Finite Group Databasebeta

← #11775129

Subgroups — #11775129

Order 1152.

708 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594892C211yesmaximal, characteristic
2C3×#4726C211yesmaximal, characteristic, complemented
3D3×C3⋊#95C211yesmaximal, characteristic, complemented
4#10589333C211yesmaximal, characteristic, complemented
5C3×#4470C211yesmaximal, characteristic, complemented
6#10589154C211yesmaximal, characteristic, complemented
7#10589150C211yesmaximal, characteristic, complemented
8#69976—31nomaximal
9#68302—31nomaximal
10C22×C3×C4×D3C2211yescharacteristic
11C22×D3×Dic3—21no—
12C2×#3795C411yescharacteristic, complemented
13#64133C2211yescharacteristic
14C3×#930C2211yescharacteristic
15C2×C3×ΓL(1,𝔽25)—21no—
16#63976—21no—
17Dic3×#67—21no—
18#63908C411yescharacteristic, complemented
19#63905—21no—
20#63879—21no—
21#63857C411yescharacteristic, complemented
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#5606—31no—
31C3×#407—31no—
32C2×C3⋊#95—31no—
33#4726D311yescharacteristic, complemented
34D3×#95—31no—
35C3×#327—31no—
36#4537—31no—
37#4470—31no—
38#4470D311yescharacteristic, complemented
39#4467—31no—
40#4467—31no—
41#4467—31no—
42#4467—61no—
43#4452—31no—
44C23×C3×D3D411yescharacteristic
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3—21no—
47C2×#634C2×C411yescharacteristic, complemented
48C2×C3×#67—21no—
49C22×C3×Dic3—21no—
50C22×C3×Dic3D411yescharacteristic
51C2×C3×D12C2×C411yescharacteristic, complemented
52C2×C3×C4×D3—42no—
53C2×C3×C4×D3C2×C411yescharacteristic
54C2×C3×C4×D3C2×C411yescharacteristic
55C2×C3×C4×D3D411yescharacteristic
56C2×C3×C4×D3D411yescharacteristic
57C2×#625—21no—
58C2×#625—21no—
59C2×D3×Dic3—24no—
60C2×D3×Dic3—21no—
61C2×D3×Dic3—42no—
62C2×D3×Dic3—42no—
63#3795—42no—
64C2×C32×C8—21no—
65#3757—21no—
66C4⋊(C3⋊Dic3)C2×C411yescharacteristic, complemented
67#3750—21no—
68C3×(C2×D3)⋊C4—21no—
69C3×C4⋊Dic3C2×C411yescharacteristic, complemented
70C2×C3×C3⋊C8—21no—
71C3×ΓL(1,𝔽25)—42no—
72Dic3⋊Dic3—21no—
73(C2×D3)⋊Dic3—21no—
74(C2×D3)⋊Dic3—21no—
75(C2×D3)⋊Dic3—21no—
76Dic32—21no—
77#1504—91noSylow
78C23×C3×C4—31no—
79C23×Dic3—61no—
80C2×#237—31no—
81C2×#235—31no—
82C22×C4×D3—61no—
83C22×C4×D3C2×D311yescharacteristic
84C2×C3×M16—61no—
85C3×#121—31no—
86#953—61no—
87#938—31no—
88#937—61no—
89D4×Dic3—61no—
90#930—31no—
91#930C2×D311yescharacteristic
92#929—61no—
93C4×#67—61no—
94C4×#67—61no—
95#926—31no—
96#924—31no—
97#924—31no—
98#924—31no—
99#924—61no—
100C2×ΓL(1,𝔽25)—21no—
101#897—31no—
102#892—31no—
103#883—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—22no—
123C22×C3×D3—22no—
124C22×C3×D3—21no—
125C22×C3×D3C22⋊C411yescharacteristic
126C22×C3×D3C22⋊C411yescharacteristic
127C2×C32×C4—41no—
128C2×C32×C4C22×C411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C3⋊Dic3—22no—
131C2×C3⋊Dic3—21no—
132C2×C3⋊Dic3—21no—
133C2×C3⋊Dic3—41no—
134C2×C3⋊Dic3—41no—
135#634—41no—
136C3×#67—41no—
137C3×#67—41no—
138C2×C3×Dic3—22no—
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×D12—41no—
146C3×C4×D3—22no—
147C3×C4×D3—22no—
148C3×C4×D3—41no—
149C3×C4×D3—41no—
150#625—42no—
151#625—42no—
152D3×Dic3—42no—
153D3×Dic3—48no—
154C32×C8—41no—
155C3×C3⋊C8—41no—
156#525—91no—
157#407—31no—
158C2×#95—91no—
159#328—91no—
160#328—91no—
161#327—31no—
162#327—91no—
163C24×C3—31no—
164C23×D3D1211yescharacteristic
165C2×C3×D4—31no—
166C2×C3×D4—61no—
167C22×C3×C4—21no—
168C22×C3×C4—31no—
169C22×C3×C4—31no—
170C22×C3×C4—31no—
171C22×C3×C4—31no—
172C22×C3×C4—31no—
173C22×C3×C4—61no—
174C22×C3×C4—122no—
175C22×C3×C4C22×D311yescharacteristic
176C22×C3×C4C22×D311yescharacteristic
177C2×#67—21no—
178C2×#67—61no—
179C2×#67—61no—
180C2×#67—61no—
181C2×#67—61no—
182C22×Dic3—21no—
183C22×Dic3—64no—
184C22×Dic3—61no—
185C22×Dic3—61no—
186C22×Dic3—61no—
187C22×Dic3—121no—
188C22×Dic3—122no—
189C22×Dic3—122no—
190C22×Dic3D1211yescharacteristic
191#237—122no—
192#235—122no—
193C2×D12C4×D311yescharacteristic, complemented
194C2×C4×D3—42no—
195C2×C4×D3—61no—
196C2×C4×D3—64no—
197C2×C4×D3—122no—
198C2×C4×D3—122no—
199C2×C4×D3C4×D311yescharacteristic
200C2×C4×D3C4×D311yescharacteristic
201C2×C4×D3#6711yescharacteristic
202C2×C4×D3#6711yescharacteristic
203C2×Dic6—31no—
204C2×Dic6—31no—
205C2×Dic6—61no—
206C3×M16—122no—
207C2×C3×C8—21no—
208C2×C3×C8—21no—
209C2×C3×C8—41no—
210C2×C3×C8—61no—
211C3×C4⋊C4—31no—
212C3×C22⋊C4—61no—
213#217—61no—
214#217—61no—
215#217—61no—
216#217—61no—
217#217—61no—
218#217—121no—
219(C2×D3)⋊C4—21no—
220(C2×D3)⋊C4—61no—
221(C2×D3)⋊C4—61no—
222(C2×D3)⋊C4—61no—
223C4⋊Dic3—31no—
224C4⋊Dic3—31no—
225C4⋊Dic3—61no—
226C4⋊Dic3—61no—
227C4⋊Dic3C4×D311yescharacteristic, complemented
228Dic3⋊C4—61no—
229Dic3⋊C4—61no—
230Dic3⋊C4—61no—
231Dic3⋊C4—121no—
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—24no—
242C2×C3×D3—24no—
243C2×C3×D3—21no—
244C2×C3×D3—21no—
245C2×C3×D3—21no—
246C2×C3×D3—21no—
247C2×C3×D3—41no—
248C2×C3×D3—41no—
249C2×C3×D3—41no—
250C2×C3×D3#9912yes—
251C2×C3×D3#10412yes—
252C32×C4—21no—
253C32×C4—21no—
254C3⋊Dic3—42no—
255C3⋊Dic3—41no—
256C3⋊Dic3—41no—
257C3×Dic3—21no—
258C3×Dic3—21no—
259C3×Dic3—42no—
260C3×Dic3—41no—
261C2×#41—91no—
262C23×C4—31no—
263C23×C4—181no—
264C2×M16—61no—
265#123—181no—
266C22⋊Q8—91no—
267C22⋊Q8—91no—
268#121—31no—
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×C3—61no—
288C23×C3C2×D1211yescharacteristic
289C23×C3D3×D411yescharacteristic
290C22×D3—21no—
291C22×D3—21no—
292C22×D3—22no—
293C22×D3—22no—
294C22×D3—21no—
295C22×D3(C2×D3)⋊C411yescharacteristic
296C22×D3(C2×D3)⋊C411yescharacteristic
297C3×D4—121no—
298C3×D4—121no—
299C3×D4—121no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—31no—
303C2×C3×C4—31no—
304C2×C3×C4—41no—
305C2×C3×C4—41no—
306C2×C3×C4—62no—
307C2×C3×C4—62no—
308C2×C3×C4—62no—
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—41no—
321#67—41no—
322#67—122no—
323#67—122no—
324#67—122no—
325#67—122no—
326C2×Dic3—22no—
327C2×Dic3—21no—
328C2×Dic3—41no—
329C2×Dic3—41no—
330C2×Dic3—41no—
331C2×Dic3—62no—
332C2×Dic3—62no—
333C2×Dic3—61no—
334C2×Dic3—61no—
335C2×Dic3—61no—
336C2×Dic3—61no—
337C2×Dic3—121no—
338C2×Dic3—121no—
339C2×Dic3—122no—
340C2×Dic3—122no—
341C2×Dic3—128no—
342C2×Dic3—121no—
343C2×Dic3—121no—
344C2×Dic3—121no—
345C2×Dic3—121no—
346C2×Dic3—241no—
347C2×Dic3—241no—
348C2×Dic3(C2×D3)⋊C411yescharacteristic
349C2×Dic3(C2×D3)⋊C411yescharacteristic
350D12—41no—
351C4×D3—22no—
352C4×D3—22no—
353C4×D3—41no—
354C4×D3—41no—
355C4×D3—122no—
356C4×D3—128no—
357Dic6—121no—
358Dic6—121no—
359Dic6—241no—
360C3×C8—41no—
361C3×C8—41no—
362C3×C8—81no—
363C3×C8—121no—
364C3⋊C8—41no—
365C2×C32—21no—
366C2×C32—21no—
367C2×C32C2×#9911yescharacteristic
368C2×C32#41711yescharacteristic
369C2×C32C2×#10411yescharacteristic
370C3×D3—22no—
371C3×D3—22no—
372C3×D3—81no—
373C24—31no—
374#41—362no—
375C2×Q8—91no—
376C2×D4—31no—
377C2×D4—61no—
378C2×D4—181no—
379C2×D4—181no—
380C22×C4—31no—
381C22×C4—31no—
382C22×C4—31no—
383C22×C4—31no—
384C22×C4—31no—
385C22×C4—61no—
386C22×C4—122no—
387C22×C4—181no—
388C22×C4—184no—
389C22×C4—181no—
390C22×C4—362no—
391C22×C4—362no—
392C22×C4C2×D3211yescharacteristic
393M16—122no—
394C2×C8—21no—
395C2×C8—61no—
396C4⋊C4—31no—
397C4⋊C4—91no—
398C4⋊C4—181no—
399C4⋊C4—181no—
400C22⋊C4—61no—
401C22⋊C4—181no—
402C22⋊C4—181no—
403C22⋊C4—181no—
404C22⋊C4—181no—
405C42—181no—
406C22×C3—21no—
407C22×C3—21no—
408C22×C3—21no—
409C22×C3—21no—
410C22×C3—21no—
411C22×C3—21no—
412C22×C3—21no—
413C22×C3—32no—
414C22×C3—32no—
415C22×C3—41no—
416C22×C3—41no—
417C22×C3—64no—
418C22×C3—64no—
419C22×C3—61no—
420C22×C3—61no—
421C22×C3—61no—
422C22×C3—61no—
423C22×C3—121no—
424C22×C3—121no—
425C22×C3—121no—
426C22×C3D3×C22⋊C411yescharacteristic
427C22×C3#90811yescharacteristic
428C22×C3#90911yescharacteristic
429C22×C3#91111yescharacteristic
430C22×C3#91511yescharacteristic
431C22×C3C2×(C2×D3)⋊C411yescharacteristic
432C2×D3—24no—
433C2×D3—24no—
434C2×D3—21no—
435C2×D3—21no—
436C2×D3—21no—
437C2×D3—21no—
438C2×D3—41no—
439C2×D3—41no—
440C2×D3—41no—
441C2×D3#80612yes—
442C2×D3#82512yes—
443C3×C4—21no—
444C3×C4—21no—
445C3×C4—21no—
446C3×C4—21no—
447C3×C4—41no—
448C3×C4—41no—
449C3×C4—61no—
450C3×C4—61no—
451C3×C4—122no—
452C3×C4—121no—
453Dic3—21no—
454Dic3—21no—
455Dic3—42no—
456Dic3—41no—
457Dic3—122no—
458Dic3—122no—
459Dic3—121no—
460Dic3—121no—
461Dic3—121no—
462Dic3—121no—
463Dic3—241no—
464Dic3—241no—
465Dic3—242no—
466C32#150411yescharacteristic, complemented, Sylow
467C23—31no—
468C23—31no—
469C23—62no—
470C23—62no—
471C23—61no—
472C23—61no—
473C23—61no—
474C23D3×D1211yescharacteristic
475Q8—361no—
476D4—121no—
477D4—121no—
478D4—121no—
479D4—362no—
480D4—362no—
481C2×C4—31no—
482C2×C4—31no—
483C2×C4—41no—
484C2×C4—62no—
485C2×C4—62no—
486C2×C4—62no—
487C2×C4—61no—
488C2×C4—121no—
489C2×C4—121no—
490C2×C4—121no—
491C2×C4—121no—
492C2×C4—121no—
493C2×C4—182no—
494C2×C4—181no—
495C2×C4—181no—
496C2×C4—362no—
497C2×C4—368no—
498C2×C4—361no—
499C2×C4—361no—
500C2×C4C4×D3211yescharacteristic
501C2×C4D3×#6711yescharacteristic
502C8—41no—
503C8—121no—
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—62no—
514C2×C3—62no—
515C2×C3—241no—
516C2×C3D3×#9911yescharacteristic
517C2×C3#477111yescharacteristic
518C2×C3D3×#10411yescharacteristic
519C2×C3C2×#80611yescharacteristic
520C2×C3#513311yescharacteristic
521C2×C3C2×#82511yescharacteristic
522D3—22no—
523D3—22no—
524D3—81no—
525C22—21no—
526C22—21no—
527C22—32no—
528C22—32no—
529C22—64no—
530C22—64no—
531C22—61no—
532C22—61no—
533C22—61no—
534C22—61no—
535C22—121no—
536C22—121no—
537C22—121no—
538C22#6379511yescharacteristic
539C22#6380011yescharacteristic
540C22D3×(C2×D3)⋊C411yescharacteristic
541C4—21no—
542C4—21no—
543C4—61no—
544C4—61no—
545C4—122no—
546C4—121no—
547C4—362no—
548C4—361no—
549C4—361no—
550C3—21no—
551C3#6830211yescharacteristic, complemented
552C3#6997611yescharacteristic, complemented
553C2—21no—
554C2—21no—
555C2—62no—
556C2—62no—
557C2—241no—
558C2D3×#80611yescharacteristic
559C2#1059067011yescharacteristic
560C2D3×#82511yescharacteristic
subgroupG/H
centerC22D3×(C2×D3)⋊C4
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32C2×C22⋊C4
prime radical#10594892C2
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. #10589333C2semidirect
5. C3×#4470C2semidirect
6. #10589154C2semidirect
7. #10589150C2semidirect
12. C2×#3795C4semidirect
18. #63908C4semidirect
21. #63857C4semidirect
22. #63841C4semidirect
33. #4726D3semidirect
38. #4470D3semidirect
47. C2×#634C2×C4semidirect
51. C2×C3×D12C2×C4semidirect
66. C4⋊(C3⋊Dic3)C2×C4semidirect
69. C3×C4⋊Dic3C2×C4semidirect
193. C2×D12C4×D3semidirect
227. C4⋊Dic3C4×D3semidirect
466. C32#1504semidirect
551. C3#68302semidirect
552. C3#69976semidirect

Maximal subgroups

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

subgroupindex
#105948922
C3×#47262
D3×C3⋊#952
#105893332
C3×#44702
#105891542
#105891502
#699763
#683023