Finite Group Databasebeta

← C2×#10593422 #11865567

Subgroups — C2×#10593422 #11865567

Order 1152.

942 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 942 conjugacy classes of subgroups — too many to draw. Only its 127 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×#3775C211yesmaximal, characteristic, complemented
2C22×#3774C211yesmaximal, characteristic
3C2×#63915C211yesmaximal, characteristic, complemented
4C2×C4×#625C211yesmaximal, characteristic, complemented
5C2×#63779C211yesmaximal, characteristic, complemented
6C2×#63740C211yesmaximal, characteristic, complemented
7C2×#63739C211yesmaximal, characteristic, complemented
8#10593422C218yesmaximal, direct product factor
9C22×C3×C4×D3—21no—
10C22×#627C2211yescharacteristic
11C22×#625C2211yescharacteristic
12C22×#625C2211yescharacteristic
13C22×#622C2211yescharacteristic
14C22×#622C2211yescharacteristic
15C2×#3775—24no—
16C2×#3775C2214yescomplemented
17C2×#3774—24no—
18C2×#3774C2214yes—
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C2×C3×(C2×D3)⋊C4—21no—
21C2×#3724C2211yescharacteristic
22C2×(C2×D3)⋊Dic3—21no—
23C2×(C2×D3)⋊Dic3—21no—
24#63915—22no—
25#63915C2214yescomplemented
26C4×#625—22no—
27C4×#625C2214yescomplemented
28#63779C2214yescomplemented
29#63740C2214yescomplemented
30#63739C2214yescomplemented
31C2×C4×#67—61no—
32C2×#885—61no—
33C23×C3×D3—21no—
34C23×C3×D3—21no—
35C22×C32×C4D411yescharacteristic
36C22×C3⋊Dic3D411yescharacteristic
37C22×C3⋊Dic3C2311yescharacteristic
38C22×C3×Dic3—21no—
39C22×C3×Dic3—21no—
40C2×C3×C4×D3—24no—
41C2×C3×C4×D3—44no—
42C2×#627—22no—
43C2×#627—22no—
44C2×#627—21no—
45C2×#627C2312yes—
46C2×#625—21no—
47C2×#625—22no—
48C2×#625—22no—
49C2×#625—22no—
50C2×#625—21no—
51C2×#625D414yes—
52C2×#625C2312yes—
53C2×#625C2312yes—
54C2×#622—22no—
55C2×#622—22no—
56C2×#622C2312yes—
57C2×#622C2312yes—
58#3775—28no—
59#3774—28no—
60C4×C3⋊Dic3D412yes—
61C4×C3⋊Dic3C2312yes—
62C3×(C2×D3)⋊C4—24no—
63#3724—21no—
64#3724C2312yes—
65(C2×D3)⋊Dic3—24no—
66(C2×D3)⋊Dic3—24no—
67C2×#463—91nomaximal, Sylow
68C23×C3×C4—61no—
69C22×#67—61no—
70C22×#67—61no—
71C22×C4×D3—21no—
72C22×Dic6—61no—
73C2×C3×C22⋊C4—61no—
74C2×#217—61no—
75C2×#217—61no—
76C4×#67—64no—
77C4×#67—64no—
78C2×(C2×D3)⋊C4—21no—
79C2×(C2×D3)⋊C4—61no—
80C2×(C2×D3)⋊C4—61no—
81C2×Dic3⋊C4—61no—
82C2×C4×Dic3—61no—
83C2×C4×Dic3—61no—
84#885—64no—
85#885—64no—
86C23×C32C2×D411yescharacteristic
87C22×C3×D3—24no—
88C22×C3×D3—22no—
89C22×C3×D3—22no—
90C22×C3×D3—42no—
91C22×C3×D3—42no—
92C22×C3×D3—42no—
93C22×C3×D3—42no—
94C22×C3×D3—42no—
95C2×C32×C4—22no—
96C2×C32×C4C2×D412yes—
97C2×C3⋊Dic3—22no—
98C2×C3⋊Dic3C2×D412yes—
99C2×C3⋊Dic3C2×D411yescharacteristic
100C2×C3⋊Dic3C2×D412yes—
101C2×C3⋊Dic3#4112yes—
102C2×C3⋊Dic3C2411yescharacteristic
103C2×C3×Dic3—22no—
104C2×C3×Dic3—22no—
105C2×C3×Dic3—42no—
106C2×C3×Dic3—42no—
107C3×C4×D3—48no—
108#627—22no—
109#627—22no—
110#627—42no—
111#625—24no—
112#625—22no—
113#625—22no—
114#625—22no—
115#625—42no—
116#625C2×D414yes—
117#622—22no—
118#622—22no—
119C22×SD16—91no—
120C22×D8—91no—
121C2×#124—91no—
122C2×C4×D4—91no—
123#463—98no—
124C2×C4⋊C8—91no—
125C2×#103—91no—
126C2×#102—91no—
127C24×C3—61no—
128C24×C3—61no—
129C23×D3—21no—
130C23×D3—21no—
131C22×C3×C4—21no—
132C22×C3×C4—21no—
133C22×C3×C4—64no—
134C22×C3×C4—61no—
135C22×C3×C4—61no—
136C22×C3×C4—124no—
137C2×#67—62no—
138C2×#67—64no—
139C2×#67—62no—
140C2×#67—62no—
141C2×#67—64no—
142C2×#67—62no—
143C2×#67—122no—
144C2×#67—122no—
145C22×Dic3—21no—
146C22×Dic3—21no—
147C22×Dic3—61no—
148C22×Dic3—61no—
149C22×Dic3—61no—
150C22×Dic3—61no—
151C2×C4×D3—24no—
152C2×C4×D3—44no—
153C2×Dic6—62no—
154C2×Dic6—62no—
155C2×Dic6—122no—
156C2×Dic6—122no—
157C3×C22⋊C4—64no—
158#217—64no—
159#217—64no—
160(C2×D3)⋊C4—24no—
161(C2×D3)⋊C4—64no—
162(C2×D3)⋊C4—64no—
163Dic3⋊C4—62no—
164Dic3⋊C4—62no—
165C4×Dic3—62no—
166C4×Dic3—62no—
167C4×Dic3—62no—
168C4×Dic3—62no—
169C22×C32#12112yes—
170C22×C32#13512yes—
171C22×C32AGL(1,ℤ/8)12yes—
172C22×C32C22×D411yescharacteristic
173C2×C3×D3—24no—
174C2×C3×D3—42no—
175C2×C3×D3—42no—
176C2×C3×D3—48no—
177C2×C3×D3—42no—
178C2×C3×D3—42no—
179C2×C3×D3—42no—
180C2×C3×D3—84no—
181C32×C4—22no—
182C3⋊Dic3—22no—
183C3⋊Dic3#12112yes—
184C3⋊Dic3C22×D411yescharacteristic
185C3⋊Dic3C2×#4111yescharacteristic
186C3×Dic3—42no—
187C3×Dic3—42no—
188C22×Q8—91no—
189C22×D4—91no—
190C22×D4—91no—
191C23×C4—61no—
192C2×SD16—94no—
193C2×SD16—184no—
194C2×D8—94no—
195C2×D8—184no—
196C22×C8—91no—
197C22×C8—91no—
198#124—94no—
199#124—182no—
200C4×D4—94no—
201C4×D4—182no—
202C2×C4⋊C4—91no—
203C2×C22⋊C4—61no—
204C2×C22⋊C4—181no—
205C2×C22⋊C4—181no—
206C2×C42—91no—
207C4⋊C8—94no—
208#103—94no—
209#102—94no—
210C23×C3—21no—
211C23×C3—21no—
212C23×C3—62no—
213C23×C3—64no—
214C23×C3—62no—
215C23×C3—122no—
216C23×C3—122no—
217C23×C3—122no—
218C23×C3—122no—
219C23×C3—122no—
220C22×D3—22no—
221C22×D3—24no—
222C22×D3—22no—
223C22×D3—42no—
224C22×D3—42no—
225C22×D3—42no—
226C22×D3—42no—
227C22×D3—42no—
228C2×C3×C4—24no—
229C2×C3×C4—22no—
230C2×C3×C4—22no—
231C2×C3×C4—42no—
232C2×C3×C4—62no—
233C2×C3×C4—62no—
234C2×C3×C4—128no—
235C2×C3×C4—122no—
236C2×C3×C4—122no—
237#67—64no—
238#67—68no—
239#67—64no—
240#67—122no—
241#67—122no—
242#67—124no—
243C2×Dic3—22no—
244C2×Dic3—22no—
245C2×Dic3—42no—
246C2×Dic3—42no—
247C2×Dic3—61no—
248C2×Dic3—61no—
249C2×Dic3—62no—
250C2×Dic3—62no—
251C2×Dic3—62no—
252C2×Dic3—62no—
253C2×Dic3—61no—
254C2×Dic3—61no—
255C2×Dic3—62no—
256C2×Dic3—62no—
257C2×Dic3—122no—
258C2×Dic3—122no—
259C4×D3—48no—
260Dic6—122no—
261Dic6—122no—
262Dic6—124no—
263C2×C32#46314yescomplemented
264C2×C32C2×#12111yescharacteristic
265C2×C32C2×#13511yescharacteristic
266C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
267C3×D3—44no—
268C3×D3—82no—
269C24—61no—
270C24—61no—
271C2×Q8—92no—
272C2×Q8—181no—
273C2×Q8—182no—
274C2×Q8—182no—
275C2×D4—92no—
276C2×D4—94no—
277C2×D4—92no—
278C2×D4—181no—
279C2×D4—182no—
280C2×D4—182no—
281C2×D4—182no—
282C2×D4—181no—
283C22×C4—61no—
284C22×C4—61no—
285C22×C4—64no—
286C22×C4—91no—
287C22×C4—91no—
288C22×C4—124no—
289C22×C4GO+(4,𝔽2)11yescharacteristic
290SD16—188no—
291D8—188no—
292C2×C8—92no—
293C2×C8—92no—
294C2×C8—182no—
295C2×C8—182no—
296C4⋊C4—92no—
297C4⋊C4—181no—
298C22⋊C4—64no—
299C22⋊C4—184no—
300C22⋊C4—184no—
301C42—92no—
302C42—92no—
303C22×C3—21no—
304C22×C3—21no—
305C22×C3—22no—
306C22×C3—22no—
307C22×C3—22no—
308C22×C3—22no—
309C22×C3—22no—
310C22×C3—22no—
311C22×C3—64no—
312C22×C3—122no—
313C22×C3—128no—
314C22×C3—122no—
315C22×C3—122no—
316C22×C3—122no—
317C22×C3—122no—
318C22×C3—244no—
319C2×D3—24no—
320C2×D3—42no—
321C2×D3—48no—
322C2×D3—42no—
323C2×D3—42no—
324C2×D3—42no—
325C2×D3—42no—
326C2×D3—84no—
327C3×C4—24no—
328C3×C4—42no—
329C3×C4—122no—
330C3×C4—122no—
331Dic3—42no—
332Dic3—42no—
333Dic3—62no—
334Dic3—61no—
335Dic3—61no—
336Dic3—62no—
337Dic3—61no—
338Dic3—61no—
339Dic3—122no—
340Dic3—122no—
341C32C2×#46311yescharacteristic, complemented, Sylow
342C23—62no—
343C23—64no—
344C23—62no—
345C23—122no—
346C23—122no—
347C23—122no—
348C23—122no—
349C23—122no—
350C23C2×GO+(4,𝔽2)11yescharacteristic
351Q8—182no—
352Q8—182no—
353Q8—362no—
354D4—94no—
355D4—182no—
356D4—184no—
357D4—182no—
358D4—182no—
359D4—362no—
360C2×C4—22no—
361C2×C4—62no—
362C2×C4—62no—
363C2×C4—91no—
364C2×C4—91no—
365C2×C4—92no—
366C2×C4—92no—
367C2×C4—92no—
368C2×C4—128no—
369C2×C4—122no—
370C2×C4—122no—
371C2×C4—182no—
372C2×C4C2×GO+(4,𝔽2)12yes—
373C8—182no—
374C8—182no—
375C2×C3—24no—
376C2×C3—24no—
377C2×C3—21no—
378C2×C3—21no—
379C2×C3—21no—
380C2×C3—21no—
381C2×C3—21no—
382C2×C3—21no—
383C2×C3—124no—
384C2×C3—242no—
385D3—44no—
386D3—82no—
387C22—64no—
388C22—128no—
389C22—122no—
390C22—122no—
391C22—122no—
392C22—122no—
393C22—122no—
394C22—244no—
395C22#6422312yes—
396C22#6423012yes—
397C22#6423612yes—
398C22C22×GO+(4,𝔽2)11yescharacteristic
399C4—22no—
400C4—91no—
401C4—91no—
402C4—92no—
403C4—122no—
404C4—122no—
405C4—182no—
406C3—21no—
407C3—21no—
408C2—124no—
409C2—242no—
410C2#1059342214yesdirect product factor
411C2C2×#6422311yescharacteristic
412C2C2×#6423011yescharacteristic
413C2C2×#6423611yescharacteristic
subgroupG/H
centerC23C2×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FrattiniC22C22×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC23×C32C2×D4
prime radicalC22×#3774C2
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#463
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
1. C22×#3775C2semidirect
3. C2×#63915C2semidirect
4. C2×C4×#625C2semidirect
5. C2×#63779C2semidirect
6. C2×#63740C2semidirect
7. C2×#63739C2semidirect
8. #10593422C2direct (N × H)
16. C2×#3775C22semidirect
25. #63915C22semidirect
27. C4×#625C22semidirect
28. #63779C22semidirect
29. #63740C22semidirect
30. #63739C22semidirect
263. C2×C32#463semidirect
341. C32C2×#463semidirect
410. C2#10593422direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37752
C22×#37742
C2×#639152
C2×C4×#6252
C2×#637792
C2×#637402
C2×#637392
#105934222
C2×#4639