Finite Group Databasebeta

← C149×#9043 #49187992

Subgroups — C149×#9043 #49187992

Order 38144.

678 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#480×C149C211yesmaximal, characteristic
2#2325×C149C211yesmaximal, characteristic
3#1823×C149C211yesmaximal, characteristic, complemented
4C2×#327×C149C211yesmaximal, characteristic
5#1445×C149C211yesmaximal, characteristic, complemented
6#1294×C149C211yesmaximal, characteristic, complemented
7#1280×C149C211yesmaximal, characteristic, complemented
8C2×#121×C149C2211yescharacteristic
9C2×C4×D4×C149—21no—
10C22×C4⋊C4×C149C2211yescharacteristic
11#480×C149—22no—
12#480×C149C414yescomplemented
13C2×#107×C149—21no—
14C2×#102×C149—21no—
15C2×C22⋊C8×C149C2211yescharacteristic
16C2×C22⋊C8×C149C2211yescharacteristic
17#388×C149—21no—
18#387×C149—21no—
19#386×C149—21no—
20#386×C149—21no—
21#385×C149—21no—
22#380×C149C2211yescharacteristic
23C2×#95×C149—21no—
24C2×#95×C149—21no—
25C2×#95×C149C2211yescharacteristic
26C2×#95×C149C2211yescharacteristic
27#340×C149—21no—
28#340×C149—21no—
29#327×C149—22no—
30C22×D4×C149—21no—
31C22×D4×C149D411yescharacteristic
32C23×C4×C149—21no—
33C23×C4×C149—21no—
34C23×C4×C149—21no—
35C23×C4×C149D411yescharacteristic
36C23×C4×C149D411yescharacteristic
37C23×C4×C149C2311yescharacteristic
38C22×C8×C149—21no—
39C22×C8×C149—21no—
40#121×C149—21no—
41#121×C149—21no—
42#121×C149C2×C412yes—
43#121×C149D412yes—
44C4×D4×C149—42no—
45C4×D4×C149—42no—
46C2×C4⋊C4×C149—21no—
47C2×C4⋊C4×C149—21no—
48C2×C4⋊C4×C149—21no—
49C2×C4⋊C4×C149—21no—
50C2×C4⋊C4×C149—21no—
51C2×C4⋊C4×C149—21no—
52C2×C4⋊C4×C149C2×C412yescomplemented
53C2×C4⋊C4×C149D411yescharacteristic
54C2×C4⋊C4×C149D411yescharacteristic
55C2×C4⋊C4×C149D411yescharacteristic
56C2×C22⋊C4×C149—21no—
57C2×C22⋊C4×C149—21no—
58C2×C22⋊C4×C149—21no—
59C2×C22⋊C4×C149—21no—
60C2×C22⋊C4×C149—21no—
61C2×C42×C149—21no—
62#107×C149—24no—
63#102×C149—24no—
64C22⋊C8×C149—21no—
65C22⋊C8×C149—21no—
66C22⋊C8×C149—21no—
67C22⋊C8×C149C2×C412yescomplemented
68#95×C149—21no—
69#95×C149—21no—
70#95×C149—21no—
71#95×C149—21no—
72#95×C149—21no—
73#95×C149—21no—
74#95×C149—21no—
75#95×C149—42no—
76#95×C149—42no—
77C24×C149—21no—
78C24×C149C2×D411yescharacteristic
79C2×D4×C149—22no—
80C2×D4×C149—22no—
81C2×D4×C149—21no—
82C2×D4×C149—41no—
83C2×D4×C149—41no—
84C2×D4×C149—41no—
85C2×D4×C149—41no—
86C2×D4×C149—41no—
87C2×D4×C149—41no—
88C2×D4×C149C22⋊C412yes—
89C22×C4×C149—21no—
90C22×C4×C149—21no—
91C22×C4×C149—21no—
92C22×C4×C149—22no—
93C22×C4×C149—22no—
94C22×C4×C149—21no—
95C22×C4×C149—21no—
96C22×C4×C149—21no—
97C22×C4×C149—21no—
98C22×C4×C149—21no—
99C22×C4×C149—41no—
100C22×C4×C149—41no—
101C22×C4×C149—42no—
102C22×C4×C149—41no—
103C22×C4×C149—41no—
104C22×C4×C149—41no—
105C22×C4×C149—41no—
106C22×C4×C149—41no—
107C22×C4×C149—41no—
108C22×C4×C149—41no—
109C22×C4×C149—41no—
110C22×C4×C149—41no—
111C22×C4×C149—41no—
112C22×C4×C149—41no—
113C22×C4×C149—41no—
114C22×C4×C149—41no—
115C22×C4×C149—41no—
116C22×C4×C149—41no—
117C22×C4×C149—41no—
118C22×C4×C149—81no—
119C22×C4×C149—81no—
120C22×C4×C149D812yes—
121C22×C4×C149C22×C411yescharacteristic
122C22×C4×C149C2×D411yescharacteristic
123C22×C4×C149C2×D411yescharacteristic
124C22×C4×C149C2×D411yescharacteristic
125C22×C4×C149#4111yescharacteristic
126C22×C4×C149#4111yescharacteristic
127C2×C8×C149—22no—
128C2×C8×C149—41no—
129C2×C8×C149—41no—
130C2×C8×C149—41no—
131C2×C8×C149—41no—
132C2×C8×C149—41no—
133C4⋊C4×C149—21no—
134C4⋊C4×C149—22no—
135C4⋊C4×C149—22no—
136C4⋊C4×C149—42no—
137C4⋊C4×C149—41no—
138C4⋊C4×C149—41no—
139C4⋊C4×C149—41no—
140C4⋊C4×C149—41no—
141C4⋊C4×C149C22⋊C412yes—
142C22⋊C4×C149—22no—
143C22⋊C4×C149—22no—
144C22⋊C4×C149—42no—
145C22⋊C4×C149—41no—
146C22⋊C4×C149—41no—
147C22⋊C4×C149—81no—
148C22⋊C4×C149—81no—
149C42×C149—42no—
150C23×C149—21no—
151C23×C149—21no—
152C23×C149—21no—
153C23×C149—21no—
154C23×C149—22no—
155C23×C149—41no—
156C23×C149—41no—
157C23×C149—41no—
158C23×C149—41no—
159C23×C149—41no—
160C23×C149—41no—
161C23×C149C4×D411yescharacteristic
162C23×C149#12011yescharacteristic
163C23×C149#12111yescharacteristic
164C23×C149C2×D811yescharacteristic
165C23×C149#13511yescharacteristic
166C23×C149AGL(1,ℤ/8)11yescharacteristic
167C23×C149AGL(1,ℤ/8)11yescharacteristic
168D4×C149—42no—
169D4×C149—42no—
170D4×C149—42no—
171D4×C149—42no—
172D4×C149—42no—
173D4×C149—81no—
174C2×C4×C149—21no—
175C2×C4×C149—21no—
176C2×C4×C149—21no—
177C2×C4×C149—21no—
178C2×C4×C149—22no—
179C2×C4×C149—22no—
180C2×C4×C149—41no—
181C2×C4×C149—41no—
182C2×C4×C149—41no—
183C2×C4×C149—41no—
184C2×C4×C149—41no—
185C2×C4×C149—41no—
186C2×C4×C149—41no—
187C2×C4×C149—41no—
188C2×C4×C149—42no—
189C2×C4×C149—42no—
190C2×C4×C149—42no—
191C2×C4×C149—42no—
192C2×C4×C149—42no—
193C2×C4×C149—42no—
194C2×C4×C149—42no—
195C2×C4×C149—42no—
196C2×C4×C149—41no—
197C2×C4×C149—41no—
198C2×C4×C149—41no—
199C2×C4×C149—41no—
200C2×C4×C149—41no—
201C2×C4×C149—41no—
202C2×C4×C149—41no—
203C2×C4×C149—41no—
204C2×C4×C149—41no—
205C2×C4×C149—81no—
206C2×C4×C149—84no—
207C2×C4×C149—81no—
208C2×C4×C149—81no—
209C2×C4×C149—81no—
210C2×C4×C149—81no—
211C2×C4×C149—81no—
212C2×C4×C149—81no—
213C2×C4×C149—81no—
214C2×C4×C149—81no—
215C2×C4×C149—81no—
216C2×C4×C149C2×C22⋊C411yescharacteristic
217C2×C4×C149C4×D411yescharacteristic
218C2×C4×C149#12111yescharacteristic
219C2×C4×C149#12311yescharacteristic
220C8×C149—42no—
221C8×C149—81no—
222C22×C149—21no—
223C22×C149—21no—
224C22×C149—21no—
225C22×C149—21no—
226C22×C149—21no—
227C22×C149—21no—
228C22×C149—21no—
229C22×C149—21no—
230C22×C149—21no—
231C22×C149—21no—
232C22×C149—21no—
233C22×C149—21no—
234C22×C149—42no—
235C22×C149—42no—
236C22×C149—42no—
237C22×C149—81no—
238C22×C149—81no—
239C22×C149—81no—
240C22×C149—81no—
241C22×C149#38611yescharacteristic
242C22×C149C4×D811yescharacteristic
243C22×C149#44211yescharacteristic
244C22×C149#44711yescharacteristic
245C22×C149#44911yescharacteristic
246C22×C149#45511yescharacteristic
247C22×C149#45611yescharacteristic
248C22×C149#45811yescharacteristic
249C22×C149#45811yescharacteristic
250C22×C149#45911yescharacteristic
251C22×C149#46311yescharacteristic
252C4×C149—21no—
253C4×C149—21no—
254C4×C149—21no—
255C4×C149—21no—
256C4×C149—42no—
257C4×C149—42no—
258C4×C149—82no—
259C4×C149—81no—
260C4×C149—81no—
261C4×C149—81no—
262C4×C149—82no—
263C2×C149—21no—
264C2×C149—21no—
265C2×C149—21no—
266C2×C149—21no—
267C2×C149—82no—
268C2×C149#160711yescharacteristic
269C2×C149#160911yescharacteristic
270C2×C149#161011yescharacteristic
271C2×C149#161211yescharacteristic
272C2×C149#187911yescharacteristic
273C2×C149#188211yescharacteristic
274C2×C149#189011yescharacteristic
275#9043C14911yesmaximal, characteristic, direct product factor, Sylow
276C149#904311yescharacteristic, direct product factor, Sylow
277C2×#480C2×C14911yescharacteristic
278#2325C2×C14911yescharacteristic
279#1823C2×C14911yescharacteristic, complemented
280C2×#327C2×C14911yescharacteristic
281#1445C2×C14911yescharacteristic, complemented
282#1294C2×C14911yescharacteristic, complemented
283#1280C2×C14911yescharacteristic, complemented
284C2×#121C22×C14911yescharacteristic
285C2×C4×D4—21no—
286C22×C4⋊C4C22×C14911yescharacteristic
287#480—22no—
288#480C4×C14914yescomplemented
289C2×#107—21no—
290C2×#102—21no—
291C2×C22⋊C8C22×C14911yescharacteristic
292C2×C22⋊C8C22×C14911yescharacteristic
293#388—21no—
294#387—21no—
295#386—21no—
296#386—21no—
297#385—21no—
298#380C22×C14911yescharacteristic
299C2×#95—21no—
300C2×#95—21no—
301C2×#95C22×C14911yescharacteristic
302C2×#95C22×C14911yescharacteristic
303#340—21no—
304#340—21no—
305#327—22no—
306C22×D4—21no—
307C22×D4D4×C14911yescharacteristic
308C23×C4—21no—
309C23×C4—21no—
310C23×C4—21no—
311C23×C4D4×C14911yescharacteristic
312C23×C4D4×C14911yescharacteristic
313C23×C4C23×C14911yescharacteristic
314C22×C8—21no—
315C22×C8—21no—
316#121—21no—
317#121—21no—
318#121C2×C4×C14912yes—
319#121D4×C14912yes—
320C4×D4—42no—
321C4×D4—42no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4C2×C4×C14912yescomplemented
329C2×C4⋊C4D4×C14911yescharacteristic
330C2×C4⋊C4D4×C14911yescharacteristic
331C2×C4⋊C4D4×C14911yescharacteristic
332C2×C22⋊C4—21no—
333C2×C22⋊C4—21no—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—21no—
336C2×C22⋊C4—21no—
337C2×C42—21no—
338#107—24no—
339#102—24no—
340C22⋊C8—21no—
341C22⋊C8—21no—
342C22⋊C8—21no—
343C22⋊C8C2×C4×C14912yescomplemented
344#95—21no—
345#95—21no—
346#95—21no—
347#95—21no—
348#95—21no—
349#95—21no—
350#95—21no—
351#95—42no—
352#95—42no—
353C24—21no—
354C24C2×D4×C14911yescharacteristic
355C2×D4—22no—
356C2×D4—22no—
357C2×D4—21no—
358C2×D4—41no—
359C2×D4—41no—
360C2×D4—41no—
361C2×D4—41no—
362C2×D4—41no—
363C2×D4—41no—
364C2×D4C22⋊C4×C14912yes—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—41no—
376C22×C4—41no—
377C22×C4—42no—
378C22×C4—41no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—41no—
384C22×C4—41no—
385C22×C4—41no—
386C22×C4—41no—
387C22×C4—41no—
388C22×C4—41no—
389C22×C4—41no—
390C22×C4—41no—
391C22×C4—41no—
392C22×C4—41no—
393C22×C4—41no—
394C22×C4—81no—
395C22×C4—81no—
396C22×C4D8×C14912yes—
397C22×C4C22×C4×C14911yescharacteristic
398C22×C4C2×D4×C14911yescharacteristic
399C22×C4C2×D4×C14911yescharacteristic
400C22×C4C2×D4×C14911yescharacteristic
401C22×C4#41×C14911yescharacteristic
402C22×C4#41×C14911yescharacteristic
403C2×C8—22no—
404C2×C8—41no—
405C2×C8—41no—
406C2×C8—41no—
407C2×C8—41no—
408C2×C8—41no—
409C4⋊C4—21no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—41no—
413C4⋊C4—41no—
414C4⋊C4—42no—
415C4⋊C4—41no—
416C4⋊C4—41no—
417C4⋊C4C22⋊C4×C14912yes—
418C22⋊C4—22no—
419C22⋊C4—22no—
420C22⋊C4—42no—
421C22⋊C4—41no—
422C22⋊C4—41no—
423C22⋊C4—81no—
424C22⋊C4—81no—
425C42—42no—
426C23—21no—
427C23—21no—
428C23—21no—
429C23—21no—
430C23—22no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23—41no—
435C23—41no—
436C23—41no—
437C23C4×D4×C14911yescharacteristic
438C23#120×C14911yescharacteristic
439C23#121×C14911yescharacteristic
440C23C2×D8×C14911yescharacteristic
441C23#135×C14911yescharacteristic
442C23AGL(1,ℤ/8)×C14911yescharacteristic
443C23AGL(1,ℤ/8)×C14911yescharacteristic
444D4—42no—
445D4—42no—
446D4—42no—
447D4—42no—
448D4—42no—
449D4—81no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—81no—
482C2×C4—84no—
483C2×C4—81no—
484C2×C4—81no—
485C2×C4—81no—
486C2×C4—81no—
487C2×C4—81no—
488C2×C4—81no—
489C2×C4—81no—
490C2×C4—81no—
491C2×C4—81no—
492C2×C4C2×C22⋊C4×C14911yescharacteristic
493C2×C4C4×D4×C14911yescharacteristic
494C2×C4#121×C14911yescharacteristic
495C2×C4#123×C14911yescharacteristic
496C8—42no—
497C8—81no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—42no—
511C22—42no—
512C22—42no—
513C22—81no—
514C22—81no—
515C22—81no—
516C22—81no—
517C22#386×C14911yescharacteristic
518C22C4×D8×C14911yescharacteristic
519C22#442×C14911yescharacteristic
520C22#447×C14911yescharacteristic
521C22#449×C14911yescharacteristic
522C22#455×C14911yescharacteristic
523C22#456×C14911yescharacteristic
524C22#458×C14911yescharacteristic
525C22#458×C14911yescharacteristic
526C22#459×C14911yescharacteristic
527C22#463×C14911yescharacteristic
528C4—21no—
529C4—21no—
530C4—21no—
531C4—21no—
532C4—42no—
533C4—42no—
534C4—82no—
535C4—81no—
536C4—81no—
537C4—81no—
538C4—82no—
539C2—21no—
540C2—21no—
541C2—21no—
542C2—21no—
543C2—82no—
544C2#1607×C14911yescharacteristic
545C2#1609×C14911yescharacteristic
546C2#1610×C14911yescharacteristic
547C2#1612×C14911yescharacteristic
548C2#1879×C14911yescharacteristic
549C2#1882×C14911yescharacteristic
550C2#1890×C14911yescharacteristic
subgroupG/H
center, socleC23×C149#120
commutatorC22×C4C22×C4×C149
Frattini, cosocleC23×C4C23×C149
prime radicalC2×#121×C149C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C149 ◁ C23×C4×C149 ◁ G

Complements

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

NH ≅ G/Ntype
3. #1823×C149C2semidirect
5. #1445×C149C2semidirect
6. #1294×C149C2semidirect
7. #1280×C149C2semidirect
12. #480×C149C4semidirect
52. C2×C4⋊C4×C149C2×C4semidirect
67. C22⋊C8×C149C2×C4semidirect
275. #9043C149direct (N × H)
276. C149#9043direct (N × H)
279. #1823C2×C149semidirect
281. #1445C2×C149semidirect
282. #1294C2×C149semidirect
283. #1280C2×C149semidirect
288. #480C4×C149semidirect
328. C2×C4⋊C4C2×C4×C149semidirect
343. C22⋊C8C2×C4×C149semidirect

Maximal subgroups

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

subgroupindex
C2×#480×C1492
#2325×C1492
#1823×C1492
C2×#327×C1492
#1445×C1492
#1294×C1492
#1280×C1492
#9043149