Finite Group Databasebeta

← #34055692

Subgroups — #34055692

Order 19072.

400 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750179C211yesmaximal, characteristic, complemented
2#124×D149C211yesmaximal, characteristic
3#23750018C211yesmaximal, characteristic, complemented
4#23750016C211yesmaximal, characteristic, complemented
5#23749986C211yesmaximal, characteristic, complemented
6#23749983C211yesmaximal, characteristic, complemented
7#23749848C211yesmaximal, characteristic, complemented
8#23749847C211yesmaximal, characteristic, complemented
9#23749844C211yesmaximal, characteristic, complemented
10#23749782C211yesmaximal, characteristic, complemented
11#23749779C211yesmaximal, characteristic, complemented
12#23749777C211yesmaximal, characteristic
13#23749774C211yesmaximal, characteristic
14#23749681C211yesmaximal, characteristic, complemented
15#464×C149C211yesmaximal, characteristic, complemented
16C2×Q8×D149C2211yescharacteristic
17C2×D4×D149C2211yescharacteristic
18C2×Dic596C2211yescharacteristic, complemented
19C2×#14558726C2211yescharacteristic, complemented
20C2×#14558726C2211yescharacteristic, complemented
21C2×#14558725C2211yescharacteristic
22C2×#14558724C2211yescharacteristic
23C2×#14558723C2211yescharacteristic
24#18011910C2211yescharacteristic, complemented
25#18011909C2211yescharacteristic, complemented
26#18011901—21no—
27#18011900C2211yescharacteristic
28#18011899C2211yescharacteristic
29#18011898C2211yescharacteristic
30#18011897—21no—
31#18011897—21no—
32#18011891C2211yescharacteristic
33#18011889—21no—
34#18011887C2211yescharacteristic
35C4×Dic298—21no—
36C4×Dic298C2211yescharacteristic, complemented
37#18011868—21no—
38C22⋊C4×D149—21no—
39C22⋊C4×D149—21no—
40C42×D149C2211yescharacteristic
41C4⋊#11924746C2211yescharacteristic, complemented
42#18011836C2211yescharacteristic, complemented
43#18011835C2211yescharacteristic, complemented
44#18011834C2211yescharacteristic, complemented
45#18011833C2211yescharacteristic
46#18011832C2211yescharacteristic
47#18011831C2211yescharacteristic
48#18011823C2211yescharacteristic
49#18011823C2211yescharacteristic
50#18011821C2211yescharacteristic, complemented
51#18011821C2211yescharacteristic, complemented
52C2×Q16×C149C2211yescharacteristic, complemented
53C2×SD16×C149C2211yescharacteristic
54#124×C149C2211yescharacteristic
55C4×Q8×C149C2211yescharacteristic, complemented
56C4⋊C8×C149C2211yescharacteristic, complemented
57#103×C149C2211yescharacteristic, complemented
58#102×C149C2211yescharacteristic
59C23×D149—21no—
60C2×Dic298—21no—
61C2×Dic298—21no—
62C2×Dic298C2311yescharacteristic
63C2×Dic298C2311yescharacteristic
64Q8×D149—41no—
65Q8×D149—41no—
66C2×D596C2311yescharacteristic
67C2×C22⋊D149—21no—
68D4×D149—41no—
69D4×D149—41no—
70C2×C4×D149—21no—
71C2×C4×D149D411yescharacteristic
72C2×C4×D149D411yescharacteristic
73C2×C4×D149C2311yescharacteristic
74Dic596—41no—
75#14558726—41no—
76#14558726—41no—
77#14558725—41no—
78#14558724—41no—
79#14558723—41no—
80C2×#11924746C2311yescharacteristic
81C2×#11924746C2311yescharacteristic
82C4⋊Dic149—21no—
83C4⋊Dic149C2311yescharacteristic
84#14558715—21no—
85#14558715—21no—
86#14558715—21no—
87#14558715—21no—
88#14558715—21no—
89C22⋊Dic149—21no—
90C22⋊Dic149—21no—
91#14558713—21no—
92#14558713—21no—
93#14558713—21no—
94#14558713—21no—
95#14558713—21no—
96#14558713—21no—
97C4×Dic149—21no—
98C4×Dic149D411yescharacteristic
99C4×Dic149D411yescharacteristic
100C4×Dic149C2311yescharacteristic
101C2×Q8×C149C2311yescharacteristic
102C2×Q8×C149C2311yescharacteristic
103C2×D4×C149C2311yescharacteristic
104Q16×C149—41no—
105SD16×C149—41no—
106C2×C8×C149C2311yescharacteristic
107C2×C8×C149C2311yescharacteristic
108C4⋊C4×C149—21no—
109C4⋊C4×C149C2311yescharacteristic
110C22⋊C4×C149—21no—
111C22⋊C4×C149—21no—
112C42×C149—21no—
113C42×C149C2311yescharacteristic
114C22×D149—21no—
115C22×D149—42no—
116C22×D149—42no—
117C22×D149—42no—
118C22×D149C2×D411yescharacteristic
119Dic298—21no—
120Dic298—21no—
121Dic298—21no—
122Dic298—21no—
123Dic298—42no—
124Dic298—42no—
125D596—21no—
126D596—21no—
127C22⋊D149—42no—
128C2×Dic149—21no—
129C2×Dic149—21no—
130C2×Dic149—21no—
131C2×Dic149C2×D411yescharacteristic
132C2×Dic149C2×D411yescharacteristic
133C2×Dic149C2×D411yescharacteristic
134C4×D149—22no—
135C4×D149—21no—
136C4×D149—21no—
137C4×D149—41no—
138C4×D149—42no—
139#11924746—21no—
140#11924746—21no—
141C23×C149—21no—
142Q8×C149—21no—
143Q8×C149—21no—
144Q8×C149—21no—
145Q8×C149—21no—
146D4×C149—21no—
147D4×C149—21no—
148C2×C4×C149—21no—
149C2×C4×C149—21no—
150C2×C4×C149—21no—
151C2×C4×C149C2×D411yescharacteristic
152C2×C4×C149C2×D411yescharacteristic
153C2×C4×C149C2411yescharacteristic
154C8×C149—21no—
155C8×C149—21no—
156C22×C149—41no—
157C22×C149—41no—
158C22×C149—41no—
159C22×C149C22×D411yescharacteristic
160C2×D149—21no—
161C2×D149—21no—
162C2×D149—41no—
163C2×D149—41no—
164C2×D149—41no—
165C2×D149—84no—
166C2×D149#13712yes—
167C4×C149—21no—
168C4×C149—21no—
169C4×C149—41no—
170C4×C149—41no—
171C4×C149—41no—
172C4×C149H(5,𝔽2)11yescharacteristic
173C4×C149H(5,𝔽2)11yescharacteristic
174Dic149—21no—
175Dic149—21no—
176Dic149—21no—
177Dic149—41no—
178Dic149—41no—
179Dic149—41no—
180C2×C149—81no—
181C2×C149#53511yescharacteristic
182C2×C149C2×#13711yescharacteristic
183C2×C149#57511yescharacteristic
184D149—22no—
185D149—81no—
186C149#321511yescharacteristic, complemented, Sylow
187#3215—1491nomaximal, Sylow
188#533—1491no—
189C2×#124—1491no—
190#497—1491no—
191#497—1491no—
192#489—1491no—
193#489—1491no—
194#464—1491no—
195#464—1491no—
196#464—1491no—
197#464D14911yescharacteristic, complemented
198#451—1491no—
199#451—1491no—
200#450—1491no—
201#450—1491no—
202#432—1491no—
203C22×Q8—1491no—
204C22×D4—1491no—
205C2×Q16—1491no—
206C2×Q16—1491no—
207C2×Q16—1491no—
208C2×Q16C2×D14911yescharacteristic, complemented
209C2×SD16—1491no—
210C2×SD16—1491no—
211C2×SD16—1491no—
212C2×SD16C2×D14911yescharacteristic
213C4⋊Q8—1491no—
214C4⋊Q8—1491no—
215#125—2981no—
216#124—2981no—
217#124—2981no—
218#124—1491no—
219#124—1491no—
220#124—1491no—
221#124C2×D14911yescharacteristic
222C22⋊Q8—2981no—
223C22⋊Q8—1491no—
224C22⋊Q8—1491no—
225C4×Q8—2981no—
226C4×Q8—1491no—
227C4×Q8C2×D14911yescharacteristic, complemented
228#117—2981no—
229C2×C22⋊C4—2981no—
230C2×C22⋊C4—2981no—
231C2×C42—1491no—
232C4⋊C8—1491no—
233C4⋊C8C2×D14911yescharacteristic, complemented
234#103—1491no—
235#103—1491no—
236#103—1491no—
237#103C2×D14911yescharacteristic, complemented
238#102—1491no—
239#102—1491no—
240#102—1491no—
241#102C2×D14911yescharacteristic
242C22⋊C8—1491no—
243C22⋊C8—1491no—
244#97—1491no—
245#97—1491no—
246C24—2981no—
247C2×Q8—2981no—
248C2×Q8—2981no—
249C2×Q8—5961no—
250C2×Q8—5961no—
251C2×Q8—1491no—
252C2×Q8—1491no—
253C2×Q8C22×D14911yescharacteristic
254C2×Q8C22×D14911yescharacteristic
255C2×D4—2981no—
256C2×D4—5961no—
257C2×D4—5961no—
258C2×D4—1491no—
259C2×D4C22×D14911yescharacteristic
260C22×C4—2981no—
261C22×C4—1491no—
262C22×C4—1491no—
263C22×C4—1491no—
264Q16—41no—
265Q16—5961no—
266Q16—5961no—
267Q16—5961no—
268SD16—41no—
269SD16—5961no—
270SD16—5961no—
271SD16—5961no—
272C2×C8—1491no—
273C2×C8—1491no—
274C2×C8C22×D14911yescharacteristic
275C2×C8C22×D14911yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—2981no—
278C4⋊C4—2981no—
279C4⋊C4—2981no—
280C4⋊C4—2981no—
281C4⋊C4—2981no—
282C4⋊C4—2981no—
283C4⋊C4—1491no—
284C4⋊C4C22×D14911yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—2981no—
288C22⋊C4—2981no—
289C22⋊C4—2981no—
290C22⋊C4—2981no—
291C22⋊C4—2981no—
292C22⋊C4—2981no—
293C22⋊C4—2981no—
294C22⋊C4—2981no—
295C42—21no—
296C42—2981no—
297C42—1491no—
298C42—1491no—
299C42—1491no—
300C42C22×D14911yescharacteristic
301C23—21no—
302C23—2981no—
303C23—5962no—
304C23—5962no—
305C23—5962no—
306C23—1491no—
307Q8—21no—
308Q8—21no—
309Q8—21no—
310Q8—21no—
311Q8—2981no—
312Q8—2981no—
313Q8—2981no—
314Q8—2981no—
315Q8—5962no—
316Q8—5962no—
317D4—21no—
318D4—21no—
319D4—2981no—
320D4—2981no—
321D4—5962no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—2982no—
326C2×C4—2981no—
327C2×C4—2981no—
328C2×C4—2981no—
329C2×C4—2981no—
330C2×C4—2981no—
331C2×C4—5961no—
332C2×C4—5962no—
333C2×C4—1491no—
334C2×C4—1491no—
335C2×C4—1491no—
336C2×C4D4×D14911yescharacteristic
337C2×C4D4×D14911yescharacteristic
338C2×C4C23×D14911yescharacteristic
339C8—21no—
340C8—21no—
341C8—2981no—
342C8—2981no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—2981no—
347C22—2981no—
348C22—5961no—
349C22—5961no—
350C22—5961no—
351C22—1492no—
352C22—11924no—
353C22C2×D4×D14911yescharacteristic
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—2981no—
360C4—2981no—
361C4—2981no—
362C4—5961no—
363C4—5961no—
364C4—5961no—
365C4#1801195611yescharacteristic
366C4#1801195711yescharacteristic
367C2—81no—
368C2—2982no—
369C2—11921no—
370C2#2375019111yescharacteristic
371C2#137×D14911yescharacteristic
372C2#2375042211yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#464×C149C2
socleC22×C149C22×D4
prime radicalC2×D4×D149C22
hypercenter#464D149
hypocenterC149#3215
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. #23750179C2semidirect
3. #23750018C2semidirect
4. #23750016C2semidirect
5. #23749986C2semidirect
6. #23749983C2semidirect
7. #23749848C2semidirect
8. #23749847C2semidirect
9. #23749844C2semidirect
10. #23749782C2semidirect
11. #23749779C2semidirect
14. #23749681C2semidirect
15. #464×C149C2semidirect
18. C2×Dic596C22semidirect
19. C2×#14558726C22semidirect
20. C2×#14558726C22semidirect
24. #18011910C22semidirect
25. #18011909C22semidirect
36. C4×Dic298C22semidirect
41. C4⋊#11924746C22semidirect
42. #18011836C22semidirect
43. #18011835C22semidirect
44. #18011834C22semidirect
50. #18011821C22semidirect
51. #18011821C22semidirect
52. C2×Q16×C149C22semidirect
55. C4×Q8×C149C22semidirect
56. C4⋊C8×C149C22semidirect
57. #103×C149C22semidirect
186. C149#3215semidirect
197. #464D149semidirect
208. C2×Q16C2×D149semidirect
227. C4×Q8C2×D149semidirect
233. C4⋊C8C2×D149semidirect
237. #103C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237501792
#124×D1492
#237500182
#237500162
#237499862
#237499832
#237498482
#237498472
#237498442
#237497822
#237497792
#237497772
#237497742
#237496812
#464×C1492
#3215149