Finite Group Databasebeta

← #26379797

Subgroups — #26379797

Order 12032.

2766 conjugacy classes of subgroups.

The subgroup lattice has 1192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689692C211yesmaximal, characteristic
2#20246559C212yesmaximal, complemented
3#20246528C212yesmaximal, complemented
4#20246498C212yesmaximal, complemented
5#20246428C211yesmaximal, characteristic, complemented
6#20246425C211yesmaximal, characteristic, complemented
7#20246406C211yesmaximal, characteristic, complemented
8#20246403C211yesmaximal, characteristic, complemented
9#20246366C212yesmaximal, complemented
10#20246273C211yesmaximal, characteristic, complemented
11C22⋊C4×D188C211yesmaximal, characteristic, complemented
12#20246208C211yesmaximal, characteristic, complemented
13#20246113C212yesmaximal, complemented
14#20246111C212yesmaximal, complemented
15#20246082C211yesmaximal, characteristic, complemented
16#20246079C211yesmaximal, characteristic, complemented
17#20246050C212yesmaximal, complemented
18#20246041C212yesmaximal, complemented
19#20245977C211yesmaximal, characteristic, complemented
20C4×#13093999C211yesmaximal, characteristic, complemented
21#20245896C211yesmaximal, characteristic, complemented
22#20245874C211yesmaximal, characteristic, complemented
23C47×#2346C211yesmaximal, characteristic, complemented
24C22×#10625350C2211yescharacteristic
25C23×D188C2211yescharacteristic
26#15689692C4116yescomplemented
27C2×#13094021C2212yes—
28C2×#13094012C2212yes—
29C2×#13093999C2211yescharacteristic
30C2×#13093999C2211yescharacteristic
31C2×#13093999C2211yescharacteristic
32C2×#13093999C2211yescharacteristic
33C2×#13093994C2212yes—
34C2×#13093994C2212yes—
35C2×C4×D188C2211yescharacteristic
36C2×C4×D188C2211yescharacteristic
37C2×C4×D188C2212yescomplemented
38C2×C4×D188C2212yescomplemented
39C2×#13093986C2211yescharacteristic
40C2×#13093986C2211yescharacteristic
41C2×#13093986C2212yescomplemented
42C2×#13093986C2212yescomplemented
43C2×#13093982C2211yescharacteristic, complemented
44C2×#13093981C2211yescharacteristic, complemented
45C2×C4⋊C4×D47C2211yescharacteristic, complemented
46C2×C22⋊C4×D47C2212yes—
47C2×C22⋊C4×D47C2212yes—
48C2×C42×D47C2211yescharacteristic, complemented
49#15689027C2211yescharacteristic, complemented
50#15689027C2212yescomplemented
51#15689027C2211yescharacteristic, complemented
52#15689025C2211yescharacteristic
53#15689025C2211yescharacteristic
54#15689025C2212yescomplemented
55#15689025C2212yescomplemented
56#15689024C2211yescharacteristic
57#15689024C2211yescharacteristic
58#15689024C2212yescomplemented
59#15689024C2212yescomplemented
60#15689023C2211yescharacteristic
61#15689023C2212yes—
62#15689023C2211yescharacteristic
63#15689022C2211yescharacteristic, complemented
64#15689022C2211yescharacteristic, complemented
65#15689016C2212yes—
66#15689016C2212yes—
67#15689015C2212yescomplemented
68#15689015C2212yescomplemented
69#15689014C2212yescomplemented
70#15689014C2212yescomplemented
71#15689013C2212yescomplemented
72#15689013C2212yescomplemented
73#15689012C2212yescomplemented
74#15689012C2212yescomplemented
75#15689001C2212yes—
76#15689001C2212yes—
77#15689001C2212yes—
78#15689001C2212yes—
79#15689001C2212yescomplemented
80#15689001C2212yescomplemented
81#15689001C2212yescomplemented
82#15689001C2212yescomplemented
83#15689001C2212yescomplemented
84#15689001C2212yescomplemented
85#15689001C2212yescomplemented
86#15689001C2212yescomplemented
87#15689001C2211yescharacteristic, complemented
88#15689001C2212yescomplemented
89#15689001C2211yescharacteristic, complemented
90#15688999C2212yes—
91#15688999C2211yescharacteristic
92#15688999C2211yescharacteristic
93#15688997C2212yescomplemented
94#15688997C2212yescomplemented
95#15688994C2212yescomplemented
96#15688994C2212yescomplemented
97#15688989C2212yescomplemented
98#15688983C2211yescharacteristic
99#15688980C2211yescharacteristic, complemented
100#15688980C2211yescharacteristic, complemented
101#15688978C2212yes—
102#15688978C2212yes—
103C4⋊C4×Dic47C2211yescharacteristic, complemented
104C4⋊C4×Dic47C2211yescharacteristic, complemented
105C4×(C2×D47)⋊C4C2212yescomplemented
106C4×(C2×D47)⋊C4C2212yescomplemented
107C4×(C2×D47)⋊C4C2211yescharacteristic, complemented
108C4×(C2×D47)⋊C4C2211yescharacteristic, complemented
109C4×C22⋊Dic47C2211yescharacteristic
110#15688970C2212yescomplemented
111#15688970C2212yescomplemented
112#15688969C2212yescomplemented
113C2×#117×C47C2211yescharacteristic
114C47×#389C2211yescharacteristic, complemented
115C47×#389C2211yescharacteristic, complemented
116C47×#388C2212yes—
117C47×#388C2212yes—
118C47×#382C2212yescomplemented
119C47×#380C2211yescharacteristic
120C4×C4⋊C4×C47C2211yescharacteristic, complemented
121C4×C4⋊C4×C47C2211yescharacteristic, complemented
122C4×C22⋊C4×C47C2211yescharacteristic
123C47×#376C2212yescomplemented
124C24×D47C2312yes—
125C2×#10625350—42no—
126C2×#10625350—42no—
127C2×#10625350C2×C418yescomplemented
128C22×Dic94C2311yescharacteristic
129C22×D188—42no—
130C22×D188—42no—
131C22×D188C2×C418yescomplemented
132C22×D188C2311yescharacteristic
133C22×D188C2311yescharacteristic
134C22×D188C2312yes—
135C22×D188C2311yescharacteristic
136C22×D188C2312yes—
137C22×D188C2312yes—
138C22×D188C2312yes—
139C22×D188C2312yes—
140C22×C22⋊D47C2311yescharacteristic
141C22×C22⋊D47C2311yescharacteristic
142C22×C4×D47C2311yescharacteristic
143C22×C4×D47C2311yescharacteristic
144C22×C4×D47C2312yes—
145C22×C4×D47C2312yes—
146C22×C4×D47C2311yescharacteristic
147C22×C4×D47C2311yescharacteristic
148C22×C4×D47C2312yes—
149C22×C4×D47C2312yes—
150C22×C4×D47C2312yes—
151#13094021C2×C4116yescomplemented
152#13094012C2×C4116yescomplemented
153#13093999C2×C418yescomplemented
154#13093999C2×C418yescomplemented
155#13093999C2×C418yescomplemented
156#13093999C2×C418yescomplemented
157#13093994C2×C4116yescomplemented
158#13093994C2×C4116yescomplemented
159C4×D188—42no—
160C4×D188—42no—
161C4×D188—44no—
162C4×D188—44no—
163#13093986—44no—
164#13093986—42no—
165#13093986—42no—
166#13093986—44no—
167#13093982—42no—
168#13093981—42no—
169C2×C4⋊Dic47C2311yescharacteristic
170C2×C4⋊Dic47C2311yescharacteristic
171C2×C4⋊Dic47C2312yes—
172C2×C4⋊Dic47C2312yes—
173C2×Dic47⋊C4C2311yescharacteristic
174C2×Dic47⋊C4C2312yes—
175C2×Dic47⋊C4C2311yescharacteristic
176C4⋊C4×D47—42no—
177C2×C22⋊Dic47C2311yescharacteristic
178C2×C22⋊Dic47C2311yescharacteristic
179C2×C22⋊Dic47C2312yes—
180C2×(C2×D47)⋊C4C2312yes—
181C2×(C2×D47)⋊C4C2312yes—
182C2×(C2×D47)⋊C4C2311yescharacteristic
183C2×(C2×D47)⋊C4C2311yescharacteristic
184C2×(C2×D47)⋊C4C2312yes—
185C2×(C2×D47)⋊C4C2312yes—
186C2×(C2×D47)⋊C4C2311yescharacteristic
187C2×(C2×D47)⋊C4C2311yescharacteristic
188C2×(C2×D47)⋊C4C2312yes—
189C2×(C2×D47)⋊C4C2312yes—
190C2×(C2×D47)⋊C4C2312yes—
191C2×(C2×D47)⋊C4C2312yes—
192C2×(C2×D47)⋊C4C2312yes—
193C2×(C2×D47)⋊C4C2312yes—
194C2×(C2×D47)⋊C4C2312yes—
195C2×(C2×D47)⋊C4C2312yes—
196C2×(C2×D47)⋊C4C2312yes—
197C2×(C2×D47)⋊C4C2312yes—
198C2×(C2×D47)⋊C4C2311yescharacteristic
199C2×(C2×D47)⋊C4C2312yes—
200C2×(C2×D47)⋊C4C2311yescharacteristic
201C2×(C2×D47)⋊C4C2312yes—
202C2×(C2×D47)⋊C4C2312yes—
203C2×(C2×D47)⋊C4C2312yes—
204C2×(C2×D47)⋊C4C2312yes—
205C22⋊C4×D47—44no—
206C22⋊C4×D47—44no—
207C2×C4×Dic47C2312yes—
208C2×C4×Dic47C2311yescharacteristic
209C2×C4×Dic47C2311yescharacteristic
210C2×C4×Dic47C2312yes—
211C2×C4×Dic47C2311yescharacteristic
212C2×C4×Dic47C2312yes—
213C2×C4×Dic47C2311yescharacteristic
214C42×D47—42no—
215C47⋊#95C2311yescharacteristic
216C47⋊#95C2312yes—
217C47⋊#95C2312yes—
218C47⋊#95C2312yes—
219C47⋊#95C2311yescharacteristic
220C47⋊#95C2312yes—
221C47⋊#95C2311yescharacteristic
222C47⋊#95C2311yescharacteristic
223C47⋊#95C2312yes—
224C47⋊#95C2311yescharacteristic
225C47⋊#95C2311yescharacteristic
226C47⋊#95C2312yes—
227C47⋊#95C2312yes—
228C23×C4×C47C2311yescharacteristic
229#117×C47C2×C418yescomplemented
230C2×C4⋊C4×C47C2311yescharacteristic
231C2×C4⋊C4×C47C2311yescharacteristic
232C2×C4⋊C4×C47C2312yes—
233C2×C4⋊C4×C47C2312yes—
234C2×C4⋊C4×C47C2311yescharacteristic
235C2×C4⋊C4×C47C2311yescharacteristic
236C2×C22⋊C4×C47C2311yescharacteristic
237C2×C22⋊C4×C47C2311yescharacteristic
238C2×C22⋊C4×C47C2312yes—
239C2×C22⋊C4×C47C2312yes—
240C2×C42×C47C2312yes—
241C2×C42×C47C2311yescharacteristic
242C2×C42×C47C2311yescharacteristic
243C2×C42×C47C2312yes—
244C2×C42×C47C2312yes—
245#95×C47C2312yes—
246#95×C47C2312yes—
247#95×C47C2312yes—
248#95×C47C2311yescharacteristic
249#95×C47C2312yes—
250#95×C47C2311yescharacteristic
251#95×C47C2312yes—
252C24×C47C2411yescharacteristic
253C23×D47—42no—
254C23×D47—42no—
255C23×D47—42no—
256C23×D47—42no—
257C23×D47—42no—
258C23×D47—42no—
259C23×D47C22×C418yes—
260C23×D47C2412yes—
261C23×D47C2412yes—
262C23×D47C2411yescharacteristic
263C23×D47C2411yescharacteristic
264C22×C4×C47—22no—
265C22×C4×C47—22no—
266C22×C4×C47C22×C414yes—
267C22×C4×C47C2411yescharacteristic
268C22×C4×C47C2411yescharacteristic
269C22×C4×C47C2412yes—
270C22×C4×C47C2411yescharacteristic
271C22×C4×C47C2412yes—
272C22×C4×C47C2412yes—
273C22×C4×C47C2411yescharacteristic
274C22×C4×C47C2412yes—
275C22×C4×C47C2411yescharacteristic
276C22×C4×C47C2411yescharacteristic
277C2×C22⋊D47—41no—
278C2×C22⋊D47—41no—
279C2×C22⋊D47—41no—
280C2×C22⋊D47—41no—
281C2×C22⋊D47C22×C414yes—
282C2×C22⋊D47C22×C414yes—
283C22×Dic47C2411yescharacteristic
284C22×Dic47C2411yescharacteristic
285C22×Dic47C2412yes—
286C22×Dic47C2411yescharacteristic
287C22×Dic47C2412yes—
288C22×Dic47C2411yescharacteristic
289C22×Dic47C2411yescharacteristic
290C22×Dic47C2411yescharacteristic
291#10625350—416no—
292C2×D188—22no—
293C2×D188—22no—
294C2×D188—22no—
295C2×D188—22no—
296C2×D188—416no—
297C2×D188—42no—
298C2×D188—42no—
299C2×D188—42no—
300C2×D188—42no—
301C2×D188—42no—
302C2×D188—42no—
303C2×D188—42no—
304C2×D188—42no—
305C2×D188—42no—
306C2×D188—42no—
307C2×D188—41no—
308C2×D188—41no—
309C2×D188C22×C414yes—
310C2×D188C22×C414yes—
311C2×D188C22×C418yes—
312C2×D188C22×C418yes—
313C2×D188C22×C418yes—
314C2×D188C22×C418yes—
315C2×D188C22×C418yes—
316C2×D188C22×C414yes—
317C2×C4×D47—22no—
318C2×C4×D47—22no—
319C2×C4×D47—22no—
320C2×C4×D47—22no—
321C2×C4×D47—22no—
322C2×C4×D47—22no—
323C2×C4×D47—24no—
324C2×C4×D47—24no—
325C2×C4×D47—41no—
326C2×C4×D47—41no—
327C2×C4×D47—41no—
328C2×C4×D47—41no—
329C2×C4×D47—42no—
330C2×C4×D47—42no—
331C2×C4×D47—42no—
332C2×C4×D47—42no—
333C2×C4×D47—42no—
334C2×C4×D47—42no—
335C2×C4×D47—42no—
336C2×C4×D47—42no—
337C2×C4×D47—42no—
338C2×C4×D47—42no—
339C2×C4×D47—42no—
340C2×C4×D47—42no—
341C2×C4×D47—42no—
342C2×C4×D47C22×C414yes—
343C2×C4×D47C22×C414yes—
344C2×Dic94—41no—
345C2×Dic94—41no—
346C2×Dic94C22×C414yes—
347C4⋊C4×C47—22no—
348C4⋊C4×C47—22no—
349C4⋊C4×C47—42no—
350C4⋊C4×C47—42no—
351C4⋊C4×C47C22×C414yes—
352C4⋊C4×C47C22×C414yes—
353C22⋊C4×C47—22no—
354C22⋊C4×C47—41no—
355C22⋊C4×C47—42no—
356C22⋊C4×C47C22×C418yes—
357C42×C47—22no—
358C42×C47—22no—
359C42×C47—24no—
360C42×C47—42no—
361C42×C47C22×C418yes—
362C22⋊Dic47—22no—
363C22⋊Dic47—42no—
364C22⋊Dic47—41no—
365(C2×D47)⋊C4—24no—
366(C2×D47)⋊C4—22no—
367(C2×D47)⋊C4—24no—
368(C2×D47)⋊C4—22no—
369(C2×D47)⋊C4—42no—
370(C2×D47)⋊C4—42no—
371(C2×D47)⋊C4—42no—
372(C2×D47)⋊C4—42no—
373(C2×D47)⋊C4—41no—
374(C2×D47)⋊C4—41no—
375(C2×D47)⋊C4—41no—
376(C2×D47)⋊C4—41no—
377(C2×D47)⋊C4—42no—
378(C2×D47)⋊C4—42no—
379(C2×D47)⋊C4—42no—
380(C2×D47)⋊C4—42no—
381(C2×D47)⋊C4—42no—
382(C2×D47)⋊C4—42no—
383(C2×D47)⋊C4—42no—
384(C2×D47)⋊C4—42no—
385(C2×D47)⋊C4—42no—
386(C2×D47)⋊C4C22×C418yes—
387(C2×D47)⋊C4C22×C418yes—
388(C2×D47)⋊C4C22×C418yes—
389(C2×D47)⋊C4C22×C418yes—
390C4⋊Dic47—22no—
391C4⋊Dic47—22no—
392C4⋊Dic47—42no—
393C4⋊Dic47—42no—
394Dic47⋊C4—42no—
395Dic47⋊C4—41no—
396Dic47⋊C4—41no—
397C4×Dic47—22no—
398C4×Dic47—22no—
399C4×Dic47—24no—
400C4×Dic47—41no—
401C4×Dic47—41no—
402C4×Dic47—42no—
403C4×Dic47—42no—
404C23×C47—21no—
405C23×C47—21no—
406C23×C47—21no—
407C23×C47—21no—
408C23×C47—21no—
409C23×C47—21no—
410C23×C47C23×C412yes—
411C23×C47C2511yescharacteristic
412C22×D47—22no—
413C22×D47—22no—
414C22×D47—21no—
415C22×D47—21no—
416C22×D47—21no—
417C22×D47—21no—
418C22×D47—21no—
419C22×D47—21no—
420C22×D47—22no—
421C22×D47—22no—
422C22×D47—22no—
423C22×D47—22no—
424C22×D47—22no—
425C22×D47—22no—
426C22×D47—21no—
427C22×D47—21no—
428C22×D47—21no—
429C22×D47—21no—
430C22×D47—22no—
431C22×D47—22no—
432C22×D47—21no—
433C22×D47—21no—
434C22×D47—22no—
435C22×D47—22no—
436C22×D47—48no—
437C22×D47—48no—
438C22×D47—48no—
439C22×D47—84no—
440C22×D47—84no—
441C22×D47—84no—
442C22×D47—84no—
443C22×D47C23×C414yes—
444C22×D47C23×C414yes—
445C22×D47C23×C412yes—
446C22×D47C23×C412yes—
447C2×C4×C47—22no—
448C2×C4×C47—21no—
449C2×C4×C47—22no—
450C2×C4×C47—21no—
451C2×C4×C47—21no—
452C2×C4×C47—22no—
453C2×C4×C47—22no—
454C2×C4×C47—21no—
455C2×C4×C47—28no—
456C2×C4×C47—21no—
457C2×C4×C47—22no—
458C2×C4×C47—21no—
459C2×C4×C47—21no—
460C2×C4×C47—22no—
461C2×C4×C47—22no—
462C2×C4×C47—21no—
463C2×C4×C47—22no—
464C2×C4×C47—21no—
465C2×C4×C47—22no—
466C2×C4×C47—21no—
467C2×C4×C47—21no—
468C2×C4×C47—22no—
469C2×C4×C47—21no—
470C2×C4×C47—21no—
471C2×C4×C47C23×C414yes—
472C2×C4×C47C23×C414yes—
473C2×C4×C47C23×C412yes—
474C2×C4×C47C23×C412yes—
475C2×C4×C47H(5,𝔽2)12yes—
476C2×C4×C47H(5,𝔽2)12yes—
477C2×C4×C47H(5,𝔽2)12yes—
478C22⋊D47—44no—
479C22⋊D47—44no—
480C2×Dic47—21no—
481C2×Dic47—21no—
482C2×Dic47—21no—
483C2×Dic47—21no—
484C2×Dic47—21no—
485C2×Dic47—21no—
486C2×Dic47—21no—
487C2×Dic47—21no—
488C2×Dic47—21no—
489C2×Dic47—22no—
490C2×Dic47—22no—
491C2×Dic47—22no—
492C2×Dic47—21no—
493C2×Dic47—21no—
494C2×Dic47—22no—
495C2×Dic47—22no—
496C2×Dic47—21no—
497C2×Dic47—21no—
498C2×Dic47—22no—
499C2×Dic47—21no—
500C2×Dic47—21no—
501C2×Dic47C23×C412yes—
502C2×Dic47C23×C412yes—
503C2×Dic47H(5,𝔽2)12yes—
504D188—28no—
505D188—28no—
506D188—48no—
507D188—48no—
508D188—48no—
509D188—48no—
510D188—48no—
511D188—44no—
512C4×D47—28no—
513C4×D47—28no—
514C4×D47—44no—
515C4×D47—44no—
516C4×D47—84no—
517C4×D47—84no—
518C4×D47—84no—
519C4×D47—84no—
520C4×D47—84no—
521Dic94—44no—
522#34415—471nomaximal, Sylow
523C22×C47—22no—
524C22×C47—22no—
525C22×C47—22no—
526C22×C47—41no—
527C22×C47—41no—
528C22×C47—41no—
529C22×C47—41no—
530C22×C47C24×C411yescharacteristic
531C22×C47C2×H(5,𝔽2)11yescharacteristic
532C22×C47C2×H(5,𝔽2)11yescharacteristic
533C22×C47C2×H(5,𝔽2)11yescharacteristic
534C22×C47C2×H(5,𝔽2)11yescharacteristic
535C22×C47#58511yescharacteristic
536C22×C47#58511yescharacteristic
537C2×D47—22no—
538C2×D47—22no—
539C2×D47—24no—
540C2×D47—24no—
541C2×D47—22no—
542C2×D47—22no—
543C2×D47—22no—
544C2×D47—22no—
545C2×D47—24no—
546C2×D47—24no—
547C2×D47—24no—
548C2×D47—24no—
549C2×D47—41no—
550C2×D47—41no—
551C2×D47—42no—
552C2×D47—42no—
553C2×D47—41no—
554C2×D47—41no—
555C2×D47—42no—
556C2×D47—42no—
557C2×D47—41no—
558C2×D47—42no—
559C2×D47—42no—
560C2×D47—41no—
561C2×D47—41no—
562C2×D47—41no—
563C2×D47—42no—
564C2×D47—42no—
565C2×D47—816no—
566C4×C47—22no—
567C4×C47—24no—
568C4×C47—24no—
569C4×C47—22no—
570C4×C47—41no—
571C4×C47—42no—
572C4×C47—41no—
573C4×C47—42no—
574C4×C47—41no—
575C4×C47#51814yes—
576Dic47—22no—
577Dic47—22no—
578Dic47—22no—
579Dic47—41no—
580Dic47—42no—
581Dic47—41no—
582Dic47—42no—
583Dic47—41no—
584C2×#535—471no—
585#2379—472no—
586#2375—472no—
587#2372—472no—
588#2363—471no—
589#2363—471no—
590#2361—471no—
591#2361—471no—
592#2358—472no—
593#2346—471no—
594#2346D4711yescharacteristic, complemented
595D4×C22⋊C4—471no—
596D4×C22⋊C4—471no—
597#2328—472no—
598#2328—472no—
599#2324—471no—
600#2324—471no—
601#2321—472no—
602#2321—472no—
603#2311—471no—
604C4×#121—471no—
605C4×#121—471no—
606#2297—471no—
607C2×C47—42no—
608C2×C47C2×#51811yescharacteristic
609C2×C47C4×H(5,𝔽2)11yescharacteristic
610C2×C47C4×H(5,𝔽2)11yescharacteristic
611C2×C47#354211yescharacteristic
612C2×C47#354211yescharacteristic
613C2×C47#354911yescharacteristic
614C2×C47#355111yescharacteristic
615D47—42no—
616D47—42no—
617D47—44no—
618D47—44no—
619C22×#41—471no—
620C23×D4—471no—
621#535—4716no—
622C2×#127—472no—
623C2×#124—472no—
624C2×#121—471no—
625C2×#121—471no—
626C2×#121—471no—
627C2×#121—471no—
628C2×#120—472no—
629C2×#120—472no—
630C2×C4×D4—472no—
631C2×C4×D4—471no—
632C2×C4×D4—472no—
633C2×C4×D4—471no—
634C2×C4×D4—472no—
635C2×C4×D4—471no—
636C2×C4×D4—472no—
637C2×C4×D4—471no—
638C2×#117—471no—
639C2×#117—471no—
640C2×#117C2×D4711yescharacteristic
641C22×C4⋊C4—471no—
642C22×C22⋊C4—472no—
643C22×C22⋊C4—472no—
644C22×C42—471no—
645#391—472no—
646#391—471no—
647#391—471no—
648#390—472no—
649#390—471no—
650#390—472no—
651#390—471no—
652#390—472no—
653#390—471no—
654#390—471no—
655#390—472no—
656#390—471no—
657#390—472no—
658#390—471no—
659#389—471no—
660#389—471no—
661#389C2×D4711yescharacteristic, complemented
662#389C2×D4711yescharacteristic, complemented
663#388—472no—
664#388—472no—
665#388—472no—
666#388—472no—
667#388—472no—
668#388—472no—
669#388—472no—
670#388—472no—
671#388—472no—
672#388—472no—
673#388C2×D4712yes—
674#388C2×D4712yes—
675#386—472no—
676#386—471no—
677#386—471no—
678#386—472no—
679#386—472no—
680#386—472no—
681#386—472no—
682#386—472no—
683#386—471no—
684#386—471no—
685#386—472no—
686#386—472no—
687#386—472no—
688#386—472no—
689#386—472no—
690#386—472no—
691#386—472no—
692#386—472no—
693#385—472no—
694#385—472no—
695#385—472no—
696#385—472no—
697#382—472no—
698#382C2×D4712yescomplemented
699#380—471no—
700#380—471no—
701#380—471no—
702#380C2×D4711yescharacteristic
703#379—472no—
704#379—472no—
705C4×C4⋊C4—471no—
706C4×C4⋊C4—471no—
707C4×C4⋊C4C2×D4711yescharacteristic, complemented
708C4×C4⋊C4C2×D4711yescharacteristic, complemented
709C4×C22⋊C4—471no—
710C4×C22⋊C4—472no—
711C4×C22⋊C4—472no—
712C4×C22⋊C4—471no—
713C4×C22⋊C4—471no—
714C4×C22⋊C4—472no—
715C4×C22⋊C4—472no—
716C4×C22⋊C4C2×D4711yescharacteristic
717#376—472no—
718#376C2×D4712yescomplemented
719C47#3441511yescharacteristic, complemented, Sylow
720C25—472no—
721C2×#41—478no—
722C2×#41—1882no—
723C2×#41—1882no—
724C22×Q8—471no—
725C22×D4—471no—
726C22×D4—471no—
727C22×D4—478no—
728C22×D4—471no—
729C22×D4—471no—
730C22×D4—472no—
731C22×D4—472no—
732C22×D4—472no—
733C22×D4—472no—
734C22×D4—472no—
735C22×D4—471no—
736C22×D4—1882no—
737C22×D4—1882no—
738C23×C4—471no—
739C23×C4—471no—
740C23×C4—472no—
741C23×C4—472no—
742C23×C4—471no—
743C23×C4—471no—
744C23×C4—472no—
745C23×C4—472no—
746C23×C4—472no—
747C23×C4C22×D4711yescharacteristic
748#127—4716no—
749#124—4716no—
750#121—478no—
751#121—478no—
752#121—478no—
753#121—478no—
754#120—4716no—
755#120—4716no—
756C4×D4—1884no—
757C4×D4—1882no—
758C4×D4—1882no—
759C4×D4—1884no—
760C4×D4—1884no—
761C4×D4—1882no—
762C4×D4—1882no—
763C4×D4—1884no—
764#117—1882no—
765#117—1882no—
766#117C4×D4718yescomplemented
767C2×C4⋊C4—471no—
768C2×C4⋊C4—471no—
769C2×C4⋊C4—472no—
770C2×C4⋊C4—471no—
771C2×C4⋊C4—471no—
772C2×C4⋊C4—472no—
773C2×C4⋊C4—472no—
774C2×C4⋊C4—1882no—
775C2×C4⋊C4C22×D4711yescharacteristic
776C2×C4⋊C4C22×D4711yescharacteristic
777C2×C4⋊C4C22×D4712yes—
778C2×C4⋊C4C22×D4712yes—
779C2×C4⋊C4C22×D4711yescharacteristic
780C2×C4⋊C4C22×D4711yescharacteristic
781C2×C22⋊C4—472no—
782C2×C22⋊C4—472no—
783C2×C22⋊C4—472no—
784C2×C22⋊C4—472no—
785C2×C22⋊C4—471no—
786C2×C22⋊C4—472no—
787C2×C22⋊C4—472no—
788C2×C22⋊C4—471no—
789C2×C22⋊C4—471no—
790C2×C22⋊C4—472no—
791C2×C22⋊C4—471no—
792C2×C22⋊C4—472no—
793C2×C22⋊C4—472no—
794C2×C22⋊C4—471no—
795C2×C22⋊C4—472no—
796C2×C22⋊C4—471no—
797C2×C22⋊C4—472no—
798C2×C22⋊C4—472no—
799C2×C22⋊C4—472no—
800C2×C22⋊C4—472no—
801C2×C22⋊C4—472no—
802C2×C22⋊C4—472no—
803C2×C22⋊C4—472no—
804C2×C22⋊C4—472no—
805C2×C22⋊C4—472no—
806C2×C22⋊C4—472no—
807C2×C22⋊C4—471no—
808C2×C22⋊C4—471no—
809C2×C22⋊C4—1884no—
810C2×C22⋊C4—1884no—
811C2×C22⋊C4C22×D4711yescharacteristic
812C2×C22⋊C4C22×D4712yes—
813C2×C22⋊C4C22×D4711yescharacteristic
814C2×C22⋊C4C22×D4712yes—
815C2×C42—471no—
816C2×C42—472no—
817C2×C42—471no—
818C2×C42—472no—
819C2×C42—472no—
820C2×C42—471no—
821C2×C42—471no—
822C2×C42—1882no—
823C2×C42C22×D4711yescharacteristic
824C2×C42C22×D4712yes—
825C2×C42C22×D4711yescharacteristic
826C2×C42C22×D4712yes—
827C2×C42C22×D4712yes—
828#95—471no—
829#95—472no—
830#95—472no—
831#95—472no—
832#95—471no—
833#95—471no—
834#95—472no—
835#95—472no—
836#95—471no—
837#95—471no—
838#95—471no—
839#95—472no—
840#95—472no—
841#95C22×D4711yescharacteristic
842#95C22×D4712yes—
843#95C22×D4712yes—
844#95C22×D4712yes—
845#95C22×D4711yescharacteristic
846#95C22×D4712yes—
847#95C22×D4712yes—
848C24—472no—
849C24—472no—
850C24—471no—
851C24—471no—
852C24—478no—
853C24—1882no—
854C24—1882no—
855C24—1882no—
856C24—1882no—
857C24—1882no—
858C24—1882no—
859C24C23×D4711yescharacteristic
860#41—18816no—
861C2×Q8—474no—
862C2×Q8—1881no—
863C2×Q8—1881no—
864C2×D4—474no—
865C2×D4—474no—
866C2×D4—474no—
867C2×D4—474no—
868C2×D4—478no—
869C2×D4—478no—
870C2×D4—478no—
871C2×D4—478no—
872C2×D4—478no—
873C2×D4—474no—
874C2×D4—942no—
875C2×D4—942no—
876C2×D4—942no—
877C2×D4—942no—
878C2×D4—18816no—
879C2×D4—1882no—
880C2×D4—1882no—
881C2×D4—1882no—
882C2×D4—1882no—
883C2×D4—1882no—
884C2×D4—1882no—
885C2×D4—1882no—
886C2×D4—1882no—
887C2×D4—1882no—
888C2×D4—1882no—
889C2×D4—1881no—
890C2×D4—1881no—
891C2×D4—1881no—
892C2×D4—1881no—
893C2×D4—1881no—
894C2×D4—1881no—
895C22×C4—22no—
896C22×C4—22no—
897C22×C4—471no—
898C22×C4—471no—
899C22×C4—471no—
900C22×C4—474no—
901C22×C4—474no—
902C22×C4—471no—
903C22×C4—471no—
904C22×C4—472no—
905C22×C4—472no—
906C22×C4—471no—
907C22×C4—944no—
908C22×C4—942no—
909C22×C4—942no—
910C22×C4—942no—
911C22×C4—942no—
912C22×C4—942no—
913C22×C4—944no—
914C22×C4—942no—
915C22×C4—1882no—
916C22×C4—1882no—
917C22×C4—1882no—
918C22×C4—1882no—
919C22×C4—1882no—
920C22×C4—1882no—
921C22×C4—1882no—
922C22×C4—1882no—
923C22×C4—1882no—
924C22×C4—1882no—
925C22×C4—1882no—
926C22×C4—1882no—
927C22×C4—1882no—
928C22×C4—1881no—
929C22×C4—1881no—
930C22×C4—1881no—
931C22×C4—1881no—
932C22×C4C2×C4×D4714yes—
933C22×C4C23×D4712yes—
934C22×C4C23×D4711yescharacteristic
935C22×C4C23×D4711yescharacteristic
936C22×C4C23×D4712yes—
937C22×C4C23×D4711yescharacteristic
938C22×C4C23×D4711yescharacteristic
939C22×C4C23×D4712yes—
940C22×C4C23×D4712yes—
941C22×C4C23×D4711yescharacteristic
942C22×C4C23×D4711yescharacteristic
943C4⋊C4—22no—
944C4⋊C4—22no—
945C4⋊C4—42no—
946C4⋊C4—42no—
947C4⋊C4—942no—
948C4⋊C4—942no—
949C4⋊C4—1882no—
950C4⋊C4—1881no—
951C4⋊C4—1881no—
952C4⋊C4—1882no—
953C4⋊C4—1882no—
954C4⋊C4C2×C4×D4714yes—
955C4⋊C4C2×C4×D4714yes—
956C22⋊C4—22no—
957C22⋊C4—42no—
958C22⋊C4—41no—
959C22⋊C4—478no—
960C22⋊C4—478no—
961C22⋊C4—478no—
962C22⋊C4—478no—
963C22⋊C4—944no—
964C22⋊C4—942no—
965C22⋊C4—942no—
966C22⋊C4—944no—
967C22⋊C4—942no—
968C22⋊C4—1882no—
969C22⋊C4—1881no—
970C22⋊C4—1882no—
971C22⋊C4—1881no—
972C22⋊C4—1882no—
973C22⋊C4—1882no—
974C22⋊C4—1881no—
975C22⋊C4—1881no—
976C22⋊C4—1882no—
977C22⋊C4—1882no—
978C22⋊C4—1882no—
979C22⋊C4—1882no—
980C22⋊C4—1882no—
981C22⋊C4—1882no—
982C22⋊C4—1882no—
983C22⋊C4—1882no—
984C22⋊C4—1882no—
985C22⋊C4—1881no—
986C22⋊C4—1882no—
987C22⋊C4C2×C4×D4718yes—
988C42—22no—
989C42—22no—
990C42—24no—
991C42—42no—
992C42—944no—
993C42—942no—
994C42—942no—
995C42—1882no—
996C42—1881no—
997C42—1881no—
998C42—1882no—
999C42C2×C4×D4718yes—
1000C23—21no—
1001C23—21no—
1002C23—21no—
1003C23—21no—
1004C23—21no—
1005C23—21no—
1006C23—474no—
1007C23—474no—
1008C23—472no—
1009C23—472no—
1010C23—942no—
1011C23—941no—
1012C23—941no—
1013C23—942no—
1014C23—942no—
1015C23—941no—
1016C23—941no—
1017C23—941no—
1018C23—941no—
1019C23—942no—
1020C23—942no—
1021C23—942no—
1022C23—942no—
1023C23—942no—
1024C23—941no—
1025C23—941no—
1026C23—941no—
1027C23—942no—
1028C23—941no—
1029C23—942no—
1030C23—941no—
1031C23—942no—
1032C23—941no—
1033C23—942no—
1034C23—3764no—
1035C23—3764no—
1036C23—3764no—
1037C23—3764no—
1038C23—1888no—
1039C23—1888no—
1040C23—1888no—
1041C23C22×C4×D4712yes—
1042C23C24×D4711yescharacteristic
1043Q8—1884no—
1044D4—948no—
1045D4—948no—
1046D4—1888no—
1047D4—1888no—
1048D4—1888no—
1049D4—1888no—
1050D4—1888no—
1051D4—1884no—
1052D4—1884no—
1053D4—1884no—
1054C2×C4—22no—
1055C2×C4—21no—
1056C2×C4—22no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—21no—
1062C2×C4—28no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—22no—
1070C2×C4—21no—
1071C2×C4—22no—
1072C2×C4—21no—
1073C2×C4—22no—
1074C2×C4—21no—
1075C2×C4—22no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—472no—
1079C2×C4—472no—
1080C2×C4—472no—
1081C2×C4—941no—
1082C2×C4—941no—
1083C2×C4—941no—
1084C2×C4—941no—
1085C2×C4—941no—
1086C2×C4—941no—
1087C2×C4—948no—
1088C2×C4—948no—
1089C2×C4—942no—
1090C2×C4—941no—
1091C2×C4—941no—
1092C2×C4—941no—
1093C2×C4—941no—
1094C2×C4—942no—
1095C2×C4—942no—
1096C2×C4—941no—
1097C2×C4—942no—
1098C2×C4—941no—
1099C2×C4—942no—
1100C2×C4—941no—
1101C2×C4—941no—
1102C2×C4—942no—
1103C2×C4—941no—
1104C2×C4—3764no—
1105C2×C4—3764no—
1106C2×C4—3764no—
1107C2×C4—3764no—
1108C2×C4—3764no—
1109C2×C4—1884no—
1110C2×C4—1884no—
1111C2×C4C22×C4×D4712yes—
1112C2×C4C22×C4×D4714yes—
1113C2×C4C22×C4×D4714yes—
1114C2×C4C22×C4×D4712yes—
1115C2×C4#1309407012yes—
1116C2×C4#1309407012yes—
1117C2×C4#1309407012yes—
1118C22—22no—
1119C22—22no—
1120C22—22no—
1121C22—41no—
1122C22—41no—
1123C22—41no—
1124C22—41no—
1125C22—942no—
1126C22—942no—
1127C22—944no—
1128C22—944no—
1129C22—942no—
1130C22—942no—
1131C22—944no—
1132C22—944no—
1133C22—942no—
1134C22—942no—
1135C22—944no—
1136C22—944no—
1137C22—37616no—
1138C22—1882no—
1139C22—1882no—
1140C22—1881no—
1141C22—1881no—
1142C22—1882no—
1143C22—1881no—
1144C22—1882no—
1145C22—1881no—
1146C22—1882no—
1147C22—1881no—
1148C22—1882no—
1149C22—1881no—
1150C22—1881no—
1151C22—1882no—
1152C22—1882no—
1153C22—1881no—
1154C22C23×C4×D4711yescharacteristic
1155C22H(5,𝔽2)×D4711yescharacteristic
1156C22C2×#1309407011yescharacteristic
1157C22C2×#1309407011yescharacteristic
1158C22C2×#1309407011yescharacteristic
1159C22#1568995911yescharacteristic
1160C22#1568996011yescharacteristic
1161C4—22no—
1162C4—24no—
1163C4—24no—
1164C4—22no—
1165C4—41no—
1166C4—42no—
1167C4—41no—
1168C4—42no—
1169C4—41no—
1170C4—942no—
1171C4—942no—
1172C4—942no—
1173C4—1881no—
1174C4—1882no—
1175C4—1881no—
1176C4—1882no—
1177C4—1881no—
1178C4#1568959714yes—
1179C2—42no—
1180C2—1884no—
1181C2—1884no—
1182C2—1882no—
1183C2—1882no—
1184C2C2×#1568959711yescharacteristic
1185C2#2025659411yescharacteristic
1186C2C4×#1309407011yescharacteristic
1187C2#2025769811yescharacteristic
1188C2#2025771111yescharacteristic
1189C2#2025778911yescharacteristic
1190C2#2025781611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D47
commutatorC22×C47C24×C4
FittingC47×#2346C2
socle, cosocleC23×C47C25
prime radicalC2×#15689692C2
hypercenter#2346D47
hypocenterC47#34415
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2346

Complements

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

NH ≅ G/Ntype
2. #20246559C2semidirect
3. #20246528C2semidirect
4. #20246498C2semidirect
5. #20246428C2semidirect
6. #20246425C2semidirect
7. #20246406C2semidirect
8. #20246403C2semidirect
9. #20246366C2semidirect
10. #20246273C2semidirect
11. C22⋊C4×D188C2semidirect
12. #20246208C2semidirect
13. #20246113C2semidirect
14. #20246111C2semidirect
15. #20246082C2semidirect
16. #20246079C2semidirect
17. #20246050C2semidirect
18. #20246041C2semidirect
19. #20245977C2semidirect
20. C4×#13093999C2semidirect
21. #20245896C2semidirect
22. #20245874C2semidirect
23. C47×#2346C2semidirect
26. #15689692C4semidirect
37. C2×C4×D188C22semidirect
38. C2×C4×D188C22semidirect
41. C2×#13093986C22semidirect
42. C2×#13093986C22semidirect
43. C2×#13093982C22semidirect
44. C2×#13093981C22semidirect
45. C2×C4⋊C4×D47C22semidirect
48. C2×C42×D47C22semidirect
49. #15689027C22semidirect
50. #15689027C22semidirect
51. #15689027C22semidirect
54. #15689025C22semidirect
55. #15689025C22semidirect
58. #15689024C22semidirect
59. #15689024C22semidirect
63. #15689022C22semidirect
64. #15689022C22semidirect
67. #15689015C22semidirect
68. #15689015C22semidirect
69. #15689014C22semidirect
70. #15689014C22semidirect
71. #15689013C22semidirect
72. #15689013C22semidirect
73. #15689012C22semidirect
74. #15689012C22semidirect
79. #15689001C22semidirect
80. #15689001C22semidirect
81. #15689001C22semidirect
82. #15689001C22semidirect
83. #15689001C22semidirect
84. #15689001C22semidirect
85. #15689001C22semidirect
86. #15689001C22semidirect
87. #15689001C22semidirect
88. #15689001C22semidirect
89. #15689001C22semidirect
93. #15688997C22semidirect
94. #15688997C22semidirect
95. #15688994C22semidirect
96. #15688994C22semidirect
97. #15688989C22semidirect
99. #15688980C22semidirect
100. #15688980C22semidirect
103. C4⋊C4×Dic47C22semidirect
104. C4⋊C4×Dic47C22semidirect
105. C4×(C2×D47)⋊C4C22semidirect
106. C4×(C2×D47)⋊C4C22semidirect
107. C4×(C2×D47)⋊C4C22semidirect
108. C4×(C2×D47)⋊C4C22semidirect
110. #15688970C22semidirect
111. #15688970C22semidirect
112. #15688969C22semidirect
114. C47×#389C22semidirect
115. C47×#389C22semidirect
118. C47×#382C22semidirect
120. C4×C4⋊C4×C47C22semidirect
121. C4×C4⋊C4×C47C22semidirect
123. C47×#376C22semidirect
127. C2×#10625350C2×C4semidirect
131. C22×D188C2×C4semidirect
151. #13094021C2×C4semidirect
152. #13094012C2×C4semidirect
153. #13093999C2×C4semidirect
154. #13093999C2×C4semidirect
155. #13093999C2×C4semidirect
156. #13093999C2×C4semidirect
157. #13093994C2×C4semidirect
158. #13093994C2×C4semidirect
229. #117×C47C2×C4semidirect
594. #2346D47semidirect
661. #389C2×D47semidirect
662. #389C2×D47semidirect
698. #382C2×D47semidirect
707. C4×C4⋊C4C2×D47semidirect
708. C4×C4⋊C4C2×D47semidirect
718. #376C2×D47semidirect
719. C47#34415semidirect
766. #117C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156896922
#202465592
#202465282
#202464982
#202464282
#202464252
#202464062
#202464032
#202463662
#202462732
C22⋊C4×D1882
#202462082
#202461132
#202461112
#202460822
#202460792
#202460502
#202460412
#202459772
C4×#130939992
#202458962
#202458742
C47×#23462
#3441547