Finite Group Databasebeta

← #26379072

Subgroups — #26379072

Order 12032.

2586 conjugacy classes of subgroups.

The subgroup lattice has 1188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689635C211yesmaximal, characteristic
2#20246552C212yesmaximal, complemented
3#20246543C212yesmaximal, complemented
4#20246470C212yesmaximal, complemented
5#20246434C212yesmaximal, complemented
6#20246339C211yesmaximal, characteristic, complemented
7#20246335C211yesmaximal, characteristic, complemented
8#20246320C211yesmaximal, characteristic, complemented
9#20246320C211yesmaximal, characteristic, complemented
10#20246314C211yesmaximal, characteristic, complemented
11#20246314C211yesmaximal, characteristic, complemented
12C4⋊C4×D188C211yesmaximal, characteristic, complemented
13#20246288C211yesmaximal, characteristic, complemented
14#20246183C212yesmaximal, complemented
15#20246171C212yesmaximal, complemented
16#20246050C212yesmaximal, complemented
17#20246041C212yesmaximal, complemented
18#20245997C211yesmaximal, characteristic, complemented
19#20245977C211yesmaximal, characteristic, complemented
20#20245977C211yesmaximal, characteristic, complemented
21#20245770C211yesmaximal, characteristic, complemented
22#380×D47C211yesmaximal, characteristic, complemented
23C47×#2314C211yesmaximal, characteristic, complemented
24C22×#10625350C2211yescharacteristic
25C23×C4×D47C2211yescharacteristic
26#15689635C4116yescomplemented
27C2×#13094008C2211yescharacteristic
28C2×#13094008C2211yescharacteristic
29C2×#13094004C2211yescharacteristic
30C2×#13094004C2211yescharacteristic
31C2×#13093999C2211yescharacteristic
32C2×#13093999C2211yescharacteristic
33C2×#13093994C2211yescharacteristic
34C2×#13093994C2211yescharacteristic
35C2×C4×D188C2212yes—
36C2×C4×D188C2211yescharacteristic
37C2×C4×D188C2211yescharacteristic
38C2×C4×D188C2211yescharacteristic
39C2×C4×D188C2211yescharacteristic
40C2×#13093986C2212yes—
41C2×#13093982C2211yescharacteristic
42C2×#13093982C2211yescharacteristic
43C2×#13093982C2211yescharacteristic, complemented
44C2×#13093982C2211yescharacteristic, complemented
45C2×C4⋊C4×D47C2211yescharacteristic
46C2×C4⋊C4×D47C2211yescharacteristic
47C2×C4⋊C4×D47C2211yescharacteristic, complemented
48C2×C4⋊C4×D47C2211yescharacteristic, complemented
49C2×C22⋊C4×D47C2212yes—
50#15689027C2212yescomplemented
51#15689027C2212yescomplemented
52#15689025C2212yes—
53#15689024C2212yes—
54#15689023C2212yes—
55#15689023C2212yes—
56#15689021C2212yescomplemented
57#15689019C2212yescomplemented
58#15689016C2212yes—
59#15689016C2212yes—
60#15689015C2212yes—
61#15689015C2212yescomplemented
62#15689014C2212yes—
63#15689014C2212yescomplemented
64#15689013C2212yes—
65#15689013C2212yescomplemented
66#15689012C2212yes—
67#15689012C2212yescomplemented
68#15689009C2212yescomplemented
69#15689009C2212yescomplemented
70#15689008C2212yescomplemented
71#15689008C2212yescomplemented
72#15689006C2212yescomplemented
73#15689006C2212yescomplemented
74#15689001C2212yes—
75#15689001C2212yes—
76#15689001C2212yes—
77#15689001C2212yes—
78#15689001C2212yescomplemented
79#15689001C2212yescomplemented
80#15688999C2212yes—
81#15688999C2212yes—
82#15688997C2212yes—
83#15688997C2212yescomplemented
84#15688994C2212yes—
85#15688994C2212yescomplemented
86#15688993C2211yescharacteristic, complemented
87#15688989C2211yescharacteristic, complemented
88#15688985C2212yes—
89#15688983C2211yescharacteristic
90#15688983C2211yescharacteristic
91#15688982C2212yes—
92#15688981C2212yes—
93#15688980C2211yescharacteristic
94#15688980C2211yescharacteristic
95#15688980C2211yescharacteristic
96#15688980C2211yescharacteristic
97#15688980C2211yescharacteristic, complemented
98#15688980C2211yescharacteristic, complemented
99#15688980C2211yescharacteristic, complemented
100#15688980C2211yescharacteristic, complemented
101#15688978C2212yes—
102C4⋊C4×Dic47C2212yescomplemented
103C4×C4⋊Dic47C2211yescharacteristic, complemented
104C4×C4⋊Dic47C2211yescharacteristic, complemented
105C4×C4⋊Dic47C2212yescomplemented
106C22⋊C4×Dic47C2212yes—
107C4×(C2×D47)⋊C4C2212yes—
108C4×(C2×D47)⋊C4C2212yescomplemented
109#15688970C2212yes—
110#15688970C2212yes—
111#15688970C2212yescomplemented
112#95×D47C2212yes—
113C2×#117×C47C2211yescharacteristic
114C47×#388C2212yes—
115C47×#388C2212yes—
116C47×#387C2212yescomplemented
117C47×#387C2212yescomplemented
118C47×#384C2211yescharacteristic, complemented
119C47×#382C2211yescharacteristic, complemented
120C47×#380C2211yescharacteristic
121C47×#380C2211yescharacteristic
122C4×C4⋊C4×C47C2211yescharacteristic, complemented
123C4×C4⋊C4×C47C2211yescharacteristic, complemented
124C24×D47C2311yescharacteristic
125C2×#10625350—42no—
126C2×#10625350—42no—
127C2×#10625350C2×C418yescomplemented
128C22×Dic94C2311yescharacteristic
129C22×D188C2311yescharacteristic
130C22×D188C2311yescharacteristic
131C22×D188C2311yescharacteristic
132C22×D188C2311yescharacteristic
133C22×D188C2311yescharacteristic
134C22×C22⋊D47C2311yescharacteristic
135C22×C22⋊D47C2311yescharacteristic
136C23×Dic47C2311yescharacteristic
137C22×C4×D47—42no—
138C22×C4×D47—42no—
139C22×C4×D47C2×C418yescomplemented
140C22×C4×D47C2311yescharacteristic
141C22×C4×D47C2311yescharacteristic
142C22×C4×D47C2311yescharacteristic
143C22×C4×D47C2311yescharacteristic
144C22×C4×D47C2312yes—
145C22×C4×D47C2312yes—
146C22×C4×D47C2312yes—
147C22×C4×D47C2312yes—
148C22×C4×D47C2311yescharacteristic
149C22×C4×D47C2311yescharacteristic
150#13094008C2×C418yescomplemented
151#13094008C2×C418yescomplemented
152#13094004C2×C418yescomplemented
153#13094004C2×C418yescomplemented
154#13093999C2×C418yes—
155#13093999C2×C418yescomplemented
156#13093994C2×C418yescomplemented
157#13093994C2×C418yescomplemented
158C4×D188—44no—
159C4×D188C2×C418yescomplemented
160C4×D188C2×C418yescomplemented
161C4×D188C2×C418yescomplemented
162C4×D188C2×C418yescomplemented
163#13093986—44no—
164#13093982—42no—
165#13093982—42no—
166#13093982—42no—
167#13093982—42no—
168C2×C4⋊Dic47C2311yescharacteristic
169C2×C4⋊Dic47C2311yescharacteristic
170C2×C4⋊Dic47C2311yescharacteristic
171C2×C4⋊Dic47C2311yescharacteristic
172C2×C4⋊Dic47C2312yes—
173C2×C4⋊Dic47C2312yes—
174C2×C4⋊Dic47C2311yescharacteristic
175C2×C4⋊Dic47C2311yescharacteristic
176C2×C4⋊Dic47C2311yescharacteristic
177C2×C4⋊Dic47C2311yescharacteristic
178C2×Dic47⋊C4C2312yes—
179C2×Dic47⋊C4C2312yes—
180C2×Dic47⋊C4C2312yes—
181C2×Dic47⋊C4C2312yes—
182C4⋊C4×D47—42no—
183C4⋊C4×D47—42no—
184C4⋊C4×D47—42no—
185C4⋊C4×D47—42no—
186C2×C22⋊Dic47C2312yes—
187C2×C22⋊Dic47C2312yes—
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)⋊C4C2312yes—
199C2×(C2×D47)⋊C4C2312yes—
200C2×(C2×D47)⋊C4C2311yescharacteristic
201C2×(C2×D47)⋊C4C2311yescharacteristic
202C2×(C2×D47)⋊C4C2311yescharacteristic
203C2×(C2×D47)⋊C4C2311yescharacteristic
204C2×(C2×D47)⋊C4C2311yescharacteristic
205C2×(C2×D47)⋊C4C2311yescharacteristic
206C2×(C2×D47)⋊C4C2311yescharacteristic
207C2×(C2×D47)⋊C4C2311yescharacteristic
208C22⋊C4×D47—44no—
209C2×C4×Dic47C2312yes—
210C2×C4×Dic47C2312yes—
211C2×C4×Dic47C2312yes—
212C2×C4×Dic47C2312yes—
213C2×C4×Dic47C2312yes—
214C2×C4×Dic47C2312yes—
215C47⋊#95C2312yes—
216C47⋊#95C2312yes—
217C47⋊#95C2312yes—
218C47⋊#95C2312yes—
219C47⋊#95C2312yes—
220C47⋊#95C2312yes—
221C47⋊#95C2312yes—
222C47⋊#95C2312yes—
223C47⋊#95C2312yes—
224C47⋊#95C2312yes—
225C47⋊#95C2312yes—
226C47⋊#95C2312yes—
227C47⋊#95C2312yes—
228C47⋊#95C2312yes—
229C23×C4×C47C2311yescharacteristic
230#117×C47C2×C418yescomplemented
231C2×C4⋊C4×C47C2311yescharacteristic
232C2×C4⋊C4×C47C2311yescharacteristic
233C2×C4⋊C4×C47C2311yescharacteristic
234C2×C4⋊C4×C47C2311yescharacteristic
235C2×C4⋊C4×C47C2312yes—
236C2×C4⋊C4×C47C2312yes—
237C2×C4⋊C4×C47C2311yescharacteristic
238C2×C4⋊C4×C47C2311yescharacteristic
239C2×C22⋊C4×C47C2312yes—
240C2×C22⋊C4×C47C2312yes—
241C2×C22⋊C4×C47C2311yescharacteristic
242C2×C22⋊C4×C47C2311yescharacteristic
243C2×C42×C47C2312yes—
244C2×C42×C47C2312yes—
245C2×C42×C47C2311yescharacteristic
246C2×C42×C47C2311yescharacteristic
247#95×C47C2312yes—
248#95×C47C2312yes—
249#95×C47C2312yes—
250#95×C47C2312yes—
251#95×C47C2312yes—
252#95×C47C2312yes—
253C24×C47C2411yescharacteristic
254C23×D47—22no—
255C23×D47—22no—
256C23×D47—41no—
257C23×D47—41no—
258C23×D47—41no—
259C23×D47—41no—
260C23×D47C22×C414yes—
261C23×D47C2411yescharacteristic
262C23×D47C2411yescharacteristic
263C23×D47C2411yescharacteristic
264C23×D47C2411yescharacteristic
265C22×C4×C47—22no—
266C22×C4×C47—22no—
267C22×C4×C47C22×C414yes—
268C22×C4×C47C2412yes—
269C22×C4×C47C2412yes—
270C22×C4×C47C2412yes—
271C22×C4×C47C2412yes—
272C22×C4×C47C2411yescharacteristic
273C22×C4×C47C2411yescharacteristic
274C22×C4×C47C2411yescharacteristic
275C22×C4×C47C2411yescharacteristic
276C22×C4×C47C2411yescharacteristic
277C22×C4×C47C2411yescharacteristic
278C2×C22⋊D47—41no—
279C2×C22⋊D47—41no—
280C2×C22⋊D47—41no—
281C2×C22⋊D47—41no—
282C2×C22⋊D47C22×C414yes—
283C2×C22⋊D47C22×C414yes—
284C22×Dic47—41no—
285C22×Dic47—41no—
286C22×Dic47C22×C414yes—
287C22×Dic47C2412yes—
288C22×Dic47C2412yes—
289C22×Dic47C2412yes—
290C22×Dic47C2412yes—
291C22×Dic47C2411yescharacteristic
292C22×Dic47C2411yescharacteristic
293C22×Dic47C2411yescharacteristic
294C22×Dic47C2411yescharacteristic
295#10625350—416no—
296C2×D188—22no—
297C2×D188—22no—
298C2×D188—22no—
299C2×D188—22no—
300C2×D188—41no—
301C2×D188—41no—
302C2×D188—41no—
303C2×D188—41no—
304C2×D188—41no—
305C2×D188—41no—
306C2×D188C22×C414yes—
307C2×D188C22×C414yes—
308C2×D188C22×C414yes—
309C2×D188C22×C414yes—
310C2×D188C22×C414yes—
311C2×C4×D47—22no—
312C2×C4×D47—22no—
313C2×C4×D47—22no—
314C2×C4×D47—22no—
315C2×C4×D47—22no—
316C2×C4×D47—22no—
317C2×C4×D47—22no—
318C2×C4×D47—22no—
319C2×C4×D47—24no—
320C2×C4×D47—24no—
321C2×C4×D47—416no—
322C2×C4×D47—41no—
323C2×C4×D47—41no—
324C2×C4×D47—41no—
325C2×C4×D47—41no—
326C2×C4×D47—42no—
327C2×C4×D47—42no—
328C2×C4×D47—42no—
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×D47C22×C414yes—
337C2×C4×D47C22×C414yes—
338C2×C4×D47C22×C414yes—
339C2×C4×D47C22×C414yes—
340C2×C4×D47C22×C414yes—
341C2×C4×D47C22×C414yes—
342C2×Dic94—41no—
343C2×Dic94—41no—
344C2×Dic94C22×C414yes—
345C4⋊C4×C47—22no—
346C4⋊C4×C47—22no—
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—42no—
354C22⋊C4×C47—42no—
355C22⋊C4×C47C22×C414yes—
356C22⋊C4×C47C22×C414yes—
357C42×C47—42no—
358C42×C47—42no—
359C42×C47C22×C414yes—
360C42×C47C22×C414yes—
361C22⋊Dic47—42no—
362C22⋊Dic47—42no—
363(C2×D47)⋊C4—24no—
364(C2×D47)⋊C4—24no—
365(C2×D47)⋊C4—42no—
366(C2×D47)⋊C4—42no—
367(C2×D47)⋊C4—42no—
368(C2×D47)⋊C4—42no—
369(C2×D47)⋊C4—42no—
370(C2×D47)⋊C4—42no—
371(C2×D47)⋊C4—42no—
372(C2×D47)⋊C4—42no—
373(C2×D47)⋊C4—42no—
374(C2×D47)⋊C4—42no—
375(C2×D47)⋊C4C22×C414yes—
376(C2×D47)⋊C4C22×C414yes—
377(C2×D47)⋊C4C22×C414yes—
378(C2×D47)⋊C4C22×C414yes—
379(C2×D47)⋊C4C22×C414yes—
380(C2×D47)⋊C4C22×C414yes—
381(C2×D47)⋊C4C22×C414yes—
382(C2×D47)⋊C4C22×C414yes—
383C4⋊Dic47—22no—
384C4⋊Dic47—22no—
385C4⋊Dic47—22no—
386C4⋊Dic47—22no—
387C4⋊Dic47—42no—
388C4⋊Dic47—42no—
389C4⋊Dic47C22×C414yes—
390C4⋊Dic47C22×C414yes—
391C4⋊Dic47C22×C414yes—
392C4⋊Dic47C22×C414yes—
393Dic47⋊C4—42no—
394Dic47⋊C4—42no—
395Dic47⋊C4—42no—
396Dic47⋊C4—42no—
397C4×Dic47—42no—
398C4×Dic47—42no—
399C4×Dic47—42no—
400C4×Dic47—42no—
401C4×Dic47—42no—
402C4×Dic47—42no—
403C23×C47—21no—
404C23×C47—21no—
405C23×C47—21no—
406C23×C47—21no—
407C23×C47—21no—
408C23×C47—21no—
409C23×C47C23×C412yes—
410C23×C47C2511yescharacteristic
411C22×D47—21no—
412C22×D47—21no—
413C22×D47—21no—
414C22×D47—21no—
415C22×D47—21no—
416C22×D47—21no—
417C22×D47—21no—
418C22×D47—21no—
419C22×D47—21no—
420C22×D47—21no—
421C22×D47—21no—
422C22×D47—21no—
423C22×D47—21no—
424C22×D47—21no—
425C22×D47—21no—
426C22×D47—21no—
427C22×D47—21no—
428C22×D47—21no—
429C22×D47—21no—
430C22×D47—21no—
431C22×D47—21no—
432C22×D47—21no—
433C22×D47—28no—
434C22×D47—44no—
435C22×D47—44no—
436C22×D47—44no—
437C22×D47—44no—
438C22×D47—44no—
439C22×D47—44no—
440C22×D47C23×C412yes—
441C22×D47C23×C412yes—
442C22×D47C23×C412yes—
443C22×D47C23×C412yes—
444C22×D47H(5,𝔽2)12yes—
445C22×D472−1+412yes—
446C2×C4×C47—21no—
447C2×C4×C47—21no—
448C2×C4×C47—21no—
449C2×C4×C47—21no—
450C2×C4×C47—21no—
451C2×C4×C47—21no—
452C2×C4×C47—21no—
453C2×C4×C47—21no—
454C2×C4×C47—21no—
455C2×C4×C47—21no—
456C2×C4×C47—28no—
457C2×C4×C47—22no—
458C2×C4×C47—22no—
459C2×C4×C47—22no—
460C2×C4×C47—22no—
461C2×C4×C47—22no—
462C2×C4×C47—22no—
463C2×C4×C47—22no—
464C2×C4×C47—22no—
465C2×C4×C47—22no—
466C2×C4×C47—22no—
467C2×C4×C47—22no—
468C2×C4×C47—22no—
469C2×C4×C47C23×C412yes—
470C2×C4×C47C23×C412yes—
471C2×C4×C47C23×C412yes—
472C2×C4×C47C23×C412yes—
473C2×C4×C47C23×C412yes—
474C2×C4×C47C23×C412yes—
475C2×C4×C47H(5,𝔽2)12yes—
476C2×C4×C47H(5,𝔽2)12yes—
477C22⋊D47—44no—
478C22⋊D47—44no—
479C2×Dic47—21no—
480C2×Dic47—21no—
481C2×Dic47—21no—
482C2×Dic47—21no—
483C2×Dic47—21no—
484C2×Dic47—21no—
485C2×Dic47—21no—
486C2×Dic47—21no—
487C2×Dic47—22no—
488C2×Dic47—22no—
489C2×Dic47—22no—
490C2×Dic47—22no—
491C2×Dic47—22no—
492C2×Dic47—22no—
493C2×Dic47—22no—
494C2×Dic47—22no—
495C2×Dic47—22no—
496C2×Dic47—22no—
497C2×Dic47—22no—
498C2×Dic47—22no—
499C2×Dic47—44no—
500C2×Dic47C23×C412yes—
501C2×Dic47C23×C412yes—
502C2×Dic47C23×C412yes—
503C2×Dic47C23×C412yes—
504D188—28no—
505D188—28no—
506D188—44no—
507D188—44no—
508D188—44no—
509C4×D47—28no—
510C4×D47—28no—
511C4×D47—28no—
512C4×D47—28no—
513C4×D47—44no—
514C4×D47—44no—
515C4×D47—84no—
516C4×D47—84no—
517C4×D47—84no—
518C4×D47—84no—
519Dic94—44no—
520#34362—471nomaximal, Sylow
521C22×C47—22no—
522C22×C47—22no—
523C22×C47—22no—
524C22×C47—41no—
525C22×C47—41no—
526C22×C47—41no—
527C22×C47—41no—
528C22×C47C24×C411yescharacteristic
529C22×C47C2×H(5,𝔽2)11yescharacteristic
530C22×C47C2×H(5,𝔽2)11yescharacteristic
531C22×C47C2×H(5,𝔽2)11yescharacteristic
532C22×C47C2×2−1+411yescharacteristic
533C22×C47#58511yescharacteristic
534C22×C47#58511yescharacteristic
535C2×D47—22no—
536C2×D47—22no—
537C2×D47—22no—
538C2×D47—22no—
539C2×D47—22no—
540C2×D47—22no—
541C2×D47—22no—
542C2×D47—22no—
543C2×D47—22no—
544C2×D47—22no—
545C2×D47—22no—
546C2×D47—22no—
547C2×D47—22no—
548C2×D47—22no—
549C2×D47—22no—
550C2×D47—416no—
551C2×D47—41no—
552C2×D47—41no—
553C2×D47—41no—
554C2×D47—41no—
555C2×D47—41no—
556C2×D47—41no—
557C2×D47—41no—
558C2×D47—41no—
559C2×D47—41no—
560C2×D47—41no—
561C2×D47—41no—
562C2×D47—41no—
563C2×D47#52014yes—
564C4×C47—22no—
565C4×C47—22no—
566C4×C47—22no—
567C4×C47—22no—
568C4×C47—22no—
569C4×C47—42no—
570C4×C47—42no—
571C4×C47—42no—
572C4×C47—42no—
573C4×C47#51814yes—
574Dic47—22no—
575Dic47—22no—
576Dic47—22no—
577Dic47—22no—
578Dic47—42no—
579Dic47—42no—
580Dic47—42no—
581Dic47—42no—
582C2×#525—471no—
583#2378—472no—
584#2377—472no—
585#2368—472no—
586#2364—472no—
587#2354—471no—
588#2354—471no—
589#2352—471no—
590#2352—471no—
591#2352—471no—
592#2352—471no—
593D4×C4⋊C4—471no—
594D4×C4⋊C4—471no—
595#2335—472no—
596#2335—472no—
597#2321—472no—
598#2321—472no—
599#2314—471no—
600#2314D4711yescharacteristic, complemented
601#2311—471no—
602#2311—471no—
603#2280—471no—
604C2×#380—471no—
605C2×C47—42no—
606C2×C47C2×#51811yescharacteristic
607C2×C47C2×#52011yescharacteristic
608C2×C47#342811yescharacteristic
609C2×C47#354111yescharacteristic
610C2×C47#354111yescharacteristic
611C2×C47#354211yescharacteristic
612C2×C47#354211yescharacteristic
613D47—24no—
614D47—42no—
615D47—42no—
616D47—42no—
617C22×#41—471no—
618C24×C4—471no—
619#525—4716no—
620C2×#123—471no—
621C2×#123—471no—
622C2×C22⋊Q8—471no—
623C2×C22⋊Q8—471no—
624C2×#121—471no—
625C2×#121—471no—
626C2×#120—471no—
627C2×#120—471no—
628C2×C4×D4—472no—
629C2×C4×D4—471no—
630C2×C4×D4—471no—
631C2×C4×D4—471no—
632C2×C4×D4—471no—
633C2×C4×D4—472no—
634C2×#117—471no—
635C2×#117—471no—
636C2×#117—471no—
637C2×#117—471no—
638C2×#117C2×D4711yescharacteristic
639C22×C4⋊C4—471no—
640C22×C4⋊C4—471no—
641C22×C4⋊C4—471no—
642C22×C4⋊C4—471no—
643C22×C22⋊C4—472no—
644#391—472no—
645#391—472no—
646#390—472no—
647#390—472no—
648#390—472no—
649#390—472no—
650#389—472no—
651#389—472no—
652#388—472no—
653#388—472no—
654#388—472no—
655#388—472no—
656#388—472no—
657#388—472no—
658#388—472no—
659#388—472no—
660#388—472no—
661#388—472no—
662#388C2×D4712yes—
663#388C2×D4712yes—
664#387—472no—
665#387—472no—
666#387—472no—
667#387—472no—
668#387—472no—
669#387—472no—
670#387C2×D4712yescomplemented
671#387C2×D4712yescomplemented
672#386—472no—
673#386—472no—
674#386—472no—
675#386—472no—
676#386—472no—
677#386—472no—
678#386—472no—
679#386—472no—
680#385—472no—
681#385—472no—
682#385—472no—
683#385—472no—
684#384—471no—
685#384C2×D4711yescharacteristic, complemented
686#382—471no—
687#382C2×D4711yescharacteristic, complemented
688#381—472no—
689#380—471no—
690#380—471no—
691#380—471no—
692#380—471no—
693#380—471no—
694#380—471no—
695#380—471no—
696#380—471no—
697#380—471no—
698#380—471no—
699#380—472no—
700#380—472no—
701#380C2×D4711yescharacteristic
702#380C2×D4711yescharacteristic
703#379—472no—
704C4×C4⋊C4—472no—
705C4×C4⋊C4—471no—
706C4×C4⋊C4—471no—
707C4×C4⋊C4—472no—
708C4×C4⋊C4C2×D4711yescharacteristic, complemented
709C4×C4⋊C4C2×D4711yescharacteristic, complemented
710C4×C22⋊C4—472no—
711C4×C22⋊C4—472no—
712C4×C22⋊C4—472no—
713C4×C22⋊C4—472no—
714C4×C22⋊C4—472no—
715C4×C22⋊C4—472no—
716C2×#95—472no—
717C47#3436211yescharacteristic, complemented, Sylow
718C25—471no—
719C2×#41—478no—
720C2×#41—1882no—
721C2×#41—1882no—
722C22×Q8—471no—
723C22×D4—471no—
724C22×D4—471no—
725C22×D4—471no—
726C22×D4—471no—
727C22×D4—471no—
728C22×D4—471no—
729C22×D4—471no—
730C23×C4—471no—
731C23×C4—471no—
732C23×C4—471no—
733C23×C4—471no—
734C23×C4—471no—
735C23×C4—478no—
736C23×C4—471no—
737C23×C4—471no—
738C23×C4—472no—
739C23×C4—472no—
740C23×C4—472no—
741C23×C4—472no—
742C23×C4—1882no—
743C23×C4—1882no—
744C23×C4C22×D4711yescharacteristic
745#123—478no—
746#123—478no—
747C22⋊Q8—478no—
748C22⋊Q8—478no—
749#121—478no—
750#121—478no—
751#120—478no—
752#120—478no—
753C4×D4—478no—
754C4×D4—478no—
755C4×D4—478no—
756C4×D4—478no—
757C4×D4—1884no—
758C4×D4—1884no—
759#117—1882no—
760#117—1882no—
761#117—1882no—
762#117—1882no—
763#117C4×D4718yescomplemented
764C2×C4⋊C4—471no—
765C2×C4⋊C4—471no—
766C2×C4⋊C4—471no—
767C2×C4⋊C4—471no—
768C2×C4⋊C4—471no—
769C2×C4⋊C4—471no—
770C2×C4⋊C4—471no—
771C2×C4⋊C4—471no—
772C2×C4⋊C4—472no—
773C2×C4⋊C4—472no—
774C2×C4⋊C4—472no—
775C2×C4⋊C4—472no—
776C2×C4⋊C4—472no—
777C2×C4⋊C4—472no—
778C2×C4⋊C4—1882no—
779C2×C4⋊C4—1882no—
780C2×C4⋊C4—1882no—
781C2×C4⋊C4—1882no—
782C2×C4⋊C4C22×D4711yescharacteristic
783C2×C4⋊C4C22×D4711yescharacteristic
784C2×C4⋊C4C22×D4711yescharacteristic
785C2×C4⋊C4C22×D4711yescharacteristic
786C2×C4⋊C4C22×D4712yes—
787C2×C4⋊C4C22×D4712yes—
788C2×C4⋊C4C22×D4711yescharacteristic
789C2×C4⋊C4C22×D4711yescharacteristic
790C2×C22⋊C4—471no—
791C2×C22⋊C4—471no—
792C2×C22⋊C4—471no—
793C2×C22⋊C4—471no—
794C2×C22⋊C4—471no—
795C2×C22⋊C4—471no—
796C2×C22⋊C4—471no—
797C2×C22⋊C4—471no—
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—472no—
808C2×C22⋊C4—472no—
809C2×C22⋊C4—472no—
810C2×C22⋊C4—472no—
811C2×C22⋊C4—472no—
812C2×C22⋊C4—1884no—
813C2×C22⋊C4C22×D4712yes—
814C2×C22⋊C4C22×D4712yes—
815C2×C22⋊C4C22×D4711yescharacteristic
816C2×C22⋊C4C22×D4711yescharacteristic
817C2×C42—472no—
818C2×C42—472no—
819C2×C42—472no—
820C2×C42—472no—
821C2×C42—472no—
822C2×C42—472no—
823C2×C42C22×D4712yes—
824C2×C42C22×D4712yes—
825C2×C42C22×D4711yescharacteristic
826C2×C42C22×D4711yescharacteristic
827#95—472no—
828#95—472no—
829#95—472no—
830#95—472no—
831#95—472no—
832#95—472no—
833#95—472no—
834#95—472no—
835#95—472no—
836#95—472no—
837#95—472no—
838#95—472no—
839#95—472no—
840#95—472no—
841#95C22×D4712yes—
842#95C22×D4712yes—
843#95C22×D4712yes—
844#95C22×D4712yes—
845#95C22×D4712yes—
846#95C22×D4712yes—
847C24—471no—
848C24—471no—
849C24—471no—
850C24—471no—
851C24—474no—
852C24—942no—
853C24—942no—
854C24—1881no—
855C24—1881no—
856C24—1881no—
857C24—1881no—
858C24C23×D4711yescharacteristic
859#41—18816no—
860C2×Q8—474no—
861C2×Q8—1881no—
862C2×Q8—1881no—
863C2×D4—474no—
864C2×D4—474no—
865C2×D4—474no—
866C2×D4—474no—
867C2×D4—474no—
868C2×D4—474no—
869C2×D4—474no—
870C2×D4—942no—
871C2×D4—942no—
872C2×D4—942no—
873C2×D4—942no—
874C2×D4—1881no—
875C2×D4—1881no—
876C2×D4—1881no—
877C2×D4—1881no—
878C2×D4—1881no—
879C2×D4—1881no—
880C2×D4—1881no—
881C2×D4—1881no—
882C2×D4—1881no—
883C2×D4—1881no—
884C22×C4—22no—
885C22×C4—22no—
886C22×C4—471no—
887C22×C4—471no—
888C22×C4—471no—
889C22×C4—471no—
890C22×C4—474no—
891C22×C4—474no—
892C22×C4—474no—
893C22×C4—474no—
894C22×C4—474no—
895C22×C4—474no—
896C22×C4—474no—
897C22×C4—472no—
898C22×C4—472no—
899C22×C4—472no—
900C22×C4—472no—
901C22×C4—944no—
902C22×C4—944no—
903C22×C4—942no—
904C22×C4—942no—
905C22×C4—942no—
906C22×C4—942no—
907C22×C4—942no—
908C22×C4—942no—
909C22×C4—942no—
910C22×C4—942no—
911C22×C4—18816no—
912C22×C4—1882no—
913C22×C4—1882no—
914C22×C4—1882no—
915C22×C4—1882no—
916C22×C4—1882no—
917C22×C4—1882no—
918C22×C4—1882no—
919C22×C4—1882no—
920C22×C4—1882no—
921C22×C4—1882no—
922C22×C4—1881no—
923C22×C4—1881no—
924C22×C4—1881no—
925C22×C4—1881no—
926C22×C4—1881no—
927C22×C4—1881no—
928C22×C4C2×C4×D4714yes—
929C22×C4C23×D4712yes—
930C22×C4C23×D4712yes—
931C22×C4C23×D4712yes—
932C22×C4C23×D4712yes—
933C22×C4C23×D4711yescharacteristic
934C22×C4C23×D4711yescharacteristic
935C22×C4C23×D4711yescharacteristic
936C22×C4C23×D4711yescharacteristic
937C22×C4C23×D4711yescharacteristic
938C22×C4C23×D4711yescharacteristic
939C4⋊C4—22no—
940C4⋊C4—22no—
941C4⋊C4—22no—
942C4⋊C4—22no—
943C4⋊C4—42no—
944C4⋊C4—42no—
945C4⋊C4—474no—
946C4⋊C4—474no—
947C4⋊C4—474no—
948C4⋊C4—474no—
949C4⋊C4—942no—
950C4⋊C4—942no—
951C4⋊C4—942no—
952C4⋊C4—942no—
953C4⋊C4—1882no—
954C4⋊C4—1882no—
955C4⋊C4—1882no—
956C4⋊C4—1882no—
957C4⋊C4—1882no—
958C4⋊C4—1882no—
959C4⋊C4C2×C4×D4714yes—
960C4⋊C4C2×C4×D4714yes—
961C22⋊C4—42no—
962C22⋊C4—42no—
963C22⋊C4—474no—
964C22⋊C4—474no—
965C22⋊C4—474no—
966C22⋊C4—474no—
967C22⋊C4—474no—
968C22⋊C4—474no—
969C22⋊C4—474no—
970C22⋊C4—474no—
971C22⋊C4—944no—
972C22⋊C4—944no—
973C22⋊C4—1882no—
974C22⋊C4—1882no—
975C22⋊C4—1882no—
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⋊C4C2×C4×D4714yes—
986C22⋊C4C2×C4×D4714yes—
987C42—42no—
988C42—42no—
989C42—1882no—
990C42—1882no—
991C42—1882no—
992C42—1882no—
993C42—1882no—
994C42—1882no—
995C42C2×C4×D4714yes—
996C42C2×C4×D4714yes—
997C23—21no—
998C23—21no—
999C23—21no—
1000C23—21no—
1001C23—21no—
1002C23—21no—
1003C23—472no—
1004C23—472no—
1005C23—472no—
1006C23—472no—
1007C23—472no—
1008C23—472no—
1009C23—948no—
1010C23—941no—
1011C23—941no—
1012C23—941no—
1013C23—941no—
1014C23—941no—
1015C23—941no—
1016C23—941no—
1017C23—941no—
1018C23—941no—
1019C23—941no—
1020C23—941no—
1021C23—941no—
1022C23—941no—
1023C23—941no—
1024C23—941no—
1025C23—941no—
1026C23—941no—
1027C23—941no—
1028C23—941no—
1029C23—941no—
1030C23—941no—
1031C23—941no—
1032C23—1884no—
1033C23—1884no—
1034C23—1884no—
1035C23—1884no—
1036C23—1884no—
1037C23—1884no—
1038C23C22×C4×D4712yes—
1039C23C24×D4711yescharacteristic
1040Q8—1884no—
1041D4—948no—
1042D4—948no—
1043D4—1884no—
1044D4—1884no—
1045D4—1884no—
1046D4—1884no—
1047D4—1884no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—28no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—472no—
1072C2×C4—472no—
1073C2×C4—472no—
1074C2×C4—472no—
1075C2×C4—941no—
1076C2×C4—941no—
1077C2×C4—941no—
1078C2×C4—941no—
1079C2×C4—941no—
1080C2×C4—941no—
1081C2×C4—941no—
1082C2×C4—941no—
1083C2×C4—948no—
1084C2×C4—948no—
1085C2×C4—948no—
1086C2×C4—948no—
1087C2×C4—942no—
1088C2×C4—942no—
1089C2×C4—942no—
1090C2×C4—942no—
1091C2×C4—942no—
1092C2×C4—942no—
1093C2×C4—942no—
1094C2×C4—942no—
1095C2×C4—942no—
1096C2×C4—942no—
1097C2×C4—942no—
1098C2×C4—942no—
1099C2×C4—3764no—
1100C2×C4—3764no—
1101C2×C4—3764no—
1102C2×C4—3764no—
1103C2×C4—1884no—
1104C2×C4—1884no—
1105C2×C4—1884no—
1106C2×C4C22×C4×D4712yes—
1107C2×C4C22×C4×D4712yes—
1108C2×C4C22×C4×D4712yes—
1109C2×C4C22×C4×D4712yes—
1110C2×C4C22×C4×D4712yes—
1111C2×C4C22×C4×D4712yes—
1112C2×C4#1309407012yes—
1113C2×C4#1309407012yes—
1114C22—22no—
1115C22—22no—
1116C22—22no—
1117C22—41no—
1118C22—41no—
1119C22—41no—
1120C22—41no—
1121C22—474no—
1122C22—942no—
1123C22—942no—
1124C22—942no—
1125C22—942no—
1126C22—942no—
1127C22—942no—
1128C22—942no—
1129C22—942no—
1130C22—942no—
1131C22—942no—
1132C22—942no—
1133C22—942no—
1134C22—942no—
1135C22—942no—
1136C22—942no—
1137C22—18816no—
1138C22—1881no—
1139C22—1881no—
1140C22—1881no—
1141C22—1881no—
1142C22—1881no—
1143C22—1881no—
1144C22—1881no—
1145C22—1881no—
1146C22—1881no—
1147C22—1881no—
1148C22—1881no—
1149C22—1881no—
1150C22C23×C4×D4711yescharacteristic
1151C22H(5,𝔽2)×D4711yescharacteristic
1152C22C2×#1309407011yescharacteristic
1153C22C2×#1309407011yescharacteristic
1154C222−1+4×D4711yescharacteristic
1155C22#1568995811yescharacteristic
1156C22#1568996011yescharacteristic
1157C4—22no—
1158C4—22no—
1159C4—22no—
1160C4—22no—
1161C4—22no—
1162C4—42no—
1163C4—42no—
1164C4—42no—
1165C4—42no—
1166C4—942no—
1167C4—942no—
1168C4—942no—
1169C4—942no—
1170C4—1882no—
1171C4—1882no—
1172C4—1882no—
1173C4—1882no—
1174C4#1568959714yes—
1175C2—42no—
1176C2—944no—
1177C2—1882no—
1178C2—1882no—
1179C2—1882no—
1180C2C2×#1568959711yescharacteristic
1181C2#520×D4711yescharacteristic
1182C2#2025658811yescharacteristic
1183C2#2025767711yescharacteristic
1184C2#2025768711yescharacteristic
1185C2#2025770011yescharacteristic
1186C2#2025771011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D47
commutatorC22×C47C24×C4
FittingC47×#2314C2
socle, cosocleC23×C47C25
prime radicalC2×#15689635C2
hypercenter#2314D47
hypocenterC47#34362
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2314

Complements

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

NH ≅ G/Ntype
2. #20246552C2semidirect
3. #20246543C2semidirect
4. #20246470C2semidirect
5. #20246434C2semidirect
6. #20246339C2semidirect
7. #20246335C2semidirect
8. #20246320C2semidirect
9. #20246320C2semidirect
10. #20246314C2semidirect
11. #20246314C2semidirect
12. C4⋊C4×D188C2semidirect
13. #20246288C2semidirect
14. #20246183C2semidirect
15. #20246171C2semidirect
16. #20246050C2semidirect
17. #20246041C2semidirect
18. #20245997C2semidirect
19. #20245977C2semidirect
20. #20245977C2semidirect
21. #20245770C2semidirect
22. #380×D47C2semidirect
23. C47×#2314C2semidirect
26. #15689635C4semidirect
43. C2×#13093982C22semidirect
44. C2×#13093982C22semidirect
47. C2×C4⋊C4×D47C22semidirect
48. C2×C4⋊C4×D47C22semidirect
50. #15689027C22semidirect
51. #15689027C22semidirect
56. #15689021C22semidirect
57. #15689019C22semidirect
61. #15689015C22semidirect
63. #15689014C22semidirect
65. #15689013C22semidirect
67. #15689012C22semidirect
68. #15689009C22semidirect
69. #15689009C22semidirect
70. #15689008C22semidirect
71. #15689008C22semidirect
72. #15689006C22semidirect
73. #15689006C22semidirect
78. #15689001C22semidirect
79. #15689001C22semidirect
83. #15688997C22semidirect
85. #15688994C22semidirect
86. #15688993C22semidirect
87. #15688989C22semidirect
97. #15688980C22semidirect
98. #15688980C22semidirect
99. #15688980C22semidirect
100. #15688980C22semidirect
102. C4⋊C4×Dic47C22semidirect
103. C4×C4⋊Dic47C22semidirect
104. C4×C4⋊Dic47C22semidirect
105. C4×C4⋊Dic47C22semidirect
108. C4×(C2×D47)⋊C4C22semidirect
111. #15688970C22semidirect
116. C47×#387C22semidirect
117. C47×#387C22semidirect
118. C47×#384C22semidirect
119. C47×#382C22semidirect
122. C4×C4⋊C4×C47C22semidirect
123. C4×C4⋊C4×C47C22semidirect
127. C2×#10625350C2×C4semidirect
139. C22×C4×D47C2×C4semidirect
150. #13094008C2×C4semidirect
151. #13094008C2×C4semidirect
152. #13094004C2×C4semidirect
153. #13094004C2×C4semidirect
155. #13093999C2×C4semidirect
156. #13093994C2×C4semidirect
157. #13093994C2×C4semidirect
159. C4×D188C2×C4semidirect
160. C4×D188C2×C4semidirect
161. C4×D188C2×C4semidirect
162. C4×D188C2×C4semidirect
230. #117×C47C2×C4semidirect
600. #2314D47semidirect
670. #387C2×D47semidirect
671. #387C2×D47semidirect
685. #384C2×D47semidirect
687. #382C2×D47semidirect
708. C4×C4⋊C4C2×D47semidirect
709. C4×C4⋊C4C2×D47semidirect
717. C47#34362semidirect
763. #117C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156896352
#202465522
#202465432
#202464702
#202464342
#202463392
#202463352
#202463202
#202463142
C4⋊C4×D1882
#202462882
#202461832
#202461712
#202460502
#202460412
#202459972
#202459772
#202457702
#380×D472
C47×#23142
#3436247