Finite Group Databasebeta

← #11778594

Subgroups — #11778594

Order 1152.

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

normal subgroups only

This group has 523 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×#4981C211yesmaximal, characteristic
3#10591124C212yesmaximal
4C3×#4528C211yesmaximal, characteristic
5#10589154C212yesmaximal
6#69713—31nomaximal
7#68140—31nomaximal
8C2×C32×C4⋊C4C2211yescharacteristic
9#64135—21no—
10#64133—21no—
11#64133C2212yes—
12#64099—22no—
13#64097—22no—
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×Dic3⋊C4—21no—
16C3×C3⋊#95—21no—
17C3×C3⋊#95C2211yescharacteristic
18C3×#830C2212yes—
19#63573—22no—
20#63567—22no—
21#5500—31no—
22#5500—31no—
23#5500—61no—
24C3×#398—31no—
25#4981D311yescharacteristic
26#4971—32no—
27#4721—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—
49C3×Dic3⋊C4—42no—
50C2×C3×C3⋊C8—22no—
51#1611—91noSylow
52C2×C3×C4⋊C4—21no—
53C2×C3×C4⋊C4—31no—
54C2×C3×C4⋊C4—61no—
55C2×C3×C4⋊C4C2×D311yescharacteristic
56C2×C3×C4⋊C4C2×D311yescharacteristic
57#926—62no—
58#926—61no—
59#926—61no—
60C2×C4⋊Dic3C2×D311yescharacteristic
61#924—32no—
62#924—32no—
63#924—62no—
64#924—62no—
65#924—61no—
66#924—61no—
67C2×Dic3⋊C4—21no—
68#890—62no—
69#890—62no—
70#890—64no—
71#888—62no—
72#888—62no—
73#888—64no—
74C3×C22⋊C8—32no—
75C3×#95—31no—
76C3×#95—61no—
77C3⋊#95—21no—
78C3⋊#95C2×D311yescharacteristic
79#830C2×D312yes—
80#817—62no—
81#816—62no—
82#810—62no—
83#808—62no—
84C23×C32C2×D411yescharacteristic
85C2×C32×C4—21no—
86C2×C32×C4—21no—
87C2×C32×C4—21no—
88C2×C32×C4—41no—
89C2×C32×C4—41no—
90C2×C32×C4SD1612yes—
91C2×C32×C4C2×D412yes—
92C2×C3⋊Dic3—22no—
93C2×C3⋊Dic3—22no—
94#634—42no—
95#634—81no—
96C2×C3×Dic3—22no—
97C2×C3×Dic3—41no—
98C2×C3×Dic3—41no—
99C2×C3×Dic3—41no—
100C2×C3×Dic3—41no—
101C2×C3×Dic3—41no—
102C3×C3⋊C8—42no—
103#544—91no—
104#483—92no—
105#398—31no—
106#328—92no—
107#324—31no—
108C22×C3×C4—21no—
109C22×C3×C4—21no—
110C22×C3×C4—21no—
111C22×C3×C4—61no—
112C22×C3×C4—61no—
113C22×C3×C4D1211yescharacteristic
114C22×C3×C4D1211yescharacteristic
115C22×C3×C4#6711yescharacteristic
116C22×C3×C4#6711yescharacteristic
117C22×C3×C4C22×D311yescharacteristic
118C22×C3×C4C22×D311yescharacteristic
119C22×Dic3—21no—
120C22×Dic3—21no—
121C2×Dic6—32no—
122C2×Dic6—32no—
123C2×Dic6—62no—
124C2×Dic6—62no—
125C2×Dic6—61no—
126C2×Dic6—61no—
127C2×C3×C8—62no—
128C3×C4⋊C4—24no—
129C3×C4⋊C4—22no—
130C3×C4⋊C4—22no—
131C3×C4⋊C4—62no—
132C3×C4⋊C4—122no—
133#217—64no—
134#217—62no—
135#217—62no—
136C4⋊Dic3—22no—
137C4⋊Dic3—32no—
138C4⋊Dic3—32no—
139C4⋊Dic3—62no—
140C4⋊Dic3—62no—
141C4⋊Dic3—61no—
142C4⋊Dic3—61no—
143C4⋊Dic3—62no—
144C4⋊Dic3—61no—
145C4⋊Dic3—61no—
146C4⋊Dic3—62no—
147C4⋊Dic3—61no—
148C4⋊Dic3—61no—
149Dic3⋊C4—42no—
150Dic3⋊C4—64no—
151Dic3⋊C4—62no—
152Dic3⋊C4—62no—
153Dic3⋊C4—64no—
154Dic3⋊C4—62no—
155Dic3⋊C4—62no—
156C4×Dic3—64no—
157C4×Dic3—62no—
158C4×Dic3—62no—
159C2×C3⋊C8—22no—
160C22×C32—21no—
161C22×C32—21no—
162C22×C32#12011yescharacteristic
163C22×C32C2×SD1611yescharacteristic
164C22×C32#13711yescharacteristic
165C32×C4—22no—
166C32×C4—22no—
167C32×C4—41no—
168C3⋊Dic3—42no—
169C3⋊Dic3—42no—
170C3×Dic3—42no—
171C3×Dic3—81no—
172C4⋊Q8—182no—
173#125—182no—
174C22⋊Q8—92no—
175C22⋊Q8—181no—
176#117—181no—
177C2×C4⋊C4—31no—
178C2×C4⋊C4—61no—
179C2×C4⋊C4D3211yescharacteristic
180#106—182no—
181#103—182no—
182C22⋊C8—32no—
183#95—31no—
184#95—61no—
185C23×C3—21no—
186C23×C3C2×D1211yescharacteristic
187C23×C3C2×#6711yescharacteristic
188C2×C3×C4—22no—
189C2×C3×C4—22no—
190C2×C3×C4—21no—
191C2×C3×C4—21no—
192C2×C3×C4—21no—
193C2×C3×C4—21no—
194C2×C3×C4—22no—
195C2×C3×C4—21no—
196C2×C3×C4—21no—
197C2×C3×C4—22no—
198C2×C3×C4—22no—
199C2×C3×C4—41no—
200C2×C3×C4—41no—
201C2×C3×C4—41no—
202C2×C3×C4—41no—
203C2×C3×C4—62no—
204C2×C3×C4—81no—
205C2×C3×C4—81no—
206C2×C3×C4—121no—
207C2×C3×C4—121no—
208C2×C3×C4—121no—
209C2×C3×C4—121no—
210C2×C3×C4—121no—
211C2×C3×C4#20412yes—
212C2×C3×C4#21412yes—
213C2×C3×C4D3×D412yes—
214C2×C3×C4D3×D412yes—
215C2×Dic3—22no—
216C2×Dic3—41no—
217C2×Dic3—41no—
218C2×Dic3—41no—
219C2×Dic3—41no—
220C2×Dic3—41no—
221C2×Dic3—64no—
222C2×Dic3—64no—
223C2×Dic3—62no—
224C2×Dic3—62no—
225C2×Dic3—62no—
226C2×Dic3—62no—
227Dic6—122no—
228Dic6—122no—
229Dic6—242no—
230Dic6—242no—
231Dic6—241no—
232Dic6—241no—
233C3×C8—122no—
234C3⋊C8—42no—
235C2×C32—21no—
236C2×C32—21no—
237C2×C32#44811yescharacteristic
238C2×C32#45611yescharacteristic
239C2×C32#45811yescharacteristic
240C2×Q8—92no—
241C2×Q8—181no—
242C22×C4—61no—
243C22×C4—61no—
244C22×C4#62611yescharacteristic
245C22×C4#62611yescharacteristic
246C22×C4C2×D3211yescharacteristic
247C2×C8—62no—
248C4⋊C4—22no—
249C4⋊C4—62no—
250C4⋊C4—92no—
251C4⋊C4—122no—
252C4⋊C4—181no—
253C4⋊C4—181no—
254C4⋊C4—181no—
255C4⋊C4—182no—
256C4⋊C4—182no—
257C22⋊C4—182no—
258C42—182no—
259C22×C3—21no—
260C22×C3—21no—
261C22×C3—21no—
262C22×C3—21no—
263C22×C3—21no—
264C22×C3—21no—
265C22×C3—21no—
266C22×C3—41no—
267C22×C3—41no—
268C22×C3#88211yescharacteristic
269C22×C3C2×#20411yescharacteristic
270C22×C3#90911yescharacteristic
271C22×C3C2×#21411yescharacteristic
272C22×C3#93711yescharacteristic
273C22×C3#95111yescharacteristic
274C3×C4—24no—
275C3×C4—22no—
276C3×C4—22no—
277C3×C4—22no—
278C3×C4—22no—
279C3×C4—42no—
280C3×C4—42no—
281C3×C4—41no—
282C3×C4—41no—
283C3×C4—122no—
284C3×C4—241no—
285Dic3—42no—
286Dic3—81no—
287Dic3—124no—
288Dic3—124no—
289Dic3—122no—
290Dic3—122no—
291Dic3—122no—
292Dic3—122no—
293C32#161111yescharacteristic, complemented, Sylow
294C23C2×#62611yescharacteristic
295Q8—362no—
296Q8—721no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—62no—
303C2×C4—121no—
304C2×C4—121no—
305C2×C4—121no—
306C2×C4—121no—
307C2×C4—121no—
308C2×C4—182no—
309C2×C4—182no—
310C2×C4#371612yes—
311C2×C4#381112yes—
312C8—122no—
313C2×C3—21no—
314C2×C3—21no—
315C2×C3—21no—
316C2×C3—21no—
317C2×C3—21no—
318C2×C3—21no—
319C2×C3—21no—
320C2×C3—41no—
321C2×C3—41no—
322C2×C3#473811yescharacteristic
323C2×C3#474211yescharacteristic
324C2×C3#475211yescharacteristic
325C2×C3#504011yescharacteristic
326C2×C3#505311yescharacteristic
327C2×C3#509511yescharacteristic
328C22—21no—
329C22—21no—
330C22C2×#371611yescharacteristic
331C22#6383111yescharacteristic
332C22#6398111yescharacteristic
333C4—22no—
334C4—22no—
335C4—41no—
336C4—122no—
337C4—241no—
338C4—362no—
339C4—362no—
340C3—21no—
341C3#6814011yescharacteristic, complemented
342C3#6971311yescharacteristic, complemented
343C2—21no—
344C2—21no—
345C2#1059118111yescharacteristic
346C2#1059153511yescharacteristic
347C2#1059165011yescharacteristic
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#1611
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
293. C32#1611semidirect
341. C3#68140semidirect
342. C3#69713semidirect

Maximal subgroups

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

subgroupindex
#105959712
C3×#49812
#105911242
C3×#45282
#105891542
#697133
#681403