Finite Group Databasebeta

← #25017965

Subgroups — #25017965

Order 11008.

2194 conjugacy classes of subgroups.

The subgroup lattice has 1180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582800C211yesmaximal, characteristic
2C2×#14582777C211yesmaximal, characteristic
3C2×#14582777C211yesmaximal, characteristic
4C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
5C2×#14582746C211yesmaximal, characteristic, complemented
6#19132833C211yesmaximal, characteristic, complemented
7#19132831C211yesmaximal, characteristic, complemented
8#19132831C211yesmaximal, characteristic, complemented
9#19132831C211yesmaximal, characteristic, complemented
10#19132827C211yesmaximal, characteristic, complemented
11#19132820C211yesmaximal, characteristic, complemented
12(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
13(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
14#95×Dic43C211yesmaximal, characteristic, complemented
15C43×#1436C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17C23×C4×D43C2211yescharacteristic
18C23×C4×D43C2211yescharacteristic
19C22×(C2×D43)⋊C4C2211yescharacteristic
20C22×(C2×D43)⋊C4C2211yescharacteristic
21C22×(C2×D43)⋊C4C2211yescharacteristic
22C22×(C2×D43)⋊C4C2211yescharacteristic
23C22×(C2×D43)⋊C4C2211yescharacteristic
24C22×(C2×D43)⋊C4C2211yescharacteristic
25C22×(C2×D43)⋊C4C2211yescharacteristic
26C22×(C2×D43)⋊C4C2211yescharacteristic
27C22×(C2×D43)⋊C4C2211yescharacteristic
28C22×(C2×D43)⋊C4C2211yescharacteristic
29C22×C4×Dic43C2211yescharacteristic
30C22×C4×Dic43C2211yescharacteristic
31C22×C4×Dic43C2211yescharacteristic
32C22×C4×Dic43C2211yescharacteristic
33#14582800C418yescomplemented
34#14582777C418yescomplemented
35#14582777C418yescomplemented
36C4×(C2×D43)⋊C4—24no—
37#14582746—24no—
38C2×C43⋊#95C2211yescharacteristic
39C2×C43⋊#95C2211yescharacteristic
40C2×C43⋊#95C2211yescharacteristic
41C2×C43⋊#95C2211yescharacteristic
42C2×C43⋊#95C2211yescharacteristic
43C2×C43⋊#95C2211yescharacteristic
44C2×C43⋊#95C2211yescharacteristic
45C2×C43⋊#95C2211yescharacteristic
46C2×C43⋊#95C2211yescharacteristic
47C2×C43⋊#95C2211yescharacteristic
48C2×C43⋊#95C2211yescharacteristic
49C22×C4⋊C4×C43C2211yescharacteristic
50C22×C42×C43C2211yescharacteristic
51C2×#95×C43C2211yescharacteristic
52C2×#95×C43C2211yescharacteristic
53C2×#95×C43C2211yescharacteristic
54C2×#95×C43C2211yescharacteristic
55C2×#95×C43C2211yescharacteristic
56C24×D43C2311yescharacteristic
57C24×D43C2311yescharacteristic
58C22×D172—41no—
59C22×D172—41no—
60C22×D172—41no—
61C22×D172—41no—
62C22×D172C2×C414yes—
63C22×D172C2×C414yes—
64C22×D172C2×C414yes—
65C23×Dic43C2311yescharacteristic
66C23×Dic43C2311yescharacteristic
67C23×Dic43C2311yescharacteristic
68C23×Dic43C2311yescharacteristic
69C23×Dic43C2311yescharacteristic
70C23×Dic43C2311yescharacteristic
71C22×C4×D43—22no—
72C22×C4×D43—22no—
73C22×C4×D43—22no—
74C22×C4×D43—22no—
75C22×C4×D43—41no—
76C22×C4×D43—41no—
77C22×C4×D43—41no—
78C22×C4×D43—41no—
79C22×C4×D43—41no—
80C22×C4×D43—41no—
81C22×C4×D43—41no—
82C22×C4×D43—41no—
83C22×C4×D43C2×C414yescomplemented
84C22×C4×D43C2×C414yescomplemented
85C2×(C2×D43)⋊C4—22no—
86C2×(C2×D43)⋊C4—22no—
87C2×(C2×D43)⋊C4—22no—
88C2×(C2×D43)⋊C4—22no—
89C2×(C2×D43)⋊C4—22no—
90C2×(C2×D43)⋊C4—22no—
91C2×(C2×D43)⋊C4—22no—
92C2×(C2×D43)⋊C4—22no—
93C2×(C2×D43)⋊C4—41no—
94C2×(C2×D43)⋊C4—41no—
95C2×(C2×D43)⋊C4—41no—
96C2×(C2×D43)⋊C4—41no—
97C2×(C2×D43)⋊C4—41no—
98C2×(C2×D43)⋊C4—41no—
99C2×(C2×D43)⋊C4—41no—
100C2×(C2×D43)⋊C4—41no—
101C2×(C2×D43)⋊C4—41no—
102C2×(C2×D43)⋊C4—41no—
103C2×(C2×D43)⋊C4—41no—
104C2×(C2×D43)⋊C4—41no—
105C2×(C2×D43)⋊C4C2×C414yes—
106C2×(C2×D43)⋊C4C2×C414yes—
107C2×(C2×D43)⋊C4C2×C414yes—
108C2×(C2×D43)⋊C4C2×C414yes—
109C2×(C2×D43)⋊C4C2×C414yescomplemented
110C2×(C2×D43)⋊C4C2×C414yescomplemented
111C2×(C2×D43)⋊C4C2×C414yescomplemented
112C2×(C2×D43)⋊C4C2×C414yescomplemented
113C2×(C2×D43)⋊C4C2×C414yescomplemented
114C2×(C2×D43)⋊C4C2×C414yescomplemented
115C2×C4×Dic43—22no—
116C2×C4×Dic43—22no—
117C2×C4×Dic43—41no—
118C2×C4×Dic43—41no—
119C2×C4×Dic43—41no—
120C2×C4×Dic43—41no—
121C2×C4×Dic43—41no—
122C2×C4×Dic43—41no—
123C2×C4×Dic43—41no—
124C2×C4×Dic43—41no—
125C2×C4×Dic43C2×C414yescomplemented
126C2×C4×Dic43D414yescomplemented
127C43⋊#95—22no—
128C43⋊#95—22no—
129C43⋊#95—22no—
130C43⋊#95—22no—
131C43⋊#95—22no—
132C43⋊#95—41no—
133C43⋊#95—41no—
134C43⋊#95—41no—
135C43⋊#95—41no—
136C43⋊#95C2×C414yescomplemented
137C43⋊#95C2×C414yescomplemented
138C23×C4×C43C2311yescharacteristic
139C23×C4×C43C2311yescharacteristic
140C23×C4×C43C2311yescharacteristic
141C23×C4×C43C2311yescharacteristic
142C23×C4×C43C2311yescharacteristic
143C23×C4×C43C2311yescharacteristic
144C23×C4×C43C2311yescharacteristic
145C2×C4⋊C4×C43—41no—
146C2×C4⋊C4×C43—41no—
147C2×C4⋊C4×C43C2×C414yescomplemented
148C2×C42×C43—22no—
149C2×C42×C43—41no—
150C2×C42×C43—41no—
151#95×C43—22no—
152#95×C43—41no—
153#95×C43—41no—
154#95×C43C2×C414yescomplemented
155#95×C43C2×C414yescomplemented
156C24×C43C2411yescharacteristic
157C23×D43—21no—
158C23×D43—21no—
159C23×D43—21no—
160C23×D43—21no—
161C23×D43—21no—
162C23×D43—21no—
163C23×D43—21no—
164C23×D43—21no—
165C23×D43—21no—
166C23×D43—21no—
167C23×D43—21no—
168C23×D43—21no—
169C23×D43—21no—
170C23×D43—21no—
171C23×D43—21no—
172C23×D43—21no—
173C23×D43—21no—
174C23×D43—21no—
175C23×D43—21no—
176C23×D43—21no—
177C23×D43—21no—
178C23×D43—21no—
179C23×D43—21no—
180C23×D43—21no—
181C23×D43C22×C412yes—
182C23×D43C22×C412yes—
183C23×D43C22×C412yes—
184C23×D43C22×C412yes—
185C23×D43C22×C412yes—
186C23×D43C22×C412yes—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43—21no—
199C22×C4×C43—21no—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43—21no—
203C22×C4×C43—21no—
204C22×C4×C43—21no—
205C22×C4×C43—21no—
206C22×C4×C43—21no—
207C22×C4×C43—21no—
208C22×C4×C43—21no—
209C22×C4×C43—21no—
210C22×C4×C43—21no—
211C22×C4×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43—21no—
215C22×C4×C43—21no—
216C22×C4×C43—21no—
217C22×C4×C43—21no—
218C22×C4×C43—21no—
219C22×C4×C43—21no—
220C22×C4×C43—21no—
221C22×C4×C43—21no—
222C22×C4×C43—21no—
223C22×C4×C43—21no—
224C22×C4×C43—21no—
225C22×C4×C43C22×C412yes—
226C22×C4×C43C22×C412yes—
227C22×C4×C43C22×C412yes—
228C22×C4×C43C22×C412yes—
229C22×C4×C43C22×C412yes—
230C22×C4×C43C22×C412yes—
231C22×C4×C43C22×C412yes—
232C22×C4×C43C22×C412yes—
233C22×C4×C43C22×C412yes—
234C22×C4×C43C2×D412yes—
235C22×C4×C43#4112yes—
236C22×Dic43—21no—
237C22×Dic43—21no—
238C22×Dic43—21no—
239C22×Dic43—21no—
240C22×Dic43—21no—
241C22×Dic43—21no—
242C22×Dic43—21no—
243C22×Dic43—21no—
244C22×Dic43—21no—
245C22×Dic43—21no—
246C22×Dic43—21no—
247C22×Dic43—21no—
248C22×Dic43—21no—
249C22×Dic43—21no—
250C22×Dic43—21no—
251C22×Dic43—21no—
252C22×Dic43—21no—
253C22×Dic43—21no—
254C22×Dic43—21no—
255C22×Dic43—21no—
256C22×Dic43—21no—
257C22×Dic43—21no—
258C22×Dic43—21no—
259C22×Dic43—21no—
260C22×Dic43—21no—
261C22×Dic43—21no—
262C22×Dic43—21no—
263C22×Dic43—21no—
264C22×Dic43—21no—
265C22×Dic43—21no—
266C22×Dic43—21no—
267C22×Dic43—21no—
268C22×Dic43C22×C412yes—
269C22×Dic43C22×C412yes—
270C22×Dic43C22×C412yes—
271C22×Dic43C22×C412yes—
272C22×Dic43C22×C412yes—
273C22×Dic43C22×C412yes—
274C22×Dic43C2×D412yes—
275C22×Dic43C2×D412yes—
276C22×Dic43#4112yes—
277C22×Dic43#4112yes—
278C2×D172—44no—
279C2×D172—44no—
280C2×D172—44no—
281C2×D172—44no—
282C2×D172—44no—
283C2×D172—44no—
284C2×D172C42116yescomplemented
285C2×C4×D43—28no—
286C2×C4×D43—28no—
287C2×C4×D43—44no—
288C2×C4×D43—44no—
289C2×C4×D43—44no—
290C2×C4×D43—44no—
291C2×C4×D43—44no—
292C2×C4×D43—44no—
293C2×C4×D43—44no—
294C2×C4×D43—44no—
295C2×C4×D43—44no—
296C2×C4×D43—44no—
297C2×C4×D43—44no—
298C2×C4×D43—44no—
299C4⋊C4×C43—44no—
300C42×C43—44no—
301(C2×D43)⋊C4—28no—
302(C2×D43)⋊C4—28no—
303(C2×D43)⋊C4—28no—
304(C2×D43)⋊C4—28no—
305(C2×D43)⋊C4—44no—
306(C2×D43)⋊C4—44no—
307(C2×D43)⋊C4—44no—
308(C2×D43)⋊C4—44no—
309(C2×D43)⋊C4—44no—
310(C2×D43)⋊C4—44no—
311C4×Dic43—44no—
312C4×Dic43—44no—
313C4×Dic43—44no—
314C4×Dic43—44no—
315C23×C43C23×C411yescharacteristic
316C23×C43C23×C411yescharacteristic
317C23×C43C23×C411yescharacteristic
318C23×C43C22×D411yescharacteristic
319C23×C43C2×#4111yescharacteristic
320C23×C43C2×#4111yescharacteristic
321C23×C43C2×#4111yescharacteristic
322C23×C43H(5,𝔽2)11yescharacteristic
323C23×C43H(5,𝔽2)11yescharacteristic
324C23×C43H(5,𝔽2)11yescharacteristic
325C23×C43H(5,𝔽2)11yescharacteristic
326C23×C43H(5,𝔽2)11yescharacteristic
327C23×C43H(5,𝔽2)11yescharacteristic
328C23×C43H(5,𝔽2)11yescharacteristic
329C23×C432−1+411yescharacteristic
330C22×D43—22no—
331C22×D43—22no—
332C22×D43—22no—
333C22×D43—22no—
334C22×D43—22no—
335C22×D43—22no—
336C22×D43—22no—
337C22×D43—22no—
338C22×D43—22no—
339C22×D43—22no—
340C22×D43—22no—
341C22×D43—22no—
342C22×D43—22no—
343C22×D43—22no—
344C22×D43—22no—
345C22×D43—22no—
346C22×D43—22no—
347C22×D43—22no—
348C22×D43—22no—
349C22×D43—22no—
350C22×D43—22no—
351C22×D43—22no—
352C22×D43—22no—
353C22×D43—22no—
354C22×D43—22no—
355C22×D43—22no—
356C22×D43—22no—
357C22×D43—22no—
358C22×D43—22no—
359C22×D43—22no—
360C22×D43—22no—
361C22×D43—22no—
362C22×D43—22no—
363C22×D43—22no—
364C22×D43—22no—
365C22×D43—22no—
366C22×D43—41no—
367C22×D43—41no—
368C22×D43—41no—
369C22×D43—41no—
370C22×D43—41no—
371C22×D43—41no—
372C22×D43—41no—
373C22×D43—41no—
374C22×D43—41no—
375C22×D43—41no—
376C22×D43—41no—
377C22×D43—41no—
378C22×D43—41no—
379C22×D43—41no—
380C22×D43—41no—
381C22×D43—41no—
382C22×D43—41no—
383C22×D43—41no—
384C22×D43—41no—
385C22×D43—41no—
386C22×D43—41no—
387C22×D43—41no—
388C22×D43—41no—
389C22×D43—41no—
390C22×D43—41no—
391C22×D43—41no—
392C22×D43—41no—
393C22×D43—41no—
394C22×D43—41no—
395C22×D43—41no—
396C22×D43—41no—
397C22×D43—41no—
398C22×D43C2×C4214yes—
399C22×D43C2×C4214yes—
400C2×C4×C43—22no—
401C2×C4×C43—22no—
402C2×C4×C43—22no—
403C2×C4×C43—22no—
404C2×C4×C43—22no—
405C2×C4×C43—22no—
406C2×C4×C43—22no—
407C2×C4×C43—22no—
408C2×C4×C43—22no—
409C2×C4×C43—22no—
410C2×C4×C43—22no—
411C2×C4×C43—22no—
412C2×C4×C43—22no—
413C2×C4×C43—22no—
414C2×C4×C43—22no—
415C2×C4×C43—22no—
416C2×C4×C43—22no—
417C2×C4×C43—22no—
418C2×C4×C43—22no—
419C2×C4×C43—22no—
420C2×C4×C43—22no—
421C2×C4×C43—22no—
422C2×C4×C43—22no—
423C2×C4×C43—22no—
424C2×C4×C43—22no—
425C2×C4×C43—22no—
426C2×C4×C43—22no—
427C2×C4×C43—41no—
428C2×C4×C43—41no—
429C2×C4×C43—41no—
430C2×C4×C43—41no—
431C2×C4×C43—41no—
432C2×C4×C43—41no—
433C2×C4×C43—41no—
434C2×C4×C43—41no—
435C2×C4×C43—41no—
436C2×C4×C43—41no—
437C2×C4×C43—41no—
438C2×C4×C43—41no—
439C2×C4×C43—41no—
440C2×C4×C43—41no—
441C2×C4×C43—41no—
442C2×C4×C43—41no—
443C2×C4×C43—41no—
444C2×C4×C43—41no—
445C2×C4×C43—41no—
446C2×C4×C43—41no—
447C2×C4×C43C2×C4214yes—
448C2×C4×C43C4×D414yes—
449C2×Dic43—22no—
450C2×Dic43—22no—
451C2×Dic43—22no—
452C2×Dic43—22no—
453C2×Dic43—22no—
454C2×Dic43—22no—
455C2×Dic43—22no—
456C2×Dic43—22no—
457C2×Dic43—22no—
458C2×Dic43—22no—
459C2×Dic43—22no—
460C2×Dic43—22no—
461C2×Dic43—22no—
462C2×Dic43—22no—
463C2×Dic43—22no—
464C2×Dic43—22no—
465C2×Dic43—22no—
466C2×Dic43—22no—
467C2×Dic43—22no—
468C2×Dic43—22no—
469C2×Dic43—22no—
470C2×Dic43—22no—
471C2×Dic43—22no—
472C2×Dic43—22no—
473C2×Dic43—41no—
474C2×Dic43—41no—
475C2×Dic43—41no—
476C2×Dic43—41no—
477C2×Dic43—41no—
478C2×Dic43—41no—
479C2×Dic43—41no—
480C2×Dic43—41no—
481C2×Dic43—41no—
482C2×Dic43—41no—
483C2×Dic43—41no—
484C2×Dic43—41no—
485C2×Dic43—41no—
486C2×Dic43—41no—
487C2×Dic43—41no—
488C2×Dic43—41no—
489C2×Dic43C4×D414yes—
490C2×Dic43C4×D414yes—
491D172—416no—
492C4×D43—416no—
493C4×D43—416no—
494#13791—431nomaximal, Sylow
495C22×C43C22×C4211yescharacteristic
496C22×C43C2×C4×D411yescharacteristic
497C22×C43C2×C4×D411yescharacteristic
498C22×C43C2×C4×D411yescharacteristic
499C22×C43C4×#4111yescharacteristic
500C22×C43C4×#4111yescharacteristic
501C22×C43C4×#4111yescharacteristic
502C22×C43#51811yescharacteristic
503C22×C43#51811yescharacteristic
504C22×C43#51811yescharacteristic
505C22×C43#51811yescharacteristic
506C22×C43#51811yescharacteristic
507C22×C43#51811yescharacteristic
508C22×C43#51811yescharacteristic
509C22×C43#51811yescharacteristic
510C22×C43#51811yescharacteristic
511C22×C43#52011yescharacteristic
512C22×C43#52011yescharacteristic
513C22×C43#52011yescharacteristic
514C22×C43#53411yescharacteristic
515C22×C43#53511yescharacteristic
516C22×C43#53511yescharacteristic
517C22×C43#53711yescharacteristic
518C22×C43#53811yescharacteristic
519C22×C43#53811yescharacteristic
520C22×C43#53811yescharacteristic
521C22×C43#53811yescharacteristic
522C22×C43#53811yescharacteristic
523C22×C43#53911yescharacteristic
524C22×C43#54011yescharacteristic
525C22×C43#54011yescharacteristic
526C22×C43#54011yescharacteristic
527C22×C43#54011yescharacteristic
528C22×C43#54211yescharacteristic
529C22×C43#54211yescharacteristic
530C2×D43—24no—
531C2×D43—24no—
532C2×D43—24no—
533C2×D43—24no—
534C2×D43—24no—
535C2×D43—24no—
536C2×D43—42no—
537C2×D43—42no—
538C2×D43—42no—
539C2×D43—42no—
540C2×D43—42no—
541C2×D43—42no—
542C2×D43—42no—
543C2×D43—42no—
544C2×D43—42no—
545C2×D43—42no—
546C2×D43—42no—
547C2×D43—42no—
548C2×D43—42no—
549C2×D43—42no—
550C2×D43—42no—
551C2×D43—42no—
552C2×D43—42no—
553C2×D43—42no—
554C2×D43—42no—
555C2×D43—42no—
556C2×D43—42no—
557C2×D43—42no—
558C2×D43—42no—
559C2×D43—42no—
560C4×C43—24no—
561C4×C43—24no—
562C4×C43—42no—
563C4×C43—42no—
564C4×C43—42no—
565C4×C43—42no—
566C4×C43—42no—
567Dic43—24no—
568Dic43—24no—
569Dic43—42no—
570Dic43—42no—
571Dic43—42no—
572Dic43—42no—
573C2×#390—431no—
574C2×#386—431no—
575C2×#386—431no—
576C2×C4×C22⋊C4—431no—
577C2×C4×C22⋊C4—431no—
578#1437—431no—
579#1437—431no—
580#1437—431no—
581#1437—431no—
582#1436—431no—
583#1436D4311yescharacteristic, complemented
584#1434—431no—
585C22⋊#95—431no—
586C22⋊#95—431no—
587C4×#95—431no—
588C2×C43C42×D411yescharacteristic
589C2×C43#227311yescharacteristic
590C2×C43#227511yescharacteristic
591C2×C43#232111yescharacteristic
592C2×C43#232111yescharacteristic
593C2×C43#232411yescharacteristic
594C2×C43#232411yescharacteristic
595C2×C43#232511yescharacteristic
596C2×C43#232811yescharacteristic
597C2×C43#233311yescharacteristic
598C2×C43#233311yescharacteristic
599C2×C43#233311yescharacteristic
600C2×C43#233511yescharacteristic
601C2×C43#233511yescharacteristic
602C2×C43#233711yescharacteristic
603D43—44no—
604D43—44no—
605C23×D4—431no—
606C24×C4—431no—
607C24×C4—431no—
608C22×C4⋊C4C2×D4311yescharacteristic
609C22×C22⋊C4—431no—
610C22×C22⋊C4—431no—
611C22×C22⋊C4—431no—
612C22×C22⋊C4—431no—
613C22×C22⋊C4—431no—
614C22×C22⋊C4—431no—
615C22×C22⋊C4—431no—
616C22×C22⋊C4—431no—
617C22×C22⋊C4—431no—
618C22×C22⋊C4—431no—
619C22×C42—431no—
620C22×C42—431no—
621C22×C42—431no—
622C22×C42—431no—
623C22×C42C2×D4311yescharacteristic
624#390—438no—
625#386—438no—
626#386—438no—
627C4×C22⋊C4—864no—
628C4×C22⋊C4—864no—
629C2×#95—431no—
630C2×#95—431no—
631C2×#95—431no—
632C2×#95—431no—
633C2×#95—431no—
634C2×#95—431no—
635C2×#95—431no—
636C2×#95—431no—
637C2×#95—431no—
638C2×#95—431no—
639C2×#95—431no—
640C2×#95C2×D4311yescharacteristic
641C2×#95C2×D4311yescharacteristic
642C2×#95C2×D4311yescharacteristic
643C2×#95C2×D4311yescharacteristic
644C2×#95C2×D4311yescharacteristic
645C43#1379111yescharacteristic, complemented, Sylow
646C25—431no—
647C25—431no—
648C22×D4—434no—
649C22×D4—434no—
650C22×D4—434no—
651C22×D4—1721no—
652C22×D4—1721no—
653C22×D4—1721no—
654C22×D4—1721no—
655C23×C4—431no—
656C23×C4—431no—
657C23×C4—431no—
658C23×C4—431no—
659C23×C4—431no—
660C23×C4—431no—
661C23×C4—434no—
662C23×C4—434no—
663C23×C4—862no—
664C23×C4—862no—
665C23×C4—862no—
666C23×C4—862no—
667C23×C4—1721no—
668C23×C4—1721no—
669C23×C4—1721no—
670C23×C4—1721no—
671C23×C4—1721no—
672C23×C4—1721no—
673C23×C4—1721no—
674C23×C4—1721no—
675C23×C4C22×D4311yescharacteristic
676C23×C4C22×D4311yescharacteristic
677C23×C4C22×D4311yescharacteristic
678C23×C4C22×D4311yescharacteristic
679C23×C4C22×D4311yescharacteristic
680C23×C4C22×D4311yescharacteristic
681C23×C4C22×D4311yescharacteristic
682C2×C4⋊C4—41no—
683C2×C4⋊C4—41no—
684C2×C4⋊C4C4×D4314yescomplemented
685C2×C22⋊C4—434no—
686C2×C22⋊C4—434no—
687C2×C22⋊C4—434no—
688C2×C22⋊C4—434no—
689C2×C22⋊C4—434no—
690C2×C22⋊C4—434no—
691C2×C22⋊C4—434no—
692C2×C22⋊C4—434no—
693C2×C22⋊C4—434no—
694C2×C22⋊C4—434no—
695C2×C22⋊C4—862no—
696C2×C22⋊C4—862no—
697C2×C22⋊C4—862no—
698C2×C22⋊C4—862no—
699C2×C22⋊C4—862no—
700C2×C22⋊C4—862no—
701C2×C22⋊C4—862no—
702C2×C22⋊C4—862no—
703C2×C22⋊C4—1721no—
704C2×C22⋊C4—1721no—
705C2×C22⋊C4—1721no—
706C2×C22⋊C4—1721no—
707C2×C22⋊C4—1721no—
708C2×C22⋊C4—1721no—
709C2×C22⋊C4—1721no—
710C2×C22⋊C4—1721no—
711C2×C22⋊C4—1721no—
712C2×C22⋊C4—1721no—
713C2×C22⋊C4—1721no—
714C2×C22⋊C4—1721no—
715C2×C42—22no—
716C2×C42—41no—
717C2×C42—41no—
718C2×C42—434no—
719C2×C42—434no—
720C2×C42—862no—
721C2×C42—862no—
722C2×C42—1721no—
723C2×C42—1721no—
724C2×C42—1721no—
725C2×C42—1721no—
726C2×C42—1721no—
727C2×C42—1721no—
728C2×C42—1721no—
729C2×C42—1721no—
730#95—22no—
731#95—41no—
732#95—41no—
733#95—434no—
734#95—434no—
735#95—862no—
736#95—862no—
737#95—862no—
738#95—862no—
739#95—862no—
740#95—1721no—
741#95—1721no—
742#95—1721no—
743#95—1721no—
744#95C4×D4314yescomplemented
745#95C4×D4314yescomplemented
746C24—432no—
747C24—432no—
748C24—432no—
749C24—432no—
750C24—432no—
751C24—432no—
752C24—861no—
753C24—861no—
754C24—861no—
755C24—861no—
756C24—861no—
757C24—861no—
758C24—861no—
759C24—861no—
760C24—861no—
761C24—861no—
762C24—861no—
763C24—861no—
764C24—861no—
765C24—861no—
766C24—861no—
767C24—861no—
768C24—861no—
769C24—861no—
770C24—861no—
771C24—861no—
772C24—861no—
773C24—861no—
774C24—861no—
775C24—861no—
776C24C23×D4311yescharacteristic
777C2×D4—4316no—
778C2×D4—1724no—
779C2×D4—1724no—
780C2×D4—1724no—
781C2×D4—1724no—
782C2×D4—1724no—
783C2×D4—1724no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—432no—
823C22×C4—432no—
824C22×C4—432no—
825C22×C4—432no—
826C22×C4—432no—
827C22×C4—432no—
828C22×C4—432no—
829C22×C4—432no—
830C22×C4—432no—
831C22×C4—432no—
832C22×C4—868no—
833C22×C4—861no—
834C22×C4—861no—
835C22×C4—861no—
836C22×C4—861no—
837C22×C4—861no—
838C22×C4—861no—
839C22×C4—861no—
840C22×C4—861no—
841C22×C4—861no—
842C22×C4—861no—
843C22×C4—861no—
844C22×C4—861no—
845C22×C4—861no—
846C22×C4—861no—
847C22×C4—861no—
848C22×C4—861no—
849C22×C4—861no—
850C22×C4—861no—
851C22×C4—861no—
852C22×C4—861no—
853C22×C4—861no—
854C22×C4—861no—
855C22×C4—861no—
856C22×C4—861no—
857C22×C4—861no—
858C22×C4—861no—
859C22×C4—861no—
860C22×C4—861no—
861C22×C4—861no—
862C22×C4—861no—
863C22×C4—861no—
864C22×C4—861no—
865C22×C4—868no—
866C22×C4—1724no—
867C22×C4—1724no—
868C22×C4—1724no—
869C22×C4—1724no—
870C22×C4—1724no—
871C22×C4—1724no—
872C22×C4—1724no—
873C22×C4—1724no—
874C22×C4—1724no—
875C22×C4—1724no—
876C22×C4—1724no—
877C22×C4—1724no—
878C22×C4C2×C4×D4312yes—
879C22×C4C2×C4×D4312yes—
880C22×C4C2×C4×D4312yes—
881C22×C4C2×C4×D4312yes—
882C22×C4C2×C4×D4312yes—
883C22×C4C2×C4×D4312yes—
884C22×C4C2×C4×D4312yes—
885C22×C4C2×C4×D4312yes—
886C22×C4C2×C4×D4312yes—
887C22×C4D4×D4312yes—
888C22×C4#1062190212yes—
889C4⋊C4—44no—
890C22⋊C4—868no—
891C22⋊C4—868no—
892C22⋊C4—868no—
893C22⋊C4—868no—
894C22⋊C4—1724no—
895C22⋊C4—1724no—
896C22⋊C4—1724no—
897C22⋊C4—1724no—
898C22⋊C4—1724no—
899C22⋊C4—1724no—
900C42—44no—
901C42—1724no—
902C42—1724no—
903C42—1724no—
904C42—1724no—
905C23—434no—
906C23—434no—
907C23—862no—
908C23—862no—
909C23—862no—
910C23—862no—
911C23—862no—
912C23—862no—
913C23—862no—
914C23—862no—
915C23—862no—
916C23—862no—
917C23—862no—
918C23—862no—
919C23—862no—
920C23—862no—
921C23—862no—
922C23—862no—
923C23—862no—
924C23—862no—
925C23—862no—
926C23—862no—
927C23—862no—
928C23—862no—
929C23—862no—
930C23—862no—
931C23—862no—
932C23—862no—
933C23—862no—
934C23—862no—
935C23—862no—
936C23—862no—
937C23—862no—
938C23—862no—
939C23—862no—
940C23—862no—
941C23—862no—
942C23—862no—
943C23—1721no—
944C23—1721no—
945C23—1721no—
946C23—1721no—
947C23—1721no—
948C23—1721no—
949C23—1721no—
950C23—1721no—
951C23—1721no—
952C23—1721no—
953C23—1721no—
954C23—1721no—
955C23—1721no—
956C23—1721no—
957C23—1721no—
958C23—1721no—
959C23—1721no—
960C23—1721no—
961C23—1721no—
962C23—1721no—
963C23—1721no—
964C23—1721no—
965C23—1721no—
966C23—1721no—
967C23—1721no—
968C23—1721no—
969C23—1721no—
970C23—1721no—
971C23—1721no—
972C23—1721no—
973C23—1721no—
974C23—1721no—
975C23C22×C4×D4311yescharacteristic
976C23C22×C4×D4311yescharacteristic
977C23C22×C4×D4311yescharacteristic
978C23C2×D4×D4311yescharacteristic
979C23#41×D4311yescharacteristic
980C23#41×D4311yescharacteristic
981C23C2×#1062190211yescharacteristic
982C23#1306337011yescharacteristic
983C23#1306337011yescharacteristic
984C23#1306337011yescharacteristic
985C23#1306337111yescharacteristic
986C23#1306337111yescharacteristic
987C23#1306337111yescharacteristic
988C23#1306337111yescharacteristic
989C23#1306337311yescharacteristic
990D4—17216no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—434no—
1039C2×C4—434no—
1040C2×C4—862no—
1041C2×C4—862no—
1042C2×C4—862no—
1043C2×C4—862no—
1044C2×C4—862no—
1045C2×C4—862no—
1046C2×C4—862no—
1047C2×C4—862no—
1048C2×C4—862no—
1049C2×C4—862no—
1050C2×C4—862no—
1051C2×C4—862no—
1052C2×C4—862no—
1053C2×C4—862no—
1054C2×C4—862no—
1055C2×C4—862no—
1056C2×C4—862no—
1057C2×C4—862no—
1058C2×C4—862no—
1059C2×C4—862no—
1060C2×C4—862no—
1061C2×C4—862no—
1062C2×C4—862no—
1063C2×C4—862no—
1064C2×C4—17216no—
1065C2×C4—17216no—
1066C2×C4—1721no—
1067C2×C4—1721no—
1068C2×C4—1721no—
1069C2×C4—1721no—
1070C2×C4—1721no—
1071C2×C4—1721no—
1072C2×C4—1721no—
1073C2×C4—1721no—
1074C2×C4—1721no—
1075C2×C4—1721no—
1076C2×C4—1721no—
1077C2×C4—1721no—
1078C2×C4—1721no—
1079C2×C4—1721no—
1080C2×C4—1721no—
1081C2×C4—1721no—
1082C2×C4C42×D4314yes—
1083C2×C4#1306328714yes—
1084C22—864no—
1085C22—864no—
1086C22—864no—
1087C22—864no—
1088C22—864no—
1089C22—864no—
1090C22—1722no—
1091C22—1722no—
1092C22—1722no—
1093C22—1722no—
1094C22—1722no—
1095C22—1722no—
1096C22—1722no—
1097C22—1722no—
1098C22—1722no—
1099C22—1722no—
1100C22—1722no—
1101C22—1722no—
1102C22—1722no—
1103C22—1722no—
1104C22—1722no—
1105C22—1722no—
1106C22—1722no—
1107C22—1722no—
1108C22—1722no—
1109C22—1722no—
1110C22—1722no—
1111C22—1722no—
1112C22—1722no—
1113C22—1722no—
1114C22C2×C42×D4311yescharacteristic
1115C22C4×D4×D4311yescharacteristic
1116C22C4×D4×D4311yescharacteristic
1117C22C2×#1306328711yescharacteristic
1118C22#1458336711yescharacteristic
1119C22C4×#1062190211yescharacteristic
1120C22C4×#1062190211yescharacteristic
1121C22#1458337111yescharacteristic
1122C22#1458337111yescharacteristic
1123C22#1458337111yescharacteristic
1124C22#1458337111yescharacteristic
1125C22#1458337111yescharacteristic
1126C22#1458337111yescharacteristic
1127C22#1458337211yescharacteristic
1128C22#1458337311yescharacteristic
1129C22#1458337311yescharacteristic
1130C22#1458338011yescharacteristic
1131C22#1458338111yescharacteristic
1132C22#1458338111yescharacteristic
1133C22#1458346011yescharacteristic
1134C22#1458346411yescharacteristic
1135C22#1458346511yescharacteristic
1136C22#1458347911yescharacteristic
1137C22#1458348311yescharacteristic
1138C22#1458348811yescharacteristic
1139C22#1458348811yescharacteristic
1140C22#1458348911yescharacteristic
1141C22#1458348911yescharacteristic
1142C22#1458349711yescharacteristic
1143C22#1458349911yescharacteristic
1144C22#1458350111yescharacteristic
1145C22#1458350111yescharacteristic
1146C22#1458350511yescharacteristic
1147C22#1458351911yescharacteristic
1148C22#1458352311yescharacteristic
1149C4—24no—
1150C4—24no—
1151C4—42no—
1152C4—42no—
1153C4—42no—
1154C4—42no—
1155C4—42no—
1156C4—864no—
1157C4—864no—
1158C4—1722no—
1159C4—1722no—
1160C4—1722no—
1161C4—1722no—
1162C2—1724no—
1163C2—1724no—
1164C2C4×#1306328711yescharacteristic
1165C2#1913694711yescharacteristic
1166C2#1913695511yescharacteristic
1167C2#1913725211yescharacteristic
1168C2#1913725711yescharacteristic
1169C2#1913728611yescharacteristic
1170C2#1913728711yescharacteristic
1171C2#1913729411yescharacteristic
1172C2#1913731611yescharacteristic
1173C2#1913735811yescharacteristic
1174C2#1913735911yescharacteristic
1175C2#1913735911yescharacteristic
1176C2#1913738811yescharacteristic
1177C2#1913739111yescharacteristic
1178C2#1913740711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC22×C43C22×C42
FittingC43×#1436C2
socle, cosocleC24×C43C24
prime radicalC23×D172C22
hypercenter#1436D43
hypocenterC43#13791
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
4. C2×C4×(C2×D43)⋊C4C2semidirect
5. C2×#14582746C2semidirect
6. #19132833C2semidirect
7. #19132831C2semidirect
8. #19132831C2semidirect
9. #19132831C2semidirect
10. #19132827C2semidirect
11. #19132820C2semidirect
12. (C2×D43)⋊#95C2semidirect
13. (C2×D43)⋊#95C2semidirect
14. #95×Dic43C2semidirect
15. C43×#1436C2semidirect
33. #14582800C4semidirect
34. #14582777C4semidirect
35. #14582777C4semidirect
83. C22×C4×D43C2×C4semidirect
84. C22×C4×D43C2×C4semidirect
109. C2×(C2×D43)⋊C4C2×C4semidirect
110. C2×(C2×D43)⋊C4C2×C4semidirect
111. C2×(C2×D43)⋊C4C2×C4semidirect
112. C2×(C2×D43)⋊C4C2×C4semidirect
113. C2×(C2×D43)⋊C4C2×C4semidirect
114. C2×(C2×D43)⋊C4C2×C4semidirect
125. C2×C4×Dic43C2×C4semidirect
126. C2×C4×Dic43D4semidirect
136. C43⋊#95C2×C4semidirect
137. C43⋊#95C2×C4semidirect
147. C2×C4⋊C4×C43C2×C4semidirect
154. #95×C43C2×C4semidirect
155. #95×C43C2×C4semidirect
284. C2×D172C42semidirect
583. #1436D43semidirect
645. C43#13791semidirect
684. C2×C4⋊C4C4×D43semidirect
744. #95C4×D43semidirect
745. #95C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145828002
C2×#145827772
C2×C4×(C2×D43)⋊C42
C2×#145827462
#191328332
#191328312
#191328272
#191328202
(C2×D43)⋊#952
#95×Dic432
C43×#14362
#1379143