Finite Group Databasebeta

← #25020180

Subgroups — #25020180

Order 11008.

1946 conjugacy classes of subgroups.

The subgroup lattice has 1158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582799C211yesmaximal, characteristic
2C2×#14582780C211yesmaximal, characteristic, complemented
3C2×#14582775C211yesmaximal, characteristic
4C2×#14582746C211yesmaximal, characteristic, complemented
5#19132861C211yesmaximal, characteristic, complemented
6#19132842C211yesmaximal, characteristic, complemented
7#19132837C211yesmaximal, characteristic, complemented
8#19132834C211yesmaximal, characteristic
9#19132833C211yesmaximal, characteristic, complemented
10#19132832C211yesmaximal, characteristic, complemented
11#19132832C211yesmaximal, characteristic, complemented
12#19132820C211yesmaximal, characteristic, complemented
13(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
14C4×C43⋊#95C211yesmaximal, characteristic, complemented
15C2×C43×#388C211yesmaximal, characteristic, complemented
16C23×C22⋊D43C2211yescharacteristic
17C23×C4×D43C2211yescharacteristic
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×C4×Dic43C2211yescharacteristic
28C22×C4×Dic43C2211yescharacteristic
29C22×C4×Dic43C2211yescharacteristic
30#14582799C418yescomplemented
31#14582780—24no—
32#14582775—24no—
33#14582746—24no—
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
46C2×C43⋊#95C2211yescharacteristic
47C2×C43⋊#95C2211yescharacteristic
48C22×C4⋊C4×C43C2211yescharacteristic
49C22×C22⋊C4×C43C2211yescharacteristic
50C22×C22⋊C4×C43C2211yescharacteristic
51C22×C22⋊C4×C43C2211yescharacteristic
52C22×C42×C43C2211yescharacteristic
53C43×#388—24no—
54C2×#95×C43C2211yescharacteristic
55C2×#95×C43C2211yescharacteristic
56C24×D43C2311yescharacteristic
57C22×C22⋊D43—22no—
58C22×C22⋊D43—22no—
59C22×C22⋊D43—22no—
60C22×C22⋊D43—22no—
61C22×C22⋊D43—41no—
62C22×C22⋊D43—41no—
63C22×C22⋊D43C2×C414yes—
64C23×Dic43C2311yescharacteristic
65C23×Dic43C2311yescharacteristic
66C23×Dic43C2311yescharacteristic
67C23×Dic43C2311yescharacteristic
68C23×Dic43C2311yescharacteristic
69C23×Dic43C2311yescharacteristic
70C23×Dic43C2311yescharacteristic
71C22×C4×D43—22no—
72C22×C4×D43—22no—
73C22×C4×D43—22no—
74C22×C4×D43—22no—
75C22×C4×D43—22no—
76C22×C4×D43—41no—
77C22×C4×D43—41no—
78C2×Dic43⋊C4—22no—
79C2×Dic43⋊C4—22no—
80C2×Dic43⋊C4C2×C414yescomplemented
81C2×C22⋊Dic43—22no—
82C2×C22⋊Dic43—22no—
83C2×C22⋊Dic43—22no—
84C2×C22⋊Dic43—22no—
85C2×C22⋊Dic43—41no—
86C2×C22⋊Dic43—41no—
87C2×C22⋊Dic43—41no—
88C2×C22⋊Dic43—41no—
89C2×C22⋊Dic43C2×C414yescomplemented
90C2×(C2×D43)⋊C4—22no—
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—41no—
100C2×(C2×D43)⋊C4—41no—
101C2×(C2×D43)⋊C4—41no—
102C2×(C2×D43)⋊C4—41no—
103C2×(C2×D43)⋊C4C2×C414yes—
104C2×(C2×D43)⋊C4C2×C414yes—
105C2×C4×Dic43—22no—
106C2×C4×Dic43—22no—
107C2×C4×Dic43—22no—
108C2×C4×Dic43—22no—
109C2×C4×Dic43—41no—
110C2×C4×Dic43—41no—
111C2×C4×Dic43—41no—
112C2×C4×Dic43—41no—
113C2×C4×Dic43C2×C414yescomplemented
114C43⋊#95—22no—
115C43⋊#95—22no—
116C43⋊#95—22no—
117C43⋊#95—22no—
118C43⋊#95—22no—
119C43⋊#95—22no—
120C43⋊#95—22no—
121C43⋊#95—22no—
122C43⋊#95—22no—
123C43⋊#95—41no—
124C43⋊#95—41no—
125C43⋊#95—41no—
126C43⋊#95—41no—
127C43⋊#95D414yes—
128C25×C43C2311yescharacteristic
129C23×C4×C43C2311yescharacteristic
130C23×C4×C43C2311yescharacteristic
131C23×C4×C43C2311yescharacteristic
132C23×C4×C43C2311yescharacteristic
133C23×C4×C43C2311yescharacteristic
134C23×C4×C43C2311yescharacteristic
135C2×C4⋊C4×C43—22no—
136C2×C4⋊C4×C43—22no—
137C2×C4⋊C4×C43—41no—
138C2×C22⋊C4×C43—22no—
139C2×C22⋊C4×C43—22no—
140C2×C22⋊C4×C43—22no—
141C2×C22⋊C4×C43—22no—
142C2×C22⋊C4×C43—22no—
143C2×C22⋊C4×C43—22no—
144C2×C22⋊C4×C43—41no—
145C2×C22⋊C4×C43—41no—
146C2×C22⋊C4×C43C2×C414yescomplemented
147C2×C42×C43—22no—
148C2×C42×C43—22no—
149C2×C42×C43—41no—
150#95×C43—22no—
151#95×C43D414yescomplemented
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×C43—21no—
161C24×C43—21no—
162C24×C43—21no—
163C24×C43—21no—
164C24×C43—21no—
165C24×C43—21no—
166C24×C43C22×C412yes—
167C24×C43C2411yescharacteristic
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×D43C22×C412yes—
181C23×D43#4112yes—
182C23×D43#4112yes—
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×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43—21no—
215C22×C4×C43—21no—
216C22×C4×C43—21no—
217C22×C4×C43C22×C412yes—
218C22×C4×C43C22×C412yes—
219C22×C4×C43C2×D412yes—
220C22×C4×C43C2×D412yes—
221C22×C4×C43C2×D412yes—
222C22×C4×C43C2×D412yes—
223C22×C4×C43#4112yes—
224C22×C4×C43#4112yes—
225C2×C22⋊D43—28no—
226C2×C22⋊D43—28no—
227C2×C22⋊D43—44no—
228C2×C22⋊D43—44no—
229C2×C22⋊D43—44no—
230C2×C22⋊D43—44no—
231C2×C22⋊D43—44no—
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×Dic43—21no—
270C22×Dic43—21no—
271C22×Dic43—21no—
272C22×Dic43C22×C412yes—
273C22×Dic43C22×C412yes—
274C22×Dic43C22×C412yes—
275C22×Dic43C2×D412yes—
276C22×Dic43C2×D412yes—
277C22×Dic43#4112yes—
278C22×Dic43#4112yes—
279C22×Dic43#4112yes—
280C22×Dic43#4112yes—
281C2×C4×D43—28no—
282C2×C4×D43—44no—
283C2×C4×D43—44no—
284C2×C4×D43—44no—
285C2×C4×D43—44no—
286C2×C4×D43—44no—
287C2×C4×D43—44no—
288C4⋊C4×C43—44no—
289C22⋊C4×C43—28no—
290C22⋊C4×C43—44no—
291C22⋊C4×C43—44no—
292C42×C43—44no—
293C22⋊Dic43—44no—
294C22⋊Dic43—44no—
295C22⋊Dic43—44no—
296(C2×D43)⋊C4—28no—
297(C2×D43)⋊C4—28no—
298(C2×D43)⋊C4—44no—
299(C2×D43)⋊C4—44no—
300(C2×D43)⋊C4—44no—
301Dic43⋊C4—28no—
302C4×Dic43—44no—
303C4×Dic43—44no—
304C4×Dic43—44no—
305C23×C43—22no—
306C23×C43—22no—
307C23×C43—22no—
308C23×C43—22no—
309C23×C43—22no—
310C23×C43—22no—
311C23×C43—22no—
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×C43—41no—
329C23×C43—41no—
330C23×C43—41no—
331C23×C43—41no—
332C23×C43—41no—
333C23×C43—41no—
334C23×C43—41no—
335C23×C43—41no—
336C23×C43—41no—
337C23×C43—41no—
338C23×C43—41no—
339C23×C43—41no—
340C23×C43C23×C411yescharacteristic
341C23×C43C22×D411yescharacteristic
342C23×C43C22×D411yescharacteristic
343C23×C43C2×#4111yescharacteristic
344C23×C43C2×#4111yescharacteristic
345C23×C43C2×#4111yescharacteristic
346C23×C43C2×#4111yescharacteristic
347C23×C43C2×#4111yescharacteristic
348C23×C43C2×#4111yescharacteristic
349C23×C43C2×#4111yescharacteristic
350C23×C43C2×#4111yescharacteristic
351C23×C43H(5,𝔽2)11yescharacteristic
352C23×C43H(5,𝔽2)11yescharacteristic
353C23×C43H(5,𝔽2)11yescharacteristic
354C23×C43H(5,𝔽2)11yescharacteristic
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—22no—
370C22×D43—22no—
371C22×D43—22no—
372C22×D43—22no—
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#11714yes—
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—22no—
397C2×C4×C43—22no—
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—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×C43—41no—
420C2×C4×C43—41no—
421C2×C4×C43—41no—
422C2×C4×C43—41no—
423C2×C4×C43—41no—
424C2×C4×C43—41no—
425C2×C4×C43—41no—
426C2×C4×C43—41no—
427C2×C4×C43—41no—
428C2×C4×C43—41no—
429C2×C4×C43—41no—
430C2×C4×C43—41no—
431C2×C4×C43C4×D414yes—
432C22⋊D43—416no—
433C2×Dic43—22no—
434C2×Dic43—22no—
435C2×Dic43—22no—
436C2×Dic43—22no—
437C2×Dic43—22no—
438C2×Dic43—22no—
439C2×Dic43—22no—
440C2×Dic43—22no—
441C2×Dic43—22no—
442C2×Dic43—22no—
443C2×Dic43—22no—
444C2×Dic43—22no—
445C2×Dic43—22no—
446C2×Dic43—22no—
447C2×Dic43—22no—
448C2×Dic43—22no—
449C2×Dic43—22no—
450C2×Dic43—22no—
451C2×Dic43—22no—
452C2×Dic43—22no—
453C2×Dic43—22no—
454C2×Dic43—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—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×Dic43C4×D414yes—
481C2×Dic43#12414yes—
482C4×D43—416no—
483#14034—431nomaximal, Sylow
484C22×C43—42no—
485C22×C43—42no—
486C22×C43—42no—
487C22×C43—42no—
488C22×C43—42no—
489C22×C43—42no—
490C22×C43—42no—
491C22×C43—81no—
492C22×C43—81no—
493C22×C43—81no—
494C22×C43—81no—
495C22×C43—81no—
496C22×C43—81no—
497C22×C43—81no—
498C22×C43—81no—
499C22×C43C2×#11711yescharacteristic
500C22×C43C2×C4×D411yescharacteristic
501C22×C43C2×C4×D411yescharacteristic
502C22×C43C4×#4111yescharacteristic
503C22×C43C4×#4111yescharacteristic
504C22×C43#51811yescharacteristic
505C22×C43#51811yescharacteristic
506C22×C43#52511yescharacteristic
507C22×C43#52511yescharacteristic
508C22×C43C2×#12411yescharacteristic
509C22×C43#52911yescharacteristic
510C22×C43#52911yescharacteristic
511C22×C43#52911yescharacteristic
512C22×C43#52911yescharacteristic
513C22×C43#53211yescharacteristic
514C22×C43#53811yescharacteristic
515C22×C43#53811yescharacteristic
516C22×C43#54011yescharacteristic
517C22×C43#54011yescharacteristic
518C22×C43D4211yescharacteristic
519C22×C43#54611yescharacteristic
520C22×C43#54611yescharacteristic
521C22×C43#54611yescharacteristic
522C22×C43#54611yescharacteristic
523C22×C43#55011yescharacteristic
524C22×C43#55011yescharacteristic
525C22×C43#55111yescharacteristic
526C22×C43#55111yescharacteristic
527C22×C43#55111yescharacteristic
528C22×C43#55111yescharacteristic
529C22×C43#55311yescharacteristic
530C22×C43#55311yescharacteristic
531C22×C43#55311yescharacteristic
532C22×C43#55311yescharacteristic
533C22×C43#55911yescharacteristic
534C2×D43—24no—
535C2×D43—24no—
536C2×D43—24no—
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—
549C4×C43—24no—
550C4×C43—42no—
551C4×C43—42no—
552C4×C43—42no—
553C4×C43—42no—
554C4×C43—42no—
555Dic43—24no—
556Dic43—24no—
557Dic43—42no—
558Dic43—42no—
559Dic43—42no—
560Dic43—81no—
561Dic43—81no—
562C2×#390—431no—
563C2×#388D4311yescharacteristic, complemented
564C2×#387—431no—
565C2×#386—431no—
566C2×C4×C22⋊C4—431no—
567#1445—431no—
568#1440—431no—
569#1439—431no—
570#1438—431no—
571#1437—431no—
572#1437—431no—
573#1437—431no—
574#1434—431no—
575C22⋊#95—431no—
576C4×#95—431no—
577C2×C43—82no—
578C2×C43#229011yescharacteristic
579C2×C43C4×#12411yescharacteristic
580C2×C43#233311yescharacteristic
581C2×C43#234211yescharacteristic
582C2×C43#235311yescharacteristic
583C2×C43#236411yescharacteristic
584C2×C43#236611yescharacteristic
585C2×C43#246411yescharacteristic
586C2×C43#246711yescharacteristic
587C2×C43#247111yescharacteristic
588C2×C43#247211yescharacteristic
589C2×C43#249011yescharacteristic
590C2×C43#251611yescharacteristic
591C2×C43#255411yescharacteristic
592C2×C43#259511yescharacteristic
593D43—44no—
594C23×D4—431no—
595C24×C4—431no—
596C22×C4⋊C4—431no—
597C22×C4⋊C4C2×D4311yescharacteristic
598C22×C22⋊C4—431no—
599C22×C22⋊C4—431no—
600C22×C22⋊C4—431no—
601C22×C22⋊C4—431no—
602C22×C22⋊C4—431no—
603C22×C22⋊C4—431no—
604C22×C22⋊C4—431no—
605C22×C22⋊C4—431no—
606C22×C22⋊C4C2×D4311yescharacteristic
607C22×C22⋊C4C2×D4311yescharacteristic
608C22×C22⋊C4C2×D4311yescharacteristic
609C22×C42—431no—
610C22×C42—431no—
611C22×C42—431no—
612C22×C42C2×D4311yescharacteristic
613#390—438no—
614#388—24no—
615#387—864no—
616#386—864no—
617C4×C22⋊C4—864no—
618C2×#95—431no—
619C2×#95—431no—
620C2×#95—431no—
621C2×#95—431no—
622C2×#95—431no—
623C2×#95—431no—
624C2×#95—431no—
625C2×#95—431no—
626C2×#95—431no—
627C2×#95—431no—
628C2×#95—431no—
629C2×#95—431no—
630C2×#95—431no—
631C2×#95—431no—
632C2×#95C2×D4311yescharacteristic
633C2×#95C2×D4311yescharacteristic
634C43#1403411yescharacteristic, complemented, Sylow
635C25—431no—
636C25C22×D4311yescharacteristic
637C22×D4—434no—
638C22×D4—862no—
639C22×D4—862no—
640C22×D4—862no—
641C22×D4—862no—
642C22×D4—1721no—
643C22×D4—1721no—
644C23×C4—431no—
645C23×C4—431no—
646C23×C4—431no—
647C23×C4—431no—
648C23×C4—431no—
649C23×C4—431no—
650C23×C4—431no—
651C23×C4—862no—
652C23×C4—862no—
653C23×C4—862no—
654C23×C4—862no—
655C23×C4—862no—
656C23×C4—1721no—
657C23×C4—1721no—
658C23×C4C22×D4311yescharacteristic
659C23×C4C22×D4311yescharacteristic
660C23×C4C22×D4311yescharacteristic
661C23×C4C22×D4311yescharacteristic
662C23×C4C22×D4311yescharacteristic
663C23×C4C22×D4311yescharacteristic
664C2×C4⋊C4—22no—
665C2×C4⋊C4—22no—
666C2×C4⋊C4—41no—
667C2×C4⋊C4—434no—
668C2×C4⋊C4—862no—
669C2×C4⋊C4—862no—
670C2×C22⋊C4—22no—
671C2×C22⋊C4—22no—
672C2×C22⋊C4—22no—
673C2×C22⋊C4—22no—
674C2×C22⋊C4—22no—
675C2×C22⋊C4—22no—
676C2×C22⋊C4—41no—
677C2×C22⋊C4—41no—
678C2×C22⋊C4—434no—
679C2×C22⋊C4—434no—
680C2×C22⋊C4—434no—
681C2×C22⋊C4—862no—
682C2×C22⋊C4—862no—
683C2×C22⋊C4—862no—
684C2×C22⋊C4—862no—
685C2×C22⋊C4—862no—
686C2×C22⋊C4—862no—
687C2×C22⋊C4—862no—
688C2×C22⋊C4—862no—
689C2×C22⋊C4—862no—
690C2×C22⋊C4—862no—
691C2×C22⋊C4—862no—
692C2×C22⋊C4—862no—
693C2×C22⋊C4—862no—
694C2×C22⋊C4—1721no—
695C2×C22⋊C4—1721no—
696C2×C22⋊C4—1721no—
697C2×C22⋊C4—1721no—
698C2×C22⋊C4—1721no—
699C2×C22⋊C4—1721no—
700C2×C22⋊C4—1721no—
701C2×C22⋊C4—1721no—
702C2×C22⋊C4C4×D4314yescomplemented
703C2×C42—22no—
704C2×C42—22no—
705C2×C42—41no—
706C2×C42—434no—
707C2×C42—862no—
708C2×C42—862no—
709C2×C42—862no—
710C2×C42—862no—
711C2×C42—1721no—
712C2×C42—1721no—
713C2×C42—1721no—
714C2×C42—1721no—
715#95—22no—
716#95—434no—
717#95—862no—
718#95—862no—
719#95—862no—
720#95—862no—
721#95—862no—
722#95—862no—
723#95—862no—
724#95—862no—
725#95—862no—
726#95—1721no—
727#95—1721no—
728#95—1721no—
729#95—1721no—
730#95C22⋊D4314yescomplemented
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24—21no—
744C24—21no—
745C24—432no—
746C24—432no—
747C24—432no—
748C24—861no—
749C24—861no—
750C24—861no—
751C24—861no—
752C24—861no—
753C24—861no—
754C24—861no—
755C24—861no—
756C24—861no—
757C24—861no—
758C24—861no—
759C24—861no—
760C24C2×C4×D4312yes—
761C24C23×D4311yescharacteristic
762C2×D4—868no—
763C2×D4—868no—
764C2×D4—1724no—
765C2×D4—1724no—
766C2×D4—1724no—
767C2×D4—1724no—
768C2×D4—1724no—
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—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—432no—
804C22×C4—432no—
805C22×C4—432no—
806C22×C4—432no—
807C22×C4—432no—
808C22×C4—432no—
809C22×C4—432no—
810C22×C4—432no—
811C22×C4—432no—
812C22×C4—868no—
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×C4—861no—
835C22×C4—861no—
836C22×C4—861no—
837C22×C4—861no—
838C22×C4—861no—
839C22×C4—861no—
840C22×C4—861no—
841C22×C4—861no—
842C22×C4—861no—
843C22×C4—861no—
844C22×C4—861no—
845C22×C4—861no—
846C22×C4—861no—
847C22×C4—861no—
848C22×C4—861no—
849C22×C4—861no—
850C22×C4—861no—
851C22×C4—861no—
852C22×C4—861no—
853C22×C4—1724no—
854C22×C4—1724no—
855C22×C4—1724no—
856C22×C4—1724no—
857C22×C4—1724no—
858C22×C4—1724no—
859C22×C4C2×C4×D4312yes—
860C22×C4C2×C4×D4312yes—
861C22×C4#1062189812yes—
862C22×C4D4×D4312yes—
863C22×C4#1062190012yes—
864C22×C4C2×C22⋊D4312yes—
865C22×C4C2×C22⋊D4312yes—
866C22×C4C2×C22⋊D4312yes—
867C4⋊C4—44no—
868C4⋊C4—868no—
869C22⋊C4—28no—
870C22⋊C4—44no—
871C22⋊C4—44no—
872C22⋊C4—868no—
873C22⋊C4—868no—
874C22⋊C4—1724no—
875C22⋊C4—1724no—
876C22⋊C4—1724no—
877C22⋊C4—1724no—
878C22⋊C4—1724no—
879C22⋊C4—1724no—
880C42—44no—
881C42—1724no—
882C42—1724no—
883C42—1724no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—41no—
892C23—41no—
893C23—41no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—434no—
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—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—
954C23C22×C4×D4311yescharacteristic
955C23C2×D4×D4311yescharacteristic
956C23C22×C22⋊D4311yescharacteristic
957C23#41×D4311yescharacteristic
958C23#41×D4311yescharacteristic
959C23#41×D4311yescharacteristic
960C23#41×D4311yescharacteristic
961C23#41×D4311yescharacteristic
962C23#41×D4311yescharacteristic
963C23C2×#1062190011yescharacteristic
964C23C2×#1062189811yescharacteristic
965C23#1306337011yescharacteristic
966C23#1306337011yescharacteristic
967C23#1306337111yescharacteristic
968C23#1306337111yescharacteristic
969D4—17216no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—434no—
1012C2×C4—434no—
1013C2×C4—862no—
1014C2×C4—862no—
1015C2×C4—862no—
1016C2×C4—862no—
1017C2×C4—862no—
1018C2×C4—862no—
1019C2×C4—862no—
1020C2×C4—862no—
1021C2×C4—862no—
1022C2×C4—862no—
1023C2×C4—862no—
1024C2×C4—862no—
1025C2×C4—862no—
1026C2×C4—862no—
1027C2×C4—862no—
1028C2×C4—862no—
1029C2×C4—862no—
1030C2×C4—862no—
1031C2×C4—862no—
1032C2×C4—862no—
1033C2×C4—862no—
1034C2×C4—17216no—
1035C2×C4—1721no—
1036C2×C4—1721no—
1037C2×C4—1721no—
1038C2×C4—1721no—
1039C2×C4—1721no—
1040C2×C4—1721no—
1041C2×C4—1721no—
1042C2×C4—1721no—
1043C2×C4—1721no—
1044C2×C4—1721no—
1045C2×C4—1721no—
1046C2×C4—1721no—
1047C2×C4—1721no—
1048C2×C4—1721no—
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×C4C4×C22⋊D4314yes—
1062C22—42no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—81no—
1070C22—81no—
1071C22—81no—
1072C22—81no—
1073C22—81no—
1074C22—81no—
1075C22—81no—
1076C22—81no—
1077C22—864no—
1078C22—864no—
1079C22—864no—
1080C22—1722no—
1081C22—1722no—
1082C22—1722no—
1083C22—1722no—
1084C22—1722no—
1085C22—1722no—
1086C22—1722no—
1087C22—1722no—
1088C22—1722no—
1089C22—1722no—
1090C22—1722no—
1091C22—1722no—
1092C22#117×D4311yescharacteristic
1093C22C4×D4×D4311yescharacteristic
1094C22C2×C4×C22⋊D4311yescharacteristic
1095C22C4×#1062190011yescharacteristic
1096C22#1458336711yescharacteristic
1097C22#1458337111yescharacteristic
1098C22#1458337111yescharacteristic
1099C22#1458340611yescharacteristic
1100C22#1458340611yescharacteristic
1101C22#124×D4311yescharacteristic
1102C22#1458342611yescharacteristic
1103C22#1458342711yescharacteristic
1104C22#1458342711yescharacteristic
1105C22#1458343211yescharacteristic
1106C22#1458344411yescharacteristic
1107C22#1458348311yescharacteristic
1108C22#1458348811yescharacteristic
1109C22#1458349911yescharacteristic
1110C22#1458350111yescharacteristic
1111C22D4×C22⋊D4311yescharacteristic
1112C22#1458353711yescharacteristic
1113C22#1458353811yescharacteristic
1114C22#1458354211yescharacteristic
1115C22#1458354311yescharacteristic
1116C22#1458356811yescharacteristic
1117C22#1458357011yescharacteristic
1118C22#1458357211yescharacteristic
1119C22#1458357411yescharacteristic
1120C22#1458357711yescharacteristic
1121C22#1458357911yescharacteristic
1122C22#1458359511yescharacteristic
1123C22#1458359611yescharacteristic
1124C22#1458359811yescharacteristic
1125C22#1458360011yescharacteristic
1126C22#1458363211yescharacteristic
1127C4—24no—
1128C4—42no—
1129C4—42no—
1130C4—42no—
1131C4—42no—
1132C4—42no—
1133C4—864no—
1134C4—864no—
1135C4—3441no—
1136C4—3441no—
1137C4—1722no—
1138C4—1722no—
1139C4—1722no—
1140C2—82no—
1141C2—1724no—
1142C2#1913703211yescharacteristic
1143C2#1913713611yescharacteristic
1144C2#1913735811yescharacteristic
1145C2#1913744311yescharacteristic
1146C2#1913753011yescharacteristic
1147C2#1913764011yescharacteristic
1148C2#1913765711yescharacteristic
1149C2#1913859711yescharacteristic
1150C2#1913864211yescharacteristic
1151C2#1913870211yescharacteristic
1152C2#1913871711yescharacteristic
1153C2#1913894611yescharacteristic
1154C2#1913923611yescharacteristic
1155C2#1913965411yescharacteristic
1156C2#1914011211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C43×#388C2
socle, cosocleC24×C43C24
prime radicalC23×C22⋊D43C22
hypercenterC2×#388D43
hypocenterC43#14034
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C2×#14582780C2semidirect
4. C2×#14582746C2semidirect
5. #19132861C2semidirect
6. #19132842C2semidirect
7. #19132837C2semidirect
9. #19132833C2semidirect
10. #19132832C2semidirect
11. #19132832C2semidirect
12. #19132820C2semidirect
13. (C2×D43)⋊#95C2semidirect
14. C4×C43⋊#95C2semidirect
15. C2×C43×#388C2semidirect
30. #14582799C4semidirect
80. C2×Dic43⋊C4C2×C4semidirect
89. C2×C22⋊Dic43C2×C4semidirect
113. C2×C4×Dic43C2×C4semidirect
146. C2×C22⋊C4×C43C2×C4semidirect
151. #95×C43D4semidirect
563. C2×#388D43semidirect
634. C43#14034semidirect
702. C2×C22⋊C4C4×D43semidirect
730. #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×#145827802
C2×#145827752
C2×#145827462
#191328612
#191328422
#191328372
#191328342
#191328332
#191328322
#191328202
(C2×D43)⋊#952
C4×C43⋊#952
C2×C43×#3882
#1403443