Finite Group Databasebeta

← #11785856

Subgroups — #11785856

Order 1152.

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

normal subgroups only

This group has 741 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
2C4×#3752C211yesmaximal, characteristic
3#10591074C211yesmaximal, characteristic
4C3×#4523C212yesmaximal, complemented
5#10589160C212yesmaximal, complemented
6#68754—32nomaximal
7C22×C4×C3⋊D3C2211yescharacteristic
8C2×C32×C42C2211yescharacteristic
9C2×#3752—21no—
10C2×C4×C3⋊Dic3C2211yescharacteristic
11C3×#926C2212yes—
12C2×C3×#208C2212yes—
13#63974—21no—
14#63957—21no—
15#63900C411yescharacteristic, complemented
16#63900C411yescharacteristic, complemented
17C4×#624—21no—
18#63874—21no—
19#63849C412yescomplemented
20#63658—21no—
21#63557—21no—
22#63557—21no—
23D3×#117—32no—
24#5126—32no—
25C4×(C2×D3)⋊C4—32no—
26C4×(C2×D3)⋊C4—61no—
27C3×#339—32no—
28#4555—32no—
29#4532—32no—
30#4523D312yescomplemented
31C23×C3⋊D3D411yescharacteristic
32C22×C32×C4—21no—
33C22×C32×C4C2311yescharacteristic
34C22×C3⋊Dic3—21no—
35C22×C3⋊Dic3D411yescharacteristic
36C2×C4×C3⋊D3—22no—
37C2×C4×C3⋊D3—22no—
38C2×C4×C3⋊D3C2×C411yescharacteristic
39C2×C4×C3⋊D3C2×C411yescharacteristic
40C2×C4×C3⋊D3D411yescharacteristic
41C2×C4×C3⋊D3D411yescharacteristic
42C2×#624—21no—
43C2×#624—21no—
44C32×C42—22no—
45#3752—24no—
46C4×C3⋊Dic3—22no—
47C3×#217—22no—
48C3×C4⋊Dic3C2×C412yes—
49C3×C4⋊Dic3C2×C412yes—
50C3×C4×Dic3—22no—
51C3×#208—22no—
52C3×#208—22no—
53C2×C3×C3⋊C8—22no—
54#3724—21no—
55#3724—21no—
56#3722—22no—
57Dic32—22no—
58#1826—91noSylow
59C22×C4×D3—32no—
60C22×C4×D3—61no—
61C2×C3×M16—32no—
62C3×#117—32no—
63C2×C3×C42—21no—
64C2×C3×C42C2×D312yes—
65C2×(C2×D3)⋊C4—62no—
66C2×(C2×D3)⋊C4—62no—
67#926C2×D312yes—
68C2×C4×Dic3—32no—
69C2×C4×Dic3—61no—
70C2×#208C2×D312yes—
71#892—32no—
72#892—32no—
73D3×C4⋊C4—32no—
74D3×C4⋊C4—32no—
75D3×C22⋊C4—62no—
76#877—62no—
77#872—62no—
78C42×D3—62no—
79C3⋊#95—62no—
80C3⋊#95—62no—
81(C2×D3)⋊C8—62no—
82(C2×D3)⋊C8—62no—
83C23×C32C2×D411yescharacteristic
84C22×C3⋊D3—22no—
85C22×C3⋊D3—21no—
86C22×C3⋊D3—21no—
87C22×C3⋊D3—41no—
88C22×C3⋊D3C22⋊C411yescharacteristic
89C22×C3⋊D3C22⋊C411yescharacteristic
90C2×C32×C4—22no—
91C2×C32×C4—41no—
92C2×C32×C4—41no—
93C2×C32×C4C22×C411yescharacteristic
94C2×C32×C4C2×D411yescharacteristic
95C2×C32×C4#4112yes—
96C2×C32×C4#4112yes—
97C2×C3⋊Dic3—22no—
98C2×C3⋊Dic3—21no—
99C2×C3⋊Dic3—21no—
100C2×C3⋊Dic3—41no—
101C2×C3⋊Dic3—41no—
102C2×C3⋊Dic3C22⋊C411yescharacteristic
103C2×C3⋊Dic3C22⋊C411yescharacteristic
104C4×C3⋊D3—22no—
105C4×C3⋊D3—22no—
106C4×C3⋊D3—22no—
107C4×C3⋊D3—22no—
108C2×C3×Dic3—22no—
109C2×C3×Dic3—22no—
110#624—42no—
111#624—42no—
112C3×C3⋊C8—42no—
113C2×#117—91no—
114#407—91no—
115C4×C22⋊C4—91no—
116#339—32no—
117#339—92no—
118C23×D3—32no—
119C23×D3—61no—
120C22×C3×C4—22no—
121C22×C3×C4—22no—
122C22×C3×C4—21no—
123C22×C3×C4C22×D312yes—
124C22×Dic3—32no—
125C22×Dic3—61no—
126C22×Dic3—62no—
127C22×Dic3—62no—
128C2×C4×D3—32no—
129C2×C4×D3—32no—
130C2×C4×D3—32no—
131C2×C4×D3—32no—
132C2×C4×D3—61no—
133C2×C4×D3—61no—
134C2×C4×D3—61no—
135C2×C4×D3—61no—
136C2×C4×D3—62no—
137C2×C4×D3—62no—
138C2×C4×D3—62no—
139C2×C4×D3—62no—
140C2×C4×D3—62no—
141C2×C4×D3—62no—
142C2×C4×D3—122no—
143C2×C4×D3—122no—
144C3×M16—62no—
145C3×M16—62no—
146C2×C3×C8—62no—
147C3×C4⋊C4—32no—
148C3×C4⋊C4—32no—
149C3×C22⋊C4—62no—
150C3×C42—22no—
151C3×C42—22no—
152C3×C42—42no—
153C3×C42—62no—
154#217—22no—
155(C2×D3)⋊C4—62no—
156(C2×D3)⋊C4—62no—
157(C2×D3)⋊C4—68no—
158(C2×D3)⋊C4—68no—
159C4⋊Dic3C4×D312yes—
160C4⋊Dic3C4×D312yes—
161Dic3⋊C4—62no—
162Dic3⋊C4—62no—
163C4×Dic3—22no—
164C4×Dic3—62no—
165C4×Dic3—62no—
166C4×Dic3—62no—
167C4×Dic3—62no—
168C4×Dic3—122no—
169#208—22no—
170#208—22no—
171C2×C3⋊C8—22no—
172C22×C32—21no—
173C22×C32—21no—
174C22×C32C2×C22⋊C411yescharacteristic
175C22×C32#12311yescharacteristic
176C22×C32#12311yescharacteristic
177C2×C3⋊D3—21no—
178C2×C3⋊D3—21no—
179C2×C3⋊D3—21no—
180C2×C3⋊D3—21no—
181C2×C3⋊D3—21no—
182C2×C3⋊D3—42no—
183C2×C3⋊D3—42no—
184C2×C3⋊D3#10412yes—
185C32×C4—42no—
186C32×C4#11712yes—
187C32×C4#12312yes—
188C3⋊Dic3—21no—
189C3⋊Dic3—21no—
190C3⋊Dic3—42no—
191C3×Dic3—42no—
192C3×Dic3—42no—
193C23×C4—91no—
194C2×M16—32no—
195#117—32no—
196#117—92no—
197#117—181no—
198#117—181no—
199C2×C4⋊C4—91no—
200C2×C4⋊C4—91no—
201C2×C22⋊C4—181no—
202C2×C22⋊C4—181no—
203C2×C42—91no—
204C2×C42—181no—
205C2×C42D3211yescharacteristic
206C22⋊C8—181no—
207C22⋊C8—181no—
208#95—181no—
209C23×C3—21no—
210C23×C3D3×D412yes—
211C22×D3—32no—
212C22×D3—32no—
213C22×D3—61no—
214C22×D3—61no—
215C22×D3—64no—
216C22×D3—64no—
217C22×D3—62no—
218C22×D3—62no—
219C22×D3—121no—
220C22×D3—121no—
221C22×D3—122no—
222C22×D3—122no—
223C2×C3×C4—24no—
224C2×C3×C4—24no—
225C2×C3×C4—22no—
226C2×C3×C4—21no—
227C2×C3×C4—21no—
228C2×C3×C4—22no—
229C2×C3×C4—42no—
230C2×C3×C4—42no—
231C2×C3×C4—42no—
232C2×C3×C4—42no—
233C2×C3×C4—62no—
234C2×C3×C4—62no—
235C2×C3×C4C2×C4×D312yes—
236C2×C3×C4#23512yes—
237C2×C3×C4#23512yes—
238C2×C3×C4D3×D412yes—
239C2×C3×C4#23712yes—
240C2×C3×C4#23912yes—
241C2×Dic3—22no—
242C2×Dic3—22no—
243C2×Dic3—32no—
244C2×Dic3—32no—
245C2×Dic3—61no—
246C2×Dic3—61no—
247C2×Dic3—62no—
248C2×Dic3—62no—
249C2×Dic3—64no—
250C2×Dic3—64no—
251C2×Dic3—121no—
252C2×Dic3—121no—
253C2×Dic3—122no—
254C2×Dic3—122no—
255C2×Dic3—122no—
256C2×Dic3—122no—
257C4×D3—62no—
258C4×D3—62no—
259C4×D3—62no—
260C4×D3—62no—
261C4×D3—62no—
262C4×D3—62no—
263C4×D3—62no—
264C4×D3—62no—
265C4×D3—122no—
266C4×D3—122no—
267C4×D3—122no—
268C4×D3—122no—
269C4×D3—124no—
270C4×D3—124no—
271C3×C8—122no—
272C3⋊C8—42no—
273C2×C32—21no—
274C2×C32—21no—
275C2×C32#38111yescharacteristic
276C2×C32C2×#10411yescharacteristic
277C2×C32#42111yescharacteristic
278C3⋊D3—22no—
279C3⋊D3—41no—
280C24—91no—
281C22×C4—21no—
282C22×C4—91no—
283C22×C4—91no—
284C22×C4—91no—
285C22×C4—91no—
286C22×C4—91no—
287C22×C4—181no—
288C22×C4—181no—
289C22×C4—182no—
290C22×C4—182no—
291C22×C4—181no—
292C22×C4C2×D3211yescharacteristic
293M16—62no—
294M16—62no—
295C2×C8—62no—
296C4⋊C4—32no—
297C4⋊C4—32no—
298C4⋊C4—181no—
299C4⋊C4—181no—
300C22⋊C4—62no—
301C22⋊C4—184no—
302C22⋊C4—182no—
303C42—22no—
304C42—62no—
305C42—182no—
306C42—182no—
307C22×C3—22no—
308C22×C3—22no—
309C22×C3—22no—
310C22×C3—22no—
311C22×C3—21no—
312C22×C3—21no—
313C22×C3—21no—
314C22×C3D3×C22⋊C412yes—
315C22×C3#88312yes—
316C22×C3#89412yes—
317C2×D3—34no—
318C2×D3—62no—
319C2×D3—62no—
320C2×D3—62no—
321C2×D3—62no—
322C2×D3—62no—
323C2×D3—62no—
324C2×D3—62no—
325C2×D3—121no—
326C2×D3—121no—
327C2×D3—121no—
328C2×D3—121no—
329C2×D3—124no—
330C2×D3—124no—
331C2×D3—124no—
332C2×D3—124no—
333C3×C4—22no—
334C3×C4—22no—
335C3×C4—44no—
336C3×C4—44no—
337C3×C4—122no—
338C3×C4—122no—
339C3×C4#87212yes—
340C3×C4#88312yes—
341C3×C4#89212yes—
342C3×C4#89412yes—
343Dic3—42no—
344Dic3—42no—
345Dic3—62no—
346Dic3—62no—
347Dic3—121no—
348Dic3—121no—
349Dic3—124no—
350Dic3—124no—
351C32#182611yescharacteristic, complemented, Sylow
352C23—91no—
353C23—91no—
354C23—182no—
355C23—181no—
356C23—181no—
357C23—361no—
358C23#381111yescharacteristic
359C2×C4—22no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—62no—
363C2×C4—62no—
364C2×C4—91no—
365C2×C4—91no—
366C2×C4—181no—
367C2×C4—181no—
368C2×C4—182no—
369C2×C4—182no—
370C2×C4—182no—
371C2×C4—182no—
372C2×C4—182no—
373C2×C4—362no—
374C2×C4—362no—
375C2×C4—361no—
376C2×C4—361no—
377C2×C4#379912yes—
378C2×C4C4×D3211yescharacteristic
379C2×C4#380211yescharacteristic
380C2×C4#380412yes—
381C8—122no—
382C2×C3—22no—
383C2×C3—22no—
384C2×C3—22no—
385C2×C3—22no—
386C2×C3—21no—
387C2×C3—21no—
388C2×C3—21no—
389C2×C3#466412yes—
390C2×C3D3×#10412yes—
391C2×C3#482112yes—
392D3—64no—
393D3—122no—
394D3—122no—
395D3—122no—
396C22—21no—
397C22—21no—
398C22—92no—
399C22—181no—
400C22—181no—
401C22—181no—
402C22—181no—
403C22—181no—
404C22—362no—
405C22—362no—
406C22#6389711yescharacteristic
407C22#6392111yescharacteristic
408C22#6397511yescharacteristic
409C4—42no—
410C4—122no—
411C4—122no—
412C4—181no—
413C4—181no—
414C4—362no—
415C4#6383612yes—
416C4#6385412yes—
417C3—21no—
418C3#6875412yescomplemented
419C2—21no—
420C2—21no—
421C2—182no—
422C2—361no—
423C2#1059039311yescharacteristic
424C2#1059039411yescharacteristic
425C2#1059137111yescharacteristic
subgroupG/H
centerC2×C4#3802
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3D4
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1826
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
4. C3×#4523C2semidirect
5. #10589160C2semidirect
15. #63900C4semidirect
16. #63900C4semidirect
19. #63849C4semidirect
30. #4523D3semidirect
351. C32#1826semidirect
418. C3#68754semidirect

Maximal subgroups

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

subgroupindex
#105949692
C4×#37522
#105910742
C3×#45232
#105891602
#687543