Finite Group Databasebeta

← #11812847

Subgroups — #11812847

Order 1152.

1467 conjugacy classes of subgroups.

The subgroup lattice has 998 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#938C211yesmaximal, characteristic
2C2×C3×#935C211yesmaximal, characteristic, complemented
3C2×Dic3×#67C211yesmaximal, characteristic, complemented
4C2×D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
5#10592921C211yesmaximal, characteristic, complemented
6#10591721C211yesmaximal, characteristic, complemented
7#10591721C211yesmaximal, characteristic, complemented
8#10591721C211yesmaximal, characteristic, complemented
9#10591717C211yesmaximal, characteristic, complemented
10#10591715C211yesmaximal, characteristic, complemented
11#10591703C211yesmaximal, characteristic, complemented
12#10591693C211yesmaximal, characteristic, complemented
13#10591342C211yesmaximal, characteristic, complemented
14#10591277C211yesmaximal, characteristic, complemented
15#10591262C211yesmaximal, characteristic, complemented
16#82897—31nomaximal
17#82655—31nomaximal
18C22×C32×D4C2211yescharacteristic
19C22×C3×#67C2211yescharacteristic
20C22×C3×#67C2211yescharacteristic
21C23×C3×Dic3C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×D3×Dic3C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic
25C2×#3757C2211yescharacteristic
26C2×#3757C2211yescharacteristic
27C2×#3757C2211yescharacteristic
28C2×#3757C2211yescharacteristic
29C2×#3750C2211yescharacteristic
30C2×C3×#217C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×#217C2211yescharacteristic
33C2×C3×#217C2211yescharacteristic
34C2×C3×#217C2211yescharacteristic
35C3×#938—24no—
36C3×#935—24no—
37C2×C3×C4⋊Dic3C2211yescharacteristic
38C2×C3×Dic3⋊C4C2211yescharacteristic
39C2×C3×Dic3⋊C4C2211yescharacteristic
40Dic3×#67—24no—
41C2×#3724C2211yescharacteristic
42C2×#3724C2211yescharacteristic
43C2×Dic3⋊Dic3C2211yescharacteristic
44C2×Dic3⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46C2×(C2×D3)⋊Dic3C2211yescharacteristic
47C2×Dic32C2211yescharacteristic
48D3×Dic3⋊C4—24no—
49#63658C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56#63579C2211yescharacteristic
57C2×C3×#123—31no—
58C2×C3×#121—31no—
59C2×#938D311yescharacteristic
60C2×#935D311yescharacteristic, complemented
61C2×D4×Dic3—31no—
62C2×C4×#67—31no—
63C22×Dic3⋊C4—31no—
64C2×D3×C4⋊C4—31no—
65#5222—31no—
66#5222—31no—
67#5222—61no—
68#5220—31no—
69#5220—31no—
70#5220—31no—
71#5210—31no—
72#5210—31no—
73#4989—31no—
74#4982—31no—
75#4981—31no—
76#4980—31no—
77#4978—31no—
78#4956—31no—
79#4956—31no—
80#4956—31no—
81#4953—31no—
82#4952—31no—
83#4949—31no—
84#4949—31no—
85#4946—31no—
86#4945—31no—
87#4944—31no—
88C24×C32C2311yescharacteristic
89C24×C32C2311yescharacteristic
90C23×C3×D3C2311yescharacteristic
91C2×C32×D4—22no—
92C2×C32×D4—22no—
93C2×C32×D4—41no—
94C22×C32×C4C2311yescharacteristic
95C22×C3⋊Dic3C2311yescharacteristic
96C22×C3⋊Dic3C2311yescharacteristic
97C22×C3⋊Dic3C2311yescharacteristic
98C22×C3⋊Dic3C2311yescharacteristic
99C2×C3×#67—22no—
100C2×C3×#67—22no—
101C2×C3×#67—22no—
102C2×C3×#67—22no—
103C2×C3×#67—22no—
104C2×C3×#67D414yes—
105C22×C3×Dic3—22no—
106C22×C3×Dic3—22no—
107C22×C3×Dic3—41no—
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C2×C3×C4×D3—22no—
116C2×C3×C4×D3—22no—
117C2×C3×C4×D3—41no—
118C2×D3×Dic3—22no—
119C2×D3×Dic3—22no—
120C2×D3×Dic3—22no—
121C2×D3×Dic3—22no—
122C2×D3×Dic3—22no—
123C2×D3×Dic3—41no—
124#3757—22no—
125#3757—22no—
126#3757—22no—
127#3757—41no—
128#3750—22no—
129C3×#217—22no—
130C3×#217—22no—
131C3×#217—22no—
132C3×#217—22no—
133C3×#217—22no—
134C3×C4⋊Dic3—22no—
135C3×Dic3⋊C4—22no—
136C3×Dic3⋊C4D414yescomplemented
137#3724—22no—
138#3724—41no—
139Dic3⋊Dic3—22no—
140Dic3⋊Dic3—22no—
141(C2×D3)⋊Dic3—22no—
142(C2×D3)⋊Dic3—22no—
143Dic32—22no—
144#2443—91noSylow
145C22×C3×D4—21no—
146C22×C3×D4—31no—
147C22×C3×D4—31no—
148C22×C3×D4C2×D311yescharacteristic
149C22×C3×D4C2×D311yescharacteristic
150C23×C3×C4—31no—
151C23×C3×C4—31no—
152C22×#67C2×D311yescharacteristic
153C22×#67C2×D311yescharacteristic
154C23×Dic3—31no—
155C23×Dic3—31no—
156C23×Dic3C2×D311yescharacteristic
157C22×C4×D3—31no—
158C22×C4×D3—31no—
159C22×C4×D3C2×D311yescharacteristic
160C3×#123—64no—
161C3×#121—64no—
162C2×C3×C4⋊C4—31no—
163C2×C3×C4⋊C4—31no—
164C2×C3×C4⋊C4—31no—
165C2×C3×C22⋊C4—31no—
166C2×C3×C22⋊C4—31no—
167C2×C3×C22⋊C4—31no—
168C2×C3×C22⋊C4—31no—
169C2×C3×C22⋊C4—31no—
170C2×#217—31no—
171C2×#217—31no—
172C2×#217—31no—
173C2×#217—31no—
174C2×#217—31no—
175C2×#217—31no—
176C2×#217—31no—
177C2×#217—31no—
178C2×#217—31no—
179C2×#217—31no—
180C2×#217—61no—
181C2×#217—61no—
182C2×#217—61no—
183C2×#217—61no—
184C2×#217C2×D311yescharacteristic
185C2×#217C2×D311yescharacteristic
186C2×#217C2×D311yescharacteristic
187C2×#217C2×D311yescharacteristic
188C2×#217C2×D311yescharacteristic
189#938—24no—
190#935—24no—
191D4×Dic3—64no—
192C4×#67—64no—
193C2×(C2×D3)⋊C4—31no—
194C2×(C2×D3)⋊C4—31no—
195C2×C4⋊Dic3—31no—
196C2×C4⋊Dic3—31no—
197C2×C4⋊Dic3C2×D311yescharacteristic
198C2×Dic3⋊C4—31no—
199C2×Dic3⋊C4—31no—
200C2×Dic3⋊C4—31no—
201C2×Dic3⋊C4—31no—
202C2×Dic3⋊C4—31no—
203C2×Dic3⋊C4—31no—
204C2×Dic3⋊C4—31no—
205C2×Dic3⋊C4—31no—
206C2×Dic3⋊C4—61no—
207C2×Dic3⋊C4—64no—
208C2×Dic3⋊C4C2×D311yescharacteristic
209C2×Dic3⋊C4C2×D311yescharacteristic
210C2×C4×Dic3—31no—
211C2×C4×Dic3—31no—
212D3×C4⋊C4—64no—
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—31no—
224C3⋊#95—31no—
225C3⋊#95—31no—
226C3⋊#95—31no—
227C3⋊#95—31no—
228C3⋊#95—31no—
229C3⋊#95—61no—
230C23×C32—21no—
231C23×C32—21no—
232C23×C32—21no—
233C23×C32—21no—
234C23×C32—21no—
235C23×C32—21no—
236C23×C32—21no—
237C23×C32—21no—
238C23×C32—21no—
239C23×C32—21no—
240C23×C32—21no—
241C23×C32—21no—
242C23×C32—21no—
243C23×C32C2×D412yes—
244C23×C32C2411yescharacteristic
245C22×C3×D3—21no—
246C22×C3×D3—21no—
247C22×C3×D3—21no—
248C22×C3×D3—21no—
249C22×C3×D3C2×D412yes—
250C22×C3×D3#4112yes—
251C22×C3×D3#4112yes—
252C32×D4—44no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4C2×D412yes—
256C2×C3⋊Dic3—21no—
257C2×C3⋊Dic3—21no—
258C2×C3⋊Dic3—21no—
259C2×C3⋊Dic3—21no—
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#4112yes—
268C3×#67—28no—
269C3×#67—44no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
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—44no—
289C2×C3×Dic3C2×D412yes—
290C2×C3×Dic3C2×D412yes—
291C2×C3×Dic3C2×D412yes—
292C3×C4×D3—44no—
293D3×Dic3—28no—
294D3×Dic3—44no—
295C2×#123—31no—
296C2×#121—31no—
297C2×C4×D4—91no—
298C22×C4⋊C4—91no—
299#399—91no—
300#398—91no—
301#397—91no—
302#394—91no—
303#388—91no—
304#387—91no—
305#386—91no—
306#386—91no—
307#386—91no—
308#385—91no—
309#385—91no—
310C24×C3—21no—
311C24×C3—21no—
312C24×C3—31no—
313C24×C3C22×D311yescharacteristic
314C24×C3C22×D311yescharacteristic
315C24×C3C22×D311yescharacteristic
316C24×C3C22×D311yescharacteristic
317C23×D3C22×D311yescharacteristic
318C2×C3×D4—22no—
319C2×C3×D4—22no—
320C2×C3×D4—22no—
321C2×C3×D4—22no—
322C2×C3×D4—34no—
323C2×C3×D4—42no—
324C2×C3×D4—42no—
325C2×C3×D4—41no—
326C2×C3×D4—41no—
327C2×C3×D4—42no—
328C2×C3×D4—62no—
329C2×C3×D4—62no—
330C2×C3×D4—62no—
331C2×C3×D4—62no—
332C2×C3×D4—62no—
333C22×C3×C4—21no—
334C22×C3×C4—31no—
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×C4—62no—
342C22×C3×C4—62no—
343C22×C3×C4—62no—
344C22×C3×C4—62no—
345C22×C3×C4—121no—
346C22×C3×C4—121no—
347C22×C3×C4C22×D311yescharacteristic
348C22×C3×C4C22×D311yescharacteristic
349C2×#67—22no—
350C2×#67—22no—
351C2×#67—22no—
352C2×#67—22no—
353C2×#67—22no—
354C2×#67#6714yes—
355C22×Dic3—22no—
356C22×Dic3—22no—
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—41no—
366C22×Dic3—61no—
367C22×Dic3—61no—
368C22×Dic3—61no—
369C22×Dic3—61no—
370C22×Dic3—62no—
371C22×Dic3—62no—
372C22×Dic3—62no—
373C22×Dic3—62no—
374C22×Dic3—62no—
375C22×Dic3—121no—
376C22×Dic3C22×D311yescharacteristic
377C22×Dic3C22×D311yescharacteristic
378C22×Dic3C22×D311yescharacteristic
379C22×Dic3C22×D311yescharacteristic
380C22×Dic3C22×D311yescharacteristic
381C22×Dic3C22×D311yescharacteristic
382C22×Dic3C22×D311yescharacteristic
383C2×C4×D3—22no—
384C2×C4×D3—22no—
385C2×C4×D3—41no—
386C2×C4×D3—62no—
387C2×C4×D3—62no—
388C2×C4×D3—62no—
389C2×C4×D3—62no—
390C2×C4×D3—62no—
391C2×C4×D3—121no—
392C3×C4⋊C4—34no—
393C3×C4⋊C4—62no—
394C3×C4⋊C4—62no—
395C3×C22⋊C4—62no—
396C3×C22⋊C4—62no—
397C3×C22⋊C4—62no—
398C3×C22⋊C4—62no—
399C3×C22⋊C4—62no—
400#217—22no—
401#217—22no—
402#217—22no—
403#217—22no—
404#217—22no—
405#217—62no—
406#217—62no—
407#217—62no—
408#217—62no—
409#217—62no—
410#217—62no—
411#217—62no—
412#217—62no—
413#217—122no—
414#217—122no—
415#217—122no—
416#217—121no—
417#217—121no—
418#217—122no—
419(C2×D3)⋊C4—62no—
420(C2×D3)⋊C4—62no—
421C4⋊Dic3—22no—
422C4⋊Dic3—62no—
423C4⋊Dic3—62no—
424Dic3⋊C4—22no—
425Dic3⋊C4—62no—
426Dic3⋊C4—62no—
427Dic3⋊C4—62no—
428Dic3⋊C4—62no—
429Dic3⋊C4—62no—
430Dic3⋊C4—62no—
431Dic3⋊C4—122no—
432Dic3⋊C4—121no—
433Dic3⋊C4—121no—
434Dic3⋊C4#6714yescomplemented
435C4×Dic3—62no—
436C4×Dic3—62no—
437C22×C32—22no—
438C22×C32—22no—
439C22×C32—22no—
440C22×C32—41no—
441C22×C32—41no—
442C22×C32—41no—
443C22×C32—41no—
444C22×C32—41no—
445C22×C32—41no—
446C22×C32—41no—
447C22×C32—41no—
448C22×C32—41no—
449C22×C32—41no—
450C22×C32—41no—
451C22×C32C22×D411yescharacteristic
452C22×C32C22×D411yescharacteristic
453C22×C32C2×#4111yescharacteristic
454C22×C32C2×#4111yescharacteristic
455C22×C32C2×#4111yescharacteristic
456C22×C32H(5,𝔽2)11yescharacteristic
457C22×C322−1+411yescharacteristic
458C2×C3×D3—22no—
459C2×C3×D3—22no—
460C2×C3×D3—22no—
461C2×C3×D3—22no—
462C2×C3×D3—22no—
463C2×C3×D3—22no—
464C2×C3×D3#12314yescomplemented
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—
476C3×Dic3—41no—
477C22×D4—31no—
478C22×D4—31no—
479C22×D4D3211yescharacteristic
480C23×C4—31no—
481C23×C4—31no—
482C23×C4—91no—
483C23×C4—91no—
484#123—64no—
485#121—64no—
486C4×D4—184no—
487C2×C4⋊C4—31no—
488C2×C4⋊C4—31no—
489C2×C4⋊C4—31no—
490C2×C4⋊C4—91no—
491C2×C4⋊C4—91no—
492C2×C4⋊C4—91no—
493C2×C4⋊C4—91no—
494C2×C4⋊C4—91no—
495C2×C4⋊C4—184no—
496C2×C22⋊C4—31no—
497C2×C22⋊C4—31no—
498C2×C22⋊C4—31no—
499C2×C22⋊C4—31no—
500C2×C22⋊C4—31no—
501C2×C22⋊C4—91no—
502C2×C22⋊C4—91no—
503C2×C22⋊C4—91no—
504C2×C22⋊C4—91no—
505C2×C22⋊C4—91no—
506C2×C22⋊C4—91no—
507C2×C42—91no—
508#95—91no—
509#95—91no—
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—21no—
526C23×C3—21no—
527C23×C3—21no—
528C23×C3—22no—
529C23×C3—21no—
530C23×C3—21no—
531C23×C3—21no—
532C23×C3—21no—
533C23×C3—21no—
534C23×C3—21no—
535C23×C3—21no—
536C23×C3—21no—
537C23×C3—21no—
538C23×C3—21no—
539C23×C3—21no—
540C23×C3—21no—
541C23×C3—21no—
542C23×C3—21no—
543C23×C3—21no—
544C23×C3—22no—
545C23×C3—32no—
546C23×C3—32no—
547C23×C3—32no—
548C23×C3—41no—
549C23×C3—41no—
550C23×C3—41no—
551C23×C3—41no—
552C23×C3—41no—
553C23×C3—41no—
554C23×C3—41no—
555C23×C3—41no—
556C23×C3—41no—
557C23×C3—41no—
558C23×C3—41no—
559C23×C3—41no—
560C23×C3—61no—
561C23×C3—61no—
562C23×C3—61no—
563C23×C3—61no—
564C23×C3D3×D412yes—
565C23×C3C2×#6712yes—
566C23×C3C23×D311yescharacteristic
567C23×C3C23×D311yescharacteristic
568C22×D3—21no—
569C22×D3—21no—
570C22×D3—21no—
571C22×D3—21no—
572C22×D3#23712yes—
573C22×D3#23712yes—
574C22×D3C2×#6712yes—
575C3×D4—44no—
576C3×D4—44no—
577C3×D4—48no—
578C3×D4—68no—
579C3×D4—124no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—22no—
585C2×C3×C4—32no—
586C2×C3×C4—32no—
587C2×C3×C4—32no—
588C2×C3×C4—41no—
589C2×C3×C4—41no—
590C2×C3×C4—61no—
591C2×C3×C4—61no—
592C2×C3×C4—61no—
593C2×C3×C4—61no—
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—124no—
609C2×C3×C4—124no—
610C2×C3×C4D3×D412yes—
611C2×C3×C4C2×#6712yes—
612#67—28no—
613#67—44no—
614C2×Dic3—21no—
615C2×Dic3—21no—
616C2×Dic3—21no—
617C2×Dic3—21no—
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—32no—
633C2×Dic3—32no—
634C2×Dic3—44no—
635C2×Dic3—62no—
636C2×Dic3—68no—
637C2×Dic3—61no—
638C2×Dic3—61no—
639C2×Dic3—61no—
640C2×Dic3—61no—
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—121no—
670C2×Dic3—124no—
671C2×Dic3C2×#6712yes—
672C2×Dic3C2×#6712yes—
673C2×Dic3C2×#6712yes—
674C4×D3—44no—
675C4×D3—68no—
676C4×D3—124no—
677C2×C32—42no—
678C2×C32—81no—
679C2×C32C2×#12311yescharacteristic
680C2×C32#52511yescharacteristic
681C2×C32#53911yescharacteristic
682C2×C32D4211yescharacteristic
683C2×C32#54711yescharacteristic
684C2×C32#54811yescharacteristic
685C2×C32#55311yescharacteristic
686C3×D3—24no—
687C24—31no—
688C24C2×D3211yescharacteristic
689C24C2×D3211yescharacteristic
690C2×D4—22no—
691C2×D4—22no—
692C2×D4—34no—
693C2×D4—41no—
694C2×D4—62no—
695C2×D4—62no—
696C2×D4—62no—
697C2×D4—62no—
698C2×D4—62no—
699C22×C4—31no—
700C22×C4—31no—
701C22×C4—31no—
702C22×C4—31no—
703C22×C4—31no—
704C22×C4—31no—
705C22×C4—31no—
706C22×C4—62no—
707C22×C4—62no—
708C22×C4—62no—
709C22×C4—62no—
710C22×C4—91no—
711C22×C4—91no—
712C22×C4—91no—
713C22×C4—91no—
714C22×C4—121no—
715C22×C4—121no—
716C22×C4—182no—
717C22×C4—182no—
718C22×C4—182no—
719C22×C4—182no—
720C22×C4—182no—
721C22×C4—361no—
722C22×C4C2×D3211yescharacteristic
723C4⋊C4—34no—
724C4⋊C4—62no—
725C4⋊C4—62no—
726C4⋊C4—182no—
727C4⋊C4—182no—
728C4⋊C4—182no—
729C4⋊C4—182no—
730C4⋊C4—361no—
731C22⋊C4—62no—
732C22⋊C4—62no—
733C22⋊C4—62no—
734C22⋊C4—62no—
735C22⋊C4—62no—
736C22⋊C4—182no—
737C22⋊C4—182no—
738C22⋊C4—182no—
739C22⋊C4—182no—
740C22⋊C4—182no—
741C22⋊C4—361no—
742C42—182no—
743C22×C3—22no—
744C22×C3—22no—
745C22×C3—22no—
746C22×C3—22no—
747C22×C3—22no—
748C22×C3—22no—
749C22×C3—21no—
750C22×C3—21no—
751C22×C3—21no—
752C22×C3—21no—
753C22×C3—21no—
754C22×C3—21no—
755C22×C3—21no—
756C22×C3—34no—
757C22×C3—42no—
758C22×C3—42no—
759C22×C3—42no—
760C22×C3—42no—
761C22×C3—42no—
762C22×C3—42no—
763C22×C3—41no—
764C22×C3—41no—
765C22×C3—41no—
766C22×C3—41no—
767C22×C3—41no—
768C22×C3—41no—
769C22×C3—41no—
770C22×C3—41no—
771C22×C3—41no—
772C22×C3—41no—
773C22×C3—41no—
774C22×C3—41no—
775C22×C3—41no—
776C22×C3—41no—
777C22×C3—41no—
778C22×C3—41no—
779C22×C3—41no—
780C22×C3—41no—
781C22×C3—41no—
782C22×C3—41no—
783C22×C3—41no—
784C22×C3—41no—
785C22×C3—62no—
786C22×C3—62no—
787C22×C3—62no—
788C22×C3—62no—
789C22×C3—62no—
790C22×C3—62no—
791C22×C3—81no—
792C22×C3—81no—
793C22×C3—81no—
794C22×C3—81no—
795C22×C3—81no—
796C22×C3—81no—
797C22×C3—81no—
798C22×C3—81no—
799C22×C3C2×D3×D411yescharacteristic
800C22×C3C2×D3×D411yescharacteristic
801C22×C3C2×#23711yescharacteristic
802C22×C3C2×#23711yescharacteristic
803C22×C3#100411yescharacteristic
804C22×C3#100411yescharacteristic
805C22×C3D3×#4111yescharacteristic
806C22×C3D3×#4111yescharacteristic
807C22×C3D3×#4111yescharacteristic
808C22×C3D3×#4111yescharacteristic
809C22×C3#101011yescharacteristic
810C22×C3#101011yescharacteristic
811C22×C3C22×#6711yescharacteristic
812C22×C3C22×#6711yescharacteristic
813C2×D3—22no—
814C2×D3—22no—
815C2×D3—22no—
816C2×D3—22no—
817C2×D3—22no—
818C2×D3—22no—
819C2×D3#93514yescomplemented
820C3×C4—22no—
821C3×C4—22no—
822C3×C4—42no—
823C3×C4—62no—
824C3×C4—62no—
825C3×C4—62no—
826C3×C4—121no—
827C3×C4—121no—
828C3×C4—121no—
829C3×C4—121no—
830Dic3—22no—
831Dic3—22no—
832Dic3—22no—
833Dic3—41no—
834Dic3—41no—
835Dic3—41no—
836Dic3—41no—
837Dic3—62no—
838Dic3—62no—
839Dic3—122no—
840Dic3—121no—
841Dic3—121no—
842Dic3—121no—
843Dic3—121no—
844Dic3—121no—
845Dic3—121no—
846Dic3—241no—
847Dic3—241no—
848Dic3—241no—
849C32#244311yescharacteristic, complemented, Sylow
850C23—21no—
851C23—21no—
852C23—21no—
853C23—21no—
854C23—21no—
855C23—21no—
856C23—21no—
857C23—21no—
858C23—21no—
859C23—21no—
860C23—21no—
861C23—21no—
862C23—21no—
863C23—32no—
864C23—32no—
865C23—32no—
866C23—61no—
867C23—61no—
868C23—61no—
869C23—61no—
870C23D3×#6712yes—
871C23C22×D3211yescharacteristic
872D4—44no—
873D4—68no—
874D4—124no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—32no—
878C2×C4—32no—
879C2×C4—32no—
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—61no—
897C2×C4—61no—
898C2×C4—92no—
899C2×C4—124no—
900C2×C4—124no—
901C2×C4—188no—
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—181no—
913C2×C4—364no—
914C2×C4D3×#6712yes—
915C2×C3—21no—
916C2×C3—21no—
917C2×C3—21no—
918C2×C3—21no—
919C2×C3—21no—
920C2×C3—21no—
921C2×C3—21no—
922C2×C3—42no—
923C2×C3—42no—
924C2×C3—64no—
925C2×C3—82no—
926C2×C3—82no—
927C2×C3—81no—
928C2×C3—81no—
929C2×C3#559811yescharacteristic
930C2×C3#560111yescharacteristic
931C2×C3#560211yescharacteristic
932C2×C3#560611yescharacteristic
933C2×C3D3×#12311yescharacteristic
934C2×C3#565511yescharacteristic
935C2×C3#566011yescharacteristic
936C2×C3#566111yescharacteristic
937C2×C3C2×#93511yescharacteristic
938C2×C3D4×#6711yescharacteristic
939C2×C3D4×#6711yescharacteristic
940C2×C3#582411yescharacteristic
941C2×C3#582811yescharacteristic
942C2×C3#583111yescharacteristic
943D3—24no—
944C22—22no—
945C22—22no—
946C22—22no—
947C22—34no—
948C22—41no—
949C22—41no—
950C22—41no—
951C22—41no—
952C22—41no—
953C22—41no—
954C22—41no—
955C22—41no—
956C22—41no—
957C22—41no—
958C22—41no—
959C22—62no—
960C22—62no—
961C22—62no—
962C22—62no—
963C22—62no—
964C22—62no—
965C22#6430911yescharacteristic
966C22D3×#23711yescharacteristic
967C22D3×#23711yescharacteristic
968C22#6431211yescharacteristic
969C22C2×D3×#6711yescharacteristic
970C22C2×D3×#6711yescharacteristic
971C22#6433011yescharacteristic
972C4—22no—
973C4—62no—
974C4—62no—
975C4—62no—
976C4—121no—
977C4—121no—
978C4—121no—
979C4—121no—
980C4—182no—
981C4—361no—
982C4—361no—
983C4—361no—
984C3—21no—
985C3#8265511yescharacteristic, complemented
986C3#8289711yescharacteristic, complemented
987C2—42no—
988C2—64no—
989C2—81no—
990C2D3×#93511yescharacteristic
991C2#1059514911yescharacteristic
992C2#1059515711yescharacteristic
993C2#1059517411yescharacteristic
994C2#1059518311yescharacteristic
995C2#1059530111yescharacteristic
996C2#67211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC22×C32×D4C22
prime radicalC2×C3×#938C2
hypercenterC22×D4D32
hypocenterC32#2443
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#935C2semidirect
3. C2×Dic3×#67C2semidirect
4. C2×D3×Dic3⋊C4C2semidirect
5. #10592921C2semidirect
6. #10591721C2semidirect
7. #10591721C2semidirect
8. #10591721C2semidirect
9. #10591717C2semidirect
10. #10591715C2semidirect
11. #10591703C2semidirect
12. #10591693C2semidirect
13. #10591342C2semidirect
14. #10591277C2semidirect
15. #10591262C2semidirect
60. C2×#935D3semidirect
136. C3×Dic3⋊C4D4semidirect
434. Dic3⋊C4#67semidirect
464. C2×C3×D3#123semidirect
819. C2×D3#935semidirect
849. C32#2443semidirect
985. C3#82655semidirect
986. C3#82897semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9382
C2×C3×#9352
C2×Dic3×#672
C2×D3×Dic3⋊C42
#105929212
#105917212
#105917172
#105917152
#105917032
#105916932
#105913422
#105912772
#105912622
#828973
#826553