Finite Group Databasebeta

← #11787073

Subgroups — #11787073

Order 1152.

891 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 891 conjugacy classes of subgroups — too many to draw. Only its 130 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#10595510C211yesmaximal, characteristic
2#10592912C211yesmaximal, characteristic
3C3×#5210C212yesmaximal, complemented
4C2×#63581C211yesmaximal, characteristic
5#10589186C212yesmaximal, complemented
6#69595—32nomaximal
7C23×C32×C4C2211yescharacteristic
8C22×#638C2211yescharacteristic
9C2×#3757C2211yescharacteristic
10C2×#3752—21no—
11C2×C3×#217C2212yes—
12C2×C3×#217C2212yes—
13C2×C3×Dic3⋊C4—22no—
14#63974—21no—
15#63957—21no—
16#63952—22no—
17#63952—22no—
18#63658—21no—
19C3×C3⋊#95—22no—
20#63581C414yescomplemented
21#5486—32no—
22C3×#385—32no—
23#5213—32no—
24#5213—61no—
25#5210D312yescomplemented
26C2×#806—32no—
27#4527—32no—
28#4526—32no—
29C24×C32C2311yescharacteristic
30C23×C3⋊D3D411yescharacteristic
31C22×C32×C4—21no—
32C22×C32×C4—22no—
33C22×C32×C4—42no—
34C2×#638—22no—
35C2×#638—22no—
36C2×#638C2×C412yes—
37C2×#638Q812yes—
38C22×C3⋊Dic3—21no—
39C22×C3⋊Dic3D411yescharacteristic
40C22×C3×Dic3—22no—
41C22×C3×Dic3D412yes—
42C22×C3×Dic3D412yes—
43C2×#624—21no—
44C2×#624—21no—
45#3757—22no—
46#3752—42no—
47C3×#217—22no—
48C3×#217—22no—
49C3×#217—22no—
50C3×#217C2×C414yescomplemented
51C3×Dic3⋊C4—44no—
52#3724—21no—
53#3724—21no—
54#3722—22no—
55Dic32—22no—
56#1867—91noSylow
57C23×C3×C4—21no—
58C23×C3×C4C2×D312yes—
59C22×#67—32no—
60C22×#67—61no—
61C2×C3×C4⋊C4—62no—
62C2×C3×C22⋊C4—32no—
63C2×C3×C22⋊C4—32no—
64C2×#217—32no—
65C2×#217—61no—
66C2×#217C2×D312yes—
67C2×#217C2×D312yes—
68C4×#67—62no—
69C4×#67—62no—
70C2×(C2×D3)⋊C4—62no—
71C2×(C2×D3)⋊C4—62no—
72C2×Dic3⋊C4—22no—
73#67⋊C4—62no—
74#67⋊C4—62no—
75D3×C22⋊C4—62no—
76#877—62no—
77C3×#95—62no—
78C3⋊#95—22no—
79C3⋊#95—62no—
80C3⋊#95—62no—
81#806—38no—
82C23×C32—41no—
83C23×C32—41no—
84C23×C32C22×C411yescharacteristic
85C23×C32C2×D411yescharacteristic
86C23×C32C2×D412yes—
87C23×C32C2×Q811yescharacteristic
88C23×C32#4112yes—
89C22×C3⋊D3—21no—
90C22×C3⋊D3—21no—
91C22×C3⋊D3—41no—
92C22×C3⋊D3—41no—
93C22×C3⋊D3C4⋊C412yescomplemented
94C2×C32×C4—22no—
95C2×C32×C4—24no—
96C2×C32×C4—41no—
97C2×C32×C4—42no—
98C2×C32×C4—41no—
99#638—24no—
100#638—24no—
101C2×C3⋊Dic3—21no—
102C2×C3⋊Dic3—21no—
103C2×C3⋊Dic3—41no—
104C2×C3⋊Dic3—41no—
105C2×C3⋊Dic3—41no—
106C2×C3⋊Dic3C4⋊C412yescomplemented
107C2×C3×Dic3—24no—
108C2×C3×Dic3—22no—
109C2×C3×Dic3—22no—
110C2×C3×Dic3—42no—
111C2×C3×Dic3—42no—
112C2×C3×Dic3—42no—
113C2×C3×Dic3—42no—
114#624—81no—
115#624—81no—
116#518—91no—
117C2×#99—91no—
118#386—91no—
119#385—32no—
120#342—92no—
121C24×C3—21no—
122C24×C3C22×D312yes—
123C23×D3—32no—
124C23×D3—61no—
125C22×C3×C4—22no—
126C22×C3×C4—22no—
127C22×C3×C4—22no—
128C22×C3×C4—22no—
129C22×C3×C4—32no—
130C22×C3×C4—32no—
131C22×C3×C4—42no—
132C22×C3×C4—44no—
133C22×C3×C4—44no—
134C22×C3×C4—62no—
135C2×#67—34no—
136C2×#67—34no—
137C2×#67—62no—
138C2×#67—62no—
139C2×#67—62no—
140C2×#67—62no—
141C2×#67—62no—
142C2×#67—62no—
143C2×#67—122no—
144C2×#67—122no—
145C22×Dic3—22no—
146C22×Dic3—32no—
147C22×Dic3—61no—
148C22×Dic3—62no—
149C22×Dic3—62no—
150C22×Dic3#6712yes—
151C22×Dic3#6712yes—
152C2×C4×D3—62no—
153C2×C4×D3—62no—
154C3×C4⋊C4—124no—
155C3×C22⋊C4—34no—
156C3×C22⋊C4—62no—
157C3×C22⋊C4—62no—
158C3×C22⋊C4—62no—
159#217—22no—
160#217—22no—
161#217—22no—
162#217—62no—
163#217—62no—
164#217—122no—
165#217C4×D314yescomplemented
166(C2×D3)⋊C4—62no—
167(C2×D3)⋊C4—62no—
168(C2×D3)⋊C4—124no—
169(C2×D3)⋊C4—124no—
170Dic3⋊C4—44no—
171Dic3⋊C4—62no—
172Dic3⋊C4—62no—
173C4×Dic3—62no—
174C4×Dic3—62no—
175C22×C32—21no—
176C22×C32—21no—
177C22×C32—22no—
178C22×C32—22no—
179C22×C32—41no—
180C22×C32—41no—
181C22×C32—42no—
182C22×C32C2×C4⋊C411yescharacteristic
183C22×C32C4×D412yes—
184C22×C32#12011yescharacteristic
185C22×C32C22⋊Q812yes—
186C22×C32#12311yescharacteristic
187C2×C3⋊D3—22no—
188C2×C3⋊D3—42no—
189C2×C3⋊D3—41no—
190C2×C3⋊D3—41no—
191C2×C3⋊D3—81no—
192C32×C4—42no—
193C3⋊Dic3—22no—
194C3⋊Dic3—81no—
195C3×Dic3—44no—
196C3×Dic3—42no—
197C3×Dic3—42no—
198C22×D4—91no—
199C23×C4D3211yescharacteristic
200C4×D4—182no—
201C4×D4—182no—
202#117—181no—
203C2×C4⋊C4—62no—
204C2×C22⋊C4—32no—
205C2×C22⋊C4—32no—
206C2×C22⋊C4—91no—
207C2×C22⋊C4—181no—
208C2×C22⋊C4—181no—
209#99—94no—
210#95—62no—
211#95—181no—
212C23×C3—21no—
213C23×C3—22no—
214C23×C3—21no—
215C23×C3—22no—
216C23×C3—21no—
217C23×C3—42no—
218C23×C3—42no—
219C23×C3—42no—
220C23×C3—42no—
221C23×C3C2×C4×D312yes—
222C23×C3#23512yes—
223C23×C3D3×D412yes—
224C23×C3D3×D412yes—
225C23×C3D3×Q812yes—
226C23×C3#23912yes—
227C23×C3C2×#6712yes—
228C22×D3—34no—
229C22×D3—62no—
230C22×D3—62no—
231C22×D3—62no—
232C22×D3—121no—
233C22×D3—121no—
234C22×D3—122no—
235C22×D3—122no—
236C22×D3—122no—
237C22×D3—122no—
238C2×C3×C4—24no—
239C2×C3×C4—24no—
240C2×C3×C4—24no—
241C2×C3×C4—24no—
242C2×C3×C4—44no—
243C2×C3×C4—42no—
244C2×C3×C4—42no—
245C2×C3×C4—42no—
246C2×C3×C4—42no—
247C2×C3×C4—42no—
248C2×C3×C4—44no—
249C2×C3×C4—42no—
250C2×C3×C4—64no—
251C2×C3×C4—62no—
252C2×C3×C4—62no—
253C2×C3×C4—122no—
254C2×C3×C4—122no—
255C2×C3×C4—122no—
256C2×C3×C4—122no—
257#67—64no—
258#67—64no—
259#67—64no—
260#67—64no—
261#67—124no—
262#67—124no—
263C2×Dic3—24no—
264C2×Dic3—22no—
265C2×Dic3—22no—
266C2×Dic3—34no—
267C2×Dic3—42no—
268C2×Dic3—42no—
269C2×Dic3—42no—
270C2×Dic3—42no—
271C2×Dic3—62no—
272C2×Dic3—62no—
273C2×Dic3—62no—
274C2×Dic3—121no—
275C2×Dic3—121no—
276C2×Dic3—122no—
277C2×Dic3—122no—
278C2×Dic3—122no—
279C2×Dic3—122no—
280C2×Dic3—122no—
281C2×Dic3—122no—
282C4×D3—242no—
283C4×D3—242no—
284C2×C32—21no—
285C2×C32—21no—
286C2×C32—22no—
287C2×C32—22no—
288C2×C32#38511yescharacteristic
289C2×C32B(4,𝔽2)11yescharacteristic
290C2×C32#45811yescharacteristic
291C3⋊D3—42no—
292C24—91no—
293C24C2×D3211yescharacteristic
294C2×D4—92no—
295C2×D4—92no—
296C2×D4—182no—
297C2×D4—182no—
298C22×C4—22no—
299C22×C4—21no—
300C22×C4—32no—
301C22×C4—32no—
302C22×C4—42no—
303C22×C4—62no—
304C22×C4—91no—
305C22×C4—181no—
306C22×C4—181no—
307C22×C4—181no—
308C4⋊C4—124no—
309C4⋊C4—181no—
310C4⋊C4—181no—
311C22⋊C4—34no—
312C22⋊C4—62no—
313C22⋊C4—62no—
314C22⋊C4—62no—
315C22⋊C4—182no—
316C22⋊C4—182no—
317C22⋊C4—362no—
318C42—182no—
319C22×C3—22no—
320C22×C3—22no—
321C22×C3—22no—
322C22×C3—22no—
323C22×C3—22no—
324C22×C3—22no—
325C22×C3—22no—
326C22×C3—22no—
327C22×C3—21no—
328C22×C3—22no—
329C22×C3—21no—
330C22×C3—22no—
331C22×C3—21no—
332C22×C3—42no—
333C22×C3—42no—
334C22×C3—42no—
335C22×C3—42no—
336C22×C3—42no—
337C22×C3—42no—
338C22×C3—42no—
339C22×C3—44no—
340C22×C3—42no—
341C22×C3D3×C4⋊C412yes—
342C22×C3#89312yes—
343C22×C3#89412yes—
344C22×C3#89612yes—
345C22×C3C4×#6712yes—
346C22×C3#93712yes—
347C22×C3#94612yes—
348C2×D3—64no—
349C2×D3—122no—
350C2×D3—122no—
351C2×D3—122no—
352C2×D3—124no—
353C2×D3—124no—
354C2×D3—241no—
355C2×D3—241no—
356C2×D3—242no—
357C2×D3—242no—
358C3×C4—44no—
359C3×C4—44no—
360C3×C4—124no—
361C3×C4—122no—
362C3×C4—122no—
363Dic3—44no—
364Dic3—42no—
365Dic3—42no—
366Dic3—64no—
367Dic3—122no—
368Dic3—242no—
369Dic3—242no—
370C32#186711yescharacteristic, complemented, Sylow
371C23—41no—
372C23—41no—
373C23—92no—
374C23—181no—
375C23—181no—
376C23—361no—
377C23—361no—
378C23#379711yescharacteristic
379C23#379912yes—
380C23C4×D3211yescharacteristic
381C23D3×#6712yes—
382C23#381111yescharacteristic
383D4—184no—
384D4—184no—
385C2×C4—22no—
386C2×C4—24no—
387C2×C4—42no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—64no—
391C2×C4—62no—
392C2×C4—62no—
393C2×C4—92no—
394C2×C4—122no—
395C2×C4—122no—
396C2×C4—122no—
397C2×C4—122no—
398C2×C4—181no—
399C2×C4—181no—
400C2×C4—361no—
401C2×C4—361no—
402C2×C4—361no—
403C2×C4—721no—
404C2×C4—721no—
405C2×C3—22no—
406C2×C3—22no—
407C2×C3—22no—
408C2×C3—22no—
409C2×C3—22no—
410C2×C3—22no—
411C2×C3—22no—
412C2×C3—22no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—21no—
416C2×C3—42no—
417C2×C3—42no—
418C2×C3#498912yes—
419C2×C3#503212yes—
420C2×C3#505312yes—
421D3—124no—
422D3—242no—
423C22—22no—
424C22—21no—
425C22—22no—
426C22—21no—
427C22—41no—
428C22—42no—
429C22—41no—
430C22—182no—
431C22—362no—
432C22—361no—
433C22—361no—
434C22—721no—
435C22#6388311yescharacteristic
436C22#6388812yes—
437C22#6389711yescharacteristic
438C22#6390412yes—
439C22#6398311yescharacteristic
440C4—42no—
441C4—124no—
442C4—122no—
443C4—122no—
444C4—182no—
445C4—721no—
446C3—21no—
447C3#6959512yescomplemented
448C2—22no—
449C2—21no—
450C2—21no—
451C2—22no—
452C2—362no—
453C2#1059137411yescharacteristic
454C2#1059139811yescharacteristic
455C2#1059172511yescharacteristic
subgroupG/H
centerC22#63983
commutatorC23×C32C22×C4
FrattiniC24C2×D32
FittingC23×C32×C4C22
socleC22×C32#120
prime radicalC22×#638C22
cosocleC24×C32C23
hypercenterC23×C4D32
hypocenterC32#1867
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
3. C3×#5210C2semidirect
5. #10589186C2semidirect
20. #63581C4semidirect
25. #5210D3semidirect
50. C3×#217C2×C4semidirect
93. C22×C3⋊D3C4⋊C4semidirect
106. C2×C3⋊Dic3C4⋊C4semidirect
165. #217C4×D3semidirect
370. C32#1867semidirect
447. C3#69595semidirect

Maximal subgroups

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

subgroupindex
#105955102
#105929122
C3×#52102
C2×#635812
#105891862
#695953