Finite Group Databasebeta

← C2×#34036811 #49172289

Subgroups — C2×#34036811 #49172289

Order 37504.

1124 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036811C2116yesmaximal, direct product factor
2C2×#22627619C211yesmaximal, characteristic, complemented
3C2×#22627619C211yesmaximal, characteristic, complemented
4C2×#22627614C211yesmaximal, characteristic, complemented
5C2×#22627614C211yesmaximal, characteristic, complemented
6C2×#22627609C211yesmaximal, characteristic
7C2×#22627609C211yesmaximal, characteristic
8C2×#22627602C211yesmaximal, characteristic, complemented
9C2×#22627602C211yesmaximal, characteristic, complemented
10C2×#22627589C211yesmaximal, characteristic, complemented
11C2×#22627586C211yesmaximal, characteristic
12C2×#22627582C211yesmaximal, characteristic, complemented
13C2×#22627581C211yesmaximal, characteristic, complemented
14C2×#22627581C211yesmaximal, characteristic, complemented
15C2×C4⋊C4×D293C211yesmaximal, characteristic, complemented
16C2×#125×C293C211yesmaximal, characteristic, complemented
17C22×Dic586C2211yescharacteristic
18C22×D1172C2211yescharacteristic
19C22×C4×D293C2211yescharacteristic
20C22×C4×D293C2211yescharacteristic
21C22×C4×D293C2211yescharacteristic
22C22×C4×D293C2211yescharacteristic
23#22627619C2218yescomplemented
24#22627619C2218yescomplemented
25#22627614C2218yescomplemented
26#22627614C2218yescomplemented
27#22627609C2218yes—
28#22627609C2218yes—
29#22627602C2218yescomplemented
30#22627602C2218yescomplemented
31#22627589C2218yescomplemented
32#22627586C2218yes—
33#22627582C2218yescomplemented
34#22627581C2218yescomplemented
35#22627581C2218yescomplemented
36C2×C4⋊Dic293C2211yescharacteristic
37C2×C4⋊Dic293C2211yescharacteristic
38C2×#17989781C2211yescharacteristic
39C2×#17989781C2211yescharacteristic
40C2×#17989781C2211yescharacteristic
41C2×#17989781C2211yescharacteristic
42C2×#17989781C2211yescharacteristic
43C2×#17989781C2211yescharacteristic
44C2×#17989781C2211yescharacteristic
45C2×#17989781C2211yescharacteristic
46C4⋊C4×D293C2218yescomplemented
47C2×#17989779C2211yescharacteristic
48C2×#17989779C2211yescharacteristic
49C2×#17989779C2211yescharacteristic
50C2×#17989779C2211yescharacteristic
51C2×#17989779C2211yescharacteristic
52C2×#17989779C2211yescharacteristic
53C2×#17989779C2211yescharacteristic
54C2×#17989779C2211yescharacteristic
55C2×C4×Dic293C2211yescharacteristic
56C2×C4×Dic293C2211yescharacteristic
57C2×C4×Dic293C2211yescharacteristic
58C2×C4×Dic293C2211yescharacteristic
59#125×C293C2218yescomplemented
60C2×C4⋊C4×C293C2211yescharacteristic
61C2×C4⋊C4×C293C2211yescharacteristic
62C2×C4⋊C4×C293C2211yescharacteristic
63C2×C4⋊C4×C293C2211yescharacteristic
64C2×C4⋊C4×C293C2211yescharacteristic
65C2×C4⋊C4×C293C2211yescharacteristic
66C2×C42×C293C2211yescharacteristic
67C23×D293C2311yescharacteristic
68C23×D293C2311yescharacteristic
69C2×Dic586—24no—
70C2×Dic586C2314yes—
71C2×D1172—24no—
72C2×D1172C2314yes—
73C22×Dic293C2311yescharacteristic
74C22×Dic293C2311yescharacteristic
75C22×Dic293C2311yescharacteristic
76C22×Dic293C2311yescharacteristic
77C22×Dic293C2311yescharacteristic
78C22×Dic293C2311yescharacteristic
79C2×C4×D293—24no—
80C2×C4×D293—24no—
81C2×C4×D293—24no—
82C2×C4×D293—24no—
83C2×C4×D293C2314yes—
84C2×C4×D293C2314yes—
85C2×C4×D293C2314yes—
86C2×C4×D293C2314yes—
87C4⋊Dic293C2314yes—
88C4⋊Dic293C2314yes—
89#17989781C2314yes—
90#17989781C2314yes—
91#17989781C2314yes—
92#17989781C2314yes—
93#17989781C2314yes—
94#17989781C2314yes—
95#17989781C2314yes—
96#17989781C2314yes—
97#17989779C2314yes—
98#17989779C2314yes—
99#17989779C2314yes—
100#17989779C2314yes—
101#17989779C2314yes—
102#17989779C2314yes—
103#17989779C2314yes—
104#17989779C2314yes—
105C4×Dic293C2314yes—
106C4×Dic293C2314yes—
107C4×Dic293C2314yes—
108C4×Dic293C2314yes—
109C22×C4×C293C2311yescharacteristic
110C22×C4×C293C2311yescharacteristic
111C22×C4×C293C2311yescharacteristic
112C22×C4×C293C2311yescharacteristic
113C22×C4×C293C2311yescharacteristic
114C22×C4×C293C2311yescharacteristic
115C22×C4×C293C2311yescharacteristic
116C4⋊C4×C293C2314yes—
117C4⋊C4×C293C2314yes—
118C4⋊C4×C293C2314yes—
119C4⋊C4×C293C2314yes—
120C4⋊C4×C293C2314yes—
121C4⋊C4×C293C2314yes—
122C42×C293C2314yes—
123C22×D293—22no—
124C22×D293—22no—
125C22×D293—22no—
126C22×D293—22no—
127C22×D293—22no—
128C22×D293#4114yes—
129C22×D293C2412yes—
130C22×D293C2412yes—
131Dic586—28no—
132D1172—28no—
133C2×Dic293—22no—
134C2×Dic293—22no—
135C2×Dic293—22no—
136C2×Dic293—22no—
137C2×Dic293—22no—
138C2×Dic293#4114yes—
139C2×Dic293C2412yes—
140C2×Dic293C2412yes—
141C2×Dic293C2412yes—
142C2×Dic293C2412yes—
143C2×Dic293C2412yes—
144C2×Dic293C2412yes—
145C4×D293—28no—
146C4×D293—28no—
147C4×D293—28no—
148C4×D293—28no—
149C23×C293C2411yescharacteristic
150C2×C4×C293—22no—
151C2×C4×C293—22no—
152C2×C4×C293—22no—
153C2×C4×C293—22no—
154C2×C4×C293—22no—
155C2×C4×C293—22no—
156C2×C4×C293—22no—
157C2×C4×C293C2412yes—
158C2×C4×C293C2412yes—
159C2×C4×C293C2412yes—
160C2×C4×C293C2412yes—
161C2×C4×C293C2412yes—
162C2×C4×C293C2412yes—
163C2×C4×C293C2412yes—
164C22×C293C2×#4112yes—
165C22×C293C2×#4112yes—
166C22×C2932−1+412yes—
167C22×C293C2511yescharacteristic
168C2×D293—28no—
169C2×D293—22no—
170C2×D293—22no—
171C2×D293—22no—
172C2×D293—22no—
173C2×D293—22no—
174C2×D293—44no—
175C2×D293C2×#4114yes—
176C4×C293—22no—
177C4×C293—22no—
178C4×C293—22no—
179C4×C293—22no—
180C4×C293—22no—
181C4×C293—22no—
182C4×C293—22no—
183Dic293—22no—
184Dic293—22no—
185Dic293—22no—
186Dic293—22no—
187Dic293—22no—
188Dic293C2×#4114yes—
189C2×C293#55214yescomplemented
190C2×C293C22×#4111yescharacteristic
191C2×C293C22×#4111yescharacteristic
192C2×C293C2×2−1+411yescharacteristic
193D293—24no—
194D293—42no—
195C293C2×#55211yescharacteristic, complemented, Sylow
196C2×#552—2931nomaximal, Sylow
197#552—29316no—
198C2×#126—2931no—
199C2×#126—2931no—
200C2×#125—2931no—
201C2×#125—2931no—
202C2×#125D29311yescharacteristic, complemented
203C2×#123—2931no—
204C2×#123—2931no—
205C2×C22⋊Q8—2931no—
206C2×C22⋊Q8—2931no—
207C2×C4×Q8—2931no—
208C2×C4×D4—2931no—
209C2×#117—2931no—
210C2×#117—2931no—
211C2×#117—2931no—
212C22×C4⋊C4—2931no—
213C22×Q8—2931no—
214C22×D4—2931no—
215C23×C4—2931no—
216C23×C4—2931no—
217C23×C4—2931no—
218C23×C4—2931no—
219#126—2938no—
220#126—2938no—
221#125—2938no—
222#125—2938no—
223#125C2×D29318yescomplemented
224#123—2938no—
225#123—2938no—
226C22⋊Q8—2938no—
227C22⋊Q8—2938no—
228C4×Q8—2938no—
229C4×D4—2938no—
230#117—2938no—
231#117—2938no—
232#117—2938no—
233C2×C4⋊C4—2931no—
234C2×C4⋊C4—2931no—
235C2×C4⋊C4—2931no—
236C2×C4⋊C4—2931no—
237C2×C4⋊C4—2931no—
238C2×C4⋊C4—2931no—
239C2×C4⋊C4—2931no—
240C2×C4⋊C4—2931no—
241C2×C4⋊C4—2931no—
242C2×C4⋊C4—2931no—
243C2×C4⋊C4—2938no—
244C2×C4⋊C4C2×D29311yescharacteristic
245C2×C4⋊C4C2×D29311yescharacteristic
246C2×C4⋊C4C2×D29311yescharacteristic
247C2×C4⋊C4C2×D29311yescharacteristic
248C2×C4⋊C4C2×D29311yescharacteristic
249C2×C4⋊C4C2×D29311yescharacteristic
250C2×C22⋊C4—2931no—
251C2×C22⋊C4—2931no—
252C2×C22⋊C4—2931no—
253C2×C22⋊C4—2931no—
254C2×C22⋊C4—2931no—
255C2×C22⋊C4—2931no—
256C2×C22⋊C4—2931no—
257C2×C22⋊C4—2931no—
258C2×C42—2931no—
259C2×C42—2931no—
260C2×C42—2931no—
261C2×C42—2931no—
262C2×C42C2×D29311yescharacteristic
263C24—2931no—
264C24—2931no—
265C2×Q8—2934no—
266C2×Q8—5864no—
267C2×D4—2934no—
268C2×D4—5864no—
269C22×C4—2931no—
270C22×C4—2931no—
271C22×C4—2931no—
272C22×C4—2931no—
273C22×C4—2931no—
274C22×C4—2931no—
275C22×C4—2934no—
276C22×C4—2934no—
277C22×C4—2934no—
278C22×C4—2934no—
279C22×C4—5864no—
280C22×C4—5864no—
281C22×C4—5864no—
282C22×C4—5864no—
283C22×C4C22×D29311yescharacteristic
284C22×C4C22×D29311yescharacteristic
285C22×C4C22×D29311yescharacteristic
286C22×C4C22×D29311yescharacteristic
287C22×C4C22×D29311yescharacteristic
288C22×C4C22×D29311yescharacteristic
289C22×C4C22×D29311yescharacteristic
290C4⋊C4—2934no—
291C4⋊C4—2934no—
292C4⋊C4—2934no—
293C4⋊C4—2934no—
294C4⋊C4—2934no—
295C4⋊C4—2934no—
296C4⋊C4—2934no—
297C4⋊C4—2934no—
298C4⋊C4—2934no—
299C4⋊C4—2934no—
300C4⋊C4C22×D29314yes—
301C4⋊C4C22×D29314yes—
302C4⋊C4C22×D29314yes—
303C4⋊C4C22×D29314yes—
304C4⋊C4C22×D29314yes—
305C4⋊C4C22×D29314yes—
306C22⋊C4—2934no—
307C22⋊C4—2934no—
308C22⋊C4—2934no—
309C22⋊C4—2934no—
310C22⋊C4—2934no—
311C22⋊C4—2934no—
312C22⋊C4—2934no—
313C22⋊C4—2934no—
314C42—2934no—
315C42—2934no—
316C42—2934no—
317C42—2934no—
318C42C22×D29314yes—
319C23—2934no—
320C23—2932no—
321C23—2932no—
322C23—5862no—
323C23—5862no—
324C23—5862no—
325C23—5862no—
326C23—5862no—
327C23C23×D29311yescharacteristic
328Q8—5868no—
329D4—5868no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—2934no—
338C2×C4—2932no—
339C2×C4—2932no—
340C2×C4—2932no—
341C2×C4—2932no—
342C2×C4—2932no—
343C2×C4—2932no—
344C2×C4—5868no—
345C2×C4—5868no—
346C2×C4—5868no—
347C2×C4—5868no—
348C2×C4—5862no—
349C2×C4—5862no—
350C2×C4—5862no—
351C2×C4—5862no—
352C2×C4—5862no—
353C2×C4C23×D29312yes—
354C2×C4C23×D29312yes—
355C2×C4C23×D29312yes—
356C2×C4C23×D29312yes—
357C2×C4C23×D29312yes—
358C2×C4C23×D29312yes—
359C2×C4C23×D29312yes—
360C22—2934no—
361C22—5868no—
362C22—5862no—
363C22—5862no—
364C22—5862no—
365C22—5862no—
366C22—5862no—
367C22—11724no—
368C22#41×D29312yes—
369C22#41×D29312yes—
370C22#2262767212yes—
371C22C24×D29311yescharacteristic
372C4—22no—
373C4—22no—
374C4—22no—
375C4—22no—
376C4—22no—
377C4—22no—
378C4—22no—
379C4—2934no—
380C4—5862no—
381C4—5862no—
382C4—5862no—
383C4—5862no—
384C4—5862no—
385C2—5864no—
386C2—11722no—
387C2#3403681114yesdirect product factor
388C2C2×#41×D29311yescharacteristic
389C2C2×#41×D29311yescharacteristic
390C2C2×#2262767211yescharacteristic
subgroupG/H
centerC23C23×D293
commutator, cosocleC22×C293C25
FrattiniC22C24×D293
FittingC2×#125×C293C2
socleC23×C293C24
prime radicalC22×D1172C22
hypercenterC2×#125D293
hypocenterC293C2×#552
LCSG ▷ C22×C293 ▷ C293
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
1. #34036811C2direct (N × H)
2. C2×#22627619C2semidirect
3. C2×#22627619C2semidirect
4. C2×#22627614C2semidirect
5. C2×#22627614C2semidirect
8. C2×#22627602C2semidirect
9. C2×#22627602C2semidirect
10. C2×#22627589C2semidirect
12. C2×#22627582C2semidirect
13. C2×#22627581C2semidirect
14. C2×#22627581C2semidirect
15. C2×C4⋊C4×D293C2semidirect
16. C2×#125×C293C2semidirect
23. #22627619C22semidirect
24. #22627619C22semidirect
25. #22627614C22semidirect
26. #22627614C22semidirect
29. #22627602C22semidirect
30. #22627602C22semidirect
31. #22627589C22semidirect
33. #22627582C22semidirect
34. #22627581C22semidirect
35. #22627581C22semidirect
46. C4⋊C4×D293C22semidirect
59. #125×C293C22semidirect
189. C2×C293#552semidirect
195. C293C2×#552semidirect
202. C2×#125D293semidirect
223. #125C2×D293semidirect
387. C2#34036811direct (N × H)

Maximal subgroups

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

subgroupindex
#340368112
C2×#226276192
C2×#226276142
C2×#226276092
C2×#226276022
C2×#226275892
C2×#226275862
C2×#226275822
C2×#226275812
C2×C4⋊C4×D2932
C2×#125×C2932
C2×#552293