Finite Group Databasebeta

← C149×#10206 #49189155

Subgroups — C149×#10206 #49189155

Order 38144.

560 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3246×C149C211yesmaximal, characteristic
2#3229×C149C211yesmaximal, characteristic, complemented
3#3152×C149C211yesmaximal, characteristic
4#1988×C149C211yesmaximal, characteristic, complemented
5#1986×C149C211yesmaximal, characteristic, complemented
6#1502×C149C211yesmaximal, characteristic
7#1283×C149C211yesmaximal, characteristic, complemented
8C2×#137×C149—22no—
9#533×C149C2211yescharacteristic
10#532×C149C2211yescharacteristic
11C2×C4⋊Q8×C149C2211yescharacteristic
12#498×C149—21no—
13#497×C149—22no—
14#494×C149—21no—
15#492×C149—21no—
16#487×C149—21no—
17#483×C149—22no—
18#476×C149—21no—
19#475×C149—22no—
20#475×C149—21no—
21#465×C149—22no—
22#461×C149—21no—
23#460×C149—21no—
24#431×C149C2211yescharacteristic
25C2×C4⋊C8×C149C2211yescharacteristic
26C4×M16×C149C2211yescharacteristic
27C4×C4⋊C4×C149C2211yescharacteristic
28#340×C149—22no—
29#339×C149—22no—
30#327×C149—22no—
31C2×#41×C149—21no—
32C22×Q8×C149—21no—
33#137×C149—44no—
34#137×C149—44no—
35C2×Q16×C149—24no—
36C2×SD16×C149—24no—
37C2×SD16×C149—22no—
38C2×M16×C149D412yes—
39C22×C8×C149D412yes—
40C4⋊Q8×C149—21no—
41C4⋊Q8×C149—21no—
42C4⋊Q8×C149—21no—
43C4⋊Q8×C149D411yescharacteristic
44C4⋊Q8×C149D411yescharacteristic
45C4⋊Q8×C149D412yes—
46C4⋊Q8×C149D411yescharacteristic
47#127×C149D411yescharacteristic
48#125×C149—21no—
49#124×C149—21no—
50C22⋊Q8×C149—21no—
51C22⋊Q8×C149—21no—
52#121×C149—21no—
53#121×C149—21no—
54C4×Q8×C149—21no—
55C4×Q8×C149—21no—
56C4×D4×C149—21no—
57C4×D4×C149—21no—
58#117×C149—21no—
59C2×C4⋊C4×C149—21no—
60C2×C4⋊C4×C149—21no—
61C2×C4⋊C4×C149—21no—
62C2×C42×C149—21no—
63C2×C42×C149C2311yescharacteristic
64#106×C149—22no—
65#106×C149—24no—
66C4⋊C8×C149—21no—
67C4⋊C8×C149—21no—
68C4⋊C8×C149—21no—
69#103×C149—22no—
70#103×C149—24no—
71#102×C149—22no—
72C22⋊C8×C149D412yes—
73#97×C149—21no—
74C4×C8×C149—21no—
75C4×C8×C149—21no—
76#95×C149—21no—
77#41×C149—42no—
78#41×C149—42no—
79C2×Q8×C149—21no—
80C2×Q8×C149—21no—
81C2×Q8×C149—21no—
82C2×Q8×C149—22no—
83C2×Q8×C149—41no—
84C2×Q8×C149—42no—
85C2×Q8×C149—42no—
86C2×D4×C149—21no—
87C2×D4×C149—21no—
88C2×D4×C149—21no—
89C2×D4×C149—41no—
90C22×C4×C149—41no—
91C22×C4×C149—41no—
92C22×C4×C149—41no—
93C22×C4×C149C2×D411yescharacteristic
94C22×C4×C149C2×D411yescharacteristic
95C22×C4×C149C2×D411yescharacteristic
96Q16×C149—48no—
97SD16×C149—48no—
98SD16×C149—82no—
99M16×C149—22no—
100M16×C149SD1614yescomplemented
101C2×C8×C149—22no—
102C2×C8×C149—22no—
103C2×C8×C149—22no—
104C2×C8×C149—42no—
105C4⋊C4×C149—22no—
106C4⋊C4×C149—21no—
107C4⋊C4×C149—22no—
108C4⋊C4×C149—21no—
109C4⋊C4×C149—21no—
110C4⋊C4×C149—22no—
111C4⋊C4×C149—21no—
112C4⋊C4×C149—21no—
113C4⋊C4×C149—21no—
114C4⋊C4×C149—41no—
115C4⋊C4×C149—41no—
116C4⋊C4×C149—41no—
117C4⋊C4×C149—41no—
118C4⋊C4×C149—41no—
119C22⋊C4×C149—41no—
120C22⋊C4×C149—41no—
121C22⋊C4×C149—41no—
122C42×C149—41no—
123C42×C149—42no—
124C42×C149C2×D411yescharacteristic
125C42×C149C2×D411yescharacteristic
126C42×C149C2×D411yescharacteristic
127C42×C149#4111yescharacteristic
128C23×C149—41no—
129C23×C149#12711yescharacteristic
130Q8×C149—42no—
131Q8×C149—44no—
132Q8×C149—42no—
133Q8×C149—41no—
134Q8×C149—41no—
135Q8×C149—82no—
136D4×C149—42no—
137D4×C149—41no—
138D4×C149—41no—
139D4×C149—81no—
140D4×C149—81no—
141D4×C149—81no—
142C2×C4×C149—21no—
143C2×C4×C149—21no—
144C2×C4×C149—41no—
145C2×C4×C149—42no—
146C2×C4×C149—41no—
147C2×C4×C149—41no—
148C2×C4×C149—41no—
149C2×C4×C149—42no—
150C2×C4×C149—81no—
151C2×C4×C149—81no—
152C2×C4×C149—81no—
153C2×C4×C149—81no—
154C2×C4×C149—82no—
155C2×C4×C149#12011yescharacteristic
156C2×C4×C149#12011yescharacteristic
157C2×C4×C149#12011yescharacteristic
158C2×C4×C149#12111yescharacteristic
159C2×C4×C149#12111yescharacteristic
160C2×C4×C149#12111yescharacteristic
161C2×C4×C149C2×SD1612yes—
162C2×C4×C149AGL(1,ℤ/8)12yes—
163C8×C149—24no—
164C8×C149—42no—
165C8×C149—42no—
166C22×C149—21no—
167C22×C149—21no—
168C22×C149—81no—
169C22×C149—81no—
170C22×C149—81no—
171C22×C149#39211yescharacteristic
172C22×C149#49211yescharacteristic
173C22×C149#49611yescharacteristic
174C4×C149—21no—
175C4×C149—21no—
176C4×C149—21no—
177C4×C149—82no—
178C4×C149—81no—
179C4×C149—81no—
180C4×C149—81no—
181C4×C149—82no—
182C4×C149#45012yes—
183C4×C149#45511yescharacteristic
184C4×C149#45611yescharacteristic
185C4×C149#46012yes—
186C2×C149—21no—
187C2×C149—21no—
188C2×C149—161no—
189C2×C149#200711yescharacteristic
190C2×C149#200911yescharacteristic
191C2×C149#201411yescharacteristic
192#10206C14911yesmaximal, characteristic, direct product factor, Sylow
193C149#1020611yescharacteristic, direct product factor, Sylow
194#3246C2×C14911yescharacteristic
195#3229C2×C14911yescharacteristic, complemented
196#3152C2×C14911yescharacteristic
197#1988C2×C14911yescharacteristic, complemented
198#1986C2×C14911yescharacteristic, complemented
199#1502C2×C14911yescharacteristic
200#1283C2×C14911yescharacteristic, complemented
201C2×#137—22no—
202#533C22×C14911yescharacteristic
203#532C22×C14911yescharacteristic
204C2×C4⋊Q8C22×C14911yescharacteristic
205#498—21no—
206#497—22no—
207#494—21no—
208#492—21no—
209#487—21no—
210#483—22no—
211#476—21no—
212#475—22no—
213#475—21no—
214#465—22no—
215#461—21no—
216#460—21no—
217#431C22×C14911yescharacteristic
218C2×C4⋊C8C22×C14911yescharacteristic
219C4×M16C22×C14911yescharacteristic
220C4×C4⋊C4C22×C14911yescharacteristic
221#340—22no—
222#339—22no—
223#327—22no—
224C2×#41—21no—
225C22×Q8—21no—
226#137—44no—
227#137—44no—
228C2×Q16—24no—
229C2×SD16—24no—
230C2×SD16—22no—
231C2×M16D4×C14912yes—
232C22×C8D4×C14912yes—
233C4⋊Q8—21no—
234C4⋊Q8—21no—
235C4⋊Q8—21no—
236C4⋊Q8D4×C14912yes—
237C4⋊Q8D4×C14911yescharacteristic
238C4⋊Q8D4×C14911yescharacteristic
239C4⋊Q8D4×C14911yescharacteristic
240#127D4×C14911yescharacteristic
241#125—21no—
242#124—21no—
243C22⋊Q8—21no—
244C22⋊Q8—21no—
245#121—21no—
246#121—21no—
247C4×Q8—21no—
248C4×Q8—21no—
249C4×D4—21no—
250C4×D4—21no—
251#117—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C42—21no—
256C2×C42C23×C14911yescharacteristic
257#106—22no—
258#106—24no—
259C4⋊C8—21no—
260C4⋊C8—21no—
261C4⋊C8—21no—
262#103—22no—
263#103—24no—
264#102—22no—
265C22⋊C8D4×C14912yes—
266#97—21no—
267C4×C8—21no—
268C4×C8—21no—
269#95—21no—
270#41—42no—
271#41—42no—
272C2×Q8—21no—
273C2×Q8—21no—
274C2×Q8—21no—
275C2×Q8—22no—
276C2×Q8—41no—
277C2×Q8—42no—
278C2×Q8—42no—
279C2×D4—21no—
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—41no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4C2×D4×C14911yescharacteristic
287C22×C4C2×D4×C14911yescharacteristic
288C22×C4C2×D4×C14911yescharacteristic
289Q16—48no—
290SD16—48no—
291SD16—82no—
292M16—22no—
293M16SD16×C14914yescomplemented
294C2×C8—22no—
295C2×C8—22no—
296C2×C8—22no—
297C2×C8—42no—
298C4⋊C4—22no—
299C4⋊C4—21no—
300C4⋊C4—22no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—22no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C22⋊C4—41no—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C42—41no—
316C42—42no—
317C42C2×D4×C14911yescharacteristic
318C42C2×D4×C14911yescharacteristic
319C42C2×D4×C14911yescharacteristic
320C42#41×C14911yescharacteristic
321C23—41no—
322C23#127×C14911yescharacteristic
323Q8—42no—
324Q8—44no—
325Q8—42no—
326Q8—41no—
327Q8—41no—
328Q8—82no—
329D4—42no—
330D4—41no—
331D4—41no—
332D4—81no—
333D4—81no—
334D4—81no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4—81no—
347C2×C4—82no—
348C2×C4#120×C14911yescharacteristic
349C2×C4#120×C14911yescharacteristic
350C2×C4#120×C14911yescharacteristic
351C2×C4#121×C14911yescharacteristic
352C2×C4#121×C14911yescharacteristic
353C2×C4#121×C14911yescharacteristic
354C2×C4C2×SD16×C14912yes—
355C2×C4AGL(1,ℤ/8)×C14912yes—
356C8—24no—
357C8—42no—
358C8—42no—
359C22—21no—
360C22—21no—
361C22—81no—
362C22—81no—
363C22—81no—
364C22#392×C14911yescharacteristic
365C22#492×C14911yescharacteristic
366C22#496×C14911yescharacteristic
367C4—21no—
368C4—21no—
369C4—21no—
370C4—82no—
371C4—81no—
372C4—81no—
373C4—81no—
374C4—82no—
375C4#450×C14912yes—
376C4#455×C14911yescharacteristic
377C4#456×C14911yescharacteristic
378C4#460×C14912yes—
379C2—21no—
380C2—21no—
381C2—161no—
382C2#2007×C14911yescharacteristic
383C2#2009×C14911yescharacteristic
384C2#2014×C14911yescharacteristic
subgroupG/H
center, socleC22×C149#392
commutator, Frattini, cosocleC2×C42C23×C149
prime radical#532×C149C22
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
2. #3229×C149C2semidirect
4. #1988×C149C2semidirect
5. #1986×C149C2semidirect
7. #1283×C149C2semidirect
100. M16×C149SD16semidirect
192. #10206C149direct (N × H)
193. C149#10206direct (N × H)
195. #3229C2×C149semidirect
197. #1988C2×C149semidirect
198. #1986C2×C149semidirect
200. #1283C2×C149semidirect
293. M16SD16×C149semidirect

Maximal subgroups

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

subgroupindex
#3246×C1492
#3229×C1492
#3152×C1492
#1988×C1492
#1986×C1492
#1502×C1492
#1283×C1492
#10206149