Finite Group Databasebeta

← C149×#13099 #49192048

Subgroups — C149×#13099 #49192048

Order 38144.

666 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3008×C149C211yesmaximal, characteristic
2#2888×C149C211yesmaximal, characteristic, complemented
3#2134×C149C211yesmaximal, characteristic, complemented
4#2122×C149C211yesmaximal, characteristic, complemented
5#1795×C149C211yesmaximal, characteristic, complemented
6#1395×C149C211yesmaximal, characteristic, complemented
7#1392×C149C211yesmaximal, characteristic, complemented
8C2×H(5,𝔽2)×C149C2211yescharacteristic
9C2×AGL(1,ℤ/8)×C149C411yescharacteristic, complemented
10C22×D8×C149C411yescharacteristic, complemented
11#568×C149—21no—
12#535×C149C2211yescharacteristic
13#449×C149—21no—
14#449×C149—21no—
15#447×C149—21no—
16#447×C149—21no—
17#421×C149—21no—
18#418×C149—21no—
19#418×C149C411yescharacteristic, complemented
20#416×C149C411yescharacteristic, complemented
21#413×C149—22no—
22#413×C149C2211yescharacteristic
23#413×C149C2211yescharacteristic
24#413×C149C2211yescharacteristic
25C2×#100×C149—21no—
26C2×#100×C149—22no—
27#410×C149C2211yescharacteristic
28#408×C149C2211yescharacteristic
29#355×C149—22no—
30AΣL(1,𝔽16)×C149—22no—
31H(5,𝔽2)×C149—42no—
32H(5,𝔽2)×C149—42no—
33C2×#41×C149—21no—
34C2×#41×C149C2×C411yescharacteristic
35C2×#41×C149D411yescharacteristic
36C2×#41×C149D411yescharacteristic
37C2×#41×C149C2311yescharacteristic
38C22×D4×C149—21no—
39C22×D4×C149—21no—
40C22×D4×C149—21no—
41C22×D4×C149C2×C411yescharacteristic
42C22×D4×C149C2×C411yescharacteristic
43C22×D4×C149D411yescharacteristic
44C22×D4×C149D411yescharacteristic
45AGL(1,ℤ/8)×C149—42no—
46C2×SD16×C149—21no—
47C2×D8×C149—21no—
48C2×D8×C149—21no—
49C2×D8×C149—21no—
50C2×D8×C149—42no—
51#131×C149—42no—
52#131×C149—42no—
53C2×M16×C149—24no—
54C2×M16×C149—21no—
55C2×M16×C149—21no—
56C2×M16×C149—21no—
57C2×M16×C149C2×C411yescharacteristic
58C22×C8×C149C2×C411yescharacteristic
59#127×C149—21no—
60#124×C149—21no—
61#121×C149—21no—
62#121×C149—21no—
63#120×C149—21no—
64#120×C149—21no—
65#117×C149—21no—
66#117×C149C2×C411yescharacteristic
67#104×C149—42no—
68#103×C149—21no—
69#102×C149—21no—
70#102×C149—21no—
71#102×C149—21no—
72#102×C149—42no—
73#101×C149—21no—
74#101×C149—21no—
75#101×C149D412yes—
76#100×C149—24no—
77#100×C149—21no—
78#100×C149—21no—
79#100×C149D412yes—
80#99×C149—21no—
81#99×C149—21no—
82C22⋊C8×C149—21no—
83C22⋊C8×C149—21no—
84C24×C149—21no—
85C24×C149—21no—
86C24×C149—21no—
87C24×C149—21no—
88#41×C149—22no—
89#41×C149—22no—
90#41×C149—22no—
91#41×C149—22no—
92#41×C149—41no—
93#41×C149—41no—
94#41×C149—41no—
95#41×C149—41no—
96#41×C149—44no—
97C2×Q8×C149C22⋊C411yescharacteristic
98C2×Q8×C149C2×D411yescharacteristic
99C2×D4×C149—21no—
100C2×D4×C149—22no—
101C2×D4×C149—22no—
102C2×D4×C149—21no—
103C2×D4×C149—21no—
104C2×D4×C149—21no—
105C2×D4×C149—21no—
106C2×D4×C149—21no—
107C2×D4×C149—21no—
108C2×D4×C149—21no—
109C2×D4×C149—41no—
110C2×D4×C149—41no—
111C2×D4×C149—41no—
112C2×D4×C149—41no—
113C2×D4×C149—44no—
114C2×D4×C149—41no—
115C2×D4×C149—41no—
116C2×D4×C149—44no—
117C2×D4×C149—44no—
118C2×D4×C149—41no—
119C2×D4×C149—41no—
120C2×D4×C149C22⋊C411yescharacteristic
121C2×D4×C149C22⋊C411yescharacteristic
122C2×D4×C149C22⋊C411yescharacteristic
123C2×D4×C149C2×D411yescharacteristic
124C2×D4×C149#4111yescharacteristic
125C2×D4×C149#4111yescharacteristic
126C22×C4×C149—21no—
127C22×C4×C149—21no—
128C22×C4×C149—21no—
129C22×C4×C149C22×C411yescharacteristic
130C22×C4×C149C2×D411yescharacteristic
131C22×C4×C149C2×D411yescharacteristic
132SD16×C149—42no—
133D8×C149—42no—
134D8×C149—42no—
135D8×C149—42no—
136M16×C149—22no—
137M16×C149—22no—
138M16×C149—44no—
139M16×C149—41no—
140M16×C149—41no—
141M16×C149—41no—
142M16×C149—41no—
143M16×C149—41no—
144C2×C8×C149—21no—
145C2×C8×C149—21no—
146C2×C8×C149—44no—
147C2×C8×C149—41no—
148C2×C8×C149—41no—
149C2×C8×C149—41no—
150C2×C8×C149—41no—
151C4⋊C4×C149—21no—
152C4⋊C4×C149—41no—
153C22⋊C4×C149—21no—
154C22⋊C4×C149—41no—
155C22⋊C4×C149—41no—
156C22⋊C4×C149—41no—
157C42×C149—21no—
158C42×C149—41no—
159C23×C149—21no—
160C23×C149—21no—
161C23×C149—21no—
162C23×C149—42no—
163C23×C149—42no—
164C23×C149—42no—
165C23×C149—41no—
166C23×C149—81no—
167C23×C149—161no—
168C23×C149—161no—
169C23×C149—161no—
170C23×C149—161no—
171C23×C149C4×D411yescharacteristic
172C23×C149#12111yescharacteristic
173C23×C149#12311yescharacteristic
174Q8×C149—21no—
175Q8×C149—41no—
176Q8×C149#9912yes—
177D4×C149—24no—
178D4×C149—21no—
179D4×C149—21no—
180D4×C149—21no—
181D4×C149—21no—
182D4×C149—21no—
183D4×C149—41no—
184D4×C149—41no—
185D4×C149—41no—
186D4×C149—42no—
187D4×C149—42no—
188D4×C149—42no—
189D4×C149—42no—
190D4×C149—42no—
191D4×C149—41no—
192D4×C149—41no—
193D4×C149—81no—
194D4×C149—161no—
195D4×C149—161no—
196D4×C149#9912yes—
197C2×C4×C149—24no—
198C2×C4×C149—21no—
199C2×C4×C149—21no—
200C2×C4×C149—21no—
201C2×C4×C149—21no—
202C2×C4×C149—21no—
203C2×C4×C149—21no—
204C2×C4×C149—21no—
205C2×C4×C149—42no—
206C2×C4×C149—42no—
207C2×C4×C149—41no—
208C2×C4×C149—81no—
209C2×C4×C149C2×C22⋊C411yescharacteristic
210C2×C4×C149C4×D411yescharacteristic
211C2×C4×C149#12011yescharacteristic
212C2×C4×C149#12111yescharacteristic
213C8×C149—42no—
214C8×C149—42no—
215C8×C149—41no—
216C8×C149—41no—
217C8×C149—81no—
218C22×C149—21no—
219C22×C149—21no—
220C22×C149—22no—
221C22×C149—21no—
222C22×C149—41no—
223C22×C149—41no—
224C22×C149—41no—
225C22×C149—41no—
226C22×C149—41no—
227C22×C149—81no—
228C22×C149—81no—
229C22×C149—81no—
230C22×C149—81no—
231C22×C149—81no—
232C22×C149—81no—
233C22×C149—162no—
234C22×C149—162no—
235C22×C149—162no—
236C22×C149—162no—
237C22×C149#38611yescharacteristic
238C4×C149—21no—
239C4×C149—21no—
240C4×C149—22no—
241C4×C149—21no—
242C4×C149—81no—
243C4×C149—161no—
244C4×C149C2×#9911yescharacteristic
245C4×C149C2×#9911yescharacteristic
246C2×C149—21no—
247C2×C149—41no—
248C2×C149—41no—
249C2×C149—41no—
250C2×C149—42no—
251C2×C149—81no—
252C2×C149—81no—
253C2×C149—161no—
254C2×C149#189811yescharacteristic
255#13099C14911yesmaximal, characteristic, direct product factor, Sylow
256C149#1309911yescharacteristic, direct product factor, Sylow
257#3008C2×C14911yescharacteristic
258#2888C2×C14911yescharacteristic, complemented
259#2134C2×C14911yescharacteristic, complemented
260#2122C2×C14911yescharacteristic, complemented
261#1795C2×C14911yescharacteristic, complemented
262#1395C2×C14911yescharacteristic, complemented
263#1392C2×C14911yescharacteristic, complemented
264C2×H(5,𝔽2)C22×C14911yescharacteristic
265C2×AGL(1,ℤ/8)C4×C14911yescharacteristic, complemented
266C22×D8C4×C14911yescharacteristic, complemented
267#568—21no—
268#535C22×C14911yescharacteristic
269#449—21no—
270#449—21no—
271#447—21no—
272#447—21no—
273#421—21no—
274#418—21no—
275#418C4×C14911yescharacteristic, complemented
276#416C4×C14911yescharacteristic, complemented
277#413—22no—
278#413C22×C14911yescharacteristic
279#413C22×C14911yescharacteristic
280#413C22×C14911yescharacteristic
281C2×#100—21no—
282C2×#100—22no—
283#410C22×C14911yescharacteristic
284#408C22×C14911yescharacteristic
285#355—22no—
286AΣL(1,𝔽16)—22no—
287H(5,𝔽2)—42no—
288H(5,𝔽2)—42no—
289C2×#41—21no—
290C2×#41C2×C4×C14911yescharacteristic
291C2×#41D4×C14911yescharacteristic
292C2×#41D4×C14911yescharacteristic
293C2×#41C23×C14911yescharacteristic
294C22×D4—21no—
295C22×D4—21no—
296C22×D4—21no—
297C22×D4C2×C4×C14911yescharacteristic
298C22×D4C2×C4×C14911yescharacteristic
299C22×D4D4×C14911yescharacteristic
300C22×D4D4×C14911yescharacteristic
301AGL(1,ℤ/8)—42no—
302C2×SD16—21no—
303C2×D8—21no—
304C2×D8—21no—
305C2×D8—21no—
306C2×D8—42no—
307#131—42no—
308#131—42no—
309C2×M16—24no—
310C2×M16—21no—
311C2×M16—21no—
312C2×M16—21no—
313C2×M16C2×C4×C14911yescharacteristic
314C22×C8C2×C4×C14911yescharacteristic
315#127—21no—
316#124—21no—
317#121—21no—
318#121—21no—
319#120—21no—
320#120—21no—
321#117—21no—
322#117C2×C4×C14911yescharacteristic
323#104—42no—
324#103—21no—
325#102—21no—
326#102—21no—
327#102—21no—
328#102—42no—
329#101—21no—
330#101—21no—
331#101D4×C14912yes—
332#100—24no—
333#100—21no—
334#100—21no—
335#100D4×C14912yes—
336#99—21no—
337#99—21no—
338C22⋊C8—21no—
339C22⋊C8—21no—
340C24—21no—
341C24—21no—
342C24—21no—
343C24—21no—
344#41—22no—
345#41—22no—
346#41—22no—
347#41—22no—
348#41—41no—
349#41—41no—
350#41—41no—
351#41—41no—
352#41—44no—
353C2×Q8C22⋊C4×C14911yescharacteristic
354C2×Q8C2×D4×C14911yescharacteristic
355C2×D4—21no—
356C2×D4—22no—
357C2×D4—22no—
358C2×D4—21no—
359C2×D4—21no—
360C2×D4—21no—
361C2×D4—21no—
362C2×D4—21no—
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—41no—
366C2×D4—41no—
367C2×D4—41no—
368C2×D4—41no—
369C2×D4—44no—
370C2×D4—41no—
371C2×D4—41no—
372C2×D4—44no—
373C2×D4—44no—
374C2×D4—41no—
375C2×D4—41no—
376C2×D4C22⋊C4×C14911yescharacteristic
377C2×D4C22⋊C4×C14911yescharacteristic
378C2×D4C22⋊C4×C14911yescharacteristic
379C2×D4C2×D4×C14911yescharacteristic
380C2×D4#41×C14911yescharacteristic
381C2×D4#41×C14911yescharacteristic
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4C22×C4×C14911yescharacteristic
386C22×C4C2×D4×C14911yescharacteristic
387C22×C4C2×D4×C14911yescharacteristic
388SD16—42no—
389D8—42no—
390D8—42no—
391D8—42no—
392M16—22no—
393M16—22no—
394M16—44no—
395M16—41no—
396M16—41no—
397M16—41no—
398M16—41no—
399M16—41no—
400C2×C8—21no—
401C2×C8—21no—
402C2×C8—44no—
403C2×C8—41no—
404C2×C8—41no—
405C2×C8—41no—
406C2×C8—41no—
407C4⋊C4—21no—
408C4⋊C4—41no—
409C22⋊C4—21no—
410C22⋊C4—41no—
411C22⋊C4—41no—
412C22⋊C4—41no—
413C42—21no—
414C42—41no—
415C23—21no—
416C23—21no—
417C23—21no—
418C23—42no—
419C23—42no—
420C23—42no—
421C23—41no—
422C23—81no—
423C23—161no—
424C23—161no—
425C23—161no—
426C23—161no—
427C23C4×D4×C14911yescharacteristic
428C23#121×C14911yescharacteristic
429C23#123×C14911yescharacteristic
430Q8—21no—
431Q8—41no—
432Q8#99×C14912yes—
433D4—24no—
434D4—21no—
435D4—21no—
436D4—21no—
437D4—21no—
438D4—21no—
439D4—41no—
440D4—41no—
441D4—41no—
442D4—42no—
443D4—42no—
444D4—42no—
445D4—42no—
446D4—42no—
447D4—41no—
448D4—41no—
449D4—81no—
450D4—161no—
451D4—161no—
452D4#99×C14912yes—
453C2×C4—24no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—41no—
464C2×C4—81no—
465C2×C4C2×C22⋊C4×C14911yescharacteristic
466C2×C4C4×D4×C14911yescharacteristic
467C2×C4#120×C14911yescharacteristic
468C2×C4#121×C14911yescharacteristic
469C8—42no—
470C8—42no—
471C8—41no—
472C8—41no—
473C8—81no—
474C22—21no—
475C22—21no—
476C22—22no—
477C22—21no—
478C22—41no—
479C22—41no—
480C22—41no—
481C22—41no—
482C22—41no—
483C22—81no—
484C22—81no—
485C22—81no—
486C22—81no—
487C22—81no—
488C22—81no—
489C22—162no—
490C22—162no—
491C22—162no—
492C22—162no—
493C22#386×C14911yescharacteristic
494C4—21no—
495C4—21no—
496C4—22no—
497C4—21no—
498C4—81no—
499C4—161no—
500C4C2×#99×C14911yescharacteristic
501C4C2×#99×C14911yescharacteristic
502C2—21no—
503C2—41no—
504C2—41no—
505C2—41no—
506C2—42no—
507C2—81no—
508C2—81no—
509C2—161no—
510C2#1898×C14911yescharacteristic
subgroupG/H
center, socleC2×C149#1898
commutatorC22×C4C22×C4×C149
Frattini, cosocleC2×#41C23×C149
prime radical#3008×C149C2
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C149 ◁ C2×C4×C149 ◁ C2×H(5,𝔽2)×C149 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2888×C149C2semidirect
3. #2134×C149C2semidirect
4. #2122×C149C2semidirect
5. #1795×C149C2semidirect
6. #1395×C149C2semidirect
7. #1392×C149C2semidirect
9. C2×AGL(1,ℤ/8)×C149C4semidirect
10. C22×D8×C149C4semidirect
19. #418×C149C4semidirect
20. #416×C149C4semidirect
255. #13099C149direct (N × H)
256. C149#13099direct (N × H)
258. #2888C2×C149semidirect
259. #2134C2×C149semidirect
260. #2122C2×C149semidirect
261. #1795C2×C149semidirect
262. #1395C2×C149semidirect
263. #1392C2×C149semidirect
265. C2×AGL(1,ℤ/8)C4×C149semidirect
266. C22×D8C4×C149semidirect
275. #418C4×C149semidirect
276. #416C4×C149semidirect

Maximal subgroups

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

subgroupindex
#3008×C1492
#2888×C1492
#2134×C1492
#2122×C1492
#1795×C1492
#1395×C1492
#1392×C1492
#13099149