Finite Group Databasebeta

← #11870831

Subgroups — #11870831

Order 1152.

644 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 644 conjugacy classes of subgroups — too many to draw. Only its 109 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#10594810C211yesmaximal, characteristic
2C2×#63838C211yesmaximal, characteristic
3#10593801C211yesmaximal, characteristic
4#10593500C212yesmaximal
5#10593499C212yesmaximal
6#10593448C212yesmaximal, complemented
7#10593445C214yesmaximal, complemented
8#10593391C212yesmaximal, complemented
9C22×#627C2211yescharacteristic
10C2×#3776C2214yes—
11C2×C4×C3⋊Dic3C2211yescharacteristic
12C3×#924—21no—
13C2×C3×Dic3⋊C4—21no—
14#63982C2212yes—
15C2×#3724C2211yescharacteristic
16#63957—21no—
17C2×Dic32—21no—
18#63919C2211yescharacteristic
19#63873C2211yescharacteristic
20#63870—21no—
21#63843—21no—
22#63838—21no—
23#63838—21no—
24#63838C2212yes—
25#63838C2212yes—
26#63838C2212yes—
27C22⋊#622C2212yes—
28#63779C2212yes—
29C4×#622C2212yes—
30#63743C2214yes—
31#63740C2214yes—
32#63740C2214yes—
33#5622—61no—
34C2×#887—61no—
35C22×C32×C4D411yescharacteristic
36C22×C3⋊Dic3D411yescharacteristic
37C22×C3⋊Dic3C2311yescharacteristic
38C22×C3×Dic3—21no—
39C22×C3×Dic3—21no—
40C2×C3×Dic6—21no—
41C2×#627—21no—
42C2×#627—24no—
43C2×#627C2312yes—
44C2×#627C2312yes—
45C2×#622C2314yes—
46#3776—28no—
47C4×C3⋊Dic3D411yescharacteristic
48C4×C3⋊Dic3D411yescharacteristic
49C4×C3⋊Dic3C2311yescharacteristic
50C4×C3⋊Dic3C2311yescharacteristic
51C3×#217—22no—
52C3×C4⋊Dic3—21no—
53C3×Dic3⋊C4—22no—
54C3×Dic3⋊C4—22no—
55C3×Dic3⋊C4—22no—
56#3724—21no—
57#3724—21no—
58#3724—21no—
59#3724C2312yes—
60#3724C2312yes—
61Dic3⋊Dic3—22no—
62Dic32—22no—
63Dic32—22no—
64Dic32—22no—
65#3104—91nomaximal, Sylow
66C22×Dic6—61no—
67C3×C22⋊Q8—61no—
68C2×C3×C4⋊C4—61no—
69Q8×Dic3—61no—
70#944—61no—
71#924—21no—
72C2×Dic3⋊C4—21no—
73C2×Dic3⋊C4—61no—
74C2×C4×Dic3—61no—
75C2×C4×Dic3—61no—
76C2×C4×Dic3—61no—
77C2×C4×Dic3—61no—
78#889—62no—
79#888—61no—
80#887—62no—
81#887—62no—
82#887—62no—
83#887—62no—
84#887—62no—
85#887—61no—
86#878—62no—
87#877—62no—
88C23×C32C2×D411yescharacteristic
89C2×C32×C4—41no—
90C2×C32×C4C2×D411yescharacteristic
91C2×C32×C4C2×D411yescharacteristic
92C2×C3⋊Dic3—22no—
93C2×C3⋊Dic3Q1614yescomplemented
94C2×C3⋊Dic3C2×D411yescharacteristic
95C2×C3⋊Dic3C2×D411yescharacteristic
96C2×C3⋊Dic3C2×D411yescharacteristic
97C2×C3⋊Dic3C2411yescharacteristic
98C2×C3×Dic3—24no—
99C2×C3×Dic3—22no—
100C2×C3×Dic3—22no—
101C2×C3×Dic3—22no—
102C2×C3×Dic3—22no—
103C2×C3×Dic3—42no—
104C3×Dic6—42no—
105#627—24no—
106#627—22no—
107#627—24no—
108#627#4114yes—
109#622—24no—
110#533—91no—
111C2×C4×Q8—91no—
112#484—92no—
113#477—92no—
114#462—92no—
115#451—92no—
116C4×Q16—94no—
117#431—91no—
118C2×C3×Q8—61no—
119C22×C3×C4—21no—
120C22×C3×C4—21no—
121C22×C3×C4—61no—
122C22×C3×C4—61no—
123C22×Dic3—21no—
124C22×Dic3—21no—
125C22×Dic3—61no—
126C22×Dic3—61no—
127C22×Dic3—61no—
128C22×Dic3—61no—
129C2×Dic6—21no—
130C2×Dic6—62no—
131C2×Dic6—62no—
132C2×Dic6—62no—
133C2×Dic6—68no—
134C3×C4⋊C4—62no—
135C3×C4⋊C4—62no—
136C3×C4⋊C4—61no—
137C3×C4⋊C4—62no—
138C3×C22⋊C4—62no—
139#217—22no—
140C4⋊Dic3—21no—
141C4⋊Dic3—62no—
142Dic3⋊C4—22no—
143Dic3⋊C4—22no—
144Dic3⋊C4—22no—
145Dic3⋊C4—62no—
146Dic3⋊C4—62no—
147Dic3⋊C4—62no—
148Dic3⋊C4—62no—
149Dic3⋊C4—62no—
150Dic3⋊C4—62no—
151C4×Dic3—61no—
152C4×Dic3—61no—
153C4×Dic3—61no—
154C4×Dic3—61no—
155C4×Dic3—61no—
156C4×Dic3—61no—
157C4×Dic3—61no—
158C4×Dic3—61no—
159C4×Dic3—62no—
160C4×Dic3—62no—
161C4×Dic3—62no—
162C4×Dic3—62no—
163C4×Dic3—62no—
164C4×Dic3—62no—
165C22×C32—21no—
166C22×C32—21no—
167C22×C32C2×Q1612yes—
168C22×C32C22×D411yescharacteristic
169C32×C4—21no—
170C32×C4—21no—
171C3⋊Dic3—21no—
172C3⋊Dic3C2×Q1612yes—
173C3⋊Dic3C2×Q1612yes—
174C3⋊Dic3C2×#4112yes—
175C3×Dic3—24no—
176C3×Dic3—42no—
177C3×Dic3—42no—
178C3×Dic3—42no—
179C22×Q8—91no—
180C2×Q16—94no—
181C4⋊Q8—91no—
182C4⋊Q8—91no—
183#125—181no—
184C22⋊Q8—61no—
185C22⋊Q8—92no—
186C4×Q8—92no—
187C4×Q8—92no—
188C4×Q8—92no—
189C4×Q8—181no—
190C4×Q8—181no—
191C4×Q8—181no—
192#117—181no—
193C2×C4⋊C4—61no—
194C2×C4⋊C4—91no—
195C2×C42—91no—
196C2×C42—181no—
197#107—94no—
198C4⋊C8—92no—
199#103—94no—
200#103—94no—
201C22⋊C8—92no—
202C4×C8—92no—
203C23×C3—21no—
204C23×C3—21no—
205C3×Q8—122no—
206C2×C3×C4—21no—
207C2×C3×C4—21no—
208C2×C3×C4—21no—
209C2×C3×C4—21no—
210C2×C3×C4—42no—
211C2×C3×C4—42no—
212C2×C3×C4—62no—
213C2×C3×C4—64no—
214C2×C3×C4—62no—
215C2×C3×C4—62no—
216C2×C3×C4—62no—
217C2×C3×C4—122no—
218C2×Dic3—22no—
219C2×Dic3—24no—
220C2×Dic3—22no—
221C2×Dic3—22no—
222C2×Dic3—22no—
223C2×Dic3—42no—
224C2×Dic3—64no—
225C2×Dic3—64no—
226C2×Dic3—61no—
227C2×Dic3—61no—
228C2×Dic3—61no—
229C2×Dic3—61no—
230C2×Dic3—61no—
231C2×Dic3—61no—
232C2×Dic3—61no—
233C2×Dic3—61no—
234C2×Dic3—64no—
235C2×Dic3—122no—
236Dic6—42no—
237Dic6—64no—
238Dic6—64no—
239Dic6—68no—
240Dic6—124no—
241C2×C32—22no—
242C2×C32#52511yescharacteristic
243C2×C32C22×Q1611yescharacteristic
244C2×C32#57511yescharacteristic
245C2×Q8—61no—
246C2×Q8—92no—
247C2×Q8—92no—
248C2×Q8—181no—
249C2×Q8—184no—
250C22×C4—61no—
251C22×C4—61no—
252C22×C4—91no—
253C22×C4—91no—
254C22×C4GO+(4,𝔽2)11yescharacteristic
255Q16—188no—
256C2×C8—94no—
257C4⋊C4—62no—
258C4⋊C4—62no—
259C4⋊C4—62no—
260C4⋊C4—61no—
261C4⋊C4—92no—
262C4⋊C4—92no—
263C4⋊C4—181no—
264C4⋊C4—181no—
265C4⋊C4—181no—
266C4⋊C4—182no—
267C22⋊C4—62no—
268C42—91no—
269C42—91no—
270C42—91no—
271C42—91no—
272C42—182no—
273C42—182no—
274C42—182no—
275C22×C3—22no—
276C22×C3—22no—
277C22×C3—21no—
278C22×C3—21no—
279C22×C3—22no—
280C22×C3—22no—
281C22×C3—41no—
282C22×C3—41no—
283C3×C4—22no—
284C3×C4—41no—
285C3×C4—41no—
286C3×C4—41no—
287C3×C4—64no—
288C3×C4—122no—
289C3×C4—122no—
290C3×C4—122no—
291Dic3—24no—
292Dic3—42no—
293Dic3—42no—
294Dic3—42no—
295Dic3—62no—
296Dic3—62no—
297Dic3—62no—
298Dic3—62no—
299Dic3—62no—
300Dic3—62no—
301Dic3—62no—
302Dic3—121no—
303C32#310411yescharacteristic, complemented, Sylow
304C23C2×GO+(4,𝔽2)11yescharacteristic
305Q8—94no—
306Q8—122no—
307Q8—182no—
308Q8—184no—
309Q8—184no—
310C2×C4—41no—
311C2×C4—64no—
312C2×C4—62no—
313C2×C4—62no—
314C2×C4—62no—
315C2×C4—62no—
316C2×C4—91no—
317C2×C4—91no—
318C2×C4—91no—
319C2×C4—94no—
320C2×C4—91no—
321C2×C4—122no—
322C2×C4—182no—
323C2×C4C2×GO+(4,𝔽2)11yescharacteristic
324C2×C4C2×GO+(4,𝔽2)11yescharacteristic
325C8—184no—
326C2×C3—24no—
327C2×C3—21no—
328C2×C3—21no—
329C2×C3—21no—
330C2×C3—21no—
331C2×C3—21no—
332C2×C3—21no—
333C2×C3—42no—
334C22—21no—
335C22—21no—
336C22#6422812yes—
337C22C22×GO+(4,𝔽2)11yescharacteristic
338C4—21no—
339C4—21no—
340C4—64no—
341C4—92no—
342C4—92no—
343C4—92no—
344C4—122no—
345C4—122no—
346C4—122no—
347C4—181no—
348C3—21no—
349C3—21no—
350C2—22no—
351C2C2×#6422811yescharacteristic
352C2#1059651011yescharacteristic
353C2#1059653211yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FittingC22×C32×C4D4
socleC22×C32C22×D4
prime radicalC23×C32C2×D4
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#3104
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
6. #10593448C2semidirect
7. #10593445C2semidirect
8. #10593391C2semidirect
93. C2×C3⋊Dic3Q16semidirect
303. C32#3104semidirect

Maximal subgroups

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

subgroupindex
#105948102
C2×#638382
#105938012
#105935002
#105934992
#105934482
#105934452
#105933912
#31049