Finite Group Databasebeta

← C2×#20247237 #26384183

Subgroups — C2×#20247237 #26384183

Order 12032.

3614 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094022C211yesmaximal, characteristic, complemented
2C22×#13094002C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D47C211yesmaximal, characteristic
4#20247237C2116yesmaximal, direct product factor
5C2×#15689046C211yesmaximal, characteristic, complemented
6C2×#15689045C211yesmaximal, characteristic, complemented
7C2×#15689035C211yesmaximal, characteristic, complemented
8C2×#15689034C211yesmaximal, characteristic, complemented
9C2×#15689023C211yesmaximal, characteristic
10C2×#15689023C211yesmaximal, characteristic
11C2×#15689018C211yesmaximal, characteristic, complemented
12C2×#15689018C211yesmaximal, characteristic, complemented
13C2×#15688996C211yesmaximal, characteristic, complemented
14C2×#15688994C211yesmaximal, characteristic, complemented
15C2×C4⋊C4×Dic47C211yesmaximal, characteristic, complemented
16C22×C22⋊Q8×C47C211yesmaximal, characteristic, complemented
17C23×Dic94C2211yescharacteristic
18C23×C22⋊D47C2211yescharacteristic
19C23×C4×D47C2211yescharacteristic
20C2×#13094022—28no—
21C2×#13094022C2218yescomplemented
22C2×#13094002—28no—
23C2×#13094002C2218yescomplemented
24C2×C4×C22⋊D47—28no—
25C2×C4×C22⋊D47C2218yes—
26C22×C4⋊Dic47C2211yescharacteristic
27C22×Dic47⋊C4C2211yescharacteristic
28C22×Dic47⋊C4C2211yescharacteristic
29C22×Dic47⋊C4C2211yescharacteristic
30C22×Dic47⋊C4C2211yescharacteristic
31C22×Dic47⋊C4C2211yescharacteristic
32C22×Dic47⋊C4C2211yescharacteristic
33C22×Dic47⋊C4C2211yescharacteristic
34C22×C22⋊Dic47C2211yescharacteristic
35C22×C22⋊Dic47C2211yescharacteristic
36C22×C22⋊Dic47C2211yescharacteristic
37C22×(C2×D47)⋊C4C2211yescharacteristic
38C22×(C2×D47)⋊C4C2211yescharacteristic
39C22×(C2×D47)⋊C4C2211yescharacteristic
40C22×(C2×D47)⋊C4C2211yescharacteristic
41C22×(C2×D47)⋊C4C2211yescharacteristic
42C22×C4×Dic47C2211yescharacteristic
43C22×C4×Dic47C2211yescharacteristic
44C22×C4×Dic47C2211yescharacteristic
45#15689046C2218yescomplemented
46#15689045C2218yescomplemented
47#15689035C2218yescomplemented
48#15689034C2218yescomplemented
49#15689023C2218yes—
50#15689023C2218yes—
51#15689018C2218yescomplemented
52#15689018C2218yescomplemented
53#15688996C2218yescomplemented
54#15688994C2218yescomplemented
55C4⋊C4×Dic47C2218yescomplemented
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×C47C2218yescomplemented
66C22×C4⋊C4×C47C2211yescharacteristic
67C22×C4⋊C4×C47C2211yescharacteristic
68C22×C4⋊C4×C47C2211yescharacteristic
69C22×C22⋊C4×C47C2211yescharacteristic
70C22×C22⋊C4×C47C2211yescharacteristic
71C24×D47C2311yescharacteristic
72C22×Dic94—24no—
73C22×Dic94—24no—
74C22×Dic94—42no—
75C22×Dic94C2314yes—
76C22×C22⋊D47—24no—
77C22×C22⋊D47—24no—
78C22×C22⋊D47Q818yescomplemented
79C22×C22⋊D47C2314yes—
80C23×Dic47C2311yescharacteristic
81C23×Dic47C2311yescharacteristic
82C23×Dic47C2311yescharacteristic
83C23×Dic47C2311yescharacteristic
84C23×Dic47C2311yescharacteristic
85C23×Dic47C2311yescharacteristic
86C23×Dic47C2311yescharacteristic
87C22×C4×D47—24no—
88C22×C4×D47—24no—
89C22×C4×D47—42no—
90C22×C4×D47C2314yes—
91#13094022—232no—
92#13094002—232no—
93C4×C22⋊D47—232no—
94C2×C4⋊Dic47—24no—
95C2×C4⋊Dic47C2314yes—
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⋊C4D418yes—
103C2×Dic47⋊C4C2314yes—
104C2×Dic47⋊C4C2314yes—
105C2×Dic47⋊C4C2314yes—
106C2×Dic47⋊C4C2314yes—
107C2×Dic47⋊C4C2314yes—
108C2×Dic47⋊C4C2314yes—
109C2×Dic47⋊C4C2314yes—
110C2×C22⋊Dic47—24no—
111C2×C22⋊Dic47—24no—
112C2×C22⋊Dic47—42no—
113C2×C22⋊Dic47C2314yes—
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—42no—
121C2×(C2×D47)⋊C4C2314yes—
122C2×(C2×D47)⋊C4C2314yes—
123C2×(C2×D47)⋊C4C2314yes—
124C2×(C2×D47)⋊C4C2314yes—
125C2×(C2×D47)⋊C4C2314yes—
126C2×C4×Dic47—24no—
127C2×C4×Dic47—24no—
128C2×C4×Dic47—24no—
129C2×C4×Dic47C2314yes—
130C2×C4×Dic47C2314yes—
131C2×C4×Dic47C2314yes—
132C47⋊#95C2314yes—
133C47⋊#95C2314yes—
134C47⋊#95C2314yes—
135C47⋊#95C2314yes—
136C47⋊#95C2314yes—
137C47⋊#95C2314yes—
138C25×C47C2311yescharacteristic
139C22×Q8×C47—24no—
140C22×Q8×C47—24no—
141C22×Q8×C47—42no—
142C22×Q8×C47C2314yes—
143C23×C4×C47—24no—
144C23×C4×C47—24no—
145C23×C4×C47—42no—
146C23×C4×C47C2311yescharacteristic
147C23×C4×C47C2311yescharacteristic
148C23×C4×C47C2314yes—
149C23×C4×C47C2311yescharacteristic
150C23×C4×C47C2311yescharacteristic
151C23×C4×C47C2311yescharacteristic
152C23×C4×C47C2311yescharacteristic
153C22⋊Q8×C47—232no—
154C2×C4⋊C4×C47—24no—
155C2×C4⋊C4×C47—24no—
156C2×C4⋊C4×C47D418yescomplemented
157C2×C4⋊C4×C47C2314yes—
158C2×C4⋊C4×C47C2314yes—
159C2×C4⋊C4×C47C2314yes—
160C2×C22⋊C4×C47—24no—
161C2×C22⋊C4×C47—24no—
162C2×C22⋊C4×C47C2314yes—
163C2×C22⋊C4×C47C2314yes—
164C24×C47—22no—
165C24×C47—22no—
166C24×C47—22no—
167C24×C47—22no—
168C24×C47—22no—
169C24×C47—22no—
170C24×C47C2×Q814yes—
171C24×C47C2412yes—
172C24×C47C2411yescharacteristic
173C23×D47—22no—
174C23×D47—22no—
175C23×D47—22no—
176C23×D47—22no—
177C23×D47—22no—
178C23×D47—22no—
179C23×D47C2×Q814yes—
180C23×D47C2412yes—
181C2×Q8×C47—28no—
182C2×Q8×C47—28no—
183C2×Q8×C47—44no—
184C2×Q8×C47—416no—
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—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—22no—
199C22×C4×C47—28no—
200C22×C4×C47—28no—
201C22×C4×C47—44no—
202C22×C4×C47—416no—
203C22×C4×C47C2×D414yes—
204C22×C4×C47C2×D414yes—
205C22×C4×C47C2×D414yes—
206C22×C4×C47C2×D414yes—
207C22×C4×C47C2412yes—
208C22×C4×C47C2412yes—
209C22×C4×C47C2412yes—
210C22×C4×C47C2412yes—
211C22×C4×C47C2412yes—
212C22×C4×C47C2412yes—
213C2×C22⋊D47—232no—
214C2×C22⋊D47—28no—
215C2×C22⋊D47—28no—
216C2×C22⋊D47C2×Q8116yescomplemented
217C22×Dic47—22no—
218C22×Dic47—22no—
219C22×Dic47—22no—
220C22×Dic47—22no—
221C22×Dic47—22no—
222C22×Dic47—22no—
223C22×Dic47—22no—
224C22×Dic47—22no—
225C22×Dic47—22no—
226C22×Dic47—22no—
227C22×Dic47—22no—
228C22×Dic47—22no—
229C22×Dic47—22no—
230C22×Dic47—22no—
231C22×Dic47—22no—
232C22×Dic47—22no—
233C22×Dic47C2×D414yes—
234C22×Dic47C2×D414yes—
235C22×Dic47C2×Q814yes—
236C22×Dic47#4114yes—
237C22×Dic47#4114yes—
238C22×Dic47C2412yes—
239C22×Dic47C2412yes—
240C22×Dic47C2412yes—
241C22×Dic47C2412yes—
242C22×Dic47C2412yes—
243C22×Dic47C2412yes—
244C22×Dic47C2412yes—
245C2×C4×D47—28no—
246C2×C4×D47—28no—
247C2×C4×D47—44no—
248C2×C4×D47—416no—
249C2×Dic94—28no—
250C2×Dic94—28no—
251C2×Dic94—44no—
252C2×Dic94—416no—
253C4⋊C4×C47—28no—
254C4⋊C4×C47—28no—
255C4⋊C4×C47C2×D4116yescomplemented
256C22⋊C4×C47—28no—
257C22⋊C4×C47—28no—
258C22⋊Dic47—28no—
259C22⋊Dic47—28no—
260C22⋊Dic47—44no—
261(C2×D47)⋊C4—28no—
262(C2×D47)⋊C4—28no—
263(C2×D47)⋊C4—28no—
264(C2×D47)⋊C4—28no—
265(C2×D47)⋊C4—44no—
266C4⋊Dic47—28no—
267Dic47⋊C4—28no—
268Dic47⋊C4—28no—
269Dic47⋊C4—28no—
270Dic47⋊C4—28no—
271Dic47⋊C4—28no—
272Dic47⋊C4—28no—
273Dic47⋊C4C2×D4116yes—
274C4×Dic47—28no—
275C4×Dic47—28no—
276C4×Dic47—28no—
277C23×C47—28no—
278C23×C47—28no—
279C23×C47—28no—
280C23×C47—22no—
281C23×C47—22no—
282C23×C47—22no—
283C23×C47—22no—
284C23×C47—22no—
285C23×C47—22no—
286C23×C47—44no—
287C23×C47—44no—
288C23×C47—44no—
289C23×C47—44no—
290C23×C47C22×D412yes—
291C23×C47C22×D412yes—
292C23×C47C22×Q814yes—
293C23×C47C22×Q812yes—
294C23×C47C2×#4112yes—
295C23×C47C2×#4112yes—
296C23×C47H(5,𝔽2)12yes—
297C23×C472−1+412yes—
298C23×C47C2511yescharacteristic
299C22×D47—28no—
300C22×D47—28no—
301C22×D47—28no—
302C22×D47—22no—
303C22×D47—22no—
304C22×D47—22no—
305C22×D47—22no—
306C22×D47—22no—
307C22×D47—22no—
308C22×D47—44no—
309C22×D47—44no—
310C22×D47—44no—
311C22×D47—44no—
312C22×D47C22×Q814yes—
313Q8×C47—416no—
314C2×C4×C47—28no—
315C2×C4×C47—28no—
316C2×C4×C47—28no—
317C2×C4×C47—28no—
318C2×C4×C47—22no—
319C2×C4×C47—22no—
320C2×C4×C47—22no—
321C2×C4×C47—22no—
322C2×C4×C47—22no—
323C2×C4×C47—22no—
324C2×C4×C47—22no—
325C2×C4×C47—22no—
326C2×C4×C47—22no—
327C2×C4×C47—22no—
328C2×C4×C47—22no—
329C2×C4×C47—22no—
330C2×C4×C47—22no—
331C2×C4×C47—22no—
332C2×C4×C47—416no—
333C2×C4×C47—44no—
334C2×C4×C47—44no—
335C2×C4×C47C22×D414yes—
336C2×C4×C47C22×D414yes—
337C2×C4×C47C22×D414yes—
338C2×C4×C47C22×D414yes—
339C22⋊D47—232no—
340C2×Dic47—28no—
341C2×Dic47—28no—
342C2×Dic47—22no—
343C2×Dic47—22no—
344C2×Dic47—22no—
345C2×Dic47—22no—
346C2×Dic47—22no—
347C2×Dic47—22no—
348C2×Dic47—22no—
349C2×Dic47—22no—
350C2×Dic47—22no—
351C2×Dic47—22no—
352C2×Dic47—22no—
353C2×Dic47—22no—
354C2×Dic47—22no—
355C2×Dic47—22no—
356C2×Dic47—22no—
357C2×Dic47—22no—
358C2×Dic47—44no—
359C2×Dic47—44no—
360C2×Dic47—44no—
361C2×Dic47—44no—
362C2×Dic47C22⋊Q8116yescomplemented
363C2×Dic47C22×D414yes—
364C2×Dic47C22×D414yes—
365C2×Dic47C22×Q814yes—
366C2×Dic47C2×#4114yes—
367C2×Dic47C2×#4114yes—
368C4×D47—416no—
369Dic94—416no—
370C2×#2452—471nomaximal, Sylow
371C22×C47—24no—
372C22×C47—24no—
373C22×C47—24no—
374C22×C47—42no—
375C22×C47—42no—
376C22×C47—42no—
377C22×C47—42no—
378C22×C47—416no—
379C22×C47C2×C22⋊Q814yes—
380C22×C47#53214yes—
381C22×C47#54214yes—
382C22×C47D4214yes—
383C22×C47#54814yes—
384C22×C47D4×Q814yes—
385C22×C47#55414yes—
386C22×C47C23×D411yescharacteristic
387C22×C47C23×D411yescharacteristic
388C22×C47C23×Q811yescharacteristic
389C22×C47C22×#4111yescharacteristic
390C22×C47C22×#4111yescharacteristic
391C22×C47C2×H(5,𝔽2)11yescharacteristic
392C22×C47C2×2−1+411yescharacteristic
393C2×D47—24no—
394C2×D47—24no—
395C2×D47—24no—
396C2×D47—42no—
397C2×D47—42no—
398C2×D47—42no—
399C2×D47—42no—
400C2×D47—416no—
401C4×C47—24no—
402C4×C47—24no—
403C4×C47—24no—
404C4×C47—24no—
405C4×C47—42no—
406C4×C47—42no—
407Dic47—24no—
408Dic47—24no—
409Dic47—42no—
410Dic47—42no—
411Dic47—42no—
412Dic47—42no—
413Dic47C2×C22⋊Q818yescomplemented
414C22×C4⋊Q8—471no—
415C22×C22⋊Q8—471no—
416C22×C22⋊Q8D4711yescharacteristic, complemented
417C22×C4×D4—471no—
418#2452—4716no—
419C2×#396—471no—
420C2×#396—471no—
421C2×#393—471no—
422C2×#393—471no—
423C2×#390—471no—
424C2×#390—471no—
425C2×#389—471no—
426C2×#389—471no—
427C2×#385—471no—
428C2×#385—471no—
429C2×C4×C4⋊C4—471no—
430C2×C47—44no—
431C2×C47#245218yescomplemented
432C2×C47C22×C22⋊Q811yescharacteristic
433C2×C47C2×#53211yescharacteristic
434C2×C47C2×#54211yescharacteristic
435C2×C47C2×D4211yescharacteristic
436C2×C47C2×#54811yescharacteristic
437C2×C47C2×D4×Q811yescharacteristic
438C2×C47C2×#55411yescharacteristic
439D47—44no—
440C23×Q8—471no—
441C23×Q8C2×D4711yescharacteristic
442C23×D4—471no—
443C24×C4—471no—
444C24×C4C2×D4711yescharacteristic
445C2×C4⋊Q8—478no—
446C2×C4⋊Q8—948no—
447C2×C22⋊Q8—28no—
448C2×C22⋊Q8—478no—
449C2×C22⋊Q8—948no—
450C2×C22⋊Q8C2×D4718yescomplemented
451C2×C4×D4—478no—
452C2×C4×D4—948no—
453C22×C4⋊C4—471no—
454C22×C4⋊C4—471no—
455C22×C4⋊C4—471no—
456C22×C4⋊C4—471no—
457C22×C4⋊C4—471no—
458C22×C4⋊C4—471no—
459C22×C4⋊C4—471no—
460C22×C4⋊C4—471no—
461C22×C4⋊C4C2×D4711yescharacteristic
462C22×C4⋊C4C2×D4711yescharacteristic
463C22×C4⋊C4C2×D4711yescharacteristic
464C22×C22⋊C4—471no—
465C22×C22⋊C4—471no—
466C22×C22⋊C4—471no—
467C22×C22⋊C4—471no—
468C22×C22⋊C4—471no—
469C22×C22⋊C4—471no—
470C22×C22⋊C4—471no—
471C22×C22⋊C4—471no—
472C22×C22⋊C4C2×D4711yescharacteristic
473C22×C22⋊C4C2×D4711yescharacteristic
474C22×C42—471no—
475C22×C42—471no—
476C22×C42—471no—
477#396—478no—
478#396—478no—
479#393—478no—
480#393—478no—
481#390—478no—
482#390—478no—
483#389—478no—
484#389—478no—
485#385—478no—
486#385—478no—
487C4×C4⋊C4—478no—
488C2×#95—471no—
489C2×#95—471no—
490C2×#95—471no—
491C2×#95—471no—
492C2×#95—471no—
493C2×#95—471no—
494C47C2×#245211yescharacteristic, complemented, Sylow
495C25—471no—
496C25C22×D4711yescharacteristic
497C22×Q8—24no—
498C22×Q8—24no—
499C22×Q8—42no—
500C22×Q8—474no—
501C22×Q8—944no—
502C22×Q8—944no—
503C22×Q8—1882no—
504C22×Q8C22×D4714yes—
505C22×D4—478no—
506C22×D4—474no—
507C22×D4—944no—
508C22×D4—944no—
509C23×C4—24no—
510C23×C4—24no—
511C23×C4—42no—
512C23×C4—471no—
513C23×C4—471no—
514C23×C4—471no—
515C23×C4—471no—
516C23×C4—471no—
517C23×C4—471no—
518C23×C4—471no—
519C23×C4—474no—
520C23×C4—944no—
521C23×C4—944no—
522C23×C4—1882no—
523C23×C4C22×D4711yescharacteristic
524C23×C4C22×D4711yescharacteristic
525C23×C4C22×D4714yes—
526C23×C4C22×D4711yescharacteristic
527C23×C4C22×D4711yescharacteristic
528C23×C4C22×D4711yescharacteristic
529C23×C4C22×D4711yescharacteristic
530C4⋊Q8—9432no—
531C22⋊Q8—232no—
532C22⋊Q8—9432no—
533C4×D4—9432no—
534C2×C4⋊C4—24no—
535C2×C4⋊C4—24no—
536C2×C4⋊C4—478no—
537C2×C4⋊C4—474no—
538C2×C4⋊C4—474no—
539C2×C4⋊C4—474no—
540C2×C4⋊C4—474no—
541C2×C4⋊C4—474no—
542C2×C4⋊C4—474no—
543C2×C4⋊C4—474no—
544C2×C4⋊C4—474no—
545C2×C4⋊C4—944no—
546C2×C4⋊C4—944no—
547C2×C4⋊C4—944no—
548C2×C4⋊C4—944no—
549C2×C4⋊C4—944no—
550C2×C4⋊C4—944no—
551C2×C4⋊C4—944no—
552C2×C4⋊C4C22⋊D4718yescomplemented
553C2×C4⋊C4C22×D4714yes—
554C2×C4⋊C4C22×D4714yes—
555C2×C4⋊C4C22×D4714yes—
556C2×C22⋊C4—24no—
557C2×C22⋊C4—24no—
558C2×C22⋊C4—474no—
559C2×C22⋊C4—474no—
560C2×C22⋊C4—474no—
561C2×C22⋊C4—474no—
562C2×C22⋊C4—474no—
563C2×C22⋊C4—474no—
564C2×C22⋊C4—474no—
565C2×C22⋊C4—474no—
566C2×C22⋊C4—944no—
567C2×C22⋊C4—944no—
568C2×C22⋊C4—944no—
569C2×C22⋊C4—944no—
570C2×C22⋊C4—944no—
571C2×C22⋊C4—944no—
572C2×C22⋊C4—1882no—
573C2×C22⋊C4—1882no—
574C2×C22⋊C4C22×D4714yes—
575C2×C22⋊C4C22×D4714yes—
576C2×C42—474no—
577C2×C42—474no—
578C2×C42—474no—
579C2×C42—944no—
580C2×C42—944no—
581C2×C42—944no—
582#95—474no—
583#95—474no—
584#95—474no—
585#95—474no—
586#95—474no—
587#95—474no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—22no—
593C24—22no—
594C24—474no—
595C24—472no—
596C24—942no—
597C24—942no—
598C24—942no—
599C24—942no—
600C24—942no—
601C24—942no—
602C24Q8×D4714yes—
603C24C23×D4712yes—
604C24C23×D4711yescharacteristic
605C2×Q8—28no—
606C2×Q8—28no—
607C2×Q8—44no—
608C2×Q8—416no—
609C2×Q8—948no—
610C2×Q8—948no—
611C2×Q8—1884no—
612C2×Q8—18816no—
613C2×D4—4716no—
614C2×D4—948no—
615C2×D4—9432no—
616C2×D4—948no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—28no—
632C22×C4—28no—
633C22×C4—44no—
634C22×C4—416no—
635C22×C4—474no—
636C22×C4—474no—
637C22×C4—474no—
638C22×C4—472no—
639C22×C4—474no—
640C22×C4—474no—
641C22×C4—472no—
642C22×C4—472no—
643C22×C4—472no—
644C22×C4—472no—
645C22×C4—472no—
646C22×C4—472no—
647C22×C4—948no—
648C22×C4—942no—
649C22×C4—942no—
650C22×C4—942no—
651C22×C4—942no—
652C22×C4—942no—
653C22×C4—942no—
654C22×C4—942no—
655C22×C4—942no—
656C22×C4—942no—
657C22×C4—942no—
658C22×C4—942no—
659C22×C4—942no—
660C22×C4—942no—
661C22×C4—942no—
662C22×C4—942no—
663C22×C4—942no—
664C22×C4—948no—
665C22×C4—1884no—
666C22×C4—18816no—
667C22×C4D4×D4714yes—
668C22×C4C2×C22⋊D4714yes—
669C22×C4C2×C22⋊D4714yes—
670C22×C4C2×C22⋊D4714yes—
671C22×C4C23×D4712yes—
672C22×C4C23×D4712yes—
673C22×C4C23×D4712yes—
674C22×C4C23×D4712yes—
675C22×C4C23×D4712yes—
676C22×C4C23×D4712yes—
677C4⋊C4—28no—
678C4⋊C4—28no—
679C4⋊C4—4716no—
680C4⋊C4—948no—
681C4⋊C4—948no—
682C4⋊C4—948no—
683C4⋊C4—948no—
684C4⋊C4—948no—
685C4⋊C4—948no—
686C4⋊C4—948no—
687C4⋊C4C2×C22⋊D47116yescomplemented
688C22⋊C4—28no—
689C22⋊C4—28no—
690C22⋊C4—948no—
691C22⋊C4—948no—
692C22⋊C4—948no—
693C22⋊C4—948no—
694C22⋊C4—948no—
695C22⋊C4—948no—
696C22⋊C4—1884no—
697C22⋊C4—1884no—
698C42—948no—
699C42—948no—
700C42—948no—
701C23—28no—
702C23—28no—
703C23—28no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—44no—
711C23—44no—
712C23—44no—
713C23—44no—
714C23—474no—
715C23—948no—
716C23—948no—
717C23—948no—
718C23—942no—
719C23—942no—
720C23—942no—
721C23—942no—
722C23—942no—
723C23—942no—
724C23—1884no—
725C23—1884no—
726C23—1884no—
727C23—1884no—
728C23C2×D4×D4712yes—
729C23C22×C22⋊D4712yes—
730C23C2×Q8×D4714yes—
731C23C2×Q8×D4712yes—
732C23#41×D4712yes—
733C23#41×D4712yes—
734C23#1309406912yes—
735C23#1309407212yes—
736C23C24×D4711yescharacteristic
737Q8—416no—
738Q8—18816no—
739D4—9432no—
740C2×C4—28no—
741C2×C4—28no—
742C2×C4—28no—
743C2×C4—28no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—416no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—4716no—
762C2×C4—474no—
763C2×C4—474no—
764C2×C4—474no—
765C2×C4—474no—
766C2×C4—474no—
767C2×C4—948no—
768C2×C4—948no—
769C2×C4—942no—
770C2×C4—942no—
771C2×C4—942no—
772C2×C4—942no—
773C2×C4—942no—
774C2×C4—942no—
775C2×C4—942no—
776C2×C4—942no—
777C2×C4—942no—
778C2×C4—942no—
779C2×C4—942no—
780C2×C4—942no—
781C2×C4—942no—
782C2×C4—942no—
783C2×C4—942no—
784C2×C4—942no—
785C2×C4—18816no—
786C2×C4—1884no—
787C2×C4—1884no—
788C2×C4—1884no—
789C2×C4—1884no—
790C2×C4C2×D4×D4714yes—
791C2×C4C22×C22⋊D4714yes—
792C2×C4C22×C22⋊D4714yes—
793C2×C4C22×C22⋊D4714yes—
794C22—24no—
795C22—24no—
796C22—24no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—416no—
801C22—42no—
802C22—944no—
803C22—944no—
804C22—944no—
805C22—1882no—
806C22—1882no—
807C22—1882no—
808C22—18816no—
809C22—1882no—
810C22C22⋊Q8×D4714yes—
811C22#1568966914yes—
812C22#1568974314yes—
813C22D4×C22⋊D4714yes—
814C22#1568978314yes—
815C22Q8×C22⋊D4714yes—
816C22#1568982714yes—
817C22C22×D4×D4711yescharacteristic
818C22C23×C22⋊D4711yescharacteristic
819C22C22×Q8×D4711yescharacteristic
820C22C2×#41×D4711yescharacteristic
821C22C2×#41×D4711yescharacteristic
822C22C2×#1309406911yescharacteristic
823C22C2×#1309407211yescharacteristic
824C4—24no—
825C4—24no—
826C4—24no—
827C4—24no—
828C4—42no—
829C4—42no—
830C4—478no—
831C4—944no—
832C4—944no—
833C4—1882no—
834C4—1882no—
835C4—1882no—
836C4—1882no—
837C2—44no—
838C2—1884no—
839C2#2024723718yesdirect product factor
840C2C2×C22⋊Q8×D4711yescharacteristic
841C2C2×#1568966911yescharacteristic
842C2C2×#1568974311yescharacteristic
843C2C2×D4×C22⋊D4711yescharacteristic
844C2C2×#1568978311yescharacteristic
845C2C2×Q8×C22⋊D4711yescharacteristic
846C2C2×#1568982711yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC22×C22⋊Q8×C47C2
socleC24×C47C24
prime radicalC23×C22⋊D47C22
hypercenterC22×C22⋊Q8D47
hypocenterC47C2×#2452
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
2. C22×#13094002C2semidirect
4. #20247237C2direct (N × H)
5. C2×#15689046C2semidirect
6. C2×#15689045C2semidirect
7. C2×#15689035C2semidirect
8. C2×#15689034C2semidirect
11. C2×#15689018C2semidirect
12. C2×#15689018C2semidirect
13. C2×#15688996C2semidirect
14. C2×#15688994C2semidirect
15. C2×C4⋊C4×Dic47C2semidirect
16. C22×C22⋊Q8×C47C2semidirect
21. C2×#13094022C22semidirect
23. C2×#13094002C22semidirect
45. #15689046C22semidirect
46. #15689045C22semidirect
47. #15689035C22semidirect
48. #15689034C22semidirect
51. #15689018C22semidirect
52. #15689018C22semidirect
53. #15688996C22semidirect
54. #15688994C22semidirect
55. C4⋊C4×Dic47C22semidirect
65. C2×C22⋊Q8×C47C22semidirect
78. C22×C22⋊D47Q8semidirect
156. C2×C4⋊C4×C47D4semidirect
216. C2×C22⋊D47C2×Q8semidirect
255. C4⋊C4×C47C2×D4semidirect
362. C2×Dic47C22⋊Q8semidirect
413. Dic47C2×C22⋊Q8semidirect
416. C22×C22⋊Q8D47semidirect
431. C2×C47#2452semidirect
450. C2×C22⋊Q8C2×D47semidirect
494. C47C2×#2452semidirect
552. C2×C4⋊C4C22⋊D47semidirect
687. C4⋊C4C2×C22⋊D47semidirect
839. C2#20247237direct (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×#130940022
C22×C4×C22⋊D472
#202472372
C2×#156890462
C2×#156890452
C2×#156890352
C2×#156890342
C2×#156890232
C2×#156890182
C2×#156889962
C2×#156889942
C2×C4⋊C4×Dic472
C22×C22⋊Q8×C472
C2×#245247