Finite Group Databasebeta

← #11774440

Subgroups — #11774440

Order 1152.

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

normal subgroups only

This group has 483 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#10592384C211yesmaximal, characteristic, complemented
3#10590256C211yesmaximal, characteristic, complemented
4C3×#4459C211yesmaximal, characteristic, complemented
5C3×#4456C211yesmaximal, characteristic, complemented
6#10589083C211yesmaximal, characteristic, complemented
7#10589080C211yesmaximal, characteristic, complemented
8#68233—31nomaximal
9#68169—31nomaximal
10C42×C3⋊D3C2211yescharacteristic
11C3×C4×D12C2211yescharacteristic
12C3×C4×Dic6C2211yescharacteristic
13#63916C411yescharacteristic
14C4×#626—21no—
15#63872C411yescharacteristic
16#63871C411yescharacteristic
17#63863C411yescharacteristic
18#63862—21no—
19#63855—21no—
20#63853—21no—
21C32×C4×C8C2211yescharacteristic
22#63647—21no—
23#63641—21no—
24C4×C3⋊(C3⋊C8)C2211yescharacteristic
25C3×C4⋊(C3⋊C8)C2211yescharacteristic
26C3×C4⋊(C3⋊C8)C2211yescharacteristic
27#63557—21no—
28#63553—21no—
29#5580—31no—
30#5557—31no—
31#4833—31no—
32#4833—31no—
33#4685—31no—
34#4685—31no—
35#4685—61no—
36C3×Q8⋊C8—31no—
37C3×D4⋊C8—31no—
38#4535—31no—
39D4⋊(C3⋊C8)—31no—
40#4484—31no—
41#4483—31no—
42#4459D311yescharacteristic, complemented
43#4456D311yescharacteristic, complemented
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—
57C3×(C2×D3)⋊C4—21no—
58C3×C4⋊Dic3C2×C411yescharacteristic
59C3×C4⋊Dic3C2×C411yescharacteristic
60C3×Dic3⋊C4—21no—
61C3×C4×Dic3—21no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64Dic3⋊Dic3—21no—
65Dic3⋊Dic3—21no—
66Dic3⋊Dic3—21no—
67#3722—21no—
68(C2×D3)⋊Dic3—21no—
69(C2×D3)⋊Dic3—21no—
70(C2×D3)⋊Dic3—21no—
71#1482—91noSylow
72C3×C4×Q8—31no—
73C3×C4×D4—31no—
74#947—31no—
75#946—31no—
76#938—31no—
77#936—31no—
78C4×#67—61no—
79#926—61no—
80#898—61no—
81#897—31no—
82#895—31no—
83#894—61no—
84#890—31no—
85#890—31no—
86#883—61no—
87#879—61no—
88C4×D12—61no—
89C4×D12C2×D311yescharacteristic
90#872—61no—
91C42×D3—31no—
92C42×D3—31no—
93C42×D3—61no—
94C4×Dic6C2×D311yescharacteristic
95C3×C4⋊C8—31no—
96C3×C4⋊C8—31no—
97C3×C4×C8—21no—
98C3×C4×C8C2×D311yescharacteristic
99C3×C4×C8C2×D311yescharacteristic
100(C2×D3)⋊C8—61no—
101(C2×D3)⋊C8—61no—
102(C2×D3)⋊C8—61no—
103(C2×D3)⋊C8—61no—
104(C2×D3)⋊C8—62no—
105Dic3⋊C8—61no—
106Dic3⋊C8—61no—
107Dic3⋊C8—62no—
108C8×Dic3—61no—
109C8×Dic3—61no—
110C4⋊(C3⋊C8)C2×D311yescharacteristic
111C4⋊(C3⋊C8)C2×D311yescharacteristic
112C4×C3⋊C8—31no—
113C4×C3⋊C8—31no—
114C4×C3⋊C8—61no—
115C22×C3⋊D3C22⋊C411yescharacteristic
116C22×C3×D3—21no—
117C2×C32×C4C22×C411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C3⋊Dic3C22⋊C411yescharacteristic
121C2×C3⋊Dic3C22⋊C411yescharacteristic
122C2×C3⋊Dic3C22⋊C411yescharacteristic
123C4×C3⋊D3—21no—
124C4×C3⋊D3—21no—
125C4×C3⋊D3—21no—
126C4×C3⋊D3—21no—
127C4×C3⋊D3—41no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—21no—
130C2×C3×Dic3—21no—
131C3×D12—21no—
132C3×D12—21no—
133C3×C4×D3—41no—
134C3×C4×D3—41no—
135C3×Dic6—21no—
136C3×Dic6—21no—
137#626—42no—
138C32×C8—41no—
139C3⋊(C3⋊C8)—41no—
140C3×C3⋊C8—41no—
141C3×C3⋊C8—41no—
142#529—91no—
143#431—91no—
144#431—91no—
145Q8⋊C8—31no—
146Q8⋊C8—91no—
147D4⋊C8—31no—
148D4⋊C8—91no—
149C2×C3×Q8—31no—
150C2×C3×D4—31no—
151C22×C3×C4—61no—
152C2×#67—61no—
153C2×D12—61no—
154C2×D12C4×D311yescharacteristic
155C2×C4×D3—21no—
156C2×C4×D3—31no—
157C2×C4×D3—31no—
158C2×C4×D3—31no—
159C2×C4×D3—31no—
160C2×C4×D3—31no—
161C2×C4×D3—31no—
162C2×C4×D3—61no—
163C2×C4×D3—61no—
164C2×C4×D3—61no—
165C2×Dic6C4×D311yescharacteristic
166C2×C3×C8—22no—
167C2×C3×C8—21no—
168C2×C3×C8—21no—
169C2×C3×C8—61no—
170C2×C3×C8—61no—
171C3×C4⋊C4—31no—
172C3×C4⋊C4—31no—
173C3×C4⋊C4—61no—
174C3×C22⋊C4—61no—
175C3×C42—21no—
176C3×C42—61no—
177C3×C42C22×D311yescharacteristic
178C3×C42C22×D311yescharacteristic
179#217—61no—
180#217—61no—
181#217—61no—
182(C2×D3)⋊C4—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—
188C4⋊Dic3—61no—
189C4⋊Dic3—61no—
190C4⋊Dic3—61no—
191C4⋊Dic3C4×D311yescharacteristic
192C4⋊Dic3C4×D311yescharacteristic
193Dic3⋊C4—21no—
194Dic3⋊C4—61no—
195Dic3⋊C4—61no—
196Dic3⋊C4—61no—
197C4×Dic3—21no—
198C4×Dic3—31no—
199C4×Dic3—31no—
200C4×Dic3—31no—
201C4×Dic3—31no—
202C4×Dic3—31no—
203C4×Dic3—31no—
204C4×Dic3—61no—
205C4×Dic3—61no—
206C4×Dic3—61no—
207C2×C3⋊C8—21no—
208C2×C3⋊C8—21no—
209C2×C3⋊C8—62no—
210C2×C3⋊C8—61no—
211C2×C3⋊C8—61no—
212C22×C32C2×C22⋊C411yescharacteristic
213C2×C3⋊D3—21no—
214C2×C3⋊D3—21no—
215C2×C3⋊D3—21no—
216C2×C3×D3—41no—
217C2×C3×D3—41no—
218C2×C3×D3—41no—
219C32×C4—21no—
220C32×C4#13111yescharacteristic
221C32×C4#13111yescharacteristic
222C32×C4#13511yescharacteristic
223C32×C4#13511yescharacteristic
224C3⋊Dic3—21no—
225C3⋊Dic3—21no—
226C3⋊Dic3—21no—
227C3×Dic3—41no—
228C3×Dic3—41no—
229C3×Dic3—41no—
230#126—181no—
231#125—91no—
232#124—91no—
233#123—181no—
234C22⋊Q8—91no—
235#121—91no—
236C4×Q8—31no—
237C4×D4—31no—
238C4×D4—181no—
239#117—181no—
240C2×C42—91no—
241C4⋊C8—31no—
242C4⋊C8—31no—
243C4⋊C8—181no—
244C22⋊C8—181no—
245C22⋊C8—181no—
246C4×C8—91no—
247C4×C8—181no—
248C4×C8D3211yescharacteristic
249C23×C3—61no—
250C22×D3—21no—
251C22×D3—31no—
252C22×D3—31no—
253C22×D3—61no—
254C3×Q8—61no—
255C3×Q8—61no—
256C3×D4—61no—
257C3×D4—61no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—61no—
262C2×C3×C4—61no—
263C2×C3×C4—61no—
264C2×C3×C4—121no—
265C2×C3×C4—121no—
266C2×C3×C4C2×C4×D311yescharacteristic
267C2×C3×C4C2×C4×D311yescharacteristic
268C2×C3×C4D3×D411yescharacteristic
269C2×C3×C4D3×D411yescharacteristic
270C2×C3×C4D3×D411yescharacteristic
271C2×C3×C4D3×D411yescharacteristic
272#67—122no—
273C2×Dic3—21no—
274C2×Dic3—21no—
275C2×Dic3—21no—
276C2×Dic3—31no—
277C2×Dic3—31no—
278C2×Dic3—31no—
279C2×Dic3—31no—
280C2×Dic3—31no—
281C2×Dic3—31no—
282C2×Dic3—61no—
283C2×Dic3—61no—
284C2×Dic3—61no—
285D12—21no—
286D12—21no—
287D12—122no—
288C4×D3—41no—
289C4×D3—41no—
290C4×D3—62no—
291C4×D3—62no—
292C4×D3—61no—
293C4×D3—61no—
294C4×D3—61no—
295C4×D3—61no—
296C4×D3—61no—
297C4×D3—61no—
298C4×D3—61no—
299C4×D3—61no—
300C4×D3—121no—
301C4×D3—121no—
302C4×D3—121no—
303C4×D3—121no—
304C4×D3—122no—
305Dic6—21no—
306Dic6—21no—
307C3×C8—42no—
308C3×C8—41no—
309C3×C8—41no—
310C3×C8—121no—
311C3×C8—121no—
312C3⋊C8—41no—
313C3⋊C8—41no—
314C3⋊C8—122no—
315C3⋊C8—121no—
316C3⋊C8—121no—
317C2×C32#40811yescharacteristic
318C2×C32#41611yescharacteristic
319C2×C32#42111yescharacteristic
320C3⋊D3—41no—
321C3×D3—81no—
322C2×Q8—31no—
323C2×D4—31no—
324C2×D4—181no—
325C22×C4—61no—
326C22×C4—91no—
327C22×C4—91no—
328C22×C4—91no—
329C2×C8—21no—
330C2×C8—61no—
331C2×C8—61no—
332C2×C8—181no—
333C4⋊C4—31no—
334C4⋊C4—31no—
335C4⋊C4—61no—
336C4⋊C4—181no—
337C4⋊C4—181no—
338C4⋊C4—181no—
339C22⋊C4—61no—
340C22⋊C4—181no—
341C22⋊C4—181no—
342C22⋊C4—181no—
343C22⋊C4—181no—
344C42—61no—
345C42—91no—
346C42—91no—
347C42—91no—
348C42C2×D3211yescharacteristic
349C22×C3—21no—
350C22×C3—121no—
351C22×C3—121no—
352C22×C3—121no—
353C22×C3D3×C22⋊C411yescharacteristic
354C22×C3D3×C22⋊C411yescharacteristic
355C2×D3—41no—
356C2×D3—41no—
357C2×D3—41no—
358C2×D3—62no—
359C2×D3—61no—
360C2×D3—61no—
361C2×D3—61no—
362C2×D3—61no—
363C2×D3—61no—
364C2×D3—61no—
365C2×D3—121no—
366C2×D3—121no—
367C3×C4—22no—
368C3×C4—21no—
369C3×C4—21no—
370C3×C4—21no—
371C3×C4—21no—
372C3×C4—21no—
373C3×C4—21no—
374C3×C4—121no—
375C3×C4—121no—
376C3×C4—121no—
377C3×C4#90111yescharacteristic
378C3×C4#90111yescharacteristic
379C3×C4#90711yescharacteristic
380C3×C4#90711yescharacteristic
381C3×C4#91211yescharacteristic
382C3×C4#91611yescharacteristic
383C3×C4#91611yescharacteristic
384C3×C4#91911yescharacteristic
385Dic3—41no—
386Dic3—41no—
387Dic3—41no—
388Dic3—62no—
389Dic3—61no—
390Dic3—61no—
391Dic3—61no—
392Dic3—61no—
393Dic3—61no—
394Dic3—61no—
395Dic3—121no—
396Dic3—121no—
397C32#148211yescharacteristic, complemented, Sylow
398C23—61no—
399C23—91no—
400Q8—61no—
401Q8—61no—
402D4—61no—
403D4—61no—
404D4—362no—
405C2×C4—61no—
406C2×C4—61no—
407C2×C4—61no—
408C2×C4—91no—
409C2×C4—91no—
410C2×C4—91no—
411C2×C4—121no—
412C2×C4—121no—
413C2×C4—181no—
414C2×C4—181no—
415C2×C4—181no—
416C2×C4—181no—
417C2×C4—361no—
418C2×C4C4×D3211yescharacteristic
419C2×C4#380211yescharacteristic
420C2×C4#381111yescharacteristic
421C8—41no—
422C8—121no—
423C8—121no—
424C8—361no—
425C2×C3—21no—
426C2×C3—21no—
427C2×C3—21no—
428C2×C3—241no—
429C2×C3#472711yescharacteristic
430C2×C3#472711yescharacteristic
431C2×C3#477211yescharacteristic
432C2×C3#480411yescharacteristic
433C2×C3#482111yescharacteristic
434C2×C3#482111yescharacteristic
435D3—81no—
436D3—122no—
437D3—121no—
438D3—121no—
439C22—121no—
440C22—121no—
441C22—121no—
442C22—181no—
443C22—181no—
444C22—181no—
445C22#6392111yescharacteristic
446C4—21no—
447C4—121no—
448C4—121no—
449C4—121no—
450C4—181no—
451C4—181no—
452C4—181no—
453C4#6380411yescharacteristic
454C4#6380411yescharacteristic
455C4#6380911yescharacteristic
456C4#6381011yescharacteristic
457C3—21no—
458C3#6816911yescharacteristic, complemented
459C3#6823311yescharacteristic, complemented
460C2—241no—
461C2—361no—
462C2#1059039411yescharacteristic
463C2#1059095611yescharacteristic
464C2#1059095911yescharacteristic
subgroupG/H
centerC2×C4#3802
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4×C8C22
socleC22×C32C2×C22⋊C4
prime radical#63916C4
cosocleC32×C42C23
hypercenterC4×C8D32
hypocenterC32#1482
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. #10592384C2semidirect
3. #10590256C2semidirect
4. C3×#4459C2semidirect
5. C3×#4456C2semidirect
6. #10589083C2semidirect
7. #10589080C2semidirect
42. #4459D3semidirect
43. #4456D3semidirect
397. C32#1482semidirect
458. C3#68169semidirect
459. C3#68233semidirect

Maximal subgroups

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

subgroupindex
#105938752
#105923842
#105902562
C3×#44592
C3×#44562
#105890832
#105890802
#682333
#681693