Finite Group Databasebeta

← C149×#11902 #49190851

Subgroups — C149×#11902 #49190851

Order 38144.

452 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 114 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#2564×C149C211yesmaximal, characteristic
2#1799×C149C211yesmaximal, characteristic
3#1460×C149C211yesmaximal, characteristic
4#1352×C149C212yesmaximal, complemented
5#1351×C149C212yesmaximal, complemented
6C2×C22⋊Q8×C149C411yescharacteristic, complemented
7C2×C4×D4×C149C2211yescharacteristic
8#431×C149—21no—
9C2×#99×C149—21no—
10#400×C149C411yescharacteristic, complemented
11#399×C149C2211yescharacteristic
12#395×C149C411yescharacteristic, complemented
13#393×C149C2211yescharacteristic
14#387×C149—21no—
15#386×C149—21no—
16#385×C149—21no—
17#380×C149—21no—
18#380×C149—21no—
19C2×#95×C149C411yescharacteristic, complemented
20#342×C149C2212yes—
21#323×C149—21no—
22#323×C149C2212yes—
23C22×Q8×C149C2×C411yescharacteristic
24C22×D4×C149D411yescharacteristic
25C23×C4×C149—21no—
26C23×C4×C149C2×C411yescharacteristic
27C23×C4×C149D411yescharacteristic
28C22⋊Q8×C149—41no—
29C22⋊Q8×C149—41no—
30C4×D4×C149—41no—
31C4×D4×C149—41no—
32C2×C4⋊C4×C149—21no—
33C2×C4⋊C4×C149—21no—
34C2×C4⋊C4×C149—21no—
35C2×C4⋊C4×C149—41no—
36C2×C4⋊C4×C149C2×C411yescharacteristic
37C2×C4⋊C4×C149C2×C411yescharacteristic
38C2×C22⋊C4×C149—21no—
39C2×C22⋊C4×C149—21no—
40C2×C22⋊C4×C149—22no—
41C2×C22⋊C4×C149—21no—
42C2×C22⋊C4×C149D411yescharacteristic
43C2×C22⋊C4×C149C2311yescharacteristic
44C2×C42×C149D411yescharacteristic
45C4⋊C8×C149—41no—
46#99×C149—42no—
47C22⋊C8×C149—22no—
48C4×C8×C149—41no—
49#95×C149—21no—
50#95×C149—21no—
51#95×C149—21no—
52#95×C149—21no—
53#95×C149—21no—
54#95×C149—41no—
55#95×C149C2×C411yescharacteristic
56#95×C149C2×C411yescharacteristic
57C24×C149C22⋊C411yescharacteristic
58C24×C149C2×D411yescharacteristic
59C2×Q8×C149—41no—
60C2×Q8×C149—81no—
61C2×D4×C149—41no—
62C2×D4×C149—41no—
63C2×D4×C149SD1612yes—
64C2×D4×C149Q1612yes—
65C22×C4×C149—21no—
66C22×C4×C149—21no—
67C22×C4×C149—21no—
68C22×C4×C149—21no—
69C22×C4×C149—21no—
70C22×C4×C149—21no—
71C22×C4×C149—21no—
72C22×C4×C149—21no—
73C22×C4×C149—42no—
74C22×C4×C149—42no—
75C22×C4×C149—42no—
76C22×C4×C149—81no—
77C22×C4×C149—81no—
78C22×C4×C149—81no—
79C22×C4×C149C22⋊C411yescharacteristic
80C22×C4×C149C22⋊C411yescharacteristic
81C22×C4×C149C22⋊C411yescharacteristic
82C22×C4×C149C22×C411yescharacteristic
83C22×C4×C149C2×D411yescharacteristic
84C2×C8×C149—42no—
85C4⋊C4×C149—41no—
86C4⋊C4×C149—42no—
87C4⋊C4×C149—41no—
88C4⋊C4×C149—41no—
89C4⋊C4×C149—41no—
90C4⋊C4×C149—81no—
91C4⋊C4×C149—82no—
92C22⋊C4×C149—41no—
93C22⋊C4×C149—41no—
94C22⋊C4×C149—42no—
95C22⋊C4×C149—42no—
96C22⋊C4×C149—42no—
97C22⋊C4×C149—42no—
98C22⋊C4×C149—81no—
99C42×C149—21no—
100C42×C149—21no—
101C23×C149—21no—
102C23×C149—21no—
103C23×C149—21no—
104C23×C149—21no—
105C23×C149—41no—
106C23×C149—41no—
107C23×C149—41no—
108C23×C149—41no—
109C23×C149#10312yes—
110C23×C149C2×C22⋊C411yescharacteristic
111C23×C149C2×SD1611yescharacteristic
112C23×C149C2×Q1611yescharacteristic
113Q8×C149—82no—
114D4×C149—42no—
115D4×C149—42no—
116C2×C4×C149—21no—
117C2×C4×C149—21no—
118C2×C4×C149—22no—
119C2×C4×C149—21no—
120C2×C4×C149—21no—
121C2×C4×C149—21no—
122C2×C4×C149—41no—
123C2×C4×C149—42no—
124C2×C4×C149—41no—
125C2×C4×C149—41no—
126C2×C4×C149—41no—
127C2×C4×C149—41no—
128C2×C4×C149—41no—
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—81no—
139C2×C4×C149—81no—
140C2×C4×C149—81no—
141C2×C4×C149—84no—
142C2×C4×C149—82no—
143C2×C4×C149—82no—
144C2×C4×C149—82no—
145C2×C4×C149#9911yescharacteristic
146C2×C4×C149#9911yescharacteristic
147C2×C4×C149#10312yes—
148C8×C149—82no—
149C22×C149—21no—
150C22×C149—21no—
151C22×C149—21no—
152C22×C149—22no—
153C22×C149—21no—
154C22×C149—42no—
155C22×C149—41no—
156C22×C149—41no—
157C22×C149—42no—
158C22×C149—41no—
159C22×C149—41no—
160C22×C149—41no—
161C22×C149—41no—
162C22×C149—81no—
163C22×C149C2×#9911yescharacteristic
164C22×C149C2×#10311yescharacteristic
165C22×C149#42111yescharacteristic
166C4×C149—21no—
167C4×C149—21no—
168C4×C149—22no—
169C4×C149—42no—
170C4×C149—41no—
171C4×C149—41no—
172C4×C149—41no—
173C4×C149—81no—
174C4×C149—81no—
175C4×C149—81no—
176C4×C149—162no—
177C2×C149—21no—
178C2×C149—21no—
179C2×C149—41no—
180C2×C149—42no—
181C2×C149—41no—
182C2×C149#152011yescharacteristic
183C2×C149#212111yescharacteristic
184C2×C149#212611yescharacteristic
185#11902C14911yesmaximal, characteristic, direct product factor, Sylow
186C149#1190211yescharacteristic, direct product factor, Sylow
187#2564C2×C14911yescharacteristic
188#1799C2×C14911yescharacteristic
189#1460C2×C14911yescharacteristic
190#1352C2×C14912yescomplemented
191#1351C2×C14912yescomplemented
192C2×C22⋊Q8C4×C14911yescharacteristic, complemented
193C2×C4×D4C22×C14911yescharacteristic
194#431—21no—
195C2×#99—21no—
196#400C4×C14911yescharacteristic, complemented
197#399C22×C14911yescharacteristic
198#395C4×C14911yescharacteristic, complemented
199#393C22×C14911yescharacteristic
200#387—21no—
201#386—21no—
202#385—21no—
203#380—21no—
204#380—21no—
205C2×#95C4×C14911yescharacteristic, complemented
206#342C22×C14912yes—
207#323—21no—
208#323C22×C14912yes—
209C22×Q8C2×C4×C14911yescharacteristic
210C22×D4D4×C14911yescharacteristic
211C23×C4—21no—
212C23×C4C2×C4×C14911yescharacteristic
213C23×C4D4×C14911yescharacteristic
214C22⋊Q8—41no—
215C22⋊Q8—41no—
216C4×D4—41no—
217C4×D4—41no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—41no—
222C2×C4⋊C4C2×C4×C14911yescharacteristic
223C2×C4⋊C4C2×C4×C14911yescharacteristic
224C2×C22⋊C4—21no—
225C2×C22⋊C4—21no—
226C2×C22⋊C4—22no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4D4×C14911yescharacteristic
229C2×C22⋊C4C23×C14911yescharacteristic
230C2×C42D4×C14911yescharacteristic
231C4⋊C8—41no—
232#99—42no—
233C22⋊C8—22no—
234C4×C8—41no—
235#95—21no—
236#95—21no—
237#95—21no—
238#95—21no—
239#95—21no—
240#95—41no—
241#95C2×C4×C14911yescharacteristic
242#95C2×C4×C14911yescharacteristic
243C24C22⋊C4×C14911yescharacteristic
244C24C2×D4×C14911yescharacteristic
245C2×Q8—41no—
246C2×Q8—81no—
247C2×D4—41no—
248C2×D4—41no—
249C2×D4SD16×C14912yes—
250C2×D4Q16×C14912yes—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—42no—
260C22×C4—42no—
261C22×C4—42no—
262C22×C4—81no—
263C22×C4—81no—
264C22×C4—81no—
265C22×C4C22⋊C4×C14911yescharacteristic
266C22×C4C22⋊C4×C14911yescharacteristic
267C22×C4C22⋊C4×C14911yescharacteristic
268C22×C4C22×C4×C14911yescharacteristic
269C22×C4C2×D4×C14911yescharacteristic
270C2×C8—42no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—42no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—81no—
277C4⋊C4—82no—
278C22⋊C4—41no—
279C22⋊C4—41no—
280C22⋊C4—42no—
281C22⋊C4—42no—
282C22⋊C4—42no—
283C22⋊C4—42no—
284C22⋊C4—81no—
285C42—21no—
286C42—21no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23—41no—
295C23#103×C14912yes—
296C23C2×C22⋊C4×C14911yescharacteristic
297C23C2×SD16×C14911yescharacteristic
298C23C2×Q16×C14911yescharacteristic
299Q8—82no—
300D4—42no—
301D4—42no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—22no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—41no—
309C2×C4—42no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
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—81no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4—84no—
328C2×C4—82no—
329C2×C4—82no—
330C2×C4—82no—
331C2×C4#99×C14911yescharacteristic
332C2×C4#99×C14911yescharacteristic
333C2×C4#103×C14912yes—
334C8—82no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—22no—
339C22—21no—
340C22—42no—
341C22—41no—
342C22—41no—
343C22—42no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—81no—
349C22C2×#99×C14911yescharacteristic
350C22C2×#103×C14911yescharacteristic
351C22#421×C14911yescharacteristic
352C4—22no—
353C4—21no—
354C4—21no—
355C4—42no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—81no—
360C4—81no—
361C4—81no—
362C4—162no—
363C2—21no—
364C2—21no—
365C2—41no—
366C2—42no—
367C2—41no—
368C2#1520×C14911yescharacteristic
369C2#2121×C14911yescharacteristic
370C2#2126×C14911yescharacteristic
subgroupG/H
center, socleC22×C149C2×#99
commutatorC22×C4C22×C4×C149
Frattini, cosocleC2×C22⋊C4C23×C149
prime radicalC22×D4×C149D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C149 ◁ C22×C4×C149 ◁ C2×C4×D4×C149 ◁ G

Complements

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

NH ≅ G/Ntype
4. #1352×C149C2semidirect
5. #1351×C149C2semidirect
6. C2×C22⋊Q8×C149C4semidirect
10. #400×C149C4semidirect
12. #395×C149C4semidirect
19. C2×#95×C149C4semidirect
185. #11902C149direct (N × H)
186. C149#11902direct (N × H)
190. #1352C2×C149semidirect
191. #1351C2×C149semidirect
192. C2×C22⋊Q8C4×C149semidirect
196. #400C4×C149semidirect
198. #395C4×C149semidirect
205. C2×#95C4×C149semidirect

Maximal subgroups

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

subgroupindex
#2564×C1492
#1799×C1492
#1460×C1492
#1352×C1492
#1351×C1492
#11902149