Finite Group Databasebeta

← #34078564

Subgroups — #34078564

Order 19328.

496 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18012762C211yesmaximal, characteristic, complemented
2C2×#18012760C211yesmaximal, characteristic, complemented
3#23752761C211yesmaximal, characteristic, complemented
4C4×#14559005C211yesmaximal, characteristic, complemented
5#23752434C211yesmaximal, characteristic, complemented
6#23752428C211yesmaximal, characteristic, complemented
7#23752424C211yesmaximal, characteristic, complemented
8#23752420C211yesmaximal, characteristic, complemented
9#23752416C211yesmaximal, characteristic, complemented
10#23752410C211yesmaximal, characteristic, complemented
11#23752406C211yesmaximal, characteristic, complemented
12C4⋊C8×D151C211yesmaximal, characteristic, complemented
13#23752207C211yesmaximal, characteristic, complemented
14#23752205C211yesmaximal, characteristic, complemented
15#464×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic
17C2×#14559005C2211yescharacteristic
18C2×#14559003C2211yescharacteristic
19#18012762—24no—
20#18012760—24no—
21C2×#14558994C2211yescharacteristic
22C2×#14558993C2211yescharacteristic
23C2×#14558991C2211yescharacteristic
24C2×#14558991C2211yescharacteristic
25C2×D1208C2211yescharacteristic
26C2×#14558989C2211yescharacteristic
27C2×C8×D151C2211yescharacteristic
28C2×C8×D151C2211yescharacteristic
29#18012737C2211yescharacteristic
30#18012735C2211yescharacteristic
31#18012727C2211yescharacteristic
32#18012712—21no—
33#18012712—21no—
34Q8×Dic151C2211yescharacteristic
35C4×D604—21no—
36C4×D604C2211yescharacteristic
37#18012701—21no—
38#18012701C2211yescharacteristic
39(C22⋊D151)⋊C4—21no—
40(C22⋊D151)⋊C4—21no—
41#18012697—21no—
42#18012697C2211yescharacteristic
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#14559005—22no—
64#14559005D414yescomplemented
65#14559003—22no—
66#14559003—22no—
67C2×Dic302C2311yescharacteristic
68C2×D604—21no—
69C2×D604—21no—
70C2×D604C2311yescharacteristic
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×D151—21no—
80C2×C4×D151D411yescharacteristic
81C2×C4×D151D411yescharacteristic
82C2×C4×D151C2311yescharacteristic
83#14558994—22no—
84#14558993—22no—
85#14558991—22no—
86#14558991—22no—
87D1208—22no—
88#14558989—22no—
89C2×C151⋊C8C2311yescharacteristic
90C2×C151⋊C8C2311yescharacteristic
91C8×D151—22no—
92C8×D151—22no—
93C4⋊Dic151—21no—
94C4⋊Dic151C2311yescharacteristic
95Dic151⋊C4—21no—
96Dic151⋊C4—21no—
97(C2×D151)⋊C4—21no—
98(C2×D151)⋊C4—21no—
99(C2×D151)⋊C4—21no—
100(C2×D151)⋊C4—21no—
101(C2×D151)⋊C4—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×D151—21no—
122C22×D151C2×D411yescharacteristic
123Dic302—21no—
124Dic302—21no—
125D604—24no—
126D604—21no—
127D604—21no—
128D604—21no—
129D604—42no—
130D604C2×D412yes—
131C22⋊D151—42no—
132C22⋊D151—42no—
133C22⋊D151—42no—
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×D151—42no—
146C4×D151C2×D412yes—
147C4×D151#4112yes—
148C151⋊C8—21no—
149C151⋊C8—21no—
150C23×C151—21no—
151Q8×C151—21no—
152Q8×C151—21no—
153Q8×C151—21no—
154Q8×C151C2×D412yes—
155D4×C151—21no—
156D4×C151—21no—
157C2×C4×C151—21no—
158C2×C4×C151—21no—
159C2×C4×C151—21no—
160C2×C4×C151C2×D411yescharacteristic
161C2×C4×C151C2×D411yescharacteristic
162C2×C4×C151C2411yescharacteristic
163C8×C151—21no—
164C8×C151—21no—
165C22×C151—41no—
166C22×C151—41no—
167C22×C151—41no—
168C22×C151C22×D411yescharacteristic
169C2×D151—21no—
170C2×D151—21no—
171C2×D151—22no—
172C2×D151—41no—
173C2×D151—41no—
174C2×D151—41no—
175C2×D151—41no—
176C2×D151—41no—
177C2×D151#12112yes—
178C4×C151—22no—
179C4×C151—21no—
180C4×C151—21no—
181C4×C151—41no—
182C4×C151—41no—
183C4×C151C22×D411yescharacteristic
184C4×C151C2×#4111yescharacteristic
185Dic151—21no—
186Dic151—41no—
187Dic151—41no—
188Dic151#12112yes—
189Dic151#13512yescomplemented
190C2×C151—81no—
191C2×C151C2×#12111yescharacteristic
192C2×C151C2×#13511yescharacteristic
193C2×C151#57511yescharacteristic
194D151—22no—
195D151—42no—
196D151—81no—
197C151#303511yescharacteristic, complemented, Sylow
198#3035—1511nomaximal, Sylow
199C2×#135—1511no—
200C2×#135—1511no—
201#532—1511no—
202C4×#41—1511no—
203#464—1511no—
204#464D15111yescharacteristic, complemented
205#463—1511no—
206#463—1511no—
207#462—1511no—
208#461—1511no—
209#460—1511no—
210#459—1511no—
211C2×C4⋊C8—1511no—
212#416—1511no—
213#416—1511no—
214C2×#41—1511no—
215C2×#41—1511no—
216C2×#41—1511no—
217#135—3024no—
218#135—3024no—
219C2×Q16—1511no—
220C2×Q16C2×D15111yescharacteristic
221C2×SD16—1511no—
222C2×SD16—1511no—
223C2×SD16—1511no—
224C2×SD16C2×D15111yescharacteristic
225C2×D8—1511no—
226C2×D8—1511no—
227C22×C8—1511no—
228C22×C8—1511no—
229C4⋊Q8—1511no—
230#127—1511no—
231#124—1511no—
232#124C2×D15111yescharacteristic
233#121—3021no—
234#121—3021no—
235C4×Q8—1511no—
236C4×Q8C2×D15111yescharacteristic
237C4×D4—3021no—
238C4×D4—3021no—
239C4×D4—3021no—
240C4×D4—3021no—
241C4×D4—1511no—
242C4×D4—1511no—
243#117—3021no—
244#117—1511no—
245C2×C42—3021no—
246C2×C42—1511no—
247C4⋊C8—1511no—
248C4⋊C8—1511no—
249C4⋊C8—1511no—
250C4⋊C8C2×D15111yescharacteristic
251#103—1511no—
252#103—1511no—
253#103—1511no—
254#103C2×D15111yescharacteristic
255#102—1511no—
256#102—1511no—
257#102—1511no—
258#102C2×D15111yescharacteristic
259#41—3022no—
260#41—3022no—
261#41—3022no—
262#41—3022no—
263#41—3022no—
264#41—1514no—
265C2×Q8—1511no—
266C2×Q8C22×D15111yescharacteristic
267C2×Q8C22×D15111yescharacteristic
268C2×D4—3021no—
269C2×D4—3021no—
270C2×D4—3021no—
271C2×D4—3021no—
272C2×D4—3021no—
273C2×D4—1511no—
274C2×D4—1511no—
275C2×D4C22×D15111yescharacteristic
276C22×C4—3021no—
277C22×C4—3021no—
278C22×C4—3021no—
279C22×C4—3021no—
280C22×C4—3021no—
281C22×C4—1511no—
282C22×C4—1511no—
283C22×C4—1511no—
284Q16—22no—
285Q16—3022no—
286SD16—22no—
287SD16—3022no—
288SD16—3022no—
289SD16—3022no—
290D8—3022no—
291D8—3022no—
292C2×C8—3022no—
293C2×C8—3022no—
294C2×C8—1511no—
295C2×C8—1511no—
296C2×C8C22×D15111yescharacteristic
297C2×C8C22×D15111yescharacteristic
298C4⋊C4—21no—
299C4⋊C4—3021no—
300C4⋊C4—3021no—
301C4⋊C4—3021no—
302C4⋊C4—1511no—
303C4⋊C4C22×D15111yescharacteristic
304C22⋊C4—21no—
305C22⋊C4—21no—
306C22⋊C4—3021no—
307C22⋊C4—3021no—
308C22⋊C4—3021no—
309C22⋊C4—3021no—
310C22⋊C4—3021no—
311C42—21no—
312C42—3021no—
313C42—3021no—
314C42—1511no—
315C42—1511no—
316C42—1511no—
317C42C22×D15111yescharacteristic
318C23—21no—
319C23—3021no—
320C23—3021no—
321C23—1511no—
322Q8—21no—
323Q8—21no—
324Q8—21no—
325Q8—3021no—
326Q8—3021no—
327Q8D4×D15112yes—
328D4—21no—
329D4—21no—
330D4—3024no—
331D4—3021no—
332D4—3021no—
333D4—3021no—
334D4—6042no—
335D4—6042no—
336D4—6042no—
337D4—6042no—
338D4—1512no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—3024no—
343C2×C4—3022no—
344C2×C4—3021no—
345C2×C4—3021no—
346C2×C4—6041no—
347C2×C4—6042no—
348C2×C4—6042no—
349C2×C4—6042no—
350C2×C4—6042no—
351C2×C4—1511no—
352C2×C4—1511no—
353C2×C4—1511no—
354C2×C4—1512no—
355C2×C4—1512no—
356C2×C4D4×D15111yescharacteristic
357C2×C4D4×D15111yescharacteristic
358C2×C4C23×D15111yescharacteristic
359C8—21no—
360C8—21no—
361C8—3021no—
362C8—3021no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—3021no—
367C22—3021no—
368C22—3022no—
369C22—6041no—
370C22—6041no—
371C22—6041no—
372C22—6041no—
373C22—6041no—
374C22—1512no—
375C22C2×D4×D15111yescharacteristic
376C4—21no—
377C4—21no—
378C4—22no—
379C4—41no—
380C4—41no—
381C4—3021no—
382C4—6041no—
383C4—6041no—
384C4—1512no—
385C4—1512no—
386C4C2×D4×D15111yescharacteristic
387C4#41×D15111yescharacteristic
388C2—81no—
389C2—3022no—
390C2—6042no—
391C2—12081no—
392C2#121×D15111yescharacteristic
393C2#135×D15111yescharacteristic
394C2#2375301111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#464×C151C2
socleC22×C151C22×D4
hypercenter#464D151
hypocenterC151#3035
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×#18012762C2semidirect
2. C2×#18012760C2semidirect
3. #23752761C2semidirect
4. C4×#14559005C2semidirect
5. #23752434C2semidirect
6. #23752428C2semidirect
7. #23752424C2semidirect
8. #23752420C2semidirect
9. #23752416C2semidirect
10. #23752410C2semidirect
11. #23752406C2semidirect
12. C4⋊C8×D151C2semidirect
13. #23752207C2semidirect
14. #23752205C2semidirect
15. #464×C151C2semidirect
64. #14559005D4semidirect
189. Dic151#135semidirect
197. C151#3035semidirect
204. #464D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127622
C2×#180127602
#237527612
C4×#145590052
#237524342
#237524282
#237524242
#237524202
#237524162
#237524102
#237524062
C4⋊C8×D1512
#237522072
#237522052
#464×C1512
#3035151