Finite Group Databasebeta

← #25021047

Subgroups — #25021047

Order 11008.

2266 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063310C211yesmaximal, characteristic
2C2×#14582789C211yesmaximal, characteristic, complemented
3C2×#14582777C211yesmaximal, characteristic
4C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
5C2×#14582746C211yesmaximal, characteristic, complemented
6#19132863C211yesmaximal, characteristic, complemented
7#19132843C211yesmaximal, characteristic, complemented
8#19132837C211yesmaximal, characteristic, complemented
9#19132835C211yesmaximal, characteristic
10#19132833C211yesmaximal, characteristic, complemented
11#19132826C211yesmaximal, characteristic, complemented
12#19132826C211yesmaximal, characteristic, complemented
13(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
14(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
15C43×C4⋊#95C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17C23×C4×D43C2211yescharacteristic
18C23×C4×D43C2211yescharacteristic
19C2×#13063310—24no—
20C2×#13063310—24no—
21C2×#13063310C418yescomplemented
22C22×Dic43⋊C4C2211yescharacteristic
23C22×(C2×D43)⋊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×(C2×D43)⋊C4C2211yescharacteristic
31C22×(C2×D43)⋊C4C2211yescharacteristic
32C22×(C2×D43)⋊C4C2211yescharacteristic
33C22×C4×Dic43C2211yescharacteristic
34C22×C4×Dic43C2211yescharacteristic
35#14582789—24no—
36#14582777—24no—
37C4×(C2×D43)⋊C4—24no—
38#14582746—24no—
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
50C2×C43⋊#95C2211yescharacteristic
51C22×C4⋊C4×C43C2211yescharacteristic
52C22×C4⋊C4×C43C2211yescharacteristic
53C22×C42×C43C2211yescharacteristic
54C2×#95×C43C2211yescharacteristic
55C2×#95×C43C2211yescharacteristic
56C2×#95×C43C2211yescharacteristic
57C2×#95×C43C2211yescharacteristic
58C24×D43C2311yescharacteristic
59C24×D43C2311yescharacteristic
60C22×D172—22no—
61C22×D172—22no—
62C22×D172—22no—
63C22×D172—22no—
64C22×D172—41no—
65C22×D172—41no—
66C22×D172C2×C414yes—
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—22no—
78C22×C4×D43—22no—
79C22×C4×D43—22no—
80C22×C4×D43—22no—
81C22×C4×D43—22no—
82C22×C4×D43—41no—
83C22×C4×D43—41no—
84C22×C4×D43—41no—
85C22×C4×D43—41no—
86C22×C4×D43C2×C414yescomplemented
87#13063310—232no—
88C2×Dic43⋊C4—22no—
89C2×Dic43⋊C4—22no—
90C2×Dic43⋊C4C2×C414yescomplemented
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—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—22no—
110C2×(C2×D43)⋊C4—22no—
111C2×(C2×D43)⋊C4—41no—
112C2×(C2×D43)⋊C4—41no—
113C2×(C2×D43)⋊C4—41no—
114C2×(C2×D43)⋊C4—41no—
115C2×(C2×D43)⋊C4C2×C414yes—
116C2×(C2×D43)⋊C4C2×C414yes—
117C2×(C2×D43)⋊C4C2×C414yescomplemented
118C2×(C2×D43)⋊C4D414yes—
119C2×(C2×D43)⋊C4D414yes—
120C2×(C2×D43)⋊C4D414yes—
121C2×C4×Dic43—22no—
122C2×C4×Dic43—22no—
123C2×C4×Dic43—22no—
124C2×C4×Dic43—22no—
125C2×C4×Dic43—41no—
126C2×C4×Dic43—41no—
127C43⋊#95—22no—
128C43⋊#95—22no—
129C43⋊#95—22no—
130C43⋊#95—22no—
131C43⋊#95—22no—
132C43⋊#95—22no—
133C43⋊#95—22no—
134C43⋊#95—22no—
135C43⋊#95—22no—
136C43⋊#95—22no—
137C43⋊#95—41no—
138C43⋊#95—41no—
139C23×C4×C43C2311yescharacteristic
140C23×C4×C43C2311yescharacteristic
141C23×C4×C43C2311yescharacteristic
142C23×C4×C43C2311yescharacteristic
143C23×C4×C43C2311yescharacteristic
144C23×C4×C43C2311yescharacteristic
145C23×C4×C43C2311yescharacteristic
146C2×C4⋊C4×C43—22no—
147C2×C4⋊C4×C43—22no—
148C2×C4⋊C4×C43—22no—
149C2×C4⋊C4×C43—22no—
150C2×C4⋊C4×C43—41no—
151C2×C4⋊C4×C43C2×C414yescomplemented
152C2×C42×C43—22no—
153C2×C42×C43—22no—
154C2×C42×C43—41no—
155#95×C43—22no—
156#95×C43—22no—
157#95×C43—41no—
158#95×C43—41no—
159C24×C43C2411yescharacteristic
160C23×D43—21no—
161C23×D43—21no—
162C23×D43—21no—
163C23×D43—21no—
164C23×D43—21no—
165C23×D43—21no—
166C23×D43—21no—
167C23×D43—21no—
168C23×D43—21no—
169C23×D43—21no—
170C23×D43—21no—
171C23×D43—21no—
172C23×D43—21no—
173C23×D43—21no—
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×D43C22×C412yes—
185C23×D43C22×C412yes—
186C23×D43C2×D412yes—
187C23×D43C2×D412yes—
188C23×D43C2×D412yes—
189C23×D43#4112yes—
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×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×C43C22×C412yes—
230C22×C4×C43C22×C412yes—
231C22×C4×C43C22×C412yes—
232C22×C4×C43C2×D412yes—
233C22×C4×C43C2×D412yes—
234C22×C4×C43C2×D412yes—
235C22×C4×C43#4112yes—
236C22×C4×C43#4112yes—
237C22×C4×C43#4112yes—
238C22×C4×C43#4112yes—
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×Dic43C22×C412yes—
275C22×Dic43C22×C412yes—
276C22×Dic43C2×D412yes—
277C22×Dic43C2×D412yes—
278C22×Dic43C2×D412yes—
279C22×Dic43#4112yes—
280C22×Dic43#4112yes—
281C2×D172—28no—
282C2×D172—28no—
283C2×D172—44no—
284C2×D172—44no—
285C2×D172—44no—
286C2×D172—44no—
287C2×D172—44no—
288C2×C4×D43—28no—
289C2×C4×D43—28no—
290C2×C4×D43—28no—
291C2×C4×D43—44no—
292C2×C4×D43—44no—
293C2×C4×D43—44no—
294C2×C4×D43—44no—
295C2×C4×D43—44no—
296C2×C4×D43—44no—
297C2×C4×D43—44no—
298C2×C4×D43—44no—
299C2×C4×D43—44no—
300C2×C4×D43—44no—
301C2×C4×D43—44no—
302C4⋊C4×C43—28no—
303C4⋊C4×C43—44no—
304C42×C43—44no—
305(C2×D43)⋊C4—28no—
306(C2×D43)⋊C4—28no—
307(C2×D43)⋊C4—28no—
308(C2×D43)⋊C4—28no—
309(C2×D43)⋊C4—28no—
310(C2×D43)⋊C4—44no—
311(C2×D43)⋊C4—44no—
312(C2×D43)⋊C4—44no—
313(C2×D43)⋊C4—44no—
314(C2×D43)⋊C4C22⋊C4116yescomplemented
315Dic43⋊C4—28no—
316C4×Dic43—44no—
317C4×Dic43—44no—
318C23×C43C23×C411yescharacteristic
319C23×C43C22×D411yescharacteristic
320C23×C43C22×D411yescharacteristic
321C23×C43C22×D411yescharacteristic
322C23×C43C2×#4111yescharacteristic
323C23×C43C2×#4111yescharacteristic
324C23×C43C2×#4111yescharacteristic
325C23×C43C2×#4111yescharacteristic
326C23×C43C2×#4111yescharacteristic
327C23×C43C2×#4111yescharacteristic
328C23×C43C2×#4111yescharacteristic
329C23×C43H(5,𝔽2)11yescharacteristic
330C23×C43H(5,𝔽2)11yescharacteristic
331C23×C43H(5,𝔽2)11yescharacteristic
332C23×C432−1+411yescharacteristic
333C22×D43—22no—
334C22×D43—22no—
335C22×D43—22no—
336C22×D43—22no—
337C22×D43—22no—
338C22×D43—22no—
339C22×D43—22no—
340C22×D43—22no—
341C22×D43—22no—
342C22×D43—22no—
343C22×D43—22no—
344C22×D43—22no—
345C22×D43—22no—
346C22×D43—22no—
347C22×D43—22no—
348C22×D43—22no—
349C22×D43—22no—
350C22×D43—22no—
351C22×D43—22no—
352C22×D43—22no—
353C22×D43—22no—
354C22×D43—22no—
355C22×D43—22no—
356C22×D43—22no—
357C22×D43—22no—
358C22×D43—22no—
359C22×D43—22no—
360C22×D43—22no—
361C22×D43—22no—
362C22×D43—22no—
363C22×D43—22no—
364C22×D43—22no—
365C22×D43—22no—
366C22×D43—22no—
367C22×D43—22no—
368C22×D43—22no—
369C22×D43—41no—
370C22×D43—41no—
371C22×D43—41no—
372C22×D43—41no—
373C22×D43—41no—
374C22×D43—41no—
375C22×D43—41no—
376C22×D43—41no—
377C22×D43—41no—
378C22×D43—41no—
379C22×D43—41no—
380C22×D43—41no—
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×D43—41no—
398C22×D43—41no—
399C22×D43—41no—
400C22×D43—41no—
401C22×D43C2×C22⋊C414yes—
402C22×D43C4×D414yes—
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—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—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×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×C43C2×C22⋊C414yes—
451C2×C4×C43#12314yescomplemented
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—22no—
466C2×Dic43—22no—
467C2×Dic43—22no—
468C2×Dic43—22no—
469C2×Dic43—22no—
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—41no—
489C2×Dic43—41no—
490C2×Dic43—41no—
491C2×Dic43—41no—
492C2×Dic43—41no—
493C2×Dic43C2×C22⋊C414yes—
494D172—416no—
495C4×D43—416no—
496C4×D43—416no—
497#14096—431nomaximal, Sylow
498C22×C43C22×C22⋊C411yescharacteristic
499C22×C43C2×C4×D411yescharacteristic
500C22×C43C4×#4111yescharacteristic
501C22×C43C4×#4111yescharacteristic
502C22×C43C4×#4111yescharacteristic
503C22×C43#51811yescharacteristic
504C22×C43#52011yescharacteristic
505C22×C43C2×#12311yescharacteristic
506C22×C43#52511yescharacteristic
507C22×C43#52511yescharacteristic
508C22×C43#52511yescharacteristic
509C22×C43#52911yescharacteristic
510C22×C43#52911yescharacteristic
511C22×C43#53211yescharacteristic
512C22×C43#53211yescharacteristic
513C22×C43#53811yescharacteristic
514C22×C43#53911yescharacteristic
515C22×C43#54011yescharacteristic
516C22×C43#54211yescharacteristic
517C22×C43D4211yescharacteristic
518C22×C43D4211yescharacteristic
519C22×C43#54611yescharacteristic
520C22×C43#54611yescharacteristic
521C22×C43#54611yescharacteristic
522C22×C43#54611yescharacteristic
523C22×C43#54611yescharacteristic
524C22×C43#54711yescharacteristic
525C22×C43#54711yescharacteristic
526C22×C43#54711yescharacteristic
527C22×C43#55111yescharacteristic
528C22×C43#55111yescharacteristic
529C22×C43#55211yescharacteristic
530C22×C43#55311yescharacteristic
531C22×C43#55311yescharacteristic
532C22×C43#55911yescharacteristic
533C2×D43—24no—
534C2×D43—24no—
535C2×D43—24no—
536C2×D43—24no—
537C2×D43—24no—
538C2×D43—24no—
539C2×D43—42no—
540C2×D43—42no—
541C2×D43—42no—
542C2×D43—42no—
543C2×D43—42no—
544C2×D43—42no—
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—
557C2×D43—42no—
558C2×D43—42no—
559C2×D43—42no—
560C2×D43—42no—
561C2×D43—42no—
562C2×D43—42no—
563C4×C43—24no—
564C4×C43—24no—
565C4×C43—42no—
566C4×C43—42no—
567C4×C43—42no—
568C4×C43—42no—
569C4×C43—81no—
570Dic43—24no—
571Dic43—42no—
572Dic43—42no—
573Dic43—42no—
574Dic43—42no—
575Dic43—81no—
576C22×#123—431no—
577C2×#388—431no—
578C2×#386—431no—
579C2×C4×C22⋊C4—431no—
580C2×C4×C22⋊C4—431no—
581#1445—431no—
582#1440—431no—
583#1439—431no—
584#1438—431no—
585#1437—431no—
586#1436—431no—
587#1436—431no—
588C4⋊#95D4311yescharacteristic, complemented
589C22⋊#95—431no—
590C22⋊#95—431no—
591C2×C43#229711yescharacteristic
592C2×C43C4×#12311yescharacteristic
593C2×C43#233511yescharacteristic
594C2×C43D4×C22⋊C411yescharacteristic
595C2×C43#233911yescharacteristic
596C2×C43#235911yescharacteristic
597C2×C43#237411yescharacteristic
598C2×C43#241811yescharacteristic
599C2×C43#242211yescharacteristic
600C2×C43#245511yescharacteristic
601C2×C43#245711yescharacteristic
602C2×C43#246411yescharacteristic
603C2×C43#247011yescharacteristic
604C2×C43#255311yescharacteristic
605C2×C43#255711yescharacteristic
606D43—44no—
607D43—44no—
608C23×D4—431no—
609C24×C4—431no—
610C24×C4—431no—
611C2×#123—438no—
612C2×#123—864no—
613C2×#123—864no—
614C22×C4⋊C4—431no—
615C22×C4⋊C4C2×D4311yescharacteristic
616C22×C4⋊C4C2×D4311yescharacteristic
617C22×C22⋊C4—431no—
618C22×C22⋊C4—431no—
619C22×C22⋊C4—431no—
620C22×C22⋊C4—431no—
621C22×C22⋊C4—431no—
622C22×C22⋊C4—431no—
623C22×C22⋊C4—431no—
624C22×C22⋊C4—431no—
625C22×C22⋊C4—431no—
626C22×C22⋊C4—431no—
627C22×C42—431no—
628C22×C42—431no—
629C22×C42C2×D4311yescharacteristic
630#388—864no—
631#386—864no—
632C4×C22⋊C4—864no—
633C4×C22⋊C4—864no—
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×#95—431no—
643C2×#95—431no—
644C2×#95—431no—
645C2×#95—431no—
646C2×#95C2×D4311yescharacteristic
647C2×#95C2×D4311yescharacteristic
648C2×#95C2×D4311yescharacteristic
649C2×#95C2×D4311yescharacteristic
650C43#1409611yescharacteristic, complemented, Sylow
651C25—431no—
652C25—431no—
653C22×D4—434no—
654C22×D4—862no—
655C22×D4—862no—
656C22×D4—862no—
657C22×D4—862no—
658C22×D4—1721no—
659C22×D4—1721no—
660C23×C4—431no—
661C23×C4—431no—
662C23×C4—431no—
663C23×C4—431no—
664C23×C4—431no—
665C23×C4—434no—
666C23×C4—431no—
667C23×C4—862no—
668C23×C4—862no—
669C23×C4—862no—
670C23×C4—862no—
671C23×C4—862no—
672C23×C4—862no—
673C23×C4—862no—
674C23×C4—862no—
675C23×C4—862no—
676C23×C4—1721no—
677C23×C4—1721no—
678C23×C4—1721no—
679C23×C4—1721no—
680C23×C4C22×D4311yescharacteristic
681C23×C4C22×D4311yescharacteristic
682C23×C4C22×D4311yescharacteristic
683C23×C4C22×D4311yescharacteristic
684C23×C4C22×D4311yescharacteristic
685C23×C4C22×D4311yescharacteristic
686C23×C4C22×D4311yescharacteristic
687#123—8632no—
688C2×C4⋊C4—22no—
689C2×C4⋊C4—22no—
690C2×C4⋊C4—22no—
691C2×C4⋊C4—22no—
692C2×C4⋊C4—41no—
693C2×C4⋊C4—434no—
694C2×C4⋊C4—862no—
695C2×C4⋊C4—862no—
696C2×C4⋊C4C4×D4314yescomplemented
697C2×C22⋊C4—434no—
698C2×C22⋊C4—434no—
699C2×C22⋊C4—434no—
700C2×C22⋊C4—434no—
701C2×C22⋊C4—434no—
702C2×C22⋊C4—434no—
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—862no—
714C2×C22⋊C4—862no—
715C2×C22⋊C4—862no—
716C2×C22⋊C4—862no—
717C2×C22⋊C4—862no—
718C2×C22⋊C4—862no—
719C2×C22⋊C4—862no—
720C2×C22⋊C4—862no—
721C2×C22⋊C4—862no—
722C2×C22⋊C4—862no—
723C2×C22⋊C4—1721no—
724C2×C22⋊C4—1721no—
725C2×C22⋊C4—1721no—
726C2×C22⋊C4—1721no—
727C2×C42—22no—
728C2×C42—22no—
729C2×C42—41no—
730C2×C42—862no—
731C2×C42—862no—
732C2×C42—862no—
733C2×C42—862no—
734C2×C42—1721no—
735C2×C42—1721no—
736#95—22no—
737#95—22no—
738#95—41no—
739#95—41no—
740#95—862no—
741#95—862no—
742#95—862no—
743#95—862no—
744#95—862no—
745#95—862no—
746#95—862no—
747#95—862no—
748#95—862no—
749#95—862no—
750#95—1721no—
751#95—1721no—
752C24—432no—
753C24—432no—
754C24—432no—
755C24—432no—
756C24—432no—
757C24—432no—
758C24—861no—
759C24—861no—
760C24—861no—
761C24—861no—
762C24—861no—
763C24—861no—
764C24—861no—
765C24—861no—
766C24—861no—
767C24—861no—
768C24—861no—
769C24—861no—
770C24—861no—
771C24—861no—
772C24—861no—
773C24—861no—
774C24—861no—
775C24—861no—
776C24—861no—
777C24—861no—
778C24—861no—
779C24—861no—
780C24—861no—
781C24—861no—
782C24C23×D4311yescharacteristic
783C2×D4—868no—
784C2×D4—868no—
785C2×D4—1724no—
786C2×D4—1724no—
787C2×D4—1724no—
788C2×D4—1724no—
789C2×D4—1724no—
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—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—432no—
830C22×C4—432no—
831C22×C4—432no—
832C22×C4—432no—
833C22×C4—432no—
834C22×C4—432no—
835C22×C4—432no—
836C22×C4—868no—
837C22×C4—868no—
838C22×C4—868no—
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—861no—
860C22×C4—861no—
861C22×C4—861no—
862C22×C4—861no—
863C22×C4—861no—
864C22×C4—861no—
865C22×C4—861no—
866C22×C4—861no—
867C22×C4—861no—
868C22×C4—861no—
869C22×C4—861no—
870C22×C4—861no—
871C22×C4—861no—
872C22×C4—861no—
873C22×C4—861no—
874C22×C4—1724no—
875C22×C4—1724no—
876C22×C4—1724no—
877C22×C4—1724no—
878C22×C4—1724no—
879C22×C4—1724no—
880C22×C4—1724no—
881C22×C4—1724no—
882C22×C4—1724no—
883C22×C4—1724no—
884C22×C4—1724no—
885C22×C4C2×C4×D4312yes—
886C22×C4C2×C4×D4312yes—
887C22×C4C2×C4×D4312yes—
888C22×C4#1062189812yes—
889C22×C4#1062189812yes—
890C22×C4D4×D4312yes—
891C22×C4D4×D4312yes—
892C22×C4D4×D4312yes—
893C22×C4#1062190212yes—
894C22×C4#1062190212yes—
895C4⋊C4—28no—
896C4⋊C4—44no—
897C4⋊C4—868no—
898C22⋊C4—4316no—
899C22⋊C4—868no—
900C22⋊C4—868no—
901C22⋊C4—868no—
902C22⋊C4—868no—
903C22⋊C4—868no—
904C22⋊C4—1724no—
905C22⋊C4—1724no—
906C22⋊C4—1724no—
907C22⋊C4—1724no—
908C42—44no—
909C42—1724no—
910C42—1724no—
911C23—434no—
912C23—434no—
913C23—862no—
914C23—862no—
915C23—862no—
916C23—862no—
917C23—862no—
918C23—862no—
919C23—862no—
920C23—862no—
921C23—862no—
922C23—862no—
923C23—862no—
924C23—862no—
925C23—862no—
926C23—862no—
927C23—862no—
928C23—862no—
929C23—862no—
930C23—862no—
931C23—862no—
932C23—862no—
933C23—862no—
934C23—862no—
935C23—862no—
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—1721no—
950C23—1721no—
951C23—1721no—
952C23—1721no—
953C23—1721no—
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—
970C23—1721no—
971C23—1721no—
972C23—1721no—
973C23—1721no—
974C23—1721no—
975C23—1721no—
976C23—1721no—
977C23—1721no—
978C23—1721no—
979C23—1721no—
980C23—1721no—
981C23C22×C4×D4311yescharacteristic
982C23C2×D4×D4311yescharacteristic
983C23C2×D4×D4311yescharacteristic
984C23C2×D4×D4311yescharacteristic
985C23#41×D4311yescharacteristic
986C23#41×D4311yescharacteristic
987C23#41×D4311yescharacteristic
988C23C2×#1062189811yescharacteristic
989C23C2×#1062189811yescharacteristic
990C23C2×#1062190211yescharacteristic
991C23C2×#1062190211yescharacteristic
992C23#1306337011yescharacteristic
993C23#1306337011yescharacteristic
994C23#1306337111yescharacteristic
995C23#1306337311yescharacteristic
996D4—17216no—
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—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—434no—
1045C2×C4—862no—
1046C2×C4—862no—
1047C2×C4—862no—
1048C2×C4—862no—
1049C2×C4—862no—
1050C2×C4—862no—
1051C2×C4—862no—
1052C2×C4—862no—
1053C2×C4—862no—
1054C2×C4—862no—
1055C2×C4—862no—
1056C2×C4—862no—
1057C2×C4—862no—
1058C2×C4—862no—
1059C2×C4—862no—
1060C2×C4—862no—
1061C2×C4—862no—
1062C2×C4—862no—
1063C2×C4—17216no—
1064C2×C4—17216no—
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×C4—1721no—
1077C2×C4—1721no—
1078C2×C4—1721no—
1079C2×C4—1721no—
1080C2×C4—1721no—
1081C2×C4—1721no—
1082C2×C4—1721no—
1083C2×C4—1721no—
1084C2×C4—1721no—
1085C2×C4—1721no—
1086C2×C4—1721no—
1087C2×C4—1721no—
1088C2×C4C22⋊C4×D4314yes—
1089C2×C4#1306331014yescomplemented
1090C22—864no—
1091C22—864no—
1092C22—864no—
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—1722no—
1109C22—1722no—
1110C22—1722no—
1111C22—1722no—
1112C22—1722no—
1113C22—1722no—
1114C22—1722no—
1115C22—1722no—
1116C22—1722no—
1117C22—1722no—
1118C22—1722no—
1119C22—1722no—
1120C22C2×C22⋊C4×D4311yescharacteristic
1121C22C4×D4×D4311yescharacteristic
1122C22C4×#1062189811yescharacteristic
1123C22C4×#1062190211yescharacteristic
1124C22C4×#1062190211yescharacteristic
1125C22#1458337111yescharacteristic
1126C22#1458338011yescharacteristic
1127C22C2×#1306331011yescharacteristic
1128C22#1458340811yescharacteristic
1129C22#1458341211yescharacteristic
1130C22#1458341211yescharacteristic
1131C22#1458342711yescharacteristic
1132C22#1458343611yescharacteristic
1133C22#1458344811yescharacteristic
1134C22#1458345011yescharacteristic
1135C22#1458348911yescharacteristic
1136C22#1458349711yescharacteristic
1137C22#1458349911yescharacteristic
1138C22#1458352311yescharacteristic
1139C22#1458353311yescharacteristic
1140C22#1458353411yescharacteristic
1141C22#1458353811yescharacteristic
1142C22#1458353911yescharacteristic
1143C22#1458353911yescharacteristic
1144C22#1458354211yescharacteristic
1145C22#1458354611yescharacteristic
1146C22#1458355011yescharacteristic
1147C22#1458355011yescharacteristic
1148C22#1458355211yescharacteristic
1149C22#1458357311yescharacteristic
1150C22#1458357611yescharacteristic
1151C22#1458358111yescharacteristic
1152C22#1458359711yescharacteristic
1153C22#1458359811yescharacteristic
1154C22#1458363411yescharacteristic
1155C4—24no—
1156C4—24no—
1157C4—42no—
1158C4—42no—
1159C4—42no—
1160C4—42no—
1161C4—81no—
1162C4—864no—
1163C4—3441no—
1164C4—1722no—
1165C4—1722no—
1166C4—1722no—
1167C4—1722no—
1168C2—1724no—
1169C2—1724no—
1170C2#1913708411yescharacteristic
1171C2C4×#1306331011yescharacteristic
1172C2#1913738811yescharacteristic
1173C2#1913741611yescharacteristic
1174C2#1913742211yescharacteristic
1175C2#1913758211yescharacteristic
1176C2#1913772411yescharacteristic
1177C2#1913806311yescharacteristic
1178C2#1913811211yescharacteristic
1179C2#1913847911yescharacteristic
1180C2#1913850911yescharacteristic
1181C2#1913860711yescharacteristic
1182C2#1913869811yescharacteristic
1183C2#1913964711yescharacteristic
1184C2#1913970111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×C4⋊#95C2
socle, cosocleC24×C43C24
prime radicalC23×D172C22
hypercenterC4⋊#95D43
hypocenterC43#14096
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#14582789C2semidirect
4. C2×C4×(C2×D43)⋊C4C2semidirect
5. C2×#14582746C2semidirect
6. #19132863C2semidirect
7. #19132843C2semidirect
8. #19132837C2semidirect
10. #19132833C2semidirect
11. #19132826C2semidirect
12. #19132826C2semidirect
13. (C2×D43)⋊#95C2semidirect
14. (C2×D43)⋊#95C2semidirect
15. C43×C4⋊#95C2semidirect
21. C2×#13063310C4semidirect
86. C22×C4×D43C2×C4semidirect
90. C2×Dic43⋊C4C2×C4semidirect
117. C2×(C2×D43)⋊C4C2×C4semidirect
151. C2×C4⋊C4×C43C2×C4semidirect
314. (C2×D43)⋊C4C22⋊C4semidirect
451. C2×C4×C43#123semidirect
588. C4⋊#95D43semidirect
650. C43#14096semidirect
696. C2×C4⋊C4C4×D43semidirect
1089. C2×C4#13063310semidirect

Maximal subgroups

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

subgroupindex
C22×#130633102
C2×#145827892
C2×#145827772
C2×C4×(C2×D43)⋊C42
C2×#145827462
#191328632
#191328432
#191328372
#191328352
#191328332
#191328262
(C2×D43)⋊#952
C43×C4⋊#952
#1409643