Finite Group Databasebeta

← C2×#21455320 #30546896

Subgroups — C2×#21455320 #30546896

Order 15616.

3074 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519804C211yesmaximal, characteristic, complemented
2C22×D8×D61C211yesmaximal, characteristic, complemented
3C2×#16840330C211yesmaximal, characteristic, complemented
4C2×#16840234C211yesmaximal, characteristic, complemented
5#21455320C2116yesmaximal, direct product factor
6C2×#16839980C211yesmaximal, characteristic, complemented
7C2×#16839979C211yesmaximal, characteristic, complemented
8C2×#16839974C211yesmaximal, characteristic, complemented
9C2×#16839958C211yesmaximal, characteristic, complemented
10C2×#16839957C211yesmaximal, characteristic, complemented
11C2×#16839956C211yesmaximal, characteristic, complemented
12C2×#16839955C211yesmaximal, characteristic, complemented
13C2×#16839787C211yesmaximal, characteristic, complemented
14C2×#16839765C211yesmaximal, characteristic, complemented
15C2×#16839757C211yesmaximal, characteristic, complemented
16C2×C61×#463C211yesmaximal, characteristic, complemented
17C22×#11758226C2211yescharacteristic
18C22×D4×D61C2211yescharacteristic
19C22×D4×D61C2211yescharacteristic
20C2×#14519804—28no—
21C2×#14519804C2218yescomplemented
22C22×#11758201C2211yescharacteristic, complemented
23C22×D488C2211yescharacteristic
24C22×D488C2211yescharacteristic, complemented
25C22×#11758199C2211yescharacteristic
26C22×#11758199C2211yescharacteristic
27C22×#11758199C2211yescharacteristic, complemented
28C2×D8×D61—28no—
29C2×D8×D61C2218yescomplemented
30C22×#11758189C2211yescharacteristic
31C22×C8×D61C2211yescharacteristic
32#16840330—24no—
33#16840330C2218yescomplemented
34C2×#14519774C2211yescharacteristic, complemented
35C2×#14519773C2211yescharacteristic, complemented
36C2×#14519766C2211yescharacteristic, complemented
37C2×#14519750—21no—
38C2×#14519750—21no—
39C2×#14519747—21no—
40C2×#14519747—21no—
41#16840234—24no—
42#16840234C2218yescomplemented
43C2×C4×D244C2211yescharacteristic, complemented
44C2×D4×Dic61C2211yescharacteristic, complemented
45C2×#14519739C2211yescharacteristic, complemented
46C2×C4×C22⋊D61—21no—
47C2×#14519737—21no—
48C2×#14519735C2211yescharacteristic
49C2×#14519734C2211yescharacteristic
50C22×#11758198—21no—
51C2×C22⋊C4×D61—21no—
52#16839980C2218yescomplemented
53#16839979C2218yescomplemented
54#16839974C2218yescomplemented
55#16839958C2218yescomplemented
56#16839957C2218yescomplemented
57#16839956C2218yescomplemented
58#16839955C2218yescomplemented
59#16839787C2218yescomplemented
60C2×C4⋊#92418C2211yescharacteristic, complemented
61C2×#14519706C2211yescharacteristic, complemented
62C2×#14519706C2211yescharacteristic, complemented
63#16839765C2218yescomplemented
64#16839757C2218yescomplemented
65C2×#14519701C2211yescharacteristic, complemented
66C2×#14519699C2211yescharacteristic, complemented
67C2×#14519699C2211yescharacteristic, complemented
68C2×#14519698C2211yescharacteristic, complemented
69C2×#14519697C2211yescharacteristic, complemented
70C2×#14519697C2211yescharacteristic, complemented
71C22×SD16×C61C2211yescharacteristic, complemented
72C22×D8×C61C2211yescharacteristic
73C2×#124×C61C2211yescharacteristic, complemented
74C2×C4×D4×C61C2211yescharacteristic, complemented
75C61×#463C2218yescomplemented
76C2×C4⋊C8×C61C2211yescharacteristic, complemented
77C2×#103×C61C2211yescharacteristic, complemented
78C2×#102×C61C2211yescharacteristic, complemented
79C24×D61—21no—
80C24×D61—21no—
81C2×#11758226—22no—
82C2×#11758226—24no—
83C2×#11758226—24no—
84C2×#11758226C2314yes—
85C22×D244—21no—
86C22×D244—21no—
87C22×D244—21no—
88C22×D244C2311yescharacteristic
89C22×D244C2311yescharacteristic
90C22×D244C2311yescharacteristic
91C22×C22⋊D61—21no—
92C22×C22⋊D61—21no—
93C22×C22⋊D61—21no—
94C22×C22⋊D61—21no—
95C2×D4×D61—22no—
96C2×D4×D61—24no—
97C2×D4×D61—22no—
98C2×D4×D61—24no—
99C2×D4×D61—24no—
100C2×D4×D61D418yescomplemented
101C2×D4×D61C2314yes—
102C2×D4×D61C2314yes—
103C23×Dic61—21no—
104C22×C4×D61—21no—
105C22×C4×D61—21no—
106C22×C4×D61—21no—
107C22×C4×D61C2311yescharacteristic
108#14519804—232no—
109C2×#11758201—24no—
110C2×#11758201C2314yescomplemented
111C2×D488—24no—
112C2×D488—24no—
113C2×D488C2314yes—
114C2×D488C2314yescomplemented
115C2×#11758199—24no—
116C2×#11758199—24no—
117C2×#11758199—24no—
118C2×#11758199C2314yes—
119C2×#11758199C2314yes—
120C2×#11758199C2314yescomplemented
121D8×D61—232no—
122C2×#11758189—24no—
123C2×#11758189C2314yes—
124C22×#92418C2311yescharacteristic
125C22×#92418C2311yescharacteristic
126C2×C8×D61—24no—
127C2×C8×D61C2314yes—
128#14519774—22no—
129#14519774C2314yescomplemented
130#14519773—22no—
131#14519773C2314yescomplemented
132#14519766—22no—
133#14519766C2314yescomplemented
134#14519750—28no—
135#14519750—28no—
136#14519747—28no—
137#14519747—28no—
138C4×D244—22no—
139C4×D244C2314yescomplemented
140D4×Dic61—22no—
141D4×Dic61C2314yescomplemented
142#14519739—22no—
143#14519739C2314yescomplemented
144C4×C22⋊D61—28no—
145#14519737—28no—
146#14519735—22no—
147#14519735C2314yes—
148#14519734D414yes—
149#14519734C2314yes—
150C2×C4⋊Dic61C2311yescharacteristic
151C2×#11758196D411yescharacteristic
152C2×#11758196D411yescharacteristic
153C2×C22⋊Dic61—21no—
154C2×#11758198—21no—
155C2×#11758198—21no—
156C2×#11758198—21no—
157C2×#11758198—21no—
158C2×#11758198—21no—
159C2×#11758198—28no—
160C2×#11758198D411yescharacteristic
161C2×#11758198D411yescharacteristic
162C22⋊C4×D61—28no—
163C2×C4×Dic61—21no—
164C2×C4×Dic61C2311yescharacteristic
165C4⋊#92418C2314yescomplemented
166#14519706C2314yescomplemented
167#14519706C2314yescomplemented
168#14519701C2314yescomplemented
169#14519699C2314yescomplemented
170#14519699C2314yescomplemented
171#14519698C2314yescomplemented
172#14519697C2314yescomplemented
173#14519697C2314yescomplemented
174C22×Q8×C61C2311yescharacteristic
175C22×D4×C61C2311yescharacteristic
176C22×D4×C61C2311yescharacteristic
177C23×C4×C61—21no—
178C2×SD16×C61—24no—
179C2×SD16×C61C2314yescomplemented
180C2×D8×C61—24no—
181C2×D8×C61C2314yes—
182C22×C8×C61C2311yescharacteristic
183C22×C8×C61C2311yescharacteristic
184#124×C61—22no—
185#124×C61C2314yescomplemented
186C4×D4×C61—22no—
187C4×D4×C61C2314yescomplemented
188C2×C4⋊C4×C61C2311yescharacteristic
189C2×C22⋊C4×C61—21no—
190C2×C22⋊C4×C61—21no—
191C2×C22⋊C4×C61—21no—
192C2×C42×C61C2311yescharacteristic
193C4⋊C8×C61C2314yescomplemented
194#103×C61C2314yescomplemented
195#102×C61C2314yescomplemented
196C24×C61—21no—
197C24×C61—21no—
198C23×D61—21no—
199C23×D61—28no—
200C23×D61—24no—
201C23×D61—21no—
202C23×D61—21no—
203C23×D61—24no—
204C23×D61—44no—
205C23×D61—82no—
206C23×D61—82no—
207C23×D61—82no—
208C23×D61—82no—
209C23×D61C2×D411yescharacteristic
210C2×Q8×C61—21no—
211C2×Q8×C61—22no—
212C2×Q8×C61—22no—
213C2×Q8×C61C2412yes—
214C2×D4×C61—21no—
215C2×D4×C61—22no—
216C2×D4×C61—21no—
217C2×D4×C61—22no—
218C2×D4×C61—22no—
219C2×D4×C61C2×D414yes—
220C2×D4×C61C2412yes—
221C2×D4×C61C2412yes—
222C22×C4×C61—21no—
223C22×C4×C61—21no—
224C22×C4×C61—24no—
225C22×C4×C61—82no—
226C22×C4×C61C2×D411yescharacteristic
227C22×C4×C61C2×D411yescharacteristic
228C22×C4×C61C2411yescharacteristic
229C2×C22⋊D61—28no—
230C2×C22⋊D61—24no—
231C2×C22⋊D61—24no—
232C2×C22⋊D61—24no—
233C2×C22⋊D61—24no—
234C2×C22⋊D61—44no—
235C2×C22⋊D61—82no—
236C2×C22⋊D61—82no—
237C22×Dic61—21no—
238C22×Dic61—24no—
239C22×Dic61—82no—
240C22×Dic61C2×D411yescharacteristic
241C22×Dic61C2×D411yescharacteristic
242C22×Dic61C2×D411yescharacteristic
243#11758226—28no—
244#11758226—28no—
245#11758226—48no—
246D4×D61—216no—
247D4×D61—28no—
248D4×D61—28no—
249D4×D61—28no—
250D4×D61—48no—
251D4×D61C2×D4116yescomplemented
252C2×D244—21no—
253C2×D244—22no—
254C2×D244—22no—
255C2×D244—22no—
256C2×D244—22no—
257C2×D244—22no—
258C2×D244—24no—
259C2×D244—21no—
260C2×D244—21no—
261C2×D244—24no—
262C2×D244—24no—
263C2×D244—44no—
264C2×D244—82no—
265C2×D244—82no—
266C2×D244C2×D414yes—
267C2×D244C2412yes—
268C2×D244C2412yes—
269C2×D244C2412yes—
270C2×C4×D61—24no—
271C2×C4×D61—24no—
272C2×C4×D61—24no—
273C2×C4×D61—44no—
274C2×C4×D61—82no—
275C2×C4×D61—82no—
276C2×C4×D61C2×D412yes—
277C2×C4×D61C2×D414yes—
278C2×C4×D61#4114yes—
279C2×C4×D61C2412yes—
280SD16×C61—28no—
281D8×C61—28no—
282C2×C8×C61—22no—
283C2×C8×C61—22no—
284C2×C8×C61C2412yes—
285C2×C8×C61C2412yes—
286C4⋊C4×C61—21no—
287C4⋊C4×C61C2412yes—
288C22⋊C4×C61—24no—
289C22⋊C4×C61—24no—
290C22⋊C4×C61—24no—
291C42×C61C2×D412yes—
292C42×C61C2412yes—
293C22⋊Dic61—24no—
294#11758201—28no—
295#11758199—28no—
296#11758199—28no—
297#11758199—28no—
298#11758198—24no—
299#11758198—24no—
300#11758198—24no—
301#11758198—24no—
302#11758198—24no—
303#11758198C2×D414yes—
304#11758198C2×D414yes—
305C4⋊Dic61—21no—
306C4⋊Dic61C2412yes—
307#11758196C2×D414yes—
308#11758196C2×D414yes—
309C4×Dic61—24no—
310C4×Dic61C2×D412yes—
311C4×Dic61C2412yes—
312C2×#92418—22no—
313C2×#92418—22no—
314C2×#92418C2412yes—
315C2×#92418C2412yes—
316D488—28no—
317D488—28no—
318#11758189—28no—
319C8×D61—28no—
320C23×C61—24no—
321C23×C61—22no—
322C23×C61—22no—
323C23×C61—42no—
324C23×C61—42no—
325C23×C61—42no—
326C23×C61—42no—
327C23×C61—42no—
328C23×C61C22×D411yescharacteristic
329C22×D61—22no—
330C22×D61—22no—
331C22×D61—24no—
332C22×D61—22no—
333C22×D61—216no—
334C22×D61—22no—
335C22×D61—22no—
336C22×D61—42no—
337C22×D61—42no—
338C22×D61—42no—
339C22×D61—42no—
340C22×D61—42no—
341C22×D61—42no—
342C22×D61—42no—
343C22×D61—42no—
344C22×D61—48no—
345C22×D61—816no—
346C22×D61—84no—
347C22×D61—84no—
348C22×D61—84no—
349C22×D61—84no—
350C22×D61—816no—
351C22×D61#12114yes—
352C22×D61C22×D412yes—
353Q8×C61—22no—
354Q8×C61—22no—
355Q8×C61—42no—
356D4×C61—24no—
357D4×C61—22no—
358D4×C61—22no—
359D4×C61—22no—
360D4×C61—42no—
361D4×C61C22×D414yes—
362C2×C4×C61—22no—
363C2×C4×C61—22no—
364C2×C4×C61—22no—
365C2×C4×C61—22no—
366C2×C4×C61—42no—
367C2×C4×C61—42no—
368C2×C4×C61—84no—
369C2×C4×C61C22×D412yes—
370C2×C4×C61C22×D412yes—
371C2×C4×C61C22×D411yescharacteristic
372C2×C4×C61C22×D412yes—
373C2×C4×C61C2×#4112yes—
374C2×C4×C61C2511yescharacteristic
375C22⋊D61—216no—
376C22⋊D61—48no—
377C22⋊D61—84no—
378C22⋊D61—84no—
379C2×Dic61—22no—
380C2×Dic61—22no—
381C2×Dic61—22no—
382C2×Dic61—42no—
383C2×Dic61—84no—
384C2×Dic61#12114yes—
385C2×Dic61C22×D412yes—
386C2×Dic61C22×D412yes—
387C2×Dic61C22×D412yes—
388D244—24no—
389D244—22no—
390D244—22no—
391D244—22no—
392D244—22no—
393D244—22no—
394D244—48no—
395D244—42no—
396D244—42no—
397D244—84no—
398D244—84no—
399D244C22×D414yes—
400C4×D61—48no—
401C4×D61—84no—
402C4×D61—84no—
403C4×D61#12118yes—
404C4×D61C22×D414yes—
405C4×D61C2×#4114yes—
406C8×C61—22no—
407C8×C61—22no—
408#92418—22no—
409#92418—22no—
410C2×#3041—611nomaximal, Sylow
411C22×C61—24no—
412C22×C61—48no—
413C22×C61—42no—
414C22×C61—42no—
415C22×C61—42no—
416C22×C61—42no—
417C22×C61—42no—
418C22×C61—84no—
419C22×C61C2×#12112yes—
420C22×C61#57612yes—
421C22×C61#57612yes—
422C22×C61C23×D411yescharacteristic
423C2×D61—28no—
424C2×D61—22no—
425C2×D61—22no—
426C2×D61—24no—
427C2×D61—48no—
428C2×D61—42no—
429C2×D61—42no—
430C2×D61—42no—
431C2×D61—42no—
432C2×D61—42no—
433C2×D61—42no—
434C2×D61—42no—
435C2×D61—42no—
436C2×D61—816no—
437C2×D61—816no—
438C2×D61—84no—
439C2×D61—84no—
440C2×D61C2×#12114yes—
441C4×C61—22no—
442C4×C61—22no—
443C4×C61—42no—
444C4×C61—42no—
445C4×C61C2×#12112yes—
446C4×C61C23×D411yescharacteristic
447C4×C61C22×#4111yescharacteristic
448Dic61—22no—
449Dic61—22no—
450Dic61—42no—
451Dic61C2×#12114yes—
452C22×AGL(1,ℤ/8)—611no—
453C23×D8—611no—
454C2×#535—611no—
455C2×#518—611no—
456#3041—6116no—
457C2×#463—611no—
458C2×#463—611no—
459C2×#463—611no—
460C2×#463D6111yescharacteristic, complemented
461C2×#459—611no—
462C2×#459—611no—
463C2×#459—611no—
464C2×#459—611no—
465C2×#424—611no—
466C2×#418—611no—
467C2×#416—611no—
468C2×C61—44no—
469C2×C61—82no—
470C2×C61#304114yescomplemented
471C2×C61C22×#12111yescharacteristic
472C2×C61C2×#57611yescharacteristic
473C2×C61C2×#57611yescharacteristic
474D61—24no—
475D61—44no—
476D61—82no—
477D61—82no—
478C22×#41—611no—
479C23×D4—611no—
480C23×D4—611no—
481C2×AGL(1,ℤ/8)—618no—
482C2×AGL(1,ℤ/8)—1228no—
483C22×SD16—611no—
484C22×SD16C2×D6111yescharacteristic, complemented
485C22×D8—611no—
486C22×D8—611no—
487C22×D8—611no—
488C22×D8—618no—
489C22×D8—611no—
490C22×D8—611no—
491C22×D8—1228no—
492C22×D8C2×D6111yescharacteristic
493C22×M16—611no—
494C23×C8—611no—
495#535—618no—
496#535—1224no—
497C2×#127—611no—
498C2×#127—611no—
499C2×#124—611no—
500C2×#124C2×D6111yescharacteristic, complemented
501C2×#121—1221no—
502C2×#121—1221no—
503C2×#120—1221no—
504C2×#120—1221no—
505#518—618no—
506#518—1224no—
507C2×C4×D4—611no—
508C2×C4×D4—611no—
509C2×C4×D4—611no—
510C2×C4×D4—1221no—
511C2×C4×D4—1221no—
512C2×C4×D4C2×D6111yescharacteristic, complemented
513C2×#117—611no—
514C2×#117—611no—
515C22×C22⋊C4—1221no—
516C22×C22⋊C4—1221no—
517#463—618no—
518#463—618no—
519#463—618no—
520#463C2×D6118yescomplemented
521#459—618no—
522#459—618no—
523#459—618no—
524#459—618no—
525#424—618no—
526C2×C4⋊C8—611no—
527C2×C4⋊C8—611no—
528C2×C4⋊C8—611no—
529C2×C4⋊C8C2×D6111yescharacteristic, complemented
530#418—618no—
531#416—618no—
532C2×#103—611no—
533C2×#103C2×D6111yescharacteristic, complemented
534C2×#102—611no—
535C2×#102—611no—
536C2×#102—611no—
537C2×#102—611no—
538C2×#102—611no—
539C2×#102C2×D6111yescharacteristic, complemented
540C61C2×#304111yescharacteristic, complemented, Sylow
541C25—1221no—
542C25—1221no—
543C2×#41—614no—
544C2×#41—1222no—
545C2×#41—1224no—
546C2×#41—1224no—
547C22×Q8C22×D6111yescharacteristic
548C22×D4—618no—
549C22×D4—614no—
550C22×D4—614no—
551C22×D4—611no—
552C22×D4—611no—
553C22×D4—611no—
554C22×D4—1221no—
555C22×D4—1222no—
556C22×D4—1224no—
557C22×D4—1224no—
558C22×D4—1224no—
559C22×D4—1222no—
560C22×D4—1221no—
561C22×D4—1221no—
562C22×D4—1221no—
563C22×D4—1221no—
564C22×D4—1221no—
565C22×D4—1221no—
566C22×D4C22×D6111yescharacteristic
567C22×D4C22×D6111yescharacteristic
568C23×C4—21no—
569C23×C4—611no—
570C23×C4—1221no—
571C23×C4—1221no—
572C23×C4—1221no—
573C23×C4—1221no—
574AGL(1,ℤ/8)—12232no—
575C2×SD16—24no—
576C2×SD16—614no—
577C2×SD16—1224no—
578C2×SD16C22×D6114yescomplemented
579C2×D8—24no—
580C2×D8—614no—
581C2×D8—614no—
582C2×D8—614no—
583C2×D8—614no—
584C2×D8—614no—
585C2×D8—1224no—
586C2×D8—1224no—
587C2×D8—12232no—
588C2×D8—1224no—
589C2×D8—1224no—
590C2×D8—1224no—
591C2×D8C22×D6114yes—
592C2×M16—614no—
593C2×M16—1224no—
594C22×C8—611no—
595C22×C8—611no—
596C22×C8—614no—
597C22×C8—1224no—
598C22×C8C22×D6111yescharacteristic
599C22×C8C22×D6111yescharacteristic
600#127—614no—
601#127—614no—
602#127—1222no—
603#127—1222no—
604#124—22no—
605#124—614no—
606#124—1222no—
607#124C22×D6114yescomplemented
608#121—1228no—
609#121—1228no—
610#120—1228no—
611#120—1228no—
612C4×D4—22no—
613C4×D4—614no—
614C4×D4—614no—
615C4×D4—614no—
616C4×D4—1222no—
617C4×D4—1222no—
618C4×D4—1228no—
619C4×D4—1228no—
620C4×D4—1222no—
621C4×D4C22×D6114yescomplemented
622#117—614no—
623#117—614no—
624#117—614no—
625#117—1222no—
626C2×C4⋊C4—611no—
627C2×C4⋊C4—611no—
628C2×C4⋊C4—611no—
629C2×C4⋊C4C22×D6111yescharacteristic
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—611no—
634C2×C22⋊C4—611no—
635C2×C22⋊C4—1228no—
636C2×C22⋊C4—1228no—
637C2×C22⋊C4—1221no—
638C2×C22⋊C4—1221no—
639C2×C22⋊C4—1221no—
640C2×C22⋊C4—1221no—
641C2×C22⋊C4—1221no—
642C2×C22⋊C4—1221no—
643C2×C42—611no—
644C2×C42—1221no—
645C2×C42C22×D6111yescharacteristic
646C4⋊C8—614no—
647C4⋊C8—614no—
648C4⋊C8—614no—
649C4⋊C8C22×D6114yescomplemented
650#103—614no—
651#103C22×D6114yescomplemented
652#102—614no—
653#102—614no—
654#102—614no—
655#102—614no—
656#102—614no—
657#102C22×D6114yescomplemented
658C24—21no—
659C24—21no—
660C24—611no—
661C24—1224no—
662C24—1228no—
663C24—1224no—
664C24—1221no—
665C24—1221no—
666C24—1221no—
667C24—4882no—
668C24—4882no—
669C24—4882no—
670C24—4882no—
671C24—2444no—
672#41—1228no—
673#41—1228no—
674#41—2448no—
675C2×Q8—21no—
676C2×Q8—22no—
677C2×Q8—22no—
678C2×Q8C23×D6112yes—
679C2×D4—21no—
680C2×D4—22no—
681C2×D4—21no—
682C2×D4—22no—
683C2×D4—22no—
684C2×D4—6116no—
685C2×D4—614no—
686C2×D4—612no—
687C2×D4—612no—
688C2×D4—612no—
689C2×D4—1224no—
690C2×D4—12216no—
691C2×D4—1228no—
692C2×D4—1228no—
693C2×D4—1228no—
694C2×D4—1224no—
695C2×D4—1228no—
696C2×D4—1224no—
697C2×D4—1224no—
698C2×D4—1224no—
699C2×D4—1221no—
700C2×D4—1222no—
701C2×D4—1222no—
702C2×D4—1224no—
703C2×D4—1224no—
704C2×D4—1221no—
705C2×D4—1221no—
706C2×D4—1222no—
707C2×D4—1222no—
708C2×D4—1222no—
709C2×D4—4882no—
710C2×D4—4882no—
711C2×D4—4882no—
712C2×D4—4882no—
713C2×D4—2444no—
714C2×D4—2448no—
715C2×D4—2444no—
716C2×D4D4×D6114yes—
717C2×D4C23×D6112yes—
718C2×D4C23×D6112yes—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—24no—
722C22×C4—82no—
723C22×C4—611no—
724C22×C4—612no—
725C22×C4—614no—
726C22×C4—614no—
727C22×C4—612no—
728C22×C4—611no—
729C22×C4—611no—
730C22×C4—1224no—
731C22×C4—1224no—
732C22×C4—1224no—
733C22×C4—1221no—
734C22×C4—1224no—
735C22×C4—4882no—
736C22×C4—4882no—
737C22×C4—4882no—
738C22×C4—2444no—
739C22×C4D4×D6111yescharacteristic
740C22×C4D4×D6111yescharacteristic
741C22×C4C23×D6111yescharacteristic
742SD16—28no—
743SD16—1228no—
744D8—28no—
745D8—1228no—
746D8—1228no—
747D8—1228no—
748D8—1228no—
749D8—1228no—
750M16—1228no—
751C2×C8—22no—
752C2×C8—22no—
753C2×C8—612no—
754C2×C8—612no—
755C2×C8—1228no—
756C2×C8—1222no—
757C2×C8—1222no—
758C2×C8C23×D6112yes—
759C2×C8C23×D6112yes—
760C4⋊C4—21no—
761C4⋊C4—614no—
762C4⋊C4—614no—
763C4⋊C4—612no—
764C4⋊C4—1221no—
765C4⋊C4C23×D6112yes—
766C22⋊C4—24no—
767C22⋊C4—24no—
768C22⋊C4—24no—
769C22⋊C4—614no—
770C22⋊C4—614no—
771C22⋊C4—1224no—
772C22⋊C4—1224no—
773C22⋊C4—1224no—
774C22⋊C4—1224no—
775C22⋊C4—1224no—
776C22⋊C4—1224no—
777C42—612no—
778C42—612no—
779C42—1224no—
780C42D4×D6112yes—
781C42C23×D6112yes—
782C23—24no—
783C23—22no—
784C23—22no—
785C23—42no—
786C23—42no—
787C23—42no—
788C23—42no—
789C23—42no—
790C23—614no—
791C23—612no—
792C23—12216no—
793C23—1222no—
794C23—1222no—
795C23—1224no—
796C23—1222no—
797C23—1222no—
798C23—1222no—
799C23—4884no—
800C23—4884no—
801C23—48816no—
802C23—4884no—
803C23—4884no—
804C23—48816no—
805C23—2448no—
806C23—2442no—
807C23—2442no—
808C23—2442no—
809C23—2442no—
810C23—2442no—
811C23—2442no—
812C23—2442no—
813C23—2442no—
814C23C2×D4×D6111yescharacteristic
815Q8—22no—
816Q8—22no—
817Q8—42no—
818D4—24no—
819D4—22no—
820D4—22no—
821D4—22no—
822D4—42no—
823D4—614no—
824D4—12216no—
825D4—1224no—
826D4—1222no—
827D4—1222no—
828D4—1222no—
829D4—1222no—
830D4—1222no—
831D4—4884no—
832D4—4884no—
833D4—4884no—
834D4—4884no—
835D4—2448no—
836D4—2448no—
837D4—2442no—
838D4—2442no—
839D4C2×D4×D6114yes—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—84no—
847C2×C4—614no—
848C2×C4—612no—
849C2×C4—618no—
850C2×C4—614no—
851C2×C4—614no—
852C2×C4—612no—
853C2×C4—612no—
854C2×C4—1222no—
855C2×C4—1222no—
856C2×C4—1222no—
857C2×C4—4884no—
858C2×C4—4884no—
859C2×C4—4884no—
860C2×C4—2448no—
861C2×C4—2442no—
862C2×C4C2×D4×D6112yes—
863C2×C4C2×D4×D6112yes—
864C2×C4C2×D4×D6111yescharacteristic
865C2×C4C2×D4×D6112yes—
866C2×C4#41×D6112yes—
867C2×C4C24×D6111yescharacteristic
868C8—22no—
869C8—22no—
870C8—1222no—
871C8—1222no—
872C22—24no—
873C22—42no—
874C22—42no—
875C22—48no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—84no—
880C22—614no—
881C22—1222no—
882C22—1222no—
883C22—1228no—
884C22—1224no—
885C22—48816no—
886C22—48816no—
887C22—4884no—
888C22—4884no—
889C22—2442no—
890C22—2442no—
891C22—2442no—
892C22—2442no—
893C22—2442no—
894C22—2442no—
895C22—2442no—
896C22—2442no—
897C22—2448no—
898C22#121×D6112yes—
899C22#1684056412yes—
900C22#1684056612yes—
901C22C22×D4×D6111yescharacteristic
902C4—22no—
903C4—22no—
904C4—42no—
905C4—42no—
906C4—614no—
907C4—1222no—
908C4—1222no—
909C4—2442no—
910C4#121×D6112yes—
911C4C22×D4×D6111yescharacteristic
912C4C2×#41×D6111yescharacteristic
913C2—44no—
914C2—82no—
915C2—1224no—
916C2—4882no—
917C2—4882no—
918C2—2444no—
919C2#2145532014yesdirect product factor
920C2C2×#121×D6111yescharacteristic
921C2C2×#1684056411yescharacteristic
922C2C2×#1684056611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#463C2
socleC23×C61C22×D4
hypercenterC2×#463D61
hypocenterC61C2×#3041
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. C22×#14519804C2semidirect
2. C22×D8×D61C2semidirect
3. C2×#16840330C2semidirect
4. C2×#16840234C2semidirect
5. #21455320C2direct (N × H)
6. C2×#16839980C2semidirect
7. C2×#16839979C2semidirect
8. C2×#16839974C2semidirect
9. C2×#16839958C2semidirect
10. C2×#16839957C2semidirect
11. C2×#16839956C2semidirect
12. C2×#16839955C2semidirect
13. C2×#16839787C2semidirect
14. C2×#16839765C2semidirect
15. C2×#16839757C2semidirect
16. C2×C61×#463C2semidirect
21. C2×#14519804C22semidirect
22. C22×#11758201C22semidirect
24. C22×D488C22semidirect
27. C22×#11758199C22semidirect
29. C2×D8×D61C22semidirect
33. #16840330C22semidirect
34. C2×#14519774C22semidirect
35. C2×#14519773C22semidirect
36. C2×#14519766C22semidirect
42. #16840234C22semidirect
43. C2×C4×D244C22semidirect
44. C2×D4×Dic61C22semidirect
45. C2×#14519739C22semidirect
52. #16839980C22semidirect
53. #16839979C22semidirect
54. #16839974C22semidirect
55. #16839958C22semidirect
56. #16839957C22semidirect
57. #16839956C22semidirect
58. #16839955C22semidirect
59. #16839787C22semidirect
60. C2×C4⋊#92418C22semidirect
61. C2×#14519706C22semidirect
62. C2×#14519706C22semidirect
63. #16839765C22semidirect
64. #16839757C22semidirect
65. C2×#14519701C22semidirect
66. C2×#14519699C22semidirect
67. C2×#14519699C22semidirect
68. C2×#14519698C22semidirect
69. C2×#14519697C22semidirect
70. C2×#14519697C22semidirect
71. C22×SD16×C61C22semidirect
73. C2×#124×C61C22semidirect
74. C2×C4×D4×C61C22semidirect
75. C61×#463C22semidirect
76. C2×C4⋊C8×C61C22semidirect
77. C2×#103×C61C22semidirect
78. C2×#102×C61C22semidirect
100. C2×D4×D61D4semidirect
110. C2×#11758201C23semidirect
114. C2×D488C23semidirect
120. C2×#11758199C23semidirect
129. #14519774C23semidirect
131. #14519773C23semidirect
133. #14519766C23semidirect
139. C4×D244C23semidirect
141. D4×Dic61C23semidirect
143. #14519739C23semidirect
165. C4⋊#92418C23semidirect
166. #14519706C23semidirect
167. #14519706C23semidirect
168. #14519701C23semidirect
169. #14519699C23semidirect
170. #14519699C23semidirect
171. #14519698C23semidirect
172. #14519697C23semidirect
173. #14519697C23semidirect
179. C2×SD16×C61C23semidirect
185. #124×C61C23semidirect
187. C4×D4×C61C23semidirect
193. C4⋊C8×C61C23semidirect
194. #103×C61C23semidirect
195. #102×C61C23semidirect
251. D4×D61C2×D4semidirect
460. C2×#463D61semidirect
470. C2×C61#3041semidirect
484. C22×SD16C2×D61semidirect
500. C2×#124C2×D61semidirect
512. C2×C4×D4C2×D61semidirect
520. #463C2×D61semidirect
529. C2×C4⋊C8C2×D61semidirect
533. C2×#103C2×D61semidirect
539. C2×#102C2×D61semidirect
540. C61C2×#3041semidirect
578. C2×SD16C22×D61semidirect
607. #124C22×D61semidirect
621. C4×D4C22×D61semidirect
649. C4⋊C8C22×D61semidirect
651. #103C22×D61semidirect
657. #102C22×D61semidirect
919. C2#21455320direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198042
C22×D8×D612
C2×#168403302
C2×#168402342
#214553202
C2×#168399802
C2×#168399792
C2×#168399742
C2×#168399582
C2×#168399572
C2×#168399562
C2×#168399552
C2×#168397872
C2×#168397652
C2×#168397572
C2×C61×#4632
C2×#304161