Finite Group Databasebeta

← #11794310

Subgroups — #11794310

Order 1152.

745 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 745 conjugacy classes of subgroups — too many to draw. Only its 120 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#10595521C211yesmaximal, characteristic
2#10592909C211yesmaximal, characteristic
3C3×#5210C212yesmaximal
4#10589187C211yesmaximal, characteristic
5#10589186C212yesmaximal
6#69594—32nomaximal
7C23×C32×C4C2211yescharacteristic
8C2×#3757C2211yescharacteristic
9C2×#3757C2211yescharacteristic
10C2×#3750—21no—
11C2×C3×#217C2212yes—
12C2×C3×#217C2212yes—
13C2×C3×Dic3⋊C4—22no—
14#63982—21no—
15#63982—21no—
16#63964—22no—
17#63964—22no—
18#63658—21no—
19C3×C3⋊#95—22no—
20#5483—32no—
21C3×#385—32no—
22#5210—32no—
23#5210—61no—
24#5210D312yes—
25#4527—32no—
26#4527—32no—
27#4526—32no—
28C24×C32C2311yescharacteristic
29C22×C32×C4—21no—
30C22×C32×C4—22no—
31C22×C32×C4—42no—
32C22×C3⋊Dic3—21no—
33C22×C3⋊Dic3D411yescharacteristic
34C22×C3⋊Dic3D411yescharacteristic
35C22×C3×Dic3—22no—
36C22×C3×Dic3D412yes—
37C22×C3×Dic3D412yes—
38C2×#627—21no—
39C2×#627—21no—
40#3757—22no—
41#3757—21no—
42#3757Q812yescomplemented
43#3750—42no—
44C3×#217—22no—
45C3×#217—22no—
46C3×#217—22no—
47C3×#217Q814yescomplemented
48C3×Dic3⋊C4—44no—
49#3724—21no—
50#3724—21no—
51Dic3⋊Dic3—22no—
52Dic3⋊Dic3—22no—
53#2062—91noSylow
54C23×C3×C4—21no—
55C23×C3×C4C2×D312yes—
56C2×C3×C4⋊C4—62no—
57C2×C3×C22⋊C4—32no—
58C2×C3×C22⋊C4—32no—
59C2×#217—32no—
60C2×#217—32no—
61C2×#217—61no—
62C2×#217—61no—
63C2×#217C2×D312yes—
64C2×#217C2×D312yes—
65#924—62no—
66#924—62no—
67C2×Dic3⋊C4—22no—
68C2×Dic3⋊C4—62no—
69C2×Dic3⋊C4—62no—
70#878—62no—
71#878—62no—
72#878—62no—
73#878—62no—
74C3×#95—62no—
75C3⋊#95—22no—
76C3⋊#95—62no—
77C3⋊#95—62no—
78C23×C32—41no—
79C23×C32—41no—
80C23×C32C2×D411yescharacteristic
81C23×C32C2×D412yes—
82C23×C32C2×Q812yes—
83C23×C32C2×Q811yescharacteristic
84C23×C32#4111yescharacteristic
85C2×C32×C4—22no—
86C2×C32×C4—24no—
87C2×C32×C4—41no—
88C2×C32×C4—42no—
89C2×C32×C4—41no—
90C2×C3⋊Dic3—22no—
91C2×C3⋊Dic3—21no—
92C2×C3⋊Dic3—21no—
93C2×C3⋊Dic3—41no—
94C2×C3⋊Dic3—41no—
95C2×C3⋊Dic3—41no—
96C2×C3⋊Dic3—41no—
97C2×C3×Dic3—22no—
98C2×C3×Dic3—22no—
99C2×C3×Dic3—24no—
100C2×C3×Dic3—42no—
101C2×C3×Dic3—42no—
102C2×C3×Dic3—42no—
103C2×C3×Dic3—42no—
104#627—81no—
105#627—81no—
106#543—91no—
107#385—32no—
108#385—91no—
109#342—92no—
110#342—91no—
111C24×C3—21no—
112C24×C3C22×D312yes—
113C22×C3×C4—22no—
114C22×C3×C4—22no—
115C22×C3×C4—22no—
116C22×C3×C4—22no—
117C22×C3×C4—32no—
118C22×C3×C4—32no—
119C22×C3×C4—42no—
120C22×C3×C4—44no—
121C22×C3×C4—44no—
122C22×C3×C4—62no—
123C22×Dic3—22no—
124C22×Dic3—32no—
125C22×Dic3—32no—
126C22×Dic3—61no—
127C22×Dic3—61no—
128C22×Dic3—62no—
129C22×Dic3—62no—
130C22×Dic3#6712yes—
131C22×Dic3#6712yes—
132C2×Dic6—62no—
133C2×Dic6—62no—
134C3×C4⋊C4—124no—
135C3×C22⋊C4—34no—
136C3×C22⋊C4—62no—
137C3×C22⋊C4—62no—
138C3×C22⋊C4—62no—
139#217—22no—
140#217—22no—
141#217—22no—
142#217—34no—
143#217—62no—
144#217—62no—
145#217—62no—
146#217—62no—
147#217—62no—
148#217—122no—
149#217Dic614yescomplemented
150C4⋊Dic3—62no—
151C4⋊Dic3—62no—
152Dic3⋊C4—44no—
153Dic3⋊C4—62no—
154Dic3⋊C4—62no—
155Dic3⋊C4—62no—
156Dic3⋊C4—62no—
157Dic3⋊C4—124no—
158Dic3⋊C4—124no—
159C22×C32—21no—
160C22×C32—21no—
161C22×C32—22no—
162C22×C32—22no—
163C22×C32—42no—
164C22×C32—41no—
165C22×C32—41no—
166C22×C32#12011yescharacteristic
167C22×C32C22⋊Q811yescharacteristic
168C22×C32C22⋊Q812yes—
169C22×C32C4⋊Q811yescharacteristic
170C22×C32C4⋊Q812yes—
171C32×C4—42no—
172C3⋊Dic3—42no—
173C3⋊Dic3—41no—
174C3⋊Dic3—41no—
175C3×Dic3—44no—
176C3×Dic3—42no—
177C3×Dic3—42no—
178C23×C4D3211yescharacteristic
179C22⋊Q8—181no—
180C22⋊Q8—181no—
181C22⋊Q8—182no—
182C22⋊Q8—182no—
183C2×C4⋊C4—62no—
184C2×C4⋊C4—181no—
185C2×C22⋊C4—32no—
186C2×C22⋊C4—32no—
187C2×C22⋊C4—91no—
188C2×C22⋊C4—91no—
189#95—62no—
190#95—181no—
191C23×C3—22no—
192C23×C3—21no—
193C23×C3—21no—
194C23×C3—22no—
195C23×C3—21no—
196C23×C3—42no—
197C23×C3—42no—
198C23×C3—42no—
199C23×C3—42no—
200C23×C3C2×Dic612yes—
201C23×C3#23512yes—
202C23×C3D3×D412yes—
203C23×C3D3×D412yes—
204C23×C3D3×Q812yes—
205C23×C3D3×Q812yes—
206C23×C3C2×#6712yes—
207C2×C3×C4—24no—
208C2×C3×C4—24no—
209C2×C3×C4—24no—
210C2×C3×C4—24no—
211C2×C3×C4—44no—
212C2×C3×C4—42no—
213C2×C3×C4—42no—
214C2×C3×C4—42no—
215C2×C3×C4—42no—
216C2×C3×C4—42no—
217C2×C3×C4—44no—
218C2×C3×C4—42no—
219C2×C3×C4—64no—
220C2×C3×C4—62no—
221C2×C3×C4—62no—
222C2×C3×C4—122no—
223C2×C3×C4—122no—
224C2×C3×C4—122no—
225C2×C3×C4—122no—
226C2×Dic3—24no—
227C2×Dic3—22no—
228C2×Dic3—22no—
229C2×Dic3—42no—
230C2×Dic3—42no—
231C2×Dic3—42no—
232C2×Dic3—42no—
233C2×Dic3—64no—
234C2×Dic3—64no—
235C2×Dic3—62no—
236C2×Dic3—62no—
237C2×Dic3—121no—
238C2×Dic3—121no—
239C2×Dic3—122no—
240C2×Dic3—122no—
241C2×Dic3—122no—
242C2×Dic3—122no—
243C2×Dic3—122no—
244C2×Dic3—122no—
245C2×Dic3—122no—
246C2×Dic3—122no—
247Dic6—242no—
248Dic6—242no—
249C2×C32—21no—
250C2×C32—21no—
251C2×C32—22no—
252C2×C32—22no—
253C2×C32#39511yescharacteristic
254C2×C32B(4,𝔽2)11yescharacteristic
255C2×C32#45811yescharacteristic
256C24C2×D3211yescharacteristic
257C2×Q8—181no—
258C2×Q8—181no—
259C22×C4—22no—
260C22×C4—21no—
261C22×C4—32no—
262C22×C4—32no—
263C22×C4—42no—
264C22×C4—62no—
265C22×C4—91no—
266C22×C4—91no—
267C22×C4—181no—
268C4⋊C4—124no—
269C4⋊C4—181no—
270C4⋊C4—181no—
271C4⋊C4—182no—
272C4⋊C4—182no—
273C4⋊C4—362no—
274C22⋊C4—34no—
275C22⋊C4—62no—
276C22⋊C4—62no—
277C22⋊C4—62no—
278C22⋊C4—92no—
279C22⋊C4—181no—
280C22⋊C4—182no—
281C22×C3—22no—
282C22×C3—22no—
283C22×C3—22no—
284C22×C3—22no—
285C22×C3—22no—
286C22×C3—22no—
287C22×C3—22no—
288C22×C3—22no—
289C22×C3—22no—
290C22×C3—21no—
291C22×C3—22no—
292C22×C3—21no—
293C22×C3—21no—
294C22×C3—42no—
295C22×C3—42no—
296C22×C3—42no—
297C22×C3—42no—
298C22×C3—42no—
299C22×C3—42no—
300C22×C3—44no—
301C22×C3—42no—
302C22×C3—42no—
303C22×C3#88812yes—
304C22×C3#88812yes—
305C22×C3#89612yes—
306C22×C3#89612yes—
307C22×C3#92412yes—
308C22×C3#93712yes—
309C22×C3#94412yes—
310C3×C4—44no—
311C3×C4—44no—
312C3×C4—124no—
313C3×C4—122no—
314C3×C4—122no—
315Dic3—44no—
316Dic3—42no—
317Dic3—42no—
318Dic3—124no—
319Dic3—124no—
320Dic3—122no—
321Dic3—122no—
322Dic3—241no—
323Dic3—241no—
324C32#206211yescharacteristic, complemented, Sylow
325C23—41no—
326C23—41no—
327C23D3×Dic612yes—
328C23#379711yescharacteristic
329C23#379811yescharacteristic
330C23D3×#6712yes—
331C23#381111yescharacteristic
332Q8—721no—
333Q8—721no—
334C2×C4—24no—
335C2×C4—22no—
336C2×C4—42no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—64no—
340C2×C4—62no—
341C2×C4—62no—
342C2×C4—122no—
343C2×C4—122no—
344C2×C4—122no—
345C2×C4—122no—
346C2×C4—182no—
347C2×C4—181no—
348C2×C4—181no—
349C2×C4—361no—
350C2×C4—361no—
351C2×C4—361no—
352C2×C4—361no—
353C2×C3—22no—
354C2×C3—22no—
355C2×C3—22no—
356C2×C3—22no—
357C2×C3—22no—
358C2×C3—22no—
359C2×C3—22no—
360C2×C3—22no—
361C2×C3—21no—
362C2×C3—21no—
363C2×C3—21no—
364C2×C3—42no—
365C2×C3—42no—
366C2×C3#497912yes—
367C2×C3#503212yes—
368C2×C3#505312yes—
369C22—22no—
370C22—21no—
371C22—22no—
372C22—21no—
373C22—42no—
374C22—41no—
375C22—41no—
376C22#6383912yes—
377C22#6384011yescharacteristic
378C22#6385112yes—
379C22#6386511yescharacteristic
380C22#6398311yescharacteristic
381C4—42no—
382C4—124no—
383C4—122no—
384C4—122no—
385C4—362no—
386C4—361no—
387C4—361no—
388C3—21no—
389C3#6959412yescomplemented
390C2—22no—
391C2—21no—
392C2—22no—
393C2—21no—
394C2#1059119511yescharacteristic
395C2#1059139811yescharacteristic
396C2#1059172511yescharacteristic
subgroupG/H
centerC22#63983
commutator, prime radical, cosocleC24×C32C23
FrattiniC24C2×D32
FittingC23×C32×C4C22
socleC22×C32#120
hypercenterC23×C4D32
hypocenterC32#2062
LCSG ▷ C24×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
42. #3757Q8semidirect
47. C3×#217Q8semidirect
149. #217Dic6semidirect
324. C32#2062semidirect
389. C3#69594semidirect

Maximal subgroups

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

subgroupindex
#105955212
#105929092
C3×#52102
#105891872
#105891862
#695943