Finite Group Databasebeta

← #11778335

Subgroups — #11778335

Order 1152.

655 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 655 conjugacy classes of subgroups — too many to draw. Only its 92 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×#5510C211yesmaximal, characteristic
2#10592678C211yesmaximal, characteristic, complemented
3#10591181C212yesmaximal, complemented
4C3×#4528C211yesmaximal, characteristic, complemented
5#10589150C212yesmaximal, complemented
6#71880—31nomaximal
7#68133—31nomaximal
8C22×#634C2211yescharacteristic
9C2×C3×#235—21no—
10C2×C32×C4⋊C4C2211yescharacteristic
11C2×#3750—21no—
12C3×#930—21no—
13C3×#930C2212yes—
14C3×#897—22no—
15C3×#895—22no—
16C2×#3716—22no—
17#63658—21no—
18#63658C2211yescharacteristic
19C3×#830C2212yes—
20#63567—22no—
21C3×#537—31no—
22#5510D311yescharacteristic
23#5040—32no—
24#4979—31no—
25#4979—31no—
26#4979—61no—
27#4738—32no—
28C3×#324—31no—
29#4537—32no—
30#4528D311yescharacteristic, complemented
31#4470—32no—
32C22×C32×C4D411yescharacteristic
33C22×C32×C4D411yescharacteristic
34C22×C32×C4C2311yescharacteristic
35C22×C3⋊Dic3—21no—
36C22×C3⋊Dic3—21no—
37C2×#634—22no—
38C2×#634—42no—
39C2×C3×#67—22no—
40C3×#235—42no—
41C3×#235—42no—
42C2×C3×D12—21no—
43C2×C3×D12—21no—
44C2×C3×D12D412yes—
45C2×C3×C4×D3—22no—
46C2×C3×Dic6—21no—
47C32×C4⋊C4—22no—
48#3750—42no—
49C3×(C2×D3)⋊C4—22no—
50C3×(C2×D3)⋊C4—22no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3D412yes—
53C2×C3×C3⋊C8—22no—
54#3716—44no—
55#1604—91noSylow
56C2×C3×#41—61no—
57C2×#235—21no—
58C22×Dic6—31no—
59C22×Dic6—31no—
60C22×Dic6—61no—
61C3×C22⋊Q8—62no—
62C3×#121—32no—
63C3×#121—62no—
64C3×#121—61no—
65C2×C3×C4⋊C4—21no—
66C2×C3×C4⋊C4C2×D311yescharacteristic
67C2×C3×C4⋊C4C2×D311yescharacteristic
68C2×#214—62no—
69#930—21no—
70#930C2×D312yes—
71C2×Dic3⋊C4—62no—
72C2×Dic3⋊C4—61no—
73C2×Dic3⋊C4—61no—
74C2×#204—62no—
75#897—22no—
76#895—22no—
77C3×C22⋊C8—32no—
78C3⋊#95—31no—
79C3⋊#95—31no—
80C3⋊#95—61no—
81C3⋊#95—62no—
82C3⋊#95—61no—
83C3⋊#95—61no—
84#830C2×D312yes—
85#816—62no—
86#810—62no—
87C23×C32C2×D411yescharacteristic
88C22×C3×D3—22no—
89C2×C32×C4—21no—
90C2×C32×C4—21no—
91C2×C32×C4—21no—
92C2×C32×C4—41no—
93C2×C32×C4—41no—
94C2×C32×C4SD1612yescomplemented
95C2×C32×C4C2×D412yes—
96C2×C3⋊Dic3—22no—
97C2×C3⋊Dic3—22no—
98C2×C3⋊Dic3—41no—
99C2×C3⋊Dic3—41no—
100C2×C3⋊Dic3—41no—
101C2×C3⋊Dic3—41no—
102#634—24no—
103#634—42no—
104C3×#67—42no—
105C3×#67—42no—
106C2×C3×Dic3—22no—
107C3×D12—42no—
108C3×D12—42no—
109C3×D12—81no—
110C3×C4×D3—44no—
111C3×Dic6—42no—
112C3×C3⋊C8—42no—
113#537—31no—
114#448—92no—
115#395—91no—
116#327—92no—
117#324—31no—
118C3×#41—122no—
119C3×#41—122no—
120C2×C3×Q8—61no—
121C2×C3×D4—32no—
122C2×C3×D4—61no—
123C2×C3×D4—61no—
124C2×C3×D4—62no—
125C22×C3×C4—21no—
126C22×C3×C4—21no—
127C22×C3×C4—21no—
128C22×C3×C4—62no—
129C22×C3×C4D1211yescharacteristic
130C22×C3×C4D1211yescharacteristic
131C22×C3×C4#6711yescharacteristic
132C22×C3×C4#6711yescharacteristic
133C22×C3×C4C22×D311yescharacteristic
134C22×C3×C4C22×D311yescharacteristic
135C2×#67—22no—
136C22×Dic3—62no—
137C22×Dic3—62no—
138C22×Dic3—61no—
139C22×Dic3—61no—
140C22×Dic3—61no—
141C22×Dic3—61no—
142#235—42no—
143#235—42no—
144C2×D12—21no—
145C2×D12—21no—
146C2×D12#6712yes—
147C2×C4×D3—22no—
148C2×Dic6—21no—
149C2×Dic6—62no—
150C2×Dic6—62no—
151C2×Dic6—122no—
152C2×Dic6—122no—
153C2×Dic6—122no—
154C2×Dic6—124no—
155C2×C3×C8—62no—
156C3×C4⋊C4—22no—
157C3×C4⋊C4—22no—
158C3×C4⋊C4—32no—
159C3×C4⋊C4—42no—
160C3×C4⋊C4—61no—
161C3×C22⋊C4—62no—
162C3×C22⋊C4—62no—
163#214—124no—
164(C2×D3)⋊C4—22no—
165(C2×D3)⋊C4—22no—
166C4⋊Dic3—21no—
167C4⋊Dic3#6712yes—
168Dic3⋊C4—122no—
169Dic3⋊C4—122no—
170Dic3⋊C4—124no—
171C2×C3⋊C8—22no—
172#204—124no—
173C22×C32—21no—
174C22×C32—21no—
175C22×C32#12011yescharacteristic
176C22×C32C2×SD1611yescharacteristic
177C22×C32AGL(1,ℤ/8)11yescharacteristic
178C2×C3×D3—42no—
179C2×C3×D3—42no—
180C2×C3×D3—42no—
181C32×C4—22no—
182C32×C4—22no—
183C32×C4—41no—
184C3⋊Dic3—42no—
185C3⋊Dic3—42no—
186C3×Dic3—42no—
187C2×#41—61no—
188C22×Q8—91no—
189C2×SD16—182no—
190C22⋊Q8—62no—
191#121—32no—
192#121—62no—
193#121—61no—
194C2×C4⋊C4—181no—
195C2×C4⋊C4D3211yescharacteristic
196#103—182no—
197C22⋊C8—32no—
198#95—91no—
199#95—181no—
200C23×C3—21no—
201C23×C3—62no—
202C23×C3C2×D1211yescharacteristic
203C23×C3C2×#6711yescharacteristic
204C22×D3—22no—
205C3×Q8—122no—
206C3×D4—122no—
207C3×D4—122no—
208C3×D4—122no—
209C3×D4—122no—
210C3×D4—241no—
211C2×C3×C4—21no—
212C2×C3×C4—21no—
213C2×C3×C4—21no—
214C2×C3×C4—21no—
215C2×C3×C4—21no—
216C2×C3×C4—21no—
217C2×C3×C4—22no—
218C2×C3×C4—22no—
219C2×C3×C4—41no—
220C2×C3×C4—41no—
221C2×C3×C4—41no—
222C2×C3×C4—41no—
223C2×C3×C4—41no—
224C2×C3×C4—42no—
225C2×C3×C4—41no—
226C2×C3×C4—41no—
227C2×C3×C4—42no—
228C2×C3×C4—62no—
229C2×C3×C4—124no—
230C2×C3×C4#20412yescomplemented
231C2×C3×C4#21412yescomplemented
232C2×C3×C4D3×D412yes—
233C2×C3×C4C2×#6712yes—
234#67—42no—
235#67—42no—
236C2×Dic3—22no—
237C2×Dic3—64no—
238C2×Dic3—62no—
239C2×Dic3—62no—
240C2×Dic3—64no—
241C2×Dic3—62no—
242C2×Dic3—62no—
243C2×Dic3—122no—
244C2×Dic3—121no—
245C2×Dic3—121no—
246C2×Dic3—122no—
247C2×Dic3—121no—
248C2×Dic3—121no—
249C2×Dic3—122no—
250C2×Dic3—122no—
251C2×Dic3—121no—
252C2×Dic3—121no—
253C2×Dic3—121no—
254C2×Dic3—121no—
255D12—42no—
256D12—42no—
257D12—81no—
258C4×D3—44no—
259Dic6—42no—
260Dic6—64no—
261Dic6—64no—
262Dic6—124no—
263Dic6—122no—
264Dic6—122no—
265Dic6—124no—
266C3×C8—122no—
267C3⋊C8—42no—
268C2×C32—21no—
269C2×C32—21no—
270C2×C32#45011yescharacteristic
271C2×C32#45611yescharacteristic
272C2×C32B(4,𝔽2)11yescharacteristic
273C3×D3—82no—
274#41—122no—
275#41—122no—
276C2×Q8—61no—
277C2×Q8—182no—
278C2×Q8—362no—
279C2×D4—32no—
280C2×D4—61no—
281C2×D4—61no—
282C2×D4—62no—
283C22×C4—62no—
284C22×C4—181no—
285C22×C4—181no—
286C22×C4#62611yescharacteristic
287C22×C4#62611yescharacteristic
288C22×C4C2×D3211yescharacteristic
289SD16—364no—
290C2×C8—62no—
291C4⋊C4—22no—
292C4⋊C4—32no—
293C4⋊C4—61no—
294C4⋊C4—362no—
295C22⋊C4—62no—
296C22⋊C4—62no—
297C22×C3—22no—
298C22×C3—22no—
299C22×C3—21no—
300C22×C3—21no—
301C22×C3—21no—
302C22×C3—21no—
303C22×C3—21no—
304C22×C3—21no—
305C22×C3—21no—
306C22×C3—122no—
307C22×C3—122no—
308C22×C3—122no—
309C22×C3#88211yescharacteristic
310C22×C3C2×#20411yescharacteristic
311C22×C3#90811yescharacteristic
312C22×C3#93211yescharacteristic
313C22×C3C2×#21411yescharacteristic
314C22×C3#95311yescharacteristic
315C2×D3—42no—
316C2×D3—42no—
317C2×D3—42no—
318C3×C4—22no—
319C3×C4—22no—
320C3×C4—22no—
321C3×C4—22no—
322C3×C4—42no—
323C3×C4—42no—
324C3×C4—41no—
325C3×C4—41no—
326C3×C4—81no—
327C3×C4—122no—
328Dic3—42no—
329Dic3—124no—
330Dic3—124no—
331Dic3—122no—
332Dic3—122no—
333Dic3—122no—
334Dic3—122no—
335C32#160411yescharacteristic, complemented, Sylow
336C23—62no—
337C23C2×#62611yescharacteristic
338Q8—122no—
339Q8—184no—
340Q8—362no—
341D4—122no—
342D4—122no—
343D4—122no—
344D4—122no—
345D4—241no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—62no—
352C2×C4—124no—
353C2×C4—182no—
354C2×C4—182no—
355C2×C4—361no—
356C2×C4—361no—
357C2×C4—361no—
358C2×C4—361no—
359C2×C4#371612yescomplemented
360C2×C4D3×#6712yes—
361C8—122no—
362C2×C3—22no—
363C2×C3—22no—
364C2×C3—21no—
365C2×C3—21no—
366C2×C3—21no—
367C2×C3—21no—
368C2×C3—21no—
369C2×C3—21no—
370C2×C3—21no—
371C2×C3—242no—
372C2×C3#473111yescharacteristic
373C2×C3#474111yescharacteristic
374C2×C3#475211yescharacteristic
375C2×C3#521811yescharacteristic
376C2×C3#524411yescharacteristic
377C2×C3#524611yescharacteristic
378D3—82no—
379C22—21no—
380C22—21no—
381C22—122no—
382C22—122no—
383C22—122no—
384C22C2×#371611yescharacteristic
385C22#6383011yescharacteristic
386C22#6397711yescharacteristic
387C4—22no—
388C4—22no—
389C4—41no—
390C4—122no—
391C4—362no—
392C4—362no—
393C3—21no—
394C3#6813311yescharacteristic, complemented
395C3#7188011yescharacteristic, complemented
396C2—21no—
397C2—21no—
398C2—242no—
399C2#1059117211yescharacteristic
400C2#1059153111yescharacteristic
401C2#1059164911yescharacteristic
subgroupG/H
centerC22#63977
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#120
prime radicalC3×#5510C2
hypercenterC2×C4⋊C4D32
hypocenterC32#1604
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #10592678C2semidirect
3. #10591181C2semidirect
4. C3×#4528C2semidirect
5. #10589150C2semidirect
30. #4528D3semidirect
94. C2×C32×C4SD16semidirect
230. C2×C3×C4#204semidirect
231. C2×C3×C4#214semidirect
335. C32#1604semidirect
359. C2×C4#3716semidirect
394. C3#68133semidirect
395. C3#71880semidirect

Maximal subgroups

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

subgroupindex
C3×#55102
#105926782
#105911812
C3×#45282
#105891502
#718803
#681333