Finite Group Databasebeta

← #11798178

Subgroups — #11798178

Order 1152.

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

normal subgroups only

This group has 545 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
2C3×#4887C211yesmaximal, characteristic, complemented
3C2×#63549C211yesmaximal, characteristic, complemented
4C2×#63547C211yesmaximal, characteristic, complemented
5#10589357C211yesmaximal, characteristic, complemented
6C3×#4491C211yesmaximal, characteristic, complemented
7(C2×D3)⋊(C3⋊C16)C211yesmaximal, characteristic, complemented
8#71085—31nomaximal
9#69193—31nomaximal
10C2×D3×D12—21no—
11C2×#3745C2211yescharacteristic
12C2×C3×Dic12C2211yescharacteristic, complemented
13C2×C3×D24C2211yescharacteristic
14C2×C3×D3×C8C2211yescharacteristic
15C3×#897—21no—
16C2×#3714—21no—
17D3×D24—22no—
18D3×D24—22no—
19C32×#107C2211yescharacteristic, complemented
20C2×C3⋊(C3⋊C16)C2211yescharacteristic, complemented
21C2×C3×C3⋊C16C2211yescharacteristic, complemented
22C3×#810—21no—
23#63549—22no—
24#63547—22no—
25C2×D3×D8—31no—
26C22×D24—31no—
27C3×#467—31no—
28C2×#828—31no—
29C2×#828—31no—
30C2×#827—31no—
31C2×#800—31no—
32#4887D311yescharacteristic, complemented
33C3×#357—31no—
34#4549—31no—
35(C2×D3)⋊C16—31no—
36#4491—31no—
37#4491—31no—
38#4491—61no—
39#4491D311yescharacteristic, complemented
40C22×D32—41no—
41C2×C4⋊(C3⋊D3)—21no—
42C2×C3×D12—21no—
43C2×C3×C4×D3D411yescharacteristic
44C2×C3×Dic6—21no—
45C2×#626—41no—
46D3×D12—24no—
47D3×D12—42no—
48C2×C32×C8C2311yescharacteristic
49C32×C4⋊C4—21no—
50#3745—21no—
51#3745D412yes—
52C3×(C2×D3)⋊C4—41no—
53C3×C4⋊Dic3—41no—
54C2×C3×C3⋊C8D411yescharacteristic
55C3×Dic12—21no—
56C3×Dic12—21no—
57C3×D24—21no—
58C3×D24D412yes—
59C3×D3×C8—21no—
60C3×D3×C8—21no—
61#3714—24no—
62C3⋊(C3⋊C16)—21no—
63C3×C3⋊C16—21no—
64#2187—91noSylow
65C2×D3×D4—61no—
66C22×D12—61no—
67C2×C3×Q16—31no—
68C2×C3×D8—31no—
69C22×C3×C8—31no—
70C3×C22⋊Q8—61no—
71C2×#213—61no—
72D3×D8—62no—
73D3×D8—62no—
74C2×Dic12C2×D311yescharacteristic, complemented
75C2×D24—31no—
76C2×D24—31no—
77C2×D24—61no—
78C2×D24—62no—
79C2×D24—61no—
80C2×D24—62no—
81C2×D24C2×D311yescharacteristic
82C2×D3×C8C2×D311yescharacteristic
83#897—21no—
84C2×C3×C16—31no—
85C3×#107—21no—
86C3×#107C2×D311yescharacteristic, complemented
87C3×#107C2×D311yescharacteristic, complemented
88C3×#103—61no—
89#828—62no—
90#828—62no—
91#827—62no—
92C2×C3⋊C16—31no—
93C2×C3⋊C16—31no—
94C2×C3⋊C16—61no—
95C2×C3⋊C16C2×D311yescharacteristic, complemented
96#810—21no—
97#800—62no—
98C22×C3⋊D3—41no—
99C22×C3×D3—41no—
100C22×C3×D3D811yescharacteristic
101C2×D32—44no—
102C2×D32—82no—
103C2×D32—82no—
104C2×C32×C4—41no—
105C2×C32×C4C2×D411yescharacteristic
106C4⋊(C3⋊D3)—22no—
107C4⋊(C3⋊D3)—41no—
108C2×C3×Dic3—41no—
109C2×C3×Dic3D811yescharacteristic
110C3×D12—22no—
111C3×D12—41no—
112C3×C4×D3—21no—
113C3×C4×D3—21no—
114C3×Dic6—41no—
115C3×Dic6—41no—
116#626—44no—
117C32×C8C2×D411yescharacteristic
118C32×C8C2×D411yescharacteristic
119C3×C3⋊C8—21no—
120C22×D8—91no—
121C2×SD32—91no—
122C2×SD32—91no—
123#467—31no—
124#357—31no—
125#357—91no—
126C22⋊C16—91no—
127C23×D3—121no—
128C23×D3—121no—
129C2×C3×Q8—61no—
130C2×C3×D4—61no—
131C22×C3×C4—31no—
132C2×#67—121no—
133D3×D4—64no—
134D3×D4—122no—
135C2×D12—21no—
136C2×D12—64no—
137C2×D12—61no—
138C2×D12—61no—
139C2×D12—121no—
140C2×D12—122no—
141C2×D12—121no—
142C2×C4×D3#6711yescharacteristic
143C2×Dic6—21no—
144C3×Q16—61no—
145C3×Q16—61no—
146C3×D8—32no—
147C3×D8—61no—
148C2×C3×C8—21no—
149C2×C3×C8—31no—
150C2×C3×C8—61no—
151C2×C3×C8—61no—
152C2×C3×C8C22×D311yescharacteristic
153C2×C3×C8C22×D311yescharacteristic
154C3×C4⋊C4—21no—
155C3×C4⋊C4—21no—
156C3×C4⋊C4—41no—
157C3×C4⋊C4—121no—
158C3×C22⋊C4—121no—
159#213—64no—
160(C2×D3)⋊C4—41no—
161C4⋊Dic3—41no—
162C2×C3⋊C8#6711yescharacteristic
163Dic12—21no—
164Dic12—21no—
165D24—21no—
166D24—32no—
167D24—32no—
168D24—62no—
169D24—64no—
170D24—61no—
171D24—61no—
172D24—121no—
173D24D1212yes—
174D3×C8—21no—
175D3×C8—21no—
176C3×C16—61no—
177C3⋊C16—21no—
178C3⋊C16—61no—
179C3⋊C16—61no—
180C3⋊C16—121no—
181C22×C32C2×D811yescharacteristic
182C2×C3⋊D3—42no—
183C2×C3⋊D3—81no—
184C2×C3⋊D3—81no—
185C2×C3×D3—21no—
186C2×C3×D3—21no—
187C2×C3×D3—42no—
188C2×C3×D3—81no—
189C2×C3×D3—81no—
190C2×C3×D3SD3212yescomplemented
191D32—88no—
192C32×C4—81no—
193C32×C4#12011yescharacteristic
194C32×C4AGL(1,ℤ/8)11yescharacteristic
195C3×Dic3—21no—
196C3×Dic3—81no—
197C22×D4—181no—
198C2×Q16—31no—
199C2×D8—31no—
200C2×D8—91no—
201C2×D8—181no—
202C2×D8—182no—
203C2×D8—182no—
204C22×C8—31no—
205C22⋊Q8—61no—
206SD32—182no—
207SD32—182no—
208C2×C16—31no—
209C2×C16—91no—
210#107D3211yescharacteristic, complemented
211#103—61no—
212C23×C3—31no—
213C23×C3—121no—
214C22×D3—41no—
215C22×D3—124no—
216C22×D3—124no—
217C22×D3—121no—
218C22×D3—121no—
219C22×D3—241no—
220C22×D3—242no—
221C22×D3—242no—
222C22×D3—242no—
223C22×D3—242no—
224C22×D3#21311yescharacteristic
225C3×Q8—121no—
226C3×Q8—121no—
227C3×D4—62no—
228C3×D4—121no—
229C2×C3×C4—21no—
230C2×C3×C4—31no—
231C2×C3×C4—41no—
232C2×C3×C4—41no—
233C2×C3×C4—61no—
234C2×C3×C4—61no—
235C2×C3×C4—81no—
236C2×C3×C4—121no—
237C2×C3×C4D3×D411yescharacteristic
238C2×C3×C4C2×#6711yescharacteristic
239#67—124no—
240C2×Dic3—41no—
241C2×Dic3#21311yescharacteristic
242D12—22no—
243D12—41no—
244D12—62no—
245D12—62no—
246D12—122no—
247D12—124no—
248D12—121no—
249D12—121no—
250D12—241no—
251C4×D3—21no—
252C4×D3—21no—
253Dic6—41no—
254Dic6—41no—
255C3×C8—21no—
256C3×C8—21no—
257C3×C8—61no—
258C3×C8C2×D1211yescharacteristic
259C3×C8D3×D411yescharacteristic
260C3×C8D3×D411yescharacteristic
261C3×C8D3×D411yescharacteristic
262C3⋊C8—21no—
263C2×C32#44711yescharacteristic
264C2×C32C2×SD3211yescharacteristic
265C2×C32#50911yescharacteristic
266C3⋊D3—82no—
267C3×D3—22no—
268C3×D3—82no—
269C24—361no—
270C2×Q8—61no—
271C2×D4—61no—
272C2×D4—184no—
273C2×D4—181no—
274C2×D4—361no—
275C2×D4—362no—
276C22×C4—31no—
277Q16—61no—
278Q16—61no—
279D8—32no—
280D8—61no—
281D8—92no—
282D8—184no—
283D8—181no—
284C2×C8—31no—
285C2×C8—61no—
286C2×C8—61no—
287C2×C8C2×D3211yescharacteristic
288C4⋊C4—21no—
289C4⋊C4—121no—
290C22⋊C4—121no—
291C16—61no—
292C16—181no—
293C22×C3—21no—
294C22×C3—32no—
295C22×C3—61no—
296C22×C3—61no—
297C22×C3—122no—
298C22×C3—241no—
299C22×C3—241no—
300C22×C3D3×D811yescharacteristic
301C22×C3C2×#21311yescharacteristic
302C2×D3—21no—
303C2×D3—21no—
304C2×D3—42no—
305C2×D3—81no—
306C2×D3—81no—
307C2×D3—122no—
308C2×D3—122no—
309C2×D3—242no—
310C2×D3—248no—
311C2×D3—248no—
312C2×D3—241no—
313C2×D3—241no—
314C2×D3—241no—
315C2×D3—241no—
316C2×D3—481no—
317C2×D3—481no—
318C2×D3#82812yescomplemented
319C3×C4—21no—
320C3×C4—21no—
321C3×C4—61no—
322C3×C4—81no—
323C3×C4—81no—
324C3×C4—161no—
325C3×C4—241no—
326C3×C4#88211yescharacteristic
327C3×C4#91411yescharacteristic
328C3×C4#93711yescharacteristic
329C3×C4#94911yescharacteristic
330Dic3—21no—
331Dic3—81no—
332C32#218711yescharacteristic, complemented, Sylow
333C23—31no—
334C23—121no—
335C23—364no—
336C23—361no—
337C23—722no—
338C23—722no—
339Q8—121no—
340Q8—121no—
341D4—62no—
342D4—121no—
343D4—182no—
344D4—364no—
345D4—361no—
346C2×C4—31no—
347C2×C4—41no—
348C2×C4—61no—
349C2×C4—61no—
350C2×C4—121no—
351C2×C4D3×#6711yescharacteristic
352C8—61no—
353C8D3×D1211yescharacteristic
354C8#380211yescharacteristic
355C2×C3—21no—
356C2×C3—21no—
357C2×C3—21no—
358C2×C3—62no—
359C2×C3—242no—
360C2×C3#477311yescharacteristic
361C2×C3#491111yescharacteristic
362C2×C3D3×SD3211yescharacteristic
363C2×C3#503611yescharacteristic
364C2×C3C2×#82811yescharacteristic
365C2×C3#519311yescharacteristic
366D3—22no—
367D3—82no—
368D3—242no—
369D3—242no—
370D3—482no—
371C22—32no—
372C22—61no—
373C22—61no—
374C22—122no—
375C22—241no—
376C22—241no—
377C22—362no—
378C22—728no—
379C22—721no—
380C22—721no—
381C22D3×#21311yescharacteristic
382C4—61no—
383C4—81no—
384C4—241no—
385C4#6392211yescharacteristic
386C4#6393911yescharacteristic
387C3—21no—
388C3#6919311yescharacteristic, complemented
389C3#7108511yescharacteristic, complemented
390C2—62no—
391C2—242no—
392C2—722no—
393C2#1059059511yescharacteristic
394C2#1059102411yescharacteristic
395C2D3×#82811yescharacteristic
subgroupG/H
centerC22D3×#213
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC32×#107C22
socleC22×C32C2×D8
prime radicalC2×D3×D24C2
hypercenter#107D32
hypocenterC32#2187
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #107

Complements

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

NH ≅ G/Ntype
2. C3×#4887C2semidirect
3. C2×#63549C2semidirect
4. C2×#63547C2semidirect
5. #10589357C2semidirect
6. C3×#4491C2semidirect
7. (C2×D3)⋊(C3⋊C16)C2semidirect
12. C2×C3×Dic12C22semidirect
19. C32×#107C22semidirect
20. C2×C3⋊(C3⋊C16)C22semidirect
21. C2×C3×C3⋊C16C22semidirect
32. #4887D3semidirect
39. #4491D3semidirect
74. C2×Dic12C2×D3semidirect
86. C3×#107C2×D3semidirect
87. C3×#107C2×D3semidirect
95. C2×C3⋊C16C2×D3semidirect
190. C2×C3×D3SD32semidirect
210. #107D32semidirect
318. C2×D3#828semidirect
332. C32#2187semidirect
388. C3#69193semidirect
389. C3#71085semidirect

Maximal subgroups

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

subgroupindex
C2×D3×D242
C3×#48872
C2×#635492
C2×#635472
#105893572
C3×#44912
(C2×D3)⋊(C3⋊C16)2
#710853
#691933