Finite Group Databasebeta

← C2×#21456108 #30548357

Subgroups — C2×#21456108 #30548357

Order 15616.

2122 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840366C211yesmaximal, characteristic
2C2×#16840238C211yesmaximal, characteristic, complemented
3#21456108C2116yesmaximal, direct product factor
4C2×#16840085C211yesmaximal, characteristic, complemented
5C2×#16840084C211yesmaximal, characteristic, complemented
6C2×#16840070C211yesmaximal, characteristic, complemented
7C2×#16840069C211yesmaximal, characteristic, complemented
8C2×#16839959C211yesmaximal, characteristic, complemented
9C2×#16839899C211yesmaximal, characteristic, complemented
10C2×#16839899C211yesmaximal, characteristic, complemented
11C2×#16839863C211yesmaximal, characteristic, complemented
12C2×#16839859C211yesmaximal, characteristic, complemented
13C2×#16839853C211yesmaximal, characteristic, complemented
14C2×SD16×Dic61C211yesmaximal, characteristic, complemented
15C2×#16839822C211yesmaximal, characteristic, complemented
16C2×C61×#460C211yesmaximal, characteristic, complemented
17C22×Q8×D61C2211yescharacteristic
18C22×#11758200C2211yescharacteristic
19C22×#11758200C2211yescharacteristic
20#16840366—24no—
21#16840366C2218yes—
22C2×#14519769C2211yescharacteristic
23C2×#14519758—21no—
24C2×#14519758—21no—
25C2×#14519749—21no—
26C2×#14519749—21no—
27C2×#14519748C2211yescharacteristic
28C2×#14519748C2211yescharacteristic
29#16840238—24no—
30#16840238C2218yescomplemented
31C2×Q8×Dic61C2211yescharacteristic
32C2×C4×Dic122—21no—
33C2×C4×Dic122C2211yescharacteristic
34C2×#14519742—21no—
35C2×#14519742C2211yescharacteristic
36C2×D4×Dic61C2211yescharacteristic
37C2×D4×Dic61C2211yescharacteristic
38C2×#14519735—21no—
39C2×#14519735C2211yescharacteristic
40C2×#14519734—21no—
41C2×#14519734C2211yescharacteristic
42#16840085C2218yescomplemented
43#16840084C2218yescomplemented
44#16840070C2218yescomplemented
45#16840069C2218yescomplemented
46#16839959C2218yescomplemented
47#16839899C2218yescomplemented
48#16839899C2218yescomplemented
49#16839863C2218yescomplemented
50#16839859C2218yescomplemented
51#16839853C2218yescomplemented
52SD16×Dic61C2218yescomplemented
53#16839822C2218yescomplemented
54C2×#14519711C2211yescharacteristic
55C2×#14519710C2211yescharacteristic
56C2×#14519709C2211yescharacteristic
57C2×#14519708C2211yescharacteristic
58C2×C4⋊#92418C2211yescharacteristic
59C2×#14519702C2211yescharacteristic
60C2×#14519702C2211yescharacteristic
61C2×#14519701C2211yescharacteristic
62C2×#14519701C2211yescharacteristic
63C2×#14519698C2211yescharacteristic
64C2×#14519698C2211yescharacteristic
65C2×#14519689C2211yescharacteristic
66C2×#14519689C2211yescharacteristic
67C2×#14519687C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C22×SD16×C61C2211yescharacteristic
70C22×SD16×C61C2211yescharacteristic
71C2×#127×C61C2211yescharacteristic
72C2×C4×Q8×C61C2211yescharacteristic
73C61×#460C2218yescomplemented
74C2×C4⋊C8×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×#102×C61C2211yescharacteristic
77C22×Dic122—21no—
78C22×Dic122C2311yescharacteristic
79C2×Q8×D61—24no—
80C2×Q8×D61—22no—
81C2×Q8×D61—24no—
82C2×Q8×D61C2314yes—
83C22×C22⋊D61—21no—
84C22×C22⋊D61—21no—
85C23×Dic61—21no—
86C23×Dic61—21no—
87C22×C4×D61—21no—
88C22×C4×D61C2311yescharacteristic
89C2×#11758200—24no—
90C2×#11758200—24no—
91C2×#11758200C2314yes—
92C2×#11758200C2314yes—
93C22×#92418C2311yescharacteristic
94C22×#92418C2311yescharacteristic
95#14519769—22no—
96#14519769C2314yes—
97#14519758—28no—
98#14519758—28no—
99#14519749—28no—
100#14519749—28no—
101#14519748—22no—
102#14519748—22no—
103#14519748C2314yes—
104#14519748C2314yes—
105Q8×Dic61—22no—
106Q8×Dic61C2314yes—
107C4×Dic122—22no—
108C4×Dic122—28no—
109C4×Dic122C2314yes—
110#14519742—28no—
111#14519742—22no—
112#14519742C2314yes—
113D4×Dic61—22no—
114D4×Dic61—22no—
115D4×Dic61C2314yes—
116D4×Dic61C2314yes—
117#14519735—22no—
118#14519735—28no—
119#14519735C2314yes—
120#14519734—28no—
121#14519734D414yes—
122#14519734C2314yes—
123C2×C4⋊Dic61—21no—
124C2×C4⋊Dic61C2311yescharacteristic
125C2×C4⋊Dic61C2311yescharacteristic
126C2×C4⋊Dic61C2311yescharacteristic
127C2×#11758196—21no—
128C2×#11758196—21no—
129C2×#11758196—21no—
130C2×#11758196—21no—
131C2×#11758196D411yescharacteristic
132C2×#11758196D411yescharacteristic
133C2×C22⋊Dic61—21no—
134C2×C22⋊Dic61—21no—
135C2×C22⋊Dic61—21no—
136C2×C22⋊Dic61—21no—
137C2×#11758198—21no—
138C2×#11758198D411yescharacteristic
139C2×#11758198D411yescharacteristic
140C2×C4×Dic61—21no—
141C2×C4×Dic61—21no—
142C2×C4×Dic61—21no—
143C2×C4×Dic61—21no—
144C2×C4×Dic61C2311yescharacteristic
145#14519711C2314yes—
146#14519710C2314yes—
147#14519709C2314yes—
148#14519708C2314yes—
149C4⋊#92418C2314yes—
150#14519702C2314yes—
151#14519702C2314yes—
152#14519701C2314yes—
153#14519701C2314yes—
154#14519698C2314yes—
155#14519698C2314yes—
156#14519689C2314yes—
157#14519689C2314yes—
158#14519687C2314yes—
159C8×Dic61C2314yes—
160C22×Q8×C61C2311yescharacteristic
161C22×D4×C61—21no—
162C22×D4×C61—21no—
163C22×D4×C61C2311yescharacteristic
164C22×D4×C61C2311yescharacteristic
165C2×SD16×C61—24no—
166C2×SD16×C61—24no—
167C2×SD16×C61C2314yes—
168C2×SD16×C61C2314yes—
169C22×C8×C61C2311yescharacteristic
170C22×C8×C61C2311yescharacteristic
171#127×C61—22no—
172#127×C61C2314yes—
173C4×Q8×C61—22no—
174C4×Q8×C61C2314yes—
175C2×C4⋊C4×C61—21no—
176C2×C4⋊C4×C61C2311yescharacteristic
177C2×C42×C61—21no—
178C2×C42×C61C2311yescharacteristic
179C4⋊C8×C61C2314yes—
180#102×C61C2314yes—
181#102×C61C2314yes—
182C24×C61—21no—
183C24×C61—21no—
184C23×D61C2×D411yescharacteristic
185C2×Q8×C61—21no—
186C2×Q8×C61—22no—
187C2×Q8×C61#4114yes—
188C2×Q8×C61C2412yes—
189C2×D4×C61—21no—
190C2×D4×C61—21no—
191C2×D4×C61—24no—
192C2×D4×C61—24no—
193C2×D4×C61—22no—
194C2×D4×C61—22no—
195C2×D4×C61—22no—
196C2×D4×C61—22no—
197C2×D4×C61—82no—
198C2×D4×C61—82no—
199C2×D4×C61C2412yes—
200C2×D4×C61C2412yes—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61C2×D411yescharacteristic
204C22×C4×C61C2×D411yescharacteristic
205C22×C4×C61C2411yescharacteristic
206C2×C22⋊D61—24no—
207C2×C22⋊D61—24no—
208C2×C22⋊D61—82no—
209C2×C22⋊D61—82no—
210C22×Dic61—21no—
211C22×Dic61—21no—
212C22×Dic61—21no—
213C22×Dic61—21no—
214C22×Dic61—24no—
215C22×Dic61—24no—
216C22×Dic61—82no—
217C22×Dic61—82no—
218C22×Dic61C2×D411yescharacteristic
219C22×Dic61C2×D411yescharacteristic
220C22×Dic61C2×D411yescharacteristic
221Q8×D61—216no—
222Q8×D61—28no—
223Q8×D61—28no—
224C2×C4×D61—28no—
225C2×C4×D61—24no—
226C2×C4×D61—22no—
227C2×C4×D61—22no—
228C2×C4×D61C2×D412yes—
229C2×C4×D61C2412yes—
230C2×Dic122—28no—
231C2×Dic122—21no—
232C2×Dic122—22no—
233C2×Dic122—24no—
234C2×Dic122#4114yes—
235C2×Dic122C2412yes—
236SD16×C61—28no—
237SD16×C61—28no—
238C2×C8×C61—22no—
239C2×C8×C61—22no—
240C2×C8×C61C2412yes—
241C2×C8×C61C2412yes—
242C4⋊C4×C61—24no—
243C4⋊C4×C61—21no—
244C4⋊C4×C61C2412yes—
245C42×C61—24no—
246C42×C61C2×D412yes—
247C42×C61C2412yes—
248C22⋊Dic61—24no—
249C22⋊Dic61—24no—
250C22⋊Dic61—24no—
251C22⋊Dic61—24no—
252#11758200—28no—
253#11758200—28no—
254#11758198—24no—
255#11758198C2×D414yes—
256#11758198C2×D414yes—
257C4⋊Dic61—21no—
258C4⋊Dic61—21no—
259C4⋊Dic61—21no—
260C4⋊Dic61—24no—
261C4⋊Dic61C2412yes—
262C4⋊Dic61C2412yes—
263C4⋊Dic61C2412yes—
264#11758196—24no—
265#11758196—24no—
266#11758196—24no—
267#11758196—24no—
268#11758196C2×D414yes—
269#11758196C2×D414yes—
270C4×Dic61—24no—
271C4×Dic61—24no—
272C4×Dic61—24no—
273C4×Dic61—24no—
274C4×Dic61C2×D412yes—
275C4×Dic61C2412yes—
276C2×#92418—22no—
277C2×#92418—22no—
278C2×#92418C2412yes—
279C2×#92418C2412yes—
280C23×C61—22no—
281C23×C61—22no—
282C23×C61—42no—
283C23×C61—42no—
284C23×C61—42no—
285C23×C61—42no—
286C23×C61—42no—
287C23×C61—42no—
288C23×C61C22×D411yescharacteristic
289C22×D61—22no—
290C22×D61—22no—
291C22×D61—22no—
292C22×D61C22×D412yes—
293Q8×C61—24no—
294Q8×C61—22no—
295Q8×C61C2×#4114yes—
296D4×C61—22no—
297D4×C61—22no—
298D4×C61—22no—
299D4×C61—22no—
300D4×C61—42no—
301D4×C61—42no—
302D4×C61—84no—
303D4×C61—84no—
304C2×C4×C61—24no—
305C2×C4×C61—22no—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—42no—
310C2×C4×C61C22×D412yes—
311C2×C4×C61C22×D412yes—
312C2×C4×C61C22×D411yescharacteristic
313C2×C4×C61C2×#4112yes—
314C2×C4×C61C2×#4112yes—
315C2×C4×C61C2511yescharacteristic
316C22⋊D61—84no—
317C22⋊D61—84no—
318C2×Dic61—22no—
319C2×Dic61—24no—
320C2×Dic61—22no—
321C2×Dic61—22no—
322C2×Dic61—22no—
323C2×Dic61—22no—
324C2×Dic61—22no—
325C2×Dic61—22no—
326C2×Dic61—42no—
327C2×Dic61—42no—
328C2×Dic61—42no—
329C2×Dic61—84no—
330C2×Dic61—84no—
331C2×Dic61C22×D412yes—
332C2×Dic61C22×D412yes—
333C2×Dic61C22×D412yes—
334C4×D61—216no—
335C4×D61—24no—
336C4×D61—22no—
337C4×D61—22no—
338Dic122—216no—
339Dic122—24no—
340Dic122—22no—
341Dic122C2×#4114yes—
342C8×C61—22no—
343C8×C61—22no—
344#92418—22no—
345#92418—22no—
346C2×#3126—611nomaximal, Sylow
347C22×C61—42no—
348C22×C61—42no—
349C22×C61—42no—
350C22×C61—42no—
351C22×C61—42no—
352C22×C61—42no—
353C22×C61—84no—
354C22×C61—84no—
355C22×C61#52512yes—
356C22×C61#57712yes—
357C22×C61#57712yes—
358C22×C61C23×D411yescharacteristic
359C2×D61—22no—
360C2×D61—22no—
361C2×D61—22no—
362C2×D61—44no—
363C4×C61—24no—
364C4×C61—22no—
365C4×C61—22no—
366C4×C61—42no—
367C4×C61#52512yes—
368C4×C61C22×#4111yescharacteristic
369C4×C61C22×#4111yescharacteristic
370Dic61—22no—
371Dic61—24no—
372Dic61—22no—
373Dic61—22no—
374Dic61—42no—
375Dic61—42no—
376Dic61—42no—
377C2×#540—611no—
378C2×#519—611no—
379#3126—6116no—
380C2×#482—611no—
381C2×#482—611no—
382C2×#479—611no—
383C2×#479—611no—
384C2×#460—611no—
385C2×#460D6111yescharacteristic, complemented
386C2×#448—611no—
387C2×#448—611no—
388C2×#440—611no—
389C2×#440—611no—
390C2×C4×SD16—611no—
391C2×C4×SD16—611no—
392C2×#433—611no—
393C2×C61—82no—
394C2×C61—82no—
395C2×C61#312614yescomplemented
396C2×C61C2×#52511yescharacteristic
397C2×C61C2×#57711yescharacteristic
398C2×C61C2×#57711yescharacteristic
399D61—42no—
400C23×Q8—611no—
401C22×SD16—611no—
402C22×SD16—611no—
403C22×SD16C2×D6111yescharacteristic
404C22×SD16C2×D6111yescharacteristic
405#540—618no—
406#540—1224no—
407C2×#127C2×D6111yescharacteristic
408C2×#125—611no—
409C2×#123—1221no—
410C2×#123—1221no—
411C2×#121—611no—
412C2×#121—611no—
413C2×#121—1221no—
414C2×#121—1221no—
415#519—618no—
416#519—1224no—
417C2×C4×Q8—611no—
418C2×C4×Q8—611no—
419C2×C4×Q8—611no—
420C2×C4×Q8—1221no—
421C2×C4×Q8—1221no—
422C2×C4×Q8C2×D6111yescharacteristic
423C2×C4×D4—611no—
424C2×C4×D4—611no—
425C2×#117—611no—
426C2×#117—611no—
427C2×#117—1221no—
428C2×#117—1221no—
429#482—618no—
430#482—618no—
431#479—618no—
432#479—618no—
433#460—618no—
434#460C2×D6118yescomplemented
435#448—618no—
436#448—618no—
437#440—618no—
438#440—618no—
439C4×SD16—618no—
440C4×SD16—618no—
441#433—618no—
442C2×#107—611no—
443C2×#107—611no—
444C2×#106—611no—
445C2×#106—611no—
446C2×C4⋊C8—611no—
447C2×C4⋊C8C2×D6111yescharacteristic
448C2×#103—611no—
449C2×#103—611no—
450C2×#103—611no—
451C2×#103—611no—
452C2×#102—611no—
453C2×#102—611no—
454C2×#102C2×D6111yescharacteristic
455C2×#102C2×D6111yescharacteristic
456C2×C22⋊C8—611no—
457C2×C22⋊C8—611no—
458C2×#97—611no—
459C2×C4×C8—611no—
460C61C2×#312611yescharacteristic, complemented, Sylow
461C22×Q8—614no—
462C22×Q8—611no—
463C22×Q8—1221no—
464C22×Q8—1222no—
465C22×Q8—1224no—
466C22×Q8—1224no—
467C22×Q8C22×D6111yescharacteristic
468C22×D4—21no—
469C22×D4—21no—
470C22×D4—1221no—
471C22×D4—1221no—
472C22×D4C22×D6111yescharacteristic
473C22×D4C22×D6111yescharacteristic
474C23×C4—611no—
475C23×C4—1221no—
476C23×C4—1221no—
477C23×C4—1221no—
478C2×SD16—24no—
479C2×SD16—24no—
480C2×SD16—614no—
481C2×SD16—614no—
482C2×SD16—1224no—
483C2×SD16—1224no—
484C2×SD16C22×D6114yes—
485C2×SD16C22×D6114yes—
486C22×C8—611no—
487C22×C8—611no—
488C22×C8C22×D6111yescharacteristic
489C22×C8C22×D6111yescharacteristic
490#127—22no—
491#127C22×D6114yes—
492#125—614no—
493#125—1222no—
494#123—1228no—
495#123—1228no—
496#121—614no—
497#121—614no—
498#121—1228no—
499#121—1228no—
500#121—1222no—
501#121—1222no—
502C4×Q8—22no—
503C4×Q8—614no—
504C4×Q8—614no—
505C4×Q8—614no—
506C4×Q8—1228no—
507C4×Q8—1222no—
508C4×Q8—1222no—
509C4×Q8—1228no—
510C4×Q8—1222no—
511C4×Q8C22×D6114yes—
512C4×D4—614no—
513C4×D4—614no—
514C4×D4—1222no—
515C4×D4—1222no—
516#117—614no—
517#117—614no—
518#117—614no—
519#117—1228no—
520#117—1228no—
521#117—1222no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—611no—
524C2×C4⋊C4—611no—
525C2×C4⋊C4—611no—
526C2×C4⋊C4—611no—
527C2×C4⋊C4—611no—
528C2×C4⋊C4—1221no—
529C2×C4⋊C4—1221no—
530C2×C4⋊C4—1221no—
531C2×C4⋊C4—1221no—
532C2×C4⋊C4—1221no—
533C2×C4⋊C4C22×D6111yescharacteristic
534C2×C22⋊C4—611no—
535C2×C22⋊C4—611no—
536C2×C22⋊C4—1221no—
537C2×C22⋊C4—1221no—
538C2×C22⋊C4—1221no—
539C2×C22⋊C4—1221no—
540C2×C22⋊C4—1221no—
541C2×C42—21no—
542C2×C42—611no—
543C2×C42—1221no—
544C2×C42—1221no—
545C2×C42—1221no—
546C2×C42—1221no—
547C2×C42C22×D6111yescharacteristic
548#107—614no—
549#107—614no—
550#106—614no—
551#106—614no—
552C4⋊C8—614no—
553C4⋊C8C22×D6114yes—
554#103—614no—
555#103—614no—
556#103—614no—
557#103—614no—
558#102—614no—
559#102—614no—
560#102C22×D6114yes—
561#102C22×D6114yes—
562C22⋊C8—614no—
563C22⋊C8—614no—
564#97—614no—
565C4×C8—614no—
566C24—21no—
567C24—21no—
568C24—611no—
569C2×Q8—21no—
570C2×Q8—22no—
571C2×Q8—614no—
572C2×Q8—612no—
573C2×Q8—1224no—
574C2×Q8—1228no—
575C2×Q8—1228no—
576C2×Q8—12216no—
577C2×Q8—1228no—
578C2×Q8—1221no—
579C2×Q8—1222no—
580C2×Q8#1175822414yes—
581C2×Q8C23×D6112yes—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—24no—
585C2×D4—24no—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—82no—
591C2×D4—82no—
592C2×D4—1224no—
593C2×D4—1224no—
594C2×D4—4882no—
595C2×D4—4882no—
596C2×D4C23×D6112yes—
597C2×D4C23×D6112yes—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—611no—
601C22×C4—611no—
602C22×C4—611no—
603C22×C4—612no—
604C22×C4—612no—
605C22×C4—1224no—
606C22×C4—1228no—
607C22×C4—1224no—
608C22×C4—1224no—
609C22×C4—1221no—
610C22×C4—1222no—
611C22×C4—1222no—
612C22×C4—1221no—
613C22×C4—1221no—
614C22×C4—1221no—
615C22×C4—4882no—
616C22×C4—4882no—
617C22×C4D4×D6111yescharacteristic
618C22×C4D4×D6111yescharacteristic
619C22×C4C23×D6111yescharacteristic
620SD16—28no—
621SD16—28no—
622SD16—1228no—
623SD16—1228no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—612no—
627C2×C8—612no—
628C2×C8—1222no—
629C2×C8—1222no—
630C2×C8C23×D6112yes—
631C2×C8C23×D6112yes—
632C4⋊C4—24no—
633C4⋊C4—21no—
634C4⋊C4—614no—
635C4⋊C4—614no—
636C4⋊C4—612no—
637C4⋊C4—612no—
638C4⋊C4—612no—
639C4⋊C4—1224no—
640C4⋊C4—1224no—
641C4⋊C4—1221no—
642C4⋊C4—1221no—
643C4⋊C4—1221no—
644C4⋊C4—1224no—
645C4⋊C4—1224no—
646C4⋊C4—1224no—
647C4⋊C4C23×D6112yes—
648C22⋊C4—614no—
649C22⋊C4—614no—
650C22⋊C4—1224no—
651C22⋊C4—1224no—
652C22⋊C4—1224no—
653C22⋊C4—1224no—
654C22⋊C4—1224no—
655C42—24no—
656C42—612no—
657C42—612no—
658C42—1224no—
659C42—1224no—
660C42—1224no—
661C42—1224no—
662C42D4×D6112yes—
663C42C23×D6112yes—
664C23—22no—
665C23—22no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—612no—
673C23—1222no—
674C23—1222no—
675C23—1222no—
676C23C2×D4×D6111yescharacteristic
677Q8—24no—
678Q8—22no—
679Q8—614no—
680Q8—12216no—
681Q8—1224no—
682Q8—1222no—
683Q8C2×#1175822414yes—
684D4—22no—
685D4—22no—
686D4—22no—
687D4—22no—
688D4—42no—
689D4—42no—
690D4—84no—
691D4—84no—
692D4—4884no—
693D4—4884no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—42no—
700C2×C4—612no—
701C2×C4—612no—
702C2×C4—612no—
703C2×C4—12216no—
704C2×C4—1222no—
705C2×C4—1224no—
706C2×C4—1222no—
707C2×C4—1222no—
708C2×C4—1222no—
709C2×C4—1224no—
710C2×C4—1222no—
711C2×C4—1222no—
712C2×C4—1222no—
713C2×C4—1222no—
714C2×C4—1222no—
715C2×C4—4884no—
716C2×C4—4884no—
717C2×C4—2442no—
718C2×C4—2442no—
719C2×C4—2442no—
720C2×C4C2×D4×D6112yes—
721C2×C4C2×D4×D6112yes—
722C2×C4C2×D4×D6111yescharacteristic
723C2×C4#41×D6112yes—
724C2×C4C2×#1175822412yes—
725C2×C4C24×D6111yescharacteristic
726C8—22no—
727C8—22no—
728C8—1222no—
729C8—1222no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—84no—
737C22—84no—
738C22—1222no—
739C22—1222no—
740C22—1222no—
741C22—2444no—
742C22#1684027212yes—
743C22#1684056812yes—
744C22#1684057212yes—
745C22C22×D4×D6111yescharacteristic
746C4—22no—
747C4—22no—
748C4—24no—
749C4—42no—
750C4—1222no—
751C4—1222no—
752C4—1222no—
753C4—1224no—
754C4—2442no—
755C4—2442no—
756C4—2442no—
757C4#1684027212yes—
758C4C2×#41×D6111yescharacteristic
759C4C22×#1175822411yescharacteristic
760C2—82no—
761C2—82no—
762C2—2442no—
763C2#2145610814yesdirect product factor
764C2C2×#1684027211yescharacteristic
765C2C2×#1684056811yescharacteristic
766C2C2×#1684057211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#460C2
socleC23×C61C22×D4
prime radicalC2×#16840366C2
hypercenterC2×#460D61
hypocenterC61C2×#3126
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#460

Complements

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

NH ≅ G/Ntype
2. C2×#16840238C2semidirect
3. #21456108C2direct (N × H)
4. C2×#16840085C2semidirect
5. C2×#16840084C2semidirect
6. C2×#16840070C2semidirect
7. C2×#16840069C2semidirect
8. C2×#16839959C2semidirect
9. C2×#16839899C2semidirect
10. C2×#16839899C2semidirect
11. C2×#16839863C2semidirect
12. C2×#16839859C2semidirect
13. C2×#16839853C2semidirect
14. C2×SD16×Dic61C2semidirect
15. C2×#16839822C2semidirect
16. C2×C61×#460C2semidirect
30. #16840238C22semidirect
42. #16840085C22semidirect
43. #16840084C22semidirect
44. #16840070C22semidirect
45. #16840069C22semidirect
46. #16839959C22semidirect
47. #16839899C22semidirect
48. #16839899C22semidirect
49. #16839863C22semidirect
50. #16839859C22semidirect
51. #16839853C22semidirect
52. SD16×Dic61C22semidirect
53. #16839822C22semidirect
73. C61×#460C22semidirect
385. C2×#460D61semidirect
395. C2×C61#3126semidirect
434. #460C2×D61semidirect
460. C61C2×#3126semidirect
763. C2#21456108direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403662
C2×#168402382
#214561082
C2×#168400852
C2×#168400842
C2×#168400702
C2×#168400692
C2×#168399592
C2×#168398992
C2×#168398632
C2×#168398592
C2×#168398532
C2×SD16×Dic612
C2×#168398222
C2×C61×#4602
C2×#312661