Finite Group Databasebeta

← #34080648

Subgroups — #34080648

Order 19328.

510 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18012765C211yesmaximal, characteristic, complemented
2C2×#18012758C211yesmaximal, characteristic, complemented
3#23752880C211yesmaximal, characteristic, complemented
4#23752856C211yesmaximal, characteristic, complemented
5#23752600C211yesmaximal, characteristic, complemented
6#23752456C211yesmaximal, characteristic, complemented
7#23752447C211yesmaximal, characteristic, complemented
8#23752433C211yesmaximal, characteristic, complemented
9#23752405C211yesmaximal, characteristic, complemented
10#23752376C211yesmaximal, characteristic, complemented
11#23752358C211yesmaximal, characteristic, complemented
12#23752354C211yesmaximal, characteristic, complemented
13#23752309C211yesmaximal, characteristic, complemented
14#23752286C211yesmaximal, characteristic, complemented
15#447×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic
17C2×#14559003C2211yescharacteristic
18C2×#14559003C2211yescharacteristic, complemented
19#18012765—24no—
20#18012758—24no—
21C2×Dic604C2211yescharacteristic, complemented
22C2×#14558993C2211yescharacteristic, complemented
23C2×#14558992C2211yescharacteristic
24C2×#14558992C2211yescharacteristic
25C2×#14558992C2211yescharacteristic, complemented
26C2×#14558989C2211yescharacteristic
27C2×#14558989C2211yescharacteristic
28C2×#14558988C2211yescharacteristic
29C2×C8×D151C2211yescharacteristic, complemented
30#18012735—21no—
31#18012735C2211yescharacteristic, complemented
32#18012726C2211yescharacteristic
33#18012720—21no—
34#18012718C2211yescharacteristic
35#18012714C2211yescharacteristic, complemented
36#18012712—21no—
37#18012711—21no—
38#18012711—21no—
39#18012710C2211yescharacteristic
40#18012708—21no—
41#18012704C2211yescharacteristic, complemented
42D4×Dic151C2211yescharacteristic
43C4×C22⋊D151C2211yescharacteristic
44(C22⋊D151)⋊C4—21no—
45C2×C22⋊Dic151—21no—
46#18012672C2211yescharacteristic, complemented
47Dic151⋊C8C2211yescharacteristic, complemented
48#18012664C2211yescharacteristic, complemented
49#18012662C2211yescharacteristic, complemented
50#18012661C2211yescharacteristic, complemented
51#18012660C2211yescharacteristic, complemented
52(C2×D151)⋊C8C2211yescharacteristic, complemented
53#18012649C2211yescharacteristic, complemented
54C22×D4×C151C2211yescharacteristic
55C2×D8×C151C2211yescharacteristic
56C2×D8×C151C2211yescharacteristic
57#121×C151C2211yescharacteristic
58#102×C151C2211yescharacteristic
59#102×C151C2211yescharacteristic
60C22⋊C8×C151C2211yescharacteristic
61#14559004—22no—
62#14559004—41no—
63#14559003—22no—
64#14559003—22no—
65#14559003—41no—
66#14559003—41no—
67C2×Dic302C2311yescharacteristic
68C2×Dic302C2311yescharacteristic
69C2×D604—21no—
70C2×D604C2311yescharacteristic
71C2×C22⋊D151—21no—
72C2×C22⋊D151—21no—
73C2×C22⋊D151—21no—
74C2×C22⋊D151—21no—
75C2×C22⋊D151—21no—
76C2×C22⋊D151—21no—
77C2×C22⋊D151D411yescharacteristic
78C22×Dic151—21no—
79C22×Dic151—21no—
80C22×Dic151—21no—
81C2×C4×D151—21no—
82C2×C4×D151C2311yescharacteristic
83Dic604—22no—
84#14558993—41no—
85#14558992—22no—
86#14558992—22no—
87#14558992D414yescomplemented
88#14558989—22no—
89#14558989—22no—
90#14558988—22no—
91C2×C151⋊C8C2311yescharacteristic
92C2×C151⋊C8C2311yescharacteristic
93C8×D151—22no—
94C4⋊Dic151C2311yescharacteristic
95Dic151⋊C4—21no—
96Dic151⋊C4—21no—
97Dic151⋊C4D411yescharacteristic
98C22⋊Dic151—21no—
99C22⋊Dic151—21no—
100C22⋊Dic151—21no—
101C22⋊Dic151—21no—
102C22⋊Dic151—21no—
103C22⋊Dic151D411yescharacteristic
104(C2×D151)⋊C4—21no—
105(C2×D151)⋊C4D411yescharacteristic
106C4×Dic151—21no—
107C4×Dic151C2311yescharacteristic
108C24×C151—21no—
109C2×D4×C151—22no—
110C2×D4×C151—21no—
111C2×D4×C151—21no—
112C2×D4×C151—41no—
113C2×D4×C151C2311yescharacteristic
114C2×D4×C151C2311yescharacteristic
115C2×D4×C151C2311yescharacteristic
116C22×C4×C151C2311yescharacteristic
117D8×C151—22no—
118D8×C151—41no—
119C2×C8×C151C2311yescharacteristic
120C2×C8×C151C2311yescharacteristic
121C4⋊C4×C151C2311yescharacteristic
122C22⋊C4×C151—21no—
123C22×D151—21no—
124C22×D151C2×D411yescharacteristic
125Dic302—21no—
126Dic302—21no—
127Dic302—21no—
128Dic302C2×D412yes—
129D604—21no—
130D604—21no—
131D604—81no—
132C22⋊D151—41no—
133C22⋊D151—42no—
134C22⋊D151—42no—
135C22⋊D151—42no—
136C22⋊D151—42no—
137C22⋊D151—81no—
138C22⋊D151—81no—
139C2×Dic151—21no—
140C2×Dic151—21no—
141C2×Dic151—21no—
142C2×Dic151—42no—
143C2×Dic151—42no—
144C2×Dic151—81no—
145C2×Dic151C2×D411yescharacteristic
146C2×Dic151C2×D411yescharacteristic
147C2×Dic151C2×D411yescharacteristic
148C4×D151—21no—
149C4×D151—21no—
150C4×D151—42no—
151C151⋊C8—21no—
152C151⋊C8C2×D412yes—
153C23×C151—21no—
154C23×C151—21no—
155C23×C151—21no—
156C23×C151—42no—
157C23×C151—42no—
158C23×C151—81no—
159C23×C151C2×D411yescharacteristic
160D4×C151—21no—
161D4×C151—21no—
162D4×C151—21no—
163D4×C151—21no—
164D4×C151—21no—
165D4×C151—42no—
166D4×C151—81no—
167D4×C151C2×D412yes—
168C2×C4×C151—21no—
169C2×C4×C151—21no—
170C2×C4×C151—21no—
171C2×C4×C151C2×D411yescharacteristic
172C2×C4×C151C2411yescharacteristic
173C8×C151—21no—
174C8×C151—21no—
175C22×C151—21no—
176C22×C151—22no—
177C22×C151—21no—
178C22×C151—21no—
179C22×C151—41no—
180C22×C151—41no—
181C22×C151—41no—
182C22×C151—41no—
183C22×C151—41no—
184C22×C151—41no—
185C22×C151—41no—
186C22×C151—41no—
187C22×C151—84no—
188C22×C151C22×D411yescharacteristic
189C2×D151—21no—
190C2×D151—21no—
191C2×D151—21no—
192C2×D151—41no—
193C2×D151—41no—
194C2×D151—41no—
195C4×C151—21no—
196C4×C151—41no—
197C4×C151C22×D411yescharacteristic
198C4×C151H(5,𝔽2)11yescharacteristic
199Dic151—21no—
200Dic151—22no—
201Dic151—21no—
202Dic151—21no—
203Dic151—41no—
204Dic151—41no—
205C2×C151—41no—
206C2×C151—42no—
207C2×C151—81no—
208C2×C151—81no—
209C2×C151D4211yescharacteristic
210C2×C151#57511yescharacteristic
211C2×C151#57611yescharacteristic
212D151—41no—
213D151—81no—
214C151#326811yescharacteristic, complemented, Sylow
215#3268—1511nomaximal, Sylow
216C2×AGL(1,ℤ/8)—1511no—
217C2×#135—1511no—
218#550—1511no—
219#546—1511no—
220#496—1511no—
221#468—1511no—
222#466—1511no—
223#464—1511no—
224#459—1511no—
225#452—1511no—
226#449—1511no—
227#449—1511no—
228#447D15111yescharacteristic, complemented
229#440—1511no—
230#435—1511no—
231C2×#41—1511no—
232C2×#41—1511no—
233C2×#41—1511no—
234C22×D4C2×D15111yescharacteristic
235AGL(1,ℤ/8)—3024no—
236#135—3024no—
237C2×Q16—1511no—
238C2×SD16—1511no—
239C2×SD16—1511no—
240C2×SD16—1511no—
241C2×SD16—1511no—
242C2×D8—1511no—
243C2×D8—1511no—
244C2×D8C2×D15111yescharacteristic
245C2×D8C2×D15111yescharacteristic
246C2×M16—1511no—
247C22×C8—1511no—
248#127—3021no—
249#127—1511no—
250#124—1511no—
251#123—3021no—
252C22⋊Q8—1511no—
253#121—3021no—
254#121—3021no—
255#121—3021no—
256#121—1511no—
257#121—1511no—
258#121C2×D15111yescharacteristic
259#120—3021no—
260C4×Q8—1511no—
261C4×D4—3021no—
262C4×D4—1511no—
263C4×D4—1511no—
264C2×C22⋊C4—3021no—
265#107—1511no—
266C4⋊C8—1511no—
267#103—1511no—
268#103—1511no—
269#102—1511no—
270#102—1511no—
271#102C2×D15111yescharacteristic
272#102C2×D15111yescharacteristic
273C22⋊C8—1511no—
274C22⋊C8C2×D15111yescharacteristic
275#97—1511no—
276C24—21no—
277#41—3022no—
278#41—3022no—
279#41—3022no—
280#41—6041no—
281#41—6041no—
282#41—6041no—
283C2×Q8—1511no—
284C2×Q8—1511no—
285C2×D4—22no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—41no—
289C2×D4—3021no—
290C2×D4—3021no—
291C2×D4—3021no—
292C2×D4—3021no—
293C2×D4—3021no—
294C2×D4—3021no—
295C2×D4—3021no—
296C2×D4—1511no—
297C2×D4—1511no—
298C2×D4C22×D15111yescharacteristic
299C2×D4C22×D15111yescharacteristic
300C2×D4C22×D15111yescharacteristic
301C22×C4—3021no—
302C22×C4—3021no—
303C22×C4—3021no—
304C22×C4—3021no—
305C22×C4—1511no—
306C22×C4C22×D15111yescharacteristic
307Q16—3022no—
308SD16—3022no—
309SD16—3022no—
310SD16—6041no—
311SD16—1514no—
312D8—22no—
313D8—41no—
314D8—3022no—
315D8—3022no—
316M16—3022no—
317C2×C8—3022no—
318C2×C8—1511no—
319C2×C8—1511no—
320C2×C8C22×D15111yescharacteristic
321C2×C8C22×D15111yescharacteristic
322C4⋊C4—3021no—
323C4⋊C4—3021no—
324C4⋊C4—1511no—
325C4⋊C4—1511no—
326C4⋊C4C22×D15111yescharacteristic
327C22⋊C4—21no—
328C22⋊C4—3021no—
329C22⋊C4—3021no—
330C22⋊C4—3021no—
331C22⋊C4—3021no—
332C22⋊C4—3021no—
333C22⋊C4—3021no—
334C22⋊C4—1511no—
335C22⋊C4—1511no—
336C42—3021no—
337C42—1511no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—42no—
342C23—42no—
343C23—81no—
344C23—3021no—
345C23—1511no—
346C23D4×D15111yescharacteristic
347Q8—3021no—
348Q8—3021no—
349Q8—3021no—
350Q8—1512no—
351D4—21no—
352D4—21no—
353D4—21no—
354D4—21no—
355D4—21no—
356D4—42no—
357D4—81no—
358D4—3021no—
359D4—3021no—
360D4—6041no—
361D4—6042no—
362D4—6042no—
363D4—6042no—
364D4—6042no—
365D4—12081no—
366D4—12081no—
367D4—12081no—
368D4D4×D15112yes—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—3021no—
373C2×C4—3021no—
374C2×C4—3021no—
375C2×C4—3021no—
376C2×C4—3021no—
377C2×C4—6042no—
378C2×C4—6042no—
379C2×C4—6042no—
380C2×C4—1511no—
381C2×C4—1511no—
382C2×C4—1511no—
383C2×C4—12081no—
384C2×C4D4×D15111yescharacteristic
385C2×C4C23×D15111yescharacteristic
386C8—21no—
387C8—21no—
388C8—3021no—
389C8—1512no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—22no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—84no—
403C22—3021no—
404C22—3021no—
405C22—3021no—
406C22—6041no—
407C22—6041no—
408C22—6041no—
409C22C2×D4×D15111yescharacteristic
410C4—21no—
411C4—41no—
412C4—3021no—
413C4—3021no—
414C4—3021no—
415C4—3022no—
416C4—6041no—
417C4—6041no—
418C4C2×D4×D15111yescharacteristic
419C4#1801278411yescharacteristic
420C2—41no—
421C2—42no—
422C2—81no—
423C2—81no—
424C2—6041no—
425C2—12081no—
426C2#2375284411yescharacteristic
427C2#2375300811yescharacteristic
428C2#2375301311yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#447×C151C2
socleC22×C151C22×D4
hypercenter#447D151
hypocenterC151#3268
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. C2×#18012765C2semidirect
2. C2×#18012758C2semidirect
3. #23752880C2semidirect
4. #23752856C2semidirect
5. #23752600C2semidirect
6. #23752456C2semidirect
7. #23752447C2semidirect
8. #23752433C2semidirect
9. #23752405C2semidirect
10. #23752376C2semidirect
11. #23752358C2semidirect
12. #23752354C2semidirect
13. #23752309C2semidirect
14. #23752286C2semidirect
15. #447×C151C2semidirect
18. C2×#14559003C22semidirect
21. C2×Dic604C22semidirect
22. C2×#14558993C22semidirect
25. C2×#14558992C22semidirect
29. C2×C8×D151C22semidirect
31. #18012735C22semidirect
35. #18012714C22semidirect
41. #18012704C22semidirect
46. #18012672C22semidirect
47. Dic151⋊C8C22semidirect
48. #18012664C22semidirect
49. #18012662C22semidirect
50. #18012661C22semidirect
51. #18012660C22semidirect
52. (C2×D151)⋊C8C22semidirect
53. #18012649C22semidirect
87. #14558992D4semidirect
214. C151#3268semidirect
228. #447D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127652
C2×#180127582
#237528802
#237528562
#237526002
#237524562
#237524472
#237524332
#237524052
#237523762
#237523582
#237523542
#237523092
#237522862
#447×C1512
#3268151