Finite Group Databasebeta

← #34061423

Subgroups — #34061423

Order 19072.

502 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18011998C211yesmaximal, characteristic, complemented
2C22×#14558745C211yesmaximal, characteristic, complemented
3#23750660C211yesmaximal, characteristic, complemented
4#23750658C211yesmaximal, characteristic, complemented
5#23750657C211yesmaximal, characteristic, complemented
6#23750656C211yesmaximal, characteristic, complemented
7#23750656C211yesmaximal, characteristic, complemented
8#23750654C211yesmaximal, characteristic, complemented
9#23750652C211yesmaximal, characteristic, complemented
10D4×#11924753C211yesmaximal, characteristic, complemented
11#23750631C211yesmaximal, characteristic, complemented
12#23750598C211yesmaximal, characteristic, complemented
13C2×C22⋊#11924753C211yesmaximal, characteristic, complemented
14#23750589C211yesmaximal, characteristic, complemented
15#23750131C211yesmaximal, characteristic
16#18011998—24no—
17C2×#14558746C2211yescharacteristic, complemented
18C2×#14558745—24no—
19C2×#14558745C2211yescharacteristic
20C2×#14558745C2211yescharacteristic
21C2×#14558745C2211yescharacteristic
22C2×#14558745C2211yescharacteristic
23C2×#14558745C2211yescharacteristic, complemented
24C2×D149⋊C8C2211yescharacteristic, complemented
25C22×#11924753C2211yescharacteristic
26C22×#11924753C2211yescharacteristic
27C22×#11924753C2211yescharacteristic
28C22×#11924753C2211yescharacteristic
29C22×#11924753C2211yescharacteristic, complemented
30#18011978C2211yescharacteristic, complemented
31#18011978C2211yescharacteristic, complemented
32C4⋊#11924753C2211yescharacteristic, complemented
33C4⋊#11924753C2211yescharacteristic, complemented
34#18011968C2211yescharacteristic, complemented
35#18011968C2211yescharacteristic, complemented
36C22⋊#11924753C2211yescharacteristic
37C22⋊#11924753C2211yescharacteristic
38C22⋊#11924753C2211yescharacteristic
39C22⋊#11924753C2211yescharacteristic
40C22⋊#11924753C2211yescharacteristic, complemented
41C22⋊#11924753C2211yescharacteristic, complemented
42#18011966C2211yescharacteristic, complemented
43#18011966C2211yescharacteristic, complemented
44C4×#11924753C2211yescharacteristic, complemented
45C4×#11924753C2211yescharacteristic, complemented
46C2×#14558735C2211yescharacteristic
47C23×Dic149C2211yescharacteristic
48#18011895C411yescharacteristic
49#18011892C411yescharacteristic
50#18011888C411yescharacteristic
51#18011888C411yescharacteristic
52#18011883C411yescharacteristic
53#18011883C411yescharacteristic
54#18011880C411yescharacteristic
55D4×Dic149C2211yescharacteristic
56D4×Dic149C2211yescharacteristic
57#18011871C2211yescharacteristic
58#18011871C2211yescharacteristic
59#18011867C2211yescharacteristic
60#120×C149C411yescharacteristic
61#14558746—22no—
62#14558745—22no—
63#14558745—22no—
64#14558745—22no—
65#14558745—22no—
66#14558745D414yescomplemented
67D149⋊C8—22no—
68C2×#11924753—22no—
69C2×#11924753—22no—
70C2×#11924753—22no—
71C2×#11924753—22no—
72C2×#11924753—22no—
73C2×#11924753C2311yescharacteristic
74C2×#11924753C2311yescharacteristic
75C2×#11924753C2311yescharacteristic
76C2×#11924753C2311yescharacteristic
77C2×#11924753C2311yescharacteristic
78C2×#11924753C2311yescharacteristic
79C2×#11924753C2311yescharacteristic
80C2×#11924753C2311yescharacteristic
81#14558735—22no—
82#14558735—22no—
83C2×Dic298C2×C411yescharacteristic
84C2×C22⋊D149C2×C411yescharacteristic
85C2×C22⋊D149C2×C411yescharacteristic
86C2×C22⋊D149C2×C411yescharacteristic
87C2×C22⋊D149C2×C411yescharacteristic
88C22×Dic149—22no—
89C22×Dic149—22no—
90C22×Dic149C2×C411yescharacteristic
91C22×Dic149C2×C411yescharacteristic
92C22×Dic149C2×C411yescharacteristic
93C22×Dic149C2311yescharacteristic
94C22×Dic149C2311yescharacteristic
95C22×Dic149C2311yescharacteristic
96C22×Dic149C2311yescharacteristic
97C2×C4×D149C2311yescharacteristic
98C4⋊Dic149C2×C411yescharacteristic
99C4⋊Dic149C2×C411yescharacteristic
100#14558715C2×C411yescharacteristic
101#14558715C2×C411yescharacteristic
102#14558715C2×C411yescharacteristic
103#14558715C2×C411yescharacteristic
104C22⋊Dic149C2×C411yescharacteristic
105C22⋊Dic149C2×C411yescharacteristic
106C22⋊Dic149C2×C411yescharacteristic
107C22⋊Dic149C2×C411yescharacteristic
108C22⋊Dic149C2×C411yescharacteristic
109#14558713C2×C411yescharacteristic
110#14558713C2×C411yescharacteristic
111C4×Dic149C2311yescharacteristic
112C4×Dic149C2311yescharacteristic
113C24×C149C2×C411yescharacteristic
114C2×D4×C149C2×C411yescharacteristic
115C2×D4×C149C2×C411yescharacteristic
116C2×D4×C149C2×C411yescharacteristic
117C22⋊C4×C149C2×C411yescharacteristic
118C22⋊C4×C149C2×C411yescharacteristic
119C22⋊C4×C149C2×C411yescharacteristic
120#11924753—21no—
121#11924753—21no—
122#11924753—21no—
123#11924753—21no—
124#11924753—21no—
125#11924753—21no—
126#11924753C2×D412yes—
127#11924753C2×D412yes—
128C22×D149C22×C411yescharacteristic
129Dic298—22no—
130C22⋊D149—22no—
131C22⋊D149—22no—
132C22⋊D149—22no—
133C22⋊D149—41no—
134C2×Dic149—22no—
135C2×Dic149—22no—
136C2×Dic149—22no—
137C2×Dic149—21no—
138C2×Dic149—21no—
139C2×Dic149—21no—
140C2×Dic149—21no—
141C2×Dic149—21no—
142C2×Dic149—21no—
143C2×Dic149C22×C411yescharacteristic
144C2×Dic149C22×C411yescharacteristic
145C2×Dic149C22×C411yescharacteristic
146C2×Dic149C22×C411yescharacteristic
147C2×Dic149C22×C411yescharacteristic
148C2×Dic149C22×C411yescharacteristic
149C2×Dic149C2×D412yes—
150C2×Dic149#4112yes—
151C2×Dic149C2411yescharacteristic
152C4×D149—21no—
153C4×D149—21no—
154C23×C149—22no—
155C23×C149—22no—
156C23×C149—41no—
157C23×C149C22×C411yescharacteristic
158C23×C149C22×C411yescharacteristic
159C23×C149C22×C411yescharacteristic
160C23×C149C22×C411yescharacteristic
161D4×C149—22no—
162D4×C149—22no—
163D4×C149—41no—
164C2×C4×C149C22×C411yescharacteristic
165C2×C4×C149C22×C411yescharacteristic
166C2×C4×C149C22×C411yescharacteristic
167C22×C149—21no—
168C22×C149—21no—
169C22×C149—21no—
170C22×C149—21no—
171C22×C149—21no—
172C22×C149—21no—
173C22×C149—21no—
174C22×C149—21no—
175C22×C149—21no—
176C22×C149—21no—
177C22×C149—44no—
178C22×C149C4×D412yes—
179C22×C149#13112yescomplemented
180C22×C149C23×C411yescharacteristic
181C2×D149—21no—
182C2×D149—21no—
183C2×D149—21no—
184C4×C149—21no—
185C4×C149—21no—
186C4×C149—21no—
187Dic149—21no—
188Dic149—21no—
189Dic149—21no—
190Dic149—21no—
191Dic149—21no—
192Dic149C4×D412yes—
193Dic149C22×D411yescharacteristic
194Dic149C2×#4111yescharacteristic
195C2×C149—22no—
196C2×C149—22no—
197C2×C149—41no—
198C2×C149—41no—
199C2×C149C2×C4×D411yescharacteristic
200C2×C149C2×#13111yescharacteristic
201C2×C149#56811yescharacteristic
202D149—41no—
203C149#293311yescharacteristic, complemented, Sylow
204#2933—1491nomaximal, Sylow
205C2×#131—1491no—
206C22×M16—1491no—
207#525—1491no—
208#436—1491no—
209#436—1491no—
210#435—1491no—
211#435—1491no—
212#435—1491no—
213#435—1491no—
214C8×D4—1491no—
215C8×D4—1491no—
216#424—1491no—
217#408—1491no—
218C2×C22⋊C8—1491no—
219#405—1491no—
220C2×#41—1491no—
221C23×C4—1491no—
222#131—2984no—
223C2×M16—2984no—
224C2×M16—1491no—
225C2×M16—1491no—
226C2×M16—1491no—
227C2×M16—1491no—
228C2×M16—1491no—
229C2×M16—1491no—
230C22×C8—1491no—
231C22×C8—1491no—
232C22×C8—1491no—
233C22×C8—1491no—
234C22×C8—1491no—
235C22×C8—1491no—
236#123—1491no—
237#123—1491no—
238C22⋊Q8—1491no—
239C22⋊Q8—1491no—
240#121—1491no—
241#121—1491no—
242#120—1491no—
243#120#1059701011yescharacteristic
244C4×D4—1491no—
245C4×D4—1491no—
246C4×D4—1491no—
247C4×D4—1491no—
248#117—1491no—
249C4⋊C8—1491no—
250C4⋊C8—1491no—
251C4⋊C8—1491no—
252C4⋊C8—1491no—
253C22⋊C8—1491no—
254C22⋊C8—1491no—
255C22⋊C8—1491no—
256C22⋊C8—1491no—
257C22⋊C8—1491no—
258C22⋊C8—1491no—
259C22⋊C8—1491no—
260C22⋊C8—1491no—
261#97—1491no—
262#97—1491no—
263C4×C8—1491no—
264C4×C8—1491no—
265C24C2×#1059701011yescharacteristic
266#41—2982no—
267#41—2982no—
268C2×Q8—1491no—
269C2×D4—1491no—
270C2×D4—1491no—
271C2×D4—1491no—
272C2×D4—1491no—
273C2×D4C2×#1059701011yescharacteristic
274C2×D4C2×#1059701011yescharacteristic
275C2×D4C2×#1059701011yescharacteristic
276C22×C4—2982no—
277C22×C4—2982no—
278C22×C4—1491no—
279C22×C4—1491no—
280C22×C4—1491no—
281C22×C4—1491no—
282C22×C4—1491no—
283C22×C4—1491no—
284C22×C4—1491no—
285C22×C4—1491no—
286M16—2982no—
287M16—2982no—
288M16—2982no—
289M16—2982no—
290M16—2982no—
291M16—1494no—
292C2×C8—2982no—
293C2×C8—2982no—
294C2×C8—2982no—
295C2×C8—2982no—
296C2×C8—2982no—
297C2×C8—2982no—
298C2×C8—1491no—
299C2×C8—1491no—
300C2×C8—1491no—
301C2×C8—1491no—
302C2×C8—1491no—
303C2×C8—1491no—
304C2×C8—1491no—
305C2×C8—1491no—
306C4⋊C4—1491no—
307C4⋊C4—1491no—
308C4⋊C4—1491no—
309C4⋊C4—1491no—
310C4⋊C4—1491no—
311C4⋊C4—1491no—
312C22⋊C4—1491no—
313C22⋊C4—1491no—
314C22⋊C4—1491no—
315C22⋊C4—1491no—
316C22⋊C4—1491no—
317C22⋊C4—1491no—
318C22⋊C4—1491no—
319C22⋊C4C2×#1059701011yescharacteristic
320C22⋊C4C2×#1059701011yescharacteristic
321C22⋊C4C2×#1059701011yescharacteristic
322C42—1491no—
323C42—1491no—
324C23—22no—
325C23—22no—
326C23—41no—
327C23—1491no—
328C23C22×#1059701011yescharacteristic
329C23C22×#1059701011yescharacteristic
330C23C22×#1059701011yescharacteristic
331C23C22×#1059701011yescharacteristic
332Q8—2982no—
333D4—22no—
334D4—22no—
335D4—41no—
336D4—2982no—
337D4—2982no—
338D4—2982no—
339D4—5961no—
340C2×C4—2981no—
341C2×C4—2981no—
342C2×C4—2982no—
343C2×C4—2981no—
344C2×C4—2981no—
345C2×C4—2981no—
346C2×C4—2981no—
347C2×C4—2981no—
348C2×C4—2982no—
349C2×C4—2982no—
350C2×C4—2981no—
351C2×C4—1491no—
352C2×C4—1491no—
353C2×C4—1491no—
354C2×C4—1491no—
355C2×C4—1491no—
356C2×C4—1492no—
357C2×C4—1492no—
358C2×C4—1491no—
359C2×C4—1491no—
360C2×C4C22×#1059701011yescharacteristic
361C2×C4C22×#1059701011yescharacteristic
362C2×C4C22×#1059701011yescharacteristic
363C8—2981no—
364C8—2981no—
365C8—2981no—
366C8—2981no—
367C8—2981no—
368C8—2981no—
369C8—1492no—
370C8—1492no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—44no—
382C22—2981no—
383C22—2981no—
384C22—2981no—
385C22D4×#1059701012yes—
386C22#1801199812yescomplemented
387C22C23×#1059701011yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—2981no—
392C4—2981no—
393C4—2981no—
394C4—2981no—
395C4—2981no—
396C4—1491no—
397C4—1491no—
398C4—1492no—
399C2—22no—
400C2—22no—
401C2—41no—
402C2—41no—
403C2—5961no—
404C2C2×D4×#1059701011yescharacteristic
405C2C2×#1801199811yescharacteristic
406C2#2375070311yescharacteristic
subgroupG/H
center, FrattiniC22C23×#10597010
commutator, socleC22×C149C23×C4
Fitting#120×C149C4
prime radical#23750131C2
cosocleC2×Dic149C24
hypercenter#120#10597010
hypocenterC149#2933
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. C2×#18011998C2semidirect
2. C22×#14558745C2semidirect
3. #23750660C2semidirect
4. #23750658C2semidirect
5. #23750657C2semidirect
6. #23750656C2semidirect
7. #23750656C2semidirect
8. #23750654C2semidirect
9. #23750652C2semidirect
10. D4×#11924753C2semidirect
11. #23750631C2semidirect
12. #23750598C2semidirect
13. C2×C22⋊#11924753C2semidirect
14. #23750589C2semidirect
17. C2×#14558746C22semidirect
23. C2×#14558745C22semidirect
24. C2×D149⋊C8C22semidirect
29. C22×#11924753C22semidirect
30. #18011978C22semidirect
31. #18011978C22semidirect
32. C4⋊#11924753C22semidirect
33. C4⋊#11924753C22semidirect
34. #18011968C22semidirect
35. #18011968C22semidirect
40. C22⋊#11924753C22semidirect
41. C22⋊#11924753C22semidirect
42. #18011966C22semidirect
43. #18011966C22semidirect
44. C4×#11924753C22semidirect
45. C4×#11924753C22semidirect
66. #14558745D4semidirect
179. C22×C149#131semidirect
203. C149#2933semidirect
386. C22#18011998semidirect

Maximal subgroups

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

subgroupindex
C2×#180119982
C22×#145587452
#237506602
#237506582
#237506572
#237506562
#237506542
#237506522
D4×#119247532
#237506312
#237505982
C2×C22⋊#119247532
#237505892
#237501312
#2933149