Finite Group Databasebeta

← #34077252

Subgroups — #34077252

Order 19328.

408 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752143C211yesmaximal, characteristic, complemented
2#23752140C211yesmaximal, characteristic, complemented
3#23752138C211yesmaximal, characteristic, complemented
4#23752138C211yesmaximal, characteristic, complemented
5#23752137C211yesmaximal, characteristic, complemented
6#23752134C211yesmaximal, characteristic, complemented
7#23752132C211yesmaximal, characteristic, complemented
8#23752127C211yesmaximal, characteristic
9#23752127C211yesmaximal, characteristic
10#23752125C211yesmaximal, characteristic, complemented
11#23752124C211yesmaximal, characteristic, complemented
12#23752112C211yesmaximal, characteristic
13#23752099C211yesmaximal, characteristic, complemented
14#23752093C211yesmaximal, characteristic, complemented
15#396×C151C211yesmaximal, characteristic, complemented
16C22×Dic302C2211yescharacteristic
17C22×C22⋊D151C2211yescharacteristic
18C2×C4⋊Dic151C2211yescharacteristic
19C2×Dic151⋊C4C2211yescharacteristic
20C2×Dic151⋊C4C2211yescharacteristic
21C2×Dic151⋊C4C2211yescharacteristic
22C2×Dic151⋊C4C2211yescharacteristic
23C2×C22⋊Dic151C2211yescharacteristic
24C2×C22⋊Dic151C2211yescharacteristic
25C2×C22⋊Dic151C2211yescharacteristic
26C2×(C2×D151)⋊C4C2211yescharacteristic
27C2×(C2×D151)⋊C4C2211yescharacteristic
28C2×(C2×D151)⋊C4C2211yescharacteristic
29C2×(C2×D151)⋊C4C2211yescharacteristic
30C2×(C2×D151)⋊C4C2211yescharacteristic
31C2×(C2×D151)⋊C4C2211yescharacteristic
32C2×C4×Dic151C2211yescharacteristic
33C151⋊#95C2211yescharacteristic
34C151⋊#95C2211yescharacteristic
35C151⋊#95C2211yescharacteristic
36C151⋊#95C2211yescharacteristic
37C151⋊#95C2211yescharacteristic
38C151⋊#95C2211yescharacteristic
39C151⋊#95C2211yescharacteristic
40C151⋊#95C2211yescharacteristic
41C151⋊#95C2211yescharacteristic
42C151⋊#95C2211yescharacteristic
43C151⋊#95C2211yescharacteristic
44C2×C4⋊C4×C151C2211yescharacteristic
45C2×C4⋊C4×C151C2211yescharacteristic
46C2×C4⋊C4×C151C2211yescharacteristic
47C2×C22⋊C4×C151C2211yescharacteristic
48C2×C22⋊C4×C151C2211yescharacteristic
49C2×C22⋊C4×C151C2211yescharacteristic
50#95×C151C2211yescharacteristic
51C23×D151C2311yescharacteristic
52C2×Dic302—41no—
53C2×Dic302—41no—
54C2×Dic302—41no—
55C2×C22⋊D151—22no—
56C2×C22⋊D151—41no—
57C2×C22⋊D151—41no—
58C22×Dic151C2311yescharacteristic
59C22×Dic151C2311yescharacteristic
60C22×Dic151C2311yescharacteristic
61C22×Dic151C2311yescharacteristic
62C22×Dic151C2311yescharacteristic
63C22×Dic151C2311yescharacteristic
64C22×Dic151C2311yescharacteristic
65C4⋊Dic151—41no—
66Dic151⋊C4—22no—
67Dic151⋊C4—22no—
68Dic151⋊C4—41no—
69Dic151⋊C4—41no—
70C22⋊Dic151—41no—
71C22⋊Dic151—41no—
72C22⋊Dic151—41no—
73(C2×D151)⋊C4—41no—
74(C2×D151)⋊C4—41no—
75(C2×D151)⋊C4—41no—
76(C2×D151)⋊C4—41no—
77(C2×D151)⋊C4—41no—
78(C2×D151)⋊C4—41no—
79C4×Dic151—41no—
80C24×C151C2311yescharacteristic
81C22×C4×C151C2311yescharacteristic
82C22×C4×C151C2311yescharacteristic
83C22×C4×C151C2311yescharacteristic
84C22×C4×C151C2311yescharacteristic
85C22×C4×C151C2311yescharacteristic
86C22×C4×C151C2311yescharacteristic
87C4⋊C4×C151—41no—
88C4⋊C4×C151—41no—
89C4⋊C4×C151—41no—
90C22⋊C4×C151—41no—
91C22⋊C4×C151—41no—
92C22⋊C4×C151—41no—
93C22×D151—21no—
94C22×D151—21no—
95C22×D151—21no—
96C22×D151—21no—
97C22×D151—21no—
98C22×D151—21no—
99C22×D151—21no—
100Dic302—44no—
101C22⋊D151—44no—
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—21no—
121C2×Dic151—21no—
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×C151C2411yescharacteristic
131C2×C4×C151—21no—
132C2×C4×C151—21no—
133C2×C4×C151—21no—
134C2×C4×C151—21no—
135C2×C4×C151—21no—
136C2×C4×C151—21no—
137C2×C4×C151—21no—
138C2×C4×C151—21no—
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—
149C22×C151—41no—
150C22×C151—41no—
151C22×C151—41no—
152C22×C151—41no—
153C22×C151—41no—
154C22×C151—41no—
155C22×C151—41no—
156C22×C151C2×#4111yescharacteristic
157C22×C151H(5,𝔽2)11yescharacteristic
158C22×C151H(5,𝔽2)11yescharacteristic
159C22×C151H(5,𝔽2)11yescharacteristic
160C22×C151H(5,𝔽2)11yescharacteristic
161C22×C1512−1+411yescharacteristic
162C22×C1512−1+411yescharacteristic
163C2×D151—41no—
164C2×D151—41no—
165C2×D151—41no—
166C2×D151—41no—
167C2×D151—41no—
168C2×D151—41no—
169C2×D151—41no—
170C4×C151—41no—
171C4×C151—41no—
172C4×C151—41no—
173C4×C151—41no—
174C4×C151—41no—
175C4×C151—41no—
176Dic151—22no—
177Dic151—41no—
178Dic151—41no—
179Dic151—41no—
180Dic151—41no—
181Dic151—41no—
182Dic151—41no—
183C2×C151—81no—
184C2×C151#53811yescharacteristic
185C2×C151#54211yescharacteristic
186C2×C151#54211yescharacteristic
187C2×C151#56011yescharacteristic
188C2×C151#56211yescharacteristic
189C2×C151#56211yescharacteristic
190C2×C151#56311yescharacteristic
191D151—81no—
192C151#283011yescharacteristic, complemented, Sylow
193#2830—1511nomaximal, Sylow
194#398—1511no—
195#397—1511no—
196#397—1511no—
197#397—1511no—
198#397—1511no—
199#396—1511no—
200#396D15111yescharacteristic, complemented
201#395—1511no—
202#394—1511no—
203#394—1511no—
204#393—1511no—
205#393—1511no—
206#390—1511no—
207#387—1511no—
208#387—1511no—
209C22×Q8—1511no—
210C22×D4—1511no—
211C2×C4⋊C4—1511no—
212C2×C4⋊C4—1511no—
213C2×C4⋊C4—1511no—
214C2×C4⋊C4—1511no—
215C2×C4⋊C4—1511no—
216C2×C4⋊C4C2×D15111yescharacteristic
217C2×C4⋊C4C2×D15111yescharacteristic
218C2×C4⋊C4C2×D15111yescharacteristic
219C2×C22⋊C4—1511no—
220C2×C22⋊C4—1511no—
221C2×C22⋊C4—1511no—
222C2×C22⋊C4—1511no—
223C2×C22⋊C4—1511no—
224C2×C22⋊C4—1511no—
225C2×C22⋊C4—1511no—
226C2×C22⋊C4—1511no—
227C2×C22⋊C4—1511no—
228C2×C22⋊C4C2×D15111yescharacteristic
229C2×C22⋊C4C2×D15111yescharacteristic
230C2×C22⋊C4C2×D15111yescharacteristic
231C2×C42—1511no—
232#95—1511no—
233#95—1511no—
234#95—1511no—
235#95—1511no—
236#95—1511no—
237#95—1511no—
238#95—1511no—
239#95—1511no—
240#95—1511no—
241#95—1511no—
242#95—1511no—
243#95C2×D15111yescharacteristic
244C24—1511no—
245C24C22×D15111yescharacteristic
246C2×Q8—6041no—
247C2×Q8—6041no—
248C2×Q8—6041no—
249C2×D4—3022no—
250C2×D4—6041no—
251C2×D4—6041no—
252C22×C4—1511no—
253C22×C4—1511no—
254C22×C4—1511no—
255C22×C4—1511no—
256C22×C4—1511no—
257C22×C4—1511no—
258C22×C4—1511no—
259C22×C4C22×D15111yescharacteristic
260C22×C4C22×D15111yescharacteristic
261C22×C4C22×D15111yescharacteristic
262C22×C4C22×D15111yescharacteristic
263C22×C4C22×D15111yescharacteristic
264C22×C4C22×D15111yescharacteristic
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—3022no—
269C4⋊C4—3022no—
270C4⋊C4—6041no—
271C4⋊C4—6041no—
272C4⋊C4—6041no—
273C22⋊C4—41no—
274C22⋊C4—41no—
275C22⋊C4—41no—
276C22⋊C4—6041no—
277C22⋊C4—6041no—
278C22⋊C4—6041no—
279C22⋊C4—6041no—
280C22⋊C4—6041no—
281C22⋊C4—6041no—
282C22⋊C4—6041no—
283C22⋊C4—6041no—
284C22⋊C4—6041no—
285C42—6041no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—3021no—
294C23—3021no—
295C23—3021no—
296C23—3021no—
297C23—3021no—
298C23—3021no—
299C23—3021no—
300C23C23×D15111yescharacteristic
301Q8—6044no—
302D4—6044no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
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—3021no—
322C2×C4—3021no—
323C2×C4—3021no—
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—1512no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—6041no—
350C22—6041no—
351C22—6041no—
352C22—6041no—
353C22—6041no—
354C22—6041no—
355C22—6041no—
356C22#41×D15111yescharacteristic
357C22#1801278411yescharacteristic
358C22#1801278411yescharacteristic
359C22#1801278411yescharacteristic
360C22#1801278511yescharacteristic
361C22#1801278611yescharacteristic
362C22#1801278711yescharacteristic
363C4—41no—
364C4—41no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—3022no—
370C4—6041no—
371C4—6041no—
372C4—6041no—
373C4—6041no—
374C4—6041no—
375C4—6041no—
376C2—81no—
377C2—12081no—
378C2#2375279411yescharacteristic
379C2#2375282811yescharacteristic
380C2#2375283211yescharacteristic
381C2#2375295011yescharacteristic
382C2#2375295711yescharacteristic
383C2#2375295811yescharacteristic
384C2#2375296311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D151
commutator, socle, cosocleC23×C151C24
Fitting#396×C151C2
prime radicalC22×C22⋊D151C22
hypercenter#396D151
hypocenterC151#2830
LCSG ▷ C23×C151 ▷ C151
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. #23752143C2semidirect
2. #23752140C2semidirect
3. #23752138C2semidirect
4. #23752138C2semidirect
5. #23752137C2semidirect
6. #23752134C2semidirect
7. #23752132C2semidirect
10. #23752125C2semidirect
11. #23752124C2semidirect
13. #23752099C2semidirect
14. #23752093C2semidirect
15. #396×C151C2semidirect
192. C151#2830semidirect
200. #396D151semidirect

Maximal subgroups

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

subgroupindex
#237521432
#237521402
#237521382
#237521372
#237521342
#237521322
#237521272
#237521252
#237521242
#237521122
#237520992
#237520932
#396×C1512
#2830151