Finite Group Databasebeta

← C2×#21458199 #30558461

Subgroups — C2×#21458199 #30558461

Order 15616.

1930 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840456C211yesmaximal, characteristic
2C2×#16840451C211yesmaximal, characteristic, complemented
3#21458199C2116yesmaximal, direct product factor
4C2×#16840162C211yesmaximal, characteristic, complemented
5C2×#16840099C211yesmaximal, characteristic, complemented
6C2×#16840103C211yesmaximal, characteristic, complemented
7C2×#16840086C211yesmaximal, characteristic, complemented
8C2×#16840077C211yesmaximal, characteristic, complemented
9C2×#16840068C211yesmaximal, characteristic, complemented
10C2×#16840065C211yesmaximal, characteristic, complemented
11C2×#16839992C211yesmaximal, characteristic, complemented
12C2×#16839991C211yesmaximal, characteristic, complemented
13C2×#16839849C211yesmaximal, characteristic, complemented
14C2×C8×C22⋊D61C211yesmaximal, characteristic, complemented
15C2×#106×D61C211yesmaximal, characteristic, complemented
16C2×C61×#427C211yesmaximal, characteristic, complemented
17C22×#11758190C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19#16840456—24no—
20#16840456C2218yes—
21#16840451—24no—
22#16840451C2218yescomplemented
23C2×#14519771—21no—
24C2×#14519770—21no—
25C2×#14519769—21no—
26C2×#14519768C2211yescharacteristic
27C2×#14519768C2211yescharacteristic
28C2×#14519759—21no—
29C2×#14519759—21no—
30C2×#14519757C2211yescharacteristic
31C2×#14519756C2211yescharacteristic
32C2×#14519752C2211yescharacteristic
33C2×#14519751C2211yescharacteristic
34C2×#14519750—21no—
35C2×#14519742C2211yescharacteristic
36C2×C4×D244—21no—
37C2×#14519739C2211yescharacteristic
38C2×C4×C22⋊D61C2211yescharacteristic
39C2×#14519734—21no—
40C2×C4⋊C4×D61C2211yescharacteristic
41C2×C4⋊C4×D61C2211yescharacteristic
42#16840162C2218yescomplemented
43#16840103C2218yescomplemented
44#16840099C2218yescomplemented
45#16840086C2218yescomplemented
46#16840077C2218yescomplemented
47#16840068C2218yescomplemented
48#16840065C2218yescomplemented
49#16839992C2218yescomplemented
50#16839991C2218yescomplemented
51#16839849C2218yescomplemented
52C8×C22⋊D61C2218yescomplemented
53C2×#14519710C2211yescharacteristic
54C2×#14519710C2211yescharacteristic
55C2×#14519709C2211yescharacteristic
56C2×#14519708C2211yescharacteristic
57C2×#14519708C2211yescharacteristic
58#106×D61C2218yescomplemented
59C2×#14519706C2211yescharacteristic
60C2×#14519702C2211yescharacteristic
61C2×#14519700C2211yescharacteristic
62C2×#14519700C2211yescharacteristic
63C2×#14519699C2211yescharacteristic
64C2×#14519697C2211yescharacteristic
65C2×#14519697C2211yescharacteristic
66C2×C22⋊#92418C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C23×C8×C61C2211yescharacteristic
70C2×#117×C61C2211yescharacteristic
71C2×#117×C61C2211yescharacteristic
72C61×#427C2218yescomplemented
73C2×#107×C61C2211yescharacteristic
74C2×#107×C61C2211yescharacteristic
75C2×#106×C61C2211yescharacteristic
76C2×#106×C61C2211yescharacteristic
77C22×Dic122C2311yescharacteristic
78C22×D244—21no—
79C22×D244C2311yescharacteristic
80C22×C22⋊D61—21no—
81C22×C22⋊D61D411yescharacteristic
82C22×C4×D61—21no—
83C22×C4×D61—21no—
84C22×C4×D61—21no—
85C22×C4×D61C2311yescharacteristic
86C2×#11758190—24no—
87C2×#11758190C2314yes—
88C22×#92418C2311yescharacteristic
89C22×#92418C2311yescharacteristic
90C2×C8×D61—24no—
91C2×C8×D61C2314yes—
92#14519771—28no—
93#14519770—28no—
94#14519769—28no—
95#14519768—22no—
96#14519768—22no—
97#14519768C2314yes—
98#14519768C2314yes—
99#14519759—28no—
100#14519759—28no—
101#14519757—22no—
102#14519757C2314yes—
103#14519756—22no—
104#14519756C2314yes—
105#14519752—22no—
106#14519752C2314yes—
107#14519751—22no—
108#14519751C2314yes—
109#14519750—28no—
110#14519742—22no—
111#14519742C2314yes—
112C4×D244—28no—
113#14519739—22no—
114#14519739C2314yes—
115C4×C22⋊D61D414yes—
116C4×C22⋊D61C2314yes—
117#14519734—28no—
118C2×C4⋊Dic61—21no—
119C2×C4⋊Dic61—21no—
120C2×C4⋊Dic61—21no—
121C2×C4⋊Dic61C2311yescharacteristic
122C2×C4⋊Dic61C2311yescharacteristic
123C2×#11758196—21no—
124C2×#11758196—21no—
125C2×#11758196—21no—
126C2×#11758196—21no—
127C2×#11758196—21no—
128C2×#11758196—21no—
129C2×#11758196D411yescharacteristic
130C4⋊C4×D61—22no—
131C4⋊C4×D61—22no—
132C4⋊C4×D61C2314yes—
133C4⋊C4×D61C2314yes—
134C2×C22⋊Dic61—21no—
135C2×C22⋊Dic61D411yescharacteristic
136C2×#11758198—21no—
137C2×#11758198—21no—
138C2×#11758198—21no—
139C2×#11758198—21no—
140C2×#11758198D411yescharacteristic
141C2×C4×Dic61—21no—
142C2×C4×Dic61C2311yescharacteristic
143#14519710C2314yes—
144#14519710C2314yes—
145#14519709C2314yes—
146#14519708C2314yes—
147#14519708C2314yes—
148#14519706C2314yes—
149#14519702C2314yes—
150#14519700C2314yes—
151#14519700C2314yes—
152#14519699C2314yes—
153#14519697C2314yes—
154#14519697C2314yes—
155C22⋊#92418C2314yes—
156#14519689C2314yes—
157C8×Dic61C2314yes—
158C23×C4×C61C2311yescharacteristic
159C22×C8×C61—24no—
160C22×C8×C61C2311yescharacteristic
161C22×C8×C61C2314yes—
162C22×C8×C61C2311yescharacteristic
163#117×C61—22no—
164#117×C61—22no—
165#117×C61C2314yes—
166#117×C61C2314yes—
167C2×C4⋊C4×C61C2311yescharacteristic
168C2×C4⋊C4×C61C2311yescharacteristic
169C2×C4⋊C4×C61C2311yescharacteristic
170C2×C4⋊C4×C61C2311yescharacteristic
171C2×C22⋊C4×C61—21no—
172C2×C22⋊C4×C61—21no—
173C2×C42×C61—21no—
174C2×C42×C61—21no—
175#107×C61C2314yes—
176#107×C61C2314yes—
177#106×C61C2314yes—
178#106×C61C2314yes—
179C24×C61C2×D411yescharacteristic
180C23×D61—21no—
181C23×D61C2×D411yescharacteristic
182C22×C4×C61—22no—
183C22×C4×C61—22no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61C2×D411yescharacteristic
189C22×C4×C61C2×D412yes—
190C22×C4×C61C2412yes—
191C22×C4×C61C2411yescharacteristic
192C2×C22⋊D61—24no—
193C2×C22⋊D61—24no—
194C2×C22⋊D61—82no—
195C2×C22⋊D61C2×D414yes—
196C22×Dic61—21no—
197C22×Dic61—21no—
198C22×Dic61—21no—
199C22×Dic61C2×D411yescharacteristic
200C22×Dic61C2×D411yescharacteristic
201C22×Dic61C2×D411yescharacteristic
202C2×D244—22no—
203C2×D244—22no—
204C2×D244—24no—
205C2×D244—21no—
206C2×D244—44no—
207C2×D244C2412yes—
208C2×C4×D61—22no—
209C2×C4×D61—22no—
210C2×C4×D61—24no—
211C2×C4×D61—24no—
212C2×C4×D61—24no—
213C2×C4×D61—44no—
214C2×C4×D61—82no—
215C2×C4×D61—82no—
216C2×C4×D61C2×D412yes—
217C2×C4×D61C2412yes—
218C2×Dic122—22no—
219C2×Dic122—22no—
220C2×Dic122—21no—
221C2×Dic122C2412yes—
222C2×C8×C61—22no—
223C2×C8×C61—28no—
224C2×C8×C61#4114yes—
225C2×C8×C61C2412yes—
226C2×C8×C61C2412yes—
227C4⋊C4×C61—21no—
228C4⋊C4×C61—21no—
229C4⋊C4×C61—21no—
230C4⋊C4×C61—21no—
231C4⋊C4×C61C2412yes—
232C4⋊C4×C61C2412yes—
233C4⋊C4×C61C2412yes—
234C4⋊C4×C61C2412yes—
235C22⋊C4×C61—24no—
236C22⋊C4×C61—24no—
237C42×C61—24no—
238C42×C61—24no—
239C22⋊Dic61—24no—
240C22⋊Dic61C2×D414yes—
241#11758198—24no—
242#11758198—24no—
243#11758198—24no—
244#11758198—24no—
245#11758198C2×D414yes—
246C4⋊Dic61—21no—
247C4⋊Dic61—21no—
248C4⋊Dic61—24no—
249C4⋊Dic61—24no—
250C4⋊Dic61—24no—
251C4⋊Dic61C2412yes—
252C4⋊Dic61C2412yes—
253#11758196—24no—
254#11758196—24no—
255#11758196—24no—
256#11758196—24no—
257#11758196—24no—
258#11758196—24no—
259#11758196C2×D414yes—
260C4×Dic61—24no—
261C4×Dic61C2×D412yes—
262C4×Dic61C2412yes—
263C2×#92418—22no—
264C2×#92418—22no—
265C2×#92418C2412yes—
266C2×#92418C2412yes—
267#11758190—28no—
268C8×D61—28no—
269C23×C61—22no—
270C23×C61—22no—
271C23×C61—22no—
272C23×C61C22×D412yes—
273C23×C61C22×D411yescharacteristic
274C22×D61—22no—
275C22×D61—22no—
276C22×D61—22no—
277C22×D61—42no—
278C22×D61—42no—
279C22×D61—42no—
280C22×D61#13514yes—
281C22×D61C22×D412yes—
282C2×C4×C61—22no—
283C2×C4×C61—24no—
284C2×C4×C61—22no—
285C2×C4×C61—22no—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—22no—
290C2×C4×C61—42no—
291C2×C4×C61—42no—
292C2×C4×C61—42no—
293C2×C4×C61—42no—
294C2×C4×C61C22×D412yes—
295C2×C4×C61C22×D411yescharacteristic
296C2×C4×C61C2×#4112yes—
297C2×C4×C612−1+412yes—
298C2×C4×C61C2511yescharacteristic
299C22⋊D61—28no—
300C22⋊D61—84no—
301C2×Dic61—22no—
302C2×Dic61—22no—
303C2×Dic61—22no—
304C2×Dic61—22no—
305C2×Dic61—22no—
306C2×Dic61—22no—
307C2×Dic61—42no—
308C2×Dic61—42no—
309C2×Dic61—42no—
310C2×Dic61C22×D412yes—
311C2×Dic61C22×D412yes—
312C2×Dic61C22×D412yes—
313D244—22no—
314D244—22no—
315D244—48no—
316D244—42no—
317C4×D61—24no—
318C4×D61—22no—
319C4×D61—22no—
320C4×D61—48no—
321C4×D61—84no—
322C4×D61—84no—
323Dic122—22no—
324Dic122—22no—
325Dic122—42no—
326C8×C61—22no—
327C8×C61C2×#4114yes—
328#92418—22no—
329#92418—22no—
330C2×#3337—611nomaximal, Sylow
331C22×C61—22no—
332C22×C61—22no—
333C22×C61—22no—
334C22×C61—44no—
335C22×C61#54712yes—
336C22×C61C2×#13512yes—
337C22×C61#57712yes—
338C22×C61C23×D411yescharacteristic
339C2×D61—28no—
340C2×D61—22no—
341C2×D61—22no—
342C2×D61—42no—
343C2×D61—42no—
344C2×D61—42no—
345C2×D61—84no—
346C2×D61C2×#13514yes—
347C4×C61—22no—
348C4×C61—42no—
349C4×C61—42no—
350C4×C61—42no—
351C4×C61—42no—
352C4×C61#54712yes—
353C4×C61C22×#4111yescharacteristic
354C4×C61C2×2−1+411yescharacteristic
355Dic61—22no—
356Dic61—22no—
357Dic61—22no—
358Dic61—42no—
359Dic61—42no—
360Dic61—42no—
361C2×#553—611no—
362C2×#552—611no—
363#3337—6116no—
364C2×#499—611no—
365C2×#484—611no—
366C2×#485—611no—
367C2×#482—611no—
368C2×#480—611no—
369C2×#479—611no—
370C2×#478—611no—
371C2×#465—611no—
372C2×#465—611no—
373C2×C4×SD16—611no—
374C2×C8×D4—611no—
375C2×#427D6111yescharacteristic, complemented
376C22×#106—611no—
377C2×C61—42no—
378C2×C61#333714yescomplemented
379C2×C61C2×#54711yescharacteristic
380C2×C61C22×#13511yescharacteristic
381C2×C61C2×#57711yescharacteristic
382D61—24no—
383D61—82no—
384C22×SD16—611no—
385C23×C8—611no—
386C23×C8C2×D6111yescharacteristic
387#553—618no—
388#553—1224no—
389#552—618no—
390#552—1224no—
391C2×#126—1221no—
392C2×#126—1221no—
393C2×#125—611no—
394C2×#125—611no—
395C2×#125—1221no—
396C2×#123—1221no—
397C2×#123—1221no—
398C2×C22⋊Q8—611no—
399C2×C22⋊Q8—611no—
400C2×#121—611no—
401C2×#121—611no—
402C2×#121—1221no—
403C2×C4×Q8—611no—
404C2×C4×D4—611no—
405C2×C4×D4—611no—
406C2×C4×D4—1221no—
407C2×#117—1221no—
408C2×#117C2×D6111yescharacteristic
409C2×#117C2×D6111yescharacteristic
410C22×C4⋊C4—611no—
411C22×C4⋊C4—611no—
412#499—618no—
413#485—618no—
414#484—618no—
415#482—618no—
416#480—618no—
417#479—618no—
418#478—618no—
419#465—618no—
420#465—618no—
421C4×SD16—618no—
422C8×D4—618no—
423#427C2×D6118yescomplemented
424C2×#107—611no—
425C2×#107—611no—
426C2×#107C2×D6111yescharacteristic
427C2×#107C2×D6111yescharacteristic
428C2×#106—611no—
429C2×#106—611no—
430C2×#106—611no—
431C2×#106—618no—
432C2×#106C2×D6111yescharacteristic
433C2×#106C2×D6111yescharacteristic
434C2×C4⋊C8—611no—
435C2×#103—611no—
436C2×#103—611no—
437C2×#103—611no—
438C2×#102—611no—
439C2×#102—611no—
440C2×#102—611no—
441C2×C22⋊C8—611no—
442C2×C22⋊C8—611no—
443C2×C4×C8—611no—
444C61C2×#333711yescharacteristic, complemented, Sylow
445C22×Q8—611no—
446C22×D4—611no—
447C22×D4—611no—
448C22×D4—1221no—
449C22×D4—1221no—
450C23×C4—611no—
451C23×C4—1221no—
452C23×C4—1221no—
453C23×C4—1221no—
454C23×C4C22×D6111yescharacteristic
455C2×SD16—614no—
456C2×SD16—1224no—
457C22×C8—24no—
458C22×C8—611no—
459C22×C8—611no—
460C22×C8—614no—
461C22×C8—1224no—
462C22×C8C22×D6111yescharacteristic
463C22×C8C22×D6114yes—
464C22×C8C22×D6111yescharacteristic
465#126—1228no—
466#126—1228no—
467#125—614no—
468#125—614no—
469#125—1228no—
470#125—1222no—
471#125—1222no—
472#123—1228no—
473#123—1228no—
474C22⋊Q8—614no—
475C22⋊Q8—614no—
476C22⋊Q8—1222no—
477C22⋊Q8—1222no—
478#121—614no—
479#121—614no—
480#121—1228no—
481#121—1222no—
482#121—1222no—
483C4×Q8—614no—
484C4×Q8—1222no—
485C4×D4—614no—
486C4×D4—614no—
487C4×D4—614no—
488C4×D4—1228no—
489C4×D4—1222no—
490#117—22no—
491#117—22no—
492#117—1228no—
493#117C22×D6114yes—
494#117C22×D6114yes—
495C2×C4⋊C4—611no—
496C2×C4⋊C4—611no—
497C2×C4⋊C4—611no—
498C2×C4⋊C4—614no—
499C2×C4⋊C4—614no—
500C2×C4⋊C4—1222no—
501C2×C4⋊C4—1222no—
502C2×C4⋊C4—1221no—
503C2×C4⋊C4—1221no—
504C2×C4⋊C4—1221no—
505C2×C4⋊C4—1221no—
506C2×C4⋊C4—1221no—
507C2×C4⋊C4—1221no—
508C2×C4⋊C4—1221no—
509C2×C4⋊C4—1221no—
510C2×C4⋊C4—1221no—
511C2×C4⋊C4C22×D6111yescharacteristic
512C2×C4⋊C4C22×D6111yescharacteristic
513C2×C4⋊C4C22×D6111yescharacteristic
514C2×C4⋊C4C22×D6111yescharacteristic
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—611no—
518C2×C22⋊C4—611no—
519C2×C22⋊C4—1221no—
520C2×C22⋊C4—1221no—
521C2×C22⋊C4—1221no—
522C2×C22⋊C4—1221no—
523C2×C22⋊C4—1221no—
524C2×C42—21no—
525C2×C42—21no—
526C2×C42—611no—
527C2×C42—1221no—
528#107—614no—
529#107—614no—
530#107C22×D6114yes—
531#107C22×D6114yes—
532#106—614no—
533#106—614no—
534#106—614no—
535#106C22×D6114yes—
536#106C22×D6114yes—
537C4⋊C8—614no—
538#103—614no—
539#103—614no—
540#103—614no—
541#102—614no—
542#102—614no—
543#102—614no—
544C22⋊C8—614no—
545C22⋊C8—614no—
546C4×C8—614no—
547C24—611no—
548C24—1221no—
549C24D4×D6111yescharacteristic
550C2×Q8—612no—
551C2×Q8—1221no—
552C2×Q8—1222no—
553C2×Q8—1222no—
554C2×D4—614no—
555C2×D4—612no—
556C2×D4—1224no—
557C2×D4—1224no—
558C2×D4—1224no—
559C2×D4—1221no—
560C2×D4—1222no—
561C2×D4—1222no—
562C2×D4—4882no—
563C2×D4—2444no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—611no—
571C22×C4—611no—
572C22×C4—611no—
573C22×C4—612no—
574C22×C4—612no—
575C22×C4—1224no—
576C22×C4—1224no—
577C22×C4—1224no—
578C22×C4—1222no—
579C22×C4—1222no—
580C22×C4—1221no—
581C22×C4—1221no—
582C22×C4—1221no—
583C22×C4—4882no—
584C22×C4—4882no—
585C22×C4—2444no—
586C22×C4D4×D6112yes—
587C22×C4D4×D6111yescharacteristic
588C22×C4C23×D6112yes—
589C22×C4C23×D6111yescharacteristic
590SD16—1228no—
591C2×C8—22no—
592C2×C8—28no—
593C2×C8—612no—
594C2×C8—612no—
595C2×C8—1222no—
596C2×C8—1222no—
597C2×C8—1228no—
598C2×C8#1175822214yes—
599C2×C8C23×D6112yes—
600C2×C8C23×D6112yes—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—614no—
606C4⋊C4—612no—
607C4⋊C4—612no—
608C4⋊C4—1224no—
609C4⋊C4—1224no—
610C4⋊C4—1224no—
611C4⋊C4—1224no—
612C4⋊C4—1224no—
613C4⋊C4—1224no—
614C4⋊C4—1224no—
615C4⋊C4—1224no—
616C4⋊C4—1221no—
617C4⋊C4—1221no—
618C4⋊C4—1224no—
619C4⋊C4C23×D6112yes—
620C4⋊C4C23×D6112yes—
621C4⋊C4C23×D6112yes—
622C4⋊C4C23×D6112yes—
623C22⋊C4—24no—
624C22⋊C4—24no—
625C22⋊C4—614no—
626C22⋊C4—614no—
627C22⋊C4—1224no—
628C22⋊C4—1224no—
629C22⋊C4—1224no—
630C22⋊C4—1224no—
631C22⋊C4—1224no—
632C42—24no—
633C42—24no—
634C42—612no—
635C42—612no—
636C42—1224no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—614no—
641C23—612no—
642C23—1222no—
643C23—1222no—
644C23—1222no—
645C23—2442no—
646C23—2442no—
647C23—2442no—
648C23C2×D4×D6112yes—
649C23C2×D4×D6111yescharacteristic
650Q8—1222no—
651Q8—1222no—
652Q8—2442no—
653D4—1228no—
654D4—1222no—
655D4—1222no—
656D4—4884no—
657D4—2448no—
658D4—2442no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—24no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—612no—
672C2×C4—612no—
673C2×C4—612no—
674C2×C4—1222no—
675C2×C4—1222no—
676C2×C4—1222no—
677C2×C4—1222no—
678C2×C4—1222no—
679C2×C4—1224no—
680C2×C4—1222no—
681C2×C4—1222no—
682C2×C4—1222no—
683C2×C4—4884no—
684C2×C4—4884no—
685C2×C4—2448no—
686C2×C4—2442no—
687C2×C4—2442no—
688C2×C4—2442no—
689C2×C4C2×D4×D6112yes—
690C2×C4C2×D4×D6111yescharacteristic
691C2×C4C2×#1175822212yes—
692C2×C4#1451982512yes—
693C2×C4C24×D6111yescharacteristic
694C8—22no—
695C8—1222no—
696C8—1222no—
697C8C2×#1175822214yes—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—44no—
702C22—614no—
703C22—1228no—
704C22—1222no—
705C22—1222no—
706C22—4884no—
707C22—2442no—
708C22—2442no—
709C22—2442no—
710C22#1684041312yes—
711C22#135×D6112yes—
712C22#1684056912yes—
713C22C22×D4×D6111yescharacteristic
714C4—22no—
715C4—42no—
716C4—42no—
717C4—42no—
718C4—42no—
719C4—1222no—
720C4—1222no—
721C4—1222no—
722C4—2442no—
723C4—2442no—
724C4—2442no—
725C4#1684041312yes—
726C4C22×#1175822211yescharacteristic
727C4C2×#1451982511yescharacteristic
728C2—42no—
729C2—1224no—
730C2—4882no—
731C2#2145819914yesdirect product factor
732C2C2×#1684041311yescharacteristic
733C2C2×#135×D6111yescharacteristic
734C2C2×#1684056911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#427C2
socleC23×C61C22×D4
prime radicalC2×#16840456C2
hypercenterC2×#427D61
hypocenterC61C2×#3337
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#427

Complements

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

NH ≅ G/Ntype
2. C2×#16840451C2semidirect
3. #21458199C2direct (N × H)
4. C2×#16840162C2semidirect
5. C2×#16840099C2semidirect
6. C2×#16840103C2semidirect
7. C2×#16840086C2semidirect
8. C2×#16840077C2semidirect
9. C2×#16840068C2semidirect
10. C2×#16840065C2semidirect
11. C2×#16839992C2semidirect
12. C2×#16839991C2semidirect
13. C2×#16839849C2semidirect
14. C2×C8×C22⋊D61C2semidirect
15. C2×#106×D61C2semidirect
16. C2×C61×#427C2semidirect
22. #16840451C22semidirect
42. #16840162C22semidirect
43. #16840103C22semidirect
44. #16840099C22semidirect
45. #16840086C22semidirect
46. #16840077C22semidirect
47. #16840068C22semidirect
48. #16840065C22semidirect
49. #16839992C22semidirect
50. #16839991C22semidirect
51. #16839849C22semidirect
52. C8×C22⋊D61C22semidirect
58. #106×D61C22semidirect
72. C61×#427C22semidirect
375. C2×#427D61semidirect
378. C2×C61#3337semidirect
423. #427C2×D61semidirect
444. C61C2×#3337semidirect
731. C2#21458199direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404562
C2×#168404512
#214581992
C2×#168401622
C2×#168400992
C2×#168401032
C2×#168400862
C2×#168400772
C2×#168400682
C2×#168400652
C2×#168399922
C2×#168399912
C2×#168398492
C2×C8×C22⋊D612
C2×#106×D612
C2×C61×#4272
C2×#333761