Finite Group Databasebeta

← C2×#20257054 #27124585

Subgroups — C2×#20257054 #27124585

Order 12032.

12366 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094070C211yesmaximal, characteristic, complemented
2C23×#10625354C211yesmaximal, characteristic, complemented
3#20257054C2132yesmaximal, direct product factor
4C2×#15689795C211yesmaximal, characteristic, complemented
5C2×#15689792C211yesmaximal, characteristic, complemented
6C2×#15689784C211yesmaximal, characteristic, complemented
7C2×#15689766C213yesmaximal, complemented
8C2×#15689764C213yesmaximal, complemented
9C2×D4×D188C213yesmaximal, complemented
10C2×#15689757C213yesmaximal, complemented
11C2×#15689703C213yesmaximal, complemented
12C2×#15689691C213yesmaximal, complemented
13C2×#15689632C213yesmaximal, complemented
14C2×#121×D47C213yesmaximal, complemented
15C2×#15689605C211yesmaximal, characteristic, complemented
16C2×C47×#548C211yesmaximal, characteristic, complemented
17C2×#13094070—216no—
18C2×#13094070C22116yescomplemented
19C22×#10625354—216no—
20C22×#10625354C2211yescharacteristic
21C22×#10625354C2213yescomplemented
22C22×#10625354C2211yescharacteristic, complemented
23C22×#10625354C2211yescharacteristic, complemented
24C22×#10625354C2213yescomplemented
25C22×#10625354C22116yescomplemented
26C22×#10625350C2213yescomplemented
27C23×D188C2213yescomplemented
28C23×D188C2213yescomplemented
29C22×D4×D47C2213yescomplemented
30C22×D4×D47C2213yescomplemented
31C22×D4×D47C2216yescomplemented
32C23×C4×D47C2213yescomplemented
33#15689795C22116yescomplemented
34#15689792C22116yescomplemented
35#15689784C22116yescomplemented
36#15689766C22148yescomplemented
37#15689764C22148yescomplemented
38D4×D188C22148yescomplemented
39#15689757C22148yescomplemented
40#15689703C22148yescomplemented
41#15689691C22148yescomplemented
42C2×#13094021C2213yescomplemented
43C2×#13094020C2213yescomplemented
44C2×#13094013C2213yescomplemented
45#15689632C22148yescomplemented
46C2×#13094009C2213yescomplemented
47C2×#13094006C2213yescomplemented
48C2×#13094002C2213yescomplemented
49C2×#13094001C2211yescharacteristic, complemented
50C2×#13094000C2213yescomplemented
51C2×#13093999C2213yescomplemented
52C2×#13093999C2216yescomplemented
53C2×#13093999C2213yescomplemented
54C2×#13093998C2213yescomplemented
55C2×#13093998C2213yescomplemented
56C2×#13093997C2216yescomplemented
57C2×#13093997C2216yescomplemented
58C2×#13093997C2213yescomplemented
59C2×#13093996C2213yescomplemented
60C2×#13093995C2213yescomplemented
61#121×D47C22148yescomplemented
62C2×#13093994C2216yescomplemented
63C2×#13093994C2213yescomplemented
64C2×#13093994C2216yescomplemented
65C2×#13093992C2213yescomplemented
66#15689605C22116yescomplemented
67C2×Q8×Dic47C2211yescharacteristic, complemented
68C2×C4×D188C2213yescomplemented
69C2×C4×D188C2213yescomplemented
70C2×#13093986C2213yescomplemented
71C2×C4×C22⋊D47C2213yescomplemented
72C2×C4×C22⋊D47C2213yescomplemented
73C2×#13093981C2213yescomplemented
74C2×C4⋊C4×D47C2213yescomplemented
75C2×C22⋊C4×D47C2216yescomplemented
76C22×#41×C47C2211yescharacteristic, complemented
77C23×Q8×C47C2211yescharacteristic, complemented
78C47×#548C22116yescomplemented
79C2×#124×C47C2213yescomplemented
80C2×C22⋊Q8×C47C2213yescomplemented
81C2×#121×C47C2213yescomplemented
82C2×C4×Q8×C47C2211yescharacteristic, complemented
83C2×C4×D4×C47C2213yescomplemented
84C24×D47C2313yes—
85C24×D47C2316yes—
86#13094070—2128no—
87C2×#10625354—28no—
88C2×#10625354—28no—
89C2×#10625354—2128no—
90C2×#10625354—224no—
91C2×#10625354—224no—
92C2×#10625354D4116yescomplemented
93C2×#10625354C2318yes—
94C2×#10625354C23124yescomplemented
95C2×#10625354C2318yescomplemented
96C2×#10625354C2318yescomplemented
97C2×#10625354C23124yescomplemented
98C2×#10625350—224no—
99C2×#10625350C23124yescomplemented
100C22×Dic94C2311yescharacteristic
101C22×D188—224no—
102C22×D188—224no—
103C22×D188C2316yes—
104C22×D188C2313yes—
105C22×D188C2313yes—
106C22×D188C2313yes—
107C22×D188C2313yes—
108C22×D188C2316yes—
109C22×D188C2313yes—
110C22×D188C23124yescomplemented
111C22×D188C23124yescomplemented
112C22×C22⋊D47C2313yes—
113C22×C22⋊D47C2313yes—
114C22×C22⋊D47C2313yes—
115C22×C22⋊D47C2313yes—
116C22×C22⋊D47C2316yes—
117C2×D4×D47—224no—
118C2×D4×D47—224no—
119C2×D4×D47—424no—
120C2×D4×D47C23124yescomplemented
121C2×D4×D47C23124yescomplemented
122C2×D4×D47C23148yescomplemented
123C23×Dic47C2311yescharacteristic
124C22×C4×D47—224no—
125C22×C4×D47C2313yes—
126C22×C4×D47C2313yes—
127C22×C4×D47C2313yes—
128C22×C4×D47C2313yes—
129C22×C4×D47C2316yes—
130C22×C4×D47C2313yes—
131C22×C4×D47C23124yescomplemented
132#13094021C23124yescomplemented
133#13094020C23124yescomplemented
134#13094013C23124yescomplemented
135#13094009C23124yescomplemented
136#13094006C23124yescomplemented
137#13094002C23124yescomplemented
138#13094001C2318yescomplemented
139#13094000C23124yescomplemented
140#13093999C23124yescomplemented
141#13093999C23148yescomplemented
142#13093999C23124yescomplemented
143#13093998C23124yescomplemented
144#13093998C23124yescomplemented
145#13093997C23148yescomplemented
146#13093997C23148yescomplemented
147#13093997C23124yescomplemented
148#13093996C23124yescomplemented
149#13093995C23124yescomplemented
150#13093994C23148yescomplemented
151#13093994C23124yescomplemented
152#13093994C23148yescomplemented
153#13093992C23124yescomplemented
154Q8×Dic47C2318yescomplemented
155C4×D188C23124yescomplemented
156C4×D188C23124yescomplemented
157#13093986C23124yescomplemented
158C4×C22⋊D47C23124yescomplemented
159C4×C22⋊D47C23124yescomplemented
160#13093981C23124yescomplemented
161C2×C4⋊Dic47C2313yes—
162C2×C4⋊Dic47C2311yescharacteristic
163C2×Dic47⋊C4C2313yes—
164C2×Dic47⋊C4C2311yescharacteristic
165C2×Dic47⋊C4C2311yescharacteristic
166C2×Dic47⋊C4C2313yes—
167C4⋊C4×D47C23124yescomplemented
168C2×C22⋊Dic47C2313yes—
169C2×C22⋊Dic47C2311yescharacteristic
170C2×(C2×D47)⋊C4C2313yes—
171C2×(C2×D47)⋊C4C2316yes—
172C2×(C2×D47)⋊C4C2313yes—
173C2×(C2×D47)⋊C4C2313yes—
174C2×(C2×D47)⋊C4C2313yes—
175C2×(C2×D47)⋊C4C2313yes—
176C2×(C2×D47)⋊C4C2313yes—
177C22⋊C4×D47C23148yescomplemented
178C2×C4×Dic47C2313yes—
179C2×#41×C47—28no—
180C2×#41×C47C2318yescomplemented
181C22×Q8×C47—28no—
182C22×Q8×C47C2313yes—
183C22×Q8×C47C2311yescharacteristic
184C22×Q8×C47C2318yescomplemented
185C22×D4×C47C2313yes—
186C22×D4×C47C2313yes—
187C23×C4×C47C2313yes—
188C23×C4×C47C2313yes—
189#124×C47C23124yescomplemented
190C22⋊Q8×C47C23124yescomplemented
191#121×C47C23124yescomplemented
192C4×Q8×C47C2318yescomplemented
193C4×D4×C47C23124yescomplemented
194C2×C4⋊C4×C47C2313yes—
195C2×C4⋊C4×C47C2313yes—
196C2×C22⋊C4×C47C2311yescharacteristic
197C2×C22⋊C4×C47C2313yes—
198C2×C22⋊C4×C47C2316yes—
199C2×C42×C47C2313yes—
200C24×C47C2413yes—
201C24×C47C2411yescharacteristic
202C23×D47—212no—
203C23×D47—212no—
204C23×D47—224no—
205C23×D47—46no—
206C23×D47—412no—
207C23×D47—412no—
208C23×D47C2413yes—
209C23×D47C2413yes—
210C23×D47C24112yes—
211C23×D47C2413yes—
212C23×D47C24124yes—
213#41×C47—232no—
214C2×Q8×C47—232no—
215C2×Q8×C47—212no—
216C2×Q8×C47C2×D418yescomplemented
217C2×Q8×C47C24112yes—
218C2×Q8×C47C2414yes—
219C2×D4×C47—212no—
220C2×D4×C47—212no—
221C2×D4×C47C24112yes—
222C2×D4×C47C24112yes—
223C22×C4×C47—212no—
224C22×C4×C47—212no—
225C22×C4×C47C2411yescharacteristic
226C22×C4×C47C2413yes—
227C22×C4×C47C2413yes—
228C22×C4×C47C2411yescharacteristic
229C22×C4×C47C24112yes—
230C22×C4×C47C24112yes—
231C22×C4×C47C2413yes—
232C2×C22⋊D47—212no—
233C2×C22⋊D47—212no—
234C2×C22⋊D47—212no—
235C2×C22⋊D47—412no—
236C2×C22⋊D47—46no—
237C2×C22⋊D47C24112yes—
238C2×C22⋊D47C24112yes—
239C2×C22⋊D47C24112yes—
240C2×C22⋊D47C24112yes—
241C2×C22⋊D47C24124yes—
242C22×Dic47—24no—
243C22×Dic47C2411yescharacteristic
244C22×Dic47C2413yes—
245C22×Dic47C2411yescharacteristic
246C22×Dic47C2411yescharacteristic
247C22×Dic47C2414yes—
248C22×Dic47C2411yescharacteristic
249#10625354—232no—
250#10625354—232no—
251#10625354—296no—
252#10625354—296no—
253#10625354C2×D4164yescomplemented
254D4×D47—296no—
255D4×D47—296no—
256D4×D47—496no—
257#10625350—296no—
258C2×D188—212no—
259C2×D188—224no—
260C2×D188—212no—
261C2×D188—212no—
262C2×D188—296no—
263C2×D188—296no—
264C2×D188—412no—
265C2×D188—46no—
266C2×D188C2×D4124yescomplemented
267C2×D188C24124yes—
268C2×D188C24112yes—
269C2×D188C24112yes—
270C2×D188C24112yes—
271C2×D188C24112yes—
272C2×D188C24124yes—
273C2×D188C24112yes—
274C2×C4×D47—212no—
275C2×C4×D47—212no—
276C2×C4×D47—212no—
277C2×C4×D47—212no—
278C2×C4×D47—296no—
279C2×C4×D47—412no—
280C2×C4×D47C2×D4124yescomplemented
281C2×C4×D47C24112yes—
282C2×C4×D47C24112yes—
283C2×C4×D47C24112yes—
284C2×C4×D47C24112yes—
285C2×C4×D47C24124yes—
286C2×C4×D47C24112yes—
287C2×Dic94—24no—
288C2×Dic94C2414yes—
289C4⋊C4×C47C24112yes—
290C4⋊C4×C47C24112yes—
291C22⋊C4×C47C2414yes—
292C22⋊C4×C47C24112yes—
293C22⋊C4×C47C24124yes—
294C42×C47C24112yes—
295C22⋊Dic47C24112yes—
296C22⋊Dic47C2414yes—
297(C2×D47)⋊C4C24112yes—
298(C2×D47)⋊C4C24124yes—
299(C2×D47)⋊C4C24112yes—
300(C2×D47)⋊C4C24112yes—
301(C2×D47)⋊C4C24112yes—
302(C2×D47)⋊C4C24112yes—
303(C2×D47)⋊C4C24112yes—
304C4⋊Dic47C24112yes—
305C4⋊Dic47C2414yes—
306Dic47⋊C4C24112yes—
307Dic47⋊C4C2414yes—
308Dic47⋊C4C2414yes—
309Dic47⋊C4C24112yes—
310C4×Dic47C24112yes—
311C23×C47—22no—
312C23×C47—22no—
313C23×C47—26no—
314C23×C47—26no—
315C23×C47—26no—
316C23×C47H(5,𝔽2)14yescomplemented
317C23×C47C2516yes—
318C23×C47C2512yes—
319C23×C47C2511yescharacteristic
320C22×D47—26no—
321C22×D47—26no—
322C22×D47—26no—
323C22×D47—26no—
324C22×D47—26no—
325C22×D47—26no—
326C22×D47—224no—
327C22×D47—26no—
328C22×D47—26no—
329C22×D47—224no—
330C22×D47—248no—
331C22×D47—412no—
332C22×D47—424no—
333C22×D47—424no—
334C22×D47—448no—
335C22×D47—848no—
336C22×D47C22×D4112yes—
337C22×D47C2516yes—
338C22×D47C2516yes—
339C22×D47C2516yes—
340Q8×C47—224no—
341Q8×C47C22×D4116yescomplemented
342D4×C47—224no—
343D4×C47—224no—
344C2×C4×C47—22no—
345C2×C4×C47—26no—
346C2×C4×C47—26no—
347C2×C4×C47—22no—
348C2×C4×C47—224no—
349C2×C4×C47—224no—
350C2×C4×C47C22×D4112yes—
351C2×C4×C47C2512yes—
352C2×C4×C47C2516yes—
353C2×C4×C47C2516yes—
354C2×C4×C47C2512yes—
355C2×C4×C47C2516yes—
356C22⋊D47—224no—
357C22⋊D47—224no—
358C22⋊D47—224no—
359C22⋊D47—424no—
360C22⋊D47—412no—
361C2×Dic47—22no—
362C2×Dic47—22no—
363C2×Dic47—26no—
364C2×Dic47—22no—
365C2×Dic47—28no—
366C2×Dic47C22×D414yes—
367C2×Dic47C2512yes—
368C2×Dic47C2516yes—
369C2×Dic47C2512yes—
370C2×Dic47C2512yes—
371C2×Dic47C2512yes—
372D188—224no—
373D188—248no—
374D188—224no—
375D188—224no—
376D188—412no—
377D188—424no—
378D188C22×D4148yescomplemented
379C4×D47—224no—
380C4×D47—224no—
381C4×D47—224no—
382C4×D47—224no—
383C4×D47—424no—
384C4×D47C22×D4148yescomplemented
385Dic94—28no—
386C2×#3488—471nomaximal, Sylow
387C22×C47—22no—
388C22×C47—22no—
389C22×C47—28no—
390C22×C47—26no—
391C22×C47—26no—
392C22×C47—26no—
393C22×C47—412no—
394C22×C47C23×D412yes—
395C22×C47C2×H(5,𝔽2)12yes—
396C22×C47C2×H(5,𝔽2)14yescomplemented
397C22×C47#58512yes—
398C22×C47C2611yescharacteristic
399C2×D47—26no—
400C2×D47—26no—
401C2×D47—224no—
402C2×D47—26no—
403C2×D47—26no—
404C2×D47—26no—
405C2×D47—26no—
406C2×D47—26no—
407C2×D47—26no—
408C2×D47—448no—
409C2×D47—412no—
410C2×D47—412no—
411C2×D47—848no—
412C2×D47C23×D4112yes—
413C4×C47—22no—
414C4×C47—26no—
415C4×C47—26no—
416C4×C47—22no—
417C4×C47C23×D4112yes—
418Dic47—22no—
419Dic47—22no—
420Dic47—26no—
421Dic47—22no—
422Dic47C23×D414yes—
423C22×H(5,𝔽2)—471no—
424C23×#41—471no—
425#3488—4732no—
426C2×#550—471no—
427C2×#550—471no—
428C2×#548—471no—
429C2×#548D4711yescharacteristic, complemented
430C2×#546—473no—
431C2×#546—473no—
432C2×D42—473no—
433C2×D42—473no—
434C2×#537—473no—
435C2×#535—473no—
436C2×#525—473no—
437C22×#121—473no—
438C2×#520—471no—
439C2×C47—24no—
440C2×C47—46no—
441C2×C47#348814yescomplemented
442C2×C47C24×D411yescharacteristic
443C2×C47C22×H(5,𝔽2)11yescharacteristic
444C2×C47C2×#58511yescharacteristic
445D47—212no—
446D47—46no—
447D47—46no—
448C2×H(5,𝔽2)—4716no—
449C2×H(5,𝔽2)—9416no—
450C22×#41—471no—
451C22×#41—473no—
452C22×#41—473no—
453C22×#41—471no—
454C22×#41—471no—
455C22×#41—4716no—
456C22×#41—473no—
457C22×#41—9416no—
458C22×#41C2×D4711yescharacteristic, complemented
459C23×Q8C2×D4711yescharacteristic, complemented
460C23×D4—473no—
461C23×D4—473no—
462C23×D4—476no—
463C23×D4—473no—
464C23×D4—473no—
465C24×C4—473no—
466#550—4716no—
467#550—4716no—
468#548—4716no—
469#548C2×D47116yescomplemented
470#546—4748no—
471#546—4748no—
472D42—4748no—
473D42—4748no—
474#537—4748no—
475#535—4748no—
476C2×#127—473no—
477C2×#127—473no—
478C2×#124—473no—
479C2×#124C2×D4713yescomplemented
480#525—4748no—
481C2×#123—473no—
482C2×#123—473no—
483C2×C22⋊Q8—473no—
484C2×C22⋊Q8—473no—
485C2×C22⋊Q8—471no—
486C2×C22⋊Q8C2×D4713yescomplemented
487C2×#121—473no—
488C2×#121—473no—
489C2×#121—473no—
490C2×#121—473no—
491C2×#121—4748no—
492C2×#121—473no—
493C2×#121—476no—
494C2×#121—473no—
495C2×#121—476no—
496C2×#121—473no—
497C2×#121—476no—
498C2×#121C2×D4713yescomplemented
499C2×#120—473no—
500C2×#120—473no—
501C2×#120—476no—
502C2×#120—476no—
503#520—4716no—
504C2×C4×Q8—471no—
505C2×C4×Q8C2×D4711yescharacteristic, complemented
506C2×C4×D4—473no—
507C2×C4×D4—473no—
508C2×C4×D4—473no—
509C2×C4×D4—473no—
510C2×C4×D4—473no—
511C2×C4×D4C2×D4713yescomplemented
512C2×#117—473no—
513C22×C4⋊C4—473no—
514C22×C22⋊C4—476no—
515C47C2×#348811yescharacteristic, complemented, Sylow
516C25—473no—
517C25—476no—
518H(5,𝔽2)—94128no—
519C2×#41—28no—
520C2×#41—4716no—
521C2×#41—478no—
522C2×#41—4724no—
523C2×#41—4724no—
524C2×#41—478no—
525C2×#41—478no—
526C2×#41—4724no—
527C2×#41—9424no—
528C2×#41—9424no—
529C2×#41—9424no—
530C2×#41—94128no—
531C2×#41—948no—
532C2×#41—948no—
533C2×#41C22×D4718yescomplemented
534C22×Q8—28no—
535C22×Q8—471no—
536C22×Q8C22×D4713yes—
537C22×Q8C22×D4711yescharacteristic
538C22×Q8C22×D4718yescomplemented
539C22×D4—473no—
540C22×D4—473no—
541C22×D4—473no—
542C22×D4—473no—
543C22×D4—476no—
544C22×D4—4724no—
545C22×D4—4724no—
546C22×D4—4748no—
547C22×D4—473no—
548C22×D4—476no—
549C22×D4—473no—
550C22×D4—473no—
551C22×D4—473no—
552C22×D4—4724no—
553C22×D4—4724no—
554C22×D4—473no—
555C22×D4—476no—
556C22×D4—9424no—
557C22×D4—9424no—
558C22×D4—9424no—
559C22×D4—9424no—
560C22×D4—18824no—
561C22×D4C22×D4713yes—
562C22×D4C22×D4713yes—
563C23×C4—473no—
564C23×C4—471no—
565C23×C4—473no—
566C23×C4—473no—
567C23×C4—473no—
568C23×C4—473no—
569C23×C4—4724no—
570C23×C4—476no—
571C23×C4—9424no—
572C23×C4C22×D4713yes—
573C23×C4C22×D4713yes—
574#127—4724no—
575#127—4724no—
576#124—4724no—
577#124C22×D47124yescomplemented
578#123—4724no—
579#123—4724no—
580C22⋊Q8—4724no—
581C22⋊Q8—4724no—
582C22⋊Q8—478no—
583C22⋊Q8C22×D47124yescomplemented
584#121—4724no—
585#121—4724no—
586#121—4724no—
587#121—4724no—
588#121—4724no—
589#121—4748no—
590#121—4724no—
591#121—4748no—
592#121—4724no—
593#121—4748no—
594#121C22×D47124yescomplemented
595#120—4724no—
596#120—4724no—
597#120—4748no—
598#120—4748no—
599C4×Q8—478no—
600C4×Q8C22×D4718yescomplemented
601C4×D4—4724no—
602C4×D4—4724no—
603C4×D4—4724no—
604C4×D4—4724no—
605C4×D4—4724no—
606C4×D4C22×D47124yescomplemented
607#117—4724no—
608C2×C4⋊C4—473no—
609C2×C4⋊C4—473no—
610C2×C4⋊C4—471no—
611C2×C4⋊C4—471no—
612C2×C4⋊C4—471no—
613C2×C4⋊C4—473no—
614C2×C4⋊C4—4724no—
615C2×C4⋊C4C22×D4713yes—
616C2×C4⋊C4C22×D4713yes—
617C2×C22⋊C4—473no—
618C2×C22⋊C4—471no—
619C2×C22⋊C4—473no—
620C2×C22⋊C4—476no—
621C2×C22⋊C4—473no—
622C2×C22⋊C4—473no—
623C2×C22⋊C4—473no—
624C2×C22⋊C4—473no—
625C2×C22⋊C4—473no—
626C2×C22⋊C4—4748no—
627C2×C22⋊C4C22×D4716yes—
628C2×C22⋊C4C22×D4711yescharacteristic
629C2×C22⋊C4C22×D4713yes—
630C2×C42—473no—
631C2×C42C22×D4713yes—
632C24—473no—
633C24—473no—
634C24—473no—
635C24—4712no—
636C24—4724no—
637C24—9424no—
638C24—9412no—
639C24—9412no—
640C24—18812no—
641C24—18812no—
642C24—1886no—
643C24C23×D4713yes—
644C24C23×D4711yescharacteristic
645#41—232no—
646#41—4764no—
647#41—9496no—
648#41—9496no—
649#41—9496no—
650#41—9432no—
651#41—9432no—
652C2×Q8—232no—
653C2×Q8—212no—
654C2×Q8—474no—
655C2×Q8—944no—
656C2×Q8D4×D4718yescomplemented
657C2×Q8C23×D47112yes—
658C2×Q8C23×D4714yes—
659C2×D4—212no—
660C2×D4—212no—
661C2×D4—4712no—
662C2×D4—4712no—
663C2×D4—4712no—
664C2×D4—4712no—
665C2×D4—4724no—
666C2×D4—4724no—
667C2×D4—4712no—
668C2×D4—4724no—
669C2×D4—4712no—
670C2×D4—4712no—
671C2×D4—4712no—
672C2×D4—4712no—
673C2×D4—4724no—
674C2×D4—9496no—
675C2×D4—9496no—
676C2×D4—9412no—
677C2×D4—9424no—
678C2×D4—9496no—
679C2×D4—9412no—
680C2×D4—9496no—
681C2×D4—9412no—
682C2×D4—9412no—
683C2×D4—9412no—
684C2×D4—9412no—
685C2×D4—1886no—
686C2×D4—18812no—
687C2×D4—1886no—
688C2×D4—18812no—
689C2×D4—18896no—
690C2×D4C23×D47112yes—
691C2×D4C23×D47112yes—
692C22×C4—212no—
693C22×C4—212no—
694C22×C4—471no—
695C22×C4—4724no—
696C22×C4—4712no—
697C22×C4—474no—
698C22×C4—471no—
699C22×C4—473no—
700C22×C4—471no—
701C22×C4—471no—
702C22×C4—4712no—
703C22×C4—4712no—
704C22×C4—4712no—
705C22×C4—4712no—
706C22×C4—4724no—
707C22×C4—9412no—
708C22×C4—9496no—
709C22×C4—9412no—
710C22×C4—944no—
711C22×C4—9412no—
712C22×C4—9412no—
713C22×C4—18812no—
714C22×C4C23×D47112yes—
715C22×C4C23×D47112yes—
716C22×C4C23×D4711yescharacteristic
717C22×C4C23×D4713yes—
718C22×C4C23×D4713yes—
719C22×C4C23×D4711yescharacteristic
720C22×C4C23×D4713yes—
721C4⋊C4—4712no—
722C4⋊C4—474no—
723C4⋊C4—474no—
724C4⋊C4—4712no—
725C4⋊C4—4712no—
726C4⋊C4—474no—
727C4⋊C4C23×D47112yes—
728C4⋊C4C23×D47112yes—
729C22⋊C4—4712no—
730C22⋊C4—474no—
731C22⋊C4—4712no—
732C22⋊C4—4724no—
733C22⋊C4—4712no—
734C22⋊C4—4712no—
735C22⋊C4—4712no—
736C22⋊C4—4712no—
737C22⋊C4—4712no—
738C22⋊C4C23×D47124yes—
739C22⋊C4C23×D4714yes—
740C22⋊C4C23×D47112yes—
741C42—4712no—
742C42C23×D47112yes—
743C23—22no—
744C23—22no—
745C23—26no—
746C23—26no—
747C23—26no—
748C23—4712no—
749C23—476no—
750C23—476no—
751C23—476no—
752C23—9448no—
753C23—9424no—
754C23—946no—
755C23—946no—
756C23—946no—
757C23—946no—
758C23—946no—
759C23—946no—
760C23—9424no—
761C23—946no—
762C23—946no—
763C23—37648no—
764C23—18824no—
765C23—18824no—
766C23—18812no—
767C23—18848no—
768C23#1309407014yescomplemented
769C23C24×D4716yes—
770C23C24×D4712yes—
771C23C24×D4711yescharacteristic
772Q8—224no—
773Q8—948no—
774Q8C2×D4×D47116yescomplemented
775D4—224no—
776D4—224no—
777D4—4748no—
778D4—9424no—
779D4—9448no—
780D4—9424no—
781D4—9424no—
782D4—9424no—
783D4—9424no—
784D4—9424no—
785D4—18812no—
786D4—18824no—
787D4—18812no—
788D4—18824no—
789C2×C4—22no—
790C2×C4—26no—
791C2×C4—26no—
792C2×C4—22no—
793C2×C4—224no—
794C2×C4—224no—
795C2×C4—474no—
796C2×C4—472no—
797C2×C4—4748no—
798C2×C4—472no—
799C2×C4—476no—
800C2×C4—472no—
801C2×C4—472no—
802C2×C4—9424no—
803C2×C4—9424no—
804C2×C4—948no—
805C2×C4—942no—
806C2×C4—942no—
807C2×C4—946no—
808C2×C4—942no—
809C2×C4—9424no—
810C2×C4—9424no—
811C2×C4—18824no—
812C2×C4C2×D4×D47112yes—
813C2×C4C24×D4712yes—
814C2×C4C24×D4716yes—
815C2×C4C24×D4716yes—
816C2×C4C24×D4712yes—
817C2×C4C24×D4716yes—
818C22—28no—
819C22—22no—
820C22—22no—
821C22—26no—
822C22—26no—
823C22—26no—
824C22—412no—
825C22—4712no—
826C22—9424no—
827C22—946no—
828C22—946no—
829C22—946no—
830C22—946no—
831C22—946no—
832C22—946no—
833C22—946no—
834C22—946no—
835C22—37648no—
836C22—18848no—
837C22—18812no—
838C22—18812no—
839C22C22×D4×D4712yes—
840C22C2×#1309407012yes—
841C22C2×#1309407014yescomplemented
842C22#1568996012yes—
843C22C25×D4711yescharacteristic
844C4—22no—
845C4—26no—
846C4—26no—
847C4—22no—
848C4—474no—
849C4—942no—
850C4—942no—
851C4—946no—
852C4—942no—
853C4C22×D4×D47112yes—
854C2—24no—
855C2—46no—
856C2—9412no—
857C2—1886no—
858C2—1886no—
859C2#2025705414yesdirect product factor
860C2C23×D4×D4711yescharacteristic
861C2C22×#1309407011yescharacteristic
862C2C2×#1568996011yescharacteristic
subgroupG/H
centerC23C24×D47
commutator, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC2×C47×#548C2
socleC23×C47C25
hypercenterC2×#548D47
hypocenterC47C2×#3488
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C22×#13094070C2semidirect
2. C23×#10625354C2semidirect
3. #20257054C2direct (N × H)
4. C2×#15689795C2semidirect
5. C2×#15689792C2semidirect
6. C2×#15689784C2semidirect
7. C2×#15689766C2semidirect
8. C2×#15689764C2semidirect
9. C2×D4×D188C2semidirect
10. C2×#15689757C2semidirect
11. C2×#15689703C2semidirect
12. C2×#15689691C2semidirect
13. C2×#15689632C2semidirect
14. C2×#121×D47C2semidirect
15. C2×#15689605C2semidirect
16. C2×C47×#548C2semidirect
18. C2×#13094070C22semidirect
21. C22×#10625354C22semidirect
22. C22×#10625354C22semidirect
23. C22×#10625354C22semidirect
24. C22×#10625354C22semidirect
25. C22×#10625354C22semidirect
26. C22×#10625350C22semidirect
27. C23×D188C22semidirect
28. C23×D188C22semidirect
29. C22×D4×D47C22semidirect
30. C22×D4×D47C22semidirect
31. C22×D4×D47C22semidirect
32. C23×C4×D47C22semidirect
33. #15689795C22semidirect
34. #15689792C22semidirect
35. #15689784C22semidirect
36. #15689766C22semidirect
37. #15689764C22semidirect
38. D4×D188C22semidirect
39. #15689757C22semidirect
40. #15689703C22semidirect
41. #15689691C22semidirect
42. C2×#13094021C22semidirect
43. C2×#13094020C22semidirect
44. C2×#13094013C22semidirect
45. #15689632C22semidirect
46. C2×#13094009C22semidirect
47. C2×#13094006C22semidirect
48. C2×#13094002C22semidirect
49. C2×#13094001C22semidirect
50. C2×#13094000C22semidirect
51. C2×#13093999C22semidirect
52. C2×#13093999C22semidirect
53. C2×#13093999C22semidirect
54. C2×#13093998C22semidirect
55. C2×#13093998C22semidirect
56. C2×#13093997C22semidirect
57. C2×#13093997C22semidirect
58. C2×#13093997C22semidirect
59. C2×#13093996C22semidirect
60. C2×#13093995C22semidirect
61. #121×D47C22semidirect
62. C2×#13093994C22semidirect
63. C2×#13093994C22semidirect
64. C2×#13093994C22semidirect
65. C2×#13093992C22semidirect
66. #15689605C22semidirect
67. C2×Q8×Dic47C22semidirect
68. C2×C4×D188C22semidirect
69. C2×C4×D188C22semidirect
70. C2×#13093986C22semidirect
71. C2×C4×C22⋊D47C22semidirect
72. C2×C4×C22⋊D47C22semidirect
73. C2×#13093981C22semidirect
74. C2×C4⋊C4×D47C22semidirect
75. C2×C22⋊C4×D47C22semidirect
76. C22×#41×C47C22semidirect
77. C23×Q8×C47C22semidirect
78. C47×#548C22semidirect
79. C2×#124×C47C22semidirect
80. C2×C22⋊Q8×C47C22semidirect
81. C2×#121×C47C22semidirect
82. C2×C4×Q8×C47C22semidirect
83. C2×C4×D4×C47C22semidirect
92. C2×#10625354D4semidirect
94. C2×#10625354C23semidirect
95. C2×#10625354C23semidirect
96. C2×#10625354C23semidirect
97. C2×#10625354C23semidirect
99. C2×#10625350C23semidirect
110. C22×D188C23semidirect
111. C22×D188C23semidirect
120. C2×D4×D47C23semidirect
121. C2×D4×D47C23semidirect
122. C2×D4×D47C23semidirect
131. C22×C4×D47C23semidirect
132. #13094021C23semidirect
133. #13094020C23semidirect
134. #13094013C23semidirect
135. #13094009C23semidirect
136. #13094006C23semidirect
137. #13094002C23semidirect
138. #13094001C23semidirect
139. #13094000C23semidirect
140. #13093999C23semidirect
141. #13093999C23semidirect
142. #13093999C23semidirect
143. #13093998C23semidirect
144. #13093998C23semidirect
145. #13093997C23semidirect
146. #13093997C23semidirect
147. #13093997C23semidirect
148. #13093996C23semidirect
149. #13093995C23semidirect
150. #13093994C23semidirect
151. #13093994C23semidirect
152. #13093994C23semidirect
153. #13093992C23semidirect
154. Q8×Dic47C23semidirect
155. C4×D188C23semidirect
156. C4×D188C23semidirect
157. #13093986C23semidirect
158. C4×C22⋊D47C23semidirect
159. C4×C22⋊D47C23semidirect
160. #13093981C23semidirect
167. C4⋊C4×D47C23semidirect
177. C22⋊C4×D47C23semidirect
180. C2×#41×C47C23semidirect
184. C22×Q8×C47C23semidirect
189. #124×C47C23semidirect
190. C22⋊Q8×C47C23semidirect
191. #121×C47C23semidirect
192. C4×Q8×C47C23semidirect
193. C4×D4×C47C23semidirect
216. C2×Q8×C47C2×D4semidirect
253. #10625354C2×D4semidirect
266. C2×D188C2×D4semidirect
280. C2×C4×D47C2×D4semidirect
316. C23×C47H(5,𝔽2)semidirect
341. Q8×C47C22×D4semidirect
378. D188C22×D4semidirect
384. C4×D47C22×D4semidirect
396. C22×C47C2×H(5,𝔽2)semidirect
429. C2×#548D47semidirect
441. C2×C47#3488semidirect
458. C22×#41C2×D47semidirect
459. C23×Q8C2×D47semidirect
469. #548C2×D47semidirect
479. C2×#124C2×D47semidirect
486. C2×C22⋊Q8C2×D47semidirect
498. C2×#121C2×D47semidirect
505. C2×C4×Q8C2×D47semidirect
511. C2×C4×D4C2×D47semidirect
515. C47C2×#3488semidirect
533. C2×#41C22×D47semidirect
538. C22×Q8C22×D47semidirect
577. #124C22×D47semidirect
583. C22⋊Q8C22×D47semidirect
594. #121C22×D47semidirect
600. C4×Q8C22×D47semidirect
606. C4×D4C22×D47semidirect
656. C2×Q8D4×D47semidirect
768. C23#13094070semidirect
774. Q8C2×D4×D47semidirect
841. C22C2×#13094070semidirect
859. C2#20257054direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940702
C23×#106253542
#202570542
C2×#156897952
C2×#156897922
C2×#156897842
C2×#156897662
C2×#156897642
C2×D4×D1882
C2×#156897572
C2×#156897032
C2×#156896912
C2×#156896322
C2×#121×D472
C2×#156896052
C2×C47×#5482
C2×#348847