Finite Group Databasebeta

← #11779223

Subgroups — #11779223

Order 1152.

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

normal subgroups only

This group has 640 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
1Q8×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
2C3×#5027C211yesmaximal, characteristic, complemented
3#10590355C211yesmaximal, characteristic
4#10590273C211yesmaximal, characteristic, complemented
5C3×#4535C211yesmaximal, characteristic, complemented
6#10589094C211yesmaximal, characteristic, complemented
7#10589082C211yesmaximal, characteristic, complemented
8#71035—31nomaximal
9#68266—31nomaximal
10C2×Q8×C3⋊D3—21no—
11C32×C4×Q8C2211yescharacteristic
12#64106—21no—
13#64106—22no—
14C4×C4⋊(C3⋊D3)—21no—
15C4×C4⋊(C3⋊D3)C2211yescharacteristic
16#64078—21no—
17#64078C2211yescharacteristic
18C2×C3×#215—21no—
19C3×#874C2211yescharacteristic
20C2×#3714—21no—
21C3×#809—21no—
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25#63563—22no—
26#63563—21no—
27Q8×D12—31no—
28Q8×D12—31no—
29Q8×D12—61no—
30C3×#460—31no—
31#5072—31no—
32#5070—31no—
33#5027D311yescharacteristic, complemented
34#4843—31no—
35#4694—31no—
36C3×Q8⋊C8—31no—
37#4535D311yescharacteristic, complemented
38#4486—31no—
39#4483—31no—
40#4482—31no—
41#4459—31no—
42C2×C32×Q8D411yescharacteristic
43Q8×C3⋊D3—42no—
44Q8×C3⋊D3—42no—
45C2×C4⋊(C3⋊D3)D411yescharacteristic
46C2×C4×C3⋊D3—22no—
47C2×C4×C3⋊D3—21no—
48C2×#634—22no—
49C2×#634—21no—
50C2×C3×D12—21no—
51C2×C3×D12—21no—
52C2×C3×D12—21no—
53C32×C4⋊C4—21no—
54C32×C4⋊C4D411yescharacteristic
55C32×C42—21no—
56C32×C42C2311yescharacteristic
57#3752—22no—
58#3752—21no—
59C4⋊(C3⋊Dic3)—22no—
60C4⋊(C3⋊Dic3)—21no—
61C4⋊(C3⋊Dic3)D411yescharacteristic
62C4⋊(C3⋊Dic3)D412yes—
63C3×#215—42no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67#3714—42no—
68#1627—91noSylow
69C2×D3×Q8—62no—
70C2×D3×Q8—61no—
71C2×D3×Q8—61no—
72C2×C3×SD16—61no—
73C3×#127—31no—
74C3×C4×Q8—21no—
75C3×C4×Q8C2×D311yescharacteristic
76C3×C4×Q8C2×D311yescharacteristic
77C2×#215—21no—
78C2×#213—61no—
79C2×D24—61no—
80#897—62no—
81#897—62no—
82#897—64no—
83#897—62no—
84#897—61no—
85#897—61no—
86#874C2×D311yescharacteristic
87C4×D12—31no—
88C4×D12—31no—
89C4×D12—61no—
90C4×D12—61no—
91C4×D12—61no—
92C4×D12—62no—
93#869—31no—
94#869—31no—
95#869—61no—
96#869—61no—
97#869—61no—
98#869—62no—
99C3×C4⋊C8—31no—
100C3×C4⋊C8—31no—
101C3×#102—61no—
102C3×C4×C8—31no—
103#832—62no—
104#832—61no—
105#821—62no—
106#821—61no—
107#809—21no—
108C4⋊(C3⋊C8)C2×D311yescharacteristic
109C4⋊(C3⋊C8)C2×D311yescharacteristic
110C4×C3⋊C8C2×D311yescharacteristic
111C22×C3⋊D3—21no—
112C22×C3×D3—41no—
113C32×Q8—21no—
114C32×Q8D812yescomplemented
115C2×C32×C4—21no—
116C2×C32×C4—21no—
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C3⋊Dic3—21no—
121C2×C3⋊Dic3—22no—
122C4⋊(C3⋊D3)—21no—
123C4⋊(C3⋊D3)SD1612yescomplemented
124C4×C3⋊D3—44no—
125C4×C3⋊D3—41no—
126C4×C3⋊D3—41no—
127#634—44no—
128#634—41no—
129#634—41no—
130C3×D12—42no—
131C3×D12—41no—
132C3×D12—41no—
133C3×D12—41no—
134C3×D12—41no—
135C3×C3⋊C8—41no—
136C3×C3⋊C8—41no—
137C3×C3⋊C8—41no—
138D4×Q8—91no—
139#486—91no—
140#460—31no—
141#459—91no—
142#332—91no—
143Q8⋊C8—31no—
144D4⋊C8—91no—
145C2×C3×Q8—21no—
146C2×C3×Q8D1211yescharacteristic
147C2×C3×Q8#6711yescharacteristic
148C2×C3×D4—61no—
149C2×C3×D4—61no—
150C2×C3×D4—61no—
151D3×Q8—124no—
152D3×Q8—122no—
153D3×Q8—122no—
154D3×Q8—124no—
155D3×Q8—122no—
156D3×Q8—122no—
157C2×D12—21no—
158C2×D12—21no—
159C2×D12—21no—
160C2×D12—31no—
161C2×D12—31no—
162C2×D12—61no—
163C2×C4×D3—64no—
164C2×C4×D3—62no—
165C2×C4×D3—62no—
166C2×C4×D3—62no—
167C2×C4×D3—61no—
168C2×C4×D3—61no—
169C2×Dic6—64no—
170C2×Dic6—62no—
171C2×Dic6—62no—
172C2×Dic6—62no—
173C2×Dic6—61no—
174C2×Dic6—61no—
175C3×SD16—122no—
176C2×C3×C8—61no—
177C2×C3×C8—61no—
178C2×C3×C8—61no—
179C3×C4⋊C4—22no—
180C3×C4⋊C4—21no—
181C3×C4⋊C4—21no—
182C3×C4⋊C4—21no—
183C3×C4⋊C4D1211yescharacteristic
184C3×C4⋊C4#6711yescharacteristic
185C3×C42—22no—
186C3×C42—21no—
187C3×C42—21no—
188C3×C42—21no—
189C3×C42C22×D311yescharacteristic
190C3×C42C22×D311yescharacteristic
191#215—42no—
192#213—122no—
193(C2×D3)⋊C4—64no—
194(C2×D3)⋊C4—62no—
195(C2×D3)⋊C4—62no—
196(C2×D3)⋊C4—62no—
197(C2×D3)⋊C4—61no—
198(C2×D3)⋊C4—61no—
199C4⋊Dic3—32no—
200C4⋊Dic3—31no—
201C4⋊Dic3—32no—
202C4⋊Dic3—31no—
203C4⋊Dic3—61no—
204C4⋊Dic3—62no—
205C4⋊Dic3—62no—
206C4⋊Dic3—64no—
207C4⋊Dic3—62no—
208C4⋊Dic3—62no—
209C4⋊Dic3—61no—
210C4⋊Dic3—61no—
211C2×C3⋊C8—21no—
212C2×C3⋊C8—21no—
213C2×C3⋊C8—21no—
214D24—122no—
215C22×C32#12011yescharacteristic
216C2×C3⋊D3—22no—
217C2×C3⋊D3—41no—
218C2×C3⋊D3—41no—
219C2×C3×D3—81no—
220C2×C3×D3—81no—
221C2×C3×D3—81no—
222C32×C4—22no—
223C32×C4—21no—
224C32×C4—41no—
225C32×C4C2×D811yescharacteristic
226C32×C4C2×SD1611yescharacteristic
227C32×C4AGL(1,ℤ/8)11yescharacteristic
228C32×C4#13711yescharacteristic
229C3⋊Dic3—41no—
230C3⋊Dic3—42no—
231C22×Q8—181no—
232C2×SD16—61no—
233C2×D8—181no—
234C4⋊Q8—91no—
235C4⋊Q8—181no—
236#127—31no—
237C22⋊Q8—182no—
238C22⋊Q8—181no—
239C4×Q8D3211yescharacteristic
240C4×D4—91no—
241C4×D4—181no—
242C4⋊C8—31no—
243C4⋊C8—31no—
244#102—61no—
245#102—181no—
246#102—182no—
247C4×C8—31no—
248C23×C3—121no—
249C22×D3—41no—
250C22×D3—62no—
251C22×D3—61no—
252C22×D3—61no—
253C3×Q8—22no—
254C3×Q8—21no—
255C3×Q8—21no—
256C3×Q8—22no—
257C3×Q8D2412yescomplemented
258C3×Q8#21312yescomplemented
259C3×D4—122no—
260C3×D4—121no—
261C3×D4—121no—
262C3×D4—121no—
263C3×D4—121no—
264C2×C3×C4—22no—
265C2×C3×C4—21no—
266C2×C3×C4—21no—
267C2×C3×C4—22no—
268C2×C3×C4—21no—
269C2×C3×C4—21no—
270C2×C3×C4—21no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4C2×D1211yescharacteristic
274C2×C3×C4D3×D411yescharacteristic
275C2×C3×C4D3×D411yescharacteristic
276C2×C3×C4D3×D411yescharacteristic
277C2×C3×C4D3×D411yescharacteristic
278C2×C3×C4C2×#6711yescharacteristic
279C2×Dic3—62no—
280C2×Dic3—64no—
281C2×Dic3—62no—
282C2×Dic3—61no—
283C2×Dic3—62no—
284C2×Dic3—61no—
285D12—32no—
286D12—32no—
287D12—42no—
288D12—41no—
289D12—41no—
290D12—41no—
291D12—41no—
292D12—62no—
293D12—62no—
294D12—61no—
295D12—61no—
296C4×D3—128no—
297C4×D3—124no—
298C4×D3—124no—
299C4×D3—122no—
300C4×D3—122no—
301C4×D3—121no—
302C4×D3—121no—
303C4×D3—121no—
304C4×D3—121no—
305Dic6—128no—
306Dic6—124no—
307Dic6—124no—
308Dic6—122no—
309Dic6—122no—
310Dic6—121no—
311Dic6—121no—
312Dic6—121no—
313Dic6—121no—
314C3×C8—121no—
315C3×C8—121no—
316C3×C8—121no—
317C3⋊C8—41no—
318C3⋊C8—41no—
319C3⋊C8—41no—
320C2×C32#44711yescharacteristic
321C2×C32#44811yescharacteristic
322C2×C32#45411yescharacteristic
323C3⋊D3—42no—
324C3×D3—161no—
325C2×Q8—182no—
326C2×Q8—181no—
327C2×Q8—362no—
328C2×Q8—362no—
329C2×Q8#62611yescharacteristic
330C2×D4—61no—
331C2×D4—61no—
332C2×D4—61no—
333C2×D4—91no—
334C22×C4—182no—
335C22×C4—181no—
336SD16—122no—
337D8—362no—
338C2×C8—61no—
339C2×C8—61no—
340C2×C8—61no—
341C4⋊C4—21no—
342C4⋊C4—91no—
343C4⋊C4—92no—
344C4⋊C4—182no—
345C4⋊C4—181no—
346C4⋊C4#62611yescharacteristic
347C22⋊C4—182no—
348C22⋊C4—181no—
349C42—21no—
350C42C2×D3211yescharacteristic
351C22×C3—21no—
352C22×C3—241no—
353C22×C3—241no—
354C22×C3—241no—
355C22×C3#88211yescharacteristic
356C22×C3#93711yescharacteristic
357C2×D3—64no—
358C2×D3—62no—
359C2×D3—62no—
360C2×D3—81no—
361C2×D3—81no—
362C2×D3—81no—
363C2×D3—122no—
364C2×D3—122no—
365C2×D3—121no—
366C2×D3—121no—
367C2×D3—121no—
368C2×D3—121no—
369C3×C4—24no—
370C3×C4—21no—
371C3×C4—22no—
372C3×C4—22no—
373C3×C4—21no—
374C3×C4—21no—
375C3×C4—21no—
376C3×C4—21no—
377C3×C4—21no—
378C3×C4—41no—
379C3×C4—42no—
380C3×C4—41no—
381C3×C4—41no—
382C3×C4C2×D2411yescharacteristic
383C3×C4#90811yescharacteristic
384C3×C4D3×SD1611yescharacteristic
385C3×C4D3×SD1611yescharacteristic
386C3×C4#91511yescharacteristic
387C3×C4#91811yescharacteristic
388C3×C4C2×#21311yescharacteristic
389C3×C4#94911yescharacteristic
390Dic3—124no—
391Dic3—122no—
392Dic3—121no—
393Dic3—122no—
394Dic3—121no—
395Dic3—122no—
396C32#162711yescharacteristic, complemented, Sylow
397C23—121no—
398C23—181no—
399Q8—21no—
400Q8—364no—
401Q8—361no—
402Q8—361no—
403Q8#371412yescomplemented
404D4—92no—
405D4—122no—
406D4—121no—
407D4—121no—
408D4—121no—
409D4—121no—
410D4—181no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—182no—
414C2×C4—181no—
415C2×C4—364no—
416C2×C4—361no—
417C2×C4—361no—
418C2×C4C2×#62611yescharacteristic
419C2×C4#381111yescharacteristic
420C2×C4#381111yescharacteristic
421C8—121no—
422C8—121no—
423C8—121no—
424C2×C3—21no—
425C2×C3—21no—
426C2×C3—21no—
427C2×C3—481no—
428C2×C3#473211yescharacteristic
429C2×C3#480611yescharacteristic
430C2×C3#482711yescharacteristic
431C2×C3#503611yescharacteristic
432C2×C3#517011yescharacteristic
433C2×C3#520111yescharacteristic
434D3—124no—
435D3—122no—
436D3—122no—
437D3—161no—
438C22—182no—
439C22—241no—
440C22—241no—
441C22—241no—
442C22—361no—
443C22—361no—
444C22#6398111yescharacteristic
445C4—22no—
446C4—21no—
447C4—41no—
448C4—362no—
449C4—361no—
450C4C2×#371411yescharacteristic
451C4#6382511yescharacteristic
452C4#6394011yescharacteristic
453C4#6395111yescharacteristic
454C3—21no—
455C3#6826611yescharacteristic, complemented
456C3#7103511yescharacteristic, complemented
457C2—362no—
458C2—481no—
459C2#1059116811yescharacteristic
460C2#1059159211yescharacteristic
461C2#1059168611yescharacteristic
subgroupG/H
centerC22#63981
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×Q8C22
socleC22×C32#120
prime radical#10590355C2
hypercenterC4×Q8D32
hypocenterC32#1627
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. Q8×C4⋊(C3⋊D3)C2semidirect
2. C3×#5027C2semidirect
4. #10590273C2semidirect
5. C3×#4535C2semidirect
6. #10589094C2semidirect
7. #10589082C2semidirect
33. #5027D3semidirect
37. #4535D3semidirect
114. C32×Q8D8semidirect
123. C4⋊(C3⋊D3)SD16semidirect
257. C3×Q8D24semidirect
258. C3×Q8#213semidirect
396. C32#1627semidirect
403. Q8#3714semidirect
455. C3#68266semidirect
456. C3#71035semidirect

Maximal subgroups

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

subgroupindex
Q8×C4⋊(C3⋊D3)2
C3×#50272
#105903552
#105902732
C3×#45352
#105890942
#105890822
#710353
#682663