Finite Group Databasebeta

← #11778821

Subgroups — #11778821

Order 1152.

507 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 507 conjugacy classes of subgroups — too many to draw. Only its 88 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#10595971C211yesmaximal, characteristic
2C3×#4986C211yesmaximal, characteristic
3#10591135C212yesmaximal
4C3×#4528C211yesmaximal, characteristic
5#10589154C212yesmaximal
6#69719—31nomaximal
7#68141—31nomaximal
8C2×C32×C4⋊C4C2211yescharacteristic
9#64135—21no—
10#64133—21no—
11#64133C2212yes—
12#64099—22no—
13#64097—22no—
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C3×C3⋊#95—21no—
16C3×C3⋊#95—21no—
17C3×C3⋊#95C2211yescharacteristic
18C3×#830C2212yes—
19#63575—22no—
20#63567—22no—
21#5500—31no—
22#5500—31no—
23#5500—61no—
24C3×#400—31no—
25#4986D311yescharacteristic
26#4970—32no—
27#4722—32no—
28C3×#324—31no—
29#4528D311yescharacteristic
30#4467—32no—
31#4452—32no—
32C22×C32×C4D411yescharacteristic
33C22×C32×C4D411yescharacteristic
34C22×C32×C4C2311yescharacteristic
35C2×#634—21no—
36C2×#634D412yes—
37C22×C3×Dic3—21no—
38C22×C3×Dic3—21no—
39C32×C4⋊C4—22no—
40#3757—22no—
41C4⋊(C3⋊Dic3)—21no—
42C4⋊(C3⋊Dic3)—21no—
43C4⋊(C3⋊Dic3)—21no—
44C4⋊(C3⋊Dic3)D412yes—
45#3750—22no—
46#3750—22no—
47C4×C3⋊Dic3—22no—
48C3×C4⋊Dic3—22no—
49C2×C3×C3⋊C8—22no—
50#1617—91noSylow
51C2×C3×C4⋊C4—21no—
52C2×C3×C4⋊C4—31no—
53C2×C3×C4⋊C4C2×D311yescharacteristic
54C2×C3×C4⋊C4C2×D311yescharacteristic
55#926—62no—
56#926—61no—
57#926—61no—
58C2×C4⋊Dic3C2×D311yescharacteristic
59#924—32no—
60#924—32no—
61#924—62no—
62#924—62no—
63#924—61no—
64#924—61no—
65#890—62no—
66#890—62no—
67#890—64no—
68#888—62no—
69#888—62no—
70#888—64no—
71C3×C22⋊C8—32no—
72C3×#95—31no—
73C3×#95—61no—
74C3×#95—61no—
75C3⋊#95—21no—
76C3⋊#95—21no—
77C3⋊#95C2×D311yescharacteristic
78#830C2×D312yes—
79#818—62no—
80#816—62no—
81#810—62no—
82#807—62no—
83C23×C32C2×D411yescharacteristic
84C2×C32×C4—21no—
85C2×C32×C4—21no—
86C2×C32×C4—21no—
87C2×C32×C4—41no—
88C2×C32×C4—41no—
89C2×C32×C4Q1612yes—
90C2×C32×C4C2×D412yes—
91C2×C3⋊Dic3—22no—
92C2×C3⋊Dic3—22no—
93#634—42no—
94#634—81no—
95C2×C3×Dic3—41no—
96C2×C3×Dic3—41no—
97C2×C3×Dic3—42no—
98C2×C3×Dic3—41no—
99C2×C3×Dic3—41no—
100C3×C3⋊C8—42no—
101#544—91no—
102#484—92no—
103#400—31no—
104#328—92no—
105#324—31no—
106C22×C3×C4—21no—
107C22×C3×C4—21no—
108C22×C3×C4—21no—
109C22×C3×C4—61no—
110C22×C3×C4—61no—
111C22×C3×C4D1211yescharacteristic
112C22×C3×C4D1211yescharacteristic
113C22×C3×C4#6711yescharacteristic
114C22×C3×C4#6711yescharacteristic
115C22×C3×C4C22×D311yescharacteristic
116C22×C3×C4C22×D311yescharacteristic
117C22×Dic3—21no—
118C22×Dic3—21no—
119C2×Dic6—32no—
120C2×Dic6—32no—
121C2×Dic6—62no—
122C2×Dic6—62no—
123C2×Dic6—61no—
124C2×Dic6—61no—
125C2×C3×C8—62no—
126C3×C4⋊C4—24no—
127C3×C4⋊C4—22no—
128C3×C4⋊C4—22no—
129C3×C4⋊C4—62no—
130#217—64no—
131#217—62no—
132#217—62no—
133C4⋊Dic3—22no—
134C4⋊Dic3—32no—
135C4⋊Dic3—32no—
136C4⋊Dic3—62no—
137C4⋊Dic3—62no—
138C4⋊Dic3—61no—
139C4⋊Dic3—61no—
140C4⋊Dic3—62no—
141C4⋊Dic3—61no—
142C4⋊Dic3—61no—
143C4⋊Dic3—62no—
144C4⋊Dic3—61no—
145C4⋊Dic3—61no—
146Dic3⋊C4—64no—
147Dic3⋊C4—62no—
148Dic3⋊C4—62no—
149Dic3⋊C4—64no—
150Dic3⋊C4—62no—
151Dic3⋊C4—62no—
152C4×Dic3—64no—
153C4×Dic3—62no—
154C4×Dic3—62no—
155C2×C3⋊C8—22no—
156C22×C32—21no—
157C22×C32—21no—
158C22×C32#12011yescharacteristic
159C22×C32C2×Q1611yescharacteristic
160C22×C32#13711yescharacteristic
161C32×C4—22no—
162C32×C4—22no—
163C32×C4—41no—
164C3⋊Dic3—42no—
165C3⋊Dic3—42no—
166C3×Dic3—81no—
167C3×Dic3—81no—
168C4⋊Q8—182no—
169#125—182no—
170C22⋊Q8—92no—
171C22⋊Q8—181no—
172#117—181no—
173C2×C4⋊C4—31no—
174C2×C4⋊C4D3211yescharacteristic
175#107—182no—
176#103—182no—
177C22⋊C8—32no—
178#95—31no—
179#95—61no—
180#95—61no—
181C23×C3—21no—
182C23×C3C2×D1211yescharacteristic
183C23×C3C2×#6711yescharacteristic
184C2×C3×C4—22no—
185C2×C3×C4—22no—
186C2×C3×C4—21no—
187C2×C3×C4—21no—
188C2×C3×C4—21no—
189C2×C3×C4—21no—
190C2×C3×C4—22no—
191C2×C3×C4—21no—
192C2×C3×C4—21no—
193C2×C3×C4—22no—
194C2×C3×C4—22no—
195C2×C3×C4—41no—
196C2×C3×C4—41no—
197C2×C3×C4—41no—
198C2×C3×C4—41no—
199C2×C3×C4—81no—
200C2×C3×C4—81no—
201C2×C3×C4—121no—
202C2×C3×C4—121no—
203C2×C3×C4—122no—
204C2×C3×C4—121no—
205C2×C3×C4—121no—
206C2×C3×C4Dic1212yes—
207C2×C3×C4#21612yes—
208C2×C3×C4D3×D412yes—
209C2×C3×C4D3×D412yes—
210C2×Dic3—41no—
211C2×Dic3—41no—
212C2×Dic3—42no—
213C2×Dic3—41no—
214C2×Dic3—41no—
215C2×Dic3—64no—
216C2×Dic3—64no—
217C2×Dic3—62no—
218C2×Dic3—62no—
219C2×Dic3—62no—
220C2×Dic3—62no—
221Dic6—122no—
222Dic6—122no—
223Dic6—242no—
224Dic6—242no—
225Dic6—241no—
226Dic6—241no—
227C3×C8—122no—
228C3⋊C8—42no—
229C2×C32—21no—
230C2×C32—21no—
231C2×C32#45111yescharacteristic
232C2×C32#45411yescharacteristic
233C2×C32#45811yescharacteristic
234C2×Q8—92no—
235C2×Q8—181no—
236C22×C4—61no—
237C22×C4—61no—
238C22×C4#62611yescharacteristic
239C22×C4#62611yescharacteristic
240C22×C4C2×D3211yescharacteristic
241C2×C8—62no—
242C4⋊C4—22no—
243C4⋊C4—62no—
244C4⋊C4—92no—
245C4⋊C4—181no—
246C4⋊C4—181no—
247C4⋊C4—181no—
248C4⋊C4—182no—
249C4⋊C4—182no—
250C22⋊C4—182no—
251C42—182no—
252C22×C3—21no—
253C22×C3—21no—
254C22×C3—21no—
255C22×C3—21no—
256C22×C3—21no—
257C22×C3—21no—
258C22×C3—21no—
259C22×C3—41no—
260C22×C3—41no—
261C22×C3#88211yescharacteristic
262C22×C3C2×Dic1211yescharacteristic
263C22×C3#90911yescharacteristic
264C22×C3#93711yescharacteristic
265C22×C3C2×#21611yescharacteristic
266C22×C3#95111yescharacteristic
267C3×C4—24no—
268C3×C4—22no—
269C3×C4—22no—
270C3×C4—22no—
271C3×C4—22no—
272C3×C4—42no—
273C3×C4—42no—
274C3×C4—41no—
275C3×C4—41no—
276C3×C4—241no—
277C3×C4—241no—
278Dic3—81no—
279Dic3—81no—
280Dic3—124no—
281Dic3—124no—
282Dic3—122no—
283Dic3—122no—
284Dic3—122no—
285Dic3—122no—
286C32#161711yescharacteristic, complemented, Sylow
287C23C2×#62611yescharacteristic
288Q8—362no—
289Q8—721no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—121no—
296C2×C4—121no—
297C2×C4—122no—
298C2×C4—121no—
299C2×C4—121no—
300C2×C4—182no—
301C2×C4—182no—
302C2×C4#371912yes—
303C2×C4#381112yes—
304C8—122no—
305C2×C3—21no—
306C2×C3—21no—
307C2×C3—21no—
308C2×C3—21no—
309C2×C3—21no—
310C2×C3—21no—
311C2×C3—21no—
312C2×C3—41no—
313C2×C3—41no—
314C2×C3#473911yescharacteristic
315C2×C3#474211yescharacteristic
316C2×C3#475311yescharacteristic
317C2×C3#505011yescharacteristic
318C2×C3#505311yescharacteristic
319C2×C3#506211yescharacteristic
320C22—21no—
321C22—21no—
322C22#6383111yescharacteristic
323C22C2×#371911yescharacteristic
324C22#6398111yescharacteristic
325C4—22no—
326C4—22no—
327C4—41no—
328C4—241no—
329C4—241no—
330C4—362no—
331C4—362no—
332C3—21no—
333C3#6814111yescharacteristic, complemented
334C3#6971911yescharacteristic, complemented
335C2—21no—
336C2—21no—
337C2#1059119011yescharacteristic
338C2#1059153511yescharacteristic
339C2#1059164711yescharacteristic
subgroupG/H
centerC22#63981
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#120
prime radicalC23×C32C2×D4
hypercenterC2×C4⋊C4D32
hypocenterC32#1617
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
286. C32#1617semidirect
333. C3#68141semidirect
334. C3#69719semidirect

Maximal subgroups

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

subgroupindex
#105959712
C3×#49862
#105911352
C3×#45282
#105891542
#697193
#681413