Finite Group Databasebeta

← #34080655

Subgroups — #34080655

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×#18012767C211yesmaximal, characteristic, complemented
2C2×#18012761C211yesmaximal, characteristic, complemented
3#23752883C211yesmaximal, characteristic, complemented
4#23752858C211yesmaximal, characteristic, complemented
5#23752601C211yesmaximal, characteristic, complemented
6#23752458C211yesmaximal, characteristic, complemented
7#23752448C211yesmaximal, characteristic, complemented
8#23752435C211yesmaximal, characteristic, complemented
9#23752408C211yesmaximal, characteristic, complemented
10#23752376C211yesmaximal, characteristic, complemented
11#23752359C211yesmaximal, characteristic, complemented
12#23752359C211yesmaximal, characteristic, complemented
13#23752348C211yesmaximal, characteristic, complemented
14#23752314C211yesmaximal, characteristic, complemented
15#435×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic
17C2×#14559004C2211yescharacteristic
18C2×#14559004C2211yescharacteristic, complemented
19C22×D604C2211yescharacteristic
20#18012767—24no—
21#18012761—24no—
22C2×Dic604C2211yescharacteristic, complemented
23C2×#14558993C2211yescharacteristic
24C2×#14558993C2211yescharacteristic
25C2×#14558993C2211yescharacteristic, complemented
26C2×#14558993C2211yescharacteristic, complemented
27C2×D1208C2211yescharacteristic
28C2×D1208C2211yescharacteristic
29C2×D1208C2211yescharacteristic
30C2×D1208C2211yescharacteristic
31#18012736C2211yescharacteristic, complemented
32#18012735—21no—
33#18012727C2211yescharacteristic
34#18012724—21no—
35#18012718C2211yescharacteristic
36#18012713C2211yescharacteristic
37#18012713C2211yescharacteristic
38#18012713C2211yescharacteristic, complemented
39#18012712—21no—
40#18012712—21no—
41#18012712—21no—
42#18012707—21no—
43C4×Dic302C2211yescharacteristic, complemented
44C4×D604C2211yescharacteristic
45#18012701—21no—
46C22⋊C4×D151—21no—
47#18012673C2211yescharacteristic, complemented
48#18012664C2211yescharacteristic, complemented
49#18012664C2211yescharacteristic, complemented
50#18012661C2211yescharacteristic
51#18012661C2211yescharacteristic
52#18012661C2211yescharacteristic, complemented
53#18012661C2211yescharacteristic, complemented
54C2×M16×C151C2211yescharacteristic
55C22×C8×C151C2211yescharacteristic, complemented
56C4×D4×C151C2211yescharacteristic
57C4⋊C8×C151C2211yescharacteristic, complemented
58C22⋊C8×C151C2211yescharacteristic
59C22⋊C8×C151C2211yescharacteristic, complemented
60#97×C151C2211yescharacteristic, complemented
61C23×D151—21no—
62#14559004—22no—
63#14559004—22no—
64#14559004—22no—
65#14559004—41no—
66#14559004—41no—
67#14559004—41no—
68C2×Dic302C2311yescharacteristic
69C2×Dic302C2311yescharacteristic
70C2×D604—22no—
71C2×D604—21no—
72C2×D604—21no—
73C2×D604—21no—
74C2×D604—41no—
75C2×D604C2311yescharacteristic
76C2×D604C2311yescharacteristic
77C2×D604C2311yescharacteristic
78C2×D604C2311yescharacteristic
79C2×C22⋊D151—21no—
80C2×C22⋊D151—21no—
81C2×C22⋊D151—21no—
82C2×C22⋊D151—21no—
83C2×C22⋊D151—21no—
84C2×C22⋊D151—21no—
85C2×C4×D151—21no—
86C2×C4×D151—21no—
87C2×C4×D151—21no—
88C2×C4×D151—21no—
89Dic604—22no—
90#14558993—22no—
91#14558993—22no—
92#14558993—41no—
93#14558993D414yescomplemented
94D1208—22no—
95D1208—22no—
96D1208—22no—
97D1208—41no—
98C4⋊Dic151C2311yescharacteristic
99C4⋊Dic151C2311yescharacteristic
100Dic151⋊C4—21no—
101Dic151⋊C4—21no—
102C22⋊Dic151—21no—
103(C2×D151)⋊C4—21no—
104(C2×D151)⋊C4—21no—
105(C2×D151)⋊C4—21no—
106(C2×D151)⋊C4—21no—
107(C2×D151)⋊C4—21no—
108(C2×D151)⋊C4—21no—
109C4×Dic151—21no—
110C2×D4×C151D411yescharacteristic
111C22×C4×C151C2311yescharacteristic
112C22×C4×C151C2311yescharacteristic
113M16×C151—22no—
114C2×C8×C151—22no—
115C2×C8×C151C2311yescharacteristic
116C2×C8×C151C2311yescharacteristic
117C2×C8×C151C2311yescharacteristic
118C2×C8×C151C2311yescharacteristic
119C4⋊C4×C151D411yescharacteristic
120C22⋊C4×C151D411yescharacteristic
121C22⋊C4×C151D411yescharacteristic
122C42×C151C2311yescharacteristic
123C22×D151—21no—
124C22×D151—21no—
125C22×D151—21no—
126C22×D151—21no—
127C22×D151—42no—
128C22×D151—42no—
129C22×D151—81no—
130Dic302—21no—
131Dic302—21no—
132Dic302—21no—
133Dic302C2×D412yes—
134D604—21no—
135D604—21no—
136D604—21no—
137D604—21no—
138D604—21no—
139D604—21no—
140D604—21no—
141D604—42no—
142D604—42no—
143D604—81no—
144D604C2×D412yes—
145C22⋊D151—42no—
146C22⋊D151—42no—
147C22⋊D151—42no—
148C22⋊D151—81no—
149C22⋊D151—81no—
150C22⋊D151—81no—
151C2×Dic151—21no—
152C2×Dic151—21no—
153C2×Dic151—21no—
154C2×Dic151—21no—
155C4×D151—42no—
156C4×D151—42no—
157C4×D151—42no—
158C4×D151—81no—
159C23×C151C2×D411yescharacteristic
160C23×C151C2×D411yescharacteristic
161D4×C151—41no—
162C2×C4×C151—21no—
163C2×C4×C151—21no—
164C2×C4×C151—21no—
165C2×C4×C151—21no—
166C2×C4×C151C2×D411yescharacteristic
167C2×C4×C151C2×D411yescharacteristic
168C2×C4×C151C2×D411yescharacteristic
169C2×C4×C151C2×D411yescharacteristic
170C2×C4×C151C2411yescharacteristic
171C8×C151—21no—
172C8×C151—21no—
173C8×C151—21no—
174C8×C151C2×D412yes—
175C22×C151—21no—
176C22×C151—21no—
177C22×C151—21no—
178C22×C151—21no—
179C22×C151—21no—
180C22×C151—21no—
181C22×C151C22×D411yescharacteristic
182C2×D151—22no—
183C2×D151—41no—
184C2×D151—41no—
185C2×D151—41no—
186C2×D151—41no—
187C2×D151—41no—
188C2×D151—41no—
189C2×D151—41no—
190C2×D151—41no—
191C2×D151—41no—
192C2×D151—41no—
193C2×D151—41no—
194C2×D151—84no—
195C4×C151—21no—
196C4×C151—21no—
197C4×C151—21no—
198C4×C151—21no—
199C4×C151C22×D411yescharacteristic
200C4×C151H(5,𝔽2)11yescharacteristic
201Dic151—22no—
202Dic151—41no—
203Dic151—41no—
204Dic151—41no—
205C2×C151—41no—
206C2×C151—41no—
207C2×C151D4211yescharacteristic
208C2×C151#57511yescharacteristic
209C2×C151#57611yescharacteristic
210D151—42no—
211D151—81no—
212D151—81no—
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#447—1511no—
229#440—1511no—
230#435D15111yescharacteristic, complemented
231C2×#41—1511no—
232C2×#41—1511no—
233C2×#41—1511no—
234C22×D4—1511no—
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×D8—1511no—
245C2×D8—1511no—
246C2×M16C2×D15111yescharacteristic
247C22×C8C2×D15111yescharacteristic, complemented
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#121—1511no—
259#120—3021no—
260C4×Q8—1511no—
261C4×D4—3021no—
262C4×D4—1511no—
263C4×D4C2×D15111yescharacteristic
264C2×C22⋊C4—3021no—
265#107—1511no—
266C4⋊C8C2×D15111yescharacteristic, complemented
267#103—1511no—
268#103—1511no—
269#102—1511no—
270#102—1511no—
271#102—1511no—
272#102—1511no—
273C22⋊C8C2×D15111yescharacteristic
274C22⋊C8C2×D15111yescharacteristic, complemented
275#97C2×D15111yescharacteristic, complemented
276C24—3021no—
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—3022no—
286C2×D4—3021no—
287C2×D4—3021no—
288C2×D4—3021no—
289C2×D4—3021no—
290C2×D4—3021no—
291C2×D4—3021no—
292C2×D4—3021no—
293C2×D4—3021no—
294C2×D4—3021no—
295C2×D4—6041no—
296C2×D4—1511no—
297C2×D4—1511no—
298C2×D4—1511no—
299C2×D4—1511no—
300C2×D4D60411yescharacteristic
301C22×C4—3021no—
302C22×C4—3021no—
303C22×C4—3021no—
304C22×C4—3021no—
305C22×C4C22×D15111yescharacteristic
306C22×C4C22×D15111yescharacteristic
307Q16—3022no—
308SD16—3022no—
309SD16—3022no—
310SD16—6041no—
311SD16—1514no—
312D8—3022no—
313D8—3022no—
314D8—3022no—
315D8—6041no—
316M16—22no—
317C2×C8—22no—
318C2×C8C22×D15111yescharacteristic
319C2×C8C22×D15111yescharacteristic
320C2×C8C22×D15111yescharacteristic
321C2×C8C22×D15111yescharacteristic
322C4⋊C4—3021no—
323C4⋊C4—3021no—
324C4⋊C4—1511no—
325C4⋊C4—1511no—
326C4⋊C4D60411yescharacteristic
327C22⋊C4—3021no—
328C22⋊C4—3021no—
329C22⋊C4—3021no—
330C22⋊C4—3021no—
331C22⋊C4—3021no—
332C22⋊C4—3021no—
333C22⋊C4—3021no—
334C22⋊C4D60411yescharacteristic
335C22⋊C4D60411yescharacteristic
336C42—3021no—
337C42C22×D15111yescharacteristic
338C23—3021no—
339C23—3021no—
340C23—3021no—
341C23—3021no—
342C23—6042no—
343C23—6042no—
344C23—12081no—
345C23C2×D60411yescharacteristic
346C23C2×D60411yescharacteristic
347Q8—3021no—
348Q8—3021no—
349Q8—3021no—
350Q8—1512no—
351D4—41no—
352D4—3021no—
353D4—3021no—
354D4—3021no—
355D4—3021no—
356D4—3021no—
357D4—3021no—
358D4—3021no—
359D4—6042no—
360D4—6042no—
361D4—6042no—
362D4—6042no—
363D4—6042no—
364D4—1512no—
365D4—12081no—
366D4—12081no—
367D4—12081no—
368D4—12081no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—3021no—
374C2×C4—3021no—
375C2×C4—3021no—
376C2×C4—3021no—
377C2×C4—6042no—
378C2×C4—6042no—
379C2×C4—6042no—
380C2×C4—12081no—
381C2×C4C2×D60411yescharacteristic
382C2×C4C2×D60411yescharacteristic
383C2×C4C2×D60411yescharacteristic
384C2×C4C2×D60411yescharacteristic
385C2×C4C23×D15111yescharacteristic
386C8—21no—
387C8—21no—
388C8—21no—
389C8D4×D15112yes—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—3022no—
397C22—6041no—
398C22—6041no—
399C22—6041no—
400C22—6041no—
401C22—6041no—
402C22—6041no—
403C22—6041no—
404C22—6041no—
405C22—6041no—
406C22—6041no—
407C22—6041no—
408C22—12084no—
409C22C22×D60411yescharacteristic
410C4—21no—
411C4—21no—
412C4—21no—
413C4—21no—
414C4—3022no—
415C4—6041no—
416C4—6041no—
417C4—6041no—
418C4C2×D4×D15111yescharacteristic
419C4#1801278511yescharacteristic
420C2—41no—
421C2—41no—
422C2—6042no—
423C2—12081no—
424C2—12081no—
425C2—12081no—
426C2D4×D60411yescharacteristic
427C2#2375301211yescharacteristic
428C2#2375301711yescharacteristic
subgroupG/H
centerC22C22×D604
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#435×C151C2
socleC22×C151C22×D4
hypercenter#435D151
hypocenterC151#3268
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#18012767C2semidirect
2. C2×#18012761C2semidirect
3. #23752883C2semidirect
4. #23752858C2semidirect
5. #23752601C2semidirect
6. #23752458C2semidirect
7. #23752448C2semidirect
8. #23752435C2semidirect
9. #23752408C2semidirect
10. #23752376C2semidirect
11. #23752359C2semidirect
12. #23752359C2semidirect
13. #23752348C2semidirect
14. #23752314C2semidirect
15. #435×C151C2semidirect
18. C2×#14559004C22semidirect
22. C2×Dic604C22semidirect
25. C2×#14558993C22semidirect
26. C2×#14558993C22semidirect
31. #18012736C22semidirect
38. #18012713C22semidirect
43. C4×Dic302C22semidirect
47. #18012673C22semidirect
48. #18012664C22semidirect
49. #18012664C22semidirect
52. #18012661C22semidirect
53. #18012661C22semidirect
55. C22×C8×C151C22semidirect
57. C4⋊C8×C151C22semidirect
59. C22⋊C8×C151C22semidirect
60. #97×C151C22semidirect
93. #14558993D4semidirect
214. C151#3268semidirect
230. #435D151semidirect
247. C22×C8C2×D151semidirect
266. C4⋊C8C2×D151semidirect
274. C22⋊C8C2×D151semidirect
275. #97C2×D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127672
C2×#180127612
#237528832
#237528582
#237526012
#237524582
#237524482
#237524352
#237524082
#237523762
#237523592
#237523482
#237523142
#435×C1512
#3268151