Finite Group Databasebeta

← #11794312

Subgroups — #11794312

Order 1152.

745 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 745 conjugacy classes of subgroups — too many to draw. Only its 126 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#10592649C211yesmaximal, characteristic
3#10591719C212yesmaximal
4C3×#4527C212yesmaximal
5#10589187C211yesmaximal, characteristic
6#68958—32nomaximal
7C23×C3⋊Dic3C2211yescharacteristic
8C2×C32×C22⋊C4C2211yescharacteristic
9C2×#3757C2211yescharacteristic
10C2×C4⋊(C3⋊Dic3)—21no—
11C2×C3×#217C2212yes—
12C2×C3×#217C2212yes—
13#63982—21no—
14#63982—21no—
15C2×Dic3⋊Dic3—22no—
16#63964—22no—
17#63964—22no—
18#63658—21no—
19#63579—22no—
20#5483—32no—
21#4950—32no—
22#4950—32no—
23#4950—61no—
24#4946—32no—
25C3×#342—32no—
26#4527—32no—
27#4527D312yes—
28C24×C32C2311yescharacteristic
29C22×C32×C4—21no—
30C22×C3⋊Dic3—21no—
31C22×C3⋊Dic3—22no—
32C22×C3⋊Dic3—42no—
33C22×C3⋊Dic3D411yescharacteristic
34C22×C3⋊Dic3D411yescharacteristic
35C22×C3×Dic3—22no—
36C22×C3×Dic3D412yes—
37C22×C3×Dic3D412yes—
38C2×#627—21no—
39C2×#627—21no—
40C32×C22⋊C4—21no—
41C32×C22⋊C4Q812yescomplemented
42#3757—22no—
43C4⋊(C3⋊Dic3)—42no—
44C3×#217—22no—
45C3×#217—22no—
46C3×#217—22no—
47C3×#217Q814yescomplemented
48#3724—21no—
49#3724—21no—
50Dic3⋊Dic3—22no—
51Dic3⋊Dic3—22no—
52Dic3⋊Dic3—44no—
53#2062—91noSylow
54C23×Dic3—32no—
55C23×Dic3—61no—
56C2×C3×C22⋊C4—21no—
57C2×C3×C22⋊C4—32no—
58C2×C3×C22⋊C4—32no—
59C2×C3×C22⋊C4C2×D312yes—
60C2×#217—32no—
61C2×#217—61no—
62C2×#217C2×D312yes—
63C2×#217C2×D312yes—
64C2×C4⋊Dic3—62no—
65C2×C4⋊Dic3—62no—
66C2×C4⋊Dic3—62no—
67#924—62no—
68#924—62no—
69C2×Dic3⋊C4—62no—
70#878—62no—
71#878—62no—
72#878—62no—
73#878—62no—
74C3⋊#95—62no—
75C3⋊#95—62no—
76C3⋊#95—62no—
77C3⋊#95—62no—
78C23×C32—41no—
79C23×C32—41no—
80C23×C32C2×D412yes—
81C23×C32C2×D411yescharacteristic
82C23×C32C2×Q811yescharacteristic
83C23×C32C2×Q812yes—
84C23×C32#4111yescharacteristic
85C2×C32×C4—22no—
86C2×C32×C4—41no—
87C2×C32×C4—41no—
88C2×C3⋊Dic3—22no—
89C2×C3⋊Dic3—24no—
90C2×C3⋊Dic3—21no—
91C2×C3⋊Dic3—21no—
92C2×C3⋊Dic3—41no—
93C2×C3⋊Dic3—42no—
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—92no—
108#385—91no—
109#342—32no—
110#342—91no—
111C24×C3—21no—
112C24×C3C22×D312yes—
113C22×C3×C4—22no—
114C22×C3×C4—22no—
115C22×C3×C4—32no—
116C22×C3×C4—32no—
117C22×C3×C4—62no—
118C22×Dic3—22no—
119C22×Dic3—32no—
120C22×Dic3—32no—
121C22×Dic3—61no—
122C22×Dic3—61no—
123C22×Dic3—62no—
124C22×Dic3—62no—
125C22×Dic3—62no—
126C22×Dic3—62no—
127C22×Dic3—122no—
128C22×Dic3—124no—
129C22×Dic3—124no—
130C22×Dic3D1212yes—
131C22×Dic3D1212yes—
132C2×Dic6—62no—
133C2×Dic6—62no—
134C3×C22⋊C4—22no—
135C3×C22⋊C4—22no—
136C3×C22⋊C4—22no—
137C3×C22⋊C4—34no—
138C3×C22⋊C4—62no—
139C3×C22⋊C4—62no—
140C3×C22⋊C4—62no—
141C3×C22⋊C4Dic614yescomplemented
142#217—22no—
143#217—22no—
144#217—22no—
145#217—62no—
146#217—62no—
147#217—122no—
148#217Dic614yescomplemented
149C4⋊Dic3—62no—
150C4⋊Dic3—62no—
151C4⋊Dic3—124no—
152C4⋊Dic3—124no—
153C4⋊Dic3—124no—
154Dic3⋊C4—62no—
155Dic3⋊C4—62no—
156Dic3⋊C4—62no—
157Dic3⋊C4—62no—
158Dic3⋊C4—124no—
159C22×C32—21no—
160C22×C32—21no—
161C22×C32—22no—
162C22×C32—22no—
163C22×C32—41no—
164C22×C32—42no—
165C22×C32—41no—
166C22×C32#12011yescharacteristic
167C22×C32C22⋊Q811yescharacteristic
168C22×C32C22⋊Q812yes—
169C22×C32C4⋊Q812yes—
170C22×C32C4⋊Q811yescharacteristic
171C32×C4—42no—
172C3⋊Dic3—42no—
173C3⋊Dic3—41no—
174C3⋊Dic3—41no—
175C3×Dic3—44no—
176C3×Dic3—42no—
177C3×Dic3—42no—
178C23×C4—91no—
179C22⋊Q8—181no—
180C22⋊Q8—181no—
181C22⋊Q8—182no—
182C22⋊Q8—182no—
183C2×C4⋊C4—181no—
184C2×C4⋊C4—182no—
185C2×C22⋊C4—32no—
186C2×C22⋊C4—32no—
187C2×C22⋊C4—91no—
188C2×C22⋊C4D3211yescharacteristic
189#95—181no—
190#95—182no—
191C23×C3—22no—
192C23×C3—22no—
193C23×C3—21no—
194C23×C3—21no—
195C23×C3—21no—
196C23×C3—42no—
197C23×C3—42no—
198C23×C3—42no—
199C23×C3—42no—
200C23×C3C2×Dic612yes—
201C23×C3C2×Dic612yes—
202C23×C3C2×D1212yes—
203C23×C3D3×D412yes—
204C23×C3D3×D412yes—
205C23×C3#23712yes—
206C23×C3D3×Q812yes—
207C2×C3×C4—24no—
208C2×C3×C4—24no—
209C2×C3×C4—42no—
210C2×C3×C4—42no—
211C2×C3×C4—42no—
212C2×C3×C4—42no—
213C2×C3×C4—62no—
214C2×C3×C4—62no—
215C2×C3×C4—64no—
216C2×C3×C4—122no—
217C2×C3×C4—122no—
218C2×C3×C4—122no—
219C2×C3×C4—122no—
220C2×Dic3—24no—
221C2×Dic3—22no—
222C2×Dic3—22no—
223C2×Dic3—42no—
224C2×Dic3—42no—
225C2×Dic3—42no—
226C2×Dic3—42no—
227C2×Dic3—64no—
228C2×Dic3—64no—
229C2×Dic3—64no—
230C2×Dic3—64no—
231C2×Dic3—62no—
232C2×Dic3—62no—
233C2×Dic3—124no—
234C2×Dic3—121no—
235C2×Dic3—121no—
236C2×Dic3—122no—
237C2×Dic3—122no—
238C2×Dic3—122no—
239C2×Dic3—122no—
240C2×Dic3—122no—
241C2×Dic3—124no—
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—21no—
260C22×C4—32no—
261C22×C4—32no—
262C22×C4—62no—
263C22×C4—91no—
264C22×C4—91no—
265C22×C4—182no—
266C22×C4—181no—
267C22×C4—362no—
268C4⋊C4—181no—
269C4⋊C4—181no—
270C4⋊C4—182no—
271C4⋊C4—182no—
272C4⋊C4—362no—
273C4⋊C4—364no—
274C22⋊C4—21no—
275C22⋊C4—34no—
276C22⋊C4—62no—
277C22⋊C4—62no—
278C22⋊C4—62no—
279C22⋊C4—182no—
280C22⋊C4#62712yescomplemented
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—21no—
290C22×C3—22no—
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#86912yes—
304C22×C3#87812yes—
305C22×C3#87812yes—
306C22×C3#88212yes—
307C22×C3#88812yes—
308C22×C3#88812yes—
309C22×C3#89712yes—
310C3×C4—44no—
311C3×C4—44no—
312C3×C4—124no—
313C3×C4—122no—
314C3×C4—122no—
315Dic3—44no—
316Dic3—42no—
317Dic3—42no—
318Dic3—124no—
319Dic3—122no—
320Dic3—124no—
321Dic3—122no—
322Dic3—241no—
323Dic3—241no—
324C32#206211yescharacteristic, complemented, Sylow
325C23—41no—
326C23—41no—
327C23D3×Dic612yes—
328C23D3×D1212yes—
329C23#380511yescharacteristic
330C23C2×#62711yescharacteristic
331C23#381111yescharacteristic
332Q8—721no—
333Q8—721no—
334C2×C4—22no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—64no—
338C2×C4—62no—
339C2×C4—62no—
340C2×C4—122no—
341C2×C4—122no—
342C2×C4—122no—
343C2×C4—122no—
344C2×C4—182no—
345C2×C4—184no—
346C2×C4—181no—
347C2×C4—181no—
348C2×C4—361no—
349C2×C4—362no—
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#465612yes—
367C2×C3#474112yes—
368C2×C3#474212yes—
369C22—21no—
370C22—22no—
371C22—21no—
372C22—22no—
373C22—42no—
374C22—41no—
375C22—41no—
376C22#6384011yescharacteristic
377C22#6389312yes—
378C22#6391812yes—
379C22#6392311yescharacteristic
380C22#6398211yescharacteristic
381C4—42no—
382C4—124no—
383C4—122no—
384C4—122no—
385C4—361no—
386C4—362no—
387C4—361no—
388C3—21no—
389C3#6895812yescomplemented
390C2—21no—
391C2—22no—
392C2—21no—
393C2—22no—
394C2#1059040911yescharacteristic
395C2#1059041011yescharacteristic
396C2#1059139711yescharacteristic
subgroupG/H
centerC22#63923
commutator, prime radical, cosocleC24×C32C23
FrattiniC24C2×D32
FittingC2×C32×C22⋊C4C22
socleC22×C32#120
hypercenterC2×C22⋊C4D32
hypocenterC32#2062
LCSG ▷ C24×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
41. C32×C22⋊C4Q8semidirect
47. C3×#217Q8semidirect
141. C3×C22⋊C4Dic6semidirect
148. #217Dic6semidirect
280. C22⋊C4#627semidirect
324. C32#2062semidirect
389. C3#68958semidirect

Maximal subgroups

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

subgroupindex
#105955212
#105926492
#105917192
C3×#45272
#105891872
#689583