Finite Group Databasebeta

← C149×#11852 #49190801

Subgroups — C149×#11852 #49190801

Order 38144.

438 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2591×C149C211yesmaximal, characteristic
2#1821×C149C211yesmaximal, characteristic, complemented
3C2×#324×C149C211yesmaximal, characteristic, complemented
4#1353×C149C212yesmaximal, complemented
5#1345×C149C212yesmaximal, complemented
6C2×#121×C149C411yescharacteristic
7C22×C4⋊C4×C149C2211yescharacteristic
8#407×C149—21no—
9C2×C22⋊C8×C149—21no—
10#400×C149C411yescharacteristic
11#400×C149C2211yescharacteristic
12#394×C149C411yescharacteristic
13#394×C149C2211yescharacteristic
14#388×C149—21no—
15#388×C149—21no—
16#386×C149—21no—
17#386×C149—21no—
18C4×C22⋊C4×C149C411yescharacteristic
19#343×C149—21no—
20#343×C149C2212yes—
21#324×C149—21no—
22#324×C149C2212yes—
23C22×D4×C149—21no—
24C22×D4×C149C2×C411yescharacteristic
25C23×C4×C149C2×C411yescharacteristic
26C23×C4×C149D411yescharacteristic
27C23×C4×C149D411yescharacteristic
28C2×M16×C149—22no—
29C22×C8×C149—41no—
30#121×C149—41no—
31#121×C149—41no—
32C2×C4⋊C4×C149—41no—
33C2×C4⋊C4×C149—41no—
34C2×C4⋊C4×C149C2×C411yescharacteristic
35C2×C4⋊C4×C149C2×C411yescharacteristic
36C2×C4⋊C4×C149D411yescharacteristic
37C2×C4⋊C4×C149D411yescharacteristic
38C2×C4⋊C4×C149C2311yescharacteristic
39C2×C22⋊C4×C149—21no—
40C2×C22⋊C4×C149—21no—
41C2×C22⋊C4×C149—21no—
42C2×C22⋊C4×C149—21no—
43C2×C22⋊C4×C149—21no—
44C2×C22⋊C4×C149—21no—
45C2×C42×C149—21no—
46C22⋊C8×C149—22no—
47C22⋊C8×C149—41no—
48C22⋊C8×C149—41no—
49C22⋊C8×C149—41no—
50#95×C149—21no—
51#95×C149—21no—
52#95×C149—21no—
53#95×C149—21no—
54#95×C149C2×C411yescharacteristic
55#95×C149C2×C411yescharacteristic
56C24×C149—21no—
57C24×C149C22⋊C411yescharacteristic
58C2×D4×C149—41no—
59C2×D4×C149—42no—
60C2×D4×C149—42no—
61C2×D4×C149—41no—
62C2×D4×C149—41no—
63C2×D4×C149—81no—
64C22×C4×C149—21no—
65C22×C4×C149—21no—
66C22×C4×C149—21no—
67C22×C4×C149—21no—
68C22×C4×C149—21no—
69C22×C4×C149—21no—
70C22×C4×C149—22no—
71C22×C4×C149—21no—
72C22×C4×C149—21no—
73C22×C4×C149—21no—
74C22×C4×C149—41no—
75C22×C4×C149—81no—
76C22×C4×C149—81no—
77C22×C4×C149C22⋊C411yescharacteristic
78C22×C4×C149C22⋊C411yescharacteristic
79C22×C4×C149C22⋊C411yescharacteristic
80C22×C4×C149C22×C411yescharacteristic
81C22×C4×C149C2×D411yescharacteristic
82C22×C4×C149C2×D411yescharacteristic
83M16×C149—42no—
84M16×C149—42no—
85C2×C8×C149—42no—
86C2×C8×C149—42no—
87C2×C8×C149—82no—
88C4⋊C4×C149—41no—
89C4⋊C4×C149—41no—
90C4⋊C4×C149—41no—
91C4⋊C4×C149—41no—
92C4⋊C4×C149—41no—
93C22⋊C4×C149—42no—
94C22⋊C4×C149—42no—
95C22⋊C4×C149—42no—
96C22⋊C4×C149—42no—
97C22⋊C4×C149—81no—
98C22⋊C4×C149—81no—
99C42×C149—81no—
100C23×C149—22no—
101C23×C149—21no—
102C23×C149—21no—
103C23×C149—41no—
104C23×C149—41no—
105C23×C149—41no—
106C23×C149—41no—
107C23×C149—41no—
108C23×C149—41no—
109C23×C149—41no—
110C23×C149—41no—
111C23×C149#9911yescharacteristic
112C23×C149#9911yescharacteristic
113C23×C149C2×C22⋊C411yescharacteristic
114D4×C149—82no—
115D4×C149—82no—
116D4×C149—82no—
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—42no—
127C2×C4×C149—42no—
128C2×C4×C149—42no—
129C2×C4×C149—41no—
130C2×C4×C149—41no—
131C2×C4×C149—41no—
132C2×C4×C149—41no—
133C2×C4×C149—41no—
134C2×C4×C149—41no—
135C2×C4×C149—41no—
136C2×C4×C149—41no—
137C2×C4×C149—41no—
138C2×C4×C149—41no—
139C2×C4×C149—41no—
140C2×C4×C149—41no—
141C2×C4×C149—41no—
142C2×C4×C149—81no—
143C2×C4×C149—81no—
144C2×C4×C149—81no—
145C2×C4×C149#13512yes—
146C8×C149—82no—
147C8×C149—82no—
148C22×C149—21no—
149C22×C149—21no—
150C22×C149—21no—
151C22×C149—21no—
152C22×C149—21no—
153C22×C149—21no—
154C22×C149—21no—
155C22×C149—42no—
156C22×C149—42no—
157C22×C149—81no—
158C22×C149—81no—
159C22×C149—81no—
160C22×C149—81no—
161C22×C149—81no—
162C22×C149—81no—
163C22×C149—81no—
164C22×C149#35512yes—
165C22×C149C2×#9911yescharacteristic
166C22×C149#41611yescharacteristic
167C22×C149#42111yescharacteristic
168C4×C149—22no—
169C4×C149—41no—
170C4×C149—41no—
171C4×C149—41no—
172C4×C149—41no—
173C4×C149—41no—
174C4×C149—81no—
175C4×C149—81no—
176C4×C149—81no—
177C2×C149—21no—
178C2×C149—21no—
179C2×C149—22no—
180C2×C149—41no—
181C2×C149—161no—
182C2×C149#151611yescharacteristic
183C2×C149#212111yescharacteristic
184C2×C149C2×#35511yescharacteristic
185#11852C14911yesmaximal, characteristic, direct product factor, Sylow
186C149#1185211yescharacteristic, direct product factor, Sylow
187#2591C2×C14911yescharacteristic
188#1821C2×C14911yescharacteristic, complemented
189C2×#324C2×C14911yescharacteristic, complemented
190#1353C2×C14912yescomplemented
191#1345C2×C14912yescomplemented
192C2×#121C4×C14911yescharacteristic
193C22×C4⋊C4C22×C14911yescharacteristic
194#407—21no—
195C2×C22⋊C8—21no—
196#400C4×C14911yescharacteristic
197#400C22×C14911yescharacteristic
198#394C4×C14911yescharacteristic
199#394C22×C14911yescharacteristic
200#388—21no—
201#388—21no—
202#386—21no—
203#386—21no—
204C4×C22⋊C4C4×C14911yescharacteristic
205#343—21no—
206#343C22×C14912yes—
207#324—21no—
208#324C22×C14912yes—
209C22×D4—21no—
210C22×D4C2×C4×C14911yescharacteristic
211C23×C4C2×C4×C14911yescharacteristic
212C23×C4D4×C14911yescharacteristic
213C23×C4D4×C14911yescharacteristic
214C2×M16—22no—
215C22×C8—41no—
216#121—41no—
217#121—41no—
218C2×C4⋊C4—41no—
219C2×C4⋊C4—41no—
220C2×C4⋊C4C2×C4×C14911yescharacteristic
221C2×C4⋊C4C2×C4×C14911yescharacteristic
222C2×C4⋊C4D4×C14911yescharacteristic
223C2×C4⋊C4D4×C14911yescharacteristic
224C2×C4⋊C4C23×C14911yescharacteristic
225C2×C22⋊C4—21no—
226C2×C22⋊C4—21no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4—21no—
229C2×C22⋊C4—21no—
230C2×C22⋊C4—21no—
231C2×C42—21no—
232C22⋊C8—22no—
233C22⋊C8—41no—
234C22⋊C8—41no—
235C22⋊C8—41no—
236#95—21no—
237#95—21no—
238#95—21no—
239#95—21no—
240#95C2×C4×C14911yescharacteristic
241#95C2×C4×C14911yescharacteristic
242C24—21no—
243C24C22⋊C4×C14911yescharacteristic
244C2×D4—41no—
245C2×D4—42no—
246C2×D4—42no—
247C2×D4—41no—
248C2×D4—41no—
249C2×D4—81no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—22no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—41no—
261C22×C4—81no—
262C22×C4—81no—
263C22×C4C22⋊C4×C14911yescharacteristic
264C22×C4C22⋊C4×C14911yescharacteristic
265C22×C4C22⋊C4×C14911yescharacteristic
266C22×C4C22×C4×C14911yescharacteristic
267C22×C4C2×D4×C14911yescharacteristic
268C22×C4C2×D4×C14911yescharacteristic
269M16—42no—
270M16—42no—
271C2×C8—42no—
272C2×C8—42no—
273C2×C8—82no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C22⋊C4—42no—
280C22⋊C4—42no—
281C22⋊C4—42no—
282C22⋊C4—42no—
283C22⋊C4—81no—
284C22⋊C4—81no—
285C42—81no—
286C23—21no—
287C23—21no—
288C23—22no—
289C23—41no—
290C23—41no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23—41no—
295C23—41no—
296C23—41no—
297C23#99×C14911yescharacteristic
298C23#99×C14911yescharacteristic
299C23C2×C22⋊C4×C14911yescharacteristic
300D4—82no—
301D4—82no—
302D4—82no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—81no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4#135×C14912yes—
332C8—82no—
333C8—82no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—42no—
342C22—42no—
343C22—81no—
344C22—81no—
345C22—81no—
346C22—81no—
347C22—81no—
348C22—81no—
349C22—81no—
350C22#355×C14912yes—
351C22C2×#99×C14911yescharacteristic
352C22#416×C14911yescharacteristic
353C22#421×C14911yescharacteristic
354C4—22no—
355C4—41no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—81no—
361C4—81no—
362C4—81no—
363C2—21no—
364C2—21no—
365C2—22no—
366C2—41no—
367C2—161no—
368C2#1516×C14911yescharacteristic
369C2#2121×C14911yescharacteristic
370C2C2×#355×C14911yescharacteristic
subgroupG/H
center, socleC22×C149C2×#99
commutatorC22×C4C22×C4×C149
Frattini, cosocleC2×C4⋊C4C23×C149
prime radicalC2×#121×C149C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C149 ◁ C24×C149 ◁ C22×C4⋊C4×C149 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1821×C149C2semidirect
3. C2×#324×C149C2semidirect
4. #1353×C149C2semidirect
5. #1345×C149C2semidirect
185. #11852C149direct (N × H)
186. C149#11852direct (N × H)
188. #1821C2×C149semidirect
189. C2×#324C2×C149semidirect
190. #1353C2×C149semidirect
191. #1345C2×C149semidirect

Maximal subgroups

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

subgroupindex
#2591×C1492
#1821×C1492
C2×#324×C1492
#1353×C1492
#1345×C1492
#11852149