Finite Group Databasebeta

← #11778516

Subgroups — #11778516

Order 1152.

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

normal subgroups only

This group has 484 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#10594973C211yesmaximal, characteristic
2#10592670C211yesmaximal, characteristic, complemented
3C3×#4983C211yesmaximal, characteristic, complemented
4C3×#4967C211yesmaximal, characteristic
5#10589154C211yesmaximal, characteristic, complemented
6#10589149C211yesmaximal, characteristic
7#10589147C211yesmaximal, characteristic, complemented
8#71166—31nomaximal
9#69711—31nomaximal
10C2×C32×C4⋊C4C2211yescharacteristic
11#64133C2211yescharacteristic
12C3×#930C2211yescharacteristic
13C2×C3×Dic3⋊C4—21no—
14C2×C3×Dic3⋊C4C2211yescharacteristic
15Dic3×#67—21no—
16#63961—21no—
17#63896—21no—
18#63884—21no—
19#63861—21no—
20#63847—21no—
21#63657C2211yescharacteristic
22#63637—21no—
23#63635—21no—
24C3×C3⋊#95—21no—
25C3×C3⋊#95C2211yescharacteristic
26C3×#830C2211yescharacteristic
27C3×#809—21no—
28C3×#807—21no—
29#5602—31no—
30#5515—31no—
31C3×#480—31no—
32C3×#398—31no—
33#4983D311yescharacteristic, complemented
34#4971—31no—
35#4971—31no—
36#4971—61no—
37#4967D311yescharacteristic
38#4537—31no—
39#4528—31no—
40#4469—31no—
41#4467—31no—
42#4452—31no—
43#4451—31no—
44C22×C32×C4—21no—
45C22×C32×C4C2311yescharacteristic
46C2×#634D411yescharacteristic
47C2×C3×#67—21no—
48C22×C3×Dic3—21no—
49C22×C3×Dic3D411yescharacteristic
50C22×C3×Dic3D411yescharacteristic
51C2×C3×D12D411yescharacteristic
52C2×D3×Dic3—21no—
53C32×C4⋊C4—21no—
54C32×C4⋊C4—21no—
55#3757—21no—
56C4⋊(C3⋊Dic3)D411yescharacteristic
57#3750—21no—
58C2×C3⋊(C3⋊C8)—21no—
59C3×(C2×D3)⋊C4—21no—
60C3×C4⋊Dic3D411yescharacteristic
61C3×Dic3⋊C4—21no—
62C3×Dic3⋊C4—21no—
63C3×Dic3⋊C4—42no—
64C2×C3×C3⋊C8—21no—
65#3724—21no—
66#3724—21no—
67Dic3⋊Dic3—21no—
68(C2×D3)⋊Dic3—21no—
69(C2×D3)⋊Dic3—21no—
70(C2×D3)⋊Dic3—21no—
71Dic32—21no—
72#1609—91noSylow
73C3×#121—31no—
74C2×C3×C4⋊C4—21no—
75C2×C3×C4⋊C4—31no—
76C2×C3×C4⋊C4—61no—
77C2×C3×C4⋊C4C2×D311yescharacteristic
78C2×C3×C4⋊C4C2×D311yescharacteristic
79#935—61no—
80#935—61no—
81D4×Dic3—61no—
82#930C2×D311yescharacteristic
83#929—61no—
84C4×#67—61no—
85#924—31no—
86#924—31no—
87#924—61no—
88C2×Dic3⋊C4—21no—
89C2×Dic3⋊C4C2×D311yescharacteristic
90#898—61no—
91#896—61no—
92#894—61no—
93#889—61no—
94#889—61no—
95#879—61no—
96#878—61no—
97C3×#107—61no—
98C3×#102—61no—
99C3×C22⋊C8—31no—
100C3×#95—31no—
101C3×#95—61no—
102C3⋊#95—21no—
103C3⋊#95C2×D311yescharacteristic
104#830—31no—
105#830—31no—
106#830—61no—
107#830C2×D311yescharacteristic
108#810—61no—
109#810—61no—
110#810—62no—
111#809—21no—
112#808—61no—
113#808—61no—
114#808—62no—
115#807—21no—
116C23×C32C2×D411yescharacteristic
117C22×C3×D3—21no—
118C2×C32×C4—41no—
119C2×C32×C4—41no—
120C2×C32×C4—41no—
121C2×C32×C4—41no—
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C3⋊Dic3—21no—
125C2×C3⋊Dic3—21no—
126#634—41no—
127C3×#67—41no—
128C3×#67—41no—
129C2×C3×Dic3—22no—
130C2×C3×Dic3—21no—
131C2×C3×Dic3—21no—
132C2×C3×Dic3—21no—
133C2×C3×Dic3—21no—
134C2×C3×Dic3—21no—
135C2×C3×Dic3—41no—
136C2×C3×Dic3—41no—
137C2×C3×Dic3—41no—
138C3×D12—41no—
139D3×Dic3—81no—
140C3⋊(C3⋊C8)—41no—
141C3×C3⋊C8—41no—
142#539—91no—
143#483—91no—
144#480—31no—
145#398—31no—
146#328—91no—
147#327—91no—
148#324—91no—
149C2×C3×D4—31no—
150C2×C3×D4—61no—
151C22×C3×C4—21no—
152C22×C3×C4—21no—
153C22×C3×C4—21no—
154C22×C3×C4—31no—
155C22×C3×C4—31no—
156C22×C3×C4—41no—
157C22×C3×C4—61no—
158C22×C3×C4C22×D311yescharacteristic
159C22×C3×C4C22×D311yescharacteristic
160C2×#67—21no—
161C22×Dic3—21no—
162C22×Dic3—61no—
163C22×Dic3#6711yescharacteristic
164C22×Dic3#6711yescharacteristic
165C2×D12#6711yescharacteristic
166C2×C4×D3—61no—
167C2×Dic6—31no—
168C2×Dic6—31no—
169C2×Dic6—61no—
170C2×C3×C8—61no—
171C3×C4⋊C4—22no—
172C3×C4⋊C4—21no—
173C3×C4⋊C4—21no—
174C3×C4⋊C4—21no—
175C3×C4⋊C4—21no—
176C3×C4⋊C4—31no—
177C3×C4⋊C4—41no—
178C3×C4⋊C4—61no—
179C3×C4⋊C4—61no—
180C3×C4⋊C4—122no—
181C3×C22⋊C4—61no—
182#217—61no—
183#217—61no—
184#217—61no—
185#217—61no—
186#217—61no—
187#217—121no—
188(C2×D3)⋊C4—21no—
189(C2×D3)⋊C4—61no—
190(C2×D3)⋊C4—61no—
191(C2×D3)⋊C4—61no—
192C4⋊Dic3—31no—
193C4⋊Dic3—31no—
194C4⋊Dic3—61no—
195C4⋊Dic3—61no—
196C4⋊Dic3#6711yescharacteristic
197Dic3⋊C4—21no—
198Dic3⋊C4—21no—
199Dic3⋊C4—42no—
200Dic3⋊C4—61no—
201Dic3⋊C4—61no—
202Dic3⋊C4—61no—
203Dic3⋊C4—61no—
204Dic3⋊C4—61no—
205Dic3⋊C4—61no—
206Dic3⋊C4—61no—
207Dic3⋊C4—121no—
208C4×Dic3—61no—
209C4×Dic3—61no—
210C2×C3⋊C8—21no—
211C2×C3⋊C8—62no—
212C2×C3⋊C8—61no—
213C2×C3⋊C8—61no—
214C22×C32—21no—
215C22×C32—21no—
216C22×C32#12011yescharacteristic
217C22×C32#13511yescharacteristic
218C22×C32AGL(1,ℤ/8)11yescharacteristic
219C2×C3×D3—41no—
220C2×C3×D3—41no—
221C2×C3×D3—41no—
222C32×C4—21no—
223C32×C4—21no—
224C32×C4—81no—
225C3⋊Dic3—41no—
226C3⋊Dic3—41no—
227C3×Dic3—42no—
228C3×Dic3—41no—
229C3×Dic3—41no—
230C3×Dic3—41no—
231#126—181no—
232#125—181no—
233#123—181no—
234#123—181no—
235C22⋊Q8—91no—
236C22⋊Q8—181no—
237#121—31no—
238C4×D4—181no—
239C2×C4⋊C4—31no—
240C2×C4⋊C4—61no—
241C2×C4⋊C4D3211yescharacteristic
242#107—61no—
243#106—181no—
244#103—181no—
245#102—61no—
246C22⋊C8—31no—
247C22⋊C8—91no—
248#95—31no—
249#95—61no—
250C23×C3—21no—
251C23×C3—61no—
252C23×C3D3×D411yescharacteristic
253C23×C3C2×#6711yescharacteristic
254C22×D3—21no—
255C3×D4—121no—
256C3×D4—121no—
257C3×D4—121no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—41no—
261C2×C3×C4—41no—
262C2×C3×C4—42no—
263C2×C3×C4—42no—
264C2×C3×C4—41no—
265C2×C3×C4—41no—
266C2×C3×C4—41no—
267C2×C3×C4—41no—
268C2×C3×C4—41no—
269C2×C3×C4—41no—
270C2×C3×C4—62no—
271C2×C3×C4—61no—
272C2×C3×C4—61no—
273C2×C3×C4—61no—
274C2×C3×C4—61no—
275C2×C3×C4—61no—
276C2×C3×C4—81no—
277C2×C3×C4—81no—
278C2×C3×C4—121no—
279C2×C3×C4—121no—
280C2×C3×C4—121no—
281C2×C3×C4D3×D411yescharacteristic
282C2×C3×C4D3×D411yescharacteristic
283C2×C3×C4D3×D411yescharacteristic
284C2×C3×C4C2×#6711yescharacteristic
285#67—41no—
286#67—41no—
287C2×Dic3—22no—
288C2×Dic3—21no—
289C2×Dic3—21no—
290C2×Dic3—21no—
291C2×Dic3—21no—
292C2×Dic3—21no—
293C2×Dic3—41no—
294C2×Dic3—41no—
295C2×Dic3—41no—
296C2×Dic3—61no—
297C2×Dic3—61no—
298C2×Dic3—61no—
299C2×Dic3—61no—
300C2×Dic3—121no—
301C2×Dic3—121no—
302C2×Dic3—241no—
303D12—41no—
304C4×D3—241no—
305Dic6—121no—
306Dic6—121no—
307Dic6—122no—
308C3×C8—121no—
309C3⋊C8—41no—
310C3⋊C8—122no—
311C3⋊C8—121no—
312C3⋊C8—121no—
313C2×C32—21no—
314C2×C32—21no—
315C2×C32#44911yescharacteristic
316C2×C32#45611yescharacteristic
317C2×C32#45811yescharacteristic
318C3×D3—81no—
319C2×Q8—91no—
320C2×D4—31no—
321C2×D4—61no—
322C22×C4—21no—
323C22×C4—31no—
324C22×C4—31no—
325C22×C4—61no—
326C22×C4—181no—
327C22×C4C2×D3211yescharacteristic
328C2×C8—61no—
329C2×C8—181no—
330C4⋊C4—21no—
331C4⋊C4—21no—
332C4⋊C4—31no—
333C4⋊C4—61no—
334C4⋊C4—61no—
335C4⋊C4—91no—
336C4⋊C4—122no—
337C4⋊C4—181no—
338C4⋊C4—181no—
339C4⋊C4—181no—
340C4⋊C4—181no—
341C22⋊C4—61no—
342C22⋊C4—181no—
343C22⋊C4—181no—
344C22⋊C4—181no—
345C22⋊C4—181no—
346C42—181no—
347C22×C3—21no—
348C22×C3—21no—
349C22×C3—21no—
350C22×C3—21no—
351C22×C3—21no—
352C22×C3—21no—
353C22×C3—21no—
354C22×C3—41no—
355C22×C3—41no—
356C22×C3—121no—
357C22×C3—121no—
358C22×C3—121no—
359C22×C3#91111yescharacteristic
360C22×C3#91211yescharacteristic
361C22×C3#93211yescharacteristic
362C22×C3#93711yescharacteristic
363C22×C3#93711yescharacteristic
364C22×C3#95011yescharacteristic
365C2×D3—41no—
366C2×D3—41no—
367C2×D3—41no—
368C3×C4—22no—
369C3×C4—21no—
370C3×C4—21no—
371C3×C4—21no—
372C3×C4—21no—
373C3×C4—41no—
374C3×C4—82no—
375C3×C4—81no—
376C3×C4—81no—
377C3×C4—122no—
378C3×C4—121no—
379C3×C4—121no—
380C3×C4—121no—
381Dic3—42no—
382Dic3—41no—
383Dic3—41no—
384Dic3—41no—
385Dic3—121no—
386Dic3—121no—
387Dic3—121no—
388Dic3—121no—
389Dic3—241no—
390Dic3—241no—
391C32#160911yescharacteristic, complemented, Sylow
392C23—61no—
393C23D3×#6711yescharacteristic
394Q8—361no—
395D4—121no—
396D4—121no—
397D4—121no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—62no—
403C2×C4—61no—
404C2×C4—61no—
405C2×C4—61no—
406C2×C4—61no—
407C2×C4—61no—
408C2×C4—121no—
409C2×C4—121no—
410C2×C4—121no—
411C2×C4—181no—
412C2×C4—181no—
413C2×C4—721no—
414C2×C4D3×#6711yescharacteristic
415C2×C4#381111yescharacteristic
416C8—121no—
417C8—361no—
418C2×C3—21no—
419C2×C3—21no—
420C2×C3—21no—
421C2×C3—21no—
422C2×C3—21no—
423C2×C3—21no—
424C2×C3—21no—
425C2×C3—41no—
426C2×C3—41no—
427C2×C3—241no—
428C2×C3#503711yescharacteristic
429C2×C3#505311yescharacteristic
430C2×C3#505311yescharacteristic
431C2×C3#509511yescharacteristic
432C2×C3#515811yescharacteristic
433C2×C3#520511yescharacteristic
434D3—81no—
435C22—21no—
436C22—21no—
437C22—121no—
438C22—121no—
439C22—121no—
440C22#6393211yescharacteristic
441C22#6393311yescharacteristic
442C22#6398311yescharacteristic
443C4—21no—
444C4—21no—
445C4—81no—
446C4—122no—
447C4—121no—
448C4—121no—
449C4—121no—
450C4—361no—
451C4—361no—
452C3—21no—
453C3#6971111yescharacteristic, complemented
454C3#7116611yescharacteristic, complemented
455C2—21no—
456C2—21no—
457C2—241no—
458C2#1059139811yescharacteristic
459C2#1059151911yescharacteristic
460C2#1059166111yescharacteristic
subgroupG/H
centerC22#63983
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. #10592670C2semidirect
3. C3×#4983C2semidirect
5. #10589154C2semidirect
7. #10589147C2semidirect
33. #4983D3semidirect
391. C32#1609semidirect
453. C3#69711semidirect
454. C3#71166semidirect

Maximal subgroups

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

subgroupindex
#105949732
#105926702
C3×#49832
C3×#49672
#105891542
#105891492
#105891472
#711663
#697113