Finite Group Databasebeta

← #25024136

Subgroups — #25024136

Order 11008.

1874 conjugacy classes of subgroups.

The subgroup lattice has 1152 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582777C211yesmaximal, characteristic
2C2×#14582777C211yesmaximal, characteristic
3C2×#14582761C211yesmaximal, characteristic, complemented
4#19132855C211yesmaximal, characteristic, complemented
5#19132850C211yesmaximal, characteristic, complemented
6#19132839C211yesmaximal, characteristic, complemented
7#19132839C211yesmaximal, characteristic, complemented
8#19132835C211yesmaximal, characteristic
9#19132831C211yesmaximal, characteristic, complemented
10#19132831C211yesmaximal, characteristic, complemented
11#19132820C211yesmaximal, characteristic, complemented
12(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
13(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
14(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
15C43×#1443C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17C23×C4×D43C2211yescharacteristic
18C23×C4×D43C2211yescharacteristic
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
26C22×(C2×D43)⋊C4C2211yescharacteristic
27C22×(C2×D43)⋊C4C2211yescharacteristic
28C22×(C2×D43)⋊C4C2211yescharacteristic
29C22×(C2×D43)⋊C4C2211yescharacteristic
30C22×C4×Dic43C2211yescharacteristic
31#14582777—24no—
32#14582777C418yescomplemented
33#14582761—24no—
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
45C2×C43⋊#95C2211yescharacteristic
46C2×C43⋊#95C2211yescharacteristic
47C2×#95×C43C2211yescharacteristic
48C2×#95×C43C2211yescharacteristic
49C2×#95×C43C2211yescharacteristic
50C2×#95×C43C2211yescharacteristic
51C2×#95×C43C2211yescharacteristic
52C2×#95×C43C2211yescharacteristic
53C2×#95×C43C2211yescharacteristic
54C24×D43C2311yescharacteristic
55C24×D43C2311yescharacteristic
56C22×D172—22no—
57C22×D172—22no—
58C22×D172—22no—
59C22×D172—22no—
60C22×D172—41no—
61C22×D172—41no—
62C22×D172C2×C414yes—
63C23×Dic43C2311yescharacteristic
64C23×Dic43C2311yescharacteristic
65C23×Dic43C2311yescharacteristic
66C23×Dic43C2311yescharacteristic
67C23×Dic43C2311yescharacteristic
68C23×Dic43C2311yescharacteristic
69C22×C4×D43—22no—
70C22×C4×D43—22no—
71C22×C4×D43—22no—
72C22×C4×D43—22no—
73C22×C4×D43—22no—
74C22×C4×D43—41no—
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×D43C2×C414yescomplemented
83C2×Dic43⋊C4—41no—
84C2×Dic43⋊C4—41no—
85C2×Dic43⋊C4—41no—
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—22no—
94C2×(C2×D43)⋊C4—22no—
95C2×(C2×D43)⋊C4—22no—
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)⋊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)⋊C4C2×C414yes—
113C2×(C2×D43)⋊C4C2×C414yes—
114C2×(C2×D43)⋊C4C2×C414yescomplemented
115C2×(C2×D43)⋊C4D414yes—
116C2×C4×Dic43—22no—
117C2×C4×Dic43—41no—
118C2×C4×Dic43—41no—
119C43⋊#95—22no—
120C43⋊#95—22no—
121C43⋊#95—22no—
122C43⋊#95—22no—
123C43⋊#95—22no—
124C43⋊#95—41no—
125C43⋊#95—41no—
126C43⋊#95—41no—
127C43⋊#95—41no—
128C43⋊#95—41no—
129C43⋊#95—41no—
130C43⋊#95—41no—
131C43⋊#95C2×C414yescomplemented
132C23×C4×C43C2311yescharacteristic
133C23×C4×C43C2311yescharacteristic
134C23×C4×C43C2311yescharacteristic
135C23×C4×C43C2311yescharacteristic
136C23×C4×C43C2311yescharacteristic
137C23×C4×C43C2311yescharacteristic
138C23×C4×C43C2311yescharacteristic
139#95×C43—22no—
140#95×C43—22no—
141#95×C43—41no—
142#95×C43—41no—
143#95×C43—41no—
144#95×C43—41no—
145#95×C43C2×C414yescomplemented
146C24×C43C2411yescharacteristic
147C23×D43—21no—
148C23×D43—21no—
149C23×D43—21no—
150C23×D43—21no—
151C23×D43—21no—
152C23×D43—21no—
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×D43C22×C412yes—
172C23×D43C22×C412yes—
173C23×D43C2×D412yes—
174C23×D43#4112yes—
175C23×D43#4112yes—
176C23×D43#4112yes—
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×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×C43C22×C412yes—
223C22×C4×C43C22×C412yes—
224C22×C4×C43C22×C412yes—
225C22×C4×C43C2×D412yes—
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×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×Dic43C22×C412yes—
264C22×Dic43C22×C412yes—
265C22×Dic43C2×D412yes—
266C22×Dic43#4112yes—
267C22×Dic43#4112yes—
268C2×D172—28no—
269C2×D172—28no—
270C2×D172—44no—
271C2×D172—44no—
272C2×D172—44no—
273C2×D172—44no—
274C2×D172—44no—
275C2×C4×D43—28no—
276C2×C4×D43—44no—
277C2×C4×D43—44no—
278C2×C4×D43—44no—
279C2×C4×D43—44no—
280C2×C4×D43—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—
289(C2×D43)⋊C4—44no—
290(C2×D43)⋊C4—44no—
291(C2×D43)⋊C4—44no—
292(C2×D43)⋊C4—44no—
293(C2×D43)⋊C4—44no—
294(C2×D43)⋊C4—44no—
295(C2×D43)⋊C4—44no—
296(C2×D43)⋊C4—44no—
297(C2×D43)⋊C4—44no—
298(C2×D43)⋊C4—44no—
299Dic43⋊C4—44no—
300C4×Dic43—44no—
301C23×C43C23×C411yescharacteristic
302C23×C43C22×D411yescharacteristic
303C23×C43C2×#4111yescharacteristic
304C23×C43C2×#4111yescharacteristic
305C23×C43C2×#4111yescharacteristic
306C23×C43C2×#4111yescharacteristic
307C23×C43C2×#4111yescharacteristic
308C23×C43H(5,𝔽2)11yescharacteristic
309C23×C43H(5,𝔽2)11yescharacteristic
310C23×C43H(5,𝔽2)11yescharacteristic
311C23×C43H(5,𝔽2)11yescharacteristic
312C23×C43H(5,𝔽2)11yescharacteristic
313C23×C43H(5,𝔽2)11yescharacteristic
314C23×C43H(5,𝔽2)11yescharacteristic
315C23×C432−1+411yescharacteristic
316C22×D43—22no—
317C22×D43—22no—
318C22×D43—22no—
319C22×D43—22no—
320C22×D43—22no—
321C22×D43—22no—
322C22×D43—22no—
323C22×D43—22no—
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—41no—
353C22×D43—41no—
354C22×D43—41no—
355C22×D43—41no—
356C22×D43—41no—
357C22×D43—41no—
358C22×D43—41no—
359C22×D43—41no—
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#11714yes—
385C22×D43C4×D414yes—
386C2×C4×C43—22no—
387C2×C4×C43—22no—
388C2×C4×C43—22no—
389C2×C4×C43—22no—
390C2×C4×C43—22no—
391C2×C4×C43—22no—
392C2×C4×C43—22no—
393C2×C4×C43—22no—
394C2×C4×C43—22no—
395C2×C4×C43—22no—
396C2×C4×C43—22no—
397C2×C4×C43—22no—
398C2×C4×C43—41no—
399C2×C4×C43—41no—
400C2×C4×C43—41no—
401C2×C4×C43—41no—
402C2×C4×C43—41no—
403C2×C4×C43—41no—
404C2×C4×C43—41no—
405C2×C4×C43—41no—
406C2×C4×C43—41no—
407C2×C4×C43—41no—
408C2×C4×C43—41no—
409C2×C4×C43—41no—
410C2×C4×C43—41no—
411C2×C4×C43—41no—
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×Dic43—22no—
436C2×Dic43—22no—
437C2×Dic43—22no—
438C2×Dic43—22no—
439C2×Dic43—22no—
440C2×Dic43—22no—
441C2×Dic43—22no—
442C2×Dic43—22no—
443C2×Dic43—22no—
444C2×Dic43—22no—
445C2×Dic43—22no—
446C2×Dic43—22no—
447C2×Dic43—22no—
448C2×Dic43—22no—
449C2×Dic43—22no—
450C2×Dic43—41no—
451C2×Dic43—41no—
452C2×Dic43—41no—
453C2×Dic43—41no—
454C2×Dic43—41no—
455C2×Dic43—41no—
456C2×Dic43—41no—
457C2×Dic43—41no—
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—
477D172—416no—
478C4×D43—416no—
479C4×D43—416no—
480#14375—431nomaximal, Sylow
481C22×C43C2×#11711yescharacteristic
482C22×C43C2×C4×D411yescharacteristic
483C22×C43C4×#4111yescharacteristic
484C22×C43#51811yescharacteristic
485C22×C43#51811yescharacteristic
486C22×C43#51811yescharacteristic
487C22×C43#52011yescharacteristic
488C22×C43#53411yescharacteristic
489C22×C43#53511yescharacteristic
490C22×C43#53811yescharacteristic
491C22×C43#53811yescharacteristic
492C22×C43#53811yescharacteristic
493C22×C43#53811yescharacteristic
494C22×C43#53811yescharacteristic
495C22×C43#53811yescharacteristic
496C22×C43#53911yescharacteristic
497C22×C43#53911yescharacteristic
498C22×C43#54011yescharacteristic
499C22×C43#54011yescharacteristic
500C22×C43#54611yescharacteristic
501C22×C43#54611yescharacteristic
502C22×C43#54611yescharacteristic
503C22×C43#54711yescharacteristic
504C22×C43#55111yescharacteristic
505C22×C43#55111yescharacteristic
506C22×C43#55111yescharacteristic
507C22×C43#55111yescharacteristic
508C22×C43#55111yescharacteristic
509C22×C43#55211yescharacteristic
510C22×C43#55311yescharacteristic
511C22×C43#55311yescharacteristic
512C22×C43#56011yescharacteristic
513C22×C43#56011yescharacteristic
514C22×C43#56211yescharacteristic
515C22×C43#56211yescharacteristic
516C2×D43—24no—
517C2×D43—24no—
518C2×D43—24no—
519C2×D43—24no—
520C2×D43—24no—
521C2×D43—24no—
522C2×D43—42no—
523C2×D43—42no—
524C2×D43—42no—
525C2×D43—42no—
526C2×D43—42no—
527C2×D43—42no—
528C2×D43—42no—
529C2×D43—42no—
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—
546C4×C43—42no—
547C4×C43—42no—
548C4×C43—42no—
549C4×C43—42no—
550C4×C43—81no—
551C4×C43—81no—
552C4×C43—81no—
553Dic43—42no—
554Dic43—42no—
555Dic43—42no—
556Dic43—42no—
557Dic43—42no—
558Dic43—81no—
559C2×#386—431no—
560C2×#386—431no—
561C2×#381—431no—
562#1443—431no—
563#1443D4311yescharacteristic, complemented
564#1442—431no—
565#1439—431no—
566#1439—431no—
567#1438—431no—
568#1437—431no—
569#1437—431no—
570#1434—431no—
571C22⋊#95—431no—
572C22⋊#95—431no—
573C22⋊#95—431no—
574C2×C43#231811yescharacteristic
575C2×C43#232111yescharacteristic
576C2×C43#233311yescharacteristic
577C2×C43#234211yescharacteristic
578C2×C43#235311yescharacteristic
579C2×C43#235911yescharacteristic
580C2×C43#237711yescharacteristic
581C2×C43#269711yescharacteristic
582C2×C43#270311yescharacteristic
583C2×C43#270611yescharacteristic
584C2×C43#270811yescharacteristic
585C2×C43#274311yescharacteristic
586C2×C43#274911yescharacteristic
587C2×C43#275011yescharacteristic
588C2×C43#276011yescharacteristic
589D43—44no—
590D43—44no—
591C23×D4—431no—
592C24×C4—431no—
593C24×C4—431no—
594C22×C4⋊C4—431no—
595C22×C22⋊C4—431no—
596C22×C22⋊C4—431no—
597C22×C22⋊C4—431no—
598C22×C22⋊C4—431no—
599C22×C22⋊C4—431no—
600C22×C22⋊C4—431no—
601C22×C22⋊C4—431no—
602C22×C22⋊C4—431no—
603C22×C22⋊C4—431no—
604C22×C22⋊C4—431no—
605C22×C42—431no—
606#386—438no—
607#386—864no—
608#381—864no—
609C2×#95—431no—
610C2×#95—431no—
611C2×#95—431no—
612C2×#95—431no—
613C2×#95—431no—
614C2×#95—431no—
615C2×#95—431no—
616C2×#95—431no—
617C2×#95—431no—
618C2×#95—431no—
619C2×#95—431no—
620C2×#95—431no—
621C2×#95—431no—
622C2×#95C2×D4311yescharacteristic
623C2×#95C2×D4311yescharacteristic
624C2×#95C2×D4311yescharacteristic
625C2×#95C2×D4311yescharacteristic
626C2×#95C2×D4311yescharacteristic
627C2×#95C2×D4311yescharacteristic
628C2×#95C2×D4311yescharacteristic
629C43#1437511yescharacteristic, complemented, Sylow
630C25—431no—
631C25—431no—
632C22×D4—434no—
633C22×D4—862no—
634C22×D4—862no—
635C22×D4—862no—
636C22×D4—862no—
637C22×D4—1721no—
638C22×D4—1721no—
639C23×C4—431no—
640C23×C4—431no—
641C23×C4—431no—
642C23×C4—431no—
643C23×C4—431no—
644C23×C4—434no—
645C23×C4—431no—
646C23×C4—862no—
647C23×C4—862no—
648C23×C4—862no—
649C23×C4—862no—
650C23×C4—862no—
651C23×C4—1721no—
652C23×C4—1721no—
653C23×C4—1721no—
654C23×C4—1721no—
655C23×C4—1721no—
656C23×C4—1721no—
657C23×C4—1721no—
658C23×C4—1721no—
659C23×C4C22×D4311yescharacteristic
660C23×C4C22×D4311yescharacteristic
661C23×C4C22×D4311yescharacteristic
662C23×C4C22×D4311yescharacteristic
663C23×C4C22×D4311yescharacteristic
664C23×C4C22×D4311yescharacteristic
665C23×C4C22×D4311yescharacteristic
666C2×C4⋊C4—1721no—
667C2×C4⋊C4—1721no—
668C2×C4⋊C4—1721no—
669C2×C22⋊C4—434no—
670C2×C22⋊C4—434no—
671C2×C22⋊C4—434no—
672C2×C22⋊C4—434no—
673C2×C22⋊C4—862no—
674C2×C22⋊C4—862no—
675C2×C22⋊C4—862no—
676C2×C22⋊C4—862no—
677C2×C22⋊C4—862no—
678C2×C22⋊C4—862no—
679C2×C22⋊C4—862no—
680C2×C22⋊C4—862no—
681C2×C22⋊C4—862no—
682C2×C22⋊C4—862no—
683C2×C22⋊C4—1721no—
684C2×C22⋊C4—1721no—
685C2×C22⋊C4—1721no—
686C2×C22⋊C4—1721no—
687C2×C22⋊C4—1721no—
688C2×C22⋊C4—1721no—
689C2×C22⋊C4—1721no—
690C2×C22⋊C4—1721no—
691C2×C22⋊C4—1721no—
692C2×C22⋊C4—1721no—
693C2×C22⋊C4—1721no—
694C2×C22⋊C4—1721no—
695C2×C22⋊C4—1721no—
696C2×C22⋊C4—1721no—
697C2×C22⋊C4—1721no—
698C2×C22⋊C4—1721no—
699C2×C42—862no—
700C2×C42—1721no—
701C2×C42—1721no—
702#95—22no—
703#95—22no—
704#95—41no—
705#95—41no—
706#95—41no—
707#95—41no—
708#95—434no—
709#95—862no—
710#95—862no—
711#95—862no—
712#95—862no—
713#95—862no—
714#95—1721no—
715#95—1721no—
716#95—1721no—
717#95—1721no—
718#95—1721no—
719#95—1721no—
720#95—1721no—
721#95C4×D4314yescomplemented
722C24—432no—
723C24—432no—
724C24—432no—
725C24—432no—
726C24—432no—
727C24—432no—
728C24—861no—
729C24—861no—
730C24—861no—
731C24—861no—
732C24—861no—
733C24—861no—
734C24—861no—
735C24—861no—
736C24—861no—
737C24—861no—
738C24—861no—
739C24—861no—
740C24—861no—
741C24—861no—
742C24—861no—
743C24—861no—
744C24—861no—
745C24—861no—
746C24—861no—
747C24—861no—
748C24—861no—
749C24—861no—
750C24—861no—
751C24—861no—
752C24C23×D4311yescharacteristic
753C2×D4—868no—
754C2×D4—868no—
755C2×D4—1724no—
756C2×D4—1724no—
757C2×D4—1724no—
758C2×D4—1724no—
759C2×D4—1724no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
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—432no—
806C22×C4—432no—
807C22×C4—432no—
808C22×C4—432no—
809C22×C4—432no—
810C22×C4—868no—
811C22×C4—861no—
812C22×C4—861no—
813C22×C4—861no—
814C22×C4—861no—
815C22×C4—861no—
816C22×C4—861no—
817C22×C4—861no—
818C22×C4—861no—
819C22×C4—861no—
820C22×C4—861no—
821C22×C4—861no—
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—1724no—
849C22×C4—1724no—
850C22×C4—1724no—
851C22×C4—1724no—
852C22×C4—1724no—
853C22×C4—1724no—
854C22×C4—1724no—
855C22×C4—1724no—
856C22×C4—1724no—
857C22×C4—1724no—
858C22×C4—1724no—
859C22×C4—1724no—
860C22×C4—1724no—
861C22×C4C2×C4×D4312yes—
862C22×C4C2×C4×D4312yes—
863C22×C4C2×C4×D4312yes—
864C22×C4D4×D4312yes—
865C4⋊C4—1724no—
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—
876C42—1724no—
877C23—434no—
878C23—434no—
879C23—862no—
880C23—862no—
881C23—862no—
882C23—862no—
883C23—862no—
884C23—862no—
885C23—862no—
886C23—862no—
887C23—862no—
888C23—862no—
889C23—862no—
890C23—862no—
891C23—862no—
892C23—862no—
893C23—862no—
894C23—862no—
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—1721no—
916C23—1721no—
917C23—1721no—
918C23—1721no—
919C23—1721no—
920C23—1721no—
921C23—1721no—
922C23—1721no—
923C23—1721no—
924C23—1721no—
925C23—1721no—
926C23—1721no—
927C23—1721no—
928C23—1721no—
929C23—1721no—
930C23—1721no—
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—
947C23C22×C4×D4311yescharacteristic
948C23C2×D4×D4311yescharacteristic
949C23#41×D4311yescharacteristic
950C23#41×D4311yescharacteristic
951C23#41×D4311yescharacteristic
952C23#41×D4311yescharacteristic
953C23#41×D4311yescharacteristic
954C23#1306337011yescharacteristic
955C23#1306337011yescharacteristic
956C23#1306337111yescharacteristic
957C23#1306337111yescharacteristic
958C23#1306337111yescharacteristic
959C23#1306337111yescharacteristic
960C23#1306337111yescharacteristic
961C23#1306337311yescharacteristic
962D4—17216no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
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—862no—
1013C2×C4—862no—
1014C2×C4—862no—
1015C2×C4—862no—
1016C2×C4—862no—
1017C2×C4—862no—
1018C2×C4—862no—
1019C2×C4—862no—
1020C2×C4—862no—
1021C2×C4—862no—
1022C2×C4—862no—
1023C2×C4—862no—
1024C2×C4—862no—
1025C2×C4—862no—
1026C2×C4—862no—
1027C2×C4—17216no—
1028C2×C4—17216no—
1029C2×C4—1721no—
1030C2×C4—1721no—
1031C2×C4—1721no—
1032C2×C4—1721no—
1033C2×C4—1721no—
1034C2×C4—1721no—
1035C2×C4—1721no—
1036C2×C4—1721no—
1037C2×C4—1721no—
1038C2×C4—1721no—
1039C2×C4—1721no—
1040C2×C4—1721no—
1041C2×C4—1721no—
1042C2×C4—1721no—
1043C2×C4—1721no—
1044C2×C4—1721no—
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—
1056C22—864no—
1057C22—864no—
1058C22—864no—
1059C22—864no—
1060C22—864no—
1061C22—864no—
1062C22—1722no—
1063C22—1722no—
1064C22—1722no—
1065C22—1722no—
1066C22—1722no—
1067C22—1722no—
1068C22—1722no—
1069C22—1722no—
1070C22—1722no—
1071C22—1722no—
1072C22—1722no—
1073C22—1722no—
1074C22—1722no—
1075C22—1722no—
1076C22—1722no—
1077C22—1722no—
1078C22—1722no—
1079C22—1722no—
1080C22—1722no—
1081C22—1722no—
1082C22—1722no—
1083C22—1722no—
1084C22—1722no—
1085C22—1722no—
1086C22#117×D4311yescharacteristic
1087C22C4×D4×D4311yescharacteristic
1088C22#1458336711yescharacteristic
1089C22#1458337111yescharacteristic
1090C22#1458337111yescharacteristic
1091C22#1458337311yescharacteristic
1092C22#1458338111yescharacteristic
1093C22#1458346011yescharacteristic
1094C22#1458346511yescharacteristic
1095C22#1458348311yescharacteristic
1096C22#1458348311yescharacteristic
1097C22#1458348511yescharacteristic
1098C22#1458348811yescharacteristic
1099C22#1458348811yescharacteristic
1100C22#1458348811yescharacteristic
1101C22#1458349511yescharacteristic
1102C22#1458349711yescharacteristic
1103C22#1458349911yescharacteristic
1104C22#1458350111yescharacteristic
1105C22#1458353811yescharacteristic
1106C22#1458354111yescharacteristic
1107C22#1458354211yescharacteristic
1108C22#1458355111yescharacteristic
1109C22#1458357411yescharacteristic
1110C22#1458357411yescharacteristic
1111C22#1458357411yescharacteristic
1112C22#1458357411yescharacteristic
1113C22#1458357711yescharacteristic
1114C22#1458358111yescharacteristic
1115C22#1458360011yescharacteristic
1116C22#1458360011yescharacteristic
1117C22#1458363911yescharacteristic
1118C22#1458364011yescharacteristic
1119C22#1458364511yescharacteristic
1120C22#1458364711yescharacteristic
1121C4—42no—
1122C4—42no—
1123C4—42no—
1124C4—42no—
1125C4—81no—
1126C4—81no—
1127C4—81no—
1128C4—3441no—
1129C4—1722no—
1130C4—1722no—
1131C4—1722no—
1132C4—1722no—
1133C4—1722no—
1134C2—1724no—
1135C2—1724no—
1136C2#1913722711yescharacteristic
1137C2#1913725711yescharacteristic
1138C2#1913735811yescharacteristic
1139C2#1913744311yescharacteristic
1140C2#1913752811yescharacteristic
1141C2#1913758011yescharacteristic
1142C2#1913775011yescharacteristic
1143C2#1914116011yescharacteristic
1144C2#1914124011yescharacteristic
1145C2#1914128911yescharacteristic
1146C2#1914131811yescharacteristic
1147C2#1914173911yescharacteristic
1148C2#1914182311yescharacteristic
1149C2#1914183811yescharacteristic
1150C2#1914197311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1443C2
socle, cosocleC24×C43C24
prime radicalC23×D172C22
hypercenter#1443D43
hypocenterC43#14375
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1443

Complements

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

NH ≅ G/Ntype
3. C2×#14582761C2semidirect
4. #19132855C2semidirect
5. #19132850C2semidirect
6. #19132839C2semidirect
7. #19132839C2semidirect
9. #19132831C2semidirect
10. #19132831C2semidirect
11. #19132820C2semidirect
12. (C2×D43)⋊#95C2semidirect
13. (C2×D43)⋊#95C2semidirect
14. (C2×D43)⋊#95C2semidirect
15. C43×#1443C2semidirect
32. #14582777C4semidirect
82. C22×C4×D43C2×C4semidirect
114. C2×(C2×D43)⋊C4C2×C4semidirect
131. C43⋊#95C2×C4semidirect
145. #95×C43C2×C4semidirect
563. #1443D43semidirect
629. C43#14375semidirect
721. #95C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145827772
C2×#145827612
#191328552
#191328502
#191328392
#191328352
#191328312
#191328202
(C2×D43)⋊#952
C43×#14432
#1437543