Finite Group Databasebeta

← #11783614

Subgroups — #11783614

Order 1152.

753 conjugacy classes of subgroups.

The subgroup lattice has 463 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63855C211yesmaximal, characteristic
2C2×C8×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C2×C3×(C2×D3)⋊C8C211yesmaximal, characteristic
4C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic
5C2×#63555C211yesmaximal, characteristic, complemented
6C3×#4550C211yesmaximal, characteristic, complemented
7#10589155C211yesmaximal, characteristic, complemented
8#69907—31nomaximal
9#68601—31nomaximal
10C22×C3×C4×D3C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C2×C3×C4×Dic3C2211yescharacteristic
15C22×C3×C3⋊C8C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C2×Dic3⋊Dic3C412yes—
18C2×(C2×D3)⋊Dic3C412yes—
19#63855—22no—
20#63855—22no—
21C8×C3⋊Dic3—22no—
22C3×(C2×D3)⋊C8C414yescomplemented
23(C2×D3)⋊(C3⋊C8)C414yescomplemented
24#63555—22no—
25C2×#926—31no—
26C2×#872—31no—
27C2×C3×C22⋊C8—31no—
28C2×#830—31no—
29C2×(C2×D3)⋊C8—31no—
30C2×(C2×D3)⋊C8D311yescharacteristic
31C2×#815—31no—
32C2×#815—31no—
33C2×C8×Dic3—31no—
34C2×C8×Dic3—31no—
35C2×C8×Dic3—61no—
36C3×#336—31no—
37#4550—31no—
38#4550D311yescharacteristic, complemented
39#4524—31no—
40C23×C3×D3C2×C411yescharacteristic
41C22×C32×C4C2311yescharacteristic
42C22×C3⋊Dic3C2×C412yes—
43C22×C3×Dic3C2×C412yes—
44C22×C3×Dic3C2×C411yescharacteristic
45C2×C3×C4×D3—21no—
46C2×C3×C4×D3—21no—
47C2×C3×C4×D3—21no—
48C2×C3×C4×D3—21no—
49C2×C3×C4×D3C2×C412yes—
50C2×C3×C4×D3C2×C412yes—
51C2×C32×C8—21no—
52C2×C32×C8—21no—
53C2×C32×C8C2×C412yes—
54C4×C3⋊Dic3D412yes—
55C4×C3⋊Dic3D412yes—
56C2×C3⋊(C3⋊C8)—21no—
57C2×C3⋊(C3⋊C8)—21no—
58C2×C3⋊(C3⋊C8)C2×C412yes—
59C3×C4×Dic3—21no—
60C3×C4×Dic3—21no—
61C2×C3×C3⋊C8—21no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8C2×C412yes—
66C2×C3×C3⋊C8C2×C412yes—
67Dic3⋊Dic3—24no—
68(C2×D3)⋊Dic3—24no—
69#1750—91noSylow
70C23×C3×C4—31no—
71C22×C4×D3C2×D311yescharacteristic
72C22×C3×C8—21no—
73C22×C3×C8—31no—
74C22×C3×C8—31no—
75C22×C3×C8C2×D311yescharacteristic
76C22×C3×C8C2×D311yescharacteristic
77C2×C3×C42—31no—
78C2×#217—32no—
79C2×(C2×D3)⋊C4—32no—
80#926—62no—
81#926—62no—
82C2×C4⋊Dic3—32no—
83C2×Dic3⋊C4—32no—
84C2×C4×Dic3—31no—
85C2×C4×Dic3—31no—
86C2×C4×Dic3—61no—
87C2×C4×Dic3C2×D311yescharacteristic
88C22×C3⋊C8—31no—
89C22×C3⋊C8—31no—
90C22×C3⋊C8—61no—
91C22×C3⋊C8C2×D311yescharacteristic
92C22×C3⋊C8C2×D311yescharacteristic
93#872—62no—
94#872—62no—
95C3×C22⋊C8—34no—
96#830—34no—
97(C2×D3)⋊C8—34no—
98(C2×D3)⋊C8Dic314yescomplemented
99#815—62no—
100#815—62no—
101C8×Dic3—62no—
102C8×Dic3—62no—
103C8×Dic3—64no—
104C23×C32C22×C411yescharacteristic
105C22×C3×D3—21no—
106C22×C3×D3—21no—
107C22×C3×D3—22no—
108C22×C3×D3—22no—
109C22×C3×D3C4212yes—
110C2×C32×C4C22×C411yescharacteristic
111C2×C32×C4C22×C411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4#4111yescharacteristic
115C2×C32×C4#4111yescharacteristic
116C2×C3⋊Dic3—22no—
117C2×C3⋊Dic3—22no—
118C2×C3⋊Dic3C22⋊C414yes—
119C2×C3×Dic3—21no—
120C2×C3×Dic3—21no—
121C2×C3×Dic3—22no—
122C2×C3×Dic3—22no—
123C2×C3×Dic3—22no—
124C2×C3×Dic3C4212yes—
125C3×C4×D3—22no—
126C3×C4×D3—22no—
127C3×C4×D3—22no—
128C3×C4×D3—22no—
129C32×C8—22no—
130C3⋊(C3⋊C8)—22no—
131C3×C3⋊C8—22no—
132C3×C3⋊C8—22no—
133C2×#117—91no—
134C2×C22⋊C8—31no—
135C2×C22⋊C8—91no—
136C2×#97—91no—
137C2×C4×C8—91no—
138#336—31no—
139#336—91no—
140C24×C3—31no—
141C23×D3C4×D311yescharacteristic
142C22×C3×C4—21no—
143C22×C3×C4—31no—
144C22×C3×C4—32no—
145C22×C3×C4—32no—
146C22×C3×C4—32no—
147C22×C3×C4—61no—
148C22×C3×C4—61no—
149C22×C3×C4—61no—
150C22×C3×C4—61no—
151C22×C3×C4C22×D311yescharacteristic
152C22×C3×C4C22×D311yescharacteristic
153C22×Dic3—32no—
154C22×Dic3—32no—
155C22×Dic3—62no—
156C22×Dic3C4×D312yes—
157C22×Dic3C4×D311yescharacteristic
158C2×C4×D3—21no—
159C2×C4×D3—21no—
160C2×C4×D3—21no—
161C2×C4×D3—21no—
162C2×C4×D3C4×D312yes—
163C2×C4×D3C2×Dic312yes—
164C2×C3×C8—22no—
165C2×C3×C8—22no—
166C2×C3×C8—21no—
167C2×C3×C8—21no—
168C2×C3×C8—21no—
169C2×C3×C8—21no—
170C2×C3×C8—22no—
171C2×C3×C8—32no—
172C2×C3×C8—32no—
173C2×C3×C8—61no—
174C2×C3×C8—61no—
175C2×C3×C8—61no—
176C2×C3×C8—61no—
177C2×C3×C8C4×D312yes—
178C2×C3×C8C2×Dic312yes—
179C3×C42—61no—
180C3×C42—61no—
181#217—64no—
182(C2×D3)⋊C4—64no—
183C4⋊Dic3—64no—
184Dic3⋊C4—64no—
185C4×Dic3—21no—
186C4×Dic3—21no—
187C4×Dic3—32no—
188C4×Dic3—32no—
189C4×Dic3—32no—
190C4×Dic3—32no—
191C4×Dic3—62no—
192C4×Dic3—62no—
193C2×C3⋊C8—21no—
194C2×C3⋊C8—21no—
195C2×C3⋊C8—21no—
196C2×C3⋊C8—21no—
197C2×C3⋊C8—32no—
198C2×C3⋊C8—32no—
199C2×C3⋊C8—62no—
200C2×C3⋊C8—62no—
201C2×C3⋊C8—62no—
202C2×C3⋊C8—61no—
203C2×C3⋊C8—61no—
204C2×C3⋊C8—61no—
205C2×C3⋊C8—61no—
206C2×C3⋊C8C4×D312yes—
207C2×C3⋊C8C2×Dic312yes—
208C22×C32C2×C4211yescharacteristic
209C22×C32C2×C22⋊C411yescharacteristic
210C22×C32#11711yescharacteristic
211C22×C32#13112yes—
212C22×C32#13112yes—
213C2×C3×D3—22no—
214C2×C3×D3—22no—
215C2×C3×D3—22no—
216C2×C3×D3—42no—
217C2×C3×D3—42no—
218C32×C4C4×D411yescharacteristic
219C32×C4C4×D411yescharacteristic
220C32×C4C4×D411yescharacteristic
221C32×C4C4×D411yescharacteristic
222C3⋊Dic3—24no—
223C3×Dic3—22no—
224C3×Dic3—42no—
225C23×C4—31no—
226C22×C8—31no—
227C22×C8—31no—
228C22×C8—91no—
229C22×C8D3211yescharacteristic
230#117—182no—
231#117—182no—
232C2×C4⋊C4—92no—
233C2×C22⋊C4—92no—
234C2×C42—31no—
235C2×C42—91no—
236C22⋊C8—34no—
237C22⋊C8—94no—
238#97—182no—
239C4×C8—182no—
240C23×C3—21no—
241C23×C3—32no—
242C23×C3—61no—
243C23×C3—61no—
244C23×C3—62no—
245C23×C3—62no—
246C23×C3C2×C4×D311yescharacteristic
247C23×C3C2×C4×D311yescharacteristic
248C22×D3—21no—
249C22×D3—21no—
250C22×D3—22no—
251C22×D3—22no—
252C22×D3C4×Dic312yes—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—32no—
260C2×C3×C4—61no—
261C2×C3×C4—61no—
262C2×C3×C4—62no—
263C2×C3×C4—62no—
264C2×C3×C4—62no—
265C2×C3×C4—62no—
266C2×C3×C4—62no—
267C2×C3×C4—62no—
268C2×C3×C4—62no—
269C2×C3×C4C2×C4×D311yescharacteristic
270C2×C3×C4C2×C4×D311yescharacteristic
271C2×C3×C4C2×C4×D311yescharacteristic
272C2×C3×C4D3×D411yescharacteristic
273C2×C3×C4D3×D411yescharacteristic
274C2×C3×C4D3×D411yescharacteristic
275C2×C3×C4D3×D411yescharacteristic
276C2×C3×C4#23711yescharacteristic
277C2×C3×C4#23711yescharacteristic
278C2×C3×C4#23711yescharacteristic
279C2×C3×C4#23911yescharacteristic
280C2×C3×C4C22×Dic311yescharacteristic
281C2×Dic3—21no—
282C2×Dic3—21no—
283C2×Dic3—22no—
284C2×Dic3—22no—
285C2×Dic3—22no—
286C2×Dic3—34no—
287C2×Dic3—34no—
288C2×Dic3—64no—
289C2×Dic3—64no—
290C2×Dic3—64no—
291C2×Dic3—62no—
292C2×Dic3—62no—
293C2×Dic3—62no—
294C2×Dic3—62no—
295C2×Dic3C4×Dic312yes—
296C4×D3—22no—
297C4×D3—22no—
298C4×D3—22no—
299C4×D3—22no—
300C3×C8—24no—
301C3×C8—22no—
302C3×C8—22no—
303C3×C8—62no—
304C3×C8—62no—
305C3⋊C8—22no—
306C3⋊C8—22no—
307C3⋊C8—64no—
308C3⋊C8—62no—
309C3⋊C8—62no—
310C2×C32C4×C22⋊C411yescharacteristic
311C2×C32#40511yescharacteristic
312C2×C32#40511yescharacteristic
313C2×C32#40812yes—
314C2×C32#43312yes—
315C3×D3—42no—
316C24—31no—
317C22×C4—31no—
318C22×C4—32no—
319C22×C4—32no—
320C22×C4—32no—
321C22×C4—61no—
322C22×C4—61no—
323C22×C4—61no—
324C22×C4—61no—
325C22×C4—92no—
326C22×C4C2×D3211yescharacteristic
327C2×C8—21no—
328C2×C8—21no—
329C2×C8—32no—
330C2×C8—32no—
331C2×C8—61no—
332C2×C8—61no—
333C2×C8—61no—
334C2×C8—61no—
335C2×C8—92no—
336C2×C8—181no—
337C2×C8—181no—
338C2×C8D3×Dic312yes—
339C4⋊C4—184no—
340C22⋊C4—184no—
341C42—61no—
342C42—61no—
343C42—92no—
344C42—92no—
345C22×C3—22no—
346C22×C3—22no—
347C22×C3—21no—
348C22×C3—21no—
349C22×C3—21no—
350C22×C3—62no—
351C22×C3—62no—
352C22×C3—62no—
353C22×C3—122no—
354C22×C3—122no—
355C22×C3C42×D311yescharacteristic
356C22×C3#87711yescharacteristic
357C22×C3D3×C22⋊C411yescharacteristic
358C22×C3D3×C22⋊C411yescharacteristic
359C22×C3#89211yescharacteristic
360C22×C3#90112yes—
361C22×C3#90112yes—
362C22×C3#90712yes—
363C22×C3#90712yes—
364C22×C3C2×C4×Dic311yescharacteristic
365C2×D3—22no—
366C2×D3—22no—
367C2×D3—22no—
368C2×D3—42no—
369C2×D3—42no—
370C3×C4—21no—
371C3×C4—21no—
372C3×C4—21no—
373C3×C4—21no—
374C3×C4—62no—
375C3×C4—122no—
376C3×C4#67⋊C411yescharacteristic
377C3×C4#67⋊C411yescharacteristic
378C3×C4#67⋊C411yescharacteristic
379C3×C4#67⋊C411yescharacteristic
380C3×C4#89311yescharacteristic
381C3×C4#89311yescharacteristic
382C3×C4D4×Dic311yescharacteristic
383C3×C4D4×Dic311yescharacteristic
384Dic3—22no—
385Dic3—42no—
386Dic3—68no—
387Dic3—64no—
388Dic3—64no—
389C32#175011yescharacteristic, complemented, Sylow
390C23—32no—
391C23—62no—
392C23—62no—
393C23—61no—
394C23—61no—
395C23C4×D3211yescharacteristic
396C2×C4—32no—
397C2×C4—61no—
398C2×C4—61no—
399C2×C4—62no—
400C2×C4—62no—
401C2×C4—62no—
402C2×C4—62no—
403C2×C4—62no—
404C2×C4—62no—
405C2×C4—62no—
406C2×C4—94no—
407C2×C4—182no—
408C2×C4—182no—
409C2×C4#379611yescharacteristic
410C2×C4C4×D3211yescharacteristic
411C2×C4#380211yescharacteristic
412C2×C4C2×D3×Dic311yescharacteristic
413C2×C4#380511yescharacteristic
414C2×C4#381111yescharacteristic
415C8—22no—
416C8—62no—
417C8—62no—
418C8—182no—
419C2×C3—21no—
420C2×C3—21no—
421C2×C3—21no—
422C2×C3—22no—
423C2×C3—22no—
424C2×C3—122no—
425C2×C3#466611yescharacteristic
426C2×C3#468911yescharacteristic
427C2×C3#470811yescharacteristic
428C2×C3#472012yes—
429C2×C3#472712yes—
430C2×C3#472712yes—
431C2×C3#484012yes—
432C2×C3Dic3×C22⋊C411yescharacteristic
433C2×C3#510111yescharacteristic
434C2×C3#512211yescharacteristic
435D3—42no—
436C22—62no—
437C22—62no—
438C22—62no—
439C22—122no—
440C22—122no—
441C22#6380312yes—
442C22#6380512yes—
443C22C4×D3×Dic311yescharacteristic
444C22#6387811yescharacteristic
445C22#6392111yescharacteristic
446C4—62no—
447C4—122no—
448C4—184no—
449C4#6388111yescharacteristic
450C4#6389811yescharacteristic
451C4#6390211yescharacteristic
452C4#67⋊Dic311yescharacteristic
453C3—21no—
454C3#6860111yescharacteristic, complemented
455C3#6990711yescharacteristic, complemented
456C2—122no—
457C2#1059069211yescharacteristic
458C2#1059069812yes—
459C2#1059090911yescharacteristic
460C2#1059095812yes—
461C2#1059136811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C2×D32
commutatorC22×C32C2×C42
FittingC22×C32×C8C22
socleC23×C32C22×C4
prime radicalC23×C3×D3C2×C4
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1750
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C2×C8×C3⋊Dic3C2semidirect
5. C2×#63555C2semidirect
6. C3×#4550C2semidirect
7. #10589155C2semidirect
22. C3×(C2×D3)⋊C8C4semidirect
23. (C2×D3)⋊(C3⋊C8)C4semidirect
38. #4550D3semidirect
98. (C2×D3)⋊C8Dic3semidirect
389. C32#1750semidirect
454. C3#68601semidirect
455. C3#69907semidirect

Maximal subgroups

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

subgroupindex
C2×#638552
C2×C8×C3⋊Dic32
C2×C3×(C2×D3)⋊C82
C2×(C2×D3)⋊(C3⋊C8)2
C2×#635552
C3×#45502
#105891552
#699073
#686013