Finite Group Databasebeta

← #25084399

Subgroups — #25084399

Order 11008.

690 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145182C211yesmaximal, characteristic
2#19145180C211yesmaximal, characteristic
3#19145180C211yesmaximal, characteristic
4#19145179C211yesmaximal, characteristic
5#19145106C211yesmaximal, characteristic
6#19145104C211yesmaximal, characteristic
7#19134275C211yesmaximal, characteristic, complemented
8#19134274C211yesmaximal, characteristic, complemented
9#19134273C211yesmaximal, characteristic, complemented
10#19134272C211yesmaximal, characteristic, complemented
11#19134271C211yesmaximal, characteristic, complemented
12#19134270C211yesmaximal, characteristic, complemented
13#19134269C211yesmaximal, characteristic, complemented
14#322×D43C211yesmaximal, characteristic
15C43×#1723C211yesmaximal, characteristic, complemented
16#14583454C2211yescharacteristic
17#14583454C2211yescharacteristic
18#14583454C2211yescharacteristic
19#14583454C2211yescharacteristic
20#14583304C2211yescharacteristic
21#14583304C2211yescharacteristic
22#14583302C2211yescharacteristic
23#14583302C2211yescharacteristic
24#14583302C2211yescharacteristic
25#14583302C2211yescharacteristic
26#14583300—22no—
27#14583299—22no—
28#14583297C2211yescharacteristic
29#14583295C2211yescharacteristic
30#14583295C2211yescharacteristic
31#14583279C2211yescharacteristic
32#14583278C2211yescharacteristic
33#14583278C2211yescharacteristic
34#14583251C2211yescharacteristic
35#14583251C2211yescharacteristic
36#14583250C2211yescharacteristic
37#14583250C2211yescharacteristic
38#14583249C2211yescharacteristic
39#14583249C2211yescharacteristic
40#14583141—22no—
41#14583139—22no—
42#14583139—22no—
43#14583137—22no—
44Q16×Dic43—22no—
45#14582993—22no—
46#14582991—22no—
47#14582991—22no—
48#14582936—22no—
49#14582934—22no—
50C4×C8×D43C2211yescharacteristic
51C4×C8×D43C2211yescharacteristic
52C4×C8×D43C2211yescharacteristic
53#14582621C2211yescharacteristic
54#14582621C2211yescharacteristic
55#14582620C2211yescharacteristic
56C43×#500C2211yescharacteristic
57C43×#500C2211yescharacteristic
58C43×#498C2211yescharacteristic
59C43×#494C2211yescharacteristic
60C43×#487C2211yescharacteristic
61C43×#487C2211yescharacteristic
62C43×#322C2211yescharacteristic
63C2×Dic172—22no—
64C2×#10621885—22no—
65C2×#10621885—22no—
66C2×C8×D43D412yes—
67C2×C8×D43D412yes—
68C2×C8×D43D412yes—
69#13063325C2311yescharacteristic
70#13063325C2311yescharacteristic
71#13063325C2311yescharacteristic
72#13063325C2311yescharacteristic
73#13063316—21no—
74#13063316—21no—
75#13063316—21no—
76#13063316—21no—
77#13063305—21no—
78#13063305—21no—
79#13063305—21no—
80#13063305—21no—
81#13063301—21no—
82#13063301—21no—
83#13063301—21no—
84#13063301—21no—
85Q8×Dic43—21no—
86Q8×Dic43—21no—
87Q8×Dic43—21no—
88Q8×Dic43—21no—
89#13063290—21no—
90#13063290—21no—
91#13063290—21no—
92#13063290—21no—
93#13063283—21no—
94#13063283—21no—
95#13063283—21no—
96#13063283—21no—
97C42×D43C2311yescharacteristic
98#13063259—22no—
99#13063259—22no—
100#13063258—22no—
101#13063258—22no—
102#13063258—22no—
103#13063258—22no—
104#13063257—22no—
105#13063256—22no—
106#13063256—22no—
107#13063250—22no—
108#13063250—22no—
109#13063249—22no—
110#13063249—22no—
111#13063248—22no—
112#13063248—22no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C4×C43⋊C8C2311yescharacteristic
116C8×Dic43D412yes—
117C8×Dic43D412yes—
118C8×Dic43D412yes—
119C2×Q16×C43—22no—
120C4⋊Q8×C43C2311yescharacteristic
121C4⋊Q8×C43C2311yescharacteristic
122C4⋊Q8×C43C2311yescharacteristic
123C4⋊Q8×C43C2311yescharacteristic
124#107×C43—22no—
125#107×C43—22no—
126#106×C43—22no—
127#103×C43—22no—
128#103×C43—22no—
129C4×C8×C43C2311yescharacteristic
130C4×C8×C43C2311yescharacteristic
131C4×C8×C43C2311yescharacteristic
132C2×Q8×C43—21no—
133C2×Q8×C43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×C4×D43C2×D411yescharacteristic
137C2×C4×D43C2×D411yescharacteristic
138C2×C4×D43C2×D411yescharacteristic
139C2×Dic86—21no—
140C2×Dic86—21no—
141C2×Dic86—21no—
142C2×Dic86—21no—
143Q16×C43—44no—
144C2×C8×C43C2×D412yes—
145C2×C8×C43C2×D412yes—
146C2×C8×C43C2×D412yes—
147C4⋊C4×C43—21no—
148C4⋊C4×C43—21no—
149C4⋊C4×C43—21no—
150C4⋊C4×C43—21no—
151C4⋊C4×C43—21no—
152C4⋊C4×C43—21no—
153C4⋊C4×C43—21no—
154C4⋊C4×C43—21no—
155C42×C43C2411yescharacteristic
156#10621885—44no—
157#10621885—44no—
158(C2×D43)⋊C4—41no—
159(C2×D43)⋊C4—41no—
160(C2×D43)⋊C4—41no—
161(C2×D43)⋊C4—41no—
162C4⋊Dic43—21no—
163C4⋊Dic43—21no—
164C4⋊Dic43—21no—
165C4⋊Dic43—21no—
166C4⋊Dic43—21no—
167C4⋊Dic43—21no—
168C4⋊Dic43—21no—
169C4⋊Dic43—21no—
170C4⋊Dic43—41no—
171C4⋊Dic43—41no—
172C4⋊Dic43—41no—
173C4⋊Dic43—41no—
174Dic43⋊C4—41no—
175Dic43⋊C4—41no—
176Dic43⋊C4—41no—
177Dic43⋊C4—41no—
178C4×Dic43—41no—
179C4×Dic43—41no—
180C4×Dic43—41no—
181C4×Dic43—41no—
182C4×Dic43C2×D411yescharacteristic
183C4×Dic43C2×D411yescharacteristic
184C4×Dic43C2×D411yescharacteristic
185C2×C43⋊C8C2×D412yes—
186C2×C43⋊C8C2×D412yes—
187C2×C43⋊C8C2×D412yes—
188Dic172—44no—
189C8×D43—42no—
190C8×D43—42no—
191C8×D43Q1618yescomplemented
192C22×D43#12711yescharacteristic
193Q8×C43—42no—
194Q8×C43—42no—
195Q8×C43—42no—
196Q8×C43—42no—
197C2×C4×C43—41no—
198C2×C4×C43—41no—
199C2×C4×C43—41no—
200C2×C4×C43—41no—
201C2×C4×C43C22×D411yescharacteristic
202C2×C4×C43C22×D411yescharacteristic
203C2×C4×C43C22×D411yescharacteristic
204C2×Dic43—41no—
205C2×Dic43—41no—
206C2×Dic43—41no—
207C2×Dic43—41no—
208C2×Dic43#12711yescharacteristic
209C2×Dic43#12711yescharacteristic
210C2×Dic43#12711yescharacteristic
211C4×D43—22no—
212C4×D43—22no—
213C4×D43C2×Q1614yes—
214Dic86—42no—
215Dic86—42no—
216Dic86—42no—
217Dic86—42no—
218C8×C43—22no—
219C8×C43—22no—
220C8×C43C2×Q1614yes—
221C43⋊C8—22no—
222C43⋊C8—22no—
223C43⋊C8C2×Q1614yes—
224#19618—431nomaximal, Sylow
225C22×C43C2×#12711yescharacteristic
226C2×D43—21no—
227C2×D43—21no—
228C2×D43#49412yes—
229C4×C43—81no—
230C4×C43—81no—
231C4×C43—81no—
232C4×C43—81no—
233C4×C43C22×Q1612yes—
234C4×C43#57512yes—
235C4×C43#57512yes—
236Dic43—21no—
237Dic43—21no—
238Dic43—81no—
239Dic43—81no—
240Dic43—81no—
241Dic43—81no—
242Dic43#49412yes—
243#3170—431no—
244#3170—431no—
245#3170—431no—
246#3170—431no—
247#3160—431no—
248#3160—431no—
249#1723—431no—
250#1723—431no—
251#1723—431no—
252#1723—431no—
253#1723—431no—
254#1723—431no—
255#1723—431no—
256#1723D4311yescharacteristic, complemented
257C2×#322—431no—
258C2×C43C2×#49411yescharacteristic
259C2×C43#315011yescharacteristic
260C2×C43#315011yescharacteristic
261D43—22no—
262#533—431no—
263#533—431no—
264#533—431no—
265#533—431no—
266#500—431no—
267#500—431no—
268#500—431no—
269#500—431no—
270#500—431no—
271#500—431no—
272#500C2×D4311yescharacteristic
273#500C2×D4311yescharacteristic
274#499—862no—
275#499—862no—
276#498—431no—
277#498—431no—
278#498—431no—
279#498C2×D4311yescharacteristic
280#494—431no—
281#494—431no—
282#494—431no—
283#494C2×D4311yescharacteristic
284#487—431no—
285#487—431no—
286#487—431no—
287#487—431no—
288#487—431no—
289#487—431no—
290#487C2×D4311yescharacteristic
291#487C2×D4311yescharacteristic
292#467—862no—
293#467—862no—
294#467—862no—
295#467—862no—
296C4×Q16—862no—
297C4×Q16—862no—
298C4×Q16—862no—
299C4×Q16—862no—
300#427—862no—
301#427—862no—
302C2×C4×C8—431no—
303C2×C4×C8—431no—
304C2×C4×C8—431no—
305#322—431no—
306#322—431no—
307#322—431no—
308#322C2×D4311yescharacteristic
309C43#1961811yescharacteristic, complemented, Sylow
310C2×Q16—22no—
311C2×Q16—862no—
312C2×Q16—862no—
313C2×Q16—862no—
314C22×C8—432no—
315C22×C8—432no—
316C22×C8—432no—
317C4⋊Q8—431no—
318C4⋊Q8—431no—
319C4⋊Q8—431no—
320C4⋊Q8—431no—
321C4⋊Q8C22×D4311yescharacteristic
322C4⋊Q8C22×D4311yescharacteristic
323C4⋊Q8C22×D4311yescharacteristic
324C4⋊Q8C22×D4311yescharacteristic
325#125—861no—
326#125—861no—
327#125—861no—
328#125—861no—
329C22⋊Q8—861no—
330C22⋊Q8—861no—
331C22⋊Q8—861no—
332C22⋊Q8—861no—
333C22⋊Q8—861no—
334C22⋊Q8—861no—
335C22⋊Q8—861no—
336C22⋊Q8—861no—
337C4×Q8—861no—
338C4×Q8—861no—
339C4×Q8—861no—
340C4×Q8—861no—
341C4×Q8—861no—
342C4×Q8—861no—
343C4×Q8—861no—
344C4×Q8—861no—
345#117—861no—
346#117—861no—
347#117—861no—
348#117—861no—
349C2×C42—431no—
350#107—22no—
351#107—22no—
352#107—862no—
353#107—862no—
354#107—862no—
355#107—862no—
356#107—862no—
357#107—862no—
358#106—22no—
359#106—862no—
360#106—862no—
361#106—862no—
362#103—22no—
363#103—22no—
364#103—862no—
365#103—862no—
366#103—862no—
367#103—862no—
368#103—862no—
369#103—862no—
370C4×C8—432no—
371C4×C8—432no—
372C4×C8—432no—
373C4×C8—431no—
374C4×C8—431no—
375C4×C8—431no—
376C4×C8C22×D4311yescharacteristic
377C4×C8C22×D4311yescharacteristic
378C4×C8C22×D4311yescharacteristic
379C2×Q8—21no—
380C2×Q8—21no—
381C2×Q8—21no—
382C2×Q8—21no—
383C2×Q8—861no—
384C2×Q8—861no—
385C2×Q8—861no—
386C2×Q8—861no—
387C22×C4—431no—
388C22×C4—431no—
389C22×C4—431no—
390Q16—44no—
391Q16—1724no—
392Q16—1724no—
393Q16—1724no—
394C2×C8—432no—
395C2×C8—438no—
396C2×C8—432no—
397C2×C8—432no—
398C2×C8—1722no—
399C2×C8—1722no—
400C2×C8D4×D4312yes—
401C2×C8D4×D4312yes—
402C2×C8D4×D4312yes—
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—21no—
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—861no—
412C4⋊C4—861no—
413C4⋊C4—861no—
414C4⋊C4—861no—
415C4⋊C4—861no—
416C4⋊C4—861no—
417C4⋊C4—861no—
418C4⋊C4—861no—
419C4⋊C4—1721no—
420C4⋊C4—1721no—
421C4⋊C4—1721no—
422C4⋊C4—1721no—
423C4⋊C4—1721no—
424C4⋊C4—1721no—
425C4⋊C4—1721no—
426C4⋊C4—1721no—
427C22⋊C4—1721no—
428C22⋊C4—1721no—
429C22⋊C4—1721no—
430C22⋊C4—1721no—
431C42—431no—
432C42—431no—
433C42—431no—
434C42—1721no—
435C42—1721no—
436C42—1721no—
437C42—1721no—
438C42C23×D4311yescharacteristic
439C23—431no—
440Q8—42no—
441Q8—42no—
442Q8—42no—
443Q8—42no—
444Q8—1722no—
445Q8—1722no—
446Q8—1722no—
447Q8—1722no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—431no—
453C2×C4—434no—
454C2×C4—431no—
455C2×C4—431no—
456C2×C4—862no—
457C2×C4—862no—
458C2×C4—1721no—
459C2×C4—1721no—
460C2×C4—1721no—
461C2×C4—1721no—
462C2×C4C2×D4×D4311yescharacteristic
463C2×C4C2×D4×D4311yescharacteristic
464C2×C4C2×D4×D4311yescharacteristic
465C8—22no—
466C8—22no—
467C8—434no—
468C8—862no—
469C8—862no—
470C8Q16×D4314yes—
471C22—432no—
472C22—861no—
473C22—861no—
474C22#127×D4311yescharacteristic
475C4—81no—
476C4—81no—
477C4—81no—
478C4—81no—
479C4—432no—
480C4—861no—
481C4—861no—
482C4—3441no—
483C4—3441no—
484C4—3441no—
485C4—3441no—
486C4C2×Q16×D4312yes—
487C4#1458369512yes—
488C4#1458369812yes—
489C2—862no—
490C2#494×D4311yescharacteristic
491C2#1914503711yescharacteristic
492C2#1914503911yescharacteristic
subgroupG/H
centerC22#127×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1723C2
socleC22×C43C2×#127
prime radicalC22×D43#127
hypercenter#1723D43
hypocenterC43#19618
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1723

Complements

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

NH ≅ G/Ntype
7. #19134275C2semidirect
8. #19134274C2semidirect
9. #19134273C2semidirect
10. #19134272C2semidirect
11. #19134271C2semidirect
12. #19134270C2semidirect
13. #19134269C2semidirect
15. C43×#1723C2semidirect
191. C8×D43Q16semidirect
256. #1723D43semidirect
309. C43#19618semidirect

Maximal subgroups

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

subgroupindex
#191451822
#191451802
#191451792
#191451062
#191451042
#191342752
#191342742
#191342732
#191342722
#191342712
#191342702
#191342692
#322×D432
C43×#17232
#1961843