Finite Group Databasebeta

← #26233021

Subgroups — #26233021

Order 12032.

1108 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689651C211yesmaximal, characteristic
2C2×#15689253C211yesmaximal, characteristic, complemented
3C2×#15689251C211yesmaximal, characteristic, complemented
4#20244186C211yesmaximal, characteristic, complemented
5#20244184C211yesmaximal, characteristic, complemented
6#20244184C211yesmaximal, characteristic, complemented
7#20244184C211yesmaximal, characteristic, complemented
8#20244182C211yesmaximal, characteristic, complemented
9#20244180C211yesmaximal, characteristic, complemented
10#20243372C211yesmaximal, characteristic, complemented
11#20243371C211yesmaximal, characteristic, complemented
12#20243367C211yesmaximal, characteristic, complemented
13#20243153C211yesmaximal, characteristic, complemented
14#20243149C211yesmaximal, characteristic, complemented
15C47×#1750C211yesmaximal, characteristic, complemented
16#15689651—24no—
17#15689651—24no—
18C2×#13094019C411yescharacteristic
19C2×#13094017C411yescharacteristic
20C2×#13094014C411yescharacteristic
21C2×#13094010C411yescharacteristic
22C2×#13094009C411yescharacteristic
23C2×#13094006C411yescharacteristic
24C2×#13094002C411yescharacteristic
25C2×#13093997C411yescharacteristic
26C2×C4×Dic94C2211yescharacteristic
27C2×C4×D188C2211yescharacteristic
28C2×C4×C22⋊D47C2211yescharacteristic
29C2×C4×C22⋊D47C2211yescharacteristic
30C2×#13093981C2211yescharacteristic
31C2×C42×D47C2211yescharacteristic
32#15689253—24no—
33#15689251—24no—
34C2×C4⋊(C47⋊C8)C2211yescharacteristic
35C2×C4⋊(C47⋊C8)C2211yescharacteristic
36C2×Dic47⋊C8C2211yescharacteristic
37C2×Dic47⋊C8C2211yescharacteristic
38C2×Dic47⋊C8C2211yescharacteristic
39C2×Dic47⋊C8C2211yescharacteristic
40C2×C22⋊(C47⋊C8)C2211yescharacteristic
41C2×C22⋊(C47⋊C8)C2211yescharacteristic
42C2×(C2×D47)⋊C8C2211yescharacteristic
43C2×(C2×D47)⋊C8C2211yescharacteristic
44C2×(C2×D47)⋊C8C2211yescharacteristic
45C2×(C2×D47)⋊C8C2211yescharacteristic
46C2×(C2×D47)⋊C8C2211yescharacteristic
47C2×(C2×D47)⋊C8C2211yescharacteristic
48C2×(C2×D47)⋊C8C2211yescharacteristic
49C2×(C2×D47)⋊C8C2211yescharacteristic
50C2×#13093934C2211yescharacteristic
51C2×#13093934C2211yescharacteristic
52C2×#13093934C2211yescharacteristic
53C2×C8×Dic47C2211yescharacteristic
54#15688878C2211yescharacteristic
55#15688878C2211yescharacteristic
56C2×#117×C47C2211yescharacteristic
57C2×C22⋊C8×C47C2211yescharacteristic
58C2×C22⋊C8×C47C2211yescharacteristic
59C2×#97×C47C2211yescharacteristic
60C2×C4×C8×C47C2211yescharacteristic
61C47×#336C2211yescharacteristic
62C47×#336C2211yescharacteristic
63C22×Dic94C2×C411yescharacteristic
64C22×D188C2×C411yescharacteristic
65C22×C22⋊D47C2×C411yescharacteristic
66C22×C22⋊D47C2×C411yescharacteristic
67C22×C4×D47C2×C411yescharacteristic
68C22×C4×D47C2×C411yescharacteristic
69C22×C4×D47C2311yescharacteristic
70C22×C4×D47C2311yescharacteristic
71C22×C47⋊C8C2311yescharacteristic
72C22×C47⋊C8C2311yescharacteristic
73C22×C47⋊C8C2311yescharacteristic
74C22×C47⋊C8C2311yescharacteristic
75#13094019—24no—
76#13094017—24no—
77#13094014—24no—
78#13094010—24no—
79#13094009—24no—
80#13094006—24no—
81#13094002—24no—
82#13093997—24no—
83C4×Dic94D414yes—
84C4×Dic94D414yes—
85C4×D188—22no—
86C4×D188—22no—
87C4×C22⋊D47—22no—
88C4×C22⋊D47—22no—
89C4×C22⋊D47—22no—
90C4×C22⋊D47—22no—
91#13093981—22no—
92#13093981—22no—
93C2×C4⋊Dic47C2×C411yescharacteristic
94C2×C4⋊Dic47C2×C411yescharacteristic
95C2×Dic47⋊C4C2×C411yescharacteristic
96C2×Dic47⋊C4C2×C411yescharacteristic
97C2×Dic47⋊C4C2×C411yescharacteristic
98C2×Dic47⋊C4C2×C411yescharacteristic
99C2×Dic47⋊C4C2×C411yescharacteristic
100C2×Dic47⋊C4C2×C411yescharacteristic
101C2×C22⋊Dic47C2×C411yescharacteristic
102C2×C22⋊Dic47C2×C411yescharacteristic
103C2×(C2×D47)⋊C4C2×C411yescharacteristic
104C2×(C2×D47)⋊C4C2×C411yescharacteristic
105C2×(C2×D47)⋊C4C2×C411yescharacteristic
106C2×(C2×D47)⋊C4C2×C411yescharacteristic
107C2×(C2×D47)⋊C4C2×C411yescharacteristic
108C2×(C2×D47)⋊C4C2×C411yescharacteristic
109C2×C4×Dic47C2×C411yescharacteristic
110C2×C4×Dic47C2×C411yescharacteristic
111C2×C4×Dic47C2311yescharacteristic
112C2×C4×Dic47C2311yescharacteristic
113C42×D47—22no—
114C42×D47—22no—
115C4⋊(C47⋊C8)—22no—
116C4⋊(C47⋊C8)—22no—
117Dic47⋊C8—22no—
118Dic47⋊C8—22no—
119Dic47⋊C8—22no—
120Dic47⋊C8—22no—
121C22⋊(C47⋊C8)—41no—
122C22⋊(C47⋊C8)—41no—
123(C2×D47)⋊C8—22no—
124(C2×D47)⋊C8—22no—
125(C2×D47)⋊C8—22no—
126(C2×D47)⋊C8—22no—
127(C2×D47)⋊C8—41no—
128(C2×D47)⋊C8—41no—
129(C2×D47)⋊C8—41no—
130(C2×D47)⋊C8—41no—
131#13093934—22no—
132#13093934—22no—
133#13093934—22no—
134C8×Dic47—22no—
135C23×C4×C47C2311yescharacteristic
136C22×C8×C47C2311yescharacteristic
137C22×C8×C47C2311yescharacteristic
138C22×C8×C47C2311yescharacteristic
139C22×C8×C47C2311yescharacteristic
140#117×C47—22no—
141#117×C47—22no—
142C2×C4⋊C4×C47C2×C411yescharacteristic
143C2×C4⋊C4×C47C2×C411yescharacteristic
144C2×C22⋊C4×C47C2×C411yescharacteristic
145C2×C22⋊C4×C47C2×C411yescharacteristic
146C2×C42×C47C2311yescharacteristic
147C2×C42×C47C2311yescharacteristic
148C22⋊C8×C47—22no—
149C22⋊C8×C47—22no—
150#97×C47—22no—
151C4×C8×C47—22no—
152C24×C47C22×C411yescharacteristic
153C23×D47C22×C411yescharacteristic
154C23×D47C22×C411yescharacteristic
155C22×C4×C47—21no—
156C22×C4×C47—21no—
157C22×C4×C47—21no—
158C22×C4×C47—21no—
159C22×C4×C47—21no—
160C22×C4×C47—21no—
161C22×C4×C47C22×C411yescharacteristic
162C22×C4×C47C22×C411yescharacteristic
163C22×C4×C47C22×C411yescharacteristic
164C22×C4×C47C22×C411yescharacteristic
165C22×C4×C47C22×C411yescharacteristic
166C22×C4×C47C2411yescharacteristic
167C2×C22⋊D47—22no—
168C2×C22⋊D47—22no—
169C2×C22⋊D47—22no—
170C2×C22⋊D47—41no—
171C2×C22⋊D47—41no—
172C2×C22⋊D47—41no—
173C22×Dic47C22×C411yescharacteristic
174C22×Dic47C22×C411yescharacteristic
175C22×Dic47C22×C411yescharacteristic
176C22×Dic47C22×C411yescharacteristic
177C22×Dic47C22×C411yescharacteristic
178C22×Dic47C22×C411yescharacteristic
179C2×D188—22no—
180C2×D188—22no—
181C2×D188—41no—
182C2×C4×D47—22no—
183C2×C4×D47—21no—
184C2×C4×D47—21no—
185C2×C4×D47—21no—
186C2×C4×D47—21no—
187C2×C4×D47—21no—
188C2×C4×D47—21no—
189C2×C4×D47—21no—
190C2×C4×D47—21no—
191C2×C4×D47—21no—
192C2×C4×D47—21no—
193C2×C4×D47—21no—
194C2×C4×D47—21no—
195C2×C4×D47—22no—
196C2×C4×D47—22no—
197C2×C4×D47—41no—
198C2×C4×D47—41no—
199C2×C4×D47—41no—
200C2×Dic94—41no—
201C2×Dic94—41no—
202C2×Dic94C22⋊C414yes—
203C2×C8×C47—21no—
204C2×C8×C47—21no—
205C2×C8×C47—21no—
206C2×C8×C47—21no—
207C2×C8×C47—21no—
208C2×C8×C47—21no—
209C2×C8×C47—21no—
210C2×C8×C47—21no—
211C2×C8×C47—21no—
212C2×C8×C47—21no—
213C2×C8×C47#4112yes—
214C2×C8×C47#4112yes—
215C4⋊C4×C47—22no—
216C4⋊C4×C47—22no—
217C22⋊C4×C47—22no—
218C22⋊C4×C47—22no—
219C42×C47—21no—
220C42×C47—21no—
221C42×C47C2×D412yes—
222C42×C47C2×D412yes—
223C22⋊Dic47—22no—
224C22⋊Dic47—22no—
225(C2×D47)⋊C4—22no—
226(C2×D47)⋊C4—22no—
227(C2×D47)⋊C4—22no—
228(C2×D47)⋊C4—22no—
229(C2×D47)⋊C4—22no—
230(C2×D47)⋊C4—22no—
231C4⋊Dic47—22no—
232C4⋊Dic47C22⋊C414yes—
233Dic47⋊C4—22no—
234Dic47⋊C4—22no—
235Dic47⋊C4—22no—
236Dic47⋊C4—22no—
237Dic47⋊C4C22⋊C414yes—
238Dic47⋊C4C22⋊C414yes—
239C4×Dic47—22no—
240C4×Dic47—22no—
241C4×Dic47C2×D412yes—
242C4×Dic47C2×D412yes—
243C4×Dic47C2×D412yes—
244C4×Dic47C2×D412yes—
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—21no—
254C2×C47⋊C8—21no—
255C2×C47⋊C8—21no—
256C2×C47⋊C8—21no—
257C23×C47—21no—
258C23×C47—21no—
259C23×C47—21no—
260C23×C47—21no—
261C23×C47—21no—
262C23×C47—21no—
263C23×C47—21no—
264C23×C47C23×C411yescharacteristic
265C22×D47—21no—
266C22×D47—21no—
267C22×D47—21no—
268C22×D47—21no—
269C22×D47—21no—
270C22×D47—21no—
271C22×D47—21no—
272C22×D47—21no—
273C22×D47—21no—
274C22×D47—21no—
275C22×D47—21no—
276C22×D47—21no—
277C22×D47—21no—
278C22×D47#13112yes—
279C2×C4×C47—21no—
280C2×C4×C47—21no—
281C2×C4×C47—21no—
282C2×C4×C47—21no—
283C2×C4×C47—21no—
284C2×C4×C47—21no—
285C2×C4×C47—21no—
286C2×C4×C47—21no—
287C2×C4×C47—21no—
288C2×C4×C47—21no—
289C2×C4×C47—21no—
290C2×C4×C47—21no—
291C2×C4×C47—21no—
292C2×C4×C47—41no—
293C2×C4×C47—41no—
294C2×C4×C47—41no—
295C2×C4×C47—41no—
296C2×C4×C47C2×C22⋊C412yes—
297C2×C4×C47C2×C22⋊C412yes—
298C2×C4×C47C22×D411yescharacteristic
299C2×C4×C47C22×D411yescharacteristic
300C2×C4×C47C2×#4111yescharacteristic
301C2×C4×C47C2×#4111yescharacteristic
302C2×C4×C47H(5,𝔽2)11yescharacteristic
303C2×C4×C472−1+411yescharacteristic
304C22⋊D47—44no—
305C22⋊D47—44no—
306C2×Dic47—21no—
307C2×Dic47—21no—
308C2×Dic47—21no—
309C2×Dic47—21no—
310C2×Dic47—21no—
311C2×Dic47—21no—
312C2×Dic47—21no—
313C2×Dic47—21no—
314C2×Dic47—21no—
315C2×Dic47—21no—
316C2×Dic47—21no—
317C2×Dic47—21no—
318C2×Dic47—21no—
319C2×Dic47—21no—
320C2×Dic47C2×C22⋊C412yes—
321C2×Dic47C2×C22⋊C412yes—
322C2×Dic47C2×C22⋊C412yes—
323C2×Dic47C2×C22⋊C412yes—
324D188—44no—
325C4×D47—44no—
326C4×D47—44no—
327C4×D47—41no—
328C4×D47—41no—
329C4×D47—41no—
330C4×D47—41no—
331C4×D47—41no—
332C4×D47—41no—
333C4×D47—41no—
334C4×D47—41no—
335Dic94—44no—
336C8×C47—22no—
337C8×C47—22no—
338C8×C47—41no—
339C8×C47—41no—
340C47⋊C8—41no—
341C47⋊C8—41no—
342C47⋊C8—41no—
343C47⋊C8—41no—
344#22533—471nomaximal, Sylow
345C22×C47—41no—
346C22×C47—41no—
347C22×C47—41no—
348C22×C47—41no—
349C22×C47—41no—
350C22×C47—41no—
351C22×C47—41no—
352C22×C47C22×C22⋊C411yescharacteristic
353C22×C47C4×#4111yescharacteristic
354C22×C47#52011yescharacteristic
355C22×C47C2×#13111yescharacteristic
356C22×C47#56811yescharacteristic
357C22×C47#56811yescharacteristic
358C22×C47#56811yescharacteristic
359C2×D47—22no—
360C2×D47—22no—
361C2×D47—22no—
362C2×D47—41no—
363C2×D47—41no—
364C2×D47—41no—
365C2×D47—41no—
366C2×D47—41no—
367C2×D47—41no—
368C2×D47—41no—
369C2×D47—41no—
370C2×D47—41no—
371C2×D47—41no—
372C2×D47—41no—
373C4×C47—22no—
374C4×C47—22no—
375C4×C47—41no—
376C4×C47—41no—
377C4×C47—41no—
378C4×C47#54811yescharacteristic
379C4×C47#54811yescharacteristic
380C4×C47#55011yescharacteristic
381C4×C47#55011yescharacteristic
382Dic47—22no—
383Dic47—22no—
384Dic47—22no—
385Dic47—22no—
386Dic47—41no—
387Dic47—41no—
388C2×#529—471no—
389C2×#446—471no—
390C2×#446—471no—
391#1955—471no—
392#1955—471no—
393#1955—471no—
394#1955—471no—
395#1954—471no—
396#1954—471no—
397#1798—471no—
398#1798—471no—
399#1797—471no—
400#1750—471no—
401#1750D4711yescharacteristic, complemented
402#1749—471no—
403C2×C47—81no—
404C2×C47#234111yescharacteristic
405C2×C47#287911yescharacteristic
406C2×C47#288011yescharacteristic
407C2×C47#296711yescharacteristic
408C2×C47#296811yescharacteristic
409C2×C47#299211yescharacteristic
410C2×C47#299511yescharacteristic
411D47—42no—
412D47—81no—
413#529—944no—
414#529—944no—
415C2×#126—471no—
416C2×#126—471no—
417C2×#125—471no—
418C2×#124—471no—
419C2×#123—471no—
420C2×#123—471no—
421C2×C22⋊Q8—471no—
422C2×#121—471no—
423C2×C4×Q8—471no—
424C2×C4×D4—471no—
425C2×C4×D4—471no—
426C2×C4×D4—471no—
427C2×#117—471no—
428C2×#117C2×D4711yescharacteristic
429C22×C42—471no—
430#446—944no—
431#446—944no—
432C2×C4⋊C8—471no—
433C2×C4⋊C8—471no—
434C2×C4⋊C8—471no—
435C2×C4⋊C8—471no—
436C2×C4⋊C8—471no—
437C2×C4⋊C8—471no—
438C2×C22⋊C8—471no—
439C2×C22⋊C8—471no—
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⋊C8C2×D4711yescharacteristic
449C2×C22⋊C8C2×D4711yescharacteristic
450C2×#97—471no—
451C2×#97—471no—
452C2×#97—471no—
453C2×#97C2×D4711yescharacteristic
454C2×C4×C8—471no—
455C2×C4×C8C2×D4711yescharacteristic
456#336—471no—
457#336—471no—
458#336C2×D4711yescharacteristic
459#336C2×D4711yescharacteristic
460C47#2253311yescharacteristic, complemented, Sylow
461C22×Q8—471no—
462C22×D4—471no—
463C22×D4—471no—
464C22×D4—471no—
465C23×C4—471no—
466C23×C4—471no—
467C23×C4—471no—
468C23×C4—471no—
469C23×C4C22×D4711yescharacteristic
470C22×C8—471no—
471C22×C8—471no—
472C22×C8—471no—
473C22×C8—471no—
474C22×C8C22×D4711yescharacteristic
475C22×C8C22×D4711yescharacteristic
476C22×C8C22×D4711yescharacteristic
477C22×C8C22×D4711yescharacteristic
478#126—944no—
479#126—944no—
480#125—944no—
481#124—944no—
482#123—944no—
483#123—944no—
484C22⋊Q8—944no—
485#121—944no—
486C4×Q8—474no—
487C4×Q8—474no—
488C4×D4—942no—
489C4×D4—942no—
490C4×D4—942no—
491C4×D4—942no—
492C4×D4—942no—
493C4×D4—942no—
494#117—22no—
495#117—22no—
496#117—942no—
497#117—942no—
498C2×C4⋊C4—471no—
499C2×C4⋊C4—471no—
500C2×C4⋊C4—471no—
501C2×C4⋊C4—471no—
502C2×C4⋊C4—471no—
503C2×C4⋊C4—471no—
504C2×C4⋊C4—471no—
505C2×C4⋊C4—471no—
506C2×C4⋊C4C4×D4711yescharacteristic
507C2×C4⋊C4C4×D4711yescharacteristic
508C2×C22⋊C4—471no—
509C2×C22⋊C4—471no—
510C2×C22⋊C4—471no—
511C2×C22⋊C4—471no—
512C2×C22⋊C4—471no—
513C2×C22⋊C4—471no—
514C2×C22⋊C4—471no—
515C2×C22⋊C4—471no—
516C2×C22⋊C4C4×D4711yescharacteristic
517C2×C22⋊C4C4×D4711yescharacteristic
518C2×C42—471no—
519C2×C42—471no—
520C2×C42—471no—
521C2×C42—471no—
522C2×C42—942no—
523C2×C42—942no—
524C2×C42C22×D4711yescharacteristic
525C2×C42C22×D4711yescharacteristic
526C4⋊C8—942no—
527C4⋊C8—942no—
528C4⋊C8—942no—
529C4⋊C8—942no—
530C4⋊C8—942no—
531C4⋊C8—942no—
532C22⋊C8—22no—
533C22⋊C8—22no—
534C22⋊C8—942no—
535C22⋊C8—942no—
536C22⋊C8—942no—
537C22⋊C8—942no—
538C22⋊C8—1881no—
539C22⋊C8—1881no—
540C22⋊C8—1881no—
541C22⋊C8—1881no—
542C22⋊C8—1881no—
543C22⋊C8—1881no—
544#97—22no—
545#97—942no—
546#97—942no—
547#97—942no—
548C4×C8—22no—
549C4×C8—942no—
550C24—471no—
551C24—471no—
552C24C2×C4×D4711yescharacteristic
553C2×Q8—474no—
554C2×Q8—1881no—
555C2×Q8—1881no—
556C2×D4—942no—
557C2×D4—942no—
558C2×D4—942no—
559C2×D4—942no—
560C2×D4—942no—
561C2×D4—1881no—
562C2×D4—1881no—
563C2×D4—1881no—
564C2×D4—1881no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—471no—
572C22×C4—471no—
573C22×C4—471no—
574C22×C4—471no—
575C22×C4—471no—
576C22×C4—471no—
577C22×C4—942no—
578C22×C4—942no—
579C22×C4—942no—
580C22×C4—941no—
581C22×C4—941no—
582C22×C4—941no—
583C22×C4—941no—
584C22×C4—941no—
585C22×C4—941no—
586C22×C4—941no—
587C22×C4—941no—
588C22×C4—941no—
589C22×C4—941no—
590C22×C4—941no—
591C22×C4—941no—
592C22×C4—1881no—
593C22×C4—1881no—
594C22×C4—1881no—
595C22×C4C2×C4×D4711yescharacteristic
596C22×C4C2×C4×D4711yescharacteristic
597C22×C4C2×C4×D4711yescharacteristic
598C22×C4C2×C4×D4711yescharacteristic
599C22×C4C2×C4×D4711yescharacteristic
600C22×C4C23×D4711yescharacteristic
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—941no—
612C2×C8—941no—
613C2×C8—941no—
614C2×C8—941no—
615C2×C8—941no—
616C2×C8—941no—
617C2×C8—941no—
618C2×C8—941no—
619C2×C8—941no—
620C2×C8—941no—
621C2×C8—941no—
622C2×C8—941no—
623C2×C8#1062535012yes—
624C2×C8#1062535012yes—
625C4⋊C4—22no—
626C4⋊C4—22no—
627C4⋊C4—474no—
628C4⋊C4—474no—
629C4⋊C4—474no—
630C4⋊C4—942no—
631C4⋊C4—942no—
632C4⋊C4—942no—
633C4⋊C4—942no—
634C4⋊C4—942no—
635C22⋊C4—22no—
636C22⋊C4—22no—
637C22⋊C4—942no—
638C22⋊C4—942no—
639C22⋊C4—942no—
640C22⋊C4—942no—
641C22⋊C4—942no—
642C22⋊C4—942no—
643C22⋊C4—942no—
644C22⋊C4—942no—
645C42—21no—
646C42—21no—
647C42—472no—
648C42—472no—
649C42—472no—
650C42—472no—
651C42—942no—
652C42—942no—
653C42D4×D4712yes—
654C42D4×D4712yes—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—472no—
663C23—941no—
664C23—941no—
665C23—941no—
666C23—941no—
667C23—941no—
668C23—941no—
669C23—941no—
670C23—941no—
671C23—941no—
672C23—941no—
673C23—941no—
674C23—941no—
675C23—941no—
676C23C22×C4×D4711yescharacteristic
677Q8—1884no—
678D4—1884no—
679D4—1884no—
680D4—1884no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—472no—
699C2×C4—472no—
700C2×C4—472no—
701C2×C4—472no—
702C2×C4—941no—
703C2×C4—941no—
704C2×C4—941no—
705C2×C4—941no—
706C2×C4—941no—
707C2×C4—941no—
708C2×C4—941no—
709C2×C4—941no—
710C2×C4—941no—
711C2×C4—941no—
712C2×C4—941no—
713C2×C4—941no—
714C2×C4—941no—
715C2×C4—941no—
716C2×C4—1884no—
717C2×C4—1884no—
718C2×C4—1881no—
719C2×C4—1881no—
720C2×C4—1881no—
721C2×C4—1881no—
722C2×C4—1881no—
723C2×C4—1881no—
724C2×C4—1881no—
725C2×C4—1881no—
726C2×C4C22⋊C4×D4712yes—
727C2×C4C22⋊C4×D4712yes—
728C2×C4C2×D4×D4711yescharacteristic
729C2×C4C2×D4×D4711yescharacteristic
730C2×C4C2×#1062535011yescharacteristic
731C2×C4C2×#1062535011yescharacteristic
732C2×C4#1309407011yescharacteristic
733C2×C4#1309407111yescharacteristic
734C8—22no—
735C8—22no—
736C8—41no—
737C8—41no—
738C8—1881no—
739C8—1881no—
740C8—1881no—
741C8—1881no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—942no—
750C22—942no—
751C22—942no—
752C22—1881no—
753C22—1881no—
754C22—1881no—
755C22—1881no—
756C22—1881no—
757C22—1881no—
758C22—1881no—
759C22—1881no—
760C22—1881no—
761C22—1881no—
762C22—1881no—
763C22C2×C22⋊C4×D4711yescharacteristic
764C22C4×#1062535011yescharacteristic
765C22#1568960311yescharacteristic
766C22#131×D4711yescharacteristic
767C22#1568988811yescharacteristic
768C22#1568988811yescharacteristic
769C22#1568988811yescharacteristic
770C4—22no—
771C4—22no—
772C4—41no—
773C4—41no—
774C4—41no—
775C4—942no—
776C4—942no—
777C4—942no—
778C4—942no—
779C4—1881no—
780C4—1881no—
781C4#1568978211yescharacteristic
782C4#1568978211yescharacteristic
783C4#1568979411yescharacteristic
784C4#1568979411yescharacteristic
785C2—81no—
786C2—3761no—
787C2—1882no—
788C2#2024622811yescharacteristic
789C2#2025183011yescharacteristic
790C2#2025183611yescharacteristic
791C2#2025236911yescharacteristic
792C2#2025237811yescharacteristic
793C2#2025252211yescharacteristic
794C2#2025255311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D47
commutator, socleC23×C47C23×C4
FittingC47×#1750C2
prime radicalC2×#13093997C4
cosocleC22×C4×C47C24
hypercenter#1750D47
hypocenterC47#22533
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ #1750

Complements

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

NH ≅ G/Ntype
2. C2×#15689253C2semidirect
3. C2×#15689251C2semidirect
4. #20244186C2semidirect
5. #20244184C2semidirect
6. #20244184C2semidirect
7. #20244184C2semidirect
8. #20244182C2semidirect
9. #20244180C2semidirect
10. #20243372C2semidirect
11. #20243371C2semidirect
12. #20243367C2semidirect
13. #20243153C2semidirect
14. #20243149C2semidirect
15. C47×#1750C2semidirect
401. #1750D47semidirect
460. C47#22533semidirect

Maximal subgroups

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

subgroupindex
C2×#156896512
C2×#156892532
C2×#156892512
#202441862
#202441842
#202441822
#202441802
#202433722
#202433712
#202433672
#202431532
#202431492
C47×#17502
#2253347