Finite Group Databasebeta

← C149×#12714 #49191663

Subgroups — C149×#12714 #49191663

Order 38144.

974 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3487×C149C211yesmaximal, characteristic
2#2134×C149C211yesmaximal, characteristic, complemented
3#2128×C149C211yesmaximal, characteristic, complemented
4#2120×C149C212yesmaximal, complemented
5#1796×C149C212yesmaximal, complemented
6C2×2−1+4×C149C2211yescharacteristic
7C22×#41×C149C411yescharacteristic, complemented
8#550×C149—22no—
9#550×C149—22no—
10#548×C149—22no—
11#548×C149—22no—
12#535×C149—22no—
13#535×C149C411yescharacteristic, complemented
14#535×C149C2211yescharacteristic
15#525×C149—22no—
16#525×C149C411yescharacteristic, complemented
17#525×C149C2211yescharacteristic
18#519×C149C411yescharacteristic, complemented
19#421×C149—22no—
20#419×C149—22no—
21#413×C149C2212yes—
22#410×C149C2212yes—
23#355×C149—22no—
24#353×C149—22no—
25#352×C149—22no—
26AΣL(1,𝔽16)×C149—22no—
272−1+4×C149—44no—
28C2×#41×C149—22no—
29C2×#41×C149—22no—
30C2×#41×C149—22no—
31C2×#41×C149—21no—
32C2×#41×C149—44no—
33C2×#41×C149C2×C411yescharacteristic
34C2×#41×C149D412yes—
35C2×#41×C149C2311yescharacteristic
36C22×Q8×C149—21no—
37C22×Q8×C149C2×C411yescharacteristic
38C22×Q8×C149D412yes—
39C22×D4×C149—21no—
40C22×D4×C149C2×C411yescharacteristic
41C23×C4×C149—21no—
42C23×C4×C149C2×C411yescharacteristic
43C2×M16×C149—22no—
44#127×C149—24no—
45#127×C149—21no—
46#127×C149D412yes—
47#124×C149—24no—
48#124×C149—21no—
49#124×C149D412yes—
50#123×C149—21no—
51#123×C149D412yes—
52C22⋊Q8×C149—24no—
53C22⋊Q8×C149—21no—
54C22⋊Q8×C149—21no—
55#121×C149—24no—
56#121×C149—24no—
57#121×C149—24no—
58#121×C149—21no—
59#121×C149—22no—
60#121×C149—21no—
61#121×C149—22no—
62#120×C149—21no—
63#120×C149—22no—
64#120×C149—22no—
65#120×C149D412yes—
66C4×Q8×C149—22no—
67C4×Q8×C149—22no—
68C4×D4×C149—24no—
69C4×D4×C149—24no—
70C4×D4×C149—22no—
71C4×D4×C149—22no—
72#117×C149—22no—
73#117×C149—22no—
74#117×C149C2×C411yescharacteristic
75#117×C149C2×C411yescharacteristic
76#104×C149—44no—
77#103×C149—44no—
78#101×C149—22no—
79#100×C149—22no—
80#99×C149—22no—
81#99×C149—22no—
82C24×C149—21no—
83C24×C149C22⋊C411yescharacteristic
84#41×C149—24no—
85#41×C149—42no—
86#41×C149—42no—
87#41×C149—42no—
88#41×C149—48no—
89#41×C149—48no—
90#41×C149—44no—
91#41×C149—44no—
92#41×C149—44no—
93C2×Q8×C149—24no—
94C2×Q8×C149—21no—
95C2×Q8×C149—22no—
96C2×Q8×C149—24no—
97C2×Q8×C149—42no—
98C2×Q8×C149—44no—
99C2×Q8×C149C22⋊C411yescharacteristic
100C2×Q8×C149C22⋊C412yes—
101C2×Q8×C149C2×D411yescharacteristic
102C2×D4×C149—24no—
103C2×D4×C149—21no—
104C2×D4×C149—22no—
105C2×D4×C149—24no—
106C2×D4×C149—22no—
107C2×D4×C149—24no—
108C2×D4×C149—22no—
109C2×D4×C149—21no—
110C2×D4×C149—44no—
111C2×D4×C149—42no—
112C2×D4×C149C22⋊C412yes—
113C2×D4×C149C22⋊C411yescharacteristic
114C2×D4×C149C2×D411yescharacteristic
115C2×D4×C149C2×D412yes—
116C22×C4×C149—21no—
117C22×C4×C149—24no—
118C22×C4×C149—22no—
119C22×C4×C149—21no—
120C22×C4×C149—21no—
121C22×C4×C149—21no—
122C22×C4×C149—22no—
123C22×C4×C149—44no—
124C22×C4×C149—42no—
125C22×C4×C149C22⋊C411yescharacteristic
126C22×C4×C149C22×C411yescharacteristic
127C22×C4×C149C2×D412yes—
128M16×C149—42no—
129M16×C149—42no—
130C2×C8×C149—42no—
131C4⋊C4×C149—24no—
132C4⋊C4×C149—22no—
133C4⋊C4×C149—21no—
134C4⋊C4×C149—21no—
135C4⋊C4×C149—22no—
136C4⋊C4×C149—42no—
137C22⋊C4×C149—22no—
138C22⋊C4×C149—24no—
139C22⋊C4×C149—22no—
140C22⋊C4×C149—21no—
141C22⋊C4×C149—22no—
142C22⋊C4×C149—24no—
143C22⋊C4×C149—22no—
144C22⋊C4×C149—42no—
145C22⋊C4×C149C22⋊C412yes—
146C42×C149—24no—
147C42×C149—21no—
148C42×C149—42no—
149C42×C149C22⋊C412yes—
150C23×C149—21no—
151C23×C149—22no—
152C23×C149—21no—
153C23×C149—42no—
154C23×C149—41no—
155C23×C149—81no—
156C23×C149—82no—
157C23×C149C2×C22⋊C411yescharacteristic
158C23×C149#12012yes—
159Q8×C149—24no—
160Q8×C149—22no—
161Q8×C149—22no—
162Q8×C149—41no—
163Q8×C149—44no—
164Q8×C149#9914yes—
165D4×C149—22no—
166D4×C149—42no—
167D4×C149—41no—
168D4×C149—44no—
169D4×C149—42no—
170D4×C149—48no—
171D4×C149—42no—
172D4×C149—42no—
173D4×C149—84no—
174D4×C149—82no—
175D4×C149—84no—
176D4×C149—82no—
177C2×C4×C149—24no—
178C2×C4×C149—22no—
179C2×C4×C149—22no—
180C2×C4×C149—22no—
181C2×C4×C149—22no—
182C2×C4×C149—22no—
183C2×C4×C149—22no—
184C2×C4×C149—21no—
185C2×C4×C149—21no—
186C2×C4×C149—44no—
187C2×C4×C149—44no—
188C2×C4×C149—48no—
189C2×C4×C149—42no—
190C2×C4×C149—42no—
191C2×C4×C149—42no—
192C2×C4×C149—41no—
193C2×C4×C149—82no—
194C2×C4×C149C2×C22⋊C411yescharacteristic
195C2×C4×C149C2×C22⋊C411yescharacteristic
196C2×C4×C149#12012yes—
197C8×C149—82no—
198C22×C149—21no—
199C22×C149—22no—
200C22×C149—42no—
201C22×C149—41no—
202C22×C149—42no—
203C22×C149—41no—
204C22×C149—41no—
205C22×C149—44no—
206C22×C149—41no—
207C22×C149—41no—
208C22×C149—42no—
209C22×C149—82no—
210C22×C149—84no—
211C22×C149#37911yescharacteristic
212C4×C149—22no—
213C4×C149—24no—
214C4×C149—21no—
215C4×C149—42no—
216C4×C149—42no—
217C4×C149—41no—
218C4×C149—41no—
219C4×C149—162no—
220C4×C149C2×#9912yes—
221C2×C149—21no—
222C2×C149—42no—
223C2×C149—41no—
224C2×C149—81no—
225C2×C149—81no—
226C2×C149—82no—
227C2×C149#178111yescharacteristic
228#12714C14911yesmaximal, characteristic, direct product factor, Sylow
229C149#1271411yescharacteristic, direct product factor, Sylow
230#3487C2×C14911yescharacteristic
231#2134C2×C14911yescharacteristic, complemented
232#2128C2×C14911yescharacteristic, complemented
233#2120C2×C14912yescomplemented
234#1796C2×C14912yescomplemented
235C2×2−1+4C22×C14911yescharacteristic
236C22×#41C4×C14911yescharacteristic, complemented
237#550—22no—
238#550—22no—
239#548—22no—
240#548—22no—
241#535—22no—
242#535C4×C14911yescharacteristic, complemented
243#535C22×C14911yescharacteristic
244#525—22no—
245#525C4×C14911yescharacteristic, complemented
246#525C22×C14911yescharacteristic
247#519C4×C14911yescharacteristic, complemented
248#421—22no—
249#419—22no—
250#413C22×C14912yes—
251#410C22×C14912yes—
252#355—22no—
253#353—22no—
254#352—22no—
255AΣL(1,𝔽16)—22no—
2562−1+4—44no—
257C2×#41—22no—
258C2×#41—22no—
259C2×#41—22no—
260C2×#41—21no—
261C2×#41—44no—
262C2×#41C2×C4×C14911yescharacteristic
263C2×#41D4×C14912yes—
264C2×#41C23×C14911yescharacteristic
265C22×Q8—21no—
266C22×Q8C2×C4×C14911yescharacteristic
267C22×Q8D4×C14912yes—
268C22×D4—21no—
269C22×D4C2×C4×C14911yescharacteristic
270C23×C4—21no—
271C23×C4C2×C4×C14911yescharacteristic
272C2×M16—22no—
273#127—24no—
274#127—21no—
275#127D4×C14912yes—
276#124—24no—
277#124—21no—
278#124D4×C14912yes—
279#123—21no—
280#123D4×C14912yes—
281C22⋊Q8—24no—
282C22⋊Q8—21no—
283C22⋊Q8—21no—
284#121—24no—
285#121—24no—
286#121—24no—
287#121—21no—
288#121—22no—
289#121—21no—
290#121—22no—
291#120—21no—
292#120—22no—
293#120—22no—
294#120D4×C14912yes—
295C4×Q8—22no—
296C4×Q8—22no—
297C4×D4—24no—
298C4×D4—24no—
299C4×D4—22no—
300C4×D4—22no—
301#117—22no—
302#117—22no—
303#117C2×C4×C14911yescharacteristic
304#117C2×C4×C14911yescharacteristic
305#104—44no—
306#103—44no—
307#101—22no—
308#100—22no—
309#99—22no—
310#99—22no—
311C24—21no—
312C24C22⋊C4×C14911yescharacteristic
313#41—24no—
314#41—42no—
315#41—42no—
316#41—42no—
317#41—48no—
318#41—48no—
319#41—44no—
320#41—44no—
321#41—44no—
322C2×Q8—24no—
323C2×Q8—21no—
324C2×Q8—22no—
325C2×Q8—24no—
326C2×Q8—42no—
327C2×Q8—44no—
328C2×Q8C22⋊C4×C14911yescharacteristic
329C2×Q8C22⋊C4×C14912yes—
330C2×Q8C2×D4×C14911yescharacteristic
331C2×D4—24no—
332C2×D4—21no—
333C2×D4—22no—
334C2×D4—24no—
335C2×D4—22no—
336C2×D4—24no—
337C2×D4—22no—
338C2×D4—21no—
339C2×D4—44no—
340C2×D4—42no—
341C2×D4C22⋊C4×C14911yescharacteristic
342C2×D4C22⋊C4×C14912yes—
343C2×D4C2×D4×C14911yescharacteristic
344C2×D4C2×D4×C14912yes—
345C22×C4—21no—
346C22×C4—24no—
347C22×C4—22no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—22no—
352C22×C4—44no—
353C22×C4—42no—
354C22×C4C22⋊C4×C14911yescharacteristic
355C22×C4C22×C4×C14911yescharacteristic
356C22×C4C2×D4×C14912yes—
357M16—42no—
358M16—42no—
359C2×C8—42no—
360C4⋊C4—24no—
361C4⋊C4—22no—
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—22no—
365C4⋊C4—42no—
366C22⋊C4—22no—
367C22⋊C4—24no—
368C22⋊C4—22no—
369C22⋊C4—21no—
370C22⋊C4—22no—
371C22⋊C4—24no—
372C22⋊C4—22no—
373C22⋊C4—42no—
374C22⋊C4C22⋊C4×C14912yes—
375C42—24no—
376C42—21no—
377C42—42no—
378C42C22⋊C4×C14912yes—
379C23—21no—
380C23—22no—
381C23—21no—
382C23—42no—
383C23—41no—
384C23—81no—
385C23—82no—
386C23C2×C22⋊C4×C14911yescharacteristic
387C23#120×C14912yes—
388Q8—24no—
389Q8—22no—
390Q8—22no—
391Q8—41no—
392Q8—44no—
393Q8#99×C14914yes—
394D4—22no—
395D4—42no—
396D4—41no—
397D4—44no—
398D4—42no—
399D4—48no—
400D4—42no—
401D4—42no—
402D4—84no—
403D4—82no—
404D4—84no—
405D4—82no—
406C2×C4—24no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—44no—
416C2×C4—44no—
417C2×C4—48no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—41no—
422C2×C4—82no—
423C2×C4C2×C22⋊C4×C14911yescharacteristic
424C2×C4C2×C22⋊C4×C14911yescharacteristic
425C2×C4#120×C14912yes—
426C8—82no—
427C22—21no—
428C22—22no—
429C22—42no—
430C22—41no—
431C22—42no—
432C22—44no—
433C22—41no—
434C22—41no—
435C22—41no—
436C22—41no—
437C22—42no—
438C22—82no—
439C22—84no—
440C22#379×C14911yescharacteristic
441C4—22no—
442C4—24no—
443C4—21no—
444C4—42no—
445C4—42no—
446C4—41no—
447C4—41no—
448C4—162no—
449C4C2×#99×C14912yes—
450C2—21no—
451C2—42no—
452C2—41no—
453C2—82no—
454C2—81no—
455C2—81no—
456C2#1781×C14911yescharacteristic
subgroupG/H
center, socleC2×C149#1781
commutatorC22×C4C22×C4×C149
Frattini, cosocleC2×#41C23×C149
prime radical#3487×C149C2
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C149 ◁ C2×C4×C149 ◁ C2×2−1+4×C149 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2134×C149C2semidirect
3. #2128×C149C2semidirect
4. #2120×C149C2semidirect
5. #1796×C149C2semidirect
7. C22×#41×C149C4semidirect
13. #535×C149C4semidirect
16. #525×C149C4semidirect
18. #519×C149C4semidirect
228. #12714C149direct (N × H)
229. C149#12714direct (N × H)
231. #2134C2×C149semidirect
232. #2128C2×C149semidirect
233. #2120C2×C149semidirect
234. #1796C2×C149semidirect
236. C22×#41C4×C149semidirect
242. #535C4×C149semidirect
245. #525C4×C149semidirect
247. #519C4×C149semidirect

Maximal subgroups

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

subgroupindex
#3487×C1492
#2134×C1492
#2128×C1492
#2120×C1492
#1796×C1492
#12714149