Finite Group Databasebeta

← #34079316

Subgroups — #34079316

Order 19328.

396 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752818C211yesmaximal, characteristic, complemented
2#23752694C211yesmaximal, characteristic, complemented
3#23752532C211yesmaximal, characteristic, complemented
4#23752527C211yesmaximal, characteristic, complemented
5#23752509C211yesmaximal, characteristic, complemented
6#23752412C211yesmaximal, characteristic, complemented
7#23752408C211yesmaximal, characteristic, complemented
8#23752360C211yesmaximal, characteristic, complemented
9#23752360C211yesmaximal, characteristic, complemented
10#23752323C211yesmaximal, characteristic, complemented
11#23752315C211yesmaximal, characteristic, complemented
12#23752297C211yesmaximal, characteristic, complemented
13#23752294C211yesmaximal, characteristic, complemented
14#23752272C211yesmaximal, characteristic, complemented
15#479×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic
17C2×#14558991C2211yescharacteristic
18C2×#14558991C2211yescharacteristic
19C2×D1208C2211yescharacteristic
20C2×D1208C2211yescharacteristic
21#18012736C2211yescharacteristic
22#18012724—21no—
23#18012724—21no—
24#18012714—21no—
25#18012714—21no—
26#18012714C2211yescharacteristic
27#18012714C2211yescharacteristic
28Q8×Dic151C2211yescharacteristic
29C4×D604—21no—
30C4×D604C2211yescharacteristic
31#18012701—21no—
32#18012701C2211yescharacteristic
33#18012701C2211yescharacteristic
34#18012701C2211yescharacteristic
35#18012696—21no—
36#18012696C2211yescharacteristic
37C4⋊C4×D151—21no—
38C4⋊C4×D151C2211yescharacteristic
39#18012672C2211yescharacteristic
40#18012670C2211yescharacteristic
41C4⋊(C151⋊C8)C2211yescharacteristic
42#18012661C2211yescharacteristic
43#18012661C2211yescharacteristic
44#18012659C2211yescharacteristic
45#18012659C2211yescharacteristic
46#18012659C2211yescharacteristic
47#18012659C2211yescharacteristic
48(C2×D151)⋊C8C2211yescharacteristic
49(C2×D151)⋊C8C2211yescharacteristic
50#18012649C2211yescharacteristic
51C8×Dic151C2211yescharacteristic
52#125×C151C2211yescharacteristic
53C4×Q8×C151C2211yescharacteristic
54#107×C151C2211yescharacteristic
55#106×C151C2211yescharacteristic
56C4⋊C8×C151C2211yescharacteristic
57#103×C151C2211yescharacteristic
58#103×C151C2211yescharacteristic
59#14559005—22no—
60#14559005—22no—
61C2×D604—21no—
62C2×D604—21no—
63C2×D604—21no—
64C2×D604—21no—
65C2×D604—21no—
66C2×D604C2311yescharacteristic
67C2×D604C2311yescharacteristic
68C2×D604C2311yescharacteristic
69C2×C4×D151—21no—
70C2×C4×D151—21no—
71C2×C4×D151—21no—
72C2×C4×D151—21no—
73C2×C4×D151—21no—
74C2×C4×D151—21no—
75C2×C4×D151C2311yescharacteristic
76#14558991—22no—
77#14558991—22no—
78D1208—22no—
79D1208—22no—
80C2×C151⋊C8C2311yescharacteristic
81C2×C151⋊C8C2311yescharacteristic
82C4⋊Dic151—21no—
83C4⋊Dic151C2311yescharacteristic
84Dic151⋊C4—21no—
85Dic151⋊C4D411yescharacteristic
86Dic151⋊C4D411yescharacteristic
87(C2×D151)⋊C4—21no—
88(C2×D151)⋊C4—21no—
89(C2×D151)⋊C4—21no—
90(C2×D151)⋊C4—21no—
91(C2×D151)⋊C4—21no—
92(C2×D151)⋊C4—21no—
93(C2×D151)⋊C4D411yescharacteristic
94(C2×D151)⋊C4D411yescharacteristic
95C4×Dic151—21no—
96C4×Dic151C2311yescharacteristic
97C2×Q8×C151C2311yescharacteristic
98C2×C8×C151C2311yescharacteristic
99C2×C8×C151C2311yescharacteristic
100C4⋊C4×C151—21no—
101C4⋊C4×C151—21no—
102C4⋊C4×C151—21no—
103C4⋊C4×C151C2311yescharacteristic
104C4⋊C4×C151C2311yescharacteristic
105C4⋊C4×C151C2311yescharacteristic
106C42×C151—21no—
107C42×C151C2311yescharacteristic
108C22×D151—21no—
109C22×D151—21no—
110C22×D151—21no—
111C22×D151C2×D411yescharacteristic
112D604—24no—
113D604—21no—
114D604—21no—
115D604—21no—
116D604—21no—
117D604—21no—
118D604—81no—
119D604—81no—
120D604—81no—
121D604—81no—
122D604#4112yes—
123C2×Dic151—21no—
124C2×Dic151C2×D411yescharacteristic
125C2×Dic151C2×D411yescharacteristic
126C2×Dic151C2×D411yescharacteristic
127C4×D151—24no—
128C4×D151—21no—
129C4×D151—21no—
130C4×D151—81no—
131C4×D151—81no—
132C4×D151—81no—
133C4×D151—81no—
134C4×D151—81no—
135C151⋊C8—21no—
136C151⋊C8—21no—
137Q8×C151—21no—
138Q8×C151#4112yes—
139C2×C4×C151—21no—
140C2×C4×C151—21no—
141C2×C4×C151—21no—
142C2×C4×C151—21no—
143C2×C4×C151C2×D411yescharacteristic
144C2×C4×C151C2×D411yescharacteristic
145C2×C4×C151C2411yescharacteristic
146C8×C151—21no—
147C8×C151—21no—
148C22×C151C22×D411yescharacteristic
149C2×D151—21no—
150C2×D151—22no—
151C2×D151—21no—
152C2×D151—21no—
153C2×D151—41no—
154C2×D151—41no—
155C2×D151—41no—
156C2×D151—41no—
157C2×D151—41no—
158C2×D151—41no—
159C2×D151—41no—
160C2×D151—41no—
161C4×C151—22no—
162C4×C151—21no—
163C4×C151—21no—
164C4×C151—41no—
165C4×C151—41no—
166C4×C151—41no—
167C4×C151C2×#4111yescharacteristic
168C4×C151C2×#4111yescharacteristic
169Dic151—21no—
170Dic151—21no—
171Dic151—21no—
172Dic151—41no—
173C2×C151#52511yescharacteristic
174C2×C151#57611yescharacteristic
175C2×C151#57711yescharacteristic
176D151—41no—
177D151—42no—
178D151—81no—
179D151—81no—
180C151#311911yescharacteristic, complemented, Sylow
181#3119—1511nomaximal, Sylow
182#540—1511no—
183#520—1511no—
184#481—1511no—
185#480—1511no—
186#479D15111yescharacteristic, complemented
187#478—1511no—
188#460—1511no—
189#459—1511no—
190#449—1511no—
191#449—1511no—
192#442—1511no—
193#440—1511no—
194C4×SD16—1511no—
195C4×D8—1511no—
196#433—1511no—
197C2×#41—1511no—
198C2×SD16—1511no—
199C2×SD16—1511no—
200C2×D8—1511no—
201C2×D8—1511no—
202#127—1511no—
203#125C2×D15111yescharacteristic
204#123—3021no—
205#123—3021no—
206#121—3021no—
207#121—3021no—
208#121—1511no—
209#121—1511no—
210C4×Q8—1511no—
211C4×Q8C2×D15111yescharacteristic
212C4×D4—3021no—
213C4×D4—3021no—
214C4×D4—1511no—
215C4×D4—1511no—
216C4×D4—1511no—
217C4×D4—1511no—
218#117—3021no—
219#117—1511no—
220C2×C4⋊C4—3021no—
221C2×C4⋊C4—1511no—
222#107—1511no—
223#107C2×D15111yescharacteristic
224#106—1511no—
225#106C2×D15111yescharacteristic
226C4⋊C8—1511no—
227C4⋊C8C2×D15111yescharacteristic
228#103C2×D15111yescharacteristic
229#103C2×D15111yescharacteristic
230#102—1511no—
231#102—1511no—
232#102—1511no—
233#102—1511no—
234#102—1511no—
235#102—1511no—
236C22⋊C8—1511no—
237C22⋊C8—1511no—
238#97—1511no—
239C4×C8—1511no—
240#41—3022no—
241#41—3022no—
242C2×Q8C22×D15111yescharacteristic
243C2×D4—3021no—
244C2×D4—3021no—
245C2×D4—3021no—
246C2×D4—3021no—
247C2×D4—3021no—
248C2×D4—1511no—
249C2×D4—1511no—
250C2×D4—1511no—
251C22×C4—3021no—
252C22×C4—3021no—
253C22×C4—3021no—
254C22×C4—3021no—
255C22×C4—3021no—
256C22×C4—3021no—
257C22×C4—1511no—
258SD16—3022no—
259SD16—3022no—
260D8—3022no—
261D8—3022no—
262C2×C8—1511no—
263C2×C8—1511no—
264C2×C8C22×D15111yescharacteristic
265C2×C8C22×D15111yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—3021no—
270C4⋊C4—3021no—
271C4⋊C4—1511no—
272C4⋊C4—1511no—
273C4⋊C4—1511no—
274C4⋊C4C22×D15111yescharacteristic
275C4⋊C4C22×D15111yescharacteristic
276C4⋊C4C22×D15111yescharacteristic
277C22⋊C4—3021no—
278C22⋊C4—3021no—
279C22⋊C4—3021no—
280C22⋊C4—3021no—
281C22⋊C4—3021no—
282C22⋊C4—3021no—
283C22⋊C4—1511no—
284C22⋊C4—1511no—
285C42—21no—
286C42—3021no—
287C42—1511no—
288C42C22×D15111yescharacteristic
289C23—3021no—
290C23—3021no—
291C23—3021no—
292C23—1511no—
293Q8—21no—
294Q8#1455900512yes—
295D4—3024no—
296D4—3021no—
297D4—3021no—
298D4—3021no—
299D4—3021no—
300D4—3021no—
301D4—1512no—
302D4—12081no—
303D4—12081no—
304D4—12081no—
305D4—12081no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—3024no—
311C2×C4—3021no—
312C2×C4—3021no—
313C2×C4—3021no—
314C2×C4—1511no—
315C2×C4—1511no—
316C2×C4—1511no—
317C2×C4—12081no—
318C2×C4—12081no—
319C2×C4—12081no—
320C2×C4—12081no—
321C2×C4—12081no—
322C2×C4D4×D15111yescharacteristic
323C2×C4D4×D15111yescharacteristic
324C2×C4C23×D15111yescharacteristic
325C8—21no—
326C8—21no—
327C8—3021no—
328C8—3021no—
329C22—3021no—
330C22—3022no—
331C22—3021no—
332C22—3021no—
333C22—6041no—
334C22—6041no—
335C22—6041no—
336C22—6041no—
337C22—6041no—
338C22—6041no—
339C22—6041no—
340C22—6041no—
341C22C2×D4×D15111yescharacteristic
342C4—22no—
343C4—21no—
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—3021no—
349C4—3021no—
350C4—3021no—
351C4—6041no—
352C4#41×D15111yescharacteristic
353C4C2×#1455900511yescharacteristic
354C2—6041no—
355C2—6042no—
356C2—12081no—
357C2—12081no—
358C2#2375272511yescharacteristic
359C2#2375301411yescharacteristic
360C2#2375302111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#479×C151C2
socleC22×C151C22×D4
hypercenter#479D151
hypocenterC151#3119
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
1. #23752818C2semidirect
2. #23752694C2semidirect
3. #23752532C2semidirect
4. #23752527C2semidirect
5. #23752509C2semidirect
6. #23752412C2semidirect
7. #23752408C2semidirect
8. #23752360C2semidirect
9. #23752360C2semidirect
10. #23752323C2semidirect
11. #23752315C2semidirect
12. #23752297C2semidirect
13. #23752294C2semidirect
14. #23752272C2semidirect
15. #479×C151C2semidirect
180. C151#3119semidirect
186. #479D151semidirect

Maximal subgroups

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

subgroupindex
#237528182
#237526942
#237525322
#237525272
#237525092
#237524122
#237524082
#237523602
#237523232
#237523152
#237522972
#237522942
#237522722
#479×C1512
#3119151