Finite Group Databasebeta

← #34052873

Subgroups — #34052873

Order 19072.

372 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
2C149⋊#401C211yesmaximal, characteristic, complemented
3#23749560C211yesmaximal, characteristic
4#23749559C211yesmaximal, characteristic, complemented
5#23749558C211yesmaximal, characteristic, complemented
6#23749558C211yesmaximal, characteristic, complemented
7#23749556C211yesmaximal, characteristic, complemented
8#23749555C211yesmaximal, characteristic, complemented
9#23749554C211yesmaximal, characteristic
10#23749552C211yesmaximal, characteristic
11#23749551C211yesmaximal, characteristic
12#23749499C211yesmaximal, characteristic
13#23749496C211yesmaximal, characteristic
14#23749496C211yesmaximal, characteristic
15#398×C149C211yesmaximal, characteristic, complemented
16C22×C4×D149C2211yescharacteristic
17C2×C4⋊Dic149C2211yescharacteristic
18C2×C4⋊Dic149C2211yescharacteristic
19C2×#14558715C2211yescharacteristic
20C2×#14558715C2211yescharacteristic
21C2×#14558715C2211yescharacteristic
22C2×#14558715C2211yescharacteristic
23C2×#14558715C2211yescharacteristic
24C2×#14558715C2211yescharacteristic
25C2×#14558713C2211yescharacteristic
26C2×#14558713C2211yescharacteristic
27C2×#14558713C2211yescharacteristic
28C2×#14558713C2211yescharacteristic
29C2×#14558713C2211yescharacteristic
30C2×#14558713C2211yescharacteristic
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×C4⋊C4×C149C2211yescharacteristic
46C2×C4⋊C4×C149C2211yescharacteristic
47C2×C4⋊C4×C149C2211yescharacteristic
48#95×C149C2211yescharacteristic
49#95×C149C2211yescharacteristic
50#95×C149C2211yescharacteristic
51C23×D149C2311yescharacteristic
52C22×Dic149C2311yescharacteristic
53C22×Dic149C2311yescharacteristic
54C22×Dic149C2311yescharacteristic
55C22×Dic149C2311yescharacteristic
56C22×Dic149C2311yescharacteristic
57C22×Dic149C2311yescharacteristic
58C22×Dic149C2311yescharacteristic
59C2×C4×D149—41no—
60C2×C4×D149—41no—
61C2×C4×D149—41no—
62C4⋊Dic149—41no—
63C4⋊Dic149—41no—
64#14558715—41no—
65#14558715—41no—
66#14558715—41no—
67#14558715—41no—
68#14558715—41no—
69#14558715—41no—
70#14558713—22no—
71#14558713—22no—
72#14558713—22no—
73#14558713—41no—
74#14558713—41no—
75#14558713—41no—
76C22×C4×C149C2311yescharacteristic
77C22×C4×C149C2311yescharacteristic
78C22×C4×C149C2311yescharacteristic
79C22×C4×C149C2311yescharacteristic
80C22×C4×C149C2311yescharacteristic
81C22×C4×C149C2311yescharacteristic
82C22×C4×C149C2311yescharacteristic
83C4⋊C4×C149—41no—
84C4⋊C4×C149—41no—
85C4⋊C4×C149—41no—
86C4⋊C4×C149—41no—
87C22×D149—21no—
88C22×D149—21no—
89C22×D149—21no—
90C22×D149—21no—
91C22×D149—21no—
92C22×D149—21no—
93C22×D149#4112yes—
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—
112C2×Dic149—21no—
113C2×Dic149—21no—
114C2×Dic149—21no—
115C4×D149—44no—
116C23×C149C2411yescharacteristic
117C2×C4×C149—21no—
118C2×C4×C149—21no—
119C2×C4×C149—21no—
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—21no—
138C22×C149C2×#4111yescharacteristic
139C22×C149H(5,𝔽2)11yescharacteristic
140C22×C149H(5,𝔽2)11yescharacteristic
141C22×C149H(5,𝔽2)11yescharacteristic
142C22×C1492−1+411yescharacteristic
143C22×C1492−1+411yescharacteristic
144C22×C1492−1+411yescharacteristic
145C2×D149—22no—
146C2×D149—22no—
147C2×D149—22no—
148C2×D149—41no—
149C2×D149—41no—
150C2×D149—41no—
151C2×D149—41no—
152C4×C149—41no—
153C4×C149—41no—
154C4×C149—41no—
155C4×C149—41no—
156C4×C149—41no—
157C4×C149—41no—
158C4×C149—41no—
159Dic149—41no—
160Dic149—41no—
161Dic149—41no—
162Dic149—41no—
163Dic149—41no—
164Dic149—41no—
165Dic149—41no—
166C2×C149#53911yescharacteristic
167C2×C149#53911yescharacteristic
168C2×C149#53911yescharacteristic
169C2×C149#56011yescharacteristic
170C2×C149#56311yescharacteristic
171C2×C149#56311yescharacteristic
172C2×C149#56311yescharacteristic
173D149—42no—
174C149#283411yescharacteristic, complemented, Sylow
175#2834—1491nomaximal, Sylow
176#401—1491no—
177#401—1491no—
178#399—1491no—
179#398—1491no—
180#398—1491no—
181#398—1491no—
182#398—1491no—
183#398—1491no—
184#398D14911yescharacteristic, complemented
185#397—1491no—
186#397—1491no—
187#397—1491no—
188#385—1491no—
189#385—1491no—
190#385—1491no—
191C23×C4—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⋊C4C2×D14911yescharacteristic
201C2×C4⋊C4C2×D14911yescharacteristic
202C2×C4⋊C4C2×D14911yescharacteristic
203C2×C4⋊C4C2×D14911yescharacteristic
204C2×C22⋊C4—1491no—
205C2×C22⋊C4—1491no—
206C2×C22⋊C4—1491no—
207C2×C22⋊C4—1491no—
208C2×C22⋊C4—1491no—
209C2×C22⋊C4—1491no—
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#95C2×D14911yescharacteristic
224#95C2×D14911yescharacteristic
225#95C2×D14911yescharacteristic
226C24—1491no—
227C22×C4—5961no—
228C22×C4—5961no—
229C22×C4—5961no—
230C22×C4—1491no—
231C22×C4—1491no—
232C22×C4—1491no—
233C22×C4—1491no—
234C22×C4—1491no—
235C22×C4—1491no—
236C22×C4—1491no—
237C22×C4C22×D14911yescharacteristic
238C22×C4C22×D14911yescharacteristic
239C22×C4C22×D14911yescharacteristic
240C22×C4C22×D14911yescharacteristic
241C22×C4C22×D14911yescharacteristic
242C22×C4C22×D14911yescharacteristic
243C22×C4C22×D14911yescharacteristic
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—5961no—
249C4⋊C4—5961no—
250C4⋊C4—5961no—
251C4⋊C4—5961no—
252C4⋊C4—5961no—
253C4⋊C4—5961no—
254C4⋊C4—5961no—
255C4⋊C4—5961no—
256C22⋊C4—2982no—
257C22⋊C4—2982no—
258C22⋊C4—2982no—
259C22⋊C4—5961no—
260C22⋊C4—5961no—
261C22⋊C4—5961no—
262C23—2981no—
263C23—2981no—
264C23—2981no—
265C23—2981no—
266C23—2981no—
267C23—2981no—
268C23—1492no—
269C23C23×D14911yescharacteristic
270C2×C4—21no—
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—21no—
289C2×C4—21no—
290C2×C4—21no—
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—5964no—
313C22—2982no—
314C22—2982no—
315C22—2982no—
316C22—5961no—
317C22—5961no—
318C22—5961no—
319C22—5961no—
320C22#41×D14911yescharacteristic
321C22#1801195611yescharacteristic
322C22#1801195611yescharacteristic
323C22#1801195711yescharacteristic
324C22#1801195811yescharacteristic
325C22#1801195911yescharacteristic
326C22#1801195911yescharacteristic
327C4—41no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—5961no—
335C4—5961no—
336C4—5961no—
337C4—5961no—
338C4—5961no—
339C4—5961no—
340C4—5961no—
341C2—5962no—
342C2#2375021811yescharacteristic
343C2#2375022111yescharacteristic
344C2#2375022311yescharacteristic
345C2#2375036311yescharacteristic
346C2#2375037411yescharacteristic
347C2#2375037611yescharacteristic
348C2#2375037911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D149
commutator, socle, cosocleC23×C149C24
Fitting#398×C149C2
prime radicalC23×D149C23
hypercenter#398D149
hypocenterC149#2834
LCSG ▷ C23×C149 ▷ C149
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C149⋊#401C2semidirect
2. C149⋊#401C2semidirect
4. #23749559C2semidirect
5. #23749558C2semidirect
6. #23749558C2semidirect
7. #23749556C2semidirect
8. #23749555C2semidirect
15. #398×C149C2semidirect
174. C149#2834semidirect
184. #398D149semidirect

Maximal subgroups

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

subgroupindex
C149⋊#4012
#237495602
#237495592
#237495582
#237495562
#237495552
#237495542
#237495522
#237495512
#237494992
#237494962
#398×C1492
#2834149