Finite Group Databasebeta

← C2×#20253251 #27083872

Subgroups — C2×#20253251 #27083872

Order 12032.

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×#15689753C211yesmaximal, characteristic, complemented
2C2×#15689602C211yesmaximal, characteristic
3#20253251C2116yesmaximal, direct product factor
4C2×#15689429C211yesmaximal, characteristic, complemented
5C2×#15689427C211yesmaximal, characteristic, complemented
6C2×#15689409C211yesmaximal, characteristic, complemented
7C2×#15689407C211yesmaximal, characteristic, complemented
8C2×#15689425C211yesmaximal, characteristic, complemented
9C2×#15689413C211yesmaximal, characteristic, complemented
10C2×#15689411C211yesmaximal, characteristic, complemented
11C2×#15689164C211yesmaximal, characteristic, complemented
12C2×#106×D47C211yesmaximal, characteristic, complemented
13C2×#15689148C211yesmaximal, characteristic, complemented
14C2×#15689121C211yesmaximal, characteristic
15C2×#15689116C211yesmaximal, characteristic
16C2×C47×#478C211yesmaximal, characteristic, complemented
17C22×#10625352C2211yescharacteristic
18C22×#10625324C2211yescharacteristic
19C22×C8×D47C2211yescharacteristic
20#15689753—24no—
21#15689753C2218yescomplemented
22C2×#13094024C2211yescharacteristic
23C2×#13094023—21no—
24C2×#13094023C2211yescharacteristic
25C2×#13094015C2211yescharacteristic
26C2×#13094014—21no—
27C2×#13094004—21no—
28C2×#13094002—21no—
29#15689602—24no—
30#15689602C2218yes—
31C2×C4×Dic94C2211yescharacteristic
32C2×#13093989C2211yescharacteristic
33C2×D4×Dic47C2211yescharacteristic
34C2×C4×C22⋊D47—21no—
35C2×(C22⋊D47)⋊C4—21no—
36C2×#13093982C2211yescharacteristic
37C2×#13093981C2211yescharacteristic
38C2×#13093980—21no—
39C22×Dic47⋊C4—21no—
40C2×C4⋊C4×D47C2211yescharacteristic
41C2×C4⋊C4×D47C2211yescharacteristic
42#15689429C2218yescomplemented
43#15689427C2218yescomplemented
44#15689425C2218yescomplemented
45#15689413C2218yescomplemented
46#15689411C2218yescomplemented
47#15689409C2218yescomplemented
48#15689407C2218yescomplemented
49#15689164C2218yescomplemented
50C2×#13093957C2211yescharacteristic
51C2×#13093956C2211yescharacteristic
52C2×#13093956C2211yescharacteristic
53C2×#13093955C2211yescharacteristic
54C2×#13093955C2211yescharacteristic
55C2×#13093955C2211yescharacteristic
56#106×D47C2218yescomplemented
57#15689148C2218yescomplemented
58C2×C4⋊(C47⋊C8)C2211yescharacteristic
59C2×Dic47⋊C8C2211yescharacteristic
60C2×Dic47⋊C8C2211yescharacteristic
61#15689121C2218yes—
62#15689116C2218yes—
63C2×#13093949C2211yescharacteristic
64C2×#13093949C2211yescharacteristic
65C2×#13093947C2211yescharacteristic
66C2×#13093947C2211yescharacteristic
67C2×#13093945C2211yescharacteristic
68C2×#13093945C2211yescharacteristic
69C2×#125×C47C2211yescharacteristic
70C2×C4×D4×C47C2211yescharacteristic
71C47×#478C2218yescomplemented
72C2×#107×C47C2211yescharacteristic
73C2×#106×C47C2211yescharacteristic
74C2×C4⋊C8×C47C2211yescharacteristic
75C2×#102×C47C2211yescharacteristic
76C2×#102×C47C2211yescharacteristic
77C2×#10625352—22no—
78C2×#10625352—24no—
79C2×#10625352Q818yescomplemented
80C2×#10625352C2314yes—
81C22×Dic94—21no—
82C22×Dic94—21no—
83C22×Dic94C2311yescharacteristic
84C22×C22⋊D47—21no—
85C23×Dic47—21no—
86C23×Dic47—21no—
87C22×C4×D47—21no—
88C22×C4×D47—21no—
89C22×C4×D47C2311yescharacteristic
90C2×#10625324—24no—
91C2×#10625324C2314yes—
92C22×C47⋊C8C2311yescharacteristic
93C22×C47⋊C8C2311yescharacteristic
94C2×C8×D47—24no—
95C2×C8×D47C2314yes—
96#13094024—22no—
97#13094024C2314yes—
98#13094023—28no—
99#13094023—22no—
100#13094023C2314yes—
101#13094015—22no—
102#13094015C2314yes—
103#13094014—28no—
104#13094004—28no—
105#13094002—28no—
106C4×Dic94—22no—
107C4×Dic94C2314yes—
108#13093989—22no—
109#13093989C2314yes—
110D4×Dic47—22no—
111D4×Dic47C2314yes—
112C4×C22⋊D47—28no—
113(C22⋊D47)⋊C4—28no—
114#13093982—22no—
115#13093982C2314yes—
116#13093981D414yes—
117#13093981C2314yes—
118#13093980—28no—
119C2×C4⋊Dic47—21no—
120C2×C4⋊Dic47—21no—
121C2×C4⋊Dic47C2311yescharacteristic
122C2×C4⋊Dic47C2311yescharacteristic
123C2×C4⋊Dic47C2311yescharacteristic
124C2×Dic47⋊C4—21no—
125C2×Dic47⋊C4—21no—
126C2×Dic47⋊C4—21no—
127C2×Dic47⋊C4—21no—
128C2×Dic47⋊C4—21no—
129C2×Dic47⋊C4—21no—
130C2×Dic47⋊C4—28no—
131C2×Dic47⋊C4D411yescharacteristic
132C2×Dic47⋊C4D411yescharacteristic
133C4⋊C4×D47—22no—
134C4⋊C4×D47—22no—
135C4⋊C4×D47C2314yes—
136C4⋊C4×D47C2314yes—
137C2×C22⋊Dic47—21no—
138C2×(C2×D47)⋊C4—21no—
139C2×(C2×D47)⋊C4D411yescharacteristic
140C2×(C2×D47)⋊C4D411yescharacteristic
141C2×C4×Dic47—21no—
142C2×C4×Dic47—21no—
143C2×C4×Dic47—21no—
144C2×C4×Dic47C2311yescharacteristic
145#13093957C2314yes—
146#13093956C2314yes—
147#13093956C2314yes—
148#13093955C2314yes—
149#13093955C2314yes—
150#13093955C2314yes—
151C4⋊(C47⋊C8)C2314yes—
152Dic47⋊C8C2314yes—
153Dic47⋊C8C2314yes—
154#13093949C2314yes—
155#13093949C2314yes—
156#13093947C2314yes—
157#13093947C2314yes—
158#13093945C2314yes—
159#13093945C2314yes—
160C22×D4×C47C2311yescharacteristic
161C23×C4×C47—21no—
162C22×C8×C47C2311yescharacteristic
163C22×C8×C47C2311yescharacteristic
164#125×C47—22no—
165#125×C47C2314yes—
166C4×D4×C47—22no—
167C4×D4×C47C2314yes—
168C2×C4⋊C4×C47—21no—
169C2×C4⋊C4×C47—21no—
170C2×C4⋊C4×C47C2311yescharacteristic
171C2×C4⋊C4×C47C2311yescharacteristic
172C2×C4⋊C4×C47C2311yescharacteristic
173C2×C22⋊C4×C47—21no—
174C2×C42×C47C2311yescharacteristic
175#107×C47C2314yes—
176#106×C47C2314yes—
177C4⋊C8×C47C2314yes—
178#102×C47C2314yes—
179#102×C47C2314yes—
180C24×C47—21no—
181C23×D47C2×D411yescharacteristic
182C2×D4×C47—21no—
183C2×D4×C47—22no—
184C2×D4×C47C2×Q814yes—
185C2×D4×C47C2412yes—
186C22×C4×C47—21no—
187C22×C4×C47—21no—
188C22×C4×C47—21no—
189C22×C4×C47—24no—
190C22×C4×C47—82no—
191C22×C4×C47C2×D411yescharacteristic
192C22×C4×C47C2×D411yescharacteristic
193C22×C4×C47C2411yescharacteristic
194C2×C22⋊D47—28no—
195C2×C22⋊D47—24no—
196C22×Dic47—21no—
197C22×Dic47—28no—
198C22×Dic47—24no—
199C22×Dic47—21no—
200C22×Dic47—21no—
201C22×Dic47—21no—
202C22×Dic47—24no—
203C22×Dic47—82no—
204C22×Dic47C2×D411yescharacteristic
205C22×Dic47C2×D411yescharacteristic
206C22×Dic47C2×D411yescharacteristic
207#10625352—216no—
208#10625352—28no—
209#10625352C2×Q8116yescomplemented
210C2×C4×D47—24no—
211C2×C4×D47—24no—
212C2×C4×D47—82no—
213C2×C4×D47—82no—
214C2×C4×D47C2×D412yes—
215C2×C4×D47C2×Q814yes—
216C2×C4×D47#4114yes—
217C2×C4×D47C2412yes—
218C2×Dic94—21no—
219C2×Dic94—22no—
220C2×Dic94—24no—
221C2×Dic94—24no—
222C2×Dic94—82no—
223C2×Dic94—82no—
224C2×Dic94C2×Q814yes—
225C2×Dic94C2412yes—
226C2×C8×C47—22no—
227C2×C8×C47—22no—
228C2×C8×C47C2412yes—
229C2×C8×C47C2412yes—
230C4⋊C4×C47—24no—
231C4⋊C4×C47—24no—
232C4⋊C4×C47—21no—
233C4⋊C4×C47—21no—
234C4⋊C4×C47—21no—
235C4⋊C4×C47C2412yes—
236C4⋊C4×C47C2412yes—
237C4⋊C4×C47C2412yes—
238C22⋊C4×C47—24no—
239C42×C47C2×D412yes—
240C42×C47C2412yes—
241C22⋊Dic47—24no—
242(C2×D47)⋊C4—24no—
243(C2×D47)⋊C4C2×D414yes—
244(C2×D47)⋊C4C2×D414yes—
245C4⋊Dic47—21no—
246C4⋊Dic47—21no—
247C4⋊Dic47—24no—
248C4⋊Dic47—21no—
249C4⋊Dic47—24no—
250C4⋊Dic47C2412yes—
251C4⋊Dic47C2412yes—
252C4⋊Dic47C2412yes—
253Dic47⋊C4—24no—
254Dic47⋊C4—24no—
255Dic47⋊C4—24no—
256Dic47⋊C4—24no—
257Dic47⋊C4—24no—
258Dic47⋊C4—24no—
259Dic47⋊C4C2×D414yes—
260Dic47⋊C4C2×D414yes—
261C4×Dic47—24no—
262C4×Dic47—24no—
263C4×Dic47—24no—
264C4×Dic47C2×D412yes—
265C4×Dic47C2412yes—
266C2×C47⋊C8—22no—
267C2×C47⋊C8—22no—
268C2×C47⋊C8C2412yes—
269C2×C47⋊C8C2412yes—
270#10625324—28no—
271C8×D47—28no—
272C23×C47—24no—
273C23×C47—22no—
274C23×C47—42no—
275C23×C47—42no—
276C23×C47C22×D411yescharacteristic
277C22×D47—22no—
278C22×D47—22no—
279C22×D47C22⋊Q814yes—
280C22×D47C22×D412yes—
281D4×C47—24no—
282D4×C47—22no—
283D4×C47C22×Q814yes—
284C2×C4×C47—22no—
285C2×C4×C47—22no—
286C2×C4×C47—22no—
287C2×C4×C47—22no—
288C2×C4×C47—22no—
289C2×C4×C47—42no—
290C2×C4×C47—42no—
291C2×C4×C47—42no—
292C2×C4×C47—84no—
293C2×C4×C47C22×D412yes—
294C2×C4×C47C22×D412yes—
295C2×C4×C47C22×D411yescharacteristic
296C2×C4×C47C22×Q812yes—
297C2×C4×C47C2×#4112yes—
298C2×C4×C47C2511yescharacteristic
299C22⋊D47—216no—
300C2×Dic47—24no—
301C2×Dic47—22no—
302C2×Dic47—22no—
303C2×Dic47—22no—
304C2×Dic47—216no—
305C2×Dic47—22no—
306C2×Dic47—22no—
307C2×Dic47—22no—
308C2×Dic47—42no—
309C2×Dic47—42no—
310C2×Dic47—42no—
311C2×Dic47—84no—
312C2×Dic47C22⋊Q814yes—
313C2×Dic47C22×D412yes—
314C2×Dic47C22×D412yes—
315C2×Dic47C22×D412yes—
316C4×D47—84no—
317C4×D47—84no—
318C4×D47C22⋊Q818yes—
319C4×D47C22×Q814yes—
320C4×D47C2×#4114yes—
321Dic94—24no—
322Dic94—22no—
323Dic94—84no—
324Dic94—84no—
325Dic94C22×Q814yes—
326C8×C47—22no—
327C8×C47—22no—
328C47⋊C8—22no—
329C47⋊C8—22no—
330C2×#3084—471nomaximal, Sylow
331C22×C47—24no—
332C22×C47—48no—
333C22×C47—42no—
334C22×C47—42no—
335C22×C47C2×C22⋊Q812yes—
336C22×C47#57712yes—
337C22×C47#57712yes—
338C22×C47C23×D411yescharacteristic
339C2×D47—28no—
340C2×D47—22no—
341C2×D47—22no—
342C2×D47C2×C22⋊Q814yes—
343C4×C47—22no—
344C4×C47—22no—
345C4×C47—42no—
346C4×C47—42no—
347C4×C47—42no—
348C4×C47C2×C22⋊Q812yes—
349C4×C47C23×Q811yescharacteristic
350C4×C47C22×#4111yescharacteristic
351Dic47—24no—
352Dic47—22no—
353Dic47—22no—
354Dic47—42no—
355Dic47—42no—
356Dic47—42no—
357Dic47C2×C22⋊Q814yes—
358C2×#544—471no—
359C2×#520—471no—
360#3084—4716no—
361C2×#479—471no—
362C2×#479—471no—
363C2×#475—471no—
364C2×#475—471no—
365C2×#478—471no—
366C2×#478D4711yescharacteristic, complemented
367C2×#476—471no—
368C2×#476—471no—
369C2×#428—471no—
370C22×#106—471no—
371C2×#424—471no—
372C2×#417—471no—
373C2×#416—471no—
374C2×C47—44no—
375C2×C47#308414yescomplemented
376C2×C47C22×C22⋊Q811yescharacteristic
377C2×C47C2×#57711yescharacteristic
378C2×C47C2×#57711yescharacteristic
379D47—24no—
380C22×#41—471no—
381C22×M16—471no—
382C23×C8—471no—
383#544—478no—
384#544—944no—
385C2×C4⋊Q8—471no—
386C2×C4⋊Q8—471no—
387C2×C4⋊Q8—941no—
388C2×#125—471no—
389C2×#125—941no—
390C2×#125C2×D4711yescharacteristic
391C2×C22⋊Q8—941no—
392C2×C22⋊Q8—941no—
393#520—478no—
394#520—944no—
395C2×C4×Q8—471no—
396C2×C4×Q8—471no—
397C2×C4×D4—471no—
398C2×C4×D4—941no—
399C2×C4×D4—941no—
400C2×C4×D4C2×D4711yescharacteristic
401C2×#117—471no—
402C2×#117—471no—
403C2×#117—941no—
404C22×C4⋊C4—471no—
405C22×C4⋊C4—471no—
406C22×C4⋊C4—941no—
407#479—478no—
408#479—478no—
409#478—478no—
410#478C2×D4718yescomplemented
411#476—478no—
412#476—478no—
413#475—478no—
414#475—478no—
415#428—478no—
416C2×#107—471no—
417C2×#107C2×D4711yescharacteristic
418C2×#106—471no—
419C2×#106—471no—
420C2×#106—471no—
421C2×#106—471no—
422C2×#106—471no—
423C2×#106—478no—
424C2×#106C2×D4711yescharacteristic
425#424—478no—
426C2×C4⋊C8—471no—
427C2×C4⋊C8—471no—
428C2×C4⋊C8—471no—
429C2×C4⋊C8C2×D4711yescharacteristic
430#417—478no—
431#416—478no—
432C2×#103—471no—
433C2×#103—471no—
434C2×#103—471no—
435C2×#103—471no—
436C2×#102—471no—
437C2×#102—471no—
438C2×#102C2×D4711yescharacteristic
439C2×#102C2×D4711yescharacteristic
440C47C2×#308411yescharacteristic, complemented, Sylow
441C2×#41—478no—
442C2×#41—474no—
443C2×#41—942no—
444C2×#41—944no—
445C22×Q8—471no—
446C22×Q8—941no—
447C22×Q8—941no—
448C22×D4—941no—
449C22×D4C22×D4711yescharacteristic
450C23×C4—21no—
451C23×C4—471no—
452C23×C4—941no—
453C23×C4—941no—
454C23×C4—941no—
455C23×C4—941no—
456C2×M16—474no—
457C2×M16—944no—
458C22×C8—471no—
459C22×C8—471no—
460C22×C8—474no—
461C22×C8—944no—
462C22×C8C22×D4711yescharacteristic
463C22×C8C22×D4711yescharacteristic
464C4⋊Q8—474no—
465C4⋊Q8—474no—
466C4⋊Q8—942no—
467C4⋊Q8—948no—
468C4⋊Q8—942no—
469#125—22no—
470#125—474no—
471#125—942no—
472#125—948no—
473#125C22×D4714yes—
474C22⋊Q8—948no—
475C22⋊Q8—948no—
476C4×Q8—474no—
477C4×Q8—474no—
478C4×Q8—942no—
479C4×Q8—942no—
480C4×D4—22no—
481C4×D4—474no—
482C4×D4—942no—
483C4×D4—948no—
484C4×D4—948no—
485C4×D4C22×D4714yes—
486#117—474no—
487#117—474no—
488#117—474no—
489#117—948no—
490#117—942no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—471no—
494C2×C4⋊C4—471no—
495C2×C4⋊C4—471no—
496C2×C4⋊C4—471no—
497C2×C4⋊C4—471no—
498C2×C4⋊C4—474no—
499C2×C4⋊C4—474no—
500C2×C4⋊C4—942no—
501C2×C4⋊C4—942no—
502C2×C4⋊C4—948no—
503C2×C4⋊C4—941no—
504C2×C4⋊C4—941no—
505C2×C4⋊C4—941no—
506C2×C4⋊C4—941no—
507C2×C4⋊C4—941no—
508C2×C4⋊C4—941no—
509C2×C4⋊C4—941no—
510C2×C4⋊C4—941no—
511C2×C4⋊C4C22×D4711yescharacteristic
512C2×C4⋊C4C22×D4711yescharacteristic
513C2×C4⋊C4C22×D4711yescharacteristic
514C2×C22⋊C4—21no—
515C2×C22⋊C4—471no—
516C2×C22⋊C4—471no—
517C2×C22⋊C4—941no—
518C2×C22⋊C4—941no—
519C2×C42—471no—
520C2×C42—941no—
521C2×C42—941no—
522C2×C42—941no—
523C2×C42C22×D4711yescharacteristic
524#107—474no—
525#107C22×D4714yes—
526#106—474no—
527#106—474no—
528#106—474no—
529#106—474no—
530#106—474no—
531#106C22×D4714yes—
532C4⋊C8—474no—
533C4⋊C8—474no—
534C4⋊C8—474no—
535C4⋊C8C22×D4714yes—
536#103—474no—
537#103—474no—
538#103—474no—
539#103—474no—
540#102—474no—
541#102—474no—
542#102C22×D4714yes—
543#102C22×D4714yes—
544C24—21no—
545C24—471no—
546#41—4716no—
547#41—9416no—
548#41—948no—
549C2×Q8—474no—
550C2×Q8—472no—
551C2×Q8—944no—
552C2×Q8—941no—
553C2×Q8—944no—
554C2×Q8—942no—
555C2×Q8—3762no—
556C2×Q8—3762no—
557C2×D4—21no—
558C2×D4—22no—
559C2×D4—944no—
560C2×D4—948no—
561C2×D4Q8×D4714yes—
562C2×D4C23×D4712yes—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—24no—
567C22×C4—82no—
568C22×C4—471no—
569C22×C4—472no—
570C22×C4—474no—
571C22×C4—474no—
572C22×C4—472no—
573C22×C4—471no—
574C22×C4—471no—
575C22×C4—944no—
576C22×C4—944no—
577C22×C4—944no—
578C22×C4—948no—
579C22×C4—944no—
580C22×C4—941no—
581C22×C4—941no—
582C22×C4—941no—
583C22×C4—941no—
584C22×C4—3762no—
585C22×C4—3762no—
586C22×C4—3762no—
587C22×C4D4×D4711yescharacteristic
588C22×C4D4×D4711yescharacteristic
589C22×C4C23×D4711yescharacteristic
590M16—948no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—472no—
594C2×C8—472no—
595C2×C8—948no—
596C2×C8—942no—
597C2×C8—942no—
598C2×C8C23×D4712yes—
599C2×C8C23×D4712yes—
600C4⋊C4—24no—
601C4⋊C4—24no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—474no—
606C4⋊C4—474no—
607C4⋊C4—472no—
608C4⋊C4—472no—
609C4⋊C4—472no—
610C4⋊C4—944no—
611C4⋊C4—944no—
612C4⋊C4—944no—
613C4⋊C4—944no—
614C4⋊C4—944no—
615C4⋊C4—944no—
616C4⋊C4—944no—
617C4⋊C4—941no—
618C4⋊C4—941no—
619C4⋊C4—941no—
620C4⋊C4—944no—
621C4⋊C4C23×D4712yes—
622C4⋊C4C23×D4712yes—
623C4⋊C4C23×D4712yes—
624C22⋊C4—24no—
625C22⋊C4—474no—
626C22⋊C4—474no—
627C22⋊C4—944no—
628C22⋊C4—944no—
629C42—472no—
630C42—472no—
631C42—944no—
632C42—944no—
633C42—944no—
634C42D4×D4712yes—
635C42C23×D4712yes—
636C23—24no—
637C23—22no—
638C23—42no—
639C23—42no—
640C23—474no—
641C23—472no—
642C23—942no—
643C23—942no—
644C23C2×D4×D4711yescharacteristic
645Q8—474no—
646Q8—944no—
647Q8—942no—
648Q8—3764no—
649Q8—3764no—
650D4—24no—
651D4—22no—
652D4—9416no—
653D4C2×Q8×D4714yes—
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—474no—
664C2×C4—472no—
665C2×C4—478no—
666C2×C4—474no—
667C2×C4—474no—
668C2×C4—472no—
669C2×C4—472no—
670C2×C4—9416no—
671C2×C4—944no—
672C2×C4—942no—
673C2×C4—942no—
674C2×C4—942no—
675C2×C4—942no—
676C2×C4—942no—
677C2×C4—942no—
678C2×C4—3764no—
679C2×C4—3764no—
680C2×C4—3764no—
681C2×C4—1882no—
682C2×C4—1882no—
683C2×C4—1882no—
684C2×C4C2×D4×D4712yes—
685C2×C4C2×D4×D4712yes—
686C2×C4C2×D4×D4711yescharacteristic
687C2×C4C2×Q8×D4712yes—
688C2×C4#41×D4712yes—
689C2×C4C24×D4711yescharacteristic
690C8—22no—
691C8—22no—
692C8—942no—
693C8—942no—
694C22—24no—
695C22—48no—
696C22—42no—
697C22—42no—
698C22—474no—
699C22—948no—
700C22—942no—
701C22—942no—
702C22C22⋊Q8×D4712yes—
703C22#1568993012yes—
704C22#1568993312yes—
705C22C22×D4×D4711yescharacteristic
706C4—22no—
707C4—22no—
708C4—42no—
709C4—42no—
710C4—42no—
711C4—474no—
712C4—942no—
713C4—942no—
714C4—944no—
715C4—1882no—
716C4—1882no—
717C4—1882no—
718C4C22⋊Q8×D4712yes—
719C4C22×Q8×D4711yescharacteristic
720C4C2×#41×D4711yescharacteristic
721C2—44no—
722C2—944no—
723C2#2025325114yesdirect product factor
724C2C2×C22⋊Q8×D4711yescharacteristic
725C2C2×#1568993011yescharacteristic
726C2C2×#1568993311yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#478C2
socleC23×C47C22×D4
prime radicalC22×#10625352C22
hypercenterC2×#478D47
hypocenterC47C2×#3084
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#15689753C2semidirect
3. #20253251C2direct (N × H)
4. C2×#15689429C2semidirect
5. C2×#15689427C2semidirect
6. C2×#15689409C2semidirect
7. C2×#15689407C2semidirect
8. C2×#15689425C2semidirect
9. C2×#15689413C2semidirect
10. C2×#15689411C2semidirect
11. C2×#15689164C2semidirect
12. C2×#106×D47C2semidirect
13. C2×#15689148C2semidirect
16. C2×C47×#478C2semidirect
21. #15689753C22semidirect
42. #15689429C22semidirect
43. #15689427C22semidirect
44. #15689425C22semidirect
45. #15689413C22semidirect
46. #15689411C22semidirect
47. #15689409C22semidirect
48. #15689407C22semidirect
49. #15689164C22semidirect
56. #106×D47C22semidirect
57. #15689148C22semidirect
71. C47×#478C22semidirect
79. C2×#10625352Q8semidirect
209. #10625352C2×Q8semidirect
366. C2×#478D47semidirect
375. C2×C47#3084semidirect
410. #478C2×D47semidirect
440. C47C2×#3084semidirect
723. C2#20253251direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897532
C2×#156896022
#202532512
C2×#156894292
C2×#156894272
C2×#156894092
C2×#156894072
C2×#156894252
C2×#156894132
C2×#156894112
C2×#156891642
C2×#106×D472
C2×#156891482
C2×#156891212
C2×#156891162
C2×C47×#4782
C2×#308447