Finite Group Databasebeta

← #11787526

Subgroups — #11787526

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×#3745C211yesmaximal, characteristic
2C2×#64102C211yesmaximal, characteristic, complemented
3#10592687C211yesmaximal, characteristic, complemented
4C2×#63636C211yesmaximal, characteristic, complemented
5C2×#63636C211yesmaximal, characteristic, complemented
6C32×#340C211yesmaximal, characteristic, complemented
7#10589416C211yesmaximal, characteristic, complemented
8#68897—34nomaximal
9C22×C4⋊(C3⋊D3)C2211yescharacteristic
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×C4×C3⋊D3—21no—
12C22×C32×C8C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×C32×C4⋊C4C2211yescharacteristic
15C2×#3752—21no—
16C2×#3752—21no—
17C2×#3752—21no—
18C2×C4×C3⋊Dic3C2211yescharacteristic
19C22×C3⋊(C3⋊C8)C2211yescharacteristic
20C2×#3745—22no—
21C2×#3745—22no—
22C2×#3745C414yescomplemented
23#64102—22no—
24#64102—22no—
25#63636—22no—
26#63636—22no—
27C22×D24—34no—
28C2×#893—34no—
29#4988—34no—
30C2×#809—34no—
31C2×#809—34no—
32C3×#340D314yescomplemented
33#4550—34no—
34C23×C3⋊D3—21no—
35C23×C3⋊D3—21no—
36C22×C32×C4—21no—
37C22×C32×C4—21no—
38C22×C32×C4C2311yescharacteristic
39C22×C3⋊Dic3D411yescharacteristic
40C22×C3⋊Dic3D411yescharacteristic
41C2×C4⋊(C3⋊D3)—21no—
42C2×C4⋊(C3⋊D3)—21no—
43C2×C4⋊(C3⋊D3)—21no—
44C2×C4⋊(C3⋊D3)—21no—
45C2×C4⋊(C3⋊D3)—21no—
46C2×C4⋊(C3⋊D3)—21no—
47C2×C4⋊(C3⋊D3)—21no—
48C2×C4⋊(C3⋊D3)—21no—
49C2×C4⋊(C3⋊D3)C2×C412yes—
50C2×C4⋊(C3⋊D3)C2×C412yescomplemented
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—
56C2×C32×C8—21no—
57C2×C32×C8—21no—
58C2×C32×C8C2×C412yescomplemented
59C32×C4⋊C4—21no—
60C32×C4⋊C4—21no—
61C32×C4⋊C4—21no—
62C32×C4⋊C4D412yes—
63#3752—24no—
64#3752—42no—
65#3752—42no—
66C4×C3⋊Dic3—21no—
67C4×C3⋊Dic3—21no—
68C2×C3⋊(C3⋊C8)—21no—
69C2×C3⋊(C3⋊C8)—21no—
70C2×C3⋊(C3⋊C8)—21no—
71#3745—28no—
72#1879—91noSylow
73C22×D12—34no—
74C22×D12—34no—
75C22×C4×D3—64no—
76C22×C3×C8C2×D314yes—
77C2×C3×C4⋊C4C2×D314yes—
78C2×C3×C4⋊C4C2×D314yes—
79C2×(C2×D3)⋊C4—64no—
80C2×(C2×D3)⋊C4—64no—
81C2×(C2×D3)⋊C4—64no—
82C2×C4×Dic3—34no—
83C22×C3⋊C8—34no—
84C2×D24—316no—
85C2×D24—68no—
86C2×D24—68no—
87#893—68no—
88#893—68no—
89#809—68no—
90#809—68no—
91C23×C32C2×D411yescharacteristic
92C22×C3⋊D3—22no—
93C22×C3⋊D3—22no—
94C22×C3⋊D3—22no—
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—
102C22×C3⋊D3—41no—
103C22×C3⋊D3—41no—
104C22×C3⋊D3—41no—
105C22×C3⋊D3—41no—
106C2×C32×C4—22no—
107C2×C32×C4—41no—
108C2×C32×C4—41no—
109C2×C32×C4—41no—
110C2×C32×C4—41no—
111C2×C32×C4—41no—
112C2×C32×C4C22×C411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4#4111yescharacteristic
117C2×C32×C4#4111yescharacteristic
118C2×C3⋊Dic3—21no—
119C2×C3⋊Dic3—21no—
120C2×C3⋊Dic3—21no—
121C2×C3⋊Dic3—21no—
122C2×C3⋊Dic3—21no—
123C2×C3⋊Dic3D812yescomplemented
124C4⋊(C3⋊D3)—22no—
125C4⋊(C3⋊D3)—22no—
126C4⋊(C3⋊D3)—22no—
127C4⋊(C3⋊D3)—22no—
128C4⋊(C3⋊D3)—22no—
129C4⋊(C3⋊D3)—41no—
130C4⋊(C3⋊D3)—41no—
131C4⋊(C3⋊D3)C22⋊C414yescomplemented
132C4×C3⋊D3—48no—
133C32×C8—22no—
134C3⋊(C3⋊C8)—41no—
135C22×D8—91no—
136C2×C4×D4—91no—
137C2×#102—91no—
138C2×#102—91no—
139#390—91no—
140#340C3⋊D311yescharacteristic, complemented
141#336—91no—
142C23×D3—64no—
143C23×D3—64no—
144C22×C3×C4—24no—
145C22×C3×C4—24no—
146C22×C3×C4C22×D314yes—
147C22×Dic3—34no—
148C22×Dic3—34no—
149C2×D12—38no—
150C2×D12—38no—
151C2×D12—38no—
152C2×D12—38no—
153C2×D12—64no—
154C2×D12—64no—
155C2×D12—64no—
156C2×D12—64no—
157C2×D12—64no—
158C2×D12—64no—
159C2×D12—64no—
160C2×D12—64no—
161C2×C4×D3—616no—
162C2×C4×D3—128no—
163C2×C4×D3—128no—
164C2×C3×C8—24no—
165C2×C3×C8—24no—
166C2×C3×C8C4×D318yescomplemented
167C3×C4⋊C4—24no—
168C3×C4⋊C4—24no—
169C3×C4⋊C4—24no—
170C3×C4⋊C4D1218yes—
171(C2×D3)⋊C4—616no—
172(C2×D3)⋊C4—128no—
173(C2×D3)⋊C4—128no—
174C4×Dic3—64no—
175C4×Dic3—64no—
176C2×C3⋊C8—64no—
177C2×C3⋊C8—64no—
178C2×C3⋊C8—64no—
179D24—632no—
180C22×C32C4×D411yescharacteristic
181C22×C32#12011yescharacteristic
182C22×C32#12111yescharacteristic
183C22×C32C2×D811yescharacteristic
184C22×C32#13511yescharacteristic
185C22×C32AGL(1,ℤ/8)11yescharacteristic
186C22×C32AGL(1,ℤ/8)11yescharacteristic
187C2×C3⋊D3—24no—
188C2×C3⋊D3—42no—
189C2×C3⋊D3—42no—
190C2×C3⋊D3—42no—
191C2×C3⋊D3—42no—
192C2×C3⋊D3—42no—
193C2×C3⋊D3—42no—
194C2×C3⋊D3—42no—
195C2×C3⋊D3—42no—
196C2×C3⋊D3—42no—
197C2×C3⋊D3—81no—
198C2×C3⋊D3—81no—
199C2×C3⋊D3—81no—
200C2×C3⋊D3—81no—
201C32×C4—42no—
202C32×C4—81no—
203C32×C4C2×C22⋊C411yescharacteristic
204C32×C4C4×D411yescharacteristic
205C32×C4#12111yescharacteristic
206C32×C4#12311yescharacteristic
207C3⋊Dic3—22no—
208C3⋊Dic3—41no—
209C22×D4—91no—
210C22×D4—91no—
211C23×C4—181no—
212C2×D8—94no—
213C2×D8—182no—
214C2×D8—182no—
215C22×C8—91no—
216C22×C8C2×C3⋊D311yescharacteristic
217C4×D4—182no—
218C4×D4—182no—
219C2×C4⋊C4C2×C3⋊D311yescharacteristic
220C2×C4⋊C4C2×C3⋊D311yescharacteristic
221C2×C22⋊C4—181no—
222C2×C22⋊C4—181no—
223C2×C22⋊C4—181no—
224C2×C42—91no—
225#102—182no—
226#102—182no—
227C23×C3D3×D414yes—
228C22×D3—68no—
229C22×D3—68no—
230C22×D3—68no—
231C22×D3—68no—
232C22×D3—124no—
233C22×D3—124no—
234C22×D3—124no—
235C22×D3—124no—
236C22×D3—124no—
237C22×D3—124no—
238C22×D3—124no—
239C22×D3—124no—
240C22×D3—124no—
241C22×D3—124no—
242C2×C3×C4—28no—
243C2×C3×C4—44no—
244C2×C3×C4—44no—
245C2×C3×C4—44no—
246C2×C3×C4—44no—
247C2×C3×C4—44no—
248C2×C3×C4C2×C4×D314yes—
249C2×C3×C4C2×D1214yes—
250C2×C3×C4#23514yes—
251C2×C3×C4D3×D414yes—
252C2×C3×C4D3×D414yes—
253C2×C3×C4#23914yes—
254C2×Dic3—38no—
255C2×Dic3—64no—
256C2×Dic3—64no—
257C2×Dic3—64no—
258C2×Dic3—64no—
259C2×Dic3—64no—
260D12—316no—
261D12—68no—
262D12—68no—
263D12—68no—
264D12—68no—
265D12—68no—
266D12—124no—
267D12—124no—
268C4×D3—1232no—
269C3×C8—28no—
270C3⋊C8—124no—
271C2×C32#38611yescharacteristic
272C2×C32C4×D811yescharacteristic
273C2×C32#44211yescharacteristic
274C2×C32#44711yescharacteristic
275C2×C32#44911yescharacteristic
276C2×C32#45911yescharacteristic
277C2×C32#46311yescharacteristic
278C3⋊D3—44no—
279C3⋊D3—82no—
280C24—181no—
281C24—181no—
282C2×D4—92no—
283C2×D4—92no—
284C2×D4—92no—
285C2×D4—92no—
286C2×D4—181no—
287C2×D4—181no—
288C2×D4—181no—
289C2×D4—181no—
290C2×D4—181no—
291C2×D4—181no—
292C2×D4—181no—
293C2×D4—181no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—91no—
297C22×C4—91no—
298C22×C4—184no—
299C22×C4—362no—
300C22×C4—362no—
301C22×C4C22×C3⋊D311yescharacteristic
302D8—188no—
303C2×C8—21no—
304C2×C8—21no—
305C2×C8—181no—
306C2×C8—181no—
307C2×C8—181no—
308C2×C8C4×C3⋊D312yescomplemented
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4C4⋊(C3⋊D3)12yes—
313C22⋊C4—184no—
314C22⋊C4—362no—
315C22⋊C4—362no—
316C42—181no—
317C42—181no—
318C22×C3#88214yes—
319C22×C3#88414yes—
320C22×C3#89314yes—
321C22×C3D3×D814yes—
322C22×C3#91414yes—
323C22×C3#91414yes—
324C22×C3#91914yes—
325C2×D3—616no—
326C2×D3—128no—
327C2×D3—128no—
328C2×D3—128no—
329C2×D3—128no—
330C2×D3—128no—
331C2×D3—128no—
332C2×D3—128no—
333C2×D3—128no—
334C2×D3—128no—
335C2×D3—244no—
336C2×D3—244no—
337C2×D3—244no—
338C2×D3—244no—
339C3×C4—48no—
340C3×C4—84no—
341C3×C4C4×D1214yes—
342C3×C4D3×C22⋊C414yes—
343C3×C4#89414yes—
344C3×C4#89514yes—
345Dic3—68no—
346Dic3—124no—
347C32#187911yescharacteristic, complemented, Sylow
348C23—182no—
349C23—182no—
350C23—182no—
351C23—182no—
352C23—361no—
353C23—361no—
354C23—361no—
355C23—361no—
356C23—361no—
357C23—361no—
358C23—361no—
359C23—361no—
360C23—361no—
361C23—361no—
362C23D4×C3⋊D311yescharacteristic
363D4—94no—
364D4—182no—
365D4—182no—
366D4—182no—
367D4—182no—
368D4—182no—
369D4—361no—
370D4—361no—
371C2×C4—22no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—92no—
378C2×C4—181no—
379C2×C4—181no—
380C2×C4—181no—
381C2×C4—181no—
382C2×C4—181no—
383C2×C4—368no—
384C2×C4C2×C4×C3⋊D311yescharacteristic
385C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
386C2×C4#382811yescharacteristic
387C2×C4D4×C3⋊D311yescharacteristic
388C2×C4D4×C3⋊D311yescharacteristic
389C2×C4#383211yescharacteristic
390C8—22no—
391C8—361no—
392C2×C3#466514yes—
393C2×C3#477314yes—
394C2×C3#478614yes—
395C2×C3#481014yes—
396C2×C3#481914yes—
397C2×C3#486914yes—
398C2×C3#487214yes—
399D3—1216no—
400D3—248no—
401C22—184no—
402C22—362no—
403C22—362no—
404C22—362no—
405C22—362no—
406C22—362no—
407C22—362no—
408C22—362no—
409C22—362no—
410C22—362no—
411C22—721no—
412C22—721no—
413C22—721no—
414C22—721no—
415C22#6409111yescharacteristic
416C22#6409311yescharacteristic
417C22#6410211yescharacteristic
418C22D8×C3⋊D311yescharacteristic
419C22#6412311yescharacteristic
420C22#6412311yescharacteristic
421C22#6412811yescharacteristic
422C4—42no—
423C4—81no—
424C4—182no—
425C4—361no—
426C4C4×C4⋊(C3⋊D3)11yescharacteristic
427C4C22⋊C4×C3⋊D311yescharacteristic
428C4#6410311yescharacteristic
429C4#6410411yescharacteristic
430C3#6889714yescomplemented
431C2—364no—
432C2—722no—
433C2#1059236411yescharacteristic
434C2#1059247211yescharacteristic
435C2#1059248511yescharacteristic
436C2#1059250911yescharacteristic
437C2#1059251811yescharacteristic
438C2#1059256811yescharacteristic
439C2#1059257111yescharacteristic
subgroupG/H
centerC23D4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#340C2
socleC23×C32C2×D4
prime radicalC22×#3745C2
cosocleC22×C32×C4C23
hypercenter#340C3⋊D3
hypocenterC32#1879
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
2. C2×#64102C2semidirect
3. #10592687C2semidirect
4. C2×#63636C2semidirect
5. C2×#63636C2semidirect
6. C32×#340C2semidirect
7. #10589416C2semidirect
22. C2×#3745C4semidirect
32. C3×#340D3semidirect
50. C2×C4⋊(C3⋊D3)C2×C4semidirect
58. C2×C32×C8C2×C4semidirect
123. C2×C3⋊Dic3D8semidirect
131. C4⋊(C3⋊D3)C22⋊C4semidirect
140. #340C3⋊D3semidirect
166. C2×C3×C8C4×D3semidirect
308. C2×C8C4×C3⋊D3semidirect
347. C32#1879semidirect
430. C3#68897semidirect

Maximal subgroups

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

subgroupindex
C22×#37452
C2×#641022
#105926872
C2×#636362
C32×#3402
#105894162
#688973