Finite Group Databasebeta

← #34078563

Subgroups — #34078563

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×#18012761C211yesmaximal, characteristic, complemented
2C2×#18012759C211yesmaximal, characteristic, complemented
3#23752758C211yesmaximal, characteristic, complemented
4#23752680C211yesmaximal, characteristic, complemented
5#23752437C211yesmaximal, characteristic, complemented
6#23752433C211yesmaximal, characteristic, complemented
7#23752430C211yesmaximal, characteristic, complemented
8#23752426C211yesmaximal, characteristic, complemented
9#23752421C211yesmaximal, characteristic, complemented
10#23752416C211yesmaximal, characteristic, complemented
11#23752411C211yesmaximal, characteristic, complemented
12#23752406C211yesmaximal, characteristic, complemented
13C2×Dic151⋊C8C211yesmaximal, characteristic, complemented
14#23752206C211yesmaximal, characteristic, complemented
15#416×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic
17C2×#14559004C2211yescharacteristic
18#18012761—24no—
19#18012759—24no—
20C2×Dic604C2211yescharacteristic
21C2×#14558994C2211yescharacteristic
22C2×#14558993C2211yescharacteristic
23C2×#14558993C2211yescharacteristic
24C2×#14558992C2211yescharacteristic
25C2×#14558991C2211yescharacteristic
26C2×D1208C2211yescharacteristic
27C2×#14558989C2211yescharacteristic
28C22×C151⋊C8C2211yescharacteristic
29#18012737C2211yescharacteristic
30#18012735C2211yescharacteristic
31#18012728C2211yescharacteristic
32#18012726C2211yescharacteristic
33#18012711—21no—
34#18012711—21no—
35#18012704C2211yescharacteristic
36#18012704C2211yescharacteristic
37#18012701C2211yescharacteristic
38#18012701C2211yescharacteristic
39C4×C22⋊D151—21no—
40C4×C22⋊D151—21no—
41(C22⋊D151)⋊C4—21no—
42(C22⋊D151)⋊C4—21no—
43#18012696—21no—
44C2×C4×Dic151C2211yescharacteristic
45C42×D151—21no—
46Dic151⋊C8C2211yescharacteristic
47Dic151⋊C8C2211yescharacteristic
48Dic151⋊C8C2211yescharacteristic
49Dic151⋊C8C2211yescharacteristic
50#18012662C2211yescharacteristic
51#18012662C2211yescharacteristic
52#18012659C2211yescharacteristic
53#18012659C2211yescharacteristic
54C2×#41×C151C2211yescharacteristic
55C22×C8×C151C2211yescharacteristic
56#117×C151C2211yescharacteristic
57#103×C151C2211yescharacteristic
58#103×C151C2211yescharacteristic
59#102×C151C2211yescharacteristic
60#102×C151C2211yescharacteristic
61#14559004—22no—
62#14559004—22no—
63#14559004—22no—
64#14559004D414yescomplemented
65C2×Dic302C2311yescharacteristic
66C2×Dic302C2311yescharacteristic
67C2×D604C2311yescharacteristic
68C2×D604C2311yescharacteristic
69C2×C22⋊D151—21no—
70C2×C22⋊D151—21no—
71C2×C22⋊D151—21no—
72C2×C22⋊D151—21no—
73C22×Dic151D411yescharacteristic
74C22×Dic151D411yescharacteristic
75C2×C4×D151—21no—
76C2×C4×D151—21no—
77C2×C4×D151—21no—
78C2×C4×D151—21no—
79Dic604—22no—
80#14558994—22no—
81#14558993—22no—
82#14558993—22no—
83#14558992—22no—
84#14558991—22no—
85D1208—22no—
86#14558989—22no—
87C2×C151⋊C8—22no—
88C2×C151⋊C8C2311yescharacteristic
89C2×C151⋊C8C2311yescharacteristic
90Dic151⋊C4—21no—
91Dic151⋊C4—21no—
92Dic151⋊C4—21no—
93Dic151⋊C4—21no—
94C22⋊Dic151—21no—
95C22⋊Dic151—21no—
96(C2×D151)⋊C4—21no—
97(C2×D151)⋊C4—21no—
98(C2×D151)⋊C4—21no—
99(C2×D151)⋊C4—21no—
100C4×Dic151—21no—
101C4×Dic151—21no—
102C4×Dic151D411yescharacteristic
103C4×Dic151D411yescharacteristic
104C4×Dic151C2311yescharacteristic
105C4×Dic151C2311yescharacteristic
106#41×C151—22no—
107#41×C151—22no—
108C2×Q8×C151C2311yescharacteristic
109C2×D4×C151—21no—
110C2×D4×C151C2311yescharacteristic
111C22×C4×C151—21no—
112C22×C4×C151C2311yescharacteristic
113C2×C8×C151—22no—
114C2×C8×C151C2311yescharacteristic
115C2×C8×C151C2311yescharacteristic
116C4⋊C4×C151C2311yescharacteristic
117C4⋊C4×C151C2311yescharacteristic
118C22⋊C4×C151—21no—
119C42×C151—21no—
120C22×D151—21no—
121C22×D151—21no—
122Dic302—21no—
123Dic302—21no—
124Dic302—21no—
125Dic302C2×D412yes—
126D604—21no—
127D604—21no—
128D604—21no—
129D604C2×D412yes—
130C22⋊D151—24no—
131C22⋊D151—42no—
132C22⋊D151—42no—
133C22⋊D151—42no—
134C2×Dic151—21no—
135C2×Dic151—22no—
136C2×Dic151—21no—
137C2×Dic151—41no—
138C2×Dic151C2×D411yescharacteristic
139C2×Dic151C2×D411yescharacteristic
140C2×Dic151C2×D411yescharacteristic
141C2×Dic151C2×D411yescharacteristic
142C4×D151—24no—
143C4×D151—42no—
144C4×D151—42no—
145C4×D151—42no—
146C151⋊C8—21no—
147C151⋊C8—21no—
148C23×C151—21no—
149C23×C151C2×D411yescharacteristic
150Q8×C151—21no—
151Q8×C151—21no—
152D4×C151—21no—
153D4×C151—21no—
154D4×C151—42no—
155C2×C4×C151—21no—
156C2×C4×C151—21no—
157C2×C4×C151—21no—
158C2×C4×C151—42no—
159C2×C4×C151C2×D412yes—
160C2×C4×C151C2×D411yescharacteristic
161C2×C4×C151#4112yes—
162C2×C4×C151C2411yescharacteristic
163C8×C151—21no—
164C8×C151—21no—
165C22×C151—21no—
166C22×C151—21no—
167C22×C151—41no—
168C22×C151—41no—
169C22×C151—41no—
170C22×C151#12112yes—
171C22×C151C22×D411yescharacteristic
172C2×D151—22no—
173C2×D151—41no—
174C2×D151—41no—
175C2×D151—41no—
176C2×D151—41no—
177C2×D151—41no—
178C4×C151—41no—
179C4×C151—41no—
180C4×C151—41no—
181C4×C151#12112yes—
182C4×C151C22×D411yescharacteristic
183C4×C151C2×#4111yescharacteristic
184Dic151—22no—
185Dic151—21no—
186Dic151—21no—
187Dic151—21no—
188Dic151—41no—
189Dic151#13512yescomplemented
190C2×C151—22no—
191C2×C151—81no—
192C2×C151C2×#12111yescharacteristic
193C2×C151C2×#13511yescharacteristic
194C2×C151#57511yescharacteristic
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#464—1511no—
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#416D15111yescharacteristic, complemented
214C2×#41—1511no—
215C2×#41—1511no—
216C2×#41C2×D15111yescharacteristic
217#135—3024no—
218#135—3024no—
219C2×Q16—1511no—
220C2×Q16—1511no—
221C2×SD16—1511no—
222C2×SD16—1511no—
223C2×SD16—1511no—
224C2×SD16—1511no—
225C2×D8—1511no—
226C2×D8—1511no—
227C22×C8—1511no—
228C22×C8C2×D15111yescharacteristic
229C4⋊Q8—1511no—
230#127—1511no—
231#124—1511no—
232#124—1511no—
233#121—3021no—
234#121—3021no—
235C4×Q8—1511no—
236C4×Q8—1511no—
237C4×D4—3021no—
238C4×D4—3021no—
239C4×D4—3021no—
240C4×D4—3021no—
241C4×D4—1511no—
242C4×D4—1511no—
243#117—3021no—
244#117C2×D15111yescharacteristic
245C2×C42—3021no—
246C2×C42—1511no—
247C4⋊C8—1511no—
248C4⋊C8—1511no—
249C4⋊C8—1511no—
250C4⋊C8—1511no—
251#103—1511no—
252#103—1511no—
253#103C2×D15111yescharacteristic
254#103C2×D15111yescharacteristic
255#102—1511no—
256#102—1511no—
257#102C2×D15111yescharacteristic
258#102C2×D15111yescharacteristic
259#41—22no—
260#41—22no—
261#41—3022no—
262#41—3022no—
263#41—3022no—
264#41—1514no—
265C2×Q8—1511no—
266C2×Q8—1511no—
267C2×Q8C22×D15111yescharacteristic
268C2×D4—21no—
269C2×D4—3021no—
270C2×D4—3021no—
271C2×D4—3021no—
272C2×D4—3021no—
273C2×D4—1511no—
274C2×D4—1511no—
275C2×D4C22×D15111yescharacteristic
276C22×C4—21no—
277C22×C4—3021no—
278C22×C4—3021no—
279C22×C4—3021no—
280C22×C4—3021no—
281C22×C4—1511no—
282C22×C4—1511no—
283C22×C4C22×D15111yescharacteristic
284Q16—3022no—
285Q16—3022no—
286SD16—3022no—
287SD16—3022no—
288SD16—3022no—
289SD16—3022no—
290D8—3022no—
291D8—3022no—
292C2×C8—22no—
293C2×C8—3022no—
294C2×C8—1511no—
295C2×C8—1511no—
296C2×C8C22×D15111yescharacteristic
297C2×C8C22×D15111yescharacteristic
298C4⋊C4—3021no—
299C4⋊C4—3021no—
300C4⋊C4—3021no—
301C4⋊C4—3021no—
302C4⋊C4C22×D15111yescharacteristic
303C4⋊C4C22×D15111yescharacteristic
304C22⋊C4—21no—
305C22⋊C4—3021no—
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—
317C42—1511no—
318C23—21no—
319C23—3021no—
320C23—3021no—
321C23D4×D15111yescharacteristic
322Q8—21no—
323Q8—21no—
324Q8—3021no—
325Q8—3021no—
326Q8—3021no—
327Q8—1512no—
328D4—21no—
329D4—21no—
330D4—42no—
331D4—3024no—
332D4—3021no—
333D4—3021no—
334D4—3021no—
335D4—6042no—
336D4—6042no—
337D4—6042no—
338D4—1512no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—42no—
343C2×C4—3021no—
344C2×C4—3022no—
345C2×C4—3024no—
346C2×C4—3021no—
347C2×C4—6042no—
348C2×C4—6042no—
349C2×C4—6041no—
350C2×C4—6042no—
351C2×C4—1511no—
352C2×C4—1511no—
353C2×C4—1511no—
354C2×C4—1511no—
355C2×C4D4×D15112yes—
356C2×C4D4×D15111yescharacteristic
357C2×C4#1455900412yes—
358C2×C4C23×D15111yescharacteristic
359C8—21no—
360C8—21no—
361C8—3021no—
362C8—3021no—
363C22—21no—
364C22—21no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—3022no—
369C22—6041no—
370C22—6041no—
371C22—6041no—
372C22—6041no—
373C22—6041no—
374C22#1801271212yes—
375C22C2×D4×D15111yescharacteristic
376C4—41no—
377C4—41no—
378C4—41no—
379C4—3021no—
380C4—3021no—
381C4—3021no—
382C4—3022no—
383C4—6041no—
384C4—1512no—
385C4#1801271212yes—
386C4C2×D4×D15111yescharacteristic
387C4C2×#1455900411yescharacteristic
388C2—22no—
389C2—81no—
390C2—6042no—
391C2—12081no—
392C2C2×#1801271211yescharacteristic
393C2#135×D15111yescharacteristic
394C2#2375300911yescharacteristic
subgroupG/H
centerC2×C4D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#416×C151C2
socleC22×C151C22×D4
hypercenter#416D151
hypocenterC151#3035
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. C2×#18012761C2semidirect
2. C2×#18012759C2semidirect
3. #23752758C2semidirect
4. #23752680C2semidirect
5. #23752437C2semidirect
6. #23752433C2semidirect
7. #23752430C2semidirect
8. #23752426C2semidirect
9. #23752421C2semidirect
10. #23752416C2semidirect
11. #23752411C2semidirect
12. #23752406C2semidirect
13. C2×Dic151⋊C8C2semidirect
14. #23752206C2semidirect
15. #416×C151C2semidirect
64. #14559004D4semidirect
189. Dic151#135semidirect
197. C151#3035semidirect
213. #416D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127612
C2×#180127592
#237527582
#237526802
#237524372
#237524332
#237524302
#237524262
#237524212
#237524162
#237524112
#237524062
C2×Dic151⋊C82
#237522062
#416×C1512
#3035151