Finite Group Databasebeta

← #11794661

Subgroups — #11794661

Order 1152.

677 conjugacy classes of subgroups; only the 140 normal subgroups are shown.

normal subgroups only

This group has 677 conjugacy classes of subgroups — too many to draw. Only its 140 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#10592687C211yesmaximal, characteristic
2#10591359C211yesmaximal, characteristic, complemented
3C2×#63564C212yesmaximal
4C3×#4529C212yesmaximal, complemented
5#10589156C211yesmaximal, characteristic, complemented
6#68902—32nomaximal
7C22×C4⋊(C3⋊D3)C2211yescharacteristic
8C2×C32×C4⋊C4C2211yescharacteristic
9C2×#3752—21no—
10C2×#3752—21no—
11C2×C4×C3⋊Dic3C2211yescharacteristic
12C2×C3×C4⋊Dic3C2212yes—
13C22×C3×C3⋊C8C2212yes—
14C2×#3724—21no—
15C2×#3724—21no—
16#63564—24no—
17C2×#821—32no—
18#4988—32no—
19#4988—61no—
20#4975—32no—
21C2×#809—32no—
22C3×#340—32no—
23#4550—32no—
24#4529D312yescomplemented
25C23×C3⋊D3—21no—
26C22×C32×C4—21no—
27C22×C32×C4C2311yescharacteristic
28C22×C3⋊Dic3D411yescharacteristic
29C22×C3⋊Dic3D411yescharacteristic
30C2×C4⋊(C3⋊D3)—22no—
31C2×C4⋊(C3⋊D3)—22no—
32C2×C4⋊(C3⋊D3)—21no—
33C2×C4⋊(C3⋊D3)D412yes—
34C22×C3×Dic3—22no—
35C32×C4⋊C4—22no—
36#3752—42no—
37#3752—42no—
38C4×C3⋊Dic3—22no—
39C3×C4⋊Dic3—22no—
40C3×C4⋊Dic3—22no—
41C2×C3×C3⋊C8—22no—
42C2×C3×C3⋊C8—22no—
43C2×C3×C3⋊C8—22no—
44#3724—42no—
45#3724—42no—
46#2071—91noSylow
47C22×D12—32no—
48C22×D12—61no—
49C22×C3×C8—32no—
50C2×C3×C4⋊C4—21no—
51C2×C3×C4⋊C4—32no—
52C2×C3×C4⋊C4C2×D312yes—
53C2×(C2×D3)⋊C4—62no—
54C2×(C2×D3)⋊C4—62no—
55C2×(C2×D3)⋊C4—62no—
56C2×(C2×D3)⋊C4—62no—
57C2×C4⋊Dic3C2×D312yes—
58C2×Dic3⋊C4—62no—
59C2×Dic3⋊C4—62no—
60C2×C4×Dic3—32no—
61C2×C4×Dic3—61no—
62C22×C3⋊C8C2×D312yes—
63#821—64no—
64#809—64no—
65C23×C32C2×D411yescharacteristic
66C22×C3⋊D3—22no—
67C22×C3⋊D3—41no—
68C22×C3⋊D3—41no—
69C22×C3⋊D3—41no—
70C22×C3⋊D3—41no—
71C22×C3⋊D3—41no—
72C22×C3⋊D3—41no—
73C2×C32×C4—41no—
74C2×C32×C4—41no—
75C2×C32×C4—41no—
76C2×C32×C4C2×D411yescharacteristic
77C2×C32×C4#4111yescharacteristic
78C2×C32×C4#4112yes—
79C2×C32×C4#4112yes—
80C2×C3⋊Dic3—21no—
81C2×C3⋊Dic3—21no—
82C2×C3⋊Dic3—21no—
83C2×C3⋊Dic3—21no—
84C2×C3⋊Dic3D812yes—
85C2×C3⋊Dic3SD1612yes—
86C4⋊(C3⋊D3)—24no—
87C4⋊(C3⋊D3)—42no—
88C2×C3×Dic3—42no—
89C2×C3×Dic3—42no—
90C2×C3×Dic3—42no—
91C3×C3⋊C8—42no—
92C2×#102—92no—
93#390—91no—
94#384—91no—
95#340—32no—
96#336—91no—
97C23×D3—62no—
98C23×D3—62no—
99C22×C3×C4—22no—
100C22×C3×C4—22no—
101C22×C3×C4—21no—
102C22×C3×C4—62no—
103C22×C3×C4C22×D312yes—
104C22×Dic3—22no—
105C22×Dic3—32no—
106C22×Dic3—32no—
107C22×Dic3—61no—
108C22×Dic3—61no—
109C2×D12—34no—
110C2×D12—62no—
111C2×D12—62no—
112C2×D12—62no—
113C2×D12—62no—
114C2×D12—62no—
115C2×D12—62no—
116C2×D12—62no—
117C2×D12—122no—
118C2×D12—122no—
119C2×C3×C8—62no—
120C2×C3×C8—62no—
121C2×C3×C8—62no—
122C3×C4⋊C4—22no—
123C3×C4⋊C4—22no—
124C3×C4⋊C4—42no—
125C3×C4⋊C4—62no—
126C3×C4⋊C4—62no—
127(C2×D3)⋊C4—124no—
128(C2×D3)⋊C4—124no—
129(C2×D3)⋊C4—124no—
130(C2×D3)⋊C4—124no—
131C4⋊Dic3—22no—
132C4⋊Dic3—22no—
133Dic3⋊C4—124no—
134Dic3⋊C4—124no—
135C4×Dic3—62no—
136C4×Dic3—62no—
137C4×Dic3—122no—
138C2×C3⋊C8—22no—
139C2×C3⋊C8—22no—
140C2×C3⋊C8—22no—
141C22×C32#12111yescharacteristic
142C22×C32#12311yescharacteristic
143C22×C32#12411yescharacteristic
144C22×C32C2×D811yescharacteristic
145C22×C32C2×SD1611yescharacteristic
146C22×C32AGL(1,ℤ/8)11yescharacteristic
147C22×C32#13711yescharacteristic
148C2×C3⋊D3—42no—
149C2×C3⋊D3—42no—
150C2×C3⋊D3—42no—
151C2×C3⋊D3—81no—
152C2×C3⋊D3—81no—
153C2×C3⋊D3—81no—
154C2×C3⋊D3—81no—
155C32×C4—81no—
156C32×C4#12312yes—
157C32×C4#12612yes—
158C3⋊Dic3—22no—
159C3⋊Dic3—22no—
160C3×Dic3—82no—
161C22×D4—91no—
162C22×C8—32no—
163C2×C4⋊C4—32no—
164C2×C4⋊C4—181no—
165C2×C4⋊C4—181no—
166C2×C4⋊C4D3211yescharacteristic
167C2×C22⋊C4—181no—
168C2×C22⋊C4—181no—
169C2×C42—91no—
170#102—184no—
171C23×C3—21no—
172C23×C3D3×D412yes—
173C22×D3—64no—
174C22×D3—64no—
175C22×D3—122no—
176C22×D3—122no—
177C22×D3—122no—
178C22×D3—122no—
179C22×D3—122no—
180C22×D3—122no—
181C22×D3—122no—
182C22×D3—122no—
183C22×D3—122no—
184C22×D3—122no—
185C22×D3—122no—
186C22×D3—122no—
187C2×C3×C4—21no—
188C2×C3×C4—22no—
189C2×C3×C4—21no—
190C2×C3×C4—22no—
191C2×C3×C4—42no—
192C2×C3×C4—42no—
193C2×C3×C4—42no—
194C2×C3×C4—42no—
195C2×C3×C4—42no—
196C2×C3×C4—42no—
197C2×C3×C4—122no—
198C2×C3×C4—122no—
199C2×C3×C4—122no—
200C2×C3×C4#23512yes—
201C2×C3×C4#23512yes—
202C2×C3×C4#23512yes—
203C2×C3×C4D3×D412yes—
204C2×C3×C4#23712yes—
205C2×C3×C4#23912yes—
206C2×Dic3—34no—
207C2×Dic3—34no—
208C2×Dic3—42no—
209C2×Dic3—42no—
210C2×Dic3—42no—
211C2×Dic3—62no—
212C2×Dic3—62no—
213C2×Dic3—62no—
214C2×Dic3—62no—
215C2×Dic3—62no—
216C2×Dic3—62no—
217C2×Dic3—121no—
218C2×Dic3—121no—
219C2×Dic3—121no—
220C2×Dic3—121no—
221D12—64no—
222D12—64no—
223D12—124no—
224D12—124no—
225D12—122no—
226D12—122no—
227C3×C8—122no—
228C3⋊C8—42no—
229C2×C32#39711yescharacteristic
230C2×C32#45911yescharacteristic
231C2×C32#46111yescharacteristic
232C2×C32#48011yescharacteristic
233C2×C32#48111yescharacteristic
234C2×C32#48611yescharacteristic
235C2×C32#48911yescharacteristic
236C3⋊D3—82no—
237C24—181no—
238C2×D4—92no—
239C2×D4—181no—
240C2×D4—182no—
241C2×D4—182no—
242C22×C4—21no—
243C22×C4—62no—
244C22×C4—91no—
245C22×C4—91no—
246C22×C4C2×D3211yescharacteristic
247C2×C8—62no—
248C2×C8—62no—
249C2×C8—62no—
250C4⋊C4—22no—
251C4⋊C4—62no—
252C4⋊C4—62no—
253C4⋊C4—362no—
254C4⋊C4—362no—
255C22⋊C4—362no—
256C22⋊C4—362no—
257C42—182no—
258C22×C3—21no—
259C22×C3—21no—
260C22×C3—21no—
261C22×C3—21no—
262C22×C3—21no—
263C22×C3—21no—
264C22×C3—21no—
265C22×C3#88412yes—
266C22×C3#88512yes—
267C22×C3#89412yes—
268C22×C3D3×D812yes—
269C22×C3D3×SD1612yes—
270C22×C3#91412yes—
271C22×C3#91812yes—
272C2×D3—124no—
273C2×D3—124no—
274C2×D3—124no—
275C2×D3—124no—
276C2×D3—124no—
277C2×D3—124no—
278C2×D3—242no—
279C2×D3—242no—
280C2×D3—242no—
281C2×D3—242no—
282C2×D3—242no—
283C2×D3—242no—
284C2×D3—242no—
285C2×D3—242no—
286C3×C4—22no—
287C3×C4—22no—
288C3×C4—82no—
289C3×C4—82no—
290C3×C4—242no—
291C3×C4#87612yes—
292C3×C4#88312yes—
293C3×C4#89412yes—
294C3×C4#89812yes—
295Dic3—64no—
296Dic3—64no—
297Dic3—82no—
298Dic3—122no—
299Dic3—122no—
300C32#207111yescharacteristic, complemented, Sylow
301C23—182no—
302C23—361no—
303C23—361no—
304C23—361no—
305C23—361no—
306C23—361no—
307C23—361no—
308C23#381111yescharacteristic
309D4—184no—
310D4—362no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—92no—
315C2×C4—92no—
316C2×C4—122no—
317C2×C4—122no—
318C2×C4—122no—
319C2×C4—181no—
320C2×C4—181no—
321C2×C4—181no—
322C2×C4—181no—
323C2×C4#379811yescharacteristic
324C2×C4#379912yes—
325C2×C4#380211yescharacteristic
326C2×C4#380412yes—
327C8—122no—
328C2×C3—21no—
329C2×C3—21no—
330C2×C3—21no—
331C2×C3—21no—
332C2×C3—21no—
333C2×C3—21no—
334C2×C3—21no—
335C2×C3#467512yes—
336C2×C3#476012yes—
337C2×C3#478612yes—
338C2×C3#479412yes—
339C2×C3#481812yes—
340C2×C3#486312yes—
341C2×C3#488212yes—
342D3—244no—
343D3—244no—
344C22—362no—
345C22—362no—
346C22—362no—
347C22—721no—
348C22—721no—
349C22—721no—
350C22—721no—
351C22#6389711yescharacteristic
352C22#6391211yescharacteristic
353C22#6392611yescharacteristic
354C22#6393011yescharacteristic
355C22#6394111yescharacteristic
356C22#6394511yescharacteristic
357C22#6395311yescharacteristic
358C4—81no—
359C4—182no—
360C4—182no—
361C4—242no—
362C4#6385412yes—
363C4#6386812yes—
364C3—21no—
365C3#6890212yescomplemented
366C2—722no—
367C2#1059044211yescharacteristic
368C2#1059044511yescharacteristic
369C2#1059055111yescharacteristic
370C2#1059056511yescharacteristic
371C2#1059121611yescharacteristic
372C2#1059140211yescharacteristic
373C2#1059163211yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC2×C4⋊C4D32
hypocenterC32#2071
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #10591359C2semidirect
4. C3×#4529C2semidirect
5. #10589156C2semidirect
24. #4529D3semidirect
300. C32#2071semidirect
365. C3#68902semidirect

Maximal subgroups

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

subgroupindex
#105926872
#105913592
C2×#635642
C3×#45292
#105891562
#689023