Finite Group Databasebeta

← #34055651

Subgroups — #34055651

Order 19072.

410 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#23750154C211yesmaximal, characteristic, complemented
2#124×D149C211yesmaximal, characteristic, complemented
3#23750007C211yesmaximal, characteristic, complemented
4#23749980C211yesmaximal, characteristic, complemented
5#23749979C211yesmaximal, characteristic, complemented
6#23749849C211yesmaximal, characteristic, complemented
7#23749845C211yesmaximal, characteristic, complemented
8#23749842C211yesmaximal, characteristic, complemented
9#23749838C211yesmaximal, characteristic, complemented
10#23749779C211yesmaximal, characteristic, complemented
11#23749774C211yesmaximal, characteristic, complemented
12#23749762C211yesmaximal, characteristic, complemented
13#23749757C211yesmaximal, characteristic
14#23749676C211yesmaximal, characteristic, complemented
15#495×C149C211yesmaximal, characteristic, complemented
16C2×Q8×D149C2211yescharacteristic
17C2×D4×D149C2211yescharacteristic
18C2×#14558726C2211yescharacteristic, complemented
19C2×#14558724C2211yescharacteristic, complemented
20C2×#14558723C2211yescharacteristic
21C2×#14558721C2211yescharacteristic
22#18011904—21no—
23#18011903C2211yescharacteristic, complemented
24#18011900C2211yescharacteristic
25#18011899C2211yescharacteristic
26#18011898C2211yescharacteristic
27#18011897—21no—
28#18011897—21no—
29#18011893—21no—
30#18011887C2211yescharacteristic
31#18011882C2211yescharacteristic
32Q8×Dic149C2211yescharacteristic, complemented
33D4×Dic149C2211yescharacteristic, complemented
34#18011871—21no—
35#18011867—21no—
36C22⋊C4×D149—21no—
37C22⋊C4×D149—21no—
38C42×D149C2211yescharacteristic
39#18011840C2211yescharacteristic, complemented
40#18011840C2211yescharacteristic, complemented
41#18011836C2211yescharacteristic, complemented
42#18011836C2211yescharacteristic, complemented
43#18011835C2211yescharacteristic, complemented
44#18011835C2211yescharacteristic, complemented
45#18011833C2211yescharacteristic
46#18011833C2211yescharacteristic
47#18011832C2211yescharacteristic
48#18011832C2211yescharacteristic
49#18011823C2211yescharacteristic
50#18011823C2211yescharacteristic
51C4×#11924746C2211yescharacteristic, complemented
52C2×Q16×C149C2211yescharacteristic, complemented
53C2×SD16×C149C2211yescharacteristic
54C2×SD16×C149C2211yescharacteristic, complemented
55C2×D8×C149C2211yescharacteristic
56#124×C149C2211yescharacteristic
57#124×C149C2211yescharacteristic, complemented
58C4×C8×C149C2211yescharacteristic, complemented
59C23×D149—21no—
60C2×Dic298—21no—
61C2×Dic298C2311yescharacteristic
62Q8×D149—41no—
63Q8×D149—41no—
64C2×D596C2311yescharacteristic
65C2×C22⋊D149—21no—
66C2×C22⋊D149—21no—
67D4×D149—41no—
68D4×D149—41no—
69C22×Dic149—21no—
70C2×C4×D149—21no—
71C2×C4×D149D411yescharacteristic
72C2×C4×D149D411yescharacteristic
73C2×C4×D149C2311yescharacteristic
74#14558726—41no—
75#14558724—41no—
76#14558723—41no—
77#14558721—41no—
78C2×#11924746C2311yescharacteristic
79C2×#11924746C2311yescharacteristic
80C4⋊Dic149—21no—
81C4⋊Dic149C2311yescharacteristic
82C4⋊Dic149C2311yescharacteristic
83#14558715—21no—
84#14558715—21no—
85#14558715—21no—
86C22⋊Dic149—21no—
87C22⋊Dic149—21no—
88C22⋊Dic149—21no—
89C22⋊Dic149—21no—
90#14558713—21no—
91#14558713—21no—
92#14558713—21no—
93#14558713—21no—
94#14558713—21no—
95C4×Dic149—21no—
96C4×Dic149D411yescharacteristic
97C4×Dic149D411yescharacteristic
98C4×Dic149C2311yescharacteristic
99C2×Q8×C149C2311yescharacteristic
100C2×Q8×C149C2311yescharacteristic
101C2×D4×C149C2311yescharacteristic
102C2×D4×C149C2311yescharacteristic
103Q16×C149—41no—
104SD16×C149—41no—
105SD16×C149—41no—
106D8×C149—41no—
107C2×C8×C149C2311yescharacteristic
108C2×C8×C149C2311yescharacteristic
109C22⋊C4×C149—21no—
110C22⋊C4×C149—21no—
111C22⋊C4×C149—21no—
112C22⋊C4×C149—21no—
113C42×C149C2311yescharacteristic
114C22×D149—21no—
115C22×D149—42no—
116C22×D149—42no—
117C22×D149—42no—
118C22×D149C2×D411yescharacteristic
119Dic298—21no—
120Dic298—21no—
121Dic298—42no—
122D596—21no—
123D596—21no—
124C22⋊D149—42no—
125C22⋊D149—42no—
126C2×Dic149—21no—
127C2×Dic149—21no—
128C2×Dic149—21no—
129C2×Dic149—42no—
130C2×Dic149C2×D411yescharacteristic
131C2×Dic149C2×D411yescharacteristic
132C2×Dic149C2×D411yescharacteristic
133C4×D149—22no—
134C4×D149—21no—
135C4×D149—21no—
136C4×D149—41no—
137C4×D149—42no—
138#11924746—21no—
139#11924746—21no—
140C23×C149—21no—
141C23×C149—21no—
142Q8×C149—21no—
143Q8×C149—21no—
144Q8×C149—21no—
145Q8×C149—21no—
146D4×C149—21no—
147D4×C149—21no—
148D4×C149—21no—
149D4×C149—21no—
150C2×C4×C149—21no—
151C2×C4×C149—21no—
152C2×C4×C149C2×D411yescharacteristic
153C2×C4×C149C2×D411yescharacteristic
154C2×C4×C149C2411yescharacteristic
155C8×C149—21no—
156C8×C149—21no—
157C22×C149—41no—
158C22×C149—41no—
159C22×C149—41no—
160C22×C149—41no—
161C22×C149—41no—
162C22×C149—41no—
163C22×C149C22×D411yescharacteristic
164C2×D149—21no—
165C2×D149—21no—
166C2×D149—41no—
167C2×D149—41no—
168C2×D149—41no—
169C2×D149—84no—
170C2×D149#13512yes—
171C4×C149—21no—
172C4×C149—21no—
173C4×C149—41no—
174C4×C149—41no—
175C4×C149H(5,𝔽2)11yescharacteristic
176C4×C149H(5,𝔽2)11yescharacteristic
177Dic149—21no—
178Dic149—21no—
179Dic149—21no—
180Dic149—41no—
181Dic149—41no—
182Dic149—41no—
183C2×C149—81no—
184C2×C149—81no—
185C2×C149#53511yescharacteristic
186C2×C149C2×#13511yescharacteristic
187C2×C149#57511yescharacteristic
188D149—22no—
189D149—81no—
190C149#321111yescharacteristic, complemented, Sylow
191#3211—1491nomaximal, Sylow
192#529—1491no—
193C2×#124—1491no—
194#495—1491no—
195#495D14911yescharacteristic, complemented
196#488—1491no—
197#488—1491no—
198#464—1491no—
199#464—1491no—
200#463—1491no—
201#463—1491no—
202#451—1491no—
203#450—1491no—
204#448—1491no—
205#447—1491no—
206#431—1491no—
207C22×Q8—1491no—
208C22×D4—1491no—
209C2×Q16—1491no—
210C2×Q16C2×D14911yescharacteristic, complemented
211C2×SD16—1491no—
212C2×SD16—1491no—
213C2×SD16C2×D14911yescharacteristic
214C2×SD16C2×D14911yescharacteristic, complemented
215C2×D8—1491no—
216C2×D8C2×D14911yescharacteristic
217#126—2981no—
218#125—1491no—
219#124—2981no—
220#124—2981no—
221#124—1491no—
222#124—1491no—
223#124—1491no—
224#124C2×D14911yescharacteristic
225#124C2×D14911yescharacteristic, complemented
226#123—2981no—
227C22⋊Q8—1491no—
228#121—1491no—
229C4×Q8—1491no—
230C4×D4—2981no—
231C4×D4—1491no—
232#117—2981no—
233C2×C22⋊C4—2981no—
234C2×C22⋊C4—2981no—
235C2×C42—1491no—
236C4⋊C8—1491no—
237C4⋊C8—1491no—
238#103—1491no—
239#103—1491no—
240#103—1491no—
241#103—1491no—
242#102—1491no—
243#102—1491no—
244#102—1491no—
245#102—1491no—
246C22⋊C8—1491no—
247C22⋊C8—1491no—
248C4×C8—1491no—
249C4×C8C2×D14911yescharacteristic, complemented
250C24—2981no—
251C2×Q8—2981no—
252C2×Q8—5961no—
253C2×Q8—5961no—
254C2×Q8—1491no—
255C2×Q8C22×D14911yescharacteristic
256C2×Q8C22×D14911yescharacteristic
257C2×D4—2981no—
258C2×D4—2981no—
259C2×D4—5961no—
260C2×D4—5961no—
261C2×D4—1491no—
262C2×D4C22×D14911yescharacteristic
263C2×D4C22×D14911yescharacteristic
264C22×C4—2981no—
265C22×C4—2981no—
266C22×C4—1491no—
267C22×C4—1491no—
268C22×C4—1491no—
269Q16—41no—
270Q16—5961no—
271SD16—41no—
272SD16—41no—
273SD16—5961no—
274SD16—5961no—
275D8—41no—
276D8—5961no—
277C2×C8—1491no—
278C2×C8—1491no—
279C2×C8C22×D14911yescharacteristic
280C2×C8C22×D14911yescharacteristic
281C4⋊C4—2981no—
282C4⋊C4—2981no—
283C4⋊C4—2981no—
284C4⋊C4—2981no—
285C4⋊C4—1491no—
286C4⋊C4—1491no—
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—21no—
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—
299C22⋊C4—2981no—
300C42—2981no—
301C42—1491no—
302C42—1491no—
303C42—1491no—
304C42C22×D14911yescharacteristic
305C23—21no—
306C23—21no—
307C23—2981no—
308C23—5962no—
309C23—5962no—
310C23—5962no—
311C23—1491no—
312Q8—21no—
313Q8—21no—
314Q8—21no—
315Q8—21no—
316Q8—2981no—
317Q8—2981no—
318Q8—5962no—
319D4—21no—
320D4—21no—
321D4—21no—
322D4—21no—
323D4—2981no—
324D4—2981no—
325D4—5962no—
326D4—5962no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—2982no—
330C2×C4—2981no—
331C2×C4—2981no—
332C2×C4—2981no—
333C2×C4—2981no—
334C2×C4—2981no—
335C2×C4—5961no—
336C2×C4—5962no—
337C2×C4—5962no—
338C2×C4—1491no—
339C2×C4—1491no—
340C2×C4—1491no—
341C2×C4D4×D14911yescharacteristic
342C2×C4D4×D14911yescharacteristic
343C2×C4C23×D14911yescharacteristic
344C8—21no—
345C8—21no—
346C8—2981no—
347C8—2981no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—2981no—
355C22—2981no—
356C22—5961no—
357C22—5961no—
358C22—5961no—
359C22—1492no—
360C22—11924no—
361C22C2×D4×D14911yescharacteristic
362C4—21no—
363C4—21no—
364C4—41no—
365C4—41no—
366C4—2981no—
367C4—2981no—
368C4—2981no—
369C4—5961no—
370C4—5961no—
371C4—5961no—
372C4#1801195611yescharacteristic
373C4#1801195611yescharacteristic
374C2—81no—
375C2—81no—
376C2—2982no—
377C2—11921no—
378C2#2375018811yescharacteristic
379C2#135×D14911yescharacteristic
380C2#2375042211yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#495×C149C2
socleC22×C149C22×D4
prime radical#23749757C2
hypercenter#495D149
hypocenterC149#3211
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. #23750154C2semidirect
2. #124×D149C2semidirect
3. #23750007C2semidirect
4. #23749980C2semidirect
5. #23749979C2semidirect
6. #23749849C2semidirect
7. #23749845C2semidirect
8. #23749842C2semidirect
9. #23749838C2semidirect
10. #23749779C2semidirect
11. #23749774C2semidirect
12. #23749762C2semidirect
14. #23749676C2semidirect
15. #495×C149C2semidirect
18. C2×#14558726C22semidirect
19. C2×#14558724C22semidirect
23. #18011903C22semidirect
32. Q8×Dic149C22semidirect
33. D4×Dic149C22semidirect
39. #18011840C22semidirect
40. #18011840C22semidirect
41. #18011836C22semidirect
42. #18011836C22semidirect
43. #18011835C22semidirect
44. #18011835C22semidirect
51. C4×#11924746C22semidirect
52. C2×Q16×C149C22semidirect
54. C2×SD16×C149C22semidirect
57. #124×C149C22semidirect
58. C4×C8×C149C22semidirect
190. C149#3211semidirect
195. #495D149semidirect
210. C2×Q16C2×D149semidirect
214. C2×SD16C2×D149semidirect
225. #124C2×D149semidirect
249. C4×C8C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237501542
#124×D1492
#237500072
#237499802
#237499792
#237498492
#237498452
#237498422
#237498382
#237497792
#237497742
#237497622
#237497572
#237496762
#495×C1492
#3211149