Finite Group Databasebeta

← #34055761

Subgroups — #34055761

Order 19072.

396 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750235C211yesmaximal, characteristic, complemented
2#23750189C211yesmaximal, characteristic
3#23750018C211yesmaximal, characteristic, complemented
4#23749996C211yesmaximal, characteristic, complemented
5#23749988C211yesmaximal, characteristic, complemented
6#23749981C211yesmaximal, characteristic, complemented
7#23749850C211yesmaximal, characteristic, complemented
8#23749849C211yesmaximal, characteristic, complemented
9#23749824C211yesmaximal, characteristic, complemented
10#23749823C211yesmaximal, characteristic, complemented
11#23749787C211yesmaximal, characteristic, complemented
12#23749778C211yesmaximal, characteristic, complemented
13#23749775C211yesmaximal, characteristic, complemented
14#23749683C211yesmaximal, characteristic, complemented
15#452×C149C211yesmaximal, characteristic, complemented
16C22×D596C2211yescharacteristic
17C2×#14558726C2211yescharacteristic, complemented
18C2×#14558725C2211yescharacteristic
19C2×#14558725C2211yescharacteristic
20C2×#14558724C2211yescharacteristic, complemented
21C2×#14558723C2211yescharacteristic
22C2×#14558723C2211yescharacteristic
23#18011909C2211yescharacteristic, complemented
24#18011907C2211yescharacteristic
25#18011907C2211yescharacteristic
26#18011904—21no—
27#18011904—21no—
28#18011902—21no—
29#18011902C2211yescharacteristic, complemented
30#18011901—21no—
31#18011900C2211yescharacteristic
32#18011900C2211yescharacteristic
33#18011890C2211yescharacteristic
34#18011885—21no—
35#18011885—21no—
36#18011879—21no—
37#18011879—21no—
38Q8×Dic149C2211yescharacteristic, complemented
39#18011876C2211yescharacteristic, complemented
40#18011870C2211yescharacteristic
41#18011840C2211yescharacteristic, complemented
42#18011840C2211yescharacteristic, complemented
43#18011835C2211yescharacteristic, complemented
44#18011833C2211yescharacteristic
45#18011833C2211yescharacteristic
46#18011832C2211yescharacteristic, complemented
47#18011831C2211yescharacteristic
48#18011831C2211yescharacteristic
49C22⋊#11924746C2211yescharacteristic
50#18011821C2211yescharacteristic, complemented
51C8×Dic149C2211yescharacteristic, complemented
52C2×#41×C149C2211yescharacteristic
53C2×Q16×C149C2211yescharacteristic, complemented
54C2×SD16×C149C2211yescharacteristic, complemented
55C22⋊Q8×C149C2211yescharacteristic
56#103×C149C2211yescharacteristic, complemented
57#102×C149C2211yescharacteristic, complemented
58C22⋊C8×C149C2211yescharacteristic
59C23×D149—21no—
60C2×Dic298C2311yescharacteristic
61C2×D596—21no—
62C2×D596—41no—
63C2×D596—41no—
64C2×D596C2311yescharacteristic
65C2×D596C2311yescharacteristic
66C2×C22⋊D149—21no—
67C2×C22⋊D149—21no—
68C2×C22⋊D149—21no—
69C2×C22⋊D149—21no—
70#14558726—41no—
71#14558725—41no—
72#14558725—41no—
73#14558724—41no—
74#14558723—41no—
75#14558723—41no—
76C2×#11924746C2311yescharacteristic
77C2×#11924746C2311yescharacteristic
78C4⋊Dic149—21no—
79C4⋊Dic149—21no—
80C4⋊Dic149D411yescharacteristic
81C4⋊Dic149D411yescharacteristic
82C4⋊Dic149C2311yescharacteristic
83#14558715—21no—
84#14558715—21no—
85#14558715—21no—
86#14558715—21no—
87#14558715—21no—
88C22⋊Dic149—21no—
89C22⋊Dic149D411yescharacteristic
90C22⋊Dic149D411yescharacteristic
91#14558713—21no—
92#14558713—21no—
93#14558713—21no—
94#14558713—21no—
95C4×Dic149—21no—
96C4×Dic149—21no—
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—
115C22×D149—21no—
116C22×D149—42no—
117C22×D149—81no—
118C22×D149—81no—
119Dic298—21no—
120Dic298—21no—
121D596—21no—
122D596—21no—
123D596—21no—
124D596—21no—
125D596—42no—
126C22⋊D149—81no—
127C22⋊D149—81no—
128C22⋊D149—81no—
129C22⋊D149—81no—
130C2×Dic149—21no—
131C2×Dic149—21no—
132C2×Dic149C2×D411yescharacteristic
133C2×Dic149C2×D411yescharacteristic
134C2×Dic149C2×D411yescharacteristic
135C2×Dic149C2×D411yescharacteristic
136#11924746—21no—
137#11924746—21no—
138C23×C149—21no—
139C23×C149C2×D411yescharacteristic
140Q8×C149—21no—
141Q8×C149—21no—
142Q8×C149—21no—
143Q8×C149—21no—
144D4×C149—21no—
145D4×C149—21no—
146D4×C149—42no—
147C2×C4×C149—21no—
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×C149C22×D411yescharacteristic
164C2×D149—41no—
165C2×D149—41no—
166C2×D149—41no—
167C2×D149—41no—
168C2×D149—41no—
169C2×D149—41no—
170C2×D149—84no—
171C4×C149—21no—
172C4×C149—41no—
173C4×C149—41no—
174C4×C149—41no—
175C4×C149H(5,𝔽2)11yescharacteristic
176C4×C149H(5,𝔽2)11yescharacteristic
177Dic149—21no—
178Dic149—21no—
179Dic149—21no—
180Dic149—21no—
181Dic149—41no—
182Dic149—41no—
183C2×C149—41no—
184C2×C149—81no—
185C2×C149#53511yescharacteristic
186C2×C149#57711yescharacteristic
187C2×C149#57711yescharacteristic
188D149—81no—
189D149—81no—
190C149#322211yescharacteristic, complemented, Sylow
191#3222—1491nomaximal, Sylow
192#541—1491no—
193#535—1491no—
194#497—1491no—
195#492—1491no—
196#490—1491no—
197#488—1491no—
198#464—1491no—
199#464—1491no—
200#460—1491no—
201#460—1491no—
202#452—1491no—
203#452D14911yescharacteristic, complemented
204#450—1491no—
205#450—1491no—
206#433—1491no—
207C2×#41C2×D14911yescharacteristic
208C22×D4—1491no—
209C2×Q16—1491no—
210C2×Q16C2×D14911yescharacteristic, complemented
211C2×SD16—1491no—
212C2×SD16—1491no—
213C2×SD16—1491no—
214C2×SD16—1491no—
215C2×SD16—1491no—
216C2×SD16C2×D14911yescharacteristic, complemented
217C4⋊Q8—1491no—
218#127—1491no—
219#127—1491no—
220#126—2981no—
221#126—2981no—
222#125—2981no—
223#125—2981no—
224#125—1491no—
225#124—1491no—
226#124—1491no—
227C22⋊Q8—1491no—
228C22⋊Q8C2×D14911yescharacteristic
229#121—2981no—
230#121—2981no—
231#120—2981no—
232#120—2981no—
233C4×Q8—1491no—
234C4×Q8—1491no—
235#117—1491no—
236C4⋊C8—1491no—
237C4⋊C8—1491no—
238#103—1491no—
239#103C2×D14911yescharacteristic, complemented
240#102—1491no—
241#102—1491no—
242#102—1491no—
243#102—1491no—
244#102—1491no—
245#102C2×D14911yescharacteristic, complemented
246C22⋊C8—1491no—
247C22⋊C8C2×D14911yescharacteristic
248#97—1491no—
249C4×C8—1491no—
250C24—2981no—
251#41—41no—
252#41—41no—
253C2×Q8—1491no—
254C2×Q8C22×D14911yescharacteristic
255C2×Q8C22×D14911yescharacteristic
256C2×D4—21no—
257C2×D4—2981no—
258C2×D4—2981no—
259C2×D4—2981no—
260C2×D4—2981no—
261C2×D4—2981no—
262C2×D4—5961no—
263C2×D4—5961no—
264C2×D4—1491no—
265C2×D4—1491no—
266C2×D4C22×D14911yescharacteristic
267C22×C4—21no—
268C22×C4C22×D14911yescharacteristic
269Q16—41no—
270Q16—5961no—
271SD16—41no—
272SD16—5961no—
273SD16—5961no—
274SD16—5961no—
275SD16—5961no—
276SD16—5961no—
277C2×C8—1491no—
278C2×C8—1491no—
279C2×C8C22×D14911yescharacteristic
280C2×C8C22×D14911yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—2981no—
283C4⋊C4—2981no—
284C4⋊C4—2981no—
285C4⋊C4—2981no—
286C4⋊C4—2981no—
287C4⋊C4—2981no—
288C4⋊C4—2981no—
289C4⋊C4—1491no—
290C4⋊C4—1491no—
291C4⋊C4—1491no—
292C4⋊C4C22×D14911yescharacteristic
293C22⋊C4—21no—
294C22⋊C4—2981no—
295C22⋊C4—2981no—
296C22⋊C4—2981no—
297C22⋊C4—2981no—
298C22⋊C4—2981no—
299C22⋊C4—1491no—
300C22⋊C4—1491no—
301C42—2981no—
302C42—2981no—
303C42—1491no—
304C42—1491no—
305C23—21no—
306C23—2981no—
307C23—2981no—
308C23—5962no—
309C23—11921no—
310C23—11921no—
311C23D4×D14911yescharacteristic
312Q8—21no—
313Q8—21no—
314Q8—21no—
315Q8—21no—
316Q8—2981no—
317Q8—2981no—
318D4—21no—
319D4—21no—
320D4—42no—
321D4—2981no—
322D4—2981no—
323D4—2981no—
324D4—2981no—
325D4—5962no—
326D4—11921no—
327D4—11921no—
328D4—11921no—
329D4—11921no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—42no—
336C2×C4—2981no—
337C2×C4—2981no—
338C2×C4—1491no—
339C2×C4—1491no—
340C2×C4—1491no—
341C2×C4—1491no—
342C2×C4D4×D14911yescharacteristic
343C2×C4C23×D14911yescharacteristic
344C8—21no—
345C8—21no—
346C8—2981no—
347C8—2981no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—5961no—
355C22—5961no—
356C22—5961no—
357C22—5961no—
358C22—5961no—
359C22—5961no—
360C22—11924no—
361C22C2×D4×D14911yescharacteristic
362C4—21no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—2981no—
367C4—2981no—
368C4—2981no—
369C4—2981no—
370C4—5961no—
371C4—5961no—
372C4#1801195611yescharacteristic
373C4#1801195611yescharacteristic
374C2—41no—
375C2—81no—
376C2—11921no—
377C2—11921no—
378C2#2375019011yescharacteristic
379C2#2375043211yescharacteristic
380C2#2375043411yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#452×C149C2
socleC22×C149C22×D4
prime radical#23750189C2
hypercenter#452D149
hypocenterC149#3222
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. #23750235C2semidirect
3. #23750018C2semidirect
4. #23749996C2semidirect
5. #23749988C2semidirect
6. #23749981C2semidirect
7. #23749850C2semidirect
8. #23749849C2semidirect
9. #23749824C2semidirect
10. #23749823C2semidirect
11. #23749787C2semidirect
12. #23749778C2semidirect
13. #23749775C2semidirect
14. #23749683C2semidirect
15. #452×C149C2semidirect
17. C2×#14558726C22semidirect
20. C2×#14558724C22semidirect
23. #18011909C22semidirect
29. #18011902C22semidirect
38. Q8×Dic149C22semidirect
39. #18011876C22semidirect
41. #18011840C22semidirect
42. #18011840C22semidirect
43. #18011835C22semidirect
46. #18011832C22semidirect
50. #18011821C22semidirect
51. C8×Dic149C22semidirect
53. C2×Q16×C149C22semidirect
54. C2×SD16×C149C22semidirect
56. #103×C149C22semidirect
57. #102×C149C22semidirect
190. C149#3222semidirect
203. #452D149semidirect
210. C2×Q16C2×D149semidirect
216. C2×SD16C2×D149semidirect
239. #103C2×D149semidirect
245. #102C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237502352
#237501892
#237500182
#237499962
#237499882
#237499812
#237498502
#237498492
#237498242
#237498232
#237497872
#237497782
#237497752
#237496832
#452×C1492
#3222149