Finite Group Databasebeta

← C149×#10275 #49189224

Subgroups — C149×#10275 #49189224

Order 38144.

562 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#487×C149C211yesmaximal, characteristic, complemented
2C2×#476×C149C211yesmaximal, characteristic
3C2×#474×C149C211yesmaximal, characteristic
4#1954×C149C211yesmaximal, characteristic
5C2×#333×C149C211yesmaximal, characteristic, complemented
6C2×#332×C149C211yesmaximal, characteristic, complemented
7#1277×C149C211yesmaximal, characteristic, complemented
8C2×C4⋊Q8×C149C2211yescharacteristic
9C2×C4⋊Q8×C149C2211yescharacteristic
10C2×C4×D4×C149C2211yescharacteristic
11#487×C149—22no—
12#487×C149—22no—
13#476×C149—22no—
14#476×C149—22no—
15#474×C149—22no—
16#474×C149—22no—
17C2×#107×C149—21no—
18C2×#106×C149—21no—
19C2×C4⋊C8×C149C2211yescharacteristic
20C2×C4⋊C8×C149C2211yescharacteristic
21C2×C4⋊C8×C149C2211yescharacteristic
22C2×#103×C149—22no—
23C2×#102×C149—21no—
24C2×#102×C149—21no—
25C2×C22⋊C8×C149—22no—
26C2×C4×C8×C149C2211yescharacteristic
27#333×C149—22no—
28#332×C149—22no—
29C22×Q8×C149—21no—
30C22×Q8×C149—21no—
31C22×D4×C149D411yescharacteristic
32C23×C4×C149—21no—
33C22×C8×C149—21no—
34C22×C8×C149—21no—
35C22×C8×C149—21no—
36C22×C8×C149D412yes—
37C4⋊Q8×C149—21no—
38C4⋊Q8×C149—21no—
39C4⋊Q8×C149—21no—
40C4⋊Q8×C149—21no—
41C4⋊Q8×C149—21no—
42C4⋊Q8×C149—21no—
43C4⋊Q8×C149D412yes—
44C4⋊Q8×C149D412yes—
45C4×D4×C149—21no—
46C4×D4×C149—21no—
47C4×D4×C149—21no—
48C4×D4×C149—21no—
49C2×C4⋊C4×C149—21no—
50C2×C4⋊C4×C149—21no—
51C2×C4⋊C4×C149—21no—
52C2×C4⋊C4×C149—21no—
53C2×C4⋊C4×C149D411yescharacteristic
54C2×C22⋊C4×C149—21no—
55C2×C42×C149C2311yescharacteristic
56#107×C149—24no—
57#106×C149—24no—
58C4⋊C8×C149—21no—
59C4⋊C8×C149—21no—
60C4⋊C8×C149—21no—
61C4⋊C8×C149—21no—
62C4⋊C8×C149D412yes—
63C4⋊C8×C149D412yes—
64#103×C149—28no—
65#102×C149—24no—
66#102×C149—24no—
67C22⋊C8×C149—44no—
68C4×C8×C149—21no—
69C4×C8×C149—21no—
70C24×C149—21no—
71C2×Q8×C149—22no—
72C2×Q8×C149—22no—
73C2×Q8×C149—41no—
74C2×Q8×C149—41no—
75C2×Q8×C149—42no—
76C2×Q8×C149—42no—
77C2×Q8×C149—82no—
78C2×D4×C149—21no—
79C2×D4×C149—21no—
80C2×D4×C149—21no—
81C2×D4×C149—21no—
82C2×D4×C149—21no—
83C2×D4×C149Q1612yes—
84C22×C4×C149—21no—
85C22×C4×C149—41no—
86C22×C4×C149—41no—
87C22×C4×C149—41no—
88C22×C4×C149—41no—
89C22×C4×C149—42no—
90C22×C4×C149—42no—
91C22×C4×C149C2×D411yescharacteristic
92C22×C4×C149C2×D411yescharacteristic
93C22×C4×C149#4111yescharacteristic
94C2×C8×C149—22no—
95C2×C8×C149—22no—
96C2×C8×C149—22no—
97C2×C8×C149—22no—
98C2×C8×C149—22no—
99C2×C8×C149—41no—
100C2×C8×C149—41no—
101C2×C8×C149—41no—
102C2×C8×C149—41no—
103C2×C8×C149—41no—
104C2×C8×C149—42no—
105C4⋊C4×C149—22no—
106C4⋊C4×C149—22no—
107C4⋊C4×C149—22no—
108C4⋊C4×C149—21no—
109C4⋊C4×C149—21no—
110C4⋊C4×C149—22no—
111C4⋊C4×C149—41no—
112C4⋊C4×C149—41no—
113C4⋊C4×C149—41no—
114C4⋊C4×C149—41no—
115C22⋊C4×C149—41no—
116C22⋊C4×C149—41no—
117C42×C149C2×D411yescharacteristic
118C42×C149C2×D411yescharacteristic
119C42×C149C2×D411yescharacteristic
120C42×C149C2×D411yescharacteristic
121C23×C149—22no—
122C23×C149—41no—
123C23×C149—42no—
124C23×C149—41no—
125C23×C149—42no—
126C23×C149#12111yescharacteristic
127Q8×C149—44no—
128Q8×C149—82no—
129Q8×C149—82no—
130Q8×C149—81no—
131Q8×C149—81no—
132D4×C149—22no—
133D4×C149—22no—
134D4×C149—41no—
135D4×C149—41no—
136C2×C4×C149—22no—
137C2×C4×C149—41no—
138C2×C4×C149—42no—
139C2×C4×C149—42no—
140C2×C4×C149—42no—
141C2×C4×C149—82no—
142C2×C4×C149—82no—
143C2×C4×C149—82no—
144C2×C4×C149—81no—
145C2×C4×C149—81no—
146C2×C4×C149#12011yescharacteristic
147C2×C4×C149#12011yescharacteristic
148C2×C4×C149#12011yescharacteristic
149C2×C4×C149#12111yescharacteristic
150C2×C4×C149#12111yescharacteristic
151C2×C4×C149#12711yescharacteristic
152C2×C4×C149C2×Q1611yescharacteristic
153C2×C4×C149#13512yes—
154C2×C4×C149#13511yescharacteristic
155C2×C4×C149AGL(1,ℤ/8)12yes—
156C2×C4×C149#13711yescharacteristic
157C2×C4×C149#13711yescharacteristic
158C8×C149—42no—
159C8×C149—42no—
160C8×C149—42no—
161C8×C149—81no—
162C22×C149—44no—
163C22×C149—42no—
164C22×C149—82no—
165C22×C149—81no—
166C22×C149—81no—
167C22×C149#39211yescharacteristic
168C22×C149#46312yes—
169C22×C149#46711yescharacteristic
170C22×C149#47011yescharacteristic
171C22×C149#47112yes—
172C4×C149—21no—
173C4×C149—21no—
174C4×C149—81no—
175C4×C149—82no—
176C4×C149—82no—
177C4×C149#44912yes—
178C4×C149#45111yescharacteristic
179C4×C149#45111yescharacteristic
180C4×C149#45211yescharacteristic
181C4×C149#45211yescharacteristic
182C4×C149#49511yescharacteristic
183C4×C149#49611yescharacteristic
184C2×C149—82no—
185C2×C149#168312yes—
186C2×C149#170312yes—
187C2×C149#200111yescharacteristic
188C2×C149#201211yescharacteristic
189C2×C149#201911yescharacteristic
190#10275C14911yesmaximal, characteristic, direct product factor, Sylow
191C149#1027511yescharacteristic, direct product factor, Sylow
192C2×#487C2×C14911yescharacteristic, complemented
193C2×#476C2×C14911yescharacteristic
194C2×#474C2×C14911yescharacteristic
195#1954C2×C14911yescharacteristic
196C2×#333C2×C14911yescharacteristic, complemented
197C2×#332C2×C14911yescharacteristic, complemented
198#1277C2×C14911yescharacteristic, complemented
199C2×C4⋊Q8C22×C14911yescharacteristic
200C2×C4⋊Q8C22×C14911yescharacteristic
201C2×C4×D4C22×C14911yescharacteristic
202#487—22no—
203#487—22no—
204#476—22no—
205#476—22no—
206#474—22no—
207#474—22no—
208C2×#107—21no—
209C2×#106—21no—
210C2×C4⋊C8C22×C14911yescharacteristic
211C2×C4⋊C8C22×C14911yescharacteristic
212C2×C4⋊C8C22×C14911yescharacteristic
213C2×#103—22no—
214C2×#102—21no—
215C2×#102—21no—
216C2×C22⋊C8—22no—
217C2×C4×C8C22×C14911yescharacteristic
218#333—22no—
219#332—22no—
220C22×Q8—21no—
221C22×Q8—21no—
222C22×D4D4×C14911yescharacteristic
223C23×C4—21no—
224C22×C8—21no—
225C22×C8—21no—
226C22×C8—21no—
227C22×C8D4×C14912yes—
228C4⋊Q8—21no—
229C4⋊Q8—21no—
230C4⋊Q8—21no—
231C4⋊Q8—21no—
232C4⋊Q8—21no—
233C4⋊Q8—21no—
234C4⋊Q8D4×C14912yes—
235C4⋊Q8D4×C14912yes—
236C4×D4—21no—
237C4×D4—21no—
238C4×D4—21no—
239C4×D4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4D4×C14911yescharacteristic
245C2×C22⋊C4—21no—
246C2×C42C23×C14911yescharacteristic
247#107—24no—
248#106—24no—
249C4⋊C8—21no—
250C4⋊C8—21no—
251C4⋊C8—21no—
252C4⋊C8—21no—
253C4⋊C8D4×C14912yes—
254C4⋊C8D4×C14912yes—
255#103—28no—
256#102—24no—
257#102—24no—
258C22⋊C8—44no—
259C4×C8—21no—
260C4×C8—21no—
261C24—21no—
262C2×Q8—22no—
263C2×Q8—22no—
264C2×Q8—41no—
265C2×Q8—41no—
266C2×Q8—42no—
267C2×Q8—42no—
268C2×Q8—82no—
269C2×D4—21no—
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4Q16×C14912yes—
275C22×C4—21no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—42no—
281C22×C4—42no—
282C22×C4C2×D4×C14911yescharacteristic
283C22×C4C2×D4×C14911yescharacteristic
284C22×C4#41×C14911yescharacteristic
285C2×C8—22no—
286C2×C8—22no—
287C2×C8—22no—
288C2×C8—22no—
289C2×C8—22no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—41no—
295C2×C8—42no—
296C4⋊C4—22no—
297C4⋊C4—22no—
298C4⋊C4—22no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—22no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C42C2×D4×C14911yescharacteristic
309C42C2×D4×C14911yescharacteristic
310C42C2×D4×C14911yescharacteristic
311C42C2×D4×C14911yescharacteristic
312C23—22no—
313C23—41no—
314C23—42no—
315C23—41no—
316C23—42no—
317C23#121×C14911yescharacteristic
318Q8—44no—
319Q8—82no—
320Q8—82no—
321Q8—81no—
322Q8—81no—
323D4—22no—
324D4—22no—
325D4—41no—
326D4—41no—
327C2×C4—22no—
328C2×C4—41no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—82no—
333C2×C4—82no—
334C2×C4—82no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4#120×C14911yescharacteristic
338C2×C4#120×C14911yescharacteristic
339C2×C4#120×C14911yescharacteristic
340C2×C4#121×C14911yescharacteristic
341C2×C4#121×C14911yescharacteristic
342C2×C4#127×C14911yescharacteristic
343C2×C4C2×Q16×C14911yescharacteristic
344C2×C4#135×C14912yes—
345C2×C4#135×C14911yescharacteristic
346C2×C4AGL(1,ℤ/8)×C14912yes—
347C2×C4#137×C14911yescharacteristic
348C2×C4#137×C14911yescharacteristic
349C8—42no—
350C8—42no—
351C8—42no—
352C8—81no—
353C22—44no—
354C22—42no—
355C22—82no—
356C22—81no—
357C22—81no—
358C22#392×C14911yescharacteristic
359C22#463×C14912yes—
360C22#467×C14911yescharacteristic
361C22#470×C14911yescharacteristic
362C22#471×C14912yes—
363C4—21no—
364C4—21no—
365C4—81no—
366C4—82no—
367C4—82no—
368C4#449×C14912yes—
369C4#451×C14911yescharacteristic
370C4#451×C14911yescharacteristic
371C4#452×C14911yescharacteristic
372C4#452×C14911yescharacteristic
373C4#495×C14911yescharacteristic
374C4#496×C14911yescharacteristic
375C2—82no—
376C2#1683×C14912yes—
377C2#1703×C14912yes—
378C2#2001×C14911yescharacteristic
379C2#2012×C14911yescharacteristic
380C2#2019×C14911yescharacteristic
subgroupG/H
center, socleC23×C149#121
commutator, Frattini, cosocleC2×C42C23×C149
prime radicalC22×D4×C149D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C149 ◁ C2×C42×C149 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#487×C149C2semidirect
5. C2×#333×C149C2semidirect
6. C2×#332×C149C2semidirect
7. #1277×C149C2semidirect
190. #10275C149direct (N × H)
191. C149#10275direct (N × H)
192. C2×#487C2×C149semidirect
196. C2×#333C2×C149semidirect
197. C2×#332C2×C149semidirect
198. #1277C2×C149semidirect

Maximal subgroups

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

subgroupindex
C2×#487×C1492
C2×#476×C1492
C2×#474×C1492
#1954×C1492
C2×#333×C1492
C2×#332×C1492
#1277×C1492
#10275149