Finite Group Databasebeta

← #25071813

Subgroups — #25071813

Order 11008.

904 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145813C211yesmaximal, characteristic, complemented
2#19145713C211yesmaximal, characteristic, complemented
3#19140716C211yesmaximal, characteristic, complemented
4#19133598C214yesmaximal, complemented
5#19133592C214yesmaximal, complemented
6#19133103C211yesmaximal, characteristic, complemented
7#19133081C211yesmaximal, characteristic, complemented
8#19132951C211yesmaximal, characteristic, complemented
9C43×#3559C211yesmaximal, characteristic
10C2×#13063325C2211yescharacteristic
11#14583309—21no—
12#14583302—21no—
13#14583258—21no—
14#14583245—21no—
15#14583227C2212yes—
16#14583210C2212yes—
17#14583210C2214yes—
18#14583194—21no—
19#14583189—21no—
20#14583179—22no—
21#14582956C2211yescharacteristic
22#14582952C2211yescharacteristic
23#14582829C2214yes—
24#14582819—22no—
25#14582768—21no—
26#14582764—21no—
27#14582745C2211yescharacteristic
28#14582636C2212yes—
29#14582633C2214yes—
30#14582633C2212yes—
31#14582625C2214yes—
32C43×#563—21no—
33C43×#562—21no—
34C43×#554—21no—
35C43×#553—21no—
36C43×#553—21no—
37C43×#547—22no—
38C43×#547—21no—
39C43×#544—21no—
40C43×#540—21no—
41C43×#539—22no—
42C43×#539C2212yes—
43C43×#537C2212yes—
44C43×#532C2211yescharacteristic
45C43×#529C2211yescharacteristic
46C2×#125×C43C2211yescharacteristic
47C22×Dic86—21no—
48#13063325—21no—
49#13063325—21no—
50#13063325—21no—
51#13063325—21no—
52C2×C4⋊Dic43—21no—
53C2×C4⋊Dic43C2312yes—
54C2×Dic43⋊C4—24no—
55C2×C4×Dic43—21no—
56#13063258—24no—
57#13063258—22no—
58#13063256—22no—
59C4⋊(C43⋊C8)—21no—
60C4⋊(C43⋊C8)—21no—
61#13063249—22no—
62#13063246—24no—
63#13063246—22no—
64C22⋊(C43⋊C8)C2312yes—
65C22⋊(C43⋊C8)C2312yes—
66#13063236—21no—
67C4×C43⋊C8—21no—
68C43⋊#95—21no—
69C43⋊#95—24no—
70C43⋊#95C2312yes—
71C2×#41×C43—21no—
72C2×#41×C43—22no—
73C4⋊Q8×C43—21no—
74C4⋊Q8×C43—22no—
75C4⋊Q8×C43D411yescharacteristic
76#127×C43D411yescharacteristic
77#126×C43—22no—
78#126×C43—22no—
79#126×C43—21no—
80#125×C43—21no—
81#125×C43—22no—
82#125×C43—21no—
83#125×C43—21no—
84#125×C43—21no—
85#125×C43—21no—
86#125×C43D411yescharacteristic
87#124×C43—21no—
88#124×C43D411yescharacteristic
89#123×C43—22no—
90#123×C43—22no—
91#123×C43—22no—
92#123×C43—22no—
93#123×C43—22no—
94#123×C43—21no—
95#123×C43—22no—
96C22⋊Q8×C43—22no—
97C22⋊Q8×C43—22no—
98C22⋊Q8×C43—22no—
99C22⋊Q8×C43—22no—
100C22⋊Q8×C43—22no—
101C22⋊Q8×C43—22no—
102C22⋊Q8×C43C2311yescharacteristic
103#121×C43—21no—
104#121×C43—22no—
105#121×C43—21no—
106#121×C43—22no—
107#121×C43—22no—
108#121×C43—21no—
109#121×C43—22no—
110#121×C43C2311yescharacteristic
111#121×C43C2312yes—
112C4×Q8×C43D411yescharacteristic
113C4×D4×C43—22no—
114C4×D4×C43—21no—
115C4×D4×C43—21no—
116C4×D4×C43—21no—
117C4×D4×C43—22no—
118C4×D4×C43—21no—
119C4×D4×C43D411yescharacteristic
120C4×D4×C43D412yes—
121#117×C43—21no—
122#117×C43—21no—
123C2×C4⋊C4×C43—22no—
124C2×C4⋊C4×C43—21no—
125C2×C4⋊C4×C43D412yes—
126C2×C4⋊C4×C43D411yescharacteristic
127C2×C4⋊C4×C43D411yescharacteristic
128C2×C4⋊C4×C43C2312yes—
129C2×C42×C43C2311yescharacteristic
130#41×C43—82no—
131#41×C43—84no—
132C2×Q8×C43—22no—
133C2×Q8×C43—21no—
134C2×Q8×C43C2×D411yescharacteristic
135C2×D4×C43—22no—
136C2×D4×C43—22no—
137C2×D4×C43—21no—
138C2×D4×C43—21no—
139C2×D4×C43—21no—
140C2×D4×C43—22no—
141C2×D4×C43C2×D411yescharacteristic
142C2×D4×C43C2×D412yes—
143C22×C4×C43—22no—
144C22×C4×C43—22no—
145C22×C4×C43—22no—
146C22×C4×C43—21no—
147C22×C4×C43—22no—
148C22×C4×C43C2×D412yes—
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D412yes—
152C22×C4×C43C2411yescharacteristic
153C22×Dic43—22no—
154C22×Dic43—22no—
155C2×Dic86—41no—
156C2×Dic86—41no—
157C2×Dic86—82no—
158C4⋊C4×C43—22no—
159C4⋊C4×C43—22no—
160C4⋊C4×C43—22no—
161C4⋊C4×C43—22no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—22no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—22no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—22no—
173C4⋊C4×C43—22no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43C2×D412yes—
176C4⋊C4×C43C2×D411yescharacteristic
177C4⋊C4×C43C2×D411yescharacteristic
178C22⋊C4×C43—22no—
179C22⋊C4×C43—22no—
180C22⋊C4×C43—22no—
181C22⋊C4×C43—22no—
182C22⋊C4×C43—22no—
183C22⋊C4×C43—21no—
184C22⋊C4×C43—21no—
185C22⋊C4×C43—21no—
186C22⋊C4×C43—22no—
187C22⋊C4×C43—21no—
188C22⋊C4×C43—22no—
189C22⋊C4×C43—21no—
190C42×C43—22no—
191C42×C43—21no—
192C42×C43C2×D411yescharacteristic
193C42×C43C2×D411yescharacteristic
194C42×C43C2×D411yescharacteristic
195C42×C43C2×D411yescharacteristic
196C4⋊Dic43—22no—
197C4⋊Dic43—22no—
198C4⋊Dic43—41no—
199C4⋊Dic43—41no—
200Dic43⋊C4—84no—
201C4×Dic43—24no—
202C2×C43⋊C8—22no—
203C2×C43⋊C8—22no—
204C23×C43—21no—
205C23×C43—22no—
206C23×C43C22×D411yescharacteristic
207Q8×C43—41no—
208Q8×C43—81no—
209Q8×C43—82no—
210D4×C43—42no—
211D4×C43—41no—
212D4×C43—44no—
213D4×C43—42no—
214D4×C43—42no—
215D4×C43—81no—
216D4×C43—82no—
217D4×C43—82no—
218C2×C4×C43—22no—
219C2×C4×C43—22no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—22no—
223C2×C4×C43—22no—
224C2×C4×C43—21no—
225C2×C4×C43—22no—
226C2×C4×C43—24no—
227C2×C4×C43—41no—
228C2×C4×C43—42no—
229C2×C4×C43—42no—
230C2×C4×C43—82no—
231C2×C4×C43—82no—
232C2×C4×C43—82no—
233C2×C4×C43—82no—
234C2×C4×C43#12011yescharacteristic
235C2×C4×C43#12011yescharacteristic
236C2×C4×C43#12011yescharacteristic
237C2×C4×C43#12011yescharacteristic
238C2×C4×C43C22×D411yescharacteristic
239C2×C4×C43C22×D411yescharacteristic
240C2×Dic43—24no—
241C2×Dic43—42no—
242C2×Dic43—42no—
243C2×Dic43—42no—
244C2×Dic43—44no—
245Dic86—82no—
246Dic86—82no—
247C43⋊C8—42no—
248C43⋊C8—42no—
249#18440—431nomaximal, Sylow
250C22×C43—21no—
251C22×C43—21no—
252C22×C43—42no—
253C22×C43—41no—
254C22×C43—41no—
255C22×C43—42no—
256C22×C43—42no—
257C22×C43—41no—
258C22×C43C2×#12011yescharacteristic
259C22×C43#57612yes—
260C4×C43—21no—
261C4×C43—21no—
262C4×C43—21no—
263C4×C43—21no—
264C4×C43—21no—
265C4×C43—42no—
266C4×C43—42no—
267C4×C43—41no—
268C4×C43—41no—
269C4×C43—42no—
270C4×C43—41no—
271C4×C43#45612yes—
272Dic43—44no—
273Dic43—82no—
274#3559D4311yescharacteristic
275#3238—431no—
276#3226—431no—
277#2660—431no—
278#1610—434no—
279#1609—434no—
280#1505—431no—
281#1500—431no—
282#1470—431no—
283C2×C43—22no—
284C2×C43—81no—
285C2×C43—82no—
286C2×C43#300811yescharacteristic
287C2×C43C2×#45611yescharacteristic
288C2×C43#302811yescharacteristic
289#563—21no—
290#562—21no—
291#554—21no—
292#553—21no—
293#553—21no—
294#547—22no—
295#547—21no—
296#544—21no—
297#540—21no—
298#539—22no—
299#539C2×D4312yes—
300#537C2×D4312yes—
301#532C2×D4311yescharacteristic
302C2×C4⋊Q8—431no—
303#529C2×D4311yescharacteristic
304C2×#125C2×D4311yescharacteristic
305#501—861no—
306#500—861no—
307#489—861no—
308#486—861no—
309#483—432no—
310#480—434no—
311#480—432no—
312#477—861no—
313#476—861no—
314#474—862no—
315#432—431no—
316#431—431no—
317#398—434no—
318#395—862no—
319#384—861no—
320#382—861no—
321#376—431no—
322#328—432no—
323#327—434no—
324#327—432no—
325#324—434no—
326C43#1844011yescharacteristic, complemented, Sylow
327C2×#41—21no—
328C2×#41—22no—
329C22×Q8—861no—
330C4⋊Q8—21no—
331C4⋊Q8—22no—
332C4⋊Q8—861no—
333C4⋊Q8—861no—
334C4⋊Q8—861no—
335C4⋊Q8—861no—
336C4⋊Q8C22⋊D4311yescharacteristic
337#127C22⋊D4311yescharacteristic
338#126—22no—
339#126—22no—
340#126—21no—
341#125—21no—
342#125—22no—
343#125—21no—
344#125—21no—
345#125—21no—
346#125—21no—
347#125C22⋊D4311yescharacteristic
348#124—21no—
349#124C22⋊D4311yescharacteristic
350#123—22no—
351#123—22no—
352#123—22no—
353#123—22no—
354#123—22no—
355#123—21no—
356#123—22no—
357C22⋊Q8—22no—
358C22⋊Q8—22no—
359C22⋊Q8—22no—
360C22⋊Q8—22no—
361C22⋊Q8—22no—
362C22⋊Q8—22no—
363C22⋊Q8C22×D4311yescharacteristic
364#121—21no—
365#121—22no—
366#121—21no—
367#121—22no—
368#121—22no—
369#121—21no—
370#121—22no—
371#121C22×D4311yescharacteristic
372#121C22×D4312yes—
373C4×Q8C22⋊D4311yescharacteristic
374C4×D4—22no—
375C4×D4—21no—
376C4×D4—21no—
377C4×D4—21no—
378C4×D4—22no—
379C4×D4—21no—
380C4×D4C22⋊D4311yescharacteristic
381C4×D4C22⋊D4312yes—
382#117—21no—
383#117—21no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—432no—
387C2×C4⋊C4—864no—
388C2×C4⋊C4—861no—
389C2×C4⋊C4C22⋊D4311yescharacteristic
390C2×C4⋊C4C22⋊D4312yes—
391C2×C4⋊C4C22⋊D4311yescharacteristic
392C2×C4⋊C4C22×D4312yes—
393C2×C42—861no—
394C2×C42C22×D4311yescharacteristic
395#107—864no—
396#107—862no—
397#106—862no—
398C4⋊C8—861no—
399C4⋊C8—861no—
400#103—862no—
401#102—864no—
402#102—862no—
403C22⋊C8—432no—
404C22⋊C8—432no—
405#97—861no—
406C4×C8—861no—
407#95—432no—
408#95—861no—
409#95—864no—
410#41—82no—
411#41—84no—
412C2×Q8—22no—
413C2×Q8—21no—
414C2×Q8—3442no—
415C2×Q8—1721no—
416C2×Q8—1721no—
417C2×Q8C2×C22⋊D4311yescharacteristic
418C2×D4—21no—
419C2×D4—22no—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4C2×C22⋊D4311yescharacteristic
425C2×D4C2×C22⋊D4312yes—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—862no—
432C22×C4—862no—
433C22×C4C2×C22⋊D4312yes—
434C22×C4C2×C22⋊D4311yescharacteristic
435C22×C4C2×C22⋊D4311yescharacteristic
436C22×C4C2×C22⋊D4312yes—
437C22×C4C23×D4311yescharacteristic
438C2×C8—862no—
439C2×C8—862no—
440C4⋊C4—22no—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—22no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—22no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—22no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—22no—
455C4⋊C4—22no—
456C4⋊C4—21no—
457C4⋊C4—862no—
458C4⋊C4—862no—
459C4⋊C4—3444no—
460C4⋊C4—1721no—
461C4⋊C4—1721no—
462C4⋊C4C2×C22⋊D4311yescharacteristic
463C4⋊C4C2×C22⋊D4312yes—
464C4⋊C4C2×C22⋊D4311yescharacteristic
465C22⋊C4—22no—
466C22⋊C4—22no—
467C22⋊C4—22no—
468C22⋊C4—22no—
469C22⋊C4—22no—
470C22⋊C4—21no—
471C22⋊C4—21no—
472C22⋊C4—21no—
473C22⋊C4—21no—
474C22⋊C4—22no—
475C22⋊C4—21no—
476C22⋊C4—22no—
477C42—22no—
478C42—21no—
479C42—864no—
480C42C2×C22⋊D4311yescharacteristic
481C42C2×C22⋊D4311yescharacteristic
482C42C2×C22⋊D4311yescharacteristic
483C42C2×C22⋊D4311yescharacteristic
484C23—21no—
485C23—22no—
486C23C22×C22⋊D4311yescharacteristic
487Q8—41no—
488Q8—81no—
489Q8—82no—
490Q8—3442no—
491Q8—3442no—
492D4—42no—
493D4—41no—
494D4—44no—
495D4—42no—
496D4—42no—
497D4—81no—
498D4—82no—
499D4—82no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—21no—
507C2×C4—22no—
508C2×C4—24no—
509C2×C4—41no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—82no—
513C2×C4—82no—
514C2×C4—82no—
515C2×C4—82no—
516C2×C4—864no—
517C2×C4—1722no—
518C2×C4—1724no—
519C2×C4—1722no—
520C2×C4—1722no—
521C2×C4#1306329411yescharacteristic
522C2×C4#1306329411yescharacteristic
523C2×C4#1306329411yescharacteristic
524C2×C4#1306329411yescharacteristic
525C2×C4C22×C22⋊D4311yescharacteristic
526C2×C4C22×C22⋊D4311yescharacteristic
527C8—1722no—
528C8—1722no—
529C22—21no—
530C22—21no—
531C22—41no—
532C22—42no—
533C22—42no—
534C22—41no—
535C22—42no—
536C22—41no—
537C22C2×#1306329411yescharacteristic
538C22#1458370212yes—
539C4—21no—
540C4—21no—
541C4—21no—
542C4—21no—
543C4—21no—
544C4—41no—
545C4—42no—
546C4—41no—
547C4—42no—
548C4—42no—
549C4—41no—
550C4—3442no—
551C4—1724no—
552C4#1458308212yes—
553C2—22no—
554C2—81no—
555C2—82no—
556C2#1914386311yescharacteristic
557C2C2×#1458308211yescharacteristic
558C2#1914400111yescharacteristic
subgroupG/H
centerC22C2×#13063294
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC43×#3559C2
socleC22×C43C2×#120
hypercenter#3559D43
hypocenterC43#18440
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3559

Complements

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

NH ≅ G/Ntype
1. #19145813C2semidirect
2. #19145713C2semidirect
3. #19140716C2semidirect
4. #19133598C2semidirect
5. #19133592C2semidirect
6. #19133103C2semidirect
7. #19133081C2semidirect
8. #19132951C2semidirect
326. C43#18440semidirect

Maximal subgroups

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

subgroupindex
#191458132
#191457132
#191407162
#191335982
#191335922
#191331032
#191330812
#191329512
C43×#35592
#1844043