Finite Group Databasebeta

← C2×#10593523 #11863587

Subgroups — C2×#10593523 #11863587

Order 1152.

1838 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 1838 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×#625C211yesmaximal, characteristic
2C22×#3775C212yesmaximal, complemented
3C2×#63982C211yesmaximal, characteristic, complemented
4C2×C22⋊#622C211yesmaximal, characteristic, complemented
5#10593523C218yesmaximal, direct product factor
6C2×#63739C212yesmaximal, complemented
7C24×C3×D3—21no—
8C23×C3⋊Dic3C2211yescharacteristic
9C22×#627C2211yescharacteristic, complemented
10C22×#625—21no—
11C22×#625—22no—
12C22×#625—28no—
13C22×#625C2214yes—
14C22×#625C2212yes—
15C22×#622C2212yescomplemented
16C2×#3775—28no—
17C2×#3775C2218yescomplemented
18C2×C3×#217—21no—
19#63982—22no—
20#63982C2214yescomplemented
21C2×#3724C2211yescharacteristic, complemented
22C2×Dic3⋊Dic3—21no—
23C22⋊#622C2214yescomplemented
24#63739C2218yescomplemented
25C23×#67—61no—
26C2×#878—61no—
27C24×C32D411yescharacteristic
28C23×C3×D3—28no—
29C23×C3×D3—24no—
30C23×C3×D3—22no—
31C23×C3×D3—44no—
32C23×C3×D3—44no—
33C22×C3⋊Dic3—24no—
34C22×C3⋊Dic3D411yescharacteristic
35C22×C3⋊Dic3D412yes—
36C22×C3⋊Dic3C2312yes—
37C22×C3⋊Dic3C2311yescharacteristic
38C22×C3×Dic3—21no—
39C22×C3×Dic3—21no—
40C2×#627—24no—
41C2×#627—21no—
42C2×#627C2312yescomplemented
43C2×#625—28no—
44C2×#625—216no—
45C2×#625—24no—
46C2×#625—22no—
47C2×#625—24no—
48C2×#625—216no—
49C2×#625D418yes—
50C2×#625C2314yes—
51C2×#622—24no—
52C2×#622C2314yescomplemented
53#3775—216no—
54C3×#217—24no—
55#3724—21no—
56#3724C2312yescomplemented
57Dic3⋊Dic3—24no—
58C2×#450—91nomaximal, Sylow
59C25×C3—61no—
60C24×D3—21no—
61C22×#67—62no—
62C22×#67—64no—
63C22×#67—64no—
64C22×#67—62no—
65C22×#67—616no—
66C23×Dic3—61no—
67C23×Dic3—61no—
68C22×Dic6—61no—
69C2×C3×C22⋊C4—61no—
70C2×#217—21no—
71C2×C4⋊Dic3—61no—
72C2×Dic3⋊C4—61no—
73C2×Dic3⋊C4—61no—
74#878—64no—
75#878—64no—
76C23×C32—22no—
77C23×C32—22no—
78C23×C32SD1614yescomplemented
79C23×C32C2×D412yes—
80C23×C32C2×D411yescharacteristic
81C22×C3×D3—216no—
82C22×C3×D3—28no—
83C22×C3×D3—24no—
84C22×C3×D3—48no—
85C22×C3×D3—432no—
86C22×C3×D3—44no—
87C22×C3×D3—48no—
88C22×C3×D3—44no—
89C2×C3⋊Dic3—22no—
90C2×C3⋊Dic3—24no—
91C2×C3⋊Dic3—24no—
92C2×C3⋊Dic3C2×D412yes—
93C2×C3⋊Dic3C2×D411yescharacteristic
94C2×C3⋊Dic3C2×D414yes—
95C2×C3⋊Dic3C2411yescharacteristic
96C2×C3×Dic3—22no—
97C2×C3×Dic3—22no—
98C2×C3×Dic3—42no—
99C2×C3×Dic3—42no—
100#627—24no—
101#627—42no—
102#625—216no—
103#625—28no—
104#625—24no—
105#625C2×D418yes—
106#622—24no—
107C23×D4—91no—
108C22×SD16—92no—
109C2×C22⋊Q8—91no—
110#450—98no—
111C2×#102—92no—
112C2×C22⋊C8—91no—
113C24×C3—21no—
114C24×C3—21no—
115C24×C3—68no—
116C24×C3—64no—
117C24×C3—62no—
118C24×C3—124no—
119C24×C3—124no—
120C23×D3—28no—
121C23×D3—24no—
122C23×D3—22no—
123C23×D3—44no—
124C23×D3—44no—
125C22×C3×C4—61no—
126C22×C3×C4—61no—
127C2×#67—68no—
128C2×#67—64no—
129C2×#67—64no—
130C2×#67—68no—
131C2×#67—68no—
132C2×#67—632no—
133C2×#67—632no—
134C2×#67—616no—
135C22×Dic3—21no—
136C22×Dic3—21no—
137C22×Dic3—61no—
138C22×Dic3—62no—
139C22×Dic3—61no—
140C22×Dic3—61no—
141C22×Dic3—62no—
142C22×Dic3—62no—
143C22×Dic3—62no—
144C22×Dic3—61no—
145C22×Dic3—68no—
146C22×Dic3—124no—
147C2×Dic6—62no—
148C2×Dic6—62no—
149C2×Dic6—124no—
150C3×C22⋊C4—64no—
151#217—24no—
152C4⋊Dic3—64no—
153Dic3⋊C4—62no—
154Dic3⋊C4—64no—
155Dic3⋊C4—62no—
156C22×C32—22no—
157C22×C32—22no—
158C22×C32—28no—
159C22×C32#12012yes—
160C22×C32C2×SD1612yes—
161C22×C32C2×SD1614yescomplemented
162C22×C32AGL(1,ℤ/8)12yes—
163C22×C32C22×D411yescharacteristic
164C2×C3×D3—28no—
165C2×C3×D3—432no—
166C2×C3×D3—44no—
167C2×C3×D3—44no—
168C2×C3×D3—416no—
169C3⋊Dic3—22no—
170C3⋊Dic3#12012yes—
171C3⋊Dic3C22×D412yes—
172C3×Dic3—42no—
173C3×Dic3—42no—
174C25—61no—
175C22×Q8—91no—
176C22×D4—92no—
177C22×D4—94no—
178C22×D4—182no—
179C22×D4—181no—
180C22×D4—188no—
181C23×C4—91no—
182C2×SD16—98no—
183C2×SD16—188no—
184C22×C8—92no—
185C22⋊Q8—94no—
186C22⋊Q8—182no—
187C2×C4⋊C4—91no—
188C2×C4⋊C4—181no—
189C2×C22⋊C4—61no—
190#102—98no—
191C22⋊C8—94no—
192C23×C3—24no—
193C23×C3—24no—
194C23×C3—22no—
195C23×C3—22no—
196C23×C3—21no—
197C23×C3—21no—
198C23×C3—24no—
199C23×C3—24no—
200C23×C3—42no—
201C23×C3—42no—
202C23×C3—616no—
203C23×C3—64no—
204C23×C3—68no—
205C23×C3—128no—
206C23×C3—1232no—
207C23×C3—124no—
208C23×C3—124no—
209C23×C3—128no—
210C22×D3—216no—
211C22×D3—24no—
212C22×D3—28no—
213C22×D3—48no—
214C22×D3—432no—
215C22×D3—44no—
216C22×D3—44no—
217C22×D3—48no—
218C2×C3×C4—62no—
219C2×C3×C4—62no—
220C2×C3×C4—122no—
221C2×C3×C4—122no—
222#67—68no—
223#67—616no—
224#67—68no—
225#67—632no—
226C2×Dic3—22no—
227C2×Dic3—22no—
228C2×Dic3—42no—
229C2×Dic3—42no—
230C2×Dic3—61no—
231C2×Dic3—64no—
232C2×Dic3—61no—
233C2×Dic3—64no—
234C2×Dic3—62no—
235C2×Dic3—61no—
236C2×Dic3—61no—
237C2×Dic3—62no—
238C2×Dic3—68no—
239C2×Dic3—68no—
240C2×Dic3—64no—
241C2×Dic3—124no—
242C2×Dic3—124no—
243C2×Dic3—122no—
244Dic6—124no—
245Dic6—124no—
246C2×C32—24no—
247C2×C32#45014yescomplemented
248C2×C32C2×#12011yescharacteristic
249C2×C32C22×SD1611yescharacteristic
250C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
251C3×D3—48no—
252C24—68no—
253C24—64no—
254C24—62no—
255C24—124no—
256C24—124no—
257C24GO+(4,𝔽2)11yescharacteristic
258C2×Q8—92no—
259C2×Q8—181no—
260C2×Q8—184no—
261C2×D4—94no—
262C2×D4—98no—
263C2×D4—182no—
264C2×D4—184no—
265C2×D4—184no—
266C2×D4—1816no—
267C2×D4—1816no—
268C2×D4—188no—
269C22×C4—61no—
270C22×C4—61no—
271C22×C4—91no—
272C22×C4—92no—
273C22×C4—92no—
274C22×C4—91no—
275C22×C4—184no—
276SD16—1816no—
277C2×C8—94no—
278C2×C8—184no—
279C4⋊C4—92no—
280C4⋊C4—181no—
281C4⋊C4—184no—
282C22⋊C4—64no—
283C22×C3—24no—
284C22×C3—24no—
285C22×C3—216no—
286C22×C3—21no—
287C22×C3—21no—
288C22×C3—22no—
289C22×C3—22no—
290C22×C3—22no—
291C22×C3—22no—
292C22×C3—24no—
293C22×C3—24no—
294C22×C3—22no—
295C22×C3—22no—
296C22×C3—42no—
297C22×C3—42no—
298C22×C3—48no—
299C22×C3—68no—
300C22×C3—1232no—
301C22×C3—124no—
302C22×C3—124no—
303C22×C3—1216no—
304C2×D3—28no—
305C2×D3—432no—
306C2×D3—44no—
307C2×D3—44no—
308C2×D3—416no—
309C3×C4—122no—
310C3×C4—122no—
311Dic3—42no—
312Dic3—42no—
313Dic3—62no—
314Dic3—62no—
315Dic3—62no—
316Dic3—62no—
317Dic3—64no—
318Dic3—122no—
319C32C2×#45011yescharacteristic, complemented, Sylow
320C23—22no—
321C23—22no—
322C23—616no—
323C23—64no—
324C23—68no—
325C23—128no—
326C23—1232no—
327C23—124no—
328C23—124no—
329C23—128no—
330C23#377514yescomplemented
331C23C2×GO+(4,𝔽2)12yes—
332C23C2×GO+(4,𝔽2)11yescharacteristic
333Q8—184no—
334Q8—362no—
335D4—98no—
336D4—184no—
337D4—188no—
338D4—1816no—
339C2×C4—62no—
340C2×C4—62no—
341C2×C4—91no—
342C2×C4—91no—
343C2×C4—94no—
344C2×C4—92no—
345C2×C4—122no—
346C2×C4—122no—
347C2×C4—184no—
348C2×C4—184no—
349C2×C4—182no—
350C8—184no—
351C2×C3—28no—
352C2×C3—21no—
353C2×C3—21no—
354C2×C3—21no—
355C2×C3—21no—
356C2×C3—21no—
357C2×C3—21no—
358C2×C3—24no—
359C2×C3—24no—
360C2×C3—44no—
361C2×C3—128no—
362D3—48no—
363C22—22no—
364C22—22no—
365C22—28no—
366C22—68no—
367C22—1232no—
368C22—124no—
369C22—124no—
370C22—1216no—
371C22#6423612yes—
372C22C2×#377512yes—
373C22C2×#377514yescomplemented
374C22#6424112yes—
375C22C22×GO+(4,𝔽2)11yescharacteristic
376C4—92no—
377C4—92no—
378C4—122no—
379C4—122no—
380C4—182no—
381C3—21no—
382C3—21no—
383C2—24no—
384C2—128no—
385C2#1059352314yesdirect product factor
386C2C2×#6423611yescharacteristic
387C2C22×#377511yescharacteristic
388C2C2×#6424111yescharacteristic
subgroupG/H
centerC23C2×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FrattiniC22C22×GO+(4,𝔽2)
FittingC24×C32D4
socleC23×C32C2×D4
prime radicalC23×#625C2
hypercenterC24GO+(4,𝔽2)
hypocenterC32C2×#450
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C24

Complements

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

NH ≅ G/Ntype
2. C22×#3775C2semidirect
3. C2×#63982C2semidirect
4. C2×C22⋊#622C2semidirect
5. #10593523C2direct (N × H)
6. C2×#63739C2semidirect
9. C22×#627C22semidirect
15. C22×#622C22semidirect
17. C2×#3775C22semidirect
20. #63982C22semidirect
21. C2×#3724C22semidirect
23. C22⋊#622C22semidirect
24. #63739C22semidirect
42. C2×#627C23semidirect
52. C2×#622C23semidirect
56. #3724C23semidirect
78. C23×C32SD16semidirect
161. C22×C32C2×SD16semidirect
247. C2×C32#450semidirect
319. C32C2×#450semidirect
330. C23#3775semidirect
373. C22C2×#3775semidirect
385. C2#10593523direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#6252
C22×#37752
C2×#639822
C2×C22⋊#6222
#105935232
C2×#637392
C2×#4509