Finite Group Databasebeta

← #11785283

Subgroups — #11785283

Order 1152.

661 conjugacy classes of subgroups.

The subgroup lattice has 389 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×Dic6C211yesmaximal, characteristic
2#10592635C211yesmaximal, characteristic
3C2×C3×C4⋊(C3⋊C8)C211yesmaximal, characteristic
4C2×#63566C212yesmaximal
5#10589164C212yesmaximal
6#71627—31nomaximal
7#70486—31nomaximal
8C22×C3×Dic6C2211yescharacteristic
9C2×C32×C42C2211yescharacteristic
10C2×C4⋊(C3⋊Dic3)C2212yes—
11C2×C3×C4⋊Dic3C2211yescharacteristic
12C2×C3×Dic3⋊C4—21no—
13C2×C3×C4×Dic3—21no—
14C22×C3×C3⋊C8C2212yes—
15C3×C4×Dic6—22no—
16C3×C4×Dic6C414yescomplemented
17#63658—21no—
18#63658—21no—
19C3×C4⋊(C3⋊C8)—22no—
20#63566—24no—
21C2×C3×C4×Q8—31no—
22C2×C4×Dic6D311yescharacteristic
23C2×C3×C4⋊C8—31no—
24C2×#835—32no—
25C2×#816—32no—
26#4936—31no—
27#4936—31no—
28#4936—61no—
29C2×C4⋊(C3⋊C8)D311yescharacteristic
30#4551—32no—
31#4529—32no—
32C22×C32×C4D411yescharacteristic
33C22×C32×C4D411yescharacteristic
34C22×C32×C4C2311yescharacteristic
35C22×C3⋊Dic3—22no—
36C22×C3×Dic3—21no—
37C22×C3×Dic3—21no—
38C2×C3×Dic6—21no—
39C2×C3×Dic6—21no—
40C2×C3×Dic6—21no—
41C2×C3×Dic6C2×C412yes—
42C2×C3×Dic6D412yes—
43C2×C3×Dic6Q812yes—
44C32×C42C2×C412yes—
45C32×C42D412yes—
46C4⋊(C3⋊Dic3)—22no—
47C4⋊(C3⋊Dic3)—22no—
48C3×C4⋊Dic3—21no—
49C3×C4⋊Dic3C2×C412yes—
50C3×Dic3⋊C4—24no—
51C3×C4×Dic3—24no—
52C2×C3×C3⋊C8—22no—
53C2×C3×C3⋊C8—22no—
54C2×C3×C3⋊C8—22no—
55#1805—91noSylow
56C22×C3×Q8—31no—
57C22×Dic6C2×D311yescharacteristic
58C22×C3×C8—32no—
59C3×C4×Q8—34no—
60C3×C4×Q8—62no—
61C2×C3×C4⋊C4—31no—
62C2×C3×C4⋊C4—61no—
63C2×C3×C42—21no—
64C2×C3×C42—61no—
65C2×C3×C42C2×D311yescharacteristic
66C2×C3×C42C2×D311yescharacteristic
67C2×C4⋊Dic3—32no—
68C2×C4⋊Dic3—32no—
69C2×C4⋊Dic3—62no—
70C2×C4⋊Dic3C2×D311yescharacteristic
71C2×Dic3⋊C4—21no—
72C2×C4×Dic3—21no—
73C22×C3⋊C8C2×D312yes—
74C4×Dic6—22no—
75C4×Dic6Dic314yescomplemented
76C3×C4⋊C8—62no—
77#835—64no—
78C3⋊#95—62no—
79C3⋊#95—62no—
80C3⋊#95—61no—
81C3⋊#95—61no—
82C3⋊#95—61no—
83C3⋊#95—61no—
84#816—64no—
85C4⋊(C3⋊C8)—22no—
86C23×C32C2×D411yescharacteristic
87C2×C32×C4—22no—
88C2×C32×C4—22no—
89C2×C32×C4C22⋊C412yes—
90C2×C32×C4C22⋊C412yes—
91C2×C32×C4C22×C411yescharacteristic
92C2×C32×C4C2×D411yescharacteristic
93C2×C32×C4C2×D411yescharacteristic
94C2×C32×C4C2×Q811yescharacteristic
95C2×C32×C4#4111yescharacteristic
96C2×C32×C4#4111yescharacteristic
97C2×C3⋊Dic3—42no—
98C2×C3⋊Dic3—42no—
99C2×C3⋊Dic3—42no—
100C2×C3×Dic3—22no—
101C2×C3×Dic3—22no—
102C2×C3×Dic3—22no—
103C2×C3×Dic3—22no—
104C2×C3×Dic3—42no—
105C3×Dic6—22no—
106C3×Dic6—22no—
107C3×Dic6—22no—
108C3×Dic6C4⋊C414yes—
109C3×C3⋊C8—42no—
110C2×C4×Q8—31no—
111C2×C4⋊C8—31no—
112C2×#103—92no—
113#382—91no—
114#340—92no—
115C2×C3×Q8—32no—
116C2×C3×Q8—32no—
117C2×C3×Q8—32no—
118C2×C3×Q8—61no—
119C2×C3×Q8—61no—
120C2×C3×Q8—61no—
121C22×C3×C4—21no—
122C22×C3×C4—21no—
123C22×C3×C4—21no—
124C22×C3×C4—61no—
125C22×C3×C4—61no—
126C22×C3×C4D1211yescharacteristic
127C22×C3×C4D1211yescharacteristic
128C22×C3×C4#6711yescharacteristic
129C22×C3×C4#6711yescharacteristic
130C22×C3×C4C22×D311yescharacteristic
131C22×C3×C4C22×D311yescharacteristic
132C22×Dic3—21no—
133C22×Dic3—21no—
134C22×Dic3—64no—
135C22×Dic3—62no—
136C22×Dic3—62no—
137C2×Dic6—21no—
138C2×Dic6—21no—
139C2×Dic6—21no—
140C2×Dic6Dic612yes—
141C2×Dic6D1212yes—
142C2×Dic6C2×Dic312yes—
143C2×C3×C8—62no—
144C2×C3×C8—62no—
145C2×C3×C8—62no—
146C3×C4⋊C4—32no—
147C3×C4⋊C4—64no—
148C3×C4⋊C4—61no—
149C3×C42—22no—
150C3×C42—22no—
151C3×C42—64no—
152C3×C42C4×D312yes—
153C3×C42C2×Dic312yes—
154C3×C42#6712yes—
155C3×C42#6712yes—
156C4⋊Dic3—21no—
157C4⋊Dic3—62no—
158C4⋊Dic3—62no—
159C4⋊Dic3—62no—
160C4⋊Dic3—62no—
161C4⋊Dic3—122no—
162C4⋊Dic3—122no—
163C4⋊Dic3C2×Dic312yes—
164Dic3⋊C4—24no—
165C4×Dic3—24no—
166C2×C3⋊C8—22no—
167C2×C3⋊C8—22no—
168C2×C3⋊C8—22no—
169C22×C32C2×C22⋊C411yescharacteristic
170C22×C32#12111yescharacteristic
171C22×C32C22⋊Q811yescharacteristic
172C22×C32#13512yes—
173C22×C32#13712yes—
174C32×C4—22no—
175C32×C4—22no—
176C32×C4C2×C4⋊C411yescharacteristic
177C32×C4#11711yescharacteristic
178C32×C4#12111yescharacteristic
179C32×C4C22⋊Q811yescharacteristic
180C3⋊Dic3—82no—
181C3×Dic3—24no—
182C3×Dic3—42no—
183C22×Q8—31no—
184C22×C8—32no—
185C4×Q8—34no—
186C4×Q8—62no—
187C2×C4⋊C4—31no—
188C2×C4⋊C4—61no—
189C2×C4⋊C4—92no—
190C2×C42—61no—
191C2×C42D3211yescharacteristic
192C4⋊C8—62no—
193#103—184no—
194#95—181no—
195#95—181no—
196C23×C3—21no—
197C23×C3C2×D1211yescharacteristic
198C23×C3C2×#6711yescharacteristic
199C3×Q8—34no—
200C3×Q8—62no—
201C3×Q8—62no—
202C3×Q8—62no—
203C2×C3×C4—22no—
204C2×C3×C4—22no—
205C2×C3×C4—22no—
206C2×C3×C4—22no—
207C2×C3×C4—22no—
208C2×C3×C4—22no—
209C2×C3×C4—21no—
210C2×C3×C4—21no—
211C2×C3×C4—21no—
212C2×C3×C4—21no—
213C2×C3×C4—21no—
214C2×C3×C4—21no—
215C2×C3×C4—42no—
216C2×C3×C4—42no—
217C2×C3×C4—62no—
218C2×C3×C4—62no—
219C2×C3×C4—62no—
220C2×C3×C4—62no—
221C2×C3×C4—122no—
222C2×C3×C4(C2×D3)⋊C412yes—
223C2×C3×C4(C2×D3)⋊C412yes—
224C2×C3×C4#21712yes—
225C2×C3×C4#21712yes—
226C2×C3×C4C2×Dic611yescharacteristic
227C2×C3×C4C2×C4×D311yescharacteristic
228C2×C3×C4C2×D1211yescharacteristic
229C2×C3×C4#23511yescharacteristic
230C2×C3×C4#23511yescharacteristic
231C2×C3×C4D3×D411yescharacteristic
232C2×C3×C4#23711yescharacteristic
233C2×C3×C4D3×Q811yescharacteristic
234C2×C3×C4#23911yescharacteristic
235C2×C3×C4C22×Dic311yescharacteristic
236C2×C3×C4C2×#6711yescharacteristic
237C2×C3×C4C2×#6711yescharacteristic
238C2×Dic3—22no—
239C2×Dic3—22no—
240C2×Dic3—22no—
241C2×Dic3—22no—
242C2×Dic3—42no—
243C2×Dic3—124no—
244C2×Dic3—124no—
245C2×Dic3—124no—
246C2×Dic3—122no—
247C2×Dic3—122no—
248C2×Dic3—122no—
249C2×Dic3—122no—
250C2×Dic3—122no—
251C2×Dic3—122no—
252Dic6—22no—
253Dic6—22no—
254Dic6—22no—
255Dic6C4⋊Dic314yes—
256C3×C8—122no—
257C3⋊C8—42no—
258C2×C32#38011yescharacteristic
259C2×C32#41611yescharacteristic
260C2×C32#41911yescharacteristic
261C2×C32#46412yes—
262C2×C32#47912yes—
263C2×Q8—32no—
264C2×Q8—32no—
265C2×Q8—32no—
266C2×Q8—61no—
267C2×Q8—61no—
268C2×Q8—61no—
269C22×C4—61no—
270C22×C4—61no—
271C22×C4—182no—
272C22×C4#62611yescharacteristic
273C22×C4#62611yescharacteristic
274C22×C4C2×D3211yescharacteristic
275C2×C8—62no—
276C2×C8—62no—
277C2×C8—62no—
278C4⋊C4—32no—
279C4⋊C4—64no—
280C4⋊C4—61no—
281C4⋊C4—182no—
282C4⋊C4—182no—
283C42—64no—
284C42D3×Dic312yes—
285C42#62512yes—
286C22×C3—22no—
287C22×C3—22no—
288C22×C3—21no—
289C22×C3—21no—
290C22×C3—21no—
291C22×C3#89511yescharacteristic
292C22×C3#89711yescharacteristic
293C22×C3#90412yes—
294C22×C3#90912yes—
295C22×C3#92411yescharacteristic
296C22×C3C2×(C2×D3)⋊C411yescharacteristic
297C22×C3#93011yescharacteristic
298C22×C3#94212yes—
299C22×C3#95012yes—
300C22×C3C2×#21711yescharacteristic
301C3×C4—22no—
302C3×C4—22no—
303C3×C4—22no—
304C3×C4—22no—
305C3×C4—21no—
306C3×C4—21no—
307C3×C4—21no—
308C3×C4—21no—
309C3×C4—42no—
310C3×C4—42no—
311C3×C4—64no—
312C3×C4—122no—
313C3×C4D3×C4⋊C411yescharacteristic
314C3×C4#89211yescharacteristic
315C3×C4#92411yescharacteristic
316C3×C4C2×C4⋊Dic311yescharacteristic
317C3×C4#92611yescharacteristic
318C3×C4#93011yescharacteristic
319C3×C4#93811yescharacteristic
320C3×C4#94611yescharacteristic
321Dic3—24no—
322Dic3—42no—
323Dic3—244no—
324Dic3—242no—
325Dic3—242no—
326C32#180511yescharacteristic, complemented, Sylow
327C23C2×#62611yescharacteristic
328Q8—34no—
329Q8—62no—
330Q8—62no—
331Q8—62no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—62no—
335C2×C4—62no—
336C2×C4—62no—
337C2×C4—62no—
338C2×C4—122no—
339C2×C4—362no—
340C2×C4—362no—
341C2×C4—362no—
342C2×C4(C2×D3)⋊Dic312yes—
343C2×C4(C2×D3)⋊Dic312yes—
344C2×C4D3×Dic611yescharacteristic
345C2×C4#379511yescharacteristic
346C2×C4#379911yescharacteristic
347C2×C4D3×D1211yescharacteristic
348C2×C4C2×D3×Dic311yescharacteristic
349C2×C4C2×#62511yescharacteristic
350C8—122no—
351C2×C3—21no—
352C2×C3—22no—
353C2×C3—21no—
354C2×C3—21no—
355C2×C3—22no—
356C2×C3#482912yes—
357C2×C3#484512yes—
358C2×C3#498711yescharacteristic
359C2×C3#502212yes—
360C2×C3#502812yes—
361C2×C3#511311yescharacteristic
362C2×C3#512011yescharacteristic
363C2×C3#521211yescharacteristic
364C2×C3#522511yescharacteristic
365C2×C3#523311yescharacteristic
366C22#6382912yes—
367C22#6383312yes—
368C22#6385711yescharacteristic
369C22#6390911yescharacteristic
370C22C2×(C2×D3)⋊Dic311yescharacteristic
371C4—22no—
372C4—22no—
373C4—64no—
374C4—122no—
375C4—722no—
376C4#6384111yescharacteristic
377C4#6385611yescharacteristic
378C4D3×C4⋊Dic311yescharacteristic
379C4#6390811yescharacteristic
380C3—21no—
381C3#7048611yescharacteristic, complemented
382C3#7162711yescharacteristic, complemented
383C2#1059030212yes—
384C2#1059036812yes—
385C2#1059108411yescharacteristic
386C2#1059110011yescharacteristic
387C2#1059131311yescharacteristic
subgroupG/H
centerC23C2×#626
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socle, prime radicalC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1805
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
16. C3×C4×Dic6C4semidirect
75. C4×Dic6Dic3semidirect
326. C32#1805semidirect
381. C3#70486semidirect
382. C3#71627semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×Dic62
#105926352
C2×C3×C4⋊(C3⋊C8)2
C2×#635662
#105891642
#716273
#704863