Finite Group Databasebeta

← C2×#21444939 #29655650

Subgroups — C2×#21444939 #29655650

Order 15616.

1074 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840497C211yesmaximal, characteristic
2C2×#16840136C211yesmaximal, characteristic
3C2×#16840054C211yesmaximal, characteristic, complemented
4#21444939C218yesmaximal, direct product factor
5C2×#16839505C211yesmaximal, characteristic
6C2×Q8⋊#92418C211yesmaximal, characteristic, complemented
7C2×#16839492C211yesmaximal, characteristic, complemented
8C2×C61×#477C211yesmaximal, characteristic, complemented
9C22×#11758201—22no—
10#16840497—22no—
11#16840497—22no—
12#16840497—22no—
13#16840497C2214yes—
14C2×#14519774C2211yescharacteristic
15C2×#14519766—21no—
16C2×#14519765—21no—
17C2×#14519762—22no—
18C2×C4×Dic122C2211yescharacteristic
19C2×C4×D244—21no—
20C2×#14519739—21no—
21#16840136—22no—
22#16840136C2214yes—
23#16840054—22no—
24#16840054C2214yescomplemented
25C2×#14519710—21no—
26C2×C4⋊#92418C2211yescharacteristic
27C2×#14519700—21no—
28C2×C4×#92418C2211yescharacteristic
29#16839505C2214yes—
30Q8⋊#92418C2214yescomplemented
31#16839492C2214yescomplemented
32C2×C4⋊Q8×C61C2211yescharacteristic
33C2×C4×Q8×C61C2211yescharacteristic
34C61×#477—22no—
35C61×#477C2214yescomplemented
36C2×#107×C61—21no—
37C2×C4⋊C8×C61C2211yescharacteristic
38C2×#103×C61—21no—
39C22×Dic122D411yescharacteristic
40C22×D244—21no—
41C22×D244—21no—
42C22×D244D412yes—
43C22×C4×D61—22no—
44C2×#11758201—28no—
45C2×#11758201—48no—
46C22×#92418—21no—
47C22×#92418—21no—
48#14519774—21no—
49#14519774—21no—
50#14519774D412yes—
51#14519774C2312yes—
52#14519766—24no—
53#14519766—24no—
54#14519765—24no—
55#14519765—24no—
56#14519762—28no—
57#14519762—28no—
58C4×Dic122—21no—
59C4×Dic122—21no—
60C4×Dic122D412yes—
61C4×Dic122C2312yes—
62C4×D244—24no—
63C4×D244—24no—
64#14519739—24no—
65#14519739—24no—
66C2×C4⋊Dic61D411yescharacteristic
67C2×#11758196—21no—
68C2×#11758198—22no—
69C2×#11758198—22no—
70C2×#11758198—22no—
71C2×C4×Dic61—21no—
72#14519710—24no—
73C4⋊#92418—21no—
74C4⋊#92418C2312yes—
75#14519700—24no—
76C4×#92418—21no—
77C4×#92418C2312yes—
78C22×Q8×C61—21no—
79C22×Q8×C61D411yescharacteristic
80C22×C8×C61—21no—
81C4⋊Q8×C61—21no—
82C4⋊Q8×C61—21no—
83C4⋊Q8×C61—21no—
84C4⋊Q8×C61C2312yes—
85C4×Q8×C61—21no—
86C4×Q8×C61—21no—
87C4×Q8×C61D412yes—
88C4×Q8×C61C2312yes—
89C2×C4⋊C4×C61—21no—
90C2×C4⋊C4×C61—21no—
91C2×C4⋊C4×C61—21no—
92C2×C4⋊C4×C61D411yescharacteristic
93C2×C42×C61—21no—
94C2×C42×C61C2311yescharacteristic
95#107×C61—24no—
96C4⋊C8×C61—21no—
97C4⋊C8×C61C2312yes—
98#103×C61—24no—
99C23×D61—22no—
100C2×Q8×C61—21no—
101C2×Q8×C61—22no—
102C2×Q8×C61—22no—
103C2×Q8×C61—22no—
104C2×Q8×C61—44no—
105C2×Q8×C61—41no—
106C2×Q8×C61C2×D412yes—
107C22×C4×C61—21no—
108C22×C4×C61—21no—
109C22×C4×C61—41no—
110C22×C4×C61C2×D411yescharacteristic
111C22×C4×C61C2×D411yescharacteristic
112C22×C4×C61C2×D411yescharacteristic
113C22×Dic61—21no—
114C22×Dic61—21no—
115C2×D244—22no—
116C2×D244—22no—
117C2×D244—22no—
118C2×D244—22no—
119C2×D244—22no—
120C2×D244—42no—
121C2×D244—42no—
122C2×D244—42no—
123C2×D244—42no—
124C2×D244—44no—
125C2×D244C2×D414yes—
126C2×C4×D61—28no—
127C2×C4×D61—84no—
128C2×Dic122—22no—
129C2×Dic122—22no—
130C2×Dic122—21no—
131C2×Dic122C2×D412yes—
132C2×C8×C61—22no—
133C2×C8×C61—42no—
134C4⋊C4×C61—22no—
135C4⋊C4×C61—21no—
136C4⋊C4×C61—22no—
137C4⋊C4×C61—22no—
138C4⋊C4×C61—22no—
139C4⋊C4×C61—41no—
140C4⋊C4×C61—41no—
141C4⋊C4×C61C2×D412yes—
142C42×C61—22no—
143C42×C61—22no—
144C42×C61C2×D411yescharacteristic
145C42×C61C2×D411yescharacteristic
146C42×C61C2×D411yescharacteristic
147C42×C61C2411yescharacteristic
148#11758201—416no—
149#11758198—28no—
150#11758198—28no—
151#11758198—28no—
152C4⋊Dic61—21no—
153C4⋊Dic61C2×D412yes—
154#11758196—22no—
155#11758196—22no—
156C4×Dic61—22no—
157C4×Dic61—22no—
158C2×#92418—24no—
159C2×#92418—22no—
160C2×#92418—22no—
161C2×#92418—42no—
162C23×C61#12011yescharacteristic
163C22×D61—24no—
164C22×D61—44no—
165C22×D61—44no—
166C22×D61—44no—
167Q8×C61—22no—
168Q8×C61—22no—
169Q8×C61—44no—
170Q8×C61—42no—
171Q8×C61—82no—
172C2×C4×C61—22no—
173C2×C4×C61—22no—
174C2×C4×C61—22no—
175C2×C4×C61—42no—
176C2×C4×C61—42no—
177C2×C4×C61—42no—
178C2×C4×C61—82no—
179C2×C4×C61#12011yescharacteristic
180C2×C4×C61#12011yescharacteristic
181C2×C4×C61#12011yescharacteristic
182C2×C4×C61#13512yes—
183C2×C4×C61#13512yes—
184C2×C4×C61#13712yes—
185C2×C4×C61#13712yes—
186C2×C4×C61C22×D411yescharacteristic
187C2×C4×C61C22×D411yescharacteristic
188C2×C4×C61C22×D411yescharacteristic
189C2×Dic61—22no—
190C2×Dic61—22no—
191C2×Dic61—42no—
192C2×Dic61—42no—
193D244—44no—
194D244—42no—
195D244—42no—
196D244—42no—
197D244—42no—
198D244—44no—
199D244—44no—
200D244—82no—
201C4×D61—88no—
202Dic122—22no—
203Dic122—22no—
204Dic122—42no—
205C8×C61—42no—
206#92418—24no—
207#92418—42no—
208C2×#1630—611nomaximal, Sylow
209C22×C61#45212yes—
210C22×C61#45212yes—
211C22×C61#45312yes—
212C22×C61C2×#12011yescharacteristic
213C2×D61—44no—
214C2×D61—44no—
215C2×D61—44no—
216C2×D61—88no—
217C4×C61—21no—
218C4×C61—21no—
219C4×C61—42no—
220C4×C61—42no—
221C4×C61—82no—
222C4×C61#45212yes—
223C4×C61#45212yes—
224C4×C61C2×#13511yescharacteristic
225C4×C61C2×#13511yescharacteristic
226C4×C61C2×#13711yescharacteristic
227C4×C61C2×#13711yescharacteristic
228Dic61—42no—
229Dic61—42no—
230C2×#559—611no—
231C2×#492—611no—
232C2×#477—611no—
233C2×#477D6111yescharacteristic, complemented
234#1630—618no—
235C2×#331—611no—
236C2×Q8⋊C8—611no—
237C2×Q8⋊C8—611no—
238C2×C61#163014yescomplemented
239C2×C61C2×#45211yescharacteristic
240C2×C61C2×#45211yescharacteristic
241C2×C61C2×#45311yescharacteristic
242D61—84no—
243C22×SD16—1222no—
244#559—614no—
245#559—1222no—
246#559—1222no—
247#559—1222no—
248C2×C4⋊Q8C2×D6111yescharacteristic
249C2×#127—611no—
250C2×#124—1221no—
251C2×#124—1221no—
252C2×#123—1222no—
253C2×C4×Q8—611no—
254C2×C4×Q8C2×D6111yescharacteristic
255C2×C4×D4—1221no—
256C2×C4×D4—1221no—
257#492—614no—
258#492—1222no—
259#477—22no—
260#477—614no—
261#477—1222no—
262#477C2×D6114yescomplemented
263C2×#107—21no—
264C2×#107—1221no—
265C2×C4⋊C8—611no—
266C2×C4⋊C8C2×D6111yescharacteristic
267C2×#103—21no—
268C2×#103—1221no—
269C2×C4×C8—611no—
270#331—614no—
271Q8⋊C8—614no—
272Q8⋊C8—614no—
273C61C2×#163011yescharacteristic, complemented, Sylow
274C22×Q8—21no—
275C22×Q8—611no—
276C22×Q8C22⋊D6111yescharacteristic
277C22×D4—612no—
278C22×D4—1221no—
279C22×D4—1221no—
280C23×C4—1222no—
281C2×SD16—1228no—
282C2×SD16—2448no—
283C22×C8—21no—
284C22×C8—1221no—
285C22×C8—1221no—
286C4⋊Q8—21no—
287C4⋊Q8—21no—
288C4⋊Q8—21no—
289C4⋊Q8C22×D6112yes—
290#127—612no—
291#127—612no—
292#127—1221no—
293#127—1221no—
294#124—1224no—
295#124—1224no—
296#124—1224no—
297#124—1224no—
298#123—1228no—
299#123—1228no—
300C4×Q8—21no—
301C4×Q8—21no—
302C4×Q8—612no—
303C4×Q8—612no—
304C4×Q8—1221no—
305C4×Q8—1221no—
306C4×Q8C22⋊D6112yes—
307C4×Q8C22×D6112yes—
308C4×D4—1224no—
309C4×D4—1224no—
310C4×D4—1224no—
311C4×D4—1224no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—611no—
316C2×C4⋊C4—1221no—
317C2×C4⋊C4C22⋊D6111yescharacteristic
318C2×C22⋊C4—1222no—
319C2×C22⋊C4—1222no—
320C2×C22⋊C4—1222no—
321C2×C42—21no—
322C2×C42—1221no—
323C2×C42C22×D6111yescharacteristic
324#107—24no—
325#107—1224no—
326C4⋊C8—21no—
327C4⋊C8—612no—
328C4⋊C8—1221no—
329C4⋊C8C22×D6112yes—
330#103—24no—
331#103—1224no—
332C4×C8—612no—
333C4×C8—1221no—
334C24—1222no—
335C2×Q8—21no—
336C2×Q8—22no—
337C2×Q8—22no—
338C2×Q8—22no—
339C2×Q8—44no—
340C2×Q8—41no—
341C2×Q8—612no—
342C2×Q8—1221no—
343C2×Q8—1222no—
344C2×Q8—1222no—
345C2×Q8C2×C22⋊D6112yes—
346C2×D4—614no—
347C2×D4—1222no—
348C2×D4—1222no—
349C2×D4—1222no—
350C2×D4—1222no—
351C2×D4—1222no—
352C2×D4—2444no—
353C2×D4—2442no—
354C2×D4—2442no—
355C2×D4—2442no—
356C2×D4—2442no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—41no—
360C22×C4—1228no—
361C22×C4—1221no—
362C22×C4—1221no—
363C22×C4—4884no—
364C22×C4D4×D6111yescharacteristic
365C22×C4D4×D6111yescharacteristic
366C22×C4C2×C22⋊D6111yescharacteristic
367SD16—24416no—
368C2×C8—22no—
369C2×C8—42no—
370C2×C8—1224no—
371C2×C8—1222no—
372C2×C8—1222no—
373C2×C8—2442no—
374C4⋊C4—22no—
375C4⋊C4—22no—
376C4⋊C4—21no—
377C4⋊C4—22no—
378C4⋊C4—22no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C4⋊C4—612no—
382C4⋊C4—1222no—
383C4⋊C4—1221no—
384C4⋊C4—1222no—
385C4⋊C4C2×C22⋊D6112yes—
386C22⋊C4—1228no—
387C22⋊C4—1228no—
388C22⋊C4—1228no—
389C42—22no—
390C42—22no—
391C42—1222no—
392C42—1222no—
393C42D4×D6111yescharacteristic
394C42D4×D6111yescharacteristic
395C42C2×C22⋊D6111yescharacteristic
396C42C23×D6111yescharacteristic
397C23—1224no—
398C23—2444no—
399C23—2444no—
400C23—2444no—
401C23#1451974511yescharacteristic
402Q8—22no—
403Q8—22no—
404Q8—44no—
405Q8—42no—
406Q8—82no—
407Q8—1222no—
408Q8—1222no—
409Q8—2442no—
410D4—4882no—
411D4—2444no—
412D4—2442no—
413D4—2442no—
414D4—2442no—
415D4—2442no—
416D4—2444no—
417D4—2444no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—82no—
425C2×C4—1222no—
426C2×C4—1222no—
427C2×C4—4888no—
428C2×C4—2442no—
429C2×C4—2442no—
430C2×C4#1451974511yescharacteristic
431C2×C4#1451974511yescharacteristic
432C2×C4#1451974511yescharacteristic
433C2×C4#1451979712yes—
434C2×C4#1451980012yes—
435C2×C4#1451980812yes—
436C2×C4#1451980912yes—
437C2×C4C2×D4×D6111yescharacteristic
438C2×C4C2×D4×D6111yescharacteristic
439C2×C4C22×C22⋊D6111yescharacteristic
440C8—42no—
441C8—1224no—
442C8—2442no—
443C22—4888no—
444C22—2444no—
445C22—2444no—
446C22—2444no—
447C22#1683992212yes—
448C22#1683992312yes—
449C22#1683992812yes—
450C22C2×#1451974511yescharacteristic
451C4—21no—
452C4—21no—
453C4—42no—
454C4—42no—
455C4—82no—
456C4—2442no—
457C4—2442no—
458C4#1683992212yes—
459C4#1683992312yes—
460C4C2×#1451979711yescharacteristic
461C4C2×#1451980011yescharacteristic
462C4C2×#1451980811yescharacteristic
463C4C2×#1451980911yescharacteristic
464C2—4884no—
465C2#2144493914yesdirect product factor
466C2C2×#1683992211yescharacteristic
467C2C2×#1683992311yescharacteristic
468C2C2×#1683992811yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×#477C2
socleC23×C61#120
prime radicalC2×#14519774C22
hypercenterC2×#477D61
hypocenterC61C2×#1630
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
3. C2×#16840054C2semidirect
4. #21444939C2direct (N × H)
6. C2×Q8⋊#92418C2semidirect
7. C2×#16839492C2semidirect
8. C2×C61×#477C2semidirect
24. #16840054C22semidirect
30. Q8⋊#92418C22semidirect
31. #16839492C22semidirect
35. C61×#477C22semidirect
233. C2×#477D61semidirect
238. C2×C61#1630semidirect
262. #477C2×D61semidirect
273. C61C2×#1630semidirect
465. C2#21444939direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404972
C2×#168401362
C2×#168400542
#214449392
C2×#168395052
C2×Q8⋊#924182
C2×#168394922
C2×C61×#4772
C2×#163061