Finite Group Databasebeta

← C2×C4×#3775 #11859911

Subgroups — C2×C4×#3775 #11859911

Order 1152.

914 conjugacy classes of subgroups; only the 183 normal subgroups are shown.

normal subgroups only

This group has 914 conjugacy classes of subgroups — too many to draw. Only its 183 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
2C2×C4×#627C211yesmaximal, characteristic, complemented
3C2×C4×#625C211yesmaximal, characteristic
4C2×C4×#622C211yesmaximal, characteristic, complemented
5C2×#63742C211yesmaximal, characteristic, complemented
6C2×#63740C211yesmaximal, characteristic, complemented
7C2×#63739C211yesmaximal, characteristic
8C4×#3775C218yesmaximal, direct product factor
9C22×C3×C4×D3—21no—
10C22×#627C2211yescharacteristic
11C22×#625C2211yescharacteristic
12C22×#622C2211yescharacteristic
13C22×#622C2211yescharacteristic
14C2×#3775C418yesdirect product factor
15C2×#3775C2214yes—
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C2×C3×C4×Dic3—21no—
18C2×#3724C2211yescharacteristic
19C2×#3724C2211yescharacteristic
20C2×Dic3⋊Dic3—21no—
21C2×(C2×D3)⋊Dic3—21no—
22C4×#627—22no—
23C4×#627C2214yescomplemented
24C4×#625—22no—
25C4×#625C2214yes—
26C4×#622C2214yescomplemented
27#63742C2214yescomplemented
28#63740C2214yescomplemented
29#63739C2214yes—
30C2×C4×#67—61no—
31C2×C4×Dic6—61no—
32C23×C3×D3—21no—
33C22×C32×C4D411yescharacteristic
34C22×C3⋊Dic3D411yescharacteristic
35C22×C3⋊Dic3C2311yescharacteristic
36C22×C3×Dic3—21no—
37C22×C3×Dic3—21no—
38C22×C3×Dic3—21no—
39C2×C3×C4×D3—24no—
40C2×C3×C4×D3—44no—
41C2×#627—21no—
42C2×#627—22no—
43C2×#627C2×C414yescomplemented
44C2×#627C2312yes—
45C2×#625—21no—
46C2×#625—22no—
47C2×#625C2×C414yes—
48C2×#625C2312yes—
49C2×#622—22no—
50C2×#622C2×C414yescomplemented
51C2×#622C2312yes—
52C2×#622C2312yes—
53#3775C2×C4116yesdirect product factor
54C4×C3⋊Dic3D412yes—
55C4×C3⋊Dic3C2312yes—
56C3×C4×Dic3—24no—
57#3724—21no—
58#3724—21no—
59#3724C2312yes—
60#3724C2312yes—
61Dic3⋊Dic3—24no—
62(C2×D3)⋊Dic3—24no—
63C2×C4×SD16—91nomaximal, Sylow
64C23×C3×C4—61no—
65C22×#67—61no—
66C22×C4×D3—21no—
67C22×Dic6—61no—
68C2×C3×C42—61no—
69C2×#217—61no—
70C4×#67—64no—
71C4×#67—64no—
72C2×(C2×D3)⋊C4—61no—
73C2×C4⋊Dic3—61no—
74C2×Dic3⋊C4—61no—
75C2×Dic3⋊C4—61no—
76C2×Dic3⋊C4—61no—
77C2×C4×Dic3—21no—
78C2×C4×Dic3—61no—
79C2×C4×Dic3—61no—
80C4×Dic6—64no—
81C4×Dic6—64no—
82C23×C32C2×D411yescharacteristic
83C22×C3×D3—24no—
84C22×C3×D3—22no—
85C22×C3×D3—42no—
86C22×C3×D3—42no—
87C2×C32×C4SD1614yescomplemented
88C2×C32×C4C2×D412yes—
89C2×C3⋊Dic3—22no—
90C2×C3⋊Dic3C22×C412yes—
91C2×C3⋊Dic3C2×D412yes—
92C2×C3⋊Dic3C2×D411yescharacteristic
93C2×C3⋊Dic3#4112yes—
94C2×C3⋊Dic3C2411yescharacteristic
95C2×C3×Dic3—24no—
96C2×C3×Dic3—22no—
97C2×C3×Dic3—22no—
98C2×C3×Dic3—22no—
99C2×C3×Dic3—42no—
100C2×C3×Dic3—42no—
101C3×C4×D3—48no—
102#627—24no—
103#627—22no—
104#627C22×C414yescomplemented
105#625—24no—
106#625—22no—
107#625C22×C414yes—
108#622—22no—
109#622C22×C414yescomplemented
110C22×SD16—91no—
111C2×C4×Q8—91no—
112C2×C4×D4—91no—
113C4×SD16—98no—
114C2×#106—91no—
115C2×#103—91no—
116C2×#102—91no—
117C2×C4×C8—91no—
118C24×C3—61no—
119C23×D3—21no—
120C22×C3×C4—21no—
121C22×C3×C4—21no—
122C22×C3×C4—64no—
123C22×C3×C4—61no—
124C22×C3×C4—61no—
125C22×C3×C4—61no—
126C22×C3×C4—124no—
127C2×#67—62no—
128C2×#67—64no—
129C2×#67—62no—
130C2×#67—64no—
131C22×Dic3—21no—
132C22×Dic3—21no—
133C22×Dic3—21no—
134C22×Dic3—61no—
135C22×Dic3—61no—
136C22×Dic3—61no—
137C22×Dic3—61no—
138C2×C4×D3—24no—
139C2×C4×D3—44no—
140C2×Dic6—62no—
141C2×Dic6—64no—
142C2×Dic6—62no—
143C2×Dic6—64no—
144C3×C42—64no—
145#217—64no—
146(C2×D3)⋊C4—64no—
147C4⋊Dic3—64no—
148Dic3⋊C4—62no—
149Dic3⋊C4—62no—
150Dic3⋊C4—64no—
151Dic3⋊C4—62no—
152Dic3⋊C4—62no—
153C4×Dic3—24no—
154C4×Dic3—62no—
155C4×Dic3—62no—
156C4×Dic3—62no—
157C4×Dic3—62no—
158C22×C32C4×D412yes—
159C22×C32C2×SD1612yes—
160C22×C32#13512yes—
161C22×C32C22×D411yescharacteristic
162C2×C3×D3—24no—
163C2×C3×D3—42no—
164C2×C3×D3—42no—
165C2×C3×D3—48no—
166C32×C4C2×SD1614yescomplemented
167C3⋊Dic3—22no—
168C3⋊Dic3C4×D412yes—
169C3⋊Dic3C23×C411yescharacteristic
170C3⋊Dic3C2×#4111yescharacteristic
171C3×Dic3—24no—
172C3×Dic3—42no—
173C3×Dic3—42no—
174C22×Q8—91no—
175C22×D4—91no—
176C23×C4—61no—
177C2×SD16—94no—
178C2×SD16—98no—
179C22×C8—91no—
180C22×C8—91no—
181C4×Q8—94no—
182C4×Q8—182no—
183C4×D4—94no—
184C4×D4—182no—
185C2×C4⋊C4—91no—
186C2×C4⋊C4—91no—
187C2×C4⋊C4—181no—
188C2×C22⋊C4—181no—
189C2×C42—61no—
190C2×C42—91no—
191#106—94no—
192#103—94no—
193#102—94no—
194C4×C8—94no—
195C23×C3—21no—
196C23×C3—21no—
197C23×C3—62no—
198C23×C3—64no—
199C23×C3—122no—
200C23×C3—122no—
201C22×D3—22no—
202C22×D3—24no—
203C22×D3—42no—
204C22×D3—42no—
205C2×C3×C4—22no—
206C2×C3×C4—22no—
207C2×C3×C4—24no—
208C2×C3×C4—24no—
209C2×C3×C4—62no—
210C2×C3×C4—64no—
211C2×C3×C4—62no—
212C2×C3×C4—62no—
213C2×C3×C4—128no—
214C2×C3×C4—122no—
215C2×C3×C4—122no—
216#67—64no—
217#67—68no—
218#67—64no—
219C2×Dic3—22no—
220C2×Dic3—24no—
221C2×Dic3—22no—
222C2×Dic3—22no—
223C2×Dic3—42no—
224C2×Dic3—42no—
225C2×Dic3—62no—
226C2×Dic3—62no—
227C2×Dic3—61no—
228C2×Dic3—61no—
229C2×Dic3—62no—
230C2×Dic3—62no—
231C2×Dic3—61no—
232C2×Dic3—61no—
233C2×Dic3—62no—
234C2×Dic3—62no—
235C2×Dic3—122no—
236C2×Dic3—122no—
237C4×D3—48no—
238Dic6—64no—
239Dic6—68no—
240Dic6—64no—
241C2×C32C4×SD1614yescomplemented
242C2×C32C2×C4×D411yescharacteristic
243C2×C32C22×SD1611yescharacteristic
244C2×C32C2×#13511yescharacteristic
245C3×D3—44no—
246C24—61no—
247C2×Q8—92no—
248C2×Q8—94no—
249C2×Q8—181no—
250C2×Q8—182no—
251C2×D4—92no—
252C2×D4—94no—
253C2×D4—181no—
254C2×D4—182no—
255C22×C4—61no—
256C22×C4—61no—
257C22×C4—61no—
258C22×C4—64no—
259C22×C4—91no—
260C22×C4—91no—
261C22×C4—124no—
262C22×C4GO+(4,𝔽2)11yescharacteristic
263SD16—916no—
264C2×C8—92no—
265C2×C8—94no—
266C2×C8—92no—
267C2×C8—182no—
268C4⋊C4—92no—
269C4⋊C4—92no—
270C4⋊C4—181no—
271C4⋊C4—181no—
272C4⋊C4—184no—
273C22⋊C4—184no—
274C42—64no—
275C42—92no—
276C42—92no—
277C22×C3—21no—
278C22×C3—21no—
279C22×C3—22no—
280C22×C3—22no—
281C22×C3—22no—
282C22×C3—22no—
283C22×C3—22no—
284C22×C3—22no—
285C22×C3—64no—
286C22×C3—122no—
287C22×C3—122no—
288C22×C3—128no—
289C2×D3—24no—
290C2×D3—42no—
291C2×D3—42no—
292C2×D3—48no—
293C3×C4—24no—
294C3×C4—24no—
295C3×C4—64no—
296C3×C4—122no—
297C3×C4—122no—
298Dic3—24no—
299Dic3—42no—
300Dic3—42no—
301Dic3—62no—
302Dic3—61no—
303Dic3—61no—
304Dic3—62no—
305Dic3—61no—
306Dic3—61no—
307Dic3—122no—
308Dic3—122no—
309C32C2×C4×SD1611yescharacteristic, complemented, Sylow
310C23—62no—
311C23—64no—
312C23—122no—
313C23—122no—
314C23C2×GO+(4,𝔽2)11yescharacteristic
315Q8—94no—
316Q8—182no—
317Q8—184no—
318D4—94no—
319D4—182no—
320D4—184no—
321C2×C4—62no—
322C2×C4—64no—
323C2×C4—62no—
324C2×C4—62no—
325C2×C4—91no—
326C2×C4—91no—
327C2×C4—92no—
328C2×C4—92no—
329C2×C4—92no—
330C2×C4—122no—
331C2×C4—122no—
332C2×C4—128no—
333C2×C4—182no—
334C2×C4#377514yesdirect product factor
335C2×C4C2×GO+(4,𝔽2)12yes—
336C8—94no—
337C8—182no—
338C2×C3—21no—
339C2×C3—21no—
340C2×C3—24no—
341C2×C3—24no—
342C2×C3—21no—
343C2×C3—21no—
344C2×C3—21no—
345C2×C3—21no—
346C2×C3—124no—
347D3—44no—
348C22—64no—
349C22—122no—
350C22—128no—
351C22—122no—
352C22#6422312yes—
353C22C4×GO+(4,𝔽2)12yes—
354C22C2×#377512yes—
355C22C22×GO+(4,𝔽2)11yescharacteristic
356C4—64no—
357C4—91no—
358C4—91no—
359C4—92no—
360C4—122no—
361C4—122no—
362C4—182no—
363C4C2×#377514yesdirect product factor
364C3—21no—
365C3—21no—
366C2—124no—
367C2C4×#377514yesdirect product factor
368C2C2×#6422311yescharacteristic
369C2C2×C4×GO+(4,𝔽2)11yescharacteristic
370C2C22×#377511yescharacteristic
subgroupG/H
center, hypercenterC22×C4GO+(4,𝔽2)
commutatorC3⋊Dic3C23×C4
FrattiniC22C22×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC23×C32C2×D4
prime radicalC22×#625C22
cosocleC2×C3⋊Dic3C24
hypocenterC32C2×C4×SD16
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×#627C2semidirect
4. C2×C4×#622C2semidirect
5. C2×#63742C2semidirect
6. C2×#63740C2semidirect
8. C4×#3775C2direct (N × H)
14. C2×#3775C4direct (N × H)
23. C4×#627C22semidirect
26. C4×#622C22semidirect
27. #63742C22semidirect
28. #63740C22semidirect
43. C2×#627C2×C4semidirect
50. C2×#622C2×C4semidirect
53. #3775C2×C4direct (N × H)
87. C2×C32×C4SD16semidirect
104. #627C22×C4semidirect
109. #622C22×C4semidirect
166. C32×C4C2×SD16semidirect
241. C2×C32C4×SD16semidirect
309. C32C2×C4×SD16semidirect
334. C2×C4#3775direct (N × H)
363. C4C2×#3775direct (N × H)
367. C2C4×#3775direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37752
C2×C4×#6272
C2×C4×#6252
C2×C4×#6222
C2×#637422
C2×#637402
C2×#637392
C4×#37752
C2×C4×SD169