Finite Group Databasebeta

← #11792662

Subgroups — #11792662

Order 1152.

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

normal subgroups only

This group has 779 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×#5822C212yesmaximal, complemented
2#10594786C211yesmaximal, characteristic, complemented
3#10592933C211yesmaximal, characteristic, complemented
4#10591071C212yesmaximal, complemented
5#10589159C211yesmaximal, characteristic, complemented
6#72121—32nomaximal
7C2×C32×#41C2211yescharacteristic
8C2×C3×#235C2212yes—
9C2×#3748C2211yescharacteristic
10C22×C3⋊(C3⋊C8)C2211yescharacteristic
11C3×#951—22no—
12C3×#950—24no—
13C3×#949—22no—
14C3×#942—22no—
15C3×#932—22no—
16C2×C3×#208C2212yes—
17#63827—22no—
18#63823—22no—
19#63822—22no—
20#63657—22no—
21(C2×D3)⋊(C3⋊C8)—24no—
22C3×#575—32no—
23#5822—32no—
24#5822D312yescomplemented
25#5234—32no—
26#5234—32no—
27#5234—61no—
28#5129—32no—
29C3⋊#338—32no—
30C32×#41—22no—
31C32×#41—22no—
32C2×C32×Q8D411yescharacteristic
33C2×C32×D4—21no—
34C2×C32×D4D411yescharacteristic
35C22×C32×C4—21no—
36C22×C32×C4C2311yescharacteristic
37C2×C3×#67—22no—
38C3×#235—22no—
39C3×#235—22no—
40C3×#235—22no—
41C3×#235—22no—
42C2×C3×D12D412yes—
43C2×C3×C4×D3—22no—
44C2×C3×Dic6D412yes—
45#3748—22no—
46C2×C3⋊(C3⋊C8)—21no—
47C2×C3⋊(C3⋊C8)—22no—
48C2×C3⋊(C3⋊C8)D412yes—
49C3×#216—24no—
50C3×#215—24no—
51C3×#214—24no—
52C3×#213—24no—
53C3×#208—22no—
54C3×#208—22no—
55C2×C3×C3⋊C8D414yes—
56#3718—22no—
57#3715—24no—
58#3713—22no—
59#2017—91noSylow
60C2×C3×#41—21no—
61C2×C3×#41—32no—
62C2×C3×#41C2×D312yes—
63C2×#235C2×D312yes—
64C3×#137—62no—
65C3×#137—62no—
66C3×AGL(1,ℤ/8)—62no—
67C3×AGL(1,ℤ/8)—62no—
68C3×#135—64no—
69C2×C3×M16—32no—
70#951—22no—
71#951—62no—
72#950—24no—
73#950—64no—
74#949—22no—
75#949—62no—
76#942—22no—
77#942—62no—
78#932—22no—
79#932—62no—
80C2×#208—32no—
81C2×#208—61no—
82C2×#208C2×D312yes—
83C22×C3⋊C8—32no—
84C22×C3⋊C8—61no—
85#830—64no—
86#830—64no—
87#830—64no—
88(C2×D3)⋊C8—64no—
89C23×C32—21no—
90C23×C32#4111yescharacteristic
91C22×C3×D3—22no—
92C32×Q8—22no—
93C32×D4—22no—
94C32×D4—42no—
95C2×C32×C4—21no—
96C2×C32×C4—41no—
97C2×C32×C4—41no—
98C2×C32×C4C2×D411yescharacteristic
99C2×C32×C4C2×D412yes—
100C2×C32×C4C2×D412yes—
101C2×C32×C4C2×D411yescharacteristic
102C3×#67—42no—
103C3×#67—42no—
104C2×C3×Dic3—22no—
105C3×D12—22no—
106C3×D12—22no—
107C3×C4×D3—42no—
108C3×C4×D3—42no—
109C3×Dic6—22no—
110C3×Dic6—22no—
111C3⋊(C3⋊C8)—22no—
112C3⋊(C3⋊C8)—41no—
113C3×C3⋊C8—24no—
114#575—32no—
115#575—91no—
116#408—92no—
117#408—91no—
118#338—91no—
119C3×#41—22no—
120C3×#41—22no—
121C3×#41—22no—
122C3×#41—22no—
123C3×#41—42no—
124C3×#41—42no—
125C3×#41—62no—
126C3×#41—62no—
127C3×#41—62no—
128C3×#41—62no—
129C2×C3×Q8—21no—
130C2×C3×Q8—32no—
131C2×C3×Q8#6712yes—
132C2×C3×D4—22no—
133C2×C3×D4—22no—
134C2×C3×D4—21no—
135C2×C3×D4—32no—
136C2×C3×D4—62no—
137C2×C3×D4#6712yes—
138C22×C3×C4—22no—
139C22×C3×C4—22no—
140C22×C3×C4—21no—
141C22×C3×C4—62no—
142C22×C3×C4C22×D312yes—
143C2×#67—22no—
144#235—22no—
145#235—22no—
146#235—22no—
147#235—22no—
148C2×D12#6712yes—
149C2×C4×D3—22no—
150C2×Dic6#6712yes—
151C3×Q16—64no—
152C3×SD16—64no—
153C3×SD16—64no—
154C3×D8—64no—
155C3×M16—62no—
156C3×M16—62no—
157C2×C3×C8—34no—
158#216—24no—
159#216—64no—
160#215—24no—
161#215—64no—
162#214—24no—
163#214—64no—
164#213—24no—
165#213—64no—
166#208—22no—
167#208—22no—
168#208—62no—
169#208—62no—
170#208—122no—
171C2×C3⋊C8—34no—
172C2×C3⋊C8—62no—
173C2×C3⋊C8—62no—
174C2×C3⋊C8—62no—
175C2×C3⋊C8—62no—
176C2×C3⋊C8—62no—
177C2×C3⋊C8—122no—
178C2×C3⋊C8#6714yes—
179C22×C32—41no—
180C22×C32—42no—
181C22×C32—41no—
182C22×C32#12112yes—
183C22×C32#12111yescharacteristic
184C2×C3×D3—44no—
185C2×C3×D3—42no—
186C32×C4—41no—
187C32×C4#12011yescharacteristic
188C32×C4#12012yes—
189C32×C4#12711yescharacteristic
190C3×Dic3—42no—
191C2×#41—32no—
192C2×#41D3211yescharacteristic
193#137—62no—
194#137—62no—
195#137—182no—
196AGL(1,ℤ/8)—62no—
197AGL(1,ℤ/8)—62no—
198AGL(1,ℤ/8)—182no—
199#135—64no—
200#135—182no—
201C2×M16—32no—
202C2×M16—91no—
203C22×C8—91no—
204C22⋊C8—184no—
205C22⋊C8—182no—
206C23×C3—22no—
207C23×C3—22no—
208C23×C3—21no—
209C23×C3—62no—
210C23×C3#23712yes—
211C22×D3—22no—
212C3×Q8—22no—
213C3×Q8—22no—
214C3×Q8—42no—
215C3×Q8—62no—
216C3×Q8—62no—
217C3×D4—22no—
218C3×D4—22no—
219C3×D4—42no—
220C3×D4—44no—
221C3×D4—42no—
222C3×D4—42no—
223C3×D4—62no—
224C3×D4—62no—
225C3×D4—122no—
226C3×D4—122no—
227C2×C3×C4—22no—
228C2×C3×C4—22no—
229C2×C3×C4—21no—
230C2×C3×C4—22no—
231C2×C3×C4—22no—
232C2×C3×C4—21no—
233C2×C3×C4—42no—
234C2×C3×C4—42no—
235C2×C3×C4—42no—
236C2×C3×C4—42no—
237C2×C3×C4—62no—
238C2×C3×C4—122no—
239C2×C3×C4—122no—
240C2×C3×C4D3×D412yes—
241C2×C3×C4D3×D412yes—
242C2×C3×C4D3×D412yes—
243C2×C3×C4C2×#6712yes—
244C2×C3×C4C2×#6712yes—
245C2×C3×C4C2×#6712yes—
246#67—42no—
247#67—42no—
248C2×Dic3—22no—
249D12—22no—
250D12—22no—
251C4×D3—42no—
252C4×D3—42no—
253Dic6—22no—
254Dic6—22no—
255C3×C8—64no—
256C3⋊C8—24no—
257C3⋊C8—64no—
258C3⋊C8—122no—
259C3⋊C8—122no—
260C3⋊C8—122no—
261C2×C32—21no—
262C2×C32—22no—
263C2×C32—81no—
264C2×C32#39211yescharacteristic
265C3×D3—82no—
266#41—22no—
267#41—22no—
268#41—62no—
269#41—62no—
270#41—62no—
271#41—62no—
272C2×Q8—32no—
273C2×Q8#62511yescharacteristic
274C2×D4—21no—
275C2×D4—32no—
276C2×D4—62no—
277C2×D4#62511yescharacteristic
278C22×C4—21no—
279C22×C4—62no—
280C22×C4C2×D3211yescharacteristic
281Q16—64no—
282Q16—182no—
283SD16—64no—
284SD16—64no—
285SD16—184no—
286D8—64no—
287D8—182no—
288M16—62no—
289M16—62no—
290M16—182no—
291C2×C8—34no—
292C2×C8—92no—
293C2×C8—182no—
294C2×C8—181no—
295C22×C3—22no—
296C22×C3—21no—
297C22×C3—42no—
298C22×C3—42no—
299C22×C3—42no—
300C22×C3—44no—
301C22×C3—44no—
302C22×C3—42no—
303C22×C3—124no—
304C22×C3—122no—
305C22×C3#93812yes—
306C22×C3#93912yes—
307C22×C3#93912yes—
308C2×D3—44no—
309C2×D3—42no—
310C3×C4—22no—
311C3×C4—21no—
312C3×C4—21no—
313C3×C4—42no—
314C3×C4—42no—
315C3×C4—122no—
316C3×C4#93712yes—
317C3×C4#93712yes—
318C3×C4#94012yes—
319C3×C4#95312yes—
320Dic3—42no—
321C32#201711yescharacteristic, complemented, Sylow
322C23—21no—
323C23—62no—
324C23#380511yescharacteristic
325Q8—22no—
326Q8—62no—
327Q8—62no—
328D4—22no—
329D4—42no—
330D4—62no—
331D4—62no—
332D4—122no—
333D4—122no—
334C2×C4—21no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—62no—
338C2×C4—122no—
339C2×C4—122no—
340C2×C4C2×#62511yescharacteristic
341C2×C4D3×#6712yes—
342C2×C4D3×#6712yes—
343C2×C4#381111yescharacteristic
344C8—64no—
345C8—182no—
346C8—361no—
347C2×C3—22no—
348C2×C3—22no—
349C2×C3—22no—
350C2×C3—22no—
351C2×C3—21no—
352C2×C3—42no—
353C2×C3—82no—
354C2×C3—82no—
355C2×C3—242no—
356C2×C3#522312yes—
357D3—82no—
358C22—41no—
359C22—42no—
360C22—41no—
361C22—124no—
362C22—122no—
363C22#6397012yes—
364C22#6398011yescharacteristic
365C4—41no—
366C4—122no—
367C4#6397612yes—
368C4#6397911yescharacteristic
369C4#6398311yescharacteristic
370C3—21no—
371C3#7212112yescomplemented
372C2—21no—
373C2—22no—
374C2—81no—
375C2—242no—
376C2#1059172311yescharacteristic
subgroupG/H
centerC4#63979
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×#41C22
socleC2×C32#392
hypercenterC2×#41D32
hypocenterC32#2017
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C3×#5822C2semidirect
2. #10594786C2semidirect
3. #10592933C2semidirect
4. #10591071C2semidirect
5. #10589159C2semidirect
24. #5822D3semidirect
321. C32#2017semidirect
371. C3#72121semidirect

Maximal subgroups

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

subgroupindex
C3×#58222
#105947862
#105929332
#105910712
#105891592
#721213