Finite Group Databasebeta

← #11788217

Subgroups — #11788217

Order 1152.

881 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 881 conjugacy classes of subgroups — too many to draw. Only its 132 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
1#10595995C211yesmaximal, characteristic
2C2×#63874C211yesmaximal, characteristic, complemented
3C2×#63570C212yesmaximal, complemented
4#10591074C211yesmaximal, characteristic, complemented
5C3×#4532C212yesmaximal, complemented
6#68757—32nomaximal
7C2×#3828C2211yescharacteristic
8C22×C4×C3⋊D3C2211yescharacteristic
9C32×#117C2211yescharacteristic
10#64106C412yescomplemented
11#64104C412yescomplemented
12#64095—21no—
13#64091—21no—
14C4×C4⋊(C3⋊D3)—22no—
15C2×C3×C4×Dic3C2212yes—
16C2×C3×#208C2212yes—
17C2×#3724—21no—
18C2×#3722—21no—
19#63874—24no—
20#63570—24no—
21#63557—22no—
22#5524—32no—
23#5524—61no—
24C2×#872—32no—
25C2×#825—32no—
26#5126—32no—
27C2×#805—32no—
28C3×#339—32no—
29#4532D312yescomplemented
30C23×C3⋊D3D411yescharacteristic
31C22×C32×C4C2311yescharacteristic
32C2×#638—21no—
33C22×C3⋊Dic3D411yescharacteristic
34#3828—22no—
35#3828—22no—
36C2×C4⋊(C3⋊D3)—22no—
37C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
38C2×C4×C3⋊D3—22no—
39C2×C4×C3⋊D3—22no—
40C2×C4×C3⋊D3—21no—
41C2×C4×C3⋊D3C2×C412yes—
42C2×C4×C3⋊D3D412yes—
43C2×#634C2×C411yescharacteristic
44C22×C3×Dic3—22no—
45C32×C4⋊C4C2×C412yes—
46C32×C22⋊C4—21no—
47C32×C42—21no—
48#3752—22no—
49#3752—22no—
50C4⋊(C3⋊Dic3)—22no—
51C3×C4×Dic3—22no—
52C3×C4×Dic3D414yescomplemented
53C3×#208—22no—
54C3×#208—22no—
55C2×C3×C3⋊C8—22no—
56#3724—24no—
57#3722—24no—
58#1897—91noSylow
59C2×#235—32no—
60C2×#235—61no—
61C22×C4×D3—32no—
62C22×C4×D3—61no—
63C2×C3×M16—32no—
64C3×#117—21no—
65C3×#117C2×D312yes—
66C2×C3×C42—32no—
67C2×(C2×D3)⋊C4—62no—
68C2×Dic3⋊C4—62no—
69C2×C4×Dic3C2×D312yes—
70C2×#208C2×D312yes—
71#897—34no—
72#897—62no—
73#895—34no—
74#895—62no—
75#886—62no—
76#886—62no—
77#882—62no—
78#882—62no—
79C4×D12—64no—
80C4×D12—64no—
81#872—64no—
82#872—64no—
83#825—64no—
84(C2×D3)⋊C8—64no—
85#805—64no—
86C23×C32C2×D411yescharacteristic
87C22×C3⋊D3—21no—
88C22×C3⋊D3—21no—
89C22×C3⋊D3—21no—
90C22×C3⋊D3—42no—
91C22×C3⋊D3C22⋊C412yes—
92C2×C32×C4—22no—
93C2×C32×C4C22×C411yescharacteristic
94C2×C32×C4C2×D412yes—
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4#4112yes—
97#638—41no—
98#638—41no—
99C2×C3⋊Dic3—21no—
100C2×C3⋊Dic3—21no—
101C2×C3⋊Dic3—21no—
102C2×C3⋊Dic3C22⋊C412yes—
103C4⋊(C3⋊D3)—22no—
104C4⋊(C3⋊D3)—44no—
105C4×C3⋊D3—24no—
106C4×C3⋊D3—24no—
107C4×C3⋊D3—42no—
108#634—22no—
109C2×C3×Dic3—24no—
110C2×C3×Dic3—44no—
111C3×C3⋊C8—42no—
112#525—91no—
113C2×#117—91no—
114C2×#104—92no—
115#407—91no—
116#339—32no—
117C23×D3—32no—
118C23×D3—61no—
119C22×C3×C4—21no—
120C22×C3×C4—62no—
121C22×C3×C4C22×D312yes—
122C2×#67—62no—
123C2×#67—62no—
124C22×Dic3—22no—
125C22×Dic3—32no—
126C22×Dic3—61no—
127#235—62no—
128#235—62no—
129#235—62no—
130#235—62no—
131#235—122no—
132#235—122no—
133C2×D12—32no—
134C2×D12—61no—
135C2×D12—64no—
136C2×D12—64no—
137C2×C4×D3—34no—
138C2×C4×D3—34no—
139C2×C4×D3—62no—
140C2×C4×D3—62no—
141C2×C4×D3—62no—
142C2×C4×D3—62no—
143C2×C4×D3—62no—
144C2×C4×D3—62no—
145C2×C4×D3—62no—
146C2×C4×D3—62no—
147C2×C4×D3—122no—
148C2×C4×D3—122no—
149C2×Dic6—32no—
150C2×Dic6—61no—
151C3×M16—62no—
152C3×M16—62no—
153C2×C3×C8—62no—
154C3×C4⋊C4—22no—
155C3×C4⋊C4C4×D314yes—
156C3×C22⋊C4—22no—
157C3×C22⋊C4—22no—
158C3×C42—22no—
159C3×C42—22no—
160C3×C42—34no—
161C3×C42—62no—
162(C2×D3)⋊C4—68no—
163(C2×D3)⋊C4—64no—
164(C2×D3)⋊C4—64no—
165(C2×D3)⋊C4—64no—
166(C2×D3)⋊C4—64no—
167C4⋊Dic3—64no—
168C4⋊Dic3—64no—
169Dic3⋊C4—68no—
170C4×Dic3—22no—
171C4×Dic3D1214yescomplemented
172#208—22no—
173#208—22no—
174C2×C3⋊C8—22no—
175C22×C32—22no—
176C22×C32C2×C22⋊C411yescharacteristic
177C22×C32#12011yescharacteristic
178C22×C32#12311yescharacteristic
179C2×C3⋊D3—22no—
180C2×C3⋊D3—22no—
181C2×C3⋊D3—22no—
182C2×C3⋊D3—42no—
183C2×C3⋊D3—42no—
184C2×C3⋊D3—41no—
185C2×C3⋊D3—42no—
186C32×C4—42no—
187C32×C4C4×D412yes—
188C32×C4#12112yes—
189C3⋊Dic3—22no—
190C3⋊Dic3—41no—
191C3×Dic3—44no—
192C2×#41—91no—
193C23×C4—91no—
194C2×M16—32no—
195#123—181no—
196C22⋊Q8—92no—
197#121—92no—
198#120—181no—
199C4×D4—182no—
200#117—184no—
201#117D3211yescharacteristic
202C2×C4⋊C4—181no—
203C2×C22⋊C4—181no—
204C2×C42—32no—
205#104—184no—
206C22⋊C8—182no—
207C23×C3—21no—
208C23×C3D3×D412yes—
209C22×D3—34no—
210C22×D3—62no—
211C22×D3—62no—
212C22×D3—62no—
213C22×D3—62no—
214C22×D3—62no—
215C22×D3—121no—
216C22×D3—121no—
217C22×D3—124no—
218C22×D3—124no—
219C2×C3×C4—24no—
220C2×C3×C4—24no—
221C2×C3×C4—22no—
222C2×C3×C4—22no—
223C2×C3×C4—21no—
224C2×C3×C4—21no—
225C2×C3×C4—64no—
226C2×C3×C4—124no—
227C2×C3×C4C2×C4×D312yes—
228C2×C3×C4C2×D1212yes—
229C2×C3×C4#23512yes—
230C2×C3×C4D3×D412yes—
231C2×C3×C4D3×D412yes—
232C2×C3×C4#23912yes—
233#67—122no—
234#67—122no—
235#67—122no—
236#67—122no—
237C2×Dic3—24no—
238C2×Dic3—34no—
239C2×Dic3—44no—
240C2×Dic3—62no—
241C2×Dic3—62no—
242C2×Dic3—62no—
243C2×Dic3—62no—
244C2×Dic3—62no—
245C2×Dic3—121no—
246C2×Dic3—121no—
247D12—62no—
248D12—62no—
249D12—122no—
250D12—128no—
251D12—128no—
252C4×D3—64no—
253C4×D3—64no—
254C4×D3—64no—
255C4×D3—64no—
256C4×D3—124no—
257C4×D3—124no—
258C4×D3—124no—
259C4×D3—122no—
260C4×D3—122no—
261Dic6—62no—
262Dic6—62no—
263Dic6—122no—
264C3×C8—122no—
265C3⋊C8—42no—
266C2×C32—21no—
267C2×C32—21no—
268C2×C32#38611yescharacteristic
269C2×C32#42112yes—
270C3⋊D3—42no—
271C3⋊D3—81no—
272C24—91no—
273#41—182no—
274#41—182no—
275C2×Q8—91no—
276C2×D4—91no—
277C2×D4—182no—
278C2×D4—181no—
279C22×C4—62no—
280C22×C4—91no—
281C22×C4—92no—
282C22×C4—92no—
283C22×C4—182no—
284C22×C4—182no—
285C22×C4—181no—
286C22×C4C2×D3211yescharacteristic
287M16—62no—
288M16—62no—
289C2×C8—62no—
290C4⋊C4—182no—
291C4⋊C4—184no—
292C4⋊C4#62412yes—
293C22⋊C4—21no—
294C22⋊C4—182no—
295C22⋊C4—182no—
296C22⋊C4—184no—
297C42—21no—
298C42—34no—
299C42—62no—
300C22×C3—24no—
301C22×C3—21no—
302C22×C3—21no—
303C22×C3—21no—
304C22×C3—42no—
305C22×C3D3×C22⋊C412yes—
306C22×C3#88212yes—
307C22×C3#89412yes—
308C2×D3—64no—
309C2×D3—64no—
310C2×D3—64no—
311C2×D3—64no—
312C2×D3—122no—
313C2×D3—122no—
314C2×D3—124no—
315C2×D3—124no—
316C2×D3—124no—
317C2×D3—124no—
318C2×D3—122no—
319C2×D3—124no—
320C2×D3—122no—
321C2×D3—124no—
322C3×C4—22no—
323C3×C4—22no—
324C3×C4—44no—
325C3×C4—44no—
326C3×C4—124no—
327C3×C4C4×D1212yes—
328C3×C4#88412yes—
329C3×C4#89312yes—
330C3×C4#89512yes—
331Dic3—44no—
332Dic3—64no—
333Dic3—122no—
334Dic3—122no—
335Dic3—122no—
336C32#189711yescharacteristic, complemented, Sylow
337C23—92no—
338C23—181no—
339C23—181no—
340C23—181no—
341C23—362no—
342C23#381111yescharacteristic
343Q8—182no—
344D4—182no—
345D4—364no—
346D4—361no—
347D4—361no—
348C2×C4—22no—
349C2×C4—64no—
350C2×C4—92no—
351C2×C4—124no—
352C2×C4—181no—
353C2×C4—181no—
354C2×C4—184no—
355C2×C4—184no—
356C2×C4—181no—
357C2×C4—362no—
358C2×C4#379912yes—
359C2×C4D3×D1212yes—
360C2×C4C2×#62411yescharacteristic
361C2×C4#381111yescharacteristic
362C8—122no—
363C2×C3—22no—
364C2×C3—22no—
365C2×C3—21no—
366C2×C3—22no—
367C2×C3—41no—
368C2×C3—41no—
369C2×C3#466512yes—
370C2×C3#482114yes—
371D3—124no—
372D3—124no—
373D3—242no—
374D3—242no—
375C22—22no—
376C22—182no—
377C22—182no—
378C22—182no—
379C22—362no—
380C22—362no—
381C22—361no—
382C22—362no—
383C22#6389711yescharacteristic
384C22#6392311yescharacteristic
385C22#6397411yescharacteristic
386C4—42no—
387C4—124no—
388C4—182no—
389C4—361no—
390C4#6389412yes—
391C4#6391012yes—
392C3—21no—
393C3#6875712yescomplemented
394C2—21no—
395C2—21no—
396C2—362no—
397C2—721no—
398C2#1059138011yescharacteristic
399C2#1059167212yes—
subgroupG/H
centerC2×C4#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC22×C32C2×C22⋊C4
prime radical#10595995C2
cosocleC22×C32×C4C23
hypercenter#117D32
hypocenterC32#1897
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C2×#63874C2semidirect
3. C2×#63570C2semidirect
4. #10591074C2semidirect
5. C3×#4532C2semidirect
10. #64106C4semidirect
11. #64104C4semidirect
29. #4532D3semidirect
52. C3×C4×Dic3D4semidirect
171. C4×Dic3D12semidirect
336. C32#1897semidirect
393. C3#68757semidirect

Maximal subgroups

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

subgroupindex
#105959952
C2×#638742
C2×#635702
#105910742
C3×#45322
#687573