Finite Group Databasebeta

← #25027872

Subgroups — #25027872

Order 11008.

1674 conjugacy classes of subgroups.

The subgroup lattice has 1000 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582790C211yesmaximal, characteristic
2C2×#14582789C211yesmaximal, characteristic
3C2×#14582789C211yesmaximal, characteristic
4C2×C42×Dic43C211yesmaximal, characteristic, complemented
5#19132831C211yesmaximal, characteristic
6#19132831C211yesmaximal, characteristic
7#19132831C211yesmaximal, characteristic
8#19132831C211yesmaximal, characteristic
9#19132830C211yesmaximal, characteristic, complemented
10#19132830C211yesmaximal, characteristic, complemented
11#19132827C211yesmaximal, characteristic, complemented
12#19132827C211yesmaximal, characteristic, complemented
13#19132821C211yesmaximal, characteristic, complemented
14#19132821C211yesmaximal, characteristic, complemented
15C2×C43×#387C211yesmaximal, characteristic, complemented
16C22×Dic43⋊C4C2211yescharacteristic
17C22×(C2×D43)⋊C4C2211yescharacteristic
18C22×(C2×D43)⋊C4C2211yescharacteristic
19C22×(C2×D43)⋊C4C2211yescharacteristic
20C22×(C2×D43)⋊C4C2211yescharacteristic
21C22×(C2×D43)⋊C4C2211yescharacteristic
22C22×(C2×D43)⋊C4C2211yescharacteristic
23C22×(C2×D43)⋊C4C2211yescharacteristic
24C22×C4×Dic43C2211yescharacteristic
25C22×C4×Dic43C2211yescharacteristic
26C22×C4×Dic43C2211yescharacteristic
27C22×C4×Dic43C2211yescharacteristic
28C22×C4×Dic43C2211yescharacteristic
29C22×C4×Dic43C2211yescharacteristic
30#14582790—24no—
31#14582789—24no—
32#14582789C418yescomplemented
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
47C42×Dic43—24no—
48C22×C4⋊C4×C43C2211yescharacteristic
49C22×C4⋊C4×C43C2211yescharacteristic
50C22×C42×C43C2211yescharacteristic
51C43×#387—24no—
52C2×#95×C43C2211yescharacteristic
53C2×#95×C43C2211yescharacteristic
54C2×#95×C43C2211yescharacteristic
55C2×#95×C43C2211yescharacteristic
56C24×D43C2311yescharacteristic
57C23×Dic43C2311yescharacteristic
58C23×Dic43C2311yescharacteristic
59C23×Dic43C2311yescharacteristic
60C23×Dic43C2311yescharacteristic
61C23×Dic43C2311yescharacteristic
62C23×Dic43C2311yescharacteristic
63C23×Dic43C2311yescharacteristic
64C2×Dic43⋊C4—22no—
65C2×Dic43⋊C4—22no—
66C2×Dic43⋊C4—22no—
67C2×(C2×D43)⋊C4—22no—
68C2×(C2×D43)⋊C4—22no—
69C2×(C2×D43)⋊C4—22no—
70C2×(C2×D43)⋊C4—22no—
71C2×(C2×D43)⋊C4—22no—
72C2×(C2×D43)⋊C4—22no—
73C2×(C2×D43)⋊C4—22no—
74C2×(C2×D43)⋊C4—22no—
75C2×(C2×D43)⋊C4—22no—
76C2×(C2×D43)⋊C4—22no—
77C2×(C2×D43)⋊C4—22no—
78C2×(C2×D43)⋊C4—22no—
79C2×(C2×D43)⋊C4—22no—
80C2×(C2×D43)⋊C4—22no—
81C2×(C2×D43)⋊C4—22no—
82C2×(C2×D43)⋊C4—22no—
83C2×(C2×D43)⋊C4—22no—
84C2×(C2×D43)⋊C4—22no—
85C2×(C2×D43)⋊C4C2×C414yes—
86C2×(C2×D43)⋊C4C2×C414yes—
87C2×(C2×D43)⋊C4C2×C414yes—
88C2×C4×Dic43—22no—
89C2×C4×Dic43—22no—
90C2×C4×Dic43—22no—
91C2×C4×Dic43—22no—
92C2×C4×Dic43—22no—
93C2×C4×Dic43—22no—
94C2×C4×Dic43—22no—
95C2×C4×Dic43—22no—
96C2×C4×Dic43—22no—
97C2×C4×Dic43—22no—
98C2×C4×Dic43—22no—
99C2×C4×Dic43—22no—
100C2×C4×Dic43—22no—
101C2×C4×Dic43—22no—
102C2×C4×Dic43—22no—
103C2×C4×Dic43—22no—
104C2×C4×Dic43C2×C414yes—
105C2×C4×Dic43D414yes—
106C43⋊#95—22no—
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—22no—
118C43⋊#95C2×C414yes—
119C43⋊#95C2×C414yes—
120C23×C4×C43C2311yescharacteristic
121C23×C4×C43C2311yescharacteristic
122C23×C4×C43C2311yescharacteristic
123C23×C4×C43C2311yescharacteristic
124C23×C4×C43C2311yescharacteristic
125C23×C4×C43C2311yescharacteristic
126C23×C4×C43C2311yescharacteristic
127C2×C4⋊C4×C43—22no—
128C2×C4⋊C4×C43—22no—
129C2×C4⋊C4×C43—22no—
130C2×C4⋊C4×C43—22no—
131C2×C4⋊C4×C43—22no—
132C2×C4⋊C4×C43C2×C414yes—
133C2×C42×C43—22no—
134C2×C42×C43—22no—
135C2×C42×C43D414yes—
136#95×C43—22no—
137#95×C43—22no—
138#95×C43—22no—
139#95×C43—22no—
140C24×C43C2411yescharacteristic
141C23×D43—21no—
142C23×D43—21no—
143C23×D43—21no—
144C23×D43—21no—
145C23×D43—21no—
146C23×D43—21no—
147C23×D43—21no—
148C23×D43—21no—
149C23×D43—21no—
150C23×D43—21no—
151C23×D43—21no—
152C23×D43—21no—
153C23×D43—21no—
154C23×D43—21no—
155C23×D43C22×C412yes—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
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×C43C22×C412yes—
195C22×C4×C43C22×C412yes—
196C22×C4×C43C22×C412yes—
197C22×C4×C43C2×D412yes—
198C22×C4×C43C2×D412yes—
199C22×C4×C43C2×D412yes—
200C22×C4×C43C2×D412yes—
201C22×C4×C43#4112yes—
202C22×C4×C43#4112yes—
203C22×C4×C43#4112yes—
204C22×C4×C43#4112yes—
205C22×Dic43—21no—
206C22×Dic43—21no—
207C22×Dic43—21no—
208C22×Dic43—21no—
209C22×Dic43—21no—
210C22×Dic43—21no—
211C22×Dic43—21no—
212C22×Dic43—21no—
213C22×Dic43—21no—
214C22×Dic43—21no—
215C22×Dic43—21no—
216C22×Dic43—21no—
217C22×Dic43—21no—
218C22×Dic43—21no—
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×Dic43C22×C412yes—
242C22×Dic43C22×C412yes—
243C22×Dic43C22×C412yes—
244C22×Dic43C2×D412yes—
245C22×Dic43C2×D412yes—
246C22×Dic43#4112yes—
247C22×Dic43#4112yes—
248C22×Dic43#4112yes—
249C22×Dic43#4112yes—
250C22×Dic43#4112yes—
251C22×Dic43#4112yes—
252C22×Dic43#4112yes—
253C22×Dic43#4112yes—
254C4⋊C4×C43—28no—
255C4⋊C4×C43—44no—
256C42×C43—28no—
257(C2×D43)⋊C4—28no—
258(C2×D43)⋊C4—28no—
259(C2×D43)⋊C4—28no—
260(C2×D43)⋊C4—44no—
261(C2×D43)⋊C4—44no—
262(C2×D43)⋊C4—44no—
263(C2×D43)⋊C4—44no—
264Dic43⋊C4—44no—
265C4×Dic43—28no—
266C4×Dic43—28no—
267C4×Dic43—28no—
268C4×Dic43—28no—
269C4×Dic43—28no—
270C4×Dic43—28no—
271C23×C43C23×C411yescharacteristic
272C23×C43C22×D411yescharacteristic
273C23×C43C22×D411yescharacteristic
274C23×C43C2×#4111yescharacteristic
275C23×C43C2×#4111yescharacteristic
276C23×C43C2×#4111yescharacteristic
277C23×C43C2×#4111yescharacteristic
278C23×C43C2×#4111yescharacteristic
279C23×C43C2×#4111yescharacteristic
280C23×C43C2×#4111yescharacteristic
281C23×C43C2×#4111yescharacteristic
282C23×C43C2×#4111yescharacteristic
283C23×C43C2×#4111yescharacteristic
284C23×C43C2×#4111yescharacteristic
285C23×C43C2×#4111yescharacteristic
286C22×D43—22no—
287C22×D43—22no—
288C22×D43—22no—
289C22×D43—22no—
290C22×D43—22no—
291C22×D43—22no—
292C22×D43—22no—
293C22×D43—41no—
294C22×D43—41no—
295C22×D43—41no—
296C22×D43—41no—
297C22×D43—41no—
298C22×D43—41no—
299C22×D43—41no—
300C22×D43—41no—
301C22×D43—41no—
302C22×D43—41no—
303C22×D43—41no—
304C22×D43—41no—
305C22×D43—41no—
306C22×D43—41no—
307C22×D43—41no—
308C22×D43—41no—
309C22×D43—41no—
310C22×D43—41no—
311C22×D43—41no—
312C22×D43—41no—
313C22×D43—41no—
314C22×D43—41no—
315C22×D43—41no—
316C22×D43—41no—
317C22×D43—41no—
318C22×D43—41no—
319C22×D43—41no—
320C22×D43—41no—
321C2×C4×C43—22no—
322C2×C4×C43—22no—
323C2×C4×C43—22no—
324C2×C4×C43—22no—
325C2×C4×C43—22no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43—22no—
330C2×C4×C43—22no—
331C2×C4×C43—22no—
332C2×C4×C43—22no—
333C2×C4×C43—22no—
334C2×C4×C43—22no—
335C2×C4×C43—22no—
336C2×C4×C43—22no—
337C2×C4×C43—22no—
338C2×C4×C43—22no—
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—41no—
346C2×C4×C43—41no—
347C2×C4×C43—41no—
348C2×C4×C43—41no—
349C2×C4×C43—41no—
350C2×C4×C43—41no—
351C2×C4×C43—41no—
352C2×C4×C43—41no—
353C2×C4×C43—41no—
354C2×C4×C43—41no—
355C2×C4×C43—41no—
356C2×C4×C43—41no—
357C2×C4×C43—41no—
358C2×C4×C43—41no—
359C2×C4×C43—41no—
360C2×C4×C43—41no—
361C2×C4×C43—41no—
362C2×C4×C43—41no—
363C2×C4×C43—41no—
364C2×C4×C43—41no—
365C2×C4×C43—41no—
366C2×C4×C43—41no—
367C2×C4×C43C4×D414yes—
368C2×C4×C43#12114yes—
369C2×C4×C43#12414yes—
370C2×Dic43—22no—
371C2×Dic43—22no—
372C2×Dic43—22no—
373C2×Dic43—22no—
374C2×Dic43—22no—
375C2×Dic43—22no—
376C2×Dic43—22no—
377C2×Dic43—22no—
378C2×Dic43—22no—
379C2×Dic43—22no—
380C2×Dic43—22no—
381C2×Dic43—22no—
382C2×Dic43—22no—
383C2×Dic43—22no—
384C2×Dic43—22no—
385C2×Dic43—22no—
386C2×Dic43—22no—
387C2×Dic43—22no—
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—41no—
398C2×Dic43—41no—
399C2×Dic43—41no—
400C2×Dic43—41no—
401C2×Dic43—41no—
402C2×Dic43—41no—
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#11714yes—
416C2×Dic43C4×D414yes—
417C2×Dic43#12314yes—
418C2×Dic43#12614yes—
419#14701—431nomaximal, Sylow
420C22×C43C2×#11711yescharacteristic
421C22×C43C2×C4×D411yescharacteristic
422C22×C43C2×C4×D411yescharacteristic
423C22×C43C4×#4111yescharacteristic
424C22×C43C4×#4111yescharacteristic
425C22×C43C4×#4111yescharacteristic
426C22×C43C4×#4111yescharacteristic
427C22×C43C2×#12111yescharacteristic
428C22×C43C2×#12311yescharacteristic
429C22×C43#52511yescharacteristic
430C22×C43#52511yescharacteristic
431C22×C43#52511yescharacteristic
432C22×C43#52511yescharacteristic
433C22×C43C2×#12411yescharacteristic
434C22×C43C2×#12611yescharacteristic
435C22×C43#52911yescharacteristic
436C22×C43#52911yescharacteristic
437C22×C43#52911yescharacteristic
438C22×C43#52911yescharacteristic
439C22×C43#52911yescharacteristic
440C22×C43#52911yescharacteristic
441C22×C43#52911yescharacteristic
442C22×C43#52911yescharacteristic
443C22×C43#52911yescharacteristic
444C22×C43#52911yescharacteristic
445C22×C43#52911yescharacteristic
446C22×C43#52911yescharacteristic
447C22×C43#52911yescharacteristic
448C22×C43#52911yescharacteristic
449C22×C43#52911yescharacteristic
450C22×C43#52911yescharacteristic
451C22×C43#53211yescharacteristic
452C22×C43#53211yescharacteristic
453C22×C43#53211yescharacteristic
454C22×C43#53211yescharacteristic
455C2×D43—42no—
456C2×D43—42no—
457C2×D43—42no—
458C2×D43—42no—
459C2×D43—42no—
460C2×D43—42no—
461C2×D43—42no—
462C2×D43—81no—
463C2×D43—81no—
464C2×D43—81no—
465C2×D43—81no—
466C2×D43—81no—
467C2×D43—81no—
468C2×D43—81no—
469C2×D43—81no—
470C4×C43—24no—
471C4×C43—24no—
472C4×C43—24no—
473C4×C43—42no—
474C4×C43—42no—
475C4×C43—81no—
476C4×C43—81no—
477Dic43—24no—
478Dic43—24no—
479Dic43—24no—
480Dic43—24no—
481Dic43—42no—
482Dic43—81no—
483Dic43—81no—
484C2×#388—431no—
485C2×#388—431no—
486C2×#388—431no—
487C2×#387D4311yescharacteristic, complemented
488C2×C43—431no—
489#1437—431no—
490#1437—431no—
491#1437—431no—
492#1437—431no—
493#1436—431no—
494#1436—431no—
495#1436—431no—
496#1436—431no—
497#1434—431no—
498#1434—431no—
499C2×C43#229011yescharacteristic
500C2×C43#229311yescharacteristic
501C2×C43#229811yescharacteristic
502C2×C43C4×#12111yescharacteristic
503C2×C43C4×#12311yescharacteristic
504C2×C43C4×#12411yescharacteristic
505C2×C43C4×#12611yescharacteristic
506C2×C43#285011yescharacteristic
507C2×C43#285211yescharacteristic
508C2×C43#285311yescharacteristic
509C2×C43#285411yescharacteristic
510C2×C43#286011yescharacteristic
511C2×C43#286111yescharacteristic
512C2×C43#286511yescharacteristic
513C2×C43#286611yescharacteristic
514D43—82no—
515C22×C4⋊C4—431no—
516C22×C4⋊C4C2×D4311yescharacteristic
517C22×C4⋊C4C2×D4311yescharacteristic
518C22×C22⋊C4—431no—
519C22×C22⋊C4—431no—
520C22×C22⋊C4—431no—
521C22×C22⋊C4—431no—
522C22×C22⋊C4—431no—
523C22×C22⋊C4—431no—
524C22×C22⋊C4—431no—
525C22×C42—431no—
526C22×C42—431no—
527C22×C42—431no—
528C22×C42—431no—
529C22×C42—431no—
530C22×C42—431no—
531C22×C42C2×D4311yescharacteristic
532#388—438no—
533#388—864no—
534#388—864no—
535#387—24no—
536C2×#95—431no—
537C2×#95—431no—
538C2×#95—431no—
539C2×#95—431no—
540C2×#95—431no—
541C2×#95—431no—
542C2×#95—431no—
543C2×#95—431no—
544C2×#95—431no—
545C2×#95—431no—
546C2×#95—431no—
547C2×#95—431no—
548C2×#95—431no—
549C2×#95—431no—
550C2×#95C2×D4311yescharacteristic
551C2×#95C2×D4311yescharacteristic
552C2×#95C2×D4311yescharacteristic
553C2×#95C2×D4311yescharacteristic
554C43—864no—
555C43#1470111yescharacteristic, complemented, Sylow
556C25—431no—
557C23×C4—431no—
558C23×C4—431no—
559C23×C4—431no—
560C23×C4—431no—
561C23×C4—431no—
562C23×C4—431no—
563C23×C4—431no—
564C23×C4C22×D4311yescharacteristic
565C23×C4C22×D4311yescharacteristic
566C23×C4C22×D4311yescharacteristic
567C23×C4C22×D4311yescharacteristic
568C23×C4C22×D4311yescharacteristic
569C23×C4C22×D4311yescharacteristic
570C23×C4C22×D4311yescharacteristic
571C2×C4⋊C4—22no—
572C2×C4⋊C4—22no—
573C2×C4⋊C4—22no—
574C2×C4⋊C4—22no—
575C2×C4⋊C4—22no—
576C2×C4⋊C4—862no—
577C2×C4⋊C4—862no—
578C2×C4⋊C4—862no—
579C2×C4⋊C4C4×D4314yes—
580C2×C22⋊C4—434no—
581C2×C22⋊C4—434no—
582C2×C22⋊C4—434no—
583C2×C22⋊C4—862no—
584C2×C22⋊C4—862no—
585C2×C22⋊C4—862no—
586C2×C22⋊C4—862no—
587C2×C22⋊C4—862no—
588C2×C22⋊C4—862no—
589C2×C22⋊C4—862no—
590C2×C22⋊C4—862no—
591C2×C22⋊C4—862no—
592C2×C22⋊C4—862no—
593C2×C22⋊C4—862no—
594C2×C22⋊C4—862no—
595C2×C22⋊C4—862no—
596C2×C22⋊C4—862no—
597C2×C22⋊C4—862no—
598C2×C22⋊C4—862no—
599C2×C22⋊C4—862no—
600C2×C22⋊C4—862no—
601C2×C42—22no—
602C2×C42—22no—
603C2×C42—434no—
604C2×C42—434no—
605C2×C42—862no—
606C2×C42—862no—
607C2×C42—862no—
608C2×C42—862no—
609C2×C42—862no—
610C2×C42—862no—
611C2×C42—862no—
612C2×C42—862no—
613C2×C42—862no—
614C2×C42—862no—
615C2×C42—862no—
616C2×C42—862no—
617C2×C42—862no—
618C2×C42—862no—
619C2×C42—862no—
620C2×C42—862no—
621C2×C42C22⋊D4314yes—
622#95—22no—
623#95—22no—
624#95—22no—
625#95—22no—
626#95—434no—
627#95—434no—
628#95—862no—
629#95—862no—
630#95—862no—
631#95—862no—
632#95—862no—
633#95—862no—
634#95—862no—
635#95—862no—
636#95—862no—
637#95—862no—
638#95—862no—
639#95—862no—
640C24—432no—
641C24—861no—
642C24—861no—
643C24—861no—
644C24—861no—
645C24—861no—
646C24—861no—
647C24—861no—
648C24—861no—
649C24—861no—
650C24—861no—
651C24—861no—
652C24—861no—
653C24—861no—
654C24—861no—
655C24C23×D4311yescharacteristic
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—432no—
695C22×C4—432no—
696C22×C4—432no—
697C22×C4—432no—
698C22×C4—432no—
699C22×C4—432no—
700C22×C4—432no—
701C22×C4—432no—
702C22×C4—432no—
703C22×C4—432no—
704C22×C4—432no—
705C22×C4—432no—
706C22×C4—432no—
707C22×C4—861no—
708C22×C4—861no—
709C22×C4—861no—
710C22×C4—861no—
711C22×C4—861no—
712C22×C4—861no—
713C22×C4—861no—
714C22×C4—861no—
715C22×C4—861no—
716C22×C4—861no—
717C22×C4—861no—
718C22×C4—861no—
719C22×C4—861no—
720C22×C4—861no—
721C22×C4—861no—
722C22×C4—861no—
723C22×C4—861no—
724C22×C4—861no—
725C22×C4—861no—
726C22×C4—861no—
727C22×C4—861no—
728C22×C4—861no—
729C22×C4—861no—
730C22×C4—861no—
731C22×C4—861no—
732C22×C4—861no—
733C22×C4—861no—
734C22×C4—861no—
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×C4C2×C4×D4312yes—
744C22×C4C2×C4×D4312yes—
745C22×C4C2×C4×D4312yes—
746C22×C4#1062189812yes—
747C22×C4D4×D4312yes—
748C22×C4#1062190012yes—
749C22×C4#1062190212yes—
750C22×C4#1062190212yes—
751C22×C4C2×C22⋊D4312yes—
752C22×C4C2×C22⋊D4312yes—
753C22×C4C2×C22⋊D4312yes—
754C4⋊C4—28no—
755C4⋊C4—44no—
756C4⋊C4—1724no—
757C22⋊C4—868no—
758C22⋊C4—868no—
759C22⋊C4—868no—
760C22⋊C4—1724no—
761C22⋊C4—1724no—
762C22⋊C4—1724no—
763C22⋊C4—1724no—
764C42—28no—
765C42—868no—
766C42—868no—
767C42—868no—
768C42—868no—
769C42—868no—
770C42—868no—
771C23—862no—
772C23—862no—
773C23—862no—
774C23—862no—
775C23—862no—
776C23—862no—
777C23—862no—
778C23—1721no—
779C23—1721no—
780C23—1721no—
781C23—1721no—
782C23—1721no—
783C23—1721no—
784C23—1721no—
785C23—1721no—
786C23—1721no—
787C23—1721no—
788C23—1721no—
789C23—1721no—
790C23—1721no—
791C23—1721no—
792C23—1721no—
793C23—1721no—
794C23—1721no—
795C23—1721no—
796C23—1721no—
797C23—1721no—
798C23—1721no—
799C23—1721no—
800C23—1721no—
801C23—1721no—
802C23—1721no—
803C23—1721no—
804C23—1721no—
805C23—1721no—
806C23C22×C4×D4311yescharacteristic
807C23C2×D4×D4311yescharacteristic
808C23C22×C22⋊D4311yescharacteristic
809C23#41×D4311yescharacteristic
810C23#41×D4311yescharacteristic
811C23#41×D4311yescharacteristic
812C23#41×D4311yescharacteristic
813C23#41×D4311yescharacteristic
814C23#41×D4311yescharacteristic
815C23#41×D4311yescharacteristic
816C23#41×D4311yescharacteristic
817C23C2×#1062190011yescharacteristic
818C23C2×#1062189811yescharacteristic
819C23C2×#1062190211yescharacteristic
820C23C2×#1062190211yescharacteristic
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—434no—
868C2×C4—434no—
869C2×C4—434no—
870C2×C4—434no—
871C2×C4—862no—
872C2×C4—862no—
873C2×C4—862no—
874C2×C4—862no—
875C2×C4—862no—
876C2×C4—862no—
877C2×C4—862no—
878C2×C4—862no—
879C2×C4—862no—
880C2×C4—862no—
881C2×C4—862no—
882C2×C4—862no—
883C2×C4—862no—
884C2×C4—862no—
885C2×C4—862no—
886C2×C4—862no—
887C2×C4—862no—
888C2×C4—862no—
889C2×C4—862no—
890C2×C4—862no—
891C2×C4—862no—
892C2×C4—862no—
893C2×C4—862no—
894C2×C4—862no—
895C2×C4—862no—
896C2×C4—862no—
897C2×C4—862no—
898C2×C4—1721no—
899C2×C4—1721no—
900C2×C4—1721no—
901C2×C4—1721no—
902C2×C4—1721no—
903C2×C4—1721no—
904C2×C4—1721no—
905C2×C4—1721no—
906C2×C4—1721no—
907C2×C4—1721no—
908C2×C4—1721no—
909C2×C4—1721no—
910C2×C4—1721no—
911C2×C4—1721no—
912C2×C4—1721no—
913C2×C4—1721no—
914C2×C4—1721no—
915C2×C4—1721no—
916C2×C4C4×C22⋊D4314yes—
917C2×C4#1306329714yes—
918C2×C4#1306331414yes—
919C22—3441no—
920C22—3441no—
921C22—3441no—
922C22—3441no—
923C22—3441no—
924C22—3441no—
925C22—3441no—
926C22—3441no—
927C22—1722no—
928C22—1722no—
929C22—1722no—
930C22—1722no—
931C22—1722no—
932C22—1722no—
933C22—1722no—
934C22#117×D4311yescharacteristic
935C22C4×D4×D4311yescharacteristic
936C22C2×C4×C22⋊D4311yescharacteristic
937C22C4×#1062190011yescharacteristic
938C22#1458336711yescharacteristic
939C22C4×#1062190211yescharacteristic
940C22C4×#1062190211yescharacteristic
941C22C2×#1306329711yescharacteristic
942C22#123×D4311yescharacteristic
943C22#1458340711yescharacteristic
944C22#1458340811yescharacteristic
945C22#1458341211yescharacteristic
946C22#1458341211yescharacteristic
947C22C2×#1306331411yescharacteristic
948C22#126×D4311yescharacteristic
949C22#1458342611yescharacteristic
950C22#1458342611yescharacteristic
951C22#1458342711yescharacteristic
952C22#1458342711yescharacteristic
953C22#1458342911yescharacteristic
954C22#1458343211yescharacteristic
955C22#1458343211yescharacteristic
956C22#1458343211yescharacteristic
957C22#1458343411yescharacteristic
958C22#1458343411yescharacteristic
959C22#1458343411yescharacteristic
960C22#1458343411yescharacteristic
961C22#1458343511yescharacteristic
962C22#1458343511yescharacteristic
963C22#1458343611yescharacteristic
964C22#1458343611yescharacteristic
965C22#1458344511yescharacteristic
966C22#1458344511yescharacteristic
967C22#1458344511yescharacteristic
968C22#1458344511yescharacteristic
969C4—24no—
970C4—24no—
971C4—24no—
972C4—42no—
973C4—42no—
974C4—81no—
975C4—81no—
976C4—864no—
977C4—864no—
978C4—864no—
979C4—864no—
980C4—3441no—
981C4—3441no—
982C4—1722no—
983C2—3442no—
984C2#1913703311yescharacteristic
985C2#1913705411yescharacteristic
986C2#1913708711yescharacteristic
987C2C4×#1306329711yescharacteristic
988C2#1913711611yescharacteristic
989C2C4×#1306331411yescharacteristic
990C2#1913714511yescharacteristic
991C2#1914289811yescharacteristic
992C2#1914291311yescharacteristic
993C2#1914291911yescharacteristic
994C2#1914292411yescharacteristic
995C2#1914296011yescharacteristic
996C2#1914296811yescharacteristic
997C2#1914298511yescharacteristic
998C2#1914298811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C43×#387C2
socle, cosocleC24×C43C24
prime radicalC24×D43C23
hypercenterC2×#387D43
hypocenterC43#14701
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
4. C2×C42×Dic43C2semidirect
9. #19132830C2semidirect
10. #19132830C2semidirect
11. #19132827C2semidirect
12. #19132827C2semidirect
13. #19132821C2semidirect
14. #19132821C2semidirect
15. C2×C43×#387C2semidirect
32. #14582789C4semidirect
487. C2×#387D43semidirect
555. C43#14701semidirect

Maximal subgroups

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

subgroupindex
C2×#145827902
C2×#145827892
C2×C42×Dic432
#191328312
#191328302
#191328272
#191328212
C2×C43×#3872
#1470143