Finite Group Databasebeta

← #13172135

Subgroups — #13172135

Order 1728.

1638 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6294C211yesmaximal, characteristic, complemented
2C2×C3×#3805C211yesmaximal, characteristic, complemented
3#11723634C211yesmaximal, characteristic, complemented
4#11723602C211yesmaximal, characteristic, complemented
5#11723595C211yesmaximal, characteristic, complemented
6C3×#63981C211yesmaximal, characteristic, complemented
7C3×#63962C211yesmaximal, characteristic, complemented
8#11722979C212yesmaximal, complemented
9#11722965C212yesmaximal, complemented
10#11722936C212yesmaximal, complemented
11#11722927C212yesmaximal, complemented
12#10595159—31nomaximal
13#10595154—31nomaximal
14#10594082—31nomaximal
15C23×C3×C3⋊D3C2211yescharacteristic
16C22×C3×C3⋊Dic3C2211yescharacteristic
17C22×C3×C3⋊Dic3C2211yescharacteristic
18C2×C32×#67C2211yescharacteristic
19C2×C32×#67C2211yescharacteristic
20C2×#6294—24no—
21C2×#6294C2212yes—
22C2×#6294C2212yes—
23C2×#6290C2212yes—
24C2×C3×#627C2211yescharacteristic, complemented
25C2×C3×#626C2212yes—
26C2×C3×#625C2211yescharacteristic, complemented
27C3×#3805—24no—
28C2×C3×D3×Dic3C2211yescharacteristic, complemented
29C2×C3×D3×Dic3C2211yescharacteristic, complemented
30#88864C2211yescharacteristic
31C32×#217C2211yescharacteristic
32#88807C2212yescomplemented
33#88806C2212yescomplemented
34#88803C2212yes—
35(C2×D3)⋊(C3⋊Dic3)C2212yescomplemented
36Dic3×C3⋊Dic3C2212yescomplemented
37C3×Dic3⋊Dic3C2212yescomplemented
38C3×#3722C2212yes—
39C3×(C2×D3)⋊Dic3C2212yescomplemented
40C2×C3×#237—31no—
41C2×C3×#237—31no—
42C22×#624—31no—
43C2×#3805D311yescharacteristic, complemented
44C22×D3×Dic3—31no—
45C22×D3×Dic3—31no—
46#64146—31no—
47#64144—31no—
48#64086—31no—
49C3×#937—31no—
50C3×#935—31no—
51C3×#886—31no—
52C3×#882—31no—
53#63981D311yescharacteristic, complemented
54#63976—31no—
55#63976—31no—
56#63976—61no—
57Dic3×#67—32no—
58#63970—32no—
59#63962D311yescharacteristic, complemented
60#63961—31no—
61#63961—31no—
62#63961—61no—
63#63958—32no—
64#63955—31no—
65#63955—31no—
66#63955—61no—
67#63952—32no—
68#63904—32no—
69#63902—32no—
70#63899—32no—
71#63898—32no—
72#63888—32no—
73#63887—32no—
74#63885—32no—
75#63879—32no—
76C23×C33C2311yescharacteristic
77C22×C3×C3⋊D3—22no—
78C22×C3×C3⋊D3—24no—
79C22×C3×C3⋊D3C2312yes—
80C22×C32×D3C2311yescharacteristic
81C22×C32×D3C2311yescharacteristic
82C2×C3⋊(C3⋊Dic3)C2312yes—
83C2×C3×C3⋊Dic3—22no—
84C2×C3×C3⋊Dic3D414yescomplemented
85C2×C3×C3⋊Dic3C2312yes—
86C2×C3×C3⋊Dic3C2311yescharacteristic
87C2×C3×C3⋊Dic3C2311yescharacteristic
88C32×#67—22no—
89C32×#67—22no—
90C2×C32×Dic3C2312yes—
91C2×C32×Dic3C2311yescharacteristic
92C2×C32×Dic3C2311yescharacteristic
93#6294—24no—
94#6294—24no—
95#6290—24no—
96C3×#627—22no—
97C3×#626—24no—
98C3×#625—22no—
99C3×D3×Dic3—22no—
100C3×D3×Dic3—22no—
101#5828—91no—
102#5656—91no—
103#5586—91no—
104C23×C3⋊D3C2×D311yescharacteristic
105C23×C3×D3—31no—
106C23×C3×D3—31no—
107C23×C3×D3—61no—
108C2×C32×D4—31no—
109C2×C32×D4—31no—
110C2×#638—32no—
111C22×C3⋊Dic3C2×D311yescharacteristic
112C22×C3⋊Dic3C2×D311yescharacteristic
113C2×C3×#67—21no—
114C2×C3×#67—21no—
115C2×C3×#67—31no—
116C2×C3×#67—31no—
117C2×C3×#67—32no—
118C2×C3×#67C2×D311yescharacteristic
119C2×C3×#67C2×D311yescharacteristic
120C2×C3×#67C2×D311yescharacteristic
121C2×C3×#67C2×D311yescharacteristic
122C22×C3×Dic3—31no—
123C22×C3×Dic3—31no—
124C22×C3×Dic3—31no—
125C22×C3×Dic3—31no—
126C22×C3×Dic3—31no—
127C22×C3×Dic3—31no—
128C22×C3×Dic3—61no—
129C22×C3×Dic3—61no—
130C3×#237—64no—
131C3×#237—64no—
132C2×C3×D12—32no—
133C2×C3×C4×D3—31no—
134C2×C3×C4×D3—31no—
135C2×C3×Dic6—31no—
136C2×C3×Dic6—31no—
137C2×#627C2×D311yescharacteristic, complemented
138C2×#626C2×D312yes—
139C2×#625—32no—
140C2×#625—32no—
141C2×#625—62no—
142C2×#625C2×D311yescharacteristic, complemented
143C2×#624—32no—
144C2×#624—32no—
145C2×#624—64no—
146#3805—24no—
147C2×D3×Dic3—32no—
148C2×D3×Dic3—32no—
149C2×D3×Dic3—32no—
150C2×D3×Dic3—32no—
151C2×D3×Dic3—64no—
152C2×D3×Dic3—64no—
153C2×D3×Dic3C2×D311yescharacteristic, complemented
154C2×D3×Dic3C2×D311yescharacteristic, complemented
155C32×C22⋊C4—31no—
156#3757—31no—
157#3757—31no—
158#3757—31no—
159#3757—32no—
160#3757—61no—
161#3757—61no—
162#3757—61no—
163#3757—121no—
164#3752—32no—
165#3750—32no—
166#3750—32no—
167C4×C3⋊Dic3—32no—
168C3×#217—21no—
169C3×#217—32no—
170C3×#217C2×D311yescharacteristic
171C3×#217C2×D311yescharacteristic
172C3×(C2×D3)⋊C4—32no—
173C3×(C2×D3)⋊C4—32no—
174C3×(C2×D3)⋊C4—32no—
175C3×C4⋊Dic3—32no—
176C3×Dic3⋊C4—32no—
177#3724—32no—
178#3724—32no—
179#3724—62no—
180Dic3⋊Dic3—32no—
181Dic3⋊Dic3—32no—
182Dic3⋊Dic3—62no—
183Dic3⋊Dic3C2×D312yescomplemented
184#3722C2×D312yes—
185(C2×D3)⋊Dic3—32no—
186(C2×D3)⋊Dic3—32no—
187(C2×D3)⋊Dic3—32no—
188(C2×D3)⋊Dic3—32no—
189(C2×D3)⋊Dic3—62no—
190(C2×D3)⋊Dic3—62no—
191(C2×D3)⋊Dic3C2×D312yescomplemented
192Dic32—32no—
193Dic32—32no—
194Dic32—62no—
195C22×C33—22no—
196C22×C33C2×D412yes—
197C22×C33C2411yescharacteristic
198C2×C3×C3⋊D3—28no—
199C2×C3×C3⋊D3—22no—
200C2×C3×C3⋊D3—22no—
201C2×C3×C3⋊D3#4114yescomplemented
202C2×C32×D3—21no—
203C2×C32×D3—21no—
204C2×C32×D3—22no—
205C2×C32×D3—22no—
206C3⋊(C3⋊Dic3)—22no—
207C3×C3⋊Dic3—22no—
208C3×C3⋊Dic3C2×D412yes—
209C3×C3⋊Dic3C2×D412yes—
210C32×Dic3—21no—
211C32×Dic3—21no—
212C32×Dic3—22no—
213C2×C3×#41—91no—
214C23×Dic3—91no—
215C2×#237—31no—
216C2×#237—31no—
217C22×C4×D3—91no—
218C22×C4×D3—91no—
219C3×#123—91no—
220C3×#120—91no—
221#953—91no—
222#946—92no—
223#939—92no—
224#938—92no—
225#937—31no—
226#937—91no—
227#937—91no—
228#937—181no—
229#935—31no—
230#935—91no—
231#935—91no—
232#935—181no—
233D4×Dic3—92no—
234#929—91no—
235C4×#67—92no—
236C4×#67—92no—
237#926—91no—
238#896—92no—
239#893—92no—
240#886—31no—
241#884—92no—
242#882—31no—
243#67⋊C4—92no—
244#67⋊C4—92no—
245#878—92no—
246#877—91no—
247#877—91no—
248#877—181no—
249C23×C32—21no—
250C23×C32—21no—
251C23×C32—21no—
252C23×C32—31no—
253C23×C32—31no—
254C23×C32—41no—
255C23×C32C22×D311yescharacteristic
256C23×C32C22×D311yescharacteristic
257C23×C32C22×D311yescharacteristic
258C22×C3⋊D3—22no—
259C22×C3⋊D3—24no—
260C22×C3⋊D3C22×D312yes—
261C22×C3×D3—21no—
262C22×C3×D3—21no—
263C22×C3×D3—32no—
264C22×C3×D3—32no—
265C22×C3×D3—62no—
266C22×C3×D3—64no—
267C22×C3×D3—64no—
268C22×C3×D3—62no—
269C22×C3×D3—62no—
270C22×C3×D3—124no—
271C22×C3×D3—122no—
272C22×C3×D3C22×D311yescharacteristic
273C22×C3×D3C22×D311yescharacteristic
274C22×C3×D3C22×D311yescharacteristic
275C22×C3×D3C22×D311yescharacteristic
276C32×D4—62no—
277C32×D4—62no—
278C2×C32×C4—31no—
279C2×C32×C4—32no—
280C2×C32×C4—31no—
281#638—64no—
282C2×C3⋊Dic3—22no—
283C2×C3⋊Dic3—32no—
284C2×C3⋊Dic3—32no—
285C2×C3⋊Dic3—32no—
286C2×C3⋊Dic3—62no—
287C2×C3⋊Dic3—62no—
288C2×C3⋊Dic3—62no—
289C2×C3⋊Dic3—122no—
290C2×C3⋊Dic3#6714yescomplemented
291C2×C3⋊Dic3C22×D312yes—
292C2×C3⋊Dic3C22×D311yescharacteristic
293C2×C3⋊Dic3C22×D311yescharacteristic
294C3×#67—22no—
295C3×#67—22no—
296C3×#67—22no—
297C3×#67—22no—
298C3×#67—42no—
299C3×#67—42no—
300C3×#67—64no—
301C3×#67—62no—
302C3×#67—62no—
303C2×C3×Dic3—22no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3—34no—
307C2×C3×Dic3—34no—
308C2×C3×Dic3—31no—
309C2×C3×Dic3—31no—
310C2×C3×Dic3—31no—
311C2×C3×Dic3—31no—
312C2×C3×Dic3—32no—
313C2×C3×Dic3—32no—
314C2×C3×Dic3—61no—
315C2×C3×Dic3—61no—
316C2×C3×Dic3—64no—
317C2×C3×Dic3—62no—
318C2×C3×Dic3—62no—
319C2×C3×Dic3—62no—
320C2×C3×Dic3—62no—
321C2×C3×Dic3—62no—
322C2×C3×Dic3—122no—
323C2×C3×Dic3C22×D312yes—
324C2×C3×Dic3C22×D312yes—
325C2×C3×Dic3C22×D311yescharacteristic
326C2×C3×Dic3C22×D311yescharacteristic
327C2×C3×Dic3C22×D311yescharacteristic
328C2×C3×Dic3C22×D311yescharacteristic
329C3×D12—64no—
330C3×C4×D3—62no—
331C3×C4×D3—62no—
332C3×Dic6—62no—
333C3×Dic6—62no—
334#627—22no—
335#626—24no—
336#625—22no—
337#625—64no—
338#625—64no—
339#625—124no—
340#624—64no—
341#624—64no—
342D3×Dic3—22no—
343D3×Dic3—22no—
344D3×Dic3—64no—
345D3×Dic3—64no—
346D3×Dic3—64no—
347D3×Dic3—64no—
348#525—271noSylow
349C2×C33—22no—
350C2×C33C22×D411yescharacteristic
351C2×C33C2×#4112yes—
352C3×C3⋊D3—24no—
353C32×D3—41no—
354C32×D3—41no—
355C24×C3—91no—
356C23×D3—31no—
357C23×D3—31no—
358C23×D3—61no—
359C3×#41—184no—
360C2×C3×Q8—91no—
361C2×C3×D4—31no—
362C2×C3×D4—31no—
363C2×C3×D4—31no—
364C2×C3×D4—31no—
365C2×C3×D4—61no—
366C2×C3×D4—61no—
367C2×C3×D4—92no—
368C2×C3×D4—91no—
369C22×C3×C4—91no—
370C22×C3×C4—91no—
371C22×C3×C4—91no—
372C22×C3×C4—91no—
373C2×#67—31no—
374C2×#67—31no—
375C2×#67—32no—
376C2×#67—92no—
377C2×#67—92no—
378C2×#67—92no—
379C2×#67—182no—
380C2×#67D3211yescharacteristic
381C2×#67D3211yescharacteristic
382C22×Dic3—31no—
383C22×Dic3—31no—
384C22×Dic3—31no—
385C22×Dic3—31no—
386C22×Dic3—31no—
387C22×Dic3—31no—
388C22×Dic3—61no—
389C22×Dic3—61no—
390C22×Dic3—92no—
391C22×Dic3—92no—
392C22×Dic3—184no—
393#237—64no—
394#237—64no—
395C2×D12—32no—
396C2×C4×D3—31no—
397C2×C4×D3—31no—
398C2×C4×D3—92no—
399C2×C4×D3—92no—
400C2×C4×D3—92no—
401C2×C4×D3—92no—
402C2×C4×D3—184no—
403C2×C4×D3—184no—
404C2×Dic6—31no—
405C2×Dic6—31no—
406C3×C4⋊C4—92no—
407C3×C22⋊C4—31no—
408C3×C22⋊C4—31no—
409C3×C22⋊C4—61no—
410C3×C22⋊C4—92no—
411C3×C22⋊C4—92no—
412#217—32no—
413#217—92no—
414#217—92no—
415#217—91no—
416#217—91no—
417#217—91no—
418#217—92no—
419#217—182no—
420#217—181no—
421#217—181no—
422#217—181no—
423#217—361no—
424#217D3211yescharacteristic
425(C2×D3)⋊C4—32no—
426(C2×D3)⋊C4—32no—
427(C2×D3)⋊C4—32no—
428(C2×D3)⋊C4—92no—
429(C2×D3)⋊C4—92no—
430(C2×D3)⋊C4—92no—
431(C2×D3)⋊C4—182no—
432C4⋊Dic3—32no—
433C4⋊Dic3—92no—
434Dic3⋊C4—32no—
435Dic3⋊C4—92no—
436Dic3⋊C4—92no—
437Dic3⋊C4—92no—
438Dic3⋊C4—92no—
439Dic3⋊C4—92no—
440Dic3⋊C4—182no—
441Dic3⋊C4—182no—
442C4×Dic3—92no—
443C4×Dic3—92no—
444C4×Dic3—92no—
445C4×Dic3—182no—
446C22×C32—22no—
447C22×C32—22no—
448C22×C32—22no—
449C22×C32—21no—
450C22×C32—21no—
451C22×C32—21no—
452C22×C32—22no—
453C22×C32—22no—
454C22×C32—22no—
455C22×C32—41no—
456C22×C32—42no—
457C22×C32—42no—
458C22×C32—42no—
459C22×C32—42no—
460C22×C32—61no—
461C22×C32—61no—
462C22×C32—62no—
463C22×C32—62no—
464C22×C32—82no—
465C22×C32D3×D412yes—
466C22×C32D3×D412yes—
467C22×C32C2×#6712yes—
468C22×C32C23×D311yescharacteristic
469C22×C32C23×D311yescharacteristic
470C22×C32C23×D311yescharacteristic
471C2×C3⋊D3—28no—
472C2×C3⋊D3—22no—
473C2×C3⋊D3—22no—
474C2×C3⋊D3#23714yescomplemented
475C2×C3×D3—21no—
476C2×C3×D3—21no—
477C2×C3×D3—22no—
478C2×C3×D3—22no—
479C2×C3×D3—22no—
480C2×C3×D3—22no—
481C2×C3×D3—21no—
482C2×C3×D3—21no—
483C2×C3×D3—34no—
484C2×C3×D3—34no—
485C2×C3×D3—42no—
486C2×C3×D3—41no—
487C2×C3×D3—41no—
488C2×C3×D3—42no—
489C2×C3×D3—64no—
490C2×C3×D3—68no—
491C2×C3×D3—68no—
492C2×C3×D3—62no—
493C2×C3×D3—62no—
494C2×C3×D3—62no—
495C2×C3×D3—62no—
496C2×C3×D3—122no—
497C2×C3×D3—122no—
498C2×C3×D3—128no—
499C32×C4—61no—
500C32×C4—61no—
501C32×C4—62no—
502C3⋊Dic3—22no—
503C3⋊Dic3—62no—
504C3⋊Dic3—62no—
505C3⋊Dic3—62no—
506C3⋊Dic3—122no—
507C3⋊Dic3—122no—
508C3⋊Dic3—122no—
509C3⋊Dic3—242no—
510C3⋊Dic3C2×#6712yes—
511C3⋊Dic3C2×#6712yes—
512C3×Dic3—21no—
513C3×Dic3—21no—
514C3×Dic3—22no—
515C3×Dic3—22no—
516C3×Dic3—21no—
517C3×Dic3—21no—
518C3×Dic3—32no—
519C3×Dic3—32no—
520C3×Dic3—32no—
521C3×Dic3—32no—
522C3×Dic3—42no—
523C3×Dic3—41no—
524C3×Dic3—41no—
525C3×Dic3—62no—
526C3×Dic3—62no—
527C3×Dic3—62no—
528C3×Dic3—62no—
529C3×Dic3—122no—
530C2×#41—91no—
531C23×C4—271no—
532#123—91no—
533#123—271no—
534C22⋊Q8—272no—
535#121—272no—
536#120—91no—
537#120—271no—
538C4×D4—272no—
539C4×D4—272no—
540#117—271no—
541C33#52511yescharacteristic, complemented, Sylow
542C23×C3—21no—
543C23×C3—21no—
544C23×C3—21no—
545C23×C3—31no—
546C23×C3—31no—
547C23×C3—31no—
548C23×C3—31no—
549C23×C3—41no—
550C23×C3—61no—
551C23×C3—61no—
552C23×C3—92no—
553C23×C3—184no—
554C23×C3—182no—
555C23×C3C2×D3211yescharacteristic
556C23×C3C2×D3211yescharacteristic
557C23×C3C2×D3211yescharacteristic
558C22×D3—32no—
559C22×D3—32no—
560C22×D3—62no—
561C22×D3—64no—
562C22×D3—64no—
563C22×D3—62no—
564C22×D3—62no—
565C22×D3—124no—
566C22×D3—122no—
567C22×D3C2×D3211yescharacteristic
568C22×D3C2×D3211yescharacteristic
569C3×Q8—182no—
570C3×D4—62no—
571C3×D4—62no—
572C3×D4—62no—
573C3×D4—62no—
574C3×D4—122no—
575C3×D4—122no—
576C3×D4—184no—
577C3×D4—182no—
578C2×C3×C4—32no—
579C2×C3×C4—32no—
580C2×C3×C4—31no—
581C2×C3×C4—31no—
582C2×C3×C4—31no—
583C2×C3×C4—31no—
584C2×C3×C4—62no—
585C2×C3×C4—61no—
586C2×C3×C4—61no—
587C2×C3×C4—91no—
588C2×C3×C4—91no—
589C2×C3×C4—94no—
590C2×C3×C4—92no—
591C2×C3×C4—182no—
592C2×C3×C4—182no—
593C2×C3×C4—182no—
594#67—22no—
595#67—22no—
596#67—64no—
597#67—62no—
598#67—62no—
599#67—184no—
600#67—184no—
601#67—184no—
602#67—364no—
603C2×Dic3—31no—
604C2×Dic3—31no—
605C2×Dic3—31no—
606C2×Dic3—31no—
607C2×Dic3—34no—
608C2×Dic3—34no—
609C2×Dic3—32no—
610C2×Dic3—32no—
611C2×Dic3—64no—
612C2×Dic3—61no—
613C2×Dic3—61no—
614C2×Dic3—62no—
615C2×Dic3—62no—
616C2×Dic3—62no—
617C2×Dic3—62no—
618C2×Dic3—62no—
619C2×Dic3—92no—
620C2×Dic3—92no—
621C2×Dic3—92no—
622C2×Dic3—122no—
623C2×Dic3—182no—
624C2×Dic3—182no—
625C2×Dic3—182no—
626C2×Dic3—184no—
627C2×Dic3—184no—
628C2×Dic3—362no—
629C2×Dic3C2×D3212yes—
630C2×Dic3C2×D3211yescharacteristic
631C2×Dic3C2×D3211yescharacteristic
632D12—64no—
633C4×D3—62no—
634C4×D3—62no—
635C4×D3—184no—
636C4×D3—184no—
637C4×D3—184no—
638C4×D3—184no—
639Dic6—62no—
640Dic6—62no—
641C2×C32—22no—
642C2×C32—22no—
643C2×C32—22no—
644C2×C32—21no—
645C2×C32—22no—
646C2×C32—22no—
647C2×C32—22no—
648C2×C32—21no—
649C2×C32—21no—
650C2×C32—41no—
651C2×C32—42no—
652C2×C32—42no—
653C2×C32—42no—
654C2×C32—42no—
655C2×C32—82no—
656C2×C32—121no—
657C2×C32—121no—
658C2×C32C2×D3×D411yescharacteristic
659C2×C32C2×D3×D411yescharacteristic
660C2×C32C2×#23712yes—
661C2×C32D3×#4112yes—
662C2×C32D3×#4112yes—
663C2×C32C22×#6711yescharacteristic
664C3⋊D3—24no—
665C3×D3—41no—
666C3×D3—41no—
667C3×D3—41no—
668C3×D3—41no—
669C3×D3—64no—
670C3×D3—64no—
671C3×D3—81no—
672C3×D3—81no—
673C3×D3—124no—
674C24—91no—
675#41—184no—
676C2×Q8—91no—
677C2×D4—31no—
678C2×D4—31no—
679C2×D4—92no—
680C2×D4—91no—
681C2×D4—272no—
682C22×C4—91no—
683C22×C4—91no—
684C22×C4—91no—
685C22×C4—91no—
686C22×C4—272no—
687C22×C4—272no—
688C22×C4—544no—
689C4⋊C4—92no—
690C4⋊C4—272no—
691C4⋊C4—272no—
692C22⋊C4—31no—
693C22⋊C4—92no—
694C22⋊C4—92no—
695C22⋊C4—272no—
696C22⋊C4—272no—
697C22⋊C4—271no—
698C42—272no—
699C22×C3—22no—
700C22×C3—22no—
701C22×C3—22no—
702C22×C3—21no—
703C22×C3—21no—
704C22×C3—21no—
705C22×C3—22no—
706C22×C3—22no—
707C22×C3—22no—
708C22×C3—42no—
709C22×C3—42no—
710C22×C3—42no—
711C22×C3—41no—
712C22×C3—42no—
713C22×C3—61no—
714C22×C3—61no—
715C22×C3—62no—
716C22×C3—62no—
717C22×C3—62no—
718C22×C3—62no—
719C22×C3—61no—
720C22×C3—61no—
721C22×C3—82no—
722C22×C3—94no—
723C22×C3—122no—
724C22×C3—121no—
725C22×C3—121no—
726C22×C3—122no—
727C22×C3—188no—
728C22×C3—182no—
729C22×C3—182no—
730C22×C3#380212yes—
731C22×C3D3×#6712yes—
732C22×C3D3×#6712yes—
733C22×C3C22×D3211yescharacteristic
734C22×C3C22×D3211yescharacteristic
735C22×C3C22×D3211yescharacteristic
736C2×D3—22no—
737C2×D3—22no—
738C2×D3—21no—
739C2×D3—21no—
740C2×D3—34no—
741C2×D3—34no—
742C2×D3—64no—
743C2×D3—68no—
744C2×D3—68no—
745C2×D3—62no—
746C2×D3—62no—
747C2×D3—62no—
748C2×D3—62no—
749C2×D3—122no—
750C2×D3—122no—
751C2×D3—128no—
752C3×C4—61no—
753C3×C4—61no—
754C3×C4—62no—
755C3×C4—62no—
756C3×C4—61no—
757C3×C4—61no—
758C3×C4—92no—
759C3×C4—92no—
760C3×C4—121no—
761C3×C4—121no—
762C3×C4—122no—
763C3×C4—182no—
764Dic3—22no—
765Dic3—21no—
766Dic3—21no—
767Dic3—32no—
768Dic3—32no—
769Dic3—32no—
770Dic3—32no—
771Dic3—62no—
772Dic3—62no—
773Dic3—62no—
774Dic3—62no—
775Dic3—122no—
776Dic3—182no—
777Dic3—182no—
778Dic3—182no—
779Dic3—362no—
780Dic3—362no—
781Dic3—362no—
782Dic3—722no—
783C32—21no—
784C32—21no—
785C32—21no—
786C32—41no—
787C32#558611yescharacteristic, complemented
788C32#565611yescharacteristic, complemented
789C32#582811yescharacteristic, complemented
790C23—31no—
791C23—31no—
792C23—92no—
793C23—184no—
794C23—182no—
795C23D3311yescharacteristic
796Q8—182no—
797D4—62no—
798D4—62no—
799D4—184no—
800D4—182no—
801D4—544no—
802C2×C4—32no—
803C2×C4—31no—
804C2×C4—31no—
805C2×C4—91no—
806C2×C4—91no—
807C2×C4—94no—
808C2×C4—92no—
809C2×C4—182no—
810C2×C4—182no—
811C2×C4—182no—
812C2×C4—272no—
813C2×C4—544no—
814C2×C4—544no—
815C2×C3—22no—
816C2×C3—22no—
817C2×C3—22no—
818C2×C3—22no—
819C2×C3—22no—
820C2×C3—22no—
821C2×C3—21no—
822C2×C3—21no—
823C2×C3—21no—
824C2×C3—42no—
825C2×C3—42no—
826C2×C3—42no—
827C2×C3—42no—
828C2×C3—41no—
829C2×C3—82no—
830C2×C3—121no—
831C2×C3—121no—
832C2×C3—121no—
833C2×C3—121no—
834C2×C3—184no—
835C2×C3—241no—
836C2×C3—241no—
837C2×C3C2×#380211yescharacteristic
838C2×C3D3×#23712yes—
839C2×C3D3×#23712yes—
840C2×C3#6431212yes—
841C2×C3C2×D3×#6711yescharacteristic
842C2×C3C2×D3×#6711yescharacteristic
843D3—41no—
844D3—41no—
845D3—64no—
846D3—64no—
847D3—124no—
848C22—22no—
849C22—62no—
850C22—62no—
851C22—61no—
852C22—61no—
853C22—94no—
854C22—188no—
855C22—182no—
856C22—182no—
857C22#8895312yes—
858C22C2×D3311yescharacteristic
859C4—62no—
860C4—61no—
861C4—61no—
862C4—92no—
863C4—92no—
864C4—182no—
865C4—542no—
866C3—21no—
867C3—21no—
868C3—21no—
869C3—41no—
870C3#1059408211yescharacteristic, complemented
871C3#1059515411yescharacteristic, complemented
872C3#1059515911yescharacteristic, complemented
873C2—22no—
874C2—121no—
875C2—121no—
876C2—184no—
877C2#1172440812yes—
878C2C2×#8895311yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
hypercenterC23D33
hypocenterC33#525
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C22×#6294C2semidirect
2. C2×C3×#3805C2semidirect
3. #11723634C2semidirect
4. #11723602C2semidirect
5. #11723595C2semidirect
6. C3×#63981C2semidirect
7. C3×#63962C2semidirect
8. #11722979C2semidirect
9. #11722965C2semidirect
10. #11722936C2semidirect
11. #11722927C2semidirect
24. C2×C3×#627C22semidirect
26. C2×C3×#625C22semidirect
28. C2×C3×D3×Dic3C22semidirect
29. C2×C3×D3×Dic3C22semidirect
32. #88807C22semidirect
33. #88806C22semidirect
35. (C2×D3)⋊(C3⋊Dic3)C22semidirect
36. Dic3×C3⋊Dic3C22semidirect
37. C3×Dic3⋊Dic3C22semidirect
39. C3×(C2×D3)⋊Dic3C22semidirect
43. C2×#3805D3semidirect
53. #63981D3semidirect
59. #63962D3semidirect
84. C2×C3×C3⋊Dic3D4semidirect
137. C2×#627C2×D3semidirect
142. C2×#625C2×D3semidirect
153. C2×D3×Dic3C2×D3semidirect
154. C2×D3×Dic3C2×D3semidirect
183. Dic3⋊Dic3C2×D3semidirect
191. (C2×D3)⋊Dic3C2×D3semidirect
201. C2×C3×C3⋊D3#41semidirect
290. C2×C3⋊Dic3#67semidirect
474. C2×C3⋊D3#237semidirect
541. C33#525semidirect
787. C32#5586semidirect
788. C32#5656semidirect
789. C32#5828semidirect
870. C3#10594082semidirect
871. C3#10595154semidirect
872. C3#10595159semidirect

Maximal subgroups

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

subgroupindex
C22×#62942
C2×C3×#38052
#117236342
#117236022
#117235952
C3×#639812
C3×#639622
#117229792
#117229652
#117229362
#117229272
#105951593
#105951543
#105940823