Finite Group Databasebeta

← C2×#20246050 #26374998

Subgroups — C2×#20246050 #26374998

Order 12032.

5094 conjugacy classes of subgroups.

The subgroup lattice has 1000 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093994C211yesmaximal, characteristic
2C22×C4×D188C211yesmaximal, characteristic, complemented
3C22×C22⋊C4×D47C211yesmaximal, characteristic, complemented
4#20246050C2116yesmaximal, direct product factor
5C2×#15689024C211yesmaximal, characteristic, complemented
6C2×#15689023C211yesmaximal, characteristic, complemented
7C2×#15689016C211yesmaximal, characteristic, complemented
8C2×#15689015C211yesmaximal, characteristic, complemented
9C2×#15689014C211yesmaximal, characteristic, complemented
10C2×#15689001C211yesmaximal, characteristic, complemented
11C2×#15689001C211yesmaximal, characteristic, complemented
12C2×#15688999C211yesmaximal, characteristic, complemented
13C2×#15688994C211yesmaximal, characteristic, complemented
14C2×#15688978C211yesmaximal, characteristic, complemented
15C2×#15688970C211yesmaximal, characteristic, complemented
16C2×C47×#388C211yesmaximal, characteristic, complemented
17C25×D47C2211yescharacteristic
18C23×D188C2211yescharacteristic
19C23×D188C2211yescharacteristic
20C23×C22⋊D47C2211yescharacteristic
21C23×C4×D47C2211yescharacteristic
22C23×C4×D47C2211yescharacteristic
23C23×C4×D47C2211yescharacteristic, complemented
24C2×#13093994C4116yescomplemented
25C2×#13093994C2218yes—
26C2×C4×D188—28no—
27C2×C4×D188C2218yescomplemented
28C22×C4⋊Dic47C2211yescharacteristic, complemented
29C22×Dic47⋊C4C2211yescharacteristic, complemented
30C22×C22⋊Dic47C2211yescharacteristic
31C22×C22⋊Dic47C2211yescharacteristic
32C22×(C2×D47)⋊C4C2211yescharacteristic
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, complemented
41C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
42C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
43C2×C22⋊C4×D47—28no—
44C2×C22⋊C4×D47C2218yescomplemented
45C22×C4×Dic47C2211yescharacteristic, complemented
46C22×C4×Dic47C2211yescharacteristic, complemented
47#15689024C2218yescomplemented
48#15689023C2218yescomplemented
49#15689016C2218yescomplemented
50#15689015C2218yescomplemented
51#15689014C2218yescomplemented
52#15689001C2218yescomplemented
53#15689001C2218yescomplemented
54#15688999C2218yescomplemented
55#15688994C2218yescomplemented
56#15688978C2218yescomplemented
57#15688970C2218yescomplemented
58C2×C47⋊#95C2211yescharacteristic, complemented
59C2×C47⋊#95C2211yescharacteristic, complemented
60C2×C47⋊#95C2211yescharacteristic, complemented
61C2×C47⋊#95C2211yescharacteristic, complemented
62C22×C4⋊C4×C47C2211yescharacteristic, complemented
63C22×C22⋊C4×C47C2211yescharacteristic
64C22×C22⋊C4×C47C2211yescharacteristic
65C22×C22⋊C4×C47C2211yescharacteristic
66C22×C42×C47C2211yescharacteristic, complemented
67C47×#388C2218yescomplemented
68C2×#95×C47C2211yescharacteristic, complemented
69C2×#95×C47C2211yescharacteristic, complemented
70C24×D47—24no—
71C24×D47—24no—
72C24×D47—42no—
73C24×D47—42no—
74C24×D47—42no—
75C24×D47—42no—
76C24×D47C2×C418yescomplemented
77C24×D47C2311yescharacteristic
78C24×D47C2311yescharacteristic
79C24×D47C2311yescharacteristic
80C24×D47C2314yes—
81C22×D188—24no—
82C22×D188—24no—
83C22×D188—42no—
84C22×D188—42no—
85C22×D188C2×C418yes—
86C22×D188C2×C418yescomplemented
87C22×D188C2314yes—
88C22×D188C2314yes—
89C22×C22⋊D47—42no—
90C22×C22⋊D47—42no—
91C22×C22⋊D47C2×C418yescomplemented
92C22×C22⋊D47C2314yes—
93C23×Dic47C2311yescharacteristic
94C23×Dic47C2311yescharacteristic
95C23×Dic47C2311yescharacteristic
96C23×Dic47C2311yescharacteristic
97C23×Dic47C2311yescharacteristic
98C22×C4×D47—24no—
99C22×C4×D47—24no—
100C22×C4×D47—42no—
101C22×C4×D47—42no—
102C22×C4×D47—42no—
103C22×C4×D47—42no—
104C22×C4×D47—42no—
105C22×C4×D47—42no—
106C22×C4×D47D418yescomplemented
107C22×C4×D47C2314yes—
108C22×C4×D47C2314yes—
109C22×C4×D47C2314yescomplemented
110#13093994C2×C4164yescomplemented
111C4×D188—232no—
112C2×C4⋊Dic47—24no—
113C2×C4⋊Dic47C2314yescomplemented
114C2×Dic47⋊C4—42no—
115C2×Dic47⋊C4C2314yescomplemented
116C2×C22⋊Dic47—24no—
117C2×C22⋊Dic47—42no—
118C2×C22⋊Dic47C2314yes—
119C2×C22⋊Dic47C2314yes—
120C2×(C2×D47)⋊C4—24no—
121C2×(C2×D47)⋊C4—24no—
122C2×(C2×D47)⋊C4—24no—
123C2×(C2×D47)⋊C4—24no—
124C2×(C2×D47)⋊C4—24no—
125C2×(C2×D47)⋊C4—42no—
126C2×(C2×D47)⋊C4—42no—
127C2×(C2×D47)⋊C4—42no—
128C2×(C2×D47)⋊C4—42no—
129C2×(C2×D47)⋊C4C2×C418yescomplemented
130C2×(C2×D47)⋊C4C2×C418yescomplemented
131C2×(C2×D47)⋊C4C2314yes—
132C2×(C2×D47)⋊C4C2314yes—
133C2×(C2×D47)⋊C4C2314yes—
134C2×(C2×D47)⋊C4C2314yes—
135C2×(C2×D47)⋊C4C2314yes—
136C2×(C2×D47)⋊C4C2314yes—
137C2×(C2×D47)⋊C4C2314yes—
138C2×(C2×D47)⋊C4C2314yes—
139C2×(C2×D47)⋊C4C2314yescomplemented
140C2×(C2×D47)⋊C4C2314yescomplemented
141C2×(C2×D47)⋊C4C2314yescomplemented
142C22⋊C4×D47—232no—
143C2×C4×Dic47—42no—
144C2×C4×Dic47—42no—
145C2×C4×Dic47C2314yescomplemented
146C2×C4×Dic47C2314yescomplemented
147C47⋊#95C2314yescomplemented
148C47⋊#95C2314yescomplemented
149C47⋊#95C2314yescomplemented
150C47⋊#95C2314yescomplemented
151C25×C47C2311yescharacteristic
152C23×C4×C47C2311yescharacteristic
153C23×C4×C47C2311yescharacteristic
154C23×C4×C47C2311yescharacteristic
155C23×C4×C47C2311yescharacteristic
156C23×C4×C47C2311yescharacteristic
157C23×C4×C47C2311yescharacteristic
158C2×C4⋊C4×C47—42no—
159C2×C4⋊C4×C47C2314yescomplemented
160C2×C22⋊C4×C47—24no—
161C2×C22⋊C4×C47—42no—
162C2×C22⋊C4×C47C2×C418yescomplemented
163C2×C22⋊C4×C47C2314yes—
164C2×C22⋊C4×C47C2314yes—
165C2×C22⋊C4×C47C2314yes—
166C2×C42×C47—24no—
167C2×C42×C47C2314yescomplemented
168#95×C47C2314yescomplemented
169#95×C47C2314yescomplemented
170C24×C47—22no—
171C24×C47—22no—
172C24×C47—22no—
173C24×C47—22no—
174C24×C47—22no—
175C24×C47—22no—
176C24×C47C22×C414yes—
177C24×C47C2412yes—
178C24×C47C2411yescharacteristic
179C23×D47—22no—
180C23×D47—22no—
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×D47—22no—
192C23×D47—22no—
193C23×D47—22no—
194C23×D47—22no—
195C23×D47—232no—
196C23×D47—28no—
197C23×D47—28no—
198C23×D47—416no—
199C23×D47—416no—
200C23×D47—44no—
201C23×D47—44no—
202C23×D47—44no—
203C23×D47—44no—
204C23×D47—416no—
205C23×D47—416no—
206C23×D47—416no—
207C23×D47—416no—
208C23×D47C22×C414yes—
209C23×D47C22×C414yes—
210C23×D47C22×C414yes—
211C23×D47C22×C4116yescomplemented
212C23×D47C2×D414yes—
213C23×D47#4114yes—
214C23×D47C2412yes—
215C23×D47C2412yes—
216C23×D47C2412yes—
217C22×C4×C47—22no—
218C22×C4×C47—22no—
219C22×C4×C47—22no—
220C22×C4×C47—22no—
221C22×C4×C47—22no—
222C22×C4×C47—22no—
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—22no—
230C22×C4×C47—22no—
231C22×C4×C47—22no—
232C22×C4×C47C22×C414yes—
233C22×C4×C47C22×C414yes—
234C22×C4×C47C2×D414yes—
235C22×C4×C47C2412yes—
236C22×C4×C47C2412yes—
237C22×C4×C47C2412yes—
238C22×C4×C47C2412yes—
239C22×C4×C47C2412yes—
240C22×C4×C47C2412yes—
241C2×C22⋊D47—416no—
242C2×C22⋊D47—44no—
243C2×C22⋊D47—44no—
244C2×C22⋊D47C22×C4116yescomplemented
245C22×Dic47—22no—
246C22×Dic47—22no—
247C22×Dic47—22no—
248C22×Dic47—22no—
249C22×Dic47—22no—
250C22×Dic47—22no—
251C22×Dic47—22no—
252C22×Dic47—22no—
253C22×Dic47—22no—
254C22×Dic47—22no—
255C22×Dic47—22no—
256C22×Dic47—22no—
257C22×Dic47—22no—
258C22×Dic47C22×C414yes—
259C22×Dic47C2×D414yes—
260C22×Dic47C2412yes—
261C22×Dic47C2412yes—
262C22×Dic47C2412yes—
263C22×Dic47C2412yes—
264C22×Dic47C2412yes—
265C2×D188—232no—
266C2×D188—28no—
267C2×D188—28no—
268C2×D188—416no—
269C2×D188—44no—
270C2×D188—44no—
271C2×D188C22×C4116yes—
272C2×D188C22×C4116yescomplemented
273C2×C4×D47—28no—
274C2×C4×D47—28no—
275C2×C4×D47—416no—
276C2×C4×D47—44no—
277C2×C4×D47—44no—
278C2×C4×D47—44no—
279C2×C4×D47—44no—
280C2×C4×D47—44no—
281C2×C4×D47—44no—
282C2×C4×D47—416no—
283C2×C4×D47—416no—
284C2×C4×D47C2×D4116yescomplemented
285C4⋊C4×C47—44no—
286C22⋊C4×C47—28no—
287C22⋊C4×C47—44no—
288C22⋊C4×C47C22×C4116yescomplemented
289C42×C47—28no—
290C22⋊Dic47—28no—
291C22⋊Dic47—44no—
292(C2×D47)⋊C4—28no—
293(C2×D47)⋊C4—28no—
294(C2×D47)⋊C4—28no—
295(C2×D47)⋊C4—28no—
296(C2×D47)⋊C4—28no—
297(C2×D47)⋊C4—44no—
298(C2×D47)⋊C4—44no—
299(C2×D47)⋊C4—44no—
300(C2×D47)⋊C4—44no—
301(C2×D47)⋊C4C22×C4116yescomplemented
302(C2×D47)⋊C4C22×C4116yescomplemented
303C4⋊Dic47—28no—
304Dic47⋊C4—44no—
305C4×Dic47—44no—
306C4×Dic47—44no—
307C23×C47—28no—
308C23×C47—28no—
309C23×C47—28no—
310C23×C47—22no—
311C23×C47—22no—
312C23×C47—22no—
313C23×C47—22no—
314C23×C47—22no—
315C23×C47—22no—
316C23×C47—44no—
317C23×C47—44no—
318C23×C47—44no—
319C23×C47—44no—
320C23×C47C23×C414yes—
321C23×C47C23×C412yes—
322C23×C47C22×D412yes—
323C23×C47C2×#4112yes—
324C23×C47H(5,𝔽2)12yes—
325C23×C47H(5,𝔽2)12yes—
326C23×C47H(5,𝔽2)12yes—
327C23×C47H(5,𝔽2)12yes—
328C23×C47C2511yescharacteristic
329C22×D47—28no—
330C22×D47—28no—
331C22×D47—28no—
332C22×D47—28no—
333C22×D47—28no—
334C22×D47—28no—
335C22×D47—22no—
336C22×D47—22no—
337C22×D47—22no—
338C22×D47—22no—
339C22×D47—28no—
340C22×D47—28no—
341C22×D47—28no—
342C22×D47—28no—
343C22×D47—28no—
344C22×D47—28no—
345C22×D47—22no—
346C22×D47—22no—
347C22×D47—22no—
348C22×D47—22no—
349C22×D47—22no—
350C22×D47—22no—
351C22×D47—22no—
352C22×D47—22no—
353C22×D47—22no—
354C22×D47—22no—
355C22×D47—22no—
356C22×D47—22no—
357C22×D47—232no—
358C22×D47—416no—
359C22×D47—416no—
360C22×D47—4128no—
361C22×D47—416no—
362C22×D47—416no—
363C22×D47—416no—
364C22×D47—416no—
365C22×D47—44no—
366C22×D47—44no—
367C22×D47—44no—
368C22×D47—44no—
369C22×D47—44no—
370C22×D47—44no—
371C22×D47—44no—
372C22×D47—44no—
373C22×D47C4×D4116yes—
374C22×D47C23×C414yes—
375C22×D47C23×C414yes—
376C22×D47C23×C414yes—
377C22×D47C22×D414yes—
378C22×D47C2×#4114yes—
379C2×C4×C47—28no—
380C2×C4×C47—28no—
381C2×C4×C47—28no—
382C2×C4×C47—22no—
383C2×C4×C47—22no—
384C2×C4×C47—22no—
385C2×C4×C47—22no—
386C2×C4×C47—22no—
387C2×C4×C47—22no—
388C2×C4×C47—22no—
389C2×C4×C47—22no—
390C2×C4×C47—22no—
391C2×C4×C47—22no—
392C2×C4×C47—22no—
393C2×C4×C47—22no—
394C2×C4×C47—22no—
395C2×C4×C47—22no—
396C2×C4×C47—22no—
397C2×C4×C47—44no—
398C2×C4×C47—44no—
399C2×C4×C47—44no—
400C2×C4×C47C23×C414yes—
401C2×C4×C47C23×C414yes—
402C2×C4×C47C22×D414yes—
403C22⋊D47—416no—
404C2×Dic47—28no—
405C2×Dic47—28no—
406C2×Dic47—22no—
407C2×Dic47—22no—
408C2×Dic47—22no—
409C2×Dic47—22no—
410C2×Dic47—22no—
411C2×Dic47—22no—
412C2×Dic47—22no—
413C2×Dic47—22no—
414C2×Dic47—22no—
415C2×Dic47—22no—
416C2×Dic47—22no—
417C2×Dic47—22no—
418C2×Dic47—22no—
419C2×Dic47—44no—
420C2×Dic47—44no—
421C2×Dic47—44no—
422C2×Dic47C23×C414yes—
423C2×Dic47C22×D414yes—
424D188—232no—
425D188—416no—
426C4×D47—416no—
427C4×D47—416no—
428C4×D47—416no—
429C2×#2321—471nomaximal, Sylow
430C22×C47—24no—
431C22×C47—24no—
432C22×C47—24no—
433C22×C47—416no—
434C22×C47—42no—
435C22×C47—42no—
436C22×C47—42no—
437C22×C47—42no—
438C22×C47C2×C4×D414yes—
439C22×C47#51814yes—
440C22×C47#51814yes—
441C22×C47#53414yes—
442C22×C47#53514yes—
443C22×C47#53814yes—
444C22×C47#53814yes—
445C22×C47C24×C411yescharacteristic
446C22×C47C23×D411yescharacteristic
447C22×C47C22×#4111yescharacteristic
448C22×C47C2×H(5,𝔽2)11yescharacteristic
449C22×C47C2×H(5,𝔽2)11yescharacteristic
450C22×C47C2×H(5,𝔽2)11yescharacteristic
451C22×C47C2×H(5,𝔽2)11yescharacteristic
452C2×D47—232no—
453C2×D47—24no—
454C2×D47—24no—
455C2×D47—24no—
456C2×D47—24no—
457C2×D47—24no—
458C2×D47—24no—
459C2×D47—24no—
460C2×D47—24no—
461C2×D47—24no—
462C2×D47—24no—
463C2×D47—24no—
464C2×D47—24no—
465C2×D47—464no—
466C2×D47—416no—
467C2×D47—416no—
468C2×D47—42no—
469C2×D47—42no—
470C2×D47—42no—
471C2×D47—42no—
472C2×D47—42no—
473C2×D47—42no—
474C2×D47—42no—
475C2×D47—42no—
476C2×D47C2×C4×D418yes—
477C4×C47—24no—
478C4×C47—24no—
479C4×C47—24no—
480C4×C47—42no—
481C4×C47—42no—
482C4×C47—42no—
483Dic47—24no—
484Dic47—24no—
485Dic47—42no—
486Dic47—42no—
487Dic47—42no—
488C22×#120—471no—
489C22×C4×D4—471no—
490C23×C22⋊C4—471no—
491#2321—4716no—
492C2×#390—471no—
493C2×#390—471no—
494C2×#388—471no—
495C2×#388—471no—
496C2×#388—471no—
497C2×#388D4711yescharacteristic, complemented
498C2×#386—471no—
499C2×#386—471no—
500C2×#386—471no—
501C2×#385—471no—
502C2×#379—471no—
503C2×C4×C22⋊C4—471no—
504C2×C47—44no—
505C2×C47#232118yescomplemented
506C2×C47C22×C4×D411yescharacteristic
507C2×C47C2×#51811yescharacteristic
508C2×C47C2×#51811yescharacteristic
509C2×C47C2×#53411yescharacteristic
510C2×C47C2×#53511yescharacteristic
511C2×C47C2×#53811yescharacteristic
512C2×C47C2×#53811yescharacteristic
513D47—28no—
514D47—44no—
515D47—44no—
516C26—471no—
517C23×D4—471no—
518C23×D4—471no—
519C23×D4—471no—
520C24×C4—471no—
521C24×C4—471no—
522C24×C4—471no—
523C2×#120—4716no—
524C2×#120—478no—
525C2×C4×D4—478no—
526C2×C4×D4—948no—
527C22×C4⋊C4—471no—
528C22×C4⋊C4—471no—
529C22×C4⋊C4C2×D4711yescharacteristic, complemented
530C22×C22⋊C4—471no—
531C22×C22⋊C4—471no—
532C22×C22⋊C4—471no—
533C22×C22⋊C4—471no—
534C22×C22⋊C4—471no—
535C22×C22⋊C4—471no—
536C22×C22⋊C4—471no—
537C22×C22⋊C4—471no—
538C22×C22⋊C4—471no—
539C22×C22⋊C4—471no—
540C22×C22⋊C4—471no—
541C22×C22⋊C4—471no—
542C22×C22⋊C4—471no—
543C22×C22⋊C4—478no—
544C22×C22⋊C4—948no—
545C22×C22⋊C4C2×D4711yescharacteristic
546C22×C22⋊C4C2×D4711yescharacteristic
547C22×C22⋊C4C2×D4711yescharacteristic
548C22×C42—471no—
549C22×C42—471no—
550C22×C42C2×D4711yescharacteristic, complemented
551#390—478no—
552#390—478no—
553#388—478no—
554#388—478no—
555#388—478no—
556#388C2×D4718yescomplemented
557#386—478no—
558#386—478no—
559#386—478no—
560#385—478no—
561#379—478no—
562C4×C22⋊C4—478no—
563C2×#95—471no—
564C2×#95—471no—
565C2×#95—471no—
566C2×#95—471no—
567C2×#95C2×D4711yescharacteristic, complemented
568C2×#95C2×D4711yescharacteristic, complemented
569C47C2×#232111yescharacteristic, complemented, Sylow
570C25—471no—
571C25—471no—
572C25—471no—
573C25—478no—
574C25—474no—
575C25—944no—
576C25—944no—
577C25—1882no—
578C25—1882no—
579C25—1882no—
580C25—1882no—
581C25C22×D4711yescharacteristic
582C22×D4—478no—
583C22×D4—474no—
584C22×D4—478no—
585C22×D4—478no—
586C22×D4—474no—
587C22×D4—474no—
588C22×D4—944no—
589C22×D4—944no—
590C22×D4—1882no—
591C22×D4—1882no—
592C22×D4—1882no—
593C22×D4—1882no—
594C23×C4—471no—
595C23×C4—471no—
596C23×C4—478no—
597C23×C4—474no—
598C23×C4—471no—
599C23×C4—471no—
600C23×C4—471no—
601C23×C4—474no—
602C23×C4—474no—
603C23×C4—944no—
604C23×C4—944no—
605C23×C4—1882no—
606C23×C4—1882no—
607C23×C4—1882no—
608C23×C4—1882no—
609C23×C4—1882no—
610C23×C4—1882no—
611C23×C4C22×D4711yescharacteristic
612C23×C4C22×D4711yescharacteristic
613C23×C4C22×D4711yescharacteristic
614C23×C4C22×D4711yescharacteristic
615C23×C4C22×D4711yescharacteristic
616C23×C4C22×D4711yescharacteristic
617#120—4764no—
618C4×D4—9432no—
619C2×C4⋊C4—42no—
620C2×C4⋊C4—474no—
621C2×C4⋊C4—474no—
622C2×C4⋊C4—944no—
623C2×C4⋊C4—1882no—
624C2×C4⋊C4C22×D4714yescomplemented
625C2×C22⋊C4—24no—
626C2×C22⋊C4—42no—
627C2×C22⋊C4—478no—
628C2×C22⋊C4—478no—
629C2×C22⋊C4—474no—
630C2×C22⋊C4—474no—
631C2×C22⋊C4—474no—
632C2×C22⋊C4—474no—
633C2×C22⋊C4—474no—
634C2×C22⋊C4—474no—
635C2×C22⋊C4—474no—
636C2×C22⋊C4—474no—
637C2×C22⋊C4—474no—
638C2×C22⋊C4—474no—
639C2×C22⋊C4—474no—
640C2×C22⋊C4—474no—
641C2×C22⋊C4—474no—
642C2×C22⋊C4—9432no—
643C2×C22⋊C4—944no—
644C2×C22⋊C4—944no—
645C2×C22⋊C4—944no—
646C2×C22⋊C4—944no—
647C2×C22⋊C4—944no—
648C2×C22⋊C4—944no—
649C2×C22⋊C4—1882no—
650C2×C22⋊C4—1882no—
651C2×C22⋊C4—1882no—
652C2×C22⋊C4—1882no—
653C2×C22⋊C4—1882no—
654C2×C22⋊C4C4×D4718yescomplemented
655C2×C22⋊C4C22×D4714yes—
656C2×C22⋊C4C22×D4714yes—
657C2×C22⋊C4C22×D4714yes—
658C2×C42—24no—
659C2×C42—474no—
660C2×C42—474no—
661C2×C42—1882no—
662C2×C42—1882no—
663C2×C42C22×D4714yescomplemented
664#95—474no—
665#95—474no—
666#95—474no—
667#95—474no—
668#95C22×D4714yescomplemented
669#95C22×D4714yescomplemented
670C24—22no—
671C24—22no—
672C24—22no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—474no—
677C24—474no—
678C24—474no—
679C24—472no—
680C24—474no—
681C24—474no—
682C24—472no—
683C24—472no—
684C24—4716no—
685C24—948no—
686C24—9432no—
687C24—948no—
688C24—942no—
689C24—942no—
690C24—942no—
691C24—942no—
692C24—942no—
693C24—942no—
694C24—942no—
695C24—942no—
696C24—942no—
697C24—942no—
698C24—942no—
699C24—942no—
700C24—942no—
701C24—942no—
702C24—942no—
703C24—942no—
704C24—18816no—
705C24—18816no—
706C24—1884no—
707C24—1884no—
708C24—1884no—
709C24—1884no—
710C24—18816no—
711C24—18816no—
712C24—18816no—
713C24—18816no—
714C24C2×C4×D4714yes—
715C24C23×D4712yes—
716C24C23×D4711yescharacteristic
717C2×D4—4716no—
718C2×D4—4716no—
719C2×D4—4716no—
720C2×D4—948no—
721C2×D4—9432no—
722C2×D4—948no—
723C2×D4—18816no—
724C2×D4—1884no—
725C2×D4—1884no—
726C2×D4—18816no—
727C2×D4—1884no—
728C2×D4—1884no—
729C22×C4—22no—
730C22×C4—22no—
731C22×C4—22no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—474no—
745C22×C4—474no—
746C22×C4—472no—
747C22×C4—472no—
748C22×C4—4716no—
749C22×C4—472no—
750C22×C4—472no—
751C22×C4—472no—
752C22×C4—948no—
753C22×C4—942no—
754C22×C4—942no—
755C22×C4—942no—
756C22×C4—942no—
757C22×C4—942no—
758C22×C4—942no—
759C22×C4—942no—
760C22×C4—942no—
761C22×C4—942no—
762C22×C4—942no—
763C22×C4—942no—
764C22×C4—942no—
765C22×C4—942no—
766C22×C4—948no—
767C22×C4—18816no—
768C22×C4—1884no—
769C22×C4—1884no—
770C22×C4—1884no—
771C22×C4—1884no—
772C22×C4—1884no—
773C22×C4—1884no—
774C22×C4—18816no—
775C22×C4—18816no—
776C22×C4C2×C4×D4714yes—
777C22×C4C2×C4×D4714yes—
778C22×C4D4×D4714yes—
779C22×C4C23×D4712yes—
780C22×C4C23×D4712yes—
781C22×C4C23×D4712yes—
782C22×C4C23×D4712yes—
783C22×C4C23×D4712yes—
784C22×C4C23×D4712yes—
785C4⋊C4—44no—
786C4⋊C4—948no—
787C4⋊C4—1884no—
788C22⋊C4—28no—
789C22⋊C4—44no—
790C22⋊C4—4716no—
791C22⋊C4—4716no—
792C22⋊C4—948no—
793C22⋊C4—948no—
794C22⋊C4—948no—
795C22⋊C4—948no—
796C22⋊C4—948no—
797C22⋊C4—948no—
798C22⋊C4—1884no—
799C22⋊C4—1884no—
800C22⋊C4—1884no—
801C22⋊C4—1884no—
802C22⋊C4—1884no—
803C22⋊C4C2×C4×D47116yescomplemented
804C42—28no—
805C42—1884no—
806C42—1884no—
807C23—28no—
808C23—28no—
809C23—28no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—44no—
817C23—44no—
818C23—44no—
819C23—44no—
820C23—4716no—
821C23—474no—
822C23—474no—
823C23—474no—
824C23—474no—
825C23—474no—
826C23—9432no—
827C23—948no—
828C23—948no—
829C23—948no—
830C23—948no—
831C23—942no—
832C23—942no—
833C23—942no—
834C23—942no—
835C23—948no—
836C23—948no—
837C23—948no—
838C23—948no—
839C23—948no—
840C23—948no—
841C23—948no—
842C23—948no—
843C23—942no—
844C23—942no—
845C23—942no—
846C23—942no—
847C23—942no—
848C23—942no—
849C23—942no—
850C23—942no—
851C23—942no—
852C23—942no—
853C23—942no—
854C23—942no—
855C23—18816no—
856C23—18816no—
857C23—188128no—
858C23—18816no—
859C23—18816no—
860C23—18816no—
861C23—18816no—
862C23—1884no—
863C23—1884no—
864C23—1884no—
865C23—1884no—
866C23—1884no—
867C23—1884no—
868C23—1884no—
869C23—1884no—
870C23C22×C4×D4714yes—
871C23C22×C4×D4712yes—
872C23C2×D4×D4712yes—
873C23#41×D4712yes—
874C23#1309406912yes—
875C23#1309407012yes—
876C23#1309407012yes—
877C23#1309407012yes—
878C23C24×D4711yescharacteristic
879D4—9432no—
880D4—18816no—
881D4—18816no—
882C2×C4—28no—
883C2×C4—28no—
884C2×C4—28no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—44no—
901C2×C4—44no—
902C2×C4—44no—
903C2×C4—474no—
904C2×C4—474no—
905C2×C4—948no—
906C2×C4—948no—
907C2×C4—942no—
908C2×C4—942no—
909C2×C4—942no—
910C2×C4—942no—
911C2×C4—942no—
912C2×C4—942no—
913C2×C4—942no—
914C2×C4—942no—
915C2×C4—942no—
916C2×C4—942no—
917C2×C4—942no—
918C2×C4—942no—
919C2×C4—942no—
920C2×C4—18816no—
921C2×C4—18816no—
922C2×C4—18816no—
923C2×C4—1884no—
924C2×C4—1884no—
925C2×C4—1884no—
926C2×C4C22×C4×D4714yes—
927C2×C4C22×C4×D4714yes—
928C2×C4C2×D4×D4714yes—
929C22—24no—
930C22—24no—
931C22—24no—
932C22—416no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—478no—
938C22—9432no—
939C22—944no—
940C22—944no—
941C22—944no—
942C22—944no—
943C22—944no—
944C22—944no—
945C22—944no—
946C22—944no—
947C22—944no—
948C22—944no—
949C22—944no—
950C22—944no—
951C22—18864no—
952C22—18816no—
953C22—18816no—
954C22—1882no—
955C22—1882no—
956C22—1882no—
957C22—1882no—
958C22—1882no—
959C22—1882no—
960C22—1882no—
961C22—1882no—
962C22C4×D4×D4714yes—
963C22#1568959514yes—
964C22#1568959714yes—
965C22#1568968414yes—
966C22#1568968914yes—
967C22#1568970714yes—
968C22#1568971214yes—
969C22C23×C4×D4711yescharacteristic
970C22C22×D4×D4711yescharacteristic
971C22C2×#41×D4711yescharacteristic
972C22C2×#1309406911yescharacteristic
973C22C2×#1309407011yescharacteristic
974C22C2×#1309407011yescharacteristic
975C22C2×#1309407011yescharacteristic
976C4—24no—
977C4—24no—
978C4—24no—
979C4—42no—
980C4—42no—
981C4—42no—
982C4—944no—
983C4—944no—
984C4—1882no—
985C4—1882no—
986C4—1882no—
987C2—44no—
988C2—948no—
989C2—1884no—
990C2—1884no—
991C2#2024605018yesdirect product factor
992C2C2×C4×D4×D4711yescharacteristic
993C2C2×#1568959511yescharacteristic
994C2C2×#1568959711yescharacteristic
995C2C2×#1568968411yescharacteristic
996C2C2×#1568968911yescharacteristic
997C2C2×#1568970711yescharacteristic
998C2C2×#1568971211yescharacteristic
subgroupG/H
centerC24C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC2×C47×#388C2
socleC24×C47C24
prime radicalC22×#13093994C2
cosocleC23×C47C25
hypercenterC2×#388D47
hypocenterC47C2×#2321
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⋊C4×D47C2semidirect
4. #20246050C2direct (N × H)
5. C2×#15689024C2semidirect
6. C2×#15689023C2semidirect
7. C2×#15689016C2semidirect
8. C2×#15689015C2semidirect
9. C2×#15689014C2semidirect
10. C2×#15689001C2semidirect
11. C2×#15689001C2semidirect
12. C2×#15688999C2semidirect
13. C2×#15688994C2semidirect
14. C2×#15688978C2semidirect
15. C2×#15688970C2semidirect
16. C2×C47×#388C2semidirect
23. C23×C4×D47C22semidirect
24. C2×#13093994C4semidirect
27. C2×C4×D188C22semidirect
28. C22×C4⋊Dic47C22semidirect
29. C22×Dic47⋊C4C22semidirect
40. C22×(C2×D47)⋊C4C22semidirect
41. C22×(C2×D47)⋊C4C22semidirect
42. C22×(C2×D47)⋊C4C22semidirect
44. C2×C22⋊C4×D47C22semidirect
45. C22×C4×Dic47C22semidirect
46. C22×C4×Dic47C22semidirect
47. #15689024C22semidirect
48. #15689023C22semidirect
49. #15689016C22semidirect
50. #15689015C22semidirect
51. #15689014C22semidirect
52. #15689001C22semidirect
53. #15689001C22semidirect
54. #15688999C22semidirect
55. #15688994C22semidirect
56. #15688978C22semidirect
57. #15688970C22semidirect
58. C2×C47⋊#95C22semidirect
59. C2×C47⋊#95C22semidirect
60. C2×C47⋊#95C22semidirect
61. C2×C47⋊#95C22semidirect
62. C22×C4⋊C4×C47C22semidirect
66. C22×C42×C47C22semidirect
67. C47×#388C22semidirect
68. C2×#95×C47C22semidirect
69. C2×#95×C47C22semidirect
76. C24×D47C2×C4semidirect
86. C22×D188C2×C4semidirect
91. C22×C22⋊D47C2×C4semidirect
106. C22×C4×D47D4semidirect
109. C22×C4×D47C23semidirect
110. #13093994C2×C4semidirect
113. C2×C4⋊Dic47C23semidirect
115. C2×Dic47⋊C4C23semidirect
129. C2×(C2×D47)⋊C4C2×C4semidirect
130. C2×(C2×D47)⋊C4C2×C4semidirect
139. C2×(C2×D47)⋊C4C23semidirect
140. C2×(C2×D47)⋊C4C23semidirect
141. C2×(C2×D47)⋊C4C23semidirect
145. C2×C4×Dic47C23semidirect
146. C2×C4×Dic47C23semidirect
147. C47⋊#95C23semidirect
148. C47⋊#95C23semidirect
149. C47⋊#95C23semidirect
150. C47⋊#95C23semidirect
159. C2×C4⋊C4×C47C23semidirect
162. C2×C22⋊C4×C47C2×C4semidirect
167. C2×C42×C47C23semidirect
168. #95×C47C23semidirect
169. #95×C47C23semidirect
211. C23×D47C22×C4semidirect
244. C2×C22⋊D47C22×C4semidirect
272. C2×D188C22×C4semidirect
284. C2×C4×D47C2×D4semidirect
288. C22⋊C4×C47C22×C4semidirect
301. (C2×D47)⋊C4C22×C4semidirect
302. (C2×D47)⋊C4C22×C4semidirect
497. C2×#388D47semidirect
505. C2×C47#2321semidirect
529. C22×C4⋊C4C2×D47semidirect
550. C22×C42C2×D47semidirect
556. #388C2×D47semidirect
567. C2×#95C2×D47semidirect
568. C2×#95C2×D47semidirect
569. C47C2×#2321semidirect
624. C2×C4⋊C4C22×D47semidirect
654. C2×C22⋊C4C4×D47semidirect
663. C2×C42C22×D47semidirect
668. #95C22×D47semidirect
669. #95C22×D47semidirect
803. C22⋊C4C2×C4×D47semidirect
991. C2#20246050direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130939942
C22×C4×D1882
C22×C22⋊C4×D472
#202460502
C2×#156890242
C2×#156890232
C2×#156890162
C2×#156890152
C2×#156890142
C2×#156890012
C2×#156889992
C2×#156889942
C2×#156889782
C2×#156889702
C2×C47×#3882
C2×#232147