Finite Group Databasebeta

← #11779140

Subgroups — #11779140

Order 1152.

553 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 553 conjugacy classes of subgroups — too many to draw. Only its 88 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#10593869C211yesmaximal, characteristic, complemented
2C3×#4843C211yesmaximal, characteristic, complemented
3#10590355C211yesmaximal, characteristic, complemented
4#10590277C211yesmaximal, characteristic, complemented
5#10589349C211yesmaximal, characteristic, complemented
6C3×#4486C211yesmaximal, characteristic, complemented
7#10589080C211yesmaximal, characteristic, complemented
8#71012—31nomaximal
9#68432—31nomaximal
10C2×#3799—21no—
11C4×C4⋊(C3⋊D3)C2211yescharacteristic
12C2×C3×D24—21no—
13C3×#874C2211yescharacteristic
14C3×C4×D12C2211yescharacteristic
15C3×#869C2211yescharacteristic
16#63916—21no—
17#63900—21no—
18#63856—21no—
19#63854—22no—
20C2×#3714—21no—
21C32×C4⋊C8C2211yescharacteristic
22C4×C3⋊(C3⋊C8)C2211yescharacteristic
23C3×#821—21no—
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25#63563—21no—
26#63562—22no—
27#5726—31no—
28#5551—31no—
29C3×#459—31no—
30#5088—31no—
31#5072—31no—
32#5070—31no—
33#4843—31no—
34#4843D311yescharacteristic, complemented
35C3×#332—31no—
36D4⋊(C3⋊C8)—31no—
37#4486D311yescharacteristic, complemented
38#4483—31no—
39#4483—31no—
40#4483—31no—
41#4483—61no—
42C2×C4⋊(C3⋊D3)D411yescharacteristic
43C2×C4×C3⋊D3—21no—
44C2×C3×D12—21no—
45C2×C3×D12—21no—
46C2×C3×D12—21no—
47C2×C3×D12D411yescharacteristic
48C2×C3×C4×D3—21no—
49C2×C3×Dic6—21no—
50C2×#626—22no—
51C2×#624—22no—
52#3799—42no—
53#3799—42no—
54C2×C32×C8—21no—
55C32×C42C2311yescharacteristic
56#3752—21no—
57C4⋊(C3⋊Dic3)D411yescharacteristic
58C2×C3⋊(C3⋊C8)—21no—
59C3×(C2×D3)⋊C4—21no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3D412yes—
62C3×C4⋊Dic3D411yescharacteristic
63C2×C3×C3⋊C8—21no—
64C3×D24—42no—
65#3724—22no—
66(C2×D3)⋊Dic3—22no—
67#3714—42no—
68#1625—91noSylow
69C2×#239—61no—
70C2×#235—61no—
71C2×C3×D8—61no—
72C3×C4⋊Q8—31no—
73C3×#127—31no—
74C3×C4×D4—31no—
75#946—61no—
76#938—61no—
77C2×#213—61no—
78#924—61no—
79C2×D24—21no—
80C2×D24—61no—
81#895—61no—
82#894—62no—
83D3×C4⋊C4—61no—
84D3×C4⋊C4—61no—
85#883—62no—
86#874C2×D311yescharacteristic
87C4×D12—31no—
88C4×D12—31no—
89C4×D12—61no—
90C4×D12C2×D311yescharacteristic
91#869C2×D311yescharacteristic
92C3×C4⋊C8—21no—
93C3×C4⋊C8—31no—
94C3×C4⋊C8C2×D311yescharacteristic
95C3×C4⋊C8C2×D311yescharacteristic
96C3×#102—61no—
97#832—61no—
98#832—62no—
99#821—21no—
100#821—61no—
101#809—62no—
102C4⋊(C3⋊C8)C2×D311yescharacteristic
103C4×C3⋊C8—31no—
104C4×C3⋊C8—31no—
105C4×C3⋊C8—61no—
106C22×C3⋊D3—21no—
107C22×C3×D3—21no—
108C22×C3×D3—41no—
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C3⋊Dic3—21no—
113C4⋊(C3⋊D3)—21no—
114C4⋊(C3⋊D3)D812yescomplemented
115C4×C3⋊D3—41no—
116C4×C3⋊D3—41no—
117C2×C3×Dic3—22no—
118C2×C3×Dic3—21no—
119C3×D12—21no—
120C3×D12—21no—
121C3×D12—42no—
122C3×D12—41no—
123C3×D12—41no—
124C3×D12—41no—
125C3×D12—41no—
126C3×C4×D3—41no—
127C3×C4×D3—41no—
128C3×Dic6—41no—
129C3×Dic6—41no—
130#626—44no—
131#624—44no—
132C32×C8—41no—
133C3⋊(C3⋊C8)—41no—
134C3×C3⋊C8—41no—
135#547—91no—
136#486—91no—
137#459—31no—
138#459—91no—
139#332—31no—
140D4⋊C8—91no—
141D4⋊C8—91no—
142C2×C3×Q8—61no—
143C2×C3×D4—31no—
144C2×C3×D4—61no—
145C2×C3×D4—61no—
146C2×C3×D4—61no—
147C22×C3×C4—61no—
148C2×#67—62no—
149#239—122no—
150#239—122no—
151#235—122no—
152#235—122no—
153C2×D12—21no—
154C2×D12—21no—
155C2×D12—21no—
156C2×D12—31no—
157C2×D12—31no—
158C2×D12—61no—
159C2×D12—62no—
160C2×D12#6711yescharacteristic
161C2×C4×D3—21no—
162C2×C4×D3—62no—
163C2×C4×D3—62no—
164C2×C4×D3—61no—
165C2×C4×D3—61no—
166C2×C4×D3—121no—
167C2×Dic6—21no—
168C3×D8—122no—
169C2×C3×C8—21no—
170C2×C3×C8—21no—
171C2×C3×C8—41no—
172C2×C3×C8—61no—
173C3×C4⋊C4—32no—
174C3×C4⋊C4—31no—
175C3×C4⋊C4—61no—
176C3×C22⋊C4—61no—
177C3×C42—21no—
178C3×C42C22×D311yescharacteristic
179C3×C42C22×D311yescharacteristic
180#217—62no—
181#213—122no—
182(C2×D3)⋊C4—21no—
183(C2×D3)⋊C4—62no—
184(C2×D3)⋊C4—61no—
185(C2×D3)⋊C4—61no—
186(C2×D3)⋊C4—121no—
187C4⋊Dic3—21no—
188C4⋊Dic3—31no—
189C4⋊Dic3—31no—
190C4⋊Dic3—61no—
191C4⋊Dic3D1212yes—
192C4⋊Dic3#6711yescharacteristic
193Dic3⋊C4—62no—
194Dic3⋊C4—62no—
195C2×C3⋊C8—21no—
196C2×C3⋊C8—61no—
197C2×C3⋊C8—61no—
198C2×C3⋊C8—121no—
199D24—42no—
200D24—122no—
201C22×C32#12011yescharacteristic
202C2×C3⋊D3—22no—
203C2×C3⋊D3—41no—
204C2×C3⋊D3—41no—
205C2×C3×D3—41no—
206C2×C3×D3—41no—
207C2×C3×D3—41no—
208C2×C3×D3—81no—
209C2×C3×D3—81no—
210C2×C3×D3—81no—
211C32×C4—21no—
212C32×C4C2×D811yescharacteristic
213C32×C4#13511yescharacteristic
214C32×C4AGL(1,ℤ/8)11yescharacteristic
215C32×C4AGL(1,ℤ/8)11yescharacteristic
216C3⋊Dic3—41no—
217C3×Dic3—41no—
218C3×Dic3—42no—
219C2×#41—181no—
220C2×D8—61no—
221C2×D8—181no—
222C4⋊Q8—31no—
223#127—31no—
224#123—182no—
225C22⋊Q8—181no—
226#121—181no—
227C4×D4—31no—
228C4×D4—91no—
229C2×C4⋊C4—181no—
230C4⋊C8—31no—
231C4⋊C8D3211yescharacteristic
232#102—61no—
233#102—182no—
234#102—181no—
235C4×C8—91no—
236C23×C3—61no—
237C23×C3—121no—
238C22×D3—21no—
239C22×D3—41no—
240C22×D3—61no—
241C22×D3—61no—
242C22×D3—121no—
243C3×Q8—121no—
244C3×Q8—121no—
245C3×D4—61no—
246C3×D4—61no—
247C3×D4—122no—
248C3×D4—121no—
249C3×D4—121no—
250C3×D4—121no—
251C3×D4—121no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—61no—
256C2×C3×C4—62no—
257C2×C3×C4—121no—
258C2×C3×C4—121no—
259C2×C3×C4C2×D1211yescharacteristic
260C2×C3×C4D3×D411yescharacteristic
261C2×C3×C4D3×D411yescharacteristic
262C2×C3×C4D3×D411yescharacteristic
263C2×C3×C4D3×D411yescharacteristic
264C2×C3×C4C2×#6711yescharacteristic
265#67—124no—
266C2×Dic3—22no—
267C2×Dic3—21no—
268C2×Dic3—61no—
269C2×Dic3—61no—
270C2×Dic3—121no—
271D12—21no—
272D12—21no—
273D12—32no—
274D12—32no—
275D12—42no—
276D12—41no—
277D12—41no—
278D12—41no—
279D12—41no—
280D12—62no—
281D12—61no—
282D12—61no—
283D12—121no—
284D12—124no—
285C4×D3—41no—
286C4×D3—41no—
287C4×D3—124no—
288C4×D3—124no—
289C4×D3—121no—
290C4×D3—121no—
291C4×D3—121no—
292C4×D3—121no—
293C4×D3—241no—
294C4×D3—241no—
295Dic6—41no—
296Dic6—41no—
297C3×C8—41no—
298C3×C8—41no—
299C3×C8—81no—
300C3×C8—121no—
301C3⋊C8—41no—
302C3⋊C8—121no—
303C3⋊C8—121no—
304C3⋊C8—122no—
305C2×C32#44711yescharacteristic
306C2×C32#44911yescharacteristic
307C2×C32#45411yescharacteristic
308C3⋊D3—42no—
309C3×D3—81no—
310C3×D3—161no—
311#41—362no—
312#41—362no—
313C2×Q8—61no—
314C2×D4—31no—
315C2×D4—61no—
316C2×D4—61no—
317C2×D4—61no—
318C2×D4—91no—
319C2×D4—182no—
320C22×C4—61no—
321C22×C4—182no—
322C22×C4—181no—
323D8—122no—
324D8—362no—
325C2×C8—21no—
326C2×C8—61no—
327C2×C8—181no—
328C4⋊C4—32no—
329C4⋊C4—31no—
330C4⋊C4—61no—
331C4⋊C4—91no—
332C4⋊C4—182no—
333C22⋊C4—61no—
334C22⋊C4—182no—
335C22⋊C4—181no—
336C42C2×D3211yescharacteristic
337C22×C3—21no—
338C22×C3—121no—
339C22×C3—121no—
340C22×C3—121no—
341C22×C3—241no—
342C22×C3—241no—
343C22×C3—241no—
344C22×C3#88211yescharacteristic
345C22×C3#93711yescharacteristic
346C2×D3—41no—
347C2×D3—41no—
348C2×D3—41no—
349C2×D3—62no—
350C2×D3—62no—
351C2×D3—81no—
352C2×D3—81no—
353C2×D3—81no—
354C2×D3—122no—
355C2×D3—121no—
356C2×D3—121no—
357C2×D3—121no—
358C2×D3—121no—
359C2×D3—241no—
360C2×D3—241no—
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—21no—
364C3×C4—21no—
365C3×C4—21no—
366C3×C4—21no—
367C3×C4—41no—
368C3×C4—122no—
369C3×C4—121no—
370C3×C4D3×D811yescharacteristic
371C3×C4D3×D811yescharacteristic
372C3×C4#91111yescharacteristic
373C3×C4#91411yescharacteristic
374C3×C4#91411yescharacteristic
375C3×C4#91911yescharacteristic
376C3×C4#93211yescharacteristic
377C3×C4#95011yescharacteristic
378Dic3—41no—
379Dic3—42no—
380Dic3—121no—
381Dic3—121no—
382Dic3—241no—
383C32#162511yescharacteristic, complemented, Sylow
384C23—61no—
385C23—121no—
386C23—181no—
387Q8—121no—
388Q8—121no—
389D4—61no—
390D4—61no—
391D4—92no—
392D4—122no—
393D4—121no—
394D4—121no—
395D4—121no—
396D4—121no—
397D4—181no—
398D4—364no—
399C2×C4—61no—
400C2×C4—62no—
401C2×C4—121no—
402C2×C4—121no—
403C2×C4—181no—
404C2×C4—364no—
405C2×C4—361no—
406C2×C4—361no—
407C2×C4D3×D1211yescharacteristic
408C2×C4#380211yescharacteristic
409C2×C4D3×#6711yescharacteristic
410C8—41no—
411C8—121no—
412C8—361no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—21no—
416C2×C3—241no—
417C2×C3—481no—
418C2×C3#475311yescharacteristic
419C2×C3#477311yescharacteristic
420C2×C3#481011yescharacteristic
421C2×C3#503711yescharacteristic
422C2×C3#515611yescharacteristic
423C2×C3#520111yescharacteristic
424D3—81no—
425D3—122no—
426D3—122no—
427D3—161no—
428D3—242no—
429C22—121no—
430C22—121no—
431C22—121no—
432C22—182no—
433C22—241no—
434C22—241no—
435C22—241no—
436C22—361no—
437C22—361no—
438C22#6392211yescharacteristic
439C4—21no—
440C4—121no—
441C4—122no—
442C4—361no—
443C4#6379711yescharacteristic
444C4#6379811yescharacteristic
445C4#6393411yescharacteristic
446C4#6394911yescharacteristic
447C3—21no—
448C3#6843211yescharacteristic, complemented
449C3#7101211yescharacteristic, complemented
450C2—241no—
451C2—362no—
452C2—481no—
453C2#1059061511yescharacteristic
454C2#1059094511yescharacteristic
455C2#1059102011yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#120
hypercenterC4⋊C8D32
hypocenterC32#1625
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. #10593869C2semidirect
2. C3×#4843C2semidirect
3. #10590355C2semidirect
4. #10590277C2semidirect
5. #10589349C2semidirect
6. C3×#4486C2semidirect
7. #10589080C2semidirect
34. #4843D3semidirect
37. #4486D3semidirect
114. C4⋊(C3⋊D3)D8semidirect
383. C32#1625semidirect
448. C3#68432semidirect
449. C3#71012semidirect

Maximal subgroups

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

subgroupindex
#105938692
C3×#48432
#105903552
#105902772
#105893492
C3×#44862
#105890802
#710123
#684323