Finite Group Databasebeta

← #34052918

Subgroups — #34052918

Order 19072.

366 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C149⋊#401C211yesmaximal, characteristic, complemented
2#23749567C211yesmaximal, characteristic, complemented
3#23749565C211yesmaximal, characteristic, complemented
4#23749561C211yesmaximal, characteristic
5#23749556C211yesmaximal, characteristic, complemented
6#23749553C211yesmaximal, characteristic
7#23749553C211yesmaximal, characteristic
8#23749550C211yesmaximal, characteristic
9#23749548C211yesmaximal, characteristic
10#23749546C211yesmaximal, characteristic, complemented
11#23749545C211yesmaximal, characteristic, complemented
12#23749537C211yesmaximal, characteristic
13#23749523C211yesmaximal, characteristic, complemented
14#23749509C211yesmaximal, characteristic, complemented
15#388×C149C211yesmaximal, characteristic
16C22×Dic298C2211yescharacteristic
17C2×C4⋊Dic149C2211yescharacteristic
18C2×C4⋊Dic149C2211yescharacteristic
19C2×C4⋊Dic149C2211yescharacteristic
20C2×#14558715C2211yescharacteristic
21C2×#14558715C2211yescharacteristic
22C2×#14558715C2211yescharacteristic
23C2×#14558715C2211yescharacteristic
24C2×#14558715C2211yescharacteristic
25C2×#14558715C2211yescharacteristic
26C2×C22⋊Dic149C2211yescharacteristic
27C2×C22⋊Dic149C2211yescharacteristic
28C2×C22⋊Dic149C2211yescharacteristic
29C2×C22⋊Dic149C2211yescharacteristic
30#18011818C2211yescharacteristic
31#18011818C2211yescharacteristic
32#18011818C2211yescharacteristic
33#18011818C2211yescharacteristic
34#18011818C2211yescharacteristic
35#18011818C2211yescharacteristic
36#18011818C2211yescharacteristic
37#18011818C2211yescharacteristic
38#18011818C2211yescharacteristic
39#18011818C2211yescharacteristic
40#18011818C2211yescharacteristic
41#18011818C2211yescharacteristic
42#18011818C2211yescharacteristic
43#18011818C2211yescharacteristic
44C2×C4⋊C4×C149C2211yescharacteristic
45C2×C22⋊C4×C149C2211yescharacteristic
46C2×C22⋊C4×C149C2211yescharacteristic
47C2×C22⋊C4×C149C2211yescharacteristic
48C2×C42×C149C2211yescharacteristic
49#95×C149C2211yescharacteristic
50#95×C149C2211yescharacteristic
51C2×Dic298—41no—
52C2×Dic298—41no—
53C2×Dic298—41no—
54C22×Dic149C2311yescharacteristic
55C22×Dic149C2311yescharacteristic
56C22×Dic149C2311yescharacteristic
57C22×Dic149C2311yescharacteristic
58C22×Dic149C2311yescharacteristic
59C22×Dic149C2311yescharacteristic
60C22×Dic149C2311yescharacteristic
61C22×Dic149C2311yescharacteristic
62C4⋊Dic149—22no—
63C4⋊Dic149—41no—
64C4⋊Dic149—41no—
65#14558715—22no—
66#14558715—41no—
67#14558715—41no—
68#14558715—41no—
69#14558715—41no—
70#14558715—41no—
71C22⋊Dic149—41no—
72C22⋊Dic149—41no—
73C22⋊Dic149—41no—
74C22⋊Dic149—41no—
75C24×C149C2311yescharacteristic
76C22×C4×C149C2311yescharacteristic
77C22×C4×C149C2311yescharacteristic
78C22×C4×C149C2311yescharacteristic
79C22×C4×C149C2311yescharacteristic
80C22×C4×C149C2311yescharacteristic
81C22×C4×C149C2311yescharacteristic
82C4⋊C4×C149—41no—
83C22⋊C4×C149—22no—
84C22⋊C4×C149—41no—
85C22⋊C4×C149—41no—
86C42×C149—41no—
87Dic298—44no—
88C2×Dic149—21no—
89C2×Dic149—21no—
90C2×Dic149—21no—
91C2×Dic149—21no—
92C2×Dic149—21no—
93C2×Dic149—21no—
94C2×Dic149—21no—
95C2×Dic149—21no—
96C2×Dic149—21no—
97C2×Dic149—21no—
98C2×Dic149—21no—
99C2×Dic149—21no—
100C2×Dic149—21no—
101C2×Dic149—21no—
102C2×Dic149—21no—
103C2×Dic149—21no—
104C2×Dic149—21no—
105C2×Dic149—21no—
106C2×Dic149—21no—
107C2×Dic149—21no—
108C2×Dic149—21no—
109C2×Dic149—21no—
110C2×Dic149—21no—
111C2×Dic149—21no—
112C23×C149—21no—
113C23×C149—21no—
114C23×C149—21no—
115C23×C149—21no—
116C23×C149—21no—
117C23×C149—21no—
118C23×C149—21no—
119C23×C149C2411yescharacteristic
120C2×C4×C149—21no—
121C2×C4×C149—21no—
122C2×C4×C149—21no—
123C2×C4×C149—21no—
124C2×C4×C149—21no—
125C2×C4×C149—21no—
126C2×C4×C149—21no—
127C2×C4×C149—21no—
128C2×C4×C149—21no—
129C2×C4×C149—21no—
130C2×C4×C149—21no—
131C2×C4×C149—21no—
132C2×C4×C149—21no—
133C2×C4×C149—21no—
134C2×C4×C149—21no—
135C2×C4×C149—21no—
136C2×C4×C149—21no—
137C2×C4×C149#4112yes—
138C22×C149—41no—
139C22×C149—41no—
140C22×C149—41no—
141C22×C149—41no—
142C22×C149—41no—
143C22×C149—41no—
144C22×C149—41no—
145C22×C149C2×#4111yescharacteristic
146C22×C149H(5,𝔽2)11yescharacteristic
147C22×C149H(5,𝔽2)11yescharacteristic
148C22×C149H(5,𝔽2)11yescharacteristic
149C22×C1492−1+411yescharacteristic
150C22×C1492−1+411yescharacteristic
151C22×C1492−1+411yescharacteristic
152C4×C149—22no—
153C4×C149—41no—
154C4×C149—41no—
155C4×C149—41no—
156C4×C149—41no—
157C4×C149—41no—
158Dic149—41no—
159Dic149—41no—
160Dic149—41no—
161Dic149—41no—
162Dic149—41no—
163Dic149—41no—
164Dic149—41no—
165Dic149—41no—
166C2×C149—81no—
167C2×C149#53911yescharacteristic
168C2×C149#54211yescharacteristic
169C2×C149#54211yescharacteristic
170C2×C149#56011yescharacteristic
171C2×C149#56311yescharacteristic
172C2×C149#56311yescharacteristic
173C2×C149#56311yescharacteristic
174C149#283811yescharacteristic, complemented, Sylow
175#2838—1491nomaximal, Sylow
176#401—1491no—
177#400—1491no—
178#400—1491no—
179#399—1491no—
180#398—1491no—
181#397—1491no—
182#397—1491no—
183#397—1491no—
184#396—1491no—
185#395—1491no—
186#395—1491no—
187#393—1491no—
188#389—1491no—
189#388D14911yescharacteristic
190#387—1491no—
191C22×Q8—1491no—
192C2×C4⋊C4—1491no—
193C2×C4⋊C4—1491no—
194C2×C4⋊C4—1491no—
195C2×C4⋊C4—1491no—
196C2×C4⋊C4—1491no—
197C2×C4⋊C4—1491no—
198C2×C4⋊C4—1491no—
199C2×C4⋊C4—1491no—
200C2×C4⋊C4—1491no—
201C2×C4⋊C4C2×D14911yescharacteristic
202C2×C22⋊C4—1491no—
203C2×C22⋊C4—1491no—
204C2×C22⋊C4—1491no—
205C2×C22⋊C4—1491no—
206C2×C22⋊C4C2×D14911yescharacteristic
207C2×C22⋊C4C2×D14911yescharacteristic
208C2×C22⋊C4C2×D14911yescharacteristic
209C2×C42C2×D14911yescharacteristic
210#95—1491no—
211#95—1491no—
212#95—1491no—
213#95—1491no—
214#95—1491no—
215#95—1491no—
216#95—1491no—
217#95—1491no—
218#95—1491no—
219#95—1491no—
220#95—1491no—
221#95—1491no—
222#95—1491no—
223#95—1491no—
224#95C2×D14911yescharacteristic
225#95C2×D14911yescharacteristic
226C24C22×D14911yescharacteristic
227C2×Q8—5961no—
228C2×Q8—5961no—
229C2×Q8—5961no—
230C22×C4—1491no—
231C22×C4—1491no—
232C22×C4—1491no—
233C22×C4—1491no—
234C22×C4—1491no—
235C22×C4—1491no—
236C22×C4—1491no—
237C22×C4—1491no—
238C22×C4C22×D14911yescharacteristic
239C22×C4C22×D14911yescharacteristic
240C22×C4C22×D14911yescharacteristic
241C22×C4C22×D14911yescharacteristic
242C22×C4C22×D14911yescharacteristic
243C22×C4C22×D14911yescharacteristic
244C4⋊C4—41no—
245C4⋊C4—2982no—
246C4⋊C4—2982no—
247C4⋊C4—5961no—
248C4⋊C4—5961no—
249C4⋊C4—5961no—
250C4⋊C4—5961no—
251C4⋊C4—5961no—
252C4⋊C4—5961no—
253C4⋊C4—5961no—
254C22⋊C4—22no—
255C22⋊C4—41no—
256C22⋊C4—41no—
257C22⋊C4—5961no—
258C22⋊C4—5961no—
259C22⋊C4—5961no—
260C22⋊C4—5961no—
261C42—41no—
262C23—21no—
263C23—21no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23—21no—
269C23C23×D14911yescharacteristic
270Q8—5964no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—2981no—
289C2×C4—2981no—
290C2×C4—2981no—
291C2×C4—2981no—
292C2×C4—2981no—
293C2×C4—2981no—
294C2×C4—2981no—
295C2×C4—2981no—
296C2×C4—2981no—
297C2×C4—2981no—
298C2×C4—2981no—
299C2×C4—2981no—
300C2×C4—2981no—
301C2×C4—2981no—
302C2×C4—2981no—
303C2×C4—2981no—
304C2×C4—2981no—
305C2×C4—2981no—
306C2×C4—2981no—
307C2×C4—2981no—
308C2×C4—2981no—
309C2×C4—2981no—
310C2×C4—2981no—
311C2×C4—2981no—
312C2×C4#1455873612yes—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22C2×#1455873611yescharacteristic
321C22#1801195611yescharacteristic
322C22#1801195611yescharacteristic
323C22#1801195711yescharacteristic
324C22#1801195811yescharacteristic
325C22#1801195811yescharacteristic
326C22#1801195811yescharacteristic
327C4—22no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—5961no—
334C4—5961no—
335C4—5961no—
336C4—5961no—
337C4—5961no—
338C4—5961no—
339C4—5961no—
340C4—5961no—
341C2—81no—
342C2#2375021711yescharacteristic
343C2#2375024011yescharacteristic
344C2#2375024611yescharacteristic
345C2#2375036311yescharacteristic
346C2#2375037511yescharacteristic
347C2#2375037711yescharacteristic
348C2#2375037811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D149
commutator, socle, cosocleC23×C149C24
Fitting#388×C149C2
prime radicalC24×C149C23
hypercenter#388D149
hypocenterC149#2838
LCSG ▷ C23×C149 ▷ C149
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C149⋊#401C2semidirect
2. #23749567C2semidirect
3. #23749565C2semidirect
5. #23749556C2semidirect
10. #23749546C2semidirect
11. #23749545C2semidirect
13. #23749523C2semidirect
14. #23749509C2semidirect
174. C149#2838semidirect

Maximal subgroups

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

subgroupindex
C149⋊#4012
#237495672
#237495652
#237495612
#237495562
#237495532
#237495502
#237495482
#237495462
#237495452
#237495372
#237495232
#237495092
#388×C1492
#2838149