Finite Group Databasebeta

← #11798067

Subgroups — #11798067

Order 1152.

581 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 581 conjugacy classes of subgroups — too many to draw. Only its 86 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
1C2×D3×D24C211yesmaximal, characteristic, complemented
2C2×#63626C211yesmaximal, characteristic, complemented
3#10590832C211yesmaximal, characteristic, complemented
4C2×#63546C211yesmaximal, characteristic, complemented
5C3×#4509C211yesmaximal, characteristic, complemented
6C3×(C2×D3)⋊C16C211yesmaximal, characteristic, complemented
7#10589116C211yesmaximal, characteristic, complemented
8#69191—31nomaximal
9#69108—31nomaximal
10C2×D3×D12—21no—
11C2×#3745C2211yescharacteristic
12C2×#3745C2211yescharacteristic, complemented
13C2×C3×D24C2211yescharacteristic
14C2×C3×D3×C8C2211yescharacteristic
15#63909—21no—
16C2×#3714—21no—
17D3×D24—22no—
18D3×D24—22no—
19C2×C32×C16C2211yescharacteristic, complemented
20#63626—22no—
21C3×#818C2211yescharacteristic, complemented
22C2×C3×C3⋊C16C2211yescharacteristic, complemented
23#63564—21no—
24#63546—22no—
25C2×D3×D8—31no—
26C22×D24—31no—
27C2×#826—31no—
28#5115—31no—
29C2×D48—31no—
30C2×D48—31no—
31C2×D48—31no—
32C2×D48—61no—
33#4883—31no—
34C3×#357—31no—
35C3×C22⋊C16—31no—
36#4509—31no—
37#4509D311yescharacteristic, complemented
38(C2×D3)⋊C16D311yescharacteristic, complemented
39#4491—31no—
40C22×D32—41no—
41C2×C4⋊(C3⋊D3)—21no—
42C2×C4⋊(C3⋊D3)—21no—
43C2×C3×D12—21no—
44C2×C3×C4×D3D411yescharacteristic
45C2×#626—41no—
46C2×#626—41no—
47D3×D12—24no—
48D3×D12—42no—
49C2×C32×C8C2311yescharacteristic
50#3745—21no—
51#3745—21no—
52#3745—21no—
53#3745D412yescomplemented
54C3×C4⋊Dic3—21no—
55C2×C3×C3⋊C8D411yescharacteristic
56C3×D24—21no—
57C3×D24D412yescomplemented
58C3×D3×C8—21no—
59C3×D3×C8—21no—
60#3722—41no—
61#3714—24no—
62C32×C16—21no—
63C3×C3⋊C16—21no—
64#2184—91noSylow
65C2×D3×D4—61no—
66C22×D12—61no—
67C2×C3×D8—31no—
68C22×C3×C8—31no—
69C2×#213—61no—
70#930—61no—
71D3×D8—62no—
72D3×D8—62no—
73C2×D24—31no—
74C2×D24—31no—
75C2×D24—31no—
76C2×D24—31no—
77C2×D24—61no—
78C2×D24—61no—
79C2×D24—62no—
80C2×D24—61no—
81C2×D24—62no—
82C2×D24C2×D311yescharacteristic
83C2×D3×C8C2×D311yescharacteristic
84#895—61no—
85C2×C3×C16—21no—
86C2×C3×C16—31no—
87C2×C3×C16C2×D311yescharacteristic, complemented
88C2×C3×C16C2×D311yescharacteristic, complemented
89C3×#107—31no—
90#826—62no—
91#821—61no—
92#818C2×D311yescharacteristic, complemented
93C2×C3⋊C16C2×D311yescharacteristic, complemented
94#809—61no—
95D48—62no—
96D48—62no—
97D48—64no—
98D48—62no—
99C22×C3⋊D3—41no—
100C22×C3⋊D3—41no—
101C22×C3×D3—41no—
102C22×C3×D3D811yescharacteristic
103C2×D32—44no—
104C2×D32—82no—
105C2×D32—82no—
106C2×C32×C4C2×D411yescharacteristic
107C4⋊(C3⋊D3)—22no—
108C4⋊(C3⋊D3)—41no—
109C4⋊(C3⋊D3)—41no—
110C4⋊(C3⋊D3)—41no—
111C2×C3×Dic3—41no—
112C2×C3×Dic3D811yescharacteristic
113C3×D12—22no—
114C3×D12—41no—
115C3×C4×D3—21no—
116C3×C4×D3—21no—
117#626—44no—
118#626—82no—
119C32×C8C2×D411yescharacteristic
120C32×C8C2×D411yescharacteristic
121C3×C3⋊C8—21no—
122C22×D8—91no—
123C2×D16—91no—
124C2×D16—91no—
125#466—91no—
126#357—31no—
127#357—91no—
128C22⋊C16—31no—
129C23×D3—121no—
130C23×D3—121no—
131C2×C3×D4—61no—
132C22×C3×C4—31no—
133C2×#67—121no—
134C2×#67—121no—
135D3×D4—64no—
136D3×D4—122no—
137C2×D12—21no—
138C2×D12—64no—
139C2×D12—61no—
140C2×D12—61no—
141C2×D12—61no—
142C2×D12—61no—
143C2×D12—121no—
144C2×D12—121no—
145C2×D12—122no—
146C2×D12—121no—
147C2×D12—121no—
148C2×C4×D3D1211yescharacteristic
149C3×D8—32no—
150C3×D8—61no—
151C2×C3×C8—21no—
152C2×C3×C8—31no—
153C2×C3×C8—61no—
154C2×C3×C8—61no—
155C2×C3×C8C22×D311yescharacteristic
156C2×C3×C8C22×D311yescharacteristic
157C3×C4⋊C4—61no—
158#213—64no—
159(C2×D3)⋊C4—121no—
160(C2×D3)⋊C4—121no—
161C4⋊Dic3—21no—
162C2×C3⋊C8D1211yescharacteristic
163D24—21no—
164D24—32no—
165D24—32no—
166D24—62no—
167D24—62no—
168D24—64no—
169D24—61no—
170D24—61no—
171D24—61no—
172D24—61no—
173D24—61no—
174D24—61no—
175D24—121no—
176D24—121no—
177D24D1212yescomplemented
178D3×C8—21no—
179D3×C8—21no—
180C3×C16—22no—
181C3×C16—21no—
182C3×C16—21no—
183C3×C16—61no—
184C3⋊C16—21no—
185C22×C32C2×D811yescharacteristic
186C2×C3⋊D3—42no—
187C2×C3⋊D3—81no—
188C2×C3⋊D3—81no—
189C2×C3⋊D3—81no—
190C2×C3⋊D3—81no—
191C2×C3⋊D3—81no—
192C2×C3×D3—21no—
193C2×C3×D3—21no—
194C2×C3×D3—42no—
195C2×C3×D3—81no—
196C2×C3×D3—81no—
197C2×C3×D3D1612yescomplemented
198D32—88no—
199C32×C4#12011yescharacteristic
200C32×C4AGL(1,ℤ/8)11yescharacteristic
201C3×Dic3—21no—
202C3×Dic3—81no—
203C22×D4—181no—
204C2×D8—31no—
205C2×D8—91no—
206C2×D8—91no—
207C2×D8—181no—
208C2×D8—182no—
209C2×D8—182no—
210C22×C8—31no—
211#121—181no—
212D16—182no—
213D16—182no—
214C2×C16—31no—
215C2×C16D3211yescharacteristic, complemented
216#107—31no—
217#102—181no—
218C23×C3—31no—
219C23×C3—121no—
220C22×D3—41no—
221C22×D3—124no—
222C22×D3—124no—
223C22×D3—121no—
224C22×D3—121no—
225C22×D3—121no—
226C22×D3—121no—
227C22×D3—241no—
228C22×D3—241no—
229C22×D3—242no—
230C22×D3—242no—
231C22×D3—242no—
232C22×D3—242no—
233C22×D3D2411yescharacteristic
234C3×D4—62no—
235C3×D4—121no—
236C2×C3×C4—21no—
237C2×C3×C4—31no—
238C2×C3×C4—61no—
239C2×C3×C4—61no—
240C2×C3×C4—121no—
241C2×C3×C4C2×D1211yescharacteristic
242C2×C3×C4D3×D411yescharacteristic
243#67—124no—
244#67—242no—
245C2×Dic3—41no—
246C2×Dic3D2411yescharacteristic
247D12—22no—
248D12—41no—
249D12—62no—
250D12—62no—
251D12—122no—
252D12—122no—
253D12—124no—
254D12—121no—
255D12—121no—
256D12—121no—
257D12—121no—
258D12—121no—
259D12—121no—
260D12—241no—
261D12—241no—
262D12—242no—
263C4×D3—21no—
264C4×D3—21no—
265C3×C8—21no—
266C3×C8—21no—
267C3×C8—61no—
268C3×C8C2×D1211yescharacteristic
269C3×C8D3×D411yescharacteristic
270C3×C8D3×D411yescharacteristic
271C3×C8D3×D411yescharacteristic
272C3⋊C8—21no—
273C2×C32#44711yescharacteristic
274C2×C32C2×D1611yescharacteristic
275C2×C32#50911yescharacteristic
276C3⋊D3—82no—
277C3⋊D3—161no—
278C3×D3—22no—
279C3×D3—82no—
280C24—361no—
281C2×D4—61no—
282C2×D4—184no—
283C2×D4—181no—
284C2×D4—181no—
285C2×D4—361no—
286C2×D4—362no—
287C2×D4—361no—
288C22×C4—31no—
289D8—32no—
290D8—61no—
291D8—92no—
292D8—184no—
293D8—181no—
294D8—181no—
295D8—181no—
296C2×C8—31no—
297C2×C8—61no—
298C2×C8—61no—
299C2×C8C2×D3211yescharacteristic
300C4⋊C4—61no—
301C22⋊C4—361no—
302C16—21no—
303C16—61no—
304C22×C3—21no—
305C22×C3—32no—
306C22×C3—61no—
307C22×C3—61no—
308C22×C3—122no—
309C22×C3—241no—
310C22×C3—241no—
311C22×C3C2×D2411yescharacteristic
312C22×C3D3×D811yescharacteristic
313C2×D3—21no—
314C2×D3—21no—
315C2×D3—42no—
316C2×D3—81no—
317C2×D3—81no—
318C2×D3—122no—
319C2×D3—122no—
320C2×D3—242no—
321C2×D3—248no—
322C2×D3—248no—
323C2×D3—241no—
324C2×D3—241no—
325C2×D3—241no—
326C2×D3—241no—
327C2×D3—242no—
328C2×D3—241no—
329C2×D3—241no—
330C2×D3—241no—
331C2×D3—241no—
332C2×D3—241no—
333C2×D3—241no—
334C2×D3—481no—
335C2×D3—481no—
336C2×D3—481no—
337C2×D3—481no—
338C2×D3D4812yescomplemented
339C3×C4—21no—
340C3×C4—21no—
341C3×C4—61no—
342C3×C4—241no—
343C3×C4#88211yescharacteristic
344C3×C4#88211yescharacteristic
345C3×C4#90811yescharacteristic
346C3×C4#91411yescharacteristic
347Dic3—21no—
348Dic3—81no—
349C32#218411yescharacteristic, complemented, Sylow
350C23—31no—
351C23—121no—
352C23—364no—
353C23—361no—
354C23—361no—
355C23—722no—
356C23—722no—
357D4—62no—
358D4—121no—
359D4—182no—
360D4—364no—
361D4—361no—
362D4—361no—
363D4—361no—
364D4—722no—
365C2×C4—31no—
366C2×C4—61no—
367C2×C4—61no—
368C2×C4—121no—
369C2×C4D3×D1211yescharacteristic
370C8—61no—
371C8D3×D1211yescharacteristic
372C8#381111yescharacteristic
373C2×C3—21no—
374C2×C3—21no—
375C2×C3—21no—
376C2×C3—62no—
377C2×C3—242no—
378C2×C3#473211yescharacteristic
379C2×C3#477311yescharacteristic
380C2×C3C2×D4811yescharacteristic
381C2×C3#490811yescharacteristic
382C2×C3D3×D1611yescharacteristic
383C2×C3#491411yescharacteristic
384D3—22no—
385D3—82no—
386D3—242no—
387D3—242no—
388D3—482no—
389D3—482no—
390D3—481no—
391D3—481no—
392C22—32no—
393C22—61no—
394C22—61no—
395C22—122no—
396C22—241no—
397C22—241no—
398C22—362no—
399C22—728no—
400C22—721no—
401C22—721no—
402C22—721no—
403C22—721no—
404C22—721no—
405C22D3×D2411yescharacteristic
406C4—61no—
407C4—241no—
408C4#6379411yescharacteristic
409C4#6392311yescharacteristic
410C3—21no—
411C3#6910811yescharacteristic, complemented
412C3#6919111yescharacteristic, complemented
413C2—62no—
414C2—242no—
415C2—722no—
416C2—1441no—
417C2D3×D4811yescharacteristic
418C2#1059023311yescharacteristic
419C2#1059094711yescharacteristic
subgroupG/H
centerC22D3×D24
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC2×C32×C16C22
socleC22×C32C2×D8
hypercenterC2×C16D32
hypocenterC32#2184
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16

Complements

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

NH ≅ G/Ntype
1. C2×D3×D24C2semidirect
2. C2×#63626C2semidirect
3. #10590832C2semidirect
4. C2×#63546C2semidirect
5. C3×#4509C2semidirect
6. C3×(C2×D3)⋊C16C2semidirect
7. #10589116C2semidirect
12. C2×#3745C22semidirect
19. C2×C32×C16C22semidirect
21. C3×#818C22semidirect
22. C2×C3×C3⋊C16C22semidirect
37. #4509D3semidirect
38. (C2×D3)⋊C16D3semidirect
53. #3745D4semidirect
57. C3×D24D4semidirect
87. C2×C3×C16C2×D3semidirect
88. C2×C3×C16C2×D3semidirect
92. #818C2×D3semidirect
93. C2×C3⋊C16C2×D3semidirect
177. D24D12semidirect
197. C2×C3×D3D16semidirect
215. C2×C16D32semidirect
338. C2×D3D48semidirect
349. C32#2184semidirect
411. C3#69108semidirect
412. C3#69191semidirect

Maximal subgroups

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

subgroupindex
C2×D3×D242
C2×#636262
#105908322
C2×#635462
C3×#45092
C3×(C2×D3)⋊C162
#105891162
#691913
#691083