Finite Group Databasebeta

← C2×#20246919 #26383749

Subgroups — C2×#20246919 #26383749

Order 12032.

5898 conjugacy classes of subgroups.

The subgroup lattice has 1112 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093999C211yesmaximal, characteristic, complemented
2C22×#13093999C211yesmaximal, characteristic, complemented
3C22×#13093994C211yesmaximal, characteristic, complemented
4C22×#13093994C211yesmaximal, characteristic, complemented
5C22×#13093986C211yesmaximal, characteristic, complemented
6C22×C22⋊C4×D47C211yesmaximal, characteristic, complemented
7#20246919C2116yesmaximal, direct product factor
8C2×#15689041C211yesmaximal, characteristic, complemented
9C2×#15689040C211yesmaximal, characteristic, complemented
10C2×#15689032C211yesmaximal, characteristic, complemented
11C2×#15689023C211yesmaximal, characteristic, complemented
12C2×#15689013C211yesmaximal, characteristic, complemented
13C2×#15689001C211yesmaximal, characteristic, complemented
14C2×#15688999C211yesmaximal, characteristic, complemented
15C2×#15688994C211yesmaximal, characteristic, complemented
16C2×C47×#396C211yesmaximal, characteristic, complemented
17C25×D47C2211yescharacteristic
18C23×D188C2211yescharacteristic
19C23×D188C2211yescharacteristic
20C23×D188C2211yescharacteristic
21C23×D188C2211yescharacteristic
22C23×D188C2211yescharacteristic, complemented
23C23×C22⋊D47C2211yescharacteristic
24C23×C22⋊D47C2211yescharacteristic
25C23×C4×D47C2211yescharacteristic
26C23×C4×D47C2211yescharacteristic
27C23×C4×D47C2211yescharacteristic, complemented
28C2×#13093999—28no—
29C2×#13093999—28no—
30C2×#13093999C2218yescomplemented
31C2×#13093999C2218yescomplemented
32C2×#13093994—28no—
33C2×#13093994—28no—
34C2×#13093994C2218yescomplemented
35C2×#13093994C2218yescomplemented
36C2×#13093986—28no—
37C2×#13093986C2218yescomplemented
38C22×Dic47⋊C4C2211yescharacteristic, complemented
39C22×C22⋊Dic47C2211yescharacteristic
40C22×(C2×D47)⋊C4C2211yescharacteristic
41C22×(C2×D47)⋊C4C2211yescharacteristic
42C22×(C2×D47)⋊C4C2211yescharacteristic
43C22×(C2×D47)⋊C4C2211yescharacteristic
44C22×(C2×D47)⋊C4C2211yescharacteristic
45C22×(C2×D47)⋊C4C2211yescharacteristic
46C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
47C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
48C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
49C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
50C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
51C2×C22⋊C4×D47—28no—
52C2×C22⋊C4×D47C2218yescomplemented
53C22×C4×Dic47C2211yescharacteristic, complemented
54#15689041C2218yescomplemented
55#15689040C2218yescomplemented
56#15689032C2218yescomplemented
57#15689023C2218yescomplemented
58#15689013C2218yescomplemented
59#15689001C2218yescomplemented
60#15688999C2218yescomplemented
61#15688994C2218yescomplemented
62C2×C47⋊#95C2211yescharacteristic, complemented
63C2×C47⋊#95C2211yescharacteristic, complemented
64C2×C47⋊#95C2211yescharacteristic, complemented
65C22×C4⋊C4×C47C2211yescharacteristic, complemented
66C22×C4⋊C4×C47C2211yescharacteristic, complemented
67C22×C4⋊C4×C47C2211yescharacteristic, complemented
68C22×C22⋊C4×C47C2211yescharacteristic
69C22×C22⋊C4×C47C2211yescharacteristic
70C22×C22⋊C4×C47C2211yescharacteristic
71C47×#396C2218yescomplemented
72C2×#95×C47C2211yescharacteristic, complemented
73C24×D47—24no—
74C24×D47—24no—
75C24×D47—24no—
76C24×D47—24no—
77C24×D47—24no—
78C24×D47—42no—
79C24×D47—42no—
80C24×D47C2311yescharacteristic
81C24×D47C2311yescharacteristic
82C24×D47C2311yescharacteristic
83C24×D47C2314yes—
84C24×D47C2311yescharacteristic
85C22×D188—24no—
86C22×D188—24no—
87C22×D188—24no—
88C22×D188—24no—
89C22×D188—24no—
90C22×D188—24no—
91C22×D188—24no—
92C22×D188—24no—
93C22×D188—24no—
94C22×D188—24no—
95C22×D188—24no—
96C22×D188—42no—
97C22×D188—42no—
98C22×D188—42no—
99C22×D188D418yescomplemented
100C22×D188C2314yes—
101C22×D188C2314yes—
102C22×D188C2314yes—
103C22×D188C2314yes—
104C22×D188C2314yescomplemented
105C22×C22⋊D47—24no—
106C22×C22⋊D47—24no—
107C22×C22⋊D47—24no—
108C22×C22⋊D47—24no—
109C22×C22⋊D47—42no—
110C22×C22⋊D47—42no—
111C22×C22⋊D47C2314yes—
112C22×C22⋊D47C2314yes—
113C23×Dic47C2311yescharacteristic
114C23×Dic47C2311yescharacteristic
115C23×Dic47C2311yescharacteristic
116C23×Dic47C2311yescharacteristic
117C22×C4×D47—24no—
118C22×C4×D47—24no—
119C22×C4×D47—24no—
120C22×C4×D47—24no—
121C22×C4×D47—24no—
122C22×C4×D47—24no—
123C22×C4×D47—42no—
124C22×C4×D47—42no—
125C22×C4×D47—42no—
126C22×C4×D47C2314yes—
127C22×C4×D47C2314yes—
128C22×C4×D47C2314yescomplemented
129#13093999—232no—
130#13093999—232no—
131#13093994—232no—
132#13093994—232no—
133#13093986—232no—
134C2×Dic47⋊C4—42no—
135C2×Dic47⋊C4C2314yescomplemented
136C2×C22⋊Dic47—24no—
137C2×C22⋊Dic47C2314yes—
138C2×(C2×D47)⋊C4—24no—
139C2×(C2×D47)⋊C4—24no—
140C2×(C2×D47)⋊C4—24no—
141C2×(C2×D47)⋊C4—24no—
142C2×(C2×D47)⋊C4—24no—
143C2×(C2×D47)⋊C4—24no—
144C2×(C2×D47)⋊C4—24no—
145C2×(C2×D47)⋊C4—24no—
146C2×(C2×D47)⋊C4—42no—
147C2×(C2×D47)⋊C4D418yescomplemented
148C2×(C2×D47)⋊C4D418yescomplemented
149C2×(C2×D47)⋊C4C2314yes—
150C2×(C2×D47)⋊C4C2314yes—
151C2×(C2×D47)⋊C4C2314yes—
152C2×(C2×D47)⋊C4C2314yes—
153C2×(C2×D47)⋊C4C2314yes—
154C2×(C2×D47)⋊C4C2314yes—
155C2×(C2×D47)⋊C4C2314yescomplemented
156C2×(C2×D47)⋊C4C2314yescomplemented
157C2×(C2×D47)⋊C4C2314yescomplemented
158C2×(C2×D47)⋊C4C2314yescomplemented
159C2×(C2×D47)⋊C4C2314yescomplemented
160C22⋊C4×D47—232no—
161C2×C4×Dic47—24no—
162C2×C4×Dic47C2314yescomplemented
163C47⋊#95C2314yescomplemented
164C47⋊#95C2314yescomplemented
165C47⋊#95C2314yescomplemented
166C25×C47C2311yescharacteristic
167C23×C4×C47C2311yescharacteristic
168C23×C4×C47C2311yescharacteristic
169C23×C4×C47C2311yescharacteristic
170C23×C4×C47C2311yescharacteristic
171C23×C4×C47C2311yescharacteristic
172C23×C4×C47C2311yescharacteristic
173C2×C4⋊C4×C47—24no—
174C2×C4⋊C4×C47—24no—
175C2×C4⋊C4×C47—24no—
176C2×C4⋊C4×C47C2314yescomplemented
177C2×C4⋊C4×C47C2314yescomplemented
178C2×C4⋊C4×C47C2314yescomplemented
179C2×C22⋊C4×C47—24no—
180C2×C22⋊C4×C47—24no—
181C2×C22⋊C4×C47—24no—
182C2×C22⋊C4×C47C2314yes—
183C2×C22⋊C4×C47C2314yes—
184C2×C22⋊C4×C47C2314yes—
185#95×C47C2314yescomplemented
186C24×C47—22no—
187C24×C47—22no—
188C24×C47—22no—
189C24×C47—22no—
190C24×C47—22no—
191C24×C47—22no—
192C24×C47#4114yes—
193C24×C47C2412yes—
194C24×C47C2411yescharacteristic
195C23×D47—22no—
196C23×D47—22no—
197C23×D47—22no—
198C23×D47—22no—
199C23×D47—232no—
200C23×D47—22no—
201C23×D47—22no—
202C23×D47—22no—
203C23×D47—22no—
204C23×D47—22no—
205C23×D47—22no—
206C23×D47—28no—
207C23×D47—22no—
208C23×D47—22no—
209C23×D47—22no—
210C23×D47—22no—
211C23×D47—22no—
212C23×D47—22no—
213C23×D47—28no—
214C23×D47—28no—
215C23×D47—22no—
216C23×D47—22no—
217C23×D47—22no—
218C23×D47—22no—
219C23×D47—22no—
220C23×D47—22no—
221C23×D47—22no—
222C23×D47—28no—
223C23×D47—28no—
224C23×D47—44no—
225C23×D47—44no—
226C23×D47—416no—
227C23×D47—416no—
228C23×D47—416no—
229C23×D47—416no—
230C23×D47—416no—
231C23×D47—416no—
232C23×D47C2×D414yes—
233C23×D47C2×D414yes—
234C23×D47C2×D414yes—
235C23×D47C2×D414yes—
236C23×D47#4114yes—
237C23×D47C2412yes—
238C23×D47C2412yes—
239C23×D47C2412yes—
240C23×D47C2412yes—
241C22×C4×C47—22no—
242C22×C4×C47—22no—
243C22×C4×C47—22no—
244C22×C4×C47—22no—
245C22×C4×C47—22no—
246C22×C4×C47—22no—
247C22×C4×C47—22no—
248C22×C4×C47—22no—
249C22×C4×C47—22no—
250C22×C4×C47—22no—
251C22×C4×C47—22no—
252C22×C4×C47—22no—
253C22×C4×C47—22no—
254C22×C4×C47—22no—
255C22×C4×C47—22no—
256C22×C4×C47C2×D414yes—
257C22×C4×C47C2×D414yes—
258C22×C4×C47C2×D414yes—
259C22×C4×C47C2412yes—
260C22×C4×C47C2412yes—
261C22×C4×C47C2412yes—
262C22×C4×C47C2412yes—
263C22×C4×C47C2412yes—
264C22×C4×C47C2412yes—
265C2×C22⋊D47—28no—
266C2×C22⋊D47—28no—
267C2×C22⋊D47—28no—
268C2×C22⋊D47—28no—
269C2×C22⋊D47—44no—
270C2×C22⋊D47—44no—
271C2×C22⋊D47—416no—
272C2×C22⋊D47—416no—
273C22×Dic47—22no—
274C22×Dic47—22no—
275C22×Dic47—22no—
276C22×Dic47—22no—
277C22×Dic47—22no—
278C22×Dic47—22no—
279C22×Dic47—22no—
280C22×Dic47—22no—
281C22×Dic47—22no—
282C22×Dic47—22no—
283C22×Dic47C2×D414yes—
284C22×Dic47C2×D414yes—
285C22×Dic47C2412yes—
286C22×Dic47C2412yes—
287C22×Dic47C2412yes—
288C22×Dic47C2412yes—
289C2×D188—232no—
290C2×D188—28no—
291C2×D188—28no—
292C2×D188—28no—
293C2×D188—28no—
294C2×D188—28no—
295C2×D188—28no—
296C2×D188—28no—
297C2×D188—28no—
298C2×D188—28no—
299C2×D188—28no—
300C2×D188—28no—
301C2×D188—44no—
302C2×D188—44no—
303C2×D188—44no—
304C2×D188—416no—
305C2×D188—416no—
306C2×D188—416no—
307C2×D188—416no—
308C2×D188C2×D4116yescomplemented
309C2×C4×D47—28no—
310C2×C4×D47—28no—
311C2×C4×D47—28no—
312C2×C4×D47—28no—
313C2×C4×D47—28no—
314C2×C4×D47—28no—
315C2×C4×D47—44no—
316C2×C4×D47—44no—
317C2×C4×D47—44no—
318C2×C4×D47—416no—
319C2×C4×D47—416no—
320C2×C4×D47—416no—
321C4⋊C4×C47—28no—
322C4⋊C4×C47—28no—
323C4⋊C4×C47—28no—
324C22⋊C4×C47—28no—
325C22⋊C4×C47—28no—
326C22⋊C4×C47—28no—
327C22⋊Dic47—28no—
328(C2×D47)⋊C4—28no—
329(C2×D47)⋊C4—28no—
330(C2×D47)⋊C4—28no—
331(C2×D47)⋊C4—28no—
332(C2×D47)⋊C4—28no—
333(C2×D47)⋊C4—28no—
334(C2×D47)⋊C4—28no—
335(C2×D47)⋊C4—28no—
336(C2×D47)⋊C4—44no—
337(C2×D47)⋊C4C2×D4116yescomplemented
338(C2×D47)⋊C4C2×D4116yescomplemented
339Dic47⋊C4—44no—
340C4×Dic47—28no—
341C23×C47—28no—
342C23×C47—28no—
343C23×C47—28no—
344C23×C47—22no—
345C23×C47—22no—
346C23×C47—22no—
347C23×C47—22no—
348C23×C47—22no—
349C23×C47—22no—
350C23×C47—44no—
351C23×C47—44no—
352C23×C47—44no—
353C23×C47—44no—
354C23×C47C22×D412yes—
355C23×C47C22×D412yes—
356C23×C47C22×D412yes—
357C23×C47C2×#4112yes—
358C23×C47C2×#4114yes—
359C23×C47C2×#4112yes—
360C23×C47H(5,𝔽2)12yes—
361C23×C47H(5,𝔽2)12yes—
362C23×C47C2511yescharacteristic
363C22×D47—28no—
364C22×D47—28no—
365C22×D47—28no—
366C22×D47—28no—
367C22×D47—28no—
368C22×D47—28no—
369C22×D47—22no—
370C22×D47—22no—
371C22×D47—22no—
372C22×D47—22no—
373C22×D47—232no—
374C22×D47—28no—
375C22×D47—28no—
376C22×D47—28no—
377C22×D47—28no—
378C22×D47—28no—
379C22×D47—28no—
380C22×D47—22no—
381C22×D47—22no—
382C22×D47—22no—
383C22×D47—22no—
384C22×D47—22no—
385C22×D47—22no—
386C22×D47—22no—
387C22×D47—22no—
388C22×D47—22no—
389C22×D47—22no—
390C22×D47—22no—
391C22×D47—22no—
392C22×D47—22no—
393C22×D47—22no—
394C22×D47—22no—
395C22×D47—22no—
396C22×D47—22no—
397C22×D47—22no—
398C22×D47—22no—
399C22×D47—416no—
400C22×D47—416no—
401C22×D47—416no—
402C22×D47—416no—
403C22×D47—4128no—
404C22×D47—416no—
405C22×D47—44no—
406C22×D47—44no—
407C22×D47—44no—
408C22×D47—44no—
409C22×D47—44no—
410C22×D47—44no—
411C22×D47—44no—
412C22×D47—44no—
413C22×D47—416no—
414C22×D47—44no—
415C22×D47—44no—
416C22×D47—44no—
417C22×D47—44no—
418C22×D47—44no—
419C22×D47—44no—
420C22×D47—44no—
421C22×D47#121116yescomplemented
422C22×D47C22×D414yes—
423C22×D47C22×D414yes—
424C22×D47C22×D414yes—
425C22×D47C22×D414yes—
426C22×D47C2×#4114yes—
427C2×C4×C47—28no—
428C2×C4×C47—28no—
429C2×C4×C47—28no—
430C2×C4×C47—22no—
431C2×C4×C47—22no—
432C2×C4×C47—22no—
433C2×C4×C47—22no—
434C2×C4×C47—22no—
435C2×C4×C47—22no—
436C2×C4×C47—22no—
437C2×C4×C47—22no—
438C2×C4×C47—22no—
439C2×C4×C47—22no—
440C2×C4×C47—22no—
441C2×C4×C47—22no—
442C2×C4×C47—22no—
443C2×C4×C47—22no—
444C2×C4×C47—22no—
445C2×C4×C47—44no—
446C2×C4×C47—44no—
447C2×C4×C47—44no—
448C2×C4×C47C22×D414yes—
449C2×C4×C47C22×D414yes—
450C2×C4×C47C22×D414yes—
451C22⋊D47—416no—
452C22⋊D47—416no—
453C2×Dic47—28no—
454C2×Dic47—28no—
455C2×Dic47—22no—
456C2×Dic47—22no—
457C2×Dic47—22no—
458C2×Dic47—22no—
459C2×Dic47—22no—
460C2×Dic47—22no—
461C2×Dic47—22no—
462C2×Dic47—22no—
463C2×Dic47—22no—
464C2×Dic47—22no—
465C2×Dic47—44no—
466C2×Dic47—44no—
467C2×Dic47C22×D414yes—
468C2×Dic47C22×D414yes—
469D188—232no—
470D188—416no—
471D188—416no—
472D188—416no—
473D188—416no—
474C4×D47—416no—
475C4×D47—416no—
476C4×D47—416no—
477C2×#2424—471nomaximal, Sylow
478C22×C47—24no—
479C22×C47—24no—
480C22×C47—24no—
481C22×C47—42no—
482C22×C47—416no—
483C22×C47—42no—
484C22×C47—42no—
485C22×C47—42no—
486C22×C47C2×#12114yes—
487C22×C47#52514yes—
488C22×C47#53814yes—
489C22×C47D4214yes—
490C22×C47D4214yes—
491C22×C47#54614yes—
492C22×C47#54614yes—
493C22×C47C23×D411yescharacteristic
494C22×C47C23×D411yescharacteristic
495C22×C47C23×D411yescharacteristic
496C22×C47C22×#4111yescharacteristic
497C22×C47C22×#4111yescharacteristic
498C22×C47C2×H(5,𝔽2)11yescharacteristic
499C22×C47C2×H(5,𝔽2)11yescharacteristic
500C2×D47—24no—
501C2×D47—232no—
502C2×D47—24no—
503C2×D47—24no—
504C2×D47—24no—
505C2×D47—24no—
506C2×D47—24no—
507C2×D47—24no—
508C2×D47—24no—
509C2×D47—24no—
510C2×D47—24no—
511C2×D47—24no—
512C2×D47—24no—
513C2×D47—464no—
514C2×D47—42no—
515C2×D47—42no—
516C2×D47—416no—
517C2×D47—416no—
518C2×D47—42no—
519C2×D47—42no—
520C2×D47—42no—
521C2×D47—42no—
522C2×D47—42no—
523C2×D47—42no—
524C2×D47—42no—
525C2×D47—42no—
526C2×D47—42no—
527C2×D47—42no—
528C2×D47—42no—
529C2×D47—42no—
530C2×D47—42no—
531C2×D47—88no—
532C2×D47C2×#12118yescomplemented
533C4×C47—24no—
534C4×C47—24no—
535C4×C47—24no—
536C4×C47—42no—
537C4×C47—42no—
538C4×C47—42no—
539Dic47—24no—
540Dic47—24no—
541Dic47—42no—
542Dic47—42no—
543C22×#121—471no—
544C22×#121—471no—
545C22×#120—471no—
546C22×#120—471no—
547C22×C4×D4—471no—
548C23×C22⋊C4—471no—
549#2424—4716no—
550C2×#396D4711yescharacteristic, complemented
551C2×#394—471no—
552C2×#394—471no—
553C2×#392—471no—
554C2×#390—471no—
555C2×#388—471no—
556C2×#386—471no—
557C2×#386—471no—
558C2×#385—471no—
559C2×C47—44no—
560C2×C47#242418yescomplemented
561C2×C47C22×#12111yescharacteristic
562C2×C47C2×#52511yescharacteristic
563C2×C47C2×#53811yescharacteristic
564C2×C47C2×D4211yescharacteristic
565C2×C47C2×D4211yescharacteristic
566C2×C47C2×#54611yescharacteristic
567C2×C47C2×#54611yescharacteristic
568D47—28no—
569D47—44no—
570D47—44no—
571D47—82no—
572C26—471no—
573C23×D4—471no—
574C23×D4—471no—
575C23×D4—471no—
576C23×D4—471no—
577C23×D4—471no—
578C23×D4—471no—
579C23×D4—471no—
580C24×C4—471no—
581C24×C4—471no—
582C24×C4—471no—
583C2×#121—478no—
584C2×#121—478no—
585C2×#121—948no—
586C2×#121—948no—
587C2×#120—478no—
588C2×#120—478no—
589C2×#120—948no—
590C2×#120—948no—
591C2×C4×D4—478no—
592C2×C4×D4—948no—
593C22×C4⋊C4—471no—
594C22×C4⋊C4C2×D4711yescharacteristic, complemented
595C22×C4⋊C4C2×D4711yescharacteristic, complemented
596C22×C4⋊C4C2×D4711yescharacteristic, complemented
597C22×C22⋊C4—471no—
598C22×C22⋊C4—471no—
599C22×C22⋊C4—471no—
600C22×C22⋊C4—471no—
601C22×C22⋊C4—471no—
602C22×C22⋊C4—471no—
603C22×C22⋊C4—471no—
604C22×C22⋊C4—471no—
605C22×C22⋊C4—471no—
606C22×C22⋊C4—471no—
607C22×C22⋊C4—471no—
608C22×C22⋊C4—471no—
609C22×C22⋊C4—478no—
610C22×C22⋊C4—948no—
611C22×C22⋊C4C2×D4711yescharacteristic
612C22×C22⋊C4C2×D4711yescharacteristic
613C22×C22⋊C4C2×D4711yescharacteristic
614C22×C42—471no—
615#396C2×D4718yescomplemented
616#394—478no—
617#394—478no—
618#392—478no—
619#390—478no—
620#388—478no—
621#386—478no—
622#386—478no—
623#385—478no—
624C2×#95—471no—
625C2×#95—471no—
626C2×#95—471no—
627C2×#95C2×D4711yescharacteristic, complemented
628C47C2×#242411yescharacteristic, complemented, Sylow
629C25—471no—
630C25—471no—
631C25—471no—
632C25—471no—
633C25—474no—
634C25—944no—
635C25—944no—
636C25—944no—
637C25—944no—
638C25—944no—
639C25—1882no—
640C25—1882no—
641C25C22×D4711yescharacteristic
642C22×D4—474no—
643C22×D4—474no—
644C22×D4—478no—
645C22×D4—474no—
646C22×D4—474no—
647C22×D4—474no—
648C22×D4—474no—
649C22×D4—474no—
650C22×D4—944no—
651C22×D4—944no—
652C22×D4—944no—
653C22×D4—944no—
654C22×D4—944no—
655C22×D4—944no—
656C22×D4—944no—
657C22×D4—944no—
658C22×D4—944no—
659C22×D4—944no—
660C22×D4—944no—
661C22×D4—944no—
662C22×D4—944no—
663C22×D4—944no—
664C22×D4—944no—
665C22×D4—1882no—
666C22×D4—1882no—
667C22×D4—1882no—
668C22×D4—1882no—
669C22×D4—1882no—
670C23×C4—471no—
671C23×C4—471no—
672C23×C4—471no—
673C23×C4—471no—
674C23×C4—474no—
675C23×C4—474no—
676C23×C4—474no—
677C23×C4—944no—
678C23×C4—944no—
679C23×C4—944no—
680C23×C4—944no—
681C23×C4—944no—
682C23×C4—944no—
683C23×C4—1882no—
684C23×C4—1882no—
685C23×C4—1882no—
686C23×C4C22×D4711yescharacteristic
687C23×C4C22×D4711yescharacteristic
688C23×C4C22×D4711yescharacteristic
689C23×C4C22×D4711yescharacteristic
690C23×C4C22×D4711yescharacteristic
691C23×C4C22×D4711yescharacteristic
692#121—9432no—
693#121—9432no—
694#120—9432no—
695#120—9432no—
696C4×D4—9432no—
697C2×C4⋊C4—24no—
698C2×C4⋊C4—24no—
699C2×C4⋊C4—24no—
700C2×C4⋊C4—474no—
701C2×C4⋊C4—1882no—
702C2×C4⋊C4C22×D4714yescomplemented
703C2×C4⋊C4C22×D4714yescomplemented
704C2×C4⋊C4C22×D4714yescomplemented
705C2×C22⋊C4—24no—
706C2×C22⋊C4—24no—
707C2×C22⋊C4—24no—
708C2×C22⋊C4—478no—
709C2×C22⋊C4—478no—
710C2×C22⋊C4—474no—
711C2×C22⋊C4—474no—
712C2×C22⋊C4—474no—
713C2×C22⋊C4—474no—
714C2×C22⋊C4—474no—
715C2×C22⋊C4—474no—
716C2×C22⋊C4—474no—
717C2×C22⋊C4—474no—
718C2×C22⋊C4—474no—
719C2×C22⋊C4—474no—
720C2×C22⋊C4—474no—
721C2×C22⋊C4—474no—
722C2×C22⋊C4—9432no—
723C2×C22⋊C4—944no—
724C2×C22⋊C4—944no—
725C2×C22⋊C4—944no—
726C2×C22⋊C4—944no—
727C2×C22⋊C4—944no—
728C2×C22⋊C4—944no—
729C2×C22⋊C4—944no—
730C2×C22⋊C4—944no—
731C2×C22⋊C4—944no—
732C2×C22⋊C4—1882no—
733C2×C22⋊C4C22×D4714yes—
734C2×C22⋊C4C22×D4714yes—
735C2×C22⋊C4C22×D4714yes—
736C2×C42—474no—
737C2×C42—944no—
738#95—474no—
739#95—474no—
740#95—474no—
741#95C22×D4714yescomplemented
742C24—22no—
743C24—22no—
744C24—22no—
745C24—22no—
746C24—22no—
747C24—22no—
748C24—474no—
749C24—474no—
750C24—474no—
751C24—472no—
752C24—474no—
753C24—474no—
754C24—472no—
755C24—472no—
756C24—472no—
757C24—948no—
758C24—948no—
759C24—948no—
760C24—948no—
761C24—9432no—
762C24—942no—
763C24—942no—
764C24—942no—
765C24—942no—
766C24—942no—
767C24—942no—
768C24—942no—
769C24—942no—
770C24—942no—
771C24—942no—
772C24—942no—
773C24—948no—
774C24—942no—
775C24—942no—
776C24—942no—
777C24—942no—
778C24—942no—
779C24—942no—
780C24—942no—
781C24—942no—
782C24—942no—
783C24—942no—
784C24—942no—
785C24—942no—
786C24—1884no—
787C24—1884no—
788C24—18816no—
789C24—18816no—
790C24—18816no—
791C24—18816no—
792C24—18816no—
793C24—18816no—
794C24#1062535414yes—
795C24C23×D4712yes—
796C24C23×D4711yescharacteristic
797C2×D4—4716no—
798C2×D4—948no—
799C2×D4—9432no—
800C2×D4—948no—
801C2×D4—948no—
802C2×D4—948no—
803C2×D4—948no—
804C2×D4—948no—
805C2×D4—948no—
806C2×D4—948no—
807C2×D4—948no—
808C2×D4—948no—
809C2×D4—948no—
810C2×D4—948no—
811C2×D4—948no—
812C2×D4—948no—
813C2×D4—948no—
814C2×D4—1884no—
815C2×D4—1884no—
816C2×D4—1884no—
817C2×D4—18816no—
818C2×D4—18816no—
819C2×D4—18816no—
820C2×D4—18816no—
821C2×D4—1884no—
822C2×D4—1884no—
823C2×D4—18816no—
824C2×D4—18816no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—474no—
841C22×C4—474no—
842C22×C4—472no—
843C22×C4—472no—
844C22×C4—472no—
845C22×C4—472no—
846C22×C4—948no—
847C22×C4—948no—
848C22×C4—948no—
849C22×C4—948no—
850C22×C4—942no—
851C22×C4—942no—
852C22×C4—942no—
853C22×C4—942no—
854C22×C4—942no—
855C22×C4—942no—
856C22×C4—942no—
857C22×C4—942no—
858C22×C4—942no—
859C22×C4—942no—
860C22×C4—948no—
861C22×C4—948no—
862C22×C4—1884no—
863C22×C4—1884no—
864C22×C4—1884no—
865C22×C4—18816no—
866C22×C4—18816no—
867C22×C4—18816no—
868C22×C4D4×D4714yes—
869C22×C4D4×D4714yes—
870C22×C4D4×D4714yes—
871C22×C4C23×D4712yes—
872C22×C4C23×D4712yes—
873C22×C4C23×D4712yes—
874C22×C4C23×D4712yes—
875C22×C4C23×D4712yes—
876C22×C4C23×D4712yes—
877C4⋊C4—28no—
878C4⋊C4—28no—
879C4⋊C4—28no—
880C4⋊C4—1884no—
881C22⋊C4—28no—
882C22⋊C4—28no—
883C22⋊C4—28no—
884C22⋊C4—4716no—
885C22⋊C4—4716no—
886C22⋊C4—948no—
887C22⋊C4—948no—
888C22⋊C4—948no—
889C22⋊C4—948no—
890C22⋊C4—948no—
891C22⋊C4—948no—
892C22⋊C4—948no—
893C22⋊C4—948no—
894C22⋊C4—948no—
895C22⋊C4—1884no—
896C42—948no—
897C23—28no—
898C23—28no—
899C23—28no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—44no—
907C23—44no—
908C23—44no—
909C23—44no—
910C23—4716no—
911C23—474no—
912C23—474no—
913C23—474no—
914C23—474no—
915C23—474no—
916C23—9432no—
917C23—948no—
918C23—948no—
919C23—948no—
920C23—948no—
921C23—948no—
922C23—942no—
923C23—942no—
924C23—942no—
925C23—942no—
926C23—948no—
927C23—948no—
928C23—948no—
929C23—948no—
930C23—948no—
931C23—948no—
932C23—948no—
933C23—942no—
934C23—942no—
935C23—942no—
936C23—942no—
937C23—942no—
938C23—942no—
939C23—942no—
940C23—942no—
941C23—942no—
942C23—942no—
943C23—942no—
944C23—942no—
945C23—942no—
946C23—942no—
947C23—942no—
948C23—942no—
949C23—942no—
950C23—942no—
951C23—942no—
952C23—18816no—
953C23—18816no—
954C23—18816no—
955C23—18816no—
956C23—18816no—
957C23—188128no—
958C23—18816no—
959C23—1884no—
960C23—1884no—
961C23—1884no—
962C23—1884no—
963C23—1884no—
964C23—1884no—
965C23—1884no—
966C23—1884no—
967C23—1884no—
968C23—1884no—
969C23—1884no—
970C23—1884no—
971C23—1884no—
972C23—1884no—
973C23—1884no—
974C23C2×D4×D4712yes—
975C23C2×D4×D4712yes—
976C23C2×D4×D4712yes—
977C23#41×D4712yes—
978C23C2×#1062535414yes—
979C23C2×#1062535412yes—
980C23#1309407012yes—
981C23#1309407012yes—
982C23C24×D4711yescharacteristic
983D4—9432no—
984D4—18816no—
985D4—18816no—
986D4—18816no—
987D4—18816no—
988D4—18816no—
989D4—18816no—
990C2×C4—28no—
991C2×C4—28no—
992C2×C4—28no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—44no—
1009C2×C4—44no—
1010C2×C4—44no—
1011C2×C4—474no—
1012C2×C4—474no—
1013C2×C4—948no—
1014C2×C4—948no—
1015C2×C4—942no—
1016C2×C4—942no—
1017C2×C4—942no—
1018C2×C4—942no—
1019C2×C4—942no—
1020C2×C4—942no—
1021C2×C4—942no—
1022C2×C4—942no—
1023C2×C4—942no—
1024C2×C4—942no—
1025C2×C4—18816no—
1026C2×C4—18816no—
1027C2×C4—18816no—
1028C2×C4—1884no—
1029C2×C4—1884no—
1030C2×C4C2×D4×D4714yes—
1031C2×C4C2×D4×D4714yes—
1032C2×C4C2×D4×D4714yes—
1033C22—24no—
1034C22—24no—
1035C22—24no—
1036C22—42no—
1037C22—42no—
1038C22—42no—
1039C22—416no—
1040C22—42no—
1041C22—478no—
1042C22—944no—
1043C22—944no—
1044C22—944no—
1045C22—944no—
1046C22—944no—
1047C22—9432no—
1048C22—944no—
1049C22—944no—
1050C22—944no—
1051C22—944no—
1052C22—944no—
1053C22—944no—
1054C22—944no—
1055C22—3768no—
1056C22—18864no—
1057C22—1882no—
1058C22—1882no—
1059C22—1882no—
1060C22—1882no—
1061C22—1882no—
1062C22—1882no—
1063C22—1882no—
1064C22—1882no—
1065C22—1882no—
1066C22—1882no—
1067C22—1882no—
1068C22—1882no—
1069C22—1882no—
1070C22—18816no—
1071C22—18816no—
1072C22—1882no—
1073C22—1882no—
1074C22#121×D4714yes—
1075C22#1568963614yes—
1076C22#1568971214yes—
1077C22#1568975714yes—
1078C22#1568975714yes—
1079C22#1568976414yes—
1080C22#1568976414yes—
1081C22C22×D4×D4711yescharacteristic
1082C22C22×D4×D4711yescharacteristic
1083C22C22×D4×D4711yescharacteristic
1084C22C2×#41×D4711yescharacteristic
1085C22C22×#1062535411yescharacteristic
1086C22C2×#1309407011yescharacteristic
1087C22C2×#1309407011yescharacteristic
1088C4—24no—
1089C4—24no—
1090C4—24no—
1091C4—42no—
1092C4—42no—
1093C4—42no—
1094C4—944no—
1095C4—944no—
1096C4—1882no—
1097C4—1882no—
1098C2—44no—
1099C2—948no—
1100C2—3762no—
1101C2—1884no—
1102C2—1884no—
1103C2#2024691918yesdirect product factor
1104C2C2×#121×D4711yescharacteristic
1105C2C2×#1568963611yescharacteristic
1106C2C2×#1568971211yescharacteristic
1107C2C2×#1568975711yescharacteristic
1108C2C2×#1568975711yescharacteristic
1109C2C2×#1568976411yescharacteristic
1110C2C2×#1568976411yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#396C2
socleC24×C47C24
hypercenterC2×#396D47
hypocenterC47C2×#2424
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C22×#13093999C2semidirect
2. C22×#13093999C2semidirect
3. C22×#13093994C2semidirect
4. C22×#13093994C2semidirect
5. C22×#13093986C2semidirect
6. C22×C22⋊C4×D47C2semidirect
7. #20246919C2direct (N × H)
8. C2×#15689041C2semidirect
9. C2×#15689040C2semidirect
10. C2×#15689032C2semidirect
11. C2×#15689023C2semidirect
12. C2×#15689013C2semidirect
13. C2×#15689001C2semidirect
14. C2×#15688999C2semidirect
15. C2×#15688994C2semidirect
16. C2×C47×#396C2semidirect
22. C23×D188C22semidirect
27. C23×C4×D47C22semidirect
30. C2×#13093999C22semidirect
31. C2×#13093999C22semidirect
34. C2×#13093994C22semidirect
35. C2×#13093994C22semidirect
37. C2×#13093986C22semidirect
38. C22×Dic47⋊C4C22semidirect
46. C22×(C2×D47)⋊C4C22semidirect
47. C22×(C2×D47)⋊C4C22semidirect
48. C22×(C2×D47)⋊C4C22semidirect
49. C22×(C2×D47)⋊C4C22semidirect
50. C22×(C2×D47)⋊C4C22semidirect
52. C2×C22⋊C4×D47C22semidirect
53. C22×C4×Dic47C22semidirect
54. #15689041C22semidirect
55. #15689040C22semidirect
56. #15689032C22semidirect
57. #15689023C22semidirect
58. #15689013C22semidirect
59. #15689001C22semidirect
60. #15688999C22semidirect
61. #15688994C22semidirect
62. C2×C47⋊#95C22semidirect
63. C2×C47⋊#95C22semidirect
64. C2×C47⋊#95C22semidirect
65. C22×C4⋊C4×C47C22semidirect
66. C22×C4⋊C4×C47C22semidirect
67. C22×C4⋊C4×C47C22semidirect
71. C47×#396C22semidirect
72. C2×#95×C47C22semidirect
99. C22×D188D4semidirect
104. C22×D188C23semidirect
128. C22×C4×D47C23semidirect
135. C2×Dic47⋊C4C23semidirect
147. C2×(C2×D47)⋊C4D4semidirect
148. C2×(C2×D47)⋊C4D4semidirect
155. C2×(C2×D47)⋊C4C23semidirect
156. C2×(C2×D47)⋊C4C23semidirect
157. C2×(C2×D47)⋊C4C23semidirect
158. C2×(C2×D47)⋊C4C23semidirect
159. C2×(C2×D47)⋊C4C23semidirect
162. C2×C4×Dic47C23semidirect
163. C47⋊#95C23semidirect
164. C47⋊#95C23semidirect
165. C47⋊#95C23semidirect
176. C2×C4⋊C4×C47C23semidirect
177. C2×C4⋊C4×C47C23semidirect
178. C2×C4⋊C4×C47C23semidirect
185. #95×C47C23semidirect
308. C2×D188C2×D4semidirect
337. (C2×D47)⋊C4C2×D4semidirect
338. (C2×D47)⋊C4C2×D4semidirect
421. C22×D47#121semidirect
532. C2×D47C2×#121semidirect
550. C2×#396D47semidirect
560. C2×C47#2424semidirect
594. C22×C4⋊C4C2×D47semidirect
595. C22×C4⋊C4C2×D47semidirect
596. C22×C4⋊C4C2×D47semidirect
615. #396C2×D47semidirect
627. C2×#95C2×D47semidirect
628. C47C2×#2424semidirect
702. C2×C4⋊C4C22×D47semidirect
703. C2×C4⋊C4C22×D47semidirect
704. C2×C4⋊C4C22×D47semidirect
741. #95C22×D47semidirect
1103. C2#20246919direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130939992
C22×#130939942
C22×#130939862
C22×C22⋊C4×D472
#202469192
C2×#156890412
C2×#156890402
C2×#156890322
C2×#156890232
C2×#156890132
C2×#156890012
C2×#156889992
C2×#156889942
C2×C47×#3962
C2×#242447