Finite Group Databasebeta

← #85514

Subgroups — #85514

Order 384.

309 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 309 conjugacy classes of subgroups — too many to draw. Only its 38 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
1A4×#41C211yesmaximal, characteristic, complemented
2#5912C211yesmaximal, characteristic, complemented
3#5417C211yesmaximal, characteristic, complemented
4#5416C211yesmaximal, characteristic, complemented
5#5415C211yesmaximal, characteristic, complemented
6#5414C211yesmaximal, characteristic, complemented
7C2×A4⋊C8C211yesmaximal, characteristic, complemented
8#3002—31nomaximal, Sylow
9Q8×A4C2211yescharacteristic
10D4×A4—21no—
11D4×A4C2211yescharacteristic
12C2×C4×A4—21no—
13C2×C4×A4C2211yescharacteristic
14GL(2,ℤ/4)—21no—
15C4⋊S4C2211yescharacteristic
16C4×S4—21no—
17A4⋊Q8C2211yescharacteristic
18#950—41nomaximal
19A4⋊C8C2211yescharacteristic
20A4⋊C8C2211yescharacteristic
21C22×#41D311yescharacteristic, complemented
22C2×#135—31no—
23C2×#135—31no—
24#525—31no—
25#452—31no—
26#452—31no—
27#451—31no—
28#450—31no—
29#449—31no—
30#449—31no—
31#448—31no—
32#447—31no—
33#416—31no—
34#416—31no—
35C2×C22⋊C8—31no—
36C22×A4—21no—
37C22×A4D411yescharacteristic
38C2×S4—21no—
39C3×#41—41no—
40#235—41no—
41C4×A4—21no—
42C4×A4D411yescharacteristic
43C4×A4C2311yescharacteristic
44SL(2,ℤ/4)—21no—
45#216—41no—
46#215—41no—
47#214—41no—
48#213—41no—
49C2×C3⋊C8—41no—
50C2×#41—31no—
51C2×#41—31no—
52C2×#41—31no—
53C2×#41—31no—
54C2×#41—31no—
55C2×#41—61no—
56C2×#41—61no—
57C22×Q8C2×D311yescharacteristic
58C22×D4—21no—
59C22×D4C2×D311yescharacteristic
60C23×C4—21no—
61C23×C4C2×D311yescharacteristic
62#135—62no—
63#135—62no—
64#135—61no—
65#135—61no—
66#135—61no—
67#135—61no—
68C2×Q16—31no—
69C2×Q16—31no—
70C2×SD16—31no—
71C2×SD16—31no—
72C2×SD16—31no—
73C2×SD16—31no—
74C2×D8—31no—
75C2×D8—31no—
76C22×C8—31no—
77C22×C8—31no—
78#123—61no—
79C22⋊Q8—31no—
80C22⋊Q8—31no—
81#121—31no—
82#121—31no—
83#120—61no—
84C4×D4—61no—
85C4×D4—61no—
86#117—31no—
87#103—31no—
88#103—31no—
89#103—31no—
90#103—31no—
91#102—31no—
92#102—31no—
93#102—31no—
94#102—31no—
95C22⋊C8—31no—
96C22⋊C8—31no—
97C22⋊C8—31no—
98C22⋊C8—31no—
99C2×A4—21no—
100C2×A4—41no—
101C2×A4C2×D411yescharacteristic
102S4—41no—
103C3×Q8—41no—
104C3×D4—41no—
105C3×D4—81no—
106C2×C3×C4—41no—
107C2×C3×C4—81no—
108#67—81no—
109D12—41no—
110C4×D3—81no—
111Dic6—41no—
112C3⋊C8—41no—
113C3⋊C8—41no—
114C24—21no—
115C24#6711yescharacteristic
116#41—32no—
117#41—32no—
118#41—31no—
119#41—31no—
120#41—31no—
121#41—61no—
122#41—61no—
123#41—61no—
124#41—61no—
125#41—61no—
126#41—61no—
127#41—62no—
128#41—62no—
129#41—61no—
130#41S411yescharacteristic, complemented
131C2×Q8—31no—
132C2×Q8—31no—
133C2×Q8—31no—
134C2×Q8—61no—
135C2×D4—31no—
136C2×D4—31no—
137C2×D4—31no—
138C2×D4—61no—
139C2×D4—61no—
140C2×D4—61no—
141C2×D4—61no—
142C2×D4—61no—
143C2×D4—61no—
144C2×D4—61no—
145C2×D4—61no—
146C22×C4—21no—
147C22×C4—31no—
148C22×C4—31no—
149C22×C4—31no—
150C22×C4—31no—
151C22×C4—61no—
152C22×C4—61no—
153C22×C4—61no—
154C22×C4—61no—
155C22×C4—61no—
156C22×C4#6711yescharacteristic
157C22×C4C22×D311yescharacteristic
158Q16—62no—
159Q16—61no—
160Q16—61no—
161SD16—62no—
162SD16—61no—
163SD16—62no—
164SD16—61no—
165SD16—61no—
166SD16—61no—
167D8—62no—
168D8—61no—
169D8—61no—
170C2×C8—31no—
171C2×C8—31no—
172C2×C8—31no—
173C2×C8—31no—
174C2×C8—61no—
175C2×C8—61no—
176C2×C8—61no—
177C2×C8—61no—
178C4⋊C4—31no—
179C4⋊C4—31no—
180C4⋊C4—61no—
181C4⋊C4—61no—
182C22⋊C4—61no—
183C22⋊C4—61no—
184C22⋊C4—61no—
185C22⋊C4—61no—
186C22⋊C4—61no—
187C42—61no—
188C22×C3—41no—
189C22×C3—81no—
190C2×D3—81no—
191A4#13511yescharacteristic, complemented
192C3×C4—41no—
193C3×C4—41no—
194C3×C4—81no—
195Dic3—81no—
196C23—21no—
197C23—31no—
198C23—31no—
199C23—41no—
200C23—61no—
201C23—61no—
202C23—61no—
203C23—61no—
204C23—121no—
205C23C2×#6711yescharacteristic
206Q8—32no—
207Q8—31no—
208Q8—61no—
209Q8—61no—
210Q8—61no—
211Q8C2×S411yescharacteristic
212D4—21no—
213D4—32no—
214D4—31no—
215D4—61no—
216D4—61no—
217D4—61no—
218D4—61no—
219D4—62no—
220D4—61no—
221D4—61no—
222D4—121no—
223D4—121no—
224D4—122no—
225D4—121no—
226D4—121no—
227D4C2×S411yescharacteristic
228C2×C4—21no—
229C2×C4—31no—
230C2×C4—31no—
231C2×C4—31no—
232C2×C4—31no—
233C2×C4—31no—
234C2×C4—31no—
235C2×C4—31no—
236C2×C4—61no—
237C2×C4—61no—
238C2×C4—61no—
239C2×C4—61no—
240C2×C4—62no—
241C2×C4—61no—
242C2×C4—61no—
243C2×C4—61no—
244C2×C4—61no—
245C2×C4—61no—
246C2×C4—121no—
247C2×C4—121no—
248C2×C4C2×S411yescharacteristic
249C8—61no—
250C8—61no—
251C8—61no—
252C8—61no—
253C2×C3—41no—
254C2×C3—81no—
255C2×C3—161no—
256D3—161no—
257C22—21no—
258C22—31no—
259C22—31no—
260C22—31no—
261C22—61no—
262C22—61no—
263C22—61no—
264C22—61no—
265C22—61no—
266C22—121no—
267C22—121no—
268C22—121no—
269C22—121no—
270C22—121no—
271C22—121no—
272C22—121no—
273C22#95011yescharacteristic, complemented
274C22GL(2,ℤ/4)11yescharacteristic
275C4—21no—
276C4—31no—
277C4—31no—
278C4—61no—
279C4—121no—
280C4—121no—
281C4—121no—
282C4GL(2,ℤ/4)11yescharacteristic
283C4C22×S411yescharacteristic
284C3—41noSylow
285C2—21no—
286C2—31no—
287C2—31no—
288C2—41no—
289C2—61no—
290C2—121no—
291C2—241no—
292C2C2×GL(2,ℤ/4)11yescharacteristic
subgroupG/H
centerC4GL(2,ℤ/4)
commutator, cosocleC4×A4C23
FrattiniC4C22×S4
FittingC22×#41D3
socleC23C2×#67
hypercenter#41S4
hypocenterA4#135
LCSG ▷ C4×A4 ▷ C2×A4 ▷ A4
UCSC1 ◁ C4 ◁ C2×C4 ◁ #41

Complements

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

NH ≅ G/Ntype
1. A4×#41C2semidirect
2. #5912C2semidirect
3. #5417C2semidirect
4. #5416C2semidirect
5. #5415C2semidirect
6. #5414C2semidirect
7. C2×A4⋊C8C2semidirect
21. C22×#41D3semidirect
130. #41S4semidirect
191. A4#135semidirect
273. C22#950semidirect

Maximal subgroups

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

subgroupindex
A4×#412
#59122
#54172
#54162
#54152
#54142
C2×A4⋊C82
#30023
#9504