Finite Group Databasebeta

← #11785855

Subgroups — #11785855

Order 1152.

777 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 777 conjugacy classes of subgroups — too many to draw. Only its 126 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
1C3⋊D3×#117C211yesmaximal, characteristic
2C4×#3722C211yesmaximal, characteristic
3#10591074C211yesmaximal, characteristic
4C3×#4532C212yesmaximal, complemented
5#10589162C212yesmaximal, complemented
6#68754—32nomaximal
7C22×C4×C3⋊D3C2211yescharacteristic
8C32×#117C2211yescharacteristic
9#64135C2211yescharacteristic
10#64101C411yescharacteristic, complemented
11#64101C411yescharacteristic, complemented
12C4⋊C4×C3⋊D3C411yescharacteristic, complemented
13C4⋊C4×C3⋊D3C411yescharacteristic, complemented
14C22⋊C4×C3⋊D3—21no—
15#64086—21no—
16#64081—21no—
17C42×C3⋊D3—21no—
18C2×C3×C4×Dic3C2212yes—
19C2×C3×#208C2212yes—
20C2×#3722—21no—
21#63579—21no—
22#63557—21no—
23#63557—21no—
24D3×#117—32no—
25D3×#117—61no—
26#5126—32no—
27C4×(C2×D3)⋊C4—32no—
28C3×#339—32no—
29#4555—32no—
30#4532D312yescomplemented
31#4523—32no—
32C23×C3⋊D3D411yescharacteristic
33C22×C32×C4C2311yescharacteristic
34C22×C3⋊Dic3D411yescharacteristic
35C2×C4×C3⋊D3—22no—
36C2×C4×C3⋊D3—22no—
37C2×C4×C3⋊D3—21no—
38C2×C4×C3⋊D3—21no—
39C2×C4×C3⋊D3C2×C411yescharacteristic
40C2×C4×C3⋊D3C2×C411yescharacteristic
41C2×C4×C3⋊D3D411yescharacteristic
42C2×C4×C3⋊D3D411yescharacteristic
43C22×C3×Dic3—22no—
44C32×C4⋊C4C2×C411yescharacteristic
45C32×C4⋊C4C2×C411yescharacteristic
46C32×C22⋊C4—21no—
47C32×C42—21no—
48#3757—21no—
49#3752—21no—
50#3752—21no—
51C4⋊(C3⋊Dic3)C2×C411yescharacteristic
52C4⋊(C3⋊Dic3)C2×C411yescharacteristic
53#3750—21no—
54#3750—21no—
55C4×C3⋊Dic3—21no—
56C4×C3⋊Dic3—21no—
57C4×C3⋊Dic3—21no—
58C3×C4×Dic3—22no—
59C3×C4×Dic3—22no—
60C3×#208—22no—
61C3×#208—22no—
62C2×C3×C3⋊C8—22no—
63#3722—24no—
64#1826—91noSylow
65C22×C4×D3—32no—
66C22×C4×D3—61no—
67C2×C3×M16—32no—
68C3×#117—21no—
69C3×#117C2×D312yes—
70C2×C3×C42—32no—
71C2×(C2×D3)⋊C4—62no—
72#926—32no—
73#926—61no—
74C2×C4×Dic3C2×D312yes—
75C2×#208C2×D312yes—
76#892—32no—
77#892—32no—
78#892—61no—
79#892—61no—
80D3×C4⋊C4—32no—
81D3×C4⋊C4—32no—
82D3×C4⋊C4—61no—
83D3×C4⋊C4—61no—
84D3×C22⋊C4—62no—
85D3×C22⋊C4—62no—
86#877—62no—
87#877—62no—
88#872—62no—
89#872—62no—
90C42×D3—62no—
91C42×D3—62no—
92C3⋊#95—62no—
93(C2×D3)⋊C8—62no—
94(C2×D3)⋊C8—62no—
95C23×C32C2×D411yescharacteristic
96C22×C3⋊D3—22no—
97C22×C3⋊D3—22no—
98C22×C3⋊D3—41no—
99C22×C3⋊D3C22⋊C411yescharacteristic
100C22×C3⋊D3C22⋊C411yescharacteristic
101C2×C32×C4—21no—
102C2×C32×C4—21no—
103C2×C32×C4C22×C411yescharacteristic
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4#4112yes—
106C2×C32×C4#4112yes—
107C2×C3⋊Dic3—22no—
108C2×C3⋊Dic3—21no—
109C2×C3⋊Dic3—21no—
110C2×C3⋊Dic3C22⋊C411yescharacteristic
111C2×C3⋊Dic3C22⋊C411yescharacteristic
112C4×C3⋊D3—21no—
113C4×C3⋊D3—21no—
114C4×C3⋊D3—21no—
115C4×C3⋊D3—21no—
116C4×C3⋊D3—22no—
117C4×C3⋊D3—22no—
118C4×C3⋊D3—42no—
119C4×C3⋊D3—42no—
120C2×C3×Dic3—24no—
121C2×C3×Dic3—42no—
122C2×C3×Dic3—42no—
123C3×C3⋊C8—42no—
124C2×#117—91no—
125#407—91no—
126C4×C22⋊C4—91no—
127#339—32no—
128#339—92no—
129C23×D3—32no—
130C23×D3—61no—
131C22×C3×C4—21no—
132C22×C3×C4—62no—
133C22×C3×C4C22×D312yes—
134C22×Dic3—22no—
135C22×Dic3—32no—
136C22×Dic3—61no—
137C2×C4×D3—32no—
138C2×C4×D3—32no—
139C2×C4×D3—32no—
140C2×C4×D3—32no—
141C2×C4×D3—61no—
142C2×C4×D3—61no—
143C2×C4×D3—61no—
144C2×C4×D3—61no—
145C2×C4×D3—64no—
146C2×C4×D3—64no—
147C2×C4×D3—62no—
148C2×C4×D3—62no—
149C2×C4×D3—62no—
150C2×C4×D3—62no—
151C2×C4×D3—62no—
152C2×C4×D3—62no—
153C2×C4×D3—62no—
154C2×C4×D3—62no—
155C3×M16—62no—
156C3×M16—62no—
157C2×C3×C8—62no—
158C3×C4⋊C4—21no—
159C3×C4⋊C4—21no—
160C3×C4⋊C4C4×D312yes—
161C3×C4⋊C4C4×D312yes—
162C3×C22⋊C4—22no—
163C3×C22⋊C4—22no—
164C3×C42—22no—
165C3×C42—22no—
166C3×C42—62no—
167C3×C42—62no—
168#217—62no—
169#217—62no—
170(C2×D3)⋊C4—68no—
171(C2×D3)⋊C4—62no—
172(C2×D3)⋊C4—62no—
173(C2×D3)⋊C4—62no—
174(C2×D3)⋊C4—62no—
175C4⋊Dic3—32no—
176C4⋊Dic3—32no—
177C4⋊Dic3—61no—
178C4⋊Dic3—61no—
179Dic3⋊C4—62no—
180Dic3⋊C4—62no—
181Dic3⋊C4—62no—
182Dic3⋊C4—62no—
183C4×Dic3—22no—
184C4×Dic3—22no—
185C4×Dic3—62no—
186C4×Dic3—62no—
187C4×Dic3—62no—
188C4×Dic3—62no—
189C4×Dic3—62no—
190C4×Dic3—62no—
191#208—22no—
192#208—22no—
193C2×C3⋊C8—22no—
194C22×C32—21no—
195C22×C32—21no—
196C22×C32C2×C22⋊C411yescharacteristic
197C22×C32#12312yes—
198C2×C3⋊D3—21no—
199C2×C3⋊D3—21no—
200C2×C3⋊D3—21no—
201C2×C3⋊D3—21no—
202C2×C3⋊D3—21no—
203C2×C3⋊D3—44no—
204C2×C3⋊D3#10412yes—
205C32×C4—41no—
206C32×C4—41no—
207C32×C4#11711yescharacteristic
208C32×C4#11711yescharacteristic
209C32×C4#12312yes—
210C3⋊Dic3—21no—
211C3⋊Dic3—21no—
212C3⋊Dic3—41no—
213C3⋊Dic3—41no—
214C3×Dic3—44no—
215C23×C4—91no—
216C2×M16—32no—
217#117—91no—
218#117—91no—
219#117—91no—
220#117—181no—
221#117—181no—
222#117D3211yescharacteristic
223C2×C4⋊C4—91no—
224C2×C4⋊C4—91no—
225C2×C22⋊C4—181no—
226C2×C22⋊C4—181no—
227C2×C42—32no—
228C2×C42—181no—
229C22⋊C8—181no—
230C22⋊C8—181no—
231#95—181no—
232C23×C3—21no—
233C23×C3D3×D412yes—
234C22×D3—32no—
235C22×D3—32no—
236C22×D3—61no—
237C22×D3—61no—
238C22×D3—64no—
239C22×D3—64no—
240C22×D3—62no—
241C22×D3—62no—
242C22×D3—122no—
243C22×D3—122no—
244C22×D3—122no—
245C2×C3×C4—22no—
246C2×C3×C4—22no—
247C2×C3×C4—22no—
248C2×C3×C4—22no—
249C2×C3×C4—22no—
250C2×C3×C4—22no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—64no—
254C2×C3×C4—122no—
255C2×C3×C4—122no—
256C2×C3×C4C2×C4×D312yes—
257C2×C3×C4#23512yes—
258C2×C3×C4#23512yes—
259C2×C3×C4D3×D412yes—
260C2×C3×C4#23712yes—
261C2×C3×C4#23912yes—
262C2×Dic3—24no—
263C2×Dic3—32no—
264C2×Dic3—32no—
265C2×Dic3—42no—
266C2×Dic3—42no—
267C2×Dic3—61no—
268C2×Dic3—61no—
269C2×Dic3—64no—
270C2×Dic3—62no—
271C2×Dic3—62no—
272C2×Dic3—62no—
273C2×Dic3—62no—
274C2×Dic3—62no—
275C2×Dic3—62no—
276C4×D3—62no—
277C4×D3—62no—
278C4×D3—64no—
279C4×D3—64no—
280C4×D3—62no—
281C4×D3—62no—
282C4×D3—62no—
283C4×D3—62no—
284C4×D3—62no—
285C4×D3—62no—
286C4×D3—62no—
287C4×D3—62no—
288C4×D3—62no—
289C4×D3—62no—
290C4×D3—124no—
291C4×D3—124no—
292C4×D3—124no—
293C4×D3—124no—
294C3×C8—122no—
295C3⋊C8—42no—
296C2×C32—22no—
297C2×C32#38111yescharacteristic
298C2×C32C2×#10411yescharacteristic
299C2×C32#42111yescharacteristic
300C3⋊D3—22no—
301C3⋊D3—41no—
302C24—91no—
303C22×C4—62no—
304C22×C4—91no—
305C22×C4—91no—
306C22×C4—91no—
307C22×C4—91no—
308C22×C4—91no—
309C22×C4—181no—
310C22×C4—181no—
311C22×C4—182no—
312C22×C4—182no—
313C22×C4C2×D3211yescharacteristic
314M16—62no—
315M16—62no—
316C2×C8—62no—
317C4⋊C4—91no—
318C4⋊C4—91no—
319C4⋊C4—181no—
320C4⋊C4—181no—
321C4⋊C4#62411yescharacteristic
322C4⋊C4#62411yescharacteristic
323C22⋊C4—21no—
324C22⋊C4—181no—
325C22⋊C4—181no—
326C22⋊C4—184no—
327C22⋊C4—181no—
328C42—21no—
329C42—62no—
330C42—62no—
331C42—181no—
332C42—181no—
333C42—181no—
334C22×C3—22no—
335C22×C3—22no—
336C22×C3—22no—
337C22×C3—21no—
338C22×C3—41no—
339C22×C3—41no—
340C22×C3D3×C22⋊C412yes—
341C22×C3#88312yes—
342C22×C3#89412yes—
343C2×D3—34no—
344C2×D3—62no—
345C2×D3—62no—
346C2×D3—62no—
347C2×D3—62no—
348C2×D3—62no—
349C2×D3—62no—
350C2×D3—62no—
351C2×D3—62no—
352C2×D3—62no—
353C2×D3—121no—
354C2×D3—121no—
355C2×D3—124no—
356C2×D3—124no—
357C2×D3—128no—
358C3×C4—21no—
359C3×C4—22no—
360C3×C4—21no—
361C3×C4—42no—
362C3×C4—42no—
363C3×C4—42no—
364C3×C4—42no—
365C3×C4—124no—
366C3×C4#87212yes—
367C3×C4#88312yes—
368C3×C4#89212yes—
369C3×C4#89412yes—
370Dic3—44no—
371Dic3—62no—
372Dic3—62no—
373Dic3—62no—
374Dic3—62no—
375Dic3—122no—
376Dic3—122no—
377Dic3—122no—
378Dic3—122no—
379C32#182611yescharacteristic, complemented, Sylow
380C23—91no—
381C23—91no—
382C23—182no—
383C23—182no—
384C23—361no—
385C23#381111yescharacteristic
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—64no—
389C2×C4—91no—
390C2×C4—91no—
391C2×C4—122no—
392C2×C4—122no—
393C2×C4—182no—
394C2×C4—181no—
395C2×C4—181no—
396C2×C4—182no—
397C2×C4—182no—
398C2×C4—181no—
399C2×C4—181no—
400C2×C4—181no—
401C2×C4—181no—
402C2×C4—362no—
403C2×C4—362no—
404C2×C4#379612yes—
405C2×C4#379812yes—
406C2×C4C2×#62411yescharacteristic
407C2×C4#381111yescharacteristic
408C8—122no—
409C2×C3—22no—
410C2×C3—22no—
411C2×C3—21no—
412C2×C3—21no—
413C2×C3—21no—
414C2×C3—42no—
415C2×C3#466412yes—
416C2×C3D3×#10412yes—
417C2×C3#482112yes—
418D3—64no—
419D3—64no—
420D3—122no—
421D3—122no—
422C22—21no—
423C22—21no—
424C22—92no—
425C22—181no—
426C22—181no—
427C22—181no—
428C22—181no—
429C22—181no—
430C22—364no—
431C22#6385312yes—
432C22#6397411yescharacteristic
433C4—41no—
434C4—41no—
435C4—124no—
436C4—181no—
437C4—181no—
438C4—361no—
439C4—361no—
440C4#6384911yescharacteristic
441C4#6385312yes—
442C4#6387411yescharacteristic
443C3—21no—
444C3#6875412yescomplemented
445C2—22no—
446C2—182no—
447C2—361no—
448C2#1059121911yescharacteristic
449C2#1059167111yescharacteristic
450C2#1059167211yescharacteristic
subgroupG/H
centerC2×C4#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3D4
cosocleC22×C32×C4C23
hypercenter#117D32
hypocenterC32#1826
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
4. C3×#4532C2semidirect
5. #10589162C2semidirect
10. #64101C4semidirect
11. #64101C4semidirect
12. C4⋊C4×C3⋊D3C4semidirect
13. C4⋊C4×C3⋊D3C4semidirect
30. #4532D3semidirect
379. C32#1826semidirect
444. C3#68754semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#1172
C4×#37222
#105910742
C3×#45322
#105891622
#687543