Finite Group Databasebeta

← #25020087

Subgroups — #25020087

Order 11008.

2574 conjugacy classes of subgroups.

The subgroup lattice has 1214 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063311C211yesmaximal, characteristic
2C22×C4×C22⋊D43C211yesmaximal, characteristic
3C2×#14582803C211yesmaximal, characteristic, complemented
4C2×#14582803C211yesmaximal, characteristic, complemented
5C2×#14582799C211yesmaximal, characteristic
6#19132844C211yesmaximal, characteristic, complemented
7#19132843C211yesmaximal, characteristic, complemented
8#19132843C211yesmaximal, characteristic, complemented
9#19132842C211yesmaximal, characteristic, complemented
10Dic43⋊#95C211yesmaximal, characteristic, complemented
11#19132818C211yesmaximal, characteristic, complemented
12(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
13(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
14#95×Dic43C211yesmaximal, characteristic, complemented
15C43×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×Dic86C2211yescharacteristic
17C23×C22⋊D43C2211yescharacteristic
18C23×C4×D43C2211yescharacteristic
19C2×#13063311—24no—
20C2×#13063311—24no—
21C2×#13063311C418yescomplemented
22C2×C4×C22⋊D43—24no—
23C2×C4×C22⋊D43—24no—
24C2×C4×C22⋊D43—24no—
25C22×Dic43⋊C4C2211yescharacteristic
26C22×Dic43⋊C4C2211yescharacteristic
27C22×C22⋊Dic43C2211yescharacteristic
28C22×C22⋊Dic43C2211yescharacteristic
29C22×C22⋊Dic43C2211yescharacteristic
30C22×(C2×D43)⋊C4C2211yescharacteristic
31C22×(C2×D43)⋊C4C2211yescharacteristic
32C22×(C2×D43)⋊C4C2211yescharacteristic
33C22×(C2×D43)⋊C4C2211yescharacteristic
34C22×(C2×D43)⋊C4C2211yescharacteristic
35C22×C4×Dic43C2211yescharacteristic
36C22×C4×Dic43C2211yescharacteristic
37C22×C4×Dic43C2211yescharacteristic
38#14582803—24no—
39#14582803—24no—
40#14582799—24no—
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
53C24×C4×C43C2211yescharacteristic
54C22×C22⋊C4×C43C2211yescharacteristic
55C22×C22⋊C4×C43C2211yescharacteristic
56C2×#95×C43C2211yescharacteristic
57C2×#95×C43C2211yescharacteristic
58C2×#95×C43C2211yescharacteristic
59C2×#95×C43C2211yescharacteristic
60C24×D43C2311yescharacteristic
61C22×Dic86—22no—
62C22×Dic86—22no—
63C22×Dic86—22no—
64C22×Dic86—22no—
65C22×Dic86—22no—
66C22×Dic86—22no—
67C22×Dic86C2×C414yescomplemented
68C22×C22⋊D43—22no—
69C22×C22⋊D43—22no—
70C22×C22⋊D43—22no—
71C22×C22⋊D43—22no—
72C22×C22⋊D43C2×C414yes—
73C22×C22⋊D43D414yes—
74C22×C22⋊D43D414yes—
75C23×Dic43C2311yescharacteristic
76C23×Dic43C2311yescharacteristic
77C23×Dic43C2311yescharacteristic
78C23×Dic43C2311yescharacteristic
79C23×Dic43C2311yescharacteristic
80C23×Dic43C2311yescharacteristic
81C23×Dic43C2311yescharacteristic
82C22×C4×D43—22no—
83C22×C4×D43—22no—
84C22×C4×D43—22no—
85C22×C4×D43—22no—
86C22×C4×D43—22no—
87C22×C4×D43—41no—
88C22×C4×D43—41no—
89#13063311—232no—
90C4×C22⋊D43—232no—
91C2×Dic43⋊C4—22no—
92C2×Dic43⋊C4—22no—
93C2×Dic43⋊C4—22no—
94C2×Dic43⋊C4—22no—
95C2×Dic43⋊C4—22no—
96C2×Dic43⋊C4D414yes—
97C2×C22⋊Dic43—22no—
98C2×C22⋊Dic43—22no—
99C2×C22⋊Dic43—22no—
100C2×C22⋊Dic43—22no—
101C2×C22⋊Dic43—22no—
102C2×C22⋊Dic43—22no—
103C2×C22⋊Dic43—22no—
104C2×C22⋊Dic43—41no—
105C2×C22⋊Dic43C2×C414yescomplemented
106C2×(C2×D43)⋊C4—22no—
107C2×(C2×D43)⋊C4—22no—
108C2×(C2×D43)⋊C4—22no—
109C2×(C2×D43)⋊C4—22no—
110C2×(C2×D43)⋊C4—22no—
111C2×(C2×D43)⋊C4—22no—
112C2×(C2×D43)⋊C4—22no—
113C2×(C2×D43)⋊C4—22no—
114C2×(C2×D43)⋊C4—22no—
115C2×(C2×D43)⋊C4—22no—
116C2×(C2×D43)⋊C4—22no—
117C2×(C2×D43)⋊C4—41no—
118C2×(C2×D43)⋊C4—41no—
119C2×(C2×D43)⋊C4C2×C414yescomplemented
120C2×(C2×D43)⋊C4C2×C414yescomplemented
121C2×C4×Dic43—22no—
122C2×C4×Dic43—22no—
123C2×C4×Dic43—22no—
124C2×C4×Dic43—22no—
125C2×C4×Dic43—22no—
126C2×C4×Dic43—22no—
127C2×C4×Dic43—22no—
128C2×C4×Dic43C2×C414yescomplemented
129C2×C4×Dic43D414yes—
130C43⋊#95—22no—
131C43⋊#95—22no—
132C43⋊#95—22no—
133C43⋊#95—22no—
134C43⋊#95—22no—
135C43⋊#95—22no—
136C43⋊#95—22no—
137C43⋊#95—22no—
138C43⋊#95—22no—
139C43⋊#95—41no—
140C43⋊#95—41no—
141C43⋊#95—41no—
142C25×C43C2311yescharacteristic
143C23×C4×C43—22no—
144C23×C4×C43—22no—
145C23×C4×C43—22no—
146C23×C4×C43—22no—
147C23×C4×C43—22no—
148C23×C4×C43—41no—
149C23×C4×C43—41no—
150C23×C4×C43C2311yescharacteristic
151C23×C4×C43C2311yescharacteristic
152C23×C4×C43C2311yescharacteristic
153C23×C4×C43C2311yescharacteristic
154C23×C4×C43C2311yescharacteristic
155C23×C4×C43C2311yescharacteristic
156C2×C22⋊C4×C43—22no—
157C2×C22⋊C4×C43—22no—
158C2×C22⋊C4×C43—22no—
159C2×C22⋊C4×C43—22no—
160C2×C22⋊C4×C43—41no—
161C2×C22⋊C4×C43C2×C414yescomplemented
162#95×C43—22no—
163#95×C43—22no—
164#95×C43—22no—
165#95×C43—41no—
166C24×C43—21no—
167C24×C43—21no—
168C24×C43—21no—
169C24×C43—21no—
170C24×C43—21no—
171C24×C43—21no—
172C24×C43—21no—
173C24×C43—21no—
174C24×C43—21no—
175C24×C43—21no—
176C24×C43—21no—
177C24×C43—21no—
178C24×C43C22×C412yes—
179C24×C43C2×D412yes—
180C24×C43C2×D412yes—
181C24×C43C2411yescharacteristic
182C23×D43—21no—
183C23×D43—21no—
184C23×D43—21no—
185C23×D43—21no—
186C23×D43—21no—
187C23×D43—21no—
188C23×D43—21no—
189C23×D43—21no—
190C23×D43—21no—
191C23×D43—21no—
192C23×D43—21no—
193C23×D43—21no—
194C23×D43C22×C412yes—
195C23×D43C2×D412yes—
196C23×D43C2×D412yes—
197C22×C4×C43—28no—
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×C43—21no—
210C22×C4×C43—21no—
211C22×C4×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43—21no—
215C22×C4×C43—21no—
216C22×C4×C43—21no—
217C22×C4×C43—21no—
218C22×C4×C43—21no—
219C22×C4×C43—21no—
220C22×C4×C43—21no—
221C22×C4×C43—21no—
222C22×C4×C43—21no—
223C22×C4×C43—21no—
224C22×C4×C43—21no—
225C22×C4×C43—21no—
226C22×C4×C43—21no—
227C22×C4×C43—21no—
228C22×C4×C43—21no—
229C22×C4×C43—21no—
230C22×C4×C43—21no—
231C22×C4×C43—21no—
232C22×C4×C43—21no—
233C22×C4×C43—44no—
234C22×C4×C43—44no—
235C22×C4×C43—44no—
236C22×C4×C43—44no—
237C22×C4×C43—44no—
238C22×C4×C43—44no—
239C22×C4×C43C22×C412yes—
240C22×C4×C43C22×C412yes—
241C22×C4×C43C2×D412yes—
242C22×C4×C43C2×D412yes—
243C22×C4×C43#4112yes—
244C22×C4×C43#4112yes—
245C22×C4×C43#4112yes—
246C2×C22⋊D43—28no—
247C2×C22⋊D43—28no—
248C2×C22⋊D43—28no—
249C2×C22⋊D43—28no—
250C2×C22⋊D43—28no—
251C2×C22⋊D43—28no—
252C2×C22⋊D43C22⋊C4116yes—
253C22×Dic43—21no—
254C22×Dic43—21no—
255C22×Dic43—21no—
256C22×Dic43—21no—
257C22×Dic43—21no—
258C22×Dic43—21no—
259C22×Dic43—21no—
260C22×Dic43—21no—
261C22×Dic43—21no—
262C22×Dic43—21no—
263C22×Dic43—21no—
264C22×Dic43—21no—
265C22×Dic43—21no—
266C22×Dic43—21no—
267C22×Dic43—21no—
268C22×Dic43—21no—
269C22×Dic43—21no—
270C22×Dic43—21no—
271C22×Dic43—21no—
272C22×Dic43—21no—
273C22×Dic43—21no—
274C22×Dic43—21no—
275C22×Dic43—21no—
276C22×Dic43—21no—
277C22×Dic43—21no—
278C22×Dic43—21no—
279C22×Dic43—21no—
280C22×Dic43—21no—
281C22×Dic43—21no—
282C22×Dic43—21no—
283C22×Dic43—21no—
284C22×Dic43—21no—
285C22×Dic43—21no—
286C22×Dic43—21no—
287C22×Dic43—21no—
288C22×Dic43—21no—
289C22×Dic43—21no—
290C22×Dic43C22×C412yes—
291C22×Dic43C22×C412yes—
292C22×Dic43C22×C412yes—
293C22×Dic43C2×D412yes—
294C22×Dic43C2×D412yes—
295C22×Dic43C2×D412yes—
296C22×Dic43C2×D412yes—
297C22×Dic43C2×D412yes—
298C22×Dic43C2×D412yes—
299C22×Dic43#4112yes—
300C22×Dic43#4112yes—
301C22×Dic43#4112yes—
302C2×C4×D43—28no—
303C2×C4×D43—44no—
304C2×C4×D43—44no—
305C2×C4×D43—44no—
306C2×C4×D43—44no—
307C2×C4×D43—44no—
308C2×C4×D43—44no—
309C2×Dic86—28no—
310C2×Dic86—28no—
311C2×Dic86—28no—
312C2×Dic86—44no—
313C2×Dic86—44no—
314C2×Dic86—44no—
315C2×Dic86—44no—
316C22⋊C4×C43—28no—
317C22⋊C4×C43—44no—
318C22⋊Dic43—28no—
319C22⋊Dic43—28no—
320C22⋊Dic43—44no—
321(C2×D43)⋊C4—28no—
322(C2×D43)⋊C4—28no—
323(C2×D43)⋊C4—28no—
324(C2×D43)⋊C4—44no—
325(C2×D43)⋊C4—44no—
326Dic43⋊C4—28no—
327Dic43⋊C4—44no—
328C4×Dic43—28no—
329C4×Dic43—28no—
330C4×Dic43—44no—
331C23×C43—22no—
332C23×C43—22no—
333C23×C43—22no—
334C23×C43—22no—
335C23×C43—22no—
336C23×C43—22no—
337C23×C43—22no—
338C23×C43—22no—
339C23×C43—22no—
340C23×C43—22no—
341C23×C43—22no—
342C23×C43—22no—
343C23×C43—22no—
344C23×C43—22no—
345C23×C43—22no—
346C23×C43—22no—
347C23×C43—22no—
348C23×C43—22no—
349C23×C43—41no—
350C23×C43—41no—
351C23×C43—41no—
352C23×C43—41no—
353C23×C43—41no—
354C23×C43—41no—
355C23×C43—41no—
356C23×C43—41no—
357C23×C43—41no—
358C23×C43—41no—
359C23×C43—41no—
360C23×C43—41no—
361C23×C43—41no—
362C23×C43—41no—
363C23×C43—41no—
364C23×C43—41no—
365C23×C43C2×C22⋊C414yes—
366C23×C43C23×C411yescharacteristic
367C23×C43C22×D411yescharacteristic
368C23×C43C22×D411yescharacteristic
369C23×C43C22×D411yescharacteristic
370C23×C43C22×D411yescharacteristic
371C23×C43C2×#4111yescharacteristic
372C23×C43C2×#4111yescharacteristic
373C23×C43C2×#4111yescharacteristic
374C23×C43C2×#4111yescharacteristic
375C23×C43C2×#4111yescharacteristic
376C23×C43C2×#4111yescharacteristic
377C23×C43H(5,𝔽2)11yescharacteristic
378C23×C43H(5,𝔽2)11yescharacteristic
379C23×C432−1+411yescharacteristic
380C23×C432−1+411yescharacteristic
381C22×D43—22no—
382C22×D43—22no—
383C22×D43—22no—
384C22×D43—22no—
385C22×D43—22no—
386C22×D43—22no—
387C22×D43—22no—
388C22×D43—22no—
389C22×D43—22no—
390C22×D43—22no—
391C22×D43—22no—
392C22×D43—22no—
393C22×D43—22no—
394C22×D43—22no—
395C22×D43—22no—
396C22×D43—22no—
397C22×D43—22no—
398C22×D43—22no—
399C22×D43—41no—
400C22×D43—41no—
401C22×D43—41no—
402C22×D43—41no—
403C22×D43—41no—
404C22×D43—41no—
405C22×D43—41no—
406C22×D43—41no—
407C22×D43—41no—
408C22×D43—41no—
409C22×D43—41no—
410C22×D43—41no—
411C22×D43—41no—
412C22×D43—41no—
413C22×D43—41no—
414C22×D43—41no—
415C22×D43C2×C22⋊C414yes—
416C2×C4×C43—22no—
417C2×C4×C43—22no—
418C2×C4×C43—22no—
419C2×C4×C43—22no—
420C2×C4×C43—22no—
421C2×C4×C43—22no—
422C2×C4×C43—22no—
423C2×C4×C43—22no—
424C2×C4×C43—22no—
425C2×C4×C43—22no—
426C2×C4×C43—22no—
427C2×C4×C43—22no—
428C2×C4×C43—22no—
429C2×C4×C43—22no—
430C2×C4×C43—22no—
431C2×C4×C43—22no—
432C2×C4×C43—22no—
433C2×C4×C43—22no—
434C2×C4×C43—416no—
435C2×C4×C43—41no—
436C2×C4×C43—41no—
437C2×C4×C43—41no—
438C2×C4×C43—41no—
439C2×C4×C43—41no—
440C2×C4×C43—41no—
441C2×C4×C43—41no—
442C2×C4×C43—41no—
443C2×C4×C43—41no—
444C2×C4×C43—41no—
445C2×C4×C43—41no—
446C2×C4×C43—41no—
447C2×C4×C43—41no—
448C2×C4×C43—41no—
449C2×C4×C43—41no—
450C2×C4×C43—41no—
451C2×C4×C43—41no—
452C2×C4×C43—41no—
453C2×C4×C43—41no—
454C2×C4×C43—41no—
455C2×C4×C43—41no—
456C2×C4×C43—41no—
457C2×C4×C43—41no—
458C2×C4×C43#12414yescomplemented
459C22⋊D43—232no—
460C2×Dic43—22no—
461C2×Dic43—22no—
462C2×Dic43—22no—
463C2×Dic43—22no—
464C2×Dic43—22no—
465C2×Dic43—22no—
466C2×Dic43—22no—
467C2×Dic43—22no—
468C2×Dic43—22no—
469C2×Dic43—22no—
470C2×Dic43—22no—
471C2×Dic43—22no—
472C2×Dic43—22no—
473C2×Dic43—22no—
474C2×Dic43—22no—
475C2×Dic43—41no—
476C2×Dic43—41no—
477C2×Dic43—41no—
478C2×Dic43—41no—
479C2×Dic43—41no—
480C2×Dic43—41no—
481C2×Dic43—41no—
482C2×Dic43—41no—
483C2×Dic43—41no—
484C2×Dic43—41no—
485C2×Dic43—41no—
486C2×Dic43—41no—
487C2×Dic43—41no—
488C2×Dic43—41no—
489C2×Dic43—41no—
490C2×Dic43—41no—
491C2×Dic43—41no—
492C2×Dic43—41no—
493C2×Dic43—41no—
494C2×Dic43—41no—
495C2×Dic43—41no—
496C2×Dic43—41no—
497C2×Dic43—41no—
498C2×Dic43—41no—
499C2×Dic43—41no—
500C2×Dic43—41no—
501C2×Dic43—41no—
502C2×Dic43C2×C22⋊C414yes—
503C2×Dic43C4×D414yes—
504C2×Dic43C4×D414yes—
505C2×Dic43#12014yes—
506C2×Dic43#12114yes—
507C2×Dic43#12114yes—
508C2×Dic43#12314yes—
509C4×D43—416no—
510Dic86—416no—
511#14027—431nomaximal, Sylow
512C22×C43—24no—
513C22×C43—24no—
514C22×C43—24no—
515C22×C43—42no—
516C22×C43—42no—
517C22×C43—42no—
518C22×C43—42no—
519C22×C43—42no—
520C22×C43—42no—
521C22×C43—42no—
522C22×C43—42no—
523C22×C43—42no—
524C22×C43—42no—
525C22×C43—42no—
526C22×C43—42no—
527C22×C43C22×C22⋊C411yescharacteristic
528C22×C43C2×C4×D411yescharacteristic
529C22×C43C2×C4×D411yescharacteristic
530C22×C43C4×#4111yescharacteristic
531C22×C43C4×#4111yescharacteristic
532C22×C43#52011yescharacteristic
533C22×C43#52011yescharacteristic
534C22×C43C2×#12011yescharacteristic
535C22×C43C2×#12111yescharacteristic
536C22×C43C2×#12111yescharacteristic
537C22×C43C2×#12311yescharacteristic
538C22×C43C2×#12411yescharacteristic
539C22×C43#52911yescharacteristic
540C22×C43#52911yescharacteristic
541C22×C43#53211yescharacteristic
542C22×C43#53511yescharacteristic
543C22×C43#53611yescharacteristic
544C22×C43#54211yescharacteristic
545C22×C43#54211yescharacteristic
546C22×C43#54611yescharacteristic
547C22×C43#54611yescharacteristic
548C22×C43#54611yescharacteristic
549C22×C43#54611yescharacteristic
550C22×C43#54611yescharacteristic
551C22×C43#54611yescharacteristic
552C22×C43#54711yescharacteristic
553C22×C43#54711yescharacteristic
554C22×C43#54711yescharacteristic
555C22×C43#54711yescharacteristic
556C22×C43#54811yescharacteristic
557C22×C43#54811yescharacteristic
558C22×C43#55611yescharacteristic
559C22×C43#55611yescharacteristic
560C22×C43#55911yescharacteristic
561C22×C43#55911yescharacteristic
562C2×D43—24no—
563C2×D43—24no—
564C2×D43—24no—
565C2×D43—42no—
566C2×D43—42no—
567C2×D43—42no—
568C2×D43—42no—
569C2×D43—42no—
570C2×D43—42no—
571C2×D43—42no—
572C2×D43—42no—
573C2×D43—42no—
574C2×D43—42no—
575C2×D43—42no—
576C2×D43—42no—
577C4×C43—24no—
578C4×C43—42no—
579C4×C43—42no—
580C4×C43—42no—
581C4×C43—42no—
582C4×C43—81no—
583Dic43—42no—
584Dic43—42no—
585Dic43—42no—
586Dic43—42no—
587Dic43—42no—
588Dic43—81no—
589Dic43#38618yes—
590C22×#124—431no—
591C22×C4×D4—431no—
592C2×#391—431no—
593C2×#391—431no—
594C2×#390—431no—
595#1440—431no—
596#1440—431no—
597#1440—431no—
598#1440—431no—
599C4⋊#95—431no—
600C22⋊#95—431no—
601C22⋊#95—431no—
602C22⋊#95—431no—
603C22⋊#95D4311yescharacteristic, complemented
604C4×#95—431no—
605C2×C43—44no—
606C2×C43C2×#38611yescharacteristic
607C2×C43C4×#12411yescharacteristic
608C2×C43#232611yescharacteristic
609C2×C43#233911yescharacteristic
610C2×C43#233911yescharacteristic
611C2×C43#236711yescharacteristic
612C2×C43#236711yescharacteristic
613C2×C43#242711yescharacteristic
614C2×C43#242711yescharacteristic
615C2×C43#243211yescharacteristic
616C2×C43#243511yescharacteristic
617C2×C43#244711yescharacteristic
618C2×C43#244711yescharacteristic
619C2×C43#254411yescharacteristic
620C2×C43#254711yescharacteristic
621D43—44no—
622C23×Q8—431no—
623C23×D4—431no—
624C24×C4—431no—
625C24×C4C2×D4311yescharacteristic
626C2×#124—438no—
627C2×#124—864no—
628C2×#124—864no—
629C2×C4×D4—864no—
630C2×C4×D4—864no—
631C2×C4×D4—864no—
632C22×C4⋊C4—431no—
633C22×C4⋊C4—431no—
634C22×C22⋊C4—431no—
635C22×C22⋊C4—431no—
636C22×C22⋊C4—431no—
637C22×C22⋊C4—431no—
638C22×C22⋊C4—431no—
639C22×C22⋊C4—431no—
640C22×C22⋊C4—431no—
641C22×C22⋊C4—431no—
642C22×C22⋊C4C2×D4311yescharacteristic
643C22×C22⋊C4C2×D4311yescharacteristic
644C22×C42—431no—
645C22×C42—431no—
646C22×C42—431no—
647#391—864no—
648#391—864no—
649#390—864no—
650C2×#95—431no—
651C2×#95—431no—
652C2×#95—431no—
653C2×#95—431no—
654C2×#95—431no—
655C2×#95—431no—
656C2×#95—431no—
657C2×#95—431no—
658C2×#95—431no—
659C2×#95—431no—
660C2×#95—431no—
661C2×#95—431no—
662C2×#95C2×D4311yescharacteristic
663C2×#95C2×D4311yescharacteristic
664C2×#95C2×D4311yescharacteristic
665C2×#95C2×D4311yescharacteristic
666C43#1402711yescharacteristic, complemented, Sylow
667C25—431no—
668C25C22×D4311yescharacteristic
669C22×Q8—434no—
670C22×Q8—862no—
671C22×Q8—862no—
672C22×Q8—862no—
673C22×Q8—862no—
674C22×Q8—862no—
675C22×Q8—862no—
676C22×D4—434no—
677C22×D4—434no—
678C22×D4—434no—
679C22×D4—862no—
680C22×D4—862no—
681C22×D4—862no—
682C22×D4—862no—
683C23×C4—22no—
684C23×C4—22no—
685C23×C4—22no—
686C23×C4—22no—
687C23×C4—22no—
688C23×C4—41no—
689C23×C4—41no—
690C23×C4—431no—
691C23×C4—431no—
692C23×C4—431no—
693C23×C4—431no—
694C23×C4—431no—
695C23×C4—431no—
696C23×C4—431no—
697C23×C4—862no—
698C23×C4—862no—
699C23×C4—862no—
700C23×C4—862no—
701C23×C4—862no—
702C23×C4—1721no—
703C23×C4—1721no—
704C23×C4C22×D4311yescharacteristic
705C23×C4C22×D4311yescharacteristic
706C23×C4C22×D4311yescharacteristic
707C23×C4C22×D4311yescharacteristic
708C23×C4C22×D4311yescharacteristic
709C23×C4C22×D4311yescharacteristic
710#124—8632no—
711C4×D4—8632no—
712C2×C4⋊C4—434no—
713C2×C4⋊C4—862no—
714C2×C4⋊C4—862no—
715C2×C4⋊C4—862no—
716C2×C4⋊C4—862no—
717C2×C4⋊C4—862no—
718C2×C22⋊C4—22no—
719C2×C22⋊C4—22no—
720C2×C22⋊C4—22no—
721C2×C22⋊C4—22no—
722C2×C22⋊C4—41no—
723C2×C22⋊C4—434no—
724C2×C22⋊C4—434no—
725C2×C22⋊C4—434no—
726C2×C22⋊C4—862no—
727C2×C22⋊C4—862no—
728C2×C22⋊C4—862no—
729C2×C22⋊C4—862no—
730C2×C22⋊C4—862no—
731C2×C22⋊C4—862no—
732C2×C22⋊C4—862no—
733C2×C22⋊C4—862no—
734C2×C22⋊C4—862no—
735C2×C22⋊C4—862no—
736C2×C22⋊C4—862no—
737C2×C22⋊C4—862no—
738C2×C22⋊C4—862no—
739C2×C22⋊C4—862no—
740C2×C22⋊C4—862no—
741C2×C22⋊C4—862no—
742C2×C22⋊C4—862no—
743C2×C22⋊C4—862no—
744C2×C22⋊C4—1721no—
745C2×C22⋊C4—1721no—
746C2×C22⋊C4—1721no—
747C2×C22⋊C4C4×D4314yescomplemented
748C2×C42—434no—
749C2×C42—434no—
750C2×C42—862no—
751C2×C42—862no—
752C2×C42—862no—
753C2×C42—862no—
754C2×C42—862no—
755C2×C42—862no—
756C2×C42—862no—
757#95—22no—
758#95—22no—
759#95—22no—
760#95—41no—
761#95—862no—
762#95—862no—
763#95—862no—
764#95—862no—
765#95—862no—
766#95—862no—
767#95—862no—
768#95—862no—
769#95—862no—
770#95—1721no—
771#95—1721no—
772#95—1721no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24—21no—
777C24—21no—
778C24—21no—
779C24—21no—
780C24—21no—
781C24—21no—
782C24—21no—
783C24—21no—
784C24—21no—
785C24—432no—
786C24—432no—
787C24—432no—
788C24—861no—
789C24—861no—
790C24—861no—
791C24—861no—
792C24—861no—
793C24—861no—
794C24—861no—
795C24—861no—
796C24—861no—
797C24—861no—
798C24—861no—
799C24—861no—
800C24C2×C4×D4312yes—
801C24D4×D4312yes—
802C24D4×D4312yes—
803C24C23×D4311yescharacteristic
804C2×Q8—868no—
805C2×Q8—868no—
806C2×Q8—868no—
807C2×Q8—1724no—
808C2×Q8—1724no—
809C2×Q8—1724no—
810C2×Q8—1724no—
811C2×D4—4316no—
812C2×D4—868no—
813C2×D4—868no—
814C2×D4—868no—
815C2×D4—868no—
816C2×D4—868no—
817C2×D4—868no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—28no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—44no—
855C22×C4—44no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4—44no—
859C22×C4—44no—
860C22×C4—432no—
861C22×C4—432no—
862C22×C4—432no—
863C22×C4—432no—
864C22×C4—432no—
865C22×C4—432no—
866C22×C4—432no—
867C22×C4—432no—
868C22×C4—432no—
869C22×C4—432no—
870C22×C4—432no—
871C22×C4—432no—
872C22×C4—868no—
873C22×C4—861no—
874C22×C4—861no—
875C22×C4—861no—
876C22×C4—861no—
877C22×C4—861no—
878C22×C4—861no—
879C22×C4—861no—
880C22×C4—861no—
881C22×C4—861no—
882C22×C4—861no—
883C22×C4—861no—
884C22×C4—861no—
885C22×C4—861no—
886C22×C4—861no—
887C22×C4—861no—
888C22×C4—861no—
889C22×C4—861no—
890C22×C4—861no—
891C22×C4—861no—
892C22×C4—861no—
893C22×C4—861no—
894C22×C4—861no—
895C22×C4—861no—
896C22×C4—861no—
897C22×C4—861no—
898C22×C4—861no—
899C22×C4—861no—
900C22×C4—861no—
901C22×C4—861no—
902C22×C4—861no—
903C22×C4—861no—
904C22×C4—861no—
905C22×C4—861no—
906C22×C4—861no—
907C22×C4—861no—
908C22×C4—861no—
909C22×C4—861no—
910C22×C4—1724no—
911C22×C4—1724no—
912C22×C4—1724no—
913C22×C4—1724no—
914C22×C4—1724no—
915C22×C4—1724no—
916C22×C4C2×C4×D4312yes—
917C22×C4C2×C4×D4312yes—
918C22×C4#1062189812yes—
919C22×C4#1062189812yes—
920C22×C4D4×D4312yes—
921C22×C4D4×D4312yes—
922C22×C4#1062190012yes—
923C4⋊C4—868no—
924C4⋊C4—1724no—
925C22⋊C4—28no—
926C22⋊C4—44no—
927C22⋊C4—868no—
928C22⋊C4—868no—
929C22⋊C4—868no—
930C22⋊C4—868no—
931C22⋊C4—868no—
932C22⋊C4—1724no—
933C22⋊C4—1724no—
934C22⋊C4—1724no—
935C42—868no—
936C42—868no—
937C42—1724no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—434no—
973C23—862no—
974C23—862no—
975C23—862no—
976C23—862no—
977C23—862no—
978C23—862no—
979C23—862no—
980C23—862no—
981C23—862no—
982C23—862no—
983C23—862no—
984C23—862no—
985C23—862no—
986C23—862no—
987C23—862no—
988C23—862no—
989C23—862no—
990C23—862no—
991C23—1721no—
992C23—1721no—
993C23—1721no—
994C23—1721no—
995C23—1721no—
996C23—1721no—
997C23—1721no—
998C23—1721no—
999C23—1721no—
1000C23—1721no—
1001C23—1721no—
1002C23—1721no—
1003C23—1721no—
1004C23—1721no—
1005C23—1721no—
1006C23—1721no—
1007C23C22⋊C4×D4314yes—
1008C23C22×C4×D4311yescharacteristic
1009C23C2×D4×D4311yescharacteristic
1010C23C2×D4×D4311yescharacteristic
1011C23C2×D4×D4311yescharacteristic
1012C23C2×D4×D4311yescharacteristic
1013C23#41×D4311yescharacteristic
1014C23#41×D4311yescharacteristic
1015C23#41×D4311yescharacteristic
1016C23C2×#1062190011yescharacteristic
1017C23C2×#1062189811yescharacteristic
1018C23C2×#1062189811yescharacteristic
1019C23#1306337011yescharacteristic
1020C23#1306337011yescharacteristic
1021C23#1306337211yescharacteristic
1022C23#1306337311yescharacteristic
1023Q8—17216no—
1024D4—8632no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—416no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—434no—
1068C2×C4—434no—
1069C2×C4—434no—
1070C2×C4—434no—
1071C2×C4—434no—
1072C2×C4—434no—
1073C2×C4—434no—
1074C2×C4—862no—
1075C2×C4—862no—
1076C2×C4—862no—
1077C2×C4—862no—
1078C2×C4—862no—
1079C2×C4—862no—
1080C2×C4—862no—
1081C2×C4—862no—
1082C2×C4—862no—
1083C2×C4—862no—
1084C2×C4—862no—
1085C2×C4—862no—
1086C2×C4—862no—
1087C2×C4—862no—
1088C2×C4—862no—
1089C2×C4—17216no—
1090C2×C4—1721no—
1091C2×C4—1721no—
1092C2×C4—1721no—
1093C2×C4—1721no—
1094C2×C4—1721no—
1095C2×C4—1721no—
1096C2×C4—1721no—
1097C2×C4—1721no—
1098C2×C4—1721no—
1099C2×C4—1721no—
1100C2×C4—1721no—
1101C2×C4—1721no—
1102C2×C4—1721no—
1103C2×C4—1721no—
1104C2×C4—1721no—
1105C2×C4—1721no—
1106C2×C4—1721no—
1107C2×C4—1721no—
1108C2×C4—1721no—
1109C2×C4—1721no—
1110C2×C4—1721no—
1111C2×C4—1721no—
1112C2×C4—1721no—
1113C2×C4—1721no—
1114C2×C4—1721no—
1115C2×C4—1721no—
1116C2×C4—1721no—
1117C2×C4#1306331114yescomplemented
1118C22—24no—
1119C22—24no—
1120C22—24no—
1121C22—42no—
1122C22—42no—
1123C22—42no—
1124C22—42no—
1125C22—42no—
1126C22—42no—
1127C22—42no—
1128C22—42no—
1129C22—42no—
1130C22—42no—
1131C22—42no—
1132C22—42no—
1133C22—864no—
1134C22—864no—
1135C22—864no—
1136C22—1722no—
1137C22—1722no—
1138C22—1722no—
1139C22—1722no—
1140C22—1722no—
1141C22—1722no—
1142C22—1722no—
1143C22—1722no—
1144C22—1722no—
1145C22—1722no—
1146C22—1722no—
1147C22—1722no—
1148C22C2×C22⋊C4×D4311yescharacteristic
1149C22C4×D4×D4311yescharacteristic
1150C22C4×D4×D4311yescharacteristic
1151C22C4×#1062190011yescharacteristic
1152C22C4×#1062189811yescharacteristic
1153C22#1458337811yescharacteristic
1154C22#1458338011yescharacteristic
1155C22#120×D4311yescharacteristic
1156C22#121×D4311yescharacteristic
1157C22#121×D4311yescharacteristic
1158C22#123×D4311yescharacteristic
1159C22C2×#1306331111yescharacteristic
1160C22#1458342711yescharacteristic
1161C22#1458342911yescharacteristic
1162C22#1458344611yescharacteristic
1163C22#1458346411yescharacteristic
1164C22#1458347211yescharacteristic
1165C22#1458351711yescharacteristic
1166C22#1458351911yescharacteristic
1167C22#1458353611yescharacteristic
1168C22#1458353611yescharacteristic
1169C22#1458353811yescharacteristic
1170C22#1458353911yescharacteristic
1171C22#1458353911yescharacteristic
1172C22#1458353911yescharacteristic
1173C22#1458354711yescharacteristic
1174C22#1458354911yescharacteristic
1175C22#1458355011yescharacteristic
1176C22#1458355011yescharacteristic
1177C22#1458355811yescharacteristic
1178C22#1458355911yescharacteristic
1179C22#1458361711yescharacteristic
1180C22#1458362011yescharacteristic
1181C22#1458363211yescharacteristic
1182C22#1458363311yescharacteristic
1183C4—24no—
1184C4—42no—
1185C4—42no—
1186C4—42no—
1187C4—42no—
1188C4—81no—
1189C4—438no—
1190C4—3441no—
1191C4—1722no—
1192C4—1722no—
1193C4—1722no—
1194C4—1722no—
1195C4—1722no—
1196C2—44no—
1197C2—1724no—
1198C2#386×D4311yescharacteristic
1199C2C4×#1306331111yescharacteristic
1200C2#1913730111yescharacteristic
1201C2#1913742111yescharacteristic
1202C2#1913742211yescharacteristic
1203C2#1913766311yescharacteristic
1204C2#1913766711yescharacteristic
1205C2#1913816911yescharacteristic
1206C2#1913817111yescharacteristic
1207C2#1913822111yescharacteristic
1208C2#1913824411yescharacteristic
1209C2#1913837911yescharacteristic
1210C2#1913838111yescharacteristic
1211C2#1913956411yescharacteristic
1212C2#1913958911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×C22⋊#95C2
socle, cosocleC24×C43C24
prime radicalC23×C22⋊D43C22
hypercenterC22⋊#95D43
hypocenterC43#14027
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×#14582803C2semidirect
4. C2×#14582803C2semidirect
6. #19132844C2semidirect
7. #19132843C2semidirect
8. #19132843C2semidirect
9. #19132842C2semidirect
10. Dic43⋊#95C2semidirect
11. #19132818C2semidirect
12. (C2×D43)⋊#95C2semidirect
13. (C2×D43)⋊#95C2semidirect
14. #95×Dic43C2semidirect
15. C43×C22⋊#95C2semidirect
21. C2×#13063311C4semidirect
67. C22×Dic86C2×C4semidirect
105. C2×C22⋊Dic43C2×C4semidirect
119. C2×(C2×D43)⋊C4C2×C4semidirect
120. C2×(C2×D43)⋊C4C2×C4semidirect
128. C2×C4×Dic43C2×C4semidirect
161. C2×C22⋊C4×C43C2×C4semidirect
458. C2×C4×C43#124semidirect
603. C22⋊#95D43semidirect
666. C43#14027semidirect
747. C2×C22⋊C4C4×D43semidirect
1117. C2×C4#13063311semidirect

Maximal subgroups

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

subgroupindex
C22×#130633112
C22×C4×C22⋊D432
C2×#145828032
C2×#145827992
#191328442
#191328432
#191328422
Dic43⋊#952
#191328182
(C2×D43)⋊#952
#95×Dic432
C43×C22⋊#952
#1402743