Finite Group Databasebeta

← #11807961

Subgroups — #11807961

Order 1152.

941 conjugacy classes of subgroups.

The subgroup lattice has 425 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63840C211yesmaximal, characteristic
2#10592628C211yesmaximal, characteristic
3C3×#4933C212yesmaximal
4#10591273C211yesmaximal, characteristic
5#10591272C212yesmaximal
6#10591254C212yesmaximal
7#10591250C212yesmaximal
8#10591248C212yesmaximal
9#10591235C212yesmaximal
10#74977—32nomaximal
11C22×#634C2211yescharacteristic
12C22×#627C2211yescharacteristic
13C2×C32×C42C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C2×C3×Dic3⋊C4C2212yes—
16C2×C3×Dic3⋊C4C2212yes—
17C2×#3724C2211yescharacteristic
18C2×Dic3⋊Dic3C2212yes—
19C2×Dic32C2212yes—
20C2×Dic32C2211yescharacteristic
21C2×Dic32C2211yescharacteristic
22#63840C418yescomplemented
23#63658C2212yes—
24#63658C2212yes—
25C3×C3⋊#95C2212yes—
26C3×C3⋊#95C2212yes—
27C3×C3⋊#95C2212yes—
28C3×C3⋊#95C2212yes—
29#63579C2212yes—
30#63579C2212yes—
31#63579C2212yes—
32#63579C2212yes—
33C2×#888—32no—
34C3×#387—32no—
35#4980—32no—
36#4978—32no—
37#4973—32no—
38#4933D312yes—
39#4929—32no—
40#4929—61no—
41#4655—32no—
42#4654—32no—
43#4653—32no—
44#4652—32no—
45#4651—32no—
46#4651—32no—
47#4646—32no—
48#4646—32no—
49C22×C32×C4C2312yes—
50C22×C32×C4C2311yescharacteristic
51C22×C3⋊Dic3C2312yes—
52C22×C3⋊Dic3C2311yescharacteristic
53C22×C3⋊Dic3C2311yescharacteristic
54C2×#634—41no—
55C2×#634—41no—
56C2×#634C2×C414yes—
57C22×C3×Dic3C2312yes—
58C22×C3×Dic3C2312yes—
59C22×C3×Dic3C2312yes—
60C22×C3×Dic3C2312yes—
61C2×#627—41no—
62C2×#627—41no—
63C2×#627C2×C414yes—
64C32×C42—41no—
65C4⋊(C3⋊Dic3)—41no—
66C3×Dic3⋊C4—42no—
67C3×Dic3⋊C4C2×C418yes—
68#3724—41no—
69Dic3⋊Dic3C2×C418yes—
70Dic32—42no—
71Dic32—41no—
72Dic32C2×C414yes—
73#2381—91noSylow
74C22×Dic6—32no—
75C22×Dic6—32no—
76C22×Dic6—61no—
77C2×C3×C4⋊C4—32no—
78C2×C3×C4⋊C4—32no—
79C2×C3×C42—21no—
80C2×C3×C42C2×D312yes—
81C2×C4⋊Dic3—32no—
82C2×C4⋊Dic3—32no—
83C2×C4⋊Dic3—61no—
84C2×Dic3⋊C4—32no—
85C2×Dic3⋊C4—32no—
86C2×Dic3⋊C4C2×D312yes—
87C2×Dic3⋊C4C2×D312yes—
88C2×C4×Dic3—32no—
89C2×C4×Dic3—32no—
90C2×C4×Dic3—32no—
91C2×C4×Dic3—32no—
92#888—316no—
93C3×#95—32no—
94C3×#95—32no—
95C3×#95—32no—
96C3×#95—32no—
97C3⋊#95—32no—
98C3⋊#95—32no—
99C3⋊#95—32no—
100C3⋊#95—32no—
101C3⋊#95—32no—
102C3⋊#95—32no—
103C3⋊#95—32no—
104C3⋊#95—32no—
105C3⋊#95—32no—
106C3⋊#95—32no—
107C3⋊#95—32no—
108C3⋊#95—32no—
109C3⋊#95—62no—
110C3⋊#95—62no—
111C3⋊#95C2×D312yes—
112C3⋊#95C2×D312yes—
113C3⋊#95C2×D312yes—
114C3⋊#95C2×D312yes—
115C23×C32C2411yescharacteristic
116C2×C32×C4—21no—
117C2×C32×C4—21no—
118C2×C32×C4—22no—
119C2×C32×C4—22no—
120C2×C32×C4—22no—
121C2×C32×C4C22×C412yes—
122C2×C3⋊Dic3—21no—
123C2×C3⋊Dic3—21no—
124C2×C3⋊Dic3—21no—
125C2×C3⋊Dic3—21no—
126C2×C3⋊Dic3—22no—
127C2×C3⋊Dic3—22no—
128C2×C3⋊Dic3—22no—
129C2×C3⋊Dic3C22×C412yes—
130C2×C3⋊Dic3C22×C412yes—
131#634—44no—
132C2×C3×Dic3—22no—
133C2×C3×Dic3—22no—
134C2×C3×Dic3—22no—
135C2×C3×Dic3—22no—
136C2×C3×Dic3—22no—
137C2×C3×Dic3—22no—
138C2×C3×Dic3—22no—
139C2×C3×Dic3—22no—
140C2×C3×Dic3—22no—
141C2×C3×Dic3—22no—
142C2×C3×Dic3C22×C414yes—
143C2×C3×Dic3C22×C414yes—
144#627—44no—
145C2×C4⋊Q8—91no—
146#391—91no—
147#391—92no—
148#391—91no—
149#387—32no—
150#387—92no—
151#387—92no—
152#387—92no—
153#383—92no—
154C22×C3×C4—21no—
155C22×C3×C4—22no—
156C22×C3×C4—32no—
157C22×C3×C4—32no—
158C22×C3×C4—32no—
159C22×C3×C4—32no—
160C22×C3×C4C22×D312yes—
161C22×C3×C4C22×D312yes—
162C22×C3×C4C22×D312yes—
163C22×Dic3—32no—
164C22×Dic3—32no—
165C22×Dic3—32no—
166C22×Dic3—32no—
167C22×Dic3—61no—
168C22×Dic3—61no—
169C22×Dic3—62no—
170C22×Dic3C22×D312yes—
171C22×Dic3C22×D312yes—
172C22×Dic3C22×D312yes—
173C22×Dic3C22×D312yes—
174C2×Dic6—38no—
175C2×Dic6—38no—
176C2×Dic6—64no—
177C2×Dic6—122no—
178C2×Dic6—122no—
179C2×Dic6—122no—
180C2×Dic6—122no—
181C2×Dic6—122no—
182C2×Dic6—122no—
183C3×C4⋊C4—38no—
184C3×C4⋊C4—122no—
185C3×C42—42no—
186C3×C42—42no—
187C4⋊Dic3—38no—
188C4⋊Dic3—122no—
189C4⋊Dic3—122no—
190Dic3⋊C4—38no—
191Dic3⋊C4—42no—
192Dic3⋊C4—122no—
193Dic3⋊C4C4×D318yes—
194C4×Dic3—38no—
195C4×Dic3—122no—
196C4×Dic3—122no—
197C4×Dic3—122no—
198C22×C32C23×C411yescharacteristic
199C22×C32H(5,𝔽2)11yescharacteristic
200C22×C32H(5,𝔽2)11yescharacteristic
201C22×C322−1+412yes—
202C22×C322−1+412yes—
203C32×C4—22no—
204C32×C4—42no—
205C3⋊Dic3—22no—
206C3⋊Dic3—22no—
207C3⋊Dic3—42no—
208C3×Dic3—24no—
209C3×Dic3—24no—
210C3×Dic3—42no—
211C3×Dic3—42no—
212C22×Q8—91no—
213C22×Q8—91no—
214C4⋊Q8—98no—
215C2×C4⋊C4—32no—
216C2×C4⋊C4—32no—
217C2×C4⋊C4—92no—
218C2×C4⋊C4—91no—
219C2×C4⋊C4—91no—
220C2×C42—91no—
221C2×C42—92no—
222C2×C42—91no—
223C2×C42D3211yescharacteristic
224#95—32no—
225#95—32no—
226#95—32no—
227#95—32no—
228#95—92no—
229#95—92no—
230#95—92no—
231#95—92no—
232#95—92no—
233#95—92no—
234C23×C3—21no—
235C23×C3C23×D312yes—
236C2×C3×C4—22no—
237C2×C3×C4—22no—
238C2×C3×C4—22no—
239C2×C3×C4—22no—
240C2×C3×C4—24no—
241C2×C3×C4—22no—
242C2×C3×C4—22no—
243C2×C3×C4—22no—
244C2×C3×C4—22no—
245C2×C3×C4—22no—
246C2×C3×C4—22no—
247C2×C3×C4—22no—
248C2×C3×C4—34no—
249C2×C3×C4—34no—
250C2×C3×C4—42no—
251C2×C3×C4—42no—
252C2×C3×C4—62no—
253C2×C3×C4—62no—
254C2×C3×C4—62no—
255C2×C3×C4—62no—
256C2×C3×C4—62no—
257C2×C3×C4—62no—
258C2×C3×C4—62no—
259C2×C3×C4—62no—
260C2×C3×C4—62no—
261C2×C3×C4—62no—
262C2×C3×C4C2×C4×D314yes—
263C2×Dic3—22no—
264C2×Dic3—22no—
265C2×Dic3—22no—
266C2×Dic3—22no—
267C2×Dic3—22no—
268C2×Dic3—22no—
269C2×Dic3—22no—
270C2×Dic3—22no—
271C2×Dic3—22no—
272C2×Dic3—22no—
273C2×Dic3—34no—
274C2×Dic3—34no—
275C2×Dic3—62no—
276C2×Dic3—62no—
277C2×Dic3—62no—
278C2×Dic3—62no—
279C2×Dic3—62no—
280C2×Dic3—62no—
281C2×Dic3—62no—
282C2×Dic3—62no—
283C2×Dic3—62no—
284C2×Dic3—62no—
285C2×Dic3—62no—
286C2×Dic3—62no—
287C2×Dic3—121no—
288C2×Dic3—121no—
289C2×Dic3—121no—
290C2×Dic3—121no—
291C2×Dic3—122no—
292C2×Dic3—122no—
293C2×Dic3—122no—
294C2×Dic3C2×C4×D314yes—
295C2×Dic3C2×C4×D314yes—
296Dic6—128no—
297Dic6—128no—
298Dic6—128no—
299C2×C32#51811yescharacteristic
300C2×C32#51912yes—
301C2×C32#56312yes—
302C2×C32#56311yescharacteristic
303C2×C32#56311yescharacteristic
304C2×Q8—94no—
305C2×Q8—94no—
306C2×Q8—361no—
307C2×Q8—361no—
308C2×Q8—361no—
309C2×Q8—361no—
310C22×C4—32no—
311C22×C4—32no—
312C22×C4—32no—
313C22×C4—32no—
314C22×C4—91no—
315C22×C4—91no—
316C22×C4—92no—
317C22×C4C2×D3212yes—
318C22×C4C2×D3211yescharacteristic
319C4⋊C4—38no—
320C4⋊C4—98no—
321C4⋊C4—122no—
322C4⋊C4—361no—
323C4⋊C4—361no—
324C42—41no—
325C42—94no—
326C42—362no—
327C42—361no—
328C22×C3—22no—
329C22×C3—22no—
330C22×C3—21no—
331C22×C3—21no—
332C22×C3—21no—
333C22×C3C22×C4×D312yes—
334C22×C3#100412yes—
335C22×C3#100712yes—
336C22×C3#100912yes—
337C22×C3#101012yes—
338C22×C3#101012yes—
339C22×C3#101012yes—
340C3×C4—24no—
341C3×C4—24no—
342C3×C4—44no—
343C3×C4—42no—
344C3×C4—42no—
345C3×C4—64no—
346C3×C4—64no—
347C3×C4—122no—
348C3×C4—122no—
349Dic3—24no—
350Dic3—24no—
351Dic3—42no—
352Dic3—42no—
353Dic3—64no—
354Dic3—64no—
355Dic3—122no—
356Dic3—122no—
357Dic3—122no—
358Dic3—122no—
359Dic3—242no—
360C32#238111yescharacteristic, complemented, Sylow
361C23C22×D3211yescharacteristic
362Q8—364no—
363Q8—364no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—34no—
370C2×C4—34no—
371C2×C4—62no—
372C2×C4—62no—
373C2×C4—62no—
374C2×C4—62no—
375C2×C4—62no—
376C2×C4—62no—
377C2×C4—62no—
378C2×C4—62no—
379C2×C4—62no—
380C2×C4—62no—
381C2×C4—92no—
382C2×C4—92no—
383C2×C4—181no—
384C2×C4—181no—
385C2×C4—181no—
386C2×C4—181no—
387C2×C4—182no—
388C2×C4—182no—
389C2×C4—182no—
390C2×C4C4×D3212yes—
391C2×C3—21no—
392C2×C3—22no—
393C2×C3—22no—
394C2×C3—21no—
395C2×C3—21no—
396C2×C3#551612yes—
397C2×C3#554512yes—
398C2×C3#557212yes—
399C2×C3#564612yes—
400C2×C3#565112yes—
401C2×C3#569912yes—
402C2×C3#571212yes—
403C22#6429712yes—
404C22#6429812yes—
405C22C2×C4×D3211yescharacteristic
406C22#6430811yescharacteristic
407C22#6433011yescharacteristic
408C4—22no—
409C4—42no—
410C4—64no—
411C4—64no—
412C4—122no—
413C4—122no—
414C4—182no—
415C4—182no—
416C4—362no—
417C3—21no—
418C3#7497712yescomplemented
419C2#1059385711yescharacteristic
420C2#1059388512yes—
421C2#1059396211yescharacteristic
422C2#1059497212yes—
423C2#1059505811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, prime radical, cosocleC23×C32C24
hypercenterC2×C42D32
hypocenterC32#2381
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
22. #63840C4semidirect
360. C32#2381semidirect
418. C3#74977semidirect

Maximal subgroups

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

subgroupindex
C2×#638402
#105926282
C3×#49332
#105912732
#105912722
#105912542
#105912502
#105912482
#105912352
#749773