Finite Group Databasebeta

← #34080833

Subgroups — #34080833

Order 19328.

494 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18012762C211yesmaximal, characteristic, complemented
2C2×#18012759C211yesmaximal, characteristic, complemented
3#23752881C211yesmaximal, characteristic, complemented
4#23752864C211yesmaximal, characteristic, complemented
5#23752583C211yesmaximal, characteristic, complemented
6#23752443C211yesmaximal, characteristic, complemented
7#23752440C211yesmaximal, characteristic, complemented
8#23752420C211yesmaximal, characteristic, complemented
9#23752406C211yesmaximal, characteristic, complemented
10#23752377C211yesmaximal, characteristic, complemented
11#23752359C211yesmaximal, characteristic, complemented
12#23752356C211yesmaximal, characteristic, complemented
13#23752297C211yesmaximal, characteristic, complemented
14(C22⋊D151)⋊C8C211yesmaximal, characteristic, complemented
15#452×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic
17C2×#14559005C2211yescharacteristic
18C2×#14559004C2211yescharacteristic
19#18012762—24no—
20#18012759—24no—
21C2×#14558994C2211yescharacteristic
22C2×#14558993C2211yescharacteristic
23C2×#14558992C2211yescharacteristic
24C2×#14558991C2211yescharacteristic
25C2×#14558991C2211yescharacteristic
26C2×D1208C2211yescharacteristic
27C2×#14558989C2211yescharacteristic
28C22×C151⋊C8C2211yescharacteristic
29C2×C8×D151C2211yescharacteristic
30#18012737C2211yescharacteristic
31#18012735—21no—
32#18012735C2211yescharacteristic
33#18012724—21no—
34#18012721—21no—
35#18012719C2211yescharacteristic
36#18012713—21no—
37#18012713C2211yescharacteristic
38#18012712—21no—
39#18012710—21no—
40#18012710C2211yescharacteristic
41Q8×Dic151C2211yescharacteristic
42#18012701C2211yescharacteristic
43C4×C22⋊D151—21no—
44C4×C22⋊D151C2211yescharacteristic
45C4⋊C4×D151—21no—
46#18012670C2211yescharacteristic
47Dic151⋊C8C2211yescharacteristic
48#18012664C2211yescharacteristic
49#18012663C2211yescharacteristic
50#18012661C2211yescharacteristic
51#18012659C2211yescharacteristic
52(C2×D151)⋊C8C2211yescharacteristic
53C8×Dic151C2211yescharacteristic
54C2×#41×C151C2211yescharacteristic
55C2×Q16×C151C2211yescharacteristic
56C2×SD16×C151C2211yescharacteristic
57C22⋊Q8×C151C2211yescharacteristic
58#103×C151C2211yescharacteristic
59#102×C151C2211yescharacteristic
60C22⋊C8×C151C2211yescharacteristic
61#14559005—22no—
62#14559005—22no—
63#14559005—41no—
64#14559005—41no—
65#14559004—22no—
66#14559004—41no—
67C2×Dic302C2311yescharacteristic
68C2×D604—21no—
69C2×D604—21no—
70C2×D604C2311yescharacteristic
71C2×D604C2311yescharacteristic
72C2×C22⋊D151—21no—
73C2×C22⋊D151—21no—
74C2×C22⋊D151—21no—
75C2×C22⋊D151—21no—
76C2×C22⋊D151—21no—
77C2×C22⋊D151D411yescharacteristic
78C2×C4×D151—21no—
79C2×C4×D151—21no—
80C2×C4×D151—21no—
81C2×C4×D151—21no—
82C2×C4×D151C2311yescharacteristic
83#14558994—22no—
84#14558993—41no—
85#14558992—22no—
86#14558991—22no—
87#14558991D414yescomplemented
88D1208—22no—
89#14558989—22no—
90C2×C151⋊C8—22no—
91C2×C151⋊C8C2311yescharacteristic
92C2×C151⋊C8C2311yescharacteristic
93C8×D151—22no—
94C4⋊Dic151—21no—
95C4⋊Dic151—21no—
96C4⋊Dic151C2311yescharacteristic
97Dic151⋊C4—21no—
98Dic151⋊C4—21no—
99Dic151⋊C4D411yescharacteristic
100C22⋊Dic151—21no—
101C22⋊Dic151D411yescharacteristic
102(C2×D151)⋊C4—21no—
103(C2×D151)⋊C4—21no—
104(C2×D151)⋊C4—21no—
105(C2×D151)⋊C4D411yescharacteristic
106C4×Dic151—21no—
107C4×Dic151C2311yescharacteristic
108#41×C151—22no—
109#41×C151—41no—
110C2×Q8×C151C2311yescharacteristic
111C2×Q8×C151C2311yescharacteristic
112C2×D4×C151—21no—
113C2×D4×C151C2311yescharacteristic
114C22×C4×C151—21no—
115C22×C4×C151C2311yescharacteristic
116Q16×C151—22no—
117SD16×C151—41no—
118C2×C8×C151C2311yescharacteristic
119C2×C8×C151C2311yescharacteristic
120C4⋊C4×C151—21no—
121C4⋊C4×C151C2311yescharacteristic
122C22⋊C4×C151—21no—
123C22×D151—21no—
124C22×D151—21no—
125C22×D151C2×D411yescharacteristic
126Dic302—21no—
127Dic302—21no—
128D604—21no—
129D604—21no—
130D604—21no—
131D604—42no—
132D604—42no—
133D604C2×D412yes—
134C22⋊D151—22no—
135C22⋊D151—42no—
136C22⋊D151—42no—
137C22⋊D151—81no—
138C22⋊D151—81no—
139C22⋊D151—81no—
140C2×Dic151—21no—
141C2×Dic151—21no—
142C2×Dic151C2×D411yescharacteristic
143C2×Dic151C2×D411yescharacteristic
144C2×Dic151C2×D411yescharacteristic
145C4×D151—21no—
146C4×D151—21no—
147C4×D151—42no—
148C4×D151—42no—
149C4×D151—42no—
150C4×D151—42no—
151C151⋊C8—21no—
152C151⋊C8C2×D412yes—
153C23×C151—21no—
154C23×C151C2×D411yescharacteristic
155Q8×C151—21no—
156Q8×C151—21no—
157Q8×C151—21no—
158Q8×C151C2×D412yes—
159D4×C151—21no—
160D4×C151—21no—
161D4×C151—42no—
162C2×C4×C151—21no—
163C2×C4×C151—21no—
164C2×C4×C151—21no—
165C2×C4×C151—21no—
166C2×C4×C151—21no—
167C2×C4×C151—42no—
168C2×C4×C151C2×D411yescharacteristic
169C2×C4×C151C2411yescharacteristic
170C8×C151—21no—
171C8×C151—21no—
172C22×C151—21no—
173C22×C151—21no—
174C22×C151—21no—
175C22×C151—41no—
176C22×C151—41no—
177C22×C151—41no—
178C22×C151C22×D411yescharacteristic
179C2×D151—21no—
180C2×D151—22no—
181C2×D151—21no—
182C2×D151—21no—
183C2×D151—41no—
184C2×D151—41no—
185C2×D151—41no—
186C2×D151—41no—
187C2×D151—41no—
188C4×C151—21no—
189C4×C151—22no—
190C4×C151—41no—
191C4×C151—41no—
192C4×C151C22×D411yescharacteristic
193C4×C151H(5,𝔽2)11yescharacteristic
194Dic151—21no—
195Dic151—21no—
196Dic151—41no—
197Dic151—41no—
198Dic151#13512yescomplemented
199C2×C151—41no—
200C2×C151—81no—
201C2×C151D4211yescharacteristic
202C2×C151C2×#13511yescharacteristic
203C2×C151#57711yescharacteristic
204D151—41no—
205D151—42no—
206D151—81no—
207C151#328411yescharacteristic, complemented, Sylow
208#3284—1511nomaximal, Sylow
209C2×#135—1511no—
210C2×#135—1511no—
211#550—1511no—
212#547—1511no—
213#492—1511no—
214#465—1511no—
215#465—1511no—
216#462—1511no—
217#459—1511no—
218#452—1511no—
219#452D15111yescharacteristic, complemented
220#449—1511no—
221#449—1511no—
222C4×SD16—1511no—
223C8×D4—1511no—
224C2×#41—1511no—
225C2×#41—1511no—
226C2×#41—1511no—
227C2×#41C2×D15111yescharacteristic
228#135—3024no—
229#135—3024no—
230C2×Q16—1511no—
231C2×Q16C2×D15111yescharacteristic
232C2×SD16—1511no—
233C2×SD16—1511no—
234C2×SD16—1511no—
235C2×SD16—1511no—
236C2×SD16C2×D15111yescharacteristic
237C2×D8—1511no—
238C2×D8—1511no—
239C22×C8—1511no—
240C22×C8—1511no—
241C4⋊Q8—1511no—
242#127—3021no—
243#127—1511no—
244#123—3021no—
245#123—3021no—
246C22⋊Q8—1511no—
247C22⋊Q8C2×D15111yescharacteristic
248#121—3021no—
249#121—3021no—
250#121—3021no—
251#121—1511no—
252#121—1511no—
253C4×Q8—1511no—
254C4×D4—3021no—
255C4×D4—1511no—
256C4×D4—1511no—
257C2×C4⋊C4—3021no—
258#106—1511no—
259C4⋊C8—1511no—
260#103—1511no—
261#103—1511no—
262#103C2×D15111yescharacteristic
263#102—1511no—
264#102—1511no—
265#102C2×D15111yescharacteristic
266C22⋊C8—1511no—
267C22⋊C8C2×D15111yescharacteristic
268C4×C8—1511no—
269#41—22no—
270#41—41no—
271#41—3022no—
272#41—3022no—
273#41—3022no—
274#41—6041no—
275#41—6041no—
276#41—6041no—
277C2×Q8—1511no—
278C2×Q8C22×D15111yescharacteristic
279C2×Q8C22×D15111yescharacteristic
280C2×D4—21no—
281C2×D4—3021no—
282C2×D4—3021no—
283C2×D4—3021no—
284C2×D4—3021no—
285C2×D4—3021no—
286C2×D4—3021no—
287C2×D4—3021no—
288C2×D4—1511no—
289C2×D4—1511no—
290C2×D4—1511no—
291C2×D4C22×D15111yescharacteristic
292C22×C4—21no—
293C22×C4—3021no—
294C22×C4—3021no—
295C22×C4—3021no—
296C22×C4—3021no—
297C22×C4—1511no—
298C22×C4C22×D15111yescharacteristic
299Q16—22no—
300Q16—3022no—
301SD16—41no—
302SD16—3022no—
303SD16—3022no—
304SD16—6041no—
305SD16—1514no—
306D8—3022no—
307D8—3022no—
308C2×C8—3022no—
309C2×C8—3022no—
310C2×C8—1511no—
311C2×C8—1511no—
312C2×C8C22×D15111yescharacteristic
313C2×C8C22×D15111yescharacteristic
314C4⋊C4—21no—
315C4⋊C4—3021no—
316C4⋊C4—3021no—
317C4⋊C4—3021no—
318C4⋊C4—3021no—
319C4⋊C4—1511no—
320C4⋊C4—1511no—
321C4⋊C4C22×D15111yescharacteristic
322C22⋊C4—21no—
323C22⋊C4—3021no—
324C22⋊C4—3021no—
325C22⋊C4—3021no—
326C22⋊C4—3021no—
327C22⋊C4—1511no—
328C22⋊C4—1511no—
329C42—3021no—
330C42—1511no—
331C23—21no—
332C23—3021no—
333C23—3021no—
334C23—1511no—
335C23D4×D15111yescharacteristic
336Q8—21no—
337Q8—21no—
338Q8—21no—
339Q8—3021no—
340Q8—3021no—
341Q8D4×D15112yes—
342D4—21no—
343D4—21no—
344D4—42no—
345D4—3022no—
346D4—3021no—
347D4—3021no—
348D4—3021no—
349D4—6042no—
350D4—6042no—
351D4—6042no—
352D4—6042no—
353D4—1512no—
354D4—12081no—
355D4—12081no—
356D4—12081no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—42no—
363C2×C4—3021no—
364C2×C4—3021no—
365C2×C4—3021no—
366C2×C4—3021no—
367C2×C4—6042no—
368C2×C4—6042no—
369C2×C4—6042no—
370C2×C4—6042no—
371C2×C4—1511no—
372C2×C4—1511no—
373C2×C4—1511no—
374C2×C4D4×D15111yescharacteristic
375C2×C4C23×D15111yescharacteristic
376C8—21no—
377C8—21no—
378C8—3021no—
379C8—1512no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—3021no—
387C22—3021no—
388C22—3021no—
389C22—3022no—
390C22—6041no—
391C22—6041no—
392C22—6041no—
393C22—6041no—
394C22—6041no—
395C22C2×D4×D15111yescharacteristic
396C4—21no—
397C4—22no—
398C4—41no—
399C4—41no—
400C4—3021no—
401C4—3021no—
402C4—6041no—
403C4—6041no—
404C4—1512no—
405C4C2×D4×D15111yescharacteristic
406C4#1801278411yescharacteristic
407C2—41no—
408C2—81no—
409C2—6041no—
410C2—6042no—
411C2—12081no—
412C2#2375284411yescharacteristic
413C2#135×D15111yescharacteristic
414C2#2375302111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#452×C151C2
socleC22×C151C22×D4
hypercenter#452D151
hypocenterC151#3284
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. C2×#18012762C2semidirect
2. C2×#18012759C2semidirect
3. #23752881C2semidirect
4. #23752864C2semidirect
5. #23752583C2semidirect
6. #23752443C2semidirect
7. #23752440C2semidirect
8. #23752420C2semidirect
9. #23752406C2semidirect
10. #23752377C2semidirect
11. #23752359C2semidirect
12. #23752356C2semidirect
13. #23752297C2semidirect
14. (C22⋊D151)⋊C8C2semidirect
15. #452×C151C2semidirect
87. #14558991D4semidirect
198. Dic151#135semidirect
207. C151#3284semidirect
219. #452D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127622
C2×#180127592
#237528812
#237528642
#237525832
#237524432
#237524402
#237524202
#237524062
#237523772
#237523592
#237523562
#237522972
(C22⋊D151)⋊C82
#452×C1512
#3284151