Finite Group Databasebeta

← C2×#1468×C149 #49196322

Subgroups — C2×#1468×C149 #49196322

Order 38144.

1490 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C149C211yesmaximal, characteristic
2C2×#407×C149C211yesmaximal, characteristic, complemented
3C22×C22⋊C8×C149C211yesmaximal, characteristic, complemented
4#1468×C149C218yesmaximal, direct product factor
5C2×#324×C149C212yesmaximal, complemented
6C2×#323×C149C212yesmaximal, complemented
7C23×D4×C149C411yescharacteristic
8C24×C4×C149C2211yescharacteristic
9C22×M16×C149—21no—
10C23×C8×C149—21no—
11C2×#123×C149—21no—
12C2×#123×C149—21no—
13C2×#123×C149—22no—
14C2×#123×C149—21no—
15C2×#123×C149—21no—
16C2×#123×C149—22no—
17C2×#123×C149C414yes—
18C2×#123×C149C2214yes—
19C22×C4⋊C4×C149C411yescharacteristic
20C22×C4⋊C4×C149C2211yescharacteristic
21C22×C22⋊C4×C149C411yescharacteristic
22C22×C22⋊C4×C149C411yescharacteristic
23C22×C22⋊C4×C149C2211yescharacteristic
24#407×C149—22no—
25#407×C149C2214yescomplemented
26C2×C22⋊C8×C149—22no—
27C2×C22⋊C8×C149—21no—
28C2×C22⋊C8×C149—21no—
29C2×C22⋊C8×C149C2212yes—
30C2×C22⋊C8×C149C2212yes—
31C2×C22⋊C8×C149C2214yescomplemented
32#324×C149C2218yescomplemented
33#323×C149C2218yescomplemented
34C25×C149C2×C411yescharacteristic
35C25×C149C2×C411yescharacteristic
36C22×D4×C149—22no—
37C22×D4×C149—21no—
38C22×D4×C149—21no—
39C22×D4×C149—44no—
40C22×D4×C149C2×C414yes—
41C23×C4×C149—44no—
42C23×C4×C149C2×C411yescharacteristic
43C23×C4×C149C2×C411yescharacteristic
44C23×C4×C149C2×C411yescharacteristic
45C23×C4×C149C2×C411yescharacteristic
46C23×C4×C149C2×C412yes—
47C23×C4×C149D411yescharacteristic
48C23×C4×C149D411yescharacteristic
49C23×C4×C149D412yes—
50C23×C4×C149D411yescharacteristic
51C23×C4×C149D411yescharacteristic
52C23×C4×C149D412yes—
53C23×C4×C149C2311yescharacteristic
54C23×C4×C149C2312yes—
55C2×M16×C149—24no—
56C2×M16×C149—44no—
57C22×C8×C149—22no—
58C22×C8×C149—22no—
59C22×C8×C149—24no—
60C22×C8×C149—44no—
61#123×C149—24no—
62#123×C149—24no—
63#123×C149—24no—
64#123×C149—24no—
65#123×C149—24no—
66#123×C149—24no—
67#123×C149—24no—
68#123×C149—24no—
69C2×C4⋊C4×C149—22no—
70C2×C4⋊C4×C149—21no—
71C2×C4⋊C4×C149—21no—
72C2×C4⋊C4×C149—21no—
73C2×C4⋊C4×C149—21no—
74C2×C4⋊C4×C149—21no—
75C2×C4⋊C4×C149—21no—
76C2×C4⋊C4×C149C2×C414yes—
77C2×C4⋊C4×C149C2×C412yes—
78C2×C4⋊C4×C149C2312yes—
79C2×C22⋊C4×C149—22no—
80C2×C22⋊C4×C149—21no—
81C2×C22⋊C4×C149—21no—
82C2×C22⋊C4×C149—22no—
83C2×C22⋊C4×C149—21no—
84C2×C22⋊C4×C149—21no—
85C2×C22⋊C4×C149—21no—
86C2×C22⋊C4×C149—21no—
87C2×C22⋊C4×C149—21no—
88C2×C22⋊C4×C149—21no—
89C2×C22⋊C4×C149C2×C414yes—
90C2×C22⋊C4×C149C2×C414yes—
91C2×C22⋊C4×C149C2×C412yes—
92C2×C22⋊C4×C149C2312yes—
93C22⋊C8×C149—22no—
94C22⋊C8×C149—24no—
95C22⋊C8×C149—24no—
96C22⋊C8×C149—22no—
97C22⋊C8×C149C2314yes—
98C22⋊C8×C149C2314yes—
99C24×C149—24no—
100C24×C149—24no—
101C24×C149—21no—
102C24×C149—21no—
103C24×C149—24no—
104C24×C149—42no—
105C24×C149—42no—
106C24×C149—42no—
107C24×C149C22⋊C411yescharacteristic
108C24×C149C22⋊C412yes—
109C24×C149C22⋊C411yescharacteristic
110C24×C149C22×C412yes—
111C24×C149C22×C411yescharacteristic
112C24×C149C22×C412yes—
113C2×D4×C149—24no—
114C2×D4×C149—24no—
115C2×D4×C149—48no—
116C2×D4×C149—44no—
117C2×D4×C149—44no—
118C2×D4×C149—48no—
119C22×C4×C149—24no—
120C22×C4×C149—24no—
121C22×C4×C149—21no—
122C22×C4×C149—21no—
123C22×C4×C149—21no—
124C22×C4×C149—21no—
125C22×C4×C149—21no—
126C22×C4×C149—21no—
127C22×C4×C149—24no—
128C22×C4×C149—42no—
129C22×C4×C149—44no—
130C22×C4×C149—44no—
131C22×C4×C149—42no—
132C22×C4×C149—42no—
133C22×C4×C149—44no—
134C22×C4×C149—42no—
135C22×C4×C149—44no—
136C22×C4×C149—42no—
137C22×C4×C149—42no—
138C22×C4×C149C22⋊C412yes—
139C22×C4×C149C22⋊C412yes—
140C22×C4×C149C22⋊C411yescharacteristic
141C22×C4×C149C22⋊C411yescharacteristic
142C22×C4×C149C22⋊C412yes—
143C22×C4×C149C22⋊C412yes—
144C22×C4×C149C22⋊C412yes—
145C22×C4×C149C22×C412yes—
146C22×C4×C149C22×C412yes—
147C22×C4×C149C22×C412yes—
148C22×C4×C149C22×C412yes—
149C22×C4×C149C22×C411yescharacteristic
150C22×C4×C149C2×D412yes—
151C22×C4×C149C2×D412yes—
152C22×C4×C149C2×D411yescharacteristic
153C22×C4×C149C2×D411yescharacteristic
154C22×C4×C149C2×D411yescharacteristic
155C22×C4×C149C2×D411yescharacteristic
156C22×C4×C149C2×D412yes—
157C22×C4×C149C2×D412yes—
158C22×C4×C149C2411yescharacteristic
159M16×C149—48no—
160C2×C8×C149—24no—
161C2×C8×C149—24no—
162C2×C8×C149—44no—
163C2×C8×C149—48no—
164C2×C8×C149—44no—
165C4⋊C4×C149—24no—
166C4⋊C4×C149—24no—
167C4⋊C4×C149—22no—
168C4⋊C4×C149—22no—
169C4⋊C4×C149—22no—
170C4⋊C4×C149—22no—
171C22⋊C4×C149—24no—
172C22⋊C4×C149—24no—
173C22⋊C4×C149—24no—
174C22⋊C4×C149—24no—
175C22⋊C4×C149—22no—
176C22⋊C4×C149—22no—
177C22⋊C4×C149—22no—
178C22⋊C4×C149—22no—
179C23×C149—22no—
180C23×C149—22no—
181C23×C149—22no—
182C23×C149—22no—
183C23×C149—24no—
184C23×C149—24no—
185C23×C149—22no—
186C23×C149—24no—
187C23×C149—22no—
188C23×C149—24no—
189C23×C149—22no—
190C23×C149—22no—
191C23×C149—24no—
192C23×C149—42no—
193C23×C149—42no—
194C23×C149—416no—
195C23×C149—42no—
196C23×C149—42no—
197C23×C149—42no—
198C23×C149—42no—
199C23×C149—42no—
200C23×C149—42no—
201C23×C149—42no—
202C23×C149—42no—
203C23×C149—88no—
204C23×C149#9914yes—
205C23×C149C2×C22⋊C412yes—
206C23×C149C2×C22⋊C411yescharacteristic
207C23×C149C2×C22⋊C412yes—
208C23×C149C2×C22⋊C411yescharacteristic
209C23×C149#13114yes—
210C23×C149C23×C411yescharacteristic
211D4×C149—48no—
212D4×C149—48no—
213C2×C4×C149—24no—
214C2×C4×C149—22no—
215C2×C4×C149—22no—
216C2×C4×C149—24no—
217C2×C4×C149—24no—
218C2×C4×C149—24no—
219C2×C4×C149—22no—
220C2×C4×C149—22no—
221C2×C4×C149—22no—
222C2×C4×C149—22no—
223C2×C4×C149—22no—
224C2×C4×C149—24no—
225C2×C4×C149—42no—
226C2×C4×C149—42no—
227C2×C4×C149—42no—
228C2×C4×C149—41no—
229C2×C4×C149—42no—
230C2×C4×C149—41no—
231C2×C4×C149—41no—
232C2×C4×C149—42no—
233C2×C4×C149—42no—
234C2×C4×C149—41no—
235C2×C4×C149—42no—
236C2×C4×C149—42no—
237C2×C4×C149—42no—
238C2×C4×C149—42no—
239C2×C4×C149—42no—
240C2×C4×C149—42no—
241C2×C4×C149—42no—
242C2×C4×C149—42no—
243C2×C4×C149C2×C22⋊C411yescharacteristic
244C2×C4×C149C2×C22⋊C411yescharacteristic
245C2×C4×C149C2×C22⋊C412yes—
246C2×C4×C149C2×C22⋊C412yes—
247C2×C4×C149C22×D411yescharacteristic
248C2×C4×C149C22×D411yescharacteristic
249C8×C149—44no—
250C8×C149—44no—
251C22×C149—22no—
252C22×C149—21no—
253C22×C149—21no—
254C22×C149—21no—
255C22×C149—21no—
256C22×C149—22no—
257C22×C149—28no—
258C22×C149—28no—
259C22×C149—22no—
260C22×C149—22no—
261C22×C149—22no—
262C22×C149—48no—
263C22×C149—48no—
264C22×C149—44no—
265C22×C149—42no—
266C22×C149—42no—
267C22×C149—42no—
268C22×C149—84no—
269C22×C149—84no—
270C22×C149—84no—
271C22×C149#40812yes—
272C22×C149#40812yes—
273C22×C149C2×#9914yes—
274C22×C149C2×#9912yes—
275C22×C149#41312yes—
276C22×C149C22×C22⋊C411yescharacteristic
277C22×C149C2×#13112yes—
278C4×C149—21no—
279C4×C149—21no—
280C4×C149—22no—
281C4×C149—21no—
282C4×C149—21no—
283C4×C149—22no—
284C4×C149—42no—
285C4×C149—42no—
286C4×C149—42no—
287C2×C149—22no—
288C2×C149—22no—
289C2×C149—24no—
290C2×C149—42no—
291C2×C149—82no—
292C2×C149#146814yesdirect product factor
293C2×C149C2×#40811yescharacteristic
294C2×C149C22×#9911yescharacteristic
295C2×C149C2×#41311yescharacteristic
296C2×#1468C14911yesmaximal, characteristic, direct product factor, Sylow
297C149C2×#146811yescharacteristic, direct product factor, Sylow
298C22×#123C2×C14911yescharacteristic
299C2×#407C2×C14911yescharacteristic, complemented
300C22×C22⋊C8C2×C14911yescharacteristic, complemented
301#1468C2×C14918yesdirect product factor
302C2×#324C2×C14912yescomplemented
303C2×#323C2×C14912yescomplemented
304C23×D4C4×C14911yescharacteristic
305C24×C4C22×C14911yescharacteristic
306C22×M16—21no—
307C23×C8—21no—
308C2×#123—21no—
309C2×#123—21no—
310C2×#123—21no—
311C2×#123—21no—
312C2×#123—22no—
313C2×#123—22no—
314C2×#123C4×C14914yes—
315C2×#123C22×C14914yes—
316C22×C4⋊C4C4×C14911yescharacteristic
317C22×C4⋊C4C22×C14911yescharacteristic
318C22×C22⋊C4C4×C14911yescharacteristic
319C22×C22⋊C4C4×C14911yescharacteristic
320C22×C22⋊C4C22×C14911yescharacteristic
321#407—22no—
322#407C22×C14914yescomplemented
323C2×C22⋊C8—22no—
324C2×C22⋊C8—21no—
325C2×C22⋊C8—21no—
326C2×C22⋊C8C22×C14912yes—
327C2×C22⋊C8C22×C14912yes—
328C2×C22⋊C8C22×C14914yescomplemented
329#324C22×C14918yescomplemented
330#323C22×C14918yescomplemented
331C25C2×C4×C14911yescharacteristic
332C25C2×C4×C14911yescharacteristic
333C22×D4—21no—
334C22×D4—22no—
335C22×D4—21no—
336C22×D4—44no—
337C22×D4C2×C4×C14914yes—
338C23×C4—44no—
339C23×C4C2×C4×C14911yescharacteristic
340C23×C4C2×C4×C14911yescharacteristic
341C23×C4C2×C4×C14911yescharacteristic
342C23×C4C2×C4×C14911yescharacteristic
343C23×C4C2×C4×C14912yes—
344C23×C4D4×C14911yescharacteristic
345C23×C4D4×C14911yescharacteristic
346C23×C4D4×C14911yescharacteristic
347C23×C4D4×C14911yescharacteristic
348C23×C4D4×C14912yes—
349C23×C4D4×C14912yes—
350C23×C4C23×C14911yescharacteristic
351C23×C4C23×C14912yes—
352C2×M16—24no—
353C2×M16—44no—
354C22×C8—22no—
355C22×C8—24no—
356C22×C8—22no—
357C22×C8—44no—
358#123—24no—
359#123—24no—
360#123—24no—
361#123—24no—
362#123—24no—
363#123—24no—
364#123—24no—
365#123—24no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4C2×C4×C14914yes—
374C2×C4⋊C4C2×C4×C14912yes—
375C2×C4⋊C4C23×C14912yes—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4C2×C4×C14914yes—
387C2×C22⋊C4C2×C4×C14914yes—
388C2×C22⋊C4C2×C4×C14912yes—
389C2×C22⋊C4C23×C14912yes—
390C22⋊C8—22no—
391C22⋊C8—24no—
392C22⋊C8—24no—
393C22⋊C8—22no—
394C22⋊C8C23×C14914yes—
395C22⋊C8C23×C14914yes—
396C24—24no—
397C24—24no—
398C24—21no—
399C24—21no—
400C24—24no—
401C24—42no—
402C24—42no—
403C24—42no—
404C24C22⋊C4×C14911yescharacteristic
405C24C22⋊C4×C14912yes—
406C24C22⋊C4×C14911yescharacteristic
407C24C22×C4×C14912yes—
408C24C22×C4×C14911yescharacteristic
409C24C22×C4×C14912yes—
410C2×D4—24no—
411C2×D4—24no—
412C2×D4—48no—
413C2×D4—44no—
414C2×D4—44no—
415C2×D4—48no—
416C22×C4—24no—
417C22×C4—24no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—24no—
425C22×C4—42no—
426C22×C4—44no—
427C22×C4—44no—
428C22×C4—42no—
429C22×C4—42no—
430C22×C4—44no—
431C22×C4—42no—
432C22×C4—44no—
433C22×C4—42no—
434C22×C4—42no—
435C22×C4C22⋊C4×C14911yescharacteristic
436C22×C4C22⋊C4×C14911yescharacteristic
437C22×C4C22⋊C4×C14912yes—
438C22×C4C22⋊C4×C14912yes—
439C22×C4C22⋊C4×C14912yes—
440C22×C4C22⋊C4×C14912yes—
441C22×C4C22⋊C4×C14912yes—
442C22×C4C22×C4×C14912yes—
443C22×C4C22×C4×C14912yes—
444C22×C4C22×C4×C14912yes—
445C22×C4C22×C4×C14912yes—
446C22×C4C22×C4×C14911yescharacteristic
447C22×C4C2×D4×C14911yescharacteristic
448C22×C4C2×D4×C14911yescharacteristic
449C22×C4C2×D4×C14912yes—
450C22×C4C2×D4×C14912yes—
451C22×C4C2×D4×C14911yescharacteristic
452C22×C4C2×D4×C14911yescharacteristic
453C22×C4C2×D4×C14912yes—
454C22×C4C2×D4×C14912yes—
455C22×C4C24×C14911yescharacteristic
456M16—48no—
457C2×C8—24no—
458C2×C8—24no—
459C2×C8—44no—
460C2×C8—48no—
461C2×C8—44no—
462C4⋊C4—24no—
463C4⋊C4—24no—
464C4⋊C4—22no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—22no—
468C22⋊C4—24no—
469C22⋊C4—24no—
470C22⋊C4—24no—
471C22⋊C4—24no—
472C22⋊C4—22no—
473C22⋊C4—22no—
474C22⋊C4—22no—
475C22⋊C4—22no—
476C23—22no—
477C23—22no—
478C23—22no—
479C23—22no—
480C23—24no—
481C23—22no—
482C23—24no—
483C23—22no—
484C23—24no—
485C23—22no—
486C23—24no—
487C23—22no—
488C23—24no—
489C23—42no—
490C23—42no—
491C23—416no—
492C23—42no—
493C23—42no—
494C23—42no—
495C23—42no—
496C23—42no—
497C23—42no—
498C23—42no—
499C23—42no—
500C23—88no—
501C23#99×C14914yes—
502C23C2×C22⋊C4×C14912yes—
503C23C2×C22⋊C4×C14911yescharacteristic
504C23C2×C22⋊C4×C14912yes—
505C23C2×C22⋊C4×C14911yescharacteristic
506C23#131×C14914yes—
507C23C23×C4×C14911yescharacteristic
508D4—48no—
509D4—48no—
510C2×C4—24no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—24no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—24no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—41no—
526C2×C4—42no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—41no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4C2×C22⋊C4×C14912yes—
541C2×C4C2×C22⋊C4×C14912yes—
542C2×C4C2×C22⋊C4×C14911yescharacteristic
543C2×C4C2×C22⋊C4×C14911yescharacteristic
544C2×C4C22×D4×C14911yescharacteristic
545C2×C4C22×D4×C14911yescharacteristic
546C8—44no—
547C8—44no—
548C22—28no—
549C22—28no—
550C22—22no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—21no—
555C22—22no—
556C22—22no—
557C22—22no—
558C22—22no—
559C22—48no—
560C22—48no—
561C22—44no—
562C22—42no—
563C22—42no—
564C22—42no—
565C22—84no—
566C22—84no—
567C22—84no—
568C22#408×C14912yes—
569C22#408×C14912yes—
570C22C2×#99×C14914yes—
571C22C2×#99×C14912yes—
572C22#413×C14912yes—
573C22C22×C22⋊C4×C14911yescharacteristic
574C22C2×#131×C14912yes—
575C4—21no—
576C4—21no—
577C4—22no—
578C4—21no—
579C4—21no—
580C4—22no—
581C4—42no—
582C4—42no—
583C4—42no—
584C2—22no—
585C2—22no—
586C2—24no—
587C2—42no—
588C2—82no—
589C2#1468×C14914yesdirect product factor
590C2C2×#408×C14911yescharacteristic
591C2C22×#99×C14911yescharacteristic
592C2C2×#413×C14911yescharacteristic
subgroupG/H
center, socleC23×C149C2×C22⋊C4
commutatorC23C23×C4×C149
Frattini, cosocleC22×C4C24×C149
prime radicalC23×D4×C149C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C149 ◁ C24×C4×C149 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#407×C149C2semidirect
3. C22×C22⋊C8×C149C2semidirect
4. #1468×C149C2direct (N × H)
5. C2×#324×C149C2semidirect
6. C2×#323×C149C2semidirect
25. #407×C149C22semidirect
31. C2×C22⋊C8×C149C22semidirect
32. #324×C149C22semidirect
33. #323×C149C22semidirect
292. C2×C149#1468direct (N × H)
296. C2×#1468C149direct (N × H)
297. C149C2×#1468direct (N × H)
299. C2×#407C2×C149semidirect
300. C22×C22⋊C8C2×C149semidirect
301. #1468C2×C149direct (N × H)
302. C2×#324C2×C149semidirect
303. C2×#323C2×C149semidirect
322. #407C22×C149semidirect
328. C2×C22⋊C8C22×C149semidirect
329. #324C22×C149semidirect
330. #323C22×C149semidirect
589. C2#1468×C149direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#123×C1492
C2×#407×C1492
C22×C22⋊C8×C1492
#1468×C1492
C2×#324×C1492
C2×#323×C1492
C2×#1468149