Finite Group Databasebeta

← #11872836

Subgroups — #11872836

Order 1152.

836 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5521C211yesmaximal, characteristic
2C3×#5518C211yesmaximal, characteristic, complemented
3#10592699C211yesmaximal, characteristic, complemented
4#10591169C212yesmaximal
5#10591102C212yesmaximal, complemented
6#10590363C212yesmaximal, complemented
7#10590358C212yesmaximal, complemented
8C4×#3715C212yesmaximal, complemented
9#10590270C212yesmaximal, complemented
10#83447—31nomaximal
11#82545—31nomaximal
12C22×C3×D12C2211yescharacteristic
13C32×#117C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C3×#924C2212yes—
16C3×#893—22no—
17C3×#889—22no—
18C3×D3×C22⋊C4—22no—
19C3×#879—22no—
20C3×C4×D12C2212yes—
21C3×C4×D12C2212yes—
22C3×#870C2211yescharacteristic, complemented
23C3×#869C2211yescharacteristic, complemented
24C3×C4×Dic6C2212yescomplemented
25C2×#3715C2212yes—
26C2×#3715C2212yes—
27#63657C2212yes—
28C4⋊(C3⋊(C3⋊C8))C2212yescomplemented
29#63630C2211yescharacteristic, complemented
30C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
31#63576C2212yescomplemented
32#63574C2212yescomplemented
33#63565C2212yescomplemented
34#63565C2212yescomplemented
35#63562C2212yes—
36#63562C2212yes—
37C3×#541—31no—
38C3×#518—31no—
39#5521D311yescharacteristic
40#5518D311yescharacteristic, complemented
41#5218—32no—
42#5083—32no—
43#5066—32no—
44#5046—32no—
45#5045—32no—
46#5026—32no—
47C4×#215—32no—
48#5019—32no—
49#5018—32no—
50C4×#214—32no—
51#5009—32no—
52#5000—31no—
53#5000—31no—
54#5000—61no—
55#4996—32no—
56C23×C3×D3—21no—
57C22×C32×C4C2311yescharacteristic
58C2×C3×D12—21no—
59C2×C3×D12—24no—
60C2×C3×D12C2312yes—
61C2×C3×C4×D3—22no—
62C2×C3×C4×D3—22no—
63C2×C3×Dic6C2312yes—
64C32×C4⋊C4D412yes—
65C32×C22⋊C4D412yes—
66C32×C42C2311yescharacteristic
67C32×C42C2311yescharacteristic
68C2×C3⋊(C3⋊C8)C2312yes—
69C2×C3⋊(C3⋊C8)C2312yes—
70C3×#217—22no—
71C3×#217—21no—
72C3×(C2×D3)⋊C4—22no—
73C3×(C2×D3)⋊C4—22no—
74C3×C4⋊Dic3—22no—
75C3×C4⋊Dic3C2312yes—
76C3×C4⋊Dic3C2312yes—
77C3×Dic3⋊C4—22no—
78C3×Dic3⋊C4—22no—
79C3×Dic3⋊C4—22no—
80C3×C4×Dic3—22no—
81C3×C4×Dic3—21no—
82#3715—24no—
83#3715—24no—
84#3123—91noSylow
85C22×C3×D4—31no—
86C22×D12C2×D311yescharacteristic
87C3×C4⋊Q8—31no—
88C3×#126—62no—
89C3×#125—31no—
90C3×#125—62no—
91C3×C22⋊Q8—32no—
92C3×C4×Q8—32no—
93C3×C4×D4—32no—
94C3×C4×D4—32no—
95C3×C4×D4—62no—
96C3×#117—21no—
97C3×#117—31no—
98C3×#117C2×D311yescharacteristic
99C3×#117C2×D311yescharacteristic
100C2×C3×C22⋊C4—62no—
101C2×#215—32no—
102C2×#215—32no—
103C2×#214—32no—
104C2×#214—32no—
105#926C2×D311yescharacteristic
106#924C2×D312yes—
107#893—22no—
108#889—22no—
109D3×C22⋊C4—22no—
110#879—22no—
111C4×D12C2×D312yes—
112C4×D12C2×D312yes—
113#870C2×D311yescharacteristic, complemented
114#869C2×D311yescharacteristic, complemented
115C4×Dic6C2×D312yescomplemented
116#835—32no—
117#835—32no—
118#832—32no—
119#832—32no—
120#830—32no—
121#830—32no—
122#830—62no—
123#810—32no—
124#810—32no—
125#809—32no—
126#809—32no—
127#808—32no—
128#808—32no—
129#807—32no—
130#807—32no—
131C4⋊(C3⋊C8)—32no—
132C4⋊(C3⋊C8)—32no—
133C4⋊(C3⋊C8)—62no—
134#803—31no—
135#803—31no—
136#803—61no—
137C4×C3⋊C8—31no—
138C4×C3⋊C8—31no—
139C4×C3⋊C8—61no—
140C23×C32C2×D411yescharacteristic
141C22×C3×D3—22no—
142C22×C3×D3—24no—
143C22×C3×D3—82no—
144C2×C32×C4—22no—
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4C2×D412yes—
147C2×C32×C4C2×D412yes—
148C2×C32×C4C2411yescharacteristic
149C2×C3×Dic3—22no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—22no—
152C3×D12—24no—
153C3×D12—22no—
154C3×D12#4114yes—
155C3×C4×D3—82no—
156C3×C4×D3—82no—
157C3×Dic6—22no—
158C3×Dic6—22no—
159C3⋊(C3⋊C8)—22no—
160C3⋊(C3⋊C8)—22no—
161#541—31no—
162#518—31no—
163#485—92no—
164#478—92no—
165#461—92no—
166#450—92no—
167#440—92no—
168C4×SD16—92no—
169#433—91no—
170C24×C3—61no—
171C23×D3—21no—
172C2×C3×Q8—32no—
173C2×C3×D4—32no—
174C2×C3×D4—64no—
175C2×C3×D4—61no—
176C22×C3×C4—21no—
177C22×C3×C4—62no—
178C22×C3×C4—62no—
179C22×C3×C4C22×D311yescharacteristic
180C22×C3×C4C22×D311yescharacteristic
181C2×D12—21no—
182C2×D12—24no—
183C2×D12C22×D312yes—
184C2×C4×D3—22no—
185C2×C4×D3—22no—
186C2×Dic6C22×D312yes—
187C3×C4⋊C4—22no—
188C3×C4⋊C4—32no—
189C3×C4⋊C4—32no—
190C3×C4⋊C4—62no—
191C3×C4⋊C4—62no—
192C3×C4⋊C4—62no—
193C3×C4⋊C4—62no—
194C3×C4⋊C4#6712yes—
195C3×C4⋊C4#6712yes—
196C3×C22⋊C4—22no—
197C3×C22⋊C4—61no—
198C3×C22⋊C4—62no—
199C3×C22⋊C4—62no—
200C3×C22⋊C4—62no—
201C3×C22⋊C4#6712yes—
202C3×C22⋊C4#6712yes—
203C3×C42—21no—
204C3×C42—21no—
205C3×C42—61no—
206C3×C42—62no—
207C3×C42C22×D311yescharacteristic
208C3×C42C22×D311yescharacteristic
209C3×C42C22×D311yescharacteristic
210C3×C42C22×D311yescharacteristic
211#217—22no—
212#217—21no—
213#215—64no—
214#215—64no—
215#214—64no—
216#214—64no—
217(C2×D3)⋊C4—22no—
218(C2×D3)⋊C4—22no—
219C4⋊Dic3—22no—
220C4⋊Dic3C22×D312yes—
221C4⋊Dic3C22×D312yes—
222Dic3⋊C4—22no—
223Dic3⋊C4—22no—
224Dic3⋊C4—22no—
225C4×Dic3—22no—
226C4×Dic3—21no—
227C2×C3⋊C8—32no—
228C2×C3⋊C8—32no—
229C2×C3⋊C8—32no—
230C2×C3⋊C8—32no—
231C2×C3⋊C8—62no—
232C2×C3⋊C8—62no—
233C22×C32—21no—
234C22×C32—22no—
235C22×C32C22×D411yescharacteristic
236C2×C3×D3—24no—
237C2×C3×D3—42no—
238C2×C3×D3—42no—
239C2×C3×D3—84no—
240C32×C4—21no—
241C32×C4—22no—
242C32×C4—22no—
243C32×C4C2×#4112yes—
244C3×Dic3—42no—
245C3×Dic3—42no—
246C3×Dic3—42no—
247C22×D4—31no—
248C2×SD16—92no—
249C2×SD16—92no—
250C4⋊Q8—31no—
251#126—62no—
252#125—31no—
253#125—62no—
254C22⋊Q8—32no—
255C4×Q8—32no—
256C4×D4—32no—
257C4×D4—32no—
258C4×D4—62no—
259#117—31no—
260#117D3211yescharacteristic
261C2×C22⋊C4—62no—
262#107—92no—
263#106—92no—
264C4⋊C8—92no—
265#103—92no—
266#103—92no—
267#102—92no—
268#102—92no—
269C22⋊C8—92no—
270#97—91no—
271C4×C8—91no—
272C23×C3—21no—
273C23×C3—64no—
274C23×C3—62no—
275C23×C3—242no—
276C23×C3C2×#6711yescharacteristic
277C23×C3C2×#6711yescharacteristic
278C22×D3—22no—
279C22×D3—24no—
280C22×D3—82no—
281C3×Q8—62no—
282C3×Q8—62no—
283C3×D4—34no—
284C3×D4—64no—
285C3×D4—62no—
286C2×C3×C4—22no—
287C2×C3×C4—22no—
288C2×C3×C4—21no—
289C2×C3×C4—22no—
290C2×C3×C4—22no—
291C2×C3×C4—21no—
292C2×C3×C4—42no—
293C2×C3×C4—62no—
294C2×C3×C4—62no—
295C2×C3×C4—62no—
296C2×C3×C4—242no—
297C2×C3×C4—242no—
298C2×C3×C4C2×#6712yes—
299C2×C3×C4C2×#6711yescharacteristic
300C2×C3×C4C2×#6711yescharacteristic
301C2×C3×C4C2×#6712yes—
302C2×C3×C4C2×#6712yes—
303C2×C3×C4C2×#6712yes—
304C2×C3×C4C23×D311yescharacteristic
305C2×C3×C4C23×D311yescharacteristic
306C2×Dic3—22no—
307C2×Dic3—22no—
308C2×Dic3—22no—
309D12—24no—
310D12—22no—
311D12#23514yes—
312C4×D3—82no—
313C4×D3—82no—
314Dic6—22no—
315Dic6—22no—
316C3⋊C8—62no—
317C3⋊C8—62no—
318C3⋊C8—62no—
319C3⋊C8—62no—
320C3⋊C8—122no—
321C3⋊C8—122no—
322C2×C32—41no—
323C2×C32#52511yescharacteristic
324C2×C32#57712yes—
325C3×D3—44no—
326C24—61no—
327C2×Q8—32no—
328C2×D4—32no—
329C2×D4—64no—
330C2×D4—61no—
331C22×C4—62no—
332C22×C4—62no—
333C22×C4C2×D3211yescharacteristic
334SD16—184no—
335SD16—184no—
336C2×C8—92no—
337C2×C8—92no—
338C4⋊C4—32no—
339C4⋊C4—32no—
340C4⋊C4—62no—
341C4⋊C4—62no—
342C4⋊C4—62no—
343C4⋊C4—62no—
344C4⋊C4#62512yes—
345C22⋊C4—61no—
346C22⋊C4—62no—
347C22⋊C4—62no—
348C22⋊C4—62no—
349C22⋊C4#62512yes—
350C42—61no—
351C42—62no—
352C42C2×D3211yescharacteristic
353C42C2×D3211yescharacteristic
354C22×C3—21no—
355C22×C3—21no—
356C22×C3—22no—
357C22×C3—22no—
358C22×C3—21no—
359C22×C3—41no—
360C22×C3—42no—
361C22×C3—64no—
362C22×C3—122no—
363C22×C3—122no—
364C22×C3—244no—
365C22×C3C22×#6711yescharacteristic
366C22×C3C22×#6711yescharacteristic
367C2×D3—24no—
368C2×D3—42no—
369C2×D3—42no—
370C2×D3—84no—
371C3×C4—21no—
372C3×C4—21no—
373C3×C4—22no—
374C3×C4—22no—
375C3×C4—22no—
376C3×C4—22no—
377C3×C4—22no—
378C3×C4—41no—
379C3×C4—42no—
380C3×C4—42no—
381C3×C4—122no—
382C3×C4—122no—
383C3×C4—122no—
384C3×C4C2×#23512yes—
385C3×C4D3×#4112yes—
386Dic3—42no—
387Dic3—42no—
388Dic3—42no—
389C32#312311yescharacteristic, complemented, Sylow
390C23—64no—
391C23—62no—
392C23—242no—
393C23C2×#62511yescharacteristic
394Q8—62no—
395Q8—62no—
396D4—34no—
397D4—64no—
398D4—62no—
399C2×C4—22no—
400C2×C4—62no—
401C2×C4—62no—
402C2×C4—62no—
403C2×C4—242no—
404C2×C4—242no—
405C2×C4C2×#62512yes—
406C2×C4C2×#62511yescharacteristic
407C2×C4C2×#62512yes—
408C2×C4C22×D3211yescharacteristic
409C8—182no—
410C8—182no—
411C2×C3—22no—
412C2×C3—21no—
413C2×C3—41no—
414C2×C3—41no—
415C2×C3—81no—
416C2×C3—124no—
417C2×C3#579111yescharacteristic
418C2×C3#582811yescharacteristic
419C2×C3#583612yes—
420C2×C3#583712yes—
421D3—44no—
422C22—22no—
423C22—21no—
424C22—64no—
425C22—122no—
426C22—122no—
427C22—244no—
428C22C22×#62511yescharacteristic
429C4—22no—
430C4—22no—
431C4—21no—
432C4—122no—
433C4—122no—
434C4—122no—
435C4D3×#23512yes—
436C3—21no—
437C3#8254511yescharacteristic, complemented
438C3#8344711yescharacteristic, complemented
439C2—41no—
440C2—124no—
441C2#1059502211yescharacteristic
442C2#1059544612yes—
subgroupG/H
centerC22C22×#625
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radicalC22×C3×D12C22
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. #10592699C2semidirect
5. #10591102C2semidirect
6. #10590363C2semidirect
7. #10590358C2semidirect
8. C4×#3715C2semidirect
9. #10590270C2semidirect
22. C3×#870C22semidirect
23. C3×#869C22semidirect
24. C3×C4×Dic6C22semidirect
28. C4⋊(C3⋊(C3⋊C8))C22semidirect
29. #63630C22semidirect
30. C4×C3⋊(C3⋊C8)C22semidirect
31. #63576C22semidirect
32. #63574C22semidirect
33. #63565C22semidirect
34. #63565C22semidirect
40. #5518D3semidirect
113. #870C2×D3semidirect
114. #869C2×D3semidirect
115. C4×Dic6C2×D3semidirect
389. C32#3123semidirect
437. C3#82545semidirect
438. C3#83447semidirect

Maximal subgroups

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

subgroupindex
C3×#55212
C3×#55182
#105926992
#105911692
#105911022
#105903632
#105903582
C4×#37152
#105902702
#834473
#825453