Finite Group Databasebeta

← #11774504

Subgroups — #11774504

Order 1152.

679 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595948C211yesmaximal, characteristic
2C3×#4925C211yesmaximal, characteristic, complemented
3C3×C4×#208C211yesmaximal, characteristic, complemented
4#10589082C214yesmaximal, complemented
5#70761—31nomaximal
6#69853—31nomaximal
7C2×#3828—21no—
8C2×C32×C42C2211yescharacteristic
9#64139—21no—
10#64139C412yes—
11#64084—21no—
12#64083C411yescharacteristic
13C4×C4⋊(C3⋊D3)—21no—
14C4×C4⋊(C3⋊D3)C2212yes—
15#64078C411yescharacteristic
16C2×C3×#208—21no—
17C3×#830—21no—
18C3×C4⋊(C3⋊C8)C2212yes—
19C3×#803—21no—
20C3×C4×C3⋊C8—21no—
21C3×C4×C3⋊C8C2212yes—
22#5477—31no—
23#5477—31no—
24#5477—61no—
25C3×#431—31no—
26C3×C4×M16—31no—
27#4925D311yescharacteristic, complemented
28C4×#208D311yescharacteristic, complemented
29#4483—34no—
30#4459—34no—
31C22×C32×C4C2×C411yescharacteristic
32C22×C32×C4D411yescharacteristic
33C22×C32×C4D411yescharacteristic
34C2×#638—22no—
35#3828—44no—
36C2×C4⋊(C3⋊D3)—21no—
37C2×C4⋊(C3⋊D3)—21no—
38C2×C4⋊(C3⋊D3)C2×C412yes—
39C2×C4×C3⋊D3—22no—
40C2×#634—21no—
41C32×C42C2×C411yescharacteristic
42C32×C42D411yescharacteristic
43C32×C42D411yescharacteristic
44C32×C42C2311yescharacteristic
45#3752—22no—
46#3752—22no—
47C4⋊(C3⋊Dic3)—21no—
48C4⋊(C3⋊Dic3)C2×C412yes—
49C3×#208—24no—
50C2×C3×C3⋊C8—22no—
51C2×C3×C3⋊C8—22no—
52#1484—91noSylow
53C2×#235—62no—
54C2×#235—61no—
55C2×#235—61no—
56C2×C3×M16—61no—
57C2×C3×C42—21no—
58C2×C3×C42C2×D311yescharacteristic
59C2×C3×C42C2×D311yescharacteristic
60#930—32no—
61#930—32no—
62#930—62no—
63#930—62no—
64#930—61no—
65#930—61no—
66C2×#208—21no—
67#875—62no—
68#875—61no—
69#875—61no—
70#874—31no—
71#874—31no—
72#874—61no—
73C4×D12—32no—
74C4×D12—32no—
75C4×D12—62no—
76C4×D12—62no—
77C4×D12—61no—
78C4×D12—61no—
79#869—31no—
80#869—31no—
81#869—61no—
82C3×C4⋊C8—32no—
83C3×C22⋊C8—61no—
84C3×#97—61no—
85C3×C4×C8—32no—
86C3×C4×C8—61no—
87#830—21no—
88C4⋊(C3⋊C8)C2×D312yes—
89#803—21no—
90C4×C3⋊C8—21no—
91C4×C3⋊C8C2×D312yes—
92C23×C32C22⋊C411yescharacteristic
93C22×C3⋊D3—22no—
94C2×C32×C4—22no—
95C2×C32×C4—22no—
96C2×C32×C4—22no—
97C2×C32×C4C22⋊C411yescharacteristic
98C2×C32×C4C22⋊C411yescharacteristic
99C2×C32×C4C22⋊C411yescharacteristic
100C2×C32×C4C22×C411yescharacteristic
101C2×C32×C4C2×D411yescharacteristic
102C2×C32×C4C2×D411yescharacteristic
103#638—44no—
104C2×C3⋊Dic3—22no—
105C4⋊(C3⋊D3)—24no—
106C4⋊(C3⋊D3)—42no—
107C4⋊(C3⋊D3)—42no—
108C4×C3⋊D3—44no—
109#634—42no—
110C3×C3⋊C8—24no—
111C3×C3⋊C8—42no—
112#532—91no—
113#431—31no—
114C4×M16—31no—
115D4⋊C8—94no—
116C22×C3×C4—21no—
117C22×C3×C4—21no—
118C22×C3×C4—21no—
119C22×C3×C4C4×D311yescharacteristic
120C22×C3×C4C4×D311yescharacteristic
121C22×C3×C4D1211yescharacteristic
122C22×C3×C4D1211yescharacteristic
123C22×C3×C4#6711yescharacteristic
124C22×C3×C4#6711yescharacteristic
125C2×#67—64no—
126C2×#67—62no—
127C2×#67—62no—
128#235—128no—
129#235—124no—
130#235—124no—
131C2×D12—32no—
132C2×D12—32no—
133C2×D12—62no—
134C2×D12—62no—
135C2×D12—62no—
136C2×D12—61no—
137C2×D12—61no—
138C2×D12—61no—
139C2×D12—61no—
140C2×C4×D3—64no—
141C2×C4×D3—62no—
142C2×C4×D3—62no—
143C2×Dic6—62no—
144C2×Dic6—61no—
145C2×Dic6—61no—
146C3×M16—64no—
147C2×C3×C8—62no—
148C2×C3×C8—62no—
149C3×C42—21no—
150C3×C42—21no—
151C3×C42—21no—
152C3×C42—21no—
153C3×C42C4×D311yescharacteristic
154C3×C42C4×D311yescharacteristic
155C3×C42D1211yescharacteristic
156C3×C42D1211yescharacteristic
157C3×C42#6711yescharacteristic
158C3×C42#6711yescharacteristic
159C3×C42C22×D311yescharacteristic
160C3×C42C22×D311yescharacteristic
161(C2×D3)⋊C4—64no—
162(C2×D3)⋊C4—64no—
163(C2×D3)⋊C4—62no—
164(C2×D3)⋊C4—62no—
165(C2×D3)⋊C4—62no—
166(C2×D3)⋊C4—62no—
167C4⋊Dic3—32no—
168C4⋊Dic3—32no—
169C4⋊Dic3—62no—
170C4⋊Dic3—62no—
171C4⋊Dic3—61no—
172C4⋊Dic3—61no—
173#208—24no—
174C2×C3⋊C8—22no—
175C2×C3⋊C8—22no—
176C22×C32—21no—
177C22×C32—21no—
178C22×C32—21no—
179C22×C32C2×C22⋊C411yescharacteristic
180C2×C3⋊D3—42no—
181C2×C3⋊D3—42no—
182C2×C3⋊D3—42no—
183C32×C4—21no—
184C32×C4—21no—
185C32×C4—21no—
186C32×C4#10412yes—
187C32×C4#13112yes—
188C32×C4AGL(1,ℤ/8)12yes—
189C3⋊Dic3—42no—
190C2×#41—181no—
191C2×M16—61no—
192C4⋊Q8—91no—
193#127—91no—
194#124—181no—
195#121—92no—
196#121—181no—
197C4×D4—92no—
198C4×D4—181no—
199C2×C42D3211yescharacteristic
200C4⋊C8—32no—
201C22⋊C8—61no—
202#97—61no—
203C4×C8—32no—
204C4×C8—61no—
205C23×C3—21no—
206C23×C3(C2×D3)⋊C411yescharacteristic
207C23×C3(C2×D3)⋊C411yescharacteristic
208C22×D3—64no—
209C22×D3—62no—
210C22×D3—62no—
211C2×C3×C4—24no—
212C2×C3×C4—22no—
213C2×C3×C4—22no—
214C2×C3×C4—22no—
215C2×C3×C4—22no—
216C2×C3×C4—22no—
217C2×C3×C4—22no—
218C2×C3×C4—21no—
219C2×C3×C4—21no—
220C2×C3×C4—21no—
221C2×C3×C4—21no—
222C2×C3×C4—21no—
223C2×C3×C4—21no—
224C2×C3×C4—42no—
225C2×C3×C4—42no—
226C2×C3×C4(C2×D3)⋊C411yescharacteristic
227C2×C3×C4(C2×D3)⋊C411yescharacteristic
228C2×C3×C4(C2×D3)⋊C411yescharacteristic
229C2×C3×C4(C2×D3)⋊C411yescharacteristic
230C2×C3×C4(C2×D3)⋊C411yescharacteristic
231C2×C3×C4(C2×D3)⋊C411yescharacteristic
232C2×C3×C4C2×C4×D311yescharacteristic
233C2×C3×C4C2×C4×D311yescharacteristic
234C2×C3×C4C2×D1211yescharacteristic
235C2×C3×C4C2×D1211yescharacteristic
236C2×C3×C4C2×#6711yescharacteristic
237C2×C3×C4C2×#6711yescharacteristic
238#67—128no—
239#67—124no—
240#67—124no—
241C2×Dic3—64no—
242C2×Dic3—62no—
243C2×Dic3—62no—
244D12—64no—
245D12—64no—
246D12—124no—
247D12—124no—
248D12—124no—
249D12—122no—
250D12—122no—
251D12—122no—
252D12—122no—
253C4×D3—128no—
254C4×D3—124no—
255C4×D3—124no—
256Dic6—124no—
257Dic6—122no—
258Dic6—122no—
259C3×C8—64no—
260C3×C8—122no—
261C3⋊C8—24no—
262C3⋊C8—42no—
263C2×C32—41no—
264C2×C32#40811yescharacteristic
265C2×C32#41811yescharacteristic
266C2×C32C2×#10411yescharacteristic
267C3⋊D3—82no—
268#41—364no—
269C2×Q8—181no—
270C2×D4—92no—
271C2×D4—182no—
272C2×D4—181no—
273C2×D4—181no—
274C22×C4—182no—
275C22×C4#62411yescharacteristic
276C22×C4#62611yescharacteristic
277C22×C4#62611yescharacteristic
278M16—64no—
279C2×C8—62no—
280C2×C8—62no—
281C4⋊C4—92no—
282C4⋊C4—181no—
283C22⋊C4—182no—
284C22⋊C4—182no—
285C42#62411yescharacteristic
286C42#62611yescharacteristic
287C42#62611yescharacteristic
288C42C2×D3211yescharacteristic
289C22×C3—22no—
290C22×C3—21no—
291C22×C3—21no—
292C22×C3—21no—
293C22×C3—21no—
294C22×C3—21no—
295C22×C3—21no—
296C22×C3—21no—
297C22×C3—41no—
298C22×C3—41no—
299C22×C3C2×(C2×D3)⋊C411yescharacteristic
300C22×C3C2×(C2×D3)⋊C411yescharacteristic
301C2×D3—124no—
302C2×D3—124no—
303C2×D3—124no—
304C2×D3—122no—
305C2×D3—122no—
306C2×D3—122no—
307C2×D3—122no—
308C2×D3—122no—
309C2×D3—122no—
310C3×C4—22no—
311C3×C4—21no—
312C3×C4—21no—
313C3×C4—21no—
314C3×C4—21no—
315C3×C4—21no—
316C3×C4—21no—
317C3×C4—22no—
318C3×C4—22no—
319C3×C4—22no—
320C3×C4—41no—
321C3×C4—41no—
322C3×C4#80512yes—
323C3×C4#82512yes—
324C3×C4#90112yes—
325C3×C4#90712yes—
326C3×C4#90812yes—
327C3×C4#94912yes—
328Dic3—124no—
329Dic3—122no—
330Dic3—122no—
331C32#148411yescharacteristic, complemented, Sylow
332C23—182no—
333C23#372211yescharacteristic
334Q8—362no—
335D4—184no—
336D4—362no—
337D4—364no—
338D4—362no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—182no—
343C2×C4—364no—
344C2×C4#372211yescharacteristic
345C2×C4#372211yescharacteristic
346C2×C4#372211yescharacteristic
347C2×C4C2×#62411yescharacteristic
348C2×C4C2×#62611yescharacteristic
349C2×C4C2×#62611yescharacteristic
350C8—64no—
351C8—122no—
352C2×C3—21no—
353C2×C3—21no—
354C2×C3—21no—
355C2×C3—42no—
356C2×C3—41no—
357C2×C3—41no—
358C2×C3C2×#80511yescharacteristic
359C2×C3#500111yescharacteristic
360C2×C3#511011yescharacteristic
361C2×C3#512911yescharacteristic
362C2×C3#513111yescharacteristic
363C2×C3C2×#82511yescharacteristic
364D3—244no—
365D3—242no—
366D3—242no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—362no—
371C22—362no—
372C22—362no—
373C22C2×#372211yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—362no—
378C4#6357012yes—
379C4#6381712yes—
380C4#6382512yes—
381C3—21no—
382C3#6985311yescharacteristic, complemented
383C3#7076111yescharacteristic, complemented
384C2—41no—
385C2—722no—
386C2#1059107311yescharacteristic
387C2#1059109611yescharacteristic
388C2C2×#6357011yescharacteristic
subgroupG/H
centerC2×C4C2×#626
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC2×C32×C42C22
socleC22×C32C2×C22⋊C4
prime radical#10595948C2
cosocleC32×C42C23
hypercenterC2×C42D32
hypocenterC32#1484
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C3×#4925C2semidirect
3. C3×C4×#208C2semidirect
4. #10589082C2semidirect
27. #4925D3semidirect
28. C4×#208D3semidirect
331. C32#1484semidirect
382. C3#69853semidirect
383. C3#70761semidirect

Maximal subgroups

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

subgroupindex
#105959482
C3×#49252
C3×C4×#2082
#105890822
#707613
#698533