Finite Group Databasebeta

← #11792251

Subgroups — #11792251

Order 1152.

861 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 861 conjugacy classes of subgroups — too many to draw. Only its 124 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
1C3×#5510C211yesmaximal, characteristic, complemented
2C2×#63823C212yesmaximal, complemented
3C3×#4988C211yesmaximal, characteristic, complemented
4C2×#63569C212yesmaximal, complemented
5#10589396C211yesmaximal, characteristic, complemented
6#71879—31nomaximal
7#69664—31nomaximal
8C2×C3×#235C2212yes—
9C22×C3×D12C2211yescharacteristic
10C2×C32×C4⋊C4C2211yescharacteristic
11C2×#3748C2212yes—
12C3×#930—22no—
13C2×C3×(C2×D3)⋊C4—22no—
14C2×C3×C4×Dic3C2211yescharacteristic
15C3×#897—22no—
16C3×#895—22no—
17C2×#3715—22no—
18#63823—24no—
19#63823—24no—
20C2×#3713—22no—
21#63569—24no—
22C3×#537—31no—
23C2×#949—32no—
24C2×#932—32no—
25#5510D311yescharacteristic, complemented
26C3×#390—31no—
27C2×#837—32no—
28#4988D311yescharacteristic, complemented
29C2×#805—32no—
30#4530—31no—
31#4530—31no—
32#4530—61no—
33C23×C3×D3—21no—
34C22×C32×C4D412yes—
35C22×C32×C4C2311yescharacteristic
36C2×C3×#67—22no—
37C22×C3×Dic3—21no—
38C3×#235—22no—
39C3×#235—22no—
40C3×#235—22no—
41C3×#235—22no—
42C2×C3×D12—22no—
43C2×C3×D12—22no—
44C2×C3×D12—21no—
45C2×C3×D12—22no—
46C2×C3×D12D412yes—
47C2×C3×D12D412yescomplemented
48C2×C3×C4×D3—22no—
49C2×C3×Dic6D412yes—
50C32×C4⋊C4—22no—
51#3748—22no—
52#3748D414yescomplemented
53C2×C3⋊(C3⋊C8)—22no—
54C3×(C2×D3)⋊C4—24no—
55C3×(C2×D3)⋊C4—44no—
56C3×C4⋊Dic3—22no—
57C3×C4×Dic3—22no—
58#3715—28no—
59#3713—28no—
60#2006—91noSylow
61C2×C3×#41—32no—
62C22×C3×D4—31no—
63C2×#235C2×D312yes—
64C22×D12C2×D311yescharacteristic
65C3×C22⋊Q8—62no—
66C3×#121—62no—
67C3×#121—62no—
68C2×C3×C4⋊C4—21no—
69C2×C3×C4⋊C4C2×D311yescharacteristic
70C2×C3×C4⋊C4C2×D311yescharacteristic
71C2×C3×C22⋊C4—62no—
72C2×C3×C42—31no—
73#949—64no—
74#949—64no—
75C2×#215—62no—
76C2×#214—62no—
77#932—64no—
78#932—64no—
79C2×#213—62no—
80C2×#213—62no—
81#930—22no—
82C2×(C2×D3)⋊C4—22no—
83C2×C4×Dic3C2×D311yescharacteristic
84C2×#208—32no—
85C2×#208—32no—
86C2×#208—62no—
87#897—22no—
88#895—22no—
89#837—64no—
90#805—64no—
91C23×C32C2×D411yescharacteristic
92C22×C3×D3—22no—
93C22×C3×D3—22no—
94C22×C3×D3—42no—
95C22×C3×D3—42no—
96C22×C3×D3—41no—
97C22×C3×D3—41no—
98C2×C32×C4—22no—
99C2×C32×C4—42no—
100C2×C32×C4C2×D411yescharacteristic
101C2×C32×C4C2×D412yes—
102C2×C32×C4C2×D412yes—
103C2×C32×C4#4111yescharacteristic
104C3×#67—42no—
105C3×#67—42no—
106C2×C3×Dic3—22no—
107C2×C3×Dic3—22no—
108C2×C3×Dic3—41no—
109C2×C3×Dic3—41no—
110C3×D12—22no—
111C3×D12—24no—
112C3×D12—22no—
113C3×D12—42no—
114C3×D12—82no—
115C3×C4×D3—42no—
116C3×C4×D3—42no—
117C3×Dic6—22no—
118C3×Dic6—22no—
119C3⋊(C3⋊C8)—24no—
120C2×AGL(1,ℤ/8)—92no—
121#537—31no—
122C2×#104—92no—
123#390—31no—
124#343—91no—
125C24×C3—61no—
126C23×D3—21no—
127C3×#41—62no—
128C3×#41—62no—
129C3×#41—62no—
130C3×#41—62no—
131C2×C3×Q8—32no—
132C2×C3×D4—32no—
133C2×C3×D4—32no—
134C2×C3×D4—62no—
135C2×C3×D4—62no—
136C2×C3×D4—62no—
137C2×C3×D4—61no—
138C2×C3×D4—62no—
139C22×C3×C4—22no—
140C22×C3×C4—21no—
141C22×C3×C4—61no—
142C22×C3×C4—62no—
143C22×C3×C4#6712yes—
144C22×C3×C4#6712yes—
145C22×C3×C4C22×D311yescharacteristic
146C22×C3×C4C22×D311yescharacteristic
147C2×#67—22no—
148C22×Dic3—21no—
149#235—22no—
150#235—22no—
151#235—22no—
152#235—22no—
153C2×D12—22no—
154C2×D12—22no—
155C2×D12—21no—
156C2×D12—22no—
157C2×D12D1212yescomplemented
158C2×D12#6712yes—
159C2×C4×D3—22no—
160C2×Dic6#6712yes—
161C3×C4⋊C4—22no—
162C3×C4⋊C4—22no—
163C3×C4⋊C4—42no—
164C3×C4⋊C4—62no—
165C3×C22⋊C4—64no—
166C3×C22⋊C4—124no—
167C3×C42—62no—
168#215—68no—
169#214—68no—
170#213—68no—
171#213—68no—
172(C2×D3)⋊C4—24no—
173(C2×D3)⋊C4—44no—
174C4⋊Dic3—22no—
175C4×Dic3—22no—
176#208—34no—
177#208—34no—
178#208—64no—
179#208—62no—
180#208—62no—
181#208—122no—
182C2×C3⋊C8—62no—
183C2×C3⋊C8—62no—
184C2×C3⋊C8—122no—
185C22×C32—21no—
186C22×C32—21no—
187C22×C32#12011yescharacteristic
188C22×C32#12111yescharacteristic
189C22×C32#12711yescharacteristic
190C2×C3×D3—44no—
191C2×C3×D3—42no—
192C2×C3×D3—42no—
193C2×C3×D3—42no—
194C2×C3×D3—42no—
195C2×C3×D3—82no—
196C2×C3×D3—81no—
197C2×C3×D3—81no—
198C32×C4—42no—
199C32×C4#12012yes—
200C32×C4#12112yes—
201C3×Dic3—42no—
202C3×Dic3—42no—
203C2×#41—32no—
204C22×D4—31no—
205AGL(1,ℤ/8)—184no—
206AGL(1,ℤ/8)—184no—
207C2×SD16—182no—
208C2×D8—182no—
209C2×M16—92no—
210C22⋊Q8—62no—
211#121—62no—
212#121—62no—
213C2×C4⋊C4D3211yescharacteristic
214C2×C22⋊C4—62no—
215C2×C42—31no—
216#104—184no—
217C23×C3—21no—
218C23×C3—62no—
219C23×C3—62no—
220C23×C3—122no—
221C23×C3—122no—
222C23×C3—121no—
223C23×C3—121no—
224C23×C3C2×#6711yescharacteristic
225C23×C3C2×#6711yescharacteristic
226C22×D3—22no—
227C22×D3—22no—
228C22×D3—42no—
229C22×D3—42no—
230C22×D3—41no—
231C22×D3—41no—
232C3×Q8—62no—
233C3×Q8—62no—
234C3×D4—62no—
235C3×D4—62no—
236C3×D4—64no—
237C3×D4—122no—
238C3×D4—122no—
239C3×D4—122no—
240C3×D4—242no—
241C2×C3×C4—22no—
242C2×C3×C4—22no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—22no—
246C2×C3×C4—22no—
247C2×C3×C4—42no—
248C2×C3×C4—42no—
249C2×C3×C4—42no—
250C2×C3×C4—62no—
251C2×C3×C4—62no—
252C2×C3×C4—82no—
253C2×C3×C4—121no—
254C2×C3×C4—121no—
255C2×C3×C4—122no—
256C2×C3×C4—122no—
257C2×C3×C4C2×D1211yescharacteristic
258C2×C3×C4#23511yescharacteristic
259C2×C3×C4D3×D411yescharacteristic
260C2×C3×C4D3×D412yes—
261C2×C3×C4D3×D412yes—
262C2×C3×C4D3×D412yes—
263C2×C3×C4#23711yescharacteristic
264C2×C3×C4C2×#6712yes—
265#67—42no—
266#67—42no—
267C2×Dic3—22no—
268C2×Dic3—22no—
269C2×Dic3—41no—
270C2×Dic3—41no—
271D12—24no—
272D12—22no—
273D12—22no—
274D12—42no—
275D12—82no—
276C4×D3—42no—
277C4×D3—42no—
278Dic6—22no—
279Dic6—22no—
280C3⋊C8—64no—
281C3⋊C8—64no—
282C3⋊C8—124no—
283C2×C32—21no—
284C2×C32—21no—
285C2×C32#39211yescharacteristic
286C2×C32#45311yescharacteristic
287C2×C32#45411yescharacteristic
288C3×D3—82no—
289C3×D3—82no—
290C24—61no—
291#41—62no—
292#41—62no—
293#41—62no—
294#41—62no—
295C2×Q8—32no—
296C2×D4—32no—
297C2×D4—32no—
298C2×D4—62no—
299C2×D4—62no—
300C2×D4—61no—
301C2×D4—62no—
302C2×D4—62no—
303C22×C4—61no—
304C22×C4—62no—
305C22×C4#62512yes—
306C22×C4C2×D3211yescharacteristic
307SD16—188no—
308D8—188no—
309M16—94no—
310M16—182no—
311C2×C8—182no—
312C4⋊C4—22no—
313C4⋊C4—62no—
314C22⋊C4—64no—
315C22⋊C4—124no—
316C42—62no—
317C22×C3—21no—
318C22×C3—21no—
319C22×C3—21no—
320C22×C3—21no—
321C22×C3—21no—
322C22×C3—21no—
323C22×C3—21no—
324C22×C3—41no—
325C22×C3—41no—
326C22×C3—124no—
327C22×C3—122no—
328C22×C3—122no—
329C22×C3—122no—
330C22×C3—122no—
331C22×C3—242no—
332C22×C3—241no—
333C22×C3—241no—
334C22×C3#93011yescharacteristic
335C22×C3#93711yescharacteristic
336C22×C3#93811yescharacteristic
337C22×C3#94011yescharacteristic
338C22×C3#94011yescharacteristic
339C22×C3#95311yescharacteristic
340C2×D3—44no—
341C2×D3—42no—
342C2×D3—42no—
343C2×D3—42no—
344C2×D3—42no—
345C2×D3—82no—
346C2×D3—81no—
347C2×D3—81no—
348C3×C4—22no—
349C3×C4—22no—
350C3×C4—42no—
351C3×C4—42no—
352C3×C4—82no—
353C3×C4—122no—
354C3×C4—122no—
355C3×C4#88212yes—
356C3×C4#88412yes—
357C3×C4#93712yes—
358C3×C4#93912yes—
359Dic3—42no—
360Dic3—42no—
361C32#200611yescharacteristic, complemented, Sylow
362C23—62no—
363C23—62no—
364C23—122no—
365C23—122no—
366C23—121no—
367C23—121no—
368C23C2×#62511yescharacteristic
369Q8—62no—
370Q8—62no—
371D4—62no—
372D4—62no—
373D4—64no—
374D4—122no—
375D4—122no—
376D4—122no—
377D4—242no—
378C2×C4—22no—
379C2×C4—42no—
380C2×C4—62no—
381C2×C4—62no—
382C2×C4—121no—
383C2×C4—121no—
384C2×C4—122no—
385C2×C4—122no—
386C2×C4#379511yescharacteristic
387C2×C4D3×D1211yescharacteristic
388C2×C4#380212yes—
389C2×C4D3×#6712yes—
390C8—184no—
391C2×C3—21no—
392C2×C3—21no—
393C2×C3—21no—
394C2×C3—21no—
395C2×C3—21no—
396C2×C3—21no—
397C2×C3—21no—
398C2×C3—41no—
399C2×C3—41no—
400C2×C3—242no—
401C2×C3—242no—
402C2×C3#496011yescharacteristic
403C2×C3#506211yescharacteristic
404C2×C3#507711yescharacteristic
405C2×C3#522311yescharacteristic
406C2×C3#524111yescharacteristic
407C2×C3#524511yescharacteristic
408D3—82no—
409D3—82no—
410C22—21no—
411C22—21no—
412C22—124no—
413C22—122no—
414C22—122no—
415C22—122no—
416C22—122no—
417C22—242no—
418C22—241no—
419C22—241no—
420C22#6390811yescharacteristic
421C22#6391411yescharacteristic
422C22#6397611yescharacteristic
423C4—42no—
424C4—122no—
425C4—122no—
426C4#6388512yes—
427C4#6392212yes—
428C3—21no—
429C3#6966411yescharacteristic, complemented
430C3#7187911yescharacteristic, complemented
431C2—21no—
432C2—21no—
433C2—242no—
434C2—242no—
435C2#1059138911yescharacteristic
436C2#1059150911yescharacteristic
437C2#1059164511yescharacteristic
subgroupG/H
centerC22#63976
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#120
hypercenterC2×C4⋊C4D32
hypocenterC32#2006
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×#5510C2semidirect
2. C2×#63823C2semidirect
3. C3×#4988C2semidirect
4. C2×#63569C2semidirect
5. #10589396C2semidirect
25. #5510D3semidirect
28. #4988D3semidirect
47. C2×C3×D12D4semidirect
52. #3748D4semidirect
157. C2×D12D12semidirect
361. C32#2006semidirect
429. C3#69664semidirect
430. C3#71879semidirect

Maximal subgroups

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

subgroupindex
C3×#55102
C2×#638232
C3×#49882
C2×#635692
#105893962
#718793
#696643