Finite Group Databasebeta

← #26376685

Subgroups — #26376685

Order 12032.

3102 conjugacy classes of subgroups.

The subgroup lattice has 1122 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#124×D47C211yesmaximal, characteristic
2C2×#15689599C211yesmaximal, characteristic, complemented
3C2×#15689595C211yesmaximal, characteristic
4#20246464C211yesmaximal, characteristic, complemented
5#20246463C211yesmaximal, characteristic, complemented
6#20246461C211yesmaximal, characteristic, complemented
7#20246459C211yesmaximal, characteristic, complemented
8#20246458C211yesmaximal, characteristic, complemented
9#20246457C211yesmaximal, characteristic, complemented
10#20246455C211yesmaximal, characteristic, complemented
11#20246236C212yesmaximal, complemented
12#20246235C212yesmaximal, complemented
13#20246232C212yesmaximal, complemented
14#20246231C212yesmaximal, complemented
15#20246097C212yesmaximal, complemented
16#20246094C212yesmaximal, complemented
17#20245971C211yesmaximal, characteristic, complemented
18#20245967C211yesmaximal, characteristic
19#20245929C212yesmaximal, complemented
20C4×#13094010C212yesmaximal, complemented
21#20245792C211yesmaximal, characteristic, complemented
22C4×#13093982C211yesmaximal, characteristic, complemented
23C47×#2367C211yesmaximal, characteristic, complemented
24C22×Q8×D47C2211yescharacteristic
25C22×D4×D47C2211yescharacteristic
26C2×#13094013C2211yescharacteristic
27C2×#13094012C2211yescharacteristic
28C2×#13094011C2211yescharacteristic
29C2×#13094010C2212yes—
30C2×#13094010C2212yes—
31#124×D47C4116yescomplemented
32#15689599—28no—
33#15689595—28no—
34C2×Q8×Dic47C2211yescharacteristic, complemented
35C2×C4×Dic94C2212yescomplemented
36C2×C4×Dic94C2211yescharacteristic, complemented
37C2×#13093989C2212yescomplemented
38C2×#13093989C2211yescharacteristic, complemented
39C2×C4×D188C2211yescharacteristic
40C2×D4×Dic47C2211yescharacteristic
41C2×#13093986C2211yescharacteristic
42C2×C4×C22⋊D47C2212yes—
43C2×(C22⋊D47)⋊C4C2212yes—
44C2×#13093982C2212yes—
45C2×#13093982C2211yescharacteristic
46C2×#13093982C2211yescharacteristic
47C2×#13093981C2211yescharacteristic
48C2×#13093981C2211yescharacteristic
49C2×#13093981C2212yes—
50C22×(C2×D47)⋊C4C2212yes—
51C2×C22⋊C4×D47C2212yes—
52C2×C22⋊C4×D47C2212yes—
53C2×C22⋊C4×D47C2212yes—
54C2×C42×D47C2211yescharacteristic
55#15689030C2211yescharacteristic, complemented
56#15689029C2211yescharacteristic, complemented
57#15689028C2211yescharacteristic, complemented
58#15689027C2212yescomplemented
59#15689027C2212yescomplemented
60#15689026C2211yescharacteristic
61#15689025C2211yescharacteristic
62#15689024C2211yescharacteristic
63#15689023C2212yes—
64#15689023C2212yes—
65#15689017C2212yescomplemented
66#15689017C2212yescomplemented
67#15689016C2212yescomplemented
68#15689016C2212yescomplemented
69#15689015C2212yescomplemented
70#15689015C2212yescomplemented
71#15689014C2212yescomplemented
72#15689014C2212yescomplemented
73#15689013C2212yescomplemented
74#15689013C2212yescomplemented
75#15689012C2212yescomplemented
76#15689012C2212yescomplemented
77#15689011C2212yescomplemented
78#15689011C2212yescomplemented
79#15688998C2212yescomplemented
80#15688997C2212yescomplemented
81#15688997C2212yescomplemented
82#15688996C2212yescomplemented
83#15688995C2212yescomplemented
84#15688994C2212yescomplemented
85#15688994C2212yescomplemented
86#15688992C2211yescharacteristic, complemented
87#15688992C2211yescharacteristic, complemented
88#15688987C2211yescharacteristic, complemented
89#15688987C2211yescharacteristic, complemented
90#15688985C2212yes—
91#15688985C2212yes—
92#15688982C2211yescharacteristic
93#15688982C2211yescharacteristic
94#15688980C2211yescharacteristic
95#15688980C2211yescharacteristic
96#15688978C2212yes—
97#15688978C2212yes—
98C4⋊C4×Dic47C2211yescharacteristic, complemented
99C4⋊C4×Dic47C2211yescharacteristic, complemented
100C4×Dic47⋊C4C2211yescharacteristic, complemented
101C4×Dic47⋊C4C2211yescharacteristic, complemented
102C4×C4⋊Dic47C2211yescharacteristic, complemented
103C4×C4⋊Dic47C2211yescharacteristic, complemented
104C22⋊C4×Dic47C2212yescomplemented
105C22⋊C4×Dic47C2212yescomplemented
106C4×(C2×D47)⋊C4C2212yes—
107C4×(C2×D47)⋊C4C2212yescomplemented
108C4×(C2×D47)⋊C4C2212yescomplemented
109C4×C22⋊Dic47C2212yescomplemented
110#15688970C2212yes—
111#15688970C2212yescomplemented
112#15688970C2212yescomplemented
113#15688968C2212yescomplemented
114C42×Dic47C2212yescomplemented
115C2×#124×C47C2211yescharacteristic
116C2×C4×Q8×C47C2211yescharacteristic, complemented
117C2×C4×D4×C47C2211yescharacteristic
118C47×#391C2211yescharacteristic, complemented
119C47×#390C2211yescharacteristic
120C47×#388C2212yescomplemented
121C47×#388C2212yescomplemented
122C47×#385C2212yescomplemented
123C4×C4⋊C4×C47C2211yescharacteristic, complemented
124C4×C4⋊C4×C47C2211yescharacteristic, complemented
125C4×C22⋊C4×C47C2212yescomplemented
126C24×D47C2312yes—
127C22×Dic94C2312yes—
128C22×Dic94C2311yescharacteristic
129C2×Q8×D47—24no—
130C2×Q8×D47—24no—
131C2×Q8×D47C2×C418yescomplemented
132C22×D188C2311yescharacteristic
133C22×C22⋊D47C2312yes—
134C2×D4×D47—24no—
135C2×D4×D47—24no—
136C2×D4×D47C2×C418yes—
137C23×Dic47C2312yes—
138C22×C4×D47C2312yes—
139C22×C4×D47C2312yes—
140C22×C4×D47C2312yes—
141C22×C4×D47C2311yescharacteristic
142C22×C4×D47C2311yescharacteristic
143C22×C4×D47C2311yescharacteristic
144#13094013C2×C418yescomplemented
145#13094012C2×C418yescomplemented
146#13094011C2×C418yescomplemented
147#13094010C2×C4116yescomplemented
148#13094010C2×C4116yescomplemented
149Q8×Dic47—24no—
150C4×Dic94—24no—
151C4×Dic94—28no—
152#13093989—24no—
153#13093989—28no—
154C4×D188—24no—
155D4×Dic47—24no—
156#13093986—24no—
157C4×C22⋊D47—28no—
158(C22⋊D47)⋊C4—28no—
159#13093982—24no—
160#13093982—28no—
161#13093982D418yes—
162#13093981—24no—
163#13093981—24no—
164#13093981—28no—
165C2×C4⋊Dic47C2311yescharacteristic
166C2×C4⋊Dic47C2312yes—
167C2×C4⋊Dic47C2311yescharacteristic
168C2×C4⋊Dic47C2311yescharacteristic
169C2×C4⋊Dic47C2311yescharacteristic
170C2×Dic47⋊C4C2311yescharacteristic
171C2×Dic47⋊C4C2311yescharacteristic
172C2×Dic47⋊C4C2311yescharacteristic
173C2×Dic47⋊C4C2311yescharacteristic
174C2×Dic47⋊C4C2312yes—
175C2×Dic47⋊C4C2312yes—
176C2×Dic47⋊C4C2311yescharacteristic
177C2×Dic47⋊C4C2311yescharacteristic
178C2×Dic47⋊C4C2311yescharacteristic
179C2×Dic47⋊C4C2311yescharacteristic
180C2×C22⋊Dic47C2312yes—
181C2×C22⋊Dic47C2312yes—
182C2×C22⋊Dic47C2312yes—
183C2×C22⋊Dic47C2312yes—
184C2×C22⋊Dic47C2312yes—
185C2×(C2×D47)⋊C4—28no—
186C2×(C2×D47)⋊C4C2312yes—
187C2×(C2×D47)⋊C4C2311yescharacteristic
188C2×(C2×D47)⋊C4C2311yescharacteristic
189C2×(C2×D47)⋊C4C2311yescharacteristic
190C2×(C2×D47)⋊C4C2311yescharacteristic
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)⋊C4C2312yes—
201C2×(C2×D47)⋊C4C2312yes—
202C22⋊C4×D47—28no—
203C22⋊C4×D47C2×C4116yescomplemented
204C22⋊C4×D47C2×C4116yescomplemented
205C2×C4×Dic47C2312yes—
206C2×C4×Dic47C2312yes—
207C2×C4×Dic47C2312yes—
208C2×C4×Dic47C2312yes—
209C2×C4×Dic47C2311yescharacteristic
210C2×C4×Dic47C2311yescharacteristic
211C2×C4×Dic47C2312yes—
212C2×C4×Dic47C2312yes—
213C2×C4×Dic47C2312yes—
214C2×C4×Dic47C2311yescharacteristic
215C2×C4×Dic47C2311yescharacteristic
216C2×C4×Dic47C2311yescharacteristic
217C2×C4×Dic47C2312yes—
218C42×D47C2×C418yescomplemented
219C47⋊#95C2312yes—
220C47⋊#95C2312yes—
221C47⋊#95C2312yes—
222C47⋊#95C2311yescharacteristic
223C47⋊#95C2312yes—
224C47⋊#95C2311yescharacteristic
225C47⋊#95C2312yes—
226C47⋊#95C2311yescharacteristic
227C47⋊#95C2311yescharacteristic
228C47⋊#95C2312yes—
229C47⋊#95C2312yes—
230C47⋊#95C2311yescharacteristic
231C47⋊#95C2311yescharacteristic
232C47⋊#95C2312yes—
233C47⋊#95C2312yes—
234C22×Q8×C47C2311yescharacteristic
235C22×D4×C47C2311yescharacteristic
236C23×C4×C47C2312yes—
237#124×C47C2×C418yescomplemented
238C4×Q8×C47—24no—
239C4×D4×C47—24no—
240C2×C4⋊C4×C47C2311yescharacteristic
241C2×C4⋊C4×C47C2312yes—
242C2×C4⋊C4×C47C2311yescharacteristic
243C2×C4⋊C4×C47C2311yescharacteristic
244C2×C4⋊C4×C47C2311yescharacteristic
245C2×C22⋊C4×C47C2312yes—
246C2×C22⋊C4×C47C2312yes—
247C2×C22⋊C4×C47C2312yes—
248C2×C22⋊C4×C47C2312yes—
249C2×C22⋊C4×C47C2312yes—
250C2×C42×C47C2312yes—
251C2×C42×C47C2311yescharacteristic
252C2×C42×C47C2311yescharacteristic
253C2×C42×C47C2312yes—
254C2×C42×C47C2311yescharacteristic
255#95×C47C2312yes—
256#95×C47C2311yescharacteristic
257#95×C47C2312yes—
258#95×C47C2311yescharacteristic
259#95×C47C2312yes—
260C24×C47C2412yes—
261C23×D47—24no—
262C23×D47—24no—
263C23×D47—42no—
264C23×D47—42no—
265C23×D47—42no—
266C23×D47—42no—
267C23×D47C22×C418yes—
268C23×D47C2412yes—
269C23×D47C2411yescharacteristic
270C2×Q8×C47—22no—
271C2×Q8×C47—22no—
272C2×Q8×C47C22×C414yes—
273C2×D4×C47—22no—
274C2×D4×C47—22no—
275C2×D4×C47C22×C414yes—
276C22×C4×C47—24no—
277C22×C4×C47—42no—
278C22×C4×C47—42no—
279C22×C4×C47C2411yescharacteristic
280C22×C4×C47C2411yescharacteristic
281C22×C4×C47C2412yes—
282C22×C4×C47C2411yescharacteristic
283C22×C4×C47C2411yescharacteristic
284C22×C4×C47C2411yescharacteristic
285C22×C4×C47C2411yescharacteristic
286C22×C4×C47C2412yes—
287C22×C4×C47C2412yes—
288C22×C4×C47C2411yescharacteristic
289C2×C22⋊D47—24no—
290C2×C22⋊D47—24no—
291C2×C22⋊D47C22×C418yes—
292C22×Dic47—24no—
293C22×Dic47—42no—
294C22×Dic47—42no—
295C22×Dic47C2412yes—
296C22×Dic47C2411yescharacteristic
297C22×Dic47C2411yescharacteristic
298C22×Dic47C2411yescharacteristic
299C22×Dic47C2411yescharacteristic
300C22×Dic47C2411yescharacteristic
301C22×Dic47C2411yescharacteristic
302C22×Dic47C2412yes—
303C22×Dic47C2412yes—
304C22×Dic47C2411yescharacteristic
305Q8×D47—232no—
306D4×D47—232no—
307C2×D188—22no—
308C2×D188—22no—
309C2×D188C22×C414yes—
310C2×C4×D47—24no—
311C2×C4×D47—24no—
312C2×C4×D47—24no—
313C2×C4×D47—24no—
314C2×C4×D47—41no—
315C2×C4×D47—41no—
316C2×C4×D47—41no—
317C2×C4×D47—41no—
318C2×C4×D47—42no—
319C2×C4×D47—42no—
320C2×C4×D47—42no—
321C2×C4×D47—42no—
322C2×C4×D47C22×C418yes—
323C2×C4×D47C22×C414yes—
324C2×C4×D47C22×C414yes—
325C2×C4×D47C22×C414yes—
326C2×C4×D47C2×D414yes—
327C2×C4×D47#4114yes—
328C2×Dic94—22no—
329C2×Dic94—22no—
330C2×Dic94—24no—
331C2×Dic94—24no—
332C2×Dic94C22×C418yes—
333C2×Dic94C22×C414yes—
334C4⋊C4×C47—24no—
335C4⋊C4×C47—22no—
336C4⋊C4×C47—41no—
337C4⋊C4×C47—41no—
338C4⋊C4×C47C2×D414yes—
339C22⋊C4×C47—24no—
340C22⋊C4×C47—42no—
341C22⋊C4×C47—42no—
342C22⋊C4×C47C22×C418yes—
343C22⋊C4×C47C22×C418yes—
344C42×C47—22no—
345C42×C47—24no—
346C42×C47—22no—
347C42×C47—42no—
348C42×C47C22×C414yes—
349C22⋊Dic47—24no—
350C22⋊Dic47—42no—
351C22⋊Dic47—42no—
352C22⋊Dic47C22×C418yes—
353C22⋊Dic47C22×C418yes—
354(C2×D47)⋊C4—22no—
355(C2×D47)⋊C4—22no—
356(C2×D47)⋊C4—22no—
357(C2×D47)⋊C4—22no—
358(C2×D47)⋊C4—24no—
359(C2×D47)⋊C4—24no—
360(C2×D47)⋊C4—24no—
361(C2×D47)⋊C4—42no—
362(C2×D47)⋊C4—42no—
363(C2×D47)⋊C4—42no—
364(C2×D47)⋊C4—42no—
365(C2×D47)⋊C4C22×C418yes—
366(C2×D47)⋊C4C22×C418yes—
367(C2×D47)⋊C4C22×C418yes—
368(C2×D47)⋊C4C22×C418yes—
369(C2×D47)⋊C4C2×D418yes—
370C4⋊Dic47—22no—
371C4⋊Dic47—24no—
372C4⋊Dic47—41no—
373C4⋊Dic47—41no—
374C4⋊Dic47C2×D414yes—
375Dic47⋊C4—24no—
376Dic47⋊C4—22no—
377Dic47⋊C4—22no—
378Dic47⋊C4—22no—
379Dic47⋊C4—24no—
380Dic47⋊C4—22no—
381Dic47⋊C4—41no—
382Dic47⋊C4—41no—
383Dic47⋊C4—41no—
384Dic47⋊C4—41no—
385C4×Dic47—22no—
386C4×Dic47—22no—
387C4×Dic47—24no—
388C4×Dic47—24no—
389C4×Dic47—24no—
390C4×Dic47—24no—
391C4×Dic47—42no—
392C4×Dic47—42no—
393C4×Dic47—42no—
394C4×Dic47C22×C414yes—
395C4×Dic47C22×C414yes—
396C4×Dic47C22×C414yes—
397C4×Dic47C2×D418yes—
398C23×C47—22no—
399C23×C47—22no—
400C23×C47—22no—
401C23×C47—22no—
402C23×C47—22no—
403C23×C47—22no—
404C23×C47C23×C414yes—
405C23×C47C2511yescharacteristic
406C22×D47—21no—
407C22×D47—21no—
408C22×D47—21no—
409C22×D47—21no—
410C22×D47—22no—
411C22×D47—22no—
412C22×D47—22no—
413C22×D47—22no—
414C22×D47—22no—
415C22×D47—22no—
416C22×D47—216no—
417C22×D47—48no—
418C22×D47—48no—
419C22×D47—84no—
420C22×D47—84no—
421C22×D47—84no—
422C22×D47—84no—
423C22×D47C23×C414yes—
424C22×D47C23×C412yes—
425C22×D47C22×D412yes—
426C22×D47C2×#4112yes—
427Q8×C47—28no—
428D4×C47—28no—
429C2×C4×C47—22no—
430C2×C4×C47—22no—
431C2×C4×C47—21no—
432C2×C4×C47—22no—
433C2×C4×C47—21no—
434C2×C4×C47—21no—
435C2×C4×C47—21no—
436C2×C4×C47—22no—
437C2×C4×C47—21no—
438C2×C4×C47—21no—
439C2×C4×C47—21no—
440C2×C4×C47—21no—
441C2×C4×C47—22no—
442C2×C4×C47—22no—
443C2×C4×C47—21no—
444C2×C4×C47—21no—
445C2×C4×C47—21no—
446C2×C4×C47—21no—
447C2×C4×C47—21no—
448C2×C4×C47—22no—
449C2×C4×C47—21no—
450C2×C4×C47—21no—
451C2×C4×C47—21no—
452C2×C4×C47—84no—
453C2×C4×C47C23×C412yes—
454C2×C4×C47C23×C412yes—
455C2×C4×C47C23×C414yes—
456C2×C4×C47C23×C412yes—
457C2×C4×C47C22×D414yes—
458C2×C4×C47C22×D412yes—
459C2×C4×C47C2×#4112yes—
460C22⋊D47—216no—
461C2×Dic47—22no—
462C2×Dic47—22no—
463C2×Dic47—21no—
464C2×Dic47—21no—
465C2×Dic47—22no—
466C2×Dic47—22no—
467C2×Dic47—21no—
468C2×Dic47—21no—
469C2×Dic47—21no—
470C2×Dic47—21no—
471C2×Dic47—21no—
472C2×Dic47—21no—
473C2×Dic47—22no—
474C2×Dic47—22no—
475C2×Dic47—22no—
476C2×Dic47—21no—
477C2×Dic47—21no—
478C2×Dic47—21no—
479C2×Dic47—21no—
480C2×Dic47—21no—
481C2×Dic47—21no—
482C2×Dic47—21no—
483C2×Dic47—21no—
484C2×Dic47—84no—
485C2×Dic47C23×C412yes—
486C2×Dic47C23×C412yes—
487C2×Dic47C23×C414yes—
488C2×Dic47C23×C412yes—
489C2×Dic47C22×D414yes—
490C2×Dic47C22×D412yes—
491C2×Dic47C2×#4112yes—
492D188—28no—
493C4×D47—216no—
494C4×D47—44no—
495C4×D47—44no—
496C4×D47—84no—
497C4×D47—84no—
498C4×D47C4×D4116yes—
499Dic94—28no—
500Dic94—216no—
501#34211—471nomaximal, Sylow
502C22×C47—24no—
503C22×C47—24no—
504C22×C47—24no—
505C22×C47—42no—
506C22×C47—42no—
507C22×C47—42no—
508C22×C47—42no—
509C22×C47C24×C411yescharacteristic
510C22×C47C23×D411yescharacteristic
511C22×C47C22×#4111yescharacteristic
512C22×C47#58511yescharacteristic
513C22×C47#58511yescharacteristic
514C22×C47#58511yescharacteristic
515C22×C47#58511yescharacteristic
516C2×D47—22no—
517C2×D47—22no—
518C2×D47—22no—
519C2×D47—22no—
520C2×D47—22no—
521C2×D47—22no—
522C2×D47—24no—
523C2×D47—24no—
524C2×D47—24no—
525C2×D47—42no—
526C2×D47—42no—
527C2×D47—42no—
528C2×D47—42no—
529C2×D47—816no—
530C2×D47C2×C4×D414yes—
531C4×C47—24no—
532C4×C47—22no—
533C4×C47—22no—
534C4×C47—24no—
535C4×C47—41no—
536C4×C47—41no—
537C4×C47—41no—
538C4×C47—41no—
539C4×C47—42no—
540C4×C47C2×C4×D414yes—
541Dic47—24no—
542Dic47—22no—
543Dic47—22no—
544Dic47—24no—
545Dic47—41no—
546Dic47—41no—
547Dic47—41no—
548Dic47—41no—
549Dic47—42no—
550Dic47C2×C4×D414yes—
551C22×#124—471no—
552C2×#519—471no—
553C2×#518—471no—
554#2367—471no—
555#2367—471no—
556#2367—471no—
557#2367—471no—
558#2367—471no—
559#2367—471no—
560#2367—471no—
561#2367D4711yescharacteristic, complemented
562#2342—472no—
563#2342—472no—
564#2342—472no—
565#2342—472no—
566#2326—472no—
567#2326—472no—
568#2310—471no—
569#2309—471no—
570C4×#124—472no—
571C4×#124—472no—
572#2285—471no—
573C4×#117—471no—
574C2×C47—44no—
575C2×C47C22×C4×D411yescharacteristic
576C2×C47#342811yescharacteristic
577C2×C47#342811yescharacteristic
578C2×C47#350011yescharacteristic
579C2×C47#350011yescharacteristic
580C2×C47#351011yescharacteristic
581C2×C47#351011yescharacteristic
582D47—24no—
583D47—44no—
584C23×Q8—471no—
585C23×D4—471no—
586C2×#124—471no—
587C2×#124—471no—
588C2×#124—4716no—
589C2×#124—472no—
590C2×#124—472no—
591C2×#124—471no—
592C2×#124C2×D4711yescharacteristic
593#519—948no—
594#518—948no—
595C2×C4×Q8—471no—
596C2×C4×Q8—472no—
597C2×C4×Q8—471no—
598C2×C4×Q8—472no—
599C2×C4×Q8—471no—
600C2×C4×Q8C2×D4711yescharacteristic, complemented
601C2×C4×D4—471no—
602C2×C4×D4—472no—
603C2×C4×D4—471no—
604C2×C4×D4—472no—
605C2×C4×D4—471no—
606C2×C4×D4C2×D4711yescharacteristic
607C2×#117—471no—
608C2×#117—471no—
609C2×#117—472no—
610C2×#117—471no—
611C2×#117—471no—
612C2×#117—472no—
613C22×C22⋊C4—472no—
614C22×C22⋊C4—472no—
615C22×C22⋊C4—472no—
616C22×C22⋊C4—472no—
617C22×C42—471no—
618#391—471no—
619#391—471no—
620#391—471no—
621#391—472no—
622#391—472no—
623#391C2×D4711yescharacteristic, complemented
624#390—471no—
625#390—471no—
626#390—472no—
627#390—472no—
628#390—471no—
629#390C2×D4711yescharacteristic
630#388—472no—
631#388—472no—
632#388—472no—
633#388—472no—
634#388—472no—
635#388—472no—
636#388—472no—
637#388—472no—
638#388—472no—
639#388—472no—
640#388—472no—
641#388—472no—
642#388—472no—
643#388—472no—
644#388C2×D4712yescomplemented
645#388C2×D4712yescomplemented
646#385—472no—
647#385—472no—
648#385—472no—
649#385—472no—
650#385—472no—
651#385—472no—
652#385—472no—
653#385C2×D4712yescomplemented
654#384—471no—
655#384—471no—
656#382—471no—
657#382—471no—
658#381—472no—
659#381—472no—
660#380—471no—
661#380—471no—
662#380—471no—
663#380—471no—
664#379—472no—
665#379—472no—
666C4×C4⋊C4—471no—
667C4×C4⋊C4—471no—
668C4×C4⋊C4—471no—
669C4×C4⋊C4—471no—
670C4×C4⋊C4—471no—
671C4×C4⋊C4—471no—
672C4×C4⋊C4C2×D4711yescharacteristic, complemented
673C4×C4⋊C4C2×D4711yescharacteristic, complemented
674C4×C22⋊C4—472no—
675C4×C22⋊C4—472no—
676C4×C22⋊C4—472no—
677C4×C22⋊C4—472no—
678C4×C22⋊C4—472no—
679C4×C22⋊C4—472no—
680C4×C22⋊C4—472no—
681C4×C22⋊C4—472no—
682C4×C22⋊C4—472no—
683C4×C22⋊C4C2×D4712yescomplemented
684#376—472no—
685C43—472no—
686C47#3421111yescharacteristic, complemented, Sylow
687C25—472no—
688C22×Q8—478no—
689C22×Q8—472no—
690C22×Q8—471no—
691C22×Q8—944no—
692C22×Q8—944no—
693C22×Q8C22×D4711yescharacteristic
694C22×D4—472no—
695C22×D4—478no—
696C22×D4—471no—
697C22×D4—944no—
698C22×D4—944no—
699C22×D4C22×D4711yescharacteristic
700C23×C4—471no—
701C23×C4—472no—
702C23×C4—471no—
703C23×C4—471no—
704C23×C4—472no—
705C23×C4—472no—
706C23×C4—472no—
707C23×C4C22×D4712yes—
708#124—478no—
709#124—478no—
710#124—4716no—
711#124—4716no—
712#124—478no—
713#124C4×D4718yescomplemented
714C4×Q8—24no—
715C4×Q8—948no—
716C4×Q8—944no—
717C4×Q8—948no—
718C4×Q8—944no—
719C4×Q8—944no—
720C4×D4—24no—
721C4×D4—944no—
722C4×D4—948no—
723C4×D4—948no—
724C4×D4—944no—
725C4×D4—944no—
726#117—478no—
727#117—948no—
728#117—944no—
729#117—944no—
730#117—948no—
731#117—944no—
732C2×C4⋊C4—471no—
733C2×C4⋊C4—471no—
734C2×C4⋊C4—471no—
735C2×C4⋊C4—471no—
736C2×C4⋊C4—471no—
737C2×C4⋊C4—472no—
738C2×C4⋊C4—472no—
739C2×C4⋊C4—472no—
740C2×C4⋊C4—471no—
741C2×C4⋊C4—471no—
742C2×C4⋊C4—471no—
743C2×C4⋊C4—471no—
744C2×C4⋊C4—471no—
745C2×C4⋊C4—471no—
746C2×C4⋊C4—471no—
747C2×C4⋊C4C22×D4712yes—
748C2×C4⋊C4C22×D4711yescharacteristic
749C2×C4⋊C4C22×D4711yescharacteristic
750C2×C4⋊C4C22×D4711yescharacteristic
751C2×C4⋊C4C22×D4711yescharacteristic
752C2×C22⋊C4—472no—
753C2×C22⋊C4—472no—
754C2×C22⋊C4—472no—
755C2×C22⋊C4—472no—
756C2×C22⋊C4—472no—
757C2×C22⋊C4—472no—
758C2×C22⋊C4—472no—
759C2×C22⋊C4—4716no—
760C2×C22⋊C4—4716no—
761C2×C22⋊C4—472no—
762C2×C22⋊C4—471no—
763C2×C22⋊C4—471no—
764C2×C22⋊C4—472no—
765C2×C22⋊C4—472no—
766C2×C22⋊C4—471no—
767C2×C22⋊C4—471no—
768C2×C22⋊C4—472no—
769C2×C22⋊C4—472no—
770C2×C22⋊C4—472no—
771C2×C22⋊C4—472no—
772C2×C22⋊C4—472no—
773C2×C22⋊C4—472no—
774C2×C22⋊C4—472no—
775C2×C22⋊C4—948no—
776C2×C22⋊C4—948no—
777C2×C22⋊C4C22×D4712yes—
778C2×C22⋊C4C22×D4712yes—
779C2×C22⋊C4C22×D4712yes—
780C2×C22⋊C4C22×D4712yes—
781C2×C22⋊C4C22×D4712yes—
782C2×C42—472no—
783C2×C42—471no—
784C2×C42—471no—
785C2×C42—471no—
786C2×C42—478no—
787C2×C42—471no—
788C2×C42—472no—
789C2×C42—472no—
790C2×C42—472no—
791C2×C42—471no—
792C2×C42—472no—
793C2×C42—472no—
794C2×C42—472no—
795C2×C42—472no—
796C2×C42C22×D4711yescharacteristic
797C2×C42C22×D4712yes—
798C2×C42C22×D4711yescharacteristic
799C2×C42C22×D4712yes—
800C2×C42C22×D4711yescharacteristic
801#95—472no—
802#95—472no—
803#95—472no—
804#95—471no—
805#95—471no—
806#95—471no—
807#95—471no—
808#95—471no—
809#95—471no—
810#95—472no—
811#95—472no—
812#95—472no—
813#95—472no—
814#95—472no—
815#95—472no—
816#95C22×D4712yes—
817#95C22×D4711yescharacteristic
818#95C22×D4712yes—
819#95C22×D4711yescharacteristic
820#95C22×D4712yes—
821C24—471no—
822C24—472no—
823C24—478no—
824C24—944no—
825C24—944no—
826C24—1882no—
827C24—1882no—
828C24—1882no—
829C24—1882no—
830C24C23×D4712yes—
831C2×Q8—22no—
832C2×Q8—22no—
833C2×Q8—478no—
834C2×Q8—474no—
835C2×Q8—944no—
836C2×Q8—944no—
837C2×Q8—9432no—
838C2×Q8—942no—
839C2×Q8—942no—
840C2×Q8C2×C4×D4714yes—
841C2×D4—22no—
842C2×D4—22no—
843C2×D4—478no—
844C2×D4—474no—
845C2×D4—9432no—
846C2×D4—944no—
847C2×D4—944no—
848C2×D4—942no—
849C2×D4—942no—
850C2×D4C2×C4×D4714yes—
851C22×C4—24no—
852C22×C4—42no—
853C22×C4—42no—
854C22×C4—471no—
855C22×C4—474no—
856C22×C4—474no—
857C22×C4—474no—
858C22×C4—471no—
859C22×C4—471no—
860C22×C4—472no—
861C22×C4—472no—
862C22×C4—478no—
863C22×C4—474no—
864C22×C4—474no—
865C22×C4—472no—
866C22×C4—471no—
867C22×C4—471no—
868C22×C4—471no—
869C22×C4—471no—
870C22×C4—944no—
871C22×C4—944no—
872C22×C4—944no—
873C22×C4—944no—
874C22×C4—944no—
875C22×C4—1882no—
876C22×C4—1882no—
877C22×C4—1882no—
878C22×C4—1882no—
879C22×C4—1881no—
880C22×C4—1881no—
881C22×C4—1881no—
882C22×C4—1881no—
883C22×C4—1882no—
884C22×C4—1882no—
885C22×C4C23×D4712yes—
886C22×C4C23×D4711yescharacteristic
887C22×C4C23×D4711yescharacteristic
888C22×C4C23×D4711yescharacteristic
889C22×C4C23×D4711yescharacteristic
890C22×C4C23×D4711yescharacteristic
891C22×C4C23×D4711yescharacteristic
892C22×C4C23×D4712yes—
893C22×C4C23×D4712yes—
894C22×C4C23×D4711yescharacteristic
895C4⋊C4—24no—
896C4⋊C4—22no—
897C4⋊C4—41no—
898C4⋊C4—41no—
899C4⋊C4—474no—
900C4⋊C4—942no—
901C4⋊C4—942no—
902C4⋊C4—942no—
903C4⋊C4—944no—
904C4⋊C4—942no—
905C4⋊C4—944no—
906C4⋊C4—944no—
907C4⋊C4—942no—
908C4⋊C4—1881no—
909C4⋊C4—1881no—
910C4⋊C4—1881no—
911C4⋊C4—1881no—
912C4⋊C4—1881no—
913C4⋊C4—1881no—
914C4⋊C4D4×D4714yes—
915C22⋊C4—24no—
916C22⋊C4—42no—
917C22⋊C4—42no—
918C22⋊C4—478no—
919C22⋊C4—478no—
920C22⋊C4—478no—
921C22⋊C4—478no—
922C22⋊C4—478no—
923C22⋊C4—478no—
924C22⋊C4—478no—
925C22⋊C4—944no—
926C22⋊C4—942no—
927C22⋊C4—942no—
928C22⋊C4—944no—
929C22⋊C4—942no—
930C22⋊C4—942no—
931C22⋊C4—944no—
932C22⋊C4—944no—
933C22⋊C4—1882no—
934C22⋊C4—1882no—
935C22⋊C4—1882no—
936C22⋊C4—1882no—
937C22⋊C4—1882no—
938C22⋊C4—1882no—
939C22⋊C4C2×C4×D4718yes—
940C22⋊C4C2×C4×D4718yes—
941C42—22no—
942C42—24no—
943C42—22no—
944C42—42no—
945C42—474no—
946C42—474no—
947C42—474no—
948C42—478no—
949C42—944no—
950C42—944no—
951C42—944no—
952C42—942no—
953C42—944no—
954C42—942no—
955C42—1882no—
956C42—1882no—
957C42—1882no—
958C42C2×C4×D4714yes—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—472no—
966C23—472no—
967C23—472no—
968C23—474no—
969C23—9416no—
970C23—941no—
971C23—941no—
972C23—941no—
973C23—941no—
974C23—942no—
975C23—942no—
976C23—942no—
977C23—942no—
978C23—942no—
979C23—942no—
980C23—3764no—
981C23—3764no—
982C23—3764no—
983C23—3764no—
984C23—1888no—
985C23—1888no—
986C23C22×C4×D4714yes—
987C23C24×D4711yescharacteristic
988Q8—28no—
989Q8—9416no—
990Q8—948no—
991D4—28no—
992D4—9416no—
993D4—948no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—21no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—22no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—84no—
1018C2×C4—472no—
1019C2×C4—472no—
1020C2×C4—472no—
1021C2×C4—4716no—
1022C2×C4—472no—
1023C2×C4—472no—
1024C2×C4—474no—
1025C2×C4—474no—
1026C2×C4—9416no—
1027C2×C4—942no—
1028C2×C4—942no—
1029C2×C4—941no—
1030C2×C4—941no—
1031C2×C4—941no—
1032C2×C4—942no—
1033C2×C4—942no—
1034C2×C4—941no—
1035C2×C4—941no—
1036C2×C4—941no—
1037C2×C4—941no—
1038C2×C4—941no—
1039C2×C4—942no—
1040C2×C4—941no—
1041C2×C4—941no—
1042C2×C4—942no—
1043C2×C4—941no—
1044C2×C4—941no—
1045C2×C4—941no—
1046C2×C4—941no—
1047C2×C4—942no—
1048C2×C4—941no—
1049C2×C4—941no—
1050C2×C4—3764no—
1051C2×C4—3764no—
1052C2×C4—3764no—
1053C2×C4—1884no—
1054C2×C4—1884no—
1055C2×C4C22×C4×D4712yes—
1056C2×C4C22×C4×D4712yes—
1057C2×C4C22×C4×D4714yes—
1058C2×C4C22×C4×D4712yes—
1059C2×C4C2×D4×D4714yes—
1060C2×C4C2×D4×D4712yes—
1061C2×C4#41×D4712yes—
1062C22—24no—
1063C22—24no—
1064C22—24no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—474no—
1070C22—942no—
1071C22—942no—
1072C22—942no—
1073C22—942no—
1074C22—942no—
1075C22—942no—
1076C22—944no—
1077C22—944no—
1078C22—944no—
1079C22—37616no—
1080C22—1882no—
1081C22—1882no—
1082C22—1882no—
1083C22—1882no—
1084C22C23×C4×D4711yescharacteristic
1085C22C22×D4×D4711yescharacteristic
1086C22C2×#41×D4711yescharacteristic
1087C22#1568995811yescharacteristic
1088C22#1568995911yescharacteristic
1089C22#1568995911yescharacteristic
1090C22#1568996011yescharacteristic
1091C4—24no—
1092C4—22no—
1093C4—22no—
1094C4—24no—
1095C4—42no—
1096C4—41no—
1097C4—41no—
1098C4—41no—
1099C4—41no—
1100C4—474no—
1101C4—944no—
1102C4—942no—
1103C4—942no—
1104C4—944no—
1105C4—1881no—
1106C4—1881no—
1107C4—1881no—
1108C4—1881no—
1109C4—1882no—
1110C4C4×D4×D4714yes—
1111C2—44no—
1112C2—944no—
1113C2—1884no—
1114C2C2×C4×D4×D4711yescharacteristic
1115C2#2025658711yescharacteristic
1116C2#2025658811yescharacteristic
1117C2#2025717411yescharacteristic
1118C2#2025717911yescharacteristic
1119C2#2025727811yescharacteristic
1120C2#2025728111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D47
commutatorC22×C47C24×C4
FittingC47×#2367C2
socle, cosocleC23×C47C25
prime radicalC22×D4×D47C22
hypercenter#2367D47
hypocenterC47#34211
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2367

Complements

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

NH ≅ G/Ntype
2. C2×#15689599C2semidirect
4. #20246464C2semidirect
5. #20246463C2semidirect
6. #20246461C2semidirect
7. #20246459C2semidirect
8. #20246458C2semidirect
9. #20246457C2semidirect
10. #20246455C2semidirect
11. #20246236C2semidirect
12. #20246235C2semidirect
13. #20246232C2semidirect
14. #20246231C2semidirect
15. #20246097C2semidirect
16. #20246094C2semidirect
17. #20245971C2semidirect
19. #20245929C2semidirect
20. C4×#13094010C2semidirect
21. #20245792C2semidirect
22. C4×#13093982C2semidirect
23. C47×#2367C2semidirect
31. #124×D47C4semidirect
34. C2×Q8×Dic47C22semidirect
35. C2×C4×Dic94C22semidirect
36. C2×C4×Dic94C22semidirect
37. C2×#13093989C22semidirect
38. C2×#13093989C22semidirect
55. #15689030C22semidirect
56. #15689029C22semidirect
57. #15689028C22semidirect
58. #15689027C22semidirect
59. #15689027C22semidirect
65. #15689017C22semidirect
66. #15689017C22semidirect
67. #15689016C22semidirect
68. #15689016C22semidirect
69. #15689015C22semidirect
70. #15689015C22semidirect
71. #15689014C22semidirect
72. #15689014C22semidirect
73. #15689013C22semidirect
74. #15689013C22semidirect
75. #15689012C22semidirect
76. #15689012C22semidirect
77. #15689011C22semidirect
78. #15689011C22semidirect
79. #15688998C22semidirect
80. #15688997C22semidirect
81. #15688997C22semidirect
82. #15688996C22semidirect
83. #15688995C22semidirect
84. #15688994C22semidirect
85. #15688994C22semidirect
86. #15688992C22semidirect
87. #15688992C22semidirect
88. #15688987C22semidirect
89. #15688987C22semidirect
98. C4⋊C4×Dic47C22semidirect
99. C4⋊C4×Dic47C22semidirect
100. C4×Dic47⋊C4C22semidirect
101. C4×Dic47⋊C4C22semidirect
102. C4×C4⋊Dic47C22semidirect
103. C4×C4⋊Dic47C22semidirect
104. C22⋊C4×Dic47C22semidirect
105. C22⋊C4×Dic47C22semidirect
107. C4×(C2×D47)⋊C4C22semidirect
108. C4×(C2×D47)⋊C4C22semidirect
109. C4×C22⋊Dic47C22semidirect
111. #15688970C22semidirect
112. #15688970C22semidirect
113. #15688968C22semidirect
114. C42×Dic47C22semidirect
116. C2×C4×Q8×C47C22semidirect
118. C47×#391C22semidirect
120. C47×#388C22semidirect
121. C47×#388C22semidirect
122. C47×#385C22semidirect
123. C4×C4⋊C4×C47C22semidirect
124. C4×C4⋊C4×C47C22semidirect
125. C4×C22⋊C4×C47C22semidirect
131. C2×Q8×D47C2×C4semidirect
144. #13094013C2×C4semidirect
145. #13094012C2×C4semidirect
146. #13094011C2×C4semidirect
147. #13094010C2×C4semidirect
148. #13094010C2×C4semidirect
203. C22⋊C4×D47C2×C4semidirect
204. C22⋊C4×D47C2×C4semidirect
218. C42×D47C2×C4semidirect
237. #124×C47C2×C4semidirect
561. #2367D47semidirect
600. C2×C4×Q8C2×D47semidirect
623. #391C2×D47semidirect
644. #388C2×D47semidirect
645. #388C2×D47semidirect
653. #385C2×D47semidirect
672. C4×C4⋊C4C2×D47semidirect
673. C4×C4⋊C4C2×D47semidirect
683. C4×C22⋊C4C2×D47semidirect
686. C47#34211semidirect
713. #124C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#124×D472
C2×#156895992
C2×#156895952
#202464642
#202464632
#202464612
#202464592
#202464582
#202464572
#202464552
#202462362
#202462352
#202462322
#202462312
#202460972
#202460942
#202459712
#202459672
#202459292
C4×#130940102
#202457922
C4×#130939822
C47×#23672
#3421147