Finite Group Databasebeta

← #34079311

Subgroups — #34079311

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#23752817C211yesmaximal, characteristic, complemented
2#23752692C211yesmaximal, characteristic, complemented
3#23752531C211yesmaximal, characteristic, complemented
4#23752526C211yesmaximal, characteristic, complemented
5#23752520C211yesmaximal, characteristic, complemented
6#23752513C211yesmaximal, characteristic, complemented
7#23752413C211yesmaximal, characteristic, complemented
8#23752408C211yesmaximal, characteristic, complemented
9#23752359C211yesmaximal, characteristic, complemented
10#23752359C211yesmaximal, characteristic, complemented
11#23752325C211yesmaximal, characteristic, complemented
12#23752314C211yesmaximal, characteristic, complemented
13C4×#14558993C211yesmaximal, characteristic, complemented
14C4×D1208C211yesmaximal, characteristic, complemented
15#433×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic
17C2×#14558993C2211yescharacteristic
18C2×#14558993C2211yescharacteristic
19C2×D1208C2211yescharacteristic
20C2×D1208C2211yescharacteristic
21#18012736C2211yescharacteristic
22#18012731C2211yescharacteristic
23#18012724—21no—
24#18012724—21no—
25#18012713C2211yescharacteristic
26#18012713C2211yescharacteristic
27#18012712—21no—
28#18012712—21no—
29C4×Dic302C2211yescharacteristic
30C4×Dic302C2211yescharacteristic
31C4×D604C2211yescharacteristic
32C4×D604C2211yescharacteristic
33C4×D604C2211yescharacteristic
34C4×D604C2211yescharacteristic
35(C22⋊D151)⋊C4—21no—
36(C22⋊D151)⋊C4—21no—
37#18012697—21no—
38C2×C4⋊Dic151C2211yescharacteristic
39C4⋊C4×D151—21no—
40#18012673C2211yescharacteristic
41#18012673C2211yescharacteristic
42#18012671C2211yescharacteristic
43#18012671C2211yescharacteristic
44#18012664C2211yescharacteristic
45#18012664C2211yescharacteristic
46#18012661C2211yescharacteristic
47#18012661C2211yescharacteristic
48#18012661C2211yescharacteristic
49#18012661C2211yescharacteristic
50#18012661C2211yescharacteristic
51#18012661C2211yescharacteristic
52#117×C151C2211yescharacteristic
53C4⋊C8×C151C2211yescharacteristic
54C4⋊C8×C151C2211yescharacteristic
55C22⋊C8×C151C2211yescharacteristic
56C22⋊C8×C151C2211yescharacteristic
57#97×C151C2211yescharacteristic
58C4×C8×C151C2211yescharacteristic
59#14559004—22no—
60#14559004—22no—
61C2×Dic302C2311yescharacteristic
62C2×D604—21no—
63C2×D604—21no—
64C2×D604C2311yescharacteristic
65C2×D604C2311yescharacteristic
66C2×D604C2311yescharacteristic
67C2×C22⋊D151—21no—
68C2×C22⋊D151—21no—
69C2×C22⋊D151—21no—
70C22×Dic151—21no—
71C2×C4×D151—21no—
72C2×C4×D151—21no—
73C2×C4×D151—21no—
74C2×C4×D151—21no—
75C2×C4×D151—21no—
76#14558993—22no—
77#14558993—22no—
78D1208—22no—
79D1208—22no—
80C4⋊Dic151—21no—
81C4⋊Dic151C2311yescharacteristic
82C4⋊Dic151C2311yescharacteristic
83C4⋊Dic151C2311yescharacteristic
84C4⋊Dic151C2311yescharacteristic
85Dic151⋊C4—21no—
86Dic151⋊C4—21no—
87Dic151⋊C4—21no—
88Dic151⋊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)⋊C4—21no—
94(C2×D151)⋊C4—21no—
95C4×Dic151—21no—
96C4×Dic151—21no—
97C22×C4×C151C2311yescharacteristic
98C2×C8×C151C2311yescharacteristic
99C2×C8×C151C2311yescharacteristic
100C2×C8×C151C2311yescharacteristic
101C2×C8×C151C2311yescharacteristic
102C4⋊C4×C151D411yescharacteristic
103C4⋊C4×C151D411yescharacteristic
104C22⋊C4×C151D411yescharacteristic
105C22⋊C4×C151D411yescharacteristic
106C42×C151C2311yescharacteristic
107C42×C151C2311yescharacteristic
108C22×D151—21no—
109C22×D151—21no—
110C22×D151—21no—
111Dic302—21no—
112Dic302#4112yes—
113D604—21no—
114D604—21no—
115D604—21no—
116D604—21no—
117D604—21no—
118D604—81no—
119D604—81no—
120D604#4112yes—
121C22⋊D151—24no—
122C22⋊D151—81no—
123C22⋊D151—81no—
124C2×Dic151—21no—
125C2×Dic151—21no—
126C2×Dic151—21no—
127C2×Dic151—21no—
128C2×Dic151—21no—
129C2×Dic151—81no—
130C4×D151—24no—
131C4×D151—81no—
132C4×D151—81no—
133C4×D151—81no—
134C4×D151—81no—
135C23×C151C2×D411yescharacteristic
136C2×C4×C151—21no—
137C2×C4×C151—21no—
138C2×C4×C151C2×D411yescharacteristic
139C2×C4×C151C2×D411yescharacteristic
140C2×C4×C151C2×D411yescharacteristic
141C2×C4×C151C2×D411yescharacteristic
142C2×C4×C151C2×D411yescharacteristic
143C2×C4×C151C2411yescharacteristic
144C8×C151—21no—
145C8×C151—21no—
146C8×C151—21no—
147C8×C151—21no—
148C22×C151—21no—
149C22×C151—21no—
150C22×C151—21no—
151C22×C151C22×D411yescharacteristic
152C2×D151—22no—
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—21no—
162C4×C151—21no—
163C4×C151—21no—
164C4×C151—21no—
165C4×C151—21no—
166C4×C151C2×#4111yescharacteristic
167C4×C151C2×#4111yescharacteristic
168Dic151—22no—
169Dic151—41no—
170Dic151—41no—
171Dic151—41no—
172Dic151—41no—
173C2×C151—41no—
174C2×C151#52511yescharacteristic
175C2×C151#57611yescharacteristic
176C2×C151#57711yescharacteristic
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#479—1511no—
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#433D15111yescharacteristic, complemented
197C2×#41—1511no—
198C2×SD16—1511no—
199C2×SD16—1511no—
200C2×D8—1511no—
201C2×D8—1511no—
202#127—1511no—
203#125—1511no—
204#123—3021no—
205#123—3021no—
206#121—3021no—
207#121—3021no—
208#121—1511no—
209#121—1511no—
210C4×Q8—1511no—
211C4×Q8—1511no—
212C4×D4—3021no—
213C4×D4—3021no—
214C4×D4—1511no—
215C4×D4—1511no—
216C4×D4—1511no—
217C4×D4—1511no—
218#117—3021no—
219#117C2×D15111yescharacteristic
220C2×C4⋊C4—3021no—
221C2×C4⋊C4—1511no—
222#107—1511no—
223#107—1511no—
224#106—1511no—
225#106—1511no—
226C4⋊C8C2×D15111yescharacteristic
227C4⋊C8C2×D15111yescharacteristic
228#103—1511no—
229#103—1511no—
230#102—1511no—
231#102—1511no—
232#102—1511no—
233#102—1511no—
234#102—1511no—
235#102—1511no—
236C22⋊C8C2×D15111yescharacteristic
237C22⋊C8C2×D15111yescharacteristic
238#97C2×D15111yescharacteristic
239C4×C8C2×D15111yescharacteristic
240#41—3022no—
241#41—3022no—
242C2×Q8—1511no—
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×C4C22×D15111yescharacteristic
258SD16—3022no—
259SD16—3022no—
260D8—3022no—
261D8—3022no—
262C2×C8C22×D15111yescharacteristic
263C2×C8C22×D15111yescharacteristic
264C2×C8C22×D15111yescharacteristic
265C2×C8C22×D15111yescharacteristic
266C4⋊C4—3021no—
267C4⋊C4—3021no—
268C4⋊C4—3021no—
269C4⋊C4—3021no—
270C4⋊C4—3021no—
271C4⋊C4—1511no—
272C4⋊C4—1511no—
273C4⋊C4—1511no—
274C4⋊C4—1511no—
275C4⋊C4D60411yescharacteristic
276C4⋊C4D60411yescharacteristic
277C22⋊C4—3021no—
278C22⋊C4—3021no—
279C22⋊C4—3021no—
280C22⋊C4—3021no—
281C22⋊C4—3021no—
282C22⋊C4—3021no—
283C22⋊C4D60411yescharacteristic
284C22⋊C4D60411yescharacteristic
285C42—3021no—
286C42—3021no—
287C42C22×D15111yescharacteristic
288C42C22×D15111yescharacteristic
289C23—3021no—
290C23—3021no—
291C23—3021no—
292C23C2×D60411yescharacteristic
293Q8—3021no—
294Q8—1512no—
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—3024no—
309C2×C4—3021no—
310C2×C4—3021no—
311C2×C4—3021no—
312C2×C4—3021no—
313C2×C4—3021no—
314C2×C4—12081no—
315C2×C4—12081no—
316C2×C4—12081no—
317C2×C4—12081no—
318C2×C4—12081no—
319C2×C4C2×D60411yescharacteristic
320C2×C4C2×D60411yescharacteristic
321C2×C4C2×D60411yescharacteristic
322C2×C4C2×D60411yescharacteristic
323C2×C4C2×D60411yescharacteristic
324C2×C4C23×D15111yescharacteristic
325C8—21no—
326C8—21no—
327C8—21no—
328C8—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—3022no—
333C22—6041no—
334C22—6041no—
335C22—6041no—
336C22—6041no—
337C22—6041no—
338C22—6041no—
339C22—6041no—
340C22—6041no—
341C22C22×D60411yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—3022no—
348C4—6041no—
349C4—6041no—
350C4—6041no—
351C4—6041no—
352C4#41×D15111yescharacteristic
353C4#41×D15111yescharacteristic
354C2—41no—
355C2—6042no—
356C2—12081no—
357C2—12081no—
358C2#2375272411yescharacteristic
359C2#2375301711yescharacteristic
360C2#2375302411yescharacteristic
subgroupG/H
centerC22C22×D604
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#433×C151C2
socleC22×C151C22×D4
hypercenter#433D151
hypocenterC151#3119
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #23752817C2semidirect
2. #23752692C2semidirect
3. #23752531C2semidirect
4. #23752526C2semidirect
5. #23752520C2semidirect
6. #23752513C2semidirect
7. #23752413C2semidirect
8. #23752408C2semidirect
9. #23752359C2semidirect
10. #23752359C2semidirect
11. #23752325C2semidirect
12. #23752314C2semidirect
13. C4×#14558993C2semidirect
14. C4×D1208C2semidirect
15. #433×C151C2semidirect
180. C151#3119semidirect
196. #433D151semidirect

Maximal subgroups

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

subgroupindex
#237528172
#237526922
#237525312
#237525262
#237525202
#237525132
#237524132
#237524082
#237523592
#237523252
#237523142
C4×#145589932
C4×D12082
#433×C1512
#3119151