Finite Group Databasebeta

← #25024765

Subgroups — #25024765

Order 11008.

2126 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063311C211yesmaximal, characteristic
2C2×#14582805C211yesmaximal, characteristic, complemented
3C2×#14582776C211yesmaximal, characteristic
4C2×#14582774C211yesmaximal, characteristic, complemented
5#19132865C211yesmaximal, characteristic, complemented
6#19132842C211yesmaximal, characteristic, complemented
7#19132841C211yesmaximal, characteristic, complemented
8#19132841C211yesmaximal, characteristic, complemented
9#19132837C211yesmaximal, characteristic, complemented
10#19132834C211yesmaximal, characteristic
11#19132833C211yesmaximal, characteristic, complemented
12#19132824C211yesmaximal, characteristic, complemented
13#19132819C211yesmaximal, characteristic, complemented
14#19132817C211yesmaximal, characteristic, complemented
15C2×C43×#388C211yesmaximal, characteristic, complemented
16C23×Dic86C2211yescharacteristic
17C23×C22⋊D43C2211yescharacteristic
18C24×Dic43C2211yescharacteristic
19C2×#13063311—24no—
20C2×#13063311—24no—
21C2×#13063311C418yescomplemented
22C22×C4⋊Dic43C2211yescharacteristic
23C22×C4⋊Dic43C2211yescharacteristic
24C22×C22⋊Dic43C2211yescharacteristic
25C22×C22⋊Dic43C2211yescharacteristic
26C22×(C2×D43)⋊C4C2211yescharacteristic
27C22×(C2×D43)⋊C4C2211yescharacteristic
28C22×(C2×D43)⋊C4C2211yescharacteristic
29C22×(C2×D43)⋊C4C2211yescharacteristic
30C22×(C2×D43)⋊C4C2211yescharacteristic
31C22×(C2×D43)⋊C4C2211yescharacteristic
32C22×C4×Dic43C2211yescharacteristic
33#14582805—24no—
34#14582776—24no—
35#14582774—24no—
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
48C2×C43⋊#95C2211yescharacteristic
49C2×C43⋊#95C2211yescharacteristic
50C22×C4⋊C4×C43C2211yescharacteristic
51C22×C22⋊C4×C43C2211yescharacteristic
52C22×C22⋊C4×C43C2211yescharacteristic
53C22×C22⋊C4×C43C2211yescharacteristic
54C22×C42×C43C2211yescharacteristic
55C43×#388—24no—
56C2×#95×C43C2211yescharacteristic
57C2×#95×C43C2211yescharacteristic
58C24×D43C2311yescharacteristic
59C22×Dic86—22no—
60C22×Dic86—22no—
61C22×Dic86—22no—
62C22×Dic86—22no—
63C22×Dic86—41no—
64C22×Dic86—41no—
65C22×Dic86C2×C414yescomplemented
66C22×C22⋊D43—22no—
67C22×C22⋊D43—22no—
68C22×C22⋊D43—22no—
69C22×C22⋊D43—22no—
70C22×C22⋊D43—41no—
71C22×C22⋊D43—41no—
72C22×C22⋊D43C2×C414yes—
73C23×Dic43—22no—
74C23×Dic43—22no—
75C23×Dic43—22no—
76C23×Dic43—41no—
77C23×Dic43—41no—
78C23×Dic43—41no—
79C23×Dic43—41no—
80C23×Dic43C2311yescharacteristic
81C23×Dic43C2311yescharacteristic
82C23×Dic43C2311yescharacteristic
83C23×Dic43C2311yescharacteristic
84C23×Dic43C2311yescharacteristic
85C23×Dic43C2311yescharacteristic
86C23×Dic43C2311yescharacteristic
87#13063311—232no—
88C2×C4⋊Dic43—22no—
89C2×C4⋊Dic43—22no—
90C2×C4⋊Dic43—22no—
91C2×C4⋊Dic43—22no—
92C2×C4⋊Dic43—41no—
93C2×C4⋊Dic43—41no—
94C2×C22⋊Dic43—22no—
95C2×C22⋊Dic43—22no—
96C2×C22⋊Dic43—22no—
97C2×C22⋊Dic43—41no—
98C2×C22⋊Dic43—41no—
99C2×C22⋊Dic43C2×C414yes—
100C2×(C2×D43)⋊C4—22no—
101C2×(C2×D43)⋊C4—22no—
102C2×(C2×D43)⋊C4—22no—
103C2×(C2×D43)⋊C4—22no—
104C2×(C2×D43)⋊C4—22no—
105C2×(C2×D43)⋊C4—22no—
106C2×(C2×D43)⋊C4—22no—
107C2×(C2×D43)⋊C4—22no—
108C2×(C2×D43)⋊C4—41no—
109C2×(C2×D43)⋊C4—41no—
110C2×(C2×D43)⋊C4—41no—
111C2×(C2×D43)⋊C4—41no—
112C2×(C2×D43)⋊C4—41no—
113C2×(C2×D43)⋊C4—41no—
114C2×(C2×D43)⋊C4—41no—
115C2×(C2×D43)⋊C4—41no—
116C2×(C2×D43)⋊C4C2×C414yescomplemented
117C2×(C2×D43)⋊C4C2×C414yescomplemented
118C2×C4×Dic43—22no—
119C2×C4×Dic43—22no—
120C2×C4×Dic43C2×C414yescomplemented
121C43⋊#95—22no—
122C43⋊#95—22no—
123C43⋊#95—22no—
124C43⋊#95—22no—
125C43⋊#95—22no—
126C43⋊#95—22no—
127C43⋊#95—22no—
128C43⋊#95—41no—
129C43⋊#95—41no—
130C43⋊#95—41no—
131C43⋊#95—41no—
132C43⋊#95—41no—
133C43⋊#95—41no—
134C43⋊#95D414yes—
135C25×C43C2311yescharacteristic
136C23×C4×C43C2311yescharacteristic
137C23×C4×C43C2311yescharacteristic
138C23×C4×C43C2311yescharacteristic
139C23×C4×C43C2311yescharacteristic
140C23×C4×C43C2311yescharacteristic
141C23×C4×C43C2311yescharacteristic
142C2×C4⋊C4×C43—22no—
143C2×C4⋊C4×C43—22no—
144C2×C4⋊C4×C43—41no—
145C2×C22⋊C4×C43—22no—
146C2×C22⋊C4×C43—22no—
147C2×C22⋊C4×C43—22no—
148C2×C22⋊C4×C43—22no—
149C2×C22⋊C4×C43—41no—
150C2×C22⋊C4×C43—41no—
151C2×C22⋊C4×C43C2×C414yes—
152C2×C22⋊C4×C43D414yes—
153C2×C22⋊C4×C43D414yes—
154C2×C42×C43—22no—
155C2×C42×C43—22no—
156C2×C42×C43—41no—
157#95×C43—22no—
158#95×C43—22no—
159C24×C43—21no—
160C24×C43—21no—
161C24×C43—21no—
162C24×C43—21no—
163C24×C43—21no—
164C24×C43—21no—
165C24×C43—21no—
166C24×C43—21no—
167C24×C43—21no—
168C24×C43—21no—
169C24×C43—21no—
170C24×C43—21no—
171C24×C43C22×C412yes—
172C24×C43C2×D412yes—
173C24×C43C2×D412yes—
174C24×C43C2411yescharacteristic
175C23×D43—21no—
176C23×D43—21no—
177C23×D43—21no—
178C23×D43—21no—
179C23×D43—21no—
180C23×D43—21no—
181C23×D43—21no—
182C23×D43—21no—
183C23×D43—21no—
184C23×D43—21no—
185C23×D43—21no—
186C23×D43—21no—
187C23×D43—21no—
188C23×D43—21no—
189C23×D43C22×C412yes—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43—21no—
199C22×C4×C43—21no—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43—21no—
203C22×C4×C43—21no—
204C22×C4×C43—21no—
205C22×C4×C43—21no—
206C22×C4×C43—21no—
207C22×C4×C43—21no—
208C22×C4×C43—21no—
209C22×C4×C43—21no—
210C22×C4×C43—21no—
211C22×C4×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43—21no—
215C22×C4×C43—21no—
216C22×C4×C43—21no—
217C22×C4×C43—21no—
218C22×C4×C43—21no—
219C22×C4×C43—21no—
220C22×C4×C43—21no—
221C22×C4×C43—21no—
222C22×C4×C43—21no—
223C22×C4×C43—21no—
224C22×C4×C43C22×C412yes—
225C22×C4×C43C22×C412yes—
226C22×C4×C43C2×D412yes—
227C22×C4×C43C2×D412yes—
228C22×C4×C43C2×D412yes—
229C22×C4×C43C2×D412yes—
230C22×C4×C43C2×D412yes—
231C22×C4×C43#4112yes—
232C2×C22⋊D43—28no—
233C2×C22⋊D43—28no—
234C2×C22⋊D43—44no—
235C2×C22⋊D43—44no—
236C2×C22⋊D43—44no—
237C2×C22⋊D43—44no—
238C2×C22⋊D43—44no—
239C22×Dic43—21no—
240C22×Dic43—21no—
241C22×Dic43—21no—
242C22×Dic43—21no—
243C22×Dic43—21no—
244C22×Dic43—21no—
245C22×Dic43—21no—
246C22×Dic43—21no—
247C22×Dic43—21no—
248C22×Dic43—21no—
249C22×Dic43—21no—
250C22×Dic43—21no—
251C22×Dic43—21no—
252C22×Dic43—21no—
253C22×Dic43—21no—
254C22×Dic43—21no—
255C22×Dic43—21no—
256C22×Dic43—21no—
257C22×Dic43—21no—
258C22×Dic43—21no—
259C22×Dic43—21no—
260C22×Dic43—21no—
261C22×Dic43—21no—
262C22×Dic43—21no—
263C22×Dic43—21no—
264C22×Dic43—21no—
265C22×Dic43—21no—
266C22×Dic43—21no—
267C22×Dic43—21no—
268C22×Dic43—21no—
269C22×Dic43—21no—
270C22×Dic43—21no—
271C22×Dic43—21no—
272C22×Dic43—21no—
273C22×Dic43—21no—
274C22×Dic43—21no—
275C22×Dic43—21no—
276C22×Dic43—21no—
277C22×Dic43—21no—
278C22×Dic43—21no—
279C22×Dic43—21no—
280C22×Dic43—21no—
281C22×Dic43—44no—
282C22×Dic43—44no—
283C22×Dic43—44no—
284C22×Dic43—44no—
285C22×Dic43—44no—
286C22×Dic43—44no—
287C22×Dic43—44no—
288C22×Dic43C22×C412yes—
289C22×Dic43C22×C412yes—
290C22×Dic43C22×C412yes—
291C22×Dic43C2×D412yes—
292C22×Dic43C2×D412yes—
293C22×Dic43#4112yes—
294C22×Dic43#4112yes—
295C2×Dic86—28no—
296C2×Dic86—28no—
297C2×Dic86—44no—
298C2×Dic86—44no—
299C2×Dic86—44no—
300C2×Dic86—44no—
301C2×Dic86—44no—
302C4⋊C4×C43—44no—
303C22⋊C4×C43—44no—
304C22⋊C4×C43—44no—
305C22⋊C4×C43C22⋊C4116yescomplemented
306C42×C43—44no—
307C22⋊Dic43—28no—
308C22⋊Dic43—44no—
309(C2×D43)⋊C4—28no—
310(C2×D43)⋊C4—28no—
311(C2×D43)⋊C4—44no—
312(C2×D43)⋊C4—44no—
313(C2×D43)⋊C4—44no—
314(C2×D43)⋊C4—44no—
315C4⋊Dic43—44no—
316C4⋊Dic43—44no—
317C4×Dic43—28no—
318C23×C43—22no—
319C23×C43—22no—
320C23×C43—22no—
321C23×C43—22no—
322C23×C43—22no—
323C23×C43—22no—
324C23×C43—22no—
325C23×C43—22no—
326C23×C43—22no—
327C23×C43—22no—
328C23×C43—22no—
329C23×C43—22no—
330C23×C43—22no—
331C23×C43—22no—
332C23×C43—22no—
333C23×C43—22no—
334C23×C43—22no—
335C23×C43—22no—
336C23×C43—41no—
337C23×C43—41no—
338C23×C43—41no—
339C23×C43—41no—
340C23×C43—41no—
341C23×C43—41no—
342C23×C43—41no—
343C23×C43—41no—
344C23×C43—41no—
345C23×C43—41no—
346C23×C43—41no—
347C23×C43—41no—
348C23×C43—41no—
349C23×C43—41no—
350C23×C43—41no—
351C23×C43—41no—
352C23×C43C2×C22⋊C414yes—
353C23×C43C23×C411yescharacteristic
354C23×C43C22×D411yescharacteristic
355C23×C43C22×D411yescharacteristic
356C23×C43C22×D411yescharacteristic
357C23×C43C2×#4111yescharacteristic
358C23×C43C2×#4111yescharacteristic
359C23×C43C2×#4111yescharacteristic
360C23×C43H(5,𝔽2)11yescharacteristic
361C23×C43H(5,𝔽2)11yescharacteristic
362C23×C43H(5,𝔽2)11yescharacteristic
363C23×C43H(5,𝔽2)11yescharacteristic
364C23×C43H(5,𝔽2)11yescharacteristic
365C23×C432−1+411yescharacteristic
366C23×C432−1+411yescharacteristic
367C23×C432−1+411yescharacteristic
368C22×D43—22no—
369C22×D43—22no—
370C22×D43—22no—
371C22×D43—22no—
372C22×D43—22no—
373C22×D43—22no—
374C22×D43—22no—
375C22×D43—41no—
376C22×D43—41no—
377C22×D43—41no—
378C22×D43—41no—
379C22×D43—41no—
380C22×D43—41no—
381C22×D43—41no—
382C22×D43—41no—
383C22×D43—41no—
384C22×D43—41no—
385C22×D43—41no—
386C22×D43—41no—
387C22×D43—41no—
388C22×D43—41no—
389C22×D43—41no—
390C22×D43—41no—
391C22×D43—41no—
392C22×D43—41no—
393C22×D43—41no—
394C22×D43—41no—
395C22×D43—41no—
396C22×D43—41no—
397C22×D43—41no—
398C22×D43—41no—
399C22×D43—41no—
400C22×D43—41no—
401C22×D43—41no—
402C22×D43—41no—
403C2×C4×C43—22no—
404C2×C4×C43—22no—
405C2×C4×C43—22no—
406C2×C4×C43—22no—
407C2×C4×C43—22no—
408C2×C4×C43—22no—
409C2×C4×C43—22no—
410C2×C4×C43—22no—
411C2×C4×C43—22no—
412C2×C4×C43—22no—
413C2×C4×C43—22no—
414C2×C4×C43—22no—
415C2×C4×C43—22no—
416C2×C4×C43—22no—
417C2×C4×C43—22no—
418C2×C4×C43—22no—
419C2×C4×C43—22no—
420C2×C4×C43—22no—
421C2×C4×C43—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×C43—41no—
432C2×C4×C43—41no—
433C2×C4×C43—41no—
434C2×C4×C43—41no—
435C2×C4×C43—41no—
436C2×C4×C43—41no—
437C2×C4×C43—41no—
438C2×C4×C43—41no—
439C2×C4×C43—41no—
440C2×C4×C43—41no—
441C2×C4×C43—41no—
442C2×C4×C43—41no—
443C2×C4×C43C2×C22⋊C414yes—
444C2×C4×C43C2×C22⋊C414yes—
445C22⋊D43—416no—
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—22no—
455C2×Dic43—22no—
456C2×Dic43—22no—
457C2×Dic43—22no—
458C2×Dic43—22no—
459C2×Dic43—22no—
460C2×Dic43—22no—
461C2×Dic43—22no—
462C2×Dic43—22no—
463C2×Dic43—22no—
464C2×Dic43—416no—
465C2×Dic43—41no—
466C2×Dic43—41no—
467C2×Dic43—41no—
468C2×Dic43—41no—
469C2×Dic43—41no—
470C2×Dic43—41no—
471C2×Dic43—41no—
472C2×Dic43—41no—
473C2×Dic43—41no—
474C2×Dic43—41no—
475C2×Dic43—41no—
476C2×Dic43—41no—
477C2×Dic43—41no—
478C2×Dic43—41no—
479C2×Dic43—41no—
480C2×Dic43—41no—
481C2×Dic43—41no—
482C2×Dic43—41no—
483C2×Dic43—41no—
484C2×Dic43—41no—
485C2×Dic43—41no—
486C2×Dic43—41no—
487C2×Dic43—41no—
488C2×Dic43—41no—
489C2×Dic43—41no—
490C2×Dic43—41no—
491C2×Dic43—41no—
492C2×Dic43—41no—
493C2×Dic43—41no—
494C2×Dic43—41no—
495C2×Dic43C4×D414yes—
496Dic86—416no—
497#14421—431nomaximal, Sylow
498C22×C43—24no—
499C22×C43—24no—
500C22×C43—24no—
501C22×C43—42no—
502C22×C43—42no—
503C22×C43—42no—
504C22×C43—42no—
505C22×C43—42no—
506C22×C43—42no—
507C22×C43—42no—
508C22×C43—42no—
509C22×C43—42no—
510C22×C43—42no—
511C22×C43—42no—
512C22×C43—42no—
513C22×C43C22×C22⋊C411yescharacteristic
514C22×C43C2×C4×D411yescharacteristic
515C22×C43C4×#4111yescharacteristic
516C22×C43#51811yescharacteristic
517C22×C43#52011yescharacteristic
518C22×C43#52011yescharacteristic
519C22×C43#52011yescharacteristic
520C22×C43#53511yescharacteristic
521C22×C43#53511yescharacteristic
522C22×C43#53611yescharacteristic
523C22×C43#53611yescharacteristic
524C22×C43#53711yescharacteristic
525C22×C43#53711yescharacteristic
526C22×C43#53811yescharacteristic
527C22×C43#53811yescharacteristic
528C22×C43#54211yescharacteristic
529C22×C43#54211yescharacteristic
530C22×C43#54211yescharacteristic
531C22×C43#54211yescharacteristic
532C22×C43D4211yescharacteristic
533C22×C43D4211yescharacteristic
534C22×C43#54611yescharacteristic
535C22×C43#54611yescharacteristic
536C22×C43#54611yescharacteristic
537C22×C43#54611yescharacteristic
538C22×C43#54611yescharacteristic
539C22×C43#54711yescharacteristic
540C22×C43#54711yescharacteristic
541C22×C43#54811yescharacteristic
542C22×C43#55611yescharacteristic
543C22×C43#55911yescharacteristic
544C22×C43H(3,𝔽4)11yescharacteristic
545C22×C43#56211yescharacteristic
546C22×C43#56211yescharacteristic
547C22×C43#56311yescharacteristic
548C2×D43—42no—
549C2×D43—42no—
550C2×D43—42no—
551C2×D43—42no—
552C2×D43—42no—
553C2×D43—42no—
554C2×D43—42no—
555C2×D43—81no—
556C2×D43—81no—
557C2×D43—81no—
558C2×D43—81no—
559C2×D43—81no—
560C2×D43—81no—
561C2×D43—81no—
562C2×D43—81no—
563C4×C43—24no—
564C4×C43—24no—
565C4×C43—42no—
566C4×C43—42no—
567C4×C43—81no—
568C4×C43—81no—
569Dic43—24no—
570Dic43—42no—
571Dic43—42no—
572Dic43—42no—
573Dic43—42no—
574Dic43—81no—
575Dic43—81no—
576C22×#124—431no—
577C2×#391—431no—
578C2×#388D4311yescharacteristic, complemented
579C2×#386—431no—
580C2×#385—431no—
581#1446—431no—
582#1440—431no—
583#1439—431no—
584#1439—431no—
585#1439—431no—
586#1438—431no—
587#1437—431no—
588C4⋊#95—431no—
589#1434—431no—
590C22⋊#95—431no—
591C2×C43—44no—
592C2×C43#231111yescharacteristic
593C2×C43#232611yescharacteristic
594C2×C43#233711yescharacteristic
595C2×C43D4×C22⋊C411yescharacteristic
596C2×C43#233911yescharacteristic
597C2×C43#236711yescharacteristic
598C2×C43#237911yescharacteristic
599C2×C43#267011yescharacteristic
600C2×C43#267211yescharacteristic
601C2×C43#267411yescharacteristic
602C2×C43#267611yescharacteristic
603C2×C43#270011yescharacteristic
604C2×C43#271011yescharacteristic
605C2×C43#271211yescharacteristic
606C2×C43#271511yescharacteristic
607D43—82no—
608C23×Q8—431no—
609C23×D4—431no—
610C24×C4—431no—
611C2×#124—438no—
612C2×#124—864no—
613C2×#124—864no—
614C22×C4⋊C4—431no—
615C22×C4⋊C4—431no—
616C22×C4⋊C4C2×D4311yescharacteristic
617C22×C22⋊C4—431no—
618C22×C22⋊C4—431no—
619C22×C22⋊C4—431no—
620C22×C22⋊C4—431no—
621C22×C22⋊C4—431no—
622C22×C22⋊C4—431no—
623C22×C22⋊C4—431no—
624C22×C22⋊C4—431no—
625C22×C22⋊C4C2×D4311yescharacteristic
626C22×C22⋊C4C2×D4311yescharacteristic
627C22×C22⋊C4C2×D4311yescharacteristic
628C22×C42—431no—
629C22×C42C2×D4311yescharacteristic
630#391—864no—
631#388—24no—
632#386—864no—
633#385—864no—
634C2×#95—431no—
635C2×#95—431no—
636C2×#95—431no—
637C2×#95—431no—
638C2×#95—431no—
639C2×#95—431no—
640C2×#95—431no—
641C2×#95—431no—
642C2×#95—431no—
643C2×#95—431no—
644C2×#95—431no—
645C2×#95—431no—
646C2×#95—431no—
647C2×#95—431no—
648C2×#95C2×D4311yescharacteristic
649C2×#95C2×D4311yescharacteristic
650C43#1442111yescharacteristic, complemented, Sylow
651C25—431no—
652C25C22×D4311yescharacteristic
653C22×Q8—434no—
654C22×Q8—862no—
655C22×Q8—862no—
656C22×Q8—862no—
657C22×Q8—862no—
658C22×Q8—1721no—
659C22×Q8—1721no—
660C22×D4—434no—
661C22×D4—862no—
662C22×D4—862no—
663C22×D4—862no—
664C22×D4—862no—
665C22×D4—1721no—
666C22×D4—1721no—
667C23×C4—431no—
668C23×C4—431no—
669C23×C4—431no—
670C23×C4—431no—
671C23×C4—431no—
672C23×C4—431no—
673C23×C4—431no—
674C23×C4—862no—
675C23×C4—862no—
676C23×C4—862no—
677C23×C4—1721no—
678C23×C4—1721no—
679C23×C4—1721no—
680C23×C4—1721no—
681C23×C4C22×D4311yescharacteristic
682C23×C4C22×D4311yescharacteristic
683C23×C4C22×D4311yescharacteristic
684C23×C4C22×D4311yescharacteristic
685C23×C4C22×D4311yescharacteristic
686C23×C4C22×D4311yescharacteristic
687#124—8632no—
688C2×C4⋊C4—22no—
689C2×C4⋊C4—22no—
690C2×C4⋊C4—41no—
691C2×C4⋊C4—862no—
692C2×C4⋊C4—862no—
693C2×C4⋊C4—862no—
694C2×C4⋊C4—862no—
695C2×C4⋊C4—1721no—
696C2×C4⋊C4—1721no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—41no—
702C2×C22⋊C4—41no—
703C2×C22⋊C4—434no—
704C2×C22⋊C4—434no—
705C2×C22⋊C4—434no—
706C2×C22⋊C4—862no—
707C2×C22⋊C4—862no—
708C2×C22⋊C4—862no—
709C2×C22⋊C4—862no—
710C2×C22⋊C4—862no—
711C2×C22⋊C4—862no—
712C2×C22⋊C4—862no—
713C2×C22⋊C4—862no—
714C2×C22⋊C4—862no—
715C2×C22⋊C4—862no—
716C2×C22⋊C4—862no—
717C2×C22⋊C4—1721no—
718C2×C22⋊C4—1721no—
719C2×C22⋊C4—1721no—
720C2×C22⋊C4—1721no—
721C2×C22⋊C4—1721no—
722C2×C22⋊C4—1721no—
723C2×C22⋊C4—1721no—
724C2×C22⋊C4—1721no—
725C2×C22⋊C4—1721no—
726C2×C22⋊C4—1721no—
727C2×C22⋊C4C4×D4314yes—
728C2×C22⋊C4D17214yes—
729C2×C22⋊C4C22⋊D4314yes—
730C2×C42—22no—
731C2×C42—22no—
732C2×C42—41no—
733C2×C42—434no—
734C2×C42—862no—
735C2×C42—862no—
736#95—22no—
737#95—22no—
738#95—434no—
739#95—862no—
740#95—862no—
741#95—862no—
742#95—862no—
743#95—862no—
744#95—862no—
745#95—862no—
746#95—1721no—
747#95—1721no—
748#95—1721no—
749#95—1721no—
750#95—1721no—
751#95—1721no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—432no—
765C24—861no—
766C24—861no—
767C24—861no—
768C24—861no—
769C24—861no—
770C24—861no—
771C24—861no—
772C24—861no—
773C24—861no—
774C24—861no—
775C24—861no—
776C24—861no—
777C24—861no—
778C24—861no—
779C24C2×C4×D4312yes—
780C24C2×D17212yes—
781C24C2×C22⋊D4312yes—
782C24C23×D4311yescharacteristic
783C2×Q8—868no—
784C2×Q8—868no—
785C2×Q8—1724no—
786C2×Q8—1724no—
787C2×Q8—1724no—
788C2×Q8—1724no—
789C2×Q8—1724no—
790C2×D4—868no—
791C2×D4—868no—
792C2×D4—1724no—
793C2×D4—1724no—
794C2×D4—1724no—
795C2×D4—1724no—
796C2×D4—1724no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—432no—
832C22×C4—432no—
833C22×C4—432no—
834C22×C4—432no—
835C22×C4—432no—
836C22×C4—432no—
837C22×C4—432no—
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—861no—
854C22×C4—861no—
855C22×C4—861no—
856C22×C4—861no—
857C22×C4—861no—
858C22×C4—861no—
859C22×C4—861no—
860C22×C4—861no—
861C22×C4—861no—
862C22×C4—861no—
863C22×C4—861no—
864C22×C4—861no—
865C22×C4—861no—
866C22×C4—861no—
867C22×C4—861no—
868C22×C4—861no—
869C22×C4—861no—
870C22×C4—861no—
871C22×C4—861no—
872C22×C4—861no—
873C22×C4—861no—
874C22×C4—861no—
875C22×C4—861no—
876C22×C4—861no—
877C22×C4—861no—
878C22×C4—861no—
879C22×C4—861no—
880C22×C4—1724no—
881C22×C4—1724no—
882C22×C4—1724no—
883C22×C4—1724no—
884C22×C4—1724no—
885C22×C4—1724no—
886C22×C4—1724no—
887C22×C4C2×C4×D4312yes—
888C22×C4C2×C4×D4312yes—
889C22×C4C2×D17212yes—
890C22×C4C2×D17212yes—
891C22×C4D4×D4312yes—
892C22×C4#1062190012yes—
893C22×C4C2×C22⋊D4312yes—
894C22×C4C2×C22⋊D4312yes—
895C4⋊C4—44no—
896C4⋊C4—1724no—
897C4⋊C4—1724no—
898C22⋊C4—44no—
899C22⋊C4—44no—
900C22⋊C4—868no—
901C22⋊C4—868no—
902C22⋊C4—868no—
903C22⋊C4—1724no—
904C22⋊C4—1724no—
905C22⋊C4—1724no—
906C22⋊C4—1724no—
907C22⋊C4—1724no—
908C22⋊C4(C2×D43)⋊C4116yescomplemented
909C42—44no—
910C42—868no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—862no—
946C23—862no—
947C23—862no—
948C23—862no—
949C23—862no—
950C23—862no—
951C23—862no—
952C23—1721no—
953C23—1721no—
954C23—1721no—
955C23—1721no—
956C23—1721no—
957C23—1721no—
958C23—1721no—
959C23—1721no—
960C23—1721no—
961C23—1721no—
962C23—1721no—
963C23—1721no—
964C23—1721no—
965C23—1721no—
966C23—1721no—
967C23—1721no—
968C23—1721no—
969C23—1721no—
970C23—1721no—
971C23—1721no—
972C23—1721no—
973C23—1721no—
974C23—1721no—
975C23—1721no—
976C23—1721no—
977C23—1721no—
978C23—1721no—
979C23—1721no—
980C23C2×(C2×D43)⋊C414yes—
981C23C22×C4×D4311yescharacteristic
982C23C2×D4×D4311yescharacteristic
983C23C22×C22⋊D4311yescharacteristic
984C23C22×D17211yescharacteristic
985C23#41×D4311yescharacteristic
986C23#41×D4311yescharacteristic
987C23C2×#1062190011yescharacteristic
988C23#1306337011yescharacteristic
989C23#1306337011yescharacteristic
990C23#1306337111yescharacteristic
991C23#1306337111yescharacteristic
992C23#1306337111yescharacteristic
993C23#1306337211yescharacteristic
994C23#1306337211yescharacteristic
995C23#1306337211yescharacteristic
996Q8—17216no—
997D4—17216no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—434no—
1039C2×C4—862no—
1040C2×C4—862no—
1041C2×C4—862no—
1042C2×C4—862no—
1043C2×C4—862no—
1044C2×C4—862no—
1045C2×C4—862no—
1046C2×C4—862no—
1047C2×C4—862no—
1048C2×C4—862no—
1049C2×C4—862no—
1050C2×C4—862no—
1051C2×C4—862no—
1052C2×C4—862no—
1053C2×C4—862no—
1054C2×C4—862no—
1055C2×C4—862no—
1056C2×C4—862no—
1057C2×C4—1721no—
1058C2×C4—1721no—
1059C2×C4—1721no—
1060C2×C4—1721no—
1061C2×C4—1721no—
1062C2×C4—1721no—
1063C2×C4—1721no—
1064C2×C4—1721no—
1065C2×C4—1721no—
1066C2×C4—1721no—
1067C2×C4—1721no—
1068C2×C4—1721no—
1069C2×C4—1721no—
1070C2×C4—1721no—
1071C2×C4—17216no—
1072C2×C4—1721no—
1073C2×C4—1721no—
1074C2×C4—1721no—
1075C2×C4—1721no—
1076C2×C4—1721no—
1077C2×C4—1721no—
1078C2×C4—1721no—
1079C2×C4—1721no—
1080C2×C4—1721no—
1081C2×C4—1721no—
1082C2×C4—1721no—
1083C2×C4—1721no—
1084C2×C4—1721no—
1085C2×C4—1721no—
1086C2×C4—1721no—
1087C2×C4—1721no—
1088C2×C4C2×(C2×D43)⋊C414yes—
1089C2×C4C2×(C2×D43)⋊C414yes—
1090C22—24no—
1091C22—24no—
1092C22—24no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—3441no—
1106C22—3441no—
1107C22—3441no—
1108C22—3441no—
1109C22—3441no—
1110C22—3441no—
1111C22—3441no—
1112C22—3441no—
1113C22—1722no—
1114C22—1722no—
1115C22—1722no—
1116C22—1722no—
1117C22—1722no—
1118C22—1722no—
1119C22—1722no—
1120C22C22×(C2×D43)⋊C411yescharacteristic
1121C22C4×D4×D4311yescharacteristic
1122C22C4×#1062190011yescharacteristic
1123C22#1458337111yescharacteristic
1124C22#1458337811yescharacteristic
1125C22#1458337911yescharacteristic
1126C22#1458337911yescharacteristic
1127C22#1458346511yescharacteristic
1128C22#1458346811yescharacteristic
1129C22#1458347111yescharacteristic
1130C22#1458347511yescharacteristic
1131C22#1458347711yescharacteristic
1132C22#1458347711yescharacteristic
1133C22#1458348611yescharacteristic
1134C22#1458348811yescharacteristic
1135C22#1458351311yescharacteristic
1136C22#1458351511yescharacteristic
1137C22#1458351711yescharacteristic
1138C22#1458351811yescharacteristic
1139C22D4×C22⋊D4311yescharacteristic
1140C22D4×D17211yescharacteristic
1141C22#1458353711yescharacteristic
1142C22#1458354111yescharacteristic
1143C22#1458354311yescharacteristic
1144C22#1458354411yescharacteristic
1145C22#1458354411yescharacteristic
1146C22#1458354811yescharacteristic
1147C22#1458355311yescharacteristic
1148C22#1458355511yescharacteristic
1149C22#1458361611yescharacteristic
1150C22#1458363111yescharacteristic
1151C22#1458364111yescharacteristic
1152C22#1458364411yescharacteristic
1153C22#1458364611yescharacteristic
1154C22#1458365111yescharacteristic
1155C4—24no—
1156C4—24no—
1157C4—42no—
1158C4—42no—
1159C4—81no—
1160C4—81no—
1161C4—864no—
1162C4—3441no—
1163C4—3441no—
1164C4—1722no—
1165C4—1722no—
1166C4—1722no—
1167C4—1722no—
1168C2—44no—
1169C2—3442no—
1170C2#1913718311yescharacteristic
1171C2#1913730411yescharacteristic
1172C2#1913740211yescharacteristic
1173C2D4×(C2×D43)⋊C411yescharacteristic
1174C2#1913742011yescharacteristic
1175C2#1913766911yescharacteristic
1176C2#1913776411yescharacteristic
1177C2#1914081911yescharacteristic
1178C2#1914084611yescharacteristic
1179C2#1914087411yescharacteristic
1180C2#1914089611yescharacteristic
1181C2#1914119111yescharacteristic
1182C2#1914133511yescharacteristic
1183C2#1914136111yescharacteristic
1184C2#1914140211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C43×#388C2
socle, cosocleC24×C43C24
prime radicalC23×C22⋊D43C22
hypercenterC2×#388D43
hypocenterC43#14421
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C2×#14582805C2semidirect
4. C2×#14582774C2semidirect
5. #19132865C2semidirect
6. #19132842C2semidirect
7. #19132841C2semidirect
8. #19132841C2semidirect
9. #19132837C2semidirect
11. #19132833C2semidirect
12. #19132824C2semidirect
13. #19132819C2semidirect
14. #19132817C2semidirect
15. C2×C43×#388C2semidirect
21. C2×#13063311C4semidirect
65. C22×Dic86C2×C4semidirect
116. C2×(C2×D43)⋊C4C2×C4semidirect
117. C2×(C2×D43)⋊C4C2×C4semidirect
120. C2×C4×Dic43C2×C4semidirect
305. C22⋊C4×C43C22⋊C4semidirect
578. C2×#388D43semidirect
650. C43#14421semidirect
908. C22⋊C4(C2×D43)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#130633112
C2×#145828052
C2×#145827762
C2×#145827742
#191328652
#191328422
#191328412
#191328372
#191328342
#191328332
#191328242
#191328192
#191328172
C2×C43×#3882
#1442143