Finite Group Databasebeta

← #34080916

Subgroups — #34080916

Order 19328.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752862C211yesmaximal, characteristic, complemented
2D4×C22⋊D151C211yesmaximal, characteristic, complemented
3#23752557C211yesmaximal, characteristic, complemented
4#23752526C211yesmaximal, characteristic, complemented
5#23752524C211yesmaximal, characteristic, complemented
6#23752490C211yesmaximal, characteristic, complemented
7#23752446C211yesmaximal, characteristic, complemented
8#23752445C211yesmaximal, characteristic, complemented
9#23752405C211yesmaximal, characteristic, complemented
10#23752344C211yesmaximal, characteristic, complemented
11D8×Dic151C211yesmaximal, characteristic, complemented
12(C22⋊D151)⋊C8C211yesmaximal, characteristic, complemented
13C2×#18012660C211yesmaximal, characteristic, complemented
14#102×D151C211yesmaximal, characteristic, complemented
15#447×C151C211yesmaximal, characteristic, complemented
16C2×#14559003—21no—
17C22×C22⋊D151—21no—
18C2×D4×D151C2211yescharacteristic
19C2×#14558989C2211yescharacteristic, complemented
20C22×C151⋊C8C2211yescharacteristic, complemented
21C2×C8×D151C2211yescharacteristic, complemented
22#18012738C2211yescharacteristic, complemented
23#18012735C2211yescharacteristic
24#18012721—21no—
25#18012720—21no—
26#18012716—21no—
27#18012713C2211yescharacteristic
28#18012711—21no—
29#18012710C2211yescharacteristic
30#18012710C2211yescharacteristic, complemented
31#18012708—21no—
32#18012707—21no—
33D4×Dic151C2211yescharacteristic
34D4×Dic151C2211yescharacteristic, complemented
35C4×C22⋊D151C2211yescharacteristic
36C2×C4⋊Dic151C2211yescharacteristic, complemented
37C4⋊C4×D151C2211yescharacteristic, complemented
38#18012673C2211yescharacteristic, complemented
39#18012673C2211yescharacteristic, complemented
40#18012672C2211yescharacteristic, complemented
41Dic151⋊C8C2211yescharacteristic, complemented
42#18012661C2211yescharacteristic, complemented
43#18012661C2211yescharacteristic, complemented
44#18012660C2211yescharacteristic
45#18012660C2211yescharacteristic
46#18012660C2211yescharacteristic, complemented
47#18012660C2211yescharacteristic, complemented
48#18012660C2211yescharacteristic, complemented
49#18012659C2211yescharacteristic, complemented
50(C2×D151)⋊C8C2211yescharacteristic, complemented
51C8×Dic151C2211yescharacteristic, complemented
52C22×D4×C151C2211yescharacteristic
53C2×D8×C151C2211yescharacteristic
54C2×D8×C151C2211yescharacteristic, complemented
55#121×C151C2211yescharacteristic, complemented
56#102×C151C2211yescharacteristic
57#102×C151C2211yescharacteristic, complemented
58C22⋊C8×C151C2211yescharacteristic, complemented
59C23×D151—21no—
60#14559003—44no—
61C2×Dic302—21no—
62C2×D604C2311yescharacteristic
63C2×C22⋊D151—21no—
64C2×C22⋊D151—21no—
65C2×C22⋊D151—21no—
66C2×C22⋊D151—21no—
67C2×C22⋊D151—21no—
68C2×C22⋊D151—21no—
69C2×C22⋊D151—44no—
70C2×C22⋊D151D411yescharacteristic
71D4×D151—22no—
72D4×D151—41no—
73C22×Dic151—21no—
74C22×Dic151—21no—
75C22×Dic151—21no—
76C2×C4×D151—21no—
77C2×C4×D151C2311yescharacteristic
78#14558989—41no—
79C2×C151⋊C8—41no—
80C2×C151⋊C8C2311yescharacteristic
81C2×C151⋊C8C2311yescharacteristic
82C8×D151—41no—
83C4⋊Dic151—21no—
84C4⋊Dic151C2311yescharacteristic
85C4⋊Dic151C2311yescharacteristic
86C4⋊Dic151C2311yescharacteristic
87Dic151⋊C4—21no—
88Dic151⋊C4—21no—
89Dic151⋊C4D411yescharacteristic
90C22⋊Dic151—21no—
91C22⋊Dic151—21no—
92C22⋊Dic151—21no—
93C22⋊Dic151—21no—
94C22⋊Dic151D411yescharacteristic
95(C2×D151)⋊C4—21no—
96(C2×D151)⋊C4D411yescharacteristic
97C4×Dic151C2311yescharacteristic
98C24×C151—21no—
99C2×D4×C151—22no—
100C2×D4×C151—21no—
101C2×D4×C151—21no—
102C2×D4×C151—41no—
103C2×D4×C151C2311yescharacteristic
104C2×D4×C151C2311yescharacteristic
105C2×D4×C151C2311yescharacteristic
106C22×C4×C151C2311yescharacteristic
107D8×C151—22no—
108D8×C151—41no—
109C2×C8×C151C2311yescharacteristic
110C2×C8×C151C2311yescharacteristic
111C4⋊C4×C151C2311yescharacteristic
112C22⋊C4×C151—21no—
113C22×D151—21no—
114C22×D151—42no—
115C22×D151—42no—
116C22×D151—81no—
117C22×D151C2×D411yescharacteristic
118Dic302—42no—
119D604—21no—
120D604—21no—
121C22⋊D151—42no—
122C22⋊D151—42no—
123C22⋊D151—42no—
124C22⋊D151—42no—
125C22⋊D151—42no—
126C22⋊D151—81no—
127C22⋊D151D814yescomplemented
128C2×Dic151—21no—
129C2×Dic151—21no—
130C2×Dic151—21no—
131C2×Dic151—42no—
132C2×Dic151—42no—
133C2×Dic151—42no—
134C2×Dic151C2×D411yescharacteristic
135C2×Dic151C2×D411yescharacteristic
136C2×Dic151C2×D411yescharacteristic
137C4×D151—21no—
138C4×D151—21no—
139C4×D151—42no—
140C151⋊C8—21no—
141C151⋊C8—21no—
142C23×C151—21no—
143C23×C151—21no—
144C23×C151—21no—
145C23×C151—42no—
146C23×C151—42no—
147C23×C151—81no—
148C23×C151C2×D411yescharacteristic
149D4×C151—21no—
150D4×C151—21no—
151D4×C151—21no—
152D4×C151—21no—
153D4×C151—21no—
154D4×C151—42no—
155D4×C151—42no—
156D4×C151#4112yescomplemented
157C2×C4×C151—21no—
158C2×C4×C151—21no—
159C2×C4×C151—21no—
160C2×C4×C151C2×D411yescharacteristic
161C2×C4×C151C2411yescharacteristic
162C8×C151—21no—
163C8×C151—21no—
164C22×C151—21no—
165C22×C151—21no—
166C22×C151—22no—
167C22×C151—41no—
168C22×C151—41no—
169C22×C151—41no—
170C22×C151—41no—
171C22×C151—41no—
172C22×C151—41no—
173C22×C151—41no—
174C22×C151—41no—
175C22×C151—84no—
176C22×C151C2×D812yes—
177C22×C151C22×D411yescharacteristic
178C2×D151—21no—
179C2×D151—21no—
180C2×D151—41no—
181C2×D151—41no—
182C2×D151—41no—
183C2×D151—84no—
184C2×D151C2×D812yes—
185C4×C151—21no—
186C4×C151—41no—
187C4×C151C2×#4111yescharacteristic
188C4×C151H(5,𝔽2)11yescharacteristic
189Dic151—21no—
190Dic151—21no—
191Dic151—41no—
192Dic151—41no—
193Dic151—41no—
194Dic151C2×D812yes—
195C2×C151—22no—
196C2×C151—42no—
197C2×C151—81no—
198C2×C151—81no—
199C2×C151#54611yescharacteristic
200C2×C151C22×D811yescharacteristic
201C2×C151#57711yescharacteristic
202D151—22no—
203D151—81no—
204C151#329411yescharacteristic, complemented, Sylow
205#3294—1511nomaximal, Sylow
206#547—1511no—
207D42—1511no—
208#486—1511no—
209#480—1511no—
210#480—1511no—
211#474—1511no—
212#466—1511no—
213#466—1511no—
214#459—1511no—
215#447—1511no—
216#447D15111yescharacteristic, complemented
217C4×D8—1511no—
218C8×D4—1511no—
219C2×#102—1511no—
220C2×#102—1511no—
221C2×#41—3021no—
222C22×D4—3021no—
223C22×D4—1511no—
224C22×D4C2×D15111yescharacteristic
225C2×D8—1511no—
226C2×D8C2×D15111yescharacteristic
227C2×D8C2×D15111yescharacteristic, complemented
228C22×C8—1511no—
229C22×C8—1511no—
230C4⋊Q8—1511no—
231#127—1511no—
232#123—3021no—
233#123—3021no—
234C22⋊Q8—3021no—
235#121—3021no—
236#121—1511no—
237#121—1511no—
238#121—1511no—
239#121C2×D15111yescharacteristic, complemented
240#120—3021no—
241#120—3021no—
242C4×D4—1511no—
243C4×D4—1511no—
244C4×D4—1511no—
245C2×C4⋊C4—1511no—
246C2×C4⋊C4—1511no—
247#107—1511no—
248#107—1511no—
249#107—1511no—
250C4⋊C8—1511no—
251#102—1511no—
252#102—1511no—
253#102—1511no—
254#102—1511no—
255#102—1511no—
256#102—1511no—
257#102—1511no—
258#102—1511no—
259#102C2×D15111yescharacteristic
260#102C2×D15111yescharacteristic, complemented
261C22⋊C8—1511no—
262C22⋊C8C2×D15111yescharacteristic, complemented
263C4×C8—1511no—
264C24—21no—
265C24—3021no—
266#41—6044no—
267C2×Q8—3021no—
268C2×D4—22no—
269C2×D4—21no—
270C2×D4—21no—
271C2×D4—41no—
272C2×D4—3022no—
273C2×D4—3021no—
274C2×D4—3021no—
275C2×D4—3021no—
276C2×D4—3021no—
277C2×D4—3021no—
278C2×D4—3021no—
279C2×D4—6041no—
280C2×D4—6044no—
281C2×D4—1511no—
282C2×D4—1511no—
283C2×D4C22×D15111yescharacteristic
284C2×D4C22×D15111yescharacteristic
285C2×D4C22×D15111yescharacteristic
286C22×C4—3021no—
287C22×C4—3021no—
288C22×C4—3021no—
289C22×C4—3021no—
290C22×C4—1511no—
291C22×C4C22×D15111yescharacteristic
292D8—22no—
293D8—41no—
294D8—6041no—
295C2×C8—6041no—
296C2×C8—6041no—
297C2×C8—1511no—
298C2×C8—1511no—
299C2×C8C22×D15111yescharacteristic
300C2×C8C22×D15111yescharacteristic
301C4⋊C4—3021no—
302C4⋊C4—3021no—
303C4⋊C4—3021no—
304C4⋊C4—1511no—
305C4⋊C4—1511no—
306C4⋊C4—1511no—
307C4⋊C4—1511no—
308C4⋊C4C22×D15111yescharacteristic
309C22⋊C4—21no—
310C22⋊C4—3021no—
311C22⋊C4—3021no—
312C22⋊C4—3021no—
313C22⋊C4—3021no—
314C22⋊C4—3021no—
315C22⋊C4—1511no—
316C22⋊C4—1511no—
317C42—1511no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—42no—
322C23—42no—
323C23—81no—
324C23—3021no—
325C23—6042no—
326C23—6042no—
327C23—1511no—
328C23—12081no—
329C23D4×D15111yescharacteristic
330Q8—6042no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—21no—
335D4—21no—
336D4—42no—
337D4—42no—
338D4—3021no—
339D4—3021no—
340D4—6042no—
341D4—6042no—
342D4—6042no—
343D4—6042no—
344D4—6042no—
345D4—1514no—
346D4—12081no—
347D4#1455900312yescomplemented
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—3021no—
352C2×C4—3021no—
353C2×C4—3021no—
354C2×C4—3021no—
355C2×C4—3021no—
356C2×C4—6042no—
357C2×C4—6042no—
358C2×C4—6042no—
359C2×C4—6042no—
360C2×C4—1511no—
361C2×C4—1511no—
362C2×C4—1511no—
363C2×C4D4×D15111yescharacteristic
364C2×C4C23×D15111yescharacteristic
365C8—21no—
366C8—21no—
367C8—3021no—
368C8—3021no—
369C22—21no—
370C22—21no—
371C22—22no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—84no—
381C22—3021no—
382C22—3021no—
383C22—6041no—
384C22—6041no—
385C22—6041no—
386C22—1512no—
387C22—12084no—
388C22D8×D15112yes—
389C22C2×D4×D15111yescharacteristic
390C4—21no—
391C4—41no—
392C4—3021no—
393C4—3021no—
394C4—6041no—
395C4—6041no—
396C4—6041no—
397C4—1512no—
398C4C2×#1455900311yescharacteristic
399C4#1801278411yescharacteristic
400C2—22no—
401C2—42no—
402C2—81no—
403C2—81no—
404C2—3022no—
405C2—12081no—
406C2#2375284911yescharacteristic
407C2C2×D8×D15111yescharacteristic
408C2#2375302211yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#447×C151C2
socleC22×C151C22×D4
hypercenter#447D151
hypocenterC151#3294
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #23752862C2semidirect
2. D4×C22⋊D151C2semidirect
3. #23752557C2semidirect
4. #23752526C2semidirect
5. #23752524C2semidirect
6. #23752490C2semidirect
7. #23752446C2semidirect
8. #23752445C2semidirect
9. #23752405C2semidirect
10. #23752344C2semidirect
11. D8×Dic151C2semidirect
12. (C22⋊D151)⋊C8C2semidirect
13. C2×#18012660C2semidirect
14. #102×D151C2semidirect
15. #447×C151C2semidirect
19. C2×#14558989C22semidirect
20. C22×C151⋊C8C22semidirect
21. C2×C8×D151C22semidirect
22. #18012738C22semidirect
30. #18012710C22semidirect
34. D4×Dic151C22semidirect
36. C2×C4⋊Dic151C22semidirect
37. C4⋊C4×D151C22semidirect
38. #18012673C22semidirect
39. #18012673C22semidirect
40. #18012672C22semidirect
41. Dic151⋊C8C22semidirect
42. #18012661C22semidirect
43. #18012661C22semidirect
46. #18012660C22semidirect
47. #18012660C22semidirect
48. #18012660C22semidirect
49. #18012659C22semidirect
50. (C2×D151)⋊C8C22semidirect
51. C8×Dic151C22semidirect
54. C2×D8×C151C22semidirect
55. #121×C151C22semidirect
57. #102×C151C22semidirect
58. C22⋊C8×C151C22semidirect
127. C22⋊D151D8semidirect
156. D4×C151#41semidirect
204. C151#3294semidirect
216. #447D151semidirect
227. C2×D8C2×D151semidirect
239. #121C2×D151semidirect
260. #102C2×D151semidirect
262. C22⋊C8C2×D151semidirect
347. D4#14559003semidirect

Maximal subgroups

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

subgroupindex
#237528622
D4×C22⋊D1512
#237525572
#237525262
#237525242
#237524902
#237524462
#237524452
#237524052
#237523442
D8×Dic1512
(C22⋊D151)⋊C82
C2×#180126602
#102×D1512
#447×C1512
#3294151