Finite Group Databasebeta

← #11795176

Subgroups — #11795176

Order 1152.

344 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 59 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
1#10593759C211yesmaximal, characteristic
2#10593344C211yesmaximal, characteristic
3#10590575C211yesmaximal, characteristic
4#10590573C211yesmaximal, characteristic
5#10590049C211yesmaximal, characteristic
6#10590049C211yesmaximal, characteristic
7#10590044C211yesmaximal, characteristic
8C2×C4⋊#157—21no—
9C2×C4⋊#157C2211yescharacteristic
10C2×C4×#157C2211yescharacteristic
11C4⋊C4×C3⋊D3C2211yescharacteristic
12#63900C2211yescharacteristic
13#63900C2211yescharacteristic
14C2×#3710C2211yescharacteristic
15C2×#3710C2211yescharacteristic
16#63781—21no—
17#63737—21no—
18#63737—21no—
19C3×#808—21no—
20C3×#807—21no—
21#63575—21no—
22#63573—21no—
23D3×#107—61no—
24D3×#106—61no—
25C22×#157—21no—
26C22×#157D411yescharacteristic
27C22×#157D411yescharacteristic
28C2×C4×C3⋊D3—21no—
29C2×C4×C3⋊D3C2311yescharacteristic
30C2×#624—21no—
31C2×#624—21no—
32C4⋊#157—21no—
33C4⋊#157—21no—
34C4⋊#157—42no—
35C4×#157—21no—
36C4×#157—21no—
37C32×C4⋊C4D411yescharacteristic
38C4⋊(C3⋊Dic3)D411yescharacteristic
39#3750—21no—
40C3×C4⋊Dic3—21no—
41C3×C4⋊Dic3—21no—
42C2×C3×C3⋊C8—21no—
43C2×C3×C3⋊C8—21no—
44#3724—21no—
45#3724—21no—
46#3710—21no—
47#3710—21no—
48#3710Q812yes—
49#3710Q812yes—
50#2085—91nomaximal, Sylow
51C2×D3×C8—61no—
52C2×D3×C8—61no—
53D3×C4⋊C4—61no—
54D3×C4⋊C4—61no—
55D3×C4⋊C4—61no—
56D3×C4⋊C4—61no—
57C3×#107—61no—
58C3×#106—61no—
59#818—61no—
60#817—61no—
61#808—21no—
62#808—61no—
63#807—21no—
64#807—61no—
65C22×C3⋊D3C2×D411yescharacteristic
66C2×#157—21no—
67C2×#157—21no—
68C2×#157—21no—
69C2×#157—21no—
70C2×#157—21no—
71C2×#157—21no—
72C2×#157—41no—
73C2×#157—41no—
74C2×#157—41no—
75C2×C32×C4—21no—
76C2×C32×C4C2×D411yescharacteristic
77C2×C3⋊Dic3—21no—
78C2×C3⋊Dic3#4111yescharacteristic
79C4×C3⋊D3—41no—
80C4×C3⋊D3—41no—
81C4×C3⋊D3C2×Q811yescharacteristic
82C4×C3⋊D3C2×Q811yescharacteristic
83C4×C3⋊D3#4111yescharacteristic
84C4×C3⋊D3#4111yescharacteristic
85C2×C3×Dic3—41no—
86C2×C3×Dic3—41no—
87#624—41no—
88#624—41no—
89#624—41no—
90#624—41no—
91C3×C3⋊C8—22no—
92C3×C3⋊C8—22no—
93C2×#107—91no—
94C2×#106—91no—
95#389—91no—
96#382—91no—
97#340—91no—
98#340—91no—
99#336—91no—
100C2×C4×D3—61no—
101C2×C4×D3—61no—
102C2×C4×D3—121no—
103C2×C4×D3—121no—
104C2×C4×D3—121no—
105C2×C4×D3—121no—
106C2×C3×C8—61no—
107C2×C3×C8—61no—
108C3×C4⋊C4—21no—
109C3×C4⋊C4—21no—
110C3×C4⋊C4—61no—
111C3×C4⋊C4—61no—
112C4⋊Dic3—21no—
113C4⋊Dic3—21no—
114C4⋊Dic3—61no—
115C4⋊Dic3—61no—
116Dic3⋊C4—121no—
117Dic3⋊C4—121no—
118Dic3⋊C4—121no—
119Dic3⋊C4—121no—
120C2×C3⋊C8—21no—
121C2×C3⋊C8—21no—
122D3×C8—62no—
123D3×C8—62no—
124D3×C8—62no—
125D3×C8—62no—
126C22×C32#12111yescharacteristic
127C2×C3⋊D3#12311yescharacteristic
128C2×C3⋊D3C4⋊Q811yescharacteristic
129C2×C3⋊D3#13511yescharacteristic
130C2×C3⋊D3#13511yescharacteristic
131C2×C3⋊D3AGL(1,ℤ/8)11yescharacteristic
132C2×C3⋊D3#13711yescharacteristic
133#157—41no—
134#157—41no—
135#157—81no—
136C32×C4—41no—
137C32×C4C22⋊Q811yescharacteristic
138C32×C4C22⋊Q811yescharacteristic
139C3⋊Dic3—41no—
140C3⋊Dic3#12511yescharacteristic
141C3⋊Dic3#12511yescharacteristic
142C3×Dic3—81no—
143C3×Dic3—81no—
144C22×C8—91no—
145C22×C8—91no—
146C2×C4⋊C4—91no—
147C2×C4⋊C4—91no—
148C2×C4⋊C4—91no—
149C2×C4⋊C4—91no—
150C2×C4⋊C4—181no—
151C2×C42—91no—
152#107—61no—
153#107—181no—
154#106—61no—
155#106—181no—
156#95—181no—
157#95—181no—
158#95—181no—
159C22×D3—61no—
160C22×D3—61no—
161C2×C3×C4—21no—
162C2×C3×C4—21no—
163C2×C3×C4—41no—
164C2×C3×C4—41no—
165C2×C3×C4—121no—
166C2×C3×C4—121no—
167C2×Dic3—41no—
168C2×Dic3—41no—
169C2×Dic3—61no—
170C2×Dic3—61no—
171C2×Dic3—121no—
172C2×Dic3—121no—
173C4×D3—61no—
174C4×D3—61no—
175C4×D3—61no—
176C4×D3—61no—
177C4×D3—61no—
178C4×D3—61no—
179C4×D3—61no—
180C4×D3—61no—
181C4×D3—241no—
182C4×D3—241no—
183C4×D3—241no—
184C4×D3—241no—
185C4×D3—241no—
186C4×D3—241no—
187C4×D3—241no—
188C4×D3—241no—
189C3×C8—62no—
190C3×C8—62no—
191C3⋊C8—22no—
192C3⋊C8—22no—
193C2×C32#39811yescharacteristic
194C2×C32#46311yescharacteristic
195C2×C32#46411yescharacteristic
196C3⋊D3#48211yescharacteristic
197C3⋊D3#48511yescharacteristic
198C3⋊D3#49911yescharacteristic
199C3⋊D3#50111yescharacteristic
200C22×C4—91no—
201C22×C4—91no—
202C22×C4—91no—
203C22×C4—181no—
204C22×C4—181no—
205C22×C4—181no—
206C22×C4—181no—
207C2×C8—61no—
208C2×C8—61no—
209C2×C8—92no—
210C2×C8—92no—
211C2×C8—181no—
212C2×C8—181no—
213C4⋊C4—61no—
214C4⋊C4—61no—
215C4⋊C4—91no—
216C4⋊C4—181no—
217C4⋊C4—181no—
218C4⋊C4—181no—
219C4⋊C4—181no—
220C4⋊C4—181no—
221C4⋊C4—362no—
222C4⋊C4GO+(4,𝔽2)11yescharacteristic
223C42—181no—
224C42—181no—
225C22×C3—21no—
226C22×C3—21no—
227C2×D3—61no—
228C2×D3—61no—
229C2×D3—61no—
230C2×D3—61no—
231C2×D3—61no—
232C2×D3—61no—
233C2×D3—61no—
234C2×D3—61no—
235C2×D3—61no—
236C2×D3—61no—
237C2×D3—61no—
238C2×D3—61no—
239C3×C4—21no—
240C3×C4—21no—
241C3×C4—21no—
242C3×C4—21no—
243C3×C4—81no—
244C3×C4—81no—
245C3×C4—241no—
246C3×C4—241no—
247Dic3—61no—
248Dic3—61no—
249Dic3—61no—
250Dic3—61no—
251Dic3—81no—
252Dic3—81no—
253Dic3—241no—
254Dic3—241no—
255C32#208511yescharacteristic, complemented, Sylow
256C23—91no—
257C2×C4—21no—
258C2×C4—91no—
259C2×C4—91no—
260C2×C4—91no—
261C2×C4—91no—
262C2×C4—91no—
263C2×C4—121no—
264C2×C4—121no—
265C2×C4—181no—
266C2×C4—181no—
267C2×C4—181no—
268C2×C4—181no—
269C2×C4—181no—
270C2×C4—181no—
271C2×C4—181no—
272C2×C4—361no—
273C2×C4—361no—
274C2×C4—361no—
275C2×C4—361no—
276C2×C4—361no—
277C2×C4—361no—
278C2×C4—361no—
279C2×C4—361no—
280C2×C4—361no—
281C2×C4C2×GO+(4,𝔽2)11yescharacteristic
282C8—62no—
283C8—62no—
284C2×C3—21no—
285C2×C3—21no—
286C2×C3—21no—
287C2×C3—21no—
288C2×C3—21no—
289C2×C3—21no—
290D3—61no—
291D3—61no—
292D3—61no—
293D3—61no—
294D3—61no—
295D3—61no—
296D3—61no—
297D3—61no—
298C22—91no—
299C22—91no—
300C22—91no—
301C22—91no—
302C22—91no—
303C22—91no—
304C22#6424211yescharacteristic
305C4—41no—
306C4—91no—
307C4—91no—
308C4—241no—
309C4—241no—
310C4—361no—
311C4—361no—
312C4—361no—
313C4—721no—
314C4D32⋊Q811yescharacteristic
315C4D32⋊Q811yescharacteristic
316C3—21no—
317C3—21no—
318C2—91no—
319C2—91no—
320C2—91no—
321C2—91no—
322C2#1059334011yescharacteristic
323C2#1059346211yescharacteristic
324C2#1059347411yescharacteristic
subgroupG/H
centerC22#64242
commutator, cosocleC2×C4×C3⋊D3C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C4⋊C4D4
socleC22×C32#121
prime radicalC22×C3⋊D3C2×D4
hypercenterC4⋊C4GO+(4,𝔽2)
hypocenterC32#2085
LCSG ▷ C2×C4×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
255. C32#2085semidirect

Maximal subgroups

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

subgroupindex
#105937592
#105933442
#105905752
#105905732
#105900492
#105900442
#20859