Finite Group Databasebeta

← #11792412

Subgroups — #11792412

Order 1152.

919 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 919 conjugacy classes of subgroups — too many to draw. Only its 116 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#10596219C211yesmaximal, characteristic, complemented
2#10595023C212yesmaximal, complemented
3C3×#5126C211yesmaximal, characteristic, complemented
4#10591113C212yesmaximal, complemented
5C3×#4557C211yesmaximal, characteristic, complemented
6#69993—31nomaximal
7#68703—31nomaximal
8C2×#3828C2212yes—
9C22×C3×C4×D3C2211yescharacteristic
10C2×C32×M16C2211yescharacteristic
11#64118—22no—
12#64117—22no—
13#64113—22no—
14C3×#926C2212yes—
15C2×C3×#208C2211yescharacteristic
16#63977—22no—
17#63966—22no—
18#63909—22no—
19C4×#626—24no—
20#63857—22no—
21C3×(C2×D3)⋊C8—22no—
22#63570—24no—
23#5791—32no—
24#5748—31no—
25#5748—31no—
26#5748—61no—
27#5524—32no—
28C3×#407—31no—
29#5139—32no—
30#5126D311yescharacteristic, complemented
31#5005—32no—
32C3×H(3,ℤ/4)—31no—
33#4557D311yescharacteristic, complemented
34C23×C3×D3D411yescharacteristic
35C22×C32×C4C2311yescharacteristic
36C2×#638—22no—
37#3828—22no—
38#3828—22no—
39#3828—22no—
40#3828—22no—
41C2×C4⋊(C3⋊D3)D412yescomplemented
42C2×C4×C3⋊D3—22no—
43C2×#634D412yescomplemented
44C22×C3×Dic3D411yescharacteristic
45C2×C3×C4×D3—22no—
46C2×C3×C4×D3—21no—
47C2×C3×C4×D3—22no—
48C2×C3×C4×D3—21no—
49C2×#626—24no—
50C32×M16—22no—
51C2×C32×C8D412yescomplemented
52#3746—22no—
53#3745—22no—
54#3744—24no—
55C3×#217—22no—
56C3×C4⋊Dic3—22no—
57C3×C4×Dic3D414yescomplemented
58C3×#208—22no—
59C2×C3×C3⋊C8—21no—
60Dic3⋊Dic3—24no—
61#3722—24no—
62(C2×D3)⋊Dic3—24no—
63#2010—91noSylow
64C23×C3×C4—31no—
65C2×#235—32no—
66C2×#235—32no—
67C2×#235—62no—
68C22×C4×D3C2×D311yescharacteristic
69C2×C3×M16—21no—
70C2×C3×M16—31no—
71C2×C3×M16C2×D311yescharacteristic
72C2×C3×M16C2×D311yescharacteristic
73C3×#117—32no—
74#953—62no—
75#930—62no—
76#929—62no—
77C4×#67—64no—
78#926C2×D312yes—
79#924—62no—
80C2×#208C2×D311yescharacteristic
81#909—62no—
82#909—62no—
83#909—64no—
84#908—62no—
85#908—62no—
86#908—64no—
87#904—64no—
88#904—62no—
89#904—62no—
90#897—62no—
91#895—62no—
92#886—62no—
93#882—62no—
94C4×D12—64no—
95C3×C22⋊C8—62no—
96#825—64no—
97(C2×D3)⋊C8—22no—
98#805—64no—
99C23×C32C2×D411yescharacteristic
100C22×C3⋊D3—22no—
101C22×C3×D3—22no—
102C22×C3×D3—21no—
103C22×C3×D3—42no—
104C2×C32×C4C2×D412yes—
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2×D412yes—
107C2×C32×C4#4111yescharacteristic
108#638—42no—
109#638—42no—
110C2×C3⋊Dic3—22no—
111C4⋊(C3⋊D3)—22no—
112C4⋊(C3⋊D3)—22no—
113C4×C3⋊D3—42no—
114C4×C3⋊D3—42no—
115#634—22no—
116#634—22no—
117C2×C3×Dic3—24no—
118C2×C3×Dic3—22no—
119C2×C3×Dic3—21no—
120C3×C4×D3—41no—
121C3×C4×D3—42no—
122C3×C4×D3—41no—
123#626—48no—
124C32×C8—22no—
125C3×C3⋊C8—41no—
126#575—91no—
127#525—92no—
128#421—92no—
129#407—31no—
130H(3,ℤ/4)—31no—
131C24×C3—31no—
132C23×D3D1211yescharacteristic
133C22×C3×C4—21no—
134C22×C3×C4—31no—
135C22×C3×C4—61no—
136C22×C3×C4—62no—
137C22×C3×C4—62no—
138C22×C3×C4—61no—
139C22×C3×C4C22×D311yescharacteristic
140C22×C3×C4C22×D311yescharacteristic
141C2×#67—64no—
142C2×#67—62no—
143C2×#67—62no—
144C2×#67—122no—
145C22×Dic3D1211yescharacteristic
146#235—64no—
147#235—64no—
148#235—62no—
149#235—62no—
150#235—62no—
151#235—62no—
152#235—62no—
153#235—62no—
154#235—62no—
155#235—62no—
156#235—122no—
157#235—122no—
158C2×D12—32no—
159C2×D12—32no—
160C2×D12—62no—
161C2×D12—64no—
162C2×C4×D3—21no—
163C2×C4×D3—22no—
164C2×C4×D3—22no—
165C2×C4×D3—21no—
166C2×C4×D3—62no—
167C2×C4×D3—62no—
168C2×C4×D3—122no—
169C2×Dic6—32no—
170C2×Dic6—32no—
171C2×Dic6—62no—
172C3×M16—24no—
173C3×M16—22no—
174C3×M16—22no—
175C3×M16—62no—
176C2×C3×C8—22no—
177C2×C3×C8—61no—
178C2×C3×C8D1212yescomplemented
179C2×C3×C8#6712yescomplemented
180C3×C4⋊C4—62no—
181C3×C22⋊C4—62no—
182C3×C42—34no—
183#217—22no—
184#217—64no—
185(C2×D3)⋊C4—64no—
186(C2×D3)⋊C4—64no—
187(C2×D3)⋊C4—64no—
188C4⋊Dic3—22no—
189C4⋊Dic3—64no—
190Dic3⋊C4—64no—
191C4×Dic3D1214yescomplemented
192#208—22no—
193C2×C3⋊C8—21no—
194Dic12—64no—
195Dic12—62no—
196Dic12—62no—
197D24—64no—
198D24—62no—
199D24—62no—
200#204—68no—
201#204—64no—
202#204—64no—
203C22×C32—41no—
204C22×C32#12012yes—
205C22×C32#12111yescharacteristic
206C2×C3⋊D3—42no—
207C2×C3⋊D3—44no—
208C2×C3×D3—24no—
209C2×C3×D3—22no—
210C2×C3×D3—42no—
211C2×C3×D3—41no—
212C2×C3×D3—41no—
213C32×C4#12011yescharacteristic
214C32×C4#12112yes—
215C32×C4#12711yescharacteristic
216C3⋊Dic3—42no—
217C3×Dic3—44no—
218C3×Dic3—41no—
219C2×#41—92no—
220C23×C4—31no—
221#137—182no—
222AGL(1,ℤ/8)—182no—
223#135—182no—
224C2×M16—31no—
225C2×M16D3211yescharacteristic
226#123—182no—
227C22⋊Q8—182no—
228#121—182no—
229#120—182no—
230C4×D4—184no—
231#117—32no—
232#104—184no—
233C22⋊C8—62no—
234C23×C3—21no—
235C23×C3—62no—
236C23×C3—61no—
237C23×C3—122no—
238C23×C3C2×D1211yescharacteristic
239C23×C3D3×D411yescharacteristic
240C22×D3—22no—
241C22×D3—21no—
242C22×D3—42no—
243C22×D3—62no—
244C22×D3—62no—
245C22×D3—122no—
246C2×C3×C4—21no—
247C2×C3×C4—22no—
248C2×C3×C4—21no—
249C2×C3×C4—22no—
250C2×C3×C4—62no—
251C2×C3×C4—64no—
252C2×C3×C4—61no—
253C2×C3×C4—121no—
254C2×C3×C4—121no—
255C2×C3×C4—122no—
256C2×C3×C4C2×D1212yes—
257C2×C3×C4C2×D1211yescharacteristic
258C2×C3×C4#23511yescharacteristic
259C2×C3×C4D3×D412yes—
260C2×C3×C4D3×D412yes—
261C2×C3×C4D3×D412yes—
262C2×C3×C4#23911yescharacteristic
263C2×C3×C4C2×#6711yescharacteristic
264#67—128no—
265#67—124no—
266#67—124no—
267#67—122no—
268#67—122no—
269#67—122no—
270#67—122no—
271C2×Dic3—24no—
272C2×Dic3—22no—
273C2×Dic3—21no—
274C2×Dic3—62no—
275C2×Dic3—62no—
276C2×Dic3—122no—
277D12—64no—
278D12—62no—
279D12—62no—
280D12—62no—
281D12—62no—
282D12—122no—
283D12—128no—
284C4×D3—42no—
285C4×D3—41no—
286C4×D3—41no—
287C4×D3—124no—
288C4×D3—124no—
289C4×D3—122no—
290C4×D3—122no—
291C4×D3—122no—
292C4×D3—122no—
293Dic6—64no—
294Dic6—62no—
295Dic6—62no—
296Dic6—62no—
297Dic6—62no—
298Dic6—122no—
299C3×C8—24no—
300C3×C8—22no—
301C3×C8—22no—
302C3×C8—121no—
303C3⋊C8—41no—
304C2×C32—22no—
305C2×C32—21no—
306C2×C32#39211yescharacteristic
307C3⋊D3—82no—
308C3×D3—42no—
309C24—31no—
310#41—182no—
311#41—182no—
312#41—182no—
313#41—182no—
314C2×Q8—92no—
315C2×D4—92no—
316C2×D4—184no—
317C2×D4—182no—
318C22×C4—31no—
319C22×C4—61no—
320C22×C4—62no—
321C22×C4—61no—
322C22×C4—62no—
323C22×C4—182no—
324C22×C4C2×D3211yescharacteristic
325Q16—182no—
326SD16—184no—
327D8—182no—
328M16—22no—
329M16—62no—
330C2×C8—61no—
331C2×C8#62612yescomplemented
332C4⋊C4—62no—
333C4⋊C4—184no—
334C22⋊C4—62no—
335C22⋊C4—184no—
336C22⋊C4—184no—
337C42—34no—
338C22×C3—21no—
339C22×C3—22no—
340C22×C3—41no—
341C22×C3—41no—
342C22×C3—64no—
343C22×C3—62no—
344C22×C3—81no—
345C22×C3—122no—
346C22×C3—121no—
347C22×C3—121no—
348C22×C3#88212yes—
349C22×C3#88212yes—
350C22×C3#89511yescharacteristic
351C22×C3#93011yescharacteristic
352C2×D3—24no—
353C2×D3—22no—
354C2×D3—42no—
355C2×D3—41no—
356C2×D3—41no—
357C2×D3—124no—
358C2×D3—124no—
359C2×D3—124no—
360C2×D3—122no—
361C2×D3—122no—
362C2×D3—244no—
363C3×C4—22no—
364C3×C4—21no—
365C3×C4—21no—
366C3×C4—124no—
367C3×C4—121no—
368C3×C4#87411yescharacteristic
369C3×C4#88211yescharacteristic
370C3×C4#88412yes—
371C3×C4#89512yes—
372C3×C4#93711yescharacteristic
373C3×C4#94011yescharacteristic
374Dic3—44no—
375Dic3—41no—
376Dic3—124no—
377Dic3—122no—
378Dic3—122no—
379C32#201011yescharacteristic, complemented, Sylow
380C23—61no—
381C23—62no—
382C23—122no—
383C23—182no—
384C23D3×D1211yescharacteristic
385Q8—182no—
386Q8—182no—
387D4—182no—
388D4—182no—
389D4—368no—
390D4—362no—
391D4—362no—
392C2×C4—61no—
393C2×C4—64no—
394C2×C4—62no—
395C2×C4—122no—
396C2×C4—121no—
397C2×C4—121no—
398C2×C4—182no—
399C2×C4—362no—
400C2×C4—362no—
401C2×C4#379911yescharacteristic
402C2×C4D3×D1212yes—
403C2×C4C2×#62611yescharacteristic
404C2×C4#381112yes—
405C8—22no—
406C8—121no—
407C2×C3—22no—
408C2×C3—21no—
409C2×C3—22no—
410C2×C3—21no—
411C2×C3—21no—
412C2×C3—42no—
413C2×C3—41no—
414C2×C3—122no—
415C2×C3#467111yescharacteristic
416C2×C3#496011yescharacteristic
417D3—42no—
418D3—244no—
419D3—242no—
420D3—242no—
421C22—41no—
422C22—64no—
423C22—62no—
424C22—122no—
425C22—121no—
426C22—121no—
427C22—364no—
428C22—362no—
429C22#6390911yescharacteristic
430C22#6392312yes—
431C4—124no—
432C4—121no—
433C4—362no—
434C4#6391012yes—
435C4#6391111yescharacteristic
436C4#6398111yescharacteristic
437C3—21no—
438C3#6870311yescharacteristic, complemented
439C3#6999311yescharacteristic, complemented
440C2—22no—
441C2—21no—
442C2—122no—
443C2—722no—
444C2#1059139511yescharacteristic
subgroupG/H
centerC4#63911
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32#392
hypercenterC2×M16D32
hypocenterC32#2010
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. #10596219C2semidirect
2. #10595023C2semidirect
3. C3×#5126C2semidirect
4. #10591113C2semidirect
5. C3×#4557C2semidirect
30. #5126D3semidirect
33. #4557D3semidirect
41. C2×C4⋊(C3⋊D3)D4semidirect
43. C2×#634D4semidirect
51. C2×C32×C8D4semidirect
57. C3×C4×Dic3D4semidirect
178. C2×C3×C8D12semidirect
179. C2×C3×C8#67semidirect
191. C4×Dic3D12semidirect
331. C2×C8#626semidirect
379. C32#2010semidirect
438. C3#68703semidirect
439. C3#69993semidirect

Maximal subgroups

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

subgroupindex
#105962192
#105950232
C3×#51262
#105911132
C3×#45572
#699933
#687033