Finite Group Databasebeta

← C2×#21446884 #29707029

Subgroups — C2×#21446884 #29707029

Order 15616.

2190 conjugacy classes of subgroups.

The subgroup lattice has 1078 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840560C211yesmaximal, characteristic, complemented
2C2×#16840273C211yesmaximal, characteristic, complemented
3C2×#16839780C211yesmaximal, characteristic, complemented
4C2×#16839779C211yesmaximal, characteristic, complemented
5C2×#16839726C211yesmaximal, characteristic, complemented
6#21446884C218yesmaximal, direct product factor
7C2×#16839518C211yesmaximal, characteristic, complemented
8C2×C61×#525C211yesmaximal, characteristic, complemented
9C22×#11758222C2211yescharacteristic
10#16840560—22no—
11#16840560—22no—
12#16840560—22no—
13#16840560C2214yescomplemented
14C2×#14519808—21no—
15C2×#14519807—21no—
16C2×#14519803—21no—
17C2×#14519802—21no—
18C2×#14519797—22no—
19C22×#11758194C2211yescharacteristic
20C22×#11758194C2211yescharacteristic
21#16840273—22no—
22#16840273—22no—
23#16840273—22no—
24#16840273C2214yescomplemented
25C2×#14519760—21no—
26C2×#14519756—21no—
27C2×#14519751—21no—
28C2×#14519746—21no—
29C2×C4×C22⋊D61—22no—
30C2×#14519736C2211yescharacteristic
31#16839780—22no—
32#16839780C2214yescomplemented
33#16839779—22no—
34#16839779C2214yescomplemented
35C2×#14519705—22no—
36C2×#14519704—22no—
37#16839726—22no—
38#16839726C2214yescomplemented
39C2×C22⋊#92418—22no—
40#16839518C2214yescomplemented
41C22×#41×C61C2211yescharacteristic
42C24×C4×C61C2211yescharacteristic
43C61×#525—22no—
44C61×#525—22no—
45C61×#525—22no—
46C61×#525C2214yescomplemented
47C2×#123×C61—21no—
48C2×C22⋊Q8×C61—21no—
49C2×#121×C61—21no—
50C2×#120×C61—21no—
51C2×C4×D4×C61—22no—
52C2×#117×C61C2211yescharacteristic
53C2×#11758222—21no—
54C2×#11758222—21no—
55C2×#11758222—21no—
56C2×#11758222—21no—
57C2×#11758222—21no—
58C2×#11758222—21no—
59C2×#11758222—21no—
60C2×#11758222—21no—
61C2×#11758222—21no—
62C2×#11758222—21no—
63C2×#11758222D412yescomplemented
64C2×#11758222C2312yes—
65C22×Dic122D411yescharacteristic, complemented
66C22×D244D411yescharacteristic, complemented
67C22×C22⋊D61—22no—
68C22×C22⋊D61—21no—
69C22×C4×D61—21no—
70#14519808—24no—
71#14519808—24no—
72#14519807—24no—
73#14519807—24no—
74#14519803—24no—
75#14519803—24no—
76#14519802—24no—
77#14519802—24no—
78#14519797—28no—
79#14519797—28no—
80C2×#11758202—22no—
81C2×#11758200—22no—
82C2×#11758201—22no—
83C2×#11758199—22no—
84C2×#11758194—21no—
85C2×#11758194—21no—
86C2×#11758194—21no—
87C2×#11758194—21no—
88C2×#11758194—21no—
89C2×#11758194—21no—
90C2×#11758194—21no—
91C2×#11758194—21no—
92C2×#11758194—21no—
93C2×#11758194D412yescomplemented
94C2×#11758194C2312yes—
95C2×#11758194C2312yes—
96C22×#92418—21no—
97C22×#92418D412yescomplemented
98#14519760—24no—
99#14519760—24no—
100#14519756—24no—
101#14519756—24no—
102#14519751—24no—
103#14519751—24no—
104#14519746—24no—
105#14519746—24no—
106C4×C22⋊D61—28no—
107C4×C22⋊D61—28no—
108#14519736—21no—
109#14519736—21no—
110#14519736D412yescomplemented
111#14519736C2312yes—
112C2×C4⋊Dic61—21no—
113C2×#11758196—22no—
114C2×C22⋊Dic61—22no—
115C2×C22⋊Dic61—21no—
116C2×#11758198—22no—
117C2×C4×Dic61D412yescomplemented
118#14519705—28no—
119#14519704—28no—
120C22⋊#92418—28no—
121C25×C61D411yescharacteristic
122C2×#41×C61—21no—
123C2×#41×C61—21no—
124C2×#41×C61—21no—
125C2×#41×C61—21no—
126C2×#41×C61—21no—
127C2×#41×C61—21no—
128C2×#41×C61—21no—
129C2×#41×C61—21no—
130C2×#41×C61—21no—
131C2×#41×C61—21no—
132C2×#41×C61D412yescomplemented
133C2×#41×C61C2312yes—
134C22×Q8×C61D411yescharacteristic, complemented
135C22×D4×C61—22no—
136C22×D4×C61—21no—
137C22×D4×C61D411yescharacteristic, complemented
138C23×C4×C61—21no—
139C23×C4×C61—21no—
140C23×C4×C61—21no—
141C23×C4×C61—21no—
142C23×C4×C61—21no—
143C23×C4×C61—21no—
144C23×C4×C61—21no—
145C23×C4×C61—21no—
146C23×C4×C61—21no—
147C23×C4×C61—21no—
148C23×C4×C61—21no—
149C23×C4×C61—21no—
150C23×C4×C61—21no—
151C23×C4×C61D411yescharacteristic
152C23×C4×C61D412yes—
153C23×C4×C61C2312yes—
154C23×C4×C61C2311yescharacteristic
155#123×C61—24no—
156#123×C61—24no—
157C22⋊Q8×C61—24no—
158C22⋊Q8×C61—24no—
159#121×C61—24no—
160#121×C61—24no—
161#120×C61—24no—
162#120×C61—24no—
163C4×D4×C61—28no—
164C4×D4×C61—28no—
165#117×C61—21no—
166#117×C61—21no—
167#117×C61D412yescomplemented
168#117×C61C2312yes—
169C2×C4⋊C4×C61—22no—
170C2×C4⋊C4×C61—21no—
171C2×C22⋊C4×C61—22no—
172C2×C22⋊C4×C61—22no—
173C2×C22⋊C4×C61—21no—
174C2×C42×C61D412yescomplemented
175C24×C61—21no—
176C24×C61—21no—
177C24×C61—21no—
178C24×C61—21no—
179C24×C61—21no—
180C24×C61—21no—
181C24×C61—21no—
182C24×C61—44no—
183C24×C61C2×D412yes—
184C24×C61C2×D411yescharacteristic
185C23×D61—21no—
186#41×C61—22no—
187#41×C61—22no—
188#41×C61—22no—
189#41×C61—22no—
190#41×C61—22no—
191#41×C61—22no—
192#41×C61—22no—
193#41×C61—22no—
194#41×C61—41no—
195#41×C61—41no—
196#41×C61—41no—
197#41×C61—41no—
198#41×C61—41no—
199#41×C61—41no—
200#41×C61—41no—
201#41×C61—41no—
202C2×Q8×C61—21no—
203C2×Q8×C61—21no—
204C2×Q8×C61—21no—
205C2×Q8×C61—21no—
206C2×Q8×C61—21no—
207C2×Q8×C61C2×D412yescomplemented
208C2×D4×C61—28no—
209C2×D4×C61—22no—
210C2×D4×C61—22no—
211C2×D4×C61—21no—
212C2×D4×C61—21no—
213C2×D4×C61—21no—
214C2×D4×C61—21no—
215C2×D4×C61—21no—
216C2×D4×C61—48no—
217C2×D4×C61—41no—
218C2×D4×C61—41no—
219C2×D4×C61—41no—
220C2×D4×C61—41no—
221C2×D4×C61C2×D412yescomplemented
222C22×C4×C61—22no—
223C22×C4×C61—21no—
224C22×C4×C61—21no—
225C22×C4×C61—21no—
226C22×C4×C61—21no—
227C22×C4×C61—21no—
228C22×C4×C61—21no—
229C22×C4×C61—21no—
230C22×C4×C61—22no—
231C22×C4×C61—22no—
232C22×C4×C61—22no—
233C22×C4×C61—22no—
234C22×C4×C61—22no—
235C22×C4×C61—22no—
236C22×C4×C61—22no—
237C22×C4×C61—22no—
238C22×C4×C61—22no—
239C22×C4×C61—22no—
240C22×C4×C61—22no—
241C22×C4×C61—22no—
242C22×C4×C61—22no—
243C22×C4×C61—22no—
244C22×C4×C61—41no—
245C22×C4×C61—41no—
246C22×C4×C61—41no—
247C22×C4×C61—41no—
248C22×C4×C61—41no—
249C22×C4×C61—41no—
250C22×C4×C61—41no—
251C22×C4×C61—41no—
252C22×C4×C61—41no—
253C22×C4×C61—41no—
254C22×C4×C61—41no—
255C22×C4×C61—41no—
256C22×C4×C61—41no—
257C22×C4×C61—41no—
258C22×C4×C61—41no—
259C22×C4×C61—41no—
260C22×C4×C61—41no—
261C22×C4×C61—41no—
262C22×C4×C61—41no—
263C22×C4×C61—41no—
264C22×C4×C61C2×D412yes—
265C22×C4×C61C2×D411yescharacteristic
266C22×C4×C61C2×D411yescharacteristic
267C22×C4×C61C2×D411yescharacteristic
268C22×C4×C61C2×D411yescharacteristic
269C22×C4×C61C2×D411yescharacteristic
270C22×C4×C61C2×D411yescharacteristic
271C22×C4×C61C2×D411yescharacteristic
272C22×C4×C61C2×D411yescharacteristic
273C22×C4×C61C2×D411yescharacteristic
274C22×C4×C61C2×D411yescharacteristic
275C22×C4×C61C2×D411yescharacteristic
276C22×C4×C61#4111yescharacteristic
277C22×C4×C61#4111yescharacteristic
278C22×C4×C61C2411yescharacteristic
279C2×C22⋊D61—28no—
280C2×C22⋊D61—22no—
281C2×C22⋊D61—22no—
282C2×C22⋊D61—48no—
283C2×C22⋊D61—41no—
284C2×C22⋊D61—41no—
285C2×C22⋊D61—41no—
286C2×C22⋊D61—41no—
287C22×Dic61—21no—
288C22×Dic61—22no—
289#11758222—22no—
290#11758222—22no—
291#11758222—22no—
292#11758222—22no—
293#11758222—22no—
294#11758222—22no—
295#11758222—22no—
296#11758222—22no—
297#11758222—41no—
298#11758222—41no—
299#11758222—41no—
300#11758222—41no—
301#11758222—41no—
302#11758222—41no—
303#11758222—41no—
304#11758222—41no—
305C2×D244—21no—
306C2×D244—21no—
307C2×D244—21no—
308C2×D244—21no—
309C2×D244—21no—
310C2×D244C2×D412yescomplemented
311C2×C4×D61—22no—
312C2×C4×D61—22no—
313C2×C4×D61—41no—
314C2×C4×D61—41no—
315C2×C4×D61—41no—
316C2×C4×D61—41no—
317C2×Dic122—21no—
318C2×Dic122—21no—
319C2×Dic122—21no—
320C2×Dic122—21no—
321C2×Dic122—21no—
322C2×Dic122C2×D412yescomplemented
323C4⋊C4×C61—28no—
324C4⋊C4×C61—22no—
325C4⋊C4×C61—22no—
326C22⋊C4×C61—28no—
327C22⋊C4×C61—28no—
328C22⋊C4×C61—22no—
329C22⋊C4×C61—22no—
330C42×C61—22no—
331C42×C61C2×D414yescomplemented
332C22⋊Dic61—28no—
333C22⋊Dic61—22no—
334C22⋊Dic61—22no—
335#11758202—28no—
336#11758201—28no—
337#11758200—28no—
338#11758199—28no—
339#11758198—28no—
340C4⋊Dic61—22no—
341C4⋊Dic61—22no—
342#11758196—28no—
343C4×Dic61—22no—
344C4×Dic61C2×D414yescomplemented
345#11758194—22no—
346#11758194—22no—
347#11758194—22no—
348#11758194—22no—
349#11758194—22no—
350#11758194—22no—
351#11758194—41no—
352#11758194—41no—
353C2×#92418—22no—
354C2×#92418—22no—
355C2×#92418—22no—
356C2×#92418—41no—
357C2×#92418—41no—
358C2×#92418C2×D414yescomplemented
359C23×C61—24no—
360C23×C61—24no—
361C23×C61—24no—
362C23×C61—22no—
363C23×C61—22no—
364C23×C61—22no—
365C23×C61—22no—
366C23×C61—42no—
367C23×C61—44no—
368C23×C61—42no—
369C23×C61—42no—
370C23×C61—42no—
371C23×C61—44no—
372C23×C61—44no—
373C23×C61—44no—
374C23×C61—44no—
375C23×C61—41no—
376C23×C61—41no—
377C23×C61—41no—
378C23×C61—41no—
379C23×C61—41no—
380C23×C61—41no—
381C23×C61#12011yescharacteristic
382C23×C61#12011yescharacteristic
383C23×C61#12011yescharacteristic
384C23×C61#12011yescharacteristic
385C23×C61#12111yescharacteristic
386C23×C61#12111yescharacteristic
387C23×C61C22×D411yescharacteristic
388C22×D61—22no—
389C22×D61—44no—
390C22×D61—41no—
391C22×D61—41no—
392Q8×C61—22no—
393Q8×C61—22no—
394Q8×C61—41no—
395Q8×C61—41no—
396D4×C61—22no—
397D4×C61—22no—
398D4×C61—416no—
399D4×C61—42no—
400D4×C61—42no—
401D4×C61—42no—
402D4×C61—42no—
403D4×C61—41no—
404D4×C61—41no—
405C2×C4×C61—22no—
406C2×C4×C61—24no—
407C2×C4×C61—22no—
408C2×C4×C61—22no—
409C2×C4×C61—22no—
410C2×C4×C61—44no—
411C2×C4×C61—41no—
412C2×C4×C61—41no—
413C2×C4×C61—41no—
414C2×C4×C61—41no—
415C2×C4×C61—41no—
416C2×C4×C61—41no—
417C2×C4×C61—42no—
418C2×C4×C61—42no—
419C2×C4×C61—42no—
420C2×C4×C61—42no—
421C2×C4×C61—42no—
422C2×C4×C61—42no—
423C2×C4×C61—42no—
424C2×C4×C61—42no—
425C2×C4×C61—42no—
426C2×C4×C61—42no—
427C2×C4×C61—42no—
428C2×C4×C61—42no—
429C2×C4×C61#12011yescharacteristic
430C2×C4×C61#12011yescharacteristic
431C2×C4×C61#12011yescharacteristic
432C2×C4×C61#12011yescharacteristic
433C2×C4×C61#12011yescharacteristic
434C2×C4×C61#12011yescharacteristic
435C2×C4×C61#12011yescharacteristic
436C2×C4×C61#12011yescharacteristic
437C2×C4×C61#12111yescharacteristic
438C2×C4×C61#12111yescharacteristic
439C2×C4×C61#12111yescharacteristic
440C2×C4×C61#12111yescharacteristic
441C2×C4×C61#12111yescharacteristic
442C2×C4×C61#12111yescharacteristic
443C2×C4×C61#12111yescharacteristic
444C2×C4×C61#12111yescharacteristic
445C2×C4×C61#12111yescharacteristic
446C2×C4×C61#12111yescharacteristic
447C2×C4×C61#12711yescharacteristic
448C2×C4×C61#12711yescharacteristic
449C2×C4×C61#12711yescharacteristic
450C2×C4×C61#12711yescharacteristic
451C2×C4×C61C22×D411yescharacteristic
452C2×C4×C61C22×D411yescharacteristic
453C2×C4×C61C22×D411yescharacteristic
454C2×C4×C61C22×D411yescharacteristic
455C2×C4×C61C22×D411yescharacteristic
456C2×C4×C61C2×#4111yescharacteristic
457C22⋊D61—416no—
458C22⋊D61—42no—
459C22⋊D61—42no—
460C22⋊D61—42no—
461C22⋊D61—42no—
462C2×Dic61—24no—
463C2×Dic61—22no—
464C2×Dic61—44no—
465C2×Dic61—41no—
466C2×Dic61—41no—
467D244—22no—
468D244—22no—
469D244—41no—
470D244—41no—
471C4×D61—42no—
472C4×D61—42no—
473C4×D61—42no—
474C4×D61—42no—
475Dic122—22no—
476Dic122—22no—
477Dic122—41no—
478Dic122—41no—
479#92418—24no—
480#92418—42no—
481C2×#2010—611nomaximal, Sylow
482C22×C61—22no—
483C22×C61—22no—
484C22×C61—22no—
485C22×C61—24no—
486C22×C61—24no—
487C22×C61—24no—
488C22×C61—41no—
489C22×C61—41no—
490C22×C61—41no—
491C22×C61—41no—
492C22×C61—42no—
493C22×C61—42no—
494C22×C61—44no—
495C22×C61—42no—
496C22×C61—44no—
497C22×C61—44no—
498C22×C61—44no—
499C22×C61—42no—
500C22×C61—44no—
501C22×C61—42no—
502C22×C61—82no—
503C22×C61—82no—
504C22×C61#39211yescharacteristic
505C22×C61#39211yescharacteristic
506C22×C61#39211yescharacteristic
507C22×C61#39211yescharacteristic
508C22×C61C2×#12011yescharacteristic
509C22×C61C2×#12011yescharacteristic
510C22×C61C2×#12111yescharacteristic
511C2×D61—44no—
512C2×D61—42no—
513C2×D61—82no—
514C2×D61—82no—
515C4×C61—44no—
516C4×C61—42no—
517C4×C61—42no—
518C4×C61#39211yescharacteristic
519C4×C61#39211yescharacteristic
520C4×C61#39211yescharacteristic
521C4×C61#39211yescharacteristic
522C4×C61C2×#12011yescharacteristic
523C4×C61C2×#12111yescharacteristic
524C4×C61C2×#12111yescharacteristic
525C4×C61C2×#12711yescharacteristic
526Dic61—44no—
527Dic61—42no—
528C2×#575—611no—
529C2×#525—611no—
530C2×#525D6111yescharacteristic, complemented
531C2×#421—611no—
532C2×#421—611no—
533C2×#407—611no—
534#2010—618no—
535C2×H(3,ℤ/4)—611no—
536C2×C61—21no—
537C2×C61—21no—
538C2×C61—21no—
539C2×C61—21no—
540C2×C61—21no—
541C2×C61—21no—
542C2×C61—44no—
543C2×C61—82no—
544C2×C61#201012yescomplemented
545C2×C61C2×#39211yescharacteristic
546D61—82no—
547C22×#41—611no—
548C22×#41C2×D6111yescharacteristic
549C24×C4C2×D6111yescharacteristic
550#575—614no—
551#575—1222no—
552#575—1222no—
553#575—1222no—
554C2×#137—1221no—
555C2×#137—1221no—
556C2×AGL(1,ℤ/8)—1221no—
557C2×AGL(1,ℤ/8)—1221no—
558C2×#135—1222no—
559C22×M16—611no—
560C22×M16—611no—
561#525—22no—
562#525—22no—
563#525—22no—
564#525—614no—
565#525—1222no—
566#525—1222no—
567#525—1222no—
568#525C2×D6114yescomplemented
569C2×#123—21no—
570C2×#123—1221no—
571C2×C22⋊Q8—21no—
572C2×C22⋊Q8—1221no—
573C2×#121—21no—
574C2×#121—1221no—
575C2×#120—21no—
576C2×#120—1221no—
577C2×C4×D4—22no—
578C2×C4×D4—1222no—
579C2×#117—611no—
580C2×#117C2×D6111yescharacteristic
581#421—614no—
582#421—614no—
583#421—1222no—
584#421—1222no—
585C2×#104—1222no—
586C2×#104—1222no—
587#407—614no—
588#407—1222no—
589C2×C22⋊C8—1222no—
590H(3,ℤ/4)—614no—
591C61C2×#201011yescharacteristic, complemented, Sylow
592C25C22⋊D6111yescharacteristic
593C2×#41—21no—
594C2×#41—21no—
595C2×#41—21no—
596C2×#41—21no—
597C2×#41—21no—
598C2×#41—21no—
599C2×#41—21no—
600C2×#41—21no—
601C2×#41—21no—
602C2×#41—21no—
603C2×#41—612no—
604C2×#41—612no—
605C2×#41—1221no—
606C2×#41—1221no—
607C2×#41—1221no—
608C2×#41—1221no—
609C2×#41—1221no—
610C2×#41—1221no—
611C2×#41—1221no—
612C2×#41—1221no—
613C2×#41—1221no—
614C2×#41—1221no—
615C2×#41C22⋊D6112yescomplemented
616C2×#41C22×D6112yes—
617C22×Q8—611no—
618C22×Q8C22⋊D6111yescharacteristic, complemented
619C22×D4—22no—
620C22×D4—21no—
621C22×D4—611no—
622C22×D4—1222no—
623C22×D4—1221no—
624C22×D4C22⋊D6111yescharacteristic, complemented
625C23×C4—21no—
626C23×C4—21no—
627C23×C4—21no—
628C23×C4—21no—
629C23×C4—21no—
630C23×C4—21no—
631C23×C4—21no—
632C23×C4—21no—
633C23×C4—21no—
634C23×C4—21no—
635C23×C4—21no—
636C23×C4—21no—
637C23×C4—21no—
638C23×C4—1221no—
639C23×C4C22⋊D6111yescharacteristic
640C23×C4C22⋊D6112yes—
641C23×C4C22×D6112yes—
642C23×C4C22×D6111yescharacteristic
643#137—1224no—
644#137—1224no—
645#137—1224no—
646#137—1224no—
647AGL(1,ℤ/8)—1224no—
648AGL(1,ℤ/8)—1224no—
649AGL(1,ℤ/8)—1224no—
650AGL(1,ℤ/8)—1224no—
651#135—1228no—
652#135—1228no—
653C2×Q16—1222no—
654C2×SD16—1222no—
655C2×SD16—1222no—
656C2×D8—1222no—
657C2×M16—612no—
658C2×M16—612no—
659C2×M16—612no—
660C2×M16—1221no—
661C2×M16—1221no—
662C2×M16—1221no—
663C2×M16—1221no—
664C2×M16—1221no—
665C2×M16—1221no—
666C2×M16—1221no—
667C2×M16—1221no—
668C2×M16—1221no—
669C22×C8—612no—
670C22×C8—1221no—
671#123—24no—
672#123—24no—
673#123—1224no—
674#123—1224no—
675C22⋊Q8—24no—
676C22⋊Q8—24no—
677C22⋊Q8—1224no—
678C22⋊Q8—1224no—
679#121—24no—
680#121—24no—
681#121—1224no—
682#121—1224no—
683#120—24no—
684#120—24no—
685#120—1224no—
686#120—1224no—
687C4×D4—28no—
688C4×D4—28no—
689C4×D4—1228no—
690C4×D4—1228no—
691#117—21no—
692#117—21no—
693#117—612no—
694#117—612no—
695#117—1221no—
696#117—1221no—
697#117C22⋊D6112yescomplemented
698#117C22×D6112yes—
699C2×C4⋊C4—22no—
700C2×C4⋊C4—21no—
701C2×C4⋊C4—1222no—
702C2×C4⋊C4—1221no—
703C2×C22⋊C4—22no—
704C2×C22⋊C4—22no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—1222no—
707C2×C22⋊C4—1222no—
708C2×C22⋊C4—1221no—
709C2×C42—612no—
710C2×C42C22⋊D6112yescomplemented
711#104—1228no—
712#104—1228no—
713C22⋊C8—1228no—
714C24—21no—
715C24—21no—
716C24—21no—
717C24—21no—
718C24—21no—
719C24—21no—
720C24—21no—
721C24—44no—
722C24—1221no—
723C24C2×C22⋊D6112yes—
724C24C2×C22⋊D6111yescharacteristic
725#41—22no—
726#41—22no—
727#41—22no—
728#41—22no—
729#41—22no—
730#41—22no—
731#41—22no—
732#41—22no—
733#41—41no—
734#41—41no—
735#41—41no—
736#41—41no—
737#41—41no—
738#41—41no—
739#41—41no—
740#41—41no—
741#41—1222no—
742#41—1222no—
743#41—1222no—
744#41—1222no—
745#41—1222no—
746#41—1222no—
747#41—1222no—
748#41—1222no—
749#41—2441no—
750#41—2441no—
751#41—2441no—
752#41—2441no—
753#41—2441no—
754#41—2441no—
755#41—2441no—
756#41—2441no—
757C2×Q8—21no—
758C2×Q8—21no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—21no—
762C2×Q8—612no—
763C2×Q8—1221no—
764C2×Q8—1221no—
765C2×Q8—1221no—
766C2×Q8—1221no—
767C2×Q8—1221no—
768C2×Q8C2×C22⋊D6112yescomplemented
769C2×D4—28no—
770C2×D4—22no—
771C2×D4—22no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—48no—
778C2×D4—41no—
779C2×D4—41no—
780C2×D4—41no—
781C2×D4—41no—
782C2×D4—612no—
783C2×D4—1228no—
784C2×D4—1222no—
785C2×D4—1222no—
786C2×D4—1221no—
787C2×D4—1221no—
788C2×D4—1221no—
789C2×D4—1221no—
790C2×D4—1221no—
791C2×D4—2448no—
792C2×D4—2441no—
793C2×D4—2441no—
794C2×D4—2441no—
795C2×D4—2441no—
796C2×D4C2×C22⋊D6112yescomplemented
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—22no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—41no—
820C22×C4—41no—
821C22×C4—41no—
822C22×C4—41no—
823C22×C4—41no—
824C22×C4—41no—
825C22×C4—41no—
826C22×C4—41no—
827C22×C4—41no—
828C22×C4—41no—
829C22×C4—41no—
830C22×C4—41no—
831C22×C4—41no—
832C22×C4—41no—
833C22×C4—41no—
834C22×C4—41no—
835C22×C4—41no—
836C22×C4—41no—
837C22×C4—41no—
838C22×C4—41no—
839C22×C4—1222no—
840C22×C4—1221no—
841C22×C4—1222no—
842C22×C4—1222no—
843C22×C4—2441no—
844C22×C4—2441no—
845C22×C4—2441no—
846C22×C4—2441no—
847C22×C4D4×D6111yescharacteristic
848C22×C4D4×D6111yescharacteristic
849C22×C4D4×D6111yescharacteristic
850C22×C4D4×D6111yescharacteristic
851C22×C4D4×D6111yescharacteristic
852C22×C4D4×D6111yescharacteristic
853C22×C4#1175822411yescharacteristic
854C22×C4#1175822411yescharacteristic
855C22×C4C2×C22⋊D6112yes—
856C22×C4C2×C22⋊D6111yescharacteristic
857C22×C4C2×C22⋊D6111yescharacteristic
858C22×C4C2×C22⋊D6111yescharacteristic
859C22×C4C2×C22⋊D6111yescharacteristic
860C22×C4C2×C22⋊D6111yescharacteristic
861C22×C4C23×D6111yescharacteristic
862Q16—1228no—
863SD16—1228no—
864SD16—1228no—
865D8—1228no—
866M16—1222no—
867M16—1222no—
868M16—1222no—
869M16—1222no—
870M16—1222no—
871M16—1222no—
872M16—2441no—
873M16—2441no—
874C2×C8—614no—
875C2×C8—1222no—
876C2×C8—1222no—
877C2×C8—1222no—
878C2×C8—2441no—
879C2×C8—2441no—
880C4⋊C4—28no—
881C4⋊C4—22no—
882C4⋊C4—22no—
883C4⋊C4—1228no—
884C4⋊C4—1222no—
885C4⋊C4—1222no—
886C22⋊C4—28no—
887C22⋊C4—28no—
888C22⋊C4—22no—
889C22⋊C4—22no—
890C22⋊C4—1228no—
891C22⋊C4—1228no—
892C22⋊C4—1222no—
893C22⋊C4—1222no—
894C42—22no—
895C42—614no—
896C42—1222no—
897C42C2×C22⋊D6114yescomplemented
898C23—24no—
899C23—24no—
900C23—24no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—42no—
906C23—44no—
907C23—42no—
908C23—42no—
909C23—42no—
910C23—44no—
911C23—44no—
912C23—44no—
913C23—44no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—1222no—
921C23—2444no—
922C23—2441no—
923C23—2441no—
924C23#1451974511yescharacteristic
925C23#1451974511yescharacteristic
926C23#1451974611yescharacteristic
927C23#1451974611yescharacteristic
928C23#1451974911yescharacteristic
929C23#1451974911yescharacteristic
930C23C22×C22⋊D6111yescharacteristic
931Q8—22no—
932Q8—22no—
933Q8—41no—
934Q8—41no—
935Q8—1222no—
936Q8—1222no—
937Q8—2441no—
938Q8—2441no—
939D4—22no—
940D4—22no—
941D4—416no—
942D4—42no—
943D4—42no—
944D4—42no—
945D4—42no—
946D4—41no—
947D4—41no—
948D4—1222no—
949D4—1222no—
950D4—24416no—
951D4—2442no—
952D4—2442no—
953D4—2442no—
954D4—2442no—
955D4—2441no—
956D4—2441no—
957C2×C4—22no—
958C2×C4—24no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—44no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—42no—
970C2×C4—42no—
971C2×C4—42no—
972C2×C4—42no—
973C2×C4—42no—
974C2×C4—42no—
975C2×C4—42no—
976C2×C4—42no—
977C2×C4—42no—
978C2×C4—42no—
979C2×C4—42no—
980C2×C4—42no—
981C2×C4—1224no—
982C2×C4—1222no—
983C2×C4—2444no—
984C2×C4—2441no—
985C2×C4—2441no—
986C2×C4—2442no—
987C2×C4—2442no—
988C2×C4—2442no—
989C2×C4—2442no—
990C2×C4#1451974511yescharacteristic
991C2×C4#1451974511yescharacteristic
992C2×C4#1451974511yescharacteristic
993C2×C4#1451974511yescharacteristic
994C2×C4#1451974511yescharacteristic
995C2×C4#1451974511yescharacteristic
996C2×C4#1451974611yescharacteristic
997C2×C4#1451974611yescharacteristic
998C2×C4#1451974811yescharacteristic
999C2×C4#1451974811yescharacteristic
1000C2×C4#1451974811yescharacteristic
1001C2×C4#1451974811yescharacteristic
1002C2×C4#1451974911yescharacteristic
1003C2×C4#1451974911yescharacteristic
1004C2×C4#1451974911yescharacteristic
1005C2×C4#1451974911yescharacteristic
1006C2×C4#1451974911yescharacteristic
1007C2×C4#1451974911yescharacteristic
1008C2×C4#1451977311yescharacteristic
1009C2×C4#1451977311yescharacteristic
1010C2×C4#1451977311yescharacteristic
1011C2×C4#1451977311yescharacteristic
1012C2×C4C2×D4×D6111yescharacteristic
1013C2×C4C2×D4×D6111yescharacteristic
1014C2×C4C2×D4×D6111yescharacteristic
1015C2×C4C22×C22⋊D6111yescharacteristic
1016C2×C4C22×C22⋊D6111yescharacteristic
1017C2×C4C2×#1175822411yescharacteristic
1018C8—1224no—
1019C8—2442no—
1020C22—22no—
1021C22—22no—
1022C22—22no—
1023C22—24no—
1024C22—24no—
1025C22—24no—
1026C22—41no—
1027C22—41no—
1028C22—41no—
1029C22—41no—
1030C22—42no—
1031C22—42no—
1032C22—42no—
1033C22—44no—
1034C22—44no—
1035C22—44no—
1036C22—44no—
1037C22—42no—
1038C22—44no—
1039C22—42no—
1040C22—82no—
1041C22—82no—
1042C22—4882no—
1043C22—4882no—
1044C22—2444no—
1045C22—2442no—
1046C22#1683967011yescharacteristic
1047C22#1683967011yescharacteristic
1048C22#1683967011yescharacteristic
1049C22#1683967011yescharacteristic
1050C22C2×#1451974511yescharacteristic
1051C22C2×#1451974611yescharacteristic
1052C22C2×#1451974911yescharacteristic
1053C4—44no—
1054C4—42no—
1055C4—42no—
1056C4—2444no—
1057C4—2442no—
1058C4#1683967011yescharacteristic
1059C4#1683967011yescharacteristic
1060C4#1683967011yescharacteristic
1061C4#1683967011yescharacteristic
1062C4C2×#1451974511yescharacteristic
1063C4C2×#1451974811yescharacteristic
1064C4C2×#1451974911yescharacteristic
1065C4C2×#1451977311yescharacteristic
1066C2—21no—
1067C2—21no—
1068C2—21no—
1069C2—21no—
1070C2—21no—
1071C2—21no—
1072C2—44no—
1073C2—82no—
1074C2—4882no—
1075C2#2144688412yesdirect product factor
1076C2C2×#1683967011yescharacteristic
subgroupG/H
centerC2×C4#14519773
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#525C2
socleC22×C61#392
hypercenterC2×#525D61
hypocenterC61C2×#2010
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. C2×#16840560C2semidirect
2. C2×#16840273C2semidirect
3. C2×#16839780C2semidirect
4. C2×#16839779C2semidirect
5. C2×#16839726C2semidirect
6. #21446884C2direct (N × H)
7. C2×#16839518C2semidirect
8. C2×C61×#525C2semidirect
13. #16840560C22semidirect
24. #16840273C22semidirect
32. #16839780C22semidirect
34. #16839779C22semidirect
38. #16839726C22semidirect
40. #16839518C22semidirect
46. C61×#525C22semidirect
63. C2×#11758222D4semidirect
65. C22×Dic122D4semidirect
66. C22×D244D4semidirect
93. C2×#11758194D4semidirect
97. C22×#92418D4semidirect
110. #14519736D4semidirect
117. C2×C4×Dic61D4semidirect
132. C2×#41×C61D4semidirect
134. C22×Q8×C61D4semidirect
137. C22×D4×C61D4semidirect
167. #117×C61D4semidirect
174. C2×C42×C61D4semidirect
207. C2×Q8×C61C2×D4semidirect
221. C2×D4×C61C2×D4semidirect
310. C2×D244C2×D4semidirect
322. C2×Dic122C2×D4semidirect
331. C42×C61C2×D4semidirect
344. C4×Dic61C2×D4semidirect
358. C2×#92418C2×D4semidirect
530. C2×#525D61semidirect
544. C2×C61#2010semidirect
568. #525C2×D61semidirect
591. C61C2×#2010semidirect
615. C2×#41C22⋊D61semidirect
618. C22×Q8C22⋊D61semidirect
624. C22×D4C22⋊D61semidirect
697. #117C22⋊D61semidirect
710. C2×C42C22⋊D61semidirect
768. C2×Q8C2×C22⋊D61semidirect
796. C2×D4C2×C22⋊D61semidirect
897. C42C2×C22⋊D61semidirect
1075. C2#21446884direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168405602
C2×#168402732
C2×#168397802
C2×#168397792
C2×#168397262
#214468842
C2×#168395182
C2×C61×#5252
C2×#201061