Finite Group Databasebeta

← #25019910

Subgroups — #25019910

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×#14582801C211yesmaximal, characteristic
2C2×#14582790C211yesmaximal, characteristic, complemented
3C2×#14582790C211yesmaximal, characteristic, complemented
4C2×#14582788C211yesmaximal, characteristic, complemented
5C2×#14582777C211yesmaximal, characteristic
6C2×#14582758C211yesmaximal, characteristic, complemented
7C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
8#19132859C211yesmaximal, characteristic, complemented
9#19132843C211yesmaximal, characteristic, complemented
10#19132839C211yesmaximal, characteristic, complemented
11#19132835C211yesmaximal, characteristic
12#19132833C211yesmaximal, characteristic, complemented
13#19132829C211yesmaximal, characteristic, complemented
14#19132828C211yesmaximal, characteristic, complemented
15C4×#95×C43C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17C23×C4×D43C2211yescharacteristic
18C22×C4⋊Dic43C2211yescharacteristic
19C22×Dic43⋊C4C2211yescharacteristic
20C22×Dic43⋊C4C2211yescharacteristic
21C22×Dic43⋊C4C2211yescharacteristic
22C22×(C2×D43)⋊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
34#14582801—24no—
35#14582790—24no—
36#14582790—24no—
37#14582788—24no—
38#14582777C418yescomplemented
39#14582758—24no—
40C4×(C2×D43)⋊C4—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
51C22×C42×C43C2211yescharacteristic
52C22×C42×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—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—22no—
88C2×Dic43⋊C4—22no—
89C2×Dic43⋊C4—41no—
90C2×Dic43⋊C4—41no—
91C2×Dic43⋊C4—41no—
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—22no—
112C2×(C2×D43)⋊C4—22no—
113C2×(C2×D43)⋊C4—22no—
114C2×(C2×D43)⋊C4—22no—
115C2×(C2×D43)⋊C4—41no—
116C2×(C2×D43)⋊C4—41no—
117C2×(C2×D43)⋊C4—41no—
118C2×(C2×D43)⋊C4—41no—
119C2×(C2×D43)⋊C4—41no—
120C2×(C2×D43)⋊C4—41no—
121C2×(C2×D43)⋊C4C2×C414yes—
122C2×(C2×D43)⋊C4C2×C414yes—
123C2×(C2×D43)⋊C4C2×C414yes—
124C2×(C2×D43)⋊C4D414yes—
125C2×C4×Dic43—22no—
126C2×C4×Dic43—22no—
127C2×C4×Dic43—41no—
128C43⋊#95—22no—
129C43⋊#95—22no—
130C43⋊#95—22no—
131C43⋊#95—22no—
132C43⋊#95—22no—
133C43⋊#95—22no—
134C43⋊#95—22no—
135C43⋊#95—41no—
136C43⋊#95C2×C414yes—
137C43⋊#95D414yescomplemented
138C23×C4×C43C2311yescharacteristic
139C23×C4×C43C2311yescharacteristic
140C23×C4×C43C2311yescharacteristic
141C23×C4×C43C2311yescharacteristic
142C23×C4×C43C2311yescharacteristic
143C23×C4×C43C2311yescharacteristic
144C23×C4×C43C2311yescharacteristic
145C2×C42×C43—22no—
146C2×C42×C43—22no—
147C2×C42×C43—22no—
148C2×C42×C43—22no—
149C2×C42×C43—22no—
150C2×C42×C43—22no—
151C2×C42×C43—22no—
152C2×C42×C43—41no—
153C2×C42×C43—41no—
154#95×C43—22no—
155#95×C43—22no—
156#95×C43C2×C414yes—
157#95×C43D414yescomplemented
158C24×C43C2411yescharacteristic
159C23×D43—21no—
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×D43—21no—
185C23×D43C22×C412yes—
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×C43—21no—
223C22×C4×C43—21no—
224C22×C4×C43—21no—
225C22×C4×C43C22×C412yes—
226C22×C4×C43C22×C412yes—
227C22×C4×C43C22×C412yes—
228C22×C4×C43C2×D412yes—
229C22×C4×C43C2×D412yes—
230C22×C4×C43C2×D412yes—
231C22×C4×C43C2×D412yes—
232C22×C4×C43C2×D412yes—
233C22×C4×C43#4112yes—
234C22×C4×C43#4112yes—
235C22×C4×C43#4112yes—
236C22×C4×C43#4112yes—
237C22×C4×C43#4112yes—
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×Dic43C22×C412yes—
275C22×Dic43C22×C412yes—
276C22×Dic43C2×D412yes—
277C22×Dic43C2×D412yes—
278C22×Dic43C2×D412yes—
279C22×Dic43#4112yes—
280C2×D172—28no—
281C2×D172—28no—
282C2×D172—44no—
283C2×D172—44no—
284C2×D172—44no—
285C2×D172—44no—
286C2×D172—44no—
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—
294C42×C43—44no—
295C42×C43—44no—
296C42×C43—44no—
297(C2×D43)⋊C4—28no—
298(C2×D43)⋊C4—28no—
299(C2×D43)⋊C4—28no—
300(C2×D43)⋊C4—28no—
301(C2×D43)⋊C4—28no—
302(C2×D43)⋊C4—44no—
303(C2×D43)⋊C4—44no—
304(C2×D43)⋊C4—44no—
305(C2×D43)⋊C4—44no—
306(C2×D43)⋊C4—44no—
307(C2×D43)⋊C4—44no—
308C4⋊Dic43—44no—
309Dic43⋊C4—44no—
310Dic43⋊C4—44no—
311Dic43⋊C4—44no—
312C4×Dic43—44no—
313C23×C43C23×C411yescharacteristic
314C23×C43C22×D411yescharacteristic
315C23×C43C22×D411yescharacteristic
316C23×C43C22×D411yescharacteristic
317C23×C43C2×#4111yescharacteristic
318C23×C43C2×#4111yescharacteristic
319C23×C43C2×#4111yescharacteristic
320C23×C43C2×#4111yescharacteristic
321C23×C43C2×#4111yescharacteristic
322C23×C43C2×#4111yescharacteristic
323C23×C43C2×#4111yescharacteristic
324C23×C43H(5,𝔽2)11yescharacteristic
325C23×C43H(5,𝔽2)11yescharacteristic
326C23×C43H(5,𝔽2)11yescharacteristic
327C23×C432−1+411yescharacteristic
328C22×D43—22no—
329C22×D43—22no—
330C22×D43—22no—
331C22×D43—22no—
332C22×D43—22no—
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—41no—
354C22×D43—41no—
355C22×D43—41no—
356C22×D43—41no—
357C22×D43—41no—
358C22×D43—41no—
359C22×D43—41no—
360C22×D43—41no—
361C22×D43—41no—
362C22×D43—41no—
363C22×D43—41no—
364C22×D43—41no—
365C22×D43—41no—
366C22×D43—41no—
367C22×D43—41no—
368C22×D43—41no—
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×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—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—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#11714yes—
445C2×C4×C43C4×D414yes—
446C2×C4×C43#12114yes—
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—41no—
463C2×Dic43—41no—
464C2×Dic43—41no—
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×Dic43C4×D414yes—
489D172—416no—
490C4×D43—416no—
491#14012—431nomaximal, Sylow
492C22×C43C2×#11711yescharacteristic
493C22×C43C2×C4×D411yescharacteristic
494C22×C43C2×C4×D411yescharacteristic
495C22×C43C2×C4×D411yescharacteristic
496C22×C43C4×#4111yescharacteristic
497C22×C43#51811yescharacteristic
498C22×C43#52011yescharacteristic
499C22×C43C2×#12111yescharacteristic
500C22×C43#52511yescharacteristic
501C22×C43#52911yescharacteristic
502C22×C43#52911yescharacteristic
503C22×C43#52911yescharacteristic
504C22×C43#53211yescharacteristic
505C22×C43#53211yescharacteristic
506C22×C43#53211yescharacteristic
507C22×C43#53811yescharacteristic
508C22×C43#53911yescharacteristic
509C22×C43#54011yescharacteristic
510C22×C43#54211yescharacteristic
511C22×C43D4211yescharacteristic
512C22×C43D4211yescharacteristic
513C22×C43#54611yescharacteristic
514C22×C43#54611yescharacteristic
515C22×C43#54611yescharacteristic
516C22×C43#54611yescharacteristic
517C22×C43#54711yescharacteristic
518C22×C43#54711yescharacteristic
519C22×C43#54811yescharacteristic
520C22×C43#55011yescharacteristic
521C22×C43#55111yescharacteristic
522C22×C43#55111yescharacteristic
523C22×C43#55111yescharacteristic
524C22×C43#55311yescharacteristic
525C22×C43#55511yescharacteristic
526C22×C43#55611yescharacteristic
527C2×D43—24no—
528C2×D43—24no—
529C2×D43—24no—
530C2×D43—42no—
531C2×D43—42no—
532C2×D43—42no—
533C2×D43—42no—
534C2×D43—42no—
535C2×D43—42no—
536C2×D43—42no—
537C2×D43—42no—
538C2×D43—42no—
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—81no—
550C2×D43—81no—
551C2×D43—81no—
552C2×D43—81no—
553C2×D43—81no—
554C2×D43—81no—
555C2×D43—81no—
556C2×D43—81no—
557C4×C43—24no—
558C4×C43—24no—
559C4×C43—24no—
560C4×C43—42no—
561C4×C43—42no—
562C4×C43—42no—
563C4×C43—42no—
564Dic43—24no—
565Dic43—42no—
566Dic43—42no—
567Dic43—42no—
568Dic43—81no—
569Dic43—81no—
570C2×#390—431no—
571C2×#388—431no—
572C2×#388—431no—
573C2×#388—431no—
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×#95D4311yescharacteristic, complemented
585C2×C43#229311yescharacteristic
586C2×C43C4×#12111yescharacteristic
587C2×C43#233511yescharacteristic
588C2×C43#234211yescharacteristic
589C2×C43#235411yescharacteristic
590C2×C43#235811yescharacteristic
591C2×C43#236111yescharacteristic
592C2×C43#242511yescharacteristic
593C2×C43#242811yescharacteristic
594C2×C43#246111yescharacteristic
595C2×C43#246711yescharacteristic
596C2×C43#252111yescharacteristic
597C2×C43#253111yescharacteristic
598C2×C43#255511yescharacteristic
599C2×C43#256011yescharacteristic
600D43—44no—
601D43—82no—
602C23×D4—431no—
603C24×C4—431no—
604C22×C4⋊C4—431no—
605C22×C4⋊C4—431no—
606C22×C4⋊C4—431no—
607C22×C4⋊C4—431no—
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⋊C4—431no—
617C22×C22⋊C4—431no—
618C22×C22⋊C4—431no—
619C22×C42—431no—
620C22×C42C2×D4311yescharacteristic
621C22×C42C2×D4311yescharacteristic
622C22×C42C2×D4311yescharacteristic
623#390—864no—
624#388—864no—
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×#95C2×D4311yescharacteristic
641C2×#95C2×D4311yescharacteristic
642C2×#95C2×D4311yescharacteristic
643C2×#95C2×D4311yescharacteristic
644C43#1401211yescharacteristic, complemented, Sylow
645C25—431no—
646C25—431no—
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—434no—
659C23×C4—431no—
660C23×C4—431no—
661C23×C4—862no—
662C23×C4—862no—
663C23×C4—862no—
664C23×C4—862no—
665C23×C4—1721no—
666C23×C4—1721no—
667C23×C4C22×D4311yescharacteristic
668C23×C4C22×D4311yescharacteristic
669C23×C4C22×D4311yescharacteristic
670C23×C4C22×D4311yescharacteristic
671C23×C4C22×D4311yescharacteristic
672C23×C4C22×D4311yescharacteristic
673C23×C4C22×D4311yescharacteristic
674C2×C4⋊C4—862no—
675C2×C4⋊C4—862no—
676C2×C4⋊C4—862no—
677C2×C4⋊C4—862no—
678C2×C4⋊C4—862no—
679C2×C4⋊C4—862no—
680C2×C4⋊C4—862no—
681C2×C4⋊C4—862no—
682C2×C4⋊C4—1721no—
683C2×C4⋊C4—1721no—
684C2×C4⋊C4—1721no—
685C2×C4⋊C4—1721no—
686C2×C22⋊C4—434no—
687C2×C22⋊C4—434no—
688C2×C22⋊C4—434no—
689C2×C22⋊C4—434no—
690C2×C22⋊C4—862no—
691C2×C22⋊C4—862no—
692C2×C22⋊C4—862no—
693C2×C22⋊C4—862no—
694C2×C22⋊C4—862no—
695C2×C22⋊C4—862no—
696C2×C22⋊C4—862no—
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⋊C4—1721no—
719C2×C42—22no—
720C2×C42—22no—
721C2×C42—22no—
722C2×C42—22no—
723C2×C42—22no—
724C2×C42—22no—
725C2×C42—22no—
726C2×C42—41no—
727C2×C42—41no—
728C2×C42—862no—
729C2×C42—862no—
730C2×C42—1721no—
731#95—22no—
732#95—22no—
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—1721no—
743#95C4×D4314yes—
744#95D17214yescomplemented
745C24—432no—
746C24—432no—
747C24—432no—
748C24—432no—
749C24—861no—
750C24—861no—
751C24—861no—
752C24—861no—
753C24—861no—
754C24—861no—
755C24—861no—
756C24—861no—
757C24—861no—
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—
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—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—432no—
820C22×C4—432no—
821C22×C4—432no—
822C22×C4—432no—
823C22×C4—432no—
824C22×C4—432no—
825C22×C4—868no—
826C22×C4—861no—
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—868no—
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—1724no—
864C22×C4—1724no—
865C22×C4—1724no—
866C22×C4—1724no—
867C22×C4—1724no—
868C22×C4C2×C4×D4312yes—
869C22×C4C2×C4×D4312yes—
870C22×C4C2×C4×D4312yes—
871C22×C4C2×D17212yes—
872C22×C4C2×D17212yes—
873C22×C4C2×D17212yes—
874C22×C4#1062189812yes—
875C22×C4#1062189812yes—
876C22×C4#1062189812yes—
877C22×C4#1062189812yes—
878C22×C4#1062189812yes—
879C22×C4D4×D4312yes—
880C22×C4D4×D4312yes—
881C4⋊C4—1724no—
882C4⋊C4—1724no—
883C4⋊C4—1724no—
884C4⋊C4—1724no—
885C22⋊C4—868no—
886C22⋊C4—868no—
887C22⋊C4—868no—
888C22⋊C4—868no—
889C22⋊C4—868no—
890C22⋊C4—1724no—
891C22⋊C4—1724no—
892C22⋊C4—1724no—
893C22⋊C4—1724no—
894C22⋊C4—1724no—
895C22⋊C4—1724no—
896C42—44no—
897C42—44no—
898C42—44no—
899C42—1724no—
900C23—434no—
901C23—862no—
902C23—862no—
903C23—862no—
904C23—862no—
905C23—862no—
906C23—862no—
907C23—862no—
908C23—862no—
909C23—862no—
910C23—862no—
911C23—862no—
912C23—862no—
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—1721no—
927C23—1721no—
928C23—1721no—
929C23—1721no—
930C23—1721no—
931C23—1721no—
932C23—1721no—
933C23—1721no—
934C23—1721no—
935C23—1721no—
936C23—1721no—
937C23—1721no—
938C23—1721no—
939C23—1721no—
940C23—1721no—
941C23—1721no—
942C23—1721no—
943C23—1721no—
944C23—1721no—
945C23—1721no—
946C23—1721no—
947C23—1721no—
948C23—1721no—
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—
970C23C22×C4×D4311yescharacteristic
971C23C2×D4×D4311yescharacteristic
972C23C2×D4×D4311yescharacteristic
973C23C22×D17211yescharacteristic
974C23#41×D4311yescharacteristic
975C23#41×D4311yescharacteristic
976C23C2×#1062189811yescharacteristic
977C23C2×#1062189811yescharacteristic
978C23C2×#1062189811yescharacteristic
979C23C2×#1062189811yescharacteristic
980C23C2×#1062189811yescharacteristic
981C23#1306337011yescharacteristic
982C23#1306337111yescharacteristic
983C23#1306337111yescharacteristic
984C23#1306337311yescharacteristic
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—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—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—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—434no—
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—17216no—
1049C2×C4—1721no—
1050C2×C4—1721no—
1051C2×C4—1721no—
1052C2×C4—1721no—
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#1306328214yes—
1076C2×C4C4×D17214yes—
1077C2×C4#1306329814yes—
1078C22—864no—
1079C22—864no—
1080C22—864no—
1081C22—3441no—
1082C22—3441no—
1083C22—3441no—
1084C22—3441no—
1085C22—3441no—
1086C22—3441no—
1087C22—3441no—
1088C22—3441no—
1089C22—1722no—
1090C22—1722no—
1091C22—1722no—
1092C22—1722no—
1093C22—1722no—
1094C22—1722no—
1095C22—1722no—
1096C22—1722no—
1097C22—1722no—
1098C22—1722no—
1099C22—1722no—
1100C22—1722no—
1101C22—1722no—
1102C22—1722no—
1103C22—1722no—
1104C22—1722no—
1105C22—1722no—
1106C22—1722no—
1107C22—1722no—
1108C22C2×#1306328211yescharacteristic
1109C22C4×D4×D4311yescharacteristic
1110C22C4×D4×D4311yescharacteristic
1111C22C2×C4×D17211yescharacteristic
1112C22C4×#1062189811yescharacteristic
1113C22#1458337111yescharacteristic
1114C22#1458338111yescharacteristic
1115C22C2×#1306329811yescharacteristic
1116C22#1458340811yescharacteristic
1117C22#1458342711yescharacteristic
1118C22#1458343311yescharacteristic
1119C22#1458343311yescharacteristic
1120C22#1458344611yescharacteristic
1121C22#1458344911yescharacteristic
1122C22#1458344911yescharacteristic
1123C22#1458348211yescharacteristic
1124C22#1458349611yescharacteristic
1125C22#1458350411yescharacteristic
1126C22#1458352111yescharacteristic
1127C22D4×D17211yescharacteristic
1128C22D4×D17211yescharacteristic
1129C22#1458353911yescharacteristic
1130C22#1458353911yescharacteristic
1131C22#1458354411yescharacteristic
1132C22#1458354511yescharacteristic
1133C22#1458355011yescharacteristic
1134C22#1458355011yescharacteristic
1135C22#1458356111yescharacteristic
1136C22#1458357011yescharacteristic
1137C22#1458357311yescharacteristic
1138C22#1458357311yescharacteristic
1139C22#1458357811yescharacteristic
1140C22#1458359311yescharacteristic
1141C22#1458361211yescharacteristic
1142C22#1458362111yescharacteristic
1143C4—24no—
1144C4—24no—
1145C4—24no—
1146C4—42no—
1147C4—42no—
1148C4—42no—
1149C4—42no—
1150C4—864no—
1151C4—3441no—
1152C4—3441no—
1153C4—1722no—
1154C4—1722no—
1155C4—1722no—
1156C2—3442no—
1157C2—1724no—
1158C2#1913705911yescharacteristic
1159C2C4×#1306329811yescharacteristic
1160C2#1913737911yescharacteristic
1161C2#1913743811yescharacteristic
1162C2#1913754011yescharacteristic
1163C2#1913757711yescharacteristic
1164C2#1913761311yescharacteristic
1165C2#1913814611yescharacteristic
1166C2#1913818311yescharacteristic
1167C2#1913856211yescharacteristic
1168C2#1913864611yescharacteristic
1169C2#1913929211yescharacteristic
1170C2#1913943611yescharacteristic
1171C2#1913966411yescharacteristic
1172C2#1913973311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC4×#95×C43C2
socle, cosocleC24×C43C24
prime radicalC23×D172C22
hypercenterC4×#95D43
hypocenterC43#14012
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
2. C2×#14582790C2semidirect
3. C2×#14582790C2semidirect
4. C2×#14582788C2semidirect
6. C2×#14582758C2semidirect
7. C2×C4×(C2×D43)⋊C4C2semidirect
8. #19132859C2semidirect
9. #19132843C2semidirect
10. #19132839C2semidirect
12. #19132833C2semidirect
13. #19132829C2semidirect
14. #19132828C2semidirect
15. C4×#95×C43C2semidirect
38. #14582777C4semidirect
137. C43⋊#95D4semidirect
157. #95×C43D4semidirect
584. C4×#95D43semidirect
644. C43#14012semidirect
744. #95D172semidirect

Maximal subgroups

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

subgroupindex
C2×#145828012
C2×#145827902
C2×#145827882
C2×#145827772
C2×#145827582
C2×C4×(C2×D43)⋊C42
#191328592
#191328432
#191328392
#191328352
#191328332
#191328292
#191328282
C4×#95×C432
#1401243