Finite Group Databasebeta

← #34055379

Subgroups — #34055379

Order 19072.

374 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750249C211yesmaximal, characteristic, complemented
2#23750231C211yesmaximal, characteristic, complemented
3#23750014C211yesmaximal, characteristic, complemented
4#23749982C211yesmaximal, characteristic, complemented
5#23749973C211yesmaximal, characteristic, complemented
6#23749879C211yesmaximal, characteristic, complemented
7#23749872C211yesmaximal, characteristic, complemented
8#23749862C211yesmaximal, characteristic, complemented
9#23749855C211yesmaximal, characteristic, complemented
10#23749736C211yesmaximal, characteristic, complemented
11#23749724C211yesmaximal, characteristic, complemented
12#23749712C211yesmaximal, characteristic, complemented
13#23749707C211yesmaximal, characteristic, complemented
14#23749582C211yesmaximal, characteristic, complemented
15#501×C149C211yesmaximal, characteristic, complemented
16C2×#14558725C2211yescharacteristic
17C2×#14558725C2211yescharacteristic
18C2×D1192C2211yescharacteristic
19C2×D1192C2211yescharacteristic
20C2×#14558719C2211yescharacteristic
21C2×C8×D149C2211yescharacteristic
22#18011908C2211yescharacteristic
23#18011906—21no—
24#18011900—21no—
25#18011899C2211yescharacteristic
26#18011896—21no—
27#18011896—21no—
28#18011896—21no—
29#18011891C2211yescharacteristic
30#18011887—21no—
31#18011886—21no—
32#18011886—21no—
33#18011886C2211yescharacteristic
34#18011886C2211yescharacteristic
35#18011886C2211yescharacteristic
36#18011876C2211yescharacteristic
37#18011873C2211yescharacteristic
38#18011873C2211yescharacteristic
39#18011873C2211yescharacteristic
40#18011868C2211yescharacteristic
41#18011834C2211yescharacteristic
42#18011834C2211yescharacteristic
43#18011831C2211yescharacteristic
44#18011831C2211yescharacteristic
45#18011831C2211yescharacteristic
46#18011831C2211yescharacteristic
47#18011831C2211yescharacteristic
48#18011831C2211yescharacteristic
49#18011821C2211yescharacteristic
50C4×#11924746C2211yescharacteristic
51C8×Dic149C2211yescharacteristic
52C4⋊Q8×C149C2211yescharacteristic
53#125×C149C2211yescharacteristic
54#107×C149C2211yescharacteristic
55#107×C149C2211yescharacteristic
56#106×C149C2211yescharacteristic
57#106×C149C2211yescharacteristic
58#97×C149C2211yescharacteristic
59C2×Dic298C2311yescharacteristic
60C2×D596—21no—
61C2×D596—21no—
62C2×D596—21no—
63C2×D596—21no—
64C2×D596—21no—
65C2×D596C2311yescharacteristic
66C2×D596C2311yescharacteristic
67C2×D596C2311yescharacteristic
68C2×C4×D149—21no—
69C2×C4×D149—21no—
70C2×C4×D149—21no—
71C2×C4×D149C2311yescharacteristic
72#14558725—22no—
73#14558725—22no—
74D1192—22no—
75D1192—22no—
76#14558719—22no—
77C2×#11924746C2311yescharacteristic
78C2×#11924746C2311yescharacteristic
79C8×D149—22no—
80C4⋊Dic149—21no—
81#14558715—21no—
82#14558715D411yescharacteristic
83#14558715D411yescharacteristic
84#14558713—21no—
85#14558713—21no—
86#14558713—21no—
87#14558713—21no—
88#14558713—21no—
89#14558713—21no—
90#14558713—21no—
91#14558713—21no—
92#14558713—21no—
93#14558713D411yescharacteristic
94#14558713D411yescharacteristic
95C4×Dic149—21no—
96C4×Dic149C2311yescharacteristic
97C2×Q8×C149—21no—
98C2×C8×C149C2311yescharacteristic
99C2×C8×C149C2311yescharacteristic
100C4⋊C4×C149—21no—
101C4⋊C4×C149—21no—
102C4⋊C4×C149—21no—
103C4⋊C4×C149C2311yescharacteristic
104C4⋊C4×C149C2311yescharacteristic
105C4⋊C4×C149C2311yescharacteristic
106C4⋊C4×C149C2311yescharacteristic
107C42×C149C2311yescharacteristic
108C22×D149—21no—
109C22×D149—21no—
110C22×D149—21no—
111C22×D149C2×D411yescharacteristic
112Dic298—21no—
113Dic298—21no—
114D596—21no—
115D596—21no—
116D596—21no—
117D596—21no—
118D596—21no—
119D596—21no—
120D596—81no—
121D596—81no—
122D596—81no—
123D596—81no—
124D596—81no—
125C2×Dic149—21no—
126C2×Dic149C2×D411yescharacteristic
127C2×Dic149C2×D411yescharacteristic
128C2×Dic149C2×D411yescharacteristic
129C4×D149—21no—
130C4×D149—21no—
131C4×D149—81no—
132C4×D149—81no—
133C4×D149—81no—
134#11924746—21no—
135#11924746—21no—
136Q8×C149—81no—
137C2×C4×C149—21no—
138C2×C4×C149—21no—
139C2×C4×C149—21no—
140C2×C4×C149—21no—
141C2×C4×C149C2×D411yescharacteristic
142C2×C4×C149C2×D411yescharacteristic
143C2×C4×C149C2411yescharacteristic
144C8×C149#4112yes—
145C8×C149#4112yes—
146C22×C149C22×D411yescharacteristic
147C2×D149—21no—
148C2×D149—21no—
149C2×D149—21no—
150C2×D149—41no—
151C2×D149—41no—
152C2×D149—41no—
153C2×D149—41no—
154C2×D149—41no—
155C2×D149—41no—
156C2×D149—41no—
157C2×D149—41no—
158C2×D149—41no—
159C4×C149—21no—
160C4×C149—21no—
161C4×C149—41no—
162C4×C149—41no—
163C4×C149—41no—
164C4×C149—41no—
165C4×C149C2×#4111yescharacteristic
166C4×C149C2×#4111yescharacteristic
167Dic149—21no—
168Dic149—21no—
169Dic149—21no—
170Dic149—41no—
171C2×C149#53211yescharacteristic
172C2×C149#57611yescharacteristic
173C2×C149#57711yescharacteristic
174D149—41no—
175D149—81no—
176D149—81no—
177D149—81no—
178C149#317911yescharacteristic, complemented, Sylow
179#3179—1491nomaximal, Sylow
180#542—1491no—
181#540—1491no—
182#501D14911yescharacteristic, complemented
183#496—1491no—
184#488—1491no—
185#486—1491no—
186#469—1491no—
187#468—1491no—
188#466—1491no—
189#465—1491no—
190#442—1491no—
191#440—1491no—
192C4×SD16—1491no—
193C4×D8—1491no—
194#405—1491no—
195C2×SD16—1491no—
196C2×SD16—1491no—
197C2×D8—1491no—
198C2×D8—1491no—
199C2×M16—1491no—
200C22×C8—1491no—
201C4⋊Q8C2×D14911yescharacteristic
202#127—1491no—
203#126—2981no—
204#125C2×D14911yescharacteristic
205#124—2981no—
206#124—1491no—
207#123—2981no—
208#123—2981no—
209#123—2981no—
210C22⋊Q8—2981no—
211C22⋊Q8—1491no—
212#121—2981no—
213#121—2981no—
214#121—1491no—
215#121—1491no—
216#121—1491no—
217C4×Q8—1491no—
218C4×D4—1491no—
219C4×D4—1491no—
220C4×D4—1491no—
221#117—1491no—
222#107C2×D14911yescharacteristic
223#107C2×D14911yescharacteristic
224#106C2×D14911yescharacteristic
225#106C2×D14911yescharacteristic
226#103—1491no—
227#103—1491no—
228#102—1491no—
229#102—1491no—
230#102—1491no—
231#102—1491no—
232#102—1491no—
233#102—1491no—
234#97—1491no—
235#97C2×D14911yescharacteristic
236C4×C8—1491no—
237C4×C8—1491no—
238C2×Q8—21no—
239C2×Q8—1491no—
240C2×D4—2981no—
241C2×D4—2981no—
242C2×D4—2981no—
243C2×D4—2981no—
244C2×D4—2981no—
245C2×D4—1491no—
246C2×D4—1491no—
247C2×D4—1491no—
248C22×C4—2981no—
249C22×C4—2981no—
250C22×C4—2981no—
251C22×C4—1491no—
252SD16—2982no—
253SD16—2982no—
254D8—2982no—
255D8—2982no—
256M16—2982no—
257C2×C8—2982no—
258C2×C8—1491no—
259C2×C8—1491no—
260C2×C8C22×D14911yescharacteristic
261C2×C8C22×D14911yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—2981no—
266C4⋊C4—2981no—
267C4⋊C4—1491no—
268C4⋊C4—1491no—
269C4⋊C4C22×D14911yescharacteristic
270C4⋊C4C22×D14911yescharacteristic
271C4⋊C4C22×D14911yescharacteristic
272C4⋊C4C22×D14911yescharacteristic
273C22⋊C4—2981no—
274C22⋊C4—2981no—
275C22⋊C4—2981no—
276C22⋊C4—2981no—
277C22⋊C4—2981no—
278C22⋊C4—2981no—
279C22⋊C4—2981no—
280C22⋊C4—2981no—
281C22⋊C4—2981no—
282C22⋊C4—1491no—
283C22⋊C4—1491no—
284C42—2981no—
285C42—1491no—
286C42C22×D14911yescharacteristic
287C23—2981no—
288C23—2981no—
289C23—2981no—
290C23—1491no—
291Q8—81no—
292Q8—2981no—
293Q8—2981no—
294D4—2981no—
295D4—2981no—
296D4—2981no—
297D4—2981no—
298D4—2981no—
299D4—2981no—
300D4—11921no—
301D4—11921no—
302D4—11921no—
303D4—11921no—
304D4—11921no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—2981no—
310C2×C4—2981no—
311C2×C4—2981no—
312C2×C4—1491no—
313C2×C4—1491no—
314C2×C4—1491no—
315C2×C4—11921no—
316C2×C4—11921no—
317C2×C4—11921no—
318C2×C4D4×D14911yescharacteristic
319C2×C4D4×D14911yescharacteristic
320C2×C4C23×D14911yescharacteristic
321C8—2981no—
322C8—2981no—
323C8#1455873712yes—
324C8#1455873712yes—
325C22—2981no—
326C22—2981no—
327C22—2981no—
328C22—5961no—
329C22—5961no—
330C22—5961no—
331C22—5961no—
332C22—5961no—
333C22—5961no—
334C22—5961no—
335C22—5961no—
336C22—5961no—
337C22C2×D4×D14911yescharacteristic
338C4—21no—
339C4—21no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—2981no—
345C4—2981no—
346C4—2981no—
347C4—5961no—
348C4C2×#1455873711yescharacteristic
349C4C2×#1455873711yescharacteristic
350C2—5961no—
351C2—11921no—
352C2—11921no—
353C2—11921no—
354C2#2375017611yescharacteristic
355C2#2375042911yescharacteristic
356C2#2375043411yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#501×C149C2
socleC22×C149C22×D4
hypercenter#501D149
hypocenterC149#3179
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
1. #23750249C2semidirect
2. #23750231C2semidirect
3. #23750014C2semidirect
4. #23749982C2semidirect
5. #23749973C2semidirect
6. #23749879C2semidirect
7. #23749872C2semidirect
8. #23749862C2semidirect
9. #23749855C2semidirect
10. #23749736C2semidirect
11. #23749724C2semidirect
12. #23749712C2semidirect
13. #23749707C2semidirect
14. #23749582C2semidirect
15. #501×C149C2semidirect
178. C149#3179semidirect
182. #501D149semidirect

Maximal subgroups

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

subgroupindex
#237502492
#237502312
#237500142
#237499822
#237499732
#237498792
#237498722
#237498622
#237498552
#237497362
#237497242
#237497122
#237497072
#237495822
#501×C1492
#3179149