Finite Group Databasebeta

← #11794007

Subgroups — #11794007

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
2C2×C32×#102C211yesmaximal, characteristic, complemented
3#10592920C211yesmaximal, characteristic, complemented
4C2×#63648C211yesmaximal, characteristic, complemented
5C2×#63641C211yesmaximal, characteristic, complemented
6#10592687C211yesmaximal, characteristic, complemented
7#10589395C211yesmaximal, characteristic, complemented
8#70212—34nomaximal
9C22×C32×D4C2211yescharacteristic
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×#3757—21no—
14C2×#3757—21no—
15C2×#3753—22no—
16C2×#3753—22no—
17C2×#3753—22no—
18C2×#3752—21no—
19C2×#3752—21no—
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C2×C4×C3⋊Dic3C2211yescharacteristic
22C22×C3⋊(C3⋊C8)C2211yescharacteristic
23C32×#102—22no—
24#63648—22no—
25#63641—22no—
26C22×#213—34no—
27C2×C3×#102D314yescomplemented
28#5221—34no—
29C2×#821—34no—
30C2×Dic3⋊C8—34no—
31#4988—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×C4C2311yescharacteristic
43C22×C3⋊Dic3—21no—
44C22×C3⋊Dic3D411yescharacteristic
45C22×C3⋊Dic3D411yescharacteristic
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—
52C2×C32×C8—21no—
53C2×C32×C8—21no—
54C2×C32×C8—21no—
55C32×C4⋊C4—21no—
56C32×C4⋊C4—21no—
57#3757—42no—
58#3757—42no—
59#3753—28no—
60#3752—42no—
61#3752—42no—
62C4⋊(C3⋊Dic3)—21no—
63C4⋊(C3⋊Dic3)—21no—
64C4×C3⋊Dic3—21no—
65C4×C3⋊Dic3—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—
72C22×C3×C8C2×D314yes—
73C2×C3×C4⋊C4C2×D314yes—
74C2×#217—64no—
75C2×#217—64no—
76C2×#213—68no—
77C2×#213—68no—
78C2×#213—68no—
79C2×(C2×D3)⋊C4—64no—
80C2×(C2×D3)⋊C4—64no—
81C2×C4⋊Dic3—34no—
82C2×C4×Dic3—34no—
83C22×C3⋊C8—34no—
84C3×#102—28no—
85#821—68no—
86Dic3⋊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—41no—
107C2×C32×C4—41no—
108C2×C32×C4—41no—
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4#4111yescharacteristic
113C2×C32×C4#4111yescharacteristic
114C2×C32×C4#4111yescharacteristic
115C2×C3⋊Dic3—21no—
116C2×C3⋊Dic3—21no—
117C2×C3⋊Dic3—21no—
118C2×C3⋊Dic3—21no—
119C2×C3⋊Dic3—21no—
120C2×C3⋊Dic3—41no—
121C2×C3⋊Dic3—41no—
122C2×C3⋊Dic3—41no—
123C2×C3⋊Dic3D812yescomplemented
124C4⋊(C3⋊D3)—22no—
125C4⋊(C3⋊D3)—22no—
126C4⋊(C3⋊D3)—41no—
127C4⋊(C3⋊D3)—41no—
128C32×C8—41no—
129C3⋊(C3⋊C8)—22no—
130C22×D8—91no—
131C2×C4⋊C8—91no—
132C2×#102—91no—
133C2×#102C3⋊D311yescharacteristic, complemented
134#390—91no—
135#390—91no—
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×D4#6718yes—
145C22×C3×C4—24no—
146C22×C3×C4C22×D314yes—
147C22×Dic3—34no—
148C22×Dic3—34no—
149C22×Dic3—64no—
150C2×D12—38no—
151C2×D12—64no—
152C2×D12—64no—
153C2×D12—64no—
154C2×D12—64no—
155C2×D12—64no—
156C2×C3×C8—24no—
157C2×C3×C8—24no—
158C2×C3×C8—24no—
159C3×C4⋊C4—24no—
160C3×C4⋊C4—24no—
161#217—128no—
162#217—128no—
163#213—632no—
164(C2×D3)⋊C4—128no—
165(C2×D3)⋊C4—128no—
166C4⋊Dic3—64no—
167C4⋊Dic3—64no—
168C4×Dic3—64no—
169C4×Dic3—64no—
170C2×C3⋊C8—38no—
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—81no—
195C32×C4#12011yescharacteristic
196C32×C4#12311yescharacteristic
197C32×C4#12311yescharacteristic
198C32×C4#12411yescharacteristic
199C3⋊Dic3—22no—
200C3⋊Dic3—41no—
201C3⋊Dic3—81no—
202C22×D4—91no—
203C22×D4C2×C3⋊D311yescharacteristic
204C2×D8—182no—
205C2×D8—182no—
206C2×D8—182no—
207C22×C8—91no—
208C22×C8C2×C3⋊D311yescharacteristic
209C2×C4⋊C4—91no—
210C2×C4⋊C4C2×C3⋊D311yescharacteristic
211C2×C22⋊C4—181no—
212C2×C22⋊C4—181no—
213C2×C22⋊C4—181no—
214C2×C22⋊C4—181no—
215C2×C42—91no—
216C4⋊C8—182no—
217#102—22no—
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×C3D3×D414yes—
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—44no—
239C2×C3×C4—44no—
240C2×C3×C4—44no—
241C2×C3×C4#23514yes—
242C2×C3×C4#23514yes—
243C2×C3×C4D3×D414yes—
244C2×C3×C4D3×D414yes—
245C2×C3×C4#23714yes—
246C2×C3×C4C2×#6714yes—
247C2×Dic3—38no—
248C2×Dic3—64no—
249C2×Dic3—64no—
250C2×Dic3—64no—
251C2×Dic3—64no—
252C2×Dic3—64no—
253C2×Dic3—124no—
254C2×Dic3—124no—
255C2×Dic3—124no—
256D12—68no—
257D12—68no—
258D12—124no—
259D12—124no—
260C3×C8—44no—
261C3⋊C8—68no—
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×D4#63812yes—
285C22×C4—21no—
286C22×C4—91no—
287C22×C4—91no—
288C22×C4—181no—
289C22×C4C22×C3⋊D311yescharacteristic
290D8—188no—
291C2×C8—21no—
292C2×C8—21no—
293C2×C8—21no—
294C2×C8—92no—
295C2×C8—181no—
296C2×C8—181no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—181no—
300C4⋊C4—181no—
301C22⋊C4—362no—
302C22⋊C4—362no—
303C22⋊C4—362no—
304C22⋊C4—362no—
305C42—181no—
306C42—181no—
307C22×C3—48no—
308C22×C3—48no—
309C22×C3—48no—
310C22×C3—84no—
311C22×C3—84no—
312C22×C3—84no—
313C22×C3—84no—
314C22×C3#88414yes—
315C22×C3#88414yes—
316C22×C3D3×D814yes—
317C22×C3#91114yes—
318C22×C3#91414yes—
319C22×C3#91614yes—
320C22×C3#93914yes—
321C2×D3—128no—
322C2×D3—128no—
323C2×D3—128no—
324C2×D3—244no—
325C2×D3—244no—
326C2×D3—244no—
327C2×D3—244no—
328C3×C4—84no—
329C3×C4#88314yes—
330C3×C4#88514yes—
331C3×C4#92914yes—
332C3×C4#93714yes—
333Dic3—68no—
334Dic3—124no—
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—
351C23D4×C3⋊D311yescharacteristic
352D4—22no—
353D4—22no—
354D4—41no—
355D4—41no—
356D4—182no—
357D4—182no—
358D4—361no—
359D4—361no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—92no—
364C2×C4—181no—
365C2×C4—181no—
366C2×C4—181no—
367C2×C4—181no—
368C2×C4—181no—
369C2×C4—361no—
370C2×C4—361no—
371C2×C4—361no—
372C2×C4#382811yescharacteristic
373C2×C4#382811yescharacteristic
374C2×C4D4×C3⋊D311yescharacteristic
375C2×C4D4×C3⋊D311yescharacteristic
376C2×C4#383011yescharacteristic
377C2×C4C2×#63811yescharacteristic
378C8—41no—
379C8—182no—
380C2×C3—88no—
381C2×C3#477514yes—
382C2×C3#478214yes—
383C2×C3#478614yes—
384C2×C3#478714yes—
385C2×C3#495914yes—
386C2×C3#515014yes—
387C2×C3#516514yes—
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#6409311yescharacteristic
404C22#6409311yescharacteristic
405C22D8×C3⋊D311yescharacteristic
406C22#6412011yescharacteristic
407C22#6412311yescharacteristic
408C22#6412511yescharacteristic
409C22#6414811yescharacteristic
410C4—81no—
411C4—182no—
412C4—361no—
413C4—721no—
414C4#6409211yescharacteristic
415C4#6409411yescharacteristic
416C4#6413811yescharacteristic
417C4#6414611yescharacteristic
418C3#7021214yescomplemented
419C2—82no—
420C2—722no—
421C2#1059247411yescharacteristic
422C2#1059248111yescharacteristic
423C2#1059248511yescharacteristic
424C2#1059248611yescharacteristic
425C2#1059265811yescharacteristic
426C2#1059284911yescharacteristic
427C2#1059286411yescharacteristic
subgroupG/H
centerC23D4×C3⋊D3
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC2×C32×#102C2
socleC23×C32C2×D4
prime radicalC22×#3753C2
hypercenterC2×#102C3⋊D3
hypocenterC32#2054
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
2. C2×C32×#102C2semidirect
3. #10592920C2semidirect
4. C2×#63648C2semidirect
5. C2×#63641C2semidirect
6. #10592687C2semidirect
7. #10589395C2semidirect
27. C2×C3×#102D3semidirect
123. C2×C3⋊Dic3D8semidirect
133. C2×#102C3⋊D3semidirect
336. C32#2054semidirect
418. C3#70212semidirect

Maximal subgroups

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

subgroupindex
C22×#37532
C2×C32×#1022
#105929202
C2×#636482
C2×#636412
#105926872
#105893952
#702123