Finite Group Databasebeta

← #11872834

Subgroups — #11872834

Order 1152.

884 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595989C211yesmaximal, characteristic, complemented
2C3×#5521C211yesmaximal, characteristic
3C3×#5000C211yesmaximal, characteristic, complemented
4#10591172C212yesmaximal
5#10591134C212yesmaximal, complemented
6#10590365C212yesmaximal, complemented
7#10590360C212yesmaximal, complemented
8C4×#3716C212yesmaximal, complemented
9#10590271C212yesmaximal, complemented
10#82545—31nomaximal
11#79387—31nomaximal
12C22×C3×D12C2211yescharacteristic
13C32×#117C2211yescharacteristic
14#64133C2212yes—
15#64098—22no—
16#64088—22no—
17#64079C2211yescharacteristic, complemented
18#64078C2211yescharacteristic, complemented
19C4×#634C2212yescomplemented
20C3×#926C2211yescharacteristic
21C3×#893—22no—
22C3×D3×C22⋊C4—22no—
23C3×C4×D12C2212yes—
24C3×C4×D12C2212yes—
25C2×#3716C2212yes—
26C2×#3716C2212yes—
27C3×#830C2212yes—
28C3×C4⋊(C3⋊C8)C2212yescomplemented
29C3×#803C2211yescharacteristic, complemented
30C3×C4×C3⋊C8C2211yescharacteristic, complemented
31#63575C2212yescomplemented
32#63573C2212yescomplemented
33#63567C2212yescomplemented
34#63567C2212yescomplemented
35#63563C2212yes—
36#63563C2212yes—
37C3×#518—31no—
38#5521D311yescharacteristic
39#5518—31no—
40#5518—31no—
41#5518—61no—
42C3×#433—31no—
43#5218—32no—
44#5019—32no—
45#5018—32no—
46C4×#214—32no—
47#5009—32no—
48#5000D311yescharacteristic, complemented
49#4996—32no—
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×#634C2312yes—
59C2×C3×D12—21no—
60C2×C3×D12—24no—
61C2×C3×D12C2312yes—
62C2×C3×C4×D3—22no—
63C2×C3×C4×D3—22no—
64C32×C4⋊C4D412yes—
65C32×C22⋊C4D412yes—
66C32×C42C2311yescharacteristic
67C32×C42C2311yescharacteristic
68#3757—22no—
69C4⋊(C3⋊Dic3)—22no—
70C4⋊(C3⋊Dic3)C2312yes—
71#3750—22no—
72#3750—22no—
73#3750—22no—
74C4×C3⋊Dic3—22no—
75C3×#217—21no—
76C3×(C2×D3)⋊C4—22no—
77C3×(C2×D3)⋊C4—22no—
78C3×C4⋊Dic3C2312yes—
79C3×C4×Dic3—21no—
80C2×C3×C3⋊C8C2312yes—
81C2×C3×C3⋊C8C2312yes—
82#3716—24no—
83#3716—24no—
84#3123—91noSylow
85C22×C3×D4—31no—
86C22×D12C2×D311yescharacteristic
87C3×C4×D4—32no—
88C3×C4×D4—32no—
89C3×C4×D4—62no—
90C3×#117—21no—
91C3×#117—31no—
92C3×#117C2×D311yescharacteristic
93C3×#117C2×D311yescharacteristic
94C2×C3×C22⋊C4—62no—
95C2×#214—32no—
96C2×#214—32no—
97#926C2×D311yescharacteristic
98#924—32no—
99#924—32no—
100#924—62no—
101C2×#204—32no—
102C2×#204—32no—
103#893—22no—
104#889—64no—
105#889—62no—
106#889—62no—
107D3×C22⋊C4—22no—
108#879—64no—
109#879—62no—
110#879—62no—
111C4×D12C2×D312yes—
112C4×D12C2×D312yes—
113#870—31no—
114#870—31no—
115#870—61no—
116#869—31no—
117#869—31no—
118#869—61no—
119C4×Dic6—32no—
120C4×Dic6—32no—
121C4×Dic6—62no—
122C3×C4⋊C8—32no—
123C3×C22⋊C8—32no—
124C3×#97—31no—
125C3×C4×C8—31no—
126#832—32no—
127#832—32no—
128#830C2×D312yes—
129#821—32no—
130#821—32no—
131#818—32no—
132#817—32no—
133#816—32no—
134#816—32no—
135#810—32no—
136#810—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×D411yescharacteristic
148C2×C32×C4C2×D412yes—
149C2×C32×C4C2×D412yes—
150C2×C32×C4C2411yescharacteristic
151C2×C3⋊Dic3—22no—
152C2×C3⋊Dic3—22no—
153#634—22no—
154#634—22no—
155C2×C3×Dic3—22no—
156C3×D12—24no—
157C3×D12—22no—
158C3×D12#4114yes—
159C3×C4×D3—82no—
160C3×C4×D3—82no—
161C3×C3⋊C8—22no—
162C3×C3⋊C8—22no—
163#541—91no—
164#518—31no—
165#485—92no—
166#478—92no—
167#461—92no—
168#450—92no—
169#440—92no—
170C4×SD16—92no—
171#433—31no—
172C24×C3—61no—
173C23×D3—21no—
174C2×C3×D4—32no—
175C2×C3×D4—64no—
176C2×C3×D4—61no—
177C22×C3×C4—21no—
178C22×C3×C4—62no—
179C22×C3×C4—62no—
180C22×C3×C4C22×D311yescharacteristic
181C22×C3×C4C22×D311yescharacteristic
182C2×D12—21no—
183C2×D12—24no—
184C2×D12C22×D312yes—
185C2×C4×D3—22no—
186C2×C4×D3—22no—
187C2×Dic6—32no—
188C2×Dic6—32no—
189C2×Dic6—62no—
190C2×C3×C8—32no—
191C2×C3×C8—32no—
192C3×C4⋊C4—22no—
193C3×C4⋊C4—32no—
194C3×C4⋊C4D1212yes—
195C3×C4⋊C4#6712yes—
196C3×C22⋊C4—22no—
197C3×C22⋊C4—61no—
198C3×C22⋊C4—62no—
199C3×C22⋊C4—62no—
200C3×C22⋊C4D1212yes—
201C3×C22⋊C4#6712yes—
202C3×C42—21no—
203C3×C42—21no—
204C3×C42—61no—
205C3×C42C22×D311yescharacteristic
206C3×C42C22×D311yescharacteristic
207C3×C42C22×D311yescharacteristic
208C3×C42C22×D311yescharacteristic
209#217—21no—
210#217—64no—
211#217—62no—
212#217—62no—
213#214—64no—
214#214—64no—
215(C2×D3)⋊C4—22no—
216(C2×D3)⋊C4—22no—
217C4⋊Dic3—32no—
218C4⋊Dic3—32no—
219C4⋊Dic3—62no—
220C4⋊Dic3—64no—
221C4⋊Dic3—62no—
222C4⋊Dic3—62no—
223C4⋊Dic3C22×D312yes—
224Dic3⋊C4—64no—
225Dic3⋊C4—64no—
226Dic3⋊C4—64no—
227Dic3⋊C4—62no—
228Dic3⋊C4—62no—
229Dic3⋊C4—62no—
230Dic3⋊C4—62no—
231Dic3⋊C4—62no—
232Dic3⋊C4—62no—
233C4×Dic3—21no—
234C4×Dic3—64no—
235C4×Dic3—62no—
236C4×Dic3—62no—
237C2×C3⋊C8C22×D312yes—
238C2×C3⋊C8C22×D312yes—
239#204—64no—
240#204—64no—
241C22×C32—21no—
242C22×C32—22no—
243C22×C32C22×D411yescharacteristic
244C2×C3×D3—24no—
245C2×C3×D3—42no—
246C2×C3×D3—42no—
247C2×C3×D3—84no—
248C32×C4—21no—
249C32×C4—22no—
250C32×C4—22no—
251C32×C4C2×#4112yes—
252C3⋊Dic3—42no—
253C3⋊Dic3—42no—
254C3×Dic3—42no—
255C22×D4—31no—
256C2×SD16—92no—
257C2×SD16—92no—
258C4⋊Q8—91no—
259#126—182no—
260#125—91no—
261#125—182no—
262C22⋊Q8—92no—
263C4×Q8—92no—
264C4×D4—32no—
265C4×D4—32no—
266C4×D4—62no—
267#117—31no—
268#117D3211yescharacteristic
269C2×C22⋊C4—62no—
270#107—92no—
271#106—92no—
272C4⋊C8—32no—
273#103—92no—
274#103—92no—
275#102—92no—
276#102—92no—
277C22⋊C8—32no—
278#97—31no—
279C4×C8—31no—
280C23×C3—21no—
281C23×C3—64no—
282C23×C3—62no—
283C23×C3—242no—
284C23×C3C2×D1211yescharacteristic
285C23×C3C2×#6711yescharacteristic
286C22×D3—22no—
287C22×D3—24no—
288C22×D3—82no—
289C3×D4—34no—
290C3×D4—64no—
291C3×D4—62no—
292C2×C3×C4—22no—
293C2×C3×C4—22no—
294C2×C3×C4—21no—
295C2×C3×C4—22no—
296C2×C3×C4—21no—
297C2×C3×C4—22no—
298C2×C3×C4—42no—
299C2×C3×C4—62no—
300C2×C3×C4—242no—
301C2×C3×C4—242no—
302C2×C3×C4C2×D1212yes—
303C2×C3×C4C2×D1211yescharacteristic
304C2×C3×C4C2×D1212yes—
305C2×C3×C4C2×#6711yescharacteristic
306C2×C3×C4C2×#6712yes—
307C2×C3×C4C2×#6712yes—
308C2×C3×C4C23×D311yescharacteristic
309C2×C3×C4C23×D311yescharacteristic
310C2×Dic3—22no—
311C2×Dic3—64no—
312C2×Dic3—64no—
313C2×Dic3—62no—
314C2×Dic3—62no—
315C2×Dic3—62no—
316C2×Dic3—62no—
317D12—24no—
318D12—22no—
319D12#23514yes—
320C4×D3—82no—
321C4×D3—82no—
322Dic6—62no—
323Dic6—62no—
324Dic6—62no—
325Dic6—62no—
326Dic6—122no—
327Dic6—122no—
328C3×C8—62no—
329C3×C8—62no—
330C3⋊C8—22no—
331C3⋊C8—22no—
332C2×C32—41no—
333C2×C32#52511yescharacteristic
334C2×C32#57712yes—
335C3×D3—44no—
336C24—61no—
337C2×Q8—92no—
338C2×D4—32no—
339C2×D4—64no—
340C2×D4—61no—
341C22×C4—62no—
342C22×C4—62no—
343C22×C4C2×D3211yescharacteristic
344SD16—184no—
345SD16—184no—
346C2×C8—32no—
347C2×C8—32no—
348C4⋊C4—32no—
349C4⋊C4—92no—
350C4⋊C4—182no—
351C4⋊C4—182no—
352C4⋊C4—182no—
353C4⋊C4—182no—
354C4⋊C4#62612yes—
355C22⋊C4—61no—
356C22⋊C4—62no—
357C22⋊C4—62no—
358C22⋊C4—182no—
359C22⋊C4#62612yes—
360C42—61no—
361C42—182no—
362C42C2×D3211yescharacteristic
363C42C2×D3211yescharacteristic
364C22×C3—22no—
365C22×C3—21no—
366C22×C3—21no—
367C22×C3—22no—
368C22×C3—21no—
369C22×C3—41no—
370C22×C3—42no—
371C22×C3—64no—
372C22×C3—122no—
373C22×C3—122no—
374C22×C3—244no—
375C22×C3C22×D1211yescharacteristic
376C22×C3C22×#6711yescharacteristic
377C2×D3—24no—
378C2×D3—42no—
379C2×D3—42no—
380C2×D3—84no—
381C3×C4—22no—
382C3×C4—22no—
383C3×C4—21no—
384C3×C4—21no—
385C3×C4—22no—
386C3×C4—22no—
387C3×C4—22no—
388C3×C4—41no—
389C3×C4—42no—
390C3×C4—42no—
391C3×C4—122no—
392C3×C4C2×#23512yes—
393C3×C4D3×#4112yes—
394Dic3—42no—
395Dic3—124no—
396Dic3—124no—
397Dic3—122no—
398Dic3—122no—
399Dic3—122no—
400Dic3—122no—
401C32#312311yescharacteristic, complemented, Sylow
402C23—64no—
403C23—62no—
404C23—242no—
405C23C2×#62611yescharacteristic
406Q8—182no—
407Q8—182no—
408D4—34no—
409D4—64no—
410D4—62no—
411C2×C4—22no—
412C2×C4—62no—
413C2×C4—182no—
414C2×C4—182no—
415C2×C4—242no—
416C2×C4—242no—
417C2×C4C2×#62611yescharacteristic
418C2×C4C2×#62612yes—
419C2×C4C2×#62612yes—
420C2×C4C22×D3211yescharacteristic
421C8—62no—
422C8—62no—
423C2×C3—22no—
424C2×C3—21no—
425C2×C3—41no—
426C2×C3—41no—
427C2×C3—81no—
428C2×C3—124no—
429C2×C3#552411yescharacteristic
430C2×C3#575112yes—
431C2×C3#579111yescharacteristic
432C2×C3#583612yes—
433D3—44no—
434C22—22no—
435C22—21no—
436C22—64no—
437C22—122no—
438C22—122no—
439C22—244no—
440C22C22×#62611yescharacteristic
441C4—22no—
442C4—22no—
443C4—21no—
444C4—122no—
445C4—362no—
446C4—362no—
447C4D3×#23512yes—
448C3—21no—
449C3#7938711yescharacteristic, complemented
450C3#8254511yescharacteristic, complemented
451C2—41no—
452C2—124no—
453C2#1059502311yescharacteristic
454C2#1059544712yes—
subgroupG/H
centerC22C22×#626
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
1. #10595989C2semidirect
3. C3×#5000C2semidirect
5. #10591134C2semidirect
6. #10590365C2semidirect
7. #10590360C2semidirect
8. C4×#3716C2semidirect
9. #10590271C2semidirect
17. #64079C22semidirect
18. #64078C22semidirect
19. C4×#634C22semidirect
28. C3×C4⋊(C3⋊C8)C22semidirect
29. C3×#803C22semidirect
30. C3×C4×C3⋊C8C22semidirect
31. #63575C22semidirect
32. #63573C22semidirect
33. #63567C22semidirect
34. #63567C22semidirect
48. #5000D3semidirect
139. C4⋊(C3⋊C8)C2×D3semidirect
140. #803C2×D3semidirect
141. C4×C3⋊C8C2×D3semidirect
401. C32#3123semidirect
449. C3#79387semidirect
450. C3#82545semidirect

Maximal subgroups

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

subgroupindex
#105959892
C3×#55212
C3×#50002
#105911722
#105911342
#105903652
#105903602
C4×#37162
#105902712
#825453
#793873