Finite Group Databasebeta

← #11792253

Subgroups — #11792253

Order 1152.

941 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 941 conjugacy classes of subgroups — too many to draw. Only its 120 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
1#10595044C211yesmaximal, characteristic, complemented
2C2×#63825C212yesmaximal, complemented
3#10592638C211yesmaximal, characteristic, complemented
4C2×C3×#805C212yesmaximal, complemented
5#10589168C211yesmaximal, characteristic, complemented
6#70392—32nomaximal
7C22×C4⋊(C3⋊D3)C2211yescharacteristic
8C2×C3×#235C2212yes—
9C2×C32×C42C2211yescharacteristic
10C2×#3752—22no—
11C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
12C2×C3×#208C2212yes—
13#63980—22no—
14#63908—22no—
15#63856—22no—
16C2×#3717—22no—
17#63825—24no—
18#63825—24no—
19C2×#3714—22no—
20C3×#805—24no—
21#5833—32no—
22C2×#949—32no—
23C2×#908—32no—
24C2×C3×#104—32no—
25#4939—32no—
26#4939—61no—
27C2×#805D312yescomplemented
28#4554—32no—
29C23×C3⋊D3—21no—
30C22×C32×C4—21no—
31C22×C32×C4C2311yescharacteristic
32C22×C3⋊Dic3D412yes—
33C2×C4⋊(C3⋊D3)—22no—
34C2×C4⋊(C3⋊D3)—22no—
35C2×C4⋊(C3⋊D3)—21no—
36C2×C4⋊(C3⋊D3)D412yescomplemented
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—
46C32×C42—22no—
47#3752—44no—
48C4⋊(C3⋊Dic3)—22no—
49C3×#208—22no—
50C3×#208D414yescomplemented
51C2×C3×C3⋊C8—22no—
52#3724—22no—
53(C2×D3)⋊Dic3—24no—
54#3717—28no—
55#3714—28no—
56#2006—91noSylow
57C2×C3×#41—32no—
58C2×#235C2×D312yes—
59C22×D12—32no—
60C22×D12—61no—
61C2×C3×M16—32no—
62C2×C3×C42—21no—
63C2×C3×C42C2×D312yes—
64#949—64no—
65#949—64no—
66#946—62no—
67C2×#215—62no—
68#939—64no—
69#938—62no—
70C2×#213—62no—
71#930—62no—
72C2×(C2×D3)⋊C4—64no—
73C2×(C2×D3)⋊C4—64no—
74C2×C4⋊Dic3—32no—
75C2×C4⋊Dic3—61no—
76#924—62no—
77C2×#208C2×D312yes—
78#908—64no—
79#908—64no—
80C2×D24—62no—
81C2×#204—62no—
82C3×#104—64no—
83#805—24no—
84C23×C32C2×D411yescharacteristic
85C22×C3⋊D3—22no—
86C22×C3⋊D3—42no—
87C22×C3⋊D3—42no—
88C22×C3⋊D3—41no—
89C22×C3⋊D3—41no—
90C22×C3×D3—22no—
91C2×C32×C4—22no—
92C2×C32×C4—41no—
93C2×C32×C4—41no—
94C2×C32×C4C2×D412yes—
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4C2×D412yes—
97C2×C32×C4#4111yescharacteristic
98C2×C3⋊Dic3—22no—
99C2×C3⋊Dic3—42no—
100C4⋊(C3⋊D3)—24no—
101C4⋊(C3⋊D3)—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)—92no—
114#537—91no—
115C2×#104—32no—
116#390—91no—
117#343—91no—
118C23×D3—62no—
119C23×D3—62no—
120C3×#41—62no—
121C3×#41—62no—
122C3×#41—62no—
123C3×#41—62no—
124C2×C3×Q8—32no—
125C2×C3×D4—32no—
126C2×C3×D4—62no—
127C22×C3×C4—22no—
128C22×C3×C4—22no—
129C22×C3×C4—21no—
130C22×C3×C4—62no—
131C22×C3×C4C22×D312yes—
132C2×#67—22no—
133C2×#67—64no—
134C22×Dic3—34no—
135C22×Dic3—62no—
136#235—22no—
137#235—22no—
138#235—22no—
139#235—22no—
140C2×D12—34no—
141C2×D12—62no—
142C2×D12—62no—
143C2×D12—62no—
144C2×D12—62no—
145C2×D12—62no—
146C2×D12—62no—
147C2×D12—62no—
148C2×D12—122no—
149C2×D12—122no—
150C2×D12D1212yes—
151C2×C4×D3—22no—
152C2×Dic6D1212yes—
153C3×M16—34no—
154C3×M16—62no—
155C2×C3×C8—62no—
156C3×C42—22no—
157C3×C42—22no—
158C3×C42—42no—
159#217—64no—
160#215—68no—
161#213—68no—
162(C2×D3)⋊C4—64no—
163(C2×D3)⋊C4—128no—
164(C2×D3)⋊C4—128no—
165C4⋊Dic3—62no—
166C4⋊Dic3—62no—
167C4⋊Dic3—122no—
168Dic3⋊C4—64no—
169#208—22no—
170#208#6714yescomplemented
171C2×C3⋊C8—22no—
172D24—68no—
173#204—68no—
174C22×C32—21no—
175C22×C32—21no—
176C22×C32#12011yescharacteristic
177C22×C32#12111yescharacteristic
178C22×C32#12711yescharacteristic
179C2×C3⋊D3—44no—
180C2×C3⋊D3—42no—
181C2×C3⋊D3—82no—
182C2×C3⋊D3—81no—
183C2×C3⋊D3—81no—
184C2×C3×D3—42no—
185C2×C3×D3—42no—
186C2×C3×D3—42no—
187C32×C4—42no—
188C32×C4#12012yes—
189C32×C4#12112yes—
190C3⋊Dic3—42no—
191C3×Dic3—42no—
192C2×#41—32no—
193C22×D4—91no—
194AGL(1,ℤ/8)—184no—
195AGL(1,ℤ/8)—184no—
196C2×SD16—182no—
197C2×D8—182no—
198C2×M16—32no—
199C22⋊Q8—182no—
200#121—182no—
201#121—182no—
202C2×C4⋊C4—91no—
203C2×C22⋊C4—182no—
204C2×C42D3211yescharacteristic
205#104—64no—
206C23×C3—21no—
207C23×C3—62no—
208C23×C3D3×D412yes—
209C22×D3—22no—
210C22×D3—64no—
211C22×D3—64no—
212C22×D3—124no—
213C22×D3—124no—
214C22×D3—122no—
215C22×D3—122no—
216C22×D3—124no—
217C22×D3—124no—
218C22×D3—122no—
219C22×D3—122no—
220C3×Q8—62no—
221C3×Q8—62no—
222C3×D4—62no—
223C3×D4—62no—
224C3×D4—122no—
225C3×D4—122no—
226C2×C3×C4—24no—
227C2×C3×C4—24no—
228C2×C3×C4—21no—
229C2×C3×C4—22no—
230C2×C3×C4—21no—
231C2×C3×C4—22no—
232C2×C3×C4—42no—
233C2×C3×C4—42no—
234C2×C3×C4—42no—
235C2×C3×C4—42no—
236C2×C3×C4—62no—
237C2×C3×C4—122no—
238C2×C3×C4—122no—
239C2×C3×C4C2×D1212yes—
240C2×C3×C4#23512yes—
241C2×C3×C4D3×D412yes—
242C2×C3×C4D3×D412yes—
243C2×C3×C4D3×D412yes—
244C2×C3×C4C2×#6712yes—
245#67—42no—
246#67—42no—
247#67—244no—
248C2×Dic3—22no—
249C2×Dic3—64no—
250C2×Dic3—122no—
251C2×Dic3—124no—
252C2×Dic3—124no—
253D12—22no—
254D12—22no—
255D12—64no—
256D12—64no—
257D12—124no—
258D12—124no—
259D12—122no—
260D12—122no—
261C4×D3—42no—
262C4×D3—42no—
263Dic6—22no—
264Dic6—22no—
265C3×C8—64no—
266C3⋊C8—24no—
267C2×C32—21no—
268C2×C32—21no—
269C2×C32#39211yescharacteristic
270C2×C32#45311yescharacteristic
271C2×C32#45411yescharacteristic
272C3⋊D3—82no—
273C3×D3—82no—
274C24—181no—
275#41—62no—
276#41—62no—
277#41—62no—
278#41—62no—
279C2×Q8—32no—
280C2×D4—32no—
281C2×D4—62no—
282C2×D4—92no—
283C2×D4—182no—
284C2×D4—181no—
285C2×D4—182no—
286C2×D4—182no—
287C22×C4—21no—
288C22×C4—62no—
289C22×C4—92no—
290C22×C4C2×D3211yescharacteristic
291SD16—188no—
292D8—188no—
293M16—34no—
294M16—62no—
295C2×C8—62no—
296C4⋊C4—182no—
297C4⋊C4—182no—
298C22⋊C4—184no—
299C22⋊C4—364no—
300C42—22no—
301C22×C3—22no—
302C22×C3—22no—
303C22×C3—22no—
304C22×C3—22no—
305C22×C3—21no—
306C22×C3—21no—
307C22×C3—21no—
308C22×C3—122no—
309C22×C3—122no—
310C22×C3—122no—
311C22×C3#88212yes—
312C22×C3#88412yes—
313C22×C3#94012yes—
314C2×D3—42no—
315C2×D3—42no—
316C2×D3—42no—
317C2×D3—124no—
318C2×D3—128no—
319C2×D3—128no—
320C2×D3—124no—
321C2×D3—244no—
322C2×D3—244no—
323C2×D3—242no—
324C2×D3—242no—
325C2×D3—242no—
326C2×D3—242no—
327C3×C4—22no—
328C3×C4—22no—
329C3×C4—44no—
330C3×C4—44no—
331C3×C4—122no—
332C3×C4#88212yes—
333C3×C4#88412yes—
334C3×C4#93012yes—
335C3×C4#93712yes—
336Dic3—42no—
337Dic3—124no—
338Dic3—242no—
339C32#200611yescharacteristic, complemented, Sylow
340C23—62no—
341C23—182no—
342C23—362no—
343C23—362no—
344C23—361no—
345C23—361no—
346C23#381111yescharacteristic
347Q8—62no—
348Q8—62no—
349D4—62no—
350D4—62no—
351D4—122no—
352D4—122no—
353D4—184no—
354D4—362no—
355D4—722no—
356C2×C4—22no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—62no—
360C2×C4—122no—
361C2×C4—122no—
362C2×C4—182no—
363C2×C4—362no—
364C2×C4#379811yescharacteristic
365C2×C4D3×D1212yes—
366C2×C4#380211yescharacteristic
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—242no—
377C2×C3#482212yes—
378C2×C3#482712yes—
379C2×C3#496012yes—
380D3—82no—
381D3—244no—
382D3—244no—
383C22—21no—
384C22—21no—
385C22—122no—
386C22—122no—
387C22—122no—
388C22—364no—
389C22—362no—
390C22—722no—
391C22—721no—
392C22—721no—
393C22#6391211yescharacteristic
394C22#6392311yescharacteristic
395C22#6397911yescharacteristic
396C4—42no—
397C4—122no—
398C4—362no—
399C4#6390612yes—
400C4#6392212yes—
401C3—21no—
402C3#7039212yescomplemented
403C2—21no—
404C2—21no—
405C2—242no—
406C2—722no—
407C2#1059039711yescharacteristic
408C2#1059040211yescharacteristic
409C2#1059139311yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC22×C32#120
hypercenterC2×C42D32
hypocenterC32#2006
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. #10595044C2semidirect
2. C2×#63825C2semidirect
3. #10592638C2semidirect
4. C2×C3×#805C2semidirect
5. #10589168C2semidirect
27. C2×#805D3semidirect
36. C2×C4⋊(C3⋊D3)D4semidirect
50. C3×#208D4semidirect
170. #208#67semidirect
339. C32#2006semidirect
402. C3#70392semidirect

Maximal subgroups

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

subgroupindex
#105950442
C2×#638252
#105926382
C2×C3×#8052
#105891682
#703923