Finite Group Databasebeta

← #11895358

Subgroups — #11895358

Order 1152.

842 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596184C211yesmaximal, characteristic, complemented
2#10593956C211yesmaximal, characteristic, complemented
3C3×#5072C211yesmaximal, characteristic
4C3×#5070C211yesmaximal, characteristic, complemented
5#10591479C212yesmaximal, complemented
6#10591435C212yesmaximal, complemented
7#10591434C212yesmaximal, complemented
8#10591403C212yesmaximal, complemented
9C4×#3716C211yesmaximal, characteristic, complemented
10#10590284C211yesmaximal, characteristic, complemented
11#10590254C211yesmaximal, characteristic, complemented
12#81585—31nomaximal
13#80319—31nomaximal
14C32×#127C2211yescharacteristic
15#64145—21no—
16#64145C2212yes—
17#64144—22no—
18D4×C3⋊Dic3—21no—
19D4×C3⋊Dic3C2212yes—
20C4×#634C2211yescharacteristic
21C4×#634C2211yescharacteristic
22C2×C3×#213C2212yes—
23C3×C4×D12C2211yescharacteristic
24C3×#869C2211yescharacteristic
25#63898C2212yes—
26D3×C4⋊Dic3—21no—
27#63887—22no—
28#63872C2212yes—
29#63857—21no—
30C2×#3716C2211yescharacteristic
31C3×#832C2212yes—
32C3×#832C2212yes—
33C3×#832C2212yes—
34C3×C4⋊(C3⋊C8)C2211yescharacteristic
35C3×C4×C3⋊C8C2211yescharacteristic
36#63575C2212yes—
37#63573C2211yescharacteristic
38#63572C2212yes—
39#63567C2212yes—
40#63567C2211yescharacteristic
41#63563C2211yescharacteristic
42#63553C2212yes—
43#5730—31no—
44#5713—31no—
45#5713—31no—
46#5713—61no—
47#5543—31no—
48C3×#486—31no—
49C3×#459—31no—
50#5153—32no—
51Dic3×D8—32no—
52#5091—31no—
53#5072D311yescharacteristic
54#5070D311yescharacteristic, complemented
55C4×#214—31no—
56#4850—31no—
57#4830—31no—
58#4787—32no—
59#4768—32no—
60#4768—32no—
61#4766—32no—
62#4763—32no—
63#4756—32no—
64C4×#204—31no—
65C8×Dic6—31no—
66C2×C32×D4—21no—
67C2×C32×D4—21no—
68C2×C32×D4C2312yes—
69C22×C3⋊Dic3—22no—
70C2×#634D411yescharacteristic
71C2×#634C2311yescharacteristic
72C2×C3×D12C2311yescharacteristic
73C2×C3×C4×D3—21no—
74C2×C3×Dic6—21no—
75C2×D3×Dic3—22no—
76C32×C42C2311yescharacteristic
77#3757—22no—
78#3757—22no—
79#3757—22no—
80C4⋊(C3⋊Dic3)D411yescharacteristic
81C4⋊(C3⋊Dic3)C2311yescharacteristic
82#3750—21no—
83#3750D412yes—
84C4×C3⋊Dic3—21no—
85C4×C3⋊Dic3C2312yes—
86C3×#213—24no—
87C3×(C2×D3)⋊C4—21no—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3C2311yescharacteristic
90C3×C4⋊Dic3C2312yes—
91C2×C3×C3⋊C8C2312yes—
92C2×C3×C3⋊C8C2311yescharacteristic
93C2×C3×C3⋊C8C2311yescharacteristic
94Dic3⋊Dic3—22no—
95Dic3⋊Dic3—22no—
96(C2×D3)⋊Dic3—22no—
97#3716—22no—
98#3361—91noSylow
99C2×C3×D8—32no—
100C3×C4⋊Q8—31no—
101C3×#127—21no—
102C3×#127C2×D311yescharacteristic
103C3×#127C2×D311yescharacteristic
104C3×C4×D4—31no—
105#946—62no—
106#936—32no—
107#936—32no—
108#936—62no—
109#936—61no—
110#936—61no—
111#936—62no—
112#935—62no—
113#935—62no—
114#935—64no—
115D4×Dic3—32no—
116D4×Dic3—32no—
117D4×Dic3—32no—
118D4×Dic3—62no—
119D4×Dic3—61no—
120D4×Dic3—61no—
121D4×Dic3—62no—
122C2×#214—31no—
123C2×#213C2×D312yes—
124C2×C4⋊Dic3—61no—
125#924—61no—
126C2×#204—31no—
127#897—61no—
128#893—32no—
129D3×C4⋊C4—61no—
130#890—32no—
131#890—32no—
132#878—62no—
133C4×D12C2×D311yescharacteristic
134#869C2×D311yescharacteristic
135C4×Dic6—31no—
136C4×Dic6—31no—
137C4×Dic6—31no—
138C4×Dic6—31no—
139C4×Dic6—61no—
140C4×Dic6—61no—
141C3×C4⋊C8—31no—
142C3×#102—32no—
143C3×#102—32no—
144C3×#102—32no—
145C3×C4×C8—31no—
146#832—31no—
147#832C2×D312yes—
148#832C2×D312yes—
149#832C2×D312yes—
150#821—31no—
151#818—32no—
152#817—31no—
153#816—32no—
154#816—31no—
155Dic3⋊C8—32no—
156Dic3⋊C8—32no—
157C8×Dic3—32no—
158C8×Dic3—32no—
159#810—31no—
160#810—32no—
161#808—31no—
162#807—32no—
163C4⋊(C3⋊C8)C2×D311yescharacteristic
164C4×C3⋊C8C2×D311yescharacteristic
165C23×C32—22no—
166C22×C3×D3—21no—
167C32×D4—22no—
168C32×D4—22no—
169C32×D4—42no—
170C32×D4—81no—
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2411yescharacteristic
174C2×C3⋊Dic3—21no—
175C2×C3⋊Dic3—21no—
176C2×C3⋊Dic3—82no—
177C2×C3⋊Dic3C2×D412yes—
178C2×C3⋊Dic3C2×D412yes—
179#634—22no—
180#634—21no—
181#634—21no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—21no—
184C3×D12—21no—
185C3×D12#4112yes—
186C3×C4×D3—42no—
187C3×Dic6—81no—
188D3×Dic3—82no—
189C3×C3⋊C8—21no—
190C3×C3⋊C8—22no—
191C3×C3⋊C8—21no—
192#559—91no—
193#554—91no—
194#488—92no—
195#486—31no—
196#478—92no—
197#477—91no—
198#463—92no—
199#459—31no—
200C8×Q8—91no—
201C4×SD16—91no—
202C4×D8—92no—
203C2×C3×Q8—61no—
204C2×C3×D4—22no—
205C2×C3×D4—22no—
206C2×C3×D4—21no—
207C2×C3×D4—21no—
208C2×C3×D4—21no—
209C2×C3×D4—21no—
210C2×C3×D4—22no—
211C2×C3×D4—31no—
212C2×C3×D4C22×D312yes—
213C2×C3×D4C22×D312yes—
214C22×C3×C4—61no—
215C22×Dic3—62no—
216C22×Dic3—62no—
217C22×Dic3—62no—
218C22×Dic3—64no—
219C2×D12C22×D311yescharacteristic
220C2×C4×D3—21no—
221C2×C4×D3—62no—
222C2×Dic6—21no—
223C2×Dic6—31no—
224C2×Dic6—31no—
225C2×Dic6—31no—
226C2×Dic6—31no—
227C2×Dic6—61no—
228C2×Dic6—61no—
229C3×D8—64no—
230C2×C3×C8—31no—
231C2×C3×C8—32no—
232C2×C3×C8—31no—
233C3×C4⋊C4—32no—
234C3×C4⋊C4—31no—
235C3×C4⋊C4—61no—
236C3×C22⋊C4—61no—
237C3×C42—21no—
238C3×C42C22×D311yescharacteristic
239C3×C42C22×D311yescharacteristic
240#217—62no—
241#217—62no—
242#217—62no—
243#217—62no—
244#217—62no—
245#217—62no—
246#217—62no—
247#217—64no—
248#217—64no—
249#217—64no—
250#214—62no—
251#213—24no—
252(C2×D3)⋊C4—21no—
253(C2×D3)⋊C4—62no—
254C4⋊Dic3—21no—
255C4⋊Dic3—31no—
256C4⋊Dic3—31no—
257C4⋊Dic3—31no—
258C4⋊Dic3—31no—
259C4⋊Dic3—61no—
260C4⋊Dic3—61no—
261C4⋊Dic3—62no—
262C4⋊Dic3—62no—
263C4⋊Dic3C22×D311yescharacteristic
264C4⋊Dic3C22×D312yes—
265Dic3⋊C4—32no—
266Dic3⋊C4—32no—
267Dic3⋊C4—62no—
268Dic3⋊C4—62no—
269Dic3⋊C4—62no—
270Dic3⋊C4—62no—
271Dic3⋊C4—61no—
272Dic3⋊C4—61no—
273C4×Dic3—32no—
274C4×Dic3—32no—
275C4×Dic3—62no—
276C4×Dic3—62no—
277C4×Dic3—61no—
278C4×Dic3—61no—
279C2×C3⋊C8C22×D311yescharacteristic
280C2×C3⋊C8C22×D311yescharacteristic
281C2×C3⋊C8C22×D312yes—
282#204—62no—
283C22×C32—42no—
284C22×C32—42no—
285C22×C32—42no—
286C22×C32C22×D411yescharacteristic
287C2×C3×D3—22no—
288C2×C3×D3—41no—
289C2×C3×D3—41no—
290C32×C4—21no—
291C32×C4#13512yes—
292C32×C4C2×#4111yescharacteristic
293C32×C42−1+411yescharacteristic
294C3⋊Dic3—22no—
295C3⋊Dic3—22no—
296C3⋊Dic3—41no—
297C3⋊Dic3—41no—
298C3×Dic3—41no—
299C3×Dic3—42no—
300C2×SD16—91no—
301C2×D8—32no—
302C4⋊Q8—31no—
303#127D3211yescharacteristic
304#125—92no—
305#124—92no—
306#124—181no—
307#123—182no—
308C22⋊Q8—182no—
309C22⋊Q8—181no—
310C4×Q8—91no—
311C4×Q8—91no—
312C4×D4—31no—
313C4×D4—92no—
314C4×D4—92no—
315C4×D4—181no—
316C2×C4⋊C4—181no—
317#107—92no—
318#106—91no—
319C4⋊C8—31no—
320C4⋊C8—92no—
321#103—91no—
322#103—92no—
323#102—32no—
324#102—32no—
325#102—32no—
326#102—91no—
327C4×C8—31no—
328C4×C8—92no—
329C23×C3—24no—
330C23×C3—22no—
331C23×C3—22no—
332C23×C3—61no—
333C22×D3—21no—
334C3×Q8—241no—
335C3×D4—22no—
336C3×D4—22no—
337C3×D4—22no—
338C3×D4—22no—
339C3×D4—32no—
340C3×D4—42no—
341C3×D4—42no—
342C3×D4—44no—
343C3×D4—42no—
344C3×D4—42no—
345C3×D4—61no—
346C3×D4—81no—
347C3×D4—81no—
348C3×D4—82no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—61no—
353C2×C3×C4—62no—
354C2×C3×C4—122no—
355C2×C3×C4D3×D411yescharacteristic
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4D3×D411yescharacteristic
358C2×C3×C4D3×D411yescharacteristic
359C2×C3×C4C23×D311yescharacteristic
360C2×C3×C4C23×D311yescharacteristic
361C2×Dic3—21no—
362C2×Dic3—22no—
363C2×Dic3—32no—
364C2×Dic3—32no—
365C2×Dic3—32no—
366C2×Dic3—32no—
367C2×Dic3—62no—
368C2×Dic3—62no—
369C2×Dic3—62no—
370C2×Dic3—62no—
371C2×Dic3—61no—
372C2×Dic3—61no—
373C2×Dic3—61no—
374C2×Dic3—61no—
375C2×Dic3—242no—
376C2×Dic3—242no—
377C2×Dic3—242no—
378C2×Dic3—244no—
379D12—21no—
380D12#23712yes—
381C4×D3—42no—
382C4×D3—242no—
383Dic6—62no—
384Dic6—62no—
385Dic6—61no—
386Dic6—61no—
387Dic6—61no—
388Dic6—61no—
389Dic6—81no—
390Dic6—122no—
391Dic6—121no—
392Dic6—121no—
393C3×C8—61no—
394C3×C8—62no—
395C3×C8—61no—
396C3⋊C8—22no—
397C3⋊C8—21no—
398C3⋊C8—21no—
399C2×C32—82no—
400C2×C32#54811yescharacteristic
401C2×C32C2×#13511yescharacteristic
402C2×C32#57611yescharacteristic
403C3×D3—42no—
404C2×Q8—61no—
405C2×Q8—91no—
406C2×Q8—91no—
407C2×D4—21no—
408C2×D4—21no—
409C2×D4—31no—
410C2×D4C2×D3212yes—
411C22×C4—61no—
412C22×C4—182no—
413C22×C4—182no—
414SD16—182no—
415D8—64no—
416C2×C8—31no—
417C2×C8—31no—
418C2×C8—32no—
419C4⋊C4—31no—
420C4⋊C4—32no—
421C4⋊C4—61no—
422C4⋊C4—91no—
423C4⋊C4—92no—
424C4⋊C4—91no—
425C4⋊C4—182no—
426C4⋊C4—182no—
427C4⋊C4—181no—
428C22⋊C4—61no—
429C22⋊C4—182no—
430C22⋊C4—182no—
431C22⋊C4—182no—
432C22⋊C4—182no—
433C42—92no—
434C42—181no—
435C42C2×D3211yescharacteristic
436C22×C3—21no—
437C22×C3—44no—
438C22×C3—44no—
439C22×C3—44no—
440C22×C3—42no—
441C22×C3—42no—
442C22×C3—42no—
443C22×C3—42no—
444C22×C3—42no—
445C22×C3—42no—
446C22×C3—62no—
447C22×C3—121no—
448C22×C3—121no—
449C22×C3C2×D3×D411yescharacteristic
450C22×C3C2×D3×D411yescharacteristic
451C2×D3—22no—
452C2×D3—41no—
453C2×D3—41no—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—21no—
457C3×C4—21no—
458C3×C4—22no—
459C3×C4—41no—
460C3×C4—121no—
461C3×C4—122no—
462C3×C4#91212yes—
463C3×C4#91612yes—
464C3×C4C2×#23711yescharacteristic
465C3×C4D3×#4111yescharacteristic
466C3×C4#101011yescharacteristic
467C3×C4#101011yescharacteristic
468Dic3—41no—
469Dic3—42no—
470Dic3—62no—
471Dic3—62no—
472Dic3—62no—
473Dic3—62no—
474Dic3—122no—
475Dic3—122no—
476Dic3—122no—
477Dic3—122no—
478Dic3—121no—
479Dic3—121no—
480Dic3—121no—
481Dic3—121no—
482C32#336111yescharacteristic, complemented, Sylow
483C23—22no—
484C23—61no—
485Q8—182no—
486Q8—181no—
487Q8—181no—
488Q8—241no—
489D4—22no—
490D4—22no—
491D4—32no—
492D4—42no—
493D4—61no—
494D4—81no—
495C2×C4—61no—
496C2×C4—62no—
497C2×C4—92no—
498C2×C4—92no—
499C2×C4—122no—
500C2×C4—181no—
501C2×C4—181no—
502C2×C4—722no—
503C2×C4—722no—
504C2×C4#381111yescharacteristic
505C2×C4#381111yescharacteristic
506C2×C4C22×D3211yescharacteristic
507C8—61no—
508C8—62no—
509C8—61no—
510C2×C3—21no—
511C2×C3—21no—
512C2×C3—21no—
513C2×C3—84no—
514C2×C3—82no—
515C2×C3—82no—
516C2×C3—122no—
517C2×C3#559811yescharacteristic
518C2×C3#567711yescharacteristic
519C2×C3C2×#91211yescharacteristic
520C2×C3#575711yescharacteristic
521C2×C3C2×#91611yescharacteristic
522C2×C3#577411yescharacteristic
523D3—42no—
524C22—42no—
525C22—42no—
526C22—42no—
527C22—62no—
528C22—121no—
529C22—121no—
530C22C2×#381111yescharacteristic
531C4—21no—
532C4—122no—
533C4—121no—
534C4—182no—
535C4—182no—
536C4—361no—
537C4—361no—
538C4#6393612yes—
539C4#6430911yescharacteristic
540C4D3×#23711yescharacteristic
541C3—21no—
542C3#8031911yescharacteristic, complemented
543C3#8158511yescharacteristic, complemented
544C2—82no—
545C2—122no—
546C2#1059510211yescharacteristic
547C2C2×#6393611yescharacteristic
548C2#1059516111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#127C22
socleC22×C32C22×D4
prime radicalC3×#5072C2
hypercenter#127D32
hypocenterC32#3361
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #10596184C2semidirect
2. #10593956C2semidirect
4. C3×#5070C2semidirect
5. #10591479C2semidirect
6. #10591435C2semidirect
7. #10591434C2semidirect
8. #10591403C2semidirect
9. C4×#3716C2semidirect
10. #10590284C2semidirect
11. #10590254C2semidirect
54. #5070D3semidirect
482. C32#3361semidirect
542. C3#80319semidirect
543. C3#81585semidirect

Maximal subgroups

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

subgroupindex
#105961842
#105939562
C3×#50722
C3×#50702
#105914792
#105914352
#105914342
#105914032
C4×#37162
#105902842
#105902542
#815853
#803193