Finite Group Databasebeta

← #25019739

Subgroups — #25019739

Order 11008.

2682 conjugacy classes of subgroups.

The subgroup lattice has 1366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063297C211yesmaximal, characteristic
2C2×#14582799C211yesmaximal, characteristic, complemented
3C2×#14582799C211yesmaximal, characteristic, complemented
4C2×#14582799C211yesmaximal, characteristic, complemented
5C2×#14582794C211yesmaximal, characteristic, complemented
6C2×#14582757C211yesmaximal, characteristic, complemented
7C2×C4×Dic43⋊C4C211yesmaximal, characteristic, complemented
8C2×C22⋊C4×Dic43C211yesmaximal, characteristic, complemented
9#19132838C211yesmaximal, characteristic, complemented
10#19132837C211yesmaximal, characteristic, complemented
11#19132836C211yesmaximal, characteristic, complemented
12#19132834C211yesmaximal, characteristic, complemented
13#19132833C211yesmaximal, characteristic, complemented
14#19132832C211yesmaximal, characteristic, complemented
15C2×C43×#390C211yesmaximal, characteristic, complemented
16C23×C22⋊D43C2211yescharacteristic
17C23×C22⋊D43C2211yescharacteristic
18C24×Dic43C2211yescharacteristic
19C2×#13063297—24no—
20C2×#13063297—24no—
21C2×#13063297C418yescomplemented
22C22×Dic43⋊C4C2211yescharacteristic
23C22×Dic43⋊C4C2211yescharacteristic
24C22×Dic43⋊C4C2211yescharacteristic
25C22×Dic43⋊C4C2211yescharacteristic
26C22×C22⋊Dic43C2211yescharacteristic
27C22×C22⋊Dic43C2211yescharacteristic
28C22×C22⋊Dic43C2211yescharacteristic
29C22×C22⋊Dic43C2211yescharacteristic
30C22×C22⋊Dic43C2211yescharacteristic
31C22×(C2×D43)⋊C4C2211yescharacteristic
32C22×(C2×D43)⋊C4C2211yescharacteristic
33C22×(C2×D43)⋊C4C2211yescharacteristic
34C22×(C2×D43)⋊C4C2211yescharacteristic
35C22×(C2×D43)⋊C4C2211yescharacteristic
36C22×C4×Dic43C2211yescharacteristic
37C22×C4×Dic43C2211yescharacteristic
38C22×C4×Dic43C2211yescharacteristic
39#14582799—24no—
40#14582799—24no—
41#14582799—24no—
42#14582794—24no—
43#14582757—24no—
44C4×Dic43⋊C4—24no—
45C22⋊C4×Dic43—24no—
46C2×C43⋊#95C2211yescharacteristic
47C2×C43⋊#95C2211yescharacteristic
48C2×C43⋊#95C2211yescharacteristic
49C2×C43⋊#95C2211yescharacteristic
50C2×C43⋊#95C2211yescharacteristic
51C2×C43⋊#95C2211yescharacteristic
52C2×C43⋊#95C2211yescharacteristic
53C2×C43⋊#95C2211yescharacteristic
54C23×D4×C43C2211yescharacteristic
55C22×C4⋊C4×C43C2211yescharacteristic
56C22×C22⋊C4×C43C2211yescharacteristic
57C22×C22⋊C4×C43C2211yescharacteristic
58C22×C22⋊C4×C43C2211yescharacteristic
59C22×C22⋊C4×C43C2211yescharacteristic
60C22×C42×C43C2211yescharacteristic
61C43×#390—24no—
62C24×D43C2311yescharacteristic
63C22×C22⋊D43—22no—
64C22×C22⋊D43—22no—
65C22×C22⋊D43—22no—
66C22×C22⋊D43—22no—
67C22×C22⋊D43—22no—
68C22×C22⋊D43—22no—
69C22×C22⋊D43—22no—
70C22×C22⋊D43—22no—
71C22×C22⋊D43—22no—
72C22×C22⋊D43—22no—
73C22×C22⋊D43—41no—
74C22×C22⋊D43—41no—
75C22×C22⋊D43C2×C414yes—
76C22×C22⋊D43C2×C414yes—
77C23×Dic43—22no—
78C23×Dic43—22no—
79C23×Dic43—22no—
80C23×Dic43—22no—
81C23×Dic43—22no—
82C23×Dic43—22no—
83C23×Dic43C2×C414yes—
84C23×Dic43C2311yescharacteristic
85C23×Dic43C2311yescharacteristic
86C23×Dic43C2311yescharacteristic
87C23×Dic43C2311yescharacteristic
88C23×Dic43C2311yescharacteristic
89C23×Dic43C2311yescharacteristic
90C23×Dic43C2311yescharacteristic
91#13063297—232no—
92C2×Dic43⋊C4—22no—
93C2×Dic43⋊C4—22no—
94C2×Dic43⋊C4—22no—
95C2×Dic43⋊C4—22no—
96C2×Dic43⋊C4—22no—
97C2×Dic43⋊C4—22no—
98C2×Dic43⋊C4—22no—
99C2×Dic43⋊C4—41no—
100C2×Dic43⋊C4C2×C414yes—
101C2×Dic43⋊C4D414yes—
102C2×Dic43⋊C4D414yes—
103C2×Dic43⋊C4D414yescomplemented
104C2×C22⋊Dic43—22no—
105C2×C22⋊Dic43—22no—
106C2×C22⋊Dic43—22no—
107C2×C22⋊Dic43—22no—
108C2×C22⋊Dic43—22no—
109C2×C22⋊Dic43—22no—
110C2×C22⋊Dic43—22no—
111C2×C22⋊Dic43—22no—
112C2×C22⋊Dic43—22no—
113C2×C22⋊Dic43—22no—
114C2×C22⋊Dic43—41no—
115C2×C22⋊Dic43—41no—
116C2×C22⋊Dic43—41no—
117C2×C22⋊Dic43—41no—
118C2×C22⋊Dic43C2×C414yes—
119C2×(C2×D43)⋊C4—22no—
120C2×(C2×D43)⋊C4—22no—
121C2×(C2×D43)⋊C4—22no—
122C2×(C2×D43)⋊C4—22no—
123C2×(C2×D43)⋊C4—22no—
124C2×(C2×D43)⋊C4—22no—
125C2×(C2×D43)⋊C4—22no—
126C2×(C2×D43)⋊C4—22no—
127C2×(C2×D43)⋊C4—22no—
128C2×(C2×D43)⋊C4—22no—
129C2×(C2×D43)⋊C4—41no—
130C2×(C2×D43)⋊C4—41no—
131C2×(C2×D43)⋊C4—41no—
132C2×(C2×D43)⋊C4—41no—
133C2×(C2×D43)⋊C4C2×C414yes—
134C2×C4×Dic43—22no—
135C2×C4×Dic43—22no—
136C2×C4×Dic43—22no—
137C2×C4×Dic43—22no—
138C2×C4×Dic43—22no—
139C2×C4×Dic43—22no—
140C2×C4×Dic43—22no—
141C2×C4×Dic43—41no—
142C2×C4×Dic43D414yescomplemented
143C43⋊#95—22no—
144C43⋊#95—22no—
145C43⋊#95—22no—
146C43⋊#95—22no—
147C43⋊#95—22no—
148C43⋊#95—22no—
149C43⋊#95—22no—
150C43⋊#95—22no—
151C25×C43C2311yescharacteristic
152C25×C43C2311yescharacteristic
153C22×D4×C43—22no—
154C22×D4×C43—22no—
155C22×D4×C43—22no—
156C22×D4×C43—22no—
157C22×D4×C43—41no—
158C22×D4×C43—41no—
159C22×D4×C43C2×C414yes—
160C23×C4×C43C2311yescharacteristic
161C23×C4×C43C2311yescharacteristic
162C23×C4×C43C2311yescharacteristic
163C23×C4×C43C2311yescharacteristic
164C23×C4×C43C2311yescharacteristic
165C2×C4⋊C4×C43—22no—
166C2×C4⋊C4×C43—22no—
167C2×C4⋊C4×C43—41no—
168C2×C22⋊C4×C43—22no—
169C2×C22⋊C4×C43—22no—
170C2×C22⋊C4×C43—22no—
171C2×C22⋊C4×C43—22no—
172C2×C22⋊C4×C43—22no—
173C2×C22⋊C4×C43—22no—
174C2×C22⋊C4×C43—22no—
175C2×C22⋊C4×C43—22no—
176C2×C22⋊C4×C43—22no—
177C2×C22⋊C4×C43—41no—
178C2×C22⋊C4×C43—41no—
179C2×C22⋊C4×C43D414yescomplemented
180C2×C42×C43—22no—
181C2×C42×C43—22no—
182C2×C42×C43—41no—
183C24×C43—21no—
184C24×C43—21no—
185C24×C43—21no—
186C24×C43—21no—
187C24×C43—21no—
188C24×C43—21no—
189C24×C43—21no—
190C24×C43—21no—
191C24×C43—21no—
192C24×C43—21no—
193C24×C43—21no—
194C24×C43—21no—
195C24×C43—21no—
196C24×C43—21no—
197C24×C43—21no—
198C24×C43—21no—
199C24×C43—21no—
200C24×C43—21no—
201C24×C43—21no—
202C24×C43—21no—
203C24×C43—21no—
204C24×C43—21no—
205C24×C43—21no—
206C24×C43—21no—
207C24×C43—21no—
208C24×C43—21no—
209C24×C43C22×C412yes—
210C24×C43C22×C412yes—
211C24×C43C2×D412yes—
212C24×C43#4112yes—
213C24×C43C2411yescharacteristic
214C23×D43—21no—
215C23×D43—21no—
216C23×D43—21no—
217C23×D43—21no—
218C23×D43—21no—
219C23×D43—21no—
220C23×D43—21no—
221C23×D43—21no—
222C23×D43—21no—
223C23×D43—21no—
224C23×D43—21no—
225C23×D43—21no—
226C23×D43—21no—
227C23×D43—21no—
228C23×D43C22×C412yes—
229C2×D4×C43—28no—
230C2×D4×C43—28no—
231C2×D4×C43—44no—
232C2×D4×C43—44no—
233C2×D4×C43—44no—
234C2×D4×C43—44no—
235C2×D4×C43—44no—
236C22×C4×C43—21no—
237C22×C4×C43—21no—
238C22×C4×C43—21no—
239C22×C4×C43—21no—
240C22×C4×C43—21no—
241C22×C4×C43—21no—
242C22×C4×C43—21no—
243C22×C4×C43—21no—
244C22×C4×C43—21no—
245C22×C4×C43—21no—
246C22×C4×C43—21no—
247C22×C4×C43—21no—
248C22×C4×C43—21no—
249C22×C4×C43—21no—
250C22×C4×C43—21no—
251C22×C4×C43—21no—
252C22×C4×C43—21no—
253C22×C4×C43—21no—
254C22×C4×C43—21no—
255C22×C4×C43—21no—
256C22×C4×C43—21no—
257C22×C4×C43—21no—
258C22×C4×C43—21no—
259C22×C4×C43—21no—
260C22×C4×C43—21no—
261C22×C4×C43—21no—
262C22×C4×C43—21no—
263C22×C4×C43C22×C412yes—
264C22×C4×C43C2×D412yes—
265C22×C4×C43C2×D412yes—
266C22×C4×C43C2×D412yes—
267C22×C4×C43C2×D412yes—
268C22×C4×C43C2×D412yes—
269C22×C4×C43C2×D412yes—
270C22×C4×C43#4112yes—
271C2×C22⋊D43—28no—
272C2×C22⋊D43—28no—
273C2×C22⋊D43—28no—
274C2×C22⋊D43—28no—
275C2×C22⋊D43—28no—
276C2×C22⋊D43—44no—
277C2×C22⋊D43—44no—
278C2×C22⋊D43—44no—
279C2×C22⋊D43—44no—
280C2×C22⋊D43—44no—
281C2×C22⋊D43—44no—
282C2×C22⋊D43—44no—
283C2×C22⋊D43—44no—
284C2×C22⋊D43—44no—
285C22×Dic43—28no—
286C22×Dic43—28no—
287C22×Dic43—28no—
288C22×Dic43—21no—
289C22×Dic43—21no—
290C22×Dic43—21no—
291C22×Dic43—21no—
292C22×Dic43—21no—
293C22×Dic43—21no—
294C22×Dic43—21no—
295C22×Dic43—21no—
296C22×Dic43—21no—
297C22×Dic43—21no—
298C22×Dic43—21no—
299C22×Dic43—21no—
300C22×Dic43—21no—
301C22×Dic43—21no—
302C22×Dic43—21no—
303C22×Dic43—21no—
304C22×Dic43—21no—
305C22×Dic43—21no—
306C22×Dic43—21no—
307C22×Dic43—21no—
308C22×Dic43—21no—
309C22×Dic43—21no—
310C22×Dic43—21no—
311C22×Dic43—21no—
312C22×Dic43—21no—
313C22×Dic43—21no—
314C22×Dic43—21no—
315C22×Dic43—21no—
316C22×Dic43—21no—
317C22×Dic43—21no—
318C22×Dic43—21no—
319C22×Dic43—21no—
320C22×Dic43—21no—
321C22×Dic43—21no—
322C22×Dic43—21no—
323C22×Dic43—44no—
324C22×Dic43—44no—
325C22×Dic43—44no—
326C22×Dic43—44no—
327C22×Dic43C22×C412yes—
328C22×Dic43C22×C412yes—
329C22×Dic43C22×C412yes—
330C22×Dic43C2×D412yes—
331C22×Dic43C2×D412yes—
332C22×Dic43C2×D412yes—
333C22×Dic43C2×D412yes—
334C22×Dic43C2×D412yes—
335C22×Dic43C2×D412yes—
336C22×Dic43C2×D412yes—
337C22×Dic43C2×D412yes—
338C22×Dic43#4112yes—
339C22×Dic43#4112yes—
340C22×Dic43#4112yes—
341C4⋊C4×C43—44no—
342C22⋊C4×C43—28no—
343C22⋊C4×C43—44no—
344C22⋊C4×C43—44no—
345C22⋊C4×C43—44no—
346C42×C43—44no—
347C22⋊Dic43—28no—
348C22⋊Dic43—28no—
349C22⋊Dic43—44no—
350C22⋊Dic43—44no—
351C22⋊Dic43—44no—
352(C2×D43)⋊C4—28no—
353(C2×D43)⋊C4—44no—
354(C2×D43)⋊C4—44no—
355(C2×D43)⋊C4—44no—
356(C2×D43)⋊C4—44no—
357Dic43⋊C4—28no—
358Dic43⋊C4—44no—
359Dic43⋊C4—44no—
360Dic43⋊C4C22⋊C4116yescomplemented
361C4×Dic43—28no—
362C4×Dic43—44no—
363C4×Dic43—44no—
364C23×C43—22no—
365C23×C43—22no—
366C23×C43—22no—
367C23×C43—22no—
368C23×C43—22no—
369C23×C43—22no—
370C23×C43—22no—
371C23×C43—22no—
372C23×C43—22no—
373C23×C43—22no—
374C23×C43—22no—
375C23×C43—22no—
376C23×C43—22no—
377C23×C43—22no—
378C23×C43—22no—
379C23×C43—22no—
380C23×C43—22no—
381C23×C43—22no—
382C23×C43—22no—
383C23×C43—22no—
384C23×C43—22no—
385C23×C43—22no—
386C23×C43—22no—
387C23×C43—22no—
388C23×C43—22no—
389C23×C43—41no—
390C23×C43—41no—
391C23×C43—41no—
392C23×C43—41no—
393C23×C43—41no—
394C23×C43—41no—
395C23×C43—41no—
396C23×C43—41no—
397C23×C43—41no—
398C23×C43—41no—
399C23×C43—41no—
400C23×C43—41no—
401C23×C43—41no—
402C23×C43—41no—
403C23×C43—41no—
404C23×C43—41no—
405C23×C43—41no—
406C23×C43—41no—
407C23×C43—41no—
408C23×C43—41no—
409C23×C43—41no—
410C23×C43—41no—
411C23×C43—41no—
412C23×C43—41no—
413C23×C43—41no—
414C23×C43—41no—
415C23×C43—41no—
416C23×C43—41no—
417C23×C43—41no—
418C23×C43—41no—
419C23×C43—41no—
420C23×C43—41no—
421C23×C43—41no—
422C23×C43—41no—
423C23×C43—41no—
424C23×C43—41no—
425C23×C43—41no—
426C23×C43—41no—
427C23×C43—41no—
428C23×C43—41no—
429C23×C43—41no—
430C23×C43—41no—
431C23×C43—41no—
432C23×C43—41no—
433C23×C43C4×D414yes—
434C23×C43C23×C411yescharacteristic
435C23×C43C22×D411yescharacteristic
436C23×C43C22×D411yescharacteristic
437C23×C43C22×D411yescharacteristic
438C23×C43C22×D411yescharacteristic
439C23×C43C22×D411yescharacteristic
440C23×C43C2×#4111yescharacteristic
441C23×C43C2×#4111yescharacteristic
442C23×C43C2×#4111yescharacteristic
443C23×C43C2×#4111yescharacteristic
444C23×C43C2×#4111yescharacteristic
445C23×C43H(5,𝔽2)11yescharacteristic
446C23×C43H(5,𝔽2)11yescharacteristic
447C23×C43H(5,𝔽2)11yescharacteristic
448C23×C432−1+411yescharacteristic
449C22×D43—22no—
450C22×D43—22no—
451C22×D43—22no—
452C22×D43—22no—
453C22×D43—22no—
454C22×D43—22no—
455C22×D43—22no—
456C22×D43—41no—
457C22×D43—41no—
458C22×D43—41no—
459C22×D43—41no—
460C22×D43—41no—
461C22×D43—41no—
462C22×D43—41no—
463C22×D43—41no—
464C22×D43—41no—
465C22×D43—41no—
466C22×D43—41no—
467C22×D43—41no—
468C22×D43—41no—
469C22×D43—41no—
470C22×D43—41no—
471C22×D43—41no—
472C22×D43—41no—
473C22×D43—41no—
474C22×D43—41no—
475C22×D43—41no—
476C22×D43—41no—
477C22×D43—41no—
478C22×D43—41no—
479C22×D43—41no—
480C22×D43—41no—
481C22×D43—41no—
482C22×D43—41no—
483C22×D43—41no—
484D4×C43—416no—
485C2×C4×C43—22no—
486C2×C4×C43—22no—
487C2×C4×C43—22no—
488C2×C4×C43—22no—
489C2×C4×C43—22no—
490C2×C4×C43—22no—
491C2×C4×C43—22no—
492C2×C4×C43—22no—
493C2×C4×C43—22no—
494C2×C4×C43—22no—
495C2×C4×C43—22no—
496C2×C4×C43—22no—
497C2×C4×C43—22no—
498C2×C4×C43—22no—
499C2×C4×C43—22no—
500C2×C4×C43—22no—
501C2×C4×C43—22no—
502C2×C4×C43—22no—
503C2×C4×C43—41no—
504C2×C4×C43—41no—
505C2×C4×C43—41no—
506C2×C4×C43—41no—
507C2×C4×C43—41no—
508C2×C4×C43—41no—
509C2×C4×C43—41no—
510C2×C4×C43—41no—
511C2×C4×C43—41no—
512C2×C4×C43—41no—
513C2×C4×C43—41no—
514C2×C4×C43—41no—
515C2×C4×C43—41no—
516C2×C4×C43—41no—
517C2×C4×C43—41no—
518C2×C4×C43C2×C22⋊C414yes—
519C2×C4×C43#12114yescomplemented
520C22⋊D43—416no—
521C22⋊D43—416no—
522C2×Dic43—22no—
523C2×Dic43—22no—
524C2×Dic43—22no—
525C2×Dic43—22no—
526C2×Dic43—22no—
527C2×Dic43—22no—
528C2×Dic43—22no—
529C2×Dic43—22no—
530C2×Dic43—22no—
531C2×Dic43—22no—
532C2×Dic43—22no—
533C2×Dic43—22no—
534C2×Dic43—22no—
535C2×Dic43—22no—
536C2×Dic43—22no—
537C2×Dic43—22no—
538C2×Dic43—22no—
539C2×Dic43—22no—
540C2×Dic43—41no—
541C2×Dic43—41no—
542C2×Dic43—41no—
543C2×Dic43—41no—
544C2×Dic43—41no—
545C2×Dic43—41no—
546C2×Dic43—41no—
547C2×Dic43—41no—
548C2×Dic43—41no—
549C2×Dic43—41no—
550C2×Dic43—41no—
551C2×Dic43—41no—
552C2×Dic43—41no—
553C2×Dic43—41no—
554C2×Dic43—41no—
555C2×Dic43—41no—
556C2×Dic43—416no—
557C2×Dic43—41no—
558C2×Dic43—41no—
559C2×Dic43—41no—
560C2×Dic43—41no—
561C2×Dic43—41no—
562C2×Dic43—41no—
563C2×Dic43—41no—
564C2×Dic43C2×C22⋊C414yes—
565C2×Dic43C2×C22⋊C414yes—
566C2×Dic43C4×D414yes—
567C2×Dic43C4×D414yes—
568C2×Dic43#12114yes—
569C2×Dic43#12114yes—
570C2×Dic43#12414yes—
571C2×Dic43#12714yes—
572#13998—431nomaximal, Sylow
573C22×C43—24no—
574C22×C43—24no—
575C22×C43—24no—
576C22×C43—42no—
577C22×C43—42no—
578C22×C43—42no—
579C22×C43—42no—
580C22×C43—42no—
581C22×C43—42no—
582C22×C43—42no—
583C22×C43—42no—
584C22×C43—42no—
585C22×C43—42no—
586C22×C43—42no—
587C22×C43—42no—
588C22×C43—42no—
589C22×C43—42no—
590C22×C43—42no—
591C22×C43—42no—
592C22×C43—42no—
593C22×C43—42no—
594C22×C43—42no—
595C22×C43—81no—
596C22×C43—81no—
597C22×C43—81no—
598C22×C43—81no—
599C22×C43—81no—
600C22×C43—81no—
601C22×C43—81no—
602C22×C43—81no—
603C22×C43C22×C22⋊C411yescharacteristic
604C22×C43C2×C4×D411yescharacteristic
605C22×C43C2×C4×D411yescharacteristic
606C22×C43C2×C4×D411yescharacteristic
607C22×C43C4×#4111yescharacteristic
608C22×C43#51811yescharacteristic
609C22×C43#52011yescharacteristic
610C22×C43C2×#12111yescharacteristic
611C22×C43C2×#12111yescharacteristic
612C22×C43C2×#12111yescharacteristic
613C22×C43#52511yescharacteristic
614C22×C43C2×#12411yescharacteristic
615C22×C43#52911yescharacteristic
616C22×C43C2×#12711yescharacteristic
617C22×C43#53211yescharacteristic
618C22×C43#53511yescharacteristic
619C22×C43#53711yescharacteristic
620C22×C43#54011yescharacteristic
621C22×C43#54211yescharacteristic
622C22×C43D4211yescharacteristic
623C22×C43D4211yescharacteristic
624C22×C43D4211yescharacteristic
625C22×C43#54611yescharacteristic
626C22×C43#54611yescharacteristic
627C22×C43#54611yescharacteristic
628C22×C43#54711yescharacteristic
629C22×C43#54811yescharacteristic
630C22×C43#54811yescharacteristic
631C22×C43#54811yescharacteristic
632C22×C43#55011yescharacteristic
633C22×C43#55011yescharacteristic
634C22×C43#55011yescharacteristic
635C22×C43#55311yescharacteristic
636C22×C43#55311yescharacteristic
637C22×C43#55511yescharacteristic
638C2×D43—42no—
639C2×D43—42no—
640C2×D43—42no—
641C2×D43—42no—
642C2×D43—42no—
643C2×D43—42no—
644C2×D43—42no—
645C2×D43—81no—
646C2×D43—81no—
647C2×D43—81no—
648C2×D43—81no—
649C2×D43—81no—
650C2×D43—81no—
651C2×D43—81no—
652C2×D43—81no—
653C4×C43—24no—
654C4×C43—24no—
655C4×C43—42no—
656C4×C43—42no—
657C4×C43—81no—
658Dic43—24no—
659Dic43—42no—
660Dic43—42no—
661Dic43—42no—
662Dic43—42no—
663Dic43—81no—
664Dic43#39018yescomplemented
665C22×#121—431no—
666C2×#390—431no—
667C2×#390—431no—
668C2×#390—431no—
669C2×#390D4311yescharacteristic, complemented
670C2×#389—431no—
671C2×#380—431no—
672C2×C4×C4⋊C4—431no—
673C2×C4×C22⋊C4—431no—
674#1439—431no—
675#1439—431no—
676#1438—431no—
677#1438—431no—
678#1437—431no—
679#1437—431no—
680C2×C43—44no—
681C2×C43—82no—
682C2×C43C2×#39011yescharacteristic
683C2×C43C4×#12111yescharacteristic
684C2×C43#232411yescharacteristic
685C2×C43D4×C22⋊C411yescharacteristic
686C2×C43#234111yescharacteristic
687C2×C43#236111yescharacteristic
688C2×C43#236311yescharacteristic
689C2×C43#241411yescharacteristic
690C2×C43#241611yescharacteristic
691C2×C43#242611yescharacteristic
692C2×C43#242811yescharacteristic
693C2×C43#249011yescharacteristic
694C2×C43#249111yescharacteristic
695C2×C43#254011yescharacteristic
696C2×C43#254111yescharacteristic
697D43—82no—
698C23×D4—431no—
699C23×D4—431no—
700C23×D4C2×D4311yescharacteristic
701C24×C4—431no—
702C2×#121—438no—
703C2×#121—864no—
704C2×#121—864no—
705C22×C4⋊C4—431no—
706C22×C4⋊C4—431no—
707C22×C4⋊C4—431no—
708C22×C4⋊C4—431no—
709C22×C4⋊C4C2×D4311yescharacteristic
710C22×C22⋊C4—431no—
711C22×C22⋊C4—431no—
712C22×C22⋊C4—431no—
713C22×C22⋊C4—431no—
714C22×C22⋊C4—431no—
715C22×C22⋊C4—431no—
716C22×C22⋊C4—431no—
717C22×C22⋊C4—431no—
718C22×C22⋊C4—431no—
719C22×C22⋊C4—431no—
720C22×C22⋊C4C2×D4311yescharacteristic
721C22×C22⋊C4C2×D4311yescharacteristic
722C22×C22⋊C4C2×D4311yescharacteristic
723C22×C22⋊C4C2×D4311yescharacteristic
724C22×C42—431no—
725C22×C42—431no—
726C22×C42—431no—
727C22×C42C2×D4311yescharacteristic
728#390—24no—
729#390—864no—
730#390—864no—
731#390—864no—
732#389—864no—
733#380—864no—
734C4×C4⋊C4—864no—
735C4×C22⋊C4—864no—
736C2×#95—431no—
737C2×#95—431no—
738C2×#95—431no—
739C2×#95—431no—
740C2×#95—431no—
741C2×#95—431no—
742C2×#95—431no—
743C2×#95—431no—
744C43#1399811yescharacteristic, complemented, Sylow
745C25—431no—
746C25C22×D4311yescharacteristic
747C25C22×D4311yescharacteristic
748C22×D4—22no—
749C22×D4—22no—
750C22×D4—22no—
751C22×D4—22no—
752C22×D4—41no—
753C22×D4—41no—
754C22×D4—434no—
755C22×D4—434no—
756C22×D4—862no—
757C22×D4—862no—
758C22×D4—862no—
759C22×D4—862no—
760C22×D4—862no—
761C22×D4—862no—
762C22×D4—862no—
763C22×D4—862no—
764C22×D4—862no—
765C22×D4—862no—
766C22×D4—1721no—
767C22×D4—1721no—
768C22×D4C4×D4314yes—
769C23×C4—431no—
770C23×C4—431no—
771C23×C4—434no—
772C23×C4—431no—
773C23×C4—431no—
774C23×C4—431no—
775C23×C4—431no—
776C23×C4—431no—
777C23×C4—862no—
778C23×C4—862no—
779C23×C4—862no—
780C23×C4—862no—
781C23×C4—862no—
782C23×C4—862no—
783C23×C4C22×D4311yescharacteristic
784C23×C4C22×D4311yescharacteristic
785C23×C4C22×D4311yescharacteristic
786C23×C4C22×D4311yescharacteristic
787C23×C4C22×D4311yescharacteristic
788#121—8632no—
789C2×C4⋊C4—22no—
790C2×C4⋊C4—22no—
791C2×C4⋊C4—41no—
792C2×C4⋊C4—434no—
793C2×C4⋊C4—434no—
794C2×C4⋊C4—434no—
795C2×C4⋊C4—434no—
796C2×C4⋊C4—862no—
797C2×C4⋊C4—862no—
798C2×C4⋊C4—862no—
799C2×C4⋊C4—862no—
800C2×C4⋊C4—862no—
801C2×C4⋊C4—862no—
802C2×C4⋊C4—862no—
803C2×C4⋊C4—1721no—
804C2×C22⋊C4—22no—
805C2×C22⋊C4—22no—
806C2×C22⋊C4—22no—
807C2×C22⋊C4—22no—
808C2×C22⋊C4—22no—
809C2×C22⋊C4—22no—
810C2×C22⋊C4—22no—
811C2×C22⋊C4—22no—
812C2×C22⋊C4—22no—
813C2×C22⋊C4—41no—
814C2×C22⋊C4—41no—
815C2×C22⋊C4—434no—
816C2×C22⋊C4—434no—
817C2×C22⋊C4—862no—
818C2×C22⋊C4—862no—
819C2×C22⋊C4—862no—
820C2×C22⋊C4—862no—
821C2×C22⋊C4—862no—
822C2×C22⋊C4—862no—
823C2×C22⋊C4—862no—
824C2×C22⋊C4—862no—
825C2×C22⋊C4—862no—
826C2×C22⋊C4—862no—
827C2×C22⋊C4—862no—
828C2×C22⋊C4—862no—
829C2×C22⋊C4—862no—
830C2×C22⋊C4—862no—
831C2×C22⋊C4—862no—
832C2×C22⋊C4—862no—
833C2×C22⋊C4—862no—
834C2×C22⋊C4—862no—
835C2×C22⋊C4—862no—
836C2×C22⋊C4—862no—
837C2×C22⋊C4—1721no—
838C2×C22⋊C4—1721no—
839C2×C22⋊C4—1721no—
840C2×C22⋊C4—1721no—
841C2×C22⋊C4—1721no—
842C2×C22⋊C4—1721no—
843C2×C22⋊C4—1721no—
844C2×C22⋊C4—1721no—
845C2×C22⋊C4C22⋊D4314yescomplemented
846C2×C42—22no—
847C2×C42—22no—
848C2×C42—41no—
849C2×C42—434no—
850C2×C42—862no—
851C2×C42—862no—
852C2×C42—862no—
853C2×C42—862no—
854C2×C42—862no—
855C2×C42—862no—
856C2×C42—862no—
857C2×C42—1721no—
858#95—862no—
859#95—862no—
860#95—862no—
861#95—862no—
862#95—862no—
863#95—862no—
864#95—862no—
865#95—862no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—21no—
872C24—21no—
873C24—21no—
874C24—21no—
875C24—21no—
876C24—21no—
877C24—21no—
878C24—21no—
879C24—21no—
880C24—21no—
881C24—21no—
882C24—21no—
883C24—21no—
884C24—21no—
885C24—21no—
886C24—21no—
887C24—21no—
888C24—21no—
889C24—21no—
890C24—21no—
891C24—21no—
892C24—432no—
893C24—861no—
894C24—861no—
895C24—861no—
896C24—861no—
897C24—861no—
898C24—861no—
899C24—861no—
900C24—861no—
901C24—861no—
902C24—861no—
903C24—861no—
904C24—861no—
905C24—861no—
906C24—861no—
907C24C2×C4×D4312yes—
908C24C2×C4×D4312yes—
909C24#1062189812yes—
910C24C2×C22⋊D4312yes—
911C24C23×D4311yescharacteristic
912C2×D4—28no—
913C2×D4—28no—
914C2×D4—44no—
915C2×D4—44no—
916C2×D4—44no—
917C2×D4—44no—
918C2×D4—44no—
919C2×D4—868no—
920C2×D4—868no—
921C2×D4—868no—
922C2×D4—868no—
923C2×D4—868no—
924C2×D4—1724no—
925C2×D4—1724no—
926C2×D4—1724no—
927C2×D4—1724no—
928C2×D4—1724no—
929C2×D4—1724no—
930C2×D4—1724no—
931C2×D4—1724no—
932C2×D4—1724no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—432no—
961C22×C4—432no—
962C22×C4—432no—
963C22×C4—432no—
964C22×C4—432no—
965C22×C4—432no—
966C22×C4—432no—
967C22×C4—432no—
968C22×C4—432no—
969C22×C4—432no—
970C22×C4—432no—
971C22×C4—432no—
972C22×C4—432no—
973C22×C4—432no—
974C22×C4—868no—
975C22×C4—868no—
976C22×C4—868no—
977C22×C4—861no—
978C22×C4—861no—
979C22×C4—861no—
980C22×C4—861no—
981C22×C4—861no—
982C22×C4—861no—
983C22×C4—861no—
984C22×C4—861no—
985C22×C4—861no—
986C22×C4—861no—
987C22×C4—861no—
988C22×C4—861no—
989C22×C4—861no—
990C22×C4—861no—
991C22×C4—861no—
992C22×C4—861no—
993C22×C4—861no—
994C22×C4—861no—
995C22×C4—861no—
996C22×C4—861no—
997C22×C4—861no—
998C22×C4—861no—
999C22×C4—861no—
1000C22×C4—861no—
1001C22×C4—861no—
1002C22×C4—861no—
1003C22×C4—861no—
1004C22×C4—861no—
1005C22×C4—861no—
1006C22×C4—861no—
1007C22×C4—861no—
1008C22×C4—861no—
1009C22×C4—861no—
1010C22×C4—861no—
1011C22×C4—861no—
1012C22×C4—1724no—
1013C22×C4—1724no—
1014C22×C4—1724no—
1015C22×C4—1724no—
1016C22×C4C2×C4×D4312yes—
1017C22×C4D4×D4312yes—
1018C22×C4D4×D4312yes—
1019C22×C4D4×D4312yes—
1020C22×C4D4×D4312yes—
1021C22×C4#1062190012yes—
1022C22×C4C2×C22⋊D4312yes—
1023C22×C4C2×C22⋊D4312yes—
1024C4⋊C4—44no—
1025C4⋊C4—4316no—
1026C4⋊C4—868no—
1027C4⋊C4—1724no—
1028C4⋊C4—1724no—
1029C22⋊C4—28no—
1030C22⋊C4—44no—
1031C22⋊C4—44no—
1032C22⋊C4—44no—
1033C22⋊C4—868no—
1034C22⋊C4—868no—
1035C22⋊C4—868no—
1036C22⋊C4—1724no—
1037C22⋊C4—1724no—
1038C22⋊C4—1724no—
1039C22⋊C4—1724no—
1040C22⋊C4—1724no—
1041C22⋊C4—1724no—
1042C22⋊C4—1724no—
1043C42—44no—
1044C42—868no—
1045C42—1724no—
1046C42—1724no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—22no—
1066C23—22no—
1067C23—22no—
1068C23—22no—
1069C23—22no—
1070C23—22no—
1071C23—22no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—862no—
1117C23—862no—
1118C23—862no—
1119C23—862no—
1120C23—862no—
1121C23—862no—
1122C23—862no—
1123C23—1721no—
1124C23—1721no—
1125C23—1721no—
1126C23—1721no—
1127C23—1721no—
1128C23—1721no—
1129C23—1721no—
1130C23—1721no—
1131C23—1721no—
1132C23—1721no—
1133C23—1721no—
1134C23—1721no—
1135C23—1721no—
1136C23—1721no—
1137C23—1721no—
1138C23—1721no—
1139C23—1721no—
1140C23—1721no—
1141C23—1721no—
1142C23—1721no—
1143C23—1721no—
1144C23—1721no—
1145C23—1721no—
1146C23—1721no—
1147C23—1721no—
1148C23—1721no—
1149C23—1721no—
1150C23—1721no—
1151C23C4×C22⋊D4314yes—
1152C23C22×C4×D4311yescharacteristic
1153C23C2×D4×D4311yescharacteristic
1154C23C2×D4×D4311yescharacteristic
1155C23C2×D4×D4311yescharacteristic
1156C23C2×D4×D4311yescharacteristic
1157C23C22×C22⋊D4311yescharacteristic
1158C23#41×D4311yescharacteristic
1159C23#41×D4311yescharacteristic
1160C23#41×D4311yescharacteristic
1161C23C2×#1062190011yescharacteristic
1162C23C2×#1062189811yescharacteristic
1163C23#1306337011yescharacteristic
1164C23#1306337011yescharacteristic
1165C23#1306337011yescharacteristic
1166C23#1306337211yescharacteristic
1167D4—416no—
1168D4—17216no—
1169D4—17216no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—434no—
1204C2×C4—434no—
1205C2×C4—434no—
1206C2×C4—434no—
1207C2×C4—434no—
1208C2×C4—434no—
1209C2×C4—434no—
1210C2×C4—434no—
1211C2×C4—862no—
1212C2×C4—862no—
1213C2×C4—862no—
1214C2×C4—862no—
1215C2×C4—862no—
1216C2×C4—862no—
1217C2×C4—862no—
1218C2×C4—862no—
1219C2×C4—862no—
1220C2×C4—862no—
1221C2×C4—862no—
1222C2×C4—862no—
1223C2×C4—862no—
1224C2×C4—862no—
1225C2×C4—862no—
1226C2×C4—862no—
1227C2×C4—862no—
1228C2×C4—862no—
1229C2×C4—17216no—
1230C2×C4—1721no—
1231C2×C4—1721no—
1232C2×C4—1721no—
1233C2×C4—1721no—
1234C2×C4—1721no—
1235C2×C4—1721no—
1236C2×C4—1721no—
1237C2×C4—1721no—
1238C2×C4—1721no—
1239C2×C4—1721no—
1240C2×C4—1721no—
1241C2×C4—1721no—
1242C2×C4—1721no—
1243C2×C4—1721no—
1244C2×C4—1721no—
1245C2×C4—1721no—
1246C2×C4—1721no—
1247C2×C4—1721no—
1248C2×C4—1721no—
1249C2×C4—1721no—
1250C2×C4—1721no—
1251C2×C4—1721no—
1252C2×C4—1721no—
1253C2×C4C22⋊C4×D4314yes—
1254C2×C4#1306329714yescomplemented
1255C22—24no—
1256C22—24no—
1257C22—24no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—42no—
1273C22—42no—
1274C22—42no—
1275C22—42no—
1276C22—42no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—3441no—
1286C22—3441no—
1287C22—3441no—
1288C22—3441no—
1289C22—3441no—
1290C22—3441no—
1291C22—3441no—
1292C22—3441no—
1293C22—1722no—
1294C22—1722no—
1295C22—1722no—
1296C22—1722no—
1297C22—1722no—
1298C22—1722no—
1299C22—1722no—
1300C22C2×C22⋊C4×D4311yescharacteristic
1301C22C4×D4×D4311yescharacteristic
1302C22C4×D4×D4311yescharacteristic
1303C22C2×C4×C22⋊D4311yescharacteristic
1304C22C4×#1062190011yescharacteristic
1305C22#1458337211yescharacteristic
1306C22#1458337811yescharacteristic
1307C22#121×D4311yescharacteristic
1308C22#121×D4311yescharacteristic
1309C22C2×#1306329711yescharacteristic
1310C22#1458340811yescharacteristic
1311C22#124×D4311yescharacteristic
1312C22#1458342911yescharacteristic
1313C22#127×D4311yescharacteristic
1314C22#1458344511yescharacteristic
1315C22#1458346211yescharacteristic
1316C22#1458347611yescharacteristic
1317C22#1458349911yescharacteristic
1318C22#1458351311yescharacteristic
1319C22D4×C22⋊D4311yescharacteristic
1320C22D4×C22⋊D4311yescharacteristic
1321C22D4×C22⋊D4311yescharacteristic
1322C22#1458353811yescharacteristic
1323C22#1458353911yescharacteristic
1324C22#1458353911yescharacteristic
1325C22#1458354811yescharacteristic
1326C22#1458355511yescharacteristic
1327C22#1458355711yescharacteristic
1328C22#1458355811yescharacteristic
1329C22#1458356711yescharacteristic
1330C22#1458356911yescharacteristic
1331C22#1458356911yescharacteristic
1332C22#1458359211yescharacteristic
1333C22#1458359811yescharacteristic
1334C22#1458361111yescharacteristic
1335C4—24no—
1336C4—24no—
1337C4—42no—
1338C4—42no—
1339C4—81no—
1340C4—438no—
1341C4—864no—
1342C4—3441no—
1343C4—1722no—
1344C4—1722no—
1345C4—1722no—
1346C4—1722no—
1347C2—44no—
1348C2—82no—
1349C2—3442no—
1350C2#390×D4311yescharacteristic
1351C2C4×#1306329711yescharacteristic
1352C2#1913728111yescharacteristic
1353C2C22⋊C4×C22⋊D4311yescharacteristic
1354C2#1913743411yescharacteristic
1355C2#1913761211yescharacteristic
1356C2#1913763011yescharacteristic
1357C2#1913801011yescharacteristic
1358C2#1913803211yescharacteristic
1359C2#1913815811yescharacteristic
1360C2#1913818011yescharacteristic
1361C2#1913894411yescharacteristic
1362C2#1913895511yescharacteristic
1363C2#1913953211yescharacteristic
1364C2#1913953911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C43×#390C2
socle, cosocleC24×C43C24
prime radicalC22×#13063297C2
hypercenterC2×#390D43
hypocenterC43#13998
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
2. C2×#14582799C2semidirect
3. C2×#14582799C2semidirect
4. C2×#14582799C2semidirect
5. C2×#14582794C2semidirect
6. C2×#14582757C2semidirect
7. C2×C4×Dic43⋊C4C2semidirect
8. C2×C22⋊C4×Dic43C2semidirect
9. #19132838C2semidirect
10. #19132837C2semidirect
11. #19132836C2semidirect
12. #19132834C2semidirect
13. #19132833C2semidirect
14. #19132832C2semidirect
15. C2×C43×#390C2semidirect
21. C2×#13063297C4semidirect
103. C2×Dic43⋊C4D4semidirect
142. C2×C4×Dic43D4semidirect
179. C2×C22⋊C4×C43D4semidirect
360. Dic43⋊C4C22⋊C4semidirect
519. C2×C4×C43#121semidirect
664. Dic43#390semidirect
669. C2×#390D43semidirect
744. C43#13998semidirect
845. C2×C22⋊C4C22⋊D43semidirect
1254. C2×C4#13063297semidirect

Maximal subgroups

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

subgroupindex
C22×#130632972
C2×#145827992
C2×#145827942
C2×#145827572
C2×C4×Dic43⋊C42
C2×C22⋊C4×Dic432
#191328382
#191328372
#191328362
#191328342
#191328332
#191328322
C2×C43×#3902
#1399843