Finite Group Databasebeta

← #34079978

Subgroups — #34079978

Order 19328.

410 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752785C211yesmaximal, characteristic, complemented
2#23752778C211yesmaximal, characteristic
3#23752555C211yesmaximal, characteristic, complemented
4#23752552C211yesmaximal, characteristic, complemented
5#23752539C211yesmaximal, characteristic, complemented
6#23752534C211yesmaximal, characteristic, complemented
7#23752458C211yesmaximal, characteristic, complemented
8#23752443C211yesmaximal, characteristic, complemented
9#23752439C211yesmaximal, characteristic, complemented
10#23752364C211yesmaximal, characteristic, complemented
11#23752361C211yesmaximal, characteristic, complemented
12#23752352C211yesmaximal, characteristic, complemented
13#23752349C211yesmaximal, characteristic, complemented
14#23752180C211yesmaximal, characteristic, complemented
15#468×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic
17C2×Q8×D151C2211yescharacteristic, complemented
18C2×D4×D151C2211yescharacteristic
19C2×#14558993C2211yescharacteristic
20C2×#14558992C2211yescharacteristic
21C2×#14558991C2211yescharacteristic
22C22×C151⋊C8C2211yescharacteristic, complemented
23#18012738—21no—
24#18012735—21no—
25#18012725—21no—
26#18012725—21no—
27#18012724—21no—
28#18012721—21no—
29#18012719C2211yescharacteristic
30#18012718C2211yescharacteristic, complemented
31#18012715C2211yescharacteristic
32#18012714C2211yescharacteristic
33#18012713C2211yescharacteristic
34#18012710C2211yescharacteristic
35#18012709—21no—
36#18012707—21no—
37#18012697C2211yescharacteristic
38#18012697C2211yescharacteristic, complemented
39#18012673C2211yescharacteristic, complemented
40#18012670C2211yescharacteristic, complemented
41#18012670C2211yescharacteristic, complemented
42#18012664C2211yescharacteristic, complemented
43#18012663C2211yescharacteristic, complemented
44#18012662C2211yescharacteristic, complemented
45#18012661C2211yescharacteristic
46#18012660C2211yescharacteristic
47#18012659C2211yescharacteristic
48(C2×D151)⋊C8C2211yescharacteristic
49(C2×D151)⋊C8C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic, complemented
51(C2×D151)⋊C8C2211yescharacteristic, complemented
52C2×SD16×C151C2211yescharacteristic
53C2×M16×C151C2211yescharacteristic, complemented
54C22⋊Q8×C151C2211yescharacteristic, complemented
55#121×C151C2211yescharacteristic
56#107×C151C2211yescharacteristic, complemented
57#103×C151C2211yescharacteristic, complemented
58#102×C151C2211yescharacteristic
59C23×D151—21no—
60#14559004—41no—
61#14559004—41no—
62C2×Dic302—21no—
63C2×Dic302D411yescharacteristic
64C2×Dic302C2311yescharacteristic
65Q8×D151—41no—
66Q8×D151—41no—
67C2×D604—21no—
68C2×D604D411yescharacteristic
69C2×D604C2311yescharacteristic
70C2×C22⋊D151—21no—
71C2×C22⋊D151—21no—
72C2×C22⋊D151—21no—
73C2×C22⋊D151D411yescharacteristic
74C2×C22⋊D151D411yescharacteristic
75D4×D151—41no—
76D4×D151—41no—
77C2×C4×D151—21no—
78C2×C4×D151C2311yescharacteristic
79C2×C4×D151C2311yescharacteristic
80#14558993—41no—
81#14558992—41no—
82#14558991—41no—
83C2×C151⋊C8—41no—
84C2×C151⋊C8C2311yescharacteristic
85C2×C151⋊C8C2311yescharacteristic
86C4⋊Dic151—21no—
87C4⋊Dic151C2311yescharacteristic
88C4⋊Dic151C2311yescharacteristic
89Dic151⋊C4—21no—
90Dic151⋊C4—21no—
91C22⋊Dic151—21no—
92C22⋊Dic151—21no—
93(C2×D151)⋊C4—21no—
94(C2×D151)⋊C4—21no—
95(C2×D151)⋊C4—21no—
96(C2×D151)⋊C4—21no—
97(C2×D151)⋊C4—21no—
98(C2×D151)⋊C4—21no—
99C4×Dic151—21no—
100C4×Dic151—21no—
101C2×Q8×C151C2311yescharacteristic
102C2×D4×C151—21no—
103C2×D4×C151C2311yescharacteristic
104C22×C4×C151C2311yescharacteristic
105SD16×C151—41no—
106M16×C151—41no—
107C2×C8×C151C2311yescharacteristic
108C2×C8×C151C2311yescharacteristic
109C4⋊C4×C151—21no—
110C4⋊C4×C151C2311yescharacteristic
111C4⋊C4×C151C2311yescharacteristic
112C22⋊C4×C151—21no—
113C22⋊C4×C151—21no—
114C22×D151—21no—
115C22×D151—42no—
116C22×D151—81no—
117C22×D151—81no—
118C22×D151C2×D411yescharacteristic
119C22×D151C2×D411yescharacteristic
120Dic302—21no—
121Dic302—21no—
122Dic302—41no—
123Dic302—42no—
124D604—21no—
125D604—21no—
126D604—41no—
127D604—81no—
128C22⋊D151—41no—
129C22⋊D151—41no—
130C22⋊D151—42no—
131C22⋊D151—81no—
132C22⋊D151—81no—
133C2×Dic151—21no—
134C2×Dic151—21no—
135C2×Dic151—21no—
136C2×Dic151C2×D411yescharacteristic
137C2×Dic151C2×D411yescharacteristic
138C4×D151—21no—
139C4×D151—21no—
140C4×D151—21no—
141C4×D151—21no—
142C4×D151—42no—
143C151⋊C8—21no—
144C151⋊C8—21no—
145C23×C151—21no—
146C23×C151C2×D411yescharacteristic
147Q8×C151—21no—
148Q8×C151—21no—
149D4×C151—21no—
150D4×C151—21no—
151D4×C151—81no—
152C2×C4×C151—21no—
153C2×C4×C151—21no—
154C2×C4×C151—21no—
155C2×C4×C151—21no—
156C2×C4×C151—21no—
157C2×C4×C151C2×D411yescharacteristic
158C2×C4×C151C2411yescharacteristic
159C8×C151—21no—
160C8×C151—21no—
161C22×C151—21no—
162C22×C151—21no—
163C22×C151—21no—
164C22×C151—41no—
165C22×C151—41no—
166C22×C151—41no—
167C22×C151C22×D411yescharacteristic
168C2×D151—21no—
169C2×D151—21no—
170C2×D151—21no—
171C2×D151—21no—
172C2×D151—21no—
173C2×D151—21no—
174C2×D151—41no—
175C2×D151—41no—
176C2×D151—41no—
177C2×D151—84no—
178C4×C151—21no—
179C4×C151—41no—
180C4×C151—41no—
181C4×C151—41no—
182C4×C151H(5,𝔽2)11yescharacteristic
183C4×C151H(5,𝔽2)11yescharacteristic
184Dic151—21no—
185Dic151—21no—
186Dic151—41no—
187Dic151—41no—
188Dic151—41no—
189C2×C151—41no—
190C2×C151—81no—
191C2×C151#53411yescharacteristic
192C2×C151#57711yescharacteristic
193C2×C151#57711yescharacteristic
194D151—41no—
195D151—41no—
196D151—81no—
197C151#320011yescharacteristic, complemented, Sylow
198#3200—1511nomaximal, Sylow
199#536—1511no—
200#535—1511no—
201#485—1511no—
202#485—1511no—
203#482—1511no—
204#482—1511no—
205#468—1511no—
206#468D15111yescharacteristic, complemented
207#465—1511no—
208#465—1511no—
209#450—1511no—
210#450—1511no—
211#448—1511no—
212#448—1511no—
213#408—1511no—
214C2×#41—1511no—
215C22×Q8—1511no—
216C22×D4—1511no—
217C2×SD16—1511no—
218C2×SD16—1511no—
219C2×SD16—1511no—
220C2×SD16C2×D15111yescharacteristic
221C2×M16C2×D15111yescharacteristic, complemented
222C22×C8—1511no—
223C4⋊Q8—3021no—
224#127—3021no—
225#124—3021no—
226#124—3021no—
227#123—3021no—
228#123—3021no—
229C22⋊Q8—1511no—
230C22⋊Q8—1511no—
231C22⋊Q8—1511no—
232C22⋊Q8C2×D15111yescharacteristic, complemented
233#121—1511no—
234#121—1511no—
235#121—1511no—
236#121C2×D15111yescharacteristic
237#120—3021no—
238#120—3021no—
239#117—1511no—
240#117—1511no—
241#107—1511no—
242#107C2×D15111yescharacteristic, complemented
243#106—1511no—
244#106—1511no—
245#103—1511no—
246#103—1511no—
247#103—1511no—
248#103C2×D15111yescharacteristic, complemented
249#102—1511no—
250#102—1511no—
251#102—1511no—
252#102C2×D15111yescharacteristic
253C22⋊C8—1511no—
254C22⋊C8—1511no—
255C22⋊C8—1511no—
256C22⋊C8—1511no—
257C24—3021no—
258#41—6041no—
259#41—6041no—
260C2×Q8—3021no—
261C2×Q8—6041no—
262C2×Q8—6041no—
263C2×Q8—1511no—
264C2×Q8—1511no—
265C2×Q8C22×D15111yescharacteristic
266C2×D4—21no—
267C2×D4—3021no—
268C2×D4—3021no—
269C2×D4—3021no—
270C2×D4—3021no—
271C2×D4—6041no—
272C2×D4—6041no—
273C2×D4—1511no—
274C2×D4—1511no—
275C2×D4—1511no—
276C2×D4—1511no—
277C2×D4C22×D15111yescharacteristic
278C22×C4—3021no—
279C22×C4—1511no—
280C22×C4—1511no—
281C22×C4C22×D15111yescharacteristic
282SD16—41no—
283SD16—6041no—
284SD16—6041no—
285SD16—6041no—
286M16—41no—
287C2×C8—6041no—
288C2×C8—1511no—
289C2×C8—1511no—
290C2×C8C22×D15111yescharacteristic
291C2×C8C22×D15111yescharacteristic
292C4⋊C4—21no—
293C4⋊C4—3021no—
294C4⋊C4—3021no—
295C4⋊C4—3021no—
296C4⋊C4—1511no—
297C4⋊C4—1511no—
298C4⋊C4C22×D15111yescharacteristic
299C4⋊C4C22×D15111yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—3021no—
303C22⋊C4—3021no—
304C22⋊C4—3021no—
305C22⋊C4—3021no—
306C22⋊C4—3021no—
307C22⋊C4—3021no—
308C22⋊C4—3021no—
309C22⋊C4—3021no—
310C42—3021no—
311C42—3021no—
312C23—21no—
313C23—3021no—
314C23—6042no—
315C23—1511no—
316C23—1511no—
317C23—12081no—
318C23—12081no—
319C23D4×D15111yescharacteristic
320Q8—21no—
321Q8—21no—
322Q8—3021no—
323Q8—3021no—
324Q8—6041no—
325Q8—6042no—
326D4—21no—
327D4—21no—
328D4—81no—
329D4—3021no—
330D4—3021no—
331D4—6041no—
332D4—6041no—
333D4—6041no—
334D4—6042no—
335D4—12081no—
336D4—12081no—
337D4—12081no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—3021no—
344C2×C4—3021no—
345C2×C4—3021no—
346C2×C4—3021no—
347C2×C4—3021no—
348C2×C4—3021no—
349C2×C4—3021no—
350C2×C4—6042no—
351C2×C4—1511no—
352C2×C4—1511no—
353C2×C4D4×D15111yescharacteristic
354C2×C4C23×D15111yescharacteristic
355C8—21no—
356C8—21no—
357C8—3021no—
358C8—3021no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—3021no—
366C22—3021no—
367C22—3021no—
368C22—3021no—
369C22—3021no—
370C22—3021no—
371C22—6041no—
372C22—6041no—
373C22—6041no—
374C22—12084no—
375C22C2×D4×D15111yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—3021no—
381C4—3021no—
382C4—6041no—
383C4—6041no—
384C4—6041no—
385C4#1801278411yescharacteristic
386C4#1801278511yescharacteristic
387C2—41no—
388C2—81no—
389C2—6041no—
390C2—6041no—
391C2—12081no—
392C2#2375277011yescharacteristic
393C2#2375302111yescharacteristic
394C2#2375302211yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#468×C151C2
socleC22×C151C22×D4
prime radical#23752778C2
hypercenter#468D151
hypocenterC151#3200
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #23752785C2semidirect
3. #23752555C2semidirect
4. #23752552C2semidirect
5. #23752539C2semidirect
6. #23752534C2semidirect
7. #23752458C2semidirect
8. #23752443C2semidirect
9. #23752439C2semidirect
10. #23752364C2semidirect
11. #23752361C2semidirect
12. #23752352C2semidirect
13. #23752349C2semidirect
14. #23752180C2semidirect
15. #468×C151C2semidirect
17. C2×Q8×D151C22semidirect
22. C22×C151⋊C8C22semidirect
30. #18012718C22semidirect
38. #18012697C22semidirect
39. #18012673C22semidirect
40. #18012670C22semidirect
41. #18012670C22semidirect
42. #18012664C22semidirect
43. #18012663C22semidirect
44. #18012662C22semidirect
50. (C2×D151)⋊C8C22semidirect
51. (C2×D151)⋊C8C22semidirect
53. C2×M16×C151C22semidirect
54. C22⋊Q8×C151C22semidirect
56. #107×C151C22semidirect
57. #103×C151C22semidirect
197. C151#3200semidirect
206. #468D151semidirect
221. C2×M16C2×D151semidirect
232. C22⋊Q8C2×D151semidirect
242. #107C2×D151semidirect
248. #103C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237527852
#237527782
#237525552
#237525522
#237525392
#237525342
#237524582
#237524432
#237524392
#237523642
#237523612
#237523522
#237523492
#237521802
#468×C1512
#3200151