Finite Group Databasebeta

← #34080619

Subgroups — #34080619

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
1C2×#18012771C211yesmaximal, characteristic, complemented
2C2×SD16×D151C211yesmaximal, characteristic, complemented
3#23752877C211yesmaximal, characteristic, complemented
4#23752855C211yesmaximal, characteristic
5#23752455C211yesmaximal, characteristic, complemented
6#23752450C211yesmaximal, characteristic, complemented
7#23752431C211yesmaximal, characteristic, complemented
8#23752414C211yesmaximal, characteristic, complemented
9#23752373C211yesmaximal, characteristic, complemented
10#23752366C211yesmaximal, characteristic, complemented
11#23752361C211yesmaximal, characteristic, complemented
12#23752349C211yesmaximal, characteristic, complemented
13#23752314C211yesmaximal, characteristic, complemented
14#23752285C211yesmaximal, characteristic, complemented
15#497×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic
17C2×Q8×D151C2211yescharacteristic
18C2×Q8×D151C2211yescharacteristic, complemented
19C2×D4×D151C2211yescharacteristic
20#18012771—24no—
21C2×#14558994C2211yescharacteristic, complemented
22C2×#14558993C2211yescharacteristic
23C2×#14558992C2211yescharacteristic
24C2×#14558991C2211yescharacteristic
25C2×#14558991C2211yescharacteristic
26SD16×D151—24no—
27C2×#14558987C2211yescharacteristic, complemented
28C2×C8×D151C2211yescharacteristic
29#18012738—21no—
30#18012721—21no—
31#18012717—21no—
32#18012717—21no—
33#18012715C2211yescharacteristic
34#18012715C2211yescharacteristic
35#18012715C2211yescharacteristic, complemented
36#18012712—21no—
37#18012710C2211yescharacteristic
38#18012709—21no—
39C4×Dic302C2211yescharacteristic, complemented
40C4×D604C2211yescharacteristic
41C4×D604C2211yescharacteristic
42#18012701—21no—
43C22⋊C4×D151—21no—
44#18012673C2211yescharacteristic, complemented
45C4⋊(C151⋊C8)C2211yescharacteristic, complemented
46#18012664C2211yescharacteristic, complemented
47#18012663C2211yescharacteristic, complemented
48#18012663C2211yescharacteristic, complemented
49#18012663C2211yescharacteristic, complemented
50#18012661C2211yescharacteristic
51#18012660C2211yescharacteristic
52(C2×D151)⋊C8C2211yescharacteristic
53(C2×D151)⋊C8C2211yescharacteristic, complemented
54C2×Q16×C151C2211yescharacteristic, complemented
55C2×Q16×C151C2211yescharacteristic, complemented
56C2×SD16×C151C2211yescharacteristic
57C2×SD16×C151C2211yescharacteristic
58C4⋊Q8×C151C2211yescharacteristic, complemented
59#124×C151C2211yescharacteristic
60#97×C151C2211yescharacteristic, complemented
61C23×D151—21no—
62#14559005—22no—
63#14559005—41no—
64C2×Dic302—21no—
65C2×Dic302—21no—
66C2×Dic302C2311yescharacteristic
67Q8×D151—22no—
68Q8×D151—22no—
69Q8×D151—41no—
70Q8×D151—41no—
71C2×D604—21no—
72C2×D604D411yescharacteristic
73C2×D604C2311yescharacteristic
74C2×C22⋊D151—21no—
75C2×C22⋊D151—21no—
76D4×D151—22no—
77D4×D151—41no—
78C2×C4×D151—21no—
79C2×C4×D151—21no—
80C2×C4×D151—21no—
81C2×C4×D151—21no—
82C2×C4×D151C2311yescharacteristic
83C2×C4×D151C2311yescharacteristic
84#14558994—22no—
85#14558993D414yescomplemented
86#14558992—22no—
87#14558991—22no—
88#14558991—22no—
89#14558987—22no—
90C2×C151⋊C8C2311yescharacteristic
91C2×C151⋊C8C2311yescharacteristic
92C8×D151—22no—
93C4⋊Dic151D411yescharacteristic
94C4⋊Dic151C2311yescharacteristic
95C4⋊Dic151C2311yescharacteristic
96Dic151⋊C4—21no—
97Dic151⋊C4—21no—
98Dic151⋊C4—21no—
99Dic151⋊C4—21no—
100C22⋊Dic151—21no—
101(C2×D151)⋊C4—21no—
102(C2×D151)⋊C4—21no—
103(C2×D151)⋊C4—21no—
104(C2×D151)⋊C4—21no—
105(C2×D151)⋊C4D411yescharacteristic
106(C2×D151)⋊C4D411yescharacteristic
107C4×Dic151—21no—
108C2×Q8×C151C2311yescharacteristic
109C2×Q8×C151C2311yescharacteristic
110C2×Q8×C151C2311yescharacteristic
111C2×D4×C151C2311yescharacteristic
112Q16×C151—22no—
113Q16×C151—41no—
114SD16×C151—22no—
115SD16×C151—41no—
116C2×C8×C151C2311yescharacteristic
117C2×C8×C151C2311yescharacteristic
118C4⋊C4×C151—21no—
119C4⋊C4×C151—21no—
120C22⋊C4×C151—21no—
121C22⋊C4×C151—21no—
122C42×C151C2311yescharacteristic
123C22×D151—21no—
124C22×D151—42no—
125C22×D151—42no—
126C22×D151—81no—
127C22×D151C2×D411yescharacteristic
128C22×D151C2×D411yescharacteristic
129Dic302—21no—
130Dic302—42no—
131Dic302—42no—
132Dic302C2×D412yes—
133D604—22no—
134D604—21no—
135D604—42no—
136D604C2×D412yes—
137C22⋊D151—42no—
138C22⋊D151—81no—
139C2×Dic151—21no—
140C2×Dic151—21no—
141C2×Dic151—21no—
142C2×Dic151C2×D411yescharacteristic
143C2×Dic151C2×D411yescharacteristic
144C4×D151—21no—
145C4×D151—21no—
146C4×D151—21no—
147C4×D151—21no—
148C4×D151—42no—
149C4×D151—42no—
150C4×D151—42no—
151C4×D151—81no—
152C151⋊C8—21no—
153C151⋊C8—21no—
154C23×C151—21no—
155Q8×C151—21no—
156Q8×C151—21no—
157Q8×C151—21no—
158Q8×C151—21no—
159Q8×C151—21no—
160Q8×C151—21no—
161D4×C151—21no—
162D4×C151—21no—
163C2×C4×C151—21no—
164C2×C4×C151—21no—
165C2×C4×C151—21no—
166C2×C4×C151C2×D411yescharacteristic
167C2×C4×C151C2×D411yescharacteristic
168C2×C4×C151C2411yescharacteristic
169C8×C151—21no—
170C8×C151C2×D412yes—
171C22×C151—41no—
172C22×C151—41no—
173C22×C151—41no—
174C22×C151C22×D411yescharacteristic
175C2×D151—21no—
176C2×D151—21no—
177C2×D151—21no—
178C2×D151—22no—
179C2×D151—21no—
180C2×D151—21no—
181C2×D151—41no—
182C2×D151—41no—
183C2×D151—84no—
184C2×D151#13712yescomplemented
185C4×C151—21no—
186C4×C151—21no—
187C4×C151—41no—
188C4×C151—41no—
189C4×C151—41no—
190C4×C151C22×D411yescharacteristic
191C4×C151H(5,𝔽2)11yescharacteristic
192Dic151—21no—
193Dic151—21no—
194Dic151—22no—
195Dic151—41no—
196Dic151—41no—
197C2×C151—81no—
198C2×C151D4211yescharacteristic
199C2×C151C2×#13711yescharacteristic
200C2×C151#57711yescharacteristic
201D151—22no—
202D151—41no—
203D151—42no—
204C151#326611yescharacteristic, complemented, Sylow
205#3266—1511nomaximal, Sylow
206C2×#137—1511no—
207C22×SD16—1511no—
208D4×Q8—1511no—
209#546—1511no—
210#497D15111yescharacteristic, complemented
211#468—1511no—
212#467—1511no—
213#464—1511no—
214#461—1511no—
215#452—1511no—
216#451—1511no—
217#450—1511no—
218#448—1511no—
219#440—1511no—
220#435—1511no—
221C2×#41—1511no—
222C22×Q8—1511no—
223C22×Q8—1511no—
224C22×D4—1511no—
225#137—3024no—
226C2×Q16—1511no—
227C2×Q16C2×D15111yescharacteristic, complemented
228C2×Q16C2×D15111yescharacteristic, complemented
229C2×SD16—3024no—
230C2×SD16—1511no—
231C2×SD16—1511no—
232C2×SD16—1511no—
233C2×SD16—1511no—
234C2×SD16C2×D15111yescharacteristic
235C2×SD16C2×D15111yescharacteristic
236C2×M16—1511no—
237C22×C8—1511no—
238C4⋊Q8—3021no—
239C4⋊Q8C2×D15111yescharacteristic, complemented
240#124C2×D15111yescharacteristic
241#123—3021no—
242C22⋊Q8—3021no—
243C22⋊Q8—3021no—
244C22⋊Q8—1511no—
245C22⋊Q8—1511no—
246C22⋊Q8—1511no—
247#121—3021no—
248#121—1511no—
249#120—3021no—
250C4×Q8—1511no—
251C4×D4—3021no—
252C4×D4—1511no—
253C4×D4—1511no—
254C2×C22⋊C4—3021no—
255#107—1511no—
256C4⋊C8—1511no—
257#103—1511no—
258#103—1511no—
259#103—1511no—
260#103—1511no—
261#102—1511no—
262#102—1511no—
263C22⋊C8—1511no—
264C22⋊C8—1511no—
265#97C2×D15111yescharacteristic, complemented
266C24—3021no—
267#41—3022no—
268#41—6041no—
269C2×Q8—3021no—
270C2×Q8—3021no—
271C2×Q8—3022no—
272C2×Q8—3022no—
273C2×Q8—6041no—
274C2×Q8—6041no—
275C2×Q8—1511no—
276C2×Q8C22×D15111yescharacteristic
277C2×Q8C22×D15111yescharacteristic
278C2×Q8C22×D15111yescharacteristic
279C2×D4—3021no—
280C2×D4—3022no—
281C2×D4—3021no—
282C2×D4—3021no—
283C2×D4—6041no—
284C2×D4—1511no—
285C2×D4—1511no—
286C2×D4C22×D15111yescharacteristic
287C22×C4—3021no—
288C22×C4—3021no—
289C22×C4—3021no—
290C22×C4—3021no—
291C22×C4—1511no—
292C22×C4—1511no—
293Q16—22no—
294Q16—41no—
295Q16—3022no—
296SD16—22no—
297SD16—41no—
298SD16—3022no—
299SD16—3022no—
300SD16—3022no—
301SD16—1514no—
302M16—3022no—
303C2×C8—3022no—
304C2×C8—1511no—
305C2×C8—1511no—
306C2×C8C22×D15111yescharacteristic
307C2×C8C22×D15111yescharacteristic
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—3021no—
311C4⋊C4—3021no—
312C4⋊C4—3021no—
313C4⋊C4—3021no—
314C4⋊C4—1511no—
315C4⋊C4—1511no—
316C4⋊C4—1511no—
317C22⋊C4—21no—
318C22⋊C4—21no—
319C22⋊C4—3021no—
320C22⋊C4—3021no—
321C22⋊C4—3021no—
322C22⋊C4—3021no—
323C22⋊C4—3021no—
324C22⋊C4—1511no—
325C22⋊C4—1511no—
326C42—3021no—
327C42C22×D15111yescharacteristic
328C23—21no—
329C23—3021no—
330C23—6042no—
331C23—6042no—
332C23—1511no—
333C23—1511no—
334C23—12081no—
335Q8—21no—
336Q8—21no—
337Q8—21no—
338Q8—21no—
339Q8—21no—
340Q8—21no—
341Q8—3021no—
342Q8—6042no—
343Q8—6042no—
344Q8—1512no—
345D4—21no—
346D4—21no—
347D4—3022no—
348D4—3021no—
349D4—6042no—
350D4—6042no—
351D4—1512no—
352D4—12081no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—3021no—
357C2×C4—3021no—
358C2×C4—3021no—
359C2×C4—3021no—
360C2×C4—3021no—
361C2×C4—3021no—
362C2×C4—3021no—
363C2×C4—6042no—
364C2×C4—6042no—
365C2×C4—6042no—
366C2×C4—1511no—
367C2×C4—1511no—
368C2×C4—12081no—
369C2×C4D4×D15111yescharacteristic
370C2×C4D4×D15111yescharacteristic
371C2×C4C23×D15111yescharacteristic
372C8—21no—
373C8—3021no—
374C8—3021no—
375C8D4×D15112yes—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—3021no—
380C22—3021no—
381C22—3021no—
382C22—3021no—
383C22—3021no—
384C22—3022no—
385C22—6041no—
386C22—6041no—
387C22—1512no—
388C22—12084no—
389C22C2×D4×D15111yescharacteristic
390C4—21no—
391C4—21no—
392C4—41no—
393C4—41no—
394C4—41no—
395C4—3021no—
396C4—3021no—
397C4—3022no—
398C4—6041no—
399C4—6041no—
400C4C2×D4×D15111yescharacteristic
401C4#1801278411yescharacteristic
402C2—81no—
403C2—3022no—
404C2—6041no—
405C2—6042no—
406C2#2375284711yescharacteristic
407C2#137×D15111yescharacteristic
408C2#2375302111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#497×C151C2
socleC22×C151C22×D4
prime radical#23752855C2
hypercenter#497D151
hypocenterC151#3266
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
1. C2×#18012771C2semidirect
2. C2×SD16×D151C2semidirect
3. #23752877C2semidirect
5. #23752455C2semidirect
6. #23752450C2semidirect
7. #23752431C2semidirect
8. #23752414C2semidirect
9. #23752373C2semidirect
10. #23752366C2semidirect
11. #23752361C2semidirect
12. #23752349C2semidirect
13. #23752314C2semidirect
14. #23752285C2semidirect
15. #497×C151C2semidirect
18. C2×Q8×D151C22semidirect
21. C2×#14558994C22semidirect
27. C2×#14558987C22semidirect
35. #18012715C22semidirect
39. C4×Dic302C22semidirect
44. #18012673C22semidirect
45. C4⋊(C151⋊C8)C22semidirect
46. #18012664C22semidirect
47. #18012663C22semidirect
48. #18012663C22semidirect
49. #18012663C22semidirect
53. (C2×D151)⋊C8C22semidirect
54. C2×Q16×C151C22semidirect
55. C2×Q16×C151C22semidirect
58. C4⋊Q8×C151C22semidirect
60. #97×C151C22semidirect
85. #14558993D4semidirect
184. C2×D151#137semidirect
204. C151#3266semidirect
210. #497D151semidirect
227. C2×Q16C2×D151semidirect
228. C2×Q16C2×D151semidirect
239. C4⋊Q8C2×D151semidirect
265. #97C2×D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127712
C2×SD16×D1512
#237528772
#237528552
#237524552
#237524502
#237524312
#237524142
#237523732
#237523662
#237523612
#237523492
#237523142
#237522852
#497×C1512
#3266151