Finite Group Databasebeta

← #11784911

Subgroups — #11784911

Order 1152.

1197 conjugacy classes of subgroups; only the 154 normal subgroups are shown.

normal subgroups only

This group has 1197 conjugacy classes of subgroups — too many to draw. Only its 154 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×#64298C211yesmaximal, characteristic
2#10592628C211yesmaximal, characteristic, complemented
3C2×C3×#805C212yesmaximal, complemented
4#10591088C212yesmaximal, complemented
5C2×#63561C211yesmaximal, characteristic, complemented
6#70387—32nomaximal
7C22×#634C2211yescharacteristic
8C2×C3×#235C2212yes—
9C2×#3805—22no—
10#64298—22no—
11#64298—24no—
12#64298C414yescomplemented
13C2×#3795—22no—
14C2×D3×Dic6—22no—
15C2×C32×C42C2211yescharacteristic
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×C3×#208C2212yes—
18#63658—22no—
19C3×#805—24no—
20#63566—22no—
21#63563—22no—
22#63561—22no—
23C2×#1010—32no—
24C2×C3×#104—32no—
25#5232—32no—
26C2×#824—32no—
27#5133—32no—
28#4929—32no—
29#4929—61no—
30C2×#805D312yescomplemented
31C22×C32×C4—21no—
32C22×C32×C4C2311yescharacteristic
33C22×C3⋊Dic3—21no—
34C22×C3⋊Dic3D412yes—
35C2×#634—22no—
36C2×#634—22no—
37C2×#634C2×C412yes—
38C2×#634D412yes—
39C2×C3×#67—22no—
40C3×#235—22no—
41C3×#235—22no—
42C3×#235C2×C414yes—
43C3×#235D414yes—
44C2×C3×D12D412yes—
45C2×C3×C4×D3—22no—
46C2×C3×Dic6D412yes—
47C2×#627—22no—
48C2×#625—22no—
49#3805—28no—
50#3805—28no—
51C2×D3×Dic3—24no—
52#3795—28no—
53#3795—28no—
54D3×Dic6—28no—
55D3×Dic6—28no—
56C32×C42—22no—
57C4⋊(C3⋊Dic3)—22no—
58C3×#208—22no—
59C3×#208—22no—
60C2×C3×C3⋊C8—22no—
61#1793—91noSylow
62C2×C3×#41—32no—
63#1010—38no—
64#1010—64no—
65#1010—64no—
66#1010—64no—
67C2×D3×Q8—62no—
68C2×#237—62no—
69C2×#237—64no—
70C2×#235—62no—
71C2×#235C2×D312yes—
72C22×Dic6—32no—
73C22×Dic6—61no—
74C22×Dic6—62no—
75C2×C3×M16—32no—
76C2×C3×C42—21no—
77C2×C3×C42C2×D312yes—
78C2×C4⋊Dic3—32no—
79C2×C4⋊Dic3—61no—
80C2×#208C2×D312yes—
81C3×#104—64no—
82#835—62no—
83#832—62no—
84C3⋊#95—64no—
85C3⋊#95—64no—
86#824—64no—
87#821—62no—
88#816—62no—
89#805—24no—
90C23×C32C2×D411yescharacteristic
91C22×C3×D3—22no—
92C2×C32×C4—22no—
93C2×C32×C4—41no—
94C2×C32×C4—41no—
95C2×C32×C4C22×C411yescharacteristic
96C2×C32×C4C2×D412yes—
97C2×C32×C4C2×D411yescharacteristic
98C2×C32×C4C2×D412yes—
99C2×C3⋊Dic3—22no—
100C2×C3⋊Dic3—22no—
101C2×C3⋊Dic3—42no—
102C2×C3⋊Dic3—41no—
103C2×C3⋊Dic3C22⋊C414yes—
104#634—24no—
105#634—24no—
106C3×#67—24no—
107C3×#67—24no—
108C2×C3×Dic3—22no—
109C3×D12—22no—
110C3×D12C22⋊C414yes—
111C3×C4×D3—24no—
112C3×C4×D3—24no—
113C3×Dic6—22no—
114C3×Dic6C22⋊C414yes—
115#627—28no—
116#625—28no—
117D3×Dic3—216no—
118C3×C3⋊C8—42no—
119C2×2−1+4—91no—
120C2×#104—32no—
121#417—92no—
122C2×#101—91no—
123#391—91no—
124C3×#41—34no—
125C3×#41—34no—
126C3×#41—62no—
127C3×#41—62no—
128C2×C3×Q8—32no—
129C2×C3×D4—32no—
130C2×C3×D4—62no—
131C22×C3×C4—22no—
132C22×C3×C4—22no—
133C22×C3×C4—21no—
134C22×C3×C4—62no—
135C22×C3×C4C22×D312yes—
136C2×#67—22no—
137C2×#67—64no—
138C22×Dic3—34no—
139C22×Dic3—62no—
140C22×Dic3—64no—
141C22×Dic3—62no—
142C22×Dic3—62no—
143D3×Q8—68no—
144D3×Q8—68no—
145#237—68no—
146#237—68no—
147#237—616no—
148#237—616no—
149#235—22no—
150#235—22no—
151#235—68no—
152#235—68no—
153#235C4×D314yes—
154#235#6714yes—
155C2×D12D1212yes—
156C2×C4×D3—22no—
157C2×C4×D3—64no—
158C2×Dic6—34no—
159C2×Dic6—34no—
160C2×Dic6—62no—
161C2×Dic6—62no—
162C2×Dic6—68no—
163C2×Dic6—64no—
164C2×Dic6—62no—
165C2×Dic6—62no—
166C2×Dic6—62no—
167C2×Dic6—62no—
168C2×Dic6—68no—
169C2×Dic6—122no—
170C2×Dic6—122no—
171C2×Dic6D1212yes—
172C3×M16—62no—
173C3×M16—62no—
174C2×C3×C8—62no—
175C3×C42—22no—
176C3×C42—22no—
177C3×C42—42no—
178C4⋊Dic3—62no—
179C4⋊Dic3—62no—
180C4⋊Dic3—122no—
181#208—22no—
182#208—22no—
183C2×C3⋊C8—22no—
184C22×C32—21no—
185C22×C32—21no—
186C22×C32C2×C22⋊C411yescharacteristic
187C22×C32#12011yescharacteristic
188C22×C32#12011yescharacteristic
189C2×C3×D3—24no—
190C2×C3×D3—42no—
191C2×C3×D3—42no—
192C32×C4—42no—
193C32×C4C2×C22⋊C412yes—
194C32×C4#12012yes—
195C3⋊Dic3—24no—
196C3⋊Dic3—81no—
197C3×Dic3—24no—
1982−1+4—94no—
1992−1+4—182no—
2002−1+4—184no—
201C2×#41—32no—
202C2×#41—182no—
203C2×#41—182no—
204C22×Q8—91no—
205C22×Q8—182no—
206C2×M16—32no—
207C2×C4⋊C4—91no—
208C2×C42D3211yescharacteristic
209#104—64no—
210#103—182no—
211#102—182no—
212#101—182no—
213#95—182no—
214C23×C3—21no—
215C23×C3—62no—
216C23×C3D3×D412yes—
217C22×D3—22no—
218C3×Q8—34no—
219C3×Q8—62no—
220C3×D4—34no—
221C3×D4—64no—
222C3×D4—64no—
223C3×D4—62no—
224C2×C3×C4—24no—
225C2×C3×C4—24no—
226C2×C3×C4—21no—
227C2×C3×C4—22no—
228C2×C3×C4—21no—
229C2×C3×C4—22no—
230C2×C3×C4—42no—
231C2×C3×C4—42no—
232C2×C3×C4—42no—
233C2×C3×C4—42no—
234C2×C3×C4—62no—
235C2×C3×C4—64no—
236C2×C3×C4—64no—
237C2×C3×C4C2×C4×D312yes—
238C2×C3×C4C2×D1212yes—
239C2×C3×C4D3×D412yes—
240C2×C3×C4D3×D412yes—
241C2×C3×C4D3×D412yes—
242C2×C3×C4C2×#6712yes—
243#67—24no—
244#67—24no—
245#67—616no—
246C2×Dic3—22no—
247C2×Dic3—38no—
248C2×Dic3—64no—
249C2×Dic3—616no—
250C2×Dic3—64no—
251C2×Dic3—64no—
252C2×Dic3—122no—
253C2×Dic3—122no—
254C2×Dic3—122no—
255C2×Dic3—124no—
256C2×Dic3—124no—
257C2×Dic3—122no—
258D12—22no—
259D12(C2×D3)⋊C414yes—
260C4×D3—24no—
261C4×D3—24no—
262C4×D3—616no—
263Dic6—22no—
264Dic6—616no—
265Dic6—64no—
266Dic6—64no—
267Dic6—64no—
268Dic6—64no—
269Dic6—124no—
270Dic6—124no—
271Dic6(C2×D3)⋊C414yes—
272C3×C8—122no—
273C3⋊C8—42no—
274C2×C32—21no—
275C2×C32—21no—
276C2×C32#37911yescharacteristic
277C2×C32#45411yescharacteristic
278C2×C32#45611yescharacteristic
279C3×D3—44no—
280#41—34no—
281#41—34no—
282#41—62no—
283#41—62no—
284#41—188no—
285#41—188no—
286#41—188no—
287#41—188no—
288C2×Q8—32no—
289C2×Q8—92no—
290C2×Q8—92no—
291C2×Q8—182no—
292C2×Q8—188no—
293C2×Q8—188no—
294C2×Q8—182no—
295C2×Q8—182no—
296C2×D4—32no—
297C2×D4—62no—
298C2×D4—182no—
299C22×C4—21no—
300C22×C4—62no—
301C22×C4—92no—
302C22×C4—184no—
303C22×C4—181no—
304C22×C4C2×D3211yescharacteristic
305M16—62no—
306M16—62no—
307C2×C8—62no—
308C4⋊C4—182no—
309C42—22no—
310C22×C3—22no—
311C22×C3—22no—
312C22×C3—22no—
313C22×C3—22no—
314C22×C3—21no—
315C22×C3—21no—
316C22×C3—21no—
317C22×C3—64no—
318C22×C3—122no—
319C22×C3—122no—
320C22×C3D3×C22⋊C412yes—
321C22×C3#88212yes—
322C22×C3#93712yes—
323C2×D3—24no—
324C2×D3—42no—
325C2×D3—42no—
326C3×C4—22no—
327C3×C4—22no—
328C3×C4—44no—
329C3×C4—44no—
330C3×C4—64no—
331C3×C4D3×C22⋊C412yes—
332C3×C4#88212yes—
333C3×C4C2×(C2×D3)⋊C412yes—
334C3×C4#93712yes—
335Dic3—24no—
336Dic3—68no—
337Dic3—124no—
338Dic3—242no—
339Dic3—242no—
340C32#179311yescharacteristic, complemented, Sylow
341C23—62no—
342C23#381111yescharacteristic
343Q8—34no—
344Q8—62no—
345Q8—188no—
346Q8—184no—
347Q8—184no—
348D4—34no—
349D4—64no—
350D4—64no—
351D4—62no—
352D4—188no—
353C2×C4—22no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—62no—
357C2×C4—64no—
358C2×C4—64no—
359C2×C4—94no—
360C2×C4—1816no—
361C2×C4—182no—
362C2×C4—182no—
363C2×C4—362no—
364C2×C4—361no—
365C2×C4C4×D3211yescharacteristic
366C2×C4D3×D1212yes—
367C2×C4#380211yescharacteristic
368C2×C4D3×#6712yes—
369C8—122no—
370C2×C3—22no—
371C2×C3—22no—
372C2×C3—22no—
373C2×C3—22no—
374C2×C3—21no—
375C2×C3—21no—
376C2×C3—21no—
377C2×C3—124no—
378C2×C3#482612yes—
379C2×C3#482712yes—
380C2×C3#495512yes—
381D3—44no—
382C22—21no—
383C22—21no—
384C22—64no—
385C22—122no—
386C22—122no—
387C22#6392111yescharacteristic
388C22#6392311yescharacteristic
389C22#6398311yescharacteristic
390C4—42no—
391C4—64no—
392C4—184no—
393C4—721no—
394C4D3×(C2×D3)⋊C412yes—
395C4#6392212yes—
396C3—21no—
397C3#7038712yescomplemented
398C2—21no—
399C2—21no—
400C2—124no—
401C2#1059040111yescharacteristic
402C2#1059040211yescharacteristic
403C2#1059139911yescharacteristic
subgroupG/H
centerC22#63923
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC22×C32#120
prime radicalC2×#64298C2
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1793
LCSG ▷ C2×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. #10592628C2semidirect
3. C2×C3×#805C2semidirect
4. #10591088C2semidirect
5. C2×#63561C2semidirect
12. #64298C4semidirect
30. C2×#805D3semidirect
340. C32#1793semidirect
397. C3#70387semidirect

Maximal subgroups

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

subgroupindex
C2×#642982
#105926282
C2×C3×#8052
#105910882
C2×#635612
#703873