Finite Group Databasebeta

← #11792242

Subgroups — #11792242

Order 1152.

941 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 941 conjugacy classes of subgroups — too many to draw. Only its 126 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×C3×#932C212yesmaximal, complemented
2#10595044C211yesmaximal, characteristic, complemented
3#10592920C211yesmaximal, characteristic, complemented
4C2×#63568C212yesmaximal, complemented
5#10589168C211yesmaximal, characteristic, complemented
6#72098—32nomaximal
7C22×C32×D4C2211yescharacteristic
8C2×C3×#235C2212yes—
9C2×#3757—22no—
10C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
11C2×C4×C3⋊Dic3C2211yescharacteristic
12C2×C3×#214—22no—
13C3×#932—24no—
14C3×#932—24no—
15C2×C3×#213—22no—
16C2×C3×#208C2212yes—
17#63980—22no—
18#63908—22no—
19#63856—22no—
20#63568—24no—
21C2×C3×AGL(1,ℤ/8)—32no—
22#5833—32no—
23C2×#932D312yescomplemented
24C2×#837—32no—
25#5221—32no—
26#5221—61no—
27C2×#825—32no—
28#4554—32no—
29C24×C32—21no—
30C2×C32×D4—22no—
31C2×C32×D4—22no—
32C2×C32×D4—21no—
33C2×C32×D4D412yescomplemented
34C22×C32×C4C2311yescharacteristic
35C22×C3⋊Dic3—21no—
36C22×C3⋊Dic3D412yes—
37C2×C3×#67—22no—
38C3×#235—22no—
39C3×#235—22no—
40C3×#235—22no—
41C3×#235—22no—
42C2×C3×D12D412yes—
43C2×C3×C4×D3—22no—
44C2×C3×Dic6D412yes—
45C2×#625—22no—
46#3757—44no—
47C4⋊(C3⋊Dic3)—22no—
48C4×C3⋊Dic3—22no—
49C3×#214—28no—
50C3×#213—28no—
51C3×#208—22no—
52C3×#208D414yescomplemented
53C2×C3×C3⋊C8—22no—
54#3724—22no—
55(C2×D3)⋊Dic3—24no—
56#2006—91noSylow
57C2×C3×#41—32no—
58C22×C3×D4—21no—
59C22×C3×D4C2×D312yes—
60C2×#235C2×D312yes—
61C3×AGL(1,ℤ/8)—64no—
62C3×AGL(1,ℤ/8)—64no—
63C2×C3×SD16—62no—
64C2×C3×D8—62no—
65C2×C3×M16—32no—
66C2×#217—64no—
67C2×#217—64no—
68#946—62no—
69#939—64no—
70#938—62no—
71C2×#214—22no—
72#932—24no—
73#932—24no—
74C2×#213—22no—
75#930—62no—
76C2×C4⋊Dic3—32no—
77C2×C4⋊Dic3—61no—
78#924—62no—
79C2×C4×Dic3—32no—
80C2×C4×Dic3—61no—
81C2×#208C2×D312yes—
82#837—64no—
83#825—64no—
84C23×C32—22no—
85C23×C32—42no—
86C23×C32—42no—
87C23×C32—41no—
88C23×C32—41no—
89C23×C32C2×D411yescharacteristic
90C22×C3×D3—22no—
91C32×D4—24no—
92C32×D4—42no—
93C2×C32×C4C2×D412yes—
94C2×C32×C4C2×D412yes—
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4#4111yescharacteristic
97C2×C3⋊Dic3—22no—
98C2×C3⋊Dic3—22no—
99C2×C3⋊Dic3—41no—
100C2×C3⋊Dic3—41no—
101C2×C3⋊Dic3—42no—
102C3×#67—42no—
103C3×#67—42no—
104C2×C3×Dic3—22no—
105C3×D12—22no—
106C3×D12—22no—
107C3×C4×D3—42no—
108C3×C4×D3—42no—
109C3×Dic6—22no—
110C3×Dic6—22no—
111#625—82no—
112C3×C3⋊C8—24no—
113C2×AGL(1,ℤ/8)—32no—
114#537—91no—
115C2×#104—92no—
116#390—91no—
117#343—91no—
118C24×C3—22no—
119C24×C3—22no—
120C3×#41—62no—
121C3×#41—62no—
122C3×#41—62no—
123C3×#41—62no—
124C2×C3×Q8—32no—
125C2×C3×D4—22no—
126C2×C3×D4—22no—
127C2×C3×D4—22no—
128C2×C3×D4—22no—
129C2×C3×D4—22no—
130C2×C3×D4—22no—
131C2×C3×D4—22no—
132C2×C3×D4—32no—
133C2×C3×D4—42no—
134C2×C3×D4—42no—
135C2×C3×D4—62no—
136C2×C3×D4#6714yescomplemented
137C22×C3×C4—21no—
138C22×C3×C4—62no—
139C22×C3×C4C22×D312yes—
140C2×#67—22no—
141C2×#67—64no—
142C22×Dic3—34no—
143C22×Dic3—62no—
144C22×Dic3—62no—
145C22×Dic3—62no—
146#235—22no—
147#235—22no—
148#235—22no—
149#235—22no—
150C2×D12#6712yes—
151C2×C4×D3—22no—
152C2×Dic6#6712yes—
153C3×SD16—68no—
154C3×D8—68no—
155C3×M16—34no—
156C3×M16—62no—
157C2×C3×C8—62no—
158#217—64no—
159#217—128no—
160#217—128no—
161#214—28no—
162#213—28no—
163(C2×D3)⋊C4—64no—
164C4⋊Dic3—62no—
165C4⋊Dic3—62no—
166C4⋊Dic3—122no—
167Dic3⋊C4—64no—
168C4×Dic3—62no—
169C4×Dic3—62no—
170C4×Dic3—122no—
171#208—22no—
172#208#6714yescomplemented
173C2×C3⋊C8—22no—
174C22×C32—21no—
175C22×C32—21no—
176C22×C32—44no—
177C22×C32—42no—
178C22×C32—82no—
179C22×C32—81no—
180C22×C32—81no—
181C22×C32#12011yescharacteristic
182C22×C32#12111yescharacteristic
183C22×C32#12711yescharacteristic
184C2×C3×D3—42no—
185C2×C3×D3—42no—
186C2×C3×D3—42no—
187C32×C4#12012yes—
188C32×C4#12112yes—
189C3⋊Dic3—42no—
190C3⋊Dic3—42no—
191C3×Dic3—42no—
192C2×#41—32no—
193C22×D4D3211yescharacteristic
194AGL(1,ℤ/8)—64no—
195AGL(1,ℤ/8)—64no—
196C2×SD16—62no—
197C2×D8—62no—
198C2×M16—32no—
199C22⋊Q8—182no—
200#121—182no—
201#121—182no—
202C2×C4⋊C4—91no—
203C2×C22⋊C4—182no—
204C2×C42—91no—
205#104—184no—
206C23×C3—24no—
207C23×C3—24no—
208C23×C3—21no—
209C23×C3—44no—
210C23×C3—44no—
211C23×C3—42no—
212C23×C3—42no—
213C23×C3—44no—
214C23×C3—44no—
215C23×C3—42no—
216C23×C3—42no—
217C23×C3—62no—
218C23×C3D3×D412yes—
219C22×D3—22no—
220C3×Q8—62no—
221C3×Q8—62no—
222C3×D4—24no—
223C3×D4—24no—
224C3×D4—44no—
225C3×D4—44no—
226C3×D4—42no—
227C3×D4—42no—
228C3×D4—62no—
229C3×D4—62no—
230C3×D4—122no—
231C3×D4—122no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—22no—
235C2×C3×C4—22no—
236C2×C3×C4—62no—
237C2×C3×C4—122no—
238C2×C3×C4—122no—
239C2×C3×C4D3×D412yes—
240C2×C3×C4D3×D412yes—
241C2×C3×C4#23712yes—
242C2×C3×C4C2×#6712yes—
243C2×C3×C4C2×#6712yes—
244C2×C3×C4C2×#6712yes—
245#67—42no—
246#67—42no—
247#67—244no—
248C2×Dic3—22no—
249C2×Dic3—64no—
250C2×Dic3—64no—
251C2×Dic3—64no—
252C2×Dic3—122no—
253C2×Dic3—122no—
254C2×Dic3—122no—
255C2×Dic3—122no—
256C2×Dic3—122no—
257C2×Dic3—124no—
258C2×Dic3—124no—
259D12—22no—
260D12—22no—
261C4×D3—42no—
262C4×D3—42no—
263Dic6—22no—
264Dic6—22no—
265C3×C8—64no—
266C3⋊C8—24no—
267C2×C32—21no—
268C2×C32—21no—
269C2×C32—82no—
270C2×C32#39211yescharacteristic
271C2×C32#45311yescharacteristic
272C2×C32#45411yescharacteristic
273C3×D3—82no—
274C24—21no—
275#41—62no—
276#41—62no—
277#41—62no—
278#41—62no—
279C2×Q8—32no—
280C2×D4—21no—
281C2×D4—22no—
282C2×D4—22no—
283C2×D4—32no—
284C2×D4—62no—
285C2×D4—182no—
286C2×D4#62512yescomplemented
287C22×C4—62no—
288C22×C4—92no—
289C22×C4—181no—
290C22×C4C2×D3211yescharacteristic
291SD16—68no—
292D8—68no—
293M16—34no—
294M16—62no—
295C2×C8—62no—
296C4⋊C4—182no—
297C4⋊C4—182no—
298C22⋊C4—184no—
299C22⋊C4—364no—
300C42—182no—
301C22×C3—22no—
302C22×C3—22no—
303C22×C3—22no—
304C22×C3—22no—
305C22×C3—21no—
306C22×C3—21no—
307C22×C3—21no—
308C22×C3—44no—
309C22×C3—48no—
310C22×C3—48no—
311C22×C3—44no—
312C22×C3—84no—
313C22×C3—84no—
314C22×C3—82no—
315C22×C3—82no—
316C22×C3—82no—
317C22×C3—82no—
318C22×C3—122no—
319C22×C3—122no—
320C22×C3—122no—
321C22×C3#93712yes—
322C22×C3#93912yes—
323C22×C3#94012yes—
324C2×D3—42no—
325C2×D3—42no—
326C2×D3—42no—
327C3×C4—22no—
328C3×C4—22no—
329C3×C4—122no—
330C3×C4#93712yes—
331C3×C4#93812yes—
332C3×C4#93912yes—
333C3×C4#95312yes—
334Dic3—42no—
335Dic3—124no—
336Dic3—124no—
337Dic3—124no—
338Dic3—242no—
339C32#200611yescharacteristic, complemented, Sylow
340C23—22no—
341C23—42no—
342C23—42no—
343C23—41no—
344C23—41no—
345C23—62no—
346C23#381111yescharacteristic
347Q8—62no—
348Q8—62no—
349D4—24no—
350D4—42no—
351D4—62no—
352D4—62no—
353D4—122no—
354D4—122no—
355D4—722no—
356C2×C4—62no—
357C2×C4—122no—
358C2×C4—122no—
359C2×C4—182no—
360C2×C4—182no—
361C2×C4—361no—
362C2×C4—361no—
363C2×C4—362no—
364C2×C4#380511yescharacteristic
365C2×C4C2×#62511yescharacteristic
366C2×C4D3×#6712yes—
367C2×C4D3×#6712yes—
368C8—64no—
369C2×C3—22no—
370C2×C3—22no—
371C2×C3—22no—
372C2×C3—22no—
373C2×C3—21no—
374C2×C3—21no—
375C2×C3—21no—
376C2×C3—84no—
377C2×C3—84no—
378C2×C3—242no—
379C2×C3#519812yes—
380C2×C3#520112yes—
381C2×C3#522312yes—
382D3—82no—
383C22—21no—
384C22—21no—
385C22—44no—
386C22—42no—
387C22—82no—
388C22—81no—
389C22—81no—
390C22—122no—
391C22—122no—
392C22—122no—
393C22#6397911yescharacteristic
394C22#6398011yescharacteristic
395C22#6398311yescharacteristic
396C4—122no—
397C4—362no—
398C4—362no—
399C4#6397012yes—
400C4#6397612yes—
401C3—21no—
402C3#7209812yescomplemented
403C2—21no—
404C2—21no—
405C2—82no—
406C2—242no—
407C2#1059152211yescharacteristic
408C2#1059152411yescharacteristic
409C2#1059172311yescharacteristic
subgroupG/H
centerC22#63983
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×D4C22
socleC22×C32#120
hypercenterC22×D4D32
hypocenterC32#2006
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#932C2semidirect
2. #10595044C2semidirect
3. #10592920C2semidirect
4. C2×#63568C2semidirect
5. #10589168C2semidirect
23. C2×#932D3semidirect
33. C2×C32×D4D4semidirect
52. C3×#208D4semidirect
136. C2×C3×D4#67semidirect
172. #208#67semidirect
286. C2×D4#625semidirect
339. C32#2006semidirect
402. C3#72098semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9322
#105950442
#105929202
C2×#635682
#105891682
#720983