Finite Group Databasebeta

← #25019217

Subgroups — #25019217

Order 11008.

1630 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582792C211yesmaximal, characteristic
2C2×C22⋊C4×Dic43C211yesmaximal, characteristic
3#19132854C211yesmaximal, characteristic, complemented
4#19132851C211yesmaximal, characteristic, complemented
5#19132838C211yesmaximal, characteristic
6#19132838C211yesmaximal, characteristic
7#19132828C211yesmaximal, characteristic, complemented
8#19132826C211yesmaximal, characteristic, complemented
9#19132824C211yesmaximal, characteristic, complemented
10Dic43⋊#95C211yesmaximal, characteristic, complemented
11#19132821C211yesmaximal, characteristic, complemented
12#19132817C211yesmaximal, characteristic
13#19132817C211yesmaximal, characteristic
14C4×C43⋊#95C211yesmaximal, characteristic, complemented
15C2×C43×#388C211yesmaximal, characteristic
16C24×Dic43C2211yescharacteristic
17C22×C4⋊Dic43C2211yescharacteristic
18C22×Dic43⋊C4C2211yescharacteristic
19C22×Dic43⋊C4C2211yescharacteristic
20C22×C22⋊Dic43C2211yescharacteristic
21C22×C22⋊Dic43C2211yescharacteristic
22C22×C22⋊Dic43C2211yescharacteristic
23C22×C4×Dic43C2211yescharacteristic
24C22×C4×Dic43C2211yescharacteristic
25C22×C4×Dic43C2211yescharacteristic
26#14582792—24no—
27C22⋊C4×Dic43C418yescomplemented
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
45C2×C43⋊#95C2211yescharacteristic
46C22×C4⋊C4×C43C2211yescharacteristic
47C22×C22⋊C4×C43C2211yescharacteristic
48C22×C22⋊C4×C43C2211yescharacteristic
49C22×C22⋊C4×C43C2211yescharacteristic
50C22×C42×C43C2211yescharacteristic
51C43×#388—24no—
52C2×#95×C43C2211yescharacteristic
53C2×#95×C43C2211yescharacteristic
54C23×Dic43—22no—
55C23×Dic43—22no—
56C23×Dic43—41no—
57C23×Dic43—41no—
58C23×Dic43—41no—
59C23×Dic43—41no—
60C23×Dic43C2×C414yes—
61C23×Dic43C2311yescharacteristic
62C23×Dic43C2311yescharacteristic
63C23×Dic43C2311yescharacteristic
64C23×Dic43C2311yescharacteristic
65C23×Dic43C2311yescharacteristic
66C23×Dic43C2311yescharacteristic
67C23×Dic43C2311yescharacteristic
68C23×Dic43C2311yescharacteristic
69C2×C4⋊Dic43—22no—
70C2×C4⋊Dic43—22no—
71C2×C4⋊Dic43—41no—
72C2×Dic43⋊C4—22no—
73C2×Dic43⋊C4—22no—
74C2×Dic43⋊C4—22no—
75C2×Dic43⋊C4—22no—
76C2×Dic43⋊C4—41no—
77C2×Dic43⋊C4—41no—
78C2×C22⋊Dic43—22no—
79C2×C22⋊Dic43—22no—
80C2×C22⋊Dic43—22no—
81C2×C22⋊Dic43—22no—
82C2×C22⋊Dic43—22no—
83C2×C22⋊Dic43—22no—
84C2×C22⋊Dic43—41no—
85C2×C22⋊Dic43—41no—
86C2×C22⋊Dic43C2×C414yes—
87C2×C4×Dic43—22no—
88C2×C4×Dic43—22no—
89C2×C4×Dic43—41no—
90C2×C4×Dic43—41no—
91C2×C4×Dic43—41no—
92C2×C4×Dic43—41no—
93C2×C4×Dic43—41no—
94C2×C4×Dic43C2×C414yes—
95C2×C4×Dic43C2×C414yes—
96C43⋊#95—22no—
97C43⋊#95—22no—
98C43⋊#95—22no—
99C43⋊#95—22no—
100C43⋊#95—22no—
101C43⋊#95—22no—
102C43⋊#95—22no—
103C43⋊#95—22no—
104C43⋊#95—22no—
105C43⋊#95—22no—
106C43⋊#95—41no—
107C43⋊#95—41no—
108C43⋊#95—41no—
109C43⋊#95—41no—
110C43⋊#95—41no—
111C43⋊#95—41no—
112C43⋊#95C2×C414yes—
113C43⋊#95C2×C414yes—
114C25×C43C2311yescharacteristic
115C23×C4×C43C2311yescharacteristic
116C23×C4×C43C2311yescharacteristic
117C23×C4×C43C2311yescharacteristic
118C23×C4×C43C2311yescharacteristic
119C23×C4×C43C2311yescharacteristic
120C23×C4×C43C2311yescharacteristic
121C2×C4⋊C4×C43—22no—
122C2×C4⋊C4×C43—22no—
123C2×C4⋊C4×C43—41no—
124C2×C22⋊C4×C43—22no—
125C2×C22⋊C4×C43—22no—
126C2×C22⋊C4×C43—22no—
127C2×C22⋊C4×C43—22no—
128C2×C22⋊C4×C43—41no—
129C2×C22⋊C4×C43—41no—
130C2×C22⋊C4×C43C2×C414yes—
131C2×C22⋊C4×C43D414yes—
132C2×C22⋊C4×C43Q814yes—
133C2×C42×C43—22no—
134C2×C42×C43—22no—
135C2×C42×C43—41no—
136#95×C43—22no—
137#95×C43—22no—
138C24×C43—21no—
139C24×C43—21no—
140C24×C43—21no—
141C24×C43—21no—
142C24×C43—21no—
143C24×C43—21no—
144C24×C43—21no—
145C24×C43—21no—
146C24×C43—21no—
147C24×C43—21no—
148C24×C43—21no—
149C24×C43—21no—
150C24×C43C22×C412yes—
151C24×C43C2×D412yes—
152C24×C43C2×Q812yes—
153C24×C43C2411yescharacteristic
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×C43C22×C412yes—
189C22×C4×C43C22×C412yes—
190C22×C4×C43C2×D412yes—
191C22×C4×C43C2×D412yes—
192C22×C4×C43C2×Q812yes—
193C22×C4×C43C2×Q812yes—
194C22×C4×C43#4112yes—
195C22×C4×C43#4112yes—
196C22×Dic43—28no—
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×Dic43—21no—
243C22×Dic43—44no—
244C22×Dic43—44no—
245C22×Dic43—44no—
246C22×Dic43—44no—
247C22×Dic43—44no—
248C22×Dic43—44no—
249C22×Dic43C22×C412yes—
250C22×Dic43C22×C412yes—
251C22×Dic43C22×C412yes—
252C22×Dic43C22×C412yes—
253C22×Dic43#4112yes—
254C22×Dic43#4112yes—
255C22×Dic43#4112yes—
256C22×Dic43#4112yes—
257C22×Dic43#4112yes—
258C22×Dic43#4112yes—
259C4⋊C4×C43—44no—
260C22⋊C4×C43—44no—
261C22⋊C4×C43—44no—
262C22⋊C4×C43C4⋊C4116yescomplemented
263C42×C43—44no—
264C22⋊Dic43—28no—
265C22⋊Dic43—44no—
266C22⋊Dic43—44no—
267C4⋊Dic43—44no—
268Dic43⋊C4—44no—
269Dic43⋊C4—44no—
270C4×Dic43—44no—
271C4×Dic43—44no—
272C4×Dic43—44no—
273C23×C43—22no—
274C23×C43—22no—
275C23×C43—22no—
276C23×C43—22no—
277C23×C43—22no—
278C23×C43—22no—
279C23×C43—22no—
280C23×C43—22no—
281C23×C43—22no—
282C23×C43—22no—
283C23×C43—22no—
284C23×C43—22no—
285C23×C43—22no—
286C23×C43—22no—
287C23×C43—22no—
288C23×C43—22no—
289C23×C43—22no—
290C23×C43—22no—
291C23×C43—41no—
292C23×C43—41no—
293C23×C43—41no—
294C23×C43—41no—
295C23×C43—41no—
296C23×C43—41no—
297C23×C43—41no—
298C23×C43—41no—
299C23×C43—41no—
300C23×C43—41no—
301C23×C43—41no—
302C23×C43—41no—
303C23×C43—41no—
304C23×C43—41no—
305C23×C43—41no—
306C23×C43—41no—
307C23×C43C2×C4⋊C414yes—
308C23×C43C23×C411yescharacteristic
309C23×C43C22×D411yescharacteristic
310C23×C43C22×Q811yescharacteristic
311C23×C43C2×#4111yescharacteristic
312C23×C43C2×#4111yescharacteristic
313C23×C43C2×#4111yescharacteristic
314C23×C43C2×#4111yescharacteristic
315C23×C43C2×#4111yescharacteristic
316C23×C43C2×#4111yescharacteristic
317C23×C43C2×#4111yescharacteristic
318C23×C43C2×#4111yescharacteristic
319C23×C43H(5,𝔽2)11yescharacteristic
320C23×C43H(5,𝔽2)11yescharacteristic
321C23×C43H(5,𝔽2)11yescharacteristic
322C23×C43H(5,𝔽2)11yescharacteristic
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—22no—
332C2×C4×C43—22no—
333C2×C4×C43—22no—
334C2×C4×C43—22no—
335C2×C4×C43—22no—
336C2×C4×C43—22no—
337C2×C4×C43—22no—
338C2×C4×C43—22no—
339C2×C4×C43—22no—
340C2×C4×C43—22no—
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×C43C2×C4⋊C414yes—
364C2×C4×C43C2×C4⋊C414yes—
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—22no—
377C2×Dic43—22no—
378C2×Dic43—22no—
379C2×Dic43—22no—
380C2×Dic43—22no—
381C2×Dic43—22no—
382C2×Dic43—22no—
383C2×Dic43—22no—
384C2×Dic43—22no—
385C2×Dic43—22no—
386C2×Dic43—22no—
387C2×Dic43—22no—
388C2×Dic43—22no—
389C2×Dic43—416no—
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—
417C2×Dic43—41no—
418C2×Dic43—41no—
419C2×Dic43—41no—
420C2×Dic43#11714yes—
421C2×Dic43#11714yes—
422#13948—431nomaximal, Sylow
423C22×C43—24no—
424C22×C43—24no—
425C22×C43—24no—
426C22×C43—42no—
427C22×C43—42no—
428C22×C43—42no—
429C22×C43—42no—
430C22×C43—42no—
431C22×C43—42no—
432C22×C43—42no—
433C22×C43—42no—
434C22×C43—42no—
435C22×C43—42no—
436C22×C43—42no—
437C22×C43—42no—
438C22×C43C22×C4⋊C411yescharacteristic
439C22×C43C2×#11711yescharacteristic
440C22×C43C2×#11711yescharacteristic
441C22×C43C4×#4111yescharacteristic
442C22×C43C4×#4111yescharacteristic
443C22×C43#51811yescharacteristic
444C22×C43#51811yescharacteristic
445C22×C43#52911yescharacteristic
446C22×C43#52911yescharacteristic
447C22×C43#52911yescharacteristic
448C22×C43#52911yescharacteristic
449C22×C43#53211yescharacteristic
450C22×C43#53211yescharacteristic
451C22×C43#53311yescharacteristic
452C22×C43#53311yescharacteristic
453C22×C43#53811yescharacteristic
454C22×C43#53811yescharacteristic
455C22×C43#53811yescharacteristic
456C22×C43#53811yescharacteristic
457C22×C43#54611yescharacteristic
458C22×C43#54611yescharacteristic
459C22×C43#54611yescharacteristic
460C22×C43#54611yescharacteristic
461C22×C43#55111yescharacteristic
462C22×C43#55111yescharacteristic
463C22×C43#55311yescharacteristic
464C22×C43#55311yescharacteristic
465C22×C43#55311yescharacteristic
466C22×C43#55311yescharacteristic
467C22×C43#55411yescharacteristic
468C22×C43#55411yescharacteristic
469C22×C43#55411yescharacteristic
470C22×C43#55411yescharacteristic
471C22×C43#55911yescharacteristic
472C22×C43#55911yescharacteristic
473C4×C43—24no—
474C4×C43—24no—
475C4×C43—42no—
476C4×C43—42no—
477C4×C43—81no—
478C4×C43—81no—
479Dic43—24no—
480Dic43—24no—
481Dic43—42no—
482Dic43—42no—
483Dic43—42no—
484Dic43—42no—
485Dic43—81no—
486Dic43—81no—
487C2×#388—431no—
488C2×#388D4311yescharacteristic
489C2×C4×C22⋊C4—431no—
490#1442—431no—
491#1442—431no—
492#1439—431no—
493#1439—431no—
494#1436—431no—
495#1436—431no—
496C4⋊#95—431no—
497C4⋊#95—431no—
498#1434—431no—
499C22⋊#95—431no—
500C22⋊#95—431no—
501C4×#95—431no—
502C2×C43—44no—
503C2×C43#228511yescharacteristic
504C2×C43#229811yescharacteristic
505C2×C43#231211yescharacteristic
506C2×C43#234911yescharacteristic
507C2×C43#234911yescharacteristic
508C2×C43#235311yescharacteristic
509C2×C43#235711yescharacteristic
510C2×C43#255711yescharacteristic
511C2×C43#255711yescharacteristic
512C2×C43#255911yescharacteristic
513C2×C43#255911yescharacteristic
514C2×C43#258711yescharacteristic
515C2×C43#258711yescharacteristic
516C2×C43#258911yescharacteristic
517C2×C43#258911yescharacteristic
518C24×C4—431no—
519C22×C4⋊C4—431no—
520C22×C4⋊C4—431no—
521C22×C4⋊C4—431no—
522C22×C4⋊C4C2×D4311yescharacteristic
523C22×C22⋊C4—431no—
524C22×C22⋊C4—431no—
525C22×C22⋊C4—431no—
526C22×C22⋊C4C2×D4311yescharacteristic
527C22×C22⋊C4C2×D4311yescharacteristic
528C22×C22⋊C4C2×D4311yescharacteristic
529C22×C42—431no—
530C22×C42—431no—
531C22×C42—431no—
532C22×C42C2×D4311yescharacteristic
533#388—24no—
534#388—864no—
535C4×C22⋊C4—438no—
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×#95—431no—
546C2×#95—431no—
547C2×#95—431no—
548C2×#95—431no—
549C2×#95—431no—
550C2×#95—431no—
551C2×#95—431no—
552C2×#95—431no—
553C2×#95—431no—
554C2×#95C2×D4311yescharacteristic
555C2×#95C2×D4311yescharacteristic
556C43#1394811yescharacteristic, complemented, Sylow
557C25C22×D4311yescharacteristic
558C23×C4—431no—
559C23×C4—431no—
560C23×C4—431no—
561C23×C4—431no—
562C23×C4—431no—
563C23×C4—431no—
564C23×C4—434no—
565C23×C4—431no—
566C23×C4—431no—
567C23×C4—862no—
568C23×C4—862no—
569C23×C4—1721no—
570C23×C4—1721no—
571C23×C4—1721no—
572C23×C4—1721no—
573C23×C4C22×D4311yescharacteristic
574C23×C4C22×D4311yescharacteristic
575C23×C4C22×D4311yescharacteristic
576C23×C4C22×D4311yescharacteristic
577C23×C4C22×D4311yescharacteristic
578C23×C4C22×D4311yescharacteristic
579C2×C4⋊C4—22no—
580C2×C4⋊C4—22no—
581C2×C4⋊C4—41no—
582C2×C4⋊C4—862no—
583C2×C4⋊C4—862no—
584C2×C4⋊C4—862no—
585C2×C4⋊C4—862no—
586C2×C4⋊C4—862no—
587C2×C4⋊C4—862no—
588C2×C4⋊C4—1721no—
589C2×C4⋊C4—1721no—
590C2×C4⋊C4—1721no—
591C2×C22⋊C4—22no—
592C2×C22⋊C4—22no—
593C2×C22⋊C4—22no—
594C2×C22⋊C4—22no—
595C2×C22⋊C4—41no—
596C2×C22⋊C4—41no—
597C2×C22⋊C4—434no—
598C2×C22⋊C4—862no—
599C2×C22⋊C4—862no—
600C2×C22⋊C4—862no—
601C2×C22⋊C4—862no—
602C2×C22⋊C4—862no—
603C2×C22⋊C4—862no—
604C2×C22⋊C4—1721no—
605C2×C22⋊C4—1721no—
606C2×C22⋊C4Dic8614yes—
607C2×C22⋊C4C4×D4314yes—
608C2×C22⋊C4C22⋊D4314yes—
609C2×C42—22no—
610C2×C42—22no—
611C2×C42—41no—
612C2×C42—434no—
613C2×C42—434no—
614C2×C42—862no—
615C2×C42—862no—
616C2×C42—1721no—
617C2×C42—1721no—
618C2×C42—1721no—
619C2×C42—1721no—
620C2×C42—1721no—
621#95—22no—
622#95—22no—
623#95—434no—
624#95—434no—
625#95—862no—
626#95—862no—
627#95—862no—
628#95—862no—
629#95—862no—
630#95—862no—
631#95—862no—
632#95—862no—
633#95—862no—
634#95—862no—
635#95—1721no—
636#95—1721no—
637#95—1721no—
638#95—1721no—
639#95—1721no—
640#95—1721no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24C2×Dic8612yes—
654C24C2×C4×D4312yes—
655C24C2×C22⋊D4312yes—
656C24C23×D4311yescharacteristic
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—432no—
692C22×C4—432no—
693C22×C4—432no—
694C22×C4—432no—
695C22×C4—432no—
696C22×C4—432no—
697C22×C4—432no—
698C22×C4—432no—
699C22×C4—432no—
700C22×C4—432no—
701C22×C4—868no—
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—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—1724no—
749C22×C4—1724no—
750C22×C4—1724no—
751C22×C4—1724no—
752C22×C4—1724no—
753C22×C4—1724no—
754C22×C4C2×Dic8612yes—
755C22×C4C2×Dic8612yes—
756C22×C4C2×C4×D4312yes—
757C22×C4C2×C4×D4312yes—
758C22×C4#1062190012yes—
759C22×C4#1062190012yes—
760C22×C4C2×C22⋊D4312yes—
761C22×C4C2×C22⋊D4312yes—
762C4⋊C4—44no—
763C4⋊C4—1724no—
764C4⋊C4—1724no—
765C4⋊C4—1724no—
766C22⋊C4—44no—
767C22⋊C4—44no—
768C22⋊C4—868no—
769C22⋊C4—1724no—
770C22⋊C4—1724no—
771C22⋊C4Dic43⋊C4116yescomplemented
772C42—44no—
773C42—1724no—
774C42—1724no—
775C42—1724no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23C2×Dic43⋊C414yes—
811C23C22×C4×D4311yescharacteristic
812C23C22×C22⋊D4311yescharacteristic
813C23C22×Dic8611yescharacteristic
814C23#41×D4311yescharacteristic
815C23#41×D4311yescharacteristic
816C23#41×D4311yescharacteristic
817C23#41×D4311yescharacteristic
818C23#41×D4311yescharacteristic
819C23#41×D4311yescharacteristic
820C23C2×#1062190011yescharacteristic
821C23C2×#1062190011yescharacteristic
822C23#1306337011yescharacteristic
823C23#1306337011yescharacteristic
824C23#1306337111yescharacteristic
825C23#1306337111yescharacteristic
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
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—434no—
867C2×C4—434no—
868C2×C4—862no—
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—862no—
882C2×C4—862no—
883C2×C4—862no—
884C2×C4—862no—
885C2×C4—862no—
886C2×C4—862no—
887C2×C4—862no—
888C2×C4—862no—
889C2×C4—862no—
890C2×C4—862no—
891C2×C4—862no—
892C2×C4—17216no—
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—
919C2×C4—1721no—
920C2×C4—1721no—
921C2×C4—1721no—
922C2×C4—1721no—
923C2×C4C2×Dic43⋊C414yes—
924C2×C4C2×Dic43⋊C414yes—
925C22—24no—
926C22—24no—
927C22—24no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22C22×Dic43⋊C411yescharacteristic
941C22#117×D4311yescharacteristic
942C22#117×D4311yescharacteristic
943C22C4×#1062190011yescharacteristic
944C22C4×#1062190011yescharacteristic
945C22#1458337111yescharacteristic
946C22#1458337111yescharacteristic
947C22#1458342611yescharacteristic
948C22#1458342811yescharacteristic
949C22#1458343011yescharacteristic
950C22#1458343211yescharacteristic
951C22#1458344511yescharacteristic
952C22#1458344511yescharacteristic
953C22#1458345211yescharacteristic
954C22#1458345211yescharacteristic
955C22#1458348111yescharacteristic
956C22#1458348311yescharacteristic
957C22#1458348511yescharacteristic
958C22#1458348811yescharacteristic
959C22#1458353711yescharacteristic
960C22#1458353711yescharacteristic
961C22#1458354311yescharacteristic
962C22#1458354311yescharacteristic
963C22#1458357211yescharacteristic
964C22#1458357911yescharacteristic
965C22#1458359211yescharacteristic
966C22#1458359611yescharacteristic
967C22#1458360011yescharacteristic
968C22#1458360011yescharacteristic
969C22#1458360611yescharacteristic
970C22#1458360611yescharacteristic
971C22#1458360811yescharacteristic
972C22#1458360811yescharacteristic
973C22#1458363111yescharacteristic
974C22#1458363311yescharacteristic
975C4—24no—
976C4—24no—
977C4—42no—
978C4—42no—
979C4—81no—
980C4—81no—
981C4—864no—
982C4—864no—
983C4—3441no—
984C4—3441no—
985C4—1722no—
986C4—1722no—
987C4—1722no—
988C4—1722no—
989C2—44no—
990C2#1913699811yescharacteristic
991C2#1913708911yescharacteristic
992C2#1913718911yescharacteristic
993C2#1913750011yescharacteristic
994C2#1913750011yescharacteristic
995C2#1913753011yescharacteristic
996C2#1913756511yescharacteristic
997C2#1913969011yescharacteristic
998C2#1913969211yescharacteristic
999C2#1913972011yescharacteristic
1000C2#1913972211yescharacteristic
1001C2#1914001211yescharacteristic
1002C2#1914001411yescharacteristic
1003C2#1914004211yescharacteristic
1004C2#1914004411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C43×#388C2
socle, cosocleC24×C43C24
prime radicalC25×C43C23
hypercenterC2×#388D43
hypocenterC43#13948
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
3. #19132854C2semidirect
4. #19132851C2semidirect
7. #19132828C2semidirect
8. #19132826C2semidirect
9. #19132824C2semidirect
10. Dic43⋊#95C2semidirect
11. #19132821C2semidirect
14. C4×C43⋊#95C2semidirect
27. C22⋊C4×Dic43C4semidirect
262. C22⋊C4×C43C4⋊C4semidirect
556. C43#13948semidirect
771. C22⋊C4Dic43⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#145827922
C2×C22⋊C4×Dic432
#191328542
#191328512
#191328382
#191328282
#191328262
#191328242
Dic43⋊#952
#191328212
#191328172
C4×C43⋊#952
C2×C43×#3882
#1394843