Finite Group Databasebeta

← C149×#8990 #49187939

Subgroups — C149×#8990 #49187939

Order 38144.

462 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3104×C149C211yesmaximal, characteristic
2Q8×M16×C149C211yesmaximal, characteristic
3#1986×C149C211yesmaximal, characteristic
4C4×#103×C149C211yesmaximal, characteristic
5#1493×C149C211yesmaximal, characteristic
6#1303×C149C211yesmaximal, characteristic
7#1278×C149C211yesmaximal, characteristic
8#533×C149C2211yescharacteristic
9C2×C4×Q8×C149C2211yescharacteristic
10#484×C149—21no—
11#477×C149C411yescharacteristic, complemented
12#477×C149C411yescharacteristic, complemented
13#462×C149C411yescharacteristic, complemented
14#462×C149C411yescharacteristic, complemented
15#451×C149—21no—
16#446×C149—21no—
17#446×C149—22no—
18C8×Q8×C149—21no—
19C4×Q16×C149—21no—
20C4×Q16×C149—21no—
21#431×C149C2211yescharacteristic
22#423×C149—21no—
23#423×C149C2211yescharacteristic
24C2×#103×C149—21no—
25C4×M16×C149—21no—
26C4×M16×C149C2211yescharacteristic
27C2×C4×C8×C149C2211yescharacteristic
28C4×C4⋊C4×C149C2211yescharacteristic
29#340×C149—21no—
30#339×C149—21no—
31#339×C149—21no—
32Q8⋊C8×C149—22no—
33C22×Q8×C149D411yescharacteristic
34C2×Q16×C149—21no—
35C2×Q16×C149—21no—
36C2×M16×C149—21no—
37C2×M16×C149D411yescharacteristic
38C2×M16×C149D411yescharacteristic
39C22×C8×C149—21no—
40C4⋊Q8×C149C2×C411yescharacteristic
41C4⋊Q8×C149C2×C411yescharacteristic
42#125×C149—21no—
43C22⋊Q8×C149—21no—
44C22⋊Q8×C149—21no—
45C4×Q8×C149—21no—
46C4×Q8×C149—21no—
47C4×Q8×C149—21no—
48C4×Q8×C149—21no—
49C4×Q8×C149C2×C411yescharacteristic
50C4×Q8×C149C2×C411yescharacteristic
51C4×Q8×C149D411yescharacteristic
52C4×Q8×C149D411yescharacteristic
53#117×C149—21no—
54C2×C4⋊C4×C149—21no—
55C2×C4⋊C4×C149—21no—
56C2×C4⋊C4×C149D411yescharacteristic
57C2×C42×C149—21no—
58C2×C42×C149—21no—
59C2×C42×C149C2311yescharacteristic
60#107×C149—21no—
61#107×C149—21no—
62C4⋊C8×C149—22no—
63C4⋊C8×C149—22no—
64C4⋊C8×C149—21no—
65C4⋊C8×C149C2×C411yescharacteristic
66C4⋊C8×C149C2×C411yescharacteristic
67C4⋊C8×C149D412yes—
68#103×C149—24no—
69#103×C149—21no—
70#103×C149—21no—
71#103×C149—21no—
72#103×C149—21no—
73C22⋊C8×C149—21no—
74#97×C149—22no—
75#97×C149—21no—
76C4×C8×C149—22no—
77C4×C8×C149—21no—
78C4×C8×C149—21no—
79C4×C8×C149—21no—
80C4×C8×C149—21no—
81#95×C149—21no—
82C2×Q8×C149—21no—
83C2×Q8×C149—22no—
84C2×Q8×C149—21no—
85C2×Q8×C149—21no—
86C2×Q8×C149—41no—
87C2×Q8×C149C22⋊C411yescharacteristic
88C2×Q8×C149C22⋊C411yescharacteristic
89C22×C4×C149—21no—
90C22×C4×C149—21no—
91C22×C4×C149—41no—
92C22×C4×C149C2×D411yescharacteristic
93C22×C4×C149C2×D411yescharacteristic
94C22×C4×C149#4111yescharacteristic
95Q16×C149—42no—
96Q16×C149—42no—
97M16×C149—21no—
98M16×C149—21no—
99M16×C149—21no—
100M16×C149—41no—
101M16×C149—41no—
102M16×C149Q1612yescomplemented
103C2×C8×C149—21no—
104C2×C8×C149—22no—
105C2×C8×C149—21no—
106C2×C8×C149—21no—
107C2×C8×C149—21no—
108C2×C8×C149—22no—
109C2×C8×C149—41no—
110C2×C8×C149—41no—
111C4⋊C4×C149—21no—
112C4⋊C4×C149—21no—
113C4⋊C4×C149—21no—
114C4⋊C4×C149—21no—
115C4⋊C4×C149—21no—
116C4⋊C4×C149—22no—
117C4⋊C4×C149—21no—
118C4⋊C4×C149—21no—
119C4⋊C4×C149—21no—
120C4⋊C4×C149—21no—
121C4⋊C4×C149—41no—
122C4⋊C4×C149—41no—
123C4⋊C4×C149—41no—
124C4⋊C4×C149C22⋊C411yescharacteristic
125C4⋊C4×C149C22⋊C411yescharacteristic
126C22⋊C4×C149—41no—
127C42×C149—21no—
128C42×C149—21no—
129C42×C149—21no—
130C42×C149—21no—
131C42×C149—41no—
132C42×C149—41no—
133C42×C149—41no—
134C42×C149C22×C411yescharacteristic
135C42×C149C2×D411yescharacteristic
136C42×C149C2×D411yescharacteristic
137C42×C149#4111yescharacteristic
138C23×C149#12111yescharacteristic
139Q8×C149—21no—
140Q8×C149—21no—
141Q8×C149—21no—
142Q8×C149—42no—
143Q8×C149—42no—
144Q8×C149—41no—
145Q8×C149—41no—
146Q8×C149#10412yes—
147C2×C4×C149—21no—
148C2×C4×C149—21no—
149C2×C4×C149—21no—
150C2×C4×C149—21no—
151C2×C4×C149—21no—
152C2×C4×C149—21no—
153C2×C4×C149—41no—
154C2×C4×C149—42no—
155C2×C4×C149—42no—
156C2×C4×C149—41no—
157C2×C4×C149—41no—
158C2×C4×C149—81no—
159C2×C4×C149—81no—
160C2×C4×C149—81no—
161C2×C4×C149C2×C22⋊C411yescharacteristic
162C2×C4×C149C4×D411yescharacteristic
163C2×C4×C149C4×D411yescharacteristic
164C2×C4×C149#12011yescharacteristic
165C2×C4×C149#12111yescharacteristic
166C2×C4×C149#12311yescharacteristic
167C2×C4×C149C2×Q1611yescharacteristic
168C2×C4×C149#13511yescharacteristic
169C2×C4×C149#13711yescharacteristic
170C2×C4×C149#13711yescharacteristic
171C8×C149—22no—
172C8×C149—42no—
173C8×C149—41no—
174C8×C149—41no—
175C8×C149—41no—
176C8×C149—42no—
177C22×C149—21no—
178C22×C149—21no—
179C22×C149#38611yescharacteristic
180C22×C149#46211yescharacteristic
181C22×C149#46411yescharacteristic
182C4×C149—21no—
183C4×C149—22no—
184C4×C149—21no—
185C4×C149—21no—
186C4×C149—41no—
187C4×C149—41no—
188C4×C149—41no—
189C4×C149—82no—
190C4×C149—81no—
191C4×C149—81no—
192C4×C149C2×#10411yescharacteristic
193C4×C149#42111yescharacteristic
194C4×C149C4×Q1611yescharacteristic
195C4×C149#44111yescharacteristic
196C4×C149#45111yescharacteristic
197C4×C149#45211yescharacteristic
198C2×C149—21no—
199C2×C149—21no—
200C2×C149#187111yescharacteristic
201C2×C149#187811yescharacteristic
202C2×C149#188111yescharacteristic
203#8990C14911yesmaximal, characteristic, direct product factor, Sylow
204C149#899011yescharacteristic, direct product factor, Sylow
205#3104C2×C14911yescharacteristic
206Q8×M16C2×C14911yescharacteristic
207#1986C2×C14911yescharacteristic
208C4×#103C2×C14911yescharacteristic
209#1493C2×C14911yescharacteristic
210#1303C2×C14911yescharacteristic
211#1278C2×C14911yescharacteristic
212#533C22×C14911yescharacteristic
213C2×C4×Q8C22×C14911yescharacteristic
214#484—21no—
215#477C4×C14911yescharacteristic, complemented
216#477C4×C14911yescharacteristic, complemented
217#462C4×C14911yescharacteristic, complemented
218#462C4×C14911yescharacteristic, complemented
219#451—21no—
220#446—21no—
221#446—22no—
222C8×Q8—21no—
223C4×Q16—21no—
224C4×Q16—21no—
225#431C22×C14911yescharacteristic
226#423—21no—
227#423C22×C14911yescharacteristic
228C2×#103—21no—
229C4×M16—21no—
230C4×M16C22×C14911yescharacteristic
231C2×C4×C8C22×C14911yescharacteristic
232C4×C4⋊C4C22×C14911yescharacteristic
233#340—21no—
234#339—21no—
235#339—21no—
236Q8⋊C8—22no—
237C22×Q8D4×C14911yescharacteristic
238C2×Q16—21no—
239C2×Q16—21no—
240C2×M16—21no—
241C2×M16D4×C14911yescharacteristic
242C2×M16D4×C14911yescharacteristic
243C22×C8—21no—
244C4⋊Q8C2×C4×C14911yescharacteristic
245C4⋊Q8C2×C4×C14911yescharacteristic
246#125—21no—
247C22⋊Q8—21no—
248C22⋊Q8—21no—
249C4×Q8—21no—
250C4×Q8—21no—
251C4×Q8—21no—
252C4×Q8—21no—
253C4×Q8C2×C4×C14911yescharacteristic
254C4×Q8C2×C4×C14911yescharacteristic
255C4×Q8D4×C14911yescharacteristic
256C4×Q8D4×C14911yescharacteristic
257#117—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4D4×C14911yescharacteristic
261C2×C42—21no—
262C2×C42—21no—
263C2×C42C23×C14911yescharacteristic
264#107—21no—
265#107—21no—
266C4⋊C8—22no—
267C4⋊C8—22no—
268C4⋊C8—21no—
269C4⋊C8C2×C4×C14911yescharacteristic
270C4⋊C8C2×C4×C14911yescharacteristic
271C4⋊C8D4×C14912yes—
272#103—24no—
273#103—21no—
274#103—21no—
275#103—21no—
276#103—21no—
277C22⋊C8—21no—
278#97—22no—
279#97—21no—
280C4×C8—22no—
281C4×C8—21no—
282C4×C8—21no—
283C4×C8—21no—
284C4×C8—21no—
285#95—21no—
286C2×Q8—21no—
287C2×Q8—22no—
288C2×Q8—21no—
289C2×Q8—21no—
290C2×Q8—41no—
291C2×Q8C22⋊C4×C14911yescharacteristic
292C2×Q8C22⋊C4×C14911yescharacteristic
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—41no—
296C22×C4C2×D4×C14911yescharacteristic
297C22×C4C2×D4×C14911yescharacteristic
298C22×C4#41×C14911yescharacteristic
299Q16—42no—
300Q16—42no—
301M16—21no—
302M16—21no—
303M16—21no—
304M16—41no—
305M16—41no—
306M16Q16×C14912yescomplemented
307C2×C8—21no—
308C2×C8—22no—
309C2×C8—21no—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—22no—
313C2×C8—41no—
314C2×C8—41no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—22no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4C22⋊C4×C14911yescharacteristic
329C4⋊C4C22⋊C4×C14911yescharacteristic
330C22⋊C4—41no—
331C42—21no—
332C42—21no—
333C42—21no—
334C42—21no—
335C42—41no—
336C42—41no—
337C42—41no—
338C42C22×C4×C14911yescharacteristic
339C42C2×D4×C14911yescharacteristic
340C42C2×D4×C14911yescharacteristic
341C42#41×C14911yescharacteristic
342C23#121×C14911yescharacteristic
343Q8—21no—
344Q8—21no—
345Q8—21no—
346Q8—42no—
347Q8—42no—
348Q8—41no—
349Q8—41no—
350Q8#104×C14912yes—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—41no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—81no—
363C2×C4—81no—
364C2×C4—81no—
365C2×C4C2×C22⋊C4×C14911yescharacteristic
366C2×C4C4×D4×C14911yescharacteristic
367C2×C4C4×D4×C14911yescharacteristic
368C2×C4#120×C14911yescharacteristic
369C2×C4#121×C14911yescharacteristic
370C2×C4#123×C14911yescharacteristic
371C2×C4C2×Q16×C14911yescharacteristic
372C2×C4#135×C14911yescharacteristic
373C2×C4#137×C14911yescharacteristic
374C2×C4#137×C14911yescharacteristic
375C8—22no—
376C8—42no—
377C8—41no—
378C8—41no—
379C8—41no—
380C8—42no—
381C22—21no—
382C22—21no—
383C22#386×C14911yescharacteristic
384C22#462×C14911yescharacteristic
385C22#464×C14911yescharacteristic
386C4—21no—
387C4—22no—
388C4—21no—
389C4—21no—
390C4—41no—
391C4—41no—
392C4—41no—
393C4—82no—
394C4—81no—
395C4—81no—
396C4C2×#104×C14911yescharacteristic
397C4#421×C14911yescharacteristic
398C4C4×Q16×C14911yescharacteristic
399C4#441×C14911yescharacteristic
400C4#451×C14911yescharacteristic
401C4#452×C14911yescharacteristic
402C2—21no—
403C2—21no—
404C2#1871×C14911yescharacteristic
405C2#1878×C14911yescharacteristic
406C2#1881×C14911yescharacteristic
subgroupG/H
centerC2×C4×C149#120
commutatorC42C22×C4×C149
Frattini, cosocleC2×C42C23×C149
socleC22×C149#386
prime radicalC23×C149#121
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C149 ◁ C2×C42×C149 ◁ G

Complements

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

NH ≅ G/Ntype
11. #477×C149C4semidirect
12. #477×C149C4semidirect
13. #462×C149C4semidirect
14. #462×C149C4semidirect
102. M16×C149Q16semidirect
203. #8990C149direct (N × H)
204. C149#8990direct (N × H)
215. #477C4×C149semidirect
216. #477C4×C149semidirect
217. #462C4×C149semidirect
218. #462C4×C149semidirect
306. M16Q16×C149semidirect

Maximal subgroups

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

subgroupindex
#3104×C1492
Q8×M16×C1492
#1986×C1492
C4×#103×C1492
#1493×C1492
#1303×C1492
#1278×C1492
#8990149