Finite Group Databasebeta

← C2×#20246286 #26375561

Subgroups — C2×#20246286 #26375561

Order 12032.

4718 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D47C211yesmaximal, characteristic
2C22×(C22⋊D47)⋊C4C211yesmaximal, characteristic
3C22×(C22⋊D47)⋊C4C211yesmaximal, characteristic
4C23×Dic47⋊C4C211yesmaximal, characteristic, complemented
5C22×C4⋊C4×D47C211yesmaximal, characteristic, complemented
6#20246286C2116yesmaximal, direct product factor
7C2×#15689020C211yesmaximal, characteristic, complemented
8C2×#15689018C211yesmaximal, characteristic, complemented
9C2×#15688998C211yesmaximal, characteristic, complemented
10C2×#15688997C211yesmaximal, characteristic, complemented
11C2×#15688994C211yesmaximal, characteristic, complemented
12C2×#15688992C211yesmaximal, characteristic, complemented
13C2×#15688982C211yesmaximal, characteristic, complemented
14C2×#15688981C211yesmaximal, characteristic, complemented
15C2×#15688974C211yesmaximal, characteristic, complemented
16C2×C47×#385C211yesmaximal, characteristic, complemented
17C23×C22⋊D47C2211yescharacteristic
18C24×Dic47C2211yescharacteristic
19C24×Dic47C2211yescharacteristic
20C23×C4×D47C2211yescharacteristic
21C23×C4×D47C2211yescharacteristic
22C23×C4×D47C2211yescharacteristic
23C2×C4×C22⋊D47—28no—
24C2×C4×C22⋊D47C2218yes—
25C2×(C22⋊D47)⋊C4—28no—
26C2×(C22⋊D47)⋊C4C4116yescomplemented
27C2×(C22⋊D47)⋊C4C2218yes—
28C2×(C22⋊D47)⋊C4C2218yes—
29C22×C4⋊Dic47C2211yescharacteristic
30C22×C4⋊Dic47C2211yescharacteristic
31C22×Dic47⋊C4—28no—
32C22×Dic47⋊C4C2211yescharacteristic
33C22×Dic47⋊C4C2211yescharacteristic
34C22×Dic47⋊C4C2211yescharacteristic
35C22×Dic47⋊C4C2211yescharacteristic
36C22×Dic47⋊C4C2211yescharacteristic
37C22×Dic47⋊C4C2211yescharacteristic
38C22×Dic47⋊C4C2211yescharacteristic
39C22×Dic47⋊C4C2211yescharacteristic
40C22×Dic47⋊C4C2211yescharacteristic
41C22×Dic47⋊C4C2218yescomplemented
42C2×C4⋊C4×D47—28no—
43C2×C4⋊C4×D47C2218yescomplemented
44C22×C22⋊Dic47C2211yescharacteristic
45C22×(C2×D47)⋊C4C2211yescharacteristic
46C22×(C2×D47)⋊C4C2211yescharacteristic
47C22×(C2×D47)⋊C4C2211yescharacteristic
48C22×C4×Dic47C2211yescharacteristic
49C22×C4×Dic47C2211yescharacteristic
50C22×C4×Dic47C2211yescharacteristic
51#15689020C2218yescomplemented
52#15689018C2218yescomplemented
53#15688998C2218yescomplemented
54#15688997C2218yescomplemented
55#15688994C2218yescomplemented
56#15688992C2218yescomplemented
57#15688982C2218yescomplemented
58#15688981C2218yescomplemented
59#15688974C2218yescomplemented
60C2×C47⋊#95C2211yescharacteristic
61C2×C47⋊#95C2211yescharacteristic
62C2×C47⋊#95C2211yescharacteristic
63C2×C47⋊#95C2211yescharacteristic
64C24×C4×C47C2211yescharacteristic
65C22×C4⋊C4×C47C2211yescharacteristic
66C22×C4⋊C4×C47C2211yescharacteristic
67C22×C22⋊C4×C47C2211yescharacteristic
68C22×C22⋊C4×C47C2211yescharacteristic
69C47×#385C2218yescomplemented
70C2×#95×C47C2211yescharacteristic
71C2×#95×C47C2211yescharacteristic
72C24×D47C2311yescharacteristic
73C22×C22⋊D47C2×C418yes—
74C22×C22⋊D47D418yes—
75C22×C22⋊D47Q818yes—
76C22×C22⋊D47C2314yes—
77C23×Dic47—24no—
78C23×Dic47—24no—
79C23×Dic47—24no—
80C23×Dic47—24no—
81C23×Dic47—42no—
82C23×Dic47C2×C418yescomplemented
83C23×Dic47C2311yescharacteristic
84C23×Dic47C2311yescharacteristic
85C23×Dic47C2311yescharacteristic
86C23×Dic47C2314yes—
87C23×Dic47C2311yescharacteristic
88C23×Dic47C2314yes—
89C23×Dic47C2311yescharacteristic
90C23×Dic47C2311yescharacteristic
91C23×Dic47C2311yescharacteristic
92C22×C4×D47—24no—
93C22×C4×D47—24no—
94C22×C4×D47—24no—
95C22×C4×D47—24no—
96C22×C4×D47—24no—
97C22×C4×D47—24no—
98C22×C4×D47—42no—
99C22×C4×D47—42no—
100C22×C4×D47C2×C418yescomplemented
101C22×C4×D47C2314yes—
102C22×C4×D47C2314yes—
103C22×C4×D47C2314yes—
104C4×C22⋊D47—232no—
105(C22⋊D47)⋊C4—232no—
106(C22⋊D47)⋊C4C2×C4164yescomplemented
107C2×C4⋊Dic47—24no—
108C2×C4⋊Dic47—42no—
109C2×C4⋊Dic47C2314yes—
110C2×C4⋊Dic47C2314yes—
111C2×Dic47⋊C4—24no—
112C2×Dic47⋊C4—24no—
113C2×Dic47⋊C4—24no—
114C2×Dic47⋊C4—24no—
115C2×Dic47⋊C4—24no—
116C2×Dic47⋊C4—24no—
117C2×Dic47⋊C4—24no—
118C2×Dic47⋊C4—232no—
119C2×Dic47⋊C4C2×C418yescomplemented
120C2×Dic47⋊C4D418yescomplemented
121C2×Dic47⋊C4C2314yes—
122C2×Dic47⋊C4C2314yes—
123C2×Dic47⋊C4C2314yes—
124C2×Dic47⋊C4C2314yes—
125C2×Dic47⋊C4C2314yes—
126C2×Dic47⋊C4C2314yes—
127C2×Dic47⋊C4C2314yes—
128C2×Dic47⋊C4C2314yes—
129C2×Dic47⋊C4C2314yes—
130C4⋊C4×D47—232no—
131C2×C22⋊Dic47—24no—
132C2×C22⋊Dic47C2314yes—
133C2×(C2×D47)⋊C4—24no—
134C2×(C2×D47)⋊C4—24no—
135C2×(C2×D47)⋊C4C2×C418yescomplemented
136C2×(C2×D47)⋊C4C2314yes—
137C2×(C2×D47)⋊C4C2314yes—
138C2×(C2×D47)⋊C4C2314yes—
139C2×C4×Dic47—24no—
140C2×C4×Dic47—24no—
141C2×C4×Dic47C2×C418yescomplemented
142C2×C4×Dic47C2314yes—
143C2×C4×Dic47C2314yes—
144C2×C4×Dic47C2314yes—
145C47⋊#95C2314yes—
146C47⋊#95C2314yes—
147C47⋊#95C2314yes—
148C47⋊#95C2314yes—
149C25×C47C2311yescharacteristic
150C23×C4×C47—24no—
151C23×C4×C47—24no—
152C23×C4×C47—42no—
153C23×C4×C47C2311yescharacteristic
154C23×C4×C47C2311yescharacteristic
155C23×C4×C47C2311yescharacteristic
156C23×C4×C47C2314yes—
157C23×C4×C47C2311yescharacteristic
158C23×C4×C47C2311yescharacteristic
159C23×C4×C47C2311yescharacteristic
160C2×C4⋊C4×C47—24no—
161C2×C4⋊C4×C47—42no—
162C2×C4⋊C4×C47C2314yes—
163C2×C4⋊C4×C47C2314yes—
164C2×C22⋊C4×C47—24no—
165C2×C22⋊C4×C47C2×C418yescomplemented
166C2×C22⋊C4×C47C2314yes—
167C2×C22⋊C4×C47C2314yes—
168#95×C47C2314yes—
169#95×C47C2314yes—
170C24×C47—22no—
171C24×C47—22no—
172C24×C47—22no—
173C24×C47—22no—
174C24×C47C22×C414yes—
175C24×C47C2×D414yes—
176C24×C47C2×Q814yes—
177C24×C47C2412yes—
178C24×C47C2411yescharacteristic
179C23×D47—22no—
180C23×D47—22no—
181C23×D47—22no—
182C23×D47—22no—
183C23×D47C22×C414yes—
184C23×D47C2×D414yes—
185C23×D47C2×Q814yes—
186C23×D47C2412yes—
187C22×C4×C47—22no—
188C22×C4×C47—22no—
189C22×C4×C47—22no—
190C22×C4×C47—22no—
191C22×C4×C47—22no—
192C22×C4×C47—22no—
193C22×C4×C47—22no—
194C22×C4×C47—22no—
195C22×C4×C47—22no—
196C22×C4×C47—22no—
197C22×C4×C47—22no—
198C22×C4×C47—28no—
199C22×C4×C47—22no—
200C22×C4×C47—22no—
201C22×C4×C47—22no—
202C22×C4×C47—22no—
203C22×C4×C47—28no—
204C22×C4×C47—44no—
205C22×C4×C47—416no—
206C22×C4×C47C22×C414yes—
207C22×C4×C47C22×C414yes—
208C22×C4×C47C2×D414yes—
209C22×C4×C47C2412yes—
210C22×C4×C47C2412yes—
211C22×C4×C47C2412yes—
212C22×C4×C47C2412yes—
213C22×C4×C47C2412yes—
214C22×C4×C47C2412yes—
215C2×C22⋊D47C4⋊C4164yescomplemented
216C2×C22⋊D47C22×C4116yes—
217C2×C22⋊D47C2×D4116yes—
218C2×C22⋊D47C2×Q8116yes—
219C22×Dic47—22no—
220C22×Dic47—22no—
221C22×Dic47—22no—
222C22×Dic47—22no—
223C22×Dic47—232no—
224C22×Dic47—28no—
225C22×Dic47—28no—
226C22×Dic47—22no—
227C22×Dic47—22no—
228C22×Dic47—22no—
229C22×Dic47—22no—
230C22×Dic47—22no—
231C22×Dic47—28no—
232C22×Dic47—22no—
233C22×Dic47—22no—
234C22×Dic47—22no—
235C22×Dic47—22no—
236C22×Dic47—28no—
237C22×Dic47—44no—
238C22×Dic47—416no—
239C22×Dic47C22×C414yes—
240C22×Dic47C22×C414yes—
241C22×Dic47C22×C414yes—
242C22×Dic47C22×C4116yescomplemented
243C22×Dic47C2×D414yes—
244C22×Dic47C2×D414yes—
245C22×Dic47C2×D414yes—
246C22×Dic47C2×Q814yes—
247C22×Dic47#4114yes—
248C22×Dic47C2412yes—
249C22×Dic47C2412yes—
250C22×Dic47C2412yes—
251C22×Dic47C2412yes—
252C22×Dic47C2412yes—
253C22×Dic47C2412yes—
254C22×Dic47C2412yes—
255C2×C4×D47—232no—
256C2×C4×D47—28no—
257C2×C4×D47—28no—
258C2×C4×D47—28no—
259C2×C4×D47—28no—
260C2×C4×D47—28no—
261C2×C4×D47—28no—
262C2×C4×D47—44no—
263C2×C4×D47—44no—
264C2×C4×D47—416no—
265C2×C4×D47—416no—
266C2×C4×D47C22×C4116yescomplemented
267C4⋊C4×C47—28no—
268C4⋊C4×C47—44no—
269C22⋊C4×C47—28no—
270C22⋊C4×C47C22×C4116yescomplemented
271C22⋊Dic47—28no—
272(C2×D47)⋊C4—28no—
273(C2×D47)⋊C4—28no—
274(C2×D47)⋊C4C22×C4116yescomplemented
275C4⋊Dic47—28no—
276C4⋊Dic47—44no—
277Dic47⋊C4—28no—
278Dic47⋊C4—28no—
279Dic47⋊C4—28no—
280Dic47⋊C4—28no—
281Dic47⋊C4—28no—
282Dic47⋊C4—28no—
283Dic47⋊C4—28no—
284Dic47⋊C4C22×C4116yescomplemented
285Dic47⋊C4C2×D4116yescomplemented
286C4×Dic47—28no—
287C4×Dic47—28no—
288C4×Dic47C22×C4116yescomplemented
289C23×C47—28no—
290C23×C47—28no—
291C23×C47—28no—
292C23×C47—28no—
293C23×C47—28no—
294C23×C47—28no—
295C23×C47—22no—
296C23×C47—22no—
297C23×C47—22no—
298C23×C47—22no—
299C23×C47C2×C4⋊C4116yescomplemented
300C23×C47C23×C414yes—
301C23×C47C23×C412yes—
302C23×C47C22×D414yes—
303C23×C47C22×D412yes—
304C23×C47C22×D412yes—
305C23×C47C22×Q814yes—
306C23×C47C22×Q812yes—
307C23×C47C2×#4112yes—
308C23×C47H(5,𝔽2)12yes—
309C23×C472−1+412yes—
310C23×C47C2511yescharacteristic
311C22×D47—28no—
312C22×D47—28no—
313C22×D47—28no—
314C22×D47—28no—
315C22×D47—28no—
316C22×D47—28no—
317C22×D47—22no—
318C22×D47—22no—
319C22×D47—22no—
320C22×D47—22no—
321C22×D47C2×C4⋊C4116yescomplemented
322C22×D47C23×C414yes—
323C22×D47C22×D414yes—
324C22×D47C22×Q814yes—
325C2×C4×C47—28no—
326C2×C4×C47—28no—
327C2×C4×C47—28no—
328C2×C4×C47—22no—
329C2×C4×C47—22no—
330C2×C4×C47—22no—
331C2×C4×C47—22no—
332C2×C4×C47—22no—
333C2×C4×C47—22no—
334C2×C4×C47—22no—
335C2×C4×C47—22no—
336C2×C4×C47—22no—
337C2×C4×C47—22no—
338C2×C4×C47—22no—
339C2×C4×C47—22no—
340C2×C4×C47—22no—
341C2×C4×C47—22no—
342C2×C4×C47—22no—
343C2×C4×C47—416no—
344C2×C4×C47—44no—
345C2×C4×C47—44no—
346C2×C4×C47—44no—
347C2×C4×C47C23×C414yes—
348C2×C4×C47C23×C414yes—
349C2×C4×C47C22×D414yes—
350C22⋊D47C2×C4⋊C4164yescomplemented
351C2×Dic47—28no—
352C2×Dic47—28no—
353C2×Dic47—22no—
354C2×Dic47—22no—
355C2×Dic47—22no—
356C2×Dic47—22no—
357C2×Dic47—232no—
358C2×Dic47—22no—
359C2×Dic47—22no—
360C2×Dic47—22no—
361C2×Dic47—22no—
362C2×Dic47—22no—
363C2×Dic47—22no—
364C2×Dic47—22no—
365C2×Dic47—22no—
366C2×Dic47—22no—
367C2×Dic47—416no—
368C2×Dic47—44no—
369C2×Dic47—44no—
370C2×Dic47—44no—
371C2×Dic47C2×C4⋊C4116yescomplemented
372C2×Dic47C4×D4116yescomplemented
373C2×Dic47C23×C414yes—
374C2×Dic47C23×C414yes—
375C2×Dic47C23×C414yes—
376C2×Dic47C22×D414yes—
377C2×Dic47C22×D414yes—
378C2×Dic47C22×D414yes—
379C2×Dic47C22×Q814yes—
380C2×Dic47C2×#4114yes—
381C4×D47—232no—
382C4×D47—416no—
383C4×D47—416no—
384C2×D4×C4⋊C4—471nomaximal, Sylow
385C22×C47—232no—
386C22×C47—24no—
387C22×C47—24no—
388C22×C47—24no—
389C22×C47—24no—
390C22×C47—24no—
391C22×C47—24no—
392C22×C47C22×C4⋊C414yes—
393C22×C47C22×C4⋊C418yescomplemented
394C22×C47C2×C4×D414yes—
395C22×C47#52014yes—
396C22×C47D4214yes—
397C22×C47#54714yes—
398C22×C47D4×Q814yes—
399C22×C47#55414yes—
400C22×C47C24×C411yescharacteristic
401C22×C47C23×D411yescharacteristic
402C22×C47C23×D411yescharacteristic
403C22×C47C23×Q811yescharacteristic
404C22×C47C22×#4111yescharacteristic
405C22×C47C2×H(5,𝔽2)11yescharacteristic
406C22×C47C2×2−1+411yescharacteristic
407C2×D47—232no—
408C2×D47—24no—
409C2×D47—24no—
410C2×D47—24no—
411C2×D47—24no—
412C2×D47—24no—
413C2×D47—24no—
414C2×D47C22×C4⋊C418yescomplemented
415C4×C47—24no—
416C4×C47—24no—
417C4×C47—24no—
418C4×C47—42no—
419C4×C47—42no—
420C4×C47—42no—
421Dic47—24no—
422Dic47—24no—
423Dic47—42no—
424Dic47—42no—
425Dic47—42no—
426Dic47C22×C4⋊C418yescomplemented
427Dic47C2×C4×D418yescomplemented
428C22×C4×D4—471no—
429C22×C4×D4—471no—
430C22×C4×D4—471no—
431C23×C4⋊C4—471no—
432C23×C4⋊C4—471no—
433D4×C4⋊C4—4716no—
434C2×#389—471no—
435C2×#389—471no—
436C2×#385—471no—
437C2×#385—471no—
438C2×#385—471no—
439C2×#385D4711yescharacteristic, complemented
440C2×#384—471no—
441C2×#380—471no—
442C2×#380—471no—
443C2×C4×C4⋊C4—471no—
444C2×C47—28no—
445C2×C47D4×C4⋊C418yescomplemented
446C2×C47C23×C4⋊C411yescharacteristic
447C2×C47C22×C4×D411yescharacteristic
448C2×C47C2×#52011yescharacteristic
449C2×C47C2×D4211yescharacteristic
450C2×C47C2×#54711yescharacteristic
451C2×C47C2×D4×Q811yescharacteristic
452C2×C47C2×#55411yescharacteristic
453D47—28no—
454C23×D4—471no—
455C24×C4—471no—
456C24×C4—471no—
457C24×C4—471no—
458C24×C4—471no—
459C24×C4—471no—
460C24×C4C2×D4711yescharacteristic
461C2×C4×D4—478no—
462C2×C4×D4—4716no—
463C2×C4×D4—478no—
464C2×C4×D4—478no—
465C2×C4×D4—948no—
466C2×C4×D4—948no—
467C22×C4⋊C4—471no—
468C22×C4⋊C4—471no—
469C22×C4⋊C4—478no—
470C22×C4⋊C4—471no—
471C22×C4⋊C4—471no—
472C22×C4⋊C4—471no—
473C22×C4⋊C4—471no—
474C22×C4⋊C4—471no—
475C22×C4⋊C4—471no—
476C22×C4⋊C4—471no—
477C22×C4⋊C4—471no—
478C22×C4⋊C4—471no—
479C22×C4⋊C4—478no—
480C22×C4⋊C4—948no—
481C22×C4⋊C4—948no—
482C22×C4⋊C4C2×D4711yescharacteristic
483C22×C4⋊C4C2×D4711yescharacteristic
484C22×C22⋊C4—471no—
485C22×C22⋊C4—471no—
486C22×C22⋊C4—471no—
487C22×C22⋊C4—471no—
488C22×C22⋊C4C2×D4711yescharacteristic
489C22×C22⋊C4C2×D4711yescharacteristic
490C22×C42—471no—
491C22×C42—471no—
492C22×C42—471no—
493#389—478no—
494#389—478no—
495#385—478no—
496#385—478no—
497#385—478no—
498#385C2×D4718yescomplemented
499#384—478no—
500#380—478no—
501#380—478no—
502C4×C4⋊C4—478no—
503C2×#95—471no—
504C2×#95—471no—
505C2×#95—471no—
506C2×#95—471no—
507C2×#95C2×D4711yescharacteristic
508C2×#95C2×D4711yescharacteristic
509C47C2×D4×C4⋊C411yescharacteristic, complemented, Sylow
510C25—471no—
511C25C22×D4711yescharacteristic
512C22×D4—478no—
513C22×D4—478no—
514C22×D4—478no—
515C22×D4—474no—
516C23×C4—24no—
517C23×C4—24no—
518C23×C4—42no—
519C23×C4—471no—
520C23×C4—471no—
521C23×C4—478no—
522C23×C4—474no—
523C23×C4—471no—
524C23×C4—471no—
525C23×C4—478no—
526C23×C4—474no—
527C23×C4—471no—
528C23×C4—471no—
529C23×C4—471no—
530C23×C4—474no—
531C23×C4—474no—
532C23×C4—474no—
533C23×C4—944no—
534C23×C4—944no—
535C23×C4—944no—
536C23×C4—944no—
537C23×C4—944no—
538C23×C4—944no—
539C23×C4—944no—
540C23×C4—944no—
541C23×C4—944no—
542C23×C4—944no—
543C23×C4—1882no—
544C23×C4—1882no—
545C23×C4—1882no—
546C23×C4C22×D4711yescharacteristic
547C23×C4C22×D4711yescharacteristic
548C23×C4C22×D4711yescharacteristic
549C23×C4C22×D4714yes—
550C23×C4C22×D4711yescharacteristic
551C23×C4C22×D4711yescharacteristic
552C23×C4C22×D4711yescharacteristic
553C4×D4—4764no—
554C4×D4—9432no—
555C4×D4—9432no—
556C2×C4⋊C4—24no—
557C2×C4⋊C4—42no—
558C2×C4⋊C4—478no—
559C2×C4⋊C4—478no—
560C2×C4⋊C4—474no—
561C2×C4⋊C4—474no—
562C2×C4⋊C4—474no—
563C2×C4⋊C4—474no—
564C2×C4⋊C4—474no—
565C2×C4⋊C4—474no—
566C2×C4⋊C4—474no—
567C2×C4⋊C4—474no—
568C2×C4⋊C4—474no—
569C2×C4⋊C4—474no—
570C2×C4⋊C4—474no—
571C2×C4⋊C4—9432no—
572C2×C4⋊C4—9432no—
573C2×C4⋊C4—944no—
574C2×C4⋊C4—944no—
575C2×C4⋊C4—944no—
576C2×C4⋊C4—944no—
577C2×C4⋊C4—944no—
578C2×C4⋊C4—944no—
579C2×C4⋊C4—944no—
580C2×C4⋊C4—944no—
581C2×C4⋊C4—1882no—
582C2×C4⋊C4C22×D4714yes—
583C2×C4⋊C4C22×D4714yes—
584C2×C22⋊C4—24no—
585C2×C22⋊C4—478no—
586C2×C22⋊C4—474no—
587C2×C22⋊C4—474no—
588C2×C22⋊C4—474no—
589C2×C22⋊C4—474no—
590C2×C22⋊C4—944no—
591C2×C22⋊C4—944no—
592C2×C22⋊C4—944no—
593C2×C22⋊C4C4×D4718yescomplemented
594C2×C22⋊C4C22×D4714yes—
595C2×C22⋊C4C22×D4714yes—
596C2×C42—478no—
597C2×C42—474no—
598C2×C42—474no—
599C2×C42—474no—
600C2×C42—944no—
601C2×C42—944no—
602#95—474no—
603#95—474no—
604#95—474no—
605#95—474no—
606#95C22×D4714yes—
607#95C22×D4714yes—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—474no—
613C24—474no—
614C24—474no—
615C24—472no—
616C24—942no—
617C24—942no—
618C24—942no—
619C24—942no—
620C24C2×C4×D4714yes—
621C24D4×D4714yes—
622C24Q8×D4714yes—
623C24C23×D4712yes—
624C24C23×D4711yescharacteristic
625C2×D4—4764no—
626C2×D4—4716no—
627C2×D4—4716no—
628C2×D4—4716no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—28no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—28no—
646C22×C4—44no—
647C22×C4—416no—
648C22×C4—474no—
649C22×C4—474no—
650C22×C4—474no—
651C22×C4—474no—
652C22×C4—474no—
653C22×C4—474no—
654C22×C4—472no—
655C22×C4—472no—
656C22×C4—474no—
657C22×C4—4716no—
658C22×C4—474no—
659C22×C4—472no—
660C22×C4—472no—
661C22×C4—4716no—
662C22×C4—472no—
663C22×C4—472no—
664C22×C4—472no—
665C22×C4—948no—
666C22×C4—9432no—
667C22×C4—948no—
668C22×C4—948no—
669C22×C4—948no—
670C22×C4—948no—
671C22×C4—948no—
672C22×C4—9432no—
673C22×C4—948no—
674C22×C4—948no—
675C22×C4—942no—
676C22×C4—942no—
677C22×C4—942no—
678C22×C4—942no—
679C22×C4—942no—
680C22×C4—942no—
681C22×C4—942no—
682C22×C4—942no—
683C22×C4—942no—
684C22×C4—948no—
685C22×C4—942no—
686C22×C4—942no—
687C22×C4—942no—
688C22×C4—942no—
689C22×C4—948no—
690C22×C4—1884no—
691C22×C4—1884no—
692C22×C4—18816no—
693C22×C4—18816no—
694C22×C4—1884no—
695C22×C4—18816no—
696C22×C4C2×C4×D4714yes—
697C22×C4C2×C4×D4714yes—
698C22×C4D4×D4714yes—
699C22×C4C23×D4712yes—
700C22×C4C23×D4712yes—
701C22×C4C23×D4712yes—
702C22×C4C23×D4712yes—
703C22×C4C23×D4712yes—
704C22×C4C23×D4712yes—
705C4⋊C4—28no—
706C4⋊C4—44no—
707C4⋊C4—4716no—
708C4⋊C4—4716no—
709C4⋊C4—948no—
710C4⋊C4—948no—
711C4⋊C4—948no—
712C4⋊C4—948no—
713C4⋊C4—948no—
714C4⋊C4—948no—
715C4⋊C4—948no—
716C4⋊C4—948no—
717C4⋊C4—1884no—
718C22⋊C4—28no—
719C22⋊C4—4716no—
720C22⋊C4—948no—
721C22⋊C4—948no—
722C22⋊C4—948no—
723C22⋊C4C2×C4×D47116yescomplemented
724C42—4716no—
725C42—948no—
726C42—948no—
727C23—28no—
728C23—28no—
729C23—28no—
730C23—28no—
731C23—28no—
732C23—28no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—4716no—
738C23—474no—
739C23—474no—
740C23—474no—
741C23—948no—
742C23—948no—
743C23—948no—
744C23—948no—
745C23—948no—
746C23—948no—
747C23—942no—
748C23—942no—
749C23—942no—
750C23—942no—
751C23C4⋊C4×D47116yescomplemented
752C23C22×C4×D4714yes—
753C23C22×C4×D4712yes—
754C23C2×D4×D4714yes—
755C23C2×D4×D4712yes—
756C23C2×D4×D4712yes—
757C23C2×Q8×D4714yes—
758C23C2×Q8×D4712yes—
759C23#41×D4712yes—
760C23#1309406912yes—
761C23#1309407112yes—
762C23C24×D4711yescharacteristic
763D4—4764no—
764C2×C4—28no—
765C2×C4—28no—
766C2×C4—28no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—416no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—4716no—
787C2×C4—4716no—
788C2×C4—474no—
789C2×C4—474no—
790C2×C4—474no—
791C2×C4—474no—
792C2×C4—474no—
793C2×C4—474no—
794C2×C4—474no—
795C2×C4—474no—
796C2×C4—9432no—
797C2×C4—9432no—
798C2×C4—948no—
799C2×C4—948no—
800C2×C4—942no—
801C2×C4—942no—
802C2×C4—942no—
803C2×C4—942no—
804C2×C4—942no—
805C2×C4—942no—
806C2×C4—942no—
807C2×C4—942no—
808C2×C4—942no—
809C2×C4—942no—
810C2×C4—942no—
811C2×C4—942no—
812C2×C4—942no—
813C2×C4—18816no—
814C2×C4—18816no—
815C2×C4—18816no—
816C2×C4—1884no—
817C2×C4—1884no—
818C2×C4—1884no—
819C2×C4C22×C4×D4714yes—
820C2×C4C22×C4×D4714yes—
821C2×C4C2×D4×D4714yes—
822C22—232no—
823C22—24no—
824C22—24no—
825C22—24no—
826C22—24no—
827C22—24no—
828C22—24no—
829C22—478no—
830C22—9432no—
831C22—944no—
832C22—944no—
833C22—944no—
834C22—944no—
835C22—944no—
836C22—944no—
837C22C2×C4⋊C4×D4714yes—
838C22C2×C4⋊C4×D4718yescomplemented
839C22C4×D4×D4714yes—
840C22#1568960214yes—
841C22#1568975514yes—
842C22#1568977114yes—
843C22#1568978614yes—
844C22#1568982714yes—
845C22C23×C4×D4711yescharacteristic
846C22C22×D4×D4711yescharacteristic
847C22C22×D4×D4711yescharacteristic
848C22C22×Q8×D4711yescharacteristic
849C22C2×#41×D4711yescharacteristic
850C22C2×#1309406911yescharacteristic
851C22C2×#1309407111yescharacteristic
852C4—24no—
853C4—24no—
854C4—24no—
855C4—42no—
856C4—42no—
857C4—42no—
858C4—478no—
859C4—478no—
860C4—944no—
861C4—944no—
862C4—1882no—
863C4—1882no—
864C4—1882no—
865C2—28no—
866C2—948no—
867C2#2024628618yesdirect product factor
868C2C22×C4⋊C4×D4711yescharacteristic
869C2C2×C4×D4×D4711yescharacteristic
870C2C2×#1568960211yescharacteristic
871C2C2×#1568975511yescharacteristic
872C2C2×#1568977111yescharacteristic
873C2C2×#1568978611yescharacteristic
874C2C2×#1568982711yescharacteristic
subgroupG/H
centerC24C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC2×C47×#385C2
socleC24×C47C24
prime radicalC23×C22⋊D47C22
cosocleC23×C47C25
hypercenterC2×#385D47
hypocenterC47C2×D4×C4⋊C4
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
4. C23×Dic47⋊C4C2semidirect
5. C22×C4⋊C4×D47C2semidirect
6. #20246286C2direct (N × H)
7. C2×#15689020C2semidirect
8. C2×#15689018C2semidirect
9. C2×#15688998C2semidirect
10. C2×#15688997C2semidirect
11. C2×#15688994C2semidirect
12. C2×#15688992C2semidirect
13. C2×#15688982C2semidirect
14. C2×#15688981C2semidirect
15. C2×#15688974C2semidirect
16. C2×C47×#385C2semidirect
26. C2×(C22⋊D47)⋊C4C4semidirect
41. C22×Dic47⋊C4C22semidirect
43. C2×C4⋊C4×D47C22semidirect
51. #15689020C22semidirect
52. #15689018C22semidirect
53. #15688998C22semidirect
54. #15688997C22semidirect
55. #15688994C22semidirect
56. #15688992C22semidirect
57. #15688982C22semidirect
58. #15688981C22semidirect
59. #15688974C22semidirect
69. C47×#385C22semidirect
82. C23×Dic47C2×C4semidirect
100. C22×C4×D47C2×C4semidirect
106. (C22⋊D47)⋊C4C2×C4semidirect
119. C2×Dic47⋊C4C2×C4semidirect
120. C2×Dic47⋊C4D4semidirect
135. C2×(C2×D47)⋊C4C2×C4semidirect
141. C2×C4×Dic47C2×C4semidirect
165. C2×C22⋊C4×C47C2×C4semidirect
215. C2×C22⋊D47C4⋊C4semidirect
242. C22×Dic47C22×C4semidirect
266. C2×C4×D47C22×C4semidirect
270. C22⋊C4×C47C22×C4semidirect
274. (C2×D47)⋊C4C22×C4semidirect
284. Dic47⋊C4C22×C4semidirect
285. Dic47⋊C4C2×D4semidirect
288. C4×Dic47C22×C4semidirect
299. C23×C47C2×C4⋊C4semidirect
321. C22×D47C2×C4⋊C4semidirect
350. C22⋊D47C2×C4⋊C4semidirect
371. C2×Dic47C2×C4⋊C4semidirect
372. C2×Dic47C4×D4semidirect
393. C22×C47C22×C4⋊C4semidirect
414. C2×D47C22×C4⋊C4semidirect
426. Dic47C22×C4⋊C4semidirect
427. Dic47C2×C4×D4semidirect
439. C2×#385D47semidirect
445. C2×C47D4×C4⋊C4semidirect
498. #385C2×D47semidirect
509. C47C2×D4×C4⋊C4semidirect
593. C2×C22⋊C4C4×D47semidirect
723. C22⋊C4C2×C4×D47semidirect
751. C23C4⋊C4×D47semidirect
838. C22C2×C4⋊C4×D47semidirect
867. C2#20246286direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D472
C22×(C22⋊D47)⋊C42
C23×Dic47⋊C42
C22×C4⋊C4×D472
#202462862
C2×#156890202
C2×#156890182
C2×#156889982
C2×#156889972
C2×#156889942
C2×#156889922
C2×#156889822
C2×#156889812
C2×#156889742
C2×C47×#3852
C2×D4×C4⋊C447