Finite Group Databasebeta

← #11774282

Subgroups — #11774282

Order 1152.

683 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 683 conjugacy classes of subgroups — too many to draw. Only its 122 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
1C4×#3830C211yesmaximal, characteristic
2#10590331C211yesmaximal, characteristic, complemented
3#10590297C211yesmaximal, characteristic, complemented
4C3×D4⋊(C3⋊C8)C212yesmaximal, complemented
5#10589085C212yesmaximal, complemented
6#68166—32nomaximal
7C2×#3830C411yescharacteristic
8C32×C4×D4C2211yescharacteristic
9D4×C3⋊Dic3C411yescharacteristic
10C4×#638—21no—
11C2×C4×C3⋊Dic3—21no—
12#64101C411yescharacteristic
13#64096C411yescharacteristic
14#64090—21no—
15#64086—21no—
16C42×C3⋊D3C2211yescharacteristic
17C4×#634C2211yescharacteristic
18C2×#3710—21no—
19C3×C4⋊(C3⋊C8)C2212yes—
20C3×C4×C3⋊C8C2212yes—
21#63572—21no—
22#63572—21no—
23#63557—21no—
24C4×#237—32no—
25C4×#237—61no—
26D3×C4⋊C8—32no—
27#4685—32no—
28C3×D4⋊C8—32no—
29D4⋊(C3⋊C8)D312yescomplemented
30#4484—32no—
31#4456—32no—
32C2×C32×D4C2×C411yescharacteristic
33C22×C32×C4—21no—
34C2×#638—21no—
35C22×C3⋊Dic3—21no—
36C22×C3⋊Dic3—21no—
37#3830—22no—
38#3830C814yescomplemented
39C2×C4×C3⋊D3C2×C411yescharacteristic
40C2×C4×C3⋊D3D411yescharacteristic
41C2×C4×C3⋊D3D411yescharacteristic
42C2×#634C2×C411yescharacteristic
43C32×C4⋊C4C2×C411yescharacteristic
44C32×C22⋊C4—21no—
45C32×C42C2311yescharacteristic
46#3757—21no—
47#3752—21no—
48C4⋊(C3⋊Dic3)C2×C411yescharacteristic
49#3750—21no—
50#3750—21no—
51C4×C3⋊Dic3—21no—
52C4×C3⋊Dic3—21no—
53C4×C3⋊Dic3—21no—
54C4×C3⋊Dic3C2×C411yescharacteristic
55C4×C3⋊Dic3D411yescharacteristic
56C4×C3⋊Dic3D411yescharacteristic
57C2×C3×C3⋊C8—22no—
58C2×C3×C3⋊C8—22no—
59#3710—42no—
60#1477—91noSylow
61C2×#237—32no—
62C2×#237—61no—
63C3×C4×D4—21no—
64C3×C4×D4C2×D312yes—
65D4×Dic3—32no—
66D4×Dic3—61no—
67C4×#67—62no—
68C4×#67—62no—
69C2×C4×Dic3—62no—
70C2×C4×Dic3—62no—
71C2×D3×C8—62no—
72#892—32no—
73#892—61no—
74#887—32no—
75#887—61no—
76#67⋊C4—62no—
77#67⋊C4—62no—
78#877—62no—
79#877—62no—
80C42×D3—32no—
81C42×D3—61no—
82C4×Dic6—32no—
83C4×Dic6—61no—
84C3×C4⋊C8—32no—
85C3×C4×C8—32no—
86(C2×D3)⋊C8—62no—
87Dic3⋊C8—62no—
88Dic3⋊C8—62no—
89C4⋊(C3⋊C8)C2×D312yes—
90C4×C3⋊C8C2×D312yes—
91C23×C32—21no—
92C22×C3⋊D3C22⋊C411yescharacteristic
93C32×D4—21no—
94C32×D4C2×C812yescomplemented
95C2×C32×C4—21no—
96C2×C32×C4—41no—
97C2×C32×C4—41no—
98C2×C32×C4C22×C411yescharacteristic
99C2×C32×C4C2×D411yescharacteristic
100C2×C32×C4C2×D411yescharacteristic
101#638—24no—
102C2×C3⋊Dic3—21no—
103C2×C3⋊Dic3—24no—
104C2×C3⋊Dic3—21no—
105C2×C3⋊Dic3—42no—
106C2×C3⋊Dic3C22⋊C411yescharacteristic
107C2×C3⋊Dic3C22⋊C411yescharacteristic
108C2×C3⋊Dic3C22⋊C411yescharacteristic
109C4×C3⋊D3—21no—
110C4×C3⋊D3—21no—
111C4×C3⋊D3—41no—
112C4×C3⋊D3C2×C812yes—
113C4×C3⋊D3M1612yes—
114#634—21no—
115#634C2×C812yescomplemented
116C3×C3⋊C8—42no—
117C3×C3⋊C8—42no—
118C4×#41—91no—
119#431—91no—
120C2×C4⋊C8—91no—
121Q8⋊C8—92no—
122D4⋊C8—32no—
123C2×C3×D4—21no—
124C2×C3×D4C4×D312yes—
125C22×C3×C4—22no—
126C22×C3×C4—22no—
127C2×#67—62no—
128C2×#67—62no—
129C22×Dic3—62no—
130C22×Dic3—62no—
131C22×Dic3—62no—
132C22×Dic3—62no—
133#237—38no—
134#237—64no—
135#237—64no—
136#237—64no—
137C2×C4×D3—32no—
138C2×C4×D3—32no—
139C2×C4×D3—32no—
140C2×C4×D3—61no—
141C2×C4×D3—61no—
142C2×C4×D3—61no—
143C2×Dic6—32no—
144C2×Dic6—61no—
145C2×C3×C8—62no—
146C2×C3×C8—62no—
147C3×C4⋊C4—21no—
148C3×C4⋊C4C4×D312yes—
149C3×C22⋊C4—22no—
150C3×C22⋊C4—22no—
151C3×C42—21no—
152C3×C42C22×D312yes—
153#217—62no—
154#217—62no—
155(C2×D3)⋊C4—62no—
156(C2×D3)⋊C4—62no—
157C4⋊Dic3—32no—
158C4⋊Dic3—61no—
159Dic3⋊C4—62no—
160Dic3⋊C4—62no—
161Dic3⋊C4—62no—
162Dic3⋊C4—62no—
163C4×Dic3—32no—
164C4×Dic3—32no—
165C4×Dic3—32no—
166C4×Dic3—61no—
167C4×Dic3—61no—
168C4×Dic3—61no—
169C4×Dic3—62no—
170C4×Dic3—62no—
171C4×Dic3—62no—
172C4×Dic3—62no—
173C4×Dic3—62no—
174C4×Dic3—62no—
175C2×C3⋊C8—22no—
176C2×C3⋊C8—22no—
177D3×C8—124no—
178C22×C32—22no—
179C22×C32—41no—
180C22×C32—41no—
181C22×C32C2×C22⋊C411yescharacteristic
182C2×C3⋊D3—21no—
183C2×C3⋊D3—21no—
184C2×C3⋊D3C22⋊C812yes—
185C32×C4—21no—
186C32×C4—41no—
187C32×C4C22×C811yescharacteristic
188C32×C4C2×M1611yescharacteristic
189C32×C4AGL(1,ℤ/8)11yescharacteristic
190C32×C4#13711yescharacteristic
191C3⋊Dic3—22no—
192C3⋊Dic3—21no—
193C3⋊Dic3—21no—
194C3⋊Dic3—41no—
195C3⋊Dic3C22⋊C812yes—
196C2×#41—91no—
197C22×C8—181no—
198C4×Q8—91no—
199C4×Q8—91no—
200C4×D4—91no—
201C4×D4—181no—
202C4×D4—181no—
203C4×D4D3211yescharacteristic
204#117—91no—
205#117—181no—
206C2×C42—91no—
207C2×C42—181no—
208C4⋊C8—32no—
209C4⋊C8—181no—
210C4⋊C8—181no—
211C22⋊C8—181no—
212C4×C8—32no—
213C23×C3—22no—
214C23×C3—22no—
215C22×D3—32no—
216C22×D3—61no—
217C3×D4—22no—
218C3×D4—22no—
219C3×D4—22no—
220C3×D4D3×C814yescomplemented
221C2×C3×C4—22no—
222C2×C3×C4—22no—
223C2×C3×C4—21no—
224C2×C3×C4—21no—
225C2×C3×C4—21no—
226C2×C3×C4—42no—
227C2×C3×C4—42no—
228C2×C3×C4—42no—
229C2×C3×C4—42no—
230C2×C3×C4C2×C4×D312yes—
231C2×C3×C4D3×D412yes—
232C2×C3×C4D3×D412yes—
233#67—68no—
234#67—68no—
235C2×Dic3—32no—
236C2×Dic3—32no—
237C2×Dic3—32no—
238C2×Dic3—61no—
239C2×Dic3—61no—
240C2×Dic3—61no—
241C2×Dic3—68no—
242C2×Dic3—62no—
243C2×Dic3—68no—
244C2×Dic3—62no—
245C2×Dic3—62no—
246C2×Dic3—62no—
247C2×Dic3—124no—
248C2×Dic3—124no—
249C4×D3—34no—
250C4×D3—34no—
251C4×D3—62no—
252C4×D3—62no—
253C4×D3—62no—
254C4×D3—62no—
255C4×D3—121no—
256C4×D3—121no—
257C4×D3—122no—
258C4×D3—122no—
259Dic6—34no—
260Dic6—62no—
261Dic6—62no—
262Dic6—62no—
263C3×C8—122no—
264C3×C8—122no—
265C3⋊C8—42no—
266C3⋊C8—42no—
267C2×C32—42no—
268C2×C32C2×C22⋊C811yescharacteristic
269C2×C32#41711yescharacteristic
270C2×C32#42111yescharacteristic
271C3⋊D3—22no—
272#41—94no—
273#41—182no—
274C2×Q8—91no—
275C2×D4—181no—
276C2×D4#62411yescharacteristic
277C22×C4—21no—
278C22×C4—91no—
279C22×C4—91no—
280C22×C4—91no—
281C22×C4—181no—
282C22×C4—181no—
283C2×C8—62no—
284C2×C8—62no—
285C2×C8—362no—
286C4⋊C4—91no—
287C4⋊C4—181no—
288C4⋊C4—181no—
289C4⋊C4#62411yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—181no—
292C22⋊C4—181no—
293C42—91no—
294C42—91no—
295C42—91no—
296C42—181no—
297C42—181no—
298C42—181no—
299C42C2×D3211yescharacteristic
300C22×C3—24no—
301C22×C3—24no—
302C22×C3—21no—
303C22×C3—42no—
304C22×C3—42no—
305C22×C3—42no—
306C22×C3—42no—
307C22×C3D3×C22⋊C412yes—
308C2×D3—34no—
309C2×D3—62no—
310C2×D3—62no—
311C2×D3—62no—
312C2×D3—121no—
313C2×D3—121no—
314C3×C4—22no—
315C3×C4—21no—
316C3×C4—21no—
317C3×C4—21no—
318C3×C4—21no—
319C3×C4—41no—
320C3×C4—42no—
321C3×C4—42no—
322C3×C4C2×D3×C812yes—
323C3×C4D3×M1612yes—
324C3×C4#91112yes—
325C3×C4#91512yes—
326Dic3—34no—
327Dic3—62no—
328Dic3—64no—
329Dic3—62no—
330Dic3—64no—
331Dic3—62no—
332Dic3—62no—
333Dic3—121no—
334Dic3—122no—
335Dic3—122no—
336C32#147711yescharacteristic, complemented, Sylow
337C23—21no—
338C23—91no—
339Q8—92no—
340Q8—181no—
341D4—21no—
342D4—184no—
343D4#371012yescomplemented
344C2×C4—21no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—91no—
348C2×C4—92no—
349C2×C4—92no—
350C2×C4—91no—
351C2×C4—91no—
352C2×C4—184no—
353C2×C4—181no—
354C2×C4—181no—
355C2×C4—181no—
356C2×C4—181no—
357C2×C4—361no—
358C2×C4—362no—
359C2×C4C2×#62411yescharacteristic
360C2×C4#381111yescharacteristic
361C2×C4#381111yescharacteristic
362C8—122no—
363C8—122no—
364C2×C3—21no—
365C2×C3—21no—
366C2×C3—21no—
367C2×C3—44no—
368C2×C3—44no—
369C2×C3D3×C22⋊C812yes—
370C2×C3#477112yes—
371C2×C3#482112yes—
372D3—64no—
373D3—122no—
374C22—22no—
375C22—41no—
376C22—41no—
377C22—92no—
378C22—181no—
379C22—181no—
380C22#6397411yescharacteristic
381C4—21no—
382C4—41no—
383C4—92no—
384C4—182no—
385C4—181no—
386C4—181no—
387C4—361no—
388C4C2×#371011yescharacteristic
389C4#6381811yescharacteristic
390C4#6392711yescharacteristic
391C4#6393111yescharacteristic
392C3—21no—
393C3#6816612yescomplemented
394C2—42no—
395C2—182no—
396C2#1059115211yescharacteristic
397C2#1059141811yescharacteristic
398C2#1059167211yescharacteristic
subgroupG/H
centerC2×C4#3811
commutatorC32×C4C22×C8
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32C2×C22⋊C4
prime radicalC2×#3830C4
cosocleC32×C42C23
hypercenterC4×D4D32
hypocenterC32#1477
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. #10590331C2semidirect
3. #10590297C2semidirect
4. C3×D4⋊(C3⋊C8)C2semidirect
5. #10589085C2semidirect
29. D4⋊(C3⋊C8)D3semidirect
38. #3830C8semidirect
94. C32×D4C2×C8semidirect
115. #634C2×C8semidirect
220. C3×D4D3×C8semidirect
336. C32#1477semidirect
343. D4#3710semidirect
393. C3#68166semidirect

Maximal subgroups

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

subgroupindex
C4×#38302
#105903312
#105902972
C3×D4⋊(C3⋊C8)2
#105890852
#681663