Finite Group Databasebeta

← C2×#21455605 #30547512

Subgroups — C2×#21455605 #30547512

Order 15616.

2162 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840315C211yesmaximal, characteristic, complemented
2C2×#16840230C211yesmaximal, characteristic
3#21455605C2116yesmaximal, direct product factor
4C2×#16840072C211yesmaximal, characteristic, complemented
5C2×#16840068C211yesmaximal, characteristic, complemented
6C2×#16840056C211yesmaximal, characteristic, complemented
7C2×#16840046C211yesmaximal, characteristic, complemented
8C2×#16840065C211yesmaximal, characteristic, complemented
9C2×#16840061C211yesmaximal, characteristic, complemented
10C2×#16840051C211yesmaximal, characteristic, complemented
11C2×#16840041C211yesmaximal, characteristic, complemented
12C2×#16839798C211yesmaximal, characteristic, complemented
13C22×#14519706C211yesmaximal, characteristic, complemented
14C2×#16839759C211yesmaximal, characteristic
15C2×#16839756C211yesmaximal, characteristic
16C2×C61×#427C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic
18C23×#92418C2211yescharacteristic
19#16840315—24no—
20#16840315C2218yescomplemented
21C2×#14519776C2211yescharacteristic
22C2×#14519776C2211yescharacteristic
23C2×#14519768C2211yescharacteristic
24C2×#14519768C2211yescharacteristic
25C2×#14519754—21no—
26C2×#14519754—21no—
27#16840230—24no—
28#16840230C2218yes—
29C2×C4×Dic122—21no—
30C2×C4×Dic122—21no—
31C2×#14519742C2211yescharacteristic
32C2×#14519742C2211yescharacteristic
33C2×#14519739C2211yescharacteristic
34C2×#14519739C2211yescharacteristic
35C2×#14519737—21no—
36C2×#14519737—21no—
37C2×#14519736C2211yescharacteristic
38C2×#14519734—21no—
39C22×C4×Dic61C2211yescharacteristic
40C2×C42×D61—21no—
41#16840072C2218yescomplemented
42#16840068C2218yescomplemented
43#16840065C2218yescomplemented
44#16840061C2218yescomplemented
45#16840056C2218yescomplemented
46#16840051C2218yescomplemented
47#16840046C2218yescomplemented
48#16840041C2218yescomplemented
49#16839798C2218yescomplemented
50C2×#14519710C2211yescharacteristic
51C2×#14519710C2211yescharacteristic
52C2×#14519708C2211yescharacteristic
53C2×#14519708C2211yescharacteristic
54C2×#14519706C2211yescharacteristic
55C2×#14519706C2211yescharacteristic
56C2×#14519706C2211yescharacteristic
57C2×#14519706C2211yescharacteristic
58C2×#14519706C2218yescomplemented
59#16839759C2218yes—
60#16839756C2218yes—
61C2×#14519702C2211yescharacteristic
62C2×#14519702C2211yescharacteristic
63C2×#14519700C2211yescharacteristic
64C2×#14519700C2211yescharacteristic
65C2×#14519699C2211yescharacteristic
66C2×#14519699C2211yescharacteristic
67C2×#14519697C2211yescharacteristic
68C2×#14519697C2211yescharacteristic
69C23×C8×C61C2211yescharacteristic
70C2×#117×C61C2211yescharacteristic
71C2×#117×C61C2211yescharacteristic
72C61×#427C2218yescomplemented
73C2×#107×C61C2211yescharacteristic
74C2×#107×C61C2211yescharacteristic
75C2×#106×C61C2211yescharacteristic
76C2×#106×C61C2211yescharacteristic
77C2×#11758222—22no—
78C2×#11758222—24no—
79C2×#11758222Q818yescomplemented
80C2×#11758222C2314yes—
81C22×Dic122—21no—
82C22×Dic122—21no—
83C22×Dic122C2311yescharacteristic
84C22×D244C2311yescharacteristic
85C22×C22⋊D61—21no—
86C23×Dic61D411yescharacteristic
87C23×Dic61D411yescharacteristic
88C22×C4×D61—21no—
89C22×C4×D61—21no—
90C22×C4×D61—21no—
91C22×#92418—24no—
92C22×#92418C2311yescharacteristic
93C22×#92418C2311yescharacteristic
94C22×#92418C2314yes—
95#14519776—22no—
96#14519776—22no—
97#14519776C2314yes—
98#14519776C2314yes—
99#14519768—22no—
100#14519768—22no—
101#14519768C2314yes—
102#14519768C2314yes—
103#14519754—28no—
104#14519754—28no—
105C4×Dic122—28no—
106C4×Dic122—28no—
107#14519742—22no—
108#14519742—22no—
109#14519742C2314yes—
110#14519742C2314yes—
111#14519739—22no—
112#14519739—22no—
113#14519739C2314yes—
114#14519739C2314yes—
115#14519737—28no—
116#14519737—28no—
117#14519736—22no—
118#14519736C2314yes—
119#14519734—28no—
120C2×C4⋊Dic61—21no—
121C2×C4⋊Dic61—21no—
122C2×C4⋊Dic61C2311yescharacteristic
123C2×C4⋊Dic61C2311yescharacteristic
124C2×#11758196—21no—
125C2×#11758196—21no—
126C2×#11758196—21no—
127C2×#11758196—21no—
128C2×#11758196—21no—
129C2×#11758196—21no—
130C2×C22⋊Dic61—21no—
131C2×#11758198—21no—
132C2×#11758198—21no—
133C2×C4×Dic61—21no—
134C2×C4×Dic61—21no—
135C2×C4×Dic61—21no—
136C2×C4×Dic61D411yescharacteristic
137C2×C4×Dic61D411yescharacteristic
138C2×C4×Dic61D414yes—
139C2×C4×Dic61C2311yescharacteristic
140C2×C4×Dic61C2311yescharacteristic
141C2×C4×Dic61C2314yes—
142C42×D61—28no—
143#14519710C2314yes—
144#14519710C2314yes—
145#14519708C2314yes—
146#14519708C2314yes—
147#14519706C2314yes—
148#14519706C2314yes—
149#14519706C2314yes—
150#14519706C2314yes—
151#14519702C2314yes—
152#14519702C2314yes—
153#14519700C2314yes—
154#14519700C2314yes—
155#14519699C2314yes—
156#14519699C2314yes—
157#14519697C2314yes—
158#14519697C2314yes—
159C23×C4×C61C2311yescharacteristic
160C22×C8×C61—24no—
161C22×C8×C61C2311yescharacteristic
162C22×C8×C61C2311yescharacteristic
163C22×C8×C61C2314yes—
164#117×C61—22no—
165#117×C61—22no—
166#117×C61C2314yes—
167#117×C61C2314yes—
168C2×C4⋊C4×C61C2311yescharacteristic
169C2×C4⋊C4×C61C2311yescharacteristic
170C2×C4⋊C4×C61C2311yescharacteristic
171C2×C4⋊C4×C61C2311yescharacteristic
172C2×C22⋊C4×C61—21no—
173C2×C22⋊C4×C61—21no—
174C2×C42×C61—21no—
175C2×C42×C61—21no—
176#107×C61C2314yes—
177#107×C61C2314yes—
178#106×C61C2314yes—
179#106×C61C2314yes—
180C24×C61C2×D411yescharacteristic
181C23×D61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61C2×D412yes—
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61C2×Q814yes—
189C22×C4×C61#4114yes—
190C22×C4×C61C2411yescharacteristic
191C22×C4×C61C2412yes—
192C2×C22⋊D61—28no—
193C2×C22⋊D61—24no—
194C22×Dic61—21no—
195C22×Dic61—24no—
196C22×Dic61—21no—
197C22×Dic61—21no—
198C22×Dic61—42no—
199C22×Dic61C2×D411yescharacteristic
200C22×Dic61C2×D411yescharacteristic
201C22×Dic61C2×D411yescharacteristic
202C22×Dic61C2×D414yes—
203C22×Dic61C2×D414yes—
204C22×Dic61C2×D411yescharacteristic
205#11758222—216no—
206#11758222—28no—
207#11758222C2×Q8116yescomplemented
208C2×D244—21no—
209C2×D244—22no—
210C2×D244C2×Q814yes—
211C2×D244C2412yes—
212C2×C4×D61—28no—
213C2×C4×D61—24no—
214C2×C4×D61—24no—
215C2×C4×D61—24no—
216C2×C4×D61—44no—
217C2×C4×D61—44no—
218C2×Dic122—21no—
219C2×Dic122—22no—
220C2×Dic122—24no—
221C2×Dic122—24no—
222C2×Dic122—44no—
223C2×Dic122—44no—
224C2×Dic122C2×Q814yes—
225C2×Dic122C2412yes—
226C2×C8×C61—22no—
227C2×C8×C61—22no—
228C2×C8×C61—28no—
229C2×C8×C61C2412yes—
230C2×C8×C61C2412yes—
231C4⋊C4×C61—21no—
232C4⋊C4×C61—21no—
233C4⋊C4×C61—21no—
234C4⋊C4×C61—21no—
235C4⋊C4×C61C2412yes—
236C4⋊C4×C61C2412yes—
237C4⋊C4×C61C2412yes—
238C4⋊C4×C61C2412yes—
239C22⋊C4×C61—24no—
240C22⋊C4×C61—24no—
241C42×C61—24no—
242C42×C61—24no—
243C22⋊Dic61—24no—
244#11758198—24no—
245#11758198—24no—
246C4⋊Dic61—21no—
247C4⋊Dic61—21no—
248C4⋊Dic61—24no—
249C4⋊Dic61—24no—
250C4⋊Dic61C2412yes—
251C4⋊Dic61C2412yes—
252#11758196—24no—
253#11758196—24no—
254#11758196—24no—
255#11758196—24no—
256#11758196—24no—
257#11758196—24no—
258C4×Dic61—24no—
259C4×Dic61—24no—
260C4×Dic61—24no—
261C4×Dic61C2×D414yes—
262C4×Dic61C2×D414yes—
263C4×Dic61C2×D412yes—
264C4×Dic61C2×D412yes—
265C4×Dic61C2412yes—
266C4×Dic61C2412yes—
267C2×#92418—22no—
268C2×#92418—22no—
269C2×#92418—28no—
270C2×#92418C2412yes—
271C2×#92418C2412yes—
272C23×C61—22no—
273C23×C61—22no—
274C23×C61C22⋊Q814yes—
275C23×C61C22×D412yes—
276C23×C61C22×D411yescharacteristic
277C22×D61—24no—
278C22×D61—22no—
279C22×D61—42no—
280C22×D61—42no—
281C2×C4×C61—22no—
282C2×C4×C61—22no—
283C2×C4×C61—22no—
284C2×C4×C61—22no—
285C2×C4×C61—42no—
286C2×C4×C61—42no—
287C2×C4×C61—42no—
288C2×C4×C61—42no—
289C2×C4×C61C22⋊Q814yes—
290C2×C4×C61C22⋊Q818yes—
291C2×C4×C61C22×D412yes—
292C2×C4×C61C22×D411yescharacteristic
293C2×C4×C61C22×Q812yes—
294C2×C4×C61C22×Q814yes—
295C2×C4×C61C2×#4112yes—
296C2×C4×C61C2×#4114yes—
297C2×C4×C61C2511yescharacteristic
298C22⋊D61—216no—
299C2×Dic61—24no—
300C2×Dic61—22no—
301C2×Dic61—22no—
302C2×Dic61—22no—
303C2×Dic61—22no—
304C2×Dic61—28no—
305C2×Dic61—22no—
306C2×Dic61—22no—
307C2×Dic61—44no—
308C2×Dic61—42no—
309C2×Dic61—42no—
310C2×Dic61#13514yes—
311C2×Dic61C22×D412yes—
312C2×Dic61C22×D412yes—
313C2×Dic61C22×D412yes—
314C2×Dic61C22×D412yes—
315D244—24no—
316D244—22no—
317D244C22×Q814yes—
318C4×D61—216no—
319C4×D61—48no—
320C4×D61—48no—
321Dic122—24no—
322Dic122—22no—
323Dic122—48no—
324Dic122—48no—
325Dic122C22×Q814yes—
326C8×C61—22no—
327C8×C61—22no—
328#92418—22no—
329#92418—22no—
330C2×#3076—611nomaximal, Sylow
331C22×C61—28no—
332C22×C61—22no—
333C22×C61—22no—
334C22×C61C2×C22⋊Q814yes—
335C22×C61C2×C22⋊Q812yes—
336C22×C61C2×#13512yes—
337C22×C61#57512yes—
338C22×C61C23×D411yescharacteristic
339C2×D61—24no—
340C2×D61—48no—
341C2×D61—42no—
342C2×D61—42no—
343C4×C61—42no—
344C4×C61—42no—
345C4×C61—42no—
346C4×C61—42no—
347C4×C61C2×C22⋊Q812yes—
348C4×C61C2×C22⋊Q814yes—
349C4×C61C23×Q811yescharacteristic
350C4×C61C22×#4111yescharacteristic
351Dic61—24no—
352Dic61—22no—
353Dic61—22no—
354Dic61—22no—
355Dic61—42no—
356Dic61—42no—
357Dic61C2×#13514yes—
358C2×#533—611no—
359C2×C4×#41—611no—
360#3076—6116no—
361C2×#479—611no—
362C2×#479—611no—
363C2×#477—611no—
364C2×#475—611no—
365C2×#478—611no—
366C2×#478—611no—
367C2×#476—611no—
368C2×#474—611no—
369C2×#427—611no—
370C2×#427D6111yescharacteristic, complemented
371C22×C4⋊C8—611no—
372C2×#416—611no—
373C2×#416—611no—
374C2×C61—24no—
375C2×C61#307614yescomplemented
376C2×C61C22×C22⋊Q811yescharacteristic
377C2×C61C22×#13511yescharacteristic
378C2×C61C2×#57511yescharacteristic
379D61—44no—
380C22×#41—611no—
381C23×C8—611no—
382C23×C8C2×D6111yescharacteristic
383#533—618no—
384#533—1224no—
385C2×C4⋊Q8—611no—
386C2×C4⋊Q8—611no—
387C2×#125—611no—
388C2×#125—611no—
389C2×C22⋊Q8—1221no—
390C2×C22⋊Q8—1221no—
391C4×#41—618no—
392C4×#41—1224no—
393C2×C4×Q8—611no—
394C2×C4×Q8—611no—
395C2×C4×Q8—1221no—
396C2×C4×Q8—1221no—
397C2×C4×D4—611no—
398C2×C4×D4—611no—
399C2×C4×D4—1221no—
400C2×C4×D4—1221no—
401C2×#117—611no—
402C2×#117—1221no—
403C2×#117C2×D6111yescharacteristic
404C2×#117C2×D6111yescharacteristic
405C22×C42—611no—
406C22×C42—1221no—
407#479—618no—
408#479—618no—
409#478—618no—
410#478—618no—
411#477—618no—
412#476—618no—
413#475—618no—
414#474—618no—
415#427—618no—
416#427C2×D6118yescomplemented
417C2×#107—611no—
418C2×#107—611no—
419C2×#107C2×D6111yescharacteristic
420C2×#107C2×D6111yescharacteristic
421C2×#106—611no—
422C2×#106—611no—
423C2×#106C2×D6111yescharacteristic
424C2×#106C2×D6111yescharacteristic
425C2×C4⋊C8—611no—
426C2×C4⋊C8—611no—
427C2×C4⋊C8—611no—
428C2×C4⋊C8—611no—
429C2×C4⋊C8—618no—
430#416—618no—
431#416—618no—
432C2×#103—611no—
433C2×#103—611no—
434C2×#103—611no—
435C2×#103—611no—
436C2×#102—611no—
437C2×#102—611no—
438C2×#102—611no—
439C2×#102—611no—
440C61C2×#307611yescharacteristic, complemented, Sylow
441C2×#41—618no—
442C2×#41—614no—
443C2×#41—1224no—
444C2×#41—1222no—
445C22×Q8—611no—
446C22×Q8—1221no—
447C22×Q8—1221no—
448C22×D4—611no—
449C22×D4—1221no—
450C23×C4—611no—
451C23×C4—611no—
452C23×C4—1221no—
453C23×C4—1221no—
454C23×C4—1221no—
455C23×C4C22×D6111yescharacteristic
456C22×C8—24no—
457C22×C8—611no—
458C22×C8—611no—
459C22×C8—614no—
460C22×C8—1224no—
461C22×C8C22×D6111yescharacteristic
462C22×C8C22×D6111yescharacteristic
463C22×C8C22×D6114yes—
464C4⋊Q8—614no—
465C4⋊Q8—614no—
466C4⋊Q8—1222no—
467C4⋊Q8—1222no—
468#125—614no—
469#125—614no—
470#125—1222no—
471#125—1222no—
472C22⋊Q8—1228no—
473C22⋊Q8—1228no—
474C4×Q8—614no—
475C4×Q8—614no—
476C4×Q8—1228no—
477C4×Q8—1228no—
478C4×Q8—1222no—
479C4×Q8—1222no—
480C4×D4—614no—
481C4×D4—614no—
482C4×D4—1222no—
483C4×D4—1222no—
484C4×D4—1228no—
485C4×D4—1228no—
486#117—22no—
487#117—22no—
488#117—614no—
489#117—1228no—
490#117—1222no—
491#117C22×D6114yes—
492#117C22×D6114yes—
493C2×C4⋊C4—611no—
494C2×C4⋊C4—611no—
495C2×C4⋊C4—1221no—
496C2×C4⋊C4—1221no—
497C2×C4⋊C4—1221no—
498C2×C4⋊C4—1221no—
499C2×C4⋊C4—1221no—
500C2×C4⋊C4—1221no—
501C2×C4⋊C4—1221no—
502C2×C4⋊C4—1221no—
503C2×C4⋊C4C22×D6111yescharacteristic
504C2×C4⋊C4C22×D6111yescharacteristic
505C2×C4⋊C4C22×D6111yescharacteristic
506C2×C4⋊C4C22×D6111yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—1221no—
510C2×C22⋊C4—1221no—
511C2×C22⋊C4—1221no—
512C2×C42—21no—
513C2×C42—21no—
514C2×C42—614no—
515C2×C42—611no—
516C2×C42—611no—
517C2×C42—611no—
518C2×C42—611no—
519C2×C42—614no—
520C2×C42—1228no—
521C2×C42—1221no—
522C2×C42—1221no—
523C2×C42—1221no—
524#107—614no—
525#107—614no—
526#107C22×D6114yes—
527#107C22×D6114yes—
528#106—614no—
529#106—614no—
530#106C22×D6114yes—
531#106C22×D6114yes—
532C4⋊C8—614no—
533C4⋊C8—614no—
534C4⋊C8—614no—
535C4⋊C8—614no—
536#103—614no—
537#103—614no—
538#103—614no—
539#103—614no—
540#102—614no—
541#102—614no—
542#102—614no—
543#102—614no—
544C24—1221no—
545C24D4×D6111yescharacteristic
546#41—6116no—
547#41—1228no—
548#41—12216no—
549C2×Q8—614no—
550C2×Q8—612no—
551C2×Q8—1224no—
552C2×Q8—1224no—
553C2×Q8—1221no—
554C2×Q8—1222no—
555C2×Q8—2444no—
556C2×Q8—2444no—
557C2×D4—614no—
558C2×D4—612no—
559C2×D4—1224no—
560C2×D4—1228no—
561C2×D4—1221no—
562C2×D4—1222no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—611no—
568C22×C4—611no—
569C22×C4—611no—
570C22×C4—611no—
571C22×C4—614no—
572C22×C4—614no—
573C22×C4—1224no—
574C22×C4—1224no—
575C22×C4—1224no—
576C22×C4—1221no—
577C22×C4—1224no—
578C22×C4—1228no—
579C22×C4—1221no—
580C22×C4—1221no—
581C22×C4—2444no—
582C22×C4—2444no—
583C22×C4—2442no—
584C22×C4#1175822214yes—
585C22×C4D4×D6112yes—
586C22×C4D4×D6111yescharacteristic
587C22×C4Q8×D6114yes—
588C22×C4C23×D6111yescharacteristic
589C22×C4C23×D6112yes—
590C2×C8—22no—
591C2×C8—22no—
592C2×C8—28no—
593C2×C8—612no—
594C2×C8—612no—
595C2×C8—1222no—
596C2×C8—1222no—
597C2×C8—1228no—
598C2×C8C23×D6112yes—
599C2×C8C23×D6112yes—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—612no—
605C4⋊C4—612no—
606C4⋊C4—1224no—
607C4⋊C4—1224no—
608C4⋊C4—1224no—
609C4⋊C4—1224no—
610C4⋊C4—1224no—
611C4⋊C4—1224no—
612C4⋊C4—1224no—
613C4⋊C4—1224no—
614C4⋊C4—1221no—
615C4⋊C4—1221no—
616C4⋊C4C23×D6112yes—
617C4⋊C4C23×D6112yes—
618C4⋊C4C23×D6112yes—
619C4⋊C4C23×D6112yes—
620C22⋊C4—24no—
621C22⋊C4—24no—
622C22⋊C4—1224no—
623C22⋊C4—1224no—
624C22⋊C4—1224no—
625C42—24no—
626C42—24no—
627C42—614no—
628C42—614no—
629C42—612no—
630C42—612no—
631C42—612no—
632C42—612no—
633C42—1224no—
634C42—1224no—
635C42—1224no—
636C23—22no—
637C23—22no—
638C23—1224no—
639C23—1222no—
640C23—2442no—
641C23—2442no—
642C23#1451975514yes—
643C23C2×D4×D6112yes—
644C23C2×D4×D6111yescharacteristic
645Q8—614no—
646Q8—1224no—
647Q8—1222no—
648Q8—2448no—
649Q8—2448no—
650D4—614no—
651D4—12216no—
652D4—1224no—
653D4—1222no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—614no—
663C2×C4—612no—
664C2×C4—612no—
665C2×C4—612no—
666C2×C4—612no—
667C2×C4—1228no—
668C2×C4—1224no—
669C2×C4—1222no—
670C2×C4—1222no—
671C2×C4—1222no—
672C2×C4—1222no—
673C2×C4—12216no—
674C2×C4—1222no—
675C2×C4—1222no—
676C2×C4—2448no—
677C2×C4—2448no—
678C2×C4—2444no—
679C2×C4—2442no—
680C2×C4—2442no—
681C2×C4#1451975514yes—
682C2×C4#1451975518yes—
683C2×C4C2×D4×D6112yes—
684C2×C4C2×D4×D6111yescharacteristic
685C2×C4C2×Q8×D6112yes—
686C2×C4C2×Q8×D6114yes—
687C2×C4C2×#1175822212yes—
688C2×C4C2×#1175822214yes—
689C2×C4C24×D6111yescharacteristic
690C8—22no—
691C8—22no—
692C8—1222no—
693C8—1222no—
694C22—22no—
695C22—22no—
696C22—28no—
697C22—1224no—
698C22—2442no—
699C22—2442no—
700C22—2448no—
701C22C2×#1451975514yes—
702C22C2×#1451975512yes—
703C22#135×D6112yes—
704C22#1684055912yes—
705C22C22×D4×D6111yescharacteristic
706C4—42no—
707C4—42no—
708C4—42no—
709C4—42no—
710C4—614no—
711C4—1222no—
712C4—1222no—
713C4—1222no—
714C4—1224no—
715C4—2442no—
716C4—2442no—
717C4C2×#1451975514yes—
718C4C2×#1451975512yes—
719C4C22×Q8×D6111yescharacteristic
720C4C22×#1175822211yescharacteristic
721C2—24no—
722C2—2444no—
723C2#2145560514yesdirect product factor
724C2C22×#1451975511yescharacteristic
725C2C2×#135×D6111yescharacteristic
726C2C2×#1684055911yescharacteristic
subgroupG/H
centerC22×C4D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#427C2
socleC23×C61C22×D4
prime radicalC22×#11758222C22
hypercenterC2×#427D61
hypocenterC61C2×#3076
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#427

Complements

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

NH ≅ G/Ntype
1. C2×#16840315C2semidirect
3. #21455605C2direct (N × H)
4. C2×#16840072C2semidirect
5. C2×#16840068C2semidirect
6. C2×#16840056C2semidirect
7. C2×#16840046C2semidirect
8. C2×#16840065C2semidirect
9. C2×#16840061C2semidirect
10. C2×#16840051C2semidirect
11. C2×#16840041C2semidirect
12. C2×#16839798C2semidirect
13. C22×#14519706C2semidirect
16. C2×C61×#427C2semidirect
20. #16840315C22semidirect
41. #16840072C22semidirect
42. #16840068C22semidirect
43. #16840065C22semidirect
44. #16840061C22semidirect
45. #16840056C22semidirect
46. #16840051C22semidirect
47. #16840046C22semidirect
48. #16840041C22semidirect
49. #16839798C22semidirect
58. C2×#14519706C22semidirect
72. C61×#427C22semidirect
79. C2×#11758222Q8semidirect
207. #11758222C2×Q8semidirect
370. C2×#427D61semidirect
375. C2×C61#3076semidirect
416. #427C2×D61semidirect
440. C61C2×#3076semidirect
723. C2#21455605direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403152
C2×#168402302
#214556052
C2×#168400722
C2×#168400682
C2×#168400562
C2×#168400462
C2×#168400652
C2×#168400612
C2×#168400512
C2×#168400412
C2×#168397982
C22×#145197062
C2×#168397592
C2×#168397562
C2×C61×#4272
C2×#307661