Finite Group Databasebeta

← #13172107

Subgroups — #13172107

Order 1728.

1766 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Dic3×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×C3×#3804C211yesmaximal, characteristic, complemented
3#11723727C211yesmaximal, characteristic, complemented
4#11723609C211yesmaximal, characteristic, complemented
5#11723603C211yesmaximal, characteristic, complemented
6C3×#63981C211yesmaximal, characteristic, complemented
7C3×#63955C211yesmaximal, characteristic, complemented
8#11722974C212yesmaximal, complemented
9#11722962C212yesmaximal, complemented
10#11722934C212yesmaximal, complemented
11Dic3×#626C212yesmaximal, complemented
12#10595154—31nomaximal
13#10595034—31nomaximal
14#10594078—31nomaximal
15C23×C3×C3⋊D3C2211yescharacteristic
16C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
17C2×C3×#638C2211yescharacteristic
18C2×C32×#67C2211yescharacteristic
19C22×C32×Dic3C2211yescharacteristic
20C2×#6295C2212yes—
21C2×Dic3×C3⋊D3—24no—
22C2×Dic3×C3⋊D3C2212yes—
23C2×Dic3×C3⋊D3C2212yes—
24C2×C3×#627C2211yescharacteristic, complemented
25C2×C3×#626C2212yes—
26C2×C3×#626C2211yescharacteristic, complemented
27C2×C3×#624C2211yescharacteristic, complemented
28C3×#3804—24no—
29C2×C3×D3×Dic3C2211yescharacteristic, complemented
30C3×#3757C2211yescharacteristic
31C32×#217C2211yescharacteristic
32#88814C2212yes—
33#88807C2212yescomplemented
34Dic3⋊(C3⋊Dic3)C2212yescomplemented
35#88803C2212yescomplemented
36(C2×D3)⋊(C3⋊Dic3)C2212yescomplemented
37C3×Dic3⋊Dic3C2212yescomplemented
38C3×#3722C2212yes—
39C3×Dic32C2212yescomplemented
40C22×C4×C3⋊D3—31no—
41C2×C3×#237—31no—
42C2×C3×#235—31no—
43C2×#3804D311yescharacteristic, complemented
44C22×D3×Dic3—31no—
45C22×D3×Dic3—31no—
46C22×D3×Dic3—61no—
47#64144—31no—
48#64095—31no—
49C3×#937—31no—
50C3×#926—31no—
51C3×#882—31no—
52C3×#877—31no—
53#63981—31no—
54#63981D311yescharacteristic, complemented
55#63977—31no—
56#63976—31no—
57Dic3×#67—32no—
58#63970—32no—
59#63962—31no—
60#63962—31no—
61#63962—31no—
62#63962—31no—
63#63962—61no—
64#63962—61no—
65#63955D311yescharacteristic, complemented
66#63916—32no—
67C4×#626—32no—
68C4×#626—32no—
69#63893—32no—
70Dic3×D12—32no—
71#63887—32no—
72#63886—32no—
73#63880—32no—
74#63879—32no—
75#63871—32no—
76C23×C33C2311yescharacteristic
77C22×C3×C3⋊D3—22no—
78C22×C3×C3⋊D3—24no—
79C22×C3×C3⋊D3C2311yescharacteristic
80C22×C3×C3⋊D3C2312yes—
81C22×C32×D3C2311yescharacteristic
82C2×C3⋊(C3⋊Dic3)—22no—
83C2×C3⋊(C3⋊Dic3)C2312yes—
84C3×#638—22no—
85C2×C3×C3⋊Dic3C2312yes—
86C2×C3×C3⋊Dic3C2311yescharacteristic
87C32×#67—22no—
88C2×C32×Dic3D414yescomplemented
89C2×C32×Dic3C2312yes—
90C2×C32×Dic3C2311yescharacteristic
91C2×C32×Dic3C2311yescharacteristic
92C2×C32×Dic3C2311yescharacteristic
93#6295—24no—
94Dic3×C3⋊D3—24no—
95Dic3×C3⋊D3—24no—
96C3×#627—22no—
97C3×#626—24no—
98C3×#626—22no—
99C3×#624—22no—
100C3×D3×Dic3—22no—
101#5828—91no—
102#5586—91no—
103#5524—91no—
104C23×C3⋊D3C2×D311yescharacteristic
105C23×C3×D3—31no—
106C23×C3×D3—31no—
107C23×C3×D3—61no—
108C2×C32×D4—31no—
109C22×C32×C4—31no—
110C2×#638C2×D311yescharacteristic
111C22×C3⋊Dic3—31no—
112C22×C3⋊Dic3—31no—
113C22×C3⋊Dic3—31no—
114C22×C3⋊Dic3—61no—
115C22×C3⋊Dic3—61no—
116C22×C3⋊Dic3—61no—
117C22×C3⋊Dic3—121no—
118C2×C4×C3⋊D3—32no—
119C2×C4×C3⋊D3—32no—
120C2×C4×C3⋊D3—64no—
121C2×C3×#67—21no—
122C2×C3×#67—31no—
123C2×C3×#67—31no—
124C2×C3×#67—32no—
125C2×C3×#67—31no—
126C2×C3×#67—61no—
127C2×C3×#67C2×D311yescharacteristic
128C2×C3×#67C2×D311yescharacteristic
129C22×C3×Dic3—21no—
130C22×C3×Dic3—31no—
131C22×C3×Dic3C2×D311yescharacteristic
132C22×C3×Dic3C2×D311yescharacteristic
133C3×#237—64no—
134C3×#235—64no—
135C2×C3×D12—32no—
136C2×C3×D12—31no—
137C2×C3×C4×D3—31no—
138C2×C3×C4×D3—31no—
139C2×C3×C4×D3—31no—
140C2×C3×Dic6—31no—
141C2×C3×Dic6—31no—
142C2×#627C2×D311yescharacteristic, complemented
143C2×#626—32no—
144C2×#626—32no—
145C2×#626C2×D312yes—
146C2×#626C2×D311yescharacteristic, complemented
147C2×#625—32no—
148C2×#624C2×D311yescharacteristic, complemented
149#3804—24no—
150C2×D3×Dic3—32no—
151C2×D3×Dic3—32no—
152C2×D3×Dic3—32no—
153C2×D3×Dic3—32no—
154C2×D3×Dic3—62no—
155C2×D3×Dic3—62no—
156C2×D3×Dic3—68no—
157C2×D3×Dic3—64no—
158C2×D3×Dic3—64no—
159C2×D3×Dic3C2×D311yescharacteristic, complemented
160C32×C22⋊C4—31no—
161#3757—32no—
162#3757C2×D311yescharacteristic
163#3752—32no—
164C4⋊(C3⋊Dic3)—32no—
165#3750—32no—
166C3×#217—21no—
167C3×#217—31no—
168C3×#217—31no—
169C3×#217—61no—
170C3×#217C2×D311yescharacteristic
171C3×#217C2×D311yescharacteristic
172C3×(C2×D3)⋊C4—32no—
173C3×(C2×D3)⋊C4—32no—
174C3×C4⋊Dic3—32no—
175C3×Dic3⋊C4—32no—
176C3×C4×Dic3—32no—
177C3×C4×Dic3—32no—
178Dic3⋊Dic3—32no—
179Dic3⋊Dic3—32no—
180Dic3⋊Dic3—32no—
181Dic3⋊Dic3—32no—
182Dic3⋊Dic3—62no—
183Dic3⋊Dic3—62no—
184Dic3⋊Dic3C2×D312yescomplemented
185#3722—32no—
186#3722C2×D312yes—
187(C2×D3)⋊Dic3—32no—
188(C2×D3)⋊Dic3—32no—
189(C2×D3)⋊Dic3—32no—
190(C2×D3)⋊Dic3—32no—
191(C2×D3)⋊Dic3—32no—
192(C2×D3)⋊Dic3—32no—
193(C2×D3)⋊Dic3—62no—
194(C2×D3)⋊Dic3—62no—
195Dic32C2×D312yescomplemented
196C22×C33—22no—
197C22×C33C2×D412yes—
198C22×C33C2411yescharacteristic
199C2×C3×C3⋊D3—28no—
200C2×C3×C3⋊D3—22no—
201C2×C3×C3⋊D3—22no—
202C2×C3×C3⋊D3—21no—
203C2×C3×C3⋊D3—22no—
204C2×C3×C3⋊D3#4114yescomplemented
205C2×C32×D3—21no—
206C2×C32×D3—22no—
207C3⋊(C3⋊Dic3)—22no—
208C3×C3⋊Dic3—21no—
209C3×C3⋊Dic3—22no—
210C32×Dic3—21no—
211C32×Dic3—22no—
212C32×Dic3C2×D412yes—
213C32×Dic3C2×D412yes—
214C2×C3×#41—91no—
215C23×Dic3—91no—
216C2×#237—31no—
217C2×#235—31no—
218C22×C4×D3—91no—
219C22×C4×D3—91no—
220C22×C4×D3—181no—
221C3×#120—91no—
222C3×#117—91no—
223#953—91no—
224#946—92no—
225#939—92no—
226#938—92no—
227#937—31no—
228#937—91no—
229#935—91no—
230#935—91no—
231#935—91no—
232#935—181no—
233D4×Dic3—92no—
234C4×#67—92no—
235C4×#67—92no—
236#926—31no—
237#897—92no—
238#895—92no—
239#886—91no—
240#886—91no—
241#886—91no—
242#886—181no—
243#882—31no—
244#882—91no—
245#67⋊C4—92no—
246#878—92no—
247#877—31no—
248C4×D12—92no—
249C4×D12—92no—
250C23×C32—21no—
251C23×C32—21no—
252C23×C32—21no—
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×D311yescharacteristic
261C22×C3⋊D3C22×D312yes—
262C22×C3×D3—21no—
263C22×C3×D3—32no—
264C22×C3×D3—32no—
265C22×C3×D3—31no—
266C22×C3×D3—31no—
267C22×C3×D3—62no—
268C22×C3×D3—61no—
269C22×C3×D3—64no—
270C22×C3×D3—64no—
271C22×C3×D3—68no—
272C22×C3×D3—64no—
273C22×C3×D3—62no—
274C22×C3×D3—62no—
275C22×C3×D3C22×D311yescharacteristic
276C22×C3×D3C22×D311yescharacteristic
277C32×D4—62no—
278C2×C32×C4—34no—
279C2×C32×C4—31no—
280C2×C32×C4—31no—
281C2×C32×C4—32no—
282C2×C32×C4—31no—
283#638—22no—
284C2×C3⋊Dic3—32no—
285C2×C3⋊Dic3—32no—
286C2×C3⋊Dic3—32no—
287C2×C3⋊Dic3—62no—
288C2×C3⋊Dic3—62no—
289C2×C3⋊Dic3—62no—
290C2×C3⋊Dic3—62no—
291C2×C3⋊Dic3—64no—
292C2×C3⋊Dic3—62no—
293C2×C3⋊Dic3—62no—
294C2×C3⋊Dic3—122no—
295C2×C3⋊Dic3—122no—
296C2×C3⋊Dic3—122no—
297C2×C3⋊Dic3—124no—
298C2×C3⋊Dic3C22×D312yes—
299C2×C3⋊Dic3C22×D311yescharacteristic
300C4×C3⋊D3—64no—
301C4×C3⋊D3—64no—
302C3×#67—22no—
303C3×#67—22no—
304C3×#67—42no—
305C3×#67—64no—
306C3×#67—62no—
307C3×#67—62no—
308C3×#67—62no—
309C3×#67—122no—
310C2×C3×Dic3—24no—
311C2×C3×Dic3—21no—
312C2×C3×Dic3—21no—
313C2×C3×Dic3—22no—
314C2×C3×Dic3—21no—
315C2×C3×Dic3—31no—
316C2×C3×Dic3—32no—
317C2×C3×Dic3—32no—
318C2×C3×Dic3—31no—
319C2×C3×Dic3—62no—
320C2×C3×Dic3—61no—
321C2×C3×Dic3—62no—
322C2×C3×Dic3D1214yescomplemented
323C2×C3×Dic3#6714yescomplemented
324C2×C3×Dic3C22×D312yes—
325C2×C3×Dic3C22×D312yes—
326C2×C3×Dic3C22×D311yescharacteristic
327C2×C3×Dic3C22×D311yescharacteristic
328C2×C3×Dic3C22×D311yescharacteristic
329C2×C3×Dic3C22×D311yescharacteristic
330C2×C3×Dic3C22×D311yescharacteristic
331C2×C3×Dic3C22×D311yescharacteristic
332C3×D12—62no—
333C3×D12—64no—
334C3×C4×D3—62no—
335C3×C4×D3—62no—
336C3×C4×D3—62no—
337C3×Dic6—62no—
338C3×Dic6—62no—
339#627—22no—
340#626—24no—
341#626—22no—
342#626—64no—
343#626—64no—
344#625—64no—
345#624—22no—
346D3×Dic3—22no—
347D3×Dic3—68no—
348D3×Dic3—68no—
349D3×Dic3—64no—
350D3×Dic3—64no—
351D3×Dic3—64no—
352D3×Dic3—64no—
353#525—271noSylow
354C2×C33—22no—
355C2×C33C22×D411yescharacteristic
356C2×C33C2×#4112yes—
357C3×C3⋊D3—24no—
358C3×C3⋊D3—41no—
359C32×D3—41no—
360C24×C3—91no—
361C23×D3—31no—
362C23×D3—31no—
363C23×D3—61no—
364C3×#41—184no—
365C2×C3×Q8—91no—
366C2×C3×D4—31no—
367C2×C3×D4—31no—
368C2×C3×D4—61no—
369C2×C3×D4—92no—
370C2×C3×D4—91no—
371C2×C3×D4—91no—
372C22×C3×C4—31no—
373C22×C3×C4—31no—
374C22×C3×C4—61no—
375C22×C3×C4—91no—
376C22×C3×C4—91no—
377C2×#67—31no—
378C2×#67—31no—
379C2×#67—32no—
380C2×#67—31no—
381C2×#67—61no—
382C2×#67—92no—
383C2×#67—92no—
384C2×#67D3211yescharacteristic
385C22×Dic3—31no—
386C22×Dic3—91no—
387C22×Dic3—91no—
388C22×Dic3—91no—
389C22×Dic3—92no—
390C22×Dic3—92no—
391C22×Dic3—181no—
392C22×Dic3—181no—
393C22×Dic3—181no—
394C22×Dic3—184no—
395C22×Dic3—361no—
396C22×Dic3D3211yescharacteristic
397#237—64no—
398#235—64no—
399C2×D12—32no—
400C2×D12—31no—
401C2×D12—92no—
402C2×C4×D3—31no—
403C2×C4×D3—31no—
404C2×C4×D3—31no—
405C2×C4×D3—92no—
406C2×C4×D3—92no—
407C2×C4×D3—92no—
408C2×C4×D3—92no—
409C2×C4×D3—182no—
410C2×C4×D3—182no—
411C2×C4×D3—184no—
412C2×C4×D3—184no—
413C2×C4×D3—188no—
414C2×Dic6—31no—
415C2×Dic6—31no—
416C3×C4⋊C4—92no—
417C3×C22⋊C4—31no—
418C3×C22⋊C4—31no—
419C3×C22⋊C4—61no—
420C3×C22⋊C4—92no—
421C3×C22⋊C4—91no—
422C3×C42—92no—
423#217—31no—
424#217—31no—
425#217—61no—
426#217—92no—
427#217—92no—
428#217—92no—
429#217—92no—
430#217—182no—
431#217D3211yescharacteristic
432(C2×D3)⋊C4—32no—
433(C2×D3)⋊C4—32no—
434(C2×D3)⋊C4—92no—
435(C2×D3)⋊C4—92no—
436(C2×D3)⋊C4—92no—
437(C2×D3)⋊C4—92no—
438(C2×D3)⋊C4—92no—
439(C2×D3)⋊C4—182no—
440C4⋊Dic3—32no—
441C4⋊Dic3—92no—
442C4⋊Dic3—92no—
443C4⋊Dic3—92no—
444C4⋊Dic3—182no—
445Dic3⋊C4—32no—
446Dic3⋊C4—92no—
447Dic3⋊C4—92no—
448Dic3⋊C4—92no—
449Dic3⋊C4—182no—
450C4×Dic3—32no—
451C4×Dic3—32no—
452C22×C32—22no—
453C22×C32—24no—
454C22×C32—22no—
455C22×C32—22no—
456C22×C32—21no—
457C22×C32—21no—
458C22×C32—21no—
459C22×C32—22no—
460C22×C32—22no—
461C22×C32—22no—
462C22×C32—42no—
463C22×C32—41no—
464C22×C32—42no—
465C22×C32—42no—
466C22×C32—44no—
467C22×C32—61no—
468C22×C32—62no—
469C22×C32C2×D1212yes—
470C22×C32D3×D412yes—
471C22×C32C2×#6712yes—
472C22×C32C23×D311yescharacteristic
473C22×C32C23×D311yescharacteristic
474C22×C32C23×D311yescharacteristic
475C2×C3⋊D3—28no—
476C2×C3⋊D3—22no—
477C2×C3⋊D3—22no—
478C2×C3⋊D3—22no—
479C2×C3⋊D3—21no—
480C2×C3⋊D3#23714yescomplemented
481C2×C3×D3—21no—
482C2×C3×D3—22no—
483C2×C3×D3—22no—
484C2×C3×D3—21no—
485C2×C3×D3—34no—
486C2×C3×D3—34no—
487C2×C3×D3—41no—
488C2×C3×D3—42no—
489C2×C3×D3—64no—
490C2×C3×D3—64no—
491C2×C3×D3—616no—
492C2×C3×D3—68no—
493C2×C3×D3—68no—
494C2×C3×D3—64no—
495C2×C3×D3—62no—
496C2×C3×D3—62no—
497C2×C3×D3—62no—
498C2×C3×D3—62no—
499C2×C3×D3—61no—
500C2×C3×D3—61no—
501C2×C3×D3—62no—
502C2×C3×D3—62no—
503C2×C3×D3—121no—
504C2×C3×D3—122no—
505C32×C4—32no—
506C32×C4—32no—
507C32×C4—61no—
508C32×C4—62no—
509C3⋊Dic3—22no—
510C3⋊Dic3—21no—
511C3⋊Dic3—62no—
512C3⋊Dic3—64no—
513C3⋊Dic3—62no—
514C3⋊Dic3—62no—
515C3⋊Dic3—122no—
516C3⋊Dic3—122no—
517C3⋊Dic3—124no—
518C3×Dic3—21no—
519C3×Dic3—22no—
520C3×Dic3—22no—
521C3×Dic3—21no—
522C3×Dic3—22no—
523C3×Dic3—22no—
524C3×Dic3—42no—
525C3×Dic3—41no—
526C3×Dic3—61no—
527C3×Dic3—61no—
528C3×Dic3—62no—
529C3×Dic3—62no—
530C3×Dic3—122no—
531C3×Dic3—121no—
532C3×Dic3C2×D1212yes—
533C3×Dic3C2×D1212yes—
534C3×Dic3C2×#6712yes—
535C3×Dic3C2×#6712yes—
536C2×#41—91no—
537C23×C4—271no—
538#123—271no—
539#123—271no—
540C22⋊Q8—272no—
541#121—272no—
542#120—91no—
543#120—271no—
544C4×D4—272no—
545C4×D4—272no—
546#117—91no—
547C33#52511yescharacteristic, complemented, Sylow
548C23×C3—21no—
549C23×C3—21no—
550C23×C3—21no—
551C23×C3—31no—
552C23×C3—31no—
553C23×C3—41no—
554C23×C3—61no—
555C23×C3—92no—
556C23×C3—91no—
557C23×C3—184no—
558C23×C3—182no—
559C23×C3C2×D3211yescharacteristic
560C23×C3C2×D3211yescharacteristic
561C23×C3C2×D3211yescharacteristic
562C22×D3—32no—
563C22×D3—32no—
564C22×D3—31no—
565C22×D3—31no—
566C22×D3—62no—
567C22×D3—61no—
568C22×D3—64no—
569C22×D3—64no—
570C22×D3—64no—
571C22×D3—68no—
572C22×D3—62no—
573C22×D3—62no—
574C22×D3C2×D3211yescharacteristic
575C3×Q8—182no—
576C3×D4—62no—
577C3×D4—62no—
578C3×D4—122no—
579C3×D4—182no—
580C3×D4—184no—
581C3×D4—182no—
582C2×C3×C4—31no—
583C2×C3×C4—31no—
584C2×C3×C4—31no—
585C2×C3×C4—31no—
586C2×C3×C4—34no—
587C2×C3×C4—34no—
588C2×C3×C4—32no—
589C2×C3×C4—31no—
590C2×C3×C4—31no—
591C2×C3×C4—32no—
592C2×C3×C4—61no—
593C2×C3×C4—61no—
594C2×C3×C4—64no—
595C2×C3×C4—61no—
596C2×C3×C4—62no—
597C2×C3×C4—91no—
598C2×C3×C4—92no—
599C2×C3×C4—182no—
600C2×C3×C4—182no—
601#67—22no—
602#67—64no—
603#67—62no—
604#67—62no—
605#67—62no—
606#67—122no—
607#67—184no—
608#67—184no—
609C2×Dic3—32no—
610C2×Dic3—32no—
611C2×Dic3—31no—
612C2×Dic3—31no—
613C2×Dic3—62no—
614C2×Dic3—61no—
615C2×Dic3—62no—
616C2×Dic3—92no—
617C2×Dic3—92no—
618C2×Dic3—92no—
619C2×Dic3—182no—
620C2×Dic3—182no—
621C2×Dic3—182no—
622C2×Dic3—184no—
623C2×Dic3—182no—
624C2×Dic3—182no—
625C2×Dic3—182no—
626C2×Dic3—184no—
627C2×Dic3—184no—
628C2×Dic3—362no—
629C2×Dic3—362no—
630C2×Dic3—362no—
631C2×Dic3—364no—
632C2×Dic3#62614yescomplemented
633C2×Dic3C2×D3212yes—
634C2×Dic3C2×D3211yescharacteristic
635C2×Dic3C2×D3211yescharacteristic
636C2×Dic3C2×D3211yescharacteristic
637D12—62no—
638D12—64no—
639D12—184no—
640C4×D3—62no—
641C4×D3—62no—
642C4×D3—62no—
643C4×D3—184no—
644C4×D3—184no—
645C4×D3—184no—
646C4×D3—184no—
647C4×D3—188no—
648C4×D3—188no—
649Dic6—62no—
650Dic6—62no—
651C2×C32—22no—
652C2×C32—24no—
653C2×C32—22no—
654C2×C32—22no—
655C2×C32—21no—
656C2×C32—22no—
657C2×C32—22no—
658C2×C32—22no—
659C2×C32—21no—
660C2×C32—21no—
661C2×C32—41no—
662C2×C32—42no—
663C2×C32—42no—
664C2×C32—42no—
665C2×C32—44no—
666C2×C32—121no—
667C2×C32C22×D1211yescharacteristic
668C2×C32C2×D3×D411yescharacteristic
669C2×C32C2×#23712yes—
670C2×C32D3×#4112yes—
671C2×C32D3×#4112yes—
672C2×C32C22×#6711yescharacteristic
673C3⋊D3—24no—
674C3⋊D3—41no—
675C3×D3—41no—
676C3×D3—41no—
677C3×D3—68no—
678C3×D3—64no—
679C3×D3—64no—
680C3×D3—81no—
681C3×D3—121no—
682C3×D3—121no—
683C3×D3—241no—
684C24—91no—
685#41—184no—
686C2×Q8—91no—
687C2×D4—31no—
688C2×D4—92no—
689C2×D4—91no—
690C2×D4—91no—
691C2×D4—272no—
692C22×C4—31no—
693C22×C4—91no—
694C22×C4—91no—
695C22×C4—272no—
696C22×C4—272no—
697C22×C4—271no—
698C22×C4—544no—
699C4⋊C4—92no—
700C4⋊C4—272no—
701C4⋊C4—272no—
702C22⋊C4—31no—
703C22⋊C4—92no—
704C22⋊C4—91no—
705C22⋊C4—272no—
706C22⋊C4—272no—
707C22⋊C4—272no—
708C42—92no—
709C22×C3—24no—
710C22×C3—22no—
711C22×C3—22no—
712C22×C3—22no—
713C22×C3—21no—
714C22×C3—21no—
715C22×C3—21no—
716C22×C3—22no—
717C22×C3—22no—
718C22×C3—22no—
719C22×C3—42no—
720C22×C3—42no—
721C22×C3—44no—
722C22×C3—41no—
723C22×C3—42no—
724C22×C3—61no—
725C22×C3—62no—
726C22×C3—62no—
727C22×C3—61no—
728C22×C3—94no—
729C22×C3—121no—
730C22×C3—122no—
731C22×C3—188no—
732C22×C3—182no—
733C22×C3—182no—
734C22×C3—181no—
735C22×C3—182no—
736C22×C3D3×D1212yes—
737C22×C3C2×#62612yes—
738C22×C3D3×#6712yes—
739C22×C3C22×D3211yescharacteristic
740C22×C3C22×D3211yescharacteristic
741C22×C3C22×D3211yescharacteristic
742C2×D3—22no—
743C2×D3—21no—
744C2×D3—34no—
745C2×D3—34no—
746C2×D3—64no—
747C2×D3—64no—
748C2×D3—616no—
749C2×D3—68no—
750C2×D3—68no—
751C2×D3—64no—
752C2×D3—62no—
753C2×D3—62no—
754C2×D3—62no—
755C2×D3—62no—
756C2×D3—62no—
757C2×D3—62no—
758C2×D3—61no—
759C2×D3—61no—
760C2×D3—121no—
761C2×D3—122no—
762C3×C4—32no—
763C3×C4—32no—
764C3×C4—32no—
765C3×C4—32no—
766C3×C4—62no—
767C3×C4—62no—
768C3×C4—61no—
769C3×C4—62no—
770C3×C4—62no—
771C3×C4—61no—
772C3×C4—121no—
773C3×C4—122no—
774C3×C4—181no—
775C3×C4—182no—
776Dic3—22no—
777Dic3—21no—
778Dic3—62no—
779Dic3—62no—
780Dic3—61no—
781Dic3—61no—
782Dic3—121no—
783Dic3—122no—
784Dic3—184no—
785Dic3—182no—
786Dic3—182no—
787Dic3—182no—
788Dic3—362no—
789Dic3—362no—
790Dic3—364no—
791Dic3C2×#62612yes—
792Dic3C2×#62612yes—
793C32—21no—
794C32—21no—
795C32—21no—
796C32—41no—
797C32#552411yescharacteristic, complemented
798C32#558611yescharacteristic, complemented
799C32#582811yescharacteristic, complemented
800C23—31no—
801C23—92no—
802C23—91no—
803C23—184no—
804C23—182no—
805C23D3311yescharacteristic
806Q8—182no—
807D4—62no—
808D4—182no—
809D4—184no—
810D4—182no—
811D4—544no—
812C2×C4—31no—
813C2×C4—31no—
814C2×C4—34no—
815C2×C4—32no—
816C2×C4—31no—
817C2×C4—92no—
818C2×C4—91no—
819C2×C4—182no—
820C2×C4—182no—
821C2×C4—272no—
822C2×C4—544no—
823C2×C4—544no—
824C2×C4—542no—
825C2×C3—24no—
826C2×C3—22no—
827C2×C3—22no—
828C2×C3—22no—
829C2×C3—22no—
830C2×C3—22no—
831C2×C3—22no—
832C2×C3—21no—
833C2×C3—21no—
834C2×C3—21no—
835C2×C3—42no—
836C2×C3—42no—
837C2×C3—44no—
838C2×C3—42no—
839C2×C3—41no—
840C2×C3—121no—
841C2×C3—121no—
842C2×C3—184no—
843C2×C3—241no—
844C2×C3—361no—
845C2×C3C2×D3×D1211yescharacteristic
846C2×C3#6430612yes—
847C2×C3D3×#23712yes—
848C2×C3D3×#23712yes—
849C2×C3C22×#62611yescharacteristic
850C2×C3C2×D3×#6711yescharacteristic
851D3—41no—
852D3—68no—
853D3—64no—
854D3—64no—
855D3—121no—
856D3—121no—
857D3—241no—
858C22—22no—
859C22—62no—
860C22—61no—
861C22—94no—
862C22—188no—
863C22—182no—
864C22—182no—
865C22—182no—
866C22—181no—
867C22D3×#62612yes—
868C22C2×D3311yescharacteristic
869C4—32no—
870C4—32no—
871C4—62no—
872C4—61no—
873C4—182no—
874C4—181no—
875C4—542no—
876C3—21no—
877C3—21no—
878C3—21no—
879C3—41no—
880C3#1059407811yescharacteristic, complemented
881C3#1059503411yescharacteristic, complemented
882C3#1059515411yescharacteristic, complemented
883C2—22no—
884C2—121no—
885C2—184no—
886C2—361no—
887C2#1172440712yes—
888C2C2×D3×#62611yescharacteristic
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×Dic3×C3⋊D3C2semidirect
2. C2×C3×#3804C2semidirect
3. #11723727C2semidirect
4. #11723609C2semidirect
5. #11723603C2semidirect
6. C3×#63981C2semidirect
7. C3×#63955C2semidirect
8. #11722974C2semidirect
9. #11722962C2semidirect
10. #11722934C2semidirect
11. Dic3×#626C2semidirect
24. C2×C3×#627C22semidirect
26. C2×C3×#626C22semidirect
27. C2×C3×#624C22semidirect
29. C2×C3×D3×Dic3C22semidirect
33. #88807C22semidirect
34. Dic3⋊(C3⋊Dic3)C22semidirect
35. #88803C22semidirect
36. (C2×D3)⋊(C3⋊Dic3)C22semidirect
37. C3×Dic3⋊Dic3C22semidirect
39. C3×Dic32C22semidirect
43. C2×#3804D3semidirect
54. #63981D3semidirect
65. #63955D3semidirect
88. C2×C32×Dic3D4semidirect
142. C2×#627C2×D3semidirect
146. C2×#626C2×D3semidirect
148. C2×#624C2×D3semidirect
159. C2×D3×Dic3C2×D3semidirect
184. Dic3⋊Dic3C2×D3semidirect
195. Dic32C2×D3semidirect
204. C2×C3×C3⋊D3#41semidirect
322. C2×C3×Dic3D12semidirect
323. C2×C3×Dic3#67semidirect
480. C2×C3⋊D3#237semidirect
547. C33#525semidirect
632. C2×Dic3#626semidirect
797. C32#5524semidirect
798. C32#5586semidirect
799. C32#5828semidirect
880. C3#10594078semidirect
881. C3#10595034semidirect
882. C3#10595154semidirect

Maximal subgroups

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

subgroupindex
C22×Dic3×C3⋊D32
C2×C3×#38042
#117237272
#117236092
#117236032
C3×#639812
C3×#639552
#117229742
#117229622
#117229342
Dic3×#6262
#105951543
#105950343
#105940783