Finite Group Databasebeta

← C2×#10590047 #11783189

Subgroups — C2×#10590047 #11783189

Order 1152.

802 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 802 conjugacy classes of subgroups — too many to draw. Only its 143 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
1C22×C4×#157C211yesmaximal, characteristic
2C2×#63874C211yesmaximal, characteristic
3C22×#3712C211yesmaximal, characteristic
4#10590047C214yesmaximal, direct product factor
5C23×#157—21no—
6C22×C4×C3⋊D3C2211yescharacteristic
7C2×C4×#157—22no—
8C2×C4×#157—21no—
9C2×C4×#157C414yescomplemented
10C2×C4×#157C2212yes—
11C2×C3×C4×Dic3—21no—
12C22×C3×C3⋊C8—21no—
13C2×#3724C412yescomplemented
14C2×#3722—21no—
15#63874—21no—
16#63874—21no—
17#63874C412yescomplemented
18#63874C2212yes—
19C2×#3712—21no—
20C2×#3712—22no—
21C2×#3712C414yescomplemented
22C2×#3712C2212yes—
23C22×ΓL(1,𝔽25)—61no—
24C2×#872—61no—
25C23×C3⋊D3D411yescharacteristic
26C22×#157—28no—
27C22×#157—24no—
28C22×#157—22no—
29C22×C32×C4D411yescharacteristic
30C22×C3⋊Dic3C2×C411yescharacteristic
31C2×C4×C3⋊D3C2×C411yescharacteristic
32C2×C4×C3⋊D3C2×C412yes—
33C2×C4×C3⋊D3C2×C412yes—
34C2×C4×C3⋊D3D411yescharacteristic
35C2×C4×C3⋊D3D411yescharacteristic
36C2×C4×C3⋊D3D412yes—
37C2×C4×C3⋊D3Q812yes—
38C2×C4×C3⋊D3C2311yescharacteristic
39C22×C3×Dic3—22no—
40C4×#157—24no—
41C4×#157—22no—
42C4×#157C2×C414yescomplemented
43C3×C4×Dic3—22no—
44C3×C4×Dic3—22no—
45C2×C3×C3⋊C8—24no—
46C2×C3×C3⋊C8—22no—
47#3724—22no—
48#3724C2×C414yescomplemented
49#3722—22no—
50#3722—22no—
51#3712—24no—
52#3712—22no—
53#3712C2×C414yescomplemented
54C2×#339—91nomaximal, Sylow
55C22×C4×D3—61no—
56C22×C4×D3—61no—
57C22×C3×C8—61no—
58C2×C3×C42—61no—
59C2×(C2×D3)⋊C4—62no—
60C2×Dic3⋊C4—62no—
61C2×C4×Dic3—21no—
62C22×C3⋊C8—21no—
63C2×ΓL(1,𝔽25)—64no—
64C2×ΓL(1,𝔽25)—62no—
65C2×ΓL(1,𝔽25)—62no—
66C2×ΓL(1,𝔽25)—64no—
67#872—62no—
68#872—62no—
69#872—62no—
70#872—62no—
71C23×C32C22⋊C411yescharacteristic
72C22×C3⋊D3—24no—
73C22×C3⋊D3C22⋊C411yescharacteristic
74C22×C3⋊D3C22⋊C412yes—
75C22×C3⋊D3C4⋊C412yes—
76C22×C3⋊D3C2×D411yescharacteristic
77C2×#157—216no—
78C2×#157—28no—
79C2×#157—24no—
80C2×C32×C4C22⋊C411yescharacteristic
81C2×C32×C4C22⋊C412yes—
82C2×C32×C4C4⋊C412yes—
83C2×C32×C4C2×D411yescharacteristic
84C2×C3⋊Dic3C4212yes—
85C2×C3⋊Dic3C22⋊C411yescharacteristic
86C2×C3⋊Dic3C4⋊C412yes—
87C2×C3⋊Dic3C22×C411yescharacteristic
88C4×C3⋊D3C4212yes—
89C4×C3⋊D3C22⋊C412yes—
90C4×C3⋊D3C22⋊C412yes—
91C4×C3⋊D3C4⋊C412yes—
92C4×C3⋊D3C4⋊C412yes—
93C4×C3⋊D3C4⋊C412yes—
94C4×C3⋊D3C22×C411yescharacteristic
95C4×C3⋊D3C22×C411yescharacteristic
96C4×C3⋊D3C2×D411yescharacteristic
97C4×C3⋊D3C2×Q811yescharacteristic
98C2×C3×Dic3—24no—
99C2×C3×Dic3—44no—
100C3×C3⋊C8—24no—
101C22×M16—91no—
102C2×#117—91no—
103C22×C42—91no—
104#339—94no—
105C23×D3—61no—
106C23×D3—61no—
107C22×C3×C4—21no—
108C22×C3×C4—21no—
109C22×C3×C4—62no—
110C22×Dic3—22no—
111C22×Dic3—61no—
112C22×Dic3—61no—
113C2×C4×D3—61no—
114C2×C4×D3—61no—
115C2×C4×D3—61no—
116C2×C4×D3—61no—
117C2×C4×D3—62no—
118C2×C4×D3—61no—
119C2×C4×D3—62no—
120C2×C4×D3—61no—
121C2×C4×D3—61no—
122C2×C4×D3—62no—
123C2×C4×D3—62no—
124C2×C4×D3—62no—
125C2×C4×D3—61no—
126C2×C4×D3—62no—
127C2×C4×D3—62no—
128C2×C4×D3—62no—
129C2×C3×C8—62no—
130C2×C3×C8—64no—
131C3×C42—62no—
132C3×C42—62no—
133(C2×D3)⋊C4—64no—
134(C2×D3)⋊C4—64no—
135Dic3⋊C4—64no—
136Dic3⋊C4—64no—
137C4×Dic3—22no—
138C4×Dic3—22no—
139C2×C3⋊C8—22no—
140C2×C3⋊C8—24no—
141ΓL(1,𝔽25)—64no—
142ΓL(1,𝔽25)—68no—
143ΓL(1,𝔽25)—64no—
144C22×C32#9512yes—
145C22×C32#10414yes—
146C22×C32C2×C22⋊C411yescharacteristic
147C2×C3⋊D3—24no—
148C2×C3⋊D3—24no—
149C2×C3⋊D3—22no—
150C2×C3⋊D3—22no—
151C2×C3⋊D3#9512yes—
152C2×C3⋊D3C2×C22⋊C411yescharacteristic
153C2×C3⋊D3C2×C4⋊C411yescharacteristic
154#157—28no—
155C32×C4#9512yes—
156C32×C4C2×C22⋊C411yescharacteristic
157C32×C4C2×C4⋊C411yescharacteristic
158C3⋊Dic3#9512yes—
159C3⋊Dic3C2×C4211yescharacteristic
160C3⋊Dic3C2×C4⋊C411yescharacteristic
161C3×Dic3—44no—
162C23×C4—91no—
163C23×C4—181no—
164C2×M16—92no—
165C2×M16—94no—
166C2×M16—181no—
167C2×M16—182no—
168C22×C8—61no—
169#117—92no—
170#117—92no—
171#117—181no—
172#117—181no—
173C2×C4⋊C4—92no—
174C2×C22⋊C4—181no—
175C2×C42—61no—
176C2×C42—94no—
177C2×C42—92no—
178C2×C42—181no—
179C2×C42—182no—
180C23×C3—21no—
181C23×C3—21no—
182C22×D3—61no—
183C22×D3—61no—
184C22×D3—62no—
185C22×D3—62no—
186C22×D3—62no—
187C22×D3—62no—
188C22×D3—61no—
189C22×D3—61no—
190C22×D3—124no—
191C22×D3—124no—
192C2×C3×C4—21no—
193C2×C3×C4—21no—
194C2×C3×C4—22no—
195C2×C3×C4—21no—
196C2×C3×C4—22no—
197C2×C3×C4—21no—
198C2×C3×C4—22no—
199C2×C3×C4—22no—
200C2×C3×C4—64no—
201C2×C3×C4—124no—
202C2×Dic3—24no—
203C2×Dic3—44no—
204C2×Dic3—62no—
205C2×Dic3—62no—
206C2×Dic3—61no—
207C2×Dic3—61no—
208C2×Dic3—62no—
209C2×Dic3—62no—
210C2×Dic3—61no—
211C2×Dic3—61no—
212C4×D3—62no—
213C4×D3—62no—
214C4×D3—62no—
215C4×D3—62no—
216C4×D3—62no—
217C4×D3—62no—
218C4×D3—62no—
219C4×D3—62no—
220C4×D3—62no—
221C4×D3—62no—
222C4×D3—62no—
223C4×D3—62no—
224C4×D3—61no—
225C4×D3—61no—
226C4×D3—61no—
227C4×D3—61no—
228C4×D3—61no—
229C4×D3—61no—
230C4×D3—61no—
231C4×D3—61no—
232C3×C8—64no—
233C3⋊C8—24no—
234C2×C32#33914yescomplemented
235C2×C32C2×#9511yescharacteristic
236C2×C32C2×#10412yes—
237C3⋊D3—21no—
238C3⋊D3—22no—
239C3⋊D3—21no—
240C24—91no—
241C22×C4—62no—
242C22×C4—91no—
243C22×C4—91no—
244C22×C4—91no—
245C22×C4—91no—
246C22×C4—92no—
247C22×C4—91no—
248C22×C4—92no—
249C22×C4—92no—
250C22×C4—92no—
251C22×C4—182no—
252C22×C4—184no—
253C22×C4—188no—
254C22×C4GO+(4,𝔽2)11yescharacteristic
255M16—94no—
256M16—182no—
257M16—184no—
258C2×C8—62no—
259C2×C8—64no—
260C4⋊C4—94no—
261C4⋊C4—182no—
262C22⋊C4—182no—
263C22⋊C4—182no—
264C42—62no—
265C42—62no—
266C42—94no—
267C42—182no—
268C42—184no—
269C22×C3—21no—
270C22×C3—21no—
271C22×C3—24no—
272C22×C3—24no—
273C22×C3—22no—
274C22×C3—22no—
275C2×D3—62no—
276C2×D3—62no—
277C2×D3—61no—
278C2×D3—61no—
279C2×D3—61no—
280C2×D3—61no—
281C2×D3—122no—
282C2×D3—122no—
283C2×D3—122no—
284C2×D3—122no—
285C2×D3—124no—
286C2×D3—124no—
287C2×D3—124no—
288C2×D3—124no—
289C3×C4—21no—
290C3×C4—21no—
291C3×C4—21no—
292C3×C4—21no—
293C3×C4—22no—
294C3×C4—22no—
295C3×C4—124no—
296Dic3—44no—
297Dic3—62no—
298Dic3—62no—
299Dic3—61no—
300Dic3—61no—
301Dic3—61no—
302Dic3—61no—
303C32C2×#33911yescharacteristic, complemented, Sylow
304C23—91no—
305C23—91no—
306C23—92no—
307C23—92no—
308C23—184no—
309C23D32⋊C411yescharacteristic
310C2×C4—64no—
311C2×C4—91no—
312C2×C4—91no—
313C2×C4—92no—
314C2×C4—92no—
315C2×C4—91no—
316C2×C4—91no—
317C2×C4—92no—
318C2×C4—91no—
319C2×C4—91no—
320C2×C4—92no—
321C2×C4—92no—
322C2×C4—92no—
323C2×C4—92no—
324C2×C4—92no—
325C2×C4—124no—
326C2×C4—184no—
327C2×C4—188no—
328C2×C4—1816no—
329C2×C4D32⋊C412yes—
330C2×C4D32⋊C411yescharacteristic
331C2×C4#377312yes—
332C2×C4C2×GO+(4,𝔽2)11yescharacteristic
333C8—64no—
334C2×C3—22no—
335C2×C3—22no—
336C2×C3—24no—
337C2×C3—24no—
338C2×C3—21no—
339C2×C3—21no—
340D3—121no—
341D3—121no—
342D3—122no—
343D3—122no—
344D3—121no—
345D3—121no—
346C22—91no—
347C22—91no—
348C22—92no—
349C22—182no—
350C22—182no—
351C22—184no—
352C22—184no—
353C22#6373114yes—
354C22#6373712yes—
355C22C2×D32⋊C411yescharacteristic
356C4—91no—
357C4—91no—
358C4—92no—
359C4—124no—
360C4—188no—
361C4#6373712yes—
362C4C2×D32⋊C411yescharacteristic
363C4C2×#377311yescharacteristic
364C3—21no—
365C3—21no—
366C2—181no—
367C2—181no—
368C2—182no—
369C2#1059004714yesdirect product factor
370C2C2×#6373112yes—
371C2C2×#6373711yescharacteristic
subgroupG/H
center, hypercenterC22×C4GO+(4,𝔽2)
commutatorC3⋊Dic3C2×C42
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC23×C32C22⋊C4
prime radicalC23×C3⋊D3D4
cosocleC2×C4×C3⋊D3C23
hypocenterC32C2×#339
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #10590047C2direct (N × H)
9. C2×C4×#157C4semidirect
13. C2×#3724C4semidirect
17. #63874C4semidirect
21. C2×#3712C4semidirect
42. C4×#157C2×C4semidirect
48. #3724C2×C4semidirect
53. #3712C2×C4semidirect
234. C2×C32#339semidirect
303. C32C2×#339semidirect
369. C2#10590047direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×#1572
C2×#638742
C22×#37122
#105900472
C2×#3399