Finite Group Databasebeta

← #11778792

Subgroups — #11778792

Order 1152.

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

normal subgroups only

This group has 537 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
2C3×#4735C211yesmaximal, characteristic, complemented
3#10591225C211yesmaximal, characteristic, complemented
4#10591125C211yesmaximal, characteristic, complemented
5#10589336C211yesmaximal, characteristic, complemented
6C3×#4469C211yesmaximal, characteristic, complemented
7#10589150C211yesmaximal, characteristic, complemented
8#71171—31nomaximal
9#68137—31nomaximal
10C2×#3804—21no—
11#64139C2211yescharacteristic
12C3×#930C2211yescharacteristic
13C2×C3×C4⋊Dic3C2211yescharacteristic
14C2×C3×Dic3⋊C4C2211yescharacteristic
15#63978—21no—
16#63910—21no—
17#63895—21no—
18#63893—21no—
19#63886—21no—
20C32×C22⋊C8C2211yescharacteristic
21#63658C2211yescharacteristic
22C3×#830C2211yescharacteristic
23C3×#821—21no—
24C3×#817—21no—
25#63579—21no—
26#63579—21no—
27#63573—21no—
28#63564—21no—
29#5597—31no—
30#5510—31no—
31C3×#481—31no—
32#4986—31no—
33#4985—31no—
34#4968—31no—
35#4735—31no—
36#4735D311yescharacteristic, complemented
37C3×#324—31no—
38#4537—31no—
39#4470—31no—
40#4470—31no—
41#4470—31no—
42#4470—61no—
43#4469D311yescharacteristic, complemented
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)D411yescharacteristic
63C3×(C2×D3)⋊C4—21no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3—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—
78C2×C3×C4⋊C4—31no—
79#939—61no—
80#939—61no—
81#930—31no—
82#930—31no—
83#930—61no—
84#930—61no—
85#930C2×D311yescharacteristic
86C2×C4⋊Dic3C2×D311yescharacteristic
87C2×Dic3⋊C4C2×D311yescharacteristic
88#897—61no—
89#897—61no—
90#896—61no—
91#895—61no—
92#895—61no—
93#884—61no—
94#878—61no—
95C3×#106—61no—
96C3×#102—61no—
97C3×C22⋊C8—21no—
98C3×C22⋊C8—31no—
99C3×C22⋊C8C2×D311yescharacteristic
100C3×C22⋊C8C2×D311yescharacteristic
101C3⋊#95—31no—
102C3⋊#95—31no—
103C3⋊#95—61no—
104C3⋊#95—61no—
105C3⋊#95—61no—
106C3⋊#95—61no—
107C3⋊#95—61no—
108#830C2×D311yescharacteristic
109#821—21no—
110#821—61no—
111#817—21no—
112#817—61no—
113#809—61no—
114#808—61no—
115C23×C32C2×D411yescharacteristic
116C22×C3⋊D3—21no—
117C22×C3×D3—21no—
118C2×C32×C4—41no—
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121#638—41no—
122#638—41no—
123C2×C3⋊Dic3—21no—
124C2×C3⋊Dic3—41no—
125C2×C3⋊Dic3—41no—
126C2×C3⋊Dic3—41no—
127C4⋊(C3⋊D3)—41no—
128C3×#67—41no—
129C3×#67—41no—
130C2×C3×Dic3—21no—
131C2×C3×Dic3—21no—
132C2×C3×Dic3—21no—
133C2×C3×Dic3—21no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3—42no—
136C2×C3×Dic3—41no—
137C2×C3×Dic3SD1612yes—
138C3×D12—41no—
139#627—42no—
140#626—42no—
141#626—81no—
142#624—42no—
143D3×Dic3—42no—
144C32×C8—41no—
145C3×C3⋊C8—41no—
146#537—91no—
147#481—31no—
148#481—91no—
149#400—91no—
150#327—91no—
151#327—91no—
152#324—31no—
153C2×C3×D4—31no—
154C2×C3×D4—61no—
155C22×C3×C4—21no—
156C22×C3×C4—31no—
157C22×C3×C4—31no—
158C22×C3×C4—61no—
159C22×C3×C4C22×D311yescharacteristic
160C22×C3×C4C22×D311yescharacteristic
161C2×#67—21no—
162C2×#67—61no—
163C2×#67—61no—
164C2×#67—61no—
165C2×#67—61no—
166C2×#67—121no—
167C22×Dic3—21no—
168C22×Dic3—61no—
169C22×Dic3—61no—
170C22×Dic3—61no—
171C22×Dic3—121no—
172C22×Dic3D1211yescharacteristic
173C22×Dic3D1211yescharacteristic
174#237—122no—
175#237—122no—
176#235—122no—
177#235—122no—
178C2×D12—31no—
179C2×D12—31no—
180C2×D12—61no—
181C2×D12—61no—
182C2×D12—61no—
183C2×D12#6711yescharacteristic
184C2×C4×D3—61no—
185C2×C4×D3—61no—
186C2×C4×D3—61no—
187C2×Dic6—61no—
188C2×Dic6—61no—
189C2×C3×C8—21no—
190C2×C3×C8—21no—
191C2×C3×C8—41no—
192C2×C3×C8—61no—
193C3×C4⋊C4—31no—
194C3×C4⋊C4—61no—
195C3×C4⋊C4—61no—
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—21no—
208C4⋊Dic3—21no—
209C4⋊Dic3—31no—
210C4⋊Dic3—31no—
211C4⋊Dic3—61no—
212C4⋊Dic3—61no—
213C4⋊Dic3#6711yescharacteristic
214Dic3⋊C4—21no—
215Dic3⋊C4—21no—
216Dic3⋊C4—61no—
217C2×C3⋊C8—21no—
218C22×C32—21no—
219C22×C32—21no—
220C22×C32#12011yescharacteristic
221C22×C32C2×SD1611yescharacteristic
222C22×C32AGL(1,ℤ/8)11yescharacteristic
223C2×C3⋊D3—41no—
224C2×C3⋊D3—41no—
225C2×C3⋊D3—41no—
226C2×C3×D3—41no—
227C2×C3×D3—41no—
228C2×C3×D3—41no—
229C32×C4—21no—
230C32×C4—21no—
231C3⋊Dic3—41no—
232C3⋊Dic3—81no—
233C3×Dic3—22no—
234C3×Dic3—41no—
235C3×Dic3—41no—
236C3×Dic3—81no—
237C2×#41—181no—
238C22⋊Q8—181no—
239C22⋊Q8—181no—
240#121—31no—
241#121—91no—
242#121—181no—
243#121—181no—
244#121—181no—
245C2×C4⋊C4—31no—
246C2×C4⋊C4—31no—
247#106—61no—
248#106—181no—
249#102—61no—
250#102—181no—
251C22⋊C8—31no—
252C22⋊C8D3211yescharacteristic
253#95—91no—
254#95—181no—
255#95—181no—
256C23×C3—21no—
257C23×C3—61no—
258C23×C3C2×D1211yescharacteristic
259C23×C3D3×D411yescharacteristic
260C22×D3—21no—
261C22×D3—61no—
262C22×D3—61no—
263C22×D3—121no—
264C3×D4—121no—
265C3×D4—121no—
266C3×D4—121no—
267C2×C3×C4—21no—
268C2×C3×C4—21no—
269C2×C3×C4—32no—
270C2×C3×C4—41no—
271C2×C3×C4—41no—
272C2×C3×C4—61no—
273C2×C3×C4—61no—
274C2×C3×C4—61no—
275C2×C3×C4—61no—
276C2×C3×C4—81no—
277C2×C3×C4—121no—
278C2×C3×C4—122no—
279C2×C3×C4—121no—
280C2×C3×C4D3×D411yescharacteristic
281C2×C3×C4D3×D411yescharacteristic
282C2×C3×C4D3×D411yescharacteristic
283C2×C3×C4C2×#6711yescharacteristic
284#67—41no—
285#67—41no—
286#67—122no—
287#67—121no—
288#67—121no—
289#67—121no—
290#67—121no—
291#67—241no—
292#67—241no—
293#67—241no—
294C2×Dic3—21no—
295C2×Dic3—21no—
296C2×Dic3—21no—
297C2×Dic3—21no—
298C2×Dic3—41no—
299C2×Dic3—42no—
300C2×Dic3—41no—
301C2×Dic3—61no—
302C2×Dic3—61no—
303C2×Dic3—121no—
304C2×Dic3—122no—
305C2×Dic3—121no—
306C2×Dic3—121no—
307C2×Dic3—121no—
308C2×Dic3—121no—
309C2×Dic3—122no—
310C2×Dic3—121no—
311C2×Dic3—121no—
312C2×Dic3—241no—
313C2×Dic3—241no—
314C2×Dic3#20412yes—
315D12—41no—
316D12—121no—
317D12—121no—
318D12—122no—
319D12—241no—
320D12—241no—
321C4×D3—122no—
322C4×D3—122no—
323C4×D3—122no—
324Dic6—122no—
325Dic6—122no—
326C3×C8—41no—
327C3×C8—41no—
328C3×C8—81no—
329C3×C8—121no—
330C3⋊C8—41no—
331C2×C32—21no—
332C2×C32—21no—
333C2×C32#45011yescharacteristic
334C2×C32#45411yescharacteristic
335C2×C32#45811yescharacteristic
336C3⋊D3—81no—
337C3×D3—81no—
338#41—362no—
339#41—362no—
340C2×Q8—181no—
341C2×D4—31no—
342C2×D4—61no—
343C2×D4—91no—
344C2×D4—181no—
345C2×D4—181no—
346C2×D4—181no—
347C22×C4—31no—
348C22×C4—31no—
349C22×C4—61no—
350C22×C4—181no—
351C22×C4—181no—
352C22×C4—181no—
353C22×C4C2×D3211yescharacteristic
354C2×C8—21no—
355C2×C8—61no—
356C4⋊C4—31no—
357C4⋊C4—61no—
358C4⋊C4—61no—
359C4⋊C4—61no—
360C4⋊C4—61no—
361C4⋊C4—91no—
362C4⋊C4—181no—
363C22⋊C4—61no—
364C22⋊C4—181no—
365C22⋊C4—181no—
366C22⋊C4—181no—
367C22×C3—21no—
368C22×C3—21no—
369C22×C3—21no—
370C22×C3—21no—
371C22×C3—21no—
372C22×C3—21no—
373C22×C3—21no—
374C22×C3—41no—
375C22×C3—41no—
376C22×C3—121no—
377C22×C3—121no—
378C22×C3—121no—
379C22×C3#88211yescharacteristic
380C22×C3C2×#20411yescharacteristic
381C22×C3#90811yescharacteristic
382C22×C3D3×SD1611yescharacteristic
383C22×C3#91411yescharacteristic
384C22×C3#93711yescharacteristic
385C2×D3—41no—
386C2×D3—41no—
387C2×D3—41no—
388C2×D3—121no—
389C2×D3—121no—
390C2×D3—121no—
391C2×D3—121no—
392C2×D3—121no—
393C2×D3—121no—
394C2×D3—241no—
395C2×D3—241no—
396C2×D3—241no—
397C3×C4—21no—
398C3×C4—21no—
399C3×C4—21no—
400C3×C4—21no—
401C3×C4—41no—
402C3×C4—41no—
403C3×C4—62no—
404C3×C4—121no—
405C3×C4—121no—
406C3×C4—241no—
407Dic3—22no—
408Dic3—41no—
409Dic3—41no—
410Dic3—81no—
411Dic3—121no—
412Dic3—121no—
413Dic3—241no—
414Dic3—241no—
415Dic3—241no—
416Dic3—242no—
417C32#161611yescharacteristic, complemented, Sylow
418C23—61no—
419C23—181no—
420C23D3×D1211yescharacteristic
421Q8—362no—
422D4—121no—
423D4—121no—
424D4—121no—
425D4—361no—
426D4—362no—
427D4—361no—
428D4—361no—
429D4—721no—
430C2×C4—32no—
431C2×C4—41no—
432C2×C4—61no—
433C2×C4—61no—
434C2×C4—61no—
435C2×C4—61no—
436C2×C4—121no—
437C2×C4—122no—
438C2×C4—121no—
439C2×C4—181no—
440C2×C4—362no—
441C2×C4—362no—
442C2×C4—361no—
443C2×C4—361no—
444C2×C4—361no—
445C2×C4#380211yescharacteristic
446C2×C4D3×#6711yescharacteristic
447C8—41no—
448C8—121no—
449C2×C3—21no—
450C2×C3—21no—
451C2×C3—21no—
452C2×C3—21no—
453C2×C3—21no—
454C2×C3—21no—
455C2×C3—21no—
456C2×C3—41no—
457C2×C3—41no—
458C2×C3—241no—
459C2×C3#473111yescharacteristic
460C2×C3#474211yescharacteristic
461C2×C3#475311yescharacteristic
462C2×C3#505311yescharacteristic
463C2×C3#516911yescharacteristic
464C2×C3#520111yescharacteristic
465D3—81no—
466D3—241no—
467D3—241no—
468D3—481no—
469C22—21no—
470C22—21no—
471C22—121no—
472C22—121no—
473C22—121no—
474C22—361no—
475C22—361no—
476C22—361no—
477C22D3×#20411yescharacteristic
478C22#6379411yescharacteristic
479C22#6392211yescharacteristic
480C4—21no—
481C4—21no—
482C4—62no—
483C4—121no—
484C4—121no—
485C4—241no—
486C4—361no—
487C4—721no—
488C3—21no—
489C3#6813711yescharacteristic, complemented
490C3#7117111yescharacteristic, complemented
491C2—21no—
492C2—21no—
493C2—241no—
494C2—721no—
495C2#1059040811yescharacteristic
496C2#1059094211yescharacteristic
497C2#1059102011yescharacteristic
subgroupG/H
centerC22#63922
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. C3×#4735C2semidirect
3. #10591225C2semidirect
4. #10591125C2semidirect
5. #10589336C2semidirect
6. C3×#4469C2semidirect
7. #10589150C2semidirect
36. #4735D3semidirect
43. #4469D3semidirect
417. C32#1616semidirect
489. C3#68137semidirect
490. C3#71171semidirect

Maximal subgroups

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

subgroupindex
#105949112
C3×#47352
#105912252
#105911252
#105893362
C3×#44692
#105891502
#711713
#681373