Finite Group Databasebeta

← #11805000

Subgroups — #11805000

Order 1152.

1701 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×(C2×D3)⋊C4C211yesmaximal, characteristic
2C2×D3×#217C211yesmaximal, characteristic
3C2×#63877C211yesmaximal, characteristic, complemented
4#10592909C211yesmaximal, characteristic, complemented
5C3×C4×#217C211yesmaximal, characteristic, complemented
6#10591706C211yesmaximal, characteristic
7Dic3×#217C211yesmaximal, characteristic, complemented
8#10591693C211yesmaximal, characteristic, complemented
9#10591369C211yesmaximal, characteristic, complemented
10Dic3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
11#10591362C211yesmaximal, characteristic, complemented
12#10591282C211yesmaximal, characteristic, complemented
13#10591281C211yesmaximal, characteristic, complemented
14#10591280C211yesmaximal, characteristic, complemented
15#10591279C211yesmaximal, characteristic, complemented
16#82098—31nomaximal
17#73574—31nomaximal
18C24×C3×D3C2211yescharacteristic
19C23×C32×C4C2211yescharacteristic
20C23×C3×Dic3C2211yescharacteristic
21C22×D3×Dic3C2211yescharacteristic
22C22×D3×Dic3C2211yescharacteristic
23C2×#3757C2211yescharacteristic
24C2×#3757C2211yescharacteristic
25C2×#3750C2211yescharacteristic, complemented
26C2×#3750C2211yescharacteristic, complemented
27C2×C3×#217C2211yescharacteristic
28C2×C3×#217C2211yescharacteristic
29C2×C3×(C2×D3)⋊C4—24no—
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×C4×Dic3C2211yescharacteristic, complemented
35C2×C3×C4×Dic3C2211yescharacteristic, complemented
36D3×#217C418yescomplemented
37C2×#3724C2211yescharacteristic, complemented
38C2×#3724C2211yescharacteristic, 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#63877—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—
58C22×(C2×D3)⋊C4D311yescharacteristic
59C2×D3×C22⋊C4—31no—
60C2×#877—31no—
61C2×#872—31no—
62C3×C4×C22⋊C4—31no—
63#5247—31no—
64#5210—31no—
65#5210—31no—
66#5210—31no—
67#5210—61no—
68C4×#217—31no—
69C4×#217D311yescharacteristic, complemented
70#4955—31no—
71#4946—31no—
72#4945—31no—
73#4945—31no—
74#4944—31no—
75#4944—31no—
76#4943—31no—
77#4942—31no—
78Dic3×C22⋊C4—31no—
79Dic3×C22⋊C4—31no—
80#4940—31no—
81#4940—31no—
82C4×(C2×D3)⋊C4—31no—
83#4669—31no—
84#4669—31no—
85#4667—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×C4—22no—
98C22×C32×C4—22no—
99C22×C32×C4—41no—
100C22×C32×C4C2311yescharacteristic
101C22×C32×C4C2311yescharacteristic
102C22×C3⋊Dic3C2311yescharacteristic
103C22×C3⋊Dic3C2311yescharacteristic
104C22×C3⋊Dic3C2311yescharacteristic
105C22×C3⋊Dic3C2311yescharacteristic
106C22×C3×Dic3—22no—
107C22×C3×Dic3—22no—
108C22×C3×Dic3—41no—
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C2×D3×Dic3—22no—
116C2×D3×Dic3—22no—
117C2×D3×Dic3—41no—
118C2×D3×Dic3—41no—
119C2×D3×Dic3C2×C414yescomplemented
120C2×D3×Dic3C2×C414yescomplemented
121#3757—22no—
122#3757C2×C414yes—
123#3750—22no—
124#3750—41no—
125C3×#217—22no—
126C3×#217C2×C414yes—
127C3×(C2×D3)⋊C4—22no—
128C3×(C2×D3)⋊C4—22no—
129C3×(C2×D3)⋊C4—22no—
130C3×(C2×D3)⋊C4D414yes—
131C3×C4×Dic3—22no—
132C3×C4×Dic3—41no—
133#3724—22no—
134#3724—41no—
135(C2×D3)⋊Dic3—22no—
136(C2×D3)⋊Dic3—22no—
137(C2×D3)⋊Dic3—41no—
138(C2×D3)⋊Dic3—41no—
139(C2×D3)⋊Dic3C2×C414yescomplemented
140(C2×D3)⋊Dic3C2×C414yescomplemented
141Dic32—22no—
142Dic32—41no—
143#2342—91noSylow
144C25×C3—31no—
145C24×D3C2×D311yescharacteristic
146C23×C3×C4—21no—
147C23×C3×C4—31no—
148C23×C3×C4C2×D311yescharacteristic
149C23×C3×C4C2×D311yescharacteristic
150C23×Dic3—31no—
151C23×Dic3—31no—
152C23×Dic3C2×D311yescharacteristic
153C22×C4×D3—31no—
154C22×C4×D3—31no—
155C2×C3×C22⋊C4—31no—
156C2×C3×C22⋊C4—31no—
157C2×C3×C22⋊C4—31no—
158C2×C3×C22⋊C4—31no—
159C2×C3×C22⋊C4—31no—
160C2×C3×C22⋊C4—31no—
161C2×C3×C22⋊C4—64no—
162C2×C3×C42—31no—
163C2×C3×C42—31no—
164C2×#217—31no—
165C2×#217—31no—
166C2×#217—31no—
167C2×#217—31no—
168C2×#217—38no—
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×#217C2×D311yescharacteristic
178C2×#217C2×D311yescharacteristic
179C2×(C2×D3)⋊C4—24no—
180C2×(C2×D3)⋊C4—31no—
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)⋊C4C2×D311yescharacteristic
187C2×(C2×D3)⋊C4C2×D311yescharacteristic
188C2×(C2×D3)⋊C4C2×D311yescharacteristic
189C2×(C2×D3)⋊C4C2×D311yescharacteristic
190C2×Dic3⋊C4—31no—
191C2×Dic3⋊C4—31no—
192C2×Dic3⋊C4—31no—
193C2×Dic3⋊C4—31no—
194C2×Dic3⋊C4—31no—
195C2×Dic3⋊C4—31no—
196C2×Dic3⋊C4—31no—
197C2×Dic3⋊C4—31no—
198C2×Dic3⋊C4—61no—
199C2×Dic3⋊C4—61no—
200C2×C4×Dic3—31no—
201C2×C4×Dic3—31no—
202C2×C4×Dic3—31no—
203C2×C4×Dic3—31no—
204C2×C4×Dic3C2×D311yescharacteristic, complemented
205C2×C4×Dic3C2×D311yescharacteristic, complemented
206D3×C22⋊C4—38no—
207#877—64no—
208#872—64no—
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×C32C22×C412yes—
232C23×C32#4112yes—
233C23×C32#4112yes—
234C23×C32C2411yescharacteristic
235C22×C3×D3—21no—
236C22×C3×D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3—21no—
239C22×C3×D3—28no—
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3—21no—
243C22×C3×D3—21no—
244C22×C3×D3—21no—
245C22×C3×D3—21no—
246C22×C3×D3—28no—
247C22×C3×D3—44no—
248C22×C3×D3—44no—
249C22×C3×D3—44no—
250C22×C3×D3—44no—
251C22×C3×D3—44no—
252C22×C3×D3C22×C412yes—
253C22×C3×D3C22×C412yes—
254C22×C3×D3C2×D412yes—
255C22×C3×D3#4112yes—
256C2×C32×C4—21no—
257C2×C32×C4—21no—
258C2×C32×C4—21no—
259C2×C32×C4—21no—
260C2×C32×C4—21no—
261C2×C32×C4—44no—
262C2×C32×C4C2×D412yes—
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⋊Dic3C22×C412yes—
274C2×C3⋊Dic3C22×C412yes—
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×Dic3—21no—
290C2×C3×Dic3—44no—
291C2×C3×Dic3C22×C412yes—
292C2×C3×Dic3C22×C412yes—
293C2×C3×Dic3C2×D412yes—
294D3×Dic3—28no—
295D3×Dic3—44no—
296C2×#117—91no—
297C22×C22⋊C4—31no—
298C22×C22⋊C4—91no—
299#388—91no—
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—31no—
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×D3C4×D314yes—
330C23×D3C22×D311yescharacteristic
331C23×D3C22×D311yescharacteristic
332C22×C3×C4—22no—
333C22×C3×C4—22no—
334C22×C3×C4—22no—
335C22×C3×C4—22no—
336C22×C3×C4—21no—
337C22×C3×C4—21no—
338C22×C3×C4—31no—
339C22×C3×C4—31no—
340C22×C3×C4—31no—
341C22×C3×C4—31no—
342C22×C3×C4—31no—
343C22×C3×C4—31no—
344C22×C3×C4—42no—
345C22×C3×C4—42no—
346C22×C3×C4—41no—
347C22×C3×C4—41no—
348C22×C3×C4—42no—
349C22×C3×C4—62no—
350C22×C3×C4—62no—
351C22×C3×C4—121no—
352C22×C3×C4C22×D311yescharacteristic
353C22×C3×C4C22×D311yescharacteristic
354C22×C3×C4C22×D311yescharacteristic
355C22×C3×C4C22×D311yescharacteristic
356C22×Dic3—22no—
357C22×Dic3—22no—
358C22×Dic3—31no—
359C22×Dic3—31no—
360C22×Dic3—31no—
361C22×Dic3—31no—
362C22×Dic3—34no—
363C22×Dic3—34no—
364C22×Dic3—31no—
365C22×Dic3—31no—
366C22×Dic3—31no—
367C22×Dic3—31no—
368C22×Dic3—41no—
369C22×Dic3—61no—
370C22×Dic3—61no—
371C22×Dic3—61no—
372C22×Dic3—61no—
373C22×Dic3—62no—
374C22×Dic3—62no—
375C22×Dic3—121no—
376C22×Dic3—121no—
377C22×Dic3C22×D311yescharacteristic
378C22×Dic3C22×D311yescharacteristic
379C22×Dic3C22×D311yescharacteristic
380C22×Dic3C22×D311yescharacteristic
381C22×Dic3C22×D311yescharacteristic
382C22×Dic3C22×D311yescharacteristic
383C2×C4×D3—34no—
384C2×C4×D3—34no—
385C2×C4×D3—62no—
386C2×C4×D3—62no—
387C2×C4×D3—121no—
388C2×C4×D3—121no—
389C3×C22⋊C4—34no—
390C3×C22⋊C4—34no—
391C3×C22⋊C4—62no—
392C3×C22⋊C4—62no—
393C3×C22⋊C4—62no—
394C3×C22⋊C4—62no—
395C3×C42—62no—
396C3×C42—121no—
397#217—22no—
398#217—34no—
399#217—34no—
400#217—34no—
401#217—34no—
402#217—64no—
403#217—62no—
404#217—62no—
405#217—62no—
406#217—62no—
407#217—122no—
408#217—121no—
409#217—121no—
410#217C4×D314yes—
411(C2×D3)⋊C4—22no—
412(C2×D3)⋊C4—22no—
413(C2×D3)⋊C4—22no—
414(C2×D3)⋊C4—34no—
415(C2×D3)⋊C4—34no—
416(C2×D3)⋊C4—62no—
417(C2×D3)⋊C4—62no—
418(C2×D3)⋊C4—121no—
419(C2×D3)⋊C4—121no—
420(C2×D3)⋊C4#6714yes—
421Dic3⋊C4—62no—
422Dic3⋊C4—62no—
423Dic3⋊C4—62no—
424Dic3⋊C4—62no—
425Dic3⋊C4—122no—
426Dic3⋊C4—121no—
427Dic3⋊C4—121no—
428Dic3⋊C4—121no—
429Dic3⋊C4—121no—
430Dic3⋊C4—122no—
431C4×Dic3—22no—
432C4×Dic3—41no—
433C4×Dic3—62no—
434C4×Dic3—62no—
435C4×Dic3—121no—
436C4×Dic3—121no—
437C22×C32—22no—
438C22×C32—22no—
439C22×C32—22no—
440C22×C32—22no—
441C22×C32—22no—
442C22×C32—22no—
443C22×C32#11714yescomplemented
444C22×C32C23×C411yescharacteristic
445C22×C32C22×D411yescharacteristic
446C22×C32C2×#4111yescharacteristic
447C22×C32C2×#4111yescharacteristic
448C22×C32C2×#4111yescharacteristic
449C22×C32H(5,𝔽2)11yescharacteristic
450C22×C32H(5,𝔽2)11yescharacteristic
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—416no—
461C2×C3×D3—41no—
462C2×C3×D3—41no—
463C2×C3×D3—41no—
464C2×C3×D3—41no—
465C2×C3×D3C4×D414yes—
466C32×C4—22no—
467C32×C4—41no—
468C3⋊Dic3—22no—
469C3⋊Dic3—22no—
470C3⋊Dic3—41no—
471C3⋊Dic3—41no—
472C3×Dic3—22no—
473C3×Dic3—22no—
474C3×Dic3—22no—
475C3×Dic3—41no—
476C3×Dic3—41no—
477C3×Dic3—41no—
478C25—31no—
479C23×C4—31no—
480C23×C4—91no—
481C23×C4—91no—
482C23×C4D3211yescharacteristic
483#117—184no—
484C2×C4⋊C4—91no—
485C2×C4⋊C4—91no—
486C2×C4⋊C4—91no—
487C2×C4⋊C4—91no—
488C2×C22⋊C4—31no—
489C2×C22⋊C4—31no—
490C2×C22⋊C4—31no—
491C2×C22⋊C4—31no—
492C2×C22⋊C4—31no—
493C2×C22⋊C4—31no—
494C2×C22⋊C4—64no—
495C2×C22⋊C4—98no—
496C2×C22⋊C4—91no—
497C2×C22⋊C4—91no—
498C2×C22⋊C4—91no—
499C2×C22⋊C4—91no—
500C2×C22⋊C4—91no—
501C2×C22⋊C4—91no—
502C2×C22⋊C4—91no—
503C2×C22⋊C4—91no—
504C2×C42—31no—
505C2×C42—31no—
506C2×C42—91no—
507C2×C42—91no—
508#95—31no—
509#95—31no—
510#95—91no—
511#95—91no—
512#95—91no—
513#95—91no—
514#95—91no—
515#95—91no—
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—22no—
526C23×C3—22no—
527C23×C3—22no—
528C23×C3—32no—
529C23×C3—32no—
530C23×C3—32no—
531C23×C3—32no—
532C23×C3—41no—
533C23×C3—41no—
534C23×C3—41no—
535C23×C3—41no—
536C23×C3—68no—
537C23×C3—61no—
538C23×C3—61no—
539C23×C3—61no—
540C23×C3—61no—
541C23×C3—68no—
542C23×C3—61no—
543C23×C3—61no—
544C23×C3—61no—
545C23×C3—61no—
546C23×C3—61no—
547C23×C3—61no—
548C23×C3—124no—
549C23×C3—124no—
550C23×C3—124no—
551C23×C3—124no—
552C23×C3—124no—
553C23×C3C2×C4×D312yes—
554C23×C3C2×C4×D312yes—
555C23×C3#23512yes—
556C23×C3#23512yes—
557C23×C3#23712yes—
558C23×C3#23712yes—
559C23×C3C23×D311yescharacteristic
560C23×C3C23×D311yescharacteristic
561C22×D3—21no—
562C22×D3—21no—
563C22×D3—21no—
564C22×D3—21no—
565C22×D3—28no—
566C22×D3—21no—
567C22×D3—21no—
568C22×D3—21no—
569C22×D3—21no—
570C22×D3—21no—
571C22×D3—21no—
572C22×D3—28no—
573C22×D3—44no—
574C22×D3—44no—
575C22×D3—44no—
576C22×D3—44no—
577C22×D3—44no—
578C22×D3C2×C4×D312yes—
579C22×D3C2×C4×D312yes—
580C22×D3#23512yes—
581C22×D3C2×#6712yes—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—22no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—22no—
594C2×C3×C4—32no—
595C2×C3×C4—32no—
596C2×C3×C4—32no—
597C2×C3×C4—41no—
598C2×C3×C4—41no—
599C2×C3×C4—41no—
600C2×C3×C4—41no—
601C2×C3×C4—44no—
602C2×C3×C4—44no—
603C2×C3×C4—48no—
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—61no—
614C2×C3×C4—61no—
615C2×C3×C4—61no—
616C2×C3×C4—61no—
617C2×C3×C4—61no—
618C2×C3×C4—61no—
619C2×C3×C4—124no—
620C2×C3×C4D3×D412yes—
621C2×C3×C4C2×#6712yes—
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—21no—
634C2×Dic3—21no—
635C2×Dic3—21no—
636C2×Dic3—21no—
637C2×Dic3—32no—
638C2×Dic3—32no—
639C2×Dic3—32no—
640C2×Dic3—32no—
641C2×Dic3—44no—
642C2×Dic3—62no—
643C2×Dic3—62no—
644C2×Dic3—68no—
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—61no—
660C2×Dic3—61no—
661C2×Dic3—61no—
662C2×Dic3—61no—
663C2×Dic3—61no—
664C2×Dic3—61no—
665C2×Dic3—121no—
666C2×Dic3—121no—
667C2×Dic3—121no—
668C2×Dic3—121no—
669C2×Dic3—121no—
670C2×Dic3—121no—
671C2×Dic3—121no—
672C2×Dic3—121no—
673C2×Dic3—121no—
674C2×Dic3—121no—
675C2×Dic3—124no—
676C2×Dic3C2×C4×D312yes—
677C2×Dic3C2×C4×D312yes—
678C2×Dic3C2×#6712yes—
679C4×D3—68no—
680C4×D3—124no—
681C2×C32—24no—
682C2×C32C2×#11711yescharacteristic
683C2×C32C2×C4×D411yescharacteristic
684C2×C32#51811yescharacteristic
685C2×C32#54611yescharacteristic
686C2×C32#54611yescharacteristic
687C2×C32#55111yescharacteristic
688C2×C32#55111yescharacteristic
689C3×D3—24no—
690C3×D3—42no—
691C24—31no—
692C24—31no—
693C24—34no—
694C24—62no—
695C24—62no—
696C24—62no—
697C24—62no—
698C24—121no—
699C24—121no—
700C24C2×D3211yescharacteristic
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—31no—
704C22×C4—31no—
705C22×C4—31no—
706C22×C4—31no—
707C22×C4—31no—
708C22×C4—31no—
709C22×C4—41no—
710C22×C4—62no—
711C22×C4—62no—
712C22×C4—94no—
713C22×C4—94no—
714C22×C4—91no—
715C22×C4—91no—
716C22×C4—91no—
717C22×C4—91no—
718C22×C4—121no—
719C22×C4—182no—
720C22×C4—182no—
721C22×C4—361no—
722C22×C4—361no—
723C22×C4C2×D3211yescharacteristic
724C22×C4C2×D3211yescharacteristic
725C4⋊C4—182no—
726C4⋊C4—182no—
727C4⋊C4—361no—
728C4⋊C4—361no—
729C22⋊C4—34no—
730C22⋊C4—34no—
731C22⋊C4—62no—
732C22⋊C4—62no—
733C22⋊C4—62no—
734C22⋊C4—62no—
735C22⋊C4—94no—
736C22⋊C4—94no—
737C22⋊C4—94no—
738C22⋊C4—182no—
739C22⋊C4—182no—
740C22⋊C4—182no—
741C22⋊C4—361no—
742C22⋊C4—361no—
743C42—62no—
744C42—121no—
745C42—182no—
746C42—361no—
747C22×C3—22no—
748C22×C3—22no—
749C22×C3—22no—
750C22×C3—22no—
751C22×C3—22no—
752C22×C3—22no—
753C22×C3—22no—
754C22×C3—22no—
755C22×C3—22no—
756C22×C3—22no—
757C22×C3—22no—
758C22×C3—22no—
759C22×C3—21no—
760C22×C3—21no—
761C22×C3—21no—
762C22×C3—21no—
763C22×C3—21no—
764C22×C3—21no—
765C22×C3—21no—
766C22×C3—24no—
767C22×C3—34no—
768C22×C3—42no—
769C22×C3—42no—
770C22×C3—42no—
771C22×C3—42no—
772C22×C3—42no—
773C22×C3—42no—
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—62no—
783C22×C3—1216no—
784C22×C3—121no—
785C22×C3—121no—
786C22×C3—121no—
787C22×C3—121no—
788C22×C3#87214yescomplemented
789C22×C3#87714yescomplemented
790C22×C3C22×C4×D311yescharacteristic
791C22×C3C22×C4×D311yescharacteristic
792C22×C3C2×#23511yescharacteristic
793C22×C3C2×#23511yescharacteristic
794C22×C3C2×#23511yescharacteristic
795C22×C3C2×D3×D411yescharacteristic
796C22×C3C2×#23711yescharacteristic
797C22×C3C2×#23711yescharacteristic
798C22×C3#100411yescharacteristic
799C22×C3#100411yescharacteristic
800C22×C3#100411yescharacteristic
801C22×C3D3×#4111yescharacteristic
802C22×C3#100911yescharacteristic
803C22×C3C22×#6711yescharacteristic
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—41no—
815C2×D3—41no—
816C2×D3—41no—
817C2×D3—41no—
818C2×D3C4×#6714yes—
819C3×C4—22no—
820C3×C4—22no—
821C3×C4—42no—
822C3×C4—42no—
823C3×C4—41no—
824C3×C4—41no—
825C3×C4—62no—
826C3×C4—62no—
827C3×C4—62no—
828C3×C4—121no—
829C3×C4—121no—
830C3×C4—121no—
831Dic3—22no—
832Dic3—22no—
833Dic3—22no—
834Dic3—41no—
835Dic3—41no—
836Dic3—41no—
837Dic3—62no—
838Dic3—62no—
839Dic3—62no—
840Dic3—62no—
841Dic3—122no—
842Dic3—122no—
843Dic3—121no—
844Dic3—121no—
845Dic3—121no—
846Dic3—121no—
847Dic3—241no—
848Dic3—241no—
849C32#234211yescharacteristic, complemented, Sylow
850C23—21no—
851C23—21no—
852C23—21no—
853C23—21no—
854C23—32no—
855C23—32no—
856C23—32no—
857C23—32no—
858C23—68no—
859C23—61no—
860C23—61no—
861C23—61no—
862C23—61no—
863C23—61no—
864C23—61no—
865C23—61no—
866C23—61no—
867C23—61no—
868C23—61no—
869C23—68no—
870C23—124no—
871C23—124no—
872C23—124no—
873C23—124no—
874C23—124no—
875C23#379512yes—
876C23C4×D3212yes—
877C23#380412yes—
878C23C22×D3211yescharacteristic
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—32no—
885C2×C4—32no—
886C2×C4—32no—
887C2×C4—44no—
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—61no—
900C2×C4—61no—
901C2×C4—61no—
902C2×C4—61no—
903C2×C4—92no—
904C2×C4—92no—
905C2×C4—124no—
906C2×C4—188no—
907C2×C4—181no—
908C2×C4—181no—
909C2×C4—181no—
910C2×C4—181no—
911C2×C4—181no—
912C2×C4—181no—
913C2×C4—181no—
914C2×C4—181no—
915C2×C4—181no—
916C2×C4—181no—
917C2×C4—364no—
918C2×C4D3×#6712yes—
919C2×C3—24no—
920C2×C3—24no—
921C2×C3—21no—
922C2×C3—21no—
923C2×C3—21no—
924C2×C3—21no—
925C2×C3—21no—
926C2×C3—21no—
927C2×C3—21no—
928C2×C3—44no—
929C2×C3—64no—
930C2×C3—122no—
931C2×C3C2×#87211yescharacteristic
932C2×C3C2×#87711yescharacteristic
933C2×C3#548611yescharacteristic
934C2×C3#549011yescharacteristic
935C2×C3#549511yescharacteristic
936C2×C3#549511yescharacteristic
937C2×C3#552711yescharacteristic
938C2×C3C4×D3×D411yescharacteristic
939C2×C3#554511yescharacteristic
940C2×C3#555011yescharacteristic
941C2×C3#555611yescharacteristic
942C2×C3C2×C4×#6711yescharacteristic
943C2×C3#580611yescharacteristic
944C2×C3#580611yescharacteristic
945D3—24no—
946D3—42no—
947C22—22no—
948C22—22no—
949C22—22no—
950C22—22no—
951C22—22no—
952C22—22no—
953C22—34no—
954C22—62no—
955C22—62no—
956C22—62no—
957C22—62no—
958C22—62no—
959C22—62no—
960C22—62no—
961C22—62no—
962C22—62no—
963C22—1216no—
964C22—121no—
965C22—121no—
966C22—121no—
967C22—121no—
968C22#6387714yescomplemented
969C22C2×#379511yescharacteristic
970C22C2×C4×D3211yescharacteristic
971C22D3×#23511yescharacteristic
972C22#6430711yescharacteristic
973C22C2×#380411yescharacteristic
974C22C2×D3×#6711yescharacteristic
975C22#6433011yescharacteristic
976C4—22no—
977C4—41no—
978C4—62no—
979C4—62no—
980C4—62no—
981C4—121no—
982C4—121no—
983C4—121no—
984C4—182no—
985C4—182no—
986C4—361no—
987C4—361no—
988C3—21no—
989C3#7357411yescharacteristic, complemented
990C3#8209811yescharacteristic, complemented
991C2—24no—
992C2—64no—
993C2—122no—
994C2C2×#6387711yescharacteristic
995C2#1059488611yescharacteristic
996C2#1059493711yescharacteristic
997C2#1059493811yescharacteristic
998C2C4×D3×#6711yescharacteristic
999C2#1059505611yescharacteristic
1000C2#1059549311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC24×C3×D3C22
hypercenterC23×C4D32
hypocenterC32#2342
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
3. C2×#63877C2semidirect
4. #10592909C2semidirect
5. C3×C4×#217C2semidirect
7. Dic3×#217C2semidirect
8. #10591693C2semidirect
9. #10591369C2semidirect
10. Dic3×(C2×D3)⋊C4C2semidirect
11. #10591362C2semidirect
12. #10591282C2semidirect
13. #10591281C2semidirect
14. #10591280C2semidirect
15. #10591279C2semidirect
25. C2×#3750C22semidirect
26. C2×#3750C22semidirect
34. C2×C3×C4×Dic3C22semidirect
35. C2×C3×C4×Dic3C22semidirect
36. D3×#217C4semidirect
37. C2×#3724C22semidirect
38. C2×#3724C22semidirect
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
69. C4×#217D3semidirect
119. C2×D3×Dic3C2×C4semidirect
120. C2×D3×Dic3C2×C4semidirect
139. (C2×D3)⋊Dic3C2×C4semidirect
140. (C2×D3)⋊Dic3C2×C4semidirect
204. C2×C4×Dic3C2×D3semidirect
205. C2×C4×Dic3C2×D3semidirect
225. C3⋊#95C2×D3semidirect
226. C3⋊#95C2×D3semidirect
443. C22×C32#117semidirect
788. C22×C3#872semidirect
789. C22×C3#877semidirect
849. C32#2342semidirect
968. C22#63877semidirect
989. C3#73574semidirect
990. C3#82098semidirect

Maximal subgroups

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

subgroupindex
C22×C3×(C2×D3)⋊C42
C2×D3×#2172
C2×#638772
#105929092
C3×C4×#2172
#105917062
Dic3×#2172
#105916932
#105913692
Dic3×(C2×D3)⋊C42
#105913622
#105912822
#105912812
#105912802
#105912792
#820983
#735743