Finite Group Databasebeta

← #29700274

Subgroups — #29700274

Order 15616.

1302 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839863C211yesmaximal, characteristic, complemented
2C22×#14519698C211yesmaximal, characteristic
3#21448828C211yesmaximal, characteristic, complemented
4D4×C22⋊Dic61C211yesmaximal, characteristic
5#21446702C211yesmaximal, characteristic, complemented
6#21446518C211yesmaximal, characteristic, complemented
7#21446441C211yesmaximal, characteristic, complemented
8#21446243C211yesmaximal, characteristic, complemented
9#21446176C211yesmaximal, characteristic, complemented
10#21446155C211yesmaximal, characteristic, complemented
11#21446068C211yesmaximal, characteristic, complemented
12#21446009C211yesmaximal, characteristic, complemented
13#21445646C211yesmaximal, characteristic, complemented
14#21445598C211yesmaximal, characteristic, complemented
15C2×C61×#450C211yesmaximal, characteristic
16C23×#92418C2211yescharacteristic
17C2×Q8×Dic61C2211yescharacteristic, complemented
18C2×D4×Dic61C2211yescharacteristic
19C2×D4×Dic61C2211yescharacteristic
20C22×C4⋊Dic61C2211yescharacteristic
21C22×C22⋊Dic61—21no—
22#16839863—24no—
23C2×#14519711C2211yescharacteristic, complemented
24C2×#14519711C2211yescharacteristic, complemented
25C2×#14519701C2211yescharacteristic, complemented
26C2×#14519701C2211yescharacteristic, complemented
27C2×#14519698—24no—
28C2×#14519698C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519698C2211yescharacteristic
32C2×#14519687C2211yescharacteristic, complemented
33C2×#14519687C2211yescharacteristic, complemented
34#16839669C2211yescharacteristic, complemented
35#16839665C2211yescharacteristic
36#16839665C2211yescharacteristic
37#16839661—21no—
38#16839661C2211yescharacteristic, complemented
39#16839648—21no—
40#16839642—21no—
41#16839642—21no—
42#16839637—21no—
43#16839622C2211yescharacteristic
44#16839618—21no—
45C4⋊C4×Dic61C2211yescharacteristic, complemented
46C22⋊C4×Dic61—21no—
47C4×C22⋊Dic61C2211yescharacteristic
48#16839525C2211yescharacteristic, complemented
49#16839525C2211yescharacteristic, complemented
50#16839524C2211yescharacteristic, complemented
51#16839524C2211yescharacteristic, complemented
52#16839516C2211yescharacteristic, complemented
53#16839516C2211yescharacteristic, complemented
54C23×D4×C61C2211yescharacteristic
55C22×SD16×C61C2211yescharacteristic
56C22×SD16×C61C2211yescharacteristic
57C2×C22⋊Q8×C61C2211yescharacteristic
58C61×#450C418yescomplemented
59C2×#102×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic
61C2×C22⋊C8×C61C2211yescharacteristic
62C23×Dic61—21no—
63C23×Dic61—21no—
64C23×Dic61—21no—
65C22×#92418—22no—
66C22×#92418—22no—
67C22×#92418—41no—
68C22×#92418C2311yescharacteristic
69C22×#92418C2311yescharacteristic
70Q8×Dic61—22no—
71Q8×Dic61—41no—
72D4×Dic61—22no—
73D4×Dic61—22no—
74D4×Dic61—41no—
75D4×Dic61—41no—
76C2×C4⋊Dic61—22no—
77C2×C4⋊Dic61—21no—
78C2×C4⋊Dic61—21no—
79C2×C4⋊Dic61—21no—
80C2×C4⋊Dic61—41no—
81C2×C4⋊Dic61C2311yescharacteristic
82C2×C4⋊Dic61C2311yescharacteristic
83C2×C4⋊Dic61C2311yescharacteristic
84C2×C4⋊Dic61C2311yescharacteristic
85C2×C22⋊Dic61—21no—
86C2×C22⋊Dic61—21no—
87C2×C22⋊Dic61—21no—
88C2×C22⋊Dic61—21no—
89C2×C22⋊Dic61—21no—
90C2×C22⋊Dic61—21no—
91C2×C22⋊Dic61—21no—
92C2×C22⋊Dic61—44no—
93C2×C22⋊Dic61D411yescharacteristic
94C2×C22⋊Dic61D411yescharacteristic
95C2×C4×Dic61—21no—
96C2×C4×Dic61—21no—
97C2×C4×Dic61C2311yescharacteristic
98C2×C4×Dic61C2311yescharacteristic
99#14519711—22no—
100#14519711—41no—
101#14519701—22no—
102#14519701—41no—
103#14519698—22no—
104#14519698—22no—
105#14519698—22no—
106#14519698D414yes—
107#14519687—22no—
108#14519687—41no—
109#14519684—21no—
110#14519684—21no—
111#14519684—21no—
112#14519684—21no—
113#14519684—21no—
114#14519684D411yescharacteristic
115#14519684D411yescharacteristic
116C25×C61—21no—
117C22×Q8×C61C2311yescharacteristic
118C22×D4×C61—22no—
119C22×D4×C61—22no—
120C22×D4×C61—21no—
121C22×D4×C61—22no—
122C22×D4×C61—41no—
123C22×D4×C61—41no—
124C22×D4×C61C2×C414yes—
125C22×D4×C61C2311yescharacteristic
126C22×D4×C61C2311yescharacteristic
127C23×C4×C61C2311yescharacteristic
128C2×SD16×C61—22no—
129C2×SD16×C61—22no—
130C2×SD16×C61—41no—
131C2×SD16×C61—41no—
132C2×SD16×C61C2×C414yescomplemented
133C2×SD16×C61C2×C414yescomplemented
134C22×C8×C61C2311yescharacteristic
135C22×C8×C61C2311yescharacteristic
136C22⋊Q8×C61—22no—
137C22⋊Q8×C61C2×C414yescomplemented
138C2×C4⋊C4×C61—21no—
139C2×C4⋊C4×C61C2311yescharacteristic
140C2×C22⋊C4×C61—21no—
141#102×C61C2×C414yescomplemented
142#102×C61C2×C414yescomplemented
143C22⋊C8×C61C2×C414yescomplemented
144C24×C61—21no—
145C24×C61—21no—
146C24×C61—24no—
147C24×C61—42no—
148C24×C61—42no—
149C24×C61—42no—
150C24×C61—42no—
151C24×C61—81no—
152C24×C61—81no—
153C24×C61C2×D411yescharacteristic
154C2×Q8×C61—21no—
155C2×Q8×C61—21no—
156C2×Q8×C61—21no—
157C2×Q8×C61—21no—
158C2×Q8×C61—21no—
159C2×Q8×C61C22×C412yes—
160C2×D4×C61—28no—
161C2×D4×C61—24no—
162C2×D4×C61—21no—
163C2×D4×C61—21no—
164C2×D4×C61—21no—
165C2×D4×C61—21no—
166C2×D4×C61—21no—
167C2×D4×C61—21no—
168C2×D4×C61—21no—
169C2×D4×C61—21no—
170C2×D4×C61—44no—
171C2×D4×C61—44no—
172C2×D4×C61—44no—
173C2×D4×C61—42no—
174C2×D4×C61—42no—
175C2×D4×C61C22×C412yes—
176C2×D4×C61C22×C412yes—
177C2×D4×C61C2×D412yes—
178C2×D4×C61#4112yes—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61C22×C412yes—
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61#4112yes—
188C22×C4×C61C2411yescharacteristic
189C22×Dic61—21no—
190C22×Dic61—21no—
191C22×Dic61—21no—
192C22×Dic61—21no—
193C22×Dic61—42no—
194C22×Dic61—42no—
195C22×Dic61—42no—
196C22×Dic61—42no—
197C22×Dic61—42no—
198C22×Dic61—42no—
199C22×Dic61—81no—
200C22×Dic61—81no—
201C22×Dic61—81no—
202C22×Dic61C2×D411yescharacteristic
203C22×Dic61C2×D411yescharacteristic
204C22×Dic61C2×D411yescharacteristic
205C22×Dic61C2×D411yescharacteristic
206SD16×C61—28no—
207SD16×C61—44no—
208C2×C8×C61—21no—
209C2×C8×C61—21no—
210C2×C8×C61—21no—
211C2×C8×C61—21no—
212C2×C8×C61C22×C412yes—
213C2×C8×C61C22×C412yes—
214C4⋊C4×C61—24no—
215C4⋊C4×C61—21no—
216C4⋊C4×C61C22×C412yes—
217C22⋊C4×C61—24no—
218C22⋊Dic61—22no—
219C22⋊Dic61—22no—
220C22⋊Dic61—42no—
221C22⋊Dic61—42no—
222C22⋊Dic61—42no—
223C22⋊Dic61—42no—
224C22⋊Dic61—42no—
225C22⋊Dic61—81no—
226C22⋊Dic61—81no—
227C4⋊Dic61—21no—
228C4⋊Dic61—21no—
229C4⋊Dic61—21no—
230C4⋊Dic61—21no—
231C4⋊Dic61—21no—
232C4⋊Dic61—21no—
233C4⋊Dic61—21no—
234C4⋊Dic61—42no—
235C4⋊Dic61—42no—
236C4⋊Dic61—81no—
237C4⋊Dic61C2×D412yes—
238C4×Dic61—21no—
239C4×Dic61—21no—
240C4×Dic61—21no—
241C4×Dic61—21no—
242C4×Dic61—42no—
243C4×Dic61—81no—
244C2×#92418—21no—
245C2×#92418—21no—
246C2×#92418—21no—
247C2×#92418—21no—
248C2×#92418—21no—
249C2×#92418—44no—
250C2×#92418C2×D412yes—
251C23×C61—21no—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61—22no—
256C23×C61—22no—
257C23×C61—22no—
258C23×C61—22no—
259C23×C61—48no—
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—48no—
271C23×C61—84no—
272C23×C61—84no—
273C23×C61—84no—
274C23×C61—84no—
275C23×C61—84no—
276C23×C61C4×D412yes—
277C23×C61AGL(1,ℤ/8)12yes—
278C23×C61#13712yes—
279C23×C61C22×D411yescharacteristic
280Q8×C61—22no—
281Q8×C61—22no—
282Q8×C61—41no—
283Q8×C61—41no—
284D4×C61—22no—
285D4×C61—22no—
286D4×C61—22no—
287D4×C61—22no—
288D4×C61—22no—
289D4×C61—48no—
290D4×C61—41no—
291D4×C61—41no—
292D4×C61C4×D414yes—
293C2×C4×C61—21no—
294C2×C4×C61—21no—
295C2×C4×C61—22no—
296C2×C4×C61—22no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61—41no—
304C2×C4×C61—41no—
305C2×C4×C61C4×D412yes—
306C2×C4×C61C23×C411yescharacteristic
307C2×C4×C61C22×D411yescharacteristic
308C2×C4×C61C2×#4111yescharacteristic
309C2×C4×C61C2×#4111yescharacteristic
310C2×C4×C61H(5,𝔽2)11yescharacteristic
311C2×C4×C61H(5,𝔽2)11yescharacteristic
312C2×Dic61—21no—
313C2×Dic61—21no—
314C2×Dic61—22no—
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—21no—
324C2×Dic61—21no—
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—41no—
336C2×Dic61—84no—
337C2×Dic61—84no—
338C2×Dic61—84no—
339C8×C61—22no—
340C8×C61—22no—
341#92418—22no—
342#92418—41no—
343#22854—611nomaximal, Sylow
344C22×C61—22no—
345C22×C61—22no—
346C22×C61—22no—
347C22×C61—22no—
348C22×C61—22no—
349C22×C61—22no—
350C22×C61—24no—
351C22×C61—42no—
352C22×C61—42no—
353C22×C61—42no—
354C22×C61—42no—
355C22×C61—42no—
356C22×C61—42no—
357C22×C61—42no—
358C22×C61—42no—
359C22×C61—42no—
360C22×C61—816no—
361C22×C61—81no—
362C22×C61—81no—
363C22×C61—81no—
364C22×C61—81no—
365C22×C61#44014yescomplemented
366C22×C61C2×C4×D411yescharacteristic
367C22×C61D4211yescharacteristic
368C22×C61#54611yescharacteristic
369C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
370C22×C61C2×#13711yescharacteristic
371C22×C61#57611yescharacteristic
372C22×C61#57711yescharacteristic
373C4×C61—22no—
374C4×C61—42no—
375C4×C61—42no—
376C4×C61C2×C4×D411yescharacteristic
377C4×C61#51811yescharacteristic
378C4×C61#54611yescharacteristic
379C4×C61#55111yescharacteristic
380Dic61—41no—
381Dic61—42no—
382Dic61—41no—
383Dic61—41no—
384Dic61—41no—
385Dic61—81no—
386Dic61—81no—
387Dic61—81no—
388C2×#450D6111yescharacteristic
389C2×#440—611no—
390C22×#102—611no—
391#2360—611no—
392D4×C22⋊C4—611no—
393#1973—611no—
394#1936—611no—
395#1925—611no—
396#1892—611no—
397#1880—611no—
398#1877—611no—
399#1862—611no—
400#1852—611no—
401#1762—611no—
402#1752—611no—
403C2×C61—24no—
404C2×C61—44no—
405C2×C61—82no—
406C2×C61#235811yescharacteristic
407C2×C61C2×#44011yescharacteristic
408C2×C61#294611yescharacteristic
409C2×C61#326411yescharacteristic
410C2×C61#326611yescharacteristic
411C2×C61#331011yescharacteristic
412C2×C61#331411yescharacteristic
413C23×D4C2×D6111yescharacteristic
414C22×SD16C2×D6111yescharacteristic
415C22×SD16C2×D6111yescharacteristic
416C23×C8—611no—
417C2×C22⋊Q8C2×D6111yescharacteristic
418C2×C4×Q8—611no—
419C2×C4×D4—611no—
420C2×C4×D4—611no—
421C22×C4⋊C4—611no—
422C22×C22⋊C4—1221no—
423#450Dic6118yescomplemented
424#440—1224no—
425C2×#107—611no—
426C2×#107—611no—
427C2×#103—611no—
428C2×#103—611no—
429C2×#102—611no—
430C2×#102—611no—
431C2×#102—611no—
432C2×#102—611no—
433C2×#102—1224no—
434C2×#102C2×D6111yescharacteristic
435C2×#102C2×D6111yescharacteristic
436C2×C22⋊C8C2×D6111yescharacteristic
437C2×#97—611no—
438C2×#97—611no—
439#391—611no—
440#390—611no—
441#390—611no—
442#389—611no—
443#389—1221no—
444#387—1221no—
445#386—1221no—
446#386—1221no—
447#385—1221no—
448#380—611no—
449#379—1221no—
450C4×C4⋊C4—611no—
451C4×C22⋊C4—611no—
452C4×C22⋊C4—1221no—
453#340—611no—
454#340—611no—
455#340—611no—
456#340—611no—
457#336—611no—
458#336—611no—
459C61#2285411yescharacteristic, complemented, Sylow
460C25—21no—
461C22×Q8C22×D6111yescharacteristic
462C22×D4—22no—
463C22×D4—22no—
464C22×D4—21no—
465C22×D4—22no—
466C22×D4—41no—
467C22×D4—41no—
468C22×D4C2×Dic6114yes—
469C22×D4C22×D6111yescharacteristic
470C22×D4C22×D6111yescharacteristic
471C23×C4—1221no—
472C23×C4—1221no—
473C23×C4—1221no—
474C23×C4C22×D6111yescharacteristic
475C2×SD16—22no—
476C2×SD16—22no—
477C2×SD16—41no—
478C2×SD16—41no—
479C2×SD16C2×Dic6114yescomplemented
480C2×SD16C2×Dic6114yescomplemented
481C22×C8—611no—
482C22×C8—611no—
483C22×C8—1222no—
484C22×C8—1222no—
485C22×C8—2441no—
486C22×C8C22×D6111yescharacteristic
487C22×C8C22×D6111yescharacteristic
488C22⋊Q8—22no—
489C22⋊Q8C2×Dic6114yescomplemented
490C4×Q8—1222no—
491C4×Q8—2441no—
492C4×D4—1222no—
493C4×D4—1222no—
494C4×D4—2441no—
495C4×D4—2441no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—611no—
498C2×C4⋊C4—611no—
499C2×C4⋊C4—611no—
500C2×C4⋊C4—611no—
501C2×C4⋊C4—1222no—
502C2×C4⋊C4—1221no—
503C2×C4⋊C4—1221no—
504C2×C4⋊C4—1221no—
505C2×C4⋊C4—2441no—
506C2×C4⋊C4C22×D6111yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—611no—
509C2×C22⋊C4—611no—
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—2444no—
518C2×C42—611no—
519C2×C42—611no—
520C2×C42—1221no—
521C2×C42—1221no—
522#107—1222no—
523#107—2441no—
524#103—1222no—
525#103—2441no—
526#102—614no—
527#102—1222no—
528#102—1222no—
529#102—1222no—
530#102C2×Dic6114yescomplemented
531#102C2×Dic6114yescomplemented
532C22⋊C8C2×Dic6114yescomplemented
533#97—1222no—
534#97—2441no—
535#95—611no—
536#95—611no—
537#95—1221no—
538#95—1221no—
539#95—1221no—
540#95—1221no—
541#95—1221no—
542C24—21no—
543C24—21no—
544C24—24no—
545C24—42no—
546C24—42no—
547C24—42no—
548C24—42no—
549C24—81no—
550C24—81no—
551C24D4×D6111yescharacteristic
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8C22×Dic6112yes—
558C2×D4—28no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—24no—
568C2×D4—44no—
569C2×D4—44no—
570C2×D4—44no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4D4×D6112yes—
574C2×D4#1175822412yes—
575C2×D4C22×Dic6112yes—
576C2×D4C22×Dic6112yes—
577C22×C4—21no—
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—4881no—
594C22×C4—2442no—
595C22×C4—2442no—
596C22×C4—2442no—
597C22×C4—2442no—
598C22×C4—2442no—
599C22×C4—2442no—
600C22×C4D4×D6111yescharacteristic
601C22×C4#1175822412yes—
602C22×C4C22×Dic6112yes—
603C22×C4C23×D6111yescharacteristic
604SD16—28no—
605SD16—44no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—612no—
611C2×C8—1221no—
612C2×C8—1221no—
613C2×C8—1221no—
614C2×C8—1221no—
615C2×C8—1221no—
616C2×C8—2444no—
617C2×C8C22×Dic6112yes—
618C2×C8C22×Dic6112yes—
619C4⋊C4—21no—
620C4⋊C4—24no—
621C4⋊C4—612no—
622C4⋊C4—1221no—
623C4⋊C4—1221no—
624C4⋊C4—1221no—
625C4⋊C4—1221no—
626C4⋊C4—1221no—
627C4⋊C4—1221no—
628C4⋊C4—1221no—
629C4⋊C4—4881no—
630C4⋊C4—2442no—
631C4⋊C4—2442no—
632C4⋊C4C22×Dic6112yes—
633C22⋊C4—24no—
634C22⋊C4—1222no—
635C22⋊C4—1222no—
636C22⋊C4—4881no—
637C22⋊C4—4881no—
638C22⋊C4—2442no—
639C22⋊C4—2442no—
640C22⋊C4—2442no—
641C22⋊C4—2442no—
642C22⋊C4—2442no—
643C42—1221no—
644C42—1221no—
645C42—1221no—
646C42—1221no—
647C42—4881no—
648C42—2442no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—48no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—48no—
667C23—41no—
668C23—41no—
669C23—84no—
670C23—84no—
671C23—84no—
672C23—84no—
673C23—84no—
674C23D4×Dic6112yes—
675C23#1451980412yes—
676C23#1451980612yes—
677C23C2×D4×D6111yescharacteristic
678Q8—22no—
679Q8—22no—
680Q8—41no—
681Q8—41no—
682D4—22no—
683D4—22no—
684D4—22no—
685D4—22no—
686D4—22no—
687D4—48no—
688D4—41no—
689D4—41no—
690D4D4×Dic6114yes—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—1221no—
704C2×C4—1221no—
705C2×C4—1221no—
706C2×C4—1221no—
707C2×C4—1221no—
708C2×C4—1221no—
709C2×C4—1221no—
710C2×C4—1221no—
711C2×C4—1221no—
712C2×C4—1221no—
713C2×C4—1222no—
714C2×C4—1221no—
715C2×C4—1221no—
716C2×C4—4884no—
717C2×C4—4884no—
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×C4D4×Dic6112yes—
731C2×C4C23×Dic6111yescharacteristic
732C2×C4C2×D4×D6111yescharacteristic
733C2×C4C2×#1175822411yescharacteristic
734C2×C4C2×#1175822411yescharacteristic
735C2×C4#1451982211yescharacteristic
736C2×C4#1451982211yescharacteristic
737C8—22no—
738C8—22no—
739C8—1222no—
740C8—2441no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—24no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—816no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22#1683986314yescomplemented
763C22C2×D4×Dic6111yescharacteristic
764C22#1684039411yescharacteristic
765C22#1684039911yescharacteristic
766C22C2×#1451980411yescharacteristic
767C22C2×#1451980611yescharacteristic
768C22#1684056611yescharacteristic
769C22#1684057211yescharacteristic
770C4—22no—
771C4—42no—
772C4—42no—
773C4—4881no—
774C4—4881no—
775C4—4881no—
776C4—2441no—
777C4—2442no—
778C4—2441no—
779C4—2441no—
780C4—2441no—
781C4C2×D4×Dic6111yescharacteristic
782C4#1684023711yescharacteristic
783C4#1684039911yescharacteristic
784C4#1684044311yescharacteristic
785C2—24no—
786C2—44no—
787C2—82no—
788C2#2144880311yescharacteristic
789C2C2×#1683986311yescharacteristic
790C2#2145465211yescharacteristic
791C2#2145730311yescharacteristic
792C2#2145733311yescharacteristic
793C2#2145784411yescharacteristic
794C2#2145790411yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#450C2
socleC23×C61C22×D4
prime radicalC23×D4×C61C22
cosocleC22×C4×C61C24
hypercenterC2×#450D61
hypocenterC61#22854
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#450

Complements

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

NH ≅ G/Ntype
1. C2×#16839863C2semidirect
3. #21448828C2semidirect
5. #21446702C2semidirect
6. #21446518C2semidirect
7. #21446441C2semidirect
8. #21446243C2semidirect
9. #21446176C2semidirect
10. #21446155C2semidirect
11. #21446068C2semidirect
12. #21446009C2semidirect
13. #21445646C2semidirect
14. #21445598C2semidirect
17. C2×Q8×Dic61C22semidirect
23. C2×#14519711C22semidirect
24. C2×#14519711C22semidirect
25. C2×#14519701C22semidirect
26. C2×#14519701C22semidirect
32. C2×#14519687C22semidirect
33. C2×#14519687C22semidirect
34. #16839669C22semidirect
38. #16839661C22semidirect
45. C4⋊C4×Dic61C22semidirect
48. #16839525C22semidirect
49. #16839525C22semidirect
50. #16839524C22semidirect
51. #16839524C22semidirect
52. #16839516C22semidirect
53. #16839516C22semidirect
58. C61×#450C4semidirect
132. C2×SD16×C61C2×C4semidirect
133. C2×SD16×C61C2×C4semidirect
137. C22⋊Q8×C61C2×C4semidirect
141. #102×C61C2×C4semidirect
142. #102×C61C2×C4semidirect
143. C22⋊C8×C61C2×C4semidirect
365. C22×C61#440semidirect
423. #450Dic61semidirect
459. C61#22854semidirect
479. C2×SD16C2×Dic61semidirect
480. C2×SD16C2×Dic61semidirect
489. C22⋊Q8C2×Dic61semidirect
530. #102C2×Dic61semidirect
531. #102C2×Dic61semidirect
532. C22⋊C8C2×Dic61semidirect
762. C22#16839863semidirect

Maximal subgroups

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

subgroupindex
C2×#168398632
C22×#145196982
#214488282
D4×C22⋊Dic612
#214467022
#214465182
#214464412
#214462432
#214461762
#214461552
#214460682
#214460092
#214456462
#214455982
C2×C61×#4502
#2285461