Finite Group Databasebeta

← #29685763

Subgroups — #29685763

Order 15616.

1476 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840245C211yesmaximal, characteristic, complemented
2C2×#16839863C211yesmaximal, characteristic, complemented
3C2×D8×Dic61C211yesmaximal, characteristic, complemented
4#21448514C211yesmaximal, characteristic, complemented
5#21446176C211yesmaximal, characteristic, complemented
6#21446169C211yesmaximal, characteristic, complemented
7#21446137C211yesmaximal, characteristic, complemented
8#21446075C211yesmaximal, characteristic, complemented
9#21446068C211yesmaximal, characteristic, complemented
10#21446009C211yesmaximal, characteristic, complemented
11#21445759C211yesmaximal, characteristic, complemented
12#21445646C211yesmaximal, characteristic, complemented
13#103×Dic61C211yesmaximal, characteristic, complemented
14#21445587C211yesmaximal, characteristic, complemented
15C2×C61×#449C211yesmaximal, characteristic
16#16840245—24no—
17#16840245—24no—
18C2×Q8×Dic61C2211yescharacteristic
19C2×Q8×Dic61C2211yescharacteristic
20C2×D4×Dic61—21no—
21C2×D4×Dic61—21no—
22C2×D4×Dic61C2211yescharacteristic
23C2×D4×Dic61C2211yescharacteristic
24C2×D4×Dic61C2211yescharacteristic
25C2×#14519736—21no—
26C2×#14519736C2211yescharacteristic
27C22×C4⋊Dic61—21no—
28C22×C4⋊Dic61C2211yescharacteristic
29#16839863—24no—
30D8×Dic61—24no—
31C2×#14519711C2211yescharacteristic
32C2×#14519711C2211yescharacteristic
33C2×#14519701C2211yescharacteristic
34C2×#14519701C2211yescharacteristic
35C2×#14519698C2211yescharacteristic
36C2×#14519698C2211yescharacteristic
37C2×#14519698C2211yescharacteristic
38C2×#14519698C2211yescharacteristic
39C2×C22⋊#92418C2211yescharacteristic
40C2×#14519687C2211yescharacteristic
41C2×C8×Dic61C2211yescharacteristic
42#16839665—21no—
43#16839665C2211yescharacteristic
44#16839661C2211yescharacteristic
45#16839655—21no—
46#16839642—21no—
47#16839637—21no—
48#16839622C2211yescharacteristic
49C4⋊C4×Dic61C2211yescharacteristic
50#16839525C2211yescharacteristic
51#16839525C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839516C2211yescharacteristic
55#16839516C2211yescharacteristic
56C22×#41×C61C2211yescharacteristic
57C22×SD16×C61C2211yescharacteristic
58C22×D8×C61C2211yescharacteristic
59C2×#121×C61C2211yescharacteristic
60C61×#449C418yescomplemented
61C2×#103×C61C2211yescharacteristic
62C2×#102×C61C2211yescharacteristic
63C2×C22⋊C8×C61C2211yescharacteristic
64C23×Dic61—21no—
65C23×Dic61—21no—
66C23×Dic61—21no—
67C23×Dic61—21no—
68C22×#92418C2311yescharacteristic
69C22×#92418C2311yescharacteristic
70Q8×Dic61—22no—
71Q8×Dic61—22no—
72Q8×Dic61—22no—
73Q8×Dic61D414yescomplemented
74D4×Dic61—28no—
75D4×Dic61—28no—
76D4×Dic61—22no—
77D4×Dic61—22no—
78D4×Dic61—22no—
79D4×Dic61—22no—
80D4×Dic61—22no—
81D4×Dic61D414yescomplemented
82#14519736—28no—
83#14519736—22no—
84#14519736—22no—
85C2×C4⋊Dic61—28no—
86C2×C4⋊Dic61—21no—
87C2×C4⋊Dic61—21no—
88C2×C4⋊Dic61—21no—
89C2×C4⋊Dic61—22no—
90C2×C4⋊Dic61—22no—
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⋊Dic61—21no—
102C2×C22⋊Dic61—21no—
103C2×C22⋊Dic61—21no—
104C2×C22⋊Dic61D411yescharacteristic
105C2×C22⋊Dic61D411yescharacteristic
106C2×C4×Dic61—21no—
107C2×C4×Dic61—21no—
108C2×C4×Dic61—21no—
109C2×C4×Dic61C2311yescharacteristic
110C2×C4×Dic61C2311yescharacteristic
111#14519711—22no—
112#14519711—22no—
113#14519701—22no—
114#14519701—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—
125C2×#41×C61—22no—
126C2×#41×C61—22no—
127C2×#41×C61—22no—
128C2×#41×C61—22no—
129C2×#41×C61—22no—
130C2×#41×C61C2×C414yescomplemented
131C22×Q8×C61C2311yescharacteristic
132C22×D4×C61—21no—
133C22×D4×C61—21no—
134C22×D4×C61C2311yescharacteristic
135C22×D4×C61C2311yescharacteristic
136C23×C4×C61—21no—
137C23×C4×C61C2311yescharacteristic
138C2×SD16×C61—22no—
139C2×SD16×C61—22no—
140C2×SD16×C61C2×C414yescomplemented
141C2×D8×C61—22no—
142C2×D8×C61—22no—
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#103×C61C2×C414yescomplemented
151#102×C61C2×C414yescomplemented
152C22⋊C8×C61C2×C414yescomplemented
153C24×C61—21no—
154C24×C61—21no—
155C24×C61C2×D411yescharacteristic
156#41×C61—28no—
157#41×C61—28no—
158#41×C61—28no—
159#41×C61—28no—
160C2×Q8×C61—21no—
161C2×Q8×C61—21no—
162C2×Q8×C61—21no—
163C2×Q8×C61C22×C412yes—
164C2×Q8×C61C2×D412yes—
165C2×Q8×C61#4112yes—
166C2×D4×C61—24no—
167C2×D4×C61—24no—
168C2×D4×C61—24no—
169C2×D4×C61—24no—
170C2×D4×C61—21no—
171C2×D4×C61—21no—
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—81no—
179C2×D4×C61—81no—
180C2×D4×C61C22×C412yes—
181C2×D4×C61C22×C412yes—
182C2×D4×C61C2×D412yes—
183C2×D4×C61#4112yes—
184C22×C4×C61—24no—
185C22×C4×C61—24no—
186C22×C4×C61—21no—
187C22×C4×C61—24no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61C22×C412yes—
194C22×C4×C61C2×D411yescharacteristic
195C22×C4×C61#4112yes—
196C22×C4×C61C2411yescharacteristic
197C22×Dic61—21no—
198C22×Dic61—21no—
199C22×Dic61—24no—
200C22×Dic61—24no—
201C22×Dic61—24no—
202C22×Dic61—21no—
203C22×Dic61—21no—
204C22×Dic61—42no—
205C22×Dic61—81no—
206C22×Dic61—81no—
207C22×Dic61—81no—
208C22×Dic61—81no—
209C22×Dic61—81no—
210C22×Dic61—81no—
211C22×Dic61—81no—
212C22×Dic61—81no—
213C22×Dic61C2×D411yescharacteristic
214C22×Dic61C2×D411yescharacteristic
215C22×Dic61C2×D411yescharacteristic
216C22×Dic61C2×D411yescharacteristic
217SD16×C61—28no—
218D8×C61—28no—
219C2×C8×C61—21no—
220C2×C8×C61—21no—
221C2×C8×C61—21no—
222C2×C8×C61—21no—
223C2×C8×C61C22×C412yes—
224C2×C8×C61C22×C412yes—
225C4⋊C4×C61—21no—
226C4⋊C4×C61C22×C412yes—
227C22⋊C4×C61—24no—
228C22⋊Dic61—24no—
229C22⋊Dic61—24no—
230C22⋊Dic61—22no—
231C22⋊Dic61—22no—
232C22⋊Dic61—42no—
233C22⋊Dic61—81no—
234C22⋊Dic61—81no—
235C22⋊Dic61—81no—
236C4⋊Dic61—24no—
237C4⋊Dic61—24no—
238C4⋊Dic61—21no—
239C4⋊Dic61—21no—
240C4⋊Dic61—22no—
241C4⋊Dic61—24no—
242C4⋊Dic61—22no—
243C4⋊Dic61—21no—
244C4⋊Dic61—21no—
245C4⋊Dic61—21no—
246C4⋊Dic61—21no—
247C4⋊Dic61—81no—
248C4⋊Dic61C2×D412yes—
249C4⋊Dic61C2×D412yes—
250C4×Dic61—24no—
251C4×Dic61—21no—
252C4×Dic61—21no—
253C4×Dic61—24no—
254C4×Dic61—81no—
255C4×Dic61C2×D412yes—
256C4×Dic61C2×D412yes—
257C2×#92418—21no—
258C2×#92418—21no—
259C2×#92418—21no—
260C2×#92418—21no—
261C2×#92418—21no—
262C2×#92418—21no—
263C23×C61—22no—
264C23×C61—21no—
265C23×C61—22no—
266C23×C61—21no—
267C23×C61—22no—
268C23×C61—21no—
269C23×C61—21no—
270C23×C61—21no—
271C23×C61—21no—
272C23×C61—22no—
273C23×C61—41no—
274C23×C61—41no—
275C23×C61—41no—
276C23×C61—41no—
277C23×C61—41no—
278C23×C61—41no—
279C23×C61—41no—
280C23×C61—41no—
281C23×C61—41no—
282C23×C61—41no—
283C23×C61C4×D412yes—
284C23×C61C22×D411yescharacteristic
285Q8×C61—22no—
286Q8×C61—22no—
287Q8×C61—22no—
288Q8×C61C4×D414yes—
289D4×C61—216no—
290D4×C61—22no—
291D4×C61—22no—
292D4×C61—22no—
293D4×C61—22no—
294D4×C61—22no—
295D4×C61—41no—
296D4×C61—41no—
297D4×C61—84no—
298D4×C61C4×D414yes—
299C2×C4×C61—216no—
300C2×C4×C61—22no—
301C2×C4×C61—22no—
302C2×C4×C61—21no—
303C2×C4×C61—21no—
304C2×C4×C61—22no—
305C2×C4×C61—22no—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—22no—
310C2×C4×C61—41no—
311C2×C4×C61—41no—
312C2×C4×C61C4×D412yes—
313C2×C4×C61C23×C411yescharacteristic
314C2×C4×C61C22×D411yescharacteristic
315C2×C4×C61C22×D411yescharacteristic
316C2×C4×C61C2×#4111yescharacteristic
317C2×C4×C61C2×#4111yescharacteristic
318C2×C4×C61C2×#4111yescharacteristic
319C2×Dic61—21no—
320C2×Dic61—21no—
321C2×Dic61—21no—
322C2×Dic61—21no—
323C2×Dic61—21no—
324C2×Dic61—21no—
325C2×Dic61—22no—
326C2×Dic61—22no—
327C2×Dic61—21no—
328C2×Dic61—21no—
329C2×Dic61—21no—
330C2×Dic61—21no—
331C2×Dic61—41no—
332C2×Dic61—41no—
333C2×Dic61—41no—
334C2×Dic61—41no—
335C2×Dic61—41no—
336C2×Dic61—41no—
337C2×Dic61—41no—
338C2×Dic61—41no—
339C2×Dic61—41no—
340C2×Dic61—41no—
341C2×Dic61—84no—
342C2×Dic61—84no—
343C2×Dic61—84no—
344C2×Dic61—84no—
345C2×Dic61#12012yes—
346C2×Dic61#12012yes—
347C8×C61—22no—
348C8×C61—22no—
349#92418—41no—
350#92418—41no—
351#21460—611nomaximal, Sylow
352C22×C61—22no—
353C22×C61—22no—
354C22×C61—22no—
355C22×C61—24no—
356C22×C61—41no—
357C22×C61—42no—
358C22×C61—41no—
359C22×C61—42no—
360C22×C61—42no—
361C22×C61—42no—
362C22×C61—41no—
363C22×C61—42no—
364C22×C61—41no—
365C22×C61—42no—
366C22×C61—42no—
367C22×C61—42no—
368C22×C61—42no—
369C22×C61—81no—
370C22×C61—81no—
371C22×C61—81no—
372C22×C61—81no—
373C22×C61C2×C4×D411yescharacteristic
374C22×C61C2×#12011yescharacteristic
375C22×C61#52511yescharacteristic
376C22×C61#57611yescharacteristic
377C22×C61#57611yescharacteristic
378C22×C61#57711yescharacteristic
379C22×C61#57811yescharacteristic
380C4×C61—22no—
381C4×C61—24no—
382C4×C61—42no—
383C4×C61C2×C4×D411yescharacteristic
384C4×C61C2×C4×D411yescharacteristic
385C4×C61#52511yescharacteristic
386C4×C61#52511yescharacteristic
387Dic61—22no—
388Dic61—22no—
389Dic61—41no—
390Dic61—42no—
391Dic61—42no—
392Dic61—41no—
393Dic61—81no—
394Dic61—81no—
395C2×#520—611no—
396C2×#449D6111yescharacteristic
397C2×#440—611no—
398C2×C4×D8—611no—
399#2324—611no—
400#1880—611no—
401#1879—611no—
402#1874—611no—
403#1863—611no—
404#1862—611no—
405#1852—611no—
406#1788—611no—
407#1762—611no—
408C4×#103—611no—
409#1750—611no—
410C2×C61—42no—
411C2×C61—44no—
412C2×C61—82no—
413C2×C61C4×#12011yescharacteristic
414C2×C61#294611yescharacteristic
415C2×C61#295111yescharacteristic
416C2×C61#300811yescharacteristic
417C2×C61#301311yescharacteristic
418C2×C61#311911yescharacteristic
419C2×C61#312411yescharacteristic
420C22×#41C2×D6111yescharacteristic
421C22×SD16C2×D6111yescharacteristic
422C22×D8C2×D6111yescharacteristic
423C2×#121C2×D6111yescharacteristic
424#520—1224no—
425#520—1224no—
426C2×C4×Q8—611no—
427C2×C4×Q8—611no—
428C2×C4×D4—611no—
429C2×C4×D4—611no—
430C2×C4×D4—611no—
431C2×C4×D4—1221no—
432C2×C4×D4—1221no—
433C2×#117—611no—
434C2×#117—1221no—
435C22×C4⋊C4—611no—
436C22×C4⋊C4—1221no—
437#449Dic6118yescomplemented
438#440—1224no—
439C4×D8—1224no—
440C2×#107—611no—
441C2×#107—611no—
442C2×#103—611no—
443C2×#103—611no—
444C2×#103C2×D6111yescharacteristic
445C2×#102—611no—
446C2×#102—611no—
447C2×#102—611no—
448C2×#102—611no—
449C2×#102C2×D6111yescharacteristic
450C2×C22⋊C8—611no—
451C2×C22⋊C8C2×D6111yescharacteristic
452C2×#97—611no—
453C2×C4×C8—611no—
454#390—611no—
455#390—1221no—
456#389—611no—
457#388—1221no—
458#386—1221no—
459#385—1221no—
460#380—611no—
461C4×C4⋊C4—611no—
462#340—611no—
463#340—611no—
464#340—611no—
465#340—611no—
466#336—611no—
467#336—611no—
468C61#2146011yescharacteristic, complemented, Sylow
469C2×#41—22no—
470C2×#41—22no—
471C2×#41—22no—
472C2×#41—22no—
473C2×#41—22no—
474C2×#41C2×Dic6114yescomplemented
475C22×Q8C22×D6111yescharacteristic
476C22×D4—21no—
477C22×D4—21no—
478C22×D4C22×D6111yescharacteristic
479C22×D4C22×D6111yescharacteristic
480C23×C4—21no—
481C23×C4—1221no—
482C23×C4—1221no—
483C23×C4—1221no—
484C23×C4—1221no—
485C23×C4C22×D6111yescharacteristic
486C2×SD16—22no—
487C2×SD16—22no—
488C2×SD16C2×Dic6114yescomplemented
489C2×D8—22no—
490C2×D8—22no—
491C2×D8C2×Dic6114yescomplemented
492C22×C8—611no—
493C22×C8—611no—
494C22×C8C22×D6111yescharacteristic
495C22×C8C22×D6111yescharacteristic
496#121—22no—
497#121C2×Dic6114yescomplemented
498C4×Q8—614no—
499C4×Q8—1222no—
500C4×Q8—1222no—
501C4×Q8—1222no—
502C4×D4—614no—
503C4×D4—1222no—
504C4×D4—1222no—
505C4×D4—1222no—
506C4×D4—1222no—
507C4×D4—1228no—
508C4×D4—1228no—
509C4×D4—1222no—
510#117—1222no—
511#117—1222no—
512#117—1228no—
513C2×C4⋊C4—611no—
514C2×C4⋊C4—611no—
515C2×C4⋊C4—611no—
516C2×C4⋊C4—611no—
517C2×C4⋊C4—611no—
518C2×C4⋊C4—611no—
519C2×C4⋊C4—1222no—
520C2×C4⋊C4—1222no—
521C2×C4⋊C4—1221no—
522C2×C4⋊C4—1221no—
523C2×C4⋊C4—1228no—
524C2×C4⋊C4—1221no—
525C2×C4⋊C4—1221no—
526C2×C4⋊C4C22×D6111yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—611no—
529C2×C22⋊C4—611no—
530C2×C22⋊C4—1221no—
531C2×C22⋊C4—1221no—
532C2×C22⋊C4—1221no—
533C2×C22⋊C4—1221no—
534C2×C22⋊C4—1221no—
535C2×C22⋊C4—1221no—
536C2×C42—611no—
537C2×C42—611no—
538C2×C42—1221no—
539C2×C42—1221no—
540C2×C42—1221no—
541#107—1222no—
542#107—1222no—
543#103—1222no—
544#103—1222no—
545#103C2×Dic6114yescomplemented
546#102—1222no—
547#102—1222no—
548#102—1222no—
549#102—1222no—
550#102C2×Dic6114yescomplemented
551C22⋊C8—1222no—
552C22⋊C8C2×Dic6114yescomplemented
553#97—1222no—
554C4×C8—1222no—
555#95—1221no—
556#95—1221no—
557#95—1221no—
558C24—21no—
559C24—21no—
560C24D4×D6111yescharacteristic
561#41—28no—
562#41—28no—
563#41—28no—
564#41—28no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8D4×D6112yes—
569C2×Q8#1175822412yes—
570C2×Q8C22×Dic6112yes—
571C2×D4—24no—
572C2×D4—24no—
573C2×D4—24no—
574C2×D4—24no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—81no—
584C2×D4—81no—
585C2×D4D4×D6112yes—
586C2×D4#1175822412yes—
587C2×D4C22×Dic6112yes—
588C2×D4C22×Dic6112yes—
589C22×C4—24no—
590C22×C4—24no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—24no—
597C22×C4—21no—
598C22×C4—611no—
599C22×C4—611no—
600C22×C4—611no—
601C22×C4—611no—
602C22×C4—1224no—
603C22×C4—1224no—
604C22×C4—1224no—
605C22×C4—1221no—
606C22×C4—1221no—
607C22×C4—1221no—
608C22×C4—1221no—
609C22×C4—4881no—
610C22×C4—4881no—
611C22×C4—4881no—
612C22×C4—4881no—
613C22×C4—4881no—
614C22×C4—4881no—
615C22×C4—4881no—
616C22×C4—4881no—
617C22×C4—2442no—
618C22×C4D4×D6111yescharacteristic
619C22×C4#1175822412yes—
620C22×C4C22×Dic6112yes—
621C22×C4C23×D6111yescharacteristic
622SD16—28no—
623D8—28no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—1221no—
629C2×C8—1221no—
630C2×C8—1221no—
631C2×C8—1221no—
632C2×C8—1221no—
633C2×C8—1221no—
634C2×C8C22×Dic6112yes—
635C2×C8C22×Dic6112yes—
636C4⋊C4—21no—
637C4⋊C4—612no—
638C4⋊C4—612no—
639C4⋊C4—1222no—
640C4⋊C4—1222no—
641C4⋊C4—1224no—
642C4⋊C4—1224no—
643C4⋊C4—1224no—
644C4⋊C4—1221no—
645C4⋊C4—1221no—
646C4⋊C4—1221no—
647C4⋊C4—1221no—
648C4⋊C4—1221no—
649C4⋊C4—1221no—
650C4⋊C4—4881no—
651C4⋊C4C22×Dic6112yes—
652C22⋊C4—24no—
653C22⋊C4—1222no—
654C22⋊C4—1222no—
655C22⋊C4—1224no—
656C22⋊C4—1224no—
657C22⋊C4—4881no—
658C22⋊C4—4881no—
659C22⋊C4—4881no—
660C22⋊C4—2442no—
661C42—612no—
662C42—612no—
663C42—1224no—
664C42—1224no—
665C42—1221no—
666C42—1221no—
667C42—4881no—
668C23—22no—
669C23—21no—
670C23—22no—
671C23—21no—
672C23—22no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—22no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23D4×Dic6112yes—
689C23C2×D4×D6111yescharacteristic
690Q8—22no—
691Q8—22no—
692Q8—22no—
693Q8D4×Dic6114yes—
694D4—216no—
695D4—22no—
696D4—22no—
697D4—22no—
698D4—22no—
699D4—22no—
700D4—41no—
701D4—41no—
702D4—84no—
703D4D4×Dic6114yes—
704C2×C4—216no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—612no—
718C2×C4—612no—
719C2×C4—1221no—
720C2×C4—1221no—
721C2×C4—1221no—
722C2×C4—1221no—
723C2×C4—1221no—
724C2×C4—1222no—
725C2×C4—1222no—
726C2×C4—1221no—
727C2×C4—1221no—
728C2×C4—1221no—
729C2×C4—1221no—
730C2×C4—1221no—
731C2×C4—4884no—
732C2×C4—4884no—
733C2×C4—4884no—
734C2×C4—4884no—
735C2×C4—2441no—
736C2×C4—2441no—
737C2×C4—2441no—
738C2×C4—2441no—
739C2×C4—2441no—
740C2×C4—2441no—
741C2×C4—2441no—
742C2×C4—2441no—
743C2×C4—2441no—
744C2×C4—2441no—
745C2×C4D4×Dic6112yes—
746C2×C4C23×Dic6111yescharacteristic
747C2×C4C2×D4×D6111yescharacteristic
748C2×C4C2×D4×D6111yescharacteristic
749C2×C4C2×#1175822411yescharacteristic
750C2×C4C2×#1175822411yescharacteristic
751C2×C4C2×#1175822411yescharacteristic
752C8—22no—
753C8—22no—
754C8—2441no—
755C8—2441no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—24no—
760C22—41no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—41no—
765C22—42no—
766C22—41no—
767C22—42no—
768C22—41no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22C2×D4×Dic6111yescharacteristic
778C22#120×D6111yescharacteristic
779C22#1684026811yescharacteristic
780C22#1684056411yescharacteristic
781C22#1684056611yescharacteristic
782C22#1684057211yescharacteristic
783C22#1684057611yescharacteristic
784C4—22no—
785C4—24no—
786C4—42no—
787C4—1222no—
788C4—1222no—
789C4—4881no—
790C4—4881no—
791C4—2441no—
792C4—2441no—
793C4—2442no—
794C4—2442no—
795C4C2×D4×Dic6111yescharacteristic
796C4C2×D4×Dic6111yescharacteristic
797C4#1684026811yescharacteristic
798C4#1684026811yescharacteristic
799C2—42no—
800C2—44no—
801C2—82no—
802C2#120×Dic6111yescharacteristic
803C2#2145465211yescharacteristic
804C2#2145469511yescharacteristic
805C2#2145508411yescharacteristic
806C2#2145513211yescharacteristic
807C2#2145601111yescharacteristic
808C2#2145607411yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
Fitting, prime radicalC2×C61×#449C2
socleC23×C61C22×D4
cosocleC22×C4×C61C24
hypercenterC2×#449D61
hypocenterC61#21460
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C2×#16840245C2semidirect
2. C2×#16839863C2semidirect
3. C2×D8×Dic61C2semidirect
4. #21448514C2semidirect
5. #21446176C2semidirect
6. #21446169C2semidirect
7. #21446137C2semidirect
8. #21446075C2semidirect
9. #21446068C2semidirect
10. #21446009C2semidirect
11. #21445759C2semidirect
12. #21445646C2semidirect
13. #103×Dic61C2semidirect
14. #21445587C2semidirect
60. C61×#449C4semidirect
73. Q8×Dic61D4semidirect
81. D4×Dic61D4semidirect
130. C2×#41×C61C2×C4semidirect
140. C2×SD16×C61C2×C4semidirect
143. C2×D8×C61C2×C4semidirect
147. #121×C61C2×C4semidirect
150. #103×C61C2×C4semidirect
151. #102×C61C2×C4semidirect
152. C22⋊C8×C61C2×C4semidirect
437. #449Dic61semidirect
468. C61#21460semidirect
474. C2×#41C2×Dic61semidirect
488. C2×SD16C2×Dic61semidirect
491. C2×D8C2×Dic61semidirect
497. #121C2×Dic61semidirect
545. #103C2×Dic61semidirect
550. #102C2×Dic61semidirect
552. 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×#168398632
C2×D8×Dic612
#214485142
#214461762
#214461692
#214461372
#214460752
#214460682
#214460092
#214457592
#214456462
#103×Dic612
#214455872
C2×C61×#4492
#2146061