Finite Group Databasebeta

← #26232516

Subgroups — #26232516

Order 12032.

1258 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689831C211yesmaximal, characteristic
2C2×(C22⋊D47)⋊C8C211yesmaximal, characteristic
3C4⋊C4×C22⋊D47C211yesmaximal, characteristic
4#20244347C211yesmaximal, characteristic, complemented
5#20244334C211yesmaximal, characteristic, complemented
6#20243812C211yesmaximal, characteristic, complemented
7#20243808C211yesmaximal, characteristic, complemented
8#20243692C211yesmaximal, characteristic, complemented
9#20243479C211yesmaximal, characteristic, complemented
10#20243477C211yesmaximal, characteristic, complemented
11#20243391C211yesmaximal, characteristic, complemented
12#103×Dic47C211yesmaximal, characteristic, complemented
13C2×#15688885C211yesmaximal, characteristic, complemented
14#340×D47C211yesmaximal, characteristic, complemented
15C47×#1872C211yesmaximal, characteristic, complemented
16C23×C47⋊C8C2211yescharacteristic
17C22×C8×D47C2211yescharacteristic
18#15689831—24no—
19#15689831C418yescomplemented
20C2×#13094023C2211yescharacteristic
21C2×#13094014—21no—
22C2×#13094004—21no—
23C2×#13094001—21no—
24C2×#13094000C2211yescharacteristic
25C2×Q8×Dic47C2211yescharacteristic
26C2×C4×C22⋊D47—21no—
27C2×C4×C22⋊D47C2211yescharacteristic
28C2×(C22⋊D47)⋊C4—21no—
29C22×C4⋊Dic47C2211yescharacteristic
30C2×C4⋊C4×D47C2211yescharacteristic
31C2×C4⋊C4×D47C2211yescharacteristic
32(C22⋊D47)⋊C8—24no—
33C2×Dic47⋊C8C2211yescharacteristic
34C2×#13093948C2211yescharacteristic
35C2×#13093948C2211yescharacteristic
36C2×(C2×D47)⋊C8C2211yescharacteristic
37C2×C8×Dic47C2211yescharacteristic
38#15689018—21no—
39#15688996—21no—
40#15688994—21no—
41#15688992C2211yescharacteristic
42#15688983C2211yescharacteristic
43#15688980C2211yescharacteristic
44C4⋊C4×Dic47C2211yescharacteristic
45#15688886C2211yescharacteristic
46#15688886C2211yescharacteristic
47#15688886C2211yescharacteristic
48#15688886C2211yescharacteristic
49#15688885C2211yescharacteristic
50#15688885C2211yescharacteristic
51#15688885C2211yescharacteristic
52#15688885C2211yescharacteristic
53#15688885C2211yescharacteristic
54#15688885C2211yescharacteristic
55C2×C22⋊Q8×C47C2211yescharacteristic
56C22×C4⋊C4×C47C2211yescharacteristic
57C2×#103×C47C2211yescharacteristic
58C2×#103×C47C2211yescharacteristic
59C2×C22⋊C8×C47C2211yescharacteristic
60C47×#340C2211yescharacteristic
61C47×#340C2211yescharacteristic
62C22×Dic94—21no—
63C22×C22⋊D47D411yescharacteristic
64C23×Dic47—21no—
65C22×C4×D47—21no—
66C22×C4×D47—21no—
67C22×C4×D47C2311yescharacteristic
68C22×C47⋊C8—22no—
69C22×C47⋊C8—22no—
70C22×C47⋊C8—41no—
71C22×C47⋊C8C2311yescharacteristic
72C22×C47⋊C8C2311yescharacteristic
73C2×C8×D47—22no—
74C2×C8×D47—22no—
75C2×C8×D47—41no—
76#13094023—22no—
77#13094023C2×C414yescomplemented
78#13094014—28no—
79#13094004—28no—
80#13094001—28no—
81#13094000—22no—
82#13094000C2×C414yescomplemented
83Q8×Dic47—22no—
84Q8×Dic47C2×C414yescomplemented
85C4×C22⋊D47—44no—
86C4×C22⋊D47C2×C414yes—
87C4×C22⋊D47D414yes—
88(C22⋊D47)⋊C4—28no—
89C2×C4⋊Dic47—22no—
90C2×C4⋊Dic47—21no—
91C2×C4⋊Dic47—21no—
92C2×C4⋊Dic47C2×C414yescomplemented
93C2×C4⋊Dic47C2311yescharacteristic
94C2×C4⋊Dic47C2311yescharacteristic
95C2×C4⋊Dic47C2311yescharacteristic
96C2×C4⋊Dic47C2311yescharacteristic
97C2×Dic47⋊C4—21no—
98C2×Dic47⋊C4—21no—
99C2×Dic47⋊C4—21no—
100C2×Dic47⋊C4—21no—
101C2×Dic47⋊C4—21no—
102C2×Dic47⋊C4—21no—
103C2×Dic47⋊C4D411yescharacteristic
104C4⋊C4×D47—22no—
105C4⋊C4×D47—22no—
106C4⋊C4×D47—41no—
107C4⋊C4×D47C2×C414yescomplemented
108C2×C22⋊Dic47—21no—
109C2×C22⋊Dic47D411yescharacteristic
110C2×(C2×D47)⋊C4—21no—
111C2×(C2×D47)⋊C4—21no—
112C2×(C2×D47)⋊C4D411yescharacteristic
113C2×C4×Dic47—21no—
114C2×C4×Dic47—21no—
115C2×C4×Dic47C2311yescharacteristic
116Dic47⋊C8—22no—
117#13093948—22no—
118#13093948—41no—
119(C2×D47)⋊C8—22no—
120C8×Dic47—22no—
121C47⋊#95—21no—
122C47⋊#95—21no—
123C47⋊#95—21no—
124C22×Q8×C47C2311yescharacteristic
125C23×C4×C47—21no—
126C23×C4×C47C2311yescharacteristic
127C22×C8×C47C2311yescharacteristic
128C22×C8×C47C2311yescharacteristic
129C22⋊Q8×C47—22no—
130C22⋊Q8×C47C2×C414yescomplemented
131C2×C4⋊C4×C47—21no—
132C2×C4⋊C4×C47—22no—
133C2×C4⋊C4×C47—21no—
134C2×C4⋊C4×C47—41no—
135C2×C4⋊C4×C47C2311yescharacteristic
136C2×C4⋊C4×C47C2311yescharacteristic
137C2×C4⋊C4×C47C2311yescharacteristic
138C2×C22⋊C4×C47—21no—
139#103×C47—22no—
140#103×C47—41no—
141C22⋊C8×C47—22no—
142C24×C47C2×D411yescharacteristic
143C23×D47C2×D411yescharacteristic
144C2×Q8×C47—21no—
145C2×Q8×C47—21no—
146C2×Q8×C47—21no—
147C2×Q8×C47—21no—
148C2×Q8×C47—21no—
149C2×Q8×C47C22×C412yes—
150C22×C4×C47—21no—
151C22×C4×C47—21no—
152C22×C4×C47—21no—
153C22×C4×C47—21no—
154C22×C4×C47—21no—
155C22×C4×C47—21no—
156C22×C4×C47—21no—
157C22×C4×C47—21no—
158C22×C4×C47—42no—
159C22×C4×C47—42no—
160C22×C4×C47—81no—
161C22×C4×C47C22×C412yes—
162C22×C4×C47C2×D411yescharacteristic
163C22×C4×C47C2×D412yes—
164C22×C4×C47C2411yescharacteristic
165C2×C22⋊D47C22⋊C414yes—
166C2×C22⋊D47SD1614yes—
167C2×C22⋊D47Q1614yes—
168C22×Dic47—21no—
169C22×Dic47—21no—
170C22×Dic47—24no—
171C22×Dic47—21no—
172C22×Dic47—21no—
173C22×Dic47—81no—
174C22×Dic47—81no—
175C22×Dic47C2×D411yescharacteristic
176C22×Dic47C2×D411yescharacteristic
177C22×Dic47C2×D411yescharacteristic
178C2×C4×D47—21no—
179C2×C4×D47—21no—
180C2×C4×D47—21no—
181C2×C4×D47—21no—
182C2×C4×D47—24no—
183C2×C4×D47—42no—
184C2×C4×D47—42no—
185C2×C4×D47—81no—
186C2×C4×D47—81no—
187C2×C4×D47—81no—
188C2×C4×D47C22×C412yes—
189C2×C4×D47C2×D412yes—
190C2×Dic94—24no—
191C2×Dic94—81no—
192C2×Dic94—81no—
193C2×C8×C47—21no—
194C2×C8×C47—21no—
195C2×C8×C47—21no—
196C2×C8×C47—21no—
197C2×C8×C47—21no—
198C2×C8×C47—21no—
199C4⋊C4×C47—24no—
200C4⋊C4×C47—21no—
201C4⋊C4×C47—21no—
202C4⋊C4×C47—21no—
203C4⋊C4×C47—21no—
204C4⋊C4×C47—42no—
205C4⋊C4×C47C22×C412yes—
206C4⋊C4×C47#4112yes—
207C22⋊C4×C47—24no—
208C22⋊Dic47—42no—
209C22⋊Dic47C22⋊C414yes—
210(C2×D47)⋊C4—24no—
211(C2×D47)⋊C4—42no—
212(C2×D47)⋊C4C22⋊C414yes—
213C4⋊Dic47—24no—
214C4⋊Dic47—21no—
215C4⋊Dic47—21no—
216C4⋊Dic47—24no—
217C4⋊Dic47—21no—
218C4⋊Dic47—21no—
219C4⋊Dic47—21no—
220C4⋊Dic47—21no—
221C4⋊Dic47C22×C412yes—
222C4⋊Dic47C22×C412yes—
223Dic47⋊C4—24no—
224Dic47⋊C4—24no—
225Dic47⋊C4—24no—
226Dic47⋊C4—42no—
227Dic47⋊C4—42no—
228Dic47⋊C4—81no—
229Dic47⋊C4C22⋊C414yes—
230C4×Dic47—24no—
231C4×Dic47—42no—
232C4×Dic47C22×C412yes—
233C4×Dic47C2×D412yes—
234C2×C47⋊C8—21no—
235C2×C47⋊C8—21no—
236C2×C47⋊C8—21no—
237C2×C47⋊C8—21no—
238C2×C47⋊C8—21no—
239C2×C47⋊C8—44no—
240C2×C47⋊C8#4112yes—
241C8×D47—44no—
242C23×C47—21no—
243C23×C47—21no—
244C23×C47—21no—
245C23×C47—21no—
246C23×C47C2×C22⋊C412yes—
247C23×C47C2×SD1612yes—
248C23×C47C2×Q1612yes—
249C23×C47C22×D411yescharacteristic
250C22×D47—21no—
251C22×D47—21no—
252C22×D47—21no—
253C22×D47—21no—
254C22×D47C2×C22⋊C412yes—
255C22×D47C2×SD1612yes—
256C22×D47C2×Q1612yes—
257Q8×C47—22no—
258Q8×C47—22no—
259Q8×C47—41no—
260Q8×C47—41no—
261C2×C4×C47—21no—
262C2×C4×C47—21no—
263C2×C4×C47—22no—
264C2×C4×C47—22no—
265C2×C4×C47—22no—
266C2×C4×C47—22no—
267C2×C4×C47—22no—
268C2×C4×C47—22no—
269C2×C4×C47—22no—
270C2×C4×C47—41no—
271C2×C4×C47—41no—
272C2×C4×C47—41no—
273C2×C4×C47—41no—
274C2×C4×C47—41no—
275C2×C4×C47—41no—
276C2×C4×C47—41no—
277C2×C4×C47—41no—
278C2×C4×C47—41no—
279C2×C4×C47—84no—
280C2×C4×C47C2×C22⋊C412yes—
281C2×C4×C47C23×C411yescharacteristic
282C2×C4×C47C22×D411yescharacteristic
283C2×C4×C47C2×#4111yescharacteristic
284C2×C4×C47C2×#4111yescharacteristic
285C2×C4×C47H(5,𝔽2)11yescharacteristic
286C2×C4×C472−1+411yescharacteristic
287C22⋊D47#103116yescomplemented
288C2×Dic47—21no—
289C2×Dic47—21no—
290C2×Dic47—21no—
291C2×Dic47—21no—
292C2×Dic47—22no—
293C2×Dic47—22no—
294C2×Dic47—41no—
295C2×Dic47—41no—
296C2×Dic47—41no—
297C2×Dic47—41no—
298C2×Dic47—41no—
299C2×Dic47—41no—
300C2×Dic47—41no—
301C2×Dic47—41no—
302C2×Dic47—41no—
303C2×Dic47—41no—
304C2×Dic47—84no—
305C2×Dic47C2×C22⋊C412yes—
306C2×Dic47C2×C22⋊C412yes—
307C2×Dic47C2×C22⋊C412yes—
308C2×Dic47C2×SD1612yes—
309C2×Dic47C2×Q1612yes—
310C4×D47—22no—
311C4×D47—22no—
312C4×D47—22no—
313C4×D47—22no—
314C4×D47—84no—
315C4×D47—84no—
316Dic94—84no—
317C8×C47—41no—
318C8×C47—41no—
319C47⋊C8—22no—
320C47⋊C8—41no—
321#22487—471nomaximal, Sylow
322C22×C47—22no—
323C22×C47—22no—
324C22×C47—22no—
325C22×C47—22no—
326C22×C47—22no—
327C22×C47—22no—
328C22×C47C2×#10314yes—
329C22×C47C22×C22⋊C411yescharacteristic
330C22×C47#54611yescharacteristic
331C22×C47#54711yescharacteristic
332C22×C47C22×SD1611yescharacteristic
333C22×C47C22×Q1611yescharacteristic
334C22×C47#57611yescharacteristic
335C22×C47#57711yescharacteristic
336C2×D47—22no—
337C2×D47—22no—
338C2×D47—22no—
339C2×D47—22no—
340C2×D47—22no—
341C2×D47—22no—
342C2×D47C2×#10314yes—
343C4×C47—22no—
344C4×C47—42no—
345C4×C47—42no—
346C4×C47—42no—
347C4×C47—81no—
348C4×C47C4×#4111yescharacteristic
349C4×C47#52011yescharacteristic
350C4×C47#54611yescharacteristic
351C4×C47#54711yescharacteristic
352Dic47—22no—
353Dic47—22no—
354Dic47—42no—
355Dic47—42no—
356Dic47—81no—
357Dic47—81no—
358Dic47C2×#10314yes—
359C2×#554—471no—
360C2×C8×D4—471no—
361D4×C4⋊C4—471no—
362#1990—471no—
363#1987—471no—
364#1892—471no—
365#1892—471no—
366#1872—471no—
367#1872D4711yescharacteristic, complemented
368#1824—471no—
369#1824—471no—
370#1803—471no—
371C4×#103—471no—
372C2×#340—471no—
373C2×#340—471no—
374C2×C47—24no—
375C2×C47#233911yescharacteristic
376C2×C47C22×#10311yescharacteristic
377C2×C47#289711yescharacteristic
378C2×C47#329511yescharacteristic
379C2×C47#329911yescharacteristic
380C2×C47#333511yescharacteristic
381C2×C47#333811yescharacteristic
382D47—24no—
383C23×C8—471no—
384C23×C8—471no—
385#554—478no—
386#554—944no—
387C2×C4⋊Q8—471no—
388C2×#125—941no—
389C2×C22⋊Q8—471no—
390C2×C22⋊Q8—941no—
391C2×C22⋊Q8—941no—
392C2×C22⋊Q8C2×D4711yescharacteristic
393C2×C4×Q8—471no—
394C2×C4×D4—471no—
395C2×C4×D4—941no—
396C2×C4×D4—941no—
397C22×C4⋊C4—471no—
398C22×C4⋊C4—471no—
399C22×C4⋊C4—471no—
400C22×C4⋊C4C2×D4711yescharacteristic
401C8×D4—944no—
402C2×C4⋊C8—471no—
403C2×#103—471no—
404C2×#103—471no—
405C2×#103C2×D4711yescharacteristic
406C2×#103C2×D4711yescharacteristic
407C2×C22⋊C8—471no—
408C2×C22⋊C8C2×D4711yescharacteristic
409C2×C4×C8—471no—
410#389—941no—
411#385—941no—
412#385—941no—
413#384—471no—
414#380—471no—
415#380—471no—
416C4×C4⋊C4—471no—
417#340—471no—
418#340—471no—
419#340—471no—
420#340—471no—
421#340—471no—
422#340—471no—
423#340—471no—
424#340—471no—
425#340—471no—
426#340—471no—
427#340C2×D4711yescharacteristic
428#340C2×D4711yescharacteristic
429C47#2248711yescharacteristic, complemented, Sylow
430C22×Q8—941no—
431C22×Q8C22×D4711yescharacteristic
432C22×D4—471no—
433C23×C4—21no—
434C23×C4—471no—
435C23×C4—941no—
436C23×C4—941no—
437C23×C4—941no—
438C23×C4C22×D4711yescharacteristic
439C22×C8—471no—
440C22×C8—471no—
441C22×C8—942no—
442C22×C8—942no—
443C22×C8—942no—
444C22×C8—942no—
445C22×C8—1881no—
446C22×C8—1881no—
447C22×C8C22×D4711yescharacteristic
448C22×C8C22×D4711yescharacteristic
449C4⋊Q8—474no—
450C4⋊Q8—942no—
451#125—948no—
452C22⋊Q8—22no—
453C22⋊Q8—474no—
454C22⋊Q8—948no—
455C22⋊Q8—948no—
456C22⋊Q8—942no—
457C22⋊Q8C4×D4714yescomplemented
458C4×Q8—474no—
459C4×Q8—942no—
460C4×D4—474no—
461C4×D4—474no—
462C4×D4—948no—
463C4×D4—1884no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—41no—
468C2×C4⋊C4—471no—
469C2×C4⋊C4—474no—
470C2×C4⋊C4—471no—
471C2×C4⋊C4—471no—
472C2×C4⋊C4—474no—
473C2×C4⋊C4—471no—
474C2×C4⋊C4—471no—
475C2×C4⋊C4—942no—
476C2×C4⋊C4—941no—
477C2×C4⋊C4—941no—
478C2×C4⋊C4—941no—
479C2×C4⋊C4—941no—
480C2×C4⋊C4—941no—
481C2×C4⋊C4—942no—
482C2×C4⋊C4—942no—
483C2×C4⋊C4—941no—
484C2×C4⋊C4—941no—
485C2×C4⋊C4—941no—
486C2×C4⋊C4—1881no—
487C2×C4⋊C4C22×D4711yescharacteristic
488C2×C4⋊C4C22×D4711yescharacteristic
489C2×C4⋊C4C22×D4711yescharacteristic
490C2×C22⋊C4—21no—
491C2×C22⋊C4—471no—
492C2×C22⋊C4—471no—
493C2×C22⋊C4—941no—
494C2×C22⋊C4—941no—
495C2×C22⋊C4—941no—
496C2×C42—471no—
497C2×C42—941no—
498C2×C42—941no—
499C4⋊C8—942no—
500#103—22no—
501#103—41no—
502#103—942no—
503#103—1881no—
504C22⋊C8—22no—
505C22⋊C8—942no—
506C4×C8—942no—
507#95—941no—
508#95—941no—
509#95—941no—
510C24—471no—
511C24D4×D4711yescharacteristic
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—944no—
518C2×Q8—3761no—
519C2×Q8—3761no—
520C2×Q8C2×C4×D4712yes—
521C2×D4—474no—
522C2×D4—474no—
523C2×D4—474no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—81no—
535C22×C4—471no—
536C22×C4—471no—
537C22×C4—471no—
538C22×C4—472no—
539C22×C4—472no—
540C22×C4—944no—
541C22×C4—941no—
542C22×C4—941no—
543C22×C4—941no—
544C22×C4—941no—
545C22×C4—944no—
546C22×C4—941no—
547C22×C4—941no—
548C22×C4—941no—
549C22×C4—941no—
550C22×C4—3761no—
551C22×C4—3761no—
552C22×C4—3761no—
553C22×C4—3761no—
554C22×C4—3761no—
555C22×C4—1882no—
556C22×C4—1882no—
557C22×C4C2×C4×D4712yes—
558C22×C4D4×D4711yescharacteristic
559C22×C4D4×D4712yes—
560C22×C4C23×D4711yescharacteristic
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—472no—
568C2×C8—941no—
569C2×C8—941no—
570C2×C8—941no—
571C2×C8—941no—
572C2×C8—941no—
573C2×C8—1884no—
574C2×C8—1884no—
575C4⋊C4—24no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—42no—
581C4⋊C4—474no—
582C4⋊C4—472no—
583C4⋊C4—472no—
584C4⋊C4—944no—
585C4⋊C4—944no—
586C4⋊C4—944no—
587C4⋊C4—944no—
588C4⋊C4—944no—
589C4⋊C4—941no—
590C4⋊C4—941no—
591C4⋊C4—941no—
592C4⋊C4—941no—
593C4⋊C4—941no—
594C4⋊C4—941no—
595C4⋊C4—3761no—
596C4⋊C4—1882no—
597C4⋊C4—1882no—
598C4⋊C4C2×C4×D4712yes—
599C4⋊C4#1062535212yes—
600C22⋊C4—24no—
601C22⋊C4—474no—
602C22⋊C4—474no—
603C22⋊C4—944no—
604C22⋊C4—1882no—
605C22⋊C4—1882no—
606C42—472no—
607C42—472no—
608C42—944no—
609C42—1882no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—472no—
615C23—472no—
616C23—472no—
617C23—941no—
618C23—941no—
619C23—941no—
620C23—941no—
621C23C22⋊C4×D4712yes—
622C23SD16×D4712yes—
623C23Q16×D4712yes—
624C23C2×D4×D4711yescharacteristic
625Q8—22no—
626Q8—22no—
627Q8—41no—
628Q8—41no—
629Q8—3764no—
630D4—4716no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—84no—
650C2×C4—472no—
651C2×C4—472no—
652C2×C4—472no—
653C2×C4—472no—
654C2×C4—472no—
655C2×C4—941no—
656C2×C4—941no—
657C2×C4—941no—
658C2×C4—941no—
659C2×C4—942no—
660C2×C4—942no—
661C2×C4—942no—
662C2×C4—942no—
663C2×C4—942no—
664C2×C4—942no—
665C2×C4—3764no—
666C2×C4—3764no—
667C2×C4—3764no—
668C2×C4—1881no—
669C2×C4—1881no—
670C2×C4—1881no—
671C2×C4—1881no—
672C2×C4—1881no—
673C2×C4—1881no—
674C2×C4—1881no—
675C2×C4—1881no—
676C2×C4—1881no—
677C2×C4—1881no—
678C2×C4C22⋊C4×D4712yes—
679C2×C4C22×C4×D4711yescharacteristic
680C2×C4C2×D4×D4711yescharacteristic
681C2×C4#41×D4711yescharacteristic
682C2×C4C2×#1062535211yescharacteristic
683C2×C4#1309406911yescharacteristic
684C2×C4#1309407111yescharacteristic
685C8—41no—
686C8—41no—
687C8—942no—
688C8—1881no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—474no—
696C22—942no—
697C22—942no—
698C22—942no—
699C22—942no—
700C22—942no—
701C22—942no—
702C22#103×D4714yes—
703C22C2×C22⋊C4×D4711yescharacteristic
704C22#1568976011yescharacteristic
705C22#1568977111yescharacteristic
706C22C2×SD16×D4711yescharacteristic
707C22C2×Q16×D4711yescharacteristic
708C22#1568992711yescharacteristic
709C22#1568993211yescharacteristic
710C4—22no—
711C4—42no—
712C4—42no—
713C4—42no—
714C4—81no—
715C4—474no—
716C4—942no—
717C4—942no—
718C4—3761no—
719C4—3761no—
720C4—1882no—
721C4—1882no—
722C4C4×#1062535211yescharacteristic
723C4#1568960211yescharacteristic
724C4#1568976211yescharacteristic
725C4#1568977311yescharacteristic
726C2—24no—
727C2—944no—
728C2#2024621411yescharacteristic
729C2C2×#103×D4711yescharacteristic
730C2#2025191211yescharacteristic
731C2#2025520511yescharacteristic
732C2#2025525711yescharacteristic
733C2#2025573811yescharacteristic
734C2#2025577511yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1872C2
socleC23×C47C22×D4
prime radicalC22×C22⋊D47D4
cosocleC22×C4×C47C24
hypercenter#1872D47
hypocenterC47#22487
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
4. #20244347C2semidirect
5. #20244334C2semidirect
6. #20243812C2semidirect
7. #20243808C2semidirect
8. #20243692C2semidirect
9. #20243479C2semidirect
10. #20243477C2semidirect
11. #20243391C2semidirect
12. #103×Dic47C2semidirect
13. C2×#15688885C2semidirect
14. #340×D47C2semidirect
15. C47×#1872C2semidirect
19. #15689831C4semidirect
77. #13094023C2×C4semidirect
82. #13094000C2×C4semidirect
84. Q8×Dic47C2×C4semidirect
92. C2×C4⋊Dic47C2×C4semidirect
107. C4⋊C4×D47C2×C4semidirect
130. C22⋊Q8×C47C2×C4semidirect
287. C22⋊D47#103semidirect
367. #1872D47semidirect
429. C47#22487semidirect
457. C22⋊Q8C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156898312
C2×(C22⋊D47)⋊C82
C4⋊C4×C22⋊D472
#202443472
#202443342
#202438122
#202438082
#202436922
#202434792
#202434772
#202433912
#103×Dic472
C2×#156888852
#340×D472
C47×#18722
#2248747