Finite Group Databasebeta

← #11779379

Subgroups — #11779379

Order 1152.

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

normal subgroups only

This group has 554 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×#5076C211yesmaximal, characteristic, complemented
3#10590310C211yesmaximal, characteristic, complemented
4#10590266C211yesmaximal, characteristic, complemented
5#10589410C211yesmaximal, characteristic, complemented
6#10589084C211yesmaximal, characteristic, complemented
7#10589081C211yesmaximal, characteristic, complemented
8#71919—31nomaximal
9#71271—31nomaximal
10C2×C3×#237—21no—
11C32×#127C2211yescharacteristic
12C3×#940—21no—
13C3×#939—22no—
14C3×#938—21no—
15C3×D4×Dic3—21no—
16C2×C3×#214—22no—
17C3×C4×D12C2211yescharacteristic
18C3×#869C2211yescharacteristic
19C3×C4×Dic6C2211yescharacteristic
20C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
21C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
22C3×C4×C3⋊C8C2211yescharacteristic
23#63576—21no—
24#63574—21no—
25#63565—21no—
26#63562—21no—
27C3×#550—31no—
28#5718D311yescharacteristic
29C3×#492—31no—
30#5091—31no—
31#5084—31no—
32#5076D311yescharacteristic, complemented
33#5021—31no—
34#5008—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×#214—44no—
59C3×(C2×D3)⋊C4—21no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3—21no—
62C3×C4⋊Dic3D411yescharacteristic
63C3×C4⋊Dic3D411yescharacteristic
64C3×Dic3⋊C4—21no—
65C3×C4×Dic3—21no—
66C2×C3×C3⋊C8—21no—
67#1631—91noSylow
68C2×C3×#41—61no—
69C2×#237—21no—
70C2×C3×SD16—62no—
71C3×C4⋊Q8—31no—
72C3×#127—21no—
73C3×#127—61no—
74C3×#127C2×D311yescharacteristic
75C3×#127C2×D311yescharacteristic
76C3×#121—61no—
77C3×#121—62no—
78C3×C4×Q8—31no—
79C3×C4×D4—31no—
80C3×C4×D4—61no—
81#940—21no—
82#939—22no—
83#938—21no—
84D4×Dic3—21no—
85C2×#214—22no—
86C4×D12C2×D311yescharacteristic
87#869C2×D311yescharacteristic
88C4×Dic6C2×D311yescharacteristic
89C3×C4×C8—31no—
90#835—61no—
91#832—61no—
92#810—61no—
93#809—61no—
94#808—61no—
95#808—61no—
96#807—61no—
97#807—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—42no—
128C3×Dic6SD1612yescomplemented
129C3⋊(C3⋊C8)—41no—
130C3⋊(C3⋊C8)—41no—
131C3×C3⋊C8—22no—
132#550—31no—
133#492—31no—
134#477—91no—
135#476—91no—
136#331—91no—
137Q8⋊C8—91no—
138D4⋊C8—91no—
139C3×#41—122no—
140C3×#41—122no—
141C2×C3×Q8—31no—
142C2×C3×Q8—61no—
143C2×C3×D4—21no—
144C2×C3×D4—21no—
145C2×C3×D4—21no—
146C2×C3×D4—21no—
147C2×C3×D4—22no—
148C2×C3×D4—31no—
149C2×C3×D4—41no—
150C2×C3×D4—41no—
151C2×C3×D4—62no—
152C2×C3×D4—62no—
153C2×C3×D4#6712yes—
154C2×C3×D4#6712yes—
155C22×C3×C4—62no—
156C22×C3×C4—61no—
157C2×#67—22no—
158C2×#67—22no—
159C22×Dic3—22no—
160#237—42no—
161#237—42no—
162C2×D12#6711yescharacteristic
163C2×C4×D3—21no—
164C2×Dic6—21no—
165C2×Dic6#6711yescharacteristic
166C3×SD16—124no—
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#214—44no—
181(C2×D3)⋊C4—21no—
182C4⋊Dic3—21no—
183C4⋊Dic3—21no—
184C4⋊Dic3#6711yescharacteristic
185C4⋊Dic3#6711yescharacteristic
186Dic3⋊C4—21no—
187C4×Dic3—21no—
188C2×C3⋊C8—21no—
189C2×C3⋊C8—61no—
190C2×C3⋊C8—61no—
191C2×C3⋊C8—61no—
192C2×C3⋊C8—61no—
193C2×C3⋊C8—121no—
194C2×C3⋊C8—121no—
195C22×C32—42no—
196C22×C32—42no—
197C22×C32—42no—
198C22×C32#12011yescharacteristic
199C2×C3×D3—41no—
200C2×C3×D3—41no—
201C2×C3×D3—41no—
202C32×C4—21no—
203C32×C4C2×SD1611yescharacteristic
204C32×C4#13511yescharacteristic
205C32×C4AGL(1,ℤ/8)11yescharacteristic
206C32×C4#13711yescharacteristic
207C3×Dic3—22no—
208C3×Dic3—41no—
209C3×Dic3—41no—
210C3×Dic3—81no—
211C2×#41—61no—
212C2×SD16—62no—
213C4⋊Q8—31no—
214#127—61no—
215#127D3211yescharacteristic
216#121—61no—
217#121—62no—
218C4×Q8—31no—
219C4×D4—31no—
220C4×D4—61no—
221#107—181no—
222#106—181no—
223C4⋊C8—91no—
224C4⋊C8—91no—
225#103—181no—
226#102—181no—
227C4×C8—31no—
228C23×C3—22no—
229C23×C3—22no—
230C23×C3—42no—
231C23×C3—61no—
232C22×D3—21no—
233C3×Q8—32no—
234C3×Q8—61no—
235C3×Q8—122no—
236C3×D4—42no—
237C3×D4—42no—
238C3×D4—41no—
239C3×D4—41no—
240C3×D4—41no—
241C3×D4—41no—
242C3×D4—41no—
243C3×D4—41no—
244C3×D4—41no—
245C3×D4—41no—
246C3×D4—61no—
247C3×D4—61no—
248C3×D4—81no—
249C3×D4—81no—
250C3×D4—81no—
251C3×D4—81no—
252C3×D4—82no—
253C3×D4—124no—
254C3×D4—242no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—61no—
259C2×C3×C4—61no—
260C2×C3×C4—61no—
261C2×C3×C4—124no—
262C2×C3×C4—121no—
263C2×C3×C4—121no—
264C2×C3×C4—121no—
265C2×C3×C4D3×D411yescharacteristic
266C2×C3×C4D3×D411yescharacteristic
267C2×C3×C4C2×#6711yescharacteristic
268C2×C3×C4C2×#6711yescharacteristic
269C2×C3×C4C2×#6711yescharacteristic
270C2×C3×C4C2×#6711yescharacteristic
271#67—44no—
272#67—82no—
273C2×Dic3—21no—
274C2×Dic3—21no—
275C2×Dic3—21no—
276C2×Dic3—44no—
277C2×Dic3—41no—
278D12—21no—
279D12—21no—
280C4×D3—41no—
281C4×D3—41no—
282Dic6—21no—
283Dic6—42no—
284Dic6#21412yescomplemented
285C3×C8—62no—
286C3⋊C8—22no—
287C3⋊C8—121no—
288C3⋊C8—121no—
289C3⋊C8—121no—
290C3⋊C8—121no—
291C3⋊C8—241no—
292C3⋊C8—241no—
293C2×C32—82no—
294C2×C32#45011yescharacteristic
295C2×C32#45211yescharacteristic
296C2×C32#45311yescharacteristic
297C3×D3—81no—
298#41—122no—
299#41—122no—
300C2×Q8—31no—
301C2×Q8—61no—
302C2×D4—21no—
303C2×D4—21no—
304C2×D4—31no—
305C2×D4—62no—
306C2×D4—62no—
307C2×D4#62512yes—
308C22×C4—62no—
309C22×C4—61no—
310SD16—124no—
311C2×C8—61no—
312C2×C8—181no—
313C2×C8—181no—
314C4⋊C4—31no—
315C4⋊C4—31no—
316C4⋊C4—61no—
317C4⋊C4—61no—
318C4⋊C4—61no—
319C22⋊C4—62no—
320C22⋊C4—61no—
321C42—61no—
322C42C2×D3211yescharacteristic
323C22×C3—21no—
324C22×C3—42no—
325C22×C3—42no—
326C22×C3—42no—
327C22×C3—42no—
328C22×C3—42no—
329C22×C3—42no—
330C22×C3—82no—
331C22×C3—82no—
332C22×C3—82no—
333C22×C3—121no—
334C22×C3—121no—
335C22×C3—121no—
336C22×C3#93711yescharacteristic
337C22×C3#95311yescharacteristic
338C2×D3—41no—
339C2×D3—41no—
340C2×D3—41no—
341C3×C4—21no—
342C3×C4—21no—
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—21no—
346C3×C4—21no—
347C3×C4—41no—
348C3×C4—62no—
349C3×C4—121no—
350C3×C4—121no—
351C3×C4—241no—
352C3×C4D3×SD1611yescharacteristic
353C3×C4#91411yescharacteristic
354C3×C4#91511yescharacteristic
355C3×C4#91611yescharacteristic
356C3×C4#93211yescharacteristic
357C3×C4C2×#21411yescharacteristic
358C3×C4#95011yescharacteristic
359C3×C4#95111yescharacteristic
360Dic3—22no—
361Dic3—41no—
362Dic3—41no—
363Dic3—81no—
364C32#163111yescharacteristic, complemented, Sylow
365C23—22no—
366C23—61no—
367Q8—32no—
368Q8—61no—
369Q8—122no—
370D4—42no—
371D4—41no—
372D4—41no—
373D4—41no—
374D4—41no—
375D4—61no—
376D4—61no—
377D4—124no—
378D4—242no—
379C2×C4—61no—
380C2×C4—61no—
381C2×C4—61no—
382C2×C4—124no—
383C2×C4—121no—
384C2×C4—121no—
385C2×C4—121no—
386C2×C4C2×#62511yescharacteristic
387C2×C4D3×#6711yescharacteristic
388C2×C4D3×#6711yescharacteristic
389C8—62no—
390C8—361no—
391C8—361no—
392C2×C3—21no—
393C2×C3—21no—
394C2×C3—21no—
395C2×C3—82no—
396C2×C3—82no—
397C2×C3—162no—
398C2×C3—241no—
399C2×C3#507711yescharacteristic
400C2×C3#516911yescharacteristic
401C2×C3#517311yescharacteristic
402C2×C3#521811yescharacteristic
403C2×C3#523911yescharacteristic
404C2×C3#524111yescharacteristic
405D3—81no—
406C22—42no—
407C22—42no—
408C22—42no—
409C22—121no—
410C22—121no—
411C22—121no—
412C22#6397611yescharacteristic
413C4—21no—
414C4—62no—
415C4—121no—
416C4—121no—
417C4—241no—
418C4D3×#21411yescharacteristic
419C4#6392911yescharacteristic
420C4#6393411yescharacteristic
421C4#6393511yescharacteristic
422C3—21no—
423C3#7127111yescharacteristic, complemented
424C3#7191911yescharacteristic, complemented
425C2—82no—
426C2—241no—
427C2#1059145811yescharacteristic
428C2#1059146111yescharacteristic
429C2#1059150911yescharacteristic
subgroupG/H
centerC22#63976
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×#127C22
socleC22×C32#120
prime radicalC3×#5718C2
hypercenter#127D32
hypocenterC32#1631
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×#5076C2semidirect
3. #10590310C2semidirect
4. #10590266C2semidirect
5. #10589410C2semidirect
6. #10589084C2semidirect
7. #10589081C2semidirect
32. #5076D3semidirect
128. C3×Dic6SD16semidirect
284. Dic6#214semidirect
364. C32#1631semidirect
423. C3#71271semidirect
424. C3#71919semidirect

Maximal subgroups

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

subgroupindex
C3×#57182
C3×#50762
#105903102
#105902662
#105894102
#105890842
#105890812
#719193
#712713