Finite Group Databasebeta

← C149×#18753 #49197702

Subgroups — C149×#18753 #49197702

Order 38144.

966 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#554×C149C211yesmaximal, characteristic
2#3209×C149C211yesmaximal, characteristic, complemented
3#3101×C149C211yesmaximal, characteristic
4#3078×C149C211yesmaximal, characteristic, complemented
5#1643×C149C214yesmaximal, complemented
6#1632×C149C214yesmaximal, complemented
7#1548×C149C211yesmaximal, characteristic, complemented
8#1486×C149C211yesmaximal, characteristic
9#1479×C149C211yesmaximal, characteristic, complemented
10#554×C149—22no—
11#554×C149—22no—
12#554×C149—22no—
13#554×C149C2214yes—
14#533×C149C2211yescharacteristic
15C2×C4⋊Q8×C149C2211yescharacteristic
16C2×#125×C149—21no—
17C2×C22⋊Q8×C149—21no—
18C2×C22⋊Q8×C149—22no—
19C2×C4×Q8×C149C2211yescharacteristic
20C2×C4×D4×C149—21no—
21C2×C4×D4×C149C2211yescharacteristic
22C22×C4⋊C4×C149—21no—
23#494×C149C2212yescomplemented
24#487×C149C2212yescomplemented
25#483×C149—21no—
26#479×C149—22no—
27#477×C149C2212yescomplemented
28#476×C149C2212yes—
29#475×C149C2212yescomplemented
30#462×C149—22no—
31#461×C149C2212yes—
32#451×C149—22no—
33#450×C149—21no—
34C4×SD16×C149—22no—
35#431×C149C2211yescharacteristic
36#431×C149C2211yescharacteristic
37#428×C149—21no—
38#423×C149C2211yescharacteristic
39#419×C149—21no—
40#333×C149C2214yescomplemented
41Q8⋊C8×C149C2214yescomplemented
42D4⋊C8×C149C2214yes—
43C22×Q8×C149D411yescharacteristic
44C22×Q8×C149D412yes—
45C22×D4×C149D411yescharacteristic
46C23×C4×C149—22no—
47C23×C4×C149—21no—
48C2×Q16×C149—24no—
49C2×SD16×C149—22no—
50C2×M16×C149—21no—
51C4⋊Q8×C149—21no—
52C4⋊Q8×C149—21no—
53C4⋊Q8×C149D412yes—
54C4⋊Q8×C149C2311yescharacteristic
55C4⋊Q8×C149C2311yescharacteristic
56C4⋊Q8×C149C2312yes—
57#125×C149—24no—
58#125×C149—24no—
59#125×C149—21no—
60C22⋊Q8×C149—24no—
61C22⋊Q8×C149—28no—
62C22⋊Q8×C149—24no—
63C22⋊Q8×C149—28no—
64C22⋊Q8×C149—21no—
65C22⋊Q8×C149—21no—
66C4×Q8×C149—21no—
67C4×Q8×C149—21no—
68C4×Q8×C149—21no—
69C4×Q8×C149—21no—
70C4×Q8×C149D412yes—
71C4×Q8×C149C2312yes—
72C4×D4×C149—24no—
73C4×D4×C149—24no—
74C4×D4×C149—21no—
75C4×D4×C149—21no—
76C4×D4×C149D412yes—
77C4×D4×C149C2312yes—
78#117×C149—21no—
79C2×C4⋊C4×C149—22no—
80C2×C4⋊C4×C149—24no—
81C2×C4⋊C4×C149—22no—
82C2×C4⋊C4×C149—21no—
83C2×C4⋊C4×C149—21no—
84C2×C4⋊C4×C149—21no—
85C2×C4⋊C4×C149—24no—
86C2×C4⋊C4×C149D411yescharacteristic
87C2×C4⋊C4×C149D411yescharacteristic
88C2×C22⋊C4×C149—22no—
89C2×C22⋊C4×C149—21no—
90C2×C42×C149—21no—
91C2×C42×C149C2311yescharacteristic
92#107×C149—22no—
93#106×C149—22no—
94#106×C149—22no—
95C4⋊C8×C149—21no—
96C4⋊C8×C149—21no—
97C4⋊C8×C149C2312yes—
98C4⋊C8×C149C2312yes—
99#103×C149—22no—
100#103×C149—22no—
101#103×C149—24no—
102#103×C149—22no—
103#102×C149—22no—
104C22⋊C8×C149—21no—
105C22⋊C8×C149—21no—
106C4×C8×C149—21no—
107C4×C8×C149C2312yes—
108C24×C149—21no—
109C2×Q8×C149—21no—
110C2×Q8×C149—22no—
111C2×Q8×C149—22no—
112C2×Q8×C149—22no—
113C2×Q8×C149—21no—
114C2×Q8×C149—21no—
115C2×Q8×C149—82no—
116C2×Q8×C149C2×D412yes—
117C2×Q8×C149C2×D414yes—
118C2×D4×C149—24no—
119C2×D4×C149—21no—
120C2×D4×C149C2×D412yes—
121C22×C4×C149—21no—
122C22×C4×C149—21no—
123C22×C4×C149—21no—
124C22×C4×C149—22no—
125C22×C4×C149—28no—
126C22×C4×C149—22no—
127C22×C4×C149—22no—
128C22×C4×C149—42no—
129C22×C4×C149—42no—
130C22×C4×C149—84no—
131C22×C4×C149C2×D411yescharacteristic
132C22×C4×C149C2×D411yescharacteristic
133C22×C4×C149C2×D411yescharacteristic
134Q16×C149—84no—
135SD16×C149—44no—
136M16×C149—42no—
137C2×C8×C149—22no—
138C2×C8×C149—22no—
139C2×C8×C149—22no—
140C4⋊C4×C149—28no—
141C4⋊C4×C149—28no—
142C4⋊C4×C149—21no—
143C4⋊C4×C149—22no—
144C4⋊C4×C149—22no—
145C4⋊C4×C149—22no—
146C4⋊C4×C149—21no—
147C4⋊C4×C149—22no—
148C4⋊C4×C149—22no—
149C4⋊C4×C149—22no—
150C4⋊C4×C149—21no—
151C4⋊C4×C149—21no—
152C4⋊C4×C149—21no—
153C4⋊C4×C149—21no—
154C4⋊C4×C149—41no—
155C4⋊C4×C149—41no—
156C4⋊C4×C149C2×D412yes—
157C4⋊C4×C149C2×D412yes—
158C22⋊C4×C149—28no—
159C22⋊C4×C149—22no—
160C22⋊C4×C149—22no—
161C22⋊C4×C149—41no—
162C42×C149—22no—
163C42×C149—22no—
164C42×C149—41no—
165C42×C149C2×D411yescharacteristic
166C42×C149C2×D411yescharacteristic
167C42×C149C2×D411yescharacteristic
168C42×C149C2411yescharacteristic
169C23×C149—24no—
170C23×C149—22no—
171C23×C149—42no—
172C23×C149—42no—
173C23×C149#12011yescharacteristic
174Q8×C149—22no—
175Q8×C149—22no—
176Q8×C149—44no—
177Q8×C149—42no—
178Q8×C149—42no—
179Q8×C149—42no—
180Q8×C149—82no—
181D4×C149—24no—
182D4×C149—22no—
183D4×C149#13714yes—
184C2×C4×C149—22no—
185C2×C4×C149—22no—
186C2×C4×C149—22no—
187C2×C4×C149—22no—
188C2×C4×C149—24no—
189C2×C4×C149—41no—
190C2×C4×C149—42no—
191C2×C4×C149—44no—
192C2×C4×C149—42no—
193C2×C4×C149—42no—
194C2×C4×C149—42no—
195C2×C4×C149—42no—
196C2×C4×C149—44no—
197C2×C4×C149—41no—
198C2×C4×C149—41no—
199C2×C4×C149—88no—
200C2×C4×C149#12011yescharacteristic
201C2×C4×C149#12011yescharacteristic
202C2×C4×C149#12011yescharacteristic
203C2×C4×C149#13512yes—
204C2×C4×C149#13712yes—
205C2×C4×C149C22×D411yescharacteristic
206C2×C4×C149C22×D411yescharacteristic
207C2×C4×C149C22×D411yescharacteristic
208C8×C149—42no—
209C8×C149—42no—
210C8×C149—42no—
211C22×C149—21no—
212C22×C149—21no—
213C22×C149—24no—
214C22×C149—48no—
215C22×C149—42no—
216C22×C149—42no—
217C22×C149#45212yes—
218C22×C149C2×#12011yescharacteristic
219C4×C149—21no—
220C4×C149—21no—
221C4×C149—21no—
222C4×C149—42no—
223C4×C149—42no—
224C4×C149—42no—
225C4×C149—44no—
226C4×C149—81no—
227C4×C149—81no—
228C4×C149#45212yes—
229C4×C149C2×#13511yescharacteristic
230C4×C149C2×#13711yescharacteristic
231C4×C149C2×#13712yes—
232C2×C149—22no—
233C2×C149—44no—
234C2×C149C2×#45211yescharacteristic
235C2×C149#300411yescharacteristic
236C2×C149#301911yescharacteristic
237#18753C14911yesmaximal, characteristic, direct product factor, Sylow
238C149#1875311yescharacteristic, direct product factor, Sylow
239C2×#554C2×C14911yescharacteristic
240#3209C2×C14911yescharacteristic, complemented
241#3101C2×C14911yescharacteristic
242#3078C2×C14911yescharacteristic, complemented
243#1643C2×C14914yescomplemented
244#1632C2×C14914yescomplemented
245#1548C2×C14911yescharacteristic, complemented
246#1486C2×C14911yescharacteristic
247#1479C2×C14911yescharacteristic, complemented
248#554—22no—
249#554—22no—
250#554—22no—
251#554C22×C14914yes—
252#533C22×C14911yescharacteristic
253C2×C4⋊Q8C22×C14911yescharacteristic
254C2×#125—21no—
255C2×C22⋊Q8—21no—
256C2×C22⋊Q8—22no—
257C2×C4×Q8C22×C14911yescharacteristic
258C2×C4×D4—21no—
259C2×C4×D4C22×C14911yescharacteristic
260C22×C4⋊C4—21no—
261#494C22×C14912yescomplemented
262#487C22×C14912yescomplemented
263#483—21no—
264#479—22no—
265#477C22×C14912yescomplemented
266#476C22×C14912yes—
267#475C22×C14912yescomplemented
268#462—22no—
269#461C22×C14912yes—
270#451—22no—
271#450—21no—
272C4×SD16—22no—
273#431C22×C14911yescharacteristic
274#431C22×C14911yescharacteristic
275#428—21no—
276#423C22×C14911yescharacteristic
277#419—21no—
278#333C22×C14914yescomplemented
279Q8⋊C8C22×C14914yescomplemented
280D4⋊C8C22×C14914yes—
281C22×Q8D4×C14911yescharacteristic
282C22×Q8D4×C14912yes—
283C22×D4D4×C14911yescharacteristic
284C23×C4—22no—
285C23×C4—21no—
286C2×Q16—24no—
287C2×SD16—22no—
288C2×M16—21no—
289C4⋊Q8—21no—
290C4⋊Q8—21no—
291C4⋊Q8D4×C14912yes—
292C4⋊Q8C23×C14911yescharacteristic
293C4⋊Q8C23×C14911yescharacteristic
294C4⋊Q8C23×C14912yes—
295#125—24no—
296#125—24no—
297#125—21no—
298C22⋊Q8—24no—
299C22⋊Q8—28no—
300C22⋊Q8—24no—
301C22⋊Q8—28no—
302C22⋊Q8—21no—
303C22⋊Q8—21no—
304C4×Q8—21no—
305C4×Q8—21no—
306C4×Q8—21no—
307C4×Q8—21no—
308C4×Q8D4×C14912yes—
309C4×Q8C23×C14912yes—
310C4×D4—24no—
311C4×D4—24no—
312C4×D4—21no—
313C4×D4—21no—
314C4×D4D4×C14912yes—
315C4×D4C23×C14912yes—
316#117—21no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4D4×C14911yescharacteristic
325C2×C4⋊C4D4×C14911yescharacteristic
326C2×C22⋊C4—22no—
327C2×C22⋊C4—21no—
328C2×C42—21no—
329C2×C42C23×C14911yescharacteristic
330#107—22no—
331#106—22no—
332#106—22no—
333C4⋊C8—21no—
334C4⋊C8—21no—
335C4⋊C8C23×C14912yes—
336C4⋊C8C23×C14912yes—
337#103—22no—
338#103—22no—
339#103—24no—
340#103—22no—
341#102—22no—
342C22⋊C8—21no—
343C22⋊C8—21no—
344C4×C8—21no—
345C4×C8C23×C14912yes—
346C24—21no—
347C2×Q8—21no—
348C2×Q8—22no—
349C2×Q8—22no—
350C2×Q8—22no—
351C2×Q8—21no—
352C2×Q8—21no—
353C2×Q8—82no—
354C2×Q8C2×D4×C14912yes—
355C2×Q8C2×D4×C14914yes—
356C2×D4—24no—
357C2×D4—21no—
358C2×D4C2×D4×C14912yes—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—22no—
363C22×C4—28no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—42no—
367C22×C4—42no—
368C22×C4—84no—
369C22×C4C2×D4×C14911yescharacteristic
370C22×C4C2×D4×C14911yescharacteristic
371C22×C4C2×D4×C14911yescharacteristic
372Q16—84no—
373SD16—44no—
374M16—42no—
375C2×C8—22no—
376C2×C8—22no—
377C2×C8—22no—
378C4⋊C4—28no—
379C4⋊C4—28no—
380C4⋊C4—21no—
381C4⋊C4—22no—
382C4⋊C4—22no—
383C4⋊C4—22no—
384C4⋊C4—21no—
385C4⋊C4—22no—
386C4⋊C4—22no—
387C4⋊C4—22no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—41no—
393C4⋊C4—41no—
394C4⋊C4C2×D4×C14912yes—
395C4⋊C4C2×D4×C14912yes—
396C22⋊C4—28no—
397C22⋊C4—22no—
398C22⋊C4—22no—
399C22⋊C4—41no—
400C42—22no—
401C42—22no—
402C42—41no—
403C42C2×D4×C14911yescharacteristic
404C42C2×D4×C14911yescharacteristic
405C42C2×D4×C14911yescharacteristic
406C42C24×C14911yescharacteristic
407C23—24no—
408C23—22no—
409C23—42no—
410C23—42no—
411C23#120×C14911yescharacteristic
412Q8—22no—
413Q8—22no—
414Q8—44no—
415Q8—42no—
416Q8—42no—
417Q8—42no—
418Q8—82no—
419D4—24no—
420D4—22no—
421D4#137×C14914yes—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—24no—
427C2×C4—41no—
428C2×C4—42no—
429C2×C4—44no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—44no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—88no—
438C2×C4#120×C14911yescharacteristic
439C2×C4#120×C14911yescharacteristic
440C2×C4#120×C14911yescharacteristic
441C2×C4#135×C14912yes—
442C2×C4#137×C14912yes—
443C2×C4C22×D4×C14911yescharacteristic
444C2×C4C22×D4×C14911yescharacteristic
445C2×C4C22×D4×C14911yescharacteristic
446C8—42no—
447C8—42no—
448C8—42no—
449C22—21no—
450C22—21no—
451C22—24no—
452C22—48no—
453C22—42no—
454C22—42no—
455C22#452×C14912yes—
456C22C2×#120×C14911yescharacteristic
457C4—21no—
458C4—21no—
459C4—21no—
460C4—42no—
461C4—42no—
462C4—42no—
463C4—44no—
464C4—81no—
465C4—81no—
466C4#452×C14912yes—
467C4C2×#135×C14911yescharacteristic
468C4C2×#137×C14911yescharacteristic
469C4C2×#137×C14912yes—
470C2—22no—
471C2—44no—
472C2C2×#452×C14911yescharacteristic
473C2#3004×C14911yescharacteristic
474C2#3019×C14911yescharacteristic
subgroupG/H
center, socleC22×C149C2×#120
commutator, Frattini, cosocleC42C24×C149
prime radicalC22×D4×C149D4
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. #3209×C149C2semidirect
4. #3078×C149C2semidirect
5. #1643×C149C2semidirect
6. #1632×C149C2semidirect
7. #1548×C149C2semidirect
9. #1479×C149C2semidirect
23. #494×C149C22semidirect
24. #487×C149C22semidirect
27. #477×C149C22semidirect
29. #475×C149C22semidirect
40. #333×C149C22semidirect
41. Q8⋊C8×C149C22semidirect
237. #18753C149direct (N × H)
238. C149#18753direct (N × H)
240. #3209C2×C149semidirect
242. #3078C2×C149semidirect
243. #1643C2×C149semidirect
244. #1632C2×C149semidirect
245. #1548C2×C149semidirect
247. #1479C2×C149semidirect
261. #494C22×C149semidirect
262. #487C22×C149semidirect
265. #477C22×C149semidirect
267. #475C22×C149semidirect
278. #333C22×C149semidirect
279. Q8⋊C8C22×C149semidirect

Maximal subgroups

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

subgroupindex
C2×#554×C1492
#3209×C1492
#3101×C1492
#3078×C1492
#1643×C1492
#1632×C1492
#1548×C1492
#1486×C1492
#1479×C1492
#18753149