Finite Group Databasebeta

← #34079994

Subgroups — #34079994

Order 19328.

390 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752790C211yesmaximal, characteristic
2#23752783C211yesmaximal, characteristic, complemented
3#23752554C211yesmaximal, characteristic, complemented
4#23752548C211yesmaximal, characteristic, complemented
5#23752543C211yesmaximal, characteristic, complemented
6#23752537C211yesmaximal, characteristic, complemented
7#23752470C211yesmaximal, characteristic, complemented
8#23752458C211yesmaximal, characteristic, complemented
9#23752453C211yesmaximal, characteristic, complemented
10#23752441C211yesmaximal, characteristic, complemented
11#23752376C211yesmaximal, characteristic, complemented
12#23752376C211yesmaximal, characteristic, complemented
13#23752370C211yesmaximal, characteristic, complemented
14#23752353C211yesmaximal, characteristic, complemented
15#408×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic
17C22×Dic302C2211yescharacteristic
18C2×Dic604C2211yescharacteristic
19C2×Dic604C2211yescharacteristic
20C2×#14558993C2211yescharacteristic
21C2×#14558993C2211yescharacteristic
22#18012737—21no—
23#18012726—21no—
24#18012720—21no—
25#18012720—21no—
26#18012718C2211yescharacteristic
27#18012718C2211yescharacteristic
28#18012718C2211yescharacteristic
29#18012718C2211yescharacteristic
30#18012718C2211yescharacteristic
31#18012718C2211yescharacteristic
32#18012715—21no—
33#18012713C2211yescharacteristic
34#18012713C2211yescharacteristic
35#18012711—21no—
36#18012711—21no—
37#18012710—21no—
38#18012698C2211yescharacteristic
39C2×C4⋊Dic151C2211yescharacteristic
40#18012673C2211yescharacteristic
41#18012673C2211yescharacteristic
42#18012671C2211yescharacteristic
43#18012671C2211yescharacteristic
44#18012664C2211yescharacteristic
45#18012664C2211yescharacteristic
46#18012664C2211yescharacteristic
47#18012664C2211yescharacteristic
48#18012664C2211yescharacteristic
49#18012664C2211yescharacteristic
50#18012661C2211yescharacteristic
51#18012661C2211yescharacteristic
52C2×#41×C151C2211yescharacteristic
53C2×M16×C151C2211yescharacteristic
54C22×C8×C151C2211yescharacteristic
55C22⋊C8×C151C2211yescharacteristic
56C22⋊C8×C151C2211yescharacteristic
57C22⋊C8×C151C2211yescharacteristic
58C22⋊C8×C151C2211yescharacteristic
59#14559004—41no—
60#14559004—41no—
61C2×Dic302—21no—
62C2×Dic302—41no—
63C2×Dic302—41no—
64C2×Dic302C2311yescharacteristic
65C2×Dic302C2311yescharacteristic
66C2×Dic302C2311yescharacteristic
67C2×D604C2311yescharacteristic
68C2×C22⋊D151—21no—
69C2×C22⋊D151—21no—
70C2×C22⋊D151—21no—
71C22×Dic151—21no—
72C22×Dic151—21no—
73C2×C4×D151—21no—
74Dic604—41no—
75Dic604—41no—
76#14558993—41no—
77#14558993—41no—
78C4⋊Dic151—21no—
79C4⋊Dic151C2311yescharacteristic
80C4⋊Dic151C2311yescharacteristic
81C4⋊Dic151C2311yescharacteristic
82C4⋊Dic151C2311yescharacteristic
83Dic151⋊C4—21no—
84Dic151⋊C4—21no—
85Dic151⋊C4—21no—
86Dic151⋊C4—21no—
87Dic151⋊C4—21no—
88Dic151⋊C4—21no—
89C22⋊Dic151—21no—
90C22⋊Dic151—21no—
91C22⋊Dic151—21no—
92C22⋊Dic151—21no—
93C22⋊Dic151—21no—
94C22⋊Dic151—21no—
95C22⋊Dic151—21no—
96(C2×D151)⋊C4—21no—
97(C2×D151)⋊C4—21no—
98C4×Dic151—21no—
99#41×C151—41no—
100#41×C151—41no—
101C2×Q8×C151D411yescharacteristic
102C2×D4×C151D411yescharacteristic
103C2×D4×C151D411yescharacteristic
104C2×D4×C151D411yescharacteristic
105C22×C4×C151C2311yescharacteristic
106C22×C4×C151C2311yescharacteristic
107C22×C4×C151C2311yescharacteristic
108M16×C151—41no—
109C2×C8×C151—41no—
110C2×C8×C151C2311yescharacteristic
111C2×C8×C151C2311yescharacteristic
112C2×C8×C151C2311yescharacteristic
113C2×C8×C151C2311yescharacteristic
114C22×D151—21no—
115Dic302—21no—
116Dic302—21no—
117Dic302—21no—
118Dic302—21no—
119Dic302—21no—
120Dic302—21no—
121Dic302—42no—
122D604—21no—
123D604—21no—
124C22⋊D151—42no—
125C22⋊D151—81no—
126C22⋊D151—81no—
127C2×Dic151—21no—
128C2×Dic151—21no—
129C2×Dic151—21no—
130C2×Dic151—21no—
131C2×Dic151—21no—
132C2×Dic151—21no—
133C2×Dic151—21no—
134C2×Dic151—42no—
135C2×Dic151—81no—
136C4×D151—42no—
137C23×C151C2×D411yescharacteristic
138C23×C151C2×D411yescharacteristic
139C23×C151C2×D411yescharacteristic
140Q8×C151—41no—
141D4×C151—41no—
142D4×C151—41no—
143D4×C151—41no—
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×C151C2×D411yescharacteristic
151C2×C4×C151C2×D411yescharacteristic
152C2×C4×C151C2×D411yescharacteristic
153C2×C4×C151C2411yescharacteristic
154C8×C151—21no—
155C8×C151—21no—
156C8×C151—21no—
157C8×C151—21no—
158C22×C151—21no—
159C22×C151—21no—
160C22×C151—21no—
161C22×C151—21no—
162C22×C151—21no—
163C22×C151—21no—
164C22×C151—21no—
165C22×C151—21no—
166C22×C151—21no—
167C22×C151C22×D411yescharacteristic
168C2×D151—41no—
169C2×D151—41no—
170C2×D151—41no—
171C4×C151—21no—
172C4×C151—21no—
173C4×C151—21no—
174C4×C151H(5,𝔽2)11yescharacteristic
175C4×C151H(5,𝔽2)11yescharacteristic
176Dic151—41no—
177Dic151—41no—
178Dic151—41no—
179Dic151—41no—
180Dic151—41no—
181Dic151—41no—
182Dic151—41no—
183C2×C151—41no—
184C2×C151—41no—
185C2×C151—41no—
186C2×C151#53411yescharacteristic
187C2×C151#57711yescharacteristic
188C2×C151#57811yescharacteristic
189D151—81no—
190C151#320111yescharacteristic, complemented, Sylow
191#3201—1511nomaximal, Sylow
192#537—1511no—
193#536—1511no—
194#485—1511no—
195#484—1511no—
196#483—1511no—
197#482—1511no—
198#470—1511no—
199#468—1511no—
200#467—1511no—
201#465—1511no—
202#452—1511no—
203#452—1511no—
204#451—1511no—
205#448—1511no—
206#408D15111yescharacteristic, complemented
207C2×#41—1511no—
208C2×#41C2×D15111yescharacteristic
209C22×Q8—1511no—
210C2×Q16—1511no—
211C2×Q16—1511no—
212C2×SD16—1511no—
213C2×SD16—1511no—
214C2×M16C2×D15111yescharacteristic
215C22×C8C2×D15111yescharacteristic
216C4⋊Q8—3021no—
217#124—3021no—
218#123—3021no—
219#123—3021no—
220C22⋊Q8—3021no—
221C22⋊Q8—1511no—
222C22⋊Q8—1511no—
223C22⋊Q8—1511no—
224C22⋊Q8—1511no—
225C22⋊Q8—1511no—
226C22⋊Q8—1511no—
227#121—3021no—
228#121—3021no—
229#121—3021no—
230#121—1511no—
231#121—1511no—
232#117—1511no—
233C2×C4⋊C4—1511no—
234#107—1511no—
235#107—1511no—
236#106—1511no—
237#106—1511no—
238#103—1511no—
239#103—1511no—
240#103—1511no—
241#103—1511no—
242#103—1511no—
243#103—1511no—
244#102—1511no—
245#102—1511no—
246C22⋊C8C2×D15111yescharacteristic
247C22⋊C8C2×D15111yescharacteristic
248C22⋊C8C2×D15111yescharacteristic
249C22⋊C8C2×D15111yescharacteristic
250#41—41no—
251#41—41no—
252#41—6041no—
253#41—6041no—
254C2×Q8—3021no—
255C2×Q8—6041no—
256C2×Q8—6041no—
257C2×Q8—1511no—
258C2×Q8—1511no—
259C2×Q8—1511no—
260C2×Q8D60411yescharacteristic
261C2×D4—3021no—
262C2×D4—3021no—
263C2×D4—3021no—
264C2×D4—1511no—
265C2×D4D60411yescharacteristic
266C2×D4D60411yescharacteristic
267C2×D4D60411yescharacteristic
268C22×C4—3021no—
269C22×C4—3021no—
270C22×C4—3021no—
271C22×C4C22×D15111yescharacteristic
272C22×C4C22×D15111yescharacteristic
273C22×C4C22×D15111yescharacteristic
274Q16—6041no—
275Q16—6041no—
276SD16—6041no—
277SD16—6041no—
278M16—41no—
279C2×C8—41no—
280C2×C8C22×D15111yescharacteristic
281C2×C8C22×D15111yescharacteristic
282C2×C8C22×D15111yescharacteristic
283C2×C8C22×D15111yescharacteristic
284C4⋊C4—3021no—
285C4⋊C4—3021no—
286C4⋊C4—3021no—
287C4⋊C4—3021no—
288C4⋊C4—3021no—
289C4⋊C4—3021no—
290C4⋊C4—3021no—
291C4⋊C4—1511no—
292C4⋊C4—1511no—
293C4⋊C4—1511no—
294C4⋊C4—1511no—
295C22⋊C4—3021no—
296C22⋊C4—3021no—
297C22⋊C4—3021no—
298C22⋊C4—3021no—
299C22⋊C4—3021no—
300C22⋊C4—3021no—
301C22⋊C4—3021no—
302C22⋊C4—3021no—
303C22⋊C4—3021no—
304C42—3021no—
305C23—3021no—
306C23C2×D60411yescharacteristic
307C23C2×D60411yescharacteristic
308C23C2×D60411yescharacteristic
309Q8—41no—
310Q8—3021no—
311Q8—3021no—
312Q8—3021no—
313Q8—3021no—
314Q8—3021no—
315Q8—3021no—
316Q8—6042no—
317D4—41no—
318D4—41no—
319D4—41no—
320D4—3021no—
321D4—3021no—
322D4—6042no—
323D4—12081no—
324D4—12081no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—3021no—
332C2×C4—3021no—
333C2×C4—3021no—
334C2×C4—3021no—
335C2×C4—3021no—
336C2×C4—3021no—
337C2×C4—3021no—
338C2×C4—6042no—
339C2×C4—6042no—
340C2×C4—12081no—
341C2×C4C2×D60411yescharacteristic
342C2×C4C2×D60411yescharacteristic
343C2×C4C2×D60411yescharacteristic
344C2×C4C23×D15111yescharacteristic
345C8—21no—
346C8—21no—
347C8—21no—
348C8—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—6041no—
359C22—6041no—
360C22—6041no—
361C22C22×D60411yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—6041no—
366C4—6041no—
367C4—6041no—
368C4—6041no—
369C4—6041no—
370C4—6041no—
371C4—6041no—
372C4#1801278411yescharacteristic
373C4#1801278411yescharacteristic
374C2—41no—
375C2—41no—
376C2—41no—
377C2—12081no—
378C2#2375277411yescharacteristic
379C2#2375302411yescharacteristic
380C2#2375302911yescharacteristic
subgroupG/H
centerC22C22×D604
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#408×C151C2
socleC22×C151C22×D4
prime radical#23752790C2
hypercenter#408D151
hypocenterC151#3201
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
2. #23752783C2semidirect
3. #23752554C2semidirect
4. #23752548C2semidirect
5. #23752543C2semidirect
6. #23752537C2semidirect
7. #23752470C2semidirect
8. #23752458C2semidirect
9. #23752453C2semidirect
10. #23752441C2semidirect
11. #23752376C2semidirect
12. #23752376C2semidirect
13. #23752370C2semidirect
14. #23752353C2semidirect
15. #408×C151C2semidirect
190. C151#3201semidirect
206. #408D151semidirect

Maximal subgroups

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

subgroupindex
#237527902
#237527832
#237525542
#237525482
#237525432
#237525372
#237524702
#237524582
#237524532
#237524412
#237523762
#237523702
#237523532
#408×C1512
#3201151