Finite Group Databasebeta

← #34080041

Subgroups — #34080041

Order 19328.

438 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752758C211yesmaximal, characteristic, complemented
2#23752757C211yesmaximal, characteristic, complemented
3#23752587C211yesmaximal, characteristic, complemented
4#23752583C211yesmaximal, characteristic, complemented
5#23752561C211yesmaximal, characteristic, complemented
6#23752557C211yesmaximal, characteristic, complemented
7#23752430C211yesmaximal, characteristic, complemented
8#23752429C211yesmaximal, characteristic, complemented
9#23752426C211yesmaximal, characteristic, complemented
10#23752425C211yesmaximal, characteristic, complemented
11#23752359C211yesmaximal, characteristic, complemented
12#23752357C211yesmaximal, characteristic, complemented
13#23752355C211yesmaximal, characteristic, complemented
14#23752262C211yesmaximal, characteristic, complemented
15#449×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic
17C2×#14559003—21no—
18C2×#14558993C2211yescharacteristic
19C2×#14558992C2211yescharacteristic
20C2×#14558991C2211yescharacteristic
21C2×D1208C2211yescharacteristic
22C2×#14558989C2211yescharacteristic
23C2×#14558989C2211yescharacteristic
24#18012738C2211yescharacteristic
25#18012737C2211yescharacteristic
26#18012735C2211yescharacteristic
27#18012735C2211yescharacteristic
28#18012728C2211yescharacteristic
29#18012726C2211yescharacteristic
30#18012725—21no—
31#18012713C2211yescharacteristic
32#18012711—21no—
33#18012711—21no—
34#18012711—21no—
35D4×Dic151C2211yescharacteristic
36#18012701C2211yescharacteristic
37C4×C22⋊D151—21no—
38C4×C22⋊D151—21no—
39(C22⋊D151)⋊C4—21no—
40C2×C4×Dic151C2211yescharacteristic
41Dic151⋊C8C2211yescharacteristic
42Dic151⋊C8C2211yescharacteristic
43#18012664C2211yescharacteristic
44#18012663C2211yescharacteristic
45#18012662C2211yescharacteristic
46#18012661C2211yescharacteristic
47#18012660C2211yescharacteristic
48#18012659C2211yescharacteristic
49C22⋊(C151⋊C8)C2211yescharacteristic
50C8×Dic151C2211yescharacteristic
51C8×Dic151C2211yescharacteristic
52C2×#41×C151C2211yescharacteristic
53C2×SD16×C151C2211yescharacteristic
54C2×D8×C151C2211yescharacteristic
55#121×C151C2211yescharacteristic
56#103×C151C2211yescharacteristic
57#102×C151C2211yescharacteristic
58C22⋊C8×C151C2211yescharacteristic
59#14559004—41no—
60#14559004—41no—
61#14559003—44no—
62C2×Dic302—21no—
63C2×Dic302C2311yescharacteristic
64C2×D604C2311yescharacteristic
65C2×D604C2311yescharacteristic
66C2×C22⋊D151—21no—
67C2×C22⋊D151—21no—
68C2×C22⋊D151—21no—
69C2×C22⋊D151—21no—
70C2×C22⋊D151—21no—
71C2×C22⋊D151—21no—
72C22×Dic151—21no—
73C22×Dic151D411yescharacteristic
74C22×Dic151D411yescharacteristic
75C2×C4×D151—21no—
76C2×C4×D151—21no—
77#14558993—41no—
78#14558992—41no—
79#14558991—41no—
80D1208—41no—
81#14558989—41no—
82#14558989—41no—
83C2×C151⋊C8C2311yescharacteristic
84C2×C151⋊C8C2311yescharacteristic
85C4⋊Dic151C2311yescharacteristic
86Dic151⋊C4—21no—
87Dic151⋊C4—21no—
88Dic151⋊C4—21no—
89C22⋊Dic151—21no—
90C22⋊Dic151—21no—
91C22⋊Dic151—21no—
92(C2×D151)⋊C4—21no—
93(C2×D151)⋊C4—21no—
94(C2×D151)⋊C4—21no—
95(C2×D151)⋊C4—21no—
96C4×Dic151D411yescharacteristic
97C4×Dic151D411yescharacteristic
98C4×Dic151C2311yescharacteristic
99C4×Dic151C2311yescharacteristic
100#41×C151—41no—
101#41×C151—41no—
102C2×Q8×C151C2311yescharacteristic
103C2×D4×C151—21no—
104C2×D4×C151—21no—
105C2×D4×C151C2311yescharacteristic
106C2×D4×C151C2311yescharacteristic
107C22×C4×C151—21no—
108C22×C4×C151C2311yescharacteristic
109SD16×C151—41no—
110D8×C151—41no—
111C2×C8×C151C2311yescharacteristic
112C2×C8×C151C2311yescharacteristic
113C4⋊C4×C151C2311yescharacteristic
114C22⋊C4×C151—21no—
115C22×D151—21no—
116C22×D151—21no—
117Dic302—21no—
118Dic302—21no—
119Dic302—42no—
120D604—21no—
121D604—21no—
122D604—21no—
123D604—21no—
124C22⋊D151—42no—
125C22⋊D151—42no—
126C22⋊D151—42no—
127C22⋊D151—42no—
128C22⋊D151—42no—
129C22⋊D151—42no—
130C2×Dic151—22no—
131C2×Dic151—22no—
132C2×Dic151—21no—
133C2×Dic151—21no—
134C2×Dic151—42no—
135C2×Dic151C2×D411yescharacteristic
136C2×Dic151C2×D411yescharacteristic
137C2×Dic151C2×D411yescharacteristic
138C2×Dic151C2×D411yescharacteristic
139C4×D151—42no—
140C4×D151—42no—
141C151⋊C8—21no—
142C151⋊C8—21no—
143C23×C151—21no—
144C23×C151—21no—
145C23×C151C2×D411yescharacteristic
146Q8×C151—21no—
147Q8×C151—21no—
148D4×C151—21no—
149D4×C151—21no—
150D4×C151—21no—
151D4×C151—21no—
152D4×C151—42no—
153D4×C151—42no—
154C2×C4×C151—21no—
155C2×C4×C151—21no—
156C2×C4×C151—21no—
157C2×C4×C151—21no—
158C2×C4×C151—42no—
159C2×C4×C151C2×D411yescharacteristic
160C2×C4×C151C2411yescharacteristic
161C8×C151—21no—
162C8×C151—21no—
163C22×C151—21no—
164C22×C151—21no—
165C22×C151—21no—
166C22×C151—41no—
167C22×C151—41no—
168C22×C151—41no—
169C22×C151—41no—
170C22×C151—41no—
171C22×C151—41no—
172C22×C151C22×D411yescharacteristic
173C2×D151—41no—
174C2×D151—41no—
175C2×D151—41no—
176C2×D151—41no—
177C2×D151—41no—
178C2×D151—41no—
179C4×C151—21no—
180C4×C151—41no—
181C4×C151—41no—
182C4×C151H(5,𝔽2)11yescharacteristic
183C4×C151H(5,𝔽2)11yescharacteristic
184Dic151—21no—
185Dic151—21no—
186Dic151—41no—
187Dic151—41no—
188Dic151#13512yes—
189Dic151AGL(1,ℤ/8)12yes—
190C2×C151—41no—
191C2×C151—81no—
192C2×C151—81no—
193C2×C151#53511yescharacteristic
194C2×C151C2×#13511yescharacteristic
195C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
196D151—81no—
197D151—81no—
198C151#320711yescharacteristic, complemented, Sylow
199#3207—1511nomaximal, Sylow
200#532—1511no—
201#532—1511no—
202#493—1511no—
203#492—1511no—
204#487—1511no—
205#486—1511no—
206#463—1511no—
207#463—1511no—
208#463—1511no—
209#463—1511no—
210#449—1511no—
211#449—1511no—
212#449—1511no—
213#449D15111yescharacteristic, complemented
214#431—1511no—
215C2×#41—3021no—
216C2×#41—1511no—
217C2×#41C2×D15111yescharacteristic
218C2×SD16—1511no—
219C2×SD16—1511no—
220C2×SD16—1511no—
221C2×SD16C2×D15111yescharacteristic
222C2×D8—1511no—
223C2×D8—1511no—
224C2×D8—1511no—
225C2×D8C2×D15111yescharacteristic
226C4⋊Q8—1511no—
227C4⋊Q8—1511no—
228#127—1511no—
229#127—1511no—
230#124—3021no—
231#124—1511no—
232#124—1511no—
233#121—3021no—
234#121—3021no—
235#121—3021no—
236#121—1511no—
237#121C2×D15111yescharacteristic
238C4×D4—3021no—
239C4×D4—3021no—
240C4×D4—3021no—
241C4×D4—1511no—
242C4×D4—1511no—
243C2×C42—1511no—
244C4⋊C8—1511no—
245C4⋊C8—1511no—
246#103—1511no—
247#103—1511no—
248#103—1511no—
249#103C2×D15111yescharacteristic
250#102—1511no—
251#102—1511no—
252#102—1511no—
253#102C2×D15111yescharacteristic
254C22⋊C8—1511no—
255C22⋊C8C2×D15111yescharacteristic
256C4×C8—1511no—
257C4×C8—1511no—
258#41—41no—
259#41—41no—
260#41—6041no—
261#41—6041no—
262#41—6044no—
263C2×Q8—3021no—
264C2×Q8—1511no—
265C2×Q8C22×D15111yescharacteristic
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—3021no—
269C2×D4—3021no—
270C2×D4—3021no—
271C2×D4—3021no—
272C2×D4—3021no—
273C2×D4—3021no—
274C2×D4—1511no—
275C2×D4—1511no—
276C2×D4C22×D15111yescharacteristic
277C2×D4C22×D15111yescharacteristic
278C22×C4—21no—
279C22×C4—3021no—
280C22×C4—3021no—
281C22×C4—3021no—
282C22×C4—1511no—
283C22×C4—1511no—
284C22×C4C22×D15111yescharacteristic
285SD16—41no—
286SD16—6041no—
287SD16—6041no—
288SD16—6041no—
289D8—41no—
290D8—6041no—
291D8—6041no—
292D8—6041no—
293C2×C8—1511no—
294C2×C8—1511no—
295C2×C8C22×D15111yescharacteristic
296C2×C8C22×D15111yescharacteristic
297C4⋊C4—3021no—
298C4⋊C4—3021no—
299C4⋊C4—3021no—
300C4⋊C4—1511no—
301C4⋊C4C22×D15111yescharacteristic
302C22⋊C4—21no—
303C22⋊C4—3021no—
304C22⋊C4—3021no—
305C22⋊C4—3021no—
306C22⋊C4—3021no—
307C22⋊C4—3021no—
308C22⋊C4—3021no—
309C22⋊C4—3021no—
310C42—1511no—
311C42—1511no—
312C42—1511no—
313C42—1511no—
314C23—21no—
315C23—21no—
316C23—3021no—
317C23—3021no—
318C23D4×D15111yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—3021no—
322Q8—3021no—
323Q8—6042no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—42no—
329D4—42no—
330D4—3021no—
331D4—3021no—
332D4—3021no—
333D4—3021no—
334D4—6042no—
335D4—6042no—
336D4—6042no—
337D4—6042no—
338D4—6042no—
339D4—6042no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—42no—
345C2×C4—3022no—
346C2×C4—3022no—
347C2×C4—3021no—
348C2×C4—3021no—
349C2×C4—6042no—
350C2×C4—6042no—
351C2×C4—6042no—
352C2×C4—1511no—
353C2×C4—1511no—
354C2×C4—1511no—
355C2×C4—1511no—
356C2×C4D4×D15111yescharacteristic
357C2×C4C23×D15111yescharacteristic
358C8—21no—
359C8—21no—
360C8—3021no—
361C8—3021no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—6041no—
372C22—6041no—
373C22—6041no—
374C22—6041no—
375C22—6041no—
376C22—6041no—
377C22C2×D4×D15111yescharacteristic
378C4—21no—
379C4—41no—
380C4—41no—
381C4—3021no—
382C4—3021no—
383C4—6041no—
384C4—6041no—
385C4—1512no—
386C4—1512no—
387C4#1801278411yescharacteristic
388C4#1801278411yescharacteristic
389C2—41no—
390C2—81no—
391C2—81no—
392C2—12081no—
393C2—12081no—
394C2#2375277711yescharacteristic
395C2#135×D15111yescharacteristic
396C2AGL(1,ℤ/8)×D15111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#449×C151C2
socleC22×C151C22×D4
hypercenter#449D151
hypocenterC151#3207
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. #23752758C2semidirect
2. #23752757C2semidirect
3. #23752587C2semidirect
4. #23752583C2semidirect
5. #23752561C2semidirect
6. #23752557C2semidirect
7. #23752430C2semidirect
8. #23752429C2semidirect
9. #23752426C2semidirect
10. #23752425C2semidirect
11. #23752359C2semidirect
12. #23752357C2semidirect
13. #23752355C2semidirect
14. #23752262C2semidirect
15. #449×C151C2semidirect
198. C151#3207semidirect
213. #449D151semidirect

Maximal subgroups

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

subgroupindex
#237527582
#237527572
#237525872
#237525832
#237525612
#237525572
#237524302
#237524292
#237524262
#237524252
#237523592
#237523572
#237523552
#237522622
#449×C1512
#3207151