Finite Group Databasebeta

← #26379237

Subgroups — #26379237

Order 12032.

3082 conjugacy classes of subgroups.

The subgroup lattice has 1198 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093996C211yesmaximal, characteristic
2#20246546C212yesmaximal, complemented
3#20246539C212yesmaximal, complemented
4#20246405C212yesmaximal, complemented
5#20246399C212yesmaximal, complemented
6#20246266C211yesmaximal, characteristic, complemented
7#20246260C211yesmaximal, characteristic, complemented
8D4×C22⋊Dic47C211yesmaximal, characteristic, complemented
9C22⋊C4×C22⋊D47C211yesmaximal, characteristic, complemented
10C22⋊C4×C22⋊D47C211yesmaximal, characteristic, complemented
11#20246204C211yesmaximal, characteristic, complemented
12#20246204C211yesmaximal, characteristic, complemented
13#20246089C212yesmaximal, complemented
14#20246086C212yesmaximal, complemented
15#20246078C212yesmaximal, complemented
16#20246074C212yesmaximal, complemented
17#20246001C211yesmaximal, characteristic, complemented
18#20246000C211yesmaximal, characteristic, complemented
19#20245984C211yesmaximal, characteristic, complemented
20#20245983C211yesmaximal, characteristic, complemented
21#20245766C211yesmaximal, characteristic, complemented
22C2×#15688981C211yesmaximal, characteristic, complemented
23D4×C22⋊C4×C47C211yesmaximal, characteristic, complemented
24C23×C22⋊D47C2211yescharacteristic
25C23×C22⋊D47C2211yescharacteristic
26C24×Dic47C2211yescharacteristic
27C2×#13093996C4116yescomplemented
28C2×#13093996C2211yescharacteristic
29C2×#13093996C2211yescharacteristic
30C2×#13093996C2211yescharacteristic
31C2×#13093996C2211yescharacteristic
32C2×#13093996C2211yescharacteristic
33C2×#13093996C2211yescharacteristic
34C2×#13093996C2211yescharacteristic
35C2×#13093996C2211yescharacteristic
36C2×D4×Dic47C2212yescomplemented
37C2×C4×C22⋊D47C2212yescomplemented
38C2×C4×C22⋊D47C2212yescomplemented
39C2×(C22⋊D47)⋊C4C2212yescomplemented
40C2×(C22⋊D47)⋊C4C2212yescomplemented
41C2×#13093980C2212yescomplemented
42C22×Dic47⋊C4C2211yescharacteristic
43C22×Dic47⋊C4C2212yescomplemented
44C22×C22⋊Dic47C2211yescharacteristic
45C22×C22⋊Dic47C2211yescharacteristic
46C22×C22⋊Dic47C2211yescharacteristic
47C22×(C2×D47)⋊C4C2211yescharacteristic
48C2×C22⋊C4×D47C2211yescharacteristic
49C2×C22⋊C4×D47C2211yescharacteristic
50#15689026C2212yescomplemented
51#15689023C2212yescomplemented
52#15689023C2212yescomplemented
53#15689023C2212yescomplemented
54#15689023C2212yescomplemented
55#15689020C2212yescomplemented
56#15689018C2212yescomplemented
57#15689017C2212yescomplemented
58#15689017C2212yescomplemented
59#15689014C2212yescomplemented
60#15689014C2212yescomplemented
61#15689012C2212yescomplemented
62#15689012C2212yescomplemented
63#15689011C2212yescomplemented
64#15689011C2212yescomplemented
65#15689010C2212yescomplemented
66#15689007C2212yescomplemented
67#15689005C2212yescomplemented
68#15689004C2212yescomplemented
69#15689003C2212yescomplemented
70#15689003C2212yescomplemented
71#15689002C2212yescomplemented
72#15689002C2212yescomplemented
73#15689000C2212yescomplemented
74#15689000C2212yescomplemented
75#15688999C2212yescomplemented
76#15688999C2212yescomplemented
77#15688999C2212yescomplemented
78#15688999C2212yescomplemented
79#15688997C2212yescomplemented
80#15688997C2212yescomplemented
81#15688996C2212yescomplemented
82#15688996C2212yescomplemented
83#15688995C2212yescomplemented
84#15688995C2212yescomplemented
85#15688994C2212yescomplemented
86#15688994C2212yescomplemented
87#15688984C2212yescomplemented
88#15688983C2211yescharacteristic
89#15688981C2211yescharacteristic
90#15688981C2211yescharacteristic
91#15688981C2211yescharacteristic
92#15688981C2211yescharacteristic
93#15688981C2211yescharacteristic
94#15688981C2211yescharacteristic
95#15688981C2211yescharacteristic
96#15688981C2211yescharacteristic
97#15688981C2212yescomplemented
98#15688981C2212yescomplemented
99#15688981C2212yescomplemented
100#15688979C2211yescharacteristic
101#15688979C2211yescharacteristic
102#15688978C2211yescharacteristic
103#15688978C2211yescharacteristic
104C4×Dic47⋊C4C2212yescomplemented
105#15688974C2212yescomplemented
106C22⋊C4×Dic47C2211yescharacteristic
107C22⋊C4×Dic47C2211yescharacteristic
108C22⋊C4×Dic47C2211yescharacteristic
109C22⋊C4×Dic47C2211yescharacteristic
110C22⋊C4×Dic47C2212yescomplemented
111C4×C22⋊Dic47C2211yescharacteristic
112C2×C47⋊#95C2212yescomplemented
113C23×D4×C47C2211yescharacteristic
114C2×C4×D4×C47C2212yescomplemented
115C22×C22⋊C4×C47C2211yescharacteristic
116C22×C22⋊C4×C47C2211yescharacteristic
117C47×#390C2212yescomplemented
118C47×#386C2212yescomplemented
119C47×#386C2212yescomplemented
120C47×#380C2211yescharacteristic
121C47×#379C2211yescharacteristic
122C47×#379C2211yescharacteristic
123C4×C22⋊C4×C47C2211yescharacteristic
124C24×D47C2311yescharacteristic
125C22×C22⋊D47—44no—
126C22×C22⋊D47—44no—
127C22×C22⋊D47C2×C418yescomplemented
128C22×C22⋊D47C2×C418yescomplemented
129C22×C22⋊D47C2311yescharacteristic
130C22×C22⋊D47C2311yescharacteristic
131C22×C22⋊D47C2311yescharacteristic
132C22×C22⋊D47C2311yescharacteristic
133C22×C22⋊D47C2311yescharacteristic
134C22×C22⋊D47C2311yescharacteristic
135C22×C22⋊D47C2311yescharacteristic
136C22×C22⋊D47C2311yescharacteristic
137C23×Dic47—44no—
138C23×Dic47C2×C418yescomplemented
139C23×Dic47C2311yescharacteristic
140C23×Dic47C2311yescharacteristic
141C23×Dic47C2311yescharacteristic
142C23×Dic47C2312yes—
143C23×Dic47C2312yes—
144C23×Dic47C2311yescharacteristic
145C23×Dic47C2311yescharacteristic
146C23×Dic47C2311yescharacteristic
147C23×Dic47C2311yescharacteristic
148C22×C4×D47C2312yes—
149C22×C4×D47C2312yes—
150#13093996C2×C418yescomplemented
151#13093996C2×C418yescomplemented
152#13093996C2×C418yescomplemented
153#13093996C2×C418yescomplemented
154#13093996C2×C418yescomplemented
155#13093996C2×C418yescomplemented
156#13093996C2×C418yescomplemented
157#13093996C2×C418yescomplemented
158D4×Dic47—44no—
159C4×C22⋊D47—44no—
160C4×C22⋊D47—44no—
161(C22⋊D47)⋊C4—44no—
162(C22⋊D47)⋊C4—44no—
163#13093980—44no—
164C2×C4⋊Dic47C2312yes—
165C2×Dic47⋊C4—44no—
166C2×Dic47⋊C4C2×C418yescomplemented
167C2×Dic47⋊C4C2312yes—
168C2×Dic47⋊C4C2312yes—
169C2×Dic47⋊C4C2312yes—
170C2×Dic47⋊C4C2312yes—
171C2×Dic47⋊C4C2312yes—
172C2×Dic47⋊C4C2312yes—
173C2×Dic47⋊C4C2312yes—
174C2×Dic47⋊C4C2312yes—
175C2×Dic47⋊C4C2311yescharacteristic
176C2×Dic47⋊C4C2311yescharacteristic
177C2×Dic47⋊C4C2311yescharacteristic
178C2×Dic47⋊C4C2311yescharacteristic
179C2×C22⋊Dic47—42no—
180C2×C22⋊Dic47—42no—
181C2×C22⋊Dic47C2×C418yescomplemented
182C2×C22⋊Dic47C2311yescharacteristic
183C2×C22⋊Dic47C2311yescharacteristic
184C2×C22⋊Dic47C2311yescharacteristic
185C2×C22⋊Dic47C2311yescharacteristic
186C2×C22⋊Dic47C2312yes—
187C2×C22⋊Dic47C2312yes—
188C2×C22⋊Dic47C2312yes—
189C2×C22⋊Dic47C2312yes—
190C2×C22⋊Dic47C2312yes—
191C2×C22⋊Dic47C2312yes—
192C2×C22⋊Dic47C2311yescharacteristic
193C2×C22⋊Dic47C2311yescharacteristic
194C2×C22⋊Dic47C2311yescharacteristic
195C2×C22⋊Dic47C2311yescharacteristic
196C2×(C2×D47)⋊C4C2×C418yescomplemented
197C2×(C2×D47)⋊C4C2312yes—
198C2×(C2×D47)⋊C4C2312yes—
199C2×(C2×D47)⋊C4C2312yes—
200C2×(C2×D47)⋊C4C2312yes—
201C2×(C2×D47)⋊C4C2312yes—
202C2×(C2×D47)⋊C4C2312yes—
203C2×(C2×D47)⋊C4C2311yescharacteristic
204C2×(C2×D47)⋊C4C2311yescharacteristic
205C2×(C2×D47)⋊C4C2311yescharacteristic
206C2×(C2×D47)⋊C4C2311yescharacteristic
207C22⋊C4×D47—42no—
208C22⋊C4×D47—42no—
209C2×C4×Dic47C2312yes—
210C2×C4×Dic47C2312yes—
211C2×C4×Dic47C2312yes—
212C2×C4×Dic47C2312yes—
213C2×C4×Dic47C2312yes—
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—
227C47⋊#95C2312yes—
228C25×C47C2311yescharacteristic
229C25×C47C2311yescharacteristic
230C22×D4×C47—44no—
231C22×D4×C47C2×C418yescomplemented
232C22×D4×C47C2311yescharacteristic
233C22×D4×C47C2311yescharacteristic
234C22×D4×C47C2311yescharacteristic
235C22×D4×C47C2311yescharacteristic
236C23×C4×C47C2312yes—
237C23×C4×C47C2312yes—
238C23×C4×C47C2311yescharacteristic
239C4×D4×C47—44no—
240C2×C4⋊C4×C47C2312yes—
241C2×C22⋊C4×C47—42no—
242C2×C22⋊C4×C47—42no—
243C2×C22⋊C4×C47C2311yescharacteristic
244C2×C22⋊C4×C47C2311yescharacteristic
245C2×C22⋊C4×C47C2311yescharacteristic
246C2×C22⋊C4×C47C2312yes—
247C2×C22⋊C4×C47C2311yescharacteristic
248C2×C22⋊C4×C47C2312yes—
249C2×C22⋊C4×C47C2312yes—
250C2×C22⋊C4×C47C2312yes—
251C2×C22⋊C4×C47C2312yes—
252C2×C22⋊C4×C47C2312yes—
253C2×C42×C47C2312yes—
254#95×C47C2312yes—
255#95×C47C2312yes—
256C24×C47—22no—
257C24×C47—24no—
258C24×C47—22no—
259C24×C47—22no—
260C24×C47—22no—
261C24×C47—42no—
262C24×C47—42no—
263C24×C47—42no—
264C24×C47C22×C414yes—
265C24×C47C22×C414yes—
266C24×C47C2411yescharacteristic
267C24×C47C2411yescharacteristic
268C24×C47C2411yescharacteristic
269C24×C47C2411yescharacteristic
270C24×C47C2411yescharacteristic
271C23×D47—22no—
272C23×D47—22no—
273C23×D47—42no—
274C23×D47—42no—
275C23×D47C22×C414yes—
276C23×D47C2411yescharacteristic
277C23×D47C2411yescharacteristic
278C2×D4×C47—24no—
279C2×D4×C47—24no—
280C2×D4×C47—42no—
281C2×D4×C47—42no—
282C2×D4×C47—416no—
283C2×D4×C47C22×C414yes—
284C2×D4×C47C22×C414yes—
285C2×D4×C47C22×C414yes—
286C2×D4×C47C22×C414yes—
287C22×C4×C47—24no—
288C22×C4×C47—42no—
289C22×C4×C47—42no—
290C22×C4×C47—42no—
291C22×C4×C47—42no—
292C22×C4×C47—42no—
293C22×C4×C47—42no—
294C22×C4×C47C22×C414yes—
295C22×C4×C47C2412yes—
296C22×C4×C47C2412yes—
297C22×C4×C47C2412yes—
298C22×C4×C47C2412yes—
299C22×C4×C47C2411yescharacteristic
300C22×C4×C47C2411yescharacteristic
301C2×C22⋊D47—24no—
302C2×C22⋊D47—24no—
303C2×C22⋊D47—24no—
304C2×C22⋊D47—24no—
305C2×C22⋊D47—416no—
306C2×C22⋊D47—42no—
307C2×C22⋊D47—42no—
308C2×C22⋊D47—42no—
309C2×C22⋊D47—42no—
310C2×C22⋊D47—416no—
311C2×C22⋊D47C22×C414yes—
312C2×C22⋊D47C22×C414yes—
313C2×C22⋊D47C22×C414yes—
314C2×C22⋊D47C22×C414yes—
315C2×C22⋊D47C22×C414yes—
316C2×C22⋊D47C22×C414yes—
317C2×C22⋊D47C22×C414yes—
318C2×C22⋊D47C22×C414yes—
319C22×Dic47—24no—
320C22×Dic47—24no—
321C22×Dic47—24no—
322C22×Dic47—24no—
323C22×Dic47—416no—
324C22×Dic47—42no—
325C22×Dic47—42no—
326C22×Dic47—42no—
327C22×Dic47—42no—
328C22×Dic47—42no—
329C22×Dic47—42no—
330C22×Dic47—42no—
331C22×Dic47—42no—
332C22×Dic47—42no—
333C22×Dic47C22×C414yes—
334C22×Dic47C22×C414yes—
335C22×Dic47C22×C414yes—
336C22×Dic47C22×C414yes—
337C22×Dic47C22×C414yes—
338C22×Dic47C22×C414yes—
339C22×Dic47C22×C414yes—
340C22×Dic47C2412yes—
341C22×Dic47C2412yes—
342C22×Dic47C2412yes—
343C22×Dic47C2412yes—
344C22×Dic47C2411yescharacteristic
345C22×Dic47C2411yescharacteristic
346C22×Dic47C2411yescharacteristic
347C22×Dic47C2411yescharacteristic
348C22×Dic47C2411yescharacteristic
349C22×Dic47C2411yescharacteristic
350C2×C4×D47—42no—
351C2×C4×D47—42no—
352C2×C4×D47—42no—
353C2×C4×D47—42no—
354C2×C4×D47—42no—
355C2×C4×D47—42no—
356C4⋊C4×C47—42no—
357C22⋊C4×C47—22no—
358C22⋊C4×C47—22no—
359C22⋊C4×C47—22no—
360C22⋊C4×C47—24no—
361C22⋊C4×C47—22no—
362C22⋊C4×C47—42no—
363C22⋊C4×C47—42no—
364C22⋊C4×C47—42no—
365C22⋊C4×C47—42no—
366C22⋊C4×C47—42no—
367C42×C47—42no—
368C22⋊Dic47—22no—
369C22⋊Dic47—22no—
370C22⋊Dic47—22no—
371C22⋊Dic47—24no—
372C22⋊Dic47—22no—
373C22⋊Dic47—42no—
374C22⋊Dic47—42no—
375C22⋊Dic47—42no—
376C22⋊Dic47—42no—
377C22⋊Dic47—42no—
378C22⋊Dic47C22×C414yes—
379C22⋊Dic47C22×C414yes—
380C22⋊Dic47C22×C414yes—
381C22⋊Dic47C22×C414yes—
382(C2×D47)⋊C4—42no—
383(C2×D47)⋊C4—42no—
384(C2×D47)⋊C4—42no—
385(C2×D47)⋊C4—42no—
386(C2×D47)⋊C4—42no—
387(C2×D47)⋊C4—42no—
388(C2×D47)⋊C4C22×C414yes—
389(C2×D47)⋊C4C22×C414yes—
390(C2×D47)⋊C4C22×C414yes—
391(C2×D47)⋊C4C22×C414yes—
392C4⋊Dic47—42no—
393Dic47⋊C4—24no—
394Dic47⋊C4—24no—
395Dic47⋊C4—42no—
396Dic47⋊C4—42no—
397Dic47⋊C4—42no—
398Dic47⋊C4—42no—
399Dic47⋊C4—42no—
400Dic47⋊C4—42no—
401Dic47⋊C4C22×C414yes—
402Dic47⋊C4C22×C414yes—
403Dic47⋊C4C22×C414yes—
404Dic47⋊C4C22×C414yes—
405C4×Dic47—24no—
406C4×Dic47—24no—
407C4×Dic47—42no—
408C4×Dic47—42no—
409C4×Dic47—42no—
410C23×C47—22no—
411C23×C47—22no—
412C23×C47—21no—
413C23×C47—22no—
414C23×C47—21no—
415C23×C47—28no—
416C23×C47—28no—
417C23×C47—21no—
418C23×C47—21no—
419C23×C47—22no—
420C23×C47—22no—
421C23×C47—22no—
422C23×C47—21no—
423C23×C47—22no—
424C23×C47—22no—
425C23×C47—22no—
426C23×C47—21no—
427C23×C47—21no—
428C23×C47—21no—
429C23×C47—28no—
430C23×C47—44no—
431C23×C47—44no—
432C23×C47—44no—
433C23×C47—48no—
434C23×C47—48no—
435C23×C47—84no—
436C23×C47—84no—
437C23×C47C23×C412yes—
438C23×C47C23×C412yes—
439C23×C47C23×C412yes—
440C23×C47C23×C412yes—
441C23×C47C23×C412yes—
442C23×C47H(5,𝔽2)14yes—
443C23×C47H(5,𝔽2)12yes—
444C23×C472−1+412yes—
445C23×C47C2511yescharacteristic
446C22×D47—21no—
447C22×D47—21no—
448C22×D47—22no—
449C22×D47—22no—
450C22×D47—22no—
451C22×D47—22no—
452C22×D47—21no—
453C22×D47—21no—
454C22×D47—28no—
455C22×D47—44no—
456C22×D47—44no—
457C22×D47—84no—
458C22×D47—84no—
459C22×D47C23×C412yes—
460C22×D47C23×C412yes—
461D4×C47—28no—
462D4×C47—28no—
463D4×C47—44no—
464D4×C47—44no—
465C2×C4×C47—22no—
466C2×C4×C47—22no—
467C2×C4×C47—22no—
468C2×C4×C47—22no—
469C2×C4×C47—22no—
470C2×C4×C47—22no—
471C2×C4×C47—22no—
472C2×C4×C47—22no—
473C2×C4×C47—22no—
474C2×C4×C47—22no—
475C2×C4×C47—22no—
476C2×C4×C47—22no—
477C2×C4×C47—22no—
478C2×C4×C47—22no—
479C2×C4×C47—44no—
480C2×C4×C47—84no—
481C2×C4×C47—84no—
482C2×C4×C47C23×C412yes—
483C2×C4×C47C23×C412yes—
484C22⋊D47—28no—
485C22⋊D47—28no—
486C22⋊D47—28no—
487C22⋊D47—28no—
488C22⋊D47—44no—
489C22⋊D47—44no—
490C22⋊D47—44no—
491C22⋊D47—44no—
492C2×Dic47—22no—
493C2×Dic47—22no—
494C2×Dic47—22no—
495C2×Dic47—22no—
496C2×Dic47—22no—
497C2×Dic47—28no—
498C2×Dic47—28no—
499C2×Dic47—28no—
500C2×Dic47—22no—
501C2×Dic47—22no—
502C2×Dic47—22no—
503C2×Dic47—22no—
504C2×Dic47—22no—
505C2×Dic47—22no—
506C2×Dic47—22no—
507C2×Dic47—22no—
508C2×Dic47—22no—
509C2×Dic47—22no—
510C2×Dic47—22no—
511C2×Dic47—22no—
512C2×Dic47—44no—
513C2×Dic47—44no—
514C2×Dic47—44no—
515C2×Dic47—44no—
516C2×Dic47—84no—
517C2×Dic47—84no—
518C2×Dic47C23×C412yes—
519C2×Dic47C23×C412yes—
520C2×Dic47C23×C412yes—
521C2×Dic47C23×C412yes—
522C2×Dic47C23×C412yes—
523C2×Dic47C23×C412yes—
524C2×Dic47H(5,𝔽2)14yes—
525C4×D47—84no—
526C4×D47—84no—
527#34379—471nomaximal, Sylow
528C22×C47—22no—
529C22×C47—22no—
530C22×C47—22no—
531C22×C47—22no—
532C22×C47—24no—
533C22×C47—24no—
534C22×C47—24no—
535C22×C47—24no—
536C22×C47—22no—
537C22×C47—22no—
538C22×C47—22no—
539C22×C47—22no—
540C22×C47—22no—
541C22×C47—22no—
542C22×C47—22no—
543C22×C47—22no—
544C22×C47—22no—
545C22×C47—416no—
546C22×C47—42no—
547C22×C47—42no—
548C22×C47—42no—
549C22×C47—42no—
550C22×C47—42no—
551C22×C47—42no—
552C22×C47—88no—
553C22×C47#51814yes—
554C22×C47#52014yes—
555C22×C47C24×C411yescharacteristic
556C22×C47C2×H(5,𝔽2)12yes—
557C22×C47C2×H(5,𝔽2)12yes—
558C22×C47C2×H(5,𝔽2)11yescharacteristic
559C22×C47C2×2−1+411yescharacteristic
560C2×D47—22no—
561C2×D47—22no—
562C2×D47—22no—
563C2×D47—22no—
564C2×D47—22no—
565C2×D47—22no—
566C2×D47—42no—
567C2×D47—42no—
568C2×D47—42no—
569C2×D47—42no—
570C2×D47—88no—
571C4×C47—22no—
572C4×C47—22no—
573C4×C47—42no—
574C4×C47—42no—
575C4×C47—42no—
576C4×C47—42no—
577Dic47—22no—
578Dic47—22no—
579Dic47—22no—
580Dic47—22no—
581Dic47—22no—
582Dic47—42no—
583Dic47—42no—
584Dic47—42no—
585Dic47—42no—
586Dic47#51814yes—
587C22×#121—471no—
588#2377—472no—
589#2377—472no—
590#2361—472no—
591#2361—472no—
592#2345—471no—
593#2345—471no—
594D4×C22⋊C4—471no—
595D4×C22⋊C4—471no—
596D4×C22⋊C4—471no—
597D4×C22⋊C4—471no—
598D4×C22⋊C4—471no—
599D4×C22⋊C4D4711yescharacteristic, complemented
600#2325—472no—
601#2325—472no—
602#2324—472no—
603#2324—472no—
604#2315—471no—
605#2315—471no—
606#2312—471no—
607#2312—471no—
608#2280—471no—
609C2×#380—471no—
610C2×C47—24no—
611C2×C47—24no—
612C2×C47—42no—
613C2×C47—42no—
614C2×C47—42no—
615C2×C47C2×#51811yescharacteristic
616C2×C47C2×#51811yescharacteristic
617C2×C47C2×#52011yescharacteristic
618C2×C47#353612yes—
619C2×C47#353712yes—
620D47—42no—
621D47—42no—
622C23×D4—471no—
623C23×D4—471no—
624C23×D4C2×D4711yescharacteristic
625C24×C4—471no—
626C2×#121—4716no—
627C2×#121—471no—
628C2×#121—471no—
629C2×#121—471no—
630C2×#121—471no—
631C2×#121—471no—
632C2×#121—471no—
633C2×#121—471no—
634C2×#121—471no—
635C2×C4×D4—472no—
636C2×C4×D4—472no—
637C2×C4×D4—472no—
638C2×C4×D4—472no—
639C2×C4×D4—472no—
640C2×C4×D4C2×D4712yescomplemented
641C2×#117—472no—
642C22×C4⋊C4—471no—
643C22×C4⋊C4—472no—
644C22×C22⋊C4—471no—
645C22×C22⋊C4—471no—
646C22×C22⋊C4—471no—
647C22×C22⋊C4—471no—
648C22×C22⋊C4—471no—
649C22×C22⋊C4—471no—
650C22×C22⋊C4C2×D4711yescharacteristic
651C22×C22⋊C4C2×D4711yescharacteristic
652#390—472no—
653#390—472no—
654#390—472no—
655#390—472no—
656#390—472no—
657#390C2×D4712yescomplemented
658#389—472no—
659#389—472no—
660#388—472no—
661#388—472no—
662#388—472no—
663#388—472no—
664#388—472no—
665#388—472no—
666#388—472no—
667#388—472no—
668#387—472no—
669#387—472no—
670#387—472no—
671#387—472no—
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#386—472no—
681#386—472no—
682#386C2×D4712yescomplemented
683#386C2×D4712yescomplemented
684#385—472no—
685#385—472no—
686#385—472no—
687#385—472no—
688#385—472no—
689#385—472no—
690#385—472no—
691#385—472no—
692#381—472no—
693#380—471no—
694#380—471no—
695#380—471no—
696#380—471no—
697#380—471no—
698#380—471no—
699#380—471no—
700#380—472no—
701#380—472no—
702#380—471no—
703#380—471no—
704#380—472no—
705#380C2×D4711yescharacteristic
706#379—471no—
707#379—471no—
708#379—471no—
709#379—471no—
710#379C2×D4711yescharacteristic
711#379C2×D4711yescharacteristic
712C4×C4⋊C4—472no—
713C4×C4⋊C4—472no—
714C4×C22⋊C4—471no—
715C4×C22⋊C4—471no—
716C4×C22⋊C4—471no—
717C4×C22⋊C4—471no—
718C4×C22⋊C4—471no—
719C4×C22⋊C4—472no—
720C4×C22⋊C4C2×D4711yescharacteristic
721C2×#95—472no—
722C47#3437911yescharacteristic, complemented, Sylow
723C25—471no—
724C25C22×D4711yescharacteristic
725C25C22×D4711yescharacteristic
726C22×D4—44no—
727C22×D4—471no—
728C22×D4—471no—
729C22×D4—471no—
730C22×D4—471no—
731C22×D4—478no—
732C22×D4—478no—
733C22×D4—471no—
734C22×D4—471no—
735C22×D4—471no—
736C22×D4—471no—
737C22×D4—1884no—
738C22×D4—1884no—
739C22×D4C4×D4718yescomplemented
740C22×D4C22×D4711yescharacteristic
741C22×D4C22×D4711yescharacteristic
742C22×D4C22×D4711yescharacteristic
743C22×D4C22×D4711yescharacteristic
744C23×C4—471no—
745C23×C4—471no—
746C23×C4—471no—
747C23×C4—478no—
748C23×C4—471no—
749C23×C4—471no—
750C23×C4—471no—
751C23×C4—471no—
752C23×C4—472no—
753C23×C4—472no—
754C23×C4—472no—
755C23×C4—472no—
756C23×C4—1884no—
757C23×C4C22×D4712yes—
758C23×C4C22×D4712yes—
759C23×C4C22×D4711yescharacteristic
760#121—478no—
761#121—478no—
762#121—478no—
763#121—478no—
764#121—478no—
765#121—478no—
766#121—478no—
767#121—478no—
768C4×D4—44no—
769C4×D4—1884no—
770C4×D4—1884no—
771C4×D4—1884no—
772C4×D4—1884no—
773C4×D4—1884no—
774#117—1884no—
775C2×C4⋊C4—478no—
776C2×C4⋊C4—471no—
777C2×C4⋊C4—471no—
778C2×C4⋊C4—471no—
779C2×C4⋊C4—471no—
780C2×C4⋊C4—472no—
781C2×C4⋊C4—472no—
782C2×C4⋊C4—472no—
783C2×C4⋊C4—472no—
784C2×C4⋊C4—472no—
785C2×C4⋊C4—472no—
786C2×C4⋊C4—472no—
787C2×C4⋊C4—472no—
788C2×C4⋊C4—472no—
789C2×C4⋊C4—1884no—
790C2×C4⋊C4C22×D4712yes—
791C2×C22⋊C4—42no—
792C2×C22⋊C4—42no—
793C2×C22⋊C4—478no—
794C2×C22⋊C4—471no—
795C2×C22⋊C4—471no—
796C2×C22⋊C4—471no—
797C2×C22⋊C4—471no—
798C2×C22⋊C4—478no—
799C2×C22⋊C4—471no—
800C2×C22⋊C4—471no—
801C2×C22⋊C4—471no—
802C2×C22⋊C4—471no—
803C2×C22⋊C4—471no—
804C2×C22⋊C4—471no—
805C2×C22⋊C4—471no—
806C2×C22⋊C4—472no—
807C2×C22⋊C4—471no—
808C2×C22⋊C4—472no—
809C2×C22⋊C4—472no—
810C2×C22⋊C4—472no—
811C2×C22⋊C4—472no—
812C2×C22⋊C4—472no—
813C2×C22⋊C4—472no—
814C2×C22⋊C4—472no—
815C2×C22⋊C4—472no—
816C2×C22⋊C4—472no—
817C2×C22⋊C4—472no—
818C2×C22⋊C4—472no—
819C2×C22⋊C4—1882no—
820C2×C22⋊C4—1882no—
821C2×C22⋊C4—1882no—
822C2×C22⋊C4—1882no—
823C2×C22⋊C4C22×D4711yescharacteristic
824C2×C22⋊C4C22×D4711yescharacteristic
825C2×C22⋊C4C22×D4711yescharacteristic
826C2×C22⋊C4C22×D4712yes—
827C2×C22⋊C4C22×D4711yescharacteristic
828C2×C22⋊C4C22×D4712yes—
829C2×C22⋊C4C22×D4712yes—
830C2×C22⋊C4C22×D4712yes—
831C2×C22⋊C4C22×D4712yes—
832C2×C22⋊C4C22×D4712yes—
833C2×C42—472no—
834C2×C42—472no—
835C2×C42—472no—
836C2×C42—472no—
837C2×C42—472no—
838C2×C42C22×D4712yes—
839#95—472no—
840#95—472no—
841#95—472no—
842#95—472no—
843#95—472no—
844#95—472no—
845#95—472no—
846#95—472no—
847#95—472no—
848#95—472no—
849#95—472no—
850#95—472no—
851#95—472no—
852#95—472no—
853#95C22×D4712yes—
854#95C22×D4712yes—
855C24—22no—
856C24—24no—
857C24—22no—
858C24—22no—
859C24—22no—
860C24—42no—
861C24—42no—
862C24—42no—
863C24—471no—
864C24—471no—
865C24—474no—
866C24—942no—
867C24—942no—
868C24—1882no—
869C24—1882no—
870C24C2×C4×D4714yes—
871C24C2×C4×D4714yes—
872C24C23×D4711yescharacteristic
873C24C23×D4711yescharacteristic
874C24C23×D4711yescharacteristic
875C24C23×D4711yescharacteristic
876C24C23×D4711yescharacteristic
877C2×D4—24no—
878C2×D4—24no—
879C2×D4—42no—
880C2×D4—42no—
881C2×D4—416no—
882C2×D4—474no—
883C2×D4—474no—
884C2×D4—474no—
885C2×D4—474no—
886C2×D4—474no—
887C2×D4—474no—
888C2×D4—474no—
889C2×D4—474no—
890C2×D4—944no—
891C2×D4—944no—
892C2×D4—944no—
893C2×D4—944no—
894C2×D4—18816no—
895C2×D4—1882no—
896C2×D4—1882no—
897C2×D4—1882no—
898C2×D4—1882no—
899C2×D4—18816no—
900C2×D4C2×C4×D4714yes—
901C2×D4C2×C4×D4714yes—
902C2×D4C2×C4×D4714yes—
903C2×D4C2×C4×D4714yes—
904C22×C4—24no—
905C22×C4—42no—
906C22×C4—42no—
907C22×C4—42no—
908C22×C4—42no—
909C22×C4—42no—
910C22×C4—42no—
911C22×C4—471no—
912C22×C4—474no—
913C22×C4—474no—
914C22×C4—474no—
915C22×C4—471no—
916C22×C4—471no—
917C22×C4—471no—
918C22×C4—471no—
919C22×C4—471no—
920C22×C4—474no—
921C22×C4—474no—
922C22×C4—474no—
923C22×C4—474no—
924C22×C4—472no—
925C22×C4—472no—
926C22×C4—472no—
927C22×C4—472no—
928C22×C4—944no—
929C22×C4—944no—
930C22×C4—944no—
931C22×C4—944no—
932C22×C4—1882no—
933C22×C4—1882no—
934C22×C4—1882no—
935C22×C4—1882no—
936C22×C4—1882no—
937C22×C4—1882no—
938C22×C4—18816no—
939C22×C4—1882no—
940C22×C4—1882no—
941C22×C4—1882no—
942C22×C4—1882no—
943C22×C4—1882no—
944C22×C4—1882no—
945C22×C4—1882no—
946C22×C4—1882no—
947C22×C4—1882no—
948C22×C4C2×C4×D4714yes—
949C22×C4C23×D4712yes—
950C22×C4C23×D4712yes—
951C22×C4C23×D4712yes—
952C22×C4C23×D4712yes—
953C22×C4C23×D4711yescharacteristic
954C22×C4C23×D4711yescharacteristic
955C4⋊C4—42no—
956C4⋊C4—474no—
957C4⋊C4—474no—
958C4⋊C4—474no—
959C4⋊C4—474no—
960C4⋊C4—944no—
961C4⋊C4—944no—
962C4⋊C4—1882no—
963C4⋊C4—1882no—
964C4⋊C4—1882no—
965C4⋊C4—1882no—
966C4⋊C4—1882no—
967C4⋊C4—1882no—
968C4⋊C4—1882no—
969C22⋊C4—22no—
970C22⋊C4—22no—
971C22⋊C4—22no—
972C22⋊C4—24no—
973C22⋊C4—22no—
974C22⋊C4—42no—
975C22⋊C4—42no—
976C22⋊C4—42no—
977C22⋊C4—42no—
978C22⋊C4—42no—
979C22⋊C4—474no—
980C22⋊C4—474no—
981C22⋊C4—474no—
982C22⋊C4—474no—
983C22⋊C4—474no—
984C22⋊C4—474no—
985C22⋊C4—474no—
986C22⋊C4—474no—
987C22⋊C4—942no—
988C22⋊C4—942no—
989C22⋊C4—942no—
990C22⋊C4—944no—
991C22⋊C4—942no—
992C22⋊C4—1882no—
993C22⋊C4—1882no—
994C22⋊C4—1882no—
995C22⋊C4—1882no—
996C22⋊C4—1882no—
997C22⋊C4—1882no—
998C22⋊C4—1882no—
999C22⋊C4—1882no—
1000C22⋊C4—1882no—
1001C22⋊C4—1882no—
1002C22⋊C4—1882no—
1003C42—42no—
1004C42—944no—
1005C42—944no—
1006C42—1882no—
1007C42—1882no—
1008C42—1882no—
1009C23—22no—
1010C23—22no—
1011C23—21no—
1012C23—22no—
1013C23—21no—
1014C23—28no—
1015C23—28no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—21no—
1020C23—21no—
1021C23—22no—
1022C23—21no—
1023C23—22no—
1024C23—22no—
1025C23—21no—
1026C23—21no—
1027C23—21no—
1028C23—28no—
1029C23—44no—
1030C23—44no—
1031C23—44no—
1032C23—48no—
1033C23—48no—
1034C23—84no—
1035C23—84no—
1036C23—472no—
1037C23—472no—
1038C23—948no—
1039C23—942no—
1040C23—942no—
1041C23—941no—
1042C23—941no—
1043C23—942no—
1044C23—942no—
1045C23—941no—
1046C23—941no—
1047C23—3764no—
1048C23—3764no—
1049C23—1884no—
1050C23—1884no—
1051C23C22×C4×D4712yes—
1052C23C22×C4×D4712yes—
1053C23C22×C4×D4712yes—
1054C23C22×C4×D4712yes—
1055C23C22×C4×D4712yes—
1056C23#1309406914yes—
1057C23#1309406912yes—
1058C23#1309407112yes—
1059C23C24×D4711yescharacteristic
1060D4—28no—
1061D4—28no—
1062D4—44no—
1063D4—44no—
1064D4—948no—
1065D4—948no—
1066D4—948no—
1067D4—948no—
1068D4—1884no—
1069D4—1884no—
1070D4—1884no—
1071D4—1884no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—44no—
1087C2×C4—84no—
1088C2×C4—84no—
1089C2×C4—472no—
1090C2×C4—474no—
1091C2×C4—472no—
1092C2×C4—472no—
1093C2×C4—472no—
1094C2×C4—472no—
1095C2×C4—472no—
1096C2×C4—948no—
1097C2×C4—948no—
1098C2×C4—948no—
1099C2×C4—942no—
1100C2×C4—942no—
1101C2×C4—942no—
1102C2×C4—942no—
1103C2×C4—942no—
1104C2×C4—942no—
1105C2×C4—942no—
1106C2×C4—942no—
1107C2×C4—942no—
1108C2×C4—942no—
1109C2×C4—942no—
1110C2×C4—942no—
1111C2×C4—942no—
1112C2×C4—942no—
1113C2×C4—942no—
1114C2×C4—942no—
1115C2×C4—942no—
1116C2×C4—3764no—
1117C2×C4—3764no—
1118C2×C4—3764no—
1119C2×C4—3764no—
1120C2×C4—1884no—
1121C2×C4—1884no—
1122C2×C4—1884no—
1123C2×C4—1884no—
1124C2×C4C22×C4×D4712yes—
1125C2×C4C22×C4×D4712yes—
1126C22—22no—
1127C22—22no—
1128C22—22no—
1129C22—24no—
1130C22—24no—
1131C22—22no—
1132C22—24no—
1133C22—24no—
1134C22—22no—
1135C22—22no—
1136C22—22no—
1137C22—22no—
1138C22—22no—
1139C22—22no—
1140C22—22no—
1141C22—22no—
1142C22—22no—
1143C22—416no—
1144C22—42no—
1145C22—42no—
1146C22—42no—
1147C22—42no—
1148C22—42no—
1149C22—42no—
1150C22—88no—
1151C22—942no—
1152C22—942no—
1153C22—942no—
1154C22—942no—
1155C22—942no—
1156C22—942no—
1157C22—3768no—
1158C22—1882no—
1159C22—1882no—
1160C22—1882no—
1161C22—1882no—
1162C22#1568959614yes—
1163C22#1568960214yes—
1164C22C23×C4×D4711yescharacteristic
1165C22H(5,𝔽2)×D4712yes—
1166C22C2×#1309406912yes—
1167C22C2×#1309406911yescharacteristic
1168C22C2×#1309407111yescharacteristic
1169C4—22no—
1170C4—22no—
1171C4—42no—
1172C4—42no—
1173C4—42no—
1174C4—42no—
1175C4—474no—
1176C4—942no—
1177C4—942no—
1178C4—942no—
1179C4—942no—
1180C4—942no—
1181C4—1882no—
1182C4—1882no—
1183C4—1882no—
1184C4—1882no—
1185C2—24no—
1186C2—24no—
1187C2—42no—
1188C2—42no—
1189C2—42no—
1190C2—1882no—
1191C2—1882no—
1192C2#518×D4711yescharacteristic
1193C2C2×#1568959611yescharacteristic
1194C2C2×#1568960211yescharacteristic
1195C2#2025760312yes—
1196C2#2025761812yes—
subgroupG/H
center, FrattiniC23C24×D47
commutatorC22×C47C24×C4
FittingD4×C22⋊C4×C47C2
socle, cosocleC23×C47C25
prime radicalC22×#13093996C2
hypercenterD4×C22⋊C4D47
hypocenterC47#34379
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #20246546C2semidirect
3. #20246539C2semidirect
4. #20246405C2semidirect
5. #20246399C2semidirect
6. #20246266C2semidirect
7. #20246260C2semidirect
8. D4×C22⋊Dic47C2semidirect
9. C22⋊C4×C22⋊D47C2semidirect
10. C22⋊C4×C22⋊D47C2semidirect
11. #20246204C2semidirect
12. #20246204C2semidirect
13. #20246089C2semidirect
14. #20246086C2semidirect
15. #20246078C2semidirect
16. #20246074C2semidirect
17. #20246001C2semidirect
18. #20246000C2semidirect
19. #20245984C2semidirect
20. #20245983C2semidirect
21. #20245766C2semidirect
22. C2×#15688981C2semidirect
23. D4×C22⋊C4×C47C2semidirect
27. C2×#13093996C4semidirect
36. C2×D4×Dic47C22semidirect
37. C2×C4×C22⋊D47C22semidirect
38. C2×C4×C22⋊D47C22semidirect
39. C2×(C22⋊D47)⋊C4C22semidirect
40. C2×(C22⋊D47)⋊C4C22semidirect
41. C2×#13093980C22semidirect
43. C22×Dic47⋊C4C22semidirect
50. #15689026C22semidirect
51. #15689023C22semidirect
52. #15689023C22semidirect
53. #15689023C22semidirect
54. #15689023C22semidirect
55. #15689020C22semidirect
56. #15689018C22semidirect
57. #15689017C22semidirect
58. #15689017C22semidirect
59. #15689014C22semidirect
60. #15689014C22semidirect
61. #15689012C22semidirect
62. #15689012C22semidirect
63. #15689011C22semidirect
64. #15689011C22semidirect
65. #15689010C22semidirect
66. #15689007C22semidirect
67. #15689005C22semidirect
68. #15689004C22semidirect
69. #15689003C22semidirect
70. #15689003C22semidirect
71. #15689002C22semidirect
72. #15689002C22semidirect
73. #15689000C22semidirect
74. #15689000C22semidirect
75. #15688999C22semidirect
76. #15688999C22semidirect
77. #15688999C22semidirect
78. #15688999C22semidirect
79. #15688997C22semidirect
80. #15688997C22semidirect
81. #15688996C22semidirect
82. #15688996C22semidirect
83. #15688995C22semidirect
84. #15688995C22semidirect
85. #15688994C22semidirect
86. #15688994C22semidirect
87. #15688984C22semidirect
97. #15688981C22semidirect
98. #15688981C22semidirect
99. #15688981C22semidirect
104. C4×Dic47⋊C4C22semidirect
105. #15688974C22semidirect
110. C22⋊C4×Dic47C22semidirect
112. C2×C47⋊#95C22semidirect
114. C2×C4×D4×C47C22semidirect
117. C47×#390C22semidirect
118. C47×#386C22semidirect
119. C47×#386C22semidirect
127. C22×C22⋊D47C2×C4semidirect
128. C22×C22⋊D47C2×C4semidirect
138. C23×Dic47C2×C4semidirect
150. #13093996C2×C4semidirect
151. #13093996C2×C4semidirect
152. #13093996C2×C4semidirect
153. #13093996C2×C4semidirect
154. #13093996C2×C4semidirect
155. #13093996C2×C4semidirect
156. #13093996C2×C4semidirect
157. #13093996C2×C4semidirect
166. C2×Dic47⋊C4C2×C4semidirect
181. C2×C22⋊Dic47C2×C4semidirect
196. C2×(C2×D47)⋊C4C2×C4semidirect
231. C22×D4×C47C2×C4semidirect
599. D4×C22⋊C4D47semidirect
640. C2×C4×D4C2×D47semidirect
657. #390C2×D47semidirect
682. #386C2×D47semidirect
683. #386C2×D47semidirect
722. C47#34379semidirect
739. C22×D4C4×D47semidirect

Maximal subgroups

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

subgroupindex
C22×#130939962
#202465462
#202465392
#202464052
#202463992
#202462662
#202462602
D4×C22⋊Dic472
C22⋊C4×C22⋊D472
#202462042
#202460892
#202460862
#202460782
#202460742
#202460012
#202460002
#202459842
#202459832
#202457662
C2×#156889812
D4×C22⋊C4×C472
#3437947