Finite Group Databasebeta

← #11787260

Subgroups — #11787260

Order 1152.

774 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 774 conjugacy classes of subgroups — too many to draw. Only its 99 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×#63982C211yesmaximal, characteristic
2C22×#3724C211yesmaximal, characteristic
3C2×C22⋊#622C211yesmaximal, characteristic
4C2×#63740C212yesmaximal, complemented
5#10590075C212yesmaximal, complemented
6C23×C3⋊Dic3C2211yescharacteristic
7C23×C3×Dic3—21no—
8C22×#627C2211yescharacteristic
9C22×#622C2212yes—
10C2×C3×#217—21no—
11#63982—22no—
12#63982C414yescomplemented
13C2×#3724—21no—
14C2×#3724—24no—
15C2×#3724C2211yescharacteristic
16C2×#3724C2212yes—
17C2×Dic3⋊Dic3—21no—
18C22⋊#622—22no—
19#63740—24no—
20C22×Dic3⋊C4—61no—
21C2×#878—61no—
22C24×C32D411yescharacteristic
23C22×C3⋊Dic3—22no—
24C22×C3⋊Dic3—22no—
25C22×C3⋊Dic3C2×C412yes—
26C22×C3⋊Dic3D411yescharacteristic
27C22×C3⋊Dic3D412yes—
28C22×C3⋊Dic3C2311yescharacteristic
29C22×C3×Dic3—24no—
30C22×C3×Dic3—21no—
31C22×C3×Dic3—21no—
32C22×C3×Dic3—22no—
33C22×C3×Dic3—42no—
34C22×C3×Dic3—42no—
35C2×#627—22no—
36C2×#627—22no—
37C2×#627—21no—
38C2×#627C2×C412yescomplemented
39C2×#622—22no—
40C2×#622—22no—
41C2×#622—22no—
42C3×#217—24no—
43#3724—24no—
44#3724—22no—
45#3724—21no—
46#3724C2×C412yescomplemented
47#3724D414yes—
48Dic3⋊Dic3—24no—
49#1872—91nomaximal, Sylow
50C23×C3×C4—61no—
51C23×Dic3—21no—
52C23×Dic3—61no—
53C23×Dic3—61no—
54C22×Dic6—61no—
55C2×C3×C22⋊C4—61no—
56C2×#217—21no—
57C2×C4⋊Dic3—61no—
58C2×Dic3⋊C4—61no—
59C2×Dic3⋊C4—62no—
60C2×Dic3⋊C4—61no—
61C2×Dic3⋊C4—68no—
62C2×Dic3⋊C4—62no—
63#878—64no—
64#878—64no—
65C23×C32—21no—
66C23×C32—21no—
67C23×C32—21no—
68C23×C32—21no—
69C23×C32C22⋊C412yes—
70C23×C32SD1612yes—
71C23×C32Q1612yes—
72C23×C32C2×D411yescharacteristic
73C2×C3⋊Dic3—21no—
74C2×C3⋊Dic3—21no—
75C2×C3⋊Dic3—24no—
76C2×C3⋊Dic3—24no—
77C2×C3⋊Dic3C22⋊C412yes—
78C2×C3⋊Dic3C22×C411yescharacteristic
79C2×C3⋊Dic3C2×D412yes—
80C2×C3⋊Dic3C2×D411yescharacteristic
81C2×C3⋊Dic3#4112yes—
82C2×C3×Dic3—22no—
83C2×C3×Dic3—22no—
84C2×C3×Dic3—24no—
85C2×C3×Dic3—48no—
86C2×C3×Dic3—41no—
87C2×C3×Dic3—41no—
88C2×C3×Dic3—42no—
89C2×C3×Dic3—41no—
90C2×C3×Dic3—42no—
91C2×C3×Dic3—41no—
92#627—24no—
93#627—42no—
94#622—42no—
95C2×C22⋊Q8—91no—
96C22×C4⋊C4—91no—
97C2×#103—92no—
98C2×C22⋊C8—91no—
99#340—92no—
100C24×C3—21no—
101C24×C3—21no—
102C22×C3×C4—64no—
103C22×C3×C4—62no—
104C22×C3×C4—61no—
105C22×C3×C4—61no—
106C22×C3×C4—122no—
107C22×C3×C4—122no—
108C22×Dic3—21no—
109C22×Dic3—24no—
110C22×Dic3—22no—
111C22×Dic3—21no—
112C22×Dic3—42no—
113C22×Dic3—42no—
114C22×Dic3—61no—
115C22×Dic3—61no—
116C22×Dic3—61no—
117C22×Dic3—62no—
118C22×Dic3—62no—
119C22×Dic3—62no—
120C22×Dic3—62no—
121C22×Dic3—61no—
122C22×Dic3—64no—
123C22×Dic3—64no—
124C22×Dic3—122no—
125C22×Dic3—122no—
126C2×Dic6—62no—
127C2×Dic6—62no—
128C2×Dic6—122no—
129C2×Dic6—122no—
130C3×C22⋊C4—64no—
131#217—24no—
132C4⋊Dic3—64no—
133Dic3⋊C4—62no—
134Dic3⋊C4—64no—
135Dic3⋊C4—64no—
136Dic3⋊C4—62no—
137Dic3⋊C4—64no—
138Dic3⋊C4—68no—
139C22×C32—22no—
140C22×C32—22no—
141C22×C32—22no—
142C22×C32—22no—
143C22×C32—22no—
144C22×C32—22no—
145C22×C32#10314yescomplemented
146C22×C32C2×C22⋊C411yescharacteristic
147C22×C32#12011yescharacteristic
148C22×C32#12311yescharacteristic
149C22×C32C2×SD1611yescharacteristic
150C22×C32C2×Q1611yescharacteristic
151C22×C32AGL(1,ℤ/8)11yescharacteristic
152C22×C32#13711yescharacteristic
153C3⋊Dic3—22no—
154C3⋊Dic3C4×D412yes—
155C3⋊Dic3#12112yes—
156C3×Dic3—42no—
157C3×Dic3—42no—
158C3×Dic3—44no—
159C22×Q8—91no—
160C23×C4—61no—
161C23×C4—91no—
162C22×C8—92no—
163C22⋊Q8—94no—
164C22⋊Q8—182no—
165C2×C4⋊C4—92no—
166C2×C4⋊C4—91no—
167C2×C4⋊C4—184no—
168C2×C4⋊C4—181no—
169C2×C4⋊C4—181no—
170C2×C22⋊C4—61no—
171#103—184no—
172C22⋊C8—182no—
173C23×C3—22no—
174C23×C3—22no—
175C23×C3—22no—
176C23×C3—22no—
177C23×C3—21no—
178C23×C3—21no—
179C23×C3—22no—
180C23×C3—22no—
181C23×C3—22no—
182C23×C3—22no—
183C23×C3—22no—
184C23×C3—22no—
185C23×C3—41no—
186C23×C3—41no—
187C23×C3—41no—
188C23×C3—41no—
189C2×C3×C4—64no—
190C2×C3×C4—62no—
191C2×C3×C4—62no—
192C2×C3×C4—121no—
193C2×C3×C4—121no—
194C2×C3×C4—121no—
195C2×C3×C4—121no—
196C2×C3×C4—128no—
197C2×C3×C4—122no—
198C2×C3×C4—122no—
199C2×Dic3—22no—
200C2×Dic3—24no—
201C2×Dic3—22no—
202C2×Dic3—41no—
203C2×Dic3—41no—
204C2×Dic3—41no—
205C2×Dic3—41no—
206C2×Dic3—48no—
207C2×Dic3—42no—
208C2×Dic3—42no—
209C2×Dic3—62no—
210C2×Dic3—61no—
211C2×Dic3—61no—
212C2×Dic3—62no—
213C2×Dic3—61no—
214C2×Dic3—62no—
215C2×Dic3—61no—
216C2×Dic3—62no—
217C2×Dic3—62no—
218C2×Dic3—62no—
219C2×Dic3—62no—
220C2×Dic3—68no—
221C2×Dic3—68no—
222C2×Dic3—62no—
223C2×Dic3—124no—
224C2×Dic3—124no—
225C2×Dic3—121no—
226C2×Dic3—121no—
227Dic6—124no—
228Dic6—124no—
229C2×C32—24no—
230C2×C32#38611yescharacteristic
231C2×C32C2×#10311yescharacteristic
232C2×C32#41711yescharacteristic
233C2×C32#45011yescharacteristic
234C2×C32#45111yescharacteristic
235C2×C32#48311yescharacteristic
236C2×C32#48411yescharacteristic
237C24GO+(4,𝔽2)11yescharacteristic
238C2×Q8—92no—
239C2×Q8—181no—
240C2×Q8—182no—
241C2×Q8—182no—
242C22×C4—64no—
243C22×C4—61no—
244C22×C4—61no—
245C22×C4—62no—
246C22×C4—91no—
247C22×C4—91no—
248C22×C4—92no—
249C22×C4—92no—
250C22×C4—122no—
251C22×C4—122no—
252C22×C4—182no—
253C22×C4—182no—
254C2×C8—182no—
255C2×C8—182no—
256C2×C8—182no—
257C4⋊C4—94no—
258C4⋊C4—92no—
259C4⋊C4—182no—
260C4⋊C4—181no—
261C4⋊C4—184no—
262C4⋊C4—184no—
263C22⋊C4—64no—
264C22×C3—24no—
265C22×C3—24no—
266C22×C3—24no—
267C22×C3—24no—
268C22×C3—24no—
269C22×C3—24no—
270C22×C3—21no—
271C22×C3—21no—
272C22×C3—21no—
273C22×C3—21no—
274C22×C3—21no—
275C22×C3—21no—
276C22×C3—21no—
277C22×C3—21no—
278C22×C3—21no—
279C22×C3—21no—
280C22×C3—21no—
281C22×C3—21no—
282C22×C3—21no—
283C22×C3—21no—
284C22×C3—24no—
285C22×C3—24no—
286C22×C3—42no—
287C22×C3—42no—
288C22×C3—42no—
289C22×C3—42no—
290C22×C3—42no—
291C22×C3—42no—
292C3×C4—122no—
293C3×C4—124no—
294C3×C4—122no—
295Dic3—42no—
296Dic3—44no—
297Dic3—42no—
298Dic3—62no—
299Dic3—62no—
300Dic3—62no—
301Dic3—62no—
302Dic3—64no—
303Dic3—122no—
304C32#187211yescharacteristic, complemented, Sylow
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23D32⋊C412yes—
310C23#377512yes—
311C23#377612yes—
312C23C2×GO+(4,𝔽2)11yescharacteristic
313Q8—184no—
314Q8—362no—
315C2×C4—62no—
316C2×C4—62no—
317C2×C4—64no—
318C2×C4—91no—
319C2×C4—91no—
320C2×C4—92no—
321C2×C4—92no—
322C2×C4—92no—
323C2×C4—128no—
324C2×C4—121no—
325C2×C4—122no—
326C2×C4—121no—
327C2×C4—122no—
328C2×C4—121no—
329C2×C4—121no—
330C2×C4—184no—
331C2×C4—184no—
332C2×C4—181no—
333C2×C4—181no—
334C8—362no—
335C2×C3—28no—
336C2×C3—21no—
337C2×C3—21no—
338C2×C3—21no—
339C2×C3—21no—
340C2×C3—21no—
341C2×C3—21no—
342C2×C3—21no—
343C2×C3—21no—
344C2×C3—21no—
345C2×C3—21no—
346C2×C3—21no—
347C2×C3—21no—
348C2×C3—21no—
349C2×C3—21no—
350C2×C3—44no—
351C22—22no—
352C22—22no—
353C22—22no—
354C22—22no—
355C22—22no—
356C22—22no—
357C22#6374014yescomplemented
358C22C2×D32⋊C411yescharacteristic
359C22#6423311yescharacteristic
360C22#6423611yescharacteristic
361C22C2×#377511yescharacteristic
362C22#6423911yescharacteristic
363C22C2×#377611yescharacteristic
364C22#6424111yescharacteristic
365C4—92no—
366C4—92no—
367C4—122no—
368C4—122no—
369C4—124no—
370C4—182no—
371C3—21no—
372C3—21no—
373C2—24no—
374C2#1059349611yescharacteristic
375C2#1059349911yescharacteristic
376C2#1059350011yescharacteristic
377C2C2×#6374011yescharacteristic
378C2#1059350411yescharacteristic
379C2#1059351411yescharacteristic
380C2#1059352311yescharacteristic
subgroupG/H
center, FrattiniC23C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
Fitting, prime radicalC24×C32D4
socleC23×C32C2×D4
cosocleC22×C3⋊Dic3C23
hypercenterC24GO+(4,𝔽2)
hypocenterC32#1872
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C24

Complements

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

NH ≅ G/Ntype
4. C2×#63740C2semidirect
5. #10590075C2semidirect
12. #63982C4semidirect
38. C2×#627C2×C4semidirect
46. #3724C2×C4semidirect
145. C22×C32#103semidirect
304. C32#1872semidirect
357. C22#63740semidirect

Maximal subgroups

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

subgroupindex
C2×#639822
C22×#37242
C2×C22⋊#6222
C2×#637402
#105900752
#18729