Finite Group Databasebeta

← #11775217

Subgroups — #11775217

Order 1152.

688 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 688 conjugacy classes of subgroups — too many to draw. Only its 61 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
1C2×#63980C211yesmaximal, characteristic
2#10593845C211yesmaximal, characteristic, complemented
3#10591705C211yesmaximal, characteristic, complemented
4#10590071C214yesmaximal, complemented
5C23×C3⋊Dic3C2211yescharacteristic
6C22×C3×#67—21no—
7C22×#625C411yescharacteristic, complemented
8C2×#3792—21no—
9C2×C3×#217—21no—
10#63980—21no—
11#63980—21no—
12#63980C412yescomplemented
13#63980C2212yes—
14C2×#3724C411yescharacteristic, complemented
15C2×(C2×D3)⋊Dic3—21no—
16C2×Dic32—21no—
17C22⋊#622—21no—
18C22⋊#622C2212yescomplemented
19#63579C2212yescomplemented
20C2×#939—61no—
21Dic3×C22⋊C4—61no—
22C24×C32D411yescharacteristic
23C23×C3×D3—21no—
24C22×C3⋊Dic3—42no—
25C22×C3⋊Dic3C2×C411yescharacteristic
26C22×C3⋊Dic3C2×C411yescharacteristic
27C22×C3⋊Dic3D411yescharacteristic
28C22×C3⋊Dic3D411yescharacteristic
29C22×C3⋊Dic3D411yescharacteristic
30C22×C3⋊Dic3C2311yescharacteristic
31C2×C3×#67—22no—
32C2×C3×#67—22no—
33C2×C3×#67—44no—
34C22×C3×Dic3—21no—
35C22×C3×Dic3—22no—
36C2×#625—21no—
37C2×#625—42no—
38C2×#625C2×C412yes—
39#3792—42no—
40C2×#622—22no—
41C3×#217—24no—
42#3724—21no—
43#3724C2×C412yes—
44(C2×D3)⋊Dic3—22no—
45(C2×D3)⋊Dic3—22no—
46Dic32—42no—
47#1507—91nomaximal, Sylow
48C22×C3×D4—61no—
49C22×#67—21no—
50C22×#67—61no—
51C23×Dic3—61no—
52C23×Dic3—61no—
53C2×C3×C22⋊C4—61no—
54C2×#217—21no—
55C2×#217—61no—
56#939—62no—
57#939—62no—
58#939—62no—
59#939—62no—
60C2×(C2×D3)⋊C4—61no—
61C2×Dic3⋊C4—61no—
62C2×C4×Dic3—62no—
63C3⋊#95—62no—
64C23×C32—22no—
65C23×C32—22no—
66C23×C32—41no—
67C23×C32C22⋊C411yescharacteristic
68C23×C32C22⋊C411yescharacteristic
69C23×C32C2×D411yescharacteristic
70C22×C3×D3—22no—
71C22×C3×D3—42no—
72C22×C3×D3—42no—
73C22×C3×D3—42no—
74C2×C3⋊Dic3—22no—
75C2×C3⋊Dic3—22no—
76C2×C3⋊Dic3—22no—
77C2×C3⋊Dic3—41no—
78C2×C3⋊Dic3—41no—
79C2×C3⋊Dic3—41no—
80C2×C3⋊Dic3C22⋊C411yescharacteristic
81C2×C3⋊Dic3C22⋊C411yescharacteristic
82C2×C3⋊Dic3C22×C411yescharacteristic
83C2×C3⋊Dic3C2×D411yescharacteristic
84C3×#67—44no—
85C3×#67—44no—
86C2×C3×Dic3—24no—
87C2×C3×Dic3—22no—
88C2×C3×Dic3—42no—
89C2×C3×Dic3—42no—
90C2×C3×Dic3—42no—
91#625—42no—
92#625—42no—
93#622—42no—
94C2×#121—91no—
95#407—91no—
96C4×C22⋊C4—91no—
97#327—94no—
98C24×C3—21no—
99C24×C3—21no—
100C24×C3—61no—
101C23×D3—21no—
102C2×C3×D4—62no—
103C2×C3×D4—62no—
104C2×C3×D4—124no—
105C22×C3×C4—62no—
106C22×C3×C4—61no—
107C2×#67—22no—
108C2×#67—22no—
109C2×#67—44no—
110C2×#67—62no—
111C2×#67—62no—
112C2×#67—124no—
113C22×Dic3—22no—
114C22×Dic3—21no—
115C22×Dic3—61no—
116C22×Dic3—61no—
117C22×Dic3—61no—
118C22×Dic3—61no—
119C22×Dic3—61no—
120C22×Dic3—61no—
121C22×Dic3—61no—
122C22×Dic3—61no—
123C22×Dic3—61no—
124C22×Dic3—61no—
125C22×Dic3—61no—
126C22×Dic3—61no—
127C22×Dic3—124no—
128C22×Dic3—124no—
129C3×C22⋊C4—64no—
130#217—24no—
131#217—62no—
132#217—62no—
133(C2×D3)⋊C4—62no—
134(C2×D3)⋊C4—62no—
135Dic3⋊C4—62no—
136Dic3⋊C4—62no—
137C4×Dic3—124no—
138C22×C32—21no—
139C22×C32—21no—
140C22×C32—21no—
141C22×C32—21no—
142C22×C32—21no—
143C22×C32—21no—
144C22×C32—21no—
145C22×C32—44no—
146C22×C32#10412yes—
147C22×C32C2×C22⋊C411yescharacteristic
148C22×C32AGL(1,ℤ/8)12yes—
149C2×C3×D3—42no—
150C2×C3×D3—42no—
151C2×C3×D3—42no—
152C2×C3×D3—84no—
153C3⋊Dic3—21no—
154C3⋊Dic3—21no—
155C3⋊Dic3—21no—
156C3⋊Dic3#9912yes—
157C3×Dic3—44no—
158C3×Dic3—42no—
159C22×D4—61no—
160C22×D4—91no—
161C23×C4—91no—
162C2×M16—181no—
163#121—92no—
164#121—92no—
165#121—181no—
166#121—181no—
167C2×C4⋊C4—91no—
168C2×C22⋊C4—61no—
169C2×C22⋊C4—181no—
170C2×C42—181no—
171C22⋊C8—92no—
172C22⋊C8—181no—
173#95—92no—
174C23×C3—22no—
175C23×C3—22no—
176C23×C3—24no—
177C23×C3—21no—
178C23×C3—21no—
179C23×C3—21no—
180C23×C3—21no—
181C23×C3—21no—
182C23×C3—21no—
183C23×C3—42no—
184C23×C3—42no—
185C23×C3—42no—
186C23×C3—42no—
187C23×C3—62no—
188C23×C3—122no—
189C23×C3—122no—
190C23×C3—122no—
191C22×D3—22no—
192C22×D3—42no—
193C22×D3—42no—
194C22×D3—42no—
195C3×D4—124no—
196C3×D4—124no—
197C2×C3×C4—62no—
198C2×C3×C4—64no—
199C2×C3×C4—122no—
200C2×C3×C4—122no—
201C2×C3×C4—122no—
202#67—44no—
203#67—44no—
204#67—124no—
205#67—124no—
206C2×Dic3—22no—
207C2×Dic3—24no—
208C2×Dic3—42no—
209C2×Dic3—42no—
210C2×Dic3—42no—
211C2×Dic3—61no—
212C2×Dic3—61no—
213C2×Dic3—61no—
214C2×Dic3—61no—
215C2×Dic3—61no—
216C2×Dic3—61no—
217C2×Dic3—61no—
218C2×Dic3—61no—
219C2×Dic3—64no—
220C2×Dic3—64no—
221C2×Dic3—122no—
222C2×Dic3—122no—
223C2×Dic3—122no—
224C2×Dic3—122no—
225C2×Dic3—122no—
226C2×Dic3—122no—
227C2×Dic3—122no—
228C2×Dic3—122no—
229C2×Dic3—122no—
230C2×Dic3—122no—
231C2×C32—22no—
232C2×C32—22no—
233C2×C32—41no—
234C2×C32C2×#9911yescharacteristic
235C2×C32#41811yescharacteristic
236C2×C32C2×#10411yescharacteristic
237C3×D3—82no—
238C24—61no—
239C24GO+(4,𝔽2)11yescharacteristic
240C2×D4—62no—
241C2×D4—62no—
242C2×D4—92no—
243C2×D4—124no—
244C2×D4—181no—
245C2×D4—362no—
246C22×C4—62no—
247C22×C4—61no—
248C22×C4—91no—
249C22×C4—91no—
250C22×C4—91no—
251C22×C4—91no—
252C22×C4—91no—
253C22×C4—91no—
254C22×C4—362no—
255M16—362no—
256C2×C8—182no—
257C4⋊C4—92no—
258C4⋊C4—181no—
259C22⋊C4—64no—
260C22⋊C4—182no—
261C22⋊C4—182no—
262C42—362no—
263C22×C3—21no—
264C22×C3—22no—
265C22×C3—22no—
266C22×C3—22no—
267C22×C3—21no—
268C22×C3—22no—
269C22×C3—22no—
270C22×C3—21no—
271C22×C3—21no—
272C22×C3—22no—
273C22×C3—22no—
274C22×C3—22no—
275C22×C3—22no—
276C22×C3—41no—
277C22×C3—41no—
278C22×C3—41no—
279C22×C3—41no—
280C22×C3—41no—
281C22×C3—41no—
282C22×C3—41no—
283C22×C3—41no—
284C22×C3—44no—
285C22×C3—44no—
286C22×C3—48no—
287C22×C3—122no—
288C22×C3—122no—
289C22×C3—122no—
290C22×C3—244no—
291C2×D3—42no—
292C2×D3—42no—
293C2×D3—42no—
294C2×D3—84no—
295C3×C4—122no—
296C3×C4—124no—
297Dic3—42no—
298Dic3—44no—
299Dic3—62no—
300Dic3—62no—
301Dic3—62no—
302Dic3—62no—
303Dic3—121no—
304Dic3—121no—
305Dic3—121no—
306Dic3—121no—
307C32#150711yescharacteristic, complemented, Sylow
308C23—22no—
309C23—22no—
310C23—41no—
311C23—62no—
312C23—122no—
313C23—122no—
314C23—122no—
315C23D32⋊C411yescharacteristic
316C23D32⋊C411yescharacteristic
317C23C2×GO+(4,𝔽2)11yescharacteristic
318D4—124no—
319D4—124no—
320D4—362no—
321D4—362no—
322C2×C4—64no—
323C2×C4—62no—
324C2×C4—91no—
325C2×C4—91no—
326C2×C4—91no—
327C2×C4—91no—
328C2×C4—122no—
329C2×C4—122no—
330C2×C4—122no—
331C2×C4—182no—
332C2×C4—182no—
333C2×C4—182no—
334C2×C4—361no—
335C2×C4—361no—
336C2×C4—361no—
337C8—362no—
338C2×C3—22no—
339C2×C3—22no—
340C2×C3—24no—
341C2×C3—21no—
342C2×C3—21no—
343C2×C3—21no—
344C2×C3—21no—
345C2×C3—21no—
346C2×C3—21no—
347C2×C3—42no—
348C2×C3—42no—
349C2×C3—42no—
350C2×C3—42no—
351C2×C3—242no—
352D3—82no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—44no—
361C22—122no—
362C22—122no—
363C22—122no—
364C22—244no—
365C22#6374112yes—
366C22C2×D32⋊C411yescharacteristic
367C22#6423612yes—
368C4—92no—
369C4—124no—
370C4—122no—
371C4—181no—
372C4—181no—
373C4—181no—
374C3—21no—
375C3—21no—
376C2—22no—
377C2—22no—
378C2—41no—
379C2—242no—
380C2#1059349011yescharacteristic
381C2#1059349311yescharacteristic
382C2C2×#6374111yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC23C2×GO+(4,𝔽2)
FittingC24×C32D4
socleC22×C32C2×C22⋊C4
prime radicalC2×#63980C2
cosocleC22×C3⋊Dic3C23
hypercenterC24GO+(4,𝔽2)
hypocenterC32#1507
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24

Complements

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

NH ≅ G/Ntype
2. #10593845C2semidirect
3. #10591705C2semidirect
4. #10590071C2semidirect
7. C22×#625C4semidirect
12. #63980C4semidirect
14. C2×#3724C4semidirect
18. C22⋊#622C22semidirect
19. #63579C22semidirect
307. C32#1507semidirect

Maximal subgroups

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

subgroupindex
C2×#639802
#105938452
#105917052
#105900712
#15079