Finite Group Databasebeta

← #34080613

Subgroups — #34080613

Order 19328.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18012771C211yesmaximal, characteristic, complemented
2C22×#14558991C211yesmaximal, characteristic, complemented
3Q8×C22⋊D151C211yesmaximal, characteristic, complemented
4#23752853C211yesmaximal, characteristic
5#23752605C211yesmaximal, characteristic, complemented
6#23752461C211yesmaximal, characteristic, complemented
7#23752451C211yesmaximal, characteristic, complemented
8#23752436C211yesmaximal, characteristic, complemented
9#23752416C211yesmaximal, characteristic, complemented
10#23752373C211yesmaximal, characteristic, complemented
11#23752365C211yesmaximal, characteristic, complemented
12#23752352C211yesmaximal, characteristic, complemented
13#23752315C211yesmaximal, characteristic, complemented
14#23752280C211yesmaximal, characteristic, complemented
15#451×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic
17C2×Q8×D151C2211yescharacteristic, complemented
18C22×D604C2211yescharacteristic
19#18012771—24no—
20C2×#14558994C2211yescharacteristic, complemented
21C2×#14558993C2211yescharacteristic
22C2×#14558993C2211yescharacteristic
23C2×#14558991—24no—
24C2×#14558991C2211yescharacteristic
25C2×#14558991C2211yescharacteristic
26C2×#14558991C2211yescharacteristic
27C2×#14558991C2211yescharacteristic
28C2×#14558987C2211yescharacteristic, complemented
29C22×C151⋊C8C2211yescharacteristic
30#18012737—21no—
31#18012737C2211yescharacteristic, complemented
32#18012728C2211yescharacteristic
33#18012724—21no—
34#18012718—21no—
35#18012718C2211yescharacteristic
36#18012715—21no—
37#18012715C2211yescharacteristic, complemented
38#18012714—21no—
39#18012714C2211yescharacteristic
40#18012709—21no—
41Q8×Dic151C2211yescharacteristic, complemented
42#18012701C2211yescharacteristic
43C4×C22⋊D151—21no—
44C4×C22⋊D151C2211yescharacteristic
45C22⋊C4×D151—21no—
46#18012672C2211yescharacteristic, complemented
47Dic151⋊C8C2211yescharacteristic, complemented
48#18012663C2211yescharacteristic, complemented
49#18012662C2211yescharacteristic, complemented
50#18012661C2211yescharacteristic
51#18012661C2211yescharacteristic
52(C2×D151)⋊C8C2211yescharacteristic, complemented
53#18012649C2211yescharacteristic, complemented
54C22×Q8×C151C2211yescharacteristic
55C2×Q16×C151C2211yescharacteristic, complemented
56C2×Q16×C151C2211yescharacteristic, complemented
57C22⋊Q8×C151C2211yescharacteristic
58#103×C151C2211yescharacteristic, complemented
59#103×C151C2211yescharacteristic, complemented
60C22⋊C8×C151C2211yescharacteristic
61C23×D151—21no—
62#14559005—22no—
63#14559005—41no—
64C2×Dic302—21no—
65C2×Dic302C2311yescharacteristic
66Q8×D151—22no—
67Q8×D151—41no—
68C2×D604—22no—
69C2×D604—21no—
70C2×D604—21no—
71C2×D604—21no—
72C2×D604—41no—
73C2×D604C2311yescharacteristic
74C2×D604C2311yescharacteristic
75C2×C22⋊D151D411yescharacteristic
76C2×C4×D151—21no—
77C2×C4×D151—21no—
78C2×C4×D151—21no—
79C2×C4×D151C2311yescharacteristic
80#14558994—22no—
81#14558993—22no—
82#14558993—41no—
83#14558991—22no—
84#14558991—22no—
85#14558991—22no—
86#14558991D414yescomplemented
87#14558987—22no—
88C2×C151⋊C8—22no—
89C2×C151⋊C8C2311yescharacteristic
90C2×C151⋊C8C2311yescharacteristic
91C4⋊Dic151—21no—
92C4⋊Dic151C2311yescharacteristic
93Dic151⋊C4—21no—
94Dic151⋊C4—21no—
95Dic151⋊C4—21no—
96Dic151⋊C4—21no—
97Dic151⋊C4D411yescharacteristic
98C22⋊Dic151—21no—
99C22⋊Dic151D411yescharacteristic
100(C2×D151)⋊C4—21no—
101(C2×D151)⋊C4—21no—
102(C2×D151)⋊C4—21no—
103(C2×D151)⋊C4—21no—
104(C2×D151)⋊C4—21no—
105(C2×D151)⋊C4D411yescharacteristic
106C4×Dic151—21no—
107C4×Dic151C2311yescharacteristic
108C2×Q8×C151—21no—
109C2×Q8×C151—22no—
110C2×Q8×C151—41no—
111C2×Q8×C151C2311yescharacteristic
112C2×Q8×C151C2311yescharacteristic
113C2×Q8×C151C2311yescharacteristic
114C22×C4×C151—21no—
115C22×C4×C151C2311yescharacteristic
116Q16×C151—22no—
117Q16×C151—41no—
118C2×C8×C151C2311yescharacteristic
119C2×C8×C151C2311yescharacteristic
120C4⋊C4×C151—21no—
121C4⋊C4×C151C2311yescharacteristic
122C22⋊C4×C151—21no—
123C22×D151—21no—
124C22×D151—21no—
125C22×D151—42no—
126C22×D151—42no—
127C22×D151—81no—
128C22×D151C2×D411yescharacteristic
129Dic302—21no—
130Dic302—21no—
131Dic302—42no—
132D604—21no—
133D604—21no—
134D604—21no—
135D604—42no—
136D604—42no—
137D604—81no—
138D604C2×D412yes—
139C22⋊D151—22no—
140C2×Dic151—21no—
141C2×Dic151—21no—
142C2×Dic151C2×D411yescharacteristic
143C2×Dic151C2×D411yescharacteristic
144C2×Dic151C2×D411yescharacteristic
145C4×D151—21no—
146C4×D151—21no—
147C4×D151—42no—
148C4×D151—42no—
149C4×D151—81no—
150C151⋊C8—21no—
151C151⋊C8C2×D412yes—
152C23×C151C2×D411yescharacteristic
153Q8×C151—21no—
154Q8×C151—21no—
155Q8×C151—21no—
156Q8×C151—21no—
157Q8×C151—21no—
158Q8×C151—42no—
159Q8×C151C2×D412yes—
160C2×C4×C151—21no—
161C2×C4×C151—21no—
162C2×C4×C151—21no—
163C2×C4×C151—21no—
164C2×C4×C151—21no—
165C2×C4×C151—21no—
166C2×C4×C151—42no—
167C2×C4×C151C2×D411yescharacteristic
168C2×C4×C151C2411yescharacteristic
169C8×C151—21no—
170C8×C151—21no—
171C22×C151—21no—
172C22×C151—21no—
173C22×C151#13712yescomplemented
174C22×C151C22×D411yescharacteristic
175C2×D151—21no—
176C2×D151—22no—
177C2×D151—21no—
178C2×D151—21no—
179C2×D151—41no—
180C2×D151—41no—
181C2×D151—41no—
182C2×D151—41no—
183C2×D151—41no—
184C2×D151—84no—
185C4×C151—21no—
186C4×C151—22no—
187C4×C151—41no—
188C4×C151—41no—
189C4×C151—41no—
190C4×C151C22×D411yescharacteristic
191C4×C151H(5,𝔽2)11yescharacteristic
192Dic151—21no—
193Dic151—21no—
194Dic151—21no—
195Dic151—41no—
196Dic151—41no—
197C2×C151—22no—
198C2×C151D4211yescharacteristic
199C2×C151C2×#13711yescharacteristic
200C2×C151#57711yescharacteristic
201D151—41no—
202D151—42no—
203D151—81no—
204C151#326611yescharacteristic, complemented, Sylow
205#3266—1511nomaximal, Sylow
206C2×#137—1511no—
207C22×SD16—1511no—
208D4×Q8—1511no—
209#546—1511no—
210#497—1511no—
211#468—1511no—
212#467—1511no—
213#464—1511no—
214#461—1511no—
215#452—1511no—
216#451D15111yescharacteristic, complemented
217#450—1511no—
218#448—1511no—
219#440—1511no—
220#435—1511no—
221C2×#41—1511no—
222C22×Q8—1511no—
223C22×Q8C2×D15111yescharacteristic
224C22×D4—1511no—
225#137—3024no—
226C2×Q16—1511no—
227C2×Q16C2×D15111yescharacteristic, complemented
228C2×Q16C2×D15111yescharacteristic, complemented
229C2×SD16—3024no—
230C2×SD16—1511no—
231C2×SD16—1511no—
232C2×SD16—1511no—
233C2×SD16—1511no—
234C2×SD16—1511no—
235C2×SD16—1511no—
236C2×M16—1511no—
237C22×C8—1511no—
238C4⋊Q8—3021no—
239C4⋊Q8—1511no—
240#124—1511no—
241#123—3021no—
242C22⋊Q8—3021no—
243C22⋊Q8—3021no—
244C22⋊Q8—1511no—
245C22⋊Q8—1511no—
246C22⋊Q8C2×D15111yescharacteristic
247#121—3021no—
248#121—1511no—
249#120—3021no—
250C4×Q8—1511no—
251C4×D4—3021no—
252C4×D4—1511no—
253C4×D4—1511no—
254C2×C22⋊C4—3021no—
255#107—1511no—
256C4⋊C8—1511no—
257#103—1511no—
258#103—1511no—
259#103C2×D15111yescharacteristic, complemented
260#103C2×D15111yescharacteristic, complemented
261#102—1511no—
262#102—1511no—
263C22⋊C8—1511no—
264C22⋊C8C2×D15111yescharacteristic
265#97—1511no—
266C24—3021no—
267#41—3022no—
268#41—6041no—
269C2×Q8—21no—
270C2×Q8—22no—
271C2×Q8—41no—
272C2×Q8—3021no—
273C2×Q8—3022no—
274C2×Q8—6041no—
275C2×Q8—1511no—
276C2×Q8C22×D15111yescharacteristic
277C2×Q8C22×D15111yescharacteristic
278C2×Q8C22×D15111yescharacteristic
279C2×D4—3022no—
280C2×D4—3021no—
281C2×D4—3021no—
282C2×D4—3021no—
283C2×D4—6041no—
284C2×D4—1511no—
285C2×D4—1511no—
286C2×D4—1511no—
287C22×C4—21no—
288C22×C4—3021no—
289C22×C4—3021no—
290C22×C4—3021no—
291C22×C4—1511no—
292C22×C4C22×D15111yescharacteristic
293Q16—22no—
294Q16—41no—
295Q16—3022no—
296SD16—3022no—
297SD16—3022no—
298SD16—3022no—
299SD16—3022no—
300SD16—6041no—
301SD16—1514no—
302M16—3022no—
303C2×C8—3022no—
304C2×C8—1511no—
305C2×C8—1511no—
306C2×C8C22×D15111yescharacteristic
307C2×C8C22×D15111yescharacteristic
308C4⋊C4—21no—
309C4⋊C4—3021no—
310C4⋊C4—3021no—
311C4⋊C4—3021no—
312C4⋊C4—3021no—
313C4⋊C4—3021no—
314C4⋊C4—1511no—
315C4⋊C4—1511no—
316C4⋊C4C22×D15111yescharacteristic
317C22⋊C4—21no—
318C22⋊C4—3021no—
319C22⋊C4—3021no—
320C22⋊C4—3021no—
321C22⋊C4—3021no—
322C22⋊C4—3021no—
323C22⋊C4—3021no—
324C22⋊C4—1511no—
325C22⋊C4—1511no—
326C42—3021no—
327C42—1511no—
328C23—3021no—
329C23—3021no—
330C23—6042no—
331C23—6042no—
332C23—1511no—
333C23—12081no—
334C23D4×D15111yescharacteristic
335Q8—21no—
336Q8—21no—
337Q8—21no—
338Q8—21no—
339Q8—21no—
340Q8—42no—
341Q8—3021no—
342Q8—3021no—
343Q8—6042no—
344Q8D4×D15112yes—
345D4—3022no—
346D4—3021no—
347D4—3021no—
348D4—3021no—
349D4—6042no—
350D4—6042no—
351D4—1512no—
352D4—12081no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—42no—
360C2×C4—3021no—
361C2×C4—3021no—
362C2×C4—3021no—
363C2×C4—3021no—
364C2×C4—6042no—
365C2×C4—6042no—
366C2×C4—1511no—
367C2×C4—1511no—
368C2×C4—1511no—
369C2×C4—12081no—
370C2×C4D4×D15111yescharacteristic
371C2×C4C23×D15111yescharacteristic
372C8—21no—
373C8—21no—
374C8—3021no—
375C8—1512no—
376C22—21no—
377C22—21no—
378C22—3021no—
379C22—3021no—
380C22—3021no—
381C22—3022no—
382C22—6041no—
383C22—6041no—
384C22—6041no—
385C22—6041no—
386C22—6041no—
387C22—12084no—
388C22#1801277112yescomplemented
389C22C2×D4×D15111yescharacteristic
390C4—21no—
391C4—22no—
392C4—41no—
393C4—41no—
394C4—41no—
395C4—3021no—
396C4—3021no—
397C4—3021no—
398C4—6041no—
399C4—6041no—
400C4C2×D4×D15111yescharacteristic
401C4#1801278411yescharacteristic
402C2—22no—
403C2—6041no—
404C2—6042no—
405C2—12081no—
406C2#2375284411yescharacteristic
407C2C2×#1801277111yescharacteristic
408C2#2375302111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#451×C151C2
socleC22×C151C22×D4
prime radical#23752853C2
hypercenter#451D151
hypocenterC151#3266
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
1. C2×#18012771C2semidirect
2. C22×#14558991C2semidirect
3. Q8×C22⋊D151C2semidirect
5. #23752605C2semidirect
6. #23752461C2semidirect
7. #23752451C2semidirect
8. #23752436C2semidirect
9. #23752416C2semidirect
10. #23752373C2semidirect
11. #23752365C2semidirect
12. #23752352C2semidirect
13. #23752315C2semidirect
14. #23752280C2semidirect
15. #451×C151C2semidirect
17. C2×Q8×D151C22semidirect
20. C2×#14558994C22semidirect
28. C2×#14558987C22semidirect
31. #18012737C22semidirect
37. #18012715C22semidirect
41. Q8×Dic151C22semidirect
46. #18012672C22semidirect
47. Dic151⋊C8C22semidirect
48. #18012663C22semidirect
49. #18012662C22semidirect
52. (C2×D151)⋊C8C22semidirect
53. #18012649C22semidirect
55. C2×Q16×C151C22semidirect
56. C2×Q16×C151C22semidirect
58. #103×C151C22semidirect
59. #103×C151C22semidirect
86. #14558991D4semidirect
173. C22×C151#137semidirect
204. C151#3266semidirect
216. #451D151semidirect
227. C2×Q16C2×D151semidirect
228. C2×Q16C2×D151semidirect
259. #103C2×D151semidirect
260. #103C2×D151semidirect
388. C22#18012771semidirect

Maximal subgroups

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

subgroupindex
C2×#180127712
C22×#145589912
Q8×C22⋊D1512
#237528532
#237526052
#237524612
#237524512
#237524362
#237524162
#237523732
#237523652
#237523522
#237523152
#237522802
#451×C1512
#3266151