Finite Group Databasebeta

← C2×#21455682 #30547607

Subgroups — C2×#21455682 #30547607

Order 15616.

2094 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×#16840392C211yesmaximal, characteristic, complemented
2C2×#16840241C211yesmaximal, characteristic
3#21455682C2116yesmaximal, direct product factor
4C2×#16840068C211yesmaximal, characteristic, complemented
5C2×#16840066C211yesmaximal, characteristic, complemented
6C2×#16840048C211yesmaximal, characteristic, complemented
7C2×#16840046C211yesmaximal, characteristic, complemented
8C2×#16840064C211yesmaximal, characteristic, complemented
9C2×#16840052C211yesmaximal, characteristic, complemented
10C2×#16840050C211yesmaximal, characteristic, complemented
11C2×#16839803C211yesmaximal, characteristic, complemented
12C2×#106×D61C211yesmaximal, characteristic, complemented
13C2×#16839787C211yesmaximal, characteristic, complemented
14C2×#16839760C211yesmaximal, characteristic
15C2×#16839755C211yesmaximal, characteristic
16C2×C61×#478C211yesmaximal, characteristic, complemented
17C22×#11758224C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19C22×C8×D61C2211yescharacteristic
20#16840392—24no—
21#16840392C2218yescomplemented
22C2×#14519777C2211yescharacteristic
23C2×#14519776—21no—
24C2×#14519776C2211yescharacteristic
25C2×#14519768C2211yescharacteristic
26C2×#14519767—21no—
27C2×#14519757—21no—
28C2×#14519755—21no—
29#16840241—24no—
30#16840241C2218yes—
31C2×C4×Dic122C2211yescharacteristic
32C2×#14519742C2211yescharacteristic
33C2×D4×Dic61C2211yescharacteristic
34C2×C4×C22⋊D61—21no—
35C2×#14519737—21no—
36C2×#14519735C2211yescharacteristic
37C2×#14519734C2211yescharacteristic
38C2×#14519733—21no—
39C22×#11758196—21no—
40C2×C4⋊C4×D61C2211yescharacteristic
41C2×C4⋊C4×D61C2211yescharacteristic
42#16840068C2218yescomplemented
43#16840066C2218yescomplemented
44#16840064C2218yescomplemented
45#16840052C2218yescomplemented
46#16840050C2218yescomplemented
47#16840048C2218yescomplemented
48#16840046C2218yescomplemented
49#16839803C2218yescomplemented
50C2×#14519710C2211yescharacteristic
51C2×#14519709C2211yescharacteristic
52C2×#14519709C2211yescharacteristic
53C2×#14519708C2211yescharacteristic
54C2×#14519708C2211yescharacteristic
55C2×#14519708C2211yescharacteristic
56#106×D61C2218yescomplemented
57#16839787C2218yescomplemented
58C2×C4⋊#92418C2211yescharacteristic
59C2×#14519706C2211yescharacteristic
60C2×#14519706C2211yescharacteristic
61#16839760C2218yes—
62#16839755C2218yes—
63C2×#14519702C2211yescharacteristic
64C2×#14519702C2211yescharacteristic
65C2×#14519700C2211yescharacteristic
66C2×#14519700C2211yescharacteristic
67C2×#14519698C2211yescharacteristic
68C2×#14519698C2211yescharacteristic
69C2×#125×C61C2211yescharacteristic
70C2×C4×D4×C61C2211yescharacteristic
71C61×#478C2218yescomplemented
72C2×#107×C61C2211yescharacteristic
73C2×#106×C61C2211yescharacteristic
74C2×C4⋊C8×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×#102×C61C2211yescharacteristic
77C2×#11758224—22no—
78C2×#11758224—24no—
79C2×#11758224Q818yescomplemented
80C2×#11758224C2314yes—
81C22×Dic122—21no—
82C22×Dic122—21no—
83C22×Dic122C2311yescharacteristic
84C22×C22⋊D61—21no—
85C23×Dic61—21no—
86C23×Dic61—21no—
87C22×C4×D61—21no—
88C22×C4×D61—21no—
89C22×C4×D61C2311yescharacteristic
90C2×#11758189—24no—
91C2×#11758189C2314yes—
92C22×#92418C2311yescharacteristic
93C22×#92418C2311yescharacteristic
94C2×C8×D61—24no—
95C2×C8×D61C2314yes—
96#14519777—22no—
97#14519777C2314yes—
98#14519776—28no—
99#14519776—22no—
100#14519776C2314yes—
101#14519768—22no—
102#14519768C2314yes—
103#14519767—28no—
104#14519757—28no—
105#14519755—28no—
106C4×Dic122—22no—
107C4×Dic122C2314yes—
108#14519742—22no—
109#14519742C2314yes—
110D4×Dic61—22no—
111D4×Dic61C2314yes—
112C4×C22⋊D61—28no—
113#14519737—28no—
114#14519735—22no—
115#14519735C2314yes—
116#14519734D414yes—
117#14519734C2314yes—
118#14519733—28no—
119C2×C4⋊Dic61—21no—
120C2×C4⋊Dic61—21no—
121C2×C4⋊Dic61C2311yescharacteristic
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×#11758196—28no—
131C2×#11758196D411yescharacteristic
132C2×#11758196D411yescharacteristic
133C4⋊C4×D61—22no—
134C4⋊C4×D61—22no—
135C4⋊C4×D61C2314yes—
136C4⋊C4×D61C2314yes—
137C2×C22⋊Dic61—21no—
138C2×#11758198—21no—
139C2×#11758198D411yescharacteristic
140C2×#11758198D411yescharacteristic
141C2×C4×Dic61—21no—
142C2×C4×Dic61—21no—
143C2×C4×Dic61—21no—
144C2×C4×Dic61C2311yescharacteristic
145#14519710C2314yes—
146#14519709C2314yes—
147#14519709C2314yes—
148#14519708C2314yes—
149#14519708C2314yes—
150#14519708C2314yes—
151C4⋊#92418C2314yes—
152#14519706C2314yes—
153#14519706C2314yes—
154#14519702C2314yes—
155#14519702C2314yes—
156#14519700C2314yes—
157#14519700C2314yes—
158#14519698C2314yes—
159#14519698C2314yes—
160C22×D4×C61C2311yescharacteristic
161C23×C4×C61—21no—
162C22×C8×C61C2311yescharacteristic
163C22×C8×C61C2311yescharacteristic
164#125×C61—22no—
165#125×C61C2314yes—
166C4×D4×C61—22no—
167C4×D4×C61C2314yes—
168C2×C4⋊C4×C61—21no—
169C2×C4⋊C4×C61—21no—
170C2×C4⋊C4×C61C2311yescharacteristic
171C2×C4⋊C4×C61C2311yescharacteristic
172C2×C4⋊C4×C61C2311yescharacteristic
173C2×C22⋊C4×C61—21no—
174C2×C42×C61C2311yescharacteristic
175#107×C61C2314yes—
176#106×C61C2314yes—
177C4⋊C8×C61C2314yes—
178#102×C61C2314yes—
179#102×C61C2314yes—
180C24×C61—21no—
181C23×D61C2×D411yescharacteristic
182C2×D4×C61—21no—
183C2×D4×C61—22no—
184C2×D4×C61C2×Q814yes—
185C2×D4×C61C2412yes—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—24no—
190C22×C4×C61—82no—
191C22×C4×C61C2×D411yescharacteristic
192C22×C4×C61C2×D411yescharacteristic
193C22×C4×C61C2411yescharacteristic
194C2×C22⋊D61—28no—
195C2×C22⋊D61—24no—
196C22×Dic61—21no—
197C22×Dic61—28no—
198C22×Dic61—24no—
199C22×Dic61—21no—
200C22×Dic61—21no—
201C22×Dic61—21no—
202C22×Dic61—24no—
203C22×Dic61—82no—
204C22×Dic61C2×D411yescharacteristic
205C22×Dic61C2×D411yescharacteristic
206C22×Dic61C2×D411yescharacteristic
207#11758224—216no—
208#11758224—28no—
209#11758224C2×Q8116yescomplemented
210C2×C4×D61—24no—
211C2×C4×D61—24no—
212C2×C4×D61—82no—
213C2×C4×D61—82no—
214C2×C4×D61C2×D412yes—
215C2×C4×D61C2×Q814yes—
216C2×C4×D61#4114yes—
217C2×C4×D61C2412yes—
218C2×Dic122—21no—
219C2×Dic122—22no—
220C2×Dic122—24no—
221C2×Dic122—24no—
222C2×Dic122—82no—
223C2×Dic122—82no—
224C2×Dic122C2×Q814yes—
225C2×Dic122C2412yes—
226C2×C8×C61—22no—
227C2×C8×C61—22no—
228C2×C8×C61C2412yes—
229C2×C8×C61C2412yes—
230C4⋊C4×C61—24no—
231C4⋊C4×C61—24no—
232C4⋊C4×C61—21no—
233C4⋊C4×C61—21no—
234C4⋊C4×C61—21no—
235C4⋊C4×C61C2412yes—
236C4⋊C4×C61C2412yes—
237C4⋊C4×C61C2412yes—
238C22⋊C4×C61—24no—
239C42×C61C2×D412yes—
240C42×C61C2412yes—
241C22⋊Dic61—24no—
242#11758198—24no—
243#11758198C2×D414yes—
244#11758198C2×D414yes—
245C4⋊Dic61—21no—
246C4⋊Dic61—21no—
247C4⋊Dic61—24no—
248C4⋊Dic61—21no—
249C4⋊Dic61—24no—
250C4⋊Dic61C2412yes—
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—
260#11758196C2×D414yes—
261C4×Dic61—24no—
262C4×Dic61—24no—
263C4×Dic61—24no—
264C4×Dic61C2×D412yes—
265C4×Dic61C2412yes—
266C2×#92418—22no—
267C2×#92418—22no—
268C2×#92418C2412yes—
269C2×#92418C2412yes—
270#11758189—28no—
271C8×D61—28no—
272C23×C61—24no—
273C23×C61—22no—
274C23×C61—42no—
275C23×C61—42no—
276C23×C61C22×D411yescharacteristic
277C22×D61—22no—
278C22×D61—22no—
279C22×D61C22⋊Q814yes—
280C22×D61C22×D412yes—
281D4×C61—24no—
282D4×C61—22no—
283D4×C61C22×Q814yes—
284C2×C4×C61—22no—
285C2×C4×C61—22no—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—42no—
290C2×C4×C61—42no—
291C2×C4×C61—42no—
292C2×C4×C61—84no—
293C2×C4×C61C22×D412yes—
294C2×C4×C61C22×D412yes—
295C2×C4×C61C22×D411yescharacteristic
296C2×C4×C61C22×Q812yes—
297C2×C4×C61C2×#4112yes—
298C2×C4×C61C2511yescharacteristic
299C22⋊D61—216no—
300C2×Dic61—24no—
301C2×Dic61—22no—
302C2×Dic61—22no—
303C2×Dic61—22no—
304C2×Dic61—216no—
305C2×Dic61—22no—
306C2×Dic61—22no—
307C2×Dic61—22no—
308C2×Dic61—42no—
309C2×Dic61—42no—
310C2×Dic61—42no—
311C2×Dic61—84no—
312C2×Dic61C22⋊Q814yes—
313C2×Dic61C22×D412yes—
314C2×Dic61C22×D412yes—
315C2×Dic61C22×D412yes—
316C4×D61—84no—
317C4×D61—84no—
318C4×D61C22⋊Q818yes—
319C4×D61C22×Q814yes—
320C4×D61C2×#4114yes—
321Dic122—24no—
322Dic122—22no—
323Dic122—84no—
324Dic122—84no—
325Dic122C22×Q814yes—
326C8×C61—22no—
327C8×C61—22no—
328#92418—22no—
329#92418—22no—
330C2×#3084—611nomaximal, Sylow
331C22×C61—24no—
332C22×C61—48no—
333C22×C61—42no—
334C22×C61—42no—
335C22×C61C2×C22⋊Q812yes—
336C22×C61#57712yes—
337C22×C61#57712yes—
338C22×C61C23×D411yescharacteristic
339C2×D61—28no—
340C2×D61—22no—
341C2×D61—22no—
342C2×D61C2×C22⋊Q814yes—
343C4×C61—22no—
344C4×C61—22no—
345C4×C61—42no—
346C4×C61—42no—
347C4×C61—42no—
348C4×C61C2×C22⋊Q812yes—
349C4×C61C23×Q811yescharacteristic
350C4×C61C22×#4111yescharacteristic
351Dic61—24no—
352Dic61—22no—
353Dic61—22no—
354Dic61—42no—
355Dic61—42no—
356Dic61—42no—
357Dic61C2×C22⋊Q814yes—
358C2×#544—611no—
359C2×#520—611no—
360#3084—6116no—
361C2×#479—611no—
362C2×#479—611no—
363C2×#475—611no—
364C2×#475—611no—
365C2×#478—611no—
366C2×#478D6111yescharacteristic, complemented
367C2×#476—611no—
368C2×#476—611no—
369C2×#428—611no—
370C22×#106—611no—
371C2×#424—611no—
372C2×#417—611no—
373C2×#416—611no—
374C2×C61—44no—
375C2×C61#308414yescomplemented
376C2×C61C22×C22⋊Q811yescharacteristic
377C2×C61C2×#57711yescharacteristic
378C2×C61C2×#57711yescharacteristic
379D61—24no—
380C22×#41—611no—
381C22×M16—611no—
382C23×C8—611no—
383#544—618no—
384#544—1224no—
385C2×C4⋊Q8—611no—
386C2×C4⋊Q8—611no—
387C2×C4⋊Q8—1221no—
388C2×#125—611no—
389C2×#125—1221no—
390C2×#125C2×D6111yescharacteristic
391C2×C22⋊Q8—1221no—
392C2×C22⋊Q8—1221no—
393#520—618no—
394#520—1224no—
395C2×C4×Q8—611no—
396C2×C4×Q8—611no—
397C2×C4×D4—611no—
398C2×C4×D4—1221no—
399C2×C4×D4—1221no—
400C2×C4×D4C2×D6111yescharacteristic
401C2×#117—611no—
402C2×#117—611no—
403C2×#117—1221no—
404C22×C4⋊C4—611no—
405C22×C4⋊C4—611no—
406C22×C4⋊C4—1221no—
407#479—618no—
408#479—618no—
409#478—618no—
410#478C2×D6118yescomplemented
411#476—618no—
412#476—618no—
413#475—618no—
414#475—618no—
415#428—618no—
416C2×#107—611no—
417C2×#107C2×D6111yescharacteristic
418C2×#106—611no—
419C2×#106—611no—
420C2×#106—611no—
421C2×#106—611no—
422C2×#106—611no—
423C2×#106—618no—
424C2×#106C2×D6111yescharacteristic
425#424—618no—
426C2×C4⋊C8—611no—
427C2×C4⋊C8—611no—
428C2×C4⋊C8—611no—
429C2×C4⋊C8C2×D6111yescharacteristic
430#417—618no—
431#416—618no—
432C2×#103—611no—
433C2×#103—611no—
434C2×#103—611no—
435C2×#103—611no—
436C2×#102—611no—
437C2×#102—611no—
438C2×#102C2×D6111yescharacteristic
439C2×#102C2×D6111yescharacteristic
440C61C2×#308411yescharacteristic, complemented, Sylow
441C2×#41—618no—
442C2×#41—614no—
443C2×#41—1222no—
444C2×#41—1224no—
445C22×Q8—611no—
446C22×Q8—1221no—
447C22×Q8—1221no—
448C22×D4—1221no—
449C22×D4C22×D6111yescharacteristic
450C23×C4—21no—
451C23×C4—611no—
452C23×C4—1221no—
453C23×C4—1221no—
454C23×C4—1221no—
455C23×C4—1221no—
456C2×M16—614no—
457C2×M16—1224no—
458C22×C8—611no—
459C22×C8—611no—
460C22×C8—614no—
461C22×C8—1224no—
462C22×C8C22×D6111yescharacteristic
463C22×C8C22×D6111yescharacteristic
464C4⋊Q8—614no—
465C4⋊Q8—614no—
466C4⋊Q8—1222no—
467C4⋊Q8—1228no—
468C4⋊Q8—1222no—
469#125—22no—
470#125—614no—
471#125—1222no—
472#125—1228no—
473#125C22×D6114yes—
474C22⋊Q8—1228no—
475C22⋊Q8—1228no—
476C4×Q8—614no—
477C4×Q8—614no—
478C4×Q8—1222no—
479C4×Q8—1222no—
480C4×D4—22no—
481C4×D4—614no—
482C4×D4—1222no—
483C4×D4—1228no—
484C4×D4—1228no—
485C4×D4C22×D6114yes—
486#117—614no—
487#117—614no—
488#117—614no—
489#117—1228no—
490#117—1222no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—611no—
494C2×C4⋊C4—611no—
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—1228no—
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×C22⋊C4—21no—
515C2×C22⋊C4—611no—
516C2×C22⋊C4—611no—
517C2×C22⋊C4—1221no—
518C2×C22⋊C4—1221no—
519C2×C42—611no—
520C2×C42—1221no—
521C2×C42—1221no—
522C2×C42—1221no—
523C2×C42C22×D6111yescharacteristic
524#107—614no—
525#107C22×D6114yes—
526#106—614no—
527#106—614no—
528#106—614no—
529#106—614no—
530#106—614no—
531#106C22×D6114yes—
532C4⋊C8—614no—
533C4⋊C8—614no—
534C4⋊C8—614no—
535C4⋊C8C22×D6114yes—
536#103—614no—
537#103—614no—
538#103—614no—
539#103—614no—
540#102—614no—
541#102—614no—
542#102C22×D6114yes—
543#102C22×D6114yes—
544C24—21no—
545C24—611no—
546#41—6116no—
547#41—12216no—
548#41—1228no—
549C2×Q8—614no—
550C2×Q8—612no—
551C2×Q8—1224no—
552C2×Q8—1221no—
553C2×Q8—1224no—
554C2×Q8—1222no—
555C2×Q8—4882no—
556C2×Q8—4882no—
557C2×D4—21no—
558C2×D4—22no—
559C2×D4—1224no—
560C2×D4—1228no—
561C2×D4Q8×D6114yes—
562C2×D4C23×D6112yes—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—24no—
567C22×C4—82no—
568C22×C4—611no—
569C22×C4—612no—
570C22×C4—614no—
571C22×C4—614no—
572C22×C4—612no—
573C22×C4—611no—
574C22×C4—611no—
575C22×C4—1224no—
576C22×C4—1224no—
577C22×C4—1224no—
578C22×C4—1228no—
579C22×C4—1224no—
580C22×C4—1221no—
581C22×C4—1221no—
582C22×C4—1221no—
583C22×C4—1221no—
584C22×C4—4882no—
585C22×C4—4882no—
586C22×C4—4882no—
587C22×C4D4×D6111yescharacteristic
588C22×C4D4×D6111yescharacteristic
589C22×C4C23×D6111yescharacteristic
590M16—1228no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—612no—
594C2×C8—612no—
595C2×C8—1228no—
596C2×C8—1222no—
597C2×C8—1222no—
598C2×C8C23×D6112yes—
599C2×C8C23×D6112yes—
600C4⋊C4—24no—
601C4⋊C4—24no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—614no—
606C4⋊C4—614no—
607C4⋊C4—612no—
608C4⋊C4—612no—
609C4⋊C4—612no—
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—1221no—
619C4⋊C4—1224no—
620C4⋊C4—1224no—
621C4⋊C4C23×D6112yes—
622C4⋊C4C23×D6112yes—
623C4⋊C4C23×D6112yes—
624C22⋊C4—24no—
625C22⋊C4—614no—
626C22⋊C4—614no—
627C22⋊C4—1224no—
628C22⋊C4—1224no—
629C42—612no—
630C42—612no—
631C42—1224no—
632C42—1224no—
633C42—1224no—
634C42D4×D6112yes—
635C42C23×D6112yes—
636C23—24no—
637C23—22no—
638C23—42no—
639C23—42no—
640C23—614no—
641C23—612no—
642C23—1222no—
643C23—1222no—
644C23C2×D4×D6111yescharacteristic
645Q8—614no—
646Q8—1224no—
647Q8—1222no—
648Q8—4884no—
649Q8—4884no—
650D4—24no—
651D4—22no—
652D4—12216no—
653D4C2×Q8×D6114yes—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—84no—
663C2×C4—614no—
664C2×C4—612no—
665C2×C4—618no—
666C2×C4—614no—
667C2×C4—614no—
668C2×C4—612no—
669C2×C4—612no—
670C2×C4—12216no—
671C2×C4—1224no—
672C2×C4—1222no—
673C2×C4—1222no—
674C2×C4—1222no—
675C2×C4—1222no—
676C2×C4—1222no—
677C2×C4—1222no—
678C2×C4—4884no—
679C2×C4—4884no—
680C2×C4—4884no—
681C2×C4—2442no—
682C2×C4—2442no—
683C2×C4—2442no—
684C2×C4C2×D4×D6112yes—
685C2×C4C2×D4×D6112yes—
686C2×C4C2×D4×D6111yescharacteristic
687C2×C4C2×Q8×D6112yes—
688C2×C4#41×D6112yes—
689C2×C4C24×D6111yescharacteristic
690C8—22no—
691C8—22no—
692C8—1222no—
693C8—1222no—
694C22—24no—
695C22—48no—
696C22—42no—
697C22—42no—
698C22—614no—
699C22—1228no—
700C22—1222no—
701C22—1222no—
702C22C22⋊Q8×D6112yes—
703C22#1684056912yes—
704C22#1684057212yes—
705C22C22×D4×D6111yescharacteristic
706C4—22no—
707C4—22no—
708C4—42no—
709C4—42no—
710C4—42no—
711C4—614no—
712C4—1222no—
713C4—1222no—
714C4—1224no—
715C4—2442no—
716C4—2442no—
717C4—2442no—
718C4C22⋊Q8×D6112yes—
719C4C22×Q8×D6111yescharacteristic
720C4C2×#41×D6111yescharacteristic
721C2—44no—
722C2—1224no—
723C2#2145568214yesdirect product factor
724C2C2×C22⋊Q8×D6111yescharacteristic
725C2C2×#1684056911yescharacteristic
726C2C2×#1684057211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#478C2
socleC23×C61C22×D4
prime radicalC22×#11758224C22
hypercenterC2×#478D61
hypocenterC61C2×#3084
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#16840392C2semidirect
3. #21455682C2direct (N × H)
4. C2×#16840068C2semidirect
5. C2×#16840066C2semidirect
6. C2×#16840048C2semidirect
7. C2×#16840046C2semidirect
8. C2×#16840064C2semidirect
9. C2×#16840052C2semidirect
10. C2×#16840050C2semidirect
11. C2×#16839803C2semidirect
12. C2×#106×D61C2semidirect
13. C2×#16839787C2semidirect
16. C2×C61×#478C2semidirect
21. #16840392C22semidirect
42. #16840068C22semidirect
43. #16840066C22semidirect
44. #16840064C22semidirect
45. #16840052C22semidirect
46. #16840050C22semidirect
47. #16840048C22semidirect
48. #16840046C22semidirect
49. #16839803C22semidirect
56. #106×D61C22semidirect
57. #16839787C22semidirect
71. C61×#478C22semidirect
79. C2×#11758224Q8semidirect
209. #11758224C2×Q8semidirect
366. C2×#478D61semidirect
375. C2×C61#3084semidirect
410. #478C2×D61semidirect
440. C61C2×#3084semidirect
723. C2#21455682direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403922
C2×#168402412
#214556822
C2×#168400682
C2×#168400662
C2×#168400482
C2×#168400462
C2×#168400642
C2×#168400522
C2×#168400502
C2×#168398032
C2×#106×D612
C2×#168397872
C2×#168397602
C2×#168397552
C2×C61×#4782
C2×#308461