Finite Group Databasebeta

← C2×#10590074 #11783191

Subgroups — C2×#10590074 #11783191

Order 1152.

902 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 902 conjugacy classes of subgroups — too many to draw. Only its 143 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×#3792C211yesmaximal, characteristic
2C2×#63957C211yesmaximal, characteristic
3C22×Dic32C211yesmaximal, characteristic
4#10590074C214yesmaximal, direct product factor
5C23×C3⋊Dic3C2211yescharacteristic
6C23×C3×Dic3—21no—
7C2×#3792—22no—
8C2×#3792—21no—
9C2×#3792C414yescomplemented
10C2×#3792C2212yes—
11C22×#622—21no—
12C2×C3×#217—21no—
13C2×#3724C412yescomplemented
14#63957—21no—
15#63957—21no—
16#63957C412yescomplemented
17#63957C2212yes—
18C2×Dic32—21no—
19C2×Dic32—22no—
20C2×Dic32—21no—
21C2×Dic32C414yescomplemented
22C2×Dic32C2212yes—
23C22×C4×Dic3—61no—
24C2×#877—61no—
25C24×C32D411yescharacteristic
26C22×C3⋊Dic3C2×C412yes—
27C22×C3⋊Dic3C2×C412yes—
28C22×C3⋊Dic3C2×C411yescharacteristic
29C22×C3⋊Dic3C2×C411yescharacteristic
30C22×C3⋊Dic3D411yescharacteristic
31C22×C3⋊Dic3D411yescharacteristic
32C22×C3⋊Dic3D412yes—
33C22×C3⋊Dic3D411yescharacteristic
34C22×C3⋊Dic3Q812yes—
35C22×C3⋊Dic3C2311yescharacteristic
36C22×C3×Dic3—28no—
37C22×C3×Dic3—24no—
38C22×C3×Dic3—22no—
39C22×C3×Dic3—22no—
40#3792—24no—
41#3792—22no—
42#3792C2×C414yescomplemented
43C2×#622—24no—
44C2×#622—22no—
45C3×#217—22no—
46C3×#217—22no—
47#3724—22no—
48#3724C2×C414yescomplemented
49Dic32—24no—
50Dic32—22no—
51Dic32—22no—
52Dic32—22no—
53Dic32C2×C414yescomplemented
54C2×#339—91nomaximal, Sylow
55C23×C3×C4—61no—
56C23×Dic3—21no—
57C23×Dic3—61no—
58C23×Dic3—61no—
59C2×C3×C22⋊C4—61no—
60C2×#217—21no—
61C2×Dic3⋊C4—62no—
62C2×C4×Dic3—64no—
63C2×C4×Dic3—62no—
64C2×C4×Dic3—62no—
65C2×C4×Dic3—62no—
66C2×C4×Dic3—64no—
67#877—62no—
68#877—62no—
69#877—62no—
70#877—62no—
71C23×C32—24no—
72C23×C32C22⋊C411yescharacteristic
73C23×C32C22⋊C412yes—
74C23×C32C22⋊C411yescharacteristic
75C23×C32C4⋊C412yes—
76C23×C32C2×D411yescharacteristic
77C2×C3⋊Dic3C4212yes—
78C2×C3⋊Dic3C4212yes—
79C2×C3⋊Dic3C22⋊C412yes—
80C2×C3⋊Dic3C22⋊C411yescharacteristic
81C2×C3⋊Dic3C22⋊C411yescharacteristic
82C2×C3⋊Dic3C22⋊C412yes—
83C2×C3⋊Dic3C22⋊C412yes—
84C2×C3⋊Dic3C4⋊C412yes—
85C2×C3⋊Dic3C4⋊C412yes—
86C2×C3⋊Dic3C4⋊C412yes—
87C2×C3⋊Dic3C4⋊C412yes—
88C2×C3⋊Dic3C4⋊C412yes—
89C2×C3⋊Dic3C22×C411yescharacteristic
90C2×C3⋊Dic3C22×C411yescharacteristic
91C2×C3⋊Dic3C22×C411yescharacteristic
92C2×C3⋊Dic3C2×D411yescharacteristic
93C2×C3⋊Dic3C2×D411yescharacteristic
94C2×C3⋊Dic3C2×Q811yescharacteristic
95C2×C3×Dic3—216no—
96C2×C3×Dic3—28no—
97C2×C3×Dic3—24no—
98C2×C3×Dic3—24no—
99C2×C3×Dic3—44no—
100#622—24no—
101C22×M16—91no—
102C2×#117—91no—
103C22×C42—91no—
104#339—94no—
105C24×C3—21no—
106C24×C3—21no—
107C22×C3×C4—62no—
108C22×C3×C4—64no—
109C22×C3×C4—68no—
110C22×C3×C4—62no—
111C22×Dic3—22no—
112C22×Dic3—24no—
113C22×Dic3—28no—
114C22×Dic3—22no—
115C22×Dic3—61no—
116C22×Dic3—61no—
117C22×Dic3—61no—
118C22×Dic3—61no—
119C22×Dic3—62no—
120C22×Dic3—61no—
121C22×Dic3—62no—
122C22×Dic3—61no—
123C22×Dic3—61no—
124C22×Dic3—61no—
125C22×Dic3—62no—
126C22×Dic3—61no—
127C22×Dic3—61no—
128C22×Dic3—62no—
129C22×Dic3—62no—
130C22×Dic3—62no—
131C22×Dic3—61no—
132C22×Dic3—61no—
133C22×Dic3—62no—
134C22×Dic3—62no—
135C3×C22⋊C4—62no—
136C3×C22⋊C4—62no—
137#217—22no—
138#217—22no—
139Dic3⋊C4—64no—
140Dic3⋊C4—64no—
141C4×Dic3—64no—
142C4×Dic3—64no—
143C4×Dic3—64no—
144C4×Dic3—68no—
145C4×Dic3—64no—
146C22×C32—24no—
147C22×C32—24no—
148C22×C32—22no—
149C22×C32—22no—
150C22×C32#9512yes—
151C22×C32#9512yes—
152C22×C32#10414yes—
153C22×C32C2×C22⋊C411yescharacteristic
154C22×C32C2×C22⋊C411yescharacteristic
155C22×C32C2×C4⋊C411yescharacteristic
156C3⋊Dic3#9512yes—
157C3⋊Dic3#9512yes—
158C3⋊Dic3C2×C4211yescharacteristic
159C3⋊Dic3C2×C22⋊C411yescharacteristic
160C3⋊Dic3C2×C4⋊C411yescharacteristic
161C3⋊Dic3C2×C4⋊C411yescharacteristic
162C3×Dic3—28no—
163C3×Dic3—44no—
164C23×C4—61no—
165C23×C4—91no—
166C2×M16—94no—
167C2×M16—92no—
168C2×M16—182no—
169C2×M16—181no—
170C22×C8—181no—
171#117—92no—
172#117—92no—
173#117—181no—
174#117—181no—
175C2×C4⋊C4—92no—
176C2×C22⋊C4—61no—
177C2×C42—92no—
178C2×C42—94no—
179C2×C42—181no—
180C2×C42—181no—
181C2×C42—182no—
182C23×C3—24no—
183C23×C3—24no—
184C23×C3—21no—
185C23×C3—21no—
186C23×C3—22no—
187C23×C3—21no—
188C23×C3—21no—
189C23×C3—22no—
190C23×C3—21no—
191C23×C3—21no—
192C23×C3—22no—
193C23×C3—22no—
194C23×C3—44no—
195C2×C3×C4—64no—
196C2×C3×C4—616no—
197C2×C3×C4—68no—
198C2×C3×C4—64no—
199C2×C3×C4—124no—
200C2×Dic3—24no—
201C2×Dic3—216no—
202C2×Dic3—28no—
203C2×Dic3—24no—
204C2×Dic3—44no—
205C2×Dic3—62no—
206C2×Dic3—62no—
207C2×Dic3—62no—
208C2×Dic3—62no—
209C2×Dic3—61no—
210C2×Dic3—62no—
211C2×Dic3—61no—
212C2×Dic3—61no—
213C2×Dic3—62no—
214C2×Dic3—61no—
215C2×Dic3—62no—
216C2×Dic3—62no—
217C2×Dic3—62no—
218C2×Dic3—62no—
219C2×Dic3—62no—
220C2×Dic3—62no—
221C2×Dic3—62no—
222C2×Dic3—62no—
223C2×Dic3—62no—
224C2×Dic3—62no—
225C2×Dic3—62no—
226C2×Dic3—62no—
227C2×Dic3—62no—
228C2×Dic3—62no—
229C2×Dic3—61no—
230C2×Dic3—61no—
231C2×Dic3—61no—
232C2×Dic3—61no—
233C2×Dic3—61no—
234C2×Dic3—61no—
235C2×Dic3—61no—
236C2×Dic3—61no—
237C2×Dic3—61no—
238C2×Dic3—61no—
239C2×Dic3—61no—
240C2×Dic3—61no—
241C2×C32—21no—
242C2×C32—22no—
243C2×C32—21no—
244C2×C32#33914yescomplemented
245C2×C32C2×#9511yescharacteristic
246C2×C32C2×#10412yes—
247C24GO+(4,𝔽2)11yescharacteristic
248C22×C4—68no—
249C22×C4—62no—
250C22×C4—64no—
251C22×C4—62no—
252C22×C4—91no—
253C22×C4—91no—
254C22×C4—92no—
255C22×C4—92no—
256C22×C4—91no—
257C22×C4—91no—
258C22×C4—91no—
259C22×C4—91no—
260C22×C4—92no—
261C22×C4—92no—
262M16—94no—
263M16—182no—
264M16—184no—
265C2×C8—182no—
266C2×C8—184no—
267C4⋊C4—94no—
268C4⋊C4—182no—
269C22⋊C4—62no—
270C22⋊C4—62no—
271C42—94no—
272C42—182no—
273C42—184no—
274C42—182no—
275C42—182no—
276C22×C3—24no—
277C22×C3—22no—
278C22×C3—24no—
279C22×C3—22no—
280C22×C3—28no—
281C22×C3—24no—
282C22×C3—21no—
283C22×C3—21no—
284C22×C3—21no—
285C22×C3—21no—
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—44no—
295C22×C3—44no—
296C22×C3—42no—
297C22×C3—42no—
298C3×C4—68no—
299C3×C4—124no—
300Dic3—28no—
301Dic3—44no—
302Dic3—62no—
303Dic3—62no—
304Dic3—62no—
305Dic3—62no—
306Dic3—61no—
307Dic3—61no—
308Dic3—61no—
309Dic3—61no—
310Dic3—61no—
311Dic3—61no—
312Dic3—61no—
313Dic3—61no—
314C32C2×#33911yescharacteristic, complemented, Sylow
315C23—24no—
316C23D32⋊C411yescharacteristic
317C23D32⋊C412yes—
318C23D32⋊C411yescharacteristic
319C23#377312yes—
320C23C2×GO+(4,𝔽2)11yescharacteristic
321C2×C4—616no—
322C2×C4—68no—
323C2×C4—64no—
324C2×C4—64no—
325C2×C4—91no—
326C2×C4—91no—
327C2×C4—91no—
328C2×C4—92no—
329C2×C4—91no—
330C2×C4—91no—
331C2×C4—91no—
332C2×C4—91no—
333C2×C4—91no—
334C2×C4—92no—
335C2×C4—92no—
336C2×C4—92no—
337C2×C4—92no—
338C2×C4—92no—
339C2×C4—92no—
340C2×C4—92no—
341C2×C4—92no—
342C2×C4—92no—
343C2×C4—124no—
344C8—184no—
345C2×C3—21no—
346C2×C3—21no—
347C2×C3—22no—
348C2×C3—24no—
349C2×C3—24no—
350C2×C3—24no—
351C2×C3—21no—
352C2×C3—21no—
353C2×C3—22no—
354C2×C3—22no—
355C2×C3—41no—
356C2×C3—41no—
357C2×C3—42no—
358C22—24no—
359C22—24no—
360C22—22no—
361C22—22no—
362C22#6373712yes—
363C22#6373712yes—
364C22#6374114yes—
365C22C2×D32⋊C411yescharacteristic
366C22C2×D32⋊C411yescharacteristic
367C22C2×#377311yescharacteristic
368C4—68no—
369C4—91no—
370C4—91no—
371C4—91no—
372C4—91no—
373C4—92no—
374C4—92no—
375C4—124no—
376C3—21no—
377C3—21no—
378C2—21no—
379C2—21no—
380C2—22no—
381C2#1059007414yesdirect product factor
382C2C2×#6373711yescharacteristic
383C2C2×#6374112yes—
subgroupG/H
centerC23D32⋊C4
commutatorC3⋊Dic3C2×C42
FrattiniC23C2×GO+(4,𝔽2)
Fitting, prime radicalC24×C32D4
socleC23×C32C22⋊C4
cosocleC22×C3⋊Dic3C23
hypercenterC24GO+(4,𝔽2)
hypocenterC32C2×#339
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C24

Complements

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

NH ≅ G/Ntype
4. #10590074C2direct (N × H)
9. C2×#3792C4semidirect
13. C2×#3724C4semidirect
16. #63957C4semidirect
21. C2×Dic32C4semidirect
42. #3792C2×C4semidirect
48. #3724C2×C4semidirect
53. Dic32C2×C4semidirect
244. C2×C32#339semidirect
314. C32C2×#339semidirect
381. C2#10590074direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37922
C2×#639572
C22×Dic322
#105900742
C2×#3399