Finite Group Databasebeta

← #25111882

Subgroups — #25111882

Order 11008.

1582 conjugacy classes of subgroups.

The subgroup lattice has 990 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583408C211yesmaximal, characteristic
2C2×#14582974C211yesmaximal, characteristic, complemented
3C2×#14582970C211yesmaximal, characteristic, complemented
4C2×#14582865C211yesmaximal, characteristic, complemented
5C2×#14582861C211yesmaximal, characteristic, complemented
6#19135391C211yesmaximal, characteristic, complemented
7#19135387C211yesmaximal, characteristic, complemented
8#19134893C211yesmaximal, characteristic, complemented
9#19134891C211yesmaximal, characteristic, complemented
10#19134891C211yesmaximal, characteristic, complemented
11#19134578C211yesmaximal, characteristic, complemented
12#19134506C211yesmaximal, characteristic, complemented
13#19134504C211yesmaximal, characteristic, complemented
14#19134360C211yesmaximal, characteristic, complemented
15C43×#1869C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C23×C4×D43C2211yescharacteristic
18C22×#10621877C2211yescharacteristic, complemented
19C22×#10621872C2211yescharacteristic
20C22×#10621872C2211yescharacteristic
21#14583408—24no—
22#14583408—24no—
23C2×#13063310C411yescharacteristic
24C2×#13063307C411yescharacteristic
25C2×#13063303C411yescharacteristic
26C2×#13063302C411yescharacteristic
27C2×#13063298C411yescharacteristic
28C2×#13063297C411yescharacteristic
29C2×#13063295C411yescharacteristic
30C2×#13063293C411yescharacteristic
31C2×C4×D172C2211yescharacteristic
32C2×C4×C22⋊D43C2211yescharacteristic
33C2×C4×C22⋊D43C2211yescharacteristic
34C2×#13063282C2211yescharacteristic
35#14582974—24no—
36#14582970—24no—
37C2×Dic43⋊C8C2211yescharacteristic, complemented
38C2×Dic43⋊C8C2211yescharacteristic, complemented
39#14582865—24no—
40#14582861—24no—
41C2×C22⋊(C43⋊C8)C2211yescharacteristic
42C2×C22⋊(C43⋊C8)C2211yescharacteristic
43C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
44C2×(C2×D43)⋊C8C2211yescharacteristic
45C2×(C2×D43)⋊C8C2211yescharacteristic
46C2×(C2×D43)⋊C8C2211yescharacteristic
47C2×(C2×D43)⋊C8C2211yescharacteristic
48C2×(C2×D43)⋊C8C2211yescharacteristic
49C2×(C2×D43)⋊C8C2211yescharacteristic
50C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
51C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
52C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
53C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
54C2×#13063235C2211yescharacteristic, complemented
55C2×C8×Dic43C2211yescharacteristic, complemented
56#14582654C2211yescharacteristic, complemented
57#14582654C2211yescharacteristic, complemented
58C23×C8×C43C2211yescharacteristic, complemented
59C2×C4×D4×C43C2211yescharacteristic
60C2×C22⋊C8×C43C2211yescharacteristic
61C2×C22⋊C8×C43C2211yescharacteristic
62C2×C22⋊C8×C43C2211yescharacteristic, complemented
63C43×#336C2211yescharacteristic, complemented
64C43×#336C2211yescharacteristic, complemented
65C24×D43C2×C411yescharacteristic
66C2×#10621898—22no—
67C2×#10621898—22no—
68C2×#10621898—22no—
69C2×#10621898—22no—
70C2×#10621898—41no—
71C2×#10621898—41no—
72C22×Dic86C2×C411yescharacteristic
73C22×D172C2×C411yescharacteristic
74C22×D172C2×C411yescharacteristic
75C22×C22⋊D43C2×C411yescharacteristic
76C22×C22⋊D43C2×C411yescharacteristic
77C22×C22⋊D43C2×C411yescharacteristic
78C22×C22⋊D43C2×C411yescharacteristic
79C23×Dic43C2×C411yescharacteristic
80C22×C4×D43—22no—
81C22×C4×D43—22no—
82C22×C4×D43—22no—
83C22×C4×D43—22no—
84C22×C4×D43—41no—
85C22×C4×D43—41no—
86C22×C4×D43C2×C411yescharacteristic
87C22×C4×D43C2×C411yescharacteristic
88C22×C4×D43C2311yescharacteristic
89C22×C4×D43C2311yescharacteristic
90C22×C4×D43C2311yescharacteristic
91C2×#10621877—22no—
92C2×#10621877—22no—
93C2×#10621877—41no—
94C2×#10621872—22no—
95C2×#10621872—22no—
96C2×#10621872—22no—
97C2×#10621872—22no—
98C2×#10621872—41no—
99C2×#10621872—41no—
100C22×C43⋊C8C2311yescharacteristic
101C22×C43⋊C8C2311yescharacteristic
102C22×C43⋊C8C2311yescharacteristic
103C22×C43⋊C8C2311yescharacteristic
104#13063310—24no—
105#13063307—24no—
106#13063303—24no—
107#13063302—24no—
108#13063298—24no—
109#13063297—24no—
110#13063295—24no—
111#13063293—24no—
112C4×D172—22no—
113C4×D172—22no—
114C4×C22⋊D43—22no—
115C4×C22⋊D43—22no—
116C4×C22⋊D43D414yes—
117C4×C22⋊D43D414yes—
118#13063282—22no—
119#13063282—22no—
120C2×C4⋊Dic43C2×C411yescharacteristic
121C2×Dic43⋊C4C2×C411yescharacteristic
122C2×Dic43⋊C4C2×C411yescharacteristic
123C2×Dic43⋊C4C2×C411yescharacteristic
124C2×Dic43⋊C4C2×C411yescharacteristic
125C2×C22⋊Dic43C2×C411yescharacteristic
126C2×C22⋊Dic43C2×C411yescharacteristic
127C2×(C2×D43)⋊C4C2×C411yescharacteristic
128C2×(C2×D43)⋊C4C2×C411yescharacteristic
129C2×(C2×D43)⋊C4C2×C411yescharacteristic
130C2×(C2×D43)⋊C4C2×C411yescharacteristic
131C2×(C2×D43)⋊C4C2×C411yescharacteristic
132C2×(C2×D43)⋊C4C2×C411yescharacteristic
133C2×C4×Dic43C2311yescharacteristic
134Dic43⋊C8—22no—
135Dic43⋊C8—22no—
136C22⋊(C43⋊C8)—22no—
137C22⋊(C43⋊C8)—22no—
138C22⋊(C43⋊C8)—41no—
139(C2×D43)⋊C8—22no—
140(C2×D43)⋊C8—22no—
141(C2×D43)⋊C8—22no—
142(C2×D43)⋊C8—22no—
143(C2×D43)⋊C8—22no—
144(C2×D43)⋊C8—22no—
145(C2×D43)⋊C8—22no—
146(C2×D43)⋊C8—41no—
147(C2×D43)⋊C8—41no—
148(C2×D43)⋊C8D414yescomplemented
149#13063235—22no—
150C8×Dic43—22no—
151C22×D4×C43C2×C411yescharacteristic
152C23×C4×C43C2311yescharacteristic
153C23×C4×C43C2311yescharacteristic
154C22×C8×C43—22no—
155C22×C8×C43—22no—
156C22×C8×C43—41no—
157C22×C8×C43C2311yescharacteristic
158C22×C8×C43C2311yescharacteristic
159C22×C8×C43C2311yescharacteristic
160C22×C8×C43C2311yescharacteristic
161C4×D4×C43—22no—
162C4×D4×C43—22no—
163C2×C4⋊C4×C43C2×C411yescharacteristic
164C2×C22⋊C4×C43C2×C411yescharacteristic
165C2×C22⋊C4×C43C2×C411yescharacteristic
166C2×C42×C43C2311yescharacteristic
167C22⋊C8×C43—22no—
168C22⋊C8×C43—22no—
169C22⋊C8×C43—41no—
170C24×C43C22×C411yescharacteristic
171C24×C43C22×C411yescharacteristic
172C23×D43—22no—
173C23×D43—22no—
174C23×D43—22no—
175C23×D43—41no—
176C23×D43—41no—
177C23×D43—41no—
178C23×D43—41no—
179C23×D43C22×C411yescharacteristic
180C23×D43C22×C411yescharacteristic
181C23×D43C22×C411yescharacteristic
182C2×D4×C43—22no—
183C2×D4×C43—22no—
184C2×D4×C43—41no—
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×C43C22×C411yescharacteristic
196C22×C4×C43C22×C411yescharacteristic
197C22×C4×C43C22×C411yescharacteristic
198C22×C4×C43C22×C411yescharacteristic
199C22×C4×C43C2×D412yes—
200C22×C4×C43C2×D412yes—
201C22×C4×C43C2411yescharacteristic
202C2×C22⋊D43—22no—
203C2×C22⋊D43—22no—
204C2×C22⋊D43—22no—
205C2×C22⋊D43—22no—
206C2×C22⋊D43—22no—
207C2×C22⋊D43—22no—
208C2×C22⋊D43—41no—
209C2×C22⋊D43—41no—
210C2×C22⋊D43—41no—
211C2×C22⋊D43—41no—
212C2×C22⋊D43—41no—
213C2×C22⋊D43C22⋊C414yes—
214C22×Dic43—22no—
215C22×Dic43—22no—
216C22×Dic43—41no—
217C22×Dic43C22×C411yescharacteristic
218C22×Dic43C22×C411yescharacteristic
219C22×Dic43C22×C411yescharacteristic
220C22×Dic43C22×C411yescharacteristic
221C22×Dic43C22×C411yescharacteristic
222#10621898—44no—
223#10621898—44no—
224#10621898—44no—
225#10621898—44no—
226C2×D172—22no—
227C2×D172—22no—
228C2×D172—22no—
229C2×D172—41no—
230C2×D172—41no—
231C2×D172—41no—
232C2×C4×D43—21no—
233C2×C4×D43—21no—
234C2×C4×D43—21no—
235C2×C4×D43—21no—
236C2×C4×D43—21no—
237C2×C4×D43—21no—
238C2×C4×D43—21no—
239C2×C4×D43—21no—
240C2×C4×D43—21no—
241C2×C4×D43—21no—
242C2×C4×D43—21no—
243C2×C4×D43—21no—
244C2×C4×D43—21no—
245C2×C4×D43—21no—
246C2×C4×D43—22no—
247C2×C4×D43—22no—
248C2×C4×D43—22no—
249C2×C4×D43—22no—
250C2×C4×D43—41no—
251C2×C4×D43—41no—
252C2×C4×D43—44no—
253C2×C4×D43—44no—
254C2×C4×D43—44no—
255C2×C4×D43—44no—
256C2×C4×D43C2×D412yes—
257C2×C4×D43C2×D412yes—
258C2×C4×D43C2×D412yes—
259C2×C4×D43#4112yes—
260C2×Dic86—22no—
261C2×Dic86—22no—
262C2×Dic86—41no—
263C2×C8×C43—21no—
264C2×C8×C43—21no—
265C2×C8×C43—21no—
266C2×C8×C43—21no—
267C2×C8×C43—21no—
268C2×C8×C43—21no—
269C2×C8×C43—21no—
270C2×C8×C43—21no—
271C2×C8×C43—21no—
272C2×C8×C43—21no—
273C2×C8×C43—21no—
274C2×C8×C43—44no—
275C2×C8×C43C2×D412yes—
276C4⋊C4×C43—22no—
277C22⋊C4×C43—22no—
278C22⋊C4×C43—22no—
279C42×C43—21no—
280C42×C43—21no—
281C22⋊Dic43—22no—
282C22⋊Dic43C22⋊C414yes—
283(C2×D43)⋊C4—22no—
284(C2×D43)⋊C4—22no—
285(C2×D43)⋊C4—22no—
286(C2×D43)⋊C4—22no—
287(C2×D43)⋊C4—22no—
288(C2×D43)⋊C4C22⋊C414yes—
289C4⋊Dic43—22no—
290Dic43⋊C4—22no—
291Dic43⋊C4—22no—
292Dic43⋊C4—22no—
293Dic43⋊C4C22⋊C414yes—
294C4×Dic43C2×D412yes—
295C4×Dic43C2×D412yes—
296#10621877—44no—
297C2×C43⋊C8—21no—
298C2×C43⋊C8—21no—
299C2×C43⋊C8—21no—
300C2×C43⋊C8—21no—
301C2×C43⋊C8—21no—
302C2×C43⋊C8—21no—
303C2×C43⋊C8—21no—
304C2×C43⋊C8—21no—
305C2×C43⋊C8—21no—
306C2×C43⋊C8—21no—
307C2×C43⋊C8—21no—
308C2×C43⋊C8C2×D412yes—
309#10621872—44no—
310#10621872—44no—
311C23×C43—21no—
312C23×C43—21no—
313C23×C43—21no—
314C23×C43—21no—
315C23×C43—21no—
316C23×C43—21no—
317C23×C43—21no—
318C23×C43—21no—
319C23×C43—21no—
320C23×C43—21no—
321C23×C43—21no—
322C23×C43—21no—
323C23×C43C2×C22⋊C412yes—
324C23×C43#13112yes—
325C23×C43C23×C411yescharacteristic
326C22×D43—21no—
327C22×D43—21no—
328C22×D43—21no—
329C22×D43—21no—
330C22×D43—21no—
331C22×D43—21no—
332C22×D43—21no—
333C22×D43—21no—
334C22×D43—21no—
335C22×D43—21no—
336C22×D43—21no—
337C22×D43—21no—
338C22×D43—21no—
339C22×D43—21no—
340C22×D43—21no—
341C22×D43—21no—
342C22×D43—21no—
343C22×D43—21no—
344C22×D43—21no—
345C22×D43—44no—
346C22×D43—44no—
347C22×D43—44no—
348C22×D43—44no—
349C22×D43—44no—
350C22×D43—44no—
351C22×D43—44no—
352C22×D43C2×C22⋊C412yes—
353C22×D43C4×D412yes—
354D4×C43—44no—
355C2×C4×C43—21no—
356C2×C4×C43—21no—
357C2×C4×C43—22no—
358C2×C4×C43—22no—
359C2×C4×C43—22no—
360C2×C4×C43—22no—
361C2×C4×C43—21no—
362C2×C4×C43—21no—
363C2×C4×C43—21no—
364C2×C4×C43—21no—
365C2×C4×C43—21no—
366C2×C4×C43—21no—
367C2×C4×C43—21no—
368C2×C4×C43—21no—
369C2×C4×C43—21no—
370C2×C4×C43—41no—
371C2×C4×C43—41no—
372C2×C4×C43—41no—
373C2×C4×C43—41no—
374C2×C4×C43C2×C22⋊C412yes—
375C2×C4×C43C22×D411yescharacteristic
376C2×C4×C43C22×D411yescharacteristic
377C2×C4×C43C22×D411yescharacteristic
378C2×C4×C43C2×#4111yescharacteristic
379C2×C4×C43H(5,𝔽2)11yescharacteristic
380C2×C4×C43H(5,𝔽2)11yescharacteristic
381C22⋊D43—44no—
382C22⋊D43—44no—
383C22⋊D43—44no—
384C22⋊D43—44no—
385C2×Dic43—21no—
386C2×Dic43—21no—
387C2×Dic43—21no—
388C2×Dic43—21no—
389C2×Dic43—21no—
390C2×Dic43—21no—
391C2×Dic43—21no—
392C2×Dic43—21no—
393C2×Dic43—21no—
394C2×Dic43—21no—
395C2×Dic43—21no—
396C2×Dic43—44no—
397C2×Dic43C2×C22⋊C412yes—
398C2×Dic43C2×C22⋊C412yes—
399C2×Dic43C2×C22⋊C412yes—
400C2×Dic43C4×D412yes—
401D172—44no—
402D172—44no—
403C4×D43—22no—
404C4×D43—22no—
405C4×D43—22no—
406C4×D43—22no—
407C4×D43—22no—
408C4×D43—22no—
409C4×D43—22no—
410C4×D43—22no—
411C4×D43—44no—
412C4×D43—44no—
413C4×D43—41no—
414C4×D43—41no—
415C4×D43—41no—
416C4×D43—41no—
417Dic86—44no—
418C8×C43—22no—
419C8×C43—41no—
420C8×C43—41no—
421C8×C43—41no—
422C43⋊C8—22no—
423C43⋊C8—41no—
424C43⋊C8—41no—
425C43⋊C8—41no—
426#22400—431nomaximal, Sylow
427C22×C43—22no—
428C22×C43—22no—
429C22×C43—22no—
430C22×C43—22no—
431C22×C43—22no—
432C22×C43—22no—
433C22×C43—41no—
434C22×C43—41no—
435C22×C43—41no—
436C22×C43—41no—
437C22×C43—41no—
438C22×C43—41no—
439C22×C43—41no—
440C22×C43—41no—
441C22×C43C22×C22⋊C411yescharacteristic
442C22×C43C2×C4×D411yescharacteristic
443C22×C43#51811yescharacteristic
444C22×C43C2×#13111yescharacteristic
445C22×C43#56811yescharacteristic
446C22×C43#56811yescharacteristic
447C22×C43#56811yescharacteristic
448C2×D43—22no—
449C2×D43—22no—
450C2×D43—22no—
451C2×D43—22no—
452C2×D43—22no—
453C2×D43—22no—
454C2×D43—416no—
455C2×D43—41no—
456C2×D43—41no—
457C2×D43—41no—
458C2×D43—41no—
459C2×D43—41no—
460C2×D43—41no—
461C2×D43—41no—
462C2×D43—41no—
463C2×D43—41no—
464C2×D43—41no—
465C2×D43—41no—
466C2×D43—41no—
467C2×D43—41no—
468C2×D43—41no—
469C2×D43—41no—
470C4×C43—22no—
471C4×C43—41no—
472C4×C43—41no—
473C4×C43—41no—
474C4×C43D4211yescharacteristic
475C4×C43D4211yescharacteristic
476C4×C43#54611yescharacteristic
477C4×C43#54611yescharacteristic
478Dic43—22no—
479Dic43—22no—
480Dic43—22no—
481Dic43—22no—
482Dic43—41no—
483C2×#525—431no—
484C2×#436—431no—
485C2×#435—431no—
486C2×#408—431no—
487C2×#407—431no—
488#1955—431no—
489#1954—431no—
490#1870—431no—
491#1870—431no—
492#1870—431no—
493#1869D4311yescharacteristic, complemented
494#1798—431no—
495#1780—431no—
496#1779—431no—
497#1750—431no—
498C2×C43—42no—
499C2×C43—42no—
500C2×C43D4×C22⋊C411yescharacteristic
501C2×C43#287911yescharacteristic
502C2×C43#288011yescharacteristic
503C2×C43#293011yescharacteristic
504C2×C43#293311yescharacteristic
505C2×C43#297611yescharacteristic
506C2×C43#297811yescharacteristic
507D43—42no—
508D43—42no—
509D43—81no—
510C22×#41—431no—
511C24×C4—431no—
512C22×M16—431no—
513C22×M16—431no—
514C22×M16—431no—
515C23×C8C2×D4311yescharacteristic, complemented
516#525—864no—
517#525—864no—
518C2×#123—431no—
519C2×#123—431no—
520C2×C22⋊Q8—431no—
521C2×C22⋊Q8—431no—
522C2×#121—431no—
523C2×#121—431no—
524C2×#120—431no—
525C2×#120—431no—
526C2×C4×D4—431no—
527C2×C4×D4—431no—
528C2×C4×D4—431no—
529C2×C4×D4C2×D4311yescharacteristic
530C2×#117—431no—
531#436—864no—
532#435—864no—
533C2×C4⋊C8—431no—
534C2×C4⋊C8—431no—
535#408—864no—
536#407—864no—
537C2×C22⋊C8—431no—
538C2×C22⋊C8—431no—
539C2×C22⋊C8—431no—
540C2×C22⋊C8—431no—
541C2×C22⋊C8—431no—
542C2×C22⋊C8—431no—
543C2×C22⋊C8—431no—
544C2×C22⋊C8—431no—
545C2×C22⋊C8—431no—
546C2×C22⋊C8—431no—
547C2×C22⋊C8—431no—
548C2×C22⋊C8—431no—
549C2×C22⋊C8—431no—
550C2×C22⋊C8C2×D4311yescharacteristic
551C2×C22⋊C8C2×D4311yescharacteristic
552C2×C22⋊C8C2×D4311yescharacteristic, complemented
553C2×#97—431no—
554C2×C4×C8—431no—
555#336—431no—
556#336—431no—
557#336C2×D4311yescharacteristic, complemented
558#336C2×D4311yescharacteristic, complemented
559C43#2240011yescharacteristic, complemented, Sylow
560C25—431no—
561C2×#41—862no—
562C2×#41—862no—
563C2×#41—862no—
564C2×#41—862no—
565C2×#41—1721no—
566C2×#41—1721no—
567C22×Q8—431no—
568C22×D4—431no—
569C22×D4—431no—
570C22×D4—431no—
571C22×D4—431no—
572C22×D4—431no—
573C22×D4—431no—
574C22×D4C4×D4311yescharacteristic
575C23×C4—431no—
576C23×C4—431no—
577C23×C4—431no—
578C23×C4—431no—
579C23×C4—431no—
580C23×C4—431no—
581C23×C4—862no—
582C23×C4—862no—
583C23×C4—862no—
584C23×C4—862no—
585C23×C4—1721no—
586C23×C4—1721no—
587C23×C4C22×D4311yescharacteristic
588C23×C4C22×D4311yescharacteristic
589C2×M16—862no—
590C2×M16—862no—
591C2×M16—862no—
592C2×M16—862no—
593C2×M16—862no—
594C2×M16—862no—
595C2×M16—1721no—
596C2×M16—1721no—
597C2×M16—1721no—
598C22×C8—22no—
599C22×C8—22no—
600C22×C8—41no—
601C22×C8—431no—
602C22×C8—431no—
603C22×C8—431no—
604C22×C8—431no—
605C22×C8C22×D4311yescharacteristic
606C22×C8C22×D4311yescharacteristic
607C22×C8C22×D4311yescharacteristic
608C22×C8C22×D4311yescharacteristic
609#123—864no—
610#123—864no—
611C22⋊Q8—864no—
612C22⋊Q8—864no—
613#121—864no—
614#121—864no—
615#120—864no—
616#120—864no—
617C4×D4—22no—
618C4×D4—22no—
619C4×D4—434no—
620C4×D4—434no—
621C4×D4—862no—
622C4×D4—862no—
623C4×D4—862no—
624C4×D4—862no—
625#117—862no—
626#117—862no—
627C2×C4⋊C4—431no—
628C2×C4⋊C4—431no—
629C2×C4⋊C4—431no—
630C2×C4⋊C4—431no—
631C2×C4⋊C4—431no—
632C2×C4⋊C4C4×D4311yescharacteristic
633C2×C22⋊C4—431no—
634C2×C22⋊C4—431no—
635C2×C22⋊C4—431no—
636C2×C22⋊C4—431no—
637C2×C22⋊C4—431no—
638C2×C22⋊C4—431no—
639C2×C22⋊C4—431no—
640C2×C22⋊C4—431no—
641C2×C22⋊C4C4×D4311yescharacteristic
642C2×C22⋊C4C4×D4311yescharacteristic
643C2×C42—431no—
644C2×C42C22×D4311yescharacteristic
645C4⋊C8—862no—
646C4⋊C8—862no—
647C22⋊C8—22no—
648C22⋊C8—22no—
649C22⋊C8—41no—
650C22⋊C8—434no—
651C22⋊C8—862no—
652C22⋊C8—862no—
653C22⋊C8—862no—
654C22⋊C8—862no—
655C22⋊C8—862no—
656C22⋊C8—862no—
657C22⋊C8—862no—
658C22⋊C8—862no—
659C22⋊C8—862no—
660C22⋊C8—1721no—
661C22⋊C8—1721no—
662C22⋊C8—1721no—
663#97—862no—
664C4×C8—862no—
665C24—431no—
666C24—431no—
667C24—431no—
668C24—862no—
669C24—862no—
670C24—862no—
671C24—1721no—
672C24—1721no—
673C24—1721no—
674C24—1721no—
675C24C2×C4×D4311yescharacteristic
676C24C2×C4×D4311yescharacteristic
677#41—1724no—
678#41—1724no—
679#41—1724no—
680#41—1724no—
681C2×Q8—862no—
682C2×Q8—862no—
683C2×Q8—1721no—
684C2×D4—22no—
685C2×D4—22no—
686C2×D4—41no—
687C2×D4—434no—
688C2×D4—862no—
689C2×D4—862no—
690C2×D4—862no—
691C2×D4—862no—
692C2×D4—862no—
693C2×D4—862no—
694C2×D4—862no—
695C2×D4—862no—
696C2×D4—862no—
697C2×D4—1721no—
698C2×D4—1721no—
699C2×D4—1721no—
700C2×D4—1721no—
701C2×D4—1721no—
702C2×D4—1721no—
703C2×D4—1721no—
704C2×D4—1721no—
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—431no—
716C22×C4—431no—
717C22×C4—431no—
718C22×C4—431no—
719C22×C4—432no—
720C22×C4—432no—
721C22×C4—432no—
722C22×C4—432no—
723C22×C4—431no—
724C22×C4—862no—
725C22×C4—862no—
726C22×C4—862no—
727C22×C4—862no—
728C22×C4—862no—
729C22×C4—862no—
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×C4—861no—
744C22×C4—1721no—
745C22×C4—1721no—
746C22×C4—1724no—
747C22×C4—1724no—
748C22×C4—1724no—
749C22×C4—1724no—
750C22×C4—1721no—
751C22×C4C2×C4×D4311yescharacteristic
752C22×C4C2×C4×D4311yescharacteristic
753C22×C4C2×C4×D4311yescharacteristic
754C22×C4C2×C4×D4311yescharacteristic
755C22×C4D4×D4312yes—
756C22×C4D4×D4312yes—
757C22×C4C23×D4311yescharacteristic
758M16—1724no—
759M16—1724no—
760M16—1724no—
761C2×C8—21no—
762C2×C8—21no—
763C2×C8—21no—
764C2×C8—21no—
765C2×C8—21no—
766C2×C8—21no—
767C2×C8—21no—
768C2×C8—21no—
769C2×C8—21no—
770C2×C8—21no—
771C2×C8—21no—
772C2×C8—44no—
773C2×C8—432no—
774C2×C8—861no—
775C2×C8—861no—
776C2×C8—861no—
777C2×C8—861no—
778C2×C8—861no—
779C2×C8—861no—
780C2×C8—861no—
781C2×C8—861no—
782C2×C8—861no—
783C2×C8—861no—
784C2×C8—861no—
785C2×C8D4×D4312yes—
786C4⋊C4—22no—
787C4⋊C4—434no—
788C4⋊C4—862no—
789C4⋊C4—862no—
790C4⋊C4—862no—
791C4⋊C4—862no—
792C22⋊C4—22no—
793C22⋊C4—22no—
794C22⋊C4—434no—
795C22⋊C4—434no—
796C22⋊C4—862no—
797C22⋊C4—862no—
798C22⋊C4—862no—
799C22⋊C4—862no—
800C22⋊C4—862no—
801C22⋊C4—862no—
802C42—21no—
803C42—21no—
804C42—432no—
805C42—432no—
806C23—21no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—21no—
817C23—21no—
818C23—432no—
819C23—432no—
820C23—861no—
821C23—861no—
822C23—861no—
823C23—861no—
824C23—861no—
825C23—861no—
826C23—861no—
827C23—861no—
828C23—861no—
829C23—861no—
830C23—861no—
831C23—861no—
832C23—861no—
833C23—861no—
834C23—861no—
835C23—861no—
836C23—861no—
837C23—861no—
838C23—861no—
839C23—1724no—
840C23—1724no—
841C23—1724no—
842C23—1724no—
843C23—1724no—
844C23—1724no—
845C23—1724no—
846C23C22⋊C4×D4312yes—
847C23#1306333112yes—
848C23C22×C4×D4311yescharacteristic
849Q8—1724no—
850D4—44no—
851D4—1724no—
852D4—1724no—
853D4—1724no—
854D4—1724no—
855D4—1724no—
856D4—1724no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—432no—
877C2×C4—432no—
878C2×C4—432no—
879C2×C4—432no—
880C2×C4—861no—
881C2×C4—861no—
882C2×C4—861no—
883C2×C4—861no—
884C2×C4—861no—
885C2×C4—861no—
886C2×C4—861no—
887C2×C4—861no—
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—861no—
897C2×C4—861no—
898C2×C4—861no—
899C2×C4—1724no—
900C2×C4—1724no—
901C2×C4—1724no—
902C2×C4—1721no—
903C2×C4—1721no—
904C2×C4—1721no—
905C2×C4—1721no—
906C2×C4C22⋊C4×D4312yes—
907C2×C4C2×D4×D4311yescharacteristic
908C2×C4C2×D4×D4311yescharacteristic
909C2×C4C2×D4×D4311yescharacteristic
910C2×C4#41×D4311yescharacteristic
911C2×C4#1306337011yescharacteristic
912C2×C4#1306337111yescharacteristic
913C8—22no—
914C8—41no—
915C8—41no—
916C8—41no—
917C8—862no—
918C8—1721no—
919C8—1721no—
920C8—1721no—
921C22—22no—
922C22—22no—
923C22—22no—
924C22—22no—
925C22—22no—
926C22—22no—
927C22—41no—
928C22—41no—
929C22—41no—
930C22—41no—
931C22—41no—
932C22—41no—
933C22—41no—
934C22—41no—
935C22—862no—
936C22—862no—
937C22—862no—
938C22—862no—
939C22—862no—
940C22—862no—
941C22—17216no—
942C22—1721no—
943C22—1721no—
944C22—1721no—
945C22—1721no—
946C22—1721no—
947C22—1721no—
948C22—1721no—
949C22—1721no—
950C22—1721no—
951C22—1721no—
952C22—1721no—
953C22—1721no—
954C22—1721no—
955C22—1721no—
956C22—1721no—
957C22C2×C22⋊C4×D4311yescharacteristic
958C22C4×D4×D4311yescharacteristic
959C22#1458337111yescharacteristic
960C22C2×#1306333111yescharacteristic
961C22#1458366411yescharacteristic
962C22#1458366411yescharacteristic
963C22#1458366511yescharacteristic
964C4—22no—
965C4—41no—
966C4—41no—
967C4—41no—
968C4—862no—
969C4—862no—
970C4—862no—
971C4—862no—
972C4—1721no—
973C4#1458353111yescharacteristic
974C4#1458353311yescharacteristic
975C4#1458353811yescharacteristic
976C4#1458354111yescharacteristic
977C2—42no—
978C2—42no—
979C2—3441no—
980C2—1722no—
981C2—1722no—
982C2#1913741311yescharacteristic
983C2#1914303711yescharacteristic
984C2#1914304111yescharacteristic
985C2#1914329311yescharacteristic
986C2#1914331511yescharacteristic
987C2#1914363711yescharacteristic
988C2#1914365411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D43
commutator, socleC23×C43C23×C4
FittingC43×#1869C2
prime radicalC2×#14583408C2
cosocleC22×C4×C43C24
hypercenter#1869D43
hypocenterC43#22400
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ #1869

Complements

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

NH ≅ G/Ntype
2. C2×#14582974C2semidirect
3. C2×#14582970C2semidirect
4. C2×#14582865C2semidirect
5. C2×#14582861C2semidirect
6. #19135391C2semidirect
7. #19135387C2semidirect
8. #19134893C2semidirect
9. #19134891C2semidirect
10. #19134891C2semidirect
11. #19134578C2semidirect
12. #19134506C2semidirect
13. #19134504C2semidirect
14. #19134360C2semidirect
15. C43×#1869C2semidirect
18. C22×#10621877C22semidirect
37. C2×Dic43⋊C8C22semidirect
38. C2×Dic43⋊C8C22semidirect
43. C2×C22⋊(C43⋊C8)C22semidirect
50. C2×(C2×D43)⋊C8C22semidirect
51. C2×(C2×D43)⋊C8C22semidirect
52. C2×(C2×D43)⋊C8C22semidirect
53. C2×(C2×D43)⋊C8C22semidirect
54. C2×#13063235C22semidirect
55. C2×C8×Dic43C22semidirect
56. #14582654C22semidirect
57. #14582654C22semidirect
58. C23×C8×C43C22semidirect
62. C2×C22⋊C8×C43C22semidirect
63. C43×#336C22semidirect
64. C43×#336C22semidirect
148. (C2×D43)⋊C8D4semidirect
493. #1869D43semidirect
515. C23×C8C2×D43semidirect
552. C2×C22⋊C8C2×D43semidirect
557. #336C2×D43semidirect
558. #336C2×D43semidirect
559. C43#22400semidirect

Maximal subgroups

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

subgroupindex
C2×#145834082
C2×#145829742
C2×#145829702
C2×#145828652
C2×#145828612
#191353912
#191353872
#191348932
#191348912
#191345782
#191345062
#191345042
#191343602
C43×#18692
#2240043