Finite Group Databasebeta

← #29685733

Subgroups — #29685733

Order 15616.

1616 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840237C211yesmaximal, characteristic, complemented
2C2×#16839874C211yesmaximal, characteristic, complemented
3C2×D8×Dic61C211yesmaximal, characteristic, complemented
4#21448514C211yesmaximal, characteristic, complemented
5#21446169C211yesmaximal, characteristic, complemented
6#21446169C211yesmaximal, characteristic, complemented
7#21446142C211yesmaximal, characteristic, complemented
8#21446082C211yesmaximal, characteristic, complemented
9#21446068C211yesmaximal, characteristic, complemented
10#21446020C211yesmaximal, characteristic, complemented
11#21445750C211yesmaximal, characteristic, complemented
12#21445646C211yesmaximal, characteristic, complemented
13#102×Dic61C211yesmaximal, characteristic, complemented
14#21445587C211yesmaximal, characteristic, complemented
15C2×C61×#447C211yesmaximal, characteristic
16#16840237—24no—
17#16840237—24no—
18C2×D4×Dic61—21no—
19C2×D4×Dic61—21no—
20C2×D4×Dic61C2211yescharacteristic
21C2×D4×Dic61C2211yescharacteristic
22C2×D4×Dic61C2211yescharacteristic
23C2×D4×Dic61C2211yescharacteristic
24C2×D4×Dic61C2211yescharacteristic, complemented
25C2×#14519736C2211yescharacteristic
26C2×#14519736C2211yescharacteristic
27C22×C22⋊Dic61—21no—
28C22×C22⋊Dic61—21no—
29#16839874—24no—
30D8×Dic61—24no—
31C2×#14519711C2211yescharacteristic, complemented
32C2×#14519709C2211yescharacteristic, complemented
33C2×#14519698C2211yescharacteristic
34C2×#14519698C2211yescharacteristic
35C2×#14519698C2211yescharacteristic
36C2×#14519698C2211yescharacteristic
37C2×#14519698C2211yescharacteristic, complemented
38C2×#14519698C2211yescharacteristic, complemented
39C2×C22⋊#92418C2211yescharacteristic
40C2×#14519687C2211yescharacteristic, complemented
41C2×C8×Dic61C2211yescharacteristic, complemented
42#16839665—21no—
43#16839665C2211yescharacteristic, complemented
44#16839661C2211yescharacteristic, complemented
45#16839655—21no—
46#16839642—21no—
47#16839637—21no—
48#16839622C2211yescharacteristic
49C4⋊C4×Dic61C2211yescharacteristic, complemented
50#16839525C2211yescharacteristic, complemented
51#16839525C2211yescharacteristic, complemented
52#16839524C2211yescharacteristic, complemented
53#16839524C2211yescharacteristic, complemented
54#16839516C2211yescharacteristic, complemented
55#16839516C2211yescharacteristic, complemented
56C23×D4×C61C2211yescharacteristic
57C22×D8×C61C2211yescharacteristic
58C22×D8×C61C2211yescharacteristic
59C2×#121×C61C2211yescharacteristic
60C61×#447C418yescomplemented
61C2×#102×C61C2211yescharacteristic
62C2×#102×C61C2211yescharacteristic
63C2×C22⋊C8×C61C2211yescharacteristic
64C23×Dic61—21no—
65C23×Dic61—21no—
66C23×Dic61—21no—
67C23×Dic61—21no—
68C23×Dic61—21no—
69C22×#92418C2311yescharacteristic
70C22×#92418C2311yescharacteristic
71D4×Dic61—28no—
72D4×Dic61—28no—
73D4×Dic61—22no—
74D4×Dic61—22no—
75D4×Dic61—22no—
76D4×Dic61—22no—
77D4×Dic61—22no—
78D4×Dic61—22no—
79D4×Dic61—22no—
80D4×Dic61—22no—
81D4×Dic61D414yescomplemented
82D4×Dic61D414yescomplemented
83#14519736—22no—
84#14519736—22no—
85#14519736—22no—
86#14519736—22no—
87C2×C4⋊Dic61—21no—
88C2×C4⋊Dic61D411yescharacteristic
89C2×C4⋊Dic61D411yescharacteristic
90C2×C4⋊Dic61C2311yescharacteristic
91C2×C4⋊Dic61C2311yescharacteristic
92C2×C4⋊Dic61C2311yescharacteristic
93C2×C4⋊Dic61C2311yescharacteristic
94C2×C22⋊Dic61—28no—
95C2×C22⋊Dic61—28no—
96C2×C22⋊Dic61—21no—
97C2×C22⋊Dic61—21no—
98C2×C22⋊Dic61—21no—
99C2×C22⋊Dic61—21no—
100C2×C22⋊Dic61—21no—
101C2×C22⋊Dic61—21no—
102C2×C22⋊Dic61—21no—
103C2×C22⋊Dic61—21no—
104C2×C22⋊Dic61—21no—
105C2×C22⋊Dic61D411yescharacteristic
106C2×C22⋊Dic61D411yescharacteristic
107C2×C4×Dic61—21no—
108C2×C4×Dic61—21no—
109C2×C4×Dic61C2311yescharacteristic
110C2×C4×Dic61C2311yescharacteristic
111#14519711—22no—
112#14519709—22no—
113#14519698—22no—
114#14519698—22no—
115#14519698—22no—
116#14519698—22no—
117#14519698—22no—
118#14519698—22no—
119C22⋊#92418—22no—
120#14519687—22no—
121C8×Dic61—22no—
122#14519684—21no—
123#14519684—21no—
124#14519684—21no—
125C25×C61—21no—
126C22×D4×C61—22no—
127C22×D4×C61—22no—
128C22×D4×C61—22no—
129C22×D4×C61—22no—
130C22×D4×C61—21no—
131C22×D4×C61—21no—
132C22×D4×C61—22no—
133C22×D4×C61C2×C414yescomplemented
134C22×D4×C61C2311yescharacteristic
135C22×D4×C61C2311yescharacteristic
136C22×D4×C61C2311yescharacteristic
137C23×C4×C61C2311yescharacteristic
138C2×D8×C61—22no—
139C2×D8×C61—22no—
140C2×D8×C61—22no—
141C2×D8×C61—22no—
142C2×D8×C61C2×C414yescomplemented
143C2×D8×C61C2×C414yescomplemented
144C22×C8×C61C2311yescharacteristic
145C22×C8×C61C2311yescharacteristic
146#121×C61—22no—
147#121×C61C2×C414yescomplemented
148C2×C4⋊C4×C61C2311yescharacteristic
149C2×C22⋊C4×C61—21no—
150#102×C61C2×C414yescomplemented
151#102×C61C2×C414yescomplemented
152C22⋊C8×C61C2×C414yescomplemented
153C24×C61—24no—
154C24×C61—24no—
155C24×C61—21no—
156C24×C61—21no—
157C24×C61—24no—
158C24×C61—21no—
159C24×C61—81no—
160C24×C61—81no—
161C24×C61—81no—
162C24×C61—81no—
163C24×C61C2×D411yescharacteristic
164C2×D4×C61—24no—
165C2×D4×C61—28no—
166C2×D4×C61—28no—
167C2×D4×C61—24no—
168C2×D4×C61—28no—
169C2×D4×C61—28no—
170C2×D4×C61—24no—
171C2×D4×C61—24no—
172C2×D4×C61—21no—
173C2×D4×C61—21no—
174C2×D4×C61—21no—
175C2×D4×C61—21no—
176C2×D4×C61—21no—
177C2×D4×C61—21no—
178C2×D4×C61—21no—
179C2×D4×C61—21no—
180C2×D4×C61—21no—
181C2×D4×C61—21no—
182C2×D4×C61—21no—
183C2×D4×C61—81no—
184C2×D4×C61—81no—
185C2×D4×C61C22×C412yes—
186C2×D4×C61C22×C412yes—
187C2×D4×C61C22×C412yes—
188C2×D4×C61C2×D412yes—
189C2×D4×C61C2×D412yes—
190C2×D4×C61#4112yes—
191C2×D4×C61#4112yes—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61C22×C412yes—
198C22×C4×C61C2×D411yescharacteristic
199C22×C4×C61#4112yes—
200C22×C4×C61C2411yescharacteristic
201C22×Dic61—21no—
202C22×Dic61—21no—
203C22×Dic61—24no—
204C22×Dic61—24no—
205C22×Dic61—24no—
206C22×Dic61—24no—
207C22×Dic61—21no—
208C22×Dic61—21no—
209C22×Dic61—42no—
210C22×Dic61—81no—
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×Dic61C2×D411yescharacteristic
221C22×Dic61C2×D411yescharacteristic
222C22×Dic61C2×D411yescharacteristic
223C22×Dic61C2×D411yescharacteristic
224D8×C61—28no—
225D8×C61—28no—
226C2×C8×C61—21no—
227C2×C8×C61—21no—
228C2×C8×C61—21no—
229C2×C8×C61—21no—
230C2×C8×C61C22×C412yes—
231C2×C8×C61C22×C412yes—
232C4⋊C4×C61—21no—
233C4⋊C4×C61C22×C412yes—
234C22⋊C4×C61—24no—
235C22⋊Dic61—24no—
236C22⋊Dic61—24no—
237C22⋊Dic61—24no—
238C22⋊Dic61—22no—
239C22⋊Dic61—22no—
240C22⋊Dic61—24no—
241C22⋊Dic61—24no—
242C22⋊Dic61—42no—
243C22⋊Dic61—81no—
244C22⋊Dic61—81no—
245C22⋊Dic61—81no—
246C4⋊Dic61—21no—
247C4⋊Dic61—21no—
248C4⋊Dic61—22no—
249C4⋊Dic61—22no—
250C4⋊Dic61—21no—
251C4⋊Dic61—21no—
252C4⋊Dic61—21no—
253C4⋊Dic61—21no—
254C4⋊Dic61—81no—
255C4⋊Dic61C2×D412yes—
256C4⋊Dic61C2×D412yes—
257C4×Dic61—24no—
258C4×Dic61—21no—
259C4×Dic61—21no—
260C4×Dic61—81no—
261C4×Dic61C2×D412yes—
262C4×Dic61C2×D412yes—
263C2×#92418—21no—
264C2×#92418—21no—
265C2×#92418—21no—
266C2×#92418—21no—
267C2×#92418—21no—
268C2×#92418—21no—
269C23×C61—216no—
270C23×C61—22no—
271C23×C61—22no—
272C23×C61—21no—
273C23×C61—22no—
274C23×C61—22no—
275C23×C61—21no—
276C23×C61—22no—
277C23×C61—22no—
278C23×C61—21no—
279C23×C61—21no—
280C23×C61—21no—
281C23×C61—21no—
282C23×C61—22no—
283C23×C61—41no—
284C23×C61—41no—
285C23×C61—41no—
286C23×C61—41no—
287C23×C61—41no—
288C23×C61—41no—
289C23×C61—41no—
290C23×C61—41no—
291C23×C61—41no—
292C23×C61—41no—
293C23×C61—41no—
294C23×C61—41no—
295C23×C61—41no—
296C23×C61—41no—
297C23×C61—84no—
298C23×C61—84no—
299C23×C61—84no—
300C23×C61—84no—
301C23×C61—84no—
302C23×C61—84no—
303C23×C61C4×D412yes—
304C23×C61C22×D411yescharacteristic
305D4×C61—216no—
306D4×C61—22no—
307D4×C61—22no—
308D4×C61—22no—
309D4×C61—22no—
310D4×C61—22no—
311D4×C61—22no—
312D4×C61—22no—
313D4×C61—22no—
314D4×C61—41no—
315D4×C61—41no—
316D4×C61—84no—
317D4×C61C4×D414yes—
318D4×C61C4×D414yes—
319C2×C4×C61—21no—
320C2×C4×C61—21no—
321C2×C4×C61—22no—
322C2×C4×C61—22no—
323C2×C4×C61—22no—
324C2×C4×C61—22no—
325C2×C4×C61—22no—
326C2×C4×C61—41no—
327C2×C4×C61—41no—
328C2×C4×C61C4×D412yes—
329C2×C4×C61C23×C411yescharacteristic
330C2×C4×C61C22×D411yescharacteristic
331C2×C4×C61C22×D411yescharacteristic
332C2×C4×C61C2×#4111yescharacteristic
333C2×C4×C61C2×#4111yescharacteristic
334C2×C4×C61C2×#4111yescharacteristic
335C2×Dic61—21no—
336C2×Dic61—21no—
337C2×Dic61—21no—
338C2×Dic61—21no—
339C2×Dic61—21no—
340C2×Dic61—21no—
341C2×Dic61—22no—
342C2×Dic61—22no—
343C2×Dic61—21no—
344C2×Dic61—21no—
345C2×Dic61—21no—
346C2×Dic61—21no—
347C2×Dic61—41no—
348C2×Dic61—41no—
349C2×Dic61—41no—
350C2×Dic61—41no—
351C2×Dic61—41no—
352C2×Dic61—41no—
353C2×Dic61—41no—
354C2×Dic61—41no—
355C2×Dic61—41no—
356C2×Dic61—41no—
357C2×Dic61—84no—
358C2×Dic61—84no—
359C2×Dic61—84no—
360C2×Dic61—84no—
361C2×Dic61—84no—
362C2×Dic61#12012yes—
363C2×Dic61#12012yes—
364C8×C61—22no—
365C8×C61—22no—
366#92418—41no—
367#92418—41no—
368#21458—611nomaximal, Sylow
369C22×C61—22no—
370C22×C61—22no—
371C22×C61—22no—
372C22×C61—24no—
373C22×C61—24no—
374C22×C61—41no—
375C22×C61—42no—
376C22×C61—42no—
377C22×C61—41no—
378C22×C61—42no—
379C22×C61—42no—
380C22×C61—42no—
381C22×C61—42no—
382C22×C61—42no—
383C22×C61—42no—
384C22×C61—42no—
385C22×C61—42no—
386C22×C61—41no—
387C22×C61—42no—
388C22×C61—42no—
389C22×C61—41no—
390C22×C61—42no—
391C22×C61—42no—
392C22×C61—42no—
393C22×C61—816no—
394C22×C61—81no—
395C22×C61—81no—
396C22×C61—81no—
397C22×C61—81no—
398C22×C61C2×C4×D411yescharacteristic
399C22×C61C2×#12011yescharacteristic
400C22×C61#52511yescharacteristic
401C22×C61#57611yescharacteristic
402C22×C61#57611yescharacteristic
403C22×C61#57611yescharacteristic
404C22×C61#57711yescharacteristic
405C4×C61—22no—
406C4×C61—42no—
407C4×C61C2×C4×D411yescharacteristic
408C4×C61C2×C4×D411yescharacteristic
409C4×C61#52511yescharacteristic
410C4×C61#52511yescharacteristic
411Dic61—22no—
412Dic61—22no—
413Dic61—41no—
414Dic61—42no—
415Dic61—41no—
416Dic61—42no—
417Dic61—81no—
418Dic61—81no—
419C2×#518—611no—
420C2×#447D6111yescharacteristic
421C2×#442—611no—
422C2×C4×D8—611no—
423#2324—611no—
424#1879—611no—
425#1879—611no—
426#1875—611no—
427#1864—611no—
428#1862—611no—
429#1854—611no—
430#1786—611no—
431#1762—611no—
432C4×#102—611no—
433#1750—611no—
434C2×C61—42no—
435C2×C61—44no—
436C2×C61—44no—
437C2×C61—82no—
438C2×C61C4×#12011yescharacteristic
439C2×C61#294611yescharacteristic
440C2×C61#294811yescharacteristic
441C2×C61#300811yescharacteristic
442C2×C61#301211yescharacteristic
443C2×C61#311811yescharacteristic
444C2×C61#312211yescharacteristic
445C23×D4C2×D6111yescharacteristic
446C22×D8C2×D6111yescharacteristic
447C22×D8C2×D6111yescharacteristic
448C2×#121C2×D6111yescharacteristic
449#518—1224no—
450#518—1224no—
451C2×C4×D4—611no—
452C2×C4×D4—611no—
453C2×C4×D4—611no—
454C2×C4×D4—611no—
455C2×C4×D4—611no—
456C2×C4×D4—1221no—
457C2×C4×D4—1221no—
458C2×#117—611no—
459C2×#117—611no—
460C22×C22⋊C4—1221no—
461C22×C22⋊C4—1221no—
462#447Dic6118yescomplemented
463#442—1224no—
464C4×D8—1224no—
465C2×#107—611no—
466C2×#106—611no—
467C2×#102—611no—
468C2×#102—611no—
469C2×#102—611no—
470C2×#102—611no—
471C2×#102—611no—
472C2×#102—611no—
473C2×#102C2×D6111yescharacteristic
474C2×#102C2×D6111yescharacteristic
475C2×C22⋊C8—611no—
476C2×C22⋊C8C2×D6111yescharacteristic
477C2×#97—611no—
478C2×C4×C8—611no—
479#390—611no—
480#390—1221no—
481#389—611no—
482#388—1221no—
483#386—1221no—
484#385—1221no—
485#380—611no—
486C4×C4⋊C4—611no—
487#340—611no—
488#340—611no—
489#340—611no—
490#340—611no—
491#336—611no—
492#336—611no—
493C61#2145811yescharacteristic, complemented, Sylow
494C25—21no—
495C22×D4—22no—
496C22×D4—22no—
497C22×D4—22no—
498C22×D4—22no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—22no—
502C22×D4C2×Dic6114yescomplemented
503C22×D4C22×D6111yescharacteristic
504C22×D4C22×D6111yescharacteristic
505C22×D4C22×D6111yescharacteristic
506C23×C4—1221no—
507C23×C4—1221no—
508C23×C4—1221no—
509C23×C4—1221no—
510C23×C4—1221no—
511C23×C4C22×D6111yescharacteristic
512C2×D8—22no—
513C2×D8—22no—
514C2×D8—22no—
515C2×D8—22no—
516C2×D8C2×Dic6114yescomplemented
517C2×D8C2×Dic6114yescomplemented
518C22×C8—611no—
519C22×C8—611no—
520C22×C8C22×D6111yescharacteristic
521C22×C8C22×D6111yescharacteristic
522#121—22no—
523#121C2×Dic6114yescomplemented
524C4×D4—614no—
525C4×D4—614no—
526C4×D4—1222no—
527C4×D4—1222no—
528C4×D4—1222no—
529C4×D4—1222no—
530C4×D4—1222no—
531C4×D4—1222no—
532C4×D4—1228no—
533C4×D4—1228no—
534C4×D4—1222no—
535C4×D4—1222no—
536#117—1222no—
537#117—1222no—
538#117—1222no—
539#117—1222no—
540C2×C4⋊C4—611no—
541C2×C4⋊C4—611no—
542C2×C4⋊C4—611no—
543C2×C4⋊C4—611no—
544C2×C4⋊C4—611no—
545C2×C4⋊C4—611no—
546C2×C4⋊C4—1221no—
547C2×C4⋊C4C22×D6111yescharacteristic
548C2×C22⋊C4—21no—
549C2×C22⋊C4—611no—
550C2×C22⋊C4—611no—
551C2×C22⋊C4—1221no—
552C2×C22⋊C4—1221no—
553C2×C22⋊C4—1221no—
554C2×C22⋊C4—1221no—
555C2×C22⋊C4—1228no—
556C2×C22⋊C4—1228no—
557C2×C22⋊C4—1221no—
558C2×C22⋊C4—1221no—
559C2×C22⋊C4—1221no—
560C2×C22⋊C4—1221no—
561C2×C22⋊C4—1221no—
562C2×C42—611no—
563C2×C42—611no—
564C2×C42—1221no—
565C2×C42—1221no—
566#107—1222no—
567#106—1222no—
568#102—1222no—
569#102—1222no—
570#102—1222no—
571#102—1222no—
572#102—1222no—
573#102—1222no—
574#102C2×Dic6114yescomplemented
575#102C2×Dic6114yescomplemented
576C22⋊C8—1222no—
577C22⋊C8C2×Dic6114yescomplemented
578#97—1222no—
579C4×C8—1222no—
580#95—1221no—
581#95—1221no—
582#95—1221no—
583C24—24no—
584C24—24no—
585C24—21no—
586C24—21no—
587C24—24no—
588C24—21no—
589C24—81no—
590C24—81no—
591C24—81no—
592C24—81no—
593C24D4×D6111yescharacteristic
594C2×D4—24no—
595C2×D4—24no—
596C2×D4—28no—
597C2×D4—28no—
598C2×D4—28no—
599C2×D4—28no—
600C2×D4—24no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—24no—
613C2×D4—81no—
614C2×D4—81no—
615C2×D4D4×D6112yes—
616C2×D4D4×D6112yes—
617C2×D4#1175822412yes—
618C2×D4#1175822412yes—
619C2×D4C22×Dic6112yes—
620C2×D4C22×Dic6112yes—
621C2×D4C22×Dic6112yes—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—611no—
628C22×C4—611no—
629C22×C4—611no—
630C22×C4—611no—
631C22×C4—1224no—
632C22×C4—1224no—
633C22×C4—1224no—
634C22×C4—1224no—
635C22×C4—1221no—
636C22×C4—1221no—
637C22×C4—1221no—
638C22×C4—1221no—
639C22×C4—4881no—
640C22×C4—4881no—
641C22×C4—4881no—
642C22×C4—4881no—
643C22×C4—4881no—
644C22×C4—4881no—
645C22×C4—4881no—
646C22×C4—4881no—
647C22×C4—4881no—
648C22×C4—4881no—
649C22×C4—2442no—
650C22×C4D4×D6111yescharacteristic
651C22×C4#1175822412yes—
652C22×C4C22×Dic6112yes—
653C22×C4C23×D6111yescharacteristic
654D8—28no—
655D8—28no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—1221no—
661C2×C8—1221no—
662C2×C8—1221no—
663C2×C8—1221no—
664C2×C8—1221no—
665C2×C8—1221no—
666C2×C8C22×Dic6112yes—
667C2×C8C22×Dic6112yes—
668C4⋊C4—21no—
669C4⋊C4—612no—
670C4⋊C4—612no—
671C4⋊C4—1222no—
672C4⋊C4—1222no—
673C4⋊C4—1221no—
674C4⋊C4—1221no—
675C4⋊C4—1221no—
676C4⋊C4—1221no—
677C4⋊C4—1221no—
678C4⋊C4—1221no—
679C4⋊C4—4881no—
680C4⋊C4C22×Dic6112yes—
681C22⋊C4—24no—
682C22⋊C4—1222no—
683C22⋊C4—1222no—
684C22⋊C4—1224no—
685C22⋊C4—1224no—
686C22⋊C4—1224no—
687C22⋊C4—1224no—
688C22⋊C4—1224no—
689C22⋊C4—4881no—
690C22⋊C4—4881no—
691C22⋊C4—4881no—
692C22⋊C4—2442no—
693C42—612no—
694C42—612no—
695C42—1224no—
696C42—1221no—
697C42—1221no—
698C42—4881no—
699C23—216no—
700C23—22no—
701C23—22no—
702C23—21no—
703C23—22no—
704C23—22no—
705C23—21no—
706C23—22no—
707C23—22no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—22no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—84no—
728C23—84no—
729C23—84no—
730C23—84no—
731C23—84no—
732C23—84no—
733C23D4×Dic6112yes—
734C23C2×D4×D6111yescharacteristic
735D4—216no—
736D4—22no—
737D4—22no—
738D4—22no—
739D4—22no—
740D4—22no—
741D4—22no—
742D4—22no—
743D4—22no—
744D4—41no—
745D4—41no—
746D4—84no—
747D4D4×Dic6114yes—
748D4D4×Dic6114yes—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—612no—
759C2×C4—612no—
760C2×C4—1221no—
761C2×C4—1221no—
762C2×C4—1221no—
763C2×C4—1221no—
764C2×C4—1222no—
765C2×C4—1222no—
766C2×C4—1221no—
767C2×C4—1221no—
768C2×C4—1221no—
769C2×C4—1221no—
770C2×C4—1221no—
771C2×C4—1221no—
772C2×C4—4884no—
773C2×C4—4884no—
774C2×C4—4884no—
775C2×C4—4884no—
776C2×C4—4884no—
777C2×C4—2441no—
778C2×C4—2441no—
779C2×C4—2441no—
780C2×C4—2441no—
781C2×C4—2441no—
782C2×C4—2441no—
783C2×C4—2441no—
784C2×C4—2441no—
785C2×C4—2441no—
786C2×C4—2441no—
787C2×C4D4×Dic6112yes—
788C2×C4C23×Dic6111yescharacteristic
789C2×C4C2×D4×D6111yescharacteristic
790C2×C4C2×D4×D6111yescharacteristic
791C2×C4C2×#1175822411yescharacteristic
792C2×C4C2×#1175822411yescharacteristic
793C2×C4C2×#1175822411yescharacteristic
794C8—22no—
795C8—22no—
796C8—2441no—
797C8—2441no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—24no—
802C22—24no—
803C22—42no—
804C22—42no—
805C22—41no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22—41no—
811C22—42no—
812C22—42no—
813C22—41no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—42no—
818C22—41no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—816no—
823C22—81no—
824C22—81no—
825C22—81no—
826C22—81no—
827C22C2×D4×Dic6111yescharacteristic
828C22#120×D6111yescharacteristic
829C22#1684026811yescharacteristic
830C22#1684056311yescharacteristic
831C22#1684056311yescharacteristic
832C22#1684056611yescharacteristic
833C22#1684057211yescharacteristic
834C4—22no—
835C4—42no—
836C4—1222no—
837C4—1222no—
838C4—4881no—
839C4—4881no—
840C4—2441no—
841C4—2442no—
842C4—2441no—
843C4—2442no—
844C4C2×D4×Dic6111yescharacteristic
845C4C2×D4×Dic6111yescharacteristic
846C4#1684026811yescharacteristic
847C4#1684026811yescharacteristic
848C2—42no—
849C2—44no—
850C2—44no—
851C2—82no—
852C2#120×Dic6111yescharacteristic
853C2#2145465211yescharacteristic
854C2#2145467111yescharacteristic
855C2#2145508211yescharacteristic
856C2#2145511811yescharacteristic
857C2#2145599611yescharacteristic
858C2#2145605611yescharacteristic
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#21458
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. C2×#16840237C2semidirect
2. C2×#16839874C2semidirect
3. C2×D8×Dic61C2semidirect
4. #21448514C2semidirect
5. #21446169C2semidirect
6. #21446169C2semidirect
7. #21446142C2semidirect
8. #21446082C2semidirect
9. #21446068C2semidirect
10. #21446020C2semidirect
11. #21445750C2semidirect
12. #21445646C2semidirect
13. #102×Dic61C2semidirect
14. #21445587C2semidirect
24. C2×D4×Dic61C22semidirect
31. C2×#14519711C22semidirect
32. C2×#14519709C22semidirect
37. C2×#14519698C22semidirect
38. C2×#14519698C22semidirect
40. C2×#14519687C22semidirect
41. C2×C8×Dic61C22semidirect
43. #16839665C22semidirect
44. #16839661C22semidirect
49. C4⋊C4×Dic61C22semidirect
50. #16839525C22semidirect
51. #16839525C22semidirect
52. #16839524C22semidirect
53. #16839524C22semidirect
54. #16839516C22semidirect
55. #16839516C22semidirect
60. C61×#447C4semidirect
81. D4×Dic61D4semidirect
82. D4×Dic61D4semidirect
133. C22×D4×C61C2×C4semidirect
142. C2×D8×C61C2×C4semidirect
143. C2×D8×C61C2×C4semidirect
147. #121×C61C2×C4semidirect
150. #102×C61C2×C4semidirect
151. #102×C61C2×C4semidirect
152. C22⋊C8×C61C2×C4semidirect
462. #447Dic61semidirect
493. C61#21458semidirect
502. C22×D4C2×Dic61semidirect
516. C2×D8C2×Dic61semidirect
517. C2×D8C2×Dic61semidirect
523. #121C2×Dic61semidirect
574. #102C2×Dic61semidirect
575. #102C2×Dic61semidirect
577. C22⋊C8C2×Dic61semidirect

Maximal subgroups

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

subgroupindex
C2×#168402372
C2×#168398742
C2×D8×Dic612
#214485142
#214461692
#214461422
#214460822
#214460682
#214460202
#214457502
#214456462
#102×Dic612
#214455872
C2×C61×#4472
#2145861