Finite Group Databasebeta

← C149×#11876 #49190825

Subgroups — C149×#11876 #49190825

Order 38144.

522 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 522 conjugacy classes of subgroups — too many to draw. Only its 114 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#2543×C149C211yesmaximal, characteristic
2#1799×C149C211yesmaximal, characteristic, complemented
3#1460×C149C211yesmaximal, characteristic, complemented
4#1344×C149C212yesmaximal, complemented
5#1343×C149C212yesmaximal, complemented
6C2×#121×C149—21no—
7C2×#121×C149C411yescharacteristic, complemented
8C2×C4×D4×C149C2211yescharacteristic
9#431×C149—21no—
10C2×#99×C149—21no—
11#398×C149C411yescharacteristic, complemented
12#397×C149C2211yescharacteristic
13#394×C149C411yescharacteristic, complemented
14#392×C149C2211yescharacteristic
15#388×C149—21no—
16#386×C149—21no—
17#386×C149—21no—
18#380×C149—21no—
19C2×#95×C149C411yescharacteristic, complemented
20#342×C149C2212yes—
21#323×C149—21no—
22#323×C149C2212yes—
23C22×D4×C149—21no—
24C22×D4×C149—21no—
25C22×D4×C149C2×C411yescharacteristic
26C22×D4×C149D411yescharacteristic
27C23×C4×C149—21no—
28C23×C4×C149C2×C411yescharacteristic
29C23×C4×C149D411yescharacteristic
30#121×C149—42no—
31#121×C149—42no—
32#121×C149—41no—
33#121×C149—41no—
34C4×D4×C149—41no—
35C4×D4×C149—41no—
36C2×C4⋊C4×C149—21no—
37C2×C4⋊C4×C149—41no—
38C2×C4⋊C4×C149C2×C411yescharacteristic
39C2×C4⋊C4×C149C2×C411yescharacteristic
40C2×C22⋊C4×C149—21no—
41C2×C22⋊C4×C149—21no—
42C2×C22⋊C4×C149—21no—
43C2×C22⋊C4×C149—21no—
44C2×C22⋊C4×C149—22no—
45C2×C22⋊C4×C149—21no—
46C2×C22⋊C4×C149D411yescharacteristic
47C2×C22⋊C4×C149C2311yescharacteristic
48C2×C42×C149D411yescharacteristic
49C4⋊C8×C149—41no—
50#99×C149—42no—
51C22⋊C8×C149—22no—
52C4×C8×C149—41no—
53#95×C149—21no—
54#95×C149—21no—
55#95×C149—21no—
56#95×C149—41no—
57#95×C149C2×C411yescharacteristic
58#95×C149C2×C411yescharacteristic
59C24×C149—21no—
60C24×C149C22⋊C411yescharacteristic
61C24×C149C2×D411yescharacteristic
62C2×D4×C149—41no—
63C2×D4×C149—41no—
64C2×D4×C149—42no—
65C2×D4×C149—41no—
66C2×D4×C149—42no—
67C2×D4×C149—42no—
68C2×D4×C149—42no—
69C2×D4×C149—41no—
70C2×D4×C149—41no—
71C2×D4×C149—81no—
72C2×D4×C149—81no—
73C2×D4×C149D812yes—
74C2×D4×C149SD1612yes—
75C22×C4×C149—21no—
76C22×C4×C149—21no—
77C22×C4×C149—21no—
78C22×C4×C149—21no—
79C22×C4×C149—21no—
80C22×C4×C149—21no—
81C22×C4×C149—21no—
82C22×C4×C149—42no—
83C22×C4×C149—42no—
84C22×C4×C149—42no—
85C22×C4×C149—81no—
86C22×C4×C149—81no—
87C22×C4×C149—81no—
88C22×C4×C149C22⋊C411yescharacteristic
89C22×C4×C149C22⋊C411yescharacteristic
90C22×C4×C149C22⋊C411yescharacteristic
91C22×C4×C149C22×C411yescharacteristic
92C22×C4×C149C2×D411yescharacteristic
93C2×C8×C149—42no—
94C4⋊C4×C149—41no—
95C4⋊C4×C149—41no—
96C4⋊C4×C149—42no—
97C4⋊C4×C149—82no—
98C22⋊C4×C149—41no—
99C22⋊C4×C149—41no—
100C22⋊C4×C149—42no—
101C22⋊C4×C149—41no—
102C22⋊C4×C149—41no—
103C22⋊C4×C149—41no—
104C22⋊C4×C149—41no—
105C22⋊C4×C149—42no—
106C22⋊C4×C149—42no—
107C22⋊C4×C149—42no—
108C22⋊C4×C149—81no—
109C42×C149—21no—
110C42×C149—21no—
111C23×C149—21no—
112C23×C149—21no—
113C23×C149—21no—
114C23×C149—21no—
115C23×C149—41no—
116C23×C149—41no—
117C23×C149—41no—
118C23×C149—41no—
119C23×C149—41no—
120C23×C149—41no—
121C23×C149—41no—
122C23×C149—41no—
123C23×C149—41no—
124C23×C149—41no—
125C23×C149—41no—
126C23×C149#10212yes—
127C23×C149C2×C22⋊C411yescharacteristic
128C23×C149C2×D811yescharacteristic
129C23×C149C2×SD1611yescharacteristic
130D4×C149—42no—
131D4×C149—42no—
132D4×C149—82no—
133D4×C149—82no—
134D4×C149—82no—
135D4×C149—84no—
136C2×C4×C149—21no—
137C2×C4×C149—21no—
138C2×C4×C149—22no—
139C2×C4×C149—21no—
140C2×C4×C149—21no—
141C2×C4×C149—21no—
142C2×C4×C149—41no—
143C2×C4×C149—42no—
144C2×C4×C149—41no—
145C2×C4×C149—41no—
146C2×C4×C149—41no—
147C2×C4×C149—41no—
148C2×C4×C149—41no—
149C2×C4×C149—41no—
150C2×C4×C149—41no—
151C2×C4×C149—41no—
152C2×C4×C149—41no—
153C2×C4×C149—41no—
154C2×C4×C149—41no—
155C2×C4×C149—81no—
156C2×C4×C149—81no—
157C2×C4×C149—81no—
158C2×C4×C149—84no—
159C2×C4×C149—82no—
160C2×C4×C149—82no—
161C2×C4×C149—82no—
162C2×C4×C149#9911yescharacteristic
163C2×C4×C149#9911yescharacteristic
164C2×C4×C149#10212yes—
165C8×C149—82no—
166C22×C149—21no—
167C22×C149—21no—
168C22×C149—21no—
169C22×C149—22no—
170C22×C149—21no—
171C22×C149—42no—
172C22×C149—41no—
173C22×C149—41no—
174C22×C149—42no—
175C22×C149—41no—
176C22×C149—41no—
177C22×C149—41no—
178C22×C149—41no—
179C22×C149—81no—
180C22×C149—81no—
181C22×C149—81no—
182C22×C149—81no—
183C22×C149—81no—
184C22×C149—81no—
185C22×C149—81no—
186C22×C149—81no—
187C22×C149C2×#9911yescharacteristic
188C22×C149C2×#10211yescharacteristic
189C22×C149#42111yescharacteristic
190C4×C149—21no—
191C4×C149—21no—
192C4×C149—22no—
193C4×C149—42no—
194C4×C149—41no—
195C4×C149—41no—
196C4×C149—41no—
197C4×C149—81no—
198C4×C149—81no—
199C4×C149—162no—
200C2×C149—21no—
201C2×C149—21no—
202C2×C149—41no—
203C2×C149—42no—
204C2×C149—41no—
205C2×C149—161no—
206C2×C149#151911yescharacteristic
207C2×C149#212111yescharacteristic
208C2×C149#212611yescharacteristic
209#11876C14911yesmaximal, characteristic, direct product factor, Sylow
210C149#1187611yescharacteristic, direct product factor, Sylow
211#2543C2×C14911yescharacteristic
212#1799C2×C14911yescharacteristic, complemented
213#1460C2×C14911yescharacteristic, complemented
214#1344C2×C14912yescomplemented
215#1343C2×C14912yescomplemented
216C2×#121—21no—
217C2×#121C4×C14911yescharacteristic, complemented
218C2×C4×D4C22×C14911yescharacteristic
219#431—21no—
220C2×#99—21no—
221#398C4×C14911yescharacteristic, complemented
222#397C22×C14911yescharacteristic
223#394C4×C14911yescharacteristic, complemented
224#392C22×C14911yescharacteristic
225#388—21no—
226#386—21no—
227#386—21no—
228#380—21no—
229C2×#95C4×C14911yescharacteristic, complemented
230#342C22×C14912yes—
231#323—21no—
232#323C22×C14912yes—
233C22×D4—21no—
234C22×D4—21no—
235C22×D4C2×C4×C14911yescharacteristic
236C22×D4D4×C14911yescharacteristic
237C23×C4—21no—
238C23×C4C2×C4×C14911yescharacteristic
239C23×C4D4×C14911yescharacteristic
240#121—42no—
241#121—42no—
242#121—41no—
243#121—41no—
244C4×D4—41no—
245C4×D4—41no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—41no—
248C2×C4⋊C4C2×C4×C14911yescharacteristic
249C2×C4⋊C4C2×C4×C14911yescharacteristic
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C2×C22⋊C4—22no—
255C2×C22⋊C4—21no—
256C2×C22⋊C4D4×C14911yescharacteristic
257C2×C22⋊C4C23×C14911yescharacteristic
258C2×C42D4×C14911yescharacteristic
259C4⋊C8—41no—
260#99—42no—
261C22⋊C8—22no—
262C4×C8—41no—
263#95—21no—
264#95—21no—
265#95—21no—
266#95—41no—
267#95C2×C4×C14911yescharacteristic
268#95C2×C4×C14911yescharacteristic
269C24—21no—
270C24C22⋊C4×C14911yescharacteristic
271C24C2×D4×C14911yescharacteristic
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—41no—
275C2×D4—42no—
276C2×D4—42no—
277C2×D4—42no—
278C2×D4—42no—
279C2×D4—41no—
280C2×D4—41no—
281C2×D4—81no—
282C2×D4—81no—
283C2×D4D8×C14912yes—
284C2×D4SD16×C14912yes—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—42no—
293C22×C4—42no—
294C22×C4—42no—
295C22×C4—81no—
296C22×C4—81no—
297C22×C4—81no—
298C22×C4C22⋊C4×C14911yescharacteristic
299C22×C4C22⋊C4×C14911yescharacteristic
300C22×C4C22⋊C4×C14911yescharacteristic
301C22×C4C22×C4×C14911yescharacteristic
302C22×C4C2×D4×C14911yescharacteristic
303C2×C8—42no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—42no—
307C4⋊C4—82no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C22⋊C4—42no—
311C22⋊C4—41no—
312C22⋊C4—41no—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C22⋊C4—42no—
316C22⋊C4—42no—
317C22⋊C4—42no—
318C22⋊C4—81no—
319C42—21no—
320C42—21no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23—41no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23—41no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23#102×C14912yes—
337C23C2×C22⋊C4×C14911yescharacteristic
338C23C2×D8×C14911yescharacteristic
339C23C2×SD16×C14911yescharacteristic
340D4—42no—
341D4—42no—
342D4—82no—
343D4—82no—
344D4—82no—
345D4—84no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—22no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—41no—
353C2×C4—42no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—81no—
366C2×C4—81no—
367C2×C4—81no—
368C2×C4—84no—
369C2×C4—82no—
370C2×C4—82no—
371C2×C4—82no—
372C2×C4#99×C14911yescharacteristic
373C2×C4#99×C14911yescharacteristic
374C2×C4#102×C14912yes—
375C8—82no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—22no—
380C22—21no—
381C22—42no—
382C22—41no—
383C22—41no—
384C22—42no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—81no—
390C22—81no—
391C22—81no—
392C22—81no—
393C22—81no—
394C22—81no—
395C22—81no—
396C22—81no—
397C22C2×#99×C14911yescharacteristic
398C22C2×#102×C14911yescharacteristic
399C22#421×C14911yescharacteristic
400C4—22no—
401C4—21no—
402C4—21no—
403C4—42no—
404C4—41no—
405C4—41no—
406C4—41no—
407C4—81no—
408C4—81no—
409C4—162no—
410C2—21no—
411C2—21no—
412C2—41no—
413C2—42no—
414C2—41no—
415C2—161no—
416C2#1519×C14911yescharacteristic
417C2#2121×C14911yescharacteristic
418C2#2126×C14911yescharacteristic
subgroupG/H
center, socleC22×C149C2×#99
commutatorC22×C4C22×C4×C149
Frattini, cosocleC2×C22⋊C4C23×C149
prime radical#2543×C149C2
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C149 ◁ C22×C4×C149 ◁ C2×C4×D4×C149 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1799×C149C2semidirect
3. #1460×C149C2semidirect
4. #1344×C149C2semidirect
5. #1343×C149C2semidirect
7. C2×#121×C149C4semidirect
11. #398×C149C4semidirect
13. #394×C149C4semidirect
19. C2×#95×C149C4semidirect
209. #11876C149direct (N × H)
210. C149#11876direct (N × H)
212. #1799C2×C149semidirect
213. #1460C2×C149semidirect
214. #1344C2×C149semidirect
215. #1343C2×C149semidirect
217. C2×#121C4×C149semidirect
221. #398C4×C149semidirect
223. #394C4×C149semidirect
229. C2×#95C4×C149semidirect

Maximal subgroups

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

subgroupindex
#2543×C1492
#1799×C1492
#1460×C1492
#1344×C1492
#1343×C1492
#11876149