Finite Group Databasebeta

← #25024518

Subgroups — #25024518

Order 11008.

2118 conjugacy classes of subgroups.

The subgroup lattice has 1196 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582801C211yesmaximal, characteristic
2C2×#14582777C211yesmaximal, characteristic
3C2×#14582777C211yesmaximal, characteristic
4C2×#14582773C211yesmaximal, characteristic, complemented
5C2×#14582773C211yesmaximal, characteristic, complemented
6C2×#14582758C211yesmaximal, characteristic, complemented
7C2×#14582756C211yesmaximal, characteristic, complemented
8#19132860C211yesmaximal, characteristic, complemented
9#19132859C211yesmaximal, characteristic, complemented
10#19132841C211yesmaximal, characteristic, complemented
11#19132839C211yesmaximal, characteristic, complemented
12#19132839C211yesmaximal, characteristic, complemented
13#19132837C211yesmaximal, characteristic, complemented
14#19132828C211yesmaximal, characteristic, complemented
15C43×#1436C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17C23×C4×D43C2211yescharacteristic
18C23×C4×D43C2211yescharacteristic
19C22×C4⋊Dic43C2211yescharacteristic
20C22×C4⋊Dic43C2211yescharacteristic
21C22×C4⋊Dic43C2211yescharacteristic
22C22×Dic43⋊C4C2211yescharacteristic
23C22×Dic43⋊C4C2211yescharacteristic
24C22×Dic43⋊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×(C2×D43)⋊C4C2211yescharacteristic
32C22×(C2×D43)⋊C4C2211yescharacteristic
33C22×(C2×D43)⋊C4C2211yescharacteristic
34C22×(C2×D43)⋊C4C2211yescharacteristic
35#14582801—24no—
36#14582777—24no—
37#14582777C418yescomplemented
38#14582773—24no—
39#14582773—24no—
40#14582758—24no—
41#14582756—24no—
42C2×C43⋊#95C2211yescharacteristic
43C2×C43⋊#95C2211yescharacteristic
44C2×C43⋊#95C2211yescharacteristic
45C2×C43⋊#95C2211yescharacteristic
46C2×C43⋊#95C2211yescharacteristic
47C2×C43⋊#95C2211yescharacteristic
48C2×C43⋊#95C2211yescharacteristic
49C2×C43⋊#95C2211yescharacteristic
50C2×C43⋊#95C2211yescharacteristic
51C22×C4⋊C4×C43C2211yescharacteristic
52C22×C42×C43C2211yescharacteristic
53C2×#95×C43C2211yescharacteristic
54C2×#95×C43C2211yescharacteristic
55C2×#95×C43C2211yescharacteristic
56C2×#95×C43C2211yescharacteristic
57C2×#95×C43C2211yescharacteristic
58C24×D43C2311yescharacteristic
59C24×D43C2311yescharacteristic
60C22×D172—41no—
61C22×D172—41no—
62C22×D172—41no—
63C22×D172—41no—
64C22×D172C2×C414yes—
65C22×D172D414yes—
66C22×D172Q814yes—
67C23×Dic43C2311yescharacteristic
68C23×Dic43C2311yescharacteristic
69C23×Dic43C2311yescharacteristic
70C23×Dic43C2311yescharacteristic
71C23×Dic43C2311yescharacteristic
72C23×Dic43C2311yescharacteristic
73C22×C4×D43—22no—
74C22×C4×D43—22no—
75C22×C4×D43—22no—
76C22×C4×D43—22no—
77C22×C4×D43—22no—
78C22×C4×D43—22no—
79C22×C4×D43—22no—
80C22×C4×D43—41no—
81C22×C4×D43—41no—
82C22×C4×D43—41no—
83C22×C4×D43—41no—
84C22×C4×D43—41no—
85C22×C4×D43—41no—
86C22×C4×D43C2×C414yescomplemented
87C2×C4⋊Dic43—22no—
88C2×C4⋊Dic43—22no—
89C2×C4⋊Dic43—22no—
90C2×C4⋊Dic43—22no—
91C2×C4⋊Dic43—41no—
92C2×C4⋊Dic43—41no—
93C2×C4⋊Dic43—41no—
94C2×C4⋊Dic43—41no—
95C2×C4⋊Dic43—41no—
96C2×Dic43⋊C4—22no—
97C2×Dic43⋊C4—22no—
98C2×Dic43⋊C4—22no—
99C2×Dic43⋊C4—22no—
100C2×Dic43⋊C4—22no—
101C2×Dic43⋊C4—41no—
102C2×Dic43⋊C4—41no—
103C2×Dic43⋊C4—41no—
104C2×Dic43⋊C4—41no—
105C2×(C2×D43)⋊C4—22no—
106C2×(C2×D43)⋊C4—22no—
107C2×(C2×D43)⋊C4—22no—
108C2×(C2×D43)⋊C4—22no—
109C2×(C2×D43)⋊C4—22no—
110C2×(C2×D43)⋊C4—22no—
111C2×(C2×D43)⋊C4—22no—
112C2×(C2×D43)⋊C4—22no—
113C2×(C2×D43)⋊C4—22no—
114C2×(C2×D43)⋊C4—22no—
115C2×(C2×D43)⋊C4—22no—
116C2×(C2×D43)⋊C4—22no—
117C2×(C2×D43)⋊C4—22no—
118C2×(C2×D43)⋊C4—22no—
119C2×(C2×D43)⋊C4—22no—
120C2×(C2×D43)⋊C4—22no—
121C2×(C2×D43)⋊C4—22no—
122C2×(C2×D43)⋊C4—41no—
123C2×(C2×D43)⋊C4—41no—
124C2×(C2×D43)⋊C4—41no—
125C2×(C2×D43)⋊C4—41no—
126C2×(C2×D43)⋊C4—41no—
127C2×(C2×D43)⋊C4—41no—
128C2×(C2×D43)⋊C4—41no—
129C2×(C2×D43)⋊C4—41no—
130C2×(C2×D43)⋊C4—41no—
131C2×(C2×D43)⋊C4—41no—
132C2×(C2×D43)⋊C4C2×C414yes—
133C2×(C2×D43)⋊C4C2×C414yes—
134C2×(C2×D43)⋊C4C2×C414yescomplemented
135C43⋊#95—22no—
136C43⋊#95—22no—
137C43⋊#95—22no—
138C43⋊#95—22no—
139C43⋊#95—41no—
140C43⋊#95—41no—
141C43⋊#95—41no—
142C43⋊#95C2×C414yescomplemented
143C43⋊#95D414yescomplemented
144C23×C4×C43C2311yescharacteristic
145C23×C4×C43C2311yescharacteristic
146C23×C4×C43C2311yescharacteristic
147C23×C4×C43C2311yescharacteristic
148C23×C4×C43C2311yescharacteristic
149C23×C4×C43C2311yescharacteristic
150C23×C4×C43C2311yescharacteristic
151C2×C4⋊C4×C43—22no—
152C2×C4⋊C4×C43—22no—
153C2×C4⋊C4×C43—41no—
154C2×C42×C43—22no—
155C2×C42×C43—41no—
156C2×C42×C43—41no—
157#95×C43—22no—
158#95×C43—22no—
159#95×C43—41no—
160#95×C43C2×C414yescomplemented
161#95×C43D414yescomplemented
162C24×C43C2411yescharacteristic
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×D43—21no—
182C23×D43—21no—
183C23×D43—21no—
184C23×D43—21no—
185C23×D43—21no—
186C23×D43—21no—
187C23×D43C22×C412yes—
188C23×D43C22×C412yes—
189C23×D43C2×D412yes—
190C23×D43C2×D412yes—
191C23×D43C2×Q812yes—
192C23×D43C2×Q812yes—
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×C43—21no—
227C22×C4×C43—21no—
228C22×C4×C43—21no—
229C22×C4×C43—21no—
230C22×C4×C43—21no—
231C22×C4×C43—21no—
232C22×C4×C43C22×C412yes—
233C22×C4×C43C22×C412yes—
234C22×C4×C43C22×C412yes—
235C22×C4×C43C2×D412yes—
236C22×C4×C43C2×D412yes—
237C22×C4×C43C2×D412yes—
238C22×C4×C43C2×D412yes—
239C22×C4×C43C2×D412yes—
240C22×C4×C43C2×Q812yes—
241C22×C4×C43#4112yes—
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×Dic43—21no—
270C22×Dic43—21no—
271C22×Dic43—21no—
272C22×Dic43—21no—
273C22×Dic43—21no—
274C22×Dic43—21no—
275C22×Dic43—21no—
276C22×Dic43—21no—
277C22×Dic43—21no—
278C22×Dic43—21no—
279C22×Dic43C22×C412yes—
280C22×Dic43C22×C412yes—
281C22×Dic43C2×D412yes—
282C22×Dic43C2×D412yes—
283C22×Dic43#4112yes—
284C2×D172—44no—
285C2×D172—44no—
286C2×D172—44no—
287C2×D172—44no—
288C2×D172—44no—
289C2×D172—44no—
290C2×D172C4⋊C4116yescomplemented
291C2×C4×D43—28no—
292C2×C4×D43—28no—
293C2×C4×D43—44no—
294C2×C4×D43—44no—
295C2×C4×D43—44no—
296C2×C4×D43—44no—
297C2×C4×D43—44no—
298C2×C4×D43—44no—
299C2×C4×D43—44no—
300C2×C4×D43—44no—
301C2×C4×D43—44no—
302C2×C4×D43—44no—
303C2×C4×D43—44no—
304C2×C4×D43—44no—
305C4⋊C4×C43—44no—
306C42×C43—44no—
307(C2×D43)⋊C4—28no—
308(C2×D43)⋊C4—28no—
309(C2×D43)⋊C4—44no—
310(C2×D43)⋊C4—44no—
311(C2×D43)⋊C4—44no—
312(C2×D43)⋊C4—44no—
313(C2×D43)⋊C4—44no—
314(C2×D43)⋊C4—44no—
315(C2×D43)⋊C4—44no—
316(C2×D43)⋊C4—44no—
317C4⋊Dic43—44no—
318C4⋊Dic43—44no—
319C4⋊Dic43—44no—
320Dic43⋊C4—44no—
321Dic43⋊C4—44no—
322Dic43⋊C4—44no—
323C23×C43C23×C411yescharacteristic
324C23×C43C22×D411yescharacteristic
325C23×C43C22×D411yescharacteristic
326C23×C43C22×D411yescharacteristic
327C23×C43C22×Q811yescharacteristic
328C23×C43C2×#4111yescharacteristic
329C23×C43C2×#4111yescharacteristic
330C23×C43H(5,𝔽2)11yescharacteristic
331C23×C43H(5,𝔽2)11yescharacteristic
332C23×C43H(5,𝔽2)11yescharacteristic
333C23×C43H(5,𝔽2)11yescharacteristic
334C23×C43H(5,𝔽2)11yescharacteristic
335C23×C43H(5,𝔽2)11yescharacteristic
336C23×C432−1+411yescharacteristic
337C23×C432−1+411yescharacteristic
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—22no—
367C22×D43—22no—
368C22×D43—22no—
369C22×D43—22no—
370C22×D43—22no—
371C22×D43—22no—
372C22×D43—22no—
373C22×D43—22no—
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×D43—41no—
399C22×D43—41no—
400C22×D43—41no—
401C22×D43—41no—
402C22×D43—41no—
403C22×D43—41no—
404C22×D43—41no—
405C22×D43—41no—
406C22×D43C2×C4⋊C414yes—
407C22×D43C2×C4⋊C414yes—
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—22no—
428C2×C4×C43—22no—
429C2×C4×C43—22no—
430C2×C4×C43—22no—
431C2×C4×C43—22no—
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×C43—41no—
448C2×C4×C43—41no—
449C2×C4×C43—41no—
450C2×C4×C43—41no—
451C2×C4×C43—41no—
452C2×C4×C43—41no—
453C2×C4×C43—41no—
454C2×C4×C43—41no—
455C2×C4×C43C2×C4⋊C414yes—
456C2×C4×C43C4×D414yes—
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—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—
485C2×Dic43—41no—
486C2×Dic43—41no—
487C2×Dic43—41no—
488C2×Dic43—41no—
489C2×Dic43—41no—
490C2×Dic43—41no—
491C2×Dic43—41no—
492C2×Dic43—41no—
493C2×Dic43—41no—
494C2×Dic43—41no—
495C2×Dic43—41no—
496C2×Dic43—41no—
497C2×Dic43—41no—
498C2×Dic43C4×D414yes—
499D172—416no—
500C4×D43—416no—
501C4×D43—416no—
502#14401—431nomaximal, Sylow
503C22×C43C22×C4⋊C411yescharacteristic
504C22×C43C2×C4×D411yescharacteristic
505C22×C43C2×C4×D411yescharacteristic
506C22×C43#51811yescharacteristic
507C22×C43#51811yescharacteristic
508C22×C43#52011yescharacteristic
509C22×C43#52011yescharacteristic
510C22×C43#53411yescharacteristic
511C22×C43#53411yescharacteristic
512C22×C43#53511yescharacteristic
513C22×C43#53511yescharacteristic
514C22×C43#53711yescharacteristic
515C22×C43#53711yescharacteristic
516C22×C43#54011yescharacteristic
517C22×C43#54011yescharacteristic
518C22×C43#54211yescharacteristic
519C22×C43#54211yescharacteristic
520C22×C43#54311yescharacteristic
521C22×C43#54311yescharacteristic
522C22×C43D4211yescharacteristic
523C22×C43D4211yescharacteristic
524C22×C43D4211yescharacteristic
525C22×C43#54611yescharacteristic
526C22×C43#54611yescharacteristic
527C22×C43#54711yescharacteristic
528C22×C43#54711yescharacteristic
529C22×C43D4×Q811yescharacteristic
530C22×C43D4×Q811yescharacteristic
531C22×C43#55111yescharacteristic
532C22×C43#55411yescharacteristic
533C22×C43#55411yescharacteristic
534C22×C43#56011yescharacteristic
535C22×C43#56211yescharacteristic
536C22×C43#56211yescharacteristic
537C22×C43#56311yescharacteristic
538C2×D43—24no—
539C2×D43—24no—
540C2×D43—24no—
541C2×D43—24no—
542C2×D43—24no—
543C2×D43—24no—
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—
560C2×D43—42no—
561C2×D43—42no—
562C2×D43—42no—
563C2×D43—42no—
564C2×D43—42no—
565C2×D43—42no—
566C2×D43—42no—
567C2×D43—42no—
568C4×C43—24no—
569C4×C43—24no—
570C4×C43—42no—
571C4×C43—42no—
572C4×C43—42no—
573C4×C43—42no—
574C4×C43—81no—
575Dic43—24no—
576Dic43—42no—
577Dic43—42no—
578Dic43—81no—
579Dic43—81no—
580Dic43—81no—
581C2×#390—431no—
582C2×#386—431no—
583C2×#386—431no—
584C2×#385—431no—
585C2×#385—431no—
586C2×#380—431no—
587C2×#380—431no—
588#1444—431no—
589#1444—431no—
590#1439—431no—
591#1439—431no—
592#1439—431no—
593#1439—431no—
594#1436—431no—
595#1436D4311yescharacteristic, complemented
596C2×C43#231511yescharacteristic
597C2×C43#232411yescharacteristic
598C2×C43#232411yescharacteristic
599C2×C43D4×C4⋊C411yescharacteristic
600C2×C43D4×C4⋊C411yescharacteristic
601C2×C43#235811yescharacteristic
602C2×C43#237611yescharacteristic
603C2×C43#266911yescharacteristic
604C2×C43#267111yescharacteristic
605C2×C43#267111yescharacteristic
606C2×C43#268311yescharacteristic
607C2×C43#269211yescharacteristic
608C2×C43#269211yescharacteristic
609C2×C43#271711yescharacteristic
610C2×C43#274811yescharacteristic
611D43—44no—
612D43—44no—
613C23×D4—431no—
614C24×C4—431no—
615C24×C4—431no—
616C22×C4⋊C4—431no—
617C22×C4⋊C4—431no—
618C22×C4⋊C4—431no—
619C22×C4⋊C4—431no—
620C22×C4⋊C4—431no—
621C22×C4⋊C4—431no—
622C22×C4⋊C4C2×D4311yescharacteristic
623C22×C22⋊C4—431no—
624C22×C22⋊C4—431no—
625C22×C22⋊C4—431no—
626C22×C22⋊C4—431no—
627C22×C22⋊C4—431no—
628C22×C22⋊C4—431no—
629C22×C22⋊C4—431no—
630C22×C22⋊C4—431no—
631C22×C22⋊C4—431no—
632C22×C22⋊C4—431no—
633C22×C42C2×D4311yescharacteristic
634#390—864no—
635#386—438no—
636#386—864no—
637#385—864no—
638#385—864no—
639#380—864no—
640#380—864no—
641C2×#95—431no—
642C2×#95—431no—
643C2×#95—431no—
644C2×#95—431no—
645C2×#95—431no—
646C2×#95—431no—
647C2×#95—431no—
648C2×#95—431no—
649C2×#95—431no—
650C2×#95C2×D4311yescharacteristic
651C2×#95C2×D4311yescharacteristic
652C2×#95C2×D4311yescharacteristic
653C2×#95C2×D4311yescharacteristic
654C2×#95C2×D4311yescharacteristic
655C43#1440111yescharacteristic, complemented, Sylow
656C25—431no—
657C25—431no—
658C22×D4—434no—
659C22×D4—434no—
660C22×D4—434no—
661C22×D4—1721no—
662C22×D4—1721no—
663C22×D4—1721no—
664C22×D4—1721no—
665C23×C4—431no—
666C23×C4—431no—
667C23×C4—431no—
668C23×C4—434no—
669C23×C4—431no—
670C23×C4—431no—
671C23×C4—431no—
672C23×C4—862no—
673C23×C4—862no—
674C23×C4—862no—
675C23×C4—862no—
676C23×C4—862no—
677C23×C4—862no—
678C23×C4—862no—
679C23×C4—1721no—
680C23×C4—1721no—
681C23×C4—1721no—
682C23×C4—1721no—
683C23×C4—1721no—
684C23×C4—1721no—
685C23×C4C22×D4311yescharacteristic
686C23×C4C22×D4311yescharacteristic
687C23×C4C22×D4311yescharacteristic
688C23×C4C22×D4311yescharacteristic
689C23×C4C22×D4311yescharacteristic
690C23×C4C22×D4311yescharacteristic
691C23×C4C22×D4311yescharacteristic
692C2×C4⋊C4—22no—
693C2×C4⋊C4—22no—
694C2×C4⋊C4—41no—
695C2×C4⋊C4—862no—
696C2×C4⋊C4—862no—
697C2×C4⋊C4—862no—
698C2×C4⋊C4—862no—
699C2×C4⋊C4—862no—
700C2×C4⋊C4—862no—
701C2×C4⋊C4—862no—
702C2×C4⋊C4—862no—
703C2×C4⋊C4—862no—
704C2×C4⋊C4—1721no—
705C2×C4⋊C4—1721no—
706C2×C4⋊C4—1721no—
707C2×C4⋊C4—1721no—
708C2×C4⋊C4—1721no—
709C2×C4⋊C4—1721no—
710C2×C4⋊C4—1721no—
711C2×C4⋊C4—1721no—
712C2×C4⋊C4—1721no—
713C2×C22⋊C4—434no—
714C2×C22⋊C4—434no—
715C2×C22⋊C4—434no—
716C2×C22⋊C4—862no—
717C2×C22⋊C4—862no—
718C2×C22⋊C4—862no—
719C2×C22⋊C4—862no—
720C2×C22⋊C4—862no—
721C2×C22⋊C4—862no—
722C2×C22⋊C4—862no—
723C2×C22⋊C4—862no—
724C2×C22⋊C4—862no—
725C2×C22⋊C4—862no—
726C2×C22⋊C4—862no—
727C2×C22⋊C4—862no—
728C2×C22⋊C4—862no—
729C2×C22⋊C4—862no—
730C2×C22⋊C4—862no—
731C2×C22⋊C4—862no—
732C2×C22⋊C4—862no—
733C2×C22⋊C4—1721no—
734C2×C22⋊C4—1721no—
735C2×C22⋊C4—1721no—
736C2×C22⋊C4—1721no—
737C2×C22⋊C4—1721no—
738C2×C22⋊C4—1721no—
739C2×C22⋊C4—1721no—
740C2×C22⋊C4—1721no—
741C2×C22⋊C4—1721no—
742C2×C22⋊C4—1721no—
743C2×C42—22no—
744C2×C42—41no—
745C2×C42—41no—
746#95—22no—
747#95—22no—
748#95—41no—
749#95—434no—
750#95—434no—
751#95—862no—
752#95—862no—
753#95—862no—
754#95—862no—
755#95—1721no—
756#95—1721no—
757#95—1721no—
758#95C4×D4314yescomplemented
759#95D17214yescomplemented
760C24—432no—
761C24—432no—
762C24—432no—
763C24—432no—
764C24—432no—
765C24—432no—
766C24—861no—
767C24—861no—
768C24—861no—
769C24—861no—
770C24—861no—
771C24—861no—
772C24—861no—
773C24—861no—
774C24—861no—
775C24—861no—
776C24—861no—
777C24—861no—
778C24—861no—
779C24—861no—
780C24—861no—
781C24—861no—
782C24—861no—
783C24—861no—
784C24—861no—
785C24—861no—
786C24—861no—
787C24—861no—
788C24—861no—
789C24—861no—
790C24C23×D4311yescharacteristic
791C2×D4—4316no—
792C2×D4—1724no—
793C2×D4—1724no—
794C2×D4—1724no—
795C2×D4—1724no—
796C2×D4—1724no—
797C2×D4—1724no—
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—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—432no—
838C22×C4—432no—
839C22×C4—432no—
840C22×C4—432no—
841C22×C4—432no—
842C22×C4—868no—
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—868no—
860C22×C4—861no—
861C22×C4—861no—
862C22×C4—861no—
863C22×C4—861no—
864C22×C4—861no—
865C22×C4—861no—
866C22×C4—861no—
867C22×C4—861no—
868C22×C4—861no—
869C22×C4—861no—
870C22×C4—861no—
871C22×C4—861no—
872C22×C4—861no—
873C22×C4—861no—
874C22×C4—861no—
875C22×C4—861no—
876C22×C4—861no—
877C22×C4—861no—
878C22×C4—861no—
879C22×C4—861no—
880C22×C4—861no—
881C22×C4—1724no—
882C22×C4—1724no—
883C22×C4—1724no—
884C22×C4—1724no—
885C22×C4—1724no—
886C22×C4—1724no—
887C22×C4—1724no—
888C22×C4—1724no—
889C22×C4—1724no—
890C22×C4—1724no—
891C22×C4—1724no—
892C22×C4—1724no—
893C22×C4C2×C4×D4312yes—
894C22×C4C2×C4×D4312yes—
895C22×C4C2×C4×D4312yes—
896C22×C4C2×D17212yes—
897C22×C4C2×D17212yes—
898C22×C4C2×D17212yes—
899C22×C4#1062189812yes—
900C22×C4D4×D4312yes—
901C22×C4D4×D4312yes—
902C22×C4Q8×D4312yes—
903C4⋊C4—44no—
904C4⋊C4—1724no—
905C4⋊C4—1724no—
906C4⋊C4—1724no—
907C4⋊C4—1724no—
908C4⋊C4—1724no—
909C4⋊C4—1724no—
910C22⋊C4—868no—
911C22⋊C4—868no—
912C22⋊C4—1724no—
913C22⋊C4—1724no—
914C22⋊C4—1724no—
915C22⋊C4—1724no—
916C22⋊C4—1724no—
917C22⋊C4—1724no—
918C22⋊C4—1724no—
919C22⋊C4—1724no—
920C42—44no—
921C23—434no—
922C23—434no—
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—862no—
944C23—862no—
945C23—862no—
946C23—862no—
947C23—862no—
948C23—862no—
949C23—862no—
950C23—862no—
951C23—862no—
952C23—862no—
953C23—862no—
954C23—862no—
955C23—862no—
956C23—862no—
957C23—862no—
958C23—862no—
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—
975C23—1721no—
976C23—1721no—
977C23—1721no—
978C23—1721no—
979C23—1721no—
980C23—1721no—
981C23—1721no—
982C23—1721no—
983C23—1721no—
984C23—1721no—
985C23—1721no—
986C23—1721no—
987C23—1721no—
988C23—1721no—
989C23—1721no—
990C23—1721no—
991C23C22×C4×D4311yescharacteristic
992C23C2×D4×D4311yescharacteristic
993C23C2×D4×D4311yescharacteristic
994C23C22×D17211yescharacteristic
995C23C2×Q8×D4311yescharacteristic
996C23#41×D4311yescharacteristic
997C23C2×#1062189811yescharacteristic
998C23#1306337011yescharacteristic
999C23#1306337011yescharacteristic
1000C23#1306337111yescharacteristic
1001C23#1306337111yescharacteristic
1002C23#1306337111yescharacteristic
1003C23#1306337111yescharacteristic
1004C23#1306337211yescharacteristic
1005C23#1306337311yescharacteristic
1006D4—17216no—
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—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—434no—
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—862no—
1065C2×C4—862no—
1066C2×C4—862no—
1067C2×C4—17216no—
1068C2×C4—17216no—
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×C4—1721no—
1083C2×C4—1721no—
1084C2×C4—1721no—
1085C2×C4—1721no—
1086C2×C4—1721no—
1087C2×C4—1721no—
1088C2×C4—1721no—
1089C2×C4—1721no—
1090C2×C4—1721no—
1091C2×C4—1721no—
1092C2×C4—1721no—
1093C2×C4—1721no—
1094C2×C4—1721no—
1095C2×C4—1721no—
1096C2×C4—1721no—
1097C2×C4—1721no—
1098C2×C4C4⋊C4×D4314yes—
1099C2×C4C4×D17214yes—
1100C22—864no—
1101C22—864no—
1102C22—864no—
1103C22—864no—
1104C22—864no—
1105C22—864no—
1106C22—1722no—
1107C22—1722no—
1108C22—1722no—
1109C22—1722no—
1110C22—1722no—
1111C22—1722no—
1112C22—1722no—
1113C22—1722no—
1114C22—1722no—
1115C22—1722no—
1116C22—1722no—
1117C22—1722no—
1118C22—1722no—
1119C22—1722no—
1120C22—1722no—
1121C22—1722no—
1122C22—1722no—
1123C22—1722no—
1124C22—1722no—
1125C22—1722no—
1126C22—1722no—
1127C22—1722no—
1128C22—1722no—
1129C22—1722no—
1130C22C2×C4⋊C4×D4311yescharacteristic
1131C22C4×D4×D4311yescharacteristic
1132C22C2×C4×D17211yescharacteristic
1133C22#1458337111yescharacteristic
1134C22#1458337111yescharacteristic
1135C22#1458337911yescharacteristic
1136C22#1458338111yescharacteristic
1137C22#1458345911yescharacteristic
1138C22#1458346011yescharacteristic
1139C22#1458346711yescharacteristic
1140C22#1458346811yescharacteristic
1141C22#1458347611yescharacteristic
1142C22#1458348011yescharacteristic
1143C22#1458350011yescharacteristic
1144C22#1458350111yescharacteristic
1145C22#1458351511yescharacteristic
1146C22#1458352111yescharacteristic
1147C22#1458352411yescharacteristic
1148C22#1458352411yescharacteristic
1149C22#1458353311yescharacteristic
1150C22D4×D17211yescharacteristic
1151C22D4×D17211yescharacteristic
1152C22#1458353911yescharacteristic
1153C22#1458354411yescharacteristic
1154C22#1458355111yescharacteristic
1155C22#1458355411yescharacteristic
1156C22#1458356411yescharacteristic
1157C22Q8×D17211yescharacteristic
1158C22#1458357311yescharacteristic
1159C22#1458360511yescharacteristic
1160C22#1458360911yescharacteristic
1161C22#1458364011yescharacteristic
1162C22#1458364511yescharacteristic
1163C22#1458364611yescharacteristic
1164C22#1458365311yescharacteristic
1165C4—24no—
1166C4—24no—
1167C4—42no—
1168C4—42no—
1169C4—42no—
1170C4—42no—
1171C4—81no—
1172C4—864no—
1173C4—3441no—
1174C4—3441no—
1175C4—3441no—
1176C4—1722no—
1177C4—1722no—
1178C2—1724no—
1179C2—1724no—
1180C2#1913720611yescharacteristic
1181C2#1913728311yescharacteristic
1182C2#1913728911yescharacteristic
1183C2#1913749611yescharacteristic
1184C2C4⋊C4×D17211yescharacteristic
1185C2#1913757711yescharacteristic
1186C2#1913774211yescharacteristic
1187C2#1914081011yescharacteristic
1188C2#1914083211yescharacteristic
1189C2#1914083411yescharacteristic
1190C2#1914096611yescharacteristic
1191C2#1914108611yescharacteristic
1192C2#1914108911yescharacteristic
1193C2#1914143511yescharacteristic
1194C2#1914180311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1436C2
socle, cosocleC24×C43C24
prime radicalC23×D172C22
hypercenter#1436D43
hypocenterC43#14401
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
4. C2×#14582773C2semidirect
5. C2×#14582773C2semidirect
6. C2×#14582758C2semidirect
7. C2×#14582756C2semidirect
8. #19132860C2semidirect
9. #19132859C2semidirect
10. #19132841C2semidirect
11. #19132839C2semidirect
12. #19132839C2semidirect
13. #19132837C2semidirect
14. #19132828C2semidirect
15. C43×#1436C2semidirect
37. #14582777C4semidirect
86. C22×C4×D43C2×C4semidirect
134. C2×(C2×D43)⋊C4C2×C4semidirect
142. C43⋊#95C2×C4semidirect
143. C43⋊#95D4semidirect
160. #95×C43C2×C4semidirect
161. #95×C43D4semidirect
290. C2×D172C4⋊C4semidirect
595. #1436D43semidirect
655. C43#14401semidirect
758. #95C4×D43semidirect
759. #95D172semidirect

Maximal subgroups

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

subgroupindex
C2×#145828012
C2×#145827772
C2×#145827732
C2×#145827582
C2×#145827562
#191328602
#191328592
#191328412
#191328392
#191328372
#191328282
C43×#14362
#1440143