Finite Group Databasebeta

← C149×#13080 #49192029

Subgroups — C149×#13080 #49192029

Order 38144.

864 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#100×C149C211yesmaximal, characteristic
2#2405×C149C211yesmaximal, characteristic
3C2×#352×C149C212yesmaximal, complemented
4#1781×C149C211yesmaximal, characteristic
5#1390×C149C212yesmaximal, complemented
6C23×D4×C149C2211yescharacteristic
7C22×M16×C149—21no—
8C2×#123×C149C411yescharacteristic, complemented
9C2×#123×C149C2211yescharacteristic
10C22×C22⋊C4×C149C411yescharacteristic, complemented
11C2×#100×C149—21no—
12C2×#100×C149—24no—
13C2×#100×C149C2212yes—
14C2×#99×C149—21no—
15C2×#99×C149C2212yes—
16#394×C149—21no—
17#394×C149—21no—
18#386×C149C411yescharacteristic, complemented
19#386×C149C2211yescharacteristic
20#385×C149—21no—
21#379×C149—21no—
22#379×C149—21no—
23#379×C149C411yescharacteristic, complemented
24#352×C149—24no—
25C25×C149C2×C411yescharacteristic
26C25×C149D411yescharacteristic
27C22×D4×C149—22no—
28C22×D4×C149—22no—
29C22×D4×C149—42no—
30C22×D4×C149—41no—
31C22×D4×C149—41no—
32C22×D4×C149C2×C411yescharacteristic
33C22×D4×C149D411yescharacteristic
34C22×D4×C149D411yescharacteristic
35C22×D4×C149C2311yescharacteristic
36C23×C4×C149C2×C411yescharacteristic
37C23×C4×C149C2×C411yescharacteristic
38C23×C4×C149D411yescharacteristic
39C2×M16×C149—24no—
40C2×M16×C149—22no—
41C2×M16×C149—41no—
42C2×M16×C149—42no—
43C22×C8×C149—41no—
44#123×C149—22no—
45#123×C149—22no—
46#123×C149—42no—
47C2×C4⋊C4×C149—21no—
48C2×C4⋊C4×C149—21no—
49C2×C22⋊C4×C149—21no—
50C2×C22⋊C4×C149—21no—
51C2×C22⋊C4×C149—21no—
52C2×C22⋊C4×C149—21no—
53C2×C22⋊C4×C149—21no—
54C2×C22⋊C4×C149—22no—
55C2×C22⋊C4×C149—21no—
56C2×C22⋊C4×C149—21no—
57C2×C22⋊C4×C149—21no—
58C2×C22⋊C4×C149—41no—
59C2×C22⋊C4×C149—41no—
60C2×C22⋊C4×C149—41no—
61C2×C22⋊C4×C149—41no—
62C2×C22⋊C4×C149C2×C411yescharacteristic
63C2×C22⋊C4×C149C2×C411yescharacteristic
64#100×C149—24no—
65#100×C149—22no—
66#100×C149D414yes—
67#99×C149—22no—
68#99×C149—22no—
69#99×C149—42no—
70#95×C149—21no—
71#95×C149—21no—
72C24×C149—21no—
73C24×C149—21no—
74C24×C149—21no—
75C24×C149—21no—
76C24×C149—22no—
77C24×C149—22no—
78C24×C149—41no—
79C24×C149—41no—
80C24×C149—42no—
81C24×C149—42no—
82C24×C149—81no—
83C24×C149—81no—
84C24×C149C22⋊C411yescharacteristic
85C24×C149C22⋊C411yescharacteristic
86C24×C149C22⋊C411yescharacteristic
87C24×C149C22×C411yescharacteristic
88C24×C149C2×D411yescharacteristic
89C2×D4×C149—22no—
90C2×D4×C149—22no—
91C2×D4×C149—22no—
92C2×D4×C149—22no—
93C2×D4×C149—21no—
94C2×D4×C149—21no—
95C2×D4×C149—41no—
96C2×D4×C149—41no—
97C2×D4×C149—41no—
98C2×D4×C149—41no—
99C2×D4×C149—41no—
100C2×D4×C149—41no—
101C2×D4×C149—44no—
102C2×D4×C149—44no—
103C2×D4×C149—44no—
104C2×D4×C149—44no—
105C2×D4×C149C2×D412yes—
106C2×D4×C149#4112yes—
107C22×C4×C149—21no—
108C22×C4×C149—21no—
109C22×C4×C149—22no—
110C22×C4×C149—21no—
111C22×C4×C149—21no—
112C22×C4×C149—21no—
113C22×C4×C149—21no—
114C22×C4×C149—21no—
115C22×C4×C149—21no—
116C22×C4×C149—22no—
117C22×C4×C149—41no—
118C22×C4×C149—41no—
119C22×C4×C149—41no—
120C22×C4×C149—42no—
121C22×C4×C149—81no—
122C22×C4×C149C22⋊C411yescharacteristic
123C22×C4×C149C2×D411yescharacteristic
124M16×C149—24no—
125M16×C149—44no—
126M16×C149—42no—
127C2×C8×C149—44no—
128C2×C8×C149—42no—
129C4⋊C4×C149—42no—
130C4⋊C4×C149—41no—
131C4⋊C4×C149—41no—
132C22⋊C4×C149—22no—
133C22⋊C4×C149—42no—
134C22⋊C4×C149—42no—
135C22⋊C4×C149—42no—
136C22⋊C4×C149—41no—
137C22⋊C4×C149—41no—
138C22⋊C4×C149—42no—
139C22⋊C4×C149—41no—
140C22⋊C4×C149—42no—
141C22⋊C4×C149—42no—
142C22⋊C4×C149—81no—
143C22⋊C4×C149—81no—
144C22⋊C4×C149—81no—
145C22⋊C4×C149—82no—
146C22⋊C4×C149—82no—
147C23×C149—22no—
148C23×C149—21no—
149C23×C149—21no—
150C23×C149—21no—
151C23×C149—21no—
152C23×C149—21no—
153C23×C149—21no—
154C23×C149—21no—
155C23×C149—21no—
156C23×C149—21no—
157C23×C149—21no—
158C23×C149—21no—
159C23×C149—21no—
160C23×C149—41no—
161C23×C149—42no—
162C23×C149—42no—
163C23×C149—42no—
164C23×C149—42no—
165C23×C149—41no—
166C23×C149—41no—
167C23×C149—41no—
168C23×C149—41no—
169C23×C149—41no—
170C23×C149—41no—
171C23×C149—42no—
172C23×C149—42no—
173C23×C149—41no—
174C23×C149—41no—
175C23×C149—42no—
176C23×C149—42no—
177C23×C149—81no—
178C23×C149—81no—
179C23×C149—81no—
180C23×C149—81no—
181C23×C149—84no—
182C23×C149—84no—
183C23×C149—84no—
184C23×C149—84no—
185C23×C149#9911yescharacteristic
186C23×C149#9911yescharacteristic
187C23×C149C2×C22⋊C411yescharacteristic
188C23×C149C4×D412yes—
189C23×C149#12112yes—
190D4×C149—42no—
191D4×C149—42no—
192D4×C149—44no—
193D4×C149—44no—
194D4×C149—42no—
195D4×C149—42no—
196C2×C4×C149—22no—
197C2×C4×C149—22no—
198C2×C4×C149—22no—
199C2×C4×C149—22no—
200C2×C4×C149—21no—
201C2×C4×C149—21no—
202C2×C4×C149—21no—
203C2×C4×C149—21no—
204C2×C4×C149—41no—
205C2×C4×C149—41no—
206C2×C4×C149—41no—
207C2×C4×C149—41no—
208C2×C4×C149—41no—
209C2×C4×C149—41no—
210C2×C4×C149—41no—
211C2×C4×C149—41no—
212C2×C4×C149—41no—
213C2×C4×C149—41no—
214C2×C4×C149—41no—
215C2×C4×C149—41no—
216C2×C4×C149—82no—
217C2×C4×C149—82no—
218C2×C4×C149—82no—
219C2×C4×C149—82no—
220C2×C4×C149—82no—
221C2×C4×C149#9912yes—
222C2×C4×C149#12011yescharacteristic
223C2×C4×C149#12311yescharacteristic
224C8×C149—44no—
225C22×C149—21no—
226C22×C149—21no—
227C22×C149—21no—
228C22×C149—21no—
229C22×C149—21no—
230C22×C149—21no—
231C22×C149—21no—
232C22×C149—22no—
233C22×C149—22no—
234C22×C149—42no—
235C22×C149—42no—
236C22×C149—42no—
237C22×C149—42no—
238C22×C149—42no—
239C22×C149—42no—
240C22×C149—41no—
241C22×C149—41no—
242C22×C149—41no—
243C22×C149—41no—
244C22×C149—41no—
245C22×C149—41no—
246C22×C149—41no—
247C22×C149—41no—
248C22×C149—41no—
249C22×C149—41no—
250C22×C149—81no—
251C22×C149—84no—
252C22×C149—84no—
253C22×C149—81no—
254C22×C149—81no—
255C22×C149—81no—
256C22×C149—84no—
257C22×C149—84no—
258C22×C149#35212yescomplemented
259C22×C149#38611yescharacteristic
260C22×C149C2×#9911yescharacteristic
261C22×C149C2×#9911yescharacteristic
262C4×C149—21no—
263C4×C149—22no—
264C4×C149—21no—
265C4×C149—81no—
266C4×C149—81no—
267C4×C149—81no—
268C4×C149—81no—
269C4×C149—162no—
270C2×C149—21no—
271C2×C149—21no—
272C2×C149—22no—
273C2×C149—42no—
274C2×C149—41no—
275C2×C149—42no—
276C2×C149—81no—
277C2×C149—81no—
278C2×C149#189811yescharacteristic
279C2×C149C2×#35211yescharacteristic
280C2×C149#212111yescharacteristic
281#13080C14911yesmaximal, characteristic, direct product factor, Sylow
282C149#1308011yescharacteristic, direct product factor, Sylow
283C22×#100C2×C14911yescharacteristic
284#2405C2×C14911yescharacteristic
285C2×#352C2×C14912yescomplemented
286#1781C2×C14911yescharacteristic
287#1390C2×C14912yescomplemented
288C23×D4C22×C14911yescharacteristic
289C22×M16—21no—
290C2×#123C4×C14911yescharacteristic, complemented
291C2×#123C22×C14911yescharacteristic
292C22×C22⋊C4C4×C14911yescharacteristic, complemented
293C2×#100—21no—
294C2×#100—24no—
295C2×#100C22×C14912yes—
296C2×#99—21no—
297C2×#99C22×C14912yes—
298#394—21no—
299#394—21no—
300#386C4×C14911yescharacteristic, complemented
301#386C22×C14911yescharacteristic
302#385—21no—
303#379—21no—
304#379—21no—
305#379C4×C14911yescharacteristic, complemented
306#352—24no—
307C25C2×C4×C14911yescharacteristic
308C25D4×C14911yescharacteristic
309C22×D4—22no—
310C22×D4—22no—
311C22×D4—42no—
312C22×D4—41no—
313C22×D4—41no—
314C22×D4C2×C4×C14911yescharacteristic
315C22×D4D4×C14911yescharacteristic
316C22×D4D4×C14911yescharacteristic
317C22×D4C23×C14911yescharacteristic
318C23×C4C2×C4×C14911yescharacteristic
319C23×C4C2×C4×C14911yescharacteristic
320C23×C4D4×C14911yescharacteristic
321C2×M16—24no—
322C2×M16—22no—
323C2×M16—41no—
324C2×M16—42no—
325C22×C8—41no—
326#123—22no—
327#123—22no—
328#123—42no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—21no—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—21no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—21no—
340C2×C22⋊C4—41no—
341C2×C22⋊C4—41no—
342C2×C22⋊C4—41no—
343C2×C22⋊C4—41no—
344C2×C22⋊C4C2×C4×C14911yescharacteristic
345C2×C22⋊C4C2×C4×C14911yescharacteristic
346#100—24no—
347#100—22no—
348#100D4×C14914yes—
349#99—22no—
350#99—22no—
351#99—42no—
352#95—21no—
353#95—21no—
354C24—21no—
355C24—21no—
356C24—21no—
357C24—21no—
358C24—22no—
359C24—22no—
360C24—41no—
361C24—41no—
362C24—42no—
363C24—42no—
364C24—81no—
365C24—81no—
366C24C22⋊C4×C14911yescharacteristic
367C24C22⋊C4×C14911yescharacteristic
368C24C22⋊C4×C14911yescharacteristic
369C24C22×C4×C14911yescharacteristic
370C24C2×D4×C14911yescharacteristic
371C2×D4—22no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—21no—
376C2×D4—21no—
377C2×D4—41no—
378C2×D4—41no—
379C2×D4—41no—
380C2×D4—41no—
381C2×D4—41no—
382C2×D4—41no—
383C2×D4—44no—
384C2×D4—44no—
385C2×D4—44no—
386C2×D4—44no—
387C2×D4C2×D4×C14912yes—
388C2×D4#41×C14912yes—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4—41no—
402C22×C4—42no—
403C22×C4—81no—
404C22×C4C22⋊C4×C14911yescharacteristic
405C22×C4C2×D4×C14911yescharacteristic
406M16—24no—
407M16—44no—
408M16—42no—
409C2×C8—44no—
410C2×C8—42no—
411C4⋊C4—42no—
412C4⋊C4—41no—
413C4⋊C4—41no—
414C22⋊C4—22no—
415C22⋊C4—42no—
416C22⋊C4—42no—
417C22⋊C4—42no—
418C22⋊C4—41no—
419C22⋊C4—41no—
420C22⋊C4—42no—
421C22⋊C4—41no—
422C22⋊C4—42no—
423C22⋊C4—42no—
424C22⋊C4—81no—
425C22⋊C4—81no—
426C22⋊C4—81no—
427C22⋊C4—82no—
428C22⋊C4—82no—
429C23—21no—
430C23—21no—
431C23—21no—
432C23—21no—
433C23—21no—
434C23—22no—
435C23—21no—
436C23—21no—
437C23—21no—
438C23—21no—
439C23—21no—
440C23—21no—
441C23—21no—
442C23—41no—
443C23—42no—
444C23—42no—
445C23—42no—
446C23—42no—
447C23—41no—
448C23—41no—
449C23—41no—
450C23—41no—
451C23—41no—
452C23—41no—
453C23—42no—
454C23—42no—
455C23—41no—
456C23—41no—
457C23—42no—
458C23—42no—
459C23—81no—
460C23—81no—
461C23—81no—
462C23—81no—
463C23—84no—
464C23—84no—
465C23—84no—
466C23—84no—
467C23#99×C14911yescharacteristic
468C23#99×C14911yescharacteristic
469C23C2×C22⋊C4×C14911yescharacteristic
470C23C4×D4×C14912yes—
471C23#121×C14912yes—
472D4—42no—
473D4—42no—
474D4—44no—
475D4—44no—
476D4—42no—
477D4—42no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—82no—
499C2×C4—82no—
500C2×C4—82no—
501C2×C4—82no—
502C2×C4—82no—
503C2×C4#99×C14912yes—
504C2×C4#120×C14911yescharacteristic
505C2×C4#123×C14911yescharacteristic
506C8—44no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—21no—
514C22—22no—
515C22—22no—
516C22—42no—
517C22—42no—
518C22—42no—
519C22—42no—
520C22—42no—
521C22—42no—
522C22—41no—
523C22—41no—
524C22—41no—
525C22—41no—
526C22—41no—
527C22—41no—
528C22—41no—
529C22—41no—
530C22—41no—
531C22—41no—
532C22—81no—
533C22—84no—
534C22—84no—
535C22—81no—
536C22—81no—
537C22—81no—
538C22—84no—
539C22—84no—
540C22#352×C14912yescomplemented
541C22#386×C14911yescharacteristic
542C22C2×#99×C14911yescharacteristic
543C22C2×#99×C14911yescharacteristic
544C4—21no—
545C4—22no—
546C4—21no—
547C4—81no—
548C4—81no—
549C4—81no—
550C4—81no—
551C4—162no—
552C2—21no—
553C2—21no—
554C2—22no—
555C2—42no—
556C2—41no—
557C2—42no—
558C2—81no—
559C2—81no—
560C2#1898×C14911yescharacteristic
561C2C2×#352×C14911yescharacteristic
562C2#2121×C14911yescharacteristic
subgroupG/H
center, socleC22×C149C2×#99
commutatorC24C22×C4×C149
Frattini, cosocleC22×D4C23×C149
prime radicalC23×D4×C149C22
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C149 ◁ C24×C149 ◁ C23×D4×C149 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×#352×C149C2semidirect
5. #1390×C149C2semidirect
8. C2×#123×C149C4semidirect
10. C22×C22⋊C4×C149C4semidirect
18. #386×C149C4semidirect
23. #379×C149C4semidirect
258. C22×C149#352semidirect
281. #13080C149direct (N × H)
282. C149#13080direct (N × H)
285. C2×#352C2×C149semidirect
287. #1390C2×C149semidirect
290. C2×#123C4×C149semidirect
292. C22×C22⋊C4C4×C149semidirect
300. #386C4×C149semidirect
305. #379C4×C149semidirect
540. C22#352×C149semidirect

Maximal subgroups

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

subgroupindex
C22×#100×C1492
#2405×C1492
C2×#352×C1492
#1781×C1492
#1390×C1492
#13080149