Finite Group Databasebeta

← #11788183

Subgroups — #11788183

Order 1152.

1049 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 1049 conjugacy classes of subgroups — too many to draw. Only its 136 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×C4×#624C211yesmaximal, characteristic, complemented
3C2×#63570C212yesmaximal, complemented
4#10591074C211yesmaximal, characteristic, complemented
5C3×#4532C212yesmaximal, complemented
6#68756—32nomaximal
7C2×#3828C2211yescharacteristic
8C22×C4×C3⋊D3C2211yescharacteristic
9C22×#624—21no—
10C32×#117C2211yescharacteristic
11#64106C412yescomplemented
12#64104C412yescomplemented
13#64095—21no—
14#64091—21no—
15C4×C4⋊(C3⋊D3)—22no—
16C2×C3×C4×Dic3C2212yes—
17C2×C3×#208C2212yes—
18C2×Dic32—21no—
19C4×#624—24no—
20#63570—24no—
21#63557—22no—
22#5524—32no—
23#5524—61no—
24C2×C42×D3—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, complemented
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, complemented
44C22×C3×Dic3—22no—
45C2×#624—28no—
46C2×#624—24no—
47C32×C4⋊C4C2×C412yescomplemented
48C32×C22⋊C4—21no—
49C32×C42—21no—
50#3752—22no—
51#3752—22no—
52C4⋊(C3⋊Dic3)—22no—
53C3×C4×Dic3—22no—
54C3×C4×Dic3D414yescomplemented
55C3×#208—22no—
56C3×#208—22no—
57C2×C3×C3⋊C8—22no—
58Dic32—24no—
59#1896—91noSylow
60C2×#235—32no—
61C2×#235—61no—
62C22×C4×D3—32no—
63C22×C4×D3—61no—
64C22×C4×D3—62no—
65C2×C3×M16—32no—
66C3×#117—21no—
67C3×#117C2×D312yes—
68C2×C3×C42—32no—
69C2×C4×Dic3—62no—
70C2×C4×Dic3C2×D312yes—
71C2×#208C2×D312yes—
72#897—34no—
73#897—62no—
74#895—34no—
75#895—62no—
76#886—62no—
77#886—62no—
78#882—62no—
79#882—62no—
80C4×D12—64no—
81C4×D12—64no—
82C42×D3—64no—
83C42×D3—64no—
84#825—64no—
85(C2×D3)⋊C8—64no—
86#805—64no—
87C23×C32C2×D411yescharacteristic
88C22×C3⋊D3—21no—
89C22×C3⋊D3—21no—
90C22×C3⋊D3—21no—
91C22×C3⋊D3—24no—
92C22×C3⋊D3C22⋊C412yes—
93C2×C32×C4—22no—
94C2×C32×C4C22×C411yescharacteristic
95C2×C32×C4C2×D412yes—
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4#4112yes—
98#638—41no—
99#638—41no—
100C2×C3⋊Dic3—21no—
101C2×C3⋊Dic3—21no—
102C2×C3⋊Dic3—21no—
103C2×C3⋊Dic3C22⋊C412yes—
104C4⋊(C3⋊D3)—22no—
105C4⋊(C3⋊D3)—44no—
106C4×C3⋊D3—24no—
107C4×C3⋊D3—24no—
108C4×C3⋊D3—42no—
109#634—22no—
110C2×C3×Dic3—28no—
111C2×C3×Dic3—24no—
112#624—216no—
113C3×C3⋊C8—42no—
114#525—91no—
115C22×C42—91no—
116C2×#104—92no—
117#407—91no—
118#339—32no—
119C23×D3—32no—
120C23×D3—61no—
121C22×C3×C4—21no—
122C22×C3×C4—62no—
123C22×C3×C4C22×D312yes—
124C2×#67—62no—
125C2×#67—62no—
126C22×Dic3—22no—
127C22×Dic3—32no—
128C22×Dic3—61no—
129#235—62no—
130#235—62no—
131#235—62no—
132#235—62no—
133#235—122no—
134#235—122no—
135C2×D12—32no—
136C2×D12—61no—
137C2×D12—64no—
138C2×D12—64no—
139C2×C4×D3—34no—
140C2×C4×D3—34no—
141C2×C4×D3—62no—
142C2×C4×D3—62no—
143C2×C4×D3—68no—
144C2×C4×D3—616no—
145C2×C4×D3—62no—
146C2×C4×D3—62no—
147C2×C4×D3—62no—
148C2×C4×D3—62no—
149C2×C4×D3—62no—
150C2×C4×D3—62no—
151C2×C4×D3—122no—
152C2×C4×D3—122no—
153C2×Dic6—32no—
154C2×Dic6—61no—
155C3×M16—62no—
156C3×M16—62no—
157C2×C3×C8—62no—
158C3×C4⋊C4—22no—
159C3×C4⋊C4C4×D314yescomplemented
160C3×C22⋊C4—22no—
161C3×C22⋊C4—22no—
162C3×C42—22no—
163C3×C42—22no—
164C3×C42—34no—
165C3×C42—62no—
166(C2×D3)⋊C4—64no—
167(C2×D3)⋊C4—64no—
168(C2×D3)⋊C4—64no—
169(C2×D3)⋊C4—64no—
170C4⋊Dic3—64no—
171C4⋊Dic3—64no—
172C4×Dic3—22no—
173C4×Dic3—68no—
174C4×Dic3D1214yescomplemented
175#208—22no—
176#208—22no—
177C2×C3⋊C8—22no—
178C22×C32—22no—
179C22×C32C2×C22⋊C411yescharacteristic
180C22×C32#12011yescharacteristic
181C22×C32#12311yescharacteristic
182C2×C3⋊D3—24no—
183C2×C3⋊D3—24no—
184C2×C3⋊D3—22no—
185C2×C3⋊D3—22no—
186C2×C3⋊D3—41no—
187C2×C3⋊D3—42no—
188C2×C3⋊D3#10414yescomplemented
189C32×C4—42no—
190C32×C4C4×D412yes—
191C32×C4#12112yes—
192C3⋊Dic3—22no—
193C3⋊Dic3—41no—
194C3×Dic3—28no—
195C2×#41—91no—
196C23×C4—91no—
197C23×C4—181no—
198C2×M16—32no—
199#123—181no—
200C22⋊Q8—92no—
201#121—92no—
202#120—181no—
203C4×D4—182no—
204#117D3211yescharacteristic
205C2×C42—32no—
206C2×C42—184no—
207C2×C42—181no—
208#104—184no—
209C22⋊C8—182no—
210C23×C3—21no—
211C23×C3D3×D412yes—
212C22×D3—34no—
213C22×D3—62no—
214C22×D3—68no—
215C22×D3—62no—
216C22×D3—62no—
217C22×D3—62no—
218C22×D3—62no—
219C22×D3—124no—
220C22×D3—121no—
221C22×D3—121no—
222C2×C3×C4—24no—
223C2×C3×C4—24no—
224C2×C3×C4—22no—
225C2×C3×C4—22no—
226C2×C3×C4—21no—
227C2×C3×C4—21no—
228C2×C3×C4—68no—
229C2×C3×C4—64no—
230C2×C3×C4C2×C4×D312yes—
231C2×C3×C4C2×D1212yes—
232C2×C3×C4#23512yes—
233C2×C3×C4D3×D412yes—
234C2×C3×C4D3×D412yes—
235C2×C3×C4#23912yes—
236#67—122no—
237#67—122no—
238#67—122no—
239#67—122no—
240C2×Dic3—28no—
241C2×Dic3—24no—
242C2×Dic3—34no—
243C2×Dic3—62no—
244C2×Dic3—62no—
245C2×Dic3—62no—
246C2×Dic3—62no—
247C2×Dic3—62no—
248C2×Dic3—121no—
249C2×Dic3—121no—
250D12—62no—
251D12—62no—
252D12—122no—
253D12—128no—
254D12—128no—
255C4×D3—632no—
256C4×D3—64no—
257C4×D3—64no—
258C4×D3—64no—
259C4×D3—64no—
260C4×D3—124no—
261C4×D3—124no—
262C4×D3—124no—
263C4×D3—122no—
264C4×D3—122no—
265Dic6—62no—
266Dic6—62no—
267Dic6—122no—
268C3×C8—122no—
269C3⋊C8—42no—
270C2×C32—21no—
271C2×C32—21no—
272C2×C32#38611yescharacteristic
273C2×C32C2×#10412yes—
274C3⋊D3—24no—
275C3⋊D3—81no—
276C24—91no—
277#41—182no—
278#41—182no—
279C2×Q8—91no—
280C2×D4—91no—
281C2×D4—182no—
282C2×D4—181no—
283C22×C4—62no—
284C22×C4—91no—
285C22×C4—92no—
286C22×C4—92no—
287C22×C4—184no—
288C22×C4—188no—
289C22×C4—182no—
290C22×C4—182no—
291C22×C4—181no—
292C22×C4C2×D3211yescharacteristic
293M16—62no—
294M16—62no—
295C2×C8—62no—
296C4⋊C4—182no—
297C4⋊C4#62412yescomplemented
298C22⋊C4—21no—
299C22⋊C4—182no—
300C22⋊C4—182no—
301C42—21no—
302C42—34no—
303C42—62no—
304C42—184no—
305C22×C3—24no—
306C22×C3—21no—
307C22×C3—21no—
308C22×C3—21no—
309C22×C3—42no—
310C22×C3D3×C22⋊C412yes—
311C22×C3#88212yes—
312C22×C3#89412yes—
313C2×D3—38no—
314C2×D3—64no—
315C2×D3—68no—
316C2×D3—68no—
317C2×D3—64no—
318C2×D3—64no—
319C2×D3—122no—
320C2×D3—122no—
321C2×D3—124no—
322C2×D3—124no—
323C2×D3—122no—
324C2×D3—124no—
325C2×D3—122no—
326C2×D3—124no—
327C3×C4—22no—
328C3×C4—22no—
329C3×C4—44no—
330C3×C4—44no—
331C3×C4—68no—
332C3×C4C4×D1212yes—
333C3×C4#88412yes—
334C3×C4#89312yes—
335C3×C4#89512yes—
336Dic3—28no—
337Dic3—64no—
338Dic3—122no—
339Dic3—122no—
340Dic3—122no—
341C32#189611yescharacteristic, complemented, Sylow
342C23—92no—
343C23—184no—
344C23—181no—
345C23—181no—
346C23—181no—
347C23#381111yescharacteristic
348Q8—182no—
349D4—182no—
350D4—364no—
351D4—361no—
352D4—361no—
353C2×C4—22no—
354C2×C4—68no—
355C2×C4—64no—
356C2×C4—92no—
357C2×C4—1816no—
358C2×C4—181no—
359C2×C4—181no—
360C2×C4—184no—
361C2×C4—184no—
362C2×C4—181no—
363C2×C4—362no—
364C2×C4#379912yes—
365C2×C4D3×D1212yes—
366C2×C4C2×#62411yescharacteristic
367C2×C4#381111yescharacteristic
368C8—122no—
369C2×C3—22no—
370C2×C3—22no—
371C2×C3—21no—
372C2×C3—22no—
373C2×C3—41no—
374C2×C3—41no—
375C2×C3#466512yes—
376C2×C3D3×#10414yes—
377D3—68no—
378D3—124no—
379D3—242no—
380D3—242no—
381C22—22no—
382C22—94no—
383C22—184no—
384C22—184no—
385C22—182no—
386C22—182no—
387C22—361no—
388C22—362no—
389C22#6389711yescharacteristic
390C22#6392311yescharacteristic
391C22#6397411yescharacteristic
392C4—42no—
393C4—68no—
394C4—182no—
395C4—361no—
396C4#6389412yes—
397C4#6391012yes—
398C3—21no—
399C3#6875612yescomplemented
400C2—21no—
401C2—21no—
402C2—184no—
403C2—721no—
404C2#1059138011yescharacteristic
405C2#1059167112yes—
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#1896
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×C4×#624C2semidirect
3. C2×#63570C2semidirect
4. #10591074C2semidirect
5. C3×#4532C2semidirect
11. #64106C4semidirect
12. #64104C4semidirect
29. #4532D3semidirect
37. C2×C4⋊(C3⋊D3)C2×C4semidirect
43. C2×#634C2×C4semidirect
47. C32×C4⋊C4C2×C4semidirect
54. C3×C4×Dic3D4semidirect
159. C3×C4⋊C4C4×D3semidirect
174. C4×Dic3D12semidirect
188. C2×C3⋊D3#104semidirect
297. C4⋊C4#624semidirect
341. C32#1896semidirect
399. C3#68756semidirect

Maximal subgroups

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

subgroupindex
#105959952
C2×C4×#6242
C2×#635702
#105910742
C3×#45322
#687563