Finite Group Databasebeta

← C2×#23750219 #34058039

Subgroups — C2×#23750219 #34058039

Order 19072.

1144 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#23750219C2116yesmaximal, direct product factor
2C2×#18011906C211yesmaximal, characteristic, complemented
3C2×#18011904C211yesmaximal, characteristic, complemented
4C2×#18011902C211yesmaximal, characteristic, complemented
5C2×#18011901C211yesmaximal, characteristic, complemented
6C2×#18011895C211yesmaximal, characteristic, complemented
7C2×#18011894C211yesmaximal, characteristic, complemented
8C2×#18011893C211yesmaximal, characteristic, complemented
9C2×#18011891C211yesmaximal, characteristic, complemented
10C2×#18011888C211yesmaximal, characteristic, complemented
11C2×#18011888C211yesmaximal, characteristic, complemented
12C2×#18011883C211yesmaximal, characteristic
13C2×D4×Dic149C211yesmaximal, characteristic, complemented
14C2×#18011871C211yesmaximal, characteristic, complemented
15C22×C4⋊Dic149C211yesmaximal, characteristic, complemented
16C2×#123×C149C211yesmaximal, characteristic, complemented
17C22×Dic298C2211yescharacteristic
18C22×C22⋊D149C2211yescharacteristic
19C22×C22⋊D149C2211yescharacteristic
20C23×Dic149C2211yescharacteristic
21C23×Dic149C2211yescharacteristic
22C23×Dic149C2211yescharacteristic
23C22×C4×D149C2211yescharacteristic
24#18011906C2218yescomplemented
25#18011904C2218yescomplemented
26#18011902C2218yescomplemented
27#18011901C2218yescomplemented
28#18011895C2218yescomplemented
29#18011894C2218yescomplemented
30#18011893C2218yescomplemented
31#18011891C2218yescomplemented
32#18011888C2218yescomplemented
33#18011888C2218yescomplemented
34#18011883C2218yes—
35D4×Dic149C2218yescomplemented
36#18011871C2218yescomplemented
37C2×C4⋊Dic149C2211yescharacteristic
38C2×C4⋊Dic149C2211yescharacteristic
39C2×C4⋊Dic149C2211yescharacteristic
40C2×C4⋊Dic149C2211yescharacteristic
41C2×C4⋊Dic149C2211yescharacteristic
42C2×C4⋊Dic149C2211yescharacteristic
43C2×C4⋊Dic149C2218yescomplemented
44C2×#14558715C2211yescharacteristic
45C2×#14558715C2211yescharacteristic
46C2×#14558715C2211yescharacteristic
47C2×#14558715C2211yescharacteristic
48C2×#14558715C2211yescharacteristic
49C2×#14558715C2211yescharacteristic
50C2×C22⋊Dic149C2211yescharacteristic
51C2×C22⋊Dic149C2211yescharacteristic
52C2×C22⋊Dic149C2211yescharacteristic
53C2×#14558713C2211yescharacteristic
54C2×#14558713C2211yescharacteristic
55C2×#14558713C2211yescharacteristic
56C2×#14558713C2211yescharacteristic
57C2×C4×Dic149C2211yescharacteristic
58C2×C4×Dic149C2211yescharacteristic
59C22×D4×C149C2211yescharacteristic
60C23×C4×C149C2211yescharacteristic
61#123×C149C2218yescomplemented
62C2×C4⋊C4×C149C2211yescharacteristic
63C2×C4⋊C4×C149C2211yescharacteristic
64C2×C22⋊C4×C149C2211yescharacteristic
65C2×C22⋊C4×C149C2211yescharacteristic
66C2×C22⋊C4×C149C2211yescharacteristic
67C23×D149C2311yescharacteristic
68C2×Dic298—42no—
69C2×Dic298C2314yes—
70C2×C22⋊D149—24no—
71C2×C22⋊D149—42no—
72C2×C22⋊D149C2314yes—
73C2×C22⋊D149C2314yes—
74C22×Dic149—42no—
75C22×Dic149—42no—
76C22×Dic149—42no—
77C22×Dic149C2311yescharacteristic
78C22×Dic149C2311yescharacteristic
79C22×Dic149C2311yescharacteristic
80C22×Dic149C2311yescharacteristic
81C22×Dic149C2311yescharacteristic
82C22×Dic149C2311yescharacteristic
83C22×Dic149C2311yescharacteristic
84C22×Dic149C2314yes—
85C22×Dic149C2314yes—
86C22×Dic149C2314yes—
87C2×C4×D149—42no—
88C2×C4×D149C2314yes—
89C4⋊Dic149C2314yes—
90C4⋊Dic149C2314yes—
91C4⋊Dic149C2314yes—
92C4⋊Dic149C2314yes—
93C4⋊Dic149C2314yes—
94C4⋊Dic149C2314yes—
95#14558715C2314yes—
96#14558715C2314yes—
97#14558715C2314yes—
98#14558715C2314yes—
99#14558715C2314yes—
100#14558715C2314yes—
101C22⋊Dic149C2314yes—
102C22⋊Dic149C2314yes—
103C22⋊Dic149C2314yes—
104#14558713C2314yes—
105#14558713C2314yes—
106#14558713C2314yes—
107#14558713C2314yes—
108C4×Dic149C2314yes—
109C4×Dic149C2314yes—
110C24×C149C2311yescharacteristic
111C24×C149C2311yescharacteristic
112C2×D4×C149—24no—
113C2×D4×C149C2314yes—
114C22×C4×C149—24no—
115C22×C4×C149C2311yescharacteristic
116C22×C4×C149C2311yescharacteristic
117C22×C4×C149C2311yescharacteristic
118C22×C4×C149C2311yescharacteristic
119C22×C4×C149C2311yescharacteristic
120C22×C4×C149C2314yes—
121C4⋊C4×C149C2314yes—
122C4⋊C4×C149C2314yes—
123C22⋊C4×C149C2314yes—
124C22⋊C4×C149C2314yes—
125C22⋊C4×C149C2314yes—
126C22×D149—22no—
127C22×D149—22no—
128C22×D149—22no—
129C22×D149C2412yes—
130Dic298—44no—
131C22⋊D149—28no—
132C22⋊D149—44no—
133C2×Dic149—22no—
134C2×Dic149—22no—
135C2×Dic149—22no—
136C2×Dic149—22no—
137C2×Dic149—22no—
138C2×Dic149—22no—
139C2×Dic149—22no—
140C2×Dic149—44no—
141C2×Dic149—44no—
142C2×Dic149—44no—
143C2×Dic149C2412yes—
144C2×Dic149C2412yes—
145C2×Dic149C2412yes—
146C2×Dic149C2412yes—
147C2×Dic149C2412yes—
148C2×Dic149C2412yes—
149C2×Dic149C2412yes—
150C4×D149—44no—
151C23×C149—22no—
152C23×C149—22no—
153C23×C149—22no—
154C23×C149—22no—
155C23×C149—22no—
156C23×C149#4114yes—
157C23×C149C2412yes—
158C23×C149C2412yes—
159C23×C149C2411yescharacteristic
160D4×C149—28no—
161C2×C4×C149—28no—
162C2×C4×C149—22no—
163C2×C4×C149—22no—
164C2×C4×C149—22no—
165C2×C4×C149—22no—
166C2×C4×C149—22no—
167C2×C4×C149C2412yes—
168C2×C4×C149C2412yes—
169C2×C4×C149C2412yes—
170C2×C4×C149C2412yes—
171C2×C4×C149C2412yes—
172C22×C149—28no—
173C22×C149—22no—
174C22×C149—22no—
175C22×C149—22no—
176C22×C149—22no—
177C22×C149—22no—
178C22×C149—44no—
179C22×C149C2×#4114yes—
180C22×C149C2×#4112yes—
181C22×C149H(5,𝔽2)12yes—
182C22×C1492−1+412yes—
183C22×C149C2511yescharacteristic
184C2×D149—22no—
185C2×D149—22no—
186C2×D149—22no—
187C2×D149—44no—
188C4×C149—22no—
189C4×C149—22no—
190C4×C149—22no—
191C4×C149—22no—
192C4×C149—22no—
193Dic149—22no—
194Dic149—22no—
195Dic149—22no—
196Dic149—22no—
197Dic149—22no—
198Dic149—22no—
199Dic149—22no—
200C2×C149—24no—
201C2×C149—42no—
202C2×C149#53914yescomplemented
203C2×C149C22×#4111yescharacteristic
204C2×C149C2×H(5,𝔽2)11yescharacteristic
205C2×C149C2×2−1+411yescharacteristic
206D149—42no—
207C149C2×#53911yescharacteristic, complemented, Sylow
208C2×#539—1491nomaximal, Sylow
209#539—14916no—
210C2×#126—1491no—
211C2×#126—1491no—
212C2×#125—1491no—
213C2×#125—1491no—
214C2×#123—1491no—
215C2×#123—1491no—
216C2×#123—1491no—
217C2×#123D14911yescharacteristic, complemented
218C2×C22⋊Q8—1491no—
219C2×C22⋊Q8—1491no—
220C2×C22⋊Q8—1491no—
221C2×#121—1491no—
222C2×C4×D4—1491no—
223C2×C4×D4—1491no—
224C22×C4⋊C4—1491no—
225C22×Q8—1491no—
226C22×D4—1491no—
227C22×D4—1491no—
228C22×D4C2×D14911yescharacteristic
229C23×C4—1491no—
230C23×C4—1491no—
231C23×C4—1491no—
232C23×C4—1491no—
233C23×C4C2×D14911yescharacteristic
234#126—1498no—
235#126—1498no—
236#125—1498no—
237#125—1498no—
238#123—1498no—
239#123—1498no—
240#123—1498no—
241#123C2×D14918yescomplemented
242C22⋊Q8—1498no—
243C22⋊Q8—1498no—
244C22⋊Q8—1498no—
245#121—1498no—
246C4×D4—1498no—
247C4×D4—1498no—
248C2×C4⋊C4—1491no—
249C2×C4⋊C4—1491no—
250C2×C4⋊C4—1491no—
251C2×C4⋊C4—1491no—
252C2×C4⋊C4—1498no—
253C2×C4⋊C4—1491no—
254C2×C4⋊C4—1491no—
255C2×C4⋊C4—1491no—
256C2×C4⋊C4—1491no—
257C2×C4⋊C4—1491no—
258C2×C4⋊C4—1491no—
259C2×C4⋊C4—1491no—
260C2×C4⋊C4—1491no—
261C2×C4⋊C4C2×D14911yescharacteristic
262C2×C4⋊C4C2×D14911yescharacteristic
263C2×C22⋊C4—1491no—
264C2×C22⋊C4—1491no—
265C2×C22⋊C4—1491no—
266C2×C22⋊C4—1491no—
267C2×C22⋊C4—1491no—
268C2×C22⋊C4—1491no—
269C2×C22⋊C4—1491no—
270C2×C22⋊C4C2×D14911yescharacteristic
271C2×C22⋊C4C2×D14911yescharacteristic
272C2×C22⋊C4C2×D14911yescharacteristic
273C2×C42—1491no—
274C2×C42—1491no—
275C24—1491no—
276C24C22×D14911yescharacteristic
277C24C22×D14911yescharacteristic
278C2×Q8—5962no—
279C2×Q8—1494no—
280C2×D4—24no—
281C2×D4—2984no—
282C2×D4—5962no—
283C2×D4—1494no—
284C2×D4—1494no—
285C2×D4C22×D14914yes—
286C22×C4—24no—
287C22×C4—5962no—
288C22×C4—5962no—
289C22×C4—5962no—
290C22×C4—5962no—
291C22×C4—1491no—
292C22×C4—1491no—
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—1494no—
302C22×C4C22×D14914yes—
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⋊C4—1494no—
316C4⋊C4—1494no—
317C4⋊C4—1494no—
318C4⋊C4—1494no—
319C4⋊C4—1494no—
320C4⋊C4C22×D14914yes—
321C4⋊C4C22×D14914yes—
322C22⋊C4—1494no—
323C22⋊C4—1494no—
324C22⋊C4—1494no—
325C22⋊C4—1494no—
326C22⋊C4—1494no—
327C22⋊C4—1494no—
328C22⋊C4—1494no—
329C22⋊C4C22×D14914yes—
330C22⋊C4C22×D14914yes—
331C22⋊C4C22×D14914yes—
332C42—1494no—
333C42—1494no—
334C23—22no—
335C23—22no—
336C23—22no—
337C23—22no—
338C23—22no—
339C23—2982no—
340C23—2982no—
341C23—2982no—
342C23—1492no—
343C23#1455873514yes—
344C23C23×D14912yes—
345C23C23×D14912yes—
346C23C23×D14911yescharacteristic
347Q8—5964no—
348D4—28no—
349D4—2988no—
350D4—5964no—
351C2×C4—28no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—2982no—
358C2×C4—2982no—
359C2×C4—2982no—
360C2×C4—2982no—
361C2×C4—2982no—
362C2×C4—2982no—
363C2×C4—2982no—
364C2×C4—5964no—
365C2×C4—5964no—
366C2×C4—5964no—
367C2×C4—5964no—
368C2×C4—1492no—
369C2×C4—1492no—
370C2×C4—1492no—
371C2×C4—1492no—
372C2×C4—1492no—
373C2×C4—1492no—
374C2×C4—1492no—
375C2×C4C23×D14912yes—
376C2×C4C23×D14912yes—
377C2×C4C23×D14912yes—
378C2×C4C23×D14912yes—
379C2×C4C23×D14912yes—
380C22—22no—
381C22—22no—
382C22—28no—
383C22—22no—
384C22—22no—
385C22—22no—
386C22—44no—
387C22—2982no—
388C22—2982no—
389C22—2982no—
390C22—5964no—
391C22C2×#1455873514yes—
392C22C2×#1455873512yes—
393C22#1801195712yes—
394C22#1801195812yes—
395C22C24×D14911yescharacteristic
396C4—22no—
397C4—22no—
398C4—22no—
399C4—22no—
400C4—22no—
401C4—2982no—
402C4—2982no—
403C4—2982no—
404C4—2982no—
405C4—2982no—
406C4—2982no—
407C4—2982no—
408C2—24no—
409C2—42no—
410C2—5962no—
411C2#2375021914yesdirect product factor
412C2C22×#1455873511yescharacteristic
413C2C2×#1801195711yescharacteristic
414C2C2×#1801195811yescharacteristic
subgroupG/H
centerC23C23×D149
commutator, cosocleC22×C149C25
FrattiniC22C24×D149
FittingC2×#123×C149C2
socleC23×C149C24
prime radicalC2×#18011883C2
hypercenterC2×#123D149
hypocenterC149C2×#539
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. #23750219C2direct (N × H)
2. C2×#18011906C2semidirect
3. C2×#18011904C2semidirect
4. C2×#18011902C2semidirect
5. C2×#18011901C2semidirect
6. C2×#18011895C2semidirect
7. C2×#18011894C2semidirect
8. C2×#18011893C2semidirect
9. C2×#18011891C2semidirect
10. C2×#18011888C2semidirect
11. C2×#18011888C2semidirect
13. C2×D4×Dic149C2semidirect
14. C2×#18011871C2semidirect
15. C22×C4⋊Dic149C2semidirect
16. C2×#123×C149C2semidirect
24. #18011906C22semidirect
25. #18011904C22semidirect
26. #18011902C22semidirect
27. #18011901C22semidirect
28. #18011895C22semidirect
29. #18011894C22semidirect
30. #18011893C22semidirect
31. #18011891C22semidirect
32. #18011888C22semidirect
33. #18011888C22semidirect
35. D4×Dic149C22semidirect
36. #18011871C22semidirect
43. C2×C4⋊Dic149C22semidirect
61. #123×C149C22semidirect
202. C2×C149#539semidirect
207. C149C2×#539semidirect
217. C2×#123D149semidirect
241. #123C2×D149semidirect
411. C2#23750219direct (N × H)

Maximal subgroups

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

subgroupindex
#237502192
C2×#180119062
C2×#180119042
C2×#180119022
C2×#180119012
C2×#180118952
C2×#180118942
C2×#180118932
C2×#180118912
C2×#180118882
C2×#180118832
C2×D4×Dic1492
C2×#180118712
C22×C4⋊Dic1492
C2×#123×C1492
C2×#539149