Finite Group Databasebeta

← #11788181

Subgroups — #11788181

Order 1152.

1049 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 1049 conjugacy classes of subgroups — too many to draw. Only its 136 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#10596299C211yesmaximal, characteristic
2C2×C4×#624C211yesmaximal, characteristic, complemented
3C2×C3×#837C212yesmaximal, complemented
4#10591074C211yesmaximal, characteristic, complemented
5#10589162C212yesmaximal, complemented
6#70382—32nomaximal
7C2×C32×#41C2211yescharacteristic
8C22×C4×C3⋊D3C2211yescharacteristic
9C22×#624—21no—
10#64155C412yescomplemented
11#64147C412yescomplemented
12#64146—21no—
13#64144—21no—
14C4×#638—22no—
15#64135C2211yescharacteristic
16C2×C3×C4×Dic3C2212yes—
17C2×C3×#208C2212yes—
18C2×Dic32—21no—
19C4×#624—24no—
20C3×#837—24no—
21#63557—22no—
22#5828—32no—
23#5828—61no—
24C2×C42×D3—32no—
25C2×C3×#104—32no—
26C2×#837D312yescomplemented
27#5126—32no—
28#4555—32no—
29#4523—32no—
30C23×C3⋊D3D411yescharacteristic
31C32×#41—22no—
32C32×#41—22no—
33C2×C32×Q8C2×C411yescharacteristic, complemented
34C2×C32×D4—21no—
35C2×C32×D4C2×C411yescharacteristic, complemented
36C22×C32×C4—21no—
37C22×C32×C4C2311yescharacteristic
38C2×#638—22no—
39C22×C3⋊Dic3D411yescharacteristic
40C2×C4×C3⋊D3—22no—
41C2×C4×C3⋊D3—22no—
42C2×C4×C3⋊D3C2×C412yes—
43C2×C4×C3⋊D3D412yes—
44C22×C3×Dic3—22no—
45C2×#624—28no—
46C2×#624—24no—
47#3757—21no—
48#3757—22no—
49#3752—22no—
50C4⋊(C3⋊Dic3)C2×C412yescomplemented
51#3750—22no—
52C4×C3⋊Dic3—21no—
53C3×C4×Dic3—22no—
54C3×C4×Dic3D414yescomplemented
55C3×#208—22no—
56C3×#208—22no—
57C2×C3×C3⋊C8—22no—
58Dic32—24no—
59#1896—91noSylow
60C2×C3×#41—21no—
61C2×C3×#41C2×D312yes—
62C22×C4×D3—32no—
63C22×C4×D3—61no—
64C22×C4×D3—62no—
65C2×C3×M16—32no—
66C2×C3×C42—32no—
67#946—34no—
68#946—62no—
69#938—34no—
70#938—62no—
71#937—62no—
72#937—62no—
73#935—62no—
74#935—62no—
75C4×#67—64no—
76C4×#67—64no—
77#926—32no—
78#926—61no—
79C2×C4×Dic3—62no—
80C2×C4×Dic3C2×D312yes—
81C2×#208C2×D312yes—
82C42×D3—64no—
83C42×D3—64no—
84C3×#104—64no—
85#837—24no—
86(C2×D3)⋊C8—64no—
87C23×C32—21no—
88C23×C32C2×D411yescharacteristic
89C22×C3⋊D3—21no—
90C22×C3⋊D3—21no—
91C22×C3⋊D3—24no—
92C22×C3⋊D3C22⋊C412yes—
93C32×Q8—22no—
94C32×D4—22no—
95C32×D4—41no—
96C32×D4—41no—
97C2×C32×C4—21no—
98C2×C32×C4—42no—
99C2×C32×C4C22×C411yescharacteristic
100C2×C32×C4C2×D411yescharacteristic
101C2×C32×C4C2×D412yes—
102C2×C32×C4#4112yes—
103#638—44no—
104C2×C3⋊Dic3—22no—
105C2×C3⋊Dic3—21no—
106C2×C3⋊Dic3—21no—
107C2×C3⋊Dic3C22⋊C412yes—
108C4×C3⋊D3—24no—
109C4×C3⋊D3—24no—
110C2×C3×Dic3—28no—
111C2×C3×Dic3—24no—
112#624—216no—
113C3×C3⋊C8—42no—
114#525—91no—
115C22×C42—91no—
116C2×#104—32no—
117#407—91no—
118#339—92no—
119C23×D3—32no—
120C23×D3—61no—
121C3×#41—22no—
122C3×#41—22no—
123C3×#41—22no—
124C3×#41—22no—
125C3×#41—42no—
126C3×#41—42no—
127C2×C3×Q8—21no—
128C2×C3×Q8C4×D312yescomplemented
129C2×C3×D4—22no—
130C2×C3×D4—22no—
131C2×C3×D4—21no—
132C2×C3×D4C4×D312yescomplemented
133C22×C3×C4—22no—
134C22×C3×C4—22no—
135C22×C3×C4—21no—
136C22×C3×C4—62no—
137C22×C3×C4C22×D312yes—
138C2×#67—64no—
139C2×#67—64no—
140C22×Dic3—22no—
141C22×Dic3—32no—
142C22×Dic3—61no—
143C2×C4×D3—34no—
144C2×C4×D3—34no—
145C2×C4×D3—62no—
146C2×C4×D3—62no—
147C2×C4×D3—68no—
148C2×C4×D3—616no—
149C2×C4×D3—62no—
150C2×C4×D3—62no—
151C2×C4×D3—62no—
152C2×C4×D3—62no—
153C2×C4×D3—122no—
154C2×C4×D3—122no—
155C3×M16—62no—
156C3×M16—62no—
157C2×C3×C8—62no—
158C3×C42—34no—
159C3×C42—62no—
160#217—64no—
161#217—62no—
162#217—64no—
163#217—62no—
164(C2×D3)⋊C4—64no—
165(C2×D3)⋊C4—64no—
166C4⋊Dic3—34no—
167C4⋊Dic3—62no—
168Dic3⋊C4—64no—
169Dic3⋊C4—64no—
170C4×Dic3—22no—
171C4×Dic3—68no—
172C4×Dic3—62no—
173C4×Dic3—62no—
174C4×Dic3#6714yescomplemented
175#208—22no—
176#208—22no—
177C2×C3⋊C8—22no—
178C22×C32—22no—
179C22×C32—41no—
180C22×C32—42no—
181C22×C32C2×C22⋊C411yescharacteristic
182C22×C32#12011yescharacteristic
183C22×C32#12311yescharacteristic
184C2×C3⋊D3—24no—
185C2×C3⋊D3—24no—
186C2×C3⋊D3—22no—
187C2×C3⋊D3—22no—
188C2×C3⋊D3#10414yescomplemented
189C32×C4—41no—
190C32×C4C4×D412yes—
191C32×C4#12112yes—
192C3⋊Dic3—22no—
193C3⋊Dic3—42no—
194C3×Dic3—28no—
195C2×#41D3211yescharacteristic
196C23×C4—91no—
197C23×C4—181no—
198C2×M16—32no—
199#123—181no—
200C22⋊Q8—92no—
201#121—92no—
202#120—181no—
203C4×D4—182no—
204#117—91no—
205C2×C42—32no—
206C2×C42—184no—
207C2×C42—181no—
208#104—64no—
209C22⋊C8—182no—
210C23×C3—22no—
211C23×C3—22no—
212C23×C3—21no—
213C23×C3D3×D412yes—
214C22×D3—34no—
215C22×D3—62no—
216C22×D3—68no—
217C22×D3—62no—
218C22×D3—62no—
219C22×D3—124no—
220C22×D3—121no—
221C22×D3—121no—
222C3×Q8—22no—
223C3×Q8—22no—
224C3×Q8—42no—
225C3×D4—22no—
226C3×D4—22no—
227C3×D4—42no—
228C3×D4—42no—
229C3×D4—42no—
230C3×D4—42no—
231C3×D4—42no—
232C2×C3×C4—22no—
233C2×C3×C4—22no—
234C2×C3×C4—22no—
235C2×C3×C4—21no—
236C2×C3×C4—22no—
237C2×C3×C4—21no—
238C2×C3×C4—44no—
239C2×C3×C4—42no—
240C2×C3×C4—42no—
241C2×C3×C4—68no—
242C2×C3×C4—64no—
243C2×C3×C4C2×C4×D312yes—
244C2×C3×C4#23512yes—
245C2×C3×C4D3×D412yes—
246C2×C3×C4D3×D412yes—
247C2×C3×C4#23712yes—
248C2×C3×C4C2×#6712yes—
249#67—128no—
250#67—128no—
251C2×Dic3—28no—
252C2×Dic3—24no—
253C2×Dic3—34no—
254C2×Dic3—62no—
255C2×Dic3—62no—
256C2×Dic3—62no—
257C2×Dic3—64no—
258C2×Dic3—64no—
259C2×Dic3—121no—
260C2×Dic3—121no—
261C4×D3—632no—
262C4×D3—64no—
263C4×D3—64no—
264C4×D3—64no—
265C4×D3—64no—
266C4×D3—124no—
267C4×D3—124no—
268C3×C8—122no—
269C3⋊C8—42no—
270C2×C32—21no—
271C2×C32—21no—
272C2×C32—81no—
273C2×C32#38611yescharacteristic
274C2×C32C2×#10412yes—
275C3⋊D3—24no—
276C24—91no—
277#41—22no—
278#41—22no—
279C2×Q8#62411yescharacteristic, complemented
280C2×D4—21no—
281C2×D4—182no—
282C2×D4#62411yescharacteristic, complemented
283C22×C4—21no—
284C22×C4—62no—
285C22×C4—91no—
286C22×C4—92no—
287C22×C4—92no—
288C22×C4—184no—
289C22×C4—188no—
290C22×C4—182no—
291C22×C4—182no—
292C22×C4C2×D3211yescharacteristic
293M16—62no—
294M16—62no—
295C2×C8—62no—
296C4⋊C4—92no—
297C4⋊C4—182no—
298C22⋊C4—182no—
299C22⋊C4—182no—
300C22⋊C4—181no—
301C42—34no—
302C42—62no—
303C42—184no—
304C42—181no—
305C22×C3—24no—
306C22×C3—21no—
307C22×C3—21no—
308C22×C3—21no—
309C22×C3—42no—
310C22×C3—44no—
311C22×C3—42no—
312C22×C3—42no—
313C22×C3—44no—
314C22×C3D3×C22⋊C412yes—
315C22×C3#88312yes—
316C22×C3#93712yes—
317C2×D3—38no—
318C2×D3—64no—
319C2×D3—68no—
320C2×D3—68no—
321C2×D3—64no—
322C2×D3—64no—
323C2×D3—122no—
324C2×D3—122no—
325C2×D3—124no—
326C2×D3—124no—
327C3×C4—22no—
328C3×C4—22no—
329C3×C4—42no—
330C3×C4—42no—
331C3×C4—68no—
332C3×C4#67⋊C412yes—
333C3×C4#88412yes—
334C3×C4C4×#6712yes—
335C3×C4#93812yes—
336Dic3—28no—
337Dic3—64no—
338Dic3—122no—
339Dic3—124no—
340Dic3—124no—
341C32#189611yescharacteristic, complemented, Sylow
342C23—21no—
343C23—92no—
344C23—184no—
345C23—181no—
346C23—181no—
347C23#381111yescharacteristic
348Q8—22no—
349D4—22no—
350D4—41no—
351D4—41no—
352D4—364no—
353C2×C4—21no—
354C2×C4—42no—
355C2×C4—68no—
356C2×C4—64no—
357C2×C4—92no—
358C2×C4—1816no—
359C2×C4—181no—
360C2×C4—181no—
361C2×C4—184no—
362C2×C4—184no—
363C2×C4—182no—
364C2×C4#380412yes—
365C2×C4C2×#62411yescharacteristic
366C2×C4D3×#6712yes—
367C2×C4#381111yescharacteristic
368C8—122no—
369C2×C3—22no—
370C2×C3—22no—
371C2×C3—22no—
372C2×C3—21no—
373C2×C3—41no—
374C2×C3—41no—
375C2×C3—82no—
376C2×C3—82no—
377C2×C3D3×#10414yes—
378C2×C3#495612yes—
379D3—68no—
380D3—124no—
381C22—22no—
382C22—42no—
383C22—41no—
384C22—94no—
385C22—184no—
386C22—184no—
387C22—182no—
388C22—182no—
389C22#6397411yescharacteristic
390C22#6397511yescharacteristic
391C22#6398311yescharacteristic
392C4—41no—
393C4—68no—
394C4—182no—
395C4—362no—
396C4#6395212yes—
397C4#6395812yes—
398C3—21no—
399C3#7038212yescomplemented
400C2—21no—
401C2—21no—
402C2—81no—
403C2—184no—
404C2#1059167112yes—
405C2#1059172211yescharacteristic
subgroupG/H
centerC2×C4#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×#41C22
socleC22×C32C2×C22⋊C4
prime radical#10596299C2
cosocleC22×C32×C4C23
hypercenterC2×#41D32
hypocenterC32#1896
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C2×C4×#624C2semidirect
3. C2×C3×#837C2semidirect
4. #10591074C2semidirect
5. #10589162C2semidirect
10. #64155C4semidirect
11. #64147C4semidirect
26. C2×#837D3semidirect
33. C2×C32×Q8C2×C4semidirect
35. C2×C32×D4C2×C4semidirect
50. C4⋊(C3⋊Dic3)C2×C4semidirect
54. C3×C4×Dic3D4semidirect
128. C2×C3×Q8C4×D3semidirect
132. C2×C3×D4C4×D3semidirect
174. C4×Dic3#67semidirect
188. C2×C3⋊D3#104semidirect
279. C2×Q8#624semidirect
282. C2×D4#624semidirect
341. C32#1896semidirect
399. C3#70382semidirect

Maximal subgroups

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

subgroupindex
#105962992
C2×C4×#6242
C2×C3×#8372
#105910742
#105891622
#703823