Finite Group Databasebeta

← C149×#10182 #49189131

Subgroups — C149×#10182 #49189131

Order 38144.

508 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3209×C149C211yesmaximal, characteristic, complemented
2#3077×C149C211yesmaximal, characteristic
3C2×#476×C149C211yesmaximal, characteristic
4#1549×C149C211yesmaximal, characteristic, complemented
5#1481×C149C211yesmaximal, characteristic, complemented
6#1460×C149C211yesmaximal, characteristic
7#1301×C149C211yesmaximal, characteristic, complemented
8#533×C149C2211yescharacteristic
9C2×C4⋊Q8×C149C2211yescharacteristic
10C2×C4×D4×C149C2211yescharacteristic
11#494×C149—21no—
12#487×C149—21no—
13#478×C149—22no—
14#476×C149—22no—
15#476×C149—21no—
16#476×C149—22no—
17#474×C149—21no—
18#462×C149—22no—
19#451×C149—22no—
20#431×C149C2211yescharacteristic
21#431×C149C2211yescharacteristic
22#428×C149—21no—
23C2×#106×C149—21no—
24#423×C149C2211yescharacteristic
25C2×C4⋊C8×C149C2211yescharacteristic
26#418×C149—21no—
27C2×#102×C149—21no—
28#332×C149—22no—
29Q8⋊C8×C149—22no—
30#323×C149—22no—
31C22×Q8×C149—21no—
32C22×D4×C149D411yescharacteristic
33C23×C4×C149—21no—
34C2×Q16×C149—24no—
35C2×M16×C149—21no—
36C22×C8×C149—21no—
37C4⋊Q8×C149—21no—
38C4⋊Q8×C149—21no—
39C4⋊Q8×C149—21no—
40C4⋊Q8×C149D412yes—
41C4⋊Q8×C149D411yescharacteristic
42C4⋊Q8×C149D411yescharacteristic
43#125×C149—21no—
44C22⋊Q8×C149—21no—
45C22⋊Q8×C149—21no—
46C4×Q8×C149—21no—
47C4×Q8×C149—21no—
48C4×D4×C149—21no—
49C4×D4×C149—21no—
50C4×D4×C149—21no—
51C4×D4×C149—21no—
52#117×C149—21no—
53C2×C4⋊C4×C149—21no—
54C2×C4⋊C4×C149—21no—
55C2×C4⋊C4×C149D411yescharacteristic
56C2×C22⋊C4×C149—21no—
57C2×C42×C149C2311yescharacteristic
58#107×C149—22no—
59#106×C149—24no—
60#106×C149—22no—
61C4⋊C8×C149—21no—
62C4⋊C8×C149—21no—
63C4⋊C8×C149—21no—
64C4⋊C8×C149—21no—
65C4⋊C8×C149D412yes—
66C4⋊C8×C149D412yes—
67#103×C149—24no—
68#102×C149—24no—
69#102×C149—22no—
70#102×C149—22no—
71C22⋊C8×C149—21no—
72C22⋊C8×C149D412yes—
73C4×C8×C149—21no—
74C4×C8×C149—21no—
75C24×C149—21no—
76C2×Q8×C149—22no—
77C2×Q8×C149—21no—
78C2×Q8×C149—21no—
79C2×Q8×C149—41no—
80C2×Q8×C149—82no—
81C2×D4×C149—21no—
82C2×D4×C149—21no—
83C2×D4×C149—21no—
84C2×D4×C149—21no—
85C2×D4×C149—21no—
86C2×D4×C149Q1612yescomplemented
87C22×C4×C149—21no—
88C22×C4×C149—41no—
89C22×C4×C149—41no—
90C22×C4×C149—41no—
91C22×C4×C149—82no—
92C22×C4×C149C2×D411yescharacteristic
93C22×C4×C149C2×D411yescharacteristic
94C22×C4×C149#4111yescharacteristic
95Q16×C149—84no—
96M16×C149—41no—
97M16×C149—41no—
98C2×C8×C149—22no—
99C2×C8×C149—22no—
100C2×C8×C149—22no—
101C2×C8×C149—41no—
102C2×C8×C149—41no—
103C2×C8×C149—41no—
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—22no—
111C4⋊C4×C149—21no—
112C4⋊C4×C149—41no—
113C4⋊C4×C149—41no—
114C4⋊C4×C149—41no—
115C4⋊C4×C149—41no—
116C22⋊C4×C149—41no—
117C22⋊C4×C149—41no—
118C22⋊C4×C149—41no—
119C42×C149—41no—
120C42×C149C2×D411yescharacteristic
121C42×C149C2×D411yescharacteristic
122C42×C149C2×D411yescharacteristic
123C42×C149C2×D411yescharacteristic
124C23×C149—22no—
125C23×C149—41no—
126C23×C149—41no—
127C23×C149—81no—
128C23×C149—81no—
129C23×C149#12111yescharacteristic
130Q8×C149—42no—
131Q8×C149—44no—
132Q8×C149—42no—
133Q8×C149—82no—
134D4×C149—22no—
135D4×C149—22no—
136D4×C149—41no—
137D4×C149—41no—
138C2×C4×C149—22no—
139C2×C4×C149—41no—
140C2×C4×C149—41no—
141C2×C4×C149—41no—
142C2×C4×C149—41no—
143C2×C4×C149—42no—
144C2×C4×C149—82no—
145C2×C4×C149—82no—
146C2×C4×C149—82no—
147C2×C4×C149—81no—
148C2×C4×C149#12011yescharacteristic
149C2×C4×C149#12011yescharacteristic
150C2×C4×C149#12011yescharacteristic
151C2×C4×C149#12111yescharacteristic
152C2×C4×C149#12111yescharacteristic
153C2×C4×C149#12711yescharacteristic
154C2×C4×C149C2×Q1611yescharacteristic
155C2×C4×C149#13511yescharacteristic
156C2×C4×C149#13711yescharacteristic
157C2×C4×C149#13711yescharacteristic
158C8×C149—42no—
159C8×C149—42no—
160C8×C149—42no—
161C8×C149—81no—
162C22×C149—21no—
163C22×C149—21no—
164C22×C149—42no—
165C22×C149—82no—
166C22×C149—82no—
167C22×C149—81no—
168C22×C149—81no—
169C22×C149#39211yescharacteristic
170C22×C149#46711yescharacteristic
171C22×C149#47011yescharacteristic
172C4×C149—21no—
173C4×C149—21no—
174C4×C149—21no—
175C4×C149—82no—
176C4×C149—81no—
177C4×C149—81no—
178C4×C149—81no—
179C4×C149#45111yescharacteristic
180C4×C149#45111yescharacteristic
181C4×C149#45211yescharacteristic
182C4×C149#45211yescharacteristic
183C4×C149#47112yes—
184C2×C149—21no—
185C2×C149—21no—
186C2×C149—82no—
187C2×C149#200111yescharacteristic
188C2×C149#200811yescharacteristic
189C2×C149#201911yescharacteristic
190#10182C14911yesmaximal, characteristic, direct product factor, Sylow
191C149#1018211yescharacteristic, direct product factor, Sylow
192#3209C2×C14911yescharacteristic, complemented
193#3077C2×C14911yescharacteristic
194C2×#476C2×C14911yescharacteristic
195#1549C2×C14911yescharacteristic, complemented
196#1481C2×C14911yescharacteristic, complemented
197#1460C2×C14911yescharacteristic
198#1301C2×C14911yescharacteristic, complemented
199#533C22×C14911yescharacteristic
200C2×C4⋊Q8C22×C14911yescharacteristic
201C2×C4×D4C22×C14911yescharacteristic
202#494—21no—
203#487—21no—
204#478—22no—
205#476—21no—
206#476—22no—
207#476—22no—
208#474—21no—
209#462—22no—
210#451—22no—
211#431C22×C14911yescharacteristic
212#431C22×C14911yescharacteristic
213#428—21no—
214C2×#106—21no—
215#423C22×C14911yescharacteristic
216C2×C4⋊C8C22×C14911yescharacteristic
217#418—21no—
218C2×#102—21no—
219#332—22no—
220Q8⋊C8—22no—
221#323—22no—
222C22×Q8—21no—
223C22×D4D4×C14911yescharacteristic
224C23×C4—21no—
225C2×Q16—24no—
226C2×M16—21no—
227C22×C8—21no—
228C4⋊Q8—21no—
229C4⋊Q8—21no—
230C4⋊Q8—21no—
231C4⋊Q8D4×C14912yes—
232C4⋊Q8D4×C14911yescharacteristic
233C4⋊Q8D4×C14911yescharacteristic
234#125—21no—
235C22⋊Q8—21no—
236C22⋊Q8—21no—
237C4×Q8—21no—
238C4×Q8—21no—
239C4×D4—21no—
240C4×D4—21no—
241C4×D4—21no—
242C4×D4—21no—
243#117—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4D4×C14911yescharacteristic
247C2×C22⋊C4—21no—
248C2×C42C23×C14911yescharacteristic
249#107—22no—
250#106—24no—
251#106—22no—
252C4⋊C8—21no—
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8—21no—
256C4⋊C8D4×C14912yes—
257C4⋊C8D4×C14912yes—
258#103—24no—
259#102—24no—
260#102—22no—
261#102—22no—
262C22⋊C8—21no—
263C22⋊C8D4×C14912yes—
264C4×C8—21no—
265C4×C8—21no—
266C24—21no—
267C2×Q8—22no—
268C2×Q8—21no—
269C2×Q8—21no—
270C2×Q8—41no—
271C2×Q8—82no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4Q16×C14912yescomplemented
278C22×C4—21no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—82no—
283C22×C4C2×D4×C14911yescharacteristic
284C22×C4C2×D4×C14911yescharacteristic
285C22×C4#41×C14911yescharacteristic
286Q16—84no—
287M16—41no—
288M16—41no—
289C2×C8—22no—
290C2×C8—22no—
291C2×C8—22no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—41no—
295C4⋊C4—22no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—22no—
302C4⋊C4—21no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C42—41no—
311C42C2×D4×C14911yescharacteristic
312C42C2×D4×C14911yescharacteristic
313C42C2×D4×C14911yescharacteristic
314C42C2×D4×C14911yescharacteristic
315C23—22no—
316C23—41no—
317C23—41no—
318C23—81no—
319C23—81no—
320C23#121×C14911yescharacteristic
321Q8—42no—
322Q8—44no—
323Q8—42no—
324Q8—82no—
325D4—22no—
326D4—22no—
327D4—41no—
328D4—41no—
329C2×C4—22no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—82no—
336C2×C4—82no—
337C2×C4—82no—
338C2×C4—81no—
339C2×C4#120×C14911yescharacteristic
340C2×C4#120×C14911yescharacteristic
341C2×C4#120×C14911yescharacteristic
342C2×C4#121×C14911yescharacteristic
343C2×C4#121×C14911yescharacteristic
344C2×C4#127×C14911yescharacteristic
345C2×C4C2×Q16×C14911yescharacteristic
346C2×C4#135×C14911yescharacteristic
347C2×C4#137×C14911yescharacteristic
348C2×C4#137×C14911yescharacteristic
349C8—42no—
350C8—42no—
351C8—42no—
352C8—81no—
353C22—21no—
354C22—21no—
355C22—42no—
356C22—82no—
357C22—82no—
358C22—81no—
359C22—81no—
360C22#392×C14911yescharacteristic
361C22#467×C14911yescharacteristic
362C22#470×C14911yescharacteristic
363C4—21no—
364C4—21no—
365C4—21no—
366C4—82no—
367C4—81no—
368C4—81no—
369C4—81no—
370C4#451×C14911yescharacteristic
371C4#451×C14911yescharacteristic
372C4#452×C14911yescharacteristic
373C4#452×C14911yescharacteristic
374C4#471×C14912yes—
375C2—21no—
376C2—21no—
377C2—82no—
378C2#2001×C14911yescharacteristic
379C2#2008×C14911yescharacteristic
380C2#2019×C14911yescharacteristic
subgroupG/H
center, socleC22×C149#392
commutator, Frattini, cosocleC2×C42C23×C149
prime radicalC22×D4×C149D4
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. #3209×C149C2semidirect
4. #1549×C149C2semidirect
5. #1481×C149C2semidirect
7. #1301×C149C2semidirect
86. C2×D4×C149Q16semidirect
190. #10182C149direct (N × H)
191. C149#10182direct (N × H)
192. #3209C2×C149semidirect
195. #1549C2×C149semidirect
196. #1481C2×C149semidirect
198. #1301C2×C149semidirect
277. C2×D4Q16×C149semidirect

Maximal subgroups

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

subgroupindex
#3209×C1492
#3077×C1492
C2×#476×C1492
#1549×C1492
#1481×C1492
#1460×C1492
#1301×C1492
#10182149