Finite Group Databasebeta

← #25026653

Subgroups — #25026653

Order 11008.

1966 conjugacy classes of subgroups.

The subgroup lattice has 1168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582817C211yesmaximal, characteristic
2C2×#14582791C211yesmaximal, characteristic, complemented
3C2×#14582789C211yesmaximal, characteristic, complemented
4C2×#14582777C211yesmaximal, characteristic
5C2×#14582777C211yesmaximal, characteristic
6#19132861C211yesmaximal, characteristic, complemented
7#19132852C211yesmaximal, characteristic, complemented
8#19132841C211yesmaximal, characteristic, complemented
9#19132837C211yesmaximal, characteristic, complemented
10#19132826C211yesmaximal, characteristic, complemented
11(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
12(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
13(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
14(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
15C43×#1442C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17C23×C4×D43C2211yescharacteristic
18C23×C4×D43C2211yescharacteristic
19C22×C4⋊Dic43C2211yescharacteristic
20C22×Dic43⋊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×(C2×D43)⋊C4C2211yescharacteristic
30C22×(C2×D43)⋊C4C2211yescharacteristic
31C22×C4×Dic43C2211yescharacteristic
32#14582817C418yescomplemented
33#14582791—24no—
34#14582789—24no—
35#14582777—24no—
36#14582777—24no—
37C2×C43⋊#95C2211yescharacteristic
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
50C2×#95×C43C2211yescharacteristic
51C2×#95×C43C2211yescharacteristic
52C2×#95×C43C2211yescharacteristic
53C2×#95×C43C2211yescharacteristic
54C2×#95×C43C2211yescharacteristic
55C2×#95×C43C2211yescharacteristic
56C24×D43C2311yescharacteristic
57C24×D43C2311yescharacteristic
58C22×D172—22no—
59C22×D172—22no—
60C22×D172—22no—
61C22×D172—22no—
62C22×D172—41no—
63C22×D172—41no—
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—22no—
76C22×C4×D43—22no—
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×D43—41no—
84C22×C4×D43—41no—
85C2×C4⋊Dic43—22no—
86C2×C4⋊Dic43—41no—
87C2×C4⋊Dic43—41no—
88C2×Dic43⋊C4—41no—
89C2×Dic43⋊C4—41no—
90C2×Dic43⋊C4C2×C414yescomplemented
91C2×(C2×D43)⋊C4—22no—
92C2×(C2×D43)⋊C4—22no—
93C2×(C2×D43)⋊C4—22no—
94C2×(C2×D43)⋊C4—22no—
95C2×(C2×D43)⋊C4—22no—
96C2×(C2×D43)⋊C4—22no—
97C2×(C2×D43)⋊C4—22no—
98C2×(C2×D43)⋊C4—22no—
99C2×(C2×D43)⋊C4—22no—
100C2×(C2×D43)⋊C4—22no—
101C2×(C2×D43)⋊C4—22no—
102C2×(C2×D43)⋊C4—22no—
103C2×(C2×D43)⋊C4—41no—
104C2×(C2×D43)⋊C4—41no—
105C2×(C2×D43)⋊C4—41no—
106C2×(C2×D43)⋊C4—41no—
107C2×(C2×D43)⋊C4—41no—
108C2×(C2×D43)⋊C4—41no—
109C2×(C2×D43)⋊C4—41no—
110C2×(C2×D43)⋊C4—41no—
111C2×(C2×D43)⋊C4—41no—
112C2×(C2×D43)⋊C4—41no—
113C2×(C2×D43)⋊C4—41no—
114C2×(C2×D43)⋊C4—41no—
115C2×(C2×D43)⋊C4C2×C414yescomplemented
116C2×(C2×D43)⋊C4C2×C414yescomplemented
117C2×(C2×D43)⋊C4C2×C414yescomplemented
118C2×(C2×D43)⋊C4C2×C414yescomplemented
119C2×(C2×D43)⋊C4D414yes—
120C2×(C2×D43)⋊C4D414yes—
121C2×C4×Dic43—22no—
122C2×C4×Dic43—22no—
123C2×C4×Dic43—41no—
124C43⋊#95—22no—
125C43⋊#95—22no—
126C43⋊#95—22no—
127C43⋊#95—22no—
128C43⋊#95—22no—
129C43⋊#95—22no—
130C43⋊#95—22no—
131C43⋊#95—41no—
132C43⋊#95—41no—
133C43⋊#95—41no—
134C43⋊#95—41no—
135C43⋊#95—41no—
136C23×C4×C43C2311yescharacteristic
137C23×C4×C43C2311yescharacteristic
138C23×C4×C43C2311yescharacteristic
139C23×C4×C43C2311yescharacteristic
140C23×C4×C43C2311yescharacteristic
141C23×C4×C43C2311yescharacteristic
142C23×C4×C43C2311yescharacteristic
143C2×C4⋊C4×C43—22no—
144C2×C4⋊C4×C43—41no—
145C2×C4⋊C4×C43—41no—
146#95×C43—22no—
147#95×C43—22no—
148#95×C43—22no—
149#95×C43—41no—
150#95×C43—41no—
151#95×C43C2×C414yescomplemented
152C24×C43C2411yescharacteristic
153C23×D43—21no—
154C23×D43—21no—
155C23×D43—21no—
156C23×D43—21no—
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×D43C22×C412yes—
178C23×D43C22×C412yes—
179C23×D43C2×D412yes—
180C23×D43C2×D412yes—
181C23×D43#4112yes—
182C23×D43#4112yes—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
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×C43—21no—
226C22×C4×C43C22×C412yes—
227C22×C4×C43C22×C412yes—
228C22×C4×C43C22×C412yes—
229C22×C4×C43C2×D412yes—
230C22×C4×C43C2×D412yes—
231C22×C4×C43#4112yes—
232C22×Dic43—21no—
233C22×Dic43—21no—
234C22×Dic43—21no—
235C22×Dic43—21no—
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×Dic43—21no—
269C22×Dic43C22×C412yes—
270C22×Dic43C22×C412yes—
271C22×Dic43C2×D412yes—
272C22×Dic43C2×D412yes—
273C22×Dic43#4112yes—
274C2×D172—28no—
275C2×D172—28no—
276C2×D172—44no—
277C2×D172—44no—
278C2×D172—44no—
279C2×D172—44no—
280C2×D172—44no—
281C2×C4×D43—44no—
282C2×C4×D43—44no—
283C2×C4×D43—44no—
284C2×C4×D43—44no—
285C2×C4×D43—44no—
286C2×C4×D43—44no—
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—
295C4⋊C4×C43—44no—
296(C2×D43)⋊C4—28no—
297(C2×D43)⋊C4—28no—
298(C2×D43)⋊C4—44no—
299(C2×D43)⋊C4—44no—
300(C2×D43)⋊C4—44no—
301(C2×D43)⋊C4—44no—
302(C2×D43)⋊C4—44no—
303(C2×D43)⋊C4—44no—
304(C2×D43)⋊C4—44no—
305(C2×D43)⋊C4—44no—
306C4⋊Dic43—44no—
307Dic43⋊C4—44no—
308C4×Dic43—44no—
309C23×C43C23×C411yescharacteristic
310C23×C43C22×D411yescharacteristic
311C23×C43C22×D411yescharacteristic
312C23×C43C2×#4111yescharacteristic
313C23×C43C2×#4111yescharacteristic
314C23×C43C2×#4111yescharacteristic
315C23×C43C2×#4111yescharacteristic
316C23×C43H(5,𝔽2)11yescharacteristic
317C23×C43H(5,𝔽2)11yescharacteristic
318C23×C43H(5,𝔽2)11yescharacteristic
319C23×C43H(5,𝔽2)11yescharacteristic
320C23×C43H(5,𝔽2)11yescharacteristic
321C23×C43H(5,𝔽2)11yescharacteristic
322C23×C432−1+411yescharacteristic
323C23×C432−1+411yescharacteristic
324C22×D43—22no—
325C22×D43—22no—
326C22×D43—22no—
327C22×D43—22no—
328C22×D43—22no—
329C22×D43—22no—
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—41no—
361C22×D43—41no—
362C22×D43—41no—
363C22×D43—41no—
364C22×D43—41no—
365C22×D43—41no—
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×D43C4×D414yes—
393C22×D43C4×D414yes—
394C2×C4×C43—22no—
395C2×C4×C43—22no—
396C2×C4×C43—22no—
397C2×C4×C43—22no—
398C2×C4×C43—22no—
399C2×C4×C43—22no—
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—41no—
413C2×C4×C43—41no—
414C2×C4×C43—41no—
415C2×C4×C43—41no—
416C2×C4×C43—41no—
417C2×C4×C43—41no—
418C2×C4×C43—41no—
419C2×C4×C43—41no—
420C2×C4×C43—41no—
421C2×C4×C43—41no—
422C2×C4×C43—41no—
423C2×C4×C43—41no—
424C2×C4×C43—41no—
425C2×C4×C43—41no—
426C2×C4×C43—41no—
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×Dic43—22no—
444C2×Dic43—22no—
445C2×Dic43—22no—
446C2×Dic43—22no—
447C2×Dic43—22no—
448C2×Dic43—22no—
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—41no—
459C2×Dic43—41no—
460C2×Dic43—41no—
461C2×Dic43—41no—
462C2×Dic43—41no—
463C2×Dic43—41no—
464C2×Dic43—41no—
465C2×Dic43—41no—
466C2×Dic43—41no—
467C2×Dic43—41no—
468C2×Dic43—41no—
469C2×Dic43—41no—
470C2×Dic43—41no—
471C2×Dic43—41no—
472C2×Dic43—41no—
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—
485D172—416no—
486C4×D43—416no—
487C4×D43—416no—
488#14571—431nomaximal, Sylow
489C22×C43C2×C4×D411yescharacteristic
490C22×C43C2×C4×D411yescharacteristic
491C22×C43C4×#4111yescharacteristic
492C22×C43#51811yescharacteristic
493C22×C43#51811yescharacteristic
494C22×C43#52011yescharacteristic
495C22×C43#52011yescharacteristic
496C22×C43#53411yescharacteristic
497C22×C43#53411yescharacteristic
498C22×C43#53711yescharacteristic
499C22×C43#53711yescharacteristic
500C22×C43#53811yescharacteristic
501C22×C43#53811yescharacteristic
502C22×C43#53811yescharacteristic
503C22×C43#53811yescharacteristic
504C22×C43#53911yescharacteristic
505C22×C43#53911yescharacteristic
506C22×C43#54011yescharacteristic
507C22×C43#54011yescharacteristic
508C22×C43D4211yescharacteristic
509C22×C43#54611yescharacteristic
510C22×C43#54611yescharacteristic
511C22×C43#54611yescharacteristic
512C22×C43#54611yescharacteristic
513C22×C43#54711yescharacteristic
514C22×C43#54711yescharacteristic
515C22×C43#55111yescharacteristic
516C22×C43#55111yescharacteristic
517C22×C43#55111yescharacteristic
518C22×C43#55211yescharacteristic
519C22×C43#55211yescharacteristic
520C22×C43H(3,𝔽4)11yescharacteristic
521C22×C43#56211yescharacteristic
522C22×C43#56211yescharacteristic
523C22×C43#56311yescharacteristic
524C2×D43—24no—
525C2×D43—24no—
526C2×D43—24no—
527C2×D43—24no—
528C2×D43—24no—
529C2×D43—24no—
530C2×D43—42no—
531C2×D43—42no—
532C2×D43—42no—
533C2×D43—42no—
534C2×D43—42no—
535C2×D43—42no—
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—
554C4×C43—42no—
555C4×C43—42no—
556C4×C43—42no—
557C4×C43—42no—
558C4×C43—42no—
559C4×C43—42no—
560C4×C43—81no—
561Dic43—42no—
562Dic43—42no—
563Dic43—42no—
564Dic43—42no—
565Dic43—42no—
566Dic43—81no—
567C2×#394—431no—
568C2×#388—431no—
569C2×#388—431no—
570C2×#386—431no—
571C2×#386—431no—
572#1445—431no—
573#1442—431no—
574#1442D4311yescharacteristic, complemented
575#1439—431no—
576#1439—431no—
577#1436—431no—
578C22⋊#95—431no—
579C22⋊#95—431no—
580C22⋊#95—431no—
581C22⋊#95—431no—
582C2×C43#232511yescharacteristic
583C2×C43#232511yescharacteristic
584C2×C43#233311yescharacteristic
585C2×C43#235811yescharacteristic
586C2×C43#235911yescharacteristic
587C2×C43#235911yescharacteristic
588C2×C43#237911yescharacteristic
589C2×C43#267111yescharacteristic
590C2×C43#267111yescharacteristic
591C2×C43#268411yescharacteristic
592C2×C43#268411yescharacteristic
593C2×C43#269511yescharacteristic
594C2×C43#269511yescharacteristic
595C2×C43#274311yescharacteristic
596C2×C43#274311yescharacteristic
597D43—44no—
598D43—44no—
599C23×D4—431no—
600C24×C4—431no—
601C24×C4—431no—
602C22×C4⋊C4—431no—
603C22×C4⋊C4—431no—
604C22×C4⋊C4C2×D4311yescharacteristic
605C22×C22⋊C4—431no—
606C22×C22⋊C4—431no—
607C22×C22⋊C4—431no—
608C22×C22⋊C4—431no—
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×C42—431no—
616#394—438no—
617#388—864no—
618#388—864no—
619#386—864no—
620#386—864no—
621C2×#95—431no—
622C2×#95—431no—
623C2×#95—431no—
624C2×#95—431no—
625C2×#95—431no—
626C2×#95—431no—
627C2×#95—431no—
628C2×#95—431no—
629C2×#95—431no—
630C2×#95—431no—
631C2×#95—431no—
632C2×#95—431no—
633C2×#95C2×D4311yescharacteristic
634C2×#95C2×D4311yescharacteristic
635C2×#95C2×D4311yescharacteristic
636C2×#95C2×D4311yescharacteristic
637C2×#95C2×D4311yescharacteristic
638C2×#95C2×D4311yescharacteristic
639C43#1457111yescharacteristic, complemented, Sylow
640C25—431no—
641C25—431no—
642C22×D4—434no—
643C22×D4—862no—
644C22×D4—862no—
645C22×D4—862no—
646C22×D4—862no—
647C22×D4—1721no—
648C22×D4—1721no—
649C23×C4—431no—
650C23×C4—431no—
651C23×C4—431no—
652C23×C4—431no—
653C23×C4—431no—
654C23×C4—431no—
655C23×C4—862no—
656C23×C4—862no—
657C23×C4—862no—
658C23×C4—862no—
659C23×C4—862no—
660C23×C4—862no—
661C23×C4—1721no—
662C23×C4—1721no—
663C23×C4—1721no—
664C23×C4—1721no—
665C23×C4—1721no—
666C23×C4—1721no—
667C23×C4—1721no—
668C23×C4—1721no—
669C23×C4C22×D4311yescharacteristic
670C23×C4C22×D4311yescharacteristic
671C23×C4C22×D4311yescharacteristic
672C23×C4C22×D4311yescharacteristic
673C23×C4C22×D4311yescharacteristic
674C23×C4C22×D4311yescharacteristic
675C23×C4C22×D4311yescharacteristic
676C2×C4⋊C4—22no—
677C2×C4⋊C4—41no—
678C2×C4⋊C4—41no—
679C2×C4⋊C4—434no—
680C2×C4⋊C4—862no—
681C2×C4⋊C4—1721no—
682C2×C4⋊C4—1721no—
683C2×C4⋊C4—1721no—
684C2×C4⋊C4—1721no—
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—862no—
692C2×C22⋊C4—862no—
693C2×C22⋊C4—862no—
694C2×C22⋊C4—862no—
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—862no—
716C2×C42—862no—
717C2×C42—1721no—
718#95—22no—
719#95—22no—
720#95—22no—
721#95—41no—
722#95—41no—
723#95—862no—
724#95—862no—
725#95—862no—
726#95—862no—
727#95—862no—
728#95—862no—
729#95—862no—
730#95—1721no—
731#95—1721no—
732#95—1721no—
733#95—1721no—
734#95—1721no—
735#95C4×D4314yescomplemented
736C24—432no—
737C24—432no—
738C24—432no—
739C24—432no—
740C24—432no—
741C24—432no—
742C24—861no—
743C24—861no—
744C24—861no—
745C24—861no—
746C24—861no—
747C24—861no—
748C24—861no—
749C24—861no—
750C24—861no—
751C24—861no—
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—
766C24C23×D4311yescharacteristic
767C2×D4—868no—
768C2×D4—868no—
769C2×D4—1724no—
770C2×D4—1724no—
771C2×D4—1724no—
772C2×D4—1724no—
773C2×D4—1724no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
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—432no—
818C22×C4—432no—
819C22×C4—432no—
820C22×C4—432no—
821C22×C4—432no—
822C22×C4—861no—
823C22×C4—861no—
824C22×C4—861no—
825C22×C4—861no—
826C22×C4—861no—
827C22×C4—861no—
828C22×C4—861no—
829C22×C4—861no—
830C22×C4—861no—
831C22×C4—861no—
832C22×C4—861no—
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—1724no—
860C22×C4—1724no—
861C22×C4—1724no—
862C22×C4—1724no—
863C22×C4—1724no—
864C22×C4—1724no—
865C22×C4—1724no—
866C22×C4—1724no—
867C22×C4—1724no—
868C22×C4—1724no—
869C22×C4—1724no—
870C22×C4—1724no—
871C22×C4—1724no—
872C22×C4—1724no—
873C22×C4C2×C4×D4312yes—
874C22×C4C2×C4×D4312yes—
875C22×C4C2×C4×D4312yes—
876C22×C4D4×D4312yes—
877C22×C4D4×D4312yes—
878C22×C4#1062190212yes—
879C4⋊C4—44no—
880C4⋊C4—1724no—
881C4⋊C4—1724no—
882C22⋊C4—868no—
883C22⋊C4—868no—
884C22⋊C4—1724no—
885C22⋊C4—1724no—
886C22⋊C4—1724no—
887C22⋊C4—1724no—
888C22⋊C4—1724no—
889C22⋊C4—1724no—
890C22⋊C4—1724no—
891C22⋊C4—1724no—
892C42—1724no—
893C23—434no—
894C23—434no—
895C23—862no—
896C23—862no—
897C23—862no—
898C23—862no—
899C23—862no—
900C23—862no—
901C23—862no—
902C23—862no—
903C23—862no—
904C23—862no—
905C23—862no—
906C23—862no—
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—1721no—
932C23—1721no—
933C23—1721no—
934C23—1721no—
935C23—1721no—
936C23—1721no—
937C23—1721no—
938C23—1721no—
939C23—1721no—
940C23—1721no—
941C23—1721no—
942C23—1721no—
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—
963C23C22×C4×D4311yescharacteristic
964C23C2×D4×D4311yescharacteristic
965C23C2×D4×D4311yescharacteristic
966C23#41×D4311yescharacteristic
967C23#41×D4311yescharacteristic
968C23#41×D4311yescharacteristic
969C23C2×#1062190211yescharacteristic
970C23#1306337011yescharacteristic
971C23#1306337011yescharacteristic
972C23#1306337111yescharacteristic
973C23#1306337111yescharacteristic
974C23#1306337111yescharacteristic
975C23#1306337111yescharacteristic
976C23#1306337211yescharacteristic
977C23#1306337311yescharacteristic
978D4—17216no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
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—862no—
1029C2×C4—862no—
1030C2×C4—862no—
1031C2×C4—862no—
1032C2×C4—862no—
1033C2×C4—862no—
1034C2×C4—862no—
1035C2×C4—862no—
1036C2×C4—862no—
1037C2×C4—862no—
1038C2×C4—862no—
1039C2×C4—862no—
1040C2×C4—862no—
1041C2×C4—862no—
1042C2×C4—862no—
1043C2×C4—17216no—
1044C2×C4—17216no—
1045C2×C4—1721no—
1046C2×C4—1721no—
1047C2×C4—1721no—
1048C2×C4—1721no—
1049C2×C4—1721no—
1050C2×C4—1721no—
1051C2×C4—1721no—
1052C2×C4—1721no—
1053C2×C4—1721no—
1054C2×C4—1721no—
1055C2×C4—1721no—
1056C2×C4—1721no—
1057C2×C4—1721no—
1058C2×C4—1721no—
1059C2×C4—1721no—
1060C2×C4—1721no—
1061C2×C4—1721no—
1062C2×C4—1721no—
1063C2×C4—1721no—
1064C2×C4—1721no—
1065C2×C4—1721no—
1066C2×C4—1721no—
1067C2×C4—1721no—
1068C2×C4—1721no—
1069C2×C4—1721no—
1070C2×C4—1721no—
1071C2×C4—1721no—
1072C22—864no—
1073C22—864no—
1074C22—864no—
1075C22—864no—
1076C22—864no—
1077C22—864no—
1078C22—1722no—
1079C22—1722no—
1080C22—1722no—
1081C22—1722no—
1082C22—1722no—
1083C22—1722no—
1084C22—1722no—
1085C22—1722no—
1086C22—1722no—
1087C22—1722no—
1088C22—1722no—
1089C22—1722no—
1090C22—1722no—
1091C22—1722no—
1092C22—1722no—
1093C22—1722no—
1094C22—1722no—
1095C22—1722no—
1096C22—1722no—
1097C22—1722no—
1098C22—1722no—
1099C22—1722no—
1100C22—1722no—
1101C22—1722no—
1102C22C4×D4×D4311yescharacteristic
1103C22C4×D4×D4311yescharacteristic
1104C22C4×#1062190211yescharacteristic
1105C22#1458337111yescharacteristic
1106C22#1458337311yescharacteristic
1107C22#1458337911yescharacteristic
1108C22#1458338011yescharacteristic
1109C22#1458345911yescharacteristic
1110C22#1458346011yescharacteristic
1111C22#1458347811yescharacteristic
1112C22#1458347911yescharacteristic
1113C22#1458348311yescharacteristic
1114C22#1458348511yescharacteristic
1115C22#1458348811yescharacteristic
1116C22#1458348911yescharacteristic
1117C22#1458349011yescharacteristic
1118C22#1458349511yescharacteristic
1119C22#1458350111yescharacteristic
1120C22#1458350511yescharacteristic
1121C22#1458353311yescharacteristic
1122C22#1458353811yescharacteristic
1123C22#1458354011yescharacteristic
1124C22#1458354111yescharacteristic
1125C22#1458354211yescharacteristic
1126C22#1458354711yescharacteristic
1127C22#1458355211yescharacteristic
1128C22#1458357411yescharacteristic
1129C22#1458357411yescharacteristic
1130C22#1458357611yescharacteristic
1131C22#1458358111yescharacteristic
1132C22#1458358711yescharacteristic
1133C22#1458364111yescharacteristic
1134C22#1458364311yescharacteristic
1135C22#1458364711yescharacteristic
1136C22#1458365311yescharacteristic
1137C4—42no—
1138C4—42no—
1139C4—42no—
1140C4—42no—
1141C4—42no—
1142C4—42no—
1143C4—81no—
1144C4—3441no—
1145C4—1722no—
1146C4—1722no—
1147C4—1722no—
1148C4—1722no—
1149C4—1722no—
1150C2—1724no—
1151C2—1724no—
1152C2#1913729211yescharacteristic
1153C2#1913729911yescharacteristic
1154C2#1913735911yescharacteristic
1155C2#1913757311yescharacteristic
1156C2#1913758211yescharacteristic
1157C2#1913759411yescharacteristic
1158C2#1913776611yescharacteristic
1159C2#1914083711yescharacteristic
1160C2#1914083811yescharacteristic
1161C2#1914097711yescharacteristic
1162C2#1914097811yescharacteristic
1163C2#1914113211yescharacteristic
1164C2#1914113511yescharacteristic
1165C2#1914173311yescharacteristic
1166C2#1914173911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1442C2
socle, cosocleC24×C43C24
prime radicalC23×D172C22
hypercenter#1442D43
hypocenterC43#14571
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
2. C2×#14582791C2semidirect
3. C2×#14582789C2semidirect
6. #19132861C2semidirect
7. #19132852C2semidirect
8. #19132841C2semidirect
9. #19132837C2semidirect
10. #19132826C2semidirect
11. (C2×D43)⋊#95C2semidirect
12. (C2×D43)⋊#95C2semidirect
13. (C2×D43)⋊#95C2semidirect
14. (C2×D43)⋊#95C2semidirect
15. C43×#1442C2semidirect
32. #14582817C4semidirect
90. C2×Dic43⋊C4C2×C4semidirect
115. C2×(C2×D43)⋊C4C2×C4semidirect
116. C2×(C2×D43)⋊C4C2×C4semidirect
117. C2×(C2×D43)⋊C4C2×C4semidirect
118. C2×(C2×D43)⋊C4C2×C4semidirect
151. #95×C43C2×C4semidirect
574. #1442D43semidirect
639. C43#14571semidirect
735. #95C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145828172
C2×#145827912
C2×#145827892
C2×#145827772
#191328612
#191328522
#191328412
#191328372
#191328262
(C2×D43)⋊#952
C43×#14422
#1457143