Finite Group Databasebeta

← #34079966

Subgroups — #34079966

Order 19328.

422 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752792C211yesmaximal, characteristic, complemented
2#23752779C211yesmaximal, characteristic, complemented
3#23752550C211yesmaximal, characteristic, complemented
4#23752537C211yesmaximal, characteristic, complemented
5#23752529C211yesmaximal, characteristic, complemented
6#23752524C211yesmaximal, characteristic, complemented
7#23752464C211yesmaximal, characteristic, complemented
8#23752455C211yesmaximal, characteristic, complemented
9#23752447C211yesmaximal, characteristic, complemented
10#23752438C211yesmaximal, characteristic, complemented
11#23752356C211yesmaximal, characteristic, complemented
12#23752356C211yesmaximal, characteristic, complemented
13#23752346C211yesmaximal, characteristic, complemented
14#23752177C211yesmaximal, characteristic, complemented
15#450×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic, complemented
17C2×#14559004C2211yescharacteristic
18C2×#14558989C2211yescharacteristic
19C2×#14558989C2211yescharacteristic
20C2×#14558987C2211yescharacteristic, complemented
21C2×C8×D151C2211yescharacteristic, complemented
22#18012735—21no—
23#18012726—21no—
24#18012717—21no—
25#18012715C2211yescharacteristic, complemented
26#18012714—21no—
27#18012714C2211yescharacteristic, complemented
28#18012713C2211yescharacteristic
29#18012712—21no—
30#18012712—21no—
31#18012710C2211yescharacteristic
32#18012710C2211yescharacteristic
33#18012710C2211yescharacteristic
34#18012710C2211yescharacteristic
35#18012708—21no—
36#18012708—21no—
37#18012698C2211yescharacteristic
38C4⋊C4×D151C2211yescharacteristic, complemented
39#18012673C2211yescharacteristic, complemented
40#18012672C2211yescharacteristic, complemented
41#18012671C2211yescharacteristic, complemented
42#18012670C2211yescharacteristic, complemented
43#18012663C2211yescharacteristic, complemented
44#18012663C2211yescharacteristic, complemented
45#18012661C2211yescharacteristic, complemented
46#18012661C2211yescharacteristic, complemented
47#18012660C2211yescharacteristic
48#18012660C2211yescharacteristic
49C22⋊(C151⋊C8)C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic, complemented
51(C2×D151)⋊C8C2211yescharacteristic, complemented
52C22×D4×C151C2211yescharacteristic
53C2×SD16×C151C2211yescharacteristic
54C2×SD16×C151C2211yescharacteristic
55C22⋊Q8×C151C2211yescharacteristic
56#102×C151C2211yescharacteristic
57#102×C151C2211yescharacteristic
58C22⋊C8×C151C2211yescharacteristic
59#14559005—41no—
60#14559005—41no—
61#14559004—41no—
62#14559004—41no—
63C2×Dic302D411yescharacteristic
64C2×D604—21no—
65C2×D604—21no—
66C2×D604D411yescharacteristic
67C2×D604C2311yescharacteristic
68C2×C22⋊D151—21no—
69C2×C22⋊D151—21no—
70C2×C22⋊D151—21no—
71C2×C22⋊D151—21no—
72C2×C22⋊D151—21no—
73C2×C22⋊D151D411yescharacteristic
74C2×C22⋊D151D411yescharacteristic
75C2×C4×D151—21no—
76C2×C4×D151—21no—
77C2×C4×D151C2311yescharacteristic
78C2×C4×D151C2311yescharacteristic
79#14558989—41no—
80#14558989—41no—
81#14558987—41no—
82C2×C151⋊C8C2311yescharacteristic
83C2×C151⋊C8C2311yescharacteristic
84C8×D151—41no—
85C4⋊Dic151C2311yescharacteristic
86C4⋊Dic151C2311yescharacteristic
87C4⋊Dic151C2311yescharacteristic
88Dic151⋊C4—21no—
89Dic151⋊C4—21no—
90C22⋊Dic151—21no—
91C22⋊Dic151—21no—
92C22⋊Dic151—21no—
93C22⋊Dic151—21no—
94C22⋊Dic151—21no—
95(C2×D151)⋊C4—21no—
96(C2×D151)⋊C4—21no—
97(C2×D151)⋊C4—21no—
98C4×Dic151—21no—
99C24×C151—21no—
100C2×Q8×C151C2311yescharacteristic
101C2×D4×C151—21no—
102C2×D4×C151—41no—
103C2×D4×C151—41no—
104C2×D4×C151C2311yescharacteristic
105C2×D4×C151C2311yescharacteristic
106C22×C4×C151C2311yescharacteristic
107SD16×C151—41no—
108SD16×C151—41no—
109C2×C8×C151C2311yescharacteristic
110C2×C8×C151C2311yescharacteristic
111C4⋊C4×C151—21no—
112C4⋊C4×C151C2311yescharacteristic
113C22⋊C4×C151—21no—
114C22×D151—21no—
115C22×D151C2×D411yescharacteristic
116C22×D151C2×D411yescharacteristic
117Dic302—41no—
118D604—21no—
119D604—21no—
120D604—41no—
121D604—42no—
122D604—81no—
123C22⋊D151—41no—
124C22⋊D151—41no—
125C22⋊D151—81no—
126C22⋊D151—81no—
127C22⋊D151—81no—
128C22⋊D151—81no—
129C22⋊D151—81no—
130C2×Dic151—21no—
131C2×Dic151—21no—
132C2×Dic151—21no—
133C2×Dic151C2×D411yescharacteristic
134C2×Dic151C2×D411yescharacteristic
135C4×D151—21no—
136C4×D151—21no—
137C4×D151—21no—
138C4×D151—21no—
139C4×D151—42no—
140C4×D151—81no—
141C151⋊C8—21no—
142C151⋊C8—21no—
143C23×C151—21no—
144C23×C151—21no—
145C23×C151—42no—
146C23×C151—81no—
147C23×C151—81no—
148C23×C151C2×D411yescharacteristic
149Q8×C151—21no—
150Q8×C151—21no—
151D4×C151—21no—
152D4×C151—21no—
153D4×C151—21no—
154D4×C151—21no—
155D4×C151—42no—
156C2×C4×C151—21no—
157C2×C4×C151—21no—
158C2×C4×C151—21no—
159C2×C4×C151—21no—
160C2×C4×C151C2×D411yescharacteristic
161C2×C4×C151C2411yescharacteristic
162C8×C151—21no—
163C8×C151—21no—
164C22×C151—21no—
165C22×C151—21no—
166C22×C151—21no—
167C22×C151—41no—
168C22×C151—41no—
169C22×C151—41no—
170C22×C151—41no—
171C22×C151—41no—
172C22×C151—41no—
173C22×C151—84no—
174C22×C151C22×D411yescharacteristic
175C2×D151—21no—
176C2×D151—21no—
177C2×D151—21no—
178C2×D151—21no—
179C2×D151—21no—
180C2×D151—21no—
181C2×D151—41no—
182C2×D151—41no—
183C2×D151—41no—
184C4×C151—21no—
185C4×C151—41no—
186C4×C151—41no—
187C4×C151H(5,𝔽2)11yescharacteristic
188C4×C151H(5,𝔽2)11yescharacteristic
189Dic151—21no—
190Dic151—21no—
191Dic151—41no—
192Dic151—41no—
193Dic151—41no—
194C2×C151—41no—
195C2×C151—81no—
196C2×C151—81no—
197C2×C151#53411yescharacteristic
198C2×C151#57611yescharacteristic
199C2×C151#57711yescharacteristic
200D151—41no—
201D151—41no—
202D151—81no—
203C151#319811yescharacteristic, complemented, Sylow
204#3198—1511nomaximal, Sylow
205#537—1511no—
206#535—1511no—
207#485—1511no—
208#482—1511no—
209#481—1511no—
210#480—1511no—
211#469—1511no—
212#468—1511no—
213#466—1511no—
214#465—1511no—
215#450D15111yescharacteristic, complemented
216#449—1511no—
217#449—1511no—
218#447—1511no—
219#408—1511no—
220C2×#41—1511no—
221C2×#41—1511no—
222C22×D4C2×D15111yescharacteristic
223C2×SD16C2×D15111yescharacteristic
224C2×SD16C2×D15111yescharacteristic
225C2×D8—1511no—
226C2×D8—1511no—
227C2×M16—1511no—
228C22×C8—1511no—
229#127—3021no—
230#124—3021no—
231C22⋊Q8—3021no—
232C22⋊Q8—1511no—
233C22⋊Q8C2×D15111yescharacteristic
234#121—3021no—
235#121—3021no—
236#121—3021no—
237#121—1511no—
238#121—1511no—
239#121—1511no—
240#121—1511no—
241#121—1511no—
242#121—1511no—
243#120—3021no—
244#120—3021no—
245#117—1511no—
246C2×C4⋊C4—1511no—
247#107—1511no—
248#107—1511no—
249#106—1511no—
250#106—1511no—
251#103—1511no—
252#103—1511no—
253#102—1511no—
254#102—1511no—
255#102—1511no—
256#102—1511no—
257#102C2×D15111yescharacteristic
258#102C2×D15111yescharacteristic
259C22⋊C8—1511no—
260C22⋊C8—1511no—
261C22⋊C8—1511no—
262C22⋊C8C2×D15111yescharacteristic
263C24—21no—
264#41—6041no—
265#41—6041no—
266#41—6041no—
267#41—6041no—
268C2×Q8—1511no—
269C2×Q8C22×D15111yescharacteristic
270C2×D4—21no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—3021no—
274C2×D4—3021no—
275C2×D4—3021no—
276C2×D4—3021no—
277C2×D4—3021no—
278C2×D4—3021no—
279C2×D4—3021no—
280C2×D4—1511no—
281C2×D4—1511no—
282C2×D4—1511no—
283C2×D4—1511no—
284C2×D4C22×D15111yescharacteristic
285C2×D4C22×D15111yescharacteristic
286C22×C4—3021no—
287C22×C4—3021no—
288C22×C4—1511no—
289C22×C4—1511no—
290C22×C4C22×D15111yescharacteristic
291SD16—41no—
292SD16—41no—
293D8—6041no—
294D8—6041no—
295M16—6041no—
296C2×C8—6041no—
297C2×C8—1511no—
298C2×C8—1511no—
299C2×C8C22×D15111yescharacteristic
300C2×C8C22×D15111yescharacteristic
301C4⋊C4—21no—
302C4⋊C4—3021no—
303C4⋊C4—3021no—
304C4⋊C4—1511no—
305C4⋊C4—1511no—
306C4⋊C4—1511no—
307C4⋊C4C22×D15111yescharacteristic
308C22⋊C4—21no—
309C22⋊C4—3021no—
310C22⋊C4—3021no—
311C22⋊C4—3021no—
312C22⋊C4—3021no—
313C22⋊C4—3021no—
314C22⋊C4—3021no—
315C22⋊C4—3021no—
316C22⋊C4—3021no—
317C42—3021no—
318C23—21no—
319C23—21no—
320C23—42no—
321C23—81no—
322C23—81no—
323C23—3021no—
324C23—1511no—
325C23—1511no—
326C23D4×D15111yescharacteristic
327Q8—21no—
328Q8—21no—
329Q8—6041no—
330D4—21no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—42no—
335D4—3021no—
336D4—3021no—
337D4—6041no—
338D4—6042no—
339D4—6041no—
340D4—6041no—
341D4—12081no—
342D4—12081no—
343D4—12081no—
344D4—12081no—
345D4—12081no—
346D4—12081no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—3021no—
352C2×C4—3021no—
353C2×C4—3021no—
354C2×C4—3021no—
355C2×C4—3021no—
356C2×C4—3021no—
357C2×C4—3021no—
358C2×C4—6042no—
359C2×C4—1511no—
360C2×C4—1511no—
361C2×C4—12081no—
362C2×C4D4×D15111yescharacteristic
363C2×C4C23×D15111yescharacteristic
364C8—21no—
365C8—21no—
366C8—3021no—
367C8—3021no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—84no—
378C22—3021no—
379C22—3021no—
380C22—3021no—
381C22—3021no—
382C22—3021no—
383C22—3021no—
384C22—6041no—
385C22—6041no—
386C22—6041no—
387C22C2×D4×D15111yescharacteristic
388C4—21no—
389C4—41no—
390C4—41no—
391C4—3021no—
392C4—3021no—
393C4—6041no—
394C4—6041no—
395C4—6041no—
396C4#1801278411yescharacteristic
397C4#1801278411yescharacteristic
398C2—41no—
399C2—81no—
400C2—81no—
401C2—6041no—
402C2—6041no—
403C2—12081no—
404C2#2375277211yescharacteristic
405C2#2375301611yescharacteristic
406C2#2375301811yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#450×C151C2
socleC22×C151C22×D4
hypercenter#450D151
hypocenterC151#3198
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #23752792C2semidirect
2. #23752779C2semidirect
3. #23752550C2semidirect
4. #23752537C2semidirect
5. #23752529C2semidirect
6. #23752524C2semidirect
7. #23752464C2semidirect
8. #23752455C2semidirect
9. #23752447C2semidirect
10. #23752438C2semidirect
11. #23752356C2semidirect
12. #23752356C2semidirect
13. #23752346C2semidirect
14. #23752177C2semidirect
15. #450×C151C2semidirect
16. C2×#14559005C22semidirect
20. C2×#14558987C22semidirect
21. C2×C8×D151C22semidirect
25. #18012715C22semidirect
27. #18012714C22semidirect
38. C4⋊C4×D151C22semidirect
39. #18012673C22semidirect
40. #18012672C22semidirect
41. #18012671C22semidirect
42. #18012670C22semidirect
43. #18012663C22semidirect
44. #18012663C22semidirect
45. #18012661C22semidirect
46. #18012661C22semidirect
50. (C2×D151)⋊C8C22semidirect
51. (C2×D151)⋊C8C22semidirect
203. C151#3198semidirect
215. #450D151semidirect

Maximal subgroups

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

subgroupindex
#237527922
#237527792
#237525502
#237525372
#237525292
#237525242
#237524642
#237524552
#237524472
#237524382
#237523562
#237523462
#237521772
#450×C1512
#3198151