Finite Group Databasebeta

← #25113704

Subgroups — #25113704

Order 11008.

962 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#103×D43C211yesmaximal, characteristic
2#19137471C211yesmaximal, characteristic
3#19137429C211yesmaximal, characteristic
4#19135287C211yesmaximal, characteristic, complemented
5#19135232C211yesmaximal, characteristic, complemented
6#19135226C211yesmaximal, characteristic, complemented
7#19134864C211yesmaximal, characteristic, complemented
8#19134862C211yesmaximal, characteristic, complemented
9#19134684C211yesmaximal, characteristic
10#19134619C211yesmaximal, characteristic
11#19134528C211yesmaximal, characteristic
12#19134426C211yesmaximal, characteristic, complemented
13#19134424C211yesmaximal, characteristic, complemented
14#19134372C211yesmaximal, characteristic
15C43×#1935C211yesmaximal, characteristic, complemented
16C22×Q8×D43C2211yescharacteristic
17C22×C8×D43C2211yescharacteristic
18C2×C4×Dic86C2211yescharacteristic
19C2×#13063290C2211yescharacteristic
20C2×C4⋊C4×D43C2211yescharacteristic
21C2×#13063256C2211yescharacteristic
22C2×#13063256C2211yescharacteristic
23C2×#13063250C2211yescharacteristic
24C2×#13063250C2211yescharacteristic
25C2×#13063249C2211yescharacteristic
26C2×#13063249C2211yescharacteristic
27C2×#13063248C2211yescharacteristic
28C2×#13063248C2211yescharacteristic
29#103×D43C418yescomplemented
30C2×(C2×D43)⋊C8C2211yescharacteristic
31C2×#13063235C2211yescharacteristic
32#14582806C2211yescharacteristic
33#14582803—21no—
34#14582803—21no—
35#14582798C2211yescharacteristic
36#14582786—21no—
37#14582780—21no—
38#14582758—21no—
39#14582756—21no—
40#14582756C2211yescharacteristic
41#14582756C2211yescharacteristic
42C4⋊C4×Dic43C2211yescharacteristic
43C4×C4⋊Dic43C2211yescharacteristic
44C4×(C2×D43)⋊C4C2211yescharacteristic
45#14582746—21no—
46#14582746—21no—
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582654C2211yescharacteristic
52#14582653C2211yescharacteristic
53C2×#103×C43C2211yescharacteristic
54C2×#103×C43C2211yescharacteristic
55C2×#97×C43C2211yescharacteristic
56C43×#391C2211yescharacteristic
57C43×#389C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C22×Dic86—21no—
61C22×Dic86C2311yescharacteristic
62C2×Q8×D43—22no—
63C2×Q8×D43—22no—
64C2×Q8×D43—22no—
65C2×Q8×D43—41no—
66C2×Q8×D43—41no—
67C2×Q8×D43C2×C414yes—
68C22×C4×D43—21no—
69C22×C4×D43—21no—
70C22×C4×D43C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73C2×C8×D43—41no—
74C2×C8×D43—41no—
75C2×C8×D43C2×C414yes—
76C4×Dic86—22no—
77C4×Dic86—41no—
78#13063290—22no—
79#13063290—41no—
80C2×C4⋊Dic43—21no—
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C4⋊C4×D43—22no—
88C4⋊C4×D43C2×C414yes—
89C2×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4D411yescharacteristic
92C2×(C2×D43)⋊C4D411yescharacteristic
93C2×C4×Dic43—21no—
94C2×C4×Dic43—21no—
95C2×C4×Dic43—21no—
96C2×C4×Dic43—21no—
97C2×C4×Dic43C2311yescharacteristic
98#13063256—41no—
99#13063256—41no—
100#13063250—22no—
101#13063250C2×C414yes—
102#13063249—41no—
103#13063249C2×C414yes—
104#13063248—22no—
105#13063248C2×C414yes—
106(C2×D43)⋊C8—22no—
107#13063235—41no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95D411yescharacteristic
116C43⋊#95D411yescharacteristic
117C22×Q8×C43C2311yescharacteristic
118C22×C8×C43C2311yescharacteristic
119C22×C8×C43C2311yescharacteristic
120C2×C4⋊C4×C43—21no—
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C42×C43C2311yescharacteristic
125#103×C43—41no—
126#103×C43C2×C414yes—
127#97×C43—41no—
128#95×C43—21no—
129#95×C43—21no—
130#95×C43—21no—
131C23×D43C2×D411yescharacteristic
132C2×Q8×C43—21no—
133C2×Q8×C43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43—21no—
137C2×Q8×C43C22×C412yes—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2411yescharacteristic
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43C2×D411yescharacteristic
150C22×Dic43C2×D411yescharacteristic
151C22×Dic43C2×D411yescharacteristic
152Q8×D43—28no—
153Q8×D43—44no—
154Q8×D43—44no—
155Q8×D43—44no—
156C2×C4×D43—21no—
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×C4×D43—21no—
160C2×C4×D43—24no—
161C2×C4×D43—24no—
162C2×C4×D43—42no—
163C2×C4×D43—42no—
164C2×C4×D43—81no—
165C2×C4×D43—81no—
166C2×C4×D43C22×C412yes—
167C2×C4×D43#4112yes—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×Dic86—24no—
172C2×Dic86—42no—
173C2×Dic86—42no—
174C2×Dic86C22×C412yes—
175C2×Dic86#4112yes—
176C2×Dic86#4112yes—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43C22×C412yes—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—81no—
189C4⋊C4×C43C22×C412yes—
190C42×C43—21no—
191C42×C43—21no—
192(C2×D43)⋊C4—22no—
193(C2×D43)⋊C4—22no—
194(C2×D43)⋊C4—42no—
195(C2×D43)⋊C4—42no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—81no—
202C4⋊Dic43C22×C412yes—
203Dic43⋊C4—24no—
204Dic43⋊C4—42no—
205Dic43⋊C4—42no—
206C4×Dic43—21no—
207C4×Dic43—21no—
208C4×Dic43—42no—
209C4×Dic43—42no—
210C4×Dic43—81no—
211C4×Dic43—81no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8C22×C412yes—
218C8×D43—44no—
219C23×C43C22×D411yescharacteristic
220C22×D43—21no—
221C22×D43—21no—
222C22×D43—21no—
223C22×D43—21no—
224C22×D43C4×D412yes—
225C22×D43#13712yes—
226C22×D43#13712yes—
227Q8×C43—22no—
228Q8×C43—22no—
229Q8×C43—41no—
230Q8×C43—41no—
231C2×C4×C43—22no—
232C2×C4×C43—22no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43C23×C411yescharacteristic
250C2×C4×C43C2×#4111yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C2×C4×C43H(5,𝔽2)11yescharacteristic
254C2×C4×C43H(5,𝔽2)11yescharacteristic
255C2×Dic43—22no—
256C2×Dic43—22no—
257C2×Dic43—22no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—22no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43C4×D412yes—
276C4×D43—22no—
277C4×D43—22no—
278C4×D43—22no—
279C4×D43—22no—
280C4×D43—48no—
281C4×D43—84no—
282Dic86—22no—
283Dic86—22no—
284Dic86—22no—
285Dic86—48no—
286Dic86#11714yes—
287C8×C43—22no—
288C8×C43—41no—
289C43⋊C8—22no—
290C43⋊C8—41no—
291#22567—431nomaximal, Sylow
292C22×C43C2×C4×D411yescharacteristic
293C22×C43#54611yescharacteristic
294C22×C43#54611yescharacteristic
295C22×C43C2×#13711yescharacteristic
296C22×C43C2×#13711yescharacteristic
297C22×C43#57711yescharacteristic
298C22×C43#57711yescharacteristic
299C2×D43—22no—
300C2×D43—22no—
301C2×D43—22no—
302C2×D43—22no—
303C2×D43—22no—
304C2×D43—22no—
305C2×D43#44114yes—
306C4×C43—42no—
307C4×C43—42no—
308C4×C43—41no—
309C4×C43—41no—
310C4×C43—81no—
311C4×C43—81no—
312C4×C43C2×#11711yescharacteristic
313C4×C43#51811yescharacteristic
314C4×C43#55111yescharacteristic
315C4×C43#55111yescharacteristic
316Dic43—24no—
317Dic43—22no—
318Dic43—42no—
319Dic43—41no—
320Dic43—41no—
321Dic43—81no—
322Dic43—81no—
323C22×#103—431no—
324#2345—431no—
325Q8×C22⋊C4—431no—
326#1935—431no—
327#1935D4311yescharacteristic, complemented
328#1927—431no—
329#1927—431no—
330#1865—431no—
331#1865—431no—
332#1824—431no—
333#1807—431no—
334#1787—431no—
335#1763—431no—
336#1763—431no—
337#1752—431no—
338C2×C43#234211yescharacteristic
339C2×C43C2×#44111yescharacteristic
340C2×C43#294911yescharacteristic
341C2×C43#331611yescharacteristic
342C2×C43#331611yescharacteristic
343C2×C43#332011yescharacteristic
344C2×C43#332011yescharacteristic
345D43—24no—
346C23×Q8—431no—
347C23×C8—431no—
348C2×C4×Q8—431no—
349C2×C4×Q8—431no—
350C22×C4⋊C4—431no—
351C2×#106—431no—
352C2×#106—431no—
353C2×#103—431no—
354C2×#103—431no—
355C2×#103—431no—
356C2×#103—438no—
357C2×#103—431no—
358C2×#103—431no—
359C2×#103—431no—
360C2×#103C2×D4311yescharacteristic
361C2×#103C2×D4311yescharacteristic
362C2×C22⋊C8—431no—
363C2×#97—431no—
364C2×#97C2×D4311yescharacteristic
365#391—431no—
366#391—861no—
367#391—861no—
368#391C2×D4311yescharacteristic
369#389—431no—
370#389C2×D4311yescharacteristic
371#387—861no—
372#387—861no—
373#380—431no—
374#380—431no—
375#380—861no—
376#380—861no—
377C4×C4⋊C4—431no—
378C4×C4⋊C4—431no—
379C4×C22⋊C4—431no—
380C4×C22⋊C4—861no—
381C4×C22⋊C4—861no—
382#340—431no—
383#340—431no—
384#340—431no—
385#340—431no—
386#340C2×D4311yescharacteristic
387#340C2×D4311yescharacteristic
388#336—431no—
389#336—431no—
390C43#2256711yescharacteristic, complemented, Sylow
391C22×Q8—434no—
392C22×Q8—431no—
393C22×Q8—861no—
394C22×Q8—862no—
395C22×Q8—862no—
396C22×Q8—862no—
397C22×Q8—1721no—
398C22×Q8—1721no—
399C22×Q8C22×D4311yescharacteristic
400C23×C4—431no—
401C23×C4—861no—
402C23×C4—861no—
403C22×C8—431no—
404C22×C8—434no—
405C22×C8—431no—
406C22×C8—1721no—
407C22×C8—1721no—
408C22×C8C22×D4311yescharacteristic
409C22×C8C22×D4311yescharacteristic
410C4×Q8—862no—
411C4×Q8—862no—
412C4×Q8—1721no—
413C4×Q8—1721no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—431no—
416C2×C4⋊C4—434no—
417C2×C4⋊C4—431no—
418C2×C4⋊C4—431no—
419C2×C4⋊C4—862no—
420C2×C4⋊C4—861no—
421C2×C4⋊C4—861no—
422C2×C4⋊C4—861no—
423C2×C4⋊C4—861no—
424C2×C4⋊C4C22×D4311yescharacteristic
425C2×C4⋊C4C22×D4311yescharacteristic
426C2×C4⋊C4C22×D4311yescharacteristic
427C2×C22⋊C4—431no—
428C2×C22⋊C4—431no—
429C2×C22⋊C4—861no—
430C2×C22⋊C4—861no—
431C2×C42—431no—
432C2×C42—861no—
433C2×C42—861no—
434C2×C42—861no—
435C2×C42—861no—
436C2×C42C22×D4311yescharacteristic
437#106—1721no—
438#106—1721no—
439#103—41no—
440#103—434no—
441#103—434no—
442#103—434no—
443#103—862no—
444#103—862no—
445#103—1721no—
446#103C4×D4314yes—
447C22⋊C8—862no—
448#97—41no—
449#97—1721no—
450#95—21no—
451#95—21no—
452#95—21no—
453#95—431no—
454#95—431no—
455#95—861no—
456#95—861no—
457#95—861no—
458#95—861no—
459#95—861no—
460#95—861no—
461#95—861no—
462C24—431no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—432no—
469C2×Q8—432no—
470C2×Q8—432no—
471C2×Q8—864no—
472C2×Q8—861no—
473C2×Q8—861no—
474C2×Q8—861no—
475C2×Q8—868no—
476C2×Q8—1722no—
477C2×Q8—1722no—
478C2×Q8—1724no—
479C2×Q8—1724no—
480C2×Q8—1724no—
481C2×Q8C2×C4×D4312yes—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—431no—
487C22×C4—432no—
488C22×C4—432no—
489C22×C4—431no—
490C22×C4—431no—
491C22×C4—864no—
492C22×C4—864no—
493C22×C4—861no—
494C22×C4—861no—
495C22×C4—861no—
496C22×C4—861no—
497C22×C4—861no—
498C22×C4—861no—
499C22×C4—861no—
500C22×C4—861no—
501C22×C4—3441no—
502C22×C4—3441no—
503C22×C4—1722no—
504C22×C4—1722no—
505C22×C4D4×D4311yescharacteristic
506C22×C4D4×D4311yescharacteristic
507C22×C4C23×D4311yescharacteristic
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—432no—
514C2×C8—861no—
515C2×C8—861no—
516C2×C8—861no—
517C2×C8—861no—
518C2×C8—861no—
519C2×C8—1724no—
520C2×C8C2×C4×D4312yes—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—81no—
527C4⋊C4—432no—
528C4⋊C4—864no—
529C4⋊C4—861no—
530C4⋊C4—861no—
531C4⋊C4—861no—
532C4⋊C4—861no—
533C4⋊C4—861no—
534C4⋊C4—3441no—
535C4⋊C4—1722no—
536C4⋊C4—1722no—
537C4⋊C4C2×C4×D4312yes—
538C22⋊C4—862no—
539C22⋊C4—862no—
540C22⋊C4—1722no—
541C22⋊C4—1722no—
542C42—21no—
543C42—21no—
544C42—861no—
545C42—861no—
546C42—3441no—
547C42—3441no—
548C42—1722no—
549C42—1722no—
550C23—432no—
551C23—432no—
552C23—432no—
553C23—861no—
554C23—861no—
555C23—861no—
556C23—861no—
557C23C2×D4×D4311yescharacteristic
558Q8—22no—
559Q8—22no—
560Q8—41no—
561Q8—41no—
562Q8—434no—
563Q8—862no—
564Q8—862no—
565Q8—862no—
566Q8—1728no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—432no—
586C2×C4—862no—
587C2×C4—862no—
588C2×C4—861no—
589C2×C4—862no—
590C2×C4—861no—
591C2×C4—862no—
592C2×C4—862no—
593C2×C4—862no—
594C2×C4—862no—
595C2×C4—862no—
596C2×C4—861no—
597C2×C4—861no—
598C2×C4—861no—
599C2×C4—861no—
600C2×C4—861no—
601C2×C4—861no—
602C2×C4—3444no—
603C2×C4—1728no—
604C2×C4—1721no—
605C2×C4—1721no—
606C2×C4—1721no—
607C2×C4—1721no—
608C2×C4—1721no—
609C2×C4—1721no—
610C2×C4—1721no—
611C2×C4—1721no—
612C2×C4C22×C4×D4311yescharacteristic
613C2×C4#41×D4311yescharacteristic
614C2×C4#41×D4311yescharacteristic
615C2×C4#41×D4311yescharacteristic
616C2×C4#1306337011yescharacteristic
617C2×C4#1306337111yescharacteristic
618C8—22no—
619C8—41no—
620C8—862no—
621C8—1721no—
622C22—434no—
623C22—862no—
624C22—862no—
625C22—862no—
626C22—862no—
627C22—862no—
628C22—862no—
629C22C4×D4×D4311yescharacteristic
630C22#1458353811yescharacteristic
631C22#1458354211yescharacteristic
632C22#137×D4311yescharacteristic
633C22#137×D4311yescharacteristic
634C22#1458370811yescharacteristic
635C22#1458370911yescharacteristic
636C4—41no—
637C4—42no—
638C4—42no—
639C4—41no—
640C4—81no—
641C4—81no—
642C4—862no—
643C4—864no—
644C4—3441no—
645C4—3441no—
646C4—1721no—
647C4—1722no—
648C4—1721no—
649C4#117×D4311yescharacteristic
650C4#1458337111yescharacteristic
651C4#1458357411yescharacteristic
652C4#1458357711yescharacteristic
653C2—864no—
654C2#1913744311yescharacteristic
655C2#441×D4311yescharacteristic
656C2#1914345111yescharacteristic
657C2#1914670111yescharacteristic
658C2#1914670511yescharacteristic
659C2#1914676111yescharacteristic
660C2#1914676511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1935C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
cosocleC22×C4×C43C24
hypercenter#1935D43
hypocenterC43#22567
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1935

Complements

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

NH ≅ G/Ntype
4. #19135287C2semidirect
5. #19135232C2semidirect
6. #19135226C2semidirect
7. #19134864C2semidirect
8. #19134862C2semidirect
12. #19134426C2semidirect
13. #19134424C2semidirect
15. C43×#1935C2semidirect
29. #103×D43C4semidirect
327. #1935D43semidirect
390. C43#22567semidirect

Maximal subgroups

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

subgroupindex
C2×#103×D432
#191374712
#191374292
#191352872
#191352322
#191352262
#191348642
#191348622
#191346842
#191346192
#191345282
#191344262
#191344242
#191343722
C43×#19352
#2256743