Finite Group Databasebeta

← #11922295

Subgroups — #11922295

Order 1152.

573 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 573 conjugacy classes of subgroups — too many to draw. Only its 67 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×#64266C211yesmaximal, characteristic
2#5827⋊C3C211yesmaximal, characteristic, complemented
3C3×#5426C211yesmaximal, characteristic, complemented
4#10593207C212yesmaximal, complemented
5#10593193C212yesmaximal, complemented
6#85365—31nomaximal
7#78868—31nomaximal
8C2×C3×#41⋊C3C2211yescharacteristic
9#64266C414yescomplemented
10C2×C3⋊GL(2,𝔽3)C2211yescharacteristic
11C2×C3⋊#226C2211yescharacteristic
12#63849—41nomaximal
13Dic3×SL(2,𝔽3)C2212yes—
14C3×#859C2212yes—
15C2×#985—31no—
16C2×#985—61no—
17#5827D311yescharacteristic, complemented
18C2×#950—31no—
19#5504—31no—
20#520⋊C3—31no—
21#5426D311yescharacteristic, complemented
22#5394—32no—
23C4×#226—32no—
24C3×#417—31no—
25#5133—31no—
26#5122—31no—
27C2×#807—31no—
28#4817—32no—
29#4790—32no—
30#4757—32no—
31#4756—32no—
32C2×C4×C3⋊D3—41no—
33C3×#41⋊C3C2×C412yescomplemented
34C2×C3×SL(2,𝔽3)C2311yescharacteristic
35C3⋊GL(2,𝔽3)C2×C412yescomplemented
36C3⋊#226C2×C412yescomplemented
37C3×C4⋊Dic3—41no—
38C3×C4⋊Dic3—41no—
39#3722—42no—
40Dic32—42no—
41#2951—91noSylow
42C2×C3×#41C2×D311yescharacteristic
43C2×#235—31no—
44C2×#41⋊C3—21no—
45C2×#41⋊C3C2×D311yescharacteristic
46#985—34no—
47#985—64no—
48C2×GL(2,𝔽3)—31no—
49C2×GL(2,𝔽3)—61no—
50C2×#226—31no—
51C2×#226—61no—
52C2×C3×M16—31no—
53C2×C3×C4⋊C4—31no—
54#950—34no—
55#950—34no—
56Q8×Dic3C2×D312yes—
57C2×#216—31no—
58C2×#215—31no—
59D4×Dic3—32no—
60C2×#214—31no—
61C2×#213—31no—
62C4×#67—62no—
63#926—31no—
64C2×C4⋊Dic3—31no—
65C22×C3⋊C8—31no—
66#893—32no—
67#892—61no—
68#892—121no—
69D3×C4⋊C4—61no—
70#887—32no—
71C4×SL(2,𝔽3)—32no—
72#859C2×D312yes—
73C3×#103—32no—
74C3×#102—32no—
75#821—32no—
76#816—32no—
77#815—32no—
78C8×Dic3—32no—
79#807—32no—
80#807—32no—
81C22×C3⋊D3—41no—
82C2×C32×C4—41no—
83C2×C3⋊Dic3—41no—
84C4×C3⋊D3—44no—
85C2×C3×Dic3—42no—
86C2×C3×Dic3—42no—
87C3×SL(2,𝔽3)C22×C411yescharacteristic
88C2×#135—91no—
89#520—31no—
90#520—91no—
91#440—92no—
92#440—92no—
93C4×Q16—92no—
94C4×D8—92no—
95C2×#107—91no—
96#417—31no—
97#417—91no—
98#405—91no—
99C3×#41—32no—
100C3×#41C4×D312yes—
101C2×C3×Q8C22×D311yescharacteristic
102C2×C3×D4—31no—
103C22×C3×C4—31no—
104C22×C3×C4—61no—
105C2×#67—61no—
106C22×Dic3—61no—
107#235—34no—
108#235—62no—
109C2×D12—31no—
110C2×C4×D3—61no—
111C2×C4×D3—62no—
112C2×C4×D3—121no—
113C2×C4×D3—241no—
114C2×Dic6—31no—
115#41⋊C3—22no—
116#41⋊C3C4×D312yescomplemented
117C2×SL(2,𝔽3)—21no—
118C2×SL(2,𝔽3)C22×D311yescharacteristic
119GL(2,𝔽3)—32no—
120GL(2,𝔽3)—62no—
121#226—32no—
122#226—62no—
123C3×M16—62no—
124C2×C3×C8—32no—
125C3×C4⋊C4—32no—
126C3×C4⋊C4—61no—
127C3×C4⋊C4—121no—
128#217—32no—
129#216—32no—
130#216—32no—
131#215—32no—
132#215—32no—
133#214—34no—
134#213—34no—
135(C2×D3)⋊C4—62no—
136(C2×D3)⋊C4—122no—
137C4⋊Dic3—31no—
138C4⋊Dic3—32no—
139C4⋊Dic3—41no—
140C4⋊Dic3S411yescharacteristic
141Dic3⋊C4—62no—
142C4×Dic3—32no—
143C4×Dic3—62no—
144C4×Dic3—122no—
145C2×C3⋊C8—31no—
146C2×C3⋊C8—31no—
147C2×C3⋊C8—34no—
148C22×C32—41no—
149C2×C3⋊D3—42no—
150C2×C3⋊D3—81no—
151C2×C3⋊D3—81no—
152C32×C4—42no—
153C3⋊Dic3—42no—
154C3×Dic3—82no—
155C3×Dic3—82no—
156C2×#41—91no—
157C2×#41D3211yescharacteristic
158#135—94no—
159#135—94no—
160C2×Q16—91no—
161C2×SD16—91no—
162C2×SD16—91no—
163C2×D8—91no—
164C2×M16—31no—
165C22×C8—91no—
166C4×Q8—32no—
167C4×Q8—92no—
168C4×D4—92no—
169C4×D4—92no—
170C4×D4—182no—
171#117—91no—
172#117—181no—
173C2×C4⋊C4—31no—
174C2×C4⋊C4—91no—
175C2×C4⋊C4—181no—
176#107—92no—
177#107—92no—
178#103—32no—
179#103—92no—
180#102—32no—
181#102—92no—
182#97—92no—
183C4×C8—92no—
184C23×C3—31no—
185C22×D3—61no—
186C22×D3—121no—
187C22×D3—241no—
188C3×Q8—31no—
189C3×Q8C2×C4×D311yescharacteristic
190C3×D4—32no—
191C3×D4—61no—
192C2×C3×C4—31no—
193C2×C3×C4—32no—
194C2×C3×C4—32no—
195C2×C3×C4—41no—
196C2×C3×C4—62no—
197C2×C3×C4—81no—
198C2×C3×C4—122no—
199C2×C3×C4—241no—
200C2×C3×C4C2×S411yescharacteristic
201#67—64no—
202C2×Dic3—32no—
203C2×Dic3—42no—
204C2×Dic3—61no—
205C2×Dic3—121no—
206C2×Dic3—241no—
207C2×Dic3—241no—
208C2×Dic3C2×S412yes—
209D12—32no—
210D12—61no—
211C4×D3—64no—
212C4×D3—124no—
213C4×D3—244no—
214C4×D3—242no—
215Dic6—32no—
216Dic6—61no—
217SL(2,𝔽3)—21no—
218SL(2,𝔽3)C2×C4×D311yescharacteristic
219C3×C8—62no—
220C3⋊C8—32no—
221C3⋊C8—32no—
222C2×C32—41no—
223C2×C32—41no—
224C2×C32—41no—
225C3⋊D3—82no—
226#41—32no—
227#41—94no—
228#41—182no—
229#41#62412yes—
230C2×Q8—91no—
231C2×Q8C2×D3211yescharacteristic
232C2×D4—31no—
233C2×D4—91no—
234C2×D4—181no—
235C22×C4—31no—
236C22×C4—61no—
237C22×C4—182no—
238C22×C4—181no—
239C22×C4—181no—
240Q16—92no—
241Q16—92no—
242SD16—94no—
243SD16—92no—
244SD16—92no—
245D8—94no—
246M16—62no—
247C2×C8—32no—
248C2×C8—91no—
249C2×C8—91no—
250C2×C8—94no—
251C4⋊C4—31no—
252C4⋊C4—32no—
253C4⋊C4—61no—
254C4⋊C4—92no—
255C4⋊C4—91no—
256C4⋊C4—182no—
257C22⋊C4—92no—
258C22⋊C4—182no—
259C42—92no—
260C42—182no—
261C22×C3—32no—
262C22×C3—41no—
263C22×C3—61no—
264C22×C3—61no—
265C22×C3—81no—
266C22×C3C22×S411yescharacteristic
267C2×D3—62no—
268C2×D3—122no—
269C2×D3—121no—
270C2×D3—121no—
271C2×D3—242no—
272C2×D3—241no—
273C2×D3—241no—
274C2×D3—242no—
275C2×D3—242no—
276C3×C4—31no—
277C3×C4—31no—
278C3×C4—42no—
279C3×C4—82no—
280C3×C4—122no—
281C3×C4—242no—
282C3×C4C4×S412yes—
283Dic3—22no—
284Dic3—62no—
285Dic3—62no—
286Dic3—82no—
287Dic3—122no—
288Dic3—242no—
289C32—41noSylow
290C23—31no—
291C23—181no—
292Q8—31no—
293Q8—92no—
294Q8—181no—
295Q8C2×#62411yescharacteristic
296D4—32no—
297D4—61no—
298D4—92no—
299D4—181no—
300D4—184no—
301C2×C4—31no—
302C2×C4—32no—
303C2×C4—32no—
304C2×C4—32no—
305C2×C4—62no—
306C2×C4—92no—
307C2×C4—181no—
308C2×C4—184no—
309C2×C4—241no—
310C2×C4—722no—
311C2×C4—721no—
312C2×C4D3×S411yescharacteristic
313C8—62no—
314C8—92no—
315C8—92no—
316C2×C3—41no—
317C2×C3—41no—
318C2×C3—41no—
319C2×C3—62no—
320C2×C3—81no—
321C2×C3—81no—
322C2×C3—81no—
323C2×C3C2×C4×S411yescharacteristic
324C2×C3#592511yescharacteristic
325C2×C3#592711yescharacteristic
326D3—122no—
327D3—242no—
328D3—244no—
329C22—32no—
330C22—61no—
331C22—61no—
332C22—182no—
333C22—361no—
334C22—361no—
335C22C2×D3×S411yescharacteristic
336C4—31no—
337C4—31no—
338C4—62no—
339C4—122no—
340C4—182no—
341C4—182no—
342C4(C3⋊S4)⋊C412yes—
343C3—41no—
344C3—81no—
345C3#8536511yescharacteristic, complemented
346C2—62no—
347C2—362no—
348C2#1059644811yescharacteristic
349C2#1059645311yescharacteristic
350C2C2×(C3⋊S4)⋊C411yescharacteristic
subgroupG/H
center, FrattiniC22C2×D3×S4
commutator, hypocenterC3×SL(2,𝔽3)C22×C4
FittingC2×C3×#41C2×D3
socleC22×C3C22×S4
prime radicalC2×#64266C2
cosocleC2×C3×SL(2,𝔽3)C23
hypercenterC2×C4D3×S4
LCSG ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. #5827⋊C3C2semidirect
3. C3×#5426C2semidirect
4. #10593207C2semidirect
5. #10593193C2semidirect
9. #64266C4semidirect
17. #5827D3semidirect
21. #5426D3semidirect
33. C3×#41⋊C3C2×C4semidirect
35. C3⋊GL(2,𝔽3)C2×C4semidirect
36. C3⋊#226C2×C4semidirect
116. #41⋊C3C4×D3semidirect
345. C3#85365semidirect

Maximal subgroups

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

subgroupindex
C2×#642662
#5827⋊C32
C3×#54262
#105932072
#105931932
#853653
#788683
#638494