Finite Group Databasebeta

← #11791433

Subgroups — #11791433

Order 1152.

745 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63873C211yesmaximal, characteristic
2C4⋊C4×C3⋊Dic3C211yesmaximal, characteristic
3C2×C3×#810C212yesmaximal
4C2×#63572C211yesmaximal, characteristic
5C2×#63566C212yesmaximal
6#70229—32nomaximal
7C22×C3×Dic6C2212yes—
8C2×C32×C4⋊C4C2211yescharacteristic
9C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
10C2×C4×C3⋊Dic3—21no—
11C2×C4×C3⋊Dic3C2211yescharacteristic
12C22×C3×C3⋊C8C2212yes—
13C2×#3724—21no—
14C2×#3724—21no—
15#63873—22no—
16#63873C414yescomplemented
17#63658—21no—
18C3×#810—24no—
19#63572—22no—
20#63566—24no—
21C2×#944—32no—
22C2×C3×#103—32no—
23C2×#835—32no—
24C2×#816—32no—
25C2×Dic3⋊C8—32no—
26Dic3×C4⋊C4—32no—
27Dic3×C4⋊C4—61no—
28C2×#810D312yes—
29C22×C32×C4—21no—
30C22×C32×C4C2311yescharacteristic
31C22×C3⋊Dic3—21no—
32C22×C3⋊Dic3D411yescharacteristic
33C22×C3⋊Dic3D411yescharacteristic
34C22×C3×Dic3—22no—
35C2×C3×Dic6—22no—
36C2×C3×Dic6—22no—
37C2×C3×Dic6—22no—
38C2×C3×Dic6—22no—
39C2×C3×Dic6—22no—
40C2×C3×Dic6C2×C414yes—
41C32×C4⋊C4—21no—
42C32×C4⋊C4D412yes—
43C4⋊(C3⋊Dic3)—21no—
44C4⋊(C3⋊Dic3)D412yes—
45C4×C3⋊Dic3—42no—
46C4×C3⋊Dic3C2×C412yes—
47C4×C3⋊Dic3D412yes—
48C2×C3×C3⋊C8—22no—
49C2×C3×C3⋊C8—22no—
50C2×C3×C3⋊C8—22no—
51#3724—24no—
52#3724—24no—
53#1981—91noSylow
54C22×C3×Q8—32no—
55C22×Dic6C2×D312yes—
56C22×C3×C8—32no—
57C2×C3×C4⋊C4—21no—
58C2×C3×C4⋊C4C2×D312yes—
59#944—38no—
60#944—64no—
61C2×C4⋊Dic3—32no—
62C2×C4⋊Dic3—61no—
63C2×Dic3⋊C4—62no—
64C2×Dic3⋊C4—62no—
65C2×C4×Dic3—32no—
66C2×C4×Dic3—61no—
67C2×C4×Dic3—62no—
68C2×C4×Dic3—62no—
69C22×C3⋊C8C2×D312yes—
70C3×#103—64no—
71#835—64no—
72C3⋊#95—62no—
73C3⋊#95—62no—
74#816—64no—
75Dic3⋊C8—64no—
76#810—24no—
77C23×C32C2×D411yescharacteristic
78C2×C32×C4—22no—
79C2×C32×C4—41no—
80C2×C32×C4—41no—
81C2×C32×C4C22×C411yescharacteristic
82C2×C32×C4C2×D411yescharacteristic
83C2×C32×C4C2×D411yescharacteristic
84C2×C32×C4C2×D411yescharacteristic
85C2×C32×C4#4111yescharacteristic
86C2×C32×C4#4111yescharacteristic
87C2×C3⋊Dic3—22no—
88C2×C3⋊Dic3—21no—
89C2×C3⋊Dic3—21no—
90C2×C3⋊Dic3—41no—
91C2×C3⋊Dic3—41no—
92C2×C3⋊Dic3C22⋊C412yes—
93C2×C3⋊Dic3C22⋊C412yes—
94C2×C3⋊Dic3SD1612yes—
95C2×C3⋊Dic3Q1612yes—
96C2×C3×Dic3—24no—
97C2×C3×Dic3—42no—
98C2×C3×Dic3—42no—
99C3×Dic6—24no—
100C3×Dic6—24no—
101C3×Dic6—42no—
102C3×Dic6—42no—
103C3×C3⋊C8—42no—
104C2×C4⋊Q8—91no—
105C2×C4⋊C8—91no—
106C2×#103—32no—
107C2×#103—92no—
108C4×C4⋊C4—91no—
109C2×C3×Q8—34no—
110C2×C3×Q8—62no—
111C2×C3×Q8—62no—
112C2×C3×Q8—62no—
113C2×C3×Q8—62no—
114C2×C3×Q8—62no—
115C22×C3×C4—22no—
116C22×C3×C4—22no—
117C22×C3×C4—21no—
118C22×C3×C4—62no—
119C22×C3×C4C22×D312yes—
120C22×Dic3—22no—
121C22×Dic3—32no—
122C22×Dic3—32no—
123C22×Dic3—61no—
124C22×Dic3—61no—
125C22×Dic3—62no—
126C22×Dic3—62no—
127C2×Dic6—22no—
128C2×Dic6—22no—
129C2×Dic6—22no—
130C2×Dic6—22no—
131C2×Dic6—22no—
132C2×Dic6C4×D314yes—
133C2×C3×C8—62no—
134C2×C3×C8—62no—
135C2×C3×C8—62no—
136C3×C4⋊C4—22no—
137C3×C4⋊C4—22no—
138C3×C4⋊C4—22no—
139C3×C4⋊C4#6714yes—
140C4⋊Dic3—34no—
141C4⋊Dic3—62no—
142C4⋊Dic3—62no—
143C4⋊Dic3—62no—
144Dic3⋊C4—68no—
145Dic3⋊C4—68no—
146C4×Dic3—34no—
147C4×Dic3—34no—
148C4×Dic3—62no—
149C4×Dic3—62no—
150C4×Dic3—124no—
151C4×Dic3—124no—
152C2×C3⋊C8—22no—
153C2×C3⋊C8—22no—
154C2×C3⋊C8—22no—
155C22×C32C2×C22⋊C411yescharacteristic
156C22×C32#12111yescharacteristic
157C22×C32#12111yescharacteristic
158C22×C32C2×SD1611yescharacteristic
159C22×C32C2×Q1611yescharacteristic
160C22×C32#13711yescharacteristic
161C22×C32#13711yescharacteristic
162C32×C4—42no—
163C32×C4C4×D411yescharacteristic
164C32×C4C4×D411yescharacteristic
165C32×C4#12411yescharacteristic
166C32×C4#12711yescharacteristic
167C3⋊Dic3—22no—
168C3⋊Dic3—42no—
169C3⋊Dic3#10314yescomplemented
170C3×Dic3—44no—
171C22×Q8—32no—
172C22×C8—32no—
173C4⋊Q8—94no—
174C4⋊Q8—182no—
175C2×C4⋊C4—91no—
176C2×C4⋊C4—181no—
177C2×C4⋊C4—181no—
178C2×C4⋊C4D3211yescharacteristic
179C2×C42—91no—
180C2×C42—181no—
181C4⋊C8—182no—
182#103—64no—
183#103—184no—
184#95—181no—
185C23×C3—21no—
186C23×C3D3×D412yes—
187C3×Q8—64no—
188C3×Q8—64no—
189C3×Q8—122no—
190C3×Q8—122no—
191C2×C3×C4—24no—
192C2×C3×C4—24no—
193C2×C3×C4—21no—
194C2×C3×C4—21no—
195C2×C3×C4—21no—
196C2×C3×C4—21no—
197C2×C3×C4—21no—
198C2×C3×C4—21no—
199C2×C3×C4—42no—
200C2×C3×C4—42no—
201C2×C3×C4—42no—
202C2×C3×C4—42no—
203C2×C3×C4—64no—
204C2×C3×C4—122no—
205C2×C3×C4—122no—
206C2×C3×C4C2×C4×D312yes—
207C2×C3×C4#23512yes—
208C2×C3×C4D3×D412yes—
209C2×C3×C4D3×D412yes—
210C2×C3×C4#23712yes—
211C2×C3×C4C2×#6712yes—
212C2×Dic3—24no—
213C2×Dic3—34no—
214C2×Dic3—34no—
215C2×Dic3—34no—
216C2×Dic3—34no—
217C2×Dic3—42no—
218C2×Dic3—42no—
219C2×Dic3—62no—
220C2×Dic3—62no—
221C2×Dic3—62no—
222C2×Dic3—62no—
223C2×Dic3—62no—
224C2×Dic3—62no—
225C2×Dic3—64no—
226C2×Dic3—64no—
227C2×Dic3—121no—
228C2×Dic3—121no—
229C2×Dic3—122no—
230C2×Dic3—122no—
231C2×Dic3—122no—
232C2×Dic3—122no—
233Dic6—24no—
234Dic6—24no—
235Dic6—42no—
236Dic6—42no—
237C3×C8—122no—
238C3⋊C8—42no—
239C2×C32#39011yescharacteristic
240C2×C32C2×#10311yescharacteristic
241C2×C32#41911yescharacteristic
242C2×C32#46111yescharacteristic
243C2×C32#46111yescharacteristic
244C2×C32#46211yescharacteristic
245C2×C32#46211yescharacteristic
246C2×Q8—34no—
247C2×Q8—62no—
248C2×Q8—62no—
249C2×Q8—62no—
250C2×Q8—62no—
251C2×Q8—62no—
252C22×C4—21no—
253C22×C4—62no—
254C22×C4—91no—
255C22×C4—91no—
256C22×C4—181no—
257C22×C4C2×D3211yescharacteristic
258C2×C8—62no—
259C2×C8—62no—
260C2×C8—62no—
261C4⋊C4—21no—
262C4⋊C4—92no—
263C4⋊C4—184no—
264C4⋊C4—184no—
265C4⋊C4—181no—
266C4⋊C4#62512yes—
267C42—92no—
268C42—92no—
269C42—362no—
270C22×C3—21no—
271C22×C3—21no—
272C22×C3—21no—
273C22×C3—21no—
274C22×C3—21no—
275C22×C3—21no—
276C22×C3—21no—
277C22×C3D3×C22⋊C412yes—
278C22×C3#88412yes—
279C22×C3D3×SD1612yes—
280C22×C3#91512yes—
281C22×C3D3×Q1612yes—
282C22×C3#91812yes—
283C22×C3#93912yes—
284C3×C4—21no—
285C3×C4—21no—
286C3×C4—21no—
287C3×C4—21no—
288C3×C4—44no—
289C3×C4—44no—
290C3×C4—124no—
291C3×C4#67⋊C412yes—
292C3×C4#88512yes—
293C3×C4C4×#6712yes—
294C3×C4#94012yes—
295Dic3—38no—
296Dic3—44no—
297Dic3—64no—
298Dic3—64no—
299Dic3—122no—
300Dic3—124no—
301Dic3—124no—
302C32#198111yescharacteristic, complemented, Sylow
303C23#381111yescharacteristic
304Q8—64no—
305Q8—64no—
306Q8—122no—
307Q8—122no—
308C2×C4—22no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—64no—
312C2×C4—92no—
313C2×C4—92no—
314C2×C4—92no—
315C2×C4—92no—
316C2×C4—122no—
317C2×C4—122no—
318C2×C4—181no—
319C2×C4—181no—
320C2×C4—182no—
321C2×C4—361no—
322C2×C4—361no—
323C2×C4#379811yescharacteristic
324C2×C4C4×D3211yescharacteristic
325C2×C4#380211yescharacteristic
326C2×C4#380211yescharacteristic
327C2×C4#380511yescharacteristic
328C2×C4C2×#62511yescharacteristic
329C8—122no—
330C2×C3—21no—
331C2×C3—21no—
332C2×C3—21no—
333C2×C3—21no—
334C2×C3—21no—
335C2×C3—21no—
336C2×C3—21no—
337C2×C3#479512yes—
338C2×C3D3×#10312yes—
339C2×C3#480212yes—
340C2×C3#481812yes—
341C2×C3#495712yes—
342C2×C3#516212yes—
343C2×C3#518212yes—
344C22#6391211yescharacteristic
345C22#6392111yescharacteristic
346C22#6393011yescharacteristic
347C22#6393111yescharacteristic
348C22#6394411yescharacteristic
349C22#6394511yescharacteristic
350C22#6398011yescharacteristic
351C4—42no—
352C4—94no—
353C4—124no—
354C4—182no—
355C4—362no—
356C4C4×#62511yescharacteristic
357C4#6390211yescharacteristic
358C4#6391411yescharacteristic
359C4#6391511yescharacteristic
360C3—21no—
361C3#7022912yescomplemented
362C2#1059056511yescharacteristic
363C2#1059056611yescharacteristic
364C2#1059060111yescharacteristic
365C2#1059060211yescharacteristic
366C2#1059138511yescharacteristic
367C2#1059149711yescharacteristic
368C2#1059163311yescharacteristic
subgroupG/H
centerC23#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socle, prime radicalC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1981
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
16. #63873C4semidirect
169. C3⋊Dic3#103semidirect
302. C32#1981semidirect
361. C3#70229semidirect

Maximal subgroups

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

subgroupindex
C2×#638732
C4⋊C4×C3⋊Dic32
C2×C3×#8102
C2×#635722
C2×#635662
#702293