Finite Group Databasebeta

← #11787778

Subgroups — #11787778

Order 1152.

719 conjugacy classes of subgroups.

The subgroup lattice has 547 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595032C211yesmaximal, characteristic
2#10594776C211yesmaximal, characteristic, complemented
3C3×#5006C211yesmaximal, characteristic, complemented
4C3×#5005C211yesmaximal, characteristic, complemented
5#10591111C211yesmaximal, characteristic, complemented
6#10589398C211yesmaximal, characteristic, complemented
7#10589160C211yesmaximal, characteristic, complemented
8#70417—31nomaximal
9#70045—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C32×#117C2211yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C3×#926C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#63980—22no—
18#63914C411yescharacteristic, complemented
19C4×#625—22no—
20#63873C411yescharacteristic, complemented
21#63863C411yescharacteristic, complemented
22#63863C411yescharacteristic, complemented
23#63815—22no—
24#63814—22no—
25D3×#208—22no—
26C3×#806—22no—
27C3×#805—22no—
28#63569—22no—
29#5832—31no—
30#5832—31no—
31#5819—31no—
32#5745—31no—
33C3×#421—31no—
34C3×#410—31no—
35#5236—31no—
36#5006D311yescharacteristic, complemented
37#5005—31no—
38#5005D311yescharacteristic, complemented
39#4555—31no—
40#4532—31no—
41#4532—31no—
42#4532—31no—
43#4532—61no—
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3—21no—
46C2×C3×#67—21no—
47C2×C3×#67D412yes—
48C3×#235—21no—
49C3×#235—21no—
50C3×#235—21no—
51C3×#235—21no—
52C3×#235—21no—
53C3×#235—21no—
54C3×#235—21no—
55C3×#235—21no—
56C2×C3×D12C2×C411yescharacteristic
57C2×C3×D12C2×C411yescharacteristic
58C2×C3×C4×D3—21no—
59C2×C3×C4×D3D412yes—
60C2×C3×Dic6C2×C411yescharacteristic
61C2×C3×Dic6C2×C411yescharacteristic
62C2×#625—22no—
63C32×C4⋊C4—21no—
64C32×C22⋊C4—21no—
65C32×C42—21no—
66C4×C3⋊Dic3—21no—
67C4×C3⋊Dic3C2×C411yescharacteristic
68C4×C3⋊Dic3C2×C411yescharacteristic
69#3748—21no—
70#3748D412yescomplemented
71C2×C3⋊(C3⋊C8)—21no—
72C3×#217—21no—
73C3×C4⋊Dic3—21no—
74C3×C4×Dic3—21no—
75C3×#208—21no—
76C3×#208D412yescomplemented
77C2×C3×C3⋊C8—21no—
78#3724—22no—
79(C2×D3)⋊Dic3—22no—
80(C2×D3)⋊Dic3—22no—
81#3711—24no—
82D3×C3⋊C8—24no—
83#1884—91noSylow
84C2×C3×#41—31no—
85C2×C3×#41—31no—
86C2×#235C2×D311yescharacteristic
87C2×#235C2×D311yescharacteristic
88C2×C3×M16—31no—
89C3×#117—21no—
90C3×#117—31no—
91C3×#117C2×D311yescharacteristic
92C3×#117C2×D311yescharacteristic
93#948—62no—
94#948—62no—
95#947—31no—
96#947—31no—
97#944—31no—
98#944—31no—
99#940—31no—
100#940—31no—
101#939—62no—
102#939—62no—
103#936—31no—
104#936—31no—
105C4×#67—62no—
106C4×#67—62no—
107#926C2×D311yescharacteristic
108C2×C4×Dic3—31no—
109C2×C4×Dic3—31no—
110C2×C4×Dic3—61no—
111C2×#208—31no—
112C2×#208—31no—
113C2×#208—61no—
114C2×#208—62no—
115C2×#208C2×D311yescharacteristic
116#907—62no—
117D3×M16—62no—
118#901—62no—
119C3×#104—62no—
120C3×#99—62no—
121#837—62no—
122#806—22no—
123#805—22no—
124#805—62no—
125C23×C32C2×D411yescharacteristic
126C22×C3×D3—21no—
127C22×C3×D3C22⋊C412yes—
128C2×C32×C4—41no—
129C2×C32×C4C22×C411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4#4111yescharacteristic
134C2×C32×C4#4111yescharacteristic
135C2×C3⋊Dic3—21no—
136C2×C3⋊Dic3—21no—
137C2×C3⋊Dic3—42no—
138C3×#67—22no—
139C3×#67—22no—
140C3×#67—41no—
141C3×#67—41no—
142C2×C3×Dic3—21no—
143C2×C3×Dic3—41no—
144C2×C3×Dic3C22⋊C412yes—
145C3×D12—21no—
146C3×D12—21no—
147C3×D12—21no—
148C3×D12—21no—
149C3×C4×D3—22no—
150C3×C4×D3—22no—
151C3×C4×D3—41no—
152C3×C4×D3—41no—
153C3×Dic6—21no—
154C3×Dic6—21no—
155C3×Dic6—21no—
156C3×Dic6—21no—
157#625—44no—
158C3⋊(C3⋊C8)—22no—
159C3×C3⋊C8—22no—
160#568—91no—
161#532—91no—
162#421—31no—
163#421—91no—
164#410—31no—
165#339—91no—
166#339—91no—
167C3×#41—61no—
168C3×#41—61no—
169C3×#41—61no—
170C3×#41—61no—
171C3×#41—61no—
172C3×#41—61no—
173C3×#41—61no—
174C3×#41—61no—
175C2×C3×Q8—31no—
176C2×C3×Q8—31no—
177C2×C3×D4—32no—
178C2×C3×D4—31no—
179C2×C3×D4—31no—
180C2×C3×D4—61no—
181C22×C3×C4—21no—
182C22×C3×C4—32no—
183C22×C3×C4—61no—
184C22×C3×C4C22×D311yescharacteristic
185C22×C3×C4C22×D311yescharacteristic
186C2×#67—21no—
187C2×#67—62no—
188C2×#67—62no—
189C2×#67#6712yes—
190C22×Dic3—61no—
191C22×Dic3—61no—
192C22×Dic3—121no—
193#235—21no—
194#235—21no—
195#235—21no—
196#235—21no—
197#235—21no—
198#235—21no—
199#235—21no—
200#235—21no—
201C2×D12C4×D311yescharacteristic
202C2×D12C4×D311yescharacteristic
203C2×C4×D3—21no—
204C2×C4×D3D1212yes—
205C2×Dic6C4×D311yescharacteristic
206C2×Dic6C4×D311yescharacteristic
207C3×M16—32no—
208C3×M16—61no—
209C2×C3×C8—61no—
210C3×C4⋊C4—22no—
211C3×C4⋊C4—21no—
212C3×C4⋊C4—21no—
213C3×C4⋊C4—61no—
214C3×C22⋊C4—21no—
215C3×C22⋊C4—21no—
216C3×C22⋊C4—41no—
217C3×C22⋊C4—61no—
218C3×C42—21no—
219C3×C42—21no—
220C3×C42—41no—
221C3×C42—61no—
222#217—21no—
223#217—62no—
224#217—62no—
225(C2×D3)⋊C4—62no—
226(C2×D3)⋊C4—62no—
227C4⋊Dic3—21no—
228Dic3⋊C4—62no—
229Dic3⋊C4—62no—
230C4×Dic3—21no—
231C4×Dic3—31no—
232C4×Dic3—31no—
233C4×Dic3—31no—
234C4×Dic3—31no—
235C4×Dic3—61no—
236C4×Dic3—61no—
237C4×Dic3—61no—
238C4×Dic3—61no—
239C4×Dic3—121no—
240#208—21no—
241#208—32no—
242#208—32no—
243#208—62no—
244#208—64no—
245#208—61no—
246#208—61no—
247#208—121no—
248#208#6712yescomplemented
249C2×C3⋊C8—21no—
250C2×C3⋊C8—64no—
251C2×C3⋊C8—61no—
252C2×C3⋊C8—61no—
253C2×C3⋊C8—121no—
254ΓL(1,𝔽25)—64no—
255D3×C8—64no—
256C22×C32—41no—
257C22×C32C2×C22⋊C411yescharacteristic
258C22×C32#12111yescharacteristic
259C22×C32#12111yescharacteristic
260C2×C3×D3—22no—
261C2×C3×D3—42no—
262C2×C3×D3—42no—
263C2×C3×D3—41no—
264C32×C4—81no—
265C32×C4C4×D411yescharacteristic
266C32×C4C4×D411yescharacteristic
267C32×C4#12011yescharacteristic
268C32×C4#12311yescharacteristic
269C3⋊Dic3—22no—
270C3⋊Dic3—41no—
271C3×Dic3—22no—
272C3×Dic3—41no—
273C3×Dic3—81no—
274C2×#41—31no—
275C2×#41—31no—
276#131—182no—
277#131—182no—
278C2×M16—31no—
279C2×M16—91no—
280C2×M16—182no—
281C4⋊Q8—91no—
282#127—91no—
283#124—91no—
284#124—91no—
285#121—182no—
286C4×D4—182no—
287#117—31no—
288#117D3211yescharacteristic
289C2×C42—91no—
290#104—62no—
291#104—182no—
292#99—62no—
293C23×C3—21no—
294C23×C3—32no—
295C23×C3—61no—
296C23×C3D3×D411yescharacteristic
297C23×C3C2×#6711yescharacteristic
298C22×D3—21no—
299C22×D3(C2×D3)⋊C412yes—
300C3×Q8—61no—
301C3×Q8—61no—
302C3×Q8—61no—
303C3×Q8—61no—
304C3×D4—62no—
305C3×D4—62no—
306C3×D4—61no—
307C3×D4—61no—
308C3×D4—61no—
309C3×D4—61no—
310C3×D4—121no—
311C3×D4—121no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—32no—
319C2×C3×C4—42no—
320C2×C3×C4—41no—
321C2×C3×C4—41no—
322C2×C3×C4—62no—
323C2×C3×C4—62no—
324C2×C3×C4—61no—
325C2×C3×C4—121no—
326C2×C3×C4—121no—
327C2×C3×C4—121no—
328C2×C3×C4C2×C4×D311yescharacteristic
329C2×C3×C4C2×C4×D311yescharacteristic
330C2×C3×C4C2×D1211yescharacteristic
331C2×C3×C4#23511yescharacteristic
332C2×C3×C4D3×D411yescharacteristic
333C2×C3×C4D3×D411yescharacteristic
334C2×C3×C4D3×D411yescharacteristic
335C2×C3×C4D3×D411yescharacteristic
336C2×C3×C4#23711yescharacteristic
337C2×C3×C4#23711yescharacteristic
338C2×C3×C4#23711yescharacteristic
339C2×C3×C4C2×#6711yescharacteristic
340#67—22no—
341#67—22no—
342#67—41no—
343#67—41no—
344#67—124no—
345#67—124no—
346C2×Dic3—21no—
347C2×Dic3—41no—
348C2×Dic3—61no—
349C2×Dic3—61no—
350C2×Dic3—61no—
351C2×Dic3—61no—
352C2×Dic3—121no—
353C2×Dic3—121no—
354C2×Dic3—122no—
355C2×Dic3—122no—
356C2×Dic3—124no—
357C2×Dic3(C2×D3)⋊C412yes—
358D12—21no—
359D12—21no—
360D12—21no—
361D12—21no—
362C4×D3—22no—
363C4×D3—22no—
364C4×D3—41no—
365C4×D3—41no—
366Dic6—21no—
367Dic6—21no—
368Dic6—21no—
369Dic6—21no—
370C3×C8—62no—
371C3⋊C8—22no—
372C3⋊C8—62no—
373C3⋊C8—62no—
374C3⋊C8—122no—
375C2×C32—21no—
376C2×C32—21no—
377C2×C32—21no—
378C2×C32#38611yescharacteristic
379C3×D3—42no—
380C3×D3—81no—
381#41—61no—
382#41—61no—
383#41—61no—
384#41—61no—
385#41—61no—
386#41—61no—
387#41—61no—
388#41—61no—
389C2×Q8—31no—
390C2×Q8—31no—
391C2×D4—32no—
392C2×D4—31no—
393C2×D4—31no—
394C2×D4—61no—
395C2×D4—182no—
396C22×C4—32no—
397C22×C4—61no—
398C22×C4—181no—
399C22×C4C2×D3211yescharacteristic
400M16—32no—
401M16—61no—
402M16—92no—
403M16—184no—
404M16—181no—
405C2×C8—61no—
406C2×C8—184no—
407C2×C8—181no—
408C4⋊C4—21no—
409C4⋊C4—61no—
410C4⋊C4—182no—
411C22⋊C4—21no—
412C22⋊C4—61no—
413C22⋊C4—182no—
414C22⋊C4—182no—
415C42—21no—
416C42—61no—
417C42—91no—
418C42—91no—
419C42—181no—
420C22×C3—21no—
421C22×C3—21no—
422C22×C3—21no—
423C22×C3—41no—
424C22×C3—41no—
425C22×C3—42no—
426C22×C3—62no—
427C22×C3—122no—
428C22×C3—122no—
429C22×C3—121no—
430C22×C3D3×C22⋊C411yescharacteristic
431C22×C3#88411yescharacteristic
432C22×C3C2×(C2×D3)⋊C411yescharacteristic
433C22×C3#93811yescharacteristic
434C22×C3#93911yescharacteristic
435C22×C3#93911yescharacteristic
436C2×D3—22no—
437C2×D3—42no—
438C2×D3—42no—
439C2×D3—41no—
440C3×C4—21no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—21no—
444C3×C4—62no—
445C3×C4—82no—
446C3×C4—81no—
447C3×C4—81no—
448C3×C4—121no—
449C3×C4—241no—
450C3×C4#67⋊C411yescharacteristic
451C3×C4#67⋊C411yescharacteristic
452C3×C4#67⋊C411yescharacteristic
453C3×C4#88211yescharacteristic
454C3×C4#88311yescharacteristic
455C3×C4#88611yescharacteristic
456C3×C4C4×#6711yescharacteristic
457C3×C4#93711yescharacteristic
458Dic3—22no—
459Dic3—41no—
460Dic3—62no—
461Dic3—62no—
462Dic3—81no—
463Dic3—122no—
464Dic3—121no—
465Dic3—121no—
466Dic3—122no—
467C32#188411yescharacteristic, complemented, Sylow
468C23—32no—
469C23—61no—
470C23D3×#6711yescharacteristic
471Q8—61no—
472Q8—61no—
473Q8—61no—
474Q8—61no—
475D4—62no—
476D4—62no—
477D4—61no—
478D4—61no—
479D4—61no—
480D4—61no—
481D4—121no—
482D4—121no—
483D4—364no—
484C2×C4—32no—
485C2×C4—41no—
486C2×C4—62no—
487C2×C4—62no—
488C2×C4—61no—
489C2×C4—121no—
490C2×C4—121no—
491C2×C4—121no—
492C2×C4—181no—
493C2×C4—181no—
494C2×C4—362no—
495C2×C4#379511yescharacteristic
496C2×C4C4×D3211yescharacteristic
497C2×C4D3×D1211yescharacteristic
498C2×C4#380211yescharacteristic
499C2×C4#380511yescharacteristic
500C2×C4D3×#6711yescharacteristic
501C8—62no—
502C8—182no—
503C2×C3—22no—
504C2×C3—21no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3—41no—
512C2×C3—41no—
513C2×C3—122no—
514C2×C3—241no—
515C2×C3#495611yescharacteristic
516C2×C3#495811yescharacteristic
517D3—42no—
518D3—81no—
519C22—41no—
520C22—62no—
521C22—122no—
522C22—122no—
523C22—121no—
524C22#6388511yescharacteristic
525C22D3×(C2×D3)⋊C411yescharacteristic
526C22#6397011yescharacteristic
527C4—62no—
528C4—81no—
529C4—121no—
530C4—182no—
531C4—241no—
532C4—361no—
533C4#6387911yescharacteristic
534C4#6389111yescharacteristic
535C4#6390211yescharacteristic
536C4#6392211yescharacteristic
537C3—21no—
538C3#7004511yescharacteristic, complemented
539C3#7041711yescharacteristic, complemented
540C2—21no—
541C2—21no—
542C2—21no—
543C2—122no—
544C2—241no—
545C2#1059136311yescharacteristic
subgroupG/H
centerC4#63922
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC2×C32#386
prime radical#10595032C2
cosocleC22×C32×C4C23
hypercenter#117D32
hypocenterC32#1884
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. #10594776C2semidirect
3. C3×#5006C2semidirect
4. C3×#5005C2semidirect
5. #10591111C2semidirect
6. #10589398C2semidirect
7. #10589160C2semidirect
18. #63914C4semidirect
20. #63873C4semidirect
21. #63863C4semidirect
22. #63863C4semidirect
36. #5006D3semidirect
38. #5005D3semidirect
70. #3748D4semidirect
76. C3×#208D4semidirect
248. #208#67semidirect
467. C32#1884semidirect
538. C3#70045semidirect
539. C3#70417semidirect

Maximal subgroups

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

subgroupindex
#105950322
#105947762
C3×#50062
C3×#50052
#105911112
#105893982
#105891602
#704173
#700453