Finite Group Databasebeta

← C149×#19081 #49198030

Subgroups — C149×#19081 #49198030

Order 38144.

880 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#3550×C149C211yesmaximal, characteristic
2#3165×C149C211yesmaximal, characteristic, complemented
3#3141×C149C211yesmaximal, characteristic
4#3139×C149C211yesmaximal, characteristic, complemented
5#1664×C149C218yesmaximal, complemented
6#1526×C149C211yesmaximal, characteristic, complemented
7#1526×C149C211yesmaximal, characteristic, complemented
8#1525×C149C211yesmaximal, characteristic
9#563×C149C2214yes—
10#559×C149—21no—
11Q82×C149—21no—
12#556×C149—21no—
13#556×C149—21no—
14D4×Q8×C149—21no—
15D4×Q8×C149—21no—
16#542×C149—22no—
17#542×C149—22no—
18#536×C149—22no—
19#533×C149C2211yescharacteristic
20#533×C149C2211yescharacteristic
21#532×C149C2211yescharacteristic
22C2×C4⋊Q8×C149C2211yescharacteristic
23#501×C149C2214yes—
24#500×C149—21no—
25#498×C149—21no—
26#491×C149C2214yes—
27#489×C149C2214yes—
28#487×C149—21no—
29#487×C149—21no—
30#487×C149—21no—
31#486×C149—21no—
32#428×C149—22no—
33#419×C149—22no—
34#417×C149—22no—
35C4×M16×C149C2211yescharacteristic
36C4×M16×C149C2211yescharacteristic
37C4×M16×C149C2211yescharacteristic
38#330×C149C2214yes—
39#330×C149C2214yes—
40#329×C149C2214yes—
41C2×#41×C149D412yes—
42C22×Q8×C149—22no—
43C22×Q8×C149—21no—
44C2×M16×C149—21no—
45C2×M16×C149—21no—
46C2×M16×C149—21no—
47C4⋊Q8×C149—22no—
48C4⋊Q8×C149—22no—
49C4⋊Q8×C149—24no—
50C4⋊Q8×C149—21no—
51C4⋊Q8×C149—21no—
52C4⋊Q8×C149—21no—
53C4⋊Q8×C149D411yescharacteristic
54C4⋊Q8×C149D411yescharacteristic
55C4⋊Q8×C149D411yescharacteristic
56C4⋊Q8×C149D411yescharacteristic
57C4⋊Q8×C149D411yescharacteristic
58C4⋊Q8×C149C2312yes—
59#127×C149D411yescharacteristic
60#126×C149—24no—
61#126×C149—24no—
62#125×C149C2312yes—
63#125×C149C2312yes—
64#124×C149—24no—
65#124×C149—22no—
66#124×C149—22no—
67#124×C149C2312yes—
68#123×C149—24no—
69#123×C149—24no—
70C22⋊Q8×C149—22no—
71C22⋊Q8×C149—22no—
72C22⋊Q8×C149—21no—
73C22⋊Q8×C149—21no—
74C22⋊Q8×C149—21no—
75C22⋊Q8×C149—21no—
76C22⋊Q8×C149—24no—
77C22⋊Q8×C149—24no—
78#121×C149—21no—
79#121×C149—21no—
80C4×Q8×C149—22no—
81C4×Q8×C149—22no—
82C4×Q8×C149—21no—
83C4×Q8×C149—21no—
84C4×Q8×C149—21no—
85C4×Q8×C149—21no—
86C4×D4×C149—22no—
87C4×D4×C149—22no—
88C4×D4×C149—21no—
89C4×D4×C149—21no—
90#117×C149—22no—
91#117×C149D412yes—
92#117×C149D412yes—
93C2×C4⋊C4×C149—21no—
94C2×C4⋊C4×C149—21no—
95C2×C42×C149C2311yescharacteristic
96#107×C149—24no—
97#106×C149—24no—
98#103×C149—24no—
99#103×C149—24no—
100#103×C149—24no—
101#102×C149—24no—
102#97×C149C2312yes—
103#97×C149C2312yes—
104#97×C149C2312yes—
105C4×C8×C149—21no—
106C4×C8×C149—21no—
107C4×C8×C149—21no—
108#41×C149—44no—
109C2×Q8×C149—24no—
110C2×Q8×C149—21no—
111C2×Q8×C149—21no—
112C2×Q8×C149—21no—
113C2×Q8×C149—21no—
114C2×Q8×C149—22no—
115C2×Q8×C149—44no—
116C2×Q8×C149—41no—
117C2×Q8×C149—84no—
118C2×Q8×C149C2×D412yes—
119C2×D4×C149—22no—
120C2×D4×C149—21no—
121C2×D4×C149—21no—
122C2×D4×C149C2×D412yes—
123C22×C4×C149—24no—
124C22×C4×C149—22no—
125C22×C4×C149—41no—
126C22×C4×C149C2×D411yescharacteristic
127C22×C4×C149C2×D411yescharacteristic
128C22×C4×C149C2×D411yescharacteristic
129M16×C149—24no—
130M16×C149—42no—
131M16×C149—42no—
132C2×C8×C149—22no—
133C2×C8×C149—22no—
134C2×C8×C149—22no—
135C4⋊C4×C149—24no—
136C4⋊C4×C149—24no—
137C4⋊C4×C149—21no—
138C4⋊C4×C149—21no—
139C4⋊C4×C149—21no—
140C4⋊C4×C149—21no—
141C4⋊C4×C149—21no—
142C4⋊C4×C149—21no—
143C4⋊C4×C149—22no—
144C4⋊C4×C149—22no—
145C4⋊C4×C149—22no—
146C4⋊C4×C149—22no—
147C4⋊C4×C149—22no—
148C4⋊C4×C149—22no—
149C4⋊C4×C149—41no—
150C4⋊C4×C149—41no—
151C4⋊C4×C149C2×D412yes—
152C4⋊C4×C149C2×D412yes—
153C4⋊C4×C149C2×D412yes—
154C4⋊C4×C149C2×D412yes—
155C22⋊C4×C149—24no—
156C22⋊C4×C149—24no—
157C22⋊C4×C149—24no—
158C22⋊C4×C149—22no—
159C22⋊C4×C149—22no—
160C22⋊C4×C149—22no—
161C22⋊C4×C149—22no—
162C42×C149—24no—
163C42×C149—22no—
164C42×C149—22no—
165C42×C149C2×D411yescharacteristic
166C42×C149C2×D411yescharacteristic
167C42×C149C2×D411yescharacteristic
168C42×C149C2411yescharacteristic
169C23×C149—22no—
170C23×C149#12011yescharacteristic
171Q8×C149—42no—
172Q8×C149—44no—
173Q8×C149—42no—
174Q8×C149—42no—
175Q8×C149—42no—
176Q8×C149—42no—
177Q8×C149—84no—
178Q8×C149—82no—
179D4×C149—42no—
180D4×C149—42no—
181D4×C149—42no—
182D4×C149—82no—
183C2×C4×C149—22no—
184C2×C4×C149—22no—
185C2×C4×C149—22no—
186C2×C4×C149—22no—
187C2×C4×C149—22no—
188C2×C4×C149—22no—
189C2×C4×C149—22no—
190C2×C4×C149—22no—
191C2×C4×C149—44no—
192C2×C4×C149—42no—
193C2×C4×C149—84no—
194C2×C4×C149—82no—
195C2×C4×C149#12011yescharacteristic
196C2×C4×C149#12011yescharacteristic
197C2×C4×C149#12011yescharacteristic
198C2×C4×C149C22×D411yescharacteristic
199C2×C4×C149C22×D411yescharacteristic
200C2×C4×C149C22×D411yescharacteristic
201C8×C149—24no—
202C8×C149—42no—
203C8×C149—42no—
204C22×C149—21no—
205C22×C149—21no—
206C22×C149—21no—
207C22×C149—42no—
208C22×C149—42no—
209C22×C149—42no—
210C22×C149C2×#12011yescharacteristic
211C4×C149—21no—
212C4×C149—21no—
213C4×C149—21no—
214C4×C149—42no—
215C4×C149—42no—
216C4×C149—42no—
217C4×C149—42no—
218C4×C149—42no—
219C4×C149—82no—
220C4×C149#45412yes—
221C4×C149#45512yes—
222C4×C149#45612yes—
223C2×C149—41no—
224C2×C149—82no—
225C2×C149C2×#45511yescharacteristic
226C2×C149C2×#45411yescharacteristic
227C2×C149C2×#45611yescharacteristic
228#19081C14911yesmaximal, characteristic, direct product factor, Sylow
229C149#1908111yescharacteristic, direct product factor, Sylow
230#3550C2×C14911yescharacteristic
231#3165C2×C14911yescharacteristic, complemented
232#3141C2×C14911yescharacteristic
233#3139C2×C14911yescharacteristic, complemented
234#1664C2×C14918yescomplemented
235#1526C2×C14911yescharacteristic, complemented
236#1526C2×C14911yescharacteristic, complemented
237#1525C2×C14911yescharacteristic
238#563C22×C14914yes—
239#559—21no—
240Q82—21no—
241#556—21no—
242#556—21no—
243D4×Q8—21no—
244D4×Q8—21no—
245#542—22no—
246#542—22no—
247#536—22no—
248#533C22×C14911yescharacteristic
249#533C22×C14911yescharacteristic
250#532C22×C14911yescharacteristic
251C2×C4⋊Q8C22×C14911yescharacteristic
252#501C22×C14914yes—
253#500—21no—
254#498—21no—
255#491C22×C14914yes—
256#489C22×C14914yes—
257#487—21no—
258#487—21no—
259#487—21no—
260#486—21no—
261#428—22no—
262#419—22no—
263#417—22no—
264C4×M16C22×C14911yescharacteristic
265C4×M16C22×C14911yescharacteristic
266C4×M16C22×C14911yescharacteristic
267#330C22×C14914yes—
268#330C22×C14914yes—
269#329C22×C14914yes—
270C2×#41D4×C14912yes—
271C22×Q8—22no—
272C22×Q8—21no—
273C2×M16—21no—
274C2×M16—21no—
275C2×M16—21no—
276C4⋊Q8—22no—
277C4⋊Q8—22no—
278C4⋊Q8—24no—
279C4⋊Q8—21no—
280C4⋊Q8—21no—
281C4⋊Q8—21no—
282C4⋊Q8D4×C14911yescharacteristic
283C4⋊Q8D4×C14911yescharacteristic
284C4⋊Q8D4×C14911yescharacteristic
285C4⋊Q8D4×C14911yescharacteristic
286C4⋊Q8D4×C14911yescharacteristic
287C4⋊Q8C23×C14912yes—
288#127D4×C14911yescharacteristic
289#126—24no—
290#126—24no—
291#125C23×C14912yes—
292#125C23×C14912yes—
293#124—24no—
294#124—22no—
295#124—22no—
296#124C23×C14912yes—
297#123—24no—
298#123—24no—
299C22⋊Q8—22no—
300C22⋊Q8—22no—
301C22⋊Q8—21no—
302C22⋊Q8—21no—
303C22⋊Q8—21no—
304C22⋊Q8—21no—
305C22⋊Q8—24no—
306C22⋊Q8—24no—
307#121—21no—
308#121—21no—
309C4×Q8—22no—
310C4×Q8—22no—
311C4×Q8—21no—
312C4×Q8—21no—
313C4×Q8—21no—
314C4×Q8—21no—
315C4×D4—22no—
316C4×D4—22no—
317C4×D4—21no—
318C4×D4—21no—
319#117—22no—
320#117D4×C14912yes—
321#117D4×C14912yes—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C42C23×C14911yescharacteristic
325#107—24no—
326#106—24no—
327#103—24no—
328#103—24no—
329#103—24no—
330#102—24no—
331#97C23×C14912yes—
332#97C23×C14912yes—
333#97C23×C14912yes—
334C4×C8—21no—
335C4×C8—21no—
336C4×C8—21no—
337#41—44no—
338C2×Q8—24no—
339C2×Q8—21no—
340C2×Q8—21no—
341C2×Q8—21no—
342C2×Q8—21no—
343C2×Q8—22no—
344C2×Q8—44no—
345C2×Q8—41no—
346C2×Q8—84no—
347C2×Q8C2×D4×C14912yes—
348C2×D4—22no—
349C2×D4—21no—
350C2×D4—21no—
351C2×D4C2×D4×C14912yes—
352C22×C4—24no—
353C22×C4—22no—
354C22×C4—41no—
355C22×C4C2×D4×C14911yescharacteristic
356C22×C4C2×D4×C14911yescharacteristic
357C22×C4C2×D4×C14911yescharacteristic
358M16—24no—
359M16—42no—
360M16—42no—
361C2×C8—22no—
362C2×C8—22no—
363C2×C8—22no—
364C4⋊C4—24no—
365C4⋊C4—24no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—22no—
373C4⋊C4—22no—
374C4⋊C4—22no—
375C4⋊C4—22no—
376C4⋊C4—22no—
377C4⋊C4—22no—
378C4⋊C4—41no—
379C4⋊C4—41no—
380C4⋊C4C2×D4×C14912yes—
381C4⋊C4C2×D4×C14912yes—
382C4⋊C4C2×D4×C14912yes—
383C4⋊C4C2×D4×C14912yes—
384C22⋊C4—24no—
385C22⋊C4—24no—
386C22⋊C4—24no—
387C22⋊C4—22no—
388C22⋊C4—22no—
389C22⋊C4—22no—
390C22⋊C4—22no—
391C42—24no—
392C42—22no—
393C42—22no—
394C42C2×D4×C14911yescharacteristic
395C42C2×D4×C14911yescharacteristic
396C42C2×D4×C14911yescharacteristic
397C42C24×C14911yescharacteristic
398C23—22no—
399C23#120×C14911yescharacteristic
400Q8—42no—
401Q8—44no—
402Q8—42no—
403Q8—42no—
404Q8—42no—
405Q8—42no—
406Q8—84no—
407Q8—82no—
408D4—42no—
409D4—42no—
410D4—42no—
411D4—82no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—44no—
421C2×C4—42no—
422C2×C4—84no—
423C2×C4—82no—
424C2×C4#120×C14911yescharacteristic
425C2×C4#120×C14911yescharacteristic
426C2×C4#120×C14911yescharacteristic
427C2×C4C22×D4×C14911yescharacteristic
428C2×C4C22×D4×C14911yescharacteristic
429C2×C4C22×D4×C14911yescharacteristic
430C8—24no—
431C8—42no—
432C8—42no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—42no—
437C22—42no—
438C22—42no—
439C22C2×#120×C14911yescharacteristic
440C4—21no—
441C4—21no—
442C4—21no—
443C4—42no—
444C4—42no—
445C4—42no—
446C4—42no—
447C4—42no—
448C4—82no—
449C4#454×C14912yes—
450C4#455×C14912yes—
451C4#456×C14912yes—
452C2—41no—
453C2—82no—
454C2C2×#455×C14911yescharacteristic
455C2C2×#454×C14911yescharacteristic
456C2C2×#456×C14911yescharacteristic
subgroupG/H
center, socleC22×C149C2×#120
commutator, Frattini, cosocleC42C24×C149
prime radical#532×C149C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C149 ◁ C2×C42×C149 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3165×C149C2semidirect
4. #3139×C149C2semidirect
5. #1664×C149C2semidirect
6. #1526×C149C2semidirect
7. #1526×C149C2semidirect
228. #19081C149direct (N × H)
229. C149#19081direct (N × H)
231. #3165C2×C149semidirect
233. #3139C2×C149semidirect
234. #1664C2×C149semidirect
235. #1526C2×C149semidirect
236. #1526C2×C149semidirect

Maximal subgroups

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

subgroupindex
#3550×C1492
#3165×C1492
#3141×C1492
#3139×C1492
#1664×C1492
#1526×C1492
#1525×C1492
#19081149