Finite Group Databasebeta

← #11775121

Subgroups — #11775121

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×D3×#95C211yesmaximal, characteristic, complemented
3#10591154C211yesmaximal, characteristic, complemented
4#10589318C211yesmaximal, characteristic, complemented
5C3×#4451C211yesmaximal, characteristic, complemented
6#10589154C211yesmaximal, characteristic, complemented
7#10589149C211yesmaximal, characteristic, complemented
8#69398—31nomaximal
9#68302—31nomaximal
10C22×C3×C4×D3—21no—
11C22×C3×C4×D3C2211yescharacteristic
12C2×#3795C411yescharacteristic, complemented
13#64133C2211yescharacteristic
14C3×#930C2211yescharacteristic
15#63976—21no—
16Dic3×#67—21no—
17#63908C411yescharacteristic, complemented
18#63905—21no—
19#63879—21no—
20#63857C411yescharacteristic, complemented
21#63841C411yescharacteristic, complemented
22C2×#3711—21no—
23C32×#95C2211yescharacteristic
24#63657C2211yescharacteristic
25C3×C3⋊#95—21no—
26C3×C3⋊#95C2211yescharacteristic
27C3×#830C2211yescharacteristic
28(C2×D3)⋊(C3⋊C8)—21no—
29#5791—31no—
30#5606—31no—
31C2×C3×#95—31no—
32#5207—31no—
33#4726—31no—
34D3×#95D311yescharacteristic, complemented
35C3×#327—31no—
36#4537—31no—
37#4467—31no—
38#4452—31no—
39#4452—31no—
40#4452—31no—
41#4452—61no—
42#4451—31no—
43#4451D311yescharacteristic, complemented
44C23×C3×D3D411yescharacteristic
45C22×C32×C4—21no—
46C22×C32×C4C2311yescharacteristic
47C2×#634C2×C411yescharacteristic, complemented
48C2×C3×#67—21no—
49C22×C3×Dic3—21no—
50C22×C3×Dic3D411yescharacteristic
51C2×C3×D12C2×C411yescharacteristic, complemented
52C2×C3×C4×D3—24no—
53C2×C3×C4×D3—42no—
54C2×C3×C4×D3—42no—
55C2×C3×C4×D3—42no—
56C2×C3×C4×D3C2×C411yescharacteristic
57C2×C3×C4×D3C2×C411yescharacteristic
58C2×C3×C4×D3D411yescharacteristic
59C2×C3×C4×D3D411yescharacteristic
60C2×#625—21no—
61C2×#625—21no—
62C2×D3×Dic3—21no—
63#3795—42no—
64#3757—21no—
65C4⋊(C3⋊Dic3)C2×C411yescharacteristic, complemented
66#3750—21no—
67C2×C3⋊(C3⋊C8)—21no—
68C3×(C2×D3)⋊C4—21no—
69C3×C4⋊Dic3C2×C411yescharacteristic, complemented
70C2×C3×C3⋊C8—21no—
71Dic3⋊Dic3—21no—
72(C2×D3)⋊Dic3—21no—
73(C2×D3)⋊Dic3—21no—
74(C2×D3)⋊Dic3—21no—
75Dic32—21no—
76#3711—42no—
77#1504—91noSylow
78C23×C3×C4—31no—
79C23×C3×C4—61no—
80C2×#237—31no—
81C2×#235—31no—
82C22×C4×D3—21no—
83C22×C4×D3C2×D311yescharacteristic
84C3×#121—31no—
85#953—61no—
86#938—31no—
87#937—61no—
88D4×Dic3—61no—
89#930—31no—
90#930C2×D311yescharacteristic
91#929—61no—
92C4×#67—61no—
93C4×#67—61no—
94#926—31no—
95#924—31no—
96#924—31no—
97#924—31no—
98#924—61no—
99C2×#208—61no—
100C2×ΓL(1,𝔽25)—61no—
101#897—31no—
102#892—31no—
103#883—61no—
104#67⋊C4—61no—
105C3×C22⋊C8—31no—
106C3×#95—21no—
107C3×#95—31no—
108C3×#95—61no—
109C3×#95C2×D311yescharacteristic
110C3×#95C2×D311yescharacteristic
111C3⋊#95—21no—
112C3⋊#95C2×D311yescharacteristic
113#830—31no—
114#830—31no—
115#830—61no—
116#830—61no—
117#830C2×D311yescharacteristic
118(C2×D3)⋊C8—61no—
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—22no—
128C2×C32×C4—41no—
129C2×C32×C4—41no—
130C2×C32×C4—41no—
131C2×C32×C4C22×C411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133C2×C3⋊Dic3—21no—
134C2×C3⋊Dic3—21no—
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—
150C3×C4×D3—48no—
151#625—42no—
152#625—42no—
153D3×Dic3—42no—
154C3⋊(C3⋊C8)—41no—
155C3×C3⋊C8—41no—
156#525—91no—
157#407—91no—
158C2×#95—31no—
159#328—91no—
160#328—91no—
161#327—31no—
162#327—91no—
163C24×C3—31no—
164C23×D3#6711yescharacteristic
165C2×C3×D4—31no—
166C2×C3×D4—61no—
167C22×C3×C4—21no—
168C22×C3×C4—21no—
169C22×C3×C4—21no—
170C22×C3×C4—31no—
171C22×C3×C4—31no—
172C22×C3×C4—31no—
173C22×C3×C4—31no—
174C22×C3×C4—31no—
175C22×C3×C4—41no—
176C22×C3×C4—64no—
177C22×C3×C4—61no—
178C22×C3×C4—122no—
179C22×C3×C4—122no—
180C22×C3×C4—122no—
181C22×C3×C4C22×D311yescharacteristic
182C22×C3×C4C22×D311yescharacteristic
183C2×#67—21no—
184C2×#67—61no—
185C2×#67—61no—
186C2×#67—61no—
187C2×#67—61no—
188C22×Dic3—21no—
189C22×Dic3—61no—
190C22×Dic3#6711yescharacteristic
191#237—122no—
192#235—122no—
193C2×D12C4×D311yescharacteristic, complemented
194C2×C4×D3—24no—
195C2×C4×D3—42no—
196C2×C4×D3—42no—
197C2×C4×D3—42no—
198C2×C4×D3—61no—
199C2×C4×D3C4×D311yescharacteristic
200C2×C4×D3C4×D311yescharacteristic
201C2×C4×D3D1211yescharacteristic
202C2×C4×D3D1211yescharacteristic
203C2×Dic6—31no—
204C2×Dic6—31no—
205C2×Dic6—61no—
206C2×C3×C8—61no—
207C3×C4⋊C4—31no—
208C3×C22⋊C4—61no—
209#217—61no—
210#217—61no—
211#217—61no—
212#217—61no—
213#217—61no—
214#217—121no—
215(C2×D3)⋊C4—21no—
216(C2×D3)⋊C4—61no—
217(C2×D3)⋊C4—61no—
218(C2×D3)⋊C4—61no—
219C4⋊Dic3—31no—
220C4⋊Dic3—31no—
221C4⋊Dic3—61no—
222C4⋊Dic3—61no—
223C4⋊Dic3C4×D311yescharacteristic, complemented
224Dic3⋊C4—61no—
225Dic3⋊C4—61no—
226Dic3⋊C4—61no—
227Dic3⋊C4—121no—
228C4×Dic3—61no—
229C4×Dic3—61no—
230#208—122no—
231C2×C3⋊C8—21no—
232C2×C3⋊C8—61no—
233C2×C3⋊C8—61no—
234C2×C3⋊C8—121no—
235ΓL(1,𝔽25)—122no—
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—
254C32×C4—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—61no—
264C2×M16—181no—
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—91no—
276C22⋊C8—181no—
277#95—31no—
278#95—61no—
279#95D3211yescharacteristic
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×C3D3×D411yescharacteristic
289C23×C3C2×#6711yescharacteristic
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—22no—
301C2×C3×C4—22no—
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—31no—
305C2×C3×C4—31no—
306C2×C3×C4—42no—
307C2×C3×C4—41no—
308C2×C3×C4—41no—
309C2×C3×C4—41no—
310C2×C3×C4—41no—
311C2×C3×C4—41no—
312C2×C3×C4—41no—
313C2×C3×C4—62no—
314C2×C3×C4—62no—
315C2×C3×C4—62no—
316C2×C3×C4—61no—
317C2×C3×C4—81no—
318C2×C3×C4—81no—
319C2×C3×C4—81no—
320C2×C3×C4—121no—
321C2×C3×C4—121no—
322C2×C3×C4—128no—
323C2×C3×C4—121no—
324C2×C3×C4—121no—
325C2×C3×C4—121no—
326C2×C3×C4C2×C4×D311yescharacteristic
327C2×C3×C4C2×C4×D311yescharacteristic
328C2×C3×C4C2×D1211yescharacteristic
329C2×C3×C4D3×D411yescharacteristic
330#67—41no—
331#67—41no—
332#67—122no—
333#67—122no—
334#67—122no—
335#67—122no—
336C2×Dic3—22no—
337C2×Dic3—21no—
338C2×Dic3—41no—
339C2×Dic3—41no—
340C2×Dic3—41no—
341C2×Dic3—61no—
342C2×Dic3—61no—
343C2×Dic3—61no—
344C2×Dic3—61no—
345C2×Dic3—121no—
346C2×Dic3—121no—
347C2×Dic3—122no—
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—48no—
356C4×D3—122no—
357Dic6—121no—
358Dic6—121no—
359Dic6—241no—
360C3×C8—121no—
361C3⋊C8—41no—
362C3⋊C8—121no—
363C3⋊C8—121no—
364C3⋊C8—241no—
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—21no—
381C22×C4—31no—
382C22×C4—31no—
383C22×C4—31no—
384C22×C4—31no—
385C22×C4—31no—
386C22×C4—64no—
387C22×C4—61no—
388C22×C4—122no—
389C22×C4—122no—
390C22×C4—122no—
391C22×C4—181no—
392C22×C4C2×D3211yescharacteristic
393M16—362no—
394C2×C8—61no—
395C2×C8—181no—
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#91111yescharacteristic
428C22×C3#91511yescharacteristic
429C22×C3C2×(C2×D3)⋊C411yescharacteristic
430C22×C3#93211yescharacteristic
431C22×C3#94211yescharacteristic
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#80512yes—
442C2×D3#80612yes—
443C3×C4—21no—
444C3×C4—21no—
445C3×C4—21no—
446C3×C4—21no—
447C3×C4—41no—
448C3×C4—41no—
449C3×C4—42no—
450C3×C4—42no—
451C3×C4—61no—
452C3×C4—61no—
453C3×C4—82no—
454C3×C4—122no—
455C3×C4—121no—
456Dic3—21no—
457Dic3—21no—
458Dic3—42no—
459Dic3—41no—
460Dic3—121no—
461Dic3—121no—
462Dic3—121no—
463Dic3—121no—
464Dic3—241no—
465Dic3—241no—
466C32#150411yescharacteristic, complemented, Sylow
467C23—31no—
468C23—31no—
469C23—62no—
470C23—62no—
471C23—61no—
472C23—61no—
473C23—61no—
474C23D3×#6711yescharacteristic
475Q8—361no—
476D4—121no—
477D4—121no—
478D4—121no—
479D4—362no—
480D4—362no—
481C2×C4—22no—
482C2×C4—31no—
483C2×C4—31no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—62no—
488C2×C4—62no—
489C2×C4—62no—
490C2×C4—61no—
491C2×C4—121no—
492C2×C4—121no—
493C2×C4—128no—
494C2×C4—121no—
495C2×C4—121no—
496C2×C4—121no—
497C2×C4—181no—
498C2×C4—181no—
499C2×C4—362no—
500C2×C4C4×D3211yescharacteristic
501C2×C4D3×D1211yescharacteristic
502C8—121no—
503C8—361no—
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×#80511yescharacteristic
520C2×C3C2×#80611yescharacteristic
521C2×C3#496611yescharacteristic
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—
538C22D3×(C2×D3)⋊C411yescharacteristic
539C22#6393211yescharacteristic
540C22#6394611yescharacteristic
541C4—21no—
542C4—21no—
543C4—42no—
544C4—61no—
545C4—61no—
546C4—122no—
547C4—121no—
548C4—361no—
549C4—361no—
550C3—21no—
551C3#6830211yescharacteristic, complemented
552C3#6939811yescharacteristic, complemented
553C2—21no—
554C2—21no—
555C2—62no—
556C2—62no—
557C2—241no—
558C2D3×#80511yescharacteristic
559C2D3×#80611yescharacteristic
560C2#1059060711yescharacteristic
subgroupG/H
centerC22D3×(C2×D3)⋊C4
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#95C22
socleC22×C32C2×C22⋊C4
prime radical#10594892C2
cosocleC22×C32×C4C23
hypercenter#95D32
hypocenterC32#1504
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C3×D3×#95C2semidirect
3. #10591154C2semidirect
4. #10589318C2semidirect
5. C3×#4451C2semidirect
6. #10589154C2semidirect
7. #10589149C2semidirect
12. C2×#3795C4semidirect
17. #63908C4semidirect
20. #63857C4semidirect
21. #63841C4semidirect
34. D3×#95D3semidirect
43. #4451D3semidirect
47. C2×#634C2×C4semidirect
51. C2×C3×D12C2×C4semidirect
65. C4⋊(C3⋊Dic3)C2×C4semidirect
69. C3×C4⋊Dic3C2×C4semidirect
193. C2×D12C4×D3semidirect
223. C4⋊Dic3C4×D3semidirect
466. C32#1504semidirect
551. C3#68302semidirect
552. C3#69398semidirect

Maximal subgroups

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

subgroupindex
#105948922
C3×D3×#952
#105911542
#105893182
C3×#44512
#105891542
#105891492
#693983
#683023