Finite Group Databasebeta

← C2×#20246851 #26383713

Subgroups — C2×#20246851 #26383713

Order 12032.

5054 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094006C211yesmaximal, characteristic, complemented
2C22×#13093994C211yesmaximal, characteristic
3C22×#13093986C211yesmaximal, characteristic, complemented
4C22×C22⋊C4×D47C211yesmaximal, characteristic, complemented
5#20246851C2116yesmaximal, direct product factor
6C2×#15689058C211yesmaximal, characteristic, complemented
7C2×#15689041C211yesmaximal, characteristic, complemented
8C2×#15689038C211yesmaximal, characteristic, complemented
9C2×#15689015C211yesmaximal, characteristic, complemented
10C2×#15689011C211yesmaximal, characteristic, complemented
11C2×#15689001C211yesmaximal, characteristic, complemented
12C2×#15689001C211yesmaximal, characteristic, complemented
13C2×#15688997C211yesmaximal, characteristic, complemented
14C2×#15688982C211yesmaximal, characteristic, complemented
15C2×#15688978C211yesmaximal, characteristic, complemented
16C2×C47×#397C211yesmaximal, characteristic, complemented
17C25×D47C2211yescharacteristic
18C23×D188C2211yescharacteristic
19C23×D188C2211yescharacteristic
20C23×C22⋊D47C2211yescharacteristic
21C23×C4×D47C2211yescharacteristic
22C23×C4×D47C2211yescharacteristic
23C23×C4×D47C2211yescharacteristic, complemented
24C2×#13094006—28no—
25C2×#13094006C2218yescomplemented
26C2×#13093994—28no—
27C2×#13093994C2218yes—
28C2×#13093986—28no—
29C2×#13093986C2218yescomplemented
30C22×C4⋊Dic47C2211yescharacteristic, complemented
31C22×Dic47⋊C4C2211yescharacteristic, complemented
32C22×Dic47⋊C4C2211yescharacteristic, complemented
33C22×Dic47⋊C4C2211yescharacteristic, complemented
34C22×C22⋊Dic47C2211yescharacteristic
35C22×C22⋊Dic47C2211yescharacteristic
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
43C22×(C2×D47)⋊C4C2211yescharacteristic
44C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
45C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
46C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
47C2×C22⋊C4×D47—28no—
48C2×C22⋊C4×D47C2218yescomplemented
49C22×C4×Dic47C2211yescharacteristic, complemented
50#15689058C2218yescomplemented
51#15689041C2218yescomplemented
52#15689038C2218yescomplemented
53#15689015C2218yescomplemented
54#15689011C2218yescomplemented
55#15689001C2218yescomplemented
56#15689001C2218yescomplemented
57#15688997C2218yescomplemented
58#15688982C2218yescomplemented
59#15688978C2218yescomplemented
60C2×C47⋊#95C2211yescharacteristic, complemented
61C2×C47⋊#95C2211yescharacteristic, complemented
62C2×C47⋊#95C2211yescharacteristic, complemented
63C22×C4⋊C4×C47C2211yescharacteristic, complemented
64C22×C22⋊C4×C47C2211yescharacteristic
65C22×C22⋊C4×C47C2211yescharacteristic
66C22×C22⋊C4×C47C2211yescharacteristic
67C47×#397C2218yescomplemented
68C2×#95×C47C2211yescharacteristic, complemented
69C2×#95×C47C2211yescharacteristic, complemented
70C2×#95×C47C2211yescharacteristic, complemented
71C24×D47—24no—
72C24×D47—24no—
73C24×D47—24no—
74C24×D47—24no—
75C24×D47—24no—
76C24×D47—42no—
77C24×D47—42no—
78C24×D47C2311yescharacteristic
79C24×D47C2311yescharacteristic
80C24×D47C2314yes—
81C24×D47C2311yescharacteristic
82C22×D188—24no—
83C22×D188—24no—
84C22×D188—24no—
85C22×D188—24no—
86C22×D188—42no—
87C22×D188D418yes—
88C22×D188C2314yes—
89C22×D188C2314yes—
90C22×C22⋊D47—24no—
91C22×C22⋊D47—24no—
92C22×C22⋊D47—42no—
93C22×C22⋊D47C2314yes—
94C23×Dic47C2311yescharacteristic
95C23×Dic47C2311yescharacteristic
96C23×Dic47C2311yescharacteristic
97C23×Dic47C2311yescharacteristic
98C23×Dic47C2311yescharacteristic
99C22×C4×D47—24no—
100C22×C4×D47—24no—
101C22×C4×D47—24no—
102C22×C4×D47—24no—
103C22×C4×D47—24no—
104C22×C4×D47—24no—
105C22×C4×D47—42no—
106C22×C4×D47—42no—
107C22×C4×D47—42no—
108C22×C4×D47C2314yes—
109C22×C4×D47C2314yes—
110C22×C4×D47C2314yescomplemented
111#13094006—232no—
112#13093994—232no—
113#13093986—232no—
114C2×C4⋊Dic47—24no—
115C2×C4⋊Dic47C2314yescomplemented
116C2×Dic47⋊C4—24no—
117C2×Dic47⋊C4—42no—
118C2×Dic47⋊C4—42no—
119C2×Dic47⋊C4C2314yescomplemented
120C2×Dic47⋊C4C2314yescomplemented
121C2×Dic47⋊C4C2314yescomplemented
122C2×C22⋊Dic47—42no—
123C2×C22⋊Dic47D418yescomplemented
124C2×C22⋊Dic47C2314yes—
125C2×C22⋊Dic47C2314yes—
126C2×(C2×D47)⋊C4—24no—
127C2×(C2×D47)⋊C4—24no—
128C2×(C2×D47)⋊C4—24no—
129C2×(C2×D47)⋊C4—24no—
130C2×(C2×D47)⋊C4—24no—
131C2×(C2×D47)⋊C4—24no—
132C2×(C2×D47)⋊C4—24no—
133C2×(C2×D47)⋊C4—24no—
134C2×(C2×D47)⋊C4—24no—
135C2×(C2×D47)⋊C4—42no—
136C2×(C2×D47)⋊C4—42no—
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×(C2×D47)⋊C4C2314yes—
144C2×(C2×D47)⋊C4C2314yes—
145C2×(C2×D47)⋊C4C2314yescomplemented
146C2×(C2×D47)⋊C4C2314yescomplemented
147C2×(C2×D47)⋊C4C2314yescomplemented
148C22⋊C4×D47—232no—
149C2×C4×Dic47—24no—
150C2×C4×Dic47C2314yescomplemented
151C47⋊#95C2314yescomplemented
152C47⋊#95C2314yescomplemented
153C47⋊#95C2314yescomplemented
154C25×C47C2311yescharacteristic
155C23×C4×C47C2311yescharacteristic
156C23×C4×C47C2311yescharacteristic
157C23×C4×C47C2311yescharacteristic
158C23×C4×C47C2311yescharacteristic
159C23×C4×C47C2311yescharacteristic
160C23×C4×C47C2311yescharacteristic
161C2×C4⋊C4×C47—24no—
162C2×C4⋊C4×C47C2314yescomplemented
163C2×C22⋊C4×C47—24no—
164C2×C22⋊C4×C47—24no—
165C2×C22⋊C4×C47—24no—
166C2×C22⋊C4×C47C2314yes—
167C2×C22⋊C4×C47C2314yes—
168C2×C22⋊C4×C47C2314yes—
169#95×C47C2314yescomplemented
170#95×C47C2314yescomplemented
171#95×C47C2314yescomplemented
172C24×C47—22no—
173C24×C47—22no—
174C24×C47—22no—
175C24×C47—22no—
176C24×C47—22no—
177C24×C47—22no—
178C24×C47C2×D414yes—
179C24×C47C2412yes—
180C24×C47C2411yescharacteristic
181C23×D47—22no—
182C23×D47—22no—
183C23×D47—22no—
184C23×D47—22no—
185C23×D47—232no—
186C23×D47—28no—
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—22no—
196C23×D47—22no—
197C23×D47—22no—
198C23×D47—22no—
199C23×D47—28no—
200C23×D47—28no—
201C23×D47—28no—
202C23×D47—28no—
203C23×D47—44no—
204C23×D47—44no—
205C23×D47—416no—
206C23×D47—416no—
207C23×D47—416no—
208C23×D47—416no—
209C23×D47—416no—
210C23×D47—416no—
211C23×D47C2×D414yes—
212C23×D47C2×D414yes—
213C23×D47#4114yes—
214C23×D47#4114yes—
215C23×D47#4114yes—
216C23×D47C2412yes—
217C23×D47C2412yes—
218C23×D47C2412yes—
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×C47—22no—
233C22×C4×C47—22no—
234C22×C4×C47—22no—
235C22×C4×C47—22no—
236C22×C4×C47C2×D414yes—
237C22×C4×C47C2412yes—
238C22×C4×C47C2412yes—
239C22×C4×C47C2412yes—
240C22×C4×C47C2412yes—
241C22×C4×C47C2412yes—
242C22×C4×C47C2412yes—
243C2×C22⋊D47—28no—
244C2×C22⋊D47—28no—
245C2×C22⋊D47—44no—
246C2×C22⋊D47—416no—
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×Dic47—22no—
259C22×Dic47—22no—
260C22×Dic47C2×D414yes—
261C22×Dic47C2×D414yes—
262C22×Dic47C2412yes—
263C22×Dic47C2412yes—
264C22×Dic47C2412yes—
265C22×Dic47C2412yes—
266C22×Dic47C2412yes—
267C2×D188—232no—
268C2×D188—28no—
269C2×D188—28no—
270C2×D188—28no—
271C2×D188—28no—
272C2×D188—44no—
273C2×D188—416no—
274C2×D188C2×D4116yes—
275C2×C4×D47—28no—
276C2×C4×D47—28no—
277C2×C4×D47—28no—
278C2×C4×D47—28no—
279C2×C4×D47—28no—
280C2×C4×D47—28no—
281C2×C4×D47—44no—
282C2×C4×D47—44no—
283C2×C4×D47—44no—
284C2×C4×D47—416no—
285C2×C4×D47—416no—
286C2×C4×D47—416no—
287C4⋊C4×C47—28no—
288C22⋊C4×C47—28no—
289C22⋊C4×C47—28no—
290C22⋊C4×C47—28no—
291C22⋊Dic47—44no—
292C22⋊Dic47C2×D4116yescomplemented
293(C2×D47)⋊C4—28no—
294(C2×D47)⋊C4—28no—
295(C2×D47)⋊C4—28no—
296(C2×D47)⋊C4—28no—
297(C2×D47)⋊C4—28no—
298(C2×D47)⋊C4—28no—
299(C2×D47)⋊C4—28no—
300(C2×D47)⋊C4—28no—
301(C2×D47)⋊C4—28no—
302(C2×D47)⋊C4—44no—
303(C2×D47)⋊C4—44no—
304C4⋊Dic47—28no—
305Dic47⋊C4—28no—
306Dic47⋊C4—44no—
307Dic47⋊C4—44no—
308C4×Dic47—28no—
309C23×C47—28no—
310C23×C47—28no—
311C23×C47—28no—
312C23×C47—22no—
313C23×C47—22no—
314C23×C47—22no—
315C23×C47—22no—
316C23×C47—22no—
317C23×C47—22no—
318C23×C47—44no—
319C23×C47—44no—
320C23×C47—44no—
321C23×C47—44no—
322C23×C47C22×D414yes—
323C23×C47C22×D412yes—
324C23×C47C22×D412yes—
325C23×C47C2×#4112yes—
326C23×C47C2×#4112yes—
327C23×C47C2×#4112yes—
328C23×C47H(5,𝔽2)12yes—
329C23×C47H(5,𝔽2)12yes—
330C23×C47C2511yescharacteristic
331C22×D47—28no—
332C22×D47—28no—
333C22×D47—28no—
334C22×D47—28no—
335C22×D47—28no—
336C22×D47—28no—
337C22×D47—22no—
338C22×D47—22no—
339C22×D47—22no—
340C22×D47—22no—
341C22×D47—232no—
342C22×D47—28no—
343C22×D47—28no—
344C22×D47—28no—
345C22×D47—28no—
346C22×D47—28no—
347C22×D47—28no—
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—22no—
358C22×D47—22no—
359C22×D47—22no—
360C22×D47—416no—
361C22×D47—416no—
362C22×D47—416no—
363C22×D47—416no—
364C22×D47—4128no—
365C22×D47—416no—
366C22×D47—44no—
367C22×D47—44no—
368C22×D47—44no—
369C22×D47—44no—
370C22×D47—44no—
371C22×D47—44no—
372C22×D47—44no—
373C22×D47—44no—
374C22×D47—416no—
375C22×D47#123116yescomplemented
376C22×D47C22×D414yes—
377C22×D47C22×D414yes—
378C22×D47C2×#4114yes—
379C22×D47C2×#4114yes—
380C22×D47C2×#4114yes—
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—22no—
398C2×C4×C47—22no—
399C2×C4×C47—44no—
400C2×C4×C47—44no—
401C2×C4×C47—44no—
402C2×C4×C47—44no—
403C2×C4×C47—44no—
404C2×C4×C47C22×D414yes—
405C22⋊D47—416no—
406C2×Dic47—28no—
407C2×Dic47—28no—
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—22no—
420C2×Dic47—22no—
421C2×Dic47—44no—
422C2×Dic47—44no—
423C2×Dic47—44no—
424C2×Dic47C22×D414yes—
425C2×Dic47C22×D414yes—
426D188—232no—
427D188—416no—
428C4×D47—416no—
429C4×D47—416no—
430C4×D47—416no—
431C2×#2418—471nomaximal, Sylow
432C22×C47—24no—
433C22×C47—24no—
434C22×C47—24no—
435C22×C47—42no—
436C22×C47—416no—
437C22×C47—42no—
438C22×C47—42no—
439C22×C47—42no—
440C22×C47C2×#12314yes—
441C22×C47#52514yes—
442C22×C47#53814yes—
443C22×C47D4214yes—
444C22×C47#54614yes—
445C22×C47#54614yes—
446C22×C47#55114yes—
447C22×C47C23×D411yescharacteristic
448C22×C47C23×D411yescharacteristic
449C22×C47C22×#4111yescharacteristic
450C22×C47C22×#4111yescharacteristic
451C22×C47C22×#4111yescharacteristic
452C22×C47C2×H(5,𝔽2)11yescharacteristic
453C22×C47C2×H(5,𝔽2)11yescharacteristic
454C2×D47—24no—
455C2×D47—232no—
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—24no—
466C2×D47—24no—
467C2×D47—464no—
468C2×D47—42no—
469C2×D47—42no—
470C2×D47—416no—
471C2×D47—416no—
472C2×D47—42no—
473C2×D47—42no—
474C2×D47—42no—
475C2×D47—42no—
476C2×D47—42no—
477C2×D47—42no—
478C2×D47C2×#12318yescomplemented
479C4×C47—24no—
480C4×C47—42no—
481C4×C47—42no—
482C4×C47—42no—
483C4×C47—42no—
484C4×C47—42no—
485Dic47—24no—
486Dic47—24no—
487Dic47—42no—
488Dic47—42no—
489Dic47—42no—
490C22×#123—471no—
491C22×#120—471no—
492C22×C4×D4—471no—
493C23×C22⋊C4—471no—
494#2418—4716no—
495C2×#399—471no—
496C2×#397D4711yescharacteristic, complemented
497C2×#394—471no—
498C2×#394—471no—
499C2×#388—471no—
500C2×#388—471no—
501C2×#386—471no—
502C2×#386—471no—
503C2×#385—471no—
504C2×#380—471no—
505C2×#379—471no—
506C2×C47—44no—
507C2×C47#241818yescomplemented
508C2×C47C22×#12311yescharacteristic
509C2×C47C2×#52511yescharacteristic
510C2×C47C2×#53811yescharacteristic
511C2×C47C2×D4211yescharacteristic
512C2×C47C2×#54611yescharacteristic
513C2×C47C2×#54611yescharacteristic
514C2×C47C2×#55111yescharacteristic
515D47—28no—
516D47—44no—
517D47—44no—
518C26—471no—
519C23×D4—471no—
520C23×D4—471no—
521C23×D4—471no—
522C24×C4—471no—
523C24×C4—471no—
524C24×C4—471no—
525C2×#123—478no—
526C2×#123—948no—
527C2×#120—478no—
528C2×#120—948no—
529C2×C4×D4—478no—
530C2×C4×D4—948no—
531C22×C4⋊C4—471no—
532C22×C4⋊C4—471no—
533C22×C4⋊C4—471no—
534C22×C4⋊C4—471no—
535C22×C4⋊C4C2×D4711yescharacteristic, complemented
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—471no—
544C22×C22⋊C4—471no—
545C22×C22⋊C4—471no—
546C22×C22⋊C4—471no—
547C22×C22⋊C4—471no—
548C22×C22⋊C4—471no—
549C22×C22⋊C4—478no—
550C22×C22⋊C4—948no—
551C22×C22⋊C4C2×D4711yescharacteristic
552C22×C22⋊C4C2×D4711yescharacteristic
553C22×C22⋊C4C2×D4711yescharacteristic
554C22×C42—471no—
555#399—478no—
556#397C2×D4718yescomplemented
557#394—478no—
558#394—478no—
559#388—478no—
560#388—478no—
561#386—478no—
562#386—478no—
563#385—478no—
564#380—478no—
565#379—478no—
566C2×#95—471no—
567C2×#95—471no—
568C2×#95—471no—
569C2×#95C2×D4711yescharacteristic, complemented
570C2×#95C2×D4711yescharacteristic, complemented
571C2×#95C2×D4711yescharacteristic, complemented
572C47C2×#241811yescharacteristic, complemented, Sylow
573C25—471no—
574C25—471no—
575C25—471no—
576C25—474no—
577C25—944no—
578C25—944no—
579C25—944no—
580C25—944no—
581C25—944no—
582C25—1882no—
583C25—1882no—
584C25C22×D4711yescharacteristic
585C22×D4—474no—
586C22×D4—478no—
587C22×D4—474no—
588C22×D4—474no—
589C22×D4—944no—
590C22×D4—944no—
591C22×D4—944no—
592C22×D4—944no—
593C22×D4—944no—
594C22×D4—944no—
595C22×D4—1882no—
596C22×D4—1882no—
597C23×C4—471no—
598C23×C4—471no—
599C23×C4—471no—
600C23×C4—471no—
601C23×C4—471no—
602C23×C4—474no—
603C23×C4—474no—
604C23×C4—474no—
605C23×C4—944no—
606C23×C4—944no—
607C23×C4—944no—
608C23×C4—944no—
609C23×C4—944no—
610C23×C4—944no—
611C23×C4—1882no—
612C23×C4—1882no—
613C23×C4—1882no—
614C23×C4C22×D4711yescharacteristic
615C23×C4C22×D4711yescharacteristic
616C23×C4C22×D4711yescharacteristic
617C23×C4C22×D4711yescharacteristic
618C23×C4C22×D4711yescharacteristic
619C23×C4C22×D4711yescharacteristic
620#123—9432no—
621#120—9432no—
622C4×D4—9432no—
623C2×C4⋊C4—24no—
624C2×C4⋊C4—474no—
625C2×C4⋊C4—474no—
626C2×C4⋊C4—474no—
627C2×C4⋊C4—474no—
628C2×C4⋊C4—944no—
629C2×C4⋊C4—944no—
630C2×C4⋊C4—1882no—
631C2×C4⋊C4—1882no—
632C2×C4⋊C4C22×D4714yescomplemented
633C2×C22⋊C4—24no—
634C2×C22⋊C4—24no—
635C2×C22⋊C4—24no—
636C2×C22⋊C4—478no—
637C2×C22⋊C4—474no—
638C2×C22⋊C4—474no—
639C2×C22⋊C4—474no—
640C2×C22⋊C4—474no—
641C2×C22⋊C4—474no—
642C2×C22⋊C4—474no—
643C2×C22⋊C4—474no—
644C2×C22⋊C4—474no—
645C2×C22⋊C4—474no—
646C2×C22⋊C4—474no—
647C2×C22⋊C4—474no—
648C2×C22⋊C4—474no—
649C2×C22⋊C4—474no—
650C2×C22⋊C4—9432no—
651C2×C22⋊C4—944no—
652C2×C22⋊C4—944no—
653C2×C22⋊C4—944no—
654C2×C22⋊C4—944no—
655C2×C22⋊C4—944no—
656C2×C22⋊C4—944no—
657C2×C22⋊C4—944no—
658C2×C22⋊C4—944no—
659C2×C22⋊C4—944no—
660C2×C22⋊C4—1882no—
661C2×C22⋊C4—1882no—
662C2×C22⋊C4—1882no—
663C2×C22⋊C4C22×D4714yes—
664C2×C22⋊C4C22×D4714yes—
665C2×C22⋊C4C22×D4714yes—
666C2×C42—474no—
667C2×C42—944no—
668#95—474no—
669#95—474no—
670#95—474no—
671#95C22×D4714yescomplemented
672#95C22×D4714yescomplemented
673#95C22×D4714yescomplemented
674C24—22no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—22no—
679C24—22no—
680C24—474no—
681C24—474no—
682C24—474no—
683C24—472no—
684C24—474no—
685C24—474no—
686C24—472no—
687C24—472no—
688C24—948no—
689C24—948no—
690C24—948no—
691C24—948no—
692C24—9432no—
693C24—942no—
694C24—942no—
695C24—942no—
696C24—942no—
697C24—948no—
698C24—942no—
699C24—942no—
700C24—942no—
701C24—942no—
702C24—942no—
703C24—942no—
704C24—942no—
705C24—942no—
706C24—942no—
707C24—942no—
708C24—942no—
709C24—942no—
710C24—1884no—
711C24—1884no—
712C24—18816no—
713C24—18816no—
714C24—18816no—
715C24—18816no—
716C24—18816no—
717C24—18816no—
718C24D4×D4714yes—
719C24C23×D4712yes—
720C24C23×D4711yescharacteristic
721C2×D4—4716no—
722C2×D4—9432no—
723C2×D4—948no—
724C2×D4—948no—
725C2×D4—948no—
726C2×D4—948no—
727C2×D4—948no—
728C2×D4—948no—
729C2×D4—1884no—
730C2×D4—18816no—
731C2×D4—1884no—
732C2×D4—18816no—
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—22no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—474no—
751C22×C4—474no—
752C22×C4—472no—
753C22×C4—472no—
754C22×C4—472no—
755C22×C4—472no—
756C22×C4—472no—
757C22×C4—948no—
758C22×C4—948no—
759C22×C4—948no—
760C22×C4—948no—
761C22×C4—948no—
762C22×C4—948no—
763C22×C4—942no—
764C22×C4—942no—
765C22×C4—942no—
766C22×C4—942no—
767C22×C4—942no—
768C22×C4—942no—
769C22×C4—942no—
770C22×C4—942no—
771C22×C4—942no—
772C22×C4—942no—
773C22×C4—942no—
774C22×C4—942no—
775C22×C4—942no—
776C22×C4—1884no—
777C22×C4—1884no—
778C22×C4—1884no—
779C22×C4—18816no—
780C22×C4—18816no—
781C22×C4—18816no—
782C22×C4D4×D4714yes—
783C22×C4C23×D4712yes—
784C22×C4C23×D4712yes—
785C22×C4C23×D4712yes—
786C22×C4C23×D4712yes—
787C22×C4C23×D4712yes—
788C22×C4C23×D4712yes—
789C4⋊C4—28no—
790C4⋊C4—948no—
791C4⋊C4—948no—
792C4⋊C4—1884no—
793C4⋊C4—1884no—
794C22⋊C4—28no—
795C22⋊C4—28no—
796C22⋊C4—28no—
797C22⋊C4—4716no—
798C22⋊C4—948no—
799C22⋊C4—948no—
800C22⋊C4—948no—
801C22⋊C4—948no—
802C22⋊C4—948no—
803C22⋊C4—948no—
804C22⋊C4—948no—
805C22⋊C4—948no—
806C22⋊C4—948no—
807C22⋊C4—1884no—
808C22⋊C4—1884no—
809C22⋊C4—1884no—
810C42—948no—
811C23—28no—
812C23—28no—
813C23—28no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—44no—
821C23—44no—
822C23—44no—
823C23—44no—
824C23—4716no—
825C23—474no—
826C23—474no—
827C23—474no—
828C23—474no—
829C23—474no—
830C23—9432no—
831C23—948no—
832C23—948no—
833C23—948no—
834C23—948no—
835C23—948no—
836C23—942no—
837C23—942no—
838C23—942no—
839C23—942no—
840C23—948no—
841C23—948no—
842C23—948no—
843C23—948no—
844C23—948no—
845C23—948no—
846C23—948no—
847C23—942no—
848C23—942no—
849C23—942no—
850C23—942no—
851C23—942no—
852C23—942no—
853C23—942no—
854C23—942no—
855C23—942no—
856C23—942no—
857C23—942no—
858C23—942no—
859C23—18816no—
860C23—18816no—
861C23—18816no—
862C23—18816no—
863C23—18816no—
864C23—188128no—
865C23—18816no—
866C23—1884no—
867C23—1884no—
868C23—1884no—
869C23—1884no—
870C23—1884no—
871C23—1884no—
872C23—1884no—
873C23—1884no—
874C23C2×D4×D4714yes—
875C23C2×D4×D4712yes—
876C23C2×D4×D4712yes—
877C23#41×D4712yes—
878C23#41×D4712yes—
879C23#41×D4712yes—
880C23#1309407012yes—
881C23#1309407012yes—
882C23C24×D4711yescharacteristic
883D4—9432no—
884D4—18816no—
885D4—18816no—
886C2×C4—28no—
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—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—44no—
905C2×C4—44no—
906C2×C4—44no—
907C2×C4—44no—
908C2×C4—44no—
909C2×C4—474no—
910C2×C4—474no—
911C2×C4—948no—
912C2×C4—948no—
913C2×C4—942no—
914C2×C4—942no—
915C2×C4—942no—
916C2×C4—942no—
917C2×C4—942no—
918C2×C4—942no—
919C2×C4—942no—
920C2×C4—942no—
921C2×C4—942no—
922C2×C4—942no—
923C2×C4—942no—
924C2×C4—942no—
925C2×C4—942no—
926C2×C4—18816no—
927C2×C4—18816no—
928C2×C4—18816no—
929C2×C4—1884no—
930C2×C4—1884no—
931C2×C4—1884no—
932C2×C4C2×D4×D4714yes—
933C22—24no—
934C22—24no—
935C22—24no—
936C22—416no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22—42no—
941C22—478no—
942C22—944no—
943C22—944no—
944C22—9432no—
945C22—944no—
946C22—944no—
947C22—944no—
948C22—944no—
949C22—944no—
950C22—944no—
951C22—944no—
952C22—944no—
953C22—944no—
954C22—944no—
955C22—18864no—
956C22—1882no—
957C22—1882no—
958C22—1882no—
959C22—18816no—
960C22—18816no—
961C22—1882no—
962C22—1882no—
963C22—1882no—
964C22—1882no—
965C22—1882no—
966C22#123×D4714yes—
967C22#1568963114yes—
968C22#1568971214yes—
969C22#1568975714yes—
970C22#1568976514yes—
971C22#1568976614yes—
972C22#1568979814yes—
973C22C22×D4×D4711yescharacteristic
974C22C22×D4×D4711yescharacteristic
975C22C2×#41×D4711yescharacteristic
976C22C2×#41×D4711yescharacteristic
977C22C2×#41×D4711yescharacteristic
978C22C2×#1309407011yescharacteristic
979C22C2×#1309407011yescharacteristic
980C4—24no—
981C4—42no—
982C4—42no—
983C4—42no—
984C4—42no—
985C4—42no—
986C4—944no—
987C4—944no—
988C4—1882no—
989C4—1882no—
990C4—1882no—
991C2—44no—
992C2—948no—
993C2—1884no—
994C2—1884no—
995C2#2024685118yesdirect product factor
996C2C2×#123×D4711yescharacteristic
997C2C2×#1568963111yescharacteristic
998C2C2×#1568971211yescharacteristic
999C2C2×#1568975711yescharacteristic
1000C2C2×#1568976511yescharacteristic
1001C2C2×#1568976611yescharacteristic
1002C2C2×#1568979811yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#397C2
socleC24×C47C24
prime radicalC22×#13093994C2
hypercenterC2×#397D47
hypocenterC47C2×#2418
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
1. C22×#13094006C2semidirect
3. C22×#13093986C2semidirect
4. C22×C22⋊C4×D47C2semidirect
5. #20246851C2direct (N × H)
6. C2×#15689058C2semidirect
7. C2×#15689041C2semidirect
8. C2×#15689038C2semidirect
9. C2×#15689015C2semidirect
10. C2×#15689011C2semidirect
11. C2×#15689001C2semidirect
12. C2×#15689001C2semidirect
13. C2×#15688997C2semidirect
14. C2×#15688982C2semidirect
15. C2×#15688978C2semidirect
16. C2×C47×#397C2semidirect
23. C23×C4×D47C22semidirect
25. C2×#13094006C22semidirect
29. C2×#13093986C22semidirect
30. C22×C4⋊Dic47C22semidirect
31. C22×Dic47⋊C4C22semidirect
32. C22×Dic47⋊C4C22semidirect
33. C22×Dic47⋊C4C22semidirect
44. C22×(C2×D47)⋊C4C22semidirect
45. C22×(C2×D47)⋊C4C22semidirect
46. C22×(C2×D47)⋊C4C22semidirect
48. C2×C22⋊C4×D47C22semidirect
49. C22×C4×Dic47C22semidirect
50. #15689058C22semidirect
51. #15689041C22semidirect
52. #15689038C22semidirect
53. #15689015C22semidirect
54. #15689011C22semidirect
55. #15689001C22semidirect
56. #15689001C22semidirect
57. #15688997C22semidirect
58. #15688982C22semidirect
59. #15688978C22semidirect
60. C2×C47⋊#95C22semidirect
61. C2×C47⋊#95C22semidirect
62. C2×C47⋊#95C22semidirect
63. C22×C4⋊C4×C47C22semidirect
67. C47×#397C22semidirect
68. C2×#95×C47C22semidirect
69. C2×#95×C47C22semidirect
70. C2×#95×C47C22semidirect
110. C22×C4×D47C23semidirect
115. C2×C4⋊Dic47C23semidirect
119. C2×Dic47⋊C4C23semidirect
120. C2×Dic47⋊C4C23semidirect
121. C2×Dic47⋊C4C23semidirect
123. C2×C22⋊Dic47D4semidirect
145. C2×(C2×D47)⋊C4C23semidirect
146. C2×(C2×D47)⋊C4C23semidirect
147. C2×(C2×D47)⋊C4C23semidirect
150. C2×C4×Dic47C23semidirect
151. C47⋊#95C23semidirect
152. C47⋊#95C23semidirect
153. C47⋊#95C23semidirect
162. C2×C4⋊C4×C47C23semidirect
169. #95×C47C23semidirect
170. #95×C47C23semidirect
171. #95×C47C23semidirect
292. C22⋊Dic47C2×D4semidirect
375. C22×D47#123semidirect
478. C2×D47C2×#123semidirect
496. C2×#397D47semidirect
507. C2×C47#2418semidirect
535. C22×C4⋊C4C2×D47semidirect
556. #397C2×D47semidirect
569. C2×#95C2×D47semidirect
570. C2×#95C2×D47semidirect
571. C2×#95C2×D47semidirect
572. C47C2×#2418semidirect
632. C2×C4⋊C4C22×D47semidirect
671. #95C22×D47semidirect
672. #95C22×D47semidirect
673. #95C22×D47semidirect
995. C2#20246851direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940062
C22×#130939942
C22×#130939862
C22×C22⋊C4×D472
#202468512
C2×#156890582
C2×#156890412
C2×#156890382
C2×#156890152
C2×#156890112
C2×#156890012
C2×#156889972
C2×#156889822
C2×#156889782
C2×C47×#3972
C2×#241847