Finite Group Databasebeta

← #11773719

Subgroups — #11773719

Order 1152.

1249 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 1249 conjugacy classes of subgroups — too many to draw. Only its 122 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
1C2×C22⋊C4×C3⋊D3C211yesmaximal, characteristic
2#10591152C212yesmaximal, complemented
3C3×#4525C212yesmaximal, complemented
4#10589146C212yesmaximal, complemented
5D3×#323—32nomaximal
6C24×C3⋊D3C411yescharacteristic
7C22×C4×C3⋊D3C411yescharacteristic
8C22×C4×C3⋊D3C2211yescharacteristic
9C2×C32×C22⋊C4C2211yescharacteristic
10C2×#3757C411yescharacteristic
11C2×#3752C411yescharacteristic
12C2×#3752C2211yescharacteristic
13C22⋊C4×C3⋊D3—22no—
14C22⋊C4×C3⋊D3—22no—
15C2×#3710—22no—
16C3×#830C2214yescomplemented
17#63557—22no—
18C2×D3×C22⋊C4—32no—
19C2×D3×C22⋊C4—61no—
20D3×C22⋊C8—34no—
21C3×#323—32no—
22#4525D312yescomplemented
23#4468—34no—
24C24×C32C2×C411yescharacteristic
25C23×C3⋊D3—21no—
26C23×C3⋊D3—21no—
27C23×C3⋊D3—22no—
28C23×C3⋊D3—42no—
29C23×C3⋊D3—42no—
30C23×C3⋊D3C814yescomplemented
31C23×C3⋊D3C2×C411yescharacteristic
32C23×C3⋊D3C2×C411yescharacteristic
33C22×C32×C4C2×C411yescharacteristic
34C22×C32×C4C2311yescharacteristic
35C22×C3⋊Dic3C2×C411yescharacteristic
36C22×C3⋊Dic3C2×C411yescharacteristic
37C2×C4×C3⋊D3—21no—
38C2×C4×C3⋊D3—21no—
39C2×C4×C3⋊D3—42no—
40C2×C4×C3⋊D3—42no—
41C2×C4×C3⋊D3D412yes—
42C2×C4×C3⋊D3D412yes—
43C32×C22⋊C4—22no—
44#3757—22no—
45#3752—22no—
46#3752—22no—
47C2×C3×C3⋊C8—24no—
48#3710—44no—
49C2×#323—91noSylow
50C24×D3—32no—
51C24×D3—61no—
52C22×C4×D3—32no—
53C22×C4×D3—32no—
54C22×C4×D3—61no—
55C22×C4×D3—61no—
56C2×C3×C22⋊C4—21no—
57C2×C3×C22⋊C4C2×D312yes—
58C2×#217—32no—
59C2×#217—61no—
60C2×(C2×D3)⋊C4—32no—
61C2×(C2×D3)⋊C4—32no—
62C2×(C2×D3)⋊C4—61no—
63C2×(C2×D3)⋊C4—61no—
64C2×D3×C8—64no—
65D3×C22⋊C4—64no—
66D3×C22⋊C4—64no—
67D3×C22⋊C4—64no—
68D3×C22⋊C4—64no—
69C3×C22⋊C8—34no—
70#830C2×D314yescomplemented
71(C2×D3)⋊C8—64no—
72C23×C32—21no—
73C23×C32—21no—
74C23×C32—41no—
75C23×C32—41no—
76C23×C32C2×C812yescomplemented
77C23×C32C22×C411yescharacteristic
78C22×C3⋊D3—22no—
79C22×C3⋊D3—22no—
80C22×C3⋊D3—21no—
81C22×C3⋊D3—21no—
82C22×C3⋊D3—24no—
83C22×C3⋊D3—24no—
84C22×C3⋊D3—42no—
85C22×C3⋊D3—42no—
86C22×C3⋊D3—48no—
87C22×C3⋊D3—48no—
88C22×C3⋊D3—42no—
89C22×C3⋊D3—42no—
90C22×C3⋊D3—41no—
91C22×C3⋊D3—41no—
92C22×C3⋊D3C22⋊C411yescharacteristic
93C22×C3⋊D3C22⋊C411yescharacteristic
94C22×C3⋊D3C2×C812yes—
95C22×C3⋊D3C2×C812yescomplemented
96C22×C3⋊D3M1612yes—
97C2×C32×C4—21no—
98C2×C32×C4—41no—
99C2×C32×C4—41no—
100C2×C32×C4C2×D412yes—
101C2×C3⋊Dic3—21no—
102C2×C3⋊Dic3—41no—
103C2×C3⋊Dic3—41no—
104C2×C3⋊Dic3C22⋊C412yes—
105C4×C3⋊D3—24no—
106C4×C3⋊D3—42no—
107C4×C3⋊D3—42no—
108C4×C3⋊D3—42no—
109C3×C3⋊C8—44no—
110C22×C22⋊C4—91no—
111C2×C22⋊C8—92no—
112#323—32no—
113#323—92no—
114C24×C3—21no—
115C24×C3C4×D312yes—
116C23×D3—32no—
117C23×D3—38no—
118C23×D3—32no—
119C23×D3—61no—
120C23×D3—64no—
121C23×D3—61no—
122C23×D3—62no—
123C23×D3—62no—
124C23×D3—64no—
125C23×D3—62no—
126C23×D3—62no—
127C23×D3—64no—
128C23×D3—124no—
129C23×D3—124no—
130C23×D3—124no—
131C23×D3—124no—
132C22×C3×C4—21no—
133C22×C3×C4—21no—
134C22×C3×C4C4×D312yes—
135C22×C3×C4C22×D312yes—
136C22×Dic3—32no—
137C22×Dic3—32no—
138C22×Dic3—61no—
139C22×Dic3—61no—
140C2×C4×D3—34no—
141C2×C4×D3—34no—
142C2×C4×D3—62no—
143C2×C4×D3—62no—
144C2×C4×D3—62no—
145C2×C4×D3—62no—
146C2×C4×D3—62no—
147C2×C4×D3—62no—
148C2×C4×D3—124no—
149C2×C4×D3—124no—
150C2×C4×D3—124no—
151C2×C4×D3—124no—
152C2×C3×C8—64no—
153C3×C22⋊C4—24no—
154C3×C22⋊C4—24no—
155#217—64no—
156#217—64no—
157(C2×D3)⋊C4—64no—
158(C2×D3)⋊C4—64no—
159(C2×D3)⋊C4—64no—
160(C2×D3)⋊C4—64no—
161C2×C3⋊C8—24no—
162D3×C8—128no—
163C22×C32—21no—
164C22×C32—21no—
165C22×C32—22no—
166C22×C32—42no—
167C22×C32—42no—
168C22×C32—41no—
169C22×C32—41no—
170C22×C32C2×C22⋊C411yescharacteristic
171C22×C32C22×C811yescharacteristic
172C22×C32C2×M1611yescharacteristic
173C2×C3⋊D3—21no—
174C2×C3⋊D3—21no—
175C2×C3⋊D3—24no—
176C2×C3⋊D3—24no—
177C2×C3⋊D3—22no—
178C2×C3⋊D3—48no—
179C2×C3⋊D3—42no—
180C2×C3⋊D3—41no—
181C2×C3⋊D3—41no—
182C2×C3⋊D3—48no—
183C2×C3⋊D3—42no—
184C2×C3⋊D3C22⋊C812yes—
185C2×C3⋊D3C22⋊C812yes—
186C2×C3⋊D3#9912yes—
187C2×C3⋊D3#10012yes—
188C32×C4—22no—
189C32×C4—41no—
190C3⋊Dic3—22no—
191C3⋊Dic3—41no—
192C25—91no—
193C23×C4—91no—
194C23×C4—91no—
195C22×C8—182no—
196C2×C22⋊C4—91no—
197C2×C22⋊C4—91no—
198C2×C22⋊C4—91no—
199C2×C22⋊C4—182no—
200C2×C22⋊C4—182no—
201C2×C22⋊C4D3211yescharacteristic
202C22⋊C8—34no—
203C22⋊C8—182no—
204C23×C3—22no—
205C23×C3—22no—
206C23×C3—22no—
207C23×C3—22no—
208C23×C3—22no—
209C23×C3—21no—
210C23×C3—42no—
211C23×C3—42no—
212C23×C3—42no—
213C23×C3—42no—
214C23×C3D3×C814yescomplemented
215C23×C3C2×C4×D312yes—
216C22×D3—32no—
217C22×D3—32no—
218C22×D3—34no—
219C22×D3—34no—
220C22×D3—34no—
221C22×D3—61no—
222C22×D3—61no—
223C22×D3—62no—
224C22×D3—62no—
225C22×D3—62no—
226C22×D3—64no—
227C22×D3—64no—
228C22×D3—68no—
229C22×D3—68no—
230C22×D3—64no—
231C22×D3—64no—
232C22×D3—62no—
233C22×D3—68no—
234C22×D3—68no—
235C22×D3—62no—
236C22×D3—62no—
237C22×D3—62no—
238C22×D3—124no—
239C22×D3—124no—
240C22×D3—124no—
241C22×D3—124no—
242C22×D3—1216no—
243C22×D3—1216no—
244C22×D3—124no—
245C22×D3—124no—
246C22×D3—1216no—
247C22×D3—124no—
248C22×D3—124no—
249C22×D3—1216no—
250C22×D3—122no—
251C22×D3—122no—
252C22×D3—122no—
253C22×D3—122no—
254C2×C3×C4—22no—
255C2×C3×C4—22no—
256C2×C3×C4—22no—
257C2×C3×C4—42no—
258C2×C3×C4—42no—
259C2×C3×C4—42no—
260C2×C3×C4—42no—
261C2×C3×C4D3×D414yes—
262C2×Dic3—34no—
263C2×Dic3—62no—
264C2×Dic3—62no—
265C2×Dic3—62no—
266C2×Dic3—122no—
267C2×Dic3—122no—
268C2×Dic3—122no—
269C2×Dic3—122no—
270C4×D3—68no—
271C4×D3—124no—
272C4×D3—124no—
273C4×D3—124no—
274C4×D3—124no—
275C4×D3—124no—
276C4×D3—124no—
277C4×D3—124no—
278C3×C8—124no—
279C3⋊C8—44no—
280C2×C32—21no—
281C2×C32—21no—
282C2×C32—42no—
283C2×C32C2×C22⋊C811yescharacteristic
284C2×C32C2×#9911yescharacteristic
285C2×C32C2×#10011yescharacteristic
286C3⋊D3—22no—
287C3⋊D3—42no—
288C3⋊D3#32314yescomplemented
289C24—91no—
290C24—94no—
291C24—91no—
292C24—181no—
293C24—181no—
294C24—182no—
295C24—362no—
296C24—362no—
297C24#62411yescharacteristic
298C22×C4—91no—
299C22×C4—92no—
300C22×C4—92no—
301C22×C4—91no—
302C22×C4—181no—
303C22×C4—181no—
304C22×C4—362no—
305C22×C4—362no—
306C22×C4#62411yescharacteristic
307C22×C4C2×D3211yescharacteristic
308C2×C8—64no—
309C2×C8—364no—
310C22⋊C4—22no—
311C22⋊C4—182no—
312C22⋊C4—182no—
313C22⋊C4—182no—
314C22×C3—22no—
315C22×C3—22no—
316C22×C3—22no—
317C22×C3—22no—
318C22×C3—24no—
319C22×C3—24no—
320C22×C3—21no—
321C22×C3—21no—
322C22×C3—21no—
323C22×C3—44no—
324C22×C3—44no—
325C22×C3—44no—
326C22×C3—44no—
327C22×C3—42no—
328C22×C3—42no—
329C22×C3—42no—
330C22×C3—42no—
331C22×C3D3×C22⋊C412yes—
332C22×C3C2×D3×C812yes—
333C22×C3D3×M1612yes—
334C2×D3—34no—
335C2×D3—34no—
336C2×D3—34no—
337C2×D3—34no—
338C2×D3—62no—
339C2×D3—62no—
340C2×D3—62no—
341C2×D3—62no—
342C2×D3—68no—
343C2×D3—68no—
344C2×D3—62no—
345C2×D3—62no—
346C2×D3—68no—
347C2×D3—68no—
348C2×D3—62no—
349C2×D3—62no—
350C2×D3—64no—
351C2×D3—64no—
352C2×D3—1216no—
353C2×D3—1216no—
354C2×D3—1216no—
355C2×D3—1216no—
356C2×D3—124no—
357C2×D3—124no—
358C2×D3—124no—
359C2×D3—122no—
360C2×D3—122no—
361C2×D3—122no—
362C2×D3—122no—
363C2×D3—124no—
364C3×C4—24no—
365C3×C4—42no—
366C3×C4—42no—
367C3×C4—42no—
368Dic3—64no—
369Dic3—122no—
370Dic3—122no—
371Dic3—122no—
372C32C2×#32311yescharacteristic, complemented, Sylow
373C23—21no—
374C23—21no—
375C23—41no—
376C23—41no—
377C23—91no—
378C23—92no—
379C23—92no—
380C23—91no—
381C23—92no—
382C23—182no—
383C23—182no—
384C23—184no—
385C23—184no—
386C23—181no—
387C23—181no—
388C23—361no—
389C23—361no—
390C23—362no—
391C23—362no—
392C23—368no—
393C23—368no—
394C23—362no—
395C23—362no—
396C23#371012yescomplemented
397C23C2×#62411yescharacteristic
398C2×C4—21no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—92no—
402C2×C4—184no—
403C2×C4—181no—
404C2×C4—362no—
405C2×C4—362no—
406C2×C4—362no—
407C2×C4—361no—
408C2×C4—361no—
409C2×C4#381112yes—
410C8—124no—
411C2×C3—22no—
412C2×C3—22no—
413C2×C3—22no—
414C2×C3—22no—
415C2×C3—21no—
416C2×C3—21no—
417C2×C3—21no—
418C2×C3—44no—
419C2×C3—44no—
420C2×C3D3×C22⋊C812yes—
421C2×C3D3×#9912yes—
422C2×C3D3×#10012yes—
423D3—38no—
424D3—64no—
425D3—64no—
426D3—64no—
427D3—124no—
428D3—124no—
429C22—21no—
430C22—21no—
431C22—22no—
432C22—42no—
433C22—42no—
434C22—41no—
435C22—41no—
436C22—92no—
437C22—92no—
438C22—92no—
439C22—92no—
440C22—184no—
441C22—184no—
442C22—181no—
443C22—181no—
444C22—182no—
445C22—362no—
446C22—362no—
447C22—368no—
448C22—368no—
449C22—361no—
450C22—361no—
451C22C2×#371011yescharacteristic
452C22#6381811yescharacteristic
453C22#6397411yescharacteristic
454C4—22no—
455C4—41no—
456C4—182no—
457C4—361no—
458C3—21no—
459C3D3×#32312yescomplemented
460C2—21no—
461C2—21no—
462C2—42no—
463C2—94no—
464C2—182no—
465C2—362no—
466C2#1059115211yescharacteristic
467C2#1059150311yescharacteristic
468C2#1059152711yescharacteristic
subgroupG/H
centerC22#63974
commutatorC22×C32C22×C8
FrattiniC22×C4C2×D32
FittingC2×C32×C22⋊C4C22
socleC22×C32C2×C22⋊C4
prime radicalC24×C3⋊D3C4
cosocleC22×C32×C4C23
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#323
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #10591152C2semidirect
3. C3×#4525C2semidirect
4. #10589146C2semidirect
16. C3×#830C22semidirect
22. #4525D3semidirect
30. C23×C3⋊D3C8semidirect
70. #830C2×D3semidirect
76. C23×C32C2×C8semidirect
95. C22×C3⋊D3C2×C8semidirect
214. C23×C3D3×C8semidirect
288. C3⋊D3#323semidirect
372. C32C2×#323semidirect
396. C23#3710semidirect
459. C3D3×#323semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C4×C3⋊D32
#105911522
C3×#45252
#105891462
D3×#3233