Finite Group Databasebeta

← #25021054

Subgroups — #25021054

Order 11008.

2266 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×#13063307C211yesmaximal, characteristic
2C2×#14582776C211yesmaximal, characteristic
3C2×C22⋊C4×Dic43C211yesmaximal, characteristic, complemented
4C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
5#19132862C211yesmaximal, characteristic, complemented
6#19132842C211yesmaximal, characteristic, complemented
7#19132837C211yesmaximal, characteristic, complemented
8#19132834C211yesmaximal, characteristic
9#19132831C211yesmaximal, characteristic, complemented
10#19132830C211yesmaximal, characteristic, complemented
11#19132828C211yesmaximal, characteristic, complemented
12#19132824C211yesmaximal, characteristic, complemented
13#19132817C211yesmaximal, characteristic, complemented
14(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
15C2×C43×#388C211yesmaximal, characteristic, complemented
16C23×C22⋊D43C2211yescharacteristic
17C24×Dic43C2211yescharacteristic
18C23×C4×D43C2211yescharacteristic
19C2×#13063307—24no—
20C2×#13063307—24no—
21C2×#13063307C418yescomplemented
22C22×C4⋊Dic43C2211yescharacteristic
23C22×Dic43⋊C4C2211yescharacteristic
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×C4×Dic43C2211yescharacteristic
32C22×C4×Dic43C2211yescharacteristic
33#14582776—24no—
34C22⋊C4×Dic43—24no—
35C4×(C2×D43)⋊C4—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×C22⋊D43—22no—
60C22×C22⋊D43—22no—
61C22×C22⋊D43—22no—
62C22×C22⋊D43—22no—
63C22×C22⋊D43—41no—
64C22×C22⋊D43—41no—
65C22×C22⋊D43C2×C414yes—
66C23×Dic43—22no—
67C23×Dic43—22no—
68C23×Dic43—22no—
69C23×Dic43—22no—
70C23×Dic43—22no—
71C23×Dic43—41no—
72C23×Dic43—41no—
73C23×Dic43C2311yescharacteristic
74C23×Dic43C2311yescharacteristic
75C23×Dic43C2311yescharacteristic
76C23×Dic43C2311yescharacteristic
77C23×Dic43C2311yescharacteristic
78C23×Dic43C2311yescharacteristic
79C23×Dic43C2311yescharacteristic
80C22×C4×D43—22no—
81C22×C4×D43—22no—
82C22×C4×D43—22no—
83C22×C4×D43—22no—
84C22×C4×D43—41no—
85C22×C4×D43—41no—
86C22×C4×D43C2×C414yescomplemented
87#13063307—232no—
88C2×C4⋊Dic43—22no—
89C2×C4⋊Dic43—22no—
90C2×C4⋊Dic43C2×C414yescomplemented
91C2×Dic43⋊C4—22no—
92C2×Dic43⋊C4—22no—
93C2×Dic43⋊C4C2×C414yescomplemented
94C2×C22⋊Dic43—22no—
95C2×C22⋊Dic43—22no—
96C2×C22⋊Dic43—22no—
97C2×C22⋊Dic43—22no—
98C2×C22⋊Dic43—22no—
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—22no—
109C2×(C2×D43)⋊C4—22no—
110C2×(C2×D43)⋊C4—22no—
111C2×(C2×D43)⋊C4—41no—
112C2×(C2×D43)⋊C4—41no—
113C2×(C2×D43)⋊C4C2×C414yescomplemented
114C2×(C2×D43)⋊C4D414yes—
115C2×C4×Dic43—22no—
116C2×C4×Dic43—22no—
117C2×C4×Dic43—22no—
118C2×C4×Dic43—22no—
119C2×C4×Dic43—41no—
120C2×C4×Dic43—41no—
121C43⋊#95—22no—
122C43⋊#95—22no—
123C43⋊#95—22no—
124C43⋊#95—22no—
125C43⋊#95—22no—
126C43⋊#95—22no—
127C43⋊#95—22no—
128C43⋊#95—22no—
129C43⋊#95—22no—
130C43⋊#95—22no—
131C43⋊#95—41no—
132C43⋊#95—41no—
133C43⋊#95—41no—
134C43⋊#95—41no—
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×D43C22×C412yes—
188C23×D43C2×D412yes—
189C23×D43#4112yes—
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—28no—
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—44no—
281C22×Dic43—44no—
282C22×Dic43—44no—
283C22×Dic43—44no—
284C22×Dic43—44no—
285C22×Dic43—44no—
286C22×Dic43C22×C412yes—
287C22×Dic43C22×C412yes—
288C22×Dic43C22×C412yes—
289C22×Dic43C2×D412yes—
290C22×Dic43#4112yes—
291C22×Dic43#4112yes—
292C22×Dic43#4112yes—
293C22×Dic43#4112yes—
294C22×Dic43#4112yes—
295C2×C4×D43—28no—
296C2×C4×D43—28no—
297C2×C4×D43—44no—
298C2×C4×D43—44no—
299C2×C4×D43—44no—
300C2×C4×D43—44no—
301C2×C4×D43—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—28no—
309(C2×D43)⋊C4—28no—
310(C2×D43)⋊C4—28no—
311(C2×D43)⋊C4—28no—
312(C2×D43)⋊C4—44no—
313(C2×D43)⋊C4—44no—
314C4⋊Dic43—28no—
315Dic43⋊C4—28no—
316C4×Dic43—44no—
317C4×Dic43—44no—
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×C43C2×#4111yescharacteristic
361C23×C43C2×#4111yescharacteristic
362C23×C43C2×#4111yescharacteristic
363C23×C43C2×#4111yescharacteristic
364C23×C43H(5,𝔽2)11yescharacteristic
365C23×C43H(5,𝔽2)11yescharacteristic
366C23×C43H(5,𝔽2)11yescharacteristic
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—22no—
376C22×D43—22no—
377C22×D43—22no—
378C22×D43—22no—
379C22×D43—22no—
380C22×D43—22no—
381C22×D43—22no—
382C22×D43—22no—
383C22×D43—22no—
384C22×D43—22no—
385C22×D43—22no—
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×D43C4×D414yes—
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—22no—
465C2×Dic43—22no—
466C2×Dic43—22no—
467C2×Dic43—22no—
468C2×Dic43—22no—
469C2×Dic43—22no—
470C2×Dic43—416no—
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×Dic43#12314yescomplemented
496C4×D43—416no—
497#14096—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×C43C4×#4111yescharacteristic
517C22×C43C4×#4111yescharacteristic
518C22×C43#51811yescharacteristic
519C22×C43#52011yescharacteristic
520C22×C43C2×#12311yescharacteristic
521C22×C43#52511yescharacteristic
522C22×C43#52511yescharacteristic
523C22×C43#52511yescharacteristic
524C22×C43#52911yescharacteristic
525C22×C43#52911yescharacteristic
526C22×C43#53211yescharacteristic
527C22×C43#53211yescharacteristic
528C22×C43#53811yescharacteristic
529C22×C43#53911yescharacteristic
530C22×C43#54011yescharacteristic
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#54711yescharacteristic
542C22×C43#55111yescharacteristic
543C22×C43#55111yescharacteristic
544C22×C43#55211yescharacteristic
545C22×C43#55311yescharacteristic
546C22×C43#55311yescharacteristic
547C22×C43#55911yescharacteristic
548C2×D43—24no—
549C2×D43—24no—
550C2×D43—24no—
551C2×D43—42no—
552C2×D43—42no—
553C2×D43—42no—
554C2×D43—42no—
555C2×D43—42no—
556C2×D43—42no—
557C2×D43—42no—
558C2×D43—42no—
559C2×D43—42no—
560C2×D43—42no—
561C2×D43—42no—
562C2×D43—42no—
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—42no—
575Dic43—42no—
576C22×#123—431no—
577C2×#388D4311yescharacteristic, complemented
578C2×#386—431no—
579C2×C4×C22⋊C4—431no—
580C2×C4×C22⋊C4—431no—
581#1445—431no—
582#1440—431no—
583#1439—431no—
584#1438—431no—
585#1437—431no—
586#1436—431no—
587#1436—431no—
588C4⋊#95—431no—
589C22⋊#95—431no—
590C22⋊#95—431no—
591C2×C43—44no—
592C2×C43#229711yescharacteristic
593C2×C43C4×#12311yescharacteristic
594C2×C43#233511yescharacteristic
595C2×C43D4×C22⋊C411yescharacteristic
596C2×C43#233911yescharacteristic
597C2×C43#235911yescharacteristic
598C2×C43#237411yescharacteristic
599C2×C43#241811yescharacteristic
600C2×C43#242211yescharacteristic
601C2×C43#245511yescharacteristic
602C2×C43#245711yescharacteristic
603C2×C43#246411yescharacteristic
604C2×C43#247011yescharacteristic
605C2×C43#255311yescharacteristic
606C2×C43#255711yescharacteristic
607D43—44no—
608C23×D4—431no—
609C24×C4—431no—
610C24×C4—431no—
611C2×#123—438no—
612C2×#123—864no—
613C2×#123—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⋊C4C2×D4311yescharacteristic
625C22×C22⋊C4C2×D4311yescharacteristic
626C22×C22⋊C4C2×D4311yescharacteristic
627C22×C42—431no—
628C22×C42—431no—
629C22×C42C2×D4311yescharacteristic
630#388—24no—
631#386—864no—
632C4×C22⋊C4—864no—
633C4×C22⋊C4—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#1409611yescharacteristic, complemented, Sylow
651C25—431no—
652C25C22×D4311yescharacteristic
653C22×D4—434no—
654C22×D4—862no—
655C22×D4—862no—
656C22×D4—862no—
657C22×D4—862no—
658C22×D4—1721no—
659C22×D4—1721no—
660C23×C4—431no—
661C23×C4—431no—
662C23×C4—431no—
663C23×C4—431no—
664C23×C4—431no—
665C23×C4—431no—
666C23×C4—431no—
667C23×C4—434no—
668C23×C4—862no—
669C23×C4—862no—
670C23×C4—862no—
671C23×C4—862no—
672C23×C4—862no—
673C23×C4—862no—
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#123—8632no—
688C2×C4⋊C4—22no—
689C2×C4⋊C4—22no—
690C2×C4⋊C4—41no—
691C2×C4⋊C4—434no—
692C2×C4⋊C4—434no—
693C2×C4⋊C4—862no—
694C2×C4⋊C4—862no—
695C2×C4⋊C4—862no—
696C2×C4⋊C4—862no—
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—862no—
718C2×C22⋊C4—862no—
719C2×C22⋊C4—862no—
720C2×C22⋊C4—862no—
721C2×C22⋊C4—862no—
722C2×C22⋊C4—1721no—
723C2×C22⋊C4—1721no—
724C2×C22⋊C4C4×D4314yes—
725C2×C22⋊C4D17214yes—
726C2×C22⋊C4C22⋊D4314yes—
727C2×C42—22no—
728C2×C42—22no—
729C2×C42—41no—
730C2×C42—862no—
731C2×C42—862no—
732C2×C42—862no—
733C2×C42—862no—
734C2×C42—1721no—
735C2×C42—1721no—
736#95—22no—
737#95—22no—
738#95—862no—
739#95—862no—
740#95—862no—
741#95—862no—
742#95—862no—
743#95—862no—
744#95—862no—
745#95—862no—
746#95—862no—
747#95—862no—
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—432no—
766C24—432no—
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×D4—868no—
784C2×D4—868no—
785C2×D4—1724no—
786C2×D4—1724no—
787C2×D4—1724no—
788C2×D4—1724no—
789C2×D4—1724no—
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—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—432no—
825C22×C4—432no—
826C22×C4—432no—
827C22×C4—432no—
828C22×C4—432no—
829C22×C4—432no—
830C22×C4—432no—
831C22×C4—432no—
832C22×C4—432no—
833C22×C4—868no—
834C22×C4—861no—
835C22×C4—861no—
836C22×C4—861no—
837C22×C4—861no—
838C22×C4—868no—
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—868no—
876C22×C4—1724no—
877C22×C4—1724no—
878C22×C4—1724no—
879C22×C4—1724no—
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—868no—
897C4⋊C4—868no—
898C22⋊C4—44no—
899C22⋊C4—44no—
900C22⋊C4—868no—
901C22⋊C4—868no—
902C22⋊C4—868no—
903C22⋊C4—868no—
904C22⋊C4—868no—
905C22⋊C4—1724no—
906C22⋊C4—1724no—
907C22⋊C4(C2×D43)⋊C4116yescomplemented
908C42—44no—
909C42—1724no—
910C42—1724no—
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—434no—
946C23—862no—
947C23—862no—
948C23—862no—
949C23—862no—
950C23—862no—
951C23—862no—
952C23—862no—
953C23—862no—
954C23—862no—
955C23—862no—
956C23—862no—
957C23—862no—
958C23—862no—
959C23—862no—
960C23—862no—
961C23—862no—
962C23—862no—
963C23—862no—
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
987C23#41×D4311yescharacteristic
988C23#41×D4311yescharacteristic
989C23#41×D4311yescharacteristic
990C23#41×D4311yescharacteristic
991C23C2×#1062190011yescharacteristic
992C23#1306337011yescharacteristic
993C23#1306337011yescharacteristic
994C23#1306337111yescharacteristic
995C23#1306337211yescharacteristic
996D4—17216no—
997C2×C4—22no—
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—41no—
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—434no—
1038C2×C4—862no—
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—862no—
1058C2×C4—862no—
1059C2×C4—862no—
1060C2×C4—862no—
1061C2×C4—862no—
1062C2×C4—17216no—
1063C2×C4—17216no—
1064C2×C4—1721no—
1065C2×C4—1721no—
1066C2×C4—1721no—
1067C2×C4—1721no—
1068C2×C4—1721no—
1069C2×C4—1721no—
1070C2×C4—1721no—
1071C2×C4—1721no—
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—864no—
1106C22—864no—
1107C22—864no—
1108C22—1722no—
1109C22—1722no—
1110C22—1722no—
1111C22—1722no—
1112C22—1722no—
1113C22—1722no—
1114C22—1722no—
1115C22—1722no—
1116C22—1722no—
1117C22—1722no—
1118C22—1722no—
1119C22—1722no—
1120C22C22×(C2×D43)⋊C411yescharacteristic
1121C22C4×D4×D4311yescharacteristic
1122C22C4×#1062190011yescharacteristic
1123C22#1458336711yescharacteristic
1124C22#1458336711yescharacteristic
1125C22#1458337111yescharacteristic
1126C22#1458337811yescharacteristic
1127C22#123×D4311yescharacteristic
1128C22#1458340911yescharacteristic
1129C22#1458341111yescharacteristic
1130C22#1458341111yescharacteristic
1131C22#1458342811yescharacteristic
1132C22#1458343211yescharacteristic
1133C22#1458344511yescharacteristic
1134C22#1458344511yescharacteristic
1135C22#1458348311yescharacteristic
1136C22#1458349011yescharacteristic
1137C22#1458349911yescharacteristic
1138C22#1458351711yescharacteristic
1139C22D4×C22⋊D4311yescharacteristic
1140C22D4×D17211yescharacteristic
1141C22#1458353711yescharacteristic
1142C22#1458354311yescharacteristic
1143C22#1458354411yescharacteristic
1144C22#1458354411yescharacteristic
1145C22#1458354611yescharacteristic
1146C22#1458354711yescharacteristic
1147C22#1458354811yescharacteristic
1148C22#1458355311yescharacteristic
1149C22#1458357411yescharacteristic
1150C22#1458357911yescharacteristic
1151C22#1458358511yescharacteristic
1152C22#1458359211yescharacteristic
1153C22#1458359411yescharacteristic
1154C22#1458363111yescharacteristic
1155C4—24no—
1156C4—24no—
1157C4—42no—
1158C4—42no—
1159C4—81no—
1160C4—81no—
1161C4—864no—
1162C4—1722no—
1163C4—1722no—
1164C4—1722no—
1165C4—1722no—
1166C4—1722no—
1167C4—1722no—
1168C2—44no—
1169C2—1724no—
1170C2#1913708311yescharacteristic
1171C2#1913712211yescharacteristic
1172C2#1913738311yescharacteristic
1173C2D4×(C2×D43)⋊C411yescharacteristic
1174C2#1913742011yescharacteristic
1175C2#1913758411yescharacteristic
1176C2#1913772311yescharacteristic
1177C2#1913806211yescharacteristic
1178C2#1913810611yescharacteristic
1179C2#1913847511yescharacteristic
1180C2#1913850011yescharacteristic
1181C2#1913860611yescharacteristic
1182C2#1913868911yescharacteristic
1183C2#1913963811yescharacteristic
1184C2#1913969211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C43×#388C2
socle, cosocleC24×C43C24
prime radicalC23×C22⋊D43C22
hypercenterC2×#388D43
hypocenterC43#14096
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
3. C2×C22⋊C4×Dic43C2semidirect
4. C2×C4×(C2×D43)⋊C4C2semidirect
5. #19132862C2semidirect
6. #19132842C2semidirect
7. #19132837C2semidirect
9. #19132831C2semidirect
10. #19132830C2semidirect
11. #19132828C2semidirect
12. #19132824C2semidirect
13. #19132817C2semidirect
14. (C2×D43)⋊#95C2semidirect
15. C2×C43×#388C2semidirect
21. C2×#13063307C4semidirect
86. C22×C4×D43C2×C4semidirect
90. C2×C4⋊Dic43C2×C4semidirect
93. C2×Dic43⋊C4C2×C4semidirect
113. C2×(C2×D43)⋊C4C2×C4semidirect
305. C22⋊C4×C43C22⋊C4semidirect
495. C2×Dic43#123semidirect
577. C2×#388D43semidirect
650. C43#14096semidirect
907. 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×#130633072
C2×#145827762
C2×C22⋊C4×Dic432
C2×C4×(C2×D43)⋊C42
#191328622
#191328422
#191328372
#191328342
#191328312
#191328302
#191328282
#191328242
#191328172
(C2×D43)⋊#952
C2×C43×#3882
#1409643