Finite Group Databasebeta

← #11775364

Subgroups — #11775364

Order 1152.

521 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5479C211yesmaximal, characteristic
2#10592635C211yesmaximal, characteristic, complemented
3C3×#4926C211yesmaximal, characteristic, complemented
4#10589152C212yesmaximal, complemented
5#10589150C212yesmaximal
6#71756—31nomaximal
7#70834—31nomaximal
8C2×C32×C42C2211yescharacteristic
9C2×C4⋊(C3⋊Dic3)—21no—
10C3×#930C2211yescharacteristic
11C3×#929—21no—
12C3×C4×#67—21no—
13C3×#924C2211yescharacteristic
14C3×#876—21no—
15C3×#875C411yescharacteristic, complemented
16C3×C4×D12C411yescharacteristic, complemented
17C3×#872—21no—
18C3×#870C411yescharacteristic, complemented
19C3×C4×Dic6C411yescharacteristic, complemented
20#63658—21no—
21#63658C2212yes—
22C3×#830C2212yes—
23C3×C4⋊(C3⋊C8)—21no—
24C3×#803—21no—
25C3×#529—31no—
26#5479D311yescharacteristic
27C3×#432—31no—
28#4936—31no—
29#4936—31no—
30#4936—61no—
31#4926D311yescharacteristic, complemented
32#4538—32no—
33#4537—32no—
34#4470—32no—
35#4467—32no—
36C22×C32×C4D411yescharacteristic
37C22×C32×C4D411yescharacteristic
38C22×C32×C4C2311yescharacteristic
39C22×C3⋊Dic3—22no—
40C2×C3×#67—21no—
41C2×C3×D12C2×C411yescharacteristic
42C2×C3×C4×D3—21no—
43C2×C3×Dic6C2×C411yescharacteristic
44C32×C42C2×C411yescharacteristic
45C32×C42C2×C411yescharacteristic
46C32×C42D411yescharacteristic
47C32×C42D411yescharacteristic
48C4⋊(C3⋊Dic3)—42no—
49C3×#217—21no—
50C3×(C2×D3)⋊C4—21no—
51C3×(C2×D3)⋊C4—21no—
52C3×(C2×D3)⋊C4—21no—
53C3×(C2×D3)⋊C4—21no—
54C3×C4⋊Dic3C2×C411yescharacteristic
55C3×C4⋊Dic3C2×C411yescharacteristic
56C3×Dic3⋊C4—21no—
57C3×Dic3⋊C4—21no—
58C3×Dic3⋊C4—21no—
59C3×Dic3⋊C4—21no—
60C3×C4×Dic3—21no—
61C2×C3×C3⋊C8—22no—
62#1512—91noSylow
63C3×#126—61no—
64C3×#125—31no—
65C3×#124—31no—
66C3×#123—61no—
67C3×C22⋊Q8—31no—
68C3×#121—31no—
69C3×C4×Q8—31no—
70C3×C4×D4—31no—
71C3×C4×D4—61no—
72C3×#117—61no—
73C2×C3×C42—21no—
74C2×C3×C42C2×D311yescharacteristic
75C2×C3×C42C2×D311yescharacteristic
76#930C2×D311yescharacteristic
77#929—21no—
78C4×#67—21no—
79C2×C4⋊Dic3—62no—
80C2×C4⋊Dic3—61no—
81C2×C4⋊Dic3—61no—
82#924C2×D311yescharacteristic
83#876—21no—
84#875Dic311yescharacteristic, complemented
85C4×D12Dic311yescharacteristic, complemented
86#872—21no—
87#870Dic311yescharacteristic, complemented
88C4×Dic6Dic311yescharacteristic, complemented
89C3×C4⋊C8—61no—
90C3×C22⋊C8—32no—
91C3×#97—61no—
92C3⋊#95—32no—
93C3⋊#95—32no—
94C3⋊#95—62no—
95C3⋊#95—62no—
96C3⋊#95—61no—
97C3⋊#95—61no—
98#830C2×D312yes—
99C4⋊(C3⋊C8)—21no—
100#803—21no—
101C23×C32C2×D411yescharacteristic
102C22×C3×D3—21no—
103C2×C32×C4—21no—
104C2×C32×C4—21no—
105C2×C32×C4—41no—
106C2×C32×C4—41no—
107C2×C32×C4C22⋊C411yescharacteristic
108C2×C32×C4C22⋊C411yescharacteristic
109C2×C32×C4C22⋊C411yescharacteristic
110C2×C32×C4C22⋊C411yescharacteristic
111C2×C32×C4C22×C411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C2×C3⋊Dic3—42no—
114C2×C3⋊Dic3—42no—
115C2×C3⋊Dic3—42no—
116C3×#67—41no—
117C3×#67—41no—
118C2×C3×Dic3—21no—
119C2×C3×Dic3—21no—
120C2×C3×Dic3—21no—
121C3×D12—41no—
122C3×C4×D3—42no—
123C3×Dic6—41no—
124C3×C3⋊C8—42no—
125#529—31no—
126#432—31no—
127#382—91no—
128#328—92no—
129#327—92no—
130C2×C3×Q8—31no—
131C2×C3×D4—31no—
132C2×C3×D4—61no—
133C22×C3×C4—21no—
134C22×C3×C4—21no—
135C22×C3×C4—21no—
136C22×C3×C4—61no—
137C22×C3×C4D1211yescharacteristic
138C22×C3×C4D1211yescharacteristic
139C22×C3×C4#6711yescharacteristic
140C22×C3×C4#6711yescharacteristic
141C22×C3×C4C22×D311yescharacteristic
142C22×C3×C4C22×D311yescharacteristic
143C2×#67—21no—
144C22×Dic3—64no—
145C22×Dic3—62no—
146C22×Dic3—62no—
147C2×D12C2×Dic311yescharacteristic
148C2×C4×D3—21no—
149C2×Dic6C2×Dic311yescharacteristic
150C2×C3×C8—62no—
151C3×C4⋊C4—31no—
152C3×C4⋊C4—31no—
153C3×C4⋊C4—61no—
154C3×C4⋊C4—61no—
155C3×C4⋊C4—61no—
156C3×C4⋊C4—61no—
157C3×C22⋊C4—61no—
158C3×C22⋊C4—61no—
159C3×C22⋊C4—61no—
160C3×C22⋊C4—61no—
161C3×C22⋊C4—61no—
162C3×C42—21no—
163C3×C42—21no—
164C3×C42—21no—
165C3×C42—21no—
166C3×C42—61no—
167C3×C42C4×D311yescharacteristic
168C3×C42C4×D311yescharacteristic
169C3×C42C2×Dic311yescharacteristic
170C3×C42C2×Dic311yescharacteristic
171C3×C42#6711yescharacteristic
172C3×C42#6711yescharacteristic
173C3×C42#6711yescharacteristic
174C3×C42#6711yescharacteristic
175#217—21no—
176(C2×D3)⋊C4—21no—
177(C2×D3)⋊C4—21no—
178(C2×D3)⋊C4—21no—
179(C2×D3)⋊C4—21no—
180C4⋊Dic3—124no—
181C4⋊Dic3—122no—
182C4⋊Dic3—122no—
183C4⋊Dic3C2×Dic311yescharacteristic
184C4⋊Dic3C2×Dic311yescharacteristic
185Dic3⋊C4—21no—
186Dic3⋊C4—21no—
187Dic3⋊C4—21no—
188Dic3⋊C4—21no—
189C4×Dic3—21no—
190C2×C3⋊C8—22no—
191C22×C32—21no—
192C22×C32—21no—
193C22×C32C2×C22⋊C411yescharacteristic
194C22×C32AGL(1,ℤ/8)11yescharacteristic
195C22×C32#13711yescharacteristic
196C2×C3×D3—41no—
197C2×C3×D3—41no—
198C2×C3×D3—41no—
199C32×C4—21no—
200C32×C4—21no—
201C32×C4—21no—
202C32×C4—21no—
203C32×C4—21no—
204C32×C4—21no—
205C3⋊Dic3—82no—
206C3×Dic3—41no—
207C3×Dic3—41no—
208C3×Dic3—41no—
209#126—61no—
210#125—31no—
211#124—31no—
212#123—61no—
213C22⋊Q8—31no—
214#121—31no—
215C4×Q8—31no—
216C4×D4—31no—
217C4×D4—61no—
218#117—61no—
219C2×C4⋊C4—181no—
220C2×C42D3211yescharacteristic
221C4⋊C8—61no—
222C22⋊C8—32no—
223#97—61no—
224#95—92no—
225#95—181no—
226C23×C3—21no—
227C23×C3—61no—
228C23×C3C2×D1211yescharacteristic
229C23×C3C2×#6711yescharacteristic
230C22×D3—21no—
231C3×Q8—121no—
232C3×D4—121no—
233C3×D4—121no—
234C3×D4—121no—
235C2×C3×C4—22no—
236C2×C3×C4—22no—
237C2×C3×C4—21no—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—41no—
248C2×C3×C4—41no—
249C2×C3×C4—41no—
250C2×C3×C4—41no—
251C2×C3×C4—42no—
252C2×C3×C4—42no—
253C2×C3×C4—61no—
254C2×C3×C4—61no—
255C2×C3×C4—61no—
256C2×C3×C4—122no—
257C2×C3×C4(C2×D3)⋊C411yescharacteristic
258C2×C3×C4(C2×D3)⋊C411yescharacteristic
259C2×C3×C4(C2×D3)⋊C411yescharacteristic
260C2×C3×C4(C2×D3)⋊C411yescharacteristic
261C2×C3×C4#21711yescharacteristic
262C2×C3×C4#21711yescharacteristic
263C2×C3×C4#21711yescharacteristic
264C2×C3×C4#21711yescharacteristic
265C2×C3×C4C2×C4×D311yescharacteristic
266C2×C3×C4C22×Dic311yescharacteristic
267C2×C3×C4C2×#6711yescharacteristic
268C2×C3×C4C2×#6711yescharacteristic
269#67—41no—
270#67—41no—
271C2×Dic3—21no—
272C2×Dic3—21no—
273C2×Dic3—21no—
274C2×Dic3—124no—
275C2×Dic3—124no—
276C2×Dic3—124no—
277C2×Dic3—122no—
278C2×Dic3—122no—
279C2×Dic3—122no—
280C2×Dic3—122no—
281C2×Dic3—122no—
282C2×Dic3—122no—
283D12—41no—
284C4×D3—42no—
285Dic6—41no—
286C3×C8—122no—
287C3⋊C8—42no—
288C2×C32—21no—
289C2×C32—21no—
290C2×C32#41011yescharacteristic
291C2×C32#41711yescharacteristic
292C2×C32#42111yescharacteristic
293C3×D3—81no—
294C2×Q8—31no—
295C2×D4—31no—
296C2×D4—61no—
297C22×C4—61no—
298C22×C4—182no—
299C22×C4#62611yescharacteristic
300C22×C4#62611yescharacteristic
301C22×C4C2×D3211yescharacteristic
302C2×C8—62no—
303C4⋊C4—31no—
304C4⋊C4—31no—
305C4⋊C4—61no—
306C4⋊C4—61no—
307C4⋊C4—61no—
308C4⋊C4—61no—
309C4⋊C4—362no—
310C22⋊C4—61no—
311C22⋊C4—61no—
312C22⋊C4—61no—
313C22⋊C4—61no—
314C22⋊C4—61no—
315C42—61no—
316C42D3×Dic311yescharacteristic
317C42D3×Dic311yescharacteristic
318C42#62511yescharacteristic
319C42#62511yescharacteristic
320C22×C3—22no—
321C22×C3—22no—
322C22×C3—21no—
323C22×C3—21no—
324C22×C3—21no—
325C22×C3—21no—
326C22×C3—21no—
327C22×C3—21no—
328C22×C3—21no—
329C22×C3—121no—
330C22×C3—121no—
331C22×C3—121no—
332C22×C3#90811yescharacteristic
333C22×C3#90911yescharacteristic
334C22×C3C2×(C2×D3)⋊C411yescharacteristic
335C22×C3#94911yescharacteristic
336C22×C3#95111yescharacteristic
337C22×C3C2×#21711yescharacteristic
338C2×D3—41no—
339C2×D3—41no—
340C2×D3—41no—
341C3×C4—22no—
342C3×C4—22no—
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—21no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—21no—
351C3×C4—21no—
352C3×C4—21no—
353C3×C4—21no—
354C3×C4—21no—
355C3×C4—41no—
356C3×C4—41no—
357C3×C4—41no—
358C3×C4—41no—
359C3×C4—121no—
360C3×C4—121no—
361C3×C4—121no—
362Dic3—41no—
363Dic3—41no—
364Dic3—41no—
365Dic3—244no—
366Dic3—242no—
367Dic3—242no—
368C32#151211yescharacteristic, complemented, Sylow
369C23—61no—
370C23C2×#62611yescharacteristic
371Q8—121no—
372D4—121no—
373D4—121no—
374D4—121no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—61no—
380C2×C4—61no—
381C2×C4—61no—
382C2×C4—122no—
383C2×C4—362no—
384C2×C4—362no—
385C2×C4—362no—
386C2×C4(C2×D3)⋊Dic311yescharacteristic
387C2×C4(C2×D3)⋊Dic311yescharacteristic
388C2×C4(C2×D3)⋊Dic311yescharacteristic
389C2×C4(C2×D3)⋊Dic311yescharacteristic
390C2×C4C2×D3×Dic311yescharacteristic
391C2×C4C2×#62511yescharacteristic
392C8—122no—
393C2×C3—22no—
394C2×C3—22no—
395C2×C3—21no—
396C2×C3—21no—
397C2×C3—21no—
398C2×C3—21no—
399C2×C3—21no—
400C2×C3—21no—
401C2×C3—21no—
402C2×C3—241no—
403C2×C3#500611yescharacteristic
404C2×C3#513311yescharacteristic
405C2×C3#513911yescharacteristic
406C2×C3#523211yescharacteristic
407C2×C3#523611yescharacteristic
408C2×C3#524011yescharacteristic
409D3—81no—
410C22—21no—
411C22—21no—
412C22—121no—
413C22—121no—
414C22—121no—
415C22#6382511yescharacteristic
416C22#6383111yescharacteristic
417C22C2×(C2×D3)⋊Dic311yescharacteristic
418C4—21no—
419C4—21no—
420C4—21no—
421C4—21no—
422C4—21no—
423C4—21no—
424C4—121no—
425C4—121no—
426C4—121no—
427C4—722no—
428C3—21no—
429C3#7083411yescharacteristic, complemented
430C3#7175611yescharacteristic, complemented
431C2—21no—
432C2—21no—
433C2—241no—
434C2#1059108811yescharacteristic
435C2#1059111011yescharacteristic
436C2#1059123111yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊Dic3
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC22×C32C2×C22⋊C4
prime radicalC3×#930C22
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1512
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. #10592635C2semidirect
3. C3×#4926C2semidirect
4. #10589152C2semidirect
15. C3×#875C4semidirect
16. C3×C4×D12C4semidirect
18. C3×#870C4semidirect
19. C3×C4×Dic6C4semidirect
31. #4926D3semidirect
84. #875Dic3semidirect
85. C4×D12Dic3semidirect
87. #870Dic3semidirect
88. C4×Dic6Dic3semidirect
368. C32#1512semidirect
429. C3#70834semidirect
430. C3#71756semidirect

Maximal subgroups

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

subgroupindex
C3×#54792
#105926352
C3×#49262
#105891522
#105891502
#717563
#708343