Finite Group Databasebeta

← #11780443

Subgroups — #11780443

Order 1152.

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

normal subgroups only

This group has 521 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#10593896C211yesmaximal, characteristic
2C3×#4680C211yesmaximal, characteristic, complemented
3#10590379C211yesmaximal, characteristic, complemented
4#10590269C211yesmaximal, characteristic, complemented
5#10589325C211yesmaximal, characteristic, complemented
6C3×#4459C211yesmaximal, characteristic, complemented
7#10589092C211yesmaximal, characteristic, complemented
8#71343—31nomaximal
9#68185—31nomaximal
10C2×#3796—21no—
11C4×C4⋊(C3⋊D3)C2211yescharacteristic
12C3×C4×D12C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C3×#869C2211yescharacteristic
15#63909—21no—
16#63890—22no—
17D3×C4⋊Dic3—21no—
18#63871—21no—
19C2×#3717—21no—
20C32×C4×C8C2211yescharacteristic
21C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
22C3×#817—22no—
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24#63576—21no—
25#63566—21no—
26#63562—21no—
27#5726—31no—
28#5555—31no—
29C3×#498—31no—
30#5087—31no—
31#5083—31no—
32#5007—31no—
33#4841—31no—
34#4680D311yescharacteristic, complemented
35C3×D4⋊C8—31no—
36#4547—31no—
37#4486—31no—
38#4459—31no—
39#4459—31no—
40#4459—61no—
41#4459D311yescharacteristic, complemented
42C2×C4⋊(C3⋊D3)D411yescharacteristic
43C2×C4×C3⋊D3—21no—
44C2×C3×D12D411yescharacteristic
45C2×C3×C4×D3—21no—
46C2×C3×Dic6—21no—
47C2×C3×Dic6—21no—
48C2×#626—22no—
49C2×D3×Dic3—22no—
50#3796—42no—
51#3796—42no—
52C2×C32×C8—21no—
53C32×C42C2311yescharacteristic
54#3752—21no—
55C4⋊(C3⋊Dic3)D411yescharacteristic
56C2×C3⋊(C3⋊C8)—21no—
57C3×(C2×D3)⋊C4—21no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3D411yescharacteristic
62C3×C4⋊Dic3D412yes—
63C2×C3×C3⋊C8—21no—
64Dic3⋊Dic3—22no—
65#3722—22no—
66#3717—42no—
67#1654—91noSylow
68C2×#239—61no—
69C2×#237—61no—
70C3×C4⋊Q8—31no—
71C3×C4⋊Q8—31no—
72C3×C4×D4—31no—
73#946—61no—
74C2×#215—61no—
75#930—61no—
76C2×C4⋊Dic3—61no—
77C2×#204—61no—
78#897—61no—
79#895—61no—
80#894—62no—
81D3×C4⋊C4—61no—
82#886—62no—
83C4×D12—31no—
84C4×D12—31no—
85C4×D12—61no—
86C4×D12C2×D311yescharacteristic
87#869C2×D311yescharacteristic
88#869C2×D311yescharacteristic
89C3×#106—62no—
90C3×C4⋊C8—31no—
91C3×C4×C8—21no—
92C3×C4×C8C2×D311yescharacteristic
93C3×C4×C8C2×D311yescharacteristic
94#835—61no—
95#832—61no—
96#817—22no—
97#816—61no—
98#809—61no—
99#807—61no—
100#807—61no—
101C4⋊(C3⋊C8)—31no—
102C4⋊(C3⋊C8)—31no—
103C4⋊(C3⋊C8)—61no—
104C4⋊(C3⋊C8)C2×D311yescharacteristic
105C22×C3⋊D3—21no—
106C22×C3×D3—21no—
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C3⋊Dic3—21no—
111C4⋊(C3⋊D3)—21no—
112C4⋊(C3⋊D3)—21no—
113C4×C3⋊D3—41no—
114C4×C3⋊D3—41no—
115C2×C3×Dic3—21no—
116C2×C3×Dic3—22no—
117C2×C3×Dic3—41no—
118C3×D12—21no—
119C3×D12SD1612yescomplemented
120C3×C4×D3—41no—
121C3×C4×D3—41no—
122C3×Dic6—41no—
123C3×Dic6—41no—
124C3×Dic6—41no—
125C3×Dic6—41no—
126#626—44no—
127D3×Dic3—44no—
128C32×C8—22no—
129C3⋊(C3⋊C8)—41no—
130C3×C3⋊C8—41no—
131#547—91no—
132#498—31no—
133#474—91no—
134#461—91no—
135#332—91no—
136D4⋊C8—31no—
137D4⋊C8—91no—
138C2×C3×Q8—61no—
139C2×C3×Q8—61no—
140C2×C3×D4—31no—
141C22×C3×C4—61no—
142C2×#67—62no—
143C22×Dic3—62no—
144#239—122no—
145#239—122no—
146#237—122no—
147#237—122no—
148C2×D12—31no—
149C2×D12—31no—
150C2×D12—61no—
151C2×D12—62no—
152C2×D12D1211yescharacteristic
153C2×C4×D3—21no—
154C2×C4×D3—62no—
155C2×C4×D3—61no—
156C2×C4×D3—61no—
157C2×C4×D3—121no—
158C2×Dic6—21no—
159C2×Dic6—21no—
160C2×C3×C8—21no—
161C2×C3×C8—21no—
162C2×C3×C8—41no—
163C2×C3×C8—61no—
164C3×C4⋊C4—31no—
165C3×C4⋊C4—32no—
166C3×C4⋊C4—61no—
167C3×C4⋊C4—61no—
168C3×C4⋊C4—61no—
169C3×C22⋊C4—61no—
170C3×C42—21no—
171C3×C42C22×D311yescharacteristic
172C3×C42C22×D311yescharacteristic
173#215—122no—
174(C2×D3)⋊C4—21no—
175(C2×D3)⋊C4—62no—
176(C2×D3)⋊C4—62no—
177(C2×D3)⋊C4—61no—
178(C2×D3)⋊C4—61no—
179(C2×D3)⋊C4—121no—
180C4⋊Dic3—21no—
181C4⋊Dic3—21no—
182C4⋊Dic3—21no—
183C4⋊Dic3—31no—
184C4⋊Dic3—31no—
185C4⋊Dic3—61no—
186C4⋊Dic3—62no—
187C4⋊Dic3D1211yescharacteristic
188C4⋊Dic3#6712yes—
189Dic3⋊C4—62no—
190C2×C3⋊C8—21no—
191C2×C3⋊C8—61no—
192C2×C3⋊C8—61no—
193C2×C3⋊C8—121no—
194#204—122no—
195C22×C32#12011yescharacteristic
196C2×C3⋊D3—41no—
197C2×C3⋊D3—41no—
198C2×C3⋊D3—41no—
199C2×C3×D3—22no—
200C2×C3×D3—41no—
201C2×C3×D3—41no—
202C32×C4—21no—
203C32×C4C2×SD1611yescharacteristic
204C32×C4#13511yescharacteristic
205C32×C4AGL(1,ℤ/8)11yescharacteristic
206C32×C4AGL(1,ℤ/8)11yescharacteristic
207C3⋊Dic3—41no—
208C3×Dic3—41no—
209C3×Dic3—42no—
210C3×Dic3—81no—
211C2×#41—181no—
212C2×SD16—181no—
213C4⋊Q8—31no—
214C4⋊Q8—31no—
215#123—182no—
216C22⋊Q8—181no—
217#121—181no—
218C4×D4—31no—
219C4×D4—91no—
220C2×C4⋊C4—181no—
221#107—181no—
222#106—62no—
223C4⋊C8—31no—
224C4⋊C8—91no—
225#103—181no—
226#102—181no—
227C4×C8D3211yescharacteristic
228C23×C3—61no—
229C22×D3—21no—
230C22×D3—61no—
231C22×D3—61no—
232C22×D3—121no—
233C3×Q8—121no—
234C3×Q8—121no—
235C3×Q8—121no—
236C3×Q8—121no—
237C3×D4—32no—
238C3×D4—61no—
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—62no—
243C2×C3×C4—61no—
244C2×C3×C4—121no—
245C2×C3×C4—121no—
246C2×C3×C4—121no—
247C2×C3×C4C2×D1211yescharacteristic
248C2×C3×C4D3×D411yescharacteristic
249C2×C3×C4D3×D411yescharacteristic
250C2×C3×C4D3×D411yescharacteristic
251C2×C3×C4D3×D411yescharacteristic
252C2×C3×C4C2×#6711yescharacteristic
253#67—124no—
254C2×Dic3—21no—
255C2×Dic3—22no—
256C2×Dic3—41no—
257C2×Dic3—61no—
258C2×Dic3—61no—
259C2×Dic3—121no—
260C2×Dic3—124no—
261D12—21no—
262D12—62no—
263D12—61no—
264D12—61no—
265D12—61no—
266D12—61no—
267D12—121no—
268D12—124no—
269D12#20412yescomplemented
270C4×D3—41no—
271C4×D3—41no—
272C4×D3—124no—
273C4×D3—121no—
274C4×D3—121no—
275C4×D3—121no—
276C4×D3—121no—
277C4×D3—241no—
278C4×D3—241no—
279Dic6—41no—
280Dic6—41no—
281Dic6—41no—
282Dic6—41no—
283C3×C8—22no—
284C3×C8—22no—
285C3×C8—42no—
286C3×C8—121no—
287C3⋊C8—41no—
288C3⋊C8—121no—
289C3⋊C8—121no—
290C3⋊C8—241no—
291C2×C32#44911yescharacteristic
292C2×C32#45011yescharacteristic
293C2×C32#45611yescharacteristic
294C3⋊D3—81no—
295C3×D3—42no—
296#41—362no—
297#41—362no—
298C2×Q8—61no—
299C2×Q8—61no—
300C2×D4—31no—
301C2×D4—91no—
302C2×D4—182no—
303C22×C4—61no—
304C22×C4—182no—
305C22×C4—181no—
306SD16—362no—
307C2×C8—21no—
308C2×C8—61no—
309C2×C8—181no—
310C4⋊C4—31no—
311C4⋊C4—32no—
312C4⋊C4—61no—
313C4⋊C4—61no—
314C4⋊C4—61no—
315C4⋊C4—91no—
316C4⋊C4—182no—
317C22⋊C4—61no—
318C22⋊C4—182no—
319C22⋊C4—181no—
320C42C2×D3211yescharacteristic
321C22×C3—21no—
322C22×C3—62no—
323C22×C3—121no—
324C22×C3—121no—
325C22×C3#88211yescharacteristic
326C22×C3#93711yescharacteristic
327C2×D3—22no—
328C2×D3—41no—
329C2×D3—41no—
330C2×D3—122no—
331C2×D3—121no—
332C2×D3—121no—
333C2×D3—121no—
334C2×D3—121no—
335C2×D3—121no—
336C2×D3—121no—
337C2×D3—241no—
338C2×D3—241no—
339C3×C4—21no—
340C3×C4—21no—
341C3×C4—21no—
342C3×C4—21no—
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—41no—
346C3×C4—121no—
347C3×C4—122no—
348C3×C4—241no—
349C3×C4C2×#20411yescharacteristic
350C3×C4#90811yescharacteristic
351C3×C4#91111yescharacteristic
352C3×C4D3×SD1611yescharacteristic
353C3×C4#91411yescharacteristic
354C3×C4#91411yescharacteristic
355C3×C4#91611yescharacteristic
356C3×C4#91611yescharacteristic
357Dic3—42no—
358Dic3—41no—
359Dic3—81no—
360Dic3—121no—
361Dic3—121no—
362Dic3—241no—
363C32#165411yescharacteristic, complemented, Sylow
364C23—61no—
365C23—181no—
366Q8—121no—
367Q8—121no—
368Q8—121no—
369Q8—121no—
370D4—32no—
371D4—61no—
372D4—181no—
373D4—181no—
374D4—364no—
375C2×C4—61no—
376C2×C4—62no—
377C2×C4—121no—
378C2×C4—121no—
379C2×C4—121no—
380C2×C4—181no—
381C2×C4—364no—
382C2×C4—361no—
383C2×C4—361no—
384C2×C4D3×D1211yescharacteristic
385C2×C4#380211yescharacteristic
386C2×C4D3×#6711yescharacteristic
387C8—22no—
388C8—121no—
389C8—361no—
390C2×C3—21no—
391C2×C3—21no—
392C2×C3—21no—
393C2×C3—122no—
394C2×C3#473111yescharacteristic
395C2×C3#478111yescharacteristic
396C2×C3#482611yescharacteristic
397C2×C3#509511yescharacteristic
398C2×C3#516911yescharacteristic
399C2×C3#517211yescharacteristic
400D3—42no—
401D3—242no—
402D3—241no—
403D3—241no—
404C22—62no—
405C22—121no—
406C22—121no—
407C22—361no—
408C22—361no—
409C22—361no—
410C22#6392211yescharacteristic
411C4—21no—
412C4—122no—
413C4—121no—
414C4—241no—
415C4—361no—
416C4D3×#20411yescharacteristic
417C4#6379411yescharacteristic
418C4#6379811yescharacteristic
419C4#6380911yescharacteristic
420C3—21no—
421C3#6818511yescharacteristic, complemented
422C3#7134311yescharacteristic, complemented
423C2—122no—
424C2—721no—
425C2#1059039911yescharacteristic
426C2#1059094211yescharacteristic
427C2#1059096411yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×C8C22
socleC22×C32#120
prime radical#10593896C2
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. C3×#4680C2semidirect
3. #10590379C2semidirect
4. #10590269C2semidirect
5. #10589325C2semidirect
6. C3×#4459C2semidirect
7. #10589092C2semidirect
34. #4680D3semidirect
41. #4459D3semidirect
119. C3×D12SD16semidirect
269. D12#204semidirect
363. C32#1654semidirect
421. C3#68185semidirect
422. C3#71343semidirect

Maximal subgroups

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

subgroupindex
#105938962
C3×#46802
#105903792
#105902692
#105893252
C3×#44592
#105890922
#713433
#681853