Finite Group Databasebeta

← #25024632

Subgroups — #25024632

Order 11008.

1866 conjugacy classes of subgroups.

The subgroup lattice has 1158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582793C211yesmaximal, characteristic, complemented
2C2×#14582775C211yesmaximal, characteristic
3C2×#14582758C211yesmaximal, characteristic, complemented
4C2×#14582756C211yesmaximal, characteristic, complemented
5#19132854C211yesmaximal, characteristic, complemented
6#19132853C211yesmaximal, characteristic, complemented
7#19132840C211yesmaximal, characteristic, complemented
8#19132838C211yesmaximal, characteristic, complemented
9#19132834C211yesmaximal, characteristic
10#19132834C211yesmaximal, characteristic
11#19132833C211yesmaximal, characteristic, complemented
12#19132831C211yesmaximal, characteristic, complemented
13#19132829C211yesmaximal, characteristic, complemented
14#19132828C211yesmaximal, characteristic, complemented
15C2×C43×#388C211yesmaximal, characteristic, complemented
16C23×C22⋊D43C2211yescharacteristic
17C23×C4×D43C2211yescharacteristic
18C22×C4⋊Dic43C2211yescharacteristic
19C22×Dic43⋊C4C2211yescharacteristic
20C22×Dic43⋊C4C2211yescharacteristic
21C22×C22⋊Dic43C2211yescharacteristic
22C22×C22⋊Dic43C2211yescharacteristic
23C22×C22⋊Dic43C2211yescharacteristic
24C22×(C2×D43)⋊C4C2211yescharacteristic
25C22×(C2×D43)⋊C4C2211yescharacteristic
26C22×(C2×D43)⋊C4C2211yescharacteristic
27C22×(C2×D43)⋊C4C2211yescharacteristic
28C22×(C2×D43)⋊C4C2211yescharacteristic
29C22×C4×Dic43C2211yescharacteristic
30#14582793—24no—
31#14582775C418yescomplemented
32#14582758—24no—
33#14582756—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
48C22×C4⋊C4×C43C2211yescharacteristic
49C22×C22⋊C4×C43C2211yescharacteristic
50C22×C22⋊C4×C43C2211yescharacteristic
51C22×C22⋊C4×C43C2211yescharacteristic
52C22×C42×C43C2211yescharacteristic
53C43×#388—24no—
54C2×#95×C43C2211yescharacteristic
55C2×#95×C43C2211yescharacteristic
56C24×D43C2311yescharacteristic
57C22×C22⋊D43—22no—
58C22×C22⋊D43—22no—
59C22×C22⋊D43—41no—
60C22×C22⋊D43—41no—
61C22×C22⋊D43—41no—
62C22×C22⋊D43—41no—
63C22×C22⋊D43C2×C414yes—
64C23×Dic43C2311yescharacteristic
65C23×Dic43C2311yescharacteristic
66C23×Dic43C2311yescharacteristic
67C23×Dic43C2311yescharacteristic
68C23×Dic43C2311yescharacteristic
69C23×Dic43C2311yescharacteristic
70C23×Dic43C2311yescharacteristic
71C22×C4×D43—22no—
72C22×C4×D43—22no—
73C22×C4×D43—22no—
74C22×C4×D43—22no—
75C22×C4×D43—41no—
76C22×C4×D43—41no—
77C22×C4×D43C2×C414yes—
78C2×C4⋊Dic43—22no—
79C2×C4⋊Dic43—22no—
80C2×C4⋊Dic43—41no—
81C2×Dic43⋊C4—22no—
82C2×Dic43⋊C4—22no—
83C2×Dic43⋊C4—22no—
84C2×Dic43⋊C4—22no—
85C2×Dic43⋊C4—41no—
86C2×Dic43⋊C4—41no—
87C2×C22⋊Dic43—22no—
88C2×C22⋊Dic43—22no—
89C2×C22⋊Dic43—22no—
90C2×C22⋊Dic43—41no—
91C2×C22⋊Dic43—41no—
92C2×C22⋊Dic43—41no—
93C2×C22⋊Dic43—41no—
94C2×C22⋊Dic43—41no—
95C2×C22⋊Dic43C2×C414yes—
96C2×(C2×D43)⋊C4—22no—
97C2×(C2×D43)⋊C4—22no—
98C2×(C2×D43)⋊C4—22no—
99C2×(C2×D43)⋊C4—22no—
100C2×(C2×D43)⋊C4—22no—
101C2×(C2×D43)⋊C4—22no—
102C2×(C2×D43)⋊C4—22no—
103C2×(C2×D43)⋊C4—22no—
104C2×(C2×D43)⋊C4—41no—
105C2×(C2×D43)⋊C4—41no—
106C2×(C2×D43)⋊C4—41no—
107C2×(C2×D43)⋊C4—41no—
108C2×(C2×D43)⋊C4—41no—
109C2×(C2×D43)⋊C4—41no—
110C2×(C2×D43)⋊C4C2×C414yes—
111C2×C4×Dic43—22no—
112C2×C4×Dic43—41no—
113C2×C4×Dic43—41no—
114C43⋊#95—22no—
115C43⋊#95—22no—
116C43⋊#95—22no—
117C43⋊#95—41no—
118C43⋊#95—41no—
119C43⋊#95—41no—
120C43⋊#95—41no—
121C43⋊#95—41no—
122C43⋊#95—41no—
123C43⋊#95—41no—
124C43⋊#95—41no—
125C43⋊#95C2×C414yes—
126C43⋊#95C2×C414yes—
127C43⋊#95D414yescomplemented
128C25×C43C2311yescharacteristic
129C23×C4×C43C2311yescharacteristic
130C23×C4×C43C2311yescharacteristic
131C23×C4×C43C2311yescharacteristic
132C23×C4×C43C2311yescharacteristic
133C23×C4×C43C2311yescharacteristic
134C23×C4×C43C2311yescharacteristic
135C2×C4⋊C4×C43—22no—
136C2×C4⋊C4×C43—22no—
137C2×C4⋊C4×C43—41no—
138C2×C22⋊C4×C43—22no—
139C2×C22⋊C4×C43—22no—
140C2×C22⋊C4×C43—22no—
141C2×C22⋊C4×C43—22no—
142C2×C22⋊C4×C43—22no—
143C2×C22⋊C4×C43—41no—
144C2×C22⋊C4×C43—41no—
145C2×C22⋊C4×C43—41no—
146C2×C22⋊C4×C43C2×C414yes—
147C2×C42×C43—22no—
148C2×C42×C43—41no—
149C2×C42×C43—41no—
150#95×C43—22no—
151#95×C43D414yescomplemented
152C24×C43—21no—
153C24×C43—21no—
154C24×C43—21no—
155C24×C43—21no—
156C24×C43—21no—
157C24×C43—21no—
158C24×C43—21no—
159C24×C43—21no—
160C24×C43—21no—
161C24×C43—21no—
162C24×C43—21no—
163C24×C43—21no—
164C24×C43—21no—
165C24×C43—21no—
166C24×C43C22×C412yes—
167C24×C43C2411yescharacteristic
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×D43—21no—
177C23×D43—21no—
178C23×D43—21no—
179C23×D43—21no—
180C23×D43C22×C412yes—
181C23×D43#4112yes—
182C23×D43#4112yes—
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×C43—21no—
216C22×C4×C43—21no—
217C22×C4×C43—21no—
218C22×C4×C43C22×C412yes—
219C22×C4×C43C22×C412yes—
220C22×C4×C43C2×D412yes—
221C22×C4×C43C2×D412yes—
222C22×C4×C43C2×D412yes—
223C22×C4×C43C2×D412yes—
224C22×C4×C43#4112yes—
225C2×C22⋊D43—28no—
226C2×C22⋊D43—44no—
227C2×C22⋊D43—44no—
228C2×C22⋊D43—44no—
229C2×C22⋊D43—44no—
230C2×C22⋊D43—44no—
231C2×C22⋊D43—44no—
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—21no—
270C22×Dic43—21no—
271C22×Dic43—21no—
272C22×Dic43—21no—
273C22×Dic43—21no—
274C22×Dic43—21no—
275C22×Dic43C22×C412yes—
276C22×Dic43C22×C412yes—
277C22×Dic43C22×C412yes—
278C22×Dic43C2×D412yes—
279C22×Dic43C2×D412yes—
280C22×Dic43#4112yes—
281C2×C4×D43—28no—
282C2×C4×D43—28no—
283C2×C4×D43—44no—
284C2×C4×D43—44no—
285C2×C4×D43—44no—
286C2×C4×D43—44no—
287C2×C4×D43—44no—
288C4⋊C4×C43—44no—
289C22⋊C4×C43—28no—
290C22⋊C4×C43—44no—
291C22⋊C4×C43—44no—
292C42×C43—44no—
293C22⋊Dic43—28no—
294C22⋊Dic43—44no—
295C22⋊Dic43—44no—
296(C2×D43)⋊C4—44no—
297(C2×D43)⋊C4—44no—
298(C2×D43)⋊C4—44no—
299(C2×D43)⋊C4—44no—
300(C2×D43)⋊C4—44no—
301C4⋊Dic43—44no—
302Dic43⋊C4—44no—
303Dic43⋊C4—44no—
304C4×Dic43—44no—
305C23×C43—22no—
306C23×C43—22no—
307C23×C43—22no—
308C23×C43—22no—
309C23×C43—22no—
310C23×C43—22no—
311C23×C43—22no—
312C23×C43—41no—
313C23×C43—41no—
314C23×C43—41no—
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—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×C43C23×C411yescharacteristic
341C23×C43C22×D411yescharacteristic
342C23×C43C22×D411yescharacteristic
343C23×C43C2×#4111yescharacteristic
344C23×C43C2×#4111yescharacteristic
345C23×C43C2×#4111yescharacteristic
346C23×C43C2×#4111yescharacteristic
347C23×C43H(5,𝔽2)11yescharacteristic
348C23×C43H(5,𝔽2)11yescharacteristic
349C23×C43H(5,𝔽2)11yescharacteristic
350C23×C43H(5,𝔽2)11yescharacteristic
351C23×C43H(5,𝔽2)11yescharacteristic
352C23×C43H(5,𝔽2)11yescharacteristic
353C23×C432−1+411yescharacteristic
354C23×C432−1+411yescharacteristic
355C22×D43—22no—
356C22×D43—22no—
357C22×D43—22no—
358C22×D43—22no—
359C22×D43—22no—
360C22×D43—22no—
361C22×D43—22no—
362C22×D43—22no—
363C22×D43—22no—
364C22×D43—22no—
365C22×D43—22no—
366C22×D43—22no—
367C22×D43—22no—
368C22×D43—22no—
369C22×D43—22no—
370C22×D43—22no—
371C22×D43—22no—
372C22×D43—22no—
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—
382C22×D43—41no—
383C22×D43—41no—
384C22×D43—41no—
385C22×D43—41no—
386C22×D43—41no—
387C22×D43—41no—
388C22×D43—41no—
389C22×D43#11714yes—
390C2×C4×C43—22no—
391C2×C4×C43—22no—
392C2×C4×C43—22no—
393C2×C4×C43—22no—
394C2×C4×C43—22no—
395C2×C4×C43—22no—
396C2×C4×C43—22no—
397C2×C4×C43—22no—
398C2×C4×C43—22no—
399C2×C4×C43—22no—
400C2×C4×C43—22no—
401C2×C4×C43—22no—
402C2×C4×C43—22no—
403C2×C4×C43—22no—
404C2×C4×C43—22no—
405C2×C4×C43—22no—
406C2×C4×C43—22no—
407C2×C4×C43—22no—
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—
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×C43C4×D414yes—
432C22⋊D43—416no—
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—22no—
444C2×Dic43—22no—
445C2×Dic43—22no—
446C2×Dic43—22no—
447C2×Dic43—22no—
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×Dic43—41no—
475C2×Dic43—41no—
476C2×Dic43—41no—
477C2×Dic43—41no—
478C2×Dic43—41no—
479C2×Dic43—41no—
480C2×Dic43—41no—
481C2×Dic43C4×D414yes—
482C4×D43—416no—
483#14410—431nomaximal, Sylow
484C22×C43—42no—
485C22×C43—42no—
486C22×C43—42no—
487C22×C43—42no—
488C22×C43—42no—
489C22×C43—42no—
490C22×C43—42no—
491C22×C43—81no—
492C22×C43—81no—
493C22×C43—81no—
494C22×C43—81no—
495C22×C43—81no—
496C22×C43—81no—
497C22×C43—81no—
498C22×C43—81no—
499C22×C43C2×#11711yescharacteristic
500C22×C43C2×C4×D411yescharacteristic
501C22×C43C2×C4×D411yescharacteristic
502C22×C43#51811yescharacteristic
503C22×C43#51811yescharacteristic
504C22×C43#52011yescharacteristic
505C22×C43#52011yescharacteristic
506C22×C43#53511yescharacteristic
507C22×C43#53511yescharacteristic
508C22×C43#53711yescharacteristic
509C22×C43#53711yescharacteristic
510C22×C43#53811yescharacteristic
511C22×C43#53811yescharacteristic
512C22×C43#53811yescharacteristic
513C22×C43#53811yescharacteristic
514C22×C43#54011yescharacteristic
515C22×C43#54011yescharacteristic
516C22×C43#54211yescharacteristic
517C22×C43#54211yescharacteristic
518C22×C43D4211yescharacteristic
519C22×C43#54611yescharacteristic
520C22×C43#54611yescharacteristic
521C22×C43#54611yescharacteristic
522C22×C43#54611yescharacteristic
523C22×C43#54811yescharacteristic
524C22×C43#54811yescharacteristic
525C22×C43#55111yescharacteristic
526C22×C43#55211yescharacteristic
527C22×C43#55211yescharacteristic
528C22×C43#55311yescharacteristic
529C22×C43#55311yescharacteristic
530C22×C43#56011yescharacteristic
531C22×C43#56211yescharacteristic
532C22×C43#56211yescharacteristic
533C22×C43#56311yescharacteristic
534C2×D43—24no—
535C2×D43—24no—
536C2×D43—24no—
537C2×D43—42no—
538C2×D43—42no—
539C2×D43—42no—
540C2×D43—42no—
541C2×D43—42no—
542C2×D43—42no—
543C2×D43—42no—
544C2×D43—42no—
545C2×D43—42no—
546C2×D43—42no—
547C2×D43—42no—
548C2×D43—42no—
549C4×C43—24no—
550C4×C43—42no—
551C4×C43—42no—
552C4×C43—42no—
553C4×C43—42no—
554C4×C43—81no—
555Dic43—24no—
556Dic43—42no—
557Dic43—42no—
558Dic43—42no—
559Dic43—81no—
560Dic43—81no—
561Dic43—81no—
562C2×#388—431no—
563C2×#388D4311yescharacteristic, complemented
564C2×#386—431no—
565C2×#380—431no—
566C2×#380—431no—
567#1442—431no—
568#1442—431no—
569#1439—431no—
570#1439—431no—
571#1438—431no—
572#1438—431no—
573#1437—431no—
574#1437—431no—
575#1436—431no—
576#1436—431no—
577C2×C43—82no—
578C2×C43#231211yescharacteristic
579C2×C43#232411yescharacteristic
580C2×C43#232411yescharacteristic
581C2×C43#235211yescharacteristic
582C2×C43#235211yescharacteristic
583C2×C43#235811yescharacteristic
584C2×C43#237611yescharacteristic
585C2×C43#267611yescharacteristic
586C2×C43#267611yescharacteristic
587C2×C43#270211yescharacteristic
588C2×C43#270211yescharacteristic
589C2×C43#270311yescharacteristic
590C2×C43#270311yescharacteristic
591C2×C43#274111yescharacteristic
592C2×C43#274111yescharacteristic
593D43—44no—
594C23×D4—431no—
595C24×C4—431no—
596C22×C4⋊C4—431no—
597C22×C4⋊C4—431no—
598C22×C4⋊C4—431no—
599C22×C4⋊C4C2×D4311yescharacteristic
600C22×C22⋊C4—431no—
601C22×C22⋊C4—431no—
602C22×C22⋊C4—431no—
603C22×C22⋊C4—431no—
604C22×C22⋊C4—431no—
605C22×C22⋊C4—431no—
606C22×C22⋊C4—431no—
607C22×C22⋊C4—431no—
608C22×C22⋊C4C2×D4311yescharacteristic
609C22×C22⋊C4C2×D4311yescharacteristic
610C22×C22⋊C4C2×D4311yescharacteristic
611C22×C42—431no—
612C22×C42C2×D4311yescharacteristic
613#388—24no—
614#388—864no—
615#386—438no—
616#380—864no—
617#380—864no—
618C2×#95—431no—
619C2×#95—431no—
620C2×#95—431no—
621C2×#95—431no—
622C2×#95—431no—
623C2×#95—431no—
624C2×#95—431no—
625C2×#95—431no—
626C2×#95—431no—
627C2×#95—431no—
628C2×#95—431no—
629C2×#95—431no—
630C2×#95—431no—
631C2×#95—431no—
632C2×#95C2×D4311yescharacteristic
633C2×#95C2×D4311yescharacteristic
634C43#1441011yescharacteristic, complemented, Sylow
635C25—431no—
636C25C22×D4311yescharacteristic
637C22×D4—434no—
638C22×D4—862no—
639C22×D4—862no—
640C22×D4—1721no—
641C22×D4—1721no—
642C22×D4—1721no—
643C22×D4—1721no—
644C23×C4—431no—
645C23×C4—431no—
646C23×C4—431no—
647C23×C4—431no—
648C23×C4—434no—
649C23×C4—431no—
650C23×C4—431no—
651C23×C4—431no—
652C23×C4—862no—
653C23×C4—862no—
654C23×C4—862no—
655C23×C4—862no—
656C23×C4—1721no—
657C23×C4—1721no—
658C23×C4C22×D4311yescharacteristic
659C23×C4C22×D4311yescharacteristic
660C23×C4C22×D4311yescharacteristic
661C23×C4C22×D4311yescharacteristic
662C23×C4C22×D4311yescharacteristic
663C23×C4C22×D4311yescharacteristic
664C2×C4⋊C4—22no—
665C2×C4⋊C4—22no—
666C2×C4⋊C4—41no—
667C2×C4⋊C4—862no—
668C2×C4⋊C4—862no—
669C2×C4⋊C4—862no—
670C2×C4⋊C4—862no—
671C2×C4⋊C4—862no—
672C2×C4⋊C4—862no—
673C2×C4⋊C4—1721no—
674C2×C4⋊C4—1721no—
675C2×C4⋊C4—1721no—
676C2×C22⋊C4—22no—
677C2×C22⋊C4—22no—
678C2×C22⋊C4—22no—
679C2×C22⋊C4—22no—
680C2×C22⋊C4—22no—
681C2×C22⋊C4—41no—
682C2×C22⋊C4—41no—
683C2×C22⋊C4—41no—
684C2×C22⋊C4—434no—
685C2×C22⋊C4—434no—
686C2×C22⋊C4—862no—
687C2×C22⋊C4—862no—
688C2×C22⋊C4—862no—
689C2×C22⋊C4—862no—
690C2×C22⋊C4—862no—
691C2×C22⋊C4—862no—
692C2×C22⋊C4—862no—
693C2×C22⋊C4—862no—
694C2×C22⋊C4—862no—
695C2×C22⋊C4—862no—
696C2×C22⋊C4—862no—
697C2×C22⋊C4—1721no—
698C2×C22⋊C4—1721no—
699C2×C22⋊C4—1721no—
700C2×C22⋊C4—1721no—
701C2×C22⋊C4—1721no—
702C2×C22⋊C4—1721no—
703C2×C22⋊C4—1721no—
704C2×C22⋊C4—1721no—
705C2×C22⋊C4—1721no—
706C2×C22⋊C4—1721no—
707C2×C22⋊C4—1721no—
708C2×C22⋊C4C4×D4314yes—
709C2×C42—22no—
710C2×C42—41no—
711C2×C42—41no—
712C2×C42—862no—
713C2×C42—1721no—
714C2×C42—1721no—
715#95—22no—
716#95—434no—
717#95—434no—
718#95—434no—
719#95—862no—
720#95—862no—
721#95—862no—
722#95—1721no—
723#95—1721no—
724#95—1721no—
725#95—1721no—
726#95—1721no—
727#95—1721no—
728#95—1721no—
729#95—1721no—
730#95C22⋊D4314yescomplemented
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24—21no—
744C24—21no—
745C24—432no—
746C24—432no—
747C24—432no—
748C24—861no—
749C24—861no—
750C24—861no—
751C24—861no—
752C24—861no—
753C24—861no—
754C24—861no—
755C24—861no—
756C24—861no—
757C24—861no—
758C24—861no—
759C24—861no—
760C24C2×C4×D4312yes—
761C24C23×D4311yescharacteristic
762C2×D4—868no—
763C2×D4—1724no—
764C2×D4—1724no—
765C2×D4—1724no—
766C2×D4—1724no—
767C2×D4—1724no—
768C2×D4—1724no—
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—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—432no—
805C22×C4—432no—
806C22×C4—432no—
807C22×C4—432no—
808C22×C4—432no—
809C22×C4—432no—
810C22×C4—868no—
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—868no—
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—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—1724no—
856C22×C4—1724no—
857C22×C4—1724no—
858C22×C4—1724no—
859C22×C4—1724no—
860C22×C4C2×C4×D4312yes—
861C22×C4C2×C4×D4312yes—
862C22×C4#1062189812yes—
863C22×C4D4×D4312yes—
864C22×C4C2×C22⋊D4312yes—
865C22×C4C2×C22⋊D4312yes—
866C22×C4C2×C22⋊D4312yes—
867C4⋊C4—44no—
868C4⋊C4—1724no—
869C4⋊C4—1724no—
870C4⋊C4—1724no—
871C22⋊C4—28no—
872C22⋊C4—44no—
873C22⋊C4—44no—
874C22⋊C4—868no—
875C22⋊C4—1724no—
876C22⋊C4—1724no—
877C22⋊C4—1724no—
878C22⋊C4—1724no—
879C22⋊C4—1724no—
880C22⋊C4—1724no—
881C22⋊C4—1724no—
882C42—44no—
883C42—1724no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—41no—
892C23—41no—
893C23—41no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—434no—
920C23—862no—
921C23—862no—
922C23—862no—
923C23—862no—
924C23—862no—
925C23—862no—
926C23—862no—
927C23—862no—
928C23—862no—
929C23—862no—
930C23—862no—
931C23—862no—
932C23—862no—
933C23—862no—
934C23—862no—
935C23—862no—
936C23—862no—
937C23—862no—
938C23—1721no—
939C23—1721no—
940C23—1721no—
941C23—1721no—
942C23—1721no—
943C23—1721no—
944C23—1721no—
945C23—1721no—
946C23—1721no—
947C23—1721no—
948C23—1721no—
949C23—1721no—
950C23—1721no—
951C23—1721no—
952C23—1721no—
953C23—1721no—
954C23C22×C4×D4311yescharacteristic
955C23C2×D4×D4311yescharacteristic
956C23C22×C22⋊D4311yescharacteristic
957C23#41×D4311yescharacteristic
958C23#41×D4311yescharacteristic
959C23#41×D4311yescharacteristic
960C23C2×#1062189811yescharacteristic
961C23#1306337011yescharacteristic
962C23#1306337011yescharacteristic
963C23#1306337011yescharacteristic
964C23#1306337111yescharacteristic
965C23#1306337111yescharacteristic
966C23#1306337111yescharacteristic
967C23#1306337211yescharacteristic
968C23#1306337211yescharacteristic
969D4—17216no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
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—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—434no—
1012C2×C4—862no—
1013C2×C4—862no—
1014C2×C4—862no—
1015C2×C4—862no—
1016C2×C4—862no—
1017C2×C4—862no—
1018C2×C4—862no—
1019C2×C4—862no—
1020C2×C4—862no—
1021C2×C4—862no—
1022C2×C4—862no—
1023C2×C4—862no—
1024C2×C4—862no—
1025C2×C4—862no—
1026C2×C4—862no—
1027C2×C4—17216no—
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—
1046C2×C4—1721no—
1047C2×C4—1721no—
1048C2×C4—1721no—
1049C2×C4—1721no—
1050C2×C4—1721no—
1051C2×C4—1721no—
1052C2×C4—1721no—
1053C2×C4—1721no—
1054C2×C4—1721no—
1055C2×C4—1721no—
1056C2×C4—1721no—
1057C2×C4—1721no—
1058C2×C4—1721no—
1059C2×C4—1721no—
1060C2×C4—1721no—
1061C2×C4C4×C22⋊D4314yes—
1062C22—42no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—81no—
1070C22—81no—
1071C22—81no—
1072C22—81no—
1073C22—81no—
1074C22—81no—
1075C22—81no—
1076C22—81no—
1077C22—864no—
1078C22—864no—
1079C22—864no—
1080C22—1722no—
1081C22—1722no—
1082C22—1722no—
1083C22—1722no—
1084C22—1722no—
1085C22—1722no—
1086C22—1722no—
1087C22—1722no—
1088C22—1722no—
1089C22—1722no—
1090C22—1722no—
1091C22—1722no—
1092C22#117×D4311yescharacteristic
1093C22C4×D4×D4311yescharacteristic
1094C22C2×C4×C22⋊D4311yescharacteristic
1095C22#1458337111yescharacteristic
1096C22#1458337111yescharacteristic
1097C22#1458337811yescharacteristic
1098C22#1458337911yescharacteristic
1099C22#1458346611yescharacteristic
1100C22#1458346711yescharacteristic
1101C22#1458347611yescharacteristic
1102C22#1458347711yescharacteristic
1103C22#1458348111yescharacteristic
1104C22#1458348311yescharacteristic
1105C22#1458348511yescharacteristic
1106C22#1458348811yescharacteristic
1107C22#1458350011yescharacteristic
1108C22#1458350111yescharacteristic
1109C22#1458351411yescharacteristic
1110C22#1458351511yescharacteristic
1111C22D4×C22⋊D4311yescharacteristic
1112C22#1458353711yescharacteristic
1113C22#1458353711yescharacteristic
1114C22#1458353811yescharacteristic
1115C22#1458354511yescharacteristic
1116C22#1458355611yescharacteristic
1117C22#1458355711yescharacteristic
1118C22#1458357811yescharacteristic
1119C22#1458358511yescharacteristic
1120C22#1458358811yescharacteristic
1121C22#1458359311yescharacteristic
1122C22#1458359411yescharacteristic
1123C22#1458363911yescharacteristic
1124C22#1458364311yescharacteristic
1125C22#1458364411yescharacteristic
1126C22#1458365111yescharacteristic
1127C4—24no—
1128C4—42no—
1129C4—42no—
1130C4—42no—
1131C4—42no—
1132C4—81no—
1133C4—864no—
1134C4—3441no—
1135C4—3441no—
1136C4—3441no—
1137C4—1722no—
1138C4—1722no—
1139C4—1722no—
1140C2—82no—
1141C2—1724no—
1142C2#1913718911yescharacteristic
1143C2#1913728211yescharacteristic
1144C2#1913728311yescharacteristic
1145C2#1913752311yescharacteristic
1146C2#1913752511yescharacteristic
1147C2#1913757211yescharacteristic
1148C2#1913773711yescharacteristic
1149C2#1914089011yescharacteristic
1150C2#1914089111yescharacteristic
1151C2#1914121711yescharacteristic
1152C2#1914121811yescharacteristic
1153C2#1914123211yescharacteristic
1154C2#1914123311yescharacteristic
1155C2#1914170811yescharacteristic
1156C2#1914171311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C43×#388C2
socle, cosocleC24×C43C24
prime radicalC23×C22⋊D43C22
hypercenterC2×#388D43
hypocenterC43#14410
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C2×#14582793C2semidirect
3. C2×#14582758C2semidirect
4. C2×#14582756C2semidirect
5. #19132854C2semidirect
6. #19132853C2semidirect
7. #19132840C2semidirect
8. #19132838C2semidirect
11. #19132833C2semidirect
12. #19132831C2semidirect
13. #19132829C2semidirect
14. #19132828C2semidirect
15. C2×C43×#388C2semidirect
31. #14582775C4semidirect
127. C43⋊#95D4semidirect
151. #95×C43D4semidirect
563. C2×#388D43semidirect
634. C43#14410semidirect
730. #95C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145827932
C2×#145827752
C2×#145827582
C2×#145827562
#191328542
#191328532
#191328402
#191328382
#191328342
#191328332
#191328312
#191328292
#191328282
C2×C43×#3882
#1441043