Finite Group Databasebeta

← #25023943

Subgroups — #25023943

Order 11008.

1910 conjugacy classes of subgroups.

The subgroup lattice has 1050 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063303C211yesmaximal, characteristic
2C2×#14582804C211yesmaximal, characteristic, complemented
3C2×#14582785C211yesmaximal, characteristic, complemented
4C2×#14582756C211yesmaximal, characteristic
5#19132865C211yesmaximal, characteristic, complemented
6#19132849C211yesmaximal, characteristic, complemented
7#19132845C211yesmaximal, characteristic, complemented
8#19132845C211yesmaximal, characteristic, complemented
9#19132837C211yesmaximal, characteristic
10#19132837C211yesmaximal, characteristic
11#19132833C211yesmaximal, characteristic
12#19132831C211yesmaximal, characteristic
13#19132828C211yesmaximal, characteristic, complemented
14(C2×D43)⋊#95C211yesmaximal, characteristic
15C2×C43×#389C211yesmaximal, characteristic, complemented
16C23×Dic86C2211yescharacteristic
17C23×C4×D43C2211yescharacteristic
18C2×#13063303—24no—
19C2×#13063303—24no—
20C2×#13063303C418yescomplemented
21C22×C4⋊Dic43C2211yescharacteristic
22C22×Dic43⋊C4C2211yescharacteristic
23C22×Dic43⋊C4C2211yescharacteristic
24C22×(C2×D43)⋊C4C2211yescharacteristic
25C22×(C2×D43)⋊C4C2211yescharacteristic
26C22×(C2×D43)⋊C4C2211yescharacteristic
27C22×(C2×D43)⋊C4C2211yescharacteristic
28C22×(C2×D43)⋊C4C2211yescharacteristic
29C22×(C2×D43)⋊C4C2211yescharacteristic
30C22×C4×Dic43C2211yescharacteristic
31#14582804—24no—
32#14582785—24no—
33#14582756—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
49C2×C43⋊#95C2211yescharacteristic
50C22×C4⋊C4×C43C2211yescharacteristic
51C22×C4⋊C4×C43C2211yescharacteristic
52C22×C4⋊C4×C43C2211yescharacteristic
53C22×C4⋊C4×C43C2211yescharacteristic
54C22×C42×C43C2211yescharacteristic
55C43×#389—24no—
56C2×#95×C43C2211yescharacteristic
57C2×#95×C43C2211yescharacteristic
58C24×D43C2311yescharacteristic
59C22×Dic86—22no—
60C22×Dic86—22no—
61C22×Dic86—22no—
62C22×Dic86—22no—
63C22×Dic86—41no—
64C22×Dic86—41no—
65C22×Dic86C2×C414yes—
66C23×Dic43C2311yescharacteristic
67C23×Dic43C2311yescharacteristic
68C23×Dic43C2311yescharacteristic
69C23×Dic43C2311yescharacteristic
70C23×Dic43C2311yescharacteristic
71C23×Dic43C2311yescharacteristic
72C23×Dic43C2311yescharacteristic
73C22×C4×D43—22no—
74C22×C4×D43—22no—
75C22×C4×D43—22no—
76C22×C4×D43—22no—
77C22×C4×D43—41no—
78C22×C4×D43—41no—
79C22×C4×D43C2×C414yes—
80#13063303—232no—
81C2×C4⋊Dic43—22no—
82C2×C4⋊Dic43—22no—
83C2×C4⋊Dic43—41no—
84C2×Dic43⋊C4—22no—
85C2×Dic43⋊C4—22no—
86C2×Dic43⋊C4—22no—
87C2×Dic43⋊C4—22no—
88C2×Dic43⋊C4C2×C414yes—
89C2×Dic43⋊C4C2×C414yes—
90C2×(C2×D43)⋊C4—22no—
91C2×(C2×D43)⋊C4—22no—
92C2×(C2×D43)⋊C4—22no—
93C2×(C2×D43)⋊C4—22no—
94C2×(C2×D43)⋊C4—22no—
95C2×(C2×D43)⋊C4—22no—
96C2×(C2×D43)⋊C4—22no—
97C2×(C2×D43)⋊C4—22no—
98C2×(C2×D43)⋊C4—22no—
99C2×(C2×D43)⋊C4—41no—
100C2×(C2×D43)⋊C4—41no—
101C2×(C2×D43)⋊C4—41no—
102C2×(C2×D43)⋊C4—41no—
103C2×(C2×D43)⋊C4—41no—
104C2×(C2×D43)⋊C4—41no—
105C2×(C2×D43)⋊C4C2×C414yes—
106C2×(C2×D43)⋊C4C2×C414yes—
107C2×(C2×D43)⋊C4Q814yescomplemented
108C2×C4×Dic43—22no—
109C2×C4×Dic43—22no—
110C2×C4×Dic43—41no—
111C43⋊#95—22no—
112C43⋊#95—22no—
113C43⋊#95—22no—
114C43⋊#95—22no—
115C43⋊#95—22no—
116C43⋊#95—22no—
117C43⋊#95—22no—
118C43⋊#95—22no—
119C43⋊#95—22no—
120C43⋊#95—41no—
121C43⋊#95—41no—
122C43⋊#95—41no—
123C43⋊#95—41no—
124C43⋊#95—41no—
125C43⋊#95—41no—
126C43⋊#95D414yes—
127C23×C4×C43C2311yescharacteristic
128C23×C4×C43C2311yescharacteristic
129C23×C4×C43C2311yescharacteristic
130C23×C4×C43C2311yescharacteristic
131C23×C4×C43C2311yescharacteristic
132C23×C4×C43C2311yescharacteristic
133C23×C4×C43C2311yescharacteristic
134C2×C4⋊C4×C43—22no—
135C2×C4⋊C4×C43—22no—
136C2×C4⋊C4×C43—22no—
137C2×C4⋊C4×C43—22no—
138C2×C4⋊C4×C43—22no—
139C2×C4⋊C4×C43—41no—
140C2×C4⋊C4×C43—41no—
141C2×C4⋊C4×C43—41no—
142C2×C4⋊C4×C43—41no—
143C2×C4⋊C4×C43C2×C414yes—
144C2×C4⋊C4×C43D414yes—
145C2×C4⋊C4×C43D414yes—
146C2×C42×C43—22no—
147C2×C42×C43—41no—
148C2×C42×C43—41no—
149#95×C43—22no—
150#95×C43—22no—
151C24×C43C2411yescharacteristic
152C23×D43—21no—
153C23×D43—21no—
154C23×D43—21no—
155C23×D43—21no—
156C23×D43—21no—
157C23×D43—21no—
158C23×D43—21no—
159C23×D43—21no—
160C23×D43—21no—
161C23×D43—21no—
162C23×D43—21no—
163C23×D43—21no—
164C23×D43C22×C412yes—
165C23×D43C2×Q812yes—
166C23×D43#4112yes—
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×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×C43C22×C412yes—
206C22×C4×C43C22×C412yes—
207C22×C4×C43C22×C412yes—
208C22×C4×C43C2×D412yes—
209C22×C4×C43C2×D412yes—
210C22×C4×C43C2×D412yes—
211C22×C4×C43C2×D412yes—
212C22×C4×C43C2×D412yes—
213C22×C4×C43C2×D412yes—
214C22×C4×C43C2×D412yes—
215C22×C4×C43C2×Q812yes—
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—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×Dic43C22×C412yes—
259C22×Dic43C22×C412yes—
260C22×Dic43C22×C412yes—
261C22×Dic43C2×D412yes—
262C22×Dic43C2×D412yes—
263C22×Dic43C2×Q812yes—
264C22×Dic43#4112yes—
265C2×C4×D43—28no—
266C2×C4×D43—28no—
267C2×C4×D43—44no—
268C2×C4×D43—44no—
269C2×C4×D43—44no—
270C2×C4×D43—44no—
271C2×C4×D43—44no—
272C2×Dic86—28no—
273C2×Dic86—28no—
274C2×Dic86—44no—
275C2×Dic86—44no—
276C2×Dic86—44no—
277C2×Dic86—44no—
278C2×Dic86—44no—
279C4⋊C4×C43—44no—
280C4⋊C4×C43—44no—
281C4⋊C4×C43—44no—
282C4⋊C4×C43C22⋊C4116yescomplemented
283C42×C43—44no—
284(C2×D43)⋊C4—28no—
285(C2×D43)⋊C4—28no—
286(C2×D43)⋊C4—44no—
287(C2×D43)⋊C4—44no—
288(C2×D43)⋊C4—44no—
289(C2×D43)⋊C4—44no—
290C4⋊Dic43—44no—
291Dic43⋊C4—28no—
292Dic43⋊C4—28no—
293C4×Dic43—44no—
294C23×C43C23×C411yescharacteristic
295C23×C43C22×D411yescharacteristic
296C23×C43C22×D411yescharacteristic
297C23×C43C22×D411yescharacteristic
298C23×C43C22×Q811yescharacteristic
299C23×C43C2×#4111yescharacteristic
300C23×C43C2×#4111yescharacteristic
301C23×C43H(5,𝔽2)11yescharacteristic
302C23×C43H(5,𝔽2)11yescharacteristic
303C23×C43H(5,𝔽2)11yescharacteristic
304C23×C43H(5,𝔽2)11yescharacteristic
305C23×C432−1+411yescharacteristic
306C23×C432−1+411yescharacteristic
307C23×C432−1+411yescharacteristic
308C23×C432−1+411yescharacteristic
309C22×D43—22no—
310C22×D43—22no—
311C22×D43—22no—
312C22×D43—22no—
313C22×D43—22no—
314C22×D43—22no—
315C22×D43—22no—
316C22×D43—22no—
317C22×D43—22no—
318C22×D43—22no—
319C22×D43—22no—
320C22×D43—22no—
321C22×D43—22no—
322C22×D43—22no—
323C22×D43—22no—
324C22×D43—22no—
325C22×D43—22no—
326C22×D43—22no—
327C22×D43—41no—
328C22×D43—41no—
329C22×D43—41no—
330C22×D43—41no—
331C22×D43—41no—
332C22×D43—41no—
333C22×D43—41no—
334C22×D43—41no—
335C22×D43—41no—
336C22×D43—41no—
337C22×D43—41no—
338C22×D43—41no—
339C22×D43—41no—
340C22×D43—41no—
341C22×D43—41no—
342C22×D43—41no—
343C22×D43C4×Q814yes—
344C2×C4×C43—22no—
345C2×C4×C43—22no—
346C2×C4×C43—22no—
347C2×C4×C43—22no—
348C2×C4×C43—22no—
349C2×C4×C43—22no—
350C2×C4×C43—22no—
351C2×C4×C43—22no—
352C2×C4×C43—22no—
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—41no—
369C2×C4×C43—41no—
370C2×C4×C43—41no—
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×C43C2×C22⋊C414yes—
391C2×C4×C43C2×C22⋊C414yes—
392C2×C4×C43C2×C22⋊C414yes—
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—22no—
407C2×Dic43—22no—
408C2×Dic43—22no—
409C2×Dic43—22no—
410C2×Dic43—22no—
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×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—41no—
436C2×Dic43—41no—
437C2×Dic43—41no—
438C2×Dic43—41no—
439C2×Dic43—41no—
440C2×Dic43—41no—
441C2×Dic43C4×D414yes—
442C4×D43—416no—
443Dic86—416no—
444#14362—431nomaximal, Sylow
445C22×C43C22×C22⋊C411yescharacteristic
446C22×C43C2×C4×D411yescharacteristic
447C22×C43C2×C4×Q811yescharacteristic
448C22×C43#51811yescharacteristic
449C22×C43#51911yescharacteristic
450C22×C43#52011yescharacteristic
451C22×C43#52011yescharacteristic
452C22×C43#53511yescharacteristic
453C22×C43#53611yescharacteristic
454C22×C43#53611yescharacteristic
455C22×C43#53711yescharacteristic
456C22×C43#53711yescharacteristic
457C22×C43#53711yescharacteristic
458C22×C43#53811yescharacteristic
459C22×C43#53911yescharacteristic
460C22×C43#54111yescharacteristic
461C22×C43#54211yescharacteristic
462C22×C43#54311yescharacteristic
463C22×C43#54411yescharacteristic
464C22×C43D4211yescharacteristic
465C22×C43D4211yescharacteristic
466C22×C43#54611yescharacteristic
467C22×C43#54611yescharacteristic
468C22×C43#54611yescharacteristic
469C22×C43#54811yescharacteristic
470C22×C43#54811yescharacteristic
471C22×C43D4×Q811yescharacteristic
472C22×C43D4×Q811yescharacteristic
473C22×C43D4×Q811yescharacteristic
474C22×C43#55211yescharacteristic
475C22×C43#55411yescharacteristic
476C22×C43#56211yescharacteristic
477C22×C43#56211yescharacteristic
478C22×C43#56311yescharacteristic
479C22×C43#56311yescharacteristic
480C2×D43—24no—
481C2×D43—24no—
482C2×D43—24no—
483C2×D43—42no—
484C2×D43—42no—
485C2×D43—42no—
486C2×D43—42no—
487C2×D43—42no—
488C2×D43—42no—
489C2×D43—42no—
490C2×D43—42no—
491C2×D43—42no—
492C2×D43—42no—
493C2×D43—42no—
494C2×D43—42no—
495C4×C43—24no—
496C4×C43—24no—
497C4×C43—24no—
498C4×C43—42no—
499C4×C43—42no—
500C4×C43—81no—
501C4×C43—81no—
502Dic43—24no—
503Dic43—42no—
504Dic43—42no—
505Dic43—42no—
506Dic43—42no—
507Dic43—81no—
508Dic43—81no—
509C22×C22⋊Q8—431no—
510C2×#391—431no—
511C2×#389D4311yescharacteristic, complemented
512C2×#387—431no—
513C2×#380—431no—
514#1446—431no—
515#1441—431no—
516#1441—431no—
517#1441—431no—
518#1439—431no—
519#1439—431no—
520#1437—431no—
521#1437—431no—
522#1436—431no—
523C22⋊#95—431no—
524C2×C43#231111yescharacteristic
525C2×C43#232311yescharacteristic
526C2×C43#232911yescharacteristic
527C2×C43D4×C22⋊C411yescharacteristic
528C2×C43Q8×C22⋊C411yescharacteristic
529C2×C43#236011yescharacteristic
530C2×C43#237811yescharacteristic
531C2×C43#267611yescharacteristic
532C2×C43#267711yescharacteristic
533C2×C43#268111yescharacteristic
534C2×C43#268311yescharacteristic
535C2×C43#269011yescharacteristic
536C2×C43#269211yescharacteristic
537C2×C43#270211yescharacteristic
538C2×C43#270411yescharacteristic
539D43—44no—
540C23×Q8—431no—
541C24×C4—431no—
542C2×C22⋊Q8—438no—
543C2×C22⋊Q8—864no—
544C2×C22⋊Q8—864no—
545C22×C4⋊C4—431no—
546C22×C4⋊C4—431no—
547C22×C4⋊C4—431no—
548C22×C4⋊C4C2×D4311yescharacteristic
549C22×C4⋊C4C2×D4311yescharacteristic
550C22×C4⋊C4C2×D4311yescharacteristic
551C22×C4⋊C4C2×D4311yescharacteristic
552C22×C22⋊C4—431no—
553C22×C22⋊C4—431no—
554C22×C22⋊C4—431no—
555C22×C22⋊C4—431no—
556C22×C22⋊C4—431no—
557C22×C22⋊C4—431no—
558C22×C42—431no—
559C22×C42C2×D4311yescharacteristic
560#391—864no—
561#389—24no—
562#387—864no—
563#380—864no—
564C2×#95—431no—
565C2×#95—431no—
566C2×#95—431no—
567C2×#95—431no—
568C2×#95—431no—
569C2×#95—431no—
570C2×#95—431no—
571C2×#95—431no—
572C2×#95—431no—
573C2×#95—431no—
574C2×#95—431no—
575C2×#95—431no—
576C2×#95—431no—
577C2×#95—431no—
578C2×#95—431no—
579C2×#95—431no—
580C2×#95C2×D4311yescharacteristic
581C2×#95C2×D4311yescharacteristic
582C43#1436211yescharacteristic, complemented, Sylow
583C25—431no—
584C22×Q8—434no—
585C22×Q8—862no—
586C22×Q8—862no—
587C22×Q8—862no—
588C22×Q8—862no—
589C22×Q8—1721no—
590C22×Q8—1721no—
591C23×C4—431no—
592C23×C4—431no—
593C23×C4—431no—
594C23×C4—431no—
595C23×C4—431no—
596C23×C4—434no—
597C23×C4—431no—
598C23×C4—431no—
599C23×C4—862no—
600C23×C4—862no—
601C23×C4—862no—
602C23×C4—862no—
603C23×C4—1721no—
604C23×C4—1721no—
605C23×C4C22×D4311yescharacteristic
606C23×C4C22×D4311yescharacteristic
607C23×C4C22×D4311yescharacteristic
608C23×C4C22×D4311yescharacteristic
609C23×C4C22×D4311yescharacteristic
610C23×C4C22×D4311yescharacteristic
611C23×C4C22×D4311yescharacteristic
612C22⋊Q8—8632no—
613C2×C4⋊C4—22no—
614C2×C4⋊C4—22no—
615C2×C4⋊C4—22no—
616C2×C4⋊C4—22no—
617C2×C4⋊C4—22no—
618C2×C4⋊C4—41no—
619C2×C4⋊C4—41no—
620C2×C4⋊C4—41no—
621C2×C4⋊C4—41no—
622C2×C4⋊C4—434no—
623C2×C4⋊C4—434no—
624C2×C4⋊C4—862no—
625C2×C4⋊C4—862no—
626C2×C4⋊C4—862no—
627C2×C4⋊C4—862no—
628C2×C4⋊C4—862no—
629C2×C4⋊C4—862no—
630C2×C4⋊C4—1721no—
631C2×C4⋊C4C4×D4314yes—
632C2×C4⋊C4D17214yes—
633C2×C4⋊C4C22⋊D4314yes—
634C2×C22⋊C4—434no—
635C2×C22⋊C4—434no—
636C2×C22⋊C4—434no—
637C2×C22⋊C4—862no—
638C2×C22⋊C4—862no—
639C2×C22⋊C4—862no—
640C2×C22⋊C4—862no—
641C2×C22⋊C4—862no—
642C2×C22⋊C4—862no—
643C2×C22⋊C4—862no—
644C2×C22⋊C4—862no—
645C2×C22⋊C4—862no—
646C2×C22⋊C4—1721no—
647C2×C22⋊C4—1721no—
648C2×C22⋊C4—1721no—
649C2×C22⋊C4—1721no—
650C2×C22⋊C4—1721no—
651C2×C22⋊C4—1721no—
652C2×C42—22no—
653C2×C42—41no—
654C2×C42—41no—
655C2×C42—862no—
656C2×C42—862no—
657C2×C42—1721no—
658#95—22no—
659#95—22no—
660#95—434no—
661#95—862no—
662#95—862no—
663#95—862no—
664#95—862no—
665#95—862no—
666#95—862no—
667#95—862no—
668#95—862no—
669#95—862no—
670#95—1721no—
671#95—1721no—
672#95—1721no—
673#95—1721no—
674#95—1721no—
675#95—1721no—
676C24—432no—
677C24—432no—
678C24—432no—
679C24—861no—
680C24—861no—
681C24—861no—
682C24—861no—
683C24—861no—
684C24—861no—
685C24—861no—
686C24—861no—
687C24—861no—
688C24—861no—
689C24—861no—
690C24—861no—
691C24C23×D4311yescharacteristic
692C2×Q8—868no—
693C2×Q8—868no—
694C2×Q8—1724no—
695C2×Q8—1724no—
696C2×Q8—1724no—
697C2×Q8—1724no—
698C2×Q8—1724no—
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—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
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—432no—
738C22×C4—432no—
739C22×C4—432no—
740C22×C4—432no—
741C22×C4—432no—
742C22×C4—432no—
743C22×C4—432no—
744C22×C4—868no—
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—861no—
765C22×C4—861no—
766C22×C4—861no—
767C22×C4—861no—
768C22×C4—861no—
769C22×C4—861no—
770C22×C4—861no—
771C22×C4—861no—
772C22×C4—861no—
773C22×C4—868no—
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—1724no—
789C22×C4—1724no—
790C22×C4—1724no—
791C22×C4—1724no—
792C22×C4—1724no—
793C22×C4C2×C4×D4312yes—
794C22×C4C2×C4×D4312yes—
795C22×C4C2×C4×D4312yes—
796C22×C4C2×D17212yes—
797C22×C4C2×D17212yes—
798C22×C4C2×D17212yes—
799C22×C4D4×D4312yes—
800C22×C4Q8×D4312yes—
801C22×C4C2×C22⋊D4312yes—
802C22×C4C2×C22⋊D4312yes—
803C22×C4C2×C22⋊D4312yes—
804C4⋊C4—44no—
805C4⋊C4—44no—
806C4⋊C4—44no—
807C4⋊C4—868no—
808C4⋊C4—868no—
809C4⋊C4—1724no—
810C4⋊C4(C2×D43)⋊C4116yescomplemented
811C22⋊C4—868no—
812C22⋊C4—868no—
813C22⋊C4—1724no—
814C22⋊C4—1724no—
815C22⋊C4—1724no—
816C22⋊C4—1724no—
817C42—44no—
818C42—1724no—
819C23—434no—
820C23—862no—
821C23—862no—
822C23—862no—
823C23—862no—
824C23—862no—
825C23—862no—
826C23—862no—
827C23—862no—
828C23—862no—
829C23—862no—
830C23—862no—
831C23—862no—
832C23—862no—
833C23—862no—
834C23—862no—
835C23—862no—
836C23—862no—
837C23—862no—
838C23—1721no—
839C23—1721no—
840C23—1721no—
841C23—1721no—
842C23—1721no—
843C23—1721no—
844C23—1721no—
845C23—1721no—
846C23—1721no—
847C23—1721no—
848C23—1721no—
849C23—1721no—
850C23—1721no—
851C23—1721no—
852C23—1721no—
853C23—1721no—
854C23C22×C4×D4311yescharacteristic
855C23C2×D4×D4311yescharacteristic
856C23C22×C22⋊D4311yescharacteristic
857C23C22×D17211yescharacteristic
858C23C2×Q8×D4311yescharacteristic
859C23#41×D4311yescharacteristic
860C23#41×D4311yescharacteristic
861C23#1306337011yescharacteristic
862C23#1306337011yescharacteristic
863C23#1306337011yescharacteristic
864C23#1306337111yescharacteristic
865C23#1306337211yescharacteristic
866C23#1306337311yescharacteristic
867C23#1306337311yescharacteristic
868C23#1306337311yescharacteristic
869Q8—17216no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
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—434no—
917C2×C4—862no—
918C2×C4—862no—
919C2×C4—862no—
920C2×C4—862no—
921C2×C4—862no—
922C2×C4—862no—
923C2×C4—862no—
924C2×C4—862no—
925C2×C4—862no—
926C2×C4—862no—
927C2×C4—862no—
928C2×C4—862no—
929C2×C4—862no—
930C2×C4—862no—
931C2×C4—862no—
932C2×C4—862no—
933C2×C4—862no—
934C2×C4—862no—
935C2×C4—17216no—
936C2×C4—1721no—
937C2×C4—1721no—
938C2×C4—1721no—
939C2×C4—1721no—
940C2×C4—1721no—
941C2×C4—1721no—
942C2×C4—1721no—
943C2×C4—1721no—
944C2×C4—1721no—
945C2×C4—1721no—
946C2×C4—1721no—
947C2×C4—1721no—
948C2×C4—1721no—
949C2×C4—1721no—
950C2×C4—1721no—
951C2×C4—1721no—
952C2×C4—1721no—
953C2×C4—1721no—
954C2×C4—1721no—
955C2×C4—1721no—
956C2×C4—1721no—
957C2×C4—1721no—
958C2×C4—1721no—
959C2×C4—1721no—
960C2×C4—1721no—
961C2×C4—1721no—
962C2×C4—1721no—
963C2×C4—1721no—
964C2×C4—1721no—
965C2×C4—1721no—
966C2×C4C2×(C2×D43)⋊C414yes—
967C2×C4C2×(C2×D43)⋊C414yes—
968C2×C4C2×(C2×D43)⋊C414yes—
969C22—864no—
970C22—864no—
971C22—864no—
972C22—1722no—
973C22—1722no—
974C22—1722no—
975C22—1722no—
976C22—1722no—
977C22—1722no—
978C22—1722no—
979C22—1722no—
980C22—1722no—
981C22—1722no—
982C22—1722no—
983C22—1722no—
984C22C22×(C2×D43)⋊C411yescharacteristic
985C22C4×D4×D4311yescharacteristic
986C22C4×Q8×D4311yescharacteristic
987C22#1458337111yescharacteristic
988C22#1458337511yescharacteristic
989C22#1458338011yescharacteristic
990C22#1458338011yescharacteristic
991C22#1458346611yescharacteristic
992C22#1458347311yescharacteristic
993C22#1458347411yescharacteristic
994C22#1458347611yescharacteristic
995C22#1458348011yescharacteristic
996C22#1458348011yescharacteristic
997C22#1458348111yescharacteristic
998C22#1458349711yescharacteristic
999C22#1458350811yescharacteristic
1000C22#1458351911yescharacteristic
1001C22#1458352411yescharacteristic
1002C22#1458352611yescharacteristic
1003C22D4×C22⋊D4311yescharacteristic
1004C22D4×D17211yescharacteristic
1005C22#1458353711yescharacteristic
1006C22#1458353811yescharacteristic
1007C22#1458354411yescharacteristic
1008C22#1458355611yescharacteristic
1009C22#1458356111yescharacteristic
1010C22Q8×C22⋊D4311yescharacteristic
1011C22#1458356411yescharacteristic
1012C22Q8×D17211yescharacteristic
1013C22#1458358111yescharacteristic
1014C22#1458360311yescharacteristic
1015C22#1458364411yescharacteristic
1016C22#1458364511yescharacteristic
1017C22#1458364811yescharacteristic
1018C22#1458365311yescharacteristic
1019C4—24no—
1020C4—24no—
1021C4—24no—
1022C4—42no—
1023C4—42no—
1024C4—81no—
1025C4—81no—
1026C4—864no—
1027C4—3441no—
1028C4—3441no—
1029C4—1722no—
1030C4—1722no—
1031C4—1722no—
1032C4—1722no—
1033C2—1724no—
1034C2#1913718811yescharacteristic
1035C2#1913727211yescharacteristic
1036C2#1913732911yescharacteristic
1037C2D4×(C2×D43)⋊C411yescharacteristic
1038C2Q8×(C2×D43)⋊C411yescharacteristic
1039C2#1913759711yescharacteristic
1040C2#1913775711yescharacteristic
1041C2#1914089011yescharacteristic
1042C2#1914090511yescharacteristic
1043C2#1914094211yescharacteristic
1044C2#1914096611yescharacteristic
1045C2#1914105511yescharacteristic
1046C2#1914108511yescharacteristic
1047C2#1914122111yescharacteristic
1048C2#1914125111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C43×#389C2
socle, cosocleC24×C43C24
prime radicalC24×D43C23
hypercenterC2×#389D43
hypocenterC43#14362
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
2. C2×#14582804C2semidirect
3. C2×#14582785C2semidirect
5. #19132865C2semidirect
6. #19132849C2semidirect
7. #19132845C2semidirect
8. #19132845C2semidirect
13. #19132828C2semidirect
15. C2×C43×#389C2semidirect
20. C2×#13063303C4semidirect
107. C2×(C2×D43)⋊C4Q8semidirect
282. C4⋊C4×C43C22⋊C4semidirect
511. C2×#389D43semidirect
582. C43#14362semidirect
810. C4⋊C4(C2×D43)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#130633032
C2×#145828042
C2×#145827852
C2×#145827562
#191328652
#191328492
#191328452
#191328372
#191328332
#191328312
#191328282
(C2×D43)⋊#952
C2×C43×#3892
#1436243