Finite Group Databasebeta

← #26376445

Subgroups — #26376445

Order 12032.

2914 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093986C211yesmaximal, characteristic
2#20246357C212yesmaximal, complemented
3#20246327C214yesmaximal, complemented
4#20246297C212yesmaximal, complemented
5#20246257C211yesmaximal, characteristic, complemented
6#20246238C212yesmaximal, complemented
7#20246230C212yesmaximal, complemented
8C22⋊C4×D188C211yesmaximal, characteristic
9#20246208C211yesmaximal, characteristic
10#20246027C212yesmaximal, complemented
11#20246020C214yesmaximal, complemented
12#20245783C211yesmaximal, characteristic, complemented
13#20245782C211yesmaximal, characteristic, complemented
14#20245767C212yesmaximal, complemented
15#381×D47C212yesmaximal, complemented
16#20245748C212yesmaximal, complemented
17C47×#2344C211yesmaximal, characteristic, complemented
18C23×D188C2211yescharacteristic
19C23×C4×D47C2212yes—
20C2×C4×D188C2212yes—
21C2×#13093986C4116yescomplemented
22C2×#13093986C2212yes—
23C2×#13093986C2211yescharacteristic
24C2×#13093986C2211yescharacteristic
25C2×#13093986C2212yes—
26C2×#13093986C2211yescharacteristic
27C2×#13093986C2212yes—
28C2×#13093986C2211yescharacteristic
29C2×#13093983C2212yes—
30C22×(C2×D47)⋊C4C2212yes—
31C2×C22⋊C4×D47C2212yes—
32C2×C22⋊C4×D47C2212yes—
33C22×C4×Dic47C2211yescharacteristic
34#15689025C2212yes—
35#15689024C2212yes—
36#15689022C2212yescomplemented
37#15689015C2214yescomplemented
38#15689014C2214yescomplemented
39#15689013C2214yescomplemented
40#15689012C2214yescomplemented
41#15689009C2214yescomplemented
42#15689001C2214yes—
43#15689001C2214yes—
44#15688997C2214yescomplemented
45#15688994C2214yescomplemented
46#15688990C2212yescomplemented
47#15688990C2212yescomplemented
48#15688988C2212yescomplemented
49#15688987C2212yescomplemented
50#15688986C2212yes—
51#15688985C2214yescomplemented
52#15688985C2214yescomplemented
53#15688984C2211yescharacteristic
54#15688984C2212yes—
55#15688984C2211yescharacteristic
56#15688983C2211yescharacteristic
57#15688981C2211yescharacteristic
58#15688981C2211yescharacteristic
59#15688980C2214yescomplemented
60#15688980C2214yescomplemented
61#15688978C2212yes—
62#15688978C2212yes—
63C4⋊C4×Dic47C2212yescomplemented
64C4⋊C4×Dic47C2212yescomplemented
65C4×Dic47⋊C4C2212yescomplemented
66C22⋊C4×Dic47C2212yes—
67C4×(C2×D47)⋊C4C2214yescomplemented
68C4×(C2×D47)⋊C4C2214yescomplemented
69C4×(C2×D47)⋊C4C2214yescomplemented
70C4×C22⋊Dic47C2211yescharacteristic
71#15688970C2214yescomplemented
72#15688969C2212yescomplemented
73#15688968C2212yescomplemented
74#95×D47C2214yescomplemented
75#95×D47C2214yescomplemented
76C2×#117×C47C2212yes—
77C22×C4⋊C4×C47C2211yescharacteristic
78C47×#389C2212yescomplemented
79C47×#387C2214yescomplemented
80C47×#381C2212yes—
81C47×#380C2211yescharacteristic
82C4×C4⋊C4×C47C2212yescomplemented
83C4×C22⋊C4×C47C2211yescharacteristic
84C24×D47C2312yes—
85C22×D188—28no—
86C22×D188C2×C418yes—
87C22×D188C2312yes—
88C22×D188C2311yescharacteristic
89C22×D188C2311yescharacteristic
90C23×Dic47C2311yescharacteristic
91C23×Dic47C2311yescharacteristic
92C22×C4×D47—44no—
93C22×C4×D47—44no—
94C22×C4×D47C2×C4116yescomplemented
95C22×C4×D47C2314yes—
96C22×C4×D47C2314yes—
97C22×C4×D47C2312yes—
98C22×C4×D47C2312yes—
99C22×C4×D47C2312yes—
100C22×C4×D47C2312yes—
101C4×D188—28no—
102#13093986—28no—
103#13093986C2×C418yes—
104#13093986C2×C418yes—
105#13093986C2×C418yescomplemented
106#13093986C2×C418yescomplemented
107#13093986C2×C4116yescomplemented
108#13093986C2×C4116yescomplemented
109#13093983—44no—
110C2×C4⋊Dic47C2312yes—
111C2×C4⋊Dic47C2314yes—
112C2×Dic47⋊C4C2312yes—
113C2×Dic47⋊C4C2312yes—
114C2×C22⋊Dic47C2311yescharacteristic
115C2×C22⋊Dic47C2311yescharacteristic
116C2×C22⋊Dic47C2312yes—
117C2×(C2×D47)⋊C4C2×C4116yescomplemented
118C2×(C2×D47)⋊C4C2314yes—
119C2×(C2×D47)⋊C4C2314yes—
120C2×(C2×D47)⋊C4C2314yes—
121C2×(C2×D47)⋊C4C2314yes—
122C2×(C2×D47)⋊C4C2314yes—
123C2×(C2×D47)⋊C4C2314yes—
124C2×(C2×D47)⋊C4C2312yes—
125C2×(C2×D47)⋊C4C2312yes—
126C2×(C2×D47)⋊C4C2312yes—
127C2×(C2×D47)⋊C4C2312yes—
128C22⋊C4×D47—44no—
129C22⋊C4×D47—44no—
130C2×C4×Dic47C2×C418yescomplemented
131C2×C4×Dic47C2312yes—
132C2×C4×Dic47C2314yes—
133C2×C4×Dic47C2314yes—
134C2×C4×Dic47C2311yescharacteristic
135C2×C4×Dic47C2311yescharacteristic
136C2×C4×Dic47C2311yescharacteristic
137C2×C4×Dic47C2311yescharacteristic
138C47⋊#95C2312yes—
139C47⋊#95C2312yes—
140C47⋊#95C2314yes—
141C47⋊#95C2314yes—
142C47⋊#95C2314yes—
143C47⋊#95C2314yes—
144C47⋊#95C2312yes—
145C47⋊#95C2312yes—
146C47⋊#95C2312yes—
147C47⋊#95C2312yes—
148C47⋊#95C2312yes—
149C47⋊#95C2312yes—
150C47⋊#95C2314yes—
151C23×C4×C47C2311yescharacteristic
152C23×C4×C47C2312yes—
153#117×C47—44no—
154C2×C4⋊C4×C47C2×C418yescomplemented
155C2×C4⋊C4×C47C2312yes—
156C2×C4⋊C4×C47C2314yes—
157C2×C4⋊C4×C47C2311yescharacteristic
158C2×C4⋊C4×C47C2312yes—
159C2×C4⋊C4×C47C2311yescharacteristic
160C2×C22⋊C4×C47C2312yes—
161C2×C22⋊C4×C47C2311yescharacteristic
162C2×C22⋊C4×C47C2311yescharacteristic
163C2×C42×C47C2312yes—
164C2×C42×C47C2314yes—
165#95×C47C2314yes—
166#95×C47C2314yes—
167#95×C47C2312yes—
168#95×C47C2312yes—
169C24×C47C2411yescharacteristic
170C23×D47—24no—
171C23×D47—24no—
172C23×D47—28no—
173C23×D47—44no—
174C23×D47C22×C418yes—
175C23×D47C2412yes—
176C23×D47C2412yes—
177C22×C4×C47—24no—
178C22×C4×C47—24no—
179C22×C4×C47—24no—
180C22×C4×C47C22×C414yes—
181C22×C4×C47C22×C418yes—
182C22×C4×C47C2412yes—
183C22×C4×C47C2414yes—
184C22×C4×C47C2412yes—
185C22×C4×C47C2412yes—
186C22×C4×C47C2412yes—
187C22×C4×C47C2411yescharacteristic
188C22×C4×C47C2411yescharacteristic
189C22×Dic47—22no—
190C22×Dic47—22no—
191C22×Dic47—42no—
192C22×Dic47C22×C414yes—
193C22×Dic47C22×C414yes—
194C22×Dic47C2412yes—
195C22×Dic47C2414yes—
196C22×Dic47C2412yes—
197C22×Dic47C2411yescharacteristic
198C22×Dic47C2411yescharacteristic
199C22×Dic47C2411yescharacteristic
200C22×Dic47C2411yescharacteristic
201C2×D188—28no—
202C2×D188—24no—
203C2×D188—232no—
204C2×D188C22×C418yes—
205C2×D188C22×C414yes—
206C2×D188C22×C414yes—
207C2×D188#4118yes—
208C2×C4×D47—28no—
209C2×C4×D47—28no—
210C2×C4×D47—432no—
211C2×C4×D47—42no—
212C2×C4×D47—42no—
213C2×C4×D47—42no—
214C2×C4×D47—42no—
215C2×C4×D47—42no—
216C2×C4×D47—42no—
217C2×C4×D47—42no—
218C2×C4×D47—42no—
219C2×C4×D47—44no—
220C2×C4×D47—44no—
221C2×C4×D47—44no—
222C2×C4×D47—44no—
223C2×C4×D47C22×C418yes—
224C2×C4×D47C22×C418yes—
225C2×C4×D47C22×C418yes—
226C2×C4×D47C22×C418yes—
227C4⋊C4×C47—24no—
228C4⋊C4×C47—44no—
229C4⋊C4×C47C22×C414yes—
230C4⋊C4×C47C22×C414yes—
231C4⋊C4×C47C22×C418yes—
232C22⋊C4×C47—22no—
233C22⋊C4×C47—24no—
234C22⋊C4×C47—22no—
235C42×C47—24no—
236C42×C47—44no—
237C22⋊Dic47—22no—
238C22⋊Dic47—24no—
239C22⋊Dic47—22no—
240(C2×D47)⋊C4—28no—
241(C2×D47)⋊C4—28no—
242(C2×D47)⋊C4—44no—
243(C2×D47)⋊C4—44no—
244(C2×D47)⋊C4—44no—
245(C2×D47)⋊C4—44no—
246(C2×D47)⋊C4C22×C418yes—
247(C2×D47)⋊C4C22×C418yes—
248(C2×D47)⋊C4C22×C418yes—
249(C2×D47)⋊C4C22×C418yes—
250C4⋊Dic47—24no—
251C4⋊Dic47—44no—
252Dic47⋊C4—42no—
253Dic47⋊C4—42no—
254C4×Dic47—24no—
255C4×Dic47—44no—
256C4×Dic47—44no—
257C4×Dic47C22×C414yes—
258C4×Dic47C22×C414yes—
259C4×Dic47C22×C414yes—
260C4×Dic47C22×C414yes—
261C23×C47—22no—
262C23×C47—22no—
263C23×C47C23×C412yes—
264C23×C47H(5,𝔽2)12yes—
265C23×C47H(5,𝔽2)12yes—
266C23×C47C2511yescharacteristic
267C22×D47—22no—
268C22×D47—22no—
269C22×D47—24no—
270C22×D47—216no—
271C22×D47—24no—
272C22×D47—22no—
273C22×D47—22no—
274C22×D47—24no—
275C22×D47—216no—
276C22×D47—48no—
277C22×D47—416no—
278C22×D47—416no—
279C22×D47C23×C414yes—
280C22×D47C23×C414yes—
281C22×D47C2×#4118yes—
282C2×C4×C47—216no—
283C2×C4×C47—22no—
284C2×C4×C47—22no—
285C2×C4×C47—22no—
286C2×C4×C47—22no—
287C2×C4×C47—22no—
288C2×C4×C47—28no—
289C2×C4×C47—22no—
290C2×C4×C47—24no—
291C2×C4×C47—22no—
292C2×C4×C47—22no—
293C2×C4×C47—24no—
294C2×C4×C47—22no—
295C2×C4×C47—24no—
296C2×C4×C47—22no—
297C2×C4×C47—22no—
298C2×C4×C47C23×C412yes—
299C2×C4×C47C23×C414yes—
300C2×C4×C47C23×C414yes—
301C2×C4×C47C23×C412yes—
302C2×C4×C47C2×#4114yes—
303C2×Dic47—28no—
304C2×Dic47—21no—
305C2×Dic47—21no—
306C2×Dic47—21no—
307C2×Dic47—21no—
308C2×Dic47—22no—
309C2×Dic47—22no—
310C2×Dic47—22no—
311C2×Dic47—22no—
312C2×Dic47—24no—
313C2×Dic47—22no—
314C2×Dic47—24no—
315C2×Dic47—22no—
316C2×Dic47—24no—
317C2×Dic47—22no—
318C2×Dic47—22no—
319C2×Dic47—44no—
320C2×Dic47C23×C412yes—
321C2×Dic47C23×C412yes—
322C2×Dic47C23×C412yes—
323C2×Dic47C23×C412yes—
324D188—216no—
325D188—28no—
326D188#117116yescomplemented
327C4×D47—48no—
328C4×D47—48no—
329C4×D47—48no—
330C4×D47—48no—
331C4×D47—88no—
332C4×D47—88no—
333#34190—471nomaximal, Sylow
334C22×C47—22no—
335C22×C47—22no—
336C22×C47—24no—
337C22×C47—24no—
338C22×C47#51814yes—
339C22×C47C24×C411yescharacteristic
340C22×C47C22×#4112yes—
341C22×C47C2×H(5,𝔽2)11yescharacteristic
342C22×C47C2×H(5,𝔽2)11yescharacteristic
343C22×C47#58512yes—
344C2×D47—24no—
345C2×D47—24no—
346C2×D47—28no—
347C2×D47—28no—
348C2×D47—24no—
349C2×D47—24no—
350C2×D47—24no—
351C2×D47—432no—
352C2×D47—44no—
353C2×D47—44no—
354C2×D47C2×#11718yes—
355C4×C47—22no—
356C4×C47—24no—
357C4×C47—24no—
358C4×C47—42no—
359C4×C47—44no—
360C4×C47—42no—
361C4×C47C2×#11714yes—
362Dic47—22no—
363Dic47—22no—
364Dic47—22no—
365Dic47—22no—
366Dic47—42no—
367Dic47—44no—
368Dic47—42no—
369C22×C4×D4—471no—
370#2357—472no—
371#2353—474no—
372#2349—472no—
373#2344—471no—
374#2344D4711yescharacteristic, complemented
375#2342—472no—
376#2342—472no—
377D4×C22⋊C4—471no—
378D4×C22⋊C4—471no—
379#2319—472no—
380#2318—474no—
381#2283—471no—
382#2283—471no—
383#2280—472no—
384C2×#381—472no—
385#2275—472no—
386C2×C47—24no—
387C2×C47C22×#11711yescharacteristic
388C2×C47C2×#51811yescharacteristic
389C2×C47#342811yescharacteristic
390C2×C47#351312yes—
391C2×C47#351312yes—
392D47—28no—
393D47—44no—
394C23×D4—471no—
395C24×C4—472no—
396C2×C4×D4—4716no—
397C2×C4×D4—472no—
398C2×C4×D4—471no—
399C2×C4×D4—471no—
400C2×C4×D4—472no—
401C2×C4×D4—471no—
402C2×C4×D4—471no—
403C2×C4×D4—472no—
404C2×C4×D4—472no—
405C2×#117—472no—
406C2×#117C2×D4712yes—
407C22×C4⋊C4C2×D4711yescharacteristic
408C22×C22⋊C4—472no—
409C22×C22⋊C4—472no—
410C22×C22⋊C4—472no—
411C22×C42—471no—
412#390—472no—
413#390—472no—
414#389—472no—
415#389C2×D4712yescomplemented
416#388—474no—
417#388—474no—
418#388—474no—
419#388—474no—
420#387—474no—
421#387C2×D4714yescomplemented
422#386—474no—
423#386—474no—
424#385—474no—
425#385—474no—
426#383—472no—
427#383—472no—
428#382—472no—
429#382—472no—
430#381—472no—
431#381—471no—
432#381—472no—
433#381—471no—
434#381—474no—
435#381—474no—
436#381C2×D4712yes—
437#380—471no—
438#380—474no—
439#380—474no—
440#380—471no—
441#380—471no—
442#380C2×D4711yescharacteristic
443#379—472no—
444#379—472no—
445C4×C4⋊C4—472no—
446C4×C4⋊C4—472no—
447C4×C4⋊C4—472no—
448C4×C4⋊C4C2×D4712yescomplemented
449C4×C22⋊C4—471no—
450C4×C22⋊C4—472no—
451C4×C22⋊C4—474no—
452C4×C22⋊C4—474no—
453C4×C22⋊C4—474no—
454C4×C22⋊C4—474no—
455C4×C22⋊C4C2×D4711yescharacteristic
456#376—472no—
457#376—472no—
458C2×#95—474no—
459C2×#95—474no—
460C47#3419011yescharacteristic, complemented, Sylow
461C25—472no—
462C22×D4—478no—
463C22×D4—471no—
464C22×D4—472no—
465C22×D4—471no—
466C22×D4—948no—
467C23×C4—471no—
468C23×C4—471no—
469C23×C4—4716no—
470C23×C4—472no—
471C23×C4—472no—
472C23×C4—472no—
473C23×C4—472no—
474C23×C4—474no—
475C23×C4—474no—
476C23×C4—1884no—
477C23×C4—1884no—
478C23×C4C22×D4712yes—
479C23×C4C22×D4711yescharacteristic
480C4×D4—478no—
481C4×D4—478no—
482C4×D4—4716no—
483C4×D4—478no—
484C4×D4—4716no—
485C4×D4—478no—
486C4×D4—948no—
487C4×D4—948no—
488#117—44no—
489#117—1884no—
490C2×C4⋊C4—472no—
491C2×C4⋊C4—474no—
492C2×C4⋊C4—472no—
493C2×C4⋊C4—472no—
494C2×C4⋊C4C4×D4718yescomplemented
495C2×C4⋊C4C22×D4712yes—
496C2×C4⋊C4C22×D4714yes—
497C2×C4⋊C4C22×D4711yescharacteristic
498C2×C4⋊C4C22×D4712yes—
499C2×C4⋊C4C22×D4711yescharacteristic
500C2×C22⋊C4—4716no—
501C2×C22⋊C4—472no—
502C2×C22⋊C4—472no—
503C2×C22⋊C4—472no—
504C2×C22⋊C4—472no—
505C2×C22⋊C4—471no—
506C2×C22⋊C4—472no—
507C2×C22⋊C4—471no—
508C2×C22⋊C4—474no—
509C2×C22⋊C4—474no—
510C2×C22⋊C4—474no—
511C2×C22⋊C4—474no—
512C2×C22⋊C4—474no—
513C2×C22⋊C4—474no—
514C2×C22⋊C4—1884no—
515C2×C22⋊C4—1884no—
516C2×C22⋊C4C22×D4711yescharacteristic
517C2×C22⋊C4C22×D4712yes—
518C2×C22⋊C4C22×D4711yescharacteristic
519C2×C42—478no—
520C2×C42—471no—
521C2×C42—471no—
522C2×C42—471no—
523C2×C42—471no—
524C2×C42—472no—
525C2×C42—474no—
526C2×C42—474no—
527C2×C42C22×D4712yes—
528C2×C42C22×D4714yes—
529#95—472no—
530#95—472no—
531#95—474no—
532#95—474no—
533#95—474no—
534#95—474no—
535#95—472no—
536#95—472no—
537#95—472no—
538#95—472no—
539#95—472no—
540#95—474no—
541#95—472no—
542#95C22×D4714yes—
543#95C22×D4714yes—
544#95C22×D4712yes—
545#95C22×D4712yes—
546C24—472no—
547C24—472no—
548C24—478no—
549C24—948no—
550C24—944no—
551C24—944no—
552C24—1884no—
553C24C23×D4711yescharacteristic
554C2×D4—474no—
555C2×D4—478no—
556C2×D4—474no—
557C2×D4—478no—
558C2×D4—9432no—
559C2×D4—948no—
560C2×D4—944no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—474no—
565C22×C4—471no—
566C22×C4—471no—
567C22×C4—471no—
568C22×C4—471no—
569C22×C4—474no—
570C22×C4—478no—
571C22×C4—478no—
572C22×C4—478no—
573C22×C4—478no—
574C22×C4—472no—
575C22×C4—474no—
576C22×C4—472no—
577C22×C4—948no—
578C22×C4—948no—
579C22×C4—942no—
580C22×C4—942no—
581C22×C4—1884no—
582C22×C4—1884no—
583C22×C4—1884no—
584C22×C4—1884no—
585C22×C4—18832no—
586C22×C4—1882no—
587C22×C4—1882no—
588C22×C4—1882no—
589C22×C4—1882no—
590C22×C4—1882no—
591C22×C4—1882no—
592C22×C4—1882no—
593C22×C4—1882no—
594C22×C4—1882no—
595C22×C4C2×C4×D4714yes—
596C22×C4C2×C4×D4718yes—
597C22×C4C23×D4712yes—
598C22×C4C23×D4714yes—
599C22×C4C23×D4712yes—
600C22×C4C23×D4711yescharacteristic
601C22×C4C23×D4712yes—
602C22×C4C23×D4712yes—
603C22×C4C23×D4711yescharacteristic
604C4⋊C4—24no—
605C4⋊C4—44no—
606C4⋊C4—944no—
607C4⋊C4—1882no—
608C4⋊C4—1882no—
609C4⋊C4—1884no—
610C4⋊C4C2×C4×D4718yes—
611C4⋊C4C2×C4×D4714yes—
612C4⋊C4C2×C4×D4714yes—
613C22⋊C4—24no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—478no—
617C22⋊C4—478no—
618C22⋊C4—478no—
619C22⋊C4—478no—
620C22⋊C4—948no—
621C22⋊C4—948no—
622C22⋊C4—942no—
623C22⋊C4—944no—
624C22⋊C4—942no—
625C22⋊C4—1884no—
626C22⋊C4—1884no—
627C22⋊C4—1884no—
628C22⋊C4—1884no—
629C42—24no—
630C42—44no—
631C42—474no—
632C42—474no—
633C42—474no—
634C42—474no—
635C42—944no—
636C42—1884no—
637C42—1884no—
638C23—22no—
639C23—22no—
640C23—474no—
641C23—478no—
642C23—474no—
643C23—9416no—
644C23—942no—
645C23—942no—
646C23—944no—
647C23—9416no—
648C23—944no—
649C23—942no—
650C23—942no—
651C23—944no—
652C23—1888no—
653C23—18816no—
654C23—18816no—
655C23C22×C4×D4712yes—
656C23#1309406912yes—
657C23#1309407012yes—
658C23C24×D4711yescharacteristic
659D4—4716no—
660D4—9416no—
661D4—948no—
662C2×C4—216no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—28no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—24no—
674C2×C4—22no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—472no—
679C2×C4—472no—
680C2×C4—472no—
681C2×C4—472no—
682C2×C4—948no—
683C2×C4—941no—
684C2×C4—941no—
685C2×C4—941no—
686C2×C4—941no—
687C2×C4—942no—
688C2×C4—942no—
689C2×C4—942no—
690C2×C4—942no—
691C2×C4—944no—
692C2×C4—942no—
693C2×C4—942no—
694C2×C4—944no—
695C2×C4—944no—
696C2×C4—942no—
697C2×C4—942no—
698C2×C4—3768no—
699C2×C4—3768no—
700C2×C4—1888no—
701C2×C4—1888no—
702C2×C4—1888no—
703C2×C4—1888no—
704C2×C4—1884no—
705C2×C4C22×C4×D4712yes—
706C2×C4C22×C4×D4714yes—
707C2×C4C22×C4×D4714yes—
708C2×C4C22×C4×D4712yes—
709C2×C4#41×D4714yes—
710C22—22no—
711C22—24no—
712C22—24no—
713C22—22no—
714C22—478no—
715C22—948no—
716C22—948no—
717C22—944no—
718C22—944no—
719C22—944no—
720C22—944no—
721C22—944no—
722C22—18832no—
723C22—1884no—
724C22—1884no—
725C22#1568959514yes—
726C22C23×C4×D4711yescharacteristic
727C22C2×#41×D4712yes—
728C22C2×#1309406911yescharacteristic
729C22C2×#1309407011yescharacteristic
730C22#1568996012yes—
731C4—22no—
732C4—24no—
733C4—24no—
734C4—44no—
735C4—42no—
736C4—42no—
737C4—942no—
738C4—942no—
739C4—942no—
740C4—942no—
741C4—1882no—
742C4—1884no—
743C4—1882no—
744C4#117×D4714yes—
745C2—24no—
746C2—948no—
747C2—1884no—
748C2C2×#117×D4711yescharacteristic
749C2C2×#1568959511yescharacteristic
750C2#2025659011yescharacteristic
751C2#2025732312yes—
752C2#2025733312yes—
subgroupG/H
center, FrattiniC23C24×D47
commutatorC22×C47C24×C4
FittingC47×#2344C2
socle, cosocleC23×C47C25
prime radicalC23×D188C22
hypercenter#2344D47
hypocenterC47#34190
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2344

Complements

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

NH ≅ G/Ntype
2. #20246357C2semidirect
3. #20246327C2semidirect
4. #20246297C2semidirect
5. #20246257C2semidirect
6. #20246238C2semidirect
7. #20246230C2semidirect
10. #20246027C2semidirect
11. #20246020C2semidirect
12. #20245783C2semidirect
13. #20245782C2semidirect
14. #20245767C2semidirect
15. #381×D47C2semidirect
16. #20245748C2semidirect
17. C47×#2344C2semidirect
21. C2×#13093986C4semidirect
36. #15689022C22semidirect
37. #15689015C22semidirect
38. #15689014C22semidirect
39. #15689013C22semidirect
40. #15689012C22semidirect
41. #15689009C22semidirect
44. #15688997C22semidirect
45. #15688994C22semidirect
46. #15688990C22semidirect
47. #15688990C22semidirect
48. #15688988C22semidirect
49. #15688987C22semidirect
51. #15688985C22semidirect
52. #15688985C22semidirect
59. #15688980C22semidirect
60. #15688980C22semidirect
63. C4⋊C4×Dic47C22semidirect
64. C4⋊C4×Dic47C22semidirect
65. C4×Dic47⋊C4C22semidirect
67. C4×(C2×D47)⋊C4C22semidirect
68. C4×(C2×D47)⋊C4C22semidirect
69. C4×(C2×D47)⋊C4C22semidirect
71. #15688970C22semidirect
72. #15688969C22semidirect
73. #15688968C22semidirect
74. #95×D47C22semidirect
75. #95×D47C22semidirect
78. C47×#389C22semidirect
79. C47×#387C22semidirect
82. C4×C4⋊C4×C47C22semidirect
94. C22×C4×D47C2×C4semidirect
105. #13093986C2×C4semidirect
106. #13093986C2×C4semidirect
107. #13093986C2×C4semidirect
108. #13093986C2×C4semidirect
117. C2×(C2×D47)⋊C4C2×C4semidirect
130. C2×C4×Dic47C2×C4semidirect
154. C2×C4⋊C4×C47C2×C4semidirect
326. D188#117semidirect
374. #2344D47semidirect
415. #389C2×D47semidirect
421. #387C2×D47semidirect
448. C4×C4⋊C4C2×D47semidirect
460. C47#34190semidirect
494. C2×C4⋊C4C4×D47semidirect

Maximal subgroups

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

subgroupindex
C22×#130939862
#202463572
#202463272
#202462972
#202462572
#202462382
#202462302
C22⋊C4×D1882
#202462082
#202460272
#202460202
#202457832
#202457822
#202457672
#381×D472
#202457482
C47×#23442
#3419047