Finite Group Databasebeta

← #34078798

Subgroups — #34078798

Order 19328.

472 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18012771C211yesmaximal, characteristic, complemented
2C2×#18012747C211yesmaximal, characteristic, complemented
3#23752792C211yesmaximal, characteristic
4#23752785C211yesmaximal, characteristic, complemented
5#23752469C211yesmaximal, characteristic, complemented
6#23752461C211yesmaximal, characteristic, complemented
7#23752458C211yesmaximal, characteristic, complemented
8#23752451C211yesmaximal, characteristic, complemented
9#23752450C211yesmaximal, characteristic, complemented
10#23752443C211yesmaximal, characteristic, complemented
11#23752442C211yesmaximal, characteristic, complemented
12#23752251C211yesmaximal, characteristic, complemented
13#23752207C211yesmaximal, characteristic, complemented
14#103×D151C211yesmaximal, characteristic, complemented
15#470×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic
17C2×#14559004C2211yescharacteristic
18C2×Q8×D151C2211yescharacteristic
19#18012771—24no—
20C2×#14558994C2211yescharacteristic
21C2×#14558993C2211yescharacteristic
22C2×#14558991C2211yescharacteristic
23#18012747—24no—
24C2×#14558987C2211yescharacteristic
25C2×#14558987C2211yescharacteristic
26C22×C151⋊C8C2211yescharacteristic
27C2×C8×D151C2211yescharacteristic
28C2×C8×D151C2211yescharacteristic
29#18012738—21no—
30#18012725—21no—
31#18012724—21no—
32#18012721—21no—
33#18012719C2211yescharacteristic
34#18012718C2211yescharacteristic
35#18012717—21no—
36#18012715C2211yescharacteristic
37#18012715C2211yescharacteristic
38#18012714—21no—
39#18012714C2211yescharacteristic
40#18012713C2211yescharacteristic
41#18012712—21no—
42#18012712—21no—
43#18012697C2211yescharacteristic
44C4⋊C4×D151C2211yescharacteristic
45#18012673C2211yescharacteristic
46#18012672C2211yescharacteristic
47#18012670C2211yescharacteristic
48#18012664C2211yescharacteristic
49#18012663C2211yescharacteristic
50#18012663C2211yescharacteristic
51#18012662C2211yescharacteristic
52#18012661C2211yescharacteristic
53#18012659C2211yescharacteristic
54C2×Q16×C151C2211yescharacteristic
55C2×M16×C151C2211yescharacteristic
56C22⋊Q8×C151C2211yescharacteristic
57C22⋊Q8×C151C2211yescharacteristic
58#106×C151C2211yescharacteristic
59#103×C151C2211yescharacteristic
60#103×C151C2211yescharacteristic
61#14559005—22no—
62#14559005—22no—
63#14559004—22no—
64#14559004—22no—
65C2×Dic302—21no—
66C2×Dic302D411yescharacteristic
67C2×Dic302C2311yescharacteristic
68Q8×D151—22no—
69Q8×D151—22no—
70C2×D604—21no—
71C2×D604—21no—
72C2×D604D411yescharacteristic
73C2×D604C2311yescharacteristic
74C2×C22⋊D151—21no—
75C2×C22⋊D151D411yescharacteristic
76C2×C22⋊D151D411yescharacteristic
77C2×C4×D151—21no—
78C2×C4×D151—21no—
79C2×C4×D151—21no—
80C2×C4×D151C2311yescharacteristic
81C2×C4×D151C2311yescharacteristic
82#14558994—22no—
83#14558993—22no—
84#14558991—22no—
85#14558987—22no—
86#14558987D414yescomplemented
87C2×C151⋊C8—22no—
88C2×C151⋊C8C2311yescharacteristic
89C2×C151⋊C8C2311yescharacteristic
90C8×D151—22no—
91C8×D151—22no—
92C4⋊Dic151—21no—
93C4⋊Dic151C2311yescharacteristic
94C4⋊Dic151C2311yescharacteristic
95Dic151⋊C4—21no—
96Dic151⋊C4—21no—
97Dic151⋊C4—21no—
98Dic151⋊C4—21no—
99C22⋊Dic151—21no—
100(C2×D151)⋊C4—21no—
101(C2×D151)⋊C4—21no—
102(C2×D151)⋊C4—21no—
103(C2×D151)⋊C4—21no—
104(C2×D151)⋊C4—21no—
105(C2×D151)⋊C4—21no—
106C4×Dic151—21no—
107C2×Q8×C151C2311yescharacteristic
108C2×Q8×C151C2311yescharacteristic
109C22×C4×C151C2311yescharacteristic
110Q16×C151—22no—
111M16×C151—22no—
112C2×C8×C151C2311yescharacteristic
113C2×C8×C151C2311yescharacteristic
114C4⋊C4×C151—21no—
115C4⋊C4×C151—21no—
116C4⋊C4×C151C2311yescharacteristic
117C4⋊C4×C151C2311yescharacteristic
118C22⋊C4×C151—21no—
119C22⋊C4×C151—21no—
120C22×D151—21no—
121C22×D151C2×D411yescharacteristic
122C22×D151C2×D411yescharacteristic
123Dic302—22no—
124Dic302—21no—
125Dic302—21no—
126Dic302—42no—
127D604—22no—
128D604—21no—
129D604—21no—
130D604—42no—
131D604—81no—
132C22⋊D151—22no—
133C22⋊D151—22no—
134C22⋊D151—81no—
135C2×Dic151—21no—
136C2×Dic151—21no—
137C2×Dic151—21no—
138C2×Dic151C2×D411yescharacteristic
139C2×Dic151C2×D411yescharacteristic
140C4×D151—21no—
141C4×D151—21no—
142C4×D151—42no—
143C4×D151—42no—
144C4×D151—81no—
145C4×D151C2×D412yes—
146C4×D151#4112yes—
147C151⋊C8—21no—
148C151⋊C8C2×D412yes—
149C23×C151C2×D411yescharacteristic
150Q8×C151—21no—
151Q8×C151—21no—
152Q8×C151—21no—
153Q8×C151—21no—
154C2×C4×C151—21no—
155C2×C4×C151—21no—
156C2×C4×C151—21no—
157C2×C4×C151—21no—
158C2×C4×C151—21no—
159C2×C4×C151—21no—
160C2×C4×C151C2×D411yescharacteristic
161C2×C4×C151C2411yescharacteristic
162C8×C151—21no—
163C8×C151C2×D412yes—
164C22×C151—21no—
165C22×C151—21no—
166C22×C151—21no—
167C22×C151C22×D411yescharacteristic
168C2×D151—21no—
169C2×D151—21no—
170C2×D151—21no—
171C2×D151—21no—
172C2×D151—21no—
173C2×D151—41no—
174C2×D151—41no—
175C2×D151—41no—
176C2×D151#12112yes—
177C4×C151—21no—
178C4×C151—41no—
179C4×C151—41no—
180C4×C151—41no—
181C4×C151—41no—
182C4×C151C22×D411yescharacteristic
183C4×C151C2×#4111yescharacteristic
184Dic151—21no—
185Dic151—41no—
186Dic151—41no—
187Dic151—41no—
188Dic151#12112yes—
189C2×C151—41no—
190C2×C151C2×#12111yescharacteristic
191C2×C151#57711yescharacteristic
192C2×C151#57811yescharacteristic
193D151—22no—
194D151—41no—
195D151—81no—
196C151#306311yescharacteristic, complemented, Sylow
197#3063—1511nomaximal, Sylow
198C2×#137—1511no—
199C2×#131—1511no—
200#537—1511no—
201#536—1511no—
202#470—1511no—
203#470D15111yescharacteristic, complemented
204#468—1511no—
205#468—1511no—
206#467—1511no—
207#467—1511no—
208#465—1511no—
209#465—1511no—
210#428—1511no—
211#416—1511no—
212C2×#103—1511no—
213C2×#41—1511no—
214C2×#41—1511no—
215C22×Q8—1511no—
216#137—3024no—
217C2×Q16—1511no—
218C2×Q16C2×D15111yescharacteristic
219C2×SD16—1511no—
220C2×SD16—1511no—
221#131—3024no—
222C2×M16—1511no—
223C2×M16—1511no—
224C2×M16C2×D15111yescharacteristic
225C22×C8—1511no—
226C22×C8—1511no—
227C22×C8—1511no—
228C4⋊Q8—3021no—
229#124—3021no—
230#123—3021no—
231#123—3021no—
232C22⋊Q8—3021no—
233C22⋊Q8—1511no—
234C22⋊Q8—1511no—
235C22⋊Q8—1511no—
236C22⋊Q8—1511no—
237C22⋊Q8C2×D15111yescharacteristic
238C22⋊Q8C2×D15111yescharacteristic
239#121—3021no—
240#121—3021no—
241#121—3021no—
242#121—1511no—
243#121—1511no—
244#117—1511no—
245C2×C4⋊C4—1511no—
246#107—1511no—
247#107—1511no—
248#106—1511no—
249#106C2×D15111yescharacteristic
250#103—1511no—
251#103—1511no—
252#103—1511no—
253#103—1511no—
254#103C2×D15111yescharacteristic
255#103C2×D15111yescharacteristic
256#102—1511no—
257#102—1511no—
258#41—3022no—
259#41—3022no—
260#41—3022no—
261#41—3022no—
262C2×Q8—3021no—
263C2×Q8—3022no—
264C2×Q8—3022no—
265C2×Q8—1511no—
266C2×Q8—1511no—
267C2×Q8C22×D15111yescharacteristic
268C2×Q8C22×D15111yescharacteristic
269C2×D4—3021no—
270C2×D4—3021no—
271C2×D4—3021no—
272C2×D4—1511no—
273C2×D4—1511no—
274C2×D4—1511no—
275C2×D4—1511no—
276C22×C4—3021no—
277C22×C4—3021no—
278C22×C4—3021no—
279C22×C4—1511no—
280C22×C4—1511no—
281C22×C4C22×D15111yescharacteristic
282Q16—22no—
283Q16—3022no—
284SD16—3022no—
285SD16—3022no—
286M16—22no—
287M16—3022no—
288M16—1514no—
289C2×C8—3022no—
290C2×C8—3022no—
291C2×C8—3022no—
292C2×C8—1511no—
293C2×C8—1511no—
294C2×C8C22×D15111yescharacteristic
295C2×C8C22×D15111yescharacteristic
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—3021no—
299C4⋊C4—3021no—
300C4⋊C4—3021no—
301C4⋊C4—3021no—
302C4⋊C4—3021no—
303C4⋊C4—1511no—
304C4⋊C4—1511no—
305C4⋊C4C22×D15111yescharacteristic
306C4⋊C4C22×D15111yescharacteristic
307C22⋊C4—21no—
308C22⋊C4—21no—
309C22⋊C4—3021no—
310C22⋊C4—3021no—
311C22⋊C4—3021no—
312C22⋊C4—3021no—
313C22⋊C4—3021no—
314C22⋊C4—3021no—
315C22⋊C4—3021no—
316C42—3021no—
317C23—3021no—
318C23—1511no—
319C23—1511no—
320C23D4×D15111yescharacteristic
321Q8—21no—
322Q8—21no—
323Q8—21no—
324Q8—21no—
325Q8—3022no—
326Q8—3021no—
327Q8—3021no—
328Q8—6042no—
329D4—3022no—
330D4—3022no—
331D4—3022no—
332D4—3021no—
333D4—3021no—
334D4—6042no—
335D4—12081no—
336D4—12081no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—3021no—
344C2×C4—3021no—
345C2×C4—3021no—
346C2×C4—3021no—
347C2×C4—3021no—
348C2×C4—6042no—
349C2×C4—6042no—
350C2×C4—1511no—
351C2×C4—1511no—
352C2×C4—1512no—
353C2×C4—1512no—
354C2×C4—12081no—
355C2×C4D4×D15111yescharacteristic
356C2×C4C23×D15111yescharacteristic
357C8—21no—
358C8—3021no—
359C8—1512no—
360C8D4×D15112yes—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—3021no—
365C22—3021no—
366C22—3021no—
367C22—3021no—
368C22—3021no—
369C22—6041no—
370C22—6041no—
371C22—6041no—
372C22—1512no—
373C22C2×D4×D15111yescharacteristic
374C4—21no—
375C4—41no—
376C4—41no—
377C4—41no—
378C4—41no—
379C4—3021no—
380C4—6041no—
381C4—6041no—
382C4—6041no—
383C4—1512no—
384C4C2×D4×D15111yescharacteristic
385C4#41×D15111yescharacteristic
386C2—41no—
387C2—3022no—
388C2—6041no—
389C2—12081no—
390C2#121×D15111yescharacteristic
391C2#2375302111yescharacteristic
392C2#2375302811yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#470×C151C2
socleC22×C151C22×D4
prime radical#23752792C2
hypercenter#470D151
hypocenterC151#3063
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. C2×#18012771C2semidirect
2. C2×#18012747C2semidirect
4. #23752785C2semidirect
5. #23752469C2semidirect
6. #23752461C2semidirect
7. #23752458C2semidirect
8. #23752451C2semidirect
9. #23752450C2semidirect
10. #23752443C2semidirect
11. #23752442C2semidirect
12. #23752251C2semidirect
13. #23752207C2semidirect
14. #103×D151C2semidirect
15. #470×C151C2semidirect
86. #14558987D4semidirect
196. C151#3063semidirect
203. #470D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127712
C2×#180127472
#237527922
#237527852
#237524692
#237524612
#237524582
#237524512
#237524502
#237524432
#237524422
#237522512
#237522072
#103×D1512
#470×C1512
#3063151