Finite Group Databasebeta

← C149×#11897 #49190846

Subgroups — C149×#11897 #49190846

Order 38144.

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

normal subgroups only

This group has 452 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#2580×C149C211yesmaximal, characteristic
2#1799×C149C211yesmaximal, characteristic
3#1459×C149C211yesmaximal, characteristic
4#1352×C149C212yesmaximal, complemented
5#1351×C149C212yesmaximal, complemented
6C2×C4×Q8×C149C411yescharacteristic, complemented
7C2×C4×D4×C149C2211yescharacteristic
8C2×#99×C149—21no—
9C2×C22⋊C8×C149—21no—
10#399×C149C411yescharacteristic, complemented
11#399×C149C2211yescharacteristic
12#393×C149C411yescharacteristic, complemented
13#393×C149C2211yescharacteristic
14#390×C149—21no—
15#389×C149—21no—
16#385×C149—21no—
17#385×C149—21no—
18#382×C149C411yescharacteristic, complemented
19#380×C149—21no—
20#342×C149C2212yes—
21#324×C149—21no—
22#323×C149C2212yes—
23C22×Q8×C149C2×C411yescharacteristic
24C22×D4×C149D411yescharacteristic
25C23×C4×C149D411yescharacteristic
26C23×C4×C149D411yescharacteristic
27C22×C8×C149—41no—
28C4×Q8×C149—41no—
29C4×Q8×C149—41no—
30C4×D4×C149—41no—
31C4×D4×C149—41no—
32C2×C4⋊C4×C149—21no—
33C2×C4⋊C4×C149—21no—
34C2×C4⋊C4×C149—21no—
35C2×C4⋊C4×C149—21no—
36C2×C4⋊C4×C149—41no—
37C2×C4⋊C4×C149C2×C411yescharacteristic
38C2×C4⋊C4×C149D411yescharacteristic
39C2×C22⋊C4×C149—21no—
40C2×C22⋊C4×C149—21no—
41C2×C22⋊C4×C149—22no—
42C2×C22⋊C4×C149—21no—
43C2×C22⋊C4×C149—21no—
44C2×C22⋊C4×C149C2×C411yescharacteristic
45C2×C22⋊C4×C149C2311yescharacteristic
46C2×C42×C149—21no—
47C2×C42×C149C2×C411yescharacteristic
48#99×C149—42no—
49C22⋊C8×C149—22no—
50C22⋊C8×C149—41no—
51#95×C149—21no—
52#95×C149—21no—
53#95×C149—21no—
54#95×C149—41no—
55#95×C149C2×C411yescharacteristic
56#95×C149C2×C411yescharacteristic
57C24×C149C22⋊C411yescharacteristic
58C24×C149C2×D411yescharacteristic
59C2×Q8×C149—42no—
60C2×Q8×C149—41no—
61C2×D4×C149—41no—
62C2×D4×C149—41no—
63C2×D4×C149SD1612yes—
64C2×D4×C149Q1612yes—
65C22×C4×C149—21no—
66C22×C4×C149—21no—
67C22×C4×C149—21no—
68C22×C4×C149—21no—
69C22×C4×C149—21no—
70C22×C4×C149—21no—
71C22×C4×C149—21no—
72C22×C4×C149—21no—
73C22×C4×C149—42no—
74C22×C4×C149—81no—
75C22×C4×C149—81no—
76C22×C4×C149C22⋊C411yescharacteristic
77C22×C4×C149C22⋊C411yescharacteristic
78C22×C4×C149C22⋊C411yescharacteristic
79C22×C4×C149C22×C411yescharacteristic
80C22×C4×C149C2×D411yescharacteristic
81C2×C8×C149—42no—
82C2×C8×C149—82no—
83C4⋊C4×C149—41no—
84C4⋊C4×C149—42no—
85C4⋊C4×C149—41no—
86C4⋊C4×C149—41no—
87C4⋊C4×C149—41no—
88C4⋊C4×C149—81no—
89C4⋊C4×C149—81no—
90C4⋊C4×C149—82no—
91C22⋊C4×C149—41no—
92C22⋊C4×C149—41no—
93C22⋊C4×C149—42no—
94C22⋊C4×C149—42no—
95C22⋊C4×C149—42no—
96C22⋊C4×C149—42no—
97C22⋊C4×C149—81no—
98C22⋊C4×C149—81no—
99C42×C149—21no—
100C42×C149—21no—
101C42×C149—42no—
102C23×C149—21no—
103C23×C149—21no—
104C23×C149—21no—
105C23×C149—21no—
106C23×C149—41no—
107C23×C149—41no—
108C23×C149—41no—
109C23×C149—41no—
110C23×C149#10312yes—
111C23×C149C2×C22⋊C411yescharacteristic
112C23×C149C2×SD1611yescharacteristic
113C23×C149C2×Q1611yescharacteristic
114Q8×C149—42no—
115Q8×C149—42no—
116D4×C149—42no—
117D4×C149—42no—
118C2×C4×C149—21no—
119C2×C4×C149—21no—
120C2×C4×C149—22no—
121C2×C4×C149—21no—
122C2×C4×C149—21no—
123C2×C4×C149—21no—
124C2×C4×C149—41no—
125C2×C4×C149—42no—
126C2×C4×C149—42no—
127C2×C4×C149—41no—
128C2×C4×C149—41no—
129C2×C4×C149—41no—
130C2×C4×C149—41no—
131C2×C4×C149—41no—
132C2×C4×C149—41no—
133C2×C4×C149—41no—
134C2×C4×C149—41no—
135C2×C4×C149—41no—
136C2×C4×C149—41no—
137C2×C4×C149—41no—
138C2×C4×C149—41no—
139C2×C4×C149—41no—
140C2×C4×C149—41no—
141C2×C4×C149—81no—
142C2×C4×C149—81no—
143C2×C4×C149—82no—
144C2×C4×C149—82no—
145C2×C4×C149—82no—
146C2×C4×C149#9911yescharacteristic
147C2×C4×C149#9911yescharacteristic
148C2×C4×C149#10312yes—
149C8×C149—82no—
150C22×C149—21no—
151C22×C149—21no—
152C22×C149—21no—
153C22×C149—22no—
154C22×C149—21no—
155C22×C149—42no—
156C22×C149—41no—
157C22×C149—41no—
158C22×C149—41no—
159C22×C149—41no—
160C22×C149—41no—
161C22×C149—41no—
162C22×C149—81no—
163C22×C149—81no—
164C22×C149C2×#9911yescharacteristic
165C22×C149C2×#10311yescharacteristic
166C22×C149#42111yescharacteristic
167C4×C149—21no—
168C4×C149—21no—
169C4×C149—22no—
170C4×C149—42no—
171C4×C149—41no—
172C4×C149—41no—
173C4×C149—41no—
174C4×C149—81no—
175C4×C149—81no—
176C4×C149—81no—
177C4×C149—162no—
178C2×C149—21no—
179C2×C149—21no—
180C2×C149—41no—
181C2×C149—42no—
182C2×C149—41no—
183C2×C149#152011yescharacteristic
184C2×C149#212011yescharacteristic
185C2×C149#212711yescharacteristic
186#11897C14911yesmaximal, characteristic, direct product factor, Sylow
187C149#1189711yescharacteristic, direct product factor, Sylow
188#2580C2×C14911yescharacteristic
189#1799C2×C14911yescharacteristic
190#1459C2×C14911yescharacteristic
191#1352C2×C14912yescomplemented
192#1351C2×C14912yescomplemented
193C2×C4×Q8C4×C14911yescharacteristic, complemented
194C2×C4×D4C22×C14911yescharacteristic
195C2×#99—21no—
196C2×C22⋊C8—21no—
197#399C4×C14911yescharacteristic, complemented
198#399C22×C14911yescharacteristic
199#393C4×C14911yescharacteristic, complemented
200#393C22×C14911yescharacteristic
201#390—21no—
202#389—21no—
203#385—21no—
204#385—21no—
205#382C4×C14911yescharacteristic, complemented
206#380—21no—
207#342C22×C14912yes—
208#324—21no—
209#323C22×C14912yes—
210C22×Q8C2×C4×C14911yescharacteristic
211C22×D4D4×C14911yescharacteristic
212C23×C4D4×C14911yescharacteristic
213C23×C4D4×C14911yescharacteristic
214C22×C8—41no—
215C4×Q8—41no—
216C4×Q8—41no—
217C4×D4—41no—
218C4×D4—41no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—41no—
224C2×C4⋊C4C2×C4×C14911yescharacteristic
225C2×C4⋊C4D4×C14911yescharacteristic
226C2×C22⋊C4—21no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4—22no—
229C2×C22⋊C4—21no—
230C2×C22⋊C4—21no—
231C2×C22⋊C4C2×C4×C14911yescharacteristic
232C2×C22⋊C4C23×C14911yescharacteristic
233C2×C42—21no—
234C2×C42C2×C4×C14911yescharacteristic
235#99—42no—
236C22⋊C8—22no—
237C22⋊C8—41no—
238#95—21no—
239#95—21no—
240#95—21no—
241#95—41no—
242#95C2×C4×C14911yescharacteristic
243#95C2×C4×C14911yescharacteristic
244C24C22⋊C4×C14911yescharacteristic
245C24C2×D4×C14911yescharacteristic
246C2×Q8—42no—
247C2×Q8—41no—
248C2×D4—41no—
249C2×D4—41no—
250C2×D4SD16×C14912yes—
251C2×D4Q16×C14912yes—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—42no—
261C22×C4—81no—
262C22×C4—81no—
263C22×C4C22⋊C4×C14911yescharacteristic
264C22×C4C22⋊C4×C14911yescharacteristic
265C22×C4C22⋊C4×C14911yescharacteristic
266C22×C4C22×C4×C14911yescharacteristic
267C22×C4C2×D4×C14911yescharacteristic
268C2×C8—42no—
269C2×C8—82no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—42no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—81no—
276C4⋊C4—81no—
277C4⋊C4—82no—
278C22⋊C4—41no—
279C22⋊C4—41no—
280C22⋊C4—42no—
281C22⋊C4—42no—
282C22⋊C4—42no—
283C22⋊C4—42no—
284C22⋊C4—81no—
285C22⋊C4—81no—
286C42—21no—
287C42—21no—
288C42—42no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—41no—
294C23—41no—
295C23—41no—
296C23—41no—
297C23#103×C14912yes—
298C23C2×C22⋊C4×C14911yescharacteristic
299C23C2×SD16×C14911yescharacteristic
300C23C2×Q16×C14911yescharacteristic
301Q8—42no—
302Q8—42no—
303D4—42no—
304D4—42no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—22no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—41no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—81no—
329C2×C4—81no—
330C2×C4—82no—
331C2×C4—82no—
332C2×C4—82no—
333C2×C4#99×C14911yescharacteristic
334C2×C4#99×C14911yescharacteristic
335C2×C4#103×C14912yes—
336C8—82no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—22no—
341C22—21no—
342C22—42no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—81no—
350C22—81no—
351C22C2×#99×C14911yescharacteristic
352C22C2×#103×C14911yescharacteristic
353C22#421×C14911yescharacteristic
354C4—22no—
355C4—21no—
356C4—21no—
357C4—42no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—81no—
362C4—81no—
363C4—81no—
364C4—162no—
365C2—21no—
366C2—21no—
367C2—41no—
368C2—42no—
369C2—41no—
370C2#1520×C14911yescharacteristic
371C2#2120×C14911yescharacteristic
372C2#2127×C14911yescharacteristic
subgroupG/H
center, socleC22×C149C2×#99
commutatorC22×C4C22×C4×C149
Frattini, cosocleC2×C22⋊C4C23×C149
prime radicalC22×D4×C149D4
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
4. #1352×C149C2semidirect
5. #1351×C149C2semidirect
6. C2×C4×Q8×C149C4semidirect
10. #399×C149C4semidirect
12. #393×C149C4semidirect
18. #382×C149C4semidirect
186. #11897C149direct (N × H)
187. C149#11897direct (N × H)
191. #1352C2×C149semidirect
192. #1351C2×C149semidirect
193. C2×C4×Q8C4×C149semidirect
197. #399C4×C149semidirect
199. #393C4×C149semidirect
205. #382C4×C149semidirect

Maximal subgroups

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

subgroupindex
#2580×C1492
#1799×C1492
#1459×C1492
#1352×C1492
#1351×C1492
#11897149