Finite Group Databasebeta

← C149×#7803 #49186752

Subgroups — C149×#7803 #49186752

Order 38144.

338 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 94 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#2810×C149C211yesmaximal, characteristic
2#2099×C149C211yesmaximal, characteristic
3#2084×C149C211yesmaximal, characteristic
4#2083×C149C211yesmaximal, characteristic
5#1271×C149C211yesmaximal, characteristic
6#1271×C149C211yesmaximal, characteristic
7#1271×C149C211yesmaximal, characteristic
8C2×#107×C149—21no—
9C2×#106×C149—21no—
10#400×C149—21no—
11#400×C149—21no—
12#400×C149—21no—
13#389×C149C2211yescharacteristic
14#389×C149C2211yescharacteristic
15#389×C149C2211yescharacteristic
16#387×C149—21no—
17#387×C149—21no—
18#387×C149—21no—
19#384×C149C2211yescharacteristic
20#340×C149—21no—
21#340×C149—21no—
22#340×C149—21no—
23#340×C149—21no—
24#336×C149C2211yescharacteristic
25#336×C149C2211yescharacteristic
26#336×C149C2211yescharacteristic
27C22×C8×C149—21no—
28C22×C8×C149—21no—
29C22×C8×C149—21no—
30C2×C4⋊C4×C149—21no—
31C2×C4⋊C4×C149—21no—
32C2×C4⋊C4×C149—21no—
33C2×C4⋊C4×C149—21no—
34C2×C4⋊C4×C149—21no—
35C2×C4⋊C4×C149—21no—
36C2×C4⋊C4×C149D411yescharacteristic
37C2×C4⋊C4×C149D411yescharacteristic
38C2×C4⋊C4×C149D411yescharacteristic
39C2×C4⋊C4×C149D411yescharacteristic
40C2×C4⋊C4×C149D411yescharacteristic
41C2×C4⋊C4×C149D411yescharacteristic
42C2×C42×C149—21no—
43C2×C42×C149C2311yescharacteristic
44#107×C149—42no—
45#106×C149—42no—
46#95×C149—21no—
47#95×C149—21no—
48#95×C149—21no—
49#95×C149—21no—
50#95×C149—21no—
51#95×C149—21no—
52#95×C149—21no—
53#95×C149—21no—
54#95×C149—21no—
55#95×C149—21no—
56C22×C4×C149—21no—
57C22×C4×C149—21no—
58C22×C4×C149—21no—
59C22×C4×C149—21no—
60C22×C4×C149—21no—
61C22×C4×C149—21no—
62C22×C4×C149—41no—
63C22×C4×C149C2×D411yescharacteristic
64C22×C4×C149C2×D411yescharacteristic
65C22×C4×C149C2×D411yescharacteristic
66C2×C8×C149—22no—
67C2×C8×C149—22no—
68C2×C8×C149—41no—
69C2×C8×C149—41no—
70C2×C8×C149—41no—
71C2×C8×C149—41no—
72C2×C8×C149—41no—
73C2×C8×C149—41no—
74C2×C8×C149—41no—
75C4⋊C4×C149—21no—
76C4⋊C4×C149—21no—
77C4⋊C4×C149—21no—
78C4⋊C4×C149—21no—
79C4⋊C4×C149—21no—
80C4⋊C4×C149—21no—
81C4⋊C4×C149—41no—
82C4⋊C4×C149—41no—
83C4⋊C4×C149—41no—
84C4⋊C4×C149—42no—
85C4⋊C4×C149—41no—
86C4⋊C4×C149—41no—
87C4⋊C4×C149—41no—
88C4⋊C4×C149—41no—
89C4⋊C4×C149—41no—
90C4⋊C4×C149—41no—
91C4⋊C4×C149—41no—
92C4⋊C4×C149—41no—
93C4⋊C4×C149—41no—
94C4⋊C4×C149—41no—
95C42×C149—41no—
96C42×C149—81no—
97C23×C149#12011yescharacteristic
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—41no—
105C2×C4×C149—41no—
106C2×C4×C149—41no—
107C2×C4×C149—41no—
108C2×C4×C149—41no—
109C2×C4×C149—41no—
110C2×C4×C149—41no—
111C2×C4×C149—41no—
112C2×C4×C149—41no—
113C2×C4×C149—41no—
114C2×C4×C149—41no—
115C2×C4×C149—41no—
116C2×C4×C149—41no—
117C2×C4×C149—41no—
118C2×C4×C149—41no—
119C2×C4×C149—41no—
120C2×C4×C149—41no—
121C2×C4×C149—41no—
122C2×C4×C149—81no—
123C2×C4×C149—81no—
124C2×C4×C149—81no—
125C2×C4×C149#13511yescharacteristic
126C2×C4×C149#13511yescharacteristic
127C2×C4×C149#13511yescharacteristic
128C2×C4×C149AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C149AGL(1,ℤ/8)11yescharacteristic
130C2×C4×C149#13711yescharacteristic
131C8×C149—42no—
132C8×C149—42no—
133C8×C149—81no—
134C22×C149#44911yescharacteristic
135C22×C149#44911yescharacteristic
136C22×C149#45211yescharacteristic
137C22×C149#45411yescharacteristic
138C22×C149#45611yescharacteristic
139C22×C149#45611yescharacteristic
140C22×C149#45811yescharacteristic
141C4×C149—21no—
142C4×C149—21no—
143C4×C149—21no—
144C4×C149—21no—
145C4×C149—21no—
146C4×C149—21no—
147C4×C149—81no—
148C4×C149—81no—
149C4×C149—81no—
150C4×C149—81no—
151C4×C149—81no—
152C4×C149—81no—
153C4×C149—161no—
154C2×C149#160911yescharacteristic
155C2×C149#160911yescharacteristic
156C2×C149#161511yescharacteristic
157C2×C149#162811yescharacteristic
158C2×C149#165011yescharacteristic
159C2×C149#165211yescharacteristic
160C2×C149#166311yescharacteristic
161#7803C14911yesmaximal, characteristic, direct product factor, Sylow
162C149#780311yescharacteristic, direct product factor, Sylow
163#2810C2×C14911yescharacteristic
164#2099C2×C14911yescharacteristic
165#2084C2×C14911yescharacteristic
166#2083C2×C14911yescharacteristic
167#1271C2×C14911yescharacteristic
168#1271C2×C14911yescharacteristic
169#1271C2×C14911yescharacteristic
170C2×#107—21no—
171C2×#106—21no—
172#400—21no—
173#400—21no—
174#400—21no—
175#389C22×C14911yescharacteristic
176#389C22×C14911yescharacteristic
177#389C22×C14911yescharacteristic
178#387—21no—
179#387—21no—
180#387—21no—
181#384C22×C14911yescharacteristic
182#340—21no—
183#340—21no—
184#340—21no—
185#340—21no—
186#336C22×C14911yescharacteristic
187#336C22×C14911yescharacteristic
188#336C22×C14911yescharacteristic
189C22×C8—21no—
190C22×C8—21no—
191C22×C8—21no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4D4×C14911yescharacteristic
199C2×C4⋊C4D4×C14911yescharacteristic
200C2×C4⋊C4D4×C14911yescharacteristic
201C2×C4⋊C4D4×C14911yescharacteristic
202C2×C4⋊C4D4×C14911yescharacteristic
203C2×C4⋊C4D4×C14911yescharacteristic
204C2×C42—21no—
205C2×C42C23×C14911yescharacteristic
206#107—42no—
207#106—42no—
208#95—21no—
209#95—21no—
210#95—21no—
211#95—21no—
212#95—21no—
213#95—21no—
214#95—21no—
215#95—21no—
216#95—21no—
217#95—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—41no—
225C22×C4C2×D4×C14911yescharacteristic
226C22×C4C2×D4×C14911yescharacteristic
227C22×C4C2×D4×C14911yescharacteristic
228C2×C8—22no—
229C2×C8—22no—
230C2×C8—41no—
231C2×C8—41no—
232C2×C8—41no—
233C2×C8—41no—
234C2×C8—41no—
235C2×C8—41no—
236C2×C8—41no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—42no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C42—41no—
258C42—81no—
259C23#120×C14911yescharacteristic
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—81no—
285C2×C4—81no—
286C2×C4—81no—
287C2×C4#135×C14911yescharacteristic
288C2×C4#135×C14911yescharacteristic
289C2×C4#135×C14911yescharacteristic
290C2×C4AGL(1,ℤ/8)×C14911yescharacteristic
291C2×C4AGL(1,ℤ/8)×C14911yescharacteristic
292C2×C4#137×C14911yescharacteristic
293C8—42no—
294C8—42no—
295C8—81no—
296C22#449×C14911yescharacteristic
297C22#449×C14911yescharacteristic
298C22#452×C14911yescharacteristic
299C22#454×C14911yescharacteristic
300C22#456×C14911yescharacteristic
301C22#456×C14911yescharacteristic
302C22#458×C14911yescharacteristic
303C4—21no—
304C4—21no—
305C4—21no—
306C4—21no—
307C4—21no—
308C4—21no—
309C4—81no—
310C4—81no—
311C4—81no—
312C4—81no—
313C4—81no—
314C4—81no—
315C4—161no—
316C2#1609×C14911yescharacteristic
317C2#1609×C14911yescharacteristic
318C2#1615×C14911yescharacteristic
319C2#1628×C14911yescharacteristic
320C2#1650×C14911yescharacteristic
321C2#1652×C14911yescharacteristic
322C2#1663×C14911yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C149#120
commutator, Frattini, cosocleC2×C42C23×C149
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C149 ◁ C2×C42×C149 ◁ G

Complements

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

NH ≅ G/Ntype
161. #7803C149direct (N × H)
162. C149#7803direct (N × H)

Maximal subgroups

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

subgroupindex
#2810×C1492
#2099×C1492
#2084×C1492
#2083×C1492
#1271×C1492
#7803149