Finite Group Databasebeta

← #11792411

Subgroups — #11792411

Order 1152.

883 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 883 conjugacy classes of subgroups — too many to draw. Only its 118 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×#5791C212yesmaximal, complemented
2#10594786C211yesmaximal, characteristic, complemented
3#10592906C211yesmaximal, characteristic, complemented
4#10591111C212yesmaximal, complemented
5#10589157C211yesmaximal, characteristic, complemented
6#71715—32nomaximal
7C23×C32×C4C2211yescharacteristic
8C2×C3×#235C2212yes—
9C2×#3748C2211yescharacteristic
10C2×#3748C2211yescharacteristic
11C3×#953—22no—
12C3×#930—22no—
13C3×#929—22no—
14C3×C4×#67—24no—
15C3×#926C2212yes—
16C3×#924—22no—
17#63827—22no—
18#63823—22no—
19#63822—22no—
20#63657—22no—
21#63569—24no—
22C3×#525—32no—
23#5822—32no—
24#5791D312yescomplemented
25#5236—32no—
26#5207—32no—
27#5207—61no—
28#5005—32no—
29#4531—32no—
30C24×C32D411yescharacteristic
31C22×C32×C4—21no—
32C22×C32×C4—22no—
33C22×C32×C4—22no—
34C22×C32×C4—21no—
35C22×C32×C4D411yescharacteristic
36C22×C32×C4C2311yescharacteristic
37C2×C3×#67—24no—
38C2×C3×#67—22no—
39C3×#235—22no—
40C3×#235—22no—
41C3×#235—22no—
42C3×#235—22no—
43C2×C3×D12D412yescomplemented
44C2×C3×C4×D3—22no—
45C2×C3×Dic6D412yescomplemented
46#3748—22no—
47#3748—22no—
48C2×C3⋊(C3⋊C8)—21no—
49C2×C3⋊(C3⋊C8)D412yescomplemented
50C3×#217—24no—
51C3×#217—22no—
52C3×(C2×D3)⋊C4—24no—
53C3×C4⋊Dic3—22no—
54C3×Dic3⋊C4—24no—
55C3×C4×Dic3D414yescomplemented
56#3718—22no—
57#3715—24no—
58#3713—22no—
59#2010—91noSylow
60C2×C3×#41—32no—
61C23×C3×C4—21no—
62C23×C3×C4C2×D312yes—
63C2×#235C2×D312yes—
64C3×#123—62no—
65C3×C22⋊Q8—62no—
66C3×#121—62no—
67C3×#120—62no—
68C3×C4×D4—64no—
69C3×#117—32no—
70#953—22no—
71#951—62no—
72#950—64no—
73#949—62no—
74#942—62no—
75#932—62no—
76#930—22no—
77#929—22no—
78C4×#67—24no—
79#926C2×D312yes—
80#924—22no—
81C2×#208—32no—
82C2×#208—32no—
83C2×#208—61no—
84C2×#208—61no—
85#837—64no—
86#830—64no—
87#830—64no—
88#805—64no—
89C23×C32—21no—
90C23×C32—22no—
91C23×C32—42no—
92C23×C32C2×D411yescharacteristic
93C22×C3×D3—22no—
94C2×C32×C4—21no—
95C2×C32×C4—22no—
96C2×C32×C4—41no—
97C2×C32×C4—42no—
98C2×C32×C4—41no—
99C2×C32×C4C2×D411yescharacteristic
100C2×C32×C4C2×D412yes—
101C2×C32×C4C2×D412yes—
102C2×C32×C4#4111yescharacteristic
103C3×#67—48no—
104C3×#67—42no—
105C3×#67—42no—
106C2×C3×Dic3—24no—
107C2×C3×Dic3—22no—
108C3×D12—22no—
109C3×D12—22no—
110C3×C4×D3—42no—
111C3×C4×D3—42no—
112C3×Dic6—22no—
113C3×Dic6—22no—
114C3⋊(C3⋊C8)—22no—
115C3⋊(C3⋊C8)—41no—
116#575—91no—
117#525—32no—
118#421—92no—
119#407—91no—
120H(3,ℤ/4)—91no—
121C24×C3—21no—
122C24×C3#6712yes—
123C3×#41—62no—
124C3×#41—62no—
125C3×#41—62no—
126C3×#41—62no—
127C2×C3×Q8—32no—
128C2×C3×D4—32no—
129C2×C3×D4—64no—
130C2×C3×D4—62no—
131C22×C3×C4—22no—
132C22×C3×C4—22no—
133C22×C3×C4—22no—
134C22×C3×C4—22no—
135C22×C3×C4—22no—
136C22×C3×C4—22no—
137C22×C3×C4—22no—
138C22×C3×C4—22no—
139C22×C3×C4—21no—
140C22×C3×C4—21no—
141C22×C3×C4—42no—
142C22×C3×C4—42no—
143C22×C3×C4—62no—
144C22×C3×C4#6712yes—
145C22×C3×C4C22×D312yes—
146C2×#67—24no—
147C2×#67—22no—
148#235—22no—
149#235—22no—
150#235—22no—
151#235—22no—
152C2×D12#6712yescomplemented
153C2×C4×D3—22no—
154C2×Dic6#6712yescomplemented
155C3×C4⋊C4—64no—
156C3×C4⋊C4—62no—
157C3×C22⋊C4—64no—
158C3×C22⋊C4—64no—
159C3×C22⋊C4—62no—
160C3×C42—34no—
161#217—24no—
162#217—22no—
163#216—64no—
164#215—64no—
165#214—64no—
166#213—64no—
167(C2×D3)⋊C4—24no—
168C4⋊Dic3—22no—
169Dic3⋊C4—24no—
170C4×Dic3#6714yescomplemented
171#208—62no—
172#208—62no—
173#208—62no—
174#208—62no—
175#208—122no—
176#208—122no—
177C2×C3⋊C8—34no—
178C2×C3⋊C8—62no—
179C2×C3⋊C8—62no—
180C2×C3⋊C8—62no—
181C22×C32—22no—
182C22×C32—24no—
183C22×C32—41no—
184C22×C32—41no—
185C22×C32—42no—
186C22×C32—41no—
187C22×C32#12012yes—
188C22×C32#12111yescharacteristic
189C2×C3×D3—44no—
190C2×C3×D3—42no—
191C32×C4—41no—
192C32×C4#12011yescharacteristic
193C32×C4#12112yes—
194C32×C4#12711yescharacteristic
195C3×Dic3—44no—
196C3×Dic3—42no—
197C2×#41—32no—
198C23×C4D3211yescharacteristic
199#137—182no—
200AGL(1,ℤ/8)—182no—
201#135—182no—
202C2×M16—91no—
203C2×M16—91no—
204#123—62no—
205C22⋊Q8—62no—
206#121—62no—
207#120—62no—
208C4×D4—64no—
209#117—32no—
210#104—184no—
211C22⋊C8—182no—
212C23×C3—22no—
213C23×C3—22no—
214C23×C3—22no—
215C23×C3—22no—
216C23×C3—21no—
217C23×C3—42no—
218C23×C3—44no—
219C23×C3—44no—
220C23×C3—62no—
221C23×C3C2×#6712yes—
222C22×D3—22no—
223C3×Q8—62no—
224C3×Q8—62no—
225C3×D4—62no—
226C3×D4—62no—
227C3×D4—128no—
228C3×D4—122no—
229C3×D4—122no—
230C2×C3×C4—22no—
231C2×C3×C4—22no—
232C2×C3×C4—22no—
233C2×C3×C4—22no—
234C2×C3×C4—21no—
235C2×C3×C4—22no—
236C2×C3×C4—22no—
237C2×C3×C4—21no—
238C2×C3×C4—42no—
239C2×C3×C4—44no—
240C2×C3×C4—42no—
241C2×C3×C4—42no—
242C2×C3×C4—42no—
243C2×C3×C4—42no—
244C2×C3×C4—42no—
245C2×C3×C4—42no—
246C2×C3×C4—64no—
247C2×C3×C4—62no—
248C2×C3×C4—122no—
249C2×C3×C4—122no—
250C2×C3×C4D3×D412yes—
251C2×C3×C4D3×D412yes—
252C2×C3×C4D3×D412yes—
253C2×C3×C4#23712yes—
254C2×C3×C4C2×#6712yes—
255C2×C3×C4C2×#6712yes—
256#67—48no—
257#67—42no—
258#67—42no—
259C2×Dic3—24no—
260C2×Dic3—22no—
261D12—22no—
262D12—22no—
263C4×D3—42no—
264C4×D3—42no—
265Dic6—22no—
266Dic6—22no—
267C3⋊C8—64no—
268C3⋊C8—122no—
269C3⋊C8—122no—
270C3⋊C8—122no—
271C2×C32—21no—
272C2×C32—22no—
273C2×C32—42no—
274C2×C32#39211yescharacteristic
275C3×D3—82no—
276C24#62511yescharacteristic
277#41—62no—
278#41—62no—
279#41—62no—
280#41—62no—
281C2×Q8—32no—
282C2×D4—32no—
283C2×D4—64no—
284C2×D4—62no—
285C22×C4—21no—
286C22×C4—22no—
287C22×C4—22no—
288C22×C4—21no—
289C22×C4—62no—
290C22×C4#62511yescharacteristic
291C22×C4C2×D3211yescharacteristic
292Q16—182no—
293SD16—184no—
294D8—182no—
295M16—182no—
296M16—182no—
297C2×C8—92no—
298C2×C8—181no—
299C4⋊C4—64no—
300C4⋊C4—62no—
301C22⋊C4—64no—
302C22⋊C4—64no—
303C22⋊C4—62no—
304C42—34no—
305C22×C3—24no—
306C22×C3—24no—
307C22×C3—24no—
308C22×C3—24no—
309C22×C3—22no—
310C22×C3—21no—
311C22×C3—44no—
312C22×C3—42no—
313C22×C3—42no—
314C22×C3—42no—
315C22×C3—42no—
316C22×C3—42no—
317C22×C3—42no—
318C22×C3—42no—
319C22×C3—44no—
320C22×C3—42no—
321C22×C3—124no—
322C22×C3—122no—
323C22×C3#93712yes—
324C22×C3#93912yes—
325C22×C3#95312yes—
326C2×D3—44no—
327C2×D3—42no—
328C3×C4—22no—
329C3×C4—21no—
330C3×C4—21no—
331C3×C4—42no—
332C3×C4—42no—
333C3×C4—124no—
334C3×C4—122no—
335C3×C4#93712yes—
336C3×C4#93812yes—
337C3×C4#93912yes—
338C3×C4#94012yes—
339Dic3—44no—
340Dic3—42no—
341C32#201011yescharacteristic, complemented, Sylow
342C23—22no—
343C23—21no—
344C23—42no—
345C23—62no—
346C23C2×#62511yescharacteristic
347Q8—62no—
348Q8—62no—
349D4—62no—
350D4—62no—
351D4—128no—
352D4—122no—
353D4—122no—
354C2×C4—22no—
355C2×C4—21no—
356C2×C4—42no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—64no—
360C2×C4—62no—
361C2×C4—122no—
362C2×C4—122no—
363C2×C4#380511yescharacteristic
364C2×C4D3×#6712yes—
365C2×C4D3×#6712yes—
366C2×C4#381111yescharacteristic
367C8—182no—
368C8—361no—
369C2×C3—22no—
370C2×C3—22no—
371C2×C3—22no—
372C2×C3—22no—
373C2×C3—21no—
374C2×C3—42no—
375C2×C3—44no—
376C2×C3—44no—
377C2×C3—242no—
378C2×C3#522312yes—
379D3—82no—
380C22—24no—
381C22—22no—
382C22—41no—
383C22—42no—
384C22—41no—
385C22—41no—
386C22—124no—
387C22—122no—
388C22#6397612yes—
389C22#6398011yescharacteristic
390C4—41no—
391C4—124no—
392C4—122no—
393C4#6397012yes—
394C4#6397911yescharacteristic
395C4#6398311yescharacteristic
396C3—21no—
397C3#7171512yescomplemented
398C2—22no—
399C2—21no—
400C2—42no—
401C2—242no—
402C2#1059172311yescharacteristic
subgroupG/H
centerC4#63979
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC23×C32×C4C22
socleC2×C32#392
hypercenterC23×C4D32
hypocenterC32#2010
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C3×#5791C2semidirect
2. #10594786C2semidirect
3. #10592906C2semidirect
4. #10591111C2semidirect
5. #10589157C2semidirect
24. #5791D3semidirect
43. C2×C3×D12D4semidirect
45. C2×C3×Dic6D4semidirect
49. C2×C3⋊(C3⋊C8)D4semidirect
55. C3×C4×Dic3D4semidirect
152. C2×D12#67semidirect
154. C2×Dic6#67semidirect
170. C4×Dic3#67semidirect
341. C32#2010semidirect
397. C3#71715semidirect

Maximal subgroups

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

subgroupindex
C3×#57912
#105947862
#105929062
#105911112
#105891572
#717153