Finite Group Databasebeta

← #11779093

Subgroups — #11779093

Order 1152.

521 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 521 conjugacy classes of subgroups — too many to draw. Only its 86 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#10593987C211yesmaximal, characteristic, complemented
2C3×#4693C211yesmaximal, characteristic, complemented
3#10590355C211yesmaximal, characteristic, complemented
4#10590347C211yesmaximal, characteristic, complemented
5#10589325C211yesmaximal, characteristic, complemented
6C3×#4459C211yesmaximal, characteristic, complemented
7#10589095C211yesmaximal, characteristic, complemented
8#71265—31nomaximal
9#68199—31nomaximal
10C4×C4⋊(C3⋊D3)C2211yescharacteristic
11C2×C3×#204—22no—
12C3×#874C2211yescharacteristic
13C3×C4×D12C2211yescharacteristic
14C3×#869C2211yescharacteristic
15#63916—21no—
16#63909—21no—
17#63907—22no—
18#63849—21no—
19#63841—21no—
20C2×#3714—21no—
21C2×#3713—21no—
22C32×C4×C8C2211yescharacteristic
23C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25#63563—21no—
26#63562—21no—
27#5734—31no—
28#5563—31no—
29C3×#492—31no—
30#5072—31no—
31#5072—31no—
32#5015—31no—
33#4843—31no—
34#4693D311yescharacteristic, complemented
35C3×D4⋊C8—31no—
36#4546—31no—
37#4481—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×D12—21no—
45C2×C3×D12—21no—
46C2×C3×D12—21no—
47C2×C3×D12D411yescharacteristic
48C2×C3×C4×D3—21no—
49C2×C3×Dic6D412yes—
50C2×#626—22no—
51C2×C32×C8—21no—
52C32×C42C2311yescharacteristic
53#3752—21no—
54C4⋊(C3⋊Dic3)D411yescharacteristic
55C2×C3⋊(C3⋊C8)—21no—
56C3×(C2×D3)⋊C4—21no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3D411yescharacteristic
60C2×C3×C3⋊C8—21no—
61C3×#204—44no—
62#3722—22no—
63(C2×D3)⋊Dic3—22no—
64Dic32—22no—
65#3714—42no—
66#3713—42no—
67#1624—91noSylow
68C2×C3×SD16—62no—
69C3×C4⋊Q8—31no—
70C3×#127—31no—
71C3×C4×D4—31no—
72#947—62no—
73#938—61no—
74C2×#213—61no—
75C2×#213—61no—
76C2×#213—61no—
77#930—61no—
78#926—61no—
79C2×D24—61no—
80C2×#204—22no—
81#895—61no—
82#895—61no—
83#892—61no—
84#892—61no—
85#892—61no—
86#885—62no—
87#874C2×D311yescharacteristic
88C4×D12—31no—
89C4×D12—31no—
90C4×D12—61no—
91C4×D12C2×D311yescharacteristic
92#869C2×D311yescharacteristic
93C3×C4⋊C8—31no—
94C3×C4×C8—21no—
95C3×C4×C8C2×D311yescharacteristic
96C3×C4×C8C2×D311yescharacteristic
97#832—61no—
98#832—61no—
99#821—61no—
100#809—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—
107C22×C3×D3—41no—
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C3⋊Dic3—21no—
112C4⋊(C3⋊D3)—21no—
113C4⋊(C3⋊D3)—21no—
114C4×C3⋊D3—41no—
115C4×C3⋊D3—41no—
116C2×C3×Dic3—21no—
117C2×C3×Dic3—22no—
118C3×D12—21no—
119C3×D12—21no—
120C3×D12—42no—
121C3×D12—41no—
122C3×D12—41no—
123C3×D12—41no—
124C3×D12—41no—
125C3×C4×D3—41no—
126C3×C4×D3—41no—
127C3×Dic6—42no—
128#626—82no—
129C32×C8—22no—
130C3⋊(C3⋊C8)—41no—
131C3×C3⋊C8—41no—
132#555—91no—
133#492—31no—
134#459—91no—
135#459—91no—
136#333—91no—
137D4⋊C8—31no—
138D4⋊C8—91no—
139C2×C3×Q8—32no—
140C2×C3×D4—31no—
141C2×C3×D4—61no—
142C2×C3×D4—61no—
143C2×C3×D4—61no—
144C22×C3×C4—61no—
145C2×#67—62no—
146C2×D12—21no—
147C2×D12—21no—
148C2×D12—21no—
149C2×D12—31no—
150C2×D12—31no—
151C2×D12—61no—
152C2×D12—62no—
153C2×D12D1211yescharacteristic
154C2×C4×D3—21no—
155C2×C4×D3—61no—
156C2×C4×D3—61no—
157C2×C4×D3—121no—
158C2×Dic6#6712yes—
159C3×SD16—124no—
160C2×C3×C8—21no—
161C2×C3×C8—21no—
162C2×C3×C8—41no—
163C2×C3×C8—61no—
164C3×C4⋊C4—31no—
165C3×C4⋊C4—61no—
166C3×C4⋊C4—61no—
167C3×C22⋊C4—61no—
168C3×C42—21no—
169C3×C42C22×D311yescharacteristic
170C3×C42C22×D311yescharacteristic
171#217—62no—
172#213—122no—
173#213—122no—
174#213—122no—
175(C2×D3)⋊C4—21no—
176(C2×D3)⋊C4—62no—
177(C2×D3)⋊C4—62no—
178(C2×D3)⋊C4—62no—
179(C2×D3)⋊C4—61no—
180(C2×D3)⋊C4—61no—
181(C2×D3)⋊C4—121no—
182C4⋊Dic3—21no—
183C4⋊Dic3—21no—
184C4⋊Dic3—31no—
185C4⋊Dic3—31no—
186C4⋊Dic3—61no—
187C4⋊Dic3D1211yescharacteristic
188C4×Dic3—62no—
189C4×Dic3—62no—
190C2×C3⋊C8—21no—
191C2×C3⋊C8—61no—
192C2×C3⋊C8—61no—
193C2×C3⋊C8—121no—
194D24—122no—
195#204—44no—
196C22×C32#12011yescharacteristic
197C2×C3⋊D3—41no—
198C2×C3⋊D3—41no—
199C2×C3⋊D3—41no—
200C2×C3×D3—41no—
201C2×C3×D3—41no—
202C2×C3×D3—41no—
203C2×C3×D3—81no—
204C2×C3×D3—81no—
205C2×C3×D3—81no—
206C32×C4—21no—
207C32×C4#13511yescharacteristic
208C32×C4#13511yescharacteristic
209C32×C4AGL(1,ℤ/8)11yescharacteristic
210C32×C4AGL(1,ℤ/8)11yescharacteristic
211C3⋊Dic3—41no—
212C3×Dic3—41no—
213C3×Dic3—42no—
214C2×SD16—62no—
215C2×D8—181no—
216C2×D8—181no—
217C4⋊Q8—31no—
218#127—31no—
219#124—182no—
220#121—181no—
221#121—181no—
222C4×D4—31no—
223C4×D4—91no—
224#117—181no—
225#117—181no—
226C4⋊C8—31no—
227C4⋊C8—91no—
228#102—181no—
229#102—181no—
230C4×C8D3211yescharacteristic
231C23×C3—61no—
232C23×C3—121no—
233C22×D3—21no—
234C22×D3—41no—
235C22×D3—61no—
236C22×D3—61no—
237C22×D3—121no—
238C3×Q8—122no—
239C3×D4—61no—
240C3×D4—61no—
241C3×D4—122no—
242C3×D4—121no—
243C3×D4—121no—
244C3×D4—121no—
245C3×D4—121no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—62no—
250C2×C3×C4—61no—
251C2×C3×C4—121no—
252C2×C3×C4—121no—
253C2×C3×C4C2×D1211yescharacteristic
254C2×C3×C4D3×D411yescharacteristic
255C2×C3×C4D3×D411yescharacteristic
256C2×C3×C4D3×D411yescharacteristic
257C2×C3×C4D3×D411yescharacteristic
258C2×C3×C4C2×#6711yescharacteristic
259#67—242no—
260C2×Dic3—21no—
261C2×Dic3—22no—
262C2×Dic3—61no—
263C2×Dic3—61no—
264C2×Dic3—121no—
265D12—21no—
266D12—21no—
267D12—42no—
268D12—41no—
269D12—41no—
270D12—41no—
271D12—41no—
272D12—62no—
273D12—61no—
274D12—61no—
275D12—61no—
276D12—61no—
277D12—121no—
278D12—242no—
279C4×D3—41no—
280C4×D3—41no—
281C4×D3—121no—
282C4×D3—121no—
283C4×D3—121no—
284C4×D3—121no—
285C4×D3—241no—
286C4×D3—241no—
287Dic6—42no—
288C3×C8—22no—
289C3×C8—22no—
290C3×C8—42no—
291C3×C8—121no—
292C3⋊C8—41no—
293C3⋊C8—121no—
294C3⋊C8—121no—
295C3⋊C8—241no—
296C2×C32#44911yescharacteristic
297C2×C32#44911yescharacteristic
298C2×C32#45311yescharacteristic
299C3⋊D3—81no—
300C3×D3—81no—
301C3×D3—161no—
302C2×Q8—32no—
303C2×D4—31no—
304C2×D4—61no—
305C2×D4—61no—
306C2×D4—61no—
307C2×D4—91no—
308C2×D4—182no—
309C22×C4—61no—
310C22×C4—181no—
311SD16—124no—
312D8—362no—
313D8—362no—
314C2×C8—21no—
315C2×C8—61no—
316C2×C8—181no—
317C4⋊C4—31no—
318C4⋊C4—61no—
319C4⋊C4—61no—
320C4⋊C4—91no—
321C22⋊C4—61no—
322C22⋊C4—182no—
323C22⋊C4—182no—
324C22⋊C4—181no—
325C42—182no—
326C42C2×D3211yescharacteristic
327C22×C3—21no—
328C22×C3—121no—
329C22×C3—121no—
330C22×C3—121no—
331C22×C3—241no—
332C22×C3—241no—
333C22×C3—241no—
334C22×C3#88211yescharacteristic
335C22×C3#93711yescharacteristic
336C2×D3—41no—
337C2×D3—41no—
338C2×D3—41no—
339C2×D3—81no—
340C2×D3—81no—
341C2×D3—81no—
342C2×D3—122no—
343C2×D3—121no—
344C2×D3—121no—
345C2×D3—121no—
346C2×D3—121no—
347C2×D3—121no—
348C2×D3—121no—
349C2×D3—241no—
350C2×D3—241no—
351C3×C4—21no—
352C3×C4—21no—
353C3×C4—21no—
354C3×C4—21no—
355C3×C4—21no—
356C3×C4—21no—
357C3×C4—41no—
358C3×C4—121no—
359C3×C4—122no—
360C3×C4#90411yescharacteristic
361C3×C4#90811yescharacteristic
362C3×C4#91111yescharacteristic
363C3×C4#91411yescharacteristic
364C3×C4#91411yescharacteristic
365C3×C4#91611yescharacteristic
366C3×C4#91611yescharacteristic
367C3×C4#91611yescharacteristic
368Dic3—41no—
369Dic3—42no—
370Dic3—121no—
371Dic3—121no—
372Dic3—241no—
373C32#162411yescharacteristic, complemented, Sylow
374C23—61no—
375C23—121no—
376C23—181no—
377Q8—122no—
378D4—61no—
379D4—61no—
380D4—122no—
381D4—121no—
382D4—121no—
383D4—121no—
384D4—121no—
385D4—181no—
386D4—181no—
387D4—722no—
388C2×C4—61no—
389C2×C4—62no—
390C2×C4—121no—
391C2×C4—121no—
392C2×C4—181no—
393C2×C4—361no—
394C2×C4—361no—
395C2×C4D3×D1211yescharacteristic
396C2×C4#380211yescharacteristic
397C2×C4D3×#6711yescharacteristic
398C8—22no—
399C8—121no—
400C8—361no—
401C2×C3—21no—
402C2×C3—21no—
403C2×C3—21no—
404C2×C3—241no—
405C2×C3—481no—
406C2×C3#473411yescharacteristic
407C2×C3#478111yescharacteristic
408C2×C3#482211yescharacteristic
409C2×C3#507711yescharacteristic
410C2×C3#517211yescharacteristic
411C2×C3#517211yescharacteristic
412D3—81no—
413D3—161no—
414D3—242no—
415D3—241no—
416D3—241no—
417C22—121no—
418C22—121no—
419C22—121no—
420C22—241no—
421C22—241no—
422C22—241no—
423C22—361no—
424C22—361no—
425C22—361no—
426C22#6392211yescharacteristic
427C4—21no—
428C4—122no—
429C4—121no—
430C4—361no—
431C4#6379411yescharacteristic
432C4#6379811yescharacteristic
433C4#6380611yescharacteristic
434C4#6380911yescharacteristic
435C3—21no—
436C3#6819911yescharacteristic, complemented
437C3#7126511yescharacteristic, complemented
438C2—241no—
439C2—481no—
440C2—721no—
441C2#1059039511yescharacteristic
442C2#1059082311yescharacteristic
443C2#1059096411yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×C8C22
socleC22×C32#120
hypercenterC4×C8D32
hypocenterC32#1624
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
1. #10593987C2semidirect
2. C3×#4693C2semidirect
3. #10590355C2semidirect
4. #10590347C2semidirect
5. #10589325C2semidirect
6. C3×#4459C2semidirect
7. #10589095C2semidirect
34. #4693D3semidirect
41. #4459D3semidirect
373. C32#1624semidirect
436. C3#68199semidirect
437. C3#71265semidirect

Maximal subgroups

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

subgroupindex
#105939872
C3×#46932
#105903552
#105903472
#105893252
C3×#44592
#105890952
#712653
#681993