Finite Group Databasebeta

← #29685778

Subgroups — #29685778

Order 15616.

1420 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840245C211yesmaximal, characteristic
2C2×#16839869C211yesmaximal, characteristic, complemented
3C2×SD16×Dic61C211yesmaximal, characteristic, complemented
4#21448503C211yesmaximal, characteristic, complemented
5#21446162C211yesmaximal, characteristic, complemented
6#21446155C211yesmaximal, characteristic, complemented
7#21446127C211yesmaximal, characteristic, complemented
8#21446089C211yesmaximal, characteristic, complemented
9#21446082C211yesmaximal, characteristic, complemented
10#21446014C211yesmaximal, characteristic, complemented
11#21445759C211yesmaximal, characteristic
12#21445646C211yesmaximal, characteristic, complemented
13#103×Dic61C211yesmaximal, characteristic, complemented
14#21445587C211yesmaximal, characteristic, complemented
15C2×C61×#452C211yesmaximal, characteristic
16#16840245—24no—
17#16840245—24no—
18C2×Q8×Dic61C2211yescharacteristic
19C2×Q8×Dic61C2211yescharacteristic
20C2×Q8×Dic61C2211yescharacteristic
21C2×D4×Dic61—21no—
22C2×D4×Dic61—21no—
23C2×D4×Dic61C2211yescharacteristic
24C2×D4×Dic61C2211yescharacteristic
25C2×#14519736—21no—
26C2×#14519736C2211yescharacteristic
27C22×C4⋊Dic61—21no—
28C22×C4⋊Dic61C2211yescharacteristic
29#16839869—24no—
30SD16×Dic61—24no—
31C2×#14519709C2211yescharacteristic
32C2×#14519709C2211yescharacteristic
33C2×#14519701C2211yescharacteristic
34C2×#14519701C2211yescharacteristic
35C2×#14519701C2211yescharacteristic
36C2×#14519701C2211yescharacteristic
37C2×#14519698C2211yescharacteristic
38C2×#14519698C2211yescharacteristic
39C2×C22⋊#92418C2211yescharacteristic
40C2×#14519687C2211yescharacteristic
41C2×C8×Dic61C2211yescharacteristic
42#16839669C2211yescharacteristic
43#16839661—21no—
44#16839661C2211yescharacteristic
45#16839655—21no—
46#16839655—21no—
47#16839648—21no—
48#16839622C2211yescharacteristic
49C4⋊C4×Dic61C2211yescharacteristic
50#16839525C2211yescharacteristic
51#16839525C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839516C2211yescharacteristic
55#16839516C2211yescharacteristic
56C22×#41×C61C2211yescharacteristic
57C22×Q16×C61C2211yescharacteristic
58C22×SD16×C61C2211yescharacteristic
59C2×C22⋊Q8×C61C2211yescharacteristic
60C61×#452C418yescomplemented
61C2×#103×C61C2211yescharacteristic
62C2×#102×C61C2211yescharacteristic
63C2×C22⋊C8×C61C2211yescharacteristic
64C23×Dic61—21no—
65C23×Dic61—21no—
66C23×Dic61—21no—
67C22×#92418C2311yescharacteristic
68C22×#92418C2311yescharacteristic
69Q8×Dic61—22no—
70Q8×Dic61—22no—
71Q8×Dic61—22no—
72Q8×Dic61—22no—
73Q8×Dic61—22no—
74Q8×Dic61D414yes—
75D4×Dic61—28no—
76D4×Dic61—28no—
77D4×Dic61—22no—
78D4×Dic61—22no—
79D4×Dic61—22no—
80D4×Dic61D414yes—
81#14519736—28no—
82#14519736—22no—
83#14519736—22no—
84C2×C4⋊Dic61—28no—
85C2×C4⋊Dic61—21no—
86C2×C4⋊Dic61—21no—
87C2×C4⋊Dic61—21no—
88C2×C4⋊Dic61—22no—
89C2×C4⋊Dic61—22no—
90C2×C4⋊Dic61—21no—
91C2×C4⋊Dic61—21no—
92C2×C4⋊Dic61D411yescharacteristic
93C2×C4⋊Dic61D411yescharacteristic
94C2×C4⋊Dic61C2311yescharacteristic
95C2×C4⋊Dic61C2311yescharacteristic
96C2×C4⋊Dic61C2311yescharacteristic
97C2×C4⋊Dic61C2311yescharacteristic
98C2×C22⋊Dic61—21no—
99C2×C22⋊Dic61—21no—
100C2×C22⋊Dic61—21no—
101C2×C22⋊Dic61D411yescharacteristic
102C2×C22⋊Dic61D411yescharacteristic
103C2×C4×Dic61—21no—
104C2×C4×Dic61—21no—
105C2×C4×Dic61—21no—
106C2×C4×Dic61—21no—
107C2×C4×Dic61C2311yescharacteristic
108C2×C4×Dic61C2311yescharacteristic
109#14519709—22no—
110#14519709—22no—
111#14519701—22no—
112#14519701—22no—
113#14519701—22no—
114#14519701—22no—
115#14519698—22no—
116#14519698—22no—
117C22⋊#92418—22no—
118#14519687—22no—
119C8×Dic61—22no—
120#14519684—21no—
121#14519684—21no—
122#14519684—21no—
123#14519684—21no—
124#14519684—21no—
125C2×#41×C61—22no—
126C2×#41×C61—22no—
127C2×#41×C61—22no—
128C2×#41×C61—22no—
129C2×#41×C61—22no—
130C2×#41×C61C2×C414yes—
131C22×Q8×C61C2311yescharacteristic
132C22×Q8×C61C2311yescharacteristic
133C22×D4×C61—21no—
134C22×D4×C61C2311yescharacteristic
135C23×C4×C61—21no—
136C23×C4×C61C2311yescharacteristic
137C2×Q16×C61—22no—
138C2×Q16×C61—22no—
139C2×Q16×C61C2×C414yescomplemented
140C2×SD16×C61—22no—
141C2×SD16×C61—22no—
142C2×SD16×C61C2×C414yescomplemented
143C22×C8×C61C2311yescharacteristic
144C22×C8×C61C2311yescharacteristic
145C22⋊Q8×C61—22no—
146C22⋊Q8×C61C2×C414yescomplemented
147C2×C4⋊C4×C61—21no—
148C2×C4⋊C4×C61C2311yescharacteristic
149C2×C22⋊C4×C61—21no—
150#103×C61C2×C414yescomplemented
151#102×C61C2×C414yescomplemented
152C22⋊C8×C61C2×C414yescomplemented
153C24×C61—21no—
154C24×C61C2×D411yescharacteristic
155#41×C61—28no—
156#41×C61—28no—
157#41×C61—28no—
158#41×C61—28no—
159C2×Q8×C61—21no—
160C2×Q8×C61—21no—
161C2×Q8×C61—21no—
162C2×Q8×C61—21no—
163C2×Q8×C61—21no—
164C2×Q8×C61—21no—
165C2×Q8×C61—21no—
166C2×Q8×C61—21no—
167C2×Q8×C61C22×C412yes—
168C2×Q8×C61C22×C412yes—
169C2×Q8×C61C2×D412yes—
170C2×Q8×C61#4112yes—
171C2×D4×C61—24no—
172C2×D4×C61—24no—
173C2×D4×C61—24no—
174C2×D4×C61—21no—
175C2×D4×C61—21no—
176C2×D4×C61—21no—
177C2×D4×C61C22×C412yes—
178C2×D4×C61C2×D412yes—
179C2×D4×C61#4112yes—
180C22×C4×C61—24no—
181C22×C4×C61—24no—
182C22×C4×C61—21no—
183C22×C4×C61—24no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61C22×C412yes—
191C22×C4×C61C2×D411yescharacteristic
192C22×C4×C61#4112yes—
193C22×C4×C61C2411yescharacteristic
194C22×Dic61—21no—
195C22×Dic61—21no—
196C22×Dic61—24no—
197C22×Dic61—24no—
198C22×Dic61—24no—
199C22×Dic61—21no—
200C22×Dic61—21no—
201C22×Dic61—81no—
202C22×Dic61—81no—
203C22×Dic61—81no—
204C22×Dic61—81no—
205C22×Dic61—81no—
206C22×Dic61—81no—
207C22×Dic61C2×D411yescharacteristic
208C22×Dic61C2×D411yescharacteristic
209C22×Dic61C2×D411yescharacteristic
210C22×Dic61C2×D411yescharacteristic
211Q16×C61—28no—
212SD16×C61—28no—
213C2×C8×C61—21no—
214C2×C8×C61—21no—
215C2×C8×C61—21no—
216C2×C8×C61—21no—
217C2×C8×C61C22×C412yes—
218C2×C8×C61C22×C412yes—
219C4⋊C4×C61—24no—
220C4⋊C4×C61—21no—
221C4⋊C4×C61C22×C412yes—
222C22⋊C4×C61—24no—
223C22⋊Dic61—24no—
224C22⋊Dic61—24no—
225C22⋊Dic61—22no—
226C22⋊Dic61—22no—
227C22⋊Dic61—81no—
228C4⋊Dic61—24no—
229C4⋊Dic61—24no—
230C4⋊Dic61—21no—
231C4⋊Dic61—21no—
232C4⋊Dic61—22no—
233C4⋊Dic61—24no—
234C4⋊Dic61—22no—
235C4⋊Dic61—21no—
236C4⋊Dic61—21no—
237C4⋊Dic61—21no—
238C4⋊Dic61—21no—
239C4⋊Dic61—42no—
240C4⋊Dic61—81no—
241C4⋊Dic61C2×D412yes—
242C4⋊Dic61C2×D412yes—
243C4×Dic61—24no—
244C4×Dic61—21no—
245C4×Dic61—21no—
246C4×Dic61—24no—
247C4×Dic61—42no—
248C4×Dic61—81no—
249C4×Dic61C2×D412yes—
250C4×Dic61C2×D412yes—
251C2×#92418—21no—
252C2×#92418—21no—
253C2×#92418—21no—
254C2×#92418—21no—
255C2×#92418—21no—
256C2×#92418—21no—
257C23×C61—22no—
258C23×C61—21no—
259C23×C61—22no—
260C23×C61—21no—
261C23×C61—22no—
262C23×C61—21no—
263C23×C61—21no—
264C23×C61—21no—
265C23×C61—21no—
266C23×C61—41no—
267C23×C61—41no—
268C23×C61—41no—
269C23×C61—41no—
270C23×C61C4×D412yes—
271C23×C61C22×D411yescharacteristic
272Q8×C61—22no—
273Q8×C61—22no—
274Q8×C61—22no—
275Q8×C61—22no—
276Q8×C61—22no—
277Q8×C61—41no—
278Q8×C61—41no—
279Q8×C61C4×D414yes—
280D4×C61—216no—
281D4×C61—22no—
282D4×C61—22no—
283D4×C61—22no—
284D4×C61C4×D414yes—
285C2×C4×C61—216no—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—21no—
289C2×C4×C61—21no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—22no—
296C2×C4×C61—22no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61—41no—
300C2×C4×C61—41no—
301C2×C4×C61C4×D412yes—
302C2×C4×C61C23×C411yescharacteristic
303C2×C4×C61C22×D411yescharacteristic
304C2×C4×C61C22×D411yescharacteristic
305C2×C4×C61C2×#4111yescharacteristic
306C2×C4×C61C2×#4111yescharacteristic
307C2×C4×C61C2×#4111yescharacteristic
308C2×Dic61—21no—
309C2×Dic61—21no—
310C2×Dic61—21no—
311C2×Dic61—21no—
312C2×Dic61—21no—
313C2×Dic61—21no—
314C2×Dic61—22no—
315C2×Dic61—22no—
316C2×Dic61—21no—
317C2×Dic61—21no—
318C2×Dic61—21no—
319C2×Dic61—21no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327C2×Dic61—41no—
328C2×Dic61—41no—
329C2×Dic61—41no—
330C2×Dic61—84no—
331C2×Dic61—84no—
332C2×Dic61—84no—
333C2×Dic61#12012yes—
334C2×Dic61#12012yes—
335C8×C61—22no—
336C8×C61—22no—
337#92418—41no—
338#92418—41no—
339#21461—611nomaximal, Sylow
340C22×C61—22no—
341C22×C61—22no—
342C22×C61—22no—
343C22×C61—24no—
344C22×C61—41no—
345C22×C61—42no—
346C22×C61—41no—
347C22×C61—42no—
348C22×C61—42no—
349C22×C61—42no—
350C22×C61—41no—
351C22×C61—42no—
352C22×C61—41no—
353C22×C61—42no—
354C22×C61C2×C4×D411yescharacteristic
355C22×C61C2×#12011yescharacteristic
356C22×C61#52511yescharacteristic
357C22×C61#57711yescharacteristic
358C22×C61#57711yescharacteristic
359C22×C61#57711yescharacteristic
360C22×C61#57811yescharacteristic
361C4×C61—22no—
362C4×C61—24no—
363C4×C61—42no—
364C4×C61—42no—
365C4×C61C2×C4×D411yescharacteristic
366C4×C61C2×C4×D411yescharacteristic
367C4×C61#52511yescharacteristic
368C4×C61#52511yescharacteristic
369Dic61—22no—
370Dic61—22no—
371Dic61—41no—
372Dic61—42no—
373Dic61—42no—
374Dic61—41no—
375Dic61—81no—
376Dic61—81no—
377C2×#520—611no—
378C2×#452D6111yescharacteristic
379C2×#441—611no—
380C2×C4×SD16—611no—
381#2323—611no—
382#1878—611no—
383#1877—611no—
384#1872—611no—
385#1865—611no—
386#1864—611no—
387#1853—611no—
388#1788—611no—
389#1762—611no—
390C4×#103—611no—
391#1750—611no—
392C2×C61—42no—
393C2×C61—44no—
394C2×C61C4×#12011yescharacteristic
395C2×C61#294711yescharacteristic
396C2×C61#295211yescharacteristic
397C2×C61#300911yescharacteristic
398C2×C61#301311yescharacteristic
399C2×C61#312011yescharacteristic
400C2×C61#312511yescharacteristic
401C22×#41C2×D6111yescharacteristic
402C22×Q16C2×D6111yescharacteristic
403C22×SD16C2×D6111yescharacteristic
404C2×C22⋊Q8C2×D6111yescharacteristic
405#520—1224no—
406#520—1224no—
407C2×C4×Q8—611no—
408C2×C4×Q8—611no—
409C2×C4×Q8—611no—
410C2×C4×D4—611no—
411C2×C4×D4—611no—
412C2×C4×D4—1221no—
413C2×C4×D4—1221no—
414C2×#117—611no—
415C2×#117—1221no—
416C22×C4⋊C4—611no—
417C22×C4⋊C4—1221no—
418#452Dic6118yescomplemented
419#441—1224no—
420C4×SD16—1224no—
421C2×#106—611no—
422C2×#106—611no—
423C2×#103—611no—
424C2×#103—611no—
425C2×#103—611no—
426C2×#103—611no—
427C2×#103C2×D6111yescharacteristic
428C2×#102—611no—
429C2×#102—611no—
430C2×#102C2×D6111yescharacteristic
431C2×C22⋊C8—611no—
432C2×C22⋊C8C2×D6111yescharacteristic
433C2×#97—611no—
434C2×C4×C8—611no—
435#391—611no—
436#389—611no—
437#389—1221no—
438#388—1221no—
439#388—1221no—
440#387—1221no—
441#380—611no—
442C4×C4⋊C4—611no—
443#340—611no—
444#340—611no—
445#340—611no—
446#340—611no—
447#336—611no—
448#336—611no—
449C61#2146111yescharacteristic, complemented, Sylow
450C2×#41—22no—
451C2×#41—22no—
452C2×#41—22no—
453C2×#41—22no—
454C2×#41—22no—
455C2×#41C2×Dic6114yes—
456C22×Q8C22×D6111yescharacteristic
457C22×Q8C22×D6111yescharacteristic
458C22×D4—21no—
459C22×D4C22×D6111yescharacteristic
460C23×C4—21no—
461C23×C4—1221no—
462C23×C4—1221no—
463C23×C4—1221no—
464C23×C4C22×D6111yescharacteristic
465C2×Q16—22no—
466C2×Q16—22no—
467C2×Q16C2×Dic6114yescomplemented
468C2×SD16—22no—
469C2×SD16—22no—
470C2×SD16C2×Dic6114yescomplemented
471C22×C8—611no—
472C22×C8—611no—
473C22×C8C22×D6111yescharacteristic
474C22×C8C22×D6111yescharacteristic
475C22⋊Q8—22no—
476C22⋊Q8C2×Dic6114yescomplemented
477C4×Q8—614no—
478C4×Q8—1222no—
479C4×Q8—1222no—
480C4×Q8—1222no—
481C4×Q8—1222no—
482C4×Q8—1222no—
483C4×D4—614no—
484C4×D4—1222no—
485C4×D4—1222no—
486C4×D4—1228no—
487C4×D4—1228no—
488C4×D4—1222no—
489#117—1222no—
490#117—1222no—
491#117—1228no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—611no—
494C2×C4⋊C4—611no—
495C2×C4⋊C4—611no—
496C2×C4⋊C4—611no—
497C2×C4⋊C4—611no—
498C2×C4⋊C4—611no—
499C2×C4⋊C4—1222no—
500C2×C4⋊C4—1222no—
501C2×C4⋊C4—1221no—
502C2×C4⋊C4—1221no—
503C2×C4⋊C4—1228no—
504C2×C4⋊C4—1221no—
505C2×C4⋊C4—1221no—
506C2×C4⋊C4—1221no—
507C2×C4⋊C4C22×D6111yescharacteristic
508C2×C22⋊C4—21no—
509C2×C22⋊C4—611no—
510C2×C22⋊C4—611no—
511C2×C22⋊C4—1221no—
512C2×C22⋊C4—1221no—
513C2×C22⋊C4—1221no—
514C2×C42—611no—
515C2×C42—611no—
516C2×C42—1221no—
517C2×C42—1221no—
518C2×C42—1221no—
519C2×C42—1221no—
520#106—1222no—
521#106—1222no—
522#103—1222no—
523#103—1222no—
524#103—1222no—
525#103—1222no—
526#103C2×Dic6114yescomplemented
527#102—1222no—
528#102—1222no—
529#102C2×Dic6114yescomplemented
530C22⋊C8—1222no—
531C22⋊C8C2×Dic6114yescomplemented
532#97—1222no—
533C4×C8—1222no—
534#95—1221no—
535#95—1221no—
536#95—1221no—
537#95—1221no—
538#95—1221no—
539C24—21no—
540C24D4×D6111yescharacteristic
541#41—28no—
542#41—28no—
543#41—28no—
544#41—28no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8D4×D6112yes—
554C2×Q8#1175822412yes—
555C2×Q8C22×Dic6112yes—
556C2×Q8C22×Dic6112yes—
557C2×D4—24no—
558C2×D4—24no—
559C2×D4—24no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4D4×D6112yes—
564C2×D4#1175822412yes—
565C2×D4C22×Dic6112yes—
566C22×C4—24no—
567C22×C4—24no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—24no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—611no—
577C22×C4—611no—
578C22×C4—611no—
579C22×C4—611no—
580C22×C4—1224no—
581C22×C4—1224no—
582C22×C4—1224no—
583C22×C4—1221no—
584C22×C4—1221no—
585C22×C4—1221no—
586C22×C4—1221no—
587C22×C4—4881no—
588C22×C4—4881no—
589C22×C4—4881no—
590C22×C4—4881no—
591C22×C4—4881no—
592C22×C4—4881no—
593C22×C4D4×D6111yescharacteristic
594C22×C4#1175822412yes—
595C22×C4C22×Dic6112yes—
596C22×C4C23×D6111yescharacteristic
597Q16—28no—
598SD16—28no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—1221no—
604C2×C8—1221no—
605C2×C8—1221no—
606C2×C8—1221no—
607C2×C8—1221no—
608C2×C8—1221no—
609C2×C8C22×Dic6112yes—
610C2×C8C22×Dic6112yes—
611C4⋊C4—21no—
612C4⋊C4—24no—
613C4⋊C4—612no—
614C4⋊C4—612no—
615C4⋊C4—1222no—
616C4⋊C4—1222no—
617C4⋊C4—1224no—
618C4⋊C4—1224no—
619C4⋊C4—1224no—
620C4⋊C4—1221no—
621C4⋊C4—1221no—
622C4⋊C4—1221no—
623C4⋊C4—1221no—
624C4⋊C4—1221no—
625C4⋊C4—1221no—
626C4⋊C4—4881no—
627C4⋊C4—2442no—
628C4⋊C4C22×Dic6112yes—
629C22⋊C4—24no—
630C22⋊C4—1222no—
631C22⋊C4—1222no—
632C22⋊C4—1224no—
633C22⋊C4—1224no—
634C22⋊C4—4881no—
635C42—612no—
636C42—612no—
637C42—1224no—
638C42—1224no—
639C42—1221no—
640C42—1221no—
641C42—4881no—
642C42—2442no—
643C23—22no—
644C23—21no—
645C23—22no—
646C23—21no—
647C23—22no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23D4×Dic6112yes—
657C23C2×D4×D6111yescharacteristic
658Q8—22no—
659Q8—22no—
660Q8—22no—
661Q8—22no—
662Q8—22no—
663Q8—41no—
664Q8—41no—
665Q8D4×Dic6114yes—
666D4—216no—
667D4—22no—
668D4—22no—
669D4—22no—
670D4D4×Dic6114yes—
671C2×C4—216no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—612no—
688C2×C4—612no—
689C2×C4—1221no—
690C2×C4—1221no—
691C2×C4—1221no—
692C2×C4—1221no—
693C2×C4—1221no—
694C2×C4—1222no—
695C2×C4—1222no—
696C2×C4—1221no—
697C2×C4—1221no—
698C2×C4—1221no—
699C2×C4—1221no—
700C2×C4—1221no—
701C2×C4—4884no—
702C2×C4—4884no—
703C2×C4—4884no—
704C2×C4—2441no—
705C2×C4—2441no—
706C2×C4—2441no—
707C2×C4—2441no—
708C2×C4—2441no—
709C2×C4—2441no—
710C2×C4—2441no—
711C2×C4—2441no—
712C2×C4—2441no—
713C2×C4—2441no—
714C2×C4D4×Dic6112yes—
715C2×C4C23×Dic6111yescharacteristic
716C2×C4C2×D4×D6111yescharacteristic
717C2×C4C2×D4×D6111yescharacteristic
718C2×C4C2×#1175822411yescharacteristic
719C2×C4C2×#1175822411yescharacteristic
720C2×C4C2×#1175822411yescharacteristic
721C8—22no—
722C8—22no—
723C8—2441no—
724C8—2441no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—24no—
729C22—41no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—41no—
734C22—42no—
735C22—41no—
736C22—42no—
737C22—41no—
738C22—42no—
739C22C2×D4×Dic6111yescharacteristic
740C22#120×D6111yescharacteristic
741C22#1684026811yescharacteristic
742C22#1684056911yescharacteristic
743C22#1684056911yescharacteristic
744C22#1684057111yescharacteristic
745C22#1684057811yescharacteristic
746C4—22no—
747C4—24no—
748C4—42no—
749C4—42no—
750C4—1222no—
751C4—1222no—
752C4—4881no—
753C4—4881no—
754C4—2441no—
755C4—2441no—
756C4—2442no—
757C4—2442no—
758C4C2×D4×Dic6111yescharacteristic
759C4C2×D4×Dic6111yescharacteristic
760C4#1684026811yescharacteristic
761C4#1684026811yescharacteristic
762C2—42no—
763C2—44no—
764C2#120×Dic6111yescharacteristic
765C2#2145466311yescharacteristic
766C2#2145470311yescharacteristic
767C2#2145509311yescharacteristic
768C2#2145513811yescharacteristic
769C2#2145602611yescharacteristic
770C2#2145608911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#452C2
socleC23×C61C22×D4
prime radicalC22×#41×C61C22
cosocleC22×C4×C61C24
hypercenterC2×#452D61
hypocenterC61#21461
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
2. C2×#16839869C2semidirect
3. C2×SD16×Dic61C2semidirect
4. #21448503C2semidirect
5. #21446162C2semidirect
6. #21446155C2semidirect
7. #21446127C2semidirect
8. #21446089C2semidirect
9. #21446082C2semidirect
10. #21446014C2semidirect
12. #21445646C2semidirect
13. #103×Dic61C2semidirect
14. #21445587C2semidirect
60. C61×#452C4semidirect
139. C2×Q16×C61C2×C4semidirect
142. C2×SD16×C61C2×C4semidirect
146. C22⋊Q8×C61C2×C4semidirect
150. #103×C61C2×C4semidirect
151. #102×C61C2×C4semidirect
152. C22⋊C8×C61C2×C4semidirect
418. #452Dic61semidirect
449. C61#21461semidirect
467. C2×Q16C2×Dic61semidirect
470. C2×SD16C2×Dic61semidirect
476. C22⋊Q8C2×Dic61semidirect
526. #103C2×Dic61semidirect
529. #102C2×Dic61semidirect
531. C22⋊C8C2×Dic61semidirect

Maximal subgroups

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

subgroupindex
C2×#168402452
C2×#168398692
C2×SD16×Dic612
#214485032
#214461622
#214461552
#214461272
#214460892
#214460822
#214460142
#214457592
#214456462
#103×Dic612
#214455872
C2×C61×#4522
#2146161