Finite Group Databasebeta

← #11805031

Subgroups — #11805031

Order 1152.

1679 conjugacy classes of subgroups.

The subgroup lattice has 999 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×C22⋊C4C211yesmaximal, characteristic
2C2×D3×#217C211yesmaximal, characteristic
3C2×#63841C211yesmaximal, characteristic, complemented
4#10592650C211yesmaximal, characteristic, complemented
5C3×#4951C211yesmaximal, characteristic, complemented
6#10591706C211yesmaximal, characteristic
7#10591702C211yesmaximal, characteristic, complemented
8#10591701C211yesmaximal, characteristic, complemented
9#10591379C211yesmaximal, characteristic, complemented
10#10591377C211yesmaximal, characteristic, complemented
11#10591368C211yesmaximal, characteristic, complemented
12Dic3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
13#10591295C211yesmaximal, characteristic, complemented
14#10591294C211yesmaximal, characteristic, complemented
15C4×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
16#82097—31nomaximal
17#75833—31nomaximal
18C24×C3×D3C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×D3×Dic3C2211yescharacteristic
22C22×D3×Dic3C2211yescharacteristic
23C2×C32×C22⋊C4C2211yescharacteristic
24C2×#3757C2211yescharacteristic
25C2×#3757C2211yescharacteristic
26C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
27C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
28C2×C3×#217C2211yescharacteristic
29C2×C3×#217C2211yescharacteristic
30C2×C3×#217C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
34C2×C3×C4×Dic3C2211yescharacteristic, complemented
35C3×D3×C22⋊C4C418yescomplemented
36D3×#217—24no—
37C2×Dic3⋊Dic3C2211yescharacteristic, complemented
38C2×Dic3⋊Dic3C2211yescharacteristic, complemented
39C2×(C2×D3)⋊Dic3C2211yescharacteristic
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×Dic32C2211yescharacteristic, complemented
46C2×Dic32C2211yescharacteristic, complemented
47#63841—24no—
48#63658C2211yescharacteristic, complemented
49#63658C2211yescharacteristic, complemented
50C3×C3⋊#95C2211yescharacteristic, complemented
51C3×C3⋊#95C2211yescharacteristic, complemented
52#63579C2211yescharacteristic, complemented
53#63579C2211yescharacteristic, complemented
54#63579C2211yescharacteristic, complemented
55#63579C2211yescharacteristic, complemented
56C22×C3×C22⋊C4—31no—
57C22×#217—31no—
58C2×#926—31no—
59C2×#892—31no—
60C2×D3×C22⋊C4—31no—
61C2×D3×C22⋊C4D311yescharacteristic
62C3×#388—31no—
63#5247—31no—
64#5212—31no—
65#5211—31no—
66C4×#217—31no—
67#4989—31no—
68#4955—31no—
69#4951—31no—
70#4951—31no—
71#4951—31no—
72#4951—31no—
73#4951—61no—
74#4951D311yescharacteristic, complemented
75#4950—31no—
76#4950—31no—
77#4945—31no—
78#4944—31no—
79Dic3×C22⋊C4—31no—
80Dic3×C22⋊C4—31no—
81C4×(C2×D3)⋊C4—31no—
82C4×(C2×D3)⋊C4—31no—
83#4668—31no—
84#4667—31no—
85#4666—31no—
86#4664—31no—
87C24×C32C2311yescharacteristic
88C23×C3×D3—22no—
89C23×C3×D3—22no—
90C23×C3×D3—22no—
91C23×C3×D3—22no—
92C23×C3×D3—41no—
93C23×C3×D3—41no—
94C23×C3×D3C2×C414yes—
95C23×C3×D3C2311yescharacteristic
96C23×C3×D3C2311yescharacteristic
97C22×C32×C4C2311yescharacteristic
98C22×C32×C4C2311yescharacteristic
99C22×C3⋊Dic3C2311yescharacteristic
100C22×C3⋊Dic3C2311yescharacteristic
101C22×C3⋊Dic3C2311yescharacteristic
102C22×C3⋊Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C2×C3×C4×D3—22no—
110C2×C3×C4×D3—22no—
111C2×C3×C4×D3—41no—
112C2×C3×C4×D3—41no—
113C2×C3×C4×D3C2×C414yescomplemented
114C2×C3×C4×D3C2×C414yescomplemented
115C2×D3×Dic3—22no—
116C2×D3×Dic3—22no—
117C2×D3×Dic3—22no—
118C2×D3×Dic3—22no—
119C2×D3×Dic3—41no—
120C2×D3×Dic3—41no—
121C32×C22⋊C4C2×C414yescomplemented
122#3757—22no—
123#3757—41no—
124C4⋊(C3⋊Dic3)—22no—
125C4×C3⋊Dic3—41no—
126C3×#217—22no—
127C3×#217—41no—
128C3×#217C2×C414yescomplemented
129C3×(C2×D3)⋊C4C2×C414yes—
130C3×(C2×D3)⋊C4C2×C414yes—
131C3×C4⋊Dic3—22no—
132C3×C4×Dic3—41no—
133Dic3⋊Dic3—41no—
134Dic3⋊Dic3—41no—
135(C2×D3)⋊Dic3—22no—
136(C2×D3)⋊Dic3—22no—
137(C2×D3)⋊Dic3—22no—
138(C2×D3)⋊Dic3—22no—
139(C2×D3)⋊Dic3—22no—
140(C2×D3)⋊Dic3D414yes—
141Dic32—22no—
142Dic32—22no—
143#2342—91noSylow
144C25×C3—31no—
145C24×D3C2×D311yescharacteristic
146C23×C3×C4—31no—
147C23×C3×C4—31no—
148C23×Dic3—31no—
149C23×Dic3—31no—
150C22×C4×D3—31no—
151C22×C4×D3—31no—
152C22×C4×D3C2×D311yescharacteristic
153C22×C4×D3C2×D311yescharacteristic
154C2×C3×C4⋊C4—31no—
155C2×C3×C22⋊C4—21no—
156C2×C3×C22⋊C4—31no—
157C2×C3×C22⋊C4—31no—
158C2×C3×C22⋊C4—31no—
159C2×C3×C22⋊C4—38no—
160C2×C3×C22⋊C4—31no—
161C2×C3×C22⋊C4—31no—
162C2×C3×C22⋊C4C2×D311yescharacteristic
163C2×C3×C22⋊C4C2×D311yescharacteristic
164C2×C3×C42—31no—
165C2×#217—31no—
166C2×#217—31no—
167C2×#217—31no—
168C2×#217—31no—
169C2×#217—31no—
170C2×#217—31no—
171C2×#217—31no—
172C2×#217—31no—
173C2×#217—31no—
174C2×#217—31no—
175C2×#217—61no—
176C2×#217—61no—
177C2×#217—64no—
178C2×#217C2×D311yescharacteristic
179C2×#217C2×D311yescharacteristic
180C2×#217C2×D311yescharacteristic
181C2×(C2×D3)⋊C4—31no—
182C2×(C2×D3)⋊C4—31no—
183C2×(C2×D3)⋊C4—31no—
184C2×(C2×D3)⋊C4—31no—
185C2×(C2×D3)⋊C4—31no—
186C2×(C2×D3)⋊C4—31no—
187C2×(C2×D3)⋊C4C2×D311yescharacteristic
188C2×(C2×D3)⋊C4C2×D311yescharacteristic
189#926—64no—
190C2×C4⋊Dic3—31no—
191C2×C4⋊Dic3—31no—
192C2×C4⋊Dic3—31no—
193C2×C4⋊Dic3—31no—
194C2×C4⋊Dic3—61no—
195C2×C4⋊Dic3C2×D311yescharacteristic, complemented
196C2×Dic3⋊C4—31no—
197C2×Dic3⋊C4—31no—
198C2×C4×Dic3—31no—
199C2×C4×Dic3—31no—
200C2×C4×Dic3—31no—
201C2×C4×Dic3—31no—
202C2×C4×Dic3—31no—
203C2×C4×Dic3—31no—
204C2×C4×Dic3—61no—
205C2×C4×Dic3C2×D311yescharacteristic, complemented
206#892—64no—
207D3×C22⋊C4—64no—
208D3×C22⋊C4Dic318yescomplemented
209C3×#95—31no—
210C3×#95—31no—
211C3⋊#95—31no—
212C3⋊#95—31no—
213C3⋊#95—31no—
214C3⋊#95—31no—
215C3⋊#95—31no—
216C3⋊#95—31no—
217C3⋊#95—31no—
218C3⋊#95—31no—
219C3⋊#95—31no—
220C3⋊#95—31no—
221C3⋊#95—31no—
222C3⋊#95—31no—
223C3⋊#95—61no—
224C3⋊#95—61no—
225C3⋊#95C2×D311yescharacteristic, complemented
226C3⋊#95C2×D311yescharacteristic, complemented
227C23×C32—21no—
228C23×C32—21no—
229C23×C32—21no—
230C23×C32—21no—
231C23×C32—21no—
232C23×C32—21no—
233C23×C32C22×C412yes—
234C23×C32C2411yescharacteristic
235C22×C3×D3—21no—
236C22×C3×D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3—21no—
239C22×C3×D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3—21no—
243C22×C3×D3—28no—
244C22×C3×D3—28no—
245C22×C3×D3—44no—
246C22×C3×D3—44no—
247C22×C3×D3—44no—
248C22×C3×D3—44no—
249C22×C3×D3—44no—
250C22×C3×D3C22×C412yes—
251C22×C3×D3C22×C412yes—
252C22×C3×D3C2×D412yes—
253C22×C3×D3#4112yes—
254C22×C3×D3#4112yes—
255C22×C3×D3#4112yes—
256C2×C32×C4—21no—
257C2×C32×C4—21no—
258C2×C32×C4—21no—
259C2×C32×C4—21no—
260C2×C32×C4C22×C412yes—
261C2×C32×C4C22×C412yes—
262C2×C3⋊Dic3—21no—
263C2×C3⋊Dic3—21no—
264C2×C3⋊Dic3—21no—
265C2×C3⋊Dic3—21no—
266C2×C3⋊Dic3—21no—
267C2×C3⋊Dic3—21no—
268C2×C3⋊Dic3—21no—
269C2×C3⋊Dic3—21no—
270C2×C3⋊Dic3—21no—
271C2×C3⋊Dic3—21no—
272C2×C3⋊Dic3—21no—
273C2×C3⋊Dic3C2×D412yes—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3—21no—
287C2×C3×Dic3—21no—
288C2×C3×Dic3—21no—
289C2×C3×Dic3C22×C412yes—
290C2×C3×Dic3C22×C412yes—
291C2×C3×Dic3C2×D412yes—
292C3×C4×D3—28no—
293C3×C4×D3—44no—
294D3×Dic3—44no—
295D3×Dic3—44no—
296C2×#117—91no—
297C22×C22⋊C4—31no—
298C22×C22⋊C4—91no—
299#388—31no—
300#388—91no—
301#388—91no—
302#388—91no—
303#385—91no—
304#385—91no—
305#381—91no—
306#380—91no—
307#379—91no—
308C4×C22⋊C4—91no—
309C4×C22⋊C4—91no—
310C4×C22⋊C4—91no—
311C24×C3—21no—
312C24×C3—31no—
313C24×C3—31no—
314C24×C3—34no—
315C24×C3—62no—
316C24×C3—62no—
317C24×C3—62no—
318C24×C3—62no—
319C24×C3—121no—
320C24×C3—121no—
321C24×C3C22×D311yescharacteristic
322C24×C3C22×D311yescharacteristic
323C23×D3—22no—
324C23×D3—22no—
325C23×D3—22no—
326C23×D3—22no—
327C23×D3—41no—
328C23×D3—41no—
329C23×D3C2×Dic314yes—
330C23×D3C22×D311yescharacteristic
331C23×D3C22×D311yescharacteristic
332C22×C3×C4—21no—
333C22×C3×C4—21no—
334C22×C3×C4—31no—
335C22×C3×C4—31no—
336C22×C3×C4—31no—
337C22×C3×C4—34no—
338C22×C3×C4—34no—
339C22×C3×C4—31no—
340C22×C3×C4—31no—
341C22×C3×C4—31no—
342C22×C3×C4—62no—
343C22×C3×C4—62no—
344C22×C3×C4—121no—
345C22×C3×C4—121no—
346C22×C3×C4C22×D311yescharacteristic
347C22×C3×C4C22×D311yescharacteristic
348C22×C3×C4C22×D311yescharacteristic
349C22×C3×C4C22×D311yescharacteristic
350C22×Dic3—31no—
351C22×Dic3—31no—
352C22×Dic3—31no—
353C22×Dic3—31no—
354C22×Dic3—31no—
355C22×Dic3—31no—
356C22×Dic3—31no—
357C22×Dic3—31no—
358C22×Dic3—61no—
359C22×Dic3—61no—
360C22×Dic3—61no—
361C22×Dic3—61no—
362C22×Dic3—62no—
363C22×Dic3—62no—
364C22×Dic3—62no—
365C22×Dic3—62no—
366C22×Dic3—121no—
367C22×Dic3—121no—
368C22×Dic3C22×D311yescharacteristic
369C22×Dic3C22×D311yescharacteristic
370C22×Dic3C22×D311yescharacteristic
371C22×Dic3C22×D311yescharacteristic
372C22×Dic3C22×D311yescharacteristic
373C22×Dic3C22×D311yescharacteristic
374C2×C4×D3—22no—
375C2×C4×D3—22no—
376C2×C4×D3—41no—
377C2×C4×D3—41no—
378C2×C4×D3—62no—
379C2×C4×D3—62no—
380C2×C4×D3—62no—
381C2×C4×D3—62no—
382C2×C4×D3—121no—
383C2×C4×D3—121no—
384C2×C4×D3C2×Dic314yescomplemented
385C2×C4×D3C2×Dic314yescomplemented
386C3×C4⋊C4—62no—
387C3×C22⋊C4—24no—
388C3×C22⋊C4—34no—
389C3×C22⋊C4—34no—
390C3×C22⋊C4—34no—
391C3×C22⋊C4—62no—
392C3×C22⋊C4—121no—
393C3×C22⋊C4C4×D314yescomplemented
394C3×C22⋊C4C2×Dic314yescomplemented
395C3×C42—121no—
396#217—22no—
397#217—34no—
398#217—41no—
399#217—62no—
400#217—62no—
401#217—62no—
402#217—62no—
403#217—62no—
404#217—62no—
405#217—62no—
406#217—122no—
407#217—121no—
408#217—121no—
409#217—122no—
410#217C2×Dic314yescomplemented
411(C2×D3)⋊C4—34no—
412(C2×D3)⋊C4—62no—
413(C2×D3)⋊C4—62no—
414(C2×D3)⋊C4—62no—
415(C2×D3)⋊C4—62no—
416(C2×D3)⋊C4—62no—
417(C2×D3)⋊C4C2×Dic314yes—
418(C2×D3)⋊C4C2×Dic314yes—
419C4⋊Dic3—22no—
420C4⋊Dic3—62no—
421C4⋊Dic3—62no—
422C4⋊Dic3—122no—
423C4⋊Dic3—121no—
424C4⋊Dic3—121no—
425Dic3⋊C4—121no—
426Dic3⋊C4—121no—
427C4×Dic3—41no—
428C4×Dic3—62no—
429C4×Dic3—62no—
430C4×Dic3—62no—
431C4×Dic3—62no—
432C4×Dic3—121no—
433C4×Dic3—121no—
434C4×Dic3—122no—
435C22×C32—22no—
436C22×C32—22no—
437C22×C32—22no—
438C22×C32—41no—
439C22×C32—41no—
440C22×C32—41no—
441C22×C32—41no—
442C22×C32C23×C411yescharacteristic
443C22×C32C22×D411yescharacteristic
444C22×C32C2×#4111yescharacteristic
445C22×C32C2×#4111yescharacteristic
446C22×C32C2×#4111yescharacteristic
447C22×C32H(5,𝔽2)11yescharacteristic
448C22×C32H(5,𝔽2)11yescharacteristic
449C2×C3×D3—22no—
450C2×C3×D3—22no—
451C2×C3×D3—22no—
452C2×C3×D3—22no—
453C2×C3×D3—22no—
454C2×C3×D3—22no—
455C2×C3×D3—22no—
456C2×C3×D3—22no—
457C2×C3×D3—22no—
458C2×C3×D3—22no—
459C2×C3×D3—22no—
460C2×C3×D3—22no—
461C2×C3×D3—416no—
462C2×C3×D3#11714yescomplemented
463C2×C3×D3C4×D414yes—
464C32×C4—22no—
465C32×C4—22no—
466C3⋊Dic3—22no—
467C3⋊Dic3—41no—
468C3⋊Dic3—41no—
469C3⋊Dic3—41no—
470C3×Dic3—22no—
471C3×Dic3—22no—
472C3×Dic3—22no—
473C3×Dic3—41no—
474C3×Dic3—41no—
475C3×Dic3—41no—
476C25—31no—
477C23×C4—31no—
478C23×C4—31no—
479C23×C4—91no—
480C23×C4—91no—
481#117—184no—
482C2×C4⋊C4—31no—
483C2×C4⋊C4—91no—
484C2×C4⋊C4—91no—
485C2×C4⋊C4—91no—
486C2×C22⋊C4—31no—
487C2×C22⋊C4—31no—
488C2×C22⋊C4—31no—
489C2×C22⋊C4—38no—
490C2×C22⋊C4—31no—
491C2×C22⋊C4—31no—
492C2×C22⋊C4—91no—
493C2×C22⋊C4—91no—
494C2×C22⋊C4—91no—
495C2×C22⋊C4—91no—
496C2×C22⋊C4—91no—
497C2×C22⋊C4—91no—
498C2×C22⋊C4—91no—
499C2×C22⋊C4—91no—
500C2×C22⋊C4—184no—
501C2×C22⋊C4D3211yescharacteristic
502C2×C42—31no—
503C2×C42—91no—
504C2×C42—91no—
505C2×C42—91no—
506#95—31no—
507#95—31no—
508#95—91no—
509#95—91no—
510#95—91no—
511#95—91no—
512#95—91no—
513#95—91no—
514C23×C3—21no—
515C23×C3—21no—
516C23×C3—21no—
517C23×C3—21no—
518C23×C3—21no—
519C23×C3—21no—
520C23×C3—21no—
521C23×C3—21no—
522C23×C3—21no—
523C23×C3—21no—
524C23×C3—21no—
525C23×C3—21no—
526C23×C3—21no—
527C23×C3—22no—
528C23×C3—32no—
529C23×C3—32no—
530C23×C3—32no—
531C23×C3—32no—
532C23×C3—32no—
533C23×C3—32no—
534C23×C3—41no—
535C23×C3—41no—
536C23×C3—41no—
537C23×C3—41no—
538C23×C3—41no—
539C23×C3—41no—
540C23×C3—68no—
541C23×C3—68no—
542C23×C3—61no—
543C23×C3—61no—
544C23×C3—61no—
545C23×C3—61no—
546C23×C3—61no—
547C23×C3—61no—
548C23×C3—61no—
549C23×C3—61no—
550C23×C3—124no—
551C23×C3—124no—
552C23×C3—124no—
553C23×C3—124no—
554C23×C3—124no—
555C23×C3C2×C4×D312yes—
556C23×C3C22×Dic312yes—
557C23×C3C23×D311yescharacteristic
558C23×C3C23×D311yescharacteristic
559C22×D3—21no—
560C22×D3—21no—
561C22×D3—21no—
562C22×D3—21no—
563C22×D3—21no—
564C22×D3—21no—
565C22×D3—21no—
566C22×D3—21no—
567C22×D3—28no—
568C22×D3—28no—
569C22×D3—44no—
570C22×D3—44no—
571C22×D3—44no—
572C22×D3—44no—
573C22×D3—44no—
574C22×D3#23512yes—
575C22×D3#23512yes—
576C22×D3D3×D412yes—
577C22×D3#23712yes—
578C22×D3C22×Dic312yes—
579C22×D3C22×Dic312yes—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—22no—
589C2×C3×C4—22no—
590C2×C3×C4—32no—
591C2×C3×C4—32no—
592C2×C3×C4—32no—
593C2×C3×C4—41no—
594C2×C3×C4—41no—
595C2×C3×C4—41no—
596C2×C3×C4—41no—
597C2×C3×C4—68no—
598C2×C3×C4—61no—
599C2×C3×C4—61no—
600C2×C3×C4—61no—
601C2×C3×C4—61no—
602C2×C3×C4—61no—
603C2×C3×C4—61no—
604C2×C3×C4—61no—
605C2×C3×C4—61no—
606C2×C3×C4—61no—
607C2×C3×C4—61no—
608C2×C3×C4—61no—
609C2×C3×C4—61no—
610C2×C3×C4—61no—
611C2×C3×C4—61no—
612C2×C3×C4—61no—
613C2×C3×C4—124no—
614C2×C3×C4C2×C4×D312yes—
615C2×C3×C4C2×C4×D312yes—
616C2×C3×C4C22×Dic312yes—
617C2×C3×C4C22×Dic312yes—
618C2×Dic3—21no—
619C2×Dic3—21no—
620C2×Dic3—21no—
621C2×Dic3—21no—
622C2×Dic3—21no—
623C2×Dic3—21no—
624C2×Dic3—21no—
625C2×Dic3—21no—
626C2×Dic3—21no—
627C2×Dic3—21no—
628C2×Dic3—21no—
629C2×Dic3—21no—
630C2×Dic3—21no—
631C2×Dic3—21no—
632C2×Dic3—21no—
633C2×Dic3—32no—
634C2×Dic3—32no—
635C2×Dic3—62no—
636C2×Dic3—61no—
637C2×Dic3—61no—
638C2×Dic3—61no—
639C2×Dic3—61no—
640C2×Dic3—62no—
641C2×Dic3—61no—
642C2×Dic3—61no—
643C2×Dic3—61no—
644C2×Dic3—61no—
645C2×Dic3—61no—
646C2×Dic3—61no—
647C2×Dic3—61no—
648C2×Dic3—61no—
649C2×Dic3—61no—
650C2×Dic3—61no—
651C2×Dic3—61no—
652C2×Dic3—61no—
653C2×Dic3—61no—
654C2×Dic3—61no—
655C2×Dic3—61no—
656C2×Dic3—61no—
657C2×Dic3—61no—
658C2×Dic3—61no—
659C2×Dic3—121no—
660C2×Dic3—121no—
661C2×Dic3—121no—
662C2×Dic3—121no—
663C2×Dic3—121no—
664C2×Dic3—121no—
665C2×Dic3—121no—
666C2×Dic3—121no—
667C2×Dic3—121no—
668C2×Dic3—121no—
669C2×Dic3—124no—
670C2×Dic3—124no—
671C2×Dic3D3×D412yes—
672C2×Dic3C22×Dic312yes—
673C2×Dic3C22×Dic312yes—
674C4×D3—28no—
675C4×D3—44no—
676C4×D3—124no—
677C4×D3—124no—
678C2×C32—42no—
679C2×C32C2×#11711yescharacteristic
680C2×C32C2×C4×D411yescharacteristic
681C2×C32#51811yescharacteristic
682C2×C32#54611yescharacteristic
683C2×C32#54611yescharacteristic
684C2×C32#55111yescharacteristic
685C2×C32#55111yescharacteristic
686C3×D3—24no—
687C3×D3—24no—
688C24—31no—
689C24—31no—
690C24—34no—
691C24—62no—
692C24—62no—
693C24—62no—
694C24—62no—
695C24—121no—
696C24—121no—
697C24C2×D3211yescharacteristic
698C22×C4—31no—
699C22×C4—31no—
700C22×C4—31no—
701C22×C4—34no—
702C22×C4—34no—
703C22×C4—31no—
704C22×C4—31no—
705C22×C4—31no—
706C22×C4—62no—
707C22×C4—62no—
708C22×C4—91no—
709C22×C4—91no—
710C22×C4—91no—
711C22×C4—91no—
712C22×C4—121no—
713C22×C4—121no—
714C22×C4—182no—
715C22×C4—182no—
716C22×C4—182no—
717C22×C4—182no—
718C22×C4—361no—
719C22×C4—361no—
720C22×C4C2×D3211yescharacteristic
721C22×C4C2×D3211yescharacteristic
722C4⋊C4—62no—
723C4⋊C4—182no—
724C4⋊C4—361no—
725C4⋊C4—361no—
726C22⋊C4—34no—
727C22⋊C4—34no—
728C22⋊C4—34no—
729C22⋊C4—62no—
730C22⋊C4—94no—
731C22⋊C4—121no—
732C22⋊C4—182no—
733C22⋊C4—182no—
734C22⋊C4—182no—
735C22⋊C4—182no—
736C22⋊C4—182no—
737C22⋊C4—182no—
738C22⋊C4—361no—
739C22⋊C4D3×Dic314yescomplemented
740C42—121no—
741C42—182no—
742C42—182no—
743C42—361no—
744C22×C3—22no—
745C22×C3—22no—
746C22×C3—22no—
747C22×C3—22no—
748C22×C3—22no—
749C22×C3—22no—
750C22×C3—21no—
751C22×C3—21no—
752C22×C3—21no—
753C22×C3—21no—
754C22×C3—21no—
755C22×C3—21no—
756C22×C3—21no—
757C22×C3—34no—
758C22×C3—34no—
759C22×C3—42no—
760C22×C3—42no—
761C22×C3—42no—
762C22×C3—41no—
763C22×C3—41no—
764C22×C3—41no—
765C22×C3—41no—
766C22×C3—41no—
767C22×C3—41no—
768C22×C3—41no—
769C22×C3—41no—
770C22×C3—62no—
771C22×C3—62no—
772C22×C3—62no—
773C22×C3—62no—
774C22×C3—62no—
775C22×C3—62no—
776C22×C3—62no—
777C22×C3—62no—
778C22×C3—62no—
779C22×C3—62no—
780C22×C3—62no—
781C22×C3—62no—
782C22×C3—81no—
783C22×C3—81no—
784C22×C3—81no—
785C22×C3—81no—
786C22×C3—1216no—
787C22×C3C22×C4×D311yescharacteristic
788C22×C3C2×#23511yescharacteristic
789C22×C3C2×#23511yescharacteristic
790C22×C3C2×D3×D411yescharacteristic
791C22×C3C2×D3×D411yescharacteristic
792C22×C3C2×#23711yescharacteristic
793C22×C3#100411yescharacteristic
794C22×C3#100411yescharacteristic
795C22×C3#100411yescharacteristic
796C22×C3D3×#4111yescharacteristic
797C22×C3D3×#4111yescharacteristic
798C22×C3D3×#4111yescharacteristic
799C22×C3#100911yescharacteristic
800C22×C3C23×Dic311yescharacteristic
801C2×D3—22no—
802C2×D3—22no—
803C2×D3—22no—
804C2×D3—22no—
805C2×D3—22no—
806C2×D3—22no—
807C2×D3—22no—
808C2×D3—22no—
809C2×D3—22no—
810C2×D3—22no—
811C2×D3—22no—
812C2×D3—22no—
813C2×D3—416no—
814C2×D3#92614yescomplemented
815C2×D3D4×Dic314yes—
816C3×C4—22no—
817C3×C4—22no—
818C3×C4—22no—
819C3×C4—22no—
820C3×C4—42no—
821C3×C4—42no—
822C3×C4—62no—
823C3×C4—62no—
824C3×C4—62no—
825C3×C4—121no—
826C3×C4—121no—
827C3×C4—121no—
828Dic3—22no—
829Dic3—22no—
830Dic3—22no—
831Dic3—41no—
832Dic3—41no—
833Dic3—41no—
834Dic3—62no—
835Dic3—62no—
836Dic3—122no—
837Dic3—122no—
838Dic3—121no—
839Dic3—121no—
840Dic3—121no—
841Dic3—121no—
842Dic3—121no—
843Dic3—121no—
844Dic3—241no—
845Dic3—241no—
846C32#234211yescharacteristic, complemented, Sylow
847C23—21no—
848C23—21no—
849C23—21no—
850C23—21no—
851C23—21no—
852C23—21no—
853C23—32no—
854C23—32no—
855C23—32no—
856C23—32no—
857C23—32no—
858C23—32no—
859C23—68no—
860C23—68no—
861C23—61no—
862C23—61no—
863C23—61no—
864C23—61no—
865C23—61no—
866C23—61no—
867C23—61no—
868C23—61no—
869C23—124no—
870C23—124no—
871C23—124no—
872C23—124no—
873C23—124no—
874C23C2×D3×Dic312yes—
875C23C22×D3211yescharacteristic
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—21no—
880C2×C4—32no—
881C2×C4—32no—
882C2×C4—32no—
883C2×C4—68no—
884C2×C4—61no—
885C2×C4—61no—
886C2×C4—61no—
887C2×C4—61no—
888C2×C4—61no—
889C2×C4—61no—
890C2×C4—61no—
891C2×C4—61no—
892C2×C4—61no—
893C2×C4—61no—
894C2×C4—61no—
895C2×C4—61no—
896C2×C4—61no—
897C2×C4—61no—
898C2×C4—61no—
899C2×C4—92no—
900C2×C4—124no—
901C2×C4—181no—
902C2×C4—181no—
903C2×C4—181no—
904C2×C4—181no—
905C2×C4—181no—
906C2×C4—181no—
907C2×C4—181no—
908C2×C4—181no—
909C2×C4—181no—
910C2×C4—181no—
911C2×C4—181no—
912C2×C4—364no—
913C2×C4—364no—
914C2×C4C2×D3×Dic312yes—
915C2×C4C2×D3×Dic312yes—
916C2×C3—21no—
917C2×C3—21no—
918C2×C3—21no—
919C2×C3—21no—
920C2×C3—21no—
921C2×C3—21no—
922C2×C3—21no—
923C2×C3—42no—
924C2×C3—42no—
925C2×C3—64no—
926C2×C3—64no—
927C2×C3—82no—
928C2×C3#549011yescharacteristic
929C2×C3#549011yescharacteristic
930C2×C3#549511yescharacteristic
931C2×C3#549511yescharacteristic
932C2×C3D3×#11711yescharacteristic
933C2×C3C4×D3×D411yescharacteristic
934C2×C3#554511yescharacteristic
935C2×C3#561011yescharacteristic
936C2×C3#565911yescharacteristic
937C2×C3#567611yescharacteristic
938C2×C3#570511yescharacteristic
939C2×C3C2×#92611yescharacteristic
940C2×C3C2×D4×Dic311yescharacteristic
941C2×C3#579811yescharacteristic
942D3—24no—
943D3—24no—
944C22—22no—
945C22—22no—
946C22—22no—
947C22—34no—
948C22—34no—
949C22—41no—
950C22—41no—
951C22—41no—
952C22—41no—
953C22—62no—
954C22—62no—
955C22—62no—
956C22—62no—
957C22—62no—
958C22—62no—
959C22—62no—
960C22—62no—
961C22—62no—
962C22—62no—
963C22—62no—
964C22—62no—
965C22—1216no—
966C22D3×#23511yescharacteristic
967C22D3×#23511yescharacteristic
968C22D32×D411yescharacteristic
969C22D3×#23711yescharacteristic
970C22#6431311yescharacteristic
971C22#6431411yescharacteristic
972C22C22×D3×Dic311yescharacteristic
973C4—22no—
974C4—22no—
975C4—62no—
976C4—62no—
977C4—62no—
978C4—121no—
979C4—121no—
980C4—121no—
981C4—182no—
982C4—361no—
983C4—361no—
984C4—361no—
985C3—21no—
986C3#7583311yescharacteristic, complemented
987C3#8209711yescharacteristic, complemented
988C2—42no—
989C2—64no—
990C2—64no—
991C2#1059409311yescharacteristic
992C2#1059419311yescharacteristic
993C2#1059427311yescharacteristic
994C2#1059428011yescharacteristic
995C2D3×#92611yescharacteristic
996C2D3×D4×Dic311yescharacteristic
997C2#1059521511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC24×C3×D3C22
hypercenterC2×C22⋊C4D32
hypocenterC32#2342
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#63841C2semidirect
4. #10592650C2semidirect
5. C3×#4951C2semidirect
7. #10591702C2semidirect
8. #10591701C2semidirect
9. #10591379C2semidirect
10. #10591377C2semidirect
11. #10591368C2semidirect
12. Dic3×(C2×D3)⋊C4C2semidirect
13. #10591295C2semidirect
14. #10591294C2semidirect
15. C4×(C2×D3)⋊Dic3C2semidirect
26. C2×C4⋊(C3⋊Dic3)C22semidirect
27. C2×C4×C3⋊Dic3C22semidirect
33. C2×C3×C4⋊Dic3C22semidirect
34. C2×C3×C4×Dic3C22semidirect
35. C3×D3×C22⋊C4C4semidirect
37. C2×Dic3⋊Dic3C22semidirect
38. C2×Dic3⋊Dic3C22semidirect
45. C2×Dic32C22semidirect
46. C2×Dic32C22semidirect
48. #63658C22semidirect
49. #63658C22semidirect
50. C3×C3⋊#95C22semidirect
51. C3×C3⋊#95C22semidirect
52. #63579C22semidirect
53. #63579C22semidirect
54. #63579C22semidirect
55. #63579C22semidirect
74. #4951D3semidirect
113. C2×C3×C4×D3C2×C4semidirect
114. C2×C3×C4×D3C2×C4semidirect
121. C32×C22⋊C4C2×C4semidirect
128. C3×#217C2×C4semidirect
195. C2×C4⋊Dic3C2×D3semidirect
205. C2×C4×Dic3C2×D3semidirect
208. D3×C22⋊C4Dic3semidirect
225. C3⋊#95C2×D3semidirect
226. C3⋊#95C2×D3semidirect
384. C2×C4×D3C2×Dic3semidirect
385. C2×C4×D3C2×Dic3semidirect
393. C3×C22⋊C4C4×D3semidirect
394. C3×C22⋊C4C2×Dic3semidirect
410. #217C2×Dic3semidirect
462. C2×C3×D3#117semidirect
739. C22⋊C4D3×Dic3semidirect
814. C2×D3#926semidirect
846. C32#2342semidirect
986. C3#75833semidirect
987. C3#82097semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×C22⋊C42
C2×D3×#2172
C2×#638412
#105926502
C3×#49512
#105917062
#105917022
#105917012
#105913792
#105913772
#105913682
Dic3×(C2×D3)⋊C42
#105912952
#105912942
C4×(C2×D3)⋊Dic32
#820973
#758333