Finite Group Databasebeta

← C149×#19078 #49198027

Subgroups — C149×#19078 #49198027

Order 38144.

944 conjugacy classes of subgroups; only the 230 normal subgroups are shown.

normal subgroups only

This group has 944 conjugacy classes of subgroups — too many to draw. Only its 230 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#3550×C149C211yesmaximal, characteristic
2#3165×C149C212yesmaximal, complemented
3#3152×C149C211yesmaximal, characteristic
4#1660×C149C218yesmaximal, complemented
5#1526×C149C212yesmaximal, complemented
6#1525×C149C211yesmaximal, characteristic
7C2×#137×C149—22no—
8#563×C149C2214yes—
9#559×C149—21no—
10Q82×C149—21no—
11#556×C149—22no—
12D4×Q8×C149—22no—
13#542×C149—24no—
14#536×C149—22no—
15#533×C149C2212yes—
16#532×C149C2211yescharacteristic
17C2×C4⋊Q8×C149C2211yescharacteristic
18#501×C149C2218yes—
19#500×C149—22no—
20#498×C149—22no—
21#497×C149C2214yes—
22#494×C149—21no—
23#492×C149—21no—
24#428×C149—24no—
25C4×M16×C149C2212yes—
26C4×M16×C149C2211yescharacteristic
27#330×C149C2218yes—
28#329×C149C2214yes—
29C2×#41×C149D412yes—
30C22×Q8×C149—22no—
31C22×Q8×C149—21no—
32#137×C149—48no—
33C2×Q16×C149—24no—
34C2×SD16×C149—24no—
35C2×M16×C149—22no—
36C2×M16×C149—21no—
37C4⋊Q8×C149—24no—
38C4⋊Q8×C149—24no—
39C4⋊Q8×C149—22no—
40C4⋊Q8×C149—21no—
41C4⋊Q8×C149D411yescharacteristic
42C4⋊Q8×C149D412yes—
43C4⋊Q8×C149D412yes—
44C4⋊Q8×C149C2312yes—
45#127×C149D411yescharacteristic
46#126×C149—28no—
47#125×C149C2314yes—
48#124×C149—24no—
49#124×C149—24no—
50#124×C149C2312yes—
51#123×C149—24no—
52#123×C149—24no—
53C22⋊Q8×C149—24no—
54C22⋊Q8×C149—22no—
55C22⋊Q8×C149—22no—
56C22⋊Q8×C149—28no—
57#121×C149—22no—
58C4×Q8×C149—24no—
59C4×Q8×C149—22no—
60C4×Q8×C149—22no—
61C4×D4×C149—24no—
62C4×D4×C149—22no—
63#117×C149—22no—
64#117×C149D414yes—
65C2×C4⋊C4×C149—22no—
66C2×C42×C149C2311yescharacteristic
67#107×C149—28no—
68#106×C149—28no—
69#97×C149C2312yes—
70#97×C149C2314yes—
71C4×C8×C149—21no—
72C4×C8×C149—22no—
73#41×C149—44no—
74C2×Q8×C149—24no—
75C2×Q8×C149—22no—
76C2×Q8×C149—22no—
77C2×Q8×C149—22no—
78C2×Q8×C149—44no—
79C2×Q8×C149—41no—
80C2×Q8×C149—84no—
81C2×Q8×C149C2×D412yes—
82C2×D4×C149—22no—
83C2×D4×C149—22no—
84C2×D4×C149C2×D412yes—
85C22×C4×C149—24no—
86C22×C4×C149—22no—
87C22×C4×C149—41no—
88C22×C4×C149C2×D412yes—
89C22×C4×C149C2×D411yescharacteristic
90Q16×C149—48no—
91SD16×C149—48no—
92M16×C149—28no—
93M16×C149—24no—
94C2×C8×C149—24no—
95C2×C8×C149—22no—
96C4⋊C4×C149—28no—
97C4⋊C4×C149—22no—
98C4⋊C4×C149—22no—
99C4⋊C4×C149—22no—
100C4⋊C4×C149—24no—
101C4⋊C4×C149—24no—
102C4⋊C4×C149—24no—
103C4⋊C4×C149—42no—
104C4⋊C4×C149C2×D414yes—
105C4⋊C4×C149C2×D414yes—
106C22⋊C4×C149—24no—
107C22⋊C4×C149—28no—
108C22⋊C4×C149—24no—
109C22⋊C4×C149—24no—
110C42×C149—24no—
111C42×C149—24no—
112C42×C149C2×D412yes—
113C42×C149C2×D411yescharacteristic
114C42×C149C2411yescharacteristic
115C23×C149—22no—
116C23×C149#12011yescharacteristic
117Q8×C149—42no—
118Q8×C149—44no—
119Q8×C149—44no—
120Q8×C149—44no—
121Q8×C149—84no—
122Q8×C149—82no—
123D4×C149—42no—
124D4×C149—44no—
125D4×C149—82no—
126C2×C4×C149—22no—
127C2×C4×C149—24no—
128C2×C4×C149—24no—
129C2×C4×C149—22no—
130C2×C4×C149—24no—
131C2×C4×C149—44no—
132C2×C4×C149—42no—
133C2×C4×C149—84no—
134C2×C4×C149—82no—
135C2×C4×C149#12011yescharacteristic
136C2×C4×C149#12012yes—
137C2×C4×C149C22×D412yes—
138C2×C4×C149C22×D411yescharacteristic
139C8×C149—28no—
140C8×C149—24no—
141C22×C149—21no—
142C22×C149—22no—
143C22×C149—42no—
144C22×C149—44no—
145C22×C149C2×#12011yescharacteristic
146C4×C149—21no—
147C4×C149—22no—
148C4×C149—42no—
149C4×C149—44no—
150C4×C149—44no—
151C4×C149—82no—
152C4×C149#45312yes—
153C4×C149#45614yes—
154C2×C149—41no—
155C2×C149—82no—
156C2×C149C2×#45311yescharacteristic
157C2×C149C2×#45612yes—
158#19078C14911yesmaximal, characteristic, direct product factor, Sylow
159C149#1907811yescharacteristic, direct product factor, Sylow
160#3550C2×C14911yescharacteristic
161#3165C2×C14912yescomplemented
162#3152C2×C14911yescharacteristic
163#1660C2×C14918yescomplemented
164#1526C2×C14912yescomplemented
165#1525C2×C14911yescharacteristic
166C2×#137—22no—
167#563C22×C14914yes—
168#559—21no—
169Q82—21no—
170#556—22no—
171D4×Q8—22no—
172#542—24no—
173#536—22no—
174#533C22×C14912yes—
175#532C22×C14911yescharacteristic
176C2×C4⋊Q8C22×C14911yescharacteristic
177#501C22×C14918yes—
178#500—22no—
179#498—22no—
180#497C22×C14914yes—
181#494—21no—
182#492—21no—
183#428—24no—
184C4×M16C22×C14911yescharacteristic
185C4×M16C22×C14912yes—
186#330C22×C14918yes—
187#329C22×C14914yes—
188C2×#41D4×C14912yes—
189C22×Q8—22no—
190C22×Q8—21no—
191#137—48no—
192C2×Q16—24no—
193C2×SD16—24no—
194C2×M16—21no—
195C2×M16—22no—
196C4⋊Q8—24no—
197C4⋊Q8—24no—
198C4⋊Q8—22no—
199C4⋊Q8—21no—
200C4⋊Q8D4×C14911yescharacteristic
201C4⋊Q8D4×C14912yes—
202C4⋊Q8D4×C14912yes—
203C4⋊Q8C23×C14912yes—
204#127D4×C14911yescharacteristic
205#126—28no—
206#125C23×C14914yes—
207#124—24no—
208#124—24no—
209#124C23×C14912yes—
210#123—24no—
211#123—24no—
212C22⋊Q8—24no—
213C22⋊Q8—22no—
214C22⋊Q8—22no—
215C22⋊Q8—28no—
216#121—22no—
217C4×Q8—24no—
218C4×Q8—22no—
219C4×Q8—22no—
220C4×D4—24no—
221C4×D4—22no—
222#117—22no—
223#117D4×C14914yes—
224C2×C4⋊C4—22no—
225C2×C42C23×C14911yescharacteristic
226#107—28no—
227#106—28no—
228#97C23×C14914yes—
229#97C23×C14912yes—
230C4×C8—21no—
231C4×C8—22no—
232#41—44no—
233C2×Q8—24no—
234C2×Q8—22no—
235C2×Q8—22no—
236C2×Q8—22no—
237C2×Q8—44no—
238C2×Q8—41no—
239C2×Q8—84no—
240C2×Q8C2×D4×C14912yes—
241C2×D4—22no—
242C2×D4—22no—
243C2×D4C2×D4×C14912yes—
244C22×C4—24no—
245C22×C4—22no—
246C22×C4—41no—
247C22×C4C2×D4×C14912yes—
248C22×C4C2×D4×C14911yescharacteristic
249Q16—48no—
250SD16—48no—
251M16—24no—
252M16—28no—
253C2×C8—24no—
254C2×C8—22no—
255C4⋊C4—28no—
256C4⋊C4—22no—
257C4⋊C4—22no—
258C4⋊C4—22no—
259C4⋊C4—24no—
260C4⋊C4—24no—
261C4⋊C4—24no—
262C4⋊C4—42no—
263C4⋊C4C2×D4×C14914yes—
264C4⋊C4C2×D4×C14914yes—
265C22⋊C4—24no—
266C22⋊C4—28no—
267C22⋊C4—24no—
268C22⋊C4—24no—
269C42—24no—
270C42—24no—
271C42C2×D4×C14912yes—
272C42C2×D4×C14911yescharacteristic
273C42C24×C14911yescharacteristic
274C23—22no—
275C23#120×C14911yescharacteristic
276Q8—42no—
277Q8—44no—
278Q8—44no—
279Q8—44no—
280Q8—84no—
281Q8—82no—
282D4—42no—
283D4—44no—
284D4—82no—
285C2×C4—22no—
286C2×C4—24no—
287C2×C4—24no—
288C2×C4—22no—
289C2×C4—24no—
290C2×C4—44no—
291C2×C4—42no—
292C2×C4—84no—
293C2×C4—82no—
294C2×C4#120×C14911yescharacteristic
295C2×C4#120×C14912yes—
296C2×C4C22×D4×C14912yes—
297C2×C4C22×D4×C14911yescharacteristic
298C8—28no—
299C8—24no—
300C22—21no—
301C22—22no—
302C22—42no—
303C22—44no—
304C22C2×#120×C14911yescharacteristic
305C4—21no—
306C4—22no—
307C4—42no—
308C4—44no—
309C4—44no—
310C4—82no—
311C4#453×C14912yes—
312C4#456×C14914yes—
313C2—41no—
314C2—82no—
315C2C2×#453×C14911yescharacteristic
316C2C2×#456×C14912yes—
subgroupG/H
center, socleC22×C149C2×#120
commutator, Frattini, cosocleC42C24×C149
prime radical#532×C149C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C149 ◁ C2×C42×C149 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3165×C149C2semidirect
4. #1660×C149C2semidirect
5. #1526×C149C2semidirect
158. #19078C149direct (N × H)
159. C149#19078direct (N × H)
161. #3165C2×C149semidirect
163. #1660C2×C149semidirect
164. #1526C2×C149semidirect

Maximal subgroups

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

subgroupindex
#3550×C1492
#3165×C1492
#3152×C1492
#1660×C1492
#1526×C1492
#1525×C1492
#19078149