×C8Q8×D6114yes—
377C2×C8Q8×D6114yes—
378C2×C8C23×D6112yes—
379C2×C8C23×D6112yes—
380C4⋊C4—28no—
381C4⋊C4—22no—
382C4⋊C4—22no—
383C4⋊C4—614no—
384C4⋊C4—614no—
385C4⋊C4—614no—
386C4⋊C4—614no—
387C4⋊C4—1228no—
388C4⋊C4—1228no—
389C4⋊C4—1228no—
390C4⋊C4—1228no—
391C4⋊C4—1222no—
392C4⋊C4—1222no—
393C4⋊C4—1228no—
394C4⋊C4—1228no—
395C4⋊C4C23×D6114yes—
396C4⋊C4C23×D6114yes—
397C22⋊C4—614no—
398C22⋊C4—614no—
399C22⋊C4—1228no—
400C42—612no—
401C42—612no—
402C42—1228no—
403C42D4×D6112yes—
404C42C23×D6112yes—
405C23—614no—
406C23—612no—
407C23—1222no—
408C23—1222no—
409C23C2×D4×D6111yescharacteristic
410Q8—88no—
411Q8—4888no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—24no—
415C2×C4—24no—
416C2×C4—44no—
417C2×C4—44no—
418C2×C4—614no—
419C2×C4—612no—
420C2×C4—618no—
421C2×C4—614no—
422C2×C4—614no—
423C2×C4—612no—
424C2×C4—612no—
425C2×C4—1222no—
426C2×C4—1222no—
427C2×C4—1224no—
428C2×C4—1224no—
429C2×C4—4888no—
430C2×C4—2444no—
431C2×C4—2444no—
432C2×C4C2×D4×D6112yes—
433C2×C4C2×D4×D6112yes—
434C2×C4C2×D4×D6111yescharacteristic
435C2×C4C2×Q8×D6112yes—
436C2×C4C2×Q8×D6112yes—
437C2×C4C24×D6111yescharacteristic
438C8—614no—
439C8—614no—
440C8C2×Q8×D6114yes—
441C8C2×Q8×D6114yes—
442C22—614no—
443C22—1222no—
444C22—1222no—
445C22—1228no—
446C22C4⋊Q8×D6112yes—
447C22#1684056312yes—
448C22#1684057512yes—
449C22C22×D4×D6111yescharacteristic
450C4—22no—
451C4—22no—
452C4—44no—
453C4—44no—
454C4—614no—
455C4—1222no—
456C4—1222no—
457C4—2444no—
458C4—2444no—
459C4C4⋊Q8×D6112yes—
460C4C22×Q8×D6111yescharacteristic
461C4C22×Q8×D6111yescharacteristic
462C2—1224no—
463C2#2145635214yesdirect product factor
464C2C2×C4⋊Q8×D6111yescharacteristic
465C2C2×#1684056311yescharacteristic
466C2C2×#1684057511yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#500C2
socleC23×C61C22×D4
prime radicalC23×D61C2×D4
hypercenterC2×#500D61
hypocenterC61C2×#3164
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#500

Complements

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

NH ≅ G/Ntype
2. #21456352C2direct (N × H)
3. C2×#16840170C2semidirect
4. C2×#16840168C2semidirect
5. C2×#16840166C2semidirect
6. C2×#16840164C2semidirect
7. C2×#16840163C2semidirect
12. C2×C61×#500C2semidirect
27. #16840170C22semidirect
28. #16840168C22semidirect
29. #16840166C22semidirect
30. #16840164C22semidirect
31. #16840163C22semidirect
47. C61×#500C22semidirect
55. C2×#11758189Q8semidirect
59. C2×C8×D61Q8semidirect
169. #11758189C2×Q8semidirect
170. C8×D61C2×Q8semidirect
234. C2×#500D61semidirect
241. C2×C61#3164semidirect
264. #500C2×D61semidirect
285. C61C2×#3164semidirect
463. C2#21456352direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403892
#214563522
C2×#168401702
C2×#168401682
C2×#168401662
C2×#168401642
C2×#168401632
C2×#168398032
C2×#168397992
C2×#107×D612
C2×#168397162
C2×C61×#5002
C2×#316461