Finite Group Databasebeta

← #26238396

Subgroups — #26238396

Order 12032.

1084 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689194C211yesmaximal, characteristic, complemented
2C2×#15689193C211yesmaximal, characteristic, complemented
3C2×C8×C22⋊D47C211yesmaximal, characteristic, complemented
4C2×#15689145C211yesmaximal, characteristic, complemented
5C4×#13093997C211yesmaximal, characteristic
6#20244180C211yesmaximal, characteristic, complemented
7#20244103C211yesmaximal, characteristic, complemented
8#20244003C211yesmaximal, characteristic, complemented
9#20244000C211yesmaximal, characteristic, complemented
10#20243684C211yesmaximal, characteristic, complemented
11#20243682C211yesmaximal, characteristic, complemented
12#20243567C211yesmaximal, characteristic, complemented
13#20243254C211yesmaximal, characteristic, complemented
14#20243145C211yesmaximal, characteristic, complemented
15C47×#1850C211yesmaximal, characteristic, complemented
16C22×#10625324C2211yescharacteristic
17C22×#10625324C2211yescharacteristic
18C22×C8×D47C2211yescharacteristic
19C2×#13093997C411yescharacteristic
20C2×C4×D188C2211yescharacteristic
21C2×C4×C22⋊D47C2211yescharacteristic
22C2×C4×C22⋊D47C2211yescharacteristic
23C2×C42×D47C2211yescharacteristic
24#15689194—24no—
25#15689193—24no—
26C8×C22⋊D47—24no—
27#15689145—24no—
28C2×C4⋊(C47⋊C8)C2211yescharacteristic
29C2×Dic47⋊C8C2211yescharacteristic
30C2×Dic47⋊C8C2211yescharacteristic
31C2×Dic47⋊C8C2211yescharacteristic
32C2×C22⋊(C47⋊C8)C2211yescharacteristic
33C2×C22⋊(C47⋊C8)C2211yescharacteristic
34C2×(C2×D47)⋊C8C2211yescharacteristic
35C2×(C2×D47)⋊C8C2211yescharacteristic
36C2×(C2×D47)⋊C8C2211yescharacteristic
37C2×(C2×D47)⋊C8C2211yescharacteristic
38C2×(C2×D47)⋊C8C2211yescharacteristic
39C2×#13093935C2211yescharacteristic
40C2×#13093934C2211yescharacteristic
41C2×C8×Dic47C2211yescharacteristic
42C2×C8×Dic47C2211yescharacteristic
43#15689023C411yescharacteristic
44#15689020C411yescharacteristic
45#15689016C411yescharacteristic
46#15689012C411yescharacteristic
47#15689001C411yescharacteristic
48#15688999C411yescharacteristic
49#15688982C411yescharacteristic
50C4×Dic47⋊C4C2211yescharacteristic
51C4×(C2×D47)⋊C4C2211yescharacteristic
52#15688878C2211yescharacteristic
53#15688878C2211yescharacteristic
54#15688877C2211yescharacteristic
55#15688877C2211yescharacteristic
56C23×C8×C47C2211yescharacteristic
57C2×C4⋊C8×C47C2211yescharacteristic
58C2×C4⋊C8×C47C2211yescharacteristic
59C2×C22⋊C8×C47C2211yescharacteristic
60C4×C22⋊C4×C47C2211yescharacteristic
61C47×#336C2211yescharacteristic
62C47×#336C2211yescharacteristic
63C22×D188C2×C411yescharacteristic
64C22×C22⋊D47C2×C411yescharacteristic
65C22×C22⋊D47C2×C411yescharacteristic
66C22×C4×D47C2×C411yescharacteristic
67C22×C4×D47C2×C411yescharacteristic
68C22×C4×D47C2311yescharacteristic
69C22×C4×D47C2311yescharacteristic
70C2×#10625324—22no—
71C2×#10625324—22no—
72C2×#10625324—22no—
73C2×#10625324—22no—
74C2×#10625324—41no—
75C2×#10625324—41no—
76C22×C47⋊C8C2311yescharacteristic
77C22×C47⋊C8C2311yescharacteristic
78C22×C47⋊C8C2311yescharacteristic
79C22×C47⋊C8C2311yescharacteristic
80C2×C8×D47—22no—
81C2×C8×D47—22no—
82C2×C8×D47—41no—
83#13093997—24no—
84C4×D188—22no—
85C4×D188—22no—
86C4×C22⋊D47—22no—
87C4×C22⋊D47—22no—
88C4×C22⋊D47—22no—
89C4×C22⋊D47—22no—
90C2×C4⋊Dic47C2×C411yescharacteristic
91C2×Dic47⋊C4C2×C411yescharacteristic
92C2×Dic47⋊C4C2×C411yescharacteristic
93C2×Dic47⋊C4C2×C411yescharacteristic
94C2×Dic47⋊C4C2×C411yescharacteristic
95C2×C22⋊Dic47C2×C411yescharacteristic
96C2×C22⋊Dic47C2×C411yescharacteristic
97C2×(C2×D47)⋊C4C2×C411yescharacteristic
98C2×(C2×D47)⋊C4C2×C411yescharacteristic
99C2×(C2×D47)⋊C4C2×C411yescharacteristic
100C2×(C2×D47)⋊C4C2×C411yescharacteristic
101C2×(C2×D47)⋊C4C2×C411yescharacteristic
102C2×(C2×D47)⋊C4C2×C411yescharacteristic
103C2×C4×Dic47C2×C411yescharacteristic
104C2×C4×Dic47C2×C411yescharacteristic
105C2×C4×Dic47C2311yescharacteristic
106C2×C4×Dic47C2311yescharacteristic
107C42×D47—22no—
108C42×D47—22no—
109C4⋊(C47⋊C8)—22no—
110Dic47⋊C8—22no—
111Dic47⋊C8—22no—
112Dic47⋊C8D414yescomplemented
113C22⋊(C47⋊C8)—22no—
114C22⋊(C47⋊C8)—22no—
115(C2×D47)⋊C8—22no—
116(C2×D47)⋊C8—22no—
117(C2×D47)⋊C8—22no—
118(C2×D47)⋊C8—41no—
119(C2×D47)⋊C8D414yescomplemented
120#13093935—22no—
121#13093934—22no—
122C8×Dic47—22no—
123C8×Dic47—22no—
124C47⋊#95C2×C411yescharacteristic
125C47⋊#95C2×C411yescharacteristic
126C47⋊#95C2×C411yescharacteristic
127C47⋊#95C2×C411yescharacteristic
128C23×C4×C47C2311yescharacteristic
129C22×C8×C47—22no—
130C22×C8×C47—22no—
131C22×C8×C47—41no—
132C22×C8×C47C2311yescharacteristic
133C22×C8×C47C2311yescharacteristic
134C22×C8×C47C2311yescharacteristic
135C22×C8×C47C2311yescharacteristic
136C2×C22⋊C4×C47C2×C411yescharacteristic
137C2×C22⋊C4×C47C2×C411yescharacteristic
138C2×C42×C47C2311yescharacteristic
139C2×C42×C47C2311yescharacteristic
140C4⋊C8×C47—22no—
141C4⋊C8×C47—22no—
142C22⋊C8×C47—41no—
143#95×C47C2×C411yescharacteristic
144#95×C47C2×C411yescharacteristic
145C24×C47C22×C411yescharacteristic
146C23×D47C22×C411yescharacteristic
147C23×D47C22×C411yescharacteristic
148C22×C4×C47—21no—
149C22×C4×C47—21no—
150C22×C4×C47—21no—
151C22×C4×C47—21no—
152C22×C4×C47—21no—
153C22×C4×C47—21no—
154C22×C4×C47C22×C411yescharacteristic
155C22×C4×C47C22×C411yescharacteristic
156C22×C4×C47C22×C411yescharacteristic
157C22×C4×C47C22×C411yescharacteristic
158C22×C4×C47C22×C411yescharacteristic
159C22×C4×C47C2411yescharacteristic
160C2×C22⋊D47—22no—
161C2×C22⋊D47—22no—
162C2×C22⋊D47—22no—
163C2×C22⋊D47—22no—
164C2×C22⋊D47—41no—
165C2×C22⋊D47M1614yescomplemented
166C22×Dic47C22×C411yescharacteristic
167C22×Dic47C22×C411yescharacteristic
168C22×Dic47C22×C411yescharacteristic
169C22×Dic47C22×C411yescharacteristic
170C22×Dic47C22×C411yescharacteristic
171C22×Dic47C22×C411yescharacteristic
172C2×D188—22no—
173C2×D188—22no—
174C2×D188—41no—
175C2×C4×D47—21no—
176C2×C4×D47—21no—
177C2×C4×D47—21no—
178C2×C4×D47—21no—
179C2×C4×D47—22no—
180C2×C4×D47—21no—
181C2×C4×D47—21no—
182C2×C4×D47—21no—
183C2×C4×D47—21no—
184C2×C4×D47—21no—
185C2×C4×D47—21no—
186C2×C4×D47—22no—
187C2×C4×D47—22no—
188C2×C4×D47—22no—
189C2×C4×D47—22no—
190C2×C4×D47—41no—
191C2×C4×D47C2×D412yes—
192C2×C4×D47#4112yes—
193C2×C8×C47—21no—
194C2×C8×C47—21no—
195C2×C8×C47—21no—
196C2×C8×C47—21no—
197C2×C8×C47—21no—
198C2×C8×C47—21no—
199C2×C8×C47—21no—
200C2×C8×C47—21no—
201C2×C8×C47—21no—
202C2×C8×C47—21no—
203C2×C8×C47—44no—
204C2×C8×C47C2×D412yes—
205C2×C8×C47C2×D412yes—
206C22⋊C4×C47—22no—
207C22⋊C4×C47—22no—
208C42×C47—21no—
209C42×C47—21no—
210C42×C47—21no—
211C42×C47—21no—
212C22⋊Dic47—22no—
213C22⋊Dic47—22no—
214(C2×D47)⋊C4—22no—
215(C2×D47)⋊C4—22no—
216(C2×D47)⋊C4—22no—
217(C2×D47)⋊C4—22no—
218(C2×D47)⋊C4—22no—
219(C2×D47)⋊C4—22no—
220C4⋊Dic47—22no—
221Dic47⋊C4—22no—
222Dic47⋊C4—22no—
223Dic47⋊C4—22no—
224Dic47⋊C4—22no—
225C4×Dic47—21no—
226C4×Dic47—21no—
227C4×Dic47—22no—
228C4×Dic47—22no—
229C4×Dic47C2×D412yes—
230C4×Dic47#4112yes—
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⋊C8C2×D412yes—
242C2×C47⋊C8C2×D412yes—
243#10625324—44no—
244#10625324—44no—
245C8×D47—44no—
246C23×C47—21no—
247C23×C47—21no—
248C23×C47—21no—
249C23×C47—21no—
250C23×C47—21no—
251C23×C47—21no—
252C23×C47C2×M1612yes—
253C23×C47C23×C411yescharacteristic
254C22×D47—21no—
255C22×D47—21no—
256C22×D47—21no—
257C22×D47—21no—
258C22×D47—21no—
259C22×D47—21no—
260C22×D47—21no—
261C22×D47—21no—
262C22×D47—21no—
263C22×D47—21no—
264C22×D47—21no—
265C22×D47—21no—
266C22×D47C4×D412yes—
267C22×D47C2×M1612yes—
268C2×C4×C47—21no—
269C2×C4×C47—21no—
270C2×C4×C47—21no—
271C2×C4×C47—21no—
272C2×C4×C47—21no—
273C2×C4×C47—21no—
274C2×C4×C47—21no—
275C2×C4×C47—21no—
276C2×C4×C47—21no—
277C2×C4×C47—21no—
278C2×C4×C47—21no—
279C2×C4×C47—21no—
280C2×C4×C47—21no—
281C2×C4×C47—21no—
282C2×C4×C47—41no—
283C2×C4×C47—41no—
284C2×C4×C47—41no—
285C2×C4×C47—41no—
286C2×C4×C47#13112yes—
287C2×C4×C47C22×D411yescharacteristic
288C2×C4×C47C22×D411yescharacteristic
289C2×C4×C47C2×#4111yescharacteristic
290C2×C4×C47C2×#4111yescharacteristic
291C2×C4×C47H(5,𝔽2)11yescharacteristic
292C2×C4×C472−1+411yescharacteristic
293C22⋊D47—28no—
294C22⋊D47—44no—
295C2×Dic47—21no—
296C2×Dic47—21no—
297C2×Dic47—21no—
298C2×Dic47—21no—
299C2×Dic47—21no—
300C2×Dic47—21no—
301C2×Dic47—21no—
302C2×Dic47—21no—
303C2×Dic47—21no—
304C2×Dic47—21no—
305C2×Dic47—21no—
306C2×Dic47—21no—
307C2×Dic47—21no—
308C2×Dic47C4×D412yes—
309C2×Dic47C4×D412yes—
310C2×Dic47C4×D412yes—
311C2×Dic47C2×M1612yes—
312C2×Dic47#13112yes—
313D188—44no—
314C4×D47—22no—
315C4×D47—22no—
316C4×D47—22no—
317C4×D47—22no—
318C4×D47—44no—
319C4×D47—41no—
320C4×D47—41no—
321C4×D47—41no—
322C4×D47—41no—
323C4×D47—44no—
324C8×C47—22no—
325C8×C47—22no—
326C8×C47—41no—
327C8×C47—41no—
328C47⋊C8—22no—
329C47⋊C8—22no—
330C47⋊C8—41no—
331C47⋊C8—41no—
332#22986—471nomaximal, Sylow
333C22×C47—22no—
334C22×C47—22no—
335C22×C47—22no—
336C22×C47—41no—
337C22×C47—41no—
338C22×C47—41no—
339C22×C47—41no—
340C22×C47C2×C4×D411yescharacteristic
341C22×C47C2×C4×D411yescharacteristic
342C22×C47#52011yescharacteristic
343C22×C47C22×M1611yescharacteristic
344C22×C47C2×#13111yescharacteristic
345C22×C47C2×#13111yescharacteristic
346C22×C47#56811yescharacteristic
347C2×D47—22no—
348C2×D47—22no—
349C2×D47—22no—
350C2×D47—22no—
351C2×D47—22no—
352C2×D47—22no—
353C2×D47—41no—
354C2×D47—41no—
355C2×D47—41no—
356C2×D47—41no—
357C2×D47—41no—
358C2×D47—41no—
359C2×D47—41no—
360C2×D47—41no—
361C4×C47—22no—
362C4×C47—41no—
363C4×C47—41no—
364C4×C47—41no—
365C4×C47—41no—
366C4×C47D4211yescharacteristic
367C4×C47#54711yescharacteristic
368C4×C47#54811yescharacteristic
369C4×C47#55311yescharacteristic
370Dic47—22no—
371Dic47—22no—
372Dic47—41no—
373Dic47—41no—
374Dic47—41no—
375Dic47#43514yescomplemented
376C2×#435—471no—
377C2×#435—471no—
378C2×C8×D4—471no—
379C2×#423—471no—
380C4×#121—471no—
381#1954—471no—
382#1939—471no—
383#1924—471no—
384#1924—471no—
385#1870—471no—
386#1870—471no—
387#1850—471no—
388#1850D4711yescharacteristic, complemented
389#1770—471no—
390C4×C22⋊C8—471no—
391C2×C47—42no—
392C2×C47#236111yescharacteristic
393C2×C47C2×#43511yescharacteristic
394C2×C47#293111yescharacteristic
395C2×C47#293311yescharacteristic
396C2×C47D4×M1611yescharacteristic
397C2×C47#299011yescharacteristic
398C2×C47#299311yescharacteristic
399D47—42no—
400D47—42no—
401C22×M16—471no—
402C22×M16—471no—
403C23×C8—471no—
404C23×C8C2×D4711yescharacteristic
405C2×#121—471no—
406C2×C4×D4—471no—
407C2×C4×D4—471no—
408C2×C4×D4—471no—
409C22×C42—471no—
410#435—944no—
411#435—944no—
412C8×D4—944no—
413#423—944no—
414C2×C4⋊C8—471no—
415C2×C4⋊C8—471no—
416C2×C4⋊C8—471no—
417C2×C4⋊C8—471no—
418C2×C4⋊C8C2×D4711yescharacteristic
419C2×C4⋊C8C2×D4711yescharacteristic
420C2×C22⋊C8—471no—
421C2×C22⋊C8—471no—
422C2×C22⋊C8—471no—
423C2×C22⋊C8—471no—
424C2×C22⋊C8—471no—
425C2×C22⋊C8—471no—
426C2×C22⋊C8—471no—
427C2×C22⋊C8C2×D4711yescharacteristic
428C2×#97—471no—
429C2×#97—471no—
430C2×C4×C8—471no—
431C2×C4×C8—471no—
432#390—471no—
433#389—471no—
434#388—471no—
435#388—471no—
436#386—471no—
437#386—471no—
438#380—471no—
439C4×C4⋊C4—471no—
440C4×C22⋊C4—471no—
441C4×C22⋊C4C2×D4711yescharacteristic
442#336—471no—
443#336—471no—
444#336—471no—
445#336—471no—
446#336C2×D4711yescharacteristic
447#336C2×D4711yescharacteristic
448C47#2298611yescharacteristic, complemented, Sylow
449C22×D4—471no—
450C22×D4—471no—
451C22×D4—471no—
452C23×C4—471no—
453C23×C4—471no—
454C23×C4—471no—
455C23×C4—471no—
456C23×C4C22×D4711yescharacteristic
457C2×M16—942no—
458C2×M16—942no—
459C2×M16—942no—
460C2×M16—942no—
461C2×M16—1881no—
462C2×M16—1881no—
463C22×C8—22no—
464C22×C8—22no—
465C22×C8—41no—
466C22×C8—471no—
467C22×C8—471no—
468C22×C8—471no—
469C22×C8—471no—
470C22×C8—942no—
471C22×C8—942no—
472C22×C8—1881no—
473C22×C8C22×D4711yescharacteristic
474C22×C8C22×D4711yescharacteristic
475C22×C8C22×D4711yescharacteristic
476C22×C8C22×D4711yescharacteristic
477#121—944no—
478C4×D4—942no—
479C4×D4—942no—
480C4×D4—942no—
481C4×D4—942no—
482C4×D4—942no—
483C4×D4—942no—
484C2×C4⋊C4—471no—
485C2×C4⋊C4—471no—
486C2×C4⋊C4—471no—
487C2×C4⋊C4—471no—
488C2×C4⋊C4—471no—
489C2×C22⋊C4—471no—
490C2×C22⋊C4—471no—
491C2×C22⋊C4—471no—
492C2×C22⋊C4—471no—
493C2×C22⋊C4—471no—
494C2×C22⋊C4—471no—
495C2×C22⋊C4—471no—
496C2×C22⋊C4—471no—
497C2×C22⋊C4C4×D4711yescharacteristic
498C2×C22⋊C4C4×D4711yescharacteristic
499C2×C42—471no—
500C2×C42—471no—
501C2×C42—471no—
502C2×C42—471no—
503C2×C42—942no—
504C2×C42—942no—
505C2×C42C22×D4711yescharacteristic
506C2×C42C22×D4711yescharacteristic
507C4⋊C8—22no—
508C4⋊C8—22no—
509C4⋊C8—474no—
510C4⋊C8—942no—
511C4⋊C8—942no—
512C4⋊C8—942no—
513C22⋊C8—41no—
514C22⋊C8—474no—
515C22⋊C8—942no—
516C22⋊C8—942no—
517C22⋊C8—942no—
518C22⋊C8—942no—
519C22⋊C8—942no—
520C22⋊C8—1881no—
521#97—942no—
522#97—942no—
523C4×C8—942no—
524C4×C8—942no—
525#95—471no—
526#95—471no—
527#95—471no—
528#95—471no—
529#95C4×D4711yescharacteristic
530#95C4×D4711yescharacteristic
531C24—471no—
532C24—471no—
533C24C2×C4×D4711yescharacteristic
534C2×D4—474no—
535C2×D4—942no—
536C2×D4—942no—
537C2×D4—942no—
538C2×D4—942no—
539C2×D4—942no—
540C2×D4—942no—
541C2×D4—1881no—
542C2×D4—1881no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—471no—
550C22×C4—471no—
551C22×C4—471no—
552C22×C4—472no—
553C22×C4—472no—
554C22×C4—471no—
555C22×C4—471no—
556C22×C4—471no—
557C22×C4—942no—
558C22×C4—942no—
559C22×C4—942no—
560C22×C4—942no—
561C22×C4—941no—
562C22×C4—941no—
563C22×C4—941no—
564C22×C4—941no—
565C22×C4—942no—
566C22×C4—941no—
567C22×C4—941no—
568C22×C4—941no—
569C22×C4—941no—
570C22×C4—941no—
571C22×C4—941no—
572C22×C4—1881no—
573C22×C4C2×C4×D4711yescharacteristic
574C22×C4C2×C4×D4711yescharacteristic
575C22×C4C2×C4×D4711yescharacteristic
576C22×C4C2×C4×D4711yescharacteristic
577C22×C4C2×C4×D4711yescharacteristic
578C22×C4C23×D4711yescharacteristic
579M16—1884no—
580M16—1884no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—44no—
592C2×C8—472no—
593C2×C8—472no—
594C2×C8—941no—
595C2×C8—941no—
596C2×C8—941no—
597C2×C8—941no—
598C2×C8—941no—
599C2×C8—941no—
600C2×C8—941no—
601C2×C8—941no—
602C2×C8—941no—
603C2×C8—941no—
604C2×C8—1884no—
605C2×C8D4×D4712yes—
606C2×C8D4×D4712yes—
607C4⋊C4—942no—
608C4⋊C4—942no—
609C4⋊C4—942no—
610C4⋊C4—942no—
611C4⋊C4—942no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—942no—
615C22⋊C4—942no—
616C22⋊C4—942no—
617C22⋊C4—942no—
618C22⋊C4—942no—
619C22⋊C4—942no—
620C22⋊C4—942no—
621C22⋊C4—942no—
622C42—21no—
623C42—21no—
624C42—21no—
625C42—21no—
626C42—472no—
627C42—472no—
628C42—942no—
629C42—942no—
630C42—941no—
631C42—941no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—472no—
639C23—472no—
640C23—941no—
641C23—941no—
642C23—941no—
643C23—941no—
644C23—941no—
645C23—941no—
646C23—941no—
647C23—941no—
648C23—941no—
649C23—941no—
650C23—941no—
651C23—941no—
652C23M16×D4712yes—
653C23C22×C4×D4711yescharacteristic
654D4—948no—
655D4—1884no—
656D4—1884no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—472no—
676C2×C4—472no—
677C2×C4—472no—
678C2×C4—472no—
679C2×C4—472no—
680C2×C4—941no—
681C2×C4—941no—
682C2×C4—941no—
683C2×C4—941no—
684C2×C4—942no—
685C2×C4—942no—
686C2×C4—942no—
687C2×C4—942no—
688C2×C4—941no—
689C2×C4—941no—
690C2×C4—941no—
691C2×C4—941no—
692C2×C4—941no—
693C2×C4—941no—
694C2×C4—941no—
695C2×C4—941no—
696C2×C4—941no—
697C2×C4—1884no—
698C2×C4—1884no—
699C2×C4—1881no—
700C2×C4—1881no—
701C2×C4—1881no—
702C2×C4—1881no—
703C2×C4#1309403012yes—
704C2×C4C2×D4×D4711yescharacteristic
705C2×C4C2×D4×D4711yescharacteristic
706C2×C4#41×D4711yescharacteristic
707C2×C4#41×D4711yescharacteristic
708C2×C4#1309406911yescharacteristic
709C2×C4#1309407211yescharacteristic
710C8—22no—
711C8—22no—
712C8—41no—
713C8—41no—
714C8—942no—
715C8—942no—
716C8—1881no—
717C8—1881no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—942no—
726C22—942no—
727C22—942no—
728C22—942no—
729C22—942no—
730C22—942no—
731C22—1881no—
732C22—1881no—
733C22—1881no—
734C22—1881no—
735C22—1881no—
736C22—1881no—
737C22—1881no—
738C22—1881no—
739C22C4×D4×D4711yescharacteristic
740C22C4×D4×D4711yescharacteristic
741C22#1568960411yescharacteristic
742C22C2×M16×D4711yescharacteristic
743C22#131×D4711yescharacteristic
744C22C2×#1309403011yescharacteristic
745C22#1568988811yescharacteristic
746C4—22no—
747C4—41no—
748C4—41no—
749C4—41no—
750C4—41no—
751C4—474no—
752C4—942no—
753C4—942no—
754C4—1881no—
755C4—1881no—
756C4—1881no—
757C4#1568975511yescharacteristic
758C4#1568977511yescharacteristic
759C4#1568978311yescharacteristic
760C4#1568981811yescharacteristic
761C2—42no—
762C2—1882no—
763C2—1882no—
764C2#2024640711yescharacteristic
765C2#435×D4711yescharacteristic
766C2#2025209511yescharacteristic
767C2#2025210811yescharacteristic
768C2#2025212111yescharacteristic
769C2#2025251011yescharacteristic
770C2#2025253511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D47
commutator, socleC23×C47C23×C4
FittingC47×#1850C2
prime radicalC2×#13093997C4
cosocleC22×C4×C47C24
hypercenter#1850D47
hypocenterC47#22986
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ #1850

Complements

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

NH ≅ G/Ntype
1. C2×#15689194C2semidirect
2. C2×#15689193C2semidirect
3. C2×C8×C22⋊D47C2semidirect
4. C2×#15689145C2semidirect
6. #20244180C2semidirect
7. #20244103C2semidirect
8. #20244003C2semidirect
9. #20244000C2semidirect
10. #20243684C2semidirect
11. #20243682C2semidirect
12. #20243567C2semidirect
13. #20243254C2semidirect
14. #20243145C2semidirect
15. C47×#1850C2semidirect
112. Dic47⋊C8D4semidirect
119. (C2×D47)⋊C8D4semidirect
165. C2×C22⋊D47M16semidirect
375. Dic47#435semidirect
388. #1850D47semidirect
448. C47#22986semidirect

Maximal subgroups

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

subgroupindex
C2×#156891942
C2×#156891932
C2×C8×C22⋊D472
C2×#156891452
C4×#130939972
#202441802
#202441032
#202440032
#202440002
#202436842
#202436822
#202435672
#202432542
#202431452
C47×#18502
#2298647