Finite Group Databasebeta

← #34080754

Subgroups — #34080754

Order 19328.

472 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18012769C211yesmaximal, characteristic, complemented
2C2×#18012768C211yesmaximal, characteristic, complemented
3#23752875C211yesmaximal, characteristic, complemented
4#23752861C211yesmaximal, characteristic
5#23752590C211yesmaximal, characteristic, complemented
6#23752469C211yesmaximal, characteristic, complemented
7#23752468C211yesmaximal, characteristic, complemented
8#23752421C211yesmaximal, characteristic, complemented
9#23752415C211yesmaximal, characteristic, complemented
10#23752375C211yesmaximal, characteristic, complemented
11#23752370C211yesmaximal, characteristic, complemented
12#23752366C211yesmaximal, characteristic, complemented
13#23752303C211yesmaximal, characteristic, complemented
14#23752287C211yesmaximal, characteristic, complemented
15#452×C151C211yesmaximal, characteristic, complemented
16C2×#14559003C2211yescharacteristic
17C22×Dic302C2211yescharacteristic
18C2×Q8×D151C2211yescharacteristic
19#18012769—24no—
20#18012768—24no—
21C2×Dic604C2211yescharacteristic
22C2×Dic604C2211yescharacteristic
23C2×#14558994C2211yescharacteristic
24C2×#14558994C2211yescharacteristic
25C2×#14558994C2211yescharacteristic
26C2×#14558992C2211yescharacteristic
27C2×#14558992C2211yescharacteristic
28C2×#14558988C2211yescharacteristic
29C2×#14558987C2211yescharacteristic
30#18012738—21no—
31#18012737C2211yescharacteristic
32#18012737C2211yescharacteristic
33#18012722—21no—
34#18012720—21no—
35#18012719C2211yescharacteristic
36#18012718C2211yescharacteristic
37#18012717—21no—
38#18012716—21no—
39#18012715C2211yescharacteristic
40#18012711—21no—
41#18012704C2211yescharacteristic
42D4×Dic151C2211yescharacteristic
43C4×C22⋊D151C2211yescharacteristic
44(C22⋊D151)⋊C4—21no—
45C2×Dic151⋊C4—21no—
46#18012670C2211yescharacteristic
47Dic151⋊C8C2211yescharacteristic
48#18012664C2211yescharacteristic
49#18012664C2211yescharacteristic
50#18012663C2211yescharacteristic
51#18012662C2211yescharacteristic
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#14559003—22no—
62#14559003—41no—
63C2×Dic302—21no—
64C2×Dic302—22no—
65C2×Dic302—21no—
66C2×Dic302—41no—
67C2×Dic302C2311yescharacteristic
68C2×Dic302C2311yescharacteristic
69C2×Dic302C2311yescharacteristic
70Q8×D151—22no—
71Q8×D151—41no—
72C2×C22⋊D151—21no—
73C2×C22⋊D151D411yescharacteristic
74C22×Dic151—21no—
75C22×Dic151—21no—
76C22×Dic151—21no—
77C2×C4×D151—21no—
78C2×C4×D151C2311yescharacteristic
79Dic604—22no—
80Dic604—41no—
81#14558994—22no—
82#14558994—22no—
83#14558994—22no—
84#14558992—22no—
85#14558992D414yescomplemented
86#14558988—22no—
87#14558987—22no—
88C2×C151⋊C8C2311yescharacteristic
89C2×C151⋊C8C2311yescharacteristic
90C4⋊Dic151—21no—
91C4⋊Dic151C2311yescharacteristic
92Dic151⋊C4—21no—
93Dic151⋊C4—21no—
94Dic151⋊C4—21no—
95Dic151⋊C4—21no—
96Dic151⋊C4—21no—
97Dic151⋊C4—21no—
98Dic151⋊C4—21no—
99Dic151⋊C4D411yescharacteristic
100C22⋊Dic151—21no—
101C22⋊Dic151—21no—
102C22⋊Dic151D411yescharacteristic
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—41no—
117SD16×C151—22no—
118C2×C8×C151C2311yescharacteristic
119C2×C8×C151C2311yescharacteristic
120C4⋊C4×C151—21no—
121C4⋊C4×C151C2311yescharacteristic
122C22⋊C4×C151—21no—
123C22×D151C2×D411yescharacteristic
124Dic302—21no—
125Dic302—21no—
126Dic302—21no—
127Dic302—21no—
128Dic302—21no—
129Dic302—42no—
130Dic302—42no—
131Dic302C2×D412yes—
132C22⋊D151—22no—
133C22⋊D151—42no—
134C2×Dic151—21no—
135C2×Dic151—21no—
136C2×Dic151—21no—
137C2×Dic151—21no—
138C2×Dic151—42no—
139C2×Dic151—42no—
140C2×Dic151—42no—
141C2×Dic151C2×D411yescharacteristic
142C2×Dic151C2×D411yescharacteristic
143C2×Dic151C2×D411yescharacteristic
144C4×D151—21no—
145C4×D151—21no—
146C4×D151—42no—
147C151⋊C8—21no—
148C151⋊C8C2×D412yes—
149C23×C151—21no—
150C23×C151C2×D411yescharacteristic
151Q8×C151—21no—
152Q8×C151—21no—
153Q8×C151—21no—
154Q8×C151—21no—
155D4×C151—21no—
156D4×C151—42no—
157D4×C151C2×D412yes—
158C2×C4×C151—21no—
159C2×C4×C151—21no—
160C2×C4×C151—21no—
161C2×C4×C151—21no—
162C2×C4×C151—21no—
163C2×C4×C151—42no—
164C2×C4×C151C2×D411yescharacteristic
165C2×C4×C151C2411yescharacteristic
166C8×C151—21no—
167C8×C151—21no—
168C22×C151—21no—
169C22×C151—22no—
170C22×C151—21no—
171C22×C151—21no—
172C22×C151—41no—
173C22×C151—41no—
174C22×C151C22×D411yescharacteristic
175C2×D151—21no—
176C2×D151—21no—
177C2×D151—21no—
178C4×C151—21no—
179C4×C151—41no—
180C4×C151—41no—
181C4×C151—41no—
182C4×C151C22×D411yescharacteristic
183C4×C151H(5,𝔽2)11yescharacteristic
184Dic151—21no—
185Dic151—22no—
186Dic151—21no—
187Dic151—41no—
188Dic151—41no—
189Dic151—41no—
190Dic151#13712yescomplemented
191C2×C151—41no—
192C2×C151—42no—
193C2×C151D4211yescharacteristic
194C2×C151C2×#13711yescharacteristic
195C2×C151#57811yescharacteristic
196D151—41no—
197C151#327611yescharacteristic, complemented, Sylow
198#3276—1511nomaximal, Sylow
199C2×#137—1511no—
200C2×#137—1511no—
201D4×Q8—1511no—
202#547—1511no—
203#494—1511no—
204#470—1511no—
205#470—1511no—
206#462—1511no—
207#461—1511no—
208#452—1511no—
209#452D15111yescharacteristic, complemented
210#451—1511no—
211#451—1511no—
212C4×SD16—1511no—
213#436—1511no—
214C2×#41—1511no—
215C2×#41C2×D15111yescharacteristic
216C22×Q8—1511no—
217C22×Q8—1511no—
218#137—3024no—
219#137—3024no—
220C2×Q16—1511no—
221C2×Q16—1511no—
222C2×Q16—1511no—
223C2×Q16—1511no—
224C2×Q16—1511no—
225C2×Q16C2×D15111yescharacteristic
226C2×SD16—1511no—
227C2×SD16—1511no—
228C2×SD16C2×D15111yescharacteristic
229C2×M16—1511no—
230C2×M16—1511no—
231C4⋊Q8—3021no—
232C4⋊Q8—1511no—
233C4⋊Q8—1511no—
234#123—3021no—
235#123—3021no—
236C22⋊Q8—3021no—
237C22⋊Q8—3021no—
238C22⋊Q8—1511no—
239C22⋊Q8—1511no—
240C22⋊Q8—1511no—
241C22⋊Q8C2×D15111yescharacteristic
242#121—3021no—
243C4×Q8—1511no—
244C4×D4—3021no—
245C4×D4—1511no—
246C4×D4—1511no—
247C2×C4⋊C4—3021no—
248#106—1511no—
249C4⋊C8—1511no—
250#103—1511no—
251#103—1511no—
252#103—1511no—
253#103—1511no—
254#103C2×D15111yescharacteristic
255#102C2×D15111yescharacteristic
256C22⋊C8—1511no—
257C22⋊C8C2×D15111yescharacteristic
258C4×C8—1511no—
259#41—22no—
260#41—41no—
261#41—3022no—
262#41—6041no—
263C2×Q8—3021no—
264C2×Q8—3022no—
265C2×Q8—3021no—
266C2×Q8—3022no—
267C2×Q8—6041no—
268C2×Q8—6041no—
269C2×Q8—1511no—
270C2×Q8—1511no—
271C2×Q8—1511no—
272C2×Q8C22×D15111yescharacteristic
273C2×Q8C22×D15111yescharacteristic
274C2×D4—21no—
275C2×D4—3021no—
276C2×D4—1511no—
277C2×D4C22×D15111yescharacteristic
278C22×C4—21no—
279C22×C4—3021no—
280C22×C4—3021no—
281C22×C4—3021no—
282C22×C4—3021no—
283C22×C4—1511no—
284C22×C4C22×D15111yescharacteristic
285Q16—41no—
286Q16—3022no—
287Q16—3022no—
288Q16—3022no—
289Q16—3022no—
290Q16—6041no—
291SD16—22no—
292SD16—3022no—
293SD16—1514no—
294M16—3022no—
295M16—3022no—
296C2×C8—1511no—
297C2×C8—1511no—
298C2×C8C22×D15111yescharacteristic
299C2×C8C22×D15111yescharacteristic
300C4⋊C4—21no—
301C4⋊C4—3021no—
302C4⋊C4—3021no—
303C4⋊C4—3021no—
304C4⋊C4—3021no—
305C4⋊C4—3021no—
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—1511no—
318C22⋊C4—1511no—
319C42—3021no—
320C42—1511no—
321C23—21no—
322C23—1511no—
323C23D4×D15111yescharacteristic
324Q8—21no—
325Q8—21no—
326Q8—21no—
327Q8—21no—
328Q8—3021no—
329Q8—3021no—
330Q8—3021no—
331Q8—3021no—
332Q8—3021no—
333Q8—6042no—
334Q8—6042no—
335Q8—1512no—
336D4—21no—
337D4—42no—
338D4—3022no—
339D4—6042no—
340D4D4×D15112yes—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—42no—
347C2×C4—3021no—
348C2×C4—3021no—
349C2×C4—3021no—
350C2×C4—3021no—
351C2×C4—3021no—
352C2×C4—3021no—
353C2×C4—6042no—
354C2×C4—6042no—
355C2×C4—6042no—
356C2×C4—6042no—
357C2×C4—1511no—
358C2×C4—1511no—
359C2×C4—1511no—
360C2×C4D4×D15111yescharacteristic
361C2×C4C23×D15111yescharacteristic
362C8—21no—
363C8—21no—
364C8—3021no—
365C8—1512no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—22no—
370C22—41no—
371C22—41no—
372C22—3021no—
373C22—3021no—
374C22—3021no—
375C22C2×D4×D15111yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—3021no—
381C4—3021no—
382C4—3022no—
383C4—6041no—
384C4—6041no—
385C4—6041no—
386C4—1512no—
387C4C2×D4×D15111yescharacteristic
388C4#1801278411yescharacteristic
389C2—41no—
390C2—42no—
391C2—6041no—
392C2#2375284411yescharacteristic
393C2#137×D15111yescharacteristic
394C2#2375302611yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#452×C151C2
socleC22×C151C22×D4
prime radical#23752861C2
hypercenter#452D151
hypocenterC151#3276
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×#18012769C2semidirect
2. C2×#18012768C2semidirect
3. #23752875C2semidirect
5. #23752590C2semidirect
6. #23752469C2semidirect
7. #23752468C2semidirect
8. #23752421C2semidirect
9. #23752415C2semidirect
10. #23752375C2semidirect
11. #23752370C2semidirect
12. #23752366C2semidirect
13. #23752303C2semidirect
14. #23752287C2semidirect
15. #452×C151C2semidirect
85. #14558992D4semidirect
190. Dic151#137semidirect
197. C151#3276semidirect
209. #452D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127692
C2×#180127682
#237528752
#237528612
#237525902
#237524692
#237524682
#237524212
#237524152
#237523752
#237523702
#237523662
#237523032
#237522872
#452×C1512
#3276151