Finite Group Databasebeta

← #103×C22⋊D47 #26231706

Subgroups — #103×C22⋊D47 #26231706

Order 12032.

1530 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×C22⋊D47C211yesmaximal, characteristic
2C2×C8×C22⋊D47C211yesmaximal, characteristic
3C2×#103×D47C211yesmaximal, characteristic, complemented
4C4⋊C4×C22⋊D47C211yesmaximal, characteristic
5#20244309C211yesmaximal, characteristic, complemented
6#20244188C211yesmaximal, characteristic, complemented
7#20243811C211yesmaximal, characteristic, complemented
8#20243808C211yesmaximal, characteristic, complemented
9#20243695C211yesmaximal, characteristic, complemented
10#20243692C211yesmaximal, characteristic, complemented
11#20243391C211yesmaximal, characteristic, complemented
12#20243323C211yesmaximal, characteristic, complemented
13#20243321C211yesmaximal, characteristic, complemented
14#103×Dic47C211yesmaximal, characteristic, complemented
15C22×#103×C47C211yesmaximal, characteristic, complemented
16C22×Q8×D47C2211yescharacteristic
17C22×C8×D47C2211yescharacteristic
18Q8×C22⋊D47—24no—
19Q8×C22⋊D47C418yescomplemented
20C2×#13094022—21no—
21C2×#13094022C2211yescharacteristic
22C2×#13094003—21no—
23C2×#13094003C2211yescharacteristic
24C2×#13094000—21no—
25C2×#13094000C2211yescharacteristic
26C2×Q8×Dic47C2211yescharacteristic
27C2×C4×C22⋊D47—21no—
28C2×C4×C22⋊D47—21no—
29C2×C4×C22⋊D47C2211yescharacteristic
30C2×C4⋊C4×D47C2211yescharacteristic
31C8×C22⋊D47—24no—
32C2×Dic47⋊C8C2211yescharacteristic
33C2×#13093949C2211yescharacteristic
34C2×#13093949C2211yescharacteristic
35C2×#13093948C2211yescharacteristic
36C2×#13093948C2211yescharacteristic
37C2×#13093948C2211yescharacteristic
38C2×#13093948C2211yescharacteristic
39C2×#13093947C2211yescharacteristic
40C2×#13093947C2211yescharacteristic
41#103×D47—24no—
42C2×C22⋊(C47⋊C8)C2211yescharacteristic
43C2×(C2×D47)⋊C8C2211yescharacteristic
44C2×C8×Dic47C2211yescharacteristic
45#15689018—21no—
46#15688996—21no—
47#15688994—21no—
48#15688992C2211yescharacteristic
49#15688983C2211yescharacteristic
50#15688980C2211yescharacteristic
51C4⋊C4×Dic47C2211yescharacteristic
52#15688886C2211yescharacteristic
53#15688886C2211yescharacteristic
54#15688885C2211yescharacteristic
55#15688885C2211yescharacteristic
56C23×Q8×C47C2211yescharacteristic
57C23×C8×C47C2211yescharacteristic
58C22×C4⋊C4×C47C2211yescharacteristic
59C2×#103×C47—24no—
60C2×#103×C47C2211yescharacteristic
61C2×#103×C47C2211yescharacteristic
62C2×#103×C47C2211yescharacteristic
63C2×#103×C47C2211yescharacteristic
64C22×Dic94—21no—
65C22×Dic94C2311yescharacteristic
66C2×Q8×D47—22no—
67C2×Q8×D47—22no—
68C2×Q8×D47—22no—
69C2×Q8×D47—41no—
70C2×Q8×D47—41no—
71C2×Q8×D47C2×C414yescomplemented
72C22×C22⋊D47D411yescharacteristic
73C22×C4×D47—21no—
74C22×C4×D47—21no—
75C22×C4×D47C2311yescharacteristic
76C22×C47⋊C8C2311yescharacteristic
77C22×C47⋊C8C2311yescharacteristic
78C2×C8×D47—22no—
79C2×C8×D47—22no—
80C2×C8×D47—41no—
81#13094022—28no—
82#13094022—22no—
83#13094022C2×C414yescomplemented
84#13094003—22no—
85#13094003—28no—
86#13094003C2×C414yescomplemented
87#13094000—22no—
88#13094000—28no—
89#13094000C2×C414yescomplemented
90Q8×Dic47—22no—
91Q8×Dic47C2×C414yescomplemented
92C4×C22⋊D47—28no—
93C4×C22⋊D47—44no—
94C4×C22⋊D47C2×C414yes—
95C4×C22⋊D47D414yes—
96C2×C4⋊Dic47—21no—
97C2×C4⋊Dic47C2311yescharacteristic
98C2×C4⋊Dic47C2311yescharacteristic
99C2×C4⋊Dic47C2311yescharacteristic
100C2×Dic47⋊C4—21no—
101C2×Dic47⋊C4—21no—
102C2×Dic47⋊C4—21no—
103C2×Dic47⋊C4—21no—
104C2×Dic47⋊C4—21no—
105C2×Dic47⋊C4—21no—
106C2×Dic47⋊C4—21no—
107C2×Dic47⋊C4D411yescharacteristic
108C4⋊C4×D47—22no—
109C4⋊C4×D47—41no—
110C2×C22⋊Dic47—21no—
111C2×C22⋊Dic47—21no—
112C2×C22⋊Dic47D411yescharacteristic
113C2×(C2×D47)⋊C4—21no—
114C2×(C2×D47)⋊C4—21no—
115C2×(C2×D47)⋊C4D411yescharacteristic
116C2×C4×Dic47—21no—
117C2×C4×Dic47—21no—
118C2×C4×Dic47C2311yescharacteristic
119Dic47⋊C8—22no—
120#13093949—22no—
121#13093949—41no—
122#13093948—22no—
123#13093948—22no—
124#13093948—41no—
125#13093948—41no—
126#13093947—22no—
127#13093947—41no—
128C22⋊(C47⋊C8)—22no—
129(C2×D47)⋊C8—22no—
130C8×Dic47—22no—
131C47⋊#95—21no—
132C47⋊#95—21no—
133C47⋊#95—21no—
134C22×Q8×C47—22no—
135C22×Q8×C47—21no—
136C22×Q8×C47—22no—
137C22×Q8×C47—22no—
138C22×Q8×C47—41no—
139C22×Q8×C47—41no—
140C22×Q8×C47C2×C414yescomplemented
141C22×Q8×C47C2311yescharacteristic
142C22×Q8×C47C2311yescharacteristic
143C23×C4×C47—21no—
144C23×C4×C47—21no—
145C23×C4×C47C2311yescharacteristic
146C22×C8×C47—22no—
147C22×C8×C47—22no—
148C22×C8×C47—41no—
149C22×C8×C47C2311yescharacteristic
150C22×C8×C47C2311yescharacteristic
151C2×C4⋊C4×C47—22no—
152C2×C4⋊C4×C47—21no—
153C2×C4⋊C4×C47—41no—
154C2×C4⋊C4×C47C2311yescharacteristic
155C2×C4⋊C4×C47C2311yescharacteristic
156#103×C47—22no—
157#103×C47—22no—
158#103×C47—22no—
159#103×C47D414yescomplemented
160C24×C47C2×D411yescharacteristic
161C23×D47C2×D411yescharacteristic
162C2×Q8×C47—24no—
163C2×Q8×C47—21no—
164C2×Q8×C47—21no—
165C2×Q8×C47—21no—
166C2×Q8×C47—21no—
167C2×Q8×C47—28no—
168C2×Q8×C47—21no—
169C2×Q8×C47—21no—
170C2×Q8×C47—21no—
171C2×Q8×C47—21no—
172C2×Q8×C47—42no—
173C2×Q8×C47—42no—
174C2×Q8×C47—44no—
175C2×Q8×C47—44no—
176C2×Q8×C47—44no—
177C2×Q8×C47C22×C412yes—
178C2×Q8×C47C22×C412yes—
179C2×Q8×C47C2×D412yes—
180C2×Q8×C47#4112yes—
181C22×C4×C47—21no—
182C22×C4×C47—21no—
183C22×C4×C47—21no—
184C22×C4×C47—21no—
185C22×C4×C47—21no—
186C22×C4×C47—24no—
187C22×C4×C47—21no—
188C22×C4×C47—21no—
189C22×C4×C47—21no—
190C22×C4×C47—42no—
191C22×C4×C47—42no—
192C22×C4×C47—42no—
193C22×C4×C47—42no—
194C22×C4×C47—81no—
195C22×C4×C47C22×C412yes—
196C22×C4×C47C2×D411yescharacteristic
197C22×C4×C47C2×D412yes—
198C22×C4×C47C2411yescharacteristic
199C2×C22⋊D47C22⋊C414yes—
200C2×C22⋊D47SD1614yes—
201C2×C22⋊D47Q1614yes—
202C22×Dic47—21no—
203C22×Dic47—21no—
204C22×Dic47—21no—
205C22×Dic47—21no—
206C22×Dic47C2×D411yescharacteristic
207C22×Dic47C2×D411yescharacteristic
208C22×Dic47C2×D411yescharacteristic
209Q8×D47—28no—
210Q8×D47—44no—
211Q8×D47—44no—
212Q8×D47—44no—
213C2×C4×D47—21no—
214C2×C4×D47—21no—
215C2×C4×D47—21no—
216C2×C4×D47—21no—
217C2×C4×D47—24no—
218C2×C4×D47—42no—
219C2×C4×D47—42no—
220C2×C4×D47—42no—
221C2×C4×D47—42no—
222C2×C4×D47—81no—
223C2×C4×D47C22×C412yes—
224C2×C4×D47C2×D412yes—
225C2×Dic94—21no—
226C2×Dic94—21no—
227C2×Dic94—21no—
228C2×Dic94—21no—
229C2×Dic94—21no—
230C2×Dic94—24no—
231C2×Dic94—42no—
232C2×Dic94—42no—
233C2×Dic94C22×C412yes—
234C2×C8×C47—21no—
235C2×C8×C47—21no—
236C2×C8×C47—21no—
237C2×C8×C47—21no—
238C2×C8×C47—21no—
239C2×C8×C47—44no—
240C2×C8×C47C2×D412yes—
241C4⋊C4×C47—21no—
242C4⋊C4×C47—21no—
243C4⋊C4×C47—21no—
244C4⋊C4×C47—42no—
245C4⋊C4×C47C2×D412yes—
246C22⋊Dic47—24no—
247C22⋊Dic47—42no—
248C22⋊Dic47C22⋊C414yes—
249(C2×D47)⋊C4—24no—
250(C2×D47)⋊C4—42no—
251(C2×D47)⋊C4C22⋊C414yes—
252C4⋊Dic47—21no—
253C4⋊Dic47—24no—
254C4⋊Dic47—21no—
255C4⋊Dic47—21no—
256C4⋊Dic47—21no—
257C4⋊Dic47—21no—
258C4⋊Dic47C22×C412yes—
259Dic47⋊C4—24no—
260Dic47⋊C4—24no—
261Dic47⋊C4—24no—
262Dic47⋊C4—24no—
263Dic47⋊C4—42no—
264Dic47⋊C4—42no—
265Dic47⋊C4—81no—
266Dic47⋊C4C22⋊C414yes—
267C4×Dic47—24no—
268C4×Dic47—42no—
269C4×Dic47C22×C412yes—
270C4×Dic47C2×D412yes—
271C2×C47⋊C8—21no—
272C2×C47⋊C8—21no—
273C2×C47⋊C8—21no—
274C2×C47⋊C8—21no—
275C2×C47⋊C8—21no—
276C2×C47⋊C8—21no—
277C8×D47—44no—
278C23×C47—21no—
279C23×C47—21no—
280C23×C47—21no—
281C23×C47—21no—
282C23×C47C2×C22⋊C412yes—
283C23×C47C2×SD1612yes—
284C23×C47C2×Q1612yes—
285C23×C47C22×D411yescharacteristic
286C22×D47—21no—
287C22×D47—21no—
288C22×D47—21no—
289C22×D47—21no—
290C22×D47C2×C22⋊C412yes—
291C22×D47C2×SD1612yes—
292C22×D47C2×Q1612yes—
293Q8×C47—22no—
294Q8×C47—22no—
295Q8×C47—22no—
296Q8×C47—22no—
297Q8×C47—22no—
298Q8×C47—48no—
299Q8×C47—41no—
300Q8×C47—41no—
301Q8×C47C4×D414yescomplemented
302C2×C4×C47—22no—
303C2×C4×C47—21no—
304C2×C4×C47—22no—
305C2×C4×C47—22no—
306C2×C4×C47—21no—
307C2×C4×C47—22no—
308C2×C4×C47—22no—
309C2×C4×C47—22no—
310C2×C4×C47—22no—
311C2×C4×C47—22no—
312C2×C4×C47—22no—
313C2×C4×C47—48no—
314C2×C4×C47—41no—
315C2×C4×C47—41no—
316C2×C4×C47—41no—
317C2×C4×C47—41no—
318C2×C4×C47—41no—
319C2×C4×C47—41no—
320C2×C4×C47—41no—
321C2×C4×C47—84no—
322C2×C4×C47C2×C22⋊C412yes—
323C2×C4×C47C23×C411yescharacteristic
324C2×C4×C47C22×D411yescharacteristic
325C2×C4×C47C22×D411yescharacteristic
326C2×C4×C47C2×#4111yescharacteristic
327C2×C4×C47H(5,𝔽2)11yescharacteristic
328C2×C4×C47H(5,𝔽2)11yescharacteristic
329C22⋊D47#103116yesdirect product factor
330C2×Dic47—21no—
331C2×Dic47—21no—
332C2×Dic47—21no—
333C2×Dic47—21no—
334C2×Dic47—22no—
335C2×Dic47—22no—
336C2×Dic47—41no—
337C2×Dic47—41no—
338C2×Dic47—41no—
339C2×Dic47—41no—
340C2×Dic47—41no—
341C2×Dic47—41no—
342C2×Dic47—41no—
343C2×Dic47—41no—
344C2×Dic47—41no—
345C2×Dic47—41no—
346C2×Dic47C2×C22⋊C412yes—
347C2×Dic47C2×C22⋊C412yes—
348C2×Dic47C2×C22⋊C412yes—
349C2×Dic47C2×SD1612yes—
350C2×Dic47C2×Q1612yes—
351C4×D47—22no—
352C4×D47—22no—
353C4×D47—22no—
354C4×D47—22no—
355C4×D47—48no—
356C4×D47—84no—
357Dic94—22no—
358Dic94—22no—
359Dic94—48no—
360Dic94—41no—
361Dic94—41no—
362C8×C47—22no—
363C8×C47—41no—
364C47⋊C8—41no—
365C47⋊C8—41no—
366D4×#103—471nomaximal, Sylow
367C22×C47—22no—
368C22×C47—22no—
369C22×C47—22no—
370C22×C47—22no—
371C22×C47—22no—
372C22×C47—22no—
373C22×C47C2×#10314yescomplemented
374C22×C47C22×C22⋊C411yescharacteristic
375C22×C47D4211yescharacteristic
376C22×C47#54611yescharacteristic
377C22×C47C22×SD1611yescharacteristic
378C22×C47C22×Q1611yescharacteristic
379C22×C47#57711yescharacteristic
380C22×C47#57811yescharacteristic
381C2×D47—22no—
382C2×D47—22no—
383C2×D47—22no—
384C2×D47—22no—
385C2×D47—22no—
386C2×D47—22no—
387C2×D47C2×#10314yescomplemented
388C4×C47—24no—
389C4×C47—22no—
390C4×C47—42no—
391C4×C47—42no—
392C4×C47—81no—
393C4×C47C2×C4×D411yescharacteristic
394C4×C47#51811yescharacteristic
395C4×C47D4211yescharacteristic
396C4×C47#54611yescharacteristic
397Dic47—22no—
398Dic47—22no—
399Dic47—42no—
400Dic47—42no—
401Dic47—81no—
402Dic47—81no—
403Dic47C2×#10314yescomplemented
404C2×D4×Q8—471no—
405C2×C8×D4—471no—
406C22×#103—471no—
407C22×#103D4711yescharacteristic, complemented
408D4×C4⋊C4—471no—
409#1981—471no—
410#1956—471no—
411#1892—471no—
412#1892—471no—
413#1872—471no—
414#1872—471no—
415#1803—471no—
416#1787—471no—
417#1787—471no—
418C4×#103—471no—
419C2×C47—24no—
420C2×C47D4×C22⋊C411yescharacteristic
421C2×C47C22×#10311yescharacteristic
422C2×C47#289811yescharacteristic
423C2×C47D4×SD1611yescharacteristic
424C2×C47D4×Q1611yescharacteristic
425C2×C47#329811yescharacteristic
426C2×C47#329911yescharacteristic
427D47—24no—
428C23×Q8—471no—
429C23×Q8C2×D4711yescharacteristic
430C23×C8—471no—
431C23×C8C2×D4711yescharacteristic
432D4×Q8—478no—
433D4×Q8—944no—
434C2×C4⋊Q8—471no—
435C2×C4⋊Q8—941no—
436C2×C22⋊Q8—471no—
437C2×C22⋊Q8—471no—
438C2×C22⋊Q8—941no—
439C2×C22⋊Q8—941no—
440C2×C4×Q8—471no—
441C2×C4×D4—471no—
442C2×C4×D4—941no—
443C2×C4×D4—941no—
444C22×C4⋊C4—471no—
445C22×C4⋊C4C2×D4711yescharacteristic
446C8×D4—944no—
447C2×C4⋊C8—471no—
448C2×#103—24no—
449C2×#103—471no—
450C2×#103—471no—
451C2×#103—471no—
452C2×#103—471no—
453C2×#103—471no—
454C2×#103—471no—
455C2×#103—471no—
456C2×#103—471no—
457C2×#103—944no—
458C2×#103C2×D4711yescharacteristic
459C2×#103C2×D4711yescharacteristic
460C2×#103C2×D4711yescharacteristic
461C2×#103C2×D4711yescharacteristic
462C2×C22⋊C8—471no—
463C2×C22⋊C8—471no—
464C2×C4×C8—471no—
465#389—941no—
466#385—941no—
467#385—941no—
468#384—471no—
469#380—471no—
470#380—471no—
471C4×C4⋊C4—471no—
472#340—471no—
473#340—471no—
474#340—471no—
475#340—471no—
476C47D4×#10311yescharacteristic, complemented, Sylow
477C22×Q8—21no—
478C22×Q8—22no—
479C22×Q8—22no—
480C22×Q8—22no—
481C22×Q8—41no—
482C22×Q8—41no—
483C22×Q8—474no—
484C22×Q8—471no—
485C22×Q8—941no—
486C22×Q8—942no—
487C22×Q8—942no—
488C22×Q8—942no—
489C22×Q8—1881no—
490C22×Q8—1881no—
491C22×Q8C4×D4714yescomplemented
492C22×Q8C22×D4711yescharacteristic
493C22×Q8C22×D4711yescharacteristic
494C22×D4—471no—
495C23×C4—21no—
496C23×C4—21no—
497C23×C4—471no—
498C23×C4—941no—
499C23×C4—941no—
500C23×C4C22×D4711yescharacteristic
501C22×C8—22no—
502C22×C8—22no—
503C22×C8—41no—
504C22×C8—471no—
505C22×C8—471no—
506C22×C8—942no—
507C22×C8—942no—
508C22×C8—1881no—
509C22×C8C22×D4711yescharacteristic
510C22×C8C22×D4711yescharacteristic
511C4⋊Q8—474no—
512C4⋊Q8—942no—
513C4⋊Q8—948no—
514C22⋊Q8—474no—
515C22⋊Q8—474no—
516C22⋊Q8—948no—
517C22⋊Q8—948no—
518C22⋊Q8—942no—
519C22⋊Q8—942no—
520C4×Q8—474no—
521C4×Q8—942no—
522C4×D4—474no—
523C4×D4—474no—
524C4×D4—948no—
525C4×D4—1884no—
526C2×C4⋊C4—22no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—41no—
529C2×C4⋊C4—471no—
530C2×C4⋊C4—471no—
531C2×C4⋊C4—471no—
532C2×C4⋊C4—471no—
533C2×C4⋊C4—941no—
534C2×C4⋊C4—941no—
535C2×C4⋊C4—941no—
536C2×C4⋊C4—941no—
537C2×C4⋊C4—941no—
538C2×C4⋊C4—942no—
539C2×C4⋊C4—941no—
540C2×C4⋊C4—941no—
541C2×C4⋊C4—941no—
542C2×C4⋊C4—1881no—
543C2×C4⋊C4C22×D4711yescharacteristic
544C2×C4⋊C4C22×D4711yescharacteristic
545C2×C22⋊C4—471no—
546C2×C22⋊C4—471no—
547C2×C22⋊C4—941no—
548C2×C22⋊C4—941no—
549C2×C22⋊C4—941no—
550C2×C22⋊C4—941no—
551C2×C42—471no—
552C2×C42—941no—
553C2×C42—941no—
554C4⋊C8—942no—
555#103—22no—
556#103—22no—
557#103—22no—
558#103—942no—
559#103—942no—
560#103—942no—
561#103—942no—
562#103—1881no—
563#103—1881no—
564#103—1881no—
565#103—1881no—
566#103C22⋊D4714yesdirect product factor
567C22⋊C8—942no—
568C22⋊C8—942no—
569C4×C8—942no—
570#95—941no—
571#95—941no—
572#95—941no—
573C24—471no—
574C24D4×D4711yescharacteristic
575C2×Q8—24no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—28no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—42no—
586C2×Q8—42no—
587C2×Q8—44no—
588C2×Q8—44no—
589C2×Q8—44no—
590C2×Q8—472no—
591C2×Q8—944no—
592C2×Q8—941no—
593C2×Q8—948no—
594C2×Q8—941no—
595C2×Q8—941no—
596C2×Q8—941no—
597C2×Q8—941no—
598C2×Q8—1882no—
599C2×Q8—1882no—
600C2×Q8—1884no—
601C2×Q8—1884no—
602C2×Q8—1884no—
603C2×Q8C2×C4×D4712yes—
604C2×Q8C2×C4×D4712yes—
605C2×Q8#1062535012yes—
606C2×Q8C2×C22⋊D4712yes—
607C2×D4—474no—
608C2×D4—474no—
609C2×D4—474no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—24no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—42no—
620C22×C4—42no—
621C22×C4—42no—
622C22×C4—42no—
623C22×C4—81no—
624C22×C4—471no—
625C22×C4—471no—
626C22×C4—471no—
627C22×C4—472no—
628C22×C4—472no—
629C22×C4—944no—
630C22×C4—941no—
631C22×C4—941no—
632C22×C4—941no—
633C22×C4—941no—
634C22×C4—941no—
635C22×C4—941no—
636C22×C4—941no—
637C22×C4—941no—
638C22×C4—3761no—
639C22×C4—1882no—
640C22×C4—1882no—
641C22×C4—1882no—
642C22×C4—1882no—
643C22×C4C2×C4×D4712yes—
644C22×C4D4×D4711yescharacteristic
645C22×C4D4×D4712yes—
646C22×C4C23×D4711yescharacteristic
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—44no—
653C2×C8—941no—
654C2×C8—941no—
655C2×C8—941no—
656C2×C8—941no—
657C2×C8—941no—
658C2×C8—941no—
659C2×C8—1884no—
660C2×C8C2×C22⋊D4712yes—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—42no—
665C4⋊C4—474no—
666C4⋊C4—472no—
667C4⋊C4—944no—
668C4⋊C4—944no—
669C4⋊C4—944no—
670C4⋊C4—944no—
671C4⋊C4—944no—
672C4⋊C4—941no—
673C4⋊C4—941no—
674C4⋊C4—941no—
675C4⋊C4—941no—
676C4⋊C4—941no—
677C4⋊C4—3761no—
678C4⋊C4—1882no—
679C4⋊C4—1882no—
680C4⋊C4C2×C22⋊D4712yes—
681C22⋊C4—474no—
682C22⋊C4—474no—
683C22⋊C4—944no—
684C22⋊C4—944no—
685C22⋊C4—1882no—
686C22⋊C4—1882no—
687C42—472no—
688C42—472no—
689C42—944no—
690C42—1882no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—472no—
696C23—472no—
697C23—472no—
698C23—941no—
699C23—941no—
700C23—941no—
701C23—941no—
702C23C22⋊C4×D4712yes—
703C23SD16×D4712yes—
704C23Q16×D4712yes—
705C23C2×D4×D4711yescharacteristic
706Q8—22no—
707Q8—22no—
708Q8—22no—
709Q8—22no—
710Q8—22no—
711Q8—48no—
712Q8—41no—
713Q8—41no—
714Q8—942no—
715Q8—942no—
716Q8—1888no—
717Q8—1881no—
718Q8—1881no—
719Q8C4×C22⋊D4714yescomplemented
720D4—4716no—
721C2×C4—21no—
722C2×C4—22no—
723C2×C4—21no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—48no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—84no—
741C2×C4—472no—
742C2×C4—472no—
743C2×C4—472no—
744C2×C4—472no—
745C2×C4—472no—
746C2×C4—941no—
747C2×C4—941no—
748C2×C4—941no—
749C2×C4—941no—
750C2×C4—942no—
751C2×C4—942no—
752C2×C4—942no—
753C2×C4—942no—
754C2×C4—942no—
755C2×C4—942no—
756C2×C4—3764no—
757C2×C4—1888no—
758C2×C4—1881no—
759C2×C4—1881no—
760C2×C4—1881no—
761C2×C4—1881no—
762C2×C4—1881no—
763C2×C4—1881no—
764C2×C4—1881no—
765C2×C4—1881no—
766C2×C4—1881no—
767C2×C4—1881no—
768C2×C4C22⋊C4×D4712yes—
769C2×C4C22×C4×D4711yescharacteristic
770C2×C4C2×D4×D4711yescharacteristic
771C2×C4C22×C22⋊D4711yescharacteristic
772C2×C4C2×#1062535011yescharacteristic
773C2×C4#1309406911yescharacteristic
774C2×C4#1309406911yescharacteristic
775C8—22no—
776C8—41no—
777C8—1881no—
778C8—1881no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—474no—
786C22—942no—
787C22—942no—
788C22—942no—
789C22—942no—
790C22—942no—
791C22—942no—
792C22#103×D4714yescomplemented
793C22C2×C22⋊C4×D4711yescharacteristic
794C22D4×C22⋊D4711yescharacteristic
795C22#1568976311yescharacteristic
796C22C2×SD16×D4711yescharacteristic
797C22C2×Q16×D4711yescharacteristic
798C22#1568992911yescharacteristic
799C22#1568993611yescharacteristic
800C4—22no—
801C4—24no—
802C4—42no—
803C4—42no—
804C4—81no—
805C4—474no—
806C4—942no—
807C4—942no—
808C4—3761no—
809C4—3761no—
810C4—1882no—
811C4—1882no—
812C4C2×C4×C22⋊D4711yescharacteristic
813C4#1568959611yescharacteristic
814C4D4×C22⋊D4711yescharacteristic
815C4#1568976311yescharacteristic
816C2—24no—
817C2—944no—
818C2C22⋊C4×C22⋊D4711yescharacteristic
819C2C2×#103×D4711yescharacteristic
820C2#2025191611yescharacteristic
821C2SD16×C22⋊D4711yescharacteristic
822C2Q16×C22⋊D4711yescharacteristic
823C2#2025524911yescharacteristic
824C2#2025526011yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC22×#103×C47C2
socleC23×C47C22×D4
prime radicalC22×C22⋊D47D4
cosocleC22×C4×C47C24
hypercenterC22×#103D47
hypocenterC47D4×#103
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
3. C2×#103×D47C2semidirect
5. #20244309C2semidirect
6. #20244188C2semidirect
7. #20243811C2semidirect
8. #20243808C2semidirect
9. #20243695C2semidirect
10. #20243692C2semidirect
11. #20243391C2semidirect
12. #20243323C2semidirect
13. #20243321C2semidirect
14. #103×Dic47C2semidirect
15. C22×#103×C47C2semidirect
19. Q8×C22⋊D47C4semidirect
71. C2×Q8×D47C2×C4semidirect
83. #13094022C2×C4semidirect
86. #13094003C2×C4semidirect
89. #13094000C2×C4semidirect
91. Q8×Dic47C2×C4semidirect
140. C22×Q8×C47C2×C4semidirect
159. #103×C47D4semidirect
301. Q8×C47C4×D4semidirect
329. C22⋊D47#103direct (N × H)
373. C22×C47C2×#103semidirect
387. C2×D47C2×#103semidirect
403. Dic47C2×#103semidirect
407. C22×#103D47semidirect
476. C47D4×#103semidirect
491. C22×Q8C4×D47semidirect
566. #103C22⋊D47direct (N × H)
719. Q8C4×C22⋊D47semidirect
792. C22#103×D47semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×C22⋊D472
C2×C8×C22⋊D472
C2×#103×D472
C4⋊C4×C22⋊D472
#202443092
#202441882
#202438112
#202438082
#202436952
#202436922
#202433912
#202433232
#202433212
#103×Dic472
C22×#103×C472
D4×#10347