Finite Group Databasebeta

← C2×#23750342 #34058234

Subgroups — C2×#23750342 #34058234

Order 19072.

1112 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#23750342C2116yesmaximal, direct product factor
2C2×#18011910C211yesmaximal, characteristic, complemented
3C2×#18011906C211yesmaximal, characteristic, complemented
4C2×#18011906C211yesmaximal, characteristic, complemented
5C2×#18011904C211yesmaximal, characteristic, complemented
6C2×#18011897C211yesmaximal, characteristic
7C2×#18011897C211yesmaximal, characteristic
8C2×#18011889C211yesmaximal, characteristic, complemented
9C2×#18011888C211yesmaximal, characteristic, complemented
10C2×C4×Dic298C211yesmaximal, characteristic, complemented
11C2×#18011876C211yesmaximal, characteristic, complemented
12C2×#18011876C211yesmaximal, characteristic, complemented
13C2×#18011871C211yesmaximal, characteristic
14C2×#18011868C211yesmaximal, characteristic, complemented
15C2×#18011867C211yesmaximal, characteristic, complemented
16C2×#126×C149C211yesmaximal, characteristic, complemented
17C22×Dic298C2211yescharacteristic
18C22×Dic298C2211yescharacteristic
19C22×Dic298C2211yescharacteristic
20C22×C22⋊D149C2211yescharacteristic
21C23×Dic149C2211yescharacteristic
22C22×C4×D149C2211yescharacteristic
23#18011910C2218yescomplemented
24#18011906C2218yescomplemented
25#18011906C2218yescomplemented
26#18011904C2218yescomplemented
27#18011897C2218yes—
28#18011897C2218yes—
29#18011889C2218yescomplemented
30#18011888C2218yescomplemented
31C4×Dic298C2218yescomplemented
32#18011876C2218yescomplemented
33#18011876C2218yescomplemented
34#18011871C2218yes—
35#18011868C2218yescomplemented
36#18011867C2218yescomplemented
37C2×C4⋊Dic149C2211yescharacteristic
38C2×C4⋊Dic149C2211yescharacteristic
39C2×#14558715C2211yescharacteristic
40C2×#14558715C2211yescharacteristic
41C2×#14558715C2211yescharacteristic
42C2×#14558715C2211yescharacteristic
43C2×#14558715C2211yescharacteristic
44C2×#14558715C2211yescharacteristic
45C2×#14558715C2211yescharacteristic
46C2×C22⋊Dic149C2211yescharacteristic
47C2×C22⋊Dic149C2211yescharacteristic
48C2×#14558713C2211yescharacteristic
49C2×#14558713C2211yescharacteristic
50C2×#14558713C2211yescharacteristic
51C2×#14558713C2211yescharacteristic
52C2×#14558713C2211yescharacteristic
53C2×C4×Dic149C2211yescharacteristic
54C2×C4×Dic149C2211yescharacteristic
55C2×C4×Dic149C2211yescharacteristic
56C2×C4×Dic149C2211yescharacteristic
57C2×C4×Dic149C2211yescharacteristic
58C2×C4×Dic149C2211yescharacteristic
59#126×C149C2218yescomplemented
60C2×C4⋊C4×C149C2211yescharacteristic
61C2×C4⋊C4×C149C2211yescharacteristic
62C2×C4⋊C4×C149C2211yescharacteristic
63C2×C22⋊C4×C149C2211yescharacteristic
64C2×C22⋊C4×C149C2211yescharacteristic
65C2×C22⋊C4×C149C2211yescharacteristic
66C2×C42×C149C2211yescharacteristic
67C23×D149C2311yescharacteristic
68C2×Dic298—24no—
69C2×Dic298—24no—
70C2×Dic298—24no—
71C2×Dic298C2314yes—
72C2×Dic298C2314yes—
73C2×Dic298C2314yes—
74C2×C22⋊D149—24no—
75C2×C22⋊D149C2314yes—
76C22×Dic149—24no—
77C22×Dic149C2311yescharacteristic
78C22×Dic149C2314yes—
79C22×Dic149C2311yescharacteristic
80C22×Dic149C2311yescharacteristic
81C22×Dic149C2311yescharacteristic
82C22×Dic149C2311yescharacteristic
83C22×Dic149C2311yescharacteristic
84C22×Dic149C2311yescharacteristic
85C2×C4×D149—24no—
86C2×C4×D149C2314yes—
87C4⋊Dic149C2314yes—
88C4⋊Dic149C2314yes—
89#14558715C2314yes—
90#14558715C2314yes—
91#14558715C2314yes—
92#14558715C2314yes—
93#14558715C2314yes—
94#14558715C2314yes—
95#14558715C2314yes—
96C22⋊Dic149C2314yes—
97C22⋊Dic149C2314yes—
98#14558713C2314yes—
99#14558713C2314yes—
100#14558713C2314yes—
101#14558713C2314yes—
102#14558713C2314yes—
103C4×Dic149C2314yes—
104C4×Dic149C2314yes—
105C4×Dic149C2314yes—
106C4×Dic149C2314yes—
107C4×Dic149C2314yes—
108C4×Dic149C2314yes—
109C24×C149C2311yescharacteristic
110C22×C4×C149C2311yescharacteristic
111C22×C4×C149C2311yescharacteristic
112C22×C4×C149C2311yescharacteristic
113C22×C4×C149C2311yescharacteristic
114C22×C4×C149C2311yescharacteristic
115C22×C4×C149C2311yescharacteristic
116C4⋊C4×C149C2314yes—
117C4⋊C4×C149C2314yes—
118C4⋊C4×C149C2314yes—
119C22⋊C4×C149C2314yes—
120C22⋊C4×C149C2314yes—
121C22⋊C4×C149C2314yes—
122C42×C149C2314yes—
123C22×D149—22no—
124C22×D149—22no—
125C22×D149—22no—
126C22×D149C2412yes—
127Dic298—28no—
128Dic298—28no—
129Dic298—28no—
130C22⋊D149—28no—
131C2×Dic149—22no—
132C2×Dic149—22no—
133C2×Dic149—22no—
134C2×Dic149—22no—
135C2×Dic149—22no—
136C2×Dic149—28no—
137C2×Dic149#4114yes—
138C2×Dic149#4114yes—
139C2×Dic149C2412yes—
140C2×Dic149C2412yes—
141C2×Dic149C2412yes—
142C2×Dic149C2412yes—
143C2×Dic149C2412yes—
144C2×Dic149C2412yes—
145C2×Dic149C2412yes—
146C4×D149—28no—
147C23×C149—22no—
148C23×C149—22no—
149C23×C149—22no—
150C23×C149C2412yes—
151C23×C149C2411yescharacteristic
152C2×C4×C149—22no—
153C2×C4×C149—22no—
154C2×C4×C149—22no—
155C2×C4×C149—22no—
156C2×C4×C149—22no—
157C2×C4×C149—22no—
158C2×C4×C149C2412yes—
159C2×C4×C149C2412yes—
160C2×C4×C149C2412yes—
161C2×C4×C149C2412yes—
162C2×C4×C149C2412yes—
163C2×C4×C149C2412yes—
164C22×C149—22no—
165C22×C149—22no—
166C22×C149—22no—
167C22×C149—44no—
168C22×C149C2×#4112yes—
169C22×C149C2×#4112yes—
170C22×C1492−1+412yes—
171C22×C149C2511yescharacteristic
172C2×D149—22no—
173C2×D149—22no—
174C2×D149—22no—
175C2×D149—44no—
176C4×C149—22no—
177C4×C149—22no—
178C4×C149—22no—
179C4×C149—22no—
180C4×C149—22no—
181C4×C149—22no—
182Dic149—22no—
183Dic149—22no—
184Dic149—22no—
185Dic149—22no—
186Dic149—22no—
187Dic149C2×#4114yes—
188Dic149C2×#4114yes—
189C2×C149—42no—
190C2×C149#55614yescomplemented
191C2×C149C22×#4111yescharacteristic
192C2×C149C22×#4111yescharacteristic
193C2×C149C2×2−1+411yescharacteristic
194D149—42no—
195C149C2×#55611yescharacteristic, complemented, Sylow
196C2×#556—1491nomaximal, Sylow
197#556—14916no—
198C2×C4⋊Q8—1491no—
199C2×#126—1491no—
200C2×#126—1491no—
201C2×#126—1491no—
202C2×#126D14911yescharacteristic, complemented
203C2×#124—1491no—
204C2×#124—1491no—
205C2×C22⋊Q8—1491no—
206C2×C22⋊Q8—1491no—
207C2×C4×Q8—1491no—
208C2×C4×Q8—1491no—
209C2×C4×Q8—1491no—
210C2×C4×D4—1491no—
211C2×#117—1491no—
212C2×#117—1491no—
213C22×Q8—1491no—
214C22×Q8—1491no—
215C22×Q8—1491no—
216C22×D4—1491no—
217C23×C4—1491no—
218C23×C4—1491no—
219C4⋊Q8—1498no—
220#126—1498no—
221#126—1498no—
222#126—1498no—
223#126C2×D14918yescomplemented
224#124—1498no—
225#124—1498no—
226C22⋊Q8—1498no—
227C22⋊Q8—1498no—
228C4×Q8—1498no—
229C4×Q8—1498no—
230C4×Q8—1498no—
231C4×D4—1498no—
232#117—1498no—
233#117—1498no—
234C2×C4⋊C4—1491no—
235C2×C4⋊C4—1491no—
236C2×C4⋊C4—1491no—
237C2×C4⋊C4—1491no—
238C2×C4⋊C4—1491no—
239C2×C4⋊C4—1491no—
240C2×C4⋊C4—1491no—
241C2×C4⋊C4—1491no—
242C2×C4⋊C4—1491no—
243C2×C4⋊C4C2×D14911yescharacteristic
244C2×C4⋊C4C2×D14911yescharacteristic
245C2×C4⋊C4C2×D14911yescharacteristic
246C2×C22⋊C4—1491no—
247C2×C22⋊C4—1491no—
248C2×C22⋊C4—1491no—
249C2×C22⋊C4—1491no—
250C2×C22⋊C4—1491no—
251C2×C22⋊C4—1491no—
252C2×C22⋊C4—1491no—
253C2×C22⋊C4C2×D14911yescharacteristic
254C2×C22⋊C4C2×D14911yescharacteristic
255C2×C22⋊C4C2×D14911yescharacteristic
256C2×C42—1491no—
257C2×C42—1491no—
258C2×C42—1491no—
259C2×C42—1491no—
260C2×C42—1491no—
261C2×C42—1491no—
262C2×C42C2×D14911yescharacteristic
263C24—1491no—
264C24C22×D14911yescharacteristic
265C2×Q8—2984no—
266C2×Q8—2984no—
267C2×Q8—2984no—
268C2×Q8—1494no—
269C2×Q8—1494no—
270C2×Q8—1494no—
271C2×D4—2984no—
272C2×D4—1494no—
273C22×C4—2984no—
274C22×C4—2984no—
275C22×C4—1494no—
276C22×C4—1491no—
277C22×C4—1491no—
278C22×C4—1491no—
279C22×C4—1491no—
280C22×C4—1491no—
281C22×C4—1494no—
282C22×C4—1491no—
283C22×C4—1491no—
284C22×C4C22×D14911yescharacteristic
285C22×C4C22×D14911yescharacteristic
286C22×C4C22×D14911yescharacteristic
287C22×C4C22×D14911yescharacteristic
288C22×C4C22×D14911yescharacteristic
289C22×C4C22×D14911yescharacteristic
290C4⋊C4—1494no—
291C4⋊C4—1494no—
292C4⋊C4—1494no—
293C4⋊C4—1494no—
294C4⋊C4—1494no—
295C4⋊C4—1494no—
296C4⋊C4—1494no—
297C4⋊C4—1494no—
298C4⋊C4—1494no—
299C4⋊C4C22×D14914yes—
300C4⋊C4C22×D14914yes—
301C4⋊C4C22×D14914yes—
302C22⋊C4—1494no—
303C22⋊C4—1494no—
304C22⋊C4—1494no—
305C22⋊C4—1494no—
306C22⋊C4—1494no—
307C22⋊C4—1494no—
308C22⋊C4—1494no—
309C22⋊C4C22×D14914yes—
310C22⋊C4C22×D14914yes—
311C22⋊C4C22×D14914yes—
312C42—1494no—
313C42—1494no—
314C42—1494no—
315C42—1494no—
316C42—1494no—
317C42—1494no—
318C42C22×D14914yes—
319C23—22no—
320C23—22no—
321C23—22no—
322C23—2982no—
323C23—2982no—
324C23—2982no—
325C23—1492no—
326C23C23×D14912yes—
327C23C23×D14911yescharacteristic
328Q8—2988no—
329Q8—2988no—
330Q8—2988no—
331D4—2988no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—2988no—
339C2×C4—2982no—
340C2×C4—2982no—
341C2×C4—2982no—
342C2×C4—2982no—
343C2×C4—2982no—
344C2×C4—2988no—
345C2×C4—1492no—
346C2×C4—1492no—
347C2×C4—1492no—
348C2×C4—1492no—
349C2×C4—1492no—
350C2×C4—1494no—
351C2×C4—1494no—
352C2×C4—1492no—
353C2×C4—1492no—
354C2×C4C23×D14912yes—
355C2×C4C23×D14912yes—
356C2×C4C23×D14912yes—
357C2×C4C23×D14912yes—
358C2×C4C23×D14912yes—
359C2×C4C23×D14912yes—
360C22—22no—
361C22—22no—
362C22—22no—
363C22—44no—
364C22—2982no—
365C22—2982no—
366C22—2982no—
367C22—5964no—
368C22#41×D14912yes—
369C22#41×D14912yes—
370C22#1801195812yes—
371C22C24×D14911yescharacteristic
372C4—22no—
373C4—22no—
374C4—22no—
375C4—22no—
376C4—22no—
377C4—22no—
378C4—2982no—
379C4—2982no—
380C4—2982no—
381C4—2982no—
382C4—2982no—
383C4—1494no—
384C4—1494no—
385C2—42no—
386C2—5962no—
387C2#2375034214yesdirect product factor
388C2C2×#41×D14911yescharacteristic
389C2C2×#41×D14911yescharacteristic
390C2C2×#1801195811yescharacteristic
subgroupG/H
centerC23C23×D149
commutator, cosocleC22×C149C25
FrattiniC22C24×D149
FittingC2×#126×C149C2
socleC23×C149C24
prime radicalC22×C22⋊D149C22
hypercenterC2×#126D149
hypocenterC149C2×#556
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. #23750342C2direct (N × H)
2. C2×#18011910C2semidirect
3. C2×#18011906C2semidirect
4. C2×#18011906C2semidirect
5. C2×#18011904C2semidirect
8. C2×#18011889C2semidirect
9. C2×#18011888C2semidirect
10. C2×C4×Dic298C2semidirect
11. C2×#18011876C2semidirect
12. C2×#18011876C2semidirect
14. C2×#18011868C2semidirect
15. C2×#18011867C2semidirect
16. C2×#126×C149C2semidirect
23. #18011910C22semidirect
24. #18011906C22semidirect
25. #18011906C22semidirect
26. #18011904C22semidirect
29. #18011889C22semidirect
30. #18011888C22semidirect
31. C4×Dic298C22semidirect
32. #18011876C22semidirect
33. #18011876C22semidirect
35. #18011868C22semidirect
36. #18011867C22semidirect
59. #126×C149C22semidirect
190. C2×C149#556semidirect
195. C149C2×#556semidirect
202. C2×#126D149semidirect
223. #126C2×D149semidirect
387. C2#23750342direct (N × H)

Maximal subgroups

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

subgroupindex
#237503422
C2×#180119102
C2×#180119062
C2×#180119042
C2×#180118972
C2×#180118892
C2×#180118882
C2×C4×Dic2982
C2×#180118762
C2×#180118712
C2×#180118682
C2×#180118672
C2×#126×C1492
C2×#556149