Finite Group Databasebeta

← C149×#13014 #49191963

Subgroups — C149×#13014 #49191963

Order 38144.

554 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×SD32×C149C211yesmaximal, characteristic
2C2×C4×D8×C149C211yesmaximal, characteristic
3C2×#358×C149C211yesmaximal, characteristic, complemented
4C2×#357×C149C211yesmaximal, characteristic
5#1969×C149C211yesmaximal, characteristic, complemented
6#1380×C149C211yesmaximal, characteristic, complemented
7#1374×C149C211yesmaximal, characteristic, complemented
8C22×Q16×C149C2211yescharacteristic
9C22×D8×C149C2211yescharacteristic
10C2×C4×D4×C149—21no—
11C2×SD32×C149—22no—
12C2×SD32×C149—22no—
13C2×SD32×C149C414yescomplemented
14C22×C16×C149C2211yescharacteristic
15C22×C16×C149C2211yescharacteristic
16C4×D8×C149—22no—
17C4×D8×C149—22no—
18C2×#107×C149C2211yescharacteristic
19C2×#107×C149C2211yescharacteristic
20C2×#103×C149—21no—
21C2×#102×C149—21no—
22C2×C4×C8×C149C2211yescharacteristic
23#391×C149—21no—
24#358×C149—22no—
25#357×C149—22no—
26C22×Q8×C149—21no—
27C22×D4×C149—21no—
28C23×C4×C149—41no—
29C2×Q16×C149—21no—
30C2×Q16×C149—21no—
31C2×Q16×C149—21no—
32C2×Q16×C149—21no—
33C2×Q16×C149—21no—
34C2×Q16×C149C2×C412yescomplemented
35C2×D8×C149—21no—
36C2×D8×C149—21no—
37C2×D8×C149—21no—
38C2×D8×C149C2×C412yes—
39C2×D8×C149D412yes—
40C2×D8×C149D412yes—
41C22×C8×C149D411yescharacteristic
42C22×C8×C149C2311yescharacteristic
43C4×D4×C149—24no—
44C4×D4×C149—42no—
45C2×C4⋊C4×C149—21no—
46C2×C4⋊C4×C149—21no—
47C2×C22⋊C4×C149—41no—
48C2×C42×C149D411yescharacteristic
49SD32×C149—28no—
50C2×C16×C149—21no—
51C2×C16×C149—21no—
52C2×C16×C149—21no—
53C2×C16×C149—21no—
54C2×C16×C149—21no—
55C2×C16×C149C2×C412yescomplemented
56#107×C149—21no—
57#107×C149—21no—
58#107×C149—21no—
59#107×C149D412yes—
60#103×C149—42no—
61#102×C149—24no—
62C4×C8×C149—21no—
63C4×C8×C149—21no—
64#95×C149—41no—
65#95×C149—41no—
66C24×C149—41no—
67C2×Q8×C149—22no—
68C2×Q8×C149—41no—
69C2×Q8×C149—41no—
70C2×Q8×C149—41no—
71C2×Q8×C149—41no—
72C2×Q8×C149—41no—
73C2×D4×C149—22no—
74C2×D4×C149—22no—
75C2×D4×C149—22no—
76C2×D4×C149—41no—
77C2×D4×C149—41no—
78C2×D4×C149—41no—
79C22×C4×C149—44no—
80C22×C4×C149—41no—
81C22×C4×C149—41no—
82C22×C4×C149—41no—
83C22×C4×C149—82no—
84C22×C4×C149—82no—
85C22×C4×C149D811yescharacteristic
86C22×C4×C149D811yescharacteristic
87C22×C4×C149C2×D411yescharacteristic
88Q16×C149—22no—
89Q16×C149—22no—
90Q16×C149—41no—
91Q16×C149—41no—
92D8×C149—22no—
93D8×C149—22no—
94D8×C149—22no—
95D8×C149C22⋊C414yes—
96C2×C8×C149—21no—
97C2×C8×C149—21no—
98C2×C8×C149—21no—
99C2×C8×C149C22×C411yescharacteristic
100C2×C8×C149C2×D411yescharacteristic
101C2×C8×C149C2×D411yescharacteristic
102C2×C8×C149C2×D411yescharacteristic
103C2×C8×C149#4111yescharacteristic
104C2×C8×C149#4111yescharacteristic
105C4⋊C4×C149—22no—
106C4⋊C4×C149—41no—
107C4⋊C4×C149—41no—
108C4⋊C4×C149—41no—
109C22⋊C4×C149—44no—
110C42×C149—21no—
111C42×C149—21no—
112C16×C149—22no—
113C16×C149—41no—
114C23×C149—42no—
115C23×C149—42no—
116C23×C149—42no—
117C23×C149—81no—
118C23×C149—81no—
119C23×C149—81no—
120C23×C149—81no—
121C23×C149C2×D811yescharacteristic
122Q8×C149—42no—
123Q8×C149—42no—
124Q8×C149—81no—
125Q8×C149—81no—
126D4×C149—24no—
127D4×C149—42no—
128D4×C149—42no—
129D4×C149—42no—
130C2×C4×C149—21no—
131C2×C4×C149—21no—
132C2×C4×C149—21no—
133C2×C4×C149—21no—
134C2×C4×C149—21no—
135C2×C4×C149—42no—
136C2×C4×C149—42no—
137C2×C4×C149—88no—
138C2×C4×C149—81no—
139C2×C4×C149—81no—
140C2×C4×C149—81no—
141C2×C4×C149—81no—
142C2×C4×C149—81no—
143C2×C4×C149—81no—
144C2×C4×C149—81no—
145C2×C4×C149SD3212yescomplemented
146C2×C4×C149C4×D411yescharacteristic
147C2×C4×C149#12011yescharacteristic
148C2×C4×C149#12111yescharacteristic
149C2×C4×C149#13511yescharacteristic
150C2×C4×C149AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C149AGL(1,ℤ/8)11yescharacteristic
152C8×C149—41no—
153C8×C149C2×C22⋊C411yescharacteristic
154C8×C149C4×D411yescharacteristic
155C8×C149#12111yescharacteristic
156C8×C149#12311yescharacteristic
157C22×C149—44no—
158C22×C149—82no—
159C22×C149—82no—
160C22×C149—82no—
161C22×C149—82no—
162C22×C149—82no—
163C22×C149—82no—
164C22×C149C4×D811yescharacteristic
165C22×C149#44711yescharacteristic
166C22×C149#45911yescharacteristic
167C22×C149C2×SD3211yescharacteristic
168C22×C149#50811yescharacteristic
169C22×C149#50911yescharacteristic
170C22×C149#51011yescharacteristic
171C4×C149—22no—
172C4×C149—41no—
173C4×C149—82no—
174C4×C149—82no—
175C4×C149—161no—
176C4×C149#38611yescharacteristic
177C4×C149#44211yescharacteristic
178C4×C149#44911yescharacteristic
179C4×C149#46311yescharacteristic
180C2×C149—84no—
181C2×C149#187911yescharacteristic
182C2×C149C4×SD3211yescharacteristic
183C2×C149#217511yescharacteristic
184C2×C149#218711yescharacteristic
185C2×C149#218911yescharacteristic
186C2×C149#220811yescharacteristic
187C2×C149#221011yescharacteristic
188#13014C14911yesmaximal, characteristic, direct product factor, Sylow
189C149#1301411yescharacteristic, direct product factor, Sylow
190C22×SD32C2×C14911yescharacteristic
191C2×C4×D8C2×C14911yescharacteristic
192C2×#358C2×C14911yescharacteristic, complemented
193C2×#357C2×C14911yescharacteristic
194#1969C2×C14911yescharacteristic, complemented
195#1380C2×C14911yescharacteristic, complemented
196#1374C2×C14911yescharacteristic, complemented
197C22×Q16C22×C14911yescharacteristic
198C22×D8C22×C14911yescharacteristic
199C2×C4×D4—21no—
200C2×SD32—22no—
201C2×SD32—22no—
202C2×SD32C4×C14914yescomplemented
203C22×C16C22×C14911yescharacteristic
204C22×C16C22×C14911yescharacteristic
205C4×D8—22no—
206C4×D8—22no—
207C2×#107C22×C14911yescharacteristic
208C2×#107C22×C14911yescharacteristic
209C2×#103—21no—
210C2×#102—21no—
211C2×C4×C8C22×C14911yescharacteristic
212#391—21no—
213#358—22no—
214#357—22no—
215C22×Q8—21no—
216C22×D4—21no—
217C23×C4—41no—
218C2×Q16—21no—
219C2×Q16—21no—
220C2×Q16—21no—
221C2×Q16—21no—
222C2×Q16—21no—
223C2×Q16C2×C4×C14912yescomplemented
224C2×D8—21no—
225C2×D8—21no—
226C2×D8—21no—
227C2×D8C2×C4×C14912yes—
228C2×D8D4×C14912yes—
229C2×D8D4×C14912yes—
230C22×C8D4×C14911yescharacteristic
231C22×C8C23×C14911yescharacteristic
232C4×D4—24no—
233C4×D4—42no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C22⋊C4—41no—
237C2×C42D4×C14911yescharacteristic
238SD32—28no—
239C2×C16—21no—
240C2×C16—21no—
241C2×C16—21no—
242C2×C16—21no—
243C2×C16—21no—
244C2×C16C2×C4×C14912yescomplemented
245#107—21no—
246#107—21no—
247#107—21no—
248#107D4×C14912yes—
249#103—42no—
250#102—24no—
251C4×C8—21no—
252C4×C8—21no—
253#95—41no—
254#95—41no—
255C24—41no—
256C2×Q8—22no—
257C2×Q8—41no—
258C2×Q8—41no—
259C2×Q8—41no—
260C2×Q8—41no—
261C2×Q8—41no—
262C2×D4—22no—
263C2×D4—22no—
264C2×D4—22no—
265C2×D4—41no—
266C2×D4—41no—
267C2×D4—41no—
268C22×C4—44no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—82no—
273C22×C4—82no—
274C22×C4D8×C14911yescharacteristic
275C22×C4D8×C14911yescharacteristic
276C22×C4C2×D4×C14911yescharacteristic
277Q16—22no—
278Q16—22no—
279Q16—41no—
280Q16—41no—
281D8—22no—
282D8—22no—
283D8—22no—
284D8C22⋊C4×C14914yes—
285C2×C8—21no—
286C2×C8—21no—
287C2×C8—21no—
288C2×C8C22×C4×C14911yescharacteristic
289C2×C8C2×D4×C14911yescharacteristic
290C2×C8C2×D4×C14911yescharacteristic
291C2×C8C2×D4×C14911yescharacteristic
292C2×C8#41×C14911yescharacteristic
293C2×C8#41×C14911yescharacteristic
294C4⋊C4—22no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C22⋊C4—44no—
299C42—21no—
300C42—21no—
301C16—22no—
302C16—41no—
303C23—42no—
304C23—42no—
305C23—42no—
306C23—81no—
307C23—81no—
308C23—81no—
309C23—81no—
310C23C2×D8×C14911yescharacteristic
311Q8—42no—
312Q8—42no—
313Q8—81no—
314Q8—81no—
315D4—24no—
316D4—42no—
317D4—42no—
318D4—42no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—88no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4SD32×C14912yescomplemented
335C2×C4C4×D4×C14911yescharacteristic
336C2×C4#120×C14911yescharacteristic
337C2×C4#121×C14911yescharacteristic
338C2×C4#135×C14911yescharacteristic
339C2×C4AGL(1,ℤ/8)×C14911yescharacteristic
340C2×C4AGL(1,ℤ/8)×C14911yescharacteristic
341C8—41no—
342C8C2×C22⋊C4×C14911yescharacteristic
343C8C4×D4×C14911yescharacteristic
344C8#121×C14911yescharacteristic
345C8#123×C14911yescharacteristic
346C22—44no—
347C22—82no—
348C22—82no—
349C22—82no—
350C22—82no—
351C22—82no—
352C22—82no—
353C22C4×D8×C14911yescharacteristic
354C22#447×C14911yescharacteristic
355C22#459×C14911yescharacteristic
356C22C2×SD32×C14911yescharacteristic
357C22#508×C14911yescharacteristic
358C22#509×C14911yescharacteristic
359C22#510×C14911yescharacteristic
360C4—22no—
361C4—41no—
362C4—82no—
363C4—82no—
364C4—161no—
365C4#386×C14911yescharacteristic
366C4#442×C14911yescharacteristic
367C4#449×C14911yescharacteristic
368C4#463×C14911yescharacteristic
369C2—84no—
370C2#1879×C14911yescharacteristic
371C2C4×SD32×C14911yescharacteristic
372C2#2175×C14911yescharacteristic
373C2#2187×C14911yescharacteristic
374C2#2189×C14911yescharacteristic
375C2#2208×C14911yescharacteristic
376C2#2210×C14911yescharacteristic
subgroupG/H
center, socleC23×C149C2×D8
commutatorC2×C8C22×C4×C149
Frattini, cosocleC22×C8C23×C149
prime radicalC22×D8×C149C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C149 ◁ C2×C42×C149 ◁ C2×C4×C8×C149 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×#358×C149C2semidirect
5. #1969×C149C2semidirect
6. #1380×C149C2semidirect
7. #1374×C149C2semidirect
13. C2×SD32×C149C4semidirect
34. C2×Q16×C149C2×C4semidirect
55. C2×C16×C149C2×C4semidirect
145. C2×C4×C149SD32semidirect
188. #13014C149direct (N × H)
189. C149#13014direct (N × H)
192. C2×#358C2×C149semidirect
194. #1969C2×C149semidirect
195. #1380C2×C149semidirect
196. #1374C2×C149semidirect
202. C2×SD32C4×C149semidirect
223. C2×Q16C2×C4×C149semidirect
244. C2×C16C2×C4×C149semidirect
334. C2×C4SD32×C149semidirect

Maximal subgroups

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

subgroupindex
C22×SD32×C1492
C2×C4×D8×C1492
C2×#358×C1492
C2×#357×C1492
#1969×C1492
#1380×C1492
#1374×C1492
#13014149