Finite Group Databasebeta

← #11775720

Subgroups — #11775720

Order 1152.

585 conjugacy classes of subgroups.

The subgroup lattice has 443 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595950C211yesmaximal, characteristic
2C3×C4×#208C211yesmaximal, characteristic, complemented
3C2×C3×#803C211yesmaximal, characteristic, complemented
4#10589089C212yesmaximal, complemented
5#10589087C212yesmaximal, complemented
6#69858—31nomaximal
7#69797—31nomaximal
8C2×C32×C42C2211yescharacteristic
9#64139C411yescharacteristic
10#64138—21no—
11C4×#638—21no—
12#64133C411yescharacteristic
13#64085—21no—
14#64084C2211yescharacteristic
15C4×C4⋊(C3⋊D3)C411yescharacteristic
16#64081—21no—
17#64079C2211yescharacteristic
18C4×#634C411yescharacteristic
19C2×C3×#208—21no—
20C22×C3×C3⋊C8—21no—
21C3×#803—21no—
22C3×#803C2212yes—
23C3×#803C2212yes—
24C3×C4×C3⋊C8—21no—
25#5479—31no—
26#5479—31no—
27#5479—61no—
28C3×C4×M16—31no—
29C2×C3×#97—31no—
30C4×#208D311yescharacteristic, complemented
31C2×#803D311yescharacteristic, complemented
32#4465—32no—
33#4465—32no—
34#4464—32no—
35#4464—32no—
36C22×C32×C4C2×C411yescharacteristic
37C22×C32×C4D411yescharacteristic
38C22×C32×C4D411yescharacteristic
39C2×#638—21no—
40C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
41C2×C4×C3⋊D3—21no—
42C2×#634C2×C411yescharacteristic
43C32×C42C2×C411yescharacteristic
44C32×C42D411yescharacteristic
45C32×C42D411yescharacteristic
46C32×C42C2311yescharacteristic
47#3757—21no—
48#3752—21no—
49#3752—21no—
50#3752—21no—
51#3752—21no—
52C4⋊(C3⋊Dic3)C2×C411yescharacteristic
53C4⋊(C3⋊Dic3)C2×C411yescharacteristic
54#3750—21no—
55#3750—21no—
56#3750—21no—
57#3750—21no—
58C4×C3⋊Dic3—21no—
59C3×#208—24no—
60C2×C3×C3⋊C8—24no—
61C2×C3×C3⋊C8—22no—
62C2×C3×C3⋊C8—22no—
63#1524—91noSylow
64C2×C3×M16—61no—
65C22×C3×C8—61no—
66C2×C3×C42—21no—
67C2×C3×C42C2×D311yescharacteristic
68C2×C3×C42C2×D311yescharacteristic
69#930—31no—
70#930—31no—
71#930—61no—
72#929—62no—
73#929—61no—
74#929—61no—
75C4×#67—62no—
76C4×#67—61no—
77C4×#67—61no—
78#924—31no—
79#924—31no—
80#924—61no—
81C2×#208—21no—
82C22×C3⋊C8—21no—
83#876—62no—
84#876—61no—
85#876—61no—
86#875—31no—
87#875—31no—
88#875—61no—
89C4×D12—31no—
90C4×D12—31no—
91C4×D12—61no—
92#872—62no—
93#872—61no—
94#872—61no—
95#870—31no—
96#870—31no—
97#870—61no—
98C4×Dic6—31no—
99C4×Dic6—31no—
100C4×Dic6—61no—
101C3×#97—32no—
102C3×#97—32no—
103C3×#97—61no—
104C3×C4×C8—61no—
105#803—21no—
106#803C2×D312yes—
107#803C2×D312yes—
108C4×C3⋊C8—21no—
109C23×C32C22⋊C411yescharacteristic
110C22×C3⋊D3—21no—
111C2×C32×C4—22no—
112C2×C32×C4—22no—
113C2×C32×C4—41no—
114C2×C32×C4C22⋊C411yescharacteristic
115C2×C32×C4C22⋊C411yescharacteristic
116C2×C32×C4C22⋊C411yescharacteristic
117C2×C32×C4C22×C411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120#638—42no—
121C2×C3⋊Dic3—21no—
122C2×C3⋊Dic3—21no—
123C2×C3⋊Dic3—21no—
124C4⋊(C3⋊D3)—41no—
125C4×C3⋊D3—42no—
126#634—41no—
127C3×C3⋊C8—24no—
128C3×C3⋊C8—24no—
129#529—91no—
130C4×M16—31no—
131C2×#97—31no—
132#330—92no—
133#329—92no—
134C22×C3×C4—21no—
135C22×C3×C4—21no—
136C22×C3×C4—21no—
137C22×C3×C4C4×D311yescharacteristic
138C22×C3×C4C4×D311yescharacteristic
139C22×C3×C4D1211yescharacteristic
140C22×C3×C4D1211yescharacteristic
141C22×C3×C4#6711yescharacteristic
142C22×C3×C4#6711yescharacteristic
143C2×#67—62no—
144C2×#67—61no—
145C2×#67—61no—
146C2×D12—31no—
147C2×D12—31no—
148C2×D12—61no—
149C2×C4×D3—62no—
150C2×C4×D3—61no—
151C2×C4×D3—61no—
152C2×Dic6—31no—
153C2×Dic6—31no—
154C2×Dic6—61no—
155C3×M16—64no—
156C2×C3×C8—64no—
157C2×C3×C8—62no—
158C2×C3×C8—62no—
159C3×C42—21no—
160C3×C42—21no—
161C3×C42—21no—
162C3×C42—21no—
163C3×C42C4×D311yescharacteristic
164C3×C42C4×D311yescharacteristic
165C3×C42D1211yescharacteristic
166C3×C42D1211yescharacteristic
167C3×C42#6711yescharacteristic
168C3×C42#6711yescharacteristic
169C3×C42C22×D311yescharacteristic
170C3×C42C22×D311yescharacteristic
171#217—62no—
172#217—61no—
173#217—61no—
174(C2×D3)⋊C4—62no—
175(C2×D3)⋊C4—62no—
176(C2×D3)⋊C4—62no—
177(C2×D3)⋊C4—62no—
178(C2×D3)⋊C4—61no—
179(C2×D3)⋊C4—61no—
180(C2×D3)⋊C4—61no—
181(C2×D3)⋊C4—61no—
182(C2×D3)⋊C4—61no—
183(C2×D3)⋊C4—61no—
184(C2×D3)⋊C4—61no—
185(C2×D3)⋊C4—61no—
186C4⋊Dic3—31no—
187C4⋊Dic3—31no—
188C4⋊Dic3—31no—
189C4⋊Dic3—31no—
190C4⋊Dic3—61no—
191C4⋊Dic3—61no—
192Dic3⋊C4—62no—
193Dic3⋊C4—62no—
194Dic3⋊C4—62no—
195Dic3⋊C4—62no—
196Dic3⋊C4—61no—
197Dic3⋊C4—61no—
198Dic3⋊C4—61no—
199Dic3⋊C4—61no—
200Dic3⋊C4—61no—
201Dic3⋊C4—61no—
202Dic3⋊C4—61no—
203Dic3⋊C4—61no—
204C4×Dic3—62no—
205C4×Dic3—61no—
206C4×Dic3—61no—
207#208—24no—
208C2×C3⋊C8—24no—
209C2×C3⋊C8—22no—
210C2×C3⋊C8—22no—
211C22×C32—21no—
212C22×C32—21no—
213C22×C32#10412yes—
214C22×C32C2×C22⋊C411yescharacteristic
215C2×C3⋊D3—41no—
216C2×C3⋊D3—41no—
217C2×C3⋊D3—41no—
218C32×C4—21no—
219C32×C4—21no—
220C32×C4—21no—
221C32×C4—21no—
222C32×C4—21no—
223C32×C4#10412yes—
224C3⋊Dic3—41no—
225C3⋊Dic3—41no—
226C3⋊Dic3—41no—
227C2×M16—61no—
228C22×C8—61no—
229#126—181no—
230#125—91no—
231#124—91no—
232#123—181no—
233C22⋊Q8—91no—
234#121—91no—
235C4×Q8—91no—
236C4×D4—91no—
237C4×D4—181no—
238#117—181no—
239C2×C42D3211yescharacteristic
240#97—32no—
241#97—32no—
242#97—61no—
243C4×C8—61no—
244C23×C3—21no—
245C23×C3(C2×D3)⋊C411yescharacteristic
246C23×C3(C2×D3)⋊C411yescharacteristic
247C22×D3—62no—
248C22×D3—61no—
249C22×D3—61no—
250C2×C3×C4—22no—
251C2×C3×C4—22no—
252C2×C3×C4—22no—
253C2×C3×C4—22no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—42no—
261C2×C3×C4—42no—
262C2×C3×C4—41no—
263C2×C3×C4—41no—
264C2×C3×C4—42no—
265C2×C3×C4(C2×D3)⋊C411yescharacteristic
266C2×C3×C4(C2×D3)⋊C411yescharacteristic
267C2×C3×C4(C2×D3)⋊C411yescharacteristic
268C2×C3×C4(C2×D3)⋊C411yescharacteristic
269C2×C3×C4(C2×D3)⋊C411yescharacteristic
270C2×C3×C4(C2×D3)⋊C411yescharacteristic
271C2×C3×C4C2×C4×D311yescharacteristic
272C2×C3×C4C2×C4×D311yescharacteristic
273C2×C3×C4C2×D1211yescharacteristic
274C2×C3×C4C2×D1211yescharacteristic
275C2×C3×C4C2×#6711yescharacteristic
276C2×C3×C4C2×#6711yescharacteristic
277#67—124no—
278#67—122no—
279#67—122no—
280C2×Dic3—62no—
281C2×Dic3—62no—
282C2×Dic3—62no—
283C2×Dic3—61no—
284C2×Dic3—61no—
285C2×Dic3—61no—
286C2×Dic3—61no—
287C2×Dic3—61no—
288C2×Dic3—61no—
289D12—121no—
290D12—121no—
291D12—122no—
292C4×D3—124no—
293C4×D3—122no—
294C4×D3—122no—
295Dic6—122no—
296Dic6—121no—
297Dic6—121no—
298C3×C8—64no—
299C3×C8—64no—
300C3⋊C8—24no—
301C3⋊C8—24no—
302C2×C32—22no—
303C2×C32#41311yescharacteristic
304C2×C32C2×#10411yescharacteristic
305C2×C32C2×#10411yescharacteristic
306C3⋊D3—81no—
307C2×Q8—91no—
308C2×D4—91no—
309C2×D4—181no—
310C22×C4—181no—
311C22×C4#62411yescharacteristic
312C22×C4#62611yescharacteristic
313C22×C4#62611yescharacteristic
314M16—64no—
315C2×C8—64no—
316C2×C8—62no—
317C2×C8—62no—
318C4⋊C4—91no—
319C4⋊C4—91no—
320C4⋊C4—181no—
321C4⋊C4—181no—
322C4⋊C4—181no—
323C4⋊C4—181no—
324C22⋊C4—181no—
325C22⋊C4—181no—
326C22⋊C4—181no—
327C22⋊C4—181no—
328C22⋊C4—181no—
329C42—181no—
330C42#62411yescharacteristic
331C42#62611yescharacteristic
332C42#62611yescharacteristic
333C42C2×D3211yescharacteristic
334C22×C3—21no—
335C22×C3—21no—
336C22×C3—21no—
337C22×C3—21no—
338C22×C3—22no—
339C22×C3—21no—
340C22×C3—41no—
341C22×C3—41no—
342C22×C3#80512yes—
343C22×C3#82512yes—
344C22×C3C2×(C2×D3)⋊C411yescharacteristic
345C22×C3C2×(C2×D3)⋊C411yescharacteristic
346C2×D3—122no—
347C2×D3—122no—
348C2×D3—122no—
349C2×D3—121no—
350C2×D3—121no—
351C2×D3—121no—
352C2×D3—121no—
353C2×D3—121no—
354C2×D3—121no—
355C3×C4—22no—
356C3×C4—21no—
357C3×C4—21no—
358C3×C4—21no—
359C3×C4—21no—
360C3×C4—21no—
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—21no—
364C3×C4—21no—
365C3×C4—21no—
366C3×C4—22no—
367C3×C4—41no—
368C3×C4—41no—
369C3×C4—41no—
370C3×C4—41no—
371C3×C4#80512yes—
372C3×C4#82512yes—
373Dic3—122no—
374Dic3—122no—
375Dic3—122no—
376Dic3—121no—
377Dic3—121no—
378Dic3—121no—
379Dic3—121no—
380Dic3—121no—
381Dic3—121no—
382C32#152411yescharacteristic, complemented, Sylow
383C23—181no—
384C23#372211yescharacteristic
385Q8—361no—
386D4—361no—
387D4—362no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—41no—
391C2×C4—181no—
392C2×C4—181no—
393C2×C4—181no—
394C2×C4—362no—
395C2×C4#372211yescharacteristic
396C2×C4#372211yescharacteristic
397C2×C4#372211yescharacteristic
398C2×C4C2×#62411yescharacteristic
399C2×C4C2×#62611yescharacteristic
400C2×C4C2×#62611yescharacteristic
401C8—64no—
402C8—64no—
403C2×C3—22no—
404C2×C3—22no—
405C2×C3—21no—
406C2×C3—21no—
407C2×C3—21no—
408C2×C3—42no—
409C2×C3C2×#80511yescharacteristic
410C2×C3C2×#80511yescharacteristic
411C2×C3#513211yescharacteristic
412C2×C3#513211yescharacteristic
413C2×C3C2×#82511yescharacteristic
414C2×C3C2×#82511yescharacteristic
415D3—242no—
416D3—241no—
417D3—241no—
418C22—21no—
419C22—21no—
420C22—361no—
421C22—361no—
422C22—361no—
423C22#6357012yes—
424C22C2×#372211yescharacteristic
425C4—21no—
426C4—21no—
427C4—21no—
428C4—21no—
429C4—21no—
430C4—361no—
431C4—361no—
432C4—361no—
433C4#6357012yes—
434C3—21no—
435C3#6979711yescharacteristic, complemented
436C3#6985811yescharacteristic, complemented
437C2—22no—
438C2—721no—
439C2#1059107811yescharacteristic
440C2C2×#6357011yescharacteristic
441C2C2×#6357011yescharacteristic
subgroupG/H
centerC2×C4#3722
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC2×C32×C42C22
socleC22×C32C2×C22⋊C4
prime radical#64139C4
cosocleC32×C42C23
hypercenterC2×C42D32
hypocenterC32#1524
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C3×C4×#208C2semidirect
3. C2×C3×#803C2semidirect
4. #10589089C2semidirect
5. #10589087C2semidirect
30. C4×#208D3semidirect
31. C2×#803D3semidirect
382. C32#1524semidirect
435. C3#69797semidirect
436. C3#69858semidirect

Maximal subgroups

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

subgroupindex
#105959502
C3×C4×#2082
C2×C3×#8032
#105890892
#105890872
#698583
#697973