Finite Group Databasebeta

← #34072098

Subgroups — #34072098

Order 19328.

652 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18012722C211yesmaximal, characteristic
2C2×C4×C22⋊D151C211yesmaximal, characteristic
3C2×#18012698C211yesmaximal, characteristic, complemented
4#23752109C211yesmaximal, characteristic, complemented
5#23752104C211yesmaximal, characteristic, complemented
6#23752101C211yesmaximal, characteristic, complemented
7#23752099C211yesmaximal, characteristic, complemented
8#23752094C211yesmaximal, characteristic, complemented
9#23752091C211yesmaximal, characteristic
10#23752086C211yesmaximal, characteristic, complemented
11#23752085C211yesmaximal, characteristic, complemented
12#23752063C211yesmaximal, characteristic, complemented
13C4×C22⋊Dic151C211yesmaximal, characteristic, complemented
14#23752059C211yesmaximal, characteristic, complemented
15C2×#95×C151C211yesmaximal, characteristic, complemented
16C22×C22⋊D151C2211yescharacteristic
17C22×C4×D151C2211yescharacteristic
18#18012722C418yescomplemented
19C4×C22⋊D151—24no—
20#18012698—24no—
21C2×C4⋊Dic151C2211yescharacteristic
22C2×C4⋊Dic151C2211yescharacteristic
23C2×Dic151⋊C4C2211yescharacteristic
24C2×Dic151⋊C4C2211yescharacteristic
25C2×Dic151⋊C4C2211yescharacteristic
26C2×Dic151⋊C4C2211yescharacteristic
27C2×Dic151⋊C4C2211yescharacteristic
28C2×C22⋊Dic151C2211yescharacteristic
29C2×C22⋊Dic151C2211yescharacteristic
30C2×C22⋊Dic151C2211yescharacteristic
31C2×(C2×D151)⋊C4C2211yescharacteristic
32C2×(C2×D151)⋊C4C2211yescharacteristic
33C2×(C2×D151)⋊C4C2211yescharacteristic
34C2×(C2×D151)⋊C4C2211yescharacteristic
35C2×(C2×D151)⋊C4C2211yescharacteristic
36C2×C4×Dic151C2211yescharacteristic
37C2×C4×Dic151C2211yescharacteristic
38C2×C4×Dic151C2211yescharacteristic
39C2×C4×Dic151C2211yescharacteristic
40C2×C4×Dic151C2211yescharacteristic
41C151⋊#95C2211yescharacteristic
42C151⋊#95C2211yescharacteristic
43C151⋊#95C2211yescharacteristic
44C151⋊#95C2211yescharacteristic
45C151⋊#95C2211yescharacteristic
46C151⋊#95C2211yescharacteristic
47C23×C4×C151C2211yescharacteristic
48C23×C4×C151C2211yescharacteristic
49C23×C4×C151C2211yescharacteristic
50#95×C151C2211yescharacteristic
51#95×C151C2211yescharacteristic
52#95×C151C2211yescharacteristic
53#95×C151C2211yescharacteristic
54C23×D151C2311yescharacteristic
55C2×C22⋊D151—22no—
56C2×C22⋊D151—22no—
57C2×C22⋊D151C2×C414yes—
58C22×Dic151C2311yescharacteristic
59C22×Dic151C2311yescharacteristic
60C22×Dic151C2311yescharacteristic
61C22×Dic151C2311yescharacteristic
62C22×Dic151C2311yescharacteristic
63C22×Dic151C2311yescharacteristic
64C22×Dic151C2311yescharacteristic
65C2×C4×D151—22no—
66C2×C4×D151—22no—
67C2×C4×D151—41no—
68C4⋊Dic151—22no—
69C4⋊Dic151—22no—
70Dic151⋊C4—22no—
71Dic151⋊C4—22no—
72Dic151⋊C4—41no—
73Dic151⋊C4C2×C414yescomplemented
74Dic151⋊C4C2×C414yescomplemented
75C22⋊Dic151—22no—
76C22⋊Dic151C2×C414yescomplemented
77C22⋊Dic151D414yes—
78(C2×D151)⋊C4—22no—
79(C2×D151)⋊C4—22no—
80(C2×D151)⋊C4—41no—
81(C2×D151)⋊C4C2×C414yescomplemented
82(C2×D151)⋊C4C2×C414yescomplemented
83C4×Dic151—22no—
84C4×Dic151—22no—
85C4×Dic151—22no—
86C4×Dic151—22no—
87C4×Dic151—41no—
88C24×C151C2311yescharacteristic
89C22×C4×C151—22no—
90C22×C4×C151—22no—
91C22×C4×C151—22no—
92C22×C4×C151—22no—
93C22×C4×C151—22no—
94C22×C4×C151—22no—
95C22×C4×C151—41no—
96C22×C4×C151—41no—
97C22×C4×C151C2×C414yescomplemented
98C22×C4×C151C2311yescharacteristic
99C22×C4×C151C2311yescharacteristic
100C22×C4×C151C2311yescharacteristic
101C22×C4×C151C2311yescharacteristic
102C22×C4×C151C2311yescharacteristic
103C22×C4×C151C2311yescharacteristic
104C22×D151—21no—
105C22×D151—21no—
106C22×D151—21no—
107C22×D151—21no—
108C22×D151—21no—
109C22×D151—21no—
110C22×D151C22×C412yes—
111C22⋊D151—28no—
112C2×Dic151—21no—
113C2×Dic151—21no—
114C2×Dic151—21no—
115C2×Dic151—21no—
116C2×Dic151—21no—
117C2×Dic151—21no—
118C2×Dic151—21no—
119C2×Dic151—21no—
120C2×Dic151—21no—
121C2×Dic151—21no—
122C2×Dic151—21no—
123C2×Dic151—21no—
124C2×Dic151—21no—
125C2×Dic151—21no—
126C2×Dic151—21no—
127C2×Dic151—21no—
128C2×Dic151C22×C412yes—
129C2×Dic151C22×C412yes—
130C2×Dic151C22×C412yes—
131C2×Dic151C2×D412yes—
132C2×Dic151C2×D412yes—
133C4×D151—44no—
134C23×C151—21no—
135C23×C151—21no—
136C23×C151—21no—
137C23×C151—21no—
138C23×C151C22×C412yes—
139C23×C151C2×D412yes—
140C23×C151#4112yes—
141C23×C151C2411yescharacteristic
142C2×C4×C151—28no—
143C2×C4×C151—21no—
144C2×C4×C151—21no—
145C2×C4×C151—21no—
146C2×C4×C151—21no—
147C2×C4×C151—21no—
148C2×C4×C151—21no—
149C2×C4×C151—21no—
150C2×C4×C151—21no—
151C2×C4×C151—21no—
152C2×C4×C151—21no—
153C2×C4×C151—21no—
154C2×C4×C151—21no—
155C2×C4×C151—21no—
156C2×C4×C151—21no—
157C2×C4×C151—44no—
158C2×C4×C151—44no—
159C2×C4×C151C22×C412yes—
160C2×C4×C151C22×C412yes—
161C2×C4×C151#4112yes—
162C2×C4×C151#4112yes—
163C22×C151—22no—
164C22×C151—22no—
165C22×C151—22no—
166C22×C151—22no—
167C22×C151—22no—
168C22×C151—22no—
169C22×C151C4×D414yes—
170C22×C151C23×C411yescharacteristic
171C22×C151C22×D411yescharacteristic
172C22×C151C2×#4111yescharacteristic
173C22×C151C2×#4111yescharacteristic
174C22×C151C2×#4111yescharacteristic
175C22×C151H(5,𝔽2)11yescharacteristic
176C22×C1512−1+411yescharacteristic
177C2×D151—22no—
178C2×D151—22no—
179C2×D151—22no—
180C2×D151—41no—
181C2×D151—41no—
182C2×D151—41no—
183C2×D151—41no—
184C4×C151—22no—
185C4×C151—22no—
186C4×C151—22no—
187C4×C151—22no—
188C4×C151—41no—
189C4×C151—41no—
190Dic151—22no—
191Dic151—22no—
192Dic151—22no—
193Dic151—22no—
194Dic151—22no—
195Dic151—41no—
196Dic151—41no—
197C2×C151—24no—
198C2×C151C2×C4×D411yescharacteristic
199C2×C151C4×#4111yescharacteristic
200C2×C151#52011yescharacteristic
201C2×C151#54611yescharacteristic
202C2×C151#54711yescharacteristic
203C2×C151#55111yescharacteristic
204C2×C151#55211yescharacteristic
205D151—42no—
206C151#235911yescharacteristic, complemented, Sylow
207#2359—1511nomaximal, Sylow
208C2×#123—1511no—
209C2×C4×D4—1511no—
210C2×#117—1511no—
211#389—1511no—
212#388—1511no—
213#388—1511no—
214#387—1511no—
215#387—1511no—
216#386—1511no—
217#385—1511no—
218#385—1511no—
219C4×C4⋊C4—1511no—
220C4×C22⋊C4—1511no—
221C4×C22⋊C4—1511no—
222C2×#95D15111yescharacteristic, complemented
223C22×D4—1511no—
224C23×C4—1511no—
225C23×C4C2×D15111yescharacteristic
226C23×C4C2×D15111yescharacteristic
227C23×C4C2×D15111yescharacteristic
228#123—1518no—
229C4×D4—3024no—
230#117—3024no—
231C2×C4⋊C4—1511no—
232C2×C4⋊C4—1511no—
233C2×C4⋊C4—1511no—
234C2×C4⋊C4—1511no—
235C2×C4⋊C4—1511no—
236C2×C4⋊C4—1511no—
237C2×C4⋊C4—1511no—
238C2×C22⋊C4—1511no—
239C2×C22⋊C4—1511no—
240C2×C22⋊C4—1511no—
241C2×C22⋊C4—1511no—
242C2×C22⋊C4—1511no—
243C2×C22⋊C4—1511no—
244C2×C22⋊C4—1511no—
245C2×C22⋊C4—1511no—
246C2×C42—1511no—
247C2×C42—1511no—
248C2×C42—1511no—
249C2×C42—1511no—
250C2×C42—1511no—
251#95—1511no—
252#95—1511no—
253#95—1511no—
254#95—1511no—
255#95—1511no—
256#95—1511no—
257#95C2×D15111yescharacteristic
258#95C2×D15111yescharacteristic
259#95C2×D15111yescharacteristic
260#95C2×D15111yescharacteristic
261C24—1511no—
262C24C22×D15111yescharacteristic
263C2×D4—3022no—
264C2×D4—3022no—
265C2×D4—1514no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4—3022no—
275C22×C4—3022no—
276C22×C4—6041no—
277C22×C4—1511no—
278C22×C4—1511no—
279C22×C4—1511no—
280C22×C4—1511no—
281C22×C4—1511no—
282C22×C4—1511no—
283C22×C4—1511no—
284C22×C4C4×D15114yescomplemented
285C22×C4C22×D15111yescharacteristic
286C22×C4C22×D15111yescharacteristic
287C22×C4C22×D15111yescharacteristic
288C22×C4C22×D15111yescharacteristic
289C22×C4C22×D15111yescharacteristic
290C22×C4C22×D15111yescharacteristic
291C4⋊C4—3022no—
292C4⋊C4—3022no—
293C4⋊C4—3022no—
294C4⋊C4—3022no—
295C4⋊C4—6041no—
296C4⋊C4—1514no—
297C4⋊C4—1514no—
298C22⋊C4—3022no—
299C22⋊C4—3022no—
300C22⋊C4—3022no—
301C22⋊C4—6041no—
302C22⋊C4—1514no—
303C22⋊C4—1514no—
304C22⋊C4—1514no—
305C22⋊C4—1514no—
306C42—3022no—
307C42—3022no—
308C42—3022no—
309C42—3022no—
310C42—6041no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—3021no—
316C23—3021no—
317C23—3021no—
318C23—3021no—
319C23—3021no—
320C23—3021no—
321C23—1512no—
322C23C2×C4×D15112yes—
323C23D4×D15112yes—
324C23#1455900312yes—
325C23C23×D15111yescharacteristic
326D4—3028no—
327C2×C4—28no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—44no—
343C2×C4—44no—
344C2×C4—3021no—
345C2×C4—3021no—
346C2×C4—3021no—
347C2×C4—3021no—
348C2×C4—3021no—
349C2×C4—3021no—
350C2×C4—3021no—
351C2×C4—3021no—
352C2×C4—3021no—
353C2×C4—3021no—
354C2×C4—3021no—
355C2×C4—3021no—
356C2×C4—3021no—
357C2×C4—3021no—
358C2×C4—3021no—
359C2×C4—3021no—
360C2×C4—6044no—
361C2×C4—1512no—
362C2×C4—1512no—
363C2×C4—1512no—
364C2×C4—1512no—
365C2×C4—1512no—
366C2×C4C2×C4×D15112yes—
367C2×C4C2×C4×D15112yes—
368C2×C4#1455900412yes—
369C2×C4#1455900412yes—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—22no—
374C22—22no—
375C22—22no—
376C22—3022no—
377C22—3022no—
378C22—3022no—
379C22—6041no—
380C22—6041no—
381C22—6041no—
382C22—6041no—
383C22(C22⋊D151)⋊C414yes—
384C22C22×C4×D15111yescharacteristic
385C22C2×D4×D15111yescharacteristic
386C22C2×#1455900311yescharacteristic
387C22C2×#1455900411yescharacteristic
388C22C2×#1455900411yescharacteristic
389C22#1801278411yescharacteristic
390C22#1801278711yescharacteristic
391C4—22no—
392C4—22no—
393C4—22no—
394C4—22no—
395C4—41no—
396C4—41no—
397C4—3022no—
398C4—3022no—
399C4—3022no—
400C4—3022no—
401C4—3022no—
402C4—6041no—
403C4—6041no—
404C2—24no—
405C2—6042no—
406C2C2×(C22⋊D151)⋊C411yescharacteristic
407C2C4×#1455900411yescharacteristic
408C2#2375269311yescharacteristic
409C2#2375285211yescharacteristic
410C2#2375286311yescharacteristic
411C2#2375288811yescharacteristic
412C2#2375289711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D151
commutatorC22×C151C23×C4
FittingC2×#95×C151C2
socle, cosocleC23×C151C24
prime radicalC22×C22⋊D151C22
hypercenterC2×#95D151
hypocenterC151#2359
LCSG ▷ C22×C151 ▷ C151
UCSC1 ◁ C23 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
3. C2×#18012698C2semidirect
4. #23752109C2semidirect
5. #23752104C2semidirect
6. #23752101C2semidirect
7. #23752099C2semidirect
8. #23752094C2semidirect
10. #23752086C2semidirect
11. #23752085C2semidirect
12. #23752063C2semidirect
13. C4×C22⋊Dic151C2semidirect
14. #23752059C2semidirect
15. C2×#95×C151C2semidirect
18. #18012722C4semidirect
73. Dic151⋊C4C2×C4semidirect
74. Dic151⋊C4C2×C4semidirect
76. C22⋊Dic151C2×C4semidirect
81. (C2×D151)⋊C4C2×C4semidirect
82. (C2×D151)⋊C4C2×C4semidirect
97. C22×C4×C151C2×C4semidirect
206. C151#2359semidirect
222. C2×#95D151semidirect
284. C22×C4C4×D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127222
C2×C4×C22⋊D1512
C2×#180126982
#237521092
#237521042
#237521012
#237520992
#237520942
#237520912
#237520862
#237520852
#237520632
C4×C22⋊Dic1512
#237520592
C2×#95×C1512
#2359151