Finite Group Databasebeta

← #11787150

Subgroups — #11787150

Order 1152.

1077 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#638C211yesmaximal, characteristic
2C23×C3×C3⋊C8C211yesmaximal, characteristic, complemented
3C2×C3×#830C211yesmaximal, characteristic, complemented
4C2×#63557C212yesmaximal, complemented
5#10589156C212yesmaximal, complemented
6#71975—31nomaximal
7#69952—31nomaximal
8C23×C32×C4C2211yescharacteristic
9C22×#638C411yescharacteristic
10C22×C4×C3⋊D3C2211yescharacteristic
11C2×#3757C411yescharacteristic
12C4×#638—22no—
13C4×#638—22no—
14C2×#3752C411yescharacteristic
15C2×#3750C411yescharacteristic
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C22×C3×C3⋊C8—22no—
18C22×C3×C3⋊C8—24no—
19C22×C3×C3⋊C8C2212yes—
20C22×C3×C3⋊C8C2212yes—
21C3×#830—22no—
22#63557—24no—
23C23×C3×C8—31no—
24C2×C4×#67—31no—
25C2×C4×#67—31no—
26C2×C4×#67—61no—
27C23×C3⋊C8D311yescharacteristic, complemented
28C2×C3×C22⋊C8—31no—
29C2×#830D311yescharacteristic, complemented
30C2×(C2×D3)⋊C8—32no—
31C2×(C2×D3)⋊C8—32no—
32#4550—32no—
33#4550—32no—
34C24×C32C2×C411yescharacteristic
35C23×C3⋊D3C2×C411yescharacteristic
36C22×C32×C4—22no—
37C22×C32×C4—22no—
38C22×C32×C4C2×C411yescharacteristic
39C22×C32×C4D412yes—
40C22×C32×C4D412yes—
41C22×C32×C4C2311yescharacteristic
42C2×#638—22no—
43C2×#638—22no—
44C2×#638C814yescomplemented
45C22×C3⋊Dic3C2×C411yescharacteristic
46C22×C3⋊Dic3C2×C411yescharacteristic
47C22×C3⋊Dic3C2×C411yescharacteristic
48C2×C4×C3⋊D3—21no—
49C2×C4×C3⋊D3—21no—
50C2×C4×C3⋊D3—22no—
51C2×C4×C3⋊D3—22no—
52#3757—22no—
53#3752—22no—
54#3750—22no—
55C4×C3⋊Dic3—21no—
56C4×C3⋊Dic3—21no—
57C2×C3×C3⋊C8—28no—
58C2×C3×C3⋊C8—22no—
59C2×C3×C3⋊C8—22no—
60C2×C3×C3⋊C8—22no—
61C2×C3×C3⋊C8—22no—
62C2×C3×C3⋊C8—22no—
63C2×C3×C3⋊C8D414yescomplemented
64#1869—91noSylow
65C23×C3×C4—21no—
66C23×C3×C4C2×D311yescharacteristic
67C23×C3×C4C2×D311yescharacteristic
68C22×#67—31no—
69C22×#67—31no—
70C22×#67—61no—
71C22×C4×D3—31no—
72C22×C4×D3—31no—
73C22×C4×D3—61no—
74C22×C3×C8—32no—
75C22×C3×C8—32no—
76C22×C3×C8—64no—
77C22×C3×C8—62no—
78C2×#217—31no—
79C2×#217—31no—
80C2×#217—61no—
81C4×#67—64no—
82C4×#67—64no—
83C4×#67—62no—
84C4×#67—62no—
85C4×#67—62no—
86C4×#67—62no—
87C2×(C2×D3)⋊C4—31no—
88C2×(C2×D3)⋊C4—31no—
89C2×(C2×D3)⋊C4—61no—
90C2×Dic3⋊C4—31no—
91C2×Dic3⋊C4—31no—
92C2×Dic3⋊C4—61no—
93C2×C4×Dic3—31no—
94C2×C4×Dic3—31no—
95C2×C4×Dic3—61no—
96C22×C3⋊C8—22no—
97C22×C3⋊C8—24no—
98C22×C3⋊C8C2×D312yes—
99C22×C3⋊C8C2×D312yes—
100C3×C22⋊C8—62no—
101#830—22no—
102(C2×D3)⋊C8—64no—
103(C2×D3)⋊C8—64no—
104C23×C32—22no—
105C23×C32—22no—
106C23×C32C22⋊C412yes—
107C23×C32C2×C812yes—
108C23×C32M1612yes—
109C23×C32C22×C411yescharacteristic
110C22×C3⋊D3—21no—
111C22×C3⋊D3—21no—
112C22×C3⋊D3—22no—
113C22×C3⋊D3—22no—
114C22×C3⋊D3C2×C812yescomplemented
115C2×C32×C4—22no—
116C2×C32×C4—22no—
117C2×C32×C4—24no—
118C2×C32×C4—22no—
119C2×C32×C4C22⋊C412yes—
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D412yes—
123C2×C32×C4#4112yes—
124#638—28no—
125C2×C3⋊Dic3—21no—
126C2×C3⋊Dic3—21no—
127C2×C3⋊Dic3—21no—
128C2×C3⋊Dic3—21no—
129C2×C3⋊Dic3—22no—
130C2×C3⋊Dic3—22no—
131C2×C3⋊Dic3C2×C812yescomplemented
132C4×C3⋊D3—41no—
133C4×C3⋊D3—42no—
134C4×C3⋊D3—41no—
135C3×C3⋊C8—24no—
136C3×C3⋊C8—42no—
137C23×C8—31no—
138C2×C4×D4—91no—
139C2×C22⋊C8—31no—
140C2×C22⋊C8—92no—
141#336—92no—
142C24×C3—21no—
143C24×C3C4×D311yescharacteristic
144C24×C3C4×D311yescharacteristic
145C23×D3—31no—
146C23×D3—31no—
147C23×D3—61no—
148C22×C3×C4—22no—
149C22×C3×C4—22no—
150C22×C3×C4—22no—
151C22×C3×C4—22no—
152C22×C3×C4—21no—
153C22×C3×C4—22no—
154C22×C3×C4—22no—
155C22×C3×C4—21no—
156C22×C3×C4—42no—
157C22×C3×C4—42no—
158C22×C3×C4C4×D311yescharacteristic
159C22×C3×C4C4×D311yescharacteristic
160C22×C3×C4D1212yes—
161C22×C3×C4D1212yes—
162C22×C3×C4#6712yes—
163C22×C3×C4#6712yes—
164C22×C3×C4C22×D311yescharacteristic
165C22×C3×C4C22×D311yescharacteristic
166C2×#67—34no—
167C2×#67—34no—
168C2×#67—64no—
169C2×#67—64no—
170C2×#67—64no—
171C2×#67—62no—
172C2×#67—62no—
173C2×#67—62no—
174C2×#67—62no—
175C22×Dic3—31no—
176C22×Dic3—31no—
177C22×Dic3—31no—
178C22×Dic3—31no—
179C22×Dic3—31no—
180C22×Dic3—31no—
181C22×Dic3—61no—
182C22×Dic3—61no—
183C22×Dic3—61no—
184C2×C4×D3—62no—
185C2×C4×D3—62no—
186C2×C4×D3—61no—
187C2×C4×D3—61no—
188C2×C4×D3—62no—
189C2×C4×D3—62no—
190C2×C4×D3—62no—
191C2×C4×D3—62no—
192C2×C4×D3—61no—
193C2×C4×D3—61no—
194C2×C4×D3—122no—
195C2×C4×D3—122no—
196C2×C3×C8—34no—
197C2×C3×C8—68no—
198C2×C3×C8—62no—
199C2×C3×C8—62no—
200C2×C3×C8—62no—
201C2×C3×C8—62no—
202C2×C3×C8—62no—
203#217—64no—
204#217—62no—
205#217—62no—
206(C2×D3)⋊C4—64no—
207(C2×D3)⋊C4—62no—
208(C2×D3)⋊C4—62no—
209Dic3⋊C4—64no—
210Dic3⋊C4—62no—
211Dic3⋊C4—62no—
212C4×Dic3—62no—
213C4×Dic3—62no—
214C4×Dic3—61no—
215C4×Dic3—61no—
216C4×Dic3—61no—
217C4×Dic3—61no—
218C2×C3⋊C8—28no—
219C2×C3⋊C8—22no—
220C2×C3⋊C8—22no—
221C2×C3⋊C8—22no—
222C2×C3⋊C8—22no—
223C2×C3⋊C8—22no—
224C2×C3⋊C8#6714yescomplemented
225C22×C32—22no—
226C22×C32—22no—
227C22×C32—24no—
228C22×C32—24no—
229C22×C32C22⋊C814yescomplemented
230C22×C32C2×C22⋊C411yescharacteristic
231C22×C32C4×D412yes—
232C22×C32C22×C811yescharacteristic
233C22×C32C2×M1611yescharacteristic
234C22×C32#13112yes—
235C2×C3⋊D3—22no—
236C2×C3⋊D3—24no—
237C2×C3⋊D3—41no—
238C2×C3⋊D3—41no—
239C2×C3⋊D3—42no—
240C32×C4—22no—
241C32×C4#12011yescharacteristic
242C32×C4#12112yes—
243C32×C4#12311yescharacteristic
244C3⋊Dic3—22no—
245C3⋊Dic3—41no—
246C3⋊Dic3—41no—
247C22×D4—91no—
248C23×C4—91no—
249C23×C4D3211yescharacteristic
250C22×C8—32no—
251C22×C8—32no—
252C22×C8—64no—
253C22×C8—62no—
254C4×D4—182no—
255C4×D4—182no—
256C2×C4⋊C4—91no—
257C2×C22⋊C4—91no—
258C2×C22⋊C4—91no—
259C2×C42—91no—
260C22⋊C8—62no—
261C22⋊C8—184no—
262C23×C3—22no—
263C23×C3—22no—
264C23×C3—22no—
265C23×C3—22no—
266C23×C3—22no—
267C23×C3—22no—
268C23×C3—22no—
269C23×C3—21no—
270C23×C3—42no—
271C23×C3—42no—
272C23×C3D3×C812yes—
273C23×C3D3×C812yes—
274C23×C3ΓL(1,𝔽25)12yes—
275C23×C3ΓL(1,𝔽25)12yes—
276C23×C3(C2×D3)⋊C412yes—
277C23×C3(C2×D3)⋊C412yes—
278C23×C3C2×C4×D311yescharacteristic
279C23×C3C2×C4×D311yescharacteristic
280C22×D3—32no—
281C22×D3—32no—
282C22×D3—62no—
283C22×D3—62no—
284C22×D3—62no—
285C22×D3—62no—
286C22×D3—61no—
287C22×D3—61no—
288C22×D3—62no—
289C22×D3—62no—
290C22×D3—61no—
291C22×D3—61no—
292C22×D3—62no—
293C22×D3—122no—
294C22×D3—122no—
295C2×C3×C4—22no—
296C2×C3×C4—22no—
297C2×C3×C4—22no—
298C2×C3×C4—22no—
299C2×C3×C4—22no—
300C2×C3×C4—24no—
301C2×C3×C4—24no—
302C2×C3×C4—22no—
303C2×C3×C4—22no—
304C2×C3×C4—22no—
305C2×C3×C4—21no—
306C2×C3×C4—21no—
307C2×C3×C4—22no—
308C2×C3×C4—42no—
309C2×C3×C4—42no—
310C2×C3×C4—44no—
311C2×C3×C4—42no—
312C2×C3×C4(C2×D3)⋊C412yes—
313C2×C3×C4(C2×D3)⋊C412yes—
314C2×C3×C4C2×D1211yescharacteristic
315C2×C3×C4C2×D1211yescharacteristic
316C2×C3×C4#23512yes—
317C2×C3×C4D3×D412yes—
318C2×C3×C4#23712yes—
319C2×C3×C4C2×#6711yescharacteristic
320C2×C3×C4C2×#6711yescharacteristic
321C2×C3×C4C2×#6712yes—
322#67—616no—
323#67—68no—
324#67—68no—
325C2×Dic3—32no—
326C2×Dic3—32no—
327C2×Dic3—62no—
328C2×Dic3—62no—
329C2×Dic3—62no—
330C2×Dic3—61no—
331C2×Dic3—61no—
332C2×Dic3—61no—
333C2×Dic3—61no—
334C2×Dic3—62no—
335C2×Dic3—62no—
336C2×Dic3—62no—
337C2×Dic3—62no—
338C2×Dic3—62no—
339C2×Dic3—61no—
340C2×Dic3—61no—
341C2×Dic3—61no—
342C2×Dic3—61no—
343C2×Dic3—62no—
344C2×Dic3—122no—
345C2×Dic3—122no—
346C4×D3—122no—
347C4×D3—122no—
348C4×D3—124no—
349C4×D3—121no—
350C4×D3—121no—
351C4×D3—121no—
352C4×D3—122no—
353C4×D3—122no—
354C4×D3—121no—
355C3×C8—64no—
356C3×C8—122no—
357C3⋊C8—24no—
358C3⋊C8—42no—
359C2×C32—24no—
360C2×C32#38611yescharacteristic
361C2×C32C2×C22⋊C811yescharacteristic
362C2×C32#40811yescharacteristic
363C2×C32C8×D412yes—
364C2×C32#43512yes—
365C3⋊D3—42no—
366C24—91no—
367C24#62411yescharacteristic
368C2×D4—94no—
369C2×D4—182no—
370C2×D4—182no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—91no—
374C22×C4—91no—
375C22×C4—91no—
376C22×C4—182no—
377C22×C4—181no—
378C22×C4—181no—
379C22×C4—182no—
380C22×C4#62411yescharacteristic
381C22×C4#62612yes—
382C22×C4#62612yes—
383C22×C4C2×D3211yescharacteristic
384C2×C8—34no—
385C2×C8—68no—
386C2×C8—62no—
387C2×C8—62no—
388C2×C8—62no—
389C2×C8—62no—
390C2×C8—62no—
391C4⋊C4—182no—
392C22⋊C4—182no—
393C22⋊C4—182no—
394C42—181no—
395C42—181no—
396C22×C3—22no—
397C22×C3—22no—
398C22×C3—22no—
399C22×C3—24no—
400C22×C3—24no—
401C22×C3—24no—
402C22×C3—22no—
403C22×C3—24no—
404C22×C3—24no—
405C22×C3—21no—
406C22×C3—22no—
407C22×C3—21no—
408C22×C3—22no—
409C22×C3—21no—
410C22×C3—42no—
411C22×C3—42no—
412C22×C3—44no—
413C22×C3—44no—
414C22×C3(C2×D3)⋊C814yescomplemented
415C22×C3(C2×D3)⋊C814yescomplemented
416C22×C3#67⋊C412yes—
417C22×C3C2×D3×C811yescharacteristic
418C22×C3C2×D3×C811yescharacteristic
419C22×C3C2×ΓL(1,𝔽25)11yescharacteristic
420C22×C3C2×ΓL(1,𝔽25)11yescharacteristic
421C22×C3#90112yes—
422C22×C3#90712yes—
423C22×C3C2×(C2×D3)⋊C411yescharacteristic
424C22×C3C2×(C2×D3)⋊C411yescharacteristic
425C22×C3C4×#6712yes—
426C2×D3—64no—
427C2×D3—64no—
428C2×D3—62no—
429C2×D3—62no—
430C2×D3—64no—
431C2×D3—124no—
432C2×D3—122no—
433C2×D3—122no—
434C2×D3—124no—
435C2×D3—121no—
436C2×D3—121no—
437C2×D3—121no—
438C2×D3—122no—
439C2×D3—121no—
440C2×D3—122no—
441C3×C4—22no—
442C3×C4—22no—
443C3×C4—21no—
444C3×C4—21no—
445C3×C4—22no—
446C3×C4—42no—
447C3×C4#88211yescharacteristic
448C3×C4#88611yescharacteristic
449C3×C4#92911yescharacteristic
450C3×C4#93012yes—
451C3×C4#93912yes—
452C3×C4#95311yescharacteristic
453Dic3—64no—
454Dic3—62no—
455Dic3—62no—
456Dic3—122no—
457Dic3—122no—
458Dic3—121no—
459Dic3—121no—
460Dic3—121no—
461Dic3—121no—
462C32#186911yescharacteristic, complemented, Sylow
463C23—22no—
464C23—22no—
465C23—92no—
466C23—182no—
467C23—181no—
468C23—182no—
469C23—181no—
470C23#371012yes—
471C23#371212yes—
472C23#372212yes—
473C23C2×#62411yescharacteristic
474D4—188no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—24no—
479C2×C4—92no—
480C2×C4—181no—
481C2×C4—181no—
482C2×C4—182no—
483C2×C4—182no—
484C2×C4—181no—
485C2×C4—181no—
486C2×C4—361no—
487C2×C4—361no—
488C2×C4—362no—
489C2×C4#372212yes—
490C2×C4#380412yes—
491C2×C4C2×#62611yescharacteristic
492C2×C4C2×#62611yescharacteristic
493C2×C4D3×#6712yes—
494C8—64no—
495C8—122no—
496C2×C3—24no—
497C2×C3—24no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—22no—
501C2×C3—22no—
502C2×C3—21no—
503C2×C3—44no—
504C2×C3#67⋊C812yes—
505C2×C3#473012yes—
506C2×C3#495811yescharacteristic
507C2×C3C2×(C2×D3)⋊C811yescharacteristic
508C2×C3C2×(C2×D3)⋊C811yescharacteristic
509C2×C3C8×#6712yes—
510C2×C3#511011yescharacteristic
511C2×C3#511112yes—
512C2×C3#512911yescharacteristic
513C2×C3#521311yescharacteristic
514D3—124no—
515D3—122no—
516D3—122no—
517C22—22no—
518C22—24no—
519C22—24no—
520C22—22no—
521C22—182no—
522C22—184no—
523C22—361no—
524C22—362no—
525C22—361no—
526C22#6355714yescomplemented
527C22C2×#371011yescharacteristic
528C22#6381712yes—
529C22C2×#371211yescharacteristic
530C22#6395212yes—
531C22C2×#372211yescharacteristic
532C4—22no—
533C4—182no—
534C4—361no—
535C4—361no—
536C4#6396611yescharacteristic
537C4#6397711yescharacteristic
538C4#6397812yes—
539C3—21no—
540C3#6995211yescharacteristic, complemented
541C3#7197511yescharacteristic, complemented
542C2—24no—
543C2—362no—
544C2C2×#6355711yescharacteristic
545C2#1059107311yescharacteristic
546C2#1059114812yes—
547C2#1059115712yes—
548C2#1059171111yescharacteristic
subgroupG/H
center, FrattiniC22×C4C2×D32
commutatorC22×C32C22×C8
FittingC23×C32×C4C22
socleC23×C32C22×C4
prime radicalC22×#638C4
cosocleC22×C32×C4C23
hypercenterC23×C4D32
hypocenterC32#1869
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C23×C3×C3⋊C8C2semidirect
3. C2×C3×#830C2semidirect
4. C2×#63557C2semidirect
5. #10589156C2semidirect
27. C23×C3⋊C8D3semidirect
29. C2×#830D3semidirect
44. C2×#638C8semidirect
63. C2×C3×C3⋊C8D4semidirect
114. C22×C3⋊D3C2×C8semidirect
131. C2×C3⋊Dic3C2×C8semidirect
224. C2×C3⋊C8#67semidirect
229. C22×C32C22⋊C8semidirect
414. C22×C3(C2×D3)⋊C8semidirect
415. C22×C3(C2×D3)⋊C8semidirect
462. C32#1869semidirect
526. C22#63557semidirect
540. C3#69952semidirect
541. C3#71975semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6382
C23×C3×C3⋊C82
C2×C3×#8302
C2×#635572
#105891562
#719753
#699523