Finite Group Databasebeta

← #11872835

Subgroups — #11872835

Order 1152.

957 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595992C211yesmaximal, characteristic
2C3×#5518C211yesmaximal, characteristic, complemented
3C3×#5000C211yesmaximal, characteristic, complemented
4#10591183C212yesmaximal
5#10591127C212yesmaximal, complemented
6#10590379C212yesmaximal, complemented
7#10590362C212yesmaximal, complemented
8C4×#3717C212yesmaximal, complemented
9#10590308C212yesmaximal, complemented
10#83447—31nomaximal
11#79387—31nomaximal
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C32×#117C2211yescharacteristic
14#64135C2211yescharacteristic
15#64102—22no—
16C22⋊C4×C3⋊D3—22no—
17C4×C4⋊(C3⋊D3)C2212yes—
18C4×C4⋊(C3⋊D3)C2212yes—
19C3×#924C2212yes—
20C3×#889—22no—
21C3×#879—22no—
22C3×#870C2211yescharacteristic, complemented
23C3×#869C2211yescharacteristic, complemented
24C3×C4×Dic6C2212yescomplemented
25C2×#3717C2212yes—
26C2×#3717C2212yes—
27C3×#830C2212yes—
28C3×C4⋊(C3⋊C8)C2212yescomplemented
29C3×#803C2211yescharacteristic, complemented
30C3×C4×C3⋊C8C2211yescharacteristic, complemented
31#63575C2212yescomplemented
32#63573C2212yescomplemented
33#63566C2212yescomplemented
34#63566C2212yescomplemented
35#63564C2212yes—
36#63564C2212yes—
37C3×#541—31no—
38#5521—31no—
39#5521—31no—
40#5521—61no—
41#5518D311yescharacteristic, complemented
42C3×#433—31no—
43#5083—32no—
44#5066—32no—
45#5046—32no—
46#5045—32no—
47#5026—32no—
48C4×#215—32no—
49#5000D311yescharacteristic, complemented
50#4847—32no—
51#4841—32no—
52#4731—32no—
53#4723—32no—
54#4710—32no—
55C4×#204—32no—
56C23×C3⋊D3—21no—
57C22×C32×C4C2311yescharacteristic
58C2×C4⋊(C3⋊D3)—21no—
59C2×C4⋊(C3⋊D3)—24no—
60C2×C4⋊(C3⋊D3)C2312yes—
61C2×C4×C3⋊D3—22no—
62C2×C4×C3⋊D3—22no—
63C2×C3×Dic6C2312yes—
64C32×C4⋊C4D412yes—
65C32×C22⋊C4D412yes—
66C32×C42C2311yescharacteristic
67C32×C42C2311yescharacteristic
68#3757—21no—
69#3752—22no—
70#3752—22no—
71C4⋊(C3⋊Dic3)C2312yes—
72C4×C3⋊Dic3—21no—
73C3×#217—22no—
74C3×C4⋊Dic3—22no—
75C3×C4⋊Dic3C2312yes—
76C3×Dic3⋊C4—22no—
77C3×Dic3⋊C4—22no—
78C3×Dic3⋊C4—22no—
79C3×C4×Dic3—22no—
80C2×C3×C3⋊C8C2312yes—
81C2×C3×C3⋊C8C2312yes—
82#3717—24no—
83#3717—24no—
84#3123—91noSylow
85C22×D12—31no—
86C22×D12—31no—
87C22×D12—61no—
88C3×C4⋊Q8—31no—
89C3×#126—62no—
90C3×#125—31no—
91C3×#125—62no—
92C3×C22⋊Q8—32no—
93C3×C4×Q8—32no—
94C3×#117—21no—
95C3×#117C2×D311yescharacteristic
96C3×#117C2×D311yescharacteristic
97C2×#215—32no—
98C2×#215—32no—
99#926—31no—
100#926—31no—
101#926—61no—
102#924C2×D312yes—
103C2×#204—32no—
104C2×#204—32no—
105#893—64no—
106#893—62no—
107#893—62no—
108#889—22no—
109D3×C22⋊C4—64no—
110D3×C22⋊C4—62no—
111D3×C22⋊C4—62no—
112#879—22no—
113C4×D12—32no—
114C4×D12—32no—
115C4×D12—32no—
116C4×D12—32no—
117C4×D12—62no—
118C4×D12—62no—
119#870C2×D311yescharacteristic, complemented
120#869C2×D311yescharacteristic, complemented
121C4×Dic6C2×D312yescomplemented
122C3×C4⋊C8—32no—
123C3×C22⋊C8—32no—
124C3×#97—31no—
125C3×C4×C8—31no—
126#835—32no—
127#835—32no—
128#830C2×D312yes—
129#821—32no—
130#821—32no—
131#818—32no—
132#817—32no—
133#816—32no—
134#816—32no—
135#809—32no—
136#809—32no—
137#808—32no—
138#807—32no—
139C4⋊(C3⋊C8)C2×D312yescomplemented
140#803C2×D311yescharacteristic, complemented
141C4×C3⋊C8C2×D311yescharacteristic, complemented
142C23×C32C2×D411yescharacteristic
143C22×C3⋊D3—22no—
144C22×C3⋊D3—24no—
145C22×C3⋊D3—82no—
146C2×C32×C4—22no—
147C2×C32×C4C2×D412yes—
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4C2×D412yes—
150C2×C32×C4C2411yescharacteristic
151C2×C3⋊Dic3—22no—
152C4⋊(C3⋊D3)—24no—
153C4⋊(C3⋊D3)—22no—
154C4⋊(C3⋊D3)#4114yes—
155C4×C3⋊D3—82no—
156C4×C3⋊D3—82no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3—22no—
159C3×Dic6—22no—
160C3×Dic6—22no—
161C3×C3⋊C8—22no—
162C3×C3⋊C8—22no—
163#541—31no—
164#518—91no—
165#485—92no—
166#478—92no—
167#461—92no—
168#450—92no—
169#440—92no—
170C4×SD16—92no—
171#433—31no—
172C23×D3—62no—
173C23×D3—61no—
174C23×D3—61no—
175C2×C3×Q8—32no—
176C22×C3×C4—21no—
177C22×C3×C4C22×D311yescharacteristic
178C22×C3×C4C22×D311yescharacteristic
179C2×D12—32no—
180C2×D12—32no—
181C2×D12—62no—
182C2×D12—64no—
183C2×D12—64no—
184C2×D12—62no—
185C2×D12—68no—
186C2×D12—61no—
187C2×D12—61no—
188C2×C4×D3—64no—
189C2×C4×D3—64no—
190C2×C4×D3—62no—
191C2×C4×D3—62no—
192C2×C4×D3—62no—
193C2×C4×D3—62no—
194C2×Dic6C22×D312yes—
195C2×C3×C8—32no—
196C2×C3×C8—32no—
197C3×C4⋊C4—22no—
198C3×C4⋊C4—32no—
199C3×C4⋊C4—62no—
200C3×C4⋊C4—62no—
201C3×C4⋊C4—62no—
202C3×C4⋊C4—62no—
203C3×C4⋊C4D1212yes—
204C3×C4⋊C4#6712yes—
205C3×C22⋊C4—22no—
206C3×C22⋊C4—62no—
207C3×C22⋊C4D1212yes—
208C3×C22⋊C4#6712yes—
209C3×C42—21no—
210C3×C42—21no—
211C3×C42—62no—
212C3×C42C22×D311yescharacteristic
213C3×C42C22×D311yescharacteristic
214C3×C42C22×D311yescharacteristic
215C3×C42C22×D311yescharacteristic
216#217—22no—
217#217—62no—
218#217—61no—
219#217—61no—
220#215—64no—
221#215—64no—
222(C2×D3)⋊C4—64no—
223(C2×D3)⋊C4—64no—
224(C2×D3)⋊C4—62no—
225(C2×D3)⋊C4—62no—
226(C2×D3)⋊C4—62no—
227(C2×D3)⋊C4—62no—
228C4⋊Dic3—22no—
229C4⋊Dic3—32no—
230C4⋊Dic3—32no—
231C4⋊Dic3—62no—
232C4⋊Dic3C22×D312yes—
233Dic3⋊C4—22no—
234Dic3⋊C4—22no—
235Dic3⋊C4—22no—
236C4×Dic3—22no—
237C4×Dic3—62no—
238C4×Dic3—61no—
239C4×Dic3—61no—
240C2×C3⋊C8C22×D312yes—
241C2×C3⋊C8C22×D312yes—
242#204—64no—
243#204—64no—
244C22×C32—21no—
245C22×C32—22no—
246C22×C32C22×D411yescharacteristic
247C2×C3⋊D3—24no—
248C2×C3⋊D3—42no—
249C2×C3⋊D3—42no—
250C2×C3⋊D3—84no—
251C32×C4—21no—
252C32×C4—22no—
253C32×C4—22no—
254C32×C4C2×#4112yes—
255C3⋊Dic3—42no—
256C3×Dic3—42no—
257C3×Dic3—42no—
258C22×D4—91no—
259C2×SD16—92no—
260C2×SD16—92no—
261C4⋊Q8—31no—
262#126—62no—
263#125—31no—
264#125—62no—
265C22⋊Q8—32no—
266C4×Q8—32no—
267C4×D4—92no—
268C4×D4—92no—
269C4×D4—182no—
270#117—91no—
271#117D3211yescharacteristic
272C2×C22⋊C4—182no—
273#107—92no—
274#106—92no—
275C4⋊C8—32no—
276#103—92no—
277#103—92no—
278#102—92no—
279#102—92no—
280C22⋊C8—32no—
281#97—31no—
282C4×C8—31no—
283C23×C3—21no—
284C23×C3C2×D1211yescharacteristic
285C23×C3C2×#6711yescharacteristic
286C22×D3—64no—
287C22×D3—62no—
288C22×D3—62no—
289C22×D3—68no—
290C22×D3—64no—
291C22×D3—64no—
292C22×D3—242no—
293C22×D3—242no—
294C22×D3—244no—
295C3×Q8—62no—
296C3×Q8—62no—
297C2×C3×C4—24no—
298C2×C3×C4—22no—
299C2×C3×C4—22no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—22no—
303C2×C3×C4—22no—
304C2×C3×C4—62no—
305C2×C3×C4—62no—
306C2×C3×C4C2×D1211yescharacteristic
307C2×C3×C4C2×D1212yes—
308C2×C3×C4C2×D1212yes—
309C2×C3×C4C2×#6712yes—
310C2×C3×C4C2×#6711yescharacteristic
311C2×C3×C4C2×#6712yes—
312C2×C3×C4C23×D311yescharacteristic
313C2×C3×C4C23×D311yescharacteristic
314C2×Dic3—22no—
315C2×Dic3—22no—
316C2×Dic3—64no—
317C2×Dic3—62no—
318C2×Dic3—62no—
319D12—34no—
320D12—34no—
321D12—64no—
322D12—68no—
323D12—64no—
324D12—64no—
325D12—64no—
326D12—62no—
327D12—62no—
328C4×D3—242no—
329C4×D3—242no—
330C4×D3—242no—
331C4×D3—242no—
332C4×D3—244no—
333C4×D3—244no—
334Dic6—22no—
335Dic6—22no—
336C3×C8—62no—
337C3×C8—62no—
338C3⋊C8—22no—
339C3⋊C8—22no—
340C2×C32—41no—
341C2×C32#52511yescharacteristic
342C2×C32#57712yes—
343C3⋊D3—44no—
344C24—181no—
345C2×Q8—32no—
346C2×D4—92no—
347C2×D4—184no—
348C2×D4—181no—
349C22×C4—182no—
350C22×C4—182no—
351C22×C4C2×D3211yescharacteristic
352SD16—184no—
353SD16—184no—
354C2×C8—32no—
355C2×C8—32no—
356C4⋊C4—32no—
357C4⋊C4—62no—
358C4⋊C4—62no—
359C4⋊C4—62no—
360C4⋊C4—62no—
361C4⋊C4—92no—
362C4⋊C4#62612yes—
363C22⋊C4—62no—
364C22⋊C4—181no—
365C22⋊C4—182no—
366C22⋊C4—182no—
367C22⋊C4#62612yes—
368C42—62no—
369C42—181no—
370C42C2×D3211yescharacteristic
371C42C2×D3211yescharacteristic
372C22×C3—22no—
373C22×C3—22no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—22no—
377C22×C3—21no—
378C22×C3—42no—
379C22×C3C22×D1211yescharacteristic
380C22×C3C22×#6711yescharacteristic
381C2×D3—68no—
382C2×D3—64no—
383C2×D3—64no—
384C2×D3—124no—
385C2×D3—124no—
386C2×D3—122no—
387C2×D3—122no—
388C2×D3—122no—
389C2×D3—122no—
390C2×D3—248no—
391C2×D3—244no—
392C2×D3—244no—
393C3×C4—22no—
394C3×C4—22no—
395C3×C4—22no—
396C3×C4—21no—
397C3×C4—21no—
398C3×C4—22no—
399C3×C4—22no—
400C3×C4—22no—
401C3×C4—42no—
402C3×C4—42no—
403C3×C4—122no—
404C3×C4—122no—
405C3×C4D3×#4112yes—
406C3×C4D3×#4112yes—
407Dic3—42no—
408Dic3—42no—
409Dic3—124no—
410Dic3—122no—
411Dic3—122no—
412C32#312311yescharacteristic, complemented, Sylow
413C23—184no—
414C23—182no—
415C23—722no—
416C23C2×#62611yescharacteristic
417Q8—62no—
418Q8—62no—
419D4—94no—
420D4—184no—
421D4—182no—
422C2×C4—22no—
423C2×C4—62no—
424C2×C4—62no—
425C2×C4—182no—
426C2×C4—722no—
427C2×C4—722no—
428C2×C4C2×#62612yes—
429C2×C4C2×#62611yescharacteristic
430C2×C4C2×#62612yes—
431C2×C4C22×D3211yescharacteristic
432C8—62no—
433C8—62no—
434C2×C3—22no—
435C2×C3—21no—
436C2×C3—42no—
437C2×C3—41no—
438C2×C3—41no—
439C2×C3#552411yescharacteristic
440C2×C3#575112yes—
441C2×C3#582811yescharacteristic
442C2×C3#583712yes—
443D3—128no—
444D3—124no—
445D3—124no—
446C22—22no—
447C22—21no—
448C22—184no—
449C22—362no—
450C22—362no—
451C22—724no—
452C22C22×#62611yescharacteristic
453C4—22no—
454C4—22no—
455C4—21no—
456C4—122no—
457C4—122no—
458C4—362no—
459C4#6430612yes—
460C3—21no—
461C3#7938711yescharacteristic, complemented
462C3#8344711yescharacteristic, complemented
463C2—41no—
464C2—364no—
465C2#1059503411yescharacteristic
466C2#1059544812yes—
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenter#117D32
hypocenterC32#3123
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C3×#5518C2semidirect
3. C3×#5000C2semidirect
5. #10591127C2semidirect
6. #10590379C2semidirect
7. #10590362C2semidirect
8. C4×#3717C2semidirect
9. #10590308C2semidirect
22. C3×#870C22semidirect
23. C3×#869C22semidirect
24. C3×C4×Dic6C22semidirect
28. C3×C4⋊(C3⋊C8)C22semidirect
29. C3×#803C22semidirect
30. C3×C4×C3⋊C8C22semidirect
31. #63575C22semidirect
32. #63573C22semidirect
33. #63566C22semidirect
34. #63566C22semidirect
41. #5518D3semidirect
49. #5000D3semidirect
119. #870C2×D3semidirect
120. #869C2×D3semidirect
121. C4×Dic6C2×D3semidirect
139. C4⋊(C3⋊C8)C2×D3semidirect
140. #803C2×D3semidirect
141. C4×C3⋊C8C2×D3semidirect
412. C32#3123semidirect
461. C3#79387semidirect
462. C3#83447semidirect

Maximal subgroups

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

subgroupindex
#105959922
C3×#55182
C3×#50002
#105911832
#105911272
#105903792
#105903622
C4×#37172
#105903082
#834473
#793873