Finite Group Databasebeta

← C149×#10246 #49189195

Subgroups — C149×#10246 #49189195

Order 38144.

740 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3208×C149C211yesmaximal, characteristic, complemented
2#3077×C149C211yesmaximal, characteristic, complemented
3#2541×C149C211yesmaximal, characteristic
4#1545×C149C211yesmaximal, characteristic, complemented
5#1503×C149C211yesmaximal, characteristic, complemented
6#1478×C149C211yesmaximal, characteristic, complemented
7#1303×C149C211yesmaximal, characteristic, complemented
8#533×C149C2211yescharacteristic
9C2×#127×C149—21no—
10C2×#127×C149C2211yescharacteristic
11C2×#121×C149—22no—
12C2×C4×D4×C149C2211yescharacteristic
13#492×C149—21no—
14#486×C149—21no—
15#478×C149—22no—
16#476×C149—21no—
17#474×C149—21no—
18#460×C149—22no—
19#450×C149—22no—
20#431×C149C2211yescharacteristic
21#431×C149C2211yescharacteristic
22#428×C149—21no—
23#423×C149C2211yescharacteristic
24#418×C149—21no—
25#392×C149—22no—
26#390×C149—21no—
27C4×C4⋊C4×C149C2211yescharacteristic
28#331×C149—22no—
29#328×C149—22no—
30D4⋊C8×C149—22no—
31C22×D4×C149—24no—
32C22×D4×C149—21no—
33C22×D4×C149—21no—
34C22×D4×C149D411yescharacteristic
35C22×D4×C149D412yes—
36C23×C4×C149—21no—
37C2×SD16×C149—24no—
38C2×M16×C149—21no—
39C4⋊Q8×C149D411yescharacteristic, complemented
40C4⋊Q8×C149D411yescharacteristic, complemented
41#127×C149—21no—
42#127×C149—21no—
43#127×C149—21no—
44#127×C149—21no—
45#127×C149—42no—
46#127×C149—42no—
47#125×C149—21no—
48C22⋊Q8×C149—21no—
49C22⋊Q8×C149—21no—
50#121×C149—48no—
51C4×Q8×C149—21no—
52C4×Q8×C149—21no—
53C4×D4×C149—21no—
54C4×D4×C149—21no—
55C4×D4×C149—21no—
56C4×D4×C149—21no—
57#117×C149—21no—
58C2×C4⋊C4×C149—21no—
59C2×C4⋊C4×C149D411yescharacteristic
60C2×C22⋊C4×C149—24no—
61C2×C22⋊C4×C149—21no—
62C2×C42×C149—21no—
63C2×C42×C149C2311yescharacteristic
64#107×C149—22no—
65#106×C149—22no—
66C4⋊C8×C149—21no—
67C4⋊C8×C149—21no—
68C4⋊C8×C149D412yescomplemented
69C4⋊C8×C149D412yescomplemented
70#102×C149—22no—
71#102×C149—22no—
72#102×C149—24no—
73C22⋊C8×C149—21no—
74C22⋊C8×C149—21no—
75C4×C8×C149—21no—
76C4×C8×C149—21no—
77#95×C149D412yes—
78C24×C149—21no—
79C24×C149—22no—
80C2×Q8×C149—21no—
81C2×Q8×C149—21no—
82C2×D4×C149—21no—
83C2×D4×C149—22no—
84C2×D4×C149—21no—
85C2×D4×C149—22no—
86C2×D4×C149—21no—
87C2×D4×C149—21no—
88C2×D4×C149—21no—
89C2×D4×C149—44no—
90C2×D4×C149—48no—
91C2×D4×C149—48no—
92C2×D4×C149—41no—
93C2×D4×C149—41no—
94C2×D4×C149—41no—
95C2×D4×C149—41no—
96C2×D4×C149—41no—
97C2×D4×C149—41no—
98C2×D4×C149—41no—
99C2×D4×C149—41no—
100C2×D4×C149—82no—
101C2×D4×C149—84no—
102C2×D4×C149SD1612yescomplemented
103C22×C4×C149—22no—
104C22×C4×C149—21no—
105C22×C4×C149—44no—
106C22×C4×C149—41no—
107C22×C4×C149—41no—
108C22×C4×C149C2×D411yescharacteristic
109C22×C4×C149C2×D411yescharacteristic
110C22×C4×C149C2×D411yescharacteristic
111SD16×C149—84no—
112M16×C149—41no—
113M16×C149—41no—
114C2×C8×C149—22no—
115C2×C8×C149—22no—
116C2×C8×C149—41no—
117C4⋊C4×C149—24no—
118C4⋊C4×C149—21no—
119C4⋊C4×C149—21no—
120C4⋊C4×C149—21no—
121C4⋊C4×C149—21no—
122C4⋊C4×C149—21no—
123C4⋊C4×C149—21no—
124C4⋊C4×C149—41no—
125C4⋊C4×C149—41no—
126C22⋊C4×C149—48no—
127C22⋊C4×C149—41no—
128C22⋊C4×C149—41no—
129C22⋊C4×C149—41no—
130C42×C149—41no—
131C42×C149—41no—
132C42×C149—41no—
133C42×C149C2×D411yescharacteristic
134C42×C149C2×D411yescharacteristic
135C42×C149C2×D411yescharacteristic
136C42×C149#4111yescharacteristic
137C23×C149—22no—
138C23×C149—42no—
139C23×C149—42no—
140C23×C149—44no—
141C23×C149—44no—
142C23×C149—41no—
143C23×C149—41no—
144C23×C149—42no—
145C23×C149—42no—
146C23×C149—42no—
147C23×C149#12011yescharacteristic
148Q8×C149—42no—
149Q8×C149—81no—
150D4×C149—22no—
151D4×C149—22no—
152D4×C149—41no—
153D4×C149—44no—
154D4×C149—41no—
155D4×C149—82no—
156D4×C149—82no—
157D4×C149—82no—
158D4×C149—816no—
159D4×C149—81no—
160D4×C149—81no—
161D4×C149—81no—
162D4×C149—81no—
163C2×C4×C149—22no—
164C2×C4×C149—24no—
165C2×C4×C149—41no—
166C2×C4×C149—42no—
167C2×C4×C149—42no—
168C2×C4×C149—42no—
169C2×C4×C149—41no—
170C2×C4×C149—41no—
171C2×C4×C149—41no—
172C2×C4×C149—82no—
173C2×C4×C149—82no—
174C2×C4×C149#12011yescharacteristic
175C2×C4×C149#12011yescharacteristic
176C2×C4×C149#12111yescharacteristic
177C2×C4×C149#12111yescharacteristic
178C2×C4×C149#12111yescharacteristic
179C2×C4×C149#12711yescharacteristic
180C2×C4×C149C2×SD1611yescharacteristic
181C2×C4×C149#13511yescharacteristic
182C2×C4×C149AGL(1,ℤ/8)11yescharacteristic
183C2×C4×C149#13711yescharacteristic
184C8×C149—42no—
185C8×C149—42no—
186C8×C149—81no—
187C22×C149—21no—
188C22×C149—21no—
189C22×C149—44no—
190C22×C149—42no—
191C22×C149—82no—
192C22×C149—84no—
193C22×C149—84no—
194C22×C149—81no—
195C22×C149—81no—
196C22×C149—82no—
197C22×C149—82no—
198C22×C149—82no—
199C22×C149#39211yescharacteristic
200C22×C149#45011yescharacteristic
201C22×C149#45211yescharacteristic
202C4×C149—21no—
203C4×C149—21no—
204C4×C149—21no—
205C4×C149—44no—
206C4×C149—81no—
207C4×C149—81no—
208C4×C149—81no—
209C4×C149#44811yescharacteristic
210C4×C149#44911yescharacteristic
211C4×C149#45312yes—
212C4×C149#46511yescharacteristic
213C4×C149#46811yescharacteristic
214C2×C149—21no—
215C2×C149—21no—
216C2×C149—82no—
217C2×C149—162no—
218C2×C149#200011yescharacteristic
219C2×C149#200211yescharacteristic
220C2×C149#200811yescharacteristic
221#10246C14911yesmaximal, characteristic, direct product factor, Sylow
222C149#1024611yescharacteristic, direct product factor, Sylow
223#3208C2×C14911yescharacteristic, complemented
224#3077C2×C14911yescharacteristic, complemented
225#2541C2×C14911yescharacteristic
226#1545C2×C14911yescharacteristic, complemented
227#1503C2×C14911yescharacteristic, complemented
228#1478C2×C14911yescharacteristic, complemented
229#1303C2×C14911yescharacteristic, complemented
230#533C22×C14911yescharacteristic
231C2×#127—21no—
232C2×#127C22×C14911yescharacteristic
233C2×#121—22no—
234C2×C4×D4C22×C14911yescharacteristic
235#492—21no—
236#486—21no—
237#478—22no—
238#476—21no—
239#474—21no—
240#460—22no—
241#450—22no—
242#431C22×C14911yescharacteristic
243#431C22×C14911yescharacteristic
244#428—21no—
245#423C22×C14911yescharacteristic
246#418—21no—
247#392—22no—
248#390—21no—
249C4×C4⋊C4C22×C14911yescharacteristic
250#331—22no—
251#328—22no—
252D4⋊C8—22no—
253C22×D4—24no—
254C22×D4—21no—
255C22×D4—21no—
256C22×D4D4×C14911yescharacteristic
257C22×D4D4×C14912yes—
258C23×C4—21no—
259C2×SD16—24no—
260C2×M16—21no—
261C4⋊Q8D4×C14911yescharacteristic, complemented
262C4⋊Q8D4×C14911yescharacteristic, complemented
263#127—21no—
264#127—21no—
265#127—21no—
266#127—21no—
267#127—42no—
268#127—42no—
269#125—21no—
270C22⋊Q8—21no—
271C22⋊Q8—21no—
272#121—48no—
273C4×Q8—21no—
274C4×Q8—21no—
275C4×D4—21no—
276C4×D4—21no—
277C4×D4—21no—
278C4×D4—21no—
279#117—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4D4×C14911yescharacteristic
282C2×C22⋊C4—24no—
283C2×C22⋊C4—21no—
284C2×C42—21no—
285C2×C42C23×C14911yescharacteristic
286#107—22no—
287#106—22no—
288C4⋊C8—21no—
289C4⋊C8—21no—
290C4⋊C8D4×C14912yescomplemented
291C4⋊C8D4×C14912yescomplemented
292#102—22no—
293#102—22no—
294#102—24no—
295C22⋊C8—21no—
296C22⋊C8—21no—
297C4×C8—21no—
298C4×C8—21no—
299#95D4×C14912yes—
300C24—21no—
301C24—22no—
302C2×Q8—21no—
303C2×Q8—21no—
304C2×D4—21no—
305C2×D4—22no—
306C2×D4—21no—
307C2×D4—22no—
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—21no—
311C2×D4—44no—
312C2×D4—48no—
313C2×D4—48no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—41no—
322C2×D4—82no—
323C2×D4—84no—
324C2×D4SD16×C14912yescomplemented
325C22×C4—22no—
326C22×C4—21no—
327C22×C4—44no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4C2×D4×C14911yescharacteristic
331C22×C4C2×D4×C14911yescharacteristic
332C22×C4C2×D4×C14911yescharacteristic
333SD16—84no—
334M16—41no—
335M16—41no—
336C2×C8—22no—
337C2×C8—22no—
338C2×C8—41no—
339C4⋊C4—24no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—41no—
347C4⋊C4—41no—
348C22⋊C4—48no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C42—41no—
353C42—41no—
354C42—41no—
355C42C2×D4×C14911yescharacteristic
356C42C2×D4×C14911yescharacteristic
357C42C2×D4×C14911yescharacteristic
358C42#41×C14911yescharacteristic
359C23—22no—
360C23—42no—
361C23—42no—
362C23—44no—
363C23—44no—
364C23—41no—
365C23—41no—
366C23—42no—
367C23—42no—
368C23—42no—
369C23#120×C14911yescharacteristic
370Q8—42no—
371Q8—81no—
372D4—22no—
373D4—22no—
374D4—41no—
375D4—44no—
376D4—41no—
377D4—82no—
378D4—82no—
379D4—82no—
380D4—816no—
381D4—81no—
382D4—81no—
383D4—81no—
384D4—81no—
385C2×C4—22no—
386C2×C4—24no—
387C2×C4—41no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—82no—
395C2×C4—82no—
396C2×C4#120×C14911yescharacteristic
397C2×C4#120×C14911yescharacteristic
398C2×C4#121×C14911yescharacteristic
399C2×C4#121×C14911yescharacteristic
400C2×C4#121×C14911yescharacteristic
401C2×C4#127×C14911yescharacteristic
402C2×C4C2×SD16×C14911yescharacteristic
403C2×C4#135×C14911yescharacteristic
404C2×C4AGL(1,ℤ/8)×C14911yescharacteristic
405C2×C4#137×C14911yescharacteristic
406C8—42no—
407C8—42no—
408C8—81no—
409C22—21no—
410C22—21no—
411C22—44no—
412C22—42no—
413C22—82no—
414C22—84no—
415C22—84no—
416C22—81no—
417C22—81no—
418C22—82no—
419C22—82no—
420C22—82no—
421C22#392×C14911yescharacteristic
422C22#450×C14911yescharacteristic
423C22#452×C14911yescharacteristic
424C4—21no—
425C4—21no—
426C4—21no—
427C4—44no—
428C4—81no—
429C4—81no—
430C4—81no—
431C4#448×C14911yescharacteristic
432C4#449×C14911yescharacteristic
433C4#453×C14912yes—
434C4#465×C14911yescharacteristic
435C4#468×C14911yescharacteristic
436C2—21no—
437C2—21no—
438C2—82no—
439C2—162no—
440C2#2000×C14911yescharacteristic
441C2#2002×C14911yescharacteristic
442C2#2008×C14911yescharacteristic
subgroupG/H
center, socleC22×C149#392
commutator, Frattini, cosocleC2×C42C23×C149
prime radical#2541×C149C2
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. #3208×C149C2semidirect
2. #3077×C149C2semidirect
4. #1545×C149C2semidirect
5. #1503×C149C2semidirect
6. #1478×C149C2semidirect
7. #1303×C149C2semidirect
39. C4⋊Q8×C149D4semidirect
40. C4⋊Q8×C149D4semidirect
68. C4⋊C8×C149D4semidirect
69. C4⋊C8×C149D4semidirect
102. C2×D4×C149SD16semidirect
221. #10246C149direct (N × H)
222. C149#10246direct (N × H)
223. #3208C2×C149semidirect
224. #3077C2×C149semidirect
226. #1545C2×C149semidirect
227. #1503C2×C149semidirect
228. #1478C2×C149semidirect
229. #1303C2×C149semidirect
261. C4⋊Q8D4×C149semidirect
262. C4⋊Q8D4×C149semidirect
290. C4⋊C8D4×C149semidirect
291. C4⋊C8D4×C149semidirect
324. C2×D4SD16×C149semidirect

Maximal subgroups

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

subgroupindex
#3208×C1492
#3077×C1492
#2541×C1492
#1545×C1492
#1503×C1492
#1478×C1492
#1303×C1492
#10246149