Finite Group Databasebeta

← C2×#21444588 #29649067

Subgroups — C2×#21444588 #29649067

Order 15616.

770 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839813C211yesmaximal, characteristic
2C2×#16839784C211yesmaximal, characteristic
3C2×C4⋊C8×D61C211yesmaximal, characteristic
4#21444588C218yesmaximal, direct product factor
5C2×#16839513C211yesmaximal, characteristic, complemented
6C2×#16839512C211yesmaximal, characteristic, complemented
7C2×#16839512C211yesmaximal, characteristic, complemented
8C2×C61×#334C211yesmaximal, characteristic, complemented
9C22×#11758189—21no—
10C22×C8×D61—21no—
11C2×C42×D61C2211yescharacteristic
12#16839813C414yes—
13#16839813C2214yes—
14#16839784—22no—
15#16839784C2214yes—
16C2×C4⋊#92418C2211yescharacteristic
17C2×C4⋊#92418C2211yescharacteristic
18C2×#14519706—21no—
19C2×#14519706—21no—
20C2×#14519706C411yescharacteristic
21C2×#14519706C411yescharacteristic
22C4⋊C8×D61—22no—
23C4⋊C8×D61C2214yes—
24C2×#14519689C411yescharacteristic
25C2×#14519689C411yescharacteristic
26C2×C4×#92418C2211yescharacteristic
27#16839513C2214yescomplemented
28#16839512C2214yescomplemented
29#16839512C2214yescomplemented
30C2×C4⋊C8×C61C2211yescharacteristic
31C2×C4⋊C8×C61C2211yescharacteristic
32C2×C4×C8×C61C2211yescharacteristic
33C61×#334C2214yescomplemented
34C22×C4×D61C2×C411yescharacteristic
35C22×C4×D61D411yescharacteristic
36C22×C4×D61Q811yescharacteristic
37C2×#11758189—24no—
38C2×#11758189—44no—
39C22×#92418—21no—
40C22×#92418—21no—
41C22×#92418C2×C411yescharacteristic
42C22×#92418C2×C411yescharacteristic
43C2×C8×D61—24no—
44C2×C8×D61—44no—
45C2×C4×Dic61C2×C411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47C2×C4×Dic61Q811yescharacteristic
48C42×D61C2×C412yes—
49C42×D61D412yes—
50C42×D61Q812yes—
51C42×D61C2312yes—
52C4⋊#92418—21no—
53C4⋊#92418—21no—
54C4⋊#92418C2312yes—
55C4⋊#92418C2312yes—
56#14519706—24no—
57#14519706—24no—
58#14519706C2×C414yes—
59#14519706C2×C414yes—
60#14519689C2×C414yes—
61#14519689C2×C414yes—
62C4×#92418C2×C412yes—
63C4×#92418C2312yes—
64C22×C8×C61—21no—
65C22×C8×C61—21no—
66C22×C8×C61C2×C411yescharacteristic
67C22×C8×C61C2×C411yescharacteristic
68C2×C42×C61C2311yescharacteristic
69C4⋊C8×C61—21no—
70C4⋊C8×C61—21no—
71C4⋊C8×C61C2312yes—
72C4⋊C8×C61C2312yes—
73C4×C8×C61C2×C412yes—
74C4×C8×C61C2312yes—
75C23×D61C4⋊C411yescharacteristic
76C22×C4×C61C22×C411yescharacteristic
77C22×C4×C61C2×D411yescharacteristic
78C22×C4×C61C2×Q811yescharacteristic
79C22×Dic61C4⋊C411yescharacteristic
80C22×Dic61C4⋊C411yescharacteristic
81C22×Dic61C4⋊C411yescharacteristic
82C2×C4×D61—22no—
83C2×C4×D61—22no—
84C2×C4×D61—42no—
85C2×C4×D61C4⋊C412yes—
86C2×C4×D61C4⋊C412yes—
87C2×C4×D61C4⋊C412yes—
88C2×C4×D61SD1614yes—
89C2×C4×D61SD1614yes—
90C2×C4×D61C22×C412yes—
91C2×C4×D61C2×D412yes—
92C2×C4×D61C2×Q812yes—
93C2×C8×C61—22no—
94C2×C8×C61—22no—
95C2×C8×C61—22no—
96C2×C8×C61—22no—
97C2×C8×C61—42no—
98C2×C8×C61—42no—
99C2×C8×C61C22×C412yes—
100C2×C8×C61C22×C412yes—
101C42×C61C22×C411yescharacteristic
102C42×C61C2×D411yescharacteristic
103C42×C61C2×Q811yescharacteristic
104C42×C61C2411yescharacteristic
105C4×Dic61C4⋊C412yes—
106C4×Dic61C4⋊C412yes—
107C4×Dic61C4⋊C412yes—
108C4×Dic61C22×C412yes—
109C4×Dic61C2×D412yes—
110C4×Dic61C2×Q812yes—
111C2×#92418—22no—
112C2×#92418—22no—
113C2×#92418—22no—
114C2×#92418—22no—
115C2×#92418—42no—
116C2×#92418—42no—
117C2×#92418C22×C412yes—
118C2×#92418C22×C412yes—
119#11758189—48no—
120C8×D61—48no—
121C23×C61C2×C4⋊C411yescharacteristic
122C22×D61—22no—
123C22×D61—22no—
124C22×D61#10614yes—
125C22×D61C2×C4⋊C412yes—
126C2×C4×C61—22no—
127C2×C4×C61C2×C4⋊C411yescharacteristic
128C2×C4×C61C2×C4⋊C411yescharacteristic
129C2×C4×C61C2×C4⋊C411yescharacteristic
130C2×C4×C61#13112yes—
131C2×C4×C61#13112yes—
132C2×C4×C61C2×SD1612yes—
133C2×C4×C61C2×SD1612yes—
134C2×C4×C61C23×C411yescharacteristic
135C2×C4×C61C22×D411yescharacteristic
136C2×C4×C61C22×Q811yescharacteristic
137C2×Dic61—22no—
138C2×Dic61—22no—
139C2×Dic61#10614yes—
140C2×Dic61C2×C4⋊C412yes—
141C2×Dic61C2×C4⋊C412yes—
142C2×Dic61C2×C4⋊C412yes—
143C4×D61—22no—
144C4×D61—22no—
145C4×D61—24no—
146C4×D61—42no—
147C4×D61—42no—
148C4×D61#10618yes—
149C4×D61C2×SD1614yes—
150C4×D61C2×SD1614yes—
151C8×C61—22no—
152C8×C61—22no—
153C8×C61—42no—
154C8×C61—42no—
155#92418—22no—
156#92418—22no—
157#92418—42no—
158#92418—42no—
159C2×#1570—611nomaximal, Sylow
160C22×C61#42412yes—
161C22×C61C2×#10612yes—
162C22×C61#43012yes—
163C22×C61C22×C4⋊C411yescharacteristic
164C2×D61—28no—
165C2×D61—22no—
166C2×D61—22no—
167C2×D61C2×#10614yes—
168C4×C61—21no—
169C4×C61—21no—
170C4×C61#42412yes—
171C4×C61C2×#10612yes—
172C4×C61C2×#13111yescharacteristic
173C4×C61C2×#13111yescharacteristic
174C4×C61C22×SD1611yescharacteristic
175C4×C61C22×SD1611yescharacteristic
176Dic61—22no—
177Dic61—22no—
178Dic61C2×#10614yes—
179C2×#431—611no—
180C2×#423—611no—
181C22×C4⋊C8—611no—
182#1570—618no—
183C2×#334—611no—
184C2×#334—611no—
185C2×#334—611no—
186C2×#334D6111yescharacteristic, complemented
187C2×C61#157014yescomplemented
188C2×C61C2×#42411yescharacteristic
189C2×C61C22×#10611yescharacteristic
190C2×C61C2×#43011yescharacteristic
191D61—24no—
192C22×M16—1221no—
193C23×C8—1221no—
194C22×C42—611no—
195#431—614no—
196#431—614no—
197#423—614no—
198#423—1222no—
199C2×C4⋊C8—611no—
200C2×C4⋊C8—611no—
201C2×C4⋊C8—611no—
202C2×C4⋊C8—611no—
203C2×C4⋊C8—614no—
204C2×C4⋊C8—1222no—
205C2×C4⋊C8—1221no—
206C2×C4⋊C8—1221no—
207C2×C4⋊C8C2×D6111yescharacteristic
208C2×C4⋊C8C2×D6111yescharacteristic
209C2×C22⋊C8—611no—
210C2×C22⋊C8—611no—
211C2×C4×C8—611no—
212C2×C4×C8C2×D6111yescharacteristic
213#334—614no—
214#334—614no—
215#334—614no—
216#334C2×D6114yescomplemented
217C61C2×#157011yescharacteristic, complemented, Sylow
218C23×C4—611no—
219C23×C4—611no—
220C23×C4—611no—
221C2×M16—1224no—
222C2×M16—2444no—
223C22×C8—21no—
224C22×C8—21no—
225C22×C8—611no—
226C22×C8—611no—
227C22×C8—1224no—
228C22×C8—1221no—
229C22×C8—1221no—
230C22×C8—2444no—
231C22×C8C4×D6111yescharacteristic
232C22×C8C4×D6111yescharacteristic
233C2×C42—611no—
234C2×C42—611no—
235C2×C42—611no—
236C2×C42—612no—
237C2×C42—612no—
238C2×C42—612no—
239C2×C42—612no—
240C2×C42C22×D6111yescharacteristic
241C4⋊C8—21no—
242C4⋊C8—21no—
243C4⋊C8—614no—
244C4⋊C8—614no—
245C4⋊C8—612no—
246C4⋊C8—612no—
247C4⋊C8—1224no—
248C4⋊C8—1224no—
249C4⋊C8—1221no—
250C4⋊C8—1221no—
251C4⋊C8C22×D6112yes—
252C4⋊C8C22×D6112yes—
253C22⋊C8—614no—
254C22⋊C8—614no—
255C4×C8—612no—
256C4×C8—612no—
257C4×C8C4×D6112yes—
258C4×C8C22×D6112yes—
259C24—611no—
260C22×C4—611no—
261C22×C4—612no—
262C22×C4—612no—
263C22×C4—614no—
264C22×C4—614no—
265C22×C4—611no—
266C22×C4—611no—
267C22×C4—612no—
268C22×C4—612no—
269C22×C4—612no—
270C22×C4—612no—
271C22×C4—1222no—
272C22×C4—1222no—
273C22×C4—2442no—
274C22×C4C2×C4×D6111yescharacteristic
275C22×C4D4×D6111yescharacteristic
276C22×C4Q8×D6111yescharacteristic
277M16—2448no—
278C2×C8—22no—
279C2×C8—22no—
280C2×C8—22no—
281C2×C8—22no—
282C2×C8—42no—
283C2×C8—42no—
284C2×C8—612no—
285C2×C8—612no—
286C2×C8—1222no—
287C2×C8—1222no—
288C2×C8—1222no—
289C2×C8—1222no—
290C2×C8—2448no—
291C2×C8—2442no—
292C2×C8—2442no—
293C2×C8C2×C4×D6112yes—
294C2×C8C2×C4×D6112yes—
295C42—612no—
296C42—612no—
297C42—612no—
298C42—612no—
299C42—612no—
300C42—612no—
301C42C2×C4×D6111yescharacteristic
302C42D4×D6111yescharacteristic
303C42Q8×D6111yescharacteristic
304C42C23×D6111yescharacteristic
305C23—612no—
306C23—614no—
307C23—1222no—
308C23—1222no—
309C23C4⋊C4×D6111yescharacteristic
310C2×C4—22no—
311C2×C4—612no—
312C2×C4—614no—
313C2×C4—614no—
314C2×C4—614no—
315C2×C4—618no—
316C2×C4—612no—
317C2×C4—612no—
318C2×C4—1222no—
319C2×C4—1222no—
320C2×C4—1222no—
321C2×C4—1222no—
322C2×C4—1224no—
323C2×C4—2442no—
324C2×C4—2442no—
325C2×C4C4⋊C4×D6111yescharacteristic
326C2×C4C4⋊C4×D6111yescharacteristic
327C2×C4C4⋊C4×D6111yescharacteristic
328C2×C4#1451978312yes—
329C2×C4#1451978512yes—
330C2×C4SD16×D6112yes—
331C2×C4SD16×D6112yes—
332C2×C4C22×C4×D6111yescharacteristic
333C2×C4C2×D4×D6111yescharacteristic
334C2×C4C2×Q8×D6111yescharacteristic
335C8—22no—
336C8—22no—
337C8—42no—
338C8—42no—
339C8—1222no—
340C8—1222no—
341C8—2442no—
342C8—2442no—
343C22—614no—
344C22—1222no—
345C22—1222no—
346C22—1228no—
347C22#1683978712yes—
348C22#106×D6112yes—
349C22#1683980912yes—
350C22C2×C4⋊C4×D6111yescharacteristic
351C4—21no—
352C4—21no—
353C4—614no—
354C4—1222no—
355C4—1222no—
356C4#1683978712yes—
357C4#106×D6112yes—
358C4C2×#1451978311yescharacteristic
359C4C2×#1451978511yescharacteristic
360C4C2×SD16×D6111yescharacteristic
361C4C2×SD16×D6111yescharacteristic
362C2—1224no—
363C2#2144458814yesdirect product factor
364C2C2×#1683978711yescharacteristic
365C2C2×#106×D6111yescharacteristic
366C2C2×#1683980911yescharacteristic
subgroupG/H
centerC22×C4D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC2×C61×#334C2
socleC23×C61C2×C4⋊C4
prime radicalC23×D61C4⋊C4
cosocleC42×C61C24
hypercenterC2×#334D61
hypocenterC61C2×#1570
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×#334

Complements

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

NH ≅ G/Ntype
4. #21444588C2direct (N × H)
5. C2×#16839513C2semidirect
6. C2×#16839512C2semidirect
7. C2×#16839512C2semidirect
8. C2×C61×#334C2semidirect
27. #16839513C22semidirect
28. #16839512C22semidirect
29. #16839512C22semidirect
33. C61×#334C22semidirect
186. C2×#334D61semidirect
187. C2×C61#1570semidirect
216. #334C2×D61semidirect
217. C61C2×#1570semidirect
363. C2#21444588direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168398132
C2×#168397842
C2×C4⋊C8×D612
#214445882
C2×#168395132
C2×#168395122
C2×C61×#3342
C2×#157061