Finite Group Databasebeta

← #25074090

Subgroups — #25074090

Order 11008.

940 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145517C211yesmaximal, characteristic, complemented
2C2×#14583302C211yesmaximal, characteristic, complemented
3#19144410C211yesmaximal, characteristic, complemented
4#19133851C214yesmaximal, complemented
5#19133830C214yesmaximal, complemented
6#19133280C211yesmaximal, characteristic, complemented
7#19133046C211yesmaximal, characteristic, complemented
8#19132977C211yesmaximal, characteristic, complemented
9C43×#3511C211yesmaximal, characteristic
10C2×#13063325C2211yescharacteristic
11#14583302—22no—
12#14583302C2214yes—
13#14583271—21no—
14#14583251—21no—
15#14583194—21no—
16#14583189—21no—
17#14583184C2212yes—
18#14583179C2212yes—
19#14583104C2214yes—
20#14583037—22no—
21#14582952C2211yescharacteristic
22#14582942—21no—
23C2×#13063258—22no—
24#14582923C2211yescharacteristic
25#14582900—21no—
26C2×C4×C43⋊C8C2211yescharacteristic
27#14582645C2214yes—
28Q8⋊(C43⋊C8)C2212yes—
29D4⋊(C43⋊C8)C2212yes—
30D4⋊(C43⋊C8)C2214yes—
31C43×#556C2212yes—
32C43×#555—21no—
33C43×#554—21no—
34C43×#553—22no—
35C43×#548—22no—
36C43×#547C2212yes—
37C43×#542—22no—
38C43×#537—21no—
39C43×#533—21no—
40C43×#532—21no—
41C43×#532C2211yescharacteristic
42C2×C4⋊Q8×C43C2211yescharacteristic
43C43×#520—21no—
44C4×#41×C43C2211yescharacteristic
45C22×Dic86—21no—
46C2×#10621883—24no—
47C2×#10621877—21no—
48C22×C43⋊C8—21no—
49#13063325—21no—
50#13063325—21no—
51#13063325—21no—
52#13063325C2312yes—
53C2×C4⋊Dic43—21no—
54C2×C4⋊Dic43—21no—
55#13063258—28no—
56#13063258—22no—
57#13063256—22no—
58C4⋊(C43⋊C8)—21no—
59C4⋊(C43⋊C8)C2312yes—
60C4⋊(C43⋊C8)C2312yes—
61#13063249—22no—
62#13063248—24no—
63#13063246—22no—
64C22⋊(C43⋊C8)—21no—
65C4×C43⋊C8—21no—
66C4×C43⋊C8—21no—
67C4×C43⋊C8C2312yes—
68C2×#41×C43—22no—
69C2×#41×C43—21no—
70C2×#41×C43D411yescharacteristic
71C22×Q8×C43—21no—
72C4⋊Q8×C43—21no—
73C4⋊Q8×C43—21no—
74C4⋊Q8×C43D412yes—
75C4⋊Q8×C43D411yescharacteristic
76C4⋊Q8×C43C2312yes—
77#127×C43D411yescharacteristic
78#126×C43—24no—
79#125×C43—22no—
80#124×C43—24no—
81#124×C43—22no—
82#124×C43—21no—
83#123×C43—24no—
84C22⋊Q8×C43—22no—
85C22⋊Q8×C43—24no—
86C22⋊Q8×C43—22no—
87C22⋊Q8×C43—22no—
88#121×C43—22no—
89#121×C43—22no—
90#121×C43—24no—
91#121×C43—22no—
92#121×C43—21no—
93#121×C43D412yes—
94C4×Q8×C43—22no—
95C4×Q8×C43—22no—
96C4×Q8×C43D411yescharacteristic
97C4×Q8×C43C2311yescharacteristic
98C4×D4×C43—22no—
99C4×D4×C43—24no—
100C4×D4×C43—22no—
101C4×D4×C43—21no—
102C4×D4×C43—21no—
103C4×D4×C43—21no—
104C4×D4×C43D411yescharacteristic
105C4×D4×C43C2311yescharacteristic
106C4×D4×C43C2312yes—
107#117×C43—22no—
108#117×C43—22no—
109#117×C43—21no—
110#117×C43D411yescharacteristic
111C2×C4⋊C4×C43—21no—
112C2×C4⋊C4×C43—22no—
113C2×C4⋊C4×C43D412yes—
114C2×C42×C43—21no—
115C2×C42×C43C2311yescharacteristic
116#41×C43—22no—
117#41×C43—22no—
118#41×C43—42no—
119#41×C43—42no—
120#41×C43—84no—
121C2×Q8×C43—21no—
122C2×Q8×C43—22no—
123C2×Q8×C43—22no—
124C2×Q8×C43—82no—
125C2×Q8×C43C2×D411yescharacteristic
126C2×D4×C43—24no—
127C2×D4×C43—21no—
128C2×D4×C43—21no—
129C2×D4×C43—21no—
130C2×D4×C43—22no—
131C2×D4×C43C2×D411yescharacteristic
132C2×D4×C43C2×D412yes—
133C22×C4×C43—24no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—22no—
138C22×C4×C43—22no—
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2×D411yescharacteristic
142C22×Dic43—41no—
143C2×Dic86—22no—
144C2×Dic86—41no—
145C2×Dic86—82no—
146C4⋊C4×C43—24no—
147C4⋊C4×C43—24no—
148C4⋊C4×C43—22no—
149C4⋊C4×C43—22no—
150C4⋊C4×C43—21no—
151C4⋊C4×C43—21no—
152C4⋊C4×C43—22no—
153C4⋊C4×C43—21no—
154C4⋊C4×C43C2×D411yescharacteristic
155C4⋊C4×C43C2×D414yes—
156C4⋊C4×C43C2×D411yescharacteristic
157C4⋊C4×C43C2×D412yes—
158C22⋊C4×C43—24no—
159C22⋊C4×C43—24no—
160C22⋊C4×C43—24no—
161C22⋊C4×C43—21no—
162C22⋊C4×C43—22no—
163C22⋊C4×C43—21no—
164C22⋊C4×C43—22no—
165C22⋊C4×C43—21no—
166C42×C43—24no—
167C42×C43—21no—
168C42×C43—21no—
169C42×C43—21no—
170C42×C43C2×D411yescharacteristic
171C42×C43C2×D411yescharacteristic
172C42×C43C2×D411yescharacteristic
173C42×C43C2411yescharacteristic
174#10621883—84no—
175C4⋊Dic43—22no—
176C4⋊Dic43—22no—
177C4⋊Dic43—41no—
178C4⋊Dic43—41no—
179#10621877—42no—
180C2×C43⋊C8—24no—
181C2×C43⋊C8—22no—
182C2×C43⋊C8—22no—
183C2×C43⋊C8—22no—
184C23×C43—21no—
185C23×C43—22no—
186C23×C43#12011yescharacteristic
187Q8×C43—21no—
188Q8×C43—21no—
189Q8×C43—44no—
190Q8×C43—42no—
191Q8×C43—82no—
192D4×C43—21no—
193D4×C43—21no—
194D4×C43—24no—
195D4×C43—42no—
196D4×C43—44no—
197D4×C43—42no—
198D4×C43—42no—
199D4×C43—84no—
200C2×C4×C43—22no—
201C2×C4×C43—22no—
202C2×C4×C43—21no—
203C2×C4×C43—21no—
204C2×C4×C43—22no—
205C2×C4×C43—21no—
206C2×C4×C43—24no—
207C2×C4×C43—42no—
208C2×C4×C43—42no—
209C2×C4×C43—42no—
210C2×C4×C43—42no—
211C2×C4×C43—42no—
212C2×C4×C43—82no—
213C2×C4×C43—84no—
214C2×C4×C43#12011yescharacteristic
215C2×C4×C43#12011yescharacteristic
216C2×C4×C43#12011yescharacteristic
217C2×C4×C43#13512yes—
218C2×C4×C43#13712yes—
219C2×C4×C43C22×D411yescharacteristic
220C2×C4×C43C22×D411yescharacteristic
221C2×C4×C43C22×D411yescharacteristic
222C2×Dic43—42no—
223C2×Dic43—82no—
224Dic86—44no—
225Dic86—82no—
226C43⋊C8—24no—
227C43⋊C8—42no—
228C43⋊C8—42no—
229#18657—431nomaximal, Sylow
230C22×C43—21no—
231C22×C43—21no—
232C22×C43—41no—
233C22×C43—42no—
234C22×C43—41no—
235C22×C43—42no—
236C22×C43—41no—
237C22×C43—42no—
238C22×C43#45212yes—
239C22×C43C2×#12011yescharacteristic
240C4×C43—21no—
241C4×C43—21no—
242C4×C43—41no—
243C4×C43—42no—
244C4×C43—41no—
245C4×C43—44no—
246C4×C43—41no—
247C4×C43#45212yes—
248C4×C43#45612yes—
249C4×C43C2×#13511yescharacteristic
250C4×C43C2×#13711yescharacteristic
251C4×C43#57612yes—
252Dic43—82no—
253#3511D4311yescharacteristic
254#3206—431no—
255C2×#500—431no—
256#3079—431no—
257#1650—434no—
258#1647—434no—
259#1549—431no—
260#1492—431no—
261#1476—431no—
262C2×C43—22no—
263C2×C43—81no—
264C2×C43—82no—
265C2×C43C2×#45211yescharacteristic
266C2×C43#300811yescharacteristic
267C2×C43C2×#45611yescharacteristic
268#556C2×D4312yes—
269#555—21no—
270#554—21no—
271#553—22no—
272#548—22no—
273#547C2×D4312yes—
274#542—22no—
275#537—21no—
276#533—21no—
277#532—21no—
278#532C2×D4311yescharacteristic
279C2×C4⋊Q8—431no—
280C2×C4⋊Q8C2×D4311yescharacteristic
281#520—21no—
282C4×#41C2×D4311yescharacteristic
283#500—434no—
284#500—862no—
285#492—861no—
286#487—861no—
287#477—861no—
288#476—861no—
289#475—432no—
290#474—432no—
291#461—434no—
292#448—862no—
293#431—431no—
294#428—861no—
295C2×#107—862no—
296#423—431no—
297#417—861no—
298C2×C4×C8—431no—
299#332—434no—
300Q8⋊C8—432no—
301D4⋊C8—432no—
302D4⋊C8—434no—
303C43#1865711yescharacteristic, complemented, Sylow
304C2×#41—22no—
305C2×#41—21no—
306C2×#41C22⋊D4311yescharacteristic
307C22×Q8—21no—
308C22×Q8—861no—
309C2×SD16—864no—
310C2×M16—861no—
311C22×C8—861no—
312C4⋊Q8—21no—
313C4⋊Q8—21no—
314C4⋊Q8—432no—
315C4⋊Q8—861no—
316C4⋊Q8—861no—
317C4⋊Q8—861no—
318C4⋊Q8C22⋊D4312yes—
319C4⋊Q8C22⋊D4311yescharacteristic
320C4⋊Q8C22×D4312yes—
321#127C22⋊D4311yescharacteristic
322#126—24no—
323#125—22no—
324#124—24no—
325#124—22no—
326#124—21no—
327#123—24no—
328C22⋊Q8—22no—
329C22⋊Q8—24no—
330C22⋊Q8—22no—
331C22⋊Q8—22no—
332#121—22no—
333#121—22no—
334#121—24no—
335#121—22no—
336#121—21no—
337#121C22⋊D4312yes—
338C4×Q8—22no—
339C4×Q8—22no—
340C4×Q8C22⋊D4311yescharacteristic
341C4×Q8C22×D4311yescharacteristic
342C4×D4—22no—
343C4×D4—24no—
344C4×D4—22no—
345C4×D4—21no—
346C4×D4—21no—
347C4×D4—21no—
348C4×D4C22⋊D4311yescharacteristic
349C4×D4C22×D4311yescharacteristic
350C4×D4C22×D4312yes—
351#117—22no—
352#117—22no—
353#117—21no—
354#117C22⋊D4311yescharacteristic
355C2×C4⋊C4—21no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—861no—
358C2×C4⋊C4—861no—
359C2×C4⋊C4C22⋊D4312yes—
360C2×C42—21no—
361C2×C42C22×D4311yescharacteristic
362#107—868no—
363#107—862no—
364#106—862no—
365C4⋊C8—432no—
366C4⋊C8—432no—
367C4⋊C8—861no—
368#103—862no—
369#103—864no—
370#102—862no—
371C22⋊C8—861no—
372C4×C8—432no—
373C4×C8—861no—
374C4×C8—861no—
375#41—22no—
376#41—22no—
377#41—42no—
378#41—42no—
379#41—84no—
380C2×Q8—21no—
381C2×Q8—22no—
382C2×Q8—22no—
383C2×Q8—82no—
384C2×Q8—862no—
385C2×Q8—3442no—
386C2×Q8—1721no—
387C2×Q8C2×C22⋊D4311yescharacteristic
388C2×D4—21no—
389C2×D4—22no—
390C2×D4—24no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4C2×C22⋊D4311yescharacteristic
394C2×D4C2×C22⋊D4312yes—
395C22×C4—24no—
396C22×C4—22no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—1721no—
402C22×C4C2×C22⋊D4311yescharacteristic
403C22×C4C2×C22⋊D4311yescharacteristic
404C22×C4C2×C22⋊D4311yescharacteristic
405SD16—3444no—
406M16—1722no—
407C2×C8—864no—
408C2×C8—862no—
409C2×C8—862no—
410C2×C8—862no—
411C4⋊C4—24no—
412C4⋊C4—24no—
413C4⋊C4—22no—
414C4⋊C4—22no—
415C4⋊C4—21no—
416C4⋊C4—21no—
417C4⋊C4—22no—
418C4⋊C4—21no—
419C4⋊C4—862no—
420C4⋊C4—862no—
421C4⋊C4—1721no—
422C4⋊C4—1721no—
423C4⋊C4C2×C22⋊D4312yes—
424C4⋊C4C2×C22⋊D4311yescharacteristic
425C4⋊C4C2×C22⋊D4311yescharacteristic
426C4⋊C4C2×C22⋊D4314yes—
427C22⋊C4—24no—
428C22⋊C4—24no—
429C22⋊C4—24no—
430C22⋊C4—21no—
431C22⋊C4—21no—
432C22⋊C4—22no—
433C22⋊C4—21no—
434C22⋊C4—22no—
435C42—24no—
436C42—21no—
437C42—21no—
438C42—21no—
439C42C2×C22⋊D4311yescharacteristic
440C42C2×C22⋊D4311yescharacteristic
441C42C2×C22⋊D4311yescharacteristic
442C42C23×D4311yescharacteristic
443C23—21no—
444C23—22no—
445C23#1306329411yescharacteristic
446Q8—21no—
447Q8—21no—
448Q8—42no—
449Q8—44no—
450Q8—82no—
451Q8—3442no—
452Q8—1724no—
453D4—21no—
454D4—21no—
455D4—24no—
456D4—42no—
457D4—44no—
458D4—42no—
459D4—42no—
460D4—84no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—22no—
466C2×C4—21no—
467C2×C4—24no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—82no—
474C2×C4—84no—
475C2×C4—3442no—
476C2×C4—1722no—
477C2×C4#1306329411yescharacteristic
478C2×C4#1306329411yescharacteristic
479C2×C4#1306329411yescharacteristic
480C2×C4#1306334512yes—
481C2×C4#1306335512yes—
482C2×C4C22×C22⋊D4311yescharacteristic
483C2×C4C22×C22⋊D4311yescharacteristic
484C2×C4C22×C22⋊D4311yescharacteristic
485C8—864no—
486C8—1722no—
487C8—1722no—
488C22—21no—
489C22—21no—
490C22—41no—
491C22—42no—
492C22—41no—
493C22—42no—
494C22—41no—
495C22—42no—
496C22#1458306112yes—
497C22C2×#1306329411yescharacteristic
498C4—21no—
499C4—21no—
500C4—41no—
501C4—41no—
502C4—42no—
503C4—41no—
504C4—44no—
505C4—3442no—
506C4#1458306112yes—
507C4#1458308212yes—
508C4C2×#1306334511yescharacteristic
509C4C2×#1306335511yescharacteristic
510C4#1458370212yes—
511C2—22no—
512C2—81no—
513C2—82no—
514C2C2×#1458306111yescharacteristic
515C2#1914386311yescharacteristic
516C2C2×#1458308211yescharacteristic
subgroupG/H
centerC22C2×#13063294
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
Fitting, prime radicalC43×#3511C2
socleC22×C43C2×#120
hypercenter#3511D43
hypocenterC43#18657
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3511

Complements

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

NH ≅ G/Ntype
1. #19145517C2semidirect
2. C2×#14583302C2semidirect
3. #19144410C2semidirect
4. #19133851C2semidirect
5. #19133830C2semidirect
6. #19133280C2semidirect
7. #19133046C2semidirect
8. #19132977C2semidirect
303. C43#18657semidirect

Maximal subgroups

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

subgroupindex
#191455172
C2×#145833022
#191444102
#191338512
#191338302
#191332802
#191330462
#191329772
C43×#35112
#1865743