Finite Group Databasebeta

← C2×#20246929 #26383747

Subgroups — C2×#20246929 #26383747

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×#13093997C211yesmaximal, characteristic, complemented
3C22×#13093994C211yesmaximal, characteristic, complemented
4C22×#13093994C211yesmaximal, characteristic, complemented
5C22×C4×D188C211yesmaximal, characteristic, complemented
6C22×C22⋊C4×D47C211yesmaximal, characteristic, complemented
7#20246929C2116yesmaximal, direct product factor
8C2×#15689045C211yesmaximal, characteristic, complemented
9C2×#15689039C211yesmaximal, characteristic, complemented
10C2×#15689039C211yesmaximal, characteristic, complemented
11C2×#15689033C211yesmaximal, characteristic, complemented
12C2×#15689025C211yesmaximal, characteristic, complemented
13C2×#15689001C211yesmaximal, characteristic, complemented
14C2×#15689001C211yesmaximal, characteristic, complemented
15C2×#15688997C211yesmaximal, characteristic, complemented
16C2×C47×#388C211yesmaximal, 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×#13093999C2218yescomplemented
30C2×#13093997—28no—
31C2×#13093997C2218yescomplemented
32C2×#13093994—28no—
33C2×#13093994—28no—
34C2×#13093994C2218yescomplemented
35C2×#13093994C2218yescomplemented
36C2×C4×D188—28no—
37C2×C4×D188C2218yescomplemented
38C22×C4⋊Dic47C2211yescharacteristic, complemented
39C22×C4⋊Dic47C2211yescharacteristic, complemented
40C22×Dic47⋊C4C2211yescharacteristic, complemented
41C22×C22⋊Dic47C2211yescharacteristic
42C22×(C2×D47)⋊C4C2211yescharacteristic
43C22×(C2×D47)⋊C4C2211yescharacteristic
44C22×(C2×D47)⋊C4C2211yescharacteristic
45C22×(C2×D47)⋊C4C2211yescharacteristic
46C22×(C2×D47)⋊C4C2211yescharacteristic
47C22×(C2×D47)⋊C4C2211yescharacteristic
48C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
49C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
50C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
51C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
52C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
53C2×C22⋊C4×D47—28no—
54C2×C22⋊C4×D47C2218yescomplemented
55#15689045C2218yescomplemented
56#15689039C2218yescomplemented
57#15689039C2218yescomplemented
58#15689033C2218yescomplemented
59#15689025C2218yescomplemented
60#15689001C2218yescomplemented
61#15689001C2218yescomplemented
62#15688997C2218yescomplemented
63C2×C47⋊#95C2211yescharacteristic, complemented
64C2×C47⋊#95C2211yescharacteristic, complemented
65C22×C4⋊C4×C47C2211yescharacteristic, complemented
66C22×C22⋊C4×C47C2211yescharacteristic
67C22×C22⋊C4×C47C2211yescharacteristic
68C22×C22⋊C4×C47C2211yescharacteristic
69C22×C42×C47C2211yescharacteristic, complemented
70C47×#388C2218yescomplemented
71C2×#95×C47C2211yescharacteristic, complemented
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#13093997—232no—
131#13093994—232no—
132#13093994—232no—
133C4×D188—232no—
134C2×C4⋊Dic47—24no—
135C2×C4⋊Dic47—42no—
136C2×C4⋊Dic47C2314yescomplemented
137C2×C4⋊Dic47C2314yescomplemented
138C2×Dic47⋊C4—24no—
139C2×Dic47⋊C4C2314yescomplemented
140C2×C22⋊Dic47—24no—
141C2×C22⋊Dic47C2314yes—
142C2×(C2×D47)⋊C4—24no—
143C2×(C2×D47)⋊C4—24no—
144C2×(C2×D47)⋊C4—24no—
145C2×(C2×D47)⋊C4—24no—
146C2×(C2×D47)⋊C4—24no—
147C2×(C2×D47)⋊C4—24no—
148C2×(C2×D47)⋊C4—24no—
149C2×(C2×D47)⋊C4—24no—
150C2×(C2×D47)⋊C4—24no—
151C2×(C2×D47)⋊C4—42no—
152C2×(C2×D47)⋊C4D418yescomplemented
153C2×(C2×D47)⋊C4C2314yes—
154C2×(C2×D47)⋊C4C2314yes—
155C2×(C2×D47)⋊C4C2314yes—
156C2×(C2×D47)⋊C4C2314yes—
157C2×(C2×D47)⋊C4C2314yes—
158C2×(C2×D47)⋊C4C2314yes—
159C2×(C2×D47)⋊C4C2314yescomplemented
160C2×(C2×D47)⋊C4C2314yescomplemented
161C2×(C2×D47)⋊C4C2314yescomplemented
162C2×(C2×D47)⋊C4C2314yescomplemented
163C2×(C2×D47)⋊C4C2314yescomplemented
164C22⋊C4×D47—232no—
165C47⋊#95C2314yescomplemented
166C47⋊#95C2314yescomplemented
167C25×C47C2311yescharacteristic
168C23×C4×C47C2311yescharacteristic
169C23×C4×C47C2311yescharacteristic
170C23×C4×C47C2311yescharacteristic
171C23×C4×C47C2311yescharacteristic
172C23×C4×C47C2311yescharacteristic
173C23×C4×C47C2311yescharacteristic
174C2×C4⋊C4×C47—24no—
175C2×C4⋊C4×C47C2314yescomplemented
176C2×C22⋊C4×C47—24no—
177C2×C22⋊C4×C47—24no—
178C2×C22⋊C4×C47D418yescomplemented
179C2×C22⋊C4×C47C2314yes—
180C2×C22⋊C4×C47C2314yes—
181C2×C22⋊C4×C47C2314yes—
182C2×C42×C47—24no—
183C2×C42×C47C2314yescomplemented
184#95×C47C2314yescomplemented
185#95×C47C2314yescomplemented
186C24×C47—22no—
187C24×C47—22no—
188C24×C47—22no—
189C24×C47—22no—
190C24×C47—22no—
191C24×C47—22no—
192C24×C47C2×D414yes—
193C24×C47C2412yes—
194C24×C47C2411yescharacteristic
195C23×D47—22no—
196C23×D47—22no—
197C23×D47—22no—
198C23×D47—22no—
199C23×D47—232no—
200C23×D47—28no—
201C23×D47—22no—
202C23×D47—22no—
203C23×D47—22no—
204C23×D47—22no—
205C23×D47—22no—
206C23×D47—22no—
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×D47#4114yes—
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×C47C2×D414yes—
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×Dic47—22no—
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—
322C22⋊C4×C47—28no—
323C22⋊C4×C47—28no—
324C22⋊C4×C47C2×D4116yescomplemented
325C42×C47—28no—
326C22⋊Dic47—28no—
327(C2×D47)⋊C4—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
338C4⋊Dic47—28no—
339C4⋊Dic47—44no—
340Dic47⋊C4—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×D414yes—
357C23×C47C22×D412yes—
358C23×C47C2×#4112yes—
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×D47C2×#4114yes—
426C22×D47C2×#4114yes—
427C2×C4×C47—28no—
428C2×C4×C47—28no—
429C2×C4×C47—28no—
430C2×C4×C47—28no—
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×C47C22×D414yes—
448C2×C4×C47C22×D414yes—
449C2×C4×C47C22×D414yes—
450C2×C4×C47C22×D414yes—
451C22⋊D47—416no—
452C22⋊D47—416no—
453C2×Dic47—28no—
454C2×Dic47—22no—
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×Dic47—44no—
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—24no—
537C4×C47—42no—
538C4×C47—42no—
539Dic47—24no—
540Dic47—42no—
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×#396—471no—
551C2×#394—471no—
552C2×#394—471no—
553C2×#392—471no—
554C2×#390—471no—
555C2×#388D4711yescharacteristic, complemented
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⋊C4—471no—
595C22×C4⋊C4—471no—
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×C42C2×D4711yescharacteristic, complemented
615#396—478no—
616#394—478no—
617#394—478no—
618#392—478no—
619#390—478no—
620#388C2×D4718yescomplemented
621#386—478no—
622#386—478no—
623#385—478no—
624C2×#95—471no—
625C2×#95—471no—
626C2×#95C2×D4711yescharacteristic, complemented
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—474no—
699C2×C4⋊C4—474no—
700C2×C4⋊C4—474no—
701C2×C4⋊C4—944no—
702C2×C4⋊C4—944no—
703C2×C4⋊C4—1882no—
704C2×C4⋊C4C22×D4714yescomplemented
705C2×C22⋊C4—24no—
706C2×C22⋊C4—24no—
707C2×C22⋊C4—478no—
708C2×C22⋊C4—474no—
709C2×C22⋊C4—474no—
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—944no—
721C2×C22⋊C4—944no—
722C2×C22⋊C4—944no—
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—9432no—
731C2×C22⋊C4—1882no—
732C2×C22⋊C4D18818yescomplemented
733C2×C22⋊C4C22×D4714yes—
734C2×C22⋊C4C22×D4714yes—
735C2×C22⋊C4C22×D4714yes—
736C2×C42—24no—
737C2×C42C22×D4714yescomplemented
738#95—474no—
739#95—474no—
740#95C22×D4714yescomplemented
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—948no—
770C24—942no—
771C24—942no—
772C24—942no—
773C24—942no—
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—
794C24C2×D18814yes—
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—474no—
840C22×C4—472no—
841C22×C4—472no—
842C22×C4—472no—
843C22×C4—472no—
844C22×C4—948no—
845C22×C4—948no—
846C22×C4—948no—
847C22×C4—942no—
848C22×C4—942no—
849C22×C4—942no—
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—948no—
859C22×C4—948no—
860C22×C4—948no—
861C22×C4—1884no—
862C22×C4—1884no—
863C22×C4—1884no—
864C22×C4—18816no—
865C22×C4—18816no—
866C22×C4—18816no—
867C22×C4C2×D18814yes—
868C22×C4C2×D18814yes—
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—948no—
879C4⋊C4—948no—
880C4⋊C4—1884no—
881C22⋊C4—28no—
882C22⋊C4—28no—
883C22⋊C4—4716no—
884C22⋊C4—948no—
885C22⋊C4—948no—
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—1884no—
895C22⋊C4C2×D188116yescomplemented
896C42—28no—
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—
976C23C22×D18814yes—
977C23C22×D18812yes—
978C23#41×D4712yes—
979C23#41×D4712yes—
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—28no—
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—474no—
1011C2×C4—948no—
1012C2×C4—942no—
1013C2×C4—942no—
1014C2×C4—942no—
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—18816no—
1024C2×C4—18816no—
1025C2×C4—18816no—
1026C2×C4—1884no—
1027C2×C4—1884no—
1028C2×C4—1884no—
1029C2×C4C2×D4×D4714yes—
1030C2×C4C2×D4×D4714yes—
1031C2×C4C22×D18814yes—
1032C2×C4C22×D18814yes—
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#1568963514yes—
1076C22#1568971214yes—
1077C22D4×D18814yes—
1078C22D4×D18814yes—
1079C22#1568976514yes—
1080C22#1568976614yes—
1081C22C22×D4×D4711yescharacteristic
1082C22C22×D4×D4711yescharacteristic
1083C22C23×D18811yescharacteristic
1084C22C2×#41×D4711yescharacteristic
1085C22C2×#41×D4711yescharacteristic
1086C22C2×#1309407011yescharacteristic
1087C22C2×#1309407011yescharacteristic
1088C4—24no—
1089C4—24no—
1090C4—24no—
1091C4—24no—
1092C4—42no—
1093C4—42no—
1094C4—944no—
1095C4—1882no—
1096C4—1882no—
1097C4—1882no—
1098C2—44no—
1099C2—948no—
1100C2—3762no—
1101C2—1884no—
1102C2—1884no—
1103C2#2024692918yesdirect product factor
1104C2C2×#121×D4711yescharacteristic
1105C2C2×#1568963511yescharacteristic
1106C2C2×#1568971211yescharacteristic
1107C2C2×D4×D18811yescharacteristic
1108C2C2×D4×D18811yescharacteristic
1109C2C2×#1568976511yescharacteristic
1110C2C2×#1568976611yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#388C2
socleC24×C47C24
hypercenterC2×#388D47
hypocenterC47C2×#2424
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×#13093999C2semidirect
2. C22×#13093997C2semidirect
3. C22×#13093994C2semidirect
4. C22×#13093994C2semidirect
5. C22×C4×D188C2semidirect
6. C22×C22⋊C4×D47C2semidirect
7. #20246929C2direct (N × H)
8. C2×#15689045C2semidirect
9. C2×#15689039C2semidirect
10. C2×#15689039C2semidirect
11. C2×#15689033C2semidirect
12. C2×#15689025C2semidirect
13. C2×#15689001C2semidirect
14. C2×#15689001C2semidirect
15. C2×#15688997C2semidirect
16. C2×C47×#388C2semidirect
22. C23×D188C22semidirect
27. C23×C4×D47C22semidirect
29. C2×#13093999C22semidirect
31. C2×#13093997C22semidirect
34. C2×#13093994C22semidirect
35. C2×#13093994C22semidirect
37. C2×C4×D188C22semidirect
38. C22×C4⋊Dic47C22semidirect
39. C22×C4⋊Dic47C22semidirect
40. C22×Dic47⋊C4C22semidirect
48. C22×(C2×D47)⋊C4C22semidirect
49. C22×(C2×D47)⋊C4C22semidirect
50. C22×(C2×D47)⋊C4C22semidirect
51. C22×(C2×D47)⋊C4C22semidirect
52. C22×(C2×D47)⋊C4C22semidirect
54. C2×C22⋊C4×D47C22semidirect
55. #15689045C22semidirect
56. #15689039C22semidirect
57. #15689039C22semidirect
58. #15689033C22semidirect
59. #15689025C22semidirect
60. #15689001C22semidirect
61. #15689001C22semidirect
62. #15688997C22semidirect
63. C2×C47⋊#95C22semidirect
64. C2×C47⋊#95C22semidirect
65. C22×C4⋊C4×C47C22semidirect
69. C22×C42×C47C22semidirect
70. C47×#388C22semidirect
71. C2×#95×C47C22semidirect
72. C2×#95×C47C22semidirect
99. C22×D188D4semidirect
104. C22×D188C23semidirect
128. C22×C4×D47C23semidirect
136. C2×C4⋊Dic47C23semidirect
137. C2×C4⋊Dic47C23semidirect
139. C2×Dic47⋊C4C23semidirect
152. C2×(C2×D47)⋊C4D4semidirect
159. C2×(C2×D47)⋊C4C23semidirect
160. C2×(C2×D47)⋊C4C23semidirect
161. C2×(C2×D47)⋊C4C23semidirect
162. C2×(C2×D47)⋊C4C23semidirect
163. C2×(C2×D47)⋊C4C23semidirect
165. C47⋊#95C23semidirect
166. C47⋊#95C23semidirect
175. C2×C4⋊C4×C47C23semidirect
178. C2×C22⋊C4×C47D4semidirect
183. C2×C42×C47C23semidirect
184. #95×C47C23semidirect
185. #95×C47C23semidirect
308. C2×D188C2×D4semidirect
324. C22⋊C4×C47C2×D4semidirect
337. (C2×D47)⋊C4C2×D4semidirect
421. C22×D47#121semidirect
532. C2×D47C2×#121semidirect
555. C2×#388D47semidirect
560. C2×C47#2424semidirect
596. C22×C4⋊C4C2×D47semidirect
614. C22×C42C2×D47semidirect
620. #388C2×D47semidirect
626. C2×#95C2×D47semidirect
627. C2×#95C2×D47semidirect
628. C47C2×#2424semidirect
704. C2×C4⋊C4C22×D47semidirect
732. C2×C22⋊C4D188semidirect
737. C2×C42C22×D47semidirect
740. #95C22×D47semidirect
741. #95C22×D47semidirect
895. C22⋊C4C2×D188semidirect
1103. C2#20246929direct (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×#130939972
C22×#130939942
C22×C4×D1882
C22×C22⋊C4×D472
#202469292
C2×#156890452
C2×#156890392
C2×#156890332
C2×#156890252
C2×#156890012
C2×#156889972
C2×C47×#3882
C2×#242447