Finite Group Databasebeta

← C2×#20247051 #26383700

Subgroups — C2×#20247051 #26383700

Order 12032.

4926 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094000C211yesmaximal, characteristic, complemented
2C23×(C2×D47)⋊C4C211yesmaximal, characteristic
3C22×C22⋊C4×D47C211yesmaximal, characteristic
4#20247051C2116yesmaximal, direct product factor
5C2×#15689058C211yesmaximal, characteristic, complemented
6C2×#15689045C211yesmaximal, characteristic, complemented
7C2×#15689045C211yesmaximal, characteristic, complemented
8C2×#15689034C211yesmaximal, characteristic, complemented
9C2×#15688998C211yesmaximal, characteristic, complemented
10C2×#15688996C211yesmaximal, characteristic, complemented
11C2×#15688994C211yesmaximal, characteristic, complemented
12C2×#15688994C211yesmaximal, characteristic, complemented
13C2×#15688981C211yesmaximal, characteristic, complemented
14C2×#15688980C211yesmaximal, characteristic, complemented
15C2×#15688978C211yesmaximal, characteristic
16C22×C22⋊Q8×C47C211yesmaximal, characteristic, complemented
17C25×D47C2211yescharacteristic
18C24×Dic47C2211yescharacteristic
19C23×C4×D47C2211yescharacteristic
20C23×C4×D47C2211yescharacteristic
21C2×#13094000—28no—
22C2×#13094000C2218yescomplemented
23C22×C4⋊Dic47C2211yescharacteristic, complemented
24C22×C4⋊Dic47C2211yescharacteristic, complemented
25C22×Dic47⋊C4C2211yescharacteristic, complemented
26C22×Dic47⋊C4C2211yescharacteristic, complemented
27C22×Dic47⋊C4C2211yescharacteristic, complemented
28C22×Dic47⋊C4C2211yescharacteristic, complemented
29C22×C22⋊Dic47C2211yescharacteristic
30C22×C22⋊Dic47C2211yescharacteristic
31C22×(C2×D47)⋊C4—28no—
32C22×(C2×D47)⋊C4C2218yes—
33C22×(C2×D47)⋊C4C2211yescharacteristic
34C22×(C2×D47)⋊C4C2211yescharacteristic
35C22×(C2×D47)⋊C4C2211yescharacteristic
36C22×(C2×D47)⋊C4C2211yescharacteristic
37C22×(C2×D47)⋊C4C2211yescharacteristic
38C22×(C2×D47)⋊C4C2211yescharacteristic
39C22×(C2×D47)⋊C4C2211yescharacteristic
40C22×(C2×D47)⋊C4C2211yescharacteristic
41C22×(C2×D47)⋊C4C2211yescharacteristic
42C22×(C2×D47)⋊C4C2211yescharacteristic
43C2×C22⋊C4×D47—28no—
44C2×C22⋊C4×D47C2218yes—
45#15689058C2218yescomplemented
46#15689045C2218yescomplemented
47#15689045C2218yescomplemented
48#15689034C2218yescomplemented
49#15688998C2218yescomplemented
50#15688996C2218yescomplemented
51#15688994C2218yescomplemented
52#15688994C2218yescomplemented
53#15688981C2218yescomplemented
54#15688980C2218yescomplemented
55#15688978C2218yes—
56C2×C47⋊#95C2211yescharacteristic, complemented
57C2×C47⋊#95C2211yescharacteristic, complemented
58C2×C47⋊#95C2211yescharacteristic, complemented
59C2×C47⋊#95C2211yescharacteristic, complemented
60C2×C47⋊#95C2211yescharacteristic, complemented
61C2×C47⋊#95C2211yescharacteristic, complemented
62C23×Q8×C47C2211yescharacteristic, complemented
63C24×C4×C47C2211yescharacteristic
64C2×C22⋊Q8×C47—28no—
65C2×C22⋊Q8×C47C2218yescomplemented
66C22×C4⋊C4×C47C2211yescharacteristic, complemented
67C22×C4⋊C4×C47C2211yescharacteristic, complemented
68C22×C4⋊C4×C47C2211yescharacteristic, complemented
69C22×C22⋊C4×C47C2211yescharacteristic
70C22×C22⋊C4×C47C2211yescharacteristic
71C24×D47—24no—
72C24×D47—24no—
73C24×D47—24no—
74C24×D47—24no—
75C24×D47—42no—
76C24×D47—42no—
77C24×D47Q818yescomplemented
78C24×D47C2311yescharacteristic
79C24×D47C2314yes—
80C24×D47C2311yescharacteristic
81C23×Dic47—24no—
82C23×Dic47—24no—
83C23×Dic47—42no—
84C23×Dic47C2311yescharacteristic
85C23×Dic47C2311yescharacteristic
86C23×Dic47C2311yescharacteristic
87C23×Dic47C2311yescharacteristic
88C23×Dic47C2311yescharacteristic
89C23×Dic47C2314yes—
90C23×Dic47C2311yescharacteristic
91C22×C4×D47—24no—
92C22×C4×D47—24no—
93C22×C4×D47—24no—
94C22×C4×D47—24no—
95C22×C4×D47—42no—
96C22×C4×D47—42no—
97C22×C4×D47C2314yes—
98C22×C4×D47C2314yes—
99#13094000—232no—
100C2×C4⋊Dic47—24no—
101C2×C4⋊Dic47—42no—
102C2×C4⋊Dic47C2314yescomplemented
103C2×C4⋊Dic47C2314yescomplemented
104C2×Dic47⋊C4—24no—
105C2×Dic47⋊C4—24no—
106C2×Dic47⋊C4—42no—
107C2×Dic47⋊C4—42no—
108C2×Dic47⋊C4C2314yescomplemented
109C2×Dic47⋊C4C2314yescomplemented
110C2×Dic47⋊C4C2314yescomplemented
111C2×Dic47⋊C4C2314yescomplemented
112C2×C22⋊Dic47—24no—
113C2×C22⋊Dic47—24no—
114C2×C22⋊Dic47C2314yes—
115C2×C22⋊Dic47C2314yes—
116C2×(C2×D47)⋊C4—24no—
117C2×(C2×D47)⋊C4—24no—
118C2×(C2×D47)⋊C4—24no—
119C2×(C2×D47)⋊C4—24no—
120C2×(C2×D47)⋊C4—24no—
121C2×(C2×D47)⋊C4—24no—
122C2×(C2×D47)⋊C4—24no—
123C2×(C2×D47)⋊C4—232no—
124C2×(C2×D47)⋊C4—42no—
125C2×(C2×D47)⋊C4—42no—
126C2×(C2×D47)⋊C4D418yes—
127C2×(C2×D47)⋊C4C2314yes—
128C2×(C2×D47)⋊C4C2314yes—
129C2×(C2×D47)⋊C4C2314yes—
130C2×(C2×D47)⋊C4C2314yes—
131C2×(C2×D47)⋊C4C2314yes—
132C2×(C2×D47)⋊C4C2314yes—
133C2×(C2×D47)⋊C4C2314yes—
134C2×(C2×D47)⋊C4C2314yes—
135C2×(C2×D47)⋊C4C2314yes—
136C2×(C2×D47)⋊C4C2314yes—
137C22⋊C4×D47—232no—
138C47⋊#95C2314yescomplemented
139C47⋊#95C2314yescomplemented
140C47⋊#95C2314yescomplemented
141C47⋊#95C2314yescomplemented
142C47⋊#95C2314yescomplemented
143C47⋊#95C2314yescomplemented
144C25×C47C2311yescharacteristic
145C22×Q8×C47—24no—
146C22×Q8×C47—24no—
147C22×Q8×C47—42no—
148C22×Q8×C47C2314yescomplemented
149C23×C4×C47—24no—
150C23×C4×C47—24no—
151C23×C4×C47—42no—
152C23×C4×C47C2311yescharacteristic
153C23×C4×C47C2311yescharacteristic
154C23×C4×C47C2311yescharacteristic
155C23×C4×C47C2314yes—
156C23×C4×C47C2311yescharacteristic
157C23×C4×C47C2311yescharacteristic
158C23×C4×C47C2311yescharacteristic
159C22⋊Q8×C47—232no—
160C2×C4⋊C4×C47—24no—
161C2×C4⋊C4×C47—24no—
162C2×C4⋊C4×C47—24no—
163C2×C4⋊C4×C47C2314yescomplemented
164C2×C4⋊C4×C47C2314yescomplemented
165C2×C4⋊C4×C47C2314yescomplemented
166C2×C22⋊C4×C47—24no—
167C2×C22⋊C4×C47D418yes—
168C2×C22⋊C4×C47C2314yes—
169C2×C22⋊C4×C47C2314yes—
170C24×C47—22no—
171C24×C47—22no—
172C24×C47—22no—
173C24×C47—22no—
174C24×C47C2×D414yes—
175C24×C47C2×Q814yes—
176C24×C47#4114yes—
177C24×C47C2412yes—
178C24×C47C2411yescharacteristic
179C23×D47—22no—
180C23×D47—22no—
181C23×D47—22no—
182C23×D47—22no—
183C23×D47—232no—
184C23×D47—28no—
185C23×D47—22no—
186C23×D47—22no—
187C23×D47—28no—
188C23×D47—22no—
189C23×D47—22no—
190C23×D47—22no—
191C23×D47—22no—
192C23×D47—232no—
193C23×D47—28no—
194C23×D47—28no—
195C23×D47—416no—
196C23×D47—44no—
197C23×D47—44no—
198C23×D47—416no—
199C23×D47—416no—
200C23×D47—416no—
201C23×D47—416no—
202C23×D47C2×D414yes—
203C23×D47C2×Q814yes—
204C23×D47C2×Q814yes—
205C23×D47C2×Q8116yescomplemented
206C23×D47#4114yes—
207C23×D47C2412yes—
208C23×D47C2412yes—
209C2×Q8×C47—28no—
210C2×Q8×C47—28no—
211C2×Q8×C47—44no—
212C2×Q8×C47—416no—
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×C47—22no—
220C22×C4×C47—22no—
221C22×C4×C47—22no—
222C22×C4×C47—28no—
223C22×C4×C47—22no—
224C22×C4×C47—22no—
225C22×C4×C47—22no—
226C22×C4×C47—22no—
227C22×C4×C47—22no—
228C22×C4×C47—22no—
229C22×C4×C47—28no—
230C22×C4×C47—44no—
231C22×C4×C47—416no—
232C22×C4×C47C2×D414yes—
233C22×C4×C47C2×D414yes—
234C22×C4×C47C2×D414yes—
235C22×C4×C47C2412yes—
236C22×C4×C47C2412yes—
237C22×C4×C47C2412yes—
238C22×C4×C47C2412yes—
239C22×C4×C47C2412yes—
240C22×C4×C47C2412yes—
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×Dic47—22no—
252C22×Dic47—28no—
253C22×Dic47—22no—
254C22×Dic47—22no—
255C22×Dic47—22no—
256C22×Dic47—22no—
257C22×Dic47—22no—
258C22×Dic47—22no—
259C22×Dic47—28no—
260C22×Dic47—44no—
261C22×Dic47—416no—
262C22×Dic47C2×D414yes—
263C22×Dic47C2412yes—
264C22×Dic47C2412yes—
265C22×Dic47C2412yes—
266C22×Dic47C2412yes—
267C22×Dic47C2412yes—
268C22×Dic47C2412yes—
269C2×C4×D47—28no—
270C2×C4×D47—28no—
271C2×C4×D47—28no—
272C2×C4×D47—28no—
273C2×C4×D47—44no—
274C2×C4×D47—44no—
275C2×C4×D47—416no—
276C2×C4×D47—416no—
277C4⋊C4×C47—28no—
278C4⋊C4×C47—28no—
279C4⋊C4×C47—28no—
280C22⋊C4×C47—28no—
281C22⋊C4×C47C2×D4116yes—
282C22⋊Dic47—28no—
283C22⋊Dic47—28no—
284(C2×D47)⋊C4—28no—
285(C2×D47)⋊C4—28no—
286(C2×D47)⋊C4—28no—
287(C2×D47)⋊C4—28no—
288(C2×D47)⋊C4—28no—
289(C2×D47)⋊C4—28no—
290(C2×D47)⋊C4—28no—
291(C2×D47)⋊C4—44no—
292(C2×D47)⋊C4—44no—
293(C2×D47)⋊C4C2×D4116yes—
294C4⋊Dic47—28no—
295C4⋊Dic47—44no—
296Dic47⋊C4—28no—
297Dic47⋊C4—28no—
298Dic47⋊C4—44no—
299Dic47⋊C4—44no—
300C23×C47—28no—
301C23×C47—28no—
302C23×C47—28no—
303C23×C47—28no—
304C23×C47—28no—
305C23×C47—28no—
306C23×C47—22no—
307C23×C47—22no—
308C23×C47—22no—
309C23×C47—22no—
310C23×C47C22⋊Q8116yescomplemented
311C23×C47C22×D412yes—
312C23×C47C22×D414yes—
313C23×C47C22×D412yes—
314C23×C47C22×Q814yes—
315C23×C47C22×Q812yes—
316C23×C47C2×#4112yes—
317C23×C47C2×#4114yes—
318C23×C47C2×#4112yes—
319C23×C47H(5,𝔽2)12yes—
320C23×C47H(5,𝔽2)12yes—
321C23×C47C2511yescharacteristic
322C22×D47—28no—
323C22×D47—28no—
324C22×D47—28no—
325C22×D47—28no—
326C22×D47—28no—
327C22×D47—28no—
328C22×D47—22no—
329C22×D47—22no—
330C22×D47—22no—
331C22×D47—22no—
332C22×D47—28no—
333C22×D47—28no—
334C22×D47—232no—
335C22×D47—28no—
336C22×D47—22no—
337C22×D47—22no—
338C22×D47—22no—
339C22×D47—22no—
340C22×D47—22no—
341C22×D47—22no—
342C22×D47—232no—
343C22×D47—416no—
344C22×D47—4128no—
345C22×D47—416no—
346C22×D47—416no—
347C22×D47—416no—
348C22×D47—416no—
349C22×D47—44no—
350C22×D47—44no—
351C22×D47—44no—
352C22×D47—44no—
353C22×D47C22⋊Q8116yescomplemented
354C22×D47C22×D414yes—
355C22×D47C22×Q814yes—
356C22×D47C22×Q814yes—
357C22×D47C2×#4114yes—
358Q8×C47—416no—
359C2×C4×C47—28no—
360C2×C4×C47—28no—
361C2×C4×C47—28no—
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—22no—
373C2×C4×C47—22no—
374C2×C4×C47—22no—
375C2×C4×C47—22no—
376C2×C4×C47—22no—
377C2×C4×C47—416no—
378C2×C4×C47—44no—
379C2×C4×C47—44no—
380C2×C4×C47—44no—
381C2×C4×C47C22×D414yes—
382C2×C4×C47C22×D414yes—
383C2×C4×C47C22×D414yes—
384C2×Dic47—28no—
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—22no—
399C2×Dic47—22no—
400C2×Dic47—22no—
401C2×Dic47—22no—
402C2×Dic47—416no—
403C2×Dic47—44no—
404C2×Dic47—44no—
405C2×Dic47—44no—
406C2×Dic47—44no—
407C2×Dic47—44no—
408C2×Dic47C22×D414yes—
409C4×D47—416no—
410C4×D47—416no—
411C2×#2437—471nomaximal, Sylow
412C22×C47—24no—
413C22×C47—24no—
414C22×C47—232no—
415C22×C47—24no—
416C22×C47—24no—
417C22×C47—24no—
418C22×C47—24no—
419C22×C47C2×C22⋊Q814yes—
420C22×C47C2×C22⋊Q814yes—
421C22×C47C2×C22⋊Q818yescomplemented
422C22×C47#54314yes—
423C22×C47D4214yes—
424C22×C47#54614yes—
425C22×C47#54614yes—
426C22×C47#55114yes—
427C22×C47C23×D411yescharacteristic
428C22×C47C23×D411yescharacteristic
429C22×C47C23×Q811yescharacteristic
430C22×C47C22×#4111yescharacteristic
431C22×C47C22×#4111yescharacteristic
432C22×C47C2×H(5,𝔽2)11yescharacteristic
433C22×C47C2×H(5,𝔽2)11yescharacteristic
434C2×D47—24no—
435C2×D47—24no—
436C2×D47—232no—
437C2×D47—24no—
438C2×D47—24no—
439C2×D47—24no—
440C2×D47—24no—
441C2×D47—24no—
442C2×D47—24no—
443C2×D47—24no—
444C2×D47—464no—
445C2×D47—416no—
446C2×D47—42no—
447C2×D47—42no—
448C2×D47—42no—
449C2×D47—42no—
450C2×D47C2×C22⋊Q818yescomplemented
451C4×C47—24no—
452C4×C47—24no—
453C4×C47—24no—
454C4×C47—42no—
455C4×C47—42no—
456C4×C47—42no—
457Dic47—24no—
458Dic47—42no—
459Dic47—42no—
460Dic47—42no—
461Dic47—42no—
462Dic47—42no—
463C22×C22⋊Q8—471no—
464C22×C22⋊Q8D4711yescharacteristic, complemented
465C23×C22⋊C4—471no—
466C23×C22⋊C4—471no—
467#2437—4716no—
468C2×#399—471no—
469C2×#396—471no—
470C2×#396—471no—
471C2×#393—471no—
472C2×#385—471no—
473C2×#385—471no—
474C2×#385—471no—
475C2×#385—471no—
476C2×#380—471no—
477C2×#380—471no—
478C2×#379—471no—
479C2×C47—28no—
480C2×C47#243718yescomplemented
481C2×C47C22×C22⋊Q811yescharacteristic
482C2×C47C22×C22⋊Q811yescharacteristic
483C2×C47C2×#54311yescharacteristic
484C2×C47C2×D4211yescharacteristic
485C2×C47C2×#54611yescharacteristic
486C2×C47C2×#54611yescharacteristic
487C2×C47C2×#55111yescharacteristic
488D47—28no—
489D47—44no—
490C26—471no—
491C23×Q8C2×D4711yescharacteristic, complemented
492C24×C4—471no—
493C24×C4—471no—
494C24×C4—471no—
495C24×C4C2×D4711yescharacteristic
496C2×C22⋊Q8—28no—
497C2×C22⋊Q8—478no—
498C2×C22⋊Q8—948no—
499C2×C22⋊Q8C2×D4718yescomplemented
500C22×C4⋊C4—471no—
501C22×C4⋊C4—471no—
502C22×C4⋊C4—471no—
503C22×C4⋊C4—471no—
504C22×C4⋊C4—471no—
505C22×C4⋊C4—471no—
506C22×C4⋊C4C2×D4711yescharacteristic, complemented
507C22×C4⋊C4C2×D4711yescharacteristic, complemented
508C22×C4⋊C4C2×D4711yescharacteristic, complemented
509C22×C22⋊C4—471no—
510C22×C22⋊C4—471no—
511C22×C22⋊C4—471no—
512C22×C22⋊C4—471no—
513C22×C22⋊C4—471no—
514C22×C22⋊C4—471no—
515C22×C22⋊C4—471no—
516C22×C22⋊C4—478no—
517C22×C22⋊C4—471no—
518C22×C22⋊C4—471no—
519C22×C22⋊C4—471no—
520C22×C22⋊C4—471no—
521C22×C22⋊C4—471no—
522C22×C22⋊C4—478no—
523C22×C22⋊C4—948no—
524C22×C22⋊C4—948no—
525C22×C22⋊C4C2×D4711yescharacteristic
526C22×C22⋊C4C2×D4711yescharacteristic
527#399—478no—
528#396—478no—
529#396—478no—
530#393—478no—
531#385—478no—
532#385—478no—
533#385—478no—
534#385—478no—
535#380—478no—
536#380—478no—
537#379—478no—
538C2×#95—471no—
539C2×#95—471no—
540C2×#95—471no—
541C2×#95—471no—
542C2×#95—471no—
543C2×#95—471no—
544C47C2×#243711yescharacteristic, complemented, Sylow
545C25—471no—
546C25—471no—
547C25—478no—
548C25—474no—
549C25—944no—
550C25—944no—
551C25—944no—
552C25—944no—
553C25—1882no—
554C25—1882no—
555C25C22×D4711yescharacteristic
556C22×Q8—24no—
557C22×Q8—24no—
558C22×Q8—42no—
559C22×Q8C22×D4714yescomplemented
560C23×C4—24no—
561C23×C4—24no—
562C23×C4—42no—
563C23×C4—471no—
564C23×C4—471no—
565C23×C4—471no—
566C23×C4—471no—
567C23×C4—471no—
568C23×C4—471no—
569C23×C4—474no—
570C23×C4—474no—
571C23×C4—474no—
572C23×C4—944no—
573C23×C4—944no—
574C23×C4—944no—
575C23×C4—944no—
576C23×C4—944no—
577C23×C4—944no—
578C23×C4—1882no—
579C23×C4—1882no—
580C23×C4—1882no—
581C23×C4C22×D4711yescharacteristic
582C23×C4C22×D4711yescharacteristic
583C23×C4C22×D4711yescharacteristic
584C23×C4C22×D4714yes—
585C23×C4C22×D4711yescharacteristic
586C23×C4C22×D4711yescharacteristic
587C23×C4C22×D4711yescharacteristic
588C22⋊Q8—232no—
589C22⋊Q8—9432no—
590C2×C4⋊C4—24no—
591C2×C4⋊C4—24no—
592C2×C4⋊C4—24no—
593C2×C4⋊C4—474no—
594C2×C4⋊C4—474no—
595C2×C4⋊C4—474no—
596C2×C4⋊C4—474no—
597C2×C4⋊C4—474no—
598C2×C4⋊C4—474no—
599C2×C4⋊C4—944no—
600C2×C4⋊C4—944no—
601C2×C4⋊C4—944no—
602C2×C4⋊C4—1882no—
603C2×C4⋊C4—1882no—
604C2×C4⋊C4—1882no—
605C2×C4⋊C4C22×D4714yescomplemented
606C2×C4⋊C4C22×D4714yescomplemented
607C2×C4⋊C4C22×D4714yescomplemented
608C2×C22⋊C4—24no—
609C2×C22⋊C4—478no—
610C2×C22⋊C4—474no—
611C2×C22⋊C4—474no—
612C2×C22⋊C4—474no—
613C2×C22⋊C4—474no—
614C2×C22⋊C4—474no—
615C2×C22⋊C4—474no—
616C2×C22⋊C4—474no—
617C2×C22⋊C4—474no—
618C2×C22⋊C4—474no—
619C2×C22⋊C4—474no—
620C2×C22⋊C4—474no—
621C2×C22⋊C4—474no—
622C2×C22⋊C4—9432no—
623C2×C22⋊C4—944no—
624C2×C22⋊C4—944no—
625C2×C22⋊C4—944no—
626C2×C22⋊C4—944no—
627C2×C22⋊C4—944no—
628C2×C22⋊C4—944no—
629C2×C22⋊C4—944no—
630C2×C22⋊C4—944no—
631C2×C22⋊C4—944no—
632C2×C22⋊C4—9432no—
633C2×C22⋊C4—1882no—
634C2×C22⋊C4—1882no—
635C2×C22⋊C4C22⋊D4718yes—
636C2×C22⋊C4C22×D4714yes—
637C2×C22⋊C4C22×D4714yes—
638#95—474no—
639#95—474no—
640#95—474no—
641#95—474no—
642#95—474no—
643#95—474no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—474no—
649C24—474no—
650C24—474no—
651C24—472no—
652C24—474no—
653C24—472no—
654C24—4716no—
655C24—948no—
656C24—9432no—
657C24—948no—
658C24—942no—
659C24—942no—
660C24—942no—
661C24—942no—
662C24—9432no—
663C24—942no—
664C24—948no—
665C24—942no—
666C24—942no—
667C24—948no—
668C24—942no—
669C24—942no—
670C24—942no—
671C24—18816no—
672C24—1884no—
673C24—1884no—
674C24—18816no—
675C24—18816no—
676C24—18816no—
677C24—18816no—
678C24Q8×D4714yes—
679C24#1062535414yes—
680C24C2×C22⋊D4714yes—
681C24C23×D4712yes—
682C24C23×D4711yescharacteristic
683C2×Q8—28no—
684C2×Q8—28no—
685C2×Q8—44no—
686C2×Q8—416no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—28no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—28no—
704C22×C4—44no—
705C22×C4—416no—
706C22×C4—474no—
707C22×C4—472no—
708C22×C4—472no—
709C22×C4—472no—
710C22×C4—472no—
711C22×C4—472no—
712C22×C4—472no—
713C22×C4—948no—
714C22×C4—948no—
715C22×C4—948no—
716C22×C4—942no—
717C22×C4—942no—
718C22×C4—942no—
719C22×C4—942no—
720C22×C4—942no—
721C22×C4—942no—
722C22×C4—942no—
723C22×C4—942no—
724C22×C4—942no—
725C22×C4—942no—
726C22×C4—942no—
727C22×C4—948no—
728C22×C4—942no—
729C22×C4—942no—
730C22×C4—942no—
731C22×C4—942no—
732C22×C4—942no—
733C22×C4—942no—
734C22×C4—948no—
735C22×C4—948no—
736C22×C4—1884no—
737C22×C4—1884no—
738C22×C4—18816no—
739C22×C4—18816no—
740C22×C4—1884no—
741C22×C4—18816no—
742C22×C4D4×D4714yes—
743C22×C4C2×C22⋊D4714yes—
744C22×C4C2×C22⋊D4714yes—
745C22×C4C23×D4712yes—
746C22×C4C23×D4712yes—
747C22×C4C23×D4712yes—
748C22×C4C23×D4712yes—
749C22×C4C23×D4712yes—
750C22×C4C23×D4712yes—
751C4⋊C4—28no—
752C4⋊C4—28no—
753C4⋊C4—28no—
754C4⋊C4—948no—
755C4⋊C4—948no—
756C4⋊C4—948no—
757C4⋊C4—1884no—
758C4⋊C4—1884no—
759C4⋊C4—1884no—
760C22⋊C4—28no—
761C22⋊C4—4716no—
762C22⋊C4—948no—
763C22⋊C4—948no—
764C22⋊C4—948no—
765C22⋊C4—948no—
766C22⋊C4—948no—
767C22⋊C4—948no—
768C22⋊C4—948no—
769C22⋊C4—948no—
770C22⋊C4—948no—
771C22⋊C4—1884no—
772C22⋊C4—1884no—
773C22⋊C4C2×C22⋊D47116yes—
774C23—28no—
775C23—28no—
776C23—28no—
777C23—28no—
778C23—28no—
779C23—28no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—4716no—
785C23—474no—
786C23—474no—
787C23—474no—
788C23—474no—
789C23—9432no—
790C23—948no—
791C23—948no—
792C23—948no—
793C23—948no—
794C23—948no—
795C23—948no—
796C23—942no—
797C23—942no—
798C23—942no—
799C23—942no—
800C23—948no—
801C23—948no—
802C23—948no—
803C23—9432no—
804C23—942no—
805C23—942no—
806C23—942no—
807C23—942no—
808C23—942no—
809C23—942no—
810C23—18816no—
811C23—188128no—
812C23—18816no—
813C23—18816no—
814C23—18816no—
815C23—18816no—
816C23—1884no—
817C23—1884no—
818C23—1884no—
819C23—1884no—
820C23#13094000116yescomplemented
821C23C2×D4×D4712yes—
822C23C22×C22⋊D4714yes—
823C23C22×C22⋊D4712yes—
824C23C2×Q8×D4714yes—
825C23C2×Q8×D4712yes—
826C23#41×D4712yes—
827C23C2×#1062535414yes—
828C23C2×#1062535412yes—
829C23#1309406912yes—
830C23#1309407012yes—
831C23C24×D4711yescharacteristic
832Q8—416no—
833C2×C4—28no—
834C2×C4—28no—
835C2×C4—28no—
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—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—416no—
852C2×C4—44no—
853C2×C4—44no—
854C2×C4—44no—
855C2×C4—474no—
856C2×C4—948no—
857C2×C4—942no—
858C2×C4—942no—
859C2×C4—942no—
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—18816no—
875C2×C4—18816no—
876C2×C4—18816no—
877C2×C4—1884no—
878C2×C4—1884no—
879C2×C4—1884no—
880C2×C4—1884no—
881C2×C4—1884no—
882C2×C4C2×D4×D4714yes—
883C2×C4C22×C22⋊D4714yes—
884C2×C4C22×C22⋊D4714yes—
885C22—232no—
886C22—24no—
887C22—24no—
888C22—24no—
889C22—24no—
890C22—24no—
891C22—24no—
892C22—478no—
893C22—9432no—
894C22—944no—
895C22—944no—
896C22—944no—
897C22—944no—
898C22—944no—
899C22—944no—
900C22—944no—
901C22—944no—
902C22—944no—
903C22—18864no—
904C22—18816no—
905C22—1882no—
906C22—1882no—
907C22—1882no—
908C22—1882no—
909C22C22⋊Q8×D4714yes—
910C22C2×#1309400014yes—
911C22C2×#1309400018yescomplemented
912C22#1568974814yes—
913C22D4×C22⋊D4714yes—
914C22#1568976114yes—
915C22#1568976414yes—
916C22#1568980014yes—
917C22C22×D4×D4711yescharacteristic
918C22C23×C22⋊D4711yescharacteristic
919C22C22×Q8×D4711yescharacteristic
920C22C2×#41×D4711yescharacteristic
921C22C22×#1062535411yescharacteristic
922C22C2×#1309406911yescharacteristic
923C22C2×#1309407011yescharacteristic
924C4—24no—
925C4—24no—
926C4—24no—
927C4—42no—
928C4—42no—
929C4—42no—
930C4—944no—
931C4—1882no—
932C4—1882no—
933C4—1882no—
934C4—1882no—
935C4—1882no—
936C2—28no—
937C2—948no—
938C2—1884no—
939C2#2024705118yesdirect product factor
940C2C2×C22⋊Q8×D4711yescharacteristic
941C2C22×#1309400011yescharacteristic
942C2C2×#1568974811yescharacteristic
943C2C2×D4×C22⋊D4711yescharacteristic
944C2C2×#1568976111yescharacteristic
945C2C2×#1568976411yescharacteristic
946C2C2×#1568980011yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC22×C22⋊Q8×C47C2
socleC24×C47C24
prime radicalC25×D47C22
hypercenterC22×C22⋊Q8D47
hypocenterC47C2×#2437
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×#13094000C2semidirect
4. #20247051C2direct (N × H)
5. C2×#15689058C2semidirect
6. C2×#15689045C2semidirect
7. C2×#15689045C2semidirect
8. C2×#15689034C2semidirect
9. C2×#15688998C2semidirect
10. C2×#15688996C2semidirect
11. C2×#15688994C2semidirect
12. C2×#15688994C2semidirect
13. C2×#15688981C2semidirect
14. C2×#15688980C2semidirect
16. C22×C22⋊Q8×C47C2semidirect
22. C2×#13094000C22semidirect
23. C22×C4⋊Dic47C22semidirect
24. C22×C4⋊Dic47C22semidirect
25. C22×Dic47⋊C4C22semidirect
26. C22×Dic47⋊C4C22semidirect
27. C22×Dic47⋊C4C22semidirect
28. C22×Dic47⋊C4C22semidirect
45. #15689058C22semidirect
46. #15689045C22semidirect
47. #15689045C22semidirect
48. #15689034C22semidirect
49. #15688998C22semidirect
50. #15688996C22semidirect
51. #15688994C22semidirect
52. #15688994C22semidirect
53. #15688981C22semidirect
54. #15688980C22semidirect
56. C2×C47⋊#95C22semidirect
57. C2×C47⋊#95C22semidirect
58. C2×C47⋊#95C22semidirect
59. C2×C47⋊#95C22semidirect
60. C2×C47⋊#95C22semidirect
61. C2×C47⋊#95C22semidirect
62. C23×Q8×C47C22semidirect
65. C2×C22⋊Q8×C47C22semidirect
66. C22×C4⋊C4×C47C22semidirect
67. C22×C4⋊C4×C47C22semidirect
68. C22×C4⋊C4×C47C22semidirect
77. C24×D47Q8semidirect
102. C2×C4⋊Dic47C23semidirect
103. C2×C4⋊Dic47C23semidirect
108. C2×Dic47⋊C4C23semidirect
109. C2×Dic47⋊C4C23semidirect
110. C2×Dic47⋊C4C23semidirect
111. C2×Dic47⋊C4C23semidirect
138. C47⋊#95C23semidirect
139. C47⋊#95C23semidirect
140. C47⋊#95C23semidirect
141. C47⋊#95C23semidirect
142. C47⋊#95C23semidirect
143. C47⋊#95C23semidirect
148. C22×Q8×C47C23semidirect
163. C2×C4⋊C4×C47C23semidirect
164. C2×C4⋊C4×C47C23semidirect
165. C2×C4⋊C4×C47C23semidirect
205. C23×D47C2×Q8semidirect
310. C23×C47C22⋊Q8semidirect
353. C22×D47C22⋊Q8semidirect
421. C22×C47C2×C22⋊Q8semidirect
450. C2×D47C2×C22⋊Q8semidirect
464. C22×C22⋊Q8D47semidirect
480. C2×C47#2437semidirect
491. C23×Q8C2×D47semidirect
499. C2×C22⋊Q8C2×D47semidirect
506. C22×C4⋊C4C2×D47semidirect
507. C22×C4⋊C4C2×D47semidirect
508. C22×C4⋊C4C2×D47semidirect
544. C47C2×#2437semidirect
559. C22×Q8C22×D47semidirect
605. C2×C4⋊C4C22×D47semidirect
606. C2×C4⋊C4C22×D47semidirect
607. C2×C4⋊C4C22×D47semidirect
820. C23#13094000semidirect
911. C22C2×#13094000semidirect
939. C2#20247051direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940002
C23×(C2×D47)⋊C42
C22×C22⋊C4×D472
#202470512
C2×#156890582
C2×#156890452
C2×#156890342
C2×#156889982
C2×#156889962
C2×#156889942
C2×#156889812
C2×#156889802
C2×#156889782
C22×C22⋊Q8×C472
C2×#243747