Finite Group Databasebeta

← #11906261

Subgroups — #11906261

Order 1152.

2892 conjugacy classes of subgroups.

The subgroup lattice has 387 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#544C211yesmaximal, characteristic
2#10596193C214yesmaximal, complemented
3#10596192C214yesmaximal, complemented
4#10596156C214yesmaximal, complemented
5#10596156C214yesmaximal, complemented
6#10596094C214yesmaximal
7#10596093C214yesmaximal
8#10595988C212yesmaximal
9#10595987C212yesmaximal
10#10595971C211yesmaximal, characteristic
11C2×#64096C211yesmaximal, characteristic
12#86585—34nomaximal
13C22×#634C2211yescharacteristic
14C32×C4⋊Q8C2214yes—
15C32×#125C2214yes—
16C32×C22⋊Q8C2214yes—
17C32×#117C2212yes—
18C2×C32×C4⋊C4C2211yescharacteristic
19Q8×C3⋊Dic3C2214yes—
20#64153C2218yes—
21#64153C2214yes—
22#64135C2212yes—
23#64133C2214yes—
24C2×#3750C2212yes—
25C2×C4×C3⋊Dic3C2211yescharacteristic
26C2×C4×C3⋊Dic3C2212yes—
27#64099C2212yes—
28#64099C2214yes—
29#64099C2212yes—
30#64098C2218yes—
31#64098C2218yes—
32#64098C2218yes—
33#64097C2212yes—
34#64097C2214yes—
35#64097C2214yes—
36#64097C2218yes—
37#64097C2212yes—
38#64096C2214yes—
39#64096C2214yes—
40#64096C2214yes—
41#64096C2214yes—
42#64096C2218yes—
43#64096C2214yes—
44#64087C2214yes—
45#64087C2214yes—
46#64086C2218yes—
47C4×#634C2214yes—
48C4×#634C2214yes—
49C4×#634C2214yes—
50C4×#634C2214yes—
51C3×#544D314yes—
52#5722—316no—
53#5721—316no—
54#5685—316no—
55#5685—316no—
56#5623—316no—
57#5622—316no—
58#5517—38no—
59#5516—38no—
60#5500—34no—
61C2×#887—34no—
62C2×C32×Q8C2314yes—
63C22×C32×C4C2312yes—
64C22×C32×C4C2311yescharacteristic
65C22×C3⋊Dic3C2311yescharacteristic
66C22×C3⋊Dic3C2311yescharacteristic
67C22×C3⋊Dic3C2312yes—
68C2×#634Q818yescomplemented
69C2×#634C2314yes—
70C2×#634C2314yes—
71C2×#634C2314yes—
72C2×#634C2314yes—
73C32×C4⋊C4C2314yes—
74C32×C4⋊C4C2312yes—
75C32×C4⋊C4C2312yes—
76C32×C4⋊C4C2314yes—
77C32×C4⋊C4C2318yes—
78C32×C22⋊C4C2314yes—
79C32×C42C2314yes—
80#3757C2314yes—
81C4⋊(C3⋊Dic3)C2312yes—
82C4⋊(C3⋊Dic3)C2312yes—
83C4⋊(C3⋊Dic3)C2314yes—
84C4⋊(C3⋊Dic3)C2314yes—
85C4⋊(C3⋊Dic3)C2314yes—
86#3750C2318yes—
87#3750C2318yes—
88#3750C2314yes—
89#3750C2314yes—
90#3750C2314yes—
91#3750C2314yes—
92#3750C2318yes—
93#3750C2318yes—
94C4×C3⋊Dic3C2312yes—
95C4×C3⋊Dic3C2314yes—
96C4×C3⋊Dic3C2312yes—
97C4×C3⋊Dic3C2318yes—
98C4×C3⋊Dic3C2318yes—
99C4×C3⋊Dic3C2314yes—
100C4×C3⋊Dic3C2314yes—
101#3502—91noSylow
102C22×Dic6—34no—
103C3×C4⋊Q8C2×D3116yes—
104C3×#125C2×D3116yes—
105C3×C22⋊Q8C2×D3116yes—
106C3×#117C2×D318yes—
107C2×C3×C4⋊C4C2×D314yes—
108Q8×Dic3—316no—
109#944—332no—
110#944—316no—
111#926—38no—
112#924—316no—
113C2×Dic3⋊C4—38no—
114C2×C4×Dic3—34no—
115C2×C4×Dic3—38no—
116#890—38no—
117#890—316no—
118#890—38no—
119#889—332no—
120#889—332no—
121#889—332no—
122#888—38no—
123#888—316no—
124#888—316no—
125#888—332no—
126#888—38no—
127#887—316no—
128#887—316no—
129#887—316no—
130#887—316no—
131#887—332no—
132#887—316no—
133#878—316no—
134#878—316no—
135#877—332no—
136C4×Dic6—316no—
137C4×Dic6—316no—
138C4×Dic6—316no—
139C4×Dic6—316no—
140C23×C32C2411yescharacteristic
141C32×Q8—44no—
142C2×C32×C4—42no—
143C2×C32×C4C2×Q814yes—
144C2×C32×C4C2414yes—
145C2×C32×C4C2414yes—
146C2×C32×C4C2414yes—
147C2×C32×C4C2412yes—
148C2×C3⋊Dic3—22no—
149C2×C3⋊Dic3—41no—
150C2×C3⋊Dic3C2×Q818yes—
151C2×C3⋊Dic3C2411yescharacteristic
152C2×C3⋊Dic3C2414yes—
153C2×C3⋊Dic3C2414yes—
154C2×C3⋊Dic3C2412yes—
155C2×C3⋊Dic3C2414yes—
156C2×C3⋊Dic3C2411yescharacteristic
157#634—28no—
158#634—44no—
159#634—44no—
160#634C2×Q8116yes—
161Q82—94no—
162#557—94no—
163#557—94no—
164#557—94no—
165#544—94no—
166#544—91no—
167#544C3⋊D311yescharacteristic
168#533—94no—
169#533—92no—
170#519—92no—
171C2×C4×Q8—91no—
172C2×C3×Q8C22×D3116yes—
173C22×C3×C4C22×D318yes—
174C22×C3×C4C22×D314yes—
175C22×Dic3—38no—
176C22×Dic3—34no—
177C22×Dic3—34no—
178C2×Dic6—332no—
179C2×Dic6—316no—
180C2×Dic6—316no—
181C2×Dic6—316no—
182C2×Dic6—316no—
183C3×C4⋊C4C22×D3116yes—
184C3×C4⋊C4C22×D318yes—
185C3×C4⋊C4C22×D318yes—
186C3×C4⋊C4C22×D3116yes—
187C3×C4⋊C4C22×D3132yes—
188C3×C22⋊C4C22×D3116yes—
189C3×C42C22×D3116yes—
190#217—316no—
191C4⋊Dic3—38no—
192C4⋊Dic3—38no—
193C4⋊Dic3—316no—
194C4⋊Dic3—316no—
195C4⋊Dic3—316no—
196Dic3⋊C4—332no—
197Dic3⋊C4—332no—
198Dic3⋊C4—316no—
199Dic3⋊C4—316no—
200Dic3⋊C4—316no—
201Dic3⋊C4—316no—
202Dic3⋊C4—332no—
203Dic3⋊C4—332no—
204C4×Dic3—38no—
205C4×Dic3—316no—
206C4×Dic3—38no—
207C4×Dic3—332no—
208C4×Dic3—332no—
209C4×Dic3—316no—
210C4×Dic3—316no—
211C22×C32—21no—
212C22×C32—21no—
213C22×C32C22×Q812yes—
214C22×C32C2511yescharacteristic
215C32×C4—24no—
216C32×C4—24no—
217C32×C4—24no—
218C32×C4C22×Q814yes—
219C3⋊Dic3—24no—
220C3⋊Dic3—21no—
221C3⋊Dic3—24no—
222C3⋊Dic3—22no—
223C3⋊Dic3C22×Q818yes—
224C3⋊Dic32−1+412yes—
225C22×Q8—91no—
226C4⋊Q8—94no—
227C4⋊Q8—98no—
228C4⋊Q8—94no—
229C4⋊Q8—92no—
230C4⋊Q8—92no—
231C4⋊Q8—98no—
232C4⋊Q8—94no—
233C4⋊Q8C2×C3⋊D314yes—
234#125—98no—
235#125—92no—
236#125—92no—
237#125—98no—
238#125—98no—
239#125—94no—
240#125C2×C3⋊D314yes—
241C22⋊Q8—94no—
242C22⋊Q8—94no—
243C22⋊Q8—94no—
244C22⋊Q8C2×C3⋊D314yes—
245C4×Q8—94no—
246C4×Q8—94no—
247C4×Q8—94no—
248C4×Q8—94no—
249C4×Q8—94no—
250C4×Q8—94no—
251C4×Q8—98no—
252C4×Q8—94no—
253C4×Q8—94no—
254C4×Q8—94no—
255C4×Q8—94no—
256#117—92no—
257#117—98no—
258#117C2×C3⋊D312yes—
259C2×C4⋊C4—92no—
260C2×C4⋊C4C2×C3⋊D311yescharacteristic
261C2×C42—92no—
262C2×C42—91no—
263C23×C3C23×D314yes—
264C3×Q8—416no—
265C2×C3×C4—48no—
266C2×C3×C4D3×Q8116yes—
267C2×C3×C4C23×D3116yes—
268C2×C3×C4C23×D3116yes—
269C2×C3×C4C23×D3116yes—
270C2×C3×C4C23×D318yes—
271C2×Dic3—332no—
272C2×Dic3—316no—
273C2×Dic3—34no—
274C2×Dic3—34no—
275C2×Dic3—316no—
276C2×Dic3—316no—
277C2×Dic3—38no—
278C2×Dic3—68no—
279C2×Dic3—124no—
280Dic6—364no—
281Dic6—632no—
282Dic6—1216no—
283Dic6—1216no—
284C2×C32—22no—
285C2×C32C23×Q811yescharacteristic
286C2×C32C2×2−1+411yescharacteristic
287C2×C32#58511yescharacteristic
288C2×Q8—94no—
289C2×Q8—94no—
290C2×Q8—94no—
291C2×Q8—94no—
292C2×Q8—98no—
293C2×Q8C22×C3⋊D314yes—
294C22×C4—92no—
295C22×C4—91no—
296C22×C4—91no—
297C22×C4C22×C3⋊D312yes—
298C22×C4C22×C3⋊D311yescharacteristic
299C4⋊C4—98no—
300C4⋊C4—98no—
301C4⋊C4—92no—
302C4⋊C4—98no—
303C4⋊C4—92no—
304C4⋊C4—94no—
305C4⋊C4—94no—
306C4⋊C4—94no—
307C4⋊C4—94no—
308C4⋊C4—94no—
309C4⋊C4—98no—
310C4⋊C4—94no—
311C4⋊C4—94no—
312C4⋊C4C22×C3⋊D314yes—
313C4⋊C4C22×C3⋊D312yes—
314C4⋊C4C22×C3⋊D312yes—
315C4⋊C4C22×C3⋊D314yes—
316C4⋊C4C22×C3⋊D318yes—
317C22⋊C4—94no—
318C22⋊C4C22×C3⋊D314yes—
319C42—94no—
320C42—92no—
321C42—94no—
322C42—92no—
323C42—98no—
324C42—98no—
325C42—94no—
326C42C22×C3⋊D314yes—
327C22×C3—24no—
328C22×C3—24no—
329C22×C3C2×D3×Q818yes—
330C22×C3C24×D314yes—
331C3×C4—216no—
332C3×C4—216no—
333C3×C4—216no—
334C3×C4C2×D3×Q8116yes—
335Dic3—332no—
336Dic3—38no—
337Dic3—616no—
338Dic3—68no—
339Dic3—616no—
340Dic3—64no—
341C32#350211yescharacteristic, complemented, Sylow
342C23C23×C3⋊D311yescharacteristic
343Q8—44no—
344Q8—916no—
345Q8—188no—
346Q8—364no—
347Q8—364no—
348C2×C4—42no—
349C2×C4—98no—
350C2×C4—94no—
351C2×C4—91no—
352C2×C4—91no—
353C2×C4—94no—
354C2×C4—94no—
355C2×C4—92no—
356C2×C4—182no—
357C2×C4—361no—
358C2×C4Q8×C3⋊D314yes—
359C2×C4C23×C3⋊D314yes—
360C2×C4C23×C3⋊D314yes—
361C2×C4C23×C3⋊D314yes—
362C2×C4C23×C3⋊D312yes—
363C2×C3—28no—
364C2×C3C22×D3×Q814yes—
365C2×C3#596614yes—
366C2×C3D3×2−1+414yes—
367C22—21no—
368C22—21no—
369C22C2×Q8×C3⋊D312yes—
370C22C24×C3⋊D311yescharacteristic
371C4—24no—
372C4—24no—
373C4—24no—
374C4—98no—
375C4—92no—
376C4—182no—
377C4—184no—
378C4—181no—
379C4—184no—
380C4C2×Q8×C3⋊D314yes—
381C3#8658514yescomplemented
382C2—22no—
383C2C22×Q8×C3⋊D311yescharacteristic
384C2#1059675811yescharacteristic
385C2C3⋊D3×2−1+411yescharacteristic
subgroupG/H
center, FrattiniC22C24×C3⋊D3
commutator, socle, cosocleC22×C32C25
FittingC32×#544C2
prime radicalC23×C32C24
hypercenter#544C3⋊D3
hypocenterC32#3502
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #544

Complements

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

NH ≅ G/Ntype
2. #10596193C2semidirect
3. #10596192C2semidirect
4. #10596156C2semidirect
5. #10596156C2semidirect
68. C2×#634Q8semidirect
341. C32#3502semidirect
381. C3#86585semidirect

Maximal subgroups

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

subgroupindex
C32×#5442
#105961932
#105961922
#105961562
#105960942
#105960932
#105959882
#105959872
#105959712
C2×#640962
#865853