Finite Group Databasebeta

← #11872732

Subgroups — #11872732

Order 1152.

1005 conjugacy classes of subgroups; only the 164 normal subgroups are shown.

normal subgroups only

This group has 1005 conjugacy classes of subgroups — too many to draw. Only its 164 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596269C211yesmaximal, characteristic, complemented
2#10595041C211yesmaximal, characteristic, complemented
3C3×#5217C212yesmaximal, complemented
4#10591486C212yesmaximal, complemented
5#10591479C212yesmaximal, complemented
6#10591436C212yesmaximal, complemented
7#10591435C212yesmaximal, complemented
8#10591093C212yesmaximal, complemented
9#10591062C211yesmaximal, characteristic, complemented
10#79993—32nomaximal
11C22×C32×D4C2211yescharacteristic
12C2×#3757—22no—
13D4×C3⋊Dic3—22no—
14D4×C3⋊Dic3C2212yes—
15D4×C3⋊Dic3C2212yes—
16#64135C2211yescharacteristic
17#64135C2211yescharacteristic
18C2×C3×#213C2212yes—
19C2×C3×#213C2212yes—
20C3×#930C2212yes—
21#63970—22no—
22#63914C2211yescharacteristic, complemented
23#63898C2212yescomplemented
24#63891—22no—
25#63872C2211yescharacteristic, complemented
26C3×#832C2212yes—
27C3×#832C2212yes—
28C3×#830C2212yes—
29#63575C2212yescomplemented
30#63573C2212yescomplemented
31#63572C2212yescomplemented
32#63563C2212yescomplemented
33#63563C2212yescomplemented
34#63555C2211yescharacteristic, complemented
35#63553C2211yescharacteristic, complemented
36#5798—32no—
37#5798—61no—
38#5619—32no—
39C3×#447—32no—
40#5217D312yescomplemented
41#5152—32no—
42#5150—32no—
43#5150—32no—
44Dic3×D8—32no—
45#5035—32no—
46#4785—32no—
47#4766—32no—
48#4763—32no—
49#4756—32no—
50#4737—32no—
51#4720—32no—
52C24×C32—21no—
53C2×C32×D4—24no—
54C2×C32×D4—21no—
55C2×C32×D4C2312yes—
56C22×C32×C4C2311yescharacteristic
57C22×C3⋊Dic3—22no—
58C22×C3⋊Dic3—22no—
59C2×C3×#67—22no—
60C2×C3×D12C2312yes—
61C2×#625—22no—
62C2×D3×Dic3—22no—
63#3757—21no—
64#3757—22no—
65#3757—22no—
66#3757D412yes—
67C4⋊(C3⋊Dic3)D412yes—
68C4⋊(C3⋊Dic3)C2312yes—
69C4×C3⋊Dic3—21no—
70C4×C3⋊Dic3C2311yescharacteristic
71C4×C3⋊Dic3C2311yescharacteristic
72C3×#213—24no—
73C3×#213—24no—
74C3×(C2×D3)⋊C4—22no—
75C3×C4⋊Dic3C2312yes—
76C2×C3×C3⋊C8C2312yes—
77C2×C3×C3⋊C8C2312yes—
78Dic3⋊Dic3—22no—
79(C2×D3)⋊Dic3—22no—
80#3122—91noSylow
81C22×C3×D4—21no—
82C22×C3×D4C2×D312yes—
83C2×C3×D8—32no—
84C2×C3×D8—32no—
85C3×#121—32no—
86C2×#217—62no—
87C2×#217—62no—
88C2×#217—64no—
89#940—32no—
90#939—62no—
91#938—62no—
92D4×Dic3—32no—
93D4×Dic3—32no—
94D4×Dic3—32no—
95D4×Dic3—32no—
96D4×Dic3—32no—
97D4×Dic3—62no—
98D4×Dic3—62no—
99D4×Dic3—62no—
100D4×Dic3—62no—
101D4×Dic3—64no—
102C2×#213C2×D312yes—
103C2×#213C2×D312yes—
104#930C2×D312yes—
105#926—32no—
106#926—32no—
107#926—61no—
108#926—61no—
109#893—32no—
110#890—32no—
111#886—62no—
112#883—62no—
113C3×#102—32no—
114C3×#102—32no—
115C3×C22⋊C8—32no—
116#832—32no—
117#832—32no—
118#832C2×D312yes—
119#832C2×D312yes—
120#830C2×D312yes—
121#821—32no—
122#821—32no—
123#818—32no—
124#817—32no—
125#815—32no—
126Dic3⋊C8—32no—
127Dic3⋊C8—32no—
128C8×Dic3—32no—
129#808—32no—
130#807—32no—
131C23×C32—24no—
132C23×C32—22no—
133C23×C32—82no—
134C23×C32C2×D411yescharacteristic
135C22×C3×D3—22no—
136C32×D4—24no—
137C32×D4—22no—
138C32×D4#4114yes—
139C2×C32×C4—22no—
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2411yescharacteristic
142C2×C3⋊Dic3—22no—
143C2×C3⋊Dic3—82no—
144C2×C3⋊Dic3—82no—
145C2×C3⋊Dic3C2×D412yes—
146C2×C3⋊Dic3C2×D412yes—
147C3×#67—82no—
148C2×C3×Dic3—22no—
149C3×D12—22no—
150C3×D12—22no—
151#625—82no—
152D3×Dic3—82no—
153C3×C3⋊C8—22no—
154C3×C3⋊C8—22no—
155#540—91no—
156#518—91no—
157#482—92no—
158#478—92no—
159#459—92no—
160#447—32no—
161#442—92no—
162C4×D8—92no—
163#433—91no—
164C24×C3—22no—
165C24×C3—22no—
166C2×C3×D4—22no—
167C2×C3×D4—28no—
168C2×C3×D4—24no—
169C2×C3×D4—24no—
170C2×C3×D4—22no—
171C2×C3×D4—22no—
172C2×C3×D4—32no—
173C2×C3×D4—62no—
174C2×C3×D4C22×D312yes—
175C2×C3×D4C22×D312yes—
176C22×C3×C4—21no—
177C22×C3×C4C22×D312yes—
178C2×#67—22no—
179C2×#67—62no—
180C2×#67—62no—
181C22×Dic3—62no—
182C22×Dic3—62no—
183C22×Dic3—62no—
184C22×Dic3—62no—
185C22×Dic3—62no—
186C22×Dic3—64no—
187C22×Dic3—64no—
188C2×D12C22×D312yes—
189C2×C4×D3—62no—
190C3×D8—64no—
191C3×D8—64no—
192C2×C3×C8—32no—
193C2×C3×C8—32no—
194C3×C4⋊C4—32no—
195C3×C22⋊C4—62no—
196#217—32no—
197#217—32no—
198#217—62no—
199#217—62no—
200#217—62no—
201#217—62no—
202#217—62no—
203#217—62no—
204#217—62no—
205#217—64no—
206#217—64no—
207#217—62no—
208#213—24no—
209#213—24no—
210(C2×D3)⋊C4—22no—
211(C2×D3)⋊C4—62no—
212C4⋊Dic3—32no—
213C4⋊Dic3—32no—
214C4⋊Dic3—32no—
215C4⋊Dic3—32no—
216C4⋊Dic3—62no—
217C4⋊Dic3—62no—
218C4⋊Dic3—62no—
219C4⋊Dic3C22×D312yes—
220Dic3⋊C4—62no—
221C4×Dic3—32no—
222C4×Dic3—32no—
223C4×Dic3—61no—
224C4×Dic3—61no—
225C4×Dic3—62no—
226C4×Dic3—62no—
227C2×C3⋊C8C22×D312yes—
228C2×C3⋊C8C22×D312yes—
229C22×C32—21no—
230C22×C32—24no—
231C22×C32—22no—
232C22×C32—42no—
233C22×C32—42no—
234C22×C32—84no—
235C22×C32C22×D411yescharacteristic
236C2×C3×D3—42no—
237C2×C3×D3—42no—
238C2×C3×D3—42no—
239C32×C4—21no—
240C32×C4C2×#4112yes—
241C3⋊Dic3—22no—
242C3⋊Dic3—22no—
243C3⋊Dic3—42no—
244C3×Dic3—42no—
245C22×D4D3211yescharacteristic
246C2×D8—32no—
247C2×D8—32no—
248#127—91no—
249#125—91no—
250#123—182no—
251#121—32no—
252#121—182no—
253C4×D4—92no—
254C4×D4—92no—
255C4×D4—92no—
256C4×D4—182no—
257#117—91no—
258#117—91no—
259C2×C22⋊C4—182no—
260#107—92no—
261#106—92no—
262C4⋊C8—92no—
263#102—32no—
264#102—32no—
265#102—92no—
266#102—92no—
267C22⋊C8—32no—
268#97—91no—
269C4×C8—91no—
270C23×C3—24no—
271C23×C3—28no—
272C23×C3—28no—
273C23×C3—22no—
274C23×C3—22no—
275C23×C3—21no—
276C23×C3—62no—
277C23×C3—82no—
278C23×C3—82no—
279C23×C3—84no—
280C23×C3D3×D412yes—
281C22×D3—22no—
282C3×D4—28no—
283C3×D4—28no—
284C3×D4—24no—
285C3×D4—22no—
286C3×D4—22no—
287C3×D4—24no—
288C3×D4—62no—
289C3×D4—62no—
290C3×D4—242no—
291C3×D4#23714yes—
292C3×D4#23714yes—
293C2×C3×C4—24no—
294C2×C3×C4—22no—
295C2×C3×C4—22no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—62no—
299C2×C3×C4D3×D412yes—
300C2×C3×C4C23×D312yes—
301#67—82no—
302#67—242no—
303#67—242no—
304C2×Dic3—22no—
305C2×Dic3—32no—
306C2×Dic3—32no—
307C2×Dic3—32no—
308C2×Dic3—32no—
309C2×Dic3—62no—
310C2×Dic3—62no—
311C2×Dic3—64no—
312C2×Dic3—62no—
313C2×Dic3—62no—
314C2×Dic3—242no—
315C2×Dic3—242no—
316C2×Dic3—242no—
317C2×Dic3—242no—
318C2×Dic3—242no—
319C2×Dic3—244no—
320C2×Dic3—244no—
321D12—22no—
322D12—22no—
323C4×D3—242no—
324C3×C8—62no—
325C3×C8—62no—
326C3⋊C8—22no—
327C3⋊C8—22no—
328C2×C32—41no—
329C2×C32—44no—
330C2×C32#52511yescharacteristic
331C2×C32#57612yes—
332C3×D3—82no—
333C24—21no—
334C2×D4—24no—
335C2×D4—21no—
336C2×D4—32no—
337C2×D4—62no—
338C2×D4—182no—
339C2×D4C2×D3212yes—
340C22×C4—182no—
341C22×C4—182no—
342C22×C4—182no—
343C22×C4C2×D3211yescharacteristic
344D8—64no—
345D8—64no—
346C2×C8—32no—
347C2×C8—32no—
348C4⋊C4—32no—
349C4⋊C4—92no—
350C4⋊C4—92no—
351C4⋊C4—182no—
352C22⋊C4—62no—
353C22⋊C4—92no—
354C22⋊C4—182no—
355C22⋊C4—182no—
356C22⋊C4—182no—
357C22⋊C4—181no—
358C42—91no—
359C42—91no—
360C42—181no—
361C22×C3—22no—
362C22×C3—28no—
363C22×C3—22no—
364C22×C3—22no—
365C22×C3—22no—
366C22×C3—24no—
367C22×C3—24no—
368C22×C3—21no—
369C22×C3—42no—
370C22×C3—44no—
371C22×C3—44no—
372C22×C3—42no—
373C22×C3—42no—
374C22×C3—42no—
375C22×C3—42no—
376C22×C3—88no—
377C22×C3—88no—
378C22×C3—122no—
379C22×C3—122no—
380C22×C3—122no—
381C22×C3C2×D3×D412yes—
382C2×D3—42no—
383C2×D3—42no—
384C2×D3—42no—
385C3×C4—22no—
386C3×C4—22no—
387C3×C4—22no—
388C3×C4—122no—
389C3×C4C2×#23712yes—
390C3×C4C2×#23712yes—
391Dic3—42no—
392Dic3—62no—
393Dic3—62no—
394Dic3—62no—
395Dic3—62no—
396Dic3—122no—
397Dic3—122no—
398Dic3—124no—
399Dic3—122no—
400Dic3—122no—
401C32#312211yescharacteristic, complemented, Sylow
402C23—24no—
403C23—22no—
404C23—62no—
405C23—82no—
406C23#381111yescharacteristic
407D4—24no—
408D4—22no—
409D4—62no—
410D4—62no—
411D4—242no—
412D4—722no—
413D4#380514yes—
414C2×C4—22no—
415C2×C4—62no—
416C2×C4—92no—
417C2×C4—92no—
418C2×C4—182no—
419C2×C4—722no—
420C2×C4—722no—
421C2×C4—722no—
422C2×C4#381111yescharacteristic
423C2×C4C22×D3211yescharacteristic
424C8—62no—
425C8—62no—
426C2×C3—22no—
427C2×C3—21no—
428C2×C3—42no—
429C2×C3—48no—
430C2×C3—42no—
431C2×C3—44no—
432C2×C3—44no—
433C2×C3—242no—
434C2×C3#558612yes—
435C2×C3#575712yes—
436C2×C3#577412yes—
437D3—82no—
438C22—22no—
439C22—21no—
440C22—24no—
441C22—42no—
442C22—42no—
443C22—84no—
444C22—122no—
445C22—122no—
446C22—122no—
447C22C2×#381111yescharacteristic
448C4—21no—
449C4—122no—
450C4—182no—
451C4—182no—
452C4—362no—
453C4C2×#380512yes—
454C3—21no—
455C3#7999312yescomplemented
456C2—41no—
457C2—44no—
458C2—242no—
459C2#1059510212yes—
460C2#1059550111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
hypercenterC22×D4D32
hypocenterC32#3122
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #10596269C2semidirect
2. #10595041C2semidirect
3. C3×#5217C2semidirect
4. #10591486C2semidirect
5. #10591479C2semidirect
6. #10591436C2semidirect
7. #10591435C2semidirect
8. #10591093C2semidirect
9. #10591062C2semidirect
22. #63914C22semidirect
23. #63898C22semidirect
25. #63872C22semidirect
29. #63575C22semidirect
30. #63573C22semidirect
31. #63572C22semidirect
32. #63563C22semidirect
33. #63563C22semidirect
34. #63555C22semidirect
35. #63553C22semidirect
40. #5217D3semidirect
401. C32#3122semidirect
455. C3#79993semidirect

Maximal subgroups

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

subgroupindex
#105962692
#105950412
C3×#52172
#105914862
#105914792
#105914362
#105914352
#105910932
#105910622
#799933