Finite Group Databasebeta

← #34080981

Subgroups — #34080981

Order 19328.

388 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752920C211yesmaximal, characteristic
2#23752875C211yesmaximal, characteristic
3#23752561C211yesmaximal, characteristic, complemented
4#23752549C211yesmaximal, characteristic, complemented
5#23752545C211yesmaximal, characteristic, complemented
6#23752506C211yesmaximal, characteristic, complemented
7#23752452C211yesmaximal, characteristic, complemented
8#23752420C211yesmaximal, characteristic, complemented
9#23752367C211yesmaximal, characteristic, complemented
10#23752366C211yesmaximal, characteristic, complemented
11#23752304C211yesmaximal, characteristic, complemented
12C8×C22⋊D151C211yesmaximal, characteristic
13C2×#18012664C211yesmaximal, characteristic, complemented
14#103×D151C211yesmaximal, characteristic, complemented
15#467×C151C211yesmaximal, characteristic, complemented
16C22×Dic302C2211yescharacteristic
17C2×Q8×D151C2211yescharacteristic
18C2×#14558994C2211yescharacteristic
19C2×#14558994C2211yescharacteristic
20C2×C8×D151C2211yescharacteristic
21#18012738—21no—
22#18012738C2211yescharacteristic
23#18012737C2211yescharacteristic
24#18012729—21no—
25#18012719—21no—
26#18012719C2211yescharacteristic
27#18012717—21no—
28#18012716—21no—
29#18012716—21no—
30#18012715C2211yescharacteristic
31Q8×Dic151C2211yescharacteristic
32#18012704C2211yescharacteristic
33C4×C22⋊D151C2211yescharacteristic
34(C22⋊D151)⋊C4—21no—
35(C22⋊D151)⋊C4—21no—
36C2×C4⋊Dic151C2211yescharacteristic
37C4⋊C4×D151C2211yescharacteristic
38#18012672C2211yescharacteristic
39#18012672C2211yescharacteristic
40Dic151⋊C8C2211yescharacteristic
41#18012664C2211yescharacteristic
42#18012664C2211yescharacteristic
43#18012664C2211yescharacteristic
44#18012664C2211yescharacteristic
45#18012663C2211yescharacteristic
46#18012663C2211yescharacteristic
47#18012662C2211yescharacteristic
48#18012662C2211yescharacteristic
49C22⋊(C151⋊C8)C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic
51C8×Dic151C2211yescharacteristic
52C2×Q16×C151C2211yescharacteristic
53C22×C8×C151C2211yescharacteristic
54C22⋊Q8×C151C2211yescharacteristic
55C22⋊Q8×C151C2211yescharacteristic
56#107×C151C2211yescharacteristic
57#103×C151C2211yescharacteristic
58#103×C151C2211yescharacteristic
59C2×Dic302—21no—
60C2×Dic302—21no—
61C2×Dic302—22no—
62C2×Dic302—21no—
63C2×Dic302—41no—
64C2×Dic302C2311yescharacteristic
65C2×Dic302C2311yescharacteristic
66Q8×D151—22no—
67Q8×D151—41no—
68C2×C22⋊D151D411yescharacteristic
69C22×Dic151—21no—
70C22×Dic151—21no—
71C2×C4×D151—21no—
72C2×C4×D151—21no—
73C2×C4×D151C2311yescharacteristic
74#14558994—22no—
75#14558994—41no—
76C2×C151⋊C8C2311yescharacteristic
77C2×C151⋊C8C2311yescharacteristic
78C8×D151—41no—
79C4⋊Dic151—21no—
80C4⋊Dic151—21no—
81C4⋊Dic151—21no—
82C4⋊Dic151C2311yescharacteristic
83C4⋊Dic151C2311yescharacteristic
84Dic151⋊C4—21no—
85Dic151⋊C4—21no—
86Dic151⋊C4—21no—
87Dic151⋊C4—21no—
88Dic151⋊C4—21no—
89Dic151⋊C4—21no—
90Dic151⋊C4D411yescharacteristic
91C22⋊Dic151D411yescharacteristic
92(C2×D151)⋊C4—21no—
93(C2×D151)⋊C4—21no—
94(C2×D151)⋊C4D411yescharacteristic
95C4×Dic151—21no—
96C4×Dic151—21no—
97C4×Dic151C2311yescharacteristic
98C2×Q8×C151C2311yescharacteristic
99C2×Q8×C151C2311yescharacteristic
100C22×C4×C151C2311yescharacteristic
101Q16×C151—41no—
102C2×C8×C151—41no—
103C2×C8×C151C2311yescharacteristic
104C2×C8×C151C2311yescharacteristic
105C4⋊C4×C151—21no—
106C4⋊C4×C151—21no—
107C4⋊C4×C151C2311yescharacteristic
108C4⋊C4×C151C2311yescharacteristic
109C22⋊C4×C151—21no—
110C22⋊C4×C151—21no—
111C22×D151C2×D411yescharacteristic
112Dic302—21no—
113Dic302—21no—
114Dic302—21no—
115Dic302—42no—
116Dic302—42no—
117Dic302—81no—
118Dic302#4112yes—
119C22⋊D151Q1614yescomplemented
120C2×Dic151—21no—
121C2×Dic151—21no—
122C2×Dic151—21no—
123C2×Dic151—21no—
124C2×Dic151—42no—
125C2×Dic151—81no—
126C2×Dic151C2×D411yescharacteristic
127C2×Dic151C2×D411yescharacteristic
128C2×Dic151C2×D411yescharacteristic
129C4×D151—21no—
130C4×D151—21no—
131C4×D151—42no—
132C4×D151—81no—
133C151⋊C8—21no—
134C151⋊C8—21no—
135C23×C151C2×D411yescharacteristic
136Q8×C151—21no—
137Q8×C151—21no—
138Q8×C151—21no—
139Q8×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×C151C2×D411yescharacteristic
147C2×C4×C151C2411yescharacteristic
148C8×C151—21no—
149C8×C151—21no—
150C22×C151—21no—
151C22×C151—21no—
152C22×C151C2×Q1612yes—
153C22×C151C22×D411yescharacteristic
154C2×D151—21no—
155C2×D151—21no—
156C2×D151C2×Q1612yes—
157C4×C151—21no—
158C4×C151—41no—
159C4×C151—41no—
160C4×C151—41no—
161C4×C151—41no—
162C4×C151C2×#4111yescharacteristic
163C4×C151H(5,𝔽2)11yescharacteristic
164Dic151—21no—
165Dic151—22no—
166Dic151—21no—
167Dic151—41no—
168Dic151—41no—
169Dic151—41no—
170Dic151C2×Q1612yes—
171C2×C151—22no—
172C2×C151#54611yescharacteristic
173C2×C151C22×Q1611yescharacteristic
174C2×C151#57711yescharacteristic
175D151—22no—
176C151#329911yescharacteristic, complemented, Sylow
177#3299—1511nomaximal, Sylow
178#554—1511no—
179D4×Q8—1511no—
180#487—1511no—
181#484—1511no—
182#484—1511no—
183#477—1511no—
184#467—1511no—
185#467D15111yescharacteristic, complemented
186#462—1511no—
187#451—1511no—
188#451—1511no—
189C4×Q16—1511no—
190C8×D4—1511no—
191C2×#103—1511no—
192C2×#103—1511no—
193C22×Q8—1511no—
194C22×Q8—1511no—
195C2×Q16—1511no—
196C2×Q16—1511no—
197C2×Q16C2×D15111yescharacteristic
198C22×C8—1511no—
199C22×C8C2×D15111yescharacteristic
200C4⋊Q8—3021no—
201C4⋊Q8—1511no—
202C4⋊Q8—1511no—
203#125—3021no—
204C22⋊Q8—3021no—
205C22⋊Q8—3021no—
206C22⋊Q8—3021no—
207C22⋊Q8—3021no—
208C22⋊Q8—1511no—
209C22⋊Q8—1511no—
210C22⋊Q8C2×D15111yescharacteristic
211C22⋊Q8C2×D15111yescharacteristic
212C4×Q8—1511no—
213C4×Q8—1511no—
214C4×D4—3021no—
215C4×D4—3021no—
216C4×D4—1511no—
217C2×C4⋊C4—1511no—
218C2×C4⋊C4—1511no—
219#107—1511no—
220#107—1511no—
221#107C2×D15111yescharacteristic
222C4⋊C8—1511no—
223#103—1511no—
224#103—1511no—
225#103—1511no—
226#103—1511no—
227#103—1511no—
228#103—1511no—
229#103—1511no—
230#103—1511no—
231#103C2×D15111yescharacteristic
232#103C2×D15111yescharacteristic
233C22⋊C8—1511no—
234C22⋊C8—1511no—
235C4×C8—1511no—
236C2×Q8—3021no—
237C2×Q8—3021no—
238C2×Q8—3022no—
239C2×Q8—3021no—
240C2×Q8—3022no—
241C2×Q8—6041no—
242C2×Q8—6041no—
243C2×Q8—1511no—
244C2×Q8—1511no—
245C2×Q8C22×D15111yescharacteristic
246C2×Q8C22×D15111yescharacteristic
247C2×D4—1511no—
248C22×C4—3021no—
249C22×C4—3021no—
250C22×C4—3021no—
251C22×C4—3021no—
252C22×C4—1511no—
253C22×C4C22×D15111yescharacteristic
254Q16—41no—
255Q16—3022no—
256Q16—6041no—
257C2×C8—41no—
258C2×C8—6041no—
259C2×C8—1511no—
260C2×C8—1511no—
261C2×C8C22×D15111yescharacteristic
262C2×C8C22×D15111yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—3021no—
266C4⋊C4—3021no—
267C4⋊C4—3021no—
268C4⋊C4—3021no—
269C4⋊C4—3021no—
270C4⋊C4—3021no—
271C4⋊C4—3021no—
272C4⋊C4—3021no—
273C4⋊C4—3021no—
274C4⋊C4—1511no—
275C4⋊C4—1511no—
276C4⋊C4—1511no—
277C4⋊C4C22×D15111yescharacteristic
278C4⋊C4C22×D15111yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—3021no—
282C22⋊C4—3021no—
283C22⋊C4—1511no—
284C22⋊C4—1511no—
285C42—3021no—
286C42—3021no—
287C42—1511no—
288C23—1511no—
289C23D4×D15111yescharacteristic
290Q8—21no—
291Q8—21no—
292Q8—21no—
293Q8—21no—
294Q8—3021no—
295Q8—3021no—
296Q8—3021no—
297Q8—6042no—
298Q8—6042no—
299Q8—1512no—
300Q8—12081no—
301D4—1514no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—3021no—
309C2×C4—3021no—
310C2×C4—3021no—
311C2×C4—3021no—
312C2×C4—3021no—
313C2×C4—3021no—
314C2×C4—6042no—
315C2×C4—6042no—
316C2×C4—1511no—
317C2×C4—1511no—
318C2×C4—1511no—
319C2×C4—12081no—
320C2×C4—12081no—
321C2×C4D4×D15111yescharacteristic
322C2×C4C23×D15111yescharacteristic
323C8—21no—
324C8—21no—
325C8—3021no—
326C8—3021no—
327C22—21no—
328C22—21no—
329C22—3021no—
330C22—3021no—
331C22—1512no—
332C22Q16×D15112yes—
333C22C2×D4×D15111yescharacteristic
334C4—21no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—3021no—
340C4—3021no—
341C4—3022no—
342C4—6041no—
343C4—6041no—
344C4—6041no—
345C4—1512no—
346C4#41×D15111yescharacteristic
347C4#1801278411yescharacteristic
348C2—22no—
349C2—3022no—
350C2#2375285111yescharacteristic
351C2C2×Q16×D15111yescharacteristic
352C2#2375301911yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#467×C151C2
socleC22×C151C22×D4
prime radicalC2×C22⋊D151D4
hypercenter#467D151
hypocenterC151#3299
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
3. #23752561C2semidirect
4. #23752549C2semidirect
5. #23752545C2semidirect
6. #23752506C2semidirect
7. #23752452C2semidirect
8. #23752420C2semidirect
9. #23752367C2semidirect
10. #23752366C2semidirect
11. #23752304C2semidirect
13. C2×#18012664C2semidirect
14. #103×D151C2semidirect
15. #467×C151C2semidirect
119. C22⋊D151Q16semidirect
176. C151#3299semidirect
185. #467D151semidirect

Maximal subgroups

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

subgroupindex
#237529202
#237528752
#237525612
#237525492
#237525452
#237525062
#237524522
#237524202
#237523672
#237523662
#237523042
C8×C22⋊D1512
C2×#180126642
#103×D1512
#467×C1512
#3299151