Finite Group Databasebeta

← #11778522

Subgroups — #11778522

Order 1152.

471 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 471 conjugacy classes of subgroups — too many to draw. Only its 84 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×#5515C211yesmaximal, characteristic
2C3×#4981C211yesmaximal, characteristic, complemented
3#10591101C211yesmaximal, characteristic, complemented
4#10591089C211yesmaximal, characteristic
5#10589394C211yesmaximal, characteristic, complemented
6#10589153C211yesmaximal, characteristic, complemented
7#10589149C211yesmaximal, characteristic
8#71886—31nomaximal
9#69711—31nomaximal
10C2×C32×C4⋊C4C2211yescharacteristic
11C3×#930C2211yescharacteristic
12C3×#929—21no—
13C3×C4×#67—21no—
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C3×#924C2211yescharacteristic
16C2×C3×Dic3⋊C4—21no—
17C3×#898—21no—
18C3×#896—21no—
19C3×#894—21no—
20C3×#889—21no—
21#63657C2211yescharacteristic
22#63657C2211yescharacteristic
23C3×C3⋊#95—21no—
24C3×C3⋊#95C2211yescharacteristic
25#63576—21no—
26#63574—21no—
27#63565—21no—
28#63562—21no—
29C3×#539—31no—
30#5515D311yescharacteristic
31C3×#398—31no—
32#5043—31no—
33#5033—31no—
34#4981D311yescharacteristic, complemented
35#4971—31no—
36#4967—31no—
37#4538—31no—
38#4537—31no—
39#4528—31no—
40#4528—31no—
41#4528—61no—
42#4452—31no—
43#4451—31no—
44C22×C32×C4D411yescharacteristic
45C22×C32×C4D411yescharacteristic
46C22×C32×C4C2311yescharacteristic
47C2×C3×#67—21no—
48C22×C3×Dic3—21no—
49C22×C3×Dic3—21no—
50C2×C3×D12D411yescharacteristic
51C2×C3×C4×D3—21no—
52C2×C3×Dic6D411yescharacteristic
53C32×C4⋊C4—21no—
54C32×C4⋊C4—21no—
55C2×C3⋊(C3⋊C8)—21no—
56C2×C3⋊(C3⋊C8)—21no—
57C3×#217—21no—
58C3×(C2×D3)⋊C4—21no—
59C3×(C2×D3)⋊C4—21no—
60C3×(C2×D3)⋊C4—21no—
61C3×(C2×D3)⋊C4—21no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3—21no—
64C3×C4⋊Dic3D411yescharacteristic
65C3×C4⋊Dic3D411yescharacteristic
66C3×Dic3⋊C4—21no—
67C3×Dic3⋊C4—21no—
68C3×Dic3⋊C4—21no—
69C3×Dic3⋊C4—21no—
70C3×Dic3⋊C4—42no—
71C3×C4×Dic3—21no—
72#1609—91noSylow
73C3×#126—61no—
74C3×#125—61no—
75C3×#123—61no—
76C3×#123—61no—
77C3×C22⋊Q8—31no—
78C3×C22⋊Q8—61no—
79C3×#121—31no—
80C3×C4×D4—61no—
81C2×C3×C4⋊C4—21no—
82C2×C3×C4⋊C4—31no—
83C2×C3×C4⋊C4—61no—
84C2×C3×C4⋊C4C2×D311yescharacteristic
85C2×C3×C4⋊C4C2×D311yescharacteristic
86#930C2×D311yescharacteristic
87#929—21no—
88C4×#67—21no—
89C2×C4⋊Dic3C2×D311yescharacteristic
90#924C2×D311yescharacteristic
91C2×Dic3⋊C4—21no—
92#898—21no—
93#896—21no—
94#894—21no—
95#889—21no—
96C3×#95—31no—
97C3×#95—61no—
98#835—61no—
99#832—61no—
100C3⋊#95—21no—
101C3⋊#95C2×D311yescharacteristic
102#830—31no—
103#830—31no—
104#830—31no—
105#830—31no—
106#830—61no—
107#830—61no—
108#810—61no—
109#809—61no—
110#808—61no—
111#808—61no—
112#807—61no—
113#807—61no—
114C23×C32C2×D411yescharacteristic
115C22×C3×D3—21no—
116C2×C32×C4—21no—
117C2×C32×C4—21no—
118C2×C32×C4—21no—
119C2×C32×C4—21no—
120C2×C32×C4—41no—
121C2×C32×C4—41no—
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C3×#67—41no—
125C3×#67—41no—
126C2×C3×Dic3—22no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—21no—
130C2×C3×Dic3—41no—
131C2×C3×Dic3—41no—
132C2×C3×Dic3—41no—
133C2×C3×Dic3—41no—
134C2×C3×Dic3—41no—
135C3×D12—41no—
136C3×C4×D3—81no—
137C3×Dic6—41no—
138C3⋊(C3⋊C8)—41no—
139C3⋊(C3⋊C8)—41no—
140#539—31no—
141#483—91no—
142#480—91no—
143#398—31no—
144#328—91no—
145#327—91no—
146#324—91no—
147C2×C3×Q8—31no—
148C2×C3×D4—31no—
149C2×C3×D4—61no—
150C22×C3×C4—21no—
151C22×C3×C4—21no—
152C22×C3×C4—21no—
153C22×C3×C4—61no—
154C22×C3×C4—61no—
155C22×C3×C4—61no—
156C22×C3×C4#6711yescharacteristic
157C22×C3×C4#6711yescharacteristic
158C22×C3×C4#6711yescharacteristic
159C22×C3×C4#6711yescharacteristic
160C22×C3×C4C22×D311yescharacteristic
161C22×C3×C4C22×D311yescharacteristic
162C2×#67—21no—
163C22×Dic3—21no—
164C22×Dic3—21no—
165C2×D12#6711yescharacteristic
166C2×C4×D3—21no—
167C2×Dic6#6711yescharacteristic
168C3×C4⋊C4—21no—
169C3×C4⋊C4—21no—
170C3×C4⋊C4—21no—
171C3×C4⋊C4—21no—
172C3×C4⋊C4—31no—
173C3×C4⋊C4—31no—
174C3×C4⋊C4—41no—
175C3×C4⋊C4—41no—
176C3×C4⋊C4—61no—
177C3×C4⋊C4—61no—
178C3×C4⋊C4—61no—
179C3×C4⋊C4—61no—
180C3×C4⋊C4—61no—
181C3×C4⋊C4—61no—
182C3×C4⋊C4—122no—
183C3×C22⋊C4—61no—
184C3×C22⋊C4—61no—
185C3×C22⋊C4—61no—
186C3×C22⋊C4—61no—
187C3×C22⋊C4—61no—
188C3×C42—61no—
189#217—21no—
190(C2×D3)⋊C4—21no—
191(C2×D3)⋊C4—21no—
192(C2×D3)⋊C4—21no—
193(C2×D3)⋊C4—21no—
194C4⋊Dic3—21no—
195C4⋊Dic3—21no—
196C4⋊Dic3#6711yescharacteristic
197C4⋊Dic3#6711yescharacteristic
198Dic3⋊C4—21no—
199Dic3⋊C4—21no—
200Dic3⋊C4—21no—
201Dic3⋊C4—21no—
202Dic3⋊C4—42no—
203C4×Dic3—21no—
204C2×C3⋊C8—61no—
205C2×C3⋊C8—61no—
206C2×C3⋊C8—61no—
207C2×C3⋊C8—61no—
208C2×C3⋊C8—121no—
209C2×C3⋊C8—121no—
210C22×C32—21no—
211C22×C32—21no—
212C22×C32#12011yescharacteristic
213C22×C32#13511yescharacteristic
214C22×C32AGL(1,ℤ/8)11yescharacteristic
215C2×C3×D3—41no—
216C2×C3×D3—41no—
217C2×C3×D3—41no—
218C32×C4—21no—
219C32×C4—21no—
220C32×C4—41no—
221C32×C4—41no—
222C3×Dic3—42no—
223C3×Dic3—41no—
224C3×Dic3—41no—
225C3×Dic3—41no—
226C3×Dic3—81no—
227#126—61no—
228#125—61no—
229#123—61no—
230#123—61no—
231C22⋊Q8—31no—
232C22⋊Q8—61no—
233#121—31no—
234C4×D4—61no—
235C2×C4⋊C4—31no—
236C2×C4⋊C4—61no—
237C2×C4⋊C4D3211yescharacteristic
238#107—181no—
239#106—181no—
240#103—181no—
241#102—181no—
242C22⋊C8—91no—
243C22⋊C8—91no—
244#95—31no—
245#95—61no—
246C23×C3—21no—
247C23×C3—61no—
248C23×C3C2×#6711yescharacteristic
249C23×C3C2×#6711yescharacteristic
250C22×D3—21no—
251C3×Q8—121no—
252C3×D4—121no—
253C3×D4—121no—
254C3×D4—121no—
255C2×C3×C4—22no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—21no—
266C2×C3×C4—41no—
267C2×C3×C4—41no—
268C2×C3×C4—41no—
269C2×C3×C4—41no—
270C2×C3×C4—41no—
271C2×C3×C4—41no—
272C2×C3×C4—41no—
273C2×C3×C4—62no—
274C2×C3×C4—61no—
275C2×C3×C4—61no—
276C2×C3×C4—61no—
277C2×C3×C4—81no—
278C2×C3×C4—81no—
279C2×C3×C4—121no—
280C2×C3×C4—121no—
281C2×C3×C4—121no—
282C2×C3×C4—121no—
283C2×C3×C4—121no—
284C2×C3×C4—241no—
285C2×C3×C4D3×D411yescharacteristic
286C2×C3×C4D3×D411yescharacteristic
287C2×C3×C4C2×#6711yescharacteristic
288C2×C3×C4C2×#6711yescharacteristic
289#67—41no—
290#67—41no—
291C2×Dic3—22no—
292C2×Dic3—21no—
293C2×Dic3—21no—
294C2×Dic3—21no—
295C2×Dic3—41no—
296C2×Dic3—41no—
297C2×Dic3—41no—
298C2×Dic3—41no—
299C2×Dic3—41no—
300D12—41no—
301C4×D3—81no—
302Dic6—41no—
303C3⋊C8—121no—
304C3⋊C8—121no—
305C3⋊C8—121no—
306C3⋊C8—121no—
307C3⋊C8—241no—
308C3⋊C8—241no—
309C2×C32—21no—
310C2×C32—21no—
311C2×C32#44911yescharacteristic
312C2×C32#45611yescharacteristic
313C2×C32#45811yescharacteristic
314C3×D3—81no—
315C2×Q8—31no—
316C2×D4—31no—
317C2×D4—61no—
318C22×C4—61no—
319C22×C4—61no—
320C22×C4—61no—
321C22×C4#62511yescharacteristic
322C22×C4#62511yescharacteristic
323C22×C4C2×D3211yescharacteristic
324C2×C8—181no—
325C2×C8—181no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—31no—
329C4⋊C4—31no—
330C4⋊C4—61no—
331C4⋊C4—61no—
332C4⋊C4—61no—
333C4⋊C4—61no—
334C4⋊C4—61no—
335C4⋊C4—61no—
336C4⋊C4—122no—
337C22⋊C4—61no—
338C22⋊C4—61no—
339C22⋊C4—61no—
340C22⋊C4—61no—
341C22⋊C4—61no—
342C42—61no—
343C22×C3—21no—
344C22×C3—21no—
345C22×C3—21no—
346C22×C3—21no—
347C22×C3—21no—
348C22×C3—21no—
349C22×C3—21no—
350C22×C3—41no—
351C22×C3—41no—
352C22×C3—121no—
353C22×C3—121no—
354C22×C3—121no—
355C22×C3#93211yescharacteristic
356C22×C3#93711yescharacteristic
357C22×C3#94911yescharacteristic
358C22×C3#95011yescharacteristic
359C22×C3#95011yescharacteristic
360C22×C3#95311yescharacteristic
361C2×D3—41no—
362C2×D3—41no—
363C2×D3—41no—
364C3×C4—21no—
365C3×C4—21no—
366C3×C4—21no—
367C3×C4—21no—
368C3×C4—41no—
369C3×C4—41no—
370C3×C4—42no—
371C3×C4—41no—
372C3×C4—41no—
373C3×C4—41no—
374C3×C4—41no—
375C3×C4—81no—
376C3×C4—122no—
377C3×C4—121no—
378C3×C4—121no—
379C3×C4—121no—
380C3×C4—241no—
381Dic3—42no—
382Dic3—41no—
383Dic3—41no—
384Dic3—41no—
385Dic3—81no—
386C32#160911yescharacteristic, complemented, Sylow
387C23—61no—
388C23C2×#62511yescharacteristic
389Q8—121no—
390D4—121no—
391D4—121no—
392D4—121no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—62no—
400C2×C4—61no—
401C2×C4—61no—
402C2×C4—61no—
403C2×C4—121no—
404C2×C4—121no—
405C2×C4—121no—
406C2×C4—121no—
407C2×C4—121no—
408C2×C4—241no—
409C2×C4D3×#6711yescharacteristic
410C2×C4D3×#6711yescharacteristic
411C8—361no—
412C8—361no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—21no—
416C2×C3—21no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3—21no—
420C2×C3—41no—
421C2×C3—41no—
422C2×C3—241no—
423C2×C3#503711yescharacteristic
424C2×C3#505311yescharacteristic
425C2×C3#509511yescharacteristic
426C2×C3#523811yescharacteristic
427C2×C3#524311yescharacteristic
428C2×C3#524611yescharacteristic
429D3—81no—
430C22—21no—
431C22—21no—
432C22—121no—
433C22—121no—
434C22—121no—
435C22#6382211yescharacteristic
436C22#6382311yescharacteristic
437C22#6397611yescharacteristic
438C4—21no—
439C4—21no—
440C4—41no—
441C4—41no—
442C4—122no—
443C4—121no—
444C4—121no—
445C4—121no—
446C4—241no—
447C3—21no—
448C3#6971111yescharacteristic, complemented
449C3#7188611yescharacteristic, complemented
450C2—21no—
451C2—21no—
452C2—241no—
453C2#1059116111yescharacteristic
454C2#1059153311yescharacteristic
455C2#1059164811yescharacteristic
subgroupG/H
centerC22#63976
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#120
prime radicalC3×#930C22
hypercenterC2×C4⋊C4D32
hypocenterC32#1609
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C3×#4981C2semidirect
3. #10591101C2semidirect
5. #10589394C2semidirect
6. #10589153C2semidirect
34. #4981D3semidirect
386. C32#1609semidirect
448. C3#69711semidirect
449. C3#71886semidirect

Maximal subgroups

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

subgroupindex
C3×#55152
C3×#49812
#105911012
#105910892
#105893942
#105891532
#105891492
#718863
#697113