Finite Group Databasebeta

← C149×#10195 #49189144

Subgroups — C149×#10195 #49189144

Order 38144.

554 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3249×C149C211yesmaximal, characteristic, complemented
2#3208×C149C211yesmaximal, characteristic
3#3138×C149C211yesmaximal, characteristic
4#1986×C149C211yesmaximal, characteristic, complemented
5#1982×C149C211yesmaximal, characteristic
6#1503×C149C211yesmaximal, characteristic, complemented
7#1283×C149C211yesmaximal, characteristic, complemented
8#533×C149C2211yescharacteristic
9#533×C149C2211yescharacteristic
10C2×#127×C149C2211yescharacteristic
11#492×C149—21no—
12#490×C149—22no—
13#486×C149—21no—
14#486×C149—21no—
15#486×C149—21no—
16#477×C149—21no—
17#477×C149—21no—
18#467×C149—22no—
19#462×C149—21no—
20#462×C149—21no—
21#460×C149—22no—
22#450×C149—22no—
23#431×C149C2211yescharacteristic
24C2×C4⋊C8×C149C2211yescharacteristic
25#418×C149—22no—
26C2×#102×C149—22no—
27C4×M16×C149C2211yescharacteristic
28C4×C4⋊C4×C149C2211yescharacteristic
29#339×C149—22no—
30#328×C149—22no—
31C22×D4×C149—21no—
32C22×D4×C149—21no—
33C22×D4×C149—21no—
34C2×Q16×C149—22no—
35C2×SD16×C149—24no—
36C2×M16×C149D412yes—
37C22×C8×C149D412yes—
38C4⋊Q8×C149D411yescharacteristic
39C4⋊Q8×C149D411yescharacteristic
40C4⋊Q8×C149D411yescharacteristic
41C4⋊Q8×C149D411yescharacteristic
42#127×C149—21no—
43#127×C149—21no—
44#127×C149—21no—
45#127×C149D412yes—
46#125×C149—21no—
47#125×C149—21no—
48C22⋊Q8×C149—21no—
49C22⋊Q8×C149—21no—
50C22⋊Q8×C149—21no—
51C22⋊Q8×C149—21no—
52C4×Q8×C149—21no—
53C4×Q8×C149—21no—
54C4×Q8×C149—21no—
55C4×Q8×C149—21no—
56#117×C149—21no—
57#117×C149—21no—
58C2×C4⋊C4×C149—21no—
59C2×C42×C149—21no—
60C2×C42×C149C2311yescharacteristic
61#107×C149—22no—
62C4⋊C8×C149—21no—
63C4⋊C8×C149—21no—
64C4⋊C8×C149—21no—
65#103×C149—22no—
66#103×C149—22no—
67#102×C149—24no—
68#102×C149—24no—
69#102×C149—24no—
70#102×C149—44no—
71C22⋊C8×C149D412yes—
72#97×C149—21no—
73C4×C8×C149—21no—
74C4×C8×C149—21no—
75#95×C149—21no—
76C24×C149—41no—
77C2×Q8×C149—21no—
78C2×Q8×C149—21no—
79C2×Q8×C149—21no—
80C2×Q8×C149—21no—
81C2×D4×C149—22no—
82C2×D4×C149—22no—
83C2×D4×C149—22no—
84C2×D4×C149—42no—
85C2×D4×C149—42no—
86C2×D4×C149—41no—
87C2×D4×C149—41no—
88C2×D4×C149—41no—
89C2×D4×C149—42no—
90C2×D4×C149—42no—
91C2×D4×C149—82no—
92C22×C4×C149—41no—
93C22×C4×C149C2×D411yescharacteristic
94C22×C4×C149C2×D411yescharacteristic
95C22×C4×C149C2×D411yescharacteristic
96Q16×C149—82no—
97SD16×C149—84no—
98M16×C149—22no—
99M16×C149—22no—
100C2×C8×C149—22no—
101C2×C8×C149—22no—
102C2×C8×C149—22no—
103C2×C8×C149—42no—
104C4⋊C4×C149—22no—
105C4⋊C4×C149—21no—
106C4⋊C4×C149—21no—
107C4⋊C4×C149—21no—
108C4⋊C4×C149—21no—
109C4⋊C4×C149—21no—
110C4⋊C4×C149—21no—
111C4⋊C4×C149—21no—
112C4⋊C4×C149—21no—
113C4⋊C4×C149—41no—
114C4⋊C4×C149—41no—
115C4⋊C4×C149—41no—
116C4⋊C4×C149—41no—
117C4⋊C4×C149—41no—
118C22⋊C4×C149—41no—
119C22⋊C4×C149—41no—
120C42×C149—41no—
121C42×C149—41no—
122C42×C149—42no—
123C42×C149C2×D411yescharacteristic
124C42×C149C2×D411yescharacteristic
125C42×C149C2×D411yescharacteristic
126C42×C149#4111yescharacteristic
127C23×C149—42no—
128C23×C149—82no—
129C23×C149—82no—
130C23×C149—81no—
131C23×C149—81no—
132C23×C149#12711yescharacteristic
133Q8×C149—42no—
134Q8×C149—41no—
135Q8×C149—41no—
136Q8×C149—41no—
137Q8×C149—41no—
138Q8×C149—81no—
139D4×C149—44no—
140D4×C149—44no—
141D4×C149—44no—
142D4×C149—82no—
143D4×C149—81no—
144D4×C149—81no—
145D4×C149—82no—
146C2×C4×C149—21no—
147C2×C4×C149—21no—
148C2×C4×C149—41no—
149C2×C4×C149—42no—
150C2×C4×C149—41no—
151C2×C4×C149—41no—
152C2×C4×C149—41no—
153C2×C4×C149—41no—
154C2×C4×C149—81no—
155C2×C4×C149—81no—
156C2×C4×C149#12011yescharacteristic
157C2×C4×C149#12011yescharacteristic
158C2×C4×C149#12011yescharacteristic
159C2×C4×C149#12111yescharacteristic
160C2×C4×C149#12111yescharacteristic
161C2×C4×C149#12111yescharacteristic
162C2×C4×C149#13512yes—
163C2×C4×C149#13712yes—
164C8×C149—42no—
165C8×C149—42no—
166C8×C149—42no—
167C22×C149—21no—
168C22×C149—21no—
169C22×C149—82no—
170C22×C149—82no—
171C22×C149—82no—
172C22×C149—162no—
173C22×C149—162no—
174C22×C149#39211yescharacteristic
175C22×C149#49511yescharacteristic
176C22×C149#49711yescharacteristic
177C4×C149—21no—
178C4×C149—21no—
179C4×C149—21no—
180C4×C149—82no—
181C4×C149—81no—
182C4×C149—81no—
183C4×C149—81no—
184C4×C149—81no—
185C4×C149#45212yes—
186C4×C149#45311yescharacteristic
187C4×C149#45411yescharacteristic
188C4×C149#46412yes—
189C2×C149—21no—
190C2×C149—21no—
191C2×C149—162no—
192C2×C149#200611yescharacteristic
193C2×C149#200811yescharacteristic
194C2×C149#201511yescharacteristic
195#10195C14911yesmaximal, characteristic, direct product factor, Sylow
196C149#1019511yescharacteristic, direct product factor, Sylow
197#3249C2×C14911yescharacteristic, complemented
198#3208C2×C14911yescharacteristic
199#3138C2×C14911yescharacteristic
200#1986C2×C14911yescharacteristic, complemented
201#1982C2×C14911yescharacteristic
202#1503C2×C14911yescharacteristic, complemented
203#1283C2×C14911yescharacteristic, complemented
204#533C22×C14911yescharacteristic
205#533C22×C14911yescharacteristic
206C2×#127C22×C14911yescharacteristic
207#492—21no—
208#490—22no—
209#486—21no—
210#486—21no—
211#486—21no—
212#477—21no—
213#477—21no—
214#467—22no—
215#462—21no—
216#462—21no—
217#460—22no—
218#450—22no—
219#431C22×C14911yescharacteristic
220C2×C4⋊C8C22×C14911yescharacteristic
221#418—22no—
222C2×#102—22no—
223C4×M16C22×C14911yescharacteristic
224C4×C4⋊C4C22×C14911yescharacteristic
225#339—22no—
226#328—22no—
227C22×D4—21no—
228C22×D4—21no—
229C22×D4—21no—
230C2×Q16—22no—
231C2×SD16—24no—
232C2×M16D4×C14912yes—
233C22×C8D4×C14912yes—
234C4⋊Q8D4×C14911yescharacteristic
235C4⋊Q8D4×C14911yescharacteristic
236C4⋊Q8D4×C14911yescharacteristic
237C4⋊Q8D4×C14911yescharacteristic
238#127—21no—
239#127—21no—
240#127—21no—
241#127D4×C14912yes—
242#125—21no—
243#125—21no—
244C22⋊Q8—21no—
245C22⋊Q8—21no—
246C22⋊Q8—21no—
247C22⋊Q8—21no—
248C4×Q8—21no—
249C4×Q8—21no—
250C4×Q8—21no—
251C4×Q8—21no—
252#117—21no—
253#117—21no—
254C2×C4⋊C4—21no—
255C2×C42—21no—
256C2×C42C23×C14911yescharacteristic
257#107—22no—
258C4⋊C8—21no—
259C4⋊C8—21no—
260C4⋊C8—21no—
261#103—22no—
262#103—22no—
263#102—24no—
264#102—24no—
265#102—24no—
266#102—44no—
267C22⋊C8D4×C14912yes—
268#97—21no—
269C4×C8—21no—
270C4×C8—21no—
271#95—21no—
272C24—41no—
273C2×Q8—21no—
274C2×Q8—21no—
275C2×Q8—21no—
276C2×Q8—21no—
277C2×D4—22no—
278C2×D4—22no—
279C2×D4—22no—
280C2×D4—42no—
281C2×D4—42no—
282C2×D4—41no—
283C2×D4—41no—
284C2×D4—41no—
285C2×D4—42no—
286C2×D4—42no—
287C2×D4—82no—
288C22×C4—41no—
289C22×C4C2×D4×C14911yescharacteristic
290C22×C4C2×D4×C14911yescharacteristic
291C22×C4C2×D4×C14911yescharacteristic
292Q16—82no—
293SD16—84no—
294M16—22no—
295M16—22no—
296C2×C8—22no—
297C2×C8—22no—
298C2×C8—22no—
299C2×C8—42no—
300C4⋊C4—22no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C42—41no—
317C42—41no—
318C42—42no—
319C42C2×D4×C14911yescharacteristic
320C42C2×D4×C14911yescharacteristic
321C42C2×D4×C14911yescharacteristic
322C42#41×C14911yescharacteristic
323C23—42no—
324C23—82no—
325C23—82no—
326C23—81no—
327C23—81no—
328C23#127×C14911yescharacteristic
329Q8—42no—
330Q8—41no—
331Q8—41no—
332Q8—41no—
333Q8—41no—
334Q8—81no—
335D4—44no—
336D4—44no—
337D4—44no—
338D4—82no—
339D4—81no—
340D4—81no—
341D4—82no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—41no—
345C2×C4—42no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—81no—
351C2×C4—81no—
352C2×C4#120×C14911yescharacteristic
353C2×C4#120×C14911yescharacteristic
354C2×C4#120×C14911yescharacteristic
355C2×C4#121×C14911yescharacteristic
356C2×C4#121×C14911yescharacteristic
357C2×C4#121×C14911yescharacteristic
358C2×C4#135×C14912yes—
359C2×C4#137×C14912yes—
360C8—42no—
361C8—42no—
362C8—42no—
363C22—21no—
364C22—21no—
365C22—82no—
366C22—82no—
367C22—82no—
368C22—162no—
369C22—162no—
370C22#392×C14911yescharacteristic
371C22#495×C14911yescharacteristic
372C22#497×C14911yescharacteristic
373C4—21no—
374C4—21no—
375C4—21no—
376C4—82no—
377C4—81no—
378C4—81no—
379C4—81no—
380C4—81no—
381C4#452×C14912yes—
382C4#453×C14911yescharacteristic
383C4#454×C14911yescharacteristic
384C4#464×C14912yes—
385C2—21no—
386C2—21no—
387C2—162no—
388C2#2006×C14911yescharacteristic
389C2#2008×C14911yescharacteristic
390C2#2015×C14911yescharacteristic
subgroupG/H
center, socleC22×C149#392
commutator, Frattini, cosocleC2×C42C23×C149
prime radicalC2×#127×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
1. #3249×C149C2semidirect
4. #1986×C149C2semidirect
6. #1503×C149C2semidirect
7. #1283×C149C2semidirect
195. #10195C149direct (N × H)
196. C149#10195direct (N × H)
197. #3249C2×C149semidirect
200. #1986C2×C149semidirect
202. #1503C2×C149semidirect
203. #1283C2×C149semidirect

Maximal subgroups

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

subgroupindex
#3249×C1492
#3208×C1492
#3138×C1492
#1986×C1492
#1982×C1492
#1503×C1492
#1283×C1492
#10195149