Finite Group Databasebeta

← C149×#18641 #49197590

Subgroups — C149×#18641 #49197590

Order 38144.

1114 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3499×C149C211yesmaximal, characteristic
2#3227×C149C211yesmaximal, characteristic, complemented
3C2×#487×C149C211yesmaximal, characteristic, complemented
4#3079×C149C211yesmaximal, characteristic, complemented
5#1637×C149C214yesmaximal, complemented
6#1635×C149C214yesmaximal, complemented
7#1546×C149C211yesmaximal, characteristic, complemented
8#1492×C149C211yesmaximal, characteristic, complemented
9#1476×C149C211yesmaximal, characteristic, complemented
10C2×2−1+4×C149—21no—
11D4×Q8×C149—21no—
12D4×Q8×C149C2212yes—
13#547×C149—22no—
14#547×C149—21no—
15#547×C149—22no—
16#547×C149C2212yes—
17#536×C149—22no—
18#536×C149—21no—
19#532×C149—21no—
20#532×C149C2211yescharacteristic
21C2×C4⋊Q8×C149—21no—
22C2×C4⋊Q8×C149C2211yescharacteristic
23C2×C4⋊Q8×C149C2211yescharacteristic
24C4×#41×C149C2211yescharacteristic
25#498×C149—21no—
26#487×C149—22no—
27#487×C149C2214yes—
28#486×C149—21no—
29#481×C149—22no—
30#477×C149C2212yes—
31#476×C149C2214yes—
32#476×C149C2212yes—
33#475×C149—21no—
34#474×C149—21no—
35#431×C149C2211yescharacteristic
36#428×C149—21no—
37#423×C149C2211yescharacteristic
38#417×C149—21no—
39C2×#103×C149—22no—
40C2×C4×C8×C149C2211yescharacteristic
41#332×C149C2214yes—
42Q8⋊C8×C149C2212yes—
43D4⋊C8×C149C2212yes—
44D4⋊C8×C149C2214yes—
452−1+4×C149—44no—
462−1+4×C149—44no—
47C2×#41×C149—22no—
48C2×#41×C149—24no—
49C2×#41×C149—22no—
50C2×#41×C149—21no—
51C2×#41×C149D411yescharacteristic
52C22×Q8×C149—22no—
53C22×Q8×C149—22no—
54C22×Q8×C149—21no—
55C22×Q8×C149—21no—
56C2×M16×C149—21no—
57C22×C8×C149—21no—
58C4⋊Q8×C149—22no—
59C4⋊Q8×C149—22no—
60C4⋊Q8×C149—22no—
61C4⋊Q8×C149—21no—
62C4⋊Q8×C149—21no—
63C4⋊Q8×C149—21no—
64C4⋊Q8×C149—21no—
65C4⋊Q8×C149—21no—
66C4⋊Q8×C149D412yes—
67C4⋊Q8×C149D411yescharacteristic
68C4⋊Q8×C149C2312yes—
69C4⋊Q8×C149C2312yes—
70#127×C149D411yescharacteristic
71#124×C149—22no—
72#124×C149—21no—
73#123×C149—24no—
74#123×C149—24no—
75#123×C149—24no—
76C22⋊Q8×C149—24no—
77C22⋊Q8×C149—22no—
78C22⋊Q8×C149—24no—
79C22⋊Q8×C149—22no—
80#121×C149—22no—
81#121×C149—22no—
82#121×C149—21no—
83#121×C149D412yes—
84C4×Q8×C149D411yescharacteristic
85C4×Q8×C149C2311yescharacteristic
86C4×D4×C149—22no—
87C4×D4×C149—22no—
88C4×D4×C149—21no—
89C4×D4×C149—21no—
90C4×D4×C149—21no—
91C4×D4×C149D411yescharacteristic
92C4×D4×C149C2311yescharacteristic
93C4×D4×C149C2312yes—
94#117×C149—21no—
95#117×C149D411yescharacteristic
96C2×C4⋊C4×C149—22no—
97C2×C4⋊C4×C149—21no—
98C2×C4⋊C4×C149—22no—
99C2×C4⋊C4×C149—21no—
100C2×C4⋊C4×C149—21no—
101C2×C4⋊C4×C149D412yes—
102C2×C42×C149—21no—
103C2×C42×C149C2311yescharacteristic
104#107×C149—22no—
105#106×C149—22no—
106#106×C149—24no—
107C4⋊C8×C149—21no—
108C4⋊C8×C149C2312yes—
109C4⋊C8×C149C2312yes—
110#103×C149—22no—
111#103×C149—28no—
112#102×C149—22no—
113#102×C149—24no—
114C22⋊C8×C149—21no—
115C4×C8×C149—21no—
116C4×C8×C149—21no—
117C4×C8×C149C2312yes—
118#41×C149—22no—
119#41×C149—48no—
120#41×C149—416no—
121#41×C149—44no—
122#41×C149—44no—
123#41×C149—42no—
124#41×C149—42no—
125#41×C149SD1614yes—
126C2×Q8×C149—24no—
127C2×Q8×C149—22no—
128C2×Q8×C149—21no—
129C2×Q8×C149—22no—
130C2×Q8×C149—22no—
131C2×Q8×C149—48no—
132C2×Q8×C149—44no—
133C2×Q8×C149—44no—
134C2×Q8×C149—44no—
135C2×Q8×C149—41no—
136C2×Q8×C149—42no—
137C2×Q8×C149—42no—
138C2×Q8×C149C2×D411yescharacteristic
139C2×D4×C149—21no—
140C2×D4×C149—24no—
141C2×D4×C149—22no—
142C2×D4×C149—21no—
143C2×D4×C149—21no—
144C2×D4×C149C2×D412yes—
145C2×D4×C149C2×D411yescharacteristic
146C22×C4×C149—21no—
147C22×C4×C149—24no—
148C22×C4×C149—24no—
149C22×C4×C149—22no—
150C22×C4×C149—21no—
151C22×C4×C149—21no—
152C22×C4×C149—22no—
153C22×C4×C149—41no—
154C22×C4×C149C2×D411yescharacteristic
155C22×C4×C149C2×D411yescharacteristic
156C22×C4×C149C2×D411yescharacteristic
157M16×C149—42no—
158C2×C8×C149—22no—
159C2×C8×C149—22no—
160C2×C8×C149—22no—
161C2×C8×C149—42no—
162C4⋊C4×C149—24no—
163C4⋊C4×C149—24no—
164C4⋊C4×C149—21no—
165C4⋊C4×C149—22no—
166C4⋊C4×C149—22no—
167C4⋊C4×C149—21no—
168C4⋊C4×C149—22no—
169C4⋊C4×C149—21no—
170C4⋊C4×C149—22no—
171C4⋊C4×C149—22no—
172C4⋊C4×C149—41no—
173C4⋊C4×C149—41no—
174C4⋊C4×C149C2×D414yes—
175C4⋊C4×C149C2×D412yes—
176C4⋊C4×C149C2×D411yescharacteristic
177C4⋊C4×C149C2×D411yescharacteristic
178C22⋊C4×C149—24no—
179C22⋊C4×C149—24no—
180C22⋊C4×C149—21no—
181C22⋊C4×C149—21no—
182C22⋊C4×C149—22no—
183C22⋊C4×C149—21no—
184C22⋊C4×C149—22no—
185C42×C149—21no—
186C42×C149—21no—
187C42×C149—21no—
188C42×C149C2×D411yescharacteristic
189C42×C149C2×D411yescharacteristic
190C42×C149C2×D411yescharacteristic
191C42×C149C2411yescharacteristic
192C23×C149—21no—
193C23×C149—22no—
194C23×C149#12011yescharacteristic
195Q8×C149—21no—
196Q8×C149—48no—
197Q8×C149—44no—
198Q8×C149—42no—
199Q8×C149—42no—
200Q8×C149—42no—
201Q8×C149—44no—
202Q8×C149—82no—
203Q8×C149C2×SD1612yes—
204D4×C149—24no—
205D4×C149—21no—
206D4×C149—24no—
207D4×C149—48no—
208D4×C149—44no—
209D4×C149—42no—
210D4×C149—42no—
211D4×C149C2×SD1612yes—
212C2×C4×C149—21no—
213C2×C4×C149—22no—
214C2×C4×C149—24no—
215C2×C4×C149—22no—
216C2×C4×C149—21no—
217C2×C4×C149—21no—
218C2×C4×C149—24no—
219C2×C4×C149—22no—
220C2×C4×C149—48no—
221C2×C4×C149—48no—
222C2×C4×C149—44no—
223C2×C4×C149—42no—
224C2×C4×C149—42no—
225C2×C4×C149—42no—
226C2×C4×C149—42no—
227C2×C4×C149—42no—
228C2×C4×C149—82no—
229C2×C4×C149#12011yescharacteristic
230C2×C4×C149#12011yescharacteristic
231C2×C4×C149#12011yescharacteristic
232C2×C4×C149C2×SD1612yes—
233C2×C4×C149AGL(1,ℤ/8)12yes—
234C2×C4×C149C22×D411yescharacteristic
235C2×C4×C149C22×D411yescharacteristic
236C2×C4×C149C22×D411yescharacteristic
237C8×C149—42no—
238C8×C149—42no—
239C8×C149—42no—
240C22×C149—21no—
241C22×C149—21no—
242C22×C149—22no—
243C22×C149—41no—
244C22×C149—41no—
245C22×C149—42no—
246C22×C149—42no—
247C22×C149—42no—
248C22×C149#45012yes—
249C22×C149C2×#12011yescharacteristic
250C4×C149—22no—
251C4×C149—21no—
252C4×C149—21no—
253C4×C149—44no—
254C4×C149—42no—
255C4×C149—41no—
256C4×C149—41no—
257C4×C149—82no—
258C4×C149#45012yes—
259C4×C149#45412yes—
260C4×C149C22×SD1611yescharacteristic
261C4×C149C2×AGL(1,ℤ/8)11yescharacteristic
262C4×C149#57812yes—
263C2×C149—22no—
264C2×C149—42no—
265C2×C149—82no—
266C2×C149C2×#45011yescharacteristic
267C2×C149#301111yescharacteristic
268C2×C149C2×#45411yescharacteristic
269#18641C14911yesmaximal, characteristic, direct product factor, Sylow
270C149#1864111yescharacteristic, direct product factor, Sylow
271#3499C2×C14911yescharacteristic
272#3227C2×C14911yescharacteristic, complemented
273C2×#487C2×C14911yescharacteristic, complemented
274#3079C2×C14911yescharacteristic, complemented
275#1637C2×C14914yescomplemented
276#1635C2×C14914yescomplemented
277#1546C2×C14911yescharacteristic, complemented
278#1492C2×C14911yescharacteristic, complemented
279#1476C2×C14911yescharacteristic, complemented
280C2×2−1+4—21no—
281D4×Q8—21no—
282D4×Q8C22×C14912yes—
283#547—22no—
284#547—21no—
285#547—22no—
286#547C22×C14912yes—
287#536—22no—
288#536—21no—
289#532—21no—
290#532C22×C14911yescharacteristic
291C2×C4⋊Q8—21no—
292C2×C4⋊Q8C22×C14911yescharacteristic
293C2×C4⋊Q8C22×C14911yescharacteristic
294C4×#41C22×C14911yescharacteristic
295#498—21no—
296#487—22no—
297#487C22×C14914yes—
298#486—21no—
299#481—22no—
300#477C22×C14912yes—
301#476C22×C14912yes—
302#476C22×C14914yes—
303#475—21no—
304#474—21no—
305#431C22×C14911yescharacteristic
306#428—21no—
307#423C22×C14911yescharacteristic
308#417—21no—
309C2×#103—22no—
310C2×C4×C8C22×C14911yescharacteristic
311#332C22×C14914yes—
312Q8⋊C8C22×C14912yes—
313D4⋊C8C22×C14912yes—
314D4⋊C8C22×C14914yes—
3152−1+4—44no—
3162−1+4—44no—
317C2×#41—22no—
318C2×#41—24no—
319C2×#41—22no—
320C2×#41—21no—
321C2×#41D4×C14911yescharacteristic
322C22×Q8—22no—
323C22×Q8—22no—
324C22×Q8—21no—
325C22×Q8—21no—
326C2×M16—21no—
327C22×C8—21no—
328C4⋊Q8—22no—
329C4⋊Q8—22no—
330C4⋊Q8—22no—
331C4⋊Q8—21no—
332C4⋊Q8—21no—
333C4⋊Q8—21no—
334C4⋊Q8—21no—
335C4⋊Q8—21no—
336C4⋊Q8D4×C14911yescharacteristic
337C4⋊Q8D4×C14912yes—
338C4⋊Q8C23×C14912yes—
339C4⋊Q8C23×C14912yes—
340#127D4×C14911yescharacteristic
341#124—22no—
342#124—21no—
343#123—24no—
344#123—24no—
345#123—24no—
346C22⋊Q8—24no—
347C22⋊Q8—22no—
348C22⋊Q8—24no—
349C22⋊Q8—22no—
350#121—22no—
351#121—22no—
352#121—21no—
353#121D4×C14912yes—
354C4×Q8D4×C14911yescharacteristic
355C4×Q8C23×C14911yescharacteristic
356C4×D4—22no—
357C4×D4—22no—
358C4×D4—21no—
359C4×D4—21no—
360C4×D4—21no—
361C4×D4D4×C14911yescharacteristic
362C4×D4C23×C14911yescharacteristic
363C4×D4C23×C14912yes—
364#117—21no—
365#117D4×C14911yescharacteristic
366C2×C4⋊C4—22no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4D4×C14912yes—
372C2×C42—21no—
373C2×C42C23×C14911yescharacteristic
374#107—22no—
375#106—22no—
376#106—24no—
377C4⋊C8—21no—
378C4⋊C8C23×C14912yes—
379C4⋊C8C23×C14912yes—
380#103—22no—
381#103—28no—
382#102—22no—
383#102—24no—
384C22⋊C8—21no—
385C4×C8—21no—
386C4×C8—21no—
387C4×C8C23×C14912yes—
388#41—22no—
389#41—48no—
390#41—416no—
391#41—44no—
392#41—44no—
393#41—42no—
394#41—42no—
395#41SD16×C14914yes—
396C2×Q8—24no—
397C2×Q8—22no—
398C2×Q8—21no—
399C2×Q8—22no—
400C2×Q8—22no—
401C2×Q8—48no—
402C2×Q8—44no—
403C2×Q8—44no—
404C2×Q8—44no—
405C2×Q8—41no—
406C2×Q8—42no—
407C2×Q8—42no—
408C2×Q8C2×D4×C14911yescharacteristic
409C2×D4—21no—
410C2×D4—24no—
411C2×D4—22no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4C2×D4×C14912yes—
415C2×D4C2×D4×C14911yescharacteristic
416C22×C4—21no—
417C22×C4—24no—
418C22×C4—24no—
419C22×C4—22no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—41no—
424C22×C4C2×D4×C14911yescharacteristic
425C22×C4C2×D4×C14911yescharacteristic
426C22×C4C2×D4×C14911yescharacteristic
427M16—42no—
428C2×C8—22no—
429C2×C8—22no—
430C2×C8—22no—
431C2×C8—42no—
432C4⋊C4—24no—
433C4⋊C4—24no—
434C4⋊C4—21no—
435C4⋊C4—22no—
436C4⋊C4—22no—
437C4⋊C4—21no—
438C4⋊C4—22no—
439C4⋊C4—21no—
440C4⋊C4—22no—
441C4⋊C4—22no—
442C4⋊C4—41no—
443C4⋊C4—41no—
444C4⋊C4C2×D4×C14914yes—
445C4⋊C4C2×D4×C14912yes—
446C4⋊C4C2×D4×C14911yescharacteristic
447C4⋊C4C2×D4×C14911yescharacteristic
448C22⋊C4—24no—
449C22⋊C4—24no—
450C22⋊C4—21no—
451C22⋊C4—21no—
452C22⋊C4—22no—
453C22⋊C4—21no—
454C22⋊C4—22no—
455C42—21no—
456C42—21no—
457C42—21no—
458C42C2×D4×C14911yescharacteristic
459C42C2×D4×C14911yescharacteristic
460C42C2×D4×C14911yescharacteristic
461C42C24×C14911yescharacteristic
462C23—21no—
463C23—22no—
464C23#120×C14911yescharacteristic
465Q8—21no—
466Q8—48no—
467Q8—44no—
468Q8—42no—
469Q8—44no—
470Q8—42no—
471Q8—42no—
472Q8—82no—
473Q8C2×SD16×C14912yes—
474D4—24no—
475D4—21no—
476D4—24no—
477D4—48no—
478D4—44no—
479D4—42no—
480D4—42no—
481D4C2×SD16×C14912yes—
482C2×C4—21no—
483C2×C4—24no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—24no—
489C2×C4—22no—
490C2×C4—48no—
491C2×C4—48no—
492C2×C4—44no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—82no—
499C2×C4#120×C14911yescharacteristic
500C2×C4#120×C14911yescharacteristic
501C2×C4#120×C14911yescharacteristic
502C2×C4C2×SD16×C14912yes—
503C2×C4AGL(1,ℤ/8)×C14912yes—
504C2×C4C22×D4×C14911yescharacteristic
505C2×C4C22×D4×C14911yescharacteristic
506C2×C4C22×D4×C14911yescharacteristic
507C8—42no—
508C8—42no—
509C8—42no—
510C22—21no—
511C22—21no—
512C22—22no—
513C22—41no—
514C22—41no—
515C22—42no—
516C22—42no—
517C22—42no—
518C22#450×C14912yes—
519C22C2×#120×C14911yescharacteristic
520C4—22no—
521C4—21no—
522C4—21no—
523C4—44no—
524C4—42no—
525C4—41no—
526C4—41no—
527C4—82no—
528C4#450×C14912yes—
529C4#454×C14912yes—
530C4C22×SD16×C14911yescharacteristic
531C4C2×AGL(1,ℤ/8)×C14911yescharacteristic
532C4#578×C14912yes—
533C2—22no—
534C2—42no—
535C2—82no—
536C2C2×#450×C14911yescharacteristic
537C2#3011×C14911yescharacteristic
538C2C2×#454×C14911yescharacteristic
subgroupG/H
center, socleC22×C149C2×#120
commutator, Frattini, cosocleC42C24×C149
prime radical#3499×C149C2
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. #3227×C149C2semidirect
3. C2×#487×C149C2semidirect
4. #3079×C149C2semidirect
5. #1637×C149C2semidirect
6. #1635×C149C2semidirect
7. #1546×C149C2semidirect
8. #1492×C149C2semidirect
9. #1476×C149C2semidirect
269. #18641C149direct (N × H)
270. C149#18641direct (N × H)
272. #3227C2×C149semidirect
273. C2×#487C2×C149semidirect
274. #3079C2×C149semidirect
275. #1637C2×C149semidirect
276. #1635C2×C149semidirect
277. #1546C2×C149semidirect
278. #1492C2×C149semidirect
279. #1476C2×C149semidirect

Maximal subgroups

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

subgroupindex
#3499×C1492
#3227×C1492
C2×#487×C1492
#3079×C1492
#1637×C1492
#1635×C1492
#1546×C1492
#1492×C1492
#1476×C1492
#18641149