Finite Group Databasebeta

← #11778937

Subgroups — #11778937

Order 1152.

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

normal subgroups only

This group has 544 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#10593951C211yesmaximal, characteristic, complemented
2#10592547C211yesmaximal, characteristic, complemented
3#10590367C211yesmaximal, characteristic, complemented
4#10590350C211yesmaximal, characteristic
5C3×#4485C211yesmaximal, characteristic, complemented
6C3×#4484C211yesmaximal, characteristic, complemented
7#10589085C211yesmaximal, characteristic, complemented
8#68402—31nomaximal
9#68258—31nomaximal
10C2×#3744—21no—
11#64083C2211yescharacteristic
12C4×#634C2211yescharacteristic
13C3×#874C2211yescharacteristic
14C3×C4×Dic6C2211yescharacteristic
15#63898—21no—
16Dic3×D12—21no—
17#63884—22no—
18#63863—21no—
19#63860—21no—
20C2×#3717—21no—
21C2×#3714—22no—
22C32×C4⋊C8C2211yescharacteristic
23#63648—21no—
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25C3×C4×C3⋊C8C2211yescharacteristic
26#63564—21no—
27#5713—31no—
28#5585—31no—
29#5073—31no—
30#5027—31no—
31#4848—31no—
32#4848—31no—
33#4848—31no—
34#4848—61no—
35#4695—31no—
36C3×#331—31no—
37C3×Q8⋊C8—31no—
38#4485D311yescharacteristic, complemented
39#4484—31no—
40#4484D311yescharacteristic, complemented
41#4456—31no—
42C2×C4⋊(C3⋊D3)—21no—
43C2×C4⋊(C3⋊D3)—21no—
44C2×C4⋊(C3⋊D3)—21no—
45C2×#634D411yescharacteristic
46C2×C3×D12—21no—
47C2×C3×D12—21no—
48C2×C3×D12D412yes—
49C2×C3×Dic6D411yescharacteristic
50C2×D3×Dic3—22no—
51C2×C32×C8—21no—
52C32×C42C2311yescharacteristic
53C4⋊(C3⋊Dic3)D411yescharacteristic
54#3750—21no—
55C4×C3⋊Dic3—21no—
56#3744—42no—
57C3×C4⋊Dic3D411yescharacteristic
58C3×Dic3⋊C4—21no—
59C3×C4×Dic3—21no—
60C2×C3×C3⋊C8—21no—
61C2×C3×C3⋊C8—21no—
62(C2×D3)⋊Dic3—22no—
63(C2×D3)⋊Dic3—22no—
64(C2×D3)⋊Dic3—22no—
65#3717—42no—
66#3714—44no—
67#1620—91noSylow
68C3×#127—31no—
69C3×C4×Q8—31no—
70#947—61no—
71C2×#215—61no—
72#936—61no—
73#936—61no—
74#935—62no—
75D4×Dic3—61no—
76D4×Dic3—61no—
77C2×#213—62no—
78C2×D24—62no—
79C2×#204—61no—
80C2×#204—61no—
81C2×#204—62no—
82C2×#204—61no—
83#894—62no—
84#893—61no—
85#875—61no—
86#874—31no—
87#874—31no—
88#874—61no—
89#874C2×D311yescharacteristic
90C4×D12—61no—
91C4×Dic6—31no—
92C4×Dic6—31no—
93C4×Dic6—61no—
94C4×Dic6C2×D311yescharacteristic
95C3×C4⋊C8—21no—
96C3×C4⋊C8—31no—
97C3×C4⋊C8C2×D311yescharacteristic
98C3×C4⋊C8C2×D311yescharacteristic
99C3×C4×C8—31no—
100#821—61no—
101#821—61no—
102#821—62no—
103#821—61no—
104#809—61no—
105C4⋊(C3⋊C8)C2×D311yescharacteristic
106C4×C3⋊C8C2×D311yescharacteristic
107C22×C3⋊D3—41no—
108C22×C3×D3—22no—
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C3⋊Dic3—21no—
113C2×C3⋊Dic3—21no—
114C4⋊(C3⋊D3)—41no—
115C4⋊(C3⋊D3)—41no—
116C4⋊(C3⋊D3)—42no—
117C4⋊(C3⋊D3)—41no—
118C4⋊(C3⋊D3)—41no—
119#634—21no—
120#634—21no—
121C2×C3×Dic3—21no—
122C2×C3×Dic3—21no—
123C3×D12—42no—
124C3×D12—41no—
125C3×D12—41no—
126C3×D12—41no—
127C3×D12—41no—
128C3×Dic6—21no—
129C3×Dic6—21no—
130D3×Dic3—82no—
131C32×C8—41no—
132C3×C3⋊C8—22no—
133C3×C3⋊C8—41no—
134#559—91no—
135#493—91no—
136#460—91no—
137#460—91no—
138#331—31no—
139Q8⋊C8—31no—
140Q8⋊C8—91no—
141C2×C3×Q8—31no—
142C2×C3×D4—32no—
143C2×C3×D4—61no—
144C2×C3×D4—61no—
145C22×Dic3—62no—
146C2×D12—21no—
147C2×D12—21no—
148C2×D12—62no—
149C2×D12—61no—
150C2×D12—61no—
151C2×D12—61no—
152C2×D12—61no—
153C2×D12—61no—
154C2×D12—61no—
155C2×D12—121no—
156C2×D12—121no—
157C2×D12D1212yes—
158C2×C4×D3—62no—
159C2×Dic6—31no—
160C2×Dic6—31no—
161C2×Dic6—61no—
162C2×Dic6D1211yescharacteristic
163C2×C3×C8—22no—
164C2×C3×C8—21no—
165C2×C3×C8—21no—
166C2×C3×C8—61no—
167C2×C3×C8—61no—
168C3×C4⋊C4—31no—
169C3×C4⋊C4—61no—
170C3×C42—21no—
171C3×C42—61no—
172C3×C42C22×D311yescharacteristic
173C3×C42C22×D311yescharacteristic
174#217—62no—
175#217—62no—
176#217—62no—
177#215—122no—
178#213—124no—
179(C2×D3)⋊C4—62no—
180(C2×D3)⋊C4—62no—
181(C2×D3)⋊C4—62no—
182C4⋊Dic3—31no—
183C4⋊Dic3—31no—
184C4⋊Dic3—61no—
185C4⋊Dic3D1211yescharacteristic
186Dic3⋊C4—21no—
187Dic3⋊C4—61no—
188Dic3⋊C4—61no—
189Dic3⋊C4—121no—
190C4×Dic3—21no—
191C4×Dic3—61no—
192C4×Dic3—61no—
193C4×Dic3—121no—
194C2×C3⋊C8—21no—
195C2×C3⋊C8—21no—
196D24—124no—
197#204—124no—
198#204—122no—
199#204—122no—
200#204—122no—
201C22×C32#12011yescharacteristic
202C2×C3⋊D3—81no—
203C2×C3⋊D3—81no—
204C2×C3⋊D3—81no—
205C2×C3×D3—42no—
206C2×C3×D3—42no—
207C2×C3×D3—42no—
208C32×C4—21no—
209C32×C4#13511yescharacteristic
210C32×C4#13511yescharacteristic
211C32×C4AGL(1,ℤ/8)11yescharacteristic
212C32×C4AGL(1,ℤ/8)11yescharacteristic
213C3⋊Dic3—41no—
214C3⋊Dic3—41no—
215C3×Dic3—41no—
216C3×Dic3—41no—
217C2×SD16—181no—
218C2×SD16—181no—
219C2×D8—182no—
220#127—31no—
221#127—91no—
222#124—181no—
223#124—181no—
224#123—182no—
225C4×Q8—31no—
226C4×Q8—91no—
227C4×D4—181no—
228C4×D4—181no—
229C4⋊C8—31no—
230C4⋊C8D3211yescharacteristic
231#102—181no—
232#102—181no—
233C4×C8—31no—
234C23×C3—62no—
235C22×D3—22no—
236C22×D3—122no—
237C22×D3—121no—
238C22×D3—121no—
239C3×Q8—61no—
240C3×Q8—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—61no—
250C2×C3×C4—61no—
251C2×C3×C4C2×D1211yescharacteristic
252C2×C3×C4C2×D1211yescharacteristic
253C2×C3×C4D3×D411yescharacteristic
254C2×C3×C4D3×D411yescharacteristic
255C2×C3×C4D3×D411yescharacteristic
256C2×C3×C4D3×D411yescharacteristic
257C2×Dic3—21no—
258C2×Dic3—21no—
259C2×Dic3—61no—
260C2×Dic3—61no—
261C2×Dic3—61no—
262C2×Dic3—61no—
263C2×Dic3—121no—
264C2×Dic3—121no—
265C2×Dic3—242no—
266D12—42no—
267D12—41no—
268D12—41no—
269D12—41no—
270D12—41no—
271D12—122no—
272D12—122no—
273D12—122no—
274D12—122no—
275D12—121no—
276D12—121no—
277D12—121no—
278D12—121no—
279D12—121no—
280D12—121no—
281D12—121no—
282D12—121no—
283D12—241no—
284D12—241no—
285D12—242no—
286C4×D3—242no—
287Dic6—21no—
288Dic6—21no—
289Dic6—62no—
290Dic6—61no—
291Dic6—61no—
292Dic6—61no—
293Dic6—61no—
294Dic6—121no—
295C3×C8—42no—
296C3×C8—41no—
297C3×C8—41no—
298C3×C8—62no—
299C3×C8—121no—
300C3⋊C8—22no—
301C3⋊C8—41no—
302C2×C32#44911yescharacteristic
303C2×C32#44911yescharacteristic
304C2×C32#45311yescharacteristic
305C3⋊D3—161no—
306C3×D3—82no—
307C2×Q8—31no—
308C2×Q8—91no—
309C2×D4—32no—
310C2×D4—61no—
311C2×D4—61no—
312C2×D4—181no—
313C2×D4—181no—
314C2×D4—181no—
315C22×C4—182no—
316SD16—362no—
317SD16—362no—
318D8—364no—
319C2×C8—21no—
320C2×C8—61no—
321C2×C8—61no—
322C4⋊C4—31no—
323C4⋊C4—61no—
324C4⋊C4—91no—
325C4⋊C4—181no—
326C22⋊C4—182no—
327C22⋊C4—182no—
328C22⋊C4—182no—
329C42—61no—
330C42—181no—
331C42C2×D3211yescharacteristic
332C22×C3—21no—
333C22×C3—122no—
334C22×C3—122no—
335C22×C3—122no—
336C22×C3#88211yescharacteristic
337C22×C3#88211yescharacteristic
338C2×D3—42no—
339C2×D3—42no—
340C2×D3—42no—
341C2×D3—242no—
342C2×D3—242no—
343C2×D3—242no—
344C2×D3—241no—
345C2×D3—241no—
346C2×D3—241no—
347C2×D3—241no—
348C2×D3—241no—
349C2×D3—241no—
350C3×C4—21no—
351C3×C4—21no—
352C3×C4—21no—
353C3×C4—21no—
354C3×C4—21no—
355C3×C4—21no—
356C3×C4—41no—
357C3×C4—121no—
358C3×C4—121no—
359C3×C4#90411yescharacteristic
360C3×C4#90811yescharacteristic
361C3×C4#91111yescharacteristic
362C3×C4#91111yescharacteristic
363C3×C4#91411yescharacteristic
364C3×C4#91611yescharacteristic
365C3×C4#91611yescharacteristic
366C3×C4#91911yescharacteristic
367Dic3—41no—
368Dic3—41no—
369Dic3—122no—
370Dic3—121no—
371Dic3—121no—
372Dic3—121no—
373Dic3—121no—
374Dic3—241no—
375C32#162011yescharacteristic, complemented, Sylow
376C23—62no—
377C23—361no—
378Q8—61no—
379Q8—61no—
380Q8—181no—
381Q8—181no—
382D4—122no—
383D4—121no—
384D4—121no—
385D4—121no—
386D4—121no—
387D4—362no—
388D4—361no—
389D4—361no—
390D4—361no—
391D4—361no—
392C2×C4—61no—
393C2×C4—61no—
394C2×C4—181no—
395C2×C4—181no—
396C2×C4—722no—
397C2×C4D3×D1211yescharacteristic
398C2×C4D3×D1211yescharacteristic
399C2×C4#381111yescharacteristic
400C8—41no—
401C8—62no—
402C8—121no—
403C2×C3—21no—
404C2×C3—21no—
405C2×C3—21no—
406C2×C3—242no—
407C2×C3#473411yescharacteristic
408C2×C3#474711yescharacteristic
409C2×C3#478111yescharacteristic
410C2×C3#478111yescharacteristic
411C2×C3#481011yescharacteristic
412C2×C3#482211yescharacteristic
413D3—82no—
414D3—482no—
415D3—481no—
416D3—481no—
417C22—122no—
418C22—122no—
419C22—122no—
420C22—721no—
421C22—721no—
422C22—721no—
423C22#6392311yescharacteristic
424C4—21no—
425C4—121no—
426C4—121no—
427C4—361no—
428C4—361no—
429C4#6379511yescharacteristic
430C4#6380611yescharacteristic
431C4#6393711yescharacteristic
432C4#6395011yescharacteristic
433C3—21no—
434C3#6825811yescharacteristic, complemented
435C3#6840211yescharacteristic, complemented
436C2—242no—
437C2—1441no—
438C2#1059061711yescharacteristic
439C2#1059096811yescharacteristic
440C2#1059101511yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#120
prime radical#10590350C2
hypercenterC4⋊C8D32
hypocenterC32#1620
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. #10593951C2semidirect
2. #10592547C2semidirect
3. #10590367C2semidirect
5. C3×#4485C2semidirect
6. C3×#4484C2semidirect
7. #10589085C2semidirect
38. #4485D3semidirect
40. #4484D3semidirect
375. C32#1620semidirect
434. C3#68258semidirect
435. C3#68402semidirect

Maximal subgroups

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

subgroupindex
#105939512
#105925472
#105903672
#105903502
C3×#44852
C3×#44842
#105890852
#684023
#682583