Finite Group Databasebeta

← #11868498

Subgroups — #11868498

Order 1152.

849 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#624C211yesmaximal, characteristic
2#10594482C211yesmaximal, characteristic
3C3⋊D3×#103C211yesmaximal, characteristic
4C3×#4799C212yesmaximal, complemented
5#10591552C211yesmaximal, characteristic
6#10591547C212yesmaximal, complemented
7#10590809C212yesmaximal, complemented
8#10590685C211yesmaximal, characteristic
9#10590658C211yesmaximal, characteristic
10#10590573C211yesmaximal, characteristic
11#10590492C212yesmaximal, complemented
12D3×#479—32nomaximal
13C2×Q8×C3⋊D3C2211yescharacteristic
14C2×C8×C3⋊D3C2211yescharacteristic
15C4⋊C4×C3⋊D3C2211yescharacteristic
16C3×Q8×Dic3C2212yes—
17C3×#890C2212yes—
18#63900—21no—
19#63900—21no—
20#63900C2211yescharacteristic
21#63900C2211yescharacteristic
22#63883—21no—
23C4×#624—21no—
24C4×#624C2211yescharacteristic
25#63869C2212yes—
26#63847—22no—
27#63844—22no—
28#63844C2212yes—
29C2×#3710C2211yescharacteristic
30C32×#103C2211yescharacteristic
31#63662C2211yescharacteristic
32#63643C2211yescharacteristic
33#63637C2211yescharacteristic
34C3×#835C2212yes—
35C3×#817C2212yes—
36C3×Dic3⋊C8C2212yes—
37C3×#807C2212yes—
38#63575C2212yes—
39#63574C2212yes—
40Dic3⋊(C3⋊C8)C2212yes—
41#63567C2212yes—
42D3×#125—32no—
43C4×D3×Q8—32no—
44C3×#479—32no—
45#5063—32no—
46#5022—32no—
47D3×#107—32no—
48#4877—32no—
49D3×#106—32no—
50#4857—32no—
51D3×C4⋊C8—32no—
52#4829—32no—
53D3×#103—32no—
54D3×#103—32no—
55D3×#103—61no—
56#4799D312yescomplemented
57#4796—32no—
58C2×C32×Q8C2311yescharacteristic
59Q8×C3⋊D3—22no—
60Q8×C3⋊D3Q814yes—
61C2×C4×C3⋊D3—21no—
62C2×C4×C3⋊D3—21no—
63C2×C4×C3⋊D3C2311yescharacteristic
64C2×#634—21no—
65C2×#634C2311yescharacteristic
66C2×#624—21no—
67C2×#624—21no—
68C2×#624D411yescharacteristic
69C2×#624D411yescharacteristic
70C2×C32×C8C2311yescharacteristic
71C32×C4⋊C4C2311yescharacteristic
72C4⋊(C3⋊Dic3)C2311yescharacteristic
73#3750—21no—
74C2×C3⋊(C3⋊C8)C2311yescharacteristic
75C8×C3⋊D3—22no—
76C3×C4⋊Dic3—22no—
77C3×C4⋊Dic3—22no—
78C3×C4⋊Dic3C2312yes—
79C3×C4⋊Dic3C2312yes—
80C3×Dic3⋊C4—22no—
81C3×C4×Dic3—22no—
82C3×C4×Dic3C2312yes—
83C2×C3×C3⋊C8C2312yes—
84#3724—21no—
85#3724—21no—
86#3724—22no—
87#3724—22no—
88Dic3⋊Dic3—22no—
89Dic32—22no—
90Dic32D412yes—
91#3710—22no—
92C2×#479—91noSylow
93C2×D3×Q8—32no—
94C2×D3×Q8—61no—
95C3×#125—32no—
96C3×C4×Q8—32no—
97Q8×Dic3C2×D312yes—
98C2×D3×C8—32no—
99C2×D3×C8—32no—
100C2×D3×C8—61no—
101D3×C4⋊C4—32no—
102D3×C4⋊C4—32no—
103D3×C4⋊C4—32no—
104D3×C4⋊C4—61no—
105D3×C4⋊C4—62no—
106D3×C4⋊C4—62no—
107D3×C4⋊C4—62no—
108#890—32no—
109#890C2×D312yes—
110#889—62no—
111#889—62no—
112#887—32no—
113#887—62no—
114C42×D3—32no—
115C42×D3—62no—
116#870—32no—
117C4×Dic6—32no—
118C4×Dic6—62no—
119C3×#107—32no—
120C3×#106—32no—
121C3×C4⋊C8—32no—
122C3×#103—21no—
123C3×#103—32no—
124C3×#103C2×D312yes—
125#835—32no—
126#835—61no—
127#835C2×D312yes—
128#818—32no—
129#817C2×D312yes—
130#816—32no—
131#816—32no—
132#816—61no—
133Dic3⋊C8—32no—
134Dic3⋊C8C2×D312yes—
135#810—32no—
136#810—32no—
137#810—61no—
138#808—32no—
139#808—32no—
140#807—32no—
141#807C2×D312yes—
142C4⋊(C3⋊C8)—32no—
143C22×C3⋊D3C2×D411yescharacteristic
144C32×Q8—21no—
145C32×Q8C2×Q812yes—
146C2×C32×C4—21no—
147C2×C32×C4—21no—
148C2×C32×C4C2411yescharacteristic
149C2×C3⋊Dic3—21no—
150C2×C3⋊Dic3—21no—
151C2×C3⋊Dic3C2×D411yescharacteristic
152C4×C3⋊D3—24no—
153C4×C3⋊D3—42no—
154C4×C3⋊D3C2×Q812yes—
155C4×C3⋊D3#4112yes—
156#634—21no—
157#634—24no—
158#634C2×Q812yes—
159C2×C3×Dic3—22no—
160C2×C3×Dic3—22no—
161C2×C3×Dic3C2×D412yes—
162C2×C3×Dic3C2×D412yes—
163#624—22no—
164#624—22no—
165#624—42no—
166#624—42no—
167C32×C8—21no—
168C3⋊(C3⋊C8)—21no—
169C3×C3⋊C8—22no—
170C2×#125—91no—
171C2×C4×Q8—91no—
172#479—32no—
173#479—92no—
174#479—92no—
175#479—92no—
176C2×#107—91no—
177C2×#106—91no—
178C2×C4⋊C8—91no—
179C2×#103—91no—
180C2×#103—91no—
181C2×C3×Q8—21no—
182C2×C3×Q8C22×D312yes—
183D3×Q8—38no—
184D3×Q8—64no—
185D3×Q8—64no—
186D3×Q8—122no—
187C2×C4×D3—32no—
188C2×C4×D3—32no—
189C2×C4×D3—32no—
190C2×C4×D3—61no—
191C2×C4×D3—62no—
192C2×C4×D3—62no—
193C2×C4×D3—62no—
194C2×C4×D3—62no—
195C2×C4×D3—121no—
196C2×C4×D3—121no—
197C2×Dic6—32no—
198C2×Dic6—61no—
199C2×Dic6—62no—
200C2×Dic6—121no—
201C2×C3×C8—21no—
202C2×C3×C8—32no—
203C2×C3×C8C22×D312yes—
204C3×C4⋊C4—21no—
205C3×C4⋊C4—32no—
206C3×C4⋊C4—32no—
207C3×C4⋊C4—62no—
208C3×C4⋊C4—62no—
209C3×C4⋊C4—62no—
210C3×C4⋊C4C22×D312yes—
211C3×C42—32no—
212C3×C42—62no—
213C4⋊Dic3—22no—
214C4⋊Dic3—22no—
215C4⋊Dic3—32no—
216C4⋊Dic3—61no—
217C4⋊Dic3—62no—
218C4⋊Dic3C22×D312yes—
219C4⋊Dic3C22×D312yes—
220Dic3⋊C4—22no—
221Dic3⋊C4—62no—
222Dic3⋊C4—62no—
223Dic3⋊C4—62no—
224Dic3⋊C4—62no—
225Dic3⋊C4—62no—
226Dic3⋊C4—62no—
227Dic3⋊C4—62no—
228Dic3⋊C4—62no—
229Dic3⋊C4—121no—
230C4×Dic3—22no—
231C4×Dic3—32no—
232C4×Dic3—32no—
233C4×Dic3—62no—
234C4×Dic3—62no—
235C4×Dic3C22×D312yes—
236C2×C3⋊C8—32no—
237C2×C3⋊C8—61no—
238C2×C3⋊C8C22×D312yes—
239D3×C8—64no—
240D3×C8—64no—
241D3×C8—122no—
242C22×C32C22×D411yescharacteristic
243C2×C3⋊D3C22⋊Q812yes—
244C2×C3⋊D3#13512yes—
245C2×C3⋊D3#13712yes—
246C32×C4—22no—
247C32×C4—41no—
248C32×C4C22×Q811yescharacteristic
249C32×C4C2×#4111yescharacteristic
250C3⋊Dic3—22no—
251C3⋊Dic3—41no—
252C3⋊Dic3C22⋊Q812yes—
253C3×Dic3—22no—
254C3×Dic3—22no—
255C3×Dic3—42no—
256C3×Dic3—42no—
257C22×Q8—91no—
258C22×C8—91no—
259C22×C8—91no—
260#125—32no—
261#125—92no—
262#125—182no—
263C4×Q8—32no—
264C4×Q8—92no—
265C4×Q8—182no—
266C2×C4⋊C4—91no—
267C2×C4⋊C4—91no—
268C2×C4⋊C4—91no—
269C2×C4⋊C4—181no—
270C2×C4⋊C4—181no—
271C2×C4⋊C4—181no—
272C2×C42—91no—
273C2×C42—181no—
274#107—32no—
275#107—92no—
276#106—32no—
277#106—92no—
278C4⋊C8—32no—
279C4⋊C8—92no—
280#103—32no—
281#103—92no—
282#103—91no—
283#103—91no—
284#103—91no—
285#103D3211yescharacteristic
286C22×D3—32no—
287C22×D3—61no—
288C3×Q8—22no—
289C3×Q8—22no—
290C3×Q8—41no—
291C3×Q8D3×Q814yes—
292C2×C3×C4—22no—
293C2×C3×C4—22no—
294C2×C3×C4—21no—
295C2×C3×C4—32no—
296C2×C3×C4—32no—
297C2×C3×C4—41no—
298C2×C3×C4—41no—
299C2×C3×C4—62no—
300C2×C3×C4—62no—
301C2×C3×C4C23×D312yes—
302C2×Dic3—22no—
303C2×Dic3—22no—
304C2×Dic3—32no—
305C2×Dic3—61no—
306C2×Dic3—62no—
307C2×Dic3—62no—
308C2×Dic3—121no—
309C2×Dic3—121no—
310C2×Dic3D3×D412yes—
311C2×Dic3D3×D412yes—
312C4×D3—34no—
313C4×D3—34no—
314C4×D3—62no—
315C4×D3—62no—
316C4×D3—64no—
317C4×D3—64no—
318C4×D3—68no—
319C4×D3—124no—
320C4×D3—124no—
321C4×D3—124no—
322C4×D3—124no—
323C4×D3—242no—
324Dic6—34no—
325Dic6—62no—
326Dic6—68no—
327Dic6—62no—
328Dic6—124no—
329Dic6—121no—
330C3×C8—22no—
331C3×C8—41no—
332C3×C8—62no—
333C3⋊C8—22no—
334C3⋊C8—62no—
335C3⋊C8—121no—
336C2×C32C2×C22⋊Q811yescharacteristic
337C2×C32C2×#13511yescharacteristic
338C2×C32C2×#13711yescharacteristic
339C3⋊D3#47914yescomplemented
340C2×Q8—94no—
341C2×Q8—91no—
342C2×Q8—181no—
343C2×Q8—182no—
344C2×Q8C2×D3211yescharacteristic
345C22×C4—91no—
346C22×C4—91no—
347C22×C4—91no—
348C22×C4—181no—
349C22×C4—181no—
350C22×C4—181no—
351C22×C4—181no—
352C2×C8—32no—
353C2×C8—91no—
354C2×C8—182no—
355C2×C8—182no—
356C2×C8C2×D3211yescharacteristic
357C4⋊C4—32no—
358C4⋊C4—32no—
359C4⋊C4—62no—
360C4⋊C4—62no—
361C4⋊C4—62no—
362C4⋊C4—91no—
363C4⋊C4—181no—
364C4⋊C4—182no—
365C4⋊C4—182no—
366C4⋊C4—182no—
367C4⋊C4—181no—
368C4⋊C4—181no—
369C4⋊C4C2×D3211yescharacteristic
370C42—32no—
371C42—62no—
372C42—92no—
373C42—182no—
374C22×C3—21no—
375C22×C3C2×D3×D412yes—
376C2×D3—34no—
377C2×D3—34no—
378C2×D3—34no—
379C2×D3—62no—
380C2×D3—62no—
381C2×D3—62no—
382C3×C4—24no—
383C3×C4—21no—
384C3×C4—21no—
385C3×C4—42no—
386C3×C4—42no—
387C3×C4—62no—
388C3×C4—62no—
389C3×C4—81no—
390C3×C4—122no—
391C3×C4—122no—
392C3×C4C2×D3×Q812yes—
393C3×C4D3×#4112yes—
394Dic3—22no—
395Dic3—22no—
396Dic3—34no—
397Dic3—42no—
398Dic3—42no—
399Dic3—62no—
400Dic3—64no—
401Dic3—122no—
402Dic3—122no—
403Dic3—241no—
404C32C2×#47911yescharacteristic, complemented, Sylow
405C23—91no—
406Q8—21no—
407Q8—92no—
408Q8—184no—
409Q8—181no—
410Q8#379712yes—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—32no—
414C2×C4—32no—
415C2×C4—62no—
416C2×C4—62no—
417C2×C4—91no—
418C2×C4—92no—
419C2×C4—92no—
420C2×C4—184no—
421C2×C4—182no—
422C2×C4—182no—
423C2×C4—181no—
424C2×C4—181no—
425C2×C4—362no—
426C2×C4—362no—
427C2×C4—362no—
428C2×C4C22×D3211yescharacteristic
429C8—21no—
430C8—62no—
431C8—181no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—21no—
435C2×C3D3×C22⋊Q812yes—
436C2×C3D3×#13512yes—
437C2×C3D3×#13712yes—
438D3—38no—
439D3—64no—
440C22—92no—
441C22—92no—
442C22—92no—
443C22D32×D411yescharacteristic
444C4—22no—
445C4—41no—
446C4—62no—
447C4—62no—
448C4—92no—
449C4—122no—
450C4—122no—
451C4—182no—
452C4—361no—
453C4C2×#379711yescharacteristic
454C4#6431211yescharacteristic
455C3—21no—
456C3D3×#47912yescomplemented
457C2—94no—
458C2#1059406711yescharacteristic
459C2#1059474711yescharacteristic
460C2#1059476011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenter#103D32
hypocenterC32C2×#479
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
4. C3×#4799C2semidirect
6. #10591547C2semidirect
7. #10590809C2semidirect
11. #10590492C2semidirect
56. #4799D3semidirect
339. C3⋊D3#479semidirect
404. C32C2×#479semidirect
456. C3D3×#479semidirect

Maximal subgroups

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

subgroupindex
Q8×#6242
#105944822
C3⋊D3×#1032
C3×#47992
#105915522
#105915472
#105908092
#105906852
#105906582
#105905732
#105904922
D3×#4793