Finite Group Databasebeta

← #26375719

Subgroups — #26375719

Order 12032.

3142 conjugacy classes of subgroups.

The subgroup lattice has 1112 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C22⋊D47)⋊C4C211yesmaximal, characteristic
2#20246358C212yesmaximal, complemented
3#20246323C212yesmaximal, complemented
4#20246322C212yesmaximal, complemented
5#20246294C212yesmaximal, complemented
6#20246266C211yesmaximal, characteristic, complemented
7#20246260C211yesmaximal, characteristic, complemented
8#20246238C211yesmaximal, characteristic, complemented
9#20246237C211yesmaximal, characteristic, complemented
10#20246230C211yesmaximal, characteristic, complemented
11C22⋊C4×C22⋊D47C211yesmaximal, characteristic
12#20246204C211yesmaximal, characteristic
13#20245848C212yesmaximal, complemented
14#20245830C212yesmaximal, complemented
15#20245824C212yesmaximal, complemented
16#20245779C211yesmaximal, characteristic, complemented
17#20245770C211yesmaximal, characteristic, complemented
18#20245766C211yesmaximal, characteristic, complemented
19C4×(C22⋊D47)⋊C4C212yesmaximal, complemented
20#117×Dic47C211yesmaximal, characteristic, complemented
21C2×C22⋊C4×Dic47C211yesmaximal, characteristic, complemented
22C4×C22⋊C4×D47C211yesmaximal, characteristic, complemented
23C47×#2342C211yesmaximal, characteristic, complemented
24C23×C22⋊D47C2211yescharacteristic
25C24×Dic47C2211yescharacteristic
26C23×C4×D47C2211yescharacteristic
27C2×C4×C22⋊D47C2212yes—
28C2×(C22⋊D47)⋊C4C4116yescomplemented
29C2×(C22⋊D47)⋊C4C2212yes—
30C2×(C22⋊D47)⋊C4C2211yescharacteristic
31C2×(C22⋊D47)⋊C4C2211yescharacteristic
32C2×(C22⋊D47)⋊C4C2211yescharacteristic
33C2×(C22⋊D47)⋊C4C2211yescharacteristic
34C2×(C22⋊D47)⋊C4C2211yescharacteristic
35C2×(C22⋊D47)⋊C4C2211yescharacteristic
36C2×(C22⋊D47)⋊C4C2211yescharacteristic
37C2×(C22⋊D47)⋊C4C2211yescharacteristic
38C2×#13093983C2211yescharacteristic
39C2×#13093982C2212yescomplemented
40C2×#13093980C2212yescomplemented
41C22×Dic47⋊C4C2211yescharacteristic
42C22×C22⋊Dic47C2211yescharacteristic
43C22×(C2×D47)⋊C4C2211yescharacteristic
44C2×C22⋊C4×D47C2211yescharacteristic
45C2×C22⋊C4×D47C2211yescharacteristic
46C22×C4×Dic47C2211yescharacteristic
47C22×C4×Dic47C2212yescomplemented
48C2×C42×D47C2212yescomplemented
49#15689023C2212yes—
50#15689023C2212yes—
51#15689020C2212yescomplemented
52#15689018C2212yescomplemented
53#15689016C2212yescomplemented
54#15689016C2212yescomplemented
55#15689015C2212yescomplemented
56#15689014C2212yescomplemented
57#15689013C2212yescomplemented
58#15689012C2212yescomplemented
59#15689010C2212yescomplemented
60#15689007C2212yescomplemented
61#15689005C2212yescomplemented
62#15689004C2212yescomplemented
63#15689002C2212yes—
64#15689000C2212yes—
65#15688999C2212yes—
66#15688999C2212yes—
67#15688998C2212yescomplemented
68#15688997C2212yescomplemented
69#15688994C2212yescomplemented
70#15688990C2212yescomplemented
71#15688987C2212yescomplemented
72#15688986C2211yescharacteristic
73#15688985C2212yescomplemented
74#15688984C2212yescomplemented
75#15688983C2211yescharacteristic
76#15688981C2211yescharacteristic
77#15688981C2211yescharacteristic
78#15688981C2211yescharacteristic
79#15688981C2211yescharacteristic
80#15688981C2212yescomplemented
81#15688980C2212yescomplemented
82#15688979C2211yescharacteristic
83#15688978C2211yescharacteristic
84#15688978C2211yescharacteristic
85C4⋊C4×Dic47C2212yescomplemented
86C4⋊C4×Dic47C2212yescomplemented
87C4×Dic47⋊C4C2212yescomplemented
88#15688974C2212yescomplemented
89#15688974C2212yescomplemented
90C22⋊C4×Dic47C2211yescharacteristic
91C22⋊C4×Dic47C2211yescharacteristic
92C22⋊C4×Dic47C2211yescharacteristic
93C22⋊C4×Dic47C2211yescharacteristic
94C22⋊C4×Dic47C2211yescharacteristic
95C22⋊C4×Dic47C2211yescharacteristic
96C22⋊C4×Dic47C2211yescharacteristic
97C22⋊C4×Dic47C2211yescharacteristic
98C22⋊C4×Dic47C2212yescomplemented
99C22⋊C4×Dic47C2212yescomplemented
100C22⋊C4×Dic47C2212yescomplemented
101C22⋊C4×Dic47C2212yescomplemented
102C4×(C2×D47)⋊C4C2212yescomplemented
103C4×(C2×D47)⋊C4C2212yescomplemented
104C4×C22⋊Dic47C2211yescharacteristic
105#15688970C2212yescomplemented
106#15688970C2212yescomplemented
107#15688970C2212yescomplemented
108#15688969C2212yescomplemented
109#15688968C2212yescomplemented
110C2×C47⋊#95C2212yescomplemented
111#95×D47C2212yescomplemented
112C42×Dic47C2212yescomplemented
113C2×#117×C47C2211yescharacteristic
114C22×C22⋊C4×C47C2211yescharacteristic
115C22×C22⋊C4×C47C2211yescharacteristic
116C47×#388C2212yescomplemented
117C47×#388C2212yescomplemented
118C47×#385C2212yescomplemented
119C47×#381C2211yescharacteristic
120C47×#380C2211yescharacteristic
121C47×#379C2211yescharacteristic
122C4×C22⋊C4×C47C2211yescharacteristic
123C4×C22⋊C4×C47C2212yescomplemented
124C24×D47C2311yescharacteristic
125C22×C22⋊D47—28no—
126C22×C22⋊D47C2×C418yes—
127C22×C22⋊D47C2311yescharacteristic
128C22×C22⋊D47C2311yescharacteristic
129C22×C22⋊D47C2311yescharacteristic
130C22×C22⋊D47C2311yescharacteristic
131C23×Dic47—44no—
132C23×Dic47C2×C418yescomplemented
133C23×Dic47C2312yes—
134C23×Dic47C2311yescharacteristic
135C23×Dic47C2311yescharacteristic
136C23×Dic47C2311yescharacteristic
137C23×Dic47C2311yescharacteristic
138C23×Dic47C2311yescharacteristic
139C23×Dic47C2311yescharacteristic
140C23×Dic47C2311yescharacteristic
141C22×C4×D47—44no—
142C22×C4×D47C2×C418yescomplemented
143C22×C4×D47C2312yes—
144C22×C4×D47C2312yes—
145C22×C4×D47C2311yescharacteristic
146C22×C4×D47C2311yescharacteristic
147C22×C4×D47C2311yescharacteristic
148C22×C4×D47C2311yescharacteristic
149C4×C22⋊D47—28no—
150(C22⋊D47)⋊C4—28no—
151(C22⋊D47)⋊C4C2×C418yes—
152(C22⋊D47)⋊C4C2×C418yes—
153(C22⋊D47)⋊C4C2×C418yescomplemented
154(C22⋊D47)⋊C4C2×C418yescomplemented
155(C22⋊D47)⋊C4C2×C418yescomplemented
156(C22⋊D47)⋊C4C2×C418yescomplemented
157(C22⋊D47)⋊C4C2×C418yescomplemented
158(C22⋊D47)⋊C4C2×C418yescomplemented
159#13093983—24no—
160#13093982—44no—
161#13093980—44no—
162C2×C4⋊Dic47C2312yes—
163C2×C4⋊Dic47C2312yes—
164C2×Dic47⋊C4C2×C418yescomplemented
165C2×Dic47⋊C4C2312yes—
166C2×Dic47⋊C4C2312yes—
167C2×Dic47⋊C4C2312yes—
168C2×Dic47⋊C4C2312yes—
169C2×Dic47⋊C4C2311yescharacteristic
170C2×Dic47⋊C4C2311yescharacteristic
171C2×Dic47⋊C4C2311yescharacteristic
172C2×Dic47⋊C4C2311yescharacteristic
173C2×C22⋊Dic47—24no—
174C2×C22⋊Dic47C2311yescharacteristic
175C2×C22⋊Dic47C2311yescharacteristic
176C2×C22⋊Dic47C2311yescharacteristic
177C2×C22⋊Dic47C2312yes—
178C2×C22⋊Dic47C2312yes—
179C2×C22⋊Dic47C2312yes—
180C2×C22⋊Dic47C2311yescharacteristic
181C2×(C2×D47)⋊C4C2×C418yescomplemented
182C2×(C2×D47)⋊C4C2312yes—
183C2×(C2×D47)⋊C4C2312yes—
184C2×(C2×D47)⋊C4C2312yes—
185C2×(C2×D47)⋊C4C2312yes—
186C2×(C2×D47)⋊C4C2312yes—
187C2×(C2×D47)⋊C4C2312yes—
188C2×(C2×D47)⋊C4C2311yescharacteristic
189C2×(C2×D47)⋊C4C2311yescharacteristic
190C2×(C2×D47)⋊C4C2311yescharacteristic
191C2×(C2×D47)⋊C4C2311yescharacteristic
192C22⋊C4×D47—24no—
193C22⋊C4×D47—24no—
194C2×C4×Dic47—44no—
195C2×C4×Dic47C2×C418yescomplemented
196C2×C4×Dic47C2312yes—
197C2×C4×Dic47C2312yes—
198C2×C4×Dic47C2312yes—
199C2×C4×Dic47C2312yes—
200C2×C4×Dic47C2312yes—
201C2×C4×Dic47C2312yes—
202C2×C4×Dic47C2312yes—
203C2×C4×Dic47C2312yes—
204C2×C4×Dic47C2312yes—
205C2×C4×Dic47C2312yes—
206C2×C4×Dic47C2311yescharacteristic
207C2×C4×Dic47C2311yescharacteristic
208C2×C4×Dic47C2311yescharacteristic
209C2×C4×Dic47C2311yescharacteristic
210C42×D47—44no—
211C47⋊#95C2312yes—
212C47⋊#95C2312yes—
213C47⋊#95C2312yes—
214C47⋊#95C2312yes—
215C47⋊#95C2312yes—
216C47⋊#95C2312yes—
217C47⋊#95C2312yes—
218C47⋊#95C2312yes—
219C47⋊#95C2312yes—
220C47⋊#95C2312yes—
221C47⋊#95C2312yes—
222C47⋊#95C2312yes—
223C47⋊#95C2312yes—
224C47⋊#95C2312yes—
225C47⋊#95C2312yes—
226C47⋊#95C2312yes—
227C25×C47C2311yescharacteristic
228C23×C4×C47C2312yes—
229C23×C4×C47C2311yescharacteristic
230C23×C4×C47C2311yescharacteristic
231#117×C47—24no—
232C2×C4⋊C4×C47C2312yes—
233C2×C4⋊C4×C47C2312yes—
234C2×C22⋊C4×C47—24no—
235C2×C22⋊C4×C47C2×C418yescomplemented
236C2×C22⋊C4×C47C2311yescharacteristic
237C2×C22⋊C4×C47C2311yescharacteristic
238C2×C22⋊C4×C47C2311yescharacteristic
239C2×C22⋊C4×C47C2312yes—
240C2×C22⋊C4×C47C2312yes—
241C2×C22⋊C4×C47C2312yes—
242C2×C22⋊C4×C47C2311yescharacteristic
243C2×C22⋊C4×C47C2311yescharacteristic
244C2×C22⋊C4×C47C2311yescharacteristic
245C2×C22⋊C4×C47C2311yescharacteristic
246C2×C22⋊C4×C47C2311yescharacteristic
247C2×C42×C47C2312yes—
248C2×C42×C47C2312yes—
249#95×C47C2312yes—
250#95×C47C2312yes—
251#95×C47C2312yes—
252#95×C47C2312yes—
253C24×C47—22no—
254C24×C47—22no—
255C24×C47—24no—
256C24×C47—42no—
257C24×C47C22×C414yes—
258C24×C47C2411yescharacteristic
259C24×C47C2411yescharacteristic
260C24×C47C2411yescharacteristic
261C23×D47—22no—
262C23×D47—22no—
263C23×D47—24no—
264C23×D47—42no—
265C23×D47C22×C414yes—
266C23×D47C2411yescharacteristic
267C23×D47C2411yescharacteristic
268C22×C4×C47—22no—
269C22×C4×C47—22no—
270C22×C4×C47—24no—
271C22×C4×C47—24no—
272C22×C4×C47—42no—
273C22×C4×C47—42no—
274C22×C4×C47C22×C414yes—
275C22×C4×C47C22×C414yes—
276C22×C4×C47C2412yes—
277C22×C4×C47C2412yes—
278C22×C4×C47C2412yes—
279C22×C4×C47C2411yescharacteristic
280C22×C4×C47C2411yescharacteristic
281C22×C4×C47C2411yescharacteristic
282C22×C4×C47C2411yescharacteristic
283C22×C4×C47C2412yes—
284C2×C22⋊D47—24no—
285C2×C22⋊D47—24no—
286C2×C22⋊D47—232no—
287C2×C22⋊D47—24no—
288C2×C22⋊D47C22×C414yes—
289C2×C22⋊D47C22×C414yes—
290C2×C22⋊D47C22×C414yes—
291C2×C22⋊D47C22×C414yes—
292C2×C22⋊D47#4118yes—
293C22×Dic47—24no—
294C22×Dic47—24no—
295C22×Dic47—24no—
296C22×Dic47—24no—
297C22×Dic47—24no—
298C22×Dic47—24no—
299C22×Dic47—416no—
300C22×Dic47—42no—
301C22×Dic47—42no—
302C22×Dic47—42no—
303C22×Dic47—42no—
304C22×Dic47C22×C414yes—
305C22×Dic47C22×C414yes—
306C22×Dic47C22×C414yes—
307C22×Dic47C22×C414yes—
308C22×Dic47C22×C414yes—
309C22×Dic47C22×C414yes—
310C22×Dic47C22×C414yes—
311C22×Dic47C2412yes—
312C22×Dic47C2412yes—
313C22×Dic47C2412yes—
314C22×Dic47C2411yescharacteristic
315C22×Dic47C2411yescharacteristic
316C22×Dic47C2411yescharacteristic
317C22×Dic47C2411yescharacteristic
318C22×Dic47C2412yes—
319C22×Dic47C2411yescharacteristic
320C22×Dic47C2411yescharacteristic
321C2×C4×D47—24no—
322C2×C4×D47—24no—
323C2×C4×D47—24no—
324C2×C4×D47—24no—
325C2×C4×D47—24no—
326C2×C4×D47—24no—
327C2×C4×D47—416no—
328C2×C4×D47—42no—
329C2×C4×D47—42no—
330C2×C4×D47—42no—
331C2×C4×D47—42no—
332C2×C4×D47C22×C414yes—
333C2×C4×D47C22×C414yes—
334C2×C4×D47C22×C414yes—
335C2×C4×D47C22×C414yes—
336C4⋊C4×C47—24no—
337C4⋊C4×C47—42no—
338C22⋊C4×C47—22no—
339C22⋊C4×C47—22no—
340C22⋊C4×C47—22no—
341C22⋊C4×C47—24no—
342C22⋊C4×C47—24no—
343C22⋊C4×C47—42no—
344C22⋊C4×C47C22×C414yes—
345C22⋊C4×C47C22×C414yes—
346C22⋊C4×C47C22×C414yes—
347C22⋊C4×C47C22×C414yes—
348C22⋊C4×C47#4114yes—
349C42×C47—24no—
350C42×C47—42no—
351C22⋊Dic47—22no—
352C22⋊Dic47—22no—
353C22⋊Dic47—22no—
354C22⋊Dic47—24no—
355C22⋊Dic47—24no—
356C22⋊Dic47—42no—
357C22⋊Dic47#4114yes—
358(C2×D47)⋊C4—24no—
359(C2×D47)⋊C4—24no—
360(C2×D47)⋊C4—24no—
361(C2×D47)⋊C4—24no—
362(C2×D47)⋊C4—42no—
363(C2×D47)⋊C4—42no—
364(C2×D47)⋊C4C22×C414yes—
365(C2×D47)⋊C4C22×C414yes—
366(C2×D47)⋊C4C22×C414yes—
367(C2×D47)⋊C4C22×C414yes—
368C4⋊Dic47—24no—
369C4⋊Dic47—42no—
370Dic47⋊C4—24no—
371Dic47⋊C4—24no—
372Dic47⋊C4—42no—
373Dic47⋊C4—42no—
374Dic47⋊C4C22×C414yes—
375Dic47⋊C4C22×C414yes—
376Dic47⋊C4C22×C414yes—
377Dic47⋊C4C22×C414yes—
378C4×Dic47—24no—
379C4×Dic47—24no—
380C4×Dic47—24no—
381C4×Dic47—24no—
382C4×Dic47—24no—
383C4×Dic47—24no—
384C4×Dic47—24no—
385C4×Dic47—42no—
386C4×Dic47—42no—
387C4×Dic47—42no—
388C4×Dic47C22×C414yes—
389C4×Dic47C22×C414yes—
390C4×Dic47C22×C414yes—
391C4×Dic47C22×C414yes—
392C23×C47—21no—
393C23×C47—22no—
394C23×C47—21no—
395C23×C47—22no—
396C23×C47—22no—
397C23×C47—28no—
398C23×C47—28no—
399C23×C47—21no—
400C23×C47—21no—
401C23×C47—22no—
402C23×C47—22no—
403C23×C47—44no—
404C23×C47—48no—
405C23×C47—48no—
406C23×C47C23×C412yes—
407C23×C47C23×C412yes—
408C23×C47C23×C412yes—
409C23×C47C2×#4114yes—
410C23×C47C2×#4112yes—
411C23×C47C2×#4112yes—
412C23×C47C2511yescharacteristic
413C22×D47—21no—
414C22×D47—21no—
415C22×D47—22no—
416C22×D47—28no—
417C22×D47—21no—
418C22×D47—21no—
419C22×D47—22no—
420C22×D47—22no—
421C22×D47—28no—
422C22×D47—44no—
423C22×D47—48no—
424C22×D47—48no—
425C22×D47C23×C412yes—
426C22×D47C23×C412yes—
427C22×D47C2×#4114yes—
428C2×C4×C47—28no—
429C2×C4×C47—21no—
430C2×C4×C47—22no—
431C2×C4×C47—21no—
432C2×C4×C47—21no—
433C2×C4×C47—21no—
434C2×C4×C47—22no—
435C2×C4×C47—22no—
436C2×C4×C47—22no—
437C2×C4×C47—22no—
438C2×C4×C47—22no—
439C2×C4×C47—22no—
440C2×C4×C47—22no—
441C2×C4×C47—22no—
442C2×C4×C47—22no—
443C2×C4×C47—22no—
444C2×C4×C47—22no—
445C2×C4×C47—22no—
446C2×C4×C47—44no—
447C2×C4×C47—48no—
448C2×C4×C47C23×C412yes—
449C2×C4×C47C23×C412yes—
450C2×C4×C47C23×C412yes—
451C2×C4×C47C23×C412yes—
452C2×C4×C47C2×#4114yes—
453C22⋊D47—28no—
454C22⋊D47—28no—
455C22⋊D47—28no—
456C22⋊D47#117116yescomplemented
457C2×Dic47—22no—
458C2×Dic47—22no—
459C2×Dic47—22no—
460C2×Dic47—22no—
461C2×Dic47—22no—
462C2×Dic47—22no—
463C2×Dic47—28no—
464C2×Dic47—28no—
465C2×Dic47—28no—
466C2×Dic47—28no—
467C2×Dic47—22no—
468C2×Dic47—22no—
469C2×Dic47—22no—
470C2×Dic47—22no—
471C2×Dic47—22no—
472C2×Dic47—22no—
473C2×Dic47—22no—
474C2×Dic47—22no—
475C2×Dic47—22no—
476C2×Dic47—44no—
477C2×Dic47—44no—
478C2×Dic47—44no—
479C2×Dic47—48no—
480C2×Dic47C23×C412yes—
481C2×Dic47C23×C412yes—
482C2×Dic47C23×C412yes—
483C2×Dic47C23×C412yes—
484C2×Dic47C23×C412yes—
485C2×Dic47C23×C412yes—
486C2×Dic47C2×#4114yes—
487C2×Dic47C2×#4114yes—
488C2×Dic47H(5,𝔽2)14yes—
489C4×D47—28no—
490C4×D47—28no—
491C4×D47—44no—
492C4×D47—44no—
493C4×D47—48no—
494C4×D47—48no—
495#34126—471nomaximal, Sylow
496C22×C47—22no—
497C22×C47—22no—
498C22×C47—22no—
499C22×C47—22no—
500C22×C47—24no—
501C22×C47—24no—
502C22×C47—24no—
503C22×C47—24no—
504C22×C47—22no—
505C22×C47—22no—
506C22×C47—22no—
507C22×C47—416no—
508C22×C47—42no—
509C22×C47—42no—
510C22×C47C2×#11714yes—
511C22×C47C4×#4114yes—
512C22×C47C24×C411yescharacteristic
513C22×C47C22×#4112yes—
514C22×C47C22×#4111yescharacteristic
515C22×C47C22×#4111yescharacteristic
516C22×C47C2×H(5,𝔽2)12yes—
517C2×D47—22no—
518C2×D47—22no—
519C2×D47—24no—
520C2×D47—24no—
521C2×D47—22no—
522C2×D47—22no—
523C2×D47—22no—
524C2×D47—416no—
525C2×D47—42no—
526C2×D47—42no—
527C2×D47C2×#11714yes—
528C4×C47—22no—
529C4×C47—22no—
530C4×C47—22no—
531C4×C47—22no—
532C4×C47—24no—
533C4×C47—42no—
534C4×C47—42no—
535C4×C47—42no—
536Dic47—22no—
537Dic47—22no—
538Dic47—22no—
539Dic47—22no—
540Dic47—24no—
541Dic47—42no—
542Dic47—42no—
543Dic47—42no—
544Dic47C2×#11714yes—
545Dic47#51814yes—
546C22×C4×D4—471no—
547#2357—472no—
548#2353—472no—
549#2353—472no—
550#2349—472no—
551#2345—471no—
552#2345—471no—
553#2342—471no—
554#2342—471no—
555#2342—471no—
556#2342D4711yescharacteristic, complemented
557D4×C22⋊C4—471no—
558D4×C22⋊C4—471no—
559#2293—472no—
560#2290—472no—
561#2290—472no—
562#2283—471no—
563#2280—471no—
564#2280—471no—
565C42×D4—472no—
566C4×#117—471no—
567C2×C4×C22⋊C4—471no—
568C2×C4×C22⋊C4—471no—
569C2×C47—24no—
570C2×C47—24no—
571C2×C47—42no—
572C2×C47C22×#11711yescharacteristic
573C2×C47C2×C4×#4111yescharacteristic
574C2×C47C2×#51811yescharacteristic
575C2×C47#348112yes—
576C2×C47#348112yes—
577D47—24no—
578D47—42no—
579C23×D4—471no—
580C24×C4—471no—
581C24×C4—471no—
582C2×C4×D4—472no—
583C2×C4×D4—4716no—
584C2×C4×D4—471no—
585C2×C4×D4—471no—
586C2×C4×D4—471no—
587C2×C4×D4—471no—
588C2×C4×D4—471no—
589C2×C4×D4—471no—
590C2×C4×D4—471no—
591C2×C4×D4—471no—
592C2×C4×D4—472no—
593C2×#117—471no—
594C2×#117—472no—
595C2×#117—472no—
596C2×#117C2×D4711yescharacteristic
597C22×C4⋊C4—471no—
598C22×C22⋊C4—471no—
599C22×C22⋊C4—471no—
600C22×C22⋊C4—471no—
601C22×C22⋊C4—471no—
602C22×C22⋊C4C2×D4711yescharacteristic
603C22×C22⋊C4C2×D4711yescharacteristic
604C22×C42—471no—
605C22×C42—472no—
606C22×C42—472no—
607#390—472no—
608#390—472no—
609#389—472no—
610#389—472no—
611#388—472no—
612#388—472no—
613#388—472no—
614#388—472no—
615#388—472no—
616#388—472no—
617#388C2×D4712yescomplemented
618#388C2×D4712yescomplemented
619#387—472no—
620#387—472no—
621#387—472no—
622#387—472no—
623#386—472no—
624#386—472no—
625#386—472no—
626#386—472no—
627#385—472no—
628#385—472no—
629#385—472no—
630#385C2×D4712yescomplemented
631#383—472no—
632#382—472no—
633#381—471no—
634#381—472no—
635#381—472no—
636#381C2×D4711yescharacteristic
637#380—471no—
638#380—472no—
639#380—471no—
640#380—471no—
641#380—471no—
642#380—471no—
643#380—472no—
644#380C2×D4711yescharacteristic
645#379—471no—
646#379—471no—
647#379—471no—
648#379C2×D4711yescharacteristic
649C4×C4⋊C4—472no—
650C4×C4⋊C4—472no—
651C4×C4⋊C4—472no—
652C4×C4⋊C4—472no—
653C4×C4⋊C4—472no—
654C4×C22⋊C4—471no—
655C4×C22⋊C4—471no—
656C4×C22⋊C4—471no—
657C4×C22⋊C4—471no—
658C4×C22⋊C4—471no—
659C4×C22⋊C4—471no—
660C4×C22⋊C4—471no—
661C4×C22⋊C4—471no—
662C4×C22⋊C4—471no—
663C4×C22⋊C4—472no—
664C4×C22⋊C4—472no—
665C4×C22⋊C4—472no—
666C4×C22⋊C4—472no—
667C4×C22⋊C4—472no—
668C4×C22⋊C4—472no—
669C4×C22⋊C4—472no—
670C4×C22⋊C4—472no—
671C4×C22⋊C4—472no—
672C4×C22⋊C4C2×D4711yescharacteristic
673C4×C22⋊C4C2×D4712yescomplemented
674#376—472no—
675#376—472no—
676C2×#95—472no—
677C2×#95—472no—
678C43—472no—
679C47#3412611yescharacteristic, complemented, Sylow
680C25—471no—
681C25C22×D4711yescharacteristic
682C22×D4—471no—
683C22×D4—478no—
684C22×D4—471no—
685C22×D4—471no—
686C22×D4—471no—
687C22×D4—948no—
688C23×C4—471no—
689C23×C4—471no—
690C23×C4—471no—
691C23×C4—471no—
692C23×C4—478no—
693C23×C4—471no—
694C23×C4—471no—
695C23×C4—471no—
696C23×C4—471no—
697C23×C4—471no—
698C23×C4—478no—
699C23×C4—471no—
700C23×C4—471no—
701C23×C4—472no—
702C23×C4—472no—
703C23×C4—472no—
704C23×C4—1884no—
705C23×C4—1884no—
706C23×C4C22×D4712yes—
707C23×C4C22×D4711yescharacteristic
708C23×C4C22×D4711yescharacteristic
709C4×D4—478no—
710C4×D4—478no—
711C4×D4—478no—
712C4×D4—478no—
713C4×D4—478no—
714C4×D4—478no—
715C4×D4—478no—
716C4×D4—478no—
717C4×D4—948no—
718C4×D4—948no—
719#117—24no—
720#117—944no—
721#117—1884no—
722#117—1884no—
723C2×C4⋊C4—478no—
724C2×C4⋊C4—471no—
725C2×C4⋊C4—471no—
726C2×C4⋊C4—471no—
727C2×C4⋊C4—471no—
728C2×C4⋊C4—472no—
729C2×C4⋊C4—472no—
730C2×C4⋊C4—472no—
731C2×C4⋊C4—472no—
732C2×C4⋊C4—472no—
733C2×C4⋊C4—472no—
734C2×C4⋊C4C22×D4712yes—
735C2×C4⋊C4C22×D4712yes—
736C2×C22⋊C4—24no—
737C2×C22⋊C4—471no—
738C2×C22⋊C4—478no—
739C2×C22⋊C4—471no—
740C2×C22⋊C4—471no—
741C2×C22⋊C4—471no—
742C2×C22⋊C4—471no—
743C2×C22⋊C4—471no—
744C2×C22⋊C4—471no—
745C2×C22⋊C4—472no—
746C2×C22⋊C4—471no—
747C2×C22⋊C4—472no—
748C2×C22⋊C4—472no—
749C2×C22⋊C4—472no—
750C2×C22⋊C4—472no—
751C2×C22⋊C4—472no—
752C2×C22⋊C4—472no—
753C2×C22⋊C4—472no—
754C2×C22⋊C4—472no—
755C2×C22⋊C4—944no—
756C2×C22⋊C4—944no—
757C2×C22⋊C4—944no—
758C2×C22⋊C4C4×D4718yescomplemented
759C2×C22⋊C4C22×D4711yescharacteristic
760C2×C22⋊C4C22×D4711yescharacteristic
761C2×C22⋊C4C22×D4712yes—
762C2×C22⋊C4C22×D4711yescharacteristic
763C2×C22⋊C4C22×D4712yes—
764C2×C22⋊C4C22×D4712yes—
765C2×C22⋊C4C22×D4711yescharacteristic
766C2×C22⋊C4C22×D4711yescharacteristic
767C2×C22⋊C4C22×D4711yescharacteristic
768C2×C22⋊C4C22×D4711yescharacteristic
769C2×C22⋊C4C22×D4711yescharacteristic
770C2×C42—478no—
771C2×C42—471no—
772C2×C42—471no—
773C2×C42—471no—
774C2×C42—471no—
775C2×C42—472no—
776C2×C42—472no—
777C2×C42—472no—
778C2×C42—472no—
779C2×C42—472no—
780C2×C42—472no—
781C2×C42—472no—
782C2×C42—472no—
783C2×C42—472no—
784C2×C42—472no—
785C2×C42—1884no—
786C2×C42—1884no—
787C2×C42C22×D4712yes—
788C2×C42C22×D4712yes—
789#95—472no—
790#95—472no—
791#95—472no—
792#95—472no—
793#95—472no—
794#95—472no—
795#95—472no—
796#95—472no—
797#95—472no—
798#95—472no—
799#95—472no—
800#95—472no—
801#95—472no—
802#95—472no—
803#95—472no—
804#95—472no—
805#95C22×D4712yes—
806#95C22×D4712yes—
807#95C22×D4712yes—
808#95C22×D4712yes—
809C24—22no—
810C24—24no—
811C24—22no—
812C24—42no—
813C24—471no—
814C24—471no—
815C24—474no—
816C24—944no—
817C24—942no—
818C24—942no—
819C24—1882no—
820C24C2×C4×D4714yes—
821C24C23×D4711yescharacteristic
822C24C23×D4711yescharacteristic
823C24C23×D4711yescharacteristic
824C2×D4—474no—
825C2×D4—478no—
826C2×D4—474no—
827C2×D4—474no—
828C2×D4—474no—
829C2×D4—944no—
830C2×D4—9432no—
831C2×D4—944no—
832C2×D4—944no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—24no—
836C22×C4—24no—
837C22×C4—42no—
838C22×C4—42no—
839C22×C4—471no—
840C22×C4—471no—
841C22×C4—474no—
842C22×C4—474no—
843C22×C4—474no—
844C22×C4—474no—
845C22×C4—471no—
846C22×C4—471no—
847C22×C4—472no—
848C22×C4—471no—
849C22×C4—471no—
850C22×C4—474no—
851C22×C4—474no—
852C22×C4—474no—
853C22×C4—474no—
854C22×C4—474no—
855C22×C4—474no—
856C22×C4—474no—
857C22×C4—472no—
858C22×C4—472no—
859C22×C4—472no—
860C22×C4—944no—
861C22×C4—944no—
862C22×C4—944no—
863C22×C4—944no—
864C22×C4—944no—
865C22×C4—944no—
866C22×C4—944no—
867C22×C4—944no—
868C22×C4—944no—
869C22×C4—944no—
870C22×C4—944no—
871C22×C4—944no—
872C22×C4—1882no—
873C22×C4—1882no—
874C22×C4—1882no—
875C22×C4—1882no—
876C22×C4—18816no—
877C22×C4—18816no—
878C22×C4—1882no—
879C22×C4—1882no—
880C22×C4—1882no—
881C22×C4—1882no—
882C22×C4C2×C4×D4714yes—
883C22×C4C2×C4×D4714yes—
884C22×C4C23×D4712yes—
885C22×C4C23×D4712yes—
886C22×C4C23×D4712yes—
887C22×C4C23×D4711yescharacteristic
888C22×C4C23×D4711yescharacteristic
889C22×C4C23×D4711yescharacteristic
890C22×C4C23×D4711yescharacteristic
891C22×C4C23×D4712yes—
892C4⋊C4—24no—
893C4⋊C4—42no—
894C4⋊C4—474no—
895C4⋊C4—474no—
896C4⋊C4—474no—
897C4⋊C4—474no—
898C4⋊C4—944no—
899C4⋊C4—944no—
900C4⋊C4—944no—
901C4⋊C4—1882no—
902C4⋊C4—1882no—
903C4⋊C4—1882no—
904C22⋊C4—22no—
905C22⋊C4—24no—
906C22⋊C4—22no—
907C22⋊C4—22no—
908C22⋊C4—24no—
909C22⋊C4—42no—
910C22⋊C4—474no—
911C22⋊C4—474no—
912C22⋊C4—474no—
913C22⋊C4—474no—
914C22⋊C4—474no—
915C22⋊C4—944no—
916C22⋊C4—944no—
917C22⋊C4—944no—
918C22⋊C4—944no—
919C22⋊C4—942no—
920C22⋊C4—942no—
921C22⋊C4—944no—
922C22⋊C4—942no—
923C22⋊C4—944no—
924C22⋊C4—1882no—
925C22⋊C4—1882no—
926C22⋊C4—1882no—
927C22⋊C4C2×C4×D4714yes—
928C22⋊C4C2×C4×D4714yes—
929C22⋊C4C2×C4×D4714yes—
930C22⋊C4C2×C4×D4714yes—
931C22⋊C4#1062535214yes—
932C42—24no—
933C42—42no—
934C42—474no—
935C42—474no—
936C42—474no—
937C42—474no—
938C42—944no—
939C42—944no—
940C42—944no—
941C42—944no—
942C42—944no—
943C42—944no—
944C42—944no—
945C42—1882no—
946C42—1882no—
947C42—1882no—
948C23—21no—
949C23—22no—
950C23—21no—
951C23—22no—
952C23—22no—
953C23—28no—
954C23—28no—
955C23—21no—
956C23—22no—
957C23—21no—
958C23—22no—
959C23—44no—
960C23—48no—
961C23—48no—
962C23—472no—
963C23—474no—
964C23—472no—
965C23—948no—
966C23—941no—
967C23—941no—
968C23—942no—
969C23—948no—
970C23—941no—
971C23—942no—
972C23—941no—
973C23—942no—
974C23—1884no—
975C23—1888no—
976C23—1888no—
977C23C22×C4×D4712yes—
978C23C22×C4×D4712yes—
979C23C22×C4×D4712yes—
980C23#41×D4714yes—
981C23#41×D4712yes—
982C23C2×#1062535212yes—
983C23C24×D4711yescharacteristic
984D4—4716no—
985D4—948no—
986D4—948no—
987D4—948no—
988C2×C4—28no—
989C2×C4—21no—
990C2×C4—22no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—44no—
1007C2×C4—48no—
1008C2×C4—472no—
1009C2×C4—472no—
1010C2×C4—474no—
1011C2×C4—474no—
1012C2×C4—472no—
1013C2×C4—472no—
1014C2×C4—472no—
1015C2×C4—472no—
1016C2×C4—474no—
1017C2×C4—948no—
1018C2×C4—948no—
1019C2×C4—948no—
1020C2×C4—948no—
1021C2×C4—948no—
1022C2×C4—948no—
1023C2×C4—942no—
1024C2×C4—942no—
1025C2×C4—942no—
1026C2×C4—942no—
1027C2×C4—942no—
1028C2×C4—942no—
1029C2×C4—942no—
1030C2×C4—942no—
1031C2×C4—942no—
1032C2×C4—942no—
1033C2×C4—942no—
1034C2×C4—942no—
1035C2×C4—942no—
1036C2×C4—942no—
1037C2×C4—942no—
1038C2×C4—1884no—
1039C2×C4—1884no—
1040C2×C4—1888no—
1041C2×C4—1888no—
1042C2×C4—1884no—
1043C2×C4—1884no—
1044C2×C4—1884no—
1045C2×C4—1888no—
1046C2×C4C22×C4×D4712yes—
1047C2×C4C22×C4×D4712yes—
1048C2×C4C22×C4×D4712yes—
1049C2×C4C22×C4×D4712yes—
1050C2×C4C2×#1062535214yes—
1051C22—22no—
1052C22—22no—
1053C22—22no—
1054C22—22no—
1055C22—24no—
1056C22—24no—
1057C22—24no—
1058C22—24no—
1059C22—22no—
1060C22—22no—
1061C22—22no—
1062C22—416no—
1063C22—42no—
1064C22—42no—
1065C22—474no—
1066C22—942no—
1067C22—942no—
1068C22—944no—
1069C22—944no—
1070C22—942no—
1071C22—942no—
1072C22—942no—
1073C22—18816no—
1074C22—1882no—
1075C22—1882no—
1076C22#117×D4714yes—
1077C22C4×#1062535214yes—
1078C22C23×C4×D4711yescharacteristic
1079C22C2×#41×D4712yes—
1080C22C2×#41×D4711yescharacteristic
1081C22C22×#1062535211yescharacteristic
1082C22H(5,𝔽2)×D4712yes—
1083C4—22no—
1084C4—22no—
1085C4—22no—
1086C4—22no—
1087C4—24no—
1088C4—42no—
1089C4—42no—
1090C4—42no—
1091C4—474no—
1092C4—474no—
1093C4—942no—
1094C4—942no—
1095C4—942no—
1096C4—942no—
1097C4—944no—
1098C4—1882no—
1099C4—1882no—
1100C4—1882no—
1101C2—24no—
1102C2—24no—
1103C2—42no—
1104C2—944no—
1105C2—1882no—
1106C2C2×#117×D4711yescharacteristic
1107C2C2×C4×#1062535211yescharacteristic
1108C2#518×D4711yescharacteristic
1109C2#2025699112yes—
1110C2#2025699312yes—
subgroupG/H
center, FrattiniC23C24×D47
commutatorC22×C47C24×C4
FittingC47×#2342C2
socle, cosocleC23×C47C25
prime radicalC23×C22⋊D47C22
hypercenter#2342D47
hypocenterC47#34126
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2342

Complements

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

NH ≅ G/Ntype
2. #20246358C2semidirect
3. #20246323C2semidirect
4. #20246322C2semidirect
5. #20246294C2semidirect
6. #20246266C2semidirect
7. #20246260C2semidirect
8. #20246238C2semidirect
9. #20246237C2semidirect
10. #20246230C2semidirect
13. #20245848C2semidirect
14. #20245830C2semidirect
15. #20245824C2semidirect
16. #20245779C2semidirect
17. #20245770C2semidirect
18. #20245766C2semidirect
19. C4×(C22⋊D47)⋊C4C2semidirect
20. #117×Dic47C2semidirect
21. C2×C22⋊C4×Dic47C2semidirect
22. C4×C22⋊C4×D47C2semidirect
23. C47×#2342C2semidirect
28. C2×(C22⋊D47)⋊C4C4semidirect
39. C2×#13093982C22semidirect
40. C2×#13093980C22semidirect
47. C22×C4×Dic47C22semidirect
48. C2×C42×D47C22semidirect
51. #15689020C22semidirect
52. #15689018C22semidirect
53. #15689016C22semidirect
54. #15689016C22semidirect
55. #15689015C22semidirect
56. #15689014C22semidirect
57. #15689013C22semidirect
58. #15689012C22semidirect
59. #15689010C22semidirect
60. #15689007C22semidirect
61. #15689005C22semidirect
62. #15689004C22semidirect
67. #15688998C22semidirect
68. #15688997C22semidirect
69. #15688994C22semidirect
70. #15688990C22semidirect
71. #15688987C22semidirect
73. #15688985C22semidirect
74. #15688984C22semidirect
80. #15688981C22semidirect
81. #15688980C22semidirect
85. C4⋊C4×Dic47C22semidirect
86. C4⋊C4×Dic47C22semidirect
87. C4×Dic47⋊C4C22semidirect
88. #15688974C22semidirect
89. #15688974C22semidirect
98. C22⋊C4×Dic47C22semidirect
99. C22⋊C4×Dic47C22semidirect
100. C22⋊C4×Dic47C22semidirect
101. C22⋊C4×Dic47C22semidirect
102. C4×(C2×D47)⋊C4C22semidirect
103. C4×(C2×D47)⋊C4C22semidirect
105. #15688970C22semidirect
106. #15688970C22semidirect
107. #15688970C22semidirect
108. #15688969C22semidirect
109. #15688968C22semidirect
110. C2×C47⋊#95C22semidirect
111. #95×D47C22semidirect
112. C42×Dic47C22semidirect
116. C47×#388C22semidirect
117. C47×#388C22semidirect
118. C47×#385C22semidirect
123. C4×C22⋊C4×C47C22semidirect
132. C23×Dic47C2×C4semidirect
142. C22×C4×D47C2×C4semidirect
153. (C22⋊D47)⋊C4C2×C4semidirect
154. (C22⋊D47)⋊C4C2×C4semidirect
155. (C22⋊D47)⋊C4C2×C4semidirect
156. (C22⋊D47)⋊C4C2×C4semidirect
157. (C22⋊D47)⋊C4C2×C4semidirect
158. (C22⋊D47)⋊C4C2×C4semidirect
164. C2×Dic47⋊C4C2×C4semidirect
181. C2×(C2×D47)⋊C4C2×C4semidirect
195. C2×C4×Dic47C2×C4semidirect
235. C2×C22⋊C4×C47C2×C4semidirect
456. C22⋊D47#117semidirect
556. #2342D47semidirect
617. #388C2×D47semidirect
618. #388C2×D47semidirect
630. #385C2×D47semidirect
673. C4×C22⋊C4C2×D47semidirect
679. C47#34126semidirect
758. C2×C22⋊C4C4×D47semidirect

Maximal subgroups

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

subgroupindex
C22×(C22⋊D47)⋊C42
#202463582
#202463232
#202463222
#202462942
#202462662
#202462602
#202462382
#202462372
#202462302
C22⋊C4×C22⋊D472
#202462042
#202458482
#202458302
#202458242
#202457792
#202457702
#202457662
C4×(C22⋊D47)⋊C42
#117×Dic472
C2×C22⋊C4×Dic472
C4×C22⋊C4×D472
C47×#23422
#3412647