Finite Group Databasebeta

← #26227400

Subgroups — #26227400

Order 12032.

1028 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689201C211yesmaximal, characteristic, complemented
2C2×#15689090C211yesmaximal, characteristic, complemented
3#20244187C211yesmaximal, characteristic, complemented
4#20244183C211yesmaximal, characteristic, complemented
5#20244003C211yesmaximal, characteristic, complemented
6#20243996C211yesmaximal, characteristic, complemented
7#20243996C211yesmaximal, characteristic, complemented
8#20243996C211yesmaximal, characteristic, complemented
9#20243686C211yesmaximal, characteristic, complemented
10#20243686C211yesmaximal, characteristic, complemented
11#20243681C211yesmaximal, characteristic, complemented
12#20243568C211yesmaximal, characteristic, complemented
13#20243300C211yesmaximal, characteristic, complemented
14#20243172C211yesmaximal, characteristic, complemented
15C47×#2388C211yesmaximal, characteristic
16C22×#10625329C2211yescharacteristic
17C22×#10625329C2211yescharacteristic
18C23×C47⋊C8C2211yescharacteristic
19#15689201—24no—
20C2×C4⋊(C47⋊C8)C2211yescharacteristic
21C2×C4⋊(C47⋊C8)C2211yescharacteristic
22C2×C4⋊(C47⋊C8)C2211yescharacteristic
23#15689090—24no—
24C2×C22⋊(C47⋊C8)C2211yescharacteristic
25C2×C22⋊(C47⋊C8)C2211yescharacteristic
26C2×C22⋊(C47⋊C8)C2211yescharacteristic
27C2×C22⋊(C47⋊C8)C2211yescharacteristic
28C2×C22⋊(C47⋊C8)C2211yescharacteristic
29C2×C22⋊(C47⋊C8)C2211yescharacteristic
30C2×C22⋊(C47⋊C8)C2211yescharacteristic
31C2×C22⋊(C47⋊C8)C2211yescharacteristic
32C2×C22⋊(C47⋊C8)C2211yescharacteristic
33C2×C22⋊(C47⋊C8)C2211yescharacteristic
34C2×C22⋊(C47⋊C8)C2211yescharacteristic
35C2×C22⋊(C47⋊C8)C2211yescharacteristic
36C2×C22⋊(C47⋊C8)C2211yescharacteristic
37C2×#13093935C2211yescharacteristic
38C2×C4×C47⋊C8C2211yescharacteristic
39C2×C4×C47⋊C8C2211yescharacteristic
40#15688878C2211yescharacteristic
41#15688878C2211yescharacteristic
42#15688878C2211yescharacteristic
43#15688878C2211yescharacteristic
44#15688878C2211yescharacteristic
45#15688878C2211yescharacteristic
46C22×#41×C47C2211yescharacteristic
47C2×C4×D4×C47C2211yescharacteristic
48C2×C4×D4×C47C2211yescharacteristic
49C2×C4×D4×C47C2211yescharacteristic
50C47×#395C411yescharacteristic
51C47×#394C411yescharacteristic
52C47×#394C411yescharacteristic
53C47×#394C411yescharacteristic
54C47×#393C411yescharacteristic
55C47×#392C411yescharacteristic
56C47×#392C411yescharacteristic
57C47×#392C411yescharacteristic
58C4×C22⋊C4×C47C2211yescharacteristic
59C4×C22⋊C4×C47C2211yescharacteristic
60C4×C22⋊C4×C47C2211yescharacteristic
61C2×#10625329—22no—
62C2×#10625329—41no—
63C2×#10625329—41no—
64C2×#10625329—41no—
65C2×#10625329—41no—
66C2×#10625329D414yescomplemented
67C22×C47⋊C8—22no—
68C22×C47⋊C8—41no—
69C22×C47⋊C8—41no—
70C22×C47⋊C8C2311yescharacteristic
71C22×C47⋊C8C2311yescharacteristic
72C22×C47⋊C8C2311yescharacteristic
73C22×C47⋊C8C2311yescharacteristic
74C22×C47⋊C8C2311yescharacteristic
75C22×C47⋊C8C2311yescharacteristic
76C22×C47⋊C8C2311yescharacteristic
77C22×C47⋊C8C2311yescharacteristic
78C4⋊(C47⋊C8)—22no—
79C4⋊(C47⋊C8)—41no—
80C4⋊(C47⋊C8)—41no—
81C22⋊(C47⋊C8)—22no—
82C22⋊(C47⋊C8)—22no—
83C22⋊(C47⋊C8)—22no—
84C22⋊(C47⋊C8)—22no—
85C22⋊(C47⋊C8)—22no—
86C22⋊(C47⋊C8)—22no—
87C22⋊(C47⋊C8)—22no—
88C22⋊(C47⋊C8)—41no—
89C22⋊(C47⋊C8)—41no—
90C22⋊(C47⋊C8)—41no—
91C22⋊(C47⋊C8)—41no—
92C22⋊(C47⋊C8)—41no—
93C22⋊(C47⋊C8)—41no—
94#13093935—41no—
95C4×C47⋊C8—22no—
96C4×C47⋊C8—41no—
97C2×#41×C47—22no—
98C2×#41×C47—22no—
99C2×#41×C47—41no—
100C2×#41×C47—41no—
101C2×#41×C47—41no—
102C2×#41×C47—41no—
103C22×Q8×C47C2×C411yescharacteristic
104C22×D4×C47C2×C411yescharacteristic
105C22×D4×C47C2×C411yescharacteristic
106C22×D4×C47C2×C411yescharacteristic
107C22×D4×C47C2×C411yescharacteristic
108C22×D4×C47C2×C411yescharacteristic
109C22×D4×C47C2×C411yescharacteristic
110C23×C4×C47C2311yescharacteristic
111C23×C4×C47C2311yescharacteristic
112C23×C4×C47C2311yescharacteristic
113C23×C4×C47C2311yescharacteristic
114C4×D4×C47—22no—
115C4×D4×C47—22no—
116C4×D4×C47—41no—
117C4×D4×C47—41no—
118C4×D4×C47—41no—
119C4×D4×C47—41no—
120C2×C4⋊C4×C47C2×C411yescharacteristic
121C2×C4⋊C4×C47C2×C411yescharacteristic
122C2×C4⋊C4×C47C2×C411yescharacteristic
123C2×C22⋊C4×C47C2×C411yescharacteristic
124C2×C22⋊C4×C47C2×C411yescharacteristic
125C2×C22⋊C4×C47C2×C411yescharacteristic
126C2×C22⋊C4×C47C2×C411yescharacteristic
127C2×C22⋊C4×C47C2×C411yescharacteristic
128C2×C22⋊C4×C47C2×C411yescharacteristic
129C2×C22⋊C4×C47C2×C411yescharacteristic
130C2×C22⋊C4×C47C2×C411yescharacteristic
131C2×C22⋊C4×C47C2×C411yescharacteristic
132C2×C22⋊C4×C47C2×C411yescharacteristic
133C2×C22⋊C4×C47C2×C411yescharacteristic
134C2×C22⋊C4×C47C2×C411yescharacteristic
135C2×C42×C47C2311yescharacteristic
136C2×C42×C47C2311yescharacteristic
137C2×C42×C47C2311yescharacteristic
138#95×C47C2×C411yescharacteristic
139#95×C47C2×C411yescharacteristic
140#95×C47C2×C411yescharacteristic
141#95×C47C2×C411yescharacteristic
142#95×C47C2×C411yescharacteristic
143#95×C47C2×C411yescharacteristic
144C24×C47C22×C411yescharacteristic
145C24×C47C22×C411yescharacteristic
146C24×C47C22×C411yescharacteristic
147C24×C47C22×C411yescharacteristic
148#41×C47—44no—
149#41×C47—44no—
150#41×C47—44no—
151#41×C47—44no—
152C2×Q8×C47—22no—
153C2×Q8×C47—41no—
154C2×Q8×C47—41no—
155C2×D4×C47—22no—
156C2×D4×C47—22no—
157C2×D4×C47—22no—
158C2×D4×C47—22no—
159C2×D4×C47—22no—
160C2×D4×C47—22no—
161C2×D4×C47—41no—
162C2×D4×C47—41no—
163C2×D4×C47—41no—
164C2×D4×C47—41no—
165C2×D4×C47—41no—
166C2×D4×C47—41no—
167C2×D4×C47—41no—
168C2×D4×C47—41no—
169C2×D4×C47—41no—
170C2×D4×C47—41no—
171C2×D4×C47—41no—
172C2×D4×C47—41no—
173C22×C4×C47—21no—
174C22×C4×C47—21no—
175C22×C4×C47—21no—
176C22×C4×C47—21no—
177C22×C4×C47—21no—
178C22×C4×C47—21no—
179C22×C4×C47—21no—
180C22×C4×C47—21no—
181C22×C4×C47—21no—
182C22×C4×C47—21no—
183C22×C4×C47—21no—
184C22×C4×C47—21no—
185C22×C4×C47—21no—
186C22×C4×C47—21no—
187C22×C4×C47—21no—
188C22×C4×C47—21no—
189C22×C4×C47—21no—
190C22×C4×C47—21no—
191C22×C4×C47—21no—
192C22×C4×C47—21no—
193C22×C4×C47—21no—
194C22×C4×C47—21no—
195C22×C4×C47C22×C411yescharacteristic
196C22×C4×C47C22×C411yescharacteristic
197C22×C4×C47C22×C411yescharacteristic
198C22×C4×C47C22×C411yescharacteristic
199C22×C4×C47C22×C411yescharacteristic
200C22×C4×C47C22×C411yescharacteristic
201C22×C4×C47C22×C411yescharacteristic
202C22×C4×C47C22×C411yescharacteristic
203C22×C4×C47C22×C411yescharacteristic
204C22×C4×C47C22×C411yescharacteristic
205C22×C4×C47C2×D412yes—
206C22×C4×C47#4112yes—
207C22×C4×C47C2411yescharacteristic
208C4⋊C4×C47—22no—
209C4⋊C4×C47—41no—
210C4⋊C4×C47—41no—
211C22⋊C4×C47—22no—
212C22⋊C4×C47—22no—
213C22⋊C4×C47—22no—
214C22⋊C4×C47—22no—
215C22⋊C4×C47—22no—
216C22⋊C4×C47—22no—
217C22⋊C4×C47—41no—
218C22⋊C4×C47—41no—
219C22⋊C4×C47—41no—
220C22⋊C4×C47—41no—
221C22⋊C4×C47—41no—
222C22⋊C4×C47—41no—
223C42×C47—21no—
224C42×C47—21no—
225C42×C47—21no—
226C42×C47—21no—
227C42×C47—21no—
228C42×C47—21no—
229#10625329—44no—
230#10625329—44no—
231C2×C47⋊C8—21no—
232C2×C47⋊C8—21no—
233C2×C47⋊C8—21no—
234C2×C47⋊C8—21no—
235C2×C47⋊C8—21no—
236C2×C47⋊C8—21no—
237C2×C47⋊C8—21no—
238C2×C47⋊C8—21no—
239C2×C47⋊C8—21no—
240C2×C47⋊C8—21no—
241C2×C47⋊C8—21no—
242C2×C47⋊C8—21no—
243C2×C47⋊C8—21no—
244C2×C47⋊C8—21no—
245C2×C47⋊C8—21no—
246C2×C47⋊C8—21no—
247C2×C47⋊C8—21no—
248C2×C47⋊C8—21no—
249C2×C47⋊C8—21no—
250C2×C47⋊C8—21no—
251C2×C47⋊C8—21no—
252C2×C47⋊C8—21no—
253C2×C47⋊C8—44no—
254C2×C47⋊C8C2×D412yes—
255C2×C47⋊C8C2×D412yes—
256C23×C47—21no—
257C23×C47—21no—
258C23×C47—21no—
259C23×C47—21no—
260C23×C47—21no—
261C23×C47—21no—
262C23×C47—21no—
263C23×C47—21no—
264C23×C47—21no—
265C23×C47—21no—
266C23×C47—21no—
267C23×C47—21no—
268C23×C47—21no—
269C23×C47—21no—
270C23×C47—21no—
271C23×C47—21no—
272C23×C47—21no—
273C23×C47—21no—
274C23×C47—21no—
275C23×C47—21no—
276C23×C47—21no—
277C23×C47—21no—
278C23×C47—21no—
279C23×C47—21no—
280C23×C47—21no—
281C23×C47—21no—
282C23×C47—21no—
283C23×C47C4×D412yes—
284C23×C47C23×C411yescharacteristic
285Q8×C47—44no—
286D4×C47—44no—
287D4×C47—44no—
288D4×C47—44no—
289D4×C47—44no—
290D4×C47—44no—
291D4×C47—44no—
292C2×C4×C47—21no—
293C2×C4×C47—21no—
294C2×C4×C47—21no—
295C2×C4×C47—21no—
296C2×C4×C47—21no—
297C2×C4×C47—21no—
298C2×C4×C47—22no—
299C2×C4×C47—22no—
300C2×C4×C47—22no—
301C2×C4×C47—22no—
302C2×C4×C47—21no—
303C2×C4×C47—21no—
304C2×C4×C47—21no—
305C2×C4×C47—21no—
306C2×C4×C47—21no—
307C2×C4×C47—21no—
308C2×C4×C47—21no—
309C2×C4×C47—21no—
310C2×C4×C47—21no—
311C2×C4×C47—21no—
312C2×C4×C47—21no—
313C2×C4×C47—21no—
314C2×C4×C47—21no—
315C2×C4×C47—21no—
316C2×C4×C47—21no—
317C2×C4×C47—21no—
318C2×C4×C47—21no—
319C2×C4×C47—21no—
320C2×C4×C47—21no—
321C2×C4×C47—21no—
322C2×C4×C47—21no—
323C2×C4×C47—41no—
324C2×C4×C47—41no—
325C2×C4×C47—41no—
326C2×C4×C47—41no—
327C2×C4×C47—41no—
328C2×C4×C47—41no—
329C2×C4×C47—41no—
330C2×C4×C47—41no—
331C2×C4×C47—41no—
332C2×C4×C47—41no—
333C2×C4×C47—41no—
334C2×C4×C47—41no—
335C2×C4×C47C4×D412yes—
336C2×C4×C47#13112yes—
337C2×C4×C47#13112yes—
338C2×C4×C47C22×D411yescharacteristic
339C2×C4×C47C2×#4111yescharacteristic
340C2×C4×C47H(5,𝔽2)11yescharacteristic
341C2×C4×C47H(5,𝔽2)11yescharacteristic
342C2×C4×C47H(5,𝔽2)11yescharacteristic
343C2×C4×C47H(5,𝔽2)11yescharacteristic
344C47⋊C8—22no—
345C47⋊C8—22no—
346C47⋊C8—41no—
347C47⋊C8—41no—
348C47⋊C8—41no—
349C47⋊C8—41no—
350C47⋊C8—41no—
351C47⋊C8—41no—
352#22039—471nomaximal, Sylow
353C22×C47—22no—
354C22×C47—22no—
355C22×C47—22no—
356C22×C47—41no—
357C22×C47—41no—
358C22×C47—41no—
359C22×C47—41no—
360C22×C47—41no—
361C22×C47—41no—
362C22×C47—41no—
363C22×C47—41no—
364C22×C47—41no—
365C22×C47—41no—
366C22×C47—41no—
367C22×C47—41no—
368C22×C47—41no—
369C22×C47—41no—
370C22×C47—41no—
371C22×C47—41no—
372C22×C47—41no—
373C22×C47—41no—
374C22×C47—41no—
375C22×C47—41no—
376C22×C47—41no—
377C22×C47—41no—
378C22×C47—41no—
379C22×C47—41no—
380C22×C47—41no—
381C22×C47C2×C4×D411yescharacteristic
382C22×C47#51811yescharacteristic
383C22×C47#51811yescharacteristic
384C22×C47C2×#13111yescharacteristic
385C22×C47C2×#13111yescharacteristic
386C22×C47#56811yescharacteristic
387C22×C47#56811yescharacteristic
388C4×C47—22no—
389C4×C47—22no—
390C4×C47—22no—
391C4×C47—41no—
392C4×C47—41no—
393C4×C47—41no—
394C4×C47—41no—
395C4×C47—41no—
396C4×C47—41no—
397C4×C47—41no—
398C4×C47#53411yescharacteristic
399C4×C47#53511yescharacteristic
400C4×C47#53811yescharacteristic
401C4×C47#53811yescharacteristic
402C2×#436—471no—
403C2×#408—471no—
404#2388D4711yescharacteristic
405#1955—471no—
406#1954—471no—
407#1924—471no—
408#1923—471no—
409#1923—471no—
410#1923—471no—
411#1870—471no—
412#1870—471no—
413#1869—471no—
414#1850—471no—
415#1780—471no—
416#1753—471no—
417C2×C47—42no—
418C2×C47—81no—
419C2×C47—81no—
420C2×C47—81no—
421C2×C47#232111yescharacteristic
422C2×C47#293311yescharacteristic
423C2×C47#293511yescharacteristic
424C2×C47#297611yescharacteristic
425C2×C47#297811yescharacteristic
426C2×C47#297911yescharacteristic
427C2×C47#298111yescharacteristic
428C22×#41C2×D4711yescharacteristic
429C22×M16—471no—
430C22×M16—471no—
431C23×C8—471no—
432C2×C4×D4C2×D4711yescharacteristic
433C2×C4×D4C2×D4711yescharacteristic
434C2×C4×D4C2×D4711yescharacteristic
435#436—944no—
436C2×C4⋊C8—471no—
437C2×C4⋊C8—471no—
438C2×C4⋊C8—471no—
439#408—944no—
440C2×C22⋊C8—471no—
441C2×C22⋊C8—471no—
442C2×C22⋊C8—471no—
443C2×C22⋊C8—471no—
444C2×C22⋊C8—471no—
445C2×C22⋊C8—471no—
446C2×C22⋊C8—471no—
447C2×C22⋊C8—471no—
448C2×C22⋊C8—471no—
449C2×C22⋊C8—471no—
450C2×C22⋊C8—471no—
451C2×C22⋊C8—471no—
452C2×C22⋊C8—471no—
453C2×#97—471no—
454C2×C4×C8—471no—
455C2×C4×C8—471no—
456#395Dic4711yescharacteristic
457#394Dic4711yescharacteristic
458#394Dic4711yescharacteristic
459#394Dic4711yescharacteristic
460#393Dic4711yescharacteristic
461#392Dic4711yescharacteristic
462#392Dic4711yescharacteristic
463#392Dic4711yescharacteristic
464C4×C22⋊C4C2×D4711yescharacteristic
465C4×C22⋊C4C2×D4711yescharacteristic
466C4×C22⋊C4C2×D4711yescharacteristic
467#336—471no—
468#336—471no—
469#336—471no—
470#336—471no—
471#336—471no—
472#336—471no—
473C47#2203911yescharacteristic, complemented, Sylow
474C2×#41—22no—
475C2×#41—22no—
476C2×#41—41no—
477C2×#41—41no—
478C2×#41—41no—
479C2×#41—41no—
480C22×Q8C2×Dic4711yescharacteristic
481C22×D4C2×Dic4711yescharacteristic
482C22×D4C2×Dic4711yescharacteristic
483C22×D4C2×Dic4711yescharacteristic
484C22×D4C2×Dic4711yescharacteristic
485C22×D4C2×Dic4711yescharacteristic
486C22×D4C2×Dic4711yescharacteristic
487C23×C4C22×D4711yescharacteristic
488C23×C4C22×D4711yescharacteristic
489C23×C4C22×D4711yescharacteristic
490C23×C4C22×D4711yescharacteristic
491C2×M16—474no—
492C2×M16—942no—
493C2×M16—1881no—
494C2×M16—1881no—
495C2×M16—1881no—
496C2×M16—1881no—
497C22×C8—471no—
498C22×C8—471no—
499C22×C8—471no—
500C22×C8—471no—
501C22×C8—471no—
502C22×C8—471no—
503C22×C8—471no—
504C22×C8—471no—
505C22×C8—942no—
506C22×C8—1881no—
507C22×C8—1881no—
508C4×D4—22no—
509C4×D4—22no—
510C4×D4—41no—
511C4×D4—41no—
512C4×D4—41no—
513C4×D4—41no—
514C2×C4⋊C4C2×Dic4711yescharacteristic
515C2×C4⋊C4C2×Dic4711yescharacteristic
516C2×C4⋊C4C2×Dic4711yescharacteristic
517C2×C22⋊C4C2×Dic4711yescharacteristic
518C2×C22⋊C4C2×Dic4711yescharacteristic
519C2×C22⋊C4C2×Dic4711yescharacteristic
520C2×C22⋊C4C2×Dic4711yescharacteristic
521C2×C22⋊C4C2×Dic4711yescharacteristic
522C2×C22⋊C4C2×Dic4711yescharacteristic
523C2×C22⋊C4C2×Dic4711yescharacteristic
524C2×C22⋊C4C2×Dic4711yescharacteristic
525C2×C22⋊C4C2×Dic4711yescharacteristic
526C2×C22⋊C4C2×Dic4711yescharacteristic
527C2×C22⋊C4C2×Dic4711yescharacteristic
528C2×C22⋊C4C2×Dic4711yescharacteristic
529C2×C42C22×D4711yescharacteristic
530C2×C42C22×D4711yescharacteristic
531C2×C42C22×D4711yescharacteristic
532C4⋊C8—942no—
533C4⋊C8—1881no—
534C4⋊C8—1881no—
535C22⋊C8—942no—
536C22⋊C8—942no—
537C22⋊C8—942no—
538C22⋊C8—942no—
539C22⋊C8—942no—
540C22⋊C8—942no—
541C22⋊C8—942no—
542C22⋊C8—1881no—
543C22⋊C8—1881no—
544C22⋊C8—1881no—
545C22⋊C8—1881no—
546C22⋊C8—1881no—
547C22⋊C8—1881no—
548#97—1881no—
549C4×C8—942no—
550C4×C8—1881no—
551#95C2×Dic4711yescharacteristic
552#95C2×Dic4711yescharacteristic
553#95C2×Dic4711yescharacteristic
554#95C2×Dic4711yescharacteristic
555#95C2×Dic4711yescharacteristic
556#95C2×Dic4711yescharacteristic
557C24C22×Dic4711yescharacteristic
558C24C22×Dic4711yescharacteristic
559C24C22×Dic4711yescharacteristic
560C24C22×Dic4711yescharacteristic
561#41—44no—
562#41—44no—
563#41—44no—
564#41—44no—
565C2×Q8—22no—
566C2×Q8—41no—
567C2×Q8—41no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—41no—
575C2×D4—41no—
576C2×D4—41no—
577C2×D4—41no—
578C2×D4—41no—
579C2×D4—41no—
580C2×D4—41no—
581C2×D4—41no—
582C2×D4—41no—
583C2×D4—41no—
584C2×D4—41no—
585C2×D4—41no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4D4×D4712yes—
609C22×C4#1062535212yes—
610C22×C4C22×Dic4711yescharacteristic
611C22×C4C22×Dic4711yescharacteristic
612C22×C4C22×Dic4711yescharacteristic
613C22×C4C22×Dic4711yescharacteristic
614C22×C4C22×Dic4711yescharacteristic
615C22×C4C22×Dic4711yescharacteristic
616C22×C4C22×Dic4711yescharacteristic
617C22×C4C22×Dic4711yescharacteristic
618C22×C4C22×Dic4711yescharacteristic
619C22×C4C22×Dic4711yescharacteristic
620C22×C4C23×D4711yescharacteristic
621M16—1884no—
622M16—1884no—
623C2×C8—472no—
624C2×C8—472no—
625C2×C8—941no—
626C2×C8—941no—
627C2×C8—941no—
628C2×C8—941no—
629C2×C8—941no—
630C2×C8—941no—
631C2×C8—941no—
632C2×C8—941no—
633C2×C8—941no—
634C2×C8—941no—
635C2×C8—941no—
636C2×C8—941no—
637C2×C8—941no—
638C2×C8—941no—
639C2×C8—941no—
640C2×C8—941no—
641C2×C8—941no—
642C2×C8—941no—
643C2×C8—941no—
644C2×C8—941no—
645C2×C8—941no—
646C2×C8—941no—
647C2×C8—1884no—
648C4⋊C4—22no—
649C4⋊C4—41no—
650C4⋊C4—41no—
651C22⋊C4—22no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—22no—
655C22⋊C4—22no—
656C22⋊C4—22no—
657C22⋊C4—41no—
658C22⋊C4—41no—
659C22⋊C4—41no—
660C22⋊C4—41no—
661C22⋊C4—41no—
662C22⋊C4—41no—
663C42—21no—
664C42—21no—
665C42—21no—
666C42—21no—
667C42—21no—
668C42—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23D4×Dic4712yes—
697C23C23×Dic4711yescharacteristic
698Q8—44no—
699D4—44no—
700D4—44no—
701D4—44no—
702D4—44no—
703D4—44no—
704D4—44no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4D4×Dic4712yes—
749C2×C4#1309403112yes—
750C2×C4#1309403112yes—
751C2×C4C2×D4×D4711yescharacteristic
752C2×C4C2×#1062535211yescharacteristic
753C2×C4#1309406911yescharacteristic
754C2×C4#1309406911yescharacteristic
755C2×C4#1309406911yescharacteristic
756C2×C4#1309406911yescharacteristic
757C8—942no—
758C8—942no—
759C8—1881no—
760C8—1881no—
761C8—1881no—
762C8—1881no—
763C8—1881no—
764C8—1881no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22C2×D4×Dic4711yescharacteristic
794C22#1568959811yescharacteristic
795C22#1568959811yescharacteristic
796C22C2×#1309403111yescharacteristic
797C22C2×#1309403111yescharacteristic
798C22#1568989011yescharacteristic
799C22#1568989011yescharacteristic
800C4—22no—
801C4—22no—
802C4—22no—
803C4—41no—
804C4—41no—
805C4—41no—
806C4—41no—
807C4—41no—
808C4—41no—
809C4—41no—
810C4#1568968311yescharacteristic
811C4#1568968811yescharacteristic
812C4#1568970811yescharacteristic
813C4#1568970811yescharacteristic
814C2—42no—
815C2—81no—
816C2—81no—
817C2—81no—
818C2#2024604911yescharacteristic
819C2#2025211511yescharacteristic
820C2#2025213211yescharacteristic
821C2#2025243611yescharacteristic
822C2#2025245011yescharacteristic
823C2#2025245511yescharacteristic
824C2#2025246411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D47
commutator, socleC23×C47C23×C4
Fitting, prime radicalC47×#2388C2
cosocleC22×C4×C47C24
hypercenter#2388D47
hypocenterC47#22039
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ #2388

Complements

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

NH ≅ G/Ntype
1. C2×#15689201C2semidirect
2. C2×#15689090C2semidirect
3. #20244187C2semidirect
4. #20244183C2semidirect
5. #20244003C2semidirect
6. #20243996C2semidirect
7. #20243996C2semidirect
8. #20243996C2semidirect
9. #20243686C2semidirect
10. #20243686C2semidirect
11. #20243681C2semidirect
12. #20243568C2semidirect
13. #20243300C2semidirect
14. #20243172C2semidirect
66. C2×#10625329D4semidirect
473. C47#22039semidirect

Maximal subgroups

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

subgroupindex
C2×#156892012
C2×#156890902
#202441872
#202441832
#202440032
#202439962
#202436862
#202436812
#202435682
#202433002
#202431722
C47×#23882
#2203947