Finite Group Databasebeta

← #25025049

Subgroups — #25025049

Order 11008.

1658 conjugacy classes of subgroups.

The subgroup lattice has 1132 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582799C211yesmaximal, characteristic
2C2×#14582791C211yesmaximal, characteristic, complemented
3#19132843C211yesmaximal, characteristic, complemented
4#19132842C211yesmaximal, characteristic, complemented
5#19132840C211yesmaximal, characteristic, complemented
6#19132837C211yesmaximal, characteristic, complemented
7#19132834C211yesmaximal, characteristic
8#19132834C211yesmaximal, characteristic
9#19132833C211yesmaximal, characteristic, complemented
10#19132832C211yesmaximal, characteristic, complemented
11#19132828C211yesmaximal, characteristic, complemented
12#19132826C211yesmaximal, characteristic, complemented
13#19132824C211yesmaximal, characteristic, complemented
14#19132820C211yesmaximal, characteristic, complemented
15C2×C43×#388C211yesmaximal, characteristic, complemented
16C23×C22⋊D43C2211yescharacteristic
17C22×C4⋊Dic43C2211yescharacteristic
18C22×Dic43⋊C4C2211yescharacteristic
19C22×C22⋊Dic43C2211yescharacteristic
20C22×C22⋊Dic43C2211yescharacteristic
21C22×C22⋊Dic43C2211yescharacteristic
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×C4×Dic43C2211yescharacteristic
29C22×C4×Dic43C2211yescharacteristic
30#14582799C418yescomplemented
31#14582791—24no—
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×#388—24no—
52C2×#95×C43C2211yescharacteristic
53C2×#95×C43C2211yescharacteristic
54C24×D43C2311yescharacteristic
55C22×C22⋊D43—22no—
56C22×C22⋊D43—22no—
57C22×C22⋊D43—41no—
58C22×C22⋊D43—41no—
59C22×C22⋊D43—41no—
60C22×C22⋊D43—41no—
61C22×C22⋊D43C2×C414yes—
62C23×Dic43C2311yescharacteristic
63C23×Dic43C2311yescharacteristic
64C23×Dic43C2311yescharacteristic
65C23×Dic43C2311yescharacteristic
66C23×Dic43C2311yescharacteristic
67C23×Dic43C2311yescharacteristic
68C23×Dic43C2311yescharacteristic
69C2×C4⋊Dic43—22no—
70C2×C4⋊Dic43—22no—
71C2×C4⋊Dic43—41no—
72C2×Dic43⋊C4—41no—
73C2×Dic43⋊C4—41no—
74C2×Dic43⋊C4C2×C414yes—
75C2×C22⋊Dic43—22no—
76C2×C22⋊Dic43—41no—
77C2×C22⋊Dic43—41no—
78C2×C22⋊Dic43—41no—
79C2×C22⋊Dic43—41no—
80C2×C22⋊Dic43—41no—
81C2×C22⋊Dic43—41no—
82C2×C22⋊Dic43—41no—
83C2×C22⋊Dic43C2×C414yes—
84C2×(C2×D43)⋊C4—22no—
85C2×(C2×D43)⋊C4—22no—
86C2×(C2×D43)⋊C4—22no—
87C2×(C2×D43)⋊C4—22no—
88C2×(C2×D43)⋊C4—22no—
89C2×(C2×D43)⋊C4—22no—
90C2×(C2×D43)⋊C4—41no—
91C2×(C2×D43)⋊C4—41no—
92C2×(C2×D43)⋊C4—41no—
93C2×(C2×D43)⋊C4—41no—
94C2×(C2×D43)⋊C4—41no—
95C2×(C2×D43)⋊C4—41no—
96C2×(C2×D43)⋊C4—41no—
97C2×(C2×D43)⋊C4—41no—
98C2×(C2×D43)⋊C4—41no—
99C2×(C2×D43)⋊C4—41no—
100C2×(C2×D43)⋊C4C2×C414yes—
101C2×(C2×D43)⋊C4C2×C414yes—
102C2×C4×Dic43—22no—
103C2×C4×Dic43—41no—
104C2×C4×Dic43—41no—
105C2×C4×Dic43—41no—
106C2×C4×Dic43—41no—
107C2×C4×Dic43C2×C414yes—
108C43⋊#95—22no—
109C43⋊#95—22no—
110C43⋊#95—22no—
111C43⋊#95—22no—
112C43⋊#95—22no—
113C43⋊#95—22no—
114C43⋊#95—41no—
115C43⋊#95—41no—
116C43⋊#95—41no—
117C43⋊#95—41no—
118C43⋊#95—41no—
119C43⋊#95—41no—
120C43⋊#95—41no—
121C43⋊#95—41no—
122C25×C43C2311yescharacteristic
123C23×C4×C43C2311yescharacteristic
124C23×C4×C43C2311yescharacteristic
125C23×C4×C43C2311yescharacteristic
126C23×C4×C43C2311yescharacteristic
127C23×C4×C43C2311yescharacteristic
128C23×C4×C43C2311yescharacteristic
129C2×C4⋊C4×C43—22no—
130C2×C4⋊C4×C43—22no—
131C2×C4⋊C4×C43—41no—
132C2×C22⋊C4×C43—22no—
133C2×C22⋊C4×C43—22no—
134C2×C22⋊C4×C43—22no—
135C2×C22⋊C4×C43—22no—
136C2×C22⋊C4×C43—22no—
137C2×C22⋊C4×C43—41no—
138C2×C22⋊C4×C43—41no—
139C2×C22⋊C4×C43—41no—
140C2×C22⋊C4×C43C2×C414yes—
141C2×C42×C43—22no—
142C2×C42×C43—41no—
143C2×C42×C43—41no—
144#95×C43—22no—
145#95×C43D414yescomplemented
146C24×C43—21no—
147C24×C43—21no—
148C24×C43—21no—
149C24×C43—21no—
150C24×C43—21no—
151C24×C43—21no—
152C24×C43—21no—
153C24×C43—21no—
154C24×C43—21no—
155C24×C43—21no—
156C24×C43—21no—
157C24×C43—21no—
158C24×C43—21no—
159C24×C43—21no—
160C24×C43C22×C412yes—
161C24×C43C2411yescharacteristic
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×D43C22×C412yes—
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×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
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×C43C22×C412yes—
213C22×C4×C43C22×C412yes—
214C22×C4×C43C2×D412yes—
215C22×C4×C43C2×D412yes—
216C22×C4×C43C2×D412yes—
217C22×C4×C43#4112yes—
218C22×C4×C43#4112yes—
219C2×C22⋊D43—28no—
220C2×C22⋊D43—44no—
221C2×C22⋊D43—44no—
222C2×C22⋊D43—44no—
223C2×C22⋊D43—44no—
224C2×C22⋊D43—44no—
225C2×C22⋊D43—44no—
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—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×Dic43C22×C412yes—
270C22×Dic43C22×C412yes—
271C22×Dic43C22×C412yes—
272C22×Dic43#4112yes—
273C22×Dic43#4112yes—
274C22×Dic43#4112yes—
275C4⋊C4×C43—44no—
276C22⋊C4×C43—28no—
277C22⋊C4×C43—44no—
278C22⋊C4×C43—44no—
279C42×C43—44no—
280C22⋊Dic43—44no—
281C22⋊Dic43—44no—
282C22⋊Dic43—44no—
283(C2×D43)⋊C4—28no—
284(C2×D43)⋊C4—44no—
285(C2×D43)⋊C4—44no—
286(C2×D43)⋊C4—44no—
287(C2×D43)⋊C4—44no—
288(C2×D43)⋊C4—44no—
289C4⋊Dic43—44no—
290Dic43⋊C4—44no—
291C4×Dic43—44no—
292C4×Dic43—44no—
293C23×C43—22no—
294C23×C43—22no—
295C23×C43—22no—
296C23×C43—22no—
297C23×C43—22no—
298C23×C43—22no—
299C23×C43—22no—
300C23×C43—41no—
301C23×C43—41no—
302C23×C43—41no—
303C23×C43—41no—
304C23×C43—41no—
305C23×C43—41no—
306C23×C43—41no—
307C23×C43—41no—
308C23×C43—41no—
309C23×C43—41no—
310C23×C43—41no—
311C23×C43—41no—
312C23×C43—41no—
313C23×C43—41no—
314C23×C43—41no—
315C23×C43—41no—
316C23×C43—41no—
317C23×C43—41no—
318C23×C43—41no—
319C23×C43—41no—
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×C43C23×C411yescharacteristic
329C23×C43C22×D411yescharacteristic
330C23×C43C2×#4111yescharacteristic
331C23×C43C2×#4111yescharacteristic
332C23×C43C2×#4111yescharacteristic
333C23×C43C2×#4111yescharacteristic
334C23×C43C2×#4111yescharacteristic
335C23×C43H(5,𝔽2)11yescharacteristic
336C23×C43H(5,𝔽2)11yescharacteristic
337C23×C43H(5,𝔽2)11yescharacteristic
338C23×C43H(5,𝔽2)11yescharacteristic
339C23×C43H(5,𝔽2)11yescharacteristic
340C23×C43H(5,𝔽2)11yescharacteristic
341C23×C43H(5,𝔽2)11yescharacteristic
342C23×C432−1+411yescharacteristic
343C22×D43—22no—
344C22×D43—22no—
345C22×D43—22no—
346C22×D43—22no—
347C22×D43—22no—
348C22×D43—22no—
349C22×D43—22no—
350C22×D43—41no—
351C22×D43—41no—
352C22×D43—41no—
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—
378C2×C4×C43—22no—
379C2×C4×C43—22no—
380C2×C4×C43—22no—
381C2×C4×C43—22no—
382C2×C4×C43—22no—
383C2×C4×C43—22no—
384C2×C4×C43—22no—
385C2×C4×C43—22no—
386C2×C4×C43—22no—
387C2×C4×C43—22no—
388C2×C4×C43—22no—
389C2×C4×C43—22no—
390C2×C4×C43—22no—
391C2×C4×C43—22no—
392C2×C4×C43—22no—
393C2×C4×C43—22no—
394C2×C4×C43—22no—
395C2×C4×C43—22no—
396C2×C4×C43—41no—
397C2×C4×C43—41no—
398C2×C4×C43—41no—
399C2×C4×C43—41no—
400C2×C4×C43—41no—
401C2×C4×C43—41no—
402C2×C4×C43—41no—
403C2×C4×C43—41no—
404C2×C4×C43—41no—
405C2×C4×C43—41no—
406C2×C4×C43—41no—
407C2×C4×C43—41no—
408C2×C4×C43—41no—
409C2×C4×C43—41no—
410C2×C4×C43—41no—
411C2×C4×C43—41no—
412C2×C4×C43—41no—
413C2×C4×C43—41no—
414C2×C4×C43—41no—
415C2×C4×C43—41no—
416C2×C4×C43—41no—
417C2×C4×C43—41no—
418C2×C4×C43—41no—
419C2×C4×C43C4×D414yes—
420C22⋊D43—416no—
421C2×Dic43—22no—
422C2×Dic43—22no—
423C2×Dic43—22no—
424C2×Dic43—22no—
425C2×Dic43—22no—
426C2×Dic43—22no—
427C2×Dic43—22no—
428C2×Dic43—22no—
429C2×Dic43—22no—
430C2×Dic43—22no—
431C2×Dic43—22no—
432C2×Dic43—22no—
433C2×Dic43—22no—
434C2×Dic43—22no—
435C2×Dic43—22no—
436C2×Dic43—41no—
437C2×Dic43—41no—
438C2×Dic43—41no—
439C2×Dic43—41no—
440C2×Dic43—41no—
441C2×Dic43—41no—
442C2×Dic43—41no—
443C2×Dic43—41no—
444C2×Dic43—41no—
445C2×Dic43—41no—
446C2×Dic43—41no—
447C2×Dic43—41no—
448C2×Dic43—41no—
449C2×Dic43—41no—
450C2×Dic43—41no—
451C2×Dic43—41no—
452C2×Dic43—41no—
453C2×Dic43—41no—
454C2×Dic43—41no—
455C2×Dic43—41no—
456C2×Dic43—41no—
457C2×Dic43—41no—
458C2×Dic43—41no—
459C2×Dic43—41no—
460C2×Dic43—41no—
461C2×Dic43—41no—
462C2×Dic43—41no—
463C2×Dic43—41no—
464C2×Dic43—41no—
465C2×Dic43—41no—
466C2×Dic43—41no—
467C2×Dic43—41no—
468C2×Dic43—41no—
469C2×Dic43#11714yes—
470#14444—431nomaximal, Sylow
471C22×C43—42no—
472C22×C43—42no—
473C22×C43—42no—
474C22×C43—42no—
475C22×C43—42no—
476C22×C43—42no—
477C22×C43—42no—
478C22×C43—81no—
479C22×C43—81no—
480C22×C43—81no—
481C22×C43—81no—
482C22×C43—81no—
483C22×C43—81no—
484C22×C43—81no—
485C22×C43—81no—
486C22×C43C2×#11711yescharacteristic
487C22×C43C2×C4×D411yescharacteristic
488C22×C43C4×#4111yescharacteristic
489C22×C43#51811yescharacteristic
490C22×C43#51811yescharacteristic
491C22×C43#51811yescharacteristic
492C22×C43#52011yescharacteristic
493C22×C43#53511yescharacteristic
494C22×C43#53511yescharacteristic
495C22×C43#53811yescharacteristic
496C22×C43#53811yescharacteristic
497C22×C43#53811yescharacteristic
498C22×C43#53811yescharacteristic
499C22×C43#53811yescharacteristic
500C22×C43#53811yescharacteristic
501C22×C43#54011yescharacteristic
502C22×C43#54011yescharacteristic
503C22×C43#54211yescharacteristic
504C22×C43#54211yescharacteristic
505C22×C43#54611yescharacteristic
506C22×C43#54611yescharacteristic
507C22×C43#54711yescharacteristic
508C22×C43#55011yescharacteristic
509C22×C43#55311yescharacteristic
510C22×C43#55311yescharacteristic
511C22×C43#55311yescharacteristic
512C22×C43#55311yescharacteristic
513C22×C43#55511yescharacteristic
514C22×C43#55611yescharacteristic
515C22×C43#55911yescharacteristic
516C22×C43#55911yescharacteristic
517C22×C43#56011yescharacteristic
518C22×C43#56011yescharacteristic
519C22×C43#56211yescharacteristic
520C22×C43#56211yescharacteristic
521C2×D43—42no—
522C2×D43—42no—
523C2×D43—42no—
524C2×D43—42no—
525C2×D43—42no—
526C2×D43—42no—
527C2×D43—42no—
528C2×D43—81no—
529C2×D43—81no—
530C2×D43—81no—
531C2×D43—81no—
532C2×D43—81no—
533C2×D43—81no—
534C2×D43—81no—
535C2×D43—81no—
536C4×C43—24no—
537C4×C43—42no—
538C4×C43—42no—
539C4×C43—42no—
540C4×C43—42no—
541C4×C43—81no—
542Dic43—24no—
543Dic43—42no—
544Dic43—42no—
545Dic43—42no—
546Dic43—81no—
547Dic43—81no—
548Dic43—81no—
549C2×#390—431no—
550C2×#388—431no—
551C2×#388D4311yescharacteristic, complemented
552#1440—431no—
553#1440—431no—
554#1439—431no—
555#1439—431no—
556#1438—431no—
557#1438—431no—
558#1437—431no—
559#1437—431no—
560#1436—431no—
561#1436—431no—
562C4⋊#95—431no—
563#1434—431no—
564C2×C43—82no—
565C2×C43#231211yescharacteristic
566C2×C43#232811yescharacteristic
567C2×C43#233711yescharacteristic
568C2×C43#235411yescharacteristic
569C2×C43#235711yescharacteristic
570C2×C43#236411yescharacteristic
571C2×C43#237711yescharacteristic
572C2×C43#271011yescharacteristic
573C2×C43#271011yescharacteristic
574C2×C43#271411yescharacteristic
575C2×C43#271411yescharacteristic
576C2×C43#280011yescharacteristic
577C2×C43#280011yescharacteristic
578C2×C43#280311yescharacteristic
579C2×C43#280311yescharacteristic
580D43—82no—
581C23×D4—431no—
582C22×C4⋊C4—431no—
583C22×C4⋊C4—431no—
584C22×C4⋊C4C2×D4311yescharacteristic
585C22×C22⋊C4—431no—
586C22×C22⋊C4—431no—
587C22×C22⋊C4—431no—
588C22×C22⋊C4—431no—
589C22×C22⋊C4—431no—
590C22×C22⋊C4—431no—
591C22×C22⋊C4—431no—
592C22×C22⋊C4—431no—
593C22×C22⋊C4—431no—
594C22×C22⋊C4C2×D4311yescharacteristic
595C22×C22⋊C4C2×D4311yescharacteristic
596C22×C22⋊C4C2×D4311yescharacteristic
597C22×C42—431no—
598C22×C42—431no—
599C22×C42C2×D4311yescharacteristic
600#390—438no—
601#388—24no—
602#388—864no—
603C2×#95—431no—
604C2×#95—431no—
605C2×#95—431no—
606C2×#95—431no—
607C2×#95—431no—
608C2×#95—431no—
609C2×#95—431no—
610C2×#95—431no—
611C2×#95—431no—
612C2×#95—431no—
613C2×#95—431no—
614C2×#95—431no—
615C2×#95—431no—
616C2×#95—431no—
617C2×#95C2×D4311yescharacteristic
618C2×#95C2×D4311yescharacteristic
619C43#1444411yescharacteristic, complemented, Sylow
620C25—431no—
621C25C22×D4311yescharacteristic
622C22×D4—434no—
623C22×D4—862no—
624C22×D4—862no—
625C22×D4—1721no—
626C22×D4—1721no—
627C22×D4—1721no—
628C22×D4—1721no—
629C23×C4—431no—
630C23×C4—431no—
631C23×C4—431no—
632C23×C4—431no—
633C23×C4—431no—
634C23×C4—431no—
635C23×C4—431no—
636C23×C4C22×D4311yescharacteristic
637C23×C4C22×D4311yescharacteristic
638C23×C4C22×D4311yescharacteristic
639C23×C4C22×D4311yescharacteristic
640C23×C4C22×D4311yescharacteristic
641C23×C4C22×D4311yescharacteristic
642C2×C4⋊C4—22no—
643C2×C4⋊C4—22no—
644C2×C4⋊C4—41no—
645C2×C4⋊C4—434no—
646C2×C4⋊C4—862no—
647C2×C4⋊C4—862no—
648C2×C4⋊C4—1721no—
649C2×C4⋊C4—1721no—
650C2×C4⋊C4—1721no—
651C2×C22⋊C4—22no—
652C2×C22⋊C4—22no—
653C2×C22⋊C4—22no—
654C2×C22⋊C4—22no—
655C2×C22⋊C4—22no—
656C2×C22⋊C4—41no—
657C2×C22⋊C4—41no—
658C2×C22⋊C4—41no—
659C2×C22⋊C4—434no—
660C2×C22⋊C4—434no—
661C2×C22⋊C4—434no—
662C2×C22⋊C4—862no—
663C2×C22⋊C4—862no—
664C2×C22⋊C4—862no—
665C2×C22⋊C4—862no—
666C2×C22⋊C4—862no—
667C2×C22⋊C4—862no—
668C2×C22⋊C4—862no—
669C2×C22⋊C4—1721no—
670C2×C22⋊C4—1721no—
671C2×C22⋊C4—1721no—
672C2×C22⋊C4—1721no—
673C2×C22⋊C4—1721no—
674C2×C22⋊C4—1721no—
675C2×C22⋊C4—1721no—
676C2×C22⋊C4—1721no—
677C2×C22⋊C4—1721no—
678C2×C22⋊C4—1721no—
679C2×C22⋊C4—1721no—
680C2×C22⋊C4—1721no—
681C2×C22⋊C4—1721no—
682C2×C22⋊C4—1721no—
683C2×C22⋊C4—1721no—
684C2×C22⋊C4—1721no—
685C2×C22⋊C4—1721no—
686C2×C22⋊C4C4×D4314yes—
687C2×C42—22no—
688C2×C42—41no—
689C2×C42—41no—
690C2×C42—434no—
691C2×C42—862no—
692C2×C42—1721no—
693C2×C42—1721no—
694C2×C42—1721no—
695C2×C42—1721no—
696#95—22no—
697#95—862no—
698#95—862no—
699#95—862no—
700#95—862no—
701#95—862no—
702#95—862no—
703#95—1721no—
704#95—1721no—
705#95—1721no—
706#95—1721no—
707#95—1721no—
708#95—1721no—
709#95—1721no—
710#95—1721no—
711#95C22⋊D4314yescomplemented
712C24—21no—
713C24—21no—
714C24—21no—
715C24—21no—
716C24—21no—
717C24—21no—
718C24—21no—
719C24—21no—
720C24—21no—
721C24—21no—
722C24—21no—
723C24—21no—
724C24—21no—
725C24—21no—
726C24—432no—
727C24—861no—
728C24—861no—
729C24—861no—
730C24—861no—
731C24—861no—
732C24—861no—
733C24—861no—
734C24—861no—
735C24—861no—
736C24—861no—
737C24—861no—
738C24—861no—
739C24—861no—
740C24—861no—
741C24C2×C4×D4312yes—
742C24C23×D4311yescharacteristic
743C2×D4—868no—
744C2×D4—1724no—
745C2×D4—1724no—
746C2×D4—1724no—
747C2×D4—1724no—
748C2×D4—1724no—
749C2×D4—1724no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—432no—
786C22×C4—432no—
787C22×C4—432no—
788C22×C4—432no—
789C22×C4—432no—
790C22×C4—432no—
791C22×C4—861no—
792C22×C4—861no—
793C22×C4—861no—
794C22×C4—861no—
795C22×C4—861no—
796C22×C4—861no—
797C22×C4—861no—
798C22×C4—861no—
799C22×C4—861no—
800C22×C4—861no—
801C22×C4—861no—
802C22×C4—861no—
803C22×C4—861no—
804C22×C4—861no—
805C22×C4—861no—
806C22×C4—861no—
807C22×C4—861no—
808C22×C4—861no—
809C22×C4—861no—
810C22×C4—861no—
811C22×C4—861no—
812C22×C4—861no—
813C22×C4—861no—
814C22×C4—861no—
815C22×C4—861no—
816C22×C4—861no—
817C22×C4—861no—
818C22×C4—861no—
819C22×C4—861no—
820C22×C4—861no—
821C22×C4—861no—
822C22×C4—861no—
823C22×C4—861no—
824C22×C4—861no—
825C22×C4—861no—
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×C4C2×C4×D4312yes—
835C22×C4C2×C4×D4312yes—
836C22×C4#1062189812yes—
837C22×C4#1062190012yes—
838C22×C4C2×C22⋊D4312yes—
839C22×C4C2×C22⋊D4312yes—
840C22×C4C2×C22⋊D4312yes—
841C4⋊C4—44no—
842C4⋊C4—1724no—
843C4⋊C4—1724no—
844C22⋊C4—28no—
845C22⋊C4—44no—
846C22⋊C4—44no—
847C22⋊C4—868no—
848C22⋊C4—1724no—
849C22⋊C4—1724no—
850C22⋊C4—1724no—
851C22⋊C4—1724no—
852C22⋊C4—1724no—
853C22⋊C4—1724no—
854C22⋊C4—1724no—
855C22⋊C4—1724no—
856C42—44no—
857C42—1724no—
858C42—1724no—
859C23—22no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—41no—
871C23—41no—
872C23—41no—
873C23—41no—
874C23—41no—
875C23—41no—
876C23—41no—
877C23—41no—
878C23—41no—
879C23—41no—
880C23—41no—
881C23—41no—
882C23—41no—
883C23—41no—
884C23—41no—
885C23—41no—
886C23—41no—
887C23—41no—
888C23—41no—
889C23—41no—
890C23—41no—
891C23—41no—
892C23—41no—
893C23—41no—
894C23—862no—
895C23—862no—
896C23—862no—
897C23—862no—
898C23—862no—
899C23—862no—
900C23—862no—
901C23—1721no—
902C23—1721no—
903C23—1721no—
904C23—1721no—
905C23—1721no—
906C23—1721no—
907C23—1721no—
908C23—1721no—
909C23—1721no—
910C23—1721no—
911C23—1721no—
912C23—1721no—
913C23—1721no—
914C23—1721no—
915C23—1721no—
916C23—1721no—
917C23—1721no—
918C23—1721no—
919C23—1721no—
920C23—1721no—
921C23—1721no—
922C23—1721no—
923C23—1721no—
924C23—1721no—
925C23—1721no—
926C23—1721no—
927C23—1721no—
928C23—1721no—
929C23C22×C4×D4311yescharacteristic
930C23C22×C22⋊D4311yescharacteristic
931C23#41×D4311yescharacteristic
932C23#41×D4311yescharacteristic
933C23#41×D4311yescharacteristic
934C23C2×#1062190011yescharacteristic
935C23C2×#1062189811yescharacteristic
936C23#1306337011yescharacteristic
937C23#1306337011yescharacteristic
938C23#1306337011yescharacteristic
939C23#1306337111yescharacteristic
940C23#1306337111yescharacteristic
941C23#1306337111yescharacteristic
942C23#1306337111yescharacteristic
943C23#1306337211yescharacteristic
944D4—17216no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—434no—
987C2×C4—862no—
988C2×C4—862no—
989C2×C4—862no—
990C2×C4—862no—
991C2×C4—862no—
992C2×C4—862no—
993C2×C4—862no—
994C2×C4—862no—
995C2×C4—862no—
996C2×C4—862no—
997C2×C4—862no—
998C2×C4—862no—
999C2×C4—862no—
1000C2×C4—862no—
1001C2×C4—862no—
1002C2×C4—1721no—
1003C2×C4—1721no—
1004C2×C4—1721no—
1005C2×C4—1721no—
1006C2×C4—1721no—
1007C2×C4—1721no—
1008C2×C4—1721no—
1009C2×C4—1721no—
1010C2×C4—1721no—
1011C2×C4—1721no—
1012C2×C4—1721no—
1013C2×C4—1721no—
1014C2×C4—1721no—
1015C2×C4—1721no—
1016C2×C4—1721no—
1017C2×C4—1721no—
1018C2×C4—1721no—
1019C2×C4—1721no—
1020C2×C4—1721no—
1021C2×C4—1721no—
1022C2×C4—1721no—
1023C2×C4—1721no—
1024C2×C4—1721no—
1025C2×C4—1721no—
1026C2×C4—1721no—
1027C2×C4—1721no—
1028C2×C4—1721no—
1029C2×C4—1721no—
1030C2×C4—1721no—
1031C2×C4—1721no—
1032C2×C4—1721no—
1033C2×C4—1721no—
1034C2×C4—1721no—
1035C2×C4C4×C22⋊D4314yes—
1036C22—42no—
1037C22—42no—
1038C22—42no—
1039C22—42no—
1040C22—42no—
1041C22—42no—
1042C22—42no—
1043C22—81no—
1044C22—81no—
1045C22—81no—
1046C22—81no—
1047C22—81no—
1048C22—81no—
1049C22—81no—
1050C22—81no—
1051C22—3441no—
1052C22—3441no—
1053C22—3441no—
1054C22—3441no—
1055C22—3441no—
1056C22—3441no—
1057C22—3441no—
1058C22—3441no—
1059C22—1722no—
1060C22—1722no—
1061C22—1722no—
1062C22—1722no—
1063C22—1722no—
1064C22—1722no—
1065C22—1722no—
1066C22#117×D4311yescharacteristic
1067C22C2×C4×C22⋊D4311yescharacteristic
1068C22C4×#1062190011yescharacteristic
1069C22#1458337111yescharacteristic
1070C22#1458337111yescharacteristic
1071C22#1458337111yescharacteristic
1072C22#1458337911yescharacteristic
1073C22#1458346311yescharacteristic
1074C22#1458346611yescharacteristic
1075C22#1458348111yescharacteristic
1076C22#1458348311yescharacteristic
1077C22#1458348511yescharacteristic
1078C22#1458348611yescharacteristic
1079C22#1458348811yescharacteristic
1080C22#1458348811yescharacteristic
1081C22#1458350011yescharacteristic
1082C22#1458350011yescharacteristic
1083C22#1458351711yescharacteristic
1084C22#1458351811yescharacteristic
1085C22#1458353711yescharacteristic
1086C22#1458354311yescharacteristic
1087C22#1458354811yescharacteristic
1088C22#1458356811yescharacteristic
1089C22#1458359211yescharacteristic
1090C22#1458359511yescharacteristic
1091C22#1458359811yescharacteristic
1092C22#1458360011yescharacteristic
1093C22#1458361211yescharacteristic
1094C22#1458361711yescharacteristic
1095C22#1458363111yescharacteristic
1096C22#1458363311yescharacteristic
1097C22#1458363711yescharacteristic
1098C22#1458364011yescharacteristic
1099C22#1458364311yescharacteristic
1100C22#1458364611yescharacteristic
1101C4—24no—
1102C4—42no—
1103C4—42no—
1104C4—42no—
1105C4—42no—
1106C4—81no—
1107C4—864no—
1108C4—3441no—
1109C4—3441no—
1110C4—3441no—
1111C4—1722no—
1112C4—1722no—
1113C4—1722no—
1114C2—82no—
1115C2—3442no—
1116C2#1913718911yescharacteristic
1117C2#1913731711yescharacteristic
1118C2#1913740211yescharacteristic
1119C2#1913754511yescharacteristic
1120C2#1913756511yescharacteristic
1121C2#1913764011yescharacteristic
1122C2#1913774811yescharacteristic
1123C2#1914133111yescharacteristic
1124C2#1914133311yescharacteristic
1125C2#1914138511yescharacteristic
1126C2#1914138711yescharacteristic
1127C2#1914248611yescharacteristic
1128C2#1914249111yescharacteristic
1129C2#1914252311yescharacteristic
1130C2#1914252811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C43×#388C2
socle, cosocleC24×C43C24
prime radicalC23×C22⋊D43C22
hypercenterC2×#388D43
hypocenterC43#14444
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C2×#14582791C2semidirect
3. #19132843C2semidirect
4. #19132842C2semidirect
5. #19132840C2semidirect
6. #19132837C2semidirect
9. #19132833C2semidirect
10. #19132832C2semidirect
11. #19132828C2semidirect
12. #19132826C2semidirect
13. #19132824C2semidirect
14. #19132820C2semidirect
15. C2×C43×#388C2semidirect
30. #14582799C4semidirect
145. #95×C43D4semidirect
551. C2×#388D43semidirect
619. C43#14444semidirect
711. #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×#145827912
#191328432
#191328422
#191328402
#191328372
#191328342
#191328332
#191328322
#191328282
#191328262
#191328242
#191328202
C2×C43×#3882
#1444443