Finite Group Databasebeta

← C2×#20248279 #26386287

Subgroups — C2×#20248279 #26386287

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×#13094009C211yesmaximal, characteristic, complemented
2C22×#13093994C211yesmaximal, characteristic
3C22×#13093986C211yesmaximal, characteristic, complemented
4C22×C22⋊C4×D47C211yesmaximal, characteristic, complemented
5#20248279C2116yesmaximal, direct product factor
6C2×#15689045C211yesmaximal, characteristic, complemented
7C2×#15689040C211yesmaximal, characteristic, complemented
8C2×#15689039C211yesmaximal, characteristic, complemented
9C2×#15689017C211yesmaximal, characteristic, complemented
10C2×#15689013C211yesmaximal, characteristic, complemented
11C2×#15689001C211yesmaximal, characteristic, complemented
12C2×#15688999C211yesmaximal, characteristic, complemented
13C2×#15688985C211yesmaximal, characteristic, complemented
14C2×#15688980C211yesmaximal, characteristic, complemented
15C2×#15688978C211yesmaximal, characteristic, complemented
16C2×C47×#396C211yesmaximal, characteristic, complemented
17C25×D47C2211yescharacteristic
18C23×D188C2211yescharacteristic
19C23×D188C2211yescharacteristic
20C23×C22⋊D47C2211yescharacteristic
21C23×C4×D47C2211yescharacteristic
22C23×C4×D47C2211yescharacteristic
23C23×C4×D47C2211yescharacteristic, complemented
24C2×#13094009—28no—
25C2×#13094009C2218yescomplemented
26C2×#13093994—28no—
27C2×#13093994C2218yes—
28C2×#13093986—28no—
29C2×#13093986C2218yescomplemented
30C22×C4⋊Dic47C2211yescharacteristic, complemented
31C22×Dic47⋊C4C2211yescharacteristic, complemented
32C22×C22⋊Dic47C2211yescharacteristic
33C22×C22⋊Dic47C2211yescharacteristic
34C22×(C2×D47)⋊C4C2211yescharacteristic
35C22×(C2×D47)⋊C4C2211yescharacteristic
36C22×(C2×D47)⋊C4C2211yescharacteristic
37C22×(C2×D47)⋊C4C2211yescharacteristic
38C22×(C2×D47)⋊C4C2211yescharacteristic
39C22×(C2×D47)⋊C4C2211yescharacteristic
40C22×(C2×D47)⋊C4C2211yescharacteristic
41C22×(C2×D47)⋊C4C2211yescharacteristic
42C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
43C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
44C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
45C2×C22⋊C4×D47—28no—
46C2×C22⋊C4×D47C2218yescomplemented
47C22×C4×Dic47C2211yescharacteristic, complemented
48#15689045C2218yescomplemented
49#15689040C2218yescomplemented
50#15689039C2218yescomplemented
51#15689017C2218yescomplemented
52#15689013C2218yescomplemented
53#15689001C2218yescomplemented
54#15688999C2218yescomplemented
55#15688985C2218yescomplemented
56#15688980C2218yescomplemented
57#15688978C2218yescomplemented
58C2×C47⋊#95C2211yescharacteristic, complemented
59C2×C47⋊#95C2211yescharacteristic, complemented
60C2×C47⋊#95C2211yescharacteristic, complemented
61C2×C47⋊#95C2211yescharacteristic, complemented
62C2×C47⋊#95C2211yescharacteristic, complemented
63C22×C4⋊C4×C47C2211yescharacteristic, complemented
64C22×C4⋊C4×C47C2211yescharacteristic, complemented
65C22×C4⋊C4×C47C2211yescharacteristic, complemented
66C22×C22⋊C4×C47C2211yescharacteristic
67C22×C22⋊C4×C47C2211yescharacteristic
68C22×C22⋊C4×C47C2211yescharacteristic
69C47×#396C2218yescomplemented
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—42no—
104C22×C4×D47—42no—
105C22×C4×D47—42no—
106C22×C4×D47—42no—
107C22×C4×D47D418yescomplemented
108C22×C4×D47C2314yes—
109C22×C4×D47C2314yes—
110C22×C4×D47C2314yescomplemented
111#13094009—232no—
112#13093994—232no—
113#13093986—232no—
114C2×C4⋊Dic47—42no—
115C2×C4⋊Dic47C2314yescomplemented
116C2×Dic47⋊C4—24no—
117C2×Dic47⋊C4C2314yescomplemented
118C2×C22⋊Dic47—24no—
119C2×C22⋊Dic47—24no—
120C2×C22⋊Dic47C2314yes—
121C2×C22⋊Dic47C2314yes—
122C2×(C2×D47)⋊C4—24no—
123C2×(C2×D47)⋊C4—24no—
124C2×(C2×D47)⋊C4—24no—
125C2×(C2×D47)⋊C4—24no—
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—42no—
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)⋊C4C2314yes—
140C2×(C2×D47)⋊C4C2314yes—
141C2×(C2×D47)⋊C4C2314yescomplemented
142C2×(C2×D47)⋊C4C2314yescomplemented
143C2×(C2×D47)⋊C4C2314yescomplemented
144C22⋊C4×D47—232no—
145C2×C4×Dic47—24no—
146C2×C4×Dic47C2314yescomplemented
147C47⋊#95C2314yescomplemented
148C47⋊#95C2314yescomplemented
149C47⋊#95C2314yescomplemented
150C47⋊#95C2314yescomplemented
151C47⋊#95C2314yescomplemented
152C25×C47C2311yescharacteristic
153C23×C4×C47C2311yescharacteristic
154C23×C4×C47C2311yescharacteristic
155C23×C4×C47C2311yescharacteristic
156C23×C4×C47C2311yescharacteristic
157C23×C4×C47C2311yescharacteristic
158C23×C4×C47C2311yescharacteristic
159C2×C4⋊C4×C47—24no—
160C2×C4⋊C4×C47—24no—
161C2×C4⋊C4×C47—42no—
162C2×C4⋊C4×C47C2314yescomplemented
163C2×C4⋊C4×C47C2314yescomplemented
164C2×C4⋊C4×C47C2314yescomplemented
165C2×C22⋊C4×C47—24no—
166C2×C22⋊C4×C47—24no—
167C2×C22⋊C4×C47—42no—
168C2×C22⋊C4×C47C2314yes—
169C2×C22⋊C4×C47C2314yes—
170C2×C22⋊C4×C47C2314yes—
171#95×C47C2314yescomplemented
172C24×C47—22no—
173C24×C47—22no—
174C24×C47—22no—
175C24×C47—22no—
176C24×C47—22no—
177C24×C47—22no—
178C24×C47#4114yes—
179C24×C47C2412yes—
180C24×C47C2411yescharacteristic
181C23×D47—22no—
182C23×D47—22no—
183C23×D47—22no—
184C23×D47—22no—
185C23×D47—232no—
186C23×D47—22no—
187C23×D47—22no—
188C23×D47—22no—
189C23×D47—22no—
190C23×D47—22no—
191C23×D47—22no—
192C23×D47—28no—
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×D47C2×D414yes—
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×C47C2×D414yes—
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×Dic47—22no—
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—416no—
280C2×C4×D47—44no—
281C2×C4×D47—44no—
282C2×C4×D47—44no—
283C2×C4×D47—44no—
284C2×C4×D47—416no—
285C2×C4×D47—416no—
286C2×C4×D47C2×D4116yescomplemented
287C4⋊C4×C47—28no—
288C4⋊C4×C47—28no—
289C4⋊C4×C47—44no—
290C22⋊C4×C47—28no—
291C22⋊C4×C47—28no—
292C22⋊C4×C47—44no—
293C22⋊Dic47—28no—
294C22⋊Dic47—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—28no—
303(C2×D47)⋊C4—28no—
304(C2×D47)⋊C4—28no—
305(C2×D47)⋊C4—44no—
306C4⋊Dic47—44no—
307Dic47⋊C4—28no—
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×D412yes—
323C23×C47C22×D412yes—
324C23×C47C2×#4112yes—
325C23×C47C2×#4112yes—
326C23×C47C2×#4114yes—
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—416no—
365C22×D47—4128no—
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#121116yes—
376C22×D47C22×D414yes—
377C22×D47C22×D414yes—
378C22×D47C22×D414yes—
379C22×D47C2×#4114yes—
380C22×D47C2×#4114yes—
381C2×C4×C47—28no—
382C2×C4×C47—28no—
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×C47C22×D414yes—
404C2×C4×C47C22×D414yes—
405C22⋊D47—416no—
406C2×Dic47—28no—
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—22no—
420C2×Dic47—22no—
421C2×Dic47—44no—
422C2×Dic47—44no—
423C2×Dic47—44no—
424C2×Dic47—44no—
425C2×Dic47C22×D414yes—
426D188—232no—
427D188—416no—
428C4×D47—416no—
429C4×D47—416no—
430C4×D47—416no—
431C2×#2534—471nomaximal, Sylow
432C22×C47—24no—
433C22×C47—24no—
434C22×C47—24no—
435C22×C47—42no—
436C22×C47—42no—
437C22×C47—42no—
438C22×C47—42no—
439C22×C47—416no—
440C22×C47C2×#12114yes—
441C22×C47#52514yes—
442C22×C47#53414yes—
443C22×C47#54614yes—
444C22×C47#54614yes—
445C22×C47#55114yes—
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—24no—
456C2×D47—24no—
457C2×D47—24no—
458C2×D47—24no—
459C2×D47—24no—
460C2×D47—232no—
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—42no—
471C2×D47—42no—
472C2×D47—42no—
473C2×D47—42no—
474C2×D47—42no—
475C2×D47—42no—
476C2×D47—416no—
477C2×D47—416no—
478C2×D47C2×#12118yes—
479C4×C47—24no—
480C4×C47—24no—
481C4×C47—42no—
482C4×C47—42no—
483C4×C47—42no—
484C4×C47—42no—
485Dic47—24no—
486Dic47—42no—
487Dic47—42no—
488Dic47—42no—
489Dic47—42no—
490C22×#123—471no—
491C22×#120—471no—
492C22×C4×D4—471no—
493C23×C22⋊C4—471no—
494#2534—4716no—
495C2×#396—471no—
496C2×#396D4711yescharacteristic, complemented
497C2×#394—471no—
498C2×#394—471no—
499C2×#388—471no—
500C2×#388—471no—
501C2×#386—471no—
502C2×#386—471no—
503C2×#381—471no—
504C2×#380—471no—
505C2×#379—471no—
506C2×C47—44no—
507C2×C47#253418yescomplemented
508C2×C47C22×#12111yescharacteristic
509C2×C47C2×#52511yescharacteristic
510C2×C47C2×#53411yescharacteristic
511C2×C47C2×#54611yescharacteristic
512C2×C47C2×#54611yescharacteristic
513C2×C47C2×#55111yescharacteristic
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⋊C4C2×D4711yescharacteristic, complemented
534C22×C4⋊C4C2×D4711yescharacteristic, complemented
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#396—478no—
556#396C2×D4718yescomplemented
557#394—478no—
558#394—478no—
559#388—478no—
560#388—478no—
561#386—478no—
562#386—478no—
563#381—478no—
564#380—478no—
565#379—478no—
566C2×#95—471no—
567C2×#95—471no—
568C2×#95—471no—
569C2×#95—471no—
570C2×#95—471no—
571C2×#95C2×D4711yescharacteristic, complemented
572C47C2×#253411yescharacteristic, 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—478no—
599C23×C4—474no—
600C23×C4—471no—
601C23×C4—471no—
602C23×C4—471no—
603C23×C4—471no—
604C23×C4—474no—
605C23×C4—474no—
606C23×C4—944no—
607C23×C4—944no—
608C23×C4—944no—
609C23×C4—944no—
610C23×C4—1882no—
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—24no—
625C2×C4⋊C4—42no—
626C2×C4⋊C4—474no—
627C2×C4⋊C4—474no—
628C2×C4⋊C4—944no—
629C2×C4⋊C4—1882no—
630C2×C4⋊C4C22×D4714yescomplemented
631C2×C4⋊C4C22×D4714yescomplemented
632C2×C4⋊C4C22×D4714yescomplemented
633C2×C22⋊C4—24no—
634C2×C22⋊C4—24no—
635C2×C22⋊C4—42no—
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—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—9432no—
650C2×C22⋊C4—944no—
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—944no—
661C2×C22⋊C4—944no—
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#95—474no—
672#95—474no—
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—942no—
698C24—942no—
699C24—942no—
700C24—942no—
701C24—942no—
702C24—942no—
703C24—942no—
704C24—948no—
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—
718C24#1062535414yes—
719C24C23×D4712yes—
720C24C23×D4711yescharacteristic
721C2×D4—4716no—
722C2×D4—948no—
723C2×D4—9432no—
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—474no—
750C22×C4—472no—
751C22×C4—4716no—
752C22×C4—472no—
753C22×C4—472no—
754C22×C4—472no—
755C22×C4—472no—
756C22×C4—948no—
757C22×C4—948no—
758C22×C4—948no—
759C22×C4—948no—
760C22×C4—942no—
761C22×C4—942no—
762C22×C4—942no—
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—18816no—
775C22×C4—1884no—
776C22×C4—1884no—
777C22×C4—1884no—
778C22×C4—1884no—
779C22×C4—18816no—
780C22×C4—18816no—
781C22×C4D4×D4714yes—
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—28no—
791C4⋊C4—44no—
792C4⋊C4—948no—
793C4⋊C4—1884no—
794C22⋊C4—28no—
795C22⋊C4—28no—
796C22⋊C4—44no—
797C22⋊C4—948no—
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—948no—
808C22⋊C4—948no—
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—948no—
837C23—942no—
838C23—942no—
839C23—942no—
840C23—942no—
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—18816no—
865C23—188128no—
866C23—1884no—
867C23—1884no—
868C23—1884no—
869C23—1884no—
870C23—1884no—
871C23—1884no—
872C23—1884no—
873C23—1884no—
874C23C2×D4×D4712yes—
875C23C2×D4×D4712yes—
876C23#41×D4712yes—
877C23#41×D4712yes—
878C23C2×#1062535414yes—
879C23C2×#1062535412yes—
880C23#1309406912yes—
881C23#1309407012yes—
882C23C24×D4711yescharacteristic
883D4—9432no—
884D4—18816no—
885D4—18816no—
886C2×C4—28no—
887C2×C4—28no—
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—474no—
909C2×C4—948no—
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—942no—
921C2×C4—942no—
922C2×C4—942no—
923C2×C4—942no—
924C2×C4—18816no—
925C2×C4—18816no—
926C2×C4—18816no—
927C2×C4—1884no—
928C2×C4—1884no—
929C2×C4—1884no—
930C2×C4—1884no—
931C2×C4C2×D4×D4714yes—
932C2×C4C2×D4×D4714yes—
933C22—24no—
934C22—24no—
935C22—24no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22—416no—
941C22—478no—
942C22—944no—
943C22—944no—
944C22—944no—
945C22—944no—
946C22—944no—
947C22—944no—
948C22—9432no—
949C22—944no—
950C22—944no—
951C22—944no—
952C22—944no—
953C22—944no—
954C22—944no—
955C22—18864no—
956C22—1882no—
957C22—1882no—
958C22—1882no—
959C22—1882no—
960C22—1882no—
961C22—1882no—
962C22—1882no—
963C22—1882no—
964C22—18816no—
965C22—18816no—
966C22#121×D4714yes—
967C22#1568963614yes—
968C22#1568968114yes—
969C22#1568976414yes—
970C22#1568977014yes—
971C22#1568979814yes—
972C22#1568980014yes—
973C22C22×D4×D4711yescharacteristic
974C22C22×D4×D4711yescharacteristic
975C22C2×#41×D4711yescharacteristic
976C22C2×#41×D4711yescharacteristic
977C22C22×#1062535411yescharacteristic
978C22C2×#1309406911yescharacteristic
979C22C2×#1309407011yescharacteristic
980C4—24no—
981C4—24no—
982C4—42no—
983C4—42no—
984C4—42no—
985C4—42no—
986C4—944no—
987C4—1882no—
988C4—1882no—
989C4—1882no—
990C4—1882no—
991C2—44no—
992C2—948no—
993C2—1884no—
994C2—1884no—
995C2#2024827918yesdirect product factor
996C2C2×#121×D4711yescharacteristic
997C2C2×#1568963611yescharacteristic
998C2C2×#1568968111yescharacteristic
999C2C2×#1568976411yescharacteristic
1000C2C2×#1568977011yescharacteristic
1001C2C2×#1568979811yescharacteristic
1002C2C2×#1568980011yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#396C2
socleC24×C47C24
prime radicalC22×#13093994C2
hypercenterC2×#396D47
hypocenterC47C2×#2534
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C22×#13094009C2semidirect
3. C22×#13093986C2semidirect
4. C22×C22⋊C4×D47C2semidirect
5. #20248279C2direct (N × H)
6. C2×#15689045C2semidirect
7. C2×#15689040C2semidirect
8. C2×#15689039C2semidirect
9. C2×#15689017C2semidirect
10. C2×#15689013C2semidirect
11. C2×#15689001C2semidirect
12. C2×#15688999C2semidirect
13. C2×#15688985C2semidirect
14. C2×#15688980C2semidirect
15. C2×#15688978C2semidirect
16. C2×C47×#396C2semidirect
23. C23×C4×D47C22semidirect
25. C2×#13094009C22semidirect
29. C2×#13093986C22semidirect
30. C22×C4⋊Dic47C22semidirect
31. C22×Dic47⋊C4C22semidirect
42. C22×(C2×D47)⋊C4C22semidirect
43. C22×(C2×D47)⋊C4C22semidirect
44. C22×(C2×D47)⋊C4C22semidirect
46. C2×C22⋊C4×D47C22semidirect
47. C22×C4×Dic47C22semidirect
48. #15689045C22semidirect
49. #15689040C22semidirect
50. #15689039C22semidirect
51. #15689017C22semidirect
52. #15689013C22semidirect
53. #15689001C22semidirect
54. #15688999C22semidirect
55. #15688985C22semidirect
56. #15688980C22semidirect
57. #15688978C22semidirect
58. C2×C47⋊#95C22semidirect
59. C2×C47⋊#95C22semidirect
60. C2×C47⋊#95C22semidirect
61. C2×C47⋊#95C22semidirect
62. C2×C47⋊#95C22semidirect
63. C22×C4⋊C4×C47C22semidirect
64. C22×C4⋊C4×C47C22semidirect
65. C22×C4⋊C4×C47C22semidirect
69. C47×#396C22semidirect
70. C2×#95×C47C22semidirect
107. C22×C4×D47D4semidirect
110. C22×C4×D47C23semidirect
115. C2×C4⋊Dic47C23semidirect
117. C2×Dic47⋊C4C23semidirect
141. C2×(C2×D47)⋊C4C23semidirect
142. C2×(C2×D47)⋊C4C23semidirect
143. C2×(C2×D47)⋊C4C23semidirect
146. C2×C4×Dic47C23semidirect
147. C47⋊#95C23semidirect
148. C47⋊#95C23semidirect
149. C47⋊#95C23semidirect
150. C47⋊#95C23semidirect
151. C47⋊#95C23semidirect
162. C2×C4⋊C4×C47C23semidirect
163. C2×C4⋊C4×C47C23semidirect
164. C2×C4⋊C4×C47C23semidirect
171. #95×C47C23semidirect
286. C2×C4×D47C2×D4semidirect
496. C2×#396D47semidirect
507. C2×C47#2534semidirect
533. C22×C4⋊C4C2×D47semidirect
534. C22×C4⋊C4C2×D47semidirect
535. C22×C4⋊C4C2×D47semidirect
556. #396C2×D47semidirect
571. C2×#95C2×D47semidirect
572. C47C2×#2534semidirect
630. C2×C4⋊C4C22×D47semidirect
631. C2×C4⋊C4C22×D47semidirect
632. C2×C4⋊C4C22×D47semidirect
673. #95C22×D47semidirect
995. C2#20248279direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940092
C22×#130939942
C22×#130939862
C22×C22⋊C4×D472
#202482792
C2×#156890452
C2×#156890402
C2×#156890392
C2×#156890172
C2×#156890132
C2×#156890012
C2×#156889992
C2×#156889852
C2×#156889802
C2×#156889782
C2×C47×#3962
C2×#253447