Finite Group Databasebeta

← #34080223

Subgroups — #34080223

Order 19328.

376 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752835C211yesmaximal, characteristic, complemented
2#23752783C211yesmaximal, characteristic, complemented
3#23752605C211yesmaximal, characteristic, complemented
4#23752593C211yesmaximal, characteristic, complemented
5#23752570C211yesmaximal, characteristic, complemented
6#23752561C211yesmaximal, characteristic, complemented
7#23752432C211yesmaximal, characteristic, complemented
8#23752426C211yesmaximal, characteristic, complemented
9#23752420C211yesmaximal, characteristic, complemented
10#23752416C211yesmaximal, characteristic, complemented
11#23752367C211yesmaximal, characteristic, complemented
12#23752357C211yesmaximal, characteristic
13#23752353C211yesmaximal, characteristic, complemented
14#23752270C211yesmaximal, characteristic, complemented
15#452×C151C211yesmaximal, characteristic, complemented
16C22×Dic302C2211yescharacteristic
17C2×#14558994C2211yescharacteristic
18C2×#14558994C2211yescharacteristic
19C2×#14558993C2211yescharacteristic
20C2×#14558993C2211yescharacteristic
21C2×#14558991C2211yescharacteristic
22C2×#14558989C2211yescharacteristic
23#18012738C2211yescharacteristic
24#18012737C2211yescharacteristic
25#18012737C2211yescharacteristic
26#18012734—21no—
27#18012728C2211yescharacteristic
28#18012726C2211yescharacteristic
29#18012726C2211yescharacteristic
30#18012725—21no—
31#18012721—21no—
32#18012720—21no—
33#18012720—21no—
34#18012719—21no—
35#18012718—21no—
36#18012718—21no—
37#18012713C2211yescharacteristic
38Q8×Dic151C2211yescharacteristic
39#18012701C2211yescharacteristic
40#18012698C2211yescharacteristic
41Dic151⋊C8C2211yescharacteristic
42Dic151⋊C8C2211yescharacteristic
43#18012664C2211yescharacteristic
44#18012664C2211yescharacteristic
45#18012663C2211yescharacteristic
46#18012662C2211yescharacteristic
47#18012662C2211yescharacteristic
48#18012660C2211yescharacteristic
49C22⋊(C151⋊C8)C2211yescharacteristic
50#18012649C2211yescharacteristic
51C8×Dic151C2211yescharacteristic
52C2×#41×C151C2211yescharacteristic
53C2×Q16×C151C2211yescharacteristic
54C2×SD16×C151C2211yescharacteristic
55C22⋊Q8×C151C2211yescharacteristic
56#103×C151C2211yescharacteristic
57#102×C151C2211yescharacteristic
58C22⋊C8×C151C2211yescharacteristic
59C2×Dic302—21no—
60C2×Dic302—21no—
61C2×Dic302—41no—
62C2×Dic302—41no—
63C2×Dic302C2311yescharacteristic
64C2×Dic302C2311yescharacteristic
65C2×D604C2311yescharacteristic
66C2×C22⋊D151—21no—
67C22×Dic151—21no—
68C2×C4×D151—21no—
69#14558994—41no—
70#14558994—41no—
71#14558993—41no—
72#14558993—41no—
73#14558991—41no—
74#14558989—41no—
75C2×C151⋊C8C2311yescharacteristic
76C2×C151⋊C8C2311yescharacteristic
77C4⋊Dic151—21no—
78C4⋊Dic151D411yescharacteristic
79C4⋊Dic151D411yescharacteristic
80C4⋊Dic151C2311yescharacteristic
81Dic151⋊C4—21no—
82Dic151⋊C4—21no—
83Dic151⋊C4—21no—
84Dic151⋊C4—21no—
85Dic151⋊C4—21no—
86C22⋊Dic151—21no—
87C22⋊Dic151—21no—
88C22⋊Dic151—21no—
89C22⋊Dic151—21no—
90C22⋊Dic151D411yescharacteristic
91C22⋊Dic151D411yescharacteristic
92(C2×D151)⋊C4—21no—
93(C2×D151)⋊C4—21no—
94(C2×D151)⋊C4—21no—
95(C2×D151)⋊C4—21no—
96C4×Dic151—21no—
97C4×Dic151C2311yescharacteristic
98C4×Dic151C2311yescharacteristic
99#41×C151—41no—
100#41×C151—41no—
101C2×Q8×C151C2311yescharacteristic
102C2×Q8×C151C2311yescharacteristic
103C2×D4×C151—21no—
104C2×D4×C151C2311yescharacteristic
105C22×C4×C151—21no—
106C22×C4×C151C2311yescharacteristic
107Q16×C151—41no—
108SD16×C151—41no—
109C2×C8×C151C2311yescharacteristic
110C2×C8×C151C2311yescharacteristic
111C4⋊C4×C151—21no—
112C4⋊C4×C151C2311yescharacteristic
113C22⋊C4×C151—21no—
114C22×D151—21no—
115Dic302—21no—
116Dic302—21no—
117Dic302—21no—
118Dic302—21no—
119Dic302—42no—
120Dic302—81no—
121D604—21no—
122D604—21no—
123C22⋊D151—81no—
124C2×Dic151—21no—
125C2×Dic151—21no—
126C2×Dic151—21no—
127C2×Dic151—42no—
128C2×Dic151C2×D411yescharacteristic
129C2×Dic151C2×D411yescharacteristic
130C2×Dic151C2×D411yescharacteristic
131C2×Dic151C2×D411yescharacteristic
132C4×D151—81no—
133C151⋊C8—21no—
134C151⋊C8—21no—
135C23×C151—21no—
136C23×C151C2×D411yescharacteristic
137Q8×C151—21no—
138Q8×C151—21no—
139Q8×C151—21no—
140Q8×C151—21no—
141D4×C151—21no—
142D4×C151—21no—
143D4×C151—42no—
144C2×C4×C151—21no—
145C2×C4×C151—21no—
146C2×C4×C151—21no—
147C2×C4×C151—21no—
148C2×C4×C151—21no—
149C2×C4×C151—42no—
150C2×C4×C151C2×D411yescharacteristic
151C2×C4×C151C2411yescharacteristic
152C8×C151—21no—
153C8×C151—21no—
154C22×C151—21no—
155C22×C151—21no—
156C22×C151—21no—
157C22×C151—41no—
158C22×C151—41no—
159C22×C151—41no—
160C22×C151C22×D411yescharacteristic
161C2×D151—41no—
162C2×D151—41no—
163C2×D151—41no—
164C4×C151—21no—
165C4×C151—41no—
166C4×C151—41no—
167C4×C151—41no—
168C4×C151H(5,𝔽2)11yescharacteristic
169C4×C151H(5,𝔽2)11yescharacteristic
170Dic151—21no—
171Dic151—21no—
172Dic151—21no—
173Dic151—21no—
174Dic151—41no—
175Dic151—41no—
176Dic151—41no—
177C2×C151—41no—
178C2×C151—81no—
179C2×C151#53511yescharacteristic
180C2×C151#57711yescharacteristic
181C2×C151#57811yescharacteristic
182D151—81no—
183C151#322511yescharacteristic, complemented, Sylow
184#3225—1511nomaximal, Sylow
185#542—1511no—
186#536—1511no—
187#497—1511no—
188#495—1511no—
189#489—1511no—
190#487—1511no—
191#464—1511no—
192#463—1511no—
193#462—1511no—
194#461—1511no—
195#452D15111yescharacteristic, complemented
196#451—1511no—
197#449—1511no—
198#448—1511no—
199#433—1511no—
200C2×#41C2×D15111yescharacteristic
201C22×Q8—1511no—
202C2×Q16—1511no—
203C2×Q16—1511no—
204C2×Q16C2×D15111yescharacteristic
205C2×SD16—1511no—
206C2×SD16—1511no—
207C2×SD16—1511no—
208C2×SD16C2×D15111yescharacteristic
209C2×D8—1511no—
210C4⋊Q8—1511no—
211C4⋊Q8—1511no—
212C4⋊Q8—1511no—
213#126—3021no—
214#124—3021no—
215#124—1511no—
216#124—1511no—
217#124—1511no—
218#123—3021no—
219#123—3021no—
220#123—3021no—
221C22⋊Q8—3021no—
222C22⋊Q8—3021no—
223C22⋊Q8—3021no—
224C22⋊Q8C2×D15111yescharacteristic
225#121—1511no—
226C4×Q8—1511no—
227C4×D4—1511no—
228#117—1511no—
229C4⋊C8—1511no—
230C4⋊C8—1511no—
231#103—1511no—
232#103—1511no—
233#103—1511no—
234#103—1511no—
235#103—1511no—
236#103C2×D15111yescharacteristic
237#102—1511no—
238#102C2×D15111yescharacteristic
239C22⋊C8—1511no—
240C22⋊C8C2×D15111yescharacteristic
241#97—1511no—
242C4×C8—1511no—
243#41—41no—
244#41—41no—
245C2×Q8—3021no—
246C2×Q8—3021no—
247C2×Q8—6041no—
248C2×Q8—6041no—
249C2×Q8—1511no—
250C2×Q8—1511no—
251C2×Q8C22×D15111yescharacteristic
252C2×Q8C22×D15111yescharacteristic
253C2×D4—21no—
254C2×D4—3021no—
255C2×D4—1511no—
256C2×D4C22×D15111yescharacteristic
257C22×C4—21no—
258C22×C4—3021no—
259C22×C4—3021no—
260C22×C4C22×D15111yescharacteristic
261Q16—41no—
262Q16—6041no—
263Q16—6041no—
264SD16—41no—
265SD16—6041no—
266SD16—6041no—
267SD16—6041no—
268D8—6041no—
269C2×C8—1511no—
270C2×C8—1511no—
271C2×C8C22×D15111yescharacteristic
272C2×C8C22×D15111yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—3021no—
275C4⋊C4—3021no—
276C4⋊C4—3021no—
277C4⋊C4—3021no—
278C4⋊C4—3021no—
279C4⋊C4—3021no—
280C4⋊C4—1511no—
281C4⋊C4—1511no—
282C4⋊C4—1511no—
283C4⋊C4C22×D15111yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—3021no—
286C22⋊C4—3021no—
287C22⋊C4—3021no—
288C22⋊C4—3021no—
289C22⋊C4—3021no—
290C22⋊C4—3021no—
291C22⋊C4—3021no—
292C22⋊C4—3021no—
293C22⋊C4—1511no—
294C22⋊C4—1511no—
295C42—3021no—
296C42—1511no—
297C42—1511no—
298C23—21no—
299C23—3021no—
300C23D4×D15111yescharacteristic
301Q8—21no—
302Q8—21no—
303Q8—21no—
304Q8—21no—
305Q8—3021no—
306Q8—3021no—
307Q8—3021no—
308Q8—3021no—
309Q8—6042no—
310Q8—12081no—
311D4—21no—
312D4—21no—
313D4—42no—
314D4—3021no—
315D4—3021no—
316D4—12081no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—3021no—
324C2×C4—3021no—
325C2×C4—3021no—
326C2×C4—6042no—
327C2×C4—1511no—
328C2×C4—1511no—
329C2×C4—1511no—
330C2×C4—1511no—
331C2×C4—12081no—
332C2×C4D4×D15111yescharacteristic
333C2×C4C23×D15111yescharacteristic
334C8—21no—
335C8—21no—
336C8—3021no—
337C8—3021no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—6041no—
345C22—6041no—
346C22—6041no—
347C22C2×D4×D15111yescharacteristic
348C4—21no—
349C4—41no—
350C4—41no—
351C4—41no—
352C4—3021no—
353C4—3021no—
354C4—3021no—
355C4—3021no—
356C4—6041no—
357C4—6041no—
358C4—6041no—
359C4#1801278411yescharacteristic
360C4#1801278411yescharacteristic
361C2—41no—
362C2—81no—
363C2—12081no—
364C2#2375277711yescharacteristic
365C2#2375301911yescharacteristic
366C2#2375302811yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#452×C151C2
socleC22×C151C22×D4
prime radical#23752357C2
hypercenter#452D151
hypocenterC151#3225
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #23752835C2semidirect
2. #23752783C2semidirect
3. #23752605C2semidirect
4. #23752593C2semidirect
5. #23752570C2semidirect
6. #23752561C2semidirect
7. #23752432C2semidirect
8. #23752426C2semidirect
9. #23752420C2semidirect
10. #23752416C2semidirect
11. #23752367C2semidirect
13. #23752353C2semidirect
14. #23752270C2semidirect
15. #452×C151C2semidirect
183. C151#3225semidirect
195. #452D151semidirect

Maximal subgroups

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

subgroupindex
#237528352
#237527832
#237526052
#237525932
#237525702
#237525612
#237524322
#237524262
#237524202
#237524162
#237523672
#237523572
#237523532
#237522702
#452×C1512
#3225151