Finite Group Databasebeta

← C2×#21455809 #30547875

Subgroups — C2×#21455809 #30547875

Order 15616.

2234 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840341C211yesmaximal, characteristic
2C2×#16840243C211yesmaximal, characteristic, complemented
3#21455809C2116yesmaximal, direct product factor
4C2×#16840079C211yesmaximal, characteristic, complemented
5C2×#16840106C211yesmaximal, characteristic, complemented
6C2×#16840104C211yesmaximal, characteristic, complemented
7C2×#16840084C211yesmaximal, characteristic, complemented
8C2×#16840083C211yesmaximal, characteristic, complemented
9C2×#16840094C211yesmaximal, characteristic, complemented
10C2×#16840092C211yesmaximal, characteristic, complemented
11C2×#16839801C211yesmaximal, characteristic, complemented
12C2×#106×D61C211yesmaximal, characteristic, complemented
13C2×#16839760C211yesmaximal, characteristic, complemented
14C2×#16839755C211yesmaximal, characteristic, complemented
15C2×#16839727C211yesmaximal, characteristic, complemented
16C2×C61×#481C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic
18C22×#11758224C2211yescharacteristic
19C22×#11758189C2211yescharacteristic
20C22×C8×D61C2211yescharacteristic
21#16840341—24no—
22#16840341C2218yes—
23C2×#14519757C2211yescharacteristic
24C2×#14519756C2211yescharacteristic
25C2×#14519754—21no—
26C2×#14519750—21no—
27C2×#14519749—21no—
28C2×#14519748—21no—
29C2×#14519748C2211yescharacteristic
30#16840243—24no—
31#16840243C2218yescomplemented
32C2×#14519742—21no—
33C2×#14519739—21no—
34C2×C4×C22⋊D61—21no—
35C2×C4×C22⋊D61—21no—
36C2×#14519736C2211yescharacteristic
37C2×#14519735C2211yescharacteristic
38C2×#14519735C2211yescharacteristic
39C2×C4⋊C4×D61C2211yescharacteristic
40C2×C4⋊C4×D61C2211yescharacteristic
41C2×C4⋊C4×D61C2211yescharacteristic
42#16840106C2218yescomplemented
43#16840104C2218yescomplemented
44#16840094C2218yescomplemented
45#16840092C2218yescomplemented
46#16840084C2218yescomplemented
47#16840083C2218yescomplemented
48#16840079C2218yescomplemented
49#16839801C2218yescomplemented
50C2×#14519711C2211yescharacteristic
51C2×#14519710C2211yescharacteristic
52C2×#14519709C2211yescharacteristic
53C2×#14519708C2211yescharacteristic
54C2×#14519708C2211yescharacteristic
55C2×#14519708C2211yescharacteristic
56#106×D61C2218yescomplemented
57#16839760C2218yescomplemented
58#16839755C2218yescomplemented
59C2×#14519702C2211yescharacteristic
60C2×#14519702C2211yescharacteristic
61C2×#14519700C2211yescharacteristic
62C2×#14519700C2211yescharacteristic
63C2×#14519698C2211yescharacteristic
64C2×#14519698C2211yescharacteristic
65#16839727C2218yescomplemented
66C2×C22⋊#92418C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×#14519689C2211yescharacteristic
69C2×#121×C61C2211yescharacteristic
70C22×C4⋊C4×C61C2211yescharacteristic
71C61×#481C2218yescomplemented
72C2×#106×C61C2211yescharacteristic
73C2×#106×C61C2211yescharacteristic
74C2×#102×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×C22⋊C8×C61C2211yescharacteristic
77C2×#11758222—24no—
78C2×#11758222—24no—
79C2×#11758222D414yes—
80C2×#11758222C2314yes—
81C2×#11758224—22no—
82C2×#11758224—24no—
83C2×#11758224—24no—
84C2×#11758224C2314yes—
85C22×Dic122D411yescharacteristic
86C22×Dic122C2311yescharacteristic
87C22×D244D411yescharacteristic
88C22×C22⋊D61—21no—
89C22×C22⋊D61—21no—
90C22×C22⋊D61D411yescharacteristic
91C22×C22⋊D61D411yescharacteristic
92C23×Dic61—21no—
93C22×C4×D61—21no—
94C22×C4×D61—21no—
95C22×C4×D61—21no—
96C22×C4×D61C2311yescharacteristic
97C22×C4×D61C2311yescharacteristic
98C2×#11758189—24no—
99C2×#11758189C2314yes—
100C22×#92418C2311yescharacteristic
101C22×#92418C2311yescharacteristic
102C2×C8×D61—24no—
103C2×C8×D61C2314yes—
104#14519757—22no—
105#14519757C2314yes—
106#14519756—22no—
107#14519756C2314yes—
108#14519754—28no—
109#14519750—28no—
110#14519749—28no—
111#14519748—28no—
112#14519748—22no—
113#14519748C2314yes—
114#14519742—28no—
115#14519739—28no—
116C4×C22⋊D61—28no—
117C4×C22⋊D61—28no—
118#14519736—22no—
119#14519736C2314yes—
120#14519735—22no—
121#14519735—22no—
122#14519735C2314yes—
123#14519735C2314yes—
124C2×C4⋊Dic61—21no—
125C2×C4⋊Dic61C2311yescharacteristic
126C2×C4⋊Dic61C2311yescharacteristic
127C2×C4⋊Dic61C2311yescharacteristic
128C2×#11758196—21no—
129C2×#11758196—21no—
130C2×#11758196—21no—
131C2×#11758196—21no—
132C4⋊C4×D61—22no—
133C4⋊C4×D61—22no—
134C4⋊C4×D61—22no—
135C4⋊C4×D61C2314yes—
136C4⋊C4×D61C2314yes—
137C4⋊C4×D61C2314yes—
138C2×C22⋊Dic61—21no—
139C2×C22⋊Dic61—21no—
140C2×C22⋊Dic61—21no—
141C2×#11758198—21no—
142C2×#11758198—21no—
143C2×#11758198—21no—
144C2×C4×Dic61—21no—
145C2×C4×Dic61—21no—
146C2×C4×Dic61—21no—
147#14519711C2314yes—
148#14519710C2314yes—
149#14519709C2314yes—
150#14519708C2314yes—
151#14519708C2314yes—
152#14519708C2314yes—
153#14519702C2314yes—
154#14519702C2314yes—
155#14519700C2314yes—
156#14519700C2314yes—
157#14519698C2314yes—
158#14519698C2314yes—
159C22⋊#92418C2314yes—
160#14519689C2314yes—
161#14519689C2314yes—
162C22×D4×C61—21no—
163C22×D4×C61C2311yescharacteristic
164C23×C4×C61—21no—
165C23×C4×C61C2311yescharacteristic
166C22×C8×C61C2311yescharacteristic
167C22×C8×C61C2311yescharacteristic
168#121×C61—22no—
169#121×C61C2314yes—
170C2×C4⋊C4×C61—21no—
171C2×C4⋊C4×C61—22no—
172C2×C4⋊C4×C61C2311yescharacteristic
173C2×C4⋊C4×C61C2311yescharacteristic
174C2×C4⋊C4×C61C2311yescharacteristic
175C2×C4⋊C4×C61C2314yes—
176C2×C22⋊C4×C61—21no—
177#106×C61C2314yes—
178#106×C61C2314yes—
179#102×C61C2314yes—
180#102×C61C2314yes—
181C22⋊C8×C61C2314yes—
182C24×C61—21no—
183C24×C61C2×D411yescharacteristic
184C23×D61C2×D411yescharacteristic
185C23×D61C2×D411yescharacteristic
186C2×D4×C61—24no—
187C2×D4×C61—21no—
188C2×D4×C61—22no—
189C2×D4×C61—22no—
190C2×D4×C61—82no—
191C2×D4×C61C2412yes—
192C22×C4×C61—22no—
193C22×C4×C61—22no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—24no—
198C22×C4×C61—82no—
199C22×C4×C61C2×D411yescharacteristic
200C22×C4×C61C2×D412yes—
201C22×C4×C61C2412yes—
202C22×C4×C61C2411yescharacteristic
203C2×C22⋊D61—24no—
204C2×C22⋊D61—24no—
205C2×C22⋊D61—24no—
206C2×C22⋊D61—24no—
207C2×C22⋊D61—44no—
208C2×C22⋊D61—82no—
209C2×C22⋊D61C2×D414yes—
210C2×C22⋊D61C2×D414yes—
211C22×Dic61—21no—
212C22×Dic61—21no—
213C22×Dic61—21no—
214C22×Dic61—21no—
215C22×Dic61—24no—
216C22×Dic61—44no—
217C22×Dic61C2×D411yescharacteristic
218C22×Dic61C2×D411yescharacteristic
219#11758224—28no—
220#11758224—28no—
221#11758224—48no—
222#11758222—216no—
223#11758222—28no—
224#11758222—28no—
225C2×D244—24no—
226C2×D244C2×D414yes—
227C2×C4×D61—22no—
228C2×C4×D61—22no—
229C2×C4×D61—24no—
230C2×C4×D61—24no—
231C2×C4×D61—24no—
232C2×C4×D61—82no—
233C2×C4×D61—82no—
234C2×C4×D61—82no—
235C2×C4×D61C2×D412yes—
236C2×C4×D61C2×D412yes—
237C2×C4×D61#4114yes—
238C2×C4×D61#4114yes—
239C2×C4×D61C2412yes—
240C2×C4×D61C2412yes—
241C2×Dic122—24no—
242C2×Dic122—22no—
243C2×Dic122—22no—
244C2×Dic122—21no—
245C2×Dic122C2×D414yes—
246C2×Dic122C2412yes—
247C2×C8×C61—22no—
248C2×C8×C61—22no—
249C2×C8×C61C2412yes—
250C2×C8×C61C2412yes—
251C4⋊C4×C61—21no—
252C4⋊C4×C61—21no—
253C4⋊C4×C61—24no—
254C4⋊C4×C61—21no—
255C4⋊C4×C61C2412yes—
256C4⋊C4×C61C2412yes—
257C4⋊C4×C61C2412yes—
258C22⋊C4×C61—24no—
259C22⋊Dic61—24no—
260C22⋊Dic61—24no—
261C22⋊Dic61—24no—
262#11758198—24no—
263#11758198—24no—
264#11758198—24no—
265C4⋊Dic61—21no—
266C4⋊Dic61—21no—
267C4⋊Dic61—21no—
268C4⋊Dic61—24no—
269C4⋊Dic61C2412yes—
270C4⋊Dic61C2412yes—
271C4⋊Dic61C2412yes—
272#11758196—24no—
273#11758196—24no—
274#11758196—24no—
275#11758196—24no—
276C4×Dic61—24no—
277C4×Dic61—24no—
278C4×Dic61—24no—
279C2×#92418—22no—
280C2×#92418—22no—
281C2×#92418C2412yes—
282C2×#92418C2412yes—
283#11758189—28no—
284C8×D61—28no—
285C23×C61—22no—
286C23×C61—22no—
287C23×C61—22no—
288C23×C61—22no—
289C23×C61—42no—
290C23×C61—42no—
291C23×C61—42no—
292C23×C61C22×D412yes—
293C23×C61C22×D411yescharacteristic
294C22×D61—22no—
295C22×D61—22no—
296C22×D61—22no—
297C22×D61—22no—
298C22×D61—22no—
299C22×D61#12314yes—
300C22×D61C22×D412yes—
301C22×D61C22×D412yes—
302D4×C61—22no—
303D4×C61—22no—
304D4×C61—42no—
305D4×C61—84no—
306C2×C4×C61—22no—
307C2×C4×C61—24no—
308C2×C4×C61—22no—
309C2×C4×C61—22no—
310C2×C4×C61—22no—
311C2×C4×C61—22no—
312C2×C4×C61—22no—
313C2×C4×C61—42no—
314C2×C4×C61—42no—
315C2×C4×C61—42no—
316C2×C4×C61—84no—
317C2×C4×C61C22×D412yes—
318C2×C4×C61C22×D411yescharacteristic
319C2×C4×C61C2×#4112yes—
320C2×C4×C61C2×#4112yes—
321C2×C4×C61C2511yescharacteristic
322C22⋊D61—28no—
323C22⋊D61—28no—
324C22⋊D61—48no—
325C22⋊D61—84no—
326C2×Dic61—22no—
327C2×Dic61—22no—
328C2×Dic61—22no—
329C2×Dic61—22no—
330C2×Dic61—22no—
331C2×Dic61—42no—
332C2×Dic61—42no—
333C2×Dic61—42no—
334C2×Dic61—42no—
335C2×Dic61—48no—
336C2×Dic61#12314yes—
337C2×Dic61C22×D412yes—
338C2×Dic61C22×D412yes—
339D244—28no—
340C4×D61—24no—
341C4×D61—22no—
342C4×D61—22no—
343C4×D61—84no—
344C4×D61—84no—
345C4×D61—84no—
346C4×D61#12318yes—
347C4×D61C2×#4114yes—
348C4×D61C2×#4114yes—
349Dic122—28no—
350Dic122—22no—
351Dic122—22no—
352Dic122—42no—
353C8×C61—22no—
354C8×C61—22no—
355#92418—22no—
356#92418—22no—
357C2×#3099—611nomaximal, Sylow
358C22×C61—22no—
359C22×C61—22no—
360C22×C61—22no—
361C22×C61—44no—
362C22×C61—42no—
363C22×C61—42no—
364C22×C61—42no—
365C22×C61—84no—
366C22×C61C2×#12312yes—
367C22×C61#57712yes—
368C22×C61#57712yes—
369C22×C61C23×D411yescharacteristic
370C2×D61—28no—
371C2×D61—22no—
372C2×D61—22no—
373C2×D61—22no—
374C2×D61—22no—
375C2×D61—22no—
376C2×D61—44no—
377C2×D61C2×#12314yes—
378C4×C61—22no—
379C4×C61—42no—
380C4×C61—42no—
381C4×C61—42no—
382C4×C61C2×#12312yes—
383C4×C61C22×#4111yescharacteristic
384C4×C61C22×#4111yescharacteristic
385Dic61—22no—
386Dic61—42no—
387Dic61—42no—
388Dic61—42no—
389Dic61—42no—
390Dic61C2×#12314yes—
391C2×#537—611no—
392C2×#520—611no—
393#3099—6116no—
394C2×#481—611no—
395C2×#481D6111yescharacteristic, complemented
396C2×#485—611no—
397C2×#485—611no—
398C2×#482—611no—
399C2×#482—611no—
400C2×#483—611no—
401C2×#483—611no—
402C2×#428—611no—
403C22×#106—611no—
404C2×#417—611no—
405C2×#416—611no—
406C2×#408—611no—
407C2×C61—42no—
408C2×C61—82no—
409C2×C61#309914yescomplemented
410C2×C61C22×#12311yescharacteristic
411C2×C61C2×#57711yescharacteristic
412C2×C61C2×#57711yescharacteristic
413D61—24no—
414D61—42no—
415C22×#41—611no—
416C22×#41—611no—
417C22×M16—611no—
418C23×C8—611no—
419#537—618no—
420#537—1224no—
421C2×C22⋊Q8—611no—
422C2×C22⋊Q8—611no—
423C2×C22⋊Q8—1221no—
424C2×#121—611no—
425C2×#121—1221no—
426C2×#121—1221no—
427C2×#121—1221no—
428C2×#121C2×D6111yescharacteristic
429#520—618no—
430#520—1224no—
431C2×C4×Q8—1221no—
432C2×C4×D4—1221no—
433C2×C4×D4—1221no—
434C2×C4×D4—1221no—
435C2×#117—611no—
436C2×#117—611no—
437C2×#117—611no—
438C22×C4⋊C4—611no—
439C22×C4⋊C4—611no—
440C22×C4⋊C4—611no—
441C22×C4⋊C4C2×D6111yescharacteristic
442#485—618no—
443#485—618no—
444#483—618no—
445#483—618no—
446#482—618no—
447#482—618no—
448#481—618no—
449#481C2×D6118yescomplemented
450#428—618no—
451C2×#107—611no—
452C2×#107—611no—
453C2×#106—611no—
454C2×#106—611no—
455C2×#106—611no—
456C2×#106—611no—
457C2×#106—618no—
458C2×#106C2×D6111yescharacteristic
459C2×#106C2×D6111yescharacteristic
460#417—618no—
461#416—618no—
462C2×#103—611no—
463C2×#103—611no—
464C2×#103—611no—
465C2×#103—611no—
466C2×#102—611no—
467C2×#102—611no—
468C2×#102C2×D6111yescharacteristic
469C2×#102C2×D6111yescharacteristic
470#408—618no—
471C2×C22⋊C8—611no—
472C2×C22⋊C8—611no—
473C2×C22⋊C8—611no—
474C2×C22⋊C8C2×D6111yescharacteristic
475C61C2×#309911yescharacteristic, complemented, Sylow
476C2×#41—614no—
477C2×#41—614no—
478C2×#41—614no—
479C2×#41—1224no—
480C2×#41—1224no—
481C2×#41—1222no—
482C2×#41—1224no—
483C2×#41—1224no—
484C22×Q8—611no—
485C22×Q8—611no—
486C22×D4—21no—
487C22×D4—611no—
488C22×D4—611no—
489C22×D4—611no—
490C22×D4—1221no—
491C22×D4—1221no—
492C22×D4C22×D6111yescharacteristic
493C23×C4—21no—
494C23×C4—611no—
495C23×C4—611no—
496C23×C4—1221no—
497C23×C4—1221no—
498C23×C4—1221no—
499C23×C4—1221no—
500C23×C4C22×D6111yescharacteristic
501C2×M16—614no—
502C2×M16—1224no—
503C22×C8—611no—
504C22×C8—611no—
505C22×C8—614no—
506C22×C8—1224no—
507C22×C8C22×D6111yescharacteristic
508C22×C8C22×D6111yescharacteristic
509C22⋊Q8—614no—
510C22⋊Q8—614no—
511C22⋊Q8—1228no—
512C22⋊Q8—1222no—
513C22⋊Q8—1222no—
514#121—22no—
515#121—614no—
516#121—1228no—
517#121—1222no—
518#121—1228no—
519#121—1228no—
520#121C22×D6114yes—
521C4×Q8—1228no—
522C4×D4—1228no—
523C4×D4—1228no—
524C4×D4—1228no—
525#117—614no—
526#117—614no—
527#117—614no—
528#117—1222no—
529#117—1222no—
530#117—1222no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—22no—
533C2×C4⋊C4—611no—
534C2×C4⋊C4—611no—
535C2×C4⋊C4—611no—
536C2×C4⋊C4—614no—
537C2×C4⋊C4—614no—
538C2×C4⋊C4—614no—
539C2×C4⋊C4—1222no—
540C2×C4⋊C4—1222no—
541C2×C4⋊C4—1222no—
542C2×C4⋊C4—1221no—
543C2×C4⋊C4—1221no—
544C2×C4⋊C4—1221no—
545C2×C4⋊C4—1221no—
546C2×C4⋊C4—1221no—
547C2×C4⋊C4C22×D6111yescharacteristic
548C2×C4⋊C4C22×D6111yescharacteristic
549C2×C4⋊C4C22×D6111yescharacteristic
550C2×C4⋊C4C22×D6114yes—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—1221no—
553C2×C22⋊C4—1221no—
554C2×C22⋊C4—1221no—
555C2×C22⋊C4—1221no—
556C2×C22⋊C4—1221no—
557C2×C22⋊C4—1221no—
558C2×C42—1221no—
559C2×C42—1221no—
560C2×C42—1221no—
561#107—614no—
562#107—614no—
563#106—614no—
564#106—614no—
565#106—614no—
566#106—614no—
567#106C22×D6114yes—
568#106C22×D6114yes—
569#103—614no—
570#103—614no—
571#103—614no—
572#103—614no—
573#102—614no—
574#102—614no—
575#102C22×D6114yes—
576#102C22×D6114yes—
577C22⋊C8—614no—
578C22⋊C8—614no—
579C22⋊C8—614no—
580C22⋊C8C22×D6114yes—
581C24—21no—
582C24—611no—
583C24—611no—
584C24D4×D6111yescharacteristic
585#41—12216no—
586#41—1228no—
587#41—1228no—
588#41—1228no—
589#41—1228no—
590#41—2448no—
591C2×Q8—614no—
592C2×Q8—612no—
593C2×Q8—1224no—
594C2×Q8—1221no—
595C2×Q8—1222no—
596C2×Q8—1222no—
597C2×D4—24no—
598C2×D4—21no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—82no—
602C2×D4—614no—
603C2×D4—614no—
604C2×D4—614no—
605C2×D4—1224no—
606C2×D4—1224no—
607C2×D4—1224no—
608C2×D4—1224no—
609C2×D4—1224no—
610C2×D4—4882no—
611C2×D4—2444no—
612C2×D4C23×D6112yes—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—24no—
619C22×C4—82no—
620C22×C4—611no—
621C22×C4—612no—
622C22×C4—614no—
623C22×C4—614no—
624C22×C4—612no—
625C22×C4—611no—
626C22×C4—612no—
627C22×C4—612no—
628C22×C4—1224no—
629C22×C4—1224no—
630C22×C4—1224no—
631C22×C4—1224no—
632C22×C4—1222no—
633C22×C4—1222no—
634C22×C4—1221no—
635C22×C4—1221no—
636C22×C4—1221no—
637C22×C4—1221no—
638C22×C4—4882no—
639C22×C4—4882no—
640C22×C4—4882no—
641C22×C4—2444no—
642C22×C4D4×D6112yes—
643C22×C4D4×D6111yescharacteristic
644C22×C4C23×D6112yes—
645C22×C4C23×D6111yescharacteristic
646M16—1228no—
647C2×C8—22no—
648C2×C8—22no—
649C2×C8—612no—
650C2×C8—612no—
651C2×C8—1228no—
652C2×C8—1222no—
653C2×C8—1222no—
654C2×C8C23×D6112yes—
655C2×C8C23×D6112yes—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—24no—
659C4⋊C4—21no—
660C4⋊C4—612no—
661C4⋊C4—612no—
662C4⋊C4—612no—
663C4⋊C4—1224no—
664C4⋊C4—1224no—
665C4⋊C4—1224no—
666C4⋊C4—1224no—
667C4⋊C4—1221no—
668C4⋊C4—1221no—
669C4⋊C4—1221no—
670C4⋊C4—1224no—
671C4⋊C4C23×D6112yes—
672C4⋊C4C23×D6112yes—
673C4⋊C4C23×D6112yes—
674C22⋊C4—24no—
675C22⋊C4—1224no—
676C22⋊C4—1224no—
677C22⋊C4—1224no—
678C22⋊C4—1224no—
679C22⋊C4—1224no—
680C22⋊C4—1224no—
681C42—1224no—
682C42—1224no—
683C42—1224no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—614no—
692C23—612no—
693C23—612no—
694C23—1222no—
695C23—1222no—
696C23—1222no—
697C23—1222no—
698C23—1222no—
699C23C2×D4×D6112yes—
700C23C2×D4×D6111yescharacteristic
701Q8—1228no—
702Q8—1222no—
703Q8—1222no—
704Q8—2442no—
705D4—22no—
706D4—22no—
707D4—42no—
708D4—84no—
709D4—1228no—
710D4—1228no—
711D4—1228no—
712D4—4884no—
713D4—2448no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—84no—
725C2×C4—614no—
726C2×C4—612no—
727C2×C4—618no—
728C2×C4—614no—
729C2×C4—614no—
730C2×C4—612no—
731C2×C4—1222no—
732C2×C4—1224no—
733C2×C4—1222no—
734C2×C4—1222no—
735C2×C4—1222no—
736C2×C4—1222no—
737C2×C4—1222no—
738C2×C4—1222no—
739C2×C4—4884no—
740C2×C4—4884no—
741C2×C4—4884no—
742C2×C4—2448no—
743C2×C4—2442no—
744C2×C4—2442no—
745C2×C4—2442no—
746C2×C4—2442no—
747C2×C4C2×D4×D6112yes—
748C2×C4C2×D4×D6111yescharacteristic
749C2×C4#41×D6112yes—
750C2×C4#41×D6112yes—
751C2×C4C24×D6111yescharacteristic
752C8—22no—
753C8—22no—
754C8—1222no—
755C8—1222no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—44no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—84no—
764C22—614no—
765C22—1222no—
766C22—1222no—
767C22—1228no—
768C22—1222no—
769C22—1222no—
770C22—1222no—
771C22—2444no—
772C22#123×D6112yes—
773C22#1684056812yes—
774C22#1684057212yes—
775C22C22×D4×D6111yescharacteristic
776C4—22no—
777C4—42no—
778C4—42no—
779C4—42no—
780C4—614no—
781C4—1222no—
782C4—2442no—
783C4—2442no—
784C4—2442no—
785C4—2442no—
786C4#123×D6112yes—
787C4C2×#41×D6111yescharacteristic
788C4C2×#41×D6111yescharacteristic
789C2—42no—
790C2—82no—
791C2—1224no—
792C2—2442no—
793C2#2145580914yesdirect product factor
794C2C2×#123×D6111yescharacteristic
795C2C2×#1684056811yescharacteristic
796C2C2×#1684057211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#481C2
socleC23×C61C22×D4
prime radicalC2×#16840341C2
hypercenterC2×#481D61
hypocenterC61C2×#3099
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#481

Complements

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

NH ≅ G/Ntype
2. C2×#16840243C2semidirect
3. #21455809C2direct (N × H)
4. C2×#16840079C2semidirect
5. C2×#16840106C2semidirect
6. C2×#16840104C2semidirect
7. C2×#16840084C2semidirect
8. C2×#16840083C2semidirect
9. C2×#16840094C2semidirect
10. C2×#16840092C2semidirect
11. C2×#16839801C2semidirect
12. C2×#106×D61C2semidirect
13. C2×#16839760C2semidirect
14. C2×#16839755C2semidirect
15. C2×#16839727C2semidirect
16. C2×C61×#481C2semidirect
31. #16840243C22semidirect
42. #16840106C22semidirect
43. #16840104C22semidirect
44. #16840094C22semidirect
45. #16840092C22semidirect
46. #16840084C22semidirect
47. #16840083C22semidirect
48. #16840079C22semidirect
49. #16839801C22semidirect
56. #106×D61C22semidirect
57. #16839760C22semidirect
58. #16839755C22semidirect
65. #16839727C22semidirect
71. C61×#481C22semidirect
395. C2×#481D61semidirect
409. C2×C61#3099semidirect
449. #481C2×D61semidirect
475. C61C2×#3099semidirect
793. C2#21455809direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403412
C2×#168402432
#214558092
C2×#168400792
C2×#168401062
C2×#168401042
C2×#168400842
C2×#168400832
C2×#168400942
C2×#168400922
C2×#168398012
C2×#106×D612
C2×#168397602
C2×#168397552
C2×#168397272
C2×C61×#4812
C2×#309961