Finite Group Databasebeta

← #11773878

Subgroups — #11773878

Order 1152.

663 conjugacy classes of subgroups.

The subgroup lattice has 427 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×C4⋊C4C211yesmaximal, characteristic
2#10591154C212yesmaximal
3#10589394C211yesmaximal, characteristic, complemented
4C3×#4528C211yesmaximal, characteristic, complemented
5#10589147C212yesmaximal, complemented
6#71552—31nomaximal
7#68144—31nomaximal
8C22×C3×C4×D3C411yescharacteristic
9C22×C3×C4×D3C411yescharacteristic
10C22×C3×C4×D3C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×C3×C4⋊Dic3C411yescharacteristic
13C2×C3×Dic3⋊C4C411yescharacteristic
14C2×C3×Dic3⋊C4C2211yescharacteristic
15C3×D3×C4⋊C4—22no—
16C3×D3×C4⋊C4—22no—
17C2×#3711—22no—
18#63657C2212yes—
19C3×#830C2212yes—
20(C2×D3)⋊(C3⋊C8)—22no—
21C22×C3×C4⋊C4—31no—
22C2×D3×C4⋊C4D311yescharacteristic
23#5207—32no—
24#4726—32no—
25C3×#324—31no—
26#4528—31no—
27#4528—31no—
28#4528—32no—
29#4528—61no—
30#4528D311yescharacteristic, complemented
31#4469—32no—
32C23×C3×D3C2×C411yescharacteristic
33C22×C32×C4C2×C411yescharacteristic
34C22×C32×C4C2×C411yescharacteristic
35C22×C32×C4C2311yescharacteristic
36C22×C3×Dic3C2×C411yescharacteristic
37C22×C3×Dic3C2×C411yescharacteristic
38C22×C3×Dic3C2×C411yescharacteristic
39C2×C3×C4×D3—21no—
40C2×C3×C4×D3—21no—
41C2×C3×C4×D3—22no—
42C2×C3×C4×D3—22no—
43C2×C3×C4×D3—21no—
44C2×C3×C4×D3—21no—
45C2×C3×C4×D3—42no—
46C2×C3×C4×D3—42no—
47C2×C3×C4×D3D412yes—
48C2×C3×C4×D3D412yes—
49C32×C4⋊C4—22no—
50C2×C3⋊(C3⋊C8)—22no—
51C3×C4⋊Dic3—22no—
52C3×Dic3⋊C4—22no—
53C3×Dic3⋊C4—22no—
54C2×C3×C3⋊C8—22no—
55#3711—44no—
56#1463—91noSylow
57C23×C3×C4—31no—
58C23×C3×C4—31no—
59C23×C3×C4—31no—
60C22×C4×D3Dic311yescharacteristic
61C22×C4×D3Dic311yescharacteristic
62C22×C4×D3C2×D311yescharacteristic
63C2×C3×C4⋊C4—21no—
64C2×C3×C4⋊C4—31no—
65C2×C3×C4⋊C4—31no—
66C2×C3×C4⋊C4—31no—
67C2×C3×C4⋊C4—62no—
68C2×C3×C4⋊C4—62no—
69C2×C3×C4⋊C4C2×D311yescharacteristic
70C2×C3×C4⋊C4C2×D311yescharacteristic
71C2×C4⋊Dic3Dic311yescharacteristic
72C2×Dic3⋊C4Dic311yescharacteristic
73C2×Dic3⋊C4C2×D311yescharacteristic
74C2×#208—62no—
75C2×ΓL(1,𝔽25)—62no—
76D3×C4⋊C4—22no—
77D3×C4⋊C4—22no—
78C3×C22⋊C8—32no—
79#830—32no—
80#830—32no—
81#830—62no—
82#830—62no—
83#830C2×D312yes—
84(C2×D3)⋊C8—62no—
85C23×C32C22×C411yescharacteristic
86C22×C3×D3—21no—
87C22×C3×D3—21no—
88C22×C3×D3—22no—
89C22×C3×D3—22no—
90C22×C3×D3C22⋊C411yescharacteristic
91C22×C3×D3C22⋊C411yescharacteristic
92C2×C32×C4—21no—
93C2×C32×C4—21no—
94C2×C32×C4—21no—
95C2×C32×C4—41no—
96C2×C32×C4—41no—
97C2×C32×C4M1612yescomplemented
98C2×C32×C4C2×D412yes—
99C2×C3×Dic3—21no—
100C2×C3×Dic3—21no—
101C2×C3×Dic3—21no—
102C2×C3×Dic3—41no—
103C2×C3×Dic3—41no—
104C2×C3×Dic3C22⋊C412yes—
105C2×C3×Dic3M1612yescomplemented
106C3×C4×D3—24no—
107C3×C4×D3—24no—
108C3×C4×D3—24no—
109C3×C4×D3—42no—
110C3×C4×D3—42no—
111C3×C4×D3—42no—
112C3⋊(C3⋊C8)—42no—
113C3×C3⋊C8—42no—
114C22×C4⋊C4—31no—
115#407—92no—
116#324—31no—
117#324—92no—
118#324—91no—
119C24×C3—31no—
120C23×D3C2×Dic311yescharacteristic
121C22×C3×C4—21no—
122C22×C3×C4—21no—
123C22×C3×C4—21no—
124C22×C3×C4—31no—
125C22×C3×C4—31no—
126C22×C3×C4—32no—
127C22×C3×C4—32no—
128C22×C3×C4—31no—
129C22×C3×C4—62no—
130C22×C3×C4—61no—
131C22×C3×C4—61no—
132C22×C3×C4—61no—
133C22×C3×C4—61no—
134C22×C3×C4—62no—
135C22×C3×C4—122no—
136C22×C3×C4—122no—
137C22×C3×C4C4×D311yescharacteristic
138C22×C3×C4C4×D311yescharacteristic
139C22×C3×C4C2×Dic311yescharacteristic
140C22×C3×C4C2×Dic311yescharacteristic
141C22×C3×C4C22×D311yescharacteristic
142C22×C3×C4C22×D311yescharacteristic
143C22×Dic3C2×Dic311yescharacteristic
144C22×Dic3C2×Dic311yescharacteristic
145C22×Dic3C2×Dic311yescharacteristic
146C2×C4×D3—21no—
147C2×C4×D3—21no—
148C2×C4×D3—22no—
149C2×C4×D3—22no—
150C2×C4×D3—21no—
151C2×C4×D3—21no—
152C2×C4×D3—42no—
153C2×C4×D3—42no—
154C2×C4×D3#6712yes—
155C2×C4×D3#6712yes—
156C2×C3×C8—62no—
157C3×C4⋊C4—22no—
158C3×C4⋊C4—22no—
159C3×C4⋊C4—42no—
160C3×C4⋊C4—62no—
161C3×C4⋊C4—62no—
162C3×C4⋊C4—62no—
163C4⋊Dic3—22no—
164Dic3⋊C4—22no—
165Dic3⋊C4—22no—
166#208—124no—
167C2×C3⋊C8—22no—
168C2×C3⋊C8—62no—
169C2×C3⋊C8—62no—
170C2×C3⋊C8—122no—
171ΓL(1,𝔽25)—124no—
172C22×C32—21no—
173C22×C32—21no—
174C22×C32C2×C22⋊C411yescharacteristic
175C22×C32C2×M1611yescharacteristic
176C22×C32C2×M1611yescharacteristic
177C2×C3×D3—24no—
178C2×C3×D3—24no—
179C2×C3×D3—21no—
180C2×C3×D3—21no—
181C2×C3×D3—21no—
182C2×C3×D3—21no—
183C2×C3×D3#9912yes—
184C2×C3×D3#10112yes—
185C32×C4—22no—
186C32×C4—22no—
187C32×C4—41no—
188C3×Dic3—22no—
189C3×Dic3—22no—
190C3×Dic3—41no—
191C23×C4—31no—
192C23×C4—31no—
193C23×C4—31no—
194C2×M16—182no—
195C2×C4⋊C4—31no—
196C2×C4⋊C4—31no—
197C2×C4⋊C4—31no—
198C2×C4⋊C4—62no—
199C2×C4⋊C4—62no—
200C2×C4⋊C4D3211yescharacteristic
201C22⋊C8—32no—
202C22⋊C8—92no—
203C22⋊C8—182no—
204C23×C3—21no—
205C23×C3—31no—
206C23×C3—31no—
207C23×C3—62no—
208C23×C3—62no—
209C23×C3—61no—
210C23×C3—61no—
211C23×C3C2×C4×D311yescharacteristic
212C23×C3C22×Dic311yescharacteristic
213C22×D3—21no—
214C22×D3—21no—
215C22×D3—22no—
216C22×D3—22no—
217C22×D3#21711yescharacteristic
218C22×D3#21711yescharacteristic
219C2×C3×C4—21no—
220C2×C3×C4—21no—
221C2×C3×C4—21no—
222C2×C3×C4—21no—
223C2×C3×C4—21no—
224C2×C3×C4—21no—
225C2×C3×C4—22no—
226C2×C3×C4—22no—
227C2×C3×C4—32no—
228C2×C3×C4—32no—
229C2×C3×C4—41no—
230C2×C3×C4—41no—
231C2×C3×C4—41no—
232C2×C3×C4—41no—
233C2×C3×C4—41no—
234C2×C3×C4—41no—
235C2×C3×C4—41no—
236C2×C3×C4—64no—
237C2×C3×C4—64no—
238C2×C3×C4—64no—
239C2×C3×C4—61no—
240C2×C3×C4—61no—
241C2×C3×C4—61no—
242C2×C3×C4—81no—
243C2×C3×C4—81no—
244C2×C3×C4—122no—
245C2×C3×C4—122no—
246C2×C3×C4—122no—
247C2×C3×C4—121no—
248C2×C3×C4—121no—
249C2×C3×C4ΓL(1,𝔽25)12yescomplemented
250C2×C3×C4#20812yescomplemented
251C2×C3×C4D3×D412yes—
252C2×C3×C4C2×#6712yes—
253C2×Dic3—21no—
254C2×Dic3—21no—
255C2×Dic3—21no—
256C2×Dic3—41no—
257C2×Dic3—41no—
258C2×Dic3#20812yescomplemented
259C2×Dic3#21712yes—
260C4×D3—24no—
261C4×D3—24no—
262C4×D3—24no—
263C4×D3—42no—
264C4×D3—42no—
265C4×D3—42no—
266C3×C8—122no—
267C3⋊C8—42no—
268C3⋊C8—122no—
269C3⋊C8—122no—
270C3⋊C8—242no—
271C2×C32—21no—
272C2×C32—21no—
273C2×C32#40711yescharacteristic
274C2×C32C2×#9911yescharacteristic
275C2×C32C2×#10111yescharacteristic
276C3×D3—22no—
277C3×D3—22no—
278C24—31no—
279C22×C4—31no—
280C22×C4—31no—
281C22×C4—32no—
282C22×C4—32no—
283C22×C4—31no—
284C22×C4—62no—
285C22×C4—61no—
286C22×C4—61no—
287C22×C4—61no—
288C22×C4—61no—
289C22×C4—62no—
290C22×C4—122no—
291C22×C4—122no—
292C22×C4D3×Dic311yescharacteristic
293C22×C4D3×Dic311yescharacteristic
294C22×C4C2×D3211yescharacteristic
295M16—364no—
296C2×C8—62no—
297C2×C8—182no—
298C4⋊C4—22no—
299C4⋊C4—62no—
300C4⋊C4—62no—
301C4⋊C4—62no—
302C22×C3—21no—
303C22×C3—21no—
304C22×C3—21no—
305C22×C3—21no—
306C22×C3—21no—
307C22×C3—21no—
308C22×C3—21no—
309C22×C3—32no—
310C22×C3—32no—
311C22×C3—41no—
312C22×C3—41no—
313C22×C3—64no—
314C22×C3—64no—
315C22×C3—61no—
316C22×C3—61no—
317C22×C3—61no—
318C22×C3—61no—
319C22×C3D3×C22⋊C411yescharacteristic
320C22×C3C2×ΓL(1,𝔽25)11yescharacteristic
321C22×C3D3×M1611yescharacteristic
322C22×C3C2×#20811yescharacteristic
323C22×C3C2×#20811yescharacteristic
324C22×C3C2×#21711yescharacteristic
325C2×D3—24no—
326C2×D3—24no—
327C2×D3—21no—
328C2×D3—21no—
329C2×D3—21no—
330C2×D3—21no—
331C2×D3#83412yes—
332C2×D3#83612yes—
333C3×C4—22no—
334C3×C4—22no—
335C3×C4—22no—
336C3×C4—22no—
337C3×C4—42no—
338C3×C4—42no—
339C3×C4—41no—
340C3×C4—41no—
341C3×C4—62no—
342C3×C4—62no—
343C3×C4—81no—
344C3×C4—121no—
345Dic3—22no—
346Dic3—22no—
347Dic3—41no—
348C32#146311yescharacteristic, complemented, Sylow
349C23—31no—
350C23—31no—
351C23—62no—
352C23—62no—
353C23—61no—
354C23—61no—
355C23C2×D3×Dic311yescharacteristic
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—32no—
360C2×C4—32no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—64no—
364C2×C4—64no—
365C2×C4—64no—
366C2×C4—61no—
367C2×C4—61no—
368C2×C4—61no—
369C2×C4—122no—
370C2×C4—122no—
371C2×C4—122no—
372C2×C4—121no—
373C2×C4—121no—
374C2×C4#371112yescomplemented
375C2×C4D3×#6712yes—
376C8—122no—
377C8—362no—
378C2×C3—21no—
379C2×C3—21no—
380C2×C3—21no—
381C2×C3—21no—
382C2×C3—21no—
383C2×C3—21no—
384C2×C3—21no—
385C2×C3—41no—
386C2×C3—41no—
387C2×C3—62no—
388C2×C3—62no—
389C2×C3#472611yescharacteristic
390C2×C3D3×#9911yescharacteristic
391C2×C3D3×#10111yescharacteristic
392C2×C3#520711yescharacteristic
393C2×C3C2×#83411yescharacteristic
394C2×C3C2×#83611yescharacteristic
395D3—22no—
396D3—22no—
397C22—21no—
398C22—21no—
399C22—32no—
400C22—32no—
401C22—64no—
402C22—64no—
403C22—61no—
404C22—61no—
405C22—61no—
406C22—61no—
407C22D3×#20811yescharacteristic
408C22C2×#371111yescharacteristic
409C22D3×#21711yescharacteristic
410C4—22no—
411C4—22no—
412C4—41no—
413C4—62no—
414C4—62no—
415C4—121no—
416C3—21no—
417C3#6814411yescharacteristic, complemented
418C3#7155211yescharacteristic, complemented
419C2—21no—
420C2—21no—
421C2—62no—
422C2—62no—
423C2#1059115411yescharacteristic
424C2D3×#83411yescharacteristic
425C2D3×#83611yescharacteristic
subgroupG/H
centerC22D3×#217
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C2×C22⋊C4
prime radicalC23×C3×D3C2×C4
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1463
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #10589394C2semidirect
4. C3×#4528C2semidirect
5. #10589147C2semidirect
30. #4528D3semidirect
97. C2×C32×C4M16semidirect
105. C2×C3×Dic3M16semidirect
249. C2×C3×C4ΓL(1,𝔽25)semidirect
250. C2×C3×C4#208semidirect
258. C2×Dic3#208semidirect
348. C32#1463semidirect
374. C2×C4#3711semidirect
417. C3#68144semidirect
418. C3#71552semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×C4⋊C42
#105911542
#105893942
C3×#45282
#105891472
#715523
#681443