Finite Group Databasebeta

← #11798209

Subgroups — #11798209

Order 1152.

461 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 461 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×Dic12C211yesmaximal, characteristic
2C3×#4887C211yesmaximal, characteristic
3C2×#63551C211yesmaximal, characteristic, complemented
4C2×#63550C211yesmaximal, characteristic, complemented
5#10589358C211yesmaximal, characteristic, complemented
6C3×#4492C211yesmaximal, characteristic, complemented
7(C2×D3)⋊(C3⋊C16)C211yesmaximal, characteristic
8#71087—31nomaximal
9#69225—31nomaximal
10C2×D3×Dic6—21no—
11C2×#3746C2211yescharacteristic
12C2×C3×Dic12C2211yescharacteristic
13C2×C3×Dic12C2211yescharacteristic
14C2×C3×D3×C8C2211yescharacteristic
15C3×#897—21no—
16C2×#3719—21no—
17D3×Dic12—22no—
18D3×Dic12—22no—
19C32×#107C2211yescharacteristic
20C2×C3⋊(C3⋊C16)C2211yescharacteristic
21C2×C3×C3⋊C16C2211yescharacteristic
22C3×#810—21no—
23#63551—22no—
24#63550—22no—
25C2×D3×Q16—31no—
26C22×Dic12—31no—
27C3×#467—31no—
28C2×#829—31no—
29C2×#829—31no—
30C2×#829—31no—
31C2×Dic24—31no—
32#4887D311yescharacteristic
33C3×#358—31no—
34#4549—31no—
35(C2×D3)⋊C16—31no—
36#4492—31no—
37#4492—31no—
38#4492—61no—
39#4492D311yescharacteristic, complemented
40C2×#634—21no—
41C2×C3×C4×D3D411yescharacteristic
42C2×C3×Dic6—21no—
43C2×C3×Dic6—21no—
44C2×#627—41no—
45C2×D3×Dic3—41no—
46D3×Dic6—24no—
47D3×Dic6—42no—
48C2×C32×C8C2311yescharacteristic
49C32×C4⋊C4—21no—
50#3746—21no—
51#3746D412yes—
52C3×(C2×D3)⋊C4—41no—
53C3×C4⋊Dic3—41no—
54C2×C3×C3⋊C8D411yescharacteristic
55C3×Dic12—21no—
56C3×Dic12—21no—
57C3×Dic12—21no—
58C3×Dic12D412yes—
59C3×D3×C8—21no—
60C3×D3×C8—21no—
61#3719—24no—
62C3⋊(C3⋊C16)—21no—
63C3×C3⋊C16—21no—
64#2188—91noSylow
65C2×D3×Q8—61no—
66C22×Dic6—61no—
67C2×C3×Q16—31no—
68C2×C3×Q16—31no—
69C22×C3×C8—31no—
70C3×C22⋊Q8—61no—
71C2×#216—61no—
72D3×Q16—62no—
73D3×Q16—62no—
74C2×Dic12—31no—
75C2×Dic12—31no—
76C2×Dic12—61no—
77C2×Dic12—62no—
78C2×Dic12—61no—
79C2×Dic12—62no—
80C2×Dic12C2×D311yescharacteristic
81C2×Dic12C2×D311yescharacteristic
82C2×D3×C8C2×D311yescharacteristic
83#897—21no—
84C2×C3×C16—31no—
85C3×#107—21no—
86C3×#107C2×D311yescharacteristic
87C3×#107C2×D311yescharacteristic
88C3×#103—61no—
89#829—62no—
90#829—62no—
91#829—62no—
92C2×C3⋊C16—31no—
93C2×C3⋊C16—31no—
94C2×C3⋊C16—61no—
95C2×C3⋊C16C2×D311yescharacteristic
96#810—21no—
97Dic24—62no—
98C22×C3×D3D811yescharacteristic
99C2×C32×C4—41no—
100C2×C32×C4C2×D411yescharacteristic
101C2×C3⋊Dic3—41no—
102#634—22no—
103#634—41no—
104C2×C3×Dic3—41no—
105C2×C3×Dic3—41no—
106C2×C3×Dic3D811yescharacteristic
107C3×C4×D3—21no—
108C3×C4×D3—21no—
109C3×Dic6—22no—
110C3×Dic6—41no—
111C3×Dic6—41no—
112C3×Dic6—41no—
113#627—44no—
114D3×Dic3—44no—
115C32×C8C2×D411yescharacteristic
116C32×C8C2×D411yescharacteristic
117C3×C3⋊C8—21no—
118C22×Q16—91no—
119C2×Q32—91no—
120C2×Q32—91no—
121#467—31no—
122#358—31no—
123#358—91no—
124C22⋊C16—91no—
125C2×C3×Q8—61no—
126C2×C3×Q8—61no—
127C22×C3×C4—31no—
128C22×Dic3—121no—
129D3×Q8—64no—
130D3×Q8—122no—
131C2×C4×D3—121no—
132C2×C4×D3#6711yescharacteristic
133C2×Dic6—21no—
134C2×Dic6—21no—
135C2×Dic6—64no—
136C2×Dic6—61no—
137C2×Dic6—61no—
138C2×Dic6—121no—
139C2×Dic6—122no—
140C2×Dic6—121no—
141C2×Dic6—121no—
142C3×Q16—32no—
143C3×Q16—61no—
144C3×Q16—61no—
145C3×Q16—61no—
146C2×C3×C8—21no—
147C2×C3×C8—31no—
148C2×C3×C8—61no—
149C2×C3×C8—61no—
150C2×C3×C8C22×D311yescharacteristic
151C2×C3×C8C22×D311yescharacteristic
152C3×C4⋊C4—21no—
153C3×C4⋊C4—21no—
154C3×C4⋊C4—41no—
155C3×C4⋊C4—121no—
156C3×C22⋊C4—121no—
157#216—64no—
158(C2×D3)⋊C4—41no—
159C4⋊Dic3—41no—
160C2×C3⋊C8#6711yescharacteristic
161Dic12—21no—
162Dic12—21no—
163Dic12—21no—
164Dic12—32no—
165Dic12—32no—
166Dic12—62no—
167Dic12—64no—
168Dic12—61no—
169Dic12—61no—
170Dic12—121no—
171Dic12D1212yes—
172D3×C8—21no—
173D3×C8—21no—
174C3×C16—61no—
175C3⋊C16—21no—
176C3⋊C16—61no—
177C3⋊C16—61no—
178C3⋊C16—121no—
179C22×C32C2×D811yescharacteristic
180C2×C3×D3—21no—
181C2×C3×D3—21no—
182C2×C3×D3Q3212yescomplemented
183C32×C4—81no—
184C32×C4#12011yescharacteristic
185C32×C4AGL(1,ℤ/8)11yescharacteristic
186C3⋊Dic3—42no—
187C3×Dic3—21no—
188C3×Dic3—42no—
189C3×Dic3—81no—
190C22×Q8—181no—
191C2×Q16—31no—
192C2×Q16—31no—
193C2×Q16—91no—
194C2×Q16—181no—
195C2×Q16—182no—
196C2×Q16—182no—
197C22×C8—31no—
198C22⋊Q8—61no—
199Q32—182no—
200Q32—182no—
201C2×C16—31no—
202C2×C16—91no—
203#107D3211yescharacteristic
204#103—61no—
205C23×C3—31no—
206C22×D3#21311yescharacteristic
207C3×Q8—62no—
208C3×Q8—121no—
209C3×Q8—121no—
210C3×Q8—121no—
211C2×C3×C4—21no—
212C2×C3×C4—31no—
213C2×C3×C4—41no—
214C2×C3×C4—41no—
215C2×C3×C4—61no—
216C2×C3×C4—61no—
217C2×C3×C4—81no—
218C2×C3×C4—121no—
219C2×C3×C4—121no—
220C2×C3×C4D3×D411yescharacteristic
221C2×C3×C4C2×#6711yescharacteristic
222C2×Dic3—41no—
223C2×Dic3—41no—
224C2×Dic3—124no—
225C2×Dic3—121no—
226C2×Dic3—121no—
227C2×Dic3—241no—
228C2×Dic3#21311yescharacteristic
229C4×D3—21no—
230C4×D3—21no—
231C4×D3—124no—
232Dic6—22no—
233Dic6—41no—
234Dic6—41no—
235Dic6—41no—
236Dic6—62no—
237Dic6—62no—
238Dic6—122no—
239Dic6—124no—
240Dic6—124no—
241Dic6—121no—
242Dic6—121no—
243Dic6—241no—
244C3×C8—21no—
245C3×C8—21no—
246C3×C8—61no—
247C3×C8C2×D1211yescharacteristic
248C3×C8D3×D411yescharacteristic
249C3×C8D3×D411yescharacteristic
250C3×C8D3×D411yescharacteristic
251C3⋊C8—21no—
252C2×C32#44711yescharacteristic
253C2×C32C2×Q3211yescharacteristic
254C2×C32#51011yescharacteristic
255C3×D3—22no—
256C2×Q8—61no—
257C2×Q8—61no—
258C2×Q8—184no—
259C2×Q8—181no—
260C2×Q8—361no—
261C2×Q8—362no—
262C22×C4—31no—
263C22×C4—361no—
264Q16—32no—
265Q16—61no—
266Q16—61no—
267Q16—61no—
268Q16—92no—
269Q16—184no—
270Q16—181no—
271C2×C8—31no—
272C2×C8—61no—
273C2×C8—61no—
274C2×C8C2×D3211yescharacteristic
275C4⋊C4—21no—
276C4⋊C4—121no—
277C22⋊C4—121no—
278C16—61no—
279C16—181no—
280C22×C3—21no—
281C22×C3—32no—
282C22×C3—61no—
283C22×C3—61no—
284C22×C3D3×D811yescharacteristic
285C22×C3C2×#21311yescharacteristic
286C2×D3—21no—
287C2×D3—21no—
288C2×D3#82912yescomplemented
289C3×C4—21no—
290C3×C4—21no—
291C3×C4—61no—
292C3×C4—81no—
293C3×C4—81no—
294C3×C4—122no—
295C3×C4—161no—
296C3×C4—241no—
297C3×C4#88211yescharacteristic
298C3×C4#91411yescharacteristic
299C3×C4#93711yescharacteristic
300C3×C4#94911yescharacteristic
301Dic3—21no—
302Dic3—42no—
303Dic3—81no—
304Dic3—122no—
305Dic3—122no—
306Dic3—242no—
307C32#218811yescharacteristic, complemented, Sylow
308C23—31no—
309Q8—62no—
310Q8—121no—
311Q8—121no—
312Q8—121no—
313Q8—182no—
314Q8—364no—
315Q8—361no—
316C2×C4—31no—
317C2×C4—41no—
318C2×C4—61no—
319C2×C4—61no—
320C2×C4—121no—
321C2×C4—121no—
322C2×C4—364no—
323C2×C4—361no—
324C2×C4D3×#6711yescharacteristic
325C8—61no—
326C8D3×D1211yescharacteristic
327C8#380211yescharacteristic
328C2×C3—21no—
329C2×C3—21no—
330C2×C3—21no—
331C2×C3—62no—
332C2×C3#477311yescharacteristic
333C2×C3#491511yescharacteristic
334C2×C3D3×Q3211yescharacteristic
335C2×C3#503611yescharacteristic
336C2×C3C2×#82911yescharacteristic
337C2×C3#519511yescharacteristic
338D3—22no—
339C22—32no—
340C22—61no—
341C22—61no—
342C22D3×#21311yescharacteristic
343C4—61no—
344C4—81no—
345C4—122no—
346C4—241no—
347C4—362no—
348C4#6392211yescharacteristic
349C4#6393911yescharacteristic
350C3—21no—
351C3#6922511yescharacteristic, complemented
352C3#7108711yescharacteristic, complemented
353C2—62no—
354C2#1059059511yescharacteristic
355C2#1059102811yescharacteristic
356C2D3×#82911yescharacteristic
subgroupG/H
centerC22D3×#213
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC32×#107C22
socleC22×C32C2×D8
prime radicalC22×C3×D3D8
hypercenter#107D32
hypocenterC32#2188
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #107

Complements

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

NH ≅ G/Ntype
3. C2×#63551C2semidirect
4. C2×#63550C2semidirect
5. #10589358C2semidirect
6. C3×#4492C2semidirect
39. #4492D3semidirect
182. C2×C3×D3Q32semidirect
288. C2×D3#829semidirect
307. C32#2188semidirect
351. C3#69225semidirect
352. C3#71087semidirect

Maximal subgroups

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

subgroupindex
C2×D3×Dic122
C3×#48872
C2×#635512
C2×#635502
#105893582
C3×#44922
(C2×D3)⋊(C3⋊C16)2
#710873
#692253