Finite Group Databasebeta

← #11793936

Subgroups — #11793936

Order 1152.

786 conjugacy classes of subgroups; only the 177 normal subgroups are shown.

normal subgroups only

This group has 786 conjugacy classes of subgroups — too many to draw. Only its 177 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×#64151C211yesmaximal, characteristic
2C2×C32×#103C211yesmaximal, characteristic, complemented
3C2×#63663C211yesmaximal, characteristic, complemented
4#10592809C211yesmaximal, characteristic
5C2×#63646C211yesmaximal, characteristic, complemented
6#10592665C211yesmaximal, characteristic
7#10589396C211yesmaximal, characteristic, complemented
8#70264—34nomaximal
9C22×C32×Q8C2211yescharacteristic
10C2×#3828C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×#3756—21no—
14#64151—22no—
15#64151—22no—
16C2×#3755—21no—
17C2×#3748C2211yescharacteristic
18C2×#3748C2211yescharacteristic
19C2×#3748C2211yescharacteristic
20C32×#103—22no—
21#63663—22no—
22#63647—22no—
23#63646—22no—
24#63637—21no—
25#63636—21no—
26C2×#942—34no—
27C2×C3×#103D314yescomplemented
28C2×#836—34no—
29#5110—34no—
30C2×#819—34no—
31#4966—34no—
32#4530—34no—
33C2×C32×Q8—21no—
34C2×C32×Q8—21no—
35C2×C32×Q8—21no—
36C2×C32×Q8—21no—
37C2×C32×Q8—21no—
38C2×C32×Q8D412yes—
39C22×C32×C4—21no—
40C22×C32×C4—21no—
41C22×C32×C4C2311yescharacteristic
42C2×#638—21no—
43#3828—21no—
44#3828—21no—
45#3828—21no—
46#3828—21no—
47C2×C4⋊(C3⋊D3)D411yescharacteristic
48C2×C4×C3⋊D3—21no—
49C2×#634D411yescharacteristic
50C2×C32×C8—21no—
51C2×C32×C8—21no—
52C2×C32×C8D412yes—
53C32×C4⋊C4—21no—
54C32×C4⋊C4—21no—
55#3756—24no—
56#3755—24no—
57#3748—21no—
58#3748—21no—
59#3748—21no—
60#3748—21no—
61#3748—21no—
62#3748D412yes—
63C2×C3⋊(C3⋊C8)—21no—
64C2×C3⋊(C3⋊C8)—21no—
65C2×C3⋊(C3⋊C8)—21no—
66#2052—91noSylow
67C22×C3×Q8C2×D314yes—
68C2×#235—34no—
69C22×C3×C8C2×D314yes—
70C2×C3×C4⋊C4C2×D314yes—
71C2×#216—64no—
72#942—68no—
73#942—68no—
74C2×#215—64no—
75C2×#208—34no—
76C2×#208—34no—
77C2×#208—34no—
78C3×#103—28no—
79#836—68no—
80(C2×D3)⋊C8—68no—
81#819—68no—
82#810—64no—
83#809—64no—
84C23×C32#4111yescharacteristic
85C22×C3⋊D3—21no—
86C32×Q8—22no—
87C32×Q8—22no—
88C32×Q8—41no—
89C32×Q8—41no—
90C2×C32×C4—22no—
91C2×C32×C4—41no—
92C2×C32×C4—41no—
93C2×C32×C4—41no—
94C2×C32×C4—81no—
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4C2×D411yescharacteristic
98C2×C32×C4C2×D411yescharacteristic
99C2×C32×C4#4111yescharacteristic
100C2×C32×C4#4111yescharacteristic
101#638—41no—
102#638—41no—
103C2×C3⋊Dic3—21no—
104C4⋊(C3⋊D3)—21no—
105C4⋊(C3⋊D3)—21no—
106C4×C3⋊D3—41no—
107C4×C3⋊D3—41no—
108#634—21no—
109#634—21no—
110C32×C8—22no—
111C3⋊(C3⋊C8)—22no—
112C3⋊(C3⋊C8)—41no—
113C3⋊(C3⋊C8)—41no—
114C2×#137—91no—
115C2×#108—91no—
116#417—91no—
117C2×#103C3⋊D311yescharacteristic, complemented
118C2×#101—91no—
119#408—91no—
120#343—91no—
121C2×C3×Q8—24no—
122C2×C3×Q8—24no—
123C2×C3×Q8—24no—
124C2×C3×Q8—24no—
125C2×C3×Q8—24no—
126C2×C3×Q8D1218yes—
127C22×C3×C4—24no—
128C22×C3×C4—24no—
129C22×C3×C4C22×D314yes—
130C2×#67—64no—
131#235—64no—
132#235—64no—
133#235—64no—
134#235—64no—
135C2×D12—34no—
136C2×C4×D3—64no—
137C2×Dic6—34no—
138C2×C3×C8—24no—
139C2×C3×C8—24no—
140C2×C3×C8#6718yes—
141C3×C4⋊C4—24no—
142C3×C4⋊C4—24no—
143#216—616no—
144#215—616no—
145#208—38no—
146#208—64no—
147#208—64no—
148#208—64no—
149#208—64no—
150#208—64no—
151C2×C3⋊C8—64no—
152C2×C3⋊C8—64no—
153C2×C3⋊C8—64no—
154C22×C32—21no—
155C22×C32—21no—
156C22×C32#12111yescharacteristic
157C22×C32#12311yescharacteristic
158C22×C32#12411yescharacteristic
159C2×C3⋊D3—41no—
160C2×C3⋊D3—41no—
161C2×C3⋊D3—41no—
162C32×C4—42no—
163C32×C4—81no—
164C32×C4#12011yescharacteristic
165C32×C4#12111yescharacteristic
166C32×C4#12111yescharacteristic
167C32×C4#12311yescharacteristic
168C3⋊Dic3—41no—
169C2×#41—91no—
170C22×Q8C2×C3⋊D311yescharacteristic
171#137—182no—
172#137—182no—
173C2×Q16—181no—
174C2×SD16—181no—
175C2×M16—91no—
176C2×M16—91no—
177C2×M16—91no—
178C22×C8C2×C3⋊D311yescharacteristic
179C2×C4⋊C4C2×C3⋊D311yescharacteristic
180#108—182no—
181#103—22no—
182#103—181no—
183#102—181no—
184#101—182no—
185C22⋊C8—182no—
186C23×C3#23714yes—
187C22×D3—64no—
188C3×Q8—28no—
189C3×Q8—28no—
190C3×Q8—44no—
191C3×Q8—44no—
192C2×C3×C4—28no—
193C2×C3×C4—44no—
194C2×C3×C4—44no—
195C2×C3×C4—44no—
196C2×C3×C4—84no—
197C2×C3×C4C2×D1214yes—
198C2×C3×C4#23514yes—
199C2×C3×C4D3×D414yes—
200C2×C3×C4D3×D414yes—
201C2×C3×C4#23714yes—
202C2×C3×C4C2×#6714yes—
203#67—124no—
204#67—124no—
205C2×Dic3—64no—
206D12—64no—
207D12—64no—
208C4×D3—124no—
209C4×D3—124no—
210Dic6—64no—
211Dic6—64no—
212C3×C8—28no—
213C3⋊C8—68no—
214C3⋊C8—124no—
215C3⋊C8—124no—
216C2×C32—21no—
217C2×C32—21no—
218C2×C32#39411yescharacteristic
219C2×C32#47111yescharacteristic
220C2×C32#47311yescharacteristic
221C3⋊D3—81no—
222#41—181no—
223#41—181no—
224#41—181no—
225#41—181no—
226C2×Q8—21no—
227C2×Q8—21no—
228C2×Q8—21no—
229C2×Q8—21no—
230C2×Q8—21no—
231C2×Q8—91no—
232C2×Q8C4⋊(C3⋊D3)12yes—
233C2×D4—91no—
234C2×D4—181no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—181no—
238C22×C4C22×C3⋊D311yescharacteristic
239Q16—184no—
240SD16—184no—
241M16—92no—
242M16—181no—
243M16—181no—
244M16—181no—
245M16—181no—
246M16—181no—
247C2×C8—21no—
248C2×C8—21no—
249C2×C8—181no—
250C2×C8—181no—
251C2×C8—181no—
252C2×C8#63812yes—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C22×C3—24no—
256C22×C3—24no—
257C22×C3#88514yes—
258C22×C3#88614yes—
259C22×C3#93814yes—
260C2×D3—124no—
261C2×D3—124no—
262C2×D3—124no—
263C3×C4—48no—
264C3×C4—84no—
265C3×C4#88214yes—
266C3×C4#88314yes—
267C3×C4#93014yes—
268C3×C4#93914yes—
269Dic3—124no—
270C32#205211yescharacteristic, complemented, Sylow
271C23—181no—
272C23#383011yescharacteristic
273Q8—22no—
274Q8—22no—
275Q8—41no—
276Q8—41no—
277Q8—181no—
278Q8—181no—
279D4—181no—
280D4—181no—
281D4—361no—
282D4—361no—
283C2×C4—22no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—81no—
288C2×C4—181no—
289C2×C4—361no—
290C2×C4—361no—
291C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
292C2×C4#382811yescharacteristic
293C2×C4D4×C3⋊D311yescharacteristic
294C2×C4D4×C3⋊D311yescharacteristic
295C2×C4#383011yescharacteristic
296C2×C4C2×#63811yescharacteristic
297C8—22no—
298C8—182no—
299C8—361no—
300C8—361no—
301C2×C3—24no—
302C2×C3—24no—
303C2×C3#496114yes—
304C2×C3#517714yes—
305C2×C3#519214yes—
306D3—244no—
307C22—21no—
308C22—21no—
309C22—361no—
310C22—361no—
311C22—361no—
312C22#6409411yescharacteristic
313C22#6409511yescharacteristic
314C22#6414711yescharacteristic
315C4—42no—
316C4—81no—
317C4—361no—
318C4#6409111yescharacteristic
319C4#6409211yescharacteristic
320C4#6413911yescharacteristic
321C4#6414811yescharacteristic
322C3#7026414yescomplemented
323C2—21no—
324C2—21no—
325C2—721no—
326C2#1059266011yescharacteristic
327C2#1059287611yescharacteristic
328C2#1059289111yescharacteristic
subgroupG/H
centerC22#64147
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC2×C32×#103C2
socleC22×C32#121
prime radicalC2×#3828C22
hypercenterC2×#103C3⋊D3
hypocenterC32#2052
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
2. C2×C32×#103C2semidirect
3. C2×#63663C2semidirect
5. C2×#63646C2semidirect
7. #10589396C2semidirect
27. C2×C3×#103D3semidirect
117. C2×#103C3⋊D3semidirect
270. C32#2052semidirect
322. C3#70264semidirect

Maximal subgroups

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

subgroupindex
C2×#641512
C2×C32×#1032
C2×#636632
#105928092
C2×#636462
#105926652
#105893962
#702643