Finite Group Databasebeta

← #34077183

Subgroups — #34077183

Order 19328.

456 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×#18012734C211yesmaximal, characteristic, complemented
2C2×#18012732C211yesmaximal, characteristic, complemented
3#23752145C211yesmaximal, characteristic, complemented
4#23752144C211yesmaximal, characteristic, complemented
5#23752143C211yesmaximal, characteristic, complemented
6#23752136C211yesmaximal, characteristic, complemented
7#23752135C211yesmaximal, characteristic, complemented
8#23752135C211yesmaximal, characteristic, complemented
9#23752134C211yesmaximal, characteristic, complemented
10#23752134C211yesmaximal, characteristic, complemented
11#23752128C211yesmaximal, characteristic
12#23752127C211yesmaximal, characteristic
13#23752127C211yesmaximal, characteristic
14#23752081C211yesmaximal, characteristic, complemented
15#396×C151C211yesmaximal, characteristic, complemented
16C22×C22⋊D151C2211yescharacteristic
17#18012734—24no—
18#18012732—24no—
19C2×C4⋊Dic151C2211yescharacteristic
20C2×C4⋊Dic151C2211yescharacteristic
21C2×C4⋊Dic151C2211yescharacteristic
22C2×C4⋊Dic151C2211yescharacteristic
23C2×Dic151⋊C4C2211yescharacteristic
24C2×Dic151⋊C4C2211yescharacteristic
25C2×Dic151⋊C4C2211yescharacteristic
26C2×Dic151⋊C4C2211yescharacteristic
27C2×Dic151⋊C4C2211yescharacteristic
28C2×Dic151⋊C4C2211yescharacteristic
29C2×Dic151⋊C4C2211yescharacteristic
30C2×Dic151⋊C4C2211yescharacteristic
31C2×C22⋊Dic151C2211yescharacteristic
32C2×C22⋊Dic151C2211yescharacteristic
33C2×C22⋊Dic151C2211yescharacteristic
34C2×(C2×D151)⋊C4C2211yescharacteristic
35C2×(C2×D151)⋊C4C2211yescharacteristic
36C2×(C2×D151)⋊C4C2211yescharacteristic
37C2×(C2×D151)⋊C4C2211yescharacteristic
38C2×(C2×D151)⋊C4C2211yescharacteristic
39C2×(C2×D151)⋊C4C2211yescharacteristic
40C2×C4×Dic151C2211yescharacteristic
41C151⋊#95C2211yescharacteristic
42C151⋊#95C2211yescharacteristic
43C151⋊#95C2211yescharacteristic
44C151⋊#95C2211yescharacteristic
45C151⋊#95C2211yescharacteristic
46C2×C4⋊C4×C151C2211yescharacteristic
47C2×C4⋊C4×C151C2211yescharacteristic
48C2×C4⋊C4×C151C2211yescharacteristic
49C2×C22⋊C4×C151C2211yescharacteristic
50C2×C22⋊C4×C151C2211yescharacteristic
51C2×C22⋊C4×C151C2211yescharacteristic
52#95×C151C2211yescharacteristic
53C23×D151C2311yescharacteristic
54C2×C22⋊D151—41no—
55C2×C22⋊D151—41no—
56C2×C22⋊D151—41no—
57C22×Dic151C2311yescharacteristic
58C22×Dic151C2311yescharacteristic
59C22×Dic151C2311yescharacteristic
60C22×Dic151C2311yescharacteristic
61C22×Dic151C2311yescharacteristic
62C22×Dic151C2311yescharacteristic
63C22×Dic151C2311yescharacteristic
64C4⋊Dic151—22no—
65C4⋊Dic151—22no—
66C4⋊Dic151—41no—
67C4⋊Dic151—41no—
68Dic151⋊C4—22no—
69Dic151⋊C4—22no—
70Dic151⋊C4—22no—
71Dic151⋊C4—41no—
72Dic151⋊C4—41no—
73Dic151⋊C4—41no—
74Dic151⋊C4—41no—
75Dic151⋊C4—41no—
76C22⋊Dic151—22no—
77C22⋊Dic151—22no—
78C22⋊Dic151—41no—
79(C2×D151)⋊C4—22no—
80(C2×D151)⋊C4—22no—
81(C2×D151)⋊C4—22no—
82(C2×D151)⋊C4—41no—
83(C2×D151)⋊C4—41no—
84(C2×D151)⋊C4—41no—
85C4×Dic151D414yescomplemented
86C24×C151C2311yescharacteristic
87C22×C4×C151C2311yescharacteristic
88C22×C4×C151C2311yescharacteristic
89C22×C4×C151C2311yescharacteristic
90C22×C4×C151C2311yescharacteristic
91C22×C4×C151C2311yescharacteristic
92C22×C4×C151C2311yescharacteristic
93C4⋊C4×C151—22no—
94C4⋊C4×C151—41no—
95C4⋊C4×C151—41no—
96C22⋊C4×C151—22no—
97C22⋊C4×C151—41no—
98C22⋊C4×C151—41no—
99C22×D151—21no—
100C22×D151—21no—
101C22×D151—21no—
102C22×D151—21no—
103C22×D151—21no—
104C22×D151—21no—
105C22×D151—21no—
106C22⋊D151—44no—
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—21no—
124C2×Dic151—21no—
125C2×Dic151—21no—
126C2×Dic151C2×D412yes—
127C2×Dic151C2×D412yes—
128C23×C151—21no—
129C23×C151—21no—
130C23×C151—21no—
131C23×C151—21no—
132C23×C151—21no—
133C23×C151—21no—
134C23×C151—21no—
135C23×C151C2411yescharacteristic
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—
150C2×C4×C151—21no—
151C2×C4×C151—21no—
152C2×C4×C151—21no—
153C2×C4×C151C2×D412yes—
154C22×C151—41no—
155C22×C151—41no—
156C22×C151—41no—
157C22×C151—41no—
158C22×C151—41no—
159C22×C151—41no—
160C22×C151—41no—
161C22×C151C22×D411yescharacteristic
162C22×C151H(5,𝔽2)11yescharacteristic
163C22×C151H(5,𝔽2)11yescharacteristic
164C22×C151H(5,𝔽2)11yescharacteristic
165C22×C1512−1+411yescharacteristic
166C22×C1512−1+411yescharacteristic
167C22×C1512−1+411yescharacteristic
168C2×D151—41no—
169C2×D151—41no—
170C2×D151—41no—
171C2×D151—41no—
172C2×D151—41no—
173C2×D151—41no—
174C2×D151—41no—
175C4×C151—22no—
176C4×C151—41no—
177C4×C151—41no—
178C4×C151—41no—
179C4×C151—41no—
180C4×C151—41no—
181Dic151—22no—
182Dic151—22no—
183Dic151—41no—
184Dic151—41no—
185Dic151—41no—
186Dic151—41no—
187Dic151—41no—
188C2×C151—81no—
189C2×C151#53711yescharacteristic
190C2×C151#53711yescharacteristic
191C2×C151#53711yescharacteristic
192C2×C151#56011yescharacteristic
193C2×C151#56311yescharacteristic
194C2×C151#56311yescharacteristic
195C2×C151#56311yescharacteristic
196D151—81no—
197C151#282311yescharacteristic, complemented, Sylow
198#2823—1511nomaximal, Sylow
199C2×#126—1511no—
200C2×#126—1511no—
201#398—1511no—
202#398—1511no—
203#398—1511no—
204#396—1511no—
205#396—1511no—
206#396—1511no—
207#396—1511no—
208#396—1511no—
209#396D15111yescharacteristic, complemented
210#394—1511no—
211#394—1511no—
212#394—1511no—
213#384—1511no—
214C22×D4—1511no—
215#126—3024no—
216#126—3024no—
217C2×C4⋊C4—1511no—
218C2×C4⋊C4—1511no—
219C2×C4⋊C4—1511no—
220C2×C4⋊C4—1511no—
221C2×C4⋊C4—1511no—
222C2×C4⋊C4—1511no—
223C2×C4⋊C4—1511no—
224C2×C4⋊C4—1511no—
225C2×C4⋊C4—1511no—
226C2×C4⋊C4—1511no—
227C2×C4⋊C4—1511no—
228C2×C4⋊C4—1511no—
229C2×C4⋊C4C2×D15111yescharacteristic
230C2×C4⋊C4C2×D15111yescharacteristic
231C2×C4⋊C4C2×D15111yescharacteristic
232C2×C22⋊C4—1511no—
233C2×C22⋊C4—1511no—
234C2×C22⋊C4—1511no—
235C2×C22⋊C4—1511no—
236C2×C22⋊C4—1511no—
237C2×C22⋊C4—1511no—
238C2×C22⋊C4—1511no—
239C2×C22⋊C4—1511no—
240C2×C22⋊C4—1511no—
241C2×C22⋊C4C2×D15111yescharacteristic
242C2×C22⋊C4C2×D15111yescharacteristic
243C2×C22⋊C4C2×D15111yescharacteristic
244C2×C42—1511no—
245#95—1511no—
246#95—1511no—
247#95—1511no—
248#95—1511no—
249#95—1511no—
250#95C2×D15111yescharacteristic
251C24—1511no—
252C24C22×D15111yescharacteristic
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—22no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—3022no—
273C4⋊C4—3022no—
274C4⋊C4—3022no—
275C4⋊C4—3022no—
276C4⋊C4—3022no—
277C4⋊C4—6041no—
278C4⋊C4—6041no—
279C4⋊C4—6041no—
280C4⋊C4—6041no—
281C4⋊C4—6041no—
282C4⋊C4—6041no—
283C4⋊C4—6041no—
284C22⋊C4—22no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—3022no—
288C22⋊C4—3022no—
289C22⋊C4—3022no—
290C22⋊C4—3022no—
291C22⋊C4—3022no—
292C22⋊C4—6041no—
293C22⋊C4—6041no—
294C22⋊C4—6041no—
295C22⋊C4—6041no—
296C42—1514no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—3021no—
305C23—3021no—
306C23—3021no—
307C23—3021no—
308C23—3021no—
309C23—3021no—
310C23—3021no—
311C23C23×D15111yescharacteristic
312D4—6044no—
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—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
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—3021no—
347C2×C4—3021no—
348C2×C4—3021no—
349C2×C4—1512no—
350C2×C4—1512no—
351C2×C4D4×D15112yes—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—6041no—
360C22—6041no—
361C22—6041no—
362C22—6041no—
363C22—6041no—
364C22—6041no—
365C22—6041no—
366C22C2×D4×D15111yescharacteristic
367C22#1801278411yescharacteristic
368C22#1801278411yescharacteristic
369C22#1801278511yescharacteristic
370C22#1801278611yescharacteristic
371C22#1801278611yescharacteristic
372C22#1801278711yescharacteristic
373C4—22no—
374C4—41no—
375C4—41no—
376C4—41no—
377C4—41no—
378C4—41no—
379C4—3022no—
380C4—3022no—
381C4—6041no—
382C4—6041no—
383C4—6041no—
384C4—6041no—
385C4—6041no—
386C2—81no—
387C2—12081no—
388C2#2375278911yescharacteristic
389C2#2375279111yescharacteristic
390C2#2375279211yescharacteristic
391C2#2375295011yescharacteristic
392C2#2375296311yescharacteristic
393C2#2375296311yescharacteristic
394C2#2375296411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D151
commutator, socle, cosocleC23×C151C24
Fitting#396×C151C2
prime radicalC22×C22⋊D151C22
hypercenter#396D151
hypocenterC151#2823
LCSG ▷ C23×C151 ▷ C151
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. C2×#18012734C2semidirect
2. C2×#18012732C2semidirect
3. #23752145C2semidirect
4. #23752144C2semidirect
5. #23752143C2semidirect
6. #23752136C2semidirect
7. #23752135C2semidirect
8. #23752135C2semidirect
9. #23752134C2semidirect
10. #23752134C2semidirect
14. #23752081C2semidirect
15. #396×C151C2semidirect
85. C4×Dic151D4semidirect
197. C151#2823semidirect
209. #396D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127342
C2×#180127322
#237521452
#237521442
#237521432
#237521362
#237521352
#237521342
#237521282
#237521272
#237520812
#396×C1512
#2823151