Finite Group Databasebeta

← C2×#21446876 #29707011

Subgroups — C2×#21446876 #29707011

Order 15616.

1926 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519807C211yesmaximal, characteristic, complemented
2C2×#16840333C211yesmaximal, characteristic, complemented
3C2×#16839779C211yesmaximal, characteristic, complemented
4C2×#16839772C211yesmaximal, characteristic, complemented
5C2×#16839736C211yesmaximal, characteristic, complemented
6#21446876C218yesmaximal, direct product factor
7C2×#16839533C211yesmaximal, characteristic, complemented
8C2×C61×#575C211yesmaximal, characteristic
9C23×Dic122C2211yescharacteristic
10C2×#14519807—22no—
11C2×#14519807—22no—
12C2×#14519807—22no—
13C2×#14519807—22no—
14C2×#14519807—22no—
15C2×#14519807C2214yescomplemented
16C22×#11758202—21no—
17C22×#11758200—21no—
18C22×#11758194C2211yescharacteristic
19#16840333—22no—
20#16840333—22no—
21#16840333—22no—
22#16840333C2214yescomplemented
23C2×#14519775—21no—
24C2×#14519764—21no—
25C2×#14519758—22no—
26C2×#14519756—22no—
27C2×#14519736C2211yescharacteristic
28C2×#14519736C2211yescharacteristic
29#16839779—22no—
30#16839779C2214yescomplemented
31C2×#14519704—22no—
32#16839772—22no—
33#16839772C2214yescomplemented
34C2×#14519702—22no—
35#16839736—22no—
36#16839736C2214yescomplemented
37C2×#14519692—22no—
38#16839533C2214yescomplemented
39C22×#41×C61C2211yescharacteristic
40C22×#41×C61C2211yescharacteristic
41C61×#575—22no—
42C61×#575—22no—
43C61×#575—22no—
44C61×#575C2214yes—
45C2×#137×C61—21no—
46C2×#137×C61—21no—
47C2×AGL(1,ℤ/8)×C61—21no—
48C2×AGL(1,ℤ/8)×C61—21no—
49C2×#135×C61—22no—
50C22×M16×C61C2211yescharacteristic
51C22×Dic122—21no—
52C22×Dic122—21no—
53C22×Dic122—21no—
54C22×Dic122—21no—
55C22×Dic122—21no—
56C22×Dic122—21no—
57C22×Dic122—21no—
58C22×Dic122—21no—
59C22×Dic122—21no—
60C22×Dic122—21no—
61C22×Dic122—21no—
62C22×Dic122D412yes—
63C22×Dic122D412yes—
64C22×Dic122C2312yes—
65C23×Dic61—21no—
66#14519807—28no—
67#14519807—28no—
68#14519807—28no—
69#14519807—28no—
70C2×#11758202—24no—
71C2×#11758202—24no—
72C2×#11758202—24no—
73C2×#11758200—24no—
74C2×#11758200—24no—
75C2×#11758200—24no—
76C2×#11758194—21no—
77C2×#11758194—21no—
78C2×#11758194—21no—
79C2×#11758194D412yes—
80C2×#11758194D412yes—
81C2×#11758194C2312yes—
82C22×#92418—21no—
83#14519775—24no—
84#14519775—24no—
85#14519764—24no—
86#14519764—24no—
87#14519758—28no—
88#14519758—28no—
89#14519756—28no—
90#14519756—28no—
91#14519736—21no—
92#14519736—21no—
93#14519736—21no—
94#14519736—21no—
95#14519736—21no—
96#14519736D412yes—
97#14519736C2312yes—
98#14519736C2312yes—
99C2×C4⋊Dic61—21no—
100C2×C4⋊Dic61—21no—
101C2×#11758196—24no—
102C2×C22⋊Dic61—24no—
103C2×C22⋊Dic61—21no—
104C2×C22⋊Dic61D412yes—
105C2×C4×Dic61—21no—
106C2×C4×Dic61—21no—
107#14519704—28no—
108#14519702—28no—
109#14519692—28no—
110C2×#41×C61—21no—
111C2×#41×C61—21no—
112C2×#41×C61—21no—
113C2×#41×C61—21no—
114C2×#41×C61—21no—
115C2×#41×C61—21no—
116C2×#41×C61—21no—
117C2×#41×C61—21no—
118C2×#41×C61—21no—
119C2×#41×C61—21no—
120C2×#41×C61—21no—
121C2×#41×C61—21no—
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×C61D412yes—
131C2×#41×C61D412yes—
132C2×#41×C61C2312yes—
133C2×#41×C61C2312yes—
134C22×Q8×C61D411yescharacteristic
135C22×Q8×C61D411yescharacteristic
136C22×D4×C61—21no—
137C22×D4×C61—21no—
138C22×D4×C61D411yescharacteristic
139C22×D4×C61D411yescharacteristic
140C23×C4×C61—21no—
141C23×C4×C61—21no—
142C23×C4×C61C2311yescharacteristic
143#137×C61—24no—
144#137×C61—24no—
145#137×C61—24no—
146#137×C61—24no—
147AGL(1,ℤ/8)×C61—24no—
148AGL(1,ℤ/8)×C61—24no—
149AGL(1,ℤ/8)×C61—24no—
150AGL(1,ℤ/8)×C61—24no—
151#135×C61—28no—
152#135×C61—28no—
153C2×Q16×C61—22no—
154C2×SD16×C61—22no—
155C2×SD16×C61—22no—
156C2×D8×C61—22no—
157C2×M16×C61—21no—
158C2×M16×C61—21no—
159C2×M16×C61—21no—
160C2×M16×C61—21no—
161C2×M16×C61D412yes—
162C2×M16×C61C2312yes—
163C22×C8×C61D412yes—
164C24×C61—21no—
165C24×C61—21no—
166C24×C61C2×D411yescharacteristic
167#41×C61—22no—
168#41×C61—22no—
169#41×C61—22no—
170#41×C61—22no—
171#41×C61—22no—
172#41×C61—22no—
173#41×C61—22no—
174#41×C61—22no—
175#41×C61—22no—
176#41×C61—22no—
177#41×C61—22no—
178#41×C61—22no—
179#41×C61—22no—
180#41×C61—22no—
181#41×C61—22no—
182#41×C61—22no—
183#41×C61—41no—
184#41×C61—41no—
185#41×C61—41no—
186#41×C61—41no—
187#41×C61—41no—
188#41×C61—41no—
189#41×C61—41no—
190#41×C61—41no—
191#41×C61—41no—
192#41×C61—41no—
193#41×C61—41no—
194#41×C61—41no—
195#41×C61—41no—
196#41×C61—41no—
197#41×C61—41no—
198#41×C61—41no—
199C2×Q8×C61—21no—
200C2×Q8×C61—21no—
201C2×Q8×C61—21no—
202C2×Q8×C61—21no—
203C2×Q8×C61—21no—
204C2×Q8×C61—21no—
205C2×Q8×C61—21no—
206C2×Q8×C61—21no—
207C2×Q8×C61—21no—
208C2×Q8×C61—21no—
209C2×Q8×C61C2×D412yes—
210C2×Q8×C61C2×D412yes—
211C2×D4×C61—22no—
212C2×D4×C61—22no—
213C2×D4×C61—22no—
214C2×D4×C61—22no—
215C2×D4×C61—21no—
216C2×D4×C61—21no—
217C2×D4×C61—21no—
218C2×D4×C61—21no—
219C2×D4×C61—21no—
220C2×D4×C61—21no—
221C2×D4×C61—21no—
222C2×D4×C61—21no—
223C2×D4×C61—21no—
224C2×D4×C61—21no—
225C2×D4×C61—41no—
226C2×D4×C61—41no—
227C2×D4×C61—41no—
228C2×D4×C61—41no—
229C2×D4×C61—41no—
230C2×D4×C61—41no—
231C2×D4×C61—41no—
232C2×D4×C61—41no—
233C2×D4×C61C2×D412yes—
234C2×D4×C61C2×D412yes—
235C22×C4×C61—21no—
236C22×C4×C61—21no—
237C22×C4×C61—22no—
238C22×C4×C61—22no—
239C22×C4×C61—22no—
240C22×C4×C61—22no—
241C22×C4×C61—41no—
242C22×C4×C61—41no—
243C22×C4×C61—41no—
244C22×C4×C61—41no—
245C22×C4×C61—41no—
246C22×C4×C61—41no—
247C22×C4×C61—41no—
248C22×C4×C61—41no—
249C22×C4×C61C2×D411yescharacteristic
250C22×C4×C61C2×D411yescharacteristic
251C22×C4×C61C2×D411yescharacteristic
252C22×C4×C61C2×D411yescharacteristic
253C22×C4×C61C2×D411yescharacteristic
254C22×C4×C61C2×D411yescharacteristic
255C22×C4×C61C2×D411yescharacteristic
256C22×C4×C61C2×D411yescharacteristic
257C22×C4×C61C2×D411yescharacteristic
258C22×C4×C61C2×D411yescharacteristic
259C22×C4×C61C2×D411yescharacteristic
260C22×C4×C61#4111yescharacteristic
261C22×C4×C61#4111yescharacteristic
262C22×C4×C61C2411yescharacteristic
263C22×Dic61—22no—
264C22×Dic61—22no—
265C22×Dic61—22no—
266C22×Dic61—22no—
267C22×Dic61—41no—
268C22×Dic61—41no—
269C22×Dic61—41no—
270C22×Dic61—41no—
271C22×Dic61—41no—
272C2×Dic122—22no—
273C2×Dic122—22no—
274C2×Dic122—22no—
275C2×Dic122—22no—
276C2×Dic122—22no—
277C2×Dic122—22no—
278C2×Dic122—22no—
279C2×Dic122—22no—
280C2×Dic122—22no—
281C2×Dic122—22no—
282C2×Dic122—22no—
283C2×Dic122—22no—
284C2×Dic122—22no—
285C2×Dic122—22no—
286C2×Dic122—22no—
287C2×Dic122—41no—
288C2×Dic122—41no—
289C2×Dic122—41no—
290C2×Dic122—41no—
291C2×Dic122—41no—
292C2×Dic122—41no—
293C2×Dic122—41no—
294C2×Dic122—41no—
295C2×Dic122—41no—
296C2×Dic122—41no—
297C2×Dic122—41no—
298C2×Dic122—41no—
299C2×Dic122C2×D414yes—
300Q16×C61—28no—
301SD16×C61—28no—
302SD16×C61—28no—
303D8×C61—28no—
304M16×C61—22no—
305M16×C61—22no—
306M16×C61—22no—
307M16×C61—22no—
308C2×C8×C61—22no—
309C2×C8×C61—22no—
310C2×C8×C61C2×D414yes—
311C22⋊Dic61—216no—
312C22⋊Dic61—22no—
313C22⋊Dic61—22no—
314C22⋊Dic61—41no—
315C22⋊Dic61C2×D414yes—
316#11758202—216no—
317#11758200—216no—
318C4⋊Dic61—22no—
319C4⋊Dic61—22no—
320C4⋊Dic61—22no—
321C4⋊Dic61—41no—
322#11758196—216no—
323C4×Dic61—22no—
324C4×Dic61—22no—
325C4×Dic61—22no—
326C4×Dic61—41no—
327#11758194—22no—
328#11758194—22no—
329#11758194—22no—
330#11758194C2×D414yes—
331C2×#92418—22no—
332C2×#92418—22no—
333C2×#92418—22no—
334C23×C61—22no—
335C23×C61—22no—
336C23×C61—42no—
337C23×C61—44no—
338C23×C61—41no—
339C23×C61—41no—
340C23×C61—41no—
341C23×C61—41no—
342C23×C61—82no—
343C23×C61#12011yescharacteristic
344C23×C61#12011yescharacteristic
345C23×C61#12111yescharacteristic
346C23×C61#12111yescharacteristic
347C23×C61#12711yescharacteristic
348C23×C61#12711yescharacteristic
349C23×C61C22×D411yescharacteristic
350Q8×C61—22no—
351Q8×C61—22no—
352Q8×C61—22no—
353Q8×C61—22no—
354Q8×C61—41no—
355Q8×C61—41no—
356Q8×C61—41no—
357Q8×C61—41no—
358D4×C61—22no—
359D4×C61—22no—
360D4×C61—22no—
361D4×C61—22no—
362D4×C61—42no—
363D4×C61—42no—
364D4×C61—42no—
365D4×C61—42no—
366D4×C61—42no—
367D4×C61—42no—
368D4×C61—42no—
369D4×C61—42no—
370D4×C61—41no—
371D4×C61—41no—
372D4×C61—41no—
373D4×C61—41no—
374C2×C4×C61—22no—
375C2×C4×C61—22no—
376C2×C4×C61—41no—
377C2×C4×C61—41no—
378C2×C4×C61—41no—
379C2×C4×C61—41no—
380C2×C4×C61—42no—
381C2×C4×C61—42no—
382C2×C4×C61—42no—
383C2×C4×C61—42no—
384C2×C4×C61—42no—
385C2×C4×C61—42no—
386C2×C4×C61—42no—
387C2×C4×C61—42no—
388C2×C4×C61#12011yescharacteristic
389C2×C4×C61#12011yescharacteristic
390C2×C4×C61#12011yescharacteristic
391C2×C4×C61#12011yescharacteristic
392C2×C4×C61#12011yescharacteristic
393C2×C4×C61#12011yescharacteristic
394C2×C4×C61#12011yescharacteristic
395C2×C4×C61#12011yescharacteristic
396C2×C4×C61#12011yescharacteristic
397C2×C4×C61#12011yescharacteristic
398C2×C4×C61#12111yescharacteristic
399C2×C4×C61#12111yescharacteristic
400C2×C4×C61#12111yescharacteristic
401C2×C4×C61#12111yescharacteristic
402C2×C4×C61#12111yescharacteristic
403C2×C4×C61#12111yescharacteristic
404C2×C4×C61#12111yescharacteristic
405C2×C4×C61#12111yescharacteristic
406C2×C4×C61#12111yescharacteristic
407C2×C4×C61#12111yescharacteristic
408C2×C4×C61#12711yescharacteristic
409C2×C4×C61#12711yescharacteristic
410C2×C4×C61C22×D411yescharacteristic
411C2×C4×C61C22×D411yescharacteristic
412C2×C4×C61C22×D411yescharacteristic
413C2×C4×C61C22×D411yescharacteristic
414C2×C4×C61C22×D411yescharacteristic
415C2×C4×C61C2×#4111yescharacteristic
416C2×Dic61—24no—
417C2×Dic61—24no—
418C2×Dic61—44no—
419C2×Dic61—42no—
420C2×Dic61—42no—
421C2×Dic61—42no—
422C2×Dic61—42no—
423C2×Dic61—42no—
424C2×Dic61—42no—
425C2×Dic61—42no—
426C2×Dic61—82no—
427Dic122—24no—
428Dic122—24no—
429Dic122—42no—
430Dic122—42no—
431Dic122—42no—
432Dic122—42no—
433Dic122—42no—
434Dic122—42no—
435C8×C61—24no—
436#92418—24no—
437C2×#2009—611nomaximal, Sylow
438C22×C61—22no—
439C22×C61—22no—
440C22×C61—22no—
441C22×C61—41no—
442C22×C61—41no—
443C22×C61—41no—
444C22×C61—41no—
445C22×C61—44no—
446C22×C61—42no—
447C22×C61—42no—
448C22×C61—82no—
449C22×C61—82no—
450C22×C61—82no—
451C22×C61—82no—
452C22×C61—82no—
453C22×C61#39211yescharacteristic
454C22×C61#39211yescharacteristic
455C22×C61#39211yescharacteristic
456C22×C61#39211yescharacteristic
457C22×C61C2×#12011yescharacteristic
458C22×C61C2×#12111yescharacteristic
459C22×C61C2×#12711yescharacteristic
460C4×C61—42no—
461C4×C61—42no—
462C4×C61#39211yescharacteristic
463C4×C61#39211yescharacteristic
464C4×C61#39211yescharacteristic
465C4×C61#39211yescharacteristic
466C4×C61C2×#12011yescharacteristic
467C4×C61C2×#12011yescharacteristic
468C4×C61C2×#12111yescharacteristic
469C4×C61C2×#12111yescharacteristic
470Dic61—44no—
471Dic61—44no—
472Dic61—82no—
473C2×#575D6111yescharacteristic
474C22×#137—611no—
475C2×#536—611no—
476C2×#421—611no—
477C2×#419—611no—
478C2×#410—611no—
479#2009—618no—
480C2×#344—611no—
481C2×C61—21no—
482C2×C61—21no—
483C2×C61—21no—
484C2×C61—21no—
485C2×C61—21no—
486C2×C61—21no—
487C2×C61—82no—
488C2×C61—82no—
489C2×C61#200912yescomplemented
490C2×C61C2×#39211yescharacteristic
491C22×#41C2×D6111yescharacteristic
492C22×#41C2×D6111yescharacteristic
493C23×Q8—611no—
494#575—22no—
495#575—22no—
496#575—22no—
497#575C2×D6114yes—
498C2×#137—21no—
499C2×#137—21no—
500C2×#137—614no—
501C2×#137—1222no—
502C2×#137—1222no—
503C2×#137—1222no—
504C2×#137—1222no—
505C2×#137—1222no—
506C2×AGL(1,ℤ/8)—21no—
507C2×AGL(1,ℤ/8)—21no—
508C2×#135—22no—
509C22×Q16—1221no—
510C22×SD16—1221no—
511C22×M16—611no—
512C22×M16C2×D6111yescharacteristic
513#536—614no—
514#536—1222no—
515#536—1222no—
516#536—1222no—
517C2×C4⋊Q8—1221no—
518C2×#124—1221no—
519C2×#123—1222no—
520C2×C22⋊Q8—1222no—
521C2×#117—611no—
522C2×#117—611no—
523#421—614no—
524#421—1222no—
525C2×#104—1222no—
526#419—614no—
527#419—1222no—
528C2×#103—1222no—
529#410—614no—
530#410—1222no—
531C2×#99—1222no—
532#344—614no—
533C61C2×#200911yescharacteristic, complemented, Sylow
534C2×#41—21no—
535C2×#41—21no—
536C2×#41—21no—
537C2×#41—21no—
538C2×#41—21no—
539C2×#41—21no—
540C2×#41—21no—
541C2×#41—21no—
542C2×#41—21no—
543C2×#41—21no—
544C2×#41—21no—
545C2×#41—21no—
546C2×#41—21no—
547C2×#41—21no—
548C2×#41—21no—
549C2×#41—21no—
550C2×#41—21no—
551C2×#41—21no—
552C2×#41—21no—
553C2×#41—21no—
554C2×#41C22⋊D6112yes—
555C2×#41C22⋊D6112yes—
556C2×#41C22×D6112yes—
557C2×#41C22×D6112yes—
558C22×Q8—612no—
559C22×Q8—612no—
560C22×Q8—612no—
561C22×Q8—1221no—
562C22×Q8—1221no—
563C22×Q8—1221no—
564C22×Q8—1221no—
565C22×Q8—1221no—
566C22×Q8—1221no—
567C22×Q8—1221no—
568C22×Q8—1221no—
569C22×Q8—1221no—
570C22×Q8—1221no—
571C22×Q8—1221no—
572C22×Q8C22⋊D6111yescharacteristic
573C22×Q8C22⋊D6111yescharacteristic
574C22×D4—21no—
575C22×D4—21no—
576C22×D4C22⋊D6111yescharacteristic
577C22×D4C22⋊D6111yescharacteristic
578C23×C4—21no—
579C23×C4—21no—
580C23×C4—1221no—
581C23×C4C22×D6111yescharacteristic
582#137—24no—
583#137—24no—
584#137—24no—
585#137—24no—
586#137—1228no—
587#137—1228no—
588#137—1228no—
589#137—1228no—
590AGL(1,ℤ/8)—24no—
591AGL(1,ℤ/8)—24no—
592AGL(1,ℤ/8)—24no—
593AGL(1,ℤ/8)—24no—
594#135—28no—
595#135—28no—
596C2×Q16—22no—
597C2×Q16—1224no—
598C2×Q16—1224no—
599C2×Q16—1224no—
600C2×SD16—22no—
601C2×SD16—22no—
602C2×SD16—1224no—
603C2×SD16—1224no—
604C2×SD16—1224no—
605C2×D8—22no—
606C2×M16—21no—
607C2×M16—21no—
608C2×M16—21no—
609C2×M16—21no—
610C2×M16—612no—
611C2×M16—612no—
612C2×M16—612no—
613C2×M16—1221no—
614C2×M16—1221no—
615C2×M16—1221no—
616C2×M16C22⋊D6112yes—
617C2×M16C22×D6112yes—
618C22×C8—1221no—
619C22×C8C22⋊D6112yes—
620C4⋊Q8—1224no—
621C4⋊Q8—1224no—
622#124—1224no—
623#124—1224no—
624#123—1228no—
625#123—1228no—
626C22⋊Q8—1228no—
627C22⋊Q8—1228no—
628#117—612no—
629#117—612no—
630#117—612no—
631#117—1221no—
632#117—1221no—
633#117—1221no—
634#117—1221no—
635#117—1221no—
636C2×C4⋊C4—1224no—
637C2×C4⋊C4—1221no—
638C2×C4⋊C4—1221no—
639C2×C22⋊C4—612no—
640C2×C22⋊C4—1224no—
641C2×C22⋊C4—1221no—
642C2×C42—1221no—
643C2×C42—1221no—
644#104—1228no—
645#103—1228no—
646#99—1228no—
647C24—21no—
648C24—21no—
649C24D4×D6111yescharacteristic
650#41—22no—
651#41—22no—
652#41—22no—
653#41—22no—
654#41—22no—
655#41—22no—
656#41—22no—
657#41—22no—
658#41—22no—
659#41—22no—
660#41—22no—
661#41—22no—
662#41—22no—
663#41—22no—
664#41—22no—
665#41—22no—
666#41—41no—
667#41—41no—
668#41—41no—
669#41—41no—
670#41—41no—
671#41—41no—
672#41—41no—
673#41—41no—
674#41—41no—
675#41—41no—
676#41—41no—
677#41—41no—
678#41—41no—
679#41—41no—
680#41—41no—
681#41—41no—
682C2×Q8—21no—
683C2×Q8—21no—
684C2×Q8—21no—
685C2×Q8—21no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—21no—
690C2×Q8—21no—
691C2×Q8—21no—
692C2×Q8—614no—
693C2×Q8—1222no—
694C2×Q8—1222no—
695C2×Q8—1222no—
696C2×Q8—1222no—
697C2×Q8—1222no—
698C2×Q8—1222no—
699C2×Q8—1222no—
700C2×Q8—1222no—
701C2×Q8—1222no—
702C2×Q8—1222no—
703C2×Q8—1222no—
704C2×Q8—1222no—
705C2×Q8—1222no—
706C2×Q8—1222no—
707C2×Q8—1222no—
708C2×Q8—2441no—
709C2×Q8—2441no—
710C2×Q8—2441no—
711C2×Q8—2441no—
712C2×Q8—2441no—
713C2×Q8—2441no—
714C2×Q8—2441no—
715C2×Q8—2441no—
716C2×Q8—2441no—
717C2×Q8—2441no—
718C2×Q8—2441no—
719C2×Q8—2441no—
720C2×Q8C2×C22⋊D6112yes—
721C2×Q8C2×C22⋊D6112yes—
722C2×D4—22no—
723C2×D4—22no—
724C2×D4—22no—
725C2×D4—22no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—41no—
737C2×D4—41no—
738C2×D4—41no—
739C2×D4—41no—
740C2×D4—41no—
741C2×D4—41no—
742C2×D4—41no—
743C2×D4—41no—
744C2×D4C2×C22⋊D6112yes—
745C2×D4C2×C22⋊D6112yes—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—41no—
753C22×C4—41no—
754C22×C4—41no—
755C22×C4—41no—
756C22×C4—41no—
757C22×C4—41no—
758C22×C4—41no—
759C22×C4—41no—
760C22×C4—1222no—
761C22×C4—1222no—
762C22×C4—1222no—
763C22×C4—1222no—
764C22×C4—2441no—
765C22×C4—2441no—
766C22×C4—2441no—
767C22×C4—2441no—
768C22×C4—2441no—
769C22×C4D4×D6111yescharacteristic
770C22×C4D4×D6111yescharacteristic
771C22×C4D4×D6111yescharacteristic
772C22×C4D4×D6111yescharacteristic
773C22×C4D4×D6111yescharacteristic
774C22×C4#1175822411yescharacteristic
775C22×C4#1175822411yescharacteristic
776C22×C4C2×C22⋊D6111yescharacteristic
777C22×C4C2×C22⋊D6111yescharacteristic
778C22×C4C2×C22⋊D6111yescharacteristic
779C22×C4C2×C22⋊D6111yescharacteristic
780C22×C4C2×C22⋊D6111yescharacteristic
781C22×C4C2×C22⋊D6111yescharacteristic
782C22×C4C23×D6111yescharacteristic
783Q16—28no—
784Q16—12216no—
785SD16—28no—
786SD16—28no—
787SD16—12216no—
788D8—28no—
789M16—22no—
790M16—22no—
791M16—22no—
792M16—22no—
793M16—614no—
794M16—1222no—
795M16—1222no—
796M16—1222no—
797C2×C8—22no—
798C2×C8—22no—
799C2×C8—1222no—
800C2×C8—1222no—
801C2×C8—1222no—
802C2×C8C2×C22⋊D6114yes—
803C4⋊C4—12216no—
804C4⋊C4—1222no—
805C4⋊C4—1222no—
806C4⋊C4—1222no—
807C4⋊C4—2441no—
808C22⋊C4—614no—
809C22⋊C4—12216no—
810C22⋊C4—1222no—
811C22⋊C4—1222no—
812C22⋊C4—2441no—
813C42—1222no—
814C42—1222no—
815C42—1222no—
816C42—2441no—
817C23—22no—
818C23—22no—
819C23—42no—
820C23—44no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—82no—
826C23#1451974511yescharacteristic
827C23#1451974511yescharacteristic
828C23#1451974911yescharacteristic
829C23#1451974911yescharacteristic
830C23#1451977311yescharacteristic
831C23#1451977311yescharacteristic
832C23C2×D4×D6111yescharacteristic
833Q8—22no—
834Q8—22no—
835Q8—22no—
836Q8—22no—
837Q8—41no—
838Q8—41no—
839Q8—41no—
840Q8—41no—
841Q8—1224no—
842Q8—1224no—
843Q8—2442no—
844Q8—2442no—
845Q8—2442no—
846Q8—2442no—
847Q8—2442no—
848Q8—2442no—
849D4—22no—
850D4—22no—
851D4—22no—
852D4—22no—
853D4—42no—
854D4—42no—
855D4—42no—
856D4—42no—
857D4—42no—
858D4—42no—
859D4—42no—
860D4—42no—
861D4—41no—
862D4—41no—
863D4—41no—
864D4—41no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—42no—
874C2×C4—42no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—42no—
879C2×C4—1224no—
880C2×C4—1224no—
881C2×C4—4882no—
882C2×C4—2442no—
883C2×C4—2444no—
884C2×C4—2442no—
885C2×C4—2442no—
886C2×C4—2442no—
887C2×C4—2442no—
888C2×C4—2442no—
889C2×C4—2442no—
890C2×C4#1451974511yescharacteristic
891C2×C4#1451974511yescharacteristic
892C2×C4#1451974511yescharacteristic
893C2×C4#1451974511yescharacteristic
894C2×C4#1451974511yescharacteristic
895C2×C4#1451974511yescharacteristic
896C2×C4#1451974611yescharacteristic
897C2×C4#1451974611yescharacteristic
898C2×C4#1451974611yescharacteristic
899C2×C4#1451974611yescharacteristic
900C2×C4#1451974811yescharacteristic
901C2×C4#1451974811yescharacteristic
902C2×C4#1451974811yescharacteristic
903C2×C4#1451974811yescharacteristic
904C2×C4#1451974911yescharacteristic
905C2×C4#1451974911yescharacteristic
906C2×C4#1451974911yescharacteristic
907C2×C4#1451974911yescharacteristic
908C2×C4#1451974911yescharacteristic
909C2×C4#1451974911yescharacteristic
910C2×C4#1451977311yescharacteristic
911C2×C4#1451977311yescharacteristic
912C2×C4C2×D4×D6111yescharacteristic
913C2×C4C2×D4×D6111yescharacteristic
914C2×C4C22×C22⋊D6111yescharacteristic
915C2×C4C22×C22⋊D6111yescharacteristic
916C2×C4C22×C22⋊D6111yescharacteristic
917C2×C4C2×#1175822411yescharacteristic
918C8—24no—
919C8—1224no—
920C22—22no—
921C22—22no—
922C22—22no—
923C22—41no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—44no—
928C22—42no—
929C22—42no—
930C22—82no—
931C22—82no—
932C22—82no—
933C22—82no—
934C22—82no—
935C22#1683967011yescharacteristic
936C22#1683967011yescharacteristic
937C22#1683967011yescharacteristic
938C22#1683967011yescharacteristic
939C22C2×#1451974511yescharacteristic
940C22C2×#1451974911yescharacteristic
941C22C2×#1451977311yescharacteristic
942C4—42no—
943C4—42no—
944C4—4882no—
945C4—2444no—
946C4—2444no—
947C4#1683967011yescharacteristic
948C4#1683967011yescharacteristic
949C4#1683967011yescharacteristic
950C4#1683967011yescharacteristic
951C4C2×#1451974511yescharacteristic
952C4C2×#1451974611yescharacteristic
953C4C2×#1451974811yescharacteristic
954C4C2×#1451974911yescharacteristic
955C2—21no—
956C2—21no—
957C2—21no—
958C2—21no—
959C2—21no—
960C2—21no—
961C2—82no—
962C2—82no—
963C2#2144687612yesdirect product factor
964C2C2×#1683967011yescharacteristic
subgroupG/H
centerC22#16839670
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
Fitting, prime radicalC2×C61×#575C2
socleC22×C61#392
hypercenterC2×#575D61
hypocenterC61C2×#2009
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#575

Complements

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

NH ≅ G/Ntype
1. C22×#14519807C2semidirect
2. C2×#16840333C2semidirect
3. C2×#16839779C2semidirect
4. C2×#16839772C2semidirect
5. C2×#16839736C2semidirect
6. #21446876C2direct (N × H)
7. C2×#16839533C2semidirect
15. C2×#14519807C22semidirect
22. #16840333C22semidirect
30. #16839779C22semidirect
33. #16839772C22semidirect
36. #16839736C22semidirect
38. #16839533C22semidirect
489. C2×C61#2009semidirect
533. C61C2×#2009semidirect
963. C2#21446876direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198072
C2×#168403332
C2×#168397792
C2×#168397722
C2×#168397362
#214468762
C2×#168395332
C2×C61×#5752
C2×#200961