Finite Group Databasebeta

← #11778514

Subgroups — #11778514

Order 1152.

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

normal subgroups only

This group has 489 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#10594980C211yesmaximal, characteristic
2#10592666C211yesmaximal, characteristic
3C3×#4983C211yesmaximal, characteristic, complemented
4C3×#4971C211yesmaximal, characteristic, complemented
5#10589153C211yesmaximal, characteristic, complemented
6#10589151C211yesmaximal, characteristic
7#10589147C211yesmaximal, characteristic, complemented
8#71174—31nomaximal
9#69711—31nomaximal
10C2×C32×C4⋊C4C2211yescharacteristic
11#64139C2211yescharacteristic
12C3×#924C2211yescharacteristic
13C2×C3×Dic3⋊C4—21no—
14C2×C3×Dic3⋊C4C2211yescharacteristic
15#63966—21no—
16#63952—21no—
17#63897—21no—
18#63888—21no—
19#63848—21no—
20#63845—21no—
21#63657C2211yescharacteristic
22#63636—21no—
23#63634—21no—
24C3×C3⋊#95—21no—
25C3×C3⋊#95C2211yescharacteristic
26C3×#830C2211yescharacteristic
27C3×#810—21no—
28C3×#808—21no—
29#5645—31no—
30#5515—31no—
31C3×#483—31no—
32C3×#398—31no—
33#4983D311yescharacteristic, complemented
34#4971D311yescharacteristic, complemented
35#4967—31no—
36#4967—31no—
37#4967—61no—
38#4538—31no—
39#4528—31no—
40#4470—31no—
41#4469—31no—
42#4452—31no—
43#4451—31no—
44C22×C32×C4—21no—
45C22×C32×C4C2311yescharacteristic
46C2×#638—21no—
47C2×C4⋊(C3⋊D3)D411yescharacteristic
48C22×C3×Dic3—21no—
49C22×C3×Dic3D411yescharacteristic
50C22×C3×Dic3D411yescharacteristic
51C2×C3×Dic6D411yescharacteristic
52C2×#624—21no—
53C32×C4⋊C4—21no—
54C32×C4⋊C4—21no—
55#3752—21no—
56C4⋊(C3⋊Dic3)D411yescharacteristic
57C2×C3⋊(C3⋊C8)—21no—
58C3×#217—21no—
59C3×C4⋊Dic3D411yescharacteristic
60C3×Dic3⋊C4—21no—
61C3×Dic3⋊C4—21no—
62C3×Dic3⋊C4—21no—
63C3×Dic3⋊C4—42no—
64C2×C3×C3⋊C8—21no—
65#3724—21no—
66Dic3⋊Dic3—21no—
67Dic3⋊Dic3—21no—
68#3722—21no—
69#3722—21no—
70#3722—21no—
71Dic32—21no—
72#1609—91noSylow
73C3×C22⋊Q8—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#946—61no—
80#930—31no—
81#930—31no—
82#930—61no—
83#929—61no—
84C4×#67—61no—
85#924C2×D311yescharacteristic
86C2×Dic3⋊C4—21no—
87C2×Dic3⋊C4C2×D311yescharacteristic
88#898—61no—
89#898—61no—
90#896—61no—
91#894—61no—
92#894—61no—
93#890—61no—
94#889—61no—
95#886—61no—
96#67⋊C4—61no—
97C3×#106—61no—
98C3×#103—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—21no—
109#809—61no—
110#809—61no—
111#809—62no—
112#808—21no—
113#807—61no—
114#807—61no—
115#807—62no—
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
124#638—41no—
125#638—41no—
126C2×C3⋊Dic3—21no—
127C4⋊(C3⋊D3)—41no—
128C2×C3×Dic3—22no—
129C2×C3×Dic3—21no—
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×Dic6—41no—
139#624—81no—
140C3⋊(C3⋊C8)—41no—
141C3×C3⋊C8—41no—
142#539—91no—
143#483—31no—
144#480—91no—
145#398—31no—
146#328—91no—
147#327—91no—
148#324—91no—
149C2×C3×Q8—31no—
150C22×C3×C4—21no—
151C22×C3×C4—21no—
152C22×C3×C4—21no—
153C22×C3×C4—31no—
154C22×C3×C4—31no—
155C22×C3×C4—41no—
156C22×C3×C4—61no—
157C22×C3×C4C22×D311yescharacteristic
158C22×C3×C4C22×D311yescharacteristic
159C2×#67—61no—
160C2×#67—61no—
161C2×#67—121no—
162C22×Dic3—21no—
163C22×Dic3#6711yescharacteristic
164C22×Dic3#6711yescharacteristic
165C2×D12—31no—
166C2×D12—31no—
167C2×D12—61no—
168C2×C4×D3—61no—
169C2×C4×D3—61no—
170C2×Dic6#6711yescharacteristic
171C2×C3×C8—61no—
172C3×C4⋊C4—22no—
173C3×C4⋊C4—21no—
174C3×C4⋊C4—21no—
175C3×C4⋊C4—21no—
176C3×C4⋊C4—21no—
177C3×C4⋊C4—31no—
178C3×C4⋊C4—41no—
179C3×C4⋊C4—61no—
180C3×C4⋊C4—61no—
181C3×C4⋊C4—61no—
182C3×C4⋊C4—122no—
183C3×C22⋊C4—61no—
184#217—21no—
185(C2×D3)⋊C4—61no—
186(C2×D3)⋊C4—61no—
187(C2×D3)⋊C4—61no—
188(C2×D3)⋊C4—61no—
189(C2×D3)⋊C4—61no—
190(C2×D3)⋊C4—61no—
191(C2×D3)⋊C4—61no—
192(C2×D3)⋊C4—61no—
193(C2×D3)⋊C4—121no—
194C4⋊Dic3—31no—
195C4⋊Dic3—31no—
196C4⋊Dic3—61no—
197C4⋊Dic3—61no—
198C4⋊Dic3—61no—
199C4⋊Dic3#6711yescharacteristic
200Dic3⋊C4—21no—
201Dic3⋊C4—21no—
202Dic3⋊C4—21no—
203Dic3⋊C4—42no—
204Dic3⋊C4—61no—
205Dic3⋊C4—61no—
206Dic3⋊C4—61no—
207Dic3⋊C4—61no—
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—42no—
227C3×Dic3—41no—
228C3×Dic3—41no—
229C3×Dic3—41no—
230C3×Dic3—41no—
231#126—181no—
232#125—181no—
233#123—181no—
234#123—181no—
235C22⋊Q8—31no—
236C22⋊Q8—181no—
237#121—91no—
238C4×D4—181no—
239C2×C4⋊C4—31no—
240C2×C4⋊C4—61no—
241C2×C4⋊C4D3211yescharacteristic
242#107—181no—
243#106—61no—
244#103—61no—
245#102—181no—
246C22⋊C8—31no—
247C22⋊C8—91no—
248#95—31no—
249#95—61no—
250C23×C3—21no—
251C23×C3D3×D411yescharacteristic
252C23×C3C2×#6711yescharacteristic
253C22×D3—61no—
254C22×D3—61no—
255C22×D3—121no—
256C3×Q8—121no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—41no—
260C2×C3×C4—41no—
261C2×C3×C4—42no—
262C2×C3×C4—42no—
263C2×C3×C4—41no—
264C2×C3×C4—41no—
265C2×C3×C4—41no—
266C2×C3×C4—41no—
267C2×C3×C4—41no—
268C2×C3×C4—41no—
269C2×C3×C4—62no—
270C2×C3×C4—61no—
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—121no—
286#67—121no—
287#67—121no—
288#67—121no—
289#67—241no—
290#67—241no—
291C2×Dic3—22no—
292C2×Dic3—21no—
293C2×Dic3—21no—
294C2×Dic3—21no—
295C2×Dic3—21no—
296C2×Dic3—21no—
297C2×Dic3—21no—
298C2×Dic3—41no—
299C2×Dic3—41no—
300C2×Dic3—41no—
301C2×Dic3—61no—
302C2×Dic3—61no—
303C2×Dic3—121no—
304D12—121no—
305D12—121no—
306D12—122no—
307C4×D3—241no—
308C4×D3—241no—
309Dic6—41no—
310C3×C8—121no—
311C3⋊C8—41no—
312C3⋊C8—122no—
313C3⋊C8—121no—
314C3⋊C8—121no—
315C2×C32—21no—
316C2×C32—21no—
317C2×C32#44911yescharacteristic
318C2×C32#45611yescharacteristic
319C2×C32#45811yescharacteristic
320C3⋊D3—81no—
321C2×Q8—31no—
322C2×D4—91no—
323C2×D4—181no—
324C22×C4—21no—
325C22×C4—31no—
326C22×C4—31no—
327C22×C4—61no—
328C22×C4—181no—
329C22×C4C2×D3211yescharacteristic
330C2×C8—61no—
331C2×C8—181no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—31no—
335C4⋊C4—61no—
336C4⋊C4—61no—
337C4⋊C4—61no—
338C4⋊C4—91no—
339C4⋊C4—122no—
340C4⋊C4—181no—
341C4⋊C4—181no—
342C4⋊C4—181no—
343C22⋊C4—61no—
344C22⋊C4—181no—
345C22⋊C4—181no—
346C22⋊C4—181no—
347C22⋊C4—181no—
348C42—181no—
349C22×C3—21no—
350C22×C3—21no—
351C22×C3—21no—
352C22×C3—21no—
353C22×C3—21no—
354C22×C3—21no—
355C22×C3—21no—
356C22×C3—41no—
357C22×C3—41no—
358C22×C3#91411yescharacteristic
359C22×C3#91611yescharacteristic
360C22×C3#93211yescharacteristic
361C22×C3#93711yescharacteristic
362C22×C3#93711yescharacteristic
363C22×C3#95011yescharacteristic
364C2×D3—121no—
365C2×D3—121no—
366C2×D3—121no—
367C2×D3—121no—
368C2×D3—121no—
369C2×D3—121no—
370C2×D3—241no—
371C2×D3—241no—
372C2×D3—241no—
373C3×C4—22no—
374C3×C4—21no—
375C3×C4—21no—
376C3×C4—21no—
377C3×C4—21no—
378C3×C4—41no—
379C3×C4—82no—
380C3×C4—81no—
381C3×C4—81no—
382C3×C4—122no—
383C3×C4—121no—
384C3×C4—121no—
385C3×C4—121no—
386C3×C4—121no—
387Dic3—42no—
388Dic3—41no—
389Dic3—41no—
390Dic3—41no—
391Dic3—41no—
392Dic3—121no—
393Dic3—121no—
394Dic3—241no—
395C32#160911yescharacteristic, complemented, Sylow
396C23—181no—
397C23D3×#6711yescharacteristic
398Q8—121no—
399D4—361no—
400D4—361no—
401D4—361no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—62no—
407C2×C4—61no—
408C2×C4—61no—
409C2×C4—61no—
410C2×C4—61no—
411C2×C4—61no—
412C2×C4—61no—
413C2×C4—121no—
414C2×C4—121no—
415C2×C4—121no—
416C2×C4—181no—
417C2×C4—721no—
418C2×C4D3×#6711yescharacteristic
419C2×C4#381111yescharacteristic
420C8—121no—
421C8—361no—
422C2×C3—21no—
423C2×C3—21no—
424C2×C3—21no—
425C2×C3—21no—
426C2×C3—21no—
427C2×C3—21no—
428C2×C3—21no—
429C2×C3—41no—
430C2×C3—41no—
431C2×C3#503711yescharacteristic
432C2×C3#505311yescharacteristic
433C2×C3#505311yescharacteristic
434C2×C3#509511yescharacteristic
435C2×C3#517211yescharacteristic
436C2×C3#520511yescharacteristic
437D3—241no—
438D3—241no—
439D3—481no—
440C22—21no—
441C22—21no—
442C22—361no—
443C22—361no—
444C22—361no—
445C22#6393411yescharacteristic
446C22#6393511yescharacteristic
447C22#6398311yescharacteristic
448C4—21no—
449C4—21no—
450C4—81no—
451C4—122no—
452C4—121no—
453C4—121no—
454C4—121no—
455C4—121no—
456C4—361no—
457C3—21no—
458C3#6971111yescharacteristic, complemented
459C3#7117411yescharacteristic, complemented
460C2—21no—
461C2—21no—
462C2—721no—
463C2#1059139811yescharacteristic
464C2#1059152111yescharacteristic
465C2#1059166111yescharacteristic
subgroupG/H
centerC22#63983
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#120
prime radical#64139C22
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
3. C3×#4983C2semidirect
4. C3×#4971C2semidirect
5. #10589153C2semidirect
7. #10589147C2semidirect
33. #4983D3semidirect
34. #4971D3semidirect
395. C32#1609semidirect
458. C3#69711semidirect
459. C3#71174semidirect

Maximal subgroups

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

subgroupindex
#105949802
#105926662
C3×#49832
C3×#49712
#105891532
#105891512
#105891472
#711743
#697113