Finite Group Databasebeta

← #11778746

Subgroups — #11778746

Order 1152.

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

normal subgroups only

This group has 483 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
2#10592685C211yesmaximal, characteristic, complemented
3#10591103C211yesmaximal, characteristic, complemented
4#10591092C211yesmaximal, characteristic
5C3×#4528C211yesmaximal, characteristic, complemented
6#10589152C211yesmaximal, characteristic, complemented
7#10589150C211yesmaximal, characteristic
8#71887—31nomaximal
9#68136—31nomaximal
10C2×C32×C4⋊C4C2211yescharacteristic
11C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
12C3×#930C2211yescharacteristic
13C3×#929—21no—
14C3×C4×#67—21no—
15C3×#924C2211yescharacteristic
16C3×#898—21no—
17C3×#896—21no—
18C3×#894—21no—
19C3×#889—21no—
20#63658—21no—
21#63658—21no—
22#63658C2211yescharacteristic
23C3×#830C2211yescharacteristic
24C3×#830C2211yescharacteristic
25#63575—21no—
26#63573—21no—
27#63566—21no—
28#63563—21no—
29C3×#539—31no—
30#5515D311yescharacteristic
31#5044—31no—
32#5034—31no—
33#4986—31no—
34#4986—31no—
35#4986—61no—
36#4735—31no—
37#4722—31no—
38C3×#324—31no—
39#4538—31no—
40#4537—31no—
41#4528D311yescharacteristic, complemented
42#4470—31no—
43#4467—31no—
44C22×C32×C4D411yescharacteristic
45C22×C32×C4D411yescharacteristic
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3—21no—
48C22×C3⋊Dic3—21no—
49C2×C3×#67—21no—
50C2×C3×D12D411yescharacteristic
51C2×C3×C4×D3—21no—
52C2×C3×Dic6D411yescharacteristic
53C32×C4⋊C4—21no—
54C32×C4⋊C4—21no—
55C4⋊(C3⋊Dic3)—21no—
56C4⋊(C3⋊Dic3)—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⋊Dic3D411yescharacteristic
63C3×C4⋊Dic3D411yescharacteristic
64C3×Dic3⋊C4—21no—
65C3×Dic3⋊C4—21no—
66C3×Dic3⋊C4—21no—
67C3×Dic3⋊C4—21no—
68C3×C4×Dic3—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71#1615—91noSylow
72C3×#126—61no—
73C3×#125—61no—
74C3×#123—61no—
75C3×#123—61no—
76C3×C22⋊Q8—31no—
77C3×C22⋊Q8—61no—
78C3×#121—31no—
79C3×C4×D4—61no—
80C2×C3×C4⋊C4—21no—
81C2×C3×C4⋊C4C2×D311yescharacteristic
82C2×C3×C4⋊C4C2×D311yescharacteristic
83#930C2×D311yescharacteristic
84#929—21no—
85C4×#67—21no—
86C2×C4⋊Dic3—31no—
87C2×C4⋊Dic3—31no—
88C2×C4⋊Dic3—61no—
89#924C2×D311yescharacteristic
90#898—21no—
91#896—21no—
92#894—21no—
93#889—21no—
94C3×C22⋊C8—31no—
95C3×C22⋊C8—31no—
96#835—61no—
97#832—61no—
98C3⋊#95—31no—
99C3⋊#95—31no—
100C3⋊#95—61no—
101C3⋊#95—62no—
102C3⋊#95—62no—
103C3⋊#95—61no—
104C3⋊#95—61no—
105C3⋊#95—61no—
106C3⋊#95—61no—
107#830C2×D311yescharacteristic
108#830C2×D311yescharacteristic
109#821—61no—
110#818—61no—
111#817—61no—
112#816—61no—
113#808—61no—
114#807—61no—
115C23×C32C2×D411yescharacteristic
116C22×C3×D3—21no—
117C2×C32×C4—21no—
118C2×C32×C4—21no—
119C2×C32×C4—21no—
120C2×C32×C4—21no—
121C2×C32×C4—41no—
122C2×C32×C4—41no—
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C3⋊Dic3—41no—
126C2×C3⋊Dic3—41no—
127C2×C3⋊Dic3—42no—
128C2×C3⋊Dic3—41no—
129C2×C3⋊Dic3—41no—
130C3×#67—41no—
131C3×#67—41no—
132C2×C3×Dic3—21no—
133C2×C3×Dic3—21no—
134C2×C3×Dic3—21no—
135C3×D12—41no—
136C3×C4×D3—81no—
137C3×Dic6—41no—
138C3×C3⋊C8—41no—
139C3×C3⋊C8—41no—
140#539—31no—
141#484—91no—
142#481—91no—
143#400—91no—
144#328—91no—
145#327—91no—
146#324—31no—
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×C4D1211yescharacteristic
155C22×C3×C4D1211yescharacteristic
156C22×C3×C4#6711yescharacteristic
157C22×C3×C4#6711yescharacteristic
158C22×C3×C4C22×D311yescharacteristic
159C22×C3×C4C22×D311yescharacteristic
160C2×#67—21no—
161C22×Dic3—62no—
162C22×Dic3—62no—
163C22×Dic3—61no—
164C22×Dic3—61no—
165C22×Dic3—61no—
166C22×Dic3—61no—
167C2×D12#6711yescharacteristic
168C2×C4×D3—21no—
169C2×Dic6#6711yescharacteristic
170C2×C3×C8—61no—
171C2×C3×C8—61no—
172C3×C4⋊C4—21no—
173C3×C4⋊C4—21no—
174C3×C4⋊C4—21no—
175C3×C4⋊C4—21no—
176C3×C4⋊C4—31no—
177C3×C4⋊C4—31no—
178C3×C4⋊C4—41no—
179C3×C4⋊C4—41no—
180C3×C4⋊C4—61no—
181C3×C4⋊C4—61no—
182C3×C4⋊C4—61no—
183C3×C4⋊C4—61no—
184C3×C22⋊C4—61no—
185C3×C22⋊C4—61no—
186C3×C22⋊C4—61no—
187C3×C22⋊C4—61no—
188C3×C22⋊C4—61no—
189C3×C42—61no—
190#217—21no—
191(C2×D3)⋊C4—21no—
192(C2×D3)⋊C4—21no—
193(C2×D3)⋊C4—21no—
194(C2×D3)⋊C4—21no—
195C4⋊Dic3—61no—
196C4⋊Dic3—61no—
197C4⋊Dic3—61no—
198C4⋊Dic3—61no—
199C4⋊Dic3—121no—
200C4⋊Dic3—121no—
201C4⋊Dic3#6711yescharacteristic
202C4⋊Dic3#6711yescharacteristic
203Dic3⋊C4—21no—
204Dic3⋊C4—21no—
205Dic3⋊C4—21no—
206Dic3⋊C4—21no—
207C4×Dic3—21no—
208C2×C3⋊C8—21no—
209C2×C3⋊C8—21no—
210C22×C32—21no—
211C22×C32—21no—
212C22×C32#12011yescharacteristic
213C22×C32#13511yescharacteristic
214C22×C32#13711yescharacteristic
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—81no—
223C3⋊Dic3—81no—
224C3×Dic3—41no—
225C3×Dic3—41no—
226C3×Dic3—41no—
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—91no—
236C2×C4⋊C4D3211yescharacteristic
237#107—181no—
238#106—181no—
239#103—181no—
240#102—181no—
241C22⋊C8—31no—
242C22⋊C8—31no—
243#95—91no—
244#95—181no—
245#95—181no—
246C23×C3—21no—
247C23×C3—61no—
248C23×C3C2×D1211yescharacteristic
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—42no—
272C2×C3×C4—41no—
273C2×C3×C4—41no—
274C2×C3×C4—42no—
275C2×C3×C4—61no—
276C2×C3×C4—61no—
277C2×C3×C4—61no—
278C2×C3×C4—241no—
279C2×C3×C4D3×D411yescharacteristic
280C2×C3×C4D3×D411yescharacteristic
281C2×C3×C4C2×#6711yescharacteristic
282C2×C3×C4C2×#6711yescharacteristic
283#67—41no—
284#67—41no—
285C2×Dic3—21no—
286C2×Dic3—21no—
287C2×Dic3—21no—
288C2×Dic3—122no—
289C2×Dic3—122no—
290C2×Dic3—124no—
291C2×Dic3—122no—
292C2×Dic3—121no—
293C2×Dic3—121no—
294C2×Dic3—121no—
295C2×Dic3—121no—
296C2×Dic3—122no—
297C2×Dic3—122no—
298C2×Dic3—122no—
299C2×Dic3—121no—
300C2×Dic3—121no—
301C2×Dic3—121no—
302C2×Dic3—121no—
303D12—41no—
304C4×D3—81no—
305Dic6—41no—
306C3×C8—121no—
307C3×C8—121no—
308C3⋊C8—41no—
309C3⋊C8—41no—
310C2×C32—21no—
311C2×C32—21no—
312C2×C32#45211yescharacteristic
313C2×C32#45411yescharacteristic
314C2×C32#45811yescharacteristic
315C3×D3—81no—
316C2×Q8—31no—
317C2×D4—31no—
318C2×D4—61no—
319C22×C4—61no—
320C22×C4—181no—
321C22×C4—181no—
322C22×C4#62611yescharacteristic
323C22×C4#62611yescharacteristic
324C22×C4C2×D3211yescharacteristic
325C2×C8—61no—
326C2×C8—61no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—31no—
330C4⋊C4—31no—
331C4⋊C4—61no—
332C4⋊C4—61no—
333C4⋊C4—61no—
334C4⋊C4—61no—
335C4⋊C4—181no—
336C4⋊C4—181no—
337C22⋊C4—61no—
338C22⋊C4—61no—
339C22⋊C4—61no—
340C22⋊C4—61no—
341C22⋊C4—61no—
342C42—61no—
343C22×C3—22no—
344C22×C3—22no—
345C22×C3—21no—
346C22×C3—21no—
347C22×C3—21no—
348C22×C3—21no—
349C22×C3—21no—
350C22×C3—21no—
351C22×C3—21no—
352C22×C3—121no—
353C22×C3—121no—
354C22×C3—121no—
355C22×C3#88211yescharacteristic
356C22×C3#90411yescharacteristic
357C22×C3#90911yescharacteristic
358C22×C3#95011yescharacteristic
359C22×C3#95111yescharacteristic
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—121no—
377C3×C4—121no—
378C3×C4—121no—
379Dic3—41no—
380Dic3—41no—
381Dic3—41no—
382Dic3—242no—
383Dic3—241no—
384Dic3—241no—
385Dic3—242no—
386Dic3—241no—
387Dic3—241no—
388C32#161511yescharacteristic, complemented, Sylow
389C23—61no—
390C23C2×#62611yescharacteristic
391Q8—121no—
392D4—121no—
393D4—121no—
394D4—121no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—61no—
402C2×C4—61no—
403C2×C4—61no—
404C2×C4—241no—
405C2×C4—361no—
406C2×C4—361no—
407C2×C4—362no—
408C2×C4—361no—
409C2×C4—361no—
410C2×C4D3×#6711yescharacteristic
411C2×C4D3×#6711yescharacteristic
412C8—121no—
413C8—121no—
414C2×C3—22no—
415C2×C3—22no—
416C2×C3—21no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3—21no—
420C2×C3—21no—
421C2×C3—21no—
422C2×C3—21no—
423C2×C3—241no—
424C2×C3#473311yescharacteristic
425C2×C3#474211yescharacteristic
426C2×C3#475311yescharacteristic
427C2×C3#523911yescharacteristic
428C2×C3#524311yescharacteristic
429C2×C3#524511yescharacteristic
430D3—81no—
431C22—21no—
432C22—21no—
433C22—121no—
434C22—121no—
435C22—121no—
436C22#6382911yescharacteristic
437C22#6383111yescharacteristic
438C22#6397711yescharacteristic
439C4—21no—
440C4—21no—
441C4—41no—
442C4—41no—
443C4—121no—
444C4—121no—
445C4—121no—
446C4—721no—
447C4—721no—
448C3—21no—
449C3#6813611yescharacteristic, complemented
450C3#7188711yescharacteristic, complemented
451C2—21no—
452C2—21no—
453C2—241no—
454C2#1059117311yescharacteristic
455C2#1059153411yescharacteristic
456C2#1059164611yescharacteristic
subgroupG/H
centerC22#63977
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#120
prime radicalC3×#930C22
hypercenterC2×C4⋊C4D32
hypocenterC32#1615
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. #10592685C2semidirect
3. #10591103C2semidirect
5. C3×#4528C2semidirect
6. #10589152C2semidirect
41. #4528D3semidirect
388. C32#1615semidirect
449. C3#68136semidirect
450. C3#71887semidirect

Maximal subgroups

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

subgroupindex
C3×#55152
#105926852
#105911032
#105910922
C3×#45282
#105891522
#105891502
#718873
#681363