Finite Group Databasebeta

← #26238408

Subgroups — #26238408

Order 12032.

1098 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×#15689196C211yesmaximal, characteristic, complemented
2C2×#15689193C211yesmaximal, characteristic, complemented
3C2×C8×D188C211yesmaximal, characteristic, complemented
4C2×C4⋊C8×D47C211yesmaximal, characteristic, complemented
5C4×#13093999C211yesmaximal, characteristic
6#20244186C211yesmaximal, characteristic, complemented
7#20244112C211yesmaximal, characteristic, complemented
8#20244001C211yesmaximal, characteristic, complemented
9#20243994C211yesmaximal, characteristic, complemented
10#20243679C211yesmaximal, characteristic, complemented
11#20243679C211yesmaximal, characteristic, complemented
12#20243572C211yesmaximal, characteristic, complemented
13#20243567C211yesmaximal, characteristic, complemented
14#20243151C211yesmaximal, characteristic, complemented
15C47×#1771C211yesmaximal, characteristic, complemented
16C22×#10625324C2211yescharacteristic
17C22×C8×D47C2211yescharacteristic
18C22×C8×D47C2211yescharacteristic
19C22×C8×D47C2211yescharacteristic
20C2×#13093999C411yescharacteristic
21C2×C4×D188C2211yescharacteristic
22C2×C4×D188C2211yescharacteristic
23C2×C4×D188C2211yescharacteristic
24C2×C42×D47C2211yescharacteristic
25#15689196—24no—
26#15689193—24no—
27C8×D188—24no—
28C2×C4⋊(C47⋊C8)C2211yescharacteristic
29C2×C4⋊(C47⋊C8)C2211yescharacteristic
30C2×C4⋊(C47⋊C8)C2211yescharacteristic
31C2×Dic47⋊C8C2211yescharacteristic
32C2×Dic47⋊C8C2211yescharacteristic
33C4⋊C8×D47—24no—
34C2×(C2×D47)⋊C8C2211yescharacteristic
35C2×(C2×D47)⋊C8C2211yescharacteristic
36C2×(C2×D47)⋊C8C2211yescharacteristic
37C2×(C2×D47)⋊C8C2211yescharacteristic
38C2×(C2×D47)⋊C8C2211yescharacteristic
39C2×(C2×D47)⋊C8C2211yescharacteristic
40C2×(C2×D47)⋊C8C2211yescharacteristic
41C2×(C2×D47)⋊C8C2211yescharacteristic
42C2×#13093935C2211yescharacteristic
43#15689024C411yescharacteristic
44#15689022C411yescharacteristic
45#15689015C411yescharacteristic
46#15689015C411yescharacteristic
47#15689001C411yescharacteristic
48#15689001C411yescharacteristic
49#15688980C411yescharacteristic
50C4×(C2×D47)⋊C4C2211yescharacteristic
51C4×(C2×D47)⋊C4C2211yescharacteristic
52#15688878C2211yescharacteristic
53#15688878C2211yescharacteristic
54#15688877C2211yescharacteristic
55#15688877C2211yescharacteristic
56C2×C4⋊C8×C47C2211yescharacteristic
57C2×#97×C47C2211yescharacteristic
58C2×#97×C47C2211yescharacteristic
59C2×C4×C8×C47C2211yescharacteristic
60C4×C4⋊C4×C47C2211yescharacteristic
61C47×#336C2211yescharacteristic
62C47×#336C2211yescharacteristic
63C22×D188C2×C411yescharacteristic
64C22×D188C2×C411yescharacteristic
65C22×D188C2×C411yescharacteristic
66C22×C4×D47C2×C411yescharacteristic
67C22×C4×D47C2×C411yescharacteristic
68C22×C4×D47C2311yescharacteristic
69C22×C4×D47C2311yescharacteristic
70C22×C4×D47C2311yescharacteristic
71C2×#10625324—22no—
72C2×#10625324—22no—
73C2×#10625324—41no—
74C22×C47⋊C8C2311yescharacteristic
75C22×C47⋊C8C2311yescharacteristic
76C22×C47⋊C8C2311yescharacteristic
77C22×C47⋊C8C2311yescharacteristic
78C2×C8×D47—22no—
79C2×C8×D47—22no—
80C2×C8×D47—22no—
81C2×C8×D47—22no—
82C2×C8×D47—22no—
83C2×C8×D47—22no—
84C2×C8×D47—41no—
85C2×C8×D47—41no—
86C2×C8×D47—41no—
87#13093999—24no—
88C4×D188—22no—
89C4×D188—22no—
90C4×D188—22no—
91C4×D188—22no—
92C4×D188—22no—
93C4×D188—22no—
94C2×C4⋊Dic47C2×C411yescharacteristic
95C2×C4⋊Dic47C2×C411yescharacteristic
96C2×C4⋊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×(C2×D47)⋊C4C2×C411yescharacteristic
104C2×(C2×D47)⋊C4C2×C411yescharacteristic
105C2×(C2×D47)⋊C4C2×C411yescharacteristic
106C2×(C2×D47)⋊C4C2×C411yescharacteristic
107C2×C4×Dic47C2×C411yescharacteristic
108C2×C4×Dic47C2×C411yescharacteristic
109C2×C4×Dic47C2311yescharacteristic
110C42×D47—22no—
111C42×D47—22no—
112C4⋊(C47⋊C8)—22no—
113C4⋊(C47⋊C8)—22no—
114C4⋊(C47⋊C8)—22no—
115Dic47⋊C8—22no—
116Dic47⋊C8—22no—
117(C2×D47)⋊C8—22no—
118(C2×D47)⋊C8—22no—
119(C2×D47)⋊C8—22no—
120(C2×D47)⋊C8—22no—
121(C2×D47)⋊C8—22no—
122(C2×D47)⋊C8—41no—
123(C2×D47)⋊C8—41no—
124(C2×D47)⋊C8D414yescomplemented
125#13093935—22no—
126C47⋊#95C2×C411yescharacteristic
127C47⋊#95C2×C411yescharacteristic
128C47⋊#95C2×C411yescharacteristic
129C47⋊#95C2×C411yescharacteristic
130C22×C8×C47C2311yescharacteristic
131C22×C8×C47C2311yescharacteristic
132C22×C8×C47C2311yescharacteristic
133C22×C8×C47C2311yescharacteristic
134C2×C4⋊C4×C47C2×C411yescharacteristic
135C2×C4⋊C4×C47C2×C411yescharacteristic
136C2×C42×C47C2311yescharacteristic
137C2×C42×C47C2311yescharacteristic
138C2×C42×C47C2311yescharacteristic
139C4⋊C8×C47D414yescomplemented
140#97×C47—22no—
141#97×C47—22no—
142C4×C8×C47—22no—
143#95×C47C2×C411yescharacteristic
144#95×C47C2×C411yescharacteristic
145C23×D47C22×C411yescharacteristic
146C23×D47C22×C411yescharacteristic
147C23×D47C22×C411yescharacteristic
148C22×C4×C47C22×C411yescharacteristic
149C22×C4×C47C22×C411yescharacteristic
150C22×C4×C47C22×C411yescharacteristic
151C22×C4×C47C22×C411yescharacteristic
152C22×C4×C47C22×C411yescharacteristic
153C22×C4×C47C22×C411yescharacteristic
154C22×C4×C47C2411yescharacteristic
155C22×Dic47C22×C411yescharacteristic
156C22×Dic47C22×C411yescharacteristic
157C22×Dic47C22×C411yescharacteristic
158C22×Dic47C22×C411yescharacteristic
159C22×Dic47C22×C411yescharacteristic
160C2×D188—22no—
161C2×D188—22no—
162C2×D188—22no—
163C2×D188—22no—
164C2×D188—22no—
165C2×D188—22no—
166C2×D188—22no—
167C2×D188—41no—
168C2×D188M1614yescomplemented
169C2×C4×D47—22no—
170C2×C4×D47—22no—
171C2×C4×D47—21no—
172C2×C4×D47—21no—
173C2×C4×D47—21no—
174C2×C4×D47—21no—
175C2×C4×D47—22no—
176C2×C4×D47—22no—
177C2×C4×D47—22no—
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—
186C2×C4×D47—21no—
187C2×C4×D47—21no—
188C2×C4×D47—21no—
189C2×C4×D47—21no—
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×C47C2×D412yes—
203C2×C8×C47C2×D412yes—
204C2×C8×C47C2×D412yes—
205C4⋊C4×C47—22no—
206C4⋊C4×C47—41no—
207C42×C47—21no—
208C42×C47—21no—
209C42×C47—21no—
210C42×C47—21no—
211C42×C47C2×D412yes—
212C42×C47#4112yes—
213(C2×D47)⋊C4—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—
220(C2×D47)⋊C4—22no—
221(C2×D47)⋊C4—22no—
222(C2×D47)⋊C4—22no—
223C4⋊Dic47—22no—
224C4⋊Dic47—22no—
225C4⋊Dic47—22no—
226C4×Dic47—22no—
227C4×Dic47—22no—
228C4×Dic47—21no—
229C4×Dic47—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—
239C2×C47⋊C8—21no—
240C2×C47⋊C8—21no—
241C2×C47⋊C8C2×D412yes—
242#10625324—44no—
243C8×D47—44no—
244C8×D47—44no—
245C8×D47—44no—
246C23×C47C23×C411yescharacteristic
247C22×D47—21no—
248C22×D47—21no—
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—21no—
263C22×D47—21no—
264C22×D47C4×D412yes—
265C22×D47C2×M1612yes—
266C22×D47C2×M1612yes—
267C22×D47#13112yes—
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—21no—
283C2×C4×C47C4×D412yes—
284C2×C4×C47C4×D412yes—
285C2×C4×C47C2×M1612yes—
286C2×C4×C47C22×D411yescharacteristic
287C2×C4×C47C22×D411yescharacteristic
288C2×C4×C47C2×#4111yescharacteristic
289C2×C4×C47C2×#4111yescharacteristic
290C2×C4×C47H(5,𝔽2)11yescharacteristic
291C2×C4×C472−1+411yescharacteristic
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×Dic47C4×D412yes—
306C2×Dic47#13112yes—
307D188—28no—
308D188—44no—
309D188—44no—
310C4×D47—28no—
311C4×D47—22no—
312C4×D47—22no—
313C4×D47—22no—
314C4×D47—22no—
315C4×D47—44no—
316C4×D47—41no—
317C4×D47—41no—
318C4×D47—41no—
319C4×D47—41no—
320C4×D47—41no—
321C4×D47—41no—
322C4×D47—41no—
323C4×D47—41no—
324C8×C47—22no—
325C8×C47—22no—
326C8×C47—22no—
327C8×C47—41no—
328C47⋊C8—22no—
329C47⋊C8—41no—
330C47⋊C8—41no—
331C47⋊C8—41no—
332#22987—471nomaximal, Sylow
333C22×C47C2×C4×D411yescharacteristic
334C22×C47C2×C4×D411yescharacteristic
335C22×C47#52011yescharacteristic
336C22×C47C22×M1611yescharacteristic
337C22×C47C2×#13111yescharacteristic
338C22×C47C2×#13111yescharacteristic
339C22×C47#56811yescharacteristic
340C2×D47—22no—
341C2×D47—22no—
342C2×D47—22no—
343C2×D47—22no—
344C2×D47—22no—
345C2×D47—22no—
346C2×D47—22no—
347C2×D47—22no—
348C2×D47—22no—
349C2×D47—41no—
350C2×D47—41no—
351C2×D47—41no—
352C2×D47—41no—
353C2×D47—41no—
354C2×D47—41no—
355C2×D47—41no—
356C2×D47—41no—
357C2×D47—41no—
358C2×D47—41no—
359C2×D47—41no—
360C2×D47#43514yescomplemented
361C4×C47—22no—
362C4×C47—22no—
363C4×C47—22no—
364C4×C47—41no—
365C4×C47—41no—
366C4×C47—41no—
367C4×C47D4211yescharacteristic
368C4×C47#54711yescharacteristic
369C4×C47#54811yescharacteristic
370C4×C47#55311yescharacteristic
371Dic47—22no—
372Dic47—22no—
373Dic47—41no—
374Dic47—41no—
375Dic47—41no—
376C2×#435—471no—
377C2×#435—471no—
378C2×C8×D4—471no—
379C22×C4⋊C8—471no—
380C4×#121—471no—
381#1955—471no—
382#1940—471no—
383#1924—471no—
384#1923—471no—
385#1869—471no—
386#1869—471no—
387#1851—471no—
388#1850—471no—
389#1771D4711yescharacteristic, complemented
390#1749—471no—
391C2×C47#236111yescharacteristic
392C2×C47C2×#43511yescharacteristic
393C2×C47#292911yescharacteristic
394C2×C47D4×M1611yescharacteristic
395C2×C47#293511yescharacteristic
396C2×C47#299011yescharacteristic
397C2×C47#299211yescharacteristic
398D47—24no—
399D47—42no—
400D47—81no—
401C22×M16—471no—
402C23×C8—471no—
403C23×C8—471no—
404C23×C8—471no—
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—
413C2×C4⋊C8—471no—
414C2×C4⋊C8—471no—
415C2×C4⋊C8—471no—
416C2×C4⋊C8—471no—
417C2×C4⋊C8—471no—
418C2×C4⋊C8—944no—
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⋊C8—471no—
428C2×#97—471no—
429C2×#97C2×D4711yescharacteristic
430C2×#97C2×D4711yescharacteristic
431C2×C4×C8C2×D4711yescharacteristic
432#390—471no—
433#389—471no—
434#388—471no—
435#388—471no—
436#386—471no—
437#386—471no—
438#380—471no—
439C4×C4⋊C4C2×D4711yescharacteristic
440C4×C22⋊C4—471no—
441C4×C22⋊C4—471no—
442#336—471no—
443#336—471no—
444#336—471no—
445#336—471no—
446#336C2×D4711yescharacteristic
447#336C2×D4711yescharacteristic
448C47#2298711yescharacteristic, complemented, Sylow
449C22×D4—471no—
450C22×D4—471no—
451C22×D4—471no—
452C23×C4—471no—
453C23×C4—471no—
454C23×C4—471no—
455C23×C4—471no—
456C23×C4—471no—
457C2×M16—942no—
458C2×M16—942no—
459C2×M16—1881no—
460C22×C8—471no—
461C22×C8—471no—
462C22×C8—471no—
463C22×C8—471no—
464C22×C8—942no—
465C22×C8—942no—
466C22×C8—942no—
467C22×C8—942no—
468C22×C8—942no—
469C22×C8—942no—
470C22×C8—1881no—
471C22×C8—1881no—
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⋊C4C4×D4711yescharacteristic
488C2×C4⋊C4C4×D4711yescharacteristic
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⋊C4—471no—
498C2×C22⋊C4—471no—
499C2×C42—471no—
500C2×C42—471no—
501C2×C42—471no—
502C2×C42—942no—
503C2×C42—942no—
504C2×C42C22×D4711yescharacteristic
505C2×C42C22×D4711yescharacteristic
506C2×C42C22×D4711yescharacteristic
507C4⋊C8—942no—
508C4⋊C8—942no—
509C4⋊C8—942no—
510C4⋊C8—942no—
511C4⋊C8—942no—
512C4⋊C8D18814yescomplemented
513C22⋊C8—474no—
514C22⋊C8—942no—
515C22⋊C8—942no—
516C22⋊C8—942no—
517C22⋊C8—942no—
518C22⋊C8—942no—
519C22⋊C8—1881no—
520C22⋊C8—1881no—
521#97—22no—
522#97—22no—
523#97—942no—
524C4×C8—22no—
525#95—471no—
526#95—471no—
527#95—471no—
528#95—471no—
529#95C4×D4711yescharacteristic
530#95C4×D4711yescharacteristic
531C24—471no—
532C24—471no—
533C24—471no—
534C2×D4—474no—
535C2×D4—942no—
536C2×D4—942no—
537C2×D4—942no—
538C2×D4—942no—
539C2×D4—942no—
540C2×D4—942no—
541C2×D4—942no—
542C2×D4—1881no—
543C22×C4—471no—
544C22×C4—471no—
545C22×C4—472no—
546C22×C4—472no—
547C22×C4—471no—
548C22×C4—471no—
549C22×C4—471no—
550C22×C4—942no—
551C22×C4—942no—
552C22×C4—942no—
553C22×C4—942no—
554C22×C4—941no—
555C22×C4—941no—
556C22×C4—941no—
557C22×C4—941no—
558C22×C4—942no—
559C22×C4—941no—
560C22×C4—941no—
561C22×C4—941no—
562C22×C4—941no—
563C22×C4—941no—
564C22×C4—941no—
565C22×C4—941no—
566C22×C4—941no—
567C22×C4—941no—
568C22×C4—941no—
569C22×C4—941no—
570C22×C4—941no—
571C22×C4—1881no—
572C22×C4C2×C4×D4711yescharacteristic
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—
580C2×C8—21no—
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—472no—
590C2×C8—941no—
591C2×C8—941no—
592C2×C8—941no—
593C2×C8—941no—
594C2×C8—941no—
595C2×C8—941no—
596C2×C8—941no—
597C2×C8—941no—
598C2×C8—941no—
599C2×C8—941no—
600C2×C8—941no—
601C2×C8—1884no—
602C2×C8—1884no—
603C2×C8—1884no—
604C2×C8C2×D18812yes—
605C2×C8C2×D18812yes—
606C2×C8D4×D4712yes—
607C4⋊C4—22no—
608C4⋊C4—41no—
609C4⋊C4—942no—
610C4⋊C4—942no—
611C4⋊C4—942no—
612C22⋊C4—942no—
613C22⋊C4—942no—
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—942no—
627C42—942no—
628C42—941no—
629C42—941no—
630C42C2×D18812yes—
631C42#1062535012yes—
632C23—472no—
633C23—472no—
634C23—472no—
635C23—472no—
636C23—941no—
637C23—941no—
638C23—941no—
639C23—941no—
640C23—941no—
641C23—941no—
642C23—941no—
643C23—941no—
644C23—941no—
645C23—941no—
646C23—941no—
647C23—941no—
648C23—941no—
649C23—941no—
650C23—941no—
651C23—941no—
652C23—941no—
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—21no—
672C2×C4—472no—
673C2×C4—472no—
674C2×C4—948no—
675C2×C4—941no—
676C2×C4—941no—
677C2×C4—941no—
678C2×C4—941no—
679C2×C4—942no—
680C2×C4—942no—
681C2×C4—942no—
682C2×C4—942no—
683C2×C4—941no—
684C2×C4—941no—
685C2×C4—941no—
686C2×C4—941no—
687C2×C4—941no—
688C2×C4—941no—
689C2×C4—941no—
690C2×C4—941no—
691C2×C4—941no—
692C2×C4—1884no—
693C2×C4—1881no—
694C2×C4—1881no—
695C2×C4—1881no—
696C2×C4—1881no—
697C2×C4—1881no—
698C2×C4—1881no—
699C2×C4—1881no—
700C2×C4—1881no—
701C2×C4C4×D18812yes—
702C2×C4C4×D18812yes—
703C2×C4M16×D4712yes—
704C2×C4C2×D4×D4711yescharacteristic
705C2×C4C22×D18811yescharacteristic
706C2×C4#41×D4711yescharacteristic
707C2×C4C2×#1062535011yescharacteristic
708C2×C4#1309407011yescharacteristic
709C2×C4#1309407211yescharacteristic
710C8—22no—
711C8—22no—
712C8—22no—
713C8—41no—
714C8—942no—
715C8—1881no—
716C8—1881no—
717C8—1881no—
718C22—474no—
719C22—942no—
720C22—942no—
721C22—942no—
722C22—942no—
723C22—942no—
724C22—942no—
725C22—942no—
726C22—942no—
727C22—942no—
728C22—1881no—
729C22—1881no—
730C22—1881no—
731C22—1881no—
732C22—1881no—
733C22—1881no—
734C22—1881no—
735C22—1881no—
736C22—1881no—
737C22—1881no—
738C22—1881no—
739C22C4×D4×D4711yescharacteristic
740C22C2×C4×D18811yescharacteristic
741C22#1568960511yescharacteristic
742C22C2×M16×D4711yescharacteristic
743C22#131×D4711yescharacteristic
744C22#131×D4711yescharacteristic
745C22#1568988911yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—41no—
750C4—41no—
751C4—41no—
752C4—942no—
753C4—942no—
754C4—1881no—
755C4—1881no—
756C4—1881no—
757C4D4×D18811yescharacteristic
758C4#1568977411yescharacteristic
759C4#1568978511yescharacteristic
760C4#1568981711yescharacteristic
761C2—944no—
762C2—3761no—
763C2—1882no—
764C2#2024640611yescharacteristic
765C2#435×D4711yescharacteristic
766C2#2025208411yescharacteristic
767C2M16×D18811yescharacteristic
768C2#2025212911yescharacteristic
769C2#2025251211yescharacteristic
770C2#2025252611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D47
commutator, socleC23×C47C23×C4
FittingC47×#1771C2
prime radicalC2×#13093999C4
cosocleC22×C4×C47C24
hypercenter#1771D47
hypocenterC47#22987
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ #1771

Complements

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

NH ≅ G/Ntype
1. C2×#15689196C2semidirect
2. C2×#15689193C2semidirect
3. C2×C8×D188C2semidirect
4. C2×C4⋊C8×D47C2semidirect
6. #20244186C2semidirect
7. #20244112C2semidirect
8. #20244001C2semidirect
9. #20243994C2semidirect
10. #20243679C2semidirect
11. #20243679C2semidirect
12. #20243572C2semidirect
13. #20243567C2semidirect
14. #20243151C2semidirect
15. C47×#1771C2semidirect
124. (C2×D47)⋊C8D4semidirect
139. C4⋊C8×C47D4semidirect
168. C2×D188M16semidirect
360. C2×D47#435semidirect
389. #1771D47semidirect
448. C47#22987semidirect
512. C4⋊C8D188semidirect

Maximal subgroups

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

subgroupindex
C2×#156891962
C2×#156891932
C2×C8×D1882
C2×C4⋊C8×D472
C4×#130939992
#202441862
#202441122
#202440012
#202439942
#202436792
#202435722
#202435672
#202431512
C47×#17712
#2298747