Finite Group Databasebeta

← #11780442

Subgroups — #11780442

Order 1152.

529 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 529 conjugacy classes of subgroups — too many to draw. Only its 90 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#10593895C211yesmaximal, characteristic
2#10592379C211yesmaximal, characteristic, complemented
3#10590365C211yesmaximal, characteristic, complemented
4#10590272C211yesmaximal, characteristic, complemented
5C3×#4459C211yesmaximal, characteristic, complemented
6C3×#4459C211yesmaximal, characteristic, complemented
7#10589094C211yesmaximal, characteristic, complemented
8#68211—31nomaximal
9#68185—31nomaximal
10C2×#3795—21no—
11#64078C2211yescharacteristic
12#64078C2211yescharacteristic
13C3×C4×D12C2211yescharacteristic
14C3×C4×D12C2211yescharacteristic
15#63908—21no—
16#63891—22no—
17D3×C4⋊Dic3—21no—
18#63857—21no—
19C2×#3716—21no—
20C32×C4×C8C2211yescharacteristic
21#63644—22no—
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24#63575—21no—
25#63567—21no—
26#63563—21no—
27#5555—31no—
28#5551—31no—
29#5019—31no—
30#5007—31no—
31#4846—31no—
32#4841—31no—
33#4680—31no—
34#4680—31no—
35#4680—61no—
36C3×D4⋊C8—31no—
37C3×D4⋊C8—31no—
38#4486—31no—
39#4482—31no—
40#4459D311yescharacteristic, complemented
41#4459D311yescharacteristic, complemented
42C2×#634—21no—
43C2×#634—21no—
44C2×C3×D12D411yescharacteristic
45C2×C3×D12D411yescharacteristic
46C2×C3×C4×D3—21no—
47C2×C3×C4×D3—21no—
48C2×#625—22no—
49C2×D3×Dic3—22no—
50#3795—42no—
51#3795—42no—
52C2×C32×C8—21no—
53C32×C42C2311yescharacteristic
54C4⋊(C3⋊Dic3)—21no—
55C4⋊(C3⋊Dic3)—21no—
56C4⋊(C3⋊Dic3)—21no—
57C4⋊(C3⋊Dic3)D412yes—
58C3×(C2×D3)⋊C4—21no—
59C3×(C2×D3)⋊C4—21no—
60C3×C4⋊Dic3D411yescharacteristic
61C3×C4⋊Dic3D411yescharacteristic
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64Dic3⋊Dic3—22no—
65(C2×D3)⋊Dic3—22no—
66#3716—42no—
67#1654—91noSylow
68C2×#237—61no—
69C2×#235—61no—
70C3×C4×D4—31no—
71C3×C4×D4—31no—
72#938—61no—
73C2×#214—61no—
74#930—61no—
75C2×C4⋊Dic3—61no—
76#924—61no—
77C2×#204—61no—
78#897—61no—
79D3×C4⋊C4—61no—
80#886—62no—
81#883—62no—
82C4×D12C2×D311yescharacteristic
83C4×D12C2×D311yescharacteristic
84#869—31no—
85#869—31no—
86#869—31no—
87#869—31no—
88#869—61no—
89#869—61no—
90C3×C4⋊C8—31no—
91C3×C4⋊C8—31no—
92C3×C4×C8—21no—
93C3×C4×C8C2×D311yescharacteristic
94C3×C4×C8C2×D311yescharacteristic
95#832—61no—
96#821—61no—
97#818—61no—
98#817—62no—
99#817—62no—
100#817—64no—
101#816—61no—
102#810—61no—
103#807—61no—
104C4⋊(C3⋊C8)C2×D311yescharacteristic
105C4⋊(C3⋊C8)C2×D311yescharacteristic
106C22×C3×D3—21no—
107C22×C3×D3—21no—
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C3⋊Dic3—22no—
112C2×C3⋊Dic3—41no—
113#634—41no—
114#634—41no—
115#634—41no—
116#634—41no—
117C2×C3×Dic3—21no—
118C2×C3×Dic3—21no—
119C3×D12—21no—
120C3×D12—21no—
121C3×D12—21no—
122C3×D12SD1612yescomplemented
123C3×C4×D3—41no—
124C3×C4×D3—41no—
125C3×C4×D3—41no—
126C3×C4×D3—41no—
127#625—44no—
128D3×Dic3—44no—
129C32×C8—22no—
130C3×C3⋊C8—41no—
131C3×C3⋊C8—41no—
132#547—91no—
133#498—91no—
134#474—91no—
135#461—91no—
136#332—91no—
137D4⋊C8—31no—
138D4⋊C8—31no—
139C2×C3×D4—31no—
140C2×C3×D4—31no—
141C22×C3×C4—61no—
142C22×C3×C4—61no—
143C2×#67—62no—
144C2×#67—62no—
145C22×Dic3—62no—
146#237—122no—
147#237—122no—
148#235—122no—
149#235—122no—
150C2×D12D1211yescharacteristic
151C2×D12D1211yescharacteristic
152C2×C4×D3—21no—
153C2×C4×D3—21no—
154C2×C4×D3—62no—
155C2×Dic6—61no—
156C2×Dic6—61no—
157C2×Dic6—61no—
158C2×Dic6—61no—
159C2×Dic6—121no—
160C2×Dic6—121no—
161C2×C3×C8—22no—
162C2×C3×C8—21no—
163C2×C3×C8—21no—
164C2×C3×C8—61no—
165C2×C3×C8—61no—
166C3×C4⋊C4—31no—
167C3×C4⋊C4—31no—
168C3×C22⋊C4—61no—
169C3×C22⋊C4—61no—
170C3×C42—21no—
171C3×C42C22×D311yescharacteristic
172C3×C42C22×D311yescharacteristic
173#217—62no—
174#214—122no—
175(C2×D3)⋊C4—21no—
176(C2×D3)⋊C4—21no—
177(C2×D3)⋊C4—62no—
178C4⋊Dic3—32no—
179C4⋊Dic3—32no—
180C4⋊Dic3—62no—
181C4⋊Dic3—62no—
182C4⋊Dic3—61no—
183C4⋊Dic3—61no—
184C4⋊Dic3—62no—
185C4⋊Dic3—61no—
186C4⋊Dic3—61no—
187C4⋊Dic3—61no—
188C4⋊Dic3—61no—
189C4⋊Dic3—121no—
190C4⋊Dic3—121no—
191C4⋊Dic3D1211yescharacteristic
192C4⋊Dic3D1211yescharacteristic
193Dic3⋊C4—62no—
194C2×C3⋊C8—21no—
195C2×C3⋊C8—21no—
196#204—122no—
197C22×C32#12011yescharacteristic
198C2×C3×D3—22no—
199C2×C3×D3—41no—
200C2×C3×D3—41no—
201C2×C3×D3—41no—
202C2×C3×D3—41no—
203C2×C3×D3—41no—
204C32×C4—21no—
205C32×C4C2×SD1611yescharacteristic
206C32×C4#13511yescharacteristic
207C32×C4AGL(1,ℤ/8)11yescharacteristic
208C32×C4AGL(1,ℤ/8)11yescharacteristic
209C3⋊Dic3—42no—
210C3⋊Dic3—81no—
211C3×Dic3—41no—
212C3×Dic3—41no—
213C2×#41—181no—
214C2×SD16—181no—
215C4⋊Q8—91no—
216C4⋊Q8—91no—
217#123—182no—
218C22⋊Q8—181no—
219#121—181no—
220C4×D4—31no—
221C4×D4—31no—
222C2×C4⋊C4—181no—
223#107—181no—
224#106—182no—
225C4⋊C8—31no—
226C4⋊C8—31no—
227#103—181no—
228#102—181no—
229C4×C8D3211yescharacteristic
230C23×C3—61no—
231C23×C3—61no—
232C22×D3—21no—
233C22×D3—21no—
234C3×D4—32no—
235C3×D4—61no—
236C3×D4—61no—
237C3×D4—61no—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—61no—
242C2×C3×C4—61no—
243C2×C3×C4—121no—
244C2×C3×C4—121no—
245C2×C3×C4—121no—
246C2×C3×C4—121no—
247C2×C3×C4C2×D1211yescharacteristic
248C2×C3×C4C2×D1211yescharacteristic
249C2×C3×C4D3×D411yescharacteristic
250C2×C3×C4D3×D411yescharacteristic
251C2×C3×C4D3×D411yescharacteristic
252C2×C3×C4D3×D411yescharacteristic
253#67—124no—
254#67—124no—
255C2×Dic3—21no—
256C2×Dic3—21no—
257C2×Dic3—62no—
258C2×Dic3—62no—
259C2×Dic3—122no—
260C2×Dic3—124no—
261C2×Dic3—122no—
262C2×Dic3—121no—
263C2×Dic3—121no—
264D12—21no—
265D12—21no—
266D12—21no—
267D12#20412yescomplemented
268C4×D3—41no—
269C4×D3—41no—
270C4×D3—41no—
271C4×D3—41no—
272C4×D3—124no—
273Dic6—121no—
274Dic6—121no—
275Dic6—121no—
276Dic6—121no—
277Dic6—121no—
278Dic6—121no—
279Dic6—121no—
280Dic6—121no—
281Dic6—241no—
282Dic6—241no—
283Dic6—241no—
284Dic6—241no—
285C3×C8—24no—
286C3×C8—22no—
287C3×C8—22no—
288C3×C8—121no—
289C3×C8—121no—
290C3⋊C8—41no—
291C3⋊C8—41no—
292C2×C32#44911yescharacteristic
293C2×C32#45011yescharacteristic
294C2×C32#45611yescharacteristic
295C3×D3—42no—
296C3×D3—81no—
297#41—362no—
298#41—362no—
299C2×Q8—181no—
300C2×Q8—181no—
301C2×D4—31no—
302C2×D4—31no—
303C2×D4—182no—
304C22×C4—61no—
305C22×C4—61no—
306C22×C4—182no—
307SD16—362no—
308C2×C8—21no—
309C2×C8—61no—
310C2×C8—61no—
311C4⋊C4—31no—
312C4⋊C4—31no—
313C4⋊C4—92no—
314C4⋊C4—182no—
315C4⋊C4—181no—
316C4⋊C4—181no—
317C4⋊C4—181no—
318C22⋊C4—61no—
319C22⋊C4—61no—
320C22⋊C4—182no—
321C42C2×D3211yescharacteristic
322C22×C3—21no—
323C22×C3—62no—
324C22×C3—121no—
325C22×C3—121no—
326C22×C3—121no—
327C22×C3—121no—
328C22×C3—121no—
329C22×C3#88211yescharacteristic
330C22×C3#88211yescharacteristic
331C2×D3—22no—
332C2×D3—41no—
333C2×D3—41no—
334C2×D3—41no—
335C2×D3—41no—
336C2×D3—41no—
337C3×C4—22no—
338C3×C4—21no—
339C3×C4—21no—
340C3×C4—21no—
341C3×C4—21no—
342C3×C4—21no—
343C3×C4—21no—
344C3×C4—121no—
345C3×C4—121no—
346C3×C4C2×#20411yescharacteristic
347C3×C4#90411yescharacteristic
348C3×C4#90811yescharacteristic
349C3×C4#90811yescharacteristic
350C3×C4#91111yescharacteristic
351C3×C4#91111yescharacteristic
352C3×C4D3×SD1611yescharacteristic
353C3×C4#91611yescharacteristic
354Dic3—41no—
355Dic3—41no—
356Dic3—122no—
357Dic3—122no—
358Dic3—242no—
359Dic3—242no—
360Dic3—241no—
361Dic3—241no—
362C32#165411yescharacteristic, complemented, Sylow
363C23—61no—
364C23—61no—
365Q8—361no—
366Q8—361no—
367Q8—361no—
368Q8—361no—
369D4—32no—
370D4—61no—
371D4—61no—
372D4—61no—
373D4—364no—
374C2×C4—61no—
375C2×C4—61no—
376C2×C4—121no—
377C2×C4—121no—
378C2×C4—121no—
379C2×C4—121no—
380C2×C4—182no—
381C2×C4—364no—
382C2×C4—361no—
383C2×C4D3×D1211yescharacteristic
384C2×C4D3×D1211yescharacteristic
385C2×C4#381111yescharacteristic
386C8—22no—
387C8—121no—
388C8—121no—
389C2×C3—21no—
390C2×C3—21no—
391C2×C3—21no—
392C2×C3—122no—
393C2×C3—241no—
394C2×C3#473111yescharacteristic
395C2×C3#473411yescharacteristic
396C2×C3#477611yescharacteristic
397C2×C3#478111yescharacteristic
398C2×C3#482611yescharacteristic
399C2×C3#482611yescharacteristic
400D3—42no—
401D3—81no—
402C22—62no—
403C22—121no—
404C22—121no—
405C22—121no—
406C22—121no—
407C22—121no—
408C22#6392311yescharacteristic
409C4—21no—
410C4—121no—
411C4—121no—
412C4—362no—
413C4—721no—
414C4D3×#20411yescharacteristic
415C4#6379511yescharacteristic
416C4#6379511yescharacteristic
417C4#6380611yescharacteristic
418C3—21no—
419C3#6818511yescharacteristic, complemented
420C3#6821111yescharacteristic, complemented
421C2—122no—
422C2—241no—
423C2#1059040111yescharacteristic
424C2#1059094611yescharacteristic
425C2#1059096811yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×C8C22
socleC22×C32#120
prime radical#10593895C2
hypercenterC4×C8D32
hypocenterC32#1654
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. #10592379C2semidirect
3. #10590365C2semidirect
4. #10590272C2semidirect
5. C3×#4459C2semidirect
6. C3×#4459C2semidirect
7. #10589094C2semidirect
40. #4459D3semidirect
41. #4459D3semidirect
122. C3×D12SD16semidirect
267. D12#204semidirect
362. C32#1654semidirect
419. C3#68185semidirect
420. C3#68211semidirect

Maximal subgroups

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

subgroupindex
#105938952
#105923792
#105903652
#105902722
C3×#44592
#105890942
#682113
#681853