Finite Group Databasebeta

← #25020403

Subgroups — #25020403

Order 11008.

2266 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063303C211yesmaximal, characteristic
2C2×#14582803C211yesmaximal, characteristic, complemented
3C2×#14582770C211yesmaximal, characteristic
4C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic
5C2×#95×D43C211yesmaximal, characteristic
6#19132865C211yesmaximal, characteristic, complemented
7#19132863C211yesmaximal, characteristic, complemented
8#19132846C211yesmaximal, characteristic, complemented
9#19132845C211yesmaximal, characteristic, complemented
10#19132828C211yesmaximal, characteristic, complemented
11#19132826C211yesmaximal, characteristic, complemented
12(C2×D43)⋊#95C211yesmaximal, characteristic
13(C2×D43)⋊#95C211yesmaximal, characteristic
14(C2×D43)⋊#95C211yesmaximal, characteristic
15C43×C4⋊#95C211yesmaximal, characteristic, complemented
16C23×Dic86C2211yescharacteristic
17C23×C4×D43C2211yescharacteristic
18C23×C4×D43C2211yescharacteristic
19C23×C4×D43C2211yescharacteristic
20C2×#13063303—24no—
21C2×#13063303—24no—
22C2×#13063303C418yescomplemented
23C22×Dic43⋊C4C2211yescharacteristic
24C22×Dic43⋊C4C2211yescharacteristic
25C22×Dic43⋊C4C2211yescharacteristic
26C22×(C2×D43)⋊C4C2211yescharacteristic
27C22×(C2×D43)⋊C4C2211yescharacteristic
28C22×(C2×D43)⋊C4C2211yescharacteristic
29C22×(C2×D43)⋊C4C2211yescharacteristic
30C22×C4×Dic43C2211yescharacteristic
31#14582803—24no—
32#14582770—24no—
33C4×(C2×D43)⋊C4—24no—
34C2×C43⋊#95C2211yescharacteristic
35C2×C43⋊#95C2211yescharacteristic
36C2×C43⋊#95C2211yescharacteristic
37C2×C43⋊#95C2211yescharacteristic
38C2×C43⋊#95C2211yescharacteristic
39C2×C43⋊#95C2211yescharacteristic
40C2×C43⋊#95C2211yescharacteristic
41C2×C43⋊#95C2211yescharacteristic
42C2×C43⋊#95C2211yescharacteristic
43C2×C43⋊#95C2211yescharacteristic
44C2×C43⋊#95C2211yescharacteristic
45C2×C43⋊#95C2211yescharacteristic
46C2×C43⋊#95C2211yescharacteristic
47C2×C43⋊#95C2211yescharacteristic
48C2×C43⋊#95C2211yescharacteristic
49C2×C43⋊#95C2211yescharacteristic
50#95×D43—24no—
51C22×C4⋊C4×C43C2211yescharacteristic
52C22×C4⋊C4×C43C2211yescharacteristic
53C22×C42×C43C2211yescharacteristic
54C2×#95×C43C2211yescharacteristic
55C2×#95×C43C2211yescharacteristic
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
66C23×Dic43C2311yescharacteristic
67C23×Dic43C2311yescharacteristic
68C23×Dic43C2311yescharacteristic
69C23×Dic43C2311yescharacteristic
70C23×Dic43C2311yescharacteristic
71C23×Dic43C2311yescharacteristic
72C23×Dic43C2311yescharacteristic
73C22×C4×D43—22no—
74C22×C4×D43—22no—
75C22×C4×D43—22no—
76C22×C4×D43—22no—
77C22×C4×D43—22no—
78C22×C4×D43—22no—
79C22×C4×D43—22no—
80C22×C4×D43—22no—
81C22×C4×D43—22no—
82C22×C4×D43—22no—
83C22×C4×D43—22no—
84C22×C4×D43—22no—
85C22×C4×D43—22no—
86C22×C4×D43—41no—
87C22×C4×D43—41no—
88C22×C4×D43—41no—
89C22×C4×D43—41no—
90C22×C4×D43—41no—
91C22×C4×D43—41no—
92C22×C4×D43C2×C414yes—
93C22×C4×D43Q814yescomplemented
94#13063303—232no—
95C2×Dic43⋊C4—22no—
96C2×Dic43⋊C4—22no—
97C2×Dic43⋊C4—22no—
98C2×Dic43⋊C4—22no—
99C2×Dic43⋊C4—22no—
100C2×Dic43⋊C4—22no—
101C2×Dic43⋊C4—41no—
102C2×Dic43⋊C4C2×C414yescomplemented
103C2×Dic43⋊C4C2×C414yescomplemented
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)⋊C4C2×C414yes—
112C2×(C2×D43)⋊C4C2×C414yes—
113C2×(C2×D43)⋊C4D414yes—
114C2×(C2×D43)⋊C4D414yes—
115C2×(C2×D43)⋊C4Q814yescomplemented
116C2×C4×Dic43—22no—
117C2×C4×Dic43—22no—
118C2×C4×Dic43—41no—
119C43⋊#95—22no—
120C43⋊#95—22no—
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—41no—
131C43⋊#95—41no—
132C43⋊#95—41no—
133C43⋊#95—41no—
134C43⋊#95D414yes—
135C23×C4×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—22no—
145C2×C4⋊C4×C43—22no—
146C2×C4⋊C4×C43—41no—
147C2×C4⋊C4×C43C2×C414yescomplemented
148C2×C42×C43—22no—
149C2×C42×C43—22no—
150C2×C42×C43—41no—
151#95×C43—22no—
152#95×C43—22no—
153#95×C43—41no—
154#95×C43—41no—
155C24×C43C2411yescharacteristic
156C23×D43—21no—
157C23×D43—21no—
158C23×D43—21no—
159C23×D43—21no—
160C23×D43—21no—
161C23×D43—21no—
162C23×D43—21no—
163C23×D43—21no—
164C23×D43C22×C412yes—
165C23×D43C2×D412yes—
166C23×D43C2×D412yes—
167C23×D43C2×Q812yes—
168C23×D43C2×Q812yes—
169C23×D43#4112yes—
170C23×D43#4112yes—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43—21no—
199C22×C4×C43—21no—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43—21no—
203C22×C4×C43—21no—
204C22×C4×C43—21no—
205C22×C4×C43—21no—
206C22×C4×C43—21no—
207C22×C4×C43—21no—
208C22×C4×C43—21no—
209C22×C4×C43—21no—
210C22×C4×C43C22×C412yes—
211C22×C4×C43C22×C412yes—
212C22×C4×C43C22×C412yes—
213C22×C4×C43C2×D412yes—
214C22×C4×C43C2×D412yes—
215C22×C4×C43C2×D412yes—
216C22×C4×C43C2×Q812yes—
217C22×C4×C43C2×Q812yes—
218C22×C4×C43#4112yes—
219C22×C4×C43#4112yes—
220C22×Dic43—21no—
221C22×Dic43—21no—
222C22×Dic43—21no—
223C22×Dic43—21no—
224C22×Dic43—21no—
225C22×Dic43—21no—
226C22×Dic43—21no—
227C22×Dic43—21no—
228C22×Dic43—21no—
229C22×Dic43—21no—
230C22×Dic43—21no—
231C22×Dic43—21no—
232C22×Dic43—21no—
233C22×Dic43—21no—
234C22×Dic43—21no—
235C22×Dic43—21no—
236C22×Dic43—21no—
237C22×Dic43—21no—
238C22×Dic43—21no—
239C22×Dic43—21no—
240C22×Dic43—21no—
241C22×Dic43—21no—
242C22×Dic43—21no—
243C22×Dic43—21no—
244C22×Dic43—21no—
245C22×Dic43—21no—
246C22×Dic43—21no—
247C22×Dic43—21no—
248C22×Dic43—21no—
249C22×Dic43—21no—
250C22×Dic43—21no—
251C22×Dic43—21no—
252C22×Dic43—21no—
253C22×Dic43—21no—
254C22×Dic43—21no—
255C22×Dic43—21no—
256C22×Dic43—21no—
257C22×Dic43—21no—
258C22×Dic43—21no—
259C22×Dic43C22×C412yes—
260C22×Dic43C22×C412yes—
261C22×Dic43C22×C412yes—
262C22×Dic43C2×D412yes—
263C22×Dic43C2×D412yes—
264C22×Dic43C2×D412yes—
265C22×Dic43C2×D412yes—
266C22×Dic43C2×Q812yes—
267C22×Dic43C2×Q812yes—
268C22×Dic43#4112yes—
269C2×C4×D43—28no—
270C2×C4×D43—28no—
271C2×C4×D43—28no—
272C2×C4×D43—28no—
273C2×C4×D43—28no—
274C2×C4×D43—44no—
275C2×C4×D43—44no—
276C2×C4×D43—44no—
277C2×C4×D43—44no—
278C2×C4×D43—44no—
279C2×C4×D43—44no—
280C2×C4×D43—44no—
281C2×C4×D43—44no—
282C2×C4×D43—44no—
283C2×C4×D43—44no—
284C2×C4×D43—44no—
285C2×C4×D43—44no—
286C2×C4×D43—44no—
287C2×C4×D43—44no—
288C2×C4×D43—44no—
289C2×C4×D43—44no—
290C2×Dic86—28no—
291C2×Dic86—28no—
292C2×Dic86—44no—
293C2×Dic86—44no—
294C2×Dic86—44no—
295C2×Dic86—44no—
296C2×Dic86—44no—
297C4⋊C4×C43—28no—
298C4⋊C4×C43—44no—
299C42×C43—44no—
300(C2×D43)⋊C4—28no—
301(C2×D43)⋊C4—28no—
302(C2×D43)⋊C4—44no—
303(C2×D43)⋊C4C22⋊C4116yes—
304Dic43⋊C4—28no—
305Dic43⋊C4—28no—
306Dic43⋊C4—44no—
307C4×Dic43—44no—
308C23×C43C23×C411yescharacteristic
309C23×C43C22×D411yescharacteristic
310C23×C43C22×D411yescharacteristic
311C23×C43C22×D411yescharacteristic
312C23×C43C22×Q811yescharacteristic
313C23×C43C22×Q811yescharacteristic
314C23×C43C2×#4111yescharacteristic
315C23×C43C2×#4111yescharacteristic
316C23×C43C2×#4111yescharacteristic
317C23×C43C2×#4111yescharacteristic
318C23×C43C2×#4111yescharacteristic
319C23×C43H(5,𝔽2)11yescharacteristic
320C23×C43H(5,𝔽2)11yescharacteristic
321C23×C43H(5,𝔽2)11yescharacteristic
322C23×C432−1+411yescharacteristic
323C22×D43—22no—
324C22×D43—22no—
325C22×D43—22no—
326C22×D43—22no—
327C22×D43—22no—
328C22×D43—22no—
329C22×D43—22no—
330C22×D43—22no—
331C22×D43—22no—
332C22×D43—22no—
333C22×D43—22no—
334C22×D43—22no—
335C22×D43—22no—
336C22×D43—22no—
337C22×D43—22no—
338C22×D43—22no—
339C22×D43—22no—
340C22×D43—22no—
341C22×D43—22no—
342C22×D43—22no—
343C22×D43—22no—
344C22×D43—22no—
345C22×D43—22no—
346C22×D43—22no—
347C22×D43—22no—
348C22×D43—22no—
349C22×D43—22no—
350C22×D43—22no—
351C22×D43C2×C22⋊C414yes—
352C22×D43C4×Q814yes—
353C22×D43C4×Q814yes—
354C22×D43C22⋊Q814yes—
355C22×D43C22⋊Q814yes—
356C22×D43#12414yes—
357C22×D43C4⋊Q814yes—
358C2×C4×C43—22no—
359C2×C4×C43—22no—
360C2×C4×C43—22no—
361C2×C4×C43—22no—
362C2×C4×C43—22no—
363C2×C4×C43—22no—
364C2×C4×C43—22no—
365C2×C4×C43—22no—
366C2×C4×C43—22no—
367C2×C4×C43—22no—
368C2×C4×C43—22no—
369C2×C4×C43—22no—
370C2×C4×C43—22no—
371C2×C4×C43—22no—
372C2×C4×C43—22no—
373C2×C4×C43—22no—
374C2×C4×C43—22no—
375C2×C4×C43—22no—
376C2×C4×C43—22no—
377C2×C4×C43—22no—
378C2×C4×C43—22no—
379C2×C4×C43—22no—
380C2×C4×C43—22no—
381C2×C4×C43—22no—
382C2×C4×C43—41no—
383C2×C4×C43—41no—
384C2×C4×C43—41no—
385C2×C4×C43—41no—
386C2×C4×C43—41no—
387C2×C4×C43—41no—
388C2×C4×C43—41no—
389C2×C4×C43—41no—
390C2×C4×C43—41no—
391C2×C4×C43—41no—
392C2×C4×C43—41no—
393C2×C4×C43—41no—
394C2×C4×C43—41no—
395C2×C4×C43—41no—
396C2×C4×C43—41no—
397C2×C4×C43—41no—
398C2×C4×C43—41no—
399C2×C4×C43—41no—
400C2×C4×C43—41no—
401C2×C4×C43—41no—
402C2×C4×C43—41no—
403C2×C4×C43—41no—
404C2×C4×C43—41no—
405C2×C4×C43C2×C22⋊C414yes—
406C2×C4×C43C22⋊Q814yescomplemented
407C2×Dic43—22no—
408C2×Dic43—22no—
409C2×Dic43—22no—
410C2×Dic43—22no—
411C2×Dic43—22no—
412C2×Dic43—22no—
413C2×Dic43—22no—
414C2×Dic43—22no—
415C2×Dic43—22no—
416C2×Dic43—22no—
417C2×Dic43—22no—
418C2×Dic43—22no—
419C2×Dic43—22no—
420C2×Dic43—22no—
421C2×Dic43—22no—
422C2×Dic43—22no—
423C2×Dic43—22no—
424C2×Dic43—22no—
425C2×Dic43—22no—
426C2×Dic43—22no—
427C2×Dic43—22no—
428C2×Dic43—22no—
429C2×Dic43—22no—
430C2×Dic43—22no—
431C2×Dic43—41no—
432C2×Dic43—41no—
433C2×Dic43—41no—
434C2×Dic43—41no—
435C2×Dic43—41no—
436C2×Dic43—41no—
437C2×Dic43—41no—
438C2×Dic43—41no—
439C2×Dic43—41no—
440C2×Dic43—41no—
441C2×Dic43—41no—
442C2×Dic43—41no—
443C2×Dic43—41no—
444C2×Dic43—41no—
445C2×Dic43—41no—
446C2×Dic43—41no—
447C2×Dic43—41no—
448C2×Dic43—41no—
449C2×Dic43—41no—
450C2×Dic43—41no—
451C2×Dic43—41no—
452C2×Dic43—41no—
453C2×Dic43—41no—
454C2×Dic43C2×C22⋊C414yes—
455C2×Dic43C4×D414yes—
456C4×D43—416no—
457C4×D43—416no—
458C4×D43—416no—
459Dic86—416no—
460#14052—431nomaximal, Sylow
461C22×C43C22×C22⋊C411yescharacteristic
462C22×C43C2×C4×D411yescharacteristic
463C22×C43C2×C4×Q811yescharacteristic
464C22×C43C2×C4×Q811yescharacteristic
465C22×C43C4×#4111yescharacteristic
466C22×C43#51811yescharacteristic
467C22×C43#52011yescharacteristic
468C22×C43C2×C22⋊Q811yescharacteristic
469C22×C43C2×C22⋊Q811yescharacteristic
470C22×C43C2×C22⋊Q811yescharacteristic
471C22×C43#52511yescharacteristic
472C22×C43C2×#12411yescharacteristic
473C22×C43#52911yescharacteristic
474C22×C43C2×C4⋊Q811yescharacteristic
475C22×C43#53311yescharacteristic
476C22×C43#53811yescharacteristic
477C22×C43#53911yescharacteristic
478C22×C43#54311yescharacteristic
479C22×C43#54411yescharacteristic
480C22×C43D4211yescharacteristic
481C22×C43D4211yescharacteristic
482C22×C43#54611yescharacteristic
483C22×C43#54611yescharacteristic
484C22×C43#54611yescharacteristic
485C22×C43#54611yescharacteristic
486C22×C43#54611yescharacteristic
487C22×C43#54711yescharacteristic
488C22×C43#54711yescharacteristic
489C22×C43D4×Q811yescharacteristic
490C22×C43#55111yescharacteristic
491C22×C43#55111yescharacteristic
492C22×C43#55211yescharacteristic
493C22×C43#55411yescharacteristic
494C22×C43#55411yescharacteristic
495C22×C43#55411yescharacteristic
496C2×D43—24no—
497C2×D43—24no—
498C2×D43—24no—
499C2×D43—24no—
500C2×D43—24no—
501C2×D43—24no—
502C2×D43—24no—
503C2×D43—24no—
504C2×D43—24no—
505C2×D43—24no—
506C2×D43—24no—
507C2×D43—24no—
508C2×D43—24no—
509C2×D43—24no—
510C2×D43#39118yescomplemented
511C4×C43—24no—
512C4×C43—24no—
513C4×C43—42no—
514C4×C43—42no—
515C4×C43—42no—
516C4×C43—42no—
517C4×C43—81no—
518Dic43—24no—
519Dic43—24no—
520Dic43—42no—
521Dic43—42no—
522Dic43—42no—
523Dic43—42no—
524Dic43—81no—
525C22×C22⋊Q8—431no—
526C2×#391—431no—
527C2×#385—431no—
528C2×C4×C22⋊C4—431no—
529C22×#95—431no—
530#1446—431no—
531#1445—431no—
532#1441—431no—
533#1441—431no—
534#1436—431no—
535#1436—431no—
536C4⋊#95D4311yescharacteristic, complemented
537C22⋊#95—431no—
538C22⋊#95—431no—
539C22⋊#95—431no—
540C2×C43C2×#39111yescharacteristic
541C2×C43C4×C22⋊Q811yescharacteristic
542C2×C43#232911yescharacteristic
543C2×C43D4×C22⋊C411yescharacteristic
544C2×C43#233911yescharacteristic
545C2×C43#236011yescharacteristic
546C2×C43#236811yescharacteristic
547C2×C43#243711yescharacteristic
548C2×C43#243811yescharacteristic
549C2×C43#244011yescharacteristic
550C2×C43#244911yescharacteristic
551C2×C43#245011yescharacteristic
552C2×C43#247211yescharacteristic
553C2×C43#248811yescharacteristic
554C2×C43#254911yescharacteristic
555D43—28no—
556C23×Q8—431no—
557C24×C4—431no—
558C24×C4—431no—
559C24×C4—431no—
560C2×C22⋊Q8—438no—
561C2×C22⋊Q8—864no—
562C2×C22⋊Q8—864no—
563C22×C4⋊C4—431no—
564C22×C4⋊C4—431no—
565C22×C4⋊C4—431no—
566C22×C4⋊C4C2×D4311yescharacteristic
567C22×C4⋊C4C2×D4311yescharacteristic
568C22×C22⋊C4—431no—
569C22×C22⋊C4—431no—
570C22×C22⋊C4—431no—
571C22×C22⋊C4—431no—
572C22×C42—431no—
573C22×C42C2×D4311yescharacteristic
574#391—864no—
575#385—864no—
576C4×C22⋊C4—864no—
577C2×#95—431no—
578C2×#95—431no—
579C2×#95—431no—
580C2×#95—431no—
581C2×#95—431no—
582C2×#95—431no—
583C2×#95—431no—
584C2×#95—431no—
585C2×#95—431no—
586C2×#95—431no—
587C2×#95—431no—
588C2×#95—431no—
589C2×#95—431no—
590C2×#95—431no—
591C2×#95—431no—
592C2×#95—431no—
593C2×#95—864no—
594C2×#95C2×D4311yescharacteristic
595C2×#95C2×D4311yescharacteristic
596C2×#95C2×D4311yescharacteristic
597C2×#95C2×D4311yescharacteristic
598C43#1405211yescharacteristic, complemented, Sylow
599C25—431no—
600C22×Q8—434no—
601C22×Q8—862no—
602C22×Q8—862no—
603C22×Q8—862no—
604C22×Q8—862no—
605C22×Q8—1721no—
606C22×Q8—1721no—
607C23×C4—431no—
608C23×C4—431no—
609C23×C4—431no—
610C23×C4—431no—
611C23×C4—431no—
612C23×C4—431no—
613C23×C4—434no—
614C23×C4—434no—
615C23×C4—431no—
616C23×C4—862no—
617C23×C4—862no—
618C23×C4—862no—
619C23×C4—862no—
620C23×C4—862no—
621C23×C4—862no—
622C23×C4—862no—
623C23×C4—862no—
624C23×C4—862no—
625C23×C4—862no—
626C23×C4—862no—
627C23×C4—862no—
628C23×C4—862no—
629C23×C4—1721no—
630C23×C4—1721no—
631C23×C4—1721no—
632C23×C4—1721no—
633C23×C4—1721no—
634C23×C4—1721no—
635C23×C4C22×D4311yescharacteristic
636C23×C4C22×D4311yescharacteristic
637C23×C4C22×D4311yescharacteristic
638C23×C4C22×D4311yescharacteristic
639C23×C4C22×D4311yescharacteristic
640C23×C4C22×D4311yescharacteristic
641C23×C4C22×D4311yescharacteristic
642C22⋊Q8—8632no—
643C2×C4⋊C4—22no—
644C2×C4⋊C4—22no—
645C2×C4⋊C4—22no—
646C2×C4⋊C4—22no—
647C2×C4⋊C4—41no—
648C2×C4⋊C4—434no—
649C2×C4⋊C4—434no—
650C2×C4⋊C4—862no—
651C2×C4⋊C4—862no—
652C2×C4⋊C4—862no—
653C2×C4⋊C4—862no—
654C2×C4⋊C4—862no—
655C2×C4⋊C4—862no—
656C2×C4⋊C4—1721no—
657C2×C4⋊C4C4×D4314yescomplemented
658C2×C22⋊C4—434no—
659C2×C22⋊C4—434no—
660C2×C22⋊C4—434no—
661C2×C22⋊C4—434no—
662C2×C22⋊C4—434no—
663C2×C22⋊C4—862no—
664C2×C22⋊C4—862no—
665C2×C22⋊C4—862no—
666C2×C22⋊C4—862no—
667C2×C22⋊C4—862no—
668C2×C22⋊C4—862no—
669C2×C22⋊C4—862no—
670C2×C42—22no—
671C2×C42—22no—
672C2×C42—41no—
673C2×C42—862no—
674C2×C42—862no—
675C2×C42—1721no—
676#95—22no—
677#95—22no—
678#95—41no—
679#95—41no—
680#95—434no—
681#95—862no—
682#95—862no—
683#95—862no—
684#95—862no—
685#95—862no—
686#95—862no—
687#95—862no—
688#95—862no—
689#95—862no—
690#95—862no—
691#95—862no—
692#95—1721no—
693#95—1721no—
694#95—1721no—
695#95—1721no—
696C24—432no—
697C24—432no—
698C24—432no—
699C24—432no—
700C24—432no—
701C24—432no—
702C24—432no—
703C24—861no—
704C24—861no—
705C24—861no—
706C24—861no—
707C24—861no—
708C24—861no—
709C24—861no—
710C24—861no—
711C24C23×D4311yescharacteristic
712C2×Q8—868no—
713C2×Q8—868no—
714C2×Q8—1724no—
715C2×Q8—1724no—
716C2×Q8—1724no—
717C2×Q8—1724no—
718C2×Q8—1724no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—432no—
759C22×C4—432no—
760C22×C4—432no—
761C22×C4—432no—
762C22×C4—432no—
763C22×C4—432no—
764C22×C4—432no—
765C22×C4—432no—
766C22×C4—432no—
767C22×C4—432no—
768C22×C4—868no—
769C22×C4—868no—
770C22×C4—868no—
771C22×C4—868no—
772C22×C4—861no—
773C22×C4—861no—
774C22×C4—861no—
775C22×C4—861no—
776C22×C4—861no—
777C22×C4—861no—
778C22×C4—861no—
779C22×C4—861no—
780C22×C4—861no—
781C22×C4—861no—
782C22×C4—861no—
783C22×C4—861no—
784C22×C4—861no—
785C22×C4—861no—
786C22×C4—861no—
787C22×C4—861no—
788C22×C4—861no—
789C22×C4—861no—
790C22×C4—861no—
791C22×C4—861no—
792C22×C4—861no—
793C22×C4—861no—
794C22×C4—861no—
795C22×C4—861no—
796C22×C4—861no—
797C22×C4—861no—
798C22×C4—861no—
799C22×C4—861no—
800C22×C4—861no—
801C22×C4—861no—
802C22×C4—861no—
803C22×C4—861no—
804C22×C4—868no—
805C22×C4—861no—
806C22×C4—861no—
807C22×C4—861no—
808C22×C4—861no—
809C22×C4—861no—
810C22×C4—861no—
811C22×C4—861no—
812C22×C4—1724no—
813C22×C4—1724no—
814C22×C4—1724no—
815C22×C4—1724no—
816C22×C4—1724no—
817C22×C4—1724no—
818C22×C4—1724no—
819C22×C4—1724no—
820C22×C4—1724no—
821C22×C4—1724no—
822C22×C4—1724no—
823C22×C4—1724no—
824C22×C4—1724no—
825C22×C4—1724no—
826C22×C4—1724no—
827C22×C4—1724no—
828C22×C4C2×C4×D4312yes—
829C22×C4C2×C4×D4312yes—
830C22×C4C2×C4×D4312yes—
831C22×C4#1062189812yes—
832C22×C4#1062189812yes—
833C22×C4D4×D4312yes—
834C22×C4D4×D4312yes—
835C22×C4D4×D4312yes—
836C22×C4Q8×D4312yes—
837C22×C4Q8×D4312yes—
838C4⋊C4—28no—
839C4⋊C4—44no—
840C4⋊C4—868no—
841C4⋊C4—868no—
842C4⋊C4—1724no—
843C22⋊C4—4316no—
844C22⋊C4—868no—
845C22⋊C4—868no—
846C22⋊C4—1724no—
847C42—44no—
848C42—1724no—
849C23—434no—
850C23—434no—
851C23—434no—
852C23—434no—
853C23—434no—
854C23—434no—
855C23—434no—
856C23—862no—
857C23—862no—
858C23—862no—
859C23—862no—
860C23—862no—
861C23—862no—
862C23—862no—
863C23—862no—
864C23—862no—
865C23—862no—
866C23—862no—
867C23—862no—
868C23—862no—
869C23—862no—
870C23—862no—
871C23—862no—
872C23—862no—
873C23—862no—
874C23—862no—
875C23—862no—
876C23—862no—
877C23—862no—
878C23—862no—
879C23—862no—
880C23—862no—
881C23—862no—
882C23—862no—
883C23—862no—
884C23C22×C4×D4311yescharacteristic
885C23C2×D4×D4311yescharacteristic
886C23C2×D4×D4311yescharacteristic
887C23C2×D4×D4311yescharacteristic
888C23C2×Q8×D4311yescharacteristic
889C23C2×Q8×D4311yescharacteristic
890C23#41×D4311yescharacteristic
891C23#41×D4311yescharacteristic
892C23#41×D4311yescharacteristic
893C23C2×#1062189811yescharacteristic
894C23C2×#1062189811yescharacteristic
895C23#1306337011yescharacteristic
896C23#1306337011yescharacteristic
897C23#1306337111yescharacteristic
898C23#1306337311yescharacteristic
899Q8—17216no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—434no—
948C2×C4—434no—
949C2×C4—862no—
950C2×C4—862no—
951C2×C4—862no—
952C2×C4—862no—
953C2×C4—862no—
954C2×C4—862no—
955C2×C4—862no—
956C2×C4—862no—
957C2×C4—862no—
958C2×C4—862no—
959C2×C4—862no—
960C2×C4—862no—
961C2×C4—862no—
962C2×C4—862no—
963C2×C4—862no—
964C2×C4—862no—
965C2×C4—862no—
966C2×C4—862no—
967C2×C4—862no—
968C2×C4—862no—
969C2×C4—862no—
970C2×C4—862no—
971C2×C4—862no—
972C2×C4—862no—
973C2×C4—17216no—
974C2×C4—17216no—
975C2×C4—17216no—
976C2×C4—1721no—
977C2×C4—1721no—
978C2×C4—1721no—
979C2×C4—1721no—
980C2×C4—1721no—
981C2×C4—1721no—
982C2×C4—1721no—
983C2×C4—1721no—
984C2×C4—1721no—
985C2×C4—1721no—
986C2×C4—1721no—
987C2×C4—1721no—
988C2×C4—1721no—
989C2×C4—1721no—
990C2×C4—1721no—
991C2×C4—1721no—
992C2×C4—1721no—
993C2×C4—1721no—
994C2×C4—1721no—
995C2×C4—1721no—
996C2×C4—1721no—
997C2×C4—1721no—
998C2×C4—1721no—
999C2×C4C22⋊C4×D4314yes—
1000C2×C4#1306330314yescomplemented
1001C22—438no—
1002C22—864no—
1003C22—864no—
1004C22—864no—
1005C22—864no—
1006C22—864no—
1007C22—864no—
1008C22—864no—
1009C22—864no—
1010C22—864no—
1011C22—864no—
1012C22—864no—
1013C22—864no—
1014C22—864no—
1015C22—864no—
1016C22C2×C22⋊C4×D4311yescharacteristic
1017C22C4×D4×D4311yescharacteristic
1018C22C4×Q8×D4311yescharacteristic
1019C22C4×Q8×D4311yescharacteristic
1020C22C4×#1062189811yescharacteristic
1021C22#1458337111yescharacteristic
1022C22#1458338011yescharacteristic
1023C22C22⋊Q8×D4311yescharacteristic
1024C22C22⋊Q8×D4311yescharacteristic
1025C22C2×#1306330311yescharacteristic
1026C22#1458340811yescharacteristic
1027C22#124×D4311yescharacteristic
1028C22#1458342711yescharacteristic
1029C22C4⋊Q8×D4311yescharacteristic
1030C22#1458345311yescharacteristic
1031C22#1458348111yescharacteristic
1032C22#1458349711yescharacteristic
1033C22#1458352411yescharacteristic
1034C22#1458352611yescharacteristic
1035C22#1458353311yescharacteristic
1036C22#1458353411yescharacteristic
1037C22#1458353811yescharacteristic
1038C22#1458353911yescharacteristic
1039C22#1458353911yescharacteristic
1040C22#1458354211yescharacteristic
1041C22#1458354611yescharacteristic
1042C22#1458355011yescharacteristic
1043C22#1458355011yescharacteristic
1044C22#1458356411yescharacteristic
1045C22#1458357311yescharacteristic
1046C22#1458357811yescharacteristic
1047C22#1458358111yescharacteristic
1048C22#1458360311yescharacteristic
1049C22#1458360411yescharacteristic
1050C22#1458360911yescharacteristic
1051C4—24no—
1052C4—24no—
1053C4—42no—
1054C4—42no—
1055C4—42no—
1056C4—42no—
1057C4—81no—
1058C4—864no—
1059C4—864no—
1060C4—3441no—
1061C4—1722no—
1062C4—1722no—
1063C4—1722no—
1064C4—1722no—
1065C2—868no—
1066C2#391×D4311yescharacteristic
1067C2C4×#1306330311yescharacteristic
1068C2#1913732911yescharacteristic
1069C2#1913741611yescharacteristic
1070C2#1913742211yescharacteristic
1071C2#1913759711yescharacteristic
1072C2#1913767911yescharacteristic
1073C2#1913826311yescharacteristic
1074C2#1913827811yescharacteristic
1075C2#1913830011yescharacteristic
1076C2#1913841111yescharacteristic
1077C2#1913842611yescharacteristic
1078C2#1913872711yescharacteristic
1079C2#1913891811yescharacteristic
1080C2#1913960411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×C4⋊#95C2
socle, cosocleC24×C43C24
prime radicalC24×D43C23
hypercenterC4⋊#95D43
hypocenterC43#14052
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#14582803C2semidirect
6. #19132865C2semidirect
7. #19132863C2semidirect
8. #19132846C2semidirect
9. #19132845C2semidirect
10. #19132828C2semidirect
11. #19132826C2semidirect
15. C43×C4⋊#95C2semidirect
22. C2×#13063303C4semidirect
65. C22×Dic86C2×C4semidirect
93. C22×C4×D43Q8semidirect
102. C2×Dic43⋊C4C2×C4semidirect
103. C2×Dic43⋊C4C2×C4semidirect
115. C2×(C2×D43)⋊C4Q8semidirect
147. C2×C4⋊C4×C43C2×C4semidirect
406. C2×C4×C43C22⋊Q8semidirect
510. C2×D43#391semidirect
536. C4⋊#95D43semidirect
598. C43#14052semidirect
657. C2×C4⋊C4C4×D43semidirect
1000. C2×C4#13063303semidirect

Maximal subgroups

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

subgroupindex
C22×#130633032
C2×#145828032
C2×#145827702
C2×C4×(C2×D43)⋊C42
C2×#95×D432
#191328652
#191328632
#191328462
#191328452
#191328282
#191328262
(C2×D43)⋊#952
C43×C4⋊#952
#1405243