Finite Group Databasebeta

← #26376993

Subgroups — #26376993

Order 12032.

2826 conjugacy classes of subgroups.

The subgroup lattice has 1158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689633C211yesmaximal, characteristic
2#20246409C211yesmaximal, characteristic, complemented
3#20246400C211yesmaximal, characteristic, complemented
4#20246395C211yesmaximal, characteristic, complemented
5#20246392C211yesmaximal, characteristic, complemented
6#20246368C212yesmaximal, complemented
7#20246365C212yesmaximal, complemented
8#20246326C212yesmaximal, complemented
9#20246293C212yesmaximal, complemented
10#20246277C211yesmaximal, characteristic, complemented
11#20246272C211yesmaximal, characteristic, complemented
12#20246227C211yesmaximal, characteristic, complemented
13#20246213C211yesmaximal, characteristic, complemented
14#20246180C212yesmaximal, complemented
15#20246176C212yesmaximal, complemented
16#20246018C212yesmaximal, complemented
17C4×#13094003C211yesmaximal, characteristic, complemented
18#20245916C211yesmaximal, characteristic, complemented
19#121×Dic47C211yesmaximal, characteristic, complemented
20#380×D47C211yesmaximal, characteristic, complemented
21#20245747C212yesmaximal, complemented
22C2×C4×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
23C4×#121×C47C211yesmaximal, characteristic, complemented
24C22×#10625352C2211yescharacteristic
25C23×C4×D47C2211yescharacteristic
26#15689633C4116yescomplemented
27C2×#13094006C2212yes—
28C2×#13094004C2211yescharacteristic
29C2×#13094003C2211yescharacteristic
30C2×#13093995C2211yescharacteristic
31C2×#13093992C2212yes—
32C2×C4×Dic94C2211yescharacteristic, complemented
33C2×#13093989C2211yescharacteristic, complemented
34C2×D4×Dic47C2212yes—
35C2×D4×Dic47C2212yes—
36C2×D4×Dic47C2211yescharacteristic, complemented
37C2×C4×C22⋊D47C2212yes—
38C2×(C22⋊D47)⋊C4C2212yes—
39C2×(C22⋊D47)⋊C4C2212yes—
40C2×#13093982C2211yescharacteristic
41C2×C4⋊C4×D47C2211yescharacteristic
42C2×C4⋊C4×D47C2211yescharacteristic
43C22×(C2×D47)⋊C4C2211yescharacteristic
44C22×(C2×D47)⋊C4C2211yescharacteristic
45C2×C22⋊C4×D47C2212yes—
46C22×C4×Dic47C2211yescharacteristic
47#15689029C2211yescharacteristic, complemented
48#15689028C2211yescharacteristic, complemented
49#15689026C2211yescharacteristic, complemented
50#15689023C2212yes—
51#15689023C2212yes—
52#15689022C2211yescharacteristic, complemented
53#15689021C2211yescharacteristic, complemented
54#15689021C2212yescomplemented
55#15689019C2211yescharacteristic, complemented
56#15689019C2212yescomplemented
57#15689017C2212yescomplemented
58#15689016C2212yescomplemented
59#15689015C2212yes—
60#15689014C2212yes—
61#15689013C2212yes—
62#15689012C2212yes—
63#15689011C2212yescomplemented
64#15689008C2212yescomplemented
65#15689007C2212yescomplemented
66#15689006C2212yescomplemented
67#15689005C2212yescomplemented
68#15689003C2212yes—
69#15689002C2212yes—
70#15689000C2212yes—
71#15688999C2212yes—
72#15688999C2212yes—
73#15688997C2212yes—
74#15688996C2212yes—
75#15688996C2212yescomplemented
76#15688995C2212yes—
77#15688995C2212yescomplemented
78#15688994C2212yes—
79#15688990C2212yescomplemented
80#15688988C2212yescomplemented
81#15688984C2212yescomplemented
82#15688983C2211yescharacteristic
83#15688982C2212yes—
84#15688981C2212yes—
85#15688981C2212yescomplemented
86#15688980C2211yescharacteristic
87#15688980C2211yescharacteristic
88C4⋊C4×Dic47C2211yescharacteristic, complemented
89C4⋊C4×Dic47C2211yescharacteristic, complemented
90C4×Dic47⋊C4C2212yescomplemented
91C4×Dic47⋊C4C2212yescomplemented
92C4×C4⋊Dic47C2211yescharacteristic, complemented
93#15688974C2212yescomplemented
94C22⋊C4×Dic47C2212yes—
95C22⋊C4×Dic47C2212yescomplemented
96C22⋊C4×Dic47C2212yescomplemented
97C4×(C2×D47)⋊C4C2211yescharacteristic
98C4×(C2×D47)⋊C4C2211yescharacteristic
99C4×(C2×D47)⋊C4C2211yescharacteristic
100C4×(C2×D47)⋊C4C2212yes—
101C4×(C2×D47)⋊C4C2211yescharacteristic
102C4×(C2×D47)⋊C4C2211yescharacteristic
103C4×(C2×D47)⋊C4C2211yescharacteristic
104C4×(C2×D47)⋊C4C2211yescharacteristic
105C4×(C2×D47)⋊C4C2211yescharacteristic
106C4×C22⋊Dic47C2212yes—
107#15688970C2212yes—
108#15688968C2212yescomplemented
109C2×C47⋊#95C2211yescharacteristic
110C2×C47⋊#95C2211yescharacteristic
111C2×C47⋊#95C2212yescomplemented
112#95×D47C2212yes—
113C2×#121×C47C2211yescharacteristic
114C2×C4×D4×C47C2212yes—
115C2×C4×D4×C47C2211yescharacteristic, complemented
116C22×C42×C47C2211yescharacteristic
117C47×#390C2211yescharacteristic, complemented
118C47×#389C2211yescharacteristic, complemented
119C47×#388C2212yescomplemented
120C47×#386C2212yes—
121C47×#380C2211yescharacteristic
122C4×C4⋊C4×C47C2211yescharacteristic, complemented
123C4×C22⋊C4×C47C2212yescomplemented
124C24×D47C2311yescharacteristic
125C2×#10625352—42no—
126C2×#10625352—42no—
127C2×#10625352C2×C418yescomplemented
128C22×Dic94C2311yescharacteristic
129C22×C22⋊D47C2312yes—
130C22×C22⋊D47C2312yes—
131C23×Dic47C2311yescharacteristic
132C23×Dic47C2311yescharacteristic
133C23×Dic47C2312yes—
134C23×Dic47C2311yescharacteristic
135C23×Dic47C2312yes—
136C22×C4×D47—42no—
137C22×C4×D47—42no—
138C22×C4×D47C2×C418yescomplemented
139C22×C4×D47C2311yescharacteristic
140C22×C4×D47C2311yescharacteristic
141C22×C4×D47C2312yes—
142C22×C4×D47C2312yes—
143C22×C4×D47C2311yescharacteristic
144C22×C4×D47C2311yescharacteristic
145#13094006C2×C4116yescomplemented
146#13094004C2×C418yescomplemented
147#13094003C2×C418yescomplemented
148#13093995C2×C418yescomplemented
149#13093992C2×C4116yescomplemented
150C4×Dic94—42no—
151#13093989—42no—
152D4×Dic47—42no—
153D4×Dic47—44no—
154D4×Dic47C2×C4116yescomplemented
155C4×C22⋊D47—28no—
156(C22⋊D47)⋊C4—28no—
157(C22⋊D47)⋊C4C2×C4116yescomplemented
158#13093982C2×C418yescomplemented
159C2×C4⋊Dic47C2311yescharacteristic
160C2×C4⋊Dic47C2311yescharacteristic
161C2×C4⋊Dic47C2312yes—
162C2×C4⋊Dic47C2311yescharacteristic
163C2×C4⋊Dic47C2312yes—
164C2×Dic47⋊C4C2312yes—
165C2×Dic47⋊C4C2312yes—
166C2×Dic47⋊C4C2312yes—
167C2×Dic47⋊C4C2312yes—
168C2×Dic47⋊C4C2312yes—
169C2×Dic47⋊C4C2312yes—
170C2×Dic47⋊C4C2312yes—
171C4⋊C4×D47—42no—
172C4⋊C4×D47—42no—
173C2×C22⋊Dic47C2312yes—
174C2×C22⋊Dic47C2312yes—
175C2×C22⋊Dic47C2312yes—
176C2×C22⋊Dic47C2312yes—
177C2×C22⋊Dic47C2312yes—
178C2×C22⋊Dic47C2312yes—
179C2×(C2×D47)⋊C4—24no—
180C2×(C2×D47)⋊C4—24no—
181C2×(C2×D47)⋊C4C2311yescharacteristic
182C2×(C2×D47)⋊C4C2311yescharacteristic
183C2×(C2×D47)⋊C4C2311yescharacteristic
184C2×(C2×D47)⋊C4C2311yescharacteristic
185C2×(C2×D47)⋊C4C2311yescharacteristic
186C2×(C2×D47)⋊C4C2311yescharacteristic
187C2×(C2×D47)⋊C4C2312yes—
188C2×(C2×D47)⋊C4C2312yes—
189C2×(C2×D47)⋊C4C2312yes—
190C2×(C2×D47)⋊C4C2312yes—
191C2×(C2×D47)⋊C4C2311yescharacteristic
192C2×(C2×D47)⋊C4C2311yescharacteristic
193C22⋊C4×D47—44no—
194C2×C4×Dic47—42no—
195C2×C4×Dic47C2312yes—
196C2×C4×Dic47C2312yes—
197C2×C4×Dic47C2311yescharacteristic
198C2×C4×Dic47C2311yescharacteristic
199C2×C4×Dic47C2312yes—
200C2×C4×Dic47C2312yes—
201C2×C4×Dic47C2311yescharacteristic
202C2×C4×Dic47C2311yescharacteristic
203C2×C4×Dic47C2312yes—
204C2×C4×Dic47C2312yes—
205C47⋊#95C2312yes—
206C47⋊#95C2312yes—
207C47⋊#95C2312yes—
208C47⋊#95C2311yescharacteristic
209C47⋊#95C2311yescharacteristic
210C47⋊#95C2311yescharacteristic
211C47⋊#95C2311yescharacteristic
212C47⋊#95C2311yescharacteristic
213C47⋊#95C2311yescharacteristic
214C47⋊#95C2311yescharacteristic
215C47⋊#95C2311yescharacteristic
216C47⋊#95C2312yes—
217C47⋊#95C2312yes—
218C47⋊#95C2312yes—
219C47⋊#95C2312yes—
220C47⋊#95C2312yes—
221C47⋊#95C2312yes—
222C47⋊#95C2312yes—
223C47⋊#95C2312yes—
224C47⋊#95C2312yes—
225C47⋊#95C2312yes—
226C22×D4×C47C2312yes—
227C22×D4×C47C2311yescharacteristic
228C23×C4×C47C2311yescharacteristic
229C23×C4×C47C2311yescharacteristic
230C23×C4×C47C2311yescharacteristic
231C23×C4×C47C2312yes—
232#121×C47C2×C418yescomplemented
233C4×D4×C47—42no—
234C4×D4×C47—44no—
235C2×C4⋊C4×C47C2311yescharacteristic
236C2×C4⋊C4×C47C2311yescharacteristic
237C2×C4⋊C4×C47C2312yes—
238C2×C4⋊C4×C47C2311yescharacteristic
239C2×C22⋊C4×C47C2312yes—
240C2×C22⋊C4×C47C2312yes—
241C2×C22⋊C4×C47C2312yes—
242C2×C22⋊C4×C47C2312yes—
243C2×C22⋊C4×C47C2312yes—
244C2×C42×C47—42no—
245C2×C42×C47C2311yescharacteristic
246C2×C42×C47C2311yescharacteristic
247C2×C42×C47C2311yescharacteristic
248C2×C42×C47C2311yescharacteristic
249C2×C42×C47C2312yes—
250#95×C47C2312yes—
251#95×C47C2312yes—
252#95×C47C2312yes—
253C24×C47C2412yes—
254C24×C47C2411yescharacteristic
255C23×D47—22no—
256C23×D47—22no—
257C23×D47—22no—
258C23×D47—22no—
259C23×D47—41no—
260C23×D47—41no—
261C23×D47C22×C414yes—
262C23×D47C2411yescharacteristic
263C23×D47C2411yescharacteristic
264C2×D4×C47—24no—
265C2×D4×C47—24no—
266C2×D4×C47—22no—
267C2×D4×C47—22no—
268C2×D4×C47C22×C418yes—
269C2×D4×C47C22×C414yes—
270C22×C4×C47—22no—
271C22×C4×C47—22no—
272C22×C4×C47—22no—
273C22×C4×C47—22no—
274C22×C4×C47—22no—
275C22×C4×C47—22no—
276C22×C4×C47—24no—
277C22×C4×C47—41no—
278C22×C4×C47—41no—
279C22×C4×C47—42no—
280C22×C4×C47—42no—
281C22×C4×C47C22×C414yes—
282C22×C4×C47C2411yescharacteristic
283C22×C4×C47C2411yescharacteristic
284C22×C4×C47C2412yes—
285C22×C4×C47C2412yes—
286C22×C4×C47C2411yescharacteristic
287C22×C4×C47C2412yes—
288C22×C4×C47C2411yescharacteristic
289C22×C4×C47C2411yescharacteristic
290C22×C4×C47C2411yescharacteristic
291C2×C22⋊D47—24no—
292C2×C22⋊D47—24no—
293C2×C22⋊D47—42no—
294C2×C22⋊D47—42no—
295C2×C22⋊D47C22×C418yes—
296C2×C22⋊D47C22×C418yes—
297C22×Dic47—22no—
298C22×Dic47—22no—
299C22×Dic47—22no—
300C22×Dic47—22no—
301C22×Dic47—24no—
302C22×Dic47—41no—
303C22×Dic47—41no—
304C22×Dic47—41no—
305C22×Dic47—41no—
306C22×Dic47—42no—
307C22×Dic47—42no—
308C22×Dic47—42no—
309C22×Dic47—42no—
310C22×Dic47C22×C418yes—
311C22×Dic47C22×C414yes—
312C22×Dic47C2411yescharacteristic
313C22×Dic47C2412yes—
314C22×Dic47C2411yescharacteristic
315C22×Dic47C2412yes—
316C22×Dic47C2411yescharacteristic
317C22×Dic47C2412yes—
318C22×Dic47C2412yes—
319C22×Dic47C2411yescharacteristic
320C22×Dic47C2411yescharacteristic
321C22×Dic47C2411yescharacteristic
322#10625352—416no—
323C2×C4×D47—22no—
324C2×C4×D47—22no—
325C2×C4×D47—22no—
326C2×C4×D47—22no—
327C2×C4×D47—24no—
328C2×C4×D47—24no—
329C2×C4×D47—416no—
330C2×C4×D47—41no—
331C2×C4×D47—41no—
332C2×C4×D47—41no—
333C2×C4×D47—41no—
334C2×C4×D47—42no—
335C2×C4×D47—42no—
336C2×C4×D47—42no—
337C2×C4×D47—42no—
338C2×C4×D47C22×C414yes—
339C2×C4×D47C22×C414yes—
340C2×C4×D47C22×C414yes—
341C2×C4×D47C22×C414yes—
342C2×Dic94—22no—
343C2×Dic94—22no—
344C2×Dic94C22×C414yes—
345C4⋊C4×C47—22no—
346C4⋊C4×C47—22no—
347C4⋊C4×C47—42no—
348C4⋊C4×C47C22×C414yes—
349C22⋊C4×C47—24no—
350C22⋊C4×C47—24no—
351C22⋊C4×C47—42no—
352C22⋊C4×C47—42no—
353C22⋊C4×C47C22×C418yes—
354C42×C47—22no—
355C42×C47—22no—
356C42×C47—41no—
357C42×C47—41no—
358C42×C47—42no—
359C22⋊Dic47—24no—
360C22⋊Dic47—24no—
361C22⋊Dic47—42no—
362C22⋊Dic47—42no—
363C22⋊Dic47C22×C418yes—
364C22⋊Dic47C22×C418yes—
365(C2×D47)⋊C4—22no—
366(C2×D47)⋊C4—22no—
367(C2×D47)⋊C4—22no—
368(C2×D47)⋊C4—22no—
369(C2×D47)⋊C4—22no—
370(C2×D47)⋊C4—22no—
371(C2×D47)⋊C4—42no—
372(C2×D47)⋊C4—42no—
373(C2×D47)⋊C4C22×C418yes—
374(C2×D47)⋊C4C22×C418yes—
375(C2×D47)⋊C4#4114yescomplemented
376(C2×D47)⋊C4#4114yescomplemented
377C4⋊Dic47—22no—
378C4⋊Dic47—22no—
379C4⋊Dic47—42no—
380C4⋊Dic47C22×C414yes—
381C4⋊Dic47C22×C418yes—
382Dic47⋊C4—24no—
383Dic47⋊C4—24no—
384Dic47⋊C4—42no—
385Dic47⋊C4—42no—
386Dic47⋊C4—42no—
387Dic47⋊C4—42no—
388Dic47⋊C4C22×C418yes—
389C4×Dic47—24no—
390C4×Dic47—22no—
391C4×Dic47—22no—
392C4×Dic47—24no—
393C4×Dic47—41no—
394C4×Dic47—41no—
395C4×Dic47—42no—
396C4×Dic47—42no—
397C4×Dic47—42no—
398C4×Dic47C22×C418yes—
399C23×C47—21no—
400C23×C47—21no—
401C23×C47—21no—
402C23×C47—21no—
403C23×C47—22no—
404C23×C47—22no—
405C23×C47—22no—
406C23×C47—22no—
407C23×C47—22no—
408C23×C47—22no—
409C23×C47C23×C414yes—
410C23×C47C23×C412yes—
411C23×C47H(5,𝔽2)12yes—
412C23×C472−1+412yes—
413C23×C47C2511yescharacteristic
414C22×D47—21no—
415C22×D47—21no—
416C22×D47—21no—
417C22×D47—21no—
418C22×D47—28no—
419C22×D47—21no—
420C22×D47—21no—
421C22×D47—21no—
422C22×D47—21no—
423C22×D47—21no—
424C22×D47—21no—
425C22×D47—28no—
426C22×D47—44no—
427C22×D47—44no—
428C22×D47—44no—
429C22×D47—44no—
430C22×D47—44no—
431C22×D47C23×C412yes—
432C22×D47C23×C412yes—
433C22×D47C2×#4112yes—
434C22×D47C2×#4112yes—
435D4×C47—216no—
436D4×C47—28no—
437C2×C4×C47—21no—
438C2×C4×C47—21no—
439C2×C4×C47—22no—
440C2×C4×C47—21no—
441C2×C4×C47—21no—
442C2×C4×C47—21no—
443C2×C4×C47—21no—
444C2×C4×C47—22no—
445C2×C4×C47—28no—
446C2×C4×C47—22no—
447C2×C4×C47—22no—
448C2×C4×C47—21no—
449C2×C4×C47—21no—
450C2×C4×C47—22no—
451C2×C4×C47—21no—
452C2×C4×C47—22no—
453C2×C4×C47—22no—
454C2×C4×C47—22no—
455C2×C4×C47—21no—
456C2×C4×C47—21no—
457C2×C4×C47—21no—
458C2×C4×C47—44no—
459C2×C4×C47—44no—
460C2×C4×C47—84no—
461C2×C4×C47C23×C414yes—
462C2×C4×C47C23×C412yes—
463C2×C4×C47C23×C412yes—
464C2×C4×C47C2×#4112yes—
465C2×C4×C47C2×#4112yes—
466C2×C4×C47H(5,𝔽2)12yes—
467C2×C4×C47H(5,𝔽2)12yes—
468C22⋊D47—216no—
469C22⋊D47—48no—
470C2×Dic47—22no—
471C2×Dic47—22no—
472C2×Dic47—21no—
473C2×Dic47—21no—
474C2×Dic47—21no—
475C2×Dic47—22no—
476C2×Dic47—22no—
477C2×Dic47—21no—
478C2×Dic47—21no—
479C2×Dic47—21no—
480C2×Dic47—21no—
481C2×Dic47—21no—
482C2×Dic47—22no—
483C2×Dic47—22no—
484C2×Dic47—21no—
485C2×Dic47—21no—
486C2×Dic47—21no—
487C2×Dic47—21no—
488C2×Dic47—22no—
489C2×Dic47—22no—
490C2×Dic47—22no—
491C2×Dic47—21no—
492C2×Dic47—22no—
493C2×Dic47—21no—
494C2×Dic47—44no—
495C2×Dic47—48no—
496C2×Dic47—44no—
497C2×Dic47—44no—
498C2×Dic47—84no—
499C2×Dic47C23×C412yes—
500C2×Dic47C23×C414yes—
501C2×Dic47C23×C414yes—
502C2×Dic47C23×C412yes—
503C2×Dic47C2×#4112yes—
504C2×Dic47C2×#4112yes—
505C4×D47—28no—
506C4×D47—28no—
507C4×D47—44no—
508C4×D47—44no—
509C4×D47—84no—
510C4×D47—84no—
511Dic94—28no—
512#34233—471nomaximal, Sylow
513C22×C47—22no—
514C22×C47—22no—
515C22×C47—22no—
516C22×C47—22no—
517C22×C47—22no—
518C22×C47—22no—
519C22×C47—24no—
520C22×C47—24no—
521C22×C47—24no—
522C22×C47—42no—
523C22×C47—42no—
524C22×C47—42no—
525C22×C47—42no—
526C22×C47#52014yes—
527C22×C47C24×C411yescharacteristic
528C22×C47C22×#4111yescharacteristic
529C22×C47C22×#4111yescharacteristic
530C22×C47C2×H(5,𝔽2)11yescharacteristic
531C22×C47C2×H(5,𝔽2)11yescharacteristic
532C22×C47C2×H(5,𝔽2)11yescharacteristic
533C22×C47C2×2−1+411yescharacteristic
534C2×D47—22no—
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—416no—
544C2×D47—41no—
545C2×D47—41no—
546C2×D47—41no—
547C2×D47—41no—
548C2×D47C4×#4114yes—
549C4×C47—22no—
550C4×C47—24no—
551C4×C47—22no—
552C4×C47—22no—
553C4×C47—42no—
554C4×C47—42no—
555C4×C47—41no—
556C4×C47—41no—
557C4×C47#51814yes—
558Dic47—24no—
559Dic47—24no—
560Dic47—22no—
561Dic47—22no—
562Dic47—22no—
563Dic47—22no—
564Dic47—42no—
565Dic47—42no—
566Dic47—41no—
567Dic47—41no—
568C2×#525—471no—
569#2361—471no—
570#2361—471no—
571#2360—471no—
572#2360—471no—
573#2358—472no—
574#2358—472no—
575#2353—472no—
576#2349—472no—
577#2347—471no—
578#2346—471no—
579#2341—471no—
580#2339—471no—
581#2335—472no—
582#2335—472no—
583#2318—472no—
584C4×C22⋊Q8—471no—
585C4×C22⋊Q8—471no—
586C4×#121—471no—
587C4×#121D4711yescharacteristic, complemented
588C2×#380—471no—
589#2275—472no—
590C2×C4×C22⋊C4—471no—
591C2×C47—24no—
592C2×C47—44no—
593C2×C47C2×C4×#4111yescharacteristic
594C2×C47C2×#51811yescharacteristic
595C2×C47C2×#52011yescharacteristic
596C2×C47#351911yescharacteristic
597C2×C47#351911yescharacteristic
598C2×C47#352011yescharacteristic
599C2×C47#352011yescharacteristic
600D47—24no—
601D47—42no—
602C22×#41—471no—
603C24×C4—471no—
604#525—4716no—
605C2×#123—472no—
606C2×C22⋊Q8—471no—
607C2×C22⋊Q8—471no—
608C2×#121—471no—
609C2×#121C2×D4711yescharacteristic
610C2×#120—472no—
611C2×C4×Q8—471no—
612C2×C4×Q8—471no—
613C2×C4×D4—472no—
614C2×C4×D4—472no—
615C2×C4×D4—471no—
616C2×C4×D4—472no—
617C2×C4×D4—472no—
618C2×C4×D4—472no—
619C2×C4×D4C2×D4712yes—
620C2×C4×D4C2×D4711yescharacteristic, complemented
621C2×#117—471no—
622C22×C4⋊C4—471no—
623C22×C4⋊C4—471no—
624C22×C22⋊C4—471no—
625C22×C22⋊C4—471no—
626C22×C22⋊C4—472no—
627C22×C42—471no—
628C22×C42C2×D4711yescharacteristic
629#391—471no—
630#391—471no—
631#390—471no—
632#390—472no—
633#390—472no—
634#390C2×D4711yescharacteristic, complemented
635#389—472no—
636#389—471no—
637#389—471no—
638#389—472no—
639#389—471no—
640#389C2×D4711yescharacteristic, complemented
641#388—472no—
642#388—472no—
643#388—472no—
644#388—472no—
645#388—472no—
646#388—472no—
647#388—472no—
648#388C2×D4712yescomplemented
649#387—472no—
650#387—472no—
651#387—472no—
652#387—472no—
653#386—472no—
654#386—472no—
655#386—472no—
656#386—472no—
657#386—472no—
658#386C2×D4712yes—
659#385—472no—
660#385—472no—
661#385—472no—
662#385—472no—
663#385—472no—
664#385—472no—
665#383—472no—
666#382—472no—
667#381—472no—
668#380—471no—
669#380—471no—
670#380—471no—
671#380—472no—
672#380—472no—
673#380—472no—
674#380C2×D4711yescharacteristic
675C4×C4⋊C4—471no—
676C4×C4⋊C4—471no—
677C4×C4⋊C4—471no—
678C4×C4⋊C4—472no—
679C4×C4⋊C4—472no—
680C4×C4⋊C4—472no—
681C4×C4⋊C4C2×D4711yescharacteristic, complemented
682C4×C22⋊C4—472no—
683C4×C22⋊C4—472no—
684C4×C22⋊C4—472no—
685C4×C22⋊C4—472no—
686C4×C22⋊C4—471no—
687C4×C22⋊C4—471no—
688C4×C22⋊C4—471no—
689C4×C22⋊C4—471no—
690C4×C22⋊C4—471no—
691C4×C22⋊C4—472no—
692C4×C22⋊C4—471no—
693C4×C22⋊C4—471no—
694C4×C22⋊C4—471no—
695C4×C22⋊C4—472no—
696C4×C22⋊C4C2×D4712yescomplemented
697#376—472no—
698C2×#95—471no—
699C2×#95—471no—
700C2×#95—472no—
701C2×#95—472no—
702C47#3423311yescharacteristic, complemented, Sylow
703C25—471no—
704C2×#41—478no—
705C2×#41—1882no—
706C2×#41—1882no—
707C22×Q8—471no—
708C22×D4—472no—
709C22×D4—472no—
710C22×D4C22×D4712yes—
711C22×D4C22×D4711yescharacteristic
712C23×C4—471no—
713C23×C4—472no—
714C23×C4—471no—
715C23×C4—471no—
716C23×C4—478no—
717C23×C4—471no—
718C23×C4—471no—
719C23×C4—471no—
720C23×C4—471no—
721C23×C4—472no—
722C23×C4—472no—
723C23×C4—472no—
724C23×C4—1882no—
725C23×C4—1882no—
726C23×C4C22×D4711yescharacteristic
727C23×C4C22×D4711yescharacteristic
728C23×C4C22×D4711yescharacteristic
729C23×C4C22×D4712yes—
730#123—4716no—
731C22⋊Q8—478no—
732C22⋊Q8—478no—
733#121—478no—
734#121C4×D4718yescomplemented
735#120—4716no—
736C4×Q8—1882no—
737C4×Q8—1882no—
738C4×D4—42no—
739C4×D4—44no—
740C4×D4—4716no—
741C4×D4—4716no—
742C4×D4—948no—
743C4×D4—948no—
744C4×D4—1882no—
745C4×D4—1884no—
746#117—478no—
747C2×C4⋊C4—471no—
748C2×C4⋊C4—472no—
749C2×C4⋊C4—472no—
750C2×C4⋊C4—471no—
751C2×C4⋊C4—471no—
752C2×C4⋊C4—472no—
753C2×C4⋊C4—472no—
754C2×C4⋊C4—472no—
755C2×C4⋊C4—472no—
756C2×C4⋊C4—472no—
757C2×C4⋊C4—472no—
758C2×C4⋊C4—472no—
759C2×C4⋊C4—1882no—
760C2×C4⋊C4—1882no—
761C2×C4⋊C4C22×D4711yescharacteristic
762C2×C4⋊C4C22×D4711yescharacteristic
763C2×C4⋊C4C22×D4712yes—
764C2×C4⋊C4C22×D4711yescharacteristic
765C2×C22⋊C4—472no—
766C2×C22⋊C4—472no—
767C2×C22⋊C4—471no—
768C2×C22⋊C4—471no—
769C2×C22⋊C4—472no—
770C2×C22⋊C4—472no—
771C2×C22⋊C4—472no—
772C2×C22⋊C4—472no—
773C2×C22⋊C4—471no—
774C2×C22⋊C4—471no—
775C2×C22⋊C4—471no—
776C2×C22⋊C4—471no—
777C2×C22⋊C4—471no—
778C2×C22⋊C4—471no—
779C2×C22⋊C4—472no—
780C2×C22⋊C4—472no—
781C2×C22⋊C4—472no—
782C2×C22⋊C4—472no—
783C2×C22⋊C4—944no—
784C2×C22⋊C4—944no—
785C2×C22⋊C4—1884no—
786C2×C22⋊C4C22×D4712yes—
787C2×C22⋊C4C22×D4712yes—
788C2×C22⋊C4C22×D4712yes—
789C2×C22⋊C4C22×D4712yes—
790C2×C22⋊C4C22×D4712yes—
791C2×C42—42no—
792C2×C42—472no—
793C2×C42—472no—
794C2×C42—472no—
795C2×C42—471no—
796C2×C42—471no—
797C2×C42—472no—
798C2×C42—472no—
799C2×C42—472no—
800C2×C42—471no—
801C2×C42—471no—
802C2×C42—1882no—
803C2×C42C22×D4711yescharacteristic
804C2×C42C22×D4711yescharacteristic
805C2×C42C22×D4712yes—
806C2×C42C22×D4711yescharacteristic
807C2×C42C22×D4711yescharacteristic
808#95—471no—
809#95—472no—
810#95—471no—
811#95—471no—
812#95—471no—
813#95—471no—
814#95—471no—
815#95—471no—
816#95—471no—
817#95—472no—
818#95—472no—
819#95—472no—
820#95—472no—
821#95—472no—
822#95—472no—
823#95—472no—
824#95—472no—
825#95—472no—
826#95—472no—
827#95—472no—
828#95—472no—
829#95C22×D4712yes—
830#95C22×D4712yes—
831#95C22×D4712yes—
832C24—471no—
833C24—471no—
834C24—474no—
835C24—942no—
836C24—942no—
837C24—942no—
838C24—942no—
839C24—1881no—
840C24—1881no—
841C24C23×D4712yes—
842C24C23×D4711yescharacteristic
843#41—18816no—
844C2×Q8—474no—
845C2×Q8—942no—
846C2×Q8—942no—
847C2×D4—24no—
848C2×D4—24no—
849C2×D4—22no—
850C2×D4—22no—
851C2×D4—478no—
852C2×D4—478no—
853C2×D4—944no—
854C2×D4—944no—
855C2×D4—1882no—
856C2×D4—1882no—
857C2×D4C2×C4×D4718yes—
858C2×D4C2×C4×D4714yes—
859C22×C4—22no—
860C22×C4—22no—
861C22×C4—22no—
862C22×C4—22no—
863C22×C4—22no—
864C22×C4—22no—
865C22×C4—24no—
866C22×C4—41no—
867C22×C4—41no—
868C22×C4—42no—
869C22×C4—42no—
870C22×C4—471no—
871C22×C4—471no—
872C22×C4—471no—
873C22×C4—472no—
874C22×C4—472no—
875C22×C4—471no—
876C22×C4—474no—
877C22×C4—478no—
878C22×C4—474no—
879C22×C4—474no—
880C22×C4—474no—
881C22×C4—474no—
882C22×C4—471no—
883C22×C4—472no—
884C22×C4—471no—
885C22×C4—472no—
886C22×C4—944no—
887C22×C4—944no—
888C22×C4—944no—
889C22×C4—942no—
890C22×C4—942no—
891C22×C4—942no—
892C22×C4—942no—
893C22×C4—942no—
894C22×C4—942no—
895C22×C4—942no—
896C22×C4—942no—
897C22×C4—18816no—
898C22×C4—1882no—
899C22×C4—1882no—
900C22×C4—1882no—
901C22×C4—1882no—
902C22×C4—1881no—
903C22×C4—1881no—
904C22×C4—1881no—
905C22×C4—1881no—
906C22×C4—1882no—
907C22×C4—1882no—
908C22×C4—1881no—
909C22×C4—1881no—
910C22×C4—1881no—
911C22×C4—1881no—
912C22×C4—1882no—
913C22×C4—1882no—
914C22×C4C2×C4×D4714yes—
915C22×C4C23×D4711yescharacteristic
916C22×C4C23×D4712yes—
917C22×C4C23×D4711yescharacteristic
918C22×C4C23×D4712yes—
919C22×C4C23×D4711yescharacteristic
920C22×C4C23×D4712yes—
921C22×C4C23×D4711yescharacteristic
922C22×C4C23×D4711yescharacteristic
923C22×C4C23×D4711yescharacteristic
924C4⋊C4—22no—
925C4⋊C4—22no—
926C4⋊C4—42no—
927C4⋊C4—478no—
928C4⋊C4—474no—
929C4⋊C4—478no—
930C4⋊C4—944no—
931C4⋊C4—944no—
932C4⋊C4—942no—
933C4⋊C4—942no—
934C4⋊C4—1882no—
935C4⋊C4—1882no—
936C4⋊C4—1882no—
937C4⋊C4—1882no—
938C4⋊C4—1882no—
939C4⋊C4C2×C4×D4714yes—
940C22⋊C4—24no—
941C22⋊C4—24no—
942C22⋊C4—42no—
943C22⋊C4—42no—
944C22⋊C4—478no—
945C22⋊C4—478no—
946C22⋊C4—478no—
947C22⋊C4—478no—
948C22⋊C4—474no—
949C22⋊C4—474no—
950C22⋊C4—942no—
951C22⋊C4—942no—
952C22⋊C4—942no—
953C22⋊C4—942no—
954C22⋊C4—944no—
955C22⋊C4—944no—
956C22⋊C4—942no—
957C22⋊C4—942no—
958C22⋊C4—1882no—
959C22⋊C4—1882no—
960C22⋊C4—1882no—
961C22⋊C4—1882no—
962C22⋊C4C2×C4×D4718yes—
963C42—22no—
964C42—22no—
965C42—41no—
966C42—41no—
967C42—42no—
968C42—478no—
969C42—944no—
970C42—944no—
971C42—942no—
972C42—942no—
973C42—1881no—
974C42—1881no—
975C42—1882no—
976C42—1882no—
977C42—1882no—
978C23—21no—
979C23—21no—
980C23—21no—
981C23—21no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—472no—
989C23—472no—
990C23—472no—
991C23—472no—
992C23—948no—
993C23—941no—
994C23—941no—
995C23—941no—
996C23—941no—
997C23—948no—
998C23—941no—
999C23—941no—
1000C23—941no—
1001C23—941no—
1002C23—941no—
1003C23—941no—
1004C23—1884no—
1005C23—1884no—
1006C23—1884no—
1007C23—1884no—
1008C23—1884no—
1009C23C22×C4×D4714yes—
1010C23C22×C4×D4712yes—
1011C23#1309406912yes—
1012C23#1309407112yes—
1013C23C24×D4711yescharacteristic
1014Q8—948no—
1015D4—216no—
1016D4—28no—
1017D4—9416no—
1018D4—1888no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—22no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—22no—
1027C2×C4—28no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—21no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—21no—
1040C2×C4—44no—
1041C2×C4—44no—
1042C2×C4—84no—
1043C2×C4—472no—
1044C2×C4—474no—
1045C2×C4—472no—
1046C2×C4—474no—
1047C2×C4—472no—
1048C2×C4—472no—
1049C2×C4—942no—
1050C2×C4—942no—
1051C2×C4—941no—
1052C2×C4—942no—
1053C2×C4—941no—
1054C2×C4—941no—
1055C2×C4—941no—
1056C2×C4—941no—
1057C2×C4—942no—
1058C2×C4—941no—
1059C2×C4—941no—
1060C2×C4—941no—
1061C2×C4—948no—
1062C2×C4—948no—
1063C2×C4—942no—
1064C2×C4—941no—
1065C2×C4—941no—
1066C2×C4—942no—
1067C2×C4—942no—
1068C2×C4—942no—
1069C2×C4—942no—
1070C2×C4—941no—
1071C2×C4—941no—
1072C2×C4—941no—
1073C2×C4—942no—
1074C2×C4—941no—
1075C2×C4—3764no—
1076C2×C4—3764no—
1077C2×C4—3764no—
1078C2×C4—1884no—
1079C2×C4—1884no—
1080C2×C4—1884no—
1081C2×C4—1888no—
1082C2×C4—1884no—
1083C2×C4—1884no—
1084C2×C4C22×C4×D4714yes—
1085C2×C4C22×C4×D4712yes—
1086C2×C4C22×C4×D4712yes—
1087C2×C4#41×D4712yes—
1088C2×C4#41×D4712yes—
1089C2×C4#1309406912yes—
1090C2×C4#1309407012yes—
1091C22—22no—
1092C22—22no—
1093C22—22no—
1094C22—22no—
1095C22—22no—
1096C22—22no—
1097C22—24no—
1098C22—24no—
1099C22—24no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—474no—
1105C22—942no—
1106C22—942no—
1107C22—942no—
1108C22—942no—
1109C22—942no—
1110C22—942no—
1111C22—942no—
1112C22—942no—
1113C22—942no—
1114C22—18816no—
1115C22—1881no—
1116C22—1881no—
1117C22—1881no—
1118C22—1881no—
1119C22#1568960214yes—
1120C22C23×C4×D4711yescharacteristic
1121C22C2×#41×D4711yescharacteristic
1122C22C2×#41×D4711yescharacteristic
1123C22C2×#1309406911yescharacteristic
1124C22C2×#1309406911yescharacteristic
1125C22C2×#1309407011yescharacteristic
1126C22C2×#1309407111yescharacteristic
1127C4—22no—
1128C4—24no—
1129C4—22no—
1130C4—22no—
1131C4—41no—
1132C4—42no—
1133C4—42no—
1134C4—41no—
1135C4—944no—
1136C4—942no—
1137C4—942no—
1138C4—944no—
1139C4—942no—
1140C4—942no—
1141C4—1882no—
1142C4—1882no—
1143C4—1881no—
1144C4—1881no—
1145C4#1568959514yes—
1146C2—24no—
1147C2—44no—
1148C2—944no—
1149C2—1882no—
1150C2C4×#41×D4711yescharacteristic
1151C2C2×#1568959511yescharacteristic
1152C2C2×#1568960211yescharacteristic
1153C2#2025741411yescharacteristic
1154C2#2025741511yescharacteristic
1155C2#2025742511yescharacteristic
1156C2#2025743911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D47
commutatorC22×C47C24×C4
FittingC4×#121×C47C2
socle, cosocleC23×C47C25
prime radicalC2×#15689633C2
hypercenterC4×#121D47
hypocenterC47#34233
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
2. #20246409C2semidirect
3. #20246400C2semidirect
4. #20246395C2semidirect
5. #20246392C2semidirect
6. #20246368C2semidirect
7. #20246365C2semidirect
8. #20246326C2semidirect
9. #20246293C2semidirect
10. #20246277C2semidirect
11. #20246272C2semidirect
12. #20246227C2semidirect
13. #20246213C2semidirect
14. #20246180C2semidirect
15. #20246176C2semidirect
16. #20246018C2semidirect
17. C4×#13094003C2semidirect
18. #20245916C2semidirect
19. #121×Dic47C2semidirect
20. #380×D47C2semidirect
21. #20245747C2semidirect
22. C2×C4×(C2×D47)⋊C4C2semidirect
23. C4×#121×C47C2semidirect
26. #15689633C4semidirect
32. C2×C4×Dic94C22semidirect
33. C2×#13093989C22semidirect
36. C2×D4×Dic47C22semidirect
47. #15689029C22semidirect
48. #15689028C22semidirect
49. #15689026C22semidirect
52. #15689022C22semidirect
53. #15689021C22semidirect
54. #15689021C22semidirect
55. #15689019C22semidirect
56. #15689019C22semidirect
57. #15689017C22semidirect
58. #15689016C22semidirect
63. #15689011C22semidirect
64. #15689008C22semidirect
65. #15689007C22semidirect
66. #15689006C22semidirect
67. #15689005C22semidirect
75. #15688996C22semidirect
77. #15688995C22semidirect
79. #15688990C22semidirect
80. #15688988C22semidirect
81. #15688984C22semidirect
85. #15688981C22semidirect
88. C4⋊C4×Dic47C22semidirect
89. C4⋊C4×Dic47C22semidirect
90. C4×Dic47⋊C4C22semidirect
91. C4×Dic47⋊C4C22semidirect
92. C4×C4⋊Dic47C22semidirect
93. #15688974C22semidirect
95. C22⋊C4×Dic47C22semidirect
96. C22⋊C4×Dic47C22semidirect
108. #15688968C22semidirect
111. C2×C47⋊#95C22semidirect
115. C2×C4×D4×C47C22semidirect
117. C47×#390C22semidirect
118. C47×#389C22semidirect
119. C47×#388C22semidirect
122. C4×C4⋊C4×C47C22semidirect
123. C4×C22⋊C4×C47C22semidirect
127. C2×#10625352C2×C4semidirect
138. C22×C4×D47C2×C4semidirect
145. #13094006C2×C4semidirect
146. #13094004C2×C4semidirect
147. #13094003C2×C4semidirect
148. #13093995C2×C4semidirect
149. #13093992C2×C4semidirect
154. D4×Dic47C2×C4semidirect
157. (C22⋊D47)⋊C4C2×C4semidirect
158. #13093982C2×C4semidirect
232. #121×C47C2×C4semidirect
375. (C2×D47)⋊C4#41semidirect
376. (C2×D47)⋊C4#41semidirect
587. C4×#121D47semidirect
620. C2×C4×D4C2×D47semidirect
634. #390C2×D47semidirect
640. #389C2×D47semidirect
648. #388C2×D47semidirect
681. C4×C4⋊C4C2×D47semidirect
696. C4×C22⋊C4C2×D47semidirect
702. C47#34233semidirect
734. #121C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156896332
#202464092
#202464002
#202463952
#202463922
#202463682
#202463652
#202463262
#202462932
#202462772
#202462722
#202462272
#202462132
#202461802
#202461762
#202460182
C4×#130940032
#202459162
#121×Dic472
#380×D472
#202457472
C2×C4×(C2×D47)⋊C42
C4×#121×C472
#3423347