Finite Group Databasebeta

← #29691358

Subgroups — #29691358

Order 15616.

1136 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21448514C211yesmaximal, characteristic, complemented
2#21448401C211yesmaximal, characteristic, complemented
3#21446696C211yesmaximal, characteristic, complemented
4#21446686C211yesmaximal, characteristic, complemented
5#21446518C211yesmaximal, characteristic, complemented
6#21446504C211yesmaximal, characteristic, complemented
7#21446448C211yesmaximal, characteristic, complemented
8#21446441C211yesmaximal, characteristic, complemented
9#21446169C211yesmaximal, characteristic, complemented
10#21446169C211yesmaximal, characteristic, complemented
11#21446142C211yesmaximal, characteristic, complemented
12#21446020C211yesmaximal, characteristic, complemented
13#21445750C211yesmaximal, characteristic, complemented
14#21445587C211yesmaximal, characteristic, complemented
15C2×C61×#447C211yesmaximal, characteristic
16C2×D4×Dic61C2211yescharacteristic, complemented
17C2×#14519736C2211yescharacteristic
18C2×#14519736C2211yescharacteristic
19C2×#14519711C2211yescharacteristic, complemented
20C2×#14519709C2211yescharacteristic, complemented
21C2×#14519698C2211yescharacteristic
22C2×#14519698C2211yescharacteristic
23C2×#14519698C2211yescharacteristic
24C2×#14519698C2211yescharacteristic
25C2×#14519698C2211yescharacteristic, complemented
26C2×#14519698C2211yescharacteristic, complemented
27C2×C22⋊#92418C2211yescharacteristic
28C2×#14519687C2211yescharacteristic, complemented
29C2×C8×Dic61C2211yescharacteristic, complemented
30#16839665—21no—
31#16839665—21no—
32#16839665—21no—
33#16839665C2211yescharacteristic
34#16839665C2211yescharacteristic
35#16839665C2211yescharacteristic
36#16839665C2211yescharacteristic
37#16839665C2211yescharacteristic, complemented
38#16839661C2211yescharacteristic, complemented
39#16839655—21no—
40#16839642—21no—
41#16839637—21no—
42#16839622C2211yescharacteristic
43#16839618—21no—
44#16839618—21no—
45C4⋊C4×Dic61C2211yescharacteristic, complemented
46#16839525C2211yescharacteristic, complemented
47#16839525C2211yescharacteristic, complemented
48#16839524C2211yescharacteristic, complemented
49#16839524C2211yescharacteristic, complemented
50#16839516C2211yescharacteristic, complemented
51#16839516C2211yescharacteristic, complemented
52C23×D4×C61C2211yescharacteristic
53C22×D8×C61C2211yescharacteristic
54C22×D8×C61C2211yescharacteristic
55C2×#121×C61C2211yescharacteristic
56C61×#447C418yescomplemented
57C2×#102×C61C2211yescharacteristic
58C2×#102×C61C2211yescharacteristic
59C2×C22⋊C8×C61C2211yescharacteristic
60C23×Dic61—21no—
61C22×#92418C2311yescharacteristic
62C22×#92418C2311yescharacteristic
63D4×Dic61—41no—
64D4×Dic61—41no—
65#14519736—41no—
66#14519736—41no—
67#14519736—41no—
68#14519736—41no—
69C2×C4⋊Dic61—21no—
70C2×C4⋊Dic61D411yescharacteristic
71C2×C4⋊Dic61D411yescharacteristic
72C2×C4⋊Dic61C2311yescharacteristic
73C2×C4⋊Dic61C2311yescharacteristic
74C2×C4⋊Dic61C2311yescharacteristic
75C2×C4⋊Dic61C2311yescharacteristic
76C2×C22⋊Dic61—21no—
77C2×C22⋊Dic61—21no—
78C2×C22⋊Dic61—21no—
79C2×C22⋊Dic61—21no—
80C2×C22⋊Dic61—21no—
81C2×C22⋊Dic61—21no—
82C2×C22⋊Dic61—21no—
83C2×C22⋊Dic61—21no—
84C2×C22⋊Dic61—21no—
85C2×C22⋊Dic61—21no—
86C2×C22⋊Dic61—21no—
87C2×C22⋊Dic61—21no—
88C2×C22⋊Dic61—21no—
89C2×C22⋊Dic61D411yescharacteristic
90C2×C22⋊Dic61D411yescharacteristic
91C2×C4×Dic61—21no—
92C2×C4×Dic61—21no—
93C2×C4×Dic61C2311yescharacteristic
94C2×C4×Dic61C2311yescharacteristic
95#14519711—41no—
96#14519709—41no—
97#14519698—41no—
98#14519698—41no—
99#14519698—41no—
100#14519698—41no—
101#14519698—41no—
102#14519698—41no—
103C22⋊#92418—22no—
104#14519687—41no—
105C8×Dic61—41no—
106#14519684—21no—
107#14519684—21no—
108#14519684—21no—
109C25×C61—21no—
110C22×D4×C61—21no—
111C22×D4×C61—21no—
112C22×D4×C61—22no—
113C22×D4×C61—41no—
114C22×D4×C61—41no—
115C22×D4×C61—41no—
116C22×D4×C61—41no—
117C22×D4×C61C2×C414yescomplemented
118C22×D4×C61C2311yescharacteristic
119C22×D4×C61C2311yescharacteristic
120C22×D4×C61C2311yescharacteristic
121C23×C4×C61C2311yescharacteristic
122C2×D8×C61—41no—
123C2×D8×C61—41no—
124C2×D8×C61—41no—
125C2×D8×C61—41no—
126C2×D8×C61C2×C414yes—
127C2×D8×C61C2×C414yes—
128C22×C8×C61C2311yescharacteristic
129C22×C8×C61C2311yescharacteristic
130#121×C61—22no—
131#121×C61C2×C414yes—
132C2×C4⋊C4×C61C2311yescharacteristic
133C2×C22⋊C4×C61—21no—
134#102×C61C2×C414yescomplemented
135#102×C61C2×C414yescomplemented
136C22⋊C8×C61C2×C414yescomplemented
137C24×C61—21no—
138C24×C61—21no—
139C24×C61—21no—
140C24×C61—24no—
141C24×C61—42no—
142C24×C61—42no—
143C24×C61—81no—
144C24×C61—81no—
145C24×C61—81no—
146C24×C61—81no—
147C24×C61C2×D411yescharacteristic
148C2×D4×C61—24no—
149C2×D4×C61—24no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—21no—
159C2×D4×C61—21no—
160C2×D4×C61—21no—
161C2×D4×C61—21no—
162C2×D4×C61—21no—
163C2×D4×C61—21no—
164C2×D4×C61—21no—
165C2×D4×C61—44no—
166C2×D4×C61—44no—
167C2×D4×C61—42no—
168C2×D4×C61—42no—
169C2×D4×C61—44no—
170C2×D4×C61—44no—
171C2×D4×C61—81no—
172C2×D4×C61—81no—
173C2×D4×C61C22×C412yes—
174C2×D4×C61C22×C412yes—
175C2×D4×C61C22×C412yes—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61C22×C412yes—
182C22×C4×C61C2×D411yescharacteristic
183C22×C4×C61#4112yes—
184C22×C4×C61C2411yescharacteristic
185C22×Dic61—21no—
186C22×Dic61—21no—
187C22×Dic61—21no—
188C22×Dic61—21no—
189C22×Dic61—42no—
190C22×Dic61—81no—
191C22×Dic61—81no—
192C22×Dic61C2×D411yescharacteristic
193C22×Dic61C2×D411yescharacteristic
194C22×Dic61C2×D411yescharacteristic
195C22×Dic61C2×D411yescharacteristic
196D8×C61—44no—
197D8×C61—44no—
198C2×C8×C61—21no—
199C2×C8×C61—21no—
200C2×C8×C61—21no—
201C2×C8×C61—21no—
202C2×C8×C61C22×C412yes—
203C2×C8×C61C22×C412yes—
204C4⋊C4×C61—21no—
205C4⋊C4×C61C22×C412yes—
206C22⋊C4×C61—24no—
207C22⋊Dic61—41no—
208C22⋊Dic61—41no—
209C22⋊Dic61—42no—
210C22⋊Dic61—42no—
211C22⋊Dic61—81no—
212C22⋊Dic61—81no—
213C22⋊Dic61—81no—
214C22⋊Dic61—81no—
215C22⋊Dic61—81no—
216C22⋊Dic61—81no—
217C22⋊Dic61—81no—
218C22⋊Dic61—81no—
219C22⋊Dic61—81no—
220C22⋊Dic61—81no—
221C22⋊Dic61—81no—
222C4⋊Dic61—21no—
223C4⋊Dic61—21no—
224C4⋊Dic61—21no—
225C4⋊Dic61—21no—
226C4⋊Dic61—21no—
227C4⋊Dic61—21no—
228C4⋊Dic61—21no—
229C4⋊Dic61—21no—
230C4⋊Dic61—41no—
231C4⋊Dic61—41no—
232C4⋊Dic61—81no—
233C4×Dic61—21no—
234C4×Dic61—21no—
235C4×Dic61—21no—
236C4×Dic61—21no—
237C4×Dic61—42no—
238C4×Dic61—81no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418—21no—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—22no—
252C23×C61—22no—
253C23×C61—22no—
254C23×C61—48no—
255C23×C61—41no—
256C23×C61—41no—
257C23×C61—41no—
258C23×C61—41no—
259C23×C61—41no—
260C23×C61—41no—
261C23×C61—41no—
262C23×C61—41no—
263C23×C61—41no—
264C23×C61—41no—
265C23×C61—41no—
266C23×C61—41no—
267C23×C61—41no—
268C23×C61—41no—
269C23×C61—41no—
270C23×C61—41no—
271C23×C61—41no—
272C23×C61—41no—
273C23×C61—84no—
274C23×C61—84no—
275C23×C61—84no—
276C23×C61—84no—
277C23×C61—84no—
278C23×C61—84no—
279C23×C61C4×D412yes—
280C23×C61C22×D411yescharacteristic
281D4×C61—22no—
282D4×C61—22no—
283D4×C61—22no—
284D4×C61—22no—
285D4×C61—22no—
286D4×C61—22no—
287D4×C61—48no—
288D4×C61—41no—
289D4×C61—41no—
290D4×C61—41no—
291D4×C61—41no—
292D4×C61—41no—
293D4×C61—41no—
294D4×C61—84no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—22no—
302C2×C4×C61—41no—
303C2×C4×C61—41no—
304C2×C4×C61C4×D412yes—
305C2×C4×C61C23×C411yescharacteristic
306C2×C4×C61C2×#4111yescharacteristic
307C2×C4×C61H(5,𝔽2)11yescharacteristic
308C2×C4×C61H(5,𝔽2)11yescharacteristic
309C2×C4×C61H(5,𝔽2)11yescharacteristic
310C2×C4×C61H(5,𝔽2)11yescharacteristic
311C2×Dic61—21no—
312C2×Dic61—21no—
313C2×Dic61—21no—
314C2×Dic61—21no—
315C2×Dic61—21no—
316C2×Dic61—21no—
317C2×Dic61—21no—
318C2×Dic61—21no—
319C2×Dic61—21no—
320C2×Dic61—21no—
321C2×Dic61—21no—
322C2×Dic61—21no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327C2×Dic61—41no—
328C2×Dic61—41no—
329C2×Dic61—41no—
330C2×Dic61—41no—
331C2×Dic61—41no—
332C2×Dic61—41no—
333C2×Dic61—41no—
334C2×Dic61—41no—
335C2×Dic61—84no—
336C8×C61—22no—
337C8×C61—22no—
338#92418—41no—
339#92418—41no—
340#22056—611nomaximal, Sylow
341C22×C61—22no—
342C22×C61—22no—
343C22×C61—22no—
344C22×C61—41no—
345C22×C61—41no—
346C22×C61—41no—
347C22×C61—41no—
348C22×C61—42no—
349C22×C61—42no—
350C22×C61—42no—
351C22×C61—42no—
352C22×C61—42no—
353C22×C61—42no—
354C22×C61—42no—
355C22×C61—42no—
356C22×C61—42no—
357C22×C61—816no—
358C22×C61—81no—
359C22×C61—81no—
360C22×C61—81no—
361C22×C61—81no—
362C22×C61—81no—
363C22×C61—81no—
364C22×C61—81no—
365C22×C61—81no—
366C22×C61—81no—
367C22×C61—81no—
368C22×C61—81no—
369C22×C61—81no—
370C22×C61C2×C4×D411yescharacteristic
371C22×C61#53411yescharacteristic
372C22×C61#53511yescharacteristic
373C22×C61#57611yescharacteristic
374C22×C61#57611yescharacteristic
375C22×C61#57611yescharacteristic
376C22×C61#57711yescharacteristic
377C4×C61—22no—
378C4×C61—42no—
379C4×C61#51811yescharacteristic
380C4×C61#51811yescharacteristic
381C4×C61#53811yescharacteristic
382C4×C61#53811yescharacteristic
383Dic61—41no—
384Dic61—41no—
385Dic61—41no—
386Dic61—41no—
387Dic61—81no—
388Dic61—81no—
389Dic61—81no—
390Dic61—81no—
391C2×#447D6111yescharacteristic
392#2324—611no—
393#2309—611no—
394#1972—611no—
395#1970—611no—
396#1936—611no—
397#1934—611no—
398#1926—611no—
399#1925—611no—
400#1879—611no—
401#1879—611no—
402#1875—611no—
403#1854—611no—
404#1786—611no—
405#1750—611no—
406C2×C61—42no—
407C2×C61—82no—
408C2×C61—82no—
409C2×C61—82no—
410C2×C61#232111yescharacteristic
411C2×C61#294611yescharacteristic
412C2×C61#294811yescharacteristic
413C2×C61#319811yescharacteristic
414C2×C61#319911yescharacteristic
415C2×C61#322011yescharacteristic
416C2×C61#322411yescharacteristic
417C23×D4C2×D6111yescharacteristic
418C22×D8C2×D6111yescharacteristic
419C22×D8C2×D6111yescharacteristic
420C2×#121C2×D6111yescharacteristic
421C2×C4×D4—611no—
422C2×#117—611no—
423C2×#117—611no—
424#447Dic6118yescomplemented
425C2×#107—611no—
426C2×#106—611no—
427C2×#102—611no—
428C2×#102—611no—
429C2×#102—611no—
430C2×#102—611no—
431C2×#102—611no—
432C2×#102—611no—
433C2×#102C2×D6111yescharacteristic
434C2×#102C2×D6111yescharacteristic
435C2×C22⋊C8—611no—
436C2×C22⋊C8C2×D6111yescharacteristic
437C2×#97—611no—
438C2×C4×C8—611no—
439#390—611no—
440#390—611no—
441#390—611no—
442#390—611no—
443#390—611no—
444#390—1221no—
445#390—1221no—
446#390—1221no—
447#389—611no—
448#388—1221no—
449#386—1221no—
450#385—1221no—
451#380—611no—
452#379—1221no—
453#379—1221no—
454C4×C4⋊C4—611no—
455#340—611no—
456#340—611no—
457#340—611no—
458#340—611no—
459#336—611no—
460#336—611no—
461C61#2205611yescharacteristic, complemented, Sylow
462C25—21no—
463C22×D4—21no—
464C22×D4—21no—
465C22×D4—22no—
466C22×D4—41no—
467C22×D4—41no—
468C22×D4—41no—
469C22×D4—41no—
470C22×D4C2×Dic6114yescomplemented
471C22×D4C22×D6111yescharacteristic
472C22×D4C22×D6111yescharacteristic
473C22×D4C22×D6111yescharacteristic
474C23×C4—1221no—
475C23×C4C22×D6111yescharacteristic
476C2×D8—41no—
477C2×D8—41no—
478C2×D8—41no—
479C2×D8—41no—
480C2×D8C2×Dic6114yes—
481C2×D8C2×Dic6114yes—
482C22×C8—611no—
483C22×C8—611no—
484C22×C8C22×D6111yescharacteristic
485C22×C8C22×D6111yescharacteristic
486#121—22no—
487#121C2×Dic6114yes—
488C4×D4—2441no—
489C4×D4—2441no—
490#117—2441no—
491#117—2441no—
492#117—2441no—
493#117—2441no—
494C2×C4⋊C4—611no—
495C2×C4⋊C4—611no—
496C2×C4⋊C4—611no—
497C2×C4⋊C4—611no—
498C2×C4⋊C4—611no—
499C2×C4⋊C4—611no—
500C2×C4⋊C4—1221no—
501C2×C4⋊C4C22×D6111yescharacteristic
502C2×C22⋊C4—21no—
503C2×C22⋊C4—611no—
504C2×C22⋊C4—611no—
505C2×C22⋊C4—1221no—
506C2×C22⋊C4—1221no—
507C2×C22⋊C4—1221no—
508C2×C22⋊C4—1221no—
509C2×C22⋊C4—1221no—
510C2×C22⋊C4—1221no—
511C2×C22⋊C4—1221no—
512C2×C22⋊C4—1221no—
513C2×C22⋊C4—1221no—
514C2×C22⋊C4—1221no—
515C2×C22⋊C4—1221no—
516C2×C22⋊C4—1221no—
517C2×C22⋊C4—1221no—
518C2×C42—611no—
519C2×C42—611no—
520C2×C42—1221no—
521C2×C42—1221no—
522#107—2441no—
523#106—2441no—
524#102—2441no—
525#102—2441no—
526#102—2441no—
527#102—2441no—
528#102—2441no—
529#102—2441no—
530#102C2×Dic6114yescomplemented
531#102C2×Dic6114yescomplemented
532C22⋊C8—1222no—
533C22⋊C8C2×Dic6114yescomplemented
534#97—2441no—
535C4×C8—2441no—
536#95—1221no—
537#95—1221no—
538#95—1221no—
539C24—21no—
540C24—21no—
541C24—21no—
542C24—24no—
543C24—42no—
544C24—42no—
545C24—81no—
546C24—81no—
547C24—81no—
548C24—81no—
549C24D4×D6111yescharacteristic
550C2×D4—24no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—24no—
567C2×D4—44no—
568C2×D4—44no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—44no—
572C2×D4—44no—
573C2×D4—81no—
574C2×D4—81no—
575C2×D4C22×Dic6112yes—
576C2×D4C22×Dic6112yes—
577C2×D4C22×Dic6112yes—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—611no—
584C22×C4—611no—
585C22×C4—611no—
586C22×C4—611no—
587C22×C4—1221no—
588C22×C4—1221no—
589C22×C4—1221no—
590C22×C4—1221no—
591C22×C4—4881no—
592C22×C4—4881no—
593C22×C4—2442no—
594C22×C4D4×D6111yescharacteristic
595C22×C4#1175822412yes—
596C22×C4C22×Dic6112yes—
597C22×C4C23×D6111yescharacteristic
598D8—44no—
599D8—44no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—1221no—
605C2×C8—1221no—
606C2×C8—1221no—
607C2×C8—1221no—
608C2×C8—1221no—
609C2×C8—1221no—
610C2×C8C22×Dic6112yes—
611C2×C8C22×Dic6112yes—
612C4⋊C4—21no—
613C4⋊C4—1221no—
614C4⋊C4—1221no—
615C4⋊C4—1221no—
616C4⋊C4—1221no—
617C4⋊C4—1221no—
618C4⋊C4—1221no—
619C4⋊C4—1221no—
620C4⋊C4—1221no—
621C4⋊C4—4881no—
622C4⋊C4—2441no—
623C4⋊C4—2441no—
624C4⋊C4C22×Dic6112yes—
625C22⋊C4—24no—
626C22⋊C4—4881no—
627C22⋊C4—4881no—
628C22⋊C4—4881no—
629C22⋊C4—4881no—
630C22⋊C4—4881no—
631C22⋊C4—4881no—
632C22⋊C4—4881no—
633C22⋊C4—4881no—
634C22⋊C4—4881no—
635C22⋊C4—4881no—
636C22⋊C4—4881no—
637C22⋊C4—2441no—
638C22⋊C4—2441no—
639C22⋊C4—2442no—
640C22⋊C4—2442no—
641C42—1221no—
642C42—1221no—
643C42—1221no—
644C42—1221no—
645C42—4881no—
646C42—2442no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—48no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—84no—
676C23—84no—
677C23—84no—
678C23—84no—
679C23—84no—
680C23—84no—
681C23D4×Dic6112yes—
682C23C2×D4×D6111yescharacteristic
683D4—22no—
684D4—22no—
685D4—22no—
686D4—22no—
687D4—22no—
688D4—22no—
689D4—48no—
690D4—41no—
691D4—41no—
692D4—41no—
693D4—41no—
694D4—41no—
695D4—41no—
696D4—84no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—1221no—
707C2×C4—1221no—
708C2×C4—1221no—
709C2×C4—1221no—
710C2×C4—1221no—
711C2×C4—1221no—
712C2×C4—1221no—
713C2×C4—1221no—
714C2×C4—1221no—
715C2×C4—1221no—
716C2×C4—1221no—
717C2×C4—1221no—
718C2×C4—4884no—
719C2×C4—2441no—
720C2×C4—2441no—
721C2×C4—2441no—
722C2×C4—2441no—
723C2×C4—2441no—
724C2×C4—2441no—
725C2×C4—2441no—
726C2×C4—2441no—
727C2×C4—2441no—
728C2×C4—2441no—
729C2×C4—2441no—
730C2×C4—2441no—
731C2×C4D4×Dic6112yes—
732C2×C4C23×Dic6111yescharacteristic
733C2×C4C2×#1175822411yescharacteristic
734C2×C4#1451982211yescharacteristic
735C2×C4#1451982211yescharacteristic
736C2×C4#1451982211yescharacteristic
737C2×C4#1451982211yescharacteristic
738C8—22no—
739C8—22no—
740C8—2441no—
741C8—2441no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—816no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22—81no—
768C22—81no—
769C22—81no—
770C22—81no—
771C22C2×D4×Dic6111yescharacteristic
772C22#1684032211yescharacteristic
773C22#1684032711yescharacteristic
774C22#1684056311yescharacteristic
775C22#1684056311yescharacteristic
776C22#1684056611yescharacteristic
777C22#1684057211yescharacteristic
778C4—22no—
779C4—42no—
780C4—4881no—
781C4—4881no—
782C4—4881no—
783C4—4881no—
784C4—2441no—
785C4—2441no—
786C4—2441no—
787C4—2441no—
788C4#1684023711yescharacteristic
789C4#1684023711yescharacteristic
790C4#1684034711yescharacteristic
791C4#1684034711yescharacteristic
792C2—42no—
793C2—82no—
794C2—82no—
795C2—82no—
796C2#2144848011yescharacteristic
797C2#2145465211yescharacteristic
798C2#2145467111yescharacteristic
799C2#2145666711yescharacteristic
800C2#2145668211yescharacteristic
801C2#2145686511yescharacteristic
802C2#2145690911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
Fitting, prime radicalC2×C61×#447C2
socleC23×C61C22×D4
cosocleC22×C4×C61C24
hypercenterC2×#447D61
hypocenterC61#22056
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#447

Complements

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

NH ≅ G/Ntype
1. #21448514C2semidirect
2. #21448401C2semidirect
3. #21446696C2semidirect
4. #21446686C2semidirect
5. #21446518C2semidirect
6. #21446504C2semidirect
7. #21446448C2semidirect
8. #21446441C2semidirect
9. #21446169C2semidirect
10. #21446169C2semidirect
11. #21446142C2semidirect
12. #21446020C2semidirect
13. #21445750C2semidirect
14. #21445587C2semidirect
16. C2×D4×Dic61C22semidirect
19. C2×#14519711C22semidirect
20. C2×#14519709C22semidirect
25. C2×#14519698C22semidirect
26. C2×#14519698C22semidirect
28. C2×#14519687C22semidirect
29. C2×C8×Dic61C22semidirect
37. #16839665C22semidirect
38. #16839661C22semidirect
45. C4⋊C4×Dic61C22semidirect
46. #16839525C22semidirect
47. #16839525C22semidirect
48. #16839524C22semidirect
49. #16839524C22semidirect
50. #16839516C22semidirect
51. #16839516C22semidirect
56. C61×#447C4semidirect
117. C22×D4×C61C2×C4semidirect
134. #102×C61C2×C4semidirect
135. #102×C61C2×C4semidirect
136. C22⋊C8×C61C2×C4semidirect
424. #447Dic61semidirect
461. C61#22056semidirect
470. C22×D4C2×Dic61semidirect
530. #102C2×Dic61semidirect
531. #102C2×Dic61semidirect
533. C22⋊C8C2×Dic61semidirect

Maximal subgroups

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

subgroupindex
#214485142
#214484012
#214466962
#214466862
#214465182
#214465042
#214464482
#214464412
#214461692
#214461422
#214460202
#214457502
#214455872
C2×C61×#4472
#2205661