Finite Group Databasebeta

← C2×#10593525 #11863633

Subgroups — C2×#10593525 #11863633

Order 1152.

1430 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 1430 conjugacy classes of subgroups — too many to draw. Only its 151 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
1C23×#627C211yesmaximal, characteristic, complemented
2C22×#3775C212yesmaximal, complemented
3C2×#63980C211yesmaximal, characteristic
4C2×C22⋊#622C211yesmaximal, characteristic, complemented
5#10593525C218yesmaximal, direct product factor
6C2×#63740C212yesmaximal, complemented
7C23×C3⋊Dic3C2211yescharacteristic
8C22×C3×#67—21no—
9C23×C3×Dic3—21no—
10C22×#627—22no—
11C22×#627—21no—
12C22×#627—28no—
13C22×#627C2212yes—
14C22×#627C2214yescomplemented
15C22×#625C2211yescharacteristic
16C22×#622C2212yes—
17C2×#3775—28no—
18C2×#3775C2218yescomplemented
19#63980—22no—
20#63980C2214yes—
21C2×#3724C2211yescharacteristic
22C2×(C2×D3)⋊Dic3—21no—
23C22⋊#622C2214yescomplemented
24#63740C2218yescomplemented
25C23×Dic6—61no—
26C2×#939—61no—
27C24×C32D411yescharacteristic
28C23×C3×D3—21no—
29C22×C3⋊Dic3—24no—
30C22×C3⋊Dic3D411yescharacteristic
31C22×C3⋊Dic3D412yes—
32C22×C3⋊Dic3C2312yes—
33C22×C3⋊Dic3C2311yescharacteristic
34C2×C3×#67—24no—
35C2×C3×#67—44no—
36C22×C3×Dic3—28no—
37C22×C3×Dic3—22no—
38C22×C3×Dic3—24no—
39C22×C3×Dic3—21no—
40C2×#627—28no—
41C2×#627—216no—
42C2×#627—22no—
43C2×#627—24no—
44C2×#627—24no—
45C2×#627—216no—
46C2×#627D418yescomplemented
47C2×#627C2314yes—
48C2×#625—24no—
49C2×#625—21no—
50C2×#625C2312yes—
51C2×#622—24no—
52C2×#622C2314yes—
53#3775—216no—
54#3724—21no—
55#3724C2312yes—
56(C2×D3)⋊Dic3—24no—
57C2×#448—91nomaximal, Sylow
58C22×C3×D4—61no—
59C23×C3×C4—61no—
60C22×#67—21no—
61C22×#67—61no—
62C23×Dic3—21no—
63C23×Dic3—61no—
64C23×Dic3—61no—
65C22×Dic6—62no—
66C22×Dic6—64no—
67C22×Dic6—64no—
68C22×Dic6—62no—
69C22×Dic6—616no—
70C2×#217—61no—
71#939—64no—
72#939—64no—
73C2×(C2×D3)⋊C4—61no—
74C2×Dic3⋊C4—61no—
75C23×C32—22no—
76C23×C32—22no—
77C23×C32SD1614yescomplemented
78C23×C32C2×D412yes—
79C23×C32C2×D411yescharacteristic
80C22×C3×D3—22no—
81C22×C3×D3—42no—
82C22×C3×D3—42no—
83C22×C3×D3—42no—
84C2×C3⋊Dic3—22no—
85C2×C3⋊Dic3—24no—
86C2×C3⋊Dic3—24no—
87C2×C3⋊Dic3C2×D412yes—
88C2×C3⋊Dic3C2×D411yescharacteristic
89C2×C3⋊Dic3C2×D414yes—
90C2×C3⋊Dic3C2411yescharacteristic
91C3×#67—48no—
92C2×C3×Dic3—216no—
93C2×C3×Dic3—28no—
94C2×C3×Dic3—24no—
95C2×C3×Dic3—22no—
96C2×C3×Dic3—42no—
97#627—216no—
98#627—28no—
99#627—24no—
100#627C2×D418yescomplemented
101#625—24no—
102#625—42no—
103#622—24no—
104C23×Q8—91no—
105C22×SD16—92no—
106C2×#121—91no—
107#448—98no—
108C2×#103—92no—
109C2×C22⋊C8—91no—
110C24×C3—21no—
111C24×C3—21no—
112C24×C3—61no—
113C23×D3—21no—
114C2×C3×D4—64no—
115C2×C3×D4—124no—
116C22×C3×C4—68no—
117C22×C3×C4—64no—
118C22×C3×C4—62no—
119C22×C3×C4—61no—
120C2×#67—24no—
121C2×#67—44no—
122C2×#67—62no—
123C2×#67—62no—
124C2×#67—124no—
125C22×Dic3—28no—
126C22×Dic3—24no—
127C22×Dic3—22no—
128C22×Dic3—21no—
129C22×Dic3—61no—
130C22×Dic3—62no—
131C22×Dic3—61no—
132C22×Dic3—61no—
133C22×Dic3—62no—
134C22×Dic3—61no—
135C22×Dic3—62no—
136C22×Dic3—62no—
137C22×Dic3—68no—
138C22×Dic3—124no—
139C2×Dic6—68no—
140C2×Dic6—64no—
141C2×Dic6—64no—
142C2×Dic6—68no—
143C2×Dic6—68no—
144C2×Dic6—632no—
145C2×Dic6—632no—
146C2×Dic6—616no—
147#217—64no—
148(C2×D3)⋊C4—64no—
149Dic3⋊C4—62no—
150Dic3⋊C4—62no—
151C22×C32—22no—
152C22×C32—22no—
153C22×C32—28no—
154C22×C32#12012yes—
155C22×C32C2×SD1612yes—
156C22×C32C2×SD1614yescomplemented
157C22×C32#13712yes—
158C22×C32C22×D411yescharacteristic
159C2×C3×D3—42no—
160C2×C3×D3—42no—
161C2×C3×D3—42no—
162C2×C3×D3—84no—
163C3⋊Dic3—22no—
164C3⋊Dic3#12012yes—
165C3⋊Dic3C22×D412yes—
166C3×Dic3—28no—
167C3×Dic3—42no—
168C22×Q8—92no—
169C22×Q8—94no—
170C22×Q8—182no—
171C22×Q8—181no—
172C22×Q8—188no—
173C22×D4—61no—
174C22×D4—91no—
175C23×C4—61no—
176C23×C4—91no—
177C2×SD16—98no—
178C2×SD16—188no—
179C22×C8—92no—
180#121—94no—
181#121—182no—
182C2×C4⋊C4—91no—
183C2×C22⋊C4—181no—
184#103—98no—
185C22⋊C8—94no—
186C23×C3—24no—
187C23×C3—24no—
188C23×C3—22no—
189C23×C3—22no—
190C23×C3—21no—
191C23×C3—21no—
192C23×C3—24no—
193C23×C3—24no—
194C23×C3—42no—
195C23×C3—42no—
196C23×C3—62no—
197C23×C3—122no—
198C23×C3—122no—
199C23×C3—122no—
200C22×D3—22no—
201C22×D3—42no—
202C22×D3—42no—
203C22×D3—42no—
204C3×D4—128no—
205C2×C3×C4—616no—
206C2×C3×C4—64no—
207C2×C3×C4—68no—
208C2×C3×C4—62no—
209C2×C3×C4—122no—
210#67—48no—
211#67—124no—
212#67—124no—
213C2×Dic3—216no—
214C2×Dic3—24no—
215C2×Dic3—28no—
216C2×Dic3—22no—
217C2×Dic3—42no—
218C2×Dic3—61no—
219C2×Dic3—61no—
220C2×Dic3—64no—
221C2×Dic3—62no—
222C2×Dic3—64no—
223C2×Dic3—61no—
224C2×Dic3—61no—
225C2×Dic3—62no—
226C2×Dic3—68no—
227C2×Dic3—68no—
228C2×Dic3—64no—
229C2×Dic3—124no—
230C2×Dic3—124no—
231C2×Dic3—122no—
232Dic6—68no—
233Dic6—616no—
234Dic6—68no—
235Dic6—632no—
236C2×C32—24no—
237C2×C32#44814yescomplemented
238C2×C32C2×#12011yescharacteristic
239C2×C32C22×SD1611yescharacteristic
240C2×C32C2×#13711yescharacteristic
241C3×D3—82no—
242C24—61no—
243C24GO+(4,𝔽2)11yescharacteristic
244C2×Q8—94no—
245C2×Q8—98no—
246C2×Q8—182no—
247C2×Q8—184no—
248C2×Q8—184no—
249C2×Q8—1816no—
250C2×Q8—1816no—
251C2×Q8—188no—
252C2×D4—64no—
253C2×D4—92no—
254C2×D4—124no—
255C2×D4—184no—
256C2×D4—181no—
257C22×C4—68no—
258C22×C4—64no—
259C22×C4—62no—
260C22×C4—61no—
261C22×C4—91no—
262C22×C4—92no—
263C22×C4—92no—
264C22×C4—91no—
265C22×C4—184no—
266SD16—1816no—
267C2×C8—94no—
268C2×C8—184no—
269C4⋊C4—92no—
270C4⋊C4—181no—
271C22⋊C4—184no—
272C22×C3—24no—
273C22×C3—24no—
274C22×C3—216no—
275C22×C3—21no—
276C22×C3—21no—
277C22×C3—22no—
278C22×C3—22no—
279C22×C3—24no—
280C22×C3—24no—
281C22×C3—22no—
282C22×C3—22no—
283C22×C3—22no—
284C22×C3—22no—
285C22×C3—42no—
286C22×C3—42no—
287C22×C3—48no—
288C22×C3—122no—
289C22×C3—122no—
290C22×C3—122no—
291C22×C3—244no—
292C2×D3—42no—
293C2×D3—42no—
294C2×D3—42no—
295C2×D3—84no—
296C3×C4—68no—
297C3×C4—122no—
298Dic3—28no—
299Dic3—42no—
300Dic3—62no—
301Dic3—62no—
302Dic3—62no—
303Dic3—62no—
304Dic3—64no—
305Dic3—122no—
306C32C2×#44811yescharacteristic, complemented, Sylow
307C23—22no—
308C23—22no—
309C23—62no—
310C23—122no—
311C23—122no—
312C23—122no—
313C23#377514yescomplemented
314C23C2×GO+(4,𝔽2)12yes—
315C23C2×GO+(4,𝔽2)11yescharacteristic
316Q8—98no—
317Q8—184no—
318Q8—188no—
319Q8—1816no—
320D4—128no—
321D4—184no—
322D4—362no—
323C2×C4—616no—
324C2×C4—64no—
325C2×C4—68no—
326C2×C4—62no—
327C2×C4—91no—
328C2×C4—91no—
329C2×C4—94no—
330C2×C4—92no—
331C2×C4—122no—
332C2×C4—184no—
333C2×C4—184no—
334C2×C4—182no—
335C8—184no—
336C2×C3—28no—
337C2×C3—21no—
338C2×C3—21no—
339C2×C3—21no—
340C2×C3—21no—
341C2×C3—21no—
342C2×C3—21no—
343C2×C3—24no—
344C2×C3—24no—
345C2×C3—44no—
346C2×C3—242no—
347D3—82no—
348C22—22no—
349C22—22no—
350C22—28no—
351C22—122no—
352C22—122no—
353C22—122no—
354C22—244no—
355C22C2×#377512yes—
356C22C2×#377514yescomplemented
357C22#6423912yes—
358C22#6424112yes—
359C22C22×GO+(4,𝔽2)11yescharacteristic
360C4—68no—
361C4—92no—
362C4—92no—
363C4—122no—
364C4—182no—
365C3—21no—
366C3—21no—
367C2—24no—
368C2—242no—
369C2#1059352514yesdirect product factor
370C2C22×#377511yescharacteristic
371C2C2×#6423911yescharacteristic
372C2C2×#6424111yescharacteristic
subgroupG/H
centerC23C2×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FrattiniC22C22×GO+(4,𝔽2)
FittingC24×C32D4
socleC23×C32C2×D4
prime radicalC2×#63980C2
hypercenterC24GO+(4,𝔽2)
hypocenterC32C2×#448
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C24

Complements

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

NH ≅ G/Ntype
1. C23×#627C2semidirect
2. C22×#3775C2semidirect
4. C2×C22⋊#622C2semidirect
5. #10593525C2direct (N × H)
6. C2×#63740C2semidirect
14. C22×#627C22semidirect
18. C2×#3775C22semidirect
23. C22⋊#622C22semidirect
24. #63740C22semidirect
46. C2×#627D4semidirect
77. C23×C32SD16semidirect
100. #627C2×D4semidirect
156. C22×C32C2×SD16semidirect
237. C2×C32#448semidirect
306. C32C2×#448semidirect
313. C23#3775semidirect
356. C22C2×#3775semidirect
369. C2#10593525direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#6272
C22×#37752
C2×#639802
C2×C22⋊#6222
#105935252
C2×#637402
C2×#4489