Finite Group Databasebeta

← #11788215

Subgroups — #11788215

Order 1152.

881 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 881 conjugacy classes of subgroups — too many to draw. Only its 132 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×#63874C211yesmaximal, characteristic, complemented
3C2×C3×#837C212yesmaximal, complemented
4#10591074C211yesmaximal, characteristic, complemented
5#10589162C212yesmaximal, complemented
6#70383—32nomaximal
7C2×C32×#41C2211yescharacteristic
8C22×C4×C3⋊D3C2211yescharacteristic
9#64155C412yescomplemented
10#64147C412yescomplemented
11#64146—21no—
12#64144—21no—
13C4×#638—22no—
14#64135C2211yescharacteristic
15C2×C3×C4×Dic3C2212yes—
16C2×C3×#208C2212yes—
17C2×#3724—21no—
18C2×#3722—21no—
19#63874—24no—
20C3×#837—24no—
21#63557—22no—
22#5828—32no—
23#5828—61no—
24C2×#872—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
34C2×C32×D4—21no—
35C2×C32×D4C2×C411yescharacteristic
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—
45#3757—21no—
46#3757—22no—
47#3752—22no—
48C4⋊(C3⋊Dic3)C2×C412yes—
49#3750—22no—
50C4×C3⋊Dic3—21no—
51C3×C4×Dic3—22no—
52C3×C4×Dic3D414yescomplemented
53C3×#208—22no—
54C3×#208—22no—
55C2×C3×C3⋊C8—22no—
56#3724—24no—
57#3722—24no—
58#1897—91noSylow
59C2×C3×#41—21no—
60C2×C3×#41C2×D312yes—
61C22×C4×D3—32no—
62C22×C4×D3—61no—
63C2×C3×M16—32no—
64C2×C3×C42—32no—
65#946—34no—
66#946—62no—
67#938—34no—
68#938—62no—
69#937—62no—
70#937—62no—
71#935—62no—
72#935—62no—
73C4×#67—64no—
74C4×#67—64no—
75C2×(C2×D3)⋊C4—62no—
76#926—32no—
77#926—61no—
78C2×Dic3⋊C4—62no—
79C2×C4×Dic3C2×D312yes—
80C2×#208C2×D312yes—
81#872—64no—
82#872—64no—
83C3×#104—64no—
84#837—24no—
85(C2×D3)⋊C8—64no—
86C23×C32—21no—
87C23×C32C2×D411yescharacteristic
88C22×C3⋊D3—21no—
89C22×C3⋊D3—21no—
90C22×C3⋊D3—42no—
91C22×C3⋊D3C22⋊C412yes—
92C32×Q8—22no—
93C32×D4—22no—
94C32×D4—41no—
95C32×D4—41no—
96C2×C32×C4—21no—
97C2×C32×C4—42no—
98C2×C32×C4C22×C411yescharacteristic
99C2×C32×C4C2×D411yescharacteristic
100C2×C32×C4C2×D412yes—
101C2×C32×C4#4112yes—
102#638—44no—
103C2×C3⋊Dic3—22no—
104C2×C3⋊Dic3—21no—
105C2×C3⋊Dic3—21no—
106C2×C3⋊Dic3C22⋊C412yes—
107C4×C3⋊D3—24no—
108C4×C3⋊D3—24no—
109C2×C3×Dic3—24no—
110C2×C3×Dic3—44no—
111C3×C3⋊C8—42no—
112#525—91no—
113C2×#117—91no—
114C2×#104—32no—
115#407—91no—
116#339—92no—
117C23×D3—32no—
118C23×D3—61no—
119C3×#41—22no—
120C3×#41—22no—
121C3×#41—22no—
122C3×#41—22no—
123C3×#41—42no—
124C3×#41—42no—
125C2×C3×Q8—21no—
126C2×C3×Q8C4×D312yes—
127C2×C3×D4—22no—
128C2×C3×D4—22no—
129C2×C3×D4—21no—
130C2×C3×D4C4×D312yes—
131C22×C3×C4—22no—
132C22×C3×C4—22no—
133C22×C3×C4—21no—
134C22×C3×C4—62no—
135C22×C3×C4C22×D312yes—
136C2×#67—64no—
137C2×#67—64no—
138C22×Dic3—22no—
139C22×Dic3—32no—
140C22×Dic3—61no—
141C2×C4×D3—34no—
142C2×C4×D3—34no—
143C2×C4×D3—62no—
144C2×C4×D3—62no—
145C2×C4×D3—62no—
146C2×C4×D3—62no—
147C2×C4×D3—62no—
148C2×C4×D3—62no—
149C2×C4×D3—122no—
150C2×C4×D3—122no—
151C3×M16—62no—
152C3×M16—62no—
153C2×C3×C8—62no—
154C3×C42—34no—
155C3×C42—62no—
156#217—64no—
157#217—62no—
158#217—64no—
159#217—62no—
160(C2×D3)⋊C4—68no—
161(C2×D3)⋊C4—64no—
162(C2×D3)⋊C4—64no—
163C4⋊Dic3—34no—
164C4⋊Dic3—62no—
165Dic3⋊C4—68no—
166Dic3⋊C4—64no—
167Dic3⋊C4—64no—
168C4×Dic3—22no—
169C4×Dic3—62no—
170C4×Dic3—62no—
171C4×Dic3#6714yescomplemented
172#208—22no—
173#208—22no—
174C2×C3⋊C8—22no—
175C22×C32—22no—
176C22×C32—41no—
177C22×C32—42no—
178C22×C32C2×C22⋊C411yescharacteristic
179C22×C32#12011yescharacteristic
180C22×C32#12311yescharacteristic
181C2×C3⋊D3—22no—
182C2×C3⋊D3—22no—
183C2×C3⋊D3—22no—
184C2×C3⋊D3—42no—
185C2×C3⋊D3—42no—
186C32×C4—41no—
187C32×C4C4×D412yes—
188C32×C4#12112yes—
189C3⋊Dic3—22no—
190C3⋊Dic3—42no—
191C3×Dic3—44no—
192C2×#41D3211yescharacteristic
193C23×C4—91no—
194C2×M16—32no—
195#123—181no—
196C22⋊Q8—92no—
197#121—92no—
198#120—181no—
199C4×D4—182no—
200#117—91no—
201#117—184no—
202C2×C4⋊C4—181no—
203C2×C22⋊C4—181no—
204C2×C42—32no—
205#104—64no—
206C22⋊C8—182no—
207C23×C3—22no—
208C23×C3—22no—
209C23×C3—21no—
210C23×C3D3×D412yes—
211C22×D3—34no—
212C22×D3—62no—
213C22×D3—62no—
214C22×D3—62no—
215C22×D3—121no—
216C22×D3—121no—
217C22×D3—124no—
218C22×D3—124no—
219C3×Q8—22no—
220C3×Q8—22no—
221C3×Q8—42no—
222C3×D4—22no—
223C3×D4—22no—
224C3×D4—42no—
225C3×D4—42no—
226C3×D4—42no—
227C3×D4—42no—
228C3×D4—42no—
229C2×C3×C4—22no—
230C2×C3×C4—22no—
231C2×C3×C4—22no—
232C2×C3×C4—21no—
233C2×C3×C4—22no—
234C2×C3×C4—21no—
235C2×C3×C4—44no—
236C2×C3×C4—42no—
237C2×C3×C4—42no—
238C2×C3×C4—64no—
239C2×C3×C4—124no—
240C2×C3×C4C2×C4×D312yes—
241C2×C3×C4#23512yes—
242C2×C3×C4D3×D412yes—
243C2×C3×C4D3×D412yes—
244C2×C3×C4#23712yes—
245C2×C3×C4C2×#6712yes—
246#67—128no—
247#67—128no—
248C2×Dic3—24no—
249C2×Dic3—34no—
250C2×Dic3—44no—
251C2×Dic3—62no—
252C2×Dic3—62no—
253C2×Dic3—62no—
254C2×Dic3—64no—
255C2×Dic3—64no—
256C2×Dic3—121no—
257C2×Dic3—121no—
258C4×D3—64no—
259C4×D3—64no—
260C4×D3—64no—
261C4×D3—64no—
262C4×D3—124no—
263C4×D3—124no—
264C3×C8—122no—
265C3⋊C8—42no—
266C2×C32—21no—
267C2×C32—21no—
268C2×C32—81no—
269C2×C32#38611yescharacteristic
270C2×C32#42112yes—
271C3⋊D3—42no—
272C24—91no—
273#41—22no—
274#41—22no—
275C2×Q8#62411yescharacteristic
276C2×D4—21no—
277C2×D4—182no—
278C2×D4#62411yescharacteristic
279C22×C4—21no—
280C22×C4—62no—
281C22×C4—91no—
282C22×C4—92no—
283C22×C4—92no—
284C22×C4—182no—
285C22×C4—182no—
286C22×C4C2×D3211yescharacteristic
287M16—62no—
288M16—62no—
289C2×C8—62no—
290C4⋊C4—92no—
291C4⋊C4—182no—
292C4⋊C4—184no—
293C22⋊C4—182no—
294C22⋊C4—184no—
295C22⋊C4—182no—
296C22⋊C4—181no—
297C42—34no—
298C42—62no—
299C42—181no—
300C22×C3—24no—
301C22×C3—21no—
302C22×C3—21no—
303C22×C3—21no—
304C22×C3—42no—
305C22×C3—44no—
306C22×C3—42no—
307C22×C3—42no—
308C22×C3—44no—
309C22×C3D3×C22⋊C412yes—
310C22×C3#88312yes—
311C22×C3#93712yes—
312C2×D3—64no—
313C2×D3—64no—
314C2×D3—64no—
315C2×D3—64no—
316C2×D3—122no—
317C2×D3—122no—
318C2×D3—124no—
319C2×D3—124no—
320C2×D3—124no—
321C2×D3—124no—
322C3×C4—22no—
323C3×C4—22no—
324C3×C4—42no—
325C3×C4—42no—
326C3×C4—124no—
327C3×C4#67⋊C412yes—
328C3×C4#88412yes—
329C3×C4C4×#6712yes—
330C3×C4#93812yes—
331Dic3—44no—
332Dic3—64no—
333Dic3—122no—
334Dic3—124no—
335Dic3—124no—
336C32#189711yescharacteristic, complemented, Sylow
337C23—21no—
338C23—92no—
339C23—181no—
340C23—181no—
341C23—362no—
342C23#381111yescharacteristic
343Q8—22no—
344D4—22no—
345D4—41no—
346D4—41no—
347D4—364no—
348C2×C4—21no—
349C2×C4—42no—
350C2×C4—64no—
351C2×C4—92no—
352C2×C4—124no—
353C2×C4—181no—
354C2×C4—181no—
355C2×C4—184no—
356C2×C4—184no—
357C2×C4—182no—
358C2×C4#380412yes—
359C2×C4C2×#62411yescharacteristic
360C2×C4D3×#6712yes—
361C2×C4#381111yescharacteristic
362C8—122no—
363C2×C3—22no—
364C2×C3—22no—
365C2×C3—22no—
366C2×C3—21no—
367C2×C3—41no—
368C2×C3—41no—
369C2×C3—82no—
370C2×C3—82no—
371C2×C3#482114yes—
372C2×C3#495612yes—
373D3—124no—
374D3—124no—
375C22—22no—
376C22—42no—
377C22—41no—
378C22—182no—
379C22—182no—
380C22—182no—
381C22—362no—
382C22—362no—
383C22#6397411yescharacteristic
384C22#6397511yescharacteristic
385C22#6398311yescharacteristic
386C4—41no—
387C4—124no—
388C4—182no—
389C4—362no—
390C4#6395212yes—
391C4#6395812yes—
392C3—21no—
393C3#7038312yescomplemented
394C2—21no—
395C2—21no—
396C2—81no—
397C2—362no—
398C2#1059167212yes—
399C2#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#1897
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×#63874C2semidirect
3. C2×C3×#837C2semidirect
4. #10591074C2semidirect
5. #10589162C2semidirect
9. #64155C4semidirect
10. #64147C4semidirect
26. C2×#837D3semidirect
52. C3×C4×Dic3D4semidirect
171. C4×Dic3#67semidirect
336. C32#1897semidirect
393. C3#70383semidirect

Maximal subgroups

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

subgroupindex
#105962992
C2×#638742
C2×C3×#8372
#105910742
#105891622
#703833