Finite Group Databasebeta

← #24988807

Subgroups — #24988807

Order 11008.

722 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#19135581C211yesmaximal, characteristic, complemented
2#19134694C211yesmaximal, characteristic, complemented
3#19134690C211yesmaximal, characteristic, complemented
4#19133138C211yesmaximal, characteristic
5#19133086C211yesmaximal, characteristic
6#19132959C211yesmaximal, characteristic, complemented
7C43×#3495C211yesmaximal, characteristic
8#14582863C2211yescharacteristic
9C2×C22⋊(C43⋊C8)C2211yescharacteristic
10#14582759C2211yescharacteristic
11C4×C22⋊Dic43C2211yescharacteristic
12#14582666—22no—
13#14582661—21no—
14#14582661—21no—
15#14582658—21no—
16#14582658—21no—
17#14582636—21no—
18#14582636—21no—
19#14582633—21no—
20#14582633—21no—
21#14582625—22no—
22C43×#556—21no—
23C43×#554—21no—
24C43×#552—21no—
25C43×#552—22no—
26C43×#552—21no—
27C43×#551—22no—
28C43×#544C411yescharacteristic, complemented
29C43×#542—21no—
30C43×#541—21no—
31C43×#536C411yescharacteristic, complemented
32C43×#533—21no—
33C43×#529—21no—
34C43×#525C2211yescharacteristic
35C2×C22⋊Q8×C43C2211yescharacteristic
36C43×#520C411yescharacteristic, complemented
37C43×#519C411yescharacteristic, complemented
38C2×#117×C43C2211yescharacteristic
39C2×#10621877—21no—
40C22×C43⋊C8—21no—
41C2×C4⋊Dic43—21no—
42C2×C22⋊Dic43—21no—
43C2×C22⋊Dic43—21no—
44C2×C4×Dic43—21no—
45C22⋊(C43⋊C8)—21no—
46C22⋊(C43⋊C8)—21no—
47C22⋊(C43⋊C8)—21no—
48C22⋊(C43⋊C8)—21no—
49C43⋊#95—21no—
50C43⋊#95—21no—
51C2×#41×C43C2×C411yescharacteristic
52C22×Q8×C43C2×C411yescharacteristic
53C23×C4×C43C2311yescharacteristic
54C4⋊Q8×C43—21no—
55C4⋊Q8×C43—21no—
56C4⋊Q8×C43—21no—
57#126×C43—22no—
58#126×C43—22no—
59#126×C43—22no—
60#126×C43—22no—
61#125×C43—22no—
62#125×C43—22no—
63#125×C43—22no—
64#125×C43—21no—
65#125×C43—21no—
66#124×C43—22no—
67#124×C43—21no—
68#123×C43—22no—
69#123×C43—22no—
70#123×C43—22no—
71#123×C43—21no—
72C22⋊Q8×C43—22no—
73C22⋊Q8×C43—22no—
74C22⋊Q8×C43—22no—
75C22⋊Q8×C43—21no—
76C22⋊Q8×C43—21no—
77C22⋊Q8×C43—21no—
78C22⋊Q8×C43—21no—
79C22⋊Q8×C43—21no—
80C22⋊Q8×C43—21no—
81C22⋊Q8×C43D411yescharacteristic
82C22⋊Q8×C43D411yescharacteristic
83#121×C43D411yescharacteristic
84#121×C43D411yescharacteristic
85#120×C43—21no—
86C4×Q8×C43—22no—
87C4×Q8×C43—21no—
88C4×Q8×C43—21no—
89C4×Q8×C43—21no—
90C4×Q8×C43—21no—
91C4×Q8×C43—21no—
92C4×D4×C43—22no—
93C4×D4×C43—21no—
94C4×D4×C43—22no—
95C4×D4×C43—21no—
96C4×D4×C43—21no—
97#117×C43—22no—
98#117×C43—22no—
99#117×C43—22no—
100#117×C43—21no—
101#117×C43—21no—
102#117×C43—21no—
103#117×C43C2×C411yescharacteristic
104#117×C43C2×C411yescharacteristic
105#117×C43C2×C411yescharacteristic
106#117×C43D411yescharacteristic
107#117×C43D411yescharacteristic
108C2×C4⋊C4×C43—21no—
109C2×C4⋊C4×C43C2×C411yescharacteristic
110C2×C4⋊C4×C43D412yes—
111C2×C4⋊C4×C43D411yescharacteristic
112C2×C4⋊C4×C43D411yescharacteristic
113C2×C22⋊C4×C43—21no—
114C2×C22⋊C4×C43D412yes—
115C2×C42×C43—21no—
116C24×C43C2×D411yescharacteristic
117#41×C43—42no—
118C2×Q8×C43—22no—
119C2×Q8×C43—21no—
120C2×Q8×C43—21no—
121C2×Q8×C43—42no—
122C2×Q8×C43C22⋊C411yescharacteristic
123C2×D4×C43—21no—
124C2×D4×C43—21no—
125C2×D4×C43—21no—
126C2×D4×C43C22⋊C411yescharacteristic
127C22×C4×C43—22no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—42no—
132C22×C4×C43C22⋊C412yes—
133C22×C4×C43C22⋊C412yes—
134C22×C4×C43C22×C411yescharacteristic
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×Dic43—41no—
141C22×Dic43—41no—
142C4⋊C4×C43—22no—
143C4⋊C4×C43—22no—
144C4⋊C4×C43—22no—
145C4⋊C4×C43—22no—
146C4⋊C4×C43—22no—
147C4⋊C4×C43—22no—
148C4⋊C4×C43—22no—
149C4⋊C4×C43—22no—
150C4⋊C4×C43—21no—
151C4⋊C4×C43—21no—
152C4⋊C4×C43—21no—
153C4⋊C4×C43—21no—
154C4⋊C4×C43—22no—
155C4⋊C4×C43—22no—
156C4⋊C4×C43—21no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43C22⋊C411yescharacteristic
159C4⋊C4×C43C22⋊C411yescharacteristic
160C4⋊C4×C43C22⋊C411yescharacteristic
161C4⋊C4×C43C22⋊C411yescharacteristic
162C4⋊C4×C43C22⋊C411yescharacteristic
163C4⋊C4×C43C22⋊C411yescharacteristic
164C22⋊C4×C43—22no—
165C22⋊C4×C43—22no—
166C22⋊C4×C43—22no—
167C22⋊C4×C43—21no—
168C22⋊C4×C43—21no—
169C22⋊C4×C43—21no—
170C22⋊C4×C43—21no—
171C22⋊C4×C43—21no—
172C22⋊C4×C43—21no—
173C22⋊C4×C43—21no—
174C22⋊C4×C43—22no—
175C22⋊C4×C43—22no—
176C22⋊C4×C43—21no—
177C22⋊C4×C43—21no—
178C42×C43—22no—
179C42×C43—22no—
180C42×C43—22no—
181C42×C43—21no—
182C42×C43—21no—
183C42×C43—21no—
184C42×C43—21no—
185C42×C43—21no—
186C22⋊Dic43—22no—
187C22⋊Dic43—41no—
188C22⋊Dic43—42no—
189C4⋊Dic43—42no—
190C4×Dic43—42no—
191#10621877—42no—
192C2×C43⋊C8—42no—
193C2×C43⋊C8—41no—
194C2×C43⋊C8—41no—
195C23×C43—21no—
196C23×C43—21no—
197C23×C43—21no—
198C23×C43—41no—
199C23×C43—41no—
200C23×C43C2×C22⋊C411yescharacteristic
201C23×C43#12011yescharacteristic
202C23×C43#12011yescharacteristic
203Q8×C43—41no—
204Q8×C43—42no—
205Q8×C43—42no—
206Q8×C43—82no—
207D4×C43—41no—
208D4×C43—42no—
209D4×C43—41no—
210D4×C43—41no—
211D4×C43—81no—
212C2×C4×C43—22no—
213C2×C4×C43—22no—
214C2×C4×C43—22no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—22no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—22no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—42no—
230C2×C4×C43—42no—
231C2×C4×C43—42no—
232C2×C4×C43—81no—
233C2×C4×C43—82no—
234C2×C4×C43C2×C22⋊C411yescharacteristic
235C2×C4×C43C2×C22⋊C411yescharacteristic
236C2×C4×C43#12011yescharacteristic
237C2×C4×C43#12011yescharacteristic
238C2×Dic43—42no—
239C2×Dic43—81no—
240C2×Dic43—81no—
241C2×Dic43—81no—
242C2×Dic43—81no—
243C2×Dic43—81no—
244C43⋊C8—81no—
245C43⋊C8—81no—
246#8468—431nomaximal, Sylow
247C22×C43—21no—
248C22×C43—21no—
249C22×C43—21no—
250C22×C43—21no—
251C22×C43—21no—
252C22×C43—21no—
253C22×C43—21no—
254C22×C43—21no—
255C22×C43—41no—
256C22×C43—41no—
257C22×C43—41no—
258C22×C43—81no—
259C22×C43—81no—
260C22×C43#37911yescharacteristic
261C22×C43#45411yescharacteristic
262C22×C43#45611yescharacteristic
263C4×C43—21no—
264C4×C43—21no—
265C4×C43—21no—
266C4×C43—41no—
267C4×C43—41no—
268C4×C43—41no—
269C4×C43—42no—
270C4×C43—41no—
271C4×C43—41no—
272C4×C43—41no—
273C4×C43—41no—
274C4×C43—42no—
275C4×C43#41012yes—
276Dic43—82no—
277Dic43—161no—
278#3495D4311yescharacteristic
279#1996—431no—
280#1826—431no—
281#1825—431no—
282#1513—431no—
283#1501—431no—
284#1472—431no—
285C2×C43—21no—
286C2×C43—21no—
287C2×C43—41no—
288C2×C43—41no—
289C2×C43—81no—
290C2×C43#178211yescharacteristic
291C2×C43#179311yescharacteristic
292C2×C43#179411yescharacteristic
293#556—21no—
294#554—21no—
295#552—21no—
296#552—22no—
297#552—21no—
298#551—22no—
299#544Dic4311yescharacteristic, complemented
300#542—21no—
301#541—21no—
302#536Dic4311yescharacteristic, complemented
303#533—21no—
304#529—21no—
305#525C2×D4311yescharacteristic
306C2×C22⋊Q8C2×D4311yescharacteristic
307#520Dic4311yescharacteristic, complemented
308#519Dic4311yescharacteristic, complemented
309C2×#117C2×D4311yescharacteristic
310#407—431no—
311C2×C22⋊C8—431no—
312#380—431no—
313C4×C22⋊C4—431no—
314#342—862no—
315#340—861no—
316#340—861no—
317#339—861no—
318#339—861no—
319#328—861no—
320#328—861no—
321#327—861no—
322#327—861no—
323#324—862no—
324C43#846811yescharacteristic, complemented, Sylow
325C2×#41C2×Dic4311yescharacteristic
326C22×Q8C2×Dic4311yescharacteristic
327C23×C4C22×D4311yescharacteristic
328C2×M16—861no—
329C22×C8—861no—
330C4⋊Q8—21no—
331C4⋊Q8—21no—
332C4⋊Q8—21no—
333#126—22no—
334#126—22no—
335#126—22no—
336#126—22no—
337#125—22no—
338#125—22no—
339#125—22no—
340#125—21no—
341#125—21no—
342#124—22no—
343#124—21no—
344#123—22no—
345#123—22no—
346#123—22no—
347#123—21no—
348C22⋊Q8—22no—
349C22⋊Q8—22no—
350C22⋊Q8—22no—
351C22⋊Q8—21no—
352C22⋊Q8—21no—
353C22⋊Q8—21no—
354C22⋊Q8—21no—
355C22⋊Q8—21no—
356C22⋊Q8—21no—
357C22⋊Q8C22⋊D4311yescharacteristic
358C22⋊Q8C22⋊D4311yescharacteristic
359#121C22⋊D4311yescharacteristic
360#121C22⋊D4311yescharacteristic
361#120—21no—
362C4×Q8—22no—
363C4×Q8—21no—
364C4×Q8—21no—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8—21no—
368C4×D4—22no—
369C4×D4—21no—
370C4×D4—22no—
371C4×D4—21no—
372C4×D4—21no—
373#117—22no—
374#117—22no—
375#117—22no—
376#117—21no—
377#117—21no—
378#117—21no—
379#117C2×Dic4311yescharacteristic
380#117C2×Dic4311yescharacteristic
381#117C2×Dic4311yescharacteristic
382#117C22⋊D4311yescharacteristic
383#117C22⋊D4311yescharacteristic
384C2×C4⋊C4—21no—
385C2×C4⋊C4—861no—
386C2×C4⋊C4C2×Dic4311yescharacteristic
387C2×C4⋊C4C22⋊D4312yes—
388C2×C4⋊C4C22⋊D4311yescharacteristic
389C2×C4⋊C4C22⋊D4311yescharacteristic
390C2×C22⋊C4—21no—
391C2×C22⋊C4—861no—
392C2×C22⋊C4—861no—
393C2×C22⋊C4C22⋊D4312yes—
394C2×C42—21no—
395C2×C42—861no—
396C22⋊C8—861no—
397C22⋊C8—861no—
398C22⋊C8—861no—
399C22⋊C8—861no—
400#95—861no—
401#95—861no—
402C24C2×C22⋊D4311yescharacteristic
403#41—42no—
404C2×Q8—22no—
405C2×Q8—21no—
406C2×Q8—21no—
407C2×Q8—42no—
408C2×Q8C22⋊Dic4311yescharacteristic
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4C22⋊Dic4311yescharacteristic
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—42no—
418C22×C4—1721no—
419C22×C4—1721no—
420C22×C4C22⋊Dic4312yes—
421C22×C4C22⋊Dic4312yes—
422C22×C4C22×Dic4311yescharacteristic
423C22×C4C2×C22⋊D4311yescharacteristic
424C22×C4C2×C22⋊D4311yescharacteristic
425C22×C4C2×C22⋊D4311yescharacteristic
426C22×C4C2×C22⋊D4311yescharacteristic
427C22×C4C2×C22⋊D4311yescharacteristic
428M16—1722no—
429C2×C8—1722no—
430C2×C8—1721no—
431C2×C8—1721no—
432C4⋊C4—22no—
433C4⋊C4—22no—
434C4⋊C4—22no—
435C4⋊C4—22no—
436C4⋊C4—22no—
437C4⋊C4—22no—
438C4⋊C4—22no—
439C4⋊C4—22no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—1722no—
449C4⋊C4C22⋊Dic4311yescharacteristic
450C4⋊C4C22⋊Dic4311yescharacteristic
451C4⋊C4C22⋊Dic4311yescharacteristic
452C4⋊C4C22⋊Dic4311yescharacteristic
453C4⋊C4C22⋊Dic4311yescharacteristic
454C4⋊C4C22⋊Dic4311yescharacteristic
455C22⋊C4—22no—
456C22⋊C4—22no—
457C22⋊C4—22no—
458C22⋊C4—21no—
459C22⋊C4—21no—
460C22⋊C4—21no—
461C22⋊C4—21no—
462C22⋊C4—21no—
463C22⋊C4—22no—
464C22⋊C4—22no—
465C22⋊C4—21no—
466C22⋊C4—21no—
467C22⋊C4—21no—
468C22⋊C4—21no—
469C22⋊C4—862no—
470C22⋊C4—1722no—
471C22⋊C4—1721no—
472C42—22no—
473C42—22no—
474C42—22no—
475C42—21no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—21no—
480C42—1722no—
481C23—21no—
482C23—21no—
483C23—21no—
484C23—41no—
485C23—41no—
486C23C2×C22⋊Dic4311yescharacteristic
487C23#1306329411yescharacteristic
488C23#1306329411yescharacteristic
489Q8—41no—
490Q8—42no—
491Q8—42no—
492Q8—82no—
493D4—41no—
494D4—42no—
495D4—41no—
496D4—41no—
497D4—81no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—22no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—22no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—81no—
519C2×C4—82no—
520C2×C4—3441no—
521C2×C4—3441no—
522C2×C4—3441no—
523C2×C4—3441no—
524C2×C4—3441no—
525C2×C4—1722no—
526C2×C4C2×C22⋊Dic4311yescharacteristic
527C2×C4C2×C22⋊Dic4311yescharacteristic
528C2×C4#1306329411yescharacteristic
529C2×C4#1306329411yescharacteristic
530C8—3441no—
531C8—3441no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—21no—
540C22—41no—
541C22—41no—
542C22—41no—
543C22—81no—
544C22—81no—
545C22#1458275511yescharacteristic
546C22#1458307211yescharacteristic
547C22#1458308211yescharacteristic
548C4—21no—
549C4—21no—
550C4—21no—
551C4—41no—
552C4—42no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4—42no—
557C4—41no—
558C4—41no—
559C4—41no—
560C4—3442no—
561C4—6881no—
562C4#1458287312yes—
563C2—21no—
564C2—21no—
565C2—41no—
566C2—41no—
567C2—81no—
568C2#1913451311yescharacteristic
569C2#1913455411yescharacteristic
570C2#1913455911yescharacteristic
subgroupG/H
centerC22#14582755
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#3495C2
socleC22×C43#379
prime radicalC43×#525C22
cosocleC23×C4×C43C23
hypercenter#3495D43
hypocenterC43#8468
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3495

Complements

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

NH ≅ G/Ntype
1. #19135581C2semidirect
2. #19134694C2semidirect
3. #19134690C2semidirect
6. #19132959C2semidirect
28. C43×#544C4semidirect
31. C43×#536C4semidirect
36. C43×#520C4semidirect
37. C43×#519C4semidirect
299. #544Dic43semidirect
302. #536Dic43semidirect
307. #520Dic43semidirect
308. #519Dic43semidirect
324. C43#8468semidirect

Maximal subgroups

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

subgroupindex
#191355812
#191346942
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