Finite Group Databasebeta

← #11790115

Subgroups — #11790115

Order 1152.

418 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 87 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
1C2×C4×#622C211yesmaximal, characteristic
2C2×#63742C211yesmaximal, characteristic
3C2×#63742C211yesmaximal, characteristic
4#10591337C211yesmaximal, characteristic
5#10591328C211yesmaximal, characteristic
6#10590075C211yesmaximal, characteristic
7#10590075C211yesmaximal, characteristic
8C22×#622C2211yescharacteristic
9C22×#622C2211yescharacteristic
10C2×C4×C3⋊Dic3C2211yescharacteristic
11C2×C3×Dic3⋊C4—21no—
12C2×#3724C2211yescharacteristic
13C2×#3724C2211yescharacteristic
14C2×#3724C2211yescharacteristic
15C2×#3724C2211yescharacteristic
16C2×Dic3⋊Dic3—21no—
17C4×#622—22no—
18#63742—22no—
19#63742C414yescomplemented
20C3×C3⋊#95—21no—
21#63579—21no—
22#4976—61no—
23#4647—61no—
24C22×C32×C4D411yescharacteristic
25C22×C3⋊Dic3D411yescharacteristic
26C22×C3⋊Dic3C2311yescharacteristic
27C22×C3×Dic3—21no—
28C22×C3×Dic3—21no—
29C22×C3×Dic3—21no—
30C22×C3×Dic3—21no—
31C2×#622—21no—
32C2×#622—21no—
33C2×#622C2×C412yes—
34C2×#622D412yes—
35C2×#622Q812yes—
36C2×#622Q812yes—
37C4×C3⋊Dic3—21no—
38C4×C3⋊Dic3—21no—
39C3×Dic3⋊C4—42no—
40#3724—21no—
41#3724—21no—
42#3724—21no—
43#3724—21no—
44#3724—21no—
45#3724—21no—
46#3724C2×C412yes—
47#3724C2×C412yes—
48Dic3⋊Dic3—42no—
49#1941—91nomaximal, Sylow
50C2×C3×C4⋊C4—61no—
51C2×C4⋊Dic3—61no—
52C2×Dic3⋊C4—21no—
53C2×Dic3⋊C4—61no—
54C2×Dic3⋊C4—61no—
55C2×Dic3⋊C4—61no—
56C2×Dic3⋊C4—61no—
57C2×Dic3⋊C4—61no—
58C2×C4×Dic3—61no—
59C2×C4×Dic3—61no—
60C3×#95—61no—
61C3⋊#95—21no—
62C3⋊#95—61no—
63C3⋊#95—61no—
64C23×C32C2×D411yescharacteristic
65C2×C32×C4—21no—
66C2×C32×C4—21no—
67C2×C32×C4SD1612yes—
68C2×C3⋊Dic3—21no—
69C2×C3⋊Dic3—21no—
70C2×C3⋊Dic3SD1612yes—
71C2×C3⋊Dic3C22×C411yescharacteristic
72C2×C3⋊Dic3C2×D411yescharacteristic
73C2×C3⋊Dic3C2×Q811yescharacteristic
74C2×C3⋊Dic3C2×Q811yescharacteristic
75C2×C3⋊Dic3#4111yescharacteristic
76C2×C3⋊Dic3#4111yescharacteristic
77C2×C3×Dic3—22no—
78C2×C3×Dic3—22no—
79C2×C3×Dic3—41no—
80C2×C3×Dic3—41no—
81C2×C3×Dic3—41no—
82C2×C3×Dic3—41no—
83C2×C3×Dic3—41no—
84C2×C3×Dic3—41no—
85C2×C3×Dic3—41no—
86C2×C3×Dic3—41no—
87C2×C3×Dic3—41no—
88C2×C3×Dic3—41no—
89#622—22no—
90#622C4⋊C414yescomplemented
91C2×#106—91no—
92C2×#106—91no—
93C2×C4×C8—91no—
94#389—91no—
95#389—91no—
96#340—91no—
97#340—91no—
98C22×C3×C4—21no—
99C22×C3×C4—21no—
100C22×C3×C4—61no—
101C22×C3×C4—61no—
102C22×C3×C4—61no—
103C22×C3×C4—61no—
104C22×Dic3—21no—
105C22×Dic3—21no—
106C22×Dic3—21no—
107C22×Dic3—21no—
108C22×Dic3—61no—
109C22×Dic3—61no—
110C22×Dic3—61no—
111C22×Dic3—61no—
112C3×C4⋊C4—122no—
113C4⋊Dic3—122no—
114Dic3⋊C4—42no—
115Dic3⋊C4—62no—
116Dic3⋊C4—62no—
117Dic3⋊C4—62no—
118Dic3⋊C4—62no—
119Dic3⋊C4—121no—
120Dic3⋊C4—121no—
121Dic3⋊C4—121no—
122Dic3⋊C4—121no—
123Dic3⋊C4—122no—
124C4×Dic3—121no—
125C4×Dic3—121no—
126C4×Dic3—121no—
127C4×Dic3—121no—
128C22×C32C4×D411yescharacteristic
129C22×C32#12111yescharacteristic
130C22×C32C4⋊Q811yescharacteristic
131C22×C32C2×SD1611yescharacteristic
132C22×C32C2×SD1611yescharacteristic
133C22×C32#13511yescharacteristic
134C22×C32#13511yescharacteristic
135C32×C4—22no—
136C3⋊Dic3—22no—
137C3⋊Dic3C2×C4⋊C411yescharacteristic
138C3⋊Dic3C4×Q811yescharacteristic
139C3⋊Dic3C22⋊Q811yescharacteristic
140C3⋊Dic3#12511yescharacteristic
141C3×Dic3—42no—
142C3×Dic3—42no—
143C3×Dic3—81no—
144C3×Dic3—81no—
145C22×C8—91no—
146C22×C8—91no—
147C2×C4⋊C4—61no—
148C2×C4⋊C4—91no—
149C2×C4⋊C4—91no—
150C2×C4⋊C4—91no—
151C2×C4⋊C4—91no—
152C2×C4⋊C4—181no—
153C2×C42—91no—
154#106—94no—
155#106—182no—
156C4×C8—182no—
157#95—61no—
158#95—181no—
159C23×C3—21no—
160C23×C3—21no—
161C2×C3×C4—22no—
162C2×C3×C4—22no—
163C2×C3×C4—41no—
164C2×C3×C4—41no—
165C2×C3×C4—41no—
166C2×C3×C4—41no—
167C2×C3×C4—62no—
168C2×C3×C4—62no—
169C2×C3×C4—121no—
170C2×C3×C4—121no—
171C2×C3×C4—121no—
172C2×C3×C4—121no—
173C2×C3×C4—121no—
174C2×C3×C4—121no—
175C2×C3×C4—121no—
176C2×C3×C4—121no—
177C2×C3×C4—121no—
178C2×C3×C4—121no—
179C2×Dic3—22no—
180C2×Dic3—22no—
181C2×Dic3—41no—
182C2×Dic3—41no—
183C2×Dic3—41no—
184C2×Dic3—41no—
185C2×Dic3—41no—
186C2×Dic3—41no—
187C2×Dic3—41no—
188C2×Dic3—41no—
189C2×Dic3—41no—
190C2×Dic3—41no—
191C2×Dic3—61no—
192C2×Dic3—61no—
193C2×Dic3—61no—
194C2×Dic3—61no—
195C2×Dic3—61no—
196C2×Dic3—61no—
197C2×Dic3—61no—
198C2×Dic3—61no—
199C2×Dic3—61no—
200C2×Dic3—61no—
201C2×Dic3—61no—
202C2×Dic3—61no—
203C2×Dic3—62no—
204C2×Dic3—62no—
205C2×Dic3—121no—
206C2×Dic3—121no—
207C2×Dic3—121no—
208C2×Dic3—121no—
209C2×C32#38911yescharacteristic
210C2×C32C4×SD1611yescharacteristic
211C2×C32C4×SD1611yescharacteristic
212C2×C32#46511yescharacteristic
213C2×C32#46511yescharacteristic
214C2×C32#49811yescharacteristic
215C2×C32#49911yescharacteristic
216C22×C4—61no—
217C22×C4—61no—
218C22×C4—61no—
219C22×C4—61no—
220C22×C4—91no—
221C22×C4—91no—
222C22×C4GO+(4,𝔽2)11yescharacteristic
223C2×C8—92no—
224C2×C8—92no—
225C2×C8—92no—
226C2×C8—92no—
227C2×C8—181no—
228C2×C8—181no—
229C4⋊C4—92no—
230C4⋊C4—92no—
231C4⋊C4—122no—
232C4⋊C4—181no—
233C4⋊C4—181no—
234C4⋊C4—181no—
235C4⋊C4—181no—
236C4⋊C4—181no—
237C4⋊C4—181no—
238C4⋊C4—362no—
239C42—181no—
240C42—181no—
241C22×C3—21no—
242C22×C3—21no—
243C22×C3—21no—
244C22×C3—21no—
245C22×C3—21no—
246C22×C3—21no—
247C22×C3—21no—
248C22×C3—21no—
249C22×C3—21no—
250C22×C3—21no—
251C22×C3—21no—
252C22×C3—21no—
253C22×C3—21no—
254C22×C3—21no—
255C3×C4—42no—
256C3×C4—42no—
257C3×C4—122no—
258C3×C4—122no—
259C3×C4—241no—
260C3×C4—241no—
261Dic3—42no—
262Dic3—42no—
263Dic3—61no—
264Dic3—61no—
265Dic3—61no—
266Dic3—61no—
267Dic3—61no—
268Dic3—61no—
269Dic3—61no—
270Dic3—61no—
271Dic3—81no—
272Dic3—81no—
273Dic3—122no—
274Dic3—122no—
275C32#194111yescharacteristic, complemented, Sylow
276C23C2×GO+(4,𝔽2)11yescharacteristic
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—62no—
280C2×C4—62no—
281C2×C4—91no—
282C2×C4—91no—
283C2×C4—91no—
284C2×C4—91no—
285C2×C4—91no—
286C2×C4—91no—
287C2×C4—92no—
288C2×C4—121no—
289C2×C4—121no—
290C2×C4—121no—
291C2×C4—121no—
292C2×C4—121no—
293C2×C4—121no—
294C2×C4—121no—
295C2×C4—121no—
296C2×C4—121no—
297C2×C4—121no—
298C2×C4—181no—
299C2×C4—181no—
300C2×C4#377512yes—
301C8—94no—
302C8—182no—
303C2×C3—21no—
304C2×C3—21no—
305C2×C3—21no—
306C2×C3—21no—
307C2×C3—21no—
308C2×C3—21no—
309C2×C3—21no—
310C2×C3—21no—
311C2×C3—21no—
312C2×C3—21no—
313C2×C3—21no—
314C2×C3—21no—
315C2×C3—21no—
316C2×C3—21no—
317C22#6422211yescharacteristic
318C22#6422311yescharacteristic
319C22#6422711yescharacteristic
320C22C4×GO+(4,𝔽2)11yescharacteristic
321C22#6423711yescharacteristic
322C22C2×#377511yescharacteristic
323C22#6424211yescharacteristic
324C4—22no—
325C4—91no—
326C4—91no—
327C4—91no—
328C4—91no—
329C4—122no—
330C4—122no—
331C4—182no—
332C4—241no—
333C4—241no—
334C3—21no—
335C3—21no—
336C2#1059338411yescharacteristic
337C2#1059339011yescharacteristic
338C2#1059341011yescharacteristic
339C2C4×#377511yescharacteristic
340C2#1059343311yescharacteristic
341C2#1059343511yescharacteristic
342C2#1059352611yescharacteristic
subgroupG/H
center, FrattiniC23C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
FittingC22×C32×C4D4
socle, prime radicalC23×C32C2×D4
cosocleC22×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1941
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
19. #63742C4semidirect
90. #622C4⋊C4semidirect
275. C32#1941semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6222
C2×#637422
#105913372
#105913282
#105900752
#19419