Finite Group Databasebeta

← #11775127

Subgroups — #11775127

Order 1152.

713 conjugacy classes of subgroups.

The subgroup lattice has 567 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595005C211yesmaximal, characteristic
2C3×#4726C211yesmaximal, characteristic, complemented
3D3×C3⋊#95C211yesmaximal, characteristic, complemented
4#10589336C211yesmaximal, characteristic, complemented
5C3×#4467C211yesmaximal, characteristic, complemented
6#10589152C211yesmaximal, characteristic, complemented
7#10589151C211yesmaximal, characteristic, complemented
8#69976—31nomaximal
9#68334—31nomaximal
10C22×C3×C4×D3C2211yescharacteristic
11C22×D3×Dic3—21no—
12C2×#3799C411yescharacteristic, complemented
13#64139C2211yescharacteristic
14C3×#924C2211yescharacteristic
15C2×C3×ΓL(1,𝔽25)—21no—
16#63977—21no—
17#63952—21no—
18#63909C411yescharacteristic, complemented
19#63904—21no—
20#63856C411yescharacteristic, complemented
21#63850—21no—
22#63841C411yescharacteristic, complemented
23C32×C22⋊C8C2211yescharacteristic
24#63658C2211yescharacteristic
25C3×C3⋊#95C2211yescharacteristic
26C3×#830C2211yescharacteristic
27C3×(C2×D3)⋊C8—21no—
28#63579—21no—
29#5791—31no—
30#5627—31no—
31C3×#407—31no—
32C2×C3⋊#95—31no—
33#4726D311yescharacteristic, complemented
34D3×#95—31no—
35C3×#328—31no—
36#4538—31no—
37#4470—31no—
38#4470—31no—
39#4470—31no—
40#4470—61no—
41#4467—31no—
42#4467D311yescharacteristic, complemented
43#4451—31no—
44C23×C3×D3D411yescharacteristic
45C22×C32×C4C2311yescharacteristic
46C2×#638—21no—
47C22×C3⋊Dic3—21no—
48C2×C4⋊(C3⋊D3)C2×C411yescharacteristic, complemented
49C22×C3×Dic3—21no—
50C22×C3×Dic3D411yescharacteristic
51C2×C3×C4×D3—42no—
52C2×C3×C4×D3C2×C411yescharacteristic
53C2×C3×C4×D3C2×C411yescharacteristic
54C2×C3×C4×D3D411yescharacteristic
55C2×C3×C4×D3D411yescharacteristic
56C2×C3×Dic6C2×C411yescharacteristic, complemented
57C2×#626—21no—
58C2×#626—21no—
59C2×#624—21no—
60C2×D3×Dic3—24no—
61C2×D3×Dic3—42no—
62C2×D3×Dic3—42no—
63#3799—42no—
64C2×C32×C8—21no—
65#3752—21no—
66C4⋊(C3⋊Dic3)C2×C411yescharacteristic, complemented
67C3×#217—21no—
68C3×C4⋊Dic3C2×C411yescharacteristic, complemented
69C3×Dic3⋊C4—21no—
70C2×C3×C3⋊C8—21no—
71C3×ΓL(1,𝔽25)—42no—
72#3724—21no—
73#3722—21no—
74(C2×D3)⋊Dic3—21no—
75(C2×D3)⋊Dic3—21no—
76Dic32—21no—
77#1504—91noSylow
78C23×C3×C4—31no—
79C23×Dic3—61no—
80C2×#239—31no—
81C2×#235—31no—
82C22×C4×D3—61no—
83C22×C4×D3C2×D311yescharacteristic
84C2×C3×M16—61no—
85C3×C22⋊Q8—31no—
86#953—61no—
87#946—31no—
88#930—31no—
89#930—31no—
90#930—31no—
91#930—61no—
92#929—61no—
93C4×#67—61no—
94C4×#67—61no—
95#926—31no—
96#924—31no—
97#924C2×D311yescharacteristic
98C2×ΓL(1,𝔽25)—21no—
99#895—31no—
100#894—61no—
101#893—61no—
102#892—31no—
103#882—61no—
104#67⋊C4—61no—
105C3×C22⋊C8—21no—
106C3×C22⋊C8—31no—
107C3×C22⋊C8—61no—
108C3×C22⋊C8C2×D311yescharacteristic
109C3×C22⋊C8C2×D311yescharacteristic
110C3×#95—31no—
111C3⋊#95—31no—
112C3⋊#95—31no—
113C3⋊#95—61no—
114C3⋊#95—61no—
115C3⋊#95—61no—
116C3⋊#95C2×D311yescharacteristic
117#830C2×D311yescharacteristic
118(C2×D3)⋊C8—21no—
119C23×C32C2×D411yescharacteristic
120C22×C3⋊D3—21no—
121C22×C3×D3—21no—
122C22×C3×D3—21no—
123C22×C3×D3—22no—
124C22×C3×D3—22no—
125C22×C3×D3C22⋊C411yescharacteristic
126C22×C3×D3C22⋊C411yescharacteristic
127C2×C32×C4—41no—
128C2×C32×C4C22×C411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130#638—41no—
131#638—41no—
132C2×C3⋊Dic3—22no—
133C2×C3⋊Dic3—21no—
134C2×C3⋊Dic3—41no—
135C2×C3⋊Dic3—41no—
136C4⋊(C3⋊D3)—41no—
137C2×C3×Dic3—22no—
138C2×C3×Dic3—21no—
139C2×C3×Dic3—21no—
140C2×C3×Dic3—41no—
141C2×C3×Dic3—41no—
142C2×C3×Dic3—41no—
143C2×C3×Dic3C22⋊C411yescharacteristic
144C2×C3×Dic3C22⋊C411yescharacteristic
145C3×C4×D3—22no—
146C3×C4×D3—22no—
147C3×C4×D3—41no—
148C3×C4×D3—41no—
149C3×Dic6—41no—
150#626—42no—
151#626—42no—
152#624—42no—
153D3×Dic3—48no—
154C32×C8—41no—
155C3×C3⋊C8—41no—
156#525—91no—
157#407—31no—
158C2×#95—91no—
159#328—31no—
160#328—91no—
161#327—91no—
162#327—91no—
163C24×C3—31no—
164C23×D3D1211yescharacteristic
165C2×C3×Q8—31no—
166C22×C3×C4—21no—
167C22×C3×C4—31no—
168C22×C3×C4—31no—
169C22×C3×C4—31no—
170C22×C3×C4—31no—
171C22×C3×C4—31no—
172C22×C3×C4—61no—
173C22×C3×C4—122no—
174C22×C3×C4C22×D311yescharacteristic
175C22×C3×C4C22×D311yescharacteristic
176C2×#67—61no—
177C2×#67—61no—
178C2×#67—61no—
179C2×#67—61no—
180C2×#67—121no—
181C22×Dic3—21no—
182C22×Dic3—64no—
183C22×Dic3—61no—
184C22×Dic3—61no—
185C22×Dic3—121no—
186C22×Dic3—122no—
187C22×Dic3—122no—
188C22×Dic3D1211yescharacteristic
189#239—122no—
190#235—122no—
191C2×D12—31no—
192C2×D12—31no—
193C2×D12—61no—
194C2×D12—61no—
195C2×D12—61no—
196C2×C4×D3—42no—
197C2×C4×D3—61no—
198C2×C4×D3—64no—
199C2×C4×D3—61no—
200C2×C4×D3—122no—
201C2×C4×D3—122no—
202C2×C4×D3C4×D311yescharacteristic
203C2×C4×D3C4×D311yescharacteristic
204C2×C4×D3#6711yescharacteristic
205C2×C4×D3#6711yescharacteristic
206C2×Dic6C4×D311yescharacteristic, complemented
207C3×M16—122no—
208C2×C3×C8—21no—
209C2×C3×C8—21no—
210C2×C3×C8—41no—
211C2×C3×C8—61no—
212C3×C4⋊C4—31no—
213C3×C4⋊C4—61no—
214C3×C22⋊C4—61no—
215#217—21no—
216#217—61no—
217#217—61no—
218(C2×D3)⋊C4—61no—
219(C2×D3)⋊C4—61no—
220(C2×D3)⋊C4—61no—
221(C2×D3)⋊C4—61no—
222(C2×D3)⋊C4—61no—
223(C2×D3)⋊C4—61no—
224(C2×D3)⋊C4—121no—
225C4⋊Dic3—31no—
226C4⋊Dic3—31no—
227C4⋊Dic3—61no—
228C4⋊Dic3C4×D311yescharacteristic, complemented
229Dic3⋊C4—21no—
230Dic3⋊C4—61no—
231Dic3⋊C4—61no—
232C4×Dic3—61no—
233C4×Dic3—61no—
234C2×C3⋊C8—21no—
235ΓL(1,𝔽25)—42no—
236C22×C32—21no—
237C22×C32—21no—
238C22×C32C2×C22⋊C411yescharacteristic
239C22×C32AGL(1,ℤ/8)11yescharacteristic
240C22×C32#13711yescharacteristic
241C2×C3⋊D3—41no—
242C2×C3⋊D3—41no—
243C2×C3⋊D3—41no—
244C2×C3×D3—24no—
245C2×C3×D3—24no—
246C2×C3×D3—21no—
247C2×C3×D3—21no—
248C2×C3×D3—21no—
249C2×C3×D3—21no—
250C2×C3×D3#9912yes—
251C2×C3×D3#10412yes—
252C32×C4—21no—
253C32×C4—21no—
254C3⋊Dic3—42no—
255C3⋊Dic3—41no—
256C3×Dic3—21no—
257C3×Dic3—21no—
258C3×Dic3—42no—
259C3×Dic3—41no—
260C3×Dic3—41no—
261C2×#41—91no—
262C23×C4—31no—
263C23×C4—181no—
264C2×M16—61no—
265#123—181no—
266C22⋊Q8—31no—
267C22⋊Q8—91no—
268#121—91no—
269#121—91no—
270#120—181no—
271C4×D4—181no—
272C4×D4—181no—
273#117—91no—
274C22⋊C8—31no—
275C22⋊C8—61no—
276C22⋊C8D3211yescharacteristic
277#95—31no—
278#95—91no—
279#95—181no—
280C23×C3—21no—
281C23×C3—31no—
282C23×C3—31no—
283C23×C3—62no—
284C23×C3—62no—
285C23×C3—61no—
286C23×C3—61no—
287C23×C3C2×D1211yescharacteristic
288C23×C3D3×D411yescharacteristic
289C22×D3—21no—
290C22×D3—21no—
291C22×D3—22no—
292C22×D3—22no—
293C22×D3—61no—
294C22×D3—61no—
295C22×D3—121no—
296C22×D3(C2×D3)⋊C411yescharacteristic
297C22×D3(C2×D3)⋊C411yescharacteristic
298C3×Q8—121no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—31no—
302C2×C3×C4—31no—
303C2×C3×C4—41no—
304C2×C3×C4—41no—
305C2×C3×C4—62no—
306C2×C3×C4—62no—
307C2×C3×C4—62no—
308C2×C3×C4—61no—
309C2×C3×C4—61no—
310C2×C3×C4—81no—
311C2×C3×C4—121no—
312C2×C3×C4—121no—
313C2×C3×C4—121no—
314C2×C3×C4—121no—
315C2×C3×C4—121no—
316C2×C3×C4C2×C4×D311yescharacteristic
317C2×C3×C4C2×C4×D311yescharacteristic
318C2×C3×C4D3×D411yescharacteristic
319C2×C3×C4C2×#6711yescharacteristic
320#67—122no—
321#67—122no—
322#67—121no—
323#67—121no—
324#67—121no—
325#67—121no—
326#67—241no—
327#67—241no—
328C2×Dic3—22no—
329C2×Dic3—21no—
330C2×Dic3—21no—
331C2×Dic3—41no—
332C2×Dic3—41no—
333C2×Dic3—41no—
334C2×Dic3—62no—
335C2×Dic3—62no—
336C2×Dic3—61no—
337C2×Dic3—61no—
338C2×Dic3—121no—
339C2×Dic3—122no—
340C2×Dic3—128no—
341C2×Dic3—121no—
342C2×Dic3—121no—
343C2×Dic3—121no—
344C2×Dic3—121no—
345C2×Dic3—241no—
346C2×Dic3—241no—
347C2×Dic3(C2×D3)⋊C411yescharacteristic
348C2×Dic3(C2×D3)⋊C411yescharacteristic
349D12—121no—
350D12—121no—
351D12—122no—
352D12—122no—
353D12—241no—
354C4×D3—22no—
355C4×D3—22no—
356C4×D3—41no—
357C4×D3—41no—
358C4×D3—122no—
359C4×D3—122no—
360C4×D3—128no—
361Dic6—41no—
362C3×C8—41no—
363C3×C8—41no—
364C3×C8—81no—
365C3×C8—121no—
366C3⋊C8—41no—
367C2×C32—21no—
368C2×C32—21no—
369C2×C32C2×#9911yescharacteristic
370C2×C32#41711yescharacteristic
371C2×C32C2×#10411yescharacteristic
372C3⋊D3—81no—
373C3×D3—22no—
374C3×D3—22no—
375C24—31no—
376#41—362no—
377C2×Q8—31no—
378C2×D4—91no—
379C2×D4—181no—
380C2×D4—181no—
381C2×D4—181no—
382C22×C4—31no—
383C22×C4—31no—
384C22×C4—31no—
385C22×C4—31no—
386C22×C4—31no—
387C22×C4—61no—
388C22×C4—122no—
389C22×C4—181no—
390C22×C4—184no—
391C22×C4—181no—
392C22×C4—362no—
393C22×C4—362no—
394C22×C4C2×D3211yescharacteristic
395M16—122no—
396C2×C8—21no—
397C2×C8—61no—
398C4⋊C4—31no—
399C4⋊C4—61no—
400C4⋊C4—91no—
401C4⋊C4—181no—
402C22⋊C4—61no—
403C22⋊C4—181no—
404C22⋊C4—181no—
405C22⋊C4—181no—
406C22⋊C4—181no—
407C42—181no—
408C22×C3—21no—
409C22×C3—21no—
410C22×C3—21no—
411C22×C3—21no—
412C22×C3—21no—
413C22×C3—21no—
414C22×C3—21no—
415C22×C3—32no—
416C22×C3—32no—
417C22×C3—41no—
418C22×C3—41no—
419C22×C3—64no—
420C22×C3—64no—
421C22×C3—61no—
422C22×C3—61no—
423C22×C3—61no—
424C22×C3—61no—
425C22×C3D3×C22⋊C411yescharacteristic
426C22×C3#90811yescharacteristic
427C22×C3#90911yescharacteristic
428C22×C3#91411yescharacteristic
429C22×C3#91811yescharacteristic
430C22×C3C2×(C2×D3)⋊C411yescharacteristic
431C2×D3—24no—
432C2×D3—24no—
433C2×D3—21no—
434C2×D3—21no—
435C2×D3—21no—
436C2×D3—21no—
437C2×D3—121no—
438C2×D3—121no—
439C2×D3—121no—
440C2×D3—121no—
441C2×D3—121no—
442C2×D3—121no—
443C2×D3—241no—
444C2×D3—241no—
445C2×D3—241no—
446C2×D3#80612yes—
447C2×D3#82512yes—
448C3×C4—21no—
449C3×C4—21no—
450C3×C4—21no—
451C3×C4—21no—
452C3×C4—41no—
453C3×C4—41no—
454C3×C4—61no—
455C3×C4—61no—
456C3×C4—122no—
457C3×C4—121no—
458C3×C4—121no—
459Dic3—21no—
460Dic3—21no—
461Dic3—42no—
462Dic3—41no—
463Dic3—41no—
464Dic3—122no—
465Dic3—122no—
466Dic3—121no—
467Dic3—121no—
468Dic3—241no—
469Dic3—242no—
470C32#150411yescharacteristic, complemented, Sylow
471C23—31no—
472C23—31no—
473C23—62no—
474C23—62no—
475C23—61no—
476C23—61no—
477C23—181no—
478C23D3×D1211yescharacteristic
479Q8—121no—
480D4—361no—
481D4—362no—
482D4—362no—
483D4—361no—
484D4—361no—
485C2×C4—31no—
486C2×C4—31no—
487C2×C4—41no—
488C2×C4—62no—
489C2×C4—62no—
490C2×C4—62no—
491C2×C4—61no—
492C2×C4—61no—
493C2×C4—121no—
494C2×C4—121no—
495C2×C4—121no—
496C2×C4—121no—
497C2×C4—121no—
498C2×C4—182no—
499C2×C4—181no—
500C2×C4—362no—
501C2×C4—368no—
502C2×C4—361no—
503C2×C4—361no—
504C2×C4C4×D3211yescharacteristic
505C2×C4D3×#6711yescharacteristic
506C8—41no—
507C8—121no—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3—21no—
512C2×C3—21no—
513C2×C3—21no—
514C2×C3—21no—
515C2×C3—41no—
516C2×C3—41no—
517C2×C3—62no—
518C2×C3—62no—
519C2×C3D3×#9911yescharacteristic
520C2×C3#480311yescharacteristic
521C2×C3D3×#10411yescharacteristic
522C2×C3C2×#80611yescharacteristic
523C2×C3#513311yescharacteristic
524C2×C3C2×#82511yescharacteristic
525D3—22no—
526D3—22no—
527D3—241no—
528D3—241no—
529D3—481no—
530C22—21no—
531C22—21no—
532C22—32no—
533C22—32no—
534C22—64no—
535C22—64no—
536C22—61no—
537C22—61no—
538C22—61no—
539C22—61no—
540C22—361no—
541C22—361no—
542C22—361no—
543C22#6379411yescharacteristic
544C22#6380111yescharacteristic
545C22D3×(C2×D3)⋊C411yescharacteristic
546C4—21no—
547C4—21no—
548C4—61no—
549C4—61no—
550C4—122no—
551C4—121no—
552C4—121no—
553C4—362no—
554C4—361no—
555C3—21no—
556C3#6833411yescharacteristic, complemented
557C3#6997611yescharacteristic, complemented
558C2—21no—
559C2—21no—
560C2—62no—
561C2—62no—
562C2—721no—
563C2D3×#80611yescharacteristic
564C2#1059067111yescharacteristic
565C2D3×#82511yescharacteristic
subgroupG/H
centerC22D3×(C2×D3)⋊C4
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32C2×C22⋊C4
prime radical#10595005C2
cosocleC22×C32×C4C23
hypercenterC22⋊C8D32
hypocenterC32#1504
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C3×#4726C2semidirect
3. D3×C3⋊#95C2semidirect
4. #10589336C2semidirect
5. C3×#4467C2semidirect
6. #10589152C2semidirect
7. #10589151C2semidirect
12. C2×#3799C4semidirect
18. #63909C4semidirect
20. #63856C4semidirect
22. #63841C4semidirect
33. #4726D3semidirect
42. #4467D3semidirect
48. C2×C4⋊(C3⋊D3)C2×C4semidirect
56. C2×C3×Dic6C2×C4semidirect
66. C4⋊(C3⋊Dic3)C2×C4semidirect
68. C3×C4⋊Dic3C2×C4semidirect
206. C2×Dic6C4×D3semidirect
228. C4⋊Dic3C4×D3semidirect
470. C32#1504semidirect
556. C3#68334semidirect
557. C3#69976semidirect

Maximal subgroups

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

subgroupindex
#105950052
C3×#47262
D3×C3⋊#952
#105893362
C3×#44672
#105891522
#105891512
#699763
#683343