Finite Group Databasebeta

← C149×#10103 #49189052

Subgroups — C149×#10103 #49189052

Order 38144.

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

normal subgroups only

This group has 458 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#3236×C149C211yesmaximal, characteristic
2#3165×C149C211yesmaximal, characteristic
3#2642×C149C211yesmaximal, characteristic
4#1556×C149C211yesmaximal, characteristic
5#1528×C149C211yesmaximal, characteristic
6#1506×C149C211yesmaximal, characteristic
7#1300×C149C211yesmaximal, characteristic
8#533×C149C2211yescharacteristic
9C2×C4⋊Q8×C149C2211yescharacteristic
10C2×#125×C149C2211yescharacteristic
11#501×C149—21no—
12#501×C149—22no—
13#500×C149—21no—
14#498×C149—21no—
15#491×C149—21no—
16#484×C149—21no—
17#483×C149—21no—
18#479×C149—22no—
19#432×C149C2211yescharacteristic
20#432×C149C2211yescharacteristic
21#428×C149—22no—
22C4×M16×C149C2211yescharacteristic
23#400×C149—22no—
24#400×C149—22no—
25#391×C149—21no—
26#391×C149—21no—
27#376×C149C2211yescharacteristic
28#332×C149—22no—
29#330×C149—22no—
30#328×C149—22no—
31C22×Q8×C149—21no—
32C2×M16×C149—21no—
33C4⋊Q8×C149—21no—
34C4⋊Q8×C149—21no—
35C4⋊Q8×C149—21no—
36C4⋊Q8×C149—21no—
37C4⋊Q8×C149D411yescharacteristic
38C4⋊Q8×C149D411yescharacteristic
39#125×C149—21no—
40#125×C149—21no—
41#125×C149—21no—
42#125×C149—21no—
43#125×C149—21no—
44C22⋊Q8×C149—21no—
45C22⋊Q8×C149—21no—
46C4×Q8×C149—21no—
47C4×Q8×C149—21no—
48#117×C149—21no—
49C2×C4⋊C4×C149—21no—
50C2×C4⋊C4×C149—21no—
51C2×C4⋊C4×C149—21no—
52C2×C4⋊C4×C149D411yescharacteristic
53C2×C4⋊C4×C149D411yescharacteristic
54C2×C4⋊C4×C149D412yes—
55C2×C42×C149—21no—
56C2×C42×C149C2311yescharacteristic
57#107×C149—24no—
58#107×C149—22no—
59#106×C149—24no—
60#106×C149—22no—
61C4⋊C8×C149—21no—
62C4⋊C8×C149D412yes—
63#103×C149—22no—
64#103×C149—22no—
65C22⋊C8×C149—21no—
66C22⋊C8×C149—21no—
67#97×C149—21no—
68#97×C149—21no—
69#97×C149D412yes—
70C4×C8×C149—21no—
71#95×C149—24no—
72#95×C149—24no—
73#95×C149—21no—
74#95×C149D412yes—
75C2×Q8×C149—21no—
76C2×Q8×C149—21no—
77C2×Q8×C149—44no—
78C2×Q8×C149—41no—
79C2×Q8×C149—41no—
80C22×C4×C149—22no—
81C22×C4×C149—21no—
82C22×C4×C149—21no—
83C22×C4×C149—22no—
84C22×C4×C149C2×D411yescharacteristic
85C22×C4×C149C2×D411yescharacteristic
86C22×C4×C149C2×D411yescharacteristic
87M16×C149—24no—
88C2×C8×C149—22no—
89C2×C8×C149—22no—
90C2×C8×C149—41no—
91C4⋊C4×C149—21no—
92C4⋊C4×C149—21no—
93C4⋊C4×C149—21no—
94C4⋊C4×C149—22no—
95C4⋊C4×C149—21no—
96C4⋊C4×C149—21no—
97C4⋊C4×C149—21no—
98C4⋊C4×C149—21no—
99C4⋊C4×C149—22no—
100C4⋊C4×C149—21no—
101C4⋊C4×C149—41no—
102C4⋊C4×C149—41no—
103C4⋊C4×C149—41no—
104C4⋊C4×C149—41no—
105C4⋊C4×C149—41no—
106C4⋊C4×C149—41no—
107C4⋊C4×C149—41no—
108C4⋊C4×C149—41no—
109C22⋊C4×C149—41no—
110C42×C149—42no—
111C42×C149—41no—
112C42×C149C2×D411yescharacteristic
113C42×C149C2×D411yescharacteristic
114C42×C149C2×D411yescharacteristic
115C42×C149#4111yescharacteristic
116C23×C149#12011yescharacteristic
117Q8×C149—42no—
118Q8×C149—81no—
119Q8×C149—82no—
120Q8×C149—82no—
121C2×C4×C149—22no—
122C2×C4×C149—22no—
123C2×C4×C149—41no—
124C2×C4×C149—42no—
125C2×C4×C149—42no—
126C2×C4×C149—42no—
127C2×C4×C149—44no—
128C2×C4×C149—41no—
129C2×C4×C149—41no—
130C2×C4×C149—41no—
131C2×C4×C149—41no—
132C2×C4×C149—42no—
133C2×C4×C149—42no—
134C2×C4×C149—42no—
135C2×C4×C149#12011yescharacteristic
136C2×C4×C149#12011yescharacteristic
137C2×C4×C149#12111yescharacteristic
138C2×C4×C149#12111yescharacteristic
139C2×C4×C149#12111yescharacteristic
140C2×C4×C149#12711yescharacteristic
141C8×C149—24no—
142C8×C149—42no—
143C8×C149—81no—
144C22×C149—21no—
145C22×C149—21no—
146C22×C149#39211yescharacteristic
147C22×C149#45612yes—
148C4×C149—21no—
149C4×C149—21no—
150C4×C149—21no—
151C4×C149—21no—
152C4×C149—21no—
153C4×C149—82no—
154C4×C149—82no—
155C4×C149—81no—
156C4×C149—81no—
157C4×C149—81no—
158C4×C149—81no—
159C4×C149#45412yes—
160C2×C149—22no—
161C2×C149#200311yescharacteristic
162C2×C149#200511yescharacteristic
163C2×C149#200911yescharacteristic
164#10103C14911yesmaximal, characteristic, direct product factor, Sylow
165C149#1010311yescharacteristic, direct product factor, Sylow
166#3236C2×C14911yescharacteristic
167#3165C2×C14911yescharacteristic
168#2642C2×C14911yescharacteristic
169#1556C2×C14911yescharacteristic
170#1528C2×C14911yescharacteristic
171#1506C2×C14911yescharacteristic
172#1300C2×C14911yescharacteristic
173#533C22×C14911yescharacteristic
174C2×C4⋊Q8C22×C14911yescharacteristic
175C2×#125C22×C14911yescharacteristic
176#501—21no—
177#501—22no—
178#500—21no—
179#498—21no—
180#491—21no—
181#484—21no—
182#483—21no—
183#479—22no—
184#432C22×C14911yescharacteristic
185#432C22×C14911yescharacteristic
186#428—22no—
187C4×M16C22×C14911yescharacteristic
188#400—22no—
189#400—22no—
190#391—21no—
191#391—21no—
192#376C22×C14911yescharacteristic
193#332—22no—
194#330—22no—
195#328—22no—
196C22×Q8—21no—
197C2×M16—21no—
198C4⋊Q8—21no—
199C4⋊Q8—21no—
200C4⋊Q8—21no—
201C4⋊Q8—21no—
202C4⋊Q8D4×C14911yescharacteristic
203C4⋊Q8D4×C14911yescharacteristic
204#125—21no—
205#125—21no—
206#125—21no—
207#125—21no—
208#125—21no—
209C22⋊Q8—21no—
210C22⋊Q8—21no—
211C4×Q8—21no—
212C4×Q8—21no—
213#117—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4D4×C14911yescharacteristic
218C2×C4⋊C4D4×C14911yescharacteristic
219C2×C4⋊C4D4×C14912yes—
220C2×C42—21no—
221C2×C42C23×C14911yescharacteristic
222#107—24no—
223#107—22no—
224#106—24no—
225#106—22no—
226C4⋊C8—21no—
227C4⋊C8D4×C14912yes—
228#103—22no—
229#103—22no—
230C22⋊C8—21no—
231C22⋊C8—21no—
232#97—21no—
233#97—21no—
234#97D4×C14912yes—
235C4×C8—21no—
236#95—24no—
237#95—24no—
238#95—21no—
239#95D4×C14912yes—
240C2×Q8—21no—
241C2×Q8—21no—
242C2×Q8—44no—
243C2×Q8—41no—
244C2×Q8—41no—
245C22×C4—22no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—22no—
249C22×C4C2×D4×C14911yescharacteristic
250C22×C4C2×D4×C14911yescharacteristic
251C22×C4C2×D4×C14911yescharacteristic
252M16—24no—
253C2×C8—22no—
254C2×C8—22no—
255C2×C8—41no—
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—22no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—22no—
265C4⋊C4—21no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C22⋊C4—41no—
275C42—42no—
276C42—41no—
277C42C2×D4×C14911yescharacteristic
278C42C2×D4×C14911yescharacteristic
279C42C2×D4×C14911yescharacteristic
280C42#41×C14911yescharacteristic
281C23#120×C14911yescharacteristic
282Q8—42no—
283Q8—81no—
284Q8—82no—
285Q8—82no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—41no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—44no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4#120×C14911yescharacteristic
301C2×C4#120×C14911yescharacteristic
302C2×C4#121×C14911yescharacteristic
303C2×C4#121×C14911yescharacteristic
304C2×C4#121×C14911yescharacteristic
305C2×C4#127×C14911yescharacteristic
306C8—24no—
307C8—42no—
308C8—81no—
309C22—21no—
310C22—21no—
311C22#392×C14911yescharacteristic
312C22#456×C14912yes—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—21no—
317C4—21no—
318C4—82no—
319C4—82no—
320C4—81no—
321C4—81no—
322C4—81no—
323C4—81no—
324C4#454×C14912yes—
325C2—22no—
326C2#2003×C14911yescharacteristic
327C2#2005×C14911yescharacteristic
328C2#2009×C14911yescharacteristic
subgroupG/H
center, socleC22×C149#392
commutator, Frattini, cosocleC2×C42C23×C149
prime radicalC23×C149#120
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C149 ◁ C2×C42×C149 ◁ G

Complements

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

NH ≅ G/Ntype
164. #10103C149direct (N × H)
165. C149#10103direct (N × H)

Maximal subgroups

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

subgroupindex
#3236×C1492
#3165×C1492
#2642×C1492
#1556×C1492
#1528×C1492
#1506×C1492
#1300×C1492
#10103149