Finite Group Databasebeta

← #34080627

Subgroups — #34080627

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×#18012772C211yesmaximal, characteristic, complemented
2C2×SD16×D151C211yesmaximal, characteristic, complemented
3#23752875C211yesmaximal, characteristic, complemented
4#23752859C211yesmaximal, characteristic
5#23752603C211yesmaximal, characteristic, complemented
6#23752454C211yesmaximal, characteristic, complemented
7#23752433C211yesmaximal, characteristic, complemented
8#23752416C211yesmaximal, characteristic, complemented
9#23752372C211yesmaximal, characteristic, complemented
10#23752369C211yesmaximal, characteristic, complemented
11#23752364C211yesmaximal, characteristic, complemented
12#23752350C211yesmaximal, characteristic, complemented
13#23752311C211yesmaximal, characteristic, complemented
14#23752281C211yesmaximal, characteristic, complemented
15#468×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic
17C22×Dic302C2211yescharacteristic, complemented
18C2×Q8×D151C2211yescharacteristic
19C2×D4×D151C2211yescharacteristic
20#18012772—24no—
21C2×Dic604C2211yescharacteristic, complemented
22C2×Dic604C2211yescharacteristic, complemented
23C2×#14558994C2211yescharacteristic, complemented
24C2×#14558993C2211yescharacteristic
25C2×#14558993C2211yescharacteristic
26C2×#14558992C2211yescharacteristic
27C2×#14558992C2211yescharacteristic
28C2×#14558991C2211yescharacteristic
29SD16×D151—24no—
30C2×C8×D151C2211yescharacteristic
31#18012738—21no—
32#18012737C2211yescharacteristic, complemented
33#18012726C2211yescharacteristic
34#18012721—21no—
35#18012719C2211yescharacteristic
36#18012719C2211yescharacteristic
37#18012717—21no—
38#18012716—21no—
39#18012710—21no—
40#18012707—21no—
41#18012704C2211yescharacteristic, complemented
42#18012701C2211yescharacteristic
43C4×C22⋊D151C2211yescharacteristic
44(C22⋊D151)⋊C4—21no—
45C22⋊C4×D151—21no—
46Dic151⋊C8C2211yescharacteristic, complemented
47#18012662C2211yescharacteristic, complemented
48#18012662C2211yescharacteristic, complemented
49#18012662C2211yescharacteristic, complemented
50#18012659C2211yescharacteristic
51C22⋊(C151⋊C8)C2211yescharacteristic, complemented
52(C2×D151)⋊C8C2211yescharacteristic
53#18012649C2211yescharacteristic, complemented
54C2×SD16×C151C2211yescharacteristic
55C2×M16×C151C2211yescharacteristic, complemented
56C22⋊Q8×C151C2211yescharacteristic, complemented
57#121×C151C2211yescharacteristic
58#107×C151C2211yescharacteristic, complemented
59#103×C151C2211yescharacteristic, complemented
60#102×C151C2211yescharacteristic
61C23×D151—21no—
62#14559004—22no—
63#14559004—41no—
64C2×Dic302—21no—
65C2×Dic302—22no—
66C2×Dic302—21no—
67C2×Dic302—41no—
68C2×Dic302C2311yescharacteristic
69C2×Dic302C2311yescharacteristic
70C2×Dic302C2311yescharacteristic
71Q8×D151—22no—
72Q8×D151—41no—
73C2×D604C2311yescharacteristic
74C2×C22⋊D151—21no—
75C2×C22⋊D151—21no—
76C2×C22⋊D151D411yescharacteristic
77D4×D151—22no—
78D4×D151—41no—
79C22×Dic151—21no—
80C2×C4×D151—21no—
81C2×C4×D151—21no—
82C2×C4×D151—21no—
83C2×C4×D151C2311yescharacteristic
84Dic604—22no—
85Dic604—22no—
86#14558994—41no—
87#14558993—22no—
88#14558993D414yescomplemented
89#14558992—22no—
90#14558992—41no—
91#14558991—22no—
92C2×C151⋊C8C2311yescharacteristic
93C2×C151⋊C8C2311yescharacteristic
94C8×D151—22no—
95C4⋊Dic151—21no—
96C4⋊Dic151—21no—
97Dic151⋊C4—21no—
98Dic151⋊C4—21no—
99Dic151⋊C4—21no—
100Dic151⋊C4D411yescharacteristic
101C22⋊Dic151—21no—
102C22⋊Dic151—21no—
103C22⋊Dic151D411yescharacteristic
104(C2×D151)⋊C4—21no—
105(C2×D151)⋊C4—21no—
106(C2×D151)⋊C4—21no—
107(C2×D151)⋊C4D411yescharacteristic
108C4×Dic151—21no—
109C4×Dic151C2311yescharacteristic
110C2×Q8×C151C2311yescharacteristic
111C2×D4×C151—21no—
112C2×D4×C151C2311yescharacteristic
113C22×C4×C151C2311yescharacteristic
114SD16×C151—22no—
115M16×C151—22no—
116C2×C8×C151C2311yescharacteristic
117C2×C8×C151C2311yescharacteristic
118C4⋊C4×C151—21no—
119C4⋊C4×C151C2311yescharacteristic
120C4⋊C4×C151C2311yescharacteristic
121C22⋊C4×C151—21no—
122C22⋊C4×C151—21no—
123C22×D151—21no—
124C22×D151—42no—
125C22×D151—42no—
126C22×D151—81no—
127C22×D151C2×D411yescharacteristic
128Dic302—21no—
129Dic302—21no—
130Dic302—21no—
131Dic302—21no—
132Dic302—21no—
133Dic302—42no—
134Dic302—42no—
135Dic302C2×D412yes—
136D604—21no—
137D604C2×D412yes—
138C22⋊D151—22no—
139C22⋊D151—42no—
140C22⋊D151—42no—
141C2×Dic151—21no—
142C2×Dic151—21no—
143C2×Dic151—21no—
144C2×Dic151—42no—
145C2×Dic151C2×D411yescharacteristic
146C2×Dic151C2×D411yescharacteristic
147C2×Dic151C2×D411yescharacteristic
148C4×D151—21no—
149C4×D151—21no—
150C4×D151—42no—
151C4×D151—42no—
152C4×D151—81no—
153C151⋊C8—21no—
154C151⋊C8—21no—
155C23×C151—21no—
156C23×C151C2×D411yescharacteristic
157Q8×C151—21no—
158Q8×C151—21no—
159D4×C151—21no—
160D4×C151—21no—
161D4×C151—81no—
162C2×C4×C151—21no—
163C2×C4×C151—21no—
164C2×C4×C151—21no—
165C2×C4×C151—21no—
166C2×C4×C151—21no—
167C2×C4×C151C2×D411yescharacteristic
168C2×C4×C151C2411yescharacteristic
169C8×C151—21no—
170C8×C151C2×D412yes—
171C22×C151—21no—
172C22×C151—21no—
173C22×C151—21no—
174C22×C151—41no—
175C22×C151—41no—
176C22×C151—41no—
177C22×C151C22×D411yescharacteristic
178C2×D151—21no—
179C2×D151—21no—
180C2×D151—22no—
181C2×D151—41no—
182C2×D151—41no—
183C2×D151—84no—
184C2×D151#13712yescomplemented
185C4×C151—21no—
186C4×C151—41no—
187C4×C151—41no—
188C4×C151—41no—
189C4×C151C22×D411yescharacteristic
190C4×C151H(5,𝔽2)11yescharacteristic
191Dic151—21no—
192Dic151—22no—
193Dic151—21no—
194Dic151—21no—
195Dic151—41no—
196Dic151—41no—
197C2×C151—41no—
198C2×C151—81no—
199C2×C151D4211yescharacteristic
200C2×C151C2×#13711yescharacteristic
201C2×C151#57711yescharacteristic
202D151—22no—
203D151—42no—
204C151#326611yescharacteristic, complemented, Sylow
205#3266—1511nomaximal, Sylow
206C2×#137—1511no—
207C22×SD16—1511no—
208D4×Q8—1511no—
209#546—1511no—
210#497—1511no—
211#468D15111yescharacteristic, complemented
212#467—1511no—
213#464—1511no—
214#461—1511no—
215#452—1511no—
216#451—1511no—
217#450—1511no—
218#448—1511no—
219#440—1511no—
220#435—1511no—
221C2×#41—1511no—
222C22×Q8—1511no—
223C22×Q8—1511no—
224C22×D4—1511no—
225#137—3024no—
226C2×Q16—1511no—
227C2×Q16—1511no—
228C2×Q16—1511no—
229C2×SD16—3024no—
230C2×SD16—1511no—
231C2×SD16—1511no—
232C2×SD16—1511no—
233C2×SD16—1511no—
234C2×SD16—1511no—
235C2×SD16C2×D15111yescharacteristic
236C2×M16C2×D15111yescharacteristic, complemented
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, complemented
247#121—3021no—
248#121C2×D15111yescharacteristic
249#120—3021no—
250C4×Q8—1511no—
251C4×D4—3021no—
252C4×D4—1511no—
253C4×D4—1511no—
254C2×C22⋊C4—3021no—
255#107C2×D15111yescharacteristic, complemented
256C4⋊C8—1511no—
257#103—1511no—
258#103—1511no—
259#103—1511no—
260#103C2×D15111yescharacteristic, complemented
261#102—1511no—
262#102C2×D15111yescharacteristic
263C22⋊C8—1511no—
264C22⋊C8—1511no—
265#97—1511no—
266C24—3021no—
267#41—3022no—
268#41—6041no—
269C2×Q8—3021no—
270C2×Q8—3022no—
271C2×Q8—3021no—
272C2×Q8—3022no—
273C2×Q8—6041no—
274C2×Q8—6041no—
275C2×Q8—1511no—
276C2×Q8—1511no—
277C2×Q8—1511no—
278C2×Q8C22×D15111yescharacteristic
279C2×D4—21no—
280C2×D4—3022no—
281C2×D4—3021no—
282C2×D4—3021no—
283C2×D4—6041no—
284C2×D4—1511no—
285C2×D4—1511no—
286C2×D4C22×D15111yescharacteristic
287C22×C4—3021no—
288C22×C4—3021no—
289C22×C4—3021no—
290C22×C4—3021no—
291C22×C4—1511no—
292C22×C4C22×D15111yescharacteristic
293Q16—3022no—
294Q16—3022no—
295Q16—6041no—
296SD16—22no—
297SD16—3022no—
298SD16—3022no—
299SD16—3022no—
300SD16—6041no—
301SD16—1514no—
302M16—22no—
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⋊C4C22×D15111yescharacteristic
316C4⋊C4C22×D15111yescharacteristic
317C22⋊C4—21no—
318C22⋊C4—21no—
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—21no—
329C23—3021no—
330C23—6042no—
331C23—6042no—
332C23—1511no—
333C23—12081no—
334C23D4×D15111yescharacteristic
335Q8—21no—
336Q8—21no—
337Q8—3021no—
338Q8—3021no—
339Q8—3021no—
340Q8—3021no—
341Q8—3021no—
342Q8—6042no—
343Q8—6042no—
344Q8—1512no—
345D4—21no—
346D4—21no—
347D4—81no—
348D4—3022no—
349D4—3021no—
350D4—6042no—
351D4—6042no—
352D4—1512no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—3021no—
359C2×C4—3021no—
360C2×C4—3021no—
361C2×C4—3021no—
362C2×C4—3021no—
363C2×C4—6042no—
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—3021no—
374C8—3021no—
375C8D4×D15112yes—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—3021no—
383C22—3021no—
384C22—3022no—
385C22—6041no—
386C22—6041no—
387C22—1512no—
388C22—12084no—
389C22C2×D4×D15111yescharacteristic
390C4—21no—
391C4—41no—
392C4—41no—
393C4—41no—
394C4—3021no—
395C4—3021no—
396C4—3021no—
397C4—3022no—
398C4—6041no—
399C4—6041no—
400C4C2×D4×D15111yescharacteristic
401C4#1801278511yescharacteristic
402C2—41no—
403C2—81no—
404C2—3022no—
405C2—6042no—
406C2#2375284611yescharacteristic
407C2#137×D15111yescharacteristic
408C2#2375302211yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#468×C151C2
socleC22×C151C22×D4
prime radical#23752859C2
hypercenter#468D151
hypocenterC151#3266
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. C2×#18012772C2semidirect
2. C2×SD16×D151C2semidirect
3. #23752875C2semidirect
5. #23752603C2semidirect
6. #23752454C2semidirect
7. #23752433C2semidirect
8. #23752416C2semidirect
9. #23752372C2semidirect
10. #23752369C2semidirect
11. #23752364C2semidirect
12. #23752350C2semidirect
13. #23752311C2semidirect
14. #23752281C2semidirect
15. #468×C151C2semidirect
17. C22×Dic302C22semidirect
21. C2×Dic604C22semidirect
22. C2×Dic604C22semidirect
23. C2×#14558994C22semidirect
32. #18012737C22semidirect
41. #18012704C22semidirect
46. Dic151⋊C8C22semidirect
47. #18012662C22semidirect
48. #18012662C22semidirect
49. #18012662C22semidirect
51. C22⋊(C151⋊C8)C22semidirect
53. #18012649C22semidirect
55. C2×M16×C151C22semidirect
56. C22⋊Q8×C151C22semidirect
58. #107×C151C22semidirect
59. #103×C151C22semidirect
88. #14558993D4semidirect
184. C2×D151#137semidirect
204. C151#3266semidirect
211. #468D151semidirect
236. C2×M16C2×D151semidirect
246. C22⋊Q8C2×D151semidirect
255. #107C2×D151semidirect
260. #103C2×D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127722
C2×SD16×D1512
#237528752
#237528592
#237526032
#237524542
#237524332
#237524162
#237523722
#237523692
#237523642
#237523502
#237523112
#237522812
#468×C1512
#3266151