Finite Group Databasebeta

← #11779868

Subgroups — #11779868

Order 1152.

542 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 96 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
1C3×#5718C211yesmaximal, characteristic
2C3×#5070C211yesmaximal, characteristic, complemented
3#10590363C211yesmaximal, characteristic, complemented
4#10590285C211yesmaximal, characteristic, complemented
5#10589410C211yesmaximal, characteristic, complemented
6#10589084C211yesmaximal, characteristic, complemented
7#10589081C211yesmaximal, characteristic, complemented
8#71921—31nomaximal
9#71199—31nomaximal
10C2×C3×#237—21no—
11C32×#127C2211yescharacteristic
12C3×#940—21no—
13C3×#939—22no—
14C3×#938—21no—
15C3×D4×Dic3—21no—
16C3×C4×D12C2211yescharacteristic
17C3×#869C2211yescharacteristic
18C3×C4×Dic6C2211yescharacteristic
19C2×#3715—21no—
20C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
21C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
22C3×#832—22no—
23C3×C4×C3⋊C8C2211yescharacteristic
24#63574—21no—
25#63565—21no—
26#63565—21no—
27C3×#550—31no—
28#5718D311yescharacteristic
29C3×#486—31no—
30#5094—31no—
31#5083—31no—
32#5070D311yescharacteristic, complemented
33#5020—31no—
34#5019—31no—
35#4544—31no—
36#4544—31no—
37#4544—61no—
38#4535—31no—
39D4⋊(C3⋊C8)—31no—
40#4459—31no—
41#4456—31no—
42C2×C32×D4—21no—
43C2×C32×D4—21no—
44C2×C32×D4D412yes—
45C2×C3×#67—22no—
46C2×C3×#67—22no—
47C22×C3×Dic3—22no—
48C3×#237—42no—
49C3×#237—42no—
50C2×C3×D12D411yescharacteristic
51C2×C3×C4×D3—21no—
52C2×C3×Dic6—21no—
53C2×C3×Dic6D411yescharacteristic
54C32×C42C2311yescharacteristic
55C2×C3⋊(C3⋊C8)—21no—
56C2×C3⋊(C3⋊C8)—21no—
57C3×#217—22no—
58C3×(C2×D3)⋊C4—21no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3D411yescharacteristic
62C3×C4⋊Dic3D411yescharacteristic
63C3×Dic3⋊C4—21no—
64C3×C4×Dic3—21no—
65C2×C3×C3⋊C8—21no—
66#3715—42no—
67#1642—91noSylow
68C2×C3×#41—61no—
69C2×#237—21no—
70C3×C4⋊Q8—31no—
71C3×#127—21no—
72C3×#127—61no—
73C3×#127C2×D311yescharacteristic
74C3×#127C2×D311yescharacteristic
75C3×#121—61no—
76C3×#121—62no—
77C3×C4×Q8—31no—
78C3×C4×D4—31no—
79C3×C4×D4—61no—
80C2×#215—61no—
81#940—21no—
82#939—22no—
83#938—21no—
84D4×Dic3—21no—
85C2×#214—61no—
86C4×D12C2×D311yescharacteristic
87#869C2×D311yescharacteristic
88C4×Dic6C2×D311yescharacteristic
89C3×#102—62no—
90C3×C4×C8—31no—
91#835—61no—
92#835—61no—
93#832—22no—
94#810—61no—
95#810—61no—
96#808—61no—
97#808—61no—
98C4⋊(C3⋊C8)—31no—
99C4⋊(C3⋊C8)—31no—
100C4⋊(C3⋊C8)—31no—
101C4⋊(C3⋊C8)—31no—
102C4⋊(C3⋊C8)—61no—
103C4⋊(C3⋊C8)—61no—
104C4×C3⋊C8C2×D311yescharacteristic
105C23×C32—22no—
106C22×C3×D3—21no—
107C32×D4—42no—
108C32×D4—41no—
109C32×D4—41no—
110C32×D4—41no—
111C32×D4—41no—
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C3×#67—44no—
116C3×#67—82no—
117C2×C3×Dic3—21no—
118C2×C3×Dic3—21no—
119C2×C3×Dic3—21no—
120C2×C3×Dic3—44no—
121C2×C3×Dic3—41no—
122C3×D12—21no—
123C3×D12—21no—
124C3×C4×D3—41no—
125C3×C4×D3—41no—
126C3×Dic6—21no—
127C3×Dic6—41no—
128C3×Dic6—41no—
129C3×Dic6SD1612yescomplemented
130C3⋊(C3⋊C8)—41no—
131C3⋊(C3⋊C8)—41no—
132C3×C3⋊C8—41no—
133#550—31no—
134#486—31no—
135#475—91no—
136#461—91no—
137#331—91no—
138Q8⋊C8—91no—
139D4⋊C8—91no—
140C3×#41—122no—
141C3×#41—122no—
142C2×C3×Q8—31no—
143C2×C3×Q8—61no—
144C2×C3×D4—21no—
145C2×C3×D4—21no—
146C2×C3×D4—21no—
147C2×C3×D4—21no—
148C2×C3×D4—22no—
149C2×C3×D4—31no—
150C2×C3×D4—41no—
151C2×C3×D4—41no—
152C2×C3×D4—62no—
153C2×C3×D4—62no—
154C2×C3×D4#6712yes—
155C2×C3×D4#6712yes—
156C22×C3×C4—62no—
157C22×C3×C4—61no—
158C2×#67—22no—
159C2×#67—22no—
160C22×Dic3—22no—
161#237—42no—
162#237—42no—
163C2×D12#6711yescharacteristic
164C2×C4×D3—21no—
165C2×Dic6—21no—
166C2×Dic6#6711yescharacteristic
167C2×C3×C8—61no—
168C3×C4⋊C4—31no—
169C3×C4⋊C4—31no—
170C3×C4⋊C4—61no—
171C3×C4⋊C4—61no—
172C3×C4⋊C4—61no—
173C3×C22⋊C4—62no—
174C3×C22⋊C4—61no—
175C3×C42—21no—
176C3×C42—61no—
177C3×C42C22×D311yescharacteristic
178C3×C42C22×D311yescharacteristic
179#217—22no—
180#215—122no—
181#214—122no—
182(C2×D3)⋊C4—21no—
183C4⋊Dic3—21no—
184C4⋊Dic3—21no—
185C4⋊Dic3#6711yescharacteristic
186C4⋊Dic3#6711yescharacteristic
187Dic3⋊C4—21no—
188C4×Dic3—21no—
189C2×C3⋊C8—21no—
190C2×C3⋊C8—61no—
191C2×C3⋊C8—61no—
192C2×C3⋊C8—61no—
193C2×C3⋊C8—61no—
194C2×C3⋊C8—121no—
195C2×C3⋊C8—121no—
196C22×C32—42no—
197C22×C32—42no—
198C22×C32—42no—
199C22×C32#12011yescharacteristic
200C2×C3×D3—41no—
201C2×C3×D3—41no—
202C2×C3×D3—41no—
203C32×C4—21no—
204C32×C4C2×SD1611yescharacteristic
205C32×C4#13511yescharacteristic
206C32×C4AGL(1,ℤ/8)11yescharacteristic
207C32×C4AGL(1,ℤ/8)11yescharacteristic
208C3×Dic3—22no—
209C3×Dic3—41no—
210C3×Dic3—41no—
211C3×Dic3—81no—
212C2×#41—61no—
213C2×SD16—181no—
214C4⋊Q8—31no—
215#127—61no—
216#127D3211yescharacteristic
217#121—61no—
218#121—62no—
219C4×Q8—31no—
220C4×D4—31no—
221C4×D4—61no—
222#106—181no—
223C4⋊C8—91no—
224C4⋊C8—91no—
225#103—181no—
226#103—181no—
227#102—62no—
228C4×C8—31no—
229C23×C3—22no—
230C23×C3—22no—
231C23×C3—42no—
232C23×C3—61no—
233C22×D3—21no—
234C3×Q8—32no—
235C3×Q8—61no—
236C3×Q8—121no—
237C3×Q8—121no—
238C3×D4—42no—
239C3×D4—42no—
240C3×D4—41no—
241C3×D4—41no—
242C3×D4—41no—
243C3×D4—41no—
244C3×D4—41no—
245C3×D4—41no—
246C3×D4—41no—
247C3×D4—41no—
248C3×D4—61no—
249C3×D4—61no—
250C3×D4—81no—
251C3×D4—81no—
252C3×D4—81no—
253C3×D4—81no—
254C3×D4—82no—
255C3×D4—124no—
256C3×D4—242no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—61no—
261C2×C3×C4—61no—
262C2×C3×C4—61no—
263C2×C3×C4—124no—
264C2×C3×C4—121no—
265C2×C3×C4—121no—
266C2×C3×C4—121no—
267C2×C3×C4D3×D411yescharacteristic
268C2×C3×C4D3×D411yescharacteristic
269C2×C3×C4C2×#6711yescharacteristic
270C2×C3×C4C2×#6711yescharacteristic
271C2×C3×C4C2×#6711yescharacteristic
272C2×C3×C4C2×#6711yescharacteristic
273#67—44no—
274#67—82no—
275C2×Dic3—21no—
276C2×Dic3—21no—
277C2×Dic3—21no—
278C2×Dic3—44no—
279C2×Dic3—41no—
280D12—21no—
281D12—21no—
282C4×D3—41no—
283C4×D3—41no—
284Dic6—21no—
285Dic6—41no—
286Dic6—41no—
287Dic6#21412yescomplemented
288C3×C8—121no—
289C3⋊C8—41no—
290C3⋊C8—121no—
291C3⋊C8—121no—
292C3⋊C8—121no—
293C3⋊C8—121no—
294C3⋊C8—241no—
295C3⋊C8—241no—
296C2×C32—82no—
297C2×C32#44911yescharacteristic
298C2×C32#45011yescharacteristic
299C2×C32#45511yescharacteristic
300C3×D3—81no—
301#41—122no—
302#41—122no—
303C2×Q8—31no—
304C2×Q8—61no—
305C2×D4—21no—
306C2×D4—21no—
307C2×D4—31no—
308C2×D4—62no—
309C2×D4—62no—
310C2×D4#62512yes—
311C22×C4—62no—
312C22×C4—61no—
313SD16—362no—
314C2×C8—61no—
315C2×C8—181no—
316C2×C8—181no—
317C4⋊C4—31no—
318C4⋊C4—31no—
319C4⋊C4—61no—
320C4⋊C4—61no—
321C4⋊C4—61no—
322C22⋊C4—62no—
323C22⋊C4—61no—
324C42—61no—
325C42C2×D3211yescharacteristic
326C22×C3—21no—
327C22×C3—42no—
328C22×C3—42no—
329C22×C3—42no—
330C22×C3—42no—
331C22×C3—42no—
332C22×C3—42no—
333C22×C3—82no—
334C22×C3—82no—
335C22×C3—82no—
336C22×C3—121no—
337C22×C3—121no—
338C22×C3—121no—
339C22×C3#93711yescharacteristic
340C22×C3#95311yescharacteristic
341C2×D3—41no—
342C2×D3—41no—
343C2×D3—41no—
344C3×C4—21no—
345C3×C4—21no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—41no—
351C3×C4—62no—
352C3×C4—121no—
353C3×C4—121no—
354C3×C4—241no—
355C3×C4#91111yescharacteristic
356C3×C4#91211yescharacteristic
357C3×C4D3×SD1611yescharacteristic
358C3×C4#91411yescharacteristic
359C3×C4#93211yescharacteristic
360C3×C4C2×#21411yescharacteristic
361C3×C4#94911yescharacteristic
362C3×C4#95011yescharacteristic
363Dic3—22no—
364Dic3—41no—
365Dic3—41no—
366Dic3—81no—
367C32#164211yescharacteristic, complemented, Sylow
368C23—22no—
369C23—61no—
370Q8—32no—
371Q8—61no—
372Q8—121no—
373Q8—121no—
374D4—42no—
375D4—41no—
376D4—41no—
377D4—41no—
378D4—41no—
379D4—61no—
380D4—61no—
381D4—124no—
382D4—242no—
383C2×C4—61no—
384C2×C4—61no—
385C2×C4—61no—
386C2×C4—124no—
387C2×C4—121no—
388C2×C4—121no—
389C2×C4—121no—
390C2×C4C2×#62511yescharacteristic
391C2×C4D3×#6711yescharacteristic
392C2×C4D3×#6711yescharacteristic
393C8—121no—
394C8—361no—
395C8—361no—
396C2×C3—21no—
397C2×C3—21no—
398C2×C3—21no—
399C2×C3—82no—
400C2×C3—82no—
401C2×C3—162no—
402C2×C3—241no—
403C2×C3#506111yescharacteristic
404C2×C3#515811yescharacteristic
405C2×C3#516911yescharacteristic
406C2×C3#521811yescharacteristic
407C2×C3#523811yescharacteristic
408C2×C3#524211yescharacteristic
409D3—81no—
410C22—42no—
411C22—42no—
412C22—42no—
413C22—121no—
414C22—121no—
415C22—121no—
416C22#6397611yescharacteristic
417C4—21no—
418C4—62no—
419C4—121no—
420C4—121no—
421C4—241no—
422C4#6392511yescharacteristic
423C4D3×#21411yescharacteristic
424C4#6393311yescharacteristic
425C4#6393411yescharacteristic
426C3—21no—
427C3#7119911yescharacteristic, complemented
428C3#7192111yescharacteristic, complemented
429C2—82no—
430C2—241no—
431C2#1059145011yescharacteristic
432C2#1059145811yescharacteristic
433C2#1059151211yescharacteristic
subgroupG/H
centerC22#63976
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×#127C22
socleC22×C32#120
prime radicalC3×#5718C2
hypercenter#127D32
hypocenterC32#1642
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
2. C3×#5070C2semidirect
3. #10590363C2semidirect
4. #10590285C2semidirect
5. #10589410C2semidirect
6. #10589084C2semidirect
7. #10589081C2semidirect
32. #5070D3semidirect
129. C3×Dic6SD16semidirect
287. Dic6#214semidirect
367. C32#1642semidirect
427. C3#71199semidirect
428. C3#71921semidirect

Maximal subgroups

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

subgroupindex
C3×#57182
C3×#50702
#105903632
#105902852
#105894102
#105890842
#105890812
#719213
#711993