Finite Group Databasebeta

← #25022237

Subgroups — #25022237

Order 11008.

1738 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582822C211yesmaximal, characteristic
2C2×#14582781C211yesmaximal, characteristic, complemented
3C2×#14582771C211yesmaximal, characteristic
4C2×C4⋊C4×Dic43C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×Dic43C211yesmaximal, characteristic
6#19132847C211yesmaximal, characteristic, complemented
7#19132845C211yesmaximal, characteristic, complemented
8#19132832C211yesmaximal, characteristic
9#19132832C211yesmaximal, characteristic
10#19132830C211yesmaximal, characteristic, complemented
11#19132826C211yesmaximal, characteristic, complemented
12Dic43⋊#95C211yesmaximal, characteristic, complemented
13#19132819C211yesmaximal, characteristic, complemented
14#19132817C211yesmaximal, characteristic
15C43×#1439C211yesmaximal, characteristic
16C24×Dic43C2211yescharacteristic
17C22×C4⋊Dic43C2211yescharacteristic
18C22×Dic43⋊C4C2211yescharacteristic
19C22×Dic43⋊C4C2211yescharacteristic
20C22×Dic43⋊C4C2211yescharacteristic
21C22×Dic43⋊C4C2211yescharacteristic
22C22×C22⋊Dic43C2211yescharacteristic
23C22×C22⋊Dic43C2211yescharacteristic
24C22×C22⋊Dic43C2211yescharacteristic
25C22×C4×Dic43C2211yescharacteristic
26C22×C4×Dic43C2211yescharacteristic
27C22×C4×Dic43C2211yescharacteristic
28C22×C4×Dic43C2211yescharacteristic
29#14582822C418yescomplemented
30#14582781—24no—
31#14582771—24no—
32C4⋊C4×Dic43—24no—
33C22⋊C4×Dic43—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×C43⋊#95C2211yescharacteristic
48C2×C43⋊#95C2211yescharacteristic
49C22×C4⋊C4×C43C2211yescharacteristic
50C22×C22⋊C4×C43C2211yescharacteristic
51C22×C22⋊C4×C43C2211yescharacteristic
52C22×C22⋊C4×C43C2211yescharacteristic
53C2×#95×C43C2211yescharacteristic
54C2×#95×C43C2211yescharacteristic
55C2×#95×C43C2211yescharacteristic
56C23×Dic43—22no—
57C23×Dic43—22no—
58C23×Dic43—22no—
59C23×Dic43—22no—
60C23×Dic43—22no—
61C23×Dic43—41no—
62C23×Dic43—41no—
63C23×Dic43C2311yescharacteristic
64C23×Dic43C2311yescharacteristic
65C23×Dic43C2311yescharacteristic
66C23×Dic43C2311yescharacteristic
67C23×Dic43C2311yescharacteristic
68C23×Dic43C2311yescharacteristic
69C23×Dic43C2311yescharacteristic
70C23×Dic43C2311yescharacteristic
71C2×C4⋊Dic43—22no—
72C2×C4⋊Dic43—22no—
73C2×C4⋊Dic43C2×C414yescomplemented
74C2×Dic43⋊C4—22no—
75C2×Dic43⋊C4—22no—
76C2×Dic43⋊C4—22no—
77C2×Dic43⋊C4—22no—
78C2×Dic43⋊C4—22no—
79C2×Dic43⋊C4—22no—
80C2×Dic43⋊C4—22no—
81C2×Dic43⋊C4—41no—
82C2×Dic43⋊C4—41no—
83C2×Dic43⋊C4—41no—
84C2×Dic43⋊C4C2×C414yescomplemented
85C2×Dic43⋊C4C2×C414yescomplemented
86C2×C22⋊Dic43—22no—
87C2×C22⋊Dic43—22no—
88C2×C22⋊Dic43—22no—
89C2×C22⋊Dic43—22no—
90C2×C22⋊Dic43—41no—
91C2×C22⋊Dic43—41no—
92C2×C22⋊Dic43C2×C414yes—
93C2×C22⋊Dic43C2×C414yes—
94C2×C22⋊Dic43Q814yes—
95C2×C4×Dic43—22no—
96C2×C4×Dic43—22no—
97C2×C4×Dic43—22no—
98C2×C4×Dic43—22no—
99C2×C4×Dic43—22no—
100C2×C4×Dic43—22no—
101C2×C4×Dic43—22no—
102C2×C4×Dic43—41no—
103C2×C4×Dic43—41no—
104C2×C4×Dic43—41no—
105C2×C4×Dic43—41no—
106C2×C4×Dic43D414yes—
107C43⋊#95—22no—
108C43⋊#95—22no—
109C43⋊#95—22no—
110C43⋊#95—22no—
111C43⋊#95—22no—
112C43⋊#95—22no—
113C43⋊#95—22no—
114C43⋊#95—22no—
115C43⋊#95—22no—
116C43⋊#95—22no—
117C43⋊#95—41no—
118C43⋊#95—41no—
119C43⋊#95—41no—
120C43⋊#95C2×C414yescomplemented
121C43⋊#95D414yes—
122C25×C43C2311yescharacteristic
123C23×C4×C43C2311yescharacteristic
124C23×C4×C43C2311yescharacteristic
125C23×C4×C43C2311yescharacteristic
126C23×C4×C43C2311yescharacteristic
127C23×C4×C43C2311yescharacteristic
128C23×C4×C43C2311yescharacteristic
129C2×C4⋊C4×C43—22no—
130C2×C4⋊C4×C43—22no—
131C2×C4⋊C4×C43—22no—
132C2×C22⋊C4×C43—22no—
133C2×C22⋊C4×C43—22no—
134C2×C22⋊C4×C43—22no—
135C2×C22⋊C4×C43—22no—
136C2×C22⋊C4×C43—22no—
137C2×C22⋊C4×C43—22no—
138C2×C22⋊C4×C43—41no—
139C2×C22⋊C4×C43—41no—
140C2×C22⋊C4×C43C2×C414yes—
141#95×C43—22no—
142#95×C43—41no—
143#95×C43—41no—
144C24×C43—21no—
145C24×C43—21no—
146C24×C43—21no—
147C24×C43—21no—
148C24×C43—21no—
149C24×C43—21no—
150C24×C43—21no—
151C24×C43—21no—
152C24×C43—21no—
153C24×C43—21no—
154C24×C43—21no—
155C24×C43—21no—
156C24×C43C22×C412yes—
157C24×C43C2×Q812yes—
158C24×C43#4112yes—
159C24×C43C2411yescharacteristic
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43C22×C412yes—
197C22×C4×C43C22×C412yes—
198C22×C4×C43C2×D412yes—
199C22×C4×C43C2×D412yes—
200C22×C4×C43#4112yes—
201C22×C4×C43#4112yes—
202C22×Dic43—28no—
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—21no—
244C22×Dic43—21no—
245C22×Dic43—44no—
246C22×Dic43—44no—
247C22×Dic43—44no—
248C22×Dic43—44no—
249C22×Dic43—44no—
250C22×Dic43—44no—
251C22×Dic43C22×C412yes—
252C22×Dic43C22×C412yes—
253C22×Dic43C22×C412yes—
254C22×Dic43C22×C412yes—
255C22×Dic43C2×D412yes—
256C22×Dic43C2×D412yes—
257C22×Dic43C2×D412yes—
258C22×Dic43C2×D412yes—
259C22×Dic43C2×Q812yes—
260C22×Dic43C2×Q812yes—
261C22×Dic43#4112yes—
262C22×Dic43#4112yes—
263C22×Dic43#4112yes—
264C22×Dic43#4112yes—
265C4⋊C4×C43—28no—
266C22⋊C4×C43—28no—
267C22⋊C4×C43—44no—
268C22⋊C4×C43—44no—
269C22⋊Dic43—28no—
270C22⋊Dic43—28no—
271C22⋊Dic43—44no—
272C4⋊Dic43—28no—
273Dic43⋊C4—28no—
274Dic43⋊C4—44no—
275Dic43⋊C4—44no—
276Dic43⋊C4—44no—
277C4×Dic43—28no—
278C4×Dic43—44no—
279C4×Dic43—44no—
280C4×Dic43—44no—
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—22no—
292C23×C43—22no—
293C23×C43—22no—
294C23×C43—22no—
295C23×C43—22no—
296C23×C43—22no—
297C23×C43—22no—
298C23×C43—22no—
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×C43—41no—
308C23×C43—41no—
309C23×C43—41no—
310C23×C43—41no—
311C23×C43—41no—
312C23×C43—41no—
313C23×C43—41no—
314C23×C43—41no—
315C23×C43C4×Q814yes—
316C23×C43C23×C411yescharacteristic
317C23×C43C22×D411yescharacteristic
318C23×C43C22×D411yescharacteristic
319C23×C43C22×Q811yescharacteristic
320C23×C43C2×#4111yescharacteristic
321C23×C43C2×#4111yescharacteristic
322C23×C43C2×#4111yescharacteristic
323C23×C43C2×#4111yescharacteristic
324C23×C43C2×#4111yescharacteristic
325C23×C43C2×#4111yescharacteristic
326C23×C43C2×#4111yescharacteristic
327C23×C43H(5,𝔽2)11yescharacteristic
328C23×C43H(5,𝔽2)11yescharacteristic
329C23×C43H(5,𝔽2)11yescharacteristic
330C23×C432−1+411yescharacteristic
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—22no—
342C2×C4×C43—22no—
343C2×C4×C43—22no—
344C2×C4×C43—22no—
345C2×C4×C43—22no—
346C2×C4×C43—41no—
347C2×C4×C43—41no—
348C2×C4×C43—41no—
349C2×C4×C43—41no—
350C2×C4×C43—41no—
351C2×C4×C43—41no—
352C2×C4×C43—41no—
353C2×C4×C43—41no—
354C2×C4×C43—41no—
355C2×C4×C43—41no—
356C2×C4×C43—41no—
357C2×C4×C43—41no—
358C2×C4×C43—41no—
359C2×C4×C43—41no—
360C2×C4×C43—41no—
361C2×C4×C43—41no—
362C2×C4×C43—41no—
363C2×C4×C43—41no—
364C2×C4×C43—41no—
365C2×C4×C43—41no—
366C2×C4×C43—41no—
367C2×C4×C43—41no—
368C2×C4×C43—41no—
369C2×C4×C43—41no—
370C2×C4×C43—41no—
371C2×C4×C43—41no—
372C2×C4×C43C4×D414yes—
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—22no—
390C2×Dic43—22no—
391C2×Dic43—22no—
392C2×Dic43—22no—
393C2×Dic43—22no—
394C2×Dic43—22no—
395C2×Dic43—22no—
396C2×Dic43—22no—
397C2×Dic43—22no—
398C2×Dic43—22no—
399C2×Dic43—22no—
400C2×Dic43—22no—
401C2×Dic43—22no—
402C2×Dic43—22no—
403C2×Dic43—22no—
404C2×Dic43—22no—
405C2×Dic43—22no—
406C2×Dic43—416no—
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—41no—
421C2×Dic43—41no—
422C2×Dic43—41no—
423C2×Dic43—41no—
424C2×Dic43—41no—
425C2×Dic43—41no—
426C2×Dic43—41no—
427C2×Dic43C4×D414yes—
428C2×Dic43#12114yes—
429C2×Dic43C22⋊Q814yes—
430#14198—431nomaximal, Sylow
431C22×C43—24no—
432C22×C43—24no—
433C22×C43—24no—
434C22×C43—42no—
435C22×C43—42no—
436C22×C43—42no—
437C22×C43—42no—
438C22×C43—42no—
439C22×C43—42no—
440C22×C43—42no—
441C22×C43—42no—
442C22×C43—42no—
443C22×C43—42no—
444C22×C43—42no—
445C22×C43—42no—
446C22×C43C2×C4×D411yescharacteristic
447C22×C43C2×C4×D411yescharacteristic
448C22×C43C2×C4×Q811yescharacteristic
449C22×C43C4×#4111yescharacteristic
450C22×C43C4×#4111yescharacteristic
451C22×C43#51811yescharacteristic
452C22×C43#52011yescharacteristic
453C22×C43C2×#12111yescharacteristic
454C22×C43C2×C22⋊Q811yescharacteristic
455C22×C43#52511yescharacteristic
456C22×C43#52511yescharacteristic
457C22×C43#52911yescharacteristic
458C22×C43#52911yescharacteristic
459C22×C43#53211yescharacteristic
460C22×C43#53311yescharacteristic
461C22×C43#53511yescharacteristic
462C22×C43#53711yescharacteristic
463C22×C43#54011yescharacteristic
464C22×C43#54211yescharacteristic
465C22×C43#54611yescharacteristic
466C22×C43#54611yescharacteristic
467C22×C43#54611yescharacteristic
468C22×C43D4×Q811yescharacteristic
469C22×C43#55111yescharacteristic
470C22×C43#55111yescharacteristic
471C22×C43#55111yescharacteristic
472C22×C43#55211yescharacteristic
473C22×C43#55211yescharacteristic
474C22×C43#55311yescharacteristic
475C22×C43#55311yescharacteristic
476C22×C43#55311yescharacteristic
477C22×C43#55411yescharacteristic
478C22×C43#55411yescharacteristic
479C22×C43#55411yescharacteristic
480C22×C43#55611yescharacteristic
481C4×C43—24no—
482C4×C43—42no—
483C4×C43—42no—
484C4×C43—42no—
485C4×C43—81no—
486C4×C43—81no—
487Dic43—24no—
488Dic43—24no—
489Dic43—24no—
490Dic43—42no—
491Dic43—42no—
492Dic43—42no—
493Dic43—42no—
494Dic43—42no—
495C2×#396—431no—
496C2×#387—431no—
497C2×#385—431no—
498C2×C4×C4⋊C4—431no—
499C2×C4×C22⋊C4—431no—
500#1441—431no—
501#1441—431no—
502#1439D4311yescharacteristic
503#1437—431no—
504#1437—431no—
505#1436—431no—
506#1436—431no—
507C4⋊#95—431no—
508#1434—431no—
509C22⋊#95—431no—
510C2×C43—44no—
511C2×C43C4×#12111yescharacteristic
512C2×C43C4×C22⋊Q811yescharacteristic
513C2×C43#232411yescharacteristic
514C2×C43#236011yescharacteristic
515C2×C43#236411yescharacteristic
516C2×C43#236811yescharacteristic
517C2×C43#237311yescharacteristic
518C2×C43#241111yescharacteristic
519C2×C43#241711yescharacteristic
520C2×C43#245711yescharacteristic
521C2×C43#246511yescharacteristic
522C2×C43#251511yescharacteristic
523C2×C43#252211yescharacteristic
524C2×C43#256611yescharacteristic
525C2×C43#260111yescharacteristic
526C24×C4—431no—
527C22×C4⋊C4—431no—
528C22×C4⋊C4—431no—
529C22×C4⋊C4—431no—
530C22×C4⋊C4—431no—
531C22×C4⋊C4—431no—
532C22×C4⋊C4C2×D4311yescharacteristic
533C22×C22⋊C4—431no—
534C22×C22⋊C4—431no—
535C22×C22⋊C4—431no—
536C22×C22⋊C4C2×D4311yescharacteristic
537C22×C22⋊C4C2×D4311yescharacteristic
538C22×C22⋊C4C2×D4311yescharacteristic
539C22×C42—431no—
540C22×C42—431no—
541C22×C42—431no—
542C22×C42—431no—
543#396—438no—
544#387—864no—
545#385—864no—
546C4×C4⋊C4—864no—
547C4×C22⋊C4—864no—
548C2×#95—431no—
549C2×#95—431no—
550C2×#95—431no—
551C2×#95—431no—
552C2×#95—431no—
553C2×#95—431no—
554C2×#95—431no—
555C2×#95—431no—
556C2×#95—431no—
557C2×#95—431no—
558C2×#95—431no—
559C2×#95—431no—
560C2×#95—431no—
561C2×#95—431no—
562C2×#95—431no—
563C2×#95C2×D4311yescharacteristic
564C2×#95C2×D4311yescharacteristic
565C2×#95C2×D4311yescharacteristic
566C43#1419811yescharacteristic, complemented, Sylow
567C25C22×D4311yescharacteristic
568C23×C4—431no—
569C23×C4—431no—
570C23×C4—431no—
571C23×C4—431no—
572C23×C4—431no—
573C23×C4—431no—
574C23×C4—431no—
575C23×C4—431no—
576C23×C4—862no—
577C23×C4—862no—
578C23×C4—862no—
579C23×C4—862no—
580C23×C4—862no—
581C23×C4—1721no—
582C23×C4—1721no—
583C23×C4C22×D4311yescharacteristic
584C23×C4C22×D4311yescharacteristic
585C23×C4C22×D4311yescharacteristic
586C23×C4C22×D4311yescharacteristic
587C23×C4C22×D4311yescharacteristic
588C23×C4C22×D4311yescharacteristic
589C2×C4⋊C4—22no—
590C2×C4⋊C4—22no—
591C2×C4⋊C4—22no—
592C2×C4⋊C4—434no—
593C2×C4⋊C4—434no—
594C2×C4⋊C4—434no—
595C2×C4⋊C4—862no—
596C2×C4⋊C4—862no—
597C2×C4⋊C4—862no—
598C2×C4⋊C4—862no—
599C2×C4⋊C4—862no—
600C2×C4⋊C4—862no—
601C2×C4⋊C4—862no—
602C2×C4⋊C4—862no—
603C2×C4⋊C4—862no—
604C2×C4⋊C4—1721no—
605C2×C4⋊C4—1721no—
606C2×C4⋊C4—1721no—
607C2×C22⋊C4—22no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4—22no—
610C2×C22⋊C4—22no—
611C2×C22⋊C4—22no—
612C2×C22⋊C4—22no—
613C2×C22⋊C4—41no—
614C2×C22⋊C4—41no—
615C2×C22⋊C4—434no—
616C2×C22⋊C4—434no—
617C2×C22⋊C4—434no—
618C2×C22⋊C4—862no—
619C2×C22⋊C4—862no—
620C2×C22⋊C4—862no—
621C2×C22⋊C4—862no—
622C2×C22⋊C4—1721no—
623C2×C22⋊C4—1721no—
624C2×C22⋊C4C4×D4314yes—
625C2×C42—434no—
626C2×C42—862no—
627C2×C42—862no—
628C2×C42—862no—
629C2×C42—862no—
630C2×C42—862no—
631C2×C42—862no—
632C2×C42—862no—
633C2×C42—1721no—
634C2×C42—1721no—
635C2×C42—1721no—
636C2×C42—1721no—
637#95—22no—
638#95—41no—
639#95—41no—
640#95—434no—
641#95—434no—
642#95—862no—
643#95—862no—
644#95—862no—
645#95—862no—
646#95—862no—
647#95—862no—
648#95—862no—
649#95—862no—
650#95—862no—
651#95—862no—
652#95—1721no—
653#95—1721no—
654#95—1721no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24C2×C4×D4312yes—
668C24#1062190012yes—
669C24Q8×D4312yes—
670C24C23×D4311yescharacteristic
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—432no—
708C22×C4—432no—
709C22×C4—432no—
710C22×C4—432no—
711C22×C4—432no—
712C22×C4—432no—
713C22×C4—432no—
714C22×C4—432no—
715C22×C4—432no—
716C22×C4—432no—
717C22×C4—432no—
718C22×C4—432no—
719C22×C4—432no—
720C22×C4—432no—
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—868no—
734C22×C4—861no—
735C22×C4—861no—
736C22×C4—861no—
737C22×C4—861no—
738C22×C4—861no—
739C22×C4—861no—
740C22×C4—861no—
741C22×C4—861no—
742C22×C4—861no—
743C22×C4—861no—
744C22×C4—861no—
745C22×C4—861no—
746C22×C4—861no—
747C22×C4—861no—
748C22×C4—861no—
749C22×C4—861no—
750C22×C4—861no—
751C22×C4—861no—
752C22×C4—861no—
753C22×C4—861no—
754C22×C4—861no—
755C22×C4—861no—
756C22×C4—861no—
757C22×C4—861no—
758C22×C4—861no—
759C22×C4—861no—
760C22×C4—861no—
761C22×C4—861no—
762C22×C4—861no—
763C22×C4—861no—
764C22×C4—1724no—
765C22×C4—1724no—
766C22×C4—1724no—
767C22×C4—1724no—
768C22×C4—1724no—
769C22×C4—1724no—
770C22×C4C2×C4×D4312yes—
771C22×C4C2×C4×D4312yes—
772C22×C4D4×D4312yes—
773C22×C4D4×D4312yes—
774C22×C4#1062190012yes—
775C22×C4#1062190012yes—
776C4⋊C4—28no—
777C4⋊C4—868no—
778C4⋊C4—868no—
779C4⋊C4—1724no—
780C4⋊C4—1724no—
781C4⋊C4—1724no—
782C22⋊C4—28no—
783C22⋊C4—44no—
784C22⋊C4—44no—
785C22⋊C4—868no—
786C22⋊C4—868no—
787C22⋊C4—1724no—
788C42—868no—
789C42—1724no—
790C42—1724no—
791C42—1724no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23#1306329014yes—
827C23C22×C4×D4311yescharacteristic
828C23C2×D4×D4311yescharacteristic
829C23C2×D4×D4311yescharacteristic
830C23C2×Q8×D4311yescharacteristic
831C23#41×D4311yescharacteristic
832C23#41×D4311yescharacteristic
833C23#41×D4311yescharacteristic
834C23#41×D4311yescharacteristic
835C23C2×#1062190011yescharacteristic
836C23C2×#1062190011yescharacteristic
837C23C2×#1062190011yescharacteristic
838C23#1306337011yescharacteristic
839C23#1306337011yescharacteristic
840C23#1306337111yescharacteristic
841C23#1306337211yescharacteristic
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—434no—
884C2×C4—434no—
885C2×C4—434no—
886C2×C4—862no—
887C2×C4—862no—
888C2×C4—862no—
889C2×C4—862no—
890C2×C4—862no—
891C2×C4—862no—
892C2×C4—862no—
893C2×C4—862no—
894C2×C4—862no—
895C2×C4—862no—
896C2×C4—862no—
897C2×C4—862no—
898C2×C4—862no—
899C2×C4—862no—
900C2×C4—862no—
901C2×C4—862no—
902C2×C4—862no—
903C2×C4—862no—
904C2×C4—862no—
905C2×C4—862no—
906C2×C4—862no—
907C2×C4—862no—
908C2×C4—862no—
909C2×C4—862no—
910C2×C4—862no—
911C2×C4—862no—
912C2×C4—862no—
913C2×C4—862no—
914C2×C4—862no—
915C2×C4—862no—
916C2×C4—862no—
917C2×C4—862no—
918C2×C4—862no—
919C2×C4—17216no—
920C2×C4—1721no—
921C2×C4—1721no—
922C2×C4—1721no—
923C2×C4—1721no—
924C2×C4—1721no—
925C2×C4—1721no—
926C2×C4—1721no—
927C2×C4—1721no—
928C2×C4—1721no—
929C2×C4—1721no—
930C2×C4—1721no—
931C2×C4—1721no—
932C2×C4—1721no—
933C2×C4—1721no—
934C2×C4—1721no—
935C2×C4—1721no—
936C2×C4—1721no—
937C2×C4—1721no—
938C2×C4—1721no—
939C2×C4—1721no—
940C2×C4(C22⋊D43)⋊C414yes—
941C22—24no—
942C22—24no—
943C22—24no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22C4×D4×D4311yescharacteristic
957C22C2×(C22⋊D43)⋊C411yescharacteristic
958C22C2×#1306329011yescharacteristic
959C22C4×#1062190011yescharacteristic
960C22#1458336711yescharacteristic
961C22#1458337111yescharacteristic
962C22#1458337811yescharacteristic
963C22#121×D4311yescharacteristic
964C22C22⋊Q8×D4311yescharacteristic
965C22#1458340511yescharacteristic
966C22#1458340911yescharacteristic
967C22#1458342611yescharacteristic
968C22#1458343011yescharacteristic
969C22#1458344411yescharacteristic
970C22#1458345111yescharacteristic
971C22#1458346511yescharacteristic
972C22#1458347811yescharacteristic
973C22#1458350311yescharacteristic
974C22#1458351811yescharacteristic
975C22#1458353611yescharacteristic
976C22#1458353811yescharacteristic
977C22#1458354211yescharacteristic
978C22#1458356211yescharacteristic
979C22#1458357211yescharacteristic
980C22#1458357711yescharacteristic
981C22#1458358011yescharacteristic
982C22#1458358511yescharacteristic
983C22#1458358611yescharacteristic
984C22#1458359211yescharacteristic
985C22#1458359411yescharacteristic
986C22#1458360011yescharacteristic
987C22#1458360311yescharacteristic
988C22#1458360311yescharacteristic
989C22#1458360711yescharacteristic
990C22#1458361811yescharacteristic
991C4—24no—
992C4—42no—
993C4—42no—
994C4—42no—
995C4—81no—
996C4—81no—
997C4—864no—
998C4—864no—
999C4—864no—
1000C4—1722no—
1001C4—1722no—
1002C4—1722no—
1003C4—1722no—
1004C4—1722no—
1005C2—44no—
1006C2#1913710511yescharacteristic
1007C2#1913712311yescharacteristic
1008C2#1913729111yescharacteristic
1009C2#1913759511yescharacteristic
1010C2#1913763911yescharacteristic
1011C2#1913767611yescharacteristic
1012C2#1913771311yescharacteristic
1013C2#1913797311yescharacteristic
1014C2#1913803911yescharacteristic
1015C2#1913849511yescharacteristic
1016C2#1913860911yescharacteristic
1017C2#1913920711yescharacteristic
1018C2#1913930611yescharacteristic
1019C2#1913979011yescharacteristic
1020C2#1914018511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1439C2
socle, cosocleC24×C43C24
prime radicalC25×C43C23
hypercenter#1439D43
hypocenterC43#14198
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C2×#14582781C2semidirect
4. C2×C4⋊C4×Dic43C2semidirect
6. #19132847C2semidirect
7. #19132845C2semidirect
10. #19132830C2semidirect
11. #19132826C2semidirect
12. Dic43⋊#95C2semidirect
13. #19132819C2semidirect
29. #14582822C4semidirect
73. C2×C4⋊Dic43C2×C4semidirect
84. C2×Dic43⋊C4C2×C4semidirect
85. C2×Dic43⋊C4C2×C4semidirect
120. C43⋊#95C2×C4semidirect
566. C43#14198semidirect

Maximal subgroups

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

subgroupindex
C2×#145828222
C2×#145827812
C2×#145827712
C2×C4⋊C4×Dic432
C2×C22⋊C4×Dic432
#191328472
#191328452
#191328322
#191328302
#191328262
Dic43⋊#952
#191328192
#191328172
C43×#14392
#1419843