Finite Group Databasebeta

← #25065857

Subgroups — #25065857

Order 11008.

588 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143562C211yesmaximal, characteristic
2#19143261C211yesmaximal, characteristic
3#19133386C211yesmaximal, characteristic, complemented
4#19133383C211yesmaximal, characteristic, complemented
5#19133381C211yesmaximal, characteristic, complemented
6#19133378C211yesmaximal, characteristic, complemented
7#19133376C211yesmaximal, characteristic, complemented
8#19133373C211yesmaximal, characteristic, complemented
9#19133363C211yesmaximal, characteristic, complemented
10#19133360C211yesmaximal, characteristic, complemented
11#19133356C211yesmaximal, characteristic, complemented
12#19133348C211yesmaximal, characteristic, complemented
13#19133345C211yesmaximal, characteristic, complemented
14#19133341C211yesmaximal, characteristic, complemented
15C43×#2925C211yesmaximal, characteristic
16#14583030C411yescharacteristic
17#14583030C411yescharacteristic
18#14582977C411yescharacteristic
19#14582977C411yescharacteristic
20#14582971C411yescharacteristic
21#14582971C411yescharacteristic
22#14582971C411yescharacteristic
23#14582971C411yescharacteristic
24#14582960—21no—
25#14582960—21no—
26#14582956C2211yescharacteristic
27#14582956C2211yescharacteristic
28#14582952C2211yescharacteristic
29#14582952C2211yescharacteristic
30#14582952C2211yescharacteristic
31#14582952C2211yescharacteristic
32#14582952C2211yescharacteristic
33#14582923C2211yescharacteristic
34C2×C4⋊(C43⋊C8)C2211yescharacteristic
35#14582866—21no—
36#14582855—21no—
37C4×#10621877C2211yescharacteristic
38C4×#10621877C2211yescharacteristic
39C2×C4×C43⋊C8C2211yescharacteristic
40#14582651C2211yescharacteristic
41#14582651C2211yescharacteristic
42#14582651C2211yescharacteristic
43#14582651C2211yescharacteristic
44#14582651C2211yescharacteristic
45#14582651C2211yescharacteristic
46#14582651C2211yescharacteristic
47#14582651C2211yescharacteristic
48#14582649C2211yescharacteristic
49#14582649C2211yescharacteristic
50#14582649C2211yescharacteristic
51#14582649C2211yescharacteristic
52#14582649C2211yescharacteristic
53#14582649C2211yescharacteristic
54#14582649C2211yescharacteristic
55#14582649C2211yescharacteristic
56C4×#41×C43C2211yescharacteristic
57C43×#433—21no—
58C43×#433—21no—
59C43×#432C2211yescharacteristic
60C43×#432C2211yescharacteristic
61C43×#431C2211yescharacteristic
62C43×#431C2211yescharacteristic
63C43×#423C2211yescharacteristic
64C2×C4⋊C8×C43C2211yescharacteristic
65C43×#408—21no—
66C43×#405—21no—
67C2×#10621877—21no—
68C2×#10621877C2×C411yescharacteristic
69C2×#10621877C2×C411yescharacteristic
70C2×#10621877C2×C411yescharacteristic
71C2×#10621877C2×C411yescharacteristic
72C22×C43⋊C8—21no—
73C22×C43⋊C8C2×C411yescharacteristic
74C22×C43⋊C8C2×C411yescharacteristic
75C4⋊(C43⋊C8)—21no—
76C4⋊(C43⋊C8)—21no—
77C4⋊(C43⋊C8)C2×C411yescharacteristic
78C4⋊(C43⋊C8)C2×C411yescharacteristic
79C4⋊(C43⋊C8)C2×C411yescharacteristic
80C4⋊(C43⋊C8)C2×C411yescharacteristic
81C4⋊(C43⋊C8)C2×C411yescharacteristic
82C4⋊(C43⋊C8)C2×C411yescharacteristic
83C4⋊(C43⋊C8)C2311yescharacteristic
84C4⋊(C43⋊C8)C2311yescharacteristic
85C4⋊(C43⋊C8)C2311yescharacteristic
86C4⋊(C43⋊C8)C2311yescharacteristic
87C22⋊(C43⋊C8)—21no—
88C22⋊(C43⋊C8)—21no—
89C22⋊(C43⋊C8)—21no—
90C22⋊(C43⋊C8)—21no—
91C22⋊(C43⋊C8)C2×C411yescharacteristic
92C22⋊(C43⋊C8)C2×C411yescharacteristic
93C22⋊(C43⋊C8)C2×C411yescharacteristic
94C22⋊(C43⋊C8)C2×C411yescharacteristic
95C22⋊(C43⋊C8)C2×C411yescharacteristic
96C22⋊(C43⋊C8)C2×C411yescharacteristic
97#13063236—21no—
98#13063236—21no—
99#13063236C2×C411yescharacteristic
100#13063236C2×C411yescharacteristic
101#13063236C2×C411yescharacteristic
102#13063236C2×C411yescharacteristic
103C4×C43⋊C8—21no—
104C4×C43⋊C8—21no—
105C4×C43⋊C8C2×C411yescharacteristic
106C4×C43⋊C8C2×C411yescharacteristic
107C4×C43⋊C8C2311yescharacteristic
108C4×C43⋊C8C2311yescharacteristic
109C4×C43⋊C8C2311yescharacteristic
110C4×C43⋊C8C2311yescharacteristic
111C2×#41×C43D411yescharacteristic
112C2×M16×C43—21no—
113C22×C8×C43—21no—
114C4×Q8×C43C2×C411yescharacteristic
115C4×Q8×C43Q811yescharacteristic
116C4×D4×C43C2×C411yescharacteristic
117C4×D4×C43C2×C411yescharacteristic
118C4×D4×C43C2×C411yescharacteristic
119C4×D4×C43Q811yescharacteristic
120C4×D4×C43Q811yescharacteristic
121C4×D4×C43Q811yescharacteristic
122#117×C43D411yescharacteristic
123#117×C43D411yescharacteristic
124#117×C43D411yescharacteristic
125C2×C42×C43C2311yescharacteristic
126C2×C42×C43C2311yescharacteristic
127C2×C42×C43C2311yescharacteristic
128C4⋊C8×C43—21no—
129C4⋊C8×C43—21no—
130C4⋊C8×C43C2311yescharacteristic
131C4⋊C8×C43C2311yescharacteristic
132C4⋊C8×C43C2311yescharacteristic
133C4⋊C8×C43C2311yescharacteristic
134C22⋊C8×C43—21no—
135C22⋊C8×C43—21no—
136C22⋊C8×C43—21no—
137C22⋊C8×C43—21no—
138#97×C43—21no—
139#97×C43—21no—
140C4×C8×C43—21no—
141C4×C8×C43—21no—
142#41×C43—41no—
143#41×C43—41no—
144C2×Q8×C43C4⋊C411yescharacteristic
145C2×D4×C43C4⋊C411yescharacteristic
146C2×D4×C43C4⋊C411yescharacteristic
147C2×D4×C43C4⋊C411yescharacteristic
148C22×C4×C43C22×C411yescharacteristic
149C22×C4×C43C22×C411yescharacteristic
150C22×C4×C43C22×C411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×Q811yescharacteristic
155C22×C4×C43C2×Q811yescharacteristic
156C22×C4×C43C2×Q811yescharacteristic
157M16×C43—42no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—42no—
163C4⋊C4×C43C4⋊C411yescharacteristic
164C4⋊C4×C43C4⋊C411yescharacteristic
165C4⋊C4×C43C4⋊C411yescharacteristic
166C4⋊C4×C43C4⋊C411yescharacteristic
167C4⋊C4×C43C4⋊C411yescharacteristic
168C4⋊C4×C43C4⋊C411yescharacteristic
169C22⋊C4×C43C4⋊C411yescharacteristic
170C22⋊C4×C43C4⋊C411yescharacteristic
171C22⋊C4×C43C4⋊C411yescharacteristic
172C22⋊C4×C43C4⋊C411yescharacteristic
173C22⋊C4×C43C4⋊C411yescharacteristic
174C22⋊C4×C43C4⋊C411yescharacteristic
175C42×C43C22×C411yescharacteristic
176C42×C43C22×C411yescharacteristic
177C42×C43C22×C411yescharacteristic
178C42×C43C2×D411yescharacteristic
179C42×C43C2×D411yescharacteristic
180C42×C43C2×D411yescharacteristic
181C42×C43C2×Q811yescharacteristic
182C42×C43C2×Q811yescharacteristic
183C42×C43C2×Q811yescharacteristic
184C42×C43C2411yescharacteristic
185#10621877—22no—
186#10621877—22no—
187#10621877—41no—
188#10621877—41no—
189#10621877—42no—
190C2×C43⋊C8—22no—
191C2×C43⋊C8—21no—
192C2×C43⋊C8—21no—
193C2×C43⋊C8—21no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—41no—
196C2×C43⋊C8—42no—
197C2×C43⋊C8C22×C411yescharacteristic
198C2×C43⋊C8C22×C411yescharacteristic
199C2×C43⋊C8C22×C411yescharacteristic
200C2×C43⋊C8C22×C411yescharacteristic
201C2×C43⋊C8C22×C411yescharacteristic
202C2×C43⋊C8C22×C411yescharacteristic
203C2×C43⋊C8C22×C411yescharacteristic
204C2×C43⋊C8C22×C411yescharacteristic
205C23×C43C2×C4⋊C411yescharacteristic
206C23×C43C2×C4⋊C411yescharacteristic
207C23×C43C2×C4⋊C411yescharacteristic
208Q8×C43—41no—
209D4×C43—41no—
210D4×C43—41no—
211D4×C43—41no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43C2×C4⋊C411yescharacteristic
228C2×C4×C43C2×C4⋊C411yescharacteristic
229C2×C4×C43C2×C4⋊C411yescharacteristic
230C2×C4×C43C2×C4⋊C411yescharacteristic
231C2×C4×C43C2×C4⋊C411yescharacteristic
232C2×C4×C43C2×C4⋊C411yescharacteristic
233C2×C4×C43C2×C4⋊C411yescharacteristic
234C2×C4×C43C2×C4⋊C411yescharacteristic
235C2×C4×C43C2×C4⋊C411yescharacteristic
236C2×C4×C43C23×C411yescharacteristic
237C2×C4×C43C22×D411yescharacteristic
238C2×C4×C43C22×Q811yescharacteristic
239C8×C43—41no—
240C8×C43—41no—
241C8×C43—41no—
242C8×C43—41no—
243C43⋊C8—21no—
244C43⋊C8—21no—
245C43⋊C8—21no—
246C43⋊C8—21no—
247C43⋊C8—21no—
248C43⋊C8—21no—
249C43⋊C8—21no—
250C43⋊C8—41no—
251C43⋊C8—41no—
252C43⋊C8—41no—
253C43⋊C8—41no—
254C43⋊C8#13112yes—
255#17831—431nomaximal, Sylow
256C22×C43—21no—
257C22×C43—21no—
258C22×C43—21no—
259C22×C43—21no—
260C22×C43—21no—
261C22×C43—21no—
262C22×C43—21no—
263C22×C43—21no—
264C22×C43—21no—
265C22×C43C22×C4⋊C411yescharacteristic
266C4×C43—21no—
267C4×C43—21no—
268C4×C43—21no—
269C4×C43—21no—
270C4×C43—21no—
271C4×C43—21no—
272C4×C43—21no—
273C4×C43—21no—
274C4×C43—21no—
275C4×C43—21no—
276C4×C43C2×#13111yescharacteristic
277C4×C43#56811yescharacteristic
278C4×C43#57511yescharacteristic
279C4×C43#57511yescharacteristic
280#2965—431no—
281#2925—431no—
282#2925D4311yescharacteristic
283#1574—431no—
284#1574—431no—
285#1573—431no—
286#1573—431no—
287#1572—431no—
288#1572—431no—
289#1569—431no—
290#1569—431no—
291#1568—431no—
292#1565—431no—
293#1565—431no—
294#1564—431no—
295C2×C43—41no—
296C2×C43—41no—
297C2×C43—41no—
298C2×C43#290611yescharacteristic
299C2×C43#291111yescharacteristic
300C2×C43#291611yescharacteristic
301C4×#41C2×D4311yescharacteristic
302#446—431no—
303#446—431no—
304#436—431no—
305#436—431no—
306#435—431no—
307#435—431no—
308#435—431no—
309#435—431no—
310#433—21no—
311#433—21no—
312#433—861no—
313#433—861no—
314#432—431no—
315#432—431no—
316#432C2×D4311yescharacteristic
317#432C2×D4311yescharacteristic
318#431—431no—
319#431—431no—
320#431—431no—
321#431—431no—
322#431—431no—
323#431C2×D4311yescharacteristic
324#431C2×D4311yescharacteristic
325#423—431no—
326#423C2×D4311yescharacteristic
327C2×C4⋊C8—431no—
328C2×C4⋊C8C2×D4311yescharacteristic
329#408—21no—
330#408—861no—
331#405—21no—
332#405—861no—
333C4×M16—431no—
334C4×M16—431no—
335C2×C4×C8—431no—
336#335—431no—
337#335—431no—
338#335—431no—
339#335—431no—
340#335—431no—
341#335—431no—
342#335—431no—
343#335—431no—
344#334—431no—
345#334—431no—
346#334—431no—
347#334—431no—
348#334—431no—
349#334—431no—
350#334—431no—
351#334—431no—
352C43#1783111yescharacteristic, complemented, Sylow
353C2×#41C22⋊D4311yescharacteristic
354C2×M16—21no—
355C2×M16—431no—
356C2×M16—431no—
357C2×M16—431no—
358C2×M16—431no—
359C2×M16—861no—
360C22×C8—21no—
361C22×C8—431no—
362C22×C8—431no—
363C22×C8—861no—
364C4×Q8Dic8611yescharacteristic
365C4×Q8C4×D4311yescharacteristic
366C4×D4Dic8611yescharacteristic
367C4×D4Dic8611yescharacteristic
368C4×D4Dic8611yescharacteristic
369C4×D4C4×D4311yescharacteristic
370C4×D4C4×D4311yescharacteristic
371C4×D4C4×D4311yescharacteristic
372#117C22⋊D4311yescharacteristic
373#117C22⋊D4311yescharacteristic
374#117C22⋊D4311yescharacteristic
375C2×C42C22×D4311yescharacteristic
376C2×C42C22×D4311yescharacteristic
377C2×C42C22×D4311yescharacteristic
378C4⋊C8—21no—
379C4⋊C8—21no—
380C4⋊C8—431no—
381C4⋊C8—431no—
382C4⋊C8—431no—
383C4⋊C8—431no—
384C4⋊C8—431no—
385C4⋊C8—431no—
386C4⋊C8—431no—
387C4⋊C8—431no—
388C4⋊C8—431no—
389C4⋊C8—431no—
390C4⋊C8—861no—
391C4⋊C8—861no—
392C4⋊C8C22×D4311yescharacteristic
393C4⋊C8C22×D4311yescharacteristic
394C4⋊C8C22×D4311yescharacteristic
395C4⋊C8C22×D4311yescharacteristic
396C22⋊C8—21no—
397C22⋊C8—21no—
398C22⋊C8—21no—
399C22⋊C8—21no—
400C22⋊C8—431no—
401C22⋊C8—431no—
402C22⋊C8—431no—
403C22⋊C8—431no—
404C22⋊C8—431no—
405C22⋊C8—431no—
406C22⋊C8—861no—
407C22⋊C8—861no—
408C22⋊C8—861no—
409C22⋊C8—861no—
410#97—21no—
411#97—21no—
412#97—431no—
413#97—431no—
414#97—431no—
415#97—431no—
416#97—861no—
417#97—861no—
418C4×C8—21no—
419C4×C8—21no—
420C4×C8—431no—
421C4×C8—431no—
422C4×C8—431no—
423C4×C8—431no—
424C4×C8—431no—
425C4×C8—431no—
426C4×C8—861no—
427C4×C8—861no—
428#41—41no—
429#41—41no—
430C2×Q8Dic43⋊C411yescharacteristic
431C2×D4Dic43⋊C411yescharacteristic
432C2×D4Dic43⋊C411yescharacteristic
433C2×D4Dic43⋊C411yescharacteristic
434C22×C4C2×Dic8611yescharacteristic
435C22×C4C2×Dic8611yescharacteristic
436C22×C4C2×Dic8611yescharacteristic
437C22×C4C2×C4×D4311yescharacteristic
438C22×C4C2×C4×D4311yescharacteristic
439C22×C4C2×C4×D4311yescharacteristic
440C22×C4C2×C22⋊D4311yescharacteristic
441C22×C4C2×C22⋊D4311yescharacteristic
442C22×C4C2×C22⋊D4311yescharacteristic
443M16—42no—
444M16—862no—
445M16—862no—
446M16—1721no—
447M16—1721no—
448M16—1722no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—42no—
454C2×C8—431no—
455C2×C8—431no—
456C2×C8—431no—
457C2×C8—431no—
458C2×C8—431no—
459C2×C8—431no—
460C2×C8—431no—
461C2×C8—431no—
462C2×C8—862no—
463C2×C8—861no—
464C2×C8—861no—
465C2×C8—861no—
466C2×C8—861no—
467C2×C8—1721no—
468C2×C8—1722no—
469C4⋊C4Dic43⋊C411yescharacteristic
470C4⋊C4Dic43⋊C411yescharacteristic
471C4⋊C4Dic43⋊C411yescharacteristic
472C4⋊C4Dic43⋊C411yescharacteristic
473C4⋊C4Dic43⋊C411yescharacteristic
474C4⋊C4Dic43⋊C411yescharacteristic
475C22⋊C4Dic43⋊C411yescharacteristic
476C22⋊C4Dic43⋊C411yescharacteristic
477C22⋊C4Dic43⋊C411yescharacteristic
478C22⋊C4Dic43⋊C411yescharacteristic
479C22⋊C4Dic43⋊C411yescharacteristic
480C22⋊C4Dic43⋊C411yescharacteristic
481C42C2×Dic8611yescharacteristic
482C42C2×Dic8611yescharacteristic
483C42C2×Dic8611yescharacteristic
484C42C2×C4×D4311yescharacteristic
485C42C2×C4×D4311yescharacteristic
486C42C2×C4×D4311yescharacteristic
487C42C2×C22⋊D4311yescharacteristic
488C42C2×C22⋊D4311yescharacteristic
489C42C2×C22⋊D4311yescharacteristic
490C42C23×D4311yescharacteristic
491C23C2×Dic43⋊C411yescharacteristic
492C23C2×Dic43⋊C411yescharacteristic
493C23C2×Dic43⋊C411yescharacteristic
494Q8—41no—
495D4—41no—
496D4—41no—
497D4—41no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4C2×Dic43⋊C411yescharacteristic
514C2×C4C2×Dic43⋊C411yescharacteristic
515C2×C4C2×Dic43⋊C411yescharacteristic
516C2×C4C2×Dic43⋊C411yescharacteristic
517C2×C4C2×Dic43⋊C411yescharacteristic
518C2×C4C2×Dic43⋊C411yescharacteristic
519C2×C4C2×Dic43⋊C411yescharacteristic
520C2×C4C2×Dic43⋊C411yescharacteristic
521C2×C4C2×Dic43⋊C411yescharacteristic
522C2×C4C22×C4×D4311yescharacteristic
523C2×C4C22×C22⋊D4311yescharacteristic
524C2×C4C22×Dic8611yescharacteristic
525C8—41no—
526C8—41no—
527C8—41no—
528C8—41no—
529C8—432no—
530C8—861no—
531C8—861no—
532C8—861no—
533C8—861no—
534C8—861no—
535C8—861no—
536C8—861no—
537C8—1721no—
538C8—1721no—
539C8—1721no—
540C8—1721no—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—21no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—21no—
549C22—21no—
550C22C22×Dic43⋊C411yescharacteristic
551C4—21no—
552C4—21no—
553C4—21no—
554C4—21no—
555C4—21no—
556C4—21no—
557C4—21no—
558C4—21no—
559C4—21no—
560C4—21no—
561C4#131×D4311yescharacteristic
562C4#1458366411yescharacteristic
563C4#1458369711yescharacteristic
564C4#1458369711yescharacteristic
565C2—41no—
566C2—41no—
567C2—41no—
568C2#1914316111yescharacteristic
569C2#1914318411yescharacteristic
570C2#1914320411yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#2925C2
socleC22×C43C22×C4⋊C4
prime radicalC2×#41×C43D4
cosocleC42×C43C24
hypercenter#2925D43
hypocenterC43#17831
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #2925

Complements

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

NH ≅ G/Ntype
3. #19133386C2semidirect
4. #19133383C2semidirect
5. #19133381C2semidirect
6. #19133378C2semidirect
7. #19133376C2semidirect
8. #19133373C2semidirect
9. #19133363C2semidirect
10. #19133360C2semidirect
11. #19133356C2semidirect
12. #19133348C2semidirect
13. #19133345C2semidirect
14. #19133341C2semidirect
352. C43#17831semidirect

Maximal subgroups

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

subgroupindex
#191435622
#191432612
#191333862
#191333832
#191333812
#191333782
#191333762
#191333732
#191333632
#191333602
#191333562
#191333482
#191333452
#191333412
C43×#29252
#1783143