Finite Group Databasebeta

← #11792250

Subgroups — #11792250

Order 1152.

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

normal subgroups only

This group has 959 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
1#10595981C211yesmaximal, characteristic, complemented
2C2×#63830C212yesmaximal, complemented
3C3×#4988C211yesmaximal, characteristic, complemented
4C2×#63570C212yesmaximal, complemented
5C3×#4530C211yesmaximal, characteristic, complemented
6#69664—31nomaximal
7#69008—31nomaximal
8C2×#3828C2212yes—
9C22×C3×D12C2211yescharacteristic
10C2×C32×C4⋊C4C2211yescharacteristic
11#64139—22no—
12#64106—22no—
13#64104—22no—
14C2×C3×(C2×D3)⋊C4—22no—
15C2×C3×C4×Dic3C2211yescharacteristic
16C2×C3×#208C2212yes—
17#63830—24no—
18#63830—24no—
19C2×#3716—22no—
20C2×#3714—22no—
21#63570—24no—
22C2×#932—32no—
23C2×#908—32no—
24#5510—31no—
25#5510—31no—
26#5510—61no—
27C3×#390—31no—
28C2×#825—32no—
29#4988D311yescharacteristic, complemented
30C2×#805—32no—
31C3×#343—31no—
32#4530D311yescharacteristic, complemented
33C23×C3×D3—21no—
34C22×C32×C4D412yes—
35C22×C32×C4C2311yescharacteristic
36C2×#638—22no—
37#3828—22no—
38#3828—22no—
39#3828—22no—
40#3828—22no—
41C2×C4⋊(C3⋊D3)—22no—
42C2×C4⋊(C3⋊D3)D412yes—
43C2×C4×C3⋊D3—22no—
44C2×#634D412yes—
45C22×C3×Dic3—21no—
46C2×C3×D12—22no—
47C2×C3×D12—22no—
48C2×C3×D12—21no—
49C2×C3×D12D412yescomplemented
50C32×C4⋊C4—22no—
51#3752—24no—
52C4⋊(C3⋊Dic3)—22no—
53C3×(C2×D3)⋊C4—44no—
54C3×C4×Dic3—22no—
55C3×#208—22no—
56C3×#208D414yescomplemented
57C2×C3×C3⋊C8—22no—
58#3716—28no—
59#3714—28no—
60#2006—91noSylow
61C22×C3×D4—31no—
62C2×#235—32no—
63C2×#235—32no—
64C2×#235—62no—
65C22×D12C2×D311yescharacteristic
66C2×C3×M16—32no—
67C2×C3×C4⋊C4—21no—
68C2×C3×C4⋊C4C2×D311yescharacteristic
69C2×C3×C4⋊C4C2×D311yescharacteristic
70C2×C3×C22⋊C4—62no—
71C2×C3×C42—31no—
72C2×#214—62no—
73#932—64no—
74#932—64no—
75C2×#213—62no—
76#930—64no—
77#930—62no—
78#930—62no—
79C2×(C2×D3)⋊C4—22no—
80C2×C4×Dic3C2×D311yescharacteristic
81C2×#208C2×D312yes—
82#908—64no—
83#908—64no—
84C2×D24—62no—
85C2×#204—62no—
86#897—62no—
87#897—62no—
88#897—64no—
89#895—62no—
90#895—62no—
91#895—64no—
92#825—64no—
93#805—64no—
94C23×C32C2×D411yescharacteristic
95C22×C3⋊D3—22no—
96C22×C3×D3—22no—
97C22×C3×D3—42no—
98C22×C3×D3—42no—
99C22×C3×D3—41no—
100C22×C3×D3—41no—
101C2×C32×C4—22no—
102C2×C32×C4—42no—
103C2×C32×C4C2×D411yescharacteristic
104C2×C32×C4C2×D412yes—
105C2×C32×C4C2×D412yes—
106C2×C32×C4#4111yescharacteristic
107#638—42no—
108#638—42no—
109C2×C3⋊Dic3—22no—
110C4⋊(C3⋊D3)—22no—
111C4⋊(C3⋊D3)—22no—
112C4⋊(C3⋊D3)—82no—
113C4×C3⋊D3—42no—
114C4×C3⋊D3—42no—
115#634—22no—
116#634—22no—
117C2×C3×Dic3—22no—
118C2×C3×Dic3—41no—
119C2×C3×Dic3—41no—
120C3×D12—24no—
121C3×D12—42no—
122C3×C3⋊C8—24no—
123C2×AGL(1,ℤ/8)—92no—
124#537—91no—
125C2×#104—92no—
126#390—31no—
127#343—31no—
128C24×C3—61no—
129C23×D3—21no—
130C2×C3×D4—32no—
131C2×C3×D4—62no—
132C2×C3×D4—62no—
133C2×C3×D4—61no—
134C22×C3×C4—22no—
135C22×C3×C4—21no—
136C22×C3×C4—61no—
137C22×C3×C4D1212yes—
138C22×C3×C4#6712yes—
139C22×C3×C4C22×D311yescharacteristic
140C22×C3×C4C22×D311yescharacteristic
141C2×#67—64no—
142C2×#67—62no—
143C2×#67—62no—
144C22×Dic3—21no—
145#235—62no—
146#235—62no—
147#235—62no—
148#235—62no—
149#235—62no—
150#235—62no—
151#235—62no—
152#235—62no—
153#235—122no—
154#235—122no—
155#235—122no—
156#235—122no—
157C2×D12—22no—
158C2×D12—22no—
159C2×D12—21no—
160C2×D12—32no—
161C2×D12—32no—
162C2×D12—62no—
163C2×D12—64no—
164C2×D12—62no—
165C2×D12—62no—
166C2×D12D1212yescomplemented
167C2×C4×D3—64no—
168C2×C4×D3—62no—
169C2×C4×D3—62no—
170C2×Dic6—32no—
171C2×Dic6—32no—
172C2×Dic6—62no—
173C3×M16—34no—
174C3×M16—62no—
175C2×C3×C8—62no—
176C3×C4⋊C4—24no—
177C3×C4⋊C4—22no—
178C3×C4⋊C4—22no—
179C3×C22⋊C4—124no—
180C3×C42—62no—
181#214—68no—
182#213—68no—
183(C2×D3)⋊C4—44no—
184(C2×D3)⋊C4—68no—
185(C2×D3)⋊C4—64no—
186(C2×D3)⋊C4—64no—
187C4⋊Dic3—64no—
188C4⋊Dic3—62no—
189C4⋊Dic3—62no—
190C4×Dic3—22no—
191#208—22no—
192#208D1214yescomplemented
193C2×C3⋊C8—22no—
194D24—68no—
195#204—68no—
196C22×C32—21no—
197C22×C32—21no—
198C22×C32#12011yescharacteristic
199C22×C32#12111yescharacteristic
200C22×C32#12711yescharacteristic
201C2×C3⋊D3—42no—
202C2×C3⋊D3—42no—
203C2×C3⋊D3—42no—
204C2×C3×D3—44no—
205C2×C3×D3—42no—
206C2×C3×D3—82no—
207C2×C3×D3—81no—
208C2×C3×D3—81no—
209C32×C4—42no—
210C32×C4#12012yes—
211C32×C4#12112yes—
212C3⋊Dic3—42no—
213C3×Dic3—42no—
214C2×#41—92no—
215C22×D4—31no—
216AGL(1,ℤ/8)—184no—
217AGL(1,ℤ/8)—184no—
218C2×SD16—182no—
219C2×D8—182no—
220C2×M16—32no—
221C22⋊Q8—182no—
222#121—182no—
223#121—182no—
224C2×C4⋊C4D3211yescharacteristic
225C2×C22⋊C4—62no—
226C2×C42—31no—
227#104—184no—
228C23×C3—21no—
229C23×C3—62no—
230C23×C3—122no—
231C23×C3—122no—
232C23×C3—121no—
233C23×C3—121no—
234C23×C3C2×D1211yescharacteristic
235C23×C3C2×#6711yescharacteristic
236C22×D3—22no—
237C22×D3—42no—
238C22×D3—42no—
239C22×D3—41no—
240C22×D3—41no—
241C22×D3—64no—
242C22×D3—62no—
243C22×D3—62no—
244C3×D4—64no—
245C3×D4—122no—
246C2×C3×C4—24no—
247C2×C3×C4—22no—
248C2×C3×C4—22no—
249C2×C3×C4—21no—
250C2×C3×C4—22no—
251C2×C3×C4—21no—
252C2×C3×C4—22no—
253C2×C3×C4—42no—
254C2×C3×C4—42no—
255C2×C3×C4—62no—
256C2×C3×C4—82no—
257C2×C3×C4—121no—
258C2×C3×C4—121no—
259C2×C3×C4C2×D1211yescharacteristic
260C2×C3×C4C2×D1212yes—
261C2×C3×C4#23511yescharacteristic
262C2×C3×C4D3×D411yescharacteristic
263C2×C3×C4D3×D412yes—
264C2×C3×C4D3×D412yes—
265C2×C3×C4D3×D412yes—
266C2×C3×C4#23911yescharacteristic
267#67—124no—
268#67—124no—
269#67—122no—
270#67—122no—
271#67—122no—
272#67—122no—
273C2×Dic3—22no—
274C2×Dic3—41no—
275C2×Dic3—41no—
276C2×Dic3—64no—
277C2×Dic3—62no—
278C2×Dic3—62no—
279D12—24no—
280D12—42no—
281D12—62no—
282D12—62no—
283D12—62no—
284D12—62no—
285D12—122no—
286D12—122no—
287D12—244no—
288D12—242no—
289D12—242no—
290C4×D3—124no—
291C4×D3—124no—
292C4×D3—122no—
293C4×D3—122no—
294C4×D3—122no—
295C4×D3—122no—
296Dic6—62no—
297Dic6—62no—
298Dic6—62no—
299Dic6—62no—
300Dic6—122no—
301Dic6—122no—
302C3×C8—64no—
303C3⋊C8—24no—
304C2×C32—21no—
305C2×C32—21no—
306C2×C32#39211yescharacteristic
307C2×C32#45311yescharacteristic
308C2×C32#45411yescharacteristic
309C3⋊D3—82no—
310C3×D3—82no—
311C24—61no—
312#41—182no—
313#41—182no—
314#41—182no—
315#41—182no—
316C2×Q8—92no—
317C2×D4—32no—
318C2×D4—61no—
319C2×D4—62no—
320C2×D4—62no—
321C2×D4—92no—
322C2×D4—182no—
323C2×D4—182no—
324C22×C4—61no—
325C22×C4—182no—
326C22×C4#62612yes—
327C22×C4C2×D3211yescharacteristic
328SD16—188no—
329D8—188no—
330M16—34no—
331M16—62no—
332C2×C8—62no—
333C4⋊C4—22no—
334C4⋊C4—182no—
335C22⋊C4—124no—
336C22⋊C4—184no—
337C42—62no—
338C22×C3—21no—
339C22×C3—21no—
340C22×C3—21no—
341C22×C3—21no—
342C22×C3—21no—
343C22×C3—21no—
344C22×C3—21no—
345C22×C3—41no—
346C22×C3—41no—
347C22×C3—124no—
348C22×C3—122no—
349C22×C3—242no—
350C22×C3—241no—
351C22×C3—241no—
352C22×C3#87411yescharacteristic
353C22×C3#88211yescharacteristic
354C22×C3#89511yescharacteristic
355C22×C3#93011yescharacteristic
356C22×C3#93711yescharacteristic
357C22×C3#94011yescharacteristic
358C2×D3—44no—
359C2×D3—42no—
360C2×D3—82no—
361C2×D3—81no—
362C2×D3—81no—
363C2×D3—124no—
364C2×D3—124no—
365C2×D3—124no—
366C2×D3—122no—
367C2×D3—122no—
368C2×D3—122no—
369C2×D3—122no—
370C2×D3—122no—
371C2×D3—122no—
372C3×C4—22no—
373C3×C4—22no—
374C3×C4—44no—
375C3×C4—42no—
376C3×C4—42no—
377C3×C4—122no—
378C3×C4#88212yes—
379C3×C4#88212yes—
380C3×C4#88412yes—
381C3×C4#89512yes—
382Dic3—42no—
383Dic3—124no—
384Dic3—122no—
385Dic3—122no—
386C32#200611yescharacteristic, complemented, Sylow
387C23—62no—
388C23—122no—
389C23—122no—
390C23—121no—
391C23—121no—
392C23—182no—
393C23C2×#62611yescharacteristic
394Q8—182no—
395Q8—182no—
396D4—64no—
397D4—122no—
398D4—182no—
399D4—182no—
400D4—362no—
401D4—362no—
402D4—722no—
403C2×C4—22no—
404C2×C4—42no—
405C2×C4—62no—
406C2×C4—121no—
407C2×C4—121no—
408C2×C4—182no—
409C2×C4—362no—
410C2×C4—362no—
411C2×C4#379911yescharacteristic
412C2×C4D3×D1212yes—
413C2×C4D3×D1211yescharacteristic
414C2×C4#381112yes—
415C8—64no—
416C2×C3—21no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3—21no—
420C2×C3—21no—
421C2×C3—21no—
422C2×C3—21no—
423C2×C3—41no—
424C2×C3—41no—
425C2×C3—242no—
426C2×C3#467111yescharacteristic
427C2×C3#474711yescharacteristic
428C2×C3#475311yescharacteristic
429C2×C3#496011yescharacteristic
430C2×C3#506211yescharacteristic
431C2×C3#507711yescharacteristic
432D3—82no—
433D3—244no—
434D3—242no—
435D3—242no—
436C22—21no—
437C22—21no—
438C22—124no—
439C22—122no—
440C22—242no—
441C22—241no—
442C22—241no—
443C22—362no—
444C22—362no—
445C22—362no—
446C22#6390911yescharacteristic
447C22#6391111yescharacteristic
448C22#6398111yescharacteristic
449C4—42no—
450C4—122no—
451C4—362no—
452C4#6391012yes—
453C4#6392312yes—
454C3—21no—
455C3#6900811yescharacteristic, complemented
456C3#6966411yescharacteristic, complemented
457C2—21no—
458C2—21no—
459C2—242no—
460C2—722no—
461C2#1059139511yescharacteristic
462C2#1059151111yescharacteristic
463C2#1059164711yescharacteristic
subgroupG/H
centerC22#63981
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. #10595981C2semidirect
2. C2×#63830C2semidirect
3. C3×#4988C2semidirect
4. C2×#63570C2semidirect
5. C3×#4530C2semidirect
29. #4988D3semidirect
32. #4530D3semidirect
49. C2×C3×D12D4semidirect
56. C3×#208D4semidirect
166. C2×D12D12semidirect
192. #208D12semidirect
386. C32#2006semidirect
455. C3#69008semidirect
456. C3#69664semidirect

Maximal subgroups

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

subgroupindex
#105959812
C2×#638302
C3×#49882
C2×#635702
C3×#45302
#696643
#690083