Finite Group Databasebeta

← C2×#23750234 #34058056

Subgroups — C2×#23750234 #34058056

Order 19072.

1004 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
1#23750234C2116yesmaximal, direct product factor
2C2×#18011910C211yesmaximal, characteristic, complemented
3C2×#18011906C211yesmaximal, characteristic
4C2×#18011906C211yesmaximal, characteristic
5C2×#18011906C211yesmaximal, characteristic
6C2×#18011905C211yesmaximal, characteristic
7C2×#18011902C211yesmaximal, characteristic, complemented
8C2×#18011901C211yesmaximal, characteristic, complemented
9C2×#18011901C211yesmaximal, characteristic, complemented
10C2×#18011901C211yesmaximal, characteristic, complemented
11C2×#18011889C211yesmaximal, characteristic
12C2×#18011889C211yesmaximal, characteristic
13C2×C4×Dic298C211yesmaximal, characteristic, complemented
14C2×#18011876C211yesmaximal, characteristic, complemented
15C2×#18011869C211yesmaximal, characteristic
16C2×#125×C149C211yesmaximal, characteristic, complemented
17C22×Dic298C2211yescharacteristic
18C22×Dic298C2211yescharacteristic
19C22×C4×D149C2211yescharacteristic
20#18011910C2218yescomplemented
21#18011906C2218yes—
22#18011906C2218yes—
23#18011906C2218yes—
24#18011905C2218yes—
25#18011902C2218yescomplemented
26#18011901C2218yescomplemented
27#18011901C2218yescomplemented
28#18011901C2218yescomplemented
29#18011889C2218yes—
30#18011889C2218yes—
31C4×Dic298C2218yescomplemented
32#18011876C2218yescomplemented
33#18011869C2218yes—
34C2×C4⋊Dic149C2211yescharacteristic
35C2×C4⋊Dic149C2211yescharacteristic
36C2×C4⋊Dic149C2211yescharacteristic
37C2×C4⋊Dic149C2211yescharacteristic
38C2×#14558715C2211yescharacteristic
39C2×#14558715C2211yescharacteristic
40C2×#14558715C2211yescharacteristic
41C2×#14558715C2211yescharacteristic
42C2×#14558715C2211yescharacteristic
43C2×#14558715C2211yescharacteristic
44C2×#14558715C2211yescharacteristic
45C2×#14558715C2211yescharacteristic
46C2×#14558715C2211yescharacteristic
47C2×#14558715C2211yescharacteristic
48C2×#14558713C2211yescharacteristic
49C2×#14558713C2211yescharacteristic
50C2×#14558713C2211yescharacteristic
51C2×#14558713C2211yescharacteristic
52C2×#14558713C2211yescharacteristic
53C2×#14558713C2211yescharacteristic
54C2×C4×Dic149C2211yescharacteristic
55C2×C4×Dic149C2211yescharacteristic
56C2×C4×Dic149C2211yescharacteristic
57C2×C4×Dic149C2211yescharacteristic
58C2×C4×Dic149C2211yescharacteristic
59#125×C149C2218yescomplemented
60C2×C4⋊C4×C149C2211yescharacteristic
61C2×C4⋊C4×C149C2211yescharacteristic
62C2×C4⋊C4×C149C2211yescharacteristic
63C2×C4⋊C4×C149C2211yescharacteristic
64C2×C4⋊C4×C149C2211yescharacteristic
65C2×C4⋊C4×C149C2211yescharacteristic
66C2×C42×C149C2211yescharacteristic
67C23×D149C2311yescharacteristic
68C2×Dic298—24no—
69C2×Dic298—24no—
70C2×Dic298C2314yes—
71C2×Dic298C2314yes—
72C22×Dic149C2311yescharacteristic
73C22×Dic149C2311yescharacteristic
74C22×Dic149C2311yescharacteristic
75C22×Dic149C2311yescharacteristic
76C22×Dic149C2311yescharacteristic
77C22×Dic149C2311yescharacteristic
78C22×Dic149C2311yescharacteristic
79C2×C4×D149—24no—
80C2×C4×D149C2314yes—
81C4⋊Dic149C2314yes—
82C4⋊Dic149C2314yes—
83C4⋊Dic149C2314yes—
84C4⋊Dic149C2314yes—
85#14558715C2314yes—
86#14558715C2314yes—
87#14558715C2314yes—
88#14558715C2314yes—
89#14558715C2314yes—
90#14558715C2314yes—
91#14558715C2314yes—
92#14558715C2314yes—
93#14558715C2314yes—
94#14558715C2314yes—
95#14558713C2314yes—
96#14558713C2314yes—
97#14558713C2314yes—
98#14558713C2314yes—
99#14558713C2314yes—
100#14558713C2314yes—
101C4×Dic149C2314yes—
102C4×Dic149C2314yes—
103C4×Dic149C2314yes—
104C4×Dic149C2314yes—
105C4×Dic149C2314yes—
106C22×C4×C149C2311yescharacteristic
107C22×C4×C149C2311yescharacteristic
108C22×C4×C149C2311yescharacteristic
109C22×C4×C149C2311yescharacteristic
110C22×C4×C149C2311yescharacteristic
111C22×C4×C149C2311yescharacteristic
112C22×C4×C149C2311yescharacteristic
113C4⋊C4×C149C2314yes—
114C4⋊C4×C149C2314yes—
115C4⋊C4×C149C2314yes—
116C4⋊C4×C149C2314yes—
117C4⋊C4×C149C2314yes—
118C4⋊C4×C149C2314yes—
119C42×C149C2314yes—
120C22×D149—22no—
121C22×D149—22no—
122C22×D149—22no—
123C22×D149C2412yes—
124Dic298—28no—
125Dic298—28no—
126C2×Dic149—22no—
127C2×Dic149—22no—
128C2×Dic149—22no—
129C2×Dic149—22no—
130C2×Dic149—22no—
131C2×Dic149—22no—
132C2×Dic149#4114yes—
133C2×Dic149C2412yes—
134C2×Dic149C2412yes—
135C2×Dic149C2412yes—
136C2×Dic149C2412yes—
137C2×Dic149C2412yes—
138C2×Dic149C2412yes—
139C2×Dic149C2412yes—
140C4×D149—28no—
141C23×C149C2411yescharacteristic
142C2×C4×C149—22no—
143C2×C4×C149—22no—
144C2×C4×C149—22no—
145C2×C4×C149—22no—
146C2×C4×C149—22no—
147C2×C4×C149—22no—
148C2×C4×C149—22no—
149C2×C4×C149C2412yes—
150C2×C4×C149C2412yes—
151C2×C4×C149C2412yes—
152C2×C4×C149C2412yes—
153C2×C4×C149C2412yes—
154C2×C4×C149C2412yes—
155C2×C4×C149C2412yes—
156C22×C149C2×#4112yes—
157C22×C1492−1+412yes—
158C22×C1492−1+412yes—
159C22×C149C2511yescharacteristic
160C2×D149—22no—
161C2×D149—22no—
162C2×D149—22no—
163C2×D149—44no—
164C4×C149—22no—
165C4×C149—22no—
166C4×C149—22no—
167C4×C149—22no—
168C4×C149—22no—
169C4×C149—22no—
170C4×C149—22no—
171Dic149—22no—
172Dic149—22no—
173Dic149—22no—
174Dic149—22no—
175Dic149—22no—
176Dic149—22no—
177Dic149C2×#4114yes—
178C2×C149#54114yescomplemented
179C2×C149C22×#4111yescharacteristic
180C2×C149C2×2−1+411yescharacteristic
181C2×C149C2×2−1+411yescharacteristic
182D149—42no—
183C149C2×#54111yescharacteristic, complemented, Sylow
184C2×#541—1491nomaximal, Sylow
185#541—14916no—
186C2×C4⋊Q8—1491no—
187C2×#126—1491no—
188C2×#126—1491no—
189C2×#126—1491no—
190C2×#126—1491no—
191C2×#125—1491no—
192C2×#125—1491no—
193C2×#125—1491no—
194C2×#125—1491no—
195C2×#125D14911yescharacteristic, complemented
196C2×C22⋊Q8—1491no—
197C2×C22⋊Q8—1491no—
198C2×C4×Q8—1491no—
199C2×C4×Q8—1491no—
200C2×#117—1491no—
201C22×Q8—1491no—
202C22×Q8—1491no—
203C23×C4—1491no—
204C4⋊Q8—1498no—
205#126—1498no—
206#126—1498no—
207#126—1498no—
208#126—1498no—
209#125—1498no—
210#125—1498no—
211#125—1498no—
212#125—1498no—
213#125C2×D14918yescomplemented
214C22⋊Q8—1498no—
215C22⋊Q8—1498no—
216C4×Q8—1498no—
217C4×Q8—1498no—
218#117—1498no—
219C2×C4⋊C4—1491no—
220C2×C4⋊C4—1491no—
221C2×C4⋊C4—1491no—
222C2×C4⋊C4—1491no—
223C2×C4⋊C4—1491no—
224C2×C4⋊C4—1491no—
225C2×C4⋊C4—1491no—
226C2×C4⋊C4—1491no—
227C2×C4⋊C4—1491no—
228C2×C4⋊C4—1491no—
229C2×C4⋊C4—1491no—
230C2×C4⋊C4—1491no—
231C2×C4⋊C4—1491no—
232C2×C4⋊C4—1491no—
233C2×C4⋊C4C2×D14911yescharacteristic
234C2×C4⋊C4C2×D14911yescharacteristic
235C2×C4⋊C4C2×D14911yescharacteristic
236C2×C4⋊C4C2×D14911yescharacteristic
237C2×C4⋊C4C2×D14911yescharacteristic
238C2×C4⋊C4C2×D14911yescharacteristic
239C2×C22⋊C4—1491no—
240C2×C22⋊C4—1491no—
241C2×C22⋊C4—1491no—
242C2×C22⋊C4—1491no—
243C2×C22⋊C4—1491no—
244C2×C22⋊C4—1491no—
245C2×C42—1491no—
246C2×C42—1491no—
247C2×C42—1491no—
248C2×C42—1491no—
249C2×C42—1491no—
250C2×C42C2×D14911yescharacteristic
251C24—1491no—
252C2×Q8—2984no—
253C2×Q8—2984no—
254C2×Q8—1494no—
255C2×Q8—1494no—
256C22×C4—2984no—
257C22×C4—1491no—
258C22×C4—1491no—
259C22×C4—1491no—
260C22×C4—1491no—
261C22×C4—1491no—
262C22×C4—1491no—
263C22×C4—1494no—
264C22×C4—1491no—
265C22×C4C22×D14911yescharacteristic
266C22×C4C22×D14911yescharacteristic
267C22×C4C22×D14911yescharacteristic
268C22×C4C22×D14911yescharacteristic
269C22×C4C22×D14911yescharacteristic
270C22×C4C22×D14911yescharacteristic
271C22×C4C22×D14911yescharacteristic
272C4⋊C4—1494no—
273C4⋊C4—1494no—
274C4⋊C4—1494no—
275C4⋊C4—1494no—
276C4⋊C4—1494no—
277C4⋊C4—1494no—
278C4⋊C4—1494no—
279C4⋊C4—1494no—
280C4⋊C4—1494no—
281C4⋊C4—1494no—
282C4⋊C4—1494no—
283C4⋊C4—1494no—
284C4⋊C4—1494no—
285C4⋊C4—1494no—
286C4⋊C4C22×D14914yes—
287C4⋊C4C22×D14914yes—
288C4⋊C4C22×D14914yes—
289C4⋊C4C22×D14914yes—
290C4⋊C4C22×D14914yes—
291C4⋊C4C22×D14914yes—
292C22⋊C4—1494no—
293C22⋊C4—1494no—
294C22⋊C4—1494no—
295C22⋊C4—1494no—
296C22⋊C4—1494no—
297C22⋊C4—1494no—
298C42—1494no—
299C42—1494no—
300C42—1494no—
301C42—1494no—
302C42—1494no—
303C42C22×D14914yes—
304C23—2982no—
305C23—2982no—
306C23—2982no—
307C23—1492no—
308C23C23×D14911yescharacteristic
309Q8—2988no—
310Q8—2988no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—2988no—
319C2×C4—2982no—
320C2×C4—2982no—
321C2×C4—2982no—
322C2×C4—2982no—
323C2×C4—2982no—
324C2×C4—2982no—
325C2×C4—1492no—
326C2×C4—1492no—
327C2×C4—1492no—
328C2×C4—1492no—
329C2×C4—1492no—
330C2×C4—1492no—
331C2×C4—1494no—
332C2×C4—1492no—
333C2×C4C23×D14912yes—
334C2×C4C23×D14912yes—
335C2×C4C23×D14912yes—
336C2×C4C23×D14912yes—
337C2×C4C23×D14912yes—
338C2×C4C23×D14912yes—
339C2×C4C23×D14912yes—
340C22—2982no—
341C22—2982no—
342C22—2982no—
343C22—5964no—
344C22#41×D14912yes—
345C22#1801195812yes—
346C22#1801195912yes—
347C22C24×D14911yescharacteristic
348C4—22no—
349C4—22no—
350C4—22no—
351C4—22no—
352C4—22no—
353C4—22no—
354C4—22no—
355C4—2982no—
356C4—2982no—
357C4—2982no—
358C4—2982no—
359C4—2982no—
360C4—2982no—
361C4—1494no—
362C2—5962no—
363C2#2375023414yesdirect product factor
364C2C2×#41×D14911yescharacteristic
365C2C2×#1801195811yescharacteristic
366C2C2×#1801195911yescharacteristic
subgroupG/H
centerC23C23×D149
commutator, cosocleC22×C149C25
FrattiniC22C24×D149
FittingC2×#125×C149C2
socleC23×C149C24
prime radicalC23×D149C23
hypercenterC2×#125D149
hypocenterC149C2×#541
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
1. #23750234C2direct (N × H)
2. C2×#18011910C2semidirect
7. C2×#18011902C2semidirect
8. C2×#18011901C2semidirect
9. C2×#18011901C2semidirect
10. C2×#18011901C2semidirect
13. C2×C4×Dic298C2semidirect
14. C2×#18011876C2semidirect
16. C2×#125×C149C2semidirect
20. #18011910C22semidirect
25. #18011902C22semidirect
26. #18011901C22semidirect
27. #18011901C22semidirect
28. #18011901C22semidirect
31. C4×Dic298C22semidirect
32. #18011876C22semidirect
59. #125×C149C22semidirect
178. C2×C149#541semidirect
183. C149C2×#541semidirect
195. C2×#125D149semidirect
213. #125C2×D149semidirect
363. C2#23750234direct (N × H)

Maximal subgroups

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

subgroupindex
#237502342
C2×#180119102
C2×#180119062
C2×#180119052
C2×#180119022
C2×#180119012
C2×#180118892
C2×C4×Dic2982
C2×#180118762
C2×#180118692
C2×#125×C1492
C2×#541149