Finite Group Databasebeta

← #34080849

Subgroups — #34080849

Order 19328.

482 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18012759C211yesmaximal, characteristic, complemented
2C2×Q16×D151C211yesmaximal, characteristic, complemented
3#23752872C211yesmaximal, characteristic, complemented
4#23752869C211yesmaximal, characteristic, complemented
5#23752593C211yesmaximal, characteristic, complemented
6#23752451C211yesmaximal, characteristic, complemented
7#23752447C211yesmaximal, characteristic, complemented
8#23752436C211yesmaximal, characteristic, complemented
9#23752433C211yesmaximal, characteristic, complemented
10#23752376C211yesmaximal, characteristic, complemented
11#23752352C211yesmaximal, characteristic, complemented
12#23752349C211yesmaximal, characteristic, complemented
13#23752304C211yesmaximal, characteristic, complemented
14(C22⋊D151)⋊C8C211yesmaximal, characteristic, complemented
15#452×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic
17C2×Q8×D151C2211yescharacteristic
18C2×Q8×D151C2211yescharacteristic
19#18012759—24no—
20C2×Dic604C2211yescharacteristic
21C2×#14558994C2211yescharacteristic
22C2×#14558994C2211yescharacteristic
23Q16×D151—24no—
24C2×#14558993C2211yescharacteristic
25C2×#14558992C2211yescharacteristic
26C2×#14558991C2211yescharacteristic
27C2×#14558989C2211yescharacteristic
28C22×C151⋊C8C2211yescharacteristic
29C2×C8×D151C2211yescharacteristic
30#18012728C2211yescharacteristic
31#18012726—21no—
32#18012726C2211yescharacteristic
33#18012725—21no—
34#18012718—21no—
35#18012718C2211yescharacteristic
36#18012717—21no—
37#18012714C2211yescharacteristic
38#18012712—21no—
39#18012710—21no—
40#18012710C2211yescharacteristic
41Q8×Dic151C2211yescharacteristic
42#18012704C2211yescharacteristic
43#18012701—21no—
44C4×C22⋊D151—21no—
45C4×C22⋊D151C2211yescharacteristic
46#18012672C2211yescharacteristic
47Dic151⋊C8C2211yescharacteristic
48#18012664C2211yescharacteristic
49#18012663C2211yescharacteristic
50#18012662C2211yescharacteristic
51#18012661C2211yescharacteristic
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#14559004—22no—
62#14559004—41no—
63C2×Dic302—21no—
64C2×Dic302—21no—
65C2×Dic302C2311yescharacteristic
66C2×Dic302C2311yescharacteristic
67Q8×D151—22no—
68Q8×D151—22no—
69Q8×D151—41no—
70Q8×D151—41no—
71C2×D604—21no—
72C2×D604C2311yescharacteristic
73C2×C22⋊D151—21no—
74C2×C22⋊D151—21no—
75C2×C22⋊D151D411yescharacteristic
76C2×C4×D151—21no—
77C2×C4×D151—21no—
78C2×C4×D151—21no—
79C2×C4×D151C2311yescharacteristic
80Dic604—22no—
81#14558994—22no—
82#14558994D414yescomplemented
83#14558993—41no—
84#14558992—22no—
85#14558991—22no—
86#14558989—22no—
87C2×C151⋊C8—22no—
88C2×C151⋊C8C2311yescharacteristic
89C2×C151⋊C8C2311yescharacteristic
90C8×D151—22no—
91C4⋊Dic151—21no—
92C4⋊Dic151C2311yescharacteristic
93Dic151⋊C4—21no—
94Dic151⋊C4—21no—
95Dic151⋊C4D411yescharacteristic
96C22⋊Dic151—21no—
97C22⋊Dic151—21no—
98C22⋊Dic151—21no—
99C22⋊Dic151—21no—
100C22⋊Dic151D411yescharacteristic
101(C2×D151)⋊C4—21no—
102(C2×D151)⋊C4—21no—
103(C2×D151)⋊C4—21no—
104(C2×D151)⋊C4D411yescharacteristic
105C4×Dic151—21no—
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×D151C2×D411yescharacteristic
125Dic302—21no—
126Dic302—21no—
127Dic302—21no—
128Dic302—42no—
129Dic302—42no—
130Dic302C2×D412yes—
131D604—21no—
132D604—21no—
133D604—42no—
134C22⋊D151—22no—
135C22⋊D151—42no—
136C22⋊D151—42no—
137C2×Dic151—21no—
138C2×Dic151—21no—
139C2×Dic151—21no—
140C2×Dic151C2×D411yescharacteristic
141C2×Dic151C2×D411yescharacteristic
142C2×Dic151C2×D411yescharacteristic
143C4×D151—21no—
144C4×D151—21no—
145C4×D151—42no—
146C4×D151—42no—
147C4×D151—42no—
148C151⋊C8—21no—
149C151⋊C8C2×D412yes—
150C23×C151—21no—
151C23×C151C2×D411yescharacteristic
152Q8×C151—21no—
153Q8×C151—21no—
154Q8×C151—21no—
155Q8×C151C2×D412yes—
156D4×C151—21no—
157D4×C151—21no—
158D4×C151—42no—
159C2×C4×C151—21no—
160C2×C4×C151—21no—
161C2×C4×C151—21no—
162C2×C4×C151—21no—
163C2×C4×C151—21no—
164C2×C4×C151—42no—
165C2×C4×C151C2×D411yescharacteristic
166C2×C4×C151C2411yescharacteristic
167C8×C151—21no—
168C8×C151—21no—
169C22×C151—21no—
170C22×C151—21no—
171C22×C151—21no—
172C22×C151—41no—
173C22×C151—41no—
174C22×C151—41no—
175C22×C151C22×D411yescharacteristic
176C2×D151—21no—
177C2×D151—21no—
178C2×D151—41no—
179C2×D151—41no—
180C2×D151—41no—
181C2×D151#13512yescomplemented
182C4×C151—21no—
183C4×C151—22no—
184C4×C151—41no—
185C4×C151—41no—
186C4×C151C22×D411yescharacteristic
187C4×C151H(5,𝔽2)11yescharacteristic
188Dic151—21no—
189Dic151—22no—
190Dic151—21no—
191Dic151—21no—
192Dic151—41no—
193Dic151—41no—
194C2×C151—41no—
195C2×C151—81no—
196C2×C151D4211yescharacteristic
197C2×C151C2×#13511yescharacteristic
198C2×C151#57811yescharacteristic
199D151—22no—
200D151—81no—
201C151#328511yescharacteristic, complemented, Sylow
202#3285—1511nomaximal, Sylow
203C2×#135—1511no—
204C22×Q16—1511no—
205#548—1511no—
206#548—1511no—
207#495—1511no—
208#467—1511no—
209#466—1511no—
210#464—1511no—
211#464—1511no—
212#452—1511no—
213#452D15111yescharacteristic, complemented
214#448—1511no—
215#448—1511no—
216C4×Q16—1511no—
217C8×D4—1511no—
218C2×#41—1511no—
219C2×#41C2×D15111yescharacteristic
220C22×Q8—1511no—
221C22×Q8—1511no—
222#135—3024no—
223C2×Q16—3024no—
224C2×Q16—1511no—
225C2×Q16—1511no—
226C2×Q16—1511no—
227C2×Q16C2×D15111yescharacteristic
228C2×SD16—1511no—
229C2×SD16—1511no—
230C2×SD16—1511no—
231C2×SD16C2×D15111yescharacteristic
232C2×D8—1511no—
233C22×C8—1511no—
234C22×C8—1511no—
235#124—3021no—
236#124—3021no—
237#124—1511no—
238#124—1511no—
239C22⋊Q8—3021no—
240C22⋊Q8—3021no—
241C22⋊Q8—1511no—
242C22⋊Q8C2×D15111yescharacteristic
243#121—3021no—
244#121—3021no—
245#121—1511no—
246#121—1511no—
247C4×Q8—1511no—
248C4×Q8—1511no—
249C4×D4—3021no—
250C4×D4—3021no—
251C4×D4—1511no—
252#107—1511no—
253C4⋊C8—1511no—
254#103—1511no—
255#103—1511no—
256#103—1511no—
257#103C2×D15111yescharacteristic
258#102—1511no—
259#102C2×D15111yescharacteristic
260C22⋊C8—1511no—
261C22⋊C8C2×D15111yescharacteristic
262C4×C8—1511no—
263#41—22no—
264#41—41no—
265#41—3022no—
266#41—6041no—
267C2×Q8—3021no—
268C2×Q8—3021no—
269C2×Q8—3022no—
270C2×Q8—3022no—
271C2×Q8—6041no—
272C2×Q8—6041no—
273C2×Q8—1511no—
274C2×Q8—1511no—
275C2×Q8C22×D15111yescharacteristic
276C2×Q8C22×D15111yescharacteristic
277C2×D4—21no—
278C2×D4—3021no—
279C2×D4—3021no—
280C2×D4—3021no—
281C2×D4—1511no—
282C2×D4—1511no—
283C2×D4C22×D15111yescharacteristic
284C22×C4—21no—
285C22×C4—3021no—
286C22×C4—3021no—
287C22×C4—3021no—
288C22×C4—1511no—
289C22×C4C22×D15111yescharacteristic
290Q16—22no—
291Q16—3022no—
292Q16—3022no—
293Q16—1514no—
294SD16—41no—
295SD16—3022no—
296SD16—3022no—
297SD16—6041no—
298D8—3022no—
299C2×C8—3022no—
300C2×C8—3022no—
301C2×C8—1511no—
302C2×C8—1511no—
303C2×C8C22×D15111yescharacteristic
304C2×C8C22×D15111yescharacteristic
305C4⋊C4—21no—
306C4⋊C4—3021no—
307C4⋊C4—3021no—
308C4⋊C4—3021no—
309C4⋊C4—1511no—
310C4⋊C4—1511no—
311C4⋊C4C22×D15111yescharacteristic
312C22⋊C4—21no—
313C22⋊C4—3021no—
314C22⋊C4—3021no—
315C22⋊C4—3021no—
316C22⋊C4—3021no—
317C22⋊C4—3021no—
318C22⋊C4—3021no—
319C22⋊C4—3021no—
320C22⋊C4—1511no—
321C22⋊C4—1511no—
322C42—3021no—
323C42—3021no—
324C42—1511no—
325C23—21no—
326C23—3021no—
327C23—1511no—
328C23D4×D15111yescharacteristic
329Q8—21no—
330Q8—21no—
331Q8—21no—
332Q8—3021no—
333Q8—3021no—
334Q8—3021no—
335Q8—6042no—
336Q8—6042no—
337Q8—1512no—
338Q8D4×D15112yes—
339D4—21no—
340D4—21no—
341D4—42no—
342D4—3022no—
343D4—3021no—
344D4—3021no—
345D4—6042no—
346D4—6042no—
347D4—6042no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—42no—
354C2×C4—3021no—
355C2×C4—3021no—
356C2×C4—3021no—
357C2×C4—3021no—
358C2×C4—3021no—
359C2×C4—6042no—
360C2×C4—6042no—
361C2×C4—6042no—
362C2×C4—1511no—
363C2×C4—1511no—
364C2×C4—1511no—
365C2×C4D4×D15111yescharacteristic
366C2×C4C23×D15111yescharacteristic
367C8—21no—
368C8—21no—
369C8—3021no—
370C8—1512no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—3021no—
378C22—3021no—
379C22—6041no—
380C22—6041no—
381C22—6041no—
382C22—1512no—
383C22C2×D4×D15111yescharacteristic
384C4—21no—
385C4—22no—
386C4—41no—
387C4—41no—
388C4—3021no—
389C4—3021no—
390C4—3021no—
391C4—3022no—
392C4—6041no—
393C4—6041no—
394C4C2×D4×D15111yescharacteristic
395C4#1801278411yescharacteristic
396C2—41no—
397C2—81no—
398C2—3022no—
399C2—12081no—
400C2#2375284411yescharacteristic
401C2#135×D15111yescharacteristic
402C2#2375302811yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#452×C151C2
socleC22×C151C22×D4
hypercenter#452D151
hypocenterC151#3285
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×#18012759C2semidirect
2. C2×Q16×D151C2semidirect
3. #23752872C2semidirect
4. #23752869C2semidirect
5. #23752593C2semidirect
6. #23752451C2semidirect
7. #23752447C2semidirect
8. #23752436C2semidirect
9. #23752433C2semidirect
10. #23752376C2semidirect
11. #23752352C2semidirect
12. #23752349C2semidirect
13. #23752304C2semidirect
14. (C22⋊D151)⋊C8C2semidirect
15. #452×C151C2semidirect
82. #14558994D4semidirect
181. C2×D151#135semidirect
201. C151#3285semidirect
213. #452D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127592
C2×Q16×D1512
#237528722
#237528692
#237525932
#237524512
#237524472
#237524362
#237524332
#237523762
#237523522
#237523492
#237523042
(C22⋊D151)⋊C82
#452×C1512
#3285151