Finite Group Databasebeta

← #34080837

Subgroups — #34080837

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×#18012761C211yesmaximal, characteristic, complemented
2C2×#18012760C211yesmaximal, characteristic, complemented
3#23752880C211yesmaximal, characteristic, complemented
4#23752864C211yesmaximal, characteristic, complemented
5#23752583C211yesmaximal, characteristic, complemented
6#23752442C211yesmaximal, characteristic, complemented
7#23752421C211yesmaximal, characteristic, complemented
8#23752406C211yesmaximal, characteristic, complemented
9#23752375C211yesmaximal, characteristic, complemented
10#23752372C211yesmaximal, characteristic, complemented
11#23752360C211yesmaximal, characteristic, complemented
12#23752355C211yesmaximal, characteristic, complemented
13#23752299C211yesmaximal, characteristic, complemented
14C8×C22⋊D151C211yesmaximal, characteristic, complemented
15#465×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic
17C2×#14559004C2211yescharacteristic
18C2×#14559004C2211yescharacteristic
19C2×#14559003C2211yescharacteristic
20#18012761—24no—
21#18012760—24no—
22C2×Dic604C2211yescharacteristic
23C2×#14558994C2211yescharacteristic
24C2×#14558993C2211yescharacteristic
25C2×#14558993C2211yescharacteristic
26C2×#14558992C2211yescharacteristic
27C2×#14558991C2211yescharacteristic
28C2×D1208C2211yescharacteristic
29C2×#14558989C2211yescharacteristic
30C2×C8×D151C2211yescharacteristic
31#18012737C2211yescharacteristic
32#18012735—21no—
33#18012735C2211yescharacteristic
34#18012724—21no—
35#18012721—21no—
36#18012719C2211yescharacteristic
37#18012714C2211yescharacteristic
38#18012712—21no—
39#18012712—21no—
40#18012711—21no—
41#18012704C2211yescharacteristic
42#18012701C2211yescharacteristic
43C4×C22⋊D151C2211yescharacteristic
44(C22⋊D151)⋊C4—21no—
45C4⋊C4×D151—21no—
46Dic151⋊C8C2211yescharacteristic
47#18012662C2211yescharacteristic
48#18012662C2211yescharacteristic
49#18012659C2211yescharacteristic
50#18012659C2211yescharacteristic
51C22⋊(C151⋊C8)C2211yescharacteristic
52(C2×D151)⋊C8C2211yescharacteristic
53C8×Dic151C2211yescharacteristic
54C2×SD16×C151C2211yescharacteristic
55C22×C8×C151C2211yescharacteristic
56C22⋊Q8×C151C2211yescharacteristic
57#121×C151C2211yescharacteristic
58#106×C151C2211yescharacteristic
59#103×C151C2211yescharacteristic
60#102×C151C2211yescharacteristic
61#14559005—22no—
62#14559005—41no—
63#14559004—22no—
64#14559004—22no—
65#14559004—41no—
66#14559004—41no—
67#14559003—22no—
68#14559003—41no—
69C2×Dic302C2311yescharacteristic
70C2×Dic302C2311yescharacteristic
71C2×D604—21no—
72C2×D604—21no—
73C2×D604C2311yescharacteristic
74C2×D604C2311yescharacteristic
75C2×C22⋊D151—21no—
76C2×C22⋊D151—21no—
77C2×C22⋊D151—21no—
78C2×C22⋊D151—21no—
79C2×C22⋊D151—21no—
80C2×C22⋊D151D411yescharacteristic
81C22×Dic151—21no—
82C2×C4×D151—21no—
83C2×C4×D151—21no—
84C2×C4×D151—21no—
85C2×C4×D151—21no—
86C2×C4×D151C2311yescharacteristic
87Dic604—22no—
88#14558994—22no—
89#14558993—22no—
90#14558993D414yescomplemented
91#14558992—41no—
92#14558991—41no—
93D1208—22no—
94#14558989—22no—
95C2×C151⋊C8C2311yescharacteristic
96C2×C151⋊C8C2311yescharacteristic
97C8×D151—22no—
98C4⋊Dic151—21no—
99Dic151⋊C4—21no—
100Dic151⋊C4—21no—
101Dic151⋊C4—21no—
102Dic151⋊C4D411yescharacteristic
103C22⋊Dic151D411yescharacteristic
104(C2×D151)⋊C4—21no—
105(C2×D151)⋊C4—21no—
106(C2×D151)⋊C4—21no—
107(C2×D151)⋊C4D411yescharacteristic
108C4×Dic151—21no—
109C4×Dic151C2311yescharacteristic
110C2×Q8×C151C2311yescharacteristic
111C2×D4×C151—21no—
112C2×D4×C151C2311yescharacteristic
113C22×C4×C151C2311yescharacteristic
114SD16×C151—22no—
115C2×C8×C151—22no—
116C2×C8×C151C2311yescharacteristic
117C2×C8×C151C2311yescharacteristic
118C4⋊C4×C151—21no—
119C4⋊C4×C151C2311yescharacteristic
120C4⋊C4×C151C2311yescharacteristic
121C22⋊C4×C151—21no—
122C22⋊C4×C151—21no—
123C22×D151—21no—
124C22×D151—21no—
125C22×D151C2×D411yescharacteristic
126Dic302—21no—
127Dic302—21no—
128Dic302—21no—
129Dic302C2×D412yes—
130D604—21no—
131D604—21no—
132D604—21no—
133D604—42no—
134D604—81no—
135D604C2×D412yes—
136C22⋊D151—22no—
137C22⋊D151—42no—
138C22⋊D151—42no—
139C22⋊D151—42no—
140C22⋊D151—42no—
141C22⋊D151—81no—
142C2×Dic151—21no—
143C2×Dic151—21no—
144C2×Dic151—42no—
145C2×Dic151C2×D411yescharacteristic
146C2×Dic151C2×D411yescharacteristic
147C2×Dic151C2×D411yescharacteristic
148C4×D151—21no—
149C4×D151—21no—
150C4×D151—42no—
151C4×D151—42no—
152C4×D151—42no—
153C4×D151—42no—
154C151⋊C8—21no—
155C151⋊C8—21no—
156C23×C151—21no—
157C23×C151C2×D411yescharacteristic
158Q8×C151—21no—
159Q8×C151—21no—
160D4×C151—21no—
161D4×C151—21no—
162D4×C151—81no—
163C2×C4×C151—21no—
164C2×C4×C151—21no—
165C2×C4×C151—21no—
166C2×C4×C151—21no—
167C2×C4×C151—21no—
168C2×C4×C151C2×D411yescharacteristic
169C2×C4×C151C2411yescharacteristic
170C8×C151—21no—
171C8×C151C2×D412yes—
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—41no—
190C4×C151—41no—
191C4×C151—41no—
192C4×C151C22×D411yescharacteristic
193C4×C151H(5,𝔽2)11yescharacteristic
194Dic151—21no—
195Dic151—22no—
196Dic151—21no—
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#465D15111yescharacteristic, complemented
216#462—1511no—
217#459—1511no—
218#452—1511no—
219#452—1511no—
220#449—1511no—
221#449—1511no—
222C4×SD16—1511no—
223C8×D4—1511no—
224C2×#41—1511no—
225C2×#41—1511no—
226C2×#41—1511no—
227C2×#41—1511no—
228#135—3024no—
229#135—3024no—
230C2×Q16—1511no—
231C2×Q16—1511no—
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×C8C2×D15111yescharacteristic
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#121C2×D15111yescharacteristic
253C4×Q8—1511no—
254C4×D4—3021no—
255C4×D4—1511no—
256C4×D4—1511no—
257C2×C4⋊C4—3021no—
258#106C2×D15111yescharacteristic
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⋊C8—1511no—
268C4×C8—1511no—
269#41—3022no—
270#41—3022no—
271#41—3022no—
272#41—3022no—
273#41—6041no—
274#41—6041no—
275#41—6041no—
276#41—6041no—
277C2×Q8—1511no—
278C2×Q8—1511no—
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—3021no—
293C22×C4—3021no—
294C22×C4—3021no—
295C22×C4—3021no—
296C22×C4—3021no—
297C22×C4—1511no—
298C22×C4C22×D15111yescharacteristic
299Q16—3022no—
300Q16—3022no—
301SD16—22no—
302SD16—3022no—
303SD16—6041no—
304SD16—6041no—
305SD16—1514no—
306D8—3022no—
307D8—3022no—
308C2×C8—22no—
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⋊C4C22×D15111yescharacteristic
321C4⋊C4C22×D15111yescharacteristic
322C22⋊C4—21no—
323C22⋊C4—21no—
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—3021no—
339Q8—3021no—
340Q8—3021no—
341Q8—1512no—
342D4—21no—
343D4—21no—
344D4—81no—
345D4—3022no—
346D4—3021no—
347D4—3021no—
348D4—3021no—
349D4—6042no—
350D4—6042no—
351D4—6042no—
352D4—6042no—
353D4—6042no—
354D4—1512no—
355D4—12081no—
356D4—12081no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—3021no—
363C2×C4—3021no—
364C2×C4—3021no—
365C2×C4—3021no—
366C2×C4—6042no—
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—3021no—
378C8—3021no—
379C8D4×D15112yes—
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—41no—
398C4—41no—
399C4—41no—
400C4—3021no—
401C4—3021no—
402C4—3022no—
403C4—6041no—
404C4—1512no—
405C4C2×D4×D15111yescharacteristic
406C4#1801278511yescharacteristic
407C2—41no—
408C2—81no—
409C2—6041no—
410C2—6042no—
411C2—12081no—
412C2#2375284611yescharacteristic
413C2#135×D15111yescharacteristic
414C2#2375301811yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#465×C151C2
socleC22×C151C22×D4
hypercenter#465D151
hypocenterC151#3284
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. C2×#18012761C2semidirect
2. C2×#18012760C2semidirect
3. #23752880C2semidirect
4. #23752864C2semidirect
5. #23752583C2semidirect
6. #23752442C2semidirect
7. #23752421C2semidirect
8. #23752406C2semidirect
9. #23752375C2semidirect
10. #23752372C2semidirect
11. #23752360C2semidirect
12. #23752355C2semidirect
13. #23752299C2semidirect
14. C8×C22⋊D151C2semidirect
15. #465×C151C2semidirect
90. #14558993D4semidirect
198. Dic151#135semidirect
207. C151#3284semidirect
215. #465D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127612
C2×#180127602
#237528802
#237528642
#237525832
#237524422
#237524212
#237524062
#237523752
#237523722
#237523602
#237523552
#237522992
C8×C22⋊D1512
#465×C1512
#3284151