Finite Group Databasebeta

← #25249947

Subgroups — #25249947

Order 11008.

660 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583338C211yesmaximal, characteristic
2#19143465C211yesmaximal, characteristic
3#19143458C211yesmaximal, characteristic, complemented
4#19136467C211yesmaximal, characteristic, complemented
5#19136463C211yesmaximal, characteristic, complemented
6#19136456C211yesmaximal, characteristic, complemented
7#19136453C211yesmaximal, characteristic, complemented
8C4×#13063271C211yesmaximal, characteristic, complemented
9SD32×Dic43C211yesmaximal, characteristic, complemented
10C4×#13063269C211yesmaximal, characteristic, complemented
11#19136380C211yesmaximal, characteristic, complemented
12#19136299C211yesmaximal, characteristic
13#358×D43C211yesmaximal, characteristic, complemented
14#19136193C211yesmaximal, characteristic, complemented
15C43×#2175C211yesmaximal, characteristic, complemented
16C2×#13063344C2211yescharacteristic
17C2×Q16×D43C2211yescharacteristic
18#14583378—21no—
19#14583375—21no—
20#14583338C418yescomplemented
21C2×Dic344C2211yescharacteristic
22C2×#13063271C2211yescharacteristic
23C2×#13063269C2211yescharacteristic
24C2×#13063264C2211yescharacteristic
25C2×C16×D43C2211yescharacteristic
26#14583004—21no—
27#14583003—21no—
28#14582999—21no—
29#14582996—21no—
30C4×Dic172C2211yescharacteristic
31C4×Dic172C2211yescharacteristic
32Q16×Dic43C2211yescharacteristic
33#14582993C2211yescharacteristic
34#14582993C2211yescharacteristic
35D8×Dic43C2211yescharacteristic
36#14582936C2211yescharacteristic
37#107×D43C2211yescharacteristic
38#14582906—21no—
39#14582897—21no—
40#14582853C2211yescharacteristic
41#14582727C2211yescharacteristic
42#14582726C2211yescharacteristic
43#14582724C2211yescharacteristic
44#14582704C2211yescharacteristic
45#14582704C2211yescharacteristic
46#14582703C2211yescharacteristic
47#14582702C2211yescharacteristic
48#14582702C2211yescharacteristic
49#14582700C2211yescharacteristic
50#14582674C2211yescharacteristic
51C4×C43⋊C16C2211yescharacteristic
52C16×Dic43C2211yescharacteristic
53C2×SD32×C43C2211yescharacteristic
54C4×Q16×C43C2211yescharacteristic
55C4×D8×C43C2211yescharacteristic
56C43×#366C2211yescharacteristic
57C43×#358C2211yescharacteristic
58C43×#357C2211yescharacteristic
59C43×#346C2211yescharacteristic
60C2×#10621900—21no—
61C2×Q8×D43—21no—
62#13063344—22no—
63#13063344C2×C414yes—
64C2×Dic172C2311yescharacteristic
65C2×Dic172C2311yescharacteristic
66C2×#10621885—21no—
67Q16×D43—22no—
68Q16×D43C2×C414yescomplemented
69C2×#10621883—21no—
70C2×#10621872D411yescharacteristic
71C2×C8×D43C2311yescharacteristic
72Q8×Dic43—21no—
73C4×Dic86—21no—
74C4×Dic86—21no—
75C4×Dic86—41no—
76#13063290—21no—
77#13063290—21no—
78#13063290—41no—
79D4×Dic43—21no—
80C4×C22⋊D43—41no—
81(C22⋊D43)⋊C4—41no—
82#13063283—21no—
83#13063283—41no—
84#13063282—41no—
85#13063282D411yescharacteristic
86#13063281—41no—
87C2×Dic43⋊C4—41no—
88C4⋊C4×D43—21no—
89Dic344C2×C414yescomplemented
90#13063271C2×C414yescomplemented
91#13063269C2×C414yescomplemented
92#13063264C2×C414yescomplemented
93C2×C43⋊C16C2311yescharacteristic
94C2×C43⋊C16C2311yescharacteristic
95C16×D43—22no—
96#13063259C2311yescharacteristic
97#13063259C2311yescharacteristic
98#13063258—21no—
99#13063256—21no—
100#13063250—21no—
101#13063250—21no—
102#13063249—21no—
103#13063248—21no—
104#13063248—21no—
105#13063246—21no—
106#13063236D411yescharacteristic
107#13063235D411yescharacteristic
108C8×Dic43C2311yescharacteristic
109C2×Q16×C43C2311yescharacteristic
110C2×D8×C43C2311yescharacteristic
111C4×Q8×C43—21no—
112C4×D4×C43—21no—
113SD32×C43C2×C414yescomplemented
114C2×C16×C43C2311yescharacteristic
115C2×C16×C43C2311yescharacteristic
116#107×C43C2311yescharacteristic
117#107×C43C2311yescharacteristic
118#103×C43—21no—
119#102×C43—21no—
120C4×C8×C43C2311yescharacteristic
121C2×Q8×C43—21no—
122C2×D4×C43—21no—
123C22×C4×C43—41no—
124C2×C22⋊D43—41no—
125C22×Dic43—41no—
126C22×Dic43—41no—
127Q8×D43—24no—
128Q8×D43—42no—
129#10621900—24no—
130#10621900—42no—
131C2×C4×D43—41no—
132C2×C4×D43—41no—
133C2×C4×D43C2×D411yescharacteristic
134C2×Dic86—21no—
135C2×Dic86—21no—
136C2×Dic86—41no—
137Q16×C43—21no—
138Q16×C43C22×C412yes—
139D8×C43—21no—
140D8×C43C22×C412yes—
141C2×C8×C43C2×D411yescharacteristic
142C2×C8×C43C2411yescharacteristic
143C4⋊C4×C43—21no—
144C4⋊C4×C43—21no—
145C4⋊C4×C43—41no—
146C22⋊C4×C43—41no—
147C42×C43—41no—
148C42×C43C2×D411yescharacteristic
149C22⋊Dic43—41no—
150#10621885—24no—
151#10621883—24no—
152(C2×D43)⋊C4—41no—
153(C2×D43)⋊C4D811yescharacteristic
154(C2×D43)⋊C4D811yescharacteristic
155C4⋊Dic43—21no—
156C4⋊Dic43—21no—
157C4⋊Dic43—41no—
158Dic43⋊C4—41no—
159Dic43⋊C4—41no—
160Dic43⋊C4—41no—
161Dic43⋊C4—41no—
162Dic43⋊C4—41no—
163Dic43⋊C4D811yescharacteristic
164Dic43⋊C4D811yescharacteristic
165C4×Dic43—41no—
166C4×Dic43—41no—
167C4×Dic43—41no—
168C4×Dic43—41no—
169C4×Dic43—41no—
170C4×Dic43—41no—
171C4×Dic43C2×D411yescharacteristic
172C2×C43⋊C8C2×D411yescharacteristic
173C2×C43⋊C8C2×D411yescharacteristic
174Dic172—21no—
175Dic172—21no—
176Dic172C22×C412yes—
177Dic172C22×C412yes—
178#10621872—22no—
179C8×D43C22×C412yes—
180C8×D43#4112yes—
181C16×C43—21no—
182C16×C43C22×C412yes—
183C43⋊C16—21no—
184C43⋊C16C22×C412yes—
185C23×C43—41no—
186C22×D43C2×D811yescharacteristic
187Q8×C43—22no—
188Q8×C43—41no—
189D4×C43—22no—
190D4×C43—41no—
191C2×C4×C43—41no—
192C2×C4×C43—41no—
193C2×C4×C43—41no—
194C2×C4×C43—161no—
195C2×C4×C43C2×D811yescharacteristic
196C2×C4×C43C2×D811yescharacteristic
197C2×C4×C43C22×D411yescharacteristic
198C22⋊D43—44no—
199C2×Dic43—41no—
200C2×Dic43—41no—
201C2×Dic43—44no—
202C2×Dic43—41no—
203C2×Dic43—41no—
204C2×Dic43—161no—
205C2×Dic43C2×D811yescharacteristic
206C2×Dic43C2×D811yescharacteristic
207C2×Dic43C2×D811yescharacteristic
208C4×D43—44no—
209C4×D43—161no—
210C4×D43C4×D412yes—
211C4×D43#13512yes—
212Dic86—22no—
213Dic86—22no—
214Dic86—41no—
215Dic86—41no—
216Dic86—44no—
217C8×C43—21no—
218C8×C43C23×C411yescharacteristic
219C8×C43C2×#4111yescharacteristic
220C43⋊C8—21no—
221C43⋊C8C4×D412yes—
222#33455—431nomaximal, Sylow
223C22×C43—42no—
224C22×C43—81no—
225C22×C43—81no—
226C22×C43C22×D811yescharacteristic
227C2×D43—21no—
228C2×D43—21no—
229C2×D43C4×D812yes—
230C4×C43—21no—
231C4×C43—21no—
232C4×C43—42no—
233C4×C43—81no—
234C4×C43—81no—
235C4×C43C2×C4×D411yescharacteristic
236C4×C43C2×#13511yescharacteristic
237Dic43—21no—
238Dic43—21no—
239Dic43—42no—
240Dic43—42no—
241Dic43—81no—
242Dic43—81no—
243Dic43C4×D812yes—
244C2×#510—431no—
245#2951—431no—
246#2950—431no—
247#2176—431no—
248#2176—431no—
249#2175—431no—
250#2175D4311yescharacteristic, complemented
251C4×Q32—431no—
252C4×Q32—431no—
253C4×SD32—431no—
254C4×SD32—431no—
255#2159—431no—
256#2138—431no—
257C2×#358—431no—
258#2108—431no—
259C2×C43—82no—
260C2×C43C2×C4×D811yescharacteristic
261C2×C43#341611yescharacteristic
262C2×C43#341711yescharacteristic
263D43—22no—
264C2×#135—431no—
265C22×Q16—431no—
266#520—861no—
267#519—861no—
268#510—438no—
269C2×Q32—431no—
270C2×Q32—431no—
271C2×SD32—431no—
272C2×SD32C2×D4311yescharacteristic
273C2×M32—431no—
274C22×C16—431no—
275#441—861no—
276#441—861no—
277#440—861no—
278#440—861no—
279C4×Q16—431no—
280C4×Q16—431no—
281C4×Q16—431no—
282C4×Q16—431no—
283C4×Q16—431no—
284C4×Q16C2×D4311yescharacteristic
285C4×D8—431no—
286C4×D8C2×D4311yescharacteristic
287#427—431no—
288C2×#107—431no—
289#419—861no—
290#417—861no—
291#405—431no—
292#367—431no—
293#367—431no—
294#366—431no—
295#366C2×D4311yescharacteristic
296#358—431no—
297#358—431no—
298#358—431no—
299#358—431no—
300#358—431no—
301#358C2×D4311yescharacteristic
302#357—431no—
303#357C2×D4311yescharacteristic
304#346—431no—
305#346C2×D4311yescharacteristic
306C4×C16—431no—
307C4×C16—431no—
308C43#3345511yescharacteristic, complemented, Sylow
309C2×#41—861no—
310C22×Q8—861no—
311#135—434no—
312#135—862no—
313C2×Q16—434no—
314C2×Q16—431no—
315C2×Q16—431no—
316C2×Q16—862no—
317C2×Q16—861no—
318C2×Q16C22×D4311yescharacteristic
319C2×SD16—861no—
320C2×D8C22×D4311yescharacteristic
321C2×M16—431no—
322C22×C8—431no—
323C4×Q8—21no—
324C4×Q8—861no—
325C4×Q8—861no—
326C4×Q8—861no—
327C4×Q8—861no—
328C4×Q8—861no—
329C4×Q8—1721no—
330C4×Q8—1721no—
331C4×D4—21no—
332C4×D4—861no—
333C4×D4—1721no—
334C4×D4—1721no—
335#117—431no—
336#117—861no—
337#117—1721no—
338#117—1721no—
339#117—1721no—
340C2×C4⋊C4—861no—
341C2×C4⋊C4—1721no—
342Q32—434no—
343Q32—434no—
344SD32—434no—
345SD32C4×D4314yescomplemented
346M32—434no—
347C2×C16—431no—
348C2×C16—431no—
349C2×C16—862no—
350C2×C16C22×D4311yescharacteristic
351C2×C16C22×D4311yescharacteristic
352#107—431no—
353#107—431no—
354#107—861no—
355#107C22×D4311yescharacteristic
356#107C22×D4311yescharacteristic
357#106—861no—
358#103—21no—
359#103—861no—
360#103—861no—
361#103—861no—
362#103—861no—
363#103—861no—
364#102—21no—
365#102—861no—
366#97—431no—
367#97—431no—
368C4×C8—431no—
369C4×C8C22×D4311yescharacteristic
370#41—864no—
371#41—1722no—
372C2×Q8—21no—
373C2×Q8—864no—
374C2×Q8—861no—
375C2×Q8—861no—
376C2×Q8—1721no—
377C2×Q8—1722no—
378C2×D4—21no—
379C2×D4—1721no—
380C22×C4—41no—
381C22×C4—431no—
382C22×C4—1721no—
383C22×C4—1721no—
384C22×C4—1721no—
385C22×C4—1721no—
386Q16—21no—
387Q16—432no—
388Q16—432no—
389Q16—864no—
390Q16—861no—
391Q16—861no—
392Q16C2×C4×D4312yes—
393SD16—864no—
394D8—21no—
395D8C2×C4×D4312yes—
396M16—862no—
397C2×C8—431no—
398C2×C8—432no—
399C2×C8—432no—
400C2×C8—431no—
401C2×C8D4×D4311yescharacteristic
402C2×C8C23×D4311yescharacteristic
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—41no—
406C4⋊C4—431no—
407C4⋊C4—431no—
408C4⋊C4—861no—
409C4⋊C4—861no—
410C4⋊C4—1721no—
411C4⋊C4—1721no—
412C4⋊C4—1721no—
413C4⋊C4—1721no—
414C4⋊C4—1721no—
415C4⋊C4—1721no—
416C22⋊C4—41no—
417C22⋊C4—431no—
418C22⋊C4—431no—
419C22⋊C4—1721no—
420C22⋊C4—1721no—
421C42—41no—
422C42—431no—
423C42—1721no—
424C42—1721no—
425C42—1721no—
426C42—1721no—
427C42—1721no—
428C42—1721no—
429C42D4×D4311yescharacteristic
430C16—21no—
431C16—432no—
432C16—861no—
433C16C2×C4×D4312yes—
434C23—41no—
435C23—431no—
436Q8—22no—
437Q8—41no—
438Q8—862no—
439Q8—862no—
440Q8—1724no—
441Q8—1721no—
442Q8—1721no—
443D4—22no—
444D4—41no—
445D4—1724no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—161no—
450C2×C4—431no—
451C2×C4—432no—
452C2×C4—432no—
453C2×C4—431no—
454C2×C4—431no—
455C2×C4—1724no—
456C2×C4—1724no—
457C2×C4—1721no—
458C2×C4—1721no—
459C2×C4—1721no—
460C2×C4—1721no—
461C2×C4—6881no—
462C2×C4—6881no—
463C2×C4D8×D4311yescharacteristic
464C2×C4D8×D4311yescharacteristic
465C2×C4C2×D4×D4311yescharacteristic
466C8—21no—
467C8—432no—
468C8—861no—
469C8C22×C4×D4311yescharacteristic
470C8#41×D4311yescharacteristic
471C22—42no—
472C22—81no—
473C22—81no—
474C22—432no—
475C22—861no—
476C22—861no—
477C22C2×D8×D4311yescharacteristic
478C4—21no—
479C4—21no—
480C4—42no—
481C4—81no—
482C4—81no—
483C4—432no—
484C4—861no—
485C4—861no—
486C4—3441no—
487C4—3441no—
488C4—1722no—
489C4—1722no—
490C4C4×D4×D4311yescharacteristic
491C4#135×D4311yescharacteristic
492C2—82no—
493C2—862no—
494C2C4×D8×D4311yescharacteristic
495C2#1914774111yescharacteristic
496C2#1914774711yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutatorC8×C43C23×C4
FrattiniC2×C8C23×D43
FittingC43×#2175C2
socleC22×C43C22×D8
prime radicalC2×#13063344C22
cosocleC2×C8×C43C24
hypercenter#2175D43
hypocenterC43#33455
LCSG ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2175

Complements

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

NH ≅ G/Ntype
3. #19143458C2semidirect
4. #19136467C2semidirect
5. #19136463C2semidirect
6. #19136456C2semidirect
7. #19136453C2semidirect
8. C4×#13063271C2semidirect
9. SD32×Dic43C2semidirect
10. C4×#13063269C2semidirect
11. #19136380C2semidirect
13. #358×D43C2semidirect
14. #19136193C2semidirect
15. C43×#2175C2semidirect
20. #14583338C4semidirect
68. Q16×D43C2×C4semidirect
89. Dic344C2×C4semidirect
90. #13063271C2×C4semidirect
91. #13063269C2×C4semidirect
92. #13063264C2×C4semidirect
113. SD32×C43C2×C4semidirect
250. #2175D43semidirect
308. C43#33455semidirect
345. SD32C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145833382
#191434652
#191434582
#191364672
#191364632
#191364562
#191364532
C4×#130632712
SD32×Dic432
C4×#130632692
#191363802
#191362992
#358×D432
#191361932
C43×#21752
#3345543