Finite Group Databasebeta

← #34071904

Subgroups — #34071904

Order 19328.

532 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752115C211yesmaximal, characteristic
2#23752111C211yesmaximal, characteristic, complemented
3#23752105C211yesmaximal, characteristic, complemented
4#23752105C211yesmaximal, characteristic, complemented
5#23752105C211yesmaximal, characteristic, complemented
6#23752105C211yesmaximal, characteristic, complemented
7#23752098C211yesmaximal, characteristic, complemented
8#23752098C211yesmaximal, characteristic, complemented
9#23752092C211yesmaximal, characteristic
10#23752087C211yesmaximal, characteristic, complemented
11#23752072C211yesmaximal, characteristic, complemented
12C4⋊C4×Dic151C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic151C211yesmaximal, characteristic, complemented
14C4×C22⋊Dic151C211yesmaximal, characteristic, complemented
15C2×#123×C151C211yesmaximal, characteristic
16C23×Dic151C2211yescharacteristic
17C2×C4⋊Dic151C2211yescharacteristic
18C2×C4⋊Dic151C2211yescharacteristic
19C2×C4⋊Dic151C2211yescharacteristic
20C2×C4⋊Dic151C2211yescharacteristic
21C2×C4⋊Dic151C2211yescharacteristic
22C2×C22⋊Dic151C2211yescharacteristic
23C2×C22⋊Dic151C2211yescharacteristic
24C2×C22⋊Dic151C2211yescharacteristic
25C2×C22⋊Dic151C2211yescharacteristic
26C2×C22⋊Dic151C2211yescharacteristic
27C2×C22⋊Dic151C2211yescharacteristic
28C2×C22⋊Dic151C2211yescharacteristic
29C2×C4×Dic151C2211yescharacteristic
30C2×C4×Dic151C2211yescharacteristic
31C2×C4×Dic151C2211yescharacteristic
32C2×C4×Dic151C2211yescharacteristic
33C2×C4×Dic151C2211yescharacteristic
34C151⋊#95C2211yescharacteristic
35C151⋊#95C2211yescharacteristic
36C151⋊#95C2211yescharacteristic
37C151⋊#95C2211yescharacteristic
38C151⋊#95C2211yescharacteristic
39C151⋊#95C2211yescharacteristic
40C151⋊#95C2211yescharacteristic
41C151⋊#95C2211yescharacteristic
42C151⋊#95C2211yescharacteristic
43C151⋊#95C2211yescharacteristic
44C22×D4×C151C2211yescharacteristic
45C23×C4×C151C2211yescharacteristic
46#123×C151C418yescomplemented
47C2×C4⋊C4×C151C2211yescharacteristic
48C2×C4⋊C4×C151C2211yescharacteristic
49C2×C22⋊C4×C151C2211yescharacteristic
50C2×C22⋊C4×C151C2211yescharacteristic
51C2×C22⋊C4×C151C2211yescharacteristic
52C22×Dic151—22no—
53C22×Dic151—41no—
54C22×Dic151—41no—
55C22×Dic151C2311yescharacteristic
56C22×Dic151C2311yescharacteristic
57C22×Dic151C2311yescharacteristic
58C22×Dic151C2311yescharacteristic
59C22×Dic151C2311yescharacteristic
60C22×Dic151C2311yescharacteristic
61C22×Dic151C2311yescharacteristic
62C22×Dic151C2311yescharacteristic
63C4⋊Dic151—22no—
64C4⋊Dic151—41no—
65C4⋊Dic151—41no—
66C4⋊Dic151—41no—
67C4⋊Dic151—41no—
68C22⋊Dic151—22no—
69C22⋊Dic151—22no—
70C22⋊Dic151—22no—
71C22⋊Dic151—41no—
72C22⋊Dic151—41no—
73C22⋊Dic151—41no—
74C22⋊Dic151—41no—
75C4×Dic151—22no—
76C4×Dic151—41no—
77C4×Dic151—41no—
78C4×Dic151—41no—
79C4×Dic151—41no—
80C24×C151C2311yescharacteristic
81C24×C151C2311yescharacteristic
82C2×D4×C151—41no—
83C2×D4×C151—41no—
84C2×D4×C151C2×C414yes—
85C22×C4×C151—41no—
86C22×C4×C151—41no—
87C22×C4×C151C2×C414yescomplemented
88C22×C4×C151C2311yescharacteristic
89C22×C4×C151C2311yescharacteristic
90C22×C4×C151C2311yescharacteristic
91C22×C4×C151C2311yescharacteristic
92C22×C4×C151C2311yescharacteristic
93C4⋊C4×C151C2×C414yescomplemented
94C4⋊C4×C151C2×C414yescomplemented
95C22⋊C4×C151C2×C414yes—
96C22⋊C4×C151C2×C414yes—
97C22⋊C4×C151C2×C414yescomplemented
98C2×Dic151—21no—
99C2×Dic151—21no—
100C2×Dic151—21no—
101C2×Dic151—21no—
102C2×Dic151—21no—
103C2×Dic151—21no—
104C2×Dic151—21no—
105C2×Dic151—21no—
106C2×Dic151—21no—
107C2×Dic151—21no—
108C2×Dic151—21no—
109C2×Dic151—21no—
110C2×Dic151—21no—
111C2×Dic151—21no—
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—44no—
121C2×Dic151#4112yes—
122C2×Dic151#4112yes—
123C23×C151—21no—
124C23×C151—21no—
125C23×C151—21no—
126C23×C151—21no—
127C23×C151—21no—
128C23×C151—21no—
129C23×C151—21no—
130C23×C151—21no—
131C23×C151—21no—
132C23×C151—21no—
133C23×C151—21no—
134C23×C151—21no—
135C23×C151C22×C412yes—
136C23×C151C22×C412yes—
137C23×C151C2411yescharacteristic
138D4×C151—44no—
139C2×C4×C151—21no—
140C2×C4×C151—21no—
141C2×C4×C151—21no—
142C2×C4×C151—21no—
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—44no—
150C2×C4×C151C22×C412yes—
151C2×C4×C151C22×C412yes—
152C2×C4×C151C22×C412yes—
153C2×C4×C151C22×C412yes—
154C2×C4×C151C22×C412yes—
155C22×C151—22no—
156C22×C151—22no—
157C22×C151—22no—
158C22×C151—22no—
159C22×C151—22no—
160C22×C151—22no—
161C22×C151—41no—
162C22×C151—41no—
163C22×C151—41no—
164C22×C151—41no—
165C22×C151—41no—
166C22×C151—41no—
167C22×C151—41no—
168C22×C151—41no—
169C22×C151C23×C411yescharacteristic
170C22×C151C2×#4111yescharacteristic
171C22×C151C2×#4111yescharacteristic
172C22×C151H(5,𝔽2)11yescharacteristic
173C22×C151H(5,𝔽2)11yescharacteristic
174C22×C151H(5,𝔽2)11yescharacteristic
175C22×C1512−1+411yescharacteristic
176C4×C151—22no—
177C4×C151—22no—
178C4×C151—22no—
179C4×C151—22no—
180C4×C151—22no—
181Dic151—22no—
182Dic151—22no—
183Dic151—41no—
184Dic151—41no—
185Dic151—41no—
186Dic151—41no—
187Dic151—41no—
188Dic151—41no—
189C2×C151—42no—
190C2×C151—42no—
191C2×C151C4×#4111yescharacteristic
192C2×C151#51811yescharacteristic
193C2×C151#52011yescharacteristic
194C2×C151#53811yescharacteristic
195C2×C151#53911yescharacteristic
196C2×C151#54011yescharacteristic
197C2×C151#54211yescharacteristic
198C151#233511yescharacteristic, complemented, Sylow
199#2335—1511nomaximal, Sylow
200C2×#123D15111yescharacteristic
201#390—1511no—
202#389—1511no—
203#388—1511no—
204#388—1511no—
205#388—1511no—
206#388—1511no—
207#387—1511no—
208#387—1511no—
209#386—1511no—
210#385—1511no—
211#380—1511no—
212C4×C4⋊C4—1511no—
213C4×C22⋊C4—1511no—
214C4×C22⋊C4—1511no—
215C22×D4C2×D15111yescharacteristic
216C23×C4—1511no—
217C23×C4C2×D15111yescharacteristic
218#123Dic15118yescomplemented
219C2×C4⋊C4—1511no—
220C2×C4⋊C4—1511no—
221C2×C4⋊C4—1511no—
222C2×C4⋊C4—1511no—
223C2×C4⋊C4—1511no—
224C2×C4⋊C4C2×D15111yescharacteristic
225C2×C4⋊C4C2×D15111yescharacteristic
226C2×C22⋊C4—1511no—
227C2×C22⋊C4—1511no—
228C2×C22⋊C4—1511no—
229C2×C22⋊C4—1511no—
230C2×C22⋊C4—1511no—
231C2×C22⋊C4—1511no—
232C2×C22⋊C4—1511no—
233C2×C22⋊C4C2×D15111yescharacteristic
234C2×C22⋊C4C2×D15111yescharacteristic
235C2×C22⋊C4C2×D15111yescharacteristic
236C2×C42—1511no—
237C2×C42—1511no—
238C2×C42—1511no—
239C2×C42—1511no—
240C2×C42—1511no—
241#95—1511no—
242#95—1511no—
243#95—1511no—
244#95—1511no—
245#95—1511no—
246#95—1511no—
247#95—1511no—
248#95—1511no—
249#95—1511no—
250#95—1511no—
251C24C22×D15111yescharacteristic
252C24C22×D15111yescharacteristic
253C2×D4—41no—
254C2×D4—41no—
255C2×D4C2×Dic15114yes—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—3022no—
259C22×C4—6041no—
260C22×C4—6041no—
261C22×C4—1511no—
262C22×C4—1511no—
263C22×C4—1511no—
264C22×C4—1511no—
265C22×C4—1511no—
266C22×C4—1511no—
267C22×C4—1511no—
268C22×C4—1511no—
269C22×C4C2×Dic15114yescomplemented
270C22×C4C22×D15111yescharacteristic
271C22×C4C22×D15111yescharacteristic
272C22×C4C22×D15111yescharacteristic
273C22×C4C22×D15111yescharacteristic
274C22×C4C22×D15111yescharacteristic
275C4⋊C4—3022no—
276C4⋊C4—6041no—
277C4⋊C4—6041no—
278C4⋊C4—6041no—
279C4⋊C4—6041no—
280C4⋊C4C2×Dic15114yescomplemented
281C4⋊C4C2×Dic15114yescomplemented
282C22⋊C4—3022no—
283C22⋊C4—3022no—
284C22⋊C4—3022no—
285C22⋊C4—6041no—
286C22⋊C4—6041no—
287C22⋊C4—6041no—
288C22⋊C4—6041no—
289C22⋊C4C2×Dic15114yes—
290C22⋊C4C2×Dic15114yes—
291C22⋊C4C2×Dic15114yescomplemented
292C42—3022no—
293C42—6041no—
294C42—6041no—
295C42—6041no—
296C42—6041no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23C22×Dic15112yes—
310C23C22×Dic15112yes—
311C23C23×D15111yescharacteristic
312D4—44no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—44no—
324C2×C4—3021no—
325C2×C4—3021no—
326C2×C4—3021no—
327C2×C4—3021no—
328C2×C4—3021no—
329C2×C4—3021no—
330C2×C4—3021no—
331C2×C4—3021no—
332C2×C4—3021no—
333C2×C4—3021no—
334C2×C4—3021no—
335C2×C4—3021no—
336C2×C4—3021no—
337C2×C4—3021no—
338C2×C4—3021no—
339C2×C4—3021no—
340C2×C4—3021no—
341C2×C4—3021no—
342C2×C4—3021no—
343C2×C4—3021no—
344C2×C4—3021no—
345C2×C4—3021no—
346C2×C4—6044no—
347C2×C4—1512no—
348C2×C4—1512no—
349C2×C4C22×Dic15112yes—
350C2×C4C22×Dic15112yes—
351C2×C4C22×Dic15112yes—
352C2×C4C22×Dic15112yes—
353C2×C4C22×Dic15112yes—
354C22—22no—
355C22—22no—
356C22—22no—
357C22—22no—
358C22—22no—
359C22—22no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22C23×Dic15111yescharacteristic
369C22#41×D15111yescharacteristic
370C22#41×D15111yescharacteristic
371C22#1801278411yescharacteristic
372C22#1801278411yescharacteristic
373C22#1801278511yescharacteristic
374C22#1801278611yescharacteristic
375C4—22no—
376C4—22no—
377C4—22no—
378C4—22no—
379C4—22no—
380C4—3022no—
381C4—3022no—
382C4—6041no—
383C4—6041no—
384C4—6041no—
385C4—6041no—
386C4—6041no—
387C4—6041no—
388C2—42no—
389C2—42no—
390C2#41×Dic15111yescharacteristic
391C2#2375268711yescharacteristic
392C2#2375269511yescharacteristic
393C2#2375279811yescharacteristic
394C2#2375280511yescharacteristic
395C2#2375281411yescharacteristic
396C2#2375283011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D151
commutatorC22×C151C23×C4
FittingC2×#123×C151C2
socle, cosocleC23×C151C24
prime radicalC22×D4×C151C22
hypercenterC2×#123D151
hypocenterC151#2335
LCSG ▷ C22×C151 ▷ C151
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
2. #23752111C2semidirect
3. #23752105C2semidirect
4. #23752105C2semidirect
5. #23752105C2semidirect
6. #23752105C2semidirect
7. #23752098C2semidirect
8. #23752098C2semidirect
10. #23752087C2semidirect
11. #23752072C2semidirect
12. C4⋊C4×Dic151C2semidirect
13. C22⋊C4×Dic151C2semidirect
14. C4×C22⋊Dic151C2semidirect
46. #123×C151C4semidirect
87. C22×C4×C151C2×C4semidirect
93. C4⋊C4×C151C2×C4semidirect
94. C4⋊C4×C151C2×C4semidirect
97. C22⋊C4×C151C2×C4semidirect
198. C151#2335semidirect
218. #123Dic151semidirect
269. C22×C4C2×Dic151semidirect
280. C4⋊C4C2×Dic151semidirect
281. C4⋊C4C2×Dic151semidirect
291. C22⋊C4C2×Dic151semidirect

Maximal subgroups

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

subgroupindex
#237521152
#237521112
#237521052
#237520982
#237520922
#237520872
#237520722
C4⋊C4×Dic1512
C22⋊C4×Dic1512
C4×C22⋊Dic1512
C2×#123×C1512
#2335151