Finite Group Databasebeta

← #11887170

Subgroups — #11887170

Order 1152.

985 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595407C211yesmaximal, characteristic, complemented
2#10594618C211yesmaximal, characteristic
3#10592487C211yesmaximal, characteristic, complemented
4C3×#4807C212yesmaximal, complemented
5#10591651C212yesmaximal, complemented
6#10591622C211yesmaximal, characteristic, complemented
7D3×#821C212yesmaximal, complemented
8#10590885C211yesmaximal, characteristic, complemented
9C8×#625C211yesmaximal, characteristic, complemented
10#10590441C212yesmaximal, complemented
11#10590433C211yesmaximal, characteristic, complemented
12#80680—32nomaximal
13C2×#3802—21no—
14C2×D3×D12C2212yes—
15Q8×C3⋊Dic3C2211yescharacteristic, complemented
16C2×#3755C2211yescharacteristic
17#64102C2211yescharacteristic
18C3×#946C2212yescomplemented
19C2×C3×#215C2212yescomplemented
20C2×C3×D3×C8C2212yescomplemented
21C3×#895C2212yes—
22#63922—22no—
23#63919C2211yescharacteristic, complemented
24#63914C2211yescharacteristic
25#63912—21no—
26#63902—21no—
27C4×#625C2211yescharacteristic
28#63893—22no—
29D3×C4⋊Dic3C2212yescomplemented
30#63870—21no—
31C32×#103C2211yescharacteristic, complemented
32#63648C2211yescharacteristic
33C8×C3⋊Dic3C2211yescharacteristic, complemented
34#63635C2211yescharacteristic, complemented
35C3×#821C2212yescomplemented
36C3×#808C2212yescomplemented
37#63572C2211yescharacteristic, complemented
38#63564C2212yes—
39#63563C2212yescomplemented
40#63562C2212yescomplemented
41(C2×D3)⋊(C3⋊C8)C2212yescomplemented
42#5635—32no—
43#5609—32no—
44C3×#465—32no—
45#5169—32no—
46#5163—32no—
47C2×#821—32no—
48C8×#67—32no—
49#5046—32no—
50#5034—32no—
51#4870—32no—
52#4863—32no—
53#4807D312yescomplemented
54#4788—32no—
55#4788—61no—
56D3×#102—32no—
57#4760—32no—
58C22×D32—22no—
59C2×C32×Q8C2311yescharacteristic
60C2×C4⋊(C3⋊D3)C2311yescharacteristic
61C2×C4×C3⋊D3—21no—
62C2×C3×D12—22no—
63C2×C3×D12C2312yes—
64C2×C3×C4×D3C2312yes—
65C2×#627—21no—
66C2×#626—22no—
67C2×#625—21no—
68C2×#625—21no—
69C2×#625D411yescharacteristic
70C2×D3×Dic3—22no—
71#3802—44no—
72D3×D12—24no—
73D3×D12—42no—
74C2×C32×C8C2311yescharacteristic
75C32×C4⋊C4C2311yescharacteristic
76#3755—22no—
77#3752—21no—
78C4⋊(C3⋊Dic3)—21no—
79C4⋊(C3⋊Dic3)C2311yescharacteristic
80C4×C3⋊Dic3—21no—
81C4×C3⋊Dic3C2311yescharacteristic
82C2×C3⋊(C3⋊C8)C2311yescharacteristic
83C3×#215—42no—
84C3×(C2×D3)⋊C4—22no—
85C3×(C2×D3)⋊C4—22no—
86C3×C4⋊Dic3C2312yes—
87C3×Dic3⋊C4—22no—
88C2×C3×C3⋊C8C2312yes—
89C3×D3×C8—42no—
90#3724—21no—
91#3724D411yescharacteristic
92Dic3⋊Dic3—22no—
93(C2×D3)⋊Dic3D412yes—
94#3295—91noSylow
95C2×D3×D4—32no—
96C2×D3×D4—62no—
97C22×D12—32no—
98C2×C3×SD16—32no—
99C22×C3×C8—32no—
100C3×C22⋊Q8—32no—
101C3×#121—32no—
102#946C2×D312yescomplemented
103Q8×Dic3—32no—
104Q8×Dic3—61no—
105C2×#215—32no—
106C2×#215—61no—
107C2×#215C2×D312yescomplemented
108#940—32no—
109#937—62no—
110C4×#67—32no—
111C2×C4⋊Dic3—32no—
112C2×D3×C8C2×D312yescomplemented
113#897—62no—
114#895C2×D312yes—
115#893—32no—
116#893—61no—
117D3×C4⋊C4—32no—
118#889—62no—
119#888—32no—
120#884—62no—
121#882—62no—
122#67⋊C4—62no—
123#878—62no—
124C3×#106—32no—
125C3×#103—21no—
126C3×#103C2×D312yescomplemented
127C3×#102—32no—
128#832—32no—
129#832—32no—
130#830—32no—
131#821—32no—
132#821—32no—
133#821—32no—
134#821—61no—
135#821C2×D312yescomplemented
136(C2×D3)⋊C8—32no—
137Dic3⋊C8—32no—
138C8×Dic3—32no—
139C8×Dic3—61no—
140#809—32no—
141#809—32no—
142#808—32no—
143#808—61no—
144#808C2×D312yescomplemented
145C22×C3⋊D3—21no—
146C22×C3×D3—22no—
147C22×C3×D3C2×D412yes—
148C2×D32—44no—
149C2×D32—44no—
150C2×D32—82no—
151C32×Q8—21no—
152C32×Q8—21no—
153C2×C32×C4—21no—
154C2×C32×C4—21no—
155C2×C32×C4C2411yescharacteristic
156C2×C3⋊Dic3—21no—
157C2×C3⋊Dic3C2×D411yescharacteristic
158C2×C3⋊Dic3C2×D411yescharacteristic
159C4⋊(C3⋊D3)—21no—
160C4⋊(C3⋊D3)#4112yes—
161C4×C3⋊D3—42no—
162C2×C3×Dic3—22no—
163C2×C3×Dic3C2×D412yes—
164C3×D12—22no—
165C3×D12—22no—
166C3×D12—44no—
167C3×C4×D3—22no—
168C3×C4×D3—22no—
169#627—81no—
170#626—44no—
171#625—42no—
172#625—81no—
173#625SD1614yescomplemented
174D3×Dic3—82no—
175C32×C8—21no—
176C3⋊(C3⋊C8)—21no—
177C3×C3⋊C8—22no—
178#554—91no—
179D42—91no—
180#486—91no—
181#481—92no—
182#476—91no—
183#465—32no—
184#460—91no—
185#450—92no—
186C4×SD16—91no—
187C8×D4—91no—
188C2×#102—92no—
189C23×D3—62no—
190C23×D3—62no—
191C2×C3×Q8—21no—
192C2×C3×Q8C22×D312yes—
193C2×C3×D4—32no—
194C2×C3×D4—62no—
195C22×C3×C4—32no—
196C2×#67—32no—
197C2×#67—62no—
198C2×#67—62no—
199C2×#67—62no—
200C22×Dic3—62no—
201D3×D4—64no—
202D3×D4—122no—
203D3×D4—128no—
204C2×D12—22no—
205C2×D12—32no—
206C2×D12—61no—
207C2×D12—64no—
208C2×D12—62no—
209C2×D12—122no—
210C2×D12C22×D312yes—
211C2×C4×D3—62no—
212C2×C4×D3—62no—
213C2×C4×D3—121no—
214C2×C4×D3C22×D312yes—
215C2×Dic6—62no—
216C3×SD16—122no—
217C2×C3×C8—21no—
218C2×C3×C8—32no—
219C2×C3×C8—122no—
220C2×C3×C8C22×D312yes—
221C3×C4⋊C4—21no—
222C3×C4⋊C4—32no—
223C3×C4⋊C4—62no—
224C3×C4⋊C4C22×D312yes—
225C3×C22⋊C4—62no—
226C3×C22⋊C4—62no—
227#217—32no—
228#215—42no—
229#215—64no—
230#215—64no—
231(C2×D3)⋊C4—22no—
232(C2×D3)⋊C4—22no—
233(C2×D3)⋊C4—32no—
234(C2×D3)⋊C4—62no—
235(C2×D3)⋊C4—121no—
236C4⋊Dic3—32no—
237C4⋊Dic3—61no—
238C4⋊Dic3—62no—
239C4⋊Dic3—62no—
240C4⋊Dic3—121no—
241C4⋊Dic3C22×D312yes—
242Dic3⋊C4—22no—
243Dic3⋊C4—32no—
244Dic3⋊C4—62no—
245Dic3⋊C4—62no—
246C4×Dic3—32no—
247C4×Dic3—61no—
248C4×Dic3—62no—
249C4×Dic3—121no—
250C2×C3⋊C8—32no—
251C2×C3⋊C8—61no—
252C2×C3⋊C8C22×D312yes—
253D3×C8—42no—
254C22×C32C22×D411yescharacteristic
255C2×C3⋊D3—22no—
256C2×C3⋊D3—41no—
257C2×C3⋊D3—41no—
258C2×C3×D3—22no—
259C2×C3×D3—22no—
260C2×C3×D3—42no—
261C2×C3×D3—42no—
262C2×C3×D3—42no—
263C2×C3×D3C2×SD1614yes—
264D32—88no—
265C32×C4—41no—
266C32×C4—41no—
267C32×C4C2×#4111yescharacteristic
268C32×C4H(5,𝔽2)11yescharacteristic
269C3⋊Dic3—21no—
270C3⋊Dic3—41no—
271C3⋊Dic3C2×SD1612yes—
272C3×Dic3—22no—
273C3×Dic3—42no—
274C22×D4—92no—
275C22×D4—181no—
276C2×SD16—32no—
277C2×SD16—91no—
278C22×C8—32no—
279C4⋊Q8—91no—
280#127—91no—
281#125—181no—
282C22⋊Q8—32no—
283C22⋊Q8—182no—
284#121—32no—
285#121—181no—
286#120—182no—
287C4×Q8—91no—
288C4×D4—91no—
289C4×D4—91no—
290C4×D4—181no—
291C2×C4⋊C4—92no—
292#106—32no—
293#106—91no—
294C4⋊C8—91no—
295#103D3211yescharacteristic, complemented
296#102—32no—
297#102—92no—
298#102—92no—
299#102—92no—
300#102—91no—
301C22⋊C8—92no—
302C4×C8—91no—
303C23×C3—32no—
304C23×C3—62no—
305C22×D3—22no—
306C22×D3—62no—
307C22×D3—121no—
308C22×D3—124no—
309C22×D3—124no—
310C22×D3—124no—
311C22×D3—124no—
312C22×D3—242no—
313C22×D3—242no—
314C22×D3D3×D412yes—
315C3×Q8—22no—
316C3×Q8—22no—
317C3×Q8—22no—
318C3×Q8—41no—
319C3×D4—62no—
320C3×D4—62no—
321C3×D4—124no—
322C2×C3×C4—22no—
323C2×C3×C4—22no—
324C2×C3×C4—21no—
325C2×C3×C4—32no—
326C2×C3×C4—41no—
327C2×C3×C4—41no—
328C2×C3×C4—62no—
329C2×C3×C4—62no—
330C2×C3×C4—62no—
331C2×C3×C4C23×D312yes—
332#67—38no—
333#67—124no—
334#67—124no—
335#67—242no—
336C2×Dic3—22no—
337C2×Dic3—32no—
338C2×Dic3—32no—
339C2×Dic3—61no—
340C2×Dic3—61no—
341C2×Dic3—62no—
342C2×Dic3—121no—
343C2×Dic3—242no—
344C2×Dic3D3×D412yes—
345D12—22no—
346D12—22no—
347D12—34no—
348D12—44no—
349D12—62no—
350D12—62no—
351D12—121no—
352D12—124no—
353C4×D3—22no—
354C4×D3—22no—
355C4×D3—124no—
356C4×D3—242no—
357C4×D3—242no—
358Dic6—242no—
359C3×C8—22no—
360C3×C8—41no—
361C3×C8—62no—
362C3⋊C8—22no—
363C3⋊C8—62no—
364C3⋊C8—62no—
365C2×C32#54611yescharacteristic
366C2×C32C22×SD1611yescharacteristic
367C2×C32#57611yescharacteristic
368C3⋊D3—42no—
369C3×D3—24no—
370C3×D3—82no—
371C24—182no—
372C2×Q8—181no—
373C2×Q8C2×D3211yescharacteristic
374C2×D4—32no—
375C2×D4—62no—
376C2×D4—91no—
377C2×D4—91no—
378C2×D4—182no—
379C2×D4—184no—
380C2×D4—181no—
381C2×D4—181no—
382C2×D4—362no—
383C2×D4—364no—
384C22×C4—32no—
385C22×C4—181no—
386C22×C4—182no—
387SD16—122no—
388SD16—182no—
389C2×C8—32no—
390C2×C8—91no—
391C2×C8—122no—
392C2×C8C2×D3211yescharacteristic
393C4⋊C4—32no—
394C4⋊C4—62no—
395C4⋊C4—91no—
396C4⋊C4—91no—
397C4⋊C4—181no—
398C4⋊C4—182no—
399C4⋊C4—181no—
400C4⋊C4C2×D3211yescharacteristic
401C22⋊C4—62no—
402C22⋊C4—62no—
403C22⋊C4—92no—
404C22⋊C4—181no—
405C42—91no—
406C42—181no—
407C22×C3—21no—
408C22×C3—34no—
409C22×C3—62no—
410C22×C3—62no—
411C22×C3—122no—
412C22×C3—122no—
413C22×C3—122no—
414C22×C3C2×D3×D412yes—
415C2×D3—22no—
416C2×D3—22no—
417C2×D3—42no—
418C2×D3—42no—
419C2×D3—42no—
420C2×D3—64no—
421C2×D3—122no—
422C2×D3—122no—
423C2×D3—122no—
424C2×D3—241no—
425C2×D3—241no—
426C2×D3—248no—
427C2×D3—248no—
428C2×D3D3×SD1614yes—
429C3×C4—21no—
430C3×C4—21no—
431C3×C4—42no—
432C3×C4—42no—
433C3×C4—42no—
434C3×C4—62no—
435C3×C4—81no—
436C3×C4—122no—
437C3×C4#100412yes—
438C3×C4D3×#4112yes—
439Dic3—22no—
440Dic3—34no—
441Dic3—42no—
442Dic3—62no—
443Dic3—62no—
444Dic3—121no—
445Dic3—122no—
446Dic3—241no—
447C32#329511yescharacteristic, complemented, Sylow
448C23—32no—
449C23—62no—
450C23—181no—
451C23—364no—
452C23—364no—
453C23—722no—
454Q8—21no—
455Q8—21no—
456Q8—721no—
457D4—62no—
458D4—62no—
459D4—94no—
460D4—92no—
461D4—124no—
462D4—181no—
463D4—364no—
464D4—362no—
465D4—721no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—32no—
469C2×C4—62no—
470C2×C4—62no—
471C2×C4—62no—
472C2×C4—91no—
473C2×C4—91no—
474C2×C4—181no—
475C2×C4—362no—
476C2×C4—722no—
477C2×C4C22×D3211yescharacteristic
478C8—21no—
479C8—62no—
480C8—181no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—21no—
484C2×C3—64no—
485C2×C3—242no—
486C2×C3#561012yes—
487C2×C3C2×D3×SD1612yes—
488C2×C3#576912yes—
489D3—24no—
490D3—82no—
491D3—124no—
492D3—242no—
493C22—34no—
494C22—62no—
495C22—62no—
496C22—122no—
497C22—122no—
498C22—122no—
499C22—182no—
500C22—361no—
501C22—361no—
502C22—728no—
503C22D32×D411yescharacteristic
504C4—41no—
505C4—41no—
506C4—62no—
507C4—92no—
508C4—122no—
509C4—181no—
510C4—361no—
511C4#6430611yescharacteristic
512C4#6431311yescharacteristic
513C3—21no—
514C3#8068012yescomplemented
515C2—64no—
516C2—242no—
517C2—362no—
518C2#1059427611yescharacteristic
519C2D32×SD1611yescharacteristic
520C2#1059477111yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radical#10594618C2
hypercenter#103D32
hypocenterC32#3295
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. #10595407C2semidirect
3. #10592487C2semidirect
4. C3×#4807C2semidirect
5. #10591651C2semidirect
6. #10591622C2semidirect
7. D3×#821C2semidirect
8. #10590885C2semidirect
9. C8×#625C2semidirect
10. #10590441C2semidirect
11. #10590433C2semidirect
15. Q8×C3⋊Dic3C22semidirect
18. C3×#946C22semidirect
19. C2×C3×#215C22semidirect
20. C2×C3×D3×C8C22semidirect
23. #63919C22semidirect
29. D3×C4⋊Dic3C22semidirect
31. C32×#103C22semidirect
33. C8×C3⋊Dic3C22semidirect
34. #63635C22semidirect
35. C3×#821C22semidirect
36. C3×#808C22semidirect
37. #63572C22semidirect
39. #63563C22semidirect
40. #63562C22semidirect
41. (C2×D3)⋊(C3⋊C8)C22semidirect
53. #4807D3semidirect
102. #946C2×D3semidirect
107. C2×#215C2×D3semidirect
112. C2×D3×C8C2×D3semidirect
126. C3×#103C2×D3semidirect
135. #821C2×D3semidirect
144. #808C2×D3semidirect
173. #625SD16semidirect
295. #103D32semidirect
447. C32#3295semidirect
514. C3#80680semidirect

Maximal subgroups

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

subgroupindex
#105954072
#105946182
#105924872
C3×#48072
#105916512
#105916222
D3×#8212
#105908852
C8×#6252
#105904412
#105904332
#806803