Finite Group Databasebeta

← #11778534

Subgroups — #11778534

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#10592420C211yesmaximal, characteristic, complemented
3#10591353C211yesmaximal, characteristic, complemented
4#10591094C211yesmaximal, characteristic
5C3×#4470C211yesmaximal, characteristic
6C3×#4469C211yesmaximal, characteristic, complemented
7#10589154C211yesmaximal, characteristic, complemented
8#68296—31nomaximal
9#68134—31nomaximal
10C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
11#64133C2211yescharacteristic
12C3×#930C2211yescharacteristic
13C2×C3×Dic3⋊C4C2211yescharacteristic
14Dic3×#67—21no—
15C2×Dic3⋊Dic3—21no—
16#63961—21no—
17#63896—21no—
18#63884—21no—
19#63861—21no—
20#63847—21no—
21C32×C22⋊C8C2211yescharacteristic
22#63644—21no—
23#63643—21no—
24C3×C3⋊#95C2211yescharacteristic
25C3×#830C2211yescharacteristic
26#63579—21no—
27#63575—21no—
28#63563—21no—
29#5602—31no—
30#5515—31no—
31#5033—31no—
32#4981—31no—
33#4736—31no—
34#4721—31no—
35#4721—31no—
36#4721—61no—
37#4661—31no—
38C3×#327—31no—
39C3×#324—31no—
40#4470D311yescharacteristic
41#4469D311yescharacteristic, complemented
42#4467—31no—
43#4452—31no—
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3—21no—
46C2×#634D411yescharacteristic
47C2×C3×#67—21no—
48C22×C3×Dic3—21no—
49C22×C3×Dic3D411yescharacteristic
50C22×C3×Dic3D411yescharacteristic
51C2×C3×D12D411yescharacteristic
52C2×D3×Dic3—21no—
53C2×C32×C8—21no—
54#3757—21no—
55C4⋊(C3⋊Dic3)—21no—
56C4⋊(C3⋊Dic3)—21no—
57C4⋊(C3⋊Dic3)D411yescharacteristic
58#3750—21no—
59C3×(C2×D3)⋊C4—21no—
60C3×C4⋊Dic3D411yescharacteristic
61C3×Dic3⋊C4—21no—
62C3×Dic3⋊C4—21no—
63C2×C3×C3⋊C8—21no—
64#3724—21no—
65#3724—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×#121—31no—
74C2×C3×C4⋊C4—31no—
75#935—61no—
76#935—61no—
77D4×Dic3—61no—
78#930C2×D311yescharacteristic
79#929—61no—
80C4×#67—61no—
81C2×C4⋊Dic3—31no—
82C2×C4⋊Dic3—31no—
83C2×C4⋊Dic3—61no—
84C2×C4⋊Dic3—61no—
85#924—31no—
86#924—31no—
87#924—61no—
88C2×Dic3⋊C4—61no—
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×C22⋊C8—21no—
98C3×C22⋊C8—31no—
99C3×C22⋊C8C2×D311yescharacteristic
100C3×C22⋊C8C2×D311yescharacteristic
101C3×#95—31no—
102#832—61no—
103C3⋊#95—61no—
104C3⋊#95—61no—
105C3⋊#95C2×D311yescharacteristic
106#830C2×D311yescharacteristic
107#821—61no—
108#818—61no—
109#817—61no—
110#817—61no—
111#817—62no—
112#816—61no—
113#816—61no—
114#816—62no—
115#807—61no—
116C23×C32C2×D411yescharacteristic
117C22×C3×D3—21no—
118C2×C32×C4—41no—
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C3⋊Dic3—21no—
122C2×C3⋊Dic3—21no—
123C2×C3⋊Dic3—41no—
124C2×C3⋊Dic3—41no—
125C2×C3⋊Dic3—41no—
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—
140C32×C8—41no—
141C3×C3⋊C8—41no—
142#539—91no—
143#483—91no—
144#480—91no—
145#398—91no—
146#328—91no—
147#327—31no—
148#324—31no—
149C2×C3×D4—31no—
150C2×C3×D4—61no—
151C22×C3×C4—21no—
152C22×C3×C4—31no—
153C22×C3×C4—31no—
154C22×C3×C4—61no—
155C22×C3×C4C22×D311yescharacteristic
156C22×C3×C4C22×D311yescharacteristic
157C2×#67—21no—
158C22×Dic3—21no—
159C22×Dic3—61no—
160C22×Dic3—61no—
161C22×Dic3—61no—
162C22×Dic3—121no—
163C22×Dic3D1211yescharacteristic
164C22×Dic3D1211yescharacteristic
165C2×D12D1211yescharacteristic
166C2×C4×D3—61no—
167C2×Dic6—31no—
168C2×Dic6—31no—
169C2×Dic6—61no—
170C2×C3×C8—22no—
171C2×C3×C8—21no—
172C2×C3×C8—21no—
173C2×C3×C8—61no—
174C3×C4⋊C4—31no—
175C3×C4⋊C4—61no—
176C3×C4⋊C4—61no—
177C3×C22⋊C4—61no—
178#217—61no—
179#217—61no—
180#217—61no—
181#217—61no—
182#217—61no—
183#217—121no—
184(C2×D3)⋊C4—21no—
185(C2×D3)⋊C4—61no—
186(C2×D3)⋊C4—61no—
187(C2×D3)⋊C4—61no—
188C4⋊Dic3—31no—
189C4⋊Dic3—31no—
190C4⋊Dic3—61no—
191C4⋊Dic3—61no—
192C4⋊Dic3—62no—
193C4⋊Dic3—61no—
194C4⋊Dic3—61no—
195C4⋊Dic3—61no—
196C4⋊Dic3—61no—
197C4⋊Dic3—121no—
198C4⋊Dic3—122no—
199C4⋊Dic3D1211yescharacteristic
200Dic3⋊C4—21no—
201Dic3⋊C4—21no—
202Dic3⋊C4—61no—
203Dic3⋊C4—61no—
204Dic3⋊C4—61no—
205Dic3⋊C4—61no—
206Dic3⋊C4—61no—
207Dic3⋊C4—61no—
208Dic3⋊C4—61no—
209Dic3⋊C4—121no—
210Dic3⋊C4—122no—
211C4×Dic3—61no—
212C4×Dic3—61no—
213C2×C3⋊C8—21no—
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—
224C3⋊Dic3—41no—
225C3⋊Dic3—41no—
226C3⋊Dic3—81no—
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—91no—
241C2×C4⋊C4—181no—
242#107—181no—
243#106—181no—
244#103—181no—
245#102—181no—
246C22⋊C8—31no—
247C22⋊C8D3211yescharacteristic
248#95—31no—
249#95—181no—
250C23×C3—21no—
251C23×C3—61no—
252C23×C3C2×D1211yescharacteristic
253C23×C3D3×D411yescharacteristic
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—62no—
264C2×C3×C4—61no—
265C2×C3×C4—61no—
266C2×C3×C4—61no—
267C2×C3×C4—61no—
268C2×C3×C4—61no—
269C2×C3×C4—121no—
270C2×C3×C4—121no—
271C2×C3×C4—121no—
272C2×C3×C4C2×D1211yescharacteristic
273C2×C3×C4D3×D411yescharacteristic
274C2×C3×C4D3×D411yescharacteristic
275C2×C3×C4D3×D411yescharacteristic
276#67—41no—
277#67—41no—
278C2×Dic3—22no—
279C2×Dic3—21no—
280C2×Dic3—21no—
281C2×Dic3—21no—
282C2×Dic3—21no—
283C2×Dic3—21no—
284C2×Dic3—41no—
285C2×Dic3—41no—
286C2×Dic3—41no—
287C2×Dic3—61no—
288C2×Dic3—61no—
289C2×Dic3—61no—
290C2×Dic3—61no—
291C2×Dic3—121no—
292C2×Dic3—121no—
293C2×Dic3—122no—
294C2×Dic3—121no—
295C2×Dic3—121no—
296C2×Dic3—121no—
297C2×Dic3—121no—
298C2×Dic3—121no—
299C2×Dic3—121no—
300C2×Dic3—241no—
301C2×Dic3—241no—
302C2×Dic3—241no—
303D12—41no—
304C4×D3—241no—
305Dic6—121no—
306Dic6—121no—
307Dic6—122no—
308C3×C8—42no—
309C3×C8—41no—
310C3×C8—41no—
311C3×C8—121no—
312C3⋊C8—41no—
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—31no—
323C22×C4—31no—
324C22×C4—61no—
325C22×C4—181no—
326C22×C4—181no—
327C22×C4C2×D3211yescharacteristic
328C2×C8—21no—
329C2×C8—61no—
330C4⋊C4—31no—
331C4⋊C4—61no—
332C4⋊C4—61no—
333C4⋊C4—91no—
334C4⋊C4—181no—
335C4⋊C4—181no—
336C4⋊C4—181no—
337C4⋊C4—181no—
338C4⋊C4—181no—
339C4⋊C4—181no—
340C4⋊C4—362no—
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#88211yescharacteristic
360C22×C3#88211yescharacteristic
361C22×C3#90411yescharacteristic
362C22×C3#90811yescharacteristic
363C22×C3#91111yescharacteristic
364C22×C3#91611yescharacteristic
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—122no—
375C3×C4—121no—
376C3×C4—121no—
377C3×C4—121no—
378Dic3—42no—
379Dic3—41no—
380Dic3—41no—
381Dic3—41no—
382Dic3—121no—
383Dic3—121no—
384Dic3—121no—
385Dic3—121no—
386Dic3—241no—
387Dic3—241no—
388Dic3—242no—
389Dic3—241no—
390Dic3—241no—
391C32#160911yescharacteristic, complemented, Sylow
392C23—61no—
393C23D3×D1211yescharacteristic
394Q8—361no—
395D4—121no—
396D4—121no—
397D4—121no—
398C2×C4—41no—
399C2×C4—62no—
400C2×C4—61no—
401C2×C4—61no—
402C2×C4—61no—
403C2×C4—61no—
404C2×C4—61no—
405C2×C4—121no—
406C2×C4—121no—
407C2×C4—121no—
408C2×C4—181no—
409C2×C4—181no—
410C2×C4—361no—
411C2×C4—361no—
412C2×C4—361no—
413C2×C4—721no—
414C2×C4D3×D1211yescharacteristic
415C2×C4#381111yescharacteristic
416C8—41no—
417C8—121no—
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#473411yescharacteristic
429C2×C3#474211yescharacteristic
430C2×C3#474211yescharacteristic
431C2×C3#475211yescharacteristic
432C2×C3#478111yescharacteristic
433C2×C3#482611yescharacteristic
434D3—81no—
435C22—21no—
436C22—21no—
437C22—121no—
438C22—121no—
439C22—121no—
440C22#6379511yescharacteristic
441C22#6380611yescharacteristic
442C22#6392311yescharacteristic
443C4—21no—
444C4—21no—
445C4—122no—
446C4—121no—
447C4—121no—
448C4—121no—
449C4—361no—
450C4—361no—
451C4—721no—
452C3—21no—
453C3#6813411yescharacteristic, complemented
454C3#6829611yescharacteristic, complemented
455C2—21no—
456C2—21no—
457C2—241no—
458C2#1059040911yescharacteristic
459C2#1059096811yescharacteristic
460C2#1059102111yescharacteristic
subgroupG/H
centerC22#63923
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. #10592420C2semidirect
3. #10591353C2semidirect
6. C3×#4469C2semidirect
7. #10589154C2semidirect
41. #4469D3semidirect
391. C32#1609semidirect
453. C3#68134semidirect
454. C3#68296semidirect

Maximal subgroups

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

subgroupindex
#105949732
#105924202
#105913532
#105910942
C3×#44702
C3×#44692
#105891542
#682963
#681343