Finite Group Databasebeta

← C2×#20246401 #26375804

Subgroups — C2×#20246401 #26375804

Order 12032.

4782 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093997C211yesmaximal, characteristic
2C22×C4×D188C211yesmaximal, characteristic, complemented
3C22×(C22⋊D47)⋊C4C211yesmaximal, characteristic, complemented
4C22×(C22⋊D47)⋊C4C211yesmaximal, characteristic, complemented
5C22×C4⋊C4×D47C211yesmaximal, characteristic, complemented
6#20246401C2116yesmaximal, direct product factor
7C2×#15689023C211yesmaximal, characteristic, complemented
8C2×#15689020C211yesmaximal, characteristic, complemented
9C2×#15689015C211yesmaximal, characteristic, complemented
10C2×#15689001C211yesmaximal, characteristic, complemented
11C2×#15688999C211yesmaximal, characteristic, complemented
12C2×#15688998C211yesmaximal, characteristic, complemented
13C2×#15688994C211yesmaximal, characteristic, complemented
14C2×C4×Dic47⋊C4C211yesmaximal, characteristic, complemented
15C2×#15688970C211yesmaximal, characteristic, complemented
16C2×C47×#388C211yesmaximal, characteristic, complemented
17C23×D188C2211yescharacteristic
18C23×C22⋊D47C2211yescharacteristic
19C23×C22⋊D47C2211yescharacteristic
20C24×Dic47C2211yescharacteristic
21C23×C4×D47C2211yescharacteristic
22C23×C4×D47C2211yescharacteristic
23C23×C4×D47C2211yescharacteristic
24C23×C4×D47C2211yescharacteristic
25C2×#13093997C4116yescomplemented
26C2×#13093997C2218yes—
27C2×C4×D188—28no—
28C2×C4×D188C2218yescomplemented
29C2×(C22⋊D47)⋊C4—28no—
30C2×(C22⋊D47)⋊C4—28no—
31C2×(C22⋊D47)⋊C4C2218yescomplemented
32C2×(C22⋊D47)⋊C4C2218yescomplemented
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×(C2×D47)⋊C4C2211yescharacteristic
43C22×(C2×D47)⋊C4C2211yescharacteristic
44C22×(C2×D47)⋊C4C2211yescharacteristic
45C22×(C2×D47)⋊C4C2211yescharacteristic
46C22×(C2×D47)⋊C4C2211yescharacteristic
47C22×(C2×D47)⋊C4C2211yescharacteristic
48C22×C4×Dic47C2211yescharacteristic
49C22×C4×Dic47C2211yescharacteristic
50C22×C4×Dic47C2211yescharacteristic
51#15689023C2218yescomplemented
52#15689020C2218yescomplemented
53#15689015C2218yescomplemented
54#15689001C2218yescomplemented
55#15688999C2218yescomplemented
56#15688998C2218yescomplemented
57#15688994C2218yescomplemented
58C4×Dic47⋊C4C2218yescomplemented
59#15688970C2218yescomplemented
60C2×C47⋊#95C2211yescharacteristic
61C2×C47⋊#95C2211yescharacteristic
62C2×C47⋊#95C2211yescharacteristic
63C2×C47⋊#95C2211yescharacteristic
64C22×C4⋊C4×C47C2211yescharacteristic
65C22×C22⋊C4×C47C2211yescharacteristic
66C22×C22⋊C4×C47C2211yescharacteristic
67C22×C22⋊C4×C47C2211yescharacteristic
68C22×C42×C47C2211yescharacteristic
69C47×#388C2218yescomplemented
70C2×#95×C47C2211yescharacteristic
71C2×#95×C47C2211yescharacteristic
72C24×D47C2311yescharacteristic
73C24×D47C2311yescharacteristic
74C22×D188—24no—
75C22×D188—24no—
76C22×D188C2×C418yescomplemented
77C22×D188C2314yes—
78C22×C22⋊D47—24no—
79C22×C22⋊D47—24no—
80C22×C22⋊D47—24no—
81C22×C22⋊D47—24no—
82C22×C22⋊D47C2×C418yescomplemented
83C22×C22⋊D47C2×C418yescomplemented
84C22×C22⋊D47C2314yes—
85C22×C22⋊D47C2314yes—
86C23×Dic47—24no—
87C23×Dic47—24no—
88C23×Dic47—42no—
89C23×Dic47C2311yescharacteristic
90C23×Dic47C2311yescharacteristic
91C23×Dic47C2314yes—
92C23×Dic47C2311yescharacteristic
93C23×Dic47C2311yescharacteristic
94C23×Dic47C2311yescharacteristic
95C23×Dic47C2311yescharacteristic
96C22×C4×D47—24no—
97C22×C4×D47—24no—
98C22×C4×D47—24no—
99C22×C4×D47—24no—
100C22×C4×D47—24no—
101C22×C4×D47—24no—
102C22×C4×D47—24no—
103C22×C4×D47—24no—
104C22×C4×D47—42no—
105C22×C4×D47—42no—
106C22×C4×D47—42no—
107C22×C4×D47C2×C418yescomplemented
108C22×C4×D47C2314yes—
109C22×C4×D47C2314yes—
110C22×C4×D47C2314yes—
111C22×C4×D47C2314yes—
112#13093997C2×C4164yescomplemented
113C4×D188—232no—
114(C22⋊D47)⋊C4—232no—
115(C22⋊D47)⋊C4—232no—
116C2×C4⋊Dic47—24no—
117C2×C4⋊Dic47—24no—
118C2×C4⋊Dic47C2314yes—
119C2×C4⋊Dic47C2314yes—
120C2×Dic47⋊C4—24no—
121C2×Dic47⋊C4—24no—
122C2×Dic47⋊C4C2×C418yescomplemented
123C2×Dic47⋊C4D418yescomplemented
124C2×Dic47⋊C4C2314yes—
125C2×Dic47⋊C4C2314yes—
126C2×Dic47⋊C4C2314yes—
127C2×Dic47⋊C4C2314yes—
128C4⋊C4×D47—232no—
129C2×C22⋊Dic47—42no—
130C2×C22⋊Dic47C2314yes—
131C2×(C2×D47)⋊C4—24no—
132C2×(C2×D47)⋊C4—24no—
133C2×(C2×D47)⋊C4—24no—
134C2×(C2×D47)⋊C4—42no—
135C2×(C2×D47)⋊C4C2×C418yescomplemented
136C2×(C2×D47)⋊C4D418yescomplemented
137C2×(C2×D47)⋊C4C2314yes—
138C2×(C2×D47)⋊C4C2314yes—
139C2×(C2×D47)⋊C4C2314yes—
140C2×(C2×D47)⋊C4C2314yes—
141C2×(C2×D47)⋊C4C2314yes—
142C2×(C2×D47)⋊C4C2314yes—
143C2×C4×Dic47—24no—
144C2×C4×Dic47—24no—
145C2×C4×Dic47—24no—
146C2×C4×Dic47C2314yes—
147C2×C4×Dic47C2314yes—
148C2×C4×Dic47C2314yes—
149C47⋊#95C2314yes—
150C47⋊#95C2314yes—
151C47⋊#95C2314yes—
152C47⋊#95C2314yes—
153C25×C47C2311yescharacteristic
154C23×C4×C47C2311yescharacteristic
155C23×C4×C47C2311yescharacteristic
156C23×C4×C47C2311yescharacteristic
157C23×C4×C47C2311yescharacteristic
158C23×C4×C47C2311yescharacteristic
159C23×C4×C47C2311yescharacteristic
160C2×C4⋊C4×C47—24no—
161C2×C4⋊C4×C47C2314yes—
162C2×C22⋊C4×C47—24no—
163C2×C22⋊C4×C47—24no—
164C2×C22⋊C4×C47C2×C418yescomplemented
165C2×C22⋊C4×C47C2314yes—
166C2×C22⋊C4×C47C2314yes—
167C2×C22⋊C4×C47C2314yes—
168C2×C42×C47—24no—
169C2×C42×C47C2314yes—
170#95×C47C2314yes—
171#95×C47C2314yes—
172C24×C47—22no—
173C24×C47—22no—
174C24×C47—22no—
175C24×C47—22no—
176C24×C47—22no—
177C24×C47—22no—
178C24×C47C22×C414yes—
179C24×C47C2412yes—
180C24×C47C2411yescharacteristic
181C23×D47—22no—
182C23×D47—22no—
183C23×D47—22no—
184C23×D47—22no—
185C23×D47—22no—
186C23×D47—22no—
187C23×D47—22no—
188C23×D47—22no—
189C23×D47—22no—
190C23×D47—22no—
191C23×D47C22×C414yes—
192C23×D47C22×C414yes—
193C23×D47C2×D414yes—
194C23×D47#4114yes—
195C23×D47C2412yes—
196C23×D47C2412yes—
197C22×C4×C47—22no—
198C22×C4×C47—22no—
199C22×C4×C47—22no—
200C22×C4×C47—22no—
201C22×C4×C47—22no—
202C22×C4×C47—22no—
203C22×C4×C47—22no—
204C22×C4×C47—22no—
205C22×C4×C47—22no—
206C22×C4×C47—22no—
207C22×C4×C47—22no—
208C22×C4×C47—22no—
209C22×C4×C47—22no—
210C22×C4×C47—22no—
211C22×C4×C47C22×C414yes—
212C22×C4×C47C22×C414yes—
213C22×C4×C47C2×D414yes—
214C22×C4×C47C2×D414yes—
215C22×C4×C47C2412yes—
216C22×C4×C47C2412yes—
217C22×C4×C47C2412yes—
218C22×C4×C47C2412yes—
219C22×C4×C47C2412yes—
220C22×C4×C47C2412yes—
221C2×C22⋊D47—232no—
222C2×C22⋊D47—28no—
223C2×C22⋊D47—28no—
224C2×C22⋊D47—232no—
225C2×C22⋊D47—28no—
226C2×C22⋊D47—28no—
227C2×C22⋊D47C22×C4116yescomplemented
228C2×C22⋊D47C22×C4116yescomplemented
229C22×Dic47—22no—
230C22×Dic47—22no—
231C22×Dic47—22no—
232C22×Dic47—22no—
233C22×Dic47—22no—
234C22×Dic47—22no—
235C22×Dic47—22no—
236C22×Dic47—22no—
237C22×Dic47—22no—
238C22×Dic47—22no—
239C22×Dic47—22no—
240C22×Dic47—22no—
241C22×Dic47—28no—
242C22×Dic47—28no—
243C22×Dic47—44no—
244C22×Dic47—416no—
245C22×Dic47C22×C414yes—
246C22×Dic47C22×C414yes—
247C22×Dic47C2×D414yes—
248C22×Dic47C2×D414yes—
249C22×Dic47C2×D414yes—
250C22×Dic47#4114yes—
251C22×Dic47C2412yes—
252C22×Dic47C2412yes—
253C22×Dic47C2412yes—
254C22×Dic47C2412yes—
255C22×Dic47C2412yes—
256C22×Dic47C2412yes—
257C2×D188—232no—
258C2×D188—28no—
259C2×D188—28no—
260C2×D188C22×C4116yescomplemented
261C2×C4×D47—232no—
262C2×C4×D47—28no—
263C2×C4×D47—28no—
264C2×C4×D47—28no—
265C2×C4×D47—28no—
266C2×C4×D47—28no—
267C2×C4×D47—28no—
268C2×C4×D47—28no—
269C2×C4×D47—28no—
270C2×C4×D47—44no—
271C2×C4×D47—44no—
272C2×C4×D47—44no—
273C2×C4×D47—416no—
274C2×C4×D47—416no—
275C2×C4×D47—416no—
276C2×C4×D47C22×C4116yescomplemented
277C4⋊C4×C47—28no—
278C22⋊C4×C47—28no—
279C22⋊C4×C47—28no—
280C22⋊C4×C47C22×C4116yescomplemented
281C42×C47—28no—
282C22⋊Dic47—44no—
283(C2×D47)⋊C4—28no—
284(C2×D47)⋊C4—28no—
285(C2×D47)⋊C4—28no—
286(C2×D47)⋊C4—44no—
287(C2×D47)⋊C4C22×C4116yescomplemented
288(C2×D47)⋊C4C2×D4116yescomplemented
289C4⋊Dic47—28no—
290C4⋊Dic47—28no—
291Dic47⋊C4—28no—
292Dic47⋊C4—28no—
293Dic47⋊C4C22×C4116yescomplemented
294Dic47⋊C4C2×D4116yescomplemented
295C4×Dic47—28no—
296C4×Dic47—28no—
297C4×Dic47—28no—
298C23×C47—28no—
299C23×C47—28no—
300C23×C47—28no—
301C23×C47—22no—
302C23×C47—22no—
303C23×C47—22no—
304C23×C47—22no—
305C23×C47—22no—
306C23×C47—22no—
307C23×C47—44no—
308C23×C47—44no—
309C23×C47—44no—
310C23×C47—44no—
311C23×C47C23×C414yes—
312C23×C47C23×C412yes—
313C23×C47C22×D412yes—
314C23×C47C22×D412yes—
315C23×C47C2×#4112yes—
316C23×C47C2×#4112yes—
317C23×C47H(5,𝔽2)12yes—
318C23×C472−1+412yes—
319C23×C47C2511yescharacteristic
320C22×D47—28no—
321C22×D47—28no—
322C22×D47—28no—
323C22×D47—28no—
324C22×D47—28no—
325C22×D47—28no—
326C22×D47—22no—
327C22×D47—22no—
328C22×D47—22no—
329C22×D47—22no—
330C22×D47—28no—
331C22×D47—28no—
332C22×D47—28no—
333C22×D47—22no—
334C22×D47—22no—
335C22×D47—22no—
336C22×D47—22no—
337C22×D47—22no—
338C22×D47—22no—
339C22×D47—44no—
340C22×D47—44no—
341C22×D47—44no—
342C22×D47—44no—
343C22×D47C4×D4116yescomplemented
344C22×D47C23×C414yes—
345C22×D47C23×C414yes—
346C22×D47C22×D414yes—
347C22×D47C2×#4114yes—
348C2×C4×C47—28no—
349C2×C4×C47—28no—
350C2×C4×C47—28no—
351C2×C4×C47—28no—
352C2×C4×C47—22no—
353C2×C4×C47—22no—
354C2×C4×C47—22no—
355C2×C4×C47—22no—
356C2×C4×C47—22no—
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—44no—
367C2×C4×C47—44no—
368C2×C4×C47C23×C414yes—
369C2×C4×C47C23×C414yes—
370C2×C4×C47C22×D414yes—
371C2×C4×C47C22×D414yes—
372C22⋊D47—232no—
373C22⋊D47—232no—
374C2×Dic47—28no—
375C2×Dic47—28no—
376C2×Dic47—28no—
377C2×Dic47—22no—
378C2×Dic47—22no—
379C2×Dic47—22no—
380C2×Dic47—22no—
381C2×Dic47—22no—
382C2×Dic47—22no—
383C2×Dic47—22no—
384C2×Dic47—22no—
385C2×Dic47—22no—
386C2×Dic47—22no—
387C2×Dic47—22no—
388C2×Dic47—22no—
389C2×Dic47—416no—
390C2×Dic47—44no—
391C2×Dic47—44no—
392C2×Dic47C4×D4116yescomplemented
393C2×Dic47C23×C414yes—
394C2×Dic47C23×C414yes—
395C2×Dic47C22×D414yes—
396C2×Dic47C22×D414yes—
397C2×Dic47C22×D414yes—
398C2×Dic47C2×#4114yes—
399D188—232no—
400C4×D47—232no—
401C4×D47—416no—
402C4×D47—416no—
403C4×D47—416no—
404C2×#2361—471nomaximal, Sylow
405C22×C47—24no—
406C22×C47—24no—
407C22×C47—24no—
408C22×C47—416no—
409C22×C47—42no—
410C22×C47—42no—
411C22×C47—42no—
412C22×C47—42no—
413C22×C47C2×C4×D414yes—
414C22×C47C2×C4×D414yes—
415C22×C47#52014yes—
416C22×C47D4214yes—
417C22×C47#54714yes—
418C22×C47#54814yes—
419C22×C47#55314yes—
420C22×C47C24×C411yescharacteristic
421C22×C47C23×D411yescharacteristic
422C22×C47C23×D411yescharacteristic
423C22×C47C22×#4111yescharacteristic
424C22×C47C22×#4111yescharacteristic
425C22×C47C2×H(5,𝔽2)11yescharacteristic
426C22×C47C2×2−1+411yescharacteristic
427C2×D47—232no—
428C2×D47—24no—
429C2×D47—24no—
430C2×D47—24no—
431C2×D47—24no—
432C2×D47—24no—
433C2×D47—24no—
434C2×D47—24no—
435C2×D47—24no—
436C2×D47—24no—
437C2×D47—416no—
438C2×D47—42no—
439C2×D47—42no—
440C2×D47—42no—
441C2×D47—42no—
442C2×D47C2×C4×D418yescomplemented
443C4×C47—24no—
444C4×C47—24no—
445C4×C47—24no—
446C4×C47—24no—
447C4×C47—42no—
448C4×C47—42no—
449Dic47—24no—
450Dic47—24no—
451Dic47—24no—
452Dic47—42no—
453Dic47—42no—
454Dic47C2×C4×D418yescomplemented
455C22×#121—471no—
456C22×C4×D4—471no—
457C22×C4×D4—471no—
458C22×C4×D4—471no—
459C23×C4⋊C4—471no—
460#2361—4716no—
461C2×#390—471no—
462C2×#389—471no—
463C2×#388—471no—
464C2×#388D4711yescharacteristic, complemented
465C2×#386—471no—
466C2×#386—471no—
467C2×#385—471no—
468C2×#385—471no—
469C2×C4×C4⋊C4—471no—
470C2×C4×C22⋊C4—471no—
471C2×C47—44no—
472C2×C47#236118yescomplemented
473C2×C47C22×C4×D411yescharacteristic
474C2×C47C22×C4×D411yescharacteristic
475C2×C47C2×#52011yescharacteristic
476C2×C47C2×D4211yescharacteristic
477C2×C47C2×#54711yescharacteristic
478C2×C47C2×#54811yescharacteristic
479C2×C47C2×#55311yescharacteristic
480D47—28no—
481D47—44no—
482C23×D4—471no—
483C23×D4—471no—
484C23×D4—471no—
485C24×C4—471no—
486C24×C4—471no—
487C24×C4—471no—
488C24×C4—471no—
489C24×C4—471no—
490C2×#121—4716no—
491C2×#121—478no—
492C2×C4×D4—478no—
493C2×C4×D4—478no—
494C2×C4×D4—478no—
495C2×C4×D4—948no—
496C2×C4×D4—948no—
497C2×C4×D4—948no—
498C22×C4⋊C4—471no—
499C22×C4⋊C4—471no—
500C22×C4⋊C4—471no—
501C22×C4⋊C4—471no—
502C22×C4⋊C4—471no—
503C22×C4⋊C4—471no—
504C22×C4⋊C4—478no—
505C22×C4⋊C4—948no—
506C22×C4⋊C4C2×D4711yescharacteristic
507C22×C22⋊C4—471no—
508C22×C22⋊C4—471no—
509C22×C22⋊C4—471no—
510C22×C22⋊C4—471no—
511C22×C22⋊C4—471no—
512C22×C22⋊C4—471no—
513C22×C22⋊C4—471no—
514C22×C22⋊C4C2×D4711yescharacteristic
515C22×C22⋊C4C2×D4711yescharacteristic
516C22×C22⋊C4C2×D4711yescharacteristic
517C22×C42—471no—
518C22×C42—471no—
519C22×C42—471no—
520C22×C42C2×D4711yescharacteristic
521#390—478no—
522#389—478no—
523#388—478no—
524#388C2×D4718yescomplemented
525#386—478no—
526#386—478no—
527#385—478no—
528#385—478no—
529C4×C4⋊C4—478no—
530C4×C22⋊C4—478no—
531C2×#95—471no—
532C2×#95—471no—
533C2×#95—471no—
534C2×#95—471no—
535C2×#95C2×D4711yescharacteristic
536C2×#95C2×D4711yescharacteristic
537C47C2×#236111yescharacteristic, complemented, Sylow
538C25—471no—
539C25—471no—
540C25C22×D4711yescharacteristic
541C22×D4—478no—
542C22×D4—478no—
543C22×D4—474no—
544C22×D4—474no—
545C22×D4—478no—
546C22×D4—474no—
547C22×D4—944no—
548C22×D4—944no—
549C22×D4—944no—
550C22×D4—944no—
551C22×D4—944no—
552C22×D4—944no—
553C23×C4—471no—
554C23×C4—471no—
555C23×C4—471no—
556C23×C4—471no—
557C23×C4—478no—
558C23×C4—474no—
559C23×C4—471no—
560C23×C4—471no—
561C23×C4—474no—
562C23×C4—474no—
563C23×C4—474no—
564C23×C4—474no—
565C23×C4—944no—
566C23×C4—944no—
567C23×C4—944no—
568C23×C4—944no—
569C23×C4—944no—
570C23×C4—944no—
571C23×C4—944no—
572C23×C4—944no—
573C23×C4—944no—
574C23×C4—944no—
575C23×C4—1882no—
576C23×C4—1882no—
577C23×C4—1882no—
578C23×C4—1882no—
579C23×C4C22×D4711yescharacteristic
580C23×C4C22×D4711yescharacteristic
581C23×C4C22×D4711yescharacteristic
582C23×C4C22×D4711yescharacteristic
583C23×C4C22×D4711yescharacteristic
584C23×C4C22×D4711yescharacteristic
585#121—4764no—
586C4×D4—9432no—
587C4×D4—9432no—
588C4×D4—9432no—
589C2×C4⋊C4—24no—
590C2×C4⋊C4—478no—
591C2×C4⋊C4—478no—
592C2×C4⋊C4—474no—
593C2×C4⋊C4—474no—
594C2×C4⋊C4—474no—
595C2×C4⋊C4—474no—
596C2×C4⋊C4—474no—
597C2×C4⋊C4—474no—
598C2×C4⋊C4—9432no—
599C2×C4⋊C4—944no—
600C2×C4⋊C4—944no—
601C2×C4⋊C4—944no—
602C2×C4⋊C4—944no—
603C2×C4⋊C4C22×D4714yes—
604C2×C22⋊C4—24no—
605C2×C22⋊C4—24no—
606C2×C22⋊C4—478no—
607C2×C22⋊C4—478no—
608C2×C22⋊C4—474no—
609C2×C22⋊C4—474no—
610C2×C22⋊C4—474no—
611C2×C22⋊C4—474no—
612C2×C22⋊C4—474no—
613C2×C22⋊C4—474no—
614C2×C22⋊C4—474no—
615C2×C22⋊C4—944no—
616C2×C22⋊C4—944no—
617C2×C22⋊C4—944no—
618C2×C22⋊C4—1882no—
619C2×C22⋊C4—1882no—
620C2×C22⋊C4C4×D4718yescomplemented
621C2×C22⋊C4C22×D4714yes—
622C2×C22⋊C4C22×D4714yes—
623C2×C22⋊C4C22×D4714yes—
624C2×C42—24no—
625C2×C42—474no—
626C2×C42—474no—
627C2×C42—474no—
628C2×C42—944no—
629C2×C42—944no—
630C2×C42—944no—
631C2×C42C22×D4714yes—
632#95—474no—
633#95—474no—
634#95—474no—
635#95—474no—
636#95C22×D4714yes—
637#95C22×D4714yes—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—474no—
645C24—474no—
646C24—474no—
647C24—472no—
648C24—474no—
649C24—472no—
650C24—942no—
651C24—942no—
652C24—942no—
653C24—942no—
654C24—942no—
655C24—942no—
656C24—942no—
657C24—942no—
658C24—942no—
659C24—942no—
660C24C2×C4×D4714yes—
661C24C23×D4712yes—
662C24C23×D4711yescharacteristic
663C2×D4—4716no—
664C2×D4—4716no—
665C2×D4—4716no—
666C2×D4—948no—
667C2×D4—9432no—
668C2×D4—948no—
669C2×D4—948no—
670C2×D4—9432no—
671C2×D4—948no—
672C2×D4—948no—
673C2×D4—9432no—
674C2×D4—948no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—474no—
690C22×C4—474no—
691C22×C4—474no—
692C22×C4—472no—
693C22×C4—474no—
694C22×C4—474no—
695C22×C4—474no—
696C22×C4—472no—
697C22×C4—472no—
698C22×C4—472no—
699C22×C4—4716no—
700C22×C4—472no—
701C22×C4—472no—
702C22×C4—948no—
703C22×C4—9432no—
704C22×C4—948no—
705C22×C4—948no—
706C22×C4—948no—
707C22×C4—948no—
708C22×C4—948no—
709C22×C4—948no—
710C22×C4—948no—
711C22×C4—942no—
712C22×C4—942no—
713C22×C4—942no—
714C22×C4—942no—
715C22×C4—942no—
716C22×C4—942no—
717C22×C4—942no—
718C22×C4—942no—
719C22×C4—942no—
720C22×C4—942no—
721C22×C4—942no—
722C22×C4—942no—
723C22×C4—948no—
724C22×C4—948no—
725C22×C4—1884no—
726C22×C4—1884no—
727C22×C4—1884no—
728C22×C4—18816no—
729C22×C4—18816no—
730C22×C4—18816no—
731C22×C4—1884no—
732C22×C4—18816no—
733C22×C4C2×C4×D4714yes—
734C22×C4C2×C4×D4714yes—
735C22×C4D4×D4714yes—
736C22×C4D4×D4714yes—
737C22×C4C23×D4712yes—
738C22×C4C23×D4712yes—
739C22×C4C23×D4712yes—
740C22×C4C23×D4712yes—
741C22×C4C23×D4712yes—
742C22×C4C23×D4712yes—
743C4⋊C4—28no—
744C4⋊C4—4716no—
745C4⋊C4—4716no—
746C4⋊C4—948no—
747C4⋊C4—948no—
748C4⋊C4—948no—
749C4⋊C4—948no—
750C22⋊C4—28no—
751C22⋊C4—28no—
752C22⋊C4—4716no—
753C22⋊C4—4716no—
754C22⋊C4—948no—
755C22⋊C4—948no—
756C22⋊C4—948no—
757C22⋊C4—1884no—
758C22⋊C4—1884no—
759C22⋊C4C2×C4×D47116yescomplemented
760C42—28no—
761C42—948no—
762C42—948no—
763C42—948no—
764C23—28no—
765C23—28no—
766C23—28no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—44no—
774C23—44no—
775C23—44no—
776C23—44no—
777C23—4716no—
778C23—474no—
779C23—474no—
780C23—474no—
781C23—474no—
782C23—948no—
783C23—948no—
784C23—948no—
785C23—948no—
786C23—948no—
787C23—948no—
788C23—942no—
789C23—942no—
790C23—942no—
791C23—942no—
792C23—948no—
793C23—948no—
794C23—948no—
795C23—942no—
796C23—942no—
797C23—942no—
798C23—942no—
799C23—942no—
800C23—942no—
801C23—1884no—
802C23—1884no—
803C23—1884no—
804C23—1884no—
805C23C22×C4×D4714yes—
806C23C22×C4×D4712yes—
807C23C2×D4×D4712yes—
808C23C2×D4×D4712yes—
809C23#41×D4712yes—
810C23#41×D4712yes—
811C23#1309407012yes—
812C23#1309407112yes—
813C23C24×D4711yescharacteristic
814D4—9432no—
815D4—9432no—
816D4—9432no—
817C2×C4—28no—
818C2×C4—28no—
819C2×C4—28no—
820C2×C4—28no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—44no—
836C2×C4—44no—
837C2×C4—4716no—
838C2×C4—474no—
839C2×C4—474no—
840C2×C4—474no—
841C2×C4—474no—
842C2×C4—474no—
843C2×C4—474no—
844C2×C4—9432no—
845C2×C4—948no—
846C2×C4—948no—
847C2×C4—948no—
848C2×C4—942no—
849C2×C4—942no—
850C2×C4—942no—
851C2×C4—942no—
852C2×C4—942no—
853C2×C4—942no—
854C2×C4—942no—
855C2×C4—942no—
856C2×C4—942no—
857C2×C4—942no—
858C2×C4—942no—
859C2×C4—942no—
860C2×C4—18816no—
861C2×C4—18816no—
862C2×C4—18816no—
863C2×C4—18816no—
864C2×C4—1884no—
865C2×C4—1884no—
866C2×C4C22×C4×D4714yes—
867C2×C4C22×C4×D4714yes—
868C2×C4C2×D4×D4714yes—
869C2×C4C2×D4×D4714yes—
870C22—24no—
871C22—24no—
872C22—24no—
873C22—42no—
874C22—42no—
875C22—42no—
876C22—416no—
877C22—42no—
878C22—478no—
879C22—944no—
880C22—944no—
881C22—944no—
882C22—944no—
883C22—944no—
884C22—9432no—
885C22—944no—
886C22—944no—
887C22—944no—
888C22—944no—
889C22—1882no—
890C22—1882no—
891C22—1882no—
892C22—18816no—
893C22—1882no—
894C22C4×D4×D4714yes—
895C22C4×D4×D4714yes—
896C22#1568960314yes—
897C22#1568975714yes—
898C22#1568977114yes—
899C22#1568978114yes—
900C22#1568982414yes—
901C22C23×C4×D4711yescharacteristic
902C22C22×D4×D4711yescharacteristic
903C22C22×D4×D4711yescharacteristic
904C22C2×#41×D4711yescharacteristic
905C22C2×#41×D4711yescharacteristic
906C22C2×#1309407011yescharacteristic
907C22C2×#1309407111yescharacteristic
908C4—24no—
909C4—24no—
910C4—24no—
911C4—24no—
912C4—42no—
913C4—42no—
914C4—478no—
915C4—944no—
916C4—944no—
917C4—944no—
918C4—1882no—
919C4—1882no—
920C2—44no—
921C2—948no—
922C2—1884no—
923C2#2024640118yesdirect product factor
924C2C2×C4×D4×D4711yescharacteristic
925C2C2×C4×D4×D4711yescharacteristic
926C2C2×#1568960311yescharacteristic
927C2C2×#1568975711yescharacteristic
928C2C2×#1568977111yescharacteristic
929C2C2×#1568978111yescharacteristic
930C2C2×#1568982411yescharacteristic
subgroupG/H
centerC24C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC2×C47×#388C2
socleC24×C47C24
prime radicalC22×#13093997C2
cosocleC23×C47C25
hypercenterC2×#388D47
hypocenterC47C2×#2361
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C22×C4×D188C2semidirect
3. C22×(C22⋊D47)⋊C4C2semidirect
4. C22×(C22⋊D47)⋊C4C2semidirect
5. C22×C4⋊C4×D47C2semidirect
6. #20246401C2direct (N × H)
7. C2×#15689023C2semidirect
8. C2×#15689020C2semidirect
9. C2×#15689015C2semidirect
10. C2×#15689001C2semidirect
11. C2×#15688999C2semidirect
12. C2×#15688998C2semidirect
13. C2×#15688994C2semidirect
14. C2×C4×Dic47⋊C4C2semidirect
15. C2×#15688970C2semidirect
16. C2×C47×#388C2semidirect
25. C2×#13093997C4semidirect
28. C2×C4×D188C22semidirect
31. C2×(C22⋊D47)⋊C4C22semidirect
32. C2×(C22⋊D47)⋊C4C22semidirect
40. C2×C4⋊C4×D47C22semidirect
51. #15689023C22semidirect
52. #15689020C22semidirect
53. #15689015C22semidirect
54. #15689001C22semidirect
55. #15688999C22semidirect
56. #15688998C22semidirect
57. #15688994C22semidirect
58. C4×Dic47⋊C4C22semidirect
59. #15688970C22semidirect
69. C47×#388C22semidirect
76. C22×D188C2×C4semidirect
82. C22×C22⋊D47C2×C4semidirect
83. C22×C22⋊D47C2×C4semidirect
107. C22×C4×D47C2×C4semidirect
112. #13093997C2×C4semidirect
122. C2×Dic47⋊C4C2×C4semidirect
123. C2×Dic47⋊C4D4semidirect
135. C2×(C2×D47)⋊C4C2×C4semidirect
136. C2×(C2×D47)⋊C4D4semidirect
164. C2×C22⋊C4×C47C2×C4semidirect
227. C2×C22⋊D47C22×C4semidirect
228. C2×C22⋊D47C22×C4semidirect
260. C2×D188C22×C4semidirect
276. C2×C4×D47C22×C4semidirect
280. C22⋊C4×C47C22×C4semidirect
287. (C2×D47)⋊C4C22×C4semidirect
288. (C2×D47)⋊C4C2×D4semidirect
293. Dic47⋊C4C22×C4semidirect
294. Dic47⋊C4C2×D4semidirect
343. C22×D47C4×D4semidirect
392. C2×Dic47C4×D4semidirect
442. C2×D47C2×C4×D4semidirect
454. Dic47C2×C4×D4semidirect
464. C2×#388D47semidirect
472. C2×C47#2361semidirect
524. #388C2×D47semidirect
537. C47C2×#2361semidirect
620. C2×C22⋊C4C4×D47semidirect
759. C22⋊C4C2×C4×D47semidirect
923. C2#20246401direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130939972
C22×C4×D1882
C22×(C22⋊D47)⋊C42
C22×C4⋊C4×D472
#202464012
C2×#156890232
C2×#156890202
C2×#156890152
C2×#156890012
C2×#156889992
C2×#156889982
C2×#156889942
C2×C4×Dic47⋊C42
C2×#156889702
C2×C47×#3882
C2×#236147