Finite Group Databasebeta

← #11778368

Subgroups — #11778368

Order 1152.

567 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 567 conjugacy classes of subgroups — too many to draw. Only its 92 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×#5500C211yesmaximal, characteristic
2#10592678C211yesmaximal, characteristic
3#10591190C212yesmaximal
4C3×#4528C211yesmaximal, characteristic
5#10589152C212yesmaximal
6#71904—31nomaximal
7#68139—31nomaximal
8C22×#634C2211yescharacteristic
9C2×C32×C4⋊C4C2211yescharacteristic
10C2×#3750—21no—
11C3×#926—21no—
12C3×#924—21no—
13C3×#924C2212yes—
14C3×#890—22no—
15C3×#888—22no—
16C2×#3719—22no—
17#63658—21no—
18#63658C2211yescharacteristic
19C3×#830C2212yes—
20#63567—22no—
21C3×#544—31no—
22#5500D311yescharacteristic
23#5050—32no—
24#4979—31no—
25#4979—31no—
26#4979—61no—
27#4739—32no—
28C3×#324—31no—
29#4538—32no—
30#4528D311yescharacteristic
31#4467—32no—
32C22×C32×C4D411yescharacteristic
33C22×C32×C4D411yescharacteristic
34C22×C32×C4C2311yescharacteristic
35C22×C3⋊Dic3—21no—
36C22×C3⋊Dic3—21no—
37C2×#634—22no—
38C2×#634—42no—
39C2×C3×Dic6—21no—
40C2×C3×Dic6D412yes—
41C32×C4⋊C4—22no—
42#3750—42no—
43C3×#217—22no—
44C3×C4⋊Dic3—21no—
45C3×C4⋊Dic3—21no—
46C3×C4⋊Dic3—21no—
47C3×C4⋊Dic3D412yes—
48C3×Dic3⋊C4—22no—
49C3×Dic3⋊C4—22no—
50C3×C4×Dic3—22no—
51C2×C3×C3⋊C8—22no—
52#3719—44no—
53#1605—91noSylow
54C22×Dic6—31no—
55C22×Dic6—31no—
56C22×Dic6—61no—
57C3×C4⋊Q8—62no—
58C3×#125—62no—
59C3×C22⋊Q8—32no—
60C3×C22⋊Q8—61no—
61C3×#117—61no—
62C2×C3×C4⋊C4—21no—
63C2×C3×C4⋊C4C2×D311yescharacteristic
64C2×C3×C4⋊C4C2×D311yescharacteristic
65C2×#216—62no—
66#926—21no—
67#924—21no—
68#924C2×D312yes—
69C2×Dic3⋊C4—62no—
70C2×Dic3⋊C4—61no—
71C2×Dic3⋊C4—61no—
72C2×Dic12—62no—
73#890—22no—
74#888—22no—
75C3×C22⋊C8—32no—
76C3⋊#95—31no—
77C3⋊#95—31no—
78C3⋊#95—61no—
79C3⋊#95—62no—
80C3⋊#95—61no—
81C3⋊#95—61no—
82#830C2×D312yes—
83#816—62no—
84#810—62no—
85C23×C32C2×D411yescharacteristic
86C2×C32×C4—21no—
87C2×C32×C4—21no—
88C2×C32×C4—21no—
89C2×C32×C4—41no—
90C2×C32×C4—41no—
91C2×C32×C4Q1612yescomplemented
92C2×C32×C4C2×D412yes—
93C2×C3⋊Dic3—22no—
94C2×C3⋊Dic3—22no—
95C2×C3⋊Dic3—41no—
96C2×C3⋊Dic3—41no—
97C2×C3⋊Dic3—41no—
98C2×C3⋊Dic3—41no—
99#634—24no—
100#634—42no—
101C2×C3×Dic3—22no—
102C2×C3×Dic3—22no—
103C3×Dic6—42no—
104C3×Dic6—81no—
105C3×C3⋊C8—42no—
106#544—31no—
107#451—92no—
108#395—91no—
109#328—92no—
110#324—31no—
111C2×C3×Q8—32no—
112C2×C3×Q8—61no—
113C22×C3×C4—21no—
114C22×C3×C4—21no—
115C22×C3×C4—21no—
116C22×C3×C4D1211yescharacteristic
117C22×C3×C4D1211yescharacteristic
118C22×C3×C4#6711yescharacteristic
119C22×C3×C4#6711yescharacteristic
120C22×C3×C4C22×D311yescharacteristic
121C22×C3×C4C22×D311yescharacteristic
122C22×Dic3—62no—
123C22×Dic3—62no—
124C22×Dic3—61no—
125C22×Dic3—61no—
126C22×Dic3—61no—
127C22×Dic3—61no—
128C2×Dic6—21no—
129C2×Dic6—62no—
130C2×Dic6—62no—
131C2×Dic6—122no—
132C2×Dic6—122no—
133C2×Dic6—122no—
134C2×Dic6—124no—
135C2×Dic6#6712yes—
136C2×C3×C8—62no—
137C3×C4⋊C4—22no—
138C3×C4⋊C4—22no—
139C3×C4⋊C4—32no—
140C3×C4⋊C4—42no—
141C3×C4⋊C4—62no—
142C3×C4⋊C4—61no—
143C3×C4⋊C4—61no—
144C3×C4⋊C4—61no—
145C3×C4⋊C4—62no—
146C3×C22⋊C4—62no—
147C3×C42—62no—
148#217—22no—
149#216—124no—
150C4⋊Dic3—21no—
151C4⋊Dic3—21no—
152C4⋊Dic3—21no—
153C4⋊Dic3#6712yes—
154Dic3⋊C4—22no—
155Dic3⋊C4—22no—
156Dic3⋊C4—122no—
157Dic3⋊C4—122no—
158Dic3⋊C4—124no—
159C4×Dic3—22no—
160C2×C3⋊C8—22no—
161Dic12—124no—
162C22×C32—21no—
163C22×C32—21no—
164C22×C32#12011yescharacteristic
165C22×C32C2×Q1611yescharacteristic
166C22×C32#13711yescharacteristic
167C32×C4—22no—
168C32×C4—22no—
169C32×C4—41no—
170C3⋊Dic3—42no—
171C3⋊Dic3—42no—
172C3×Dic3—42no—
173C3×Dic3—42no—
174C22×Q8—91no—
175C2×Q16—182no—
176C4⋊Q8—62no—
177#125—62no—
178C22⋊Q8—32no—
179C22⋊Q8—61no—
180#117—61no—
181C2×C4⋊C4—181no—
182C2×C4⋊C4D3211yescharacteristic
183#103—182no—
184C22⋊C8—32no—
185#95—91no—
186#95—181no—
187C23×C3—21no—
188C23×C3C2×D1211yescharacteristic
189C23×C3C2×#6711yescharacteristic
190C3×Q8—122no—
191C3×Q8—241no—
192C2×C3×C4—21no—
193C2×C3×C4—21no—
194C2×C3×C4—21no—
195C2×C3×C4—21no—
196C2×C3×C4—21no—
197C2×C3×C4—21no—
198C2×C3×C4—22no—
199C2×C3×C4—22no—
200C2×C3×C4—41no—
201C2×C3×C4—41no—
202C2×C3×C4—41no—
203C2×C3×C4—41no—
204C2×C3×C4—41no—
205C2×C3×C4—42no—
206C2×C3×C4—41no—
207C2×C3×C4—41no—
208C2×C3×C4—42no—
209C2×C3×C4—62no—
210C2×C3×C4—62no—
211C2×C3×C4Dic1212yescomplemented
212C2×C3×C4#21612yescomplemented
213C2×C3×C4D3×D412yes—
214C2×C3×C4C2×#6712yes—
215C2×Dic3—22no—
216C2×Dic3—22no—
217C2×Dic3—64no—
218C2×Dic3—62no—
219C2×Dic3—62no—
220C2×Dic3—64no—
221C2×Dic3—62no—
222C2×Dic3—62no—
223C2×Dic3—122no—
224C2×Dic3—121no—
225C2×Dic3—121no—
226C2×Dic3—122no—
227C2×Dic3—121no—
228C2×Dic3—121no—
229C2×Dic3—122no—
230C2×Dic3—122no—
231C2×Dic3—121no—
232C2×Dic3—121no—
233C2×Dic3—121no—
234C2×Dic3—121no—
235Dic6—42no—
236Dic6—64no—
237Dic6—64no—
238Dic6—81no—
239Dic6—124no—
240Dic6—122no—
241Dic6—122no—
242Dic6—124no—
243C3×C8—122no—
244C3⋊C8—42no—
245C2×C32—21no—
246C2×C32—21no—
247C2×C32#45111yescharacteristic
248C2×C32#45611yescharacteristic
249C2×C32B(4,𝔽2)11yescharacteristic
250C2×Q8—32no—
251C2×Q8—61no—
252C2×Q8—182no—
253C2×Q8—362no—
254C22×C4—181no—
255C22×C4—181no—
256C22×C4#62611yescharacteristic
257C22×C4#62611yescharacteristic
258C22×C4C2×D3211yescharacteristic
259Q16—364no—
260C2×C8—62no—
261C4⋊C4—22no—
262C4⋊C4—32no—
263C4⋊C4—61no—
264C4⋊C4—61no—
265C4⋊C4—61no—
266C4⋊C4—62no—
267C4⋊C4—62no—
268C4⋊C4—362no—
269C22⋊C4—62no—
270C42—62no—
271C22×C3—22no—
272C22×C3—22no—
273C22×C3—21no—
274C22×C3—21no—
275C22×C3—21no—
276C22×C3—21no—
277C22×C3—21no—
278C22×C3—21no—
279C22×C3—21no—
280C22×C3#88211yescharacteristic
281C22×C3C2×Dic1211yescharacteristic
282C22×C3#90911yescharacteristic
283C22×C3#94211yescharacteristic
284C22×C3C2×#21611yescharacteristic
285C22×C3#95311yescharacteristic
286C3×C4—22no—
287C3×C4—22no—
288C3×C4—22no—
289C3×C4—22no—
290C3×C4—42no—
291C3×C4—42no—
292C3×C4—41no—
293C3×C4—41no—
294C3×C4—81no—
295C3×C4—122no—
296C3×C4—122no—
297Dic3—42no—
298Dic3—42no—
299Dic3—124no—
300Dic3—124no—
301Dic3—122no—
302Dic3—122no—
303Dic3—122no—
304Dic3—122no—
305C32#160511yescharacteristic, complemented, Sylow
306C23C2×#62611yescharacteristic
307Q8—122no—
308Q8—184no—
309Q8—241no—
310Q8—362no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—62no—
317C2×C4—62no—
318C2×C4—182no—
319C2×C4—182no—
320C2×C4—361no—
321C2×C4—361no—
322C2×C4—361no—
323C2×C4—361no—
324C2×C4#371912yescomplemented
325C2×C4D3×#6712yes—
326C8—122no—
327C2×C3—22no—
328C2×C3—22no—
329C2×C3—21no—
330C2×C3—21no—
331C2×C3—21no—
332C2×C3—21no—
333C2×C3—21no—
334C2×C3—21no—
335C2×C3—21no—
336C2×C3#473911yescharacteristic
337C2×C3#474111yescharacteristic
338C2×C3#475211yescharacteristic
339C2×C3#522811yescharacteristic
340C2×C3#524411yescharacteristic
341C2×C3#524611yescharacteristic
342C22—21no—
343C22—21no—
344C22#6383311yescharacteristic
345C22C2×#371911yescharacteristic
346C22#6397711yescharacteristic
347C4—22no—
348C4—22no—
349C4—41no—
350C4—122no—
351C4—122no—
352C4—362no—
353C4—362no—
354C3—21no—
355C3#6813911yescharacteristic, complemented
356C3#7190411yescharacteristic, complemented
357C2—21no—
358C2—21no—
359C2#1059118611yescharacteristic
360C2#1059153111yescharacteristic
361C2#1059164911yescharacteristic
subgroupG/H
centerC22#63977
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#120
prime radicalC23×C32C2×D4
hypercenterC2×C4⋊C4D32
hypocenterC32#1605
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
91. C2×C32×C4Q16semidirect
211. C2×C3×C4Dic12semidirect
212. C2×C3×C4#216semidirect
305. C32#1605semidirect
324. C2×C4#3719semidirect
355. C3#68139semidirect
356. C3#71904semidirect

Maximal subgroups

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

subgroupindex
C3×#55002
#105926782
#105911902
C3×#45282
#105891522
#719043
#681393