Finite Group Databasebeta

← #34080863

Subgroups — #34080863

Order 19328.

504 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18012760C211yesmaximal, characteristic, complemented
2C2×#18012759C211yesmaximal, characteristic, complemented
3#23752881C211yesmaximal, characteristic, complemented
4#23752880C211yesmaximal, characteristic, complemented
5#23752587C211yesmaximal, characteristic, complemented
6#23752447C211yesmaximal, characteristic, complemented
7#23752446C211yesmaximal, characteristic, complemented
8#23752411C211yesmaximal, characteristic, complemented
9#23752410C211yesmaximal, characteristic, complemented
10#23752360C211yesmaximal, characteristic, complemented
11#23752359C211yesmaximal, characteristic, complemented
12#23752354C211yesmaximal, characteristic, complemented
13#23752304C211yesmaximal, characteristic, complemented
14(C22⋊D151)⋊C8C211yesmaximal, characteristic, complemented
15#449×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic
17C2×#14559004C2211yescharacteristic
18C2×#14559003C2211yescharacteristic
19#18012760—24no—
20#18012759—24no—
21C2×#14558994C2211yescharacteristic
22C2×#14558993C2211yescharacteristic
23C2×#14558992C2211yescharacteristic
24C2×#14558991C2211yescharacteristic
25C2×D1208C2211yescharacteristic
26C2×#14558989C2211yescharacteristic
27C2×#14558989C2211yescharacteristic
28C22×C151⋊C8C2211yescharacteristic
29C2×C8×D151C2211yescharacteristic
30#18012735—21no—
31#18012735—21no—
32#18012735C2211yescharacteristic
33#18012735C2211yescharacteristic
34#18012714C2211yescharacteristic
35#18012713—21no—
36#18012713C2211yescharacteristic
37#18012712—21no—
38#18012711—21no—
39#18012710—21no—
40#18012710C2211yescharacteristic
41Q8×Dic151C2211yescharacteristic
42#18012704C2211yescharacteristic
43C4×C22⋊D151—21no—
44C4×C22⋊D151C2211yescharacteristic
45(C22⋊D151)⋊C4—21no—
46#18012672C2211yescharacteristic
47Dic151⋊C8C2211yescharacteristic
48#18012664C2211yescharacteristic
49#18012661C2211yescharacteristic
50#18012660C2211yescharacteristic
51#18012659C2211yescharacteristic
52(C2×D151)⋊C8C2211yescharacteristic
53C8×Dic151C2211yescharacteristic
54C2×#41×C151C2211yescharacteristic
55C2×SD16×C151C2211yescharacteristic
56C2×D8×C151C2211yescharacteristic
57#121×C151C2211yescharacteristic
58#103×C151C2211yescharacteristic
59#102×C151C2211yescharacteristic
60C22⋊C8×C151C2211yescharacteristic
61#14559005—22no—
62#14559005—41no—
63#14559004—22no—
64#14559004—41no—
65#14559003—22no—
66#14559003—41no—
67C2×Dic302C2311yescharacteristic
68C2×D604—21no—
69C2×D604—21no—
70C2×D604C2311yescharacteristic
71C2×D604C2311yescharacteristic
72C2×C22⋊D151—21no—
73C2×C22⋊D151—21no—
74C2×C22⋊D151—21no—
75C2×C22⋊D151—21no—
76C2×C22⋊D151—21no—
77C2×C22⋊D151—21no—
78C2×C22⋊D151—21no—
79C2×C22⋊D151—21no—
80C2×C22⋊D151D411yescharacteristic
81C22×Dic151—21no—
82C2×C4×D151—21no—
83C2×C4×D151—21no—
84C2×C4×D151C2311yescharacteristic
85#14558994D414yescomplemented
86#14558993—22no—
87#14558992—22no—
88#14558991—22no—
89D1208—41no—
90#14558989—22no—
91#14558989—22no—
92C2×C151⋊C8—22no—
93C2×C151⋊C8C2311yescharacteristic
94C2×C151⋊C8C2311yescharacteristic
95C8×D151—22no—
96C4⋊Dic151—21no—
97C4⋊Dic151C2311yescharacteristic
98Dic151⋊C4—21no—
99Dic151⋊C4D411yescharacteristic
100C22⋊Dic151—21no—
101C22⋊Dic151D411yescharacteristic
102(C2×D151)⋊C4—21no—
103(C2×D151)⋊C4—21no—
104(C2×D151)⋊C4D411yescharacteristic
105C4×Dic151—21no—
106C4×Dic151—21no—
107C4×Dic151C2311yescharacteristic
108#41×C151—22no—
109#41×C151—41no—
110C2×Q8×C151C2311yescharacteristic
111C2×D4×C151—21no—
112C2×D4×C151—21no—
113C2×D4×C151C2311yescharacteristic
114C2×D4×C151C2311yescharacteristic
115C22×C4×C151—21no—
116C22×C4×C151C2311yescharacteristic
117SD16×C151—22no—
118D8×C151—41no—
119C2×C8×C151C2311yescharacteristic
120C2×C8×C151C2311yescharacteristic
121C4⋊C4×C151C2311yescharacteristic
122C22⋊C4×C151—21no—
123C22×D151—21no—
124C22×D151—21no—
125C22×D151C2×D411yescharacteristic
126Dic302—21no—
127Dic302C2×D412yes—
128D604—21no—
129D604—21no—
130D604—21no—
131D604—21no—
132D604—42no—
133D604—81no—
134C22⋊D151—22no—
135C22⋊D151—42no—
136C22⋊D151—42no—
137C22⋊D151—42no—
138C22⋊D151—42no—
139C22⋊D151—81no—
140C22⋊D151—81no—
141C22⋊D151—81no—
142C22⋊D151—81no—
143C2×Dic151—21no—
144C2×Dic151—21no—
145C2×Dic151—42no—
146C2×Dic151C2×D411yescharacteristic
147C2×Dic151C2×D411yescharacteristic
148C2×Dic151C2×D411yescharacteristic
149C4×D151—21no—
150C4×D151—21no—
151C4×D151—42no—
152C4×D151—42no—
153C151⋊C8—21no—
154C151⋊C8C2×D412yes—
155C23×C151—21no—
156C23×C151—21no—
157C23×C151C2×D411yescharacteristic
158Q8×C151—21no—
159Q8×C151C2×D412yes—
160D4×C151—21no—
161D4×C151—21no—
162D4×C151—21no—
163D4×C151—21no—
164D4×C151—42no—
165D4×C151—81no—
166C2×C4×C151—21no—
167C2×C4×C151—21no—
168C2×C4×C151—21no—
169C2×C4×C151—21no—
170C2×C4×C151—42no—
171C2×C4×C151C2×D411yescharacteristic
172C2×C4×C151C2411yescharacteristic
173C8×C151—21no—
174C8×C151—21no—
175C22×C151—21no—
176C22×C151—21no—
177C22×C151—21no—
178C22×C151—41no—
179C22×C151—41no—
180C22×C151—41no—
181C22×C151—41no—
182C22×C151—41no—
183C22×C151—41no—
184C22×C151C22×D411yescharacteristic
185C2×D151—21no—
186C2×D151—21no—
187C2×D151—21no—
188C2×D151—41no—
189C2×D151—41no—
190C2×D151—41no—
191C2×D151—41no—
192C2×D151—41no—
193C2×D151—41no—
194C4×C151—21no—
195C4×C151—22no—
196C4×C151—41no—
197C4×C151C22×D411yescharacteristic
198C4×C151H(5,𝔽2)11yescharacteristic
199Dic151—21no—
200Dic151—22no—
201Dic151—21no—
202Dic151—41no—
203Dic151#13512yescomplemented
204C2×C151—41no—
205C2×C151—81no—
206C2×C151—81no—
207C2×C151D4211yescharacteristic
208C2×C151C2×#13511yescharacteristic
209C2×C151#57611yescharacteristic
210D151—41no—
211D151—81no—
212D151—81no—
213C151#328711yescharacteristic, complemented, Sylow
214#3287—1511nomaximal, Sylow
215C2×#135—1511no—
216C2×#135—1511no—
217#550—1511no—
218#550—1511no—
219#493—1511no—
220#466—1511no—
221#466—1511no—
222#460—1511no—
223#460—1511no—
224#449—1511no—
225#449—1511no—
226#449—1511no—
227#449D15111yescharacteristic, complemented
228C4×Q16—1511no—
229C8×D4—1511no—
230C2×#41—1511no—
231C2×#41—1511no—
232C2×#41—1511no—
233C2×#41C2×D15111yescharacteristic
234#135—3024no—
235#135—3024no—
236C2×Q16—1511no—
237C2×SD16—1511no—
238C2×SD16—1511no—
239C2×SD16—1511no—
240C2×SD16C2×D15111yescharacteristic
241C2×D8—1511no—
242C2×D8—1511no—
243C2×D8—1511no—
244C2×D8C2×D15111yescharacteristic
245C22×C8—1511no—
246C22×C8—1511no—
247#127—3021no—
248#127—3021no—
249#127—1511no—
250#127—1511no—
251#121—3021no—
252#121—3021no—
253#121—3021no—
254#121—3021no—
255#121—1511no—
256#121—1511no—
257#121—1511no—
258#121C2×D15111yescharacteristic
259C4×Q8—1511no—
260C4×Q8—1511no—
261C4×D4—3021no—
262C4×D4—3021no—
263C4×D4—1511no—
264#107—1511no—
265C4⋊C8—1511no—
266#103—1511no—
267#103C2×D15111yescharacteristic
268#102—1511no—
269#102—1511no—
270#102—1511no—
271#102C2×D15111yescharacteristic
272C22⋊C8—1511no—
273C22⋊C8C2×D15111yescharacteristic
274C4×C8—1511no—
275#41—22no—
276#41—41no—
277#41—3022no—
278#41—3022no—
279#41—3022no—
280#41—6041no—
281#41—6041no—
282#41—6041no—
283C2×Q8—1511no—
284C2×Q8C22×D15111yescharacteristic
285C2×D4—21no—
286C2×D4—21no—
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—3021no—
296C2×D4—3021no—
297C2×D4—1511no—
298C2×D4—1511no—
299C2×D4—1511no—
300C2×D4C22×D15111yescharacteristic
301C2×D4C22×D15111yescharacteristic
302C22×C4—21no—
303C22×C4—3021no—
304C22×C4—3021no—
305C22×C4—3021no—
306C22×C4—1511no—
307C22×C4C22×D15111yescharacteristic
308Q16—1514no—
309SD16—22no—
310SD16—3022no—
311SD16—3022no—
312SD16—3022no—
313D8—41no—
314D8—3022no—
315D8—3022no—
316D8—6041no—
317C2×C8—3022no—
318C2×C8—3022no—
319C2×C8—1511no—
320C2×C8—1511no—
321C2×C8C22×D15111yescharacteristic
322C2×C8C22×D15111yescharacteristic
323C4⋊C4—3021no—
324C4⋊C4—3021no—
325C4⋊C4—1511no—
326C4⋊C4—1511no—
327C4⋊C4C22×D15111yescharacteristic
328C22⋊C4—21no—
329C22⋊C4—3021no—
330C22⋊C4—3021no—
331C22⋊C4—3021no—
332C22⋊C4—1511no—
333C22⋊C4—1511no—
334C42—3021no—
335C42—3021no—
336C42—1511no—
337C23—21no—
338C23—21no—
339C23—3021no—
340C23—3021no—
341C23—1511no—
342C23D4×D15111yescharacteristic
343Q8—21no—
344Q8—3021no—
345Q8—1512no—
346Q8D4×D15112yes—
347D4—21no—
348D4—21no—
349D4—21no—
350D4—21no—
351D4—42no—
352D4—81no—
353D4—3022no—
354D4—3021no—
355D4—3021no—
356D4—3021no—
357D4—3021no—
358D4—6042no—
359D4—6042no—
360D4—6042no—
361D4—6042no—
362D4—6042no—
363D4—12081no—
364D4—12081no—
365D4—12081no—
366D4—12081no—
367D4—12081no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—42no—
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×C4D4×D15111yescharacteristic
384C2×C4C23×D15111yescharacteristic
385C8—21no—
386C8—21no—
387C8—3021no—
388C8—1512no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—3021no—
399C22—3021no—
400C22—3021no—
401C22—6041no—
402C22—6041no—
403C22—6041no—
404C22—6041no—
405C22—6041no—
406C22—6041no—
407C22C2×D4×D15111yescharacteristic
408C4—21no—
409C4—22no—
410C4—41no—
411C4—3021no—
412C4—3021no—
413C4—3022no—
414C4—6041no—
415C4—1512no—
416C4C2×D4×D15111yescharacteristic
417C4#1801278411yescharacteristic
418C2—41no—
419C2—81no—
420C2—81no—
421C2—6041no—
422C2—12081no—
423C2—12081no—
424C2#2375284411yescharacteristic
425C2#135×D15111yescharacteristic
426C2#2375301611yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#449×C151C2
socleC22×C151C22×D4
hypercenter#449D151
hypocenterC151#3287
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. C2×#18012760C2semidirect
2. C2×#18012759C2semidirect
3. #23752881C2semidirect
4. #23752880C2semidirect
5. #23752587C2semidirect
6. #23752447C2semidirect
7. #23752446C2semidirect
8. #23752411C2semidirect
9. #23752410C2semidirect
10. #23752360C2semidirect
11. #23752359C2semidirect
12. #23752354C2semidirect
13. #23752304C2semidirect
14. (C22⋊D151)⋊C8C2semidirect
15. #449×C151C2semidirect
85. #14558994D4semidirect
203. Dic151#135semidirect
213. C151#3287semidirect
227. #449D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127602
C2×#180127592
#237528812
#237528802
#237525872
#237524472
#237524462
#237524112
#237524102
#237523602
#237523592
#237523542
#237523042
(C22⋊D151)⋊C82
#449×C1512
#3287151