Finite Group Databasebeta

← #11778755

Subgroups — #11778755

Order 1152.

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

normal subgroups only

This group has 468 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×#5645C211yesmaximal, characteristic
2#10592743C211yesmaximal, characteristic, complemented
3#10591226C211yesmaximal, characteristic, complemented
4#10591092C211yesmaximal, characteristic
5C3×#4538C211yesmaximal, characteristic, complemented
6#10589149C211yesmaximal, characteristic
7#10589147C211yesmaximal, characteristic, complemented
8#71887—31nomaximal
9#68330—31nomaximal
10C32×C22⋊Q8C2211yescharacteristic
11C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
12C3×#946—21no—
13C3×#930C2211yescharacteristic
14C2×C3×Dic3⋊C4C2211yescharacteristic
15C3×#898—21no—
16C3×#894—21no—
17C3×#890—21no—
18C3×#886—21no—
19C3×#67⋊C4—21no—
20#63662—21no—
21#63657C2211yescharacteristic
22#63634—21no—
23C3×C3⋊#95C2211yescharacteristic
24C3×#830C2211yescharacteristic
25#63579—21no—
26#63579—21no—
27#63573—21no—
28#63563—21no—
29C3×#539—31no—
30#5645D311yescharacteristic
31#5044—31no—
32#5044—31no—
33#5044—61no—
34#5034—31no—
35#4986—31no—
36#4735—31no—
37#4659—31no—
38C3×#328—31no—
39#4538D311yescharacteristic, complemented
40#4537—31no—
41#4528—31no—
42#4469—31no—
43#4451—31no—
44C2×C32×Q8D411yescharacteristic
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3—21no—
47C2×C3×#67—21no—
48C22×C3×Dic3—21no—
49C22×C3×Dic3D411yescharacteristic
50C22×C3×Dic3D411yescharacteristic
51C2×C3×D12D411yescharacteristic
52C2×C3×C4×D3—21no—
53C32×C4⋊C4—21no—
54C32×C4⋊C4D411yescharacteristic
55C32×C22⋊C4—21no—
56C4⋊(C3⋊Dic3)—21no—
57C4⋊(C3⋊Dic3)—21no—
58C2×C3⋊(C3⋊C8)—21no—
59C3×(C2×D3)⋊C4—21no—
60C3×(C2×D3)⋊C4—21no—
61C3×(C2×D3)⋊C4—21no—
62C3×(C2×D3)⋊C4—21no—
63C3×C4⋊Dic3—21no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3D411yescharacteristic
66C3×Dic3⋊C4—21no—
67C3×Dic3⋊C4—21no—
68C3×Dic3⋊C4—21no—
69C3×C4×Dic3—21no—
70C2×C3×C3⋊C8—21no—
71#1615—91noSylow
72C3×#126—61no—
73C3×#125—61no—
74C3×#123—61no—
75C3×#123—61no—
76C3×C22⋊Q8—21no—
77C3×C22⋊Q8—61no—
78C3×C22⋊Q8C2×D311yescharacteristic
79C3×C22⋊Q8C2×D311yescharacteristic
80C3×#121—31no—
81C3×C4×D4—61no—
82C2×C3×C4⋊C4—31no—
83#946—21no—
84#930C2×D311yescharacteristic
85C2×C4⋊Dic3—31no—
86C2×C4⋊Dic3—31no—
87C2×C4⋊Dic3—61no—
88C2×Dic3⋊C4C2×D311yescharacteristic
89#898—21no—
90#894—21no—
91#890—21no—
92#886—21no—
93#67⋊C4—21no—
94C3×C22⋊C8—31no—
95C3×#95—31no—
96#835—62no—
97#835—61no—
98#835—61no—
99#832—61no—
100C3⋊#95—61no—
101C3⋊#95—61no—
102C3⋊#95—61no—
103C3⋊#95—61no—
104C3⋊#95C2×D311yescharacteristic
105#830—31no—
106#830—31no—
107#830—61no—
108#830C2×D311yescharacteristic
109#821—61no—
110#817—61no—
111#808—61no—
112#807—62no—
113#807—61no—
114#807—61no—
115C23×C32C2×D411yescharacteristic
116C22×C3×D3—21no—
117C32×Q8—41no—
118C2×C32×C4—21no—
119C2×C32×C4—21no—
120C2×C32×C4—41no—
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C3⋊Dic3—41no—
124C2×C3⋊Dic3—42no—
125C3×#67—41no—
126C3×#67—41no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—21no—
130C2×C3×Dic3—21no—
131C2×C3×Dic3—21no—
132C2×C3×Dic3—41no—
133C2×C3×Dic3—41no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3—41no—
136C3×D12—41no—
137C3×C4×D3—81no—
138C3⋊(C3⋊C8)—41no—
139C3×C3⋊C8—41no—
140#539—31no—
141#484—91no—
142#481—91no—
143#400—91no—
144#328—31no—
145#327—91no—
146#324—91no—
147C2×C3×Q8—21no—
148C2×C3×Q8D1211yescharacteristic
149C2×C3×Q8#6711yescharacteristic
150C2×C3×D4—31no—
151C2×C3×D4—61no—
152C22×C3×C4—21no—
153C22×C3×C4—31no—
154C22×C3×C4—31no—
155C22×C3×C4—61no—
156C22×C3×C4—61no—
157C22×C3×C4C22×D311yescharacteristic
158C22×C3×C4C22×D311yescharacteristic
159C2×#67—21no—
160C22×Dic3—21no—
161C22×Dic3—61no—
162C22×Dic3—61no—
163C22×Dic3—121no—
164C22×Dic3#6711yescharacteristic
165C22×Dic3#6711yescharacteristic
166C2×D12#6711yescharacteristic
167C2×C4×D3—21no—
168C2×C3×C8—61no—
169C3×C4⋊C4—21no—
170C3×C4⋊C4—21no—
171C3×C4⋊C4—21no—
172C3×C4⋊C4—31no—
173C3×C4⋊C4—41no—
174C3×C4⋊C4—61no—
175C3×C4⋊C4—61no—
176C3×C4⋊C4—61no—
177C3×C4⋊C4—61no—
178C3×C4⋊C4—61no—
179C3×C4⋊C4D1211yescharacteristic
180C3×C4⋊C4#6711yescharacteristic
181C3×C22⋊C4—21no—
182C3×C22⋊C4—21no—
183C3×C22⋊C4—41no—
184C3×C22⋊C4—61no—
185C3×C22⋊C4—61no—
186C3×C22⋊C4—61no—
187C3×C22⋊C4—61no—
188C3×C42—61no—
189(C2×D3)⋊C4—21no—
190(C2×D3)⋊C4—21no—
191(C2×D3)⋊C4—21no—
192(C2×D3)⋊C4—21no—
193C4⋊Dic3—21no—
194C4⋊Dic3—21no—
195C4⋊Dic3—62no—
196C4⋊Dic3—61no—
197C4⋊Dic3—61no—
198C4⋊Dic3—61no—
199C4⋊Dic3—61no—
200C4⋊Dic3—121no—
201C4⋊Dic3#6711yescharacteristic
202Dic3⋊C4—21no—
203Dic3⋊C4—21no—
204Dic3⋊C4—21no—
205C4×Dic3—21no—
206C2×C3⋊C8—21no—
207C2×C3⋊C8—62no—
208C2×C3⋊C8—61no—
209C2×C3⋊C8—61no—
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—41no—
224C3×Dic3—41no—
225C3×Dic3—41no—
226C3×Dic3—81no—
227#126—61no—
228#125—61no—
229#123—61no—
230#123—61no—
231C22⋊Q8—61no—
232C22⋊Q8D3211yescharacteristic
233#121—31no—
234C4×D4—61no—
235C2×C4⋊C4—31no—
236C2×C4⋊C4—91no—
237#107—181no—
238#106—181no—
239#103—181no—
240#102—181no—
241C22⋊C8—31no—
242C22⋊C8—91no—
243#95—31no—
244#95—181no—
245#95—181no—
246C23×C3—21no—
247C23×C3—61no—
248C23×C3D3×D411yescharacteristic
249C23×C3C2×#6711yescharacteristic
250C22×D3—21no—
251C3×Q8—41no—
252C3×Q8—41no—
253C3×Q8—42no—
254C3×D4—121no—
255C3×D4—121no—
256C3×D4—121no—
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—41no—
264C2×C3×C4—41no—
265C2×C3×C4—41no—
266C2×C3×C4—41no—
267C2×C3×C4—42no—
268C2×C3×C4—61no—
269C2×C3×C4—61no—
270C2×C3×C4—61no—
271C2×C3×C4—61no—
272C2×C3×C4—61no—
273C2×C3×C4—121no—
274C2×C3×C4—121no—
275C2×C3×C4—121no—
276C2×C3×C4—121no—
277C2×C3×C4—241no—
278C2×C3×C4C2×D1211yescharacteristic
279C2×C3×C4D3×D411yescharacteristic
280C2×C3×C4C2×#6711yescharacteristic
281C2×C3×C4C2×#6711yescharacteristic
282#67—41no—
283#67—41no—
284C2×Dic3—21no—
285C2×Dic3—21no—
286C2×Dic3—21no—
287C2×Dic3—21no—
288C2×Dic3—21no—
289C2×Dic3—41no—
290C2×Dic3—41no—
291C2×Dic3—41no—
292C2×Dic3—41no—
293C2×Dic3—122no—
294C2×Dic3—122no—
295C2×Dic3—122no—
296C2×Dic3—121no—
297C2×Dic3—121no—
298C2×Dic3—242no—
299D12—41no—
300C4×D3—81no—
301C3×C8—121no—
302C3⋊C8—41no—
303C3⋊C8—122no—
304C3⋊C8—121no—
305C3⋊C8—121no—
306C2×C32—21no—
307C2×C32—21no—
308C2×C32#45211yescharacteristic
309C2×C32#45411yescharacteristic
310C2×C32#45811yescharacteristic
311C3×D3—81no—
312C2×Q8#62611yescharacteristic
313C2×D4—31no—
314C2×D4—61no—
315C22×C4—31no—
316C22×C4—31no—
317C22×C4—61no—
318C22×C4—61no—
319C22×C4—181no—
320C22×C4C2×D3211yescharacteristic
321C2×C8—61no—
322C2×C8—181no—
323C4⋊C4—21no—
324C4⋊C4—31no—
325C4⋊C4—61no—
326C4⋊C4—61no—
327C4⋊C4—61no—
328C4⋊C4—61no—
329C4⋊C4—61no—
330C4⋊C4—181no—
331C4⋊C4—181no—
332C4⋊C4#62611yescharacteristic
333C22⋊C4—21no—
334C22⋊C4—61no—
335C22⋊C4—61no—
336C22⋊C4—61no—
337C22⋊C4—61no—
338C42—61no—
339C22×C3—21no—
340C22×C3—21no—
341C22×C3—21no—
342C22×C3—21no—
343C22×C3—21no—
344C22×C3—21no—
345C22×C3—21no—
346C22×C3—41no—
347C22×C3—41no—
348C22×C3—121no—
349C22×C3—121no—
350C22×C3—121no—
351C22×C3#88211yescharacteristic
352C22×C3#91611yescharacteristic
353C22×C3#91811yescharacteristic
354C22×C3#95011yescharacteristic
355C22×C3#95111yescharacteristic
356C22×C3#95311yescharacteristic
357C2×D3—41no—
358C2×D3—41no—
359C2×D3—41no—
360C3×C4—22no—
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—21no—
364C3×C4—21no—
365C3×C4—41no—
366C3×C4—41no—
367C3×C4—41no—
368C3×C4—41no—
369C3×C4—41no—
370C3×C4—81no—
371C3×C4—81no—
372C3×C4—121no—
373C3×C4—121no—
374C3×C4—121no—
375C3×C4—241no—
376Dic3—41no—
377Dic3—41no—
378Dic3—41no—
379Dic3—81no—
380Dic3—242no—
381Dic3—241no—
382Dic3—241no—
383C32#161511yescharacteristic, complemented, Sylow
384C23—61no—
385C23D3×#6711yescharacteristic
386Q8—41no—
387D4—121no—
388D4—121no—
389D4—121no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—41no—
393C2×C4—61no—
394C2×C4—61no—
395C2×C4—61no—
396C2×C4—61no—
397C2×C4—61no—
398C2×C4—121no—
399C2×C4—121no—
400C2×C4—121no—
401C2×C4—121no—
402C2×C4—241no—
403C2×C4—362no—
404C2×C4—361no—
405C2×C4C2×#62611yescharacteristic
406C2×C4D3×#6711yescharacteristic
407C8—121no—
408C8—361no—
409C2×C3—21no—
410C2×C3—21no—
411C2×C3—21no—
412C2×C3—21no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—21no—
416C2×C3—41no—
417C2×C3—41no—
418C2×C3—241no—
419C2×C3#474211yescharacteristic
420C2×C3#480811yescharacteristic
421C2×C3#482711yescharacteristic
422C2×C3#523911yescharacteristic
423C2×C3#524311yescharacteristic
424C2×C3#524511yescharacteristic
425D3—81no—
426C22—21no—
427C22—21no—
428C22—121no—
429C22—121no—
430C22—121no—
431C22#6394311yescharacteristic
432C22#6394711yescharacteristic
433C22#6397711yescharacteristic
434C4—21no—
435C4—21no—
436C4—41no—
437C4—41no—
438C4—121no—
439C4—121no—
440C4—121no—
441C4—241no—
442C4—721no—
443C3—21no—
444C3#6833011yescharacteristic, complemented
445C3#7188711yescharacteristic, complemented
446C2—21no—
447C2—21no—
448C2—241no—
449C2#1059153411yescharacteristic
450C2#1059159911yescharacteristic
451C2#1059168511yescharacteristic
subgroupG/H
centerC22#63977
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×C22⋊Q8C22
socleC22×C32#120
prime radicalC3×#930C22
hypercenterC22⋊Q8D32
hypocenterC32#1615
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #10592743C2semidirect
3. #10591226C2semidirect
5. C3×#4538C2semidirect
7. #10589147C2semidirect
39. #4538D3semidirect
383. C32#1615semidirect
444. C3#68330semidirect
445. C3#71887semidirect

Maximal subgroups

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

subgroupindex
C3×#56452
#105927432
#105912262
#105910922
C3×#45382
#105891492
#105891472
#718873
#683303