Finite Group Databasebeta

← #25027386

Subgroups — #25027386

Order 11008.

1442 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582812C211yesmaximal, characteristic
2#19132865C211yesmaximal, characteristic, complemented
3#19132865C211yesmaximal, characteristic, complemented
4#19132854C211yesmaximal, characteristic, complemented
5#19132853C211yesmaximal, characteristic, complemented
6#19132852C211yesmaximal, characteristic, complemented
7#19132851C211yesmaximal, characteristic, complemented
8#19132850C211yesmaximal, characteristic, complemented
9#19132841C211yesmaximal, characteristic
10#19132839C211yesmaximal, characteristic
11#19132837C211yesmaximal, characteristic
12(C2×D43)⋊#95C211yesmaximal, characteristic
13(C2×D43)⋊#95C211yesmaximal, characteristic
14(C2×D43)⋊#95C211yesmaximal, characteristic
15C43×#1442C211yesmaximal, characteristic, complemented
16C23×Dic86C2211yescharacteristic
17C23×C4×D43C2211yescharacteristic
18C22×C4⋊Dic43C2211yescharacteristic
19C22×Dic43⋊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
26#14582812C418yescomplemented
27C2×C43⋊#95C2211yescharacteristic
28C2×C43⋊#95C2211yescharacteristic
29C2×C43⋊#95C2211yescharacteristic
30C2×C43⋊#95C2211yescharacteristic
31C2×C43⋊#95C2211yescharacteristic
32C2×C43⋊#95C2211yescharacteristic
33C2×C43⋊#95C2211yescharacteristic
34C2×C43⋊#95C2211yescharacteristic
35C2×C43⋊#95C2211yescharacteristic
36C2×C43⋊#95C2211yescharacteristic
37C2×C43⋊#95C2211yescharacteristic
38C2×C43⋊#95C2211yescharacteristic
39C2×C43⋊#95C2211yescharacteristic
40C2×C43⋊#95C2211yescharacteristic
41C2×C43⋊#95C2211yescharacteristic
42C2×C43⋊#95C2211yescharacteristic
43C2×C43⋊#95C2211yescharacteristic
44C2×C43⋊#95C2211yescharacteristic
45C22×C4⋊C4×C43C2211yescharacteristic
46C2×#95×C43C2211yescharacteristic
47C2×#95×C43C2211yescharacteristic
48C2×#95×C43C2211yescharacteristic
49C2×#95×C43C2211yescharacteristic
50C2×#95×C43C2211yescharacteristic
51C2×#95×C43C2211yescharacteristic
52C24×D43C2311yescharacteristic
53C22×Dic86—41no—
54C22×Dic86—41no—
55C22×Dic86—41no—
56C22×Dic86—41no—
57C22×Dic86—41no—
58C22×Dic86—41no—
59C22×Dic86C2×C414yescomplemented
60C23×Dic43C2311yescharacteristic
61C23×Dic43C2311yescharacteristic
62C23×Dic43C2311yescharacteristic
63C23×Dic43C2311yescharacteristic
64C23×Dic43C2311yescharacteristic
65C23×Dic43C2311yescharacteristic
66C23×Dic43C2311yescharacteristic
67C22×C4×D43—41no—
68C22×C4×D43—41no—
69C22×C4×D43—41no—
70C22×C4×D43—41no—
71C22×C4×D43—41no—
72C22×C4×D43—41no—
73C22×C4×D43Q814yescomplemented
74C2×C4⋊Dic43—41no—
75C2×C4⋊Dic43—41no—
76C2×C4⋊Dic43—41no—
77C2×Dic43⋊C4—41no—
78C2×Dic43⋊C4—41no—
79C2×Dic43⋊C4—41no—
80C2×(C2×D43)⋊C4—22no—
81C2×(C2×D43)⋊C4—22no—
82C2×(C2×D43)⋊C4—22no—
83C2×(C2×D43)⋊C4—41no—
84C2×(C2×D43)⋊C4—41no—
85C2×(C2×D43)⋊C4—41no—
86C2×(C2×D43)⋊C4—41no—
87C2×(C2×D43)⋊C4—41no—
88C2×(C2×D43)⋊C4—41no—
89C2×(C2×D43)⋊C4—41no—
90C2×(C2×D43)⋊C4—41no—
91C2×(C2×D43)⋊C4—41no—
92C2×(C2×D43)⋊C4—41no—
93C2×(C2×D43)⋊C4—41no—
94C2×(C2×D43)⋊C4—41no—
95C2×(C2×D43)⋊C4C2×C414yes—
96C2×(C2×D43)⋊C4C2×C414yes—
97C2×(C2×D43)⋊C4C2×C414yes—
98C43⋊#95—41no—
99C43⋊#95—41no—
100C43⋊#95—41no—
101C43⋊#95—41no—
102C43⋊#95—41no—
103C43⋊#95—41no—
104C43⋊#95—41no—
105C43⋊#95—41no—
106C43⋊#95—41no—
107C43⋊#95—41no—
108C43⋊#95—41no—
109C43⋊#95—41no—
110C43⋊#95—41no—
111C43⋊#95—41no—
112C43⋊#95—41no—
113C43⋊#95—41no—
114C43⋊#95C2×C414yescomplemented
115C43⋊#95C2×C414yescomplemented
116C23×C4×C43C2311yescharacteristic
117C23×C4×C43C2311yescharacteristic
118C23×C4×C43C2311yescharacteristic
119C23×C4×C43C2311yescharacteristic
120C23×C4×C43C2311yescharacteristic
121C23×C4×C43C2311yescharacteristic
122C23×C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43—41no—
124C2×C4⋊C4×C43—41no—
125C2×C4⋊C4×C43—41no—
126#95×C43—41no—
127#95×C43—41no—
128#95×C43—41no—
129#95×C43—41no—
130#95×C43—41no—
131#95×C43C2×C414yescomplemented
132C24×C43C2411yescharacteristic
133C23×D43—21no—
134C23×D43—21no—
135C23×D43—21no—
136C23×D43—21no—
137C23×D43—21no—
138C23×D43—21no—
139C23×D43—21no—
140C23×D43—21no—
141C23×D43—21no—
142C23×D43—21no—
143C23×D43—21no—
144C23×D43—21no—
145C23×D43C22×C412yes—
146C23×D43C2×Q812yes—
147C23×D43#4112yes—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
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×C43C22×C412yes—
194C22×C4×C43C22×C412yes—
195C22×C4×C43C22×C412yes—
196C22×C4×C43C2×Q812yes—
197C22×Dic43—21no—
198C22×Dic43—21no—
199C22×Dic43—21no—
200C22×Dic43—21no—
201C22×Dic43—21no—
202C22×Dic43—21no—
203C22×Dic43—21no—
204C22×Dic43—21no—
205C22×Dic43—21no—
206C22×Dic43—21no—
207C22×Dic43—21no—
208C22×Dic43—21no—
209C22×Dic43—21no—
210C22×Dic43—21no—
211C22×Dic43—21no—
212C22×Dic43—21no—
213C22×Dic43—21no—
214C22×Dic43—21no—
215C22×Dic43—21no—
216C22×Dic43—21no—
217C22×Dic43—21no—
218C22×Dic43—21no—
219C22×Dic43—21no—
220C22×Dic43—21no—
221C22×Dic43—21no—
222C22×Dic43—21no—
223C22×Dic43—21no—
224C22×Dic43—21no—
225C22×Dic43—21no—
226C22×Dic43—21no—
227C22×Dic43—21no—
228C22×Dic43—21no—
229C22×Dic43—21no—
230C22×Dic43—21no—
231C22×Dic43—21no—
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×Dic43C22×C412yes—
243C22×Dic43C22×C412yes—
244C22×Dic43C22×C412yes—
245C22×Dic43C2×Q812yes—
246C2×C4×D43—44no—
247C2×C4×D43—44no—
248C2×C4×D43—44no—
249C2×C4×D43—44no—
250C2×C4×D43—44no—
251C2×C4×D43—44no—
252C2×C4×D43—44no—
253C2×Dic86—44no—
254C2×Dic86—44no—
255C2×Dic86—44no—
256C2×Dic86—44no—
257C2×Dic86—44no—
258C2×Dic86—44no—
259C2×Dic86—44no—
260C4⋊C4×C43—44no—
261(C2×D43)⋊C4—44no—
262(C2×D43)⋊C4—44no—
263(C2×D43)⋊C4—44no—
264(C2×D43)⋊C4—44no—
265(C2×D43)⋊C4—44no—
266(C2×D43)⋊C4—44no—
267C4⋊Dic43—44no—
268Dic43⋊C4—44no—
269C23×C43C23×C411yescharacteristic
270C23×C43C22×Q811yescharacteristic
271C23×C43C2×#4111yescharacteristic
272C23×C43H(5,𝔽2)11yescharacteristic
273C23×C43H(5,𝔽2)11yescharacteristic
274C23×C43H(5,𝔽2)11yescharacteristic
275C23×C43H(5,𝔽2)11yescharacteristic
276C23×C43H(5,𝔽2)11yescharacteristic
277C23×C43H(5,𝔽2)11yescharacteristic
278C23×C43H(5,𝔽2)11yescharacteristic
279C23×C43H(5,𝔽2)11yescharacteristic
280C23×C43H(5,𝔽2)11yescharacteristic
281C23×C432−1+411yescharacteristic
282C23×C432−1+411yescharacteristic
283C23×C432−1+411yescharacteristic
284C22×D43—22no—
285C22×D43—22no—
286C22×D43—22no—
287C22×D43—22no—
288C22×D43—22no—
289C22×D43—22no—
290C22×D43—22no—
291C22×D43—22no—
292C22×D43—22no—
293C22×D43—22no—
294C22×D43—22no—
295C22×D43—22no—
296C22×D43—22no—
297C22×D43—22no—
298C22×D43—22no—
299C22×D43—22no—
300C22×D43—22no—
301C22×D43—22no—
302C22×D43—41no—
303C22×D43—41no—
304C22×D43—41no—
305C22×D43—41no—
306C22×D43—41no—
307C22×D43—41no—
308C22×D43—41no—
309C22×D43—41no—
310C22×D43—41no—
311C22×D43—41no—
312C22×D43—41no—
313C22×D43—41no—
314C22×D43—41no—
315C22×D43—41no—
316C22×D43—41no—
317C22×D43—41no—
318C22×D43C4×Q814yes—
319C2×C4×C43—22no—
320C2×C4×C43—22no—
321C2×C4×C43—22no—
322C2×C4×C43—22no—
323C2×C4×C43—22no—
324C2×C4×C43—22no—
325C2×C4×C43—22no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43—22no—
330C2×C4×C43—22no—
331C2×C4×C43—41no—
332C2×C4×C43—41no—
333C2×C4×C43—41no—
334C2×C4×C43—41no—
335C2×C4×C43—41no—
336C2×C4×C43—41no—
337C2×C4×C43—41no—
338C2×C4×C43—41no—
339C2×C4×C43—41no—
340C2×C4×C43—41no—
341C2×C4×C43—41no—
342C2×C4×C43—41no—
343C2×C4×C43—41no—
344C2×C4×C43—41no—
345C2×C4×C43—41no—
346C2×C4×C43—41no—
347C2×C4×C43—41no—
348C2×C4×C43—41no—
349C2×C4×C43—41no—
350C2×C4×C43—41no—
351C2×C4×C43—41no—
352C2×C4×C43—41no—
353C2×C4×C43—41no—
354C2×C4×C43—41no—
355C2×C4×C43—41no—
356C2×C4×C43—41no—
357C2×C4×C43—41no—
358C2×C4×C43—41no—
359C2×C4×C43—41no—
360C2×C4×C43—41no—
361C2×C4×C43—41no—
362C2×C4×C43—41no—
363C2×C4×C43—41no—
364C2×C4×C43—41no—
365C2×C4×C43—41no—
366C2×C4×C43—41no—
367C2×C4×C43—41no—
368C2×Dic43—22no—
369C2×Dic43—22no—
370C2×Dic43—22no—
371C2×Dic43—22no—
372C2×Dic43—22no—
373C2×Dic43—22no—
374C2×Dic43—22no—
375C2×Dic43—22no—
376C2×Dic43—22no—
377C2×Dic43—22no—
378C2×Dic43—22no—
379C2×Dic43—22no—
380C2×Dic43—41no—
381C2×Dic43—41no—
382C2×Dic43—41no—
383C2×Dic43—41no—
384C2×Dic43—41no—
385C2×Dic43—41no—
386C2×Dic43—41no—
387C2×Dic43—41no—
388C2×Dic43—41no—
389C2×Dic43—41no—
390C2×Dic43—41no—
391C2×Dic43—41no—
392C2×Dic43—41no—
393C2×Dic43—41no—
394C2×Dic43—41no—
395C2×Dic43—41no—
396C2×Dic43—41no—
397C2×Dic43—41no—
398C2×Dic43—41no—
399C2×Dic43—41no—
400C2×Dic43—41no—
401C2×Dic43—41no—
402C2×Dic43—41no—
403C2×Dic43—41no—
404C2×Dic43—41no—
405C2×Dic43—41no—
406C2×Dic43—41no—
407C2×Dic43—41no—
408C2×Dic43—41no—
409C2×Dic43—41no—
410C2×Dic43—41no—
411C2×Dic43—41no—
412C2×Dic43—41no—
413C2×Dic43—41no—
414C2×Dic43—41no—
415C2×Dic43—41no—
416C2×Dic43—41no—
417C4×D43—416no—
418Dic86—416no—
419#14635—431nomaximal, Sylow
420C22×C43C2×C4×Q811yescharacteristic
421C22×C43#51811yescharacteristic
422C22×C43#51811yescharacteristic
423C22×C43#51811yescharacteristic
424C22×C43#52011yescharacteristic
425C22×C43#52011yescharacteristic
426C22×C43#52011yescharacteristic
427C22×C43#53811yescharacteristic
428C22×C43#53811yescharacteristic
429C22×C43#53811yescharacteristic
430C22×C43#53911yescharacteristic
431C22×C43#53911yescharacteristic
432C22×C43#53911yescharacteristic
433C22×C43#54311yescharacteristic
434C22×C43#54311yescharacteristic
435C22×C43#54311yescharacteristic
436C22×C43#54411yescharacteristic
437C22×C43#54411yescharacteristic
438C22×C43#54411yescharacteristic
439C22×C43#56011yescharacteristic
440C22×C43#56011yescharacteristic
441C22×C43#56011yescharacteristic
442C22×C43H(3,𝔽4)11yescharacteristic
443C22×C43H(3,𝔽4)11yescharacteristic
444C22×C43H(3,𝔽4)11yescharacteristic
445C22×C43H(3,𝔽4)11yescharacteristic
446C22×C43#56211yescharacteristic
447C22×C43#56211yescharacteristic
448C22×C43#56211yescharacteristic
449C22×C43#56211yescharacteristic
450C22×C43#56211yescharacteristic
451C22×C43#56211yescharacteristic
452C22×C43#56311yescharacteristic
453C22×C43#56311yescharacteristic
454C22×C43#56311yescharacteristic
455C2×D43—24no—
456C2×D43—24no—
457C2×D43—24no—
458C2×D43—42no—
459C2×D43—42no—
460C2×D43—42no—
461C2×D43—42no—
462C2×D43—42no—
463C2×D43—42no—
464C2×D43—42no—
465C2×D43—42no—
466C2×D43—42no—
467C2×D43—42no—
468C2×D43—42no—
469C2×D43—42no—
470C4×C43—42no—
471C4×C43—42no—
472C4×C43—42no—
473C4×C43—42no—
474C4×C43—81no—
475C4×C43—81no—
476C4×C43—81no—
477Dic43—42no—
478Dic43—42no—
479Dic43—42no—
480Dic43—42no—
481Dic43—81no—
482Dic43—81no—
483Dic43—81no—
484C2×#393—431no—
485#1446—431no—
486#1446—431no—
487#1442—431no—
488#1442—431no—
489#1442—431no—
490#1442—431no—
491#1442—431no—
492#1442D4311yescharacteristic, complemented
493#1439—431no—
494#1439—431no—
495#1439—431no—
496C22⋊#95—431no—
497C22⋊#95—431no—
498C22⋊#95—431no—
499C2×C43#232911yescharacteristic
500C2×C43#232911yescharacteristic
501C2×C43#232911yescharacteristic
502C2×C43#237511yescharacteristic
503C2×C43#237911yescharacteristic
504C2×C43#237911yescharacteristic
505C2×C43#237911yescharacteristic
506C2×C43#282411yescharacteristic
507C2×C43#282411yescharacteristic
508C2×C43#282411yescharacteristic
509C2×C43#283511yescharacteristic
510C2×C43#284011yescharacteristic
511C2×C43#284111yescharacteristic
512C2×C43#284111yescharacteristic
513C2×C43#284111yescharacteristic
514D43—44no—
515C23×Q8—431no—
516C24×C4—431no—
517C22×C4⋊C4—431no—
518C22×C4⋊C4—431no—
519C22×C4⋊C4C2×D4311yescharacteristic
520C22×C22⋊C4—431no—
521C22×C22⋊C4—431no—
522C22×C22⋊C4—431no—
523C22×C22⋊C4—431no—
524C22×C22⋊C4—431no—
525C22×C22⋊C4—431no—
526#393—438no—
527C2×#95—431no—
528C2×#95—431no—
529C2×#95—431no—
530C2×#95—431no—
531C2×#95—431no—
532C2×#95—431no—
533C2×#95—431no—
534C2×#95—431no—
535C2×#95—431no—
536C2×#95—431no—
537C2×#95—431no—
538C2×#95—431no—
539C2×#95—431no—
540C2×#95—431no—
541C2×#95—431no—
542C2×#95—431no—
543C2×#95—431no—
544C2×#95—431no—
545C2×#95C2×D4311yescharacteristic
546C2×#95C2×D4311yescharacteristic
547C2×#95C2×D4311yescharacteristic
548C2×#95C2×D4311yescharacteristic
549C2×#95C2×D4311yescharacteristic
550C2×#95C2×D4311yescharacteristic
551C43#1463511yescharacteristic, complemented, Sylow
552C25—431no—
553C22×Q8—434no—
554C22×Q8—1721no—
555C22×Q8—1721no—
556C22×Q8—1721no—
557C22×Q8—1721no—
558C22×Q8—1721no—
559C22×Q8—1721no—
560C23×C4—431no—
561C23×C4—431no—
562C23×C4—431no—
563C23×C4—431no—
564C23×C4—434no—
565C23×C4—431no—
566C23×C4—431no—
567C23×C4—431no—
568C23×C4—1721no—
569C23×C4—1721no—
570C23×C4—1721no—
571C23×C4—1721no—
572C23×C4—1721no—
573C23×C4—1721no—
574C23×C4C22×D4311yescharacteristic
575C23×C4C22×D4311yescharacteristic
576C23×C4C22×D4311yescharacteristic
577C23×C4C22×D4311yescharacteristic
578C23×C4C22×D4311yescharacteristic
579C23×C4C22×D4311yescharacteristic
580C23×C4C22×D4311yescharacteristic
581C2×C4⋊C4—41no—
582C2×C4⋊C4—41no—
583C2×C4⋊C4—41no—
584C2×C4⋊C4—1721no—
585C2×C4⋊C4—1721no—
586C2×C4⋊C4—1721no—
587C2×C4⋊C4—1721no—
588C2×C4⋊C4—1721no—
589C2×C4⋊C4—1721no—
590C2×C22⋊C4—434no—
591C2×C22⋊C4—434no—
592C2×C22⋊C4—434no—
593C2×C22⋊C4—862no—
594C2×C22⋊C4—862no—
595C2×C22⋊C4—862no—
596C2×C22⋊C4—1721no—
597C2×C22⋊C4—1721no—
598C2×C22⋊C4—1721no—
599C2×C22⋊C4—1721no—
600C2×C22⋊C4—1721no—
601C2×C22⋊C4—1721no—
602C2×C22⋊C4—1721no—
603C2×C22⋊C4—1721no—
604C2×C22⋊C4—1721no—
605C2×C22⋊C4—1721no—
606C2×C22⋊C4—1721no—
607C2×C22⋊C4—1721no—
608#95—41no—
609#95—41no—
610#95—41no—
611#95—41no—
612#95—41no—
613#95—434no—
614#95—434no—
615#95—1721no—
616#95—1721no—
617#95—1721no—
618#95—1721no—
619#95—1721no—
620#95—1721no—
621#95—1721no—
622#95—1721no—
623#95—1721no—
624#95—1721no—
625#95—1721no—
626#95—1721no—
627#95—1721no—
628#95—1721no—
629#95—1721no—
630#95—1721no—
631#95C4×D4314yescomplemented
632C24—432no—
633C24—432no—
634C24—432no—
635C24—861no—
636C24—861no—
637C24—861no—
638C24—861no—
639C24—861no—
640C24—861no—
641C24—861no—
642C24—861no—
643C24—861no—
644C24—861no—
645C24—861no—
646C24—861no—
647C24C23×D4311yescharacteristic
648C2×Q8—1724no—
649C2×Q8—1724no—
650C2×Q8—1724no—
651C2×Q8—1724no—
652C2×Q8—1724no—
653C2×Q8—1724no—
654C2×Q8—1724no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—432no—
701C22×C4—432no—
702C22×C4—432no—
703C22×C4—432no—
704C22×C4—861no—
705C22×C4—861no—
706C22×C4—861no—
707C22×C4—861no—
708C22×C4—861no—
709C22×C4—861no—
710C22×C4—861no—
711C22×C4—861no—
712C22×C4—861no—
713C22×C4—861no—
714C22×C4—861no—
715C22×C4—861no—
716C22×C4—861no—
717C22×C4—861no—
718C22×C4—861no—
719C22×C4—861no—
720C22×C4—861no—
721C22×C4—861no—
722C22×C4—861no—
723C22×C4—861no—
724C22×C4—861no—
725C22×C4—861no—
726C22×C4—861no—
727C22×C4—861no—
728C22×C4—861no—
729C22×C4—861no—
730C22×C4—861no—
731C22×C4—861no—
732C22×C4—861no—
733C22×C4—861no—
734C22×C4—861no—
735C22×C4—861no—
736C22×C4—861no—
737C22×C4—861no—
738C22×C4—861no—
739C22×C4—861no—
740C22×C4—861no—
741C22×C4—861no—
742C22×C4—861no—
743C22×C4—861no—
744C22×C4—861no—
745C22×C4—861no—
746C22×C4—861no—
747C22×C4—861no—
748C22×C4—861no—
749C22×C4—1724no—
750C22×C4—1724no—
751C22×C4—1724no—
752C22×C4—1724no—
753C22×C4—1724no—
754C22×C4—1724no—
755C22×C4—1724no—
756C22×C4C2×C4×D4312yes—
757C22×C4C2×C4×D4312yes—
758C22×C4C2×C4×D4312yes—
759C22×C4Q8×D4312yes—
760C4⋊C4—44no—
761C4⋊C4—1724no—
762C4⋊C4—1724no—
763C22⋊C4—1724no—
764C22⋊C4—1724no—
765C22⋊C4—1724no—
766C22⋊C4—1724no—
767C22⋊C4—1724no—
768C22⋊C4—1724no—
769C23—434no—
770C23—862no—
771C23—862no—
772C23—862no—
773C23—862no—
774C23—862no—
775C23—862no—
776C23—862no—
777C23—862no—
778C23—862no—
779C23—862no—
780C23—862no—
781C23—862no—
782C23—862no—
783C23—862no—
784C23—862no—
785C23—862no—
786C23—862no—
787C23—862no—
788C23—1721no—
789C23—1721no—
790C23—1721no—
791C23—1721no—
792C23—1721no—
793C23—1721no—
794C23—1721no—
795C23—1721no—
796C23—1721no—
797C23—1721no—
798C23—1721no—
799C23—1721no—
800C23—1721no—
801C23—1721no—
802C23—1721no—
803C23—1721no—
804C23C22×C4×D4311yescharacteristic
805C23C2×Q8×D4311yescharacteristic
806C23#41×D4311yescharacteristic
807C23#1306337011yescharacteristic
808C23#1306337011yescharacteristic
809C23#1306337011yescharacteristic
810C23#1306337011yescharacteristic
811C23#1306337111yescharacteristic
812C23#1306337111yescharacteristic
813C23#1306337111yescharacteristic
814C23#1306337111yescharacteristic
815C23#1306337111yescharacteristic
816C23#1306337211yescharacteristic
817C23#1306337211yescharacteristic
818C23#1306337311yescharacteristic
819Q8—17216no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—862no—
870C2×C4—862no—
871C2×C4—862no—
872C2×C4—862no—
873C2×C4—862no—
874C2×C4—862no—
875C2×C4—862no—
876C2×C4—862no—
877C2×C4—862no—
878C2×C4—862no—
879C2×C4—862no—
880C2×C4—862no—
881C2×C4—17216no—
882C2×C4—1721no—
883C2×C4—1721no—
884C2×C4—1721no—
885C2×C4—1721no—
886C2×C4—1721no—
887C2×C4—1721no—
888C2×C4—1721no—
889C2×C4—1721no—
890C2×C4—1721no—
891C2×C4—1721no—
892C2×C4—1721no—
893C2×C4—1721no—
894C2×C4—1721no—
895C2×C4—1721no—
896C2×C4—1721no—
897C2×C4—1721no—
898C2×C4—1721no—
899C2×C4—1721no—
900C2×C4—1721no—
901C2×C4—1721no—
902C2×C4—1721no—
903C2×C4—1721no—
904C2×C4—1721no—
905C2×C4—1721no—
906C2×C4—1721no—
907C2×C4—1721no—
908C2×C4—1721no—
909C2×C4—1721no—
910C2×C4—1721no—
911C2×C4—1721no—
912C2×C4—1721no—
913C2×C4—1721no—
914C2×C4—1721no—
915C2×C4—1721no—
916C2×C4—1721no—
917C2×C4—1721no—
918C2×C4—1721no—
919C22—864no—
920C22—864no—
921C22—864no—
922C22—1722no—
923C22—1722no—
924C22—1722no—
925C22—1722no—
926C22—1722no—
927C22—1722no—
928C22—1722no—
929C22—1722no—
930C22—1722no—
931C22—1722no—
932C22—1722no—
933C22—1722no—
934C22C4×Q8×D4311yescharacteristic
935C22#1458337111yescharacteristic
936C22#1458337111yescharacteristic
937C22#1458337311yescharacteristic
938C22#1458337811yescharacteristic
939C22#1458337911yescharacteristic
940C22#1458338011yescharacteristic
941C22#1458348111yescharacteristic
942C22#1458348511yescharacteristic
943C22#1458348811yescharacteristic
944C22#1458349011yescharacteristic
945C22#1458349211yescharacteristic
946C22#1458349711yescharacteristic
947C22#1458352411yescharacteristic
948C22#1458352411yescharacteristic
949C22#1458352411yescharacteristic
950C22#1458352611yescharacteristic
951C22#1458352911yescharacteristic
952C22#1458352911yescharacteristic
953C22#1458363711yescharacteristic
954C22#1458363911yescharacteristic
955C22#1458364011yescharacteristic
956C22#1458364111yescharacteristic
957C22#1458364111yescharacteristic
958C22#1458364111yescharacteristic
959C22#1458364211yescharacteristic
960C22#1458364311yescharacteristic
961C22#1458364411yescharacteristic
962C22#1458364511yescharacteristic
963C22#1458364611yescharacteristic
964C22#1458364611yescharacteristic
965C22#1458364711yescharacteristic
966C22#1458365011yescharacteristic
967C22#1458365111yescharacteristic
968C22#1458365311yescharacteristic
969C4—42no—
970C4—42no—
971C4—42no—
972C4—42no—
973C4—81no—
974C4—81no—
975C4—81no—
976C4—3441no—
977C4—3441no—
978C4—3441no—
979C4—1722no—
980C4—1722no—
981C4—1722no—
982C4—1722no—
983C2—1724no—
984C2#1913732211yescharacteristic
985C2#1913732411yescharacteristic
986C2#1913732911yescharacteristic
987C2#1913773511yescharacteristic
988C2#1913776411yescharacteristic
989C2#1913776611yescharacteristic
990C2#1913776811yescharacteristic
991C2#1914267111yescharacteristic
992C2#1914267311yescharacteristic
993C2#1914267611yescharacteristic
994C2#1914278211yescharacteristic
995C2#1914284711yescharacteristic
996C2#1914285111yescharacteristic
997C2#1914285311yescharacteristic
998C2#1914285411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1442C2
socle, cosocleC24×C43C24
prime radicalC24×D43C23
hypercenter#1442D43
hypocenterC43#14635
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
2. #19132865C2semidirect
3. #19132865C2semidirect
4. #19132854C2semidirect
5. #19132853C2semidirect
6. #19132852C2semidirect
7. #19132851C2semidirect
8. #19132850C2semidirect
15. C43×#1442C2semidirect
26. #14582812C4semidirect
59. C22×Dic86C2×C4semidirect
73. C22×C4×D43Q8semidirect
114. C43⋊#95C2×C4semidirect
115. C43⋊#95C2×C4semidirect
131. #95×C43C2×C4semidirect
492. #1442D43semidirect
551. C43#14635semidirect
631. #95C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145828122
#191328652
#191328542
#191328532
#191328522
#191328512
#191328502
#191328412
#191328392
#191328372
(C2×D43)⋊#952
C43×#14422
#1463543