Finite Group Databasebeta

← #25025796

Subgroups — #25025796

Order 11008.

1406 conjugacy classes of subgroups.

The subgroup lattice has 978 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582761C211yesmaximal, characteristic
2#19132856C211yesmaximal, characteristic, complemented
3#19132855C211yesmaximal, characteristic, complemented
4#19132854C211yesmaximal, characteristic, complemented
5#19132839C211yesmaximal, characteristic
6#19132837C211yesmaximal, characteristic
7#19132831C211yesmaximal, characteristic
8#19132831C211yesmaximal, characteristic
9#19132830C211yesmaximal, characteristic, complemented
10#19132826C211yesmaximal, characteristic, complemented
11#19132820C211yesmaximal, characteristic, complemented
12#19132819C211yesmaximal, characteristic, complemented
13(C2×D43)⋊#95C211yesmaximal, characteristic
14(C2×D43)⋊#95C211yesmaximal, characteristic
15C43×#1442C211yesmaximal, characteristic, complemented
16C23×C4×D43C2211yescharacteristic
17C22×Dic43⋊C4C2211yescharacteristic
18C22×(C2×D43)⋊C4C2211yescharacteristic
19C22×(C2×D43)⋊C4C2211yescharacteristic
20C22×(C2×D43)⋊C4C2211yescharacteristic
21C22×(C2×D43)⋊C4C2211yescharacteristic
22C22×(C2×D43)⋊C4C2211yescharacteristic
23C22×(C2×D43)⋊C4C2211yescharacteristic
24C22×C4×Dic43C2211yescharacteristic
25C22×C4×Dic43C2211yescharacteristic
26#14582761C418yescomplemented
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
53C23×Dic43C2311yescharacteristic
54C23×Dic43C2311yescharacteristic
55C23×Dic43C2311yescharacteristic
56C23×Dic43C2311yescharacteristic
57C23×Dic43C2311yescharacteristic
58C23×Dic43C2311yescharacteristic
59C23×Dic43C2311yescharacteristic
60C22×C4×D43—22no—
61C22×C4×D43—22no—
62C22×C4×D43—41no—
63C22×C4×D43—41no—
64C22×C4×D43—41no—
65C22×C4×D43—41no—
66C22×C4×D43C2×C414yes—
67C2×Dic43⋊C4—22no—
68C2×Dic43⋊C4—22no—
69C2×Dic43⋊C4—41no—
70C2×(C2×D43)⋊C4—22no—
71C2×(C2×D43)⋊C4—22no—
72C2×(C2×D43)⋊C4—22no—
73C2×(C2×D43)⋊C4—22no—
74C2×(C2×D43)⋊C4—22no—
75C2×(C2×D43)⋊C4—22no—
76C2×(C2×D43)⋊C4—22no—
77C2×(C2×D43)⋊C4—22no—
78C2×(C2×D43)⋊C4—41no—
79C2×(C2×D43)⋊C4—41no—
80C2×(C2×D43)⋊C4—41no—
81C2×(C2×D43)⋊C4—41no—
82C2×(C2×D43)⋊C4—41no—
83C2×(C2×D43)⋊C4—41no—
84C2×(C2×D43)⋊C4—41no—
85C2×(C2×D43)⋊C4—41no—
86C2×(C2×D43)⋊C4C2×C414yes—
87C2×(C2×D43)⋊C4C2×C414yes—
88C2×C4×Dic43—22no—
89C2×C4×Dic43—22no—
90C2×C4×Dic43—41no—
91C2×C4×Dic43—41no—
92C2×C4×Dic43—41no—
93C2×C4×Dic43—41no—
94C43⋊#95—22no—
95C43⋊#95—22no—
96C43⋊#95—22no—
97C43⋊#95—22no—
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⋊#95C2×C414yes—
110C43⋊#95C2×C414yes—
111C43⋊#95C2×C414yes—
112C23×C4×C43C2311yescharacteristic
113C23×C4×C43C2311yescharacteristic
114C23×C4×C43C2311yescharacteristic
115C23×C4×C43C2311yescharacteristic
116C23×C4×C43C2311yescharacteristic
117C23×C4×C43C2311yescharacteristic
118C23×C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43—41no—
120C2×C4⋊C4×C43—41no—
121C2×C4⋊C4×C43—41no—
122#95×C43—41no—
123#95×C43—41no—
124#95×C43—41no—
125#95×C43—41no—
126#95×C43—41no—
127#95×C43C2×C414yes—
128C24×C43C2411yescharacteristic
129C23×D43—21no—
130C23×D43—21no—
131C23×D43—21no—
132C23×D43—21no—
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×D43C22×C412yes—
142C23×D43#4112yes—
143C23×D43#4112yes—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
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×C43C22×C412yes—
190C22×C4×C43C22×C412yes—
191C22×C4×C43C22×C412yes—
192C22×C4×C43#4112yes—
193C22×Dic43—21no—
194C22×Dic43—21no—
195C22×Dic43—21no—
196C22×Dic43—21no—
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×Dic43C22×C412yes—
237C22×Dic43C22×C412yes—
238C22×Dic43C22×C412yes—
239C22×Dic43#4112yes—
240C22×Dic43#4112yes—
241C22×Dic43#4112yes—
242C2×C4×D43—28no—
243C2×C4×D43—44no—
244C2×C4×D43—44no—
245C2×C4×D43—44no—
246C2×C4×D43—44no—
247C2×C4×D43—44no—
248C2×C4×D43—44no—
249C4⋊C4×C43—44no—
250(C2×D43)⋊C4—44no—
251(C2×D43)⋊C4—44no—
252(C2×D43)⋊C4—44no—
253(C2×D43)⋊C4—44no—
254(C2×D43)⋊C4—44no—
255(C2×D43)⋊C4—44no—
256Dic43⋊C4—44no—
257C4×Dic43—44no—
258C4×Dic43—44no—
259C23×C43C23×C411yescharacteristic
260C23×C43C2×#4111yescharacteristic
261C23×C43C2×#4111yescharacteristic
262C23×C43C2×#4111yescharacteristic
263C23×C43C2×#4111yescharacteristic
264C23×C43C2×#4111yescharacteristic
265C23×C43C2×#4111yescharacteristic
266C23×C43H(5,𝔽2)11yescharacteristic
267C23×C43H(5,𝔽2)11yescharacteristic
268C23×C43H(5,𝔽2)11yescharacteristic
269C23×C43H(5,𝔽2)11yescharacteristic
270C23×C43H(5,𝔽2)11yescharacteristic
271C23×C43H(5,𝔽2)11yescharacteristic
272C23×C432−1+411yescharacteristic
273C23×C432−1+411yescharacteristic
274C22×D43—22no—
275C22×D43—22no—
276C22×D43—22no—
277C22×D43—22no—
278C22×D43—22no—
279C22×D43—22no—
280C22×D43—22no—
281C22×D43—22no—
282C22×D43—22no—
283C22×D43—22no—
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—41no—
293C22×D43—41no—
294C22×D43—41no—
295C22×D43—41no—
296C22×D43—41no—
297C22×D43—41no—
298C22×D43—41no—
299C22×D43—41no—
300C22×D43—41no—
301C22×D43—41no—
302C22×D43—41no—
303C22×D43—41no—
304C22×D43—41no—
305C22×D43—41no—
306C22×D43—41no—
307C22×D43—41no—
308C22×D43#11714yes—
309C2×C4×C43—22no—
310C2×C4×C43—22no—
311C2×C4×C43—22no—
312C2×C4×C43—22no—
313C2×C4×C43—22no—
314C2×C4×C43—22no—
315C2×C4×C43—22no—
316C2×C4×C43—22no—
317C2×C4×C43—22no—
318C2×C4×C43—22no—
319C2×C4×C43—22no—
320C2×C4×C43—22no—
321C2×C4×C43—41no—
322C2×C4×C43—41no—
323C2×C4×C43—41no—
324C2×C4×C43—41no—
325C2×C4×C43—41no—
326C2×C4×C43—41no—
327C2×C4×C43—41no—
328C2×C4×C43—41no—
329C2×C4×C43—41no—
330C2×C4×C43—41no—
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×Dic43—22no—
359C2×Dic43—22no—
360C2×Dic43—22no—
361C2×Dic43—22no—
362C2×Dic43—22no—
363C2×Dic43—22no—
364C2×Dic43—22no—
365C2×Dic43—22no—
366C2×Dic43—22no—
367C2×Dic43—22no—
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—41no—
377C2×Dic43—41no—
378C2×Dic43—41no—
379C2×Dic43—41no—
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—
407C4×D43—416no—
408#14508—431nomaximal, Sylow
409C22×C43C2×#11711yescharacteristic
410C22×C43C4×#4111yescharacteristic
411C22×C43C4×#4111yescharacteristic
412C22×C43#51811yescharacteristic
413C22×C43#51811yescharacteristic
414C22×C43#52011yescharacteristic
415C22×C43#52011yescharacteristic
416C22×C43#53811yescharacteristic
417C22×C43#53811yescharacteristic
418C22×C43#53811yescharacteristic
419C22×C43#53811yescharacteristic
420C22×C43#53811yescharacteristic
421C22×C43#53811yescharacteristic
422C22×C43#53911yescharacteristic
423C22×C43#53911yescharacteristic
424C22×C43#54011yescharacteristic
425C22×C43#54011yescharacteristic
426C22×C43#54211yescharacteristic
427C22×C43#54211yescharacteristic
428C22×C43#55111yescharacteristic
429C22×C43#55111yescharacteristic
430C22×C43#55111yescharacteristic
431C22×C43#55111yescharacteristic
432C22×C43#55111yescharacteristic
433C22×C43#55211yescharacteristic
434C22×C43#55211yescharacteristic
435C22×C43#55211yescharacteristic
436C22×C43#55211yescharacteristic
437C22×C43#55311yescharacteristic
438C22×C43#55311yescharacteristic
439C22×C43#55911yescharacteristic
440C22×C43#56011yescharacteristic
441C22×C43#56211yescharacteristic
442C22×C43#56211yescharacteristic
443C22×C43#56311yescharacteristic
444C2×D43—24no—
445C2×D43—24no—
446C2×D43—24no—
447C2×D43—42no—
448C2×D43—42no—
449C2×D43—42no—
450C2×D43—42no—
451C2×D43—42no—
452C2×D43—42no—
453C2×D43—42no—
454C2×D43—42no—
455C2×D43—42no—
456C2×D43—42no—
457C2×D43—42no—
458C2×D43—42no—
459C4×C43—42no—
460C4×C43—42no—
461C4×C43—42no—
462C4×C43—42no—
463C4×C43—81no—
464C4×C43—81no—
465C4×C43—81no—
466Dic43—42no—
467Dic43—42no—
468Dic43—42no—
469Dic43—42no—
470Dic43—42no—
471Dic43—42no—
472Dic43—81no—
473C2×#381—431no—
474#1443—431no—
475#1443—431no—
476#1442—431no—
477#1442D4311yescharacteristic, complemented
478#1439—431no—
479#1439—431no—
480#1437—431no—
481#1437—431no—
482#1436—431no—
483#1436—431no—
484#1434—431no—
485#1434—431no—
486C22⋊#95—431no—
487C22⋊#95—431no—
488C2×C43#231211yescharacteristic
489C2×C43#233511yescharacteristic
490C2×C43#233511yescharacteristic
491C2×C43#234311yescharacteristic
492C2×C43#234311yescharacteristic
493C2×C43#237411yescharacteristic
494C2×C43#237611yescharacteristic
495C2×C43#275011yescharacteristic
496C2×C43#275011yescharacteristic
497C2×C43#275211yescharacteristic
498C2×C43#276011yescharacteristic
499C2×C43#276111yescharacteristic
500C2×C43#276111yescharacteristic
501C2×C43#276411yescharacteristic
502C2×C43#277111yescharacteristic
503D43—44no—
504C24×C4—431no—
505C22×C4⋊C4—431no—
506C22×C4⋊C4C2×D4311yescharacteristic
507C22×C22⋊C4—431no—
508C22×C22⋊C4—431no—
509C22×C22⋊C4—431no—
510C22×C22⋊C4—431no—
511C22×C22⋊C4—431no—
512C22×C22⋊C4—431no—
513C22×C42—431no—
514C22×C42—431no—
515#381—438no—
516C2×#95—431no—
517C2×#95—431no—
518C2×#95—431no—
519C2×#95—431no—
520C2×#95—431no—
521C2×#95—431no—
522C2×#95—431no—
523C2×#95—431no—
524C2×#95—431no—
525C2×#95—431no—
526C2×#95—431no—
527C2×#95—431no—
528C2×#95—431no—
529C2×#95—431no—
530C2×#95—431no—
531C2×#95—431no—
532C2×#95—431no—
533C2×#95—431no—
534C2×#95C2×D4311yescharacteristic
535C2×#95C2×D4311yescharacteristic
536C2×#95C2×D4311yescharacteristic
537C2×#95C2×D4311yescharacteristic
538C2×#95C2×D4311yescharacteristic
539C2×#95C2×D4311yescharacteristic
540C43#1450811yescharacteristic, complemented, Sylow
541C25—431no—
542C23×C4—431no—
543C23×C4—431no—
544C23×C4—431no—
545C23×C4—431no—
546C23×C4—431no—
547C23×C4—431no—
548C23×C4—434no—
549C23×C4—431no—
550C23×C4—862no—
551C23×C4—862no—
552C23×C4—1721no—
553C23×C4—1721no—
554C23×C4—1721no—
555C23×C4—1721no—
556C23×C4C22×D4311yescharacteristic
557C23×C4C22×D4311yescharacteristic
558C23×C4C22×D4311yescharacteristic
559C23×C4C22×D4311yescharacteristic
560C23×C4C22×D4311yescharacteristic
561C23×C4C22×D4311yescharacteristic
562C23×C4C22×D4311yescharacteristic
563C2×C4⋊C4—41no—
564C2×C4⋊C4—41no—
565C2×C4⋊C4—41no—
566C2×C4⋊C4—862no—
567C2×C4⋊C4—862no—
568C2×C4⋊C4—1721no—
569C2×C22⋊C4—434no—
570C2×C22⋊C4—434no—
571C2×C22⋊C4—862no—
572C2×C22⋊C4—862no—
573C2×C22⋊C4—862no—
574C2×C22⋊C4—862no—
575C2×C22⋊C4—862no—
576C2×C22⋊C4—862no—
577C2×C22⋊C4—862no—
578C2×C22⋊C4—862no—
579C2×C22⋊C4—1721no—
580C2×C22⋊C4—1721no—
581C2×C22⋊C4—1721no—
582C2×C22⋊C4—1721no—
583C2×C22⋊C4—1721no—
584C2×C22⋊C4—1721no—
585C2×C22⋊C4—1721no—
586C2×C22⋊C4—1721no—
587C2×C42—862no—
588C2×C42—862no—
589C2×C42—1721no—
590C2×C42—1721no—
591C2×C42—1721no—
592C2×C42—1721no—
593#95—41no—
594#95—41no—
595#95—41no—
596#95—41no—
597#95—41no—
598#95—434no—
599#95—434no—
600#95—434no—
601#95—862no—
602#95—862no—
603#95—862no—
604#95—862no—
605#95—1721no—
606#95—1721no—
607#95—1721no—
608#95—1721no—
609#95—1721no—
610#95—1721no—
611#95—1721no—
612#95—1721no—
613#95—1721no—
614#95—1721no—
615#95—1721no—
616#95C4×D4314yes—
617C24—432no—
618C24—432no—
619C24—432no—
620C24—861no—
621C24—861no—
622C24—861no—
623C24—861no—
624C24—861no—
625C24—861no—
626C24—861no—
627C24—861no—
628C24—861no—
629C24—861no—
630C24—861no—
631C24—861no—
632C24C23×D4311yescharacteristic
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
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—432no—
679C22×C4—432no—
680C22×C4—432no—
681C22×C4—432no—
682C22×C4—432no—
683C22×C4—432no—
684C22×C4—868no—
685C22×C4—861no—
686C22×C4—861no—
687C22×C4—861no—
688C22×C4—861no—
689C22×C4—861no—
690C22×C4—861no—
691C22×C4—861no—
692C22×C4—861no—
693C22×C4—861no—
694C22×C4—861no—
695C22×C4—861no—
696C22×C4—861no—
697C22×C4—861no—
698C22×C4—861no—
699C22×C4—861no—
700C22×C4—861no—
701C22×C4—861no—
702C22×C4—861no—
703C22×C4—861no—
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—1724no—
729C22×C4—1724no—
730C22×C4—1724no—
731C22×C4—1724no—
732C22×C4—1724no—
733C22×C4—1724no—
734C22×C4C2×C4×D4312yes—
735C22×C4C2×C4×D4312yes—
736C22×C4C2×C4×D4312yes—
737C22×C4#1062190212yes—
738C4⋊C4—44no—
739C4⋊C4—1724no—
740C22⋊C4—1724no—
741C22⋊C4—1724no—
742C22⋊C4—1724no—
743C22⋊C4—1724no—
744C22⋊C4—1724no—
745C22⋊C4—1724no—
746C42—1724no—
747C42—1724no—
748C23—434no—
749C23—862no—
750C23—862no—
751C23—862no—
752C23—862no—
753C23—862no—
754C23—862no—
755C23—862no—
756C23—862no—
757C23—862no—
758C23—862no—
759C23—862no—
760C23—862no—
761C23—862no—
762C23—862no—
763C23—862no—
764C23—862no—
765C23—862no—
766C23—862no—
767C23—1721no—
768C23—1721no—
769C23—1721no—
770C23—1721no—
771C23—1721no—
772C23—1721no—
773C23—1721no—
774C23—1721no—
775C23—1721no—
776C23—1721no—
777C23—1721no—
778C23—1721no—
779C23—1721no—
780C23—1721no—
781C23—1721no—
782C23—1721no—
783C23C22×C4×D4311yescharacteristic
784C23#41×D4311yescharacteristic
785C23#41×D4311yescharacteristic
786C23#41×D4311yescharacteristic
787C23#41×D4311yescharacteristic
788C23#41×D4311yescharacteristic
789C23C2×#1062190211yescharacteristic
790C23#1306337011yescharacteristic
791C23#1306337011yescharacteristic
792C23#1306337011yescharacteristic
793C23#1306337011yescharacteristic
794C23#1306337111yescharacteristic
795C23#1306337111yescharacteristic
796C23#1306337211yescharacteristic
797C23#1306337311yescharacteristic
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
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—862no—
848C2×C4—862no—
849C2×C4—862no—
850C2×C4—862no—
851C2×C4—862no—
852C2×C4—862no—
853C2×C4—862no—
854C2×C4—862no—
855C2×C4—862no—
856C2×C4—862no—
857C2×C4—862no—
858C2×C4—862no—
859C2×C4—862no—
860C2×C4—862no—
861C2×C4—862no—
862C2×C4—862no—
863C2×C4—862no—
864C2×C4—862no—
865C2×C4—17216no—
866C2×C4—1721no—
867C2×C4—1721no—
868C2×C4—1721no—
869C2×C4—1721no—
870C2×C4—1721no—
871C2×C4—1721no—
872C2×C4—1721no—
873C2×C4—1721no—
874C2×C4—1721no—
875C2×C4—1721no—
876C2×C4—1721no—
877C2×C4—1721no—
878C2×C4—1721no—
879C2×C4—1721no—
880C2×C4—1721no—
881C2×C4—1721no—
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—
897C22—864no—
898C22—864no—
899C22—864no—
900C22—1722no—
901C22—1722no—
902C22—1722no—
903C22—1722no—
904C22—1722no—
905C22—1722no—
906C22—1722no—
907C22—1722no—
908C22—1722no—
909C22—1722no—
910C22—1722no—
911C22—1722no—
912C22#117×D4311yescharacteristic
913C22#1458336711yescharacteristic
914C22C4×#1062190211yescharacteristic
915C22#1458337111yescharacteristic
916C22#1458337111yescharacteristic
917C22#1458337811yescharacteristic
918C22#1458338011yescharacteristic
919C22#1458348111yescharacteristic
920C22#1458348311yescharacteristic
921C22#1458348311yescharacteristic
922C22#1458348511yescharacteristic
923C22#1458348811yescharacteristic
924C22#1458348911yescharacteristic
925C22#1458349011yescharacteristic
926C22#1458349711yescharacteristic
927C22#1458349911yescharacteristic
928C22#1458349911yescharacteristic
929C22#1458351711yescharacteristic
930C22#1458352311yescharacteristic
931C22#1458357611yescharacteristic
932C22#1458357611yescharacteristic
933C22#1458357711yescharacteristic
934C22#1458357911yescharacteristic
935C22#1458357911yescharacteristic
936C22#1458358111yescharacteristic
937C22#1458358111yescharacteristic
938C22#1458358511yescharacteristic
939C22#1458358711yescharacteristic
940C22#1458360011yescharacteristic
941C22#1458360211yescharacteristic
942C22#1458363311yescharacteristic
943C22#1458363811yescharacteristic
944C22#1458364511yescharacteristic
945C22#1458364611yescharacteristic
946C22#1458365011yescharacteristic
947C4—42no—
948C4—42no—
949C4—42no—
950C4—42no—
951C4—81no—
952C4—81no—
953C4—81no—
954C4—3441no—
955C4—1722no—
956C4—1722no—
957C4—1722no—
958C4—1722no—
959C4—1722no—
960C4—1722no—
961C2—1724no—
962C2#1913718911yescharacteristic
963C2#1913738311yescharacteristic
964C2#1913738811yescharacteristic
965C2#1913744811yescharacteristic
966C2#1913745411yescharacteristic
967C2#1913772711yescharacteristic
968C2#1913774411yescharacteristic
969C2#1914183211yescharacteristic
970C2#1914183811yescharacteristic
971C2#1914186111yescharacteristic
972C2#1914197011yescharacteristic
973C2#1914197511yescharacteristic
974C2#1914198911yescharacteristic
975C2#1914201411yescharacteristic
976C2#1914210711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1442C2
socle, cosocleC24×C43C24
prime radicalC24×D43C23
hypercenter#1442D43
hypocenterC43#14508
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
2. #19132856C2semidirect
3. #19132855C2semidirect
4. #19132854C2semidirect
9. #19132830C2semidirect
10. #19132826C2semidirect
11. #19132820C2semidirect
12. #19132819C2semidirect
15. C43×#1442C2semidirect
26. #14582761C4semidirect
477. #1442D43semidirect
540. C43#14508semidirect

Maximal subgroups

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

subgroupindex
C2×#145827612
#191328562
#191328552
#191328542
#191328392
#191328372
#191328312
#191328302
#191328262
#191328202
#191328192
(C2×D43)⋊#952
C43×#14422
#1450843