Finite Group Databasebeta

← C2×#20247087 #26384103

Subgroups — C2×#20247087 #26384103

Order 12032.

3550 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094022C211yesmaximal, characteristic, complemented
2C22×#13094001C211yesmaximal, characteristic
3C23×Dic47⋊C4C211yesmaximal, characteristic
4#20247087C2116yesmaximal, direct product factor
5C2×#15689054C211yesmaximal, characteristic, complemented
6C2×#15689053C211yesmaximal, characteristic, complemented
7C2×#15689043C211yesmaximal, characteristic, complemented
8C2×#15689042C211yesmaximal, characteristic, complemented
9C2×#15689018C211yesmaximal, characteristic, complemented
10C2×#15689018C211yesmaximal, characteristic, complemented
11C2×#15688996C211yesmaximal, characteristic
12C2×#15688995C211yesmaximal, characteristic
13C2×#15688992C211yesmaximal, characteristic, complemented
14C2×#15688981C211yesmaximal, characteristic
15C2×C22⋊C4×Dic47C211yesmaximal, characteristic
16C22×C22⋊Q8×C47C211yesmaximal, characteristic
17C23×Dic94C2211yescharacteristic
18C24×Dic47C2211yescharacteristic
19C24×Dic47C2211yescharacteristic
20C2×#13094022—28no—
21C2×#13094022C2218yescomplemented
22C2×#13094001—28no—
23C2×#13094001C2218yes—
24C22×C4⋊Dic47C2211yescharacteristic
25C22×Dic47⋊C4—28no—
26C22×Dic47⋊C4C2211yescharacteristic
27C22×Dic47⋊C4C2211yescharacteristic
28C22×Dic47⋊C4C2218yes—
29C22×Dic47⋊C4C2211yescharacteristic
30C22×Dic47⋊C4C2211yescharacteristic
31C22×Dic47⋊C4C2211yescharacteristic
32C22×Dic47⋊C4C2211yescharacteristic
33C22×Dic47⋊C4C2211yescharacteristic
34C22×Dic47⋊C4C2211yescharacteristic
35C22×Dic47⋊C4C2211yescharacteristic
36C22×Dic47⋊C4C2211yescharacteristic
37C22×Dic47⋊C4C2211yescharacteristic
38C22×Dic47⋊C4C2211yescharacteristic
39C22×C22⋊Dic47C2211yescharacteristic
40C22×C22⋊Dic47C2211yescharacteristic
41C22×C4×Dic47C2211yescharacteristic
42C22×C4×Dic47C2211yescharacteristic
43#15689054C2218yescomplemented
44#15689053C2218yescomplemented
45#15689043C2218yescomplemented
46#15689042C2218yescomplemented
47#15689018C2218yescomplemented
48#15689018C2218yescomplemented
49#15688996C2218yes—
50#15688995C2218yes—
51#15688992C2218yescomplemented
52#15688981C2218yes—
53C22⋊C4×Dic47C2218yes—
54C2×C47⋊#95C2211yescharacteristic
55C2×C47⋊#95C2211yescharacteristic
56C2×C47⋊#95C2211yescharacteristic
57C2×C47⋊#95C2211yescharacteristic
58C2×C47⋊#95C2211yescharacteristic
59C2×C47⋊#95C2211yescharacteristic
60C2×C47⋊#95C2211yescharacteristic
61C2×C47⋊#95C2211yescharacteristic
62C23×Q8×C47C2211yescharacteristic
63C24×C4×C47C2211yescharacteristic
64C2×C22⋊Q8×C47—28no—
65C2×C22⋊Q8×C47C2218yes—
66C22×C4⋊C4×C47C2211yescharacteristic
67C22×C4⋊C4×C47C2211yescharacteristic
68C22×C4⋊C4×C47C2211yescharacteristic
69C22×C22⋊C4×C47C2211yescharacteristic
70C22×C22⋊C4×C47C2211yescharacteristic
71C22×Dic94—24no—
72C22×Dic94—24no—
73C22×Dic94—42no—
74C22×Dic94C2314yes—
75C23×Dic47—24no—
76C23×Dic47—24no—
77C23×Dic47—24no—
78C23×Dic47—24no—
79C23×Dic47—42no—
80C23×Dic47Q818yescomplemented
81C23×Dic47C2311yescharacteristic
82C23×Dic47C2311yescharacteristic
83C23×Dic47C2311yescharacteristic
84C23×Dic47C2314yes—
85C23×Dic47C2311yescharacteristic
86C23×Dic47C2311yescharacteristic
87C23×Dic47C2311yescharacteristic
88C23×Dic47C2311yescharacteristic
89C23×Dic47C2314yes—
90C23×Dic47C2311yescharacteristic
91#13094022—232no—
92#13094001—232no—
93C2×C4⋊Dic47—24no—
94C2×C4⋊Dic47C2314yes—
95C2×Dic47⋊C4—24no—
96C2×Dic47⋊C4—24no—
97C2×Dic47⋊C4—24no—
98C2×Dic47⋊C4—24no—
99C2×Dic47⋊C4—24no—
100C2×Dic47⋊C4—24no—
101C2×Dic47⋊C4—24no—
102C2×Dic47⋊C4—24no—
103C2×Dic47⋊C4—24no—
104C2×Dic47⋊C4—232no—
105C2×Dic47⋊C4—42no—
106C2×Dic47⋊C4—42no—
107C2×Dic47⋊C4D418yes—
108C2×Dic47⋊C4C2314yes—
109C2×Dic47⋊C4C2314yes—
110C2×Dic47⋊C4C2314yes—
111C2×Dic47⋊C4C2314yes—
112C2×Dic47⋊C4C2314yes—
113C2×Dic47⋊C4C2314yes—
114C2×Dic47⋊C4C2314yes—
115C2×Dic47⋊C4C2314yes—
116C2×Dic47⋊C4C2314yes—
117C2×Dic47⋊C4C2314yes—
118C2×Dic47⋊C4C2314yes—
119C2×Dic47⋊C4C2314yes—
120C2×C22⋊Dic47—24no—
121C2×C22⋊Dic47Q818yescomplemented
122C2×C22⋊Dic47C2314yes—
123C2×C22⋊Dic47C2314yes—
124C2×C4×Dic47—24no—
125C2×C4×Dic47—24no—
126C2×C4×Dic47C2314yes—
127C2×C4×Dic47C2314yes—
128C47⋊#95C2314yes—
129C47⋊#95C2314yes—
130C47⋊#95C2314yes—
131C47⋊#95C2314yes—
132C47⋊#95C2314yes—
133C47⋊#95C2314yes—
134C47⋊#95C2314yes—
135C47⋊#95C2314yes—
136C25×C47C2311yescharacteristic
137C22×Q8×C47—24no—
138C22×Q8×C47—24no—
139C22×Q8×C47—42no—
140C22×Q8×C47C2314yes—
141C23×C4×C47—24no—
142C23×C4×C47—24no—
143C23×C4×C47—42no—
144C23×C4×C47C2311yescharacteristic
145C23×C4×C47C2311yescharacteristic
146C23×C4×C47C2311yescharacteristic
147C23×C4×C47C2314yes—
148C23×C4×C47C2311yescharacteristic
149C23×C4×C47C2311yescharacteristic
150C23×C4×C47C2311yescharacteristic
151C22⋊Q8×C47—232no—
152C2×C4⋊C4×C47—24no—
153C2×C4⋊C4×C47—24no—
154C2×C4⋊C4×C47—24no—
155C2×C4⋊C4×C47C2314yes—
156C2×C4⋊C4×C47C2314yes—
157C2×C4⋊C4×C47C2314yes—
158C2×C22⋊C4×C47—24no—
159C2×C22⋊C4×C47D418yes—
160C2×C22⋊C4×C47C2314yes—
161C2×C22⋊C4×C47C2314yes—
162C24×C47—22no—
163C24×C47—22no—
164C24×C47—22no—
165C24×C47—22no—
166C24×C47C2×D414yes—
167C24×C47C2×Q814yes—
168C24×C47C2×Q814yes—
169C24×C47C2412yes—
170C24×C47C2411yescharacteristic
171C2×Q8×C47—28no—
172C2×Q8×C47—28no—
173C2×Q8×C47—44no—
174C2×Q8×C47—416no—
175C22×C4×C47—22no—
176C22×C4×C47—22no—
177C22×C4×C47—22no—
178C22×C4×C47—22no—
179C22×C4×C47—22no—
180C22×C4×C47—22no—
181C22×C4×C47—22no—
182C22×C4×C47—22no—
183C22×C4×C47—22no—
184C22×C4×C47—28no—
185C22×C4×C47—22no—
186C22×C4×C47—22no—
187C22×C4×C47—22no—
188C22×C4×C47—22no—
189C22×C4×C47—22no—
190C22×C4×C47—22no—
191C22×C4×C47—28no—
192C22×C4×C47—44no—
193C22×C4×C47—416no—
194C22×C4×C47C2×D414yes—
195C22×C4×C47C2×D414yes—
196C22×C4×C47C2×D414yes—
197C22×C4×C47C2412yes—
198C22×C4×C47C2412yes—
199C22×C4×C47C2412yes—
200C22×C4×C47C2412yes—
201C22×C4×C47C2412yes—
202C22×C4×C47C2412yes—
203C22×Dic47—22no—
204C22×Dic47—22no—
205C22×Dic47—22no—
206C22×Dic47—22no—
207C22×Dic47—22no—
208C22×Dic47—22no—
209C22×Dic47—22no—
210C22×Dic47—22no—
211C22×Dic47—232no—
212C22×Dic47—28no—
213C22×Dic47—28no—
214C22×Dic47—22no—
215C22×Dic47—22no—
216C22×Dic47—22no—
217C22×Dic47—22no—
218C22×Dic47—22no—
219C22×Dic47—28no—
220C22×Dic47—22no—
221C22×Dic47—22no—
222C22×Dic47—22no—
223C22×Dic47—22no—
224C22×Dic47—28no—
225C22×Dic47—44no—
226C22×Dic47—416no—
227C22×Dic47C2×D414yes—
228C22×Dic47C2×D414yes—
229C22×Dic47C2×Q814yes—
230C22×Dic47C2×Q814yes—
231C22×Dic47C2×Q814yes—
232C22×Dic47C2×Q814yes—
233C22×Dic47C2×Q8116yescomplemented
234C22×Dic47#4114yes—
235C22×Dic47C2412yes—
236C22×Dic47C2412yes—
237C22×Dic47C2412yes—
238C22×Dic47C2412yes—
239C22×Dic47C2412yes—
240C22×Dic47C2412yes—
241C22×Dic47C2412yes—
242C22×Dic47C2412yes—
243C2×Dic94—28no—
244C2×Dic94—28no—
245C2×Dic94—44no—
246C2×Dic94—416no—
247C4⋊C4×C47—28no—
248C4⋊C4×C47—28no—
249C4⋊C4×C47—28no—
250C22⋊C4×C47—28no—
251C22⋊C4×C47C2×D4116yes—
252C22⋊Dic47—28no—
253C22⋊Dic47C2×Q8116yescomplemented
254C4⋊Dic47—28no—
255Dic47⋊C4—28no—
256Dic47⋊C4—28no—
257Dic47⋊C4—28no—
258Dic47⋊C4—28no—
259Dic47⋊C4—28no—
260Dic47⋊C4—28no—
261Dic47⋊C4—28no—
262Dic47⋊C4—28no—
263Dic47⋊C4—28no—
264Dic47⋊C4—44no—
265Dic47⋊C4—44no—
266Dic47⋊C4C2×D4116yes—
267C4×Dic47—28no—
268C4×Dic47—28no—
269C23×C47—28no—
270C23×C47—28no—
271C23×C47—28no—
272C23×C47—28no—
273C23×C47—28no—
274C23×C47—28no—
275C23×C47—22no—
276C23×C47—22no—
277C23×C47—22no—
278C23×C47—22no—
279C23×C47C4⋊Q8116yescomplemented
280C23×C47C22×D412yes—
281C23×C47C22×D414yes—
282C23×C47C22×D412yes—
283C23×C47C22×Q814yes—
284C23×C47C22×Q814yes—
285C23×C47C22×Q812yes—
286C23×C47C22×Q812yes—
287C23×C47C2×#4112yes—
288C23×C47H(5,𝔽2)12yes—
289C23×C472−1+412yes—
290C23×C47C2511yescharacteristic
291Q8×C47—416no—
292C2×C4×C47—28no—
293C2×C4×C47—28no—
294C2×C4×C47—28no—
295C2×C4×C47—22no—
296C2×C4×C47—22no—
297C2×C4×C47—22no—
298C2×C4×C47—22no—
299C2×C4×C47—22no—
300C2×C4×C47—22no—
301C2×C4×C47—22no—
302C2×C4×C47—22no—
303C2×C4×C47—22no—
304C2×C4×C47—22no—
305C2×C4×C47—22no—
306C2×C4×C47—22no—
307C2×C4×C47—22no—
308C2×C4×C47—22no—
309C2×C4×C47—22no—
310C2×C4×C47—416no—
311C2×C4×C47—44no—
312C2×C4×C47—44no—
313C2×C4×C47—44no—
314C2×C4×C47C22×D414yes—
315C2×C4×C47C22×D414yes—
316C2×C4×C47C22×D414yes—
317C2×Dic47—28no—
318C2×Dic47—28no—
319C2×Dic47—28no—
320C2×Dic47—28no—
321C2×Dic47—22no—
322C2×Dic47—22no—
323C2×Dic47—22no—
324C2×Dic47—22no—
325C2×Dic47—22no—
326C2×Dic47—22no—
327C2×Dic47—22no—
328C2×Dic47—22no—
329C2×Dic47—232no—
330C2×Dic47—22no—
331C2×Dic47—22no—
332C2×Dic47—22no—
333C2×Dic47—22no—
334C2×Dic47—22no—
335C2×Dic47—22no—
336C2×Dic47—22no—
337C2×Dic47—22no—
338C2×Dic47—22no—
339C2×Dic47—416no—
340C2×Dic47—44no—
341C2×Dic47—44no—
342C2×Dic47—44no—
343C2×Dic47C22⋊Q8116yescomplemented
344C2×Dic47C22×D414yes—
345C2×Dic47C22×D414yes—
346C2×Dic47C22×Q814yes—
347C2×Dic47C22×Q814yes—
348C2×Dic47C22×Q814yes—
349C2×Dic47C22×Q814yes—
350C2×Dic47C2×#4114yes—
351Dic94—416no—
352C2×#2440—471nomaximal, Sylow
353C22×C47—24no—
354C22×C47—24no—
355C22×C47—24no—
356C22×C47—232no—
357C22×C47—24no—
358C22×C47—24no—
359C22×C47—24no—
360C22×C47C2×C22⋊Q814yes—
361C22×C47C2×C4⋊Q814yes—
362C22×C47C2×C4⋊Q818yescomplemented
363C22×C47#54414yes—
364C22×C47D4214yes—
365C22×C47#54714yes—
366C22×C47D4×Q814yes—
367C22×C47#55414yes—
368C22×C47C23×D411yescharacteristic
369C22×C47C23×D411yescharacteristic
370C22×C47C23×Q811yescharacteristic
371C22×C47C23×Q811yescharacteristic
372C22×C47C22×#4111yescharacteristic
373C22×C47C2×H(5,𝔽2)11yescharacteristic
374C22×C47C2×2−1+411yescharacteristic
375C4×C47—24no—
376C4×C47—24no—
377C4×C47—24no—
378C4×C47—42no—
379C4×C47—42no—
380C4×C47—42no—
381Dic47—24no—
382Dic47—24no—
383Dic47—24no—
384Dic47—24no—
385Dic47—42no—
386Dic47—42no—
387Dic47—42no—
388Dic47C2×C22⋊Q818yescomplemented
389C22×C4⋊Q8—471no—
390C22×C22⋊Q8—471no—
391C22×C22⋊Q8D4711yescharacteristic
392C23×C4⋊C4—471no—
393#2440—4716no—
394C2×#398—471no—
395C2×#398—471no—
396C2×#395—471no—
397C2×#395—471no—
398C2×#389—471no—
399C2×#389—471no—
400C2×#385—471no—
401C2×#385—471no—
402C2×#384—471no—
403C2×#380—471no—
404C2×C4×C22⋊C4—471no—
405C2×C47—28no—
406C2×C47#244018yescomplemented
407C2×C47C22×C22⋊Q811yescharacteristic
408C2×C47C22×C4⋊Q811yescharacteristic
409C2×C47C2×#54411yescharacteristic
410C2×C47C2×D4211yescharacteristic
411C2×C47C2×#54711yescharacteristic
412C2×C47C2×D4×Q811yescharacteristic
413C2×C47C2×#55411yescharacteristic
414C23×Q8—471no—
415C23×Q8C2×D4711yescharacteristic
416C24×C4—471no—
417C24×C4—471no—
418C24×C4C2×D4711yescharacteristic
419C2×C4⋊Q8—478no—
420C2×C4⋊Q8—948no—
421C2×C22⋊Q8—28no—
422C2×C22⋊Q8—478no—
423C2×C22⋊Q8—948no—
424C2×C22⋊Q8C2×D4718yes—
425C22×C4⋊C4—471no—
426C22×C4⋊C4—471no—
427C22×C4⋊C4—471no—
428C22×C4⋊C4—471no—
429C22×C4⋊C4—471no—
430C22×C4⋊C4—471no—
431C22×C4⋊C4—471no—
432C22×C4⋊C4—471no—
433C22×C4⋊C4—478no—
434C22×C4⋊C4—471no—
435C22×C4⋊C4—471no—
436C22×C4⋊C4—471no—
437C22×C4⋊C4—471no—
438C22×C4⋊C4—471no—
439C22×C4⋊C4—948no—
440C22×C4⋊C4C2×D4711yescharacteristic
441C22×C4⋊C4C2×D4711yescharacteristic
442C22×C4⋊C4C2×D4711yescharacteristic
443C22×C22⋊C4—471no—
444C22×C22⋊C4—471no—
445C22×C22⋊C4C2×D4711yescharacteristic
446C22×C22⋊C4C2×D4711yescharacteristic
447C22×C42—471no—
448C22×C42—471no—
449#398—478no—
450#398—478no—
451#395—478no—
452#395—478no—
453#389—478no—
454#389—478no—
455#385—478no—
456#385—478no—
457#384—478no—
458#380—478no—
459C4×C22⋊C4—478no—
460C2×#95—471no—
461C2×#95—471no—
462C2×#95—471no—
463C2×#95—471no—
464C2×#95—471no—
465C2×#95—471no—
466C2×#95—471no—
467C2×#95—471no—
468C47C2×#244011yescharacteristic, complemented, Sylow
469C25C22×D4711yescharacteristic
470C22×Q8—24no—
471C22×Q8—24no—
472C22×Q8—42no—
473C22×Q8—474no—
474C22×Q8—944no—
475C22×Q8—944no—
476C22×Q8—1882no—
477C22×Q8C22×D4714yes—
478C23×C4—24no—
479C23×C4—24no—
480C23×C4—42no—
481C23×C4—471no—
482C23×C4—478no—
483C23×C4—474no—
484C23×C4—471no—
485C23×C4—471no—
486C23×C4—471no—
487C23×C4—471no—
488C23×C4—471no—
489C23×C4—471no—
490C23×C4—471no—
491C23×C4—474no—
492C23×C4—944no—
493C23×C4—944no—
494C23×C4—944no—
495C23×C4—944no—
496C23×C4—1882no—
497C23×C4C22×D4711yescharacteristic
498C23×C4C22×D4711yescharacteristic
499C23×C4C22×D4711yescharacteristic
500C23×C4C22×D4714yes—
501C23×C4C22×D4711yescharacteristic
502C23×C4C22×D4711yescharacteristic
503C23×C4C22×D4711yescharacteristic
504C4⋊Q8—9432no—
505C22⋊Q8—232no—
506C22⋊Q8—9432no—
507C2×C4⋊C4—24no—
508C2×C4⋊C4—24no—
509C2×C4⋊C4—24no—
510C2×C4⋊C4—478no—
511C2×C4⋊C4—474no—
512C2×C4⋊C4—474no—
513C2×C4⋊C4—474no—
514C2×C4⋊C4—474no—
515C2×C4⋊C4—474no—
516C2×C4⋊C4—474no—
517C2×C4⋊C4—474no—
518C2×C4⋊C4—474no—
519C2×C4⋊C4—474no—
520C2×C4⋊C4—474no—
521C2×C4⋊C4—474no—
522C2×C4⋊C4—474no—
523C2×C4⋊C4—474no—
524C2×C4⋊C4—9432no—
525C2×C4⋊C4—944no—
526C2×C4⋊C4—944no—
527C2×C4⋊C4—944no—
528C2×C4⋊C4—944no—
529C2×C4⋊C4—944no—
530C2×C4⋊C4—944no—
531C2×C4⋊C4—944no—
532C2×C4⋊C4—944no—
533C2×C4⋊C4—944no—
534C2×C4⋊C4—944no—
535C2×C4⋊C4—1882no—
536C2×C4⋊C4—1882no—
537C2×C4⋊C4C22×D4714yes—
538C2×C4⋊C4C22×D4714yes—
539C2×C4⋊C4C22×D4714yes—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—478no—
542C2×C22⋊C4—474no—
543C2×C22⋊C4—474no—
544C2×C22⋊C4—944no—
545C2×C22⋊C4C22⋊D4718yes—
546C2×C22⋊C4C22×D4714yes—
547C2×C22⋊C4C22×D4714yes—
548C2×C42—474no—
549C2×C42—474no—
550C2×C42—944no—
551C2×C42—944no—
552#95—474no—
553#95—474no—
554#95—474no—
555#95—474no—
556#95—474no—
557#95—474no—
558#95—474no—
559#95—474no—
560C24—22no—
561C24—22no—
562C24—22no—
563C24—22no—
564C24Q8×D4714yes—
565C24Q8×D4714yes—
566C24C2×C22⋊D4714yes—
567C24C23×D4712yes—
568C24C23×D4711yescharacteristic
569C2×Q8—28no—
570C2×Q8—28no—
571C2×Q8—44no—
572C2×Q8—416no—
573C2×Q8—948no—
574C2×Q8—948no—
575C2×Q8—1884no—
576C2×Q8—18816no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—28no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—28no—
594C22×C4—44no—
595C22×C4—416no—
596C22×C4—474no—
597C22×C4—474no—
598C22×C4—474no—
599C22×C4—472no—
600C22×C4—474no—
601C22×C4—474no—
602C22×C4—474no—
603C22×C4—474no—
604C22×C4—4716no—
605C22×C4—472no—
606C22×C4—472no—
607C22×C4—472no—
608C22×C4—472no—
609C22×C4—472no—
610C22×C4—472no—
611C22×C4—472no—
612C22×C4—948no—
613C22×C4—9432no—
614C22×C4—948no—
615C22×C4—948no—
616C22×C4—942no—
617C22×C4—942no—
618C22×C4—942no—
619C22×C4—942no—
620C22×C4—942no—
621C22×C4—942no—
622C22×C4—942no—
623C22×C4—942no—
624C22×C4—942no—
625C22×C4—942no—
626C22×C4—942no—
627C22×C4—942no—
628C22×C4—942no—
629C22×C4—948no—
630C22×C4—942no—
631C22×C4—942no—
632C22×C4—942no—
633C22×C4—942no—
634C22×C4—1884no—
635C22×C4—18816no—
636C22×C4D4×D4714yes—
637C22×C4C2×C22⋊D4714yes—
638C22×C4C2×C22⋊D4714yes—
639C22×C4C23×D4712yes—
640C22×C4C23×D4712yes—
641C22×C4C23×D4712yes—
642C22×C4C23×D4712yes—
643C22×C4C23×D4712yes—
644C22×C4C23×D4712yes—
645C4⋊C4—28no—
646C4⋊C4—28no—
647C4⋊C4—28no—
648C4⋊C4—4716no—
649C4⋊C4—948no—
650C4⋊C4—948no—
651C4⋊C4—948no—
652C4⋊C4—948no—
653C4⋊C4—948no—
654C4⋊C4—948no—
655C4⋊C4—948no—
656C4⋊C4—948no—
657C4⋊C4—948no—
658C4⋊C4—948no—
659C4⋊C4—1884no—
660C4⋊C4—1884no—
661C22⋊C4—28no—
662C22⋊C4—4716no—
663C22⋊C4—948no—
664C22⋊C4C2×C22⋊D47116yes—
665C42—948no—
666C42—948no—
667C23—28no—
668C23—28no—
669C23—28no—
670C23—28no—
671C23—28no—
672C23—28no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23#13094022116yescomplemented
678C23C2×D4×D4712yes—
679C23C22×C22⋊D4714yes—
680C23C22×C22⋊D4712yes—
681C23C2×Q8×D4714yes—
682C23C2×Q8×D4714yes—
683C23C2×Q8×D4712yes—
684C23C2×Q8×D4712yes—
685C23#41×D4712yes—
686C23#1309406912yes—
687C23#1309407112yes—
688C23C24×D4711yescharacteristic
689Q8—416no—
690Q8—18816no—
691C2×C4—28no—
692C2×C4—28no—
693C2×C4—28no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—416no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—4716no—
714C2×C4—474no—
715C2×C4—474no—
716C2×C4—474no—
717C2×C4—474no—
718C2×C4—474no—
719C2×C4—474no—
720C2×C4—474no—
721C2×C4—9432no—
722C2×C4—948no—
723C2×C4—948no—
724C2×C4—948no—
725C2×C4—948no—
726C2×C4—942no—
727C2×C4—942no—
728C2×C4—942no—
729C2×C4—942no—
730C2×C4—942no—
731C2×C4—942no—
732C2×C4—942no—
733C2×C4—942no—
734C2×C4—942no—
735C2×C4—942no—
736C2×C4—942no—
737C2×C4—942no—
738C2×C4—942no—
739C2×C4—942no—
740C2×C4—942no—
741C2×C4—942no—
742C2×C4—942no—
743C2×C4—18816no—
744C2×C4—1884no—
745C2×C4—1884no—
746C2×C4—1884no—
747C2×C4C2×D4×D4714yes—
748C2×C4C22×C22⋊D4714yes—
749C2×C4C22×C22⋊D4714yes—
750C22—24no—
751C22—232no—
752C22—24no—
753C22—24no—
754C22—24no—
755C22—24no—
756C22—24no—
757C22C22⋊Q8×D4714yes—
758C22C2×#1309402214yes—
759C22C2×#1309402218yescomplemented
760C22#1568975214yes—
761C22D4×C22⋊D4714yes—
762C22#1568977214yes—
763C22#1568978614yes—
764C22#1568982714yes—
765C22C22×D4×D4711yescharacteristic
766C22C23×C22⋊D4711yescharacteristic
767C22C22×Q8×D4711yescharacteristic
768C22C22×Q8×D4711yescharacteristic
769C22C2×#41×D4711yescharacteristic
770C22C2×#1309406911yescharacteristic
771C22C2×#1309407111yescharacteristic
772C4—24no—
773C4—24no—
774C4—24no—
775C4—42no—
776C4—42no—
777C4—42no—
778C4—478no—
779C4—944no—
780C4—944no—
781C4—944no—
782C4—944no—
783C4—1882no—
784C4—1882no—
785C4—1882no—
786C2—28no—
787C2#2024708718yesdirect product factor
788C2C2×C22⋊Q8×D4711yescharacteristic
789C2C22×#1309402211yescharacteristic
790C2C2×#1568975211yescharacteristic
791C2C2×D4×C22⋊D4711yescharacteristic
792C2C2×#1568977211yescharacteristic
793C2C2×#1568978611yescharacteristic
794C2C2×#1568982711yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC22×C22⋊Q8×C47C2
socleC24×C47C24
prime radicalC25×C47C23
hypercenterC22×C22⋊Q8D47
hypocenterC47C2×#2440
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×#13094022C2semidirect
4. #20247087C2direct (N × H)
5. C2×#15689054C2semidirect
6. C2×#15689053C2semidirect
7. C2×#15689043C2semidirect
8. C2×#15689042C2semidirect
9. C2×#15689018C2semidirect
10. C2×#15689018C2semidirect
13. C2×#15688992C2semidirect
21. C2×#13094022C22semidirect
43. #15689054C22semidirect
44. #15689053C22semidirect
45. #15689043C22semidirect
46. #15689042C22semidirect
47. #15689018C22semidirect
48. #15689018C22semidirect
51. #15688992C22semidirect
80. C23×Dic47Q8semidirect
121. C2×C22⋊Dic47Q8semidirect
233. C22×Dic47C2×Q8semidirect
253. C22⋊Dic47C2×Q8semidirect
279. C23×C47C4⋊Q8semidirect
343. C2×Dic47C22⋊Q8semidirect
362. C22×C47C2×C4⋊Q8semidirect
388. Dic47C2×C22⋊Q8semidirect
406. C2×C47#2440semidirect
468. C47C2×#2440semidirect
677. C23#13094022semidirect
759. C22C2×#13094022semidirect
787. C2#20247087direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940222
C22×#130940012
C23×Dic47⋊C42
#202470872
C2×#156890542
C2×#156890532
C2×#156890432
C2×#156890422
C2×#156890182
C2×#156889962
C2×#156889952
C2×#156889922
C2×#156889812
C2×C22⋊C4×Dic472
C22×C22⋊Q8×C472
C2×#244047