Finite Group Databasebeta

← C149×#14506 #49193455

Subgroups — C149×#14506 #49193455

Order 38144.

1962 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C149C211yesmaximal, characteristic
2C2×#388×C149C212yesmaximal, complemented
3#1445×C149C212yesmaximal, complemented
4#1439×C149C212yesmaximal, complemented
5#1438×C149C211yesmaximal, characteristic
6#1438×C149C211yesmaximal, characteristic
7#1437×C149C212yesmaximal, complemented
8C4⋊#95×C149C212yesmaximal, complemented
9C22⋊#95×C149C212yesmaximal, complemented
10C23×D4×C149C2211yescharacteristic
11C24×C4×C149C2211yescharacteristic
12C2×#123×C149—28no—
13C2×#123×C149C418yescomplemented
14C22×C4⋊C4×C149C2212yes—
15C22×C4⋊C4×C149C2212yes—
16C22×C22⋊C4×C149C2212yes—
17C22×C22⋊C4×C149C2212yes—
18C22×C22⋊C4×C149C2211yescharacteristic
19C22×C22⋊C4×C149C2212yes—
20C22×C22⋊C4×C149C2212yes—
21C22×C22⋊C4×C149C2211yescharacteristic
22C22×C22⋊C4×C149C2211yescharacteristic
23C22×C42×C149C2212yes—
24#388×C149—28no—
25C2×#95×C149C2212yes—
26C2×#95×C149C2212yes—
27C2×#95×C149C2212yes—
28C2×#95×C149C2212yes—
29C2×#95×C149C2212yes—
30C2×#95×C149C2212yes—
31C2×#95×C149C2211yescharacteristic
32C2×#95×C149C2212yes—
33C2×#95×C149C2211yescharacteristic
34C25×C149C2311yescharacteristic
35C25×C149C2311yescharacteristic
36C22×D4×C149—24no—
37C22×D4×C149—42no—
38C22×D4×C149—41no—
39C22×D4×C149—41no—
40C22×D4×C149C2×C414yes—
41C23×C4×C149—24no—
42C23×C4×C149—42no—
43C23×C4×C149—41no—
44C23×C4×C149—41no—
45C23×C4×C149C2×C414yes—
46C23×C4×C149C2312yes—
47C23×C4×C149C2312yes—
48C23×C4×C149C2312yes—
49C23×C4×C149C2311yescharacteristic
50C23×C4×C149C2312yes—
51C23×C4×C149C2312yes—
52C23×C4×C149C2312yes—
53#123×C149—232no—
54C2×C4⋊C4×C149—24no—
55C2×C4⋊C4×C149—24no—
56C2×C4⋊C4×C149—24no—
57C2×C4⋊C4×C149—24no—
58C2×C4⋊C4×C149—42no—
59C2×C4⋊C4×C149C2×C418yes—
60C2×C22⋊C4×C149—24no—
61C2×C22⋊C4×C149—24no—
62C2×C22⋊C4×C149—24no—
63C2×C22⋊C4×C149—24no—
64C2×C22⋊C4×C149—24no—
65C2×C22⋊C4×C149—24no—
66C2×C22⋊C4×C149—24no—
67C2×C22⋊C4×C149—24no—
68C2×C22⋊C4×C149—41no—
69C2×C22⋊C4×C149—42no—
70C2×C22⋊C4×C149—42no—
71C2×C22⋊C4×C149—42no—
72C2×C22⋊C4×C149—42no—
73C2×C22⋊C4×C149—41no—
74C2×C22⋊C4×C149—42no—
75C2×C22⋊C4×C149C2×C418yes—
76C2×C22⋊C4×C149C2×C414yes—
77C2×C22⋊C4×C149D418yes—
78C2×C42×C149—24no—
79C2×C42×C149—24no—
80C2×C42×C149—42no—
81#95×C149—24no—
82#95×C149—24no—
83#95×C149—41no—
84#95×C149—42no—
85#95×C149—42no—
86#95×C149—42no—
87#95×C149—42no—
88#95×C149—42no—
89#95×C149—41no—
90C24×C149—22no—
91C24×C149—22no—
92C24×C149—22no—
93C24×C149—22no—
94C24×C149—21no—
95C24×C149—21no—
96C24×C149—22no—
97C24×C149—22no—
98C24×C149—22no—
99C24×C149—22no—
100C24×C149—22no—
101C24×C149—22no—
102C24×C149—21no—
103C24×C149—21no—
104C24×C149—22no—
105C24×C149C22×C412yes—
106C24×C149C22×C412yes—
107C24×C149C2×D414yes—
108C24×C149C2411yescharacteristic
109C2×D4×C149—28no—
110C2×D4×C149—44no—
111C2×D4×C149—44no—
112C2×D4×C149—48no—
113C2×D4×C149—48no—
114C22×C4×C149—22no—
115C22×C4×C149—22no—
116C22×C4×C149—22no—
117C22×C4×C149—22no—
118C22×C4×C149—28no—
119C22×C4×C149—22no—
120C22×C4×C149—22no—
121C22×C4×C149—22no—
122C22×C4×C149—22no—
123C22×C4×C149—22no—
124C22×C4×C149—22no—
125C22×C4×C149—22no—
126C22×C4×C149—22no—
127C22×C4×C149—22no—
128C22×C4×C149—22no—
129C22×C4×C149—22no—
130C22×C4×C149—22no—
131C22×C4×C149—22no—
132C22×C4×C149—22no—
133C22×C4×C149—22no—
134C22×C4×C149—22no—
135C22×C4×C149—21no—
136C22×C4×C149—21no—
137C22×C4×C149—22no—
138C22×C4×C149—22no—
139C22×C4×C149—22no—
140C22×C4×C149—22no—
141C22×C4×C149—22no—
142C22×C4×C149—22no—
143C22×C4×C149—22no—
144C22×C4×C149—22no—
145C22×C4×C149—22no—
146C22×C4×C149—22no—
147C22×C4×C149—22no—
148C22×C4×C149—22no—
149C22×C4×C149—22no—
150C22×C4×C149—22no—
151C22×C4×C149—22no—
152C22×C4×C149—22no—
153C22×C4×C149—22no—
154C22×C4×C149—22no—
155C22×C4×C149—44no—
156C22×C4×C149—44no—
157C22×C4×C149—48no—
158C22×C4×C149—48no—
159C22×C4×C149C22×C414yes—
160C22×C4×C149C22×C412yes—
161C22×C4×C149C22×C414yes—
162C22×C4×C149C2×D414yes—
163C22×C4×C149C2×D414yes—
164C22×C4×C149#4114yes—
165C22×C4×C149#4114yes—
166C4⋊C4×C149—216no—
167C4⋊C4×C149—48no—
168C22⋊C4×C149—216no—
169C22⋊C4×C149—44no—
170C22⋊C4×C149—48no—
171C22⋊C4×C149—48no—
172C22⋊C4×C149—48no—
173C22⋊C4×C149—44no—
174C22⋊C4×C149C22⋊C4116yescomplemented
175C42×C149—48no—
176C23×C149—24no—
177C23×C149—22no—
178C23×C149—22no—
179C23×C149—24no—
180C23×C149—24no—
181C23×C149—24no—
182C23×C149—24no—
183C23×C149—24no—
184C23×C149—24no—
185C23×C149—24no—
186C23×C149—22no—
187C23×C149—24no—
188C23×C149—22no—
189C23×C149—22no—
190C23×C149—24no—
191C23×C149—42no—
192C23×C149—42no—
193C23×C149—42no—
194C23×C149—42no—
195C23×C149—41no—
196C23×C149—42no—
197C23×C149—41no—
198C23×C149—41no—
199C23×C149—42no—
200C23×C149—41no—
201C23×C149—42no—
202C23×C149—42no—
203C23×C149—42no—
204C23×C149—42no—
205C23×C149—42no—
206C23×C149—42no—
207C23×C149—42no—
208C23×C149—42no—
209C23×C149—42no—
210C23×C149—42no—
211C23×C149—41no—
212C23×C149—42no—
213C23×C149—41no—
214C23×C149—41no—
215C23×C149—42no—
216C23×C149—41no—
217C23×C149C2×C22⋊C414yes—
218C23×C149C23×C411yescharacteristic
219C23×C149C22×D412yes—
220C23×C149C2×#4112yes—
221C23×C149C2×#4112yes—
222C23×C149H(5,𝔽2)12yes—
223C23×C149H(5,𝔽2)11yescharacteristic
224C23×C149H(5,𝔽2)11yescharacteristic
225C23×C149H(5,𝔽2)12yes—
226C23×C1492−1+412yes—
227D4×C149—416no—
228C2×C4×C149—24no—
229C2×C4×C149—24no—
230C2×C4×C149—24no—
231C2×C4×C149—24no—
232C2×C4×C149—24no—
233C2×C4×C149—24no—
234C2×C4×C149—24no—
235C2×C4×C149—22no—
236C2×C4×C149—24no—
237C2×C4×C149—24no—
238C2×C4×C149—22no—
239C2×C4×C149—22no—
240C2×C4×C149—24no—
241C2×C4×C149—24no—
242C2×C4×C149—24no—
243C2×C4×C149—24no—
244C2×C4×C149—24no—
245C2×C4×C149—24no—
246C2×C4×C149—416no—
247C2×C4×C149—42no—
248C2×C4×C149—42no—
249C2×C4×C149—42no—
250C2×C4×C149—42no—
251C2×C4×C149—42no—
252C2×C4×C149—42no—
253C2×C4×C149—42no—
254C2×C4×C149—42no—
255C2×C4×C149—42no—
256C2×C4×C149—42no—
257C2×C4×C149—42no—
258C2×C4×C149—42no—
259C2×C4×C149—42no—
260C2×C4×C149—42no—
261C2×C4×C149—42no—
262C2×C4×C149—42no—
263C2×C4×C149—42no—
264C2×C4×C149—42no—
265C2×C4×C149—42no—
266C2×C4×C149—42no—
267C2×C4×C149—42no—
268C2×C4×C149—42no—
269C2×C4×C149—42no—
270C2×C4×C149—42no—
271C2×C4×C149—42no—
272C2×C4×C149—42no—
273C2×C4×C149—42no—
274C2×C4×C149—42no—
275C2×C4×C149C2×C22⋊C418yes—
276C22×C149—24no—
277C22×C149—28no—
278C22×C149—44no—
279C22×C149—42no—
280C22×C149—42no—
281C22×C149—44no—
282C22×C149—44no—
283C22×C149—44no—
284C22×C149—44no—
285C22×C149—42no—
286C22×C149—44no—
287C22×C149—44no—
288C22×C149—42no—
289C22×C149—42no—
290C22×C149—82no—
291C22×C149—82no—
292C22×C149—82no—
293C22×C149—82no—
294C22×C149C22×C22⋊C411yescharacteristic
295C22×C149C4×#4112yes—
296C22×C149#51811yescharacteristic
297C22×C149#51811yescharacteristic
298C22×C149#52012yes—
299C22×C149#53512yes—
300C22×C149#53512yes—
301C22×C149#53812yes—
302C22×C149#53912yes—
303C22×C149#54012yes—
304C22×C149#54212yes—
305C22×C149#54612yes—
306C22×C149#54612yes—
307C22×C149#54712yes—
308C22×C149#54712yes—
309C22×C149#55111yescharacteristic
310C22×C149#55312yes—
311C22×C149#55911yescharacteristic
312C22×C149#56011yescharacteristic
313C22×C149#56212yes—
314C22×C149#56311yescharacteristic
315C4×C149—28no—
316C4×C149—44no—
317C4×C149—42no—
318C4×C149—44no—
319C4×C149—44no—
320C4×C149—82no—
321C4×C149—82no—
322C2×C149—44no—
323C2×C149—82no—
324C2×C149#230911yescharacteristic
325C2×C149#233512yes—
326C2×C149#233912yes—
327C2×C149#237411yescharacteristic
328C2×C149#237611yescharacteristic
329C2×C149#270312yes—
330C2×C149#270612yes—
331C2×C149#271012yes—
332C2×C149#271812yes—
333#14506C14911yesmaximal, characteristic, direct product factor, Sylow
334C149#1450611yescharacteristic, direct product factor, Sylow
335C22×#123C2×C14911yescharacteristic
336C2×#388C2×C14912yescomplemented
337#1445C2×C14912yescomplemented
338#1439C2×C14912yescomplemented
339#1438C2×C14911yescharacteristic
340#1438C2×C14911yescharacteristic
341#1437C2×C14912yescomplemented
342C4⋊#95C2×C14912yescomplemented
343C22⋊#95C2×C14912yescomplemented
344C23×D4C22×C14911yescharacteristic
345C24×C4C22×C14911yescharacteristic
346C2×#123—28no—
347C2×#123C4×C14918yescomplemented
348C22×C4⋊C4C22×C14912yes—
349C22×C4⋊C4C22×C14912yes—
350C22×C22⋊C4C22×C14912yes—
351C22×C22⋊C4C22×C14912yes—
352C22×C22⋊C4C22×C14911yescharacteristic
353C22×C22⋊C4C22×C14912yes—
354C22×C22⋊C4C22×C14912yes—
355C22×C22⋊C4C22×C14911yescharacteristic
356C22×C22⋊C4C22×C14911yescharacteristic
357C22×C42C22×C14912yes—
358#388—28no—
359C2×#95C22×C14912yes—
360C2×#95C22×C14912yes—
361C2×#95C22×C14912yes—
362C2×#95C22×C14912yes—
363C2×#95C22×C14912yes—
364C2×#95C22×C14912yes—
365C2×#95C22×C14911yescharacteristic
366C2×#95C22×C14912yes—
367C2×#95C22×C14911yescharacteristic
368C25C23×C14911yescharacteristic
369C25C23×C14911yescharacteristic
370C22×D4—24no—
371C22×D4—42no—
372C22×D4—41no—
373C22×D4—41no—
374C22×D4C2×C4×C14914yes—
375C23×C4—24no—
376C23×C4—42no—
377C23×C4—41no—
378C23×C4—41no—
379C23×C4C2×C4×C14914yes—
380C23×C4C23×C14912yes—
381C23×C4C23×C14912yes—
382C23×C4C23×C14912yes—
383C23×C4C23×C14911yescharacteristic
384C23×C4C23×C14912yes—
385C23×C4C23×C14912yes—
386C23×C4C23×C14912yes—
387#123—232no—
388C2×C4⋊C4—24no—
389C2×C4⋊C4—24no—
390C2×C4⋊C4—24no—
391C2×C4⋊C4—24no—
392C2×C4⋊C4—42no—
393C2×C4⋊C4C2×C4×C14918yes—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—41no—
403C2×C22⋊C4—42no—
404C2×C22⋊C4—42no—
405C2×C22⋊C4—42no—
406C2×C22⋊C4—42no—
407C2×C22⋊C4—41no—
408C2×C22⋊C4—42no—
409C2×C22⋊C4C2×C4×C14918yes—
410C2×C22⋊C4C2×C4×C14914yes—
411C2×C22⋊C4D4×C14918yes—
412C2×C42—24no—
413C2×C42—24no—
414C2×C42—42no—
415#95—24no—
416#95—24no—
417#95—41no—
418#95—42no—
419#95—42no—
420#95—42no—
421#95—42no—
422#95—42no—
423#95—41no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—21no—
429C24—21no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—21no—
437C24—21no—
438C24—22no—
439C24C22×C4×C14912yes—
440C24C22×C4×C14912yes—
441C24C2×D4×C14914yes—
442C24C24×C14911yescharacteristic
443C2×D4—28no—
444C2×D4—44no—
445C2×D4—44no—
446C2×D4—48no—
447C2×D4—48no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—28no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—44no—
490C22×C4—44no—
491C22×C4—48no—
492C22×C4—48no—
493C22×C4C22×C4×C14914yes—
494C22×C4C22×C4×C14912yes—
495C22×C4C22×C4×C14914yes—
496C22×C4C2×D4×C14914yes—
497C22×C4C2×D4×C14914yes—
498C22×C4#41×C14914yes—
499C22×C4#41×C14914yes—
500C4⋊C4—216no—
501C4⋊C4—48no—
502C22⋊C4—216no—
503C22⋊C4—44no—
504C22⋊C4—48no—
505C22⋊C4—48no—
506C22⋊C4—48no—
507C22⋊C4—44no—
508C22⋊C4C22⋊C4×C149116yescomplemented
509C42—48no—
510C23—24no—
511C23—22no—
512C23—22no—
513C23—24no—
514C23—24no—
515C23—24no—
516C23—24no—
517C23—24no—
518C23—24no—
519C23—24no—
520C23—22no—
521C23—24no—
522C23—22no—
523C23—22no—
524C23—24no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—41no—
530C23—42no—
531C23—41no—
532C23—41no—
533C23—42no—
534C23—41no—
535C23—42no—
536C23—42no—
537C23—42no—
538C23—42no—
539C23—42no—
540C23—42no—
541C23—42no—
542C23—42no—
543C23—42no—
544C23—42no—
545C23—41no—
546C23—42no—
547C23—41no—
548C23—41no—
549C23—42no—
550C23—41no—
551C23C2×C22⋊C4×C14914yes—
552C23C23×C4×C14911yescharacteristic
553C23C22×D4×C14912yes—
554C23C2×#41×C14912yes—
555C23C2×#41×C14912yes—
556C23H(5,𝔽2)×C14912yes—
557C23H(5,𝔽2)×C14911yescharacteristic
558C23H(5,𝔽2)×C14911yescharacteristic
559C23H(5,𝔽2)×C14912yes—
560C232−1+4×C14912yes—
561D4—416no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—22no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—416no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4C2×C22⋊C4×C14918yes—
610C22—24no—
611C22—28no—
612C22—44no—
613C22—44no—
614C22—44no—
615C22—44no—
616C22—44no—
617C22—42no—
618C22—42no—
619C22—42no—
620C22—44no—
621C22—44no—
622C22—42no—
623C22—42no—
624C22—82no—
625C22—82no—
626C22—82no—
627C22—82no—
628C22C22×C22⋊C4×C14911yescharacteristic
629C22C4×#41×C14912yes—
630C22#518×C14911yescharacteristic
631C22#518×C14911yescharacteristic
632C22#520×C14912yes—
633C22#535×C14912yes—
634C22#535×C14912yes—
635C22#538×C14912yes—
636C22#539×C14912yes—
637C22#540×C14912yes—
638C22#542×C14912yes—
639C22#546×C14912yes—
640C22#546×C14912yes—
641C22#547×C14912yes—
642C22#547×C14912yes—
643C22#551×C14911yescharacteristic
644C22#553×C14912yes—
645C22#559×C14911yescharacteristic
646C22#560×C14911yescharacteristic
647C22#562×C14912yes—
648C22#563×C14911yescharacteristic
649C4—28no—
650C4—44no—
651C4—44no—
652C4—44no—
653C4—42no—
654C4—82no—
655C4—82no—
656C2—44no—
657C2—82no—
658C2#2309×C14911yescharacteristic
659C2#2335×C14912yes—
660C2#2339×C14912yes—
661C2#2374×C14911yescharacteristic
662C2#2376×C14911yescharacteristic
663C2#2703×C14912yes—
664C2#2706×C14912yes—
665C2#2710×C14912yes—
666C2#2718×C14912yes—
subgroupG/H
center, socleC24×C149C24
commutatorC23C23×C4×C149
Frattini, cosocleC24C24×C149
prime radicalC23×D4×C149C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C149 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#388×C149C2semidirect
3. #1445×C149C2semidirect
4. #1439×C149C2semidirect
7. #1437×C149C2semidirect
8. C4⋊#95×C149C2semidirect
9. C22⋊#95×C149C2semidirect
13. C2×#123×C149C4semidirect
174. C22⋊C4×C149C22⋊C4semidirect
333. #14506C149direct (N × H)
334. C149#14506direct (N × H)
336. C2×#388C2×C149semidirect
337. #1445C2×C149semidirect
338. #1439C2×C149semidirect
341. #1437C2×C149semidirect
342. C4⋊#95C2×C149semidirect
343. C22⋊#95C2×C149semidirect
347. C2×#123C4×C149semidirect
508. C22⋊C4C22⋊C4×C149semidirect

Maximal subgroups

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

subgroupindex
C22×#123×C1492
C2×#388×C1492
#1445×C1492
#1439×C1492
#1438×C1492
#1437×C1492
C4⋊#95×C1492
C22⋊#95×C1492
#14506149