Finite Group Databasebeta

← #11812881

Subgroups — #11812881

Order 1152.

1557 conjugacy classes of subgroups.

The subgroup lattice has 995 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
2C2×#63980C211yesmaximal, characteristic
3C2×#67⋊Dic3C211yesmaximal, characteristic, complemented
4C2×#63891C211yesmaximal, characteristic, complemented
5C3×#5213C211yesmaximal, characteristic, complemented
6C3×#5213C211yesmaximal, characteristic, complemented
7#10591719C211yesmaximal, characteristic, complemented
8#10591713C211yesmaximal, characteristic, complemented
9#10591394C211yesmaximal, characteristic, complemented
10#10591379C211yesmaximal, characteristic, complemented
11#10591351C211yesmaximal, characteristic, complemented
12#10591317C211yesmaximal, characteristic, complemented
13#10591316C211yesmaximal, characteristic, complemented
14#10591315C211yesmaximal, characteristic, complemented
15#10591271C211yesmaximal, characteristic, complemented
16#74704—31nomaximal
17#74703—31nomaximal
18C23×C32×C4C2211yescharacteristic
19C23×C3⋊Dic3C2211yescharacteristic
20C23×C3⋊Dic3C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C22×#625C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic
25C2×C4⋊(C3⋊Dic3)—24no—
26C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
27C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
28C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
29C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
30C2×C3×#217C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36#63980—24no—
37#67⋊Dic3—24no—
38C2×#3724C2211yescharacteristic
39C2×Dic3⋊Dic3C2211yescharacteristic
40C2×Dic3⋊Dic3C2211yescharacteristic
41C2×Dic3⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46C2×(C2×D3)⋊Dic3C2211yescharacteristic
47C2×Dic32C2211yescharacteristic
48#63891—24no—
49C3×C3⋊#95C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56#63579C2211yescharacteristic
57C2×#939—31no—
58C2×#939—31no—
59C2×D4×Dic3—31no—
60C22×C4⋊Dic3—31no—
61C22×C4⋊Dic3—31no—
62C22×C4⋊Dic3—61no—
63C2×#886—31no—
64C2×#883—31no—
65C2×#67⋊C4—31no—
66C3×#386—31no—
67C3×#386—31no—
68#5220—31no—
69#5213D311yescharacteristic, complemented
70#5213D311yescharacteristic, complemented
71#4961—31no—
72#4961—31no—
73#4958—31no—
74#4953—31no—
75#4951—31no—
76#4950—31no—
77#4950—31no—
78#4949—31no—
79#4946—31no—
80#4677—31no—
81#4674—31no—
82#4670—31no—
83#4668—31no—
84#4661—31no—
85#4657—31no—
86#4654—31no—
87#4653—31no—
88C24×C32C2311yescharacteristic
89C23×C3×D3C2311yescharacteristic
90C23×C3×D3C2311yescharacteristic
91C22×C32×C4—22no—
92C22×C32×C4—22no—
93C22×C32×C4—22no—
94C22×C32×C4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C22×C3⋊Dic3—22no—
97C22×C3⋊Dic3—22no—
98C22×C3⋊Dic3—22no—
99C22×C3⋊Dic3—22no—
100C22×C3⋊Dic3—41no—
101C22×C3⋊Dic3—41no—
102C22×C3⋊Dic3C2311yescharacteristic
103C22×C3⋊Dic3C2311yescharacteristic
104C22×C3⋊Dic3C2311yescharacteristic
105C22×C3⋊Dic3C2311yescharacteristic
106C2×C3×#67—22no—
107C2×C3×#67—22no—
108C2×C3×#67—22no—
109C2×C3×#67—22no—
110C2×C3×#67—22no—
111C2×C3×#67D414yes—
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C22×C3×Dic3C2311yescharacteristic
116C22×C3×Dic3C2311yescharacteristic
117C22×C3×Dic3C2311yescharacteristic
118C2×#625—22no—
119C2×#625—22no—
120C2×#625—41no—
121C2×D3×Dic3—22no—
122C2×D3×Dic3—22no—
123C2×D3×Dic3—41no—
124C4⋊(C3⋊Dic3)—22no—
125C4⋊(C3⋊Dic3)—22no—
126C4⋊(C3⋊Dic3)—22no—
127C4⋊(C3⋊Dic3)D414yescomplemented
128C3×#217—22no—
129C3×#217—22no—
130C3×(C2×D3)⋊C4—22no—
131C3×(C2×D3)⋊C4—22no—
132C3×(C2×D3)⋊C4—22no—
133C3×(C2×D3)⋊C4—22no—
134#3724—22no—
135Dic3⋊Dic3—22no—
136Dic3⋊Dic3—22no—
137Dic3⋊Dic3—41no—
138(C2×D3)⋊Dic3—22no—
139(C2×D3)⋊Dic3—22no—
140(C2×D3)⋊Dic3—22no—
141(C2×D3)⋊Dic3—22no—
142(C2×D3)⋊Dic3—41no—
143Dic32—22no—
144#2443—91noSylow
145C22×C3×D4—31no—
146C22×C3×D4—31no—
147C23×C3×C4—21no—
148C23×C3×C4C2×D311yescharacteristic
149C23×C3×C4C2×D311yescharacteristic
150C22×#67—31no—
151C22×#67—31no—
152C22×#67C2×D311yescharacteristic
153C22×#67C2×D311yescharacteristic
154C23×Dic3—31no—
155C23×Dic3—31no—
156C23×Dic3—31no—
157C23×Dic3—31no—
158C23×Dic3—31no—
159C23×Dic3—61no—
160C23×Dic3—61no—
161C22×C4×D3—31no—
162C2×C3×C22⋊C4—31no—
163C2×C3×C22⋊C4—31no—
164C2×C3×C22⋊C4—31no—
165C2×C3×C22⋊C4—31no—
166C2×C3×C22⋊C4—31no—
167C2×C3×C22⋊C4—31no—
168C2×#217—31no—
169C2×#217—31no—
170C2×#217—31no—
171C2×#217—31no—
172C2×#217—31no—
173C2×#217C2×D311yescharacteristic
174C2×#217C2×D311yescharacteristic
175#939—64no—
176#939—64no—
177D4×Dic3—64no—
178C2×(C2×D3)⋊C4—31no—
179C2×(C2×D3)⋊C4—31no—
180C2×(C2×D3)⋊C4—31no—
181C2×(C2×D3)⋊C4—31no—
182C2×(C2×D3)⋊C4—31no—
183C2×(C2×D3)⋊C4C2×D311yescharacteristic
184C2×(C2×D3)⋊C4C2×D311yescharacteristic
185C2×(C2×D3)⋊C4C2×D311yescharacteristic
186C2×(C2×D3)⋊C4C2×D311yescharacteristic
187C2×C4⋊Dic3—31no—
188C2×C4⋊Dic3—31no—
189C2×C4⋊Dic3—31no—
190C2×C4⋊Dic3—31no—
191C2×C4⋊Dic3—31no—
192C2×C4⋊Dic3—31no—
193C2×C4⋊Dic3—31no—
194C2×C4⋊Dic3—31no—
195C2×C4⋊Dic3—31no—
196C2×C4⋊Dic3—31no—
197C2×C4⋊Dic3—31no—
198C2×C4⋊Dic3—61no—
199C2×C4⋊Dic3—61no—
200C2×C4⋊Dic3—61no—
201C2×C4⋊Dic3—61no—
202C2×C4⋊Dic3—64no—
203C2×C4⋊Dic3—64no—
204C2×C4⋊Dic3—68no—
205C2×Dic3⋊C4—31no—
206C2×Dic3⋊C4—31no—
207C2×Dic3⋊C4—31no—
208C2×Dic3⋊C4—31no—
209C2×Dic3⋊C4—31no—
210C2×C4×Dic3—31no—
211C2×C4×Dic3—31no—
212#886—64no—
213#883—64no—
214#67⋊C4—64no—
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—31no—
224C3⋊#95—31no—
225C3⋊#95—31no—
226C3⋊#95—31no—
227C3⋊#95C2×D311yescharacteristic
228C3⋊#95C2×D311yescharacteristic
229C3⋊#95C2×D311yescharacteristic
230C3⋊#95C2×D311yescharacteristic
231C23×C32—21no—
232C23×C32—21no—
233C23×C32—21no—
234C23×C32—21no—
235C23×C32C2×D412yes—
236C23×C32#4112yes—
237C23×C32#4112yes—
238C23×C32C2411yescharacteristic
239C22×C3×D3—21no—
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—21no—
247C22×C3×D3—21no—
248C22×C3×D3—21no—
249C22×C3×D3—21no—
250C22×C3×D3—21no—
251C22×C3×D3—21no—
252C22×C3×D3C2×D412yes—
253C2×C32×C4—28no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4—21no—
258C2×C32×C4C2×D412yes—
259C2×C32×C4#4112yes—
260C2×C3⋊Dic3—21no—
261C2×C3⋊Dic3—21no—
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—44no—
271C2×C3⋊Dic3—44no—
272C2×C3⋊Dic3C2×D412yes—
273C2×C3⋊Dic3C2×D412yes—
274C3×#67—28no—
275C3×#67—44no—
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—21no—
291C2×C3×Dic3—21no—
292C2×C3×Dic3—21no—
293C2×C3×Dic3C2×D412yes—
294#625—44no—
295D3×Dic3—44no—
296C2×#123—91no—
297C2×#121—91no—
298C2×C4×D4—91no—
299C22×C4⋊C4—91no—
300#399—91no—
301#398—91no—
302#397—91no—
303#394—91no—
304#388—91no—
305#387—91no—
306#386—31no—
307#386—31no—
308#386—91no—
309#385—91no—
310#385—91no—
311C24×C3—21no—
312C24×C3—31no—
313C24×C3—31no—
314C24×C3C22×D311yescharacteristic
315C24×C3C22×D311yescharacteristic
316C23×D3C22×D311yescharacteristic
317C23×D3C22×D311yescharacteristic
318C2×C3×D4—34no—
319C2×C3×D4—62no—
320C2×C3×D4—62no—
321C2×C3×D4—62no—
322C2×C3×D4—62no—
323C2×C3×D4—62no—
324C22×C3×C4—24no—
325C22×C3×C4—24no—
326C22×C3×C4—24no—
327C22×C3×C4—22no—
328C22×C3×C4—22no—
329C22×C3×C4—22no—
330C22×C3×C4—22no—
331C22×C3×C4—22no—
332C22×C3×C4—22no—
333C22×C3×C4—21no—
334C22×C3×C4—21no—
335C22×C3×C4—31no—
336C22×C3×C4—31no—
337C22×C3×C4—31no—
338C22×C3×C4—31no—
339C22×C3×C4—31no—
340C22×C3×C4—31no—
341C22×C3×C4C22×D311yescharacteristic
342C22×C3×C4C22×D311yescharacteristic
343C22×C3×C4C22×D311yescharacteristic
344C22×C3×C4C22×D311yescharacteristic
345C2×#67—22no—
346C2×#67—22no—
347C2×#67—22no—
348C2×#67—22no—
349C2×#67—22no—
350C2×#67—62no—
351C2×#67—62no—
352C2×#67—62no—
353C2×#67—62no—
354C2×#67—121no—
355C2×#67—121no—
356C2×#67D1214yes—
357C22×Dic3—31no—
358C22×Dic3—31no—
359C22×Dic3—31no—
360C22×Dic3—31no—
361C22×Dic3—31no—
362C22×Dic3—31no—
363C22×Dic3—31no—
364C22×Dic3—31no—
365C22×Dic3—61no—
366C22×Dic3—61no—
367C22×Dic3—61no—
368C22×Dic3—61no—
369C22×Dic3—62no—
370C22×Dic3—62no—
371C22×Dic3—62no—
372C22×Dic3—62no—
373C22×Dic3—62no—
374C22×Dic3—62no—
375C22×Dic3—64no—
376C22×Dic3—64no—
377C22×Dic3—62no—
378C22×Dic3—62no—
379C22×Dic3—62no—
380C22×Dic3—62no—
381C22×Dic3—122no—
382C22×Dic3—122no—
383C22×Dic3—121no—
384C22×Dic3—121no—
385C22×Dic3—121no—
386C22×Dic3—121no—
387C22×Dic3—121no—
388C22×Dic3—122no—
389C22×Dic3—122no—
390C22×Dic3C22×D311yescharacteristic
391C22×Dic3C22×D311yescharacteristic
392C22×Dic3C22×D311yescharacteristic
393C22×Dic3C22×D311yescharacteristic
394C22×Dic3C22×D311yescharacteristic
395C22×Dic3C22×D311yescharacteristic
396C2×C4×D3—62no—
397C2×C4×D3—62no—
398C2×C4×D3—121no—
399C3×C22⋊C4—62no—
400C3×C22⋊C4—62no—
401C3×C22⋊C4—62no—
402C3×C22⋊C4—62no—
403C3×C22⋊C4—62no—
404C3×C22⋊C4—62no—
405#217—22no—
406#217—22no—
407#217—62no—
408#217—62no—
409#217—62no—
410#217—62no—
411#217—121no—
412(C2×D3)⋊C4—22no—
413(C2×D3)⋊C4—22no—
414(C2×D3)⋊C4—22no—
415(C2×D3)⋊C4—22no—
416(C2×D3)⋊C4—62no—
417(C2×D3)⋊C4—62no—
418(C2×D3)⋊C4—62no—
419(C2×D3)⋊C4—62no—
420(C2×D3)⋊C4—121no—
421C4⋊Dic3—34no—
422C4⋊Dic3—34no—
423C4⋊Dic3—64no—
424C4⋊Dic3—62no—
425C4⋊Dic3—62no—
426C4⋊Dic3—62no—
427C4⋊Dic3—62no—
428C4⋊Dic3—62no—
429C4⋊Dic3—62no—
430C4⋊Dic3—64no—
431C4⋊Dic3—64no—
432C4⋊Dic3—64no—
433C4⋊Dic3—62no—
434C4⋊Dic3—62no—
435C4⋊Dic3—121no—
436Dic3⋊C4—62no—
437Dic3⋊C4—62no—
438Dic3⋊C4—62no—
439Dic3⋊C4—62no—
440Dic3⋊C4—121no—
441C4×Dic3—62no—
442C4×Dic3—62no—
443C22×C32—22no—
444C22×C32—22no—
445C22×C32—22no—
446C22×C32—22no—
447C22×C32—22no—
448C22×C32—22no—
449C22×C32#12314yescomplemented
450C22×C32C22×D411yescharacteristic
451C22×C32C22×D411yescharacteristic
452C22×C32C2×#4111yescharacteristic
453C22×C32C2×#4111yescharacteristic
454C22×C32C2×#4111yescharacteristic
455C22×C32H(5,𝔽2)11yescharacteristic
456C22×C322−1+411yescharacteristic
457C2×C3×D3—22no—
458C2×C3×D3—22no—
459C2×C3×D3—22no—
460C2×C3×D3—41no—
461C2×C3×D3—41no—
462C2×C3×D3—41no—
463C2×C3×D3—41no—
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C2×C3×D3—41no—
467C2×C3×D3—41no—
468C2×C3×D3—41no—
469C2×C3×D3—41no—
470C2×C3×D3—41no—
471C32×C4—22no—
472C32×C4—22no—
473C3⋊Dic3—22no—
474C3⋊Dic3—22no—
475C3⋊Dic3—41no—
476C3⋊Dic3—41no—
477C3×Dic3—22no—
478C3×Dic3—41no—
479C3×Dic3—41no—
480C3×Dic3—41no—
481C3×Dic3—41no—
482C3×Dic3—41no—
483C22×D4—31no—
484C22×D4—31no—
485C22×D4—91no—
486C23×C4—91no—
487C23×C4—91no—
488C23×C4—91no—
489C23×C4D3211yescharacteristic
490#123—184no—
491#121—184no—
492C4×D4—184no—
493C2×C4⋊C4—91no—
494C2×C4⋊C4—91no—
495C2×C4⋊C4—91no—
496C2×C4⋊C4—91no—
497C2×C4⋊C4—91no—
498C2×C4⋊C4—91no—
499C2×C4⋊C4—91no—
500C2×C4⋊C4—91no—
501C2×C4⋊C4—184no—
502C2×C22⋊C4—31no—
503C2×C22⋊C4—31no—
504C2×C22⋊C4—31no—
505C2×C22⋊C4—31no—
506C2×C22⋊C4—31no—
507C2×C22⋊C4—31no—
508C2×C22⋊C4—91no—
509C2×C22⋊C4—91no—
510C2×C22⋊C4—91no—
511C2×C22⋊C4—91no—
512C2×C22⋊C4—91no—
513C2×C42—91no—
514#95—31no—
515#95—31no—
516#95—31no—
517#95—31no—
518#95—91no—
519#95—91no—
520#95—91no—
521#95—91no—
522C23×C3—22no—
523C23×C3—22no—
524C23×C3—22no—
525C23×C3—22no—
526C23×C3—21no—
527C23×C3—21no—
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—21no—
531C23×C3—21no—
532C23×C3—21no—
533C23×C3—21no—
534C23×C3—21no—
535C23×C3—22no—
536C23×C3—22no—
537C23×C3—22no—
538C23×C3—32no—
539C23×C3—61no—
540C23×C3—61no—
541C23×C3—61no—
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—61no—
551C23×C3—61no—
552C23×C3C2×D1212yes—
553C23×C3#23512yes—
554C23×C3D3×D412yes—
555C23×C3#23712yes—
556C23×C3#23712yes—
557C23×C3#23712yes—
558C23×C3C23×D311yescharacteristic
559C23×C3C23×D311yescharacteristic
560C22×D3—21no—
561C22×D3—21no—
562C22×D3—21no—
563C22×D3—21no—
564C22×D3—21no—
565C22×D3—21no—
566C22×D3—21no—
567C22×D3—21no—
568C22×D3—21no—
569C22×D3—21no—
570C22×D3—21no—
571C22×D3—21no—
572C22×D3—21no—
573C22×D3C2×D1212yes—
574C3×D4—68no—
575C3×D4—124no—
576C2×C3×C4—22no—
577C2×C3×C4—216no—
578C2×C3×C4—28no—
579C2×C3×C4—28no—
580C2×C3×C4—22no—
581C2×C3×C4—22no—
582C2×C3×C4—22no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—21no—
591C2×C3×C4—22no—
592C2×C3×C4—22no—
593C2×C3×C4—32no—
594C2×C3×C4—61no—
595C2×C3×C4—61no—
596C2×C3×C4—61no—
597C2×C3×C4—61no—
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×C4D3×D412yes—
612C2×C3×C4D3×D412yes—
613C2×C3×C4#23712yes—
614C2×C3×C4#23712yes—
615#67—28no—
616#67—44no—
617#67—124no—
618#67—124no—
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—21no—
634C2×Dic3—21no—
635C2×Dic3—21no—
636C2×Dic3—32no—
637C2×Dic3—32no—
638C2×Dic3—32no—
639C2×Dic3—32no—
640C2×Dic3—62no—
641C2×Dic3—62no—
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—62no—
651C2×Dic3—62no—
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—121no—
665C2×Dic3—121no—
666C2×Dic3—121no—
667C2×Dic3—121no—
668C2×Dic3—121no—
669C2×Dic3—121no—
670C2×Dic3—121no—
671C2×Dic3—121no—
672C2×Dic3—124no—
673C2×Dic3—124no—
674C2×Dic3—124no—
675C2×Dic3—124no—
676C2×Dic3—124no—
677C2×Dic3—128no—
678C2×Dic3—128no—
679C2×Dic3C2×D1212yes—
680C4×D3—124no—
681C2×C32—24no—
682C2×C32C2×#12311yescharacteristic
683C2×C32#52511yescharacteristic
684C2×C32#53911yescharacteristic
685C2×C32D4211yescharacteristic
686C2×C32#54711yescharacteristic
687C2×C32#54811yescharacteristic
688C2×C32#55311yescharacteristic
689C3×D3—42no—
690C3×D3—81no—
691C24—31no—
692C24—31no—
693C24C2×D3211yescharacteristic
694C2×D4—34no—
695C2×D4—62no—
696C2×D4—62no—
697C2×D4—62no—
698C2×D4—62no—
699C2×D4—62no—
700C2×D4—182no—
701C2×D4—182no—
702C2×D4—361no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—22no—
706C22×C4—31no—
707C22×C4—31no—
708C22×C4—31no—
709C22×C4—31no—
710C22×C4—31no—
711C22×C4—31no—
712C22×C4—91no—
713C22×C4—91no—
714C22×C4—91no—
715C22×C4—91no—
716C22×C4—182no—
717C22×C4—182no—
718C22×C4—182no—
719C22×C4—182no—
720C22×C4—182no—
721C22×C4—182no—
722C22×C4—361no—
723C22×C4—361no—
724C22×C4—361no—
725C22×C4C2×D3211yescharacteristic
726C22×C4C2×D3211yescharacteristic
727C4⋊C4—94no—
728C4⋊C4—182no—
729C4⋊C4—182no—
730C4⋊C4—182no—
731C4⋊C4—182no—
732C4⋊C4—182no—
733C4⋊C4—182no—
734C4⋊C4—361no—
735C22⋊C4—62no—
736C22⋊C4—62no—
737C22⋊C4—62no—
738C22⋊C4—62no—
739C22⋊C4—62no—
740C22⋊C4—62no—
741C22⋊C4—182no—
742C22⋊C4—182no—
743C22⋊C4—182no—
744C22⋊C4—182no—
745C22⋊C4—361no—
746C42—182no—
747C22×C3—24no—
748C22×C3—24no—
749C22×C3—24no—
750C22×C3—24no—
751C22×C3—24no—
752C22×C3—24no—
753C22×C3—22no—
754C22×C3—22no—
755C22×C3—22no—
756C22×C3—22no—
757C22×C3—22no—
758C22×C3—22no—
759C22×C3—22no—
760C22×C3—22no—
761C22×C3—22no—
762C22×C3—22no—
763C22×C3—22no—
764C22×C3—22no—
765C22×C3—21no—
766C22×C3—21no—
767C22×C3—21no—
768C22×C3—21no—
769C22×C3—21no—
770C22×C3—21no—
771C22×C3—21no—
772C22×C3—24no—
773C22×C3—62no—
774C22×C3—62no—
775C22×C3—62no—
776C22×C3—121no—
777C22×C3—121no—
778C22×C3—121no—
779C22×C3—121no—
780C22×C3—121no—
781C22×C3—121no—
782C22×C3—121no—
783C22×C3—121no—
784C22×C3—121no—
785C22×C3—121no—
786C22×C3—121no—
787C22×C3#88314yescomplemented
788C22×C3#88614yescomplemented
789C22×C3C22×D1211yescharacteristic
790C22×C3C2×#23511yescharacteristic
791C22×C3C2×D3×D411yescharacteristic
792C22×C3C2×D3×D411yescharacteristic
793C22×C3C2×D3×D411yescharacteristic
794C22×C3C2×#23711yescharacteristic
795C22×C3C2×#23711yescharacteristic
796C22×C3C2×#23711yescharacteristic
797C22×C3C2×#23711yescharacteristic
798C22×C3C2×#23711yescharacteristic
799C22×C3#100911yescharacteristic
800C22×C3#100911yescharacteristic
801C22×C3#101011yescharacteristic
802C22×C3#101011yescharacteristic
803C2×D3—22no—
804C2×D3—22no—
805C2×D3—22no—
806C2×D3—41no—
807C2×D3—41no—
808C2×D3—41no—
809C2×D3—41no—
810C2×D3—41no—
811C2×D3—41no—
812C2×D3—41no—
813C2×D3—41no—
814C2×D3—41no—
815C2×D3—41no—
816C2×D3—41no—
817C3×C4—24no—
818C3×C4—24no—
819C3×C4—22no—
820C3×C4—22no—
821C3×C4—22no—
822C3×C4—22no—
823C3×C4—62no—
824C3×C4—121no—
825C3×C4—121no—
826C3×C4—121no—
827C3×C4—121no—
828C3×C4—121no—
829Dic3—22no—
830Dic3—41no—
831Dic3—41no—
832Dic3—41no—
833Dic3—41no—
834Dic3—41no—
835Dic3—62no—
836Dic3—62no—
837Dic3—62no—
838Dic3—62no—
839Dic3—122no—
840Dic3—122no—
841Dic3—122no—
842Dic3—122no—
843Dic3—121no—
844Dic3—121no—
845Dic3—121no—
846Dic3—121no—
847C32#244311yescharacteristic, complemented, Sylow
848C23—21no—
849C23—21no—
850C23—21no—
851C23—21no—
852C23—32no—
853C23—61no—
854C23—61no—
855C23—61no—
856C23—61no—
857C23—61no—
858C23—61no—
859C23—61no—
860C23—61no—
861C23—61no—
862C23—61no—
863C23—61no—
864C23—61no—
865C23—61no—
866C23#379512yes—
867C23D3×D1212yes—
868C23#380512yes—
869C23C22×D3211yescharacteristic
870D4—68no—
871D4—124no—
872D4—364no—
873C2×C4—28no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—32no—
879C2×C4—61no—
880C2×C4—61no—
881C2×C4—61no—
882C2×C4—61no—
883C2×C4—61no—
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—92no—
897C2×C4—92no—
898C2×C4—181no—
899C2×C4—181no—
900C2×C4—181no—
901C2×C4—181no—
902C2×C4—181no—
903C2×C4—181no—
904C2×C4—181no—
905C2×C4—181no—
906C2×C4—181no—
907C2×C4—181no—
908C2×C4—364no—
909C2×C4—364no—
910C2×C4—364no—
911C2×C4#380512yes—
912C2×C4#381112yes—
913C2×C3—28no—
914C2×C3—24no—
915C2×C3—24no—
916C2×C3—21no—
917C2×C3—21no—
918C2×C3—21no—
919C2×C3—21no—
920C2×C3—21no—
921C2×C3—21no—
922C2×C3—21no—
923C2×C3—122no—
924C2×C3—241no—
925C2×C3C2×#88311yescharacteristic
926C2×C3C2×#88611yescharacteristic
927C2×C3D4×D1211yescharacteristic
928C2×C3#555211yescharacteristic
929C2×C3#555511yescharacteristic
930C2×C3#556511yescharacteristic
931C2×C3#558611yescharacteristic
932C2×C3#558611yescharacteristic
933C2×C3#559811yescharacteristic
934C2×C3#560911yescharacteristic
935C2×C3#561111yescharacteristic
936C2×C3#561811yescharacteristic
937C2×C3#566511yescharacteristic
938C2×C3#566511yescharacteristic
939D3—42no—
940D3—81no—
941C22—22no—
942C22—22no—
943C22—22no—
944C22—22no—
945C22—22no—
946C22—22no—
947C22—62no—
948C22—62no—
949C22—62no—
950C22—121no—
951C22—121no—
952C22—121no—
953C22—121no—
954C22—121no—
955C22—121no—
956C22—121no—
957C22—121no—
958C22—121no—
959C22—121no—
960C22—121no—
961C22#6389114yescomplemented
962C22C2×#379511yescharacteristic
963C22#6429811yescharacteristic
964C22C2×D3×D1211yescharacteristic
965C22#6430811yescharacteristic
966C22C2×#380511yescharacteristic
967C22C2×#380511yescharacteristic
968C22C2×#381111yescharacteristic
969C4—22no—
970C4—22no—
971C4—62no—
972C4—121no—
973C4—121no—
974C4—121no—
975C4—121no—
976C4—121no—
977C4—182no—
978C4—182no—
979C4—361no—
980C4—361no—
981C3—21no—
982C3#7470311yescharacteristic, complemented
983C3#7470411yescharacteristic, complemented
984C2—24no—
985C2—122no—
986C2—241no—
987C2C2×#6389111yescharacteristic
988C2#1059490711yescharacteristic
989C2#1059491811yescharacteristic
990C2#1059499411yescharacteristic
991C2#1059499511yescharacteristic
992C2#1059507411yescharacteristic
993C2#1059550111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC23×C32×C4C22
prime radicalC2×#63980C2
hypercenterC23×C4D32
hypocenterC32#2443
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×C4⋊(C3⋊Dic3)C2semidirect
3. C2×#67⋊Dic3C2semidirect
4. C2×#63891C2semidirect
5. C3×#5213C2semidirect
6. C3×#5213C2semidirect
7. #10591719C2semidirect
8. #10591713C2semidirect
9. #10591394C2semidirect
10. #10591379C2semidirect
11. #10591351C2semidirect
12. #10591317C2semidirect
13. #10591316C2semidirect
14. #10591315C2semidirect
15. #10591271C2semidirect
69. #5213D3semidirect
70. #5213D3semidirect
127. C4⋊(C3⋊Dic3)D4semidirect
449. C22×C32#123semidirect
787. C22×C3#883semidirect
788. C22×C3#886semidirect
847. C32#2443semidirect
961. C22#63891semidirect
982. C3#74703semidirect
983. C3#74704semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊(C3⋊Dic3)2
C2×#639802
C2×#67⋊Dic32
C2×#638912
C3×#52132
#105917192
#105917132
#105913942
#105913792
#105913512
#105913172
#105913162
#105913152
#105912712
#747043
#747033