Finite Group Databasebeta

← #11801804

Subgroups — #11801804

Order 1152.

1129 conjugacy classes of subgroups.

The subgroup lattice has 485 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63838C211yesmaximal, characteristic
2C42×C3⋊Dic3C211yesmaximal, characteristic
3C3×#4933C212yesmaximal
4#10591396C211yesmaximal, characteristic
5#10591396C211yesmaximal, characteristic
6#10591337C211yesmaximal, characteristic
7#10591328C211yesmaximal, characteristic
8#10591257C211yesmaximal, characteristic
9#10591252C212yesmaximal
10#10591241C212yesmaximal
11#10591192C212yesmaximal
12#74938—32nomaximal
13C22×#627C2211yescharacteristic
14C2×C32×C42C2211yescharacteristic
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C2×C4×C3⋊Dic3C2211yescharacteristic
18C2×C4×C3⋊Dic3C2211yescharacteristic
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C2×C4×C3⋊Dic3C2211yescharacteristic
21C2×C3×Dic3⋊C4C2212yes—
22C2×C3×Dic3⋊C4C2212yes—
23C2×#3724C2211yescharacteristic
24C2×#3724C2211yescharacteristic
25C2×#3724C2211yescharacteristic
26C2×Dic3⋊Dic3C2212yes—
27C2×Dic32C2212yes—
28C2×Dic32C2212yes—
29#63838C418yescomplemented
30C3×C3⋊#95C2212yes—
31C3×C3⋊#95C2212yes—
32C3×C3⋊#95C2212yes—
33C3×C3⋊#95C2212yes—
34#63579C2212yes—
35#63579C2212yes—
36#63579C2212yes—
37C2×#887—32no—
38C3×#387—32no—
39#4980—32no—
40#4976—32no—
41Dic3×C4⋊C4—32no—
42#4933D312yes—
43C42×Dic3—32no—
44C42×Dic3—61no—
45#4652—32no—
46#4649—32no—
47#4649—32no—
48#4648—32no—
49#4648—32no—
50#4647—32no—
51#4646—32no—
52#4646—32no—
53C22×C32×C4C2311yescharacteristic
54C22×C32×C4C2311yescharacteristic
55C22×C32×C4C2311yescharacteristic
56C22×C3⋊Dic3C2311yescharacteristic
57C22×C3⋊Dic3C2311yescharacteristic
58C22×C3⋊Dic3C2311yescharacteristic
59C22×C3⋊Dic3C2311yescharacteristic
60C22×C3×Dic3C2312yes—
61C22×C3×Dic3C2312yes—
62C22×C3×Dic3C2312yes—
63C22×C3×Dic3C2312yes—
64C2×#627—22no—
65C2×#627—22no—
66C2×#627C2×C414yes—
67C32×C42—22no—
68C4×C3⋊Dic3—22no—
69C4×C3⋊Dic3—22no—
70C4×C3⋊Dic3—22no—
71C4×C3⋊Dic3—22no—
72C4×C3⋊Dic3C2×C414yes—
73C4×C3⋊Dic3Q814yescomplemented
74C3×Dic3⋊C4—24no—
75C3×Dic3⋊C4C2×C418yes—
76#3724—22no—
77#3724—22no—
78#3724C2×C414yes—
79Dic3⋊Dic3—24no—
80Dic32—24no—
81Dic32C2×C418yes—
82#2295—91noSylow
83C22×Dic6—32no—
84C2×C3×C4⋊C4—32no—
85C2×C3×C4⋊C4—32no—
86C2×C3×C42—21no—
87C2×C3×C42C2×D312yes—
88C2×C4⋊Dic3—32no—
89C2×Dic3⋊C4—32no—
90C2×Dic3⋊C4—32no—
91C2×Dic3⋊C4—32no—
92C2×Dic3⋊C4—32no—
93C2×Dic3⋊C4C2×D312yes—
94C2×Dic3⋊C4C2×D312yes—
95C2×C4×Dic3—32no—
96C2×C4×Dic3—32no—
97C2×C4×Dic3—32no—
98C2×C4×Dic3—32no—
99C2×C4×Dic3—32no—
100C2×C4×Dic3—32no—
101C2×C4×Dic3—32no—
102C2×C4×Dic3—32no—
103C2×C4×Dic3—32no—
104C2×C4×Dic3—32no—
105C2×C4×Dic3—61no—
106C2×C4×Dic3—61no—
107C2×C4×Dic3—61no—
108C2×C4×Dic3—61no—
109C2×C4×Dic3—61no—
110C2×C4×Dic3—61no—
111#887—316no—
112C3×#95—32no—
113C3×#95—32no—
114C3×#95—32no—
115C3×#95—32no—
116C3⋊#95—32no—
117C3⋊#95—32no—
118C3⋊#95—32no—
119C3⋊#95—32no—
120C3⋊#95—32no—
121C3⋊#95—32no—
122C3⋊#95C2×D312yes—
123C3⋊#95C2×D312yes—
124C3⋊#95C2×D312yes—
125C3⋊#95C2×D312yes—
126C23×C32C2411yescharacteristic
127C2×C32×C4—21no—
128C2×C32×C4—21no—
129C2×C32×C4—21no—
130C2×C32×C4—21no—
131C2×C32×C4—21no—
132C2×C32×C4—21no—
133C2×C32×C4C22×C412yes—
134C2×C32×C4C2×Q812yes—
135C2×C32×C4#4112yes—
136C2×C3⋊Dic3—21no—
137C2×C3⋊Dic3—21no—
138C2×C3⋊Dic3—21no—
139C2×C3⋊Dic3—21no—
140C2×C3⋊Dic3C22×C412yes—
141C2×C3⋊Dic3C22×C412yes—
142C2×C3⋊Dic3C2×Q812yes—
143C2×C3⋊Dic3C2×Q812yes—
144C2×C3⋊Dic3#4112yes—
145C2×C3⋊Dic3#4112yes—
146C2×C3⋊Dic3#4112yes—
147C2×C3⋊Dic3#4112yes—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—22no—
155C2×C3×Dic3—22no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3C22×C414yes—
159C2×C3×Dic3C22×C414yes—
160#627—28no—
161C2×C4×Q8—91no—
162#391—91no—
163#391—91no—
164#389—91no—
165#389—91no—
166#387—32no—
167#387—92no—
168C4×C4⋊C4—91no—
169C4×C4⋊C4—92no—
170#376—92no—
171C43—91no—
172C22×C3×C4—21no—
173C22×C3×C4—21no—
174C22×C3×C4—21no—
175C22×C3×C4—32no—
176C22×C3×C4—32no—
177C22×C3×C4—32no—
178C22×C3×C4—32no—
179C22×C3×C4C22×D312yes—
180C22×C3×C4C22×D312yes—
181C22×C3×C4C22×D312yes—
182C22×Dic3—32no—
183C22×Dic3—32no—
184C22×Dic3—32no—
185C22×Dic3—32no—
186C22×Dic3—61no—
187C22×Dic3—61no—
188C22×Dic3—61no—
189C22×Dic3—61no—
190C22×Dic3C22×D312yes—
191C22×Dic3C22×D312yes—
192C22×Dic3C22×D312yes—
193C22×Dic3C22×D312yes—
194C2×Dic6—38no—
195C2×Dic6—64no—
196C2×Dic6—64no—
197C3×C4⋊C4—38no—
198C3×C4⋊C4—64no—
199C3×C42—24no—
200C3×C42—24no—
201C4⋊Dic3—64no—
202Dic3⋊C4—24no—
203Dic3⋊C4—38no—
204Dic3⋊C4—64no—
205Dic3⋊C4—64no—
206Dic3⋊C4—64no—
207Dic3⋊C4C4×D318yes—
208C4×Dic3—38no—
209C4×Dic3—38no—
210C4×Dic3—38no—
211C4×Dic3—38no—
212C4×Dic3—64no—
213C4×Dic3—64no—
214C4×Dic3—64no—
215C4×Dic3—64no—
216C4×Dic3—64no—
217C4×Dic3—64no—
218C4×Dic3—64no—
219C4×Dic3—64no—
220C4×Dic3—64no—
221C4×Dic3—64no—
222C4×Dic3—64no—
223C4×Dic3—64no—
224C22×C32C23×C411yescharacteristic
225C22×C32C22×Q811yescharacteristic
226C22×C32C2×#4111yescharacteristic
227C22×C32C2×#4111yescharacteristic
228C22×C32C2×#4111yescharacteristic
229C22×C32C2×#4111yescharacteristic
230C22×C32C2×#4111yescharacteristic
231C32×C4—22no—
232C32×C4—22no—
233C32×C4—22no—
234C3⋊Dic3—22no—
235C3⋊Dic3—22no—
236C3⋊Dic3#11714yes—
237C3⋊Dic3C4×Q814yes—
238C3×Dic3—24no—
239C3×Dic3—24no—
240C3×Dic3—42no—
241C3×Dic3—42no—
242C22×Q8—91no—
243C4×Q8—98no—
244C2×C4⋊C4—32no—
245C2×C4⋊C4—32no—
246C2×C4⋊C4—91no—
247C2×C4⋊C4—92no—
248C2×C4⋊C4—91no—
249C2×C4⋊C4—91no—
250C2×C42—92no—
251C2×C42—91no—
252C2×C42—91no—
253C2×C42—92no—
254C2×C42—91no—
255C2×C42—91no—
256C2×C42—91no—
257C2×C42—91no—
258C2×C42D3211yescharacteristic
259#95—32no—
260#95—32no—
261#95—32no—
262#95—32no—
263#95—92no—
264#95—92no—
265#95—92no—
266C23×C3—21no—
267C23×C3C23×D312yes—
268C2×C3×C4—22no—
269C2×C3×C4—22no—
270C2×C3×C4—22no—
271C2×C3×C4—22no—
272C2×C3×C4—22no—
273C2×C3×C4—22no—
274C2×C3×C4—22no—
275C2×C3×C4—22no—
276C2×C3×C4—22no—
277C2×C3×C4—22no—
278C2×C3×C4—22no—
279C2×C3×C4—22no—
280C2×C3×C4—22no—
281C2×C3×C4—22no—
282C2×C3×C4—22no—
283C2×C3×C4—34no—
284C2×C3×C4—34no—
285C2×C3×C4—62no—
286C2×C3×C4—62no—
287C2×C3×C4—62no—
288C2×C3×C4—62no—
289C2×C3×C4—62no—
290C2×C3×C4—62no—
291C2×C3×C4—62no—
292C2×C3×C4—62no—
293C2×C3×C4—62no—
294C2×C3×C4—62no—
295C2×C3×C4C2×C4×D314yes—
296C2×C3×C4#23714yes—
297C2×C3×C4D3×Q814yes—
298C2×Dic3—22no—
299C2×Dic3—22no—
300C2×Dic3—22no—
301C2×Dic3—22no—
302C2×Dic3—22no—
303C2×Dic3—22no—
304C2×Dic3—22no—
305C2×Dic3—22no—
306C2×Dic3—22no—
307C2×Dic3—22no—
308C2×Dic3—34no—
309C2×Dic3—34no—
310C2×Dic3—34no—
311C2×Dic3—34no—
312C2×Dic3—34no—
313C2×Dic3—34no—
314C2×Dic3—34no—
315C2×Dic3—34no—
316C2×Dic3—62no—
317C2×Dic3—62no—
318C2×Dic3—62no—
319C2×Dic3—62no—
320C2×Dic3—62no—
321C2×Dic3—62no—
322C2×Dic3—62no—
323C2×Dic3—62no—
324C2×Dic3—62no—
325C2×Dic3—62no—
326C2×Dic3—62no—
327C2×Dic3—62no—
328C2×Dic3—62no—
329C2×Dic3—62no—
330C2×Dic3—62no—
331C2×Dic3—62no—
332C2×Dic3C2×C4×D314yes—
333C2×Dic3C2×C4×D314yes—
334Dic6—616no—
335C2×C32C2×#11711yescharacteristic
336C2×C32C2×C4×Q811yescharacteristic
337C2×C32C4×#4111yescharacteristic
338C2×C32#52911yescharacteristic
339C2×C32#52911yescharacteristic
340C2×C32#53311yescharacteristic
341C2×C32#53311yescharacteristic
342C2×Q8—94no—
343C2×Q8—182no—
344C2×Q8—182no—
345C22×C4—32no—
346C22×C4—32no—
347C22×C4—32no—
348C22×C4—32no—
349C22×C4—91no—
350C22×C4—91no—
351C22×C4—91no—
352C22×C4—91no—
353C22×C4C2×D3211yescharacteristic
354C22×C4C2×D3211yescharacteristic
355C22×C4C2×D3211yescharacteristic
356C4⋊C4—38no—
357C4⋊C4—64no—
358C4⋊C4—94no—
359C4⋊C4—182no—
360C4⋊C4—182no—
361C4⋊C4—184no—
362C42—22no—
363C42—98no—
364C42—94no—
365C42—94no—
366C42—182no—
367C42—182no—
368C42—182no—
369C42—182no—
370C42—184no—
371C22×C3—21no—
372C22×C3—21no—
373C22×C3—21no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—21no—
377C22×C3—21no—
378C22×C3C22×C4×D312yes—
379C22×C3C2×#23712yes—
380C22×C3C2×D3×Q812yes—
381C22×C3D3×#4112yes—
382C22×C3D3×#4112yes—
383C22×C3D3×#4112yes—
384C22×C3D3×#4112yes—
385C3×C4—24no—
386C3×C4—24no—
387C3×C4—24no—
388C3×C4—24no—
389C3×C4—24no—
390C3×C4—24no—
391C3×C4—64no—
392C3×C4—64no—
393C3×C4—122no—
394C3×C4—122no—
395Dic3—24no—
396Dic3—24no—
397Dic3—38no—
398Dic3—38no—
399Dic3—42no—
400Dic3—42no—
401Dic3—64no—
402Dic3—64no—
403Dic3—64no—
404Dic3—64no—
405Dic3—64no—
406Dic3—64no—
407C32#229511yescharacteristic, complemented, Sylow
408C23C22×D3211yescharacteristic
409Q8—188no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—34no—
417C2×C4—34no—
418C2×C4—62no—
419C2×C4—62no—
420C2×C4—62no—
421C2×C4—62no—
422C2×C4—62no—
423C2×C4—62no—
424C2×C4—62no—
425C2×C4—62no—
426C2×C4—62no—
427C2×C4—62no—
428C2×C4—92no—
429C2×C4—92no—
430C2×C4—92no—
431C2×C4—92no—
432C2×C4—92no—
433C2×C4—92no—
434C2×C4—92no—
435C2×C4—92no—
436C2×C4—181no—
437C2×C4—181no—
438C2×C4—181no—
439C2×C4—181no—
440C2×C4#379712yes—
441C2×C4C4×D3212yes—
442C2×C4#380512yes—
443C2×C3—21no—
444C2×C3—21no—
445C2×C3—21no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3—21no—
450C2×C3D3×#11712yes—
451C2×C3C4×#23712yes—
452C2×C3C4×D3×Q812yes—
453C2×C3#562212yes—
454C2×C3#564912yes—
455C2×C3#568812yes—
456C2×C3#570612yes—
457C22C2×#379711yescharacteristic
458C22C2×C4×D3211yescharacteristic
459C22#6430611yescharacteristic
460C22#6430611yescharacteristic
461C22#6430611yescharacteristic
462C22#6430611yescharacteristic
463C22C2×#380511yescharacteristic
464C4—22no—
465C4—22no—
466C4—22no—
467C4—64no—
468C4—64no—
469C4—94no—
470C4—94no—
471C4—122no—
472C4—122no—
473C4—182no—
474C4—182no—
475C3—21no—
476C3#7493812yescomplemented
477C2#1059385411yescharacteristic
478C2C4×#379711yescharacteristic
479C2#1059397911yescharacteristic
480C2#1059399211yescharacteristic
481C2#1059481011yescharacteristic
482C2C4×#380511yescharacteristic
483C2#1059496311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, prime radical, cosocleC23×C32C24
hypercenterC2×C42D32
hypocenterC32#2295
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
29. #63838C4semidirect
73. C4×C3⋊Dic3Q8semidirect
407. C32#2295semidirect
476. C3#74938semidirect

Maximal subgroups

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

subgroupindex
C2×#638382
C42×C3⋊Dic32
C3×#49332
#105913962
#105913372
#105913282
#105912572
#105912522
#105912412
#105911922
#749383