Finite Group Databasebeta

← #11779974

Subgroups — #11779974

Order 1152.

470 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 100 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×#5543C211yesmaximal, characteristic
2#10592706C211yesmaximal, characteristic
3#10590385C211yesmaximal, characteristic, complemented
4#10590287C211yesmaximal, characteristic, complemented
5C3×D4⋊(C3⋊C8)C211yesmaximal, characteristic
6#10589095C211yesmaximal, characteristic, complemented
7#10589084C211yesmaximal, characteristic, complemented
8#71926—31nomaximal
9#68191—31nomaximal
10C32×C4×D4C2211yescharacteristic
11#64078C2211yescharacteristic
12C3×D4×Dic3—21no—
13C2×C3×C4⋊Dic3—21no—
14C3×#924—21no—
15C3×#890—21no—
16C3×#878—22no—
17C3×#869C2211yescharacteristic
18C3×C4×Dic6C2211yescharacteristic
19C2×#3719—21no—
20#63659—21no—
21#63634—21no—
22C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25#63567—21no—
26#63566—22no—
27C3×#554—31no—
28#5543D311yescharacteristic
29#5079—31no—
30#5031—31no—
31#5007—31no—
32#5007—31no—
33#5007—61no—
34#4849—31no—
35#4681—31no—
36C3×D4⋊C8—31no—
37#4546—31no—
38#4535—31no—
39D4⋊(C3⋊C8)D311yescharacteristic
40#4481—31no—
41#4456—31no—
42C2×C32×D4D411yescharacteristic
43C22×C32×C4—21no—
44C2×#634—21no—
45C22×C3×Dic3—22no—
46C2×C3×Dic6D411yescharacteristic
47C2×C3×Dic6D412yes—
48C32×C4⋊C4D411yescharacteristic
49C32×C22⋊C4—21no—
50C32×C42C2311yescharacteristic
51C4⋊(C3⋊Dic3)—21no—
52C4⋊(C3⋊Dic3)—21no—
53C2×C3⋊(C3⋊C8)—21no—
54C3×#217—22no—
55C3×C4⋊Dic3—22no—
56C3×C4⋊Dic3—21no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3D411yescharacteristic
59C3×Dic3⋊C4—22no—
60C3×Dic3⋊C4—21no—
61C3×C4×Dic3—21no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64#3719—42no—
65#1644—91noSylow
66C3×C4⋊Q8—31no—
67C3×#125—61no—
68C3×C22⋊Q8—62no—
69C3×C22⋊Q8—61no—
70C3×C4×Q8—31no—
71C3×C4×D4—21no—
72C3×C4×D4—61no—
73C3×C4×D4C2×D311yescharacteristic
74C3×C4×D4C2×D311yescharacteristic
75C2×C3×C4⋊C4—61no—
76C2×#216—61no—
77D4×Dic3—21no—
78C2×C4⋊Dic3—21no—
79#924—21no—
80C2×Dic12—61no—
81#890—21no—
82#878—22no—
83#869—31no—
84#869—31no—
85#869—61no—
86#869C2×D311yescharacteristic
87C4×Dic6C2×D311yescharacteristic
88C3×C4⋊C8—31no—
89C3×C4×C8—31no—
90#835—62no—
91#832—62no—
92#832—61no—
93#832—61no—
94#816—62no—
95#816—61no—
96#810—61no—
97#807—62no—
98#807—61no—
99#807—61no—
100C4⋊(C3⋊C8)—31no—
101C4⋊(C3⋊C8)—31no—
102C4⋊(C3⋊C8)—61no—
103C4⋊(C3⋊C8)C2×D311yescharacteristic
104C4×C3⋊C8C2×D311yescharacteristic
105C23×C32—21no—
106C32×D4—21no—
107C32×D4Q1612yescomplemented
108C2×C32×C4—21no—
109C2×C32×C4—41no—
110C2×C32×C4—41no—
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C2×C3⋊Dic3—41no—
115#634—41no—
116#634—41no—
117C2×C3×Dic3—21no—
118C2×C3×Dic3—21no—
119C2×C3×Dic3—22no—
120C2×C3×Dic3—82no—
121C3×Dic6—21no—
122C3×Dic6—21no—
123C3×Dic6—42no—
124C3⋊(C3⋊C8)—41no—
125C3×C3⋊C8—41no—
126C3×C3⋊C8—41no—
127#554—31no—
128#487—91no—
129#474—91no—
130#462—91no—
131#333—91no—
132Q8⋊C8—91no—
133D4⋊C8—31no—
134C2×C3×Q8—31no—
135C2×C3×Q8—32no—
136C2×C3×D4—21no—
137C2×C3×D4D1211yescharacteristic
138C2×C3×D4#6711yescharacteristic
139C22×C3×C4—21no—
140C22×C3×C4—21no—
141C22×C3×C4—41no—
142C22×C3×C4—62no—
143C22×Dic3—22no—
144C2×Dic6—61no—
145C2×Dic6—61no—
146C2×Dic6—121no—
147C2×Dic6#6711yescharacteristic
148C2×Dic6#6712yes—
149C2×C3×C8—61no—
150C2×C3×C8—61no—
151C3×C4⋊C4—21no—
152C3×C4⋊C4—31no—
153C3×C4⋊C4—62no—
154C3×C4⋊C4—62no—
155C3×C4⋊C4—61no—
156C3×C4⋊C4—61no—
157C3×C4⋊C4—61no—
158C3×C4⋊C4D1211yescharacteristic
159C3×C4⋊C4#6711yescharacteristic
160C3×C22⋊C4—21no—
161C3×C22⋊C4—21no—
162C3×C22⋊C4—41no—
163C3×C22⋊C4—62no—
164C3×C42—21no—
165C3×C42—61no—
166C3×C42C22×D311yescharacteristic
167C3×C42C22×D311yescharacteristic
168#217—22no—
169#216—122no—
170C4⋊Dic3—22no—
171C4⋊Dic3—21no—
172C4⋊Dic3—21no—
173C4⋊Dic3—62no—
174C4⋊Dic3—61no—
175C4⋊Dic3—61no—
176C4⋊Dic3—61no—
177C4⋊Dic3—61no—
178C4⋊Dic3—121no—
179C4⋊Dic3#6711yescharacteristic
180Dic3⋊C4—22no—
181Dic3⋊C4—21no—
182C4×Dic3—21no—
183C2×C3⋊C8—21no—
184C2×C3⋊C8—21no—
185C2×C3⋊C8—62no—
186C2×C3⋊C8—61no—
187C2×C3⋊C8—61no—
188Dic12—122no—
189C22×C32—22no—
190C22×C32—41no—
191C22×C32—41no—
192C22×C32#12011yescharacteristic
193C32×C4—21no—
194C32×C4—41no—
195C32×C4C2×Q1611yescharacteristic
196C32×C4#13511yescharacteristic
197C32×C4AGL(1,ℤ/8)11yescharacteristic
198C32×C4#13711yescharacteristic
199C3⋊Dic3—81no—
200C3×Dic3—41no—
201C3×Dic3—42no—
202C3×Dic3—41no—
203C2×Q16—181no—
204C4⋊Q8—31no—
205C4⋊Q8—91no—
206#125—61no—
207C22⋊Q8—62no—
208C22⋊Q8—61no—
209C4×Q8—31no—
210C4×D4—61no—
211C4×D4D3211yescharacteristic
212C2×C4⋊C4—61no—
213#107—181no—
214C4⋊C8—31no—
215C4⋊C8—91no—
216#103—181no—
217#103—182no—
218#102—181no—
219C4×C8—31no—
220C23×C3—21no—
221C23×C3—21no—
222C23×C3—41no—
223C3×Q8—61no—
224C3×Q8—61no—
225C3×Q8—122no—
226C3×D4—21no—
227C3×D4—21no—
228C3×D4—22no—
229C3×D4—41no—
230C3×D4Dic1212yescomplemented
231C3×D4#21612yescomplemented
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—41no—
238C2×C3×C4—41no—
239C2×C3×C4—41no—
240C2×C3×C4—41no—
241C2×C3×C4—41no—
242C2×C3×C4—61no—
243C2×C3×C4—61no—
244C2×C3×C4—62no—
245C2×C3×C4—81no—
246C2×C3×C4—81no—
247C2×C3×C4—242no—
248C2×C3×C4C2×D1211yescharacteristic
249C2×C3×C4D3×D411yescharacteristic
250C2×C3×C4D3×D411yescharacteristic
251C2×C3×C4C2×#6711yescharacteristic
252C2×C3×C4C2×#6711yescharacteristic
253C2×C3×C4C2×#6711yescharacteristic
254C2×Dic3—21no—
255C2×Dic3—21no—
256C2×Dic3—22no—
257C2×Dic3—82no—
258C2×Dic3—122no—
259C2×Dic3—121no—
260C2×Dic3—121no—
261Dic6—21no—
262Dic6—21no—
263Dic6—42no—
264Dic6—121no—
265Dic6—121no—
266Dic6—121no—
267Dic6—121no—
268Dic6—241no—
269Dic6—241no—
270C3×C8—121no—
271C3×C8—121no—
272C3⋊C8—41no—
273C3⋊C8—41no—
274C3⋊C8—122no—
275C3⋊C8—121no—
276C3⋊C8—121no—
277C2×C32—42no—
278C2×C32#44911yescharacteristic
279C2×C32#45111yescharacteristic
280C2×C32#45511yescharacteristic
281C2×Q8—31no—
282C2×Q8—32no—
283C2×Q8—181no—
284C2×D4#62611yescharacteristic
285C22×C4—21no—
286C22×C4—62no—
287Q16—362no—
288C2×C8—61no—
289C2×C8—61no—
290C2×C8—181no—
291C4⋊C4—31no—
292C4⋊C4—62no—
293C4⋊C4—62no—
294C4⋊C4—61no—
295C4⋊C4—61no—
296C4⋊C4—61no—
297C4⋊C4—181no—
298C4⋊C4—181no—
299C4⋊C4#62611yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—62no—
302C42—61no—
303C42C2×D3211yescharacteristic
304C22×C3—22no—
305C22×C3—22no—
306C22×C3—21no—
307C22×C3—42no—
308C22×C3—41no—
309C22×C3—41no—
310C22×C3—41no—
311C22×C3—41no—
312C22×C3—81no—
313C22×C3—81no—
314C22×C3#88211yescharacteristic
315C22×C3#95311yescharacteristic
316C3×C4—21no—
317C3×C4—21no—
318C3×C4—21no—
319C3×C4—21no—
320C3×C4—21no—
321C3×C4—21no—
322C3×C4—41no—
323C3×C4—41no—
324C3×C4—41no—
325C3×C4—81no—
326C3×C4—121no—
327C3×C4—121no—
328C3×C4—122no—
329C3×C4C2×Dic1211yescharacteristic
330C3×C4#90911yescharacteristic
331C3×C4#91111yescharacteristic
332C3×C4#91611yescharacteristic
333C3×C4#94211yescharacteristic
334C3×C4C2×#21611yescharacteristic
335C3×C4#94911yescharacteristic
336C3×C4#95011yescharacteristic
337Dic3—41no—
338Dic3—42no—
339Dic3—41no—
340Dic3—242no—
341Dic3—241no—
342Dic3—241no—
343C32#164411yescharacteristic, complemented, Sylow
344C23—21no—
345Q8—61no—
346Q8—61no—
347Q8—122no—
348Q8—361no—
349Q8—361no—
350D4—21no—
351D4#371912yescomplemented
352C2×C4—21no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—61no—
356C2×C4—61no—
357C2×C4—62no—
358C2×C4—242no—
359C2×C4—361no—
360C2×C4C2×#62611yescharacteristic
361C2×C4D3×#6711yescharacteristic
362C2×C4D3×#6711yescharacteristic
363C8—121no—
364C8—121no—
365C8—361no—
366C2×C3—21no—
367C2×C3—21no—
368C2×C3—21no—
369C2×C3—42no—
370C2×C3—42no—
371C2×C3—82no—
372C2×C3#473911yescharacteristic
373C2×C3#478111yescharacteristic
374C2×C3#482511yescharacteristic
375C2×C3#522811yescharacteristic
376C2×C3#523811yescharacteristic
377C2×C3#524211yescharacteristic
378C22—22no—
379C22—41no—
380C22—41no—
381C22#6397711yescharacteristic
382C4—21no—
383C4—41no—
384C4—121no—
385C4—122no—
386C4—121no—
387C4—721no—
388C4#6383311yescharacteristic
389C4C2×#371911yescharacteristic
390C4#6392511yescharacteristic
391C4#6393511yescharacteristic
392C3—21no—
393C3#6819111yescharacteristic, complemented
394C3#7192611yescharacteristic, complemented
395C2—42no—
396C2#1059118611yescharacteristic
397C2#1059145211yescharacteristic
398C2#1059168811yescharacteristic
subgroupG/H
centerC22#63977
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32#120
prime radicalC2×C32×D4D4
hypercenterC4×D4D32
hypocenterC32#1644
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. #10590385C2semidirect
4. #10590287C2semidirect
6. #10589095C2semidirect
7. #10589084C2semidirect
107. C32×D4Q16semidirect
230. C3×D4Dic12semidirect
231. C3×D4#216semidirect
343. C32#1644semidirect
351. D4#3719semidirect
393. C3#68191semidirect
394. C3#71926semidirect

Maximal subgroups

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

subgroupindex
C3×#55432
#105927062
#105903852
#105902872
C3×D4⋊(C3⋊C8)2
#105890952
#105890842
#719263
#681913