Finite Group Databasebeta

← #11779865

Subgroups — #11779865

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#10592793C211yesmaximal, characteristic, complemented
3C3×#5088C211yesmaximal, characteristic, complemented
4C3×#5083C211yesmaximal, characteristic, complemented
5#10589090C211yesmaximal, characteristic, complemented
6#10589085C211yesmaximal, characteristic, complemented
7#10589081C211yesmaximal, characteristic, complemented
8#71199—31nomaximal
9#71045—31nomaximal
10C2×#3795—21no—
11C32×C4⋊Q8C2211yescharacteristic
12C4×#634C2211yescharacteristic
13C2×C3×#215—21no—
14C3×#874C2211yescharacteristic
15C3×C4×D12C2211yescharacteristic
16#63914—21no—
17#63908—21no—
18#63898—21no—
19#63885—22no—
20#63637—21no—
21#63635—21no—
22C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
23C3×#835—21no—
24C3×#809—22no—
25C3×C4⋊(C3⋊C8)C2211yescharacteristic
26C3×C4×C3⋊C8C2211yescharacteristic
27#5718—31no—
28#5553—31no—
29C3×#486—31no—
30C3×#461—31no—
31#5094—31no—
32#5094—31no—
33#5094—61no—
34#5088D311yescharacteristic, complemented
35#5083D311yescharacteristic, complemented
36#4544—31no—
37D4⋊(C3⋊C8)—31no—
38#4485—31no—
39#4484—31no—
40#4459—31no—
41#4456—31no—
42C2×C32×Q8—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—
54C32×C4⋊C4—21no—
55C32×C4⋊C4—21no—
56C32×C42C2311yescharacteristic
57C4⋊(C3⋊Dic3)D411yescharacteristic
58#3750—21no—
59C4×C3⋊Dic3—21no—
60C2×C3⋊(C3⋊C8)—21no—
61C3×#215—42no—
62C3×(C2×D3)⋊C4—21no—
63C3×C4⋊Dic3D411yescharacteristic
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66(C2×D3)⋊Dic3—22no—
67#1642—91noSylow
68C2×#237—61no—
69C2×#235—61no—
70C2×C3×SD16—61no—
71C3×C4⋊Q8—21no—
72C3×C4⋊Q8C2×D311yescharacteristic
73C3×C4⋊Q8C2×D311yescharacteristic
74C3×#127—31no—
75C3×C4×D4—31no—
76C2×#215—21no—
77#940—61no—
78#940—61no—
79#939—62no—
80#938—61no—
81D4×Dic3—61no—
82#930—61no—
83#893—61no—
84#884—62no—
85#874C2×D311yescharacteristic
86C4×D12C2×D311yescharacteristic
87C4×Dic6—31no—
88C4×Dic6—31no—
89C4×Dic6—61no—
90C3×C4⋊C8—31no—
91C3×#103—61no—
92C3×#102—62no—
93C3×C4×C8—31no—
94#835—21no—
95#810—61no—
96#810—61no—
97#810—62no—
98#809—22no—
99#808—61no—
100#808—61no—
101#808—62no—
102C4⋊(C3⋊C8)—31no—
103C4⋊(C3⋊C8)—31no—
104C4⋊(C3⋊C8)—61no—
105C4⋊(C3⋊C8)C2×D311yescharacteristic
106C4×C3⋊C8C2×D311yescharacteristic
107C22×C3×D3—22no—
108C22×C3×D3—21no—
109C32×Q8—41no—
110C32×Q8—41no—
111C2×C32×C4—41no—
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C3⋊Dic3—21no—
116C2×C3⋊Dic3—21no—
117#634—21no—
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—
132C3⋊(C3⋊C8)—41no—
133C3×C3⋊C8—41no—
134C3×C3⋊C8—41no—
135#550—91no—
136#486—31no—
137#475—91no—
138#461—31no—
139#331—91no—
140Q8⋊C8—91no—
141D4⋊C8—91no—
142C2×C3×Q8—21no—
143C2×C3×Q8—21no—
144C2×C3×Q8—41no—
145C2×C3×D4—31no—
146C2×C3×D4—32no—
147C2×C3×D4—61no—
148C2×C3×D4—61no—
149C22×C3×C4—61no—
150C2×#67—62no—
151C2×#67—62no—
152C2×#67—62no—
153C2×#67—62no—
154C22×Dic3—62no—
155#237—122no—
156#237—122no—
157#235—122no—
158#235—122no—
159C2×D12—21no—
160C2×D12—21no—
161C2×D12#6711yescharacteristic
162C2×D12#6712yes—
163C2×C4×D3—21no—
164C2×C4×D3—62no—
165C2×Dic6—31no—
166C2×Dic6—31no—
167C2×Dic6—61no—
168C3×SD16—122no—
169C2×C3×C8—61no—
170C2×C3×C8—61no—
171C3×C4⋊C4—22no—
172C3×C4⋊C4—21no—
173C3×C4⋊C4—21no—
174C3×C4⋊C4—21no—
175C3×C4⋊C4—21no—
176C3×C4⋊C4—31no—
177C3×C4⋊C4—41no—
178C3×C22⋊C4—61no—
179C3×C42—21no—
180C3×C42C22×D311yescharacteristic
181C3×C42C22×D311yescharacteristic
182#217—62no—
183#215—42no—
184(C2×D3)⋊C4—21no—
185(C2×D3)⋊C4—62no—
186C4⋊Dic3—31no—
187C4⋊Dic3—31no—
188C4⋊Dic3—61no—
189C4⋊Dic3#6711yescharacteristic
190Dic3⋊C4—61no—
191Dic3⋊C4—61no—
192Dic3⋊C4—121no—
193C4×Dic3—61no—
194C4×Dic3—61no—
195C4×Dic3—121no—
196C2×C3⋊C8—21no—
197C2×C3⋊C8—21no—
198C2×C3⋊C8—62no—
199C2×C3⋊C8—61no—
200C2×C3⋊C8—61no—
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×C4—81no—
210C32×C4C2×SD1611yescharacteristic
211C32×C4#13511yescharacteristic
212C32×C4AGL(1,ℤ/8)11yescharacteristic
213C32×C4AGL(1,ℤ/8)11yescharacteristic
214C3⋊Dic3—22no—
215C3⋊Dic3—41no—
216C3×Dic3—41no—
217C2×#41—181no—
218C2×SD16—61no—
219C4⋊Q8D3211yescharacteristic
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⋊C8—91no—
230#103—61no—
231#103—181no—
232#102—62no—
233C4×C8—31no—
234C23×C3—62no—
235C23×C3—61no—
236C22×D3—21no—
237C22×D3—22no—
238C3×Q8—41no—
239C3×Q8—41no—
240C3×Q8—41no—
241C3×Q8—41no—
242C3×Q8—81no—
243C3×Q8—81no—
244C3×D4—61no—
245C3×D4—61no—
246C3×D4—122no—
247C3×D4—121no—
248C3×D4—121no—
249C3×D4—121no—
250C3×D4—121no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—42no—
255C2×C3×C4—41no—
256C2×C3×C4—41no—
257C2×C3×C4—61no—
258C2×C3×C4—121no—
259C2×C3×C4—121no—
260C2×C3×C4D3×D411yescharacteristic
261C2×C3×C4D3×D411yescharacteristic
262C2×C3×C4D3×D411yescharacteristic
263C2×C3×C4D3×D411yescharacteristic
264C2×C3×C4C2×#6711yescharacteristic
265C2×C3×C4C2×#6711yescharacteristic
266#67—124no—
267#67—124no—
268#67—242no—
269#67—242no—
270C2×Dic3—21no—
271C2×Dic3—61no—
272C2×Dic3—61no—
273C2×Dic3—61no—
274C2×Dic3—61no—
275C2×Dic3—121no—
276C2×Dic3—121no—
277C2×Dic3—124no—
278D12—21no—
279D12—21no—
280D12—42no—
281D12—41no—
282D12—41no—
283D12—41no—
284D12—41no—
285C4×D3—41no—
286C4×D3—41no—
287C4×D3—124no—
288Dic6—32no—
289Dic6—32no—
290Dic6—62no—
291Dic6—61no—
292Dic6—61no—
293Dic6—121no—
294C3×C8—121no—
295C3×C8—121no—
296C3⋊C8—41no—
297C3⋊C8—41no—
298C3⋊C8—122no—
299C3⋊C8—121no—
300C3⋊C8—121no—
301C2×C32#44911yescharacteristic
302C2×C32#45011yescharacteristic
303C2×C32#45511yescharacteristic
304C3×D3—82no—
305C3×D3—81no—
306#41—362no—
307#41—362no—
308C2×Q8—21no—
309C2×Q8—91no—
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—122no—
319C2×C8—61no—
320C2×C8—61no—
321C2×C8—181no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—31no—
325C4⋊C4—91no—
326C4⋊C4—181no—
327C22⋊C4—61no—
328C22⋊C4—182no—
329C42—181no—
330C42C2×D3211yescharacteristic
331C22×C3—21no—
332C22×C3—121no—
333C22×C3—122no—
334C22×C3—121no—
335C22×C3—122no—
336C22×C3—122no—
337C22×C3—121no—
338C22×C3#93711yescharacteristic
339C22×C3#93711yescharacteristic
340C2×D3—42no—
341C2×D3—41no—
342C2×D3—42no—
343C2×D3—41no—
344C2×D3—41no—
345C2×D3—42no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—21no—
351C3×C4—21no—
352C3×C4—41no—
353C3×C4—82no—
354C3×C4—81no—
355C3×C4—81no—
356C3×C4—121no—
357C3×C4#91111yescharacteristic
358C3×C4#91211yescharacteristic
359C3×C4D3×SD1611yescharacteristic
360C3×C4D3×SD1611yescharacteristic
361C3×C4#91411yescharacteristic
362C3×C4#91411yescharacteristic
363C3×C4#93211yescharacteristic
364C3×C4#95011yescharacteristic
365Dic3—41no—
366Dic3—62no—
367Dic3—62no—
368Dic3—122no—
369Dic3—121no—
370Dic3—121no—
371Dic3—241no—
372C32#164211yescharacteristic, complemented, Sylow
373C23—61no—
374C23—62no—
375Q8—41no—
376Q8—41no—
377Q8—92no—
378Q8—181no—
379D4—61no—
380D4—61no—
381D4—122no—
382D4—121no—
383D4—121no—
384D4—121no—
385D4—121no—
386D4—364no—
387D4—722no—
388C2×C4—41no—
389C2×C4—61no—
390C2×C4—121no—
391C2×C4—121no—
392C2×C4—181no—
393C2×C4—181no—
394C2×C4—364no—
395C2×C4D3×#6711yescharacteristic
396C2×C4D3×#6711yescharacteristic
397C2×C4#381111yescharacteristic
398C8—121no—
399C8—121no—
400C8—361no—
401C2×C3—21no—
402C2×C3—21no—
403C2×C3—21no—
404C2×C3—241no—
405C2×C3—242no—
406C2×C3#503711yescharacteristic
407C2×C3#506111yescharacteristic
408C2×C3#515811yescharacteristic
409C2×C3#516911yescharacteristic
410C2×C3#516911yescharacteristic
411C2×C3#520211yescharacteristic
412D3—82no—
413D3—81no—
414C22—121no—
415C22—122no—
416C22—121no—
417C22—122no—
418C22—122no—
419C22—121no—
420C22#6398311yescharacteristic
421C4—21no—
422C4—81no—
423C4—121no—
424C4—182no—
425C4—361no—
426C4#6393211yescharacteristic
427C4#6393311yescharacteristic
428C4#6394011yescharacteristic
429C4#6394111yescharacteristic
430C3—21no—
431C3#7104511yescharacteristic, complemented
432C3#7119911yescharacteristic, complemented
433C2—241no—
434C2—242no—
435C2#1059151911yescharacteristic
436C2#1059165211yescharacteristic
437C2#1059165911yescharacteristic
subgroupG/H
centerC22#63983
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socleC22×C32#120
prime radical#10593906C2
hypercenterC4⋊Q8D32
hypocenterC32#1642
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #10592793C2semidirect
3. C3×#5088C2semidirect
4. C3×#5083C2semidirect
5. #10589090C2semidirect
6. #10589085C2semidirect
7. #10589081C2semidirect
34. #5088D3semidirect
35. #5083D3semidirect
118. #634SD16semidirect
372. C32#1642semidirect
431. C3#71045semidirect
432. C3#71199semidirect

Maximal subgroups

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

subgroupindex
#105939062
#105927932
C3×#50882
C3×#50832
#105890902
#105890852
#105890812
#711993
#710453