Finite Group Databasebeta

← #11778533

Subgroups — #11778533

Order 1152.

471 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 471 conjugacy classes of subgroups — too many to draw. Only its 78 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
1#10594974C211yesmaximal, characteristic
2C3×#4721C211yesmaximal, characteristic, complemented
3#10591358C211yesmaximal, characteristic, complemented
4#10591089C211yesmaximal, characteristic
5#10589335C211yesmaximal, characteristic, complemented
6C3×#4470C211yesmaximal, characteristic
7#10589153C211yesmaximal, characteristic, complemented
8#71174—31nomaximal
9#68296—31nomaximal
10C2×#3750C2211yescharacteristic
11C3×#930C2211yescharacteristic
12C2×C3×C4⋊Dic3C2211yescharacteristic
13C3×#924C2211yescharacteristic
14#67⋊Dic3—21no—
15C2×Dic3⋊Dic3—21no—
16#63962—21no—
17#63887—21no—
18#63884—21no—
19#63858—21no—
20#63846—21no—
21C32×C22⋊C8C2211yescharacteristic
22#63657C2211yescharacteristic
23C3×C3⋊#95C2211yescharacteristic
24C3×#817—21no—
25C3×#816—21no—
26#63579—21no—
27#63576—21no—
28#63562—21no—
29#5645—31no—
30#5602—31no—
31C3×#483—31no—
32#5033—31no—
33#4983—31no—
34#4967—31no—
35#4721D311yescharacteristic, complemented
36#4661—31no—
37C3×#327—31no—
38#4538—31no—
39#4470D311yescharacteristic
40#4469—31no—
41#4469—31no—
42#4469—61no—
43#4452—31no—
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3D411yescharacteristic
46C22×C3⋊Dic3D411yescharacteristic
47C2×C3×#67—21no—
48C22×C3×Dic3—21no—
49C22×C3×Dic3—21no—
50C2×C3×D12D411yescharacteristic
51C2×C3×Dic6D411yescharacteristic
52C2×D3×Dic3—21no—
53C2×C32×C8—21no—
54#3750—21no—
55#3750—21no—
56C2×C3⋊(C3⋊C8)—21no—
57C3×#217—21no—
58C3×(C2×D3)⋊C4—21no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3D411yescharacteristic
62C3×C4⋊Dic3D411yescharacteristic
63C3×Dic3⋊C4—21no—
64Dic3⋊Dic3—21no—
65Dic3⋊Dic3—21no—
66Dic3⋊Dic3—21no—
67Dic3⋊Dic3—42no—
68(C2×D3)⋊Dic3—21no—
69(C2×D3)⋊Dic3—21no—
70(C2×D3)⋊Dic3—21no—
71Dic32—21no—
72#1609—91noSylow
73C3×C22⋊Q8—31no—
74C3×#121—31no—
75C2×C3×C4⋊C4—31no—
76#946—61no—
77#935—61no—
78#935—61no—
79D4×Dic3—61no—
80#930C2×D311yescharacteristic
81C2×C4⋊Dic3—61no—
82C2×C4⋊Dic3C2×D311yescharacteristic
83#924C2×D311yescharacteristic
84C2×Dic3⋊C4—31no—
85C2×Dic3⋊C4—31no—
86C2×Dic3⋊C4—61no—
87C2×Dic3⋊C4—61no—
88#898—61no—
89#894—61no—
90#890—61no—
91#889—61no—
92#886—61no—
93#67⋊C4—61no—
94#879—61no—
95#878—61no—
96C3×#106—61no—
97C3×#103—61no—
98C3×C22⋊C8—21no—
99C3×C22⋊C8C2×D311yescharacteristic
100C3×C22⋊C8C2×D311yescharacteristic
101C3×#95—31no—
102#832—61no—
103C3⋊#95—61no—
104C3⋊#95—61no—
105C3⋊#95C2×D311yescharacteristic
106#830—31no—
107#830—31no—
108#830—61no—
109#817—21no—
110#816—21no—
111#809—61no—
112#807—61no—
113#807—61no—
114C23×C32C2×D411yescharacteristic
115C22×C3×D3—21no—
116C2×C32×C4—41no—
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C3⋊Dic3—21no—
120C2×C3⋊Dic3—21no—
121C2×C3⋊Dic3—21no—
122C2×C3⋊Dic3—21no—
123C2×C3⋊Dic3—41no—
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×Dic6—41no—
137D3×Dic3—81no—
138C32×C8—41no—
139C3⋊(C3⋊C8)—41no—
140#539—91no—
141#483—31no—
142#480—91no—
143#398—91no—
144#328—91no—
145#327—31no—
146#324—91no—
147C2×C3×Q8—31no—
148C2×C3×D4—31no—
149C2×C3×D4—61no—
150C22×C3×C4—21no—
151C22×C3×C4—61no—
152C22×C3×C4—61no—
153C22×C3×C4C22×D311yescharacteristic
154C22×C3×C4C22×D311yescharacteristic
155C2×#67—21no—
156C22×Dic3—21no—
157C22×Dic3—21no—
158C22×Dic3—31no—
159C22×Dic3—31no—
160C22×Dic3—31no—
161C22×Dic3—31no—
162C22×Dic3—61no—
163C22×Dic3—61no—
164C22×Dic3—61no—
165C2×D12D1211yescharacteristic
166C2×C4×D3—61no—
167C2×Dic6#6711yescharacteristic
168C2×C3×C8—21no—
169C2×C3×C8—21no—
170C2×C3×C8—41no—
171C3×C4⋊C4—31no—
172C3×C4⋊C4—31no—
173C3×C4⋊C4—61no—
174C3×C4⋊C4—61no—
175C3×C4⋊C4—61no—
176C3×C22⋊C4—61no—
177C3×C22⋊C4—61no—
178#217—21no—
179#217—61no—
180#217—61no—
181#217—61no—
182(C2×D3)⋊C4—21no—
183(C2×D3)⋊C4—61no—
184(C2×D3)⋊C4—61no—
185(C2×D3)⋊C4—61no—
186C4⋊Dic3—21no—
187C4⋊Dic3—21no—
188C4⋊Dic3—61no—
189C4⋊Dic3—61no—
190C4⋊Dic3—61no—
191C4⋊Dic3—122no—
192C4⋊Dic3D1211yescharacteristic
193C4⋊Dic3#6711yescharacteristic
194Dic3⋊C4—21no—
195Dic3⋊C4—61no—
196Dic3⋊C4—61no—
197Dic3⋊C4—61no—
198Dic3⋊C4—61no—
199Dic3⋊C4—61no—
200Dic3⋊C4—61no—
201Dic3⋊C4—61no—
202Dic3⋊C4—121no—
203Dic3⋊C4—121no—
204Dic3⋊C4—122no—
205C4×Dic3—61no—
206C4×Dic3—61no—
207C2×C3⋊C8—61no—
208C2×C3⋊C8—61no—
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—
220C3⋊Dic3—41no—
221C3⋊Dic3—41no—
222C3×Dic3—42no—
223C3×Dic3—41no—
224C3×Dic3—41no—
225C3×Dic3—41no—
226C3×Dic3—81no—
227#126—181no—
228#125—181no—
229#123—181no—
230#123—181no—
231C22⋊Q8—31no—
232C22⋊Q8—181no—
233#121—31no—
234C4×D4—181no—
235C2×C4⋊C4—31no—
236C2×C4⋊C4—91no—
237C2×C4⋊C4—181no—
238#107—181no—
239#106—61no—
240#103—61no—
241#102—181no—
242C22⋊C8—91no—
243C22⋊C8D3211yescharacteristic
244#95—31no—
245#95—181no—
246C23×C3—21no—
247C23×C3—61no—
248C23×C3D3×D411yescharacteristic
249C23×C3D3×D411yescharacteristic
250C22×D3—21no—
251C3×Q8—121no—
252C3×D4—121no—
253C3×D4—121no—
254C3×D4—121no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—41no—
258C2×C3×C4—41no—
259C2×C3×C4—62no—
260C2×C3×C4—61no—
261C2×C3×C4—61no—
262C2×C3×C4—61no—
263C2×C3×C4—81no—
264C2×C3×C4—121no—
265C2×C3×C4—121no—
266C2×C3×C4—121no—
267C2×C3×C4—121no—
268C2×C3×C4—121no—
269C2×C3×C4C2×D1211yescharacteristic
270C2×C3×C4D3×D411yescharacteristic
271C2×C3×C4D3×D411yescharacteristic
272C2×C3×C4C2×#6711yescharacteristic
273#67—41no—
274#67—41no—
275C2×Dic3—22no—
276C2×Dic3—21no—
277C2×Dic3—21no—
278C2×Dic3—21no—
279C2×Dic3—41no—
280C2×Dic3—41no—
281C2×Dic3—41no—
282C2×Dic3—41no—
283C2×Dic3—41no—
284C2×Dic3—62no—
285C2×Dic3—61no—
286C2×Dic3—61no—
287C2×Dic3—61no—
288C2×Dic3—61no—
289C2×Dic3—61no—
290C2×Dic3—61no—
291C2×Dic3—61no—
292C2×Dic3—61no—
293C2×Dic3—121no—
294C2×Dic3—121no—
295C2×Dic3—121no—
296C2×Dic3—121no—
297C2×Dic3—121no—
298C2×Dic3—241no—
299C2×Dic3—241no—
300D12—41no—
301C4×D3—241no—
302Dic6—41no—
303C3×C8—41no—
304C3×C8—41no—
305C3×C8—81no—
306C3⋊C8—121no—
307C3⋊C8—121no—
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—91no—
321C22×C4—91no—
322C22×C4—181no—
323C22×C4C2×D3211yescharacteristic
324C2×C8—21no—
325C2×C8—181no—
326C4⋊C4—31no—
327C4⋊C4—31no—
328C4⋊C4—61no—
329C4⋊C4—61no—
330C4⋊C4—61no—
331C4⋊C4—181no—
332C4⋊C4—181no—
333C4⋊C4—181no—
334C4⋊C4—181no—
335C4⋊C4—181no—
336C4⋊C4—362no—
337C22⋊C4—61no—
338C22⋊C4—61no—
339C22⋊C4—181no—
340C22⋊C4—181no—
341C22⋊C4—181no—
342C42—181no—
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#88211yescharacteristic
356C22×C3#91111yescharacteristic
357C22×C3#91411yescharacteristic
358C22×C3#91611yescharacteristic
359C22×C3#91611yescharacteristic
360C22×C3#93711yescharacteristic
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—122no—
371C3×C4—121no—
372C3×C4—121no—
373C3×C4—121no—
374C3×C4—241no—
375Dic3—42no—
376Dic3—41no—
377Dic3—41no—
378Dic3—41no—
379Dic3—81no—
380Dic3—122no—
381Dic3—121no—
382Dic3—121no—
383Dic3—121no—
384Dic3—121no—
385Dic3—241no—
386C32#160911yescharacteristic, complemented, Sylow
387C23—61no—
388C23#380211yescharacteristic
389Q8—121no—
390D4—121no—
391D4—121no—
392D4—121no—
393C2×C4—41no—
394C2×C4—62no—
395C2×C4—61no—
396C2×C4—61no—
397C2×C4—61no—
398C2×C4—121no—
399C2×C4—121no—
400C2×C4—121no—
401C2×C4—121no—
402C2×C4—121no—
403C2×C4—181no—
404C2×C4—181no—
405C2×C4—181no—
406C2×C4—181no—
407C2×C4—361no—
408C2×C4—721no—
409C2×C4D3×D1211yescharacteristic
410C2×C4D3×#6711yescharacteristic
411C8—41no—
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#474211yescharacteristic
424C2×C3#478111yescharacteristic
425C2×C3#482611yescharacteristic
426C2×C3#505311yescharacteristic
427C2×C3#517211yescharacteristic
428C2×C3#520511yescharacteristic
429D3—81no—
430C22—21no—
431C22—21no—
432C22—121no—
433C22—121no—
434C22—121no—
435C22#6379811yescharacteristic
436C22#6380911yescharacteristic
437C22#6392211yescharacteristic
438C4—21no—
439C4—21no—
440C4—122no—
441C4—121no—
442C4—121no—
443C4—121no—
444C4—241no—
445C4—361no—
446C4—361no—
447C3—21no—
448C3#6829611yescharacteristic, complemented
449C3#7117411yescharacteristic, complemented
450C2—21no—
451C2—21no—
452C2—241no—
453C2#1059040811yescharacteristic
454C2#1059096411yescharacteristic
455C2#1059101711yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32#120
prime radicalC3×#930C22
hypercenterC22⋊C8D32
hypocenterC32#1609
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C3×#4721C2semidirect
3. #10591358C2semidirect
5. #10589335C2semidirect
7. #10589153C2semidirect
35. #4721D3semidirect
386. C32#1609semidirect
448. C3#68296semidirect
449. C3#71174semidirect

Maximal subgroups

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

subgroupindex
#105949742
C3×#47212
#105913582
#105910892
#105893352
C3×#44702
#105891532
#711743
#682963