Finite Group Databasebeta

← #11774843

Subgroups — #11774843

Order 1152.

549 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 549 conjugacy classes of subgroups — too many to draw. Only its 100 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
2#10590340C211yesmaximal, characteristic, complemented
3#10590297C211yesmaximal, characteristic, complemented
4C3×D4⋊(C3⋊C8)C212yesmaximal, complemented
5#10589085C212yesmaximal, complemented
6#68178—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—
19C3×C4⋊(C3⋊C8)C2212yes—
20C3×C4×C3⋊C8C2212yes—
21#63572—21no—
22#63572—21no—
23#63557—21no—
24#5557—32no—
25#5557—61no—
26#4837—32no—
27#4685—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—42no—
58#1495—91noSylow
59C3×C4×D4—21no—
60C3×C4×D4C2×D312yes—
61#938—32no—
62#938—61no—
63#936—32no—
64#936—61no—
65C4×#67—62no—
66C4×#67—62no—
67#926—62no—
68#926—62no—
69C2×ΓL(1,𝔽25)—62no—
70#897—32no—
71#897—61no—
72#890—32no—
73#890—61no—
74#883—62no—
75#883—62no—
76#879—62no—
77#879—62no—
78C42×D3—32no—
79C42×D3—61no—
80C4×Dic6—32no—
81C4×Dic6—61no—
82C3×C4⋊C8—32no—
83C3×C4×C8—32no—
84(C2×D3)⋊C8—62no—
85Dic3⋊C8—62no—
86Dic3⋊C8—62no—
87C4⋊(C3⋊C8)C2×D312yes—
88C4×C3⋊C8C2×D312yes—
89C23×C32—21no—
90C22×C3⋊D3C22⋊C411yescharacteristic
91C32×D4—22no—
92C2×C32×C4—21no—
93C2×C32×C4—41no—
94C2×C32×C4—41no—
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⋊Dic3C22⋊C411yescharacteristic
102C2×C3⋊Dic3C22⋊C411yescharacteristic
103C2×C3⋊Dic3C22⋊C411yescharacteristic
104C4×C3⋊D3—22no—
105C4×C3⋊D3—21no—
106C4×C3⋊D3—21no—
107C4×C3⋊D3—41no—
108#634—22no—
109C3×C3⋊C8—42no—
110C3×C3⋊C8—42no—
111#529—91no—
112#431—91no—
113#423—91no—
114Q8⋊C8—92no—
115D4⋊C8—32no—
116C2×C3×D4—21no—
117C2×C3×D4C4×D312yes—
118C22×C3×C4—22no—
119C22×C3×C4—22no—
120C2×#67—62no—
121C2×#67—62no—
122C2×C4×D3—32no—
123C2×C4×D3—32no—
124C2×C4×D3—32no—
125C2×C4×D3—61no—
126C2×C4×D3—61no—
127C2×C4×D3—61no—
128C2×Dic6—32no—
129C2×Dic6—61no—
130C2×C3×C8—62no—
131C2×C3×C8—62no—
132C3×C4⋊C4—21no—
133C3×C4⋊C4C4×D312yes—
134C3×C22⋊C4—22no—
135C3×C22⋊C4—22no—
136C3×C42—21no—
137C3×C42C22×D312yes—
138#217—62no—
139#217—62no—
140#217—62no—
141#217—62no—
142#217—62no—
143#217—62no—
144(C2×D3)⋊C4—62no—
145(C2×D3)⋊C4—62no—
146C4⋊Dic3—32no—
147C4⋊Dic3—61no—
148C4⋊Dic3—62no—
149C4⋊Dic3—62no—
150C4⋊Dic3—62no—
151C4⋊Dic3—62no—
152Dic3⋊C4—62no—
153Dic3⋊C4—62no—
154Dic3⋊C4—62no—
155Dic3⋊C4—62no—
156C4×Dic3—32no—
157C4×Dic3—32no—
158C4×Dic3—32no—
159C4×Dic3—61no—
160C4×Dic3—61no—
161C4×Dic3—61no—
162C4×Dic3—62no—
163C4×Dic3—62no—
164C2×C3⋊C8—22no—
165C2×C3⋊C8—22no—
166ΓL(1,𝔽25)—124no—
167C22×C32—41no—
168C22×C32—41no—
169C22×C32—41no—
170C22×C32C2×C22⋊C411yescharacteristic
171C2×C3⋊D3—21no—
172C2×C3⋊D3—21no—
173C2×C3⋊D3—21no—
174C32×C4—21no—
175C32×C4—41no—
176C32×C4#13112yes—
177C32×C4AGL(1,ℤ/8)11yescharacteristic
178C32×C4#13711yescharacteristic
179C3⋊Dic3—21no—
180C3⋊Dic3—21no—
181C3⋊Dic3—21no—
182C3⋊Dic3—41no—
183C3⋊Dic3—41no—
184C2×M16—181no—
185#126—181no—
186#125—91no—
187#124—91no—
188#123—181no—
189C22⋊Q8—91no—
190#121—91no—
191C4×Q8—91no—
192C4×D4—181no—
193C4×D4D3211yescharacteristic
194#117—181no—
195C2×C42—91no—
196C4⋊C8—32no—
197C4⋊C8—181no—
198C4⋊C8—181no—
199C22⋊C8—181no—
200C4×C8—32no—
201C23×C3—22no—
202C23×C3—22no—
203C22×D3—32no—
204C22×D3—61no—
205C3×D4—22no—
206C3×D4—22no—
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×C4—42no—
214C2×C3×C4—42no—
215C2×C3×C4—42no—
216C2×C3×C4—42no—
217C2×C3×C4C2×C4×D312yes—
218C2×C3×C4D3×D412yes—
219C2×C3×C4D3×D412yes—
220#67—124no—
221#67—124no—
222C2×Dic3—32no—
223C2×Dic3—32no—
224C2×Dic3—32no—
225C2×Dic3—61no—
226C2×Dic3—61no—
227C2×Dic3—61no—
228C2×Dic3—62no—
229C2×Dic3—62no—
230C2×Dic3—62no—
231C2×Dic3—62no—
232C4×D3—62no—
233C4×D3—62no—
234C4×D3—62no—
235C4×D3—62no—
236C4×D3—122no—
237C4×D3—121no—
238C4×D3—121no—
239C4×D3—122no—
240C4×D3—122no—
241Dic6—62no—
242Dic6—62no—
243Dic6—122no—
244C3×C8—122no—
245C3×C8—122no—
246C3⋊C8—42no—
247C3⋊C8—42no—
248C2×C32—81no—
249C2×C32#40811yescharacteristic
250C2×C32#41711yescharacteristic
251C2×C32#42111yescharacteristic
252C3⋊D3—41no—
253C2×Q8—91no—
254C2×D4—181no—
255C2×D4#62411yescharacteristic
256C22×C4—21no—
257C22×C4—91no—
258C22×C4—91no—
259C22×C4—91no—
260M16—362no—
261C2×C8—62no—
262C2×C8—62no—
263C4⋊C4—91no—
264C4⋊C4—181no—
265C4⋊C4—181no—
266C4⋊C4—181no—
267C4⋊C4—181no—
268C4⋊C4#62411yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—181no—
271C22⋊C4—181no—
272C22⋊C4—181no—
273C22⋊C4—181no—
274C42—91no—
275C42—91no—
276C42—91no—
277C42—181no—
278C42C2×D3211yescharacteristic
279C22×C3—21no—
280C22×C3—42no—
281C22×C3—42no—
282C22×C3—42no—
283C22×C3—42no—
284C22×C3—42no—
285C22×C3—42no—
286C22×C3D3×C22⋊C412yes—
287C2×D3—62no—
288C2×D3—62no—
289C2×D3—62no—
290C2×D3—62no—
291C2×D3—121no—
292C2×D3—121no—
293C3×C4—22no—
294C3×C4—22no—
295C3×C4—21no—
296C3×C4—21no—
297C3×C4—41no—
298C3×C4—42no—
299C3×C4—42no—
300C3×C4#90112yes—
301C3×C4#90712yes—
302C3×C4#91112yes—
303C3×C4#91512yes—
304Dic3—62no—
305Dic3—62no—
306Dic3—62no—
307Dic3—121no—
308Dic3—121no—
309Dic3—121no—
310Dic3—122no—
311Dic3—122no—
312Dic3—122no—
313Dic3—122no—
314C32#149511yescharacteristic, complemented, Sylow
315C23—21no—
316C23—91no—
317Q8—182no—
318D4—22no—
319D4—362no—
320C2×C4—21no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—91no—
324C2×C4—91no—
325C2×C4—91no—
326C2×C4—182no—
327C2×C4—181no—
328C2×C4—181no—
329C2×C4—181no—
330C2×C4—181no—
331C2×C4—361no—
332C2×C4C2×#62411yescharacteristic
333C2×C4#381111yescharacteristic
334C2×C4#381111yescharacteristic
335C8—122no—
336C8—122no—
337C2×C3—21no—
338C2×C3—21no—
339C2×C3—21no—
340C2×C3—82no—
341C2×C3—82no—
342C2×C3#472712yes—
343C2×C3#477112yes—
344C2×C3#482112yes—
345D3—122no—
346D3—122no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—181no—
351C22—181no—
352C22—181no—
353C22#6397411yescharacteristic
354C4—21no—
355C4—41no—
356C4—181no—
357C4—181no—
358C4—181no—
359C4—361no—
360C4—361no—
361C4#6381712yes—
362C4#6392711yescharacteristic
363C4#6393111yescharacteristic
364C3—21no—
365C3#6817812yescomplemented
366C2—81no—
367C2—361no—
368C2#1059115311yescharacteristic
369C2#1059141811yescharacteristic
370C2#1059167211yescharacteristic
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#1495
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. #10590340C2semidirect
3. #10590297C2semidirect
4. C3×D4⋊(C3⋊C8)C2semidirect
5. #10589085C2semidirect
29. D4⋊(C3⋊C8)D3semidirect
314. C32#1495semidirect
365. C3#68178semidirect

Maximal subgroups

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

subgroupindex
#105960282
#105903402
#105902972
C3×D4⋊(C3⋊C8)2
#105890852
#681783