Finite Group Databasebeta

← #34080221

Subgroups — #34080221

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#23752833C211yesmaximal, characteristic, complemented
2#23752788C211yesmaximal, characteristic, complemented
3#23752606C211yesmaximal, characteristic, complemented
4#23752596C211yesmaximal, characteristic, complemented
5#23752572C211yesmaximal, characteristic, complemented
6#23752563C211yesmaximal, characteristic, complemented
7#23752435C211yesmaximal, characteristic, complemented
8#23752428C211yesmaximal, characteristic, complemented
9#23752423C211yesmaximal, characteristic, complemented
10#23752418C211yesmaximal, characteristic, complemented
11#23752376C211yesmaximal, characteristic, complemented
12#23752370C211yesmaximal, characteristic, complemented
13#23752359C211yesmaximal, characteristic
14#23752353C211yesmaximal, characteristic, complemented
15#433×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic
17C22×Dic302C2211yescharacteristic
18C2×Dic604C2211yescharacteristic
19C2×Dic604C2211yescharacteristic
20C2×Dic604C2211yescharacteristic
21C2×#14558993C2211yescharacteristic
22C2×#14558993C2211yescharacteristic
23C2×#14558993C2211yescharacteristic
24C2×#14558993C2211yescharacteristic
25C2×D1208C2211yescharacteristic
26#18012739C2211yescharacteristic
27#18012739C2211yescharacteristic
28#18012739C2211yescharacteristic
29#18012734—21no—
30#18012727C2211yescharacteristic
31#18012727C2211yescharacteristic
32#18012727C2211yescharacteristic
33#18012725—21no—
34#18012723—21no—
35#18012723—21no—
36#18012721—21no—
37#18012719—21no—
38#18012719—21no—
39#18012718C2211yescharacteristic
40#18012717—21no—
41#18012713C2211yescharacteristic
42C4×Dic302C2211yescharacteristic
43C4×D604C2211yescharacteristic
44#18012664C2211yescharacteristic
45#18012664C2211yescharacteristic
46#18012664C2211yescharacteristic
47#18012664C2211yescharacteristic
48#18012664C2211yescharacteristic
49#18012664C2211yescharacteristic
50#18012661C2211yescharacteristic
51#18012661C2211yescharacteristic
52#117×C151C2211yescharacteristic
53C4⋊C8×C151C2211yescharacteristic
54C4⋊C8×C151C2211yescharacteristic
55C22⋊C8×C151C2211yescharacteristic
56C22⋊C8×C151C2211yescharacteristic
57#97×C151C2211yescharacteristic
58C4×C8×C151C2211yescharacteristic
59#14559004—41no—
60#14559004—41no—
61C2×Dic302—21no—
62C2×Dic302—21no—
63C2×Dic302—41no—
64C2×Dic302—41no—
65C2×Dic302C2311yescharacteristic
66C2×Dic302C2311yescharacteristic
67C2×Dic302C2311yescharacteristic
68C2×Dic302C2311yescharacteristic
69C2×D604C2311yescharacteristic
70C2×D604C2311yescharacteristic
71C2×C22⋊D151—21no—
72C2×C22⋊D151—21no—
73C22×Dic151—21no—
74C2×C4×D151—21no—
75C2×C4×D151—21no—
76Dic604—41no—
77Dic604—41no—
78Dic604—41no—
79#14558993—41no—
80#14558993—41no—
81#14558993—41no—
82#14558993—41no—
83D1208—41no—
84C4⋊Dic151—21no—
85C4⋊Dic151—21no—
86C4⋊Dic151—21no—
87C4⋊Dic151—21no—
88C4⋊Dic151—21no—
89C4⋊Dic151C2311yescharacteristic
90C4⋊Dic151C2311yescharacteristic
91Dic151⋊C4—21no—
92Dic151⋊C4—21no—
93C22⋊Dic151—21no—
94(C2×D151)⋊C4—21no—
95(C2×D151)⋊C4—21no—
96(C2×D151)⋊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—
103C22×C4×C151C2311yescharacteristic
104C2×C8×C151C2311yescharacteristic
105C2×C8×C151C2311yescharacteristic
106C2×C8×C151C2311yescharacteristic
107C2×C8×C151C2311yescharacteristic
108C4⋊C4×C151D411yescharacteristic
109C4⋊C4×C151D411yescharacteristic
110C22⋊C4×C151D411yescharacteristic
111C22⋊C4×C151D411yescharacteristic
112C42×C151C2311yescharacteristic
113C42×C151C2311yescharacteristic
114C22×D151—21no—
115C22×D151—21no—
116Dic302—21no—
117Dic302—21no—
118Dic302—21no—
119Dic302—21no—
120Dic302—21no—
121Dic302—21no—
122Dic302—21no—
123Dic302—21no—
124Dic302—42no—
125Dic302—81no—
126D604—21no—
127D604—21no—
128D604—21no—
129D604—21no—
130C22⋊D151—42no—
131C22⋊D151—81no—
132C2×Dic151—21no—
133C2×Dic151—21no—
134C2×Dic151—21no—
135C2×Dic151—21no—
136C2×Dic151—21no—
137C2×Dic151—21no—
138C2×Dic151—42no—
139C4×D151—42no—
140C4×D151—81no—
141C23×C151C2×D411yescharacteristic
142C2×C4×C151—21no—
143C2×C4×C151—21no—
144C2×C4×C151C2×D411yescharacteristic
145C2×C4×C151C2×D411yescharacteristic
146C2×C4×C151C2×D411yescharacteristic
147C2×C4×C151C2×D411yescharacteristic
148C2×C4×C151C2×D411yescharacteristic
149C2×C4×C151C2411yescharacteristic
150C8×C151—21no—
151C8×C151—21no—
152C8×C151—21no—
153C8×C151—21no—
154C22×C151—21no—
155C22×C151—21no—
156C22×C151—21no—
157C22×C151C22×D411yescharacteristic
158C2×D151—41no—
159C2×D151—41no—
160C2×D151—41no—
161C2×D151—41no—
162C2×D151—41no—
163C2×D151—41no—
164C4×C151—21no—
165C4×C151—21no—
166C4×C151—21no—
167C4×C151—21no—
168C4×C151—21no—
169C4×C151H(5,𝔽2)11yescharacteristic
170C4×C151H(5,𝔽2)11yescharacteristic
171Dic151—41no—
172Dic151—41no—
173Dic151—41no—
174Dic151—41no—
175Dic151—41no—
176Dic151—41no—
177C2×C151—41no—
178C2×C151#53511yescharacteristic
179C2×C151#57711yescharacteristic
180C2×C151#57811yescharacteristic
181D151—81no—
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#452—1511no—
196#451—1511no—
197#449—1511no—
198#448—1511no—
199#433D15111yescharacteristic, complemented
200C2×#41—1511no—
201C22×Q8—1511no—
202C2×Q16—1511no—
203C2×Q16—1511no—
204C2×Q16—1511no—
205C2×SD16—1511no—
206C2×SD16—1511no—
207C2×SD16—1511no—
208C2×SD16—1511no—
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⋊Q8—1511no—
225#121—1511no—
226C4×Q8—1511no—
227C4×D4—1511no—
228#117C2×D15111yescharacteristic
229C4⋊C8C2×D15111yescharacteristic
230C4⋊C8C2×D15111yescharacteristic
231#103—1511no—
232#103—1511no—
233#103—1511no—
234#103—1511no—
235#103—1511no—
236#103—1511no—
237#102—1511no—
238#102—1511no—
239C22⋊C8C2×D15111yescharacteristic
240C22⋊C8C2×D15111yescharacteristic
241#97C2×D15111yescharacteristic
242C4×C8C2×D15111yescharacteristic
243#41—6041no—
244#41—6041no—
245C2×Q8—3021no—
246C2×Q8—3021no—
247C2×Q8—6041no—
248C2×Q8—6041no—
249C2×Q8—1511no—
250C2×Q8—1511no—
251C2×Q8—1511no—
252C2×Q8—1511no—
253C2×D4—3021no—
254C2×D4—3021no—
255C2×D4—1511no—
256C2×D4—1511no—
257C22×C4—3021no—
258C22×C4—3021no—
259C22×C4—3021no—
260C22×C4C22×D15111yescharacteristic
261Q16—6041no—
262Q16—6041no—
263Q16—6041no—
264SD16—6041no—
265SD16—6041no—
266SD16—6041no—
267SD16—6041no—
268D8—6041no—
269C2×C8C22×D15111yescharacteristic
270C2×C8C22×D15111yescharacteristic
271C2×C8C22×D15111yescharacteristic
272C2×C8C22×D15111yescharacteristic
273C4⋊C4—3021no—
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⋊C4D60411yescharacteristic
283C4⋊C4D60411yescharacteristic
284C22⋊C4—3021no—
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⋊C4D60411yescharacteristic
294C22⋊C4D60411yescharacteristic
295C42—3021no—
296C42C22×D15111yescharacteristic
297C42C22×D15111yescharacteristic
298C23—3021no—
299C23—3021no—
300C23C2×D60411yescharacteristic
301Q8—3021no—
302Q8—3021no—
303Q8—3021no—
304Q8—3021no—
305Q8—3021no—
306Q8—3021no—
307Q8—3021no—
308Q8—3021no—
309Q8—6042no—
310Q8—12081no—
311D4—3021no—
312D4—3021no—
313D4—3021no—
314D4—3021no—
315D4—6042no—
316D4—12081no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—3021no—
320C2×C4—3021no—
321C2×C4—3021no—
322C2×C4—3021no—
323C2×C4—3021no—
324C2×C4—3021no—
325C2×C4—6042no—
326C2×C4—6042no—
327C2×C4—12081no—
328C2×C4C2×D60411yescharacteristic
329C2×C4C2×D60411yescharacteristic
330C2×C4C2×D60411yescharacteristic
331C2×C4C2×D60411yescharacteristic
332C2×C4C2×D60411yescharacteristic
333C2×C4C23×D15111yescharacteristic
334C8—21no—
335C8—21no—
336C8—21no—
337C8—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—6041no—
342C22—6041no—
343C22—6041no—
344C22—6041no—
345C22—6041no—
346C22—6041no—
347C22C22×D60411yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—6041no—
354C4—6041no—
355C4—6041no—
356C4—6041no—
357C4—6041no—
358C4—6041no—
359C4#1801278511yescharacteristic
360C4#1801278511yescharacteristic
361C2—41no—
362C2—12081no—
363C2—12081no—
364C2#2375278111yescharacteristic
365C2#2375302411yescharacteristic
366C2#2375302911yescharacteristic
subgroupG/H
centerC22C22×D604
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#433×C151C2
socleC22×C151C22×D4
prime radical#23752359C2
hypercenter#433D151
hypocenterC151#3225
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #23752833C2semidirect
2. #23752788C2semidirect
3. #23752606C2semidirect
4. #23752596C2semidirect
5. #23752572C2semidirect
6. #23752563C2semidirect
7. #23752435C2semidirect
8. #23752428C2semidirect
9. #23752423C2semidirect
10. #23752418C2semidirect
11. #23752376C2semidirect
12. #23752370C2semidirect
14. #23752353C2semidirect
15. #433×C151C2semidirect
183. C151#3225semidirect
199. #433D151semidirect

Maximal subgroups

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

subgroupindex
#237528332
#237527882
#237526062
#237525962
#237525722
#237525632
#237524352
#237524282
#237524232
#237524182
#237523762
#237523702
#237523592
#237523532
#433×C1512
#3225151