Finite Group Databasebeta

← #11805267

Subgroups — #11805267

Order 1152.

1225 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63900C211yesmaximal, characteristic
2#10592365C211yesmaximal, characteristic
3C3×#4654C212yesmaximal, complemented
4#10591367C212yesmaximal
5#10591355C211yesmaximal, characteristic
6#10591337C211yesmaximal, characteristic, complemented
7C4×#3724C211yesmaximal, characteristic, complemented
8#10591328C211yesmaximal, characteristic, complemented
9#10591269C212yesmaximal, complemented
10#10591257C211yesmaximal, characteristic, complemented
11#10591233C212yesmaximal
12#74962—32nomaximal
13C22×C4×C3⋊D3C2211yescharacteristic
14C22×#624C2212yes—
15C2×#3752C2211yescharacteristic
16C2×#3752C2211yescharacteristic
17C2×C4×C3⋊Dic3C2211yescharacteristic
18C2×C4×C3⋊Dic3C2211yescharacteristic
19C2×C3×C4⋊Dic3C2212yes—
20C2×C3×Dic3⋊C4C2212yes—
21C2×C3×C4×Dic3C2212yes—
22C2×#3724C2211yescharacteristic
23C2×#3724C2211yescharacteristic
24C2×#3724C2211yescharacteristic
25C2×#3724C2211yescharacteristic
26C2×Dic3⋊Dic3C2212yes—
27C2×#3722C2212yes—
28C2×Dic32C2212yes—
29#63900C418yescomplemented
30C32×#95C2211yescharacteristic
31#63658C2211yescharacteristic
32C3×C3⋊#95C2212yes—
33C3×C3⋊#95C2212yes—
34C3×C3⋊#95C2212yes—
35#63579C2212yes—
36#63579C2212yes—
37C2×D3×C4⋊C4—32no—
38C3×#387—32no—
39#4987—32no—
40#4980—32no—
41#4976—32no—
42C4×(C2×D3)⋊C4—32no—
43C4×Dic3⋊C4—32no—
44#4667—32no—
45#4667—32no—
46#4666—32no—
47#4666—32no—
48#4666—61no—
49#4654D312yescomplemented
50#4653—32no—
51#4649—32no—
52#4647—32no—
53C23×C3⋊D3C2311yescharacteristic
54C22×C32×C4C2311yescharacteristic
55C22×C32×C4C2311yescharacteristic
56C22×C32×C4C2311yescharacteristic
57C22×C3⋊Dic3C2311yescharacteristic
58C22×C3⋊Dic3C2311yescharacteristic
59C22×C3⋊Dic3C2311yescharacteristic
60C2×C4×C3⋊D3—22no—
61C2×C4×C3⋊D3—22no—
62C2×C4×C3⋊D3C2×C414yes—
63C22×C3×Dic3C2312yes—
64C22×C3×Dic3C2312yes—
65C22×C3×Dic3C2312yes—
66C22×C3×Dic3C2312yes—
67C2×#624—42no—
68C2×#624—42no—
69C2×#624C2×C418yes—
70#3752—22no—
71#3752Q814yes—
72C4×C3⋊Dic3—22no—
73C4×C3⋊Dic3—22no—
74C3×C4⋊Dic3C2×C418yes—
75C3×Dic3⋊C4—42no—
76C3×C4×Dic3—42no—
77#3724—22no—
78#3724—22no—
79#3724C2×C414yes—
80#3724C2×C414yes—
81Dic3⋊Dic3—42no—
82#3722—24no—
83Dic32—42no—
84#2345—91noSylow
85C22×C4×D3—32no—
86C22×C4×D3—32no—
87C22×C4×D3—32no—
88C22×C4×D3—61no—
89C2×C3×C4⋊C4—32no—
90C2×C3×C4⋊C4—32no—
91C2×C3×C42—32no—
92C2×(C2×D3)⋊C4—32no—
93C2×(C2×D3)⋊C4—32no—
94C2×(C2×D3)⋊C4—32no—
95C2×(C2×D3)⋊C4—32no—
96C2×(C2×D3)⋊C4—61no—
97C2×(C2×D3)⋊C4—61no—
98C2×C4⋊Dic3—32no—
99C2×C4⋊Dic3C2×D312yes—
100C2×Dic3⋊C4—32no—
101C2×Dic3⋊C4—32no—
102C2×Dic3⋊C4—32no—
103C2×Dic3⋊C4—32no—
104C2×Dic3⋊C4—32no—
105C2×Dic3⋊C4C2×D312yes—
106C2×C4×Dic3—32no—
107C2×C4×Dic3—32no—
108C2×C4×Dic3—32no—
109C2×C4×Dic3—32no—
110C2×C4×Dic3—61no—
111C2×C4×Dic3—61no—
112C2×C4×Dic3C2×D312yes—
113D3×C4⋊C4—316no—
114C3×#95—21no—
115C3×#95—32no—
116C3×#95—32no—
117C3×#95—32no—
118C3×#95C2×D312yes—
119C3⋊#95—32no—
120C3⋊#95—32no—
121C3⋊#95—32no—
122C3⋊#95—32no—
123C3⋊#95—32no—
124C3⋊#95—61no—
125C3⋊#95C2×D312yes—
126C3⋊#95C2×D312yes—
127C3⋊#95C2×D312yes—
128C23×C32C2411yescharacteristic
129C22×C3⋊D3—21no—
130C22×C3⋊D3—21no—
131C22×C3⋊D3—21no—
132C22×C3⋊D3—21no—
133C22×C3⋊D3C22×C412yes—
134C22×C3⋊D3C2×Q812yes—
135C22×C3⋊D3#4112yes—
136C2×C32×C4—21no—
137C2×C32×C4—21no—
138C2×C32×C4—21no—
139C2×C32×C4—21no—
140C2×C32×C4—21no—
141C2×C32×C4—21no—
142C2×C32×C4—21no—
143C2×C32×C4C22×C412yes—
144C2×C32×C4C2×Q812yes—
145C2×C3⋊Dic3—21no—
146C2×C3⋊Dic3—21no—
147C2×C3⋊Dic3—21no—
148C2×C3⋊Dic3—21no—
149C2×C3⋊Dic3—21no—
150C2×C3⋊Dic3C22×C412yes—
151C2×C3⋊Dic3C2×Q812yes—
152C2×C3⋊Dic3#4112yes—
153C2×C3⋊Dic3#4112yes—
154C4×C3⋊D3—28no—
155C2×C3×Dic3—22no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3—22no—
159C2×C3×Dic3—22no—
160C2×C3×Dic3—22no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—22no—
163C2×C3×Dic3—22no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3C22×C414yes—
166C2×C3×Dic3C22×C414yes—
167#624—48no—
168C22×C4⋊C4—91no—
169#389—91no—
170#389—91no—
171#387—32no—
172#387—92no—
173#380—91no—
174#380—92no—
175C4×C4⋊C4—91no—
176C4×C4⋊C4—91no—
177C4×C22⋊C4—92no—
178C4×C22⋊C4—91no—
179C23×D3—32no—
180C23×D3—61no—
181C22×C3×C4—21no—
182C22×C3×C4—21no—
183C22×C3×C4—21no—
184C22×C3×C4—32no—
185C22×C3×C4—32no—
186C22×C3×C4—32no—
187C22×C3×C4—32no—
188C22×C3×C4C22×D312yes—
189C22×C3×C4C22×D312yes—
190C22×C3×C4C22×D312yes—
191C22×Dic3—32no—
192C22×Dic3—32no—
193C22×Dic3—32no—
194C22×Dic3—61no—
195C22×Dic3—61no—
196C22×Dic3—61no—
197C22×Dic3C22×D312yes—
198C22×Dic3C22×D312yes—
199C22×Dic3C22×D312yes—
200C22×Dic3C22×D312yes—
201C2×C4×D3—38no—
202C2×C4×D3—38no—
203C2×C4×D3—38no—
204C2×C4×D3—64no—
205C2×C4×D3—64no—
206C2×C4×D3—64no—
207C2×C4×D3—122no—
208C2×C4×D3—122no—
209C2×C4×D3—122no—
210C2×C4×D3—122no—
211C2×C4×D3—122no—
212C2×C4×D3—122no—
213C3×C4⋊C4—38no—
214C3×C4⋊C4—122no—
215C3×C42—122no—
216(C2×D3)⋊C4—38no—
217(C2×D3)⋊C4—64no—
218(C2×D3)⋊C4—64no—
219(C2×D3)⋊C4—64no—
220(C2×D3)⋊C4—64no—
221(C2×D3)⋊C4—64no—
222C4⋊Dic3—122no—
223C4⋊Dic3C4×D318yes—
224Dic3⋊C4—38no—
225Dic3⋊C4—38no—
226Dic3⋊C4—42no—
227Dic3⋊C4—64no—
228Dic3⋊C4—64no—
229Dic3⋊C4—122no—
230C4×Dic3—42no—
231C4×Dic3—64no—
232C4×Dic3—64no—
233C4×Dic3—122no—
234C4×Dic3—122no—
235C4×Dic3—122no—
236C4×Dic3—122no—
237C22×C32C23×C411yescharacteristic
238C22×C32C22×Q811yescharacteristic
239C22×C32C2×#4111yescharacteristic
240C22×C32C2×#4111yescharacteristic
241C22×C32C2×#4111yescharacteristic
242C22×C32H(5,𝔽2)11yescharacteristic
243C22×C32H(5,𝔽2)11yescharacteristic
244C2×C3⋊D3—22no—
245C2×C3⋊D3—22no—
246C2×C3⋊D3—22no—
247C2×C3⋊D3—22no—
248C2×C3⋊D3—22no—
249C2×C3⋊D3—22no—
250C2×C3⋊D3C4×Q814yes—
251C32×C4—22no—
252C32×C4—22no—
253C32×C4—41no—
254C3⋊Dic3—22no—
255C3⋊Dic3—41no—
256C3⋊Dic3#11714yes—
257C3×Dic3—24no—
258C3×Dic3—24no—
259C3×Dic3—42no—
260C3×Dic3—42no—
261C23×C4—92no—
262C23×C4—91no—
263C2×C4⋊C4—32no—
264C2×C4⋊C4—32no—
265C2×C4⋊C4—98no—
266C2×C4⋊C4—91no—
267C2×C4⋊C4—91no—
268C2×C4⋊C4—91no—
269C2×C4⋊C4—91no—
270C2×C4⋊C4—92no—
271C2×C22⋊C4—91no—
272C2×C22⋊C4—92no—
273C2×C22⋊C4—91no—
274C2×C42—32no—
275C2×C42—91no—
276C2×C42—91no—
277C2×C42—92no—
278#95—32no—
279#95—32no—
280#95—32no—
281#95—92no—
282#95—92no—
283#95—91no—
284#95D3211yescharacteristic
285C23×C3—21no—
286C23×C3C23×D312yes—
287C22×D3—34no—
288C22×D3—34no—
289C22×D3—34no—
290C22×D3—62no—
291C22×D3—62no—
292C22×D3—62no—
293C22×D3—62no—
294C22×D3—62no—
295C22×D3—62no—
296C22×D3—62no—
297C22×D3—121no—
298C22×D3—121no—
299C22×D3—121no—
300C22×D3—121no—
301C2×C3×C4—22no—
302C2×C3×C4—22no—
303C2×C3×C4—22no—
304C2×C3×C4—22no—
305C2×C3×C4—22no—
306C2×C3×C4—22no—
307C2×C3×C4—22no—
308C2×C3×C4—22no—
309C2×C3×C4—22no—
310C2×C3×C4—22no—
311C2×C3×C4—34no—
312C2×C3×C4—34no—
313C2×C3×C4—41no—
314C2×C3×C4—41no—
315C2×C3×C4—41no—
316C2×C3×C4—41no—
317C2×C3×C4—41no—
318C2×C3×C4—41no—
319C2×C3×C4—62no—
320C2×C3×C4—62no—
321C2×C3×C4—62no—
322C2×C3×C4—62no—
323C2×C3×C4—62no—
324C2×C3×C4—62no—
325C2×C3×C4—62no—
326C2×C3×C4—62no—
327C2×C3×C4—62no—
328C2×C3×C4—62no—
329C2×C3×C4C2×C4×D314yes—
330C2×C3×C4D3×Q814yes—
331C2×Dic3—22no—
332C2×Dic3—22no—
333C2×Dic3—22no—
334C2×Dic3—22no—
335C2×Dic3—22no—
336C2×Dic3—22no—
337C2×Dic3—22no—
338C2×Dic3—22no—
339C2×Dic3—22no—
340C2×Dic3—22no—
341C2×Dic3—34no—
342C2×Dic3—34no—
343C2×Dic3—34no—
344C2×Dic3—34no—
345C2×Dic3—62no—
346C2×Dic3—62no—
347C2×Dic3—62no—
348C2×Dic3—62no—
349C2×Dic3—62no—
350C2×Dic3—62no—
351C2×Dic3—62no—
352C2×Dic3—62no—
353C2×Dic3—62no—
354C2×Dic3—62no—
355C2×Dic3—121no—
356C2×Dic3—121no—
357C2×Dic3—121no—
358C2×Dic3—121no—
359C2×Dic3C2×C4×D314yes—
360C2×Dic3C2×C4×D314yes—
361C4×D3—616no—
362C4×D3—128no—
363C4×D3—128no—
364C4×D3—128no—
365C2×C32C2×#11711yescharacteristic
366C2×C32C2×C4×Q811yescharacteristic
367C2×C32#51811yescharacteristic
368C2×C32#55311yescharacteristic
369C2×C32#55311yescharacteristic
370C2×C32#55411yescharacteristic
371C2×C32#55411yescharacteristic
372C3⋊D3—24no—
373C24—91no—
374C22×C4—32no—
375C22×C4—32no—
376C22×C4—32no—
377C22×C4—32no—
378C22×C4—98no—
379C22×C4—91no—
380C22×C4—91no—
381C22×C4—94no—
382C22×C4—91no—
383C22×C4—182no—
384C22×C4—182no—
385C22×C4—362no—
386C22×C4—362no—
387C22×C4C2×D3211yescharacteristic
388C22×C4C2×D3211yescharacteristic
389C22×C4C2×D3211yescharacteristic
390C4⋊C4—38no—
391C4⋊C4—94no—
392C4⋊C4—94no—
393C4⋊C4—122no—
394C4⋊C4—182no—
395C4⋊C4—182no—
396C4⋊C4—362no—
397C22⋊C4—94no—
398C22⋊C4—182no—
399C22⋊C4—184no—
400C42—122no—
401C42—182no—
402C42—182no—
403C42—362no—
404C22×C3—21no—
405C22×C3—21no—
406C22×C3—21no—
407C22×C3—21no—
408C22×C3—21no—
409C22×C3—21no—
410C22×C3—21no—
411C22×C3C22×C4×D312yes—
412C22×C3#100412yes—
413C22×C3C2×D3×Q812yes—
414C22×C3D3×#4112yes—
415C22×C3D3×#4112yes—
416C22×C3D3×#4112yes—
417C22×C3#100912yes—
418C2×D3—38no—
419C2×D3—64no—
420C2×D3—64no—
421C2×D3—64no—
422C2×D3—64no—
423C2×D3—64no—
424C2×D3—64no—
425C2×D3—64no—
426C2×D3—122no—
427C2×D3—122no—
428C2×D3—122no—
429C2×D3—122no—
430C2×D3—122no—
431C2×D3—122no—
432C3×C4—24no—
433C3×C4—24no—
434C3×C4—42no—
435C3×C4—42no—
436C3×C4—42no—
437C3×C4—42no—
438C3×C4—64no—
439C3×C4—64no—
440C3×C4—122no—
441C3×C4—122no—
442Dic3—24no—
443Dic3—24no—
444Dic3—38no—
445Dic3—42no—
446Dic3—42no—
447Dic3—64no—
448Dic3—64no—
449Dic3—122no—
450Dic3—122no—
451Dic3—122no—
452C32#234511yescharacteristic, complemented, Sylow
453C23—92no—
454C23—92no—
455C23—92no—
456C23—181no—
457C23—181no—
458C23—181no—
459C23—181no—
460C23C22×D3211yescharacteristic
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—34no—
469C2×C4—34no—
470C2×C4—62no—
471C2×C4—62no—
472C2×C4—62no—
473C2×C4—62no—
474C2×C4—62no—
475C2×C4—62no—
476C2×C4—62no—
477C2×C4—62no—
478C2×C4—62no—
479C2×C4—62no—
480C2×C4—92no—
481C2×C4—92no—
482C2×C4—92no—
483C2×C4—92no—
484C2×C4—188no—
485C2×C4—181no—
486C2×C4—181no—
487C2×C4—181no—
488C2×C4—181no—
489C2×C4—181no—
490C2×C4—368no—
491C2×C4#379712yes—
492C2×C4C4×D3212yes—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3D3×#11712yes—
501C2×C3#554512yes—
502C2×C3C4×D3×Q812yes—
503C2×C3#563612yes—
504C2×C3#566112yes—
505C2×C3#569012yes—
506C2×C3#570912yes—
507D3—68no—
508D3—124no—
509C22—94no—
510C22—182no—
511C22—182no—
512C22—182no—
513C22—182no—
514C22—182no—
515C22—182no—
516C22C2×#379711yescharacteristic
517C22C2×C4×D3211yescharacteristic
518C22#6430611yescharacteristic
519C22#6431211yescharacteristic
520C22#6431211yescharacteristic
521C22#6431311yescharacteristic
522C22#6432011yescharacteristic
523C4—22no—
524C4—22no—
525C4—41no—
526C4—64no—
527C4—64no—
528C4—94no—
529C4—122no—
530C4—122no—
531C4—182no—
532C4—361no—
533C3—21no—
534C3#7496212yescomplemented
535C2—184no—
536C2C4×#379711yescharacteristic
537C2#1059405211yescharacteristic
538C2#1059416811yescharacteristic
539C2#1059422911yescharacteristic
540C2#1059447511yescharacteristic
541C2#1059448411yescharacteristic
542C2#1059460611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenter#95D32
hypocenterC32#2345
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
3. C3×#4654C2semidirect
6. #10591337C2semidirect
7. C4×#3724C2semidirect
8. #10591328C2semidirect
9. #10591269C2semidirect
10. #10591257C2semidirect
29. #63900C4semidirect
49. #4654D3semidirect
452. C32#2345semidirect
534. C3#74962semidirect

Maximal subgroups

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

subgroupindex
C2×#639002
#105923652
C3×#46542
#105913672
#105913552
#105913372
C4×#37242
#105913282
#105912692
#105912572
#105912332
#749623