Finite Group Databasebeta

← #24988068

Subgroups — #24988068

Order 11008.

846 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583428C211yesmaximal, characteristic
2#19134358C211yesmaximal, characteristic, complemented
3#19134358C211yesmaximal, characteristic, complemented
4C2×#14582640C211yesmaximal, characteristic, complemented
5C2×#14582640C211yesmaximal, characteristic, complemented
6C2×#14582639C211yesmaximal, characteristic, complemented
7C2×C43×#329C211yesmaximal, characteristic, complemented
8#14583428—22no—
9#14583428—22no—
10#14583428—22no—
11#14583428—22no—
12C2×#13063318—21no—
13C2×#13063317C2211yescharacteristic
14C2×#13063307—21no—
15C2×#13063301C411yescharacteristic
16C2×#13063296C411yescharacteristic
17C2×Q8×Dic43C411yescharacteristic
18C2×D4×Dic43C411yescharacteristic
19C2×(C22⋊D43)⋊C4—21no—
20C2×#13063281—21no—
21C2×C42×D43C2211yescharacteristic
22C2×(C2×D43)⋊C8—21no—
23C2×(C2×D43)⋊C8—21no—
24C2×#13063236C2211yescharacteristic
25C2×#13063236C2211yescharacteristic
26#14582653—21no—
27#14582653—21no—
28#14582640—22no—
29#14582640—22no—
30#14582639—22no—
31C2×#124×C43C2211yescharacteristic
32C2×#97×C43C2211yescharacteristic
33C2×#97×C43C2211yescharacteristic
34C43×#329—22no—
35C22×C22⋊D43—21no—
36C23×Dic43—21no—
37C22×C4×D43C2×C411yescharacteristic
38C22×C4×D43D411yescharacteristic
39C22×C4×D43D411yescharacteristic
40C22×C43⋊C8—21no—
41C22×C43⋊C8—21no—
42#13063318—24no—
43#13063318—24no—
44#13063317—21no—
45#13063317—21no—
46#13063317D412yes—
47#13063317D412yes—
48#13063307—24no—
49#13063307—24no—
50#13063301—22no—
51#13063301—22no—
52#13063296—22no—
53#13063296—22no—
54Q8×Dic43—22no—
55Q8×Dic43—22no—
56D4×Dic43—22no—
57D4×Dic43—22no—
58(C22⋊D43)⋊C4—24no—
59(C22⋊D43)⋊C4—24no—
60#13063281—24no—
61#13063281—24no—
62C2×C4⋊Dic43—21no—
63C2×C4⋊Dic43C2×C411yescharacteristic
64C2×C4⋊Dic43C2×C411yescharacteristic
65C2×Dic43⋊C4—21no—
66C2×Dic43⋊C4—21no—
67C2×Dic43⋊C4—21no—
68C2×C22⋊Dic43—21no—
69C2×C22⋊Dic43—21no—
70C2×(C2×D43)⋊C4—21no—
71C2×C4×Dic43—21no—
72C2×C4×Dic43C2×C411yescharacteristic
73C2×C4×Dic43D411yescharacteristic
74C2×C4×Dic43D411yescharacteristic
75C42×D43—21no—
76C42×D43—21no—
77C42×D43—21no—
78C42×D43—21no—
79(C2×D43)⋊C8—24no—
80(C2×D43)⋊C8—24no—
81#13063236—21no—
82#13063236—21no—
83#13063236—21no—
84#13063236—21no—
85C22×Q8×C43C2×C411yescharacteristic
86C22×D4×C43C2×C411yescharacteristic
87C22×C8×C43—21no—
88C22×C8×C43—21no—
89#124×C43—21no—
90#124×C43—21no—
91#124×C43D412yes—
92#124×C43D412yes—
93C2×C22⋊C4×C43—21no—
94C2×C22⋊C4×C43—21no—
95C2×C42×C43C2311yescharacteristic
96#97×C43—21no—
97#97×C43—21no—
98#97×C43—21no—
99#97×C43—21no—
100C24×C43—21no—
101C23×D43C22⋊C411yescharacteristic
102C2×Q8×C43—21no—
103C2×Q8×C43—41no—
104C2×Q8×C43—41no—
105C2×Q8×C43C22⋊C412yes—
106C2×D4×C43—21no—
107C2×D4×C43—41no—
108C2×D4×C43—41no—
109C2×D4×C43C22⋊C412yes—
110C22×C4×C43—21no—
111C22×C4×C43C22×C411yescharacteristic
112C22×C4×C43C2×D411yescharacteristic
113C22×C4×C43C2×D411yescharacteristic
114C2×C22⋊D43—24no—
115C2×C22⋊D43—42no—
116C2×C22⋊D43—42no—
117C22×Dic43—24no—
118C22×Dic43—21no—
119C22×Dic43—21no—
120C22×Dic43—42no—
121C22×Dic43—42no—
122C22×Dic43C22⋊C411yescharacteristic
123C22×Dic43C22⋊C411yescharacteristic
124C22×Dic43C22⋊C411yescharacteristic
125C2×C4×D43—21no—
126C2×C4×D43—21no—
127C2×C4×D43—21no—
128C2×C4×D43—21no—
129C2×C4×D43—21no—
130C2×C4×D43—21no—
131C2×C4×D43—22no—
132C2×C4×D43—22no—
133C2×C4×D43—41no—
134C2×C4×D43—41no—
135C2×C4×D43—41no—
136C2×C4×D43—41no—
137C2×C8×C43—22no—
138C2×C8×C43—22no—
139C2×C8×C43—41no—
140C2×C8×C43—41no—
141C2×C8×C43—41no—
142C2×C8×C43—41no—
143C22⋊C4×C43—22no—
144C22⋊C4×C43—22no—
145C22⋊C4×C43—22no—
146C22⋊C4×C43—22no—
147C42×C43C2×D411yescharacteristic
148C42×C43C2×D411yescharacteristic
149C42×C43C2×D411yescharacteristic
150C42×C43C2×D411yescharacteristic
151C22⋊Dic43—24no—
152C22⋊Dic43—24no—
153(C2×D43)⋊C4—24no—
154C4⋊Dic43—24no—
155C4⋊Dic43—21no—
156C4⋊Dic43—21no—
157C4⋊Dic43C22⋊C412yes—
158C4⋊Dic43C22⋊C412yes—
159Dic43⋊C4—24no—
160Dic43⋊C4—22no—
161Dic43⋊C4—22no—
162Dic43⋊C4—22no—
163Dic43⋊C4—22no—
164C4×Dic43—24no—
165C4×Dic43—21no—
166C4×Dic43—21no—
167C4×Dic43—21no—
168C4×Dic43—21no—
169C4×Dic43—21no—
170C4×Dic43—21no—
171C2×C43⋊C8—22no—
172C2×C43⋊C8—22no—
173C2×C43⋊C8—41no—
174C2×C43⋊C8—41no—
175C2×C43⋊C8—41no—
176C2×C43⋊C8—41no—
177C23×C43—22no—
178C23×C43—41no—
179C23×C43—41no—
180C23×C43—41no—
181C23×C43—41no—
182C23×C43—41no—
183C23×C43—41no—
184C23×C43C2×C22⋊C411yescharacteristic
185C22×D43—21no—
186C22×D43—21no—
187C22×D43—21no—
188C22×D43—21no—
189C22×D43—21no—
190C22×D43—21no—
191C22×D43#10412yes—
192Q8×C43—42no—
193Q8×C43—42no—
194D4×C43—42no—
195D4×C43—42no—
196C2×C4×C43—21no—
197C2×C4×C43—21no—
198C2×C4×C43—21no—
199C2×C4×C43—21no—
200C2×C4×C43—21no—
201C2×C4×C43—21no—
202C2×C4×C43—22no—
203C2×C4×C43—41no—
204C2×C4×C43—41no—
205C2×C4×C43C2×C22⋊C411yescharacteristic
206C2×C4×C43C2×C22⋊C411yescharacteristic
207C2×C4×C43#12011yescharacteristic
208C2×C4×C43#12011yescharacteristic
209C2×C4×C43#12011yescharacteristic
210C2×C4×C43#12011yescharacteristic
211C22⋊D43—48no—
212C2×Dic43—21no—
213C2×Dic43—21no—
214C2×Dic43—21no—
215C2×Dic43—21no—
216C2×Dic43—22no—
217C2×Dic43—22no—
218C2×Dic43—21no—
219C2×Dic43—21no—
220C2×Dic43—21no—
221C2×Dic43—21no—
222C2×Dic43—48no—
223C2×Dic43—41no—
224C2×Dic43—41no—
225C2×Dic43—41no—
226C2×Dic43—41no—
227C2×Dic43#10412yes—
228C4×D43—42no—
229C4×D43—42no—
230C4×D43—42no—
231C4×D43—42no—
232C4×D43—42no—
233C4×D43—42no—
234C8×C43—42no—
235C8×C43—42no—
236C43⋊C8—42no—
237C43⋊C8—42no—
238#8336—431nomaximal, Sylow
239C22×C43—42no—
240C22×C43—42no—
241C22×C43—42no—
242C22×C43—81no—
243C22×C43—81no—
244C22×C43—81no—
245C22×C43—81no—
246C22×C43#37911yescharacteristic
247C22×C43#41311yescharacteristic
248C22×C43#41311yescharacteristic
249C22×C43C2×#10411yescharacteristic
250C22×C43C2×#10411yescharacteristic
251C22×C43#42111yescharacteristic
252C22×C43#42111yescharacteristic
253C2×D43—22no—
254C2×D43—22no—
255C2×D43—22no—
256C2×D43—41no—
257C2×D43—41no—
258C2×D43—41no—
259C2×D43—41no—
260C4×C43—21no—
261C4×C43—21no—
262C4×C43—21no—
263C4×C43—21no—
264C4×C43—21no—
265C4×C43—21no—
266C4×C43—42no—
267Dic43—22no—
268Dic43—41no—
269Dic43—41no—
270Dic43—42no—
271Dic43—42no—
272C2×#529—431no—
273#1749—431no—
274#1749—431no—
275C2×#330—431no—
276C2×#330—431no—
277C2×#329—431no—
278C2×#329D4311yescharacteristic, complemented
279C2×C43—82no—
280C2×C43#152411yescharacteristic
281C2×C43#152911yescharacteristic
282C2×C43#153211yescharacteristic
283C2×C43#153511yescharacteristic
284C2×C43#178511yescharacteristic
285C2×C43#178911yescharacteristic
286C2×C43#178911yescharacteristic
287D43—42no—
288#529—862no—
289#529—862no—
290#529—862no—
291#529—862no—
292C2×#126—861no—
293C2×#125—431no—
294C2×#124C2×D4311yescharacteristic
295C2×#123—861no—
296C2×C22⋊Q8—431no—
297C2×#121—431no—
298C2×C4×Q8—431no—
299C2×C4×D4—431no—
300C2×C4×D4—861no—
301C2×#117—861no—
302C22×C42—431no—
303C2×C22⋊C8—861no—
304C2×C22⋊C8—861no—
305C2×#97—431no—
306C2×#97—431no—
307C2×#97C2×D4311yescharacteristic
308C2×#97C2×D4311yescharacteristic
309#336—861no—
310#336—861no—
311#330—862no—
312#330—862no—
313#329—22no—
314#329—862no—
315C43#833611yescharacteristic, complemented, Sylow
316C22×Q8C4×D4311yescharacteristic
317C22×D4—861no—
318C22×D4C4×D4311yescharacteristic
319C23×C4—431no—
320C23×C4—431no—
321C23×C4—431no—
322C23×C4—861no—
323C22×C8—21no—
324C22×C8—21no—
325C22×C8—861no—
326C22×C8—861no—
327#126—864no—
328#126—864no—
329#125—432no—
330#125—432no—
331#125—861no—
332#125—861no—
333#124—21no—
334#124—21no—
335#124D17212yes—
336#124C22⋊D4312yes—
337#123—864no—
338#123—864no—
339C22⋊Q8—862no—
340C22⋊Q8—862no—
341#121—862no—
342#121—862no—
343C4×Q8—862no—
344C4×Q8—862no—
345C4×D4—864no—
346C4×D4—864no—
347C4×D4—862no—
348C4×D4—862no—
349#117—864no—
350#117—864no—
351C2×C4⋊C4—431no—
352C2×C4⋊C4—431no—
353C2×C4⋊C4—861no—
354C2×C4⋊C4—861no—
355C2×C4⋊C4—861no—
356C2×C4⋊C4—861no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—861no—
360C2×C22⋊C4—861no—
361C2×C22⋊C4—861no—
362C2×C42—431no—
363C2×C42—431no—
364C2×C42—431no—
365C2×C42—861no—
366C2×C42—861no—
367C2×C42—861no—
368C2×C42—861no—
369C2×C42—861no—
370C2×C42C22×D4311yescharacteristic
371C22⋊C8—864no—
372C22⋊C8—864no—
373#97—21no—
374#97—21no—
375#97—21no—
376#97—21no—
377#97—861no—
378#97—861no—
379#97—861no—
380#97—861no—
381C24—21no—
382C24—431no—
383C2×Q8—21no—
384C2×Q8—41no—
385C2×Q8—41no—
386C2×Q8(C2×D43)⋊C412yes—
387C2×D4—21no—
388C2×D4—41no—
389C2×D4—41no—
390C2×D4—864no—
391C2×D4—1722no—
392C2×D4—1722no—
393C2×D4(C2×D43)⋊C412yes—
394C22×C4—21no—
395C22×C4—431no—
396C22×C4—431no—
397C22×C4—431no—
398C22×C4—862no—
399C22×C4—862no—
400C22×C4—864no—
401C22×C4—861no—
402C22×C4—861no—
403C22×C4—861no—
404C22×C4—861no—
405C22×C4—861no—
406C22×C4—861no—
407C22×C4—861no—
408C22×C4—861no—
409C22×C4—1721no—
410C22×C4—1721no—
411C22×C4—1721no—
412C22×C4—1721no—
413C22×C4—1722no—
414C22×C4—1722no—
415C22×C4C2×C4×D4311yescharacteristic
416C22×C4D4×D4311yescharacteristic
417C22×C4D4×D4311yescharacteristic
418C2×C8—22no—
419C2×C8—22no—
420C2×C8—41no—
421C2×C8—41no—
422C2×C8—41no—
423C2×C8—41no—
424C2×C8—862no—
425C2×C8—862no—
426C2×C8—1721no—
427C2×C8—1721no—
428C2×C8—1721no—
429C2×C8—1721no—
430C4⋊C4—432no—
431C4⋊C4—432no—
432C4⋊C4—864no—
433C4⋊C4—864no—
434C4⋊C4—861no—
435C4⋊C4—861no—
436C4⋊C4—862no—
437C4⋊C4—862no—
438C4⋊C4—862no—
439C4⋊C4—862no—
440C22⋊C4—22no—
441C22⋊C4—22no—
442C22⋊C4—22no—
443C22⋊C4—22no—
444C22⋊C4—864no—
445C22⋊C4—864no—
446C22⋊C4—864no—
447C42—864no—
448C42—861no—
449C42—861no—
450C42—861no—
451C42—861no—
452C42—861no—
453C42—861no—
454C42C2×D17211yescharacteristic
455C42D4×D4311yescharacteristic
456C42D4×D4311yescharacteristic
457C42C2×C22⋊D4311yescharacteristic
458C23—22no—
459C23—41no—
460C23—41no—
461C23—41no—
462C23—41no—
463C23—41no—
464C23—41no—
465C23—432no—
466C23—861no—
467C23—861no—
468C23—861no—
469C23—861no—
470C23—861no—
471C23—861no—
472C23C22⋊C4×D4311yescharacteristic
473Q8—42no—
474Q8—42no—
475D4—42no—
476D4—42no—
477D4—1728no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—22no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—432no—
488C2×C4—861no—
489C2×C4—861no—
490C2×C4—861no—
491C2×C4—861no—
492C2×C4—861no—
493C2×C4—861no—
494C2×C4—861no—
495C2×C4—861no—
496C2×C4—862no—
497C2×C4—862no—
498C2×C4—1722no—
499C2×C4—1722no—
500C2×C4—1722no—
501C2×C4—1722no—
502C2×C4—1722no—
503C2×C4—1722no—
504C2×C4—1728no—
505C2×C4—1721no—
506C2×C4—1721no—
507C2×C4—1721no—
508C2×C4—1721no—
509C2×C4C22⋊C4×D4311yescharacteristic
510C2×C4C2×(C2×D43)⋊C411yescharacteristic
511C2×C4#1306329311yescharacteristic
512C2×C4#1306329311yescharacteristic
513C2×C4#1306329511yescharacteristic
514C2×C4#1306329511yescharacteristic
515C8—42no—
516C8—42no—
517C8—1722no—
518C8—1722no—
519C22—42no—
520C22—42no—
521C22—42no—
522C22—81no—
523C22—81no—
524C22—81no—
525C22—81no—
526C22—862no—
527C22—862no—
528C22—862no—
529C22—1721no—
530C22—1721no—
531C22—1721no—
532C22—1721no—
533C22#1458275411yescharacteristic
534C22#1458288011yescharacteristic
535C22#1458288011yescharacteristic
536C22#104×D4311yescharacteristic
537C22#104×D4311yescharacteristic
538C22#1458291411yescharacteristic
539C22#1458291411yescharacteristic
540C4—21no—
541C4—21no—
542C4—21no—
543C4—21no—
544C4—21no—
545C4—21no—
546C4—42no—
547C4—862no—
548C4—1721no—
549C4—1721no—
550C4—1722no—
551C4—1722no—
552C2—82no—
553C2—1722no—
554C2#1913318011yescharacteristic
555C2#1913319911yescharacteristic
556C2#1913321211yescharacteristic
557C2#1913322311yescharacteristic
558C2#1913452011yescharacteristic
559C2#1913453711yescharacteristic
560C2#1913453711yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC2×C43×#329C2
socleC23×C43C2×C22⋊C4
prime radicalC2×#13063296C4
cosocleC2×C42×C43C23
hypercenterC2×#329D43
hypocenterC43#8336
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#329

Complements

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

NH ≅ G/Ntype
2. #19134358C2semidirect
3. #19134358C2semidirect
4. C2×#14582640C2semidirect
5. C2×#14582640C2semidirect
6. C2×#14582639C2semidirect
7. C2×C43×#329C2semidirect
278. C2×#329D43semidirect
315. C43#8336semidirect

Maximal subgroups

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

subgroupindex
C2×#145834282
#191343582
C2×#145826402
C2×#145826392
C2×C43×#3292
#833643