Finite Group Databasebeta

← #11779227

Subgroups — #11779227

Order 1152.

541 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 541 conjugacy classes of subgroups — too many to draw. Only its 92 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#10593903C211yesmaximal, characteristic, complemented
2C3×#4694C211yesmaximal, characteristic, complemented
3#10590364C211yesmaximal, characteristic, complemented
4#10590355C211yesmaximal, characteristic
5#10589325C211yesmaximal, characteristic, complemented
6C3×#4456C211yesmaximal, characteristic, complemented
7#10589092C211yesmaximal, characteristic, complemented
8#71205—31nomaximal
9#68266—31nomaximal
10C2×#3797—21no—
11C4×C4⋊(C3⋊D3)C2211yescharacteristic
12C3×#874C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C3×C4×Dic6C2211yescharacteristic
15#63918—21no—
16#63895—22no—
17#63894—21no—
18#63871—21no—
19C2×#3715—21no—
20C2×#3714—21no—
21C32×C4×C8C2211yescharacteristic
22C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
23C3×#821—22no—
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25#63563—21no—
26#63562—21no—
27#5727—31no—
28Q8×D12—31no—
29C3×#486—31no—
30#5075—31no—
31#5072—31no—
32#5027—31no—
33#4843—31no—
34#4694D311yescharacteristic, complemented
35C3×Q8⋊C8—31no—
36#4547—31no—
37#4486—31no—
38#4459—31no—
39#4459—31no—
40#4459—61no—
41#4456D311yescharacteristic, 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×Dic6—21no—
48C2×C3×Dic6D411yescharacteristic
49C2×#627—22no—
50C2×#624—22no—
51#3797—42no—
52#3797—42no—
53C2×C32×C8—21no—
54C32×C42C2311yescharacteristic
55#3752—21no—
56C4⋊(C3⋊Dic3)D411yescharacteristic
57C2×C3⋊(C3⋊C8)—21no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3D411yescharacteristic
60C3×C4⋊Dic3D412yes—
61C3×Dic3⋊C4—21no—
62C3×C4×Dic3—21no—
63C2×C3×C3⋊C8—21no—
64Dic3⋊Dic3—22no—
65#3722—22no—
66#3715—42no—
67#3714—42no—
68#1627—91noSylow
69C2×D3×Q8—61no—
70C2×D3×Q8—61no—
71C3×C4⋊Q8—31no—
72C3×#127—31no—
73C3×C4×Q8—31no—
74#946—61no—
75C2×#215—61no—
76C2×#214—61no—
77C2×#213—61no—
78C2×D24—61no—
79#897—61no—
80#897—62no—
81#896—62no—
82#893—61no—
83#888—61no—
84#874C2×D311yescharacteristic
85C4×D12—31no—
86C4×D12—31no—
87C4×D12—61no—
88C4×D12—61no—
89#869—61no—
90#869C2×D311yescharacteristic
91C4×Dic6C2×D311yescharacteristic
92C3×C4⋊C8—31no—
93C3×#102—62no—
94C3×C4×C8—21no—
95C3×C4×C8C2×D311yescharacteristic
96C3×C4×C8C2×D311yescharacteristic
97#832—61no—
98#832—61no—
99#821—22no—
100#821—61no—
101#809—61no—
102C4⋊(C3⋊C8)—31no—
103C4⋊(C3⋊C8)—31no—
104C4⋊(C3⋊C8)—61no—
105C4⋊(C3⋊C8)C2×D311yescharacteristic
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)SD1612yescomplemented
114C4×C3⋊D3—41no—
115C4×C3⋊D3—41no—
116C2×C3×Dic3—21no—
117C2×C3×Dic3—21no—
118C2×C3×Dic3—22no—
119C3×D12—42no—
120C3×D12—41no—
121C3×D12—41no—
122C3×D12—41no—
123C3×D12—41no—
124C3×Dic6—21no—
125C3×Dic6—41no—
126C3×Dic6—41no—
127C3×Dic6D812yescomplemented
128#627—44no—
129#624—44no—
130C32×C8—41no—
131C3⋊(C3⋊C8)—41no—
132C3×C3⋊C8—41no—
133D4×Q8—91no—
134#486—31no—
135#460—91no—
136#459—91no—
137#332—91no—
138Q8⋊C8—31no—
139D4⋊C8—91no—
140C2×C3×Q8—31no—
141C2×C3×Q8—61no—
142C2×C3×D4—61no—
143C2×C3×D4—61no—
144C2×C3×D4—61no—
145D3×Q8—122no—
146D3×Q8—122no—
147D3×Q8—122no—
148D3×Q8—122no—
149C2×D12—21no—
150C2×D12—21no—
151C2×D12—21no—
152C2×D12—31no—
153C2×D12—31no—
154C2×D12—61no—
155C2×C4×D3—62no—
156C2×C4×D3—62no—
157C2×C4×D3—61no—
158C2×C4×D3—61no—
159C2×C4×D3—121no—
160C2×Dic6—21no—
161C2×Dic6—62no—
162C2×Dic6—62no—
163C2×Dic6D1211yescharacteristic
164C2×C3×C8—21no—
165C2×C3×C8—21no—
166C2×C3×C8—41no—
167C2×C3×C8—61no—
168C3×C4⋊C4—31no—
169C3×C4⋊C4—32no—
170C3×C4⋊C4—61no—
171C3×C4⋊C4—61no—
172C3×C42—21no—
173C3×C42—61no—
174C3×C42C22×D311yescharacteristic
175C3×C42C22×D311yescharacteristic
176#215—122no—
177#214—122no—
178#213—122no—
179(C2×D3)⋊C4—62no—
180(C2×D3)⋊C4—62no—
181(C2×D3)⋊C4—61no—
182(C2×D3)⋊C4—61no—
183(C2×D3)⋊C4—121no—
184C4⋊Dic3—21no—
185C4⋊Dic3—31no—
186C4⋊Dic3—31no—
187C4⋊Dic3—61no—
188C4⋊Dic3—62no—
189C4⋊Dic3D1211yescharacteristic
190C4⋊Dic3#6712yes—
191Dic3⋊C4—21no—
192Dic3⋊C4—62no—
193C4×Dic3—21no—
194C2×C3⋊C8—21no—
195C2×C3⋊C8—61no—
196C2×C3⋊C8—61no—
197C2×C3⋊C8—121no—
198D24—122no—
199C22×C32#12011yescharacteristic
200C2×C3⋊D3—22no—
201C2×C3⋊D3—41no—
202C2×C3⋊D3—41no—
203C2×C3×D3—81no—
204C2×C3×D3—81no—
205C2×C3×D3—81no—
206C32×C4—21no—
207C32×C4C2×D811yescharacteristic
208C32×C4C2×SD1611yescharacteristic
209C32×C4AGL(1,ℤ/8)11yescharacteristic
210C32×C4#13711yescharacteristic
211C3⋊Dic3—41no—
212C3×Dic3—22no—
213C3×Dic3—42no—
214C3×Dic3—41no—
215C22×Q8—181no—
216C2×SD16—181no—
217C2×D8—181no—
218C4⋊Q8—31no—
219C4⋊Q8—181no—
220#127—31no—
221C22⋊Q8—182no—
222C22⋊Q8—181no—
223C4×Q8—31no—
224C4×D4—91no—
225C4×D4—181no—
226C4⋊C8—31no—
227C4⋊C8—91no—
228#102—62no—
229#102—181no—
230#102—181no—
231C4×C8D3211yescharacteristic
232C23×C3—121no—
233C22×D3—41no—
234C22×D3—61no—
235C22×D3—61no—
236C22×D3—121no—
237C3×Q8—32no—
238C3×Q8—61no—
239C3×Q8—121no—
240C3×Q8—121no—
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—61no—
250C2×C3×C4—62no—
251C2×C3×C4—61no—
252C2×C3×C4C2×D1211yescharacteristic
253C2×C3×C4D3×D411yescharacteristic
254C2×C3×C4D3×D411yescharacteristic
255C2×C3×C4D3×D411yescharacteristic
256C2×C3×C4D3×D411yescharacteristic
257C2×C3×C4C2×#6711yescharacteristic
258C2×Dic3—21no—
259C2×Dic3—21no—
260C2×Dic3—22no—
261C2×Dic3—61no—
262C2×Dic3—61no—
263C2×Dic3—121no—
264D12—32no—
265D12—32no—
266D12—42no—
267D12—41no—
268D12—41no—
269D12—41no—
270D12—41no—
271D12—62no—
272D12—61no—
273D12—61no—
274D12—121no—
275C4×D3—124no—
276C4×D3—124no—
277C4×D3—121no—
278C4×D3—121no—
279C4×D3—121no—
280C4×D3—121no—
281C4×D3—241no—
282C4×D3—241no—
283Dic6—21no—
284Dic6—41no—
285Dic6—41no—
286Dic6—124no—
287Dic6—124no—
288Dic6D2412yescomplemented
289C3×C8—41no—
290C3×C8—41no—
291C3×C8—42no—
292C3×C8—121no—
293C3⋊C8—41no—
294C3⋊C8—121no—
295C3⋊C8—121no—
296C3⋊C8—241no—
297C2×C32#44711yescharacteristic
298C2×C32#44811yescharacteristic
299C2×C32#45411yescharacteristic
300C3⋊D3—42no—
301C3×D3—161no—
302C2×Q8—31no—
303C2×Q8—61no—
304C2×Q8—182no—
305C2×Q8—362no—
306C2×Q8—362no—
307C2×D4—61no—
308C2×D4—61no—
309C2×D4—61no—
310C2×D4—91no—
311C22×C4—182no—
312C22×C4—181no—
313SD16—362no—
314D8—362no—
315C2×C8—21no—
316C2×C8—61no—
317C2×C8—181no—
318C4⋊C4—31no—
319C4⋊C4—32no—
320C4⋊C4—61no—
321C4⋊C4—61no—
322C4⋊C4—91no—
323C4⋊C4—182no—
324C22⋊C4—182no—
325C22⋊C4—181no—
326C42—61no—
327C42C2×D3211yescharacteristic
328C22×C3—21no—
329C22×C3—241no—
330C22×C3—241no—
331C22×C3—241no—
332C22×C3#88211yescharacteristic
333C22×C3#93711yescharacteristic
334C2×D3—62no—
335C2×D3—62no—
336C2×D3—81no—
337C2×D3—81no—
338C2×D3—81no—
339C2×D3—122no—
340C2×D3—121no—
341C2×D3—121no—
342C2×D3—121no—
343C2×D3—121no—
344C2×D3—241no—
345C2×D3—241no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—21no—
351C3×C4—21no—
352C3×C4—41no—
353C3×C4—62no—
354C3×C4—122no—
355C3×C4—121no—
356C3×C4C2×D2411yescharacteristic
357C3×C4#90811yescharacteristic
358C3×C4D3×D811yescharacteristic
359C3×C4#91111yescharacteristic
360C3×C4D3×SD1611yescharacteristic
361C3×C4D3×SD1611yescharacteristic
362C3×C4#91511yescharacteristic
363C3×C4#91811yescharacteristic
364Dic3—22no—
365Dic3—42no—
366Dic3—41no—
367Dic3—121no—
368Dic3—121no—
369Dic3—241no—
370C32#162711yescharacteristic, complemented, Sylow
371C23—121no—
372C23—181no—
373Q8—32no—
374Q8—61no—
375Q8—121no—
376Q8—121no—
377Q8—364no—
378D4—92no—
379D4—122no—
380D4—121no—
381D4—121no—
382D4—121no—
383D4—121no—
384D4—181no—
385C2×C4—61no—
386C2×C4—61no—
387C2×C4—62no—
388C2×C4—181no—
389C2×C4—364no—
390C2×C4—361no—
391C2×C4—361no—
392C2×C4D3×D1211yescharacteristic
393C2×C4#380211yescharacteristic
394C2×C4D3×#6711yescharacteristic
395C8—41no—
396C8—121no—
397C8—361no—
398C2×C3—21no—
399C2×C3—21no—
400C2×C3—21no—
401C2×C3—481no—
402C2×C3#473211yescharacteristic
403C2×C3#480611yescharacteristic
404C2×C3#482711yescharacteristic
405C2×C3#506211yescharacteristic
406C2×C3#515611yescharacteristic
407C2×C3#517011yescharacteristic
408D3—122no—
409D3—122no—
410D3—161no—
411D3—242no—
412C22—182no—
413C22—241no—
414C22—241no—
415C22—241no—
416C22—361no—
417C22—361no—
418C22#6392211yescharacteristic
419C4—21no—
420C4—62no—
421C4—121no—
422C4—122no—
423C4—361no—
424C4D3×D2411yescharacteristic
425C4#6379511yescharacteristic
426C4#6379611yescharacteristic
427C4#6381111yescharacteristic
428C3—21no—
429C3#6826611yescharacteristic, complemented
430C3#7120511yescharacteristic, complemented
431C2—362no—
432C2—481no—
433C2#1059040011yescharacteristic
434C2#1059082411yescharacteristic
435C2#1059094411yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×C8C22
socleC22×C32#120
prime radical#10590355C2
hypercenterC4×C8D32
hypocenterC32#1627
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. #10593903C2semidirect
2. C3×#4694C2semidirect
3. #10590364C2semidirect
5. #10589325C2semidirect
6. C3×#4456C2semidirect
7. #10589092C2semidirect
34. #4694D3semidirect
41. #4456D3semidirect
113. C4⋊(C3⋊D3)SD16semidirect
127. C3×Dic6D8semidirect
288. Dic6D24semidirect
370. C32#1627semidirect
429. C3#68266semidirect
430. C3#71205semidirect

Maximal subgroups

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

subgroupindex
#105939032
C3×#46942
#105903642
#105903552
#105893252
C3×#44562
#105890922
#712053
#682663