Finite Group Databasebeta

← #25111913

Subgroups — #25111913

Order 11008.

1512 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583446C211yesmaximal, characteristic
2C2×#14582973C211yesmaximal, characteristic, complemented
3C2×#14582970C211yesmaximal, characteristic, complemented
4C2×#14582865C211yesmaximal, characteristic, complemented
5C2×#14582864C211yesmaximal, characteristic, complemented
6#19135391C211yesmaximal, characteristic, complemented
7#19135391C211yesmaximal, characteristic, complemented
8#19134893C211yesmaximal, characteristic, complemented
9#19134891C211yesmaximal, characteristic, complemented
10#19134886C211yesmaximal, characteristic, complemented
11#19134574C211yesmaximal, characteristic, complemented
12#19134506C211yesmaximal, characteristic, complemented
13#19134506C211yesmaximal, characteristic, complemented
14#19134356C211yesmaximal, characteristic, complemented
15C43×#1869C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C22×#10621898C2211yescharacteristic
18C22×#10621877C2211yescharacteristic
19C22×#10621872C2211yescharacteristic
20C22×C8×D43C2211yescharacteristic
21#14583446—24no—
22#14583446—24no—
23C2×#13063324C411yescharacteristic
24C2×#13063321C411yescharacteristic
25C2×#13063311C411yescharacteristic
26C2×#13063311C411yescharacteristic
27C2×#13063300C411yescharacteristic
28C2×#13063298C411yescharacteristic
29C2×#13063298C411yescharacteristic
30C2×#13063296C411yescharacteristic
31C2×C4×D172C2211yescharacteristic
32C2×C4×C22⋊D43C2211yescharacteristic
33C2×C4×C22⋊D43C2211yescharacteristic
34C2×C42×D43C2211yescharacteristic
35#14582973—24no—
36#14582970—24no—
37C2×Dic43⋊C8C2211yescharacteristic
38C2×Dic43⋊C8C2211yescharacteristic
39#14582865—24no—
40#14582864—24no—
41C2×C22⋊(C43⋊C8)C2211yescharacteristic
42C2×C22⋊(C43⋊C8)C2211yescharacteristic
43C2×C22⋊(C43⋊C8)C2211yescharacteristic
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
51C2×(C2×D43)⋊C8C2211yescharacteristic
52C2×(C2×D43)⋊C8C2211yescharacteristic
53C2×(C2×D43)⋊C8C2211yescharacteristic
54C2×#13063235C2211yescharacteristic
55C2×#13063235C2211yescharacteristic
56#14582654C2211yescharacteristic
57#14582654C2211yescharacteristic
58C23×C8×C43C2211yescharacteristic
59C2×C4×D4×C43C2211yescharacteristic
60C2×C22⋊C8×C43C2211yescharacteristic
61C2×C22⋊C8×C43C2211yescharacteristic
62C2×C22⋊C8×C43C2211yescharacteristic
63C43×#336C2211yescharacteristic
64C43×#336C2211yescharacteristic
65C2×#10621898—22no—
66C2×#10621898—22no—
67C2×#10621898—22no—
68C2×#10621898—22no—
69C2×#10621898—22no—
70C2×#10621898—22no—
71C2×#10621898—22no—
72C2×#10621898—22no—
73C2×#10621898—41no—
74C2×#10621898—41no—
75C2×#10621898—41no—
76C2×#10621898—41no—
77C22×Dic86C2×C411yescharacteristic
78C22×Dic86C2×C411yescharacteristic
79C22×D172C2×C411yescharacteristic
80C22×D172C2×C411yescharacteristic
81C22×D172C2×C411yescharacteristic
82C22×C22⋊D43C2×C411yescharacteristic
83C22×C22⋊D43C2×C411yescharacteristic
84C22×C22⋊D43C2×C411yescharacteristic
85C22×C22⋊D43C2×C411yescharacteristic
86C22×C22⋊D43C2×C411yescharacteristic
87C22×C22⋊D43C2×C411yescharacteristic
88C22×C4×D43C2×C411yescharacteristic
89C22×C4×D43C2×C411yescharacteristic
90C22×C4×D43C2311yescharacteristic
91C22×C4×D43C2311yescharacteristic
92C22×C4×D43C2311yescharacteristic
93C2×#10621877—22no—
94C2×#10621877—22no—
95C2×#10621877—41no—
96C2×#10621872—22no—
97C2×#10621872—22no—
98C2×#10621872—41no—
99C22×C43⋊C8C2311yescharacteristic
100C22×C43⋊C8C2311yescharacteristic
101C22×C43⋊C8C2311yescharacteristic
102C22×C43⋊C8C2311yescharacteristic
103C2×C8×D43—22no—
104C2×C8×D43—22no—
105C2×C8×D43—41no—
106#13063324—24no—
107#13063321—24no—
108#13063311—24no—
109#13063311—24no—
110#13063300—24no—
111#13063298—24no—
112#13063298—24no—
113#13063296—24no—
114C4×D172—22no—
115C4×D172—22no—
116C4×C22⋊D43—22no—
117C4×C22⋊D43—22no—
118C4×C22⋊D43D414yes—
119C4×C22⋊D43D414yes—
120C2×C4⋊Dic43C2×C411yescharacteristic
121C2×Dic43⋊C4C2×C411yescharacteristic
122C2×Dic43⋊C4C2×C411yescharacteristic
123C2×C22⋊Dic43C2×C411yescharacteristic
124C2×C22⋊Dic43C2×C411yescharacteristic
125C2×(C2×D43)⋊C4C2×C411yescharacteristic
126C2×(C2×D43)⋊C4C2×C411yescharacteristic
127C2×(C2×D43)⋊C4C2×C411yescharacteristic
128C2×(C2×D43)⋊C4C2×C411yescharacteristic
129C2×C4×Dic43C2×C411yescharacteristic
130C2×C4×Dic43C2×C411yescharacteristic
131C2×C4×Dic43C2311yescharacteristic
132C42×D43—22no—
133C42×D43—22no—
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—
150#13063235—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×D43C22×C411yescharacteristic
173C23×D43C22×C411yescharacteristic
174C23×D43C22×C411yescharacteristic
175C2×D4×C43—22no—
176C2×D4×C43—22no—
177C2×D4×C43—41no—
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×C43C22×C411yescharacteristic
189C22×C4×C43C22×C411yescharacteristic
190C22×C4×C43C22×C411yescharacteristic
191C22×C4×C43C22×C411yescharacteristic
192C22×C4×C43C2×D412yes—
193C22×C4×C43C2×D412yes—
194C22×C4×C43C2411yescharacteristic
195C2×C22⋊D43—22no—
196C2×C22⋊D43—22no—
197C2×C22⋊D43—22no—
198C2×C22⋊D43—22no—
199C2×C22⋊D43—22no—
200C2×C22⋊D43—22no—
201C2×C22⋊D43—22no—
202C2×C22⋊D43—22no—
203C2×C22⋊D43—22no—
204C2×C22⋊D43—41no—
205C2×C22⋊D43—41no—
206C2×C22⋊D43—41no—
207C2×C22⋊D43—41no—
208C2×C22⋊D43—41no—
209C2×C22⋊D43—41no—
210C2×C22⋊D43—41no—
211C2×C22⋊D43—41no—
212C2×C22⋊D43C22⋊C414yes—
213C22×Dic43C22×C411yescharacteristic
214C22×Dic43C22×C411yescharacteristic
215C22×Dic43C22×C411yescharacteristic
216C22×Dic43C22×C411yescharacteristic
217C22×Dic43C22×C411yescharacteristic
218#10621898—44no—
219#10621898—44no—
220#10621898—44no—
221#10621898—44no—
222#10621898—44no—
223#10621898—44no—
224#10621898—44no—
225#10621898—44no—
226C2×D172—22no—
227C2×D172—22no—
228C2×D172—22no—
229C2×D172—22no—
230C2×D172—22no—
231C2×D172—22no—
232C2×D172—41no—
233C2×D172—41no—
234C2×D172—41no—
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—22no—
244C2×C4×D43—21no—
245C2×C4×D43—21no—
246C2×C4×D43—21no—
247C2×C4×D43—21no—
248C2×C4×D43—21no—
249C2×C4×D43—21no—
250C2×C4×D43—22no—
251C2×C4×D43—22no—
252C2×C4×D43—41no—
253C2×C4×D43—41no—
254C2×C4×D43—41no—
255C2×C4×D43C2×D412yes—
256C2×C4×D43C2×D412yes—
257C2×C4×D43C2×D412yes—
258C2×C4×D43#4112yes—
259C2×Dic86—22no—
260C2×Dic86—22no—
261C2×Dic86—22no—
262C2×Dic86—22no—
263C2×Dic86—41no—
264C2×Dic86—41no—
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—21no—
275C2×C8×C43—21no—
276C2×C8×C43—44no—
277C2×C8×C43C2×D412yes—
278C4⋊C4×C43—22no—
279C22⋊C4×C43—22no—
280C22⋊C4×C43—22no—
281C42×C43—21no—
282C42×C43—21no—
283C22⋊Dic43—22no—
284C22⋊Dic43C22⋊C414yes—
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⋊C4C22⋊C414yes—
292C4×Dic43—22no—
293C4×Dic43—22no—
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—
310C8×D43—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×C43—21no—
324C23×C43C2×C22⋊C412yes—
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×D43C2×C22⋊C412yes—
346C22×D43C4×D412yes—
347D4×C43—44no—
348C2×C4×C43—21no—
349C2×C4×C43—21no—
350C2×C4×C43—21no—
351C2×C4×C43—21no—
352C2×C4×C43—22no—
353C2×C4×C43—22no—
354C2×C4×C43—22no—
355C2×C4×C43—22no—
356C2×C4×C43—21no—
357C2×C4×C43—21no—
358C2×C4×C43—21no—
359C2×C4×C43—21no—
360C2×C4×C43—21no—
361C2×C4×C43—21no—
362C2×C4×C43—41no—
363C2×C4×C43—41no—
364C2×C4×C43—41no—
365C2×C4×C43—41no—
366C2×C4×C43C2×C22⋊C412yes—
367C2×C4×C43#13112yes—
368C2×C4×C43C22×D411yescharacteristic
369C2×C4×C43C22×D411yescharacteristic
370C2×C4×C43C22×D411yescharacteristic
371C2×C4×C43C2×#4111yescharacteristic
372C2×C4×C43H(5,𝔽2)11yescharacteristic
373C2×C4×C43H(5,𝔽2)11yescharacteristic
374C22⋊D43—44no—
375C22⋊D43—44no—
376C22⋊D43—44no—
377C22⋊D43—44no—
378C22⋊D43—44no—
379C22⋊D43—44no—
380C2×Dic43—21no—
381C2×Dic43—21no—
382C2×Dic43—21no—
383C2×Dic43—21no—
384C2×Dic43—21no—
385C2×Dic43—21no—
386C2×Dic43—21no—
387C2×Dic43—21no—
388C2×Dic43—21no—
389C2×Dic43—21no—
390C2×Dic43—21no—
391C2×Dic43C2×C22⋊C412yes—
392C2×Dic43C2×C22⋊C412yes—
393C2×Dic43C2×C22⋊C412yes—
394C2×Dic43C4×D412yes—
395D172—44no—
396D172—44no—
397D172—44no—
398C4×D43—22no—
399C4×D43—22no—
400C4×D43—22no—
401C4×D43—22no—
402C4×D43—22no—
403C4×D43—22no—
404C4×D43—22no—
405C4×D43—22no—
406C4×D43—44no—
407C4×D43—44no—
408C4×D43—41no—
409C4×D43—41no—
410C4×D43—41no—
411C4×D43—41no—
412Dic86—44no—
413Dic86—44no—
414C8×C43—22no—
415C8×C43—41no—
416C8×C43—41no—
417C8×C43—41no—
418C43⋊C8—22no—
419C43⋊C8—41no—
420C43⋊C8—41no—
421C43⋊C8—41no—
422#22403—431nomaximal, Sylow
423C22×C43—22no—
424C22×C43—22no—
425C22×C43—22no—
426C22×C43—41no—
427C22×C43—41no—
428C22×C43—41no—
429C22×C43—41no—
430C22×C43—41no—
431C22×C43—41no—
432C22×C43—41no—
433C22×C43—41no—
434C22×C43—41no—
435C22×C43—41no—
436C22×C43—41no—
437C22×C43C22×C22⋊C411yescharacteristic
438C22×C43C2×C4×D411yescharacteristic
439C22×C43#51811yescharacteristic
440C22×C43C2×#13111yescharacteristic
441C22×C43#56811yescharacteristic
442C22×C43#56811yescharacteristic
443C22×C43#56811yescharacteristic
444C2×D43—22no—
445C2×D43—22no—
446C2×D43—22no—
447C2×D43—22no—
448C2×D43—22no—
449C2×D43—22no—
450C2×D43—41no—
451C2×D43—41no—
452C2×D43—41no—
453C2×D43—41no—
454C2×D43—41no—
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—
465C4×C43—22no—
466C4×C43—22no—
467C4×C43—41no—
468C4×C43—41no—
469C4×C43D4211yescharacteristic
470C4×C43D4211yescharacteristic
471C4×C43#54611yescharacteristic
472C4×C43#54611yescharacteristic
473Dic43—22no—
474Dic43—22no—
475Dic43—22no—
476Dic43—22no—
477Dic43—41no—
478C2×#532—431no—
479C2×#435—431no—
480C2×#435—431no—
481C2×#408—431no—
482C2×#408—431no—
483#1955—431no—
484#1955—431no—
485#1870—431no—
486#1870—431no—
487#1869—431no—
488#1869D4311yescharacteristic, complemented
489#1797—431no—
490#1780—431no—
491#1780—431no—
492#1749—431no—
493C2×C43—42no—
494C2×C43—81no—
495C2×C43D4×C22⋊C411yescharacteristic
496C2×C43#287911yescharacteristic
497C2×C43#288011yescharacteristic
498C2×C43#293211yescharacteristic
499C2×C43#293511yescharacteristic
500C2×C43#298011yescharacteristic
501C2×C43#298111yescharacteristic
502D43—42no—
503D43—42no—
504D43—81no—
505C22×#41—431no—
506C22×#41—431no—
507C22×M16—431no—
508C22×M16—431no—
509C23×C8—431no—
510C23×C8C2×D4311yescharacteristic
511#532—864no—
512#532—864no—
513C2×C4⋊Q8—431no—
514C2×#127—431no—
515C2×#124—431no—
516C2×#124—431no—
517C2×#121—431no—
518C2×#121—431no—
519C2×#121—431no—
520C2×#121—431no—
521C2×C4×D4—431no—
522C2×C4×D4—431no—
523C2×C4×D4—431no—
524C2×C4×D4C2×D4311yescharacteristic
525C22×C42—431no—
526#435—864no—
527#435—864no—
528C2×C4⋊C8—431no—
529C2×C4⋊C8—431no—
530#408—864no—
531#408—864no—
532C2×C22⋊C8—431no—
533C2×C22⋊C8—431no—
534C2×C22⋊C8—431no—
535C2×C22⋊C8—431no—
536C2×C22⋊C8—431no—
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⋊C8C2×D4311yescharacteristic
546C2×C22⋊C8C2×D4311yescharacteristic
547C2×C22⋊C8C2×D4311yescharacteristic
548C2×#97—431no—
549C2×#97—431no—
550#336—431no—
551#336—431no—
552#336C2×D4311yescharacteristic
553#336C2×D4311yescharacteristic
554C43#2240311yescharacteristic, complemented, Sylow
555C2×#41—862no—
556C2×#41—862no—
557C2×#41—862no—
558C2×#41—862no—
559C2×#41—862no—
560C2×#41—862no—
561C2×#41—862no—
562C2×#41—862no—
563C2×#41—1721no—
564C2×#41—1721no—
565C2×#41—1721no—
566C2×#41—1721no—
567C22×Q8—431no—
568C22×Q8—431no—
569C22×D4—431no—
570C22×D4—431no—
571C22×D4—431no—
572C22×D4—431no—
573C22×D4—431no—
574C22×D4—431no—
575C22×D4—431no—
576C22×D4—431no—
577C22×D4—431no—
578C22×D4C4×D4311yescharacteristic
579C23×C4—431no—
580C23×C4—431no—
581C23×C4—431no—
582C23×C4—431no—
583C23×C4—431no—
584C23×C4C22×D4311yescharacteristic
585C23×C4C22×D4311yescharacteristic
586C2×M16—862no—
587C2×M16—862no—
588C2×M16—862no—
589C2×M16—862no—
590C2×M16—1721no—
591C2×M16—1721no—
592C22×C8—22no—
593C22×C8—22no—
594C22×C8—41no—
595C22×C8—431no—
596C22×C8—431no—
597C22×C8—431no—
598C22×C8—431no—
599C22×C8—862no—
600C22×C8—862no—
601C22×C8—1721no—
602C22×C8C22×D4311yescharacteristic
603C22×C8C22×D4311yescharacteristic
604C22×C8C22×D4311yescharacteristic
605C22×C8C22×D4311yescharacteristic
606C4⋊Q8—864no—
607#127—864no—
608#124—864no—
609#124—864no—
610#121—864no—
611#121—864no—
612#121—864no—
613#121—864no—
614C4×D4—22no—
615C4×D4—22no—
616C4×D4—434no—
617C4×D4—434no—
618C4×D4—862no—
619C4×D4—862no—
620C4×D4—862no—
621C4×D4—862no—
622C2×C4⋊C4—431no—
623C2×C4⋊C4—431no—
624C2×C4⋊C4—431no—
625C2×C4⋊C4C4×D4311yescharacteristic
626C2×C22⋊C4—431no—
627C2×C22⋊C4—431no—
628C2×C22⋊C4—431no—
629C2×C22⋊C4—431no—
630C2×C22⋊C4—431no—
631C2×C22⋊C4—431no—
632C2×C22⋊C4C4×D4311yescharacteristic
633C2×C22⋊C4C4×D4311yescharacteristic
634C2×C42—431no—
635C2×C42—431no—
636C2×C42—431no—
637C2×C42—862no—
638C2×C42—862no—
639C2×C42C22×D4311yescharacteristic
640C4⋊C8—862no—
641C4⋊C8—862no—
642C22⋊C8—22no—
643C22⋊C8—22no—
644C22⋊C8—41no—
645C22⋊C8—434no—
646C22⋊C8—862no—
647C22⋊C8—862no—
648C22⋊C8—862no—
649C22⋊C8—862no—
650C22⋊C8—862no—
651C22⋊C8—862no—
652C22⋊C8—862no—
653C22⋊C8—862no—
654C22⋊C8—862no—
655C22⋊C8—1721no—
656C22⋊C8—1721no—
657C22⋊C8—1721no—
658#97—862no—
659#97—862no—
660C24—431no—
661C24—431no—
662C24—431no—
663C24C2×C4×D4311yescharacteristic
664C24C2×C4×D4311yescharacteristic
665#41—1724no—
666#41—1724no—
667#41—1724no—
668#41—1724no—
669#41—1724no—
670#41—1724no—
671#41—1724no—
672#41—1724no—
673C2×Q8—862no—
674C2×Q8—862no—
675C2×Q8—862no—
676C2×Q8—862no—
677C2×Q8—1721no—
678C2×Q8—1721no—
679C2×D4—22no—
680C2×D4—22no—
681C2×D4—41no—
682C2×D4—434no—
683C2×D4—862no—
684C2×D4—862no—
685C2×D4—862no—
686C2×D4—862no—
687C2×D4—862no—
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—862no—
698C2×D4—1721no—
699C2×D4—1721no—
700C2×D4—1721no—
701C2×D4—1721no—
702C2×D4—1721no—
703C2×D4—1721no—
704C2×D4—1721no—
705C2×D4—1721no—
706C2×D4—1721no—
707C2×D4—1721no—
708C2×D4—1721no—
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—431no—
720C22×C4—431no—
721C22×C4—431no—
722C22×C4—431no—
723C22×C4—432no—
724C22×C4—432no—
725C22×C4—432no—
726C22×C4—432no—
727C22×C4—431no—
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—862no—
739C22×C4—861no—
740C22×C4—861no—
741C22×C4—861no—
742C22×C4—861no—
743C22×C4—861no—
744C22×C4—861no—
745C22×C4—1721no—
746C22×C4—1721no—
747C22×C4—1721no—
748C22×C4C2×C4×D4311yescharacteristic
749C22×C4C2×C4×D4311yescharacteristic
750C22×C4C2×C4×D4311yescharacteristic
751C22×C4C2×C4×D4311yescharacteristic
752C22×C4D4×D4312yes—
753C22×C4D4×D4312yes—
754C22×C4C23×D4311yescharacteristic
755M16—1724no—
756M16—1724no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—21no—
761C2×C8—21no—
762C2×C8—21no—
763C2×C8—21no—
764C2×C8—21no—
765C2×C8—21no—
766C2×C8—21no—
767C2×C8—21no—
768C2×C8—44no—
769C2×C8—432no—
770C2×C8—861no—
771C2×C8—861no—
772C2×C8—861no—
773C2×C8—861no—
774C2×C8—861no—
775C2×C8—861no—
776C2×C8—861no—
777C2×C8—861no—
778C2×C8—861no—
779C2×C8—861no—
780C2×C8—861no—
781C2×C8—1724no—
782C2×C8D4×D4312yes—
783C4⋊C4—22no—
784C4⋊C4—434no—
785C4⋊C4—862no—
786C4⋊C4—862no—
787C22⋊C4—22no—
788C22⋊C4—22no—
789C22⋊C4—434no—
790C22⋊C4—434no—
791C22⋊C4—862no—
792C22⋊C4—862no—
793C22⋊C4—862no—
794C22⋊C4—862no—
795C42—21no—
796C42—21no—
797C42—432no—
798C42—432no—
799C42—862no—
800C42—862no—
801C23—21no—
802C23—21no—
803C23—21no—
804C23—21no—
805C23—21no—
806C23—21no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—432no—
815C23—432no—
816C23—861no—
817C23—861no—
818C23—861no—
819C23—861no—
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—
835C23C22⋊C4×D4312yes—
836C23C22×C4×D4311yescharacteristic
837Q8—1724no—
838Q8—1724no—
839D4—44no—
840D4—1724no—
841D4—1724no—
842D4—1724no—
843D4—1724no—
844D4—1724no—
845D4—1724no—
846D4—1724no—
847D4—1724no—
848D4—1724no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—432no—
868C2×C4—432no—
869C2×C4—432no—
870C2×C4—432no—
871C2×C4—861no—
872C2×C4—861no—
873C2×C4—861no—
874C2×C4—861no—
875C2×C4—861no—
876C2×C4—861no—
877C2×C4—861no—
878C2×C4—861no—
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—861no—
888C2×C4—861no—
889C2×C4—861no—
890C2×C4—1724no—
891C2×C4—1724no—
892C2×C4—1721no—
893C2×C4—1721no—
894C2×C4—1721no—
895C2×C4—1721no—
896C2×C4C22⋊C4×D4312yes—
897C2×C4#1306333112yes—
898C2×C4C2×D4×D4311yescharacteristic
899C2×C4C2×D4×D4311yescharacteristic
900C2×C4C2×D4×D4311yescharacteristic
901C2×C4#41×D4311yescharacteristic
902C2×C4#1306337011yescharacteristic
903C2×C4#1306337111yescharacteristic
904C8—22no—
905C8—41no—
906C8—41no—
907C8—41no—
908C8—862no—
909C8—1721no—
910C8—1721no—
911C8—1721no—
912C22—22no—
913C22—22no—
914C22—22no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—41no—
925C22—41no—
926C22—862no—
927C22—862no—
928C22—862no—
929C22—862no—
930C22—862no—
931C22—862no—
932C22—1721no—
933C22—1721no—
934C22—1721no—
935C22—1721no—
936C22—1721no—
937C22—1721no—
938C22—1721no—
939C22—1721no—
940C22—1721no—
941C22—1721no—
942C22—1721no—
943C22—1721no—
944C22—1721no—
945C22—1721no—
946C22—1721no—
947C22C2×C22⋊C4×D4311yescharacteristic
948C22C4×D4×D4311yescharacteristic
949C22#1458337111yescharacteristic
950C22C2×#1306333111yescharacteristic
951C22#1458366411yescharacteristic
952C22#1458366411yescharacteristic
953C22#1458366511yescharacteristic
954C4—22no—
955C4—22no—
956C4—41no—
957C4—41no—
958C4—862no—
959C4—862no—
960C4—862no—
961C4—862no—
962C4—1721no—
963C4#1458353111yescharacteristic
964C4#1458353311yescharacteristic
965C4#1458353811yescharacteristic
966C4#1458354111yescharacteristic
967C2—42no—
968C2—81no—
969C2—3441no—
970C2—1722no—
971C2—1722no—
972C2#1913741311yescharacteristic
973C2#1914303711yescharacteristic
974C2#1914304111yescharacteristic
975C2#1914330911yescharacteristic
976C2#1914333411yescharacteristic
977C2#1914366311yescharacteristic
978C2#1914366911yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D43
commutator, socleC23×C43C23×C4
FittingC43×#1869C2
prime radicalC2×#14583446C2
cosocleC22×C4×C43C24
hypercenter#1869D43
hypocenterC43#22403
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ #1869

Complements

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

NH ≅ G/Ntype
2. C2×#14582973C2semidirect
3. C2×#14582970C2semidirect
4. C2×#14582865C2semidirect
5. C2×#14582864C2semidirect
6. #19135391C2semidirect
7. #19135391C2semidirect
8. #19134893C2semidirect
9. #19134891C2semidirect
10. #19134886C2semidirect
11. #19134574C2semidirect
12. #19134506C2semidirect
13. #19134506C2semidirect
14. #19134356C2semidirect
15. C43×#1869C2semidirect
148. (C2×D43)⋊C8D4semidirect
488. #1869D43semidirect
554. C43#22403semidirect

Maximal subgroups

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

subgroupindex
C2×#145834462
C2×#145829732
C2×#145829702
C2×#145828652
C2×#145828642
#191353912
#191348932
#191348912
#191348862
#191345742
#191345062
#191343562
C43×#18692
#2240343