Finite Group Databasebeta

← #34055726

Subgroups — #34055726

Order 19072.

396 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750171C211yesmaximal, characteristic, complemented
2#23750156C211yesmaximal, characteristic, complemented
3#23750016C211yesmaximal, characteristic, complemented
4#23750013C211yesmaximal, characteristic, complemented
5#23749992C211yesmaximal, characteristic, complemented
6#23749988C211yesmaximal, characteristic, complemented
7#23749850C211yesmaximal, characteristic, complemented
8#23749846C211yesmaximal, characteristic, complemented
9#23749842C211yesmaximal, characteristic, complemented
10#23749838C211yesmaximal, characteristic, complemented
11#23749789C211yesmaximal, characteristic, complemented
12#23749787C211yesmaximal, characteristic, complemented
13#23749768C211yesmaximal, characteristic, complemented
14#23749679C211yesmaximal, characteristic, complemented
15#449×C149C211yesmaximal, characteristic, complemented
16C2×#14558736C2211yescharacteristic
17C2×Dic596C2211yescharacteristic
18C2×#14558726C2211yescharacteristic
19C2×#14558725C2211yescharacteristic
20C2×#14558724C2211yescharacteristic
21C2×#14558724C2211yescharacteristic
22C2×#14558721C2211yescharacteristic
23#18011909C2211yescharacteristic
24#18011907C2211yescharacteristic
25#18011904—21no—
26#18011902C2211yescharacteristic
27#18011900C2211yescharacteristic
28#18011898C2211yescharacteristic
29#18011898C2211yescharacteristic
30#18011892—21no—
31#18011890C2211yescharacteristic
32#18011883—21no—
33#18011883—21no—
34#18011876C2211yescharacteristic
35D4×Dic149—21no—
36D4×Dic149C2211yescharacteristic
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
50#18011821C2211yescharacteristic
51#18011821C2211yescharacteristic
52C2×#41×C149C2211yescharacteristic
53C2×SD16×C149C2211yescharacteristic
54C2×D8×C149C2211yescharacteristic
55#121×C149C2211yescharacteristic
56#103×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic
58C22⋊C8×C149C2211yescharacteristic
59#14558736—41no—
60#14558736—41no—
61C2×Dic298C2311yescharacteristic
62C2×Dic298C2311yescharacteristic
63C2×D596C2311yescharacteristic
64C2×C22⋊D149—21no—
65C2×C22⋊D149—21no—
66C2×C22⋊D149—21no—
67C22×Dic149—21no—
68C22×Dic149D411yescharacteristic
69C22×Dic149D411yescharacteristic
70C2×C4×D149—21no—
71Dic596—41no—
72#14558726—41no—
73#14558725—41no—
74#14558724—41no—
75#14558724—41no—
76#14558721—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—
86C22⋊Dic149—21no—
87C22⋊Dic149—21no—
88C22⋊Dic149—21no—
89C22⋊Dic149—21no—
90C22⋊Dic149—21no—
91C22⋊Dic149—21no—
92#14558713—21no—
93#14558713—21no—
94C4×Dic149—21no—
95C4×Dic149D411yescharacteristic
96C4×Dic149D411yescharacteristic
97C4×Dic149C2311yescharacteristic
98C4×Dic149C2311yescharacteristic
99#41×C149—41no—
100#41×C149—41no—
101C2×Q8×C149C2311yescharacteristic
102C2×D4×C149—21no—
103C2×D4×C149—21no—
104C2×D4×C149C2311yescharacteristic
105C2×D4×C149C2311yescharacteristic
106C22×C4×C149—21no—
107C22×C4×C149C2311yescharacteristic
108SD16×C149—41no—
109D8×C149—41no—
110C2×C8×C149C2311yescharacteristic
111C2×C8×C149C2311yescharacteristic
112C4⋊C4×C149C2311yescharacteristic
113C22⋊C4×C149—21no—
114C22×D149—21no—
115Dic298—21no—
116Dic298—21no—
117Dic298—21no—
118Dic298—21no—
119D596—21no—
120D596—21no—
121C22⋊D149—42no—
122C22⋊D149—42no—
123C22⋊D149—42no—
124C2×Dic149—21no—
125C2×Dic149—21no—
126C2×Dic149—21no—
127C2×Dic149—41no—
128C2×Dic149—41no—
129C2×Dic149—42no—
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×C149—21no—
139C23×C149C2×D411yescharacteristic
140Q8×C149—21no—
141Q8×C149—21no—
142D4×C149—21no—
143D4×C149—21no—
144D4×C149—21no—
145D4×C149—21no—
146D4×C149—42no—
147D4×C149—42no—
148C2×C4×C149—21no—
149C2×C4×C149—21no—
150C2×C4×C149—21no—
151C2×C4×C149—21no—
152C2×C4×C149—42no—
153C2×C4×C149C2×D411yescharacteristic
154C2×C4×C149C2411yescharacteristic
155C8×C149—21no—
156C8×C149—21no—
157C22×C149—21no—
158C22×C149—21no—
159C22×C149—21no—
160C22×C149—41no—
161C22×C149—41no—
162C22×C149—41no—
163C22×C149—41no—
164C22×C149—41no—
165C22×C149—41no—
166C22×C149C22×D411yescharacteristic
167C2×D149—41no—
168C2×D149—41no—
169C2×D149—41no—
170C4×C149—21no—
171C4×C149—41no—
172C4×C149—41no—
173C4×C149H(5,𝔽2)11yescharacteristic
174C4×C149H(5,𝔽2)11yescharacteristic
175Dic149—21no—
176Dic149—21no—
177Dic149—21no—
178Dic149—21no—
179Dic149—41no—
180Dic149—41no—
181Dic149—41no—
182C2×C149—41no—
183C2×C149—81no—
184C2×C149—81no—
185C2×C149#53511yescharacteristic
186C2×C149#57511yescharacteristic
187C2×C149#57511yescharacteristic
188D149—81no—
189C149#321911yescharacteristic, complemented, Sylow
190#3219—1491nomaximal, Sylow
191#532—1491no—
192#529—1491no—
193#497—1491no—
194#496—1491no—
195#491—1491no—
196#490—1491no—
197#464—1491no—
198#464—1491no—
199#463—1491no—
200#463—1491no—
201#452—1491no—
202#452—1491no—
203#449—1491no—
204#449D14911yescharacteristic, complemented
205#432—1491no—
206C2×#41—1491no—
207C2×#41C2×D14911yescharacteristic
208C2×Q16—1491no—
209C2×Q16—1491no—
210C2×SD16—1491no—
211C2×SD16—1491no—
212C2×SD16—1491no—
213C2×SD16C2×D14911yescharacteristic
214C2×D8—1491no—
215C2×D8C2×D14911yescharacteristic
216C4⋊Q8—1491no—
217#127—1491no—
218#126—2981no—
219#125—1491no—
220#124—1491no—
221#124—1491no—
222#124—1491no—
223#123—2981no—
224C22⋊Q8—1491no—
225#121—2981no—
226#121—2981no—
227#121C2×D14911yescharacteristic
228C4×Q8—1491no—
229C4×D4—2981no—
230C4×D4—2981no—
231C4×D4—2981no—
232C4×D4—1491no—
233#117—2981no—
234C2×C42—1491no—
235C4⋊C8—1491no—
236C4⋊C8—1491no—
237#103—1491no—
238#103—1491no—
239#103—1491no—
240#103C2×D14911yescharacteristic
241#102—1491no—
242#102—1491no—
243#102—1491no—
244#102C2×D14911yescharacteristic
245C22⋊C8—1491no—
246C22⋊C8C2×D14911yescharacteristic
247#97—1491no—
248#97—1491no—
249#41—41no—
250#41—41no—
251#41—5961no—
252#41—5961no—
253C2×Q8—1491no—
254C2×Q8—1491no—
255C2×Q8C22×D14911yescharacteristic
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—2981no—
259C2×D4—2981no—
260C2×D4—2981no—
261C2×D4—1491no—
262C2×D4C22×D14911yescharacteristic
263C2×D4C22×D14911yescharacteristic
264C22×C4—21no—
265C22×C4—2981no—
266C22×C4—2981no—
267C22×C4—1491no—
268C22×C4—1491no—
269C22×C4C22×D14911yescharacteristic
270Q16—5961no—
271Q16—5961no—
272SD16—41no—
273SD16—5961no—
274SD16—5961no—
275SD16—5961no—
276D8—41no—
277D8—5961no—
278C2×C8—1491no—
279C2×C8—1491no—
280C2×C8C22×D14911yescharacteristic
281C2×C8C22×D14911yescharacteristic
282C4⋊C4—2981no—
283C4⋊C4—2981no—
284C4⋊C4—2981no—
285C4⋊C4—2981no—
286C4⋊C4—2981no—
287C4⋊C4—2981no—
288C4⋊C4—1491no—
289C4⋊C4C22×D14911yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—2981no—
292C22⋊C4—2981no—
293C22⋊C4—2981no—
294C22⋊C4—2981no—
295C22⋊C4—2981no—
296C22⋊C4—2981no—
297C22⋊C4—2981no—
298C22⋊C4—2981no—
299C42—2981no—
300C42—1491no—
301C42—1491no—
302C42—1491no—
303C42—1491no—
304C23—21no—
305C23—21no—
306C23—2981no—
307C23D4×D14911yescharacteristic
308Q8—21no—
309Q8—21no—
310Q8—2981no—
311Q8—2981no—
312Q8—2981no—
313Q8—2981no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—21no—
318D4—42no—
319D4—42no—
320D4—2981no—
321D4—2981no—
322D4—5962no—
323D4—5962no—
324D4—5962no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—42no—
330C2×C4—2981no—
331C2×C4—2981no—
332C2×C4—2981no—
333C2×C4—5962no—
334C2×C4—5961no—
335C2×C4—5961no—
336C2×C4—5962no—
337C2×C4—1491no—
338C2×C4—1491no—
339C2×C4—1491no—
340C2×C4—1491no—
341C2×C4D4×D14911yescharacteristic
342C2×C4C23×D14911yescharacteristic
343C8—21no—
344C8—21no—
345C8—2981no—
346C8—2981no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—5961no—
357C22—5961no—
358C22—5961no—
359C22C2×D4×D14911yescharacteristic
360C4—21no—
361C4—41no—
362C4—41no—
363C4—2981no—
364C4—2981no—
365C4—2981no—
366C4—2981no—
367C4—5961no—
368C4—5961no—
369C4—5961no—
370C4#1801195611yescharacteristic
371C4#1801195611yescharacteristic
372C2—41no—
373C2—81no—
374C2—81no—
375C2—11921no—
376C2#2375019011yescharacteristic
377C2#2375042111yescharacteristic
378C2#2375042211yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#449×C149C2
socleC22×C149C22×D4
hypercenter#449D149
hypocenterC149#3219
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #23750171C2semidirect
2. #23750156C2semidirect
3. #23750016C2semidirect
4. #23750013C2semidirect
5. #23749992C2semidirect
6. #23749988C2semidirect
7. #23749850C2semidirect
8. #23749846C2semidirect
9. #23749842C2semidirect
10. #23749838C2semidirect
11. #23749789C2semidirect
12. #23749787C2semidirect
13. #23749768C2semidirect
14. #23749679C2semidirect
15. #449×C149C2semidirect
189. C149#3219semidirect
204. #449D149semidirect

Maximal subgroups

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

subgroupindex
#237501712
#237501562
#237500162
#237500132
#237499922
#237499882
#237498502
#237498462
#237498422
#237498382
#237497892
#237497872
#237497682
#237496792
#449×C1492
#3219149