Finite Group Databasebeta

← #11870829

Subgroups — #11870829

Order 1152.

644 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 644 conjugacy classes of subgroups — too many to draw. Only its 117 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#10595050C211yesmaximal, characteristic
2C2×C4×#627C211yesmaximal, characteristic
3#10593795C211yesmaximal, characteristic
4#10593500C212yesmaximal
5#10593499C212yesmaximal
6#10593447C212yesmaximal, complemented
7C4×#3776C214yesmaximal, complemented
8#10593393C212yesmaximal, complemented
9C22×#627C2211yescharacteristic
10C2×#3776C2214yes—
11C2×C4×C3⋊Dic3C2211yescharacteristic
12C3×#926—21no—
13C2×C3×C4×Dic3—21no—
14#63982—21no—
15#63982C2212yes—
16C2×#3724C2211yescharacteristic
17C2×Dic3⋊Dic3—21no—
18#63919C2211yescharacteristic
19#63919C2211yescharacteristic
20C4×#627—21no—
21C4×#627—21no—
22C4×#627—21no—
23C4×#627C2212yes—
24C4×#627C2212yes—
25C4×#627C2212yes—
26#63872—21no—
27C22⋊#622C2212yes—
28C4⋊#622C2212yes—
29C4×#622C2212yes—
30#63743C2214yes—
31#63740C2214yes—
32#63740C2214yes—
33#5517—61no—
34C2×C4×Dic6—61no—
35C22×C32×C4D411yescharacteristic
36C22×C3⋊Dic3D411yescharacteristic
37C22×C3⋊Dic3C2311yescharacteristic
38C22×C3×Dic3—21no—
39C22×C3×Dic3—21no—
40C2×#627—21no—
41C2×#627—24no—
42C2×#627—21no—
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×C4⋊Dic3—21no—
54C3×C4×Dic3—22no—
55C3×C4×Dic3—22no—
56C3×C4×Dic3—22no—
57#3724—21no—
58#3724—21no—
59#3724C2312yes—
60#3724C2312yes—
61Dic3⋊Dic3—22no—
62Dic3⋊Dic3—22no—
63Dic3⋊Dic3—22no—
64Dic3⋊Dic3—22no—
65#3104—91nomaximal, Sylow
66C22×Dic6—61no—
67C3×#117—61no—
68C2×C3×C42—61no—
69#926—21no—
70C2×C4⋊Dic3—61no—
71C2×Dic3⋊C4—61no—
72C2×Dic3⋊C4—61no—
73C2×C4×Dic3—21no—
74C2×C4×Dic3—61no—
75C2×C4×Dic3—61no—
76#890—61no—
77#890—61no—
78#888—61no—
79#888—61no—
80#878—62no—
81#878—62no—
82C4×Dic6—62no—
83C4×Dic6—62no—
84C4×Dic6—62no—
85C4×Dic6—62no—
86C4×Dic6—62no—
87C4×Dic6—62no—
88C23×C32C2×D411yescharacteristic
89C2×C32×C4Q1614yescomplemented
90C2×C32×C4C2×D411yescharacteristic
91C2×C32×C4C2×D411yescharacteristic
92C2×C3⋊Dic3—22no—
93C2×C3⋊Dic3—41no—
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—
104#627—24no—
105#627—22no—
106#627—24no—
107#627—42no—
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—
118C22×C3×C4—21no—
119C22×C3×C4—21no—
120C22×C3×C4—61no—
121C22×C3×C4—61no—
122C22×Dic3—21no—
123C22×Dic3—21no—
124C22×Dic3—61no—
125C22×Dic3—61no—
126C22×Dic3—61no—
127C22×Dic3—61no—
128C2×Dic6—62no—
129C2×Dic6—62no—
130C2×Dic6—62no—
131C2×Dic6—68no—
132C2×Dic6—62no—
133C3×C4⋊C4—61no—
134C3×C4⋊C4—61no—
135C3×C22⋊C4—62no—
136C3×C42—62no—
137C3×C42—62no—
138C3×C42—62no—
139#217—22no—
140C4⋊Dic3—21no—
141C4⋊Dic3—21no—
142C4⋊Dic3—62no—
143C4⋊Dic3—62no—
144C4⋊Dic3—62no—
145C4⋊Dic3—62no—
146Dic3⋊C4—62no—
147Dic3⋊C4—62no—
148Dic3⋊C4—62no—
149Dic3⋊C4—62no—
150Dic3⋊C4—62no—
151Dic3⋊C4—62no—
152Dic3⋊C4—62no—
153Dic3⋊C4—62no—
154C4×Dic3—22no—
155C4×Dic3—22no—
156C4×Dic3—22no—
157C4×Dic3—61no—
158C4×Dic3—61no—
159C4×Dic3—61no—
160C4×Dic3—61no—
161C4×Dic3—61no—
162C4×Dic3—61no—
163C4×Dic3—61no—
164C4×Dic3—61no—
165C22×C32—21no—
166C22×C32—21no—
167C22×C32C2×Q1612yes—
168C22×C32C22×D411yescharacteristic
169C32×C4C2×Q1612yes—
170C32×C4C2×Q1612yes—
171C3⋊Dic3—21no—
172C3⋊Dic3—21no—
173C3⋊Dic3—21no—
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—92no—
185C22⋊Q8—181no—
186C4×Q8—92no—
187C4×Q8—92no—
188C4×Q8—92no—
189C4×Q8—181no—
190C4×Q8—181no—
191C4×Q8—181no—
192#117—61no—
193C2×C4⋊C4—91no—
194C2×C4⋊C4—181no—
195C2×C42—61no—
196C2×C42—91no—
197#107—94no—
198C4⋊C8—92no—
199#103—94no—
200#103—94no—
201C22⋊C8—92no—
202C4×C8—92no—
203C23×C3—21no—
204C23×C3—21no—
205C2×C3×C4—21no—
206C2×C3×C4—21no—
207C2×C3×C4—21no—
208C2×C3×C4—21no—
209C2×C3×C4—24no—
210C2×C3×C4—24no—
211C2×C3×C4—62no—
212C2×C3×C4—64no—
213C2×C3×C4—62no—
214C2×C3×C4—62no—
215C2×C3×C4—62no—
216C2×C3×C4—122no—
217C2×Dic3—22no—
218C2×Dic3—24no—
219C2×Dic3—22no—
220C2×Dic3—22no—
221C2×Dic3—22no—
222C2×Dic3—42no—
223C2×Dic3—61no—
224C2×Dic3—61no—
225C2×Dic3—61no—
226C2×Dic3—61no—
227C2×Dic3—61no—
228C2×Dic3—61no—
229C2×Dic3—61no—
230C2×Dic3—61no—
231C2×Dic3—64no—
232C2×Dic3—122no—
233C2×Dic3—122no—
234C2×Dic3—122no—
235Dic6—64no—
236Dic6—64no—
237Dic6—68no—
238Dic6—124no—
239Dic6—124no—
240C2×C32—22no—
241C2×C32#52511yescharacteristic
242C2×C32C22×Q1611yescharacteristic
243C2×C32#57511yescharacteristic
244C2×Q8—92no—
245C2×Q8—92no—
246C2×Q8—181no—
247C2×Q8—181no—
248C2×Q8—184no—
249C22×C4—61no—
250C22×C4—61no—
251C22×C4—91no—
252C22×C4—91no—
253C22×C4GO+(4,𝔽2)11yescharacteristic
254Q16—188no—
255C2×C8—94no—
256C4⋊C4—61no—
257C4⋊C4—61no—
258C4⋊C4—92no—
259C4⋊C4—92no—
260C4⋊C4—181no—
261C4⋊C4—182no—
262C4⋊C4—182no—
263C4⋊C4—182no—
264C4⋊C4—182no—
265C4⋊C4—181no—
266C22⋊C4—62no—
267C42—62no—
268C42—62no—
269C42—62no—
270C42—91no—
271C42—91no—
272C42—91no—
273C42—91no—
274C22×C3—22no—
275C22×C3—22no—
276C22×C3—21no—
277C22×C3—21no—
278C22×C3—22no—
279C22×C3—22no—
280C22×C3—41no—
281C22×C3—41no—
282C3×C4—22no—
283C3×C4—22no—
284C3×C4—22no—
285C3×C4—22no—
286C3×C4—64no—
287C3×C4—122no—
288C3×C4—122no—
289C3×C4—122no—
290Dic3—24no—
291Dic3—42no—
292Dic3—42no—
293Dic3—42no—
294Dic3—62no—
295Dic3—62no—
296Dic3—62no—
297Dic3—62no—
298Dic3—121no—
299Dic3—121no—
300Dic3—121no—
301Dic3—121no—
302C32#310411yescharacteristic, complemented, Sylow
303C23C2×GO+(4,𝔽2)11yescharacteristic
304Q8—94no—
305Q8—182no—
306Q8—184no—
307Q8—184no—
308Q8—362no—
309C2×C4—64no—
310C2×C4—62no—
311C2×C4—62no—
312C2×C4—62no—
313C2×C4—62no—
314C2×C4—91no—
315C2×C4—91no—
316C2×C4—91no—
317C2×C4—91no—
318C2×C4—122no—
319C2×C4—182no—
320C2×C4—361no—
321C2×C4#377614yescomplemented
322C2×C4C2×GO+(4,𝔽2)11yescharacteristic
323C2×C4C2×GO+(4,𝔽2)11yescharacteristic
324C8—184no—
325C2×C3—24no—
326C2×C3—21no—
327C2×C3—21no—
328C2×C3—21no—
329C2×C3—21no—
330C2×C3—21no—
331C2×C3—21no—
332C2×C3—42no—
333C22—21no—
334C22—21no—
335C22C2×#377612yes—
336C22C22×GO+(4,𝔽2)11yescharacteristic
337C4—64no—
338C4—92no—
339C4—122no—
340C4—122no—
341C4—122no—
342C4—181no—
343C4—181no—
344C4—181no—
345C4C2×#377612yes—
346C4C2×#377612yes—
347C3—21no—
348C3—21no—
349C2—22no—
350C2#1059649911yescharacteristic
351C2#1059651011yescharacteristic
352C2C22×#377611yescharacteristic
subgroupG/H
centerC2×C4C2×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FrattiniC22C22×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C22×D4
prime radicalC23×C32C2×D4
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#3104
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
6. #10593447C2semidirect
7. C4×#3776C2semidirect
8. #10593393C2semidirect
89. C2×C32×C4Q16semidirect
302. C32#3104semidirect
321. C2×C4#3776semidirect

Maximal subgroups

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

subgroupindex
#105950502
C2×C4×#6272
#105937952
#105935002
#105934992
#105934472
C4×#37762
#105933932
#31049