Finite Group Databasebeta

← #26384462

Subgroups — #26384462

Order 12032.

2992 conjugacy classes of subgroups.

The subgroup lattice has 1166 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689655C211yesmaximal, characteristic, complemented
2C2×C4×D4×D47C211yesmaximal, characteristic, complemented
3#20247632C212yesmaximal, complemented
4#20247452C212yesmaximal, complemented
5#20247293C212yesmaximal, complemented
6#20247258C211yesmaximal, characteristic, complemented
7#20247173C211yesmaximal, characteristic, complemented
8#20247110C211yesmaximal, characteristic, complemented
9#20247038C211yesmaximal, characteristic, complemented
10#20246963C211yesmaximal, characteristic, complemented
11#20246878C211yesmaximal, characteristic, complemented
12#20246855C212yesmaximal, complemented
13#20246837C211yesmaximal, characteristic, complemented
14#20246742C211yesmaximal, characteristic
15#20246648C212yesmaximal, complemented
16#20246624C212yesmaximal, complemented
17C4×#13094012C211yesmaximal, characteristic, complemented
18C4×#13094004C211yesmaximal, characteristic, complemented
19C4×#13093999C211yesmaximal, characteristic, complemented
20C4×#13093994C212yesmaximal, complemented
21#20245767C212yesmaximal, complemented
22C42×D188C211yesmaximal, characteristic, complemented
23C47×#2293C211yesmaximal, characteristic, complemented
24C22×D4×D47C2211yescharacteristic
25C23×C4×D47C2212yes—
26#15689655—28no—
27C2×#13094017C2212yescomplemented
28C2×#13094015C2211yescharacteristic, complemented
29C2×#13094012C2211yescharacteristic
30C2×#13094011C2211yescharacteristic
31C2×#13094006C2212yescomplemented
32C2×#13094004C2211yescharacteristic
33C2×#13094004C2211yescharacteristic, complemented
34C2×#13093999C2211yescharacteristic
35C2×#13093995C2211yescharacteristic
36C2×#13093994C2212yes—
37C2×C4×Dic94C2211yescharacteristic, complemented
38C2×C4×D188C2211yescharacteristic
39C2×C4×D188C2211yescharacteristic
40C2×C4×D188C2211yescharacteristic
41C2×C4×D188C2211yescharacteristic
42C2×C4×D188C2212yescomplemented
43C2×D4×Dic47C2211yescharacteristic
44C2×#13093986C2211yescharacteristic
45C2×C4×C22⋊D47C2212yes—
46C2×C4×C22⋊D47C2212yescomplemented
47C2×(C22⋊D47)⋊C4C2212yes—
48C4×D4×D47—28no—
49C2×#13093983C2212yescomplemented
50C2×C4⋊C4×D47C2211yescharacteristic
51C2×C22⋊C4×D47C2212yes—
52C2×C42×D47C2211yescharacteristic
53C2×C42×D47C2211yescharacteristic, complemented
54#15689063C2212yescomplemented
55#15689060C2212yescomplemented
56#15689055C2212yescomplemented
57#15689053C2212yescomplemented
58#15689050C2212yescomplemented
59#15689048C2212yescomplemented
60#15689048C2212yescomplemented
61#15689048C2212yescomplemented
62#15689045C2212yescomplemented
63#15689045C2212yescomplemented
64#15689040C2212yescomplemented
65#15689039C2212yes—
66#15689039C2212yes—
67#15689039C2212yes—
68#15689039C2212yescomplemented
69#15689032C2212yes—
70#15689029C2211yescharacteristic, complemented
71#15689028C2211yescharacteristic, complemented
72#15689025C2211yescharacteristic
73#15689024C2211yescharacteristic
74#15689022C2211yescharacteristic, complemented
75#15689022C2211yescharacteristic, complemented
76#15689015C2212yescomplemented
77#15689014C2212yescomplemented
78#15689014C2212yescomplemented
79#15689008C2212yescomplemented
80#15689001C2212yes—
81#15689001C2212yescomplemented
82#15689001C2212yescomplemented
83#15689000C2212yescomplemented
84#15688998C2212yescomplemented
85#15688997C2212yes—
86#15688997C2212yes—
87#15688997C2212yescomplemented
88#15688989C2211yescharacteristic, complemented
89#15688984C2212yescomplemented
90#15688984C2212yescomplemented
91#15688980C2212yes—
92#15688980C2212yes—
93#15688980C2211yescharacteristic
94#15688980C2212yescomplemented
95#15688980C2212yescomplemented
96#15688980C2211yescharacteristic, complemented
97#15688978C2212yes—
98#15688978C2212yes—
99#15688978C2212yes—
100C4×C4⋊Dic47C2212yescomplemented
101C4×C4⋊Dic47C2211yescharacteristic, complemented
102C4×C4⋊Dic47C2211yescharacteristic, complemented
103C4×C4⋊Dic47C2211yescharacteristic, complemented
104C4×(C2×D47)⋊C4C2211yescharacteristic
105C4×(C2×D47)⋊C4C2212yes—
106C4×(C2×D47)⋊C4C2211yescharacteristic
107C4×(C2×D47)⋊C4C2211yescharacteristic
108C4×(C2×D47)⋊C4C2212yescomplemented
109C4×(C2×D47)⋊C4C2212yescomplemented
110C4×(C2×D47)⋊C4C2211yescharacteristic, complemented
111C4×(C2×D47)⋊C4C2211yescharacteristic, complemented
112C4×(C2×D47)⋊C4C2212yescomplemented
113C4×(C2×D47)⋊C4C2211yescharacteristic, complemented
114C2×C4×D4×C47C2211yescharacteristic
115C2×#117×C47C2212yescomplemented
116C47×#390C2211yescharacteristic
117C47×#390C2211yescharacteristic
118C47×#389C2211yescharacteristic, complemented
119C47×#389C2211yescharacteristic, complemented
120C47×#388C2212yescomplemented
121C47×#388C2212yescomplemented
122C4×C4⋊C4×C47C2211yescharacteristic, complemented
123C4×C22⋊C4×C47C2212yescomplemented
124C43×C47C2211yescharacteristic, complemented
125C24×D47C2312yes—
126C22×Dic94C2311yescharacteristic
127C22×D188C2312yes—
128C22×D188C2311yescharacteristic
129C22×D188C2311yescharacteristic
130C22×C22⋊D47C2312yes—
131C22×C22⋊D47C2312yes—
132C2×D4×D47—24no—
133C2×D4×D47—24no—
134C2×D4×D47—24no—
135C23×Dic47C2312yes—
136C22×C4×D47—28no—
137C22×C4×D47—28no—
138C22×C4×D47—44no—
139C22×C4×D47C2312yes—
140C22×C4×D47C2311yescharacteristic
141C22×C4×D47C2311yescharacteristic
142C22×C4×D47C2311yescharacteristic
143C22×C4×D47C2311yescharacteristic
144C22×C4×D47C2312yes—
145C22×C4×D47C2312yes—
146C22×C4×D47C2311yescharacteristic
147C22×C4×D47C2311yescharacteristic
148#13094017—28no—
149#13094015—24no—
150#13094012—24no—
151#13094011—24no—
152#13094006—28no—
153#13094004—24no—
154#13094004—24no—
155#13093999—24no—
156#13093995—24no—
157#13093994—28no—
158C4×Dic94—24no—
159C4×D188—24no—
160C4×D188—24no—
161C4×D188—24no—
162C4×D188—24no—
163C4×D188—44no—
164D4×Dic47—24no—
165#13093986—24no—
166C4×C22⋊D47—28no—
167C4×C22⋊D47—28no—
168(C22⋊D47)⋊C4—28no—
169#13093983—28no—
170C2×C4⋊Dic47C2311yescharacteristic
171C2×C4⋊Dic47C2311yescharacteristic
172C2×C4⋊Dic47C2311yescharacteristic
173C2×C4⋊Dic47C2312yes—
174C2×C4⋊Dic47C2312yes—
175C2×C4⋊Dic47C2312yes—
176C2×C4⋊Dic47C2311yescharacteristic
177C2×C4⋊Dic47C2311yescharacteristic
178C2×C4⋊Dic47C2312yes—
179C2×C4⋊Dic47C2312yes—
180C2×Dic47⋊C4C2312yes—
181C2×Dic47⋊C4C2312yes—
182C2×Dic47⋊C4C2312yes—
183C4⋊C4×D47—24no—
184C2×C22⋊Dic47C2312yes—
185C2×C22⋊Dic47C2312yes—
186C2×C22⋊Dic47C2312yes—
187C2×C22⋊Dic47C2312yes—
188C2×(C2×D47)⋊C4C2311yescharacteristic
189C2×(C2×D47)⋊C4C2311yescharacteristic
190C2×(C2×D47)⋊C4C2311yescharacteristic
191C2×(C2×D47)⋊C4C2312yes—
192C2×(C2×D47)⋊C4C2312yes—
193C2×(C2×D47)⋊C4C2311yescharacteristic
194C2×(C2×D47)⋊C4C2311yescharacteristic
195C2×(C2×D47)⋊C4C2311yescharacteristic
196C2×(C2×D47)⋊C4C2312yes—
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)⋊C4C2312yes—
204C2×(C2×D47)⋊C4C2312yes—
205C2×(C2×D47)⋊C4C2312yes—
206C2×(C2×D47)⋊C4C2312yes—
207C22⋊C4×D47—28no—
208C2×C4×Dic47C2311yescharacteristic
209C2×C4×Dic47C2312yes—
210C2×C4×Dic47C2311yescharacteristic
211C2×C4×Dic47C2311yescharacteristic
212C2×C4×Dic47C2311yescharacteristic
213C2×C4×Dic47C2311yescharacteristic
214C2×C4×Dic47C2311yescharacteristic
215C42×D47—24no—
216C42×D47—24no—
217C47⋊#95C2311yescharacteristic
218C47⋊#95C2311yescharacteristic
219C47⋊#95C2311yescharacteristic
220C47⋊#95C2311yescharacteristic
221C47⋊#95C2311yescharacteristic
222C47⋊#95C2311yescharacteristic
223C47⋊#95C2312yes—
224C47⋊#95C2312yes—
225C47⋊#95C2312yes—
226C47⋊#95C2312yes—
227C47⋊#95C2312yes—
228C47⋊#95C2312yes—
229C47⋊#95C2312yes—
230C47⋊#95C2312yes—
231C47⋊#95C2312yes—
232C47⋊#95C2312yes—
233C22×D4×C47C2311yescharacteristic
234C23×C4×C47C2312yes—
235C4×D4×C47D418yescomplemented
236#117×C47—44no—
237C2×C4⋊C4×C47C2311yescharacteristic
238C2×C4⋊C4×C47C2311yescharacteristic
239C2×C4⋊C4×C47C2312yes—
240C2×C4⋊C4×C47C2312yes—
241C2×C4⋊C4×C47C2311yescharacteristic
242C2×C22⋊C4×C47C2312yes—
243C2×C22⋊C4×C47C2312yes—
244C2×C22⋊C4×C47C2312yes—
245C2×C22⋊C4×C47C2312yes—
246C2×C22⋊C4×C47C2312yes—
247C2×C42×C47C2311yescharacteristic
248C2×C42×C47C2312yes—
249C2×C42×C47C2311yescharacteristic
250C2×C42×C47C2311yescharacteristic
251C2×C42×C47C2311yescharacteristic
252C2×C42×C47C2311yescharacteristic
253C2×C42×C47C2311yescharacteristic
254C2×C42×C47C2311yescharacteristic
255#95×C47C2312yes—
256#95×C47C2312yes—
257#95×C47C2312yes—
258C24×C47C2412yes—
259C23×D47—24no—
260C23×D47—24no—
261C23×D47—24no—
262C23×D47—24no—
263C23×D47—24no—
264C23×D47—42no—
265C23×D47—42no—
266C23×D47C2412yes—
267C23×D47C2411yescharacteristic
268C23×D47C2411yescharacteristic
269C2×D4×C47—22no—
270C2×D4×C47—22no—
271C2×D4×C47C2×D414yes—
272C22×C4×C47—24no—
273C22×C4×C47—24no—
274C22×C4×C47C2×D418yes—
275C22×C4×C47C2411yescharacteristic
276C22×C4×C47C2411yescharacteristic
277C22×C4×C47C2411yescharacteristic
278C22×C4×C47C2412yes—
279C22×C4×C47C2412yes—
280C22×C4×C47C2411yescharacteristic
281C22×C4×C47C2412yes—
282C22×C4×C47C2411yescharacteristic
283C22×C4×C47C2411yescharacteristic
284C22×C4×C47C2411yescharacteristic
285C2×C22⋊D47—24no—
286C2×C22⋊D47—24no—
287C2×C22⋊D47—24no—
288C2×C22⋊D47—24no—
289C2×C22⋊D47—24no—
290C2×C22⋊D47—42no—
291C22×Dic47—24no—
292C22×Dic47—24no—
293C22×Dic47—42no—
294C22×Dic47C2412yes—
295C22×Dic47C2411yescharacteristic
296C22×Dic47C2411yescharacteristic
297C22×Dic47C2411yescharacteristic
298C22×Dic47C2412yes—
299C22×Dic47C2412yes—
300C22×Dic47C2411yescharacteristic
301C22×Dic47C2411yescharacteristic
302C22×Dic47C2411yescharacteristic
303D4×D47—232no—
304C2×D188—22no—
305C2×D188—22no—
306C2×D188—22no—
307C2×D188—22no—
308C2×D188—24no—
309C2×D188—24no—
310C2×D188—42no—
311C2×D188#4114yes—
312C2×D188#4114yes—
313C2×C4×D47—22no—
314C2×C4×D47—22no—
315C2×C4×D47—22no—
316C2×C4×D47—22no—
317C2×C4×D47—22no—
318C2×C4×D47—22no—
319C2×C4×D47—24no—
320C2×C4×D47—22no—
321C2×C4×D47—22no—
322C2×C4×D47—22no—
323C2×C4×D47—22no—
324C2×C4×D47—24no—
325C2×C4×D47—24no—
326C2×C4×D47—24no—
327C2×C4×D47—22no—
328C2×C4×D47—22no—
329C2×C4×D47—22no—
330C2×C4×D47—24no—
331C2×C4×D47—22no—
332C2×C4×D47—24no—
333C2×C4×D47—24no—
334C2×C4×D47—432no—
335C2×C4×D47—42no—
336C2×C4×D47—42no—
337C2×C4×D47—41no—
338C2×C4×D47—41no—
339C2×C4×D47#4114yes—
340C2×C4×D47#4114yes—
341C2×Dic94—22no—
342C2×Dic94—22no—
343C2×Dic94—22no—
344C4⋊C4×C47—22no—
345C4⋊C4×C47—22no—
346C4⋊C4×C47—42no—
347C4⋊C4×C47—42no—
348C4⋊C4×C47C2×D414yes—
349C22⋊C4×C47—24no—
350C22⋊C4×C47—42no—
351C22⋊C4×C47—42no—
352C22⋊C4×C47—42no—
353C22⋊C4×C47C2×D418yes—
354C42×C47—22no—
355C42×C47—22no—
356C42×C47—22no—
357C42×C47—22no—
358C42×C47—22no—
359C42×C47—24no—
360C42×C47—41no—
361C42×C47C2×D414yes—
362C22⋊Dic47—24no—
363C22⋊Dic47—24no—
364C22⋊Dic47—24no—
365C22⋊Dic47—24no—
366(C2×D47)⋊C4—22no—
367(C2×D47)⋊C4—22no—
368(C2×D47)⋊C4—22no—
369(C2×D47)⋊C4—22no—
370(C2×D47)⋊C4—24no—
371(C2×D47)⋊C4—24no—
372(C2×D47)⋊C4—24no—
373(C2×D47)⋊C4—24no—
374(C2×D47)⋊C4—24no—
375(C2×D47)⋊C4—24no—
376(C2×D47)⋊C4—24no—
377(C2×D47)⋊C4—24no—
378(C2×D47)⋊C4—24no—
379(C2×D47)⋊C4—22no—
380(C2×D47)⋊C4—22no—
381(C2×D47)⋊C4—42no—
382(C2×D47)⋊C4—42no—
383(C2×D47)⋊C4—42no—
384(C2×D47)⋊C4—42no—
385C4⋊Dic47—22no—
386C4⋊Dic47—24no—
387C4⋊Dic47—24no—
388C4⋊Dic47—22no—
389C4⋊Dic47—22no—
390C4⋊Dic47—22no—
391C4⋊Dic47—22no—
392C4⋊Dic47—24no—
393C4⋊Dic47—42no—
394C4⋊Dic47—42no—
395Dic47⋊C4—24no—
396Dic47⋊C4—24no—
397Dic47⋊C4—24no—
398C4×Dic47—22no—
399C4×Dic47—22no—
400C4×Dic47—22no—
401C4×Dic47—22no—
402C4×Dic47—22no—
403C4×Dic47—22no—
404C4×Dic47—24no—
405C23×C47—22no—
406C23×C47—22no—
407C23×C47—22no—
408C23×C47—22no—
409C23×C47—22no—
410C23×C47—22no—
411C23×C47C22×D414yes—
412C23×C47C2511yescharacteristic
413C22×D47—21no—
414C22×D47—21no—
415C22×D47—21no—
416C22×D47—21no—
417C22×D47—216no—
418C22×D47—21no—
419C22×D47—22no—
420C22×D47—21no—
421C22×D47—21no—
422C22×D47—22no—
423C22×D47—22no—
424C22×D47—21no—
425C22×D47—22no—
426C22×D47—21no—
427C22×D47—22no—
428C22×D47—22no—
429C22×D47—21no—
430C22×D47—48no—
431C22×D47—48no—
432C22×D47—48no—
433C22×D47—48no—
434C22×D47—48no—
435C22×D47—48no—
436C22×D47C2×#4114yes—
437C22×D47C2×#4112yes—
438C22×D47C2×#4112yes—
439C22×D47C2×#4112yes—
440C22×D47C2×#4112yes—
441D4×C47—28no—
442C2×C4×C47—21no—
443C2×C4×C47—21no—
444C2×C4×C47—21no—
445C2×C4×C47—22no—
446C2×C4×C47—22no—
447C2×C4×C47—21no—
448C2×C4×C47—216no—
449C2×C4×C47—22no—
450C2×C4×C47—21no—
451C2×C4×C47—21no—
452C2×C4×C47—21no—
453C2×C4×C47—21no—
454C2×C4×C47—21no—
455C2×C4×C47—22no—
456C2×C4×C47—22no—
457C2×C4×C47—22no—
458C2×C4×C47—22no—
459C2×C4×C47—21no—
460C2×C4×C47—21no—
461C2×C4×C47—22no—
462C2×C4×C47—21no—
463C2×C4×C47—21no—
464C2×C4×C47C22×D412yes—
465C2×C4×C47C22×D414yes—
466C2×C4×C47C22×D412yes—
467C2×C4×C47C22×D412yes—
468C2×C4×C47C2×#4112yes—
469C2×C4×C47C2×#4112yes—
470C2×C4×C47C2×#4112yes—
471C2×C4×C47C2×#4112yes—
472C2×C4×C47H(5,𝔽2)12yes—
473C22⋊D47—216no—
474C22⋊D47—48no—
475C2×Dic47—21no—
476C2×Dic47—21no—
477C2×Dic47—21no—
478C2×Dic47—21no—
479C2×Dic47—21no—
480C2×Dic47—21no—
481C2×Dic47—21no—
482C2×Dic47—21no—
483C2×Dic47—22no—
484C2×Dic47—22no—
485C2×Dic47—22no—
486C2×Dic47—22no—
487C2×Dic47—21no—
488C2×Dic47—21no—
489C2×Dic47—21no—
490C2×Dic47—21no—
491C2×Dic47—22no—
492C2×Dic47—21no—
493C2×Dic47—22no—
494C2×Dic47—22no—
495C2×Dic47—21no—
496C2×Dic47—22no—
497C2×Dic47—21no—
498C2×Dic47—22no—
499C2×Dic47—21no—
500C2×Dic47—48no—
501C2×Dic47C2×#4112yes—
502C2×Dic47C2×#4112yes—
503D188—28no—
504D188—28no—
505D188—48no—
506C4×D47—28no—
507C4×D47—28no—
508C4×D47—48no—
509C4×D47—44no—
510C4×D47—44no—
511C4×D47—48no—
512C4×D47—44no—
513C4×D47—44no—
514C4×D47—48no—
515Dic94—44no—
516#34700—471nomaximal, Sylow
517C22×C47—24no—
518C22×C47—24no—
519C22×C47—24no—
520C22×C47—42no—
521C22×C47—42no—
522C22×C47—42no—
523C22×C47—42no—
524C22×C47C23×D411yescharacteristic
525C22×C47C22×#4111yescharacteristic
526C22×C47C22×#4111yescharacteristic
527C22×C47C22×#4111yescharacteristic
528C22×C47C22×#4111yescharacteristic
529C22×C47C2×H(5,𝔽2)11yescharacteristic
530C22×C47#58511yescharacteristic
531C2×D47—22no—
532C2×D47—22no—
533C2×D47—22no—
534C2×D47—22no—
535C2×D47—22no—
536C2×D47—22no—
537C2×D47—24no—
538C2×D47—22no—
539C2×D47—22no—
540C2×D47—24no—
541C2×D47—22no—
542C2×D47—24no—
543C2×D47—432no—
544C2×D47—41no—
545C2×D47—42no—
546C2×D47—41no—
547C2×D47—42no—
548C2×D47—42no—
549C2×D47—41no—
550C2×D47—42no—
551C2×D47—41no—
552C2×D47#52914yescomplemented
553C4×C47—22no—
554C4×C47—24no—
555C4×C47—22no—
556C4×C47—42no—
557C4×C47—41no—
558C4×C47—41no—
559C4×C47—42no—
560C4×C47—41no—
561C4×C47#52514yes—
562C4×C47#54614yes—
563Dic47—22no—
564Dic47—22no—
565Dic47—42no—
566Dic47—41no—
567Dic47—42no—
568Dic47—41no—
569Dic47—41no—
570Dic47—41no—
571Dic47—42no—
572C2×#529—471no—
573C22×C4×D4—471no—
574#2480—472no—
575#2468—472no—
576#2457—472no—
577#2454—471no—
578#2447—471no—
579#2442—471no—
580#2435—471no—
581#2427—471no—
582#2420—471no—
583#2418—472no—
584#2417—471no—
585#2408—471no—
586#2395—472no—
587#2392—472no—
588C4×#124—471no—
589C4×C22⋊Q8—471no—
590C4×#121—471no—
591C4×#120—472no—
592#2293D4711yescharacteristic, complemented
593#2280—472no—
594C42×D4—471no—
595C2×C47—44no—
596C2×C47C2×#52511yescharacteristic
597C2×C47C2×#52911yescharacteristic
598C2×C47#346011yescharacteristic
599C2×C47C2×#54611yescharacteristic
600C2×C47D4×#4111yescharacteristic
601C2×C47#347511yescharacteristic
602C2×C47#348111yescharacteristic
603D47—24no—
604D47—42no—
605D47—44no—
606C23×D4—471no—
607C24×C4—472no—
608#529—948no—
609C2×#126—472no—
610C2×#125—471no—
611C2×#124—471no—
612C2×#124—471no—
613C2×#123—472no—
614C2×C22⋊Q8—471no—
615C2×C22⋊Q8—471no—
616C2×#121—471no—
617C2×#121—471no—
618C2×#120—472no—
619C2×C4×Q8—471no—
620C2×C4×D4—471no—
621C2×C4×D4—472no—
622C2×C4×D4—472no—
623C2×C4×D4—471no—
624C2×C4×D4—472no—
625C2×C4×D4—471no—
626C2×C4×D4—471no—
627C2×C4×D4—471no—
628C2×C4×D4—471no—
629C2×C4×D4—472no—
630C2×C4×D4—948no—
631C2×C4×D4C2×D4711yescharacteristic
632C2×#117—472no—
633C2×#117C2×D4712yescomplemented
634C22×C4⋊C4—471no—
635C22×C22⋊C4—472no—
636C22×C42—471no—
637C22×C42—471no—
638#400—472no—
639#399—472no—
640#398—472no—
641#398—472no—
642#397—472no—
643#397—472no—
644#397—472no—
645#397—472no—
646#396—472no—
647#396—472no—
648#394—472no—
649#394—472no—
650#394—472no—
651#394—472no—
652#394—472no—
653#392—472no—
654#391—471no—
655#391—471no—
656#390—471no—
657#390—471no—
658#390C2×D4711yescharacteristic
659#390C2×D4711yescharacteristic
660#389—471no—
661#389—471no—
662#389C2×D4711yescharacteristic, complemented
663#389C2×D4711yescharacteristic, complemented
664#388—472no—
665#388—472no—
666#388—472no—
667#388C2×D4712yescomplemented
668#388C2×D4712yescomplemented
669#387—472no—
670#386—472no—
671#386—472no—
672#386—472no—
673#386—472no—
674#385—472no—
675#385—472no—
676#385—472no—
677#385—472no—
678#382—471no—
679#381—472no—
680#381—472no—
681#380—471no—
682#380—472no—
683#380—472no—
684#380—471no—
685#380—472no—
686#380—472no—
687#379—472no—
688#379—472no—
689#379—472no—
690C4×C4⋊C4—472no—
691C4×C4⋊C4—471no—
692C4×C4⋊C4—471no—
693C4×C4⋊C4—471no—
694C4×C4⋊C4C2×D4711yescharacteristic, complemented
695C4×C22⋊C4—471no—
696C4×C22⋊C4—471no—
697C4×C22⋊C4—471no—
698C4×C22⋊C4—472no—
699C4×C22⋊C4—471no—
700C4×C22⋊C4—472no—
701C4×C22⋊C4—472no—
702C4×C22⋊C4—472no—
703C4×C22⋊C4—471no—
704C4×C22⋊C4—471no—
705C4×C22⋊C4C2×D4712yescomplemented
706C43C2×D4711yescharacteristic, complemented
707C47#3470011yescharacteristic, complemented, Sylow
708C25—472no—
709C22×Q8—471no—
710C22×D4—472no—
711C22×D4—472no—
712C22×D4—471no—
713C22×D4—471no—
714C22×D4—472no—
715C22×D4—944no—
716C22×D4—944no—
717C22×D4—944no—
718C22×D4C22×D4711yescharacteristic
719C23×C4—471no—
720C23×C4—471no—
721C23×C4—472no—
722C23×C4—471no—
723C23×C4—471no—
724C23×C4—472no—
725C23×C4—471no—
726C23×C4—472no—
727C23×C4—472no—
728C23×C4—471no—
729C23×C4—948no—
730C23×C4—948no—
731C23×C4—1884no—
732C23×C4C22×D4712yes—
733#126—948no—
734#125—944no—
735#124—944no—
736#124—944no—
737#123—948no—
738C22⋊Q8—944no—
739C22⋊Q8—944no—
740#121—944no—
741#121—944no—
742#120—948no—
743C4×Q8—944no—
744C4×D4—944no—
745C4×D4—944no—
746C4×D4—944no—
747C4×D4—944no—
748C4×D4—948no—
749C4×D4—948no—
750C4×D4—944no—
751C4×D4—948no—
752C4×D4—944no—
753C4×D4—1884no—
754C4×D4D18818yescomplemented
755#117—44no—
756#117—948no—
757C2×C4⋊C4—472no—
758C2×C4⋊C4—471no—
759C2×C4⋊C4—472no—
760C2×C4⋊C4—472no—
761C2×C4⋊C4—472no—
762C2×C4⋊C4—471no—
763C2×C4⋊C4—471no—
764C2×C4⋊C4—471no—
765C2×C4⋊C4—471no—
766C2×C4⋊C4—472no—
767C2×C4⋊C4—472no—
768C2×C4⋊C4—472no—
769C2×C4⋊C4—472no—
770C2×C4⋊C4—944no—
771C2×C4⋊C4C22×D4711yescharacteristic
772C2×C4⋊C4C22×D4711yescharacteristic
773C2×C4⋊C4C22×D4712yes—
774C2×C4⋊C4C22×D4712yes—
775C2×C4⋊C4C22×D4711yescharacteristic
776C2×C22⋊C4—472no—
777C2×C22⋊C4—472no—
778C2×C22⋊C4—472no—
779C2×C22⋊C4—472no—
780C2×C22⋊C4—472no—
781C2×C22⋊C4—472no—
782C2×C22⋊C4—472no—
783C2×C22⋊C4—471no—
784C2×C22⋊C4—471no—
785C2×C22⋊C4—471no—
786C2×C22⋊C4—471no—
787C2×C22⋊C4—471no—
788C2×C22⋊C4—471no—
789C2×C22⋊C4—472no—
790C2×C22⋊C4—472no—
791C2×C22⋊C4—472no—
792C2×C22⋊C4—472no—
793C2×C22⋊C4—472no—
794C2×C22⋊C4—472no—
795C2×C22⋊C4—472no—
796C2×C22⋊C4—472no—
797C2×C22⋊C4—472no—
798C2×C22⋊C4—472no—
799C2×C22⋊C4—948no—
800C2×C22⋊C4C22×D4712yes—
801C2×C22⋊C4C22×D4712yes—
802C2×C22⋊C4C22×D4712yes—
803C2×C22⋊C4C22×D4712yes—
804C2×C22⋊C4C22×D4712yes—
805C2×C42—471no—
806C2×C42—471no—
807C2×C42—471no—
808C2×C42—471no—
809C2×C42—471no—
810C2×C42—472no—
811C2×C42—471no—
812C2×C42—944no—
813C2×C42—944no—
814C2×C42C22×D4711yescharacteristic
815C2×C42C22×D4711yescharacteristic
816C2×C42C22×D4711yescharacteristic
817C2×C42C22×D4711yescharacteristic
818C2×C42C22×D4712yes—
819C2×C42C22×D4711yescharacteristic
820C2×C42C22×D4711yescharacteristic
821C2×C42C22×D4711yescharacteristic
822#95—471no—
823#95—471no—
824#95—471no—
825#95—471no—
826#95—471no—
827#95—471no—
828#95—472no—
829#95—472no—
830#95—472no—
831#95—472no—
832#95—472no—
833#95—472no—
834#95—472no—
835#95—472no—
836#95—472no—
837#95—472no—
838#95C22×D4712yes—
839#95C22×D4712yes—
840#95C22×D4712yes—
841C24—471no—
842C24—472no—
843C24—471no—
844C24—944no—
845C24—944no—
846C24—944no—
847C24—944no—
848C24—944no—
849C24—1882no—
850C24—1882no—
851C24C23×D4712yes—
852C2×Q8—942no—
853C2×Q8—942no—
854C2×Q8—942no—
855C2×D4—22no—
856C2×D4—22no—
857C2×D4—474no—
858C2×D4—474no—
859C2×D4—942no—
860C2×D4—942no—
861C2×D4—944no—
862C2×D4—944no—
863C2×D4—944no—
864C2×D4—9432no—
865C2×D4—944no—
866C2×D4—944no—
867C2×D4—944no—
868C2×D4—944no—
869C2×D4—942no—
870C2×D4—942no—
871C2×D4—1882no—
872C2×D4—1882no—
873C2×D4C2×D18814yes—
874C22×C4—24no—
875C22×C4—24no—
876C22×C4—471no—
877C22×C4—471no—
878C22×C4—474no—
879C22×C4—474no—
880C22×C4—472no—
881C22×C4—471no—
882C22×C4—471no—
883C22×C4—471no—
884C22×C4—472no—
885C22×C4—472no—
886C22×C4—471no—
887C22×C4—944no—
888C22×C4—942no—
889C22×C4—942no—
890C22×C4—944no—
891C22×C4—944no—
892C22×C4—942no—
893C22×C4—942no—
894C22×C4—942no—
895C22×C4—942no—
896C22×C4—944no—
897C22×C4—942no—
898C22×C4—942no—
899C22×C4—942no—
900C22×C4—942no—
901C22×C4—944no—
902C22×C4—944no—
903C22×C4—944no—
904C22×C4—942no—
905C22×C4—942no—
906C22×C4—942no—
907C22×C4—944no—
908C22×C4—942no—
909C22×C4—944no—
910C22×C4—1881no—
911C22×C4—1881no—
912C22×C4—1882no—
913C22×C4—1882no—
914C22×C4—18832no—
915C22×C4—1882no—
916C22×C4C2×D18818yes—
917C22×C4C23×D4711yescharacteristic
918C22×C4C23×D4712yes—
919C22×C4C23×D4711yescharacteristic
920C22×C4C23×D4711yescharacteristic
921C22×C4C23×D4712yes—
922C22×C4C23×D4711yescharacteristic
923C22×C4C23×D4712yes—
924C22×C4C23×D4711yescharacteristic
925C22×C4C23×D4711yescharacteristic
926C22×C4C23×D4711yescharacteristic
927C4⋊C4—22no—
928C4⋊C4—22no—
929C4⋊C4—42no—
930C4⋊C4—42no—
931C4⋊C4—942no—
932C4⋊C4—942no—
933C4⋊C4—944no—
934C4⋊C4—944no—
935C4⋊C4—944no—
936C4⋊C4—944no—
937C4⋊C4—942no—
938C4⋊C4—944no—
939C4⋊C4—944no—
940C4⋊C4—942no—
941C4⋊C4—942no—
942C4⋊C4—1882no—
943C4⋊C4—1882no—
944C4⋊C4C2×D18814yes—
945C22⋊C4—24no—
946C22⋊C4—42no—
947C22⋊C4—42no—
948C22⋊C4—42no—
949C22⋊C4—942no—
950C22⋊C4—942no—
951C22⋊C4—942no—
952C22⋊C4—942no—
953C22⋊C4—942no—
954C22⋊C4—942no—
955C22⋊C4—944no—
956C22⋊C4—944no—
957C22⋊C4—944no—
958C22⋊C4—944no—
959C22⋊C4—944no—
960C22⋊C4—944no—
961C22⋊C4—944no—
962C22⋊C4—944no—
963C22⋊C4—944no—
964C22⋊C4—944no—
965C22⋊C4—944no—
966C22⋊C4—944no—
967C22⋊C4—944no—
968C22⋊C4—1882no—
969C22⋊C4—1882no—
970C22⋊C4—1882no—
971C22⋊C4—1882no—
972C22⋊C4C2×D18818yes—
973C42—22no—
974C42—22no—
975C42—22no—
976C42—22no—
977C42—22no—
978C42—24no—
979C42—41no—
980C42—942no—
981C42—942no—
982C42—942no—
983C42—942no—
984C42—942no—
985C42—942no—
986C42—944no—
987C42C2×D18814yes—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—472no—
995C23—472no—
996C23—472no—
997C23—474no—
998C23—472no—
999C23—9416no—
1000C23—941no—
1001C23—941no—
1002C23—941no—
1003C23—941no—
1004C23—941no—
1005C23—942no—
1006C23—941no—
1007C23—941no—
1008C23—942no—
1009C23—942no—
1010C23—941no—
1011C23—942no—
1012C23—941no—
1013C23—942no—
1014C23—942no—
1015C23—941no—
1016C23—1888no—
1017C23—1888no—
1018C23—1888no—
1019C23—1888no—
1020C23—1888no—
1021C23—1888no—
1022C23C22×D18814yes—
1023C23C24×D4711yescharacteristic
1024Q8—1884no—
1025D4—28no—
1026D4—948no—
1027D4—9416no—
1028D4—948no—
1029D4—1888no—
1030D4—1888no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—21no—
1037C2×C4—216no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—22no—
1053C2×C4—472no—
1054C2×C4—472no—
1055C2×C4—941no—
1056C2×C4—941no—
1057C2×C4—941no—
1058C2×C4—941no—
1059C2×C4—948no—
1060C2×C4—948no—
1061C2×C4—941no—
1062C2×C4—941no—
1063C2×C4—941no—
1064C2×C4—941no—
1065C2×C4—942no—
1066C2×C4—942no—
1067C2×C4—942no—
1068C2×C4—941no—
1069C2×C4—942no—
1070C2×C4—942no—
1071C2×C4—941no—
1072C2×C4—941no—
1073C2×C4—941no—
1074C2×C4—941no—
1075C2×C4—942no—
1076C2×C4—942no—
1077C2×C4—941no—
1078C2×C4—942no—
1079C2×C4—941no—
1080C2×C4—942no—
1081C2×C4—941no—
1082C2×C4—1888no—
1083C2×C4—1884no—
1084C2×C4—1884no—
1085C2×C4—1888no—
1086C2×C4—1888no—
1087C2×C4—1884no—
1088C2×C4—1888no—
1089C2×C4—1884no—
1090C2×C4C22×D18812yes—
1091C2×C4C22×D18814yes—
1092C2×C4C22×D18812yes—
1093C2×C4C22×D18812yes—
1094C2×C4#41×D4712yes—
1095C2×C4#41×D4712yes—
1096C2×C4#41×D4712yes—
1097C2×C4#41×D4712yes—
1098C2×C4#1309406912yes—
1099C22—24no—
1100C22—24no—
1101C22—24no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—474no—
1107C22—942no—
1108C22—942no—
1109C22—942no—
1110C22—942no—
1111C22—942no—
1112C22—942no—
1113C22—942no—
1114C22—944no—
1115C22—942no—
1116C22—944no—
1117C22—942no—
1118C22—944no—
1119C22—18832no—
1120C22—1882no—
1121C22—1881no—
1122C22—1882no—
1123C22—1881no—
1124C22—1882no—
1125C22—1881no—
1126C22—1882no—
1127C22—1881no—
1128C22C23×D18811yescharacteristic
1129C22C2×#41×D4711yescharacteristic
1130C22C2×#41×D4711yescharacteristic
1131C22C2×#41×D4711yescharacteristic
1132C22C2×#41×D4711yescharacteristic
1133C22C2×#1309406911yescharacteristic
1134C22#1568995911yescharacteristic
1135C4—24no—
1136C4—22no—
1137C4—22no—
1138C4—41no—
1139C4—42no—
1140C4—41no—
1141C4—42no—
1142C4—41no—
1143C4—942no—
1144C4—942no—
1145C4—1882no—
1146C4—1881no—
1147C4—1881no—
1148C4—1881no—
1149C4—1882no—
1150C4—1881no—
1151C4—1882no—
1152C4#1568963514yes—
1153C4#1568976814yes—
1154C2—44no—
1155C2—944no—
1156C2—1884no—
1157C2—1882no—
1158C2C2×#1568963511yescharacteristic
1159C2#529×D4711yescharacteristic
1160C2#2025680211yescharacteristic
1161C2C2×#1568976811yescharacteristic
1162C2#41×D18811yescharacteristic
1163C2#2025694411yescharacteristic
1164C2#2025699611yescharacteristic
subgroupG/H
centerC22×C4C23×D47
commutator, socle, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC47×#2293C2
prime radical#20246742C2
hypercenter#2293D47
hypocenterC47#34700
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ #2293

Complements

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

NH ≅ G/Ntype
1. C2×#15689655C2semidirect
2. C2×C4×D4×D47C2semidirect
3. #20247632C2semidirect
4. #20247452C2semidirect
5. #20247293C2semidirect
6. #20247258C2semidirect
7. #20247173C2semidirect
8. #20247110C2semidirect
9. #20247038C2semidirect
10. #20246963C2semidirect
11. #20246878C2semidirect
12. #20246855C2semidirect
13. #20246837C2semidirect
15. #20246648C2semidirect
16. #20246624C2semidirect
17. C4×#13094012C2semidirect
18. C4×#13094004C2semidirect
19. C4×#13093999C2semidirect
20. C4×#13093994C2semidirect
21. #20245767C2semidirect
22. C42×D188C2semidirect
23. C47×#2293C2semidirect
27. C2×#13094017C22semidirect
28. C2×#13094015C22semidirect
31. C2×#13094006C22semidirect
33. C2×#13094004C22semidirect
37. C2×C4×Dic94C22semidirect
42. C2×C4×D188C22semidirect
46. C2×C4×C22⋊D47C22semidirect
49. C2×#13093983C22semidirect
53. C2×C42×D47C22semidirect
54. #15689063C22semidirect
55. #15689060C22semidirect
56. #15689055C22semidirect
57. #15689053C22semidirect
58. #15689050C22semidirect
59. #15689048C22semidirect
60. #15689048C22semidirect
61. #15689048C22semidirect
62. #15689045C22semidirect
63. #15689045C22semidirect
64. #15689040C22semidirect
68. #15689039C22semidirect
70. #15689029C22semidirect
71. #15689028C22semidirect
74. #15689022C22semidirect
75. #15689022C22semidirect
76. #15689015C22semidirect
77. #15689014C22semidirect
78. #15689014C22semidirect
79. #15689008C22semidirect
81. #15689001C22semidirect
82. #15689001C22semidirect
83. #15689000C22semidirect
84. #15688998C22semidirect
87. #15688997C22semidirect
88. #15688989C22semidirect
89. #15688984C22semidirect
90. #15688984C22semidirect
94. #15688980C22semidirect
95. #15688980C22semidirect
96. #15688980C22semidirect
100. C4×C4⋊Dic47C22semidirect
101. C4×C4⋊Dic47C22semidirect
102. C4×C4⋊Dic47C22semidirect
103. C4×C4⋊Dic47C22semidirect
108. C4×(C2×D47)⋊C4C22semidirect
109. C4×(C2×D47)⋊C4C22semidirect
110. C4×(C2×D47)⋊C4C22semidirect
111. C4×(C2×D47)⋊C4C22semidirect
112. C4×(C2×D47)⋊C4C22semidirect
113. C4×(C2×D47)⋊C4C22semidirect
115. C2×#117×C47C22semidirect
118. C47×#389C22semidirect
119. C47×#389C22semidirect
120. C47×#388C22semidirect
121. C47×#388C22semidirect
122. C4×C4⋊C4×C47C22semidirect
123. C4×C22⋊C4×C47C22semidirect
124. C43×C47C22semidirect
235. C4×D4×C47D4semidirect
552. C2×D47#529semidirect
592. #2293D47semidirect
633. C2×#117C2×D47semidirect
662. #389C2×D47semidirect
663. #389C2×D47semidirect
667. #388C2×D47semidirect
668. #388C2×D47semidirect
694. C4×C4⋊C4C2×D47semidirect
705. C4×C22⋊C4C2×D47semidirect
706. C43C2×D47semidirect
707. C47#34700semidirect
754. C4×D4D188semidirect

Maximal subgroups

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

subgroupindex
C2×#156896552
C2×C4×D4×D472
#202476322
#202474522
#202472932
#202472582
#202471732
#202471102
#202470382
#202469632
#202468782
#202468552
#202468372
#202467422
#202466482
#202466242
C4×#130940122
C4×#130940042
C4×#130939992
C4×#130939942
#202457672
C42×D1882
C47×#22932
#3470047