Finite Group Databasebeta

← #25020078

Subgroups — #25020078

Order 11008.

2358 conjugacy classes of subgroups.

The subgroup lattice has 1194 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063311C211yesmaximal, characteristic
2C22×C4×Dic86C211yesmaximal, characteristic, complemented
3C2×#14582803C211yesmaximal, characteristic, complemented
4C2×#14582799C211yesmaximal, characteristic
5C2×#14582799C211yesmaximal, characteristic
6#19132841C211yesmaximal, characteristic, complemented
7#19132840C211yesmaximal, characteristic, complemented
8#19132839C211yesmaximal, characteristic, complemented
9#19132838C211yesmaximal, characteristic, complemented
10#19132833C211yesmaximal, characteristic, complemented
11#19132832C211yesmaximal, characteristic, complemented
12#19132831C211yesmaximal, characteristic, complemented
13Dic43⋊#95C211yesmaximal, characteristic, complemented
14#95×Dic43C211yesmaximal, characteristic, complemented
15C43×#1437C211yesmaximal, characteristic, complemented
16C23×Dic86C2211yescharacteristic
17C23×C22⋊D43C2211yescharacteristic
18C2×#13063311—24no—
19C2×#13063311—24no—
20C2×#13063311C418yescomplemented
21C2×C4×Dic86—24no—
22C2×C4×Dic86—24no—
23C2×C4×Dic86—24no—
24C22×C4⋊Dic43C2211yescharacteristic
25C22×Dic43⋊C4C2211yescharacteristic
26C22×Dic43⋊C4C2211yescharacteristic
27C22×Dic43⋊C4C2211yescharacteristic
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×(C2×D43)⋊C4C2211yescharacteristic
37C22×C4×Dic43C2211yescharacteristic
38C22×C4×Dic43C2211yescharacteristic
39C22×C4×Dic43C2211yescharacteristic
40C22×C4×Dic43C2211yescharacteristic
41#14582803—24no—
42#14582799—24no—
43#14582799—24no—
44C2×C43⋊#95C2211yescharacteristic
45C2×C43⋊#95C2211yescharacteristic
46C2×C43⋊#95C2211yescharacteristic
47C2×C43⋊#95C2211yescharacteristic
48C2×C43⋊#95C2211yescharacteristic
49C2×C43⋊#95C2211yescharacteristic
50C2×C43⋊#95C2211yescharacteristic
51C2×C43⋊#95C2211yescharacteristic
52C2×C43⋊#95C2211yescharacteristic
53C22×C22⋊C4×C43C2211yescharacteristic
54C22×C22⋊C4×C43C2211yescharacteristic
55C22×C22⋊C4×C43C2211yescharacteristic
56C22×C42×C43C2211yescharacteristic
57C2×#95×C43C2211yescharacteristic
58C2×#95×C43C2211yescharacteristic
59C2×#95×C43C2211yescharacteristic
60C24×D43C2311yescharacteristic
61C22×Dic86—22no—
62C22×Dic86—22no—
63C22×Dic86—22no—
64C22×Dic86—22no—
65C22×Dic86C2×C414yes—
66C22×Dic86D414yes—
67C22×Dic86D414yes—
68C22×C22⋊D43—22no—
69C22×C22⋊D43—22no—
70C22×C22⋊D43—22no—
71C22×C22⋊D43—22no—
72C22×C22⋊D43—22no—
73C22×C22⋊D43—22no—
74C22×C22⋊D43C2×C414yes—
75C23×Dic43C2311yescharacteristic
76C23×Dic43C2311yescharacteristic
77C23×Dic43C2311yescharacteristic
78C23×Dic43C2311yescharacteristic
79C23×Dic43C2311yescharacteristic
80C23×Dic43C2311yescharacteristic
81C23×Dic43C2311yescharacteristic
82#13063311—232no—
83C4×Dic86—232no—
84C2×C4⋊Dic43—22no—
85C2×C4⋊Dic43—22no—
86C2×C4⋊Dic43—22no—
87C2×Dic43⋊C4—22no—
88C2×Dic43⋊C4—22no—
89C2×Dic43⋊C4—22no—
90C2×Dic43⋊C4—22no—
91C2×Dic43⋊C4—22no—
92C2×Dic43⋊C4—22no—
93C2×Dic43⋊C4—22no—
94C2×Dic43⋊C4—22no—
95C2×Dic43⋊C4D414yes—
96C2×C22⋊Dic43—22no—
97C2×C22⋊Dic43—22no—
98C2×C22⋊Dic43—22no—
99C2×C22⋊Dic43—22no—
100C2×C22⋊Dic43—22no—
101C2×C22⋊Dic43—41no—
102C2×C22⋊Dic43—41no—
103C2×C22⋊Dic43—41no—
104C2×C22⋊Dic43C2×C414yes—
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—22no—
112C2×(C2×D43)⋊C4—22no—
113C2×(C2×D43)⋊C4—22no—
114C2×(C2×D43)⋊C4—22no—
115C2×(C2×D43)⋊C4—22no—
116C2×(C2×D43)⋊C4—22no—
117C2×(C2×D43)⋊C4—41no—
118C2×(C2×D43)⋊C4—41no—
119C2×(C2×D43)⋊C4—41no—
120C2×(C2×D43)⋊C4—41no—
121C2×(C2×D43)⋊C4C2×C414yes—
122C2×(C2×D43)⋊C4C2×C414yes—
123C2×C4×Dic43—22no—
124C2×C4×Dic43—22no—
125C2×C4×Dic43—22no—
126C2×C4×Dic43—22no—
127C2×C4×Dic43—22no—
128C2×C4×Dic43—22no—
129C2×C4×Dic43—22no—
130C2×C4×Dic43—22no—
131C2×C4×Dic43—22no—
132C2×C4×Dic43—22no—
133C2×C4×Dic43C2×C414yes—
134C2×C4×Dic43D414yes—
135C43⋊#95—22no—
136C43⋊#95—22no—
137C43⋊#95—22no—
138C43⋊#95—22no—
139C43⋊#95—22no—
140C43⋊#95—22no—
141C43⋊#95—41no—
142C43⋊#95—41no—
143C43⋊#95—41no—
144C25×C43C2311yescharacteristic
145C23×C4×C43C2311yescharacteristic
146C23×C4×C43C2311yescharacteristic
147C23×C4×C43C2311yescharacteristic
148C23×C4×C43C2311yescharacteristic
149C23×C4×C43C2311yescharacteristic
150C23×C4×C43C2311yescharacteristic
151C2×C22⋊C4×C43—22no—
152C2×C22⋊C4×C43—22no—
153C2×C22⋊C4×C43—22no—
154C2×C22⋊C4×C43—22no—
155C2×C22⋊C4×C43—22no—
156C2×C22⋊C4×C43—22no—
157C2×C22⋊C4×C43—22no—
158C2×C22⋊C4×C43—41no—
159C2×C22⋊C4×C43C2×C414yes—
160C2×C42×C43—22no—
161C2×C42×C43—22no—
162C2×C42×C43—22no—
163#95×C43—22no—
164#95×C43—22no—
165#95×C43—41no—
166C24×C43—21no—
167C24×C43—21no—
168C24×C43—21no—
169C24×C43—21no—
170C24×C43—21no—
171C24×C43—21no—
172C24×C43—21no—
173C24×C43—21no—
174C24×C43—21no—
175C24×C43—21no—
176C24×C43—21no—
177C24×C43—21no—
178C24×C43—21no—
179C24×C43—21no—
180C24×C43C22×C412yes—
181C24×C43C2411yescharacteristic
182C23×D43—21no—
183C23×D43—21no—
184C23×D43—21no—
185C23×D43—21no—
186C23×D43—21no—
187C23×D43—21no—
188C23×D43—21no—
189C23×D43—21no—
190C23×D43—21no—
191C23×D43—21no—
192C23×D43—21no—
193C23×D43—21no—
194C23×D43—21no—
195C23×D43—21no—
196C23×D43C22×C412yes—
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×C43—21no—
225C22×C4×C43—21no—
226C22×C4×C43—21no—
227C22×C4×C43—21no—
228C22×C4×C43—21no—
229C22×C4×C43—21no—
230C22×C4×C43C22×C412yes—
231C22×C4×C43C22×C412yes—
232C22×C4×C43C2×D412yes—
233C22×C4×C43C2×D412yes—
234C22×C4×C43C2×D412yes—
235C22×C4×C43C2×D412yes—
236C22×C4×C43#4112yes—
237C22×C4×C43#4112yes—
238C22×C4×C43#4112yes—
239C2×C22⋊D43—28no—
240C2×C22⋊D43—28no—
241C2×C22⋊D43—28no—
242C2×C22⋊D43—44no—
243C2×C22⋊D43—44no—
244C2×C22⋊D43—44no—
245C2×C22⋊D43—44no—
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×Dic43C22×C412yes—
282C22×Dic43C22×C412yes—
283C22×Dic43C22×C412yes—
284C22×Dic43C2×D412yes—
285C22×Dic43C2×D412yes—
286C22×Dic43C2×D412yes—
287C22×Dic43C2×D412yes—
288C22×Dic43C2×D412yes—
289C22×Dic43C2×D412yes—
290C22×Dic43C2×D412yes—
291C22×Dic43C2×D412yes—
292C22×Dic43#4112yes—
293C22×Dic43#4112yes—
294C22×Dic43#4112yes—
295C2×Dic86—28no—
296C2×Dic86—28no—
297C2×Dic86—28no—
298C2×Dic86—28no—
299C2×Dic86—28no—
300C2×Dic86—28no—
301C2×Dic86C22⋊C4116yescomplemented
302C22⋊C4×C43—28no—
303C22⋊C4×C43—44no—
304C22⋊C4×C43—44no—
305C42×C43—28no—
306C22⋊Dic43—28no—
307C22⋊Dic43—44no—
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—28no—
316Dic43⋊C4—28no—
317Dic43⋊C4—28no—
318Dic43⋊C4—44no—
319C4×Dic43—28no—
320C4×Dic43—28no—
321C4×Dic43—28no—
322C4×Dic43—44no—
323C23×C43—22no—
324C23×C43—22no—
325C23×C43—22no—
326C23×C43—22no—
327C23×C43—22no—
328C23×C43—22no—
329C23×C43—22no—
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×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×C43—41no—
353C23×C43—41no—
354C23×C43—41no—
355C23×C43—41no—
356C23×C43—41no—
357C23×C43—41no—
358C23×C43C23×C411yescharacteristic
359C23×C43C22×D411yescharacteristic
360C23×C43C22×D411yescharacteristic
361C23×C43C22×D411yescharacteristic
362C23×C43C22×D411yescharacteristic
363C23×C43C2×#4111yescharacteristic
364C23×C43C2×#4111yescharacteristic
365C23×C43C2×#4111yescharacteristic
366C23×C43C2×#4111yescharacteristic
367C23×C43C2×#4111yescharacteristic
368C23×C43C2×#4111yescharacteristic
369C23×C43H(5,𝔽2)11yescharacteristic
370C23×C43H(5,𝔽2)11yescharacteristic
371C23×C432−1+411yescharacteristic
372C23×C432−1+411yescharacteristic
373C22×D43—22no—
374C22×D43—22no—
375C22×D43—22no—
376C22×D43—22no—
377C22×D43—22no—
378C22×D43—22no—
379C22×D43—22no—
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—
403C22×D43—41no—
404C22×D43—41no—
405C22×D43—41no—
406C22×D43—41no—
407C22×D43—41no—
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—22no—
422C2×C4×C43—22no—
423C2×C4×C43—22no—
424C2×C4×C43—22no—
425C2×C4×C43—22no—
426C2×C4×C43—22no—
427C2×C4×C43—22no—
428C2×C4×C43—22no—
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×C43—41no—
444C2×C4×C43—41no—
445C2×C4×C43—41no—
446C2×C4×C43—41no—
447C2×C4×C43—41no—
448C2×C4×C43C2×C22⋊C414yes—
449C2×C4×C43#12414yescomplemented
450C22⋊D43—416no—
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—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×Dic43C2×C22⋊C414yes—
493C2×Dic43C2×C22⋊C414yes—
494C2×Dic43C4×D414yes—
495C2×Dic43C4×D414yes—
496C2×Dic43#12014yes—
497C2×Dic43#12114yes—
498C2×Dic43#12114yes—
499C2×Dic43#12314yes—
500Dic86—232no—
501#14026—431nomaximal, Sylow
502C22×C43—42no—
503C22×C43—42no—
504C22×C43—42no—
505C22×C43—42no—
506C22×C43—42no—
507C22×C43—42no—
508C22×C43—42no—
509C22×C43—81no—
510C22×C43—81no—
511C22×C43—81no—
512C22×C43—81no—
513C22×C43—81no—
514C22×C43—81no—
515C22×C43—81no—
516C22×C43—81no—
517C22×C43C22×C22⋊C411yescharacteristic
518C22×C43C2×C4×D411yescharacteristic
519C22×C43C2×C4×D411yescharacteristic
520C22×C43C4×#4111yescharacteristic
521C22×C43C4×#4111yescharacteristic
522C22×C43#52011yescharacteristic
523C22×C43#52011yescharacteristic
524C22×C43C2×#12011yescharacteristic
525C22×C43C2×#12111yescharacteristic
526C22×C43C2×#12111yescharacteristic
527C22×C43C2×#12311yescharacteristic
528C22×C43C2×#12411yescharacteristic
529C22×C43#52911yescharacteristic
530C22×C43#52911yescharacteristic
531C22×C43#53211yescharacteristic
532C22×C43#53511yescharacteristic
533C22×C43#53611yescharacteristic
534C22×C43#54211yescharacteristic
535C22×C43#54211yescharacteristic
536C22×C43#54611yescharacteristic
537C22×C43#54611yescharacteristic
538C22×C43#54811yescharacteristic
539C22×C43#54811yescharacteristic
540C22×C43#54811yescharacteristic
541C22×C43#54811yescharacteristic
542C22×C43#54811yescharacteristic
543C22×C43#54811yescharacteristic
544C22×C43#55011yescharacteristic
545C22×C43#55011yescharacteristic
546C22×C43#55011yescharacteristic
547C22×C43#55011yescharacteristic
548C22×C43#55611yescharacteristic
549C22×C43#55611yescharacteristic
550C22×C43#55911yescharacteristic
551C22×C43#55911yescharacteristic
552C2×D43—42no—
553C2×D43—42no—
554C2×D43—42no—
555C2×D43—42no—
556C2×D43—42no—
557C2×D43—42no—
558C2×D43—42no—
559C2×D43—81no—
560C2×D43—81no—
561C2×D43—81no—
562C2×D43—81no—
563C2×D43—81no—
564C2×D43—81no—
565C2×D43—81no—
566C2×D43—81no—
567C4×C43—24no—
568C4×C43—24no—
569C4×C43—42no—
570C4×C43—42no—
571C4×C43—42no—
572C4×C43—81no—
573Dic43—24no—
574Dic43—42no—
575Dic43—42no—
576Dic43—42no—
577Dic43—42no—
578Dic43—81no—
579Dic43#38618yes—
580C22×#124—431no—
581C22×C4×Q8—431no—
582C2×#391—431no—
583C2×#390—431no—
584C2×#390—431no—
585#1439—431no—
586#1439—431no—
587#1439—431no—
588#1439—431no—
589#1437—431no—
590#1437—431no—
591#1437—431no—
592#1437D4311yescharacteristic, complemented
593C4⋊#95—431no—
594C4×#95—431no—
595C2×C43—82no—
596C2×C43C2×#38611yescharacteristic
597C2×C43C4×#12411yescharacteristic
598C2×C43#232611yescharacteristic
599C2×C43#234111yescharacteristic
600C2×C43#234111yescharacteristic
601C2×C43#236711yescharacteristic
602C2×C43#236711yescharacteristic
603C2×C43#242611yescharacteristic
604C2×C43#242611yescharacteristic
605C2×C43#243111yescharacteristic
606C2×C43#243611yescharacteristic
607C2×C43#244811yescharacteristic
608C2×C43#244811yescharacteristic
609C2×C43#254511yescharacteristic
610C2×C43#254811yescharacteristic
611D43—82no—
612C23×Q8—431no—
613C23×D4—431no—
614C2×#124—438no—
615C2×#124—864no—
616C2×#124—864no—
617C2×C4×Q8—864no—
618C2×C4×Q8—864no—
619C2×C4×Q8—864no—
620C22×C4⋊C4—431no—
621C22×C4⋊C4—431no—
622C22×C4⋊C4—431no—
623C22×C4⋊C4—431no—
624C22×C22⋊C4—431no—
625C22×C22⋊C4—431no—
626C22×C22⋊C4—431no—
627C22×C22⋊C4—431no—
628C22×C22⋊C4—431no—
629C22×C22⋊C4—431no—
630C22×C22⋊C4—431no—
631C22×C22⋊C4—431no—
632C22×C22⋊C4—431no—
633C22×C22⋊C4C2×D4311yescharacteristic
634C22×C22⋊C4C2×D4311yescharacteristic
635C22×C22⋊C4C2×D4311yescharacteristic
636C22×C42—431no—
637C22×C42—431no—
638C22×C42—431no—
639C22×C42—431no—
640C22×C42C2×D4311yescharacteristic
641#391—864no—
642#390—864no—
643#390—864no—
644C2×#95—431no—
645C2×#95—431no—
646C2×#95—431no—
647C2×#95—431no—
648C2×#95—431no—
649C2×#95—431no—
650C2×#95—431no—
651C2×#95—431no—
652C2×#95—431no—
653C2×#95C2×D4311yescharacteristic
654C2×#95C2×D4311yescharacteristic
655C2×#95C2×D4311yescharacteristic
656C43#1402611yescharacteristic, complemented, Sylow
657C25—431no—
658C25C22×D4311yescharacteristic
659C22×Q8—434no—
660C22×Q8—434no—
661C22×Q8—434no—
662C22×Q8—862no—
663C22×Q8—862no—
664C22×Q8—862no—
665C22×Q8—862no—
666C22×D4—434no—
667C22×D4—862no—
668C22×D4—862no—
669C22×D4—862no—
670C22×D4—862no—
671C22×D4—862no—
672C22×D4—862no—
673C23×C4—431no—
674C23×C4—431no—
675C23×C4—431no—
676C23×C4—431no—
677C23×C4—431no—
678C23×C4—431no—
679C23×C4—431no—
680C23×C4C22×D4311yescharacteristic
681C23×C4C22×D4311yescharacteristic
682C23×C4C22×D4311yescharacteristic
683C23×C4C22×D4311yescharacteristic
684C23×C4C22×D4311yescharacteristic
685C23×C4C22×D4311yescharacteristic
686#124—8632no—
687C4×Q8—8632no—
688C2×C4⋊C4—434no—
689C2×C4⋊C4—862no—
690C2×C4⋊C4—862no—
691C2×C4⋊C4—862no—
692C2×C4⋊C4—862no—
693C2×C4⋊C4—862no—
694C2×C4⋊C4—862no—
695C2×C4⋊C4—862no—
696C2×C4⋊C4—862no—
697C2×C4⋊C4—862no—
698C2×C4⋊C4—862no—
699C2×C4⋊C4—862no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—22no—
703C2×C22⋊C4—22no—
704C2×C22⋊C4—22no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—41no—
708C2×C22⋊C4—434no—
709C2×C22⋊C4—434no—
710C2×C22⋊C4—434no—
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—862no—
723C2×C22⋊C4—862no—
724C2×C22⋊C4—862no—
725C2×C22⋊C4—862no—
726C2×C22⋊C4—862no—
727C2×C22⋊C4—862no—
728C2×C22⋊C4—1721no—
729C2×C22⋊C4—1721no—
730C2×C22⋊C4—1721no—
731C2×C22⋊C4—1721no—
732C2×C22⋊C4—1721no—
733C2×C22⋊C4—1721no—
734C2×C22⋊C4—1721no—
735C2×C22⋊C4C4×D4314yes—
736C2×C42—22no—
737C2×C42—22no—
738C2×C42—22no—
739C2×C42—434no—
740C2×C42—434no—
741C2×C42—862no—
742C2×C42—862no—
743C2×C42—862no—
744C2×C42—862no—
745C2×C42—862no—
746C2×C42—862no—
747C2×C42—862no—
748C2×C42—862no—
749C2×C42—862no—
750C2×C42—862no—
751#95—22no—
752#95—22no—
753#95—41no—
754#95—862no—
755#95—862no—
756#95—862no—
757#95—862no—
758#95—862no—
759#95—862no—
760#95—1721no—
761#95—1721no—
762#95—1721no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24—21no—
777C24—432no—
778C24—861no—
779C24—861no—
780C24—861no—
781C24—861no—
782C24—861no—
783C24—861no—
784C24—861no—
785C24—861no—
786C24—861no—
787C24—861no—
788C24—861no—
789C24—861no—
790C24—861no—
791C24—861no—
792C24C2×C4×D4312yes—
793C24C23×D4311yescharacteristic
794C2×Q8—4316no—
795C2×Q8—868no—
796C2×Q8—868no—
797C2×Q8—868no—
798C2×Q8—868no—
799C2×Q8—868no—
800C2×Q8—868no—
801C2×D4—868no—
802C2×D4—868no—
803C2×D4—868no—
804C2×D4—1724no—
805C2×D4—1724no—
806C2×D4—1724no—
807C2×D4—1724no—
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—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—432no—
842C22×C4—432no—
843C22×C4—432no—
844C22×C4—432no—
845C22×C4—432no—
846C22×C4—432no—
847C22×C4—432no—
848C22×C4—432no—
849C22×C4—432no—
850C22×C4—432no—
851C22×C4—432no—
852C22×C4—432no—
853C22×C4—432no—
854C22×C4—432no—
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—861no—
881C22×C4—861no—
882C22×C4—861no—
883C22×C4—861no—
884C22×C4—861no—
885C22×C4—861no—
886C22×C4—861no—
887C22×C4—861no—
888C22×C4—861no—
889C22×C4—861no—
890C22×C4C2×C4×D4312yes—
891C22×C4C2×C4×D4312yes—
892C22×C4#1062189812yes—
893C22×C4#1062189812yes—
894C22×C4D4×D4312yes—
895C22×C4D4×D4312yes—
896C22×C4D4×D4312yes—
897C22×C4D4×D4312yes—
898C22×C4#1062190012yes—
899C4⋊C4—868no—
900C4⋊C4—868no—
901C4⋊C4—868no—
902C4⋊C4—1724no—
903C22⋊C4—28no—
904C22⋊C4—44no—
905C22⋊C4—44no—
906C22⋊C4—868no—
907C22⋊C4—868no—
908C22⋊C4—868no—
909C22⋊C4—1724no—
910C22⋊C4—1724no—
911C22⋊C4—1724no—
912C22⋊C4—1724no—
913C22⋊C4—1724no—
914C22⋊C4—1724no—
915C42—28no—
916C42—868no—
917C42—868no—
918C42—868no—
919C42—1724no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—41no—
928C23—41no—
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—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—862no—
956C23—862no—
957C23—862no—
958C23—862no—
959C23—862no—
960C23—862no—
961C23—862no—
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—
980C23—1721no—
981C23—1721no—
982C23—1721no—
983C23—1721no—
984C23—1721no—
985C23—1721no—
986C23—1721no—
987C23—1721no—
988C23—1721no—
989C23—1721no—
990C23C22×C4×D4311yescharacteristic
991C23C2×D4×D4311yescharacteristic
992C23C2×D4×D4311yescharacteristic
993C23C2×D4×D4311yescharacteristic
994C23C2×D4×D4311yescharacteristic
995C23#41×D4311yescharacteristic
996C23#41×D4311yescharacteristic
997C23#41×D4311yescharacteristic
998C23C2×#1062190011yescharacteristic
999C23C2×#1062189811yescharacteristic
1000C23C2×#1062189811yescharacteristic
1001C23#1306337011yescharacteristic
1002C23#1306337111yescharacteristic
1003C23#1306337211yescharacteristic
1004C23#1306337211yescharacteristic
1005Q8—8632no—
1006D4—17216no—
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—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
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—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—434no—
1048C2×C4—434no—
1049C2×C4—434no—
1050C2×C4—434no—
1051C2×C4—434no—
1052C2×C4—434no—
1053C2×C4—434no—
1054C2×C4—434no—
1055C2×C4—862no—
1056C2×C4—862no—
1057C2×C4—862no—
1058C2×C4—862no—
1059C2×C4—862no—
1060C2×C4—862no—
1061C2×C4—862no—
1062C2×C4—862no—
1063C2×C4—862no—
1064C2×C4—862no—
1065C2×C4—862no—
1066C2×C4—862no—
1067C2×C4—862no—
1068C2×C4—862no—
1069C2×C4—862no—
1070C2×C4—862no—
1071C2×C4—862no—
1072C2×C4—862no—
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×C4—1721no—
1089C2×C4—1721no—
1090C2×C4—1721no—
1091C2×C4—1721no—
1092C2×C4—1721no—
1093C2×C4—1721no—
1094C2×C4—1721no—
1095C2×C4—1721no—
1096C2×C4C22⋊C4×D4314yes—
1097C2×C4#1306331114yescomplemented
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—81no—
1106C22—81no—
1107C22—81no—
1108C22—81no—
1109C22—81no—
1110C22—81no—
1111C22—81no—
1112C22—81no—
1113C22—3441no—
1114C22—3441no—
1115C22—3441no—
1116C22—3441no—
1117C22—3441no—
1118C22—3441no—
1119C22—3441no—
1120C22—3441no—
1121C22—1722no—
1122C22—1722no—
1123C22—1722no—
1124C22—1722no—
1125C22—1722no—
1126C22—1722no—
1127C22—1722no—
1128C22C2×C22⋊C4×D4311yescharacteristic
1129C22C4×D4×D4311yescharacteristic
1130C22C4×D4×D4311yescharacteristic
1131C22C4×#1062190011yescharacteristic
1132C22C4×#1062189811yescharacteristic
1133C22#1458337811yescharacteristic
1134C22#1458337911yescharacteristic
1135C22#120×D4311yescharacteristic
1136C22#121×D4311yescharacteristic
1137C22#121×D4311yescharacteristic
1138C22#123×D4311yescharacteristic
1139C22C2×#1306331111yescharacteristic
1140C22#1458342711yescharacteristic
1141C22#1458342911yescharacteristic
1142C22#1458344611yescharacteristic
1143C22#1458346511yescharacteristic
1144C22#1458347111yescharacteristic
1145C22#1458351311yescharacteristic
1146C22#1458351511yescharacteristic
1147C22#1458353911yescharacteristic
1148C22#1458354111yescharacteristic
1149C22#1458355511yescharacteristic
1150C22#1458355511yescharacteristic
1151C22#1458355711yescharacteristic
1152C22#1458355811yescharacteristic
1153C22#1458355811yescharacteristic
1154C22#1458355811yescharacteristic
1155C22#1458356711yescharacteristic
1156C22#1458356911yescharacteristic
1157C22#1458357011yescharacteristic
1158C22#1458357011yescharacteristic
1159C22#1458361611yescharacteristic
1160C22#1458361711yescharacteristic
1161C22#1458363111yescharacteristic
1162C22#1458363211yescharacteristic
1163C4—24no—
1164C4—24no—
1165C4—42no—
1166C4—42no—
1167C4—42no—
1168C4—81no—
1169C4—438no—
1170C4—864no—
1171C4—3441no—
1172C4—1722no—
1173C4—1722no—
1174C4—1722no—
1175C4—1722no—
1176C2—82no—
1177C2—3442no—
1178C2#386×D4311yescharacteristic
1179C2C4×#1306331111yescharacteristic
1180C2#1913730411yescharacteristic
1181C2#1913743411yescharacteristic
1182C2#1913743511yescharacteristic
1183C2#1913766711yescharacteristic
1184C2#1913766911yescharacteristic
1185C2#1913815811yescharacteristic
1186C2#1913816011yescharacteristic
1187C2#1913821211yescharacteristic
1188C2#1913825111yescharacteristic
1189C2#1913839011yescharacteristic
1190C2#1913839211yescharacteristic
1191C2#1913957311yescharacteristic
1192C2#1913959611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1437C2
socle, cosocleC24×C43C24
prime radicalC23×C22⋊D43C22
hypercenter#1437D43
hypocenterC43#14026
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic86C2semidirect
3. C2×#14582803C2semidirect
6. #19132841C2semidirect
7. #19132840C2semidirect
8. #19132839C2semidirect
9. #19132838C2semidirect
10. #19132833C2semidirect
11. #19132832C2semidirect
12. #19132831C2semidirect
13. Dic43⋊#95C2semidirect
14. #95×Dic43C2semidirect
15. C43×#1437C2semidirect
20. C2×#13063311C4semidirect
301. C2×Dic86C22⋊C4semidirect
449. C2×C4×C43#124semidirect
592. #1437D43semidirect
656. C43#14026semidirect
1097. C2×C4#13063311semidirect

Maximal subgroups

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

subgroupindex
C22×#130633112
C22×C4×Dic862
C2×#145828032
C2×#145827992
#191328412
#191328402
#191328392
#191328382
#191328332
#191328322
#191328312
Dic43⋊#952
#95×Dic432
C43×#14372
#1402643