Finite Group Databasebeta

← C149×#18382 #49197331

Subgroups — C149×#18382 #49197331

Order 38144.

1056 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3501×C149C211yesmaximal, characteristic, complemented
2#3187×C149C212yesmaximal, complemented
3#2543×C149C211yesmaximal, characteristic
4#1611×C149C212yesmaximal, complemented
5#1608×C149C212yesmaximal, complemented
6#1599×C149C212yesmaximal, complemented
7#1596×C149C212yesmaximal, complemented
8C2×#328×C149C212yesmaximal, complemented
9#1459×C149C211yesmaximal, characteristic, complemented
10#554×C149—24no—
11#554×C149—22no—
12D4×Q8×C149—22no—
13#544×C149C2212yes—
14#543×C149—21no—
15#543×C149C2212yes—
16#533×C149—21no—
17C2×C22⋊Q8×C149—21no—
18C2×C22⋊Q8×C149C2212yes—
19C2×#121×C149—21no—
20C2×#121×C149C2211yescharacteristic
21#518×C149—21no—
22C2×C4×D4×C149C2211yescharacteristic
23#483×C149C2214yes—
24#481×C149—22no—
25#465×C149—24no—
26#450×C149C2214yes—
27#448×C149—22no—
28C2×C22⋊C8×C149C2212yes—
29#398×C149C2211yescharacteristic
30#397×C149C2211yescharacteristic
31#394×C149C2211yescharacteristic
32#392×C149C2211yescharacteristic
33#388×C149—21no—
34#386×C149—21no—
35#386×C149—21no—
36C2×#95×C149C2211yescharacteristic
37#328×C149C2214yes—
38#328×C149C2214yes—
39#324×C149C2212yes—
40#323×C149C2212yes—
41C22×Q8×C149—21no—
42C22×Q8×C149D412yescomplemented
43C22×D4×C149—21no—
44C22×D4×C149—21no—
45C22×D4×C149D411yescharacteristic
46C22×D4×C149C2311yescharacteristic
47C23×C4×C149—21no—
48C23×C4×C149D411yescharacteristic
49C23×C4×C149C2311yescharacteristic
50C2×SD16×C149—24no—
51C22×C8×C149—22no—
52C4⋊Q8×C149—21no—
53C4⋊Q8×C149—21no—
54C4⋊Q8×C149—24no—
55#125×C149—22no—
56#125×C149—24no—
57C22⋊Q8×C149—22no—
58C22⋊Q8×C149—22no—
59C22⋊Q8×C149—24no—
60C22⋊Q8×C149—24no—
61C22⋊Q8×C149—24no—
62C22⋊Q8×C149—22no—
63C22⋊Q8×C149—22no—
64C22⋊Q8×C149—22no—
65C22⋊Q8×C149—22no—
66C22⋊Q8×C149—24no—
67C22⋊Q8×C149D414yescomplemented
68C22⋊Q8×C149C2314yes—
69#121×C149—22no—
70#121×C149—22no—
71#121×C149—44no—
72C4×Q8×C149—22no—
73C4×Q8×C149—22no—
74C4×D4×C149—24no—
75C4×D4×C149—24no—
76C4×D4×C149—22no—
77C4×D4×C149—22no—
78#117×C149—22no—
79C2×C4⋊C4×C149—21no—
80C2×C4⋊C4×C149—22no—
81C2×C4⋊C4×C149—22no—
82C2×C4⋊C4×C149—21no—
83C2×C4⋊C4×C149D412yescomplemented
84C2×C4⋊C4×C149C2311yescharacteristic
85C2×C4⋊C4×C149C2311yescharacteristic
86C2×C22⋊C4×C149—22no—
87C2×C22⋊C4×C149—22no—
88C2×C22⋊C4×C149—21no—
89C2×C22⋊C4×C149—21no—
90C2×C22⋊C4×C149—21no—
91C2×C22⋊C4×C149—21no—
92C2×C22⋊C4×C149—21no—
93C2×C22⋊C4×C149D411yescharacteristic
94C2×C22⋊C4×C149C2311yescharacteristic
95C2×C42×C149D411yescharacteristic
96#106×C149—24no—
97#103×C149—24no—
98#102×C149—24no—
99C22⋊C8×C149—22no—
100C22⋊C8×C149C2314yes—
101#95×C149—21no—
102#95×C149—21no—
103#95×C149—21no—
104#95×C149C2311yescharacteristic
105#95×C149C2311yescharacteristic
106C24×C149—21no—
107C24×C149C2×D411yescharacteristic
108C24×C149C2×D411yescharacteristic
109C2×Q8×C149—22no—
110C2×Q8×C149—22no—
111C2×Q8×C149—22no—
112C2×Q8×C149—82no—
113C2×Q8×C149—82no—
114C2×Q8×C149C2×D414yes—
115C2×D4×C149—22no—
116C2×D4×C149—22no—
117C2×D4×C149—22no—
118C2×D4×C149—42no—
119C2×D4×C149—42no—
120C2×D4×C149—42no—
121C2×D4×C149—42no—
122C2×D4×C149—42no—
123C2×D4×C149—81no—
124C2×D4×C149—81no—
125C2×D4×C149SD1614yescomplemented
126C22×C4×C149—21no—
127C22×C4×C149—22no—
128C22×C4×C149—22no—
129C22×C4×C149—22no—
130C22×C4×C149—22no—
131C22×C4×C149—21no—
132C22×C4×C149—21no—
133C22×C4×C149—21no—
134C22×C4×C149—21no—
135C22×C4×C149—42no—
136C22×C4×C149—42no—
137C22×C4×C149—81no—
138C22×C4×C149—81no—
139C22×C4×C149—81no—
140C22×C4×C149C2×D411yescharacteristic
141C22×C4×C149C2×D411yescharacteristic
142C22×C4×C149C2×D411yescharacteristic
143C22×C4×C149C2×D411yescharacteristic
144C22×C4×C149C2×D412yes—
145C22×C4×C149C2×D412yes—
146C22×C4×C149C2411yescharacteristic
147SD16×C149—84no—
148C2×C8×C149—24no—
149C2×C8×C149—82no—
150C4⋊C4×C149—22no—
151C4⋊C4×C149—24no—
152C4⋊C4×C149—22no—
153C4⋊C4×C149—22no—
154C4⋊C4×C149—24no—
155C4⋊C4×C149—22no—
156C4⋊C4×C149—24no—
157C4⋊C4×C149—22no—
158C4⋊C4×C149—24no—
159C4⋊C4×C149—22no—
160C4⋊C4×C149—22no—
161C4⋊C4×C149—42no—
162C4⋊C4×C149C2×D414yes—
163C22⋊C4×C149—24no—
164C22⋊C4×C149—24no—
165C22⋊C4×C149—22no—
166C22⋊C4×C149—24no—
167C22⋊C4×C149—22no—
168C22⋊C4×C149—42no—
169C22⋊C4×C149—42no—
170C22⋊C4×C149—41no—
171C22⋊C4×C149—41no—
172C22⋊C4×C149—42no—
173C22⋊C4×C149—81no—
174C42×C149—24no—
175C42×C149—21no—
176C42×C149—21no—
177C23×C149—21no—
178C23×C149—21no—
179C23×C149—41no—
180C23×C149—41no—
181C23×C149—41no—
182C23×C149—41no—
183C23×C149—41no—
184C23×C149—41no—
185C23×C149—41no—
186C23×C149—41no—
187C23×C149—41no—
188C23×C149—41no—
189C23×C149—41no—
190C23×C149#12012yes—
191C23×C149C2×SD1612yes—
192C23×C149C2×SD1612yes—
193C23×C149#13712yes—
194C23×C149C22×D411yescharacteristic
195Q8×C149—44no—
196Q8×C149—44no—
197Q8×C149—82no—
198Q8×C149—82no—
199D4×C149—28no—
200D4×C149—44no—
201D4×C149—84no—
202D4×C149—84no—
203C2×C4×C149—21no—
204C2×C4×C149—21no—
205C2×C4×C149—22no—
206C2×C4×C149—21no—
207C2×C4×C149—24no—
208C2×C4×C149—24no—
209C2×C4×C149—21no—
210C2×C4×C149—42no—
211C2×C4×C149—41no—
212C2×C4×C149—42no—
213C2×C4×C149—41no—
214C2×C4×C149—42no—
215C2×C4×C149—41no—
216C2×C4×C149—41no—
217C2×C4×C149—41no—
218C2×C4×C149—41no—
219C2×C4×C149—41no—
220C2×C4×C149—41no—
221C2×C4×C149—41no—
222C2×C4×C149—41no—
223C2×C4×C149—41no—
224C2×C4×C149—41no—
225C2×C4×C149—81no—
226C2×C4×C149—82no—
227C2×C4×C149—82no—
228C2×C4×C149—82no—
229C2×C4×C149—82no—
230C2×C4×C149—84no—
231C2×C4×C149#12011yescharacteristic
232C2×C4×C149#12011yescharacteristic
233C2×C4×C149C2×SD1612yes—
234C2×C4×C149C22×D412yes—
235C8×C149—44no—
236C22×C149—21no—
237C22×C149—22no—
238C22×C149—21no—
239C22×C149—22no—
240C22×C149—22no—
241C22×C149—42no—
242C22×C149—42no—
243C22×C149—42no—
244C22×C149—41no—
245C22×C149—41no—
246C22×C149—81no—
247C22×C149—81no—
248C22×C149—81no—
249C22×C149—81no—
250C22×C149—81no—
251C22×C149—81no—
252C22×C149—81no—
253C22×C149—81no—
254C22×C149#44814yes—
255C22×C149C2×#12011yescharacteristic
256C22×C149C22×SD1611yescharacteristic
257C22×C149C2×#13711yescharacteristic
258C4×C149—22no—
259C4×C149—22no—
260C4×C149—21no—
261C4×C149—21no—
262C4×C149—42no—
263C4×C149—41no—
264C4×C149—44no—
265C4×C149—41no—
266C4×C149—44no—
267C4×C149—81no—
268C4×C149—81no—
269C2×C149—21no—
270C2×C149—21no—
271C2×C149—24no—
272C2×C149—42no—
273C2×C149—161no—
274C2×C149C2×#44811yescharacteristic
275C2×C149#301811yescharacteristic
276C2×C149#302611yescharacteristic
277#18382C14911yesmaximal, characteristic, direct product factor, Sylow
278C149#1838211yescharacteristic, direct product factor, Sylow
279#3501C2×C14911yescharacteristic, complemented
280#3187C2×C14912yescomplemented
281#2543C2×C14911yescharacteristic
282#1611C2×C14912yescomplemented
283#1608C2×C14912yescomplemented
284#1599C2×C14912yescomplemented
285#1596C2×C14912yescomplemented
286C2×#328C2×C14912yescomplemented
287#1459C2×C14911yescharacteristic, complemented
288#554—24no—
289#554—22no—
290D4×Q8—22no—
291#544C22×C14912yes—
292#543—21no—
293#543C22×C14912yes—
294#533—21no—
295C2×C22⋊Q8—21no—
296C2×C22⋊Q8C22×C14912yes—
297C2×#121—21no—
298C2×#121C22×C14911yescharacteristic
299#518—21no—
300C2×C4×D4C22×C14911yescharacteristic
301#483C22×C14914yes—
302#481—22no—
303#465—24no—
304#450C22×C14914yes—
305#448—22no—
306C2×C22⋊C8C22×C14912yes—
307#398C22×C14911yescharacteristic
308#397C22×C14911yescharacteristic
309#394C22×C14911yescharacteristic
310#392C22×C14911yescharacteristic
311#388—21no—
312#386—21no—
313#386—21no—
314C2×#95C22×C14911yescharacteristic
315#328C22×C14914yes—
316#328C22×C14914yes—
317#324C22×C14912yes—
318#323C22×C14912yes—
319C22×Q8—21no—
320C22×Q8D4×C14912yescomplemented
321C22×D4—21no—
322C22×D4—21no—
323C22×D4D4×C14911yescharacteristic
324C22×D4C23×C14911yescharacteristic
325C23×C4—21no—
326C23×C4D4×C14911yescharacteristic
327C23×C4C23×C14911yescharacteristic
328C2×SD16—24no—
329C22×C8—22no—
330C4⋊Q8—21no—
331C4⋊Q8—21no—
332C4⋊Q8—24no—
333#125—22no—
334#125—24no—
335C22⋊Q8—22no—
336C22⋊Q8—22no—
337C22⋊Q8—24no—
338C22⋊Q8—24no—
339C22⋊Q8—24no—
340C22⋊Q8—22no—
341C22⋊Q8—22no—
342C22⋊Q8—22no—
343C22⋊Q8—22no—
344C22⋊Q8—24no—
345C22⋊Q8D4×C14914yescomplemented
346C22⋊Q8C23×C14914yes—
347#121—22no—
348#121—22no—
349#121—44no—
350C4×Q8—22no—
351C4×Q8—22no—
352C4×D4—24no—
353C4×D4—24no—
354C4×D4—22no—
355C4×D4—22no—
356#117—22no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4D4×C14912yescomplemented
362C2×C4⋊C4C23×C14911yescharacteristic
363C2×C4⋊C4C23×C14911yescharacteristic
364C2×C22⋊C4—22no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4D4×C14911yescharacteristic
372C2×C22⋊C4C23×C14911yescharacteristic
373C2×C42D4×C14911yescharacteristic
374#106—24no—
375#103—24no—
376#102—24no—
377C22⋊C8—22no—
378C22⋊C8C23×C14914yes—
379#95—21no—
380#95—21no—
381#95—21no—
382#95C23×C14911yescharacteristic
383#95C23×C14911yescharacteristic
384C24—21no—
385C24C2×D4×C14911yescharacteristic
386C24C2×D4×C14911yescharacteristic
387C2×Q8—22no—
388C2×Q8—22no—
389C2×Q8—22no—
390C2×Q8—82no—
391C2×Q8—82no—
392C2×Q8C2×D4×C14914yes—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4—22no—
396C2×D4—42no—
397C2×D4—42no—
398C2×D4—42no—
399C2×D4—42no—
400C2×D4—42no—
401C2×D4—81no—
402C2×D4—81no—
403C2×D4SD16×C14914yescomplemented
404C22×C4—21no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—42no—
414C22×C4—42no—
415C22×C4—81no—
416C22×C4—81no—
417C22×C4—81no—
418C22×C4C2×D4×C14911yescharacteristic
419C22×C4C2×D4×C14911yescharacteristic
420C22×C4C2×D4×C14911yescharacteristic
421C22×C4C2×D4×C14911yescharacteristic
422C22×C4C2×D4×C14912yes—
423C22×C4C2×D4×C14912yes—
424C22×C4C24×C14911yescharacteristic
425SD16—84no—
426C2×C8—24no—
427C2×C8—82no—
428C4⋊C4—22no—
429C4⋊C4—24no—
430C4⋊C4—22no—
431C4⋊C4—22no—
432C4⋊C4—24no—
433C4⋊C4—22no—
434C4⋊C4—24no—
435C4⋊C4—22no—
436C4⋊C4—24no—
437C4⋊C4—22no—
438C4⋊C4—22no—
439C4⋊C4—42no—
440C4⋊C4C2×D4×C14914yes—
441C22⋊C4—24no—
442C22⋊C4—24no—
443C22⋊C4—22no—
444C22⋊C4—24no—
445C22⋊C4—22no—
446C22⋊C4—42no—
447C22⋊C4—42no—
448C22⋊C4—41no—
449C22⋊C4—41no—
450C22⋊C4—42no—
451C22⋊C4—81no—
452C42—24no—
453C42—21no—
454C42—21no—
455C23—21no—
456C23—21no—
457C23—41no—
458C23—41no—
459C23—41no—
460C23—41no—
461C23—41no—
462C23—41no—
463C23—41no—
464C23—41no—
465C23—41no—
466C23—41no—
467C23—41no—
468C23#120×C14912yes—
469C23C2×SD16×C14912yes—
470C23C2×SD16×C14912yes—
471C23#137×C14912yes—
472C23C22×D4×C14911yescharacteristic
473Q8—44no—
474Q8—44no—
475Q8—82no—
476Q8—82no—
477D4—28no—
478D4—44no—
479D4—84no—
480D4—84no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—22no—
484C2×C4—21no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—21no—
488C2×C4—42no—
489C2×C4—41no—
490C2×C4—42no—
491C2×C4—41no—
492C2×C4—42no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—81no—
504C2×C4—82no—
505C2×C4—82no—
506C2×C4—82no—
507C2×C4—82no—
508C2×C4—84no—
509C2×C4#120×C14911yescharacteristic
510C2×C4#120×C14911yescharacteristic
511C2×C4C2×SD16×C14912yes—
512C2×C4C22×D4×C14912yes—
513C8—44no—
514C22—21no—
515C22—22no—
516C22—21no—
517C22—22no—
518C22—22no—
519C22—42no—
520C22—42no—
521C22—42no—
522C22—41no—
523C22—41no—
524C22—81no—
525C22—81no—
526C22—81no—
527C22—81no—
528C22—81no—
529C22—81no—
530C22—81no—
531C22—81no—
532C22#448×C14914yes—
533C22C2×#120×C14911yescharacteristic
534C22C22×SD16×C14911yescharacteristic
535C22C2×#137×C14911yescharacteristic
536C4—22no—
537C4—22no—
538C4—21no—
539C4—21no—
540C4—42no—
541C4—41no—
542C4—44no—
543C4—41no—
544C4—44no—
545C4—81no—
546C4—81no—
547C2—21no—
548C2—21no—
549C2—24no—
550C2—42no—
551C2—161no—
552C2C2×#448×C14911yescharacteristic
553C2#3018×C14911yescharacteristic
554C2#3026×C14911yescharacteristic
subgroupG/H
center, socleC22×C149C2×#120
commutator, Frattini, cosocleC22×C4C24×C149
prime radical#2543×C149C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C149 ◁ C23×C4×C149 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3501×C149C2semidirect
2. #3187×C149C2semidirect
4. #1611×C149C2semidirect
5. #1608×C149C2semidirect
6. #1599×C149C2semidirect
7. #1596×C149C2semidirect
8. C2×#328×C149C2semidirect
9. #1459×C149C2semidirect
42. C22×Q8×C149D4semidirect
67. C22⋊Q8×C149D4semidirect
83. C2×C4⋊C4×C149D4semidirect
125. C2×D4×C149SD16semidirect
277. #18382C149direct (N × H)
278. C149#18382direct (N × H)
279. #3501C2×C149semidirect
280. #3187C2×C149semidirect
282. #1611C2×C149semidirect
283. #1608C2×C149semidirect
284. #1599C2×C149semidirect
285. #1596C2×C149semidirect
286. C2×#328C2×C149semidirect
287. #1459C2×C149semidirect
320. C22×Q8D4×C149semidirect
345. C22⋊Q8D4×C149semidirect
361. C2×C4⋊C4D4×C149semidirect
403. C2×D4SD16×C149semidirect

Maximal subgroups

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

subgroupindex
#3501×C1492
#3187×C1492
#2543×C1492
#1611×C1492
#1608×C1492
#1599×C1492
#1596×C1492
C2×#328×C1492
#1459×C1492
#18382149