Finite Group Databasebeta

← #25253467

Subgroups — #25253467

Order 11008.

580 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#19146939C211yesmaximal, characteristic
2#19146344C211yesmaximal, characteristic, complemented
3#19136821C211yesmaximal, characteristic, complemented
4#19136794C211yesmaximal, characteristic, complemented
5#19136790C211yesmaximal, characteristic, complemented
6#19136736C211yesmaximal, characteristic, complemented
7#19136690C211yesmaximal, characteristic, complemented
8#19136638C211yesmaximal, characteristic, complemented
9#19136511C211yesmaximal, characteristic, complemented
10#19136510C211yesmaximal, characteristic, complemented
11#19136450C211yesmaximal, characteristic, complemented
12C16×C22⋊D43C211yesmaximal, characteristic, complemented
13C2×#14582704C211yesmaximal, characteristic, complemented
14#358×D43C211yesmaximal, characteristic, complemented
15C43×#2217C211yesmaximal, characteristic, complemented
16C22×Dic172C2211yescharacteristic
17C2×Q16×D43C2211yescharacteristic
18#14583562—21no—
19#14583549—21no—
20C2×#13063269C2211yescharacteristic
21C2×#13063269C2211yescharacteristic
22C2×C16×D43C2211yescharacteristic
23#14583303C2211yescharacteristic
24#14583277C2211yescharacteristic
25#14583211—21no—
26#14583210—21no—
27#14583177—21no—
28#14583141C2211yescharacteristic
29#14583132C2211yescharacteristic
30#14583108—21no—
31#14583056—21no—
32#14583054—21no—
33#14582993C2211yescharacteristic
34D8×Dic43C2211yescharacteristic
35C8×C22⋊D43C2211yescharacteristic
36C2×#13063259C2211yescharacteristic
37#107×D43C2211yescharacteristic
38#14582726C2211yescharacteristic
39#14582726C2211yescharacteristic
40Dic43⋊C16C2211yescharacteristic
41#14582704C2211yescharacteristic
42#14582704C2211yescharacteristic
43#14582704C2211yescharacteristic
44#14582704C2211yescharacteristic
45#14582703C2211yescharacteristic
46#14582703C2211yescharacteristic
47#14582702C2211yescharacteristic
48#14582702C2211yescharacteristic
49C22⋊(C43⋊C16)C2211yescharacteristic
50(C2×D43)⋊C16C2211yescharacteristic
51C16×Dic43C2211yescharacteristic
52C2×SD32×C43C2211yescharacteristic
53C22×C16×C43C2211yescharacteristic
54C43×#467C2211yescharacteristic
55C43×#466C2211yescharacteristic
56C43×#367C2211yescharacteristic
57C43×#358C2211yescharacteristic
58C43×#357C2211yescharacteristic
59C2×#10621900—41no—
60C22×Dic86—21no—
61C2×Q8×D43—21no—
62C2×Dic172—22no—
63C2×Dic172—21no—
64C2×Dic172—41no—
65C2×Dic172C2311yescharacteristic
66C2×Dic172C2311yescharacteristic
67C2×#10621885—21no—
68C2×#10621885—21no—
69Q16×D43—22no—
70Q16×D43—41no—
71C2×C8×D43C2311yescharacteristic
72#13063324—21no—
73#13063324—41no—
74#13063323—21no—
75#13063307—41no—
76#13063306—41no—
77#13063305—21no—
78#13063303—41no—
79#13063302—41no—
80#13063302—41no—
81#13063296—21no—
82#13063290—21no—
83D4×Dic43—21no—
84C4×C22⋊D43D411yescharacteristic
85(C22⋊D43)⋊C4—41no—
86C2×C4⋊Dic43—21no—
87C4⋊C4×D43—21no—
88#13063269—22no—
89#13063269—41no—
90C2×C43⋊C16C2311yescharacteristic
91C2×C43⋊C16C2311yescharacteristic
92C16×D43—41no—
93#13063259—21no—
94#13063259C2311yescharacteristic
95#13063259C2311yescharacteristic
96#13063258—21no—
97#13063258—21no—
98Dic43⋊C8D411yescharacteristic
99#13063248—21no—
100#13063248—21no—
101#13063246—21no—
102#13063246—21no—
103C22⋊(C43⋊C8)D411yescharacteristic
104(C2×D43)⋊C8D411yescharacteristic
105C8×Dic43C2311yescharacteristic
106C2×Q16×C43C2311yescharacteristic
107C2×D8×C43C2311yescharacteristic
108C22×C8×C43C2311yescharacteristic
109C22⋊Q8×C43—21no—
110#121×C43—21no—
111SD32×C43—41no—
112C2×C16×C43—41no—
113C2×C16×C43C2311yescharacteristic
114C2×C16×C43C2311yescharacteristic
115#107×C43C2311yescharacteristic
116#107×C43C2311yescharacteristic
117#103×C43—21no—
118#102×C43—21no—
119C2×Q8×C43—21no—
120C2×D4×C43—21no—
121C2×D4×C43—41no—
122C22×C4×C43C2×D411yescharacteristic
123C2×C22⋊D43—41no—
124C2×C22⋊D43D811yescharacteristic
125C22×Dic43—41no—
126C22×Dic43—41no—
127C22×Dic43—41no—
128Q8×D43—42no—
129Q8×D43—81no—
130#10621900—84no—
131C2×C4×D43—41no—
132C2×C4×D43—41no—
133C2×C4×D43C2×D411yescharacteristic
134C2×Dic86—21no—
135C2×Dic86—21no—
136C2×Dic86—42no—
137C2×Dic86—41no—
138C2×Dic86—41no—
139C2×Dic86—41no—
140C2×Dic86—81no—
141Q16×C43—21no—
142Q16×C43—21no—
143D8×C43—21no—
144D8×C43—21no—
145C2×C8×C43—21no—
146C2×C8×C43—21no—
147C2×C8×C43C2×D411yescharacteristic
148C2×C8×C43C2411yescharacteristic
149C4⋊C4×C43—21no—
150C4⋊C4×C43—21no—
151C4⋊C4×C43—41no—
152C22⋊C4×C43—41no—
153C22⋊C4×C43—41no—
154C22⋊Dic43—41no—
155C22⋊Dic43—41no—
156C22⋊Dic43D811yescharacteristic
157#10621885—42no—
158#10621885—81no—
159(C2×D43)⋊C4—41no—
160(C2×D43)⋊C4D811yescharacteristic
161C4⋊Dic43—21no—
162C4⋊Dic43—21no—
163C4⋊Dic43—41no—
164C4⋊Dic43—41no—
165Dic43⋊C4—41no—
166Dic43⋊C4—41no—
167Dic43⋊C4—41no—
168Dic43⋊C4—41no—
169Dic43⋊C4—41no—
170Dic43⋊C4D811yescharacteristic
171C4×Dic43—41no—
172C4×Dic43C2×D411yescharacteristic
173C2×C43⋊C8C2×D411yescharacteristic
174C2×C43⋊C8C2×D411yescharacteristic
175Dic172—21no—
176Dic172—21no—
177Dic172—21no—
178Dic172—42no—
179Dic172#4112yescomplemented
180C8×D43—21no—
181C8×D43—21no—
182C16×C43—21no—
183C16×C43—21no—
184C43⋊C16—21no—
185C43⋊C16—21no—
186C23×C43—41no—
187C23×C43C2×D811yescharacteristic
188C22×D43C2×D811yescharacteristic
189Q8×C43—41no—
190Q8×C43—41no—
191D4×C43—41no—
192D4×C43—41no—
193D4×C43—82no—
194C2×C4×C43—21no—
195C2×C4×C43—21no—
196C2×C4×C43—41no—
197C2×C4×C43—41no—
198C2×C4×C43—41no—
199C2×C4×C43C2×D811yescharacteristic
200C2×C4×C43C22×D411yescharacteristic
201C22⋊D43—82no—
202C22⋊D43SD3214yescomplemented
203C2×Dic43—41no—
204C2×Dic43—41no—
205C2×Dic43—41no—
206C2×Dic43—41no—
207C2×Dic43—82no—
208C2×Dic43—82no—
209C2×Dic43—82no—
210C2×Dic43C2×D811yescharacteristic
211C2×Dic43C2×D811yescharacteristic
212C2×Dic43C2×D811yescharacteristic
213C4×D43—21no—
214C4×D43—21no—
215C4×D43—82no—
216C4×D43—82no—
217Dic86—22no—
218Dic86—41no—
219Dic86—41no—
220Dic86—41no—
221Dic86—82no—
222Dic86—82no—
223Dic86—82no—
224C8×C43—21no—
225C8×C43C2×#4111yescharacteristic
226C8×C43H(5,𝔽2)11yescharacteristic
227C43⋊C8—21no—
228C43⋊C8—21no—
229#33865—431nomaximal, Sylow
230C22×C43—21no—
231C22×C43—21no—
232C22×C43—81no—
233C22×C43—81no—
234C22×C43—81no—
235C22×C43C2×SD3212yes—
236C22×C43C22×D811yescharacteristic
237C2×D43—21no—
238C2×D43—21no—
239C2×D43C2×SD3212yes—
240C4×C43—21no—
241C4×C43—81no—
242C4×C43—81no—
243C4×C43—81no—
244C4×C43#54611yescharacteristic
245C4×C43#57711yescharacteristic
246Dic43—21no—
247Dic43—21no—
248Dic43—42no—
249Dic43—81no—
250Dic43—81no—
251Dic43—81no—
252Dic43C2×SD3212yes—
253#3334—431no—
254D4×Q16—431no—
255#2241—431no—
256#2235—431no—
257#2235—431no—
258#2225—431no—
259#2217—431no—
260#2217D4311yescharacteristic, complemented
261#2208—431no—
262#2185—431no—
263#2185—431no—
264C4×SD32—431no—
265D4×C16—431no—
266C2×#358—431no—
267C2×#358—431no—
268C2×C43—22no—
269C2×C43—161no—
270C2×C43#329411yescharacteristic
271C2×C43C22×SD3211yescharacteristic
272C2×C43#341711yescharacteristic
273D43—22no—
274C22×Q16—431no—
275C22×Q16—431no—
276D4×Q8—861no—
277#547—861no—
278C2×SD32—431no—
279C2×SD32—431no—
280C2×SD32C2×D4311yescharacteristic
281C22×C16—431no—
282C22×C16C2×D4311yescharacteristic
283#500—431no—
284#494—431no—
285#480—861no—
286#480—861no—
287#474—861no—
288#467—431no—
289#467C2×D4311yescharacteristic
290#466—431no—
291#466C2×D4311yescharacteristic
292#462—861no—
293#451—861no—
294#451—861no—
295C4×Q16—431no—
296C4×D8—431no—
297C8×D4—431no—
298C2×#107—431no—
299C2×#107—431no—
300#367—431no—
301#367—431no—
302#367C2×D4311yescharacteristic
303C4⋊C16—431no—
304#358—431no—
305#358—431no—
306#358—431no—
307#358—431no—
308#358—431no—
309#358—431no—
310#358—431no—
311#358—431no—
312#358C2×D4311yescharacteristic
313#357C2×D4311yescharacteristic
314C22⋊C16—431no—
315C22⋊C16—431no—
316C4×C16—431no—
317C43#3386511yescharacteristic, complemented, Sylow
318C2×#41—1721no—
319C22×Q8—861no—
320C22×Q8—861no—
321C2×Q16—431no—
322C2×Q16—431no—
323C2×Q16—862no—
324C2×Q16—861no—
325C2×Q16—861no—
326C2×Q16—862no—
327C2×Q16—861no—
328C2×Q16—1721no—
329C2×Q16—1721no—
330C2×Q16C22×D4311yescharacteristic
331C2×D8C22×D4311yescharacteristic
332C22×C8—431no—
333C22×C8C22×D4311yescharacteristic
334C4⋊Q8—861no—
335C4⋊Q8—861no—
336C4⋊Q8—1721no—
337#123—1721no—
338#123—1721no—
339C22⋊Q8—21no—
340C22⋊Q8—861no—
341C22⋊Q8—1721no—
342C22⋊Q8—1721no—
343C22⋊Q8—1721no—
344#121—21no—
345#121—861no—
346C4×Q8—861no—
347C4×D4—431no—
348C4×D4—861no—
349C4×D4—1721no—
350C2×C4⋊C4—861no—
351C2×C4⋊C4—861no—
352SD32—41no—
353SD32—862no—
354SD32—1721no—
355C2×C16—41no—
356C2×C16—431no—
357C2×C16—431no—
358C2×C16—1721no—
359C2×C16C22×D4311yescharacteristic
360C2×C16C22×D4311yescharacteristic
361#107—431no—
362#107—431no—
363#107—861no—
364#107—861no—
365#107—861no—
366#107C22×D4311yescharacteristic
367#107C22×D4311yescharacteristic
368C4⋊C8—431no—
369#103—21no—
370#103—861no—
371#103—861no—
372#102—21no—
373#102—861no—
374#102—861no—
375C22⋊C8—431no—
376C22⋊C8—431no—
377C4×C8—431no—
378#41—3444no—
379C2×Q8—21no—
380C2×Q8—861no—
381C2×Q8—861no—
382C2×Q8—3441no—
383C2×Q8—3441no—
384C2×Q8—1722no—
385C2×Q8—1721no—
386C2×Q8—1721no—
387C2×Q8—1722no—
388C2×Q8—1721no—
389C2×D4—21no—
390C2×D4—41no—
391C2×D4—431no—
392C2×D4—1721no—
393C22×C4—431no—
394C22×C4—1721no—
395C22×C4—1721no—
396C22×C4—1721no—
397C22×C4—1721no—
398C22×C4—1721no—
399C22×C4D4×D4311yescharacteristic
400Q16—21no—
401Q16—21no—
402Q16—432no—
403Q16—861no—
404Q16—861no—
405Q16—861no—
406Q16—3441no—
407Q16—1722no—
408Q16—1722no—
409D8—21no—
410D8—21no—
411C2×C8—21no—
412C2×C8—21no—
413C2×C8—431no—
414C2×C8—431no—
415C2×C8—861no—
416C2×C8—861no—
417C2×C8D4×D4311yescharacteristic
418C2×C8C23×D4311yescharacteristic
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—41no—
422C4⋊C4—431no—
423C4⋊C4—861no—
424C4⋊C4—861no—
425C4⋊C4—1721no—
426C4⋊C4—1721no—
427C4⋊C4—1721no—
428C4⋊C4—1721no—
429C4⋊C4—1721no—
430C4⋊C4—1721no—
431C4⋊C4—1721no—
432C22⋊C4—41no—
433C22⋊C4—41no—
434C22⋊C4—431no—
435C22⋊C4—431no—
436C22⋊C4—1721no—
437C22⋊C4—1721no—
438C22⋊C4—1721no—
439C42—431no—
440C42—1721no—
441C16—21no—
442C16—21no—
443C16—861no—
444C16—861no—
445C23—41no—
446C23—431no—
447C23D8×D4311yescharacteristic
448Q8—41no—
449Q8—41no—
450Q8—862no—
451Q8—3442no—
452Q8—3442no—
453Q8—3442no—
454Q8—1721no—
455Q8—1721no—
456Q8—1721no—
457D4—41no—
458D4—41no—
459D4—82no—
460D4—434no—
461D4—3442no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—431no—
468C2×C4—431no—
469C2×C4—431no—
470C2×C4—861no—
471C2×C4—861no—
472C2×C4—3442no—
473C2×C4—3442no—
474C2×C4—3442no—
475C2×C4—3442no—
476C2×C4—3442no—
477C2×C4—1721no—
478C2×C4—1721no—
479C2×C4—1721no—
480C2×C4—1721no—
481C2×C4D8×D4311yescharacteristic
482C2×C4C2×D4×D4311yescharacteristic
483C8—21no—
484C8—861no—
485C8—861no—
486C8#41×D4311yescharacteristic
487C8#1306337011yescharacteristic
488C22—21no—
489C22—21no—
490C22—81no—
491C22—81no—
492C22—81no—
493C22—432no—
494C22—861no—
495C22—861no—
496C22SD32×D4312yes—
497C22C2×D8×D4311yescharacteristic
498C4—21no—
499C4—81no—
500C4—81no—
501C4—81no—
502C4—432no—
503C4—861no—
504C4—861no—
505C4—3441no—
506C4—3441no—
507C4—3441no—
508C4—1722no—
509C4#1458353811yescharacteristic
510C4#1458370611yescharacteristic
511C2—22no—
512C2—161no—
513C2—862no—
514C2#1914640311yescharacteristic
515C2C2×SD32×D4311yescharacteristic
516C2#1914774511yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2217C2
socleC22×C43C22×D8
prime radical#19146939C2
hypercenter#2217D43
hypocenterC43#33865
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2217

Complements

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

NH ≅ G/Ntype
2. #19146344C2semidirect
3. #19136821C2semidirect
4. #19136794C2semidirect
5. #19136790C2semidirect
6. #19136736C2semidirect
7. #19136690C2semidirect
8. #19136638C2semidirect
9. #19136511C2semidirect
10. #19136510C2semidirect
11. #19136450C2semidirect
12. C16×C22⋊D43C2semidirect
13. C2×#14582704C2semidirect
14. #358×D43C2semidirect
15. C43×#2217C2semidirect
179. Dic172#41semidirect
202. C22⋊D43SD32semidirect
260. #2217D43semidirect
317. C43#33865semidirect

Maximal subgroups

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

subgroupindex
#191469392
#191463442
#191368212
#191367942
#191367902
#191367362
#191366902
#191366382
#191365112
#191365102
#191364502
C16×C22⋊D432
C2×#145827042
#358×D432
C43×#22172
#3386543