Finite Group Databasebeta

← #11779643

Subgroups — #11779643

Order 1152.

497 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 497 conjugacy classes of subgroups — too many to draw. Only its 104 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
1C3×D4×Dic6C211yesmaximal, characteristic
2C3×#5008C211yesmaximal, characteristic
3#10590310C211yesmaximal, characteristic, complemented
4#10590290C211yesmaximal, characteristic, complemented
5D4⋊(C3⋊(C3⋊C8))C211yesmaximal, characteristic
6#10589092C211yesmaximal, characteristic, complemented
7#10589083C211yesmaximal, characteristic, complemented
8#71915—31nomaximal
9#71142—31nomaximal
10C22×C3×Dic6—21no—
11C32×C4×D4C2211yescharacteristic
12C3×D4×Dic3—21no—
13C3×#924—21no—
14C3×#888—21no—
15C3×#878—22no—
16C3×#869C2211yescharacteristic
17C3×#869C2211yescharacteristic
18C3×C4×Dic6C2211yescharacteristic
19C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
20C4×C3⋊(C3⋊C8)C2211yescharacteristic
21C3×#832—21no—
22C3×#808—21no—
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24#63576—21no—
25#63565—21no—
26#63565—22no—
27C3×D4×Q8—31no—
28D4×Dic6D311yescharacteristic
29C3×#476—31no—
30#5093—31no—
31#5091—31no—
32#5079—31no—
33#5021—31no—
34#5008D311yescharacteristic
35#4547—31no—
36#4535—31no—
37D4⋊(C3⋊C8)—31no—
38D4⋊(C3⋊C8)—31no—
39D4⋊(C3⋊C8)—61no—
40#4486—31no—
41#4484—31no—
42C2×C32×D4D411yescharacteristic
43C22×C32×C4—21no—
44C22×C3×Dic3—22no—
45C2×C3×Dic6—22no—
46C2×C3×Dic6—21no—
47C2×C3×Dic6—21no—
48C2×C3×Dic6—42no—
49C2×C3×Dic6—42no—
50C2×C3×Dic6D411yescharacteristic
51C32×C4⋊C4D411yescharacteristic
52C32×C22⋊C4—21no—
53C32×C42C2311yescharacteristic
54C2×C3⋊(C3⋊C8)—21no—
55C2×C3⋊(C3⋊C8)—21no—
56C3×#217—22no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3D412yes—
61C3×C4⋊Dic3D411yescharacteristic
62C3×Dic3⋊C4—22no—
63C3×Dic3⋊C4—21no—
64C3×C4×Dic3—21no—
65C2×C3×C3⋊C8—21no—
66#1637—91noSylow
67C22×C3×Q8—61no—
68C22×Dic6—21no—
69C3×C4⋊Q8—31no—
70C3×C4⋊Q8—31no—
71C3×C4⋊Q8—61no—
72C3×C22⋊Q8—62no—
73C3×C22⋊Q8—61no—
74C3×C4×Q8—31no—
75C3×C4×D4—21no—
76C3×C4×D4—61no—
77C3×C4×D4C2×D311yescharacteristic
78C3×C4×D4C2×D311yescharacteristic
79D4×Dic3—21no—
80#924—21no—
81#888—21no—
82#878—22no—
83#869C2×D311yescharacteristic
84#869C2×D311yescharacteristic
85C4×Dic6C2×D311yescharacteristic
86C3×#106—61no—
87C3×C4⋊C8—31no—
88C3×#102—61no—
89#835—61no—
90#835—62no—
91#832—21no—
92#810—62no—
93#810—61no—
94#808—21no—
95#807—61no—
96#807—61no—
97C4⋊(C3⋊C8)—31no—
98C4⋊(C3⋊C8)—31no—
99C4⋊(C3⋊C8)—61no—
100C4⋊(C3⋊C8)C2×D311yescharacteristic
101C4×C3⋊C8—31no—
102C4×C3⋊C8—31no—
103C4×C3⋊C8—61no—
104C23×C32—21no—
105C32×D4—21no—
106C32×D4Q1612yes—
107C2×C32×C4—21no—
108C2×C32×C4—41no—
109C2×C32×C4—41no—
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C2×C3×Dic3—21no—
114C2×C3×Dic3—21no—
115C2×C3×Dic3—22no—
116C2×C3×Dic3—44no—
117C2×C3×Dic3—41no—
118C3×Dic6—21no—
119C3×Dic6—44no—
120C3×Dic6—41no—
121C3×Dic6—41no—
122C3×Dic6—42no—
123C3×Dic6SD1612yes—
124C3⋊(C3⋊C8)—41no—
125C3⋊(C3⋊C8)—41no—
126C3×C3⋊C8—41no—
127D4×Q8—31no—
128#487—91no—
129#477—91no—
130#476—31no—
131#332—91no—
132Q8⋊C8—91no—
133D4⋊C8—91no—
134C2×C3×Q8—31no—
135C2×C3×Q8—62no—
136C2×C3×Q8—61no—
137C2×C3×Q8—61no—
138C2×C3×Q8—122no—
139C2×C3×Q8—122no—
140C2×C3×D4—21no—
141C2×C3×D4#6711yescharacteristic
142C2×C3×D4#6711yescharacteristic
143C22×C3×C4—21no—
144C22×C3×C4—21no—
145C22×C3×C4—41no—
146C22×C3×C4—62no—
147C22×Dic3—22no—
148C2×Dic6—22no—
149C2×Dic6—21no—
150C2×Dic6—21no—
151C2×Dic6—42no—
152C2×Dic6—42no—
153C2×Dic6#6711yescharacteristic
154C2×C3×C8—61no—
155C3×C4⋊C4—21no—
156C3×C4⋊C4—31no—
157C3×C4⋊C4—32no—
158C3×C4⋊C4—62no—
159C3×C4⋊C4—61no—
160C3×C4⋊C4—61no—
161C3×C4⋊C4—61no—
162C3×C4⋊C4—61no—
163C3×C4⋊C4#6711yescharacteristic
164C3×C4⋊C4#6711yescharacteristic
165C3×C22⋊C4—21no—
166C3×C22⋊C4—21no—
167C3×C22⋊C4—41no—
168C3×C22⋊C4—62no—
169C3×C42—21no—
170C3×C42—61no—
171C3×C42C22×D311yescharacteristic
172C3×C42C22×D311yescharacteristic
173#217—22no—
174C4⋊Dic3—21no—
175C4⋊Dic3—21no—
176C4⋊Dic3—21no—
177C4⋊Dic3#6711yescharacteristic
178C4⋊Dic3#6712yes—
179Dic3⋊C4—22no—
180Dic3⋊C4—21no—
181C4×Dic3—21no—
182C2×C3⋊C8—21no—
183C2×C3⋊C8—61no—
184C2×C3⋊C8—61no—
185C2×C3⋊C8—61no—
186C2×C3⋊C8—61no—
187C2×C3⋊C8—121no—
188C2×C3⋊C8—121no—
189C22×C32—22no—
190C22×C32—41no—
191C22×C32—41no—
192C22×C32#12011yescharacteristic
193C32×C4—21no—
194C32×C4—41no—
195C32×C4C2×SD1611yescharacteristic
196C32×C4C2×Q1611yescharacteristic
197C32×C4AGL(1,ℤ/8)11yescharacteristic
198C32×C4#13711yescharacteristic
199C3×Dic3—22no—
200C3×Dic3—42no—
201C3×Dic3—41no—
202C3×Dic3—81no—
203C22×Q8—61no—
204C4⋊Q8—31no—
205C4⋊Q8—31no—
206C4⋊Q8—61no—
207C22⋊Q8—62no—
208C22⋊Q8—61no—
209C4×Q8—31no—
210C4×D4—61no—
211C4×D4D3211yescharacteristic
212#107—181no—
213#106—61no—
214C4⋊C8—31no—
215C4⋊C8—91no—
216#103—182no—
217#103—181no—
218#102—61no—
219C4×C8—91no—
220C23×C3—21no—
221C23×C3—21no—
222C23×C3—41no—
223C3×Q8—32no—
224C3×Q8—61no—
225C3×Q8—122no—
226C3×Q8—124no—
227C3×Q8—121no—
228C3×Q8—121no—
229C3×D4—21no—
230C3×D4—21no—
231C3×D4—22no—
232C3×D4—41no—
233C3×D4#21612yes—
234C3×D4#21612yes—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—21no—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—41no—
241C2×C3×C4—41no—
242C2×C3×C4—41no—
243C2×C3×C4—41no—
244C2×C3×C4—41no—
245C2×C3×C4—61no—
246C2×C3×C4—61no—
247C2×C3×C4—62no—
248C2×C3×C4—81no—
249C2×C3×C4—81no—
250C2×C3×C4—124no—
251C2×C3×C4—121no—
252C2×C3×C4D3×D411yescharacteristic
253C2×C3×C4D3×D411yescharacteristic
254C2×C3×C4C2×#6711yescharacteristic
255C2×C3×C4C2×#6711yescharacteristic
256C2×C3×C4C2×#6711yescharacteristic
257C2×C3×C4C2×#6711yescharacteristic
258C2×Dic3—21no—
259C2×Dic3—21no—
260C2×Dic3—22no—
261C2×Dic3—44no—
262C2×Dic3—41no—
263Dic6—21no—
264Dic6—44no—
265Dic6—41no—
266Dic6—41no—
267Dic6—42no—
268Dic6#21412yes—
269C3×C8—121no—
270C3⋊C8—41no—
271C3⋊C8—121no—
272C3⋊C8—121no—
273C3⋊C8—122no—
274C3⋊C8—121no—
275C3⋊C8—121no—
276C3⋊C8—241no—
277C2×C32—42no—
278C2×C32#45011yescharacteristic
279C2×C32#45111yescharacteristic
280C2×C32#45411yescharacteristic
281C2×Q8—31no—
282C2×Q8—62no—
283C2×Q8—61no—
284C2×Q8—61no—
285C2×Q8—122no—
286C2×Q8—122no—
287C2×D4#62511yescharacteristic
288C22×C4—21no—
289C22×C4—62no—
290C2×C8—61no—
291C2×C8—181no—
292C2×C8—181no—
293C4⋊C4—32no—
294C4⋊C4—31no—
295C4⋊C4—62no—
296C4⋊C4—61no—
297C4⋊C4—61no—
298C4⋊C4—61no—
299C4⋊C4—61no—
300C4⋊C4#62511yescharacteristic
301C22⋊C4—21no—
302C22⋊C4—62no—
303C42—61no—
304C42C2×D3211yescharacteristic
305C22×C3—22no—
306C22×C3—22no—
307C22×C3—21no—
308C22×C3—42no—
309C22×C3—41no—
310C22×C3—41no—
311C22×C3—41no—
312C22×C3—41no—
313C22×C3—81no—
314C22×C3—81no—
315C22×C3#93711yescharacteristic
316C22×C3#95311yescharacteristic
317C3×C4—21no—
318C3×C4—21no—
319C3×C4—21no—
320C3×C4—21no—
321C3×C4—21no—
322C3×C4—21no—
323C3×C4—41no—
324C3×C4—41no—
325C3×C4—41no—
326C3×C4—62no—
327C3×C4—81no—
328C3×C4—122no—
329C3×C4—121no—
330C3×C4—241no—
331C3×C4D3×SD1611yescharacteristic
332C3×C4#91411yescharacteristic
333C3×C4#93211yescharacteristic
334C3×C4C2×#21411yescharacteristic
335C3×C4#94211yescharacteristic
336C3×C4C2×#21611yescharacteristic
337C3×C4C2×#21611yescharacteristic
338C3×C4#95111yescharacteristic
339Dic3—22no—
340Dic3—42no—
341Dic3—41no—
342Dic3—81no—
343C32#163711yescharacteristic, complemented, Sylow
344C23—21no—
345Q8—32no—
346Q8—61no—
347Q8—122no—
348Q8—124no—
349Q8—121no—
350Q8—121no—
351D4—21no—
352D4#371812yes—
353C2×C4—21no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—61no—
357C2×C4—61no—
358C2×C4—62no—
359C2×C4—124no—
360C2×C4—121no—
361C2×C4C2×#62511yescharacteristic
362C2×C4D3×#6711yescharacteristic
363C2×C4D3×#6711yescharacteristic
364C8—121no—
365C8—361no—
366C8—361no—
367C2×C3—21no—
368C2×C3—21no—
369C2×C3—21no—
370C2×C3—42no—
371C2×C3—42no—
372C2×C3—82no—
373C2×C3#505011yescharacteristic
374C2×C3#516911yescharacteristic
375C2×C3#520111yescharacteristic
376C2×C3#521811yescharacteristic
377C2×C3#522811yescharacteristic
378C2×C3#524511yescharacteristic
379C22—22no—
380C22—41no—
381C22—41no—
382C22#6397611yescharacteristic
383C4—21no—
384C4—41no—
385C4—62no—
386C4—121no—
387C4—122no—
388C4—241no—
389C4#6382711yescharacteristic
390C4C2×#371811yescharacteristic
391C4D3×#21411yescharacteristic
392C4#6393411yescharacteristic
393C3—21no—
394C3#7114211yescharacteristic, complemented
395C3#7191511yescharacteristic, complemented
396C2—42no—
397C2#1059118511yescharacteristic
398C2#1059145811yescharacteristic
399C2#1059168411yescharacteristic
subgroupG/H
centerC22#63976
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32#120
prime radicalC2×C32×D4D4
hypercenterC4×D4D32
hypocenterC32#1637
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
3. #10590310C2semidirect
4. #10590290C2semidirect
6. #10589092C2semidirect
7. #10589083C2semidirect
343. C32#1637semidirect
394. C3#71142semidirect
395. C3#71915semidirect

Maximal subgroups

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

subgroupindex
C3×D4×Dic62
C3×#50082
#105903102
#105902902
D4⋊(C3⋊(C3⋊C8))2
#105890922
#105890832
#719153
#711423