Finite Group Databasebeta

← #34055805

Subgroups — #34055805

Order 19072.

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#23750247C211yesmaximal, characteristic, complemented
2#23750195C211yesmaximal, characteristic, complemented
3#23750018C211yesmaximal, characteristic, complemented
4#23750006C211yesmaximal, characteristic, complemented
5#23749983C211yesmaximal, characteristic, complemented
6#23749974C211yesmaximal, characteristic, complemented
7#23749837C211yesmaximal, characteristic, complemented
8#23749835C211yesmaximal, characteristic, complemented
9#23749831C211yesmaximal, characteristic, complemented
10#23749784C211yesmaximal, characteristic, complemented
11#23749779C211yesmaximal, characteristic, complemented
12#23749771C211yesmaximal, characteristic
13#23749765C211yesmaximal, characteristic, complemented
14#23749685C211yesmaximal, characteristic, complemented
15#464×C149C211yesmaximal, characteristic, complemented
16C2×#14558735C2211yescharacteristic
17C2×Q8×D149C2211yescharacteristic
18C2×#14558726C2211yescharacteristic
19C2×#14558726C2211yescharacteristic
20C2×#14558725C2211yescharacteristic
21C2×#14558725C2211yescharacteristic
22C2×#14558723C2211yescharacteristic
23C2×#14558721C2211yescharacteristic
24#18011911C2211yescharacteristic
25#18011910C2211yescharacteristic
26#18011909C2211yescharacteristic
27#18011905—21no—
28#18011900C2211yescharacteristic
29#18011899—21no—
30#18011898C2211yescharacteristic
31#18011896—21no—
32#18011893—21no—
33#18011893—21no—
34#18011889—21no—
35#18011888—21no—
36#18011888—21no—
37#18011887C2211yescharacteristic
38#18011886C2211yescharacteristic
39C4×D596C2211yescharacteristic
40#18011868C2211yescharacteristic
41C4⋊#11924746C2211yescharacteristic
42#18011836C2211yescharacteristic
43#18011836C2211yescharacteristic
44#18011835C2211yescharacteristic
45#18011834C2211yescharacteristic
46#18011834C2211yescharacteristic
47#18011832C2211yescharacteristic
48#18011823C2211yescharacteristic
49#18011823C2211yescharacteristic
50#18011821C2211yescharacteristic
51C8×Dic149C2211yescharacteristic
52C2×Q16×C149C2211yescharacteristic
53C2×SD16×C149C2211yescharacteristic
54#124×C149C2211yescharacteristic
55C4×Q8×C149C2211yescharacteristic
56C4⋊C8×C149C2211yescharacteristic
57#103×C149C2211yescharacteristic
58#102×C149C2211yescharacteristic
59#14558735—41no—
60#14558735—41no—
61C2×Dic298—21no—
62C2×Dic298—21no—
63C2×Dic298C2311yescharacteristic
64C2×Dic298C2311yescharacteristic
65Q8×D149—41no—
66Q8×D149—41no—
67C2×D596—21no—
68C2×D596C2311yescharacteristic
69C2×C22⋊D149—21no—
70C22×Dic149—21no—
71C2×C4×D149—21no—
72C2×C4×D149—21no—
73C2×C4×D149C2311yescharacteristic
74#14558726—41no—
75#14558726—41no—
76#14558725—41no—
77#14558725—41no—
78#14558723—41no—
79#14558721—41no—
80C2×#11924746C2311yescharacteristic
81C2×#11924746C2311yescharacteristic
82C4⋊Dic149—21no—
83C4⋊Dic149—21no—
84C4⋊Dic149C2311yescharacteristic
85#14558715—21no—
86#14558715—21no—
87#14558715—21no—
88#14558715—21no—
89#14558715D411yescharacteristic
90#14558715D411yescharacteristic
91C22⋊Dic149—21no—
92C22⋊Dic149—21no—
93#14558713—21no—
94#14558713—21no—
95#14558713—21no—
96#14558713—21no—
97#14558713—21no—
98#14558713D411yescharacteristic
99#14558713D411yescharacteristic
100C4×Dic149C2311yescharacteristic
101C2×Q8×C149C2311yescharacteristic
102C2×Q8×C149C2311yescharacteristic
103C2×D4×C149C2311yescharacteristic
104Q16×C149—41no—
105SD16×C149—41no—
106C2×C8×C149C2311yescharacteristic
107C2×C8×C149C2311yescharacteristic
108C4⋊C4×C149—21no—
109C4⋊C4×C149C2311yescharacteristic
110C22⋊C4×C149—21no—
111C22⋊C4×C149—21no—
112C42×C149—21no—
113C42×C149C2311yescharacteristic
114C22×D149—21no—
115C22×D149C2×D411yescharacteristic
116Dic298—21no—
117Dic298—21no—
118Dic298—21no—
119Dic298—21no—
120Dic298—42no—
121Dic298—81no—
122D596—21no—
123D596—21no—
124D596—81no—
125C22⋊D149—42no—
126C2×Dic149—21no—
127C2×Dic149—21no—
128C2×Dic149—21no—
129C2×Dic149—42no—
130C2×Dic149C2×D411yescharacteristic
131C2×Dic149C2×D411yescharacteristic
132C2×Dic149C2×D411yescharacteristic
133C4×D149—21no—
134C4×D149—21no—
135C4×D149—42no—
136C4×D149—81no—
137#11924746—21no—
138#11924746—21no—
139C23×C149—21no—
140Q8×C149—21no—
141Q8×C149—21no—
142Q8×C149—21no—
143Q8×C149—21no—
144D4×C149—21no—
145D4×C149—21no—
146C2×C4×C149—21no—
147C2×C4×C149—21no—
148C2×C4×C149—21no—
149C2×C4×C149C2×D411yescharacteristic
150C2×C4×C149C2×D411yescharacteristic
151C2×C4×C149C2411yescharacteristic
152C8×C149—21no—
153C8×C149—21no—
154C22×C149—41no—
155C22×C149—41no—
156C22×C149—41no—
157C22×C149C22×D411yescharacteristic
158C2×D149—21no—
159C2×D149—21no—
160C2×D149—21no—
161C2×D149—41no—
162C2×D149—41no—
163C2×D149—41no—
164C4×C149—21no—
165C4×C149—21no—
166C4×C149—41no—
167C4×C149—41no—
168C4×C149—41no—
169C4×C149H(5,𝔽2)11yescharacteristic
170C4×C149H(5,𝔽2)11yescharacteristic
171Dic149—21no—
172Dic149—21no—
173Dic149—21no—
174Dic149—41no—
175Dic149—41no—
176Dic149—41no—
177C2×C149—81no—
178C2×C149#53511yescharacteristic
179C2×C149#57711yescharacteristic
180C2×C149#57811yescharacteristic
181D149—41no—
182D149—81no—
183C149#322511yescharacteristic, complemented, Sylow
184#3225—1491nomaximal, Sylow
185#542—1491no—
186#536—1491no—
187#497—1491no—
188#495—1491no—
189#489—1491no—
190#487—1491no—
191#464D14911yescharacteristic, complemented
192#463—1491no—
193#462—1491no—
194#461—1491no—
195#452—1491no—
196#451—1491no—
197#449—1491no—
198#448—1491no—
199#433—1491no—
200C2×#41—1491no—
201C22×Q8—1491no—
202C2×Q16—1491no—
203C2×Q16—1491no—
204C2×Q16C2×D14911yescharacteristic
205C2×SD16—1491no—
206C2×SD16—1491no—
207C2×SD16—1491no—
208C2×SD16C2×D14911yescharacteristic
209C2×D8—1491no—
210C4⋊Q8—1491no—
211C4⋊Q8—1491no—
212C4⋊Q8—1491no—
213#126—2981no—
214#124—2981no—
215#124—1491no—
216#124—1491no—
217#124C2×D14911yescharacteristic
218#123—2981no—
219#123—2981no—
220#123—2981no—
221C22⋊Q8—2981no—
222C22⋊Q8—2981no—
223C22⋊Q8—2981no—
224C22⋊Q8—1491no—
225#121—1491no—
226C4×Q8C2×D14911yescharacteristic
227C4×D4—1491no—
228#117—1491no—
229C4⋊C8—1491no—
230C4⋊C8C2×D14911yescharacteristic
231#103—1491no—
232#103—1491no—
233#103—1491no—
234#103—1491no—
235#103—1491no—
236#103C2×D14911yescharacteristic
237#102—1491no—
238#102C2×D14911yescharacteristic
239C22⋊C8—1491no—
240C22⋊C8—1491no—
241#97—1491no—
242C4×C8—1491no—
243#41—5961no—
244#41—5961no—
245C2×Q8—2981no—
246C2×Q8—2981no—
247C2×Q8—5961no—
248C2×Q8—5961no—
249C2×Q8—1491no—
250C2×Q8—1491no—
251C2×Q8C22×D14911yescharacteristic
252C2×Q8C22×D14911yescharacteristic
253C2×D4—2981no—
254C2×D4—2981no—
255C2×D4—1491no—
256C2×D4C22×D14911yescharacteristic
257C22×C4—2981no—
258C22×C4—2981no—
259C22×C4—2981no—
260C22×C4—1491no—
261Q16—41no—
262Q16—5961no—
263Q16—5961no—
264SD16—41no—
265SD16—5961no—
266SD16—5961no—
267SD16—5961no—
268D8—5961no—
269C2×C8—1491no—
270C2×C8—1491no—
271C2×C8C22×D14911yescharacteristic
272C2×C8C22×D14911yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—2981no—
275C4⋊C4—2981no—
276C4⋊C4—2981no—
277C4⋊C4—2981no—
278C4⋊C4—2981no—
279C4⋊C4—2981no—
280C4⋊C4—1491no—
281C4⋊C4—1491no—
282C4⋊C4—1491no—
283C4⋊C4C22×D14911yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—2981no—
287C22⋊C4—2981no—
288C22⋊C4—2981no—
289C22⋊C4—2981no—
290C22⋊C4—2981no—
291C22⋊C4—2981no—
292C22⋊C4—2981no—
293C22⋊C4—1491no—
294C22⋊C4—1491no—
295C42—21no—
296C42—1491no—
297C42C22×D14911yescharacteristic
298C23—21no—
299C23—2981no—
300C23—1491no—
301Q8—21no—
302Q8—21no—
303Q8—21no—
304Q8—21no—
305Q8—2981no—
306Q8—2981no—
307Q8—2981no—
308Q8—2981no—
309Q8—5962no—
310Q8—11921no—
311D4—21no—
312D4—21no—
313D4—2981no—
314D4—2981no—
315D4—5962no—
316D4—11921no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—2981no—
321C2×C4—2981no—
322C2×C4—2981no—
323C2×C4—2981no—
324C2×C4—2981no—
325C2×C4—5962no—
326C2×C4—5962no—
327C2×C4—1491no—
328C2×C4—1491no—
329C2×C4—1491no—
330C2×C4—11921no—
331C2×C4D4×D14911yescharacteristic
332C2×C4D4×D14911yescharacteristic
333C2×C4C23×D14911yescharacteristic
334C8—21no—
335C8—21no—
336C8—2981no—
337C8—2981no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—2981no—
342C22—2981no—
343C22—2981no—
344C22—5961no—
345C22—5961no—
346C22—5961no—
347C22C2×D4×D14911yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—2981no—
354C4—2981no—
355C4—2981no—
356C4—5961no—
357C4—5961no—
358C4—5961no—
359C4#1801195611yescharacteristic
360C4#1801195711yescharacteristic
361C2—81no—
362C2—5961no—
363C2—11921no—
364C2#2375019111yescharacteristic
365C2#2375043211yescharacteristic
366C2#2375044111yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#464×C149C2
socleC22×C149C22×D4
prime radical#23749771C2
hypercenter#464D149
hypocenterC149#3225
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. #23750247C2semidirect
2. #23750195C2semidirect
3. #23750018C2semidirect
4. #23750006C2semidirect
5. #23749983C2semidirect
6. #23749974C2semidirect
7. #23749837C2semidirect
8. #23749835C2semidirect
9. #23749831C2semidirect
10. #23749784C2semidirect
11. #23749779C2semidirect
13. #23749765C2semidirect
14. #23749685C2semidirect
15. #464×C149C2semidirect
183. C149#3225semidirect
191. #464D149semidirect

Maximal subgroups

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

subgroupindex
#237502472
#237501952
#237500182
#237500062
#237499832
#237499742
#237498372
#237498352
#237498312
#237497842
#237497792
#237497712
#237497652
#237496852
#464×C1492
#3225149