Finite Group Databasebeta

← #26222424

Subgroups — #26222424

Order 12032.

1052 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689196C211yesmaximal, characteristic, complemented
2C2×#15689194C211yesmaximal, characteristic, complemented
3C2×C8×C22⋊D47C211yesmaximal, characteristic, complemented
4#20246624C211yesmaximal, characteristic
5#20244182C211yesmaximal, characteristic, complemented
6#20244106C211yesmaximal, characteristic, complemented
7#20243994C211yesmaximal, characteristic, complemented
8#20243994C211yesmaximal, characteristic, complemented
9#20243685C211yesmaximal, characteristic, complemented
10#20243685C211yesmaximal, characteristic, complemented
11#20243372C211yesmaximal, characteristic, complemented
12#20243260C211yesmaximal, characteristic, complemented
13#20243173C211yesmaximal, characteristic, complemented
14#20243165C211yesmaximal, characteristic, complemented
15C2×C47×#405C211yesmaximal, characteristic, complemented
16C22×#10625324C2211yescharacteristic
17C22×C8×D47C2211yescharacteristic
18C2×C4×D188C2211yescharacteristic
19C2×C4×C22⋊D47C2211yescharacteristic
20C2×C4×C22⋊D47C2211yescharacteristic
21#15689196—24no—
22#15689194—24no—
23C8×C22⋊D47—24no—
24C2×C4⋊(C47⋊C8)C2211yescharacteristic
25C2×C4⋊(C47⋊C8)C2211yescharacteristic
26C2×Dic47⋊C8C2211yescharacteristic
27C2×Dic47⋊C8C2211yescharacteristic
28C2×C22⋊(C47⋊C8)C2211yescharacteristic
29C2×C22⋊(C47⋊C8)C2211yescharacteristic
30C2×(C2×D47)⋊C8C2211yescharacteristic
31C2×(C2×D47)⋊C8C2211yescharacteristic
32C2×(C2×D47)⋊C8C2211yescharacteristic
33C2×(C2×D47)⋊C8C2211yescharacteristic
34C2×(C2×D47)⋊C8C2211yescharacteristic
35C2×(C2×D47)⋊C8C2211yescharacteristic
36C2×#13093934C2211yescharacteristic
37C2×C8×Dic47C2211yescharacteristic
38#15689053C411yescharacteristic
39#15689048C411yescharacteristic
40#15689045C411yescharacteristic
41#15689045C411yescharacteristic
42#15689040C411yescharacteristic
43#15689039C411yescharacteristic
44#15689039C411yescharacteristic
45#15689032C411yescharacteristic
46C4×C4⋊Dic47C2211yescharacteristic
47C4×(C2×D47)⋊C4C2211yescharacteristic
48C4×(C2×D47)⋊C4C2211yescharacteristic
49#15688878C2211yescharacteristic
50#15688878C2211yescharacteristic
51#15688877C2211yescharacteristic
52#15688877C2211yescharacteristic
53#15688877C2211yescharacteristic
54#15688877C2211yescharacteristic
55C22×M16×C47C2211yescharacteristic
56C23×C8×C47C2211yescharacteristic
57C2×#117×C47C2211yescharacteristic
58C47×#405—24no—
59C2×#97×C47C2211yescharacteristic
60C2×#97×C47C2211yescharacteristic
61C2×C4×C8×C47C2211yescharacteristic
62C2×C4×C8×C47C2211yescharacteristic
63C22×D188C2×C411yescharacteristic
64C22×C22⋊D47C2×C411yescharacteristic
65C22×C22⋊D47C2×C411yescharacteristic
66C22×C4×D47C2311yescharacteristic
67C22×C4×D47C2311yescharacteristic
68C2×#10625324—22no—
69C2×#10625324—22no—
70C2×#10625324—22no—
71C22×C47⋊C8C2311yescharacteristic
72C22×C47⋊C8C2311yescharacteristic
73C22×C47⋊C8C2311yescharacteristic
74C22×C47⋊C8C2311yescharacteristic
75C2×C8×D47—22no—
76C2×C8×D47—22no—
77C2×C8×D47—22no—
78C4×D188—22no—
79C4×D188—22no—
80C4×C22⋊D47—22no—
81C4×C22⋊D47—22no—
82C4×C22⋊D47—22no—
83C4×C22⋊D47—22no—
84C2×C4⋊Dic47C2×C411yescharacteristic
85C2×C4⋊Dic47C2×C411yescharacteristic
86C2×C4⋊Dic47C2×C411yescharacteristic
87C2×Dic47⋊C4C2×C411yescharacteristic
88C2×Dic47⋊C4C2×C411yescharacteristic
89C2×C22⋊Dic47C2×C411yescharacteristic
90C2×C22⋊Dic47C2×C411yescharacteristic
91C2×(C2×D47)⋊C4C2×C411yescharacteristic
92C2×(C2×D47)⋊C4C2×C411yescharacteristic
93C2×(C2×D47)⋊C4C2×C411yescharacteristic
94C2×(C2×D47)⋊C4C2×C411yescharacteristic
95C2×(C2×D47)⋊C4C2×C411yescharacteristic
96C2×(C2×D47)⋊C4C2×C411yescharacteristic
97C2×(C2×D47)⋊C4C2×C411yescharacteristic
98C2×(C2×D47)⋊C4C2×C411yescharacteristic
99C2×C4×Dic47C2311yescharacteristic
100C2×C4×Dic47C2311yescharacteristic
101C4⋊(C47⋊C8)—22no—
102C4⋊(C47⋊C8)—22no—
103Dic47⋊C8—22no—
104Dic47⋊C8—22no—
105C22⋊(C47⋊C8)—22no—
106C22⋊(C47⋊C8)—22no—
107(C2×D47)⋊C8—22no—
108(C2×D47)⋊C8—22no—
109(C2×D47)⋊C8—22no—
110(C2×D47)⋊C8—22no—
111(C2×D47)⋊C8—22no—
112(C2×D47)⋊C8—22no—
113#13093934—22no—
114C8×Dic47—22no—
115C47⋊#95C2×C411yescharacteristic
116C47⋊#95C2×C411yescharacteristic
117C47⋊#95C2×C411yescharacteristic
118C47⋊#95C2×C411yescharacteristic
119C47⋊#95C2×C411yescharacteristic
120C47⋊#95C2×C411yescharacteristic
121C23×C4×C47C2311yescharacteristic
122C2×M16×C47—22no—
123C2×M16×C47—22no—
124C2×M16×C47—22no—
125C22×C8×C47—22no—
126C22×C8×C47—22no—
127C22×C8×C47D414yescomplemented
128C22×C8×C47C2311yescharacteristic
129C22×C8×C47C2311yescharacteristic
130C22×C8×C47C2311yescharacteristic
131C22×C8×C47C2311yescharacteristic
132#117×C47—22no—
133#117×C47—22no—
134C2×C4⋊C4×C47C2×C411yescharacteristic
135C2×C4⋊C4×C47C2×C411yescharacteristic
136C2×C22⋊C4×C47C2×C411yescharacteristic
137C2×C22⋊C4×C47C2×C411yescharacteristic
138C2×C42×C47C2311yescharacteristic
139C2×C42×C47C2311yescharacteristic
140#97×C47—22no—
141#97×C47D414yescomplemented
142C4×C8×C47—22no—
143C4×C8×C47—22no—
144C24×C47C22×C411yescharacteristic
145C23×D47C22×C411yescharacteristic
146C23×D47C22×C411yescharacteristic
147C22×C4×C47—21no—
148C22×C4×C47—21no—
149C22×C4×C47—21no—
150C22×C4×C47—21no—
151C22×C4×C47C22×C411yescharacteristic
152C22×C4×C47C22×C411yescharacteristic
153C22×C4×C47C22×C411yescharacteristic
154C22×C4×C47C22×C411yescharacteristic
155C22×C4×C47C22×C411yescharacteristic
156C22×C4×C47C2×D412yes—
157C22×C4×C47#4112yes—
158C22×C4×C47C2411yescharacteristic
159C2×C22⋊D47—22no—
160C2×C22⋊D47—22no—
161C2×C22⋊D47—22no—
162C2×C22⋊D47—22no—
163C2×C22⋊D47—41no—
164C2×C22⋊D47—41no—
165C22×Dic47C22×C411yescharacteristic
166C22×Dic47C22×C411yescharacteristic
167C22×Dic47C22×C411yescharacteristic
168C22×Dic47C22×C411yescharacteristic
169C22×Dic47C22×C411yescharacteristic
170C22×Dic47C22×C411yescharacteristic
171C2×D188—22no—
172C2×D188—22no—
173C2×D188—41no—
174C2×C4×D47—21no—
175C2×C4×D47—21no—
176C2×C4×D47—21no—
177C2×C4×D47—21no—
178C2×C4×D47—21no—
179C2×C4×D47—21no—
180C2×C4×D47—21no—
181C2×C4×D47—21no—
182C2×C4×D47—21no—
183C2×C4×D47—21no—
184C2×C4×D47—21no—
185C2×C4×D47—21no—
186M16×C47—28no—
187C2×C8×C47—21no—
188C2×C8×C47—21no—
189C2×C8×C47—21no—
190C2×C8×C47—21no—
191C2×C8×C47—21no—
192C2×C8×C47—21no—
193C2×C8×C47—28no—
194C2×C8×C47C2×D412yes—
195C2×C8×C47C2×D412yes—
196C2×C8×C47C2×D412yes—
197C2×C8×C47C2×D412yes—
198C2×C8×C47#4112yes—
199C2×C8×C47#4112yes—
200C4⋊C4×C47—22no—
201C4⋊C4×C47—22no—
202C22⋊C4×C47—22no—
203C22⋊C4×C47—22no—
204C42×C47—21no—
205C42×C47—21no—
206C42×C47C2×D412yes—
207C42×C47#4112yes—
208C22⋊Dic47—22no—
209C22⋊Dic47—22no—
210(C2×D47)⋊C4—22no—
211(C2×D47)⋊C4—22no—
212(C2×D47)⋊C4—22no—
213(C2×D47)⋊C4—22no—
214(C2×D47)⋊C4—22no—
215(C2×D47)⋊C4—22no—
216(C2×D47)⋊C4—41no—
217(C2×D47)⋊C4—41no—
218C4⋊Dic47—22no—
219C4⋊Dic47—22no—
220C4⋊Dic47—41no—
221Dic47⋊C4—22no—
222Dic47⋊C4—22no—
223C4×Dic47—21no—
224C4×Dic47—21no—
225C4×Dic47—21no—
226C4×Dic47—21no—
227C2×C47⋊C8—21no—
228C2×C47⋊C8—21no—
229C2×C47⋊C8—21no—
230C2×C47⋊C8—21no—
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—
239#10625324—44no—
240C8×D47—44no—
241C23×C47—21no—
242C23×C47—21no—
243C23×C47—21no—
244C23×C47—21no—
245C23×C47—21no—
246C23×C47—21no—
247C23×C47C4×D412yes—
248C23×C47C23×C411yescharacteristic
249C22×D47—21no—
250C22×D47—21no—
251C22×D47—21no—
252C22×D47—21no—
253C22×D47—21no—
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#13112yes—
263C2×C4×C47—21no—
264C2×C4×C47—21no—
265C2×C4×C47—21no—
266C2×C4×C47—21no—
267C2×C4×C47—21no—
268C2×C4×C47—21no—
269C2×C4×C47—22no—
270C2×C4×C47—22no—
271C2×C4×C47—22no—
272C2×C4×C47—22no—
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×C47C4×D412yes—
280C2×C4×C47C4×D412yes—
281C2×C4×C47C4×D412yes—
282C2×C4×C47C22×D411yescharacteristic
283C2×C4×C47C22×D411yescharacteristic
284C2×C4×C47C2×#4111yescharacteristic
285C2×C4×C47C2×#4111yescharacteristic
286C2×C4×C47C2×#4111yescharacteristic
287C2×C4×C47C2×#4111yescharacteristic
288C22⋊D47—28no—
289C22⋊D47—44no—
290C2×Dic47—21no—
291C2×Dic47—21no—
292C2×Dic47—21no—
293C2×Dic47—21no—
294C2×Dic47—21no—
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#13112yes—
308D188—44no—
309C4×D47—41no—
310C4×D47—41no—
311C4×D47—41no—
312C4×D47—41no—
313C4×D47—41no—
314C4×D47—41no—
315C4×D47—41no—
316C4×D47—41no—
317C8×C47—22no—
318C8×C47—22no—
319C8×C47—22no—
320C8×C47#12114yes—
321C47⋊C8—41no—
322C47⋊C8—41no—
323C47⋊C8—41no—
324C47⋊C8—41no—
325#21495—471nomaximal, Sylow
326C22×C47—22no—
327C22×C47—22no—
328C22×C47—22no—
329C22×C47—41no—
330C22×C47—41no—
331C22×C47—41no—
332C22×C47—41no—
333C22×C47C2×C4×D411yescharacteristic
334C22×C47C2×C4×D411yescharacteristic
335C22×C47C4×#4111yescharacteristic
336C22×C47C2×#13111yescharacteristic
337C22×C47C2×#13111yescharacteristic
338C22×C47#56811yescharacteristic
339C22×C47#56811yescharacteristic
340C2×D47—22no—
341C2×D47—22no—
342C2×D47—22no—
343C2×D47—41no—
344C2×D47—41no—
345C2×D47—41no—
346C2×D47—41no—
347C2×D47—41no—
348C2×D47—41no—
349C2×D47—41no—
350C2×D47—41no—
351C2×D47—41no—
352C2×D47—41no—
353C2×D47—41no—
354C4×C47—22no—
355C4×C47—22no—
356C4×C47—22no—
357C4×C47—41no—
358C4×C47—41no—
359C4×C47C2×#12111yescharacteristic
360C4×C47#52511yescharacteristic
361C4×C47#52911yescharacteristic
362C4×C47#53211yescharacteristic
363Dic47—22no—
364Dic47—41no—
365Dic47—41no—
366Dic47—41no—
367Dic47—41no—
368Dic47—41no—
369C2×#435—471no—
370C2×#435—471no—
371C2×C8×D4—471no—
372C2×#405D4711yescharacteristic, complemented
373#2392—471no—
374#1954—471no—
375#1939—471no—
376#1923—471no—
377#1923—471no—
378#1870—471no—
379#1870—471no—
380#1798—471no—
381#1771—471no—
382#1753—471no—
383#1752—471no—
384C2×C47—42no—
385C2×C47C4×#12111yescharacteristic
386C2×C47#292911yescharacteristic
387C2×C47#293011yescharacteristic
388C2×C47#293311yescharacteristic
389C2×C47#293511yescharacteristic
390C2×C47#296811yescharacteristic
391C2×C47#296911yescharacteristic
392D47—42no—
393D47—81no—
394C22×M16—471no—
395C22×M16C2×D4711yescharacteristic
396C23×C8—471no—
397C23×C8C2×D4711yescharacteristic
398C2×C4×D4—471no—
399C2×C4×D4—471no—
400C2×C4×D4—471no—
401C2×#117C2×D4711yescharacteristic
402#435—944no—
403#435—944no—
404C8×D4—944no—
405C2×C4⋊C8—471no—
406C2×C4⋊C8—471no—
407C2×C4⋊C8—471no—
408C2×C4⋊C8—471no—
409C2×C22⋊C8—471no—
410C2×C22⋊C8—471no—
411C2×C22⋊C8—471no—
412C2×C22⋊C8—471no—
413C2×C22⋊C8—471no—
414C2×C22⋊C8—471no—
415C2×C22⋊C8—471no—
416C2×C22⋊C8—471no—
417#405—24no—
418C2×#97—471no—
419C2×#97C2×D4711yescharacteristic
420C2×#97C2×D4711yescharacteristic
421C2×C4×C8—471no—
422C2×C4×C8C2×D4711yescharacteristic
423C2×C4×C8C2×D4711yescharacteristic
424#398—471no—
425#397—471no—
426#396—471no—
427#396—471no—
428#394—471no—
429#394—471no—
430#394—471no—
431#392—471no—
432C4×C4⋊C4—471no—
433C4×C22⋊C4—471no—
434C4×C22⋊C4—471no—
435#336—471no—
436#336—471no—
437#336—471no—
438#336—471no—
439#336—471no—
440#336—471no—
441C47#2149511yescharacteristic, complemented, Sylow
442C22×D4—471no—
443C22×D4—471no—
444C22×D4—471no—
445C23×C4—471no—
446C23×C4—471no—
447C23×C4C22×D4711yescharacteristic
448C2×M16—22no—
449C2×M16—22no—
450C2×M16—22no—
451C2×M16—942no—
452C2×M16—942no—
453C2×M16—942no—
454C22×C8—22no—
455C22×C8—22no—
456C22×C8—471no—
457C22×C8—471no—
458C22×C8—471no—
459C22×C8—471no—
460C22×C8—942no—
461C22×C8—942no—
462C22×C8—942no—
463C22×C8D18814yescomplemented
464C22×C8C22×D4711yescharacteristic
465C22×C8C22×D4711yescharacteristic
466C22×C8C22×D4711yescharacteristic
467C22×C8C22×D4711yescharacteristic
468C4×D4—942no—
469C4×D4—942no—
470C4×D4—942no—
471C4×D4—942no—
472C4×D4—942no—
473C4×D4—942no—
474#117—22no—
475#117—22no—
476C2×C4⋊C4—471no—
477C2×C4⋊C4—471no—
478C2×C4⋊C4—471no—
479C2×C4⋊C4—471no—
480C2×C4⋊C4—471no—
481C2×C4⋊C4C4×D4711yescharacteristic
482C2×C4⋊C4C4×D4711yescharacteristic
483C2×C22⋊C4—471no—
484C2×C22⋊C4—471no—
485C2×C22⋊C4—471no—
486C2×C22⋊C4—471no—
487C2×C22⋊C4—471no—
488C2×C22⋊C4—471no—
489C2×C22⋊C4—471no—
490C2×C22⋊C4—471no—
491C2×C22⋊C4—471no—
492C2×C22⋊C4—471no—
493C2×C22⋊C4C4×D4711yescharacteristic
494C2×C22⋊C4C4×D4711yescharacteristic
495C2×C42—471no—
496C2×C42—471no—
497C2×C42C22×D4711yescharacteristic
498C2×C42C22×D4711yescharacteristic
499C4⋊C8—942no—
500C4⋊C8—942no—
501C4⋊C8—942no—
502C4⋊C8—942no—
503C22⋊C8—942no—
504C22⋊C8—942no—
505C22⋊C8—942no—
506C22⋊C8—942no—
507C22⋊C8—942no—
508C22⋊C8—942no—
509C22⋊C8—942no—
510C22⋊C8—942no—
511#97—22no—
512#97—942no—
513#97C22⋊D4714yescomplemented
514C4×C8—22no—
515C4×C8—22no—
516C4×C8—942no—
517#95—471no—
518#95—471no—
519#95—471no—
520#95—471no—
521#95—471no—
522#95—471no—
523C24—471no—
524C24—471no—
525C24C2×C4×D4711yescharacteristic
526C2×D4—942no—
527C2×D4—942no—
528C2×D4—942no—
529C2×D4—942no—
530C2×D4—942no—
531C2×D4—942no—
532C2×D4—1881no—
533C2×D4—1881no—
534C2×D4—1881no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—471no—
540C22×C4—471no—
541C22×C4—471no—
542C22×C4—471no—
543C22×C4—471no—
544C22×C4—471no—
545C22×C4—941no—
546C22×C4—941no—
547C22×C4—941no—
548C22×C4—941no—
549C22×C4—941no—
550C22×C4—941no—
551C22×C4—941no—
552C22×C4—941no—
553C22×C4—941no—
554C22×C4—941no—
555C22×C4—941no—
556C22×C4—941no—
557C22×C4C2×C4×D4711yescharacteristic
558C22×C4C2×C4×D4711yescharacteristic
559C22×C4C2×C4×D4711yescharacteristic
560C22×C4C2×C4×D4711yescharacteristic
561C22×C4C2×C4×D4711yescharacteristic
562C22×C4C2×D18812yes—
563C22×C4#1062535012yes—
564C22×C4C23×D4711yescharacteristic
565M16—28no—
566M16—1884no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—28no—
574C2×C8—941no—
575C2×C8—941no—
576C2×C8—941no—
577C2×C8—941no—
578C2×C8—941no—
579C2×C8—941no—
580C2×C8—941no—
581C2×C8—941no—
582C2×C8—941no—
583C2×C8—941no—
584C2×C8—941no—
585C2×C8—941no—
586C2×C8—1884no—
587C2×C8C2×D18812yes—
588C2×C8C2×D18812yes—
589C2×C8#1062535012yes—
590C2×C8#1062535012yes—
591C2×C8C2×C22⋊D4712yes—
592C2×C8C2×C22⋊D4712yes—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—942no—
596C4⋊C4—942no—
597C4⋊C4—942no—
598C4⋊C4—942no—
599C4⋊C4—1881no—
600C22⋊C4—22no—
601C22⋊C4—22no—
602C22⋊C4—942no—
603C22⋊C4—942no—
604C22⋊C4—942no—
605C22⋊C4—942no—
606C22⋊C4—942no—
607C22⋊C4—942no—
608C22⋊C4—942no—
609C22⋊C4—942no—
610C22⋊C4—1881no—
611C22⋊C4—1881no—
612C42—21no—
613C42—21no—
614C42—941no—
615C42—941no—
616C42—941no—
617C42—941no—
618C42#1062535012yes—
619C42C2×C22⋊D4712yes—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—472no—
627C23—941no—
628C23—941no—
629C23—941no—
630C23—941no—
631C23—941no—
632C23—941no—
633C23—941no—
634C23—941no—
635C23—941no—
636C23—941no—
637C23—941no—
638C23—941no—
639C23—941no—
640C23C4×D18812yes—
641C23C22×C4×D4711yescharacteristic
642D4—948no—
643D4—1884no—
644D4—1884no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—472no—
662C2×C4—941no—
663C2×C4—941no—
664C2×C4—941no—
665C2×C4—941no—
666C2×C4—941no—
667C2×C4—941no—
668C2×C4—941no—
669C2×C4—941no—
670C2×C4—941no—
671C2×C4—941no—
672C2×C4—941no—
673C2×C4—941no—
674C2×C4—941no—
675C2×C4—941no—
676C2×C4—941no—
677C2×C4—941no—
678C2×C4—941no—
679C2×C4—1881no—
680C2×C4—1881no—
681C2×C4—1881no—
682C2×C4—1881no—
683C2×C4—1881no—
684C2×C4—1881no—
685C2×C4—1881no—
686C2×C4—1881no—
687C2×C4C4×C22⋊D4712yes—
688C2×C4C4×C22⋊D4712yes—
689C2×C4C4×D18812yes—
690C2×C4C22×C22⋊D4711yescharacteristic
691C2×C4C22×D18811yescharacteristic
692C2×C4C2×#1062535011yescharacteristic
693C2×C4C2×#1062535011yescharacteristic
694C2×C4C2×#1062535011yescharacteristic
695C2×C4C2×#1062535011yescharacteristic
696C8—22no—
697C8—22no—
698C8—22no—
699C8—1881no—
700C8—1881no—
701C8—1881no—
702C8—1881no—
703C8#1309399814yes—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—942no—
712C22—942no—
713C22—942no—
714C22—1881no—
715C22—1881no—
716C22—1881no—
717C22—1881no—
718C22—1881no—
719C22—1881no—
720C22—1881no—
721C22—1881no—
722C22—1881no—
723C22—1881no—
724C22—1881no—
725C22C2×C4×C22⋊D4711yescharacteristic
726C22C2×C4×D18811yescharacteristic
727C22C4×#1062535011yescharacteristic
728C22#131×D4711yescharacteristic
729C22#131×D4711yescharacteristic
730C22#1568988811yescharacteristic
731C22#1568988811yescharacteristic
732C4—22no—
733C4—22no—
734C4—22no—
735C4—41no—
736C4—41no—
737C4—942no—
738C4—1881no—
739C4—1881no—
740C4—1881no—
741C4—1881no—
742C4—1881no—
743C4C2×#1309399811yescharacteristic
744C4#1568963411yescharacteristic
745C4#1568965711yescharacteristic
746C4#1568967311yescharacteristic
747C2—42no—
748C2—3761no—
749C2—1882no—
750C2C4×#1309399811yescharacteristic
751C2#2025208411yescharacteristic
752C2#2025209311yescharacteristic
753C2#2025211011yescharacteristic
754C2#2025213011yescharacteristic
755C2#2025237811yescharacteristic
756C2#2025238811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D47
commutator, socleC23×C47C23×C4
FittingC2×C47×#405C2
prime radical#15689032C4
cosocleC22×C4×C47C24
hypercenterC2×#405D47
hypocenterC47#21495
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×#405

Complements

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

NH ≅ G/Ntype
1. C2×#15689196C2semidirect
2. C2×#15689194C2semidirect
3. C2×C8×C22⋊D47C2semidirect
5. #20244182C2semidirect
6. #20244106C2semidirect
7. #20243994C2semidirect
8. #20243994C2semidirect
9. #20243685C2semidirect
10. #20243685C2semidirect
11. #20243372C2semidirect
12. #20243260C2semidirect
13. #20243173C2semidirect
14. #20243165C2semidirect
15. C2×C47×#405C2semidirect
127. C22×C8×C47D4semidirect
141. #97×C47D4semidirect
372. C2×#405D47semidirect
441. C47#21495semidirect
463. C22×C8D188semidirect
513. #97C22⋊D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156891962
C2×#156891942
C2×C8×C22⋊D472
#202466242
#202441822
#202441062
#202439942
#202436852
#202433722
#202432602
#202431732
#202431652
C2×C47×#4052
#2149547