Finite Group Databasebeta

← #34055554

Subgroups — #34055554

Order 19072.

442 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750192C211yesmaximal, characteristic, complemented
2#23750191C211yesmaximal, characteristic, complemented
3#23749950C211yesmaximal, characteristic, complemented
4#23749948C211yesmaximal, characteristic, complemented
5#23749947C211yesmaximal, characteristic, complemented
6#23749946C211yesmaximal, characteristic, complemented
7#23749877C211yesmaximal, characteristic, complemented
8#23749875C211yesmaximal, characteristic, complemented
9#23749860C211yesmaximal, characteristic, complemented
10#23749858C211yesmaximal, characteristic, complemented
11#23749759C211yesmaximal, characteristic, complemented
12#23749757C211yesmaximal, characteristic, complemented
13#23749757C211yesmaximal, characteristic, complemented
14#23749590C211yesmaximal, characteristic, complemented
15#447×C149C211yesmaximal, characteristic, complemented
16C2×#14558736C2211yescharacteristic
17C2×D4×D149C2211yescharacteristic, complemented
18C2×#14558721C2211yescharacteristic
19C2×#14558721C2211yescharacteristic
20C2×#14558719C2211yescharacteristic, complemented
21C2×C8×D149C2211yescharacteristic, complemented
22#18011907—21no—
23#18011907—21no—
24#18011898—21no—
25#18011897—21no—
26#18011886C2211yescharacteristic, complemented
27#18011885C2211yescharacteristic
28#18011882C2211yescharacteristic
29#18011882C2211yescharacteristic
30#18011882C2211yescharacteristic, complemented
31#18011882C2211yescharacteristic, complemented
32#18011882C2211yescharacteristic, complemented
33#18011881—21no—
34#18011880—21no—
35#18011880—21no—
36#18011879—21no—
37#18011870C2211yescharacteristic, complemented
38#18011869C2211yescharacteristic, complemented
39#18011845C2211yescharacteristic, complemented
40#18011844C2211yescharacteristic, complemented
41#18011843C2211yescharacteristic, complemented
42#18011842C2211yescharacteristic, complemented
43#18011833C2211yescharacteristic, complemented
44#18011833C2211yescharacteristic, complemented
45#18011832C2211yescharacteristic, complemented
46#18011832C2211yescharacteristic, complemented
47#18011832C2211yescharacteristic, complemented
48#18011832C2211yescharacteristic, complemented
49C22⋊#11924746C2211yescharacteristic, complemented
50#18011823C2211yescharacteristic, complemented
51#18011823C2211yescharacteristic, complemented
52C22×D4×C149C2211yescharacteristic, complemented
53C2×D8×C149C2211yescharacteristic
54C2×D8×C149C2211yescharacteristic
55#121×C149C2211yescharacteristic
56#102×C149C2211yescharacteristic, complemented
57#102×C149C2211yescharacteristic, complemented
58C22⋊C8×C149C2211yescharacteristic, complemented
59C23×D149—21no—
60#14558736—41no—
61#14558736—41no—
62C2×Dic298D411yescharacteristic
63C2×D596—21no—
64C2×D596D411yescharacteristic
65C2×D596C2311yescharacteristic
66C2×C22⋊D149—21no—
67C2×C22⋊D149—21no—
68C2×C22⋊D149—21no—
69C2×C22⋊D149—21no—
70C2×C22⋊D149—21no—
71C2×C22⋊D149—21no—
72C2×C22⋊D149—21no—
73C2×C22⋊D149D411yescharacteristic
74C2×C22⋊D149D411yescharacteristic
75D4×D149—41no—
76D4×D149—41no—
77C2×C4×D149C2311yescharacteristic
78C2×C4×D149C2311yescharacteristic
79#14558721—41no—
80#14558721—41no—
81#14558719—41no—
82C2×#11924746C2311yescharacteristic
83C2×#11924746C2311yescharacteristic
84C8×D149—41no—
85C4⋊Dic149C2311yescharacteristic
86C4⋊Dic149C2311yescharacteristic
87C4⋊Dic149C2311yescharacteristic
88C22⋊Dic149—21no—
89C22⋊Dic149—21no—
90C22⋊Dic149—21no—
91C22⋊Dic149—21no—
92C22⋊Dic149—21no—
93C22⋊Dic149—21no—
94#14558713—21no—
95#14558713—21no—
96#14558713—21no—
97C4×Dic149—21no—
98C4×Dic149—21no—
99C24×C149—21no—
100C2×D4×C149—21no—
101C2×D4×C149—21no—
102C2×D4×C149—41no—
103C2×D4×C149—41no—
104C2×D4×C149C2311yescharacteristic
105C2×D4×C149C2311yescharacteristic
106C2×D4×C149C2311yescharacteristic
107C22×C4×C149C2311yescharacteristic
108D8×C149—41no—
109D8×C149—41no—
110C2×C8×C149C2311yescharacteristic
111C2×C8×C149C2311yescharacteristic
112C4⋊C4×C149C2311yescharacteristic
113C22⋊C4×C149—21no—
114C22×D149—21no—
115C22×D149—42no—
116C22×D149—81no—
117C22×D149—81no—
118C22×D149C2×D411yescharacteristic
119C22×D149C2×D411yescharacteristic
120Dic298—41no—
121D596—21no—
122D596—21no—
123D596—41no—
124D596—81no—
125C22⋊D149—41no—
126C22⋊D149—41no—
127C22⋊D149—42no—
128C22⋊D149—81no—
129C22⋊D149—81no—
130C22⋊D149—81no—
131C22⋊D149—81no—
132C22⋊D149—81no—
133C22⋊D149—81no—
134C2×Dic149—21no—
135C2×Dic149—21no—
136C2×Dic149—21no—
137C2×Dic149C2×D411yescharacteristic
138C2×Dic149C2×D411yescharacteristic
139C4×D149—21no—
140C4×D149—21no—
141C4×D149—21no—
142C4×D149—21no—
143#11924746—21no—
144#11924746—21no—
145C23×C149—21no—
146C23×C149—21no—
147C23×C149—21no—
148C23×C149—42no—
149C23×C149—81no—
150C23×C149—81no—
151C23×C149C2×D411yescharacteristic
152D4×C149—21no—
153D4×C149—21no—
154D4×C149—21no—
155D4×C149—21no—
156D4×C149—21no—
157D4×C149—21no—
158D4×C149—42no—
159D4×C149—81no—
160C2×C4×C149—21no—
161C2×C4×C149—21no—
162C2×C4×C149—21no—
163C2×C4×C149C2×D411yescharacteristic
164C2×C4×C149C2411yescharacteristic
165C8×C149—21no—
166C8×C149—21no—
167C22×C149—21no—
168C22×C149—21no—
169C22×C149—21no—
170C22×C149—41no—
171C22×C149—41no—
172C22×C149—41no—
173C22×C149—41no—
174C22×C149—41no—
175C22×C149—41no—
176C22×C149—41no—
177C22×C149—41no—
178C22×C149—41no—
179C22×C149—84no—
180C22×C149C22×D411yescharacteristic
181C2×D149—21no—
182C2×D149—21no—
183C2×D149—21no—
184C2×D149—21no—
185C2×D149—21no—
186C2×D149—21no—
187C2×D149—41no—
188C2×D149—41no—
189C2×D149—41no—
190C2×D149—84no—
191C4×C149—21no—
192C4×C149—41no—
193C4×C149H(5,𝔽2)11yescharacteristic
194C4×C149H(5,𝔽2)11yescharacteristic
195Dic149—21no—
196Dic149—21no—
197Dic149—41no—
198Dic149—41no—
199Dic149—41no—
200C2×C149—41no—
201C2×C149—81no—
202C2×C149—81no—
203C2×C149—81no—
204C2×C149#53411yescharacteristic
205C2×C149#57611yescharacteristic
206C2×C149#57611yescharacteristic
207D149—41no—
208D149—41no—
209D149—81no—
210C149#319911yescharacteristic, complemented, Sylow
211#3199—1491nomaximal, Sylow
212#535—1491no—
213#535—1491no—
214#482—1491no—
215#482—1491no—
216#482—1491no—
217#482—1491no—
218#469—1491no—
219#469—1491no—
220#466—1491no—
221#466—1491no—
222#447—1491no—
223#447—1491no—
224#447—1491no—
225#447D14911yescharacteristic, complemented
226#408—1491no—
227C2×#41—1491no—
228C22×D4—1491no—
229C22×D4C2×D14911yescharacteristic, complemented
230C2×D8—1491no—
231C2×D8—1491no—
232C2×D8C2×D14911yescharacteristic
233C2×D8C2×D14911yescharacteristic
234C2×M16—1491no—
235C22×C8—1491no—
236#127—2981no—
237#127—2981no—
238#124—2981no—
239#124—2981no—
240#121—1491no—
241#121—1491no—
242#121—1491no—
243#121—1491no—
244#121—1491no—
245#121—1491no—
246#121—1491no—
247#121C2×D14911yescharacteristic
248#120—2981no—
249#120—2981no—
250#120—2981no—
251#120—2981no—
252#117—1491no—
253#117—1491no—
254#107—1491no—
255#107—1491no—
256#106—1491no—
257#106—1491no—
258#102—1491no—
259#102—1491no—
260#102—1491no—
261#102—1491no—
262#102—1491no—
263#102—1491no—
264#102C2×D14911yescharacteristic, complemented
265#102C2×D14911yescharacteristic, complemented
266C22⋊C8—1491no—
267C22⋊C8—1491no—
268C22⋊C8—1491no—
269C22⋊C8C2×D14911yescharacteristic, complemented
270C24—21no—
271C24—2981no—
272#41—5961no—
273#41—5961no—
274C2×Q8—1491no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4—41no—
278C2×D4—41no—
279C2×D4—2981no—
280C2×D4—2981no—
281C2×D4—2981no—
282C2×D4—2981no—
283C2×D4—2981no—
284C2×D4—2981no—
285C2×D4—2981no—
286C2×D4—2981no—
287C2×D4—5961no—
288C2×D4—5961no—
289C2×D4—1491no—
290C2×D4—1491no—
291C2×D4—1491no—
292C2×D4—1491no—
293C2×D4C22×D14911yescharacteristic
294C2×D4C22×D14911yescharacteristic
295C2×D4C22×D14911yescharacteristic
296C22×C4—1491no—
297C22×C4—1491no—
298C22×C4C22×D14911yescharacteristic
299D8—41no—
300D8—41no—
301D8—5961no—
302D8—5961no—
303M16—5961no—
304C2×C8—5961no—
305C2×C8—1491no—
306C2×C8—1491no—
307C2×C8C22×D14911yescharacteristic
308C2×C8C22×D14911yescharacteristic
309C4⋊C4—1491no—
310C4⋊C4—1491no—
311C4⋊C4—1491no—
312C4⋊C4C22×D14911yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—2981no—
315C22⋊C4—2981no—
316C22⋊C4—2981no—
317C22⋊C4—2981no—
318C22⋊C4—2981no—
319C22⋊C4—2981no—
320C22⋊C4—2981no—
321C22⋊C4—2981no—
322C22⋊C4—2981no—
323C42—2981no—
324C42—2981no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—42no—
329C23—81no—
330C23—81no—
331C23—2981no—
332C23—5962no—
333C23—1491no—
334C23—1491no—
335C23—11921no—
336C23—11921no—
337C23D4×D14911yescharacteristic
338Q8—5961no—
339D4—21no—
340D4—21no—
341D4—21no—
342D4—21no—
343D4—21no—
344D4—21no—
345D4—42no—
346D4—81no—
347D4—2981no—
348D4—2981no—
349D4—5961no—
350D4—5961no—
351D4—5961no—
352D4—5962no—
353D4—11921no—
354D4—11921no—
355D4—11921no—
356D4—11921no—
357D4—11921no—
358D4—11921no—
359D4—11921no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—2981no—
364C2×C4—2981no—
365C2×C4—2981no—
366C2×C4—2981no—
367C2×C4—2981no—
368C2×C4—2981no—
369C2×C4—2981no—
370C2×C4—1491no—
371C2×C4—1491no—
372C2×C4D4×D14911yescharacteristic
373C2×C4C23×D14911yescharacteristic
374C8—21no—
375C8—21no—
376C8—2981no—
377C8—2981no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—84no—
391C22—2981no—
392C22—2981no—
393C22—2981no—
394C22—2981no—
395C22—2981no—
396C22—2981no—
397C22—5961no—
398C22—5961no—
399C22—5961no—
400C22—11924no—
401C22C2×D4×D14911yescharacteristic
402C4—21no—
403C4—41no—
404C4—2981no—
405C4—2981no—
406C4—5961no—
407C4—5961no—
408C4—5961no—
409C4#1801195611yescharacteristic
410C4#1801195611yescharacteristic
411C2—41no—
412C2—81no—
413C2—81no—
414C2—81no—
415C2—5961no—
416C2—5961no—
417C2—11921no—
418C2#2375018511yescharacteristic
419C2#2375042611yescharacteristic
420C2#2375042911yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#447×C149C2
socleC22×C149C22×D4
hypercenter#447D149
hypocenterC149#3199
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #23750192C2semidirect
2. #23750191C2semidirect
3. #23749950C2semidirect
4. #23749948C2semidirect
5. #23749947C2semidirect
6. #23749946C2semidirect
7. #23749877C2semidirect
8. #23749875C2semidirect
9. #23749860C2semidirect
10. #23749858C2semidirect
11. #23749759C2semidirect
12. #23749757C2semidirect
13. #23749757C2semidirect
14. #23749590C2semidirect
15. #447×C149C2semidirect
17. C2×D4×D149C22semidirect
20. C2×#14558719C22semidirect
21. C2×C8×D149C22semidirect
26. #18011886C22semidirect
30. #18011882C22semidirect
31. #18011882C22semidirect
32. #18011882C22semidirect
37. #18011870C22semidirect
38. #18011869C22semidirect
39. #18011845C22semidirect
40. #18011844C22semidirect
41. #18011843C22semidirect
42. #18011842C22semidirect
43. #18011833C22semidirect
44. #18011833C22semidirect
45. #18011832C22semidirect
46. #18011832C22semidirect
47. #18011832C22semidirect
48. #18011832C22semidirect
49. C22⋊#11924746C22semidirect
50. #18011823C22semidirect
51. #18011823C22semidirect
52. C22×D4×C149C22semidirect
56. #102×C149C22semidirect
57. #102×C149C22semidirect
58. C22⋊C8×C149C22semidirect
210. C149#3199semidirect
225. #447D149semidirect
229. C22×D4C2×D149semidirect
264. #102C2×D149semidirect
265. #102C2×D149semidirect
269. C22⋊C8C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237501922
#237501912
#237499502
#237499482
#237499472
#237499462
#237498772
#237498752
#237498602
#237498582
#237497592
#237497572
#237495902
#447×C1492
#3199149