Finite Group Databasebeta

← C2×#20246721 #26384965

Subgroups — C2×#20246721 #26384965

Order 12032.

5718 conjugacy classes of subgroups.

The subgroup lattice has 944 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#10625350C211yesmaximal, characteristic
2C22×#13094009C211yesmaximal, characteristic, complemented
3C22×#13094006C211yesmaximal, characteristic, complemented
4C22×C4⋊C4×D47C211yesmaximal, characteristic, complemented
5#20246721C2116yesmaximal, direct product factor
6C2×#15689044C211yesmaximal, characteristic, complemented
7C2×#15689043C211yesmaximal, characteristic, complemented
8C2×#15689039C211yesmaximal, characteristic, complemented
9C2×#15689038C211yesmaximal, characteristic, complemented
10C2×#15689001C211yesmaximal, characteristic, complemented
11C2×#15688999C211yesmaximal, characteristic, complemented
12C2×#15688997C211yesmaximal, characteristic, complemented
13C2×#15688996C211yesmaximal, characteristic, complemented
14C2×#15688994C211yesmaximal, characteristic, complemented
15C2×#15688985C211yesmaximal, characteristic, complemented
16C2×C47×#385C211yesmaximal, characteristic, complemented
17C22×#10625350—28no—
18C22×#10625350—28no—
19C22×#10625350—28no—
20C22×#10625350C2218yes—
21C23×Dic94C2211yescharacteristic
22C23×D188C2211yescharacteristic
23C23×C22⋊D47C2211yescharacteristic
24C23×C22⋊D47C2211yescharacteristic
25C23×C4×D47C2211yescharacteristic
26C23×C4×D47C2211yescharacteristic
27C23×C4×D47C2211yescharacteristic
28C23×C4×D47C2211yescharacteristic
29C2×#13094009—28no—
30C2×#13094009C2218yescomplemented
31C2×#13094006—28no—
32C2×#13094006C2218yescomplemented
33C22×C4⋊Dic47C2211yescharacteristic
34C22×C4⋊Dic47C2211yescharacteristic
35C22×Dic47⋊C4C2211yescharacteristic
36C22×Dic47⋊C4C2211yescharacteristic
37C22×Dic47⋊C4C2211yescharacteristic
38C22×Dic47⋊C4C2211yescharacteristic
39C2×C4⋊C4×D47—28no—
40C2×C4⋊C4×D47C2218yescomplemented
41C22×C22⋊Dic47C2211yescharacteristic
42C22×C22⋊Dic47C2211yescharacteristic
43C22×(C2×D47)⋊C4C2211yescharacteristic
44C22×(C2×D47)⋊C4C2211yescharacteristic
45C22×(C2×D47)⋊C4C2211yescharacteristic
46C22×(C2×D47)⋊C4C2211yescharacteristic
47C22×(C2×D47)⋊C4C2211yescharacteristic
48C22×(C2×D47)⋊C4C2211yescharacteristic
49#15689044C2218yescomplemented
50#15689043C2218yescomplemented
51#15689039C2218yescomplemented
52#15689038C2218yescomplemented
53#15689001C2218yescomplemented
54#15688999C2218yescomplemented
55#15688997C2218yescomplemented
56#15688996C2218yescomplemented
57#15688994C2218yescomplemented
58#15688985C2218yescomplemented
59C2×C47⋊#95C2211yescharacteristic
60C2×C47⋊#95C2211yescharacteristic
61C2×C47⋊#95C2211yescharacteristic
62C2×C47⋊#95C2211yescharacteristic
63C2×C47⋊#95C2211yescharacteristic
64C2×C47⋊#95C2211yescharacteristic
65C24×C4×C47C2211yescharacteristic
66C22×C4⋊C4×C47C2211yescharacteristic
67C22×C4⋊C4×C47C2211yescharacteristic
68C22×C22⋊C4×C47C2211yescharacteristic
69C22×C22⋊C4×C47C2211yescharacteristic
70C47×#385C2218yescomplemented
71C2×#95×C47C2211yescharacteristic
72C2×#95×C47C2211yescharacteristic
73C24×D47C2311yescharacteristic
74C24×D47C2311yescharacteristic
75C2×#10625350—2128no—
76C2×#10625350—232no—
77C2×#10625350—232no—
78C2×#10625350—232no—
79C22×Dic94—24no—
80C22×Dic94—24no—
81C22×Dic94—24no—
82C22×Dic94C2314yes—
83C22×D188—24no—
84C22×D188—24no—
85C22×D188D418yes—
86C22×D188C2314yes—
87C22×C22⋊D47—24no—
88C22×C22⋊D47—24no—
89C22×C22⋊D47—24no—
90C22×C22⋊D47—24no—
91C22×C22⋊D47—24no—
92C22×C22⋊D47D418yes—
93C22×C22⋊D47C2314yes—
94C22×C22⋊D47C2314yes—
95C23×Dic47C2311yescharacteristic
96C23×Dic47C2311yescharacteristic
97C23×Dic47C2311yescharacteristic
98C23×Dic47C2311yescharacteristic
99C23×Dic47C2311yescharacteristic
100C23×Dic47C2311yescharacteristic
101C22×C4×D47—24no—
102C22×C4×D47—24no—
103C22×C4×D47—24no—
104C22×C4×D47—24no—
105C22×C4×D47—24no—
106C22×C4×D47—24no—
107C22×C4×D47—24no—
108C22×C4×D47—24no—
109C22×C4×D47—24no—
110C22×C4×D47—24no—
111C22×C4×D47—24no—
112C22×C4×D47D418yes—
113C22×C4×D47C2314yes—
114C22×C4×D47C2314yes—
115C22×C4×D47C2314yes—
116C22×C4×D47C2314yes—
117#13094009—232no—
118#13094006—232no—
119C2×C4⋊Dic47—24no—
120C2×C4⋊Dic47—24no—
121C2×C4⋊Dic47C2314yes—
122C2×C4⋊Dic47C2314yes—
123C2×Dic47⋊C4—24no—
124C2×Dic47⋊C4—24no—
125C2×Dic47⋊C4—24no—
126C2×Dic47⋊C4—24no—
127C2×Dic47⋊C4C2314yes—
128C2×Dic47⋊C4C2314yes—
129C2×Dic47⋊C4C2314yes—
130C2×Dic47⋊C4C2314yes—
131C4⋊C4×D47—232no—
132C2×C22⋊Dic47—24no—
133C2×C22⋊Dic47—24no—
134C2×C22⋊Dic47C2314yes—
135C2×C22⋊Dic47C2314yes—
136C2×(C2×D47)⋊C4—24no—
137C2×(C2×D47)⋊C4—24no—
138C2×(C2×D47)⋊C4—24no—
139C2×(C2×D47)⋊C4—24no—
140C2×(C2×D47)⋊C4—24no—
141C2×(C2×D47)⋊C4—24no—
142C2×(C2×D47)⋊C4C2314yes—
143C2×(C2×D47)⋊C4C2314yes—
144C2×(C2×D47)⋊C4C2314yes—
145C2×(C2×D47)⋊C4C2314yes—
146C2×(C2×D47)⋊C4C2314yes—
147C2×(C2×D47)⋊C4C2314yes—
148C47⋊#95C2314yes—
149C47⋊#95C2314yes—
150C47⋊#95C2314yes—
151C47⋊#95C2314yes—
152C47⋊#95C2314yes—
153C47⋊#95C2314yes—
154C25×C47C2311yescharacteristic
155C23×C4×C47—24no—
156C23×C4×C47—24no—
157C23×C4×C47—24no—
158C23×C4×C47C2311yescharacteristic
159C23×C4×C47C2311yescharacteristic
160C23×C4×C47C2314yes—
161C23×C4×C47C2311yescharacteristic
162C23×C4×C47C2311yescharacteristic
163C23×C4×C47C2311yescharacteristic
164C23×C4×C47C2311yescharacteristic
165C2×C4⋊C4×C47—24no—
166C2×C4⋊C4×C47—24no—
167C2×C4⋊C4×C47C2314yes—
168C2×C4⋊C4×C47C2314yes—
169C2×C22⋊C4×C47—24no—
170C2×C22⋊C4×C47—24no—
171C2×C22⋊C4×C47C2314yes—
172C2×C22⋊C4×C47C2314yes—
173#95×C47C2314yes—
174#95×C47C2314yes—
175C24×C47—22no—
176C24×C47—22no—
177C24×C47—22no—
178C24×C47—22no—
179C24×C47—22no—
180C24×C47—22no—
181C24×C47C2×D414yes—
182C24×C47C2412yes—
183C24×C47C2411yescharacteristic
184C23×D47—22no—
185C23×D47—22no—
186C23×D47—22no—
187C23×D47—22no—
188C23×D47—22no—
189C23×D47—22no—
190C23×D47—22no—
191C23×D47—22no—
192C23×D47—22no—
193C23×D47—22no—
194C23×D47C2×D414yes—
195C23×D47C2×D414yes—
196C23×D47C2×D414yes—
197C23×D47C2×D414yes—
198C23×D47C2412yes—
199C23×D47C2412yes—
200C22×C4×C47—232no—
201C22×C4×C47—22no—
202C22×C4×C47—22no—
203C22×C4×C47—22no—
204C22×C4×C47—22no—
205C22×C4×C47—22no—
206C22×C4×C47—28no—
207C22×C4×C47—22no—
208C22×C4×C47—28no—
209C22×C4×C47—28no—
210C22×C4×C47—22no—
211C22×C4×C47—22no—
212C22×C4×C47—22no—
213C22×C4×C47—22no—
214C22×C4×C47—22no—
215C22×C4×C47—22no—
216C22×C4×C47—22no—
217C22×C4×C47—22no—
218C22×C4×C47—22no—
219C22×C4×C47C2×D414yes—
220C22×C4×C47C2×D414yes—
221C22×C4×C47#4114yescomplemented
222C22×C4×C47C2412yes—
223C22×C4×C47C2412yes—
224C22×C4×C47C2412yes—
225C22×C4×C47C2412yes—
226C22×C4×C47C2412yes—
227C22×C4×C47C2412yes—
228C2×C22⋊D47—232no—
229C2×C22⋊D47—28no—
230C2×C22⋊D47—232no—
231C2×C22⋊D47—28no—
232C2×C22⋊D47—28no—
233C2×C22⋊D47—28no—
234C2×C22⋊D47—28no—
235C2×C22⋊D47C2×D4116yes—
236C22×Dic47—22no—
237C22×Dic47—22no—
238C22×Dic47—22no—
239C22×Dic47—22no—
240C22×Dic47—22no—
241C22×Dic47—22no—
242C22×Dic47—22no—
243C22×Dic47—22no—
244C22×Dic47—22no—
245C22×Dic47—22no—
246C22×Dic47—22no—
247C22×Dic47—22no—
248C22×Dic47—22no—
249C22×Dic47—22no—
250C22×Dic47—22no—
251C22×Dic47C2×D414yes—
252C22×Dic47C2×D414yes—
253C22×Dic47#4114yescomplemented
254C22×Dic47C2412yes—
255C22×Dic47C2412yes—
256C22×Dic47C2412yes—
257C22×Dic47C2412yes—
258C22×Dic47C2412yes—
259C22×Dic47C2412yes—
260#10625350—2256no—
261C2×D188—232no—
262C2×D188—28no—
263C2×D188—28no—
264C2×D188C2×D4116yes—
265C2×C4×D47—232no—
266C2×C4×D47—232no—
267C2×C4×D47—232no—
268C2×C4×D47—28no—
269C2×C4×D47—28no—
270C2×C4×D47—28no—
271C2×C4×D47—28no—
272C2×C4×D47—28no—
273C2×C4×D47—28no—
274C2×C4×D47—28no—
275C2×C4×D47—28no—
276C2×C4×D47—28no—
277C2×C4×D47—28no—
278C2×C4×D47—28no—
279C2×C4×D47—416no—
280C2×C4×D47C2×D4116yes—
281C2×Dic94—232no—
282C2×Dic94—28no—
283C2×Dic94—28no—
284C2×Dic94—28no—
285C4⋊C4×C47—28no—
286C4⋊C4×C47—28no—
287C22⋊C4×C47—28no—
288C22⋊C4×C47—28no—
289C22⋊Dic47—28no—
290C22⋊Dic47—28no—
291(C2×D47)⋊C4—28no—
292(C2×D47)⋊C4—28no—
293(C2×D47)⋊C4—28no—
294(C2×D47)⋊C4—28no—
295(C2×D47)⋊C4—28no—
296(C2×D47)⋊C4—28no—
297C4⋊Dic47—28no—
298C4⋊Dic47—28no—
299Dic47⋊C4—28no—
300Dic47⋊C4—28no—
301Dic47⋊C4—28no—
302Dic47⋊C4—28no—
303C23×C47—28no—
304C23×C47—28no—
305C23×C47—28no—
306C23×C47—22no—
307C23×C47—22no—
308C23×C47—22no—
309C23×C47—22no—
310C23×C47—22no—
311C23×C47—22no—
312C23×C47—44no—
313C23×C47—44no—
314C23×C47—44no—
315C23×C47—44no—
316C23×C47C22×D414yes—
317C23×C47C22×D412yes—
318C23×C47C22×D412yes—
319C23×C47C22×D412yes—
320C23×C47C2×#4112yes—
321C23×C47C2×#4112yes—
322C23×C472−1+412yes—
323C23×C472−1+412yes—
324C23×C47C2511yescharacteristic
325C22×D47—28no—
326C22×D47—28no—
327C22×D47—28no—
328C22×D47—28no—
329C22×D47—28no—
330C22×D47—28no—
331C22×D47—22no—
332C22×D47—22no—
333C22×D47—22no—
334C22×D47—22no—
335C22×D47—28no—
336C22×D47—28no—
337C22×D47—28no—
338C22×D47—22no—
339C22×D47—22no—
340C22×D47—22no—
341C22×D47—22no—
342C22×D47—22no—
343C22×D47—22no—
344C22×D47—44no—
345C22×D47—44no—
346C22×D47—44no—
347C22×D47—44no—
348C22×D47#120116yes—
349C22×D47C22×D414yes—
350C22×D47C22×D414yes—
351C22×D47C22×D414yes—
352C22×D47C22×D414yes—
353C2×C4×C47—232no—
354C2×C4×C47—28no—
355C2×C4×C47—28no—
356C2×C4×C47—28no—
357C2×C4×C47—22no—
358C2×C4×C47—22no—
359C2×C4×C47—22no—
360C2×C4×C47—22no—
361C2×C4×C47—22no—
362C2×C4×C47—22no—
363C2×C4×C47—22no—
364C2×C4×C47—22no—
365C2×C4×C47—22no—
366C2×C4×C47—22no—
367C2×C4×C47—22no—
368C2×C4×C47—22no—
369C2×C4×C47—22no—
370C2×C4×C47—22no—
371C2×C4×C47—22no—
372C2×C4×C47—44no—
373C2×C4×C47—44no—
374C2×C4×C47—44no—
375C2×C4×C47C22×D414yes—
376C2×C4×C47C22×D414yes—
377C2×C4×C47C2×#4114yescomplemented
378C22⋊D47—232no—
379C22⋊D47—232no—
380C2×Dic47—28no—
381C2×Dic47—28no—
382C2×Dic47—28no—
383C2×Dic47—22no—
384C2×Dic47—22no—
385C2×Dic47—22no—
386C2×Dic47—22no—
387C2×Dic47—22no—
388C2×Dic47—22no—
389C2×Dic47—22no—
390C2×Dic47—22no—
391C2×Dic47—22no—
392C2×Dic47—22no—
393C2×Dic47—22no—
394C2×Dic47—22no—
395C2×Dic47—22no—
396C2×Dic47—22no—
397C2×Dic47—22no—
398C2×Dic47—44no—
399C2×Dic47—44no—
400C2×Dic47—44no—
401C2×Dic47C22×D414yes—
402C2×Dic47C22×D414yes—
403C2×Dic47C2×#4114yescomplemented
404D188—232no—
405C4×D47—232no—
406C4×D47—232no—
407C4×D47—232no—
408C4×D47—416no—
409Dic94—232no—
410C2×#2406—471nomaximal, Sylow
411C22×C47—24no—
412C22×C47—24no—
413C22×C47—24no—
414C22×C47—416no—
415C22×C47—42no—
416C22×C47—42no—
417C22×C47—42no—
418C22×C47—42no—
419C22×C47C2×#12014yes—
420C22×C47#52514yes—
421C22×C47#53614yes—
422C22×C47#54714yes—
423C22×C47#54714yes—
424C22×C47#54714yes—
425C22×C47#54714yes—
426C22×C47C23×D411yescharacteristic
427C22×C47C23×D411yescharacteristic
428C22×C47C23×D411yescharacteristic
429C22×C47C22×#4111yescharacteristic
430C22×C47C22×#4111yescharacteristic
431C22×C47C2×2−1+411yescharacteristic
432C22×C47C2×2−1+411yescharacteristic
433C2×D47—232no—
434C2×D47—24no—
435C2×D47—24no—
436C2×D47—24no—
437C2×D47—24no—
438C2×D47—24no—
439C2×D47—24no—
440C2×D47—24no—
441C2×D47—24no—
442C2×D47—24no—
443C2×D47—416no—
444C2×D47—42no—
445C2×D47—42no—
446C2×D47—42no—
447C2×D47—42no—
448C2×D47C2×#12018yes—
449C4×C47—24no—
450C4×C47—24no—
451C4×C47—24no—
452C4×C47—42no—
453C4×C47—42no—
454C4×C47—42no—
455Dic47—24no—
456Dic47—24no—
457Dic47—24no—
458Dic47—42no—
459Dic47—42no—
460Dic47—42no—
461C23×#41—471no—
462C22×#123—471no—
463C22×#123—471no—
464C23×C4⋊C4—471no—
465#2406—4716no—
466C2×#395—471no—
467C2×#395—471no—
468C2×#394—471no—
469C2×#394—471no—
470C2×#386—471no—
471C2×#386—471no—
472C2×#385—471no—
473C2×#385—471no—
474C2×#385—471no—
475C2×#385D4711yescharacteristic, complemented
476C2×#381—471no—
477C2×C47—44no—
478C2×C47#240618yescomplemented
479C2×C47C22×#12011yescharacteristic
480C2×C47C2×#52511yescharacteristic
481C2×C47C2×#53611yescharacteristic
482C2×C47C2×#54711yescharacteristic
483C2×C47C2×#54711yescharacteristic
484C2×C47C2×#54711yescharacteristic
485C2×C47C2×#54711yescharacteristic
486D47—28no—
487D47—44no—
488C22×#41—478no—
489C22×#41—948no—
490C22×#41—948no—
491C22×#41—948no—
492C23×Q8—471no—
493C23×D4—471no—
494C23×D4—471no—
495C23×D4—471no—
496C24×C4—471no—
497C24×C4—471no—
498C24×C4—471no—
499C24×C4—471no—
500C24×C4C2×D4711yescharacteristic
501C2×#123—478no—
502C2×#123—478no—
503C2×#123—948no—
504C2×#123—948no—
505C22×C4⋊C4—471no—
506C22×C4⋊C4—471no—
507C22×C4⋊C4—471no—
508C22×C4⋊C4—471no—
509C22×C4⋊C4—471no—
510C22×C4⋊C4—471no—
511C22×C4⋊C4—478no—
512C22×C4⋊C4—948no—
513C22×C4⋊C4C2×D4711yescharacteristic
514C22×C4⋊C4C2×D4711yescharacteristic
515C22×C22⋊C4—471no—
516C22×C22⋊C4—471no—
517C22×C22⋊C4—471no—
518C22×C22⋊C4—471no—
519C22×C22⋊C4—471no—
520C22×C22⋊C4—471no—
521C22×C22⋊C4—471no—
522C22×C22⋊C4—471no—
523C22×C22⋊C4C2×D4711yescharacteristic
524C22×C22⋊C4C2×D4711yescharacteristic
525#395—478no—
526#395—478no—
527#394—478no—
528#394—478no—
529#386—478no—
530#386—478no—
531#385—478no—
532#385—478no—
533#385—478no—
534#385C2×D4718yescomplemented
535#381—478no—
536C2×#95—471no—
537C2×#95—471no—
538C2×#95—471no—
539C2×#95—471no—
540C2×#95—471no—
541C2×#95—471no—
542C2×#95C2×D4711yescharacteristic
543C2×#95C2×D4711yescharacteristic
544C47C2×#240611yescharacteristic, complemented, Sylow
545C25—471no—
546C25—471no—
547C25C22×D4711yescharacteristic
548C2×#41—9432no—
549C2×#41—9432no—
550C2×#41—9432no—
551C2×#41—94128no—
552C22×Q8—474no—
553C22×Q8—944no—
554C22×Q8—944no—
555C22×Q8—944no—
556C22×D4—478no—
557C22×D4—474no—
558C22×D4—474no—
559C22×D4—478no—
560C22×D4—474no—
561C22×D4—944no—
562C22×D4—944no—
563C22×D4—944no—
564C22×D4—944no—
565C22×D4—944no—
566C22×D4—944no—
567C22×D4—944no—
568C23×C4—24no—
569C23×C4—24no—
570C23×C4—24no—
571C23×C4—471no—
572C23×C4—471no—
573C23×C4—471no—
574C23×C4—478no—
575C23×C4—474no—
576C23×C4—471no—
577C23×C4—471no—
578C23×C4—471no—
579C23×C4—474no—
580C23×C4—474no—
581C23×C4—474no—
582C23×C4—944no—
583C23×C4—944no—
584C23×C4—944no—
585C23×C4—944no—
586C23×C4—944no—
587C23×C4—944no—
588C23×C4—944no—
589C23×C4—944no—
590C23×C4—944no—
591C23×C4—944no—
592C23×C4—944no—
593C23×C4C22×D4714yes—
594C23×C4C22×D4711yescharacteristic
595C23×C4C22×D4711yescharacteristic
596C23×C4C22×D4711yescharacteristic
597C23×C4C22×D4711yescharacteristic
598C23×C4C22×D4711yescharacteristic
599C23×C4C22×D4711yescharacteristic
600#123—9432no—
601#123—9432no—
602C2×C4⋊C4—24no—
603C2×C4⋊C4—24no—
604C2×C4⋊C4—474no—
605C2×C4⋊C4—474no—
606C2×C4⋊C4—474no—
607C2×C4⋊C4—474no—
608C2×C4⋊C4—474no—
609C2×C4⋊C4—474no—
610C2×C4⋊C4—9432no—
611C2×C4⋊C4—944no—
612C2×C4⋊C4—944no—
613C2×C4⋊C4—944no—
614C2×C4⋊C4—944no—
615C2×C4⋊C4—944no—
616C2×C4⋊C4—944no—
617C2×C4⋊C4C22×D4714yes—
618C2×C4⋊C4C22×D4714yes—
619C2×C22⋊C4—24no—
620C2×C22⋊C4—24no—
621C2×C22⋊C4—474no—
622C2×C22⋊C4—474no—
623C2×C22⋊C4—474no—
624C2×C22⋊C4—474no—
625C2×C22⋊C4—474no—
626C2×C22⋊C4—474no—
627C2×C22⋊C4—474no—
628C2×C22⋊C4—474no—
629C2×C22⋊C4—944no—
630C2×C22⋊C4—944no—
631C2×C22⋊C4—944no—
632C2×C22⋊C4—944no—
633C2×C22⋊C4—944no—
634C2×C22⋊C4—944no—
635C2×C22⋊C4—944no—
636C2×C22⋊C4—944no—
637C2×C22⋊C4C22×D4714yes—
638C2×C22⋊C4C22×D4714yes—
639#95—474no—
640#95—474no—
641#95—474no—
642#95—474no—
643#95—474no—
644#95—474no—
645#95C22×D4714yes—
646#95C22×D4714yes—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—474no—
654C24—474no—
655C24—474no—
656C24—472no—
657C24—474no—
658C24—472no—
659C24—942no—
660C24—942no—
661C24—942no—
662C24—942no—
663C24—942no—
664C24—942no—
665C24—942no—
666C24—942no—
667C24—942no—
668C24—942no—
669C24D4×D4714yes—
670C24C23×D4712yes—
671C24C23×D4711yescharacteristic
672#41—94256no—
673C2×Q8—948no—
674C2×Q8—948no—
675C2×Q8—9432no—
676C2×Q8—948no—
677C2×D4—4716no—
678C2×D4—4716no—
679C2×D4—9432no—
680C2×D4—948no—
681C2×D4—948no—
682C2×D4—948no—
683C2×D4—9432no—
684C2×D4—948no—
685C2×D4—948no—
686C2×D4—948no—
687C2×D4—9432no—
688C2×D4—948no—
689C22×C4—232no—
690C22×C4—22no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—28no—
696C22×C4—22no—
697C22×C4—28no—
698C22×C4—28no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—22no—
706C22×C4—22no—
707C22×C4—22no—
708C22×C4—474no—
709C22×C4—474no—
710C22×C4—474no—
711C22×C4—472no—
712C22×C4—472no—
713C22×C4—472no—
714C22×C4—4716no—
715C22×C4—472no—
716C22×C4—472no—
717C22×C4—472no—
718C22×C4—948no—
719C22×C4—948no—
720C22×C4—948no—
721C22×C4—9432no—
722C22×C4—948no—
723C22×C4—948no—
724C22×C4—948no—
725C22×C4—9432no—
726C22×C4—9432no—
727C22×C4—948no—
728C22×C4—948no—
729C22×C4—948no—
730C22×C4—942no—
731C22×C4—942no—
732C22×C4—942no—
733C22×C4—942no—
734C22×C4—942no—
735C22×C4—942no—
736C22×C4—948no—
737C22×C4—948no—
738C22×C4—942no—
739C22×C4—942no—
740C22×C4—942no—
741C22×C4—942no—
742C22×C4—942no—
743C22×C4—942no—
744C22×C4—942no—
745C22×C4—942no—
746C22×C4—942no—
747C22×C4—18816no—
748C22×C4#1062535014yescomplemented
749C22×C4D4×D4714yes—
750C22×C4D4×D4714yes—
751C22×C4C23×D4712yes—
752C22×C4C23×D4712yes—
753C22×C4C23×D4712yes—
754C22×C4C23×D4712yes—
755C22×C4C23×D4712yes—
756C22×C4C23×D4712yes—
757C4⋊C4—28no—
758C4⋊C4—28no—
759C4⋊C4—948no—
760C4⋊C4—948no—
761C4⋊C4—948no—
762C4⋊C4—948no—
763C4⋊C4—948no—
764C4⋊C4—948no—
765C22⋊C4—28no—
766C22⋊C4—28no—
767C22⋊C4—948no—
768C22⋊C4—948no—
769C22⋊C4—948no—
770C22⋊C4—948no—
771C22⋊C4—948no—
772C22⋊C4—948no—
773C22⋊C4—948no—
774C22⋊C4—948no—
775C23—28no—
776C23—28no—
777C23—28no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—44no—
785C23—44no—
786C23—44no—
787C23—44no—
788C23—4716no—
789C23—474no—
790C23—474no—
791C23—474no—
792C23—474no—
793C23—948no—
794C23—948no—
795C23—948no—
796C23—948no—
797C23—948no—
798C23—942no—
799C23—942no—
800C23—948no—
801C23—942no—
802C23—942no—
803C23—948no—
804C23—948no—
805C23—948no—
806C23—942no—
807C23—942no—
808C23—942no—
809C23—942no—
810C23—942no—
811C23—942no—
812C23—1884no—
813C23—1884no—
814C23—1884no—
815C23—1884no—
816C23C2×D4×D4714yes—
817C23C2×D4×D4712yes—
818C23C2×D4×D4712yes—
819C23C2×D4×D4712yes—
820C23#41×D4712yes—
821C23C2×#1062535012yes—
822C23#1309407112yes—
823C23#1309407212yes—
824C23C24×D4711yescharacteristic
825Q8—9432no—
826D4—9432no—
827D4—9432no—
828D4—9432no—
829C2×C4—232no—
830C2×C4—28no—
831C2×C4—28no—
832C2×C4—28no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—44no—
849C2×C4—44no—
850C2×C4—44no—
851C2×C4—474no—
852C2×C4—474no—
853C2×C4—474no—
854C2×C4—9432no—
855C2×C4—9432no—
856C2×C4—9432no—
857C2×C4—948no—
858C2×C4—948no—
859C2×C4—948no—
860C2×C4—942no—
861C2×C4—942no—
862C2×C4—942no—
863C2×C4—942no—
864C2×C4—942no—
865C2×C4—942no—
866C2×C4—942no—
867C2×C4—942no—
868C2×C4—942no—
869C2×C4—942no—
870C2×C4—942no—
871C2×C4—942no—
872C2×C4—942no—
873C2×C4—942no—
874C2×C4—942no—
875C2×C4—18816no—
876C2×C4—1884no—
877C2×C4—1884no—
878C2×C4—1884no—
879C2×C4C2×D4×D4714yes—
880C2×C4C2×D4×D4714yes—
881C2×C4C2×#1062535014yescomplemented
882C22—24no—
883C22—24no—
884C22—24no—
885C22—42no—
886C22—42no—
887C22—42no—
888C22—42no—
889C22—416no—
890C22—478no—
891C22—944no—
892C22—944no—
893C22—944no—
894C22—944no—
895C22—944no—
896C22—944no—
897C22—9432no—
898C22—944no—
899C22—944no—
900C22—944no—
901C22—1882no—
902C22—1882no—
903C22—1882no—
904C22—1882no—
905C22—18816no—
906C22#120×D4714yes—
907C22#1568963214yes—
908C22#1568969614yes—
909C22#1568977114yes—
910C22#1568977414yes—
911C22#1568977514yes—
912C22#1568977814yes—
913C22C22×D4×D4711yescharacteristic
914C22C22×D4×D4711yescharacteristic
915C22C22×D4×D4711yescharacteristic
916C22C2×#41×D4711yescharacteristic
917C22C22×#1062535011yescharacteristic
918C22C2×#1309407111yescharacteristic
919C22C2×#1309407211yescharacteristic
920C4—24no—
921C4—24no—
922C4—24no—
923C4—42no—
924C4—42no—
925C4—42no—
926C4—944no—
927C4—944no—
928C4—944no—
929C4—1882no—
930C4—1882no—
931C4—1882no—
932C2—44no—
933C2—948no—
934C2—1884no—
935C2#2024672118yesdirect product factor
936C2C2×#120×D4711yescharacteristic
937C2C2×#1568963211yescharacteristic
938C2C2×#1568969611yescharacteristic
939C2C2×#1568977111yescharacteristic
940C2C2×#1568977411yescharacteristic
941C2C2×#1568977511yescharacteristic
942C2C2×#1568977811yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#385C2
socleC24×C47C24
prime radicalC23×#10625350C2
hypercenterC2×#385D47
hypocenterC47C2×#2406
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C22×#13094009C2semidirect
3. C22×#13094006C2semidirect
4. C22×C4⋊C4×D47C2semidirect
5. #20246721C2direct (N × H)
6. C2×#15689044C2semidirect
7. C2×#15689043C2semidirect
8. C2×#15689039C2semidirect
9. C2×#15689038C2semidirect
10. C2×#15689001C2semidirect
11. C2×#15688999C2semidirect
12. C2×#15688997C2semidirect
13. C2×#15688996C2semidirect
14. C2×#15688994C2semidirect
15. C2×#15688985C2semidirect
16. C2×C47×#385C2semidirect
30. C2×#13094009C22semidirect
32. C2×#13094006C22semidirect
40. C2×C4⋊C4×D47C22semidirect
49. #15689044C22semidirect
50. #15689043C22semidirect
51. #15689039C22semidirect
52. #15689038C22semidirect
53. #15689001C22semidirect
54. #15688999C22semidirect
55. #15688997C22semidirect
56. #15688996C22semidirect
57. #15688994C22semidirect
58. #15688985C22semidirect
70. C47×#385C22semidirect
221. C22×C4×C47#41semidirect
253. C22×Dic47#41semidirect
377. C2×C4×C47C2×#41semidirect
403. C2×Dic47C2×#41semidirect
475. C2×#385D47semidirect
478. C2×C47#2406semidirect
534. #385C2×D47semidirect
544. C47C2×#2406semidirect
748. C22×C4#10625350semidirect
881. C2×C4C2×#10625350semidirect
935. C2#20246721direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#106253502
C22×#130940092
C22×#130940062
C22×C4⋊C4×D472
#202467212
C2×#156890442
C2×#156890432
C2×#156890392
C2×#156890382
C2×#156890012
C2×#156889992
C2×#156889972
C2×#156889962
C2×#156889942
C2×#156889852
C2×C47×#3852
C2×#240647