Finite Group Databasebeta

← #25024702

Subgroups — #25024702

Order 11008.

1766 conjugacy classes of subgroups.

The subgroup lattice has 1142 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582788C211yesmaximal, characteristic, complemented
2C2×#14582776C211yesmaximal, characteristic
3C2×#14582757C211yesmaximal, characteristic, complemented
4#19132856C211yesmaximal, characteristic, complemented
5#19132850C211yesmaximal, characteristic, complemented
6#19132843C211yesmaximal, characteristic, complemented
7#19132839C211yesmaximal, characteristic, complemented
8#19132834C211yesmaximal, characteristic
9#19132834C211yesmaximal, characteristic
10#19132833C211yesmaximal, characteristic, complemented
11#19132832C211yesmaximal, characteristic, complemented
12#19132828C211yesmaximal, characteristic, complemented
13#19132820C211yesmaximal, characteristic, complemented
14#19132817C211yesmaximal, characteristic, complemented
15C43×#1437C211yesmaximal, characteristic, complemented
16C23×C22⋊D43C2211yescharacteristic
17C24×Dic43C2211yescharacteristic
18C22×Dic43⋊C4C2211yescharacteristic
19C22×Dic43⋊C4C2211yescharacteristic
20C22×C22⋊Dic43C2211yescharacteristic
21C22×C22⋊Dic43C2211yescharacteristic
22C22×(C2×D43)⋊C4C2211yescharacteristic
23C22×(C2×D43)⋊C4C2211yescharacteristic
24C22×(C2×D43)⋊C4C2211yescharacteristic
25C22×(C2×D43)⋊C4C2211yescharacteristic
26C22×(C2×D43)⋊C4C2211yescharacteristic
27C22×(C2×D43)⋊C4C2211yescharacteristic
28C22×C4×Dic43C2211yescharacteristic
29#14582788—24no—
30#14582776C418yescomplemented
31#14582757—24no—
32C2×C43⋊#95C2211yescharacteristic
33C2×C43⋊#95C2211yescharacteristic
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
47C22×C22⋊C4×C43C2211yescharacteristic
48C22×C22⋊C4×C43C2211yescharacteristic
49C22×C22⋊C4×C43C2211yescharacteristic
50C22×C42×C43C2211yescharacteristic
51C2×#95×C43C2211yescharacteristic
52C2×#95×C43C2211yescharacteristic
53C2×#95×C43C2211yescharacteristic
54C24×D43C2311yescharacteristic
55C22×C22⋊D43—22no—
56C22×C22⋊D43—22no—
57C22×C22⋊D43—41no—
58C22×C22⋊D43—41no—
59C22×C22⋊D43—41no—
60C22×C22⋊D43—41no—
61C22×C22⋊D43C2×C414yes—
62C23×Dic43—22no—
63C23×Dic43—22no—
64C23×Dic43—41no—
65C23×Dic43—41no—
66C23×Dic43—41no—
67C23×Dic43—41no—
68C23×Dic43C2×C414yes—
69C23×Dic43C2311yescharacteristic
70C23×Dic43C2311yescharacteristic
71C23×Dic43C2311yescharacteristic
72C23×Dic43C2311yescharacteristic
73C23×Dic43C2311yescharacteristic
74C23×Dic43C2311yescharacteristic
75C23×Dic43C2311yescharacteristic
76C2×Dic43⋊C4—22no—
77C2×Dic43⋊C4—41no—
78C2×Dic43⋊C4—41no—
79C2×Dic43⋊C4—41no—
80C2×Dic43⋊C4—41no—
81C2×Dic43⋊C4D414yescomplemented
82C2×C22⋊Dic43—22no—
83C2×C22⋊Dic43—22no—
84C2×C22⋊Dic43—22no—
85C2×C22⋊Dic43—22no—
86C2×C22⋊Dic43—41no—
87C2×C22⋊Dic43—41no—
88C2×(C2×D43)⋊C4—22no—
89C2×(C2×D43)⋊C4—22no—
90C2×(C2×D43)⋊C4—22no—
91C2×(C2×D43)⋊C4—22no—
92C2×(C2×D43)⋊C4—22no—
93C2×(C2×D43)⋊C4—22no—
94C2×(C2×D43)⋊C4—41no—
95C2×(C2×D43)⋊C4—41no—
96C2×(C2×D43)⋊C4—41no—
97C2×(C2×D43)⋊C4—41no—
98C2×(C2×D43)⋊C4—41no—
99C2×(C2×D43)⋊C4—41no—
100C2×(C2×D43)⋊C4—41no—
101C2×(C2×D43)⋊C4—41no—
102C2×(C2×D43)⋊C4—41no—
103C2×(C2×D43)⋊C4—41no—
104C2×(C2×D43)⋊C4C2×C414yes—
105C2×(C2×D43)⋊C4C2×C414yes—
106C2×C4×Dic43—22no—
107C2×C4×Dic43—22no—
108C2×C4×Dic43—41no—
109C43⋊#95—22no—
110C43⋊#95—22no—
111C43⋊#95—22no—
112C43⋊#95—22no—
113C43⋊#95—41no—
114C43⋊#95—41no—
115C43⋊#95—41no—
116C43⋊#95—41no—
117C43⋊#95—41no—
118C43⋊#95—41no—
119C43⋊#95—41no—
120C43⋊#95—41no—
121C43⋊#95—41no—
122C43⋊#95C2×C414yes—
123C43⋊#95C2×C414yes—
124C25×C43C2311yescharacteristic
125C23×C4×C43C2311yescharacteristic
126C23×C4×C43C2311yescharacteristic
127C23×C4×C43C2311yescharacteristic
128C23×C4×C43C2311yescharacteristic
129C23×C4×C43C2311yescharacteristic
130C23×C4×C43C2311yescharacteristic
131C2×C22⋊C4×C43—22no—
132C2×C22⋊C4×C43—22no—
133C2×C22⋊C4×C43—22no—
134C2×C22⋊C4×C43—22no—
135C2×C22⋊C4×C43—41no—
136C2×C22⋊C4×C43—41no—
137C2×C22⋊C4×C43—41no—
138C2×C22⋊C4×C43—41no—
139C2×C22⋊C4×C43C2×C414yes—
140C2×C42×C43—41no—
141C2×C42×C43—41no—
142C2×C42×C43—41no—
143#95×C43—22no—
144#95×C43—22no—
145#95×C43—41no—
146C24×C43—21no—
147C24×C43—21no—
148C24×C43—21no—
149C24×C43—21no—
150C24×C43—21no—
151C24×C43—21no—
152C24×C43—21no—
153C24×C43—21no—
154C24×C43—21no—
155C24×C43—21no—
156C24×C43—21no—
157C24×C43—21no—
158C24×C43C22×C412yes—
159C24×C43#4112yes—
160C24×C43#4112yes—
161C24×C43C2411yescharacteristic
162C23×D43—21no—
163C23×D43—21no—
164C23×D43—21no—
165C23×D43—21no—
166C23×D43—21no—
167C23×D43—21no—
168C23×D43—21no—
169C23×D43—21no—
170C23×D43—21no—
171C23×D43—21no—
172C23×D43—21no—
173C23×D43—21no—
174C23×D43—21no—
175C23×D43—21no—
176C23×D43C22×C412yes—
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×C43—21no—
211C22×C4×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43—21no—
215C22×C4×C43C22×C412yes—
216C22×C4×C43C22×C412yes—
217C22×C4×C43C2×D412yes—
218C22×C4×C43#4112yes—
219C2×C22⋊D43—28no—
220C2×C22⋊D43—44no—
221C2×C22⋊D43—44no—
222C2×C22⋊D43—44no—
223C2×C22⋊D43—44no—
224C2×C22⋊D43—44no—
225C2×C22⋊D43—44no—
226C22×Dic43—28no—
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×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—44no—
270C22×Dic43—44no—
271C22×Dic43—44no—
272C22×Dic43—44no—
273C22×Dic43—44no—
274C22×Dic43—44no—
275C22×Dic43C22×C412yes—
276C22×Dic43C22×C412yes—
277C22×Dic43C22×C412yes—
278C22×Dic43C2×D412yes—
279C22×Dic43C2×D412yes—
280C22×Dic43#4112yes—
281C22×Dic43#4112yes—
282C22⋊C4×C43—44no—
283C22⋊C4×C43—44no—
284C22⋊C4×C43—44no—
285C42×C43—44no—
286C22⋊Dic43—44no—
287C22⋊Dic43—44no—
288(C2×D43)⋊C4—28no—
289(C2×D43)⋊C4—44no—
290(C2×D43)⋊C4—44no—
291(C2×D43)⋊C4—44no—
292(C2×D43)⋊C4—44no—
293(C2×D43)⋊C4—44no—
294Dic43⋊C4—44no—
295Dic43⋊C4—44no—
296C4×Dic43—44no—
297C23×C43—22no—
298C23×C43—22no—
299C23×C43—22no—
300C23×C43—22no—
301C23×C43—22no—
302C23×C43—22no—
303C23×C43—22no—
304C23×C43—22no—
305C23×C43—22no—
306C23×C43—22no—
307C23×C43—22no—
308C23×C43—22no—
309C23×C43—22no—
310C23×C43—22no—
311C23×C43—22no—
312C23×C43—22no—
313C23×C43—22no—
314C23×C43—22no—
315C23×C43—41no—
316C23×C43—41no—
317C23×C43—41no—
318C23×C43—41no—
319C23×C43—41no—
320C23×C43—41no—
321C23×C43—41no—
322C23×C43—41no—
323C23×C43—41no—
324C23×C43—41no—
325C23×C43—41no—
326C23×C43—41no—
327C23×C43—41no—
328C23×C43—41no—
329C23×C43—41no—
330C23×C43—41no—
331C23×C43#11714yes—
332C23×C43C23×C411yescharacteristic
333C23×C43C22×D411yescharacteristic
334C23×C43C2×#4111yescharacteristic
335C23×C43C2×#4111yescharacteristic
336C23×C43C2×#4111yescharacteristic
337C23×C43C2×#4111yescharacteristic
338C23×C43C2×#4111yescharacteristic
339C23×C43H(5,𝔽2)11yescharacteristic
340C23×C43H(5,𝔽2)11yescharacteristic
341C23×C43H(5,𝔽2)11yescharacteristic
342C23×C43H(5,𝔽2)11yescharacteristic
343C23×C43H(5,𝔽2)11yescharacteristic
344C23×C43H(5,𝔽2)11yescharacteristic
345C23×C43H(5,𝔽2)11yescharacteristic
346C23×C432−1+411yescharacteristic
347C22×D43—22no—
348C22×D43—22no—
349C22×D43—22no—
350C22×D43—22no—
351C22×D43—22no—
352C22×D43—22no—
353C22×D43—22no—
354C22×D43—41no—
355C22×D43—41no—
356C22×D43—41no—
357C22×D43—41no—
358C22×D43—41no—
359C22×D43—41no—
360C22×D43—41no—
361C22×D43—41no—
362C22×D43—41no—
363C22×D43—41no—
364C22×D43—41no—
365C22×D43—41no—
366C22×D43—41no—
367C22×D43—41no—
368C22×D43—41no—
369C22×D43—41no—
370C22×D43—41no—
371C22×D43—41no—
372C22×D43—41no—
373C22×D43—41no—
374C22×D43—41no—
375C22×D43—41no—
376C22×D43—41no—
377C22×D43—41no—
378C22×D43—41no—
379C22×D43—41no—
380C22×D43—41no—
381C22×D43—41no—
382C2×C4×C43—22no—
383C2×C4×C43—22no—
384C2×C4×C43—22no—
385C2×C4×C43—22no—
386C2×C4×C43—22no—
387C2×C4×C43—22no—
388C2×C4×C43—22no—
389C2×C4×C43—22no—
390C2×C4×C43—22no—
391C2×C4×C43—22no—
392C2×C4×C43—22no—
393C2×C4×C43—22no—
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×C43—41no—
406C2×C4×C43—41no—
407C2×C4×C43—41no—
408C2×C4×C43—41no—
409C2×C4×C43—41no—
410C2×C4×C43—41no—
411C2×C4×C43—41no—
412C2×C4×C43—41no—
413C2×C4×C43—41no—
414C2×C4×C43—41no—
415C2×C4×C43—41no—
416C2×C4×C43—41no—
417C2×C4×C43—41no—
418C2×C4×C43—41no—
419C2×C4×C43—41no—
420C2×C4×C43—41no—
421C2×C4×C43—41no—
422C2×C4×C43—41no—
423C2×C4×C43—41no—
424C22⋊D43—416no—
425C2×Dic43—22no—
426C2×Dic43—22no—
427C2×Dic43—22no—
428C2×Dic43—22no—
429C2×Dic43—22no—
430C2×Dic43—22no—
431C2×Dic43—22no—
432C2×Dic43—22no—
433C2×Dic43—22no—
434C2×Dic43—22no—
435C2×Dic43—22no—
436C2×Dic43—22no—
437C2×Dic43—22no—
438C2×Dic43—22no—
439C2×Dic43—22no—
440C2×Dic43—22no—
441C2×Dic43—22no—
442C2×Dic43—22no—
443C2×Dic43—416no—
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×Dic43—41no—
455C2×Dic43—41no—
456C2×Dic43—41no—
457C2×Dic43—41no—
458C2×Dic43—41no—
459C2×Dic43—41no—
460C2×Dic43—41no—
461C2×Dic43—41no—
462C2×Dic43—41no—
463C2×Dic43—41no—
464C2×Dic43—41no—
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×Dic43C4×D414yes—
475#14415—431nomaximal, Sylow
476C22×C43—24no—
477C22×C43—24no—
478C22×C43—24no—
479C22×C43—42no—
480C22×C43—42no—
481C22×C43—42no—
482C22×C43—42no—
483C22×C43—42no—
484C22×C43—42no—
485C22×C43—42no—
486C22×C43—42no—
487C22×C43—42no—
488C22×C43—42no—
489C22×C43—42no—
490C22×C43—42no—
491C22×C43C2×#11711yescharacteristic
492C22×C43C2×C4×D411yescharacteristic
493C22×C43C4×#4111yescharacteristic
494C22×C43#51811yescharacteristic
495C22×C43#51811yescharacteristic
496C22×C43#51811yescharacteristic
497C22×C43#52011yescharacteristic
498C22×C43#53411yescharacteristic
499C22×C43#53511yescharacteristic
500C22×C43#53811yescharacteristic
501C22×C43#53811yescharacteristic
502C22×C43#53811yescharacteristic
503C22×C43#53811yescharacteristic
504C22×C43#53811yescharacteristic
505C22×C43#53811yescharacteristic
506C22×C43#53811yescharacteristic
507C22×C43#53911yescharacteristic
508C22×C43#54011yescharacteristic
509C22×C43#54211yescharacteristic
510C22×C43#54611yescharacteristic
511C22×C43#54611yescharacteristic
512C22×C43#54811yescharacteristic
513C22×C43#55011yescharacteristic
514C22×C43#55111yescharacteristic
515C22×C43#55111yescharacteristic
516C22×C43#55211yescharacteristic
517C22×C43#55311yescharacteristic
518C22×C43#55311yescharacteristic
519C22×C43#55311yescharacteristic
520C22×C43#55311yescharacteristic
521C22×C43#55511yescharacteristic
522C22×C43#56011yescharacteristic
523C22×C43#56011yescharacteristic
524C22×C43#56211yescharacteristic
525C22×C43#56211yescharacteristic
526C2×D43—42no—
527C2×D43—42no—
528C2×D43—42no—
529C2×D43—42no—
530C2×D43—42no—
531C2×D43—42no—
532C2×D43—42no—
533C2×D43—81no—
534C2×D43—81no—
535C2×D43—81no—
536C2×D43—81no—
537C2×D43—81no—
538C2×D43—81no—
539C2×D43—81no—
540C2×D43—81no—
541C4×C43—42no—
542C4×C43—42no—
543C4×C43—42no—
544C4×C43—42no—
545C4×C43—81no—
546C4×C43—81no—
547Dic43—24no—
548Dic43—42no—
549Dic43—42no—
550Dic43—42no—
551Dic43—42no—
552Dic43—81no—
553Dic43—81no—
554C2×#388—431no—
555C2×#386—431no—
556C2×#380—431no—
557#1443—431no—
558#1442—431no—
559#1440—431no—
560#1439—431no—
561#1438—431no—
562#1438—431no—
563#1437—431no—
564#1437—431no—
565#1437D4311yescharacteristic, complemented
566#1436—431no—
567#1434—431no—
568C22⋊#95—431no—
569C2×C43—44no—
570C2×C43#231211yescharacteristic
571C2×C43#232111yescharacteristic
572C2×C43#233511yescharacteristic
573C2×C43#235211yescharacteristic
574C2×C43#235311yescharacteristic
575C2×C43#236311yescharacteristic
576C2×C43#237711yescharacteristic
577C2×C43#268811yescharacteristic
578C2×C43#269611yescharacteristic
579C2×C43#271411yescharacteristic
580C2×C43#273011yescharacteristic
581C2×C43#275611yescharacteristic
582C2×C43#277811yescharacteristic
583C2×C43#277911yescharacteristic
584C2×C43#278111yescharacteristic
585D43—82no—
586C23×D4—431no—
587C24×C4—431no—
588C22×C4⋊C4—431no—
589C22×C4⋊C4—431no—
590C22×C22⋊C4—431no—
591C22×C22⋊C4—431no—
592C22×C22⋊C4—431no—
593C22×C22⋊C4—431no—
594C22×C22⋊C4—431no—
595C22×C22⋊C4—431no—
596C22×C22⋊C4—431no—
597C22×C22⋊C4—431no—
598C22×C22⋊C4C2×D4311yescharacteristic
599C22×C22⋊C4C2×D4311yescharacteristic
600C22×C22⋊C4C2×D4311yescharacteristic
601C22×C42—431no—
602C22×C42C2×D4311yescharacteristic
603#388—864no—
604#386—438no—
605#380—864no—
606C2×#95—431no—
607C2×#95—431no—
608C2×#95—431no—
609C2×#95—431no—
610C2×#95—431no—
611C2×#95—431no—
612C2×#95—431no—
613C2×#95—431no—
614C2×#95—431no—
615C2×#95—431no—
616C2×#95—431no—
617C2×#95—431no—
618C2×#95—431no—
619C2×#95—431no—
620C2×#95—431no—
621C2×#95C2×D4311yescharacteristic
622C2×#95C2×D4311yescharacteristic
623C2×#95C2×D4311yescharacteristic
624C43#1441511yescharacteristic, complemented, Sylow
625C25—431no—
626C25C22×D4311yescharacteristic
627C22×D4—434no—
628C22×D4—862no—
629C22×D4—862no—
630C22×D4—1721no—
631C22×D4—1721no—
632C22×D4—1721no—
633C22×D4—1721no—
634C23×C4—431no—
635C23×C4—431no—
636C23×C4—431no—
637C23×C4—431no—
638C23×C4—431no—
639C23×C4—434no—
640C23×C4—431no—
641C23×C4—431no—
642C23×C4—862no—
643C23×C4—862no—
644C23×C4—1721no—
645C23×C4—1721no—
646C23×C4—1721no—
647C23×C4—1721no—
648C23×C4C22×D4311yescharacteristic
649C23×C4C22×D4311yescharacteristic
650C23×C4C22×D4311yescharacteristic
651C23×C4C22×D4311yescharacteristic
652C23×C4C22×D4311yescharacteristic
653C23×C4C22×D4311yescharacteristic
654C2×C4⋊C4—434no—
655C2×C4⋊C4—862no—
656C2×C4⋊C4—1721no—
657C2×C4⋊C4—1721no—
658C2×C4⋊C4—1721no—
659C2×C4⋊C4—1721no—
660C2×C22⋊C4—22no—
661C2×C22⋊C4—22no—
662C2×C22⋊C4—22no—
663C2×C22⋊C4—22no—
664C2×C22⋊C4—41no—
665C2×C22⋊C4—41no—
666C2×C22⋊C4—41no—
667C2×C22⋊C4—41no—
668C2×C22⋊C4—434no—
669C2×C22⋊C4—434no—
670C2×C22⋊C4—862no—
671C2×C22⋊C4—862no—
672C2×C22⋊C4—862no—
673C2×C22⋊C4—862no—
674C2×C22⋊C4—862no—
675C2×C22⋊C4—862no—
676C2×C22⋊C4—862no—
677C2×C22⋊C4—862no—
678C2×C22⋊C4—862no—
679C2×C22⋊C4—862no—
680C2×C22⋊C4—1721no—
681C2×C22⋊C4—1721no—
682C2×C22⋊C4—1721no—
683C2×C22⋊C4—1721no—
684C2×C22⋊C4—1721no—
685C2×C22⋊C4—1721no—
686C2×C22⋊C4—1721no—
687C2×C22⋊C4—1721no—
688C2×C22⋊C4—1721no—
689C2×C22⋊C4—1721no—
690C2×C22⋊C4—1721no—
691C2×C22⋊C4—1721no—
692C2×C22⋊C4C4×D4314yes—
693C2×C42—41no—
694C2×C42—41no—
695C2×C42—41no—
696C2×C42—862no—
697C2×C42—862no—
698C2×C42—1721no—
699#95—22no—
700#95—22no—
701#95—41no—
702#95—434no—
703#95—434no—
704#95—862no—
705#95—862no—
706#95—862no—
707#95—862no—
708#95—1721no—
709#95—1721no—
710#95—1721no—
711#95—1721no—
712#95—1721no—
713#95—1721no—
714#95—1721no—
715#95—1721no—
716#95—1721no—
717C24—21no—
718C24—21no—
719C24—21no—
720C24—21no—
721C24—21no—
722C24—21no—
723C24—21no—
724C24—21no—
725C24—21no—
726C24—21no—
727C24—21no—
728C24—21no—
729C24—432no—
730C24—861no—
731C24—861no—
732C24—861no—
733C24—861no—
734C24—861no—
735C24—861no—
736C24—861no—
737C24—861no—
738C24—861no—
739C24—861no—
740C24—861no—
741C24—861no—
742C24—861no—
743C24—861no—
744C24C2×C4×D4312yes—
745C24#1062189812yes—
746C24#1062189812yes—
747C24C23×D4311yescharacteristic
748C2×D4—868no—
749C2×D4—1724no—
750C2×D4—1724no—
751C2×D4—1724no—
752C2×D4—1724no—
753C2×D4—1724no—
754C2×D4—1724no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—432no—
794C22×C4—432no—
795C22×C4—432no—
796C22×C4—432no—
797C22×C4—432no—
798C22×C4—432no—
799C22×C4—432no—
800C22×C4—868no—
801C22×C4—861no—
802C22×C4—861no—
803C22×C4—861no—
804C22×C4—861no—
805C22×C4—861no—
806C22×C4—861no—
807C22×C4—861no—
808C22×C4—861no—
809C22×C4—861no—
810C22×C4—861no—
811C22×C4—861no—
812C22×C4—861no—
813C22×C4—861no—
814C22×C4—861no—
815C22×C4—861no—
816C22×C4—861no—
817C22×C4—861no—
818C22×C4—861no—
819C22×C4—861no—
820C22×C4—861no—
821C22×C4—861no—
822C22×C4—861no—
823C22×C4—861no—
824C22×C4—861no—
825C22×C4—861no—
826C22×C4—861no—
827C22×C4—861no—
828C22×C4—861no—
829C22×C4—861no—
830C22×C4—861no—
831C22×C4—861no—
832C22×C4—861no—
833C22×C4—861no—
834C22×C4—861no—
835C22×C4—861no—
836C22×C4—861no—
837C22×C4—861no—
838C22×C4—861no—
839C22×C4—861no—
840C22×C4—861no—
841C22×C4—861no—
842C22×C4—861no—
843C22×C4—1724no—
844C22×C4—1724no—
845C22×C4—1724no—
846C22×C4—1724no—
847C22×C4—1724no—
848C22×C4—1724no—
849C22×C4C2×C4×D4312yes—
850C22×C4C2×C4×D4312yes—
851C22×C4D4×D4312yes—
852C22×C4#1062190012yes—
853C4⋊C4—1724no—
854C4⋊C4—1724no—
855C22⋊C4—44no—
856C22⋊C4—44no—
857C22⋊C4—44no—
858C22⋊C4—868no—
859C22⋊C4—1724no—
860C22⋊C4—1724no—
861C22⋊C4—1724no—
862C22⋊C4—1724no—
863C22⋊C4—1724no—
864C22⋊C4—1724no—
865C22⋊C4—1724no—
866C42—44no—
867C42—1724no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23—22no—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—41no—
887C23—41no—
888C23—41no—
889C23—41no—
890C23—41no—
891C23—41no—
892C23—41no—
893C23—41no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—862no—
903C23—862no—
904C23—862no—
905C23—862no—
906C23—862no—
907C23—862no—
908C23—862no—
909C23—1721no—
910C23—1721no—
911C23—1721no—
912C23—1721no—
913C23—1721no—
914C23—1721no—
915C23—1721no—
916C23—1721no—
917C23—1721no—
918C23—1721no—
919C23—1721no—
920C23—1721no—
921C23—1721no—
922C23—1721no—
923C23—1721no—
924C23—1721no—
925C23—1721no—
926C23—1721no—
927C23—1721no—
928C23—1721no—
929C23—1721no—
930C23—1721no—
931C23—1721no—
932C23—1721no—
933C23—1721no—
934C23—1721no—
935C23—1721no—
936C23—1721no—
937C23#1306328214yes—
938C23C22×C4×D4311yescharacteristic
939C23C2×D4×D4311yescharacteristic
940C23#41×D4311yescharacteristic
941C23#41×D4311yescharacteristic
942C23C2×#1062190011yescharacteristic
943C23C2×#1062189811yescharacteristic
944C23C2×#1062189811yescharacteristic
945C23#1306337011yescharacteristic
946C23#1306337011yescharacteristic
947C23#1306337011yescharacteristic
948C23#1306337011yescharacteristic
949C23#1306337111yescharacteristic
950C23#1306337111yescharacteristic
951C23#1306337111yescharacteristic
952C23#1306337211yescharacteristic
953D4—17216no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—434no—
997C2×C4—862no—
998C2×C4—862no—
999C2×C4—862no—
1000C2×C4—862no—
1001C2×C4—862no—
1002C2×C4—862no—
1003C2×C4—862no—
1004C2×C4—862no—
1005C2×C4—862no—
1006C2×C4—862no—
1007C2×C4—862no—
1008C2×C4—862no—
1009C2×C4—862no—
1010C2×C4—862no—
1011C2×C4—862no—
1012C2×C4—862no—
1013C2×C4—862no—
1014C2×C4—862no—
1015C2×C4—17216no—
1016C2×C4—1721no—
1017C2×C4—1721no—
1018C2×C4—1721no—
1019C2×C4—1721no—
1020C2×C4—1721no—
1021C2×C4—1721no—
1022C2×C4—1721no—
1023C2×C4—1721no—
1024C2×C4—1721no—
1025C2×C4—1721no—
1026C2×C4—1721no—
1027C2×C4—1721no—
1028C2×C4—1721no—
1029C2×C4—1721no—
1030C2×C4—1721no—
1031C2×C4—1721no—
1032C2×C4—1721no—
1033C2×C4—1721no—
1034C2×C4—1721no—
1035C2×C4—1721no—
1036C2×C4—1721no—
1037C2×C4—1721no—
1038C2×C4—1721no—
1039C2×C4—1721no—
1040C2×C4—1721no—
1041C2×C4—1721no—
1042C2×C4—1721no—
1043C2×C4—1721no—
1044C2×C4—1721no—
1045C2×C4—1721no—
1046C22—24no—
1047C22—24no—
1048C22—24no—
1049C22—42no—
1050C22—42no—
1051C22—42no—
1052C22—42no—
1053C22—42no—
1054C22—42no—
1055C22—42no—
1056C22—42no—
1057C22—42no—
1058C22—42no—
1059C22—42no—
1060C22—42no—
1061C22—3441no—
1062C22—3441no—
1063C22—3441no—
1064C22—3441no—
1065C22—3441no—
1066C22—3441no—
1067C22—3441no—
1068C22—3441no—
1069C22—1722no—
1070C22—1722no—
1071C22—1722no—
1072C22—1722no—
1073C22—1722no—
1074C22—1722no—
1075C22—1722no—
1076C22C2×#1306328211yescharacteristic
1077C22C4×D4×D4311yescharacteristic
1078C22C4×#1062190011yescharacteristic
1079C22#1458337111yescharacteristic
1080C22#1458337211yescharacteristic
1081C22#1458337311yescharacteristic
1082C22#1458337811yescharacteristic
1083C22#1458345711yescharacteristic
1084C22#1458346711yescharacteristic
1085C22#1458348211yescharacteristic
1086C22#1458348211yescharacteristic
1087C22#1458348211yescharacteristic
1088C22#1458348211yescharacteristic
1089C22#1458348511yescharacteristic
1090C22#1458348611yescharacteristic
1091C22#1458348811yescharacteristic
1092C22#1458349011yescharacteristic
1093C22#1458350111yescharacteristic
1094C22#1458351811yescharacteristic
1095C22#1458353811yescharacteristic
1096C22#1458353911yescharacteristic
1097C22#1458355811yescharacteristic
1098C22#1458356911yescharacteristic
1099C22#1458357311yescharacteristic
1100C22#1458357511yescharacteristic
1101C22#1458358211yescharacteristic
1102C22#1458359211yescharacteristic
1103C22#1458359511yescharacteristic
1104C22#1458359811yescharacteristic
1105C22#1458359811yescharacteristic
1106C22#1458361111yescharacteristic
1107C22#1458363711yescharacteristic
1108C22#1458363811yescharacteristic
1109C22#1458364411yescharacteristic
1110C22#1458364611yescharacteristic
1111C4—42no—
1112C4—42no—
1113C4—42no—
1114C4—42no—
1115C4—81no—
1116C4—81no—
1117C4—864no—
1118C4—3441no—
1119C4—3441no—
1120C4—1722no—
1121C4—1722no—
1122C4—1722no—
1123C4—1722no—
1124C2—44no—
1125C2—3442no—
1126C2#1913719011yescharacteristic
1127C2#1913724811yescharacteristic
1128C2#1913737811yescharacteristic
1129C2#1913751811yescharacteristic
1130C2#1913752911yescharacteristic
1131C2#1913763011yescharacteristic
1132C2#1913775311yescharacteristic
1133C2#1914102811yescharacteristic
1134C2#1914114211yescharacteristic
1135C2#1914138611yescharacteristic
1136C2#1914158711yescharacteristic
1137C2#1914191211yescharacteristic
1138C2#1914221411yescharacteristic
1139C2#1914222911yescharacteristic
1140C2#1914225311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1437C2
socle, cosocleC24×C43C24
prime radicalC23×C22⋊D43C22
hypercenter#1437D43
hypocenterC43#14415
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
1. C2×#14582788C2semidirect
3. C2×#14582757C2semidirect
4. #19132856C2semidirect
5. #19132850C2semidirect
6. #19132843C2semidirect
7. #19132839C2semidirect
10. #19132833C2semidirect
11. #19132832C2semidirect
12. #19132828C2semidirect
13. #19132820C2semidirect
14. #19132817C2semidirect
15. C43×#1437C2semidirect
30. #14582776C4semidirect
81. C2×Dic43⋊C4D4semidirect
565. #1437D43semidirect
624. C43#14415semidirect

Maximal subgroups

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

subgroupindex
C2×#145827882
C2×#145827762
C2×#145827572
#191328562
#191328502
#191328432
#191328392
#191328342
#191328332
#191328322
#191328282
#191328202
#191328172
C43×#14372
#1441543