Finite Group Databasebeta

← #11779136

Subgroups — #11779136

Order 1152.

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

normal subgroups only

This group has 582 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×#5551C211yesmaximal, characteristic, complemented
2#10592714C211yesmaximal, characteristic, complemented
3#10590349C211yesmaximal, characteristic, complemented
4#10590281C211yesmaximal, characteristic, complemented
5C3×D4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6#10589093C211yesmaximal, characteristic, complemented
7#10589081C211yesmaximal, characteristic, complemented
8#71910—31nomaximal
9#68180—31nomaximal
10C2×C3×#235—21no—
11C32×C4×D4C2211yescharacteristic
12C2×#3753—21no—
13#64083C2211yescharacteristic
14C3×#938—21no—
15C3×#924—21no—
16C3×D3×C4⋊C4—21no—
17C3×#883—22no—
18C3×C4×D12C2211yescharacteristic
19C3×#869C2211yescharacteristic
20C2×#3714—21no—
21#63636—21no—
22C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25#63564—22no—
26#63564—21no—
27C3×#547—31no—
28#5551D311yescharacteristic, complemented
29#5088—31no—
30#5015—31no—
31#5015—31no—
32#5015—31no—
33#5015—61no—
34#4843—31no—
35#4694—31no—
36C3×D4⋊C8—31no—
37#4547—31no—
38D4⋊(C3⋊C8)—31no—
39D4⋊(C3⋊C8)D311yescharacteristic, complemented
40#4482—31no—
41#4459—31no—
42C2×C32×D4D411yescharacteristic
43C22×C32×C4—21no—
44C2×C4⋊(C3⋊D3)—21no—
45C2×C4⋊(C3⋊D3)—21no—
46C2×C4⋊(C3⋊D3)—21no—
47C2×C3×#67—22no—
48C3×#235—42no—
49C3×#235—42no—
50C2×C3×D12D411yescharacteristic
51C2×C3×C4×D3—22no—
52C2×C3×C4×D3—21no—
53C2×C3×Dic6—21no—
54C32×C4⋊C4D411yescharacteristic
55C32×C22⋊C4—21no—
56C32×C42C2311yescharacteristic
57#3753—42no—
58C2×C3⋊(C3⋊C8)—21no—
59C3×#217—22no—
60C3×(C2×D3)⋊C4—21no—
61C3×C4⋊Dic3—21no—
62C3×C4⋊Dic3D412yes—
63C3×C4⋊Dic3D411yescharacteristic
64C3×Dic3⋊C4—22no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67#3714—42no—
68#1625—91noSylow
69C2×C3×#41—61no—
70C2×#235—21no—
71C3×C4⋊Q8—31no—
72C3×#123—62no—
73C3×C22⋊Q8—61no—
74C3×#121—61no—
75C3×C4×D4—21no—
76C3×C4×D4—31no—
77C3×C4×D4C2×D311yescharacteristic
78C3×C4×D4C2×D311yescharacteristic
79C2×C3×C4⋊C4—61no—
80#938—21no—
81C2×#213—61no—
82C2×#213—62no—
83C2×#213—61no—
84C2×#213—61no—
85#924—21no—
86C2×D24—61no—
87D3×C4⋊C4—21no—
88#883—22no—
89#874—31no—
90#874—31no—
91#874—61no—
92C4×D12C2×D311yescharacteristic
93#869C2×D311yescharacteristic
94C3×C4⋊C8—31no—
95C3×C4×C8—31no—
96#821—62no—
97#821—61no—
98#809—61no—
99#809—62no—
100#809—62no—
101#809—61no—
102#809—61no—
103C4⋊(C3⋊C8)—31no—
104C4⋊(C3⋊C8)—31no—
105C4⋊(C3⋊C8)—61no—
106C4⋊(C3⋊C8)C2×D311yescharacteristic
107C4×C3⋊C8C2×D311yescharacteristic
108C23×C32—21no—
109C22×C3⋊D3—41no—
110C22×C3×D3—21no—
111C32×D4—21no—
112C32×D4—21no—
113C2×C32×C4—21no—
114C2×C32×C4—41no—
115C2×C32×C4—41no—
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C4⋊(C3⋊D3)—41no—
120C4⋊(C3⋊D3)—41no—
121C4⋊(C3⋊D3)—42no—
122C4⋊(C3⋊D3)—41no—
123C4⋊(C3⋊D3)—41no—
124C3×#67—44no—
125C2×C3×Dic3—21no—
126C2×C3×Dic3—22no—
127C3×D12—21no—
128C3×D12D812yescomplemented
129C3×C4×D3—44no—
130C3×C4×D3—41no—
131C3×C4×D3—41no—
132C3×Dic6—41no—
133C3×Dic6—41no—
134C3⋊(C3⋊C8)—41no—
135C3×C3⋊C8—41no—
136C3×C3⋊C8—41no—
137#547—31no—
138#486—91no—
139#459—91no—
140#459—91no—
141#332—91no—
142D4⋊C8—31no—
143D4⋊C8—91no—
144C3×#41—122no—
145C3×#41—122no—
146C2×C3×Q8—61no—
147C2×C3×D4—21no—
148C2×C3×D4—31no—
149C2×C3×D4—62no—
150C2×C3×D4D1211yescharacteristic
151C2×C3×D4#6711yescharacteristic
152C22×C3×C4—21no—
153C22×C3×C4—21no—
154C22×C3×C4—41no—
155C22×C3×C4—62no—
156C22×C3×C4—61no—
157C2×#67—22no—
158#235—42no—
159#235—42no—
160C2×D12—62no—
161C2×D12—61no—
162C2×D12—61no—
163C2×D12—61no—
164C2×D12—61no—
165C2×D12—61no—
166C2×D12—61no—
167C2×D12—121no—
168C2×D12—121no—
169C2×D12#6711yescharacteristic
170C2×C4×D3—22no—
171C2×C4×D3—21no—
172C2×Dic6—21no—
173C2×C3×C8—61no—
174C2×C3×C8—61no—
175C3×C4⋊C4—21no—
176C3×C4⋊C4—31no—
177C3×C4⋊C4—32no—
178C3×C4⋊C4—62no—
179C3×C4⋊C4—61no—
180C3×C4⋊C4D1211yescharacteristic
181C3×C4⋊C4#6711yescharacteristic
182C3×C22⋊C4—21no—
183C3×C22⋊C4—21no—
184C3×C22⋊C4—41no—
185C3×C22⋊C4—62no—
186C3×C22⋊C4—61no—
187C3×C42—21no—
188C3×C42C22×D311yescharacteristic
189C3×C42C22×D311yescharacteristic
190#217—22no—
191#213—122no—
192#213—124no—
193#213—122no—
194#213—122no—
195(C2×D3)⋊C4—21no—
196C4⋊Dic3—21no—
197C4⋊Dic3#6712yes—
198C4⋊Dic3#6711yescharacteristic
199Dic3⋊C4—22no—
200C2×C3⋊C8—21no—
201C2×C3⋊C8—21no—
202C2×C3⋊C8—62no—
203C2×C3⋊C8—61no—
204C2×C3⋊C8—61no—
205D24—122no—
206C22×C32—41no—
207C22×C32—41no—
208C22×C32—41no—
209C22×C32#12011yescharacteristic
210C2×C3⋊D3—81no—
211C2×C3⋊D3—81no—
212C2×C3⋊D3—81no—
213C2×C3×D3—22no—
214C2×C3×D3—41no—
215C2×C3×D3—41no—
216C32×C4—21no—
217C32×C4—41no—
218C32×C4C2×D811yescharacteristic
219C32×C4#13511yescharacteristic
220C32×C4AGL(1,ℤ/8)11yescharacteristic
221C32×C4AGL(1,ℤ/8)11yescharacteristic
222C3×Dic3—42no—
223C3×Dic3—41no—
224C2×#41—61no—
225C2×D8—181no—
226C2×D8—181no—
227C4⋊Q8—31no—
228#127—91no—
229#123—62no—
230C22⋊Q8—61no—
231#121—61no—
232C4×D4—31no—
233C4×D4D3211yescharacteristic
234C2×C4⋊C4—61no—
235C4⋊C8—31no—
236C4⋊C8—91no—
237#102—181no—
238#102—182no—
239#102—181no—
240C4×C8—31no—
241C23×C3—21no—
242C23×C3—21no—
243C23×C3—41no—
244C23×C3—61no—
245C22×D3—21no—
246C22×D3—122no—
247C22×D3—121no—
248C22×D3—121no—
249C3×Q8—121no—
250C3×Q8—121no—
251C3×D4—22no—
252C3×D4—21no—
253C3×D4—21no—
254C3×D4—21no—
255C3×D4—21no—
256C3×D4—32no—
257C3×D4—41no—
258C3×D4—61no—
259C3×D4—124no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—41no—
266C2×C3×C4—41no—
267C2×C3×C4—41no—
268C2×C3×C4—41no—
269C2×C3×C4—41no—
270C2×C3×C4—61no—
271C2×C3×C4—62no—
272C2×C3×C4—81no—
273C2×C3×C4—81no—
274C2×C3×C4—124no—
275C2×C3×C4—121no—
276C2×C3×C4—121no—
277C2×C3×C4C2×D1211yescharacteristic
278C2×C3×C4D3×D411yescharacteristic
279C2×C3×C4D3×D411yescharacteristic
280C2×C3×C4C2×#6711yescharacteristic
281C2×C3×C4C2×#6711yescharacteristic
282C2×C3×C4C2×#6711yescharacteristic
283#67—44no—
284C2×Dic3—21no—
285C2×Dic3—22no—
286D12—21no—
287D12—122no—
288D12—122no—
289D12—122no—
290D12—122no—
291D12—121no—
292D12—121no—
293D12—121no—
294D12—121no—
295D12—121no—
296D12—121no—
297D12—121no—
298D12—121no—
299D12—241no—
300D12—241no—
301D12—242no—
302D12#21312yescomplemented
303C4×D3—44no—
304C4×D3—41no—
305C4×D3—41no—
306Dic6—41no—
307Dic6—41no—
308C3×C8—121no—
309C3×C8—121no—
310C3⋊C8—41no—
311C3⋊C8—41no—
312C3⋊C8—122no—
313C3⋊C8—121no—
314C3⋊C8—121no—
315C2×C32—81no—
316C2×C32#44711yescharacteristic
317C2×C32#44911yescharacteristic
318C2×C32#45411yescharacteristic
319C3⋊D3—161no—
320C3×D3—42no—
321#41—122no—
322#41—122no—
323C2×Q8—61no—
324C2×D4—31no—
325C2×D4—62no—
326C2×D4—181no—
327C2×D4—181no—
328C2×D4—181no—
329C2×D4#62611yescharacteristic
330C22×C4—21no—
331C22×C4—62no—
332C22×C4—61no—
333D8—362no—
334D8—362no—
335C2×C8—61no—
336C2×C8—61no—
337C2×C8—181no—
338C4⋊C4—31no—
339C4⋊C4—32no—
340C4⋊C4—62no—
341C4⋊C4—61no—
342C4⋊C4#62611yescharacteristic
343C22⋊C4—21no—
344C22⋊C4—62no—
345C22⋊C4—61no—
346C42C2×D3211yescharacteristic
347C22×C3—21no—
348C22×C3—42no—
349C22×C3—41no—
350C22×C3—41no—
351C22×C3—41no—
352C22×C3—41no—
353C22×C3—41no—
354C22×C3—41no—
355C22×C3—62no—
356C22×C3—81no—
357C22×C3—81no—
358C22×C3—121no—
359C22×C3—121no—
360C22×C3#88211yescharacteristic
361C22×C3#95311yescharacteristic
362C2×D3—22no—
363C2×D3—41no—
364C2×D3—41no—
365C2×D3—242no—
366C2×D3—242no—
367C2×D3—242no—
368C2×D3—241no—
369C2×D3—241no—
370C2×D3—241no—
371C2×D3—241no—
372C2×D3—241no—
373C2×D3—241no—
374C3×C4—21no—
375C3×C4—21no—
376C3×C4—21no—
377C3×C4—21no—
378C3×C4—21no—
379C3×C4—21no—
380C3×C4—41no—
381C3×C4—41no—
382C3×C4—41no—
383C3×C4—81no—
384C3×C4—121no—
385C3×C4—122no—
386C3×C4#90411yescharacteristic
387C3×C4#90811yescharacteristic
388C3×C4D3×D811yescharacteristic
389C3×C4#91411yescharacteristic
390C3×C4C2×#21311yescharacteristic
391C3×C4#93211yescharacteristic
392C3×C4#94911yescharacteristic
393C3×C4#95011yescharacteristic
394Dic3—42no—
395Dic3—41no—
396C32#162511yescharacteristic, complemented, Sylow
397C23—21no—
398C23—61no—
399C23—361no—
400Q8—121no—
401Q8—121no—
402D4—21no—
403D4—21no—
404D4—32no—
405D4—61no—
406D4—124no—
407D4—362no—
408D4—361no—
409D4—361no—
410D4—361no—
411D4—361no—
412C2×C4—21no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—61no—
416C2×C4—62no—
417C2×C4—124no—
418C2×C4—121no—
419C2×C4—121no—
420C2×C4C2×#62611yescharacteristic
421C2×C4D3×#6711yescharacteristic
422C2×C4D3×#6711yescharacteristic
423C8—121no—
424C8—121no—
425C8—361no—
426C2×C3—21no—
427C2×C3—21no—
428C2×C3—21no—
429C2×C3—82no—
430C2×C3—81no—
431C2×C3—81no—
432C2×C3—122no—
433C2×C3#473411yescharacteristic
434C2×C3#477311yescharacteristic
435C2×C3#482711yescharacteristic
436C2×C3#521711yescharacteristic
437C2×C3#523811yescharacteristic
438C2×C3#524511yescharacteristic
439D3—42no—
440D3—482no—
441D3—481no—
442D3—481no—
443C22—41no—
444C22—41no—
445C22—41no—
446C22—62no—
447C22—121no—
448C22—121no—
449C22—721no—
450C22—721no—
451C22—721no—
452C22#6397711yescharacteristic
453C4—21no—
454C4—41no—
455C4—121no—
456C4—122no—
457C4#6382511yescharacteristic
458C4#6382911yescharacteristic
459C4D3×#21311yescharacteristic
460C4#6393411yescharacteristic
461C3—21no—
462C3#6818011yescharacteristic, complemented
463C3#7191011yescharacteristic, complemented
464C2—81no—
465C2—122no—
466C2—1441no—
467C2#1059116311yescharacteristic
468C2#1059144811yescharacteristic
469C2#1059168511yescharacteristic
subgroupG/H
centerC22#63977
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32#120
hypercenterC4×D4D32
hypocenterC32#1625
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C3×#5551C2semidirect
2. #10592714C2semidirect
3. #10590349C2semidirect
4. #10590281C2semidirect
5. C3×D4⋊(C3⋊C8)C2semidirect
6. #10589093C2semidirect
7. #10589081C2semidirect
28. #5551D3semidirect
39. D4⋊(C3⋊C8)D3semidirect
128. C3×D12D8semidirect
302. D12#213semidirect
396. C32#1625semidirect
462. C3#68180semidirect
463. C3#71910semidirect

Maximal subgroups

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

subgroupindex
C3×#55512
#105927142
#105903492
#105902812
C3×D4⋊(C3⋊C8)2
#105890932
#105890812
#719103
#681803