Finite Group Databasebeta

← #11792413

Subgroups — #11792413

Order 1152.

883 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 883 conjugacy classes of subgroups — too many to draw. Only its 118 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×#5748C211yesmaximal, characteristic, complemented
2#10595034C212yesmaximal, complemented
3#10592825C211yesmaximal, characteristic, complemented
4#10591111C212yesmaximal, complemented
5C3×#4557C211yesmaximal, characteristic, complemented
6#72118—31nomaximal
7#68703—31nomaximal
8C22×C4×C3⋊D3C2211yescharacteristic
9C2×C3×#235C2212yes—
10C2×C32×M16C2211yescharacteristic
11C2×#3748C2211yescharacteristic
12C3×#926C2212yes—
13C3×#909—22no—
14C3×#908—22no—
15C3×#904—22no—
16#63981—22no—
17#63962—22no—
18#63916—22no—
19C4×#626—24no—
20#63871—22no—
21#63647—22no—
22#63569—24no—
23C3×#575—31no—
24#5828—32no—
25#5748D311yescharacteristic, complemented
26#5524—32no—
27#5236—32no—
28#5126—31no—
29#5126—31no—
30#5126—61no—
31#5005—32no—
32C3×H(3,ℤ/4)—31no—
33#4557D311yescharacteristic, complemented
34C23×C3⋊D3D411yescharacteristic
35C22×C32×C4C2311yescharacteristic
36C22×C3⋊Dic3D411yescharacteristic
37C2×C4×C3⋊D3—21no—
38C2×C4×C3⋊D3—22no—
39C2×C4×C3⋊D3—22no—
40C2×C4×C3⋊D3—21no—
41C2×C3×#67—22no—
42C3×#235—22no—
43C3×#235—22no—
44C3×#235—22no—
45C3×#235—22no—
46C2×C3×D12D412yescomplemented
47C2×C3×C4×D3—22no—
48C2×C3×Dic6D412yescomplemented
49C2×#626—24no—
50C32×M16—22no—
51C2×C32×C8D412yescomplemented
52#3748—22no—
53C2×C3⋊(C3⋊C8)—21no—
54C3×#217—22no—
55C3×C4⋊Dic3—22no—
56C3×C4×Dic3D414yescomplemented
57C3×Dic12—22no—
58C3×D24—22no—
59C3×#204—24no—
60Dic3⋊Dic3—24no—
61#3722—24no—
62(C2×D3)⋊Dic3—24no—
63#2010—91noSylow
64C2×C3×#41—32no—
65C2×#235C2×D312yes—
66C22×C4×D3—31no—
67C22×C4×D3—31no—
68C22×C4×D3—61no—
69C3×#137—62no—
70C3×AGL(1,ℤ/8)—62no—
71C3×#135—62no—
72C2×C3×M16—21no—
73C2×C3×M16C2×D311yescharacteristic
74C2×C3×M16C2×D311yescharacteristic
75C3×#117—32no—
76#946—62no—
77#938—62no—
78#937—62no—
79#935—62no—
80C4×#67—64no—
81#926C2×D312yes—
82C2×#208—31no—
83C2×#208—31no—
84C2×#208—61no—
85#909—22no—
86#908—22no—
87#904—22no—
88#897—62no—
89#895—62no—
90#886—62no—
91#882—62no—
92C4×D12—64no—
93#837—64no—
94(C2×D3)⋊C8—64no—
95(C2×D3)⋊C8—62no—
96(C2×D3)⋊C8—62no—
97#805—64no—
98C23×C32C2×D411yescharacteristic
99C22×C3⋊D3—21no—
100C22×C3⋊D3—22no—
101C22×C3⋊D3—42no—
102C22×C3×D3—22no—
103C2×C32×C4C2×D412yes—
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4C2×D412yes—
106C2×C32×C4#4111yescharacteristic
107C2×C3⋊Dic3—21no—
108C2×C3⋊Dic3—22no—
109C4×C3⋊D3—41no—
110C4×C3⋊D3—42no—
111C4×C3⋊D3—41no—
112C3×#67—42no—
113C3×#67—42no—
114C2×C3×Dic3—24no—
115C2×C3×Dic3—22no—
116C3×D12—22no—
117C3×D12—22no—
118C3×C4×D3—42no—
119C3×C4×D3—42no—
120C3×Dic6—22no—
121C3×Dic6—22no—
122#626—48no—
123C32×C8—22no—
124C3⋊(C3⋊C8)—41no—
125#575—31no—
126#525—92no—
127#421—92no—
128#407—91no—
129H(3,ℤ/4)—31no—
130C23×D3—31no—
131C23×D3—31no—
132C23×D3—61no—
133C3×#41—62no—
134C3×#41—62no—
135C3×#41—62no—
136C3×#41—62no—
137C2×C3×Q8—32no—
138C2×C3×D4—32no—
139C2×C3×D4—62no—
140C22×C3×C4—21no—
141C22×C3×C4—62no—
142C22×C3×C4C22×D311yescharacteristic
143C22×C3×C4C22×D311yescharacteristic
144C2×#67—22no—
145C2×#67—64no—
146C22×Dic3—31no—
147C22×Dic3—31no—
148C22×Dic3—61no—
149#235—22no—
150#235—22no—
151#235—22no—
152#235—22no—
153C2×D12—64no—
154C2×D12#6712yescomplemented
155C2×C4×D3—22no—
156C2×C4×D3—62no—
157C2×C4×D3—62no—
158C2×C4×D3—61no—
159C2×C4×D3—62no—
160C2×C4×D3—62no—
161C2×C4×D3—62no—
162C2×C4×D3—61no—
163C2×C4×D3—61no—
164C2×C4×D3—61no—
165C2×C4×D3—62no—
166C2×C4×D3—122no—
167C2×C4×D3—122no—
168C2×Dic6#6712yescomplemented
169C3×Q16—62no—
170C3×SD16—64no—
171C3×D8—62no—
172C3×M16—22no—
173C3×M16—22no—
174C3×M16—42no—
175C2×C3×C8—22no—
176C2×C3×C8D1212yescomplemented
177C2×C3×C8#6712yescomplemented
178C3×C4⋊C4—62no—
179C3×C22⋊C4—62no—
180C3×C42—34no—
181#217—22no—
182#217—64no—
183(C2×D3)⋊C4—64no—
184(C2×D3)⋊C4—64no—
185(C2×D3)⋊C4—64no—
186C4⋊Dic3—22no—
187C4⋊Dic3—64no—
188Dic3⋊C4—64no—
189C4×Dic3D1214yescomplemented
190#208—62no—
191#208—62no—
192#208—122no—
193C2×C3⋊C8—62no—
194C2×C3⋊C8—61no—
195C2×C3⋊C8—61no—
196Dic12—22no—
197D24—22no—
198#204—24no—
199C22×C32—41no—
200C22×C32#12012yes—
201C22×C32#12111yescharacteristic
202C2×C3⋊D3—22no—
203C2×C3⋊D3—24no—
204C2×C3⋊D3—41no—
205C2×C3⋊D3—42no—
206C2×C3⋊D3—41no—
207C2×C3×D3—44no—
208C2×C3×D3—42no—
209C32×C4#12011yescharacteristic
210C32×C4#12112yes—
211C32×C4#12711yescharacteristic
212C3⋊Dic3—41no—
213C3×Dic3—44no—
214C3×Dic3—42no—
215C2×#41—32no—
216C23×C4—91no—
217#137—62no—
218AGL(1,ℤ/8)—62no—
219#135—62no—
220C2×M16—91no—
221C2×M16D3211yescharacteristic
222#123—182no—
223C22⋊Q8—182no—
224#121—182no—
225#120—182no—
226C4×D4—184no—
227#117—32no—
228#104—184no—
229C22⋊C8—182no—
230C23×C3—21no—
231C23×C3—62no—
232C23×C3D3×D411yescharacteristic
233C23×C3D3×D411yescharacteristic
234C22×D3—22no—
235C22×D3—62no—
236C22×D3—62no—
237C22×D3—61no—
238C22×D3—62no—
239C22×D3—61no—
240C22×D3—122no—
241C22×D3—122no—
242C22×D3—122no—
243C22×D3—124no—
244C3×Q8—62no—
245C3×Q8—62no—
246C3×D4—62no—
247C3×D4—62no—
248C3×D4—122no—
249C3×D4—122no—
250C2×C3×C4—21no—
251C2×C3×C4—22no—
252C2×C3×C4—21no—
253C2×C3×C4—22no—
254C2×C3×C4—62no—
255C2×C3×C4—64no—
256C2×C3×C4—122no—
257C2×C3×C4—122no—
258C2×C3×C4C2×D1212yes—
259C2×C3×C4C2×D1211yescharacteristic
260C2×C3×C4D3×D412yes—
261C2×C3×C4D3×D412yes—
262C2×C3×C4#23711yescharacteristic
263C2×C3×C4#23911yescharacteristic
264C2×C3×C4C2×#6711yescharacteristic
265C2×C3×C4C2×#6712yes—
266#67—42no—
267#67—42no—
268#67—128no—
269C2×Dic3—24no—
270C2×Dic3—22no—
271C2×Dic3—62no—
272C2×Dic3—62no—
273C2×Dic3—61no—
274C2×Dic3—62no—
275C2×Dic3—61no—
276C2×Dic3—122no—
277D12—22no—
278D12—22no—
279D12—128no—
280C4×D3—42no—
281C4×D3—42no—
282C4×D3—124no—
283C4×D3—122no—
284C4×D3—122no—
285C4×D3—121no—
286C4×D3—121no—
287C4×D3—122no—
288C4×D3—122no—
289C4×D3—121no—
290C4×D3—121no—
291Dic6—22no—
292Dic6—22no—
293C3×C8—22no—
294C3×C8—22no—
295C3×C8—42no—
296C3⋊C8—122no—
297C3⋊C8—121no—
298C3⋊C8—121no—
299C2×C32—21no—
300C2×C32—22no—
301C2×C32#39211yescharacteristic
302C3⋊D3—42no—
303C3×D3—82no—
304C24—91no—
305#41—62no—
306#41—62no—
307#41—62no—
308#41—62no—
309C2×Q8—32no—
310C2×D4—32no—
311C2×D4—62no—
312C2×D4—184no—
313C22×C4—62no—
314C22×C4—91no—
315C22×C4—181no—
316C22×C4—182no—
317C22×C4—181no—
318C22×C4—182no—
319C22×C4C2×D3211yescharacteristic
320Q16—62no—
321SD16—64no—
322D8—62no—
323M16—22no—
324M16—182no—
325C2×C8—181no—
326C2×C8#62612yescomplemented
327C4⋊C4—62no—
328C4⋊C4—184no—
329C22⋊C4—62no—
330C22⋊C4—184no—
331C22⋊C4—184no—
332C42—34no—
333C22×C3—21no—
334C22×C3—22no—
335C22×C3—41no—
336C22×C3—41no—
337C22×C3—42no—
338C22×C3—124no—
339C22×C3—122no—
340C22×C3#88212yes—
341C22×C3#89511yescharacteristic
342C22×C3#93712yes—
343C22×C3#93811yescharacteristic
344C2×D3—44no—
345C2×D3—42no—
346C2×D3—64no—
347C2×D3—64no—
348C2×D3—64no—
349C2×D3—62no—
350C2×D3—62no—
351C2×D3—124no—
352C2×D3—122no—
353C2×D3—122no—
354C2×D3—122no—
355C2×D3—121no—
356C2×D3—122no—
357C2×D3—121no—
358C2×D3—124no—
359C2×D3—121no—
360C2×D3—121no—
361C3×C4—22no—
362C3×C4—21no—
363C3×C4—21no—
364C3×C4—124no—
365C3×C4—122no—
366C3×C4#87411yescharacteristic
367C3×C4#88211yescharacteristic
368C3×C4#89512yes—
369C3×C4#93912yes—
370C3×C4#94011yescharacteristic
371C3×C4#95311yescharacteristic
372Dic3—44no—
373Dic3—42no—
374Dic3—122no—
375Dic3—121no—
376Dic3—121no—
377C32#201011yescharacteristic, complemented, Sylow
378C23—62no—
379C23—181no—
380C23—182no—
381C23—362no—
382C23#380211yescharacteristic
383Q8—62no—
384Q8—62no—
385D4—62no—
386D4—62no—
387D4—122no—
388D4—122no—
389D4—368no—
390C2×C4—64no—
391C2×C4—62no—
392C2×C4—122no—
393C2×C4—122no—
394C2×C4—181no—
395C2×C4—182no—
396C2×C4—362no—
397C2×C4—361no—
398C2×C4—361no—
399C2×C4#379611yescharacteristic
400C2×C4D3×D1212yes—
401C2×C4C2×#62611yescharacteristic
402C2×C4D3×#6712yes—
403C8—22no—
404C8—361no—
405C2×C3—22no—
406C2×C3—22no—
407C2×C3—21no—
408C2×C3—22no—
409C2×C3—21no—
410C2×C3—21no—
411C2×C3—42no—
412C2×C3—242no—
413C2×C3#467111yescharacteristic
414C2×C3#522311yescharacteristic
415D3—82no—
416D3—124no—
417D3—122no—
418D3—122no—
419C22—41no—
420C22—124no—
421C22—122no—
422C22—184no—
423C22—182no—
424C22—362no—
425C22—361no—
426C22—361no—
427C22#6391611yescharacteristic
428C22#6392212yes—
429C4—124no—
430C4—122no—
431C4—361no—
432C4#6388612yes—
433C4#6391111yescharacteristic
434C4#6397711yescharacteristic
435C3—21no—
436C3#6870311yescharacteristic, complemented
437C3#7211811yescharacteristic, complemented
438C2—22no—
439C2—21no—
440C2—242no—
441C2—362no—
442C2#1059139111yescharacteristic
subgroupG/H
centerC4#63911
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32#392
hypercenterC2×M16D32
hypocenterC32#2010
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C3×#5748C2semidirect
2. #10595034C2semidirect
3. #10592825C2semidirect
4. #10591111C2semidirect
5. C3×#4557C2semidirect
25. #5748D3semidirect
33. #4557D3semidirect
46. C2×C3×D12D4semidirect
48. C2×C3×Dic6D4semidirect
51. C2×C32×C8D4semidirect
56. C3×C4×Dic3D4semidirect
154. C2×D12#67semidirect
168. C2×Dic6#67semidirect
176. C2×C3×C8D12semidirect
177. C2×C3×C8#67semidirect
189. C4×Dic3D12semidirect
326. C2×C8#626semidirect
377. C32#2010semidirect
436. C3#68703semidirect
437. C3#72118semidirect

Maximal subgroups

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

subgroupindex
C3×#57482
#105950342
#105928252
#105911112
C3×#45572
#721183
#687033