Finite Group Databasebeta

← #11787532

Subgroups — #11787532

Order 1152.

1314 conjugacy classes of subgroups.

The subgroup lattice has 441 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3753C211yesmaximal, characteristic
2C2×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
3C32×#390C211yesmaximal, characteristic, complemented
4C2×#63659C211yesmaximal, characteristic, complemented
5C2×#63636C211yesmaximal, characteristic, complemented
6#10589395C211yesmaximal, characteristic, complemented
7#10589390C211yesmaximal, characteristic, complemented
8#69657—34nomaximal
9C22×C32×D4C2211yescharacteristic
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×C4×C3⋊D3—21no—
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×C32×C22⋊C4—21no—
14C2×C32×C22⋊C4—21no—
15C2×C32×C42C2211yescharacteristic
16C2×#3753—22no—
17C2×#3753—22no—
18C2×#3753C414yescomplemented
19C2×#3752—21no—
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C22×C3⋊(C3⋊C8)C2211yescharacteristic
22C22×C3⋊(C3⋊C8)C2211yescharacteristic
23C4×C4⋊(C3⋊D3)—22no—
24C4×C4⋊(C3⋊D3)—22no—
25#63659—22no—
26#63636—22no—
27C22×#213—34no—
28C2×C4×D12—34no—
29C3×#390D314yescomplemented
30C2×#832—34no—
31C2×#809—34no—
32#4529—34no—
33#4524—34no—
34C24×C32—21no—
35C23×C3⋊D3—21no—
36C2×C32×D4—21no—
37C2×C32×D4—21no—
38C2×C32×D4—21no—
39C2×C32×D4—21no—
40C2×C32×D4—21no—
41C2×C32×D4C2×C412yescomplemented
42C22×C32×C4—21no—
43C22×C32×C4D411yescharacteristic
44C22×C32×C4D411yescharacteristic
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3—21no—
47C2×C4⋊(C3⋊D3)—21no—
48C2×C4⋊(C3⋊D3)—21no—
49C2×C4⋊(C3⋊D3)—21no—
50C2×C4⋊(C3⋊D3)C2×C412yes—
51C2×C4⋊(C3⋊D3)D412yes—
52C2×C4⋊(C3⋊D3)D412yes—
53C2×C4×C3⋊D3—24no—
54C2×C4×C3⋊D3—42no—
55C2×C4×C3⋊D3—42no—
56C32×C4⋊C4—21no—
57C32×C4⋊C4—21no—
58C32×C22⋊C4—42no—
59C32×C22⋊C4—42no—
60C32×C42—21no—
61C32×C42—21no—
62#3753—28no—
63#3752—24no—
64C4⋊(C3⋊Dic3)—21no—
65C4⋊(C3⋊Dic3)D412yes—
66C2×C3⋊(C3⋊C8)—21no—
67C2×C3⋊(C3⋊C8)—21no—
68C2×C3⋊(C3⋊C8)—21no—
69C2×C3⋊(C3⋊C8)—21no—
70C2×C3⋊(C3⋊C8)—21no—
71C2×C3⋊(C3⋊C8)C2×C412yescomplemented
72#1879—91noSylow
73C22×C3×D4C2×D314yes—
74C22×D12—34no—
75C22×C4×D3—64no—
76C2×C3×C4⋊C4C2×D314yes—
77C2×C3×C22⋊C4—24no—
78C2×C3×C22⋊C4—24no—
79C2×C3×C42C2×D314yes—
80C2×#213—316no—
81C2×#213—68no—
82C2×#213—68no—
83C2×(C2×D3)⋊C4—64no—
84C2×C4⋊Dic3—34no—
85C22×C3⋊C8—34no—
86C22×C3⋊C8—34no—
87C4×D12—68no—
88C4×D12—68no—
89#832—68no—
90#809—68no—
91C23×C32—22no—
92C23×C32—41no—
93C23×C32—41no—
94C23×C32—41no—
95C23×C32—41no—
96C23×C32—41no—
97C23×C32—41no—
98C23×C32C2×D411yescharacteristic
99C22×C3⋊D3—22no—
100C22×C3⋊D3—22no—
101C22×C3⋊D3—22no—
102C22×C3⋊D3—41no—
103C22×C3⋊D3—41no—
104C22×C3⋊D3—41no—
105C22×C3⋊D3—41no—
106C32×D4—22no—
107C32×D4—22no—
108C32×D4—41no—
109C32×D4—41no—
110C2×C32×C4—21no—
111C2×C32×C4—21no—
112C2×C32×C4—21no—
113C2×C32×C4—21no—
114C2×C32×C4—21no—
115C2×C32×C4—41no—
116C2×C32×C4—41no—
117C2×C32×C4—41no—
118C2×C32×C4D812yescomplemented
119C2×C32×C4C22×C411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4#4111yescharacteristic
124C2×C32×C4#4111yescharacteristic
125C2×C3⋊Dic3—22no—
126C2×C3⋊Dic3—41no—
127C2×C3⋊Dic3—41no—
128C4⋊(C3⋊D3)—22no—
129C4⋊(C3⋊D3)—22no—
130C4⋊(C3⋊D3)—22no—
131C4⋊(C3⋊D3)C22⋊C414yescomplemented
132C4×C3⋊D3—48no—
133C3⋊(C3⋊C8)—22no—
134C3⋊(C3⋊C8)—41no—
135C22×D8—91no—
136C2×C4×D4—91no—
137C2×#102—91no—
138C2×#102—91no—
139#390C3⋊D311yescharacteristic, complemented
140#340—91no—
141#336—91no—
142C24×C3—24no—
143C23×D3—64no—
144C2×C3×D4—24no—
145C2×C3×D4—24no—
146C2×C3×D4—24no—
147C2×C3×D4—24no—
148C2×C3×D4—24no—
149C2×C3×D4C4×D318yescomplemented
150C22×C3×C4—24no—
151C22×C3×C4#6714yes—
152C22×C3×C4#6714yes—
153C22×C3×C4C22×D314yes—
154C22×Dic3—64no—
155C2×D12—38no—
156C2×D12—38no—
157C2×D12—38no—
158C2×D12—64no—
159C2×D12—64no—
160C2×D12—64no—
161C2×C4×D3—616no—
162C2×C4×D3—128no—
163C2×C4×D3—128no—
164C3×C4⋊C4—24no—
165C3×C4⋊C4—24no—
166C3×C22⋊C4—48no—
167C3×C22⋊C4—48no—
168C3×C42—24no—
169C3×C42—24no—
170#213—632no—
171(C2×D3)⋊C4—616no—
172C4⋊Dic3—38no—
173C4⋊Dic3—64no—
174C2×C3⋊C8—38no—
175C2×C3⋊C8—64no—
176C2×C3⋊C8—64no—
177C2×C3⋊C8—64no—
178C2×C3⋊C8—64no—
179C2×C3⋊C8—64no—
180C22×C32—42no—
181C22×C32—42no—
182C22×C32—42no—
183C22×C32—81no—
184C22×C32—81no—
185C22×C32—81no—
186C22×C32—81no—
187C22×C32C4×D411yescharacteristic
188C22×C32#12011yescharacteristic
189C22×C32#12111yescharacteristic
190C22×C32C2×D811yescharacteristic
191C22×C32#13511yescharacteristic
192C22×C32AGL(1,ℤ/8)11yescharacteristic
193C22×C32AGL(1,ℤ/8)11yescharacteristic
194C2×C3⋊D3—24no—
195C2×C3⋊D3—42no—
196C2×C3⋊D3—42no—
197C2×C3⋊D3—42no—
198C2×C3⋊D3—42no—
199C2×C3⋊D3—42no—
200C2×C3⋊D3—42no—
201C32×C4—22no—
202C32×C4—41no—
203C32×C4—81no—
204C32×C4C2×C22⋊C411yescharacteristic
205C32×C4C4×D411yescharacteristic
206C32×C4#12111yescharacteristic
207C32×C4#12311yescharacteristic
208C3⋊Dic3—42no—
209C22×D4—91no—
210C22×D4C2×C3⋊D311yescharacteristic
211C23×C4—181no—
212C2×D8—94no—
213C2×D8—182no—
214C2×D8—182no—
215C22×C8—91no—
216C22×C8—91no—
217C4×D4—182no—
218C4×D4—182no—
219C2×C4⋊C4—91no—
220C2×C4⋊C4C2×C3⋊D311yescharacteristic
221C2×C22⋊C4—21no—
222C2×C22⋊C4—21no—
223C2×C22⋊C4—181no—
224C2×C42C2×C3⋊D311yescharacteristic
225#102—182no—
226#102—182no—
227C23×C3—28no—
228C23×C3—44no—
229C23×C3—44no—
230C23×C3—44no—
231C23×C3—44no—
232C23×C3—44no—
233C23×C3—44no—
234C23×C3C2×#6714yes—
235C22×D3—68no—
236C22×D3—68no—
237C22×D3—68no—
238C22×D3—124no—
239C22×D3—124no—
240C22×D3—124no—
241C22×D3—124no—
242C3×D4—28no—
243C3×D4—28no—
244C3×D4—44no—
245C3×D4—44no—
246C2×C3×C4—24no—
247C2×C3×C4—24no—
248C2×C3×C4—24no—
249C2×C3×C4—24no—
250C2×C3×C4—24no—
251C2×C3×C4—44no—
252C2×C3×C4—44no—
253C2×C3×C4—44no—
254C2×C3×C4#21318yescomplemented
255C2×C3×C4C2×C4×D314yes—
256C2×C3×C4#23514yes—
257C2×C3×C4D3×D414yes—
258C2×C3×C4D3×D414yes—
259C2×C3×C4D3×D414yes—
260C2×C3×C4#23714yes—
261C2×Dic3—68no—
262C2×Dic3—124no—
263C2×Dic3—124no—
264D12—316no—
265D12—68no—
266D12—68no—
267D12—68no—
268C4×D3—1232no—
269C3⋊C8—68no—
270C3⋊C8—124no—
271C2×C32—82no—
272C2×C32#38611yescharacteristic
273C2×C32C4×D811yescharacteristic
274C2×C32#44211yescharacteristic
275C2×C32#44711yescharacteristic
276C2×C32#44911yescharacteristic
277C2×C32#45911yescharacteristic
278C2×C32#46311yescharacteristic
279C3⋊D3—44no—
280C24—21no—
281C24—181no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—21no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—92no—
288C2×D4—92no—
289C2×D4—92no—
290C2×D4—181no—
291C2×D4—181no—
292C2×D4—181no—
293C2×D4C4×C3⋊D312yescomplemented
294C22×C4—21no—
295C22×C4—184no—
296C22×C4—181no—
297C22×C4—362no—
298C22×C4—362no—
299C22×C4#63811yescharacteristic
300C22×C4#63811yescharacteristic
301C22×C4C22×C3⋊D311yescharacteristic
302D8—188no—
303C2×C8—92no—
304C2×C8—181no—
305C2×C8—181no—
306C2×C8—181no—
307C2×C8—181no—
308C2×C8—181no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—92no—
312C4⋊C4—181no—
313C22⋊C4—42no—
314C22⋊C4—42no—
315C22⋊C4—184no—
316C42—21no—
317C42—21no—
318C22×C3—48no—
319C22×C3—48no—
320C22×C3—48no—
321C22×C3—84no—
322C22×C3—84no—
323C22×C3—84no—
324C22×C3—84no—
325C22×C3C4×#6714yes—
326C22×C3C2×#21314yes—
327C22×C3#93214yes—
328C22×C3#93714yes—
329C22×C3#93814yes—
330C22×C3#94914yes—
331C22×C3#95014yes—
332C2×D3—616no—
333C2×D3—128no—
334C2×D3—128no—
335C2×D3—128no—
336C2×D3—128no—
337C2×D3—128no—
338C2×D3—128no—
339C3×C4—28no—
340C3×C4—44no—
341C3×C4—84no—
342C3×C4D3×C22⋊C414yes—
343C3×C4#67⋊C414yes—
344C3×C4#88314yes—
345C3×C4#88414yes—
346Dic3—128no—
347C32#187911yescharacteristic, complemented, Sylow
348C23—22no—
349C23—41no—
350C23—41no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—182no—
356C23—182no—
357C23—182no—
358C23—361no—
359C23—361no—
360C23—361no—
361C23—361no—
362C23C2×#63811yescharacteristic
363D4—22no—
364D4—22no—
365D4—41no—
366D4—41no—
367D4—94no—
368D4—182no—
369D4—182no—
370D4—182no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—182no—
380C2×C4—368no—
381C2×C4—361no—
382C2×C4—361no—
383C2×C4#375312yescomplemented
384C2×C4C2×C4×C3⋊D311yescharacteristic
385C2×C4#382811yescharacteristic
386C2×C4D4×C3⋊D311yescharacteristic
387C2×C4D4×C3⋊D311yescharacteristic
388C2×C4D4×C3⋊D311yescharacteristic
389C2×C4#383011yescharacteristic
390C8—182no—
391C8—361no—
392C2×C3—88no—
393C2×C3#495614yes—
394C2×C3C4×#21314yes—
395C2×C3#501414yes—
396C2×C3#503614yes—
397C2×C3#503714yes—
398C2×C3#505714yes—
399C2×C3#507214yes—
400D3—1216no—
401C22—42no—
402C22—42no—
403C22—42no—
404C22—81no—
405C22—81no—
406C22—81no—
407C22—81no—
408C22—184no—
409C22—362no—
410C22—362no—
411C22—362no—
412C22—362no—
413C22—362no—
414C22—362no—
415C22C4×#63811yescharacteristic
416C22C2×#375311yescharacteristic
417C22#6414111yescharacteristic
418C22#6414611yescharacteristic
419C22#6414711yescharacteristic
420C22#6415811yescharacteristic
421C22#6415911yescharacteristic
422C4—22no—
423C4—41no—
424C4—81no—
425C4—362no—
426C4C22⋊C4×C3⋊D311yescharacteristic
427C4#6409011yescharacteristic
428C4#6409211yescharacteristic
429C4#6409311yescharacteristic
430C3#6965714yescomplemented
431C2—82no—
432C2—364no—
433C2#1059265511yescharacteristic
434C2C4×#375311yescharacteristic
435C2#1059271311yescharacteristic
436C2#1059273511yescharacteristic
437C2#1059273611yescharacteristic
438C2#1059275611yescharacteristic
439C2#1059277111yescharacteristic
subgroupG/H
centerC23C2×#638
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#390C2
socleC23×C32C2×D4
prime radicalC22×#3753C2
cosocleC22×C32×C4C23
hypercenter#390C3⋊D3
hypocenterC32#1879
LCSG ▷ C2×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. C2×C4×C4⋊(C3⋊D3)C2semidirect
3. C32×#390C2semidirect
4. C2×#63659C2semidirect
5. C2×#63636C2semidirect
6. #10589395C2semidirect
7. #10589390C2semidirect
18. C2×#3753C4semidirect
29. C3×#390D3semidirect
41. C2×C32×D4C2×C4semidirect
71. C2×C3⋊(C3⋊C8)C2×C4semidirect
118. C2×C32×C4D8semidirect
131. C4⋊(C3⋊D3)C22⋊C4semidirect
139. #390C3⋊D3semidirect
149. C2×C3×D4C4×D3semidirect
254. C2×C3×C4#213semidirect
293. C2×D4C4×C3⋊D3semidirect
347. C32#1879semidirect
383. C2×C4#3753semidirect
430. C3#69657semidirect

Maximal subgroups

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

subgroupindex
C22×#37532
C2×C4×C4⋊(C3⋊D3)2
C32×#3902
C2×#636592
C2×#636362
#105893952
#105893902
#696573