Finite Group Databasebeta

← #25019384

Subgroups — #25019384

Order 11008.

2266 conjugacy classes of subgroups.

The subgroup lattice has 1068 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063302C211yesmaximal, characteristic
2C22×#13063290C211yesmaximal, characteristic, complemented
3C2×#14582803C211yesmaximal, characteristic, complemented
4C2×#14582757C211yesmaximal, characteristic
5C2×C22⋊C4×Dic43C211yesmaximal, characteristic
6#19132847C211yesmaximal, characteristic, complemented
7#19132845C211yesmaximal, characteristic, complemented
8#19132838C211yesmaximal, characteristic
9#19132832C211yesmaximal, characteristic
10#19132832C211yesmaximal, characteristic
11#19132830C211yesmaximal, characteristic, complemented
12#19132829C211yesmaximal, characteristic, complemented
13Dic43⋊#95C211yesmaximal, characteristic, complemented
14Dic43⋊#95C211yesmaximal, characteristic, complemented
15C43×#1439C211yesmaximal, characteristic
16C23×Dic86C2211yescharacteristic
17C24×Dic43C2211yescharacteristic
18C2×#13063302—24no—
19C2×#13063302—24no—
20C2×#13063302C418yescomplemented
21C2×#13063290—24no—
22C2×#13063290—24no—
23C2×#13063290—24no—
24C22×C4⋊Dic43C2211yescharacteristic
25C22×Dic43⋊C4C2211yescharacteristic
26C22×Dic43⋊C4C2211yescharacteristic
27C22×Dic43⋊C4C2211yescharacteristic
28C22×Dic43⋊C4C2211yescharacteristic
29C22×Dic43⋊C4C2211yescharacteristic
30C22×C22⋊Dic43C2211yescharacteristic
31C22×C22⋊Dic43C2211yescharacteristic
32C22×C22⋊Dic43C2211yescharacteristic
33C22×C4×Dic43C2211yescharacteristic
34C22×C4×Dic43C2211yescharacteristic
35C22×C4×Dic43C2211yescharacteristic
36C22×C4×Dic43C2211yescharacteristic
37#14582803—24no—
38#14582757—24no—
39C22⋊C4×Dic43—24no—
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
49C2×C43⋊#95C2211yescharacteristic
50C2×C43⋊#95C2211yescharacteristic
51C2×C43⋊#95C2211yescharacteristic
52C2×C43⋊#95C2211yescharacteristic
53C22×C4⋊C4×C43C2211yescharacteristic
54C22×C22⋊C4×C43C2211yescharacteristic
55C22×C22⋊C4×C43C2211yescharacteristic
56C22×C22⋊C4×C43C2211yescharacteristic
57C2×#95×C43C2211yescharacteristic
58C2×#95×C43C2211yescharacteristic
59C2×#95×C43C2211yescharacteristic
60C22×Dic86—22no—
61C22×Dic86—22no—
62C22×Dic86—22no—
63C22×Dic86—22no—
64C22×Dic86C2×C414yes—
65C22×Dic86D414yes—
66C22×Dic86D414yes—
67C23×Dic43—22no—
68C23×Dic43—22no—
69C23×Dic43—22no—
70C23×Dic43—22no—
71C23×Dic43—22no—
72C23×Dic43—22no—
73C23×Dic43C2×C414yes—
74C23×Dic43C2311yescharacteristic
75C23×Dic43C2311yescharacteristic
76C23×Dic43C2311yescharacteristic
77C23×Dic43C2311yescharacteristic
78C23×Dic43C2311yescharacteristic
79C23×Dic43C2311yescharacteristic
80C23×Dic43C2311yescharacteristic
81C23×Dic43C2311yescharacteristic
82#13063302—232no—
83#13063290—232no—
84C2×C4⋊Dic43—22no—
85C2×C4⋊Dic43—22no—
86C2×C4⋊Dic43C2×C414yes—
87C2×Dic43⋊C4—22no—
88C2×Dic43⋊C4—22no—
89C2×Dic43⋊C4—22no—
90C2×Dic43⋊C4—22no—
91C2×Dic43⋊C4—22no—
92C2×Dic43⋊C4—22no—
93C2×Dic43⋊C4—22no—
94C2×Dic43⋊C4—22no—
95C2×Dic43⋊C4—22no—
96C2×Dic43⋊C4—22no—
97C2×Dic43⋊C4—22no—
98C2×Dic43⋊C4—22no—
99C2×Dic43⋊C4C2×C414yes—
100C2×Dic43⋊C4C2×C414yes—
101C2×Dic43⋊C4D414yes—
102C2×C22⋊Dic43—22no—
103C2×C22⋊Dic43—22no—
104C2×C22⋊Dic43—22no—
105C2×C22⋊Dic43—22no—
106C2×C22⋊Dic43—22no—
107C2×C22⋊Dic43—22no—
108C2×C22⋊Dic43—41no—
109C2×C22⋊Dic43C2×C414yes—
110C2×C22⋊Dic43Q814yescomplemented
111C2×C4×Dic43—22no—
112C2×C4×Dic43—22no—
113C2×C4×Dic43—22no—
114C2×C4×Dic43—22no—
115C2×C4×Dic43—22no—
116C2×C4×Dic43—22no—
117C2×C4×Dic43—22no—
118C2×C4×Dic43—22no—
119C2×C4×Dic43—22no—
120C2×C4×Dic43—22no—
121C2×C4×Dic43—22no—
122C2×C4×Dic43D414yes—
123C43⋊#95—22no—
124C43⋊#95—22no—
125C43⋊#95—22no—
126C43⋊#95—22no—
127C43⋊#95—22no—
128C43⋊#95—22no—
129C43⋊#95—22no—
130C43⋊#95—22no—
131C43⋊#95—22no—
132C43⋊#95—22no—
133C43⋊#95—41no—
134C43⋊#95—41no—
135C43⋊#95—41no—
136C25×C43C2311yescharacteristic
137C23×C4×C43C2311yescharacteristic
138C23×C4×C43C2311yescharacteristic
139C23×C4×C43C2311yescharacteristic
140C23×C4×C43C2311yescharacteristic
141C23×C4×C43C2311yescharacteristic
142C23×C4×C43C2311yescharacteristic
143C2×C4⋊C4×C43—22no—
144C2×C4⋊C4×C43—22no—
145C2×C4⋊C4×C43—22no—
146C2×C22⋊C4×C43—22no—
147C2×C22⋊C4×C43—22no—
148C2×C22⋊C4×C43—22no—
149C2×C22⋊C4×C43—22no—
150C2×C22⋊C4×C43—22no—
151C2×C22⋊C4×C43—22no—
152C2×C22⋊C4×C43—22no—
153C2×C22⋊C4×C43—41no—
154C2×C22⋊C4×C43C2×C414yes—
155#95×C43—22no—
156#95×C43—22no—
157#95×C43—41no—
158C24×C43—21no—
159C24×C43—21no—
160C24×C43—21no—
161C24×C43—21no—
162C24×C43—21no—
163C24×C43—21no—
164C24×C43—21no—
165C24×C43—21no—
166C24×C43—21no—
167C24×C43—21no—
168C24×C43—21no—
169C24×C43—21no—
170C24×C43C22×C412yes—
171C24×C43C2×Q812yes—
172C24×C43#4112yes—
173C24×C43C2411yescharacteristic
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×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×C43C22×C412yes—
210C22×C4×C43C22×C412yes—
211C22×C4×C43C2×D412yes—
212C22×C4×C43C2×D412yes—
213C22×C4×C43C2×D412yes—
214C22×C4×C43C2×D412yes—
215C22×C4×C43#4112yes—
216C22×Dic43—28no—
217C22×Dic43—28no—
218C22×Dic43—28no—
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—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—44no—
259C22×Dic43—44no—
260C22×Dic43—44no—
261C22×Dic43—44no—
262C22×Dic43C22×C412yes—
263C22×Dic43C22×C412yes—
264C22×Dic43C22×C412yes—
265C22×Dic43C22×C412yes—
266C22×Dic43C2×D412yes—
267C22×Dic43C2×D412yes—
268C22×Dic43C2×D412yes—
269C22×Dic43C2×D412yes—
270C22×Dic43C2×D412yes—
271C22×Dic43C2×D412yes—
272C22×Dic43C2×D412yes—
273C22×Dic43C2×D412yes—
274C22×Dic43C2×Q812yes—
275C22×Dic43C2×Q812yes—
276C22×Dic43#4112yes—
277C22×Dic43#4112yes—
278C22×Dic43#4112yes—
279C2×Dic86—28no—
280C2×Dic86—28no—
281C2×Dic86—28no—
282C2×Dic86—28no—
283C2×Dic86—28no—
284C2×Dic86—28no—
285C2×Dic86C22⋊C4116yescomplemented
286C4⋊C4×C43—28no—
287C22⋊C4×C43—28no—
288C22⋊C4×C43—28no—
289C22⋊C4×C43—44no—
290C22⋊Dic43—28no—
291C22⋊Dic43—28no—
292C22⋊Dic43—44no—
293C4⋊Dic43—28no—
294Dic43⋊C4—28no—
295Dic43⋊C4—28no—
296Dic43⋊C4—28no—
297Dic43⋊C4—28no—
298Dic43⋊C4—44no—
299C4×Dic43—28no—
300C4×Dic43—28no—
301C4×Dic43—28no—
302C4×Dic43—44no—
303C23×C43—22no—
304C23×C43—22no—
305C23×C43—22no—
306C23×C43—22no—
307C23×C43—22no—
308C23×C43—22no—
309C23×C43—22no—
310C23×C43—22no—
311C23×C43—22no—
312C23×C43—22no—
313C23×C43—22no—
314C23×C43—22no—
315C23×C43—22no—
316C23×C43—22no—
317C23×C43—22no—
318C23×C43—22no—
319C23×C43—22no—
320C23×C43—22no—
321C23×C43—41no—
322C23×C43—41no—
323C23×C43—41no—
324C23×C43—41no—
325C23×C43—41no—
326C23×C43—41no—
327C23×C43—41no—
328C23×C43—41no—
329C23×C43—41no—
330C23×C43—41no—
331C23×C43—41no—
332C23×C43—41no—
333C23×C43—41no—
334C23×C43—41no—
335C23×C43—41no—
336C23×C43—41no—
337C23×C43C4×Q814yescomplemented
338C23×C43C23×C411yescharacteristic
339C23×C43C22×D411yescharacteristic
340C23×C43C22×D411yescharacteristic
341C23×C43C22×D411yescharacteristic
342C23×C43C22×D411yescharacteristic
343C23×C43C22×Q811yescharacteristic
344C23×C43C2×#4111yescharacteristic
345C23×C43C2×#4111yescharacteristic
346C23×C43C2×#4111yescharacteristic
347C23×C43C2×#4111yescharacteristic
348C23×C43C2×#4111yescharacteristic
349C23×C43H(5,𝔽2)11yescharacteristic
350C23×C432−1+411yescharacteristic
351C23×C432−1+411yescharacteristic
352C23×C432−1+411yescharacteristic
353C2×C4×C43—22no—
354C2×C4×C43—22no—
355C2×C4×C43—22no—
356C2×C4×C43—22no—
357C2×C4×C43—22no—
358C2×C4×C43—22no—
359C2×C4×C43—22no—
360C2×C4×C43—22no—
361C2×C4×C43—22no—
362C2×C4×C43—22no—
363C2×C4×C43—22no—
364C2×C4×C43—22no—
365C2×C4×C43—22no—
366C2×C4×C43—22no—
367C2×C4×C43—22no—
368C2×C4×C43—22no—
369C2×C4×C43—22no—
370C2×C4×C43—22no—
371C2×C4×C43—41no—
372C2×C4×C43—41no—
373C2×C4×C43—41no—
374C2×C4×C43—41no—
375C2×C4×C43—41no—
376C2×C4×C43—41no—
377C2×C4×C43—41no—
378C2×C4×C43—41no—
379C2×C4×C43—41no—
380C2×C4×C43—41no—
381C2×C4×C43—41no—
382C2×C4×C43—41no—
383C2×C4×C43—41no—
384C2×C4×C43—41no—
385C2×C4×C43—41no—
386C2×C4×C43—41no—
387C2×C4×C43—41no—
388C2×C4×C43—41no—
389C2×C4×C43—41no—
390C2×C4×C43—41no—
391C2×C4×C43—41no—
392C2×C4×C43—41no—
393C2×C4×C43—41no—
394C2×C4×C43C2×C22⋊C414yes—
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—22no—
407C2×Dic43—22no—
408C2×Dic43—22no—
409C2×Dic43—22no—
410C2×Dic43—22no—
411C2×Dic43—22no—
412C2×Dic43—22no—
413C2×Dic43—22no—
414C2×Dic43—22no—
415C2×Dic43—22no—
416C2×Dic43—22no—
417C2×Dic43—22no—
418C2×Dic43—22no—
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×Dic43—41no—
428C2×Dic43—41no—
429C2×Dic43—41no—
430C2×Dic43—41no—
431C2×Dic43—41no—
432C2×Dic43—41no—
433C2×Dic43—41no—
434C2×Dic43—41no—
435C2×Dic43—416no—
436C2×Dic43—41no—
437C2×Dic43—41no—
438C2×Dic43—41no—
439C2×Dic43—41no—
440C2×Dic43—41no—
441C2×Dic43—41no—
442C2×Dic43—41no—
443C2×Dic43C2×C22⋊C414yes—
444C2×Dic43C2×C22⋊C414yes—
445C2×Dic43C4×D414yes—
446C2×Dic43C4×D414yes—
447C2×Dic43#12014yes—
448C2×Dic43#12114yes—
449C2×Dic43#12114yes—
450C2×Dic43C22⋊Q814yescomplemented
451C2×Dic43#12314yes—
452Dic86—232no—
453#13969—431nomaximal, Sylow
454C22×C43—24no—
455C22×C43—24no—
456C22×C43—24no—
457C22×C43—42no—
458C22×C43—42no—
459C22×C43—42no—
460C22×C43—42no—
461C22×C43—42no—
462C22×C43—42no—
463C22×C43—42no—
464C22×C43—42no—
465C22×C43—42no—
466C22×C43—42no—
467C22×C43—42no—
468C22×C43—42no—
469C22×C43C22×C22⋊C411yescharacteristic
470C22×C43C2×C4×D411yescharacteristic
471C22×C43C2×C4×D411yescharacteristic
472C22×C43C2×C4×Q811yescharacteristic
473C22×C43C4×#4111yescharacteristic
474C22×C43#51911yescharacteristic
475C22×C43#52011yescharacteristic
476C22×C43C2×#12011yescharacteristic
477C22×C43C2×#12111yescharacteristic
478C22×C43C2×#12111yescharacteristic
479C22×C43C2×C22⋊Q811yescharacteristic
480C22×C43C2×#12311yescharacteristic
481C22×C43#52511yescharacteristic
482C22×C43#52911yescharacteristic
483C22×C43#53311yescharacteristic
484C22×C43#53611yescharacteristic
485C22×C43#53711yescharacteristic
486C22×C43#54111yescharacteristic
487C22×C43#54211yescharacteristic
488C22×C43#54611yescharacteristic
489C22×C43#54711yescharacteristic
490C22×C43#54811yescharacteristic
491C22×C43#54811yescharacteristic
492C22×C43#54811yescharacteristic
493C22×C43#54811yescharacteristic
494C22×C43#54811yescharacteristic
495C22×C43D4×Q811yescharacteristic
496C22×C43D4×Q811yescharacteristic
497C22×C43D4×Q811yescharacteristic
498C22×C43#55011yescharacteristic
499C22×C43#55011yescharacteristic
500C22×C43#55211yescharacteristic
501C22×C43#55211yescharacteristic
502C22×C43#55411yescharacteristic
503C22×C43#55611yescharacteristic
504C4×C43—24no—
505C4×C43—42no—
506C4×C43—42no—
507C4×C43—42no—
508C4×C43—42no—
509C4×C43—81no—
510Dic43—24no—
511Dic43—24no—
512Dic43—42no—
513Dic43—42no—
514Dic43—42no—
515Dic43—42no—
516Dic43—81no—
517Dic43#38618yes—
518C22×C22⋊Q8—431no—
519C22×C4×Q8—431no—
520C2×#391—431no—
521C2×#380—431no—
522C2×C4×C22⋊C4—431no—
523#1441—431no—
524#1441—431no—
525#1439—431no—
526#1439D4311yescharacteristic
527#1437—431no—
528#1437—431no—
529#1436—431no—
530#1436—431no—
531C4⋊#95—431no—
532C4⋊#95—431no—
533C2×C43—44no—
534C2×C43C2×#38611yescharacteristic
535C2×C43C4×C22⋊Q811yescharacteristic
536C2×C43#232311yescharacteristic
537C2×C43Q8×C22⋊C411yescharacteristic
538C2×C43#234111yescharacteristic
539C2×C43#236011yescharacteristic
540C2×C43#236211yescharacteristic
541C2×C43#240711yescharacteristic
542C2×C43#240911yescharacteristic
543C2×C43#242111yescharacteristic
544C2×C43#242311yescharacteristic
545C2×C43#242611yescharacteristic
546C2×C43#242911yescharacteristic
547C2×C43#253611yescharacteristic
548C2×C43#253811yescharacteristic
549C23×Q8—431no—
550C24×C4—431no—
551C2×C22⋊Q8—438no—
552C2×C22⋊Q8—864no—
553C2×C22⋊Q8—864no—
554C2×C4×Q8—864no—
555C2×C4×Q8—864no—
556C2×C4×Q8—864no—
557C22×C4⋊C4—431no—
558C22×C4⋊C4—431no—
559C22×C4⋊C4—431no—
560C22×C4⋊C4—431no—
561C22×C4⋊C4—431no—
562C22×C4⋊C4—431no—
563C22×C4⋊C4C2×D4311yescharacteristic
564C22×C22⋊C4—431no—
565C22×C22⋊C4—431no—
566C22×C22⋊C4—431no—
567C22×C22⋊C4C2×D4311yescharacteristic
568C22×C22⋊C4C2×D4311yescharacteristic
569C22×C22⋊C4C2×D4311yescharacteristic
570C22×C42—431no—
571C22×C42—431no—
572C22×C42—431no—
573C22×C42—431no—
574#391—864no—
575#380—864no—
576C4×C22⋊C4—864no—
577C2×#95—431no—
578C2×#95—431no—
579C2×#95—431no—
580C2×#95—431no—
581C2×#95—431no—
582C2×#95—431no—
583C2×#95—431no—
584C2×#95—431no—
585C2×#95—431no—
586C2×#95—431no—
587C2×#95—431no—
588C2×#95—431no—
589C2×#95—431no—
590C2×#95C2×D4311yescharacteristic
591C2×#95C2×D4311yescharacteristic
592C2×#95C2×D4311yescharacteristic
593C43#1396911yescharacteristic, complemented, Sylow
594C25C22×D4311yescharacteristic
595C22×Q8—434no—
596C22×Q8—434no—
597C22×Q8—434no—
598C22×Q8—862no—
599C22×Q8—862no—
600C22×Q8—862no—
601C22×Q8—862no—
602C23×C4—431no—
603C23×C4—431no—
604C23×C4—431no—
605C23×C4—434no—
606C23×C4—431no—
607C23×C4—431no—
608C23×C4—431no—
609C23×C4—431no—
610C23×C4—431no—
611C23×C4—862no—
612C23×C4—862no—
613C23×C4—862no—
614C23×C4—862no—
615C23×C4—862no—
616C23×C4—862no—
617C23×C4C22×D4311yescharacteristic
618C23×C4C22×D4311yescharacteristic
619C23×C4C22×D4311yescharacteristic
620C23×C4C22×D4311yescharacteristic
621C23×C4C22×D4311yescharacteristic
622C23×C4C22×D4311yescharacteristic
623C22⋊Q8—8632no—
624C4×Q8—8632no—
625C2×C4⋊C4—22no—
626C2×C4⋊C4—22no—
627C2×C4⋊C4—22no—
628C2×C4⋊C4—434no—
629C2×C4⋊C4—434no—
630C2×C4⋊C4—434no—
631C2×C4⋊C4—434no—
632C2×C4⋊C4—862no—
633C2×C4⋊C4—862no—
634C2×C4⋊C4—862no—
635C2×C4⋊C4—862no—
636C2×C4⋊C4—862no—
637C2×C4⋊C4—862no—
638C2×C4⋊C4—862no—
639C2×C4⋊C4—862no—
640C2×C4⋊C4—862no—
641C2×C4⋊C4—862no—
642C2×C4⋊C4—862no—
643C2×C4⋊C4—862no—
644C2×C4⋊C4—862no—
645C2×C4⋊C4—862no—
646C2×C22⋊C4—22no—
647C2×C22⋊C4—22no—
648C2×C22⋊C4—22no—
649C2×C22⋊C4—22no—
650C2×C22⋊C4—22no—
651C2×C22⋊C4—22no—
652C2×C22⋊C4—22no—
653C2×C22⋊C4—41no—
654C2×C22⋊C4—434no—
655C2×C22⋊C4—434no—
656C2×C22⋊C4—862no—
657C2×C22⋊C4—862no—
658C2×C22⋊C4—862no—
659C2×C22⋊C4—862no—
660C2×C22⋊C4—862no—
661C2×C22⋊C4—862no—
662C2×C22⋊C4—1721no—
663C2×C22⋊C4C4×D4314yes—
664C2×C42—434no—
665C2×C42—862no—
666C2×C42—862no—
667C2×C42—862no—
668C2×C42—862no—
669C2×C42—862no—
670C2×C42—862no—
671C2×C42—862no—
672C2×C42—862no—
673C2×C42—862no—
674C2×C42—862no—
675C2×C42—862no—
676#95—22no—
677#95—22no—
678#95—41no—
679#95—862no—
680#95—862no—
681#95—862no—
682#95—862no—
683#95—862no—
684#95—862no—
685#95—862no—
686#95—862no—
687#95—862no—
688#95—862no—
689#95—1721no—
690#95—1721no—
691#95—1721no—
692C24—21no—
693C24—21no—
694C24—21no—
695C24—21no—
696C24—21no—
697C24—21no—
698C24—21no—
699C24—21no—
700C24—21no—
701C24—21no—
702C24—21no—
703C24—21no—
704C24C2×C4×D4312yes—
705C24#1062190012yes—
706C24Q8×D4312yes—
707C24C23×D4311yescharacteristic
708C2×Q8—4316no—
709C2×Q8—868no—
710C2×Q8—868no—
711C2×Q8—868no—
712C2×Q8—868no—
713C2×Q8—868no—
714C2×Q8—868no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—432no—
751C22×C4—432no—
752C22×C4—432no—
753C22×C4—432no—
754C22×C4—432no—
755C22×C4—432no—
756C22×C4—432no—
757C22×C4—432no—
758C22×C4—432no—
759C22×C4—432no—
760C22×C4—432no—
761C22×C4—432no—
762C22×C4—432no—
763C22×C4—432no—
764C22×C4—432no—
765C22×C4—432no—
766C22×C4—432no—
767C22×C4—868no—
768C22×C4—868no—
769C22×C4—868no—
770C22×C4—861no—
771C22×C4—861no—
772C22×C4—861no—
773C22×C4—861no—
774C22×C4—861no—
775C22×C4—861no—
776C22×C4—861no—
777C22×C4—861no—
778C22×C4—861no—
779C22×C4—861no—
780C22×C4—861no—
781C22×C4—861no—
782C22×C4—861no—
783C22×C4—861no—
784C22×C4—861no—
785C22×C4—861no—
786C22×C4—861no—
787C22×C4—861no—
788C22×C4—861no—
789C22×C4—861no—
790C22×C4—861no—
791C22×C4—861no—
792C22×C4—861no—
793C22×C4—861no—
794C22×C4—861no—
795C22×C4—861no—
796C22×C4—861no—
797C22×C4—861no—
798C22×C4—861no—
799C22×C4—861no—
800C22×C4—861no—
801C22×C4—861no—
802C22×C4—861no—
803C22×C4—861no—
804C22×C4—861no—
805C22×C4—861no—
806C22×C4—861no—
807C22×C4—861no—
808C22×C4—861no—
809C22×C4—1724no—
810C22×C4—1724no—
811C22×C4—1724no—
812C22×C4—1724no—
813C22×C4C2×C4×D4312yes—
814C22×C4C2×C4×D4312yes—
815C22×C4D4×D4312yes—
816C22×C4D4×D4312yes—
817C22×C4D4×D4312yes—
818C22×C4D4×D4312yes—
819C22×C4#1062190012yes—
820C4⋊C4—28no—
821C4⋊C4—868no—
822C4⋊C4—868no—
823C4⋊C4—868no—
824C4⋊C4—868no—
825C4⋊C4—868no—
826C4⋊C4—1724no—
827C22⋊C4—28no—
828C22⋊C4—28no—
829C22⋊C4—44no—
830C22⋊C4—868no—
831C22⋊C4—868no—
832C22⋊C4—1724no—
833C42—868no—
834C42—868no—
835C42—868no—
836C42—1724no—
837C23—22no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—41no—
871C23#1306329014yescomplemented
872C23C22×C4×D4311yescharacteristic
873C23C2×D4×D4311yescharacteristic
874C23C2×D4×D4311yescharacteristic
875C23C2×D4×D4311yescharacteristic
876C23C2×D4×D4311yescharacteristic
877C23C2×Q8×D4311yescharacteristic
878C23#41×D4311yescharacteristic
879C23#41×D4311yescharacteristic
880C23#41×D4311yescharacteristic
881C23C2×#1062190011yescharacteristic
882C23C2×#1062190011yescharacteristic
883C23#1306337011yescharacteristic
884C23#1306337211yescharacteristic
885C23#1306337211yescharacteristic
886C23#1306337211yescharacteristic
887Q8—8632no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—434no—
930C2×C4—434no—
931C2×C4—434no—
932C2×C4—434no—
933C2×C4—434no—
934C2×C4—434no—
935C2×C4—434no—
936C2×C4—434no—
937C2×C4—434no—
938C2×C4—862no—
939C2×C4—862no—
940C2×C4—862no—
941C2×C4—862no—
942C2×C4—862no—
943C2×C4—862no—
944C2×C4—862no—
945C2×C4—862no—
946C2×C4—862no—
947C2×C4—862no—
948C2×C4—862no—
949C2×C4—862no—
950C2×C4—862no—
951C2×C4—862no—
952C2×C4—862no—
953C2×C4—862no—
954C2×C4—862no—
955C2×C4—862no—
956C2×C4—862no—
957C2×C4—862no—
958C2×C4—862no—
959C2×C4—862no—
960C2×C4—862no—
961C2×C4—862no—
962C2×C4—17216no—
963C2×C4—1721no—
964C2×C4—1721no—
965C2×C4—1721no—
966C2×C4—1721no—
967C2×C4—1721no—
968C2×C4—1721no—
969C2×C4—1721no—
970C2×C4—1721no—
971C2×C4—1721no—
972C2×C4—1721no—
973C2×C4—1721no—
974C2×C4—1721no—
975C2×C4—1721no—
976C2×C4—1721no—
977C2×C4—1721no—
978C2×C4—1721no—
979C2×C4—1721no—
980C2×C4—1721no—
981C2×C4—1721no—
982C2×C4—1721no—
983C2×C4—1721no—
984C2×C4—1721no—
985C2×C4—1721no—
986C2×C4C22⋊C4×D4314yes—
987C22—24no—
988C22—24no—
989C22—24no—
990C22—42no—
991C22—42no—
992C22—42no—
993C22—42no—
994C22—42no—
995C22—42no—
996C22—42no—
997C22—42no—
998C22—42no—
999C22—42no—
1000C22—42no—
1001C22—42no—
1002C22C2×C22⋊C4×D4311yescharacteristic
1003C22C4×D4×D4311yescharacteristic
1004C22C4×D4×D4311yescharacteristic
1005C22C2×#1306329011yescharacteristic
1006C22C4×#1062190011yescharacteristic
1007C22#1458337611yescharacteristic
1008C22#1458337811yescharacteristic
1009C22#120×D4311yescharacteristic
1010C22#121×D4311yescharacteristic
1011C22#121×D4311yescharacteristic
1012C22C22⋊Q8×D4311yescharacteristic
1013C22#123×D4311yescharacteristic
1014C22#1458340511yescharacteristic
1015C22#1458342611yescharacteristic
1016C22#1458345111yescharacteristic
1017C22#1458346911yescharacteristic
1018C22#1458347611yescharacteristic
1019C22#1458350611yescharacteristic
1020C22#1458351711yescharacteristic
1021C22#1458353611yescharacteristic
1022C22#1458354911yescharacteristic
1023C22#1458355511yescharacteristic
1024C22#1458355511yescharacteristic
1025C22#1458355511yescharacteristic
1026C22#1458355711yescharacteristic
1027C22#1458355711yescharacteristic
1028C22#1458356211yescharacteristic
1029C22#1458356211yescharacteristic
1030C22#1458356211yescharacteristic
1031C22#1458356711yescharacteristic
1032C22#1458356911yescharacteristic
1033C22#1458358611yescharacteristic
1034C22#1458358611yescharacteristic
1035C22#1458360311yescharacteristic
1036C22#1458361611yescharacteristic
1037C4—24no—
1038C4—42no—
1039C4—42no—
1040C4—42no—
1041C4—42no—
1042C4—81no—
1043C4—438no—
1044C4—864no—
1045C4—864no—
1046C4—3441no—
1047C4—1722no—
1048C4—1722no—
1049C4—1722no—
1050C4—1722no—
1051C2—44no—
1052C2#386×D4311yescharacteristic
1053C2#1913712711yescharacteristic
1054C2#1913727011yescharacteristic
1055C2#1913742711yescharacteristic
1056C2#1913743411yescharacteristic
1057C2#1913759511yescharacteristic
1058C2#1913761911yescharacteristic
1059C2#1913793311yescharacteristic
1060C2#1913795311yescharacteristic
1061C2#1913809111yescharacteristic
1062C2#1913811311yescharacteristic
1063C2#1913815411yescharacteristic
1064C2#1913818711yescharacteristic
1065C2#1913949911yescharacteristic
1066C2#1913951211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1439C2
socle, cosocleC24×C43C24
prime radicalC25×C43C23
hypercenter#1439D43
hypocenterC43#13969
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C22×#13063290C2semidirect
3. C2×#14582803C2semidirect
6. #19132847C2semidirect
7. #19132845C2semidirect
11. #19132830C2semidirect
12. #19132829C2semidirect
13. Dic43⋊#95C2semidirect
14. Dic43⋊#95C2semidirect
20. C2×#13063302C4semidirect
110. C2×C22⋊Dic43Q8semidirect
285. C2×Dic86C22⋊C4semidirect
337. C23×C43C4×Q8semidirect
450. C2×Dic43C22⋊Q8semidirect
593. C43#13969semidirect
871. C23#13063290semidirect

Maximal subgroups

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

subgroupindex
C22×#130633022
C22×#130632902
C2×#145828032
C2×#145827572
C2×C22⋊C4×Dic432
#191328472
#191328452
#191328382
#191328322
#191328302
#191328292
Dic43⋊#952
C43×#14392
#1396943