Finite Group Databasebeta

← #11785849

Subgroups — #11785849

Order 1152.

707 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 707 conjugacy classes of subgroups — too many to draw. Only its 124 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#10594969C211yesmaximal, characteristic
2#10592825C211yesmaximal, characteristic
3C4×#3722C211yesmaximal, characteristic
4C3×#4555C212yesmaximal, complemented
5#10589161C212yesmaximal, complemented
6#68754—32nomaximal
7C22×C4×C3⋊D3C2211yescharacteristic
8C2×C32×M16C2211yescharacteristic
9C2×#3748C2211yescharacteristic
10C3×#926C2212yes—
11C2×C3×C4×Dic3C2212yes—
12#63974—21no—
13C2×#3722—21no—
14#63957—21no—
15#63900C411yescharacteristic, complemented
16#63900C411yescharacteristic, complemented
17C4×#624—21no—
18#63874—21no—
19#63849C412yescomplemented
20#63647—21no—
21#63647—21no—
22#63579—21no—
23D3×#117—32no—
24#5126—32no—
25#5126—61no—
26C4×(C2×D3)⋊C4—32no—
27C3×#339—32no—
28#4555D312yescomplemented
29#4532—32no—
30#4523—32no—
31C23×C3⋊D3D411yescharacteristic
32C22×C32×C4C2311yescharacteristic
33C22×C3⋊Dic3D411yescharacteristic
34C2×C4×C3⋊D3—22no—
35C2×C4×C3⋊D3—22no—
36C2×C4×C3⋊D3C2×C411yescharacteristic
37C2×C4×C3⋊D3C2×C411yescharacteristic
38C2×C4×C3⋊D3D411yescharacteristic
39C2×C4×C3⋊D3D411yescharacteristic
40C22×C3×Dic3—22no—
41C2×#624—21no—
42C2×#624—21no—
43C32×M16—22no—
44C2×C32×C8—21no—
45#3748—22no—
46C2×C3⋊(C3⋊C8)—21no—
47C3×#217—22no—
48C3×C4⋊Dic3C2×C412yes—
49C3×C4⋊Dic3C2×C412yes—
50C3×C4×Dic3—22no—
51C3×C4×Dic3—22no—
52C3×C4×Dic3—22no—
53#3724—21no—
54#3724—21no—
55#3722—24no—
56#3722—22no—
57Dic32—22no—
58#1826—91noSylow
59C22×C4×D3—32no—
60C22×C4×D3—61no—
61C2×C3×M16—21no—
62C2×C3×M16C2×D312yes—
63C3×#117—32no—
64C2×C3×C42—32no—
65C2×(C2×D3)⋊C4—62no—
66#926C2×D312yes—
67C2×C4×Dic3C2×D312yes—
68C2×#208—32no—
69C2×#208—61no—
70#892—32no—
71#892—32no—
72D3×C4⋊C4—32no—
73D3×C4⋊C4—32no—
74D3×C22⋊C4—62no—
75#877—62no—
76#872—62no—
77C42×D3—62no—
78C3⋊#95—62no—
79(C2×D3)⋊C8—62no—
80(C2×D3)⋊C8—62no—
81(C2×D3)⋊C8—62no—
82(C2×D3)⋊C8—62no—
83C23×C32C2×D411yescharacteristic
84C22×C3⋊D3—22no—
85C22×C3⋊D3—22no—
86C22×C3⋊D3—41no—
87C22×C3⋊D3C22⋊C411yescharacteristic
88C22×C3⋊D3C22⋊C411yescharacteristic
89C2×C32×C4C22×C411yescharacteristic
90C2×C32×C4C2×D411yescharacteristic
91C2×C32×C4#4112yes—
92C2×C32×C4#4112yes—
93C2×C3⋊Dic3—22no—
94C2×C3⋊Dic3C22⋊C411yescharacteristic
95C2×C3⋊Dic3C22⋊C411yescharacteristic
96C4×C3⋊D3—22no—
97C4×C3⋊D3—22no—
98C4×C3⋊D3—21no—
99C4×C3⋊D3—21no—
100C4×C3⋊D3—21no—
101C4×C3⋊D3—21no—
102C2×C3×Dic3—24no—
103C2×C3×Dic3—22no—
104C2×C3×Dic3—22no—
105C2×C3×Dic3—42no—
106C2×C3×Dic3—42no—
107#624—42no—
108#624—42no—
109C32×C8—41no—
110C3⋊(C3⋊C8)—41no—
111C2×#117—91no—
112#407—91no—
113C4×C22⋊C4—91no—
114#339—32no—
115#339—92no—
116C23×D3—32no—
117C23×D3—61no—
118C22×C3×C4—21no—
119C22×C3×C4—62no—
120C22×C3×C4C22×D312yes—
121C22×Dic3—22no—
122C22×Dic3—32no—
123C22×Dic3—61no—
124C2×C4×D3—32no—
125C2×C4×D3—32no—
126C2×C4×D3—32no—
127C2×C4×D3—32no—
128C2×C4×D3—61no—
129C2×C4×D3—61no—
130C2×C4×D3—61no—
131C2×C4×D3—61no—
132C2×C4×D3—62no—
133C2×C4×D3—62no—
134C2×C4×D3—62no—
135C2×C4×D3—62no—
136C2×C4×D3—62no—
137C2×C4×D3—62no—
138C2×C4×D3—122no—
139C2×C4×D3—122no—
140C3×M16—22no—
141C3×M16—22no—
142C3×M16—42no—
143C2×C3×C8—22no—
144C2×C3×C8—22no—
145C3×C4⋊C4—32no—
146C3×C4⋊C4—32no—
147C3×C22⋊C4—62no—
148C3×C42—62no—
149C3×C42—62no—
150C3×C42—62no—
151#217—22no—
152(C2×D3)⋊C4—62no—
153(C2×D3)⋊C4—62no—
154(C2×D3)⋊C4—68no—
155C4⋊Dic3C4×D312yes—
156C4⋊Dic3C4×D312yes—
157Dic3⋊C4—62no—
158Dic3⋊C4—62no—
159C4×Dic3—22no—
160C4×Dic3—22no—
161C4×Dic3—22no—
162C4×Dic3—62no—
163C4×Dic3—62no—
164#208—62no—
165#208—62no—
166#208—122no—
167C2×C3⋊C8—62no—
168C2×C3⋊C8—62no—
169C22×C32—21no—
170C22×C32—21no—
171C22×C32C2×C22⋊C411yescharacteristic
172C22×C32#12312yes—
173C2×C3⋊D3—21no—
174C2×C3⋊D3—21no—
175C2×C3⋊D3—21no—
176C2×C3⋊D3—21no—
177C2×C3⋊D3—21no—
178C2×C3⋊D3—44no—
179C2×C3⋊D3#10412yes—
180C32×C4#11712yes—
181C32×C4#12311yescharacteristic
182C32×C4#12311yescharacteristic
183C3⋊Dic3—21no—
184C3⋊Dic3—21no—
185C3×Dic3—44no—
186C3×Dic3—42no—
187C3×Dic3—42no—
188C23×C4—91no—
189C2×M16—91no—
190C2×M16D3211yescharacteristic
191#117—32no—
192#117—92no—
193#117—181no—
194#117—181no—
195C2×C4⋊C4—91no—
196C2×C4⋊C4—91no—
197C2×C22⋊C4—181no—
198C2×C22⋊C4—181no—
199C2×C42—32no—
200C2×C42—181no—
201C22⋊C8—181no—
202C22⋊C8—181no—
203#95—181no—
204C23×C3—21no—
205C23×C3D3×D412yes—
206C22×D3—32no—
207C22×D3—32no—
208C22×D3—61no—
209C22×D3—61no—
210C22×D3—64no—
211C22×D3—62no—
212C22×D3—62no—
213C22×D3—122no—
214C22×D3—122no—
215C22×D3—122no—
216C22×D3—122no—
217C2×C3×C4—22no—
218C2×C3×C4—21no—
219C2×C3×C4—22no—
220C2×C3×C4—21no—
221C2×C3×C4—64no—
222C2×C3×C4—62no—
223C2×C3×C4—62no—
224C2×C3×C4—122no—
225C2×C3×C4—122no—
226C2×C3×C4C2×C4×D312yes—
227C2×C3×C4#23512yes—
228C2×C3×C4#23512yes—
229C2×C3×C4D3×D412yes—
230C2×C3×C4#23712yes—
231C2×C3×C4#23912yes—
232C2×Dic3—24no—
233C2×Dic3—22no—
234C2×Dic3—22no—
235C2×Dic3—32no—
236C2×Dic3—32no—
237C2×Dic3—42no—
238C2×Dic3—42no—
239C2×Dic3—61no—
240C2×Dic3—61no—
241C2×Dic3—62no—
242C2×Dic3—62no—
243C2×Dic3—122no—
244C4×D3—62no—
245C4×D3—62no—
246C4×D3—62no—
247C4×D3—62no—
248C4×D3—62no—
249C4×D3—62no—
250C4×D3—62no—
251C4×D3—62no—
252C4×D3—122no—
253C4×D3—122no—
254C4×D3—121no—
255C4×D3—121no—
256C4×D3—121no—
257C4×D3—121no—
258C4×D3—124no—
259C4×D3—124no—
260C3×C8—42no—
261C3×C8—42no—
262C3⋊C8—122no—
263C3⋊C8—122no—
264C2×C32—22no—
265C2×C32#38111yescharacteristic
266C2×C32C2×#10411yescharacteristic
267C2×C32#42111yescharacteristic
268C3⋊D3—22no—
269C3⋊D3—41no—
270C24—91no—
271C22×C4—62no—
272C22×C4—91no—
273C22×C4—91no—
274C22×C4—91no—
275C22×C4—91no—
276C22×C4—91no—
277C22×C4—181no—
278C22×C4—181no—
279C22×C4—182no—
280C22×C4—182no—
281C22×C4C2×D3211yescharacteristic
282M16—22no—
283M16—182no—
284C2×C8—21no—
285C2×C8—181no—
286C4⋊C4—32no—
287C4⋊C4—32no—
288C4⋊C4—181no—
289C4⋊C4—181no—
290C22⋊C4—62no—
291C22⋊C4—182no—
292C22⋊C4—184no—
293C42—62no—
294C42—62no—
295C42—62no—
296C42—182no—
297C22×C3—22no—
298C22×C3—22no—
299C22×C3—22no—
300C22×C3—21no—
301C22×C3—41no—
302C22×C3—41no—
303C22×C3D3×C22⋊C412yes—
304C22×C3#88312yes—
305C22×C3#89412yes—
306C2×D3—34no—
307C2×D3—62no—
308C2×D3—62no—
309C2×D3—62no—
310C2×D3—62no—
311C2×D3—62no—
312C2×D3—62no—
313C2×D3—62no—
314C2×D3—121no—
315C2×D3—121no—
316C2×D3—121no—
317C2×D3—121no—
318C2×D3—124no—
319C2×D3—124no—
320C2×D3—128no—
321C3×C4—22no—
322C3×C4—21no—
323C3×C4—21no—
324C3×C4—124no—
325C3×C4—122no—
326C3×C4—122no—
327C3×C4#87212yes—
328C3×C4#88312yes—
329C3×C4#89212yes—
330C3×C4#89412yes—
331Dic3—44no—
332Dic3—42no—
333Dic3—42no—
334Dic3—62no—
335Dic3—62no—
336Dic3—121no—
337Dic3—121no—
338C32#182611yescharacteristic, complemented, Sylow
339C23—91no—
340C23—91no—
341C23—182no—
342C23—182no—
343C23—361no—
344C23#380211yescharacteristic
345C2×C4—64no—
346C2×C4—62no—
347C2×C4—62no—
348C2×C4—91no—
349C2×C4—91no—
350C2×C4—122no—
351C2×C4—122no—
352C2×C4—182no—
353C2×C4—182no—
354C2×C4—182no—
355C2×C4—181no—
356C2×C4—181no—
357C2×C4—181no—
358C2×C4—181no—
359C2×C4—362no—
360C2×C4—362no—
361C2×C4#379912yes—
362C2×C4C4×D3211yescharacteristic
363C2×C4#380412yes—
364C2×C4#381111yescharacteristic
365C8—41no—
366C8—361no—
367C2×C3—22no—
368C2×C3—22no—
369C2×C3—21no—
370C2×C3—21no—
371C2×C3—21no—
372C2×C3—42no—
373C2×C3#466412yes—
374C2×C3D3×#10412yes—
375C2×C3#482112yes—
376D3—64no—
377D3—122no—
378D3—122no—
379D3—122no—
380C22—21no—
381C22—21no—
382C22—92no—
383C22—181no—
384C22—181no—
385C22—181no—
386C22—181no—
387C22—181no—
388C22—364no—
389C22#6385412yes—
390C22#6392111yescharacteristic
391C4—124no—
392C4—122no—
393C4—122no—
394C4—181no—
395C4—181no—
396C4#6383612yes—
397C4#6389711yescharacteristic
398C4#6397511yescharacteristic
399C3—21no—
400C3#6875412yescomplemented
401C2—22no—
402C2—182no—
403C2—361no—
404C2#1059100811yescharacteristic
405C2#1059100911yescharacteristic
406C2#1059137111yescharacteristic
subgroupG/H
centerC2×C4#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3D4
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1826
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
4. C3×#4555C2semidirect
5. #10589161C2semidirect
15. #63900C4semidirect
16. #63900C4semidirect
19. #63849C4semidirect
28. #4555D3semidirect
338. C32#1826semidirect
400. C3#68754semidirect

Maximal subgroups

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

subgroupindex
#105949692
#105928252
C4×#37222
C3×#45552
#105891612
#687543