Finite Group Databasebeta

← C2×#23750241 #34058064

Subgroups — C2×#23750241 #34058064

Order 19072.

1132 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750241C2116yesmaximal, direct product factor
2C2×#18011910C211yesmaximal, characteristic, complemented
3C2×#18011906C211yesmaximal, characteristic, complemented
4C2×#18011899C211yesmaximal, characteristic, complemented
5C2×#18011897C211yesmaximal, characteristic, complemented
6C2×#18011897C211yesmaximal, characteristic, complemented
7C2×#18011896C211yesmaximal, characteristic, complemented
8C2×#18011895C211yesmaximal, characteristic, complemented
9C2×#18011891C211yesmaximal, characteristic, complemented
10C2×#18011889C211yesmaximal, characteristic, complemented
11C2×#18011888C211yesmaximal, characteristic, complemented
12C2×#18011884C211yesmaximal, characteristic
13C2×C4×Dic298C211yesmaximal, characteristic, complemented
14C2×#18011871C211yesmaximal, characteristic, complemented
15C2×#18011869C211yesmaximal, characteristic, complemented
16C2×#126×C149C211yesmaximal, characteristic, complemented
17C22×Dic298C2211yescharacteristic
18C22×Dic298C2211yescharacteristic
19C22×Dic298C2211yescharacteristic
20C22×D596C2211yescharacteristic
21C22×C22⋊D149C2211yescharacteristic
22C22×C22⋊D149C2211yescharacteristic
23C23×Dic149C2211yescharacteristic
24C22×C4×D149C2211yescharacteristic
25C22×C4×D149C2211yescharacteristic
26#18011910C2218yescomplemented
27#18011906C2218yescomplemented
28#18011899C2218yescomplemented
29#18011897C2218yescomplemented
30#18011897C2218yescomplemented
31#18011896C2218yescomplemented
32#18011895C2218yescomplemented
33#18011891C2218yescomplemented
34#18011889C2218yescomplemented
35#18011888C2218yescomplemented
36#18011884C2218yes—
37C4×Dic298C2218yescomplemented
38#18011871C2218yescomplemented
39#18011869C2218yescomplemented
40C2×C4⋊Dic149C2211yescharacteristic
41C2×C4⋊Dic149C2211yescharacteristic
42C2×C4⋊Dic149C2211yescharacteristic
43C2×#14558715C2211yescharacteristic
44C2×#14558715C2211yescharacteristic
45C2×#14558715C2211yescharacteristic
46C2×#14558715C2211yescharacteristic
47C2×C22⋊Dic149C2211yescharacteristic
48C2×#14558713C2211yescharacteristic
49C2×#14558713C2211yescharacteristic
50C2×#14558713C2211yescharacteristic
51C2×#14558713C2211yescharacteristic
52C2×#14558713C2211yescharacteristic
53C2×#14558713C2211yescharacteristic
54C2×#14558713C2211yescharacteristic
55C2×#14558713C2211yescharacteristic
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
68C23×D149C2311yescharacteristic
69C2×Dic298—24no—
70C2×Dic298—42no—
71C2×Dic298—42no—
72C2×Dic298C2314yes—
73C2×Dic298C2314yes—
74C2×Dic298C2314yes—
75C2×D596—42no—
76C2×D596C2314yes—
77C2×C22⋊D149—24no—
78C2×C22⋊D149—42no—
79C2×C22⋊D149C2314yes—
80C2×C22⋊D149C2314yes—
81C22×Dic149—42no—
82C22×Dic149C2311yescharacteristic
83C22×Dic149C2311yescharacteristic
84C22×Dic149C2311yescharacteristic
85C22×Dic149C2311yescharacteristic
86C22×Dic149C2311yescharacteristic
87C22×Dic149C2314yes—
88C22×Dic149C2311yescharacteristic
89C2×C4×D149—24no—
90C2×C4×D149—42no—
91C2×C4×D149C2314yes—
92C2×C4×D149C2314yes—
93C4⋊Dic149C2314yes—
94C4⋊Dic149C2314yes—
95C4⋊Dic149C2314yes—
96#14558715C2314yes—
97#14558715C2314yes—
98#14558715C2314yes—
99#14558715C2314yes—
100C22⋊Dic149C2314yes—
101#14558713C2314yes—
102#14558713C2314yes—
103#14558713C2314yes—
104#14558713C2314yes—
105#14558713C2314yes—
106#14558713C2314yes—
107#14558713C2314yes—
108#14558713C2314yes—
109C4×Dic149C2314yes—
110C4×Dic149C2314yes—
111C4×Dic149C2314yes—
112C24×C149C2311yescharacteristic
113C22×C4×C149C2311yescharacteristic
114C22×C4×C149C2311yescharacteristic
115C22×C4×C149C2311yescharacteristic
116C22×C4×C149C2311yescharacteristic
117C22×C4×C149C2311yescharacteristic
118C22×C4×C149C2311yescharacteristic
119C4⋊C4×C149C2314yes—
120C4⋊C4×C149C2314yes—
121C4⋊C4×C149C2314yes—
122C22⋊C4×C149C2314yes—
123C22⋊C4×C149C2314yes—
124C22⋊C4×C149C2314yes—
125C42×C149C2314yes—
126C22×D149—22no—
127C22×D149—22no—
128C22×D149—22no—
129C22×D149—22no—
130C22×D149—22no—
131C22×D149—22no—
132C22×D149C2412yes—
133C22×D149C2412yes—
134Dic298—28no—
135Dic298—44no—
136Dic298—44no—
137D596—44no—
138C22⋊D149—28no—
139C22⋊D149—44no—
140C2×Dic149—22no—
141C2×Dic149—22no—
142C2×Dic149—22no—
143C2×Dic149—22no—
144C2×Dic149—22no—
145C2×Dic149—44no—
146C2×Dic149#4114yes—
147C2×Dic149C2412yes—
148C2×Dic149C2412yes—
149C2×Dic149C2412yes—
150C2×Dic149C2412yes—
151C2×Dic149C2412yes—
152C2×Dic149C2412yes—
153C4×D149—28no—
154C4×D149—44no—
155C23×C149—22no—
156C23×C149—22no—
157C23×C149—22no—
158C23×C149C2412yes—
159C23×C149C2411yescharacteristic
160C2×C4×C149—22no—
161C2×C4×C149—22no—
162C2×C4×C149—22no—
163C2×C4×C149—22no—
164C2×C4×C149—22no—
165C2×C4×C149—22no—
166C2×C4×C149C2412yes—
167C2×C4×C149C2412yes—
168C2×C4×C149C2412yes—
169C2×C4×C149C2412yes—
170C2×C4×C149C2412yes—
171C2×C4×C149C2412yes—
172C22×C149—22no—
173C22×C149—22no—
174C22×C149—22no—
175C22×C149—44no—
176C22×C149C2×#4112yes—
177C22×C149H(5,𝔽2)12yes—
178C22×C1492−1+412yes—
179C22×C149C2511yescharacteristic
180C2×D149—22no—
181C2×D149—22no—
182C2×D149—22no—
183C2×D149—22no—
184C2×D149—22no—
185C2×D149—22no—
186C2×D149—44no—
187C2×D149—44no—
188C4×C149—22no—
189C4×C149—22no—
190C4×C149—22no—
191C4×C149—22no—
192C4×C149—22no—
193C4×C149—22no—
194Dic149—22no—
195Dic149—22no—
196Dic149—22no—
197Dic149—22no—
198Dic149—22no—
199Dic149C2×#4114yes—
200C2×C149—42no—
201C2×C149#54214yescomplemented
202C2×C149C22×#4111yescharacteristic
203C2×C149C2×H(5,𝔽2)11yescharacteristic
204C2×C149C2×2−1+411yescharacteristic
205D149—42no—
206D149—42no—
207C149C2×#54211yescharacteristic, complemented, Sylow
208C2×#542—1491nomaximal, Sylow
209#542—14916no—
210C2×C4⋊Q8—1491no—
211C2×#126—1491no—
212C2×#126D14911yescharacteristic, complemented
213C2×#124—1491no—
214C2×#124—1491no—
215C2×#124—1491no—
216C2×#123—1491no—
217C2×#123—1491no—
218C2×C22⋊Q8—1491no—
219C2×C22⋊Q8—1491no—
220C2×C22⋊Q8—1491no—
221C2×#121—1491no—
222C2×C4×Q8—1491no—
223C2×C4×D4—1491no—
224C2×#117—1491no—
225C22×Q8—1491no—
226C22×Q8—1491no—
227C22×Q8—1491no—
228C22×D4—1491no—
229C22×D4—1491no—
230C22×D4—1491no—
231C23×C4—1491no—
232C23×C4—1491no—
233C23×C4—1491no—
234C4⋊Q8—1498no—
235#126—1498no—
236#126C2×D14918yescomplemented
237#124—1498no—
238#124—1498no—
239#124—1498no—
240#123—1498no—
241#123—1498no—
242C22⋊Q8—1498no—
243C22⋊Q8—1498no—
244C22⋊Q8—1498no—
245#121—1498no—
246C4×Q8—1498no—
247C4×D4—1498no—
248#117—1498no—
249C2×C4⋊C4—1491no—
250C2×C4⋊C4—1491no—
251C2×C4⋊C4—1491no—
252C2×C4⋊C4—1491no—
253C2×C4⋊C4—1491no—
254C2×C4⋊C4—1491no—
255C2×C4⋊C4—1491no—
256C2×C4⋊C4C2×D14911yescharacteristic
257C2×C4⋊C4C2×D14911yescharacteristic
258C2×C4⋊C4C2×D14911yescharacteristic
259C2×C22⋊C4—1491no—
260C2×C22⋊C4—1491no—
261C2×C22⋊C4—1491no—
262C2×C22⋊C4—1491no—
263C2×C22⋊C4—1491no—
264C2×C22⋊C4—1491no—
265C2×C22⋊C4—1491no—
266C2×C22⋊C4—1491no—
267C2×C22⋊C4—1491no—
268C2×C22⋊C4C2×D14911yescharacteristic
269C2×C22⋊C4C2×D14911yescharacteristic
270C2×C22⋊C4C2×D14911yescharacteristic
271C2×C42—1491no—
272C2×C42—1491no—
273C2×C42—1491no—
274C2×C42C2×D14911yescharacteristic
275C24—1491no—
276C24—1491no—
277C24C22×D14911yescharacteristic
278C2×Q8—2984no—
279C2×Q8—5962no—
280C2×Q8—5962no—
281C2×Q8—1494no—
282C2×Q8—1494no—
283C2×Q8—1494no—
284C2×D4—2984no—
285C2×D4—5962no—
286C2×D4—5962no—
287C2×D4—1494no—
288C2×D4—1494no—
289C2×D4—1494no—
290C22×C4—2984no—
291C22×C4—5962no—
292C22×C4—5962no—
293C22×C4—1491no—
294C22×C4—1491no—
295C22×C4—1491no—
296C22×C4—1491no—
297C22×C4—1491no—
298C22×C4—1494no—
299C22×C4—1494no—
300C22×C4—1494no—
301C22×C4—1491no—
302C22×C4C22×D14911yescharacteristic
303C22×C4C22×D14911yescharacteristic
304C22×C4C22×D14911yescharacteristic
305C22×C4C22×D14911yescharacteristic
306C22×C4C22×D14911yescharacteristic
307C22×C4C22×D14911yescharacteristic
308C4⋊C4—1494no—
309C4⋊C4—1494no—
310C4⋊C4—1494no—
311C4⋊C4—1494no—
312C4⋊C4—1494no—
313C4⋊C4—1494no—
314C4⋊C4—1494no—
315C4⋊C4C22×D14914yes—
316C4⋊C4C22×D14914yes—
317C4⋊C4C22×D14914yes—
318C22⋊C4—1494no—
319C22⋊C4—1494no—
320C22⋊C4—1494no—
321C22⋊C4—1494no—
322C22⋊C4—1494no—
323C22⋊C4—1494no—
324C22⋊C4—1494no—
325C22⋊C4—1494no—
326C22⋊C4—1494no—
327C22⋊C4C22×D14914yes—
328C22⋊C4C22×D14914yes—
329C22⋊C4C22×D14914yes—
330C42—1494no—
331C42—1494no—
332C42—1494no—
333C42C22×D14914yes—
334C23—22no—
335C23—22no—
336C23—22no—
337C23—2982no—
338C23—2982no—
339C23—2982no—
340C23—2982no—
341C23—2982no—
342C23—2982no—
343C23—1492no—
344C23—1492no—
345C23C23×D14912yes—
346C23C23×D14911yescharacteristic
347Q8—2988no—
348Q8—5964no—
349Q8—5964no—
350D4—2988no—
351D4—5964no—
352D4—5964no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—2988no—
360C2×C4—2982no—
361C2×C4—2982no—
362C2×C4—2982no—
363C2×C4—2982no—
364C2×C4—2982no—
365C2×C4—5964no—
366C2×C4—5964no—
367C2×C4—1492no—
368C2×C4—1492no—
369C2×C4—1492no—
370C2×C4—1492no—
371C2×C4—1492no—
372C2×C4—1494no—
373C2×C4—1492no—
374C2×C4C23×D14912yes—
375C2×C4C23×D14912yes—
376C2×C4C23×D14912yes—
377C2×C4C23×D14912yes—
378C2×C4C23×D14912yes—
379C2×C4C23×D14912yes—
380C22—22no—
381C22—22no—
382C22—22no—
383C22—44no—
384C22—2982no—
385C22—2982no—
386C22—2982no—
387C22—2982no—
388C22—2982no—
389C22—2982no—
390C22—5964no—
391C22—5964no—
392C22#41×D14912yes—
393C22#1801195712yes—
394C22#1801195812yes—
395C22C24×D14911yescharacteristic
396C4—22no—
397C4—22no—
398C4—22no—
399C4—22no—
400C4—22no—
401C4—22no—
402C4—2982no—
403C4—2982no—
404C4—2982no—
405C4—2982no—
406C4—2982no—
407C4—1494no—
408C2—42no—
409C2—5962no—
410C2—5962no—
411C2#2375024114yesdirect product factor
412C2C2×#41×D14911yescharacteristic
413C2C2×#1801195711yescharacteristic
414C2C2×#1801195811yescharacteristic
subgroupG/H
centerC23C23×D149
commutator, cosocleC22×C149C25
FrattiniC22C24×D149
FittingC2×#126×C149C2
socleC23×C149C24
prime radicalC2×#18011884C2
hypercenterC2×#126D149
hypocenterC149C2×#542
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. #23750241C2direct (N × H)
2. C2×#18011910C2semidirect
3. C2×#18011906C2semidirect
4. C2×#18011899C2semidirect
5. C2×#18011897C2semidirect
6. C2×#18011897C2semidirect
7. C2×#18011896C2semidirect
8. C2×#18011895C2semidirect
9. C2×#18011891C2semidirect
10. C2×#18011889C2semidirect
11. C2×#18011888C2semidirect
13. C2×C4×Dic298C2semidirect
14. C2×#18011871C2semidirect
15. C2×#18011869C2semidirect
16. C2×#126×C149C2semidirect
26. #18011910C22semidirect
27. #18011906C22semidirect
28. #18011899C22semidirect
29. #18011897C22semidirect
30. #18011897C22semidirect
31. #18011896C22semidirect
32. #18011895C22semidirect
33. #18011891C22semidirect
34. #18011889C22semidirect
35. #18011888C22semidirect
37. C4×Dic298C22semidirect
38. #18011871C22semidirect
39. #18011869C22semidirect
59. #126×C149C22semidirect
201. C2×C149#542semidirect
207. C149C2×#542semidirect
212. C2×#126D149semidirect
236. #126C2×D149semidirect
411. C2#23750241direct (N × H)

Maximal subgroups

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

subgroupindex
#237502412
C2×#180119102
C2×#180119062
C2×#180118992
C2×#180118972
C2×#180118962
C2×#180118952
C2×#180118912
C2×#180118892
C2×#180118882
C2×#180118842
C2×C4×Dic2982
C2×#180118712
C2×#180118692
C2×#126×C1492
C2×#542149