Finite Group Databasebeta

← #34081055

Subgroups — #34081055

Order 19328.

408 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#23752926C211yesmaximal, characteristic, complemented
2#23752880C211yesmaximal, characteristic, complemented
3#23752557C211yesmaximal, characteristic, complemented
4#23752539C211yesmaximal, characteristic, complemented
5#23752533C211yesmaximal, characteristic, complemented
6#23752506C211yesmaximal, characteristic, complemented
7#23752447C211yesmaximal, characteristic, complemented
8#23752405C211yesmaximal, characteristic, complemented
9#23752355C211yesmaximal, characteristic, complemented
10#23752354C211yesmaximal, characteristic, complemented
11#23752303C211yesmaximal, characteristic, complemented
12C8×C22⋊D151C211yesmaximal, characteristic, complemented
13#23752209C211yesmaximal, characteristic, complemented
14#23752205C211yesmaximal, characteristic, complemented
15#466×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic
17C2×#14559003C2211yescharacteristic
18C2×#14558992C2211yescharacteristic
19C2×#14558989C2211yescharacteristic
20C2×C8×D151C2211yescharacteristic
21#18012738C2211yescharacteristic
22#18012735—21no—
23#18012735C2211yescharacteristic
24#18012726—21no—
25#18012725—21no—
26#18012714C2211yescharacteristic
27#18012712—21no—
28#18012711—21no—
29#18012711—21no—
30#18012710C2211yescharacteristic
31#18012704C2211yescharacteristic
32D4×Dic151C2211yescharacteristic
33C4×C22⋊D151C2211yescharacteristic
34(C22⋊D151)⋊C4—21no—
35#18012698C2211yescharacteristic
36#18012697C2211yescharacteristic
37#18012695—21no—
38#18012672C2211yescharacteristic
39#18012670C2211yescharacteristic
40Dic151⋊C8C2211yescharacteristic
41#18012664C2211yescharacteristic
42#18012664C2211yescharacteristic
43#18012662C2211yescharacteristic
44#18012661C2211yescharacteristic
45#18012661C2211yescharacteristic
46#18012660C2211yescharacteristic
47#18012660C2211yescharacteristic
48#18012659C2211yescharacteristic
49C22⋊(C151⋊C8)C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic
51C8×Dic151C2211yescharacteristic
52C2×D8×C151C2211yescharacteristic
53C22×C8×C151C2211yescharacteristic
54#121×C151C2211yescharacteristic
55#121×C151C2211yescharacteristic
56#107×C151C2211yescharacteristic
57#102×C151C2211yescharacteristic
58#102×C151C2211yescharacteristic
59#14559004—22no—
60#14559004—41no—
61#14559003—22no—
62#14559003—41no—
63C2×Dic302—21no—
64C2×Dic302C2311yescharacteristic
65C2×D604—21no—
66C2×D604C2311yescharacteristic
67C2×C22⋊D151—21no—
68C2×C22⋊D151—21no—
69C2×C22⋊D151—21no—
70C2×C22⋊D151—21no—
71C2×C22⋊D151—21no—
72C2×C22⋊D151D411yescharacteristic
73C22×Dic151—21no—
74C22×Dic151—21no—
75C2×C4×D151—21no—
76C2×C4×D151C2311yescharacteristic
77#14558992—22no—
78#14558989—41no—
79C2×C151⋊C8C2311yescharacteristic
80C2×C151⋊C8C2311yescharacteristic
81C8×D151—41no—
82C4⋊Dic151C2311yescharacteristic
83C4⋊Dic151C2311yescharacteristic
84Dic151⋊C4—21no—
85Dic151⋊C4—21no—
86Dic151⋊C4D411yescharacteristic
87C22⋊Dic151—21no—
88C22⋊Dic151—21no—
89C22⋊Dic151—21no—
90C22⋊Dic151D411yescharacteristic
91(C2×D151)⋊C4—21no—
92(C2×D151)⋊C4—21no—
93(C2×D151)⋊C4D411yescharacteristic
94C4×Dic151—21no—
95C4×Dic151—21no—
96C4×Dic151—21no—
97C4×Dic151C2311yescharacteristic
98C2×D4×C151—21no—
99C2×D4×C151—21no—
100C2×D4×C151C2311yescharacteristic
101C2×D4×C151C2311yescharacteristic
102C22×C4×C151C2311yescharacteristic
103D8×C151—41no—
104C2×C8×C151—41no—
105C2×C8×C151C2311yescharacteristic
106C2×C8×C151C2311yescharacteristic
107C4⋊C4×C151C2311yescharacteristic
108C4⋊C4×C151C2311yescharacteristic
109C22⋊C4×C151—21no—
110C22⋊C4×C151—21no—
111C22×D151—21no—
112C22×D151C2×D411yescharacteristic
113Dic302—21no—
114Dic302—81no—
115Dic302#4112yes—
116D604—21no—
117D604—21no—
118D604—81no—
119C22⋊D151—22no—
120C22⋊D151—42no—
121C22⋊D151—42no—
122C22⋊D151—42no—
123C22⋊D151—81no—
124C22⋊D151—81no—
125C2×Dic151—21no—
126C2×Dic151—21no—
127C2×Dic151—21no—
128C2×Dic151—42no—
129C2×Dic151—42no—
130C2×Dic151C2×D411yescharacteristic
131C2×Dic151C2×D411yescharacteristic
132C2×Dic151C2×D411yescharacteristic
133C4×D151—21no—
134C4×D151—21no—
135C4×D151—42no—
136C151⋊C8—21no—
137C151⋊C8—21no—
138C23×C151—21no—
139C23×C151—21no—
140C23×C151C2×D411yescharacteristic
141D4×C151—21no—
142D4×C151—21no—
143D4×C151—21no—
144D4×C151—21no—
145D4×C151—81no—
146D4×C151—81no—
147C2×C4×C151—21no—
148C2×C4×C151—21no—
149C2×C4×C151—21no—
150C2×C4×C151—21no—
151C2×C4×C151C2×D411yescharacteristic
152C2×C4×C151C2411yescharacteristic
153C8×C151—21no—
154C8×C151—21no—
155C22×C151—21no—
156C22×C151—21no—
157C22×C151—21no—
158C22×C151—41no—
159C22×C151—41no—
160C22×C151—41no—
161C22×C151—41no—
162C22×C151—41no—
163C22×C151—41no—
164C22×C151C22×D411yescharacteristic
165C2×D151—21no—
166C2×D151—21no—
167C2×D151—21no—
168C2×D151—41no—
169C2×D151—41no—
170C2×D151—41no—
171C4×C151—21no—
172C4×C151—41no—
173C4×C151—41no—
174C4×C151C2×#4111yescharacteristic
175C4×C151H(5,𝔽2)11yescharacteristic
176Dic151—21no—
177Dic151—22no—
178Dic151—21no—
179Dic151—41no—
180Dic151—41no—
181Dic151#13512yes—
182C2×C151—41no—
183C2×C151—81no—
184C2×C151—81no—
185C2×C151#54611yescharacteristic
186C2×C151C2×#13511yescharacteristic
187C2×C151#57611yescharacteristic
188D151—41no—
189D151—81no—
190C151#330511yescharacteristic, complemented, Sylow
191#3305—1511nomaximal, Sylow
192#555—1511no—
193#550—1511no—
194#486—1511no—
195#482—1511no—
196#482—1511no—
197#477—1511no—
198#466—1511no—
199#466D15111yescharacteristic, complemented
200#459—1511no—
201#449—1511no—
202#449—1511no—
203C4×SD16—1511no—
204C8×D4—1511no—
205#416—1511no—
206#416—1511no—
207C2×#41—1511no—
208C2×#41—1511no—
209C2×SD16—1511no—
210C2×D8—1511no—
211C2×D8C2×D15111yescharacteristic
212C22×C8—1511no—
213C22×C8C2×D15111yescharacteristic
214C4⋊Q8—1511no—
215#127—3021no—
216#127—1511no—
217#124—3021no—
218#124—3021no—
219#121—3021no—
220#121—3021no—
221#121—3021no—
222#121—1511no—
223#121—1511no—
224#121C2×D15111yescharacteristic
225#121C2×D15111yescharacteristic
226C4×Q8—1511no—
227C4×D4—3021no—
228C4×D4—1511no—
229C4×D4—1511no—
230#117—3021no—
231#117—1511no—
232#117—1511no—
233#107—1511no—
234#107C2×D15111yescharacteristic
235#106—1511no—
236C4⋊C8—1511no—
237#103—1511no—
238#103—1511no—
239#103—1511no—
240#102—1511no—
241#102—1511no—
242#102—1511no—
243#102—1511no—
244#102—1511no—
245#102C2×D15111yescharacteristic
246#102C2×D15111yescharacteristic
247C22⋊C8—1511no—
248C22⋊C8—1511no—
249C4×C8—1511no—
250#41—3022no—
251#41—3022no—
252#41—6041no—
253#41—6041no—
254C2×Q8—3021no—
255C2×Q8—1511no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—3021no—
259C2×D4—3021no—
260C2×D4—3021no—
261C2×D4—3021no—
262C2×D4—3021no—
263C2×D4—3021no—
264C2×D4—1511no—
265C2×D4—1511no—
266C2×D4C22×D15111yescharacteristic
267C2×D4C22×D15111yescharacteristic
268C22×C4—3021no—
269C22×C4—3021no—
270C22×C4—3021no—
271C22×C4—1511no—
272C22×C4C22×D15111yescharacteristic
273SD16—3022no—
274D8—41no—
275D8—6041no—
276C2×C8—41no—
277C2×C8—6041no—
278C2×C8—1511no—
279C2×C8—1511no—
280C2×C8C22×D15111yescharacteristic
281C2×C8C22×D15111yescharacteristic
282C4⋊C4—3021no—
283C4⋊C4—3021no—
284C4⋊C4—1511no—
285C4⋊C4—1511no—
286C4⋊C4—1511no—
287C4⋊C4C22×D15111yescharacteristic
288C4⋊C4C22×D15111yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—3021no—
292C22⋊C4—3021no—
293C22⋊C4—3021no—
294C22⋊C4—3021no—
295C22⋊C4—3021no—
296C22⋊C4—1511no—
297C22⋊C4—1511no—
298C42—3021no—
299C42—3021no—
300C42—3021no—
301C42—1511no—
302C23—21no—
303C23—21no—
304C23—3021no—
305C23—1511no—
306C23D4×D15111yescharacteristic
307Q8—3021no—
308Q8—1512no—
309Q8—12081no—
310D4—21no—
311D4—21no—
312D4—21no—
313D4—21no—
314D4—81no—
315D4—81no—
316D4—3022no—
317D4—3021no—
318D4—3021no—
319D4—6042no—
320D4—6042no—
321D4—6042no—
322D4—12081no—
323D4—12081no—
324D4—12081no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—3021no—
330C2×C4—3021no—
331C2×C4—3021no—
332C2×C4—3021no—
333C2×C4—3021no—
334C2×C4—6042no—
335C2×C4—6042no—
336C2×C4—6042no—
337C2×C4—1511no—
338C2×C4—1511no—
339C2×C4—1511no—
340C2×C4D4×D15111yescharacteristic
341C2×C4C23×D15111yescharacteristic
342C8—21no—
343C8—21no—
344C8—3021no—
345C8—3021no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—3021no—
356C22—3021no—
357C22—3021no—
358C22—6041no—
359C22—6041no—
360C22—6041no—
361C22C2×D4×D15111yescharacteristic
362C4—21no—
363C4—41no—
364C4—41no—
365C4—3021no—
366C4—3021no—
367C4—3022no—
368C4—6041no—
369C4—6041no—
370C4—1512no—
371C4#41×D15111yescharacteristic
372C4#1801278411yescharacteristic
373C2—41no—
374C2—81no—
375C2—81no—
376C2—6041no—
377C2—12081no—
378C2#2375285111yescharacteristic
379C2#135×D15111yescharacteristic
380C2#2375301311yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#466×C151C2
socleC22×C151C22×D4
hypercenter#466D151
hypocenterC151#3305
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #23752926C2semidirect
2. #23752880C2semidirect
3. #23752557C2semidirect
4. #23752539C2semidirect
5. #23752533C2semidirect
6. #23752506C2semidirect
7. #23752447C2semidirect
8. #23752405C2semidirect
9. #23752355C2semidirect
10. #23752354C2semidirect
11. #23752303C2semidirect
12. C8×C22⋊D151C2semidirect
13. #23752209C2semidirect
14. #23752205C2semidirect
15. #466×C151C2semidirect
190. C151#3305semidirect
199. #466D151semidirect

Maximal subgroups

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

subgroupindex
#237529262
#237528802
#237525572
#237525392
#237525332
#237525062
#237524472
#237524052
#237523552
#237523542
#237523032
C8×C22⋊D1512
#237522092
#237522052
#466×C1512
#3305151