Finite Group Databasebeta

← C149×#11069 #49190018

Subgroups — C149×#11069 #49190018

Order 38144.

2538 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2315×C149C211yesmaximal, characteristic, complemented
2C2×#379×C149C212yesmaximal
3C2×#379×C149C211yesmaximal, characteristic
4C2×#342×C149C212yesmaximal, complemented
5C2×#342×C149C211yesmaximal, characteristic, complemented
6C26×C149C2211yescharacteristic
7C22×C22⋊C4×C149—24no—
8C22×C22⋊C4×C149—22no—
9C22×C22⋊C4×C149C2212yes—
10C22×C22⋊C4×C149C2211yescharacteristic
11C22×C22⋊C4×C149C2212yes—
12C22×C22⋊C4×C149C2211yescharacteristic
13#385×C149—24no—
14#380×C149—22no—
15#379×C149—24no—
16#379×C149—24no—
17#379×C149—22no—
18#379×C149C414yescomplemented
19#342×C149—22no—
20#342×C149—24no—
21C25×C149—21no—
22C25×C149—22no—
23C25×C149—21no—
24C25×C149—22no—
25C25×C149—22no—
26C25×C149—21no—
27C25×C149—21no—
28C25×C149—22no—
29C25×C149—48no—
30C25×C149C2×C412yes—
31C25×C149D412yes—
32C25×C149Q812yes—
33C25×C149C2311yescharacteristic
34C23×C4×C149—21no—
35C23×C4×C149—22no—
36C23×C4×C149D414yes—
37C23×C4×C149D412yes—
38C2×C4⋊C4×C149—24no—
39C2×C22⋊C4×C149—22no—
40C2×C22⋊C4×C149—22no—
41C2×C22⋊C4×C149—22no—
42C2×C22⋊C4×C149—22no—
43C2×C22⋊C4×C149—22no—
44C2×C22⋊C4×C149—22no—
45C2×C22⋊C4×C149—22no—
46C2×C22⋊C4×C149—22no—
47C2×C22⋊C4×C149—216no—
48C2×C22⋊C4×C149—22no—
49C2×C22⋊C4×C149—21no—
50C2×C22⋊C4×C149—22no—
51C2×C22⋊C4×C149—22no—
52C2×C22⋊C4×C149—22no—
53C2×C22⋊C4×C149—22no—
54C2×C22⋊C4×C149—22no—
55C2×C22⋊C4×C149—22no—
56C2×C22⋊C4×C149—28no—
57C2×C22⋊C4×C149—48no—
58C2×C22⋊C4×C149—416no—
59C2×C22⋊C4×C149C2×C412yes—
60C2×C22⋊C4×C149C2×C412yes—
61C2×C22⋊C4×C149D414yes—
62C2×C22⋊C4×C149D412yes—
63#95×C149—24no—
64C24×C149—28no—
65C24×C149—216no—
66C24×C149—22no—
67C24×C149—24no—
68C24×C149—24no—
69C24×C149—22no—
70C24×C149—22no—
71C24×C149—24no—
72C24×C149—22no—
73C24×C149—24no—
74C24×C149—22no—
75C24×C149—22no—
76C24×C149—24no—
77C24×C149—24no—
78C24×C149—48no—
79C24×C149—48no—
80C24×C149—48no—
81C24×C149—44no—
82C24×C149—44no—
83C24×C149—48no—
84C24×C149—48no—
85C24×C149—416no—
86C24×C149—416no—
87C24×C149—48no—
88C24×C149—48no—
89C24×C149—416no—
90C24×C149—41no—
91C24×C149—42no—
92C24×C149—42no—
93C24×C149—42no—
94C24×C149—41no—
95C24×C149—42no—
96C24×C149—42no—
97C24×C149—41no—
98C24×C149—42no—
99C24×C149—41no—
100C24×C149C4⋊C414yescomplemented
101C24×C149C22×C411yescharacteristic
102C24×C149C2×D411yescharacteristic
103C24×C149C2×D412yes—
104C24×C149C2×D411yescharacteristic
105C24×C149C2×D411yescharacteristic
106C24×C149C2×D412yes—
107C24×C149C2×Q811yescharacteristic
108C24×C149#4111yescharacteristic
109C24×C149#4111yescharacteristic
110C24×C149#4112yes—
111C24×C149#4112yes—
112C22×C4×C149—22no—
113C22×C4×C149—22no—
114C22×C4×C149—22no—
115C22×C4×C149—24no—
116C22×C4×C149—24no—
117C22×C4×C149—24no—
118C22×C4×C149—24no—
119C22×C4×C149—44no—
120C22×C4×C149—48no—
121C22×C4×C149—44no—
122C22×C4×C149—48no—
123C22×C4×C149—42no—
124C22×C4×C149—41no—
125C22×C4×C149—42no—
126C22×C4×C149—41no—
127C22×C4×C149C22⋊C414yescomplemented
128C4⋊C4×C149—84no—
129C22⋊C4×C149—24no—
130C22⋊C4×C149—24no—
131C22⋊C4×C149—24no—
132C22⋊C4×C149—24no—
133C22⋊C4×C149—24no—
134C22⋊C4×C149—416no—
135C22⋊C4×C149—432no—
136C22⋊C4×C149—42no—
137C22⋊C4×C149—42no—
138C22⋊C4×C149—42no—
139C22⋊C4×C149—42no—
140C22⋊C4×C149—42no—
141C22⋊C4×C149—42no—
142C22⋊C4×C149—42no—
143C23×C149—24no—
144C23×C149—28no—
145C23×C149—28no—
146C23×C149—216no—
147C23×C149—216no—
148C23×C149—28no—
149C23×C149—28no—
150C23×C149—216no—
151C23×C149—24no—
152C23×C149—28no—
153C23×C149—48no—
154C23×C149—42no—
155C23×C149—42no—
156C23×C149—42no—
157C23×C149—44no—
158C23×C149—42no—
159C23×C149—44no—
160C23×C149—42no—
161C23×C149—42no—
162C23×C149—44no—
163C23×C149—44no—
164C23×C149—416no—
165C23×C149—48no—
166C23×C149—48no—
167C23×C149—48no—
168C23×C149—416no—
169C23×C149—48no—
170C23×C149—44no—
171C23×C149—48no—
172C23×C149—416no—
173C23×C149—44no—
174C23×C149—48no—
175C23×C149—48no—
176C23×C149—416no—
177C23×C149—48no—
178C23×C149—48no—
179C23×C149—416no—
180C23×C149—416no—
181C23×C149—416no—
182C23×C149—416no—
183C23×C149—416no—
184C23×C149—42no—
185C23×C149—44no—
186C23×C149—42no—
187C23×C149—42no—
188C23×C149—42no—
189C23×C149—44no—
190C23×C149—44no—
191C23×C149—42no—
192C23×C149—42no—
193C23×C149—48no—
194C23×C149C2×C22⋊C411yescharacteristic
195C23×C149C2×C4⋊C411yescharacteristic
196C23×C149#11711yescharacteristic
197C23×C149C4×D412yes—
198C23×C149C4×D412yes—
199C23×C149#12012yes—
200C23×C149#12011yescharacteristic
201C23×C149#12111yescharacteristic
202C23×C149#12112yes—
203C23×C149#12112yes—
204C23×C149#12111yescharacteristic
205C23×C149#12112yes—
206C23×C149C22⋊Q811yescharacteristic
207C23×C149C22⋊Q812yes—
208C23×C149C22⋊Q811yescharacteristic
209C23×C149C22⋊Q812yes—
210C23×C149#12311yescharacteristic
211C23×C149#12312yes—
212C23×C149#12312yes—
213C23×C149#12412yes—
214C23×C149#12411yescharacteristic
215C23×C149#12612yes—
216C23×C149#12711yescharacteristic
217C2×C4×C149—24no—
218C2×C4×C149—44no—
219C2×C4×C149—44no—
220C2×C4×C149—44no—
221C2×C4×C149—48no—
222C2×C4×C149—48no—
223C2×C4×C149—42no—
224C2×C4×C149—44no—
225C2×C4×C149—44no—
226C2×C4×C149—48no—
227C2×C4×C149—82no—
228C2×C4×C149—84no—
229C2×C4×C149—82no—
230C2×C4×C149—82no—
231C2×C4×C149—84no—
232C2×C4×C149—84no—
233C22×C149—22no—
234C22×C149—24no—
235C22×C149—22no—
236C22×C149—24no—
237C22×C149—24no—
238C22×C149—24no—
239C22×C149—22no—
240C22×C149—22no—
241C22×C149—22no—
242C22×C149—24no—
243C22×C149—22no—
244C22×C149—24no—
245C22×C149—28no—
246C22×C149—216no—
247C22×C149—41no—
248C22×C149—41no—
249C22×C149—42no—
250C22×C149—42no—
251C22×C149—41no—
252C22×C149—41no—
253C22×C149—42no—
254C22×C149—42no—
255C22×C149—42no—
256C22×C149—42no—
257C22×C149—48no—
258C22×C149—416no—
259C22×C149—44no—
260C22×C149—48no—
261C22×C149—416no—
262C22×C149—416no—
263C22×C149—48no—
264C22×C149—48no—
265C22×C149—48no—
266C22×C149—44no—
267C22×C149—48no—
268C22×C149—48no—
269C22×C149#38011yescharacteristic
270C22×C149#38512yes—
271C22×C149#38611yescharacteristic
272C22×C149#38812yes—
273C22×C149#39011yescharacteristic
274C22×C149#39211yescharacteristic
275C22×C149#39311yescharacteristic
276C22×C149#39412yes—
277C22×C149#39612yes—
278C22×C149#39711yescharacteristic
279C22×C149#39911yescharacteristic
280C22×C149B(4,𝔽2)14yes—
281C4×C149—44no—
282C4×C149—82no—
283C4×C149—84no—
284C4×C149—84no—
285C2×C149—21no—
286C2×C149—22no—
287C2×C149—21no—
288C2×C149—22no—
289C2×C149—22no—
290C2×C149—22no—
291C2×C149—21no—
292C2×C149—21no—
293C2×C149—48no—
294C2×C149#143911yescharacteristic
295C2×C149#188912yes—
296C2×C149#202112yes—
297C2×C149#202912yes—
298#11069C14911yesmaximal, characteristic, direct product factor, Sylow
299C149#1106911yescharacteristic, direct product factor, Sylow
300#2315C2×C14911yescharacteristic, complemented
301C2×#379C2×C14912yes—
302C2×#379C2×C14911yescharacteristic
303C2×#342C2×C14912yescomplemented
304C2×#342C2×C14911yescharacteristic, complemented
305C26C22×C14911yescharacteristic
306C22×C22⋊C4—24no—
307C22×C22⋊C4—22no—
308C22×C22⋊C4C22×C14912yes—
309C22×C22⋊C4C22×C14911yescharacteristic
310C22×C22⋊C4C22×C14912yes—
311C22×C22⋊C4C22×C14911yescharacteristic
312#385—24no—
313#380—22no—
314#379—24no—
315#379—24no—
316#379—22no—
317#379C4×C14914yescomplemented
318#342—22no—
319#342—24no—
320C25—21no—
321C25—22no—
322C25—21no—
323C25—22no—
324C25—22no—
325C25—21no—
326C25—21no—
327C25—22no—
328C25—48no—
329C25C2×C4×C14912yes—
330C25D4×C14912yes—
331C25Q8×C14912yes—
332C25C23×C14911yescharacteristic
333C23×C4—21no—
334C23×C4—22no—
335C23×C4D4×C14914yes—
336C23×C4D4×C14912yes—
337C2×C4⋊C4—24no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—22no—
340C2×C22⋊C4—22no—
341C2×C22⋊C4—22no—
342C2×C22⋊C4—22no—
343C2×C22⋊C4—22no—
344C2×C22⋊C4—22no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—216no—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—21no—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—28no—
356C2×C22⋊C4—48no—
357C2×C22⋊C4—416no—
358C2×C22⋊C4C2×C4×C14912yes—
359C2×C22⋊C4C2×C4×C14912yes—
360C2×C22⋊C4D4×C14914yes—
361C2×C22⋊C4D4×C14912yes—
362#95—24no—
363C24—216no—
364C24—28no—
365C24—22no—
366C24—24no—
367C24—24no—
368C24—22no—
369C24—22no—
370C24—24no—
371C24—22no—
372C24—24no—
373C24—22no—
374C24—22no—
375C24—24no—
376C24—24no—
377C24—48no—
378C24—48no—
379C24—48no—
380C24—44no—
381C24—48no—
382C24—44no—
383C24—416no—
384C24—48no—
385C24—48no—
386C24—48no—
387C24—416no—
388C24—416no—
389C24—41no—
390C24—42no—
391C24—42no—
392C24—42no—
393C24—41no—
394C24—42no—
395C24—42no—
396C24—41no—
397C24—42no—
398C24—41no—
399C24C4⋊C4×C14914yescomplemented
400C24C22×C4×C14911yescharacteristic
401C24C2×D4×C14911yescharacteristic
402C24C2×D4×C14912yes—
403C24C2×D4×C14911yescharacteristic
404C24C2×D4×C14911yescharacteristic
405C24C2×D4×C14912yes—
406C24C2×Q8×C14911yescharacteristic
407C24#41×C14911yescharacteristic
408C24#41×C14911yescharacteristic
409C24#41×C14912yes—
410C24#41×C14912yes—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—24no—
415C22×C4—24no—
416C22×C4—24no—
417C22×C4—24no—
418C22×C4—44no—
419C22×C4—48no—
420C22×C4—48no—
421C22×C4—44no—
422C22×C4—42no—
423C22×C4—41no—
424C22×C4—42no—
425C22×C4—41no—
426C22×C4C22⋊C4×C14914yescomplemented
427C4⋊C4—84no—
428C22⋊C4—24no—
429C22⋊C4—24no—
430C22⋊C4—24no—
431C22⋊C4—24no—
432C22⋊C4—24no—
433C22⋊C4—416no—
434C22⋊C4—432no—
435C22⋊C4—42no—
436C22⋊C4—42no—
437C22⋊C4—42no—
438C22⋊C4—42no—
439C22⋊C4—42no—
440C22⋊C4—42no—
441C22⋊C4—42no—
442C23—28no—
443C23—24no—
444C23—216no—
445C23—28no—
446C23—28no—
447C23—28no—
448C23—216no—
449C23—216no—
450C23—24no—
451C23—28no—
452C23—48no—
453C23—42no—
454C23—42no—
455C23—44no—
456C23—42no—
457C23—42no—
458C23—42no—
459C23—42no—
460C23—44no—
461C23—44no—
462C23—48no—
463C23—416no—
464C23—48no—
465C23—44no—
466C23—48no—
467C23—416no—
468C23—44no—
469C23—48no—
470C23—44no—
471C23—416no—
472C23—48no—
473C23—48no—
474C23—48no—
475C23—416no—
476C23—48no—
477C23—48no—
478C23—416no—
479C23—416no—
480C23—416no—
481C23—416no—
482C23—416no—
483C23—42no—
484C23—44no—
485C23—42no—
486C23—42no—
487C23—42no—
488C23—44no—
489C23—44no—
490C23—42no—
491C23—42no—
492C23—48no—
493C23C2×C22⋊C4×C14911yescharacteristic
494C23C2×C4⋊C4×C14911yescharacteristic
495C23#117×C14911yescharacteristic
496C23C4×D4×C14912yes—
497C23C4×D4×C14912yes—
498C23#120×C14912yes—
499C23#120×C14911yescharacteristic
500C23#121×C14911yescharacteristic
501C23#121×C14912yes—
502C23#121×C14912yes—
503C23#121×C14911yescharacteristic
504C23#121×C14912yes—
505C23C22⋊Q8×C14911yescharacteristic
506C23C22⋊Q8×C14912yes—
507C23C22⋊Q8×C14911yescharacteristic
508C23C22⋊Q8×C14912yes—
509C23#123×C14911yescharacteristic
510C23#123×C14912yes—
511C23#123×C14912yes—
512C23#124×C14912yes—
513C23#124×C14911yescharacteristic
514C23#126×C14912yes—
515C23#127×C14911yescharacteristic
516C2×C4—24no—
517C2×C4—44no—
518C2×C4—44no—
519C2×C4—48no—
520C2×C4—44no—
521C2×C4—48no—
522C2×C4—42no—
523C2×C4—44no—
524C2×C4—44no—
525C2×C4—48no—
526C2×C4—82no—
527C2×C4—82no—
528C2×C4—82no—
529C2×C4—84no—
530C2×C4—84no—
531C2×C4—84no—
532C22—24no—
533C22—24no—
534C22—22no—
535C22—22no—
536C22—22no—
537C22—24no—
538C22—22no—
539C22—24no—
540C22—22no—
541C22—24no—
542C22—22no—
543C22—24no—
544C22—28no—
545C22—216no—
546C22—41no—
547C22—41no—
548C22—42no—
549C22—42no—
550C22—41no—
551C22—41no—
552C22—42no—
553C22—42no—
554C22—42no—
555C22—42no—
556C22—48no—
557C22—416no—
558C22—44no—
559C22—48no—
560C22—416no—
561C22—416no—
562C22—48no—
563C22—48no—
564C22—44no—
565C22—48no—
566C22—48no—
567C22—48no—
568C22#380×C14911yescharacteristic
569C22#385×C14912yes—
570C22#386×C14911yescharacteristic
571C22#388×C14912yes—
572C22#390×C14911yescharacteristic
573C22#392×C14911yescharacteristic
574C22#393×C14911yescharacteristic
575C22#394×C14912yes—
576C22#396×C14912yes—
577C22#397×C14911yescharacteristic
578C22#399×C14911yescharacteristic
579C22B(4,𝔽2)×C14914yes—
580C4—44no—
581C4—82no—
582C4—84no—
583C4—84no—
584C2—21no—
585C2—22no—
586C2—21no—
587C2—22no—
588C2—22no—
589C2—22no—
590C2—21no—
591C2—21no—
592C2—48no—
593C2#1439×C14911yescharacteristic
594C2#1889×C14912yes—
595C2#2021×C14912yes—
596C2#2029×C14912yes—
subgroupG/H
center, socleC23×C149#120
commutatorC24C22×C4×C149
Frattini, cosocleC25C23×C149
prime radicalC26×C149C22
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C149 ◁ C25×C149 ◁ G

Complements

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

NH ≅ G/Ntype
1. #2315×C149C2semidirect
4. C2×#342×C149C2semidirect
5. C2×#342×C149C2semidirect
18. #379×C149C4semidirect
100. C24×C149C4⋊C4semidirect
127. C22×C4×C149C22⋊C4semidirect
298. #11069C149direct (N × H)
299. C149#11069direct (N × H)
300. #2315C2×C149semidirect
303. C2×#342C2×C149semidirect
304. C2×#342C2×C149semidirect
317. #379C4×C149semidirect
399. C24C4⋊C4×C149semidirect
426. C22×C4C22⋊C4×C149semidirect

Maximal subgroups

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

subgroupindex
#2315×C1492
C2×#379×C1492
C2×#342×C1492
#11069149