Finite Group Databasebeta

← #2836×C149 #34041749

Subgroups — #2836×C149 #34041749

Order 19072.

358 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#400×C149C211yesmaximal, characteristic, complemented
2#400×C149C211yesmaximal, characteristic, complemented
3#399×C149C211yesmaximal, characteristic
4#398×C149C211yesmaximal, characteristic, complemented
5#398×C149C211yesmaximal, characteristic, complemented
6#398×C149C211yesmaximal, characteristic, complemented
7#398×C149C211yesmaximal, characteristic, complemented
8#397×C149C211yesmaximal, characteristic
9#397×C149C211yesmaximal, characteristic
10#397×C149C211yesmaximal, characteristic
11#396×C149C211yesmaximal, characteristic
12#396×C149C211yesmaximal, characteristic
13#389×C149C211yesmaximal, characteristic, complemented
14#388×C149C211yesmaximal, characteristic
15#387×C149C211yesmaximal, characteristic, complemented
16C2×C4⋊C4×C149C2211yescharacteristic
17C2×C4⋊C4×C149C2211yescharacteristic
18C2×C4⋊C4×C149C2211yescharacteristic
19C2×C4⋊C4×C149C2211yescharacteristic
20C2×C4⋊C4×C149C2211yescharacteristic
21C2×C4⋊C4×C149C2211yescharacteristic
22C2×C4⋊C4×C149C2211yescharacteristic
23C2×C4⋊C4×C149C2211yescharacteristic
24C2×C4⋊C4×C149C2211yescharacteristic
25C2×C4⋊C4×C149C2211yescharacteristic
26C2×C4⋊C4×C149C2211yescharacteristic
27C2×C4⋊C4×C149C2211yescharacteristic
28C2×C4⋊C4×C149C2211yescharacteristic
29C2×C22⋊C4×C149C2211yescharacteristic
30C2×C22⋊C4×C149C2211yescharacteristic
31C2×C22⋊C4×C149C2211yescharacteristic
32C2×C22⋊C4×C149C2211yescharacteristic
33C2×C22⋊C4×C149C2211yescharacteristic
34C2×C22⋊C4×C149C2211yescharacteristic
35C2×C22⋊C4×C149C2211yescharacteristic
36C2×C42×C149C2211yescharacteristic
37#95×C149C2211yescharacteristic
38#95×C149C2211yescharacteristic
39#95×C149C2211yescharacteristic
40#95×C149C2211yescharacteristic
41#95×C149C2211yescharacteristic
42#95×C149C2211yescharacteristic
43#95×C149C2211yescharacteristic
44#95×C149C2211yescharacteristic
45#95×C149C2211yescharacteristic
46#95×C149C2211yescharacteristic
47#95×C149C2211yescharacteristic
48#95×C149C2211yescharacteristic
49#95×C149C2211yescharacteristic
50#95×C149C2211yescharacteristic
51C24×C149C2311yescharacteristic
52C22×C4×C149C2311yescharacteristic
53C22×C4×C149C2311yescharacteristic
54C22×C4×C149C2311yescharacteristic
55C22×C4×C149C2311yescharacteristic
56C22×C4×C149C2311yescharacteristic
57C22×C4×C149C2311yescharacteristic
58C22×C4×C149C2311yescharacteristic
59C22×C4×C149C2311yescharacteristic
60C22×C4×C149C2311yescharacteristic
61C22×C4×C149C2311yescharacteristic
62C22×C4×C149C2311yescharacteristic
63C22×C4×C149C2311yescharacteristic
64C22×C4×C149C2311yescharacteristic
65C22×C4×C149C2311yescharacteristic
66C4⋊C4×C149—22no—
67C4⋊C4×C149—22no—
68C4⋊C4×C149—41no—
69C4⋊C4×C149—41no—
70C4⋊C4×C149—41no—
71C4⋊C4×C149—41no—
72C4⋊C4×C149—41no—
73C4⋊C4×C149—41no—
74C4⋊C4×C149—41no—
75C4⋊C4×C149—41no—
76C4⋊C4×C149—41no—
77C4⋊C4×C149—41no—
78C4⋊C4×C149—41no—
79C22⋊C4×C149—22no—
80C22⋊C4×C149—41no—
81C22⋊C4×C149—41no—
82C22⋊C4×C149—41no—
83C22⋊C4×C149—41no—
84C22⋊C4×C149—41no—
85C22⋊C4×C149—41no—
86C42×C149—41no—
87C23×C149—21no—
88C23×C149—21no—
89C23×C149—21no—
90C23×C149—21no—
91C23×C149—21no—
92C23×C149—21no—
93C23×C149—21no—
94C23×C149C2411yescharacteristic
95C2×C4×C149—21no—
96C2×C4×C149—21no—
97C2×C4×C149—21no—
98C2×C4×C149—21no—
99C2×C4×C149—21no—
100C2×C4×C149—21no—
101C2×C4×C149—21no—
102C2×C4×C149—21no—
103C2×C4×C149—21no—
104C2×C4×C149—21no—
105C2×C4×C149—21no—
106C2×C4×C149—21no—
107C2×C4×C149—21no—
108C2×C4×C149—21no—
109C2×C4×C149—21no—
110C2×C4×C149—21no—
111C2×C4×C149—21no—
112C2×C4×C149—21no—
113C2×C4×C149—21no—
114C2×C4×C149—21no—
115C2×C4×C149—21no—
116C2×C4×C149—21no—
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#4112yes—
137C22×C149—41no—
138C22×C149—41no—
139C22×C149—41no—
140C22×C149—41no—
141C22×C149—41no—
142C22×C149—41no—
143C22×C149—41no—
144C22×C149C2×#4111yescharacteristic
145C22×C149H(5,𝔽2)11yescharacteristic
146C22×C149H(5,𝔽2)11yescharacteristic
147C22×C149H(5,𝔽2)11yescharacteristic
148C22×C1492−1+411yescharacteristic
149C22×C1492−1+411yescharacteristic
150C22×C1492−1+411yescharacteristic
151C4×C149—22no—
152C4×C149—41no—
153C4×C149—41no—
154C4×C149—41no—
155C4×C149—41no—
156C4×C149—41no—
157C4×C149—41no—
158C4×C149—41no—
159C4×C149—41no—
160C4×C149—41no—
161C4×C149—41no—
162C4×C149—41no—
163C4×C149—41no—
164C4×C149—41no—
165C2×C149—81no—
166C2×C149#53911yescharacteristic
167C2×C149#54011yescharacteristic
168C2×C149#54111yescharacteristic
169C2×C149#56211yescharacteristic
170C2×C149#56211yescharacteristic
171C2×C149#56311yescharacteristic
172C2×C149#56311yescharacteristic
173C149#283611yescharacteristic, direct product factor, Sylow
174#2836C14911yesmaximal, characteristic, direct product factor, Sylow
175#400C2×C14911yescharacteristic, complemented
176#400C2×C14911yescharacteristic, complemented
177#399C2×C14911yescharacteristic
178#398C2×C14911yescharacteristic, complemented
179#398C2×C14911yescharacteristic, complemented
180#398C2×C14911yescharacteristic, complemented
181#398C2×C14911yescharacteristic, complemented
182#397C2×C14911yescharacteristic
183#397C2×C14911yescharacteristic
184#397C2×C14911yescharacteristic
185#396C2×C14911yescharacteristic
186#396C2×C14911yescharacteristic
187#389C2×C14911yescharacteristic, complemented
188#388C2×C14911yescharacteristic
189#387C2×C14911yescharacteristic, complemented
190C2×C4⋊C4C22×C14911yescharacteristic
191C2×C4⋊C4C22×C14911yescharacteristic
192C2×C4⋊C4C22×C14911yescharacteristic
193C2×C4⋊C4C22×C14911yescharacteristic
194C2×C4⋊C4C22×C14911yescharacteristic
195C2×C4⋊C4C22×C14911yescharacteristic
196C2×C4⋊C4C22×C14911yescharacteristic
197C2×C4⋊C4C22×C14911yescharacteristic
198C2×C4⋊C4C22×C14911yescharacteristic
199C2×C4⋊C4C22×C14911yescharacteristic
200C2×C4⋊C4C22×C14911yescharacteristic
201C2×C4⋊C4C22×C14911yescharacteristic
202C2×C4⋊C4C22×C14911yescharacteristic
203C2×C22⋊C4C22×C14911yescharacteristic
204C2×C22⋊C4C22×C14911yescharacteristic
205C2×C22⋊C4C22×C14911yescharacteristic
206C2×C22⋊C4C22×C14911yescharacteristic
207C2×C22⋊C4C22×C14911yescharacteristic
208C2×C22⋊C4C22×C14911yescharacteristic
209C2×C22⋊C4C22×C14911yescharacteristic
210C2×C42C22×C14911yescharacteristic
211#95C22×C14911yescharacteristic
212#95C22×C14911yescharacteristic
213#95C22×C14911yescharacteristic
214#95C22×C14911yescharacteristic
215#95C22×C14911yescharacteristic
216#95C22×C14911yescharacteristic
217#95C22×C14911yescharacteristic
218#95C22×C14911yescharacteristic
219#95C22×C14911yescharacteristic
220#95C22×C14911yescharacteristic
221#95C22×C14911yescharacteristic
222#95C22×C14911yescharacteristic
223#95C22×C14911yescharacteristic
224#95C22×C14911yescharacteristic
225C24C23×C14911yescharacteristic
226C22×C4C23×C14911yescharacteristic
227C22×C4C23×C14911yescharacteristic
228C22×C4C23×C14911yescharacteristic
229C22×C4C23×C14911yescharacteristic
230C22×C4C23×C14911yescharacteristic
231C22×C4C23×C14911yescharacteristic
232C22×C4C23×C14911yescharacteristic
233C22×C4C23×C14911yescharacteristic
234C22×C4C23×C14911yescharacteristic
235C22×C4C23×C14911yescharacteristic
236C22×C4C23×C14911yescharacteristic
237C22×C4C23×C14911yescharacteristic
238C22×C4C23×C14911yescharacteristic
239C22×C4C23×C14911yescharacteristic
240C4⋊C4—22no—
241C4⋊C4—22no—
242C4⋊C4—41no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C22⋊C4—22no—
254C22⋊C4—41no—
255C22⋊C4—41no—
256C22⋊C4—41no—
257C22⋊C4—41no—
258C22⋊C4—41no—
259C22⋊C4—41no—
260C42—41no—
261C23—21no—
262C23—21no—
263C23—21no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23C24×C14911yescharacteristic
269C2×C4—21no—
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—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4#41×C14912yes—
311C22—41no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22C2×#41×C14911yescharacteristic
319C22H(5,𝔽2)×C14911yescharacteristic
320C22H(5,𝔽2)×C14911yescharacteristic
321C22H(5,𝔽2)×C14911yescharacteristic
322C222−1+4×C14911yescharacteristic
323C222−1+4×C14911yescharacteristic
324C222−1+4×C14911yescharacteristic
325C4—22no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—41no—
339C2—81no—
340C2#539×C14911yescharacteristic
341C2#540×C14911yescharacteristic
342C2#541×C14911yescharacteristic
343C2#562×C14911yescharacteristic
344C2#562×C14911yescharacteristic
345C2#563×C14911yescharacteristic
346C2#563×C14911yescharacteristic
subgroupG/H
center, socleC23×C149C24
commutator, Frattini, cosocleC23C24×C149
prime radicalC24×C149C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C149 ◁ G

Complements

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

NH ≅ G/Ntype
1. #400×C149C2semidirect
2. #400×C149C2semidirect
4. #398×C149C2semidirect
5. #398×C149C2semidirect
6. #398×C149C2semidirect
7. #398×C149C2semidirect
13. #389×C149C2semidirect
15. #387×C149C2semidirect
173. C149#2836direct (N × H)
174. #2836C149direct (N × H)
175. #400C2×C149semidirect
176. #400C2×C149semidirect
178. #398C2×C149semidirect
179. #398C2×C149semidirect
180. #398C2×C149semidirect
181. #398C2×C149semidirect
187. #389C2×C149semidirect
189. #387C2×C149semidirect

Maximal subgroups

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

subgroupindex
#400×C1492
#399×C1492
#398×C1492
#397×C1492
#396×C1492
#389×C1492
#388×C1492
#387×C1492
#2836149