Finite Group Databasebeta

← #25023972

Subgroups — #25023972

Order 11008.

1866 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063301C211yesmaximal, characteristic
2C2×#14582790C211yesmaximal, characteristic
3C2×#14582789C211yesmaximal, characteristic
4C2×#14582761C211yesmaximal, characteristic
5#19132866C211yesmaximal, characteristic, complemented
6#19132861C211yesmaximal, characteristic, complemented
7#19132847C211yesmaximal, characteristic, complemented
8#19132845C211yesmaximal, characteristic, complemented
9#19132843C211yesmaximal, characteristic
10#19132843C211yesmaximal, characteristic
11#19132829C211yesmaximal, characteristic, complemented
12#19132828C211yesmaximal, characteristic, complemented
13Dic43⋊#95C211yesmaximal, characteristic, complemented
14(C2×D43)⋊#95C211yesmaximal, characteristic
15C2×C43×#391C211yesmaximal, characteristic, complemented
16C23×C4×D43C2211yescharacteristic
17C2×#13063301—24no—
18C2×#13063301—24no—
19C2×#13063301C418yescomplemented
20C22×C4⋊Dic43C2211yescharacteristic
21C22×Dic43⋊C4C2211yescharacteristic
22C22×Dic43⋊C4C2211yescharacteristic
23C22×Dic43⋊C4C2211yescharacteristic
24C22×(C2×D43)⋊C4C2211yescharacteristic
25C22×(C2×D43)⋊C4C2211yescharacteristic
26C22×(C2×D43)⋊C4C2211yescharacteristic
27C22×(C2×D43)⋊C4C2211yescharacteristic
28C22×(C2×D43)⋊C4C2211yescharacteristic
29C22×(C2×D43)⋊C4C2211yescharacteristic
30C22×C4×Dic43C2211yescharacteristic
31#14582790—24no—
32#14582789—24no—
33#14582761—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
50C23×Q8×C43C2211yescharacteristic
51C22×C4⋊C4×C43C2211yescharacteristic
52C22×C42×C43C2211yescharacteristic
53C43×#391—24no—
54C2×#95×C43C2211yescharacteristic
55C2×#95×C43C2211yescharacteristic
56C2×#95×C43C2211yescharacteristic
57C2×#95×C43C2211yescharacteristic
58C24×D43C2311yescharacteristic
59C23×Dic43C2311yescharacteristic
60C23×Dic43C2311yescharacteristic
61C23×Dic43C2311yescharacteristic
62C23×Dic43C2311yescharacteristic
63C23×Dic43C2311yescharacteristic
64C23×Dic43C2311yescharacteristic
65C23×Dic43C2311yescharacteristic
66C22×C4×D43—22no—
67C22×C4×D43—22no—
68C22×C4×D43—22no—
69C22×C4×D43—22no—
70C22×C4×D43—41no—
71C22×C4×D43—41no—
72C22×C4×D43C2×C414yes—
73#13063301—232no—
74C2×C4⋊Dic43—22no—
75C2×C4⋊Dic43—22no—
76C2×C4⋊Dic43C2×C414yes—
77C2×Dic43⋊C4—22no—
78C2×Dic43⋊C4—22no—
79C2×Dic43⋊C4—22no—
80C2×Dic43⋊C4—22no—
81C2×Dic43⋊C4—22no—
82C2×Dic43⋊C4—22no—
83C2×Dic43⋊C4—41no—
84C2×Dic43⋊C4C2×C414yes—
85C2×Dic43⋊C4C2×C414yes—
86C2×(C2×D43)⋊C4—22no—
87C2×(C2×D43)⋊C4—22no—
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—22no—
95C2×(C2×D43)⋊C4—22no—
96C2×(C2×D43)⋊C4—41no—
97C2×(C2×D43)⋊C4—41no—
98C2×(C2×D43)⋊C4—41no—
99C2×(C2×D43)⋊C4—41no—
100C2×(C2×D43)⋊C4C2×C414yes—
101C2×(C2×D43)⋊C4C2×C414yes—
102C2×(C2×D43)⋊C4D414yes—
103C2×(C2×D43)⋊C4D414yes—
104C2×C4×Dic43—22no—
105C2×C4×Dic43—22no—
106C2×C4×Dic43—41no—
107C43⋊#95—22no—
108C43⋊#95—22no—
109C43⋊#95—22no—
110C43⋊#95—22no—
111C43⋊#95—22no—
112C43⋊#95—22no—
113C43⋊#95—22no—
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—
123C22×Q8×C43—22no—
124C22×Q8×C43—22no—
125C22×Q8×C43—22no—
126C22×Q8×C43—22no—
127C22×Q8×C43—41no—
128C22×Q8×C43—41no—
129C22×Q8×C43C2×C414yes—
130C23×C4×C43C2311yescharacteristic
131C23×C4×C43C2311yescharacteristic
132C23×C4×C43C2311yescharacteristic
133C23×C4×C43C2311yescharacteristic
134C23×C4×C43C2311yescharacteristic
135C23×C4×C43C2311yescharacteristic
136C23×C4×C43C2311yescharacteristic
137C2×C4⋊C4×C43—22no—
138C2×C4⋊C4×C43—22no—
139C2×C4⋊C4×C43—41no—
140C2×C42×C43—22no—
141C2×C42×C43—22no—
142C2×C42×C43—41no—
143#95×C43—22no—
144#95×C43—22no—
145#95×C43—22no—
146#95×C43D414yes—
147C24×C43C2411yescharacteristic
148C23×D43—21no—
149C23×D43—21no—
150C23×D43—21no—
151C23×D43—21no—
152C23×D43—21no—
153C23×D43—21no—
154C23×D43—21no—
155C23×D43—21no—
156C23×D43—21no—
157C23×D43—21no—
158C23×D43—21no—
159C23×D43—21no—
160C23×D43C22×C412yes—
161C23×D43C2×D412yes—
162C23×D43C2×D412yes—
163C2×Q8×C43—28no—
164C2×Q8×C43—28no—
165C2×Q8×C43—44no—
166C2×Q8×C43—44no—
167C2×Q8×C43—44no—
168C2×Q8×C43—44no—
169C2×Q8×C43—44no—
170C22×C4×C43—21no—
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×C43C22×C412yes—
210C22×C4×C43C22×C412yes—
211C22×C4×C43C22×C412yes—
212C22×C4×C43C2×D412yes—
213C22×C4×C43C2×D412yes—
214C22×C4×C43C2×D412yes—
215C22×C4×C43C2×D412yes—
216C22×C4×C43C2×D412yes—
217C22×C4×C43#4112yes—
218C22×C4×C43#4112yes—
219C22×Dic43—21no—
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×Dic43—21no—
260C22×Dic43—21no—
261C22×Dic43—21no—
262C22×Dic43C22×C412yes—
263C22×Dic43C22×C412yes—
264C22×Dic43C22×C412yes—
265C22×Dic43C2×D412yes—
266C22×Dic43C2×D412yes—
267C22×Dic43#4112yes—
268C2×C4×D43—28no—
269C2×C4×D43—28no—
270C2×C4×D43—44no—
271C2×C4×D43—44no—
272C2×C4×D43—44no—
273C2×C4×D43—44no—
274C2×C4×D43—44no—
275C4⋊C4×C43—44no—
276C42×C43—44no—
277(C2×D43)⋊C4—28no—
278(C2×D43)⋊C4—44no—
279(C2×D43)⋊C4—44no—
280(C2×D43)⋊C4—44no—
281(C2×D43)⋊C4—44no—
282(C2×D43)⋊C4C22⋊C4116yes—
283C4⋊Dic43—28no—
284Dic43⋊C4—28no—
285Dic43⋊C4—28no—
286Dic43⋊C4—44no—
287C4×Dic43—44no—
288C23×C43C23×C411yescharacteristic
289C23×C43C22×D411yescharacteristic
290C23×C43C22×D411yescharacteristic
291C23×C43C22×D411yescharacteristic
292C23×C43C2×#4111yescharacteristic
293C23×C43C2×#4111yescharacteristic
294C23×C43C2×#4111yescharacteristic
295C23×C43H(5,𝔽2)11yescharacteristic
296C23×C43H(5,𝔽2)11yescharacteristic
297C23×C43H(5,𝔽2)11yescharacteristic
298C23×C432−1+411yescharacteristic
299C23×C432−1+411yescharacteristic
300C23×C432−1+411yescharacteristic
301C23×C432−1+411yescharacteristic
302C23×C432−1+411yescharacteristic
303C22×D43—22no—
304C22×D43—22no—
305C22×D43—22no—
306C22×D43—22no—
307C22×D43—22no—
308C22×D43—22no—
309C22×D43—22no—
310C22×D43—22no—
311C22×D43—22no—
312C22×D43—22no—
313C22×D43—22no—
314C22×D43—22no—
315C22×D43—22no—
316C22×D43—22no—
317C22×D43—22no—
318C22×D43—22no—
319C22×D43—22no—
320C22×D43—22no—
321C22×D43—41no—
322C22×D43—41no—
323C22×D43—41no—
324C22×D43—41no—
325C22×D43—41no—
326C22×D43—41no—
327C22×D43—41no—
328C22×D43—41no—
329C22×D43—41no—
330C22×D43—41no—
331C22×D43—41no—
332C22×D43—41no—
333C22×D43—41no—
334C22×D43—41no—
335C22×D43—41no—
336C22×D43—41no—
337C22×D43C2×C22⋊C414yes—
338Q8×C43—416no—
339C2×C4×C43—22no—
340C2×C4×C43—22no—
341C2×C4×C43—22no—
342C2×C4×C43—22no—
343C2×C4×C43—22no—
344C2×C4×C43—22no—
345C2×C4×C43—22no—
346C2×C4×C43—22no—
347C2×C4×C43—22no—
348C2×C4×C43—22no—
349C2×C4×C43—22no—
350C2×C4×C43—22no—
351C2×C4×C43—22no—
352C2×C4×C43—22no—
353C2×C4×C43—22no—
354C2×C4×C43—22no—
355C2×C4×C43—22no—
356C2×C4×C43—22no—
357C2×C4×C43—22no—
358C2×C4×C43—22no—
359C2×C4×C43—22no—
360C2×C4×C43—22no—
361C2×C4×C43—22no—
362C2×C4×C43—22no—
363C2×C4×C43—41no—
364C2×C4×C43—41no—
365C2×C4×C43—41no—
366C2×C4×C43—41no—
367C2×C4×C43—41no—
368C2×C4×C43—41no—
369C2×C4×C43—41no—
370C2×C4×C43—41no—
371C2×C4×C43—41no—
372C2×C4×C43—41no—
373C2×C4×C43—41no—
374C2×C4×C43—41no—
375C2×C4×C43—41no—
376C2×C4×C43—41no—
377C2×C4×C43—41no—
378C2×C4×C43—41no—
379C2×C4×C43—41no—
380C2×C4×C43—41no—
381C2×C4×C43—41no—
382C2×C4×C43—41no—
383C2×C4×C43—41no—
384C2×C4×C43—41no—
385C2×C4×C43—41no—
386C2×C4×C43C2×C22⋊C414yes—
387C2×C4×C43C4×D414yes—
388C2×Dic43—22no—
389C2×Dic43—22no—
390C2×Dic43—22no—
391C2×Dic43—22no—
392C2×Dic43—22no—
393C2×Dic43—22no—
394C2×Dic43—22no—
395C2×Dic43—22no—
396C2×Dic43—22no—
397C2×Dic43—22no—
398C2×Dic43—22no—
399C2×Dic43—22no—
400C2×Dic43—22no—
401C2×Dic43—22no—
402C2×Dic43—22no—
403C2×Dic43—41no—
404C2×Dic43—41no—
405C2×Dic43—41no—
406C2×Dic43—41no—
407C2×Dic43—41no—
408C2×Dic43—41no—
409C2×Dic43—41no—
410C2×Dic43—41no—
411C2×Dic43—41no—
412C2×Dic43—41no—
413C2×Dic43—41no—
414C2×Dic43—41no—
415C2×Dic43—41no—
416C2×Dic43—41no—
417C2×Dic43—41no—
418C2×Dic43—41no—
419C2×Dic43—41no—
420C2×Dic43—41no—
421C2×Dic43—41no—
422C2×Dic43—41no—
423C2×Dic43—41no—
424C2×Dic43—41no—
425C2×Dic43—41no—
426C2×Dic43—41no—
427C2×Dic43—41no—
428C2×Dic43—41no—
429C2×Dic43—41no—
430C2×Dic43—41no—
431C2×Dic43—41no—
432C2×Dic43—41no—
433C2×Dic43—41no—
434C2×Dic43—41no—
435C2×Dic43—41no—
436C2×Dic43C2×C22⋊C414yes—
437C4×D43—416no—
438#14364—431nomaximal, Sylow
439C22×C43C22×C22⋊C411yescharacteristic
440C22×C43C2×C4×D411yescharacteristic
441C22×C43C4×#4111yescharacteristic
442C22×C43#51811yescharacteristic
443C22×C43#51911yescharacteristic
444C22×C43#51911yescharacteristic
445C22×C43#52011yescharacteristic
446C22×C43#53611yescharacteristic
447C22×C43#53611yescharacteristic
448C22×C43#53611yescharacteristic
449C22×C43#53611yescharacteristic
450C22×C43#53611yescharacteristic
451C22×C43#53711yescharacteristic
452C22×C43#53911yescharacteristic
453C22×C43#53911yescharacteristic
454C22×C43#54111yescharacteristic
455C22×C43#54211yescharacteristic
456C22×C43#54211yescharacteristic
457C22×C43#54211yescharacteristic
458C22×C43D4211yescharacteristic
459C22×C43D4211yescharacteristic
460C22×C43#54611yescharacteristic
461C22×C43#54611yescharacteristic
462C22×C43#54611yescharacteristic
463C22×C43#54611yescharacteristic
464C22×C43#54711yescharacteristic
465C22×C43#54711yescharacteristic
466C22×C43#54711yescharacteristic
467C22×C43#54811yescharacteristic
468C22×C43#55211yescharacteristic
469C22×C43#55611yescharacteristic
470C22×C43#56211yescharacteristic
471C22×C43#56211yescharacteristic
472C22×C43#56311yescharacteristic
473C22×C43#56311yescharacteristic
474C2×D43—24no—
475C2×D43—24no—
476C2×D43—24no—
477C2×D43—42no—
478C2×D43—42no—
479C2×D43—42no—
480C2×D43—42no—
481C2×D43—42no—
482C2×D43—42no—
483C2×D43—42no—
484C2×D43—42no—
485C2×D43—42no—
486C2×D43—42no—
487C2×D43—42no—
488C2×D43—42no—
489C4×C43—24no—
490C4×C43—24no—
491C4×C43—42no—
492C4×C43—42no—
493C4×C43—42no—
494C4×C43—42no—
495C4×C43—81no—
496Dic43—24no—
497Dic43—42no—
498Dic43—42no—
499Dic43—42no—
500Dic43—81no—
501Dic43—81no—
502Dic43—81no—
503C22×C22⋊Q8—431no—
504C2×#391D4311yescharacteristic, complemented
505C2×#388—431no—
506C2×#388—431no—
507C2×#381—431no—
508#1446—431no—
509#1445—431no—
510#1441—431no—
511#1441—431no—
512#1440—431no—
513#1440—431no—
514#1436—431no—
515#1436—431no—
516C4⋊#95—431no—
517C22⋊#95—431no—
518C2×C43#231011yescharacteristic
519C2×C43#232311yescharacteristic
520C2×C43#233211yescharacteristic
521C2×C43D4×C22⋊C411yescharacteristic
522C2×C43#233911yescharacteristic
523C2×C43#236211yescharacteristic
524C2×C43#237811yescharacteristic
525C2×C43#267211yescharacteristic
526C2×C43#267411yescharacteristic
527C2×C43#268011yescharacteristic
528C2×C43#268111yescharacteristic
529C2×C43#268711yescharacteristic
530C2×C43#268911yescharacteristic
531C2×C43#269811yescharacteristic
532C2×C43#270011yescharacteristic
533D43—44no—
534C23×Q8C2×D4311yescharacteristic
535C24×C4—431no—
536C2×C22⋊Q8—438no—
537C2×C22⋊Q8—864no—
538C2×C22⋊Q8—864no—
539C22×C4⋊C4—431no—
540C22×C4⋊C4—431no—
541C22×C4⋊C4—431no—
542C22×C4⋊C4—431no—
543C22×C4⋊C4C2×D4311yescharacteristic
544C22×C22⋊C4—431no—
545C22×C22⋊C4—431no—
546C22×C22⋊C4—431no—
547C22×C22⋊C4—431no—
548C22×C22⋊C4—431no—
549C22×C22⋊C4—431no—
550C22×C42—431no—
551C22×C42C2×D4311yescharacteristic
552#391—24no—
553#388—864no—
554#388—864no—
555#381—864no—
556C2×#95—431no—
557C2×#95—431no—
558C2×#95—431no—
559C2×#95—431no—
560C2×#95—431no—
561C2×#95—431no—
562C2×#95—431no—
563C2×#95—431no—
564C2×#95—431no—
565C2×#95—431no—
566C2×#95—431no—
567C2×#95—431no—
568C2×#95—431no—
569C2×#95—431no—
570C2×#95—431no—
571C2×#95—431no—
572C2×#95C2×D4311yescharacteristic
573C2×#95C2×D4311yescharacteristic
574C2×#95C2×D4311yescharacteristic
575C2×#95C2×D4311yescharacteristic
576C43#1436411yescharacteristic, complemented, Sylow
577C25—431no—
578C22×Q8—22no—
579C22×Q8—22no—
580C22×Q8—22no—
581C22×Q8—22no—
582C22×Q8—41no—
583C22×Q8—41no—
584C22×Q8C4×D4314yes—
585C23×C4—431no—
586C23×C4—431no—
587C23×C4—431no—
588C23×C4—431no—
589C23×C4—434no—
590C23×C4—431no—
591C23×C4—431no—
592C23×C4—431no—
593C23×C4—862no—
594C23×C4—862no—
595C23×C4—862no—
596C23×C4—862no—
597C23×C4—1721no—
598C23×C4—1721no—
599C23×C4C22×D4311yescharacteristic
600C23×C4C22×D4311yescharacteristic
601C23×C4C22×D4311yescharacteristic
602C23×C4C22×D4311yescharacteristic
603C23×C4C22×D4311yescharacteristic
604C23×C4C22×D4311yescharacteristic
605C23×C4C22×D4311yescharacteristic
606C22⋊Q8—8632no—
607C2×C4⋊C4—22no—
608C2×C4⋊C4—22no—
609C2×C4⋊C4—41no—
610C2×C4⋊C4—434no—
611C2×C4⋊C4—434no—
612C2×C4⋊C4—434no—
613C2×C4⋊C4—862no—
614C2×C4⋊C4—862no—
615C2×C4⋊C4—862no—
616C2×C4⋊C4—862no—
617C2×C4⋊C4—862no—
618C2×C4⋊C4—862no—
619C2×C4⋊C4—862no—
620C2×C4⋊C4—862no—
621C2×C4⋊C4—1721no—
622C2×C22⋊C4—434no—
623C2×C22⋊C4—434no—
624C2×C22⋊C4—434no—
625C2×C22⋊C4—434no—
626C2×C22⋊C4—862no—
627C2×C22⋊C4—862no—
628C2×C22⋊C4—862no—
629C2×C22⋊C4—862no—
630C2×C22⋊C4—862no—
631C2×C22⋊C4—862no—
632C2×C22⋊C4—862no—
633C2×C22⋊C4—862no—
634C2×C22⋊C4—862no—
635C2×C22⋊C4—862no—
636C2×C22⋊C4—1721no—
637C2×C22⋊C4—1721no—
638C2×C22⋊C4—1721no—
639C2×C22⋊C4—1721no—
640C2×C42—22no—
641C2×C42—22no—
642C2×C42—41no—
643C2×C42—862no—
644C2×C42—862no—
645C2×C42—1721no—
646#95—22no—
647#95—22no—
648#95—22no—
649#95—862no—
650#95—862no—
651#95—862no—
652#95—862no—
653#95—862no—
654#95—862no—
655#95—862no—
656#95—862no—
657#95—862no—
658#95—862no—
659#95—1721no—
660#95—1721no—
661#95—1721no—
662#95—1721no—
663#95—1721no—
664#95—1721no—
665#95C22⋊D4314yes—
666C24—432no—
667C24—432no—
668C24—432no—
669C24—861no—
670C24—861no—
671C24—861no—
672C24—861no—
673C24—861no—
674C24—861no—
675C24—861no—
676C24—861no—
677C24—861no—
678C24—861no—
679C24—861no—
680C24—861no—
681C24C23×D4311yescharacteristic
682C2×Q8—28no—
683C2×Q8—28no—
684C2×Q8—44no—
685C2×Q8—44no—
686C2×Q8—44no—
687C2×Q8—44no—
688C2×Q8—44no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
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—432no—
729C22×C4—432no—
730C22×C4—432no—
731C22×C4—432no—
732C22×C4—432no—
733C22×C4—432no—
734C22×C4—868no—
735C22×C4—861no—
736C22×C4—861no—
737C22×C4—861no—
738C22×C4—861no—
739C22×C4—861no—
740C22×C4—861no—
741C22×C4—861no—
742C22×C4—861no—
743C22×C4—861no—
744C22×C4—861no—
745C22×C4—861no—
746C22×C4—861no—
747C22×C4—861no—
748C22×C4—861no—
749C22×C4—861no—
750C22×C4—861no—
751C22×C4—861no—
752C22×C4—861no—
753C22×C4—861no—
754C22×C4—861no—
755C22×C4—861no—
756C22×C4—861no—
757C22×C4—868no—
758C22×C4—861no—
759C22×C4—861no—
760C22×C4—861no—
761C22×C4—861no—
762C22×C4—861no—
763C22×C4—861no—
764C22×C4—861no—
765C22×C4—861no—
766C22×C4—861no—
767C22×C4—861no—
768C22×C4—861no—
769C22×C4—861no—
770C22×C4—861no—
771C22×C4—861no—
772C22×C4—861no—
773C22×C4—861no—
774C22×C4—861no—
775C22×C4—861no—
776C22×C4—861no—
777C22×C4—861no—
778C22×C4—861no—
779C22×C4—1724no—
780C22×C4—1724no—
781C22×C4—1724no—
782C22×C4—1724no—
783C22×C4—1724no—
784C22×C4C2×C4×D4312yes—
785C22×C4C2×C4×D4312yes—
786C22×C4C2×C4×D4312yes—
787C22×C4#1062189812yes—
788C22×C4D4×D4312yes—
789C22×C4D4×D4312yes—
790C22×C4#1062190212yes—
791C22×C4C2×C22⋊D4312yes—
792C22×C4C2×C22⋊D4312yes—
793C22×C4C2×C22⋊D4312yes—
794C4⋊C4—44no—
795C4⋊C4—868no—
796C4⋊C4—868no—
797C4⋊C4—868no—
798C4⋊C4—1724no—
799C22⋊C4—4316no—
800C22⋊C4—868no—
801C22⋊C4—1724no—
802C22⋊C4—1724no—
803C22⋊C4—1724no—
804C22⋊C4—1724no—
805C42—44no—
806C42—1724no—
807C23—434no—
808C23—862no—
809C23—862no—
810C23—862no—
811C23—862no—
812C23—862no—
813C23—862no—
814C23—862no—
815C23—862no—
816C23—862no—
817C23—862no—
818C23—862no—
819C23—862no—
820C23—862no—
821C23—862no—
822C23—862no—
823C23—862no—
824C23—862no—
825C23—862no—
826C23—1721no—
827C23—1721no—
828C23—1721no—
829C23—1721no—
830C23—1721no—
831C23—1721no—
832C23—1721no—
833C23—1721no—
834C23—1721no—
835C23—1721no—
836C23—1721no—
837C23—1721no—
838C23—1721no—
839C23—1721no—
840C23—1721no—
841C23—1721no—
842C23C22×C4×D4311yescharacteristic
843C23C2×D4×D4311yescharacteristic
844C23C2×D4×D4311yescharacteristic
845C23C22×C22⋊D4311yescharacteristic
846C23#41×D4311yescharacteristic
847C23C2×#1062189811yescharacteristic
848C23C2×#1062190211yescharacteristic
849C23#1306337011yescharacteristic
850C23#1306337011yescharacteristic
851C23#1306337111yescharacteristic
852C23#1306337211yescharacteristic
853C23#1306337211yescharacteristic
854C23#1306337311yescharacteristic
855C23#1306337311yescharacteristic
856C23#1306337311yescharacteristic
857Q8—416no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—434no—
906C2×C4—862no—
907C2×C4—862no—
908C2×C4—862no—
909C2×C4—862no—
910C2×C4—862no—
911C2×C4—862no—
912C2×C4—862no—
913C2×C4—862no—
914C2×C4—862no—
915C2×C4—862no—
916C2×C4—862no—
917C2×C4—862no—
918C2×C4—862no—
919C2×C4—862no—
920C2×C4—862no—
921C2×C4—17216no—
922C2×C4—1721no—
923C2×C4—1721no—
924C2×C4—1721no—
925C2×C4—1721no—
926C2×C4—1721no—
927C2×C4—1721no—
928C2×C4—1721no—
929C2×C4—1721no—
930C2×C4—1721no—
931C2×C4—1721no—
932C2×C4—1721no—
933C2×C4—1721no—
934C2×C4—1721no—
935C2×C4—1721no—
936C2×C4—1721no—
937C2×C4—1721no—
938C2×C4—1721no—
939C2×C4—1721no—
940C2×C4—1721no—
941C2×C4—1721no—
942C2×C4—1721no—
943C2×C4—1721no—
944C2×C4—1721no—
945C2×C4—1721no—
946C2×C4—1721no—
947C2×C4—1721no—
948C2×C4—1721no—
949C2×C4—1721no—
950C2×C4—1721no—
951C2×C4—1721no—
952C2×C4—1721no—
953C2×C4—1721no—
954C2×C4—1721no—
955C2×C4C22⋊C4×D4314yes—
956C2×C4C4×C22⋊D4314yes—
957C22—864no—
958C22—864no—
959C22—864no—
960C22—1722no—
961C22—1722no—
962C22—1722no—
963C22—1722no—
964C22—1722no—
965C22—1722no—
966C22—1722no—
967C22—1722no—
968C22—1722no—
969C22—1722no—
970C22—1722no—
971C22—1722no—
972C22C2×C22⋊C4×D4311yescharacteristic
973C22C2×C4×C22⋊D4311yescharacteristic
974C22C4×#1062190211yescharacteristic
975C22#1458337211yescharacteristic
976C22#1458337511yescharacteristic
977C22#1458337511yescharacteristic
978C22#1458338111yescharacteristic
979C22#1458346911yescharacteristic
980C22#1458347211yescharacteristic
981C22#1458347211yescharacteristic
982C22#1458347311yescharacteristic
983C22#1458347411yescharacteristic
984C22#1458347711yescharacteristic
985C22#1458349511yescharacteristic
986C22#1458349811yescharacteristic
987C22#1458350711yescharacteristic
988C22#1458351311yescharacteristic
989C22#1458352111yescharacteristic
990C22#1458352311yescharacteristic
991C22D4×C22⋊D4311yescharacteristic
992C22D4×C22⋊D4311yescharacteristic
993C22#1458353911yescharacteristic
994C22#1458353911yescharacteristic
995C22#1458354011yescharacteristic
996C22#1458354211yescharacteristic
997C22#1458354811yescharacteristic
998C22#1458355111yescharacteristic
999C22#1458355211yescharacteristic
1000C22#1458356011yescharacteristic
1001C22#1458359011yescharacteristic
1002C22#1458362211yescharacteristic
1003C22#1458364311yescharacteristic
1004C22#1458364511yescharacteristic
1005C22#1458364811yescharacteristic
1006C22#1458365011yescharacteristic
1007C4—24no—
1008C4—24no—
1009C4—42no—
1010C4—42no—
1011C4—42no—
1012C4—42no—
1013C4—81no—
1014C4—864no—
1015C4—3441no—
1016C4—3441no—
1017C4—3441no—
1018C4—1722no—
1019C4—1722no—
1020C4—1722no—
1021C2—1724no—
1022C2#1913717811yescharacteristic
1023C2#1913727111yescharacteristic
1024C2#1913735011yescharacteristic
1025C2C22⋊C4×C22⋊D4311yescharacteristic
1026C2#1913742411yescharacteristic
1027C2#1913761811yescharacteristic
1028C2#1913775611yescharacteristic
1029C2#1914084111yescharacteristic
1030C2#1914087111yescharacteristic
1031C2#1914093411yescharacteristic
1032C2#1914095011yescharacteristic
1033C2#1914101111yescharacteristic
1034C2#1914104111yescharacteristic
1035C2#1914117211yescharacteristic
1036C2#1914119611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C43×#391C2
socle, cosocleC24×C43C24
prime radicalC24×D43C23
hypercenterC2×#391D43
hypocenterC43#14364
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
5. #19132866C2semidirect
6. #19132861C2semidirect
7. #19132847C2semidirect
8. #19132845C2semidirect
11. #19132829C2semidirect
12. #19132828C2semidirect
13. Dic43⋊#95C2semidirect
15. C2×C43×#391C2semidirect
19. C2×#13063301C4semidirect
504. C2×#391D43semidirect
576. C43#14364semidirect

Maximal subgroups

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

subgroupindex
C22×#130633012
C2×#145827902
C2×#145827892
C2×#145827612
#191328662
#191328612
#191328472
#191328452
#191328432
#191328292
#191328282
Dic43⋊#952
(C2×D43)⋊#952
C2×C43×#3912
#1436443