Finite Group Databasebeta

← #11778790

Subgroups — #11778790

Order 1152.

549 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 549 conjugacy classes of subgroups — too many to draw. Only its 82 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#10594911C211yesmaximal, characteristic
2#10592434C211yesmaximal, characteristic, complemented
3#10591226C211yesmaximal, characteristic, complemented
4#10591092C211yesmaximal, characteristic, complemented
5C3×#4470C211yesmaximal, characteristic, complemented
6C3×#4469C211yesmaximal, characteristic, complemented
7#10589151C211yesmaximal, characteristic, complemented
8#68299—31nomaximal
9#68137—31nomaximal
10C2×#3804—21no—
11#64139C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C3×#930C2211yescharacteristic
14C2×C3×Dic3⋊C4C2211yescharacteristic
15#63978—21no—
16#63910—21no—
17#63895—21no—
18#63893—21no—
19#63886—21no—
20C32×C22⋊C8C2211yescharacteristic
21#63648—21no—
22#63644—21no—
23C3×C3⋊#95C2211yescharacteristic
24C3×#830C2211yescharacteristic
25#63579—21no—
26#63579—21no—
27#63573—21no—
28#63563—21no—
29#5597—31no—
30#5510—31no—
31#5034—31no—
32#4986—31no—
33#4735—31no—
34#4735—31no—
35#4735—31no—
36#4735—61no—
37#4659—31no—
38C3×#327—31no—
39C3×#324—31no—
40#4470—31no—
41#4470D311yescharacteristic, complemented
42#4469D311yescharacteristic, complemented
43#4451—31no—
44C22×C32×C4C2311yescharacteristic
45C2×#638—21no—
46C22×C3⋊Dic3—21no—
47C2×C4⋊(C3⋊D3)D411yescharacteristic
48C2×C3×#67—21no—
49C22×C3×Dic3—21no—
50C22×C3×Dic3D411yescharacteristic
51C22×C3×Dic3D411yescharacteristic
52C2×C3×D12D411yescharacteristic
53C2×#627—21no—
54C2×#626—21no—
55C2×#626—21no—
56C2×#624—21no—
57#3804—42no—
58#3804—42no—
59C2×D3×Dic3—21no—
60C2×C32×C8—21no—
61#3752—21no—
62C4⋊(C3⋊Dic3)—21no—
63C4⋊(C3⋊Dic3)—21no—
64C4⋊(C3⋊Dic3)D411yescharacteristic
65C3×(C2×D3)⋊C4—21no—
66C3×C4⋊Dic3D411yescharacteristic
67C3×Dic3⋊C4—21no—
68C3×Dic3⋊C4—21no—
69C2×C3×C3⋊C8—21no—
70Dic3⋊Dic3—21no—
71#3722—21no—
72(C2×D3)⋊Dic3—21no—
73#1616—91noSylow
74C2×#237—61no—
75C2×#235—61no—
76C3×#121—31no—
77C2×C3×C4⋊C4—31no—
78#939—61no—
79#939—61no—
80#930—31no—
81#930—31no—
82#930—61no—
83#930—61no—
84#930C2×D311yescharacteristic
85C2×C4⋊Dic3—31no—
86C2×C4⋊Dic3—31no—
87C2×C4⋊Dic3—61no—
88C2×Dic3⋊C4C2×D311yescharacteristic
89#897—61no—
90#897—61no—
91#896—61no—
92#895—61no—
93#895—61no—
94#884—61no—
95#878—61no—
96C3×C22⋊C8—21no—
97C3×C22⋊C8—31no—
98C3×C22⋊C8C2×D311yescharacteristic
99C3×C22⋊C8C2×D311yescharacteristic
100C3×#95—31no—
101#832—61no—
102C3⋊#95—61no—
103C3⋊#95—61no—
104C3⋊#95—61no—
105C3⋊#95—61no—
106C3⋊#95C2×D311yescharacteristic
107#830C2×D311yescharacteristic
108#821—61no—
109#821—61no—
110#821—62no—
111#821—61no—
112#817—61no—
113#817—61no—
114#817—62no—
115#817—61no—
116#808—61no—
117C23×C32C2×D411yescharacteristic
118C22×C3⋊D3—21no—
119C22×C3×D3—21no—
120C2×C32×C4—41no—
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123#638—41no—
124#638—41no—
125C2×C3⋊Dic3—21no—
126C2×C3⋊Dic3—41no—
127C2×C3⋊Dic3—42no—
128C4⋊(C3⋊D3)—41no—
129C3×#67—41no—
130C3×#67—41no—
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—
138C2×C3×Dic3—41no—
139C2×C3×Dic3SD1612yes—
140C3×D12—41no—
141#627—42no—
142#626—42no—
143#626—81no—
144#624—42no—
145D3×Dic3—42no—
146C32×C8—41no—
147C3×C3⋊C8—41no—
148#537—91no—
149#481—91no—
150#481—91no—
151#400—91no—
152#327—31no—
153#327—91no—
154#324—31no—
155C2×C3×D4—31no—
156C2×C3×D4—61no—
157C22×C3×C4—21no—
158C22×C3×C4—31no—
159C22×C3×C4—31no—
160C22×C3×C4—61no—
161C22×C3×C4C22×D311yescharacteristic
162C22×C3×C4C22×D311yescharacteristic
163C2×#67—21no—
164C2×#67—61no—
165C2×#67—61no—
166C2×#67—61no—
167C2×#67—61no—
168C2×#67—121no—
169C22×Dic3—21no—
170C22×Dic3—61no—
171C22×Dic3—61no—
172C22×Dic3—61no—
173C22×Dic3—121no—
174C22×Dic3D1211yescharacteristic
175C22×Dic3D1211yescharacteristic
176#237—122no—
177#237—122no—
178#235—122no—
179#235—122no—
180C2×D12—31no—
181C2×D12—31no—
182C2×D12—61no—
183C2×D12—61no—
184C2×D12—61no—
185C2×D12D1211yescharacteristic
186C2×C4×D3—61no—
187C2×C4×D3—61no—
188C2×C4×D3—61no—
189C2×Dic6—61no—
190C2×Dic6—61no—
191C2×C3×C8—22no—
192C2×C3×C8—21no—
193C2×C3×C8—21no—
194C2×C3×C8—61no—
195C3×C4⋊C4—31no—
196C3×C4⋊C4—61no—
197C3×C4⋊C4—61no—
198C3×C22⋊C4—61no—
199#217—61no—
200(C2×D3)⋊C4—21no—
201(C2×D3)⋊C4—61no—
202(C2×D3)⋊C4—61no—
203(C2×D3)⋊C4—61no—
204(C2×D3)⋊C4—61no—
205(C2×D3)⋊C4—61no—
206(C2×D3)⋊C4—121no—
207C4⋊Dic3—31no—
208C4⋊Dic3—31no—
209C4⋊Dic3—61no—
210C4⋊Dic3—61no—
211C4⋊Dic3—62no—
212C4⋊Dic3—61no—
213C4⋊Dic3—61no—
214C4⋊Dic3—61no—
215C4⋊Dic3—61no—
216C4⋊Dic3—121no—
217C4⋊Dic3D1211yescharacteristic
218Dic3⋊C4—21no—
219Dic3⋊C4—21no—
220Dic3⋊C4—61no—
221C2×C3⋊C8—21no—
222C22×C32—21no—
223C22×C32—21no—
224C22×C32#12011yescharacteristic
225C22×C32C2×SD1611yescharacteristic
226C22×C32AGL(1,ℤ/8)11yescharacteristic
227C2×C3⋊D3—41no—
228C2×C3⋊D3—41no—
229C2×C3⋊D3—41no—
230C2×C3×D3—41no—
231C2×C3×D3—41no—
232C2×C3×D3—41no—
233C32×C4—21no—
234C32×C4—21no—
235C3⋊Dic3—41no—
236C3⋊Dic3—81no—
237C3×Dic3—22no—
238C3×Dic3—41no—
239C3×Dic3—41no—
240C3×Dic3—81no—
241C2×#41—181no—
242C22⋊Q8—181no—
243C22⋊Q8—181no—
244#121—31no—
245#121—91no—
246#121—181no—
247#121—181no—
248#121—181no—
249C2×C4⋊C4—31no—
250C2×C4⋊C4—91no—
251#106—181no—
252#106—181no—
253#102—181no—
254#102—181no—
255C22⋊C8—31no—
256C22⋊C8D3211yescharacteristic
257#95—31no—
258#95—181no—
259#95—181no—
260C23×C3—21no—
261C23×C3—61no—
262C23×C3C2×D1211yescharacteristic
263C23×C3D3×D411yescharacteristic
264C22×D3—21no—
265C22×D3—61no—
266C22×D3—61no—
267C22×D3—121no—
268C3×D4—121no—
269C3×D4—121no—
270C3×D4—121no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—32no—
274C2×C3×C4—41no—
275C2×C3×C4—41no—
276C2×C3×C4—42no—
277C2×C3×C4—61no—
278C2×C3×C4—61no—
279C2×C3×C4—61no—
280C2×C3×C4—61no—
281C2×C3×C4—121no—
282C2×C3×C4—121no—
283C2×C3×C4—121no—
284C2×C3×C4—121no—
285C2×C3×C4C2×D1211yescharacteristic
286C2×C3×C4D3×D411yescharacteristic
287C2×C3×C4D3×D411yescharacteristic
288C2×C3×C4D3×D411yescharacteristic
289#67—41no—
290#67—41no—
291#67—122no—
292#67—121no—
293#67—121no—
294#67—121no—
295#67—121no—
296#67—241no—
297#67—241no—
298#67—241no—
299C2×Dic3—21no—
300C2×Dic3—21no—
301C2×Dic3—21no—
302C2×Dic3—21no—
303C2×Dic3—41no—
304C2×Dic3—41no—
305C2×Dic3—41no—
306C2×Dic3—41no—
307C2×Dic3—61no—
308C2×Dic3—61no—
309C2×Dic3—121no—
310C2×Dic3—122no—
311C2×Dic3—122no—
312C2×Dic3—122no—
313C2×Dic3—122no—
314C2×Dic3—121no—
315C2×Dic3—121no—
316C2×Dic3—242no—
317C2×Dic3#20412yes—
318D12—41no—
319D12—121no—
320D12—121no—
321D12—122no—
322D12—122no—
323D12—241no—
324C4×D3—122no—
325C4×D3—122no—
326C4×D3—122no—
327Dic6—122no—
328Dic6—122no—
329C3×C8—42no—
330C3×C8—41no—
331C3×C8—41no—
332C3×C8—121no—
333C3⋊C8—41no—
334C2×C32—21no—
335C2×C32—21no—
336C2×C32#45011yescharacteristic
337C2×C32#45411yescharacteristic
338C2×C32#45811yescharacteristic
339C3⋊D3—81no—
340C3×D3—81no—
341#41—362no—
342#41—362no—
343C2×Q8—181no—
344C2×D4—31no—
345C2×D4—61no—
346C2×D4—91no—
347C2×D4—181no—
348C2×D4—181no—
349C2×D4—181no—
350C22×C4—31no—
351C22×C4—31no—
352C22×C4—61no—
353C22×C4—181no—
354C22×C4—181no—
355C22×C4—181no—
356C22×C4C2×D3211yescharacteristic
357C2×C8—21no—
358C2×C8—61no—
359C4⋊C4—31no—
360C4⋊C4—61no—
361C4⋊C4—61no—
362C4⋊C4—91no—
363C4⋊C4—181no—
364C4⋊C4—181no—
365C4⋊C4—181no—
366C22⋊C4—61no—
367C22⋊C4—181no—
368C22⋊C4—181no—
369C22⋊C4—181no—
370C22×C3—21no—
371C22×C3—21no—
372C22×C3—21no—
373C22×C3—21no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—21no—
377C22×C3—41no—
378C22×C3—41no—
379C22×C3—121no—
380C22×C3—121no—
381C22×C3—121no—
382C22×C3#88211yescharacteristic
383C22×C3#88211yescharacteristic
384C22×C3C2×#20411yescharacteristic
385C22×C3#90811yescharacteristic
386C22×C3#91111yescharacteristic
387C22×C3D3×SD1611yescharacteristic
388C2×D3—41no—
389C2×D3—41no—
390C2×D3—41no—
391C2×D3—121no—
392C2×D3—121no—
393C2×D3—121no—
394C2×D3—121no—
395C2×D3—121no—
396C2×D3—121no—
397C2×D3—241no—
398C2×D3—241no—
399C2×D3—241no—
400C3×C4—22no—
401C3×C4—21no—
402C3×C4—21no—
403C3×C4—21no—
404C3×C4—21no—
405C3×C4—41no—
406C3×C4—62no—
407C3×C4—121no—
408C3×C4—121no—
409C3×C4—241no—
410Dic3—22no—
411Dic3—41no—
412Dic3—41no—
413Dic3—81no—
414Dic3—121no—
415Dic3—121no—
416Dic3—241no—
417Dic3—242no—
418Dic3—241no—
419Dic3—241no—
420C32#161611yescharacteristic, complemented, Sylow
421C23—61no—
422C23—181no—
423C23D3×D1211yescharacteristic
424Q8—362no—
425D4—121no—
426D4—121no—
427D4—121no—
428D4—361no—
429D4—362no—
430D4—361no—
431D4—361no—
432D4—721no—
433C2×C4—32no—
434C2×C4—41no—
435C2×C4—61no—
436C2×C4—61no—
437C2×C4—61no—
438C2×C4—61no—
439C2×C4—121no—
440C2×C4—121no—
441C2×C4—121no—
442C2×C4—121no—
443C2×C4—181no—
444C2×C4—362no—
445C2×C4—362no—
446C2×C4—362no—
447C2×C4—361no—
448C2×C4D3×D1211yescharacteristic
449C2×C4#381111yescharacteristic
450C8—41no—
451C8—121no—
452C2×C3—21no—
453C2×C3—21no—
454C2×C3—21no—
455C2×C3—21no—
456C2×C3—21no—
457C2×C3—21no—
458C2×C3—21no—
459C2×C3—41no—
460C2×C3—41no—
461C2×C3—241no—
462C2×C3#473111yescharacteristic
463C2×C3#474211yescharacteristic
464C2×C3#474211yescharacteristic
465C2×C3#475311yescharacteristic
466C2×C3#477611yescharacteristic
467C2×C3#482711yescharacteristic
468D3—81no—
469D3—241no—
470D3—241no—
471D3—481no—
472C22—21no—
473C22—21no—
474C22—121no—
475C22—121no—
476C22—121no—
477C22—361no—
478C22—361no—
479C22—361no—
480C22D3×#20411yescharacteristic
481C22#6379511yescharacteristic
482C22#6392311yescharacteristic
483C4—21no—
484C4—21no—
485C4—62no—
486C4—121no—
487C4—121no—
488C4—241no—
489C4—361no—
490C4—721no—
491C3—21no—
492C3#6813711yescharacteristic, complemented
493C3#6829911yescharacteristic, complemented
494C2—21no—
495C2—21no—
496C2—241no—
497C2—721no—
498C2#1059040911yescharacteristic
499C2#1059094611yescharacteristic
500C2#1059102211yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32#120
prime radical#10594911C2
hypercenterC22⋊C8D32
hypocenterC32#1616
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. #10592434C2semidirect
3. #10591226C2semidirect
4. #10591092C2semidirect
5. C3×#4470C2semidirect
6. C3×#4469C2semidirect
7. #10589151C2semidirect
41. #4470D3semidirect
42. #4469D3semidirect
420. C32#1616semidirect
492. C3#68137semidirect
493. C3#68299semidirect

Maximal subgroups

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

subgroupindex
#105949112
#105924342
#105912262
#105910922
C3×#44702
C3×#44692
#105891512
#682993
#681373