Finite Group Databasebeta

← #11778968

Subgroups — #11778968

Order 1152.

598 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 598 conjugacy classes of subgroups — too many to draw. Only its 96 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
1C3×#5718C211yesmaximal, characteristic, complemented
2C3×#5073C211yesmaximal, characteristic, complemented
3#10590364C211yesmaximal, characteristic, complemented
4#10590347C211yesmaximal, characteristic, complemented
5#10589410C211yesmaximal, characteristic, complemented
6#10589084C211yesmaximal, characteristic, complemented
7#10589081C211yesmaximal, characteristic, complemented
8#71918—31nomaximal
9#71285—31nomaximal
10C2×C3×#237—21no—
11C32×#127C2211yescharacteristic
12C3×#940—21no—
13C3×#939—22no—
14C3×#938—21no—
15C3×D4×Dic3—21no—
16C2×C3×#213—22no—
17C3×#874C2211yescharacteristic
18C3×C4×D12C2211yescharacteristic
19C3×C4×Dic6C2211yescharacteristic
20C2×#3715—21no—
21C2×#3713—21no—
22C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
23C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25#63562—21no—
26#63562—21no—
27C3×#550—31no—
28#5718D311yescharacteristic, complemented
29C3×#493—31no—
30#5075—31no—
31#5073D311yescharacteristic, complemented
32#5072—31no—
33#5027—31no—
34#5015—31no—
35#4544—31no—
36#4544—31no—
37#4544—61no—
38#4535—31no—
39D4⋊(C3⋊C8)—31no—
40#4459—31no—
41#4456—31no—
42C2×C32×D4—21no—
43C2×C32×D4—21no—
44C2×C32×D4D412yes—
45C2×C3×#67—22no—
46C2×C3×#67—22no—
47C22×C3×Dic3—22no—
48C3×#237—42no—
49C3×#237—42no—
50C2×C3×D12—21no—
51C2×C3×D12—21no—
52C2×C3×D12—21no—
53C2×C3×D12D411yescharacteristic
54C2×C3×C4×D3—21no—
55C2×C3×Dic6D411yescharacteristic
56C32×C42C2311yescharacteristic
57C2×C3⋊(C3⋊C8)—21no—
58C2×C3⋊(C3⋊C8)—21no—
59C3×#217—22no—
60C3×#213—44no—
61C3×(C2×D3)⋊C4—21no—
62C3×C4⋊Dic3D411yescharacteristic
63C3×C4⋊Dic3D411yescharacteristic
64C3×Dic3⋊C4—21no—
65C3×C4×Dic3—21no—
66C2×C3×C3⋊C8—21no—
67#3715—42no—
68#3713—42no—
69#1621—91noSylow
70C2×C3×#41—61no—
71C2×#237—21no—
72C2×C3×D8—62no—
73C3×#127—21no—
74C3×#127—31no—
75C3×#127—61no—
76C3×#127C2×D311yescharacteristic
77C3×#127C2×D311yescharacteristic
78C3×#121—61no—
79C3×#121—62no—
80C3×C4×Q8—31no—
81C3×C4×D4—31no—
82C3×C4×D4—61no—
83C2×#215—61no—
84#940—21no—
85#939—22no—
86#938—21no—
87D4×Dic3—21no—
88C2×#214—61no—
89C2×#213—22no—
90C2×#213—61no—
91C2×#213—61no—
92#874C2×D311yescharacteristic
93C4×D12C2×D311yescharacteristic
94C4×Dic6C2×D311yescharacteristic
95C3×C4×C8—31no—
96#832—61no—
97#832—61no—
98#809—61no—
99#809—61no—
100C4⋊(C3⋊C8)—31no—
101C4⋊(C3⋊C8)—31no—
102C4⋊(C3⋊C8)—31no—
103C4⋊(C3⋊C8)—31no—
104C4⋊(C3⋊C8)—61no—
105C4⋊(C3⋊C8)—61no—
106C4×C3⋊C8C2×D311yescharacteristic
107C23×C32—22no—
108C22×C3×D3—21no—
109C22×C3×D3—41no—
110C32×D4—42no—
111C32×D4—41no—
112C32×D4—41no—
113C32×D4—41no—
114C32×D4—41no—
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C3×#67—44no—
119C3×#67—82no—
120C2×C3×Dic3—21no—
121C2×C3×Dic3—21no—
122C2×C3×Dic3—21no—
123C2×C3×Dic3—44no—
124C3×D12—21no—
125C3×D12—21no—
126C3×D12—42no—
127C3×D12—41no—
128C3×D12—41no—
129C3×D12—41no—
130C3×D12—41no—
131C3×C4×D3—41no—
132C3×C4×D3—41no—
133C3×Dic6—21no—
134C3×Dic6D812yescomplemented
135C3⋊(C3⋊C8)—41no—
136C3⋊(C3⋊C8)—41no—
137C3×C3⋊C8—22no—
138#550—31no—
139#493—31no—
140#460—91no—
141#459—91no—
142#331—91no—
143Q8⋊C8—91no—
144D4⋊C8—91no—
145C3×#41—122no—
146C3×#41—122no—
147C2×C3×Q8—31no—
148C2×C3×D4—21no—
149C2×C3×D4—21no—
150C2×C3×D4—21no—
151C2×C3×D4—21no—
152C2×C3×D4—22no—
153C2×C3×D4—31no—
154C2×C3×D4—41no—
155C2×C3×D4—41no—
156C2×C3×D4—62no—
157C2×C3×D4—62no—
158C2×C3×D4—61no—
159C2×C3×D4—61no—
160C2×C3×D4—61no—
161C2×C3×D4#6712yes—
162C2×C3×D4#6712yes—
163C22×C3×C4—62no—
164C22×C3×C4—61no—
165C2×#67—22no—
166C2×#67—22no—
167C22×Dic3—22no—
168#237—42no—
169#237—42no—
170C2×D12—21no—
171C2×D12—21no—
172C2×D12—21no—
173C2×D12#6711yescharacteristic
174C2×C4×D3—21no—
175C2×Dic6#6711yescharacteristic
176C3×D8—124no—
177C2×C3×C8—61no—
178C3×C4⋊C4—31no—
179C3×C4⋊C4—31no—
180C3×C4⋊C4—61no—
181C3×C22⋊C4—62no—
182C3×C22⋊C4—61no—
183C3×C42—21no—
184C3×C42—61no—
185C3×C42C22×D311yescharacteristic
186C3×C42C22×D311yescharacteristic
187#217—22no—
188#215—122no—
189#214—122no—
190#213—44no—
191#213—122no—
192#213—122no—
193(C2×D3)⋊C4—21no—
194C4⋊Dic3#6711yescharacteristic
195C4⋊Dic3#6711yescharacteristic
196Dic3⋊C4—21no—
197C4×Dic3—21no—
198C2×C3⋊C8—21no—
199C2×C3⋊C8—61no—
200C2×C3⋊C8—61no—
201C2×C3⋊C8—61no—
202C2×C3⋊C8—61no—
203C2×C3⋊C8—121no—
204C2×C3⋊C8—121no—
205C22×C32—42no—
206C22×C32—42no—
207C22×C32—42no—
208C22×C32#12011yescharacteristic
209C2×C3×D3—41no—
210C2×C3×D3—41no—
211C2×C3×D3—41no—
212C2×C3×D3—81no—
213C2×C3×D3—81no—
214C2×C3×D3—81no—
215C32×C4—21no—
216C32×C4C2×D811yescharacteristic
217C32×C4#13511yescharacteristic
218C32×C4AGL(1,ℤ/8)11yescharacteristic
219C32×C4AGL(1,ℤ/8)11yescharacteristic
220C3×Dic3—22no—
221C3×Dic3—41no—
222C3×Dic3—41no—
223C2×#41—61no—
224C2×SD16—181no—
225C2×D8—62no—
226C2×D8—181no—
227#127—31no—
228#127—61no—
229#127D3211yescharacteristic
230#121—61no—
231#121—62no—
232C4×Q8—31no—
233C4×D4—31no—
234C4×D4—61no—
235C4⋊C8—91no—
236C4⋊C8—91no—
237#102—181no—
238#102—181no—
239C4×C8—31no—
240C23×C3—22no—
241C23×C3—22no—
242C23×C3—42no—
243C23×C3—61no—
244C23×C3—121no—
245C22×D3—21no—
246C22×D3—41no—
247C3×Q8—32no—
248C3×Q8—61no—
249C3×D4—42no—
250C3×D4—42no—
251C3×D4—41no—
252C3×D4—41no—
253C3×D4—41no—
254C3×D4—41no—
255C3×D4—41no—
256C3×D4—41no—
257C3×D4—41no—
258C3×D4—41no—
259C3×D4—61no—
260C3×D4—61no—
261C3×D4—81no—
262C3×D4—81no—
263C3×D4—81no—
264C3×D4—81no—
265C3×D4—82no—
266C3×D4—122no—
267C3×D4—124no—
268C3×D4—121no—
269C3×D4—121no—
270C3×D4—121no—
271C3×D4—121no—
272C3×D4—242no—
273C2×C3×C4—21no—
274C2×C3×C4—21no—
275C2×C3×C4—21no—
276C2×C3×C4—61no—
277C2×C3×C4—61no—
278C2×C3×C4—61no—
279C2×C3×C4—124no—
280C2×C3×C4—121no—
281C2×C3×C4—121no—
282C2×C3×C4D3×D411yescharacteristic
283C2×C3×C4D3×D411yescharacteristic
284C2×C3×C4C2×#6711yescharacteristic
285C2×C3×C4C2×#6711yescharacteristic
286C2×C3×C4C2×#6711yescharacteristic
287C2×C3×C4C2×#6711yescharacteristic
288#67—44no—
289#67—82no—
290C2×Dic3—21no—
291C2×Dic3—21no—
292C2×Dic3—21no—
293C2×Dic3—44no—
294D12—21no—
295D12—21no—
296D12—42no—
297D12—41no—
298D12—41no—
299D12—41no—
300D12—41no—
301C4×D3—41no—
302C4×D3—41no—
303Dic6—21no—
304Dic6#21312yescomplemented
305C3×C8—62no—
306C3⋊C8—22no—
307C3⋊C8—121no—
308C3⋊C8—121no—
309C3⋊C8—121no—
310C3⋊C8—121no—
311C3⋊C8—241no—
312C3⋊C8—241no—
313C2×C32—82no—
314C2×C32#44711yescharacteristic
315C2×C32#44911yescharacteristic
316C2×C32#45311yescharacteristic
317C3×D3—81no—
318C3×D3—161no—
319#41—122no—
320#41—122no—
321C2×Q8—31no—
322C2×D4—21no—
323C2×D4—21no—
324C2×D4—31no—
325C2×D4—62no—
326C2×D4—62no—
327C2×D4—61no—
328C2×D4—61no—
329C2×D4—61no—
330C2×D4#62512yes—
331C22×C4—62no—
332C22×C4—61no—
333SD16—362no—
334D8—124no—
335D8—362no—
336C2×C8—61no—
337C2×C8—181no—
338C2×C8—181no—
339C4⋊C4—31no—
340C4⋊C4—31no—
341C4⋊C4—61no—
342C22⋊C4—62no—
343C22⋊C4—61no—
344C42—61no—
345C42C2×D3211yescharacteristic
346C22×C3—21no—
347C22×C3—42no—
348C22×C3—42no—
349C22×C3—42no—
350C22×C3—42no—
351C22×C3—42no—
352C22×C3—42no—
353C22×C3—82no—
354C22×C3—82no—
355C22×C3—82no—
356C22×C3—121no—
357C22×C3—121no—
358C22×C3—121no—
359C22×C3—241no—
360C22×C3—241no—
361C22×C3—241no—
362C22×C3#93711yescharacteristic
363C22×C3#95311yescharacteristic
364C2×D3—41no—
365C2×D3—41no—
366C2×D3—41no—
367C2×D3—81no—
368C2×D3—81no—
369C2×D3—81no—
370C3×C4—21no—
371C3×C4—21no—
372C3×C4—21no—
373C3×C4—21no—
374C3×C4—21no—
375C3×C4—21no—
376C3×C4—41no—
377C3×C4—62no—
378C3×C4—121no—
379C3×C4—121no—
380C3×C4D3×D811yescharacteristic
381C3×C4#91111yescharacteristic
382C3×C4#91111yescharacteristic
383C3×C4#91211yescharacteristic
384C3×C4C2×#21311yescharacteristic
385C3×C4#93211yescharacteristic
386C3×C4#94911yescharacteristic
387C3×C4#95011yescharacteristic
388Dic3—22no—
389Dic3—41no—
390Dic3—41no—
391C32#162111yescharacteristic, complemented, Sylow
392C23—22no—
393C23—61no—
394C23—121no—
395Q8—32no—
396Q8—61no—
397D4—42no—
398D4—41no—
399D4—41no—
400D4—41no—
401D4—41no—
402D4—61no—
403D4—61no—
404D4—122no—
405D4—124no—
406D4—121no—
407D4—121no—
408D4—121no—
409D4—121no—
410D4—242no—
411C2×C4—61no—
412C2×C4—61no—
413C2×C4—61no—
414C2×C4—124no—
415C2×C4—121no—
416C2×C4—121no—
417C2×C4C2×#62511yescharacteristic
418C2×C4D3×#6711yescharacteristic
419C2×C4D3×#6711yescharacteristic
420C8—62no—
421C8—361no—
422C8—361no—
423C2×C3—21no—
424C2×C3—21no—
425C2×C3—21no—
426C2×C3—82no—
427C2×C3—82no—
428C2×C3—162no—
429C2×C3—241no—
430C2×C3—481no—
431C2×C3#507711yescharacteristic
432C2×C3#515611yescharacteristic
433C2×C3#515811yescharacteristic
434C2×C3#521711yescharacteristic
435C2×C3#523811yescharacteristic
436C2×C3#524111yescharacteristic
437D3—81no—
438D3—161no—
439C22—42no—
440C22—42no—
441C22—42no—
442C22—121no—
443C22—121no—
444C22—121no—
445C22—241no—
446C22—241no—
447C22—241no—
448C22#6397611yescharacteristic
449C4—21no—
450C4—62no—
451C4—121no—
452C4—121no—
453C4D3×#21311yescharacteristic
454C4#6392511yescharacteristic
455C4#6393211yescharacteristic
456C4#6393311yescharacteristic
457C3—21no—
458C3#7128511yescharacteristic, complemented
459C3#7191811yescharacteristic, complemented
460C2—82no—
461C2—241no—
462C2—481no—
463C2#1059144711yescharacteristic
464C2#1059145011yescharacteristic
465C2#1059150911yescharacteristic
subgroupG/H
centerC22#63976
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×#127C22
socleC22×C32#120
hypercenter#127D32
hypocenterC32#1621
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. C3×#5718C2semidirect
2. C3×#5073C2semidirect
3. #10590364C2semidirect
4. #10590347C2semidirect
5. #10589410C2semidirect
6. #10589084C2semidirect
7. #10589081C2semidirect
28. #5718D3semidirect
31. #5073D3semidirect
134. C3×Dic6D8semidirect
304. Dic6#213semidirect
391. C32#1621semidirect
458. C3#71285semidirect
459. C3#71918semidirect

Maximal subgroups

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

subgroupindex
C3×#57182
C3×#50732
#105903642
#105903472
#105894102
#105890842
#105890812
#719183
#712853