Finite Group Databasebeta

← #34055645

Subgroups — #34055645

Order 19072.

394 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750177C211yesmaximal, characteristic, complemented
2#23750171C211yesmaximal, characteristic
3#23750003C211yesmaximal, characteristic, complemented
4#23749996C211yesmaximal, characteristic, complemented
5#23749974C211yesmaximal, characteristic, complemented
6#23749970C211yesmaximal, characteristic, complemented
7#23749850C211yesmaximal, characteristic, complemented
8#23749849C211yesmaximal, characteristic, complemented
9#23749846C211yesmaximal, characteristic, complemented
10#23749845C211yesmaximal, characteristic, complemented
11#23749789C211yesmaximal, characteristic, complemented
12#23749787C211yesmaximal, characteristic, complemented
13#23749785C211yesmaximal, characteristic, complemented
14#23749675C211yesmaximal, characteristic, complemented
15#452×C149C211yesmaximal, characteristic, complemented
16C2×#14558736C2211yescharacteristic
17C2×Dic596C2211yescharacteristic
18C2×#14558726C2211yescharacteristic
19C2×#14558726C2211yescharacteristic
20C2×#14558725C2211yescharacteristic
21C2×#14558724C2211yescharacteristic
22C2×#14558723C2211yescharacteristic
23#18011910C2211yescharacteristic
24#18011909C2211yescharacteristic
25#18011909C2211yescharacteristic
26#18011907C2211yescharacteristic
27#18011901—21no—
28#18011900C2211yescharacteristic
29#18011898C2211yescharacteristic
30#18011890C2211yescharacteristic
31#18011888—21no—
32#18011883—21no—
33#18011883—21no—
34Q8×Dic149C2211yescharacteristic
35#18011876—21no—
36#18011876C2211yescharacteristic
37C4×C22⋊D149—21no—
38C4×C22⋊D149—21no—
39#18011867—21no—
40C2×C4×Dic149C2211yescharacteristic
41#18011840C2211yescharacteristic
42#18011840C2211yescharacteristic
43#18011836C2211yescharacteristic
44#18011835C2211yescharacteristic
45#18011834C2211yescharacteristic
46#18011833C2211yescharacteristic
47#18011832C2211yescharacteristic
48#18011831C2211yescharacteristic
49C22⋊#11924746C2211yescharacteristic
50C8×Dic149C2211yescharacteristic
51C8×Dic149C2211yescharacteristic
52C2×#41×C149C2211yescharacteristic
53C2×Q16×C149C2211yescharacteristic
54C2×SD16×C149C2211yescharacteristic
55C22⋊Q8×C149C2211yescharacteristic
56#103×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic
58C22⋊C8×C149C2211yescharacteristic
59#14558736—41no—
60#14558736—41no—
61C2×Dic298—21no—
62C2×Dic298C2311yescharacteristic
63C2×Dic298C2311yescharacteristic
64C2×D596C2311yescharacteristic
65C2×C22⋊D149—21no—
66C2×C22⋊D149—21no—
67C2×C22⋊D149—21no—
68C22×Dic149D411yescharacteristic
69C22×Dic149D411yescharacteristic
70C2×C4×D149—21no—
71Dic596—41no—
72#14558726—41no—
73#14558726—41no—
74#14558725—41no—
75#14558724—41no—
76#14558723—41no—
77C2×#11924746C2311yescharacteristic
78C2×#11924746C2311yescharacteristic
79C4⋊Dic149—21no—
80C4⋊Dic149C2311yescharacteristic
81#14558715—21no—
82#14558715—21no—
83#14558715—21no—
84#14558715—21no—
85#14558715—21no—
86#14558715—21no—
87#14558715—21no—
88C22⋊Dic149—21no—
89C22⋊Dic149—21no—
90C22⋊Dic149—21no—
91#14558713—21no—
92#14558713—21no—
93C4×Dic149—21no—
94C4×Dic149—21no—
95C4×Dic149D411yescharacteristic
96C4×Dic149D411yescharacteristic
97C4×Dic149C2311yescharacteristic
98C4×Dic149C2311yescharacteristic
99#41×C149—41no—
100#41×C149—41no—
101C2×Q8×C149C2311yescharacteristic
102C2×Q8×C149C2311yescharacteristic
103C2×D4×C149—21no—
104C2×D4×C149C2311yescharacteristic
105C22×C4×C149—21no—
106C22×C4×C149C2311yescharacteristic
107Q16×C149—41no—
108SD16×C149—41no—
109C2×C8×C149C2311yescharacteristic
110C2×C8×C149C2311yescharacteristic
111C4⋊C4×C149—21no—
112C4⋊C4×C149C2311yescharacteristic
113C22⋊C4×C149—21no—
114C22×D149—21no—
115Dic298—21no—
116Dic298—21no—
117Dic298—21no—
118Dic298—21no—
119Dic298—42no—
120D596—21no—
121D596—21no—
122C22⋊D149—42no—
123C22⋊D149—42no—
124C22⋊D149—42no—
125C2×Dic149—22no—
126C2×Dic149—22no—
127C2×Dic149—21no—
128C2×Dic149—21no—
129C2×Dic149—21no—
130C2×Dic149C2×D411yescharacteristic
131C2×Dic149C2×D411yescharacteristic
132C2×Dic149C2×D411yescharacteristic
133C2×Dic149C2×D411yescharacteristic
134C4×D149—42no—
135#11924746—21no—
136#11924746—21no—
137C23×C149—21no—
138C23×C149C2×D411yescharacteristic
139Q8×C149—21no—
140Q8×C149—21no—
141Q8×C149—21no—
142Q8×C149—21no—
143D4×C149—21no—
144D4×C149—21no—
145D4×C149—42no—
146C2×C4×C149—21no—
147C2×C4×C149—21no—
148C2×C4×C149—21no—
149C2×C4×C149—21no—
150C2×C4×C149—21no—
151C2×C4×C149—42no—
152C2×C4×C149C2×D411yescharacteristic
153C2×C4×C149C2411yescharacteristic
154C8×C149—21no—
155C8×C149—21no—
156C22×C149—21no—
157C22×C149—21no—
158C22×C149—21no—
159C22×C149—41no—
160C22×C149—41no—
161C22×C149—41no—
162C22×C149C22×D411yescharacteristic
163C2×D149—41no—
164C2×D149—41no—
165C2×D149—41no—
166C4×C149—21no—
167C4×C149—41no—
168C4×C149—41no—
169C4×C149—41no—
170C4×C149H(5,𝔽2)11yescharacteristic
171C4×C149H(5,𝔽2)11yescharacteristic
172Dic149—21no—
173Dic149—21no—
174Dic149—41no—
175Dic149—41no—
176Dic149—41no—
177Dic149#13512yes—
178Dic149#13712yes—
179C2×C149—41no—
180C2×C149—81no—
181C2×C149#53511yescharacteristic
182C2×C149C2×#13511yescharacteristic
183C2×C149C2×#13711yescharacteristic
184D149—81no—
185C149#321011yescharacteristic, complemented, Sylow
186#3210—1491nomaximal, Sylow
187#533—1491no—
188#532—1491no—
189#494—1491no—
190#492—1491no—
191#487—1491no—
192#486—1491no—
193#464—1491no—
194#464—1491no—
195#464—1491no—
196#464—1491no—
197#452—1491no—
198#452—1491no—
199#452—1491no—
200#452D14911yescharacteristic, complemented
201#431—1491no—
202C2×#41—1491no—
203C2×#41C2×D14911yescharacteristic
204C2×Q16—1491no—
205C2×Q16—1491no—
206C2×Q16—1491no—
207C2×Q16C2×D14911yescharacteristic
208C2×SD16—1491no—
209C2×SD16—1491no—
210C2×SD16—1491no—
211C2×SD16C2×D14911yescharacteristic
212C4⋊Q8—1491no—
213C4⋊Q8—1491no—
214C4⋊Q8—1491no—
215#127—1491no—
216#125—2981no—
217#124—1491no—
218#124—1491no—
219C22⋊Q8—2981no—
220C22⋊Q8—1491no—
221C22⋊Q8C2×D14911yescharacteristic
222#121—2981no—
223#121—2981no—
224C4×Q8—2981no—
225C4×Q8—1491no—
226C4×Q8—1491no—
227C4×D4—2981no—
228C4×D4—2981no—
229#117—2981no—
230C2×C42—1491no—
231C4⋊C8—1491no—
232C4⋊C8—1491no—
233#103—1491no—
234#103—1491no—
235#103—1491no—
236#103C2×D14911yescharacteristic
237#102—1491no—
238#102—1491no—
239#102—1491no—
240#102C2×D14911yescharacteristic
241C22⋊C8—1491no—
242C22⋊C8C2×D14911yescharacteristic
243C4×C8—1491no—
244C4×C8—1491no—
245#41—41no—
246#41—41no—
247#41—5961no—
248#41—5961no—
249C2×Q8—2981no—
250C2×Q8—1491no—
251C2×Q8—1491no—
252C2×Q8C22×D14911yescharacteristic
253C2×Q8C22×D14911yescharacteristic
254C2×D4—21no—
255C2×D4—2981no—
256C2×D4—2981no—
257C2×D4—2981no—
258C2×D4—1491no—
259C2×D4C22×D14911yescharacteristic
260C22×C4—21no—
261C22×C4—2981no—
262C22×C4—1491no—
263C22×C4—1491no—
264C22×C4C22×D14911yescharacteristic
265Q16—41no—
266Q16—5961no—
267Q16—5961no—
268Q16—5961no—
269SD16—41no—
270SD16—5961no—
271SD16—5961no—
272SD16—5961no—
273C2×C8—1491no—
274C2×C8—1491no—
275C2×C8C22×D14911yescharacteristic
276C2×C8C22×D14911yescharacteristic
277C4⋊C4—21no—
278C4⋊C4—2981no—
279C4⋊C4—2981no—
280C4⋊C4—2981no—
281C4⋊C4—2981no—
282C4⋊C4—2981no—
283C4⋊C4—2981no—
284C4⋊C4—2981no—
285C4⋊C4—2981no—
286C4⋊C4—1491no—
287C4⋊C4C22×D14911yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—2981no—
290C22⋊C4—2981no—
291C22⋊C4—2981no—
292C22⋊C4—2981no—
293C22⋊C4—2981no—
294C42—2981no—
295C42—2981no—
296C42—1491no—
297C42—1491no—
298C42—1491no—
299C42—1491no—
300C23—21no—
301C23—2981no—
302C23D4×D14911yescharacteristic
303Q8—21no—
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—2981no—
308Q8—2981no—
309Q8—2981no—
310Q8—2981no—
311Q8—5962no—
312D4—21no—
313D4—21no—
314D4—42no—
315D4—2981no—
316D4—2981no—
317D4—5962no—
318D4—5962no—
319D4—5962no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—42no—
326C2×C4—2982no—
327C2×C4—2982no—
328C2×C4—2981no—
329C2×C4—2981no—
330C2×C4—2981no—
331C2×C4—5962no—
332C2×C4—1491no—
333C2×C4—1491no—
334C2×C4—1491no—
335C2×C4—1491no—
336C2×C4D4×D14911yescharacteristic
337C2×C4C23×D14911yescharacteristic
338C8—21no—
339C8—21no—
340C8—2981no—
341C8—2981no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—5961no—
349C22—5961no—
350C22—5961no—
351C22C2×D4×D14911yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—2981no—
357C4—2981no—
358C4—5961no—
359C4—5961no—
360C4—5961no—
361C4—1492no—
362C4—1492no—
363C4#1801195611yescharacteristic
364C4#1801195611yescharacteristic
365C2—41no—
366C2—81no—
367C2—11921no—
368C2#2375019011yescharacteristic
369C2#135×D14911yescharacteristic
370C2#137×D14911yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#452×C149C2
socleC22×C149C22×D4
prime radical#23750171C2
hypercenter#452D149
hypocenterC149#3210
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #23750177C2semidirect
3. #23750003C2semidirect
4. #23749996C2semidirect
5. #23749974C2semidirect
6. #23749970C2semidirect
7. #23749850C2semidirect
8. #23749849C2semidirect
9. #23749846C2semidirect
10. #23749845C2semidirect
11. #23749789C2semidirect
12. #23749787C2semidirect
13. #23749785C2semidirect
14. #23749675C2semidirect
15. #452×C149C2semidirect
185. C149#3210semidirect
200. #452D149semidirect

Maximal subgroups

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

subgroupindex
#237501772
#237501712
#237500032
#237499962
#237499742
#237499702
#237498502
#237498492
#237498462
#237498452
#237497892
#237497872
#237497852
#237496752
#452×C1492
#3210149