Finite Group Databasebeta

← #11779883

Subgroups — #11779883

Order 1152.

548 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 88 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#10593906C211yesmaximal, characteristic
2#10592550C211yesmaximal, characteristic, complemented
3#10590365C211yesmaximal, characteristic, complemented
4#10590273C211yesmaximal, characteristic, complemented
5C3×#4485C211yesmaximal, characteristic, complemented
6C3×#4483C211yesmaximal, characteristic, complemented
7#10589085C211yesmaximal, characteristic, complemented
8#68393—31nomaximal
9#68197—31nomaximal
10C2×#3795—21no—
11#64078C2211yescharacteristic
12C4×#634C2211yescharacteristic
13C3×#874C2211yescharacteristic
14C3×C4×D12C2211yescharacteristic
15#63914—21no—
16#63908—21no—
17#63898—21no—
18#63885—22no—
19C2×#3716—21no—
20C32×C4⋊C8C2211yescharacteristic
21#63644—21no—
22#63643—21no—
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25#63567—21no—
26#63563—22no—
27#5718—31no—
28#5553—31no—
29#5070—31no—
30#5019—31no—
31#4851—31no—
32#4851—31no—
33#4851—61no—
34#4841—31no—
35#4694—31no—
36C3×#331—31no—
37C3×D4⋊C8—31no—
38#4485D311yescharacteristic, complemented
39#4484—31no—
40#4483D311yescharacteristic, complemented
41#4456—31no—
42C2×#634—21no—
43C2×#634D411yescharacteristic
44C2×C3×D12—21no—
45C2×C3×D12—21no—
46C2×C3×D12D411yescharacteristic
47C2×C3×D12D412yes—
48C2×C3×C4×D3—21no—
49C2×#625—22no—
50C2×#625—22no—
51C2×D3×Dic3—22no—
52#3795—42no—
53#3795—42no—
54C2×C32×C8—21no—
55C32×C42C2311yescharacteristic
56C4⋊(C3⋊Dic3)—21no—
57C4⋊(C3⋊Dic3)—21no—
58C4⋊(C3⋊Dic3)D411yescharacteristic
59#3750—21no—
60C4×C3⋊Dic3—21no—
61C3×(C2×D3)⋊C4—21no—
62C3×C4⋊Dic3D411yescharacteristic
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65(C2×D3)⋊Dic3—22no—
66#3716—42no—
67#1642—91noSylow
68C2×#237—61no—
69C2×#235—61no—
70C3×#127—31no—
71C3×C4×D4—31no—
72#940—61no—
73#940—61no—
74#939—62no—
75#938—61no—
76D4×Dic3—61no—
77C2×#214—61no—
78#930—61no—
79C2×#204—61no—
80#893—61no—
81#884—62no—
82#874C2×D311yescharacteristic
83C4×D12C2×D311yescharacteristic
84#869—31no—
85#869—31no—
86#869—61no—
87C4×Dic6—31no—
88C4×Dic6—31no—
89C4×Dic6—61no—
90C3×C4⋊C8—21no—
91C3×C4⋊C8—31no—
92C3×C4⋊C8C2×D311yescharacteristic
93C3×C4⋊C8C2×D311yescharacteristic
94C3×C4×C8—31no—
95#832—62no—
96#821—62no—
97#817—61no—
98#817—61no—
99#817—62no—
100#816—61no—
101#816—61no—
102#816—62no—
103#816—61no—
104#810—61no—
105C4⋊(C3⋊C8)C2×D311yescharacteristic
106C4×C3⋊C8C2×D311yescharacteristic
107C22×C3×D3—22no—
108C22×C3×D3—21no—
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C3⋊Dic3—21no—
113C2×C3⋊Dic3—21no—
114C2×C3⋊Dic3—41no—
115#634—21no—
116#634—41no—
117#634—41no—
118#634SD1612yescomplemented
119C2×C3×Dic3—21no—
120C3×D12—21no—
121C3×D12—21no—
122C3×D12—42no—
123C3×D12—41no—
124C3×D12—41no—
125C3×D12—41no—
126C3×D12—41no—
127C3×C4×D3—41no—
128C3×C4×D3—41no—
129#625—44no—
130#625—82no—
131D3×Dic3—44no—
132C32×C8—41no—
133C3×C3⋊C8—41no—
134C3×C3⋊C8—41no—
135#550—91no—
136#486—91no—
137#475—91no—
138#461—91no—
139#331—31no—
140Q8⋊C8—91no—
141D4⋊C8—31no—
142C2×C3×D4—31no—
143C2×C3×D4—32no—
144C2×C3×D4—61no—
145C2×C3×D4—61no—
146C22×C3×C4—61no—
147C2×#67—62no—
148C2×#67—62no—
149C2×#67—62no—
150C2×#67—62no—
151C22×Dic3—62no—
152#237—122no—
153#237—122no—
154#235—122no—
155#235—122no—
156C2×D12—21no—
157C2×D12—21no—
158C2×D12D1211yescharacteristic
159C2×D12D1212yes—
160C2×C4×D3—21no—
161C2×C4×D3—62no—
162C2×Dic6—31no—
163C2×Dic6—31no—
164C2×Dic6—61no—
165C2×Dic6—61no—
166C2×Dic6—61no—
167C2×Dic6—121no—
168C2×C3×C8—22no—
169C2×C3×C8—21no—
170C2×C3×C8—21no—
171C2×C3×C8—61no—
172C2×C3×C8—61no—
173C3×C4⋊C4—31no—
174C3×C22⋊C4—61no—
175C3×C42—21no—
176C3×C42C22×D311yescharacteristic
177C3×C42C22×D311yescharacteristic
178#217—62no—
179#214—122no—
180(C2×D3)⋊C4—21no—
181(C2×D3)⋊C4—62no—
182C4⋊Dic3—31no—
183C4⋊Dic3—31no—
184C4⋊Dic3—61no—
185C4⋊Dic3—62no—
186C4⋊Dic3—61no—
187C4⋊Dic3—61no—
188C4⋊Dic3—61no—
189C4⋊Dic3—61no—
190C4⋊Dic3—121no—
191C4⋊Dic3D1211yescharacteristic
192Dic3⋊C4—61no—
193Dic3⋊C4—61no—
194Dic3⋊C4—121no—
195C4×Dic3—61no—
196C4×Dic3—61no—
197C4×Dic3—121no—
198C2×C3⋊C8—21no—
199C2×C3⋊C8—21no—
200#204—122no—
201C22×C32#12011yescharacteristic
202C2×C3×D3—41no—
203C2×C3×D3—42no—
204C2×C3×D3—42no—
205C2×C3×D3—41no—
206C2×C3×D3—41no—
207C2×C3×D3—42no—
208C32×C4—21no—
209C32×C4C2×SD1611yescharacteristic
210C32×C4#13511yescharacteristic
211C32×C4AGL(1,ℤ/8)11yescharacteristic
212C32×C4AGL(1,ℤ/8)11yescharacteristic
213C3⋊Dic3—22no—
214C3⋊Dic3—41no—
215C3⋊Dic3—81no—
216C3×Dic3—41no—
217C2×#41—181no—
218C2×SD16—181no—
219C4⋊Q8—91no—
220#127—31no—
221#127—181no—
222#121—182no—
223#121—181no—
224C4×Q8—91no—
225C4×D4—31no—
226C4×D4—181no—
227#106—181no—
228C4⋊C8—31no—
229C4⋊C8D3211yescharacteristic
230#103—181no—
231#103—181no—
232#102—182no—
233C4×C8—31no—
234C23×C3—62no—
235C23×C3—61no—
236C22×D3—21no—
237C22×D3—22no—
238C3×D4—61no—
239C3×D4—61no—
240C3×D4—122no—
241C3×D4—121no—
242C3×D4—121no—
243C3×D4—121no—
244C3×D4—121no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—61no—
249C2×C3×C4—121no—
250C2×C3×C4—121no—
251C2×C3×C4C2×D1211yescharacteristic
252C2×C3×C4C2×D1211yescharacteristic
253C2×C3×C4D3×D411yescharacteristic
254C2×C3×C4D3×D411yescharacteristic
255C2×C3×C4D3×D411yescharacteristic
256C2×C3×C4D3×D411yescharacteristic
257#67—124no—
258#67—124no—
259#67—242no—
260#67—242no—
261C2×Dic3—21no—
262C2×Dic3—61no—
263C2×Dic3—61no—
264C2×Dic3—61no—
265C2×Dic3—61no—
266C2×Dic3—121no—
267C2×Dic3—121no—
268C2×Dic3—124no—
269C2×Dic3—122no—
270C2×Dic3—121no—
271C2×Dic3—121no—
272D12—21no—
273D12—21no—
274D12—42no—
275D12—41no—
276D12—41no—
277D12—41no—
278D12—41no—
279C4×D3—41no—
280C4×D3—41no—
281C4×D3—124no—
282Dic6—32no—
283Dic6—32no—
284Dic6—62no—
285Dic6—61no—
286Dic6—61no—
287Dic6—121no—
288Dic6—121no—
289Dic6—121no—
290Dic6—121no—
291Dic6—121no—
292Dic6—241no—
293Dic6—241no—
294C3×C8—42no—
295C3×C8—41no—
296C3×C8—41no—
297C3×C8—121no—
298C3×C8—121no—
299C3⋊C8—41no—
300C3⋊C8—41no—
301C2×C32#44911yescharacteristic
302C2×C32#45011yescharacteristic
303C2×C32#45511yescharacteristic
304C3×D3—82no—
305C3×D3—81no—
306#41—362no—
307#41—362no—
308C2×Q8—91no—
309C2×Q8—181no—
310C2×D4—31no—
311C2×D4—32no—
312C2×D4—61no—
313C2×D4—61no—
314C2×D4—182no—
315C2×D4—182no—
316C22×C4—61no—
317C22×C4—182no—
318SD16—362no—
319C2×C8—21no—
320C2×C8—61no—
321C2×C8—61no—
322C4⋊C4—31no—
323C4⋊C4—91no—
324C4⋊C4—181no—
325C4⋊C4—181no—
326C4⋊C4—181no—
327C22⋊C4—61no—
328C22⋊C4—182no—
329C42—181no—
330C42C2×D3211yescharacteristic
331C22×C3—21no—
332C22×C3—122no—
333C22×C3—121no—
334C22×C3—122no—
335C22×C3—121no—
336C22×C3—121no—
337C22×C3—122no—
338C22×C3#88211yescharacteristic
339C22×C3#88211yescharacteristic
340C2×D3—41no—
341C2×D3—42no—
342C2×D3—41no—
343C2×D3—42no—
344C2×D3—42no—
345C2×D3—41no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—21no—
351C3×C4—21no—
352C3×C4—41no—
353C3×C4—121no—
354C3×C4#90411yescharacteristic
355C3×C4#90811yescharacteristic
356C3×C4#91111yescharacteristic
357C3×C4#91111yescharacteristic
358C3×C4#91111yescharacteristic
359C3×C4D3×SD1611yescharacteristic
360C3×C4D3×SD1611yescharacteristic
361C3×C4#91611yescharacteristic
362Dic3—41no—
363Dic3—62no—
364Dic3—62no—
365Dic3—122no—
366Dic3—121no—
367Dic3—121no—
368Dic3—241no—
369Dic3—242no—
370Dic3—241no—
371Dic3—241no—
372C32#164211yescharacteristic, complemented, Sylow
373C23—61no—
374C23—62no—
375Q8—92no—
376Q8—181no—
377Q8—361no—
378Q8—361no—
379D4—61no—
380D4—61no—
381D4—122no—
382D4—121no—
383D4—121no—
384D4—121no—
385D4—121no—
386D4—364no—
387D4—722no—
388C2×C4—61no—
389C2×C4—121no—
390C2×C4—121no—
391C2×C4—181no—
392C2×C4—181no—
393C2×C4—364no—
394C2×C4—361no—
395C2×C4D3×D1211yescharacteristic
396C2×C4D3×D1211yescharacteristic
397C2×C4#381111yescharacteristic
398C8—41no—
399C8—121no—
400C8—121no—
401C2×C3—21no—
402C2×C3—21no—
403C2×C3—21no—
404C2×C3—241no—
405C2×C3—242no—
406C2×C3#473411yescharacteristic
407C2×C3#474611yescharacteristic
408C2×C3#477611yescharacteristic
409C2×C3#477611yescharacteristic
410C2×C3#478111yescharacteristic
411C2×C3#482511yescharacteristic
412D3—82no—
413D3—81no—
414C22—122no—
415C22—121no—
416C22—121no—
417C22—122no—
418C22—121no—
419C22—122no—
420C22#6392311yescharacteristic
421C4—21no—
422C4—121no—
423C4—182no—
424C4—361no—
425C4—721no—
426C4#6379511yescharacteristic
427C4#6380611yescharacteristic
428C4#6392711yescharacteristic
429C4#6394011yescharacteristic
430C3—21no—
431C3#6819711yescharacteristic, complemented
432C3#6839311yescharacteristic, complemented
433C2—242no—
434C2—241no—
435C2#1059059711yescharacteristic
436C2#1059096811yescharacteristic
437C2#1059101611yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#120
prime radical#10593906C2
hypercenterC4⋊C8D32
hypocenterC32#1642
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. #10592550C2semidirect
3. #10590365C2semidirect
4. #10590273C2semidirect
5. C3×#4485C2semidirect
6. C3×#4483C2semidirect
7. #10589085C2semidirect
38. #4485D3semidirect
40. #4483D3semidirect
118. #634SD16semidirect
372. C32#1642semidirect
431. C3#68197semidirect
432. C3#68393semidirect

Maximal subgroups

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

subgroupindex
#105939062
#105925502
#105903652
#105902732
C3×#44852
C3×#44832
#105890852
#683933
#681973