Finite Group Databasebeta

← #11791499

Subgroups — #11791499

Order 1152.

853 conjugacy classes of subgroups; only the 164 normal subgroups are shown.

normal subgroups only

This group has 853 conjugacy classes of subgroups — too many to draw. Only its 164 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×#64145C211yesmaximal, characteristic
2C2×C3×#832C212yesmaximal
3#10591274C211yesmaximal, characteristic, complemented
4C2×#63572C211yesmaximal, characteristic, complemented
5C2×#63567C212yesmaximal, complemented
6#70162—32nomaximal
7C22×C32×D4C2211yescharacteristic
8C22×#634C2211yescharacteristic
9C2×#3757—21no—
10C2×#3757—21no—
11#64145—22no—
12#64145C414yescomplemented
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C2×C3×C4⋊Dic3C2212yes—
15C22×C3×C3⋊C8C2212yes—
16C2×Dic32—21no—
17C3×#832—24no—
18#63579—21no—
19#63572—22no—
20#63567—24no—
21C2×#936—32no—
22C2×#936—61no—
23C2×C3×#102—32no—
24C2×#832D312yes—
25C2×#816—32no—
26C2×Dic3⋊C8—32no—
27Dic3×C4⋊C4—32no—
28C2×#810—32no—
29C24×C32—21no—
30C2×C32×D4—22no—
31C2×C32×D4—21no—
32C2×C32×D4—22no—
33C2×C32×D4C2×C412yes—
34C22×C32×C4C2311yescharacteristic
35C22×C3⋊Dic3—21no—
36C22×C3⋊Dic3D411yescharacteristic
37C22×C3⋊Dic3D411yescharacteristic
38C2×#634—22no—
39C2×#634—22no—
40C2×#634—21no—
41C2×#634C2×C412yes—
42C22×C3×Dic3—22no—
43#3757—24no—
44#3757—24no—
45C4×C3⋊Dic3C2×C412yes—
46C4×C3⋊Dic3D412yes—
47C3×C4⋊Dic3—22no—
48C3×C4⋊Dic3D414yes—
49C2×C3×C3⋊C8—22no—
50C2×C3×C3⋊C8—22no—
51C2×C3×C3⋊C8—22no—
52Dic32—42no—
53#1983—91noSylow
54C22×C3×D4—21no—
55C22×C3×D4C2×D312yes—
56C22×Dic6—32no—
57C22×Dic6—61no—
58C22×C3×C8—32no—
59C2×C3×C4⋊C4—32no—
60C2×#217—62no—
61C2×#217—62no—
62C2×#217—62no—
63C2×#217—62no—
64#936—38no—
65#936—64no—
66#936—64no—
67#936—64no—
68C2×C4⋊Dic3C2×D312yes—
69C2×C4×Dic3—32no—
70C2×C4×Dic3—61no—
71C2×C4×Dic3—62no—
72C22×C3⋊C8C2×D312yes—
73C3×#102—64no—
74#832—24no—
75C3⋊#95—62no—
76#816—64no—
77Dic3⋊C8—64no—
78#810—64no—
79C23×C32—22no—
80C23×C32—42no—
81C23×C32—42no—
82C23×C32—41no—
83C23×C32—41no—
84C23×C32C2×D411yescharacteristic
85C32×D4—24no—
86C32×D4—41no—
87C32×D4—41no—
88C2×C32×C4C22×C411yescharacteristic
89C2×C32×C4C2×D411yescharacteristic
90C2×C32×C4C2×D412yes—
91C2×C32×C4#4112yes—
92C2×C3⋊Dic3—22no—
93C2×C3⋊Dic3—22no—
94C2×C3⋊Dic3—21no—
95C2×C3⋊Dic3—21no—
96C2×C3⋊Dic3—42no—
97C2×C3⋊Dic3C22⋊C412yes—
98C2×C3⋊Dic3C22⋊C412yes—
99#634—24no—
100#634—41no—
101#634—41no—
102C2×C3×Dic3—24no—
103C2×C3×Dic3—42no—
104C2×C3×Dic3—42no—
105C3×C3⋊C8—42no—
106C2×#124—91no—
107C2×C4⋊C8—91no—
108C2×#103—92no—
109C2×#102—32no—
110C4×C4⋊C4—91no—
111C24×C3—22no—
112C24×C3—22no—
113C2×C3×D4—22no—
114C2×C3×D4—22no—
115C2×C3×D4—22no—
116C2×C3×D4—22no—
117C2×C3×D4—22no—
118C2×C3×D4—22no—
119C2×C3×D4—22no—
120C2×C3×D4—42no—
121C2×C3×D4—42no—
122C2×C3×D4C4×D314yes—
123C22×C3×C4—21no—
124C22×C3×C4—62no—
125C22×C3×C4C22×D312yes—
126C22×Dic3—22no—
127C22×Dic3—32no—
128C22×Dic3—32no—
129C22×Dic3—61no—
130C22×Dic3—61no—
131C22×Dic3—62no—
132C22×Dic3—62no—
133C2×Dic6—34no—
134C2×Dic6—62no—
135C2×Dic6—62no—
136C2×Dic6—62no—
137C2×Dic6—62no—
138C2×Dic6—62no—
139C2×Dic6—62no—
140C2×Dic6—62no—
141C2×Dic6—122no—
142C2×Dic6—122no—
143C2×C3×C8—62no—
144C2×C3×C8—62no—
145C2×C3×C8—62no—
146C3×C4⋊C4—34no—
147C3×C4⋊C4—62no—
148#217—68no—
149#217—68no—
150#217—68no—
151#217—68no—
152C4⋊Dic3—22no—
153C4⋊Dic3#6714yes—
154C4×Dic3—34no—
155C4×Dic3—34no—
156C4×Dic3—62no—
157C4×Dic3—62no—
158C4×Dic3—124no—
159C2×C3⋊C8—22no—
160C2×C3⋊C8—22no—
161C2×C3⋊C8—22no—
162C22×C32—42no—
163C22×C32—42no—
164C22×C32—42no—
165C22×C32—82no—
166C22×C32—82no—
167C22×C32C2×C22⋊C411yescharacteristic
168C22×C32#12112yes—
169C22×C32#13512yes—
170C22×C32AGL(1,ℤ/8)11yescharacteristic
171C22×C32#13711yescharacteristic
172C32×C4C4×D412yes—
173C32×C4#12411yescharacteristic
174C32×C4#12711yescharacteristic
175C3⋊Dic3—22no—
176C3⋊Dic3—22no—
177C3⋊Dic3—42no—
178C3×Dic3—44no—
179C22×Q8—91no—
180C22×D4D3211yescharacteristic
181C22×C8—32no—
182#124—94no—
183#124—182no—
184C2×C4⋊C4—32no—
185C2×C22⋊C4—181no—
186C2×C22⋊C4—181no—
187C2×C42—91no—
188C2×C42—181no—
189C4⋊C8—182no—
190#103—184no—
191#102—64no—
192#95—181no—
193C23×C3—24no—
194C23×C3—24no—
195C23×C3—21no—
196C23×C3—44no—
197C23×C3—42no—
198C23×C3—42no—
199C23×C3—44no—
200C23×C3—42no—
201C23×C3—42no—
202C23×C3—42no—
203C23×C3—42no—
204C23×C3—42no—
205C23×C3—42no—
206C23×C3D3×D412yes—
207C3×D4—24no—
208C3×D4—24no—
209C3×D4—44no—
210C3×D4—42no—
211C3×D4—42no—
212C3×D4—42no—
213C3×D4—42no—
214C2×C3×C4—22no—
215C2×C3×C4—21no—
216C2×C3×C4—22no—
217C2×C3×C4—21no—
218C2×C3×C4—64no—
219C2×C3×C4—122no—
220C2×C3×C4—122no—
221C2×C3×C4C2×C4×D312yes—
222C2×C3×C4#23512yes—
223C2×C3×C4D3×D412yes—
224C2×C3×C4D3×D412yes—
225C2×C3×C4#23712yes—
226C2×C3×C4C2×#6712yes—
227C2×Dic3—24no—
228C2×Dic3—34no—
229C2×Dic3—34no—
230C2×Dic3—42no—
231C2×Dic3—42no—
232C2×Dic3—62no—
233C2×Dic3—62no—
234C2×Dic3—62no—
235C2×Dic3—62no—
236C2×Dic3—62no—
237C2×Dic3—62no—
238C2×Dic3—64no—
239C2×Dic3—64no—
240C2×Dic3—121no—
241C2×Dic3—121no—
242C2×Dic3—122no—
243C2×Dic3—124no—
244C2×Dic3—122no—
245C2×Dic3—122no—
246Dic6—64no—
247Dic6—64no—
248Dic6—124no—
249Dic6—122no—
250Dic6—122no—
251Dic6—122no—
252Dic6—122no—
253C3×C8—122no—
254C3⋊C8—42no—
255C2×C32—82no—
256C2×C32#39011yescharacteristic
257C2×C32#41611yescharacteristic
258C2×C32#41711yescharacteristic
259C2×C32#46312yes—
260C2×C32#46412yes—
261C24—21no—
262C2×Q8—92no—
263C2×Q8—181no—
264C2×Q8—182no—
265C2×Q8—182no—
266C2×D4—22no—
267C2×D4—22no—
268C2×D4—21no—
269C2×D4#62412yes—
270C22×C4—62no—
271C22×C4—91no—
272C22×C4—91no—
273C22×C4—181no—
274C22×C4C2×D3211yescharacteristic
275C2×C8—62no—
276C2×C8—62no—
277C2×C8—62no—
278C4⋊C4—34no—
279C4⋊C4—62no—
280C22⋊C4—184no—
281C22⋊C4—184no—
282C42—92no—
283C42—92no—
284C42—362no—
285C22×C3—21no—
286C22×C3—21no—
287C22×C3—22no—
288C22×C3—22no—
289C22×C3—21no—
290C22×C3—44no—
291C22×C3—44no—
292C22×C3—44no—
293C22×C3—44no—
294C22×C3—44no—
295C22×C3—44no—
296C22×C3—84no—
297C22×C3—84no—
298C22×C3—82no—
299C22×C3—82no—
300C22×C3—82no—
301C22×C3—82no—
302C22×C3D3×C22⋊C412yes—
303C22×C3#88412yes—
304C22×C3#91112yes—
305C22×C3#91212yes—
306C22×C3#91512yes—
307C22×C3#91612yes—
308C22×C3#93912yes—
309C3×C4—22no—
310C3×C4—21no—
311C3×C4—21no—
312C3×C4—124no—
313C3×C4#67⋊C412yes—
314C3×C4#88512yes—
315C3×C4C4×#6712yes—
316C3×C4#94012yes—
317Dic3—44no—
318Dic3—64no—
319Dic3—64no—
320Dic3—122no—
321Dic3—122no—
322Dic3—124no—
323Dic3—124no—
324C32#198311yescharacteristic, complemented, Sylow
325C23—22no—
326C23—41no—
327C23—41no—
328C23—42no—
329C23—42no—
330C23#381111yescharacteristic
331Q8—184no—
332Q8—361no—
333Q8—361no—
334D4—24no—
335D4—41no—
336D4—41no—
337C2×C4—64no—
338C2×C4—92no—
339C2×C4—92no—
340C2×C4—122no—
341C2×C4—122no—
342C2×C4—181no—
343C2×C4—181no—
344C2×C4—182no—
345C2×C4—182no—
346C2×C4—362no—
347C2×C4#380412yes—
348C2×C4C2×#62411yescharacteristic
349C2×C4D3×#6712yes—
350C2×C4#381111yescharacteristic
351C8—122no—
352C2×C3—21no—
353C2×C3—21no—
354C2×C3—22no—
355C2×C3—22no—
356C2×C3—21no—
357C2×C3—84no—
358C2×C3—84no—
359C2×C3#476712yes—
360C2×C3#477112yes—
361C2×C3#477212yes—
362C2×C3#478712yes—
363C2×C3#495712yes—
364C2×C3#515312yes—
365C2×C3#516612yes—
366C22—42no—
367C22—42no—
368C22—42no—
369C22—82no—
370C22—82no—
371C22#6392711yescharacteristic
372C22#6393111yescharacteristic
373C22#6393612yes—
374C22#6397112yes—
375C22#6397411yescharacteristic
376C4—124no—
377C4—182no—
378C4—182no—
379C4—362no—
380C4#6395212yes—
381C4#6395311yescharacteristic
382C4#6397911yescharacteristic
383C3—21no—
384C3#7016212yescomplemented
385C2—82no—
386C2#1059141811yescharacteristic
387C2#1059142411yescharacteristic
388C2#1059143412yes—
389C2#1059144312yes—
390C2#1059170411yescharacteristic
subgroupG/H
centerC23#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
Fitting, prime radicalC22×C32×D4C22
socleC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenterC22×D4D32
hypocenterC32#1983
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
3. #10591274C2semidirect
4. C2×#63572C2semidirect
5. C2×#63567C2semidirect
12. #64145C4semidirect
324. C32#1983semidirect
384. C3#70162semidirect

Maximal subgroups

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

subgroupindex
C2×#641452
C2×C3×#8322
#105912742
C2×#635722
C2×#635672
#701623