Finite Group Databasebeta

← #11774471

Subgroups — #11774471

Order 1152.

585 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 585 conjugacy classes of subgroups — too many to draw. Only its 102 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#10596028C211yesmaximal, characteristic
2C4×#3712C211yesmaximal, characteristic, complemented
3#10590331C211yesmaximal, characteristic, complemented
4C3×D4⋊(C3⋊C8)C212yesmaximal, complemented
5#10589085C212yesmaximal, complemented
6#68170—32nomaximal
7C32×C4×D4C2211yescharacteristic
8#64147C411yescharacteristic
9#64145C411yescharacteristic
10C4×#638—21no—
11#64135—21no—
12#64106C411yescharacteristic
13#64099C411yescharacteristic
14#64092—21no—
15#64088—21no—
16C42×C3⋊D3C2211yescharacteristic
17C4×#634C2211yescharacteristic
18C2×#3712—21no—
19C2×#3710—21no—
20C3×C4⋊(C3⋊C8)C2212yes—
21C3×C4×C3⋊C8C2212yes—
22#63572—21no—
23#63555—21no—
24#5557—32no—
25#5557—61no—
26D3×C4⋊C8—32no—
27C4×ΓL(1,𝔽25)—32no—
28C3×D4⋊C8—32no—
29D4⋊(C3⋊C8)D312yescomplemented
30#4484—32no—
31#4456—32no—
32C2×C32×D4C2×C411yescharacteristic
33C22×C32×C4—21no—
34C2×#638—21no—
35C2×C4×C3⋊D3C2×C411yescharacteristic
36C2×C4×C3⋊D3D411yescharacteristic
37C2×C4×C3⋊D3D411yescharacteristic
38C2×#634C2×C411yescharacteristic
39C32×C4⋊C4C2×C411yescharacteristic
40C32×C22⋊C4—21no—
41C32×C42C2311yescharacteristic
42#3757—21no—
43#3757—21no—
44#3757—21no—
45#3752—21no—
46C4⋊(C3⋊Dic3)—21no—
47C4⋊(C3⋊Dic3)—21no—
48C4⋊(C3⋊Dic3)C2×C411yescharacteristic
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—42no—
59#1483—91noSylow
60C3×C4×D4—21no—
61C3×C4×D4C2×D312yes—
62#938—32no—
63#938—61no—
64#936—32no—
65#936—61no—
66C4×#67—62no—
67C4×#67—62no—
68#926—62no—
69#926—62no—
70C2×ΓL(1,𝔽25)—62no—
71C2×D3×C8—62no—
72#897—32no—
73#897—61no—
74#890—32no—
75#890—61no—
76#883—62no—
77#883—62no—
78#879—62no—
79#879—62no—
80C42×D3—32no—
81C42×D3—61no—
82C4×Dic6—32no—
83C4×Dic6—61no—
84C3×C4⋊C8—32no—
85C3×C4×C8—32no—
86#815—62no—
87Dic3⋊C8—62no—
88C4⋊(C3⋊C8)C2×D312yes—
89C4×C3⋊C8C2×D312yes—
90C23×C32—21no—
91C22×C3⋊D3C22⋊C411yescharacteristic
92C32×D4—22no—
93C2×C32×C4—21no—
94C2×C32×C4—41no—
95C2×C32×C4—41no—
96C2×C32×C4C22×C411yescharacteristic
97C2×C32×C4C2×D411yescharacteristic
98C2×C32×C4C2×D411yescharacteristic
99#638—42no—
100C2×C3⋊Dic3—21no—
101C2×C3⋊Dic3—21no—
102C2×C3⋊Dic3C22⋊C411yescharacteristic
103C2×C3⋊Dic3C22⋊C411yescharacteristic
104C2×C3⋊Dic3C22⋊C411yescharacteristic
105C4×C3⋊D3—22no—
106C4×C3⋊D3—22no—
107C4×C3⋊D3—21no—
108C4×C3⋊D3—21no—
109#634—22no—
110C3×C3⋊C8—24no—
111C3×C3⋊C8—42no—
112#529—91no—
113C2×C4⋊C8—91no—
114C4×M16—91no—
115Q8⋊C8—92no—
116D4⋊C8—32no—
117C2×C3×D4—21no—
118C2×C3×D4C4×D312yes—
119C22×C3×C4—22no—
120C22×C3×C4—22no—
121C2×#67—62no—
122C2×#67—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×Dic6—32no—
130C2×Dic6—61no—
131C2×C3×C8—62no—
132C2×C3×C8—62no—
133C3×C4⋊C4—21no—
134C3×C4⋊C4C4×D312yes—
135C3×C22⋊C4—22no—
136C3×C22⋊C4—22no—
137C3×C42—21no—
138C3×C42C22×D312yes—
139#217—62no—
140#217—62no—
141#217—62no—
142#217—62no—
143#217—62no—
144#217—62no—
145(C2×D3)⋊C4—62no—
146(C2×D3)⋊C4—62no—
147C4⋊Dic3—32no—
148C4⋊Dic3—61no—
149C4⋊Dic3—62no—
150C4⋊Dic3—62no—
151C4⋊Dic3—62no—
152C4⋊Dic3—62no—
153Dic3⋊C4—62no—
154Dic3⋊C4—62no—
155Dic3⋊C4—62no—
156Dic3⋊C4—62no—
157C4×Dic3—32no—
158C4×Dic3—32no—
159C4×Dic3—32no—
160C4×Dic3—61no—
161C4×Dic3—61no—
162C4×Dic3—61no—
163C4×Dic3—62no—
164C4×Dic3—62no—
165C2×C3⋊C8—22no—
166C2×C3⋊C8—22no—
167ΓL(1,𝔽25)—68no—
168D3×C8—124no—
169C22×C32—41no—
170C22×C32—41no—
171C22×C32—41no—
172C22×C32C2×C22⋊C411yescharacteristic
173C2×C3⋊D3—21no—
174C2×C3⋊D3—21no—
175C2×C3⋊D3#10412yes—
176C32×C4—21no—
177C32×C4—41no—
178C32×C4#13112yes—
179C32×C4AGL(1,ℤ/8)11yescharacteristic
180C32×C4#13711yescharacteristic
181C3⋊Dic3—21no—
182C3⋊Dic3—21no—
183C3⋊Dic3—21no—
184C3⋊Dic3—41no—
185C3⋊Dic3—41no—
186C2×M16—181no—
187C22×C8—181no—
188#126—181no—
189#125—91no—
190#124—91no—
191#123—181no—
192C22⋊Q8—91no—
193#121—91no—
194C4×Q8—91no—
195C4×D4—181no—
196C4×D4D3211yescharacteristic
197#117—181no—
198C2×C42—91no—
199C4⋊C8—32no—
200C4⋊C8—181no—
201#97—181no—
202C4×C8—32no—
203C23×C3—22no—
204C23×C3—22no—
205C22×D3—32no—
206C22×D3—61no—
207C3×D4—22no—
208C3×D4—22no—
209C3×D4—42no—
210C2×C3×C4—22no—
211C2×C3×C4—22no—
212C2×C3×C4—21no—
213C2×C3×C4—21no—
214C2×C3×C4—21no—
215C2×C3×C4—42no—
216C2×C3×C4—42no—
217C2×C3×C4—42no—
218C2×C3×C4—42no—
219C2×C3×C4C2×C4×D312yes—
220C2×C3×C4D3×D412yes—
221C2×C3×C4D3×D412yes—
222#67—124no—
223#67—124no—
224C2×Dic3—32no—
225C2×Dic3—32no—
226C2×Dic3—32no—
227C2×Dic3—61no—
228C2×Dic3—61no—
229C2×Dic3—61no—
230C2×Dic3—62no—
231C2×Dic3—62no—
232C2×Dic3—62no—
233C2×Dic3—62no—
234C4×D3—64no—
235C4×D3—62no—
236C4×D3—62no—
237C4×D3—62no—
238C4×D3—62no—
239C4×D3—122no—
240C4×D3—121no—
241C4×D3—121no—
242C4×D3—122no—
243Dic6—62no—
244Dic6—62no—
245Dic6—122no—
246C3×C8—64no—
247C3×C8—122no—
248C3⋊C8—24no—
249C3⋊C8—42no—
250C2×C32—81no—
251C2×C32#40811yescharacteristic
252C2×C32#41711yescharacteristic
253C2×C32C2×#10411yescharacteristic
254C3⋊D3—22no—
255C2×Q8—91no—
256C2×D4—181no—
257C2×D4#62411yescharacteristic
258C22×C4—21no—
259C22×C4—91no—
260C22×C4—91no—
261C22×C4—91no—
262M16—184no—
263C2×C8—62no—
264C2×C8—62no—
265C2×C8—362no—
266C4⋊C4—91no—
267C4⋊C4—181no—
268C4⋊C4—181no—
269C4⋊C4—181no—
270C4⋊C4—181no—
271C4⋊C4#62411yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—181no—
274C22⋊C4—181no—
275C22⋊C4—181no—
276C22⋊C4—181no—
277C42—91no—
278C42—91no—
279C42—91no—
280C42—181no—
281C42C2×D3211yescharacteristic
282C22×C3—21no—
283C22×C3—42no—
284C22×C3—42no—
285C22×C3—42no—
286C22×C3—42no—
287C22×C3—42no—
288C22×C3—42no—
289C22×C3D3×C22⋊C412yes—
290C2×D3—34no—
291C2×D3—62no—
292C2×D3—62no—
293C2×D3—62no—
294C2×D3—121no—
295C2×D3—121no—
296C3×C4—22no—
297C3×C4—22no—
298C3×C4—21no—
299C3×C4—21no—
300C3×C4—41no—
301C3×C4—42no—
302C3×C4—42no—
303C3×C4#90112yes—
304C3×C4#90712yes—
305C3×C4#91112yes—
306C3×C4#91512yes—
307Dic3—62no—
308Dic3—62no—
309Dic3—62no—
310Dic3—121no—
311Dic3—121no—
312Dic3—121no—
313Dic3—122no—
314Dic3—122no—
315Dic3—122no—
316Dic3—122no—
317C32#148311yescharacteristic, complemented, Sylow
318C23—21no—
319C23—91no—
320Q8—182no—
321D4—22no—
322D4—362no—
323C2×C4—21no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—91no—
327C2×C4—91no—
328C2×C4—91no—
329C2×C4—182no—
330C2×C4—182no—
331C2×C4—181no—
332C2×C4—181no—
333C2×C4—181no—
334C2×C4—181no—
335C2×C4C2×#62411yescharacteristic
336C2×C4#381111yescharacteristic
337C2×C4#381111yescharacteristic
338C8—64no—
339C8—122no—
340C2×C3—21no—
341C2×C3—21no—
342C2×C3—21no—
343C2×C3—82no—
344C2×C3—82no—
345C2×C3#472712yes—
346C2×C3#477112yes—
347C2×C3D3×#10412yes—
348D3—64no—
349D3—122no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—92no—
354C22—181no—
355C22—181no—
356C22#6397411yescharacteristic
357C4—21no—
358C4—41no—
359C4—181no—
360C4—181no—
361C4—181no—
362C4—361no—
363C4—361no—
364C4#6381712yes—
365C4#6392711yescharacteristic
366C4#6393111yescharacteristic
367C3—21no—
368C3#6817012yescomplemented
369C2—81no—
370C2—182no—
371C2#1059115311yescharacteristic
372C2#1059141811yescharacteristic
373C2#1059167111yescharacteristic
subgroupG/H
centerC2×C4#3811
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32C2×C22⋊C4
prime radical#64147C4
cosocleC32×C42C23
hypercenterC4×D4D32
hypocenterC32#1483
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C4×#3712C2semidirect
3. #10590331C2semidirect
4. C3×D4⋊(C3⋊C8)C2semidirect
5. #10589085C2semidirect
29. D4⋊(C3⋊C8)D3semidirect
317. C32#1483semidirect
368. C3#68170semidirect

Maximal subgroups

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

subgroupindex
#105960282
C4×#37122
#105903312
C3×D4⋊(C3⋊C8)2
#105890852
#681703