Finite Group Databasebeta

← C2×#21455603 #30547510

Subgroups — C2×#21455603 #30547510

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×#41×Dic61C211yesmaximal, characteristic
3#21455603C2116yesmaximal, direct product factor
4C2×#16840071C211yesmaximal, characteristic, complemented
5C2×#16840067C211yesmaximal, characteristic, complemented
6C2×#16840055C211yesmaximal, characteristic, complemented
7C2×#16840045C211yesmaximal, characteristic, complemented
8C2×#16840064C211yesmaximal, characteristic, complemented
9C2×#16840060C211yesmaximal, characteristic, complemented
10C2×#16840050C211yesmaximal, characteristic, complemented
11C2×#16840040C211yesmaximal, characteristic, complemented
12C2×#16839800C211yesmaximal, characteristic, complemented
13C2×#16839798C211yesmaximal, characteristic, complemented
14C22×#14519706C211yesmaximal, characteristic, complemented
15C2×#16839758C211yesmaximal, characteristic
16C2×C61×#416C211yesmaximal, characteristic
17C23×#92418C2211yescharacteristic
18#16840315—24no—
19#16840315C2218yescomplemented
20C2×#14519776C2211yescharacteristic
21C2×#14519776C2211yescharacteristic
22C2×#14519768C2211yescharacteristic
23C2×#14519768C2211yescharacteristic
24C2×#14519754—21no—
25C2×#14519754—21no—
26#41×Dic61—24no—
27#41×Dic61C2218yes—
28C2×Q8×Dic61C2211yescharacteristic
29C2×Q8×Dic61C2211yescharacteristic
30C2×C4×Dic122—21no—
31C2×C4×Dic122—21no—
32C2×D4×Dic61—21no—
33C2×D4×Dic61—21no—
34C2×D4×Dic61C2211yescharacteristic
35C2×D4×Dic61C2211yescharacteristic
36C2×#14519736—21no—
37C2×#14519736C2211yescharacteristic
38C2×#14519736C2211yescharacteristic
39C22×C4×Dic61—21no—
40C22×C4×Dic61C2211yescharacteristic
41#16840071C2218yescomplemented
42#16840067C2218yescomplemented
43#16840064C2218yescomplemented
44#16840060C2218yescomplemented
45#16840055C2218yescomplemented
46#16840050C2218yescomplemented
47#16840045C2218yescomplemented
48#16840040C2218yescomplemented
49#16839800C2218yescomplemented
50#16839798C2218yescomplemented
51C2×#14519711C2211yescharacteristic
52C2×#14519711C2211yescharacteristic
53C2×#14519710C2211yescharacteristic
54C2×#14519710C2211yescharacteristic
55C2×#14519709C2211yescharacteristic
56C2×#14519709C2211yescharacteristic
57C2×#14519708C2211yescharacteristic
58C2×#14519708C2211yescharacteristic
59C2×#14519706C2211yescharacteristic
60C2×#14519706C2211yescharacteristic
61C2×#14519706C2211yescharacteristic
62C2×#14519706C2211yescharacteristic
63C2×#14519706C2218yescomplemented
64#16839758C2218yes—
65C2×#14519701C2211yescharacteristic
66C2×#14519701C2211yescharacteristic
67C2×#14519698C2211yescharacteristic
68C2×#14519698C2211yescharacteristic
69C22×#41×C61C2211yescharacteristic
70C23×C8×C61C2211yescharacteristic
71C2×#117×C61C2211yescharacteristic
72C61×#416C2218yes—
73C2×#103×C61C2211yescharacteristic
74C2×#103×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×#102×C61C2211yescharacteristic
77C22×Dic122—21no—
78C22×Dic122—21no—
79C23×Dic61—21no—
80C23×Dic61—21no—
81C23×Dic61D411yescharacteristic
82C23×Dic61D411yescharacteristic
83C22×#92418—24no—
84C22×#92418C2311yescharacteristic
85C22×#92418C2311yescharacteristic
86C22×#92418C2314yes—
87#14519776—22no—
88#14519776—22no—
89#14519776C2314yes—
90#14519776C2314yes—
91#14519768—22no—
92#14519768—22no—
93#14519768C2314yes—
94#14519768C2314yes—
95#14519754—28no—
96#14519754—28no—
97Q8×Dic61—22no—
98Q8×Dic61—22no—
99Q8×Dic61C2314yes—
100Q8×Dic61C2314yes—
101C4×Dic122—28no—
102C4×Dic122—28no—
103D4×Dic61—28no—
104D4×Dic61—28no—
105D4×Dic61—22no—
106D4×Dic61—22no—
107D4×Dic61C2314yes—
108D4×Dic61C2314yes—
109#14519736—22no—
110#14519736—22no—
111#14519736—28no—
112#14519736C2314yes—
113#14519736C2314yes—
114C2×C4⋊Dic61—21no—
115C2×C4⋊Dic61—21no—
116C2×C4⋊Dic61—21no—
117C2×C4⋊Dic61—21no—
118C2×C4⋊Dic61C2311yescharacteristic
119C2×C4⋊Dic61C2311yescharacteristic
120C2×C4⋊Dic61C2311yescharacteristic
121C2×C4⋊Dic61C2311yescharacteristic
122C2×#11758196—21no—
123C2×#11758196—21no—
124C2×#11758196—21no—
125C2×#11758196—21no—
126C2×C22⋊Dic61—21no—
127C2×C22⋊Dic61—21no—
128C2×C22⋊Dic61—21no—
129C2×C22⋊Dic61—21no—
130C2×C4×Dic61—21no—
131C2×C4×Dic61—21no—
132C2×C4×Dic61—21no—
133C2×C4×Dic61—21no—
134C2×C4×Dic61—28no—
135C2×C4×Dic61D411yescharacteristic
136C2×C4×Dic61D411yescharacteristic
137C2×C4×Dic61D414yes—
138C2×C4×Dic61C2311yescharacteristic
139C2×C4×Dic61C2311yescharacteristic
140C2×C4×Dic61C2314yes—
141#14519711C2314yes—
142#14519711C2314yes—
143#14519710C2314yes—
144#14519710C2314yes—
145#14519709C2314yes—
146#14519709C2314yes—
147#14519708C2314yes—
148#14519708C2314yes—
149#14519706C2314yes—
150#14519706C2314yes—
151#14519706C2314yes—
152#14519706C2314yes—
153#14519701C2314yes—
154#14519701C2314yes—
155#14519698C2314yes—
156#14519698C2314yes—
157C2×#41×C61—22no—
158C2×#41×C61—24no—
159C2×#41×C61Q818yescomplemented
160C2×#41×C61C2314yes—
161C22×Q8×C61C2311yescharacteristic
162C22×D4×C61—21no—
163C22×D4×C61C2311yescharacteristic
164C23×C4×C61—21no—
165C23×C4×C61C2311yescharacteristic
166C22×C8×C61—24no—
167C22×C8×C61C2311yescharacteristic
168C22×C8×C61C2311yescharacteristic
169C22×C8×C61C2314yes—
170#117×C61—22no—
171#117×C61C2314yes—
172C2×C4⋊C4×C61C2311yescharacteristic
173C2×C4⋊C4×C61C2311yescharacteristic
174C2×C22⋊C4×C61—21no—
175C2×C42×C61—21no—
176#103×C61C2314yes—
177#103×C61C2314yes—
178#102×C61C2314yes—
179#102×C61C2314yes—
180C24×C61—21no—
181C24×C61C2×D411yescharacteristic
182#41×C61—216no—
183#41×C61—28no—
184#41×C61C2×Q8116yescomplemented
185C2×Q8×C61—21no—
186C2×Q8×C61—22no—
187C2×Q8×C61C2×Q814yes—
188C2×Q8×C61C2412yes—
189C2×D4×C61—28no—
190C2×D4×C61—24no—
191C2×D4×C61—21no—
192C2×D4×C61—22no—
193C2×D4×C61C2×Q814yes—
194C2×D4×C61C2412yes—
195C22×C4×C61—21no—
196C22×C4×C61—28no—
197C22×C4×C61—24no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61C2×D412yes—
201C22×C4×C61C2×D411yescharacteristic
202C22×C4×C61C2×Q814yes—
203C22×C4×C61#4114yes—
204C22×C4×C61C2411yescharacteristic
205C22×C4×C61C2412yes—
206C22×Dic61—24no—
207C22×Dic61—21no—
208C22×Dic61—21no—
209C22×Dic61—21no—
210C22×Dic61—21no—
211C22×Dic61—24no—
212C22×Dic61—24no—
213C22×Dic61—42no—
214C22×Dic61—44no—
215C22×Dic61—44no—
216C22×Dic61C2×D411yescharacteristic
217C22×Dic61C2×D411yescharacteristic
218C22×Dic61C2×D411yescharacteristic
219C22×Dic61C2×D414yes—
220C22×Dic61C2×D414yes—
221C22×Dic61C2×D411yescharacteristic
222C2×Dic122—24no—
223C2×Dic122—24no—
224C2×Dic122—44no—
225C2×Dic122—44no—
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×C61C2412yes—
234C4⋊C4×C61C2412yes—
235C22⋊C4×C61—24no—
236C42×C61—24no—
237C22⋊Dic61—24no—
238C22⋊Dic61—24no—
239C22⋊Dic61—24no—
240C22⋊Dic61—24no—
241C4⋊Dic61—21no—
242C4⋊Dic61—21no—
243C4⋊Dic61—21no—
244C4⋊Dic61—21no—
245C4⋊Dic61—24no—
246C4⋊Dic61—24no—
247C4⋊Dic61—24no—
248C4⋊Dic61—24no—
249C4⋊Dic61C2412yes—
250C4⋊Dic61C2412yes—
251C4⋊Dic61C2412yes—
252C4⋊Dic61C2412yes—
253#11758196—24no—
254#11758196—24no—
255#11758196—24no—
256#11758196—24no—
257C4×Dic61—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×C61—24no—
275C23×C61—22no—
276C23×C61—42no—
277C23×C61—42no—
278C23×C61C22⋊Q814yes—
279C23×C61C22×D412yes—
280C23×C61C22×D411yescharacteristic
281Q8×C61—24no—
282Q8×C61—22no—
283Q8×C61C22×Q814yes—
284D4×C61—216no—
285D4×C61—24no—
286D4×C61—22no—
287D4×C61C22×Q814yes—
288C2×C4×C61—24no—
289C2×C4×C61—22no—
290C2×C4×C61—216no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—42no—
294C2×C4×C61—42no—
295C2×C4×C61C22⋊Q814yes—
296C2×C4×C61C22⋊Q818yes—
297C2×C4×C61C22×D412yes—
298C2×C4×C61C22×D411yescharacteristic
299C2×C4×C61C22×Q812yes—
300C2×C4×C61C22×Q814yes—
301C2×C4×C61C2×#4112yes—
302C2×C4×C61C2×#4114yes—
303C2×C4×C61C2511yescharacteristic
304C2×Dic61—22no—
305C2×Dic61—22no—
306C2×Dic61—22no—
307C2×Dic61—28no—
308C2×Dic61—22no—
309C2×Dic61—22no—
310C2×Dic61—22no—
311C2×Dic61—22no—
312C2×Dic61—44no—
313C2×Dic61—48no—
314C2×Dic61—42no—
315C2×Dic61—42no—
316C2×Dic61—42no—
317C2×Dic61—42no—
318C2×Dic61—48no—
319C2×Dic61#13514yes—
320C2×Dic61C22×D412yes—
321C2×Dic61C22×D412yes—
322C2×Dic61C22×D412yes—
323C2×Dic61C22×D412yes—
324Dic122—48no—
325Dic122—48no—
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×C61—24no—
335C22×C61—48no—
336C22×C61—42no—
337C22×C61—42no—
338C22×C61C2×C22⋊Q814yes—
339C22×C61C2×C22⋊Q812yes—
340C22×C61C2×#13512yes—
341C22×C61#57512yes—
342C22×C61C23×D411yescharacteristic
343C4×C61—24no—
344C4×C61—42no—
345C4×C61—42no—
346C4×C61C2×C22⋊Q814yes—
347C4×C61C2×C22⋊Q812yes—
348C4×C61C23×Q811yescharacteristic
349C4×C61C22×#4111yescharacteristic
350Dic61—22no—
351Dic61—22no—
352Dic61—22no—
353Dic61—42no—
354Dic61—42no—
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×#427—611no—
371C22×C4⋊C8—611no—
372C2×#416—611no—
373C2×#416D6111yescharacteristic
374C2×C61—24no—
375C2×C61—44no—
376C2×C61#307614yescomplemented
377C2×C61C22×C22⋊Q811yescharacteristic
378C2×C61C22×#13511yescharacteristic
379C2×C61C2×#57511yescharacteristic
380C22×#41C2×D6111yescharacteristic
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—611no—
403C2×#117—1221no—
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#427—618no—
417C2×#107—611no—
418C2×#107—611no—
419C2×#107—611no—
420C2×#107—611no—
421C2×#106—611no—
422C2×#106—611no—
423C2×#106—611no—
424C2×#106—611no—
425C2×C4⋊C8—611no—
426C2×C4⋊C8—611no—
427C2×C4⋊C8—611no—
428C2×C4⋊C8—611no—
429C2×C4⋊C8—618no—
430#416—618no—
431#416C2×D6118yes—
432C2×#103—611no—
433C2×#103—611no—
434C2×#103C2×D6111yescharacteristic
435C2×#103C2×D6111yescharacteristic
436C2×#102—611no—
437C2×#102—611no—
438C2×#102C2×D6111yescharacteristic
439C2×#102C2×D6111yescharacteristic
440C61C2×#307611yescharacteristic, complemented, Sylow
441C2×#41—22no—
442C2×#41—24no—
443C2×#41Dic12218yescomplemented
444C2×#41C22×D6114yes—
445C22×Q8—1221no—
446C22×Q8—1221no—
447C22×Q8C22×D6111yescharacteristic
448C22×D4—21no—
449C22×D4C22×D6111yescharacteristic
450C23×C4—21no—
451C23×C4—611no—
452C23×C4—611no—
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—614no—
488#117—614no—
489#117—1228no—
490#117—1222no—
491#117—1222no—
492#117C22×D6114yes—
493C2×C4⋊C4—611no—
494C2×C4⋊C4—611no—
495C2×C4⋊C4—611no—
496C2×C4⋊C4—611no—
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⋊C4—1221no—
504C2×C4⋊C4—1221no—
505C2×C4⋊C4C22×D6111yescharacteristic
506C2×C4⋊C4C22×D6111yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—1221no—
509C2×C22⋊C4—1221no—
510C2×C22⋊C4—1221no—
511C2×C22⋊C4—1221no—
512C2×C42—21no—
513C2×C42—614no—
514C2×C42—611no—
515C2×C42—611no—
516C2×C42—611no—
517C2×C42—611no—
518C2×C42—614no—
519C2×C42—1228no—
520C2×C42—1221no—
521C2×C42—1221no—
522C2×C42—1221no—
523C2×C42—1221no—
524#107—614no—
525#107—614no—
526#107—614no—
527#107—614no—
528#106—614no—
529#106—614no—
530#106—614no—
531#106—614no—
532C4⋊C8—614no—
533C4⋊C8—614no—
534C4⋊C8—614no—
535C4⋊C8—614no—
536#103—614no—
537#103—614no—
538#103C22×D6114yes—
539#103C22×D6114yes—
540#102—614no—
541#102—614no—
542#102C22×D6114yes—
543#102C22×D6114yes—
544C24—21no—
545C24D4×D6111yescharacteristic
546#41—28no—
547#41—216no—
548#41C2×Dic122116yescomplemented
549C2×Q8—21no—
550C2×Q8—22no—
551C2×Q8—1224no—
552C2×Q8—1224no—
553C2×Q8—2444no—
554C2×Q8—2444no—
555C2×Q8C2×Dic12214yes—
556C2×Q8C23×D6112yes—
557C2×D4—24no—
558C2×D4—28no—
559C2×D4—21no—
560C2×D4—22no—
561C2×D4C2×Dic12214yes—
562C2×D4C23×D6112yes—
563C22×C4—21no—
564C22×C4—24no—
565C22×C4—28no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—611no—
569C22×C4—611no—
570C22×C4—611no—
571C22×C4—611no—
572C22×C4—614no—
573C22×C4—614no—
574C22×C4—1224no—
575C22×C4—1224no—
576C22×C4—1224no—
577C22×C4—1221no—
578C22×C4—1221no—
579C22×C4—1221no—
580C22×C4—1221no—
581C22×C4—2444no—
582C22×C4—2442no—
583C22×C4—2444no—
584C22×C4C2×Dic12214yes—
585C22×C4D4×D6112yes—
586C22×C4D4×D6111yescharacteristic
587C22×C4#1175822414yes—
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—612no—
603C4⋊C4—612no—
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⋊C4—1221no—
617C4⋊C4—1221no—
618C4⋊C4C23×D6112yes—
619C4⋊C4C23×D6112yes—
620C22⋊C4—24no—
621C22⋊C4—1224no—
622C22⋊C4—1224no—
623C22⋊C4—1224no—
624C22⋊C4—1224no—
625C42—24no—
626C42—614no—
627C42—614no—
628C42—612no—
629C42—612no—
630C42—612no—
631C42—612no—
632C42—1224no—
633C42—1224no—
634C42—1224no—
635C42—1224no—
636C23—22no—
637C23—22no—
638C23—24no—
639C23—22no—
640C23—42no—
641C23—42no—
642C23#1451975414yes—
643C23C2×D4×D6112yes—
644C23C2×D4×D6111yescharacteristic
645Q8—24no—
646Q8—22no—
647Q8—2448no—
648Q8—2448no—
649Q8C22×Dic12214yes—
650D4—216no—
651D4—24no—
652D4—22no—
653D4C22×Dic12214yes—
654C2×C4—24no—
655C2×C4—22no—
656C2×C4—216no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—614no—
662C2×C4—612no—
663C2×C4—612no—
664C2×C4—612no—
665C2×C4—612no—
666C2×C4—1228no—
667C2×C4—1222no—
668C2×C4—1222no—
669C2×C4—1222no—
670C2×C4—1222no—
671C2×C4—1222no—
672C2×C4—1222no—
673C2×C4—1222no—
674C2×C4—2448no—
675C2×C4—2444no—
676C2×C4—2448no—
677C2×C4—2442no—
678C2×C4—2442no—
679C2×C4—2442no—
680C2×C4—2442no—
681C2×C4#1451975414yes—
682C2×C4#1451975418yes—
683C2×C4C2×D4×D6112yes—
684C2×C4C2×D4×D6111yescharacteristic
685C2×C4C22×Dic12212yes—
686C2×C4C22×Dic12214yes—
687C2×C4C2×#1175822412yes—
688C2×C4C2×#1175822414yes—
689C2×C4C24×D6111yescharacteristic
690C8—22no—
691C8—22no—
692C8—1222no—
693C8—1222no—
694C22—22no—
695C22—22no—
696C22—28no—
697C22—24no—
698C22—42no—
699C22—42no—
700C22—48no—
701C22C2×#1451975414yes—
702C22C2×#1451975412yes—
703C22#135×D6112yes—
704C22#1684055912yes—
705C22C22×D4×D6111yescharacteristic
706C4—24no—
707C4—42no—
708C4—42no—
709C4—614no—
710C4—1222no—
711C4—1222no—
712C4—1222no—
713C4—2442no—
714C4—2442no—
715C4—2442no—
716C4—2442no—
717C4C2×#1451975414yes—
718C4C2×#1451975412yes—
719C4C23×Dic12211yescharacteristic
720C4C22×#1175822411yescharacteristic
721C2—24no—
722C2—44no—
723C2#2145560314yesdirect product factor
724C2C22×#1451975411yescharacteristic
725C2C2×#135×D6111yescharacteristic
726C2C2×#1684055911yescharacteristic
subgroupG/H
centerC22×C4D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#416C2
socleC23×C61C22×D4
prime radicalC22×#41×C61C22
hypercenterC2×#416D61
hypocenterC61C2×#3076
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
1. C2×#16840315C2semidirect
3. #21455603C2direct (N × H)
4. C2×#16840071C2semidirect
5. C2×#16840067C2semidirect
6. C2×#16840055C2semidirect
7. C2×#16840045C2semidirect
8. C2×#16840064C2semidirect
9. C2×#16840060C2semidirect
10. C2×#16840050C2semidirect
11. C2×#16840040C2semidirect
12. C2×#16839800C2semidirect
13. C2×#16839798C2semidirect
14. C22×#14519706C2semidirect
19. #16840315C22semidirect
41. #16840071C22semidirect
42. #16840067C22semidirect
43. #16840064C22semidirect
44. #16840060C22semidirect
45. #16840055C22semidirect
46. #16840050C22semidirect
47. #16840045C22semidirect
48. #16840040C22semidirect
49. #16839800C22semidirect
50. #16839798C22semidirect
63. C2×#14519706C22semidirect
159. C2×#41×C61Q8semidirect
184. #41×C61C2×Q8semidirect
376. C2×C61#3076semidirect
440. C61C2×#3076semidirect
443. C2×#41Dic122semidirect
548. #41C2×Dic122semidirect
723. C2#21455603direct (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×#41×Dic612
#214556032
C2×#168400712
C2×#168400672
C2×#168400552
C2×#168400452
C2×#168400642
C2×#168400602
C2×#168400502
C2×#168400402
C2×#168398002
C2×#168397982
C22×#145197062
C2×#168397582
C2×C61×#4162
C2×#307661