Finite Group Databasebeta

← #11774840

Subgroups — #11774840

Order 1152.

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

normal subgroups only

This group has 495 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#10593875C211yesmaximal, characteristic
2#10592536C211yesmaximal, characteristic, complemented
3#10590297C211yesmaximal, characteristic, complemented
4C3×#4484C211yesmaximal, characteristic, complemented
5C3×#4483C211yesmaximal, characteristic, complemented
6#10589084C211yesmaximal, characteristic, complemented
7#10589081C211yesmaximal, characteristic, complemented
8#68242—31nomaximal
9#68178—31nomaximal
10C2×#3743—21no—
11C42×C3⋊D3C2211yescharacteristic
12C3×C4×D12C2211yescharacteristic
13C3×C4×Dic6C2211yescharacteristic
14#63916C411yescharacteristic
15C4×#626—21no—
16#63872C411yescharacteristic
17#63871C411yescharacteristic
18#63863C411yescharacteristic
19#63862—21no—
20#63855—21no—
21#63853—21no—
22C32×C4⋊C8C2211yescharacteristic
23#63641—21no—
24C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
25C3×C4×C3⋊C8C2211yescharacteristic
26C3×C4×C3⋊C8C2211yescharacteristic
27#63572—21no—
28#63557—21no—
29#5580—31no—
30#5557—31no—
31#4837—31no—
32#4837—31no—
33#4837—61no—
34#4685—31no—
35#4685—31no—
36C3×Q8⋊C8—31no—
37C3×D4⋊C8—31no—
38#4535—31no—
39D4⋊(C3⋊C8)—31no—
40#4484D311yescharacteristic, complemented
41#4483D311yescharacteristic, complemented
42#4459—31no—
43#4456—31no—
44C2×C4×C3⋊D3C2×C411yescharacteristic
45C2×C4×C3⋊D3D411yescharacteristic
46C2×C4×C3⋊D3D411yescharacteristic
47C2×C3×D12C2×C411yescharacteristic
48C2×C3×C4×D3—21no—
49C2×C3×Dic6C2×C411yescharacteristic
50C2×#626—21no—
51C2×C32×C8—21no—
52C32×C42C2311yescharacteristic
53C4×C3⋊Dic3C2×C411yescharacteristic
54C4×C3⋊Dic3D411yescharacteristic
55C4×C3⋊Dic3D411yescharacteristic
56C2×C3⋊(C3⋊C8)—21no—
57#3743—42no—
58C3×(C2×D3)⋊C4—21no—
59C3×C4⋊Dic3C2×C411yescharacteristic
60C3×C4⋊Dic3C2×C411yescharacteristic
61C3×Dic3⋊C4—21no—
62C3×C4×Dic3—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65Dic3⋊Dic3—21no—
66Dic3⋊Dic3—21no—
67Dic3⋊Dic3—21no—
68#3722—21no—
69(C2×D3)⋊Dic3—21no—
70(C2×D3)⋊Dic3—21no—
71(C2×D3)⋊Dic3—21no—
72#1495—91noSylow
73C3×C4×Q8—31no—
74C3×C4×D4—31no—
75#947—31no—
76#946—31no—
77#938—31no—
78#936—31no—
79C4×#67—61no—
80#926—61no—
81C2×ΓL(1,𝔽25)—61no—
82C2×ΓL(1,𝔽25)—61no—
83C2×ΓL(1,𝔽25)—62no—
84#898—61no—
85#897—31no—
86#895—31no—
87#894—61no—
88#890—31no—
89#890—31no—
90#883—61no—
91#879—61no—
92C4×D12—61no—
93C4×D12C2×D311yescharacteristic
94#872—61no—
95C42×D3—31no—
96C42×D3—31no—
97C42×D3—61no—
98C4×Dic6C2×D311yescharacteristic
99C3×C4⋊C8—21no—
100C3×C4⋊C8C2×D311yescharacteristic
101C3×C4⋊C8C2×D311yescharacteristic
102C3×C4×C8—31no—
103C3×C4×C8—31no—
104(C2×D3)⋊C8—61no—
105(C2×D3)⋊C8—61no—
106Dic3⋊C8—61no—
107Dic3⋊C8—61no—
108Dic3⋊C8—61no—
109Dic3⋊C8—61no—
110Dic3⋊C8—62no—
111C4⋊(C3⋊C8)—31no—
112C4⋊(C3⋊C8)—31no—
113C4⋊(C3⋊C8)—61no—
114C4×C3⋊C8C2×D311yescharacteristic
115C4×C3⋊C8C2×D311yescharacteristic
116C22×C3⋊D3C22⋊C411yescharacteristic
117C22×C3×D3—21no—
118C2×C32×C4C22×C411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C3⋊Dic3C22⋊C411yescharacteristic
122C2×C3⋊Dic3C22⋊C411yescharacteristic
123C2×C3⋊Dic3C22⋊C411yescharacteristic
124C4×C3⋊D3—21no—
125C4×C3⋊D3—21no—
126C4×C3⋊D3—21no—
127C4×C3⋊D3—21no—
128C4×C3⋊D3—41no—
129C2×C3×Dic3—21no—
130C2×C3×Dic3—21no—
131C2×C3×Dic3—21no—
132C3×D12—21no—
133C3×D12—21no—
134C3×C4×D3—41no—
135C3×C4×D3—41no—
136C3×Dic6—21no—
137C3×Dic6—21no—
138#626—42no—
139C32×C8—41no—
140C3⋊(C3⋊C8)—41no—
141C3×C3⋊C8—41no—
142C3×C3⋊C8—41no—
143#529—91no—
144#431—91no—
145#423—91no—
146Q8⋊C8—31no—
147Q8⋊C8—91no—
148D4⋊C8—31no—
149D4⋊C8—91no—
150C2×C3×Q8—31no—
151C2×C3×D4—31no—
152C22×C3×C4—61no—
153C2×#67—61no—
154C2×D12—61no—
155C2×D12C4×D311yescharacteristic
156C2×C4×D3—21no—
157C2×C4×D3—31no—
158C2×C4×D3—31no—
159C2×C4×D3—31no—
160C2×C4×D3—31no—
161C2×C4×D3—31no—
162C2×C4×D3—31no—
163C2×C4×D3—61no—
164C2×C4×D3—61no—
165C2×C4×D3—61no—
166C2×Dic6C4×D311yescharacteristic
167C2×C3×C8—22no—
168C2×C3×C8—21no—
169C2×C3×C8—21no—
170C2×C3×C8—61no—
171C2×C3×C8—61no—
172C3×C4⋊C4—31no—
173C3×C4⋊C4—31no—
174C3×C4⋊C4—61no—
175C3×C22⋊C4—61no—
176C3×C42—21no—
177C3×C42—61no—
178C3×C42C22×D311yescharacteristic
179C3×C42C22×D311yescharacteristic
180#217—61no—
181#217—61no—
182#217—61no—
183(C2×D3)⋊C4—21no—
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—
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—
198C4×Dic3—21no—
199C4×Dic3—31no—
200C4×Dic3—31no—
201C4×Dic3—31no—
202C4×Dic3—31no—
203C4×Dic3—31no—
204C4×Dic3—31no—
205C4×Dic3—61no—
206C4×Dic3—61no—
207C4×Dic3—61no—
208C2×C3⋊C8—21no—
209C2×C3⋊C8—21no—
210C2×C3⋊C8—62no—
211C2×C3⋊C8—61no—
212C2×C3⋊C8—61no—
213ΓL(1,𝔽25)—124no—
214ΓL(1,𝔽25)—122no—
215ΓL(1,𝔽25)—122no—
216C22×C32C2×C22⋊C411yescharacteristic
217C2×C3⋊D3—21no—
218C2×C3⋊D3—21no—
219C2×C3⋊D3—21no—
220C2×C3×D3—41no—
221C2×C3×D3—41no—
222C2×C3×D3—41no—
223C32×C4—21no—
224C32×C4#13111yescharacteristic
225C32×C4#13111yescharacteristic
226C32×C4AGL(1,ℤ/8)11yescharacteristic
227C32×C4#13711yescharacteristic
228C3⋊Dic3—21no—
229C3⋊Dic3—21no—
230C3⋊Dic3—21no—
231C3×Dic3—41no—
232C3×Dic3—41no—
233C3×Dic3—41no—
234C2×M16—181no—
235#126—181no—
236#125—91no—
237#124—91no—
238#123—181no—
239C22⋊Q8—91no—
240#121—91no—
241C4×Q8—31no—
242C4×D4—31no—
243C4×D4—181no—
244#117—181no—
245C2×C42—91no—
246C4⋊C8—91no—
247C4⋊C8—181no—
248C4⋊C8—181no—
249C4⋊C8D3211yescharacteristic
250C22⋊C8—181no—
251C4×C8—31no—
252C4×C8—31no—
253C23×C3—61no—
254C22×D3—21no—
255C22×D3—31no—
256C22×D3—31no—
257C22×D3—61no—
258C3×Q8—61no—
259C3×Q8—61no—
260C3×D4—61no—
261C3×D4—61no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—61no—
266C2×C3×C4—61no—
267C2×C3×C4—61no—
268C2×C3×C4—121no—
269C2×C3×C4—121no—
270C2×C3×C4C2×C4×D311yescharacteristic
271C2×C3×C4C2×C4×D311yescharacteristic
272C2×C3×C4D3×D411yescharacteristic
273C2×C3×C4D3×D411yescharacteristic
274C2×C3×C4D3×D411yescharacteristic
275C2×C3×C4D3×D411yescharacteristic
276#67—122no—
277C2×Dic3—21no—
278C2×Dic3—21no—
279C2×Dic3—21no—
280C2×Dic3—31no—
281C2×Dic3—31no—
282C2×Dic3—31no—
283C2×Dic3—31no—
284C2×Dic3—31no—
285C2×Dic3—31no—
286C2×Dic3—61no—
287C2×Dic3—61no—
288C2×Dic3—61no—
289D12—21no—
290D12—21no—
291D12—122no—
292C4×D3—41no—
293C4×D3—41no—
294C4×D3—62no—
295C4×D3—62no—
296C4×D3—61no—
297C4×D3—61no—
298C4×D3—61no—
299C4×D3—61no—
300C4×D3—61no—
301C4×D3—61no—
302C4×D3—61no—
303C4×D3—61no—
304C4×D3—121no—
305C4×D3—121no—
306C4×D3—121no—
307C4×D3—121no—
308C4×D3—122no—
309Dic6—21no—
310Dic6—21no—
311C3×C8—42no—
312C3×C8—41no—
313C3×C8—41no—
314C3×C8—121no—
315C3×C8—121no—
316C3⋊C8—41no—
317C3⋊C8—41no—
318C3⋊C8—122no—
319C3⋊C8—121no—
320C3⋊C8—121no—
321C2×C32#40811yescharacteristic
322C2×C32#41711yescharacteristic
323C2×C32#42111yescharacteristic
324C3⋊D3—41no—
325C3×D3—81no—
326C2×Q8—31no—
327C2×D4—31no—
328C2×D4—181no—
329C22×C4—61no—
330C22×C4—91no—
331C22×C4—91no—
332C22×C4—91no—
333M16—362no—
334C2×C8—21no—
335C2×C8—61no—
336C2×C8—61no—
337C2×C8—181no—
338C4⋊C4—31no—
339C4⋊C4—31no—
340C4⋊C4—61no—
341C4⋊C4—181no—
342C4⋊C4—181no—
343C4⋊C4—181no—
344C22⋊C4—61no—
345C22⋊C4—181no—
346C22⋊C4—181no—
347C22⋊C4—181no—
348C22⋊C4—181no—
349C42—61no—
350C42—91no—
351C42—91no—
352C42—91no—
353C42C2×D3211yescharacteristic
354C22×C3—21no—
355C22×C3—121no—
356C22×C3—121no—
357C22×C3—121no—
358C22×C3D3×C22⋊C411yescharacteristic
359C22×C3D3×C22⋊C411yescharacteristic
360C2×D3—41no—
361C2×D3—41no—
362C2×D3—41no—
363C2×D3—62no—
364C2×D3—61no—
365C2×D3—61no—
366C2×D3—61no—
367C2×D3—61no—
368C2×D3—61no—
369C2×D3—61no—
370C2×D3—121no—
371C2×D3—121no—
372C3×C4—21no—
373C3×C4—21no—
374C3×C4—21no—
375C3×C4—21no—
376C3×C4—21no—
377C3×C4—21no—
378C3×C4—41no—
379C3×C4—121no—
380C3×C4—121no—
381C3×C4—121no—
382C3×C4#90111yescharacteristic
383C3×C4#90111yescharacteristic
384C3×C4#90711yescharacteristic
385C3×C4#90711yescharacteristic
386C3×C4#91111yescharacteristic
387C3×C4#91411yescharacteristic
388C3×C4#91511yescharacteristic
389C3×C4#91811yescharacteristic
390Dic3—41no—
391Dic3—41no—
392Dic3—41no—
393Dic3—62no—
394Dic3—62no—
395Dic3—61no—
396Dic3—61no—
397Dic3—61no—
398Dic3—61no—
399Dic3—61no—
400Dic3—61no—
401Dic3—121no—
402C32#149511yescharacteristic, complemented, Sylow
403C23—61no—
404C23—91no—
405Q8—61no—
406Q8—61no—
407D4—61no—
408D4—61no—
409D4—362no—
410C2×C4—61no—
411C2×C4—61no—
412C2×C4—61no—
413C2×C4—91no—
414C2×C4—91no—
415C2×C4—91no—
416C2×C4—121no—
417C2×C4—121no—
418C2×C4—181no—
419C2×C4—181no—
420C2×C4—181no—
421C2×C4—181no—
422C2×C4—361no—
423C2×C4C4×D3211yescharacteristic
424C2×C4#380211yescharacteristic
425C2×C4#381111yescharacteristic
426C8—41no—
427C8—121no—
428C8—121no—
429C8—361no—
430C2×C3—21no—
431C2×C3—21no—
432C2×C3—21no—
433C2×C3—241no—
434C2×C3#472711yescharacteristic
435C2×C3#472711yescharacteristic
436C2×C3#477111yescharacteristic
437C2×C3#480311yescharacteristic
438C2×C3#482111yescharacteristic
439C2×C3#482111yescharacteristic
440D3—81no—
441D3—122no—
442D3—121no—
443D3—121no—
444C22—121no—
445C22—121no—
446C22—121no—
447C22—181no—
448C22—181no—
449C22—181no—
450C22#6392111yescharacteristic
451C4—21no—
452C4—121no—
453C4—121no—
454C4—121no—
455C4—181no—
456C4—181no—
457C4—181no—
458C4#6380411yescharacteristic
459C4#6380411yescharacteristic
460C4#6393711yescharacteristic
461C4#6395111yescharacteristic
462C3—21no—
463C3#6817811yescharacteristic, complemented
464C3#6824211yescharacteristic, complemented
465C2—241no—
466C2—361no—
467C2#1059061211yescharacteristic
468C2#1059095911yescharacteristic
469C2#1059100911yescharacteristic
subgroupG/H
centerC2×C4#3811
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32C2×C22⋊C4
prime radical#63916C4
cosocleC32×C42C23
hypercenterC4⋊C8D32
hypocenterC32#1495
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10592536C2semidirect
3. #10590297C2semidirect
4. C3×#4484C2semidirect
5. C3×#4483C2semidirect
6. #10589084C2semidirect
7. #10589081C2semidirect
40. #4484D3semidirect
41. #4483D3semidirect
402. C32#1495semidirect
463. C3#68178semidirect
464. C3#68242semidirect

Maximal subgroups

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

subgroupindex
#105938752
#105925362
#105902972
C3×#44842
C3×#44832
#105890842
#105890812
#682423
#681783