Finite Group Databasebeta

← #34078580

Subgroups — #34078580

Order 19328.

484 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18012771C211yesmaximal, characteristic, complemented
2C2×#18012768C211yesmaximal, characteristic, complemented
3#23752761C211yesmaximal, characteristic
4C4×Q8×D151C211yesmaximal, characteristic, complemented
5#23752435C211yesmaximal, characteristic, complemented
6#23752434C211yesmaximal, characteristic, complemented
7#23752431C211yesmaximal, characteristic, complemented
8#23752421C211yesmaximal, characteristic, complemented
9#23752420C211yesmaximal, characteristic, complemented
10#23752411C211yesmaximal, characteristic, complemented
11#23752410C211yesmaximal, characteristic, complemented
12#23752234C211yesmaximal, characteristic, complemented
13#23752212C211yesmaximal, characteristic, complemented
14#23752210C211yesmaximal, characteristic, complemented
15#464×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic
17C2×#14559003C2211yescharacteristic
18C2×Q8×D151C2211yescharacteristic
19#18012771—24no—
20#18012768—24no—
21C2×Dic604C2211yescharacteristic
22C2×#14558994C2211yescharacteristic
23C2×#14558994C2211yescharacteristic
24C2×#14558993C2211yescharacteristic
25C2×#14558992C2211yescharacteristic
26C2×#14558991C2211yescharacteristic
27C2×#14558987C2211yescharacteristic
28C2×#14558987C2211yescharacteristic
29#18012737C2211yescharacteristic
30#18012735C2211yescharacteristic
31#18012727C2211yescharacteristic
32#18012712—21no—
33#18012712—21no—
34Q8×Dic151C2211yescharacteristic
35C4×Dic302—21no—
36C4×Dic302C2211yescharacteristic
37#18012704—21no—
38#18012704C2211yescharacteristic
39(C22⋊D151)⋊C4—21no—
40(C22⋊D151)⋊C4—21no—
41C4⋊C4×D151—21no—
42C4⋊C4×D151C2211yescharacteristic
43C42×D151—21no—
44C42×D151C2211yescharacteristic
45C4⋊(C151⋊C8)C2211yescharacteristic
46Dic151⋊C8C2211yescharacteristic
47Dic151⋊C8C2211yescharacteristic
48#18012664C2211yescharacteristic
49#18012663C2211yescharacteristic
50#18012662C2211yescharacteristic
51#18012661C2211yescharacteristic
52#18012660C2211yescharacteristic
53#18012659C2211yescharacteristic
54C2×Q16×C151C2211yescharacteristic
55C2×SD16×C151C2211yescharacteristic
56#124×C151C2211yescharacteristic
57C4×Q8×C151C2211yescharacteristic
58C4⋊C8×C151C2211yescharacteristic
59#103×C151C2211yescharacteristic
60#102×C151C2211yescharacteristic
61#14559005—22no—
62#14559005—22no—
63#14559003—22no—
64#14559003—22no—
65C2×Dic302—21no—
66C2×Dic302C2311yescharacteristic
67C2×Dic302C2311yescharacteristic
68Q8×D151—22no—
69Q8×D151D414yescomplemented
70C2×D604—21no—
71C2×D604C2311yescharacteristic
72C2×C22⋊D151—21no—
73C2×C22⋊D151—21no—
74C2×C22⋊D151—21no—
75C22×Dic151—21no—
76C2×C4×D151—21no—
77C2×C4×D151—21no—
78C2×C4×D151—21no—
79C2×C4×D151D411yescharacteristic
80C2×C4×D151D411yescharacteristic
81C2×C4×D151C2311yescharacteristic
82Dic604—22no—
83#14558994—22no—
84#14558994—22no—
85#14558993—22no—
86#14558992—22no—
87#14558991—22no—
88#14558987—22no—
89#14558987—22no—
90C2×C151⋊C8C2311yescharacteristic
91C2×C151⋊C8C2311yescharacteristic
92C4⋊Dic151—21no—
93C4⋊Dic151C2311yescharacteristic
94Dic151⋊C4—21no—
95Dic151⋊C4—21no—
96Dic151⋊C4—21no—
97Dic151⋊C4—21no—
98Dic151⋊C4—21no—
99(C2×D151)⋊C4—21no—
100(C2×D151)⋊C4—21no—
101C4×Dic151—21no—
102C4×Dic151—21no—
103C4×Dic151—21no—
104C4×Dic151D411yescharacteristic
105C4×Dic151D411yescharacteristic
106C4×Dic151C2311yescharacteristic
107C2×Q8×C151C2311yescharacteristic
108C2×Q8×C151C2311yescharacteristic
109C2×D4×C151C2311yescharacteristic
110Q16×C151—22no—
111SD16×C151—22no—
112C2×C8×C151C2311yescharacteristic
113C2×C8×C151C2311yescharacteristic
114C4⋊C4×C151—21no—
115C4⋊C4×C151C2311yescharacteristic
116C22⋊C4×C151—21no—
117C22⋊C4×C151—21no—
118C42×C151—21no—
119C42×C151C2311yescharacteristic
120C22×D151—21no—
121C22×D151C2×D411yescharacteristic
122Dic302—21no—
123Dic302—24no—
124Dic302—21no—
125Dic302—21no—
126Dic302C2×D412yes—
127D604—21no—
128D604—21no—
129D604—42no—
130C22⋊D151—42no—
131C22⋊D151—42no—
132C22⋊D151—42no—
133C2×Dic151—21no—
134C2×Dic151—21no—
135C2×Dic151—21no—
136C2×Dic151—42no—
137C2×Dic151C2×D411yescharacteristic
138C2×Dic151C2×D411yescharacteristic
139C2×Dic151C2×D411yescharacteristic
140C4×D151—24no—
141C4×D151—22no—
142C4×D151—41no—
143C4×D151—42no—
144C4×D151—42no—
145C4×D151C2×D412yes—
146C4×D151#4112yes—
147C151⋊C8—21no—
148C151⋊C8—21no—
149C23×C151—21no—
150Q8×C151—21no—
151Q8×C151—21no—
152Q8×C151—21no—
153Q8×C151C2×D412yes—
154D4×C151—21no—
155D4×C151—21no—
156C2×C4×C151—21no—
157C2×C4×C151—21no—
158C2×C4×C151—21no—
159C2×C4×C151C2×D411yescharacteristic
160C2×C4×C151C2×D411yescharacteristic
161C2×C4×C151C2411yescharacteristic
162C8×C151—21no—
163C8×C151—21no—
164C22×C151—41no—
165C22×C151—41no—
166C22×C151—41no—
167C22×C151C22×D411yescharacteristic
168C2×D151—21no—
169C2×D151—21no—
170C2×D151—41no—
171C2×D151—41no—
172C2×D151—41no—
173C2×D151#12112yes—
174C4×C151—22no—
175C4×C151—21no—
176C4×C151—21no—
177C4×C151—41no—
178C4×C151—41no—
179C4×C151C22×D411yescharacteristic
180C4×C151C2×#4111yescharacteristic
181Dic151—22no—
182Dic151—21no—
183Dic151—41no—
184Dic151—41no—
185Dic151#12112yes—
186Dic151#13712yescomplemented
187C2×C151—81no—
188C2×C151C2×#12111yescharacteristic
189C2×C151C2×#13711yescharacteristic
190C2×C151#57511yescharacteristic
191D151—22no—
192D151—81no—
193C151#303711yescharacteristic, complemented, Sylow
194#3037—1511nomaximal, Sylow
195C2×#137—1511no—
196C2×#137—1511no—
197#532—1511no—
198C2×C4×Q8—1511no—
199#464—1511no—
200#464—1511no—
201#464—1511no—
202#464D15111yescharacteristic, complemented
203#462—1511no—
204#462—1511no—
205#460—1511no—
206#460—1511no—
207#423—1511no—
208#417—1511no—
209#417—1511no—
210C2×#41—1511no—
211C2×#41—1511no—
212C22×Q8—1511no—
213#137—3024no—
214#137—3024no—
215C2×Q16—1511no—
216C2×Q16—1511no—
217C2×Q16—1511no—
218C2×Q16C2×D15111yescharacteristic
219C2×SD16—1511no—
220C2×SD16—1511no—
221C2×SD16—1511no—
222C2×SD16C2×D15111yescharacteristic
223C2×M16—1511no—
224C2×M16—1511no—
225C4⋊Q8—1511no—
226#127—1511no—
227#124—1511no—
228#124C2×D15111yescharacteristic
229#121—3021no—
230#121—3021no—
231C4×Q8—3021no—
232C4×Q8—3021no—
233C4×Q8—1511no—
234C4×Q8—1511no—
235C4×Q8—1511no—
236C4×Q8C2×D15111yescharacteristic
237C4×D4—3021no—
238C4×D4—3021no—
239C2×C4⋊C4—3021no—
240C2×C4⋊C4—1511no—
241C2×C42—3021no—
242C2×C42—1511no—
243C4⋊C8—1511no—
244C4⋊C8—1511no—
245C4⋊C8—1511no—
246C4⋊C8C2×D15111yescharacteristic
247#103—1511no—
248#103—1511no—
249#103—1511no—
250#103C2×D15111yescharacteristic
251#102—1511no—
252#102—1511no—
253#102—1511no—
254#102C2×D15111yescharacteristic
255#41—3022no—
256#41—3022no—
257#41—3022no—
258#41—3022no—
259C2×Q8—3021no—
260C2×Q8—3022no—
261C2×Q8—1514no—
262C2×Q8—1511no—
263C2×Q8—1511no—
264C2×Q8C22×D15111yescharacteristic
265C2×Q8C22×D15111yescharacteristic
266C2×D4—3021no—
267C2×D4—3021no—
268C2×D4—3021no—
269C2×D4—3021no—
270C2×D4—1511no—
271C2×D4C22×D15111yescharacteristic
272C22×C4—3021no—
273C22×C4—3021no—
274C22×C4—3021no—
275C22×C4—3021no—
276C22×C4—1511no—
277C22×C4—1511no—
278C22×C4—1511no—
279Q16—22no—
280Q16—3022no—
281Q16—3022no—
282Q16—3022no—
283SD16—22no—
284SD16—3022no—
285SD16—3022no—
286SD16—3022no—
287M16—3022no—
288M16—3022no—
289C2×C8—1511no—
290C2×C8—1511no—
291C2×C8C22×D15111yescharacteristic
292C2×C8C22×D15111yescharacteristic
293C4⋊C4—21no—
294C4⋊C4—3021no—
295C4⋊C4—3021no—
296C4⋊C4—3021no—
297C4⋊C4—3021no—
298C4⋊C4—3021no—
299C4⋊C4—3021no—
300C4⋊C4—1511no—
301C4⋊C4C22×D15111yescharacteristic
302C22⋊C4—21no—
303C22⋊C4—21no—
304C22⋊C4—3021no—
305C22⋊C4—3021no—
306C42—21no—
307C42—3021no—
308C42—3021no—
309C42—3021no—
310C42—1511no—
311C42—1511no—
312C42—1511no—
313C42C22×D15111yescharacteristic
314C23—21no—
315C23—3021no—
316C23—1511no—
317Q8—21no—
318Q8—21no—
319Q8—21no—
320Q8—3024no—
321Q8—3021no—
322Q8—3021no—
323Q8—3021no—
324Q8—1512no—
325Q8D4×D15112yes—
326D4—21no—
327D4—21no—
328D4—3021no—
329D4—3021no—
330D4—6042no—
331D4—6042no—
332D4—6042no—
333D4—6042no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—3024no—
338C2×C4—3022no—
339C2×C4—3021no—
340C2×C4—3021no—
341C2×C4—3021no—
342C2×C4—6041no—
343C2×C4—6042no—
344C2×C4—6042no—
345C2×C4—6042no—
346C2×C4—1511no—
347C2×C4—1511no—
348C2×C4—1511no—
349C2×C4—1512no—
350C2×C4—1512no—
351C2×C4D4×D15111yescharacteristic
352C2×C4D4×D15111yescharacteristic
353C2×C4C23×D15111yescharacteristic
354C8—21no—
355C8—21no—
356C8—3021no—
357C8—3021no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—3021no—
362C22—3021no—
363C22—6041no—
364C22—6041no—
365C22—6041no—
366C22—1512no—
367C22C2×D4×D15111yescharacteristic
368C4—21no—
369C4—21no—
370C4—22no—
371C4—41no—
372C4—41no—
373C4—3021no—
374C4—3022no—
375C4—6041no—
376C4—6041no—
377C4—1512no—
378C4—1512no—
379C4C2×D4×D15111yescharacteristic
380C4#41×D15111yescharacteristic
381C2—81no—
382C2—3022no—
383C2—12081no—
384C2#121×D15111yescharacteristic
385C2#137×D15111yescharacteristic
386C2#2375300911yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#464×C151C2
socleC22×C151C22×D4
prime radical#23752761C2
hypercenter#464D151
hypocenterC151#3037
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. C2×#18012771C2semidirect
2. C2×#18012768C2semidirect
4. C4×Q8×D151C2semidirect
5. #23752435C2semidirect
6. #23752434C2semidirect
7. #23752431C2semidirect
8. #23752421C2semidirect
9. #23752420C2semidirect
10. #23752411C2semidirect
11. #23752410C2semidirect
12. #23752234C2semidirect
13. #23752212C2semidirect
14. #23752210C2semidirect
15. #464×C151C2semidirect
69. Q8×D151D4semidirect
186. Dic151#137semidirect
193. C151#3037semidirect
202. #464D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127712
C2×#180127682
#237527612
C4×Q8×D1512
#237524352
#237524342
#237524312
#237524212
#237524202
#237524112
#237524102
#237522342
#237522122
#237522102
#464×C1512
#3037151