Finite Group Databasebeta

← #34080224

Subgroups — #34080224

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#23752834C211yesmaximal, characteristic, complemented
2#23752782C211yesmaximal, characteristic, complemented
3#23752605C211yesmaximal, characteristic, complemented
4#23752593C211yesmaximal, characteristic, complemented
5#23752570C211yesmaximal, characteristic, complemented
6#23752561C211yesmaximal, characteristic, complemented
7#23752424C211yesmaximal, characteristic, complemented
8#23752422C211yesmaximal, characteristic, complemented
9#23752418C211yesmaximal, characteristic, complemented
10#23752371C211yesmaximal, characteristic, complemented
11#23752366C211yesmaximal, characteristic, complemented
12#23752358C211yesmaximal, characteristic
13#23752352C211yesmaximal, characteristic, complemented
14#23752272C211yesmaximal, characteristic, complemented
15#464×C151C211yesmaximal, characteristic, complemented
16C2×#14559003C2211yescharacteristic
17C2×Q8×D151C2211yescharacteristic
18C2×#14558994C2211yescharacteristic
19C2×#14558994C2211yescharacteristic
20C2×#14558993C2211yescharacteristic
21C2×#14558993C2211yescharacteristic
22C2×#14558991C2211yescharacteristic
23C2×#14558989C2211yescharacteristic
24#18012739C2211yescharacteristic
25#18012738C2211yescharacteristic
26#18012737C2211yescharacteristic
27#18012733—21no—
28#18012728C2211yescharacteristic
29#18012727—21no—
30#18012726C2211yescharacteristic
31#18012724—21no—
32#18012721—21no—
33#18012721—21no—
34#18012717—21no—
35#18012716—21no—
36#18012716—21no—
37#18012715C2211yescharacteristic
38#18012714C2211yescharacteristic
39C4×D604C2211yescharacteristic
40#18012696C2211yescharacteristic
41C4⋊(C151⋊C8)C2211yescharacteristic
42#18012664C2211yescharacteristic
43#18012664C2211yescharacteristic
44#18012663C2211yescharacteristic
45#18012662C2211yescharacteristic
46#18012662C2211yescharacteristic
47#18012660C2211yescharacteristic
48(C2×D151)⋊C8C2211yescharacteristic
49(C2×D151)⋊C8C2211yescharacteristic
50#18012649C2211yescharacteristic
51C8×Dic151C2211yescharacteristic
52C2×Q16×C151C2211yescharacteristic
53C2×SD16×C151C2211yescharacteristic
54#124×C151C2211yescharacteristic
55C4×Q8×C151C2211yescharacteristic
56C4⋊C8×C151C2211yescharacteristic
57#103×C151C2211yescharacteristic
58#102×C151C2211yescharacteristic
59#14559003—41no—
60#14559003—41no—
61C2×Dic302—21no—
62C2×Dic302—21no—
63C2×Dic302C2311yescharacteristic
64C2×Dic302C2311yescharacteristic
65Q8×D151—41no—
66Q8×D151—41no—
67C2×D604—21no—
68C2×D604C2311yescharacteristic
69C2×C22⋊D151—21no—
70C22×Dic151—21no—
71C2×C4×D151—21no—
72C2×C4×D151—21no—
73C2×C4×D151C2311yescharacteristic
74#14558994—41no—
75#14558994—41no—
76#14558993—41no—
77#14558993—41no—
78#14558991—41no—
79#14558989—41no—
80C2×C151⋊C8C2311yescharacteristic
81C2×C151⋊C8C2311yescharacteristic
82C4⋊Dic151—21no—
83C4⋊Dic151—21no—
84C4⋊Dic151C2311yescharacteristic
85Dic151⋊C4—21no—
86Dic151⋊C4—21no—
87Dic151⋊C4—21no—
88Dic151⋊C4—21no—
89Dic151⋊C4D411yescharacteristic
90Dic151⋊C4D411yescharacteristic
91C22⋊Dic151—21no—
92C22⋊Dic151—21no—
93(C2×D151)⋊C4—21no—
94(C2×D151)⋊C4—21no—
95(C2×D151)⋊C4—21no—
96(C2×D151)⋊C4—21no—
97(C2×D151)⋊C4—21no—
98(C2×D151)⋊C4D411yescharacteristic
99(C2×D151)⋊C4D411yescharacteristic
100C4×Dic151C2311yescharacteristic
101C2×Q8×C151C2311yescharacteristic
102C2×Q8×C151C2311yescharacteristic
103C2×D4×C151C2311yescharacteristic
104Q16×C151—41no—
105SD16×C151—41no—
106C2×C8×C151C2311yescharacteristic
107C2×C8×C151C2311yescharacteristic
108C4⋊C4×C151—21no—
109C4⋊C4×C151C2311yescharacteristic
110C22⋊C4×C151—21no—
111C22⋊C4×C151—21no—
112C42×C151—21no—
113C42×C151C2311yescharacteristic
114C22×D151—21no—
115C22×D151C2×D411yescharacteristic
116Dic302—21no—
117Dic302—21no—
118Dic302—21no—
119Dic302—21no—
120Dic302—42no—
121Dic302—81no—
122D604—21no—
123D604—21no—
124D604—81no—
125C22⋊D151—42no—
126C2×Dic151—21no—
127C2×Dic151—21no—
128C2×Dic151—21no—
129C2×Dic151—42no—
130C2×Dic151C2×D411yescharacteristic
131C2×Dic151C2×D411yescharacteristic
132C2×Dic151C2×D411yescharacteristic
133C4×D151—21no—
134C4×D151—21no—
135C4×D151—42no—
136C4×D151—81no—
137C151⋊C8—21no—
138C151⋊C8—21no—
139C23×C151—21no—
140Q8×C151—21no—
141Q8×C151—21no—
142Q8×C151—21no—
143Q8×C151—21no—
144D4×C151—21no—
145D4×C151—21no—
146C2×C4×C151—21no—
147C2×C4×C151—21no—
148C2×C4×C151—21no—
149C2×C4×C151C2×D411yescharacteristic
150C2×C4×C151C2×D411yescharacteristic
151C2×C4×C151C2411yescharacteristic
152C8×C151—21no—
153C8×C151—21no—
154C22×C151—41no—
155C22×C151—41no—
156C22×C151—41no—
157C22×C151C22×D411yescharacteristic
158C2×D151—21no—
159C2×D151—21no—
160C2×D151—21no—
161C2×D151—41no—
162C2×D151—41no—
163C2×D151—41no—
164C4×C151—21no—
165C4×C151—21no—
166C4×C151—41no—
167C4×C151—41no—
168C4×C151—41no—
169C4×C151H(5,𝔽2)11yescharacteristic
170C4×C151H(5,𝔽2)11yescharacteristic
171Dic151—21no—
172Dic151—21no—
173Dic151—21no—
174Dic151—41no—
175Dic151—41no—
176Dic151—41no—
177C2×C151—81no—
178C2×C151#53511yescharacteristic
179C2×C151#57711yescharacteristic
180C2×C151#57811yescharacteristic
181D151—41no—
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#464D15111yescharacteristic, complemented
192#463—1511no—
193#462—1511no—
194#461—1511no—
195#452—1511no—
196#451—1511no—
197#449—1511no—
198#448—1511no—
199#433—1511no—
200C2×#41—1511no—
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#124C2×D15111yescharacteristic
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×Q8C2×D15111yescharacteristic
227C4×D4—1511no—
228#117—1511no—
229C4⋊C8—1511no—
230C4⋊C8C2×D15111yescharacteristic
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⋊C8—1511no—
241#97—1511no—
242C4×C8—1511no—
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×Q8C22×D15111yescharacteristic
252C2×Q8C22×D15111yescharacteristic
253C2×D4—3021no—
254C2×D4—3021no—
255C2×D4—1511no—
256C2×D4C22×D15111yescharacteristic
257C22×C4—3021no—
258C22×C4—3021no—
259C22×C4—3021no—
260C22×C4—1511no—
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—21no—
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—21no—
296C42—1511no—
297C42C22×D15111yescharacteristic
298C23—21no—
299C23—3021no—
300C23—1511no—
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—3021no—
314D4—3021no—
315D4—6042no—
316D4—12081no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—3021no—
321C2×C4—3021no—
322C2×C4—3021no—
323C2×C4—3021no—
324C2×C4—3021no—
325C2×C4—6042no—
326C2×C4—6042no—
327C2×C4—1511no—
328C2×C4—1511no—
329C2×C4—1511no—
330C2×C4—12081no—
331C2×C4D4×D15111yescharacteristic
332C2×C4D4×D15111yescharacteristic
333C2×C4C23×D15111yescharacteristic
334C8—21no—
335C8—21no—
336C8—3021no—
337C8—3021no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—3021no—
342C22—3021no—
343C22—3021no—
344C22—6041no—
345C22—6041no—
346C22—6041no—
347C22C2×D4×D15111yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—3021no—
354C4—3021no—
355C4—3021no—
356C4—6041no—
357C4—6041no—
358C4—6041no—
359C4#1801278411yescharacteristic
360C4#1801278511yescharacteristic
361C2—81no—
362C2—6041no—
363C2—12081no—
364C2#2375277811yescharacteristic
365C2#2375301911yescharacteristic
366C2#2375302811yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#464×C151C2
socleC22×C151C22×D4
prime radical#23752358C2
hypercenter#464D151
hypocenterC151#3225
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. #23752834C2semidirect
2. #23752782C2semidirect
3. #23752605C2semidirect
4. #23752593C2semidirect
5. #23752570C2semidirect
6. #23752561C2semidirect
7. #23752424C2semidirect
8. #23752422C2semidirect
9. #23752418C2semidirect
10. #23752371C2semidirect
11. #23752366C2semidirect
13. #23752352C2semidirect
14. #23752272C2semidirect
15. #464×C151C2semidirect
183. C151#3225semidirect
191. #464D151semidirect

Maximal subgroups

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

subgroupindex
#237528342
#237527822
#237526052
#237525932
#237525702
#237525612
#237524242
#237524222
#237524182
#237523712
#237523662
#237523582
#237523522
#237522722
#464×C1512
#3225151