Finite Group Databasebeta

← #11787979

Subgroups — #11787979

Order 1152.

943 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 943 conjugacy classes of subgroups — too many to draw. Only its 132 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×#64138C211yesmaximal, characteristic
2#10595510C211yesmaximal, characteristic
3C3×#5211C212yesmaximal, complemented
4C2×#63581C211yesmaximal, characteristic
5#10589186C212yesmaximal, complemented
6#69538—32nomaximal
7C23×C32×C4C2211yescharacteristic
8C22×#638C2211yescharacteristic
9C2×#3757C2211yescharacteristic
10#64138—22no—
11#64138C414yescomplemented
12C2×#3752—21no—
13C2×#3750—21no—
14C2×C3×#217C2212yes—
15C2×C3×#217C2212yes—
16#63974—21no—
17#63957—21no—
18#63952—24no—
19C3×C3⋊#95—24no—
20#63581—22no—
21C2×#929—32no—
22C2×#929—61no—
23#5486—32no—
24C3×#381—32no—
25#5211D312yescomplemented
26C2×#806—32no—
27#4527—32no—
28#4526—32no—
29C24×C32C2311yescharacteristic
30C23×C3⋊D3D411yescharacteristic
31C22×C32×C4—21no—
32C22×C32×C4—21no—
33C22×C32×C4—22no—
34C22×C32×C4—22no—
35C22×C32×C4C2×C412yescomplemented
36C2×#638—22no—
37C2×#638—22no—
38C2×#638C2×C412yes—
39C2×#638D412yes—
40C22×C3⋊Dic3—21no—
41C22×C3⋊Dic3D411yescharacteristic
42C22×C3×Dic3—22no—
43C22×C3×Dic3D414yes—
44C2×#624—22no—
45#3757—21no—
46#3757C2×C412yescomplemented
47#3752—24no—
48#3750—24no—
49C3×#217—22no—
50C3×#217—22no—
51C3×#217—22no—
52C3×#217—22no—
53#3724—22no—
54#3722—22no—
55Dic32—22no—
56#1890—91noSylow
57C23×C3×C4—21no—
58C23×C3×C4C2×D312yes—
59C22×#67—32no—
60C22×#67—61no—
61C2×C3×C22⋊C4—32no—
62C2×C3×C22⋊C4—32no—
63C2×#217—32no—
64C2×#217—61no—
65C2×#217C2×D312yes—
66C2×#217C2×D312yes—
67#929—38no—
68#929—64no—
69#929—64no—
70#929—64no—
71C4×#67—64no—
72C2×(C2×D3)⋊C4—62no—
73C2×(C2×D3)⋊C4—62no—
74C2×Dic3⋊C4—62no—
75C2×Dic3⋊C4—62no—
76#67⋊C4—64no—
77D3×C22⋊C4—62no—
78#877—62no—
79C3×#95—64no—
80C3⋊#95—24no—
81#806—64no—
82C23×C32—42no—
83C23×C32C22×C411yescharacteristic
84C23×C32C2×D411yescharacteristic
85C23×C32C2×D411yescharacteristic
86C23×C32C2×D412yes—
87C23×C32#4112yes—
88C22×C3⋊D3—21no—
89C22×C3⋊D3—21no—
90C22×C3⋊D3—42no—
91C22×C3⋊D3C22⋊C412yes—
92C2×C32×C4—22no—
93C2×C32×C4—24no—
94C2×C32×C4—41no—
95C2×C32×C4—42no—
96C2×C32×C4—41no—
97#638—24no—
98#638—24no—
99C2×C3⋊Dic3—22no—
100C2×C3⋊Dic3—21no—
101C2×C3⋊Dic3—21no—
102C2×C3⋊Dic3—42no—
103C2×C3⋊Dic3C22⋊C412yes—
104C2×C3×Dic3—24no—
105C2×C3×Dic3—44no—
106C2×C3×Dic3—44no—
107C2×C3×Dic3—42no—
108#624—82no—
109C2×#123—91no—
110#518—91no—
111C2×#99—91no—
112#381—32no—
113#342—92no—
114C24×C3—21no—
115C24×C3C22×D312yes—
116C23×D3—32no—
117C23×D3—61no—
118C22×C3×C4—22no—
119C22×C3×C4—22no—
120C22×C3×C4—22no—
121C22×C3×C4—22no—
122C22×C3×C4—22no—
123C22×C3×C4—22no—
124C22×C3×C4—22no—
125C22×C3×C4—22no—
126C22×C3×C4—22no—
127C22×C3×C4—34no—
128C22×C3×C4—42no—
129C22×C3×C4—42no—
130C22×C3×C4—62no—
131C22×C3×C4C4×D314yescomplemented
132C2×#67—34no—
133C2×#67—34no—
134C2×#67—62no—
135C2×#67—62no—
136C2×#67—62no—
137C2×#67—62no—
138C2×#67—62no—
139C2×#67—62no—
140C2×#67—122no—
141C2×#67—122no—
142C22×Dic3—22no—
143C22×Dic3—32no—
144C22×Dic3—61no—
145C22×Dic3—62no—
146C22×Dic3—62no—
147C22×Dic3#6714yes—
148C2×C4×D3—64no—
149C3×C22⋊C4—62no—
150C3×C22⋊C4—62no—
151C3×C22⋊C4—62no—
152C3×C22⋊C4—62no—
153#217—22no—
154#217—22no—
155#217—22no—
156#217—22no—
157#217—34no—
158#217—62no—
159#217—62no—
160#217—62no—
161(C2×D3)⋊C4—64no—
162(C2×D3)⋊C4—68no—
163(C2×D3)⋊C4—68no—
164Dic3⋊C4—64no—
165Dic3⋊C4—68no—
166Dic3⋊C4—68no—
167C4×Dic3—64no—
168C22×C32—22no—
169C22×C32—24no—
170C22×C32—41no—
171C22×C32—41no—
172C22×C32—42no—
173C22×C32C2×C22⋊C411yescharacteristic
174C22×C32C4×D412yes—
175C22×C32#12011yescharacteristic
176C22×C32#12112yes—
177C22×C32#12311yescharacteristic
178C2×C3⋊D3—22no—
179C2×C3⋊D3—42no—
180C2×C3⋊D3—42no—
181C2×C3⋊D3—81no—
182C32×C4—42no—
183C3⋊Dic3—22no—
184C3⋊Dic3—42no—
185C3×Dic3—44no—
186C3×Dic3—82no—
187C22×D4—91no—
188C23×C4D3211yescharacteristic
189#123—94no—
190#123—182no—
191C4×D4—184no—
192#117—181no—
193C2×C4⋊C4—181no—
194C2×C22⋊C4—32no—
195C2×C22⋊C4—32no—
196C2×C22⋊C4—91no—
197C2×C22⋊C4—181no—
198C2×C22⋊C4—181no—
199#99—182no—
200#95—64no—
201C23×C3—22no—
202C23×C3—21no—
203C23×C3—22no—
204C23×C3—21no—
205C23×C3—21no—
206C23×C3—44no—
207C23×C3—44no—
208C23×C3C2×C4×D312yes—
209C23×C3#23512yes—
210C23×C3D3×D412yes—
211C23×C3D3×D412yes—
212C23×C3D3×D412yes—
213C23×C3#23712yes—
214C23×C3C2×#6712yes—
215C22×D3—34no—
216C22×D3—62no—
217C22×D3—62no—
218C22×D3—62no—
219C22×D3—121no—
220C22×D3—121no—
221C22×D3—124no—
222C22×D3—124no—
223C2×C3×C4—24no—
224C2×C3×C4—24no—
225C2×C3×C4—24no—
226C2×C3×C4—24no—
227C2×C3×C4—44no—
228C2×C3×C4—44no—
229C2×C3×C4—42no—
230C2×C3×C4—42no—
231C2×C3×C4—42no—
232C2×C3×C4—42no—
233C2×C3×C4—42no—
234C2×C3×C4—42no—
235C2×C3×C4—64no—
236C2×C3×C4—124no—
237C2×C3×C4—124no—
238C2×C3×C4—122no—
239#67—64no—
240#67—64no—
241#67—64no—
242#67—64no—
243#67—124no—
244#67—124no—
245C2×Dic3—24no—
246C2×Dic3—34no—
247C2×Dic3—44no—
248C2×Dic3—44no—
249C2×Dic3—42no—
250C2×Dic3—62no—
251C2×Dic3—62no—
252C2×Dic3—62no—
253C2×Dic3—64no—
254C2×Dic3—64no—
255C2×Dic3—121no—
256C2×Dic3—121no—
257C2×Dic3—124no—
258C2×Dic3—124no—
259C4×D3—244no—
260C2×C32—21no—
261C2×C32—21no—
262C2×C32—22no—
263C2×C32—22no—
264C2×C32#38611yescharacteristic
265C2×C32#45812yes—
266C3⋊D3—42no—
267C24—91no—
268C24C2×D3211yescharacteristic
269C2×D4—92no—
270C2×D4—92no—
271C2×D4—182no—
272C2×D4—182no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—34no—
278C22×C4—62no—
279C22×C4—91no—
280C22×C4—182no—
281C22×C4—181no—
282C22×C4#62412yescomplemented
283C4⋊C4—184no—
284C4⋊C4—182no—
285C22⋊C4—62no—
286C22⋊C4—62no—
287C22⋊C4—62no—
288C22⋊C4—62no—
289C22⋊C4—92no—
290C22⋊C4—184no—
291C22⋊C4—182no—
292C22⋊C4—181no—
293C42—182no—
294C22×C3—24no—
295C22×C3—24no—
296C22×C3—24no—
297C22×C3—24no—
298C22×C3—22no—
299C22×C3—22no—
300C22×C3—21no—
301C22×C3—21no—
302C22×C3—21no—
303C22×C3—44no—
304C22×C3—42no—
305C22×C3—42no—
306C22×C3—42no—
307C22×C3—42no—
308C22×C3—44no—
309C22×C3—42no—
310C22×C3—42no—
311C22×C3D3×C22⋊C412yes—
312C22×C3#67⋊C412yes—
313C22×C3#88312yes—
314C22×C3#88412yes—
315C22×C3C4×#6712yes—
316C22×C3#93712yes—
317C22×C3#93812yes—
318C2×D3—64no—
319C2×D3—122no—
320C2×D3—124no—
321C2×D3—124no—
322C2×D3—124no—
323C2×D3—242no—
324C2×D3—242no—
325C2×D3—242no—
326C3×C4—44no—
327C3×C4—44no—
328C3×C4—124no—
329C3×C4—242no—
330Dic3—44no—
331Dic3—64no—
332Dic3—82no—
333Dic3—122no—
334Dic3—124no—
335Dic3—124no—
336C32#189011yescharacteristic, complemented, Sylow
337C23—42no—
338C23—92no—
339C23—181no—
340C23—181no—
341C23—362no—
342C23#380412yes—
343C23C2×#62411yescharacteristic
344C23D3×#6712yes—
345C23#381111yescharacteristic
346C23#381111yescharacteristic
347D4—184no—
348D4—184no—
349C2×C4—24no—
350C2×C4—22no—
351C2×C4—42no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—64no—
355C2×C4—92no—
356C2×C4—124no—
357C2×C4—124no—
358C2×C4—122no—
359C2×C4—181no—
360C2×C4—181no—
361C2×C4—182no—
362C2×C4—362no—
363C2×C4—722no—
364C2×C3—22no—
365C2×C3—22no—
366C2×C3—22no—
367C2×C3—22no—
368C2×C3—22no—
369C2×C3—22no—
370C2×C3—22no—
371C2×C3—22no—
372C2×C3—22no—
373C2×C3—21no—
374C2×C3—42no—
375C2×C3—42no—
376C2×C3#495612yes—
377C2×C3#505314yes—
378D3—124no—
379D3—242no—
380C22—24no—
381C22—22no—
382C22—42no—
383C22—41no—
384C22—41no—
385C22—182no—
386C22—362no—
387C22—362no—
388C22—721no—
389C22#6395212yes—
390C22#6395812yes—
391C22#6397411yescharacteristic
392C22#6397511yescharacteristic
393C22#6398311yescharacteristic
394C4—42no—
395C4—124no—
396C4—182no—
397C4—242no—
398C4—362no—
399C3—21no—
400C3#6953812yescomplemented
401C2—22no—
402C2—21no—
403C2—21no—
404C2—22no—
405C2—362no—
406C2#1059139812yes—
407C2#1059172211yescharacteristic
subgroupG/H
centerC22#63983
commutatorC23×C32C22×C4
FrattiniC24C2×D32
FittingC23×C32×C4C22
socleC22×C32#120
prime radicalC22×#638C22
cosocleC24×C32C23
hypercenterC23×C4D32
hypocenterC32#1890
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
3. C3×#5211C2semidirect
5. #10589186C2semidirect
11. #64138C4semidirect
25. #5211D3semidirect
35. C22×C32×C4C2×C4semidirect
46. #3757C2×C4semidirect
131. C22×C3×C4C4×D3semidirect
282. C22×C4#624semidirect
336. C32#1890semidirect
400. C3#69538semidirect

Maximal subgroups

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

subgroupindex
C2×#641382
#105955102
C3×#52112
C2×#635812
#105891862
#695383