Finite Group Databasebeta

← C2×#10593342 #11801739

Subgroups — C2×#10593342 #11801739

Order 1152.

1562 conjugacy classes of subgroups; only the 263 normal subgroups are shown.

normal subgroups only

This group has 1562 conjugacy classes of subgroups — too many to draw. Only its 263 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×#3797C211yesmaximal, characteristic
2C22×C4×#157C211yesmaximal, characteristic
3C2×#63900C211yesmaximal, characteristic
4C2×#63737C214yesmaximal
5#10593342C218yesmaximal, direct product factor
6C23×#157C2212yes—
7C22×C4×C3⋊D3C2211yescharacteristic
8C22×C3×Dic6—21no—
9C22×#627—21no—
10C22×#624C2212yes—
11C22×#624C2212yes—
12C2×#3797—22no—
13C2×#3797—24no—
14C2×#3797C418yescomplemented
15C2×#3797C2214yes—
16C2×C4×#157—24no—
17C2×C4×#157C2214yes—
18C2×C3×C4⋊Dic3—21no—
19C2×#3724—21no—
20#63900—22no—
21#63900C2214yes—
22#63737C22116yes—
23C22×D3×Q8—61no—
24C2×D3×C4⋊C4—61no—
25C23×C3⋊D3C2311yescharacteristic
26C22×#157—24no—
27C22×#157—24no—
28C22×#157Q818yescomplemented
29C22×#157C2314yes—
30C22×C32×C4D411yescharacteristic
31C22×C3⋊Dic3D411yescharacteristic
32C2×C4×C3⋊D3C2×C414yes—
33C2×C4×C3⋊D3D412yes—
34C2×C4×C3⋊D3D414yes—
35C2×C4×C3⋊D3C2312yes—
36C22×C3×Dic3—22no—
37C22×C3×Dic3—22no—
38C2×C3×Dic6—28no—
39C2×C3×Dic6—24no—
40C2×#627—28no—
41C2×#627—24no—
42C2×#624—22no—
43C2×#624—24no—
44C2×#624—28no—
45C2×#624—22no—
46C2×#624C2×C418yes—
47C2×#624C2314yes—
48C2×#624C2314yes—
49#3797—216no—
50#3797—28no—
51#3797C2×C4116yescomplemented
52C4×#157—28no—
53C3×C4⋊Dic3—24no—
54#3724—24no—
55C2×#391—91nomaximal, Sylow
56C22×C3×Q8—61no—
57C2×D3×Q8—68no—
58C2×D3×Q8—64no—
59C2×D3×Q8—64no—
60C2×D3×Q8—68no—
61C22×C4×D3—62no—
62C22×C4×D3—61no—
63C22×C4×D3—61no—
64C22×C4×D3—62no—
65C22×Dic6—21no—
66C22×Dic6—62no—
67C2×C3×C4⋊C4—61no—
68C2×C4⋊Dic3—21no—
69C2×Dic3⋊C4—62no—
70D3×C4⋊C4—64no—
71D3×C4⋊C4—64no—
72C23×C32C2×D411yescharacteristic
73C22×C3⋊D3C22×C412yes—
74C22×C3⋊D3C2×D411yescharacteristic
75C22×C3⋊D3C2×D412yes—
76C22×C3⋊D3C2×Q814yes—
77C22×C3⋊D3#4114yes—
78C22×C3⋊D3C2411yescharacteristic
79C2×#157—216no—
80C2×#157—24no—
81C2×#157—24no—
82C2×#157C2×Q818yescomplemented
83C2×C32×C4C22⋊C414yes—
84C2×C32×C4C2×D412yes—
85C2×C3⋊Dic3C22⋊C414yes—
86C2×C3⋊Dic3C2×D412yes—
87C4×C3⋊D3C22⋊C418yes—
88C4×C3⋊D3C22×C414yes—
89C4×C3⋊D3C2×D414yes—
90C2×C3×Dic3—28no—
91C2×C3×Dic3—24no—
92C2×C3×Dic3—24no—
93C2×C3×Dic3—44no—
94C3×Dic6—216no—
95#627—216no—
96#624—28no—
97#624—24no—
98#624—28no—
99#624—44no—
100#624C22×C418yes—
101C23×Q8—91no—
102C22×C4⋊C4—91no—
103C22×C42—91no—
104#391—98no—
105C2×#95—94no—
106C23×D3—61no—
107C23×D3—61no—
108C2×C3×Q8—64no—
109C2×C3×Q8—68no—
110C22×C3×C4—21no—
111C22×C3×C4—21no—
112C22×C3×C4—62no—
113C22×C3×C4—62no—
114C22×Dic3—22no—
115C22×Dic3—22no—
116C22×Dic3—61no—
117C22×Dic3—61no—
118D3×Q8—616no—
119D3×Q8—632no—
120D3×Q8—616no—
121C2×C4×D3—68no—
122C2×C4×D3—64no—
123C2×C4×D3—62no—
124C2×C4×D3—62no—
125C2×C4×D3—64no—
126C2×C4×D3—62no—
127C2×C4×D3—64no—
128C2×C4×D3—62no—
129C2×C4×D3—64no—
130C2×C4×D3—64no—
131C2×C4×D3—64no—
132C2×C4×D3—64no—
133C2×C4×D3—68no—
134C2×C4×D3—64no—
135C2×C4×D3—128no—
136C2×Dic6—24no—
137C2×Dic6—28no—
138C2×Dic6—616no—
139C2×Dic6—68no—
140C3×C4⋊C4—64no—
141C4⋊Dic3—24no—
142Dic3⋊C4—68no—
143C22×C32C2×C22⋊C412yes—
144C22×C32#12412yes—
145C22×C32C4⋊Q812yes—
146C22×C32C22×D411yescharacteristic
147C2×C3⋊D3C2×C22⋊C412yes—
148C2×C3⋊D3C4×Q818yes—
149C2×C3⋊D3C22⋊Q818yes—
150C2×C3⋊D3#12412yes—
151C2×C3⋊D3C4⋊Q812yes—
152C2×C3⋊D3C23×C411yescharacteristic
153C2×C3⋊D3C22×D411yescharacteristic
154C2×C3⋊D3C22×Q812yes—
155C2×C3⋊D3C2×#4112yes—
156#157—28no—
157C32×C4C2×C22⋊C414yes—
158C3⋊Dic3C2×C22⋊C414yes—
159C3×Dic3—28no—
160C3×Dic3—44no—
161C22×Q8—61no—
162C22×Q8—94no—
163C22×Q8—98no—
164C22×Q8—181no—
165C22×Q8—182no—
166C22×Q8—184no—
167C23×C4—92no—
168C23×C4—92no—
169C23×C4—91no—
170C23×C4—92no—
171C2×C4⋊C4—61no—
172C2×C4⋊C4—94no—
173C2×C4⋊C4—182no—
174C2×C4⋊C4—181no—
175C2×C42—94no—
176C2×C42—184no—
177#95—916no—
178C23×C3—21no—
179C23×C3—21no—
180C22×D3—62no—
181C22×D3—62no—
182C22×D3—61no—
183C22×D3—61no—
184C22×D3—62no—
185C22×D3—62no—
186C22×D3—64no—
187C22×D3—64no—
188C22×D3—64no—
189C22×D3—64no—
190C22×D3—61no—
191C22×D3—61no—
192C3×Q8—616no—
193C2×C3×C4—22no—
194C2×C3×C4—22no—
195C2×C3×C4—24no—
196C2×C3×C4—24no—
197C2×C3×C4—64no—
198C2×C3×C4—68no—
199C2×C3×C4—64no—
200C2×C3×C4—124no—
201C2×Dic3—24no—
202C2×Dic3—28no—
203C2×Dic3—24no—
204C2×Dic3—44no—
205C2×Dic3—64no—
206C2×Dic3—64no—
207C2×Dic3—62no—
208C2×Dic3—62no—
209C4×D3—68no—
210C4×D3—68no—
211C4×D3—68no—
212C4×D3—64no—
213C4×D3—64no—
214C4×D3—64no—
215C4×D3—64no—
216C4×D3—616no—
217C4×D3—68no—
218C4×D3—128no—
219C4×D3—128no—
220Dic6—216no—
221Dic6—632no—
222C2×C32#39114yescomplemented
223C2×C32C22×C22⋊C411yescharacteristic
224C2×C32C2×#12411yescharacteristic
225C2×C32C2×C4⋊Q811yescharacteristic
226C3⋊D3#39114yescomplemented
227C3⋊D3C2×C4×Q812yes—
228C3⋊D3C2×C22⋊Q812yes—
229C24—91no—
230C2×Q8—64no—
231C2×Q8—68no—
232C2×Q8—916no—
233C2×Q8—184no—
234C2×Q8—188no—
235C2×Q8—188no—
236C2×Q8—1816no—
237C22×C4—62no—
238C22×C4—62no—
239C22×C4—94no—
240C22×C4—98no—
241C22×C4—94no—
242C22×C4—91no—
243C22×C4—92no—
244C22×C4—92no—
245C22×C4—94no—
246C22×C4—94no—
247C22×C4—98no—
248C22×C4—94no—
249C22×C4—182no—
250C22×C4—184no—
251C22×C4—182no—
252C22×C4—188no—
253C22×C4—184no—
254C22×C4—184no—
255C22×C4GO+(4,𝔽2)11yescharacteristic
256C4⋊C4—64no—
257C4⋊C4—184no—
258C42—188no—
259C22×C3—21no—
260C22×C3—21no—
261C22×C3—22no—
262C22×C3—22no—
263C22×C3—22no—
264C22×C3—22no—
265C22×C3—22no—
266C22×C3—22no—
267C2×D3—62no—
268C2×D3—61no—
269C2×D3—61no—
270C2×D3—62no—
271C2×D3—61no—
272C2×D3—61no—
273C2×D3—62no—
274C2×D3—62no—
275C2×D3—68no—
276C2×D3—68no—
277C2×D3—68no—
278C2×D3—68no—
279C2×D3—62no—
280C2×D3—62no—
281C2×D3—62no—
282C2×D3—62no—
283C2×D3—62no—
284C2×D3—62no—
285C3×C4—24no—
286C3×C4—24no—
287C3×C4—68no—
288C3×C4—124no—
289Dic3—28no—
290Dic3—44no—
291Dic3—64no—
292Dic3—64no—
293C32C2×#39111yescharacteristic, complemented, Sylow
294C23—91no—
295C23—91no—
296C23—94no—
297C23—94no—
298C23—92no—
299C23—92no—
300C23C2×GO+(4,𝔽2)11yescharacteristic
301Q8—616no—
302Q8—1816no—
303C2×C4—64no—
304C2×C4—68no—
305C2×C4—64no—
306C2×C4—98no—
307C2×C4—92no—
308C2×C4—94no—
309C2×C4—94no—
310C2×C4—94no—
311C2×C4—98no—
312C2×C4—98no—
313C2×C4—124no—
314C2×C4—184no—
315C2×C4—188no—
316C2×C4—188no—
317C2×C4—184no—
318C2×C4—1816no—
319C2×C4—184no—
320C2×C4—364no—
321C2×C4D32⋊C414yes—
322C2×C4C2×GO+(4,𝔽2)12yes—
323C2×C3—24no—
324C2×C3—24no—
325C2×C3—21no—
326C2×C3—21no—
327C2×C3—21no—
328C2×C3—21no—
329C2×C3—21no—
330C2×C3—21no—
331D3—62no—
332D3—62no—
333D3—62no—
334D3—62no—
335D3—64no—
336D3—64no—
337C22—98no—
338C22—98no—
339C22—92no—
340C22—92no—
341C22—92no—
342C22—92no—
343C22—91no—
344C22—91no—
345C22—92no—
346C22#6422112yes—
347C22#6422212yes—
348C22C2×D32⋊C412yes—
349C22C22×GO+(4,𝔽2)11yescharacteristic
350C4—68no—
351C4—94no—
352C4—124no—
353C4—188no—
354C4C2×D32⋊C414yes—
355C3—21no—
356C3—21no—
357C2—92no—
358C2—94no—
359C2—92no—
360C2#1059334214yesdirect product factor
361C2C2×#6422111yescharacteristic
362C2C2×#6422211yescharacteristic
363C2C22×D32⋊C411yescharacteristic
subgroupG/H
centerC23C2×GO+(4,𝔽2)
commutatorC2×C3⋊D3C23×C4
FrattiniC22C22×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC23×C32C2×D4
prime radicalC23×C3⋊D3C23
cosocleC22×C3⋊D3C24
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#391
LCSG ▷ C2×C3⋊D3 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
5. #10593342C2direct (N × H)
14. C2×#3797C4semidirect
28. C22×#157Q8semidirect
51. #3797C2×C4semidirect
82. C2×#157C2×Q8semidirect
222. C2×C32#391semidirect
226. C3⋊D3#391semidirect
293. C32C2×#391semidirect
360. C2#10593342direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37972
C22×C4×#1572
C2×#639002
C2×#637372
#105933422
C2×#3919