Finite Group Databasebeta

← #11794010

Subgroups — #11794010

Order 1152.

1080 conjugacy classes of subgroups.

The subgroup lattice has 429 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3753C211yesmaximal, characteristic
2C32×#390C211yesmaximal, characteristic, complemented
3C2×#63659C211yesmaximal, characteristic, complemented
4C2×#63636C211yesmaximal, characteristic, complemented
5#10592638C211yesmaximal, characteristic, complemented
6C2×C4⋊(C3⋊(C3⋊C8))C211yesmaximal, characteristic, complemented
7#10589395C211yesmaximal, characteristic, complemented
8#69650—34nomaximal
9C22×C32×D4C2211yescharacteristic
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×C32×C22⋊C4—21no—
13C2×C32×C22⋊C4—21no—
14C2×C32×C42C2211yescharacteristic
15C2×#3753—22no—
16C2×#3753—22no—
17C2×#3753—22no—
18C2×#3752—21no—
19C2×#3752—21no—
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C22×C3⋊(C3⋊C8)C2211yescharacteristic
22C22×C3⋊(C3⋊C8)C2211yescharacteristic
23#63659—22no—
24#63636—22no—
25C4⋊(C3⋊(C3⋊C8))—22no—
26C22×#213—34no—
27C3×#390D314yescomplemented
28C2×#832—34no—
29C2×#809—34no—
30#4939—34no—
31C2×C4⋊(C3⋊C8)—34no—
32#4529—34no—
33C24×C32—21no—
34C23×C3⋊D3—21no—
35C2×C32×D4—21no—
36C2×C32×D4—21no—
37C2×C32×D4—21no—
38C2×C32×D4—21no—
39C2×C32×D4—21no—
40C2×C32×D4D412yes—
41C22×C32×C4—21no—
42C22×C32×C4D411yescharacteristic
43C22×C32×C4D411yescharacteristic
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3—21no—
46C2×C4⋊(C3⋊D3)—21no—
47C2×C4⋊(C3⋊D3)—21no—
48C2×C4⋊(C3⋊D3)—21no—
49C2×C4⋊(C3⋊D3)—21no—
50C2×C4⋊(C3⋊D3)—21no—
51C2×C4⋊(C3⋊D3)D412yes—
52C32×C4⋊C4—21no—
53C32×C4⋊C4—21no—
54C32×C22⋊C4—42no—
55C32×C22⋊C4—42no—
56C32×C42—21no—
57C32×C42—21no—
58#3753—28no—
59#3752—42no—
60#3752—42no—
61C4⋊(C3⋊Dic3)—21no—
62C4⋊(C3⋊Dic3)—21no—
63C2×C3⋊(C3⋊C8)—21no—
64C2×C3⋊(C3⋊C8)—21no—
65C2×C3⋊(C3⋊C8)—21no—
66C2×C3⋊(C3⋊C8)—21no—
67C2×C3⋊(C3⋊C8)—21no—
68C2×C3⋊(C3⋊C8)D412yes—
69#2054—91noSylow
70C22×C3×D4C2×D314yes—
71C22×D12—34no—
72C2×C3×C4⋊C4C2×D314yes—
73C2×C3×C22⋊C4—24no—
74C2×C3×C22⋊C4—24no—
75C2×C3×C42C2×D314yes—
76C2×#213—68no—
77C2×#213—68no—
78C2×#213—68no—
79C2×(C2×D3)⋊C4—64no—
80C2×(C2×D3)⋊C4—64no—
81C2×C4⋊Dic3—34no—
82C22×C3⋊C8—34no—
83C22×C3⋊C8—34no—
84#832—68no—
85#809—68no—
86C4⋊(C3⋊C8)—68no—
87C23×C32—22no—
88C23×C32—41no—
89C23×C32—41no—
90C23×C32—41no—
91C23×C32—41no—
92C23×C32—41no—
93C23×C32—41no—
94C23×C32C2×D411yescharacteristic
95C22×C3⋊D3—22no—
96C22×C3⋊D3—41no—
97C22×C3⋊D3—41no—
98C22×C3⋊D3—41no—
99C22×C3⋊D3—41no—
100C22×C3⋊D3—41no—
101C22×C3⋊D3—41no—
102C32×D4—22no—
103C32×D4—22no—
104C32×D4—41no—
105C32×D4—41no—
106C2×C32×C4—21no—
107C2×C32×C4—21no—
108C2×C32×C4—21no—
109C2×C32×C4—21no—
110C2×C32×C4—21no—
111C2×C32×C4—41no—
112C2×C32×C4—41no—
113C2×C32×C4—41no—
114C2×C32×C4D812yescomplemented
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4#4111yescharacteristic
119C2×C32×C4#4111yescharacteristic
120C2×C32×C4#4111yescharacteristic
121C2×C3⋊Dic3—41no—
122C2×C3⋊Dic3—41no—
123C2×C3⋊Dic3—41no—
124C4⋊(C3⋊D3)—22no—
125C4⋊(C3⋊D3)—22no—
126C4⋊(C3⋊D3)—41no—
127C4⋊(C3⋊D3)—41no—
128C3⋊(C3⋊C8)—22no—
129C3⋊(C3⋊C8)—41no—
130C22×D8—91no—
131C2×C4⋊C8—91no—
132C2×#102—91no—
133C2×#102—91no—
134#390—91no—
135#390C3⋊D311yescharacteristic, complemented
136#340—91no—
137C24×C3—24no—
138C23×D3—64no—
139C2×C3×D4—24no—
140C2×C3×D4—24no—
141C2×C3×D4—24no—
142C2×C3×D4—24no—
143C2×C3×D4—24no—
144C2×C3×D4D1218yes—
145C22×C3×C4—24no—
146C22×C3×C4#6714yes—
147C22×C3×C4#6714yes—
148C22×C3×C4C22×D314yes—
149C22×Dic3—64no—
150C2×D12—38no—
151C2×D12—64no—
152C2×D12—64no—
153C2×D12—64no—
154C2×D12—64no—
155C2×D12—64no—
156C3×C4⋊C4—24no—
157C3×C4⋊C4—24no—
158C3×C22⋊C4—48no—
159C3×C22⋊C4—48no—
160C3×C42—24no—
161C3×C42—24no—
162#213—632no—
163(C2×D3)⋊C4—128no—
164(C2×D3)⋊C4—128no—
165C4⋊Dic3—64no—
166C4⋊Dic3—64no—
167C2×C3⋊C8—38no—
168C2×C3⋊C8—64no—
169C2×C3⋊C8—64no—
170C2×C3⋊C8—64no—
171C2×C3⋊C8—64no—
172C2×C3⋊C8—64no—
173C22×C32—42no—
174C22×C32—42no—
175C22×C32—42no—
176C22×C32—81no—
177C22×C32—81no—
178C22×C32—81no—
179C22×C32—81no—
180C22×C32#12111yescharacteristic
181C22×C32#12111yescharacteristic
182C22×C32#12111yescharacteristic
183C22×C32C2×D811yescharacteristic
184C22×C32#13511yescharacteristic
185C22×C32AGL(1,ℤ/8)11yescharacteristic
186C22×C32AGL(1,ℤ/8)11yescharacteristic
187C2×C3⋊D3—42no—
188C2×C3⋊D3—42no—
189C2×C3⋊D3—42no—
190C2×C3⋊D3—81no—
191C2×C3⋊D3—81no—
192C2×C3⋊D3—81no—
193C2×C3⋊D3—81no—
194C32×C4—22no—
195C32×C4—41no—
196C32×C4—81no—
197C32×C4#12011yescharacteristic
198C32×C4#12311yescharacteristic
199C32×C4#12311yescharacteristic
200C32×C4#12411yescharacteristic
201C3⋊Dic3—81no—
202C22×D4—91no—
203C22×D4C2×C3⋊D311yescharacteristic
204C2×D8—182no—
205C2×D8—182no—
206C2×D8—182no—
207C22×C8—91no—
208C22×C8—91no—
209C2×C4⋊C4—91no—
210C2×C4⋊C4C2×C3⋊D311yescharacteristic
211C2×C22⋊C4—21no—
212C2×C22⋊C4—21no—
213C2×C22⋊C4—181no—
214C2×C22⋊C4—181no—
215C2×C42C2×C3⋊D311yescharacteristic
216C4⋊C8—182no—
217#102—182no—
218#102—182no—
219C23×C3—28no—
220C23×C3—44no—
221C23×C3—44no—
222C23×C3—44no—
223C23×C3—44no—
224C23×C3—44no—
225C23×C3—44no—
226C23×C3C2×#6714yes—
227C22×D3—68no—
228C22×D3—124no—
229C22×D3—124no—
230C22×D3—124no—
231C22×D3—124no—
232C22×D3—124no—
233C22×D3—124no—
234C3×D4—28no—
235C3×D4—28no—
236C3×D4—44no—
237C3×D4—44no—
238C2×C3×C4—24no—
239C2×C3×C4—24no—
240C2×C3×C4—24no—
241C2×C3×C4—24no—
242C2×C3×C4—24no—
243C2×C3×C4—44no—
244C2×C3×C4—44no—
245C2×C3×C4—44no—
246C2×C3×C4#21318yescomplemented
247C2×C3×C4C2×D1214yes—
248C2×C3×C4#23514yes—
249C2×C3×C4D3×D414yes—
250C2×C3×C4D3×D414yes—
251C2×C3×C4#23714yes—
252C2×C3×C4#23714yes—
253C2×Dic3—124no—
254C2×Dic3—124no—
255C2×Dic3—124no—
256D12—68no—
257D12—68no—
258D12—124no—
259D12—124no—
260C3⋊C8—68no—
261C3⋊C8—124no—
262C2×C32—82no—
263C2×C32#39411yescharacteristic
264C2×C32#45911yescharacteristic
265C2×C32#45911yescharacteristic
266C2×C32#46311yescharacteristic
267C2×C32#46311yescharacteristic
268C2×C32#46611yescharacteristic
269C2×C32#46911yescharacteristic
270C3⋊D3—82no—
271C24—21no—
272C24—181no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—92no—
279C2×D4—181no—
280C2×D4—181no—
281C2×D4—181no—
282C2×D4—181no—
283C2×D4—181no—
284C2×D4C4⋊(C3⋊D3)12yes—
285C22×C4—21no—
286C22×C4—181no—
287C22×C4#63811yescharacteristic
288C22×C4#63811yescharacteristic
289C22×C4C22×C3⋊D311yescharacteristic
290D8—188no—
291C2×C8—92no—
292C2×C8—181no—
293C2×C8—181no—
294C2×C8—181no—
295C2×C8—181no—
296C2×C8—181no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—181no—
300C4⋊C4—181no—
301C22⋊C4—42no—
302C22⋊C4—42no—
303C22⋊C4—362no—
304C22⋊C4—362no—
305C42—21no—
306C42—21no—
307C22×C3—48no—
308C22×C3—48no—
309C22×C3—48no—
310C22×C3—84no—
311C22×C3—84no—
312C22×C3—84no—
313C22×C3—84no—
314C22×C3#93014yes—
315C22×C3C2×#21314yes—
316C22×C3#93214yes—
317C22×C3#93814yes—
318C22×C3#93914yes—
319C22×C3#94914yes—
320C22×C3#95014yes—
321C2×D3—128no—
322C2×D3—128no—
323C2×D3—128no—
324C2×D3—244no—
325C2×D3—244no—
326C2×D3—244no—
327C2×D3—244no—
328C3×C4—28no—
329C3×C4—44no—
330C3×C4—84no—
331C3×C4#88214yes—
332C3×C4#88314yes—
333C3×C4#88514yes—
334C3×C4#88614yes—
335Dic3—244no—
336C32#205411yescharacteristic, complemented, Sylow
337C23—22no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23—182no—
345C23—361no—
346C23—361no—
347C23—361no—
348C23—361no—
349C23—361no—
350C23—361no—
351C23C2×#63811yescharacteristic
352D4—22no—
353D4—22no—
354D4—41no—
355D4—41no—
356D4—182no—
357D4—182no—
358D4—361no—
359D4—361no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—361no—
369C2×C4—361no—
370C2×C4—361no—
371C2×C4#375312yescomplemented
372C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
373C2×C4#382811yescharacteristic
374C2×C4D4×C3⋊D311yescharacteristic
375C2×C4D4×C3⋊D311yescharacteristic
376C2×C4#383011yescharacteristic
377C2×C4#383011yescharacteristic
378C8—182no—
379C8—361no—
380C2×C3—88no—
381C2×C3#496114yes—
382C2×C3#501514yes—
383C2×C3#501614yes—
384C2×C3#503814yes—
385C2×C3#503914yes—
386C2×C3#505714yes—
387C2×C3#507214yes—
388D3—248no—
389C22—42no—
390C22—42no—
391C22—42no—
392C22—81no—
393C22—81no—
394C22—81no—
395C22—81no—
396C22—362no—
397C22—362no—
398C22—362no—
399C22—721no—
400C22—721no—
401C22—721no—
402C22—721no—
403C22#6413911yescharacteristic
404C22C2×#375311yescharacteristic
405C22#6414111yescharacteristic
406C22#6414711yescharacteristic
407C22#6414811yescharacteristic
408C22#6415811yescharacteristic
409C22#6415911yescharacteristic
410C4—22no—
411C4—41no—
412C4—81no—
413C4—721no—
414C4#6409111yescharacteristic
415C4#6409211yescharacteristic
416C4#6409411yescharacteristic
417C4#6409511yescharacteristic
418C3#6965014yescomplemented
419C2—82no—
420C2—722no—
421C2#1059266011yescharacteristic
422C2#1059271411yescharacteristic
423C2#1059271511yescharacteristic
424C2#1059273711yescharacteristic
425C2#1059273811yescharacteristic
426C2#1059275611yescharacteristic
427C2#1059277111yescharacteristic
subgroupG/H
centerC23C2×#638
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC32×#390C2
socleC23×C32C2×D4
prime radicalC22×#3753C2
hypercenter#390C3⋊D3
hypocenterC32#2054
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C32×#390C2semidirect
3. C2×#63659C2semidirect
4. C2×#63636C2semidirect
5. #10592638C2semidirect
6. C2×C4⋊(C3⋊(C3⋊C8))C2semidirect
7. #10589395C2semidirect
27. C3×#390D3semidirect
114. C2×C32×C4D8semidirect
135. #390C3⋊D3semidirect
246. C2×C3×C4#213semidirect
336. C32#2054semidirect
371. C2×C4#3753semidirect
418. C3#69650semidirect

Maximal subgroups

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

subgroupindex
C22×#37532
C32×#3902
C2×#636592
C2×#636362
#105926382
C2×C4⋊(C3⋊(C3⋊C8))2
#105893952
#696503