Finite Group Databasebeta

← #11775369

Subgroups — #11775369

Order 1152.

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

normal subgroups only

This group has 484 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#10594949C211yesmaximal, characteristic
2C3×#4719C211yesmaximal, characteristic, complemented
3#10591206C211yesmaximal, characteristic, complemented
4#10589333C211yesmaximal, characteristic, complemented
5C3×#4470C211yesmaximal, characteristic
6#10589154C211yesmaximal, characteristic, complemented
7#10589150C211yesmaximal, characteristic
8#70834—31nomaximal
9#68280—31nomaximal
10#64133C2211yescharacteristic
11C3×#930C2211yescharacteristic
12C2×C3×C4×Dic3C2211yescharacteristic
13Dic3×#67—21no—
14C2×Dic3⋊Dic3—21no—
15#63961—21no—
16Dic3×D12C411yescharacteristic, complemented
17#63877—21no—
18#63869C411yescharacteristic, complemented
19#63860C411yescharacteristic, complemented
20#63859—21no—
21#63844C411yescharacteristic, complemented
22C32×C22⋊C8C2211yescharacteristic
23#63658C2211yescharacteristic
24C3×C3⋊#95C2211yescharacteristic
25C3×#830C2211yescharacteristic
26C3×#815—21no—
27C3×Dic3⋊C8—21no—
28#63579—21no—
29#5600—31no—
30#5479—31no—
31C3×#432—31no—
32#4936—31no—
33#4719D311yescharacteristic, complemented
34#4650—31no—
35C3×#327—31no—
36#4537—31no—
37#4470—31no—
38#4470D311yescharacteristic
39#4467—31no—
40#4467—31no—
41#4467—31no—
42#4467—61no—
43#4452—31no—
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3—21no—
46C2×#634C2×C411yescharacteristic
47C2×C3×#67—21no—
48C22×C3×Dic3—21no—
49C22×C3×Dic3D411yescharacteristic
50C22×C3×Dic3D411yescharacteristic
51C2×C3×D12C2×C411yescharacteristic
52C2×D3×Dic3—21no—
53C2×C32×C8—21no—
54#3757—21no—
55C4⋊(C3⋊Dic3)C2×C411yescharacteristic
56#3750—21no—
57C3×(C2×D3)⋊C4—21no—
58C3×C4⋊Dic3C2×C411yescharacteristic
59C3×C4×Dic3C2×C411yescharacteristic
60C3×C4×Dic3C2×C411yescharacteristic
61C3×C4×Dic3D411yescharacteristic
62C3×C4×Dic3D411yescharacteristic
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#1512—91noSylow
73C3×#121—31no—
74C2×C3×C42—31no—
75#936—31no—
76#935—61no—
77D4×Dic3—31no—
78D4×Dic3—61no—
79#930C2×D311yescharacteristic
80#929—61no—
81C4×#67—61no—
82C2×C4⋊Dic3—61no—
83#924—31no—
84#924—31no—
85#924—61no—
86C2×Dic3⋊C4—61no—
87C2×C4×Dic3C2×D311yescharacteristic
88#890—31no—
89#887—31no—
90#879—61no—
91#877—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
119C2×C3⋊Dic3—21no—
120C2×C3⋊Dic3—21no—
121C2×C3⋊Dic3—41no—
122C2×C3⋊Dic3—41no—
123C2×C3⋊Dic3—41no—
124#634—41no—
125C3×#67—41no—
126C3×#67—41no—
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×D12—41no—
139D3×Dic3—42no—
140C32×C8—41no—
141C3×C3⋊C8—41no—
142#529—91no—
143#432—31no—
144#382—91no—
145#328—91no—
146#328—91no—
147#327—31no—
148#327—91no—
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×D12C4×D311yescharacteristic
166C2×C4×D3—61no—
167C2×Dic6—31no—
168C2×Dic6—31no—
169C2×Dic6—61no—
170C2×C3×C8—21no—
171C2×C3×C8—21no—
172C2×C3×C8—41no—
173C2×C3×C8—61no—
174C3×C4⋊C4—31no—
175C3×C22⋊C4—61no—
176C3×C42—31no—
177C3×C42—31no—
178C3×C42—31no—
179C3×C42—31no—
180#217—61no—
181#217—61no—
182#217—61no—
183#217—61no—
184#217—61no—
185#217—121no—
186(C2×D3)⋊C4—21no—
187(C2×D3)⋊C4—61no—
188(C2×D3)⋊C4—61no—
189(C2×D3)⋊C4—61no—
190C4⋊Dic3—31no—
191C4⋊Dic3—31no—
192C4⋊Dic3—61no—
193C4⋊Dic3—61no—
194C4⋊Dic3—122no—
195C4⋊Dic3C4×D311yescharacteristic
196Dic3⋊C4—61no—
197Dic3⋊C4—61no—
198Dic3⋊C4—61no—
199Dic3⋊C4—61no—
200Dic3⋊C4—61no—
201Dic3⋊C4—61no—
202Dic3⋊C4—61no—
203Dic3⋊C4—121no—
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—41no—
224C3⋊Dic3—81no—
225C3×Dic3—21no—
226C3×Dic3—21no—
227C3×Dic3—21no—
228C3×Dic3—21no—
229C3×Dic3—41no—
230C3×Dic3—81no—
231#126—181no—
232#125—91no—
233#124—91no—
234#123—181no—
235C22⋊Q8—91no—
236#121—31no—
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×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—31no—
261C2×C3×C4—31no—
262C2×C3×C4—31no—
263C2×C3×C4—31no—
264C2×C3×C4—41no—
265C2×C3×C4—41no—
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—41no—
279#67—41no—
280C2×Dic3—21no—
281C2×Dic3—21no—
282C2×Dic3—21no—
283C2×Dic3—41no—
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—122no—
299C2×Dic3—121no—
300C2×Dic3—121no—
301C2×Dic3—241no—
302C2×Dic3—241no—
303C2×Dic3(C2×D3)⋊C411yescharacteristic
304C2×Dic3(C2×D3)⋊C411yescharacteristic
305C2×Dic3(C2×D3)⋊C411yescharacteristic
306C2×Dic3(C2×D3)⋊C411yescharacteristic
307D12—41no—
308C4×D3—122no—
309Dic6—121no—
310Dic6—121no—
311Dic6—241no—
312C3×C8—41no—
313C3×C8—41no—
314C3×C8—81no—
315C3×C8—121no—
316C3⋊C8—41no—
317C2×C32—21no—
318C2×C32—21no—
319C2×C32#41011yescharacteristic
320C2×C32#41711yescharacteristic
321C2×C32#42111yescharacteristic
322C3×D3—81no—
323C2×Q8—91no—
324C2×D4—31no—
325C2×D4—61no—
326C22×C4—31no—
327C22×C4—31no—
328C22×C4—61no—
329C22×C4—181no—
330C22×C4—181no—
331C22×C4C2×D3211yescharacteristic
332C2×C8—21no—
333C2×C8—61no—
334C4⋊C4—31no—
335C4⋊C4—91no—
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—31no—
347C42—31no—
348C42—31no—
349C42—31no—
350C42—181no—
351C22×C3—21no—
352C22×C3—21no—
353C22×C3—21no—
354C22×C3—21no—
355C22×C3—21no—
356C22×C3—21no—
357C22×C3—21no—
358C22×C3—41no—
359C22×C3—41no—
360C22×C3—121no—
361C22×C3—121no—
362C22×C3—121no—
363C22×C3D3×C22⋊C411yescharacteristic
364C22×C3#90811yescharacteristic
365C22×C3#90911yescharacteristic
366C22×C3#91111yescharacteristic
367C22×C3#91511yescharacteristic
368C22×C3C2×(C2×D3)⋊C411yescharacteristic
369C2×D3—41no—
370C2×D3—41no—
371C2×D3—41no—
372C3×C4—21no—
373C3×C4—21no—
374C3×C4—21no—
375C3×C4—21no—
376C3×C4—41no—
377C3×C4—41no—
378C3×C4—61no—
379C3×C4—61no—
380C3×C4—61no—
381C3×C4—61no—
382C3×C4—121no—
383C3×C4—241no—
384Dic3—21no—
385Dic3—21no—
386Dic3—21no—
387Dic3—21no—
388Dic3—41no—
389Dic3—81no—
390Dic3—121no—
391Dic3—121no—
392Dic3—121no—
393Dic3—121no—
394Dic3—241no—
395Dic3—241no—
396Dic3—241no—
397Dic3—241no—
398Dic3—242no—
399C32#151211yescharacteristic, complemented, Sylow
400C23—61no—
401C23D3×D1211yescharacteristic
402Q8—361no—
403D4—121no—
404D4—121no—
405D4—121no—
406C2×C4—31no—
407C2×C4—31no—
408C2×C4—31no—
409C2×C4—31no—
410C2×C4—41no—
411C2×C4—61no—
412C2×C4—61no—
413C2×C4—61no—
414C2×C4—121no—
415C2×C4—121no—
416C2×C4—121no—
417C2×C4—121no—
418C2×C4—181no—
419C2×C4—181no—
420C2×C4—362no—
421C2×C4—361no—
422C2×C4—361no—
423C2×C4—361no—
424C2×C4C4×D3211yescharacteristic
425C2×C4D3×#6711yescharacteristic
426C8—41no—
427C8—121no—
428C2×C3—21no—
429C2×C3—21no—
430C2×C3—21no—
431C2×C3—21no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—21no—
435C2×C3—41no—
436C2×C3—41no—
437C2×C3—241no—
438C2×C3#474011yescharacteristic
439C2×C3#477111yescharacteristic
440C2×C3#482111yescharacteristic
441C2×C3#500611yescharacteristic
442C2×C3#513311yescharacteristic
443C2×C3#513911yescharacteristic
444D3—81no—
445C22—21no—
446C22—21no—
447C22—121no—
448C22—121no—
449C22—121no—
450C22#6379511yescharacteristic
451C22#6380011yescharacteristic
452C22D3×(C2×D3)⋊C411yescharacteristic
453C4—21no—
454C4—21no—
455C4—61no—
456C4—61no—
457C4—61no—
458C4—61no—
459C4—121no—
460C4—241no—
461C4—361no—
462C4—361no—
463C4—721no—
464C3—21no—
465C3#6828011yescharacteristic, complemented
466C3#7083411yescharacteristic, complemented
467C2—21no—
468C2—21no—
469C2—241no—
470C2#1059040511yescharacteristic
471C2#1059067011yescharacteristic
472C2#1059100511yescharacteristic
subgroupG/H
centerC22D3×(C2×D3)⋊C4
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32C2×C22⋊C4
prime radicalC3×#930C22
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
4. #10589333C2semidirect
6. #10589154C2semidirect
16. Dic3×D12C4semidirect
18. #63869C4semidirect
19. #63860C4semidirect
21. #63844C4semidirect
33. #4719D3semidirect
399. C32#1512semidirect
465. C3#68280semidirect
466. C3#70834semidirect

Maximal subgroups

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

subgroupindex
#105949492
C3×#47192
#105912062
#105893332
C3×#44702
#105891542
#105891502
#708343
#682803