Finite Group Databasebeta

← #11775136

Subgroups — #11775136

Order 1152.

408 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 80 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#10589698C211yesmaximal, characteristic
2#10588399C211yesmaximal, characteristic, complemented
3#10588328C211yesmaximal, characteristic, complemented
4C9×#327C211yesmaximal, characteristic, complemented
5#10588214C211yesmaximal, characteristic, complemented
6#10588147C211yesmaximal, characteristic, complemented
7#10588129C211yesmaximal, characteristic, complemented
8#68278—31nomaximal
9C2×#3699—21no—
10C9×#121C2211yescharacteristic
11#63502C411yescharacteristic, complemented
12#63501—21no—
13D4×Dic9C411yescharacteristic, complemented
14#63492C2211yescharacteristic
15C2×C4×Dic9—21no—
16C2×C4×Dic9C2211yescharacteristic
17#63455C411yescharacteristic, complemented
18#63450C411yescharacteristic, complemented
19#63447—21no—
20#611⋊C4—21no—
21C9×C22⋊C8C2211yescharacteristic
22C9×#95C2211yescharacteristic
23C9⋊#95—21no—
24C9⋊#95C2211yescharacteristic
25#63389C2211yescharacteristic
26#63375—21no—
27Dic9⋊C8—21no—
28#5596—31no—
29#4719—31no—
30#4648—31no—
31C3×#327D311yescharacteristic
32#4537—31no—
33#4470—31no—
34#4451—31no—
35C2×D4×C9—21no—
36C2×D4×C9C2×C411yescharacteristic
37C22×C4×C9—21no—
38C22×C4×C9C2311yescharacteristic
39C2×#611—21no—
40C2×#611—21no—
41C2×#611—21no—
42C22×Dic9—21no—
43C22×Dic9—21no—
44C22×Dic9D411yescharacteristic
45C22×Dic9D411yescharacteristic
46#3699—42no—
47#3699—42no—
48C2×D36C2×C411yescharacteristic
49C2×C4×D9—21no—
50C2×Dic18—21no—
51C2×C8×C9—21no—
52C9×C4⋊C4C2×C411yescharacteristic
53C9×C22⋊C4—21no—
54#3676—21no—
55(C2×D9)⋊C4—21no—
56(C2×D9)⋊C4—21no—
57C4⋊Dic9C2×C411yescharacteristic
58Dic9⋊C4—21no—
59C4×Dic9—24no—
60C4×Dic9C2×C411yescharacteristic
61C4×Dic9C2×C411yescharacteristic
62C4×Dic9D411yescharacteristic
63C4×Dic9D411yescharacteristic
64C2×C9⋊C8—21no—
65#1505—91noSylow
66C2×#237—61no—
67C3×#121C2×D311yescharacteristic
68#940—31no—
69#939—61no—
70D4×Dic3—31no—
71#930—31no—
72C2×C4×Dic3—31no—
73C2×C4×Dic3—61no—
74#893—31no—
75#888—31no—
76#885—61no—
77#67⋊C4—61no—
78C3×C22⋊C8C2×D311yescharacteristic
79C3×#95C2×D311yescharacteristic
80C3⋊#95—31no—
81C3⋊#95—61no—
82#830—31no—
83#815—61no—
84Dic3⋊C8—61no—
85C23×C9—21no—
86C23×C9C2×D411yescharacteristic
87C22×D9—21no—
88D4×C9—41no—
89D4×C9—41no—
90D4×C9—41no—
91C2×C4×C9—22no—
92C2×C4×C9—21no—
93C2×C4×C9—41no—
94C2×C4×C9—41no—
95C2×C4×C9—41no—
96C2×C4×C9C22×C411yescharacteristic
97C2×C4×C9C2×D411yescharacteristic
98#611—42no—
99#611—41no—
100#611—41no—
101#611—42no—
102C2×Dic9—21no—
103C2×Dic9—21no—
104C2×Dic9—22no—
105C2×Dic9—22no—
106C2×Dic9—21no—
107C2×Dic9—42no—
108C2×Dic9—41no—
109C2×Dic9—41no—
110C2×Dic9C22⋊C411yescharacteristic
111C2×Dic9C22⋊C411yescharacteristic
112C2×Dic9C22⋊C411yescharacteristic
113C2×Dic9C22⋊C411yescharacteristic
114D36—41no—
115C4×D9—42no—
116Dic18—42no—
117C8×C9—41no—
118C9⋊C8—41no—
119#532—91no—
120#432—91no—
121#376—91no—
122#327—91no—
123#327—91no—
124#327—91no—
125#327D911yescharacteristic, complemented
126C2×C3×D4—21no—
127C2×C3×D4C4×D311yescharacteristic
128C22×C3×C4—21no—
129C22×C3×C4C22×D311yescharacteristic
130C2×#67—61no—
131C2×#67—61no—
132C2×#67—61no—
133C22×Dic3—31no—
134C22×Dic3—31no—
135C22×Dic3—61no—
136C22×Dic3—61no—
137#237—122no—
138#237—122no—
139C2×D12—31no—
140C2×C4×D3—61no—
141C2×Dic6—61no—
142C2×C3×C8—21no—
143C3×C4⋊C4C4×D311yescharacteristic
144C3×C22⋊C4—21no—
145#217—61no—
146(C2×D3)⋊C4—61no—
147(C2×D3)⋊C4—61no—
148C4⋊Dic3—31no—
149Dic3⋊C4—61no—
150C4×Dic3—31no—
151C4×Dic3—31no—
152C4×Dic3—31no—
153C4×Dic3—31no—
154C4×Dic3—64no—
155C2×C3⋊C8—61no—
156C22×C9—21no—
157C22×C9—21no—
158C22×C9—41no—
159C22×C9—41no—
160C22×C9—41no—
161C22×C9C2×C22⋊C411yescharacteristic
162C22×C9AGL(1,ℤ/8)11yescharacteristic
163C22×C9AGL(1,ℤ/8)11yescharacteristic
164C2×D9—41no—
165C2×D9—41no—
166C2×D9—41no—
167C4×C9—21no—
168C4×C9—21no—
169C4×C9—42no—
170C4×C9—41no—
171Dic9—21no—
172Dic9—21no—
173Dic9—21no—
174Dic9—42no—
175Dic9—41no—
176Dic9#10412yes—
177C2×#41—181no—
178C4⋊Q8—91no—
179#127—91no—
180#124—181no—
181#121—91no—
182#121—181no—
183#121C2×D911yescharacteristic
184C4×D4—91no—
185C4×D4—91no—
186C4×D4—181no—
187C2×C42—91no—
188C2×C42—181no—
189C4⋊C8—181no—
190C22⋊C8—91no—
191C22⋊C8C2×D911yescharacteristic
192#97—181no—
193#95—91no—
194#95—181no—
195#95C2×D911yescharacteristic
196C23×C3—21no—
197C23×C3D3×D411yescharacteristic
198C22×D3—61no—
199C3×D4—41no—
200C3×D4—41no—
201C3×D4—41no—
202C2×C3×C4—22no—
203C2×C3×C4—21no—
204C2×C3×C4—41no—
205C2×C3×C4—41no—
206C2×C3×C4—41no—
207C2×C3×C4C2×C4×D311yescharacteristic
208C2×C3×C4D3×D411yescharacteristic
209#67—122no—
210#67—122no—
211#67—121no—
212#67—121no—
213C2×Dic3—31no—
214C2×Dic3—31no—
215C2×Dic3—31no—
216C2×Dic3—31no—
217C2×Dic3—62no—
218C2×Dic3—61no—
219C2×Dic3—61no—
220C2×Dic3—62no—
221C2×Dic3—61no—
222C2×Dic3—122no—
223C2×Dic3—121no—
224C2×Dic3—121no—
225D12—121no—
226C4×D3—122no—
227Dic6—122no—
228C3×C8—41no—
229C3⋊C8—121no—
230C2×C9—21no—
231C2×C9—21no—
232C2×C9—81no—
233C2×C9#41011yescharacteristic
234C2×C9#41811yescharacteristic
235C2×C9C2×#10411yescharacteristic
236D9—81no—
237#41—362no—
238#41—362no—
239C2×Q8—181no—
240C2×D4—21no—
241C2×D4—91no—
242C2×D4—181no—
243C2×D4—181no—
244C2×D4—181no—
245C2×D4C4×D911yescharacteristic
246C22×C4—21no—
247C22×C4—91no—
248C22×C4—91no—
249C22×C4—181no—
250C22×C4—181no—
251C22×C4—181no—
252C22×C4C22×D911yescharacteristic
253C2×C8—21no—
254C2×C8—181no—
255C4⋊C4—91no—
256C4⋊C4—181no—
257C4⋊C4C4×D911yescharacteristic
258C22⋊C4—21no—
259C22⋊C4—181no—
260C22⋊C4—181no—
261C22⋊C4—181no—
262C42—91no—
263C42—91no—
264C42—91no—
265C42—91no—
266C42—184no—
267C22×C3—21no—
268C22×C3—21no—
269C22×C3—41no—
270C22×C3—41no—
271C22×C3—41no—
272C22×C3D3×C22⋊C411yescharacteristic
273C22×C3#91111yescharacteristic
274C22×C3#91411yescharacteristic
275C2×D3—121no—
276C2×D3—121no—
277C2×D3—121no—
278C3×C4—21no—
279C3×C4—21no—
280C3×C4—42no—
281C3×C4—41no—
282Dic3—32no—
283Dic3—61no—
284Dic3—61no—
285Dic3—61no—
286Dic3—122no—
287Dic3—121no—
288C9#150511yescharacteristic, complemented, Sylow
289C23—21no—
290C23—181no—
291C23D4×D911yescharacteristic
292Q8—362no—
293D4—41no—
294D4—41no—
295D4—41no—
296D4—361no—
297D4—362no—
298D4—362no—
299D4—361no—
300D4—361no—
301C2×C4—22no—
302C2×C4—21no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—91no—
307C2×C4—91no—
308C2×C4—91no—
309C2×C4—91no—
310C2×C4—182no—
311C2×C4—181no—
312C2×C4—181no—
313C2×C4—182no—
314C2×C4—181no—
315C2×C4—362no—
316C2×C4—362no—
317C2×C4—361no—
318C2×C4—361no—
319C2×C4C2×C4×D911yescharacteristic
320C2×C4D4×D911yescharacteristic
321C8—41no—
322C8—361no—
323C2×C3—21no—
324C2×C3—21no—
325C2×C3—81no—
326C2×C3#474011yescharacteristic
327C2×C3#477011yescharacteristic
328C2×C3D3×#10411yescharacteristic
329D3—241no—
330C22—21no—
331C22—21no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—361no—
336C22—361no—
337C22—361no—
338C22C22⋊C4×D911yescharacteristic
339C22#6347311yescharacteristic
340C22#6347611yescharacteristic
341C4—21no—
342C4—21no—
343C4—42no—
344C4—41no—
345C4—92no—
346C4—181no—
347C4—181no—
348C4—181no—
349C4—362no—
350C4—361no—
351C3#6827811yescharacteristic
352C2—21no—
353C2—21no—
354C2—81no—
355C2—721no—
356C2#1058842011yescharacteristic
357C2#1058845011yescharacteristic
358C2D9×#10411yescharacteristic
subgroupG/H
centerC22C22⋊C4×D9
commutatorC2×C4×C9C22×C4
FrattiniC22×C3×C4C22×D3
FittingC9×#327C2
socleC22×C3D3×C22⋊C4
prime radical#10589698C2
cosocleC22×C4×C9C23
hypercenter#327D9
hypocenterC9#1505
LCSG ▷ C2×C4×C9 ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #10588399C2semidirect
3. #10588328C2semidirect
4. C9×#327C2semidirect
5. #10588214C2semidirect
6. #10588147C2semidirect
7. #10588129C2semidirect
11. #63502C4semidirect
13. D4×Dic9C4semidirect
17. #63455C4semidirect
18. #63450C4semidirect
125. #327D9semidirect
288. C9#1505semidirect

Maximal subgroups

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

subgroupindex
#105896982
#105883992
#105883282
C9×#3272
#105882142
#105881472
#105881292
#682783