Finite Group Databasebeta

← #11775718

Subgroups — #11775718

Order 1152.

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

normal subgroups only

This group has 585 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#10596151C211yesmaximal, characteristic
2#10590322C211yesmaximal, characteristic, complemented
3#10590247C211yesmaximal, characteristic, complemented
4C3×#4540C212yesmaximal, complemented
5#10589089C212yesmaximal, complemented
6#68341—32nomaximal
7C32×#124C2211yescharacteristic
8#64155C411yescharacteristic
9Q8×C3⋊Dic3C411yescharacteristic
10#64147C411yescharacteristic
11D4×C3⋊Dic3C411yescharacteristic
12#64092—21no—
13#64090—21no—
14#64088—21no—
15#64086—21no—
16C42×C3⋊D3C2211yescharacteristic
17#64079C2211yescharacteristic
18C2×#3712—21no—
19C2×#3710—21no—
20C3×#803C2212yes—
21C3×#803C2212yes—
22#63555—21no—
23#63553—21no—
24#5680—32no—
25#5680—61no—
26#4707—32no—
27D3×#97—32no—
28C3×#329—32no—
29#4540D312yescomplemented
30#4465—32no—
31#4465—32no—
32C2×C32×Q8C2×C411yescharacteristic
33C2×C32×D4C2×C411yescharacteristic
34C2×#638—21no—
35C22×C3⋊Dic3—21no—
36C2×C4×C3⋊D3C2×C411yescharacteristic
37C2×C4×C3⋊D3D411yescharacteristic
38C2×C4×C3⋊D3D411yescharacteristic
39C32×C22⋊C4—21no—
40C32×C22⋊C4—21no—
41C32×C42C2311yescharacteristic
42#3757—21no—
43#3757—21no—
44#3752—21no—
45C4⋊(C3⋊Dic3)—21no—
46C4⋊(C3⋊Dic3)C2×C411yescharacteristic
47C4⋊(C3⋊Dic3)C2×C411yescharacteristic
48#3750—21no—
49#3750—21no—
50#3750—21no—
51C4×C3⋊Dic3—21no—
52C4×C3⋊Dic3C2×C411yescharacteristic
53C4×C3⋊Dic3D411yescharacteristic
54C4×C3⋊Dic3D411yescharacteristic
55C2×C3×C3⋊C8—22no—
56C2×C3×C3⋊C8—22no—
57#3712—24no—
58#3710—24no—
59#1524—91noSylow
60C3×#124—21no—
61C3×#124C2×D312yes—
62#946—32no—
63#946—61no—
64Q8×Dic3—32no—
65Q8×Dic3—61no—
66#938—32no—
67#938—61no—
68D4×Dic3—32no—
69D4×Dic3—61no—
70C2×ΓL(1,𝔽25)—62no—
71C2×D3×C8—62no—
72#883—62no—
73#883—62no—
74#67⋊C4—62no—
75#67⋊C4—62no—
76#879—62no—
77#879—62no—
78#877—62no—
79#877—62no—
80C42×D3—32no—
81C42×D3—61no—
82#870—32no—
83#870—61no—
84C3×#97—32no—
85C3×#97—32no—
86#815—62no—
87C8×Dic3—62no—
88#803C2×D312yes—
89#803C2×D312yes—
90C23×C32—21no—
91C22×C3⋊D3C22⋊C411yescharacteristic
92C32×Q8—41no—
93C32×D4—41no—
94C2×C32×C4—21no—
95C2×C32×C4C22×C411yescharacteristic
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4C2×D411yescharacteristic
98#638—42no—
99C2×C3⋊Dic3—21no—
100C2×C3⋊Dic3—21no—
101C2×C3⋊Dic3—42no—
102C2×C3⋊Dic3C22⋊C411yescharacteristic
103C2×C3⋊Dic3C22⋊C411yescharacteristic
104C2×C3⋊Dic3C22⋊C411yescharacteristic
105C4×C3⋊D3—22no—
106C4×C3⋊D3—22no—
107C4×C3⋊D3—41no—
108C3×C3⋊C8—24no—
109C3×C3⋊C8—24no—
110#529—91no—
111C4×M16—91no—
112C2×#97—91no—
113#330—92no—
114#329—32no—
115C2×C3×Q8—21no—
116C2×C3×Q8C4×D312yes—
117C2×C3×D4—21no—
118C2×C3×D4C4×D312yes—
119C2×#67—62no—
120C2×#67—62no—
121C22×Dic3—62no—
122C22×Dic3—62no—
123C2×C4×D3—32no—
124C2×C4×D3—32no—
125C2×C4×D3—32no—
126C2×C4×D3—61no—
127C2×C4×D3—61no—
128C2×C4×D3—61no—
129C2×C3×C8—62no—
130C2×C3×C8—62no—
131C3×C22⋊C4—22no—
132C3×C22⋊C4—22no—
133C3×C22⋊C4—22no—
134C3×C22⋊C4—22no—
135C3×C42—21no—
136C3×C42C22×D312yes—
137#217—62no—
138#217—62no—
139#217—62no—
140#217—62no—
141(C2×D3)⋊C4—62no—
142(C2×D3)⋊C4—62no—
143C4⋊Dic3—32no—
144C4⋊Dic3—32no—
145C4⋊Dic3—61no—
146C4⋊Dic3—61no—
147C4⋊Dic3—62no—
148C4⋊Dic3—62no—
149Dic3⋊C4—62no—
150Dic3⋊C4—62no—
151Dic3⋊C4—62no—
152Dic3⋊C4—62no—
153Dic3⋊C4—62no—
154Dic3⋊C4—62no—
155C4×Dic3—32no—
156C4×Dic3—32no—
157C4×Dic3—32no—
158C4×Dic3—61no—
159C4×Dic3—61no—
160C4×Dic3—61no—
161C4×Dic3—62no—
162C4×Dic3—62no—
163C2×C3⋊C8—22no—
164C2×C3⋊C8—22no—
165ΓL(1,𝔽25)—68no—
166D3×C8—68no—
167C22×C32—41no—
168C22×C32—41no—
169C22×C32—41no—
170C22×C32C2×C22⋊C411yescharacteristic
171C2×C3⋊D3—21no—
172C2×C3⋊D3—21no—
173C2×C3⋊D3#10412yes—
174C32×C4—21no—
175C32×C4—21no—
176C32×C4—21no—
177C32×C4—41no—
178C3⋊Dic3—21no—
179C3⋊Dic3—21no—
180C3⋊Dic3—41no—
181C3⋊Dic3—41no—
182C3⋊Dic3#10412yes—
183C2×M16—181no—
184C22×C8—181no—
185#126—181no—
186#125—91no—
187#124D3211yescharacteristic
188#123—181no—
189C22⋊Q8—91no—
190#121—91no—
191C4×Q8—91no—
192C4×D4—91no—
193C4×D4—181no—
194#117—181no—
195C2×C42—91no—
196#97—32no—
197#97—32no—
198#97—181no—
199C4×C8—181no—
200C23×C3—22no—
201C23×C3—22no—
202C22×D3—32no—
203C22×D3—61no—
204C3×Q8—42no—
205C3×Q8—42no—
206C3×D4—42no—
207C3×D4—42no—
208C2×C3×C4—22no—
209C2×C3×C4—22no—
210C2×C3×C4—21no—
211C2×C3×C4—21no—
212C2×C3×C4—21no—
213C2×C3×C4C2×C4×D312yes—
214C2×C3×C4D3×D412yes—
215C2×C3×C4D3×D412yes—
216#67—124no—
217#67—124no—
218C2×Dic3—32no—
219C2×Dic3—32no—
220C2×Dic3—32no—
221C2×Dic3—61no—
222C2×Dic3—61no—
223C2×Dic3—61no—
224C2×Dic3—62no—
225C2×Dic3—62no—
226C2×Dic3—62no—
227C2×Dic3—62no—
228C2×Dic3—124no—
229C2×Dic3—124no—
230C4×D3—64no—
231C4×D3—64no—
232C4×D3—122no—
233C4×D3—122no—
234C4×D3—122no—
235C4×D3—122no—
236C3×C8—64no—
237C3×C8—64no—
238C3⋊C8—24no—
239C3⋊C8—24no—
240C2×C32—81no—
241C2×C32#41311yescharacteristic
242C2×C32C2×#10411yescharacteristic
243C2×C32C2×#10411yescharacteristic
244C3⋊D3—22no—
245C2×Q8#62411yescharacteristic
246C2×D4—181no—
247C2×D4#62411yescharacteristic
248C22×C4—91no—
249C22×C4—91no—
250C22×C4—91no—
251C22×C4—181no—
252M16—184no—
253C2×C8—62no—
254C2×C8—62no—
255C2×C8—184no—
256C4⋊C4—91no—
257C4⋊C4—91no—
258C4⋊C4—181no—
259C4⋊C4—181no—
260C4⋊C4—181no—
261C4⋊C4—181no—
262C22⋊C4—21no—
263C22⋊C4—21no—
264C22⋊C4—181no—
265C22⋊C4—181no—
266C22⋊C4—181no—
267C42—91no—
268C42—91no—
269C42—91no—
270C42—181no—
271C42C2×D3211yescharacteristic
272C22×C3—21no—
273C22×C3—42no—
274C22×C3—42no—
275C22×C3—42no—
276C22×C3—42no—
277C22×C3—42no—
278C22×C3—42no—
279C22×C3D3×C22⋊C412yes—
280C2×D3—34no—
281C2×D3—62no—
282C2×D3—62no—
283C2×D3—62no—
284C2×D3—121no—
285C2×D3—121no—
286C3×C4—22no—
287C3×C4—22no—
288C3×C4—22no—
289C3×C4—22no—
290C3×C4—41no—
291C3×C4—41no—
292C3×C4—42no—
293C3×C4—42no—
294Dic3—34no—
295Dic3—62no—
296Dic3—62no—
297Dic3—62no—
298Dic3—121no—
299Dic3—121no—
300Dic3—122no—
301Dic3—122no—
302Dic3—122no—
303Dic3—122no—
304C32#152411yescharacteristic, complemented, Sylow
305C23—21no—
306C23—91no—
307Q8—41no—
308D4—41no—
309D4—362no—
310C2×C4—21no—
311C2×C4—91no—
312C2×C4—91no—
313C2×C4—91no—
314C2×C4—182no—
315C2×C4—182no—
316C2×C4—181no—
317C2×C4—181no—
318C2×C4—361no—
319C2×C4—362no—
320C2×C4C2×#62411yescharacteristic
321C2×C4#381111yescharacteristic
322C2×C4#381111yescharacteristic
323C8—64no—
324C8—64no—
325C2×C3—21no—
326C2×C3—21no—
327C2×C3—21no—
328C2×C3—82no—
329C2×C3—82no—
330C2×C3#474512yes—
331C2×C3D3×#10412yes—
332C2×C3D3×#10412yes—
333D3—64no—
334D3—122no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—92no—
339C22—181no—
340C22—181no—
341C22#6397411yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—41no—
346C4—92no—
347C4—181no—
348C4—181no—
349C4—361no—
350C4—361no—
351C3—21no—
352C3#6834112yescomplemented
353C2—81no—
354C2—182no—
355C2#1059150411yescharacteristic
356C2#1059167111yescharacteristic
357C2#1059167111yescharacteristic
subgroupG/H
centerC22#63974
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×#124C22
socleC22×C32C2×C22⋊C4
prime radical#64147C4
cosocleC32×C42C23
hypercenter#124D32
hypocenterC32#1524
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
2. #10590322C2semidirect
3. #10590247C2semidirect
4. C3×#4540C2semidirect
5. #10589089C2semidirect
29. #4540D3semidirect
304. C32#1524semidirect
352. C3#68341semidirect

Maximal subgroups

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

subgroupindex
#105961512
#105903222
#105902472
C3×#45402
#105890892
#683413