Finite Group Databasebeta

← #34077274

Subgroups — #34077274

Order 19328.

416 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752152C211yesmaximal, characteristic, complemented
2#23752151C211yesmaximal, characteristic, complemented
3#23752141C211yesmaximal, characteristic, complemented
4#23752133C211yesmaximal, characteristic, complemented
5#23752128C211yesmaximal, characteristic
6#23752128C211yesmaximal, characteristic
7#23752127C211yesmaximal, characteristic
8#23752125C211yesmaximal, characteristic, complemented
9#23752125C211yesmaximal, characteristic, complemented
10#23752124C211yesmaximal, characteristic, complemented
11#23752124C211yesmaximal, characteristic, complemented
12#23752116C211yesmaximal, characteristic, complemented
13#23752102C211yesmaximal, characteristic, complemented
14#23752100C211yesmaximal, characteristic, complemented
15#397×C151C211yesmaximal, characteristic, complemented
16C22×Dic302C2211yescharacteristic
17C22×Dic302C2211yescharacteristic
18C22×C22⋊D151C2211yescharacteristic
19C2×C4⋊Dic151C2211yescharacteristic
20C2×C4⋊Dic151C2211yescharacteristic
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×C22⋊C4×C151C2211yescharacteristic
46C2×C22⋊C4×C151C2211yescharacteristic
47C2×C22⋊C4×C151C2211yescharacteristic
48#95×C151C2211yescharacteristic
49#95×C151C2211yescharacteristic
50#95×C151C2211yescharacteristic
51C23×D151C2311yescharacteristic
52C2×Dic302—22no—
53C2×Dic302—41no—
54C2×Dic302—41no—
55C2×Dic302—41no—
56C2×Dic302—41no—
57C2×Dic302—41no—
58C2×C22⋊D151—41no—
59C2×C22⋊D151—41no—
60C2×C22⋊D151—41no—
61C22×Dic151C2311yescharacteristic
62C22×Dic151C2311yescharacteristic
63C22×Dic151C2311yescharacteristic
64C22×Dic151C2311yescharacteristic
65C22×Dic151C2311yescharacteristic
66C22×Dic151C2311yescharacteristic
67C22×Dic151C2311yescharacteristic
68C4⋊Dic151—41no—
69C4⋊Dic151—41no—
70Dic151⋊C4—41no—
71Dic151⋊C4—41no—
72C22⋊Dic151—22no—
73C22⋊Dic151—41no—
74C22⋊Dic151—41no—
75(C2×D151)⋊C4—22no—
76(C2×D151)⋊C4—41no—
77(C2×D151)⋊C4—41no—
78(C2×D151)⋊C4—41no—
79(C2×D151)⋊C4—41no—
80(C2×D151)⋊C4—41no—
81C4×Dic151—41no—
82C24×C151C2311yescharacteristic
83C22×C4×C151C2311yescharacteristic
84C22×C4×C151C2311yescharacteristic
85C22×C4×C151C2311yescharacteristic
86C22×C4×C151C2311yescharacteristic
87C22×C4×C151C2311yescharacteristic
88C22×C4×C151C2311yescharacteristic
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—
101Dic302—44no—
102C22⋊D151—44no—
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—21no—
123C2×Dic151#4112yes—
124C23×C151—21no—
125C23×C151—21no—
126C23×C151—21no—
127C23×C151—21no—
128C23×C151—21no—
129C23×C151—21no—
130C23×C151—21no—
131C23×C151C2411yescharacteristic
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—
149C2×C4×C151—21no—
150C22×C151—41no—
151C22×C151—41no—
152C22×C151—41no—
153C22×C151—41no—
154C22×C151—41no—
155C22×C151—41no—
156C22×C151—41no—
157C22×C151C2×#4111yescharacteristic
158C22×C151H(5,𝔽2)11yescharacteristic
159C22×C151H(5,𝔽2)11yescharacteristic
160C22×C151H(5,𝔽2)11yescharacteristic
161C22×C151H(5,𝔽2)11yescharacteristic
162C22×C1512−1+411yescharacteristic
163C22×C1512−1+411yescharacteristic
164C2×D151—41no—
165C2×D151—41no—
166C2×D151—41no—
167C2×D151—41no—
168C2×D151—41no—
169C2×D151—41no—
170C2×D151—41no—
171C4×C151—41no—
172C4×C151—41no—
173C4×C151—41no—
174C4×C151—41no—
175C4×C151—41no—
176C4×C151—41no—
177Dic151—22no—
178Dic151—41no—
179Dic151—41no—
180Dic151—41no—
181Dic151—41no—
182Dic151—41no—
183Dic151—41no—
184C2×C151—81no—
185C2×C151#53811yescharacteristic
186C2×C151#54211yescharacteristic
187C2×C151#54211yescharacteristic
188C2×C151H(3,𝔽4)11yescharacteristic
189C2×C151#56211yescharacteristic
190C2×C151#56211yescharacteristic
191C2×C151#56311yescharacteristic
192D151—81no—
193C151#283211yescharacteristic, complemented, Sylow
194#2832—1511nomaximal, Sylow
195#400—1511no—
196#400—1511no—
197#397—1511no—
198#397D15111yescharacteristic, complemented
199#395—1511no—
200#394—1511no—
201#394—1511no—
202#394—1511no—
203#393—1511no—
204#393—1511no—
205#393—1511no—
206#393—1511no—
207#391—1511no—
208#388—1511no—
209#388—1511no—
210C22×Q8—1511no—
211C22×Q8—1511no—
212C22×D4—1511no—
213C2×C4⋊C4—1511no—
214C2×C4⋊C4—1511no—
215C2×C4⋊C4—1511no—
216C2×C4⋊C4—1511no—
217C2×C4⋊C4C2×D15111yescharacteristic
218C2×C22⋊C4—1511no—
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⋊C4C2×D15111yescharacteristic
228C2×C22⋊C4C2×D15111yescharacteristic
229C2×C22⋊C4C2×D15111yescharacteristic
230C2×C42—1511no—
231#95—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#95C2×D15111yescharacteristic
243#95C2×D15111yescharacteristic
244#95C2×D15111yescharacteristic
245C24—1511no—
246C24C22×D15111yescharacteristic
247C2×Q8—3022no—
248C2×Q8—6041no—
249C2×Q8—6041no—
250C2×Q8—6041no—
251C2×Q8—6041no—
252C2×Q8—6041no—
253C2×D4—6041no—
254C2×D4—6041no—
255C2×D4—6041no—
256C22×C4—1511no—
257C22×C4—1511no—
258C22×C4—1511no—
259C22×C4—1511no—
260C22×C4—1511no—
261C22×C4—1511no—
262C22×C4—1511no—
263C22×C4C22×D15111yescharacteristic
264C22×C4C22×D15111yescharacteristic
265C22×C4C22×D15111yescharacteristic
266C22×C4C22×D15111yescharacteristic
267C22×C4C22×D15111yescharacteristic
268C22×C4C22×D15111yescharacteristic
269C4⋊C4—41no—
270C4⋊C4—6041no—
271C4⋊C4—6041no—
272C4⋊C4—6041no—
273C4⋊C4—6041no—
274C22⋊C4—41no—
275C22⋊C4—41no—
276C22⋊C4—41no—
277C22⋊C4—3022no—
278C22⋊C4—3022no—
279C22⋊C4—6041no—
280C22⋊C4—6041no—
281C22⋊C4—6041no—
282C22⋊C4—6041no—
283C22⋊C4—6041no—
284C22⋊C4—6041no—
285C22⋊C4—6041no—
286C42—6041no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—3021no—
295C23—3021no—
296C23—3021no—
297C23—3021no—
298C23—3021no—
299C23—3021no—
300C23—3021no—
301C23C23×D15111yescharacteristic
302Q8—6044no—
303Q8—6044no—
304D4—6044no—
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—21no—
322C2×C4—21no—
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—3021no—
342C2×C4—3021no—
343C2×C4—1512no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—6041no—
352C22—6041no—
353C22—6041no—
354C22—6041no—
355C22—6041no—
356C22—6041no—
357C22—6041no—
358C22#41×D15111yescharacteristic
359C22#1801278411yescharacteristic
360C22#1801278411yescharacteristic
361C22#1801278511yescharacteristic
362C22#1801278511yescharacteristic
363C22#1801278611yescharacteristic
364C22#1801278611yescharacteristic
365C4—41no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4—41no—
371C4—3022no—
372C4—6041no—
373C4—6041no—
374C4—6041no—
375C4—6041no—
376C4—6041no—
377C4—6041no—
378C2—81no—
379C2—12081no—
380C2#2375279811yescharacteristic
381C2#2375282811yescharacteristic
382C2#2375283011yescharacteristic
383C2#2375295411yescharacteristic
384C2#2375295711yescharacteristic
385C2#2375295911yescharacteristic
386C2#2375296411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D151
commutator, socle, cosocleC23×C151C24
Fitting#397×C151C2
prime radicalC22×C22⋊D151C22
hypercenter#397D151
hypocenterC151#2832
LCSG ▷ C23×C151 ▷ C151
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. #23752152C2semidirect
2. #23752151C2semidirect
3. #23752141C2semidirect
4. #23752133C2semidirect
8. #23752125C2semidirect
9. #23752125C2semidirect
10. #23752124C2semidirect
11. #23752124C2semidirect
12. #23752116C2semidirect
13. #23752102C2semidirect
14. #23752100C2semidirect
15. #397×C151C2semidirect
193. C151#2832semidirect
198. #397D151semidirect

Maximal subgroups

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

subgroupindex
#237521522
#237521512
#237521412
#237521332
#237521282
#237521272
#237521252
#237521242
#237521162
#237521022
#237521002
#397×C1512
#2832151