Finite Group Databasebeta

← #11802684

Subgroups — #11802684

Order 1152.

1677 conjugacy classes of subgroups.

The subgroup lattice has 491 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3797C211yesmaximal, characteristic
2C2×#63836C212yesmaximal
3#10592363C211yesmaximal, characteristic
4C3×#4646C212yesmaximal, complemented
5#10591371C212yesmaximal
6#10591261C212yesmaximal, complemented
7#10591235C212yesmaximal, complemented
8#10591219C211yesmaximal, characteristic
9#10591191C212yesmaximal, complemented
10#76610—32nomaximal
11C22×C4×C3⋊D3C2211yescharacteristic
12C22×C3×Dic6C2212yes—
13C22×#627C2212yes—
14C22×#624C2211yescharacteristic
15C22×#624C2211yescharacteristic
16C2×#3797—28no—
17C2×#3797C418yescomplemented
18C2×#3752C2212yes—
19C2×C3×Dic3⋊C4C2212yes—
20C2×C3×C4×Dic3C2212yes—
21C2×Dic3⋊Dic3C2212yes—
22C2×#3722C2212yes—
23C2×Dic32C2212yes—
24#63836—28no—
25C32×#95C2211yescharacteristic
26#63658C2212yes—
27#63658C2211yescharacteristic
28C3×C3⋊#95C2212yes—
29C3×C3⋊#95C2212yes—
30C3×C3⋊#95C2212yes—
31#63579C2211yescharacteristic
32#63579C2212yes—
33#63579C2212yes—
34#63579C2211yescharacteristic
35C22×D3×Q8—32no—
36C2×#892—32no—
37C2×#872—32no—
38C3×#391—32no—
39#5229—32no—
40#4973—32no—
41#4929—32no—
42#4664—32no—
43#4664—32no—
44#4664—32no—
45#4664—32no—
46#4664—61no—
47#4646—32no—
48#4646—32no—
49#4646—32no—
50#4646D312yescomplemented
51C23×C3⋊D3C2311yescharacteristic
52C22×C32×C4C2312yes—
53C22×C32×C4C2311yescharacteristic
54C22×C3⋊Dic3C2312yes—
55C22×C3⋊Dic3C2311yescharacteristic
56C2×C4×C3⋊D3—24no—
57C2×C4×C3⋊D3C2×C414yes—
58C22×C3×Dic3C2312yes—
59C22×C3×Dic3C2312yes—
60C22×C3×Dic3C2312yes—
61C22×C3×Dic3C2312yes—
62C2×C3×Dic6—24no—
63C2×C3×Dic6—24no—
64C2×C3×Dic6C2×C418yes—
65C2×#627—24no—
66C2×#627—24no—
67C2×#627C2×C418yes—
68C2×#624—24no—
69C2×#624C2×C414yes—
70C2×#624C2×C414yes—
71C2×#624D418yes—
72#3797—232no—
73#3752—24no—
74C3×Dic3⋊C4—24no—
75C3×C4×Dic3—24no—
76Dic3⋊Dic3—24no—
77#3722—24no—
78Dic32—24no—
79#2310—91noSylow
80C22×C3×Q8—32no—
81C2×D3×Q8—316no—
82C2×D3×Q8—68no—
83C2×D3×Q8—68no—
84C22×C4×D3—32no—
85C22×C4×D3—32no—
86C22×C4×D3—32no—
87C22×C4×D3—61no—
88C22×Dic6—32no—
89C22×Dic6—32no—
90C22×Dic6C2×D312yes—
91C2×C3×C4⋊C4—32no—
92C2×C3×C42—32no—
93C2×(C2×D3)⋊C4—32no—
94C2×(C2×D3)⋊C4—32no—
95C2×(C2×D3)⋊C4—32no—
96C2×(C2×D3)⋊C4—32no—
97C2×(C2×D3)⋊C4—62no—
98C2×C4⋊Dic3—32no—
99C2×Dic3⋊C4—32no—
100C2×Dic3⋊C4C2×D312yes—
101C2×C4×Dic3—32no—
102C2×C4×Dic3—32no—
103C2×C4×Dic3C2×D312yes—
104#892—68no—
105#872—68no—
106C3×#95—21no—
107C3×#95—32no—
108C3×#95—32no—
109C3×#95—32no—
110C3×#95C2×D312yes—
111C3⋊#95—32no—
112C3⋊#95—32no—
113C3⋊#95—32no—
114C3⋊#95—32no—
115C3⋊#95—32no—
116C3⋊#95—32no—
117C3⋊#95—32no—
118C3⋊#95—32no—
119C3⋊#95—32no—
120C3⋊#95—62no—
121C3⋊#95—61no—
122C3⋊#95C2×D312yes—
123C3⋊#95C2×D312yes—
124C3⋊#95C2×D312yes—
125C23×C32C2411yescharacteristic
126C22×C3⋊D3—21no—
127C22×C3⋊D3—22no—
128C22×C3⋊D3—21no—
129C22×C3⋊D3C22×C412yes—
130C22×C3⋊D3C2×D414yes—
131C2×C32×C4—22no—
132C2×C32×C4—22no—
133C2×C32×C4—22no—
134C2×C32×C4—22no—
135C2×C32×C4C22×C412yes—
136C2×C3⋊Dic3—22no—
137C2×C3⋊Dic3—22no—
138C2×C3⋊Dic3—22no—
139C2×C3⋊Dic3—22no—
140C2×C3⋊Dic3C22×C412yes—
141C4×C3⋊D3—28no—
142C2×C3×Dic3—22no—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—22no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—22no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3C22×C414yes—
151C2×C3×Dic3C22×C414yes—
152C2×C3×Dic3C2×D414yes—
153C2×C3×Dic3C2×D414yes—
154C3×Dic6—216no—
155#627—216no—
156#624—28no—
157#624C22⋊C4116yes—
158C23×Q8—91no—
159C2×#117—92no—
160#391—32no—
161#391—92no—
162#391—92no—
163#391—92no—
164#381—91no—
165#381—92no—
166#381—91no—
167C23×D3—32no—
168C23×D3—61no—
169C2×C3×Q8—38no—
170C2×C3×Q8—64no—
171C2×C3×Q8—64no—
172C22×C3×C4—21no—
173C22×C3×C4—22no—
174C22×C3×C4—32no—
175C22×C3×C4—32no—
176C22×C3×C4—32no—
177C22×C3×C4—32no—
178C22×C3×C4C22×D312yes—
179C22×C3×C4C22×D312yes—
180C22×C3×C4C22×D312yes—
181C22×Dic3—32no—
182C22×Dic3—32no—
183C22×Dic3—32no—
184C22×Dic3—61no—
185C22×Dic3—62no—
186C22×Dic3C22×D312yes—
187C22×Dic3C22×D312yes—
188C22×Dic3C22×D312yes—
189C22×Dic3C22×D312yes—
190D3×Q8—664no—
191C2×C4×D3—38no—
192C2×C4×D3—38no—
193C2×C4×D3—38no—
194C2×C4×D3—38no—
195C2×C4×D3—38no—
196C2×C4×D3—64no—
197C2×C4×D3—64no—
198C2×C4×D3—64no—
199C2×C4×D3—64no—
200C2×C4×D3—64no—
201C2×C4×D3—124no—
202C2×Dic6—24no—
203C2×Dic6—24no—
204C2×Dic6—38no—
205C2×Dic6—38no—
206C2×Dic6—64no—
207C2×Dic6—64no—
208C2×Dic6—64no—
209C2×Dic6—64no—
210C2×Dic6C4×D318yes—
211C3×C4⋊C4—64no—
212C3×C42—64no—
213(C2×D3)⋊C4—64no—
214(C2×D3)⋊C4—64no—
215(C2×D3)⋊C4—64no—
216(C2×D3)⋊C4—64no—
217(C2×D3)⋊C4—124no—
218C4⋊Dic3—64no—
219Dic3⋊C4—24no—
220Dic3⋊C4—64no—
221C4×Dic3—24no—
222C4×Dic3—64no—
223C4×Dic3—64no—
224C22×C32C23×C411yescharacteristic
225C22×C32C22×D412yes—
226C22×C322−1+411yescharacteristic
227C22×C322−1+412yes—
228C22×C322−1+411yescharacteristic
229C2×C3⋊D3—22no—
230C2×C3⋊D3—22no—
231C2×C3⋊D3—24no—
232C2×C3⋊D3—24no—
233C2×C3⋊D3C2×C22⋊C414yes—
234C32×C4—22no—
235C32×C4—42no—
236C3⋊Dic3—22no—
237C3⋊Dic3—42no—
238C3×Dic3—24no—
239C3×Dic3—42no—
240C3×Dic3—42no—
241C3×Dic3C2×C22⋊C418yes—
242C22×Q8—32no—
243C22×Q8—92no—
244C22×Q8—98no—
245C22×Q8—188no—
246C23×C4—91no—
247C23×C4—91no—
248C23×C4—91no—
249#117—188no—
250C2×C4⋊C4—32no—
251C2×C4⋊C4—92no—
252C2×C22⋊C4—92no—
253C2×C22⋊C4—92no—
254C2×C42—32no—
255C2×C42—92no—
256#95—32no—
257#95—32no—
258#95—32no—
259#95—92no—
260#95—92no—
261#95—91no—
262#95—91no—
263#95—92no—
264#95—91no—
265#95D3211yescharacteristic
266C23×C3—21no—
267C23×C3C23×D312yes—
268C22×D3—34no—
269C22×D3—34no—
270C22×D3—34no—
271C22×D3—62no—
272C22×D3—64no—
273C22×D3—62no—
274C22×D3—62no—
275C22×D3—62no—
276C22×D3—62no—
277C22×D3—122no—
278C22×D3—121no—
279C22×D3—121no—
280C3×Q8—616no—
281C2×C3×C4—22no—
282C2×C3×C4—22no—
283C2×C3×C4—22no—
284C2×C3×C4—22no—
285C2×C3×C4—22no—
286C2×C3×C4—22no—
287C2×C3×C4—22no—
288C2×C3×C4—22no—
289C2×C3×C4—22no—
290C2×C3×C4—34no—
291C2×C3×C4—34no—
292C2×C3×C4—34no—
293C2×C3×C4—34no—
294C2×C3×C4—42no—
295C2×C3×C4—42no—
296C2×C3×C4—42no—
297C2×C3×C4—42no—
298C2×C3×C4—62no—
299C2×C3×C4—62no—
300C2×C3×C4—62no—
301C2×C3×C4—62no—
302C2×C3×C4—62no—
303C2×C3×C4—62no—
304C2×C3×C4—62no—
305C2×C3×C4—62no—
306C2×C3×C4C2×C4×D314yes—
307C2×Dic3—22no—
308C2×Dic3—22no—
309C2×Dic3—22no—
310C2×Dic3—22no—
311C2×Dic3—22no—
312C2×Dic3—22no—
313C2×Dic3—22no—
314C2×Dic3—22no—
315C2×Dic3—34no—
316C2×Dic3—62no—
317C2×Dic3—62no—
318C2×Dic3—62no—
319C2×Dic3—62no—
320C2×Dic3—62no—
321C2×Dic3—62no—
322C2×Dic3—62no—
323C2×Dic3—62no—
324C2×Dic3—62no—
325C2×Dic3—122no—
326C2×Dic3—122no—
327C2×Dic3—122no—
328C2×Dic3—122no—
329C2×Dic3C2×C4×D314yes—
330C2×Dic3C2×C4×D314yes—
331C2×Dic3D3×D414yes—
332C2×Dic3D3×D414yes—
333C4×D3—332no—
334C4×D3—616no—
335C4×D3—616no—
336C4×D3—128no—
337Dic6—216no—
338Dic6—616no—
339Dic6—616no—
340C2×C32C22×C22⋊C411yescharacteristic
341C2×C32#51911yescharacteristic
342C2×C32#51911yescharacteristic
343C2×C32#53612yes—
344C2×C32#53612yes—
345C3⋊D3—24no—
346C24—91no—
347C2×Q8—38no—
348C2×Q8—64no—
349C2×Q8—64no—
350C2×Q8—98no—
351C2×Q8—184no—
352C2×Q8—184no—
353C2×Q8—1832no—
354C22×C4—32no—
355C22×C4—32no—
356C22×C4—32no—
357C22×C4—32no—
358C22×C4—98no—
359C22×C4—94no—
360C22×C4—94no—
361C22×C4—91no—
362C22×C4—94no—
363C22×C4—92no—
364C22×C4—184no—
365C22×C4—184no—
366C22×C4C2×D3212yes—
367C22×C4C2×D3211yescharacteristic
368C4⋊C4—64no—
369C4⋊C4—184no—
370C22⋊C4—184no—
371C22⋊C4—184no—
372C42—64no—
373C42—184no—
374C22×C3—22no—
375C22×C3—21no—
376C22×C3—21no—
377C22×C3—22no—
378C22×C3—21no—
379C22×C3C22×C4×D312yes—
380C22×C3C2×D3×D412yes—
381C22×C3C2×D3×D412yes—
382C22×C3#100712yes—
383C22×C3#100712yes—
384C22×C3#101012yes—
385C22×C3#101012yes—
386C2×D3—38no—
387C2×D3—64no—
388C2×D3—64no—
389C2×D3—64no—
390C2×D3—64no—
391C2×D3—64no—
392C2×D3—64no—
393C2×D3—64no—
394C2×D3—124no—
395C2×D3—124no—
396C2×D3—122no—
397C2×D3—122no—
398C3×C4—24no—
399C3×C4—38no—
400C3×C4—42no—
401C3×C4—42no—
402C3×C4—42no—
403C3×C4—64no—
404C3×C4—82no—
405C3×C4—122no—
406C3×C4—122no—
407Dic3—24no—
408Dic3—42no—
409Dic3—42no—
410Dic3—64no—
411Dic3—122no—
412Dic3—122no—
413Dic3—122no—
414Dic3—242no—
415Dic3D3×C22⋊C418yes—
416C32#231011yescharacteristic, complemented, Sylow
417C23—92no—
418C23—94no—
419C23—182no—
420C23—181no—
421C23—181no—
422C23C22×D3211yescharacteristic
423Q8—616no—
424Q8—1816no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—34no—
430C2×C4—34no—
431C2×C4—34no—
432C2×C4—34no—
433C2×C4—62no—
434C2×C4—62no—
435C2×C4—62no—
436C2×C4—62no—
437C2×C4—62no—
438C2×C4—62no—
439C2×C4—62no—
440C2×C4—62no—
441C2×C4—916no—
442C2×C4—92no—
443C2×C4—188no—
444C2×C4—188no—
445C2×C4—182no—
446C2×C4—182no—
447C2×C4—182no—
448C2×C4—182no—
449C2×C4C4×D3212yes—
450C2×C3—22no—
451C2×C3—22no—
452C2×C3—21no—
453C2×C3—21no—
454C2×C3—21no—
455C2×C3C2×D3×C22⋊C412yes—
456C2×C3#557212yes—
457C2×C3#557212yes—
458C2×C3#562812yes—
459C2×C3#562812yes—
460C2×C3#567512yes—
461C2×C3#572412yes—
462D3—68no—
463D3—124no—
464C22—94no—
465C22—184no—
466C22—184no—
467C22—182no—
468C22—182no—
469C22#6429712yes—
470C22C2×C4×D3211yescharacteristic
471C22#6430911yescharacteristic
472C22D32×D412yes—
473C22#6431611yescharacteristic
474C4—22no—
475C4—38no—
476C4—42no—
477C4—64no—
478C4—122no—
479C4—122no—
480C4—182no—
481C4—362no—
482C3—21no—
483C3#7661012yescomplemented
484C2—184no—
485C2#1059384811yescharacteristic
486C2#1059407012yes—
487C2D32×C22⋊C411yescharacteristic
488C2#1059432812yes—
489C2#1059434711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenter#95D32
hypocenterC32#2310
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
4. C3×#4646C2semidirect
6. #10591261C2semidirect
7. #10591235C2semidirect
9. #10591191C2semidirect
17. C2×#3797C4semidirect
50. #4646D3semidirect
416. C32#2310semidirect
483. C3#76610semidirect

Maximal subgroups

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

subgroupindex
C22×#37972
C2×#638362
#105923632
C3×#46462
#105913712
#105912612
#105912352
#105912192
#105911912
#766103