Finite Group Databasebeta

← #11805312

Subgroups — #11805312

Order 1152.

1097 conjugacy classes of subgroups.

The subgroup lattice has 535 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63855C211yesmaximal, characteristic
2#10592347C211yesmaximal, characteristic, complemented
3C3×#4666C211yesmaximal, characteristic
4C3×#4648C211yesmaximal, characteristic, complemented
5#10591360C211yesmaximal, characteristic, complemented
6C4×Dic3⋊Dic3C212yesmaximal, complemented
7#10591327C212yesmaximal, complemented
8#10591295C211yesmaximal, characteristic
9#10591287C212yesmaximal
10#10591279C212yesmaximal
11#10591206C211yesmaximal, characteristic, complemented
12#73459—31nomaximal
13#73392—31nomaximal
14C22×C3×C4×D3C2211yescharacteristic
15C2×C4×C3⋊Dic3C2212yes—
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C2×C3×(C2×D3)⋊C4C2212yes—
18C2×C3×C4×Dic3C2212yes—
19C2×C3×C4×Dic3C2212yes—
20C2×C3×C4×Dic3C2211yescharacteristic
21C2×#3724C2212yes—
22C2×Dic3⋊Dic3C2212yes—
23C2×Dic3⋊Dic3C2212yes—
24C2×Dic3⋊Dic3C2211yescharacteristic
25C2×Dic3⋊Dic3C2211yescharacteristic
26C2×(C2×D3)⋊Dic3C2212yes—
27C2×(C2×D3)⋊Dic3C2211yescharacteristic
28C2×(C2×D3)⋊Dic3C2211yescharacteristic
29#63855C418yescomplemented
30C32×#95C2211yescharacteristic
31#63658C2212yes—
32#63658C2211yescharacteristic
33C3×C3⋊#95C2212yes—
34C3×C3⋊#95C2211yescharacteristic
35C3×C3⋊#95C2211yescharacteristic
36#63579C2212yes—
37#63579C2212yes—
38C2×#926—31no—
39C2×#872—31no—
40C3×C4×C22⋊C4—31no—
41C3×#376—31no—
42#5212—31no—
43#4944—32no—
44#4944—32no—
45#4940—32no—
46#4936—31no—
47C4×C4⋊Dic3—32no—
48C4×Dic3⋊C4—32no—
49#4928—32no—
50#4670—32no—
51#4667—31no—
52#4666D311yescharacteristic
53#4650—31no—
54#4650—31no—
55#4650—31no—
56#4648—31no—
57#4648—31no—
58#4648—61no—
59#4648D311yescharacteristic, complemented
60#4647—32no—
61C23×C3×D3C2311yescharacteristic
62C22×C32×C4C2311yescharacteristic
63C22×C32×C4C2312yes—
64C22×C3⋊Dic3C2312yes—
65C22×C3⋊Dic3C2311yescharacteristic
66C22×C3⋊Dic3C2311yescharacteristic
67C22×C3×Dic3C2312yes—
68C22×C3×Dic3C2312yes—
69C22×C3×Dic3C2311yescharacteristic
70C22×C3×Dic3C2311yescharacteristic
71C22×C3×Dic3C2311yescharacteristic
72C2×C3×C4×D3—24no—
73C2×C3×C4×D3C2×C414yes—
74C4×C3⋊Dic3—24no—
75C4×C3⋊Dic3C2×C414yes—
76C3×(C2×D3)⋊C4—24no—
77C3×C4×Dic3—24no—
78C3×C4×Dic3—24no—
79C3×C4×Dic3C2×C414yes—
80#3724—42no—
81Dic3⋊Dic3—24no—
82Dic3⋊Dic3—42no—
83Dic3⋊Dic3C2×C414yes—
84Dic3⋊Dic3C2×C414yes—
85(C2×D3)⋊Dic3—42no—
86(C2×D3)⋊Dic3C2×C414yes—
87(C2×D3)⋊Dic3C2×C414yes—
88#2346—91noSylow
89C23×C3×C4—31no—
90C22×C4×D3C2×D311yescharacteristic
91C2×C3×C22⋊C4—32no—
92C2×C3×C42—31no—
93C2×C3×C42—32no—
94C2×C3×C42—32no—
95C2×#217—31no—
96C2×#217—31no—
97C2×#217—32no—
98C2×(C2×D3)⋊C4—31no—
99C2×(C2×D3)⋊C4—31no—
100C2×(C2×D3)⋊C4—32no—
101C2×(C2×D3)⋊C4C2×D312yes—
102#926—38no—
103C2×C4⋊Dic3—31no—
104C2×C4⋊Dic3—31no—
105C2×C4⋊Dic3—32no—
106C2×C4⋊Dic3—32no—
107C2×Dic3⋊C4—31no—
108C2×Dic3⋊C4—31no—
109C2×Dic3⋊C4—32no—
110C2×Dic3⋊C4—32no—
111C2×Dic3⋊C4—32no—
112C2×Dic3⋊C4—32no—
113C2×C4×Dic3—31no—
114C2×C4×Dic3—31no—
115C2×C4×Dic3—32no—
116C2×C4×Dic3—32no—
117C2×C4×Dic3—61no—
118C2×C4×Dic3—62no—
119C2×C4×Dic3C2×D312yes—
120C2×C4×Dic3C2×D312yes—
121C2×C4×Dic3C2×D311yescharacteristic
122#872—38no—
123C3×#95—21no—
124C3×#95—32no—
125C3×#95—31no—
126C3×#95—31no—
127C3×#95C2×D311yescharacteristic
128C3×#95C2×D311yescharacteristic
129C3⋊#95—32no—
130C3⋊#95—31no—
131C3⋊#95—31no—
132C3⋊#95—32no—
133C3⋊#95—32no—
134C3⋊#95—32no—
135C3⋊#95—32no—
136C3⋊#95—32no—
137C3⋊#95—61no—
138C3⋊#95—62no—
139C3⋊#95C2×D311yescharacteristic
140C3⋊#95C2×D312yes—
141C3⋊#95C2×D311yescharacteristic
142C23×C32C2411yescharacteristic
143C22×C3×D3—22no—
144C22×C3×D3—22no—
145C22×C3×D3—21no—
146C22×C3×D3—21no—
147C22×C3×D3C22×C412yes—
148C2×C32×C4—22no—
149C2×C32×C4—22no—
150C2×C32×C4—22no—
151C2×C32×C4C22×C412yes—
152C2×C32×C4#4114yes—
153C2×C3⋊Dic3—22no—
154C2×C3⋊Dic3—22no—
155C2×C3⋊Dic3—21no—
156C2×C3⋊Dic3—21no—
157C2×C3⋊Dic3—22no—
158C2×C3⋊Dic3—22no—
159C2×C3⋊Dic3C22×C412yes—
160C2×C3⋊Dic3C22×C412yes—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—21no—
163C2×C3×Dic3—21no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3C22×C412yes—
171C2×C3×Dic3C22×C412yes—
172C2×C3×Dic3C22×C412yes—
173C2×C3×Dic3#4114yes—
174C3×C4×D3—28no—
175C2×#117—91no—
176#389—92no—
177#388—92no—
178#388—92no—
179#382—91no—
180#382—91no—
181#380—91no—
182C4×C4⋊C4—92no—
183C4×C22⋊C4—31no—
184#376—31no—
185#376—91no—
186C24×C3—31no—
187C23×D3C22×D311yescharacteristic
188C22×C3×C4—22no—
189C22×C3×C4—21no—
190C22×C3×C4—31no—
191C22×C3×C4—31no—
192C22×C3×C4—31no—
193C22×C3×C4—34no—
194C22×C3×C4—32no—
195C22×C3×C4—32no—
196C22×C3×C4—64no—
197C22×C3×C4C22×D311yescharacteristic
198C22×C3×C4C22×D311yescharacteristic
199C22×C3×C4C22×D312yes—
200C22×C3×C4C22×D312yes—
201C22×Dic3—31no—
202C22×Dic3—31no—
203C22×Dic3—31no—
204C22×Dic3—31no—
205C22×Dic3—32no—
206C22×Dic3—32no—
207C22×Dic3—61no—
208C22×Dic3—61no—
209C22×Dic3—62no—
210C22×Dic3C22×D312yes—
211C22×Dic3C22×D312yes—
212C22×Dic3C22×D311yescharacteristic
213C22×Dic3C22×D311yescharacteristic
214C22×Dic3C22×D311yescharacteristic
215C2×C4×D3—24no—
216C2×C4×D3C4×D314yes—
217C3×C22⋊C4—64no—
218C3×C42—34no—
219C3×C42—64no—
220C3×C42—64no—
221#217—34no—
222#217—34no—
223#217—122no—
224(C2×D3)⋊C4—24no—
225(C2×D3)⋊C4—34no—
226(C2×D3)⋊C4—34no—
227(C2×D3)⋊C4—122no—
228C4⋊Dic3—34no—
229C4⋊Dic3—34no—
230C4⋊Dic3—64no—
231C4⋊Dic3—122no—
232Dic3⋊C4—34no—
233Dic3⋊C4—34no—
234Dic3⋊C4—64no—
235Dic3⋊C4—122no—
236Dic3⋊C4—122no—
237Dic3⋊C4—122no—
238C4×Dic3—24no—
239C4×Dic3—24no—
240C4×Dic3—34no—
241C4×Dic3—34no—
242C4×Dic3—64no—
243C4×Dic3—68no—
244C4×Dic3—64no—
245C4×Dic3—64no—
246C4×Dic3C4×D314yes—
247C22×C32C23×C411yescharacteristic
248C22×C32C2×#4112yes—
249C22×C32C2×#4112yes—
250C22×C32H(5,𝔽2)11yescharacteristic
251C22×C322−1+411yescharacteristic
252C2×C3×D3—22no—
253C2×C3×D3—22no—
254C2×C3×D3—22no—
255C2×C3×D3—42no—
256C2×C3×D3—42no—
257C32×C4—22no—
258C32×C4—24no—
259C3⋊Dic3—22no—
260C3⋊Dic3—22no—
261C3⋊Dic3—42no—
262C3×Dic3—22no—
263C3×Dic3—22no—
264C3×Dic3—42no—
265C3×Dic3—42no—
266C3×Dic3#11714yes—
267C23×C4—31no—
268#117—98no—
269C2×C4⋊C4—91no—
270C2×C4⋊C4—91no—
271C2×C4⋊C4—92no—
272C2×C4⋊C4—92no—
273C2×C4⋊C4—92no—
274C2×C22⋊C4—32no—
275C2×C22⋊C4—91no—
276C2×C22⋊C4—91no—
277C2×C22⋊C4—92no—
278C2×C42—31no—
279C2×C42—32no—
280C2×C42—32no—
281C2×C42—91no—
282C2×C42—92no—
283#95—31no—
284#95—32no—
285#95—31no—
286#95—92no—
287#95—92no—
288#95—91no—
289#95—92no—
290#95D3211yescharacteristic
291C23×C3—21no—
292C23×C3—32no—
293C23×C3—62no—
294C23×C3—62no—
295C23×C3—61no—
296C23×C3—61no—
297C23×C3C23×D311yescharacteristic
298C23×C3C23×D311yescharacteristic
299C22×D3—22no—
300C22×D3—22no—
301C22×D3—21no—
302C22×D3—21no—
303C22×D3C2×C4×D312yes—
304C2×C3×C4—22no—
305C2×C3×C4—22no—
306C2×C3×C4—22no—
307C2×C3×C4—22no—
308C2×C3×C4—22no—
309C2×C3×C4—22no—
310C2×C3×C4—24no—
311C2×C3×C4—22no—
312C2×C3×C4—32no—
313C2×C3×C4—34no—
314C2×C3×C4—32no—
315C2×C3×C4—32no—
316C2×C3×C4—42no—
317C2×C3×C4—42no—
318C2×C3×C4—42no—
319C2×C3×C4—68no—
320C2×C3×C4—62no—
321C2×C3×C4—61no—
322C2×C3×C4—61no—
323C2×C3×C4—62no—
324C2×C3×C4—62no—
325C2×C3×C4—62no—
326C2×C3×C4—62no—
327C2×C3×C4—62no—
328C2×C3×C4—62no—
329C2×C3×C4C2×C4×D312yes—
330C2×C3×C4C2×C4×D312yes—
331C2×C3×C4#23514yes—
332C2×C3×C4#23514yes—
333C2×Dic3—22no—
334C2×Dic3—21no—
335C2×Dic3—21no—
336C2×Dic3—22no—
337C2×Dic3—22no—
338C2×Dic3—22no—
339C2×Dic3—22no—
340C2×Dic3—22no—
341C2×Dic3—22no—
342C2×Dic3—32no—
343C2×Dic3—32no—
344C2×Dic3—32no—
345C2×Dic3—32no—
346C2×Dic3—62no—
347C2×Dic3—62no—
348C2×Dic3—64no—
349C2×Dic3—62no—
350C2×Dic3—62no—
351C2×Dic3—61no—
352C2×Dic3—61no—
353C2×Dic3—61no—
354C2×Dic3—61no—
355C2×Dic3—64no—
356C2×Dic3—62no—
357C2×Dic3—62no—
358C2×Dic3—62no—
359C2×Dic3—62no—
360C2×Dic3—62no—
361C2×Dic3—62no—
362C2×Dic3—121no—
363C2×Dic3—121no—
364C2×Dic3—122no—
365C2×Dic3—122no—
366C2×Dic3C2×C4×D312yes—
367C2×Dic3C2×C4×D312yes—
368C2×Dic3C2×C4×D312yes—
369C2×Dic3#23714yes—
370C4×D3—28no—
371C2×C32C2×#11711yescharacteristic
372C2×C32C4×#4111yescharacteristic
373C2×C32#52011yescharacteristic
374C2×C32#55212yes—
375C2×C32#55512yes—
376C3×D3—42no—
377C24—31no—
378C22×C4—31no—
379C22×C4—31no—
380C22×C4—31no—
381C22×C4—34no—
382C22×C4—32no—
383C22×C4—32no—
384C22×C4—64no—
385C22×C4—91no—
386C22×C4—91no—
387C22×C4—92no—
388C22×C4C2×D3212yes—
389C22×C4C2×D3211yescharacteristic
390C4⋊C4—94no—
391C4⋊C4—94no—
392C4⋊C4—184no—
393C4⋊C4—362no—
394C4⋊C4—362no—
395C22⋊C4—64no—
396C22⋊C4—94no—
397C22⋊C4—94no—
398C22⋊C4—362no—
399C42—34no—
400C42—64no—
401C42—64no—
402C42—94no—
403C42—184no—
404C22×C3—22no—
405C22×C3—21no—
406C22×C3—21no—
407C22×C3—22no—
408C22×C3—21no—
409C22×C3—62no—
410C22×C3—62no—
411C22×C3—62no—
412C22×C3—122no—
413C22×C3—122no—
414C22×C3C22×C4×D311yescharacteristic
415C22×C3C22×C4×D311yescharacteristic
416C22×C3C2×#23512yes—
417C22×C3C2×#23512yes—
418C22×C3C2×#23712yes—
419C22×C3D3×#4112yes—
420C22×C3#100911yescharacteristic
421C22×C3#100911yescharacteristic
422C22×C3#101011yescharacteristic
423C22×C3#101011yescharacteristic
424C2×D3—22no—
425C2×D3—22no—
426C2×D3—22no—
427C2×D3—42no—
428C2×D3—42no—
429C3×C4—22no—
430C3×C4—22no—
431C3×C4—24no—
432C3×C4—24no—
433C3×C4—34no—
434C3×C4—44no—
435C3×C4—42no—
436C3×C4—62no—
437C3×C4—62no—
438C3×C4—122no—
439C3×C4—122no—
440Dic3—22no—
441Dic3—22no—
442Dic3—42no—
443Dic3—42no—
444Dic3—64no—
445Dic3—62no—
446Dic3—62no—
447Dic3—62no—
448Dic3—62no—
449Dic3—122no—
450Dic3—124no—
451Dic3—122no—
452Dic3—122no—
453Dic3#87714yes—
454C32#234611yescharacteristic, complemented, Sylow
455C23—32no—
456C23—62no—
457C23—61no—
458C23—62no—
459C23—61no—
460C23C22×D3211yescharacteristic
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—32no—
465C2×C4—34no—
466C2×C4—32no—
467C2×C4—32no—
468C2×C4—68no—
469C2×C4—62no—
470C2×C4—61no—
471C2×C4—61no—
472C2×C4—62no—
473C2×C4—62no—
474C2×C4—62no—
475C2×C4—62no—
476C2×C4—62no—
477C2×C4—62no—
478C2×C4—92no—
479C2×C4—92no—
480C2×C4—182no—
481C2×C4—181no—
482C2×C4—181no—
483C2×C4—182no—
484C2×C4—182no—
485C2×C4—182no—
486C2×C4#379814yes—
487C2×C4C4×D3212yes—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—22no—
491C2×C3—22no—
492C2×C3—21no—
493C2×C3—122no—
494C2×C3C4×#23511yescharacteristic
495C2×C3C4×#23511yescharacteristic
496C2×C3C2×#87711yescharacteristic
497C2×C3D3×#11711yescharacteristic
498C2×C3#552311yescharacteristic
499C2×C3#552311yescharacteristic
500C2×C3#553112yes—
501C2×C3#553212yes—
502C2×C3#554112yes—
503C2×C3#556312yes—
504D3—42no—
505C22—62no—
506C22—62no—
507C22—62no—
508C22—122no—
509C22—122no—
510C22C2×#379812yes—
511C22C2×C4×D3211yescharacteristic
512C22#6430911yescharacteristic
513C22D3×#23712yes—
514C22#6432011yescharacteristic
515C4—24no—
516C4—22no—
517C4—34no—
518C4—62no—
519C4—62no—
520C4—122no—
521C4—122no—
522C4—182no—
523C4—182no—
524C4—362no—
525C3—21no—
526C3#7339211yescharacteristic, complemented
527C3#7345911yescharacteristic, complemented
528C2—122no—
529C2C4×#379811yescharacteristic
530C2#1059403912yes—
531C2D3×#87711yescharacteristic
532C2#1059451111yescharacteristic
533C2#1059455512yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC23×C3×D3C23
hypercenter#95D32
hypocenterC32#2346
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. #10592347C2semidirect
4. C3×#4648C2semidirect
5. #10591360C2semidirect
6. C4×Dic3⋊Dic3C2semidirect
7. #10591327C2semidirect
11. #10591206C2semidirect
29. #63855C4semidirect
59. #4648D3semidirect
454. C32#2346semidirect
526. C3#73392semidirect
527. C3#73459semidirect

Maximal subgroups

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

subgroupindex
C2×#638552
#105923472
C3×#46662
C3×#46482
#105913602
C4×Dic3⋊Dic32
#105913272
#105912952
#105912872
#105912792
#105912062
#734593
#733923