Finite Group Databasebeta

← #11774473

Subgroups — #11774473

Order 1152.

585 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595950C211yesmaximal, characteristic
2C2×C3×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
3C3×C4×#208C211yesmaximal, characteristic, complemented
4#10589085C212yesmaximal, complemented
5#10589082C212yesmaximal, complemented
6#70427—31nomaximal
7#69852—31nomaximal
8C2×C32×C42C2211yescharacteristic
9#64139C411yescharacteristic
10#64138—21no—
11C4×#638—21no—
12#64133C411yescharacteristic
13#64085—21no—
14#64084C411yescharacteristic
15C4×C4⋊(C3⋊D3)C2211yescharacteristic
16#64081—21no—
17#64079C411yescharacteristic
18C4×#634C2211yescharacteristic
19C2×C3×#208—21no—
20C22×C3×C3⋊C8—21no—
21C3×C4⋊(C3⋊C8)—21no—
22C3×C4⋊(C3⋊C8)C2212yes—
23C3×#803—21no—
24C3×C4×C3⋊C8C2212yes—
25#5479—31no—
26#5479—31no—
27#5479—61no—
28C2×C3×C4⋊C8—31no—
29C3×C4×M16—31no—
30C2×C4⋊(C3⋊C8)D311yescharacteristic, complemented
31C4×#208D311yescharacteristic, complemented
32#4484—32no—
33#4483—32no—
34#4459—32no—
35#4456—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—22no—
61C2×C3×C3⋊C8—22no—
62C2×C3×C3⋊C8—42no—
63#1483—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×C4⋊C8—32no—
102C3×C4⋊C8—61no—
103C3×#97—61no—
104C3×C4×C8—32no—
105C4⋊(C3⋊C8)—21no—
106C4⋊(C3⋊C8)C2×D312yes—
107#803—21no—
108C4×C3⋊C8C2×D312yes—
109C23×C32C22⋊C411yescharacteristic
110C22×C3⋊D3—21no—
111C2×C32×C4—22no—
112C2×C32×C4—22no—
113C2×C32×C4—21no—
114C2×C32×C4—21no—
115C2×C32×C4C22⋊C411yescharacteristic
116C2×C32×C4C22⋊C411yescharacteristic
117C2×C32×C4C22⋊C411yescharacteristic
118C2×C32×C4C22×C411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121#638—42no—
122C2×C3⋊Dic3—21no—
123C2×C3⋊Dic3—21no—
124C2×C3⋊Dic3—21no—
125C4⋊(C3⋊D3)—22no—
126C4×C3⋊D3—41no—
127C4×C3⋊D3—41no—
128#634—22no—
129C3×C3⋊C8—24no—
130C3×C3⋊C8—42no—
131#529—91no—
132C2×C4⋊C8—31no—
133C4×M16—31no—
134Q8⋊C8—92no—
135D4⋊C8—92no—
136C22×C3×C4—21no—
137C22×C3×C4—21no—
138C22×C3×C4—21no—
139C22×C3×C4C4×D311yescharacteristic
140C22×C3×C4C4×D311yescharacteristic
141C22×C3×C4D1211yescharacteristic
142C22×C3×C4D1211yescharacteristic
143C22×C3×C4#6711yescharacteristic
144C22×C3×C4#6711yescharacteristic
145C2×#67—62no—
146C2×#67—61no—
147C2×#67—61no—
148C2×D12—31no—
149C2×D12—31no—
150C2×D12—61no—
151C2×C4×D3—62no—
152C2×C4×D3—61no—
153C2×C4×D3—61no—
154C2×Dic6—31no—
155C2×Dic6—31no—
156C2×Dic6—61no—
157C3×M16—64no—
158C2×C3×C8—62no—
159C2×C3×C8—62no—
160C2×C3×C8—122no—
161C3×C42—21no—
162C3×C42—21no—
163C3×C42—21no—
164C3×C42—21no—
165C3×C42C4×D311yescharacteristic
166C3×C42C4×D311yescharacteristic
167C3×C42D1211yescharacteristic
168C3×C42D1211yescharacteristic
169C3×C42#6711yescharacteristic
170C3×C42#6711yescharacteristic
171C3×C42C22×D311yescharacteristic
172C3×C42C22×D311yescharacteristic
173#217—62no—
174#217—61no—
175#217—61no—
176(C2×D3)⋊C4—62no—
177(C2×D3)⋊C4—62no—
178(C2×D3)⋊C4—62no—
179(C2×D3)⋊C4—62no—
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—
186(C2×D3)⋊C4—61no—
187(C2×D3)⋊C4—61no—
188C4⋊Dic3—31no—
189C4⋊Dic3—31no—
190C4⋊Dic3—31no—
191C4⋊Dic3—31no—
192C4⋊Dic3—61no—
193C4⋊Dic3—61no—
194Dic3⋊C4—62no—
195Dic3⋊C4—62no—
196Dic3⋊C4—62no—
197Dic3⋊C4—62no—
198Dic3⋊C4—61no—
199Dic3⋊C4—61no—
200Dic3⋊C4—61no—
201Dic3⋊C4—61no—
202Dic3⋊C4—61no—
203Dic3⋊C4—61no—
204Dic3⋊C4—61no—
205Dic3⋊C4—61no—
206C4×Dic3—62no—
207C4×Dic3—61no—
208C4×Dic3—61no—
209#208—24no—
210C2×C3⋊C8—22no—
211C2×C3⋊C8—22no—
212C2×C3⋊C8—42no—
213C22×C32—21no—
214C22×C32—21no—
215C22×C32#10412yes—
216C22×C32C2×C22⋊C411yescharacteristic
217C2×C3⋊D3—41no—
218C2×C3⋊D3—41no—
219C2×C3⋊D3—41no—
220C32×C4—21no—
221C32×C4—21no—
222C32×C4—21no—
223C32×C4—21no—
224C32×C4#13112yes—
225C32×C4AGL(1,ℤ/8)11yescharacteristic
226C32×C4#13711yescharacteristic
227C3⋊Dic3—41no—
228C3⋊Dic3—41no—
229C3⋊Dic3—41no—
230C2×M16—61no—
231C22×C8—61no—
232#126—181no—
233#125—91no—
234#124—91no—
235#123—181no—
236C22⋊Q8—91no—
237#121—91no—
238C4×Q8—91no—
239C4×D4—91no—
240C4×D4—181no—
241#117—181no—
242C2×C42D3211yescharacteristic
243C4⋊C8—32no—
244C4⋊C8—61no—
245#97—61no—
246C4×C8—32no—
247C23×C3—21no—
248C23×C3(C2×D3)⋊C411yescharacteristic
249C23×C3(C2×D3)⋊C411yescharacteristic
250C22×D3—62no—
251C22×D3—61no—
252C22×D3—61no—
253C2×C3×C4—22no—
254C2×C3×C4—22no—
255C2×C3×C4—22no—
256C2×C3×C4—22no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—21no—
266C2×C3×C4—21no—
267C2×C3×C4—42no—
268C2×C3×C4—41no—
269C2×C3×C4—41no—
270C2×C3×C4—42no—
271C2×C3×C4(C2×D3)⋊C411yescharacteristic
272C2×C3×C4(C2×D3)⋊C411yescharacteristic
273C2×C3×C4(C2×D3)⋊C411yescharacteristic
274C2×C3×C4(C2×D3)⋊C411yescharacteristic
275C2×C3×C4(C2×D3)⋊C411yescharacteristic
276C2×C3×C4(C2×D3)⋊C411yescharacteristic
277C2×C3×C4C2×C4×D311yescharacteristic
278C2×C3×C4C2×C4×D311yescharacteristic
279C2×C3×C4C2×D1211yescharacteristic
280C2×C3×C4C2×D1211yescharacteristic
281C2×C3×C4C2×#6711yescharacteristic
282C2×C3×C4C2×#6711yescharacteristic
283#67—124no—
284#67—122no—
285#67—122no—
286C2×Dic3—62no—
287C2×Dic3—62no—
288C2×Dic3—62no—
289C2×Dic3—61no—
290C2×Dic3—61no—
291C2×Dic3—61no—
292C2×Dic3—61no—
293C2×Dic3—61no—
294C2×Dic3—61no—
295D12—62no—
296D12—62no—
297D12—122no—
298C4×D3—122no—
299C4×D3—122no—
300C4×D3—121no—
301C4×D3—121no—
302C4×D3—121no—
303C4×D3—121no—
304Dic6—62no—
305Dic6—62no—
306Dic6—122no—
307C3×C8—64no—
308C3×C8—122no—
309C3⋊C8—24no—
310C3⋊C8—42no—
311C2×C32—22no—
312C2×C32#40811yescharacteristic
313C2×C32#41711yescharacteristic
314C2×C32C2×#10411yescharacteristic
315C3⋊D3—81no—
316C2×Q8—91no—
317C2×D4—91no—
318C2×D4—181no—
319C22×C4—181no—
320C22×C4#62411yescharacteristic
321C22×C4#62611yescharacteristic
322C22×C4#62611yescharacteristic
323M16—64no—
324C2×C8—62no—
325C2×C8—62no—
326C2×C8—122no—
327C4⋊C4—91no—
328C4⋊C4—91no—
329C4⋊C4—181no—
330C4⋊C4—181no—
331C4⋊C4—181no—
332C4⋊C4—181no—
333C22⋊C4—181no—
334C22⋊C4—181no—
335C22⋊C4—181no—
336C22⋊C4—181no—
337C22⋊C4—181no—
338C42—181no—
339C42#62411yescharacteristic
340C42#62611yescharacteristic
341C42#62611yescharacteristic
342C42C2×D3211yescharacteristic
343C22×C3—21no—
344C22×C3—21no—
345C22×C3—21no—
346C22×C3—21no—
347C22×C3—22no—
348C22×C3—21no—
349C22×C3—41no—
350C22×C3—41no—
351C22×C3#80512yes—
352C22×C3#82512yes—
353C22×C3C2×(C2×D3)⋊C411yescharacteristic
354C22×C3C2×(C2×D3)⋊C411yescharacteristic
355C2×D3—122no—
356C2×D3—122no—
357C2×D3—122no—
358C2×D3—121no—
359C2×D3—121no—
360C2×D3—121no—
361C2×D3—121no—
362C2×D3—121no—
363C2×D3—121no—
364C3×C4—21no—
365C3×C4—21no—
366C3×C4—21no—
367C3×C4—21no—
368C3×C4—21no—
369C3×C4—21no—
370C3×C4—21no—
371C3×C4—21no—
372C3×C4—22no—
373C3×C4—21no—
374C3×C4—21no—
375C3×C4—41no—
376C3×C4—41no—
377C3×C4—41no—
378C3×C4—41no—
379C3×C4#90112yes—
380C3×C4#90712yes—
381C3×C4#90811yescharacteristic
382C3×C4#90911yescharacteristic
383C3×C4#93211yescharacteristic
384C3×C4#94211yescharacteristic
385Dic3—122no—
386Dic3—122no—
387Dic3—122no—
388Dic3—121no—
389Dic3—121no—
390Dic3—121no—
391Dic3—121no—
392Dic3—121no—
393Dic3—121no—
394C32#148311yescharacteristic, complemented, Sylow
395C23—181no—
396C23#372211yescharacteristic
397Q8—182no—
398D4—182no—
399D4—362no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—181no—
405C2×C4—181no—
406C2×C4—181no—
407C2×C4—361no—
408C2×C4—361no—
409C2×C4#372211yescharacteristic
410C2×C4#372211yescharacteristic
411C2×C4#372211yescharacteristic
412C2×C4C2×#62411yescharacteristic
413C2×C4C2×#62611yescharacteristic
414C2×C4C2×#62611yescharacteristic
415C8—64no—
416C8—122no—
417C2×C3—22no—
418C2×C3—22no—
419C2×C3—21no—
420C2×C3—21no—
421C2×C3—21no—
422C2×C3—42no—
423C2×C3C2×#80511yescharacteristic
424C2×C3#496611yescharacteristic
425C2×C3#511011yescharacteristic
426C2×C3#512911yescharacteristic
427C2×C3#513311yescharacteristic
428C2×C3C2×#82511yescharacteristic
429D3—242no—
430D3—241no—
431D3—241no—
432C22—21no—
433C22—21no—
434C22—361no—
435C22—361no—
436C22—361no—
437C22#6357012yes—
438C22C2×#372211yescharacteristic
439C4—21no—
440C4—21no—
441C4—21no—
442C4—21no—
443C4—361no—
444C4—361no—
445C4—361no—
446C4#6381712yes—
447C4#6383011yescharacteristic
448C4#6383311yescharacteristic
449C3—21no—
450C3#6985211yescharacteristic, complemented
451C3#7042711yescharacteristic, complemented
452C2—22no—
453C2—721no—
454C2#1059107311yescharacteristic
455C2#1059110611yescharacteristic
456C2C2×#6357011yescharacteristic
subgroupG/H
centerC2×C4C2×#626
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC2×C32×C42C22
socleC22×C32C2×C22⋊C4
prime radical#64139C4
cosocleC32×C42C23
hypercenterC2×C42D32
hypocenterC32#1483
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×C3×C4⋊(C3⋊C8)C2semidirect
3. C3×C4×#208C2semidirect
4. #10589085C2semidirect
5. #10589082C2semidirect
30. C2×C4⋊(C3⋊C8)D3semidirect
31. C4×#208D3semidirect
394. C32#1483semidirect
450. C3#69852semidirect
451. C3#70427semidirect

Maximal subgroups

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

subgroupindex
#105959502
C2×C3×C4⋊(C3⋊C8)2
C3×C4×#2082
#105890852
#105890822
#704273
#698523