Finite Group Databasebeta

← #11792286

Subgroups — #11792286

Order 1152.

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

normal subgroups only

This group has 833 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
2C2×#63831C212yesmaximal, complemented
3#10592628C211yesmaximal, characteristic, complemented
4C2×C3×#805C212yesmaximal, complemented
5#10589168C211yesmaximal, characteristic, complemented
6#70393—32nomaximal
7C22×#634C2211yescharacteristic
8C2×C3×#235C2212yes—
9C2×C32×C42C2211yescharacteristic
10C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
11C2×C3×#208C2212yes—
12#63980—22no—
13#63908—22no—
14#63856—22no—
15C2×#3719—22no—
16#63831—24no—
17#63831—24no—
18C2×#3716—22no—
19#63658—22no—
20C3×#805—24no—
21#5833—32no—
22C2×#951—32no—
23C2×#909—32no—
24C2×C3×#104—32no—
25#4929—32no—
26#4929—61no—
27C2×#805D312yescomplemented
28#4554—32no—
29C22×C32×C4—21no—
30C22×C32×C4C2311yescharacteristic
31C22×C3⋊Dic3—21no—
32C22×C3⋊Dic3D412yes—
33C2×#634—22no—
34C2×#634—22no—
35C2×#634—21no—
36C2×#634D412yescomplemented
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—
47C4⋊(C3⋊Dic3)—22no—
48C3×#208—22no—
49C3×#208D414yescomplemented
50C2×C3×C3⋊C8—22no—
51#3724—22no—
52(C2×D3)⋊Dic3—24no—
53#3719—28no—
54#3716—28no—
55#2007—91noSylow
56C2×C3×#41—32no—
57C2×#235C2×D312yes—
58C22×Dic6—32no—
59C22×Dic6—61no—
60C2×C3×M16—32no—
61C2×C3×C42—21no—
62C2×C3×C42C2×D312yes—
63#951—64no—
64#951—64no—
65#946—62no—
66C2×#216—62no—
67#939—64no—
68#938—62no—
69C2×#214—62no—
70#930—62no—
71C2×C4⋊Dic3—32no—
72C2×C4⋊Dic3—61no—
73#924—62no—
74C2×#208C2×D312yes—
75#909—64no—
76#909—64no—
77C2×Dic12—62no—
78C2×#204—62no—
79C3×#104—64no—
80C3⋊#95—64no—
81C3⋊#95—64no—
82#805—24no—
83C23×C32C2×D411yescharacteristic
84C22×C3×D3—22no—
85C2×C32×C4—22no—
86C2×C32×C4—41no—
87C2×C32×C4—41no—
88C2×C32×C4C2×D412yes—
89C2×C32×C4C2×D411yescharacteristic
90C2×C32×C4C2×D412yes—
91C2×C32×C4#4111yescharacteristic
92C2×C3⋊Dic3—22no—
93C2×C3⋊Dic3—22no—
94C2×C3⋊Dic3—41no—
95C2×C3⋊Dic3—41no—
96C2×C3⋊Dic3—42no—
97#634—24no—
98#634—42no—
99C3×#67—42no—
100C3×#67—42no—
101C2×C3×Dic3—22no—
102C3×D12—22no—
103C3×D12—22no—
104C3×C4×D3—42no—
105C3×C4×D3—42no—
106C3×Dic6—22no—
107C3×Dic6—22no—
108#625—82no—
109C3×C3⋊C8—24no—
110C2×#137—92no—
111#537—91no—
112C2×#104—32no—
113#391—91no—
114#343—91no—
115C3×#41—62no—
116C3×#41—62no—
117C3×#41—62no—
118C3×#41—62no—
119C2×C3×Q8—32no—
120C2×C3×D4—32no—
121C2×C3×D4—62no—
122C22×C3×C4—22no—
123C22×C3×C4—22no—
124C22×C3×C4—21no—
125C22×C3×C4—62no—
126C22×C3×C4C22×D312yes—
127C2×#67—22no—
128C2×#67—64no—
129C22×Dic3—34no—
130C22×Dic3—62no—
131C22×Dic3—62no—
132C22×Dic3—62no—
133#235—22no—
134#235—22no—
135#235—22no—
136#235—22no—
137C2×D12D1212yes—
138C2×C4×D3—22no—
139C2×Dic6—34no—
140C2×Dic6—62no—
141C2×Dic6—62no—
142C2×Dic6—62no—
143C2×Dic6—62no—
144C2×Dic6—62no—
145C2×Dic6—62no—
146C2×Dic6—62no—
147C2×Dic6—122no—
148C2×Dic6—122no—
149C2×Dic6D1212yes—
150C3×M16—34no—
151C3×M16—62no—
152C2×C3×C8—62no—
153C3×C42—22no—
154C3×C42—22no—
155C3×C42—42no—
156#217—64no—
157#216—68no—
158#214—68no—
159(C2×D3)⋊C4—64no—
160C4⋊Dic3—62no—
161C4⋊Dic3—62no—
162C4⋊Dic3—122no—
163Dic3⋊C4—64no—
164#208—22no—
165#208#6714yescomplemented
166C2×C3⋊C8—22no—
167Dic12—68no—
168#204—68no—
169C22×C32—21no—
170C22×C32—21no—
171C22×C32#12011yescharacteristic
172C22×C32#12111yescharacteristic
173C22×C32#12711yescharacteristic
174C2×C3×D3—42no—
175C2×C3×D3—42no—
176C2×C3×D3—42no—
177C32×C4—42no—
178C32×C4#12012yes—
179C32×C4#12112yes—
180C3⋊Dic3—42no—
181C3⋊Dic3—42no—
182C3×Dic3—42no—
183C2×#41—32no—
184C22×Q8—91no—
185#137—184no—
186#137—184no—
187C2×Q16—182no—
188C2×SD16—182no—
189C2×M16—32no—
190C22⋊Q8—182no—
191#121—182no—
192#121—182no—
193C2×C4⋊C4—91no—
194C2×C42D3211yescharacteristic
195#104—64no—
196#95—182no—
197C23×C3—21no—
198C23×C3—62no—
199C23×C3D3×D412yes—
200C22×D3—22no—
201C3×Q8—62no—
202C3×Q8—62no—
203C3×D4—62no—
204C3×D4—62no—
205C3×D4—122no—
206C3×D4—122no—
207C2×C3×C4—24no—
208C2×C3×C4—24no—
209C2×C3×C4—21no—
210C2×C3×C4—22no—
211C2×C3×C4—21no—
212C2×C3×C4—22no—
213C2×C3×C4—42no—
214C2×C3×C4—42no—
215C2×C3×C4—42no—
216C2×C3×C4—42no—
217C2×C3×C4—62no—
218C2×C3×C4—122no—
219C2×C3×C4—122no—
220C2×C3×C4C2×D1212yes—
221C2×C3×C4#23512yes—
222C2×C3×C4D3×D412yes—
223C2×C3×C4D3×D412yes—
224C2×C3×C4D3×D412yes—
225C2×C3×C4C2×#6712yes—
226#67—42no—
227#67—42no—
228#67—244no—
229C2×Dic3—22no—
230C2×Dic3—64no—
231C2×Dic3—64no—
232C2×Dic3—64no—
233C2×Dic3—122no—
234C2×Dic3—122no—
235C2×Dic3—122no—
236C2×Dic3—122no—
237C2×Dic3—122no—
238C2×Dic3—124no—
239C2×Dic3—124no—
240D12—22no—
241D12—22no—
242C4×D3—42no—
243C4×D3—42no—
244Dic6—22no—
245Dic6—22no—
246Dic6—64no—
247Dic6—64no—
248Dic6—124no—
249Dic6—124no—
250Dic6—122no—
251Dic6—122no—
252C3×C8—64no—
253C3⋊C8—24no—
254C2×C32—21no—
255C2×C32—21no—
256C2×C32#39211yescharacteristic
257C2×C32#45511yescharacteristic
258C2×C32#45611yescharacteristic
259C3×D3—82no—
260#41—62no—
261#41—62no—
262#41—62no—
263#41—62no—
264C2×Q8—32no—
265C2×Q8—92no—
266C2×Q8—181no—
267C2×Q8—182no—
268C2×Q8—182no—
269C2×D4—32no—
270C2×D4—62no—
271C2×D4—182no—
272C22×C4—21no—
273C22×C4—62no—
274C22×C4—92no—
275C22×C4—181no—
276C22×C4C2×D3211yescharacteristic
277Q16—188no—
278SD16—188no—
279M16—34no—
280M16—62no—
281C2×C8—62no—
282C4⋊C4—182no—
283C4⋊C4—182no—
284C22⋊C4—184no—
285C42—22no—
286C22×C3—22no—
287C22×C3—22no—
288C22×C3—22no—
289C22×C3—22no—
290C22×C3—21no—
291C22×C3—21no—
292C22×C3—21no—
293C22×C3—122no—
294C22×C3—122no—
295C22×C3—122no—
296C22×C3#88212yes—
297C22×C3#88412yes—
298C22×C3#94012yes—
299C2×D3—42no—
300C2×D3—42no—
301C2×D3—42no—
302C3×C4—22no—
303C3×C4—22no—
304C3×C4—44no—
305C3×C4—44no—
306C3×C4—122no—
307C3×C4#88212yes—
308C3×C4#88412yes—
309C3×C4#93012yes—
310C3×C4#93712yes—
311Dic3—42no—
312Dic3—124no—
313Dic3—124no—
314Dic3—124no—
315Dic3—242no—
316C32#200711yescharacteristic, complemented, Sylow
317C23—62no—
318C23#381111yescharacteristic
319Q8—62no—
320Q8—62no—
321Q8—184no—
322Q8—362no—
323D4—62no—
324D4—62no—
325D4—122no—
326D4—122no—
327D4—722no—
328C2×C4—22no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—62no—
332C2×C4—122no—
333C2×C4—122no—
334C2×C4—182no—
335C2×C4—182no—
336C2×C4—361no—
337C2×C4—361no—
338C2×C4—362no—
339C2×C4#379811yescharacteristic
340C2×C4D3×D1212yes—
341C2×C4#380211yescharacteristic
342C2×C4D3×#6712yes—
343C8—64no—
344C2×C3—22no—
345C2×C3—22no—
346C2×C3—22no—
347C2×C3—22no—
348C2×C3—21no—
349C2×C3—21no—
350C2×C3—21no—
351C2×C3—242no—
352C2×C3#482512yes—
353C2×C3#482612yes—
354C2×C3#496012yes—
355D3—82no—
356C22—21no—
357C22—21no—
358C22—122no—
359C22—122no—
360C22—122no—
361C22#6391211yescharacteristic
362C22#6392311yescharacteristic
363C22#6397911yescharacteristic
364C4—42no—
365C4—122no—
366C4—362no—
367C4—362no—
368C4#6390612yes—
369C4#6392212yes—
370C3—21no—
371C3#7039312yescomplemented
372C2—21no—
373C2—21no—
374C2—242no—
375C2#1059039811yescharacteristic
376C2#1059040111yescharacteristic
377C2#1059139311yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC22×C32#120
prime radical#10595044C2
hypercenterC2×C42D32
hypocenterC32#2007
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
2. C2×#63831C2semidirect
3. #10592628C2semidirect
4. C2×C3×#805C2semidirect
5. #10589168C2semidirect
27. C2×#805D3semidirect
36. C2×#634D4semidirect
49. C3×#208D4semidirect
165. #208#67semidirect
316. C32#2007semidirect
371. C3#70393semidirect

Maximal subgroups

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

subgroupindex
#105950442
C2×#638312
#105926282
C2×C3×#8052
#105891682
#703933