Finite Group Databasebeta

← #11798177

Subgroups — #11798177

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
2C2×C3×#800C211yesmaximal, characteristic, complemented
3#10590851C211yesmaximal, characteristic, complemented
4C2×#63549C211yesmaximal, characteristic, complemented
5#10589375C211yesmaximal, characteristic, complemented
6C3×(C2×D3)⋊C16C211yesmaximal, characteristic, complemented
7#10589115C211yesmaximal, characteristic, complemented
8#71485—31nomaximal
9#69110—31nomaximal
10C2×D3×D12—21no—
11C2×#3745C2211yescharacteristic
12C2×C3×Dic12C2211yescharacteristic, complemented
13C2×C3×D24C2211yescharacteristic
14C2×C3×D3×C8C2211yescharacteristic
15#63856—21no—
16C2×#3714—21no—
17D3×D24—22no—
18D3×D24—22no—
19C2×C32×C16C2211yescharacteristic, complemented
20#63645C2211yescharacteristic, complemented
21C2×C3×C3⋊C16C2211yescharacteristic, complemented
22C3×#800—22no—
23#63566—21no—
24#63549—22no—
25C2×D3×D8—31no—
26C22×D24—31no—
27C2×C3×SD32—31no—
28#5188—31no—
29C2×#828—31no—
30#5116—31no—
31C2×#800—31no—
32C2×#800D311yescharacteristic, complemented
33C3×C22⋊C16—31no—
34#4562—31no—
35#4509—31no—
36#4509—31no—
37#4509—31no—
38#4509—61no—
39(C2×D3)⋊C16D311yescharacteristic, 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
49C4⋊(C3⋊Dic3)—21no—
50#3745—21no—
51#3745D412yes—
52C2×C3×C3⋊C8D411yescharacteristic
53C3×Dic12—21no—
54C3×Dic12—21no—
55C3×D24—21no—
56C3×D24D412yes—
57C3×D3×C8—21no—
58C3×D3×C8—21no—
59#3724—41no—
60(C2×D3)⋊Dic3—41no—
61#3714—24no—
62C32×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—
70#946—61no—
71C2×#213—61no—
72#924—61no—
73D3×D8—62no—
74D3×D8—62no—
75C2×Dic12C2×D311yescharacteristic, complemented
76C2×D24—31no—
77C2×D24—31no—
78C2×D24—61no—
79C2×D24—62no—
80C2×D24—61no—
81C2×D24—62no—
82C2×D24C2×D311yescharacteristic
83C2×D3×C8C2×D311yescharacteristic
84C3×SD32—62no—
85C2×C3×C16—21no—
86C2×C3×C16—31no—
87C2×C3×C16C2×D311yescharacteristic, complemented
88C2×C3×C16C2×D311yescharacteristic, complemented
89#835—61no—
90#828—62no—
91#818—31no—
92#818—31no—
93#818—61no—
94#816—61no—
95C2×C3⋊C16C2×D311yescharacteristic, complemented
96#800—22no—
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×C4C2×D411yescharacteristic
105C2×C3⋊Dic3—41no—
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—31no—
122C2×SD32—91no—
123#467—91no—
124#357—91no—
125#357—91no—
126C22⋊C16—31no—
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×D3D1211yescharacteristic
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
154#217—121no—
155#213—64no—
156(C2×D3)⋊C4—121no—
157C4⋊Dic3—61no—
158C4⋊Dic3—61no—
159C4⋊Dic3—121no—
160Dic3⋊C4—121no—
161Dic3⋊C4—121no—
162C2×C3⋊C8D1211yescharacteristic
163Dic12—21no—
164Dic12—21no—
165D24—21no—
166D24—32no—
167D24—32no—
168D24—62no—
169D24—64no—
170D24—61no—
171D24—61no—
172D24—121no—
173D24#6712yes—
174D3×C8—21no—
175D3×C8—21no—
176C3×C16—21no—
177C3×C16—21no—
178C3×C16—41no—
179C3×C16—61no—
180C3⋊C16—21no—
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#12011yescharacteristic
193C32×C4AGL(1,ℤ/8)11yescharacteristic
194C3⋊Dic3—81no—
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—181no—
206SD32—62no—
207SD32—182no—
208C2×C16—31no—
209C2×C16D3211yescharacteristic, complemented
210#107—91no—
211#103—181no—
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×D3D2411yescharacteristic
225C3×Q8—121no—
226C3×Q8—121no—
227C3×D4—62no—
228C3×D4—121no—
229C2×C3×C4—21no—
230C2×C3×C4—31no—
231C2×C3×C4—61no—
232C2×C3×C4—61no—
233C2×C3×C4—121no—
234C2×C3×C4C2×D1211yescharacteristic
235C2×C3×C4D3×D411yescharacteristic
236#67—124no—
237C2×Dic3—41no—
238C2×Dic3—121no—
239C2×Dic3—121no—
240C2×Dic3—241no—
241C2×Dic3D2411yescharacteristic
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×C8D3×D411yescharacteristic
259C3×C8D3×D411yescharacteristic
260C3×C8D3×D411yescharacteristic
261C3×C8C2×#6711yescharacteristic
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—181no—
289C4⋊C4—361no—
290C22⋊C4—361no—
291C16—21no—
292C16—61no—
293C22×C3—21no—
294C22×C3—32no—
295C22×C3—61no—
296C22×C3—61no—
297C22×C3—122no—
298C22×C3—241no—
299C22×C3—241no—
300C22×C3C2×D2411yescharacteristic
301C22×C3D3×D811yescharacteristic
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#80012yescomplemented
319C3×C4—21no—
320C3×C4—21no—
321C3×C4—61no—
322C3×C4—241no—
323C3×C4#88211yescharacteristic
324C3×C4#90811yescharacteristic
325C3×C4#91111yescharacteristic
326C3×C4#93711yescharacteristic
327Dic3—21no—
328Dic3—81no—
329Dic3—241no—
330Dic3—241no—
331Dic3—481no—
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—61no—
348C2×C4—61no—
349C2×C4—121no—
350C2×C4—361no—
351C2×C4D3×D1211yescharacteristic
352C8—61no—
353C8#380211yescharacteristic
354C8D3×#6711yescharacteristic
355C2×C3—21no—
356C2×C3—21no—
357C2×C3—21no—
358C2×C3—62no—
359C2×C3—242no—
360C2×C3#473211yescharacteristic
361C2×C3C2×#80011yescharacteristic
362C2×C3#490811yescharacteristic
363C2×C3D3×SD3211yescharacteristic
364C2×C3#491411yescharacteristic
365C2×C3#515611yescharacteristic
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×D2411yescharacteristic
382C4—61no—
383C4—241no—
384C4—721no—
385C4#6379511yescharacteristic
386C4#6392211yescharacteristic
387C3—21no—
388C3#6911011yescharacteristic, complemented
389C3#7148511yescharacteristic, complemented
390C2—62no—
391C2—242no—
392C2—722no—
393C2D3×#80011yescharacteristic
394C2#1059023311yescharacteristic
395C2#1059094411yescharacteristic
subgroupG/H
centerC22D3×D24
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC2×C32×C16C22
socleC22×C32C2×D8
prime radicalC2×D3×D24C2
hypercenterC2×C16D32
hypocenterC32#2187
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
2. C2×C3×#800C2semidirect
3. #10590851C2semidirect
4. C2×#63549C2semidirect
5. #10589375C2semidirect
6. C3×(C2×D3)⋊C16C2semidirect
7. #10589115C2semidirect
12. C2×C3×Dic12C22semidirect
19. C2×C32×C16C22semidirect
20. #63645C22semidirect
21. C2×C3×C3⋊C16C22semidirect
32. C2×#800D3semidirect
39. (C2×D3)⋊C16D3semidirect
75. C2×Dic12C2×D3semidirect
87. C2×C3×C16C2×D3semidirect
88. C2×C3×C16C2×D3semidirect
95. C2×C3⋊C16C2×D3semidirect
190. C2×C3×D3SD32semidirect
209. C2×C16D32semidirect
318. C2×D3#800semidirect
332. C32#2187semidirect
388. C3#69110semidirect
389. C3#71485semidirect

Maximal subgroups

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

subgroupindex
C2×D3×D242
C2×C3×#8002
#105908512
C2×#635492
#105893752
C3×(C2×D3)⋊C162
#105891152
#714853
#691103