Finite Group Databasebeta

← #25019923

Subgroups — #25019923

Order 11008.

2046 conjugacy classes of subgroups.

The subgroup lattice has 1174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582799C211yesmaximal, characteristic
2C2×#14582790C211yesmaximal, characteristic, complemented
3C2×#14582787C211yesmaximal, characteristic, complemented
4C2×#14582775C211yesmaximal, characteristic
5C2×#14582756C211yesmaximal, characteristic, complemented
6C2×#14582746C211yesmaximal, characteristic, complemented
7#19132858C211yesmaximal, characteristic, complemented
8#19132843C211yesmaximal, characteristic, complemented
9#19132840C211yesmaximal, characteristic, complemented
10#19132834C211yesmaximal, characteristic
11#19132832C211yesmaximal, characteristic, complemented
12#19132829C211yesmaximal, characteristic, complemented
13#19132826C211yesmaximal, characteristic, complemented
14C4×C43⋊#95C211yesmaximal, characteristic, complemented
15C2×C43×#388C211yesmaximal, characteristic, complemented
16C23×C22⋊D43C2211yescharacteristic
17C23×C4×D43C2211yescharacteristic
18C22×C4⋊Dic43C2211yescharacteristic
19C22×Dic43⋊C4C2211yescharacteristic
20C22×Dic43⋊C4C2211yescharacteristic
21C22×C22⋊Dic43C2211yescharacteristic
22C22×C22⋊Dic43C2211yescharacteristic
23C22×C22⋊Dic43C2211yescharacteristic
24C22×(C2×D43)⋊C4C2211yescharacteristic
25C22×(C2×D43)⋊C4C2211yescharacteristic
26C22×(C2×D43)⋊C4C2211yescharacteristic
27C22×(C2×D43)⋊C4C2211yescharacteristic
28C22×(C2×D43)⋊C4C2211yescharacteristic
29C22×C4×Dic43C2211yescharacteristic
30C22×C4×Dic43C2211yescharacteristic
31C22×C4×Dic43C2211yescharacteristic
32#14582799—24no—
33#14582790—24no—
34#14582787—24no—
35#14582775C418yescomplemented
36#14582756—24no—
37#14582746—24no—
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×C22⋊C4×C43C2211yescharacteristic
52C22×C22⋊C4×C43C2211yescharacteristic
53C22×C22⋊C4×C43C2211yescharacteristic
54C22×C42×C43C2211yescharacteristic
55C43×#388—24no—
56C2×#95×C43C2211yescharacteristic
57C2×#95×C43C2211yescharacteristic
58C24×D43C2311yescharacteristic
59C22×C22⋊D43—22no—
60C22×C22⋊D43—22no—
61C22×C22⋊D43—22no—
62C22×C22⋊D43—22no—
63C22×C22⋊D43—41no—
64C22×C22⋊D43—41no—
65C22×C22⋊D43C2×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—
80C2×C4⋊Dic43—22no—
81C2×C4⋊Dic43—22no—
82C2×C4⋊Dic43—41no—
83C2×Dic43⋊C4—22no—
84C2×Dic43⋊C4—22no—
85C2×Dic43⋊C4—22no—
86C2×Dic43⋊C4—22no—
87C2×Dic43⋊C4—41no—
88C2×Dic43⋊C4—41no—
89C2×C22⋊Dic43—22no—
90C2×C22⋊Dic43—22no—
91C2×C22⋊Dic43—22no—
92C2×C22⋊Dic43—22no—
93C2×C22⋊Dic43—22no—
94C2×C22⋊Dic43—41no—
95C2×C22⋊Dic43—41no—
96C2×C22⋊Dic43—41no—
97C2×C22⋊Dic43C2×C414yes—
98C2×(C2×D43)⋊C4—22no—
99C2×(C2×D43)⋊C4—22no—
100C2×(C2×D43)⋊C4—22no—
101C2×(C2×D43)⋊C4—22no—
102C2×(C2×D43)⋊C4—22no—
103C2×(C2×D43)⋊C4—22no—
104C2×(C2×D43)⋊C4—22no—
105C2×(C2×D43)⋊C4—22no—
106C2×(C2×D43)⋊C4—22no—
107C2×(C2×D43)⋊C4—22no—
108C2×(C2×D43)⋊C4—22no—
109C2×(C2×D43)⋊C4—41no—
110C2×(C2×D43)⋊C4—41no—
111C2×(C2×D43)⋊C4C2×C414yes—
112C2×(C2×D43)⋊C4D414yes—
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—41no—
120C2×C4×Dic43—41no—
121C2×C4×Dic43—41no—
122C43⋊#95—22no—
123C43⋊#95—22no—
124C43⋊#95—22no—
125C43⋊#95—22no—
126C43⋊#95—22no—
127C43⋊#95—22no—
128C43⋊#95—22no—
129C43⋊#95—22no—
130C43⋊#95—41no—
131C43⋊#95C2×C414yes—
132C43⋊#95C2×C414yes—
133C43⋊#95D414yescomplemented
134C25×C43C2311yescharacteristic
135C23×C4×C43C2311yescharacteristic
136C23×C4×C43C2311yescharacteristic
137C23×C4×C43C2311yescharacteristic
138C23×C4×C43C2311yescharacteristic
139C23×C4×C43C2311yescharacteristic
140C23×C4×C43C2311yescharacteristic
141C2×C4⋊C4×C43—22no—
142C2×C4⋊C4×C43—22no—
143C2×C4⋊C4×C43—41no—
144C2×C22⋊C4×C43—22no—
145C2×C22⋊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—41no—
152C2×C22⋊C4×C43C2×C414yes—
153C2×C42×C43—22no—
154C2×C42×C43—22no—
155C2×C42×C43—22no—
156#95×C43—22no—
157#95×C43D414yescomplemented
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×C43—21no—
171C24×C43—21no—
172C24×C43C22×C412yes—
173C24×C43C2411yescharacteristic
174C23×D43—21no—
175C23×D43—21no—
176C23×D43—21no—
177C23×D43—21no—
178C23×D43—21no—
179C23×D43—21no—
180C23×D43—21no—
181C23×D43—21no—
182C23×D43—21no—
183C23×D43—21no—
184C23×D43—21no—
185C23×D43—21no—
186C23×D43C22×C412yes—
187C23×D43C2×D412yes—
188C23×D43#4112yes—
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×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×C43C22×C412yes—
223C22×C4×C43C22×C412yes—
224C22×C4×C43C2×D412yes—
225C22×C4×C43C2×D412yes—
226C22×C4×C43C2×D412yes—
227C22×C4×C43C2×D412yes—
228C22×C4×C43C2×D412yes—
229C22×C4×C43#4112yes—
230C22×C4×C43#4112yes—
231C2×C22⋊D43—28no—
232C2×C22⋊D43—28no—
233C2×C22⋊D43—44no—
234C2×C22⋊D43—44no—
235C2×C22⋊D43—44no—
236C2×C22⋊D43—44no—
237C2×C22⋊D43—44no—
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—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×Dic43C22×C412yes—
278C22×Dic43C22×C412yes—
279C22×Dic43C22×C412yes—
280C22×Dic43C2×D412yes—
281C22×Dic43C2×D412yes—
282C22×Dic43C2×D412yes—
283C22×Dic43#4112yes—
284C22×Dic43#4112yes—
285C22×Dic43#4112yes—
286C22×Dic43#4112yes—
287C2×C4×D43—28no—
288C2×C4×D43—28no—
289C2×C4×D43—44no—
290C2×C4×D43—44no—
291C2×C4×D43—44no—
292C2×C4×D43—44no—
293C2×C4×D43—44no—
294C4⋊C4×C43—44no—
295C22⋊C4×C43—28no—
296C22⋊C4×C43—44no—
297C22⋊C4×C43—44no—
298C42×C43—44no—
299C22⋊Dic43—28no—
300C22⋊Dic43—44no—
301C22⋊Dic43—44no—
302(C2×D43)⋊C4—28no—
303(C2×D43)⋊C4—28no—
304(C2×D43)⋊C4—28no—
305(C2×D43)⋊C4—44no—
306(C2×D43)⋊C4—44no—
307C4⋊Dic43—44no—
308Dic43⋊C4—44no—
309Dic43⋊C4—44no—
310C4×Dic43—44no—
311C4×Dic43—44no—
312C4×Dic43—44no—
313C23×C43—22no—
314C23×C43—22no—
315C23×C43—22no—
316C23×C43—22no—
317C23×C43—22no—
318C23×C43—22no—
319C23×C43—22no—
320C23×C43—41no—
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×C43—41no—
338C23×C43—41no—
339C23×C43—41no—
340C23×C43—41no—
341C23×C43—41no—
342C23×C43—41no—
343C23×C43—41no—
344C23×C43—41no—
345C23×C43—41no—
346C23×C43—41no—
347C23×C43—41no—
348C23×C43C23×C411yescharacteristic
349C23×C43C22×D411yescharacteristic
350C23×C43C22×D411yescharacteristic
351C23×C43C22×D411yescharacteristic
352C23×C43C2×#4111yescharacteristic
353C23×C43C2×#4111yescharacteristic
354C23×C43C2×#4111yescharacteristic
355C23×C43C2×#4111yescharacteristic
356C23×C43C2×#4111yescharacteristic
357C23×C43C2×#4111yescharacteristic
358C23×C43C2×#4111yescharacteristic
359C23×C43H(5,𝔽2)11yescharacteristic
360C23×C43H(5,𝔽2)11yescharacteristic
361C23×C43H(5,𝔽2)11yescharacteristic
362C23×C432−1+411yescharacteristic
363C22×D43—22no—
364C22×D43—22no—
365C22×D43—22no—
366C22×D43—22no—
367C22×D43—22no—
368C22×D43—22no—
369C22×D43—22no—
370C22×D43—22no—
371C22×D43—22no—
372C22×D43—22no—
373C22×D43—22no—
374C22×D43—22no—
375C22×D43—22no—
376C22×D43—22no—
377C22×D43—22no—
378C22×D43—22no—
379C22×D43—22no—
380C22×D43—22no—
381C22×D43—41no—
382C22×D43—41no—
383C22×D43—41no—
384C22×D43—41no—
385C22×D43—41no—
386C22×D43—41no—
387C22×D43—41no—
388C22×D43—41no—
389C22×D43—41no—
390C22×D43—41no—
391C22×D43—41no—
392C22×D43—41no—
393C22×D43—41no—
394C22×D43—41no—
395C22×D43—41no—
396C22×D43—41no—
397C22×D43C4×D414yes—
398C2×C4×C43—22no—
399C2×C4×C43—22no—
400C2×C4×C43—22no—
401C2×C4×C43—22no—
402C2×C4×C43—22no—
403C2×C4×C43—22no—
404C2×C4×C43—22no—
405C2×C4×C43—22no—
406C2×C4×C43—22no—
407C2×C4×C43—22no—
408C2×C4×C43—22no—
409C2×C4×C43—22no—
410C2×C4×C43—22no—
411C2×C4×C43—22no—
412C2×C4×C43—22no—
413C2×C4×C43—22no—
414C2×C4×C43—22no—
415C2×C4×C43—22no—
416C2×C4×C43—22no—
417C2×C4×C43—22no—
418C2×C4×C43—22no—
419C2×C4×C43—41no—
420C2×C4×C43—41no—
421C2×C4×C43—41no—
422C2×C4×C43—41no—
423C2×C4×C43—41no—
424C2×C4×C43—41no—
425C2×C4×C43—41no—
426C2×C4×C43—41no—
427C2×C4×C43—41no—
428C2×C4×C43—41no—
429C2×C4×C43—41no—
430C2×C4×C43—41no—
431C2×C4×C43—41no—
432C2×C4×C43—41no—
433C2×C4×C43—41no—
434C2×C4×C43—41no—
435C2×C4×C43—41no—
436C2×C4×C43—41no—
437C2×C4×C43—41no—
438C2×C4×C43C4×D414yes—
439C2×C4×C43#12114yes—
440C22⋊D43—416no—
441C2×Dic43—22no—
442C2×Dic43—22no—
443C2×Dic43—22no—
444C2×Dic43—22no—
445C2×Dic43—22no—
446C2×Dic43—22no—
447C2×Dic43—22no—
448C2×Dic43—22no—
449C2×Dic43—22no—
450C2×Dic43—22no—
451C2×Dic43—22no—
452C2×Dic43—22no—
453C2×Dic43—22no—
454C2×Dic43—22no—
455C2×Dic43—22no—
456C2×Dic43—22no—
457C2×Dic43—22no—
458C2×Dic43—22no—
459C2×Dic43—22no—
460C2×Dic43—22no—
461C2×Dic43—22no—
462C2×Dic43—22no—
463C2×Dic43—22no—
464C2×Dic43—22no—
465C2×Dic43—41no—
466C2×Dic43—41no—
467C2×Dic43—41no—
468C2×Dic43—41no—
469C2×Dic43—41no—
470C2×Dic43—41no—
471C2×Dic43—41no—
472C2×Dic43—41no—
473C2×Dic43—41no—
474C2×Dic43—41no—
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#11714yes—
489C2×Dic43C4×D414yes—
490C4×D43—416no—
491#14012—431nomaximal, Sylow
492C22×C43—42no—
493C22×C43—42no—
494C22×C43—42no—
495C22×C43—42no—
496C22×C43—42no—
497C22×C43—42no—
498C22×C43—42no—
499C22×C43—81no—
500C22×C43—81no—
501C22×C43—81no—
502C22×C43—81no—
503C22×C43—81no—
504C22×C43—81no—
505C22×C43—81no—
506C22×C43—81no—
507C22×C43C2×#11711yescharacteristic
508C22×C43C2×C4×D411yescharacteristic
509C22×C43C2×C4×D411yescharacteristic
510C22×C43C2×C4×D411yescharacteristic
511C22×C43C4×#4111yescharacteristic
512C22×C43#51811yescharacteristic
513C22×C43#52011yescharacteristic
514C22×C43C2×#12111yescharacteristic
515C22×C43#52511yescharacteristic
516C22×C43#52911yescharacteristic
517C22×C43#52911yescharacteristic
518C22×C43#52911yescharacteristic
519C22×C43#53211yescharacteristic
520C22×C43#53211yescharacteristic
521C22×C43#53211yescharacteristic
522C22×C43#53811yescharacteristic
523C22×C43#53911yescharacteristic
524C22×C43#54011yescharacteristic
525C22×C43#54211yescharacteristic
526C22×C43D4211yescharacteristic
527C22×C43D4211yescharacteristic
528C22×C43#54611yescharacteristic
529C22×C43#54611yescharacteristic
530C22×C43#54611yescharacteristic
531C22×C43#54611yescharacteristic
532C22×C43#54711yescharacteristic
533C22×C43#54711yescharacteristic
534C22×C43#54811yescharacteristic
535C22×C43#55011yescharacteristic
536C22×C43#55111yescharacteristic
537C22×C43#55111yescharacteristic
538C22×C43#55111yescharacteristic
539C22×C43#55311yescharacteristic
540C22×C43#55511yescharacteristic
541C22×C43#55611yescharacteristic
542C2×D43—24no—
543C2×D43—24no—
544C2×D43—24no—
545C2×D43—42no—
546C2×D43—42no—
547C2×D43—42no—
548C2×D43—42no—
549C2×D43—42no—
550C2×D43—42no—
551C2×D43—42no—
552C2×D43—42no—
553C2×D43—42no—
554C2×D43—42no—
555C2×D43—42no—
556C2×D43—42no—
557C4×C43—24no—
558C4×C43—24no—
559C4×C43—42no—
560C4×C43—42no—
561C4×C43—42no—
562C4×C43—81no—
563Dic43—24no—
564Dic43—24no—
565Dic43—42no—
566Dic43—42no—
567Dic43—42no—
568Dic43—42no—
569Dic43—81no—
570C2×#390—431no—
571C2×#388—431no—
572C2×#388—431no—
573C2×#388D4311yescharacteristic, complemented
574C2×#386—431no—
575C2×#380—431no—
576C2×C4×C22⋊C4—431no—
577#1444—431no—
578#1440—431no—
579#1439—431no—
580#1438—431no—
581#1437—431no—
582#1436—431no—
583#1436—431no—
584C4×#95—431no—
585C2×C43—82no—
586C2×C43#229311yescharacteristic
587C2×C43C4×#12111yescharacteristic
588C2×C43#233511yescharacteristic
589C2×C43#234211yescharacteristic
590C2×C43#235411yescharacteristic
591C2×C43#235811yescharacteristic
592C2×C43#236111yescharacteristic
593C2×C43#242511yescharacteristic
594C2×C43#242811yescharacteristic
595C2×C43#246111yescharacteristic
596C2×C43#246711yescharacteristic
597C2×C43#252111yescharacteristic
598C2×C43#253111yescharacteristic
599C2×C43#255511yescharacteristic
600C2×C43#256011yescharacteristic
601D43—44no—
602C23×D4—431no—
603C24×C4—431no—
604C22×C4⋊C4—431no—
605C22×C4⋊C4—431no—
606C22×C4⋊C4—431no—
607C22×C4⋊C4C2×D4311yescharacteristic
608C22×C22⋊C4—431no—
609C22×C22⋊C4—431no—
610C22×C22⋊C4—431no—
611C22×C22⋊C4—431no—
612C22×C22⋊C4—431no—
613C22×C22⋊C4—431no—
614C22×C22⋊C4—431no—
615C22×C22⋊C4—431no—
616C22×C22⋊C4C2×D4311yescharacteristic
617C22×C22⋊C4C2×D4311yescharacteristic
618C22×C22⋊C4C2×D4311yescharacteristic
619C22×C42—431no—
620C22×C42—431no—
621C22×C42—431no—
622C22×C42C2×D4311yescharacteristic
623#390—864no—
624#388—24no—
625#388—864no—
626#388—864no—
627#386—438no—
628#380—864no—
629C4×C22⋊C4—864no—
630C2×#95—431no—
631C2×#95—431no—
632C2×#95—431no—
633C2×#95—431no—
634C2×#95—431no—
635C2×#95—431no—
636C2×#95—431no—
637C2×#95—431no—
638C2×#95—431no—
639C2×#95—431no—
640C2×#95—431no—
641C2×#95—431no—
642C2×#95C2×D4311yescharacteristic
643C2×#95C2×D4311yescharacteristic
644C43#1401211yescharacteristic, complemented, Sylow
645C25—431no—
646C25C22×D4311yescharacteristic
647C22×D4—434no—
648C22×D4—862no—
649C22×D4—862no—
650C22×D4—862no—
651C22×D4—862no—
652C22×D4—1721no—
653C22×D4—1721no—
654C23×C4—431no—
655C23×C4—431no—
656C23×C4—431no—
657C23×C4—431no—
658C23×C4—431no—
659C23×C4—431no—
660C23×C4—434no—
661C23×C4—431no—
662C23×C4—862no—
663C23×C4—862no—
664C23×C4—862no—
665C23×C4—862no—
666C23×C4—1721no—
667C23×C4—1721no—
668C23×C4C22×D4311yescharacteristic
669C23×C4C22×D4311yescharacteristic
670C23×C4C22×D4311yescharacteristic
671C23×C4C22×D4311yescharacteristic
672C23×C4C22×D4311yescharacteristic
673C23×C4C22×D4311yescharacteristic
674C2×C4⋊C4—22no—
675C2×C4⋊C4—22no—
676C2×C4⋊C4—41no—
677C2×C4⋊C4—862no—
678C2×C4⋊C4—862no—
679C2×C4⋊C4—862no—
680C2×C4⋊C4—862no—
681C2×C4⋊C4—862no—
682C2×C4⋊C4—862no—
683C2×C4⋊C4—1721no—
684C2×C4⋊C4—1721no—
685C2×C4⋊C4—1721no—
686C2×C22⋊C4—22no—
687C2×C22⋊C4—22no—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—22no—
690C2×C22⋊C4—22no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—41no—
694C2×C22⋊C4—434no—
695C2×C22⋊C4—434no—
696C2×C22⋊C4—434no—
697C2×C22⋊C4—862no—
698C2×C22⋊C4—862no—
699C2×C22⋊C4—862no—
700C2×C22⋊C4—862no—
701C2×C22⋊C4—862no—
702C2×C22⋊C4—862no—
703C2×C22⋊C4—862no—
704C2×C22⋊C4—862no—
705C2×C22⋊C4—862no—
706C2×C22⋊C4—862no—
707C2×C22⋊C4—862no—
708C2×C22⋊C4—862no—
709C2×C22⋊C4—862no—
710C2×C22⋊C4—862no—
711C2×C22⋊C4—862no—
712C2×C22⋊C4—862no—
713C2×C22⋊C4—1721no—
714C2×C22⋊C4—1721no—
715C2×C22⋊C4—1721no—
716C2×C22⋊C4—1721no—
717C2×C22⋊C4—1721no—
718C2×C22⋊C4C4×D4314yes—
719C2×C42—22no—
720C2×C42—22no—
721C2×C42—22no—
722C2×C42—862no—
723C2×C42—862no—
724C2×C42—862no—
725C2×C42—862no—
726C2×C42—862no—
727C2×C42—862no—
728C2×C42—1721no—
729C2×C42—1721no—
730C2×C42—1721no—
731#95—22no—
732#95—434no—
733#95—434no—
734#95—434no—
735#95—862no—
736#95—862no—
737#95—862no—
738#95—862no—
739#95—862no—
740#95—862no—
741#95—862no—
742#95—862no—
743#95—1721no—
744#95C22⋊D4314yescomplemented
745C24—21no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—432no—
760C24—432no—
761C24—432no—
762C24—861no—
763C24—861no—
764C24—861no—
765C24—861no—
766C24—861no—
767C24—861no—
768C24—861no—
769C24—861no—
770C24—861no—
771C24—861no—
772C24—861no—
773C24—861no—
774C24C2×C4×D4312yes—
775C24C23×D4311yescharacteristic
776C2×D4—868no—
777C2×D4—868no—
778C2×D4—1724no—
779C2×D4—1724no—
780C2×D4—1724no—
781C2×D4—1724no—
782C2×D4—1724no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—432no—
817C22×C4—432no—
818C22×C4—432no—
819C22×C4—432no—
820C22×C4—432no—
821C22×C4—432no—
822C22×C4—432no—
823C22×C4—432no—
824C22×C4—432no—
825C22×C4—432no—
826C22×C4—868no—
827C22×C4—861no—
828C22×C4—861no—
829C22×C4—861no—
830C22×C4—861no—
831C22×C4—861no—
832C22×C4—861no—
833C22×C4—861no—
834C22×C4—861no—
835C22×C4—861no—
836C22×C4—861no—
837C22×C4—861no—
838C22×C4—861no—
839C22×C4—861no—
840C22×C4—861no—
841C22×C4—861no—
842C22×C4—861no—
843C22×C4—861no—
844C22×C4—861no—
845C22×C4—861no—
846C22×C4—861no—
847C22×C4—861no—
848C22×C4—861no—
849C22×C4—861no—
850C22×C4—861no—
851C22×C4—861no—
852C22×C4—861no—
853C22×C4—861no—
854C22×C4—861no—
855C22×C4—861no—
856C22×C4—861no—
857C22×C4—861no—
858C22×C4—861no—
859C22×C4—868no—
860C22×C4—861no—
861C22×C4—861no—
862C22×C4—861no—
863C22×C4—861no—
864C22×C4—861no—
865C22×C4—861no—
866C22×C4—861no—
867C22×C4—1724no—
868C22×C4—1724no—
869C22×C4—1724no—
870C22×C4—1724no—
871C22×C4—1724no—
872C22×C4C2×C4×D4312yes—
873C22×C4C2×C4×D4312yes—
874C22×C4#1062189812yes—
875C22×C4D4×D4312yes—
876C22×C4D4×D4312yes—
877C22×C4#1062190012yes—
878C22×C4C2×C22⋊D4312yes—
879C22×C4C2×C22⋊D4312yes—
880C22×C4C2×C22⋊D4312yes—
881C4⋊C4—44no—
882C4⋊C4—1724no—
883C4⋊C4—1724no—
884C4⋊C4—1724no—
885C22⋊C4—28no—
886C22⋊C4—44no—
887C22⋊C4—44no—
888C22⋊C4—868no—
889C22⋊C4—868no—
890C22⋊C4—868no—
891C22⋊C4—868no—
892C22⋊C4—1724no—
893C22⋊C4—1724no—
894C22⋊C4—1724no—
895C22⋊C4—1724no—
896C42—44no—
897C42—1724no—
898C42—1724no—
899C42—1724no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—434no—
936C23—862no—
937C23—862no—
938C23—862no—
939C23—862no—
940C23—862no—
941C23—862no—
942C23—862no—
943C23—862no—
944C23—862no—
945C23—862no—
946C23—862no—
947C23—862no—
948C23—862no—
949C23—862no—
950C23—862no—
951C23—862no—
952C23—862no—
953C23—862no—
954C23—1721no—
955C23—1721no—
956C23—1721no—
957C23—1721no—
958C23—1721no—
959C23—1721no—
960C23—1721no—
961C23—1721no—
962C23—1721no—
963C23—1721no—
964C23—1721no—
965C23—1721no—
966C23—1721no—
967C23—1721no—
968C23—1721no—
969C23—1721no—
970C23C22×C4×D4311yescharacteristic
971C23C2×D4×D4311yescharacteristic
972C23C2×D4×D4311yescharacteristic
973C23C22×C22⋊D4311yescharacteristic
974C23#41×D4311yescharacteristic
975C23#41×D4311yescharacteristic
976C23#41×D4311yescharacteristic
977C23#41×D4311yescharacteristic
978C23#41×D4311yescharacteristic
979C23C2×#1062190011yescharacteristic
980C23C2×#1062189811yescharacteristic
981C23#1306337011yescharacteristic
982C23#1306337111yescharacteristic
983C23#1306337111yescharacteristic
984C23#1306337211yescharacteristic
985D4—17216no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—434no—
1027C2×C4—434no—
1028C2×C4—862no—
1029C2×C4—862no—
1030C2×C4—862no—
1031C2×C4—862no—
1032C2×C4—862no—
1033C2×C4—862no—
1034C2×C4—862no—
1035C2×C4—862no—
1036C2×C4—862no—
1037C2×C4—862no—
1038C2×C4—862no—
1039C2×C4—862no—
1040C2×C4—862no—
1041C2×C4—862no—
1042C2×C4—862no—
1043C2×C4—862no—
1044C2×C4—862no—
1045C2×C4—862no—
1046C2×C4—862no—
1047C2×C4—862no—
1048C2×C4—862no—
1049C2×C4—862no—
1050C2×C4—862no—
1051C2×C4—862no—
1052C2×C4—17216no—
1053C2×C4—1721no—
1054C2×C4—1721no—
1055C2×C4—1721no—
1056C2×C4—1721no—
1057C2×C4—1721no—
1058C2×C4—1721no—
1059C2×C4—1721no—
1060C2×C4—1721no—
1061C2×C4—1721no—
1062C2×C4—1721no—
1063C2×C4—1721no—
1064C2×C4—1721no—
1065C2×C4—1721no—
1066C2×C4—1721no—
1067C2×C4—1721no—
1068C2×C4—1721no—
1069C2×C4—1721no—
1070C2×C4—1721no—
1071C2×C4—1721no—
1072C2×C4—1721no—
1073C2×C4—1721no—
1074C2×C4—1721no—
1075C2×C4—1721no—
1076C2×C4C4×C22⋊D4314yes—
1077C2×C4#1306329614yes—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—81no—
1086C22—81no—
1087C22—81no—
1088C22—81no—
1089C22—81no—
1090C22—81no—
1091C22—81no—
1092C22—81no—
1093C22—864no—
1094C22—864no—
1095C22—864no—
1096C22—1722no—
1097C22—1722no—
1098C22—1722no—
1099C22—1722no—
1100C22—1722no—
1101C22—1722no—
1102C22—1722no—
1103C22—1722no—
1104C22—1722no—
1105C22—1722no—
1106C22—1722no—
1107C22—1722no—
1108C22#117×D4311yescharacteristic
1109C22C4×D4×D4311yescharacteristic
1110C22C4×D4×D4311yescharacteristic
1111C22C2×C4×C22⋊D4311yescharacteristic
1112C22C4×#1062190011yescharacteristic
1113C22#1458337111yescharacteristic
1114C22#1458337911yescharacteristic
1115C22C2×#1306329611yescharacteristic
1116C22#1458340611yescharacteristic
1117C22#1458342611yescharacteristic
1118C22#1458343111yescharacteristic
1119C22#1458343211yescharacteristic
1120C22#1458344411yescharacteristic
1121C22#1458344611yescharacteristic
1122C22#1458344811yescharacteristic
1123C22#1458348811yescharacteristic
1124C22#1458349311yescharacteristic
1125C22#1458350211yescharacteristic
1126C22#1458351311yescharacteristic
1127C22D4×C22⋊D4311yescharacteristic
1128C22#1458353311yescharacteristic
1129C22#1458353711yescharacteristic
1130C22#1458354111yescharacteristic
1131C22#1458354511yescharacteristic
1132C22#1458354611yescharacteristic
1133C22#1458354711yescharacteristic
1134C22#1458354811yescharacteristic
1135C22#1458355711yescharacteristic
1136C22#1458356811yescharacteristic
1137C22#1458357411yescharacteristic
1138C22#1458357811yescharacteristic
1139C22#1458357911yescharacteristic
1140C22#1458360011yescharacteristic
1141C22#1458361211yescharacteristic
1142C22#1458361711yescharacteristic
1143C4—24no—
1144C4—24no—
1145C4—42no—
1146C4—42no—
1147C4—42no—
1148C4—81no—
1149C4—864no—
1150C4—864no—
1151C4—3441no—
1152C4—1722no—
1153C4—1722no—
1154C4—1722no—
1155C4—1722no—
1156C2—82no—
1157C2—1724no—
1158C2#1913705511yescharacteristic
1159C2C4×#1306329611yescharacteristic
1160C2#1913739211yescharacteristic
1161C2#1913743911yescharacteristic
1162C2#1913754511yescharacteristic
1163C2#1913757211yescharacteristic
1164C2#1913760811yescharacteristic
1165C2#1913814211yescharacteristic
1166C2#1913817911yescharacteristic
1167C2#1913855811yescharacteristic
1168C2#1913864211yescharacteristic
1169C2#1913930511yescharacteristic
1170C2#1913944111yescharacteristic
1171C2#1913967111yescharacteristic
1172C2#1913973811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C43×#388C2
socle, cosocleC24×C43C24
prime radicalC23×C22⋊D43C22
hypercenterC2×#388D43
hypocenterC43#14012
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C2×#14582790C2semidirect
3. C2×#14582787C2semidirect
5. C2×#14582756C2semidirect
6. C2×#14582746C2semidirect
7. #19132858C2semidirect
8. #19132843C2semidirect
9. #19132840C2semidirect
11. #19132832C2semidirect
12. #19132829C2semidirect
13. #19132826C2semidirect
14. C4×C43⋊#95C2semidirect
15. C2×C43×#388C2semidirect
35. #14582775C4semidirect
133. C43⋊#95D4semidirect
157. #95×C43D4semidirect
573. C2×#388D43semidirect
644. C43#14012semidirect
744. #95C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145827992
C2×#145827902
C2×#145827872
C2×#145827752
C2×#145827562
C2×#145827462
#191328582
#191328432
#191328402
#191328342
#191328322
#191328292
#191328262
C4×C43⋊#952
C2×C43×#3882
#1401243