Finite Group Databasebeta

← #11798617

Subgroups — #11798617

Order 1152.

535 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 535 conjugacy classes of subgroups — too many to draw. Only its 68 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×#5713C211yesmaximal, characteristic, complemented
2C3×#5077C211yesmaximal, characteristic
3#10591533C212yesmaximal, complemented
4#10589411C211yesmaximal, characteristic, complemented
5#10589176C212yesmaximal, complemented
6#71946—31nomaximal
7#70986—31nomaximal
8C3×#1004C2211yescharacteristic
9C32×#127C2211yescharacteristic
10C3×#936—22no—
11C3×#935—21no—
12C3×#935C2212yes—
13C3×D4×Dic3—22no—
14C3×#932—21no—
15C3×C4×Dic6—21no—
16#63961—22no—
17#63661C2212yes—
18C3×#833C2211yescharacteristic
19C3×#805—21no—
20#63580—22no—
21C3×#559—31no—
22#5713D311yescharacteristic, complemented
23C3×#453—31no—
24#5243—32no—
25#5077D311yescharacteristic
26#5053—32no—
27#4545—31no—
28#4545—31no—
29#4545—61no—
30#4539—32no—
31#4476—32no—
32C2×C32×D4—22no—
33C2×C32×D4D411yescharacteristic
34C2×C32×D4C2311yescharacteristic
35C2×C3×#67—22no—
36C22×C3×Dic3—21no—
37C22×C3×Dic3D412yes—
38C3×#237—41no—
39C3×D3×D4—41no—
40C3×#235—21no—
41C2×C3×Dic6—21no—
42C32×C42D411yescharacteristic
43#3757—22no—
44C3×#217—22no—
45C3×#217—21no—
46C3×#217—22no—
47C3×#217D412yes—
48C3×#214—41no—
49C3×#213—41no—
50C3×C4⋊Dic3—21no—
51C3×Dic3⋊C4—22no—
52C3×C4×Dic3—22no—
53C3×#208—21no—
54#3724—42no—
55(C2×D3)⋊Dic3—42no—
56#2198—91noSylow
57C3×H(5,𝔽2)—31no—
58#1004C2×D311yescharacteristic
59C3×AGL(1,ℤ/8)—61no—
60C3×#127—21no—
61C3×#127C2×D311yescharacteristic
62C3×#127C2×D311yescharacteristic
63C3×#124—62no—
64C3×#123—32no—
65C3×#123—61no—
66C3×C4×Q8—61no—
67C3×C4×D4—62no—
68#936—22no—
69#935—21no—
70#935—62no—
71#935C2×D312yes—
72D4×Dic3—22no—
73#932—21no—
74#929—62no—
75C4×Dic6—21no—
76C3×#104—61no—
77C3×#100—31no—
78#834—32no—
79#834—32no—
80#834—62no—
81#834—62no—
82#833C2×D311yescharacteristic
83#806—62no—
84#805—21no—
85C23×C32—21no—
86C23×C32C2×D412yes—
87C22×C3×D3—22no—
88C32×D4—41no—
89C32×D4—41no—
90C32×D4—44no—
91C2×C32×C4—21no—
92C2×C32×C4C2×D411yescharacteristic
93C2×C3⋊Dic3—42no—
94C3×#67—42no—
95C3×#67—41no—
96C2×C3×Dic3—22no—
97C2×C3×Dic3—22no—
98C2×C3×Dic3—22no—
99C2×C3×Dic3—42no—
100C2×C3×Dic3—81no—
101C3×D12—21no—
102C3×C4×D3—41no—
103C3×Dic6—21no—
104C3×Dic6—42no—
105C3×C3⋊C8—41no—
106#559—31no—
107#458—92no—
108#453—31no—
109#353—91no—
110#352—92no—
111C3×#41—61no—
112C3×#41—121no—
113C2×C3×Q8—61no—
114C2×C3×D4—22no—
115C2×C3×D4—22no—
116C2×C3×D4—21no—
117C2×C3×D4—21no—
118C2×C3×D4—42no—
119C2×C3×D4—62no—
120C2×C3×D4—121no—
121C2×C3×D4#6711yescharacteristic
122C2×C3×D4#6711yescharacteristic
123C2×C3×D4C22×D311yescharacteristic
124C2×C3×D4C22×D311yescharacteristic
125C22×C3×C4—32no—
126C22×C3×C4—61no—
127C2×#67—22no—
128C22×Dic3—21no—
129C22×Dic3#6712yes—
130#237—41no—
131D3×D4—41no—
132#235—21no—
133C2×Dic6—21no—
134C3×SD16—121no—
135C3×D8—121no—
136C3×M16—61no—
137C3×C4⋊C4—61no—
138C3×C4⋊C4—62no—
139C3×C22⋊C4—32no—
140C3×C22⋊C4—62no—
141C3×C22⋊C4—61no—
142C3×C22⋊C4—62no—
143C3×C42—21no—
144C3×C42—62no—
145C3×C42#6711yescharacteristic
146C3×C42#6711yescharacteristic
147#217—22no—
148#217—21no—
149#217—22no—
150#217—62no—
151#217—62no—
152#217—122no—
153#217—122no—
154#217#6712yes—
155#214—41no—
156#213—41no—
157(C2×D3)⋊C4—122no—
158C4⋊Dic3—21no—
159Dic3⋊C4—22no—
160Dic3⋊C4—122no—
161Dic3⋊C4—122no—
162C4×Dic3—22no—
163#208—21no—
164C22×C32—22no—
165C22×C32—42no—
166C22×C32—42no—
167C22×C32—41no—
168C22×C32#12011yescharacteristic
169C2×C3×D3—41no—
170C2×C3×D3—82no—
171C32×C4—22no—
172C32×C4—21no—
173C3⋊Dic3—82no—
174C3×Dic3—42no—
175C3×Dic3—41no—
176C3×Dic3—42no—
177H(5,𝔽2)—31no—
178AGL(1,ℤ/8)—61no—
179#127D3211yescharacteristic
180#124—62no—
181#123—32no—
182#123—61no—
183#123—182no—
184C4×Q8—61no—
185C4×D4—62no—
186#104—61no—
187#100—31no—
188#99—92no—
189#99—182no—
190C23×C3—21no—
191C23×C3—21no—
192C23×C3—22no—
193C23×C3—41no—
194C23×C3—62no—
195C23×C3D3×D412yes—
196C23×C3C2×#6712yes—
197C22×D3—22no—
198C3×Q8—61no—
199C3×Q8—122no—
200C3×D4—41no—
201C3×D4—41no—
202C3×D4—41no—
203C3×D4—41no—
204C3×D4—44no—
205C3×D4—44no—
206C3×D4—61no—
207C3×D4—81no—
208C3×D4—81no—
209C3×D4—84no—
210C3×D4—122no—
211C3×D4—121no—
212C2×C3×C4—21no—
213C2×C3×C4—21no—
214C2×C3×C4—21no—
215C2×C3×C4—41no—
216C2×C3×C4—62no—
217C2×C3×C4—62no—
218C2×C3×C4—62no—
219C2×C3×C4—121no—
220C2×C3×C4—122no—
221C2×C3×C4—241no—
222C2×C3×C4C2×#6711yescharacteristic
223C2×C3×C4C2×#6711yescharacteristic
224#67—42no—
225#67—41no—
226C2×Dic3—22no—
227C2×Dic3—22no—
228C2×Dic3—22no—
229C2×Dic3—42no—
230C2×Dic3—81no—
231C2×Dic3—122no—
232C2×Dic3—122no—
233C2×Dic3—242no—
234D12—21no—
235C4×D3—41no—
236Dic6—21no—
237Dic6—42no—
238C3×C8—121no—
239C3⋊C8—41no—
240C2×C32—21no—
241C2×C32—42no—
242C2×C32—81no—
243C2×C32B(4,𝔽2)11yescharacteristic
244C3×D3—81no—
245#41—61no—
246#41—121no—
247C2×Q8—61no—
248C2×D4—22no—
249C2×D4—62no—
250C2×D4—121no—
251C2×D4#62511yescharacteristic
252C2×D4C2×D3211yescharacteristic
253C22×C4—32no—
254C22×C4—61no—
255SD16—121no—
256D8—121no—
257M16—61no—
258C4⋊C4—61no—
259C4⋊C4—62no—
260C4⋊C4—362no—
261C22⋊C4—32no—
262C22⋊C4—62no—
263C22⋊C4—61no—
264C22⋊C4—62no—
265C22⋊C4—182no—
266C22⋊C4—362no—
267C42—62no—
268C42#62511yescharacteristic
269C22×C3—22no—
270C22×C3—22no—
271C22×C3—21no—
272C22×C3—42no—
273C22×C3—42no—
274C22×C3—42no—
275C22×C3—42no—
276C22×C3—42no—
277C22×C3—41no—
278C22×C3—41no—
279C22×C3—81no—
280C22×C3—82no—
281C22×C3—82no—
282C22×C3—121no—
283C22×C3—242no—
284C22×C3#93711yescharacteristic
285C22×C3#95311yescharacteristic
286C2×D3—41no—
287C2×D3—82no—
288C3×C4—22no—
289C3×C4—22no—
290C3×C4—21no—
291C3×C4—21no—
292C3×C4—41no—
293C3×C4—42no—
294C3×C4—122no—
295C3×C4—121no—
296C3×C4—122no—
297Dic3—42no—
298Dic3—42no—
299Dic3—41no—
300Dic3—242no—
301Dic3—242no—
302Dic3—482no—
303C32#219811yescharacteristic, complemented, Sylow
304C23—21no—
305C23—62no—
306C23D3×#6712yes—
307Q8—61no—
308Q8—122no—
309D4—41no—
310D4—41no—
311D4—44no—
312D4—61no—
313D4—122no—
314D4—121no—
315C2×C4—21no—
316C2×C4—62no—
317C2×C4—62no—
318C2×C4—62no—
319C2×C4—121no—
320C2×C4—122no—
321C2×C4—241no—
322C2×C4—362no—
323C2×C4C2×#62511yescharacteristic
324C8—121no—
325C2×C3—21no—
326C2×C3—21no—
327C2×C3—21no—
328C2×C3—41no—
329C2×C3—42no—
330C2×C3—42no—
331C2×C3—82no—
332C2×C3—81no—
333C2×C3—81no—
334C2×C3—161no—
335C2×C3—241no—
336C2×C3#503211yescharacteristic
337C2×C3#524411yescharacteristic
338D3—81no—
339C22—22no—
340C22—42no—
341C22—42no—
342C22—41no—
343C22—121no—
344C22—242no—
345C22#6397611yescharacteristic
346C4—22no—
347C4—21no—
348C4—122no—
349C4—121no—
350C4—122no—
351C4—722no—
352C3—21no—
353C3#7098611yescharacteristic, complemented
354C3#7194611yescharacteristic, complemented
355C2—21no—
356C2—42no—
357C2—81no—
358C2—241no—
359C2#1059153011yescharacteristic
subgroupG/H
centerC2#10591530
commutator, cosocleC2×C32×D4C23
FrattiniC2×D4C2×D32
FittingC32×#127C22
socleC2×C32B(4,𝔽2)
prime radicalC3×#5077C2
hypercenter#127D32
hypocenterC32#2198
LCSG ▷ C2×C32×D4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #127

Complements

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

NH ≅ G/Ntype
1. C3×#5713C2semidirect
3. #10591533C2semidirect
4. #10589411C2semidirect
5. #10589176C2semidirect
22. #5713D3semidirect
303. C32#2198semidirect
353. C3#70986semidirect
354. C3#71946semidirect

Maximal subgroups

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

subgroupindex
C3×#57132
C3×#50772
#105915332
#105894112
#105891762
#719463
#709863