Finite Group Databasebeta

← #13172161

Subgroups — #13172161

Order 1728.

1726 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89049C211yesmaximal, characteristic
2#11723626C212yesmaximal, complemented
3C2×#88803C211yesmaximal, characteristic, complemented
4C3×#63974C211yesmaximal, characteristic, complemented
5C3×#63952C212yesmaximal, complemented
6#11722934C212yesmaximal, complemented
7#11722931C212yesmaximal, complemented
8#11722922C212yesmaximal, complemented
9#11722905C212yesmaximal, complemented
10#10595058—31nomaximal
11#10594254—32nomaximal
12C23×C3×C3⋊D3C2211yescharacteristic
13C22×#1113C2211yescharacteristic
14C22×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
15C2×C3×#638C2212yes—
16C22×C32×Dic3C2211yescharacteristic, complemented
17#89049C418yescomplemented
18C2×#6295C2212yes—
19C2×#6294C2211yescharacteristic
20C2×Dic3×C3⋊D3C2212yescomplemented
21C2×C3×#624C2212yescomplemented
22C2×C3×#624C2211yescharacteristic, complemented
23C2×C3×#624C2211yescharacteristic, complemented
24C32×#217C2212yescomplemented
25#88807C2212yescomplemented
26#88803C2212yes—
27#88803C2212yescomplemented
28#88803C2212yescomplemented
29Dic3×C3⋊Dic3C2212yescomplemented
30C3×#3724C2212yescomplemented
31C3×#3722C2212yes—
32C3×#3722C2212yescomplemented
33C3×Dic32C2212yescomplemented
34C2×#3811—31no—
35C2×D3×#67—32no—
36C2×#3752—31no—
37#64090—32no—
38C3×C4×#67—32no—
39C3×#67⋊C4—32no—
40C3×D3×C22⋊C4—32no—
41#63974D311yescharacteristic, complemented
42#67⋊Dic3—32no—
43#67⋊Dic3—32no—
44#67⋊Dic3—62no—
45C2×(C2×D3)⋊Dic3—32no—
46C2×(C2×D3)⋊Dic3—61no—
47#63952D312yescomplemented
48#63921—32no—
49D3×(C2×D3)⋊C4—32no—
50D3×(C2×D3)⋊C4—32no—
51#63904—32no—
52#63904—32no—
53C4×#626—32no—
54C4×#625—32no—
55#63880—32no—
56#63879—32no—
57#63878—32no—
58#63877—32no—
59#63836—32no—
60C23×C33C2311yescharacteristic
61C22×C3×C3⋊D3—41no—
62C22×C3×C3⋊D3—41no—
63C22×C3×C3⋊D3C2×C414yescomplemented
64C22×C3×C3⋊D3C2311yescharacteristic
65C22×C3×C3⋊D3C2312yes—
66C22×C3×C3⋊D3C2311yescharacteristic
67C2×#1113—41no—
68C2×#1113—41no—
69C2×#1113C2×C414yescomplemented
70C2×C3⋊(C3⋊Dic3)—41no—
71C2×C3⋊(C3⋊Dic3)C2312yes—
72C3×#638C2×C418yescomplemented
73C2×C3×C3⋊Dic3C2312yes—
74C2×C32×Dic3—41no—
75C2×C32×Dic3C2312yes—
76C2×C32×Dic3C2312yes—
77C2×C32×Dic3C2312yes—
78#6295C2×C418yescomplemented
79#6294C2×C414yescomplemented
80Dic3×C3⋊D3—42no—
81C3×#624—41no—
82C3×#624—42no—
83C3×#624—41no—
84#5545—92no—
85#5486—91no—
86C23×C3⋊D3C2×D311yescharacteristic
87C23×C3×D3—32no—
88C23×C3×D3—61no—
89C22×D32—32no—
90C22×D32—31no—
91C22×C32×C4—31no—
92C2×#638C2×D312yes—
93C22×C3⋊Dic3—32no—
94C22×C3⋊Dic3—31no—
95C22×C3⋊Dic3—61no—
96C22×C3⋊Dic3—62no—
97C22×C3⋊Dic3—121no—
98C2×C4×C3⋊D3—32no—
99C2×C3×#67—32no—
100C2×C3×#67—32no—
101C2×C3×#67—62no—
102C22×C3×Dic3—21no—
103C22×C3×Dic3C2×D312yescomplemented
104C2×C3×C4×D3—32no—
105C2×C3×C4×D3—32no—
106C2×C3×C4×D3—32no—
107C2×C3×C4×D3—32no—
108#3811—38no—
109D3×#67—316no—
110C2×#626—32no—
111C2×#626—32no—
112C2×#625—32no—
113C2×#624—31no—
114C2×#624C2×D311yescharacteristic, complemented
115C2×#624C2×D311yescharacteristic, complemented
116C2×#624C2×D312yescomplemented
117C2×D3×Dic3—32no—
118C2×D3×Dic3—32no—
119C2×D3×Dic3—32no—
120C2×D3×Dic3—62no—
121C32×C22⋊C4—32no—
122#3752—32no—
123#3752—32no—
124#3752—32no—
125#3750—32no—
126C4×C3⋊Dic3—32no—
127C3×#217—22no—
128C3×#217C2×D312yescomplemented
129C3×#217C2×D312yescomplemented
130C3×(C2×D3)⋊C4—32no—
131C3×(C2×D3)⋊C4—32no—
132C3×(C2×D3)⋊C4—32no—
133C3×(C2×D3)⋊C4—32no—
134C3×Dic3⋊C4—32no—
135C3×Dic3⋊C4—32no—
136C3×C4×Dic3—32no—
137C3×C4×Dic3—32no—
138#3724C2×D312yescomplemented
139Dic3⋊Dic3—32no—
140Dic3⋊Dic3—32no—
141Dic3⋊Dic3—62no—
142#3722C2×D312yes—
143#3722C2×D312yescomplemented
144(C2×D3)⋊Dic3—32no—
145(C2×D3)⋊Dic3—32no—
146(C2×D3)⋊Dic3—32no—
147(C2×D3)⋊Dic3—32no—
148(C2×D3)⋊Dic3—32no—
149(C2×D3)⋊Dic3—32no—
150(C2×D3)⋊Dic3—62no—
151(C2×D3)⋊Dic3—62no—
152(C2×D3)⋊Dic3—62no—
153Dic32—32no—
154Dic32—32no—
155Dic32—62no—
156Dic32C2×D312yescomplemented
157C22×C33—21no—
158C22×C33—21no—
159C22×C33C22×C412yes—
160C22×C33C2411yescharacteristic
161C2×C3×C3⋊D3—22no—
162C2×C3×C3⋊D3—21no—
163C2×C3×C3⋊D3—21no—
164C2×C3×C3⋊D3—22no—
165C2×C3×C3⋊D3—21no—
166C2×C3×C3⋊D3—21no—
167C2×C3×C3⋊D3—44no—
168C2×C3×C3⋊D3C22×C412yes—
169C2×C3×C3⋊D3C22×C412yes—
170C2×C3×C3⋊D3C22×C414yes—
171#1113—44no—
172C3⋊(C3⋊Dic3)—22no—
173C3×C3⋊Dic3C22×C414yes—
174C32×Dic3—22no—
175C32×Dic3—22no—
176C32×Dic3—22no—
177C22×#67—91no—
178C2×D3×D4—92no—
179C3×C4×D4—92no—
180C2×C3×C22⋊C4—91no—
181C2×#217—91no—
182D4×Dic3—92no—
183C4×#67—32no—
184C4×#67—92no—
185C4×#67—92no—
186C4×#67—92no—
187C2×(C2×D3)⋊C4—92no—
188C2×(C2×D3)⋊C4—92no—
189C2×(C2×D3)⋊C4—181no—
190#893—92no—
191#892—92no—
192#67⋊C4—32no—
193#67⋊C4—92no—
194#67⋊C4—92no—
195#67⋊C4—92no—
196#67⋊C4—182no—
197D3×C22⋊C4—32no—
198D3×C22⋊C4—92no—
199D3×C22⋊C4—92no—
200#877—92no—
201C4×D12—92no—
202#872—92no—
203C23×C32—21no—
204C23×C32—22no—
205C23×C32—41no—
206C23×C32C22×D312yes—
207C23×C32C22×D311yescharacteristic
208C22×C3⋊D3—41no—
209C22×C3⋊D3—41no—
210C22×C3⋊D3C4×D314yescomplemented
211C22×C3⋊D3C22×D311yescharacteristic
212C22×C3⋊D3C22×D312yes—
213C22×C3⋊D3C22×D311yescharacteristic
214C22×C3×D3—32no—
215C22×C3×D3—32no—
216C22×C3×D3—32no—
217C22×C3×D3—32no—
218C22×C3×D3—38no—
219C22×C3×D3—61no—
220C22×C3×D3—61no—
221C22×C3×D3—64no—
222C22×C3×D3—62no—
223C22×C3×D3—122no—
224C22×C3×D3—122no—
225C22×C3×D3—122no—
226C22×C3×D3—122no—
227C2×D32—38no—
228C2×D32—34no—
229C2×D32—121no—
230C2×D32—121no—
231C2×D32—122no—
232C2×D32—122no—
233C2×C32×C4—32no—
234C2×C32×C4—32no—
235C2×C32×C4—32no—
236C2×C32×C4—121no—
237#638C4×D318yescomplemented
238C2×C3⋊Dic3—32no—
239C2×C3⋊Dic3—32no—
240C2×C3⋊Dic3—32no—
241C2×C3⋊Dic3—62no—
242C2×C3⋊Dic3—62no—
243C2×C3⋊Dic3—62no—
244C2×C3⋊Dic3—122no—
245C2×C3⋊Dic3—122no—
246C2×C3⋊Dic3—121no—
247C2×C3⋊Dic3—124no—
248C2×C3⋊Dic3—122no—
249C2×C3⋊Dic3—124no—
250C2×C3⋊Dic3C22×D312yes—
251C4×C3⋊D3—122no—
252C3×#67—38no—
253C3×#67—38no—
254C3×#67—68no—
255C2×C3×Dic3—22no—
256C2×C3×Dic3—22no—
257C2×C3×Dic3—22no—
258C2×C3×Dic3—32no—
259C2×C3×Dic3—32no—
260C2×C3×Dic3—42no—
261C2×C3×Dic3—42no—
262C2×C3×Dic3—62no—
263C2×C3×Dic3C22×D312yes—
264C2×C3×Dic3C22×D312yes—
265C2×C3×Dic3C22×D312yes—
266C2×C3×Dic3C22×D312yes—
267C2×C3×Dic3C22×D312yes—
268C2×C3×Dic3C22×D312yes—
269C3×C4×D3—122no—
270C3×C4×D3—122no—
271C3×C4×D3—122no—
272C3×C4×D3—122no—
273#626—38no—
274#626—38no—
275#625—38no—
276#624—34no—
277#624—41no—
278#624—41no—
279#624—42no—
280D3×Dic3—38no—
281D3×Dic3—122no—
282D3×Dic3—122no—
283D3×Dic3—124no—
284#518—271noSylow
285C2×C33—22no—
286C2×C33C23×C411yescharacteristic
287C2×C33H(5,𝔽2)11yescharacteristic
288C2×C33H(5,𝔽2)11yescharacteristic
289C3×C3⋊D3—22no—
290C3×C3⋊D3—24no—
291C3×C3⋊D3—22no—
292C24×C3—91no—
293C23×D3—32no—
294C23×D3—61no—
295C23×D3—91no—
296C23×D3—92no—
297C2×C3×D4—92no—
298C22×C3×C4—32no—
299C22×C3×C4—61no—
300C22×C3×C4—92no—
301C22×C3×C4—91no—
302C22×C3×C4—91no—
303C2×#67—32no—
304C2×#67—32no—
305C2×#67—62no—
306C2×#67—92no—
307C2×#67—92no—
308C2×#67—98no—
309C22×Dic3—91no—
310C22×Dic3—91no—
311C22×Dic3—92no—
312C22×Dic3—92no—
313C22×Dic3—182no—
314C22×Dic3—181no—
315C22×Dic3—361no—
316C22×Dic3D3211yescharacteristic, complemented
317D3×D4—916no—
318C2×D12—92no—
319C2×C4×D3—32no—
320C2×C4×D3—32no—
321C2×C4×D3—32no—
322C2×C4×D3—32no—
323C2×C4×D3—92no—
324C2×C4×D3—92no—
325C2×C4×D3—92no—
326C2×C4×D3—182no—
327C3×C4⋊C4—92no—
328C3×C22⋊C4—32no—
329C3×C22⋊C4—32no—
330C3×C22⋊C4—62no—
331C3×C22⋊C4—92no—
332C3×C22⋊C4—92no—
333C3×C42—92no—
334#217—92no—
335#217—92no—
336#217—92no—
337#217D3212yescomplemented
338(C2×D3)⋊C4—32no—
339(C2×D3)⋊C4—32no—
340(C2×D3)⋊C4—32no—
341(C2×D3)⋊C4—32no—
342(C2×D3)⋊C4—92no—
343(C2×D3)⋊C4—92no—
344(C2×D3)⋊C4—92no—
345(C2×D3)⋊C4—92no—
346(C2×D3)⋊C4—92no—
347(C2×D3)⋊C4—92no—
348(C2×D3)⋊C4—182no—
349(C2×D3)⋊C4—182no—
350(C2×D3)⋊C4—182no—
351C4⋊Dic3—92no—
352Dic3⋊C4—32no—
353Dic3⋊C4—32no—
354Dic3⋊C4—92no—
355Dic3⋊C4—92no—
356Dic3⋊C4—182no—
357C4×Dic3—32no—
358C4×Dic3—32no—
359C4×Dic3—92no—
360C4×Dic3—92no—
361C4×Dic3—92no—
362C4×Dic3—182no—
363C22×C32—21no—
364C22×C32—21no—
365C22×C32—22no—
366C22×C32—22no—
367C22×C32—22no—
368C22×C32—22no—
369C22×C32—22no—
370C22×C32—21no—
371C22×C32—22no—
372C22×C32—24no—
373C22×C32—42no—
374C22×C32—41no—
375C22×C32—42no—
376C22×C32—42no—
377C22×C32—42no—
378C22×C32—42no—
379C22×C32C2×C4×D312yes—
380C22×C32C2×C4×D314yes—
381C22×C32C23×D311yescharacteristic
382C22×C32C23×D312yes—
383C2×C3⋊D3—22no—
384C2×C3⋊D3—21no—
385C2×C3⋊D3—21no—
386C2×C3⋊D3—21no—
387C2×C3⋊D3—21no—
388C2×C3⋊D3—22no—
389C2×C3⋊D3—44no—
390C2×C3⋊D3C2×C4×D312yes—
391C2×C3⋊D3C2×C4×D312yes—
392C2×C3⋊D3C2×C4×D314yes—
393C2×C3×D3—34no—
394C2×C3×D3—34no—
395C2×C3×D3—34no—
396C2×C3×D3—34no—
397C2×C3×D3—64no—
398C2×C3×D3—62no—
399C2×C3×D3—62no—
400C2×C3×D3—62no—
401C2×C3×D3—62no—
402C2×C3×D3—62no—
403C2×C3×D3—62no—
404C2×C3×D3—62no—
405C2×C3×D3—62no—
406C2×C3×D3—62no—
407C2×C3×D3—62no—
408C2×C3×D3—122no—
409C2×C3×D3—122no—
410C2×C3×D3—121no—
411C2×C3×D3—121no—
412C2×C3×D3—121no—
413C2×C3×D3—121no—
414C2×C3×D3—128no—
415C2×C3×D3—128no—
416D32—124no—
417D32—128no—
418C32×C4—62no—
419C32×C4—62no—
420C32×C4—62no—
421C3⋊Dic3—62no—
422C3⋊Dic3—64no—
423C3⋊Dic3—62no—
424C3⋊Dic3—62no—
425C3⋊Dic3—122no—
426C3⋊Dic3—122no—
427C3⋊Dic3—124no—
428C3⋊Dic3C2×C4×D314yes—
429C3×Dic3—22no—
430C3×Dic3—22no—
431C3×Dic3—22no—
432C3×Dic3—22no—
433C3×Dic3—22no—
434C3×Dic3—22no—
435C3×Dic3—34no—
436C3×Dic3—34no—
437C3×Dic3—42no—
438C3×Dic3—42no—
439C3×Dic3—42no—
440C3×Dic3—64no—
441C22×D4—271no—
442C4×D4—92no—
443C4×D4—272no—
444C4×D4—272no—
445C4×D4—272no—
446#117—272no—
447C2×C22⋊C4—91no—
448C2×C22⋊C4—272no—
449C2×C22⋊C4—271no—
450C33#51811yescharacteristic, complemented, Sylow
451C23×C3—21no—
452C23×C3—22no—
453C23×C3—41no—
454C23×C3—91no—
455C23×C3—91no—
456C23×C3—92no—
457C23×C3—94no—
458C23×C3—361no—
459C23×C3—361no—
460C23×C3C2×D3212yes—
461C23×C3C2×D3211yescharacteristic
462C22×D3—32no—
463C22×D3—32no—
464C22×D3—32no—
465C22×D3—32no—
466C22×D3—38no—
467C22×D3—64no—
468C22×D3—61no—
469C22×D3—61no—
470C22×D3—62no—
471C22×D3—98no—
472C22×D3—94no—
473C22×D3—122no—
474C22×D3—122no—
475C22×D3—122no—
476C22×D3—122no—
477C22×D3—361no—
478C22×D3—362no—
479C22×D3—362no—
480C22×D3—361no—
481C3×D4—98no—
482C2×C3×C4—32no—
483C2×C3×C4—32no—
484C2×C3×C4—32no—
485C2×C3×C4—32no—
486C2×C3×C4—32no—
487C2×C3×C4—32no—
488C2×C3×C4—62no—
489C2×C3×C4—62no—
490C2×C3×C4—62no—
491C2×C3×C4—92no—
492C2×C3×C4—122no—
493C2×C3×C4—122no—
494C2×C3×C4—361no—
495C2×C3×C4—362no—
496C2×C3×C4—361no—
497#67—38no—
498#67—38no—
499#67—68no—
500#67—98no—
501#67—98no—
502C2×Dic3—32no—
503C2×Dic3—32no—
504C2×Dic3—41no—
505C2×Dic3—62no—
506C2×Dic3—94no—
507C2×Dic3—92no—
508C2×Dic3—92no—
509C2×Dic3—92no—
510C2×Dic3—182no—
511C2×Dic3—182no—
512C2×Dic3—182no—
513C2×Dic3—362no—
514C2×Dic3—362no—
515C2×Dic3—361no—
516C2×Dic3—362no—
517C2×Dic3—364no—
518C2×Dic3—362no—
519C2×Dic3—364no—
520C2×Dic3C2×D3212yes—
521C2×Dic3C2×D3212yes—
522C2×Dic3C2×D3212yes—
523D12—98no—
524C4×D3—98no—
525C4×D3—122no—
526C4×D3—122no—
527C4×D3—122no—
528C4×D3—122no—
529C4×D3—362no—
530C4×D3—362no—
531C4×D3—364no—
532C2×C32—22no—
533C2×C32—24no—
534C2×C32—24no—
535C2×C32—22no—
536C2×C32—21no—
537C2×C32—21no—
538C2×C32—22no—
539C2×C32—22no—
540C2×C32—21no—
541C2×C32—41no—
542C2×C32—41no—
543C2×C32—41no—
544C2×C32—44no—
545C2×C32—44no—
546C2×C32C22×C4×D311yescharacteristic
547C2×C32C22×C4×D312yes—
548C2×C32#100411yescharacteristic
549C2×C32#100412yes—
550C2×C32#100411yescharacteristic
551C2×C32#100912yes—
552C3⋊D3—22no—
553C3⋊D3—22no—
554C3⋊D3—24no—
555C3×D3—64no—
556C3×D3—64no—
557C3×D3—64no—
558C3×D3—64no—
559C3×D3—124no—
560C3×D3—122no—
561C3×D3—122no—
562C24—91no—
563C24—271no—
564C2×D4—92no—
565C2×D4—272no—
566C2×D4—278no—
567C22×C4—31no—
568C22×C4—91no—
569C22×C4—91no—
570C22×C4—92no—
571C22×C4—272no—
572C22×C4—271no—
573C22×C4—271no—
574C4⋊C4—92no—
575C4⋊C4—272no—
576C22⋊C4—32no—
577C22⋊C4—92no—
578C22⋊C4—92no—
579C22⋊C4—272no—
580C22⋊C4—272no—
581C22⋊C4—272no—
582C42—92no—
583C42—272no—
584C22×C3—22no—
585C22×C3—22no—
586C22×C3—21no—
587C22×C3—22no—
588C22×C3—22no—
589C22×C3—21no—
590C22×C3—22no—
591C22×C3—21no—
592C22×C3—22no—
593C22×C3—24no—
594C22×C3—42no—
595C22×C3—42no—
596C22×C3—42no—
597C22×C3—42no—
598C22×C3—41no—
599C22×C3—42no—
600C22×C3—92no—
601C22×C3—92no—
602C22×C3—94no—
603C22×C3—181no—
604C22×C3—181no—
605C22×C3—182no—
606C22×C3—182no—
607C22×C3—181no—
608C22×C3—181no—
609C22×C3—364no—
610C22×C3C4×D3212yes—
611C22×C3C4×D3214yes—
612C22×C3C22×D3211yescharacteristic
613C22×C3C22×D3212yes—
614C2×D3—34no—
615C2×D3—34no—
616C2×D3—34no—
617C2×D3—34no—
618C2×D3—64no—
619C2×D3—62no—
620C2×D3—62no—
621C2×D3—62no—
622C2×D3—62no—
623C2×D3—62no—
624C2×D3—62no—
625C2×D3—62no—
626C2×D3—62no—
627C2×D3—62no—
628C2×D3—62no—
629C2×D3—122no—
630C2×D3—121no—
631C2×D3—121no—
632C2×D3—121no—
633C2×D3—121no—
634C2×D3—122no—
635C2×D3—128no—
636C2×D3—128no—
637C2×D3—368no—
638C2×D3—364no—
639C3×C4—62no—
640C3×C4—62no—
641C3×C4—62no—
642C3×C4—62no—
643C3×C4—62no—
644C3×C4—62no—
645C3×C4—94no—
646C3×C4—122no—
647C3×C4—122no—
648C3×C4—122no—
649Dic3—22no—
650Dic3—22no—
651Dic3—22no—
652Dic3—34no—
653Dic3—34no—
654Dic3—64no—
655Dic3—184no—
656Dic3—182no—
657Dic3—182no—
658Dic3—182no—
659Dic3—362no—
660Dic3—362no—
661Dic3—364no—
662C32—22no—
663C32—21no—
664C32—41no—
665C32#548611yescharacteristic, complemented
666C32#554512yescomplemented
667C23—91no—
668C23—92no—
669C23—91no—
670C23—94no—
671C23—274no—
672C23—361no—
673C23—361no—
674C23—1081no—
675C23—1081no—
676C23D3311yescharacteristic
677D4—98no—
678D4—278no—
679C2×C4—32no—
680C2×C4—32no—
681C2×C4—32no—
682C2×C4—92no—
683C2×C4—121no—
684C2×C4—274no—
685C2×C4—272no—
686C2×C4—362no—
687C2×C4—361no—
688C2×C4—361no—
689C2×C4—1082no—
690C2×C4—1081no—
691C2×C3—24no—
692C2×C3—24no—
693C2×C3—22no—
694C2×C3—22no—
695C2×C3—21no—
696C2×C3—21no—
697C2×C3—22no—
698C2×C3—22no—
699C2×C3—21no—
700C2×C3—44no—
701C2×C3—44no—
702C2×C3—41no—
703C2×C3—41no—
704C2×C3—41no—
705C2×C3—184no—
706C2×C3—182no—
707C2×C3—182no—
708C2×C3C2×C4×D3212yes—
709C2×C3C2×C4×D3211yescharacteristic
710C2×C3#6430811yescharacteristic
711C2×C3#6431312yes—
712C2×C3#6431412yes—
713C2×C3#6433011yescharacteristic
714D3—64no—
715D3—64no—
716D3—64no—
717D3—64no—
718D3—122no—
719D3—122no—
720D3—124no—
721C22—21no—
722C22—21no—
723C22—92no—
724C22—94no—
725C22—92no—
726C22—181no—
727C22—182no—
728C22—181no—
729C22—181no—
730C22—182no—
731C22—181no—
732C22—364no—
733C22—1084no—
734C22#8894912yes—
735C22C2×D3311yescharacteristic
736C4—62no—
737C4—62no—
738C4—62no—
739C4—94no—
740C4—542no—
741C3—21no—
742C3—22no—
743C3—41no—
744C3#1059425412yescomplemented
745C3#1059505811yescharacteristic, complemented
746C2—22no—
747C2—182no—
748C2—182no—
749C2—184no—
750C2C2×#8894911yescharacteristic
751C2#1172441511yescharacteristic
752C2#1172442011yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutatorC2×C33C23×C4
FittingC23×C33C23
socle, cosocleC22×C33C24
prime radicalC2×#89049C2
hypercenterC23D33
hypocenterC33#518
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
2. #11723626C2semidirect
3. C2×#88803C2semidirect
4. C3×#63974C2semidirect
5. C3×#63952C2semidirect
6. #11722934C2semidirect
7. #11722931C2semidirect
8. #11722922C2semidirect
9. #11722905C2semidirect
14. C22×C3⋊(C3⋊Dic3)C22semidirect
16. C22×C32×Dic3C22semidirect
17. #89049C4semidirect
20. C2×Dic3×C3⋊D3C22semidirect
21. C2×C3×#624C22semidirect
22. C2×C3×#624C22semidirect
23. C2×C3×#624C22semidirect
24. C32×#217C22semidirect
25. #88807C22semidirect
27. #88803C22semidirect
28. #88803C22semidirect
29. Dic3×C3⋊Dic3C22semidirect
30. C3×#3724C22semidirect
32. C3×#3722C22semidirect
33. C3×Dic32C22semidirect
41. #63974D3semidirect
47. #63952D3semidirect
63. C22×C3×C3⋊D3C2×C4semidirect
69. C2×#1113C2×C4semidirect
72. C3×#638C2×C4semidirect
78. #6295C2×C4semidirect
79. #6294C2×C4semidirect
103. C22×C3×Dic3C2×D3semidirect
114. C2×#624C2×D3semidirect
115. C2×#624C2×D3semidirect
116. C2×#624C2×D3semidirect
128. C3×#217C2×D3semidirect
129. C3×#217C2×D3semidirect
138. #3724C2×D3semidirect
143. #3722C2×D3semidirect
156. Dic32C2×D3semidirect
210. C22×C3⋊D3C4×D3semidirect
237. #638C4×D3semidirect
316. C22×Dic3D32semidirect
337. #217D32semidirect
450. C33#518semidirect
665. C32#5486semidirect
666. C32#5545semidirect
744. C3#10594254semidirect
745. C3#10595058semidirect

Maximal subgroups

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

subgroupindex
C2×#890492
#117236262
C2×#888032
C3×#639742
C3×#639522
#117229342
#117229312
#117229222
#117229052
#105950583
#105942543