Finite Group Databasebeta

← #11786376

Subgroups — #11786376

Order 1152.

586 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 586 conjugacy classes of subgroups — too many to draw. Only its 89 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×D32×C8C211yesmaximal, characteristic
2C4×D32⋊C4C211yesmaximal, characteristic
3C2×#63732C211yesmaximal, characteristic, complemented
4C2×D32⋊C8C211yesmaximal, characteristic
5#10590658C211yesmaximal, characteristic, complemented
6#10590181C211yesmaximal, characteristic, complemented
7#10590043C211yesmaximal, characteristic, complemented
8C2×C4×D32C2211yescharacteristic
9C2×C4×#157C2211yescharacteristic
10C2×#3787C2211yescharacteristic
11C2×D32⋊C4C411yescharacteristic
12C2×D32⋊C4C411yescharacteristic
13C2×C8×C3⋊D3C2211yescharacteristic
14C2×C3×D3×C8—21no—
15C4×#624C2211yescharacteristic
16C2×#3710C2211yescharacteristic
17C2×#3710C2211yescharacteristic
18C2×D3×C3⋊C8—21no—
19D32×C8—22no—
20D32×C8—22no—
21#63737C411yescharacteristic
22#63737C411yescharacteristic
23#63732—22no—
24D32⋊C8—22no—
25C3×Dic3⋊C8—21no—
26Dic3⋊(C3⋊C8)—21no—
27C22×D3×C8—61no—
28D3×C4⋊C8—61no—
29C22×D32C2×C411yescharacteristic
30C22×#157C2×C411yescharacteristic
31C22×#157C2×C411yescharacteristic
32C2×C4×C3⋊D3C2311yescharacteristic
33C2×C3×C4×D3—21no—
34C2×#624C2×C411yescharacteristic
35C2×#624C2×C411yescharacteristic
36C2×#624C2×C411yescharacteristic
37C2×D3×Dic3—21no—
38C4×D32—21no—
39C4×D32—21no—
40C4×D32D412yes—
41C4×D32Q812yes—
42C2×#622—21no—
43C4×#157—21no—
44C4×#157—21no—
45#3787—21no—
46#3787—21no—
47D32⋊C4—22no—
48D32⋊C4C814yescomplemented
49C2×C32×C8D411yescharacteristic
50C2×C3⋊(C3⋊C8)D411yescharacteristic
51C8×C3⋊D3—21no—
52C8×C3⋊D3—21no—
53C3×C4×Dic3—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8—21no—
56C3×D3×C8—24no—
57Dic32—21no—
58#3710—21no—
59#3710—21no—
60#3710—21no—
61#3710D412yes—
62D3×C3⋊C8—24no—
63#1850—91nomaximal, Sylow
64C22×C4×D3—61no—
65C22×C3×C8—61no—
66C22×C3⋊C8—61no—
67C2×D3×C8—21no—
68C2×D3×C8—61no—
69C2×D3×C8—61no—
70C2×D3×C8—61no—
71C2×D3×C8—61no—
72C2×D3×C8—64no—
73C2×D3×C8—64no—
74C2×D3×C8—61no—
75C42×D3—61no—
76C3×C4⋊C8—61no—
77Dic3⋊C8—21no—
78Dic3⋊C8—61no—
79C4⋊(C3⋊C8)—61no—
80C22×C3⋊D3C22×C411yescharacteristic
81C22×C3×D3—21no—
82C2×D32—21no—
83C2×D32—21no—
84C2×D32—21no—
85C2×D32C4⋊C412yes—
86C2×D32C2×C812yes—
87C2×D32M1612yes—
88C2×#157—21no—
89C2×#157—21no—
90C2×#157—21no—
91C2×#157—21no—
92C2×#157—21no—
93C2×#157C2×C812yescomplemented
94C2×C32×C4C2×D411yescharacteristic
95C2×C3⋊Dic3#4111yescharacteristic
96C4×C3⋊D3C2×D411yescharacteristic
97C4×C3⋊D3C2×D411yescharacteristic
98C4×C3⋊D3C2×Q811yescharacteristic
99C4×C3⋊D3#4111yescharacteristic
100C2×C3×Dic3—21no—
101C2×C3×Dic3—21no—
102C2×C3×Dic3—21no—
103C3×C4×D3—22no—
104C3×C4×D3—22no—
105#624—21no—
106#624—21no—
107#624—21no—
108#624—21no—
109#624C4⋊C412yes—
110#624C2×C812yescomplemented
111D3×Dic3—22no—
112D3×Dic3—22no—
113#622—41no—
114C32×C8—21no—
115C3⋊(C3⋊C8)—21no—
116C3×C3⋊C8—22no—
117C3×C3⋊C8—41no—
118C23×C8—91no—
119C2×C4⋊C8—91no—
120C2×C4⋊C8—91no—
121C2×C22⋊C8—91no—
122C4×C22⋊C4—91no—
123#336—91no—
124#336—91no—
125C23×D3—61no—
126C22×C3×C4—61no—
127C22×Dic3—61no—
128C2×C4×D3—21no—
129C2×C4×D3—62no—
130C2×C4×D3—62no—
131C2×C4×D3—61no—
132C2×C4×D3—61no—
133C2×C4×D3—61no—
134C2×C4×D3—61no—
135C2×C4×D3—61no—
136C2×C4×D3—62no—
137C2×C4×D3—62no—
138C2×C4×D3—61no—
139C2×C3×C8—21no—
140C2×C3×C8—21no—
141C2×C3×C8—64no—
142C2×C3×C8—61no—
143C2×C3×C8—61no—
144C3×C42—61no—
145C4×Dic3—21no—
146C4×Dic3—61no—
147C4×Dic3—61no—
148C2×C3⋊C8—21no—
149C2×C3⋊C8—21no—
150C2×C3⋊C8—61no—
151C2×C3⋊C8—61no—
152C2×C3⋊C8—64no—
153D3×C8—24no—
154D3×C8—62no—
155D3×C8—62no—
156D3×C8—62no—
157D3×C8—62no—
158D3×C8—64no—
159D3×C8—121no—
160D3×C8—121no—
161D3×C8—121no—
162D3×C8—121no—
163C22×C32C4×D411yescharacteristic
164C2×C3⋊D3C2×C4⋊C411yescharacteristic
165C2×C3⋊D3C4×D411yescharacteristic
166C2×C3⋊D3C22×C811yescharacteristic
167C2×C3⋊D3C2×M1611yescharacteristic
168C2×C3⋊D3#13111yescharacteristic
169C2×C3⋊D3#13111yescharacteristic
170C2×C3×D3—22no—
171C2×C3×D3—22no—
172C2×C3×D3—22no—
173D32—22no—
174D32—22no—
175D32—22no—
176D32C4⋊C814yescomplemented
177#157—22no—
178#157—41no—
179C32×C4#12011yescharacteristic
180C32×C4C22⋊Q811yescharacteristic
181C3⋊Dic3C22⋊Q811yescharacteristic
182C3⋊Dic3#12311yescharacteristic
183C3×Dic3—22no—
184C3×Dic3—22no—
185C3×Dic3—41no—
186C23×C4—91no—
187C22×C8—61no—
188C22×C8—91no—
189C22×C8—91no—
190C22×C8—91no—
191C22×C8—91no—
192C22×C8—182no—
193C22×C8—182no—
194C22×C8—181no—
195C2×C22⋊C4—91no—
196C2×C22⋊C4—91no—
197C2×C42—91no—
198C2×C42—91no—
199C4⋊C8—61no—
200C4⋊C8—181no—
201C4⋊C8—182no—
202C22⋊C8—182no—
203#95—91no—
204#95—91no—
205C23×C3—61no—
206C22×D3—21no—
207C22×D3—62no—
208C22×D3—62no—
209C22×D3—62no—
210C22×D3—61no—
211C22×D3—61no—
212C22×D3—62no—
213C22×D3—62no—
214C22×D3—62no—
215C2×C3×C4—21no—
216C2×C3×C4—21no—
217C2×C3×C4—62no—
218C2×C3×C4—62no—
219C2×C3×C4—61no—
220C2×C3×C4—61no—
221C2×C3×C4—61no—
222C2×Dic3—21no—
223C2×Dic3—21no—
224C2×Dic3—21no—
225C2×Dic3—61no—
226C2×Dic3—61no—
227C2×Dic3—62no—
228C2×Dic3—62no—
229C4×D3—22no—
230C4×D3—22no—
231C4×D3—62no—
232C4×D3—62no—
233C4×D3—61no—
234C4×D3—61no—
235C4×D3—61no—
236C4×D3—61no—
237C4×D3—61no—
238C4×D3—61no—
239C4×D3—61no—
240C4×D3—61no—
241C4×D3—62no—
242C4×D3—62no—
243C4×D3—62no—
244C4×D3—62no—
245C4×D3—121no—
246C4×D3—121no—
247C3×C8—22no—
248C3×C8—41no—
249C3×C8—62no—
250C3×C8—121no—
251C3⋊C8—22no—
252C3⋊C8—41no—
253C3⋊C8—62no—
254C3⋊C8—121no—
255C2×C32#38511yescharacteristic
256C2×C32C8×D411yescharacteristic
257C2×C32#43511yescharacteristic
258C3⋊D3C2×C4⋊C811yescharacteristic
259C3⋊D3#42411yescharacteristic
260C3⋊D3C8×D411yescharacteristic
261C3⋊D3#43511yescharacteristic
262C3×D3—24no—
263C24—91no—
264C22×C4—61no—
265C22×C4—91no—
266C22×C4—91no—
267C22×C4—92no—
268C22×C4—92no—
269C22×C4—91no—
270C22×C4—91no—
271C22×C4—91no—
272C22×C4—91no—
273C22×C4—181no—
274C22×C4—181no—
275C22×C4—181no—
276C2×C8—64no—
277C2×C8—61no—
278C2×C8—61no—
279C2×C8—92no—
280C2×C8—91no—
281C2×C8—181no—
282C2×C8—181no—
283C2×C8—181no—
284C2×C8—184no—
285C2×C8—181no—
286C2×C8—181no—
287C2×C8—181no—
288C2×C8—181no—
289C2×C8—181no—
290C2×C8GO+(4,𝔽2)11yescharacteristic
291C22⋊C4—94no—
292C22⋊C4—182no—
293C42—61no—
294C42—181no—
295C42—181no—
296C42—181no—
297C22×C3—21no—
298C22×C3—21no—
299C22×C3—62no—
300C22×C3—62no—
301C22×C3—62no—
302C2×D3—22no—
303C2×D3—22no—
304C2×D3—22no—
305C2×D3—64no—
306C2×D3—61no—
307C2×D3—61no—
308C2×D3—61no—
309C2×D3—61no—
310C2×D3—61no—
311C2×D3—61no—
312C2×D3—61no—
313C2×D3—61no—
314C2×D3—61no—
315C2×D3—61no—
316C2×D3—61no—
317C2×D3—61no—
318C2×D3—64no—
319C2×D3—64no—
320C2×D3—64no—
321C3×C4—21no—
322C3×C4—21no—
323C3×C4—21no—
324C3×C4—21no—
325C3×C4—62no—
326C3×C4—62no—
327C3×C4—121no—
328Dic3—22no—
329Dic3—22no—
330Dic3—41no—
331Dic3—61no—
332Dic3—61no—
333Dic3—61no—
334Dic3—61no—
335C32#185011yescharacteristic, complemented, Sylow
336C23—61no—
337C23—92no—
338C23—92no—
339C23—92no—
340C23—91no—
341C23—181no—
342C23—181no—
343C23—181no—
344C2×C4—61no—
345C2×C4—61no—
346C2×C4—62no—
347C2×C4—62no—
348C2×C4—61no—
349C2×C4—92no—
350C2×C4—92no—
351C2×C4—91no—
352C2×C4—91no—
353C2×C4—91no—
354C2×C4—91no—
355C2×C4—91no—
356C2×C4—92no—
357C2×C4—181no—
358C2×C4—181no—
359C2×C4—182no—
360C2×C4—182no—
361C2×C4—181no—
362C2×C4—181no—
363C2×C4—181no—
364C2×C4—181no—
365C2×C4—181no—
366C2×C4—181no—
367C2×C4—181no—
368C2×C4C2×GO+(4,𝔽2)11yescharacteristic
369C8—21no—
370C8—62no—
371C8—121no—
372C8—181no—
373C8—361no—
374C2×C3—21no—
375C2×C3—21no—
376C2×C3—21no—
377C2×C3—21no—
378C2×C3—21no—
379C2×C3—21no—
380C2×C3—64no—
381D3—24no—
382D3—61no—
383D3—61no—
384D3—61no—
385D3—61no—
386D3—61no—
387D3—61no—
388D3—61no—
389D3—61no—
390C22—62no—
391C22—62no—
392C22—62no—
393C22—94no—
394C22—91no—
395C22—91no—
396C22—91no—
397C22—91no—
398C22—91no—
399C22—91no—
400C22—182no—
401C22—182no—
402C22—182no—
403C22C4×GO+(4,𝔽2)11yescharacteristic
404C4—62no—
405C4—62no—
406C4—91no—
407C4—91no—
408C4—121no—
409C4—182no—
410C4—361no—
411C4D32⋊Q811yescharacteristic
412C4#6424111yescharacteristic
413C3—21no—
414C3—21no—
415C2—64no—
416C2—91no—
417C2—91no—
418C2—91no—
419C2—91no—
420C2C8×GO+(4,𝔽2)11yescharacteristic
421C2#1059328211yescharacteristic
422C2#1059339811yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×GO+(4,𝔽2)
commutatorC2×C3⋊D3C22×C8
FittingC2×C32×C8D4
socleC22×C32C4×D4
prime radicalC22×D32C2×C4
cosocleC2×C4×C3⋊D3C23
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#1850
LCSG ▷ C2×C3⋊D3 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
3. C2×#63732C2semidirect
5. #10590658C2semidirect
6. #10590181C2semidirect
7. #10590043C2semidirect
48. D32⋊C4C8semidirect
93. C2×#157C2×C8semidirect
110. #624C2×C8semidirect
176. D32C4⋊C8semidirect
335. C32#1850semidirect

Maximal subgroups

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

subgroupindex
C2×D32×C82
C4×D32⋊C42
C2×#637322
C2×D32⋊C82
#105906582
#105901812
#105900432
#18509