Finite Group Databasebeta

← #11775367

Subgroups — #11775367

Order 1152.

489 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 489 conjugacy classes of subgroups — too many to draw. Only its 98 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#10594955C211yesmaximal, characteristic
2C3×#4719C211yesmaximal, characteristic, complemented
3#10591206C211yesmaximal, characteristic, complemented
4#10589336C211yesmaximal, characteristic
5C3×#4467C211yesmaximal, characteristic, complemented
6#10589152C211yesmaximal, characteristic, complemented
7#10589151C211yesmaximal, characteristic
8#70834—31nomaximal
9#68312—31nomaximal
10#64139C2211yescharacteristic
11C3×#924C2211yescharacteristic
12C2×C3×C4×Dic3C2211yescharacteristic
13#63966—21no—
14C2×Dic3⋊Dic3—21no—
15#63952—21no—
16#63894C411yescharacteristic, complemented
17#63869C411yescharacteristic, complemented
18#63868—21no—
19#63864C411yescharacteristic, complemented
20Dic3×Dic6C411yescharacteristic, complemented
21#63836—21no—
22C32×C22⋊C8C2211yescharacteristic
23#63658C2211yescharacteristic
24C3×C3⋊#95C2211yescharacteristic
25C3×#830C2211yescharacteristic
26C3×#815—21no—
27C3×Dic3⋊C8—21no—
28#63579—21no—
29#5624—31no—
30#5479—31no—
31C3×#432—31no—
32#4936—31no—
33#4719D311yescharacteristic, complemented
34#4650—31no—
35C3×#328—31no—
36#4538—31no—
37#4470—31no—
38#4470—31no—
39#4470—31no—
40#4470—61no—
41#4467—31no—
42#4467D311yescharacteristic, complemented
43#4451—31no—
44C22×C32×C4C2311yescharacteristic
45C2×#638—21no—
46C22×C3⋊Dic3—21no—
47C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
48C22×C3×Dic3—21no—
49C22×C3×Dic3D411yescharacteristic
50C22×C3×Dic3D411yescharacteristic
51C2×C3×Dic6C2×C411yescharacteristic
52C2×#624—21no—
53C2×C32×C8—21no—
54#3752—21no—
55C4⋊(C3⋊Dic3)C2×C411yescharacteristic
56C3×#217—21no—
57C3×C4⋊Dic3C2×C411yescharacteristic
58C3×Dic3⋊C4—21no—
59C3×C4×Dic3C2×C411yescharacteristic
60C3×C4×Dic3C2×C411yescharacteristic
61C3×C4×Dic3D411yescharacteristic
62C3×C4×Dic3D411yescharacteristic
63C2×C3×C3⋊C8—21no—
64#3724—21no—
65Dic3⋊Dic3—21no—
66Dic3⋊Dic3—21no—
67Dic3⋊Dic3—42no—
68#3722—21no—
69#3722—21no—
70#3722—21no—
71Dic32—21no—
72#1512—91noSylow
73C3×C22⋊Q8—31no—
74C2×C3×C42—31no—
75#947—31no—
76Q8×Dic3—31no—
77#930—31no—
78#930—31no—
79#930—61no—
80#929—61no—
81C4×#67—61no—
82C2×C4⋊Dic3—61no—
83#924C2×D311yescharacteristic
84C2×Dic3⋊C4—61no—
85C2×C4×Dic3C2×D311yescharacteristic
86#898—61no—
87#893—31no—
88#892—61no—
89#890—31no—
90#886—61no—
91#67⋊C4—61no—
92#876—61no—
93#875—31no—
94C4×D12—31no—
95#872—61no—
96#870—31no—
97C4×Dic6—31no—
98C3×C4⋊C8—61no—
99C3×C22⋊C8—21no—
100C3×C22⋊C8—31no—
101C3×C22⋊C8C2×D311yescharacteristic
102C3×C22⋊C8C2×D311yescharacteristic
103C3×#97—61no—
104C3×#95—31no—
105C3⋊#95—31no—
106C3⋊#95—31no—
107C3⋊#95—61no—
108C3⋊#95—61no—
109C3⋊#95—61no—
110C3⋊#95C2×D311yescharacteristic
111#830C2×D311yescharacteristic
112#815—21no—
113Dic3⋊C8—21no—
114C23×C32C2×D411yescharacteristic
115C22×C3⋊D3—21no—
116C2×C32×C4—41no—
117C2×C32×C4C22×C411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119#638—41no—
120#638—41no—
121C2×C3⋊Dic3—21no—
122C2×C3⋊Dic3—41no—
123C2×C3⋊Dic3—41no—
124C2×C3⋊Dic3—41no—
125C4⋊(C3⋊D3)—41no—
126C2×C3×Dic3—21no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—21no—
130C2×C3×Dic3—41no—
131C2×C3×Dic3—41no—
132C2×C3×Dic3—41no—
133C2×C3×Dic3—41no—
134C2×C3×Dic3C22⋊C411yescharacteristic
135C2×C3×Dic3C22⋊C411yescharacteristic
136C2×C3×Dic3C22⋊C411yescharacteristic
137C2×C3×Dic3C22⋊C411yescharacteristic
138C3×Dic6—41no—
139#624—42no—
140C32×C8—41no—
141C3×C3⋊C8—41no—
142#529—91no—
143#432—31no—
144#382—91no—
145#328—31no—
146#328—91no—
147#327—91no—
148#327—91no—
149C2×C3×Q8—31no—
150C22×C3×C4—21no—
151C22×C3×C4—31no—
152C22×C3×C4—31no—
153C22×C3×C4—61no—
154C22×C3×C4C22×D311yescharacteristic
155C22×C3×C4C22×D311yescharacteristic
156C2×#67—61no—
157C2×#67—61no—
158C2×#67—121no—
159C22×Dic3—21no—
160C22×Dic3—61no—
161C22×Dic3—61no—
162C22×Dic3—121no—
163C22×Dic3D1211yescharacteristic
164C22×Dic3D1211yescharacteristic
165C2×D12—31no—
166C2×D12—31no—
167C2×D12—61no—
168C2×C4×D3—61no—
169C2×C4×D3—61no—
170C2×Dic6C4×D311yescharacteristic
171C2×C3×C8—21no—
172C2×C3×C8—21no—
173C2×C3×C8—41no—
174C2×C3×C8—61no—
175C3×C4⋊C4—31no—
176C3×C4⋊C4—61no—
177C3×C22⋊C4—61no—
178C3×C42—31no—
179C3×C42—31no—
180C3×C42—31no—
181C3×C42—31no—
182#217—21no—
183(C2×D3)⋊C4—61no—
184(C2×D3)⋊C4—61no—
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—121no—
192C4⋊Dic3—31no—
193C4⋊Dic3—31no—
194C4⋊Dic3—61no—
195C4⋊Dic3—61no—
196C4⋊Dic3—61no—
197C4⋊Dic3—122no—
198C4⋊Dic3C4×D311yescharacteristic
199Dic3⋊C4—21no—
200Dic3⋊C4—61no—
201Dic3⋊C4—61no—
202Dic3⋊C4—61no—
203Dic3⋊C4—61no—
204Dic3⋊C4—122no—
205C4×Dic3—61no—
206C4×Dic3—61no—
207C4×Dic3C4×D311yescharacteristic
208C4×Dic3C4×D311yescharacteristic
209C4×Dic3#6711yescharacteristic
210C4×Dic3#6711yescharacteristic
211C2×C3⋊C8—21no—
212C22×C32—21no—
213C22×C32—21no—
214C22×C32C2×C22⋊C411yescharacteristic
215C22×C32AGL(1,ℤ/8)11yescharacteristic
216C22×C32#13711yescharacteristic
217C2×C3⋊D3—41no—
218C2×C3⋊D3—41no—
219C2×C3⋊D3—41no—
220C32×C4—21no—
221C32×C4—21no—
222C3⋊Dic3—41no—
223C3⋊Dic3—81no—
224C3×Dic3—21no—
225C3×Dic3—21no—
226C3×Dic3—21no—
227C3×Dic3—21no—
228C3×Dic3—41no—
229C3×Dic3—41no—
230C3×Dic3—81no—
231#126—181no—
232#125—91no—
233#124—91no—
234#123—181no—
235C22⋊Q8—31no—
236#121—91no—
237C4×Q8—91no—
238C4×D4—91no—
239C4×D4—181no—
240#117—181no—
241C2×C4⋊C4—181no—
242C2×C42—31no—
243C4⋊C8—61no—
244C22⋊C8—31no—
245C22⋊C8D3211yescharacteristic
246#97—61no—
247#95—31no—
248#95—91no—
249#95—181no—
250C23×C3—21no—
251C23×C3C2×D1211yescharacteristic
252C23×C3D3×D411yescharacteristic
253C22×D3—61no—
254C22×D3—61no—
255C22×D3—121no—
256C3×Q8—121no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—31no—
260C2×C3×C4—31no—
261C2×C3×C4—31no—
262C2×C3×C4—31no—
263C2×C3×C4—41no—
264C2×C3×C4—41no—
265C2×C3×C4—61no—
266C2×C3×C4—61no—
267C2×C3×C4—61no—
268C2×C3×C4—61no—
269C2×C3×C4—81no—
270C2×C3×C4—121no—
271C2×C3×C4—121no—
272C2×C3×C4—121no—
273C2×C3×C4—121no—
274C2×C3×C4C2×C4×D311yescharacteristic
275C2×C3×C4C2×C4×D311yescharacteristic
276C2×C3×C4D3×D411yescharacteristic
277C2×C3×C4C2×#6711yescharacteristic
278#67—121no—
279#67—121no—
280#67—121no—
281#67—121no—
282#67—241no—
283#67—241no—
284C2×Dic3—21no—
285C2×Dic3—21no—
286C2×Dic3—21no—
287C2×Dic3—21no—
288C2×Dic3—41no—
289C2×Dic3—41no—
290C2×Dic3—41no—
291C2×Dic3—41no—
292C2×Dic3—61no—
293C2×Dic3—61no—
294C2×Dic3—121no—
295C2×Dic3—121no—
296C2×Dic3—121no—
297C2×Dic3—121no—
298C2×Dic3—121no—
299C2×Dic3—122no—
300C2×Dic3—121no—
301C2×Dic3—121no—
302C2×Dic3—241no—
303C2×Dic3—241no—
304C2×Dic3(C2×D3)⋊C411yescharacteristic
305C2×Dic3(C2×D3)⋊C411yescharacteristic
306C2×Dic3(C2×D3)⋊C411yescharacteristic
307C2×Dic3(C2×D3)⋊C411yescharacteristic
308D12—121no—
309D12—121no—
310D12—241no—
311C4×D3—122no—
312C4×D3—122no—
313Dic6—41no—
314C3×C8—41no—
315C3×C8—41no—
316C3×C8—81no—
317C3×C8—121no—
318C3⋊C8—41no—
319C2×C32—21no—
320C2×C32—21no—
321C2×C32#41011yescharacteristic
322C2×C32#41711yescharacteristic
323C2×C32#42111yescharacteristic
324C3⋊D3—81no—
325C2×Q8—31no—
326C2×D4—91no—
327C2×D4—181no—
328C22×C4—31no—
329C22×C4—31no—
330C22×C4—61no—
331C22×C4—181no—
332C22×C4—181no—
333C22×C4C2×D3211yescharacteristic
334C2×C8—21no—
335C2×C8—61no—
336C4⋊C4—31no—
337C4⋊C4—61no—
338C4⋊C4—91no—
339C4⋊C4—181no—
340C4⋊C4—181no—
341C4⋊C4—181no—
342C4⋊C4—362no—
343C22⋊C4—61no—
344C22⋊C4—181no—
345C22⋊C4—181no—
346C22⋊C4—181no—
347C22⋊C4—181no—
348C42—31no—
349C42—31no—
350C42—31no—
351C42—31no—
352C42—181no—
353C22×C3—21no—
354C22×C3—21no—
355C22×C3—21no—
356C22×C3—21no—
357C22×C3—21no—
358C22×C3—21no—
359C22×C3—21no—
360C22×C3—41no—
361C22×C3—41no—
362C22×C3D3×C22⋊C411yescharacteristic
363C22×C3#90811yescharacteristic
364C22×C3#90911yescharacteristic
365C22×C3#91411yescharacteristic
366C22×C3#91811yescharacteristic
367C22×C3C2×(C2×D3)⋊C411yescharacteristic
368C2×D3—121no—
369C2×D3—121no—
370C2×D3—121no—
371C2×D3—121no—
372C2×D3—121no—
373C2×D3—121no—
374C2×D3—241no—
375C2×D3—241no—
376C2×D3—241no—
377C3×C4—21no—
378C3×C4—21no—
379C3×C4—21no—
380C3×C4—21no—
381C3×C4—41no—
382C3×C4—41no—
383C3×C4—61no—
384C3×C4—61no—
385C3×C4—61no—
386C3×C4—61no—
387C3×C4—121no—
388C3×C4—121no—
389C3×C4—241no—
390Dic3—21no—
391Dic3—21no—
392Dic3—21no—
393Dic3—21no—
394Dic3—41no—
395Dic3—41no—
396Dic3—81no—
397Dic3—121no—
398Dic3—121no—
399Dic3—241no—
400Dic3—241no—
401Dic3—241no—
402Dic3—242no—
403C32#151211yescharacteristic, complemented, Sylow
404C23—181no—
405C23D3×D1211yescharacteristic
406Q8—121no—
407D4—361no—
408D4—361no—
409D4—361no—
410C2×C4—31no—
411C2×C4—31no—
412C2×C4—31no—
413C2×C4—31no—
414C2×C4—41no—
415C2×C4—61no—
416C2×C4—61no—
417C2×C4—61no—
418C2×C4—61no—
419C2×C4—121no—
420C2×C4—121no—
421C2×C4—121no—
422C2×C4—121no—
423C2×C4—181no—
424C2×C4—362no—
425C2×C4—361no—
426C2×C4—361no—
427C2×C4—361no—
428C2×C4C4×D3211yescharacteristic
429C2×C4D3×#6711yescharacteristic
430C8—41no—
431C8—121no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—21no—
435C2×C3—21no—
436C2×C3—21no—
437C2×C3—21no—
438C2×C3—21no—
439C2×C3—41no—
440C2×C3—41no—
441C2×C3#474011yescharacteristic
442C2×C3#480311yescharacteristic
443C2×C3#482111yescharacteristic
444C2×C3#500611yescharacteristic
445C2×C3#513311yescharacteristic
446C2×C3#513911yescharacteristic
447D3—241no—
448D3—241no—
449D3—481no—
450C22—21no—
451C22—21no—
452C22—361no—
453C22—361no—
454C22—361no—
455C22#6379411yescharacteristic
456C22#6380111yescharacteristic
457C22D3×(C2×D3)⋊C411yescharacteristic
458C4—21no—
459C4—21no—
460C4—61no—
461C4—61no—
462C4—61no—
463C4—61no—
464C4—121no—
465C4—121no—
466C4—241no—
467C4—361no—
468C4—721no—
469C3—21no—
470C3#6831211yescharacteristic, complemented
471C3#7083411yescharacteristic, complemented
472C2—21no—
473C2—21no—
474C2—721no—
475C2#1059040511yescharacteristic
476C2#1059067111yescharacteristic
477C2#1059100511yescharacteristic
subgroupG/H
centerC22D3×(C2×D3)⋊C4
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32C2×C22⋊C4
prime radical#64139C22
cosocleC22×C32×C4C23
hypercenterC22⋊C8D32
hypocenterC32#1512
LCSG ▷ C2×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×#4719C2semidirect
3. #10591206C2semidirect
5. C3×#4467C2semidirect
6. #10589152C2semidirect
16. #63894C4semidirect
17. #63869C4semidirect
19. #63864C4semidirect
20. Dic3×Dic6C4semidirect
33. #4719D3semidirect
42. #4467D3semidirect
403. C32#1512semidirect
470. C3#68312semidirect
471. C3#70834semidirect

Maximal subgroups

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

subgroupindex
#105949552
C3×#47192
#105912062
#105893362
C3×#44672
#105891522
#105891512
#708343
#683123