Finite Group Databasebeta

← #11775360

Subgroups — #11775360

Order 1152.

521 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 521 conjugacy classes of subgroups — too many to draw. Only its 90 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#10594965C211yesmaximal, characteristic
2#10592349C211yesmaximal, characteristic, complemented
3#10591066C211yesmaximal, characteristic, complemented
4C3×#4452C211yesmaximal, characteristic, complemented
5C3×#4451C211yesmaximal, characteristic
6#10589152C211yesmaximal, characteristic, complemented
7#10589150C211yesmaximal, characteristic
8#68312—31nomaximal
9#68280—31nomaximal
10C2×#3750—21no—
11C2×C4×C3⋊Dic3C2211yescharacteristic
12C3×#930C2211yescharacteristic
13C3×#924C2211yescharacteristic
14#67⋊Dic3—21no—
15#63962—21no—
16#63898C411yescharacteristic, complemented
17#63878—21no—
18#63872C411yescharacteristic, complemented
19#63863C411yescharacteristic, complemented
20#63862—21no—
21#63843C411yescharacteristic, complemented
22C32×#95C2211yescharacteristic
23#63658—21no—
24#63658C2211yescharacteristic
25C3×#830C2211yescharacteristic
26C3×#830C2211yescharacteristic
27#63572—21no—
28#63555—21no—
29#5624—31no—
30#5600—31no—
31#4719—31no—
32#4719—31no—
33#4650—31no—
34#4650—31no—
35#4650—61no—
36C3×#328—31no—
37C3×#327—31no—
38#4538—31no—
39#4537—31no—
40#4470—31no—
41#4467—31no—
42#4452D311yescharacteristic, complemented
43#4451D311yescharacteristic
44C22×C32×C4—21no—
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3—21no—
47C22×C3⋊Dic3D411yescharacteristic
48C22×C3⋊Dic3D411yescharacteristic
49C2×C3×#67—21no—
50C2×C3×D12C2×C411yescharacteristic
51C2×C3×Dic6C2×C411yescharacteristic
52C2×D3×Dic3—21no—
53#3750—42no—
54C4×C3⋊Dic3C2×C411yescharacteristic
55C4×C3⋊Dic3C2×C411yescharacteristic
56C4×C3⋊Dic3D411yescharacteristic
57C4×C3⋊Dic3D411yescharacteristic
58C3×#217—21no—
59C3×(C2×D3)⋊C4—21no—
60C3×C4⋊Dic3C2×C411yescharacteristic
61C3×C4⋊Dic3C2×C411yescharacteristic
62C3×Dic3⋊C4—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65Dic3⋊Dic3—21no—
66Dic3⋊Dic3—21no—
67Dic3⋊Dic3—21no—
68(C2×D3)⋊Dic3—21no—
69(C2×D3)⋊Dic3—21no—
70(C2×D3)⋊Dic3—21no—
71Dic32—21no—
72#1512—91noSylow
73C3×C22⋊Q8—31no—
74C3×#121—31no—
75#947—31no—
76Q8×Dic3—31no—
77#936—31no—
78#935—61no—
79D4×Dic3—31no—
80D4×Dic3—61no—
81#930C2×D311yescharacteristic
82#924C2×D311yescharacteristic
83C2×Dic3⋊C4—61no—
84C2×Dic3⋊C4—61no—
85C2×Dic3⋊C4—62no—
86C2×C4×Dic3—31no—
87C2×C4×Dic3—31no—
88C2×C4×Dic3—61no—
89#898—61no—
90#893—31no—
91#892—61no—
92#890—31no—
93#890—31no—
94#887—31no—
95#886—61no—
96#67⋊C4—61no—
97#879—61no—
98#877—61no—
99C3×C22⋊C8—31no—
100C3×C22⋊C8—31no—
101C3×#95—21no—
102C3×#95C2×D311yescharacteristic
103C3×#95C2×D311yescharacteristic
104C3⋊#95—31no—
105C3⋊#95—31no—
106C3⋊#95—61no—
107C3⋊#95—61no—
108C3⋊#95—61no—
109C3⋊#95—62no—
110#830C2×D311yescharacteristic
111#830C2×D311yescharacteristic
112#815—61no—
113#815—61no—
114Dic3⋊C8—61no—
115Dic3⋊C8—61no—
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×C4C22×C411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C3⋊Dic3—21no—
125C2×C3⋊Dic3—21no—
126C2×C3⋊Dic3—41no—
127C2×C3⋊Dic3—41no—
128C2×C3⋊Dic3—41no—
129C2×C3⋊Dic3—41no—
130C2×C3⋊Dic3C22⋊C411yescharacteristic
131C2×C3⋊Dic3C22⋊C411yescharacteristic
132C2×C3⋊Dic3C22⋊C411yescharacteristic
133C2×C3⋊Dic3C22⋊C411yescharacteristic
134C3×#67—41no—
135C3×#67—41no—
136C2×C3×Dic3—21no—
137C2×C3×Dic3—21no—
138C2×C3×Dic3—21no—
139C3×D12—41no—
140C3×Dic6—41no—
141D3×Dic3—42no—
142C3×C3⋊C8—41no—
143C3×C3⋊C8—41no—
144#529—91no—
145#432—91no—
146#382—91no—
147#328—31no—
148#328—91no—
149#327—31no—
150#327—91no—
151C2×C3×Q8—31no—
152C2×C3×D4—31no—
153C2×C3×D4—61no—
154C22×C3×C4—22no—
155C22×C3×C4—21no—
156C22×C3×C4—21no—
157C22×C3×C4—21no—
158C22×C3×C4C22×D311yescharacteristic
159C22×C3×C4C22×D311yescharacteristic
160C2×#67—21no—
161C22×Dic3—31no—
162C22×Dic3—31no—
163C22×Dic3—31no—
164C22×Dic3—31no—
165C22×Dic3—61no—
166C22×Dic3—61no—
167C22×Dic3—61no—
168C22×Dic3—62no—
169C22×Dic3—61no—
170C22×Dic3—61no—
171C2×D12C4×D311yescharacteristic
172C2×C4×D3—61no—
173C2×Dic6C4×D311yescharacteristic
174C2×C3×C8—61no—
175C2×C3×C8—61no—
176C3×C4⋊C4—31no—
177C3×C4⋊C4—31no—
178C3×C4⋊C4—61no—
179C3×C22⋊C4—61no—
180C3×C22⋊C4—61no—
181#217—21no—
182#217—61no—
183#217—61no—
184#217—61no—
185(C2×D3)⋊C4—21no—
186(C2×D3)⋊C4—61no—
187(C2×D3)⋊C4—61no—
188(C2×D3)⋊C4—61no—
189C4⋊Dic3—61no—
190C4⋊Dic3—61no—
191C4⋊Dic3—61no—
192C4⋊Dic3C4×D311yescharacteristic
193C4⋊Dic3C4×D311yescharacteristic
194Dic3⋊C4—21no—
195Dic3⋊C4—61no—
196Dic3⋊C4—61no—
197Dic3⋊C4—61no—
198Dic3⋊C4—124no—
199Dic3⋊C4—122no—
200Dic3⋊C4—122no—
201C4×Dic3—31no—
202C4×Dic3—31no—
203C4×Dic3—31no—
204C4×Dic3—31no—
205C4×Dic3—31no—
206C4×Dic3—31no—
207C4×Dic3—31no—
208C4×Dic3—31no—
209C4×Dic3—61no—
210C4×Dic3—61no—
211C4×Dic3—61no—
212C4×Dic3—61no—
213C4×Dic3—61no—
214C4×Dic3—61no—
215C2×C3⋊C8—21no—
216C2×C3⋊C8—21no—
217C22×C32—21no—
218C22×C32—21no—
219C22×C32C2×C22⋊C411yescharacteristic
220C22×C32AGL(1,ℤ/8)11yescharacteristic
221C22×C32#13711yescharacteristic
222C2×C3×D3—41no—
223C2×C3×D3—41no—
224C2×C3×D3—41no—
225C32×C4—21no—
226C32×C4—21no—
227C32×C4—81no—
228C3⋊Dic3—21no—
229C3⋊Dic3—21no—
230C3⋊Dic3—21no—
231C3⋊Dic3—21no—
232C3⋊Dic3—81no—
233C3×Dic3—41no—
234C3×Dic3—41no—
235C3×Dic3—41no—
236#126—181no—
237#125—91no—
238#124—91no—
239#123—181no—
240C22⋊Q8—31no—
241#121—31no—
242C4×Q8—91no—
243C4×D4—91no—
244C4×D4—181no—
245#117—181no—
246C2×C4⋊C4—181no—
247C2×C42—91no—
248C4⋊C8—181no—
249C22⋊C8—31no—
250C22⋊C8—31no—
251#97—181no—
252#95—91no—
253#95—181no—
254#95D3211yescharacteristic
255C23×C3—21no—
256C23×C3—61no—
257C23×C3D3×D411yescharacteristic
258C23×C3D3×D411yescharacteristic
259C22×D3—21no—
260C3×Q8—121no—
261C3×D4—121no—
262C3×D4—121no—
263C3×D4—121no—
264C2×C3×C4—21no—
265C2×C3×C4—21no—
266C2×C3×C4—41no—
267C2×C3×C4—41no—
268C2×C3×C4—42no—
269C2×C3×C4—42no—
270C2×C3×C4—42no—
271C2×C3×C4—42no—
272C2×C3×C4—41no—
273C2×C3×C4—41no—
274C2×C3×C4—41no—
275C2×C3×C4—41no—
276C2×C3×C4—41no—
277C2×C3×C4—41no—
278C2×C3×C4—61no—
279C2×C3×C4—61no—
280C2×C3×C4—61no—
281C2×C3×C4C2×C4×D311yescharacteristic
282C2×C3×C4C2×C4×D311yescharacteristic
283C2×C3×C4D3×D411yescharacteristic
284C2×C3×C4D3×D411yescharacteristic
285#67—41no—
286#67—41no—
287C2×Dic3—21no—
288C2×Dic3—21no—
289C2×Dic3—21no—
290C2×Dic3—31no—
291C2×Dic3—31no—
292C2×Dic3—31no—
293C2×Dic3—31no—
294C2×Dic3—31no—
295C2×Dic3—31no—
296C2×Dic3—31no—
297C2×Dic3—31no—
298C2×Dic3—61no—
299C2×Dic3—61no—
300C2×Dic3—61no—
301C2×Dic3—61no—
302C2×Dic3—62no—
303C2×Dic3—62no—
304C2×Dic3—61no—
305C2×Dic3—61no—
306C2×Dic3—61no—
307C2×Dic3—61no—
308C2×Dic3—122no—
309C2×Dic3—121no—
310C2×Dic3—121no—
311C2×Dic3—122no—
312C2×Dic3—122no—
313C2×Dic3—122no—
314C2×Dic3—122no—
315C2×Dic3—121no—
316C2×Dic3—121no—
317C2×Dic3—121no—
318C2×Dic3—121no—
319C2×Dic3—121no—
320C2×Dic3—121no—
321D12—41no—
322C4×D3—122no—
323Dic6—41no—
324C3×C8—121no—
325C3×C8—121no—
326C3⋊C8—41no—
327C3⋊C8—41no—
328C2×C32—21no—
329C2×C32—21no—
330C2×C32#41011yescharacteristic
331C2×C32#41711yescharacteristic
332C2×C32#42111yescharacteristic
333C3×D3—81no—
334C2×Q8—31no—
335C2×D4—31no—
336C2×D4—61no—
337C22×C4—21no—
338C22×C4—91no—
339C22×C4—91no—
340C22×C4—181no—
341C22×C4—181no—
342C22×C4C2×D3211yescharacteristic
343C2×C8—61no—
344C2×C8—61no—
345C4⋊C4—31no—
346C4⋊C4—31no—
347C4⋊C4—61no—
348C4⋊C4—181no—
349C4⋊C4—181no—
350C4⋊C4—181no—
351C4⋊C4—362no—
352C22⋊C4—61no—
353C22⋊C4—61no—
354C22⋊C4—181no—
355C22⋊C4—181no—
356C22⋊C4—181no—
357C42—91no—
358C42—91no—
359C42—91no—
360C42—91no—
361C42—181no—
362C22×C3—22no—
363C22×C3—22no—
364C22×C3—21no—
365C22×C3—21no—
366C22×C3—21no—
367C22×C3—21no—
368C22×C3—21no—
369C22×C3—21no—
370C22×C3—21no—
371C22×C3—121no—
372C22×C3—121no—
373C22×C3—121no—
374C22×C3D3×C22⋊C411yescharacteristic
375C22×C3D3×C22⋊C411yescharacteristic
376C22×C3#91111yescharacteristic
377C22×C3#91411yescharacteristic
378C22×C3#91511yescharacteristic
379C22×C3#91811yescharacteristic
380C2×D3—41no—
381C2×D3—41no—
382C2×D3—41no—
383C3×C4—21no—
384C3×C4—21no—
385C3×C4—21no—
386C3×C4—21no—
387C3×C4—41no—
388C3×C4—41no—
389C3×C4—82no—
390C3×C4—81no—
391C3×C4—81no—
392C3×C4—121no—
393C3×C4—121no—
394C3×C4—121no—
395Dic3—41no—
396Dic3—41no—
397Dic3—41no—
398Dic3—62no—
399Dic3—62no—
400Dic3—61no—
401Dic3—61no—
402Dic3—61no—
403Dic3—61no—
404Dic3—61no—
405Dic3—61no—
406Dic3—61no—
407Dic3—61no—
408Dic3—121no—
409Dic3—121no—
410Dic3—242no—
411Dic3—241no—
412Dic3—241no—
413C32#151211yescharacteristic, complemented, Sylow
414C23—61no—
415C23#381111yescharacteristic
416Q8—121no—
417D4—121no—
418D4—121no—
419D4—121no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—61no—
425C2×C4—61no—
426C2×C4—61no—
427C2×C4—91no—
428C2×C4—91no—
429C2×C4—91no—
430C2×C4—91no—
431C2×C4—181no—
432C2×C4—181no—
433C2×C4—362no—
434C2×C4—361no—
435C2×C4—361no—
436C2×C4—361no—
437C2×C4—361no—
438C2×C4C4×D3211yescharacteristic
439C2×C4#380211yescharacteristic
440C8—121no—
441C8—121no—
442C2×C3—22no—
443C2×C3—22no—
444C2×C3—21no—
445C2×C3—21no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3—21no—
450C2×C3—21no—
451C2×C3—241no—
452C2×C3#474011yescharacteristic
453C2×C3#474011yescharacteristic
454C2×C3#477111yescharacteristic
455C2×C3#480311yescharacteristic
456C2×C3#482111yescharacteristic
457C2×C3#482111yescharacteristic
458D3—81no—
459C22—21no—
460C22—21no—
461C22—121no—
462C22—121no—
463C22—121no—
464C22#6392111yescharacteristic
465C22#6393711yescharacteristic
466C22#6395111yescharacteristic
467C4—21no—
468C4—21no—
469C4—81no—
470C4—121no—
471C4—121no—
472C4—121no—
473C4—181no—
474C4—181no—
475C4—181no—
476C4—181no—
477C4—721no—
478C3—21no—
479C3#6828011yescharacteristic, complemented
480C3#6831211yescharacteristic, complemented
481C2—21no—
482C2—21no—
483C2—241no—
484C2#1059039411yescharacteristic
485C2#1059040611yescharacteristic
486C2#1059061211yescharacteristic
subgroupG/H
centerC22#63921
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#95C22
socleC22×C32C2×C22⋊C4
prime radicalC3×#930C22
cosocleC22×C32×C4C23
hypercenter#95D32
hypocenterC32#1512
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #10592349C2semidirect
3. #10591066C2semidirect
4. C3×#4452C2semidirect
6. #10589152C2semidirect
16. #63898C4semidirect
18. #63872C4semidirect
19. #63863C4semidirect
21. #63843C4semidirect
42. #4452D3semidirect
413. C32#1512semidirect
479. C3#68280semidirect
480. C3#68312semidirect

Maximal subgroups

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

subgroupindex
#105949652
#105923492
#105910662
C3×#44522
C3×#44512
#105891522
#105891502
#683123
#682803