Finite Group Databasebeta

← #25017928

Subgroups — #25017928

Order 11008.

1710 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582792C211yesmaximal, characteristic
2C2×C22⋊C4×Dic43C211yesmaximal, characteristic
3#19132832C211yesmaximal, characteristic
4#19132832C211yesmaximal, characteristic
5#19132829C211yesmaximal, characteristic, complemented
6#19132827C211yesmaximal, characteristic, complemented
7#19132824C211yesmaximal, characteristic, complemented
8#19132822C211yesmaximal, characteristic, complemented
9#19132820C211yesmaximal, characteristic, complemented
10#19132820C211yesmaximal, characteristic, complemented
11#19132817C211yesmaximal, characteristic
12#19132817C211yesmaximal, characteristic
13C4×C43⋊#95C211yesmaximal, characteristic, complemented
14#95×Dic43C211yesmaximal, characteristic, complemented
15C2×C43×#388C211yesmaximal, characteristic
16C24×Dic43C2211yescharacteristic
17C22×C4⋊Dic43C2211yescharacteristic
18C22×C22⋊Dic43C2211yescharacteristic
19C22×C22⋊Dic43C2211yescharacteristic
20C22×C22⋊Dic43C2211yescharacteristic
21C22×C4×Dic43C2211yescharacteristic
22C22×C4×Dic43C2211yescharacteristic
23C22×C4×Dic43C2211yescharacteristic
24C22×C4×Dic43C2211yescharacteristic
25C22×C4×Dic43C2211yescharacteristic
26#14582792C418yescomplemented
27C22⋊C4×Dic43C418yescomplemented
28C2×C43⋊#95C2211yescharacteristic
29C2×C43⋊#95C2211yescharacteristic
30C2×C43⋊#95C2211yescharacteristic
31C2×C43⋊#95C2211yescharacteristic
32C2×C43⋊#95C2211yescharacteristic
33C2×C43⋊#95C2211yescharacteristic
34C2×C43⋊#95C2211yescharacteristic
35C2×C43⋊#95C2211yescharacteristic
36C2×C43⋊#95C2211yescharacteristic
37C2×C43⋊#95C2211yescharacteristic
38C2×C43⋊#95C2211yescharacteristic
39C2×C43⋊#95C2211yescharacteristic
40C2×C43⋊#95C2211yescharacteristic
41C2×C43⋊#95C2211yescharacteristic
42C2×C43⋊#95C2211yescharacteristic
43C2×C43⋊#95C2211yescharacteristic
44C2×C43⋊#95C2211yescharacteristic
45C2×C43⋊#95C2211yescharacteristic
46C22×C4⋊C4×C43C2211yescharacteristic
47C22×C22⋊C4×C43C2211yescharacteristic
48C22×C22⋊C4×C43C2211yescharacteristic
49C22×C22⋊C4×C43C2211yescharacteristic
50C22×C42×C43C2211yescharacteristic
51C43×#388C418yescomplemented
52C2×#95×C43C2211yescharacteristic
53C2×#95×C43C2211yescharacteristic
54C23×Dic43—22no—
55C23×Dic43—22no—
56C23×Dic43—41no—
57C23×Dic43—41no—
58C23×Dic43—41no—
59C23×Dic43—41no—
60C23×Dic43C2×C414yes—
61C23×Dic43C2311yescharacteristic
62C23×Dic43C2311yescharacteristic
63C23×Dic43C2311yescharacteristic
64C23×Dic43C2311yescharacteristic
65C23×Dic43C2311yescharacteristic
66C23×Dic43C2311yescharacteristic
67C23×Dic43C2311yescharacteristic
68C23×Dic43C2311yescharacteristic
69C2×C4⋊Dic43—41no—
70C2×C4⋊Dic43—41no—
71C2×C4⋊Dic43C2×C414yescomplemented
72C2×C22⋊Dic43—22no—
73C2×C22⋊Dic43—22no—
74C2×C22⋊Dic43—41no—
75C2×C22⋊Dic43—41no—
76C2×C22⋊Dic43—41no—
77C2×C22⋊Dic43—41no—
78C2×C22⋊Dic43C2×C414yes—
79C2×C22⋊Dic43C2×C414yes—
80C2×C22⋊Dic43C2×C414yes—
81C2×C4×Dic43—22no—
82C2×C4×Dic43—22no—
83C2×C4×Dic43—41no—
84C2×C4×Dic43—41no—
85C2×C4×Dic43—41no—
86C2×C4×Dic43—41no—
87C2×C4×Dic43—41no—
88C2×C4×Dic43—41no—
89C2×C4×Dic43—41no—
90C2×C4×Dic43—41no—
91C2×C4×Dic43—41no—
92C2×C4×Dic43—41no—
93C2×C4×Dic43C2×C414yes—
94C2×C4×Dic43C2×C414yes—
95C2×C4×Dic43C2×C414yescomplemented
96C43⋊#95—22no—
97C43⋊#95—22no—
98C43⋊#95—22no—
99C43⋊#95—22no—
100C43⋊#95—22no—
101C43⋊#95—22no—
102C43⋊#95—41no—
103C43⋊#95—41no—
104C43⋊#95—41no—
105C43⋊#95—41no—
106C43⋊#95—41no—
107C43⋊#95—41no—
108C43⋊#95—41no—
109C43⋊#95—41no—
110C43⋊#95C2×C414yes—
111C43⋊#95C2×C414yes—
112C43⋊#95C2×C414yescomplemented
113C43⋊#95C2×C414yescomplemented
114C25×C43C2311yescharacteristic
115C23×C4×C43C2311yescharacteristic
116C23×C4×C43C2311yescharacteristic
117C23×C4×C43C2311yescharacteristic
118C23×C4×C43C2311yescharacteristic
119C23×C4×C43C2311yescharacteristic
120C23×C4×C43C2311yescharacteristic
121C2×C4⋊C4×C43—41no—
122C2×C4⋊C4×C43—41no—
123C2×C4⋊C4×C43C2×C414yescomplemented
124C2×C22⋊C4×C43—41no—
125C2×C22⋊C4×C43—41no—
126C2×C22⋊C4×C43—41no—
127C2×C22⋊C4×C43—41no—
128C2×C22⋊C4×C43C2×C414yes—
129C2×C22⋊C4×C43C2×C414yes—
130C2×C22⋊C4×C43C2×C414yes—
131C2×C22⋊C4×C43C2×C414yes—
132C2×C22⋊C4×C43C2×C414yes—
133C2×C42×C43—41no—
134C2×C42×C43—41no—
135C2×C42×C43C2×C414yescomplemented
136#95×C43C2×C414yescomplemented
137#95×C43C2×C414yescomplemented
138C24×C43—21no—
139C24×C43—21no—
140C24×C43—21no—
141C24×C43—21no—
142C24×C43—21no—
143C24×C43—21no—
144C24×C43—21no—
145C24×C43—21no—
146C24×C43—21no—
147C24×C43—21no—
148C24×C43—21no—
149C24×C43—21no—
150C24×C43C22×C412yes—
151C24×C43C22×C412yes—
152C24×C43C22×C412yes—
153C24×C43C2411yescharacteristic
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43C22×C412yes—
187C22×C4×C43C22×C412yes—
188C22×C4×C43C22×C412yes—
189C22×C4×C43C22×C412yes—
190C22×C4×C43C22×C412yes—
191C22×C4×C43C22×C412yes—
192C22×C4×C43C22×C412yes—
193C22×C4×C43C22×C412yes—
194C22×C4×C43C22×C412yes—
195C22×C4×C43C22×C412yes—
196C22×Dic43—28no—
197C22×Dic43—21no—
198C22×Dic43—21no—
199C22×Dic43—21no—
200C22×Dic43—21no—
201C22×Dic43—21no—
202C22×Dic43—21no—
203C22×Dic43—21no—
204C22×Dic43—21no—
205C22×Dic43—21no—
206C22×Dic43—21no—
207C22×Dic43—21no—
208C22×Dic43—21no—
209C22×Dic43—21no—
210C22×Dic43—21no—
211C22×Dic43—21no—
212C22×Dic43—21no—
213C22×Dic43—21no—
214C22×Dic43—21no—
215C22×Dic43—21no—
216C22×Dic43—21no—
217C22×Dic43—21no—
218C22×Dic43—21no—
219C22×Dic43—21no—
220C22×Dic43—21no—
221C22×Dic43—21no—
222C22×Dic43—21no—
223C22×Dic43—21no—
224C22×Dic43—21no—
225C22×Dic43—21no—
226C22×Dic43—21no—
227C22×Dic43—21no—
228C22×Dic43—21no—
229C22×Dic43—21no—
230C22×Dic43—21no—
231C22×Dic43—21no—
232C22×Dic43—21no—
233C22×Dic43—21no—
234C22×Dic43—21no—
235C22×Dic43—21no—
236C22×Dic43—21no—
237C22×Dic43—21no—
238C22×Dic43—21no—
239C22×Dic43—21no—
240C22×Dic43—21no—
241C22×Dic43—44no—
242C22×Dic43—44no—
243C22×Dic43—44no—
244C22×Dic43—44no—
245C22×Dic43—44no—
246C22×Dic43—44no—
247C22×Dic43C22×C412yes—
248C22×Dic43C22×C412yes—
249C22×Dic43C22×C412yes—
250C22×Dic43C22×C412yes—
251C22×Dic43C22×C412yes—
252C22×Dic43C22×C412yes—
253C22×Dic43C22×C412yes—
254C22×Dic43C22×C412yes—
255C22×Dic43#4112yes—
256C22×Dic43#4112yes—
257C22×Dic43#4112yes—
258C22×Dic43#4112yes—
259C4⋊C4×C43—44no—
260C22⋊C4×C43—44no—
261C22⋊C4×C43—44no—
262C22⋊C4×C43C42116yescomplemented
263C42×C43—44no—
264C22⋊Dic43—28no—
265C22⋊Dic43—44no—
266C22⋊Dic43—44no—
267C4⋊Dic43—44no—
268C4×Dic43—44no—
269C4×Dic43—44no—
270C4×Dic43—44no—
271C4×Dic43—44no—
272C4×Dic43—44no—
273C23×C43—22no—
274C23×C43—22no—
275C23×C43—22no—
276C23×C43—22no—
277C23×C43—22no—
278C23×C43—22no—
279C23×C43—22no—
280C23×C43—22no—
281C23×C43—22no—
282C23×C43—22no—
283C23×C43—22no—
284C23×C43—22no—
285C23×C43—22no—
286C23×C43—22no—
287C23×C43—22no—
288C23×C43—22no—
289C23×C43—22no—
290C23×C43—22no—
291C23×C43—41no—
292C23×C43—41no—
293C23×C43—41no—
294C23×C43—41no—
295C23×C43—41no—
296C23×C43—41no—
297C23×C43—41no—
298C23×C43—41no—
299C23×C43—41no—
300C23×C43—41no—
301C23×C43—41no—
302C23×C43—41no—
303C23×C43—41no—
304C23×C43—41no—
305C23×C43—41no—
306C23×C43—41no—
307C23×C43C2×C4214yes—
308C23×C43C23×C411yescharacteristic
309C23×C43C23×C411yescharacteristic
310C23×C43C23×C411yescharacteristic
311C23×C43C2×#4111yescharacteristic
312C23×C43C2×#4111yescharacteristic
313C23×C43C2×#4111yescharacteristic
314C23×C43C2×#4111yescharacteristic
315C23×C43H(5,𝔽2)11yescharacteristic
316C23×C43H(5,𝔽2)11yescharacteristic
317C23×C43H(5,𝔽2)11yescharacteristic
318C23×C43H(5,𝔽2)11yescharacteristic
319C23×C43H(5,𝔽2)11yescharacteristic
320C23×C43H(5,𝔽2)11yescharacteristic
321C23×C432−1+411yescharacteristic
322C23×C432−1+411yescharacteristic
323C2×C4×C43—22no—
324C2×C4×C43—22no—
325C2×C4×C43—22no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43—22no—
330C2×C4×C43—22no—
331C2×C4×C43—22no—
332C2×C4×C43—22no—
333C2×C4×C43—22no—
334C2×C4×C43—22no—
335C2×C4×C43—22no—
336C2×C4×C43—22no—
337C2×C4×C43—22no—
338C2×C4×C43—22no—
339C2×C4×C43—22no—
340C2×C4×C43—22no—
341C2×C4×C43—22no—
342C2×C4×C43—22no—
343C2×C4×C43—22no—
344C2×C4×C43—22no—
345C2×C4×C43—22no—
346C2×C4×C43—22no—
347C2×C4×C43—41no—
348C2×C4×C43—41no—
349C2×C4×C43—41no—
350C2×C4×C43—41no—
351C2×C4×C43—41no—
352C2×C4×C43—41no—
353C2×C4×C43—41no—
354C2×C4×C43—41no—
355C2×C4×C43—41no—
356C2×C4×C43—41no—
357C2×C4×C43—41no—
358C2×C4×C43—41no—
359C2×C4×C43—41no—
360C2×C4×C43—41no—
361C2×C4×C43—41no—
362C2×C4×C43—41no—
363C2×C4×C43C2×C4214yes—
364C2×C4×C43C2×C4214yes—
365C2×Dic43—22no—
366C2×Dic43—22no—
367C2×Dic43—22no—
368C2×Dic43—22no—
369C2×Dic43—22no—
370C2×Dic43—22no—
371C2×Dic43—22no—
372C2×Dic43—22no—
373C2×Dic43—22no—
374C2×Dic43—22no—
375C2×Dic43—22no—
376C2×Dic43—22no—
377C2×Dic43—22no—
378C2×Dic43—22no—
379C2×Dic43—22no—
380C2×Dic43—22no—
381C2×Dic43—22no—
382C2×Dic43—22no—
383C2×Dic43—22no—
384C2×Dic43—22no—
385C2×Dic43—22no—
386C2×Dic43—22no—
387C2×Dic43—22no—
388C2×Dic43—22no—
389C2×Dic43—22no—
390C2×Dic43—22no—
391C2×Dic43—22no—
392C2×Dic43—22no—
393C2×Dic43—22no—
394C2×Dic43—22no—
395C2×Dic43—416no—
396C2×Dic43—41no—
397C2×Dic43—41no—
398C2×Dic43—41no—
399C2×Dic43—41no—
400C2×Dic43—41no—
401C2×Dic43—41no—
402C2×Dic43—41no—
403C2×Dic43—41no—
404C2×Dic43—41no—
405C2×Dic43—41no—
406C2×Dic43—41no—
407C2×Dic43—41no—
408C2×Dic43—41no—
409C2×Dic43—41no—
410C2×Dic43—41no—
411C2×Dic43—41no—
412C2×Dic43—41no—
413C2×Dic43—41no—
414C2×Dic43—41no—
415C2×Dic43—41no—
416C2×Dic43—41no—
417C2×Dic43—41no—
418C2×Dic43—41no—
419C2×Dic43—41no—
420C2×Dic43#11714yes—
421C2×Dic43#11714yes—
422#13788—431nomaximal, Sylow
423C22×C43—24no—
424C22×C43—24no—
425C22×C43—24no—
426C22×C43—42no—
427C22×C43—42no—
428C22×C43—42no—
429C22×C43—42no—
430C22×C43—42no—
431C22×C43—42no—
432C22×C43—42no—
433C22×C43—42no—
434C22×C43—42no—
435C22×C43—42no—
436C22×C43—42no—
437C22×C43—42no—
438C22×C43C22×C4211yescharacteristic
439C22×C43C2×#11711yescharacteristic
440C22×C43C2×#11711yescharacteristic
441C22×C43C4×#4111yescharacteristic
442C22×C43C4×#4111yescharacteristic
443C22×C43C4×#4111yescharacteristic
444C22×C43C4×#4111yescharacteristic
445C22×C43#51811yescharacteristic
446C22×C43#51811yescharacteristic
447C22×C43#51811yescharacteristic
448C22×C43#51811yescharacteristic
449C22×C43#51811yescharacteristic
450C22×C43#51811yescharacteristic
451C22×C43#52011yescharacteristic
452C22×C43#52011yescharacteristic
453C22×C43#52011yescharacteristic
454C22×C43#52011yescharacteristic
455C22×C43#52011yescharacteristic
456C22×C43#52011yescharacteristic
457C22×C43#53811yescharacteristic
458C22×C43#53811yescharacteristic
459C22×C43#53811yescharacteristic
460C22×C43#53811yescharacteristic
461C22×C43#53811yescharacteristic
462C22×C43#53811yescharacteristic
463C22×C43#53911yescharacteristic
464C22×C43#53911yescharacteristic
465C22×C43#54011yescharacteristic
466C22×C43#54011yescharacteristic
467C22×C43#54011yescharacteristic
468C22×C43#54111yescharacteristic
469C22×C43#54211yescharacteristic
470C22×C43#54211yescharacteristic
471C22×C43#54211yescharacteristic
472C22×C43#54211yescharacteristic
473C4×C43—24no—
474C4×C43—24no—
475C4×C43—42no—
476C4×C43—42no—
477C4×C43—42no—
478C4×C43—42no—
479Dic43—24no—
480Dic43—24no—
481Dic43—42no—
482Dic43—42no—
483Dic43—42no—
484Dic43—42no—
485Dic43—42no—
486Dic43—42no—
487C2×#388—431no—
488C2×#388D4311yescharacteristic
489C2×C4×C22⋊C4—431no—
490#1437—431no—
491#1437—431no—
492#1436—431no—
493#1436—431no—
494C4⋊#95—431no—
495#1434—431no—
496#1434—431no—
497#1434—431no—
498C22⋊#95—431no—
499C22⋊#95—431no—
500C4×#95—431no—
501C4×#95—431no—
502C2×C43—44no—
503C2×C43C4×#11711yescharacteristic
504C2×C43#227511yescharacteristic
505C2×C43#227511yescharacteristic
506C2×C43#231211yescharacteristic
507C2×C43#231411yescharacteristic
508C2×C43#231811yescharacteristic
509C2×C43#231911yescharacteristic
510C2×C43#233311yescharacteristic
511C2×C43#233311yescharacteristic
512C2×C43#233411yescharacteristic
513C2×C43#233411yescharacteristic
514C2×C43#233511yescharacteristic
515C2×C43#233511yescharacteristic
516C2×C43#233711yescharacteristic
517C2×C43#233711yescharacteristic
518C24×C4—431no—
519C22×C4⋊C4—431no—
520C22×C4⋊C4C2×D4311yescharacteristic
521C22×C22⋊C4—431no—
522C22×C22⋊C4—431no—
523C22×C22⋊C4—431no—
524C22×C22⋊C4C2×D4311yescharacteristic
525C22×C22⋊C4C2×D4311yescharacteristic
526C22×C22⋊C4C2×D4311yescharacteristic
527C22×C42—431no—
528C22×C42—431no—
529C22×C42—431no—
530C22×C42—431no—
531C22×C42—431no—
532C22×C42C2×D4311yescharacteristic
533#388—438no—
534#388Dic4318yescomplemented
535C4×C22⋊C4—438no—
536C2×#95—431no—
537C2×#95—431no—
538C2×#95—431no—
539C2×#95—431no—
540C2×#95—431no—
541C2×#95—431no—
542C2×#95—431no—
543C2×#95—431no—
544C2×#95—431no—
545C2×#95—431no—
546C2×#95—431no—
547C2×#95—431no—
548C2×#95—431no—
549C2×#95—431no—
550C2×#95—431no—
551C2×#95—431no—
552C2×#95—431no—
553C2×#95—431no—
554C2×#95C2×D4311yescharacteristic
555C2×#95C2×D4311yescharacteristic
556C43#1378811yescharacteristic, complemented, Sylow
557C25C22×D4311yescharacteristic
558C23×C4—431no—
559C23×C4—431no—
560C23×C4—431no—
561C23×C4—431no—
562C23×C4—431no—
563C23×C4—431no—
564C23×C4—431no—
565C23×C4—431no—
566C23×C4—434no—
567C23×C4—862no—
568C23×C4—862no—
569C23×C4—1721no—
570C23×C4—1721no—
571C23×C4—1721no—
572C23×C4—1721no—
573C23×C4C22×D4311yescharacteristic
574C23×C4C22×D4311yescharacteristic
575C23×C4C22×D4311yescharacteristic
576C23×C4C22×D4311yescharacteristic
577C23×C4C22×D4311yescharacteristic
578C23×C4C22×D4311yescharacteristic
579C2×C4⋊C4—41no—
580C2×C4⋊C4—41no—
581C2×C4⋊C4—434no—
582C2×C4⋊C4—1721no—
583C2×C4⋊C4—1721no—
584C2×C4⋊C4C2×Dic4314yescomplemented
585C2×C22⋊C4—41no—
586C2×C22⋊C4—41no—
587C2×C22⋊C4—41no—
588C2×C22⋊C4—41no—
589C2×C22⋊C4—434no—
590C2×C22⋊C4—434no—
591C2×C22⋊C4—434no—
592C2×C22⋊C4—862no—
593C2×C22⋊C4—862no—
594C2×C22⋊C4—1721no—
595C2×C22⋊C4—1721no—
596C2×C22⋊C4—1721no—
597C2×C22⋊C4—1721no—
598C2×C22⋊C4C4×D4314yes—
599C2×C22⋊C4C4×D4314yes—
600C2×C22⋊C4C2×Dic4314yes—
601C2×C22⋊C4C2×Dic4314yes—
602C2×C22⋊C4C2×Dic4314yes—
603C2×C42—41no—
604C2×C42—41no—
605C2×C42—434no—
606C2×C42—434no—
607C2×C42—434no—
608C2×C42—862no—
609C2×C42—862no—
610C2×C42—1721no—
611C2×C42—1721no—
612C2×C42—1721no—
613C2×C42—1721no—
614C2×C42—1721no—
615C2×C42—1721no—
616C2×C42—1721no—
617C2×C42—1721no—
618C2×C42—1721no—
619C2×C42—1721no—
620C2×C42C2×Dic4314yescomplemented
621#95—434no—
622#95—434no—
623#95—434no—
624#95—434no—
625#95—862no—
626#95—862no—
627#95—862no—
628#95—862no—
629#95—862no—
630#95—862no—
631#95—1721no—
632#95—1721no—
633#95—1721no—
634#95—1721no—
635#95—1721no—
636#95—1721no—
637#95—1721no—
638#95—1721no—
639#95C2×Dic4314yescomplemented
640#95C2×Dic4314yescomplemented
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24C2×C4×D4312yes—
654C24C2×C4×D4312yes—
655C24C22×Dic4312yes—
656C24C23×D4311yescharacteristic
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—432no—
690C22×C4—432no—
691C22×C4—432no—
692C22×C4—432no—
693C22×C4—432no—
694C22×C4—432no—
695C22×C4—432no—
696C22×C4—432no—
697C22×C4—432no—
698C22×C4—432no—
699C22×C4—432no—
700C22×C4—432no—
701C22×C4—868no—
702C22×C4—861no—
703C22×C4—861no—
704C22×C4—861no—
705C22×C4—861no—
706C22×C4—861no—
707C22×C4—861no—
708C22×C4—861no—
709C22×C4—861no—
710C22×C4—861no—
711C22×C4—861no—
712C22×C4—861no—
713C22×C4—861no—
714C22×C4—861no—
715C22×C4—861no—
716C22×C4—861no—
717C22×C4—861no—
718C22×C4—861no—
719C22×C4—861no—
720C22×C4—861no—
721C22×C4—861no—
722C22×C4—861no—
723C22×C4—861no—
724C22×C4—861no—
725C22×C4—861no—
726C22×C4—861no—
727C22×C4—861no—
728C22×C4—861no—
729C22×C4—861no—
730C22×C4—861no—
731C22×C4—861no—
732C22×C4—861no—
733C22×C4—861no—
734C22×C4—861no—
735C22×C4—861no—
736C22×C4—861no—
737C22×C4—861no—
738C22×C4—861no—
739C22×C4—861no—
740C22×C4—861no—
741C22×C4—861no—
742C22×C4—861no—
743C22×C4—861no—
744C22×C4—861no—
745C22×C4—861no—
746C22×C4—1724no—
747C22×C4—1724no—
748C22×C4—1724no—
749C22×C4—1724no—
750C22×C4—1724no—
751C22×C4—1724no—
752C22×C4C2×C4×D4312yes—
753C22×C4C2×C4×D4312yes—
754C22×C4C2×C4×D4312yes—
755C22×C4C2×C4×D4312yes—
756C22×C4C22×Dic4312yes—
757C22×C4C22×Dic4312yes—
758C22×C4C22×Dic4312yes—
759C22×C4C22×Dic4312yes—
760C22×C4C22×Dic4312yes—
761C22×C4C22×Dic4312yes—
762C4⋊C4—44no—
763C4⋊C4—1724no—
764C22⋊C4—44no—
765C22⋊C4—44no—
766C22⋊C4—868no—
767C22⋊C4—1724no—
768C22⋊C4—1724no—
769C22⋊C4C4×Dic43116yescomplemented
770C42—44no—
771C42—1724no—
772C42—1724no—
773C42—1724no—
774C42—1724no—
775C42—1724no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23C2×C4×Dic4314yes—
811C23C22×C4×D4311yescharacteristic
812C23C22×C4×D4311yescharacteristic
813C23C23×Dic4311yescharacteristic
814C23#41×D4311yescharacteristic
815C23#41×D4311yescharacteristic
816C23#41×D4311yescharacteristic
817C23#41×D4311yescharacteristic
818C23#1306337011yescharacteristic
819C23#1306337011yescharacteristic
820C23#1306337011yescharacteristic
821C23#1306337011yescharacteristic
822C23#1306337111yescharacteristic
823C23#1306337111yescharacteristic
824C23#1306337211yescharacteristic
825C23#1306337211yescharacteristic
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—434no—
867C2×C4—434no—
868C2×C4—862no—
869C2×C4—862no—
870C2×C4—862no—
871C2×C4—862no—
872C2×C4—862no—
873C2×C4—862no—
874C2×C4—862no—
875C2×C4—862no—
876C2×C4—862no—
877C2×C4—862no—
878C2×C4—862no—
879C2×C4—862no—
880C2×C4—862no—
881C2×C4—862no—
882C2×C4—862no—
883C2×C4—862no—
884C2×C4—862no—
885C2×C4—862no—
886C2×C4—862no—
887C2×C4—862no—
888C2×C4—862no—
889C2×C4—862no—
890C2×C4—862no—
891C2×C4—862no—
892C2×C4—862no—
893C2×C4—862no—
894C2×C4—862no—
895C2×C4—862no—
896C2×C4—862no—
897C2×C4—862no—
898C2×C4—17216no—
899C2×C4—1721no—
900C2×C4—1721no—
901C2×C4—1721no—
902C2×C4—1721no—
903C2×C4—1721no—
904C2×C4—1721no—
905C2×C4—1721no—
906C2×C4—1721no—
907C2×C4—1721no—
908C2×C4—1721no—
909C2×C4—1721no—
910C2×C4—1721no—
911C2×C4—1721no—
912C2×C4—1721no—
913C2×C4—1721no—
914C2×C4—1721no—
915C2×C4—1721no—
916C2×C4—1721no—
917C2×C4—1721no—
918C2×C4—1721no—
919C2×C4—1721no—
920C2×C4—1721no—
921C2×C4—1721no—
922C2×C4—1721no—
923C2×C4C2×C4×Dic4314yes—
924C2×C4C2×C4×Dic4314yes—
925C22—24no—
926C22—24no—
927C22—24no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22C22×C4×Dic4311yescharacteristic
941C22#117×D4311yescharacteristic
942C22#117×D4311yescharacteristic
943C22#1458336711yescharacteristic
944C22#1458336711yescharacteristic
945C22#41×Dic4311yescharacteristic
946C22#41×Dic4311yescharacteristic
947C22#1458337111yescharacteristic
948C22#1458337111yescharacteristic
949C22#1458337111yescharacteristic
950C22#1458337111yescharacteristic
951C22#1458337411yescharacteristic
952C22#1458337411yescharacteristic
953C22#1458337811yescharacteristic
954C22#1458337811yescharacteristic
955C22#1458337811yescharacteristic
956C22#1458337811yescharacteristic
957C22#1458338211yescharacteristic
958C22#1458338211yescharacteristic
959C22#1458348111yescharacteristic
960C22#1458348111yescharacteristic
961C22#1458348311yescharacteristic
962C22#1458348311yescharacteristic
963C22#1458348511yescharacteristic
964C22#1458348811yescharacteristic
965C22#1458349011yescharacteristic
966C22#1458349211yescharacteristic
967C22#1458349911yescharacteristic
968C22#1458349911yescharacteristic
969C22#1458350111yescharacteristic
970C22#1458350611yescharacteristic
971C22#1458351311yescharacteristic
972C22#1458351311yescharacteristic
973C22#1458351511yescharacteristic
974C22#1458351711yescharacteristic
975C4—24no—
976C4—24no—
977C4—42no—
978C4—42no—
979C4—42no—
980C4—42no—
981C4—864no—
982C4—864no—
983C4—1722no—
984C4—1722no—
985C4—1722no—
986C4—1722no—
987C4—1722no—
988C4—1722no—
989C2—44no—
990C2#117×Dic4311yescharacteristic
991C2#1913695611yescharacteristic
992C2#1913695611yescharacteristic
993C2#1913718911yescharacteristic
994C2#1913719911yescharacteristic
995C2#1913722511yescharacteristic
996C2#1913723611yescharacteristic
997C2#1913735811yescharacteristic
998C2#1913736211yescharacteristic
999C2#1913736811yescharacteristic
1000C2#1913737411yescharacteristic
1001C2#1913738311yescharacteristic
1002C2#1913738911yescharacteristic
1003C2#1913740611yescharacteristic
1004C2#1913741011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC22×C43C22×C42
FittingC2×C43×#388C2
socle, cosocleC24×C43C24
prime radicalC25×C43C23
hypercenterC2×#388D43
hypocenterC43#13788
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
5. #19132829C2semidirect
6. #19132827C2semidirect
7. #19132824C2semidirect
8. #19132822C2semidirect
9. #19132820C2semidirect
10. #19132820C2semidirect
13. C4×C43⋊#95C2semidirect
14. #95×Dic43C2semidirect
26. #14582792C4semidirect
27. C22⋊C4×Dic43C4semidirect
51. C43×#388C4semidirect
71. C2×C4⋊Dic43C2×C4semidirect
95. C2×C4×Dic43C2×C4semidirect
112. C43⋊#95C2×C4semidirect
113. C43⋊#95C2×C4semidirect
123. C2×C4⋊C4×C43C2×C4semidirect
135. C2×C42×C43C2×C4semidirect
136. #95×C43C2×C4semidirect
137. #95×C43C2×C4semidirect
262. C22⋊C4×C43C42semidirect
534. #388Dic43semidirect
556. C43#13788semidirect
584. C2×C4⋊C4C2×Dic43semidirect
620. C2×C42C2×Dic43semidirect
639. #95C2×Dic43semidirect
640. #95C2×Dic43semidirect
769. C22⋊C4C4×Dic43semidirect

Maximal subgroups

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

subgroupindex
C2×#145827922
C2×C22⋊C4×Dic432
#191328322
#191328292
#191328272
#191328242
#191328222
#191328202
#191328172
C4×C43⋊#952
#95×Dic432
C2×C43×#3882
#1378843