Finite Group Databasebeta

← #13172661

Subgroups — #13172661

Order 1728.

1722 conjugacy classes of subgroups.

The subgroup lattice has 1388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3804C211yesmaximal, characteristic, complemented
2C2×D3×#626C211yesmaximal, characteristic, complemented
3#11723728C211yesmaximal, characteristic, complemented
4#11723643C211yesmaximal, characteristic, complemented
5#11723633C211yesmaximal, characteristic, complemented
6#11723632C211yesmaximal, characteristic, complemented
7C3×#63983C211yesmaximal, characteristic, complemented
8C3×#63978C211yesmaximal, characteristic, complemented
9#11723007C211yesmaximal, characteristic, complemented
10#11723005C211yesmaximal, characteristic, complemented
11#11722961C211yesmaximal, characteristic, complemented
12#11722957C211yesmaximal, characteristic, complemented
13#11722950C211yesmaximal, characteristic, complemented
14#11722947C211yesmaximal, characteristic, complemented
15#11722914C211yesmaximal, characteristic, complemented
16#10595285—31nomaximal
17#10595238—31nomaximal
18#10595064—31nomaximal
19C22×D3×C3⋊D3C2211yescharacteristic
20C22×C3×D32C2211yescharacteristic
21C2×#6312C2211yescharacteristic, complemented
22C2×C3×#638C2211yescharacteristic, complemented
23C2×C3×#638C2211yescharacteristic, complemented
24C2×C3×#638C2211yescharacteristic, complemented
25C2×C32×#67C2211yescharacteristic
26C2×C32×#67C2211yescharacteristic, complemented
27C22×C32×Dic3C2211yescharacteristic, complemented
28C2×#6295C2211yescharacteristic
29C2×#6295C2211yescharacteristic, complemented
30C2×#6295C2211yescharacteristic, complemented
31C2×#6292C2211yescharacteristic
32C2×#6292C2211yescharacteristic, complemented
33C2×#6291C2211yescharacteristic
34C2×#6290C2211yescharacteristic, complemented
35C2×C3×#627C2211yescharacteristic, complemented
36C2×C3×#626C2211yescharacteristic
37C2×C3×#626C2211yescharacteristic
38C2×C3×#624C2211yescharacteristic, complemented
39C3×#3804—24no—
40C2×C3×D3×Dic3C2211yescharacteristic
41D3×#626—24no—
42#88813C2211yescharacteristic, complemented
43Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
44#88804C2211yescharacteristic, complemented
45#88804C2211yescharacteristic, complemented
46#88803C2211yescharacteristic, complemented
47#88803C2211yescharacteristic, complemented
48(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
49Dic3×C3⋊Dic3C2211yescharacteristic, complemented
50C3×Dic3⋊Dic3C2211yescharacteristic, complemented
51C3×#3722C2211yescharacteristic, complemented
52C3×#3722C2211yescharacteristic, complemented
53C3×(C2×D3)⋊Dic3C2211yescharacteristic
54C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
55C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
56C2×C3×#237—31no—
57C2×C3×#235—31no—
58C2×D3×#67—31no—
59C22×#626—31no—
60C2×#3804D311yescharacteristic, complemented
61C2×D3×D12—31no—
62#64149—31no—
63#64146—31no—
64#64139—31no—
65C3×#939—31no—
66C3×#937—31no—
67C3×#937—31no—
68C3×#930—31no—
69#63983—31no—
70#63983—31no—
71#63983—61no—
72#63983D311yescharacteristic, complemented
73#63981—31no—
74#63979—31no—
75#63979—31no—
76#63979—31no—
77#63979—31no—
78#63979—31no—
79#63979—61no—
80#63978—31no—
81#63978—31no—
82#63978—61no—
83#63978D311yescharacteristic, complemented
84#63977—31no—
85#63976—31no—
86#63958—31no—
87#63955—31no—
88#63953—31no—
89#63923—31no—
90#63922—31no—
91#63922—31no—
92#63915—31no—
93#63910—31no—
94#63909—31no—
95#63908—31no—
96#63907—31no—
97#63907—31no—
98#63907—31no—
99#63907—31no—
100#63906—31no—
101#63906—31no—
102#63878—31no—
103#63841—31no—
104C23×C33C2311yescharacteristic
105C22×C3⋊(C3⋊D3)C2311yescharacteristic
106C22×C3×C3⋊D3C2311yescharacteristic
107C22×C3×C3⋊D3C2311yescharacteristic
108C22×C3×C3⋊D3C2311yescharacteristic
109C22×C32×D3C2311yescharacteristic
110C22×C32×D3C2311yescharacteristic
111C2×D3×C3⋊D3—22no—
112C2×D3×C3⋊D3—41no—
113C2×D3×C3⋊D3—41no—
114C2×C3×D32—22no—
115C2×C3×D32—41no—
116C2×C3×D32—41no—
117#6312—41no—
118C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
119C3×#638—22no—
120C3×#638—41no—
121C3×#638—41no—
122C2×C3×C3⋊Dic3C2311yescharacteristic
123C2×C3×C3⋊Dic3C2311yescharacteristic
124C2×C3×C3⋊Dic3C2311yescharacteristic
125C32×#67—22no—
126C32×#67—41no—
127C2×C32×Dic3—22no—
128C2×C32×Dic3C2311yescharacteristic
129C2×C32×Dic3C2311yescharacteristic
130C2×C32×Dic3C2311yescharacteristic
131C2×C32×Dic3C2311yescharacteristic
132#6295—22no—
133#6295—41no—
134#6295—41no—
135#6292—22no—
136#6292—41no—
137#6291—22no—
138#6290—41no—
139C3×#627—22no—
140C3×#626—22no—
141C3×#626—22no—
142C3×#624—22no—
143C3×D3×Dic3D414yescomplemented
144#5830—91no—
145#5607—91no—
146#5592—91no—
147C23×C3⋊D3—31no—
148C23×C3×D3—31no—
149C23×C3×D3—31no—
150C22×D32—31no—
151C22×D32—31no—
152C22×D32—61no—
153C22×D32C2×D311yescharacteristic
154C2×C32×D4—31no—
155C2×C32×D4—31no—
156C22×C32×C4—31no—
157C2×#638—31no—
158C2×#638—31no—
159C2×#638—31no—
160C2×#638—31no—
161C2×#638—31no—
162C2×#638—61no—
163C2×#638—61no—
164C2×#638—61no—
165C2×#638—121no—
166C2×#638C2×D311yescharacteristic, complemented
167C2×#638C2×D311yescharacteristic, complemented
168C2×#638C2×D311yescharacteristic, complemented
169C2×C4⋊(C3⋊D3)—31no—
170C2×C4⋊(C3⋊D3)—31no—
171C2×C3×#67—21no—
172C2×C3×#67—21no—
173C2×C3×#67—31no—
174C2×C3×#67—31no—
175C2×C3×#67—31no—
176C2×C3×#67—31no—
177C2×C3×#67—31no—
178C2×C3×#67—31no—
179C2×C3×#67—31no—
180C2×C3×#67—31no—
181C2×C3×#67—61no—
182C2×C3×#67—61no—
183C2×C3×#67—61no—
184C2×C3×#67C2×D311yescharacteristic
185C2×C3×#67C2×D311yescharacteristic
186C2×C3×#67C2×D311yescharacteristic, complemented
187C2×C3×#67C2×D311yescharacteristic, complemented
188C22×C3×Dic3—21no—
189C22×C3×Dic3—31no—
190C22×C3×Dic3C2×D311yescharacteristic, complemented
191C22×C3×Dic3C2×D311yescharacteristic, complemented
192C3×#237—64no—
193C3×#235—64no—
194C2×C3×D12—31no—
195C2×C3×D12—31no—
196C2×C3×C4×D3—31no—
197C2×C3×C4×D3—31no—
198C2×C3×C4×D3—31no—
199C2×C3×Dic6—31no—
200C2×C3×Dic6—31no—
201D3×#67—64no—
202C2×#627C2×D311yescharacteristic, complemented
203C2×#626—31no—
204C2×#626—31no—
205C2×#626—31no—
206C2×#626—31no—
207C2×#626—31no—
208C2×#626—31no—
209C2×#626—31no—
210C2×#626—31no—
211C2×#626—31no—
212C2×#626—31no—
213C2×#626—31no—
214C2×#626—31no—
215C2×#626—64no—
216C2×#626—61no—
217C2×#626—61no—
218C2×#626—61no—
219C2×#626C2×D311yescharacteristic
220C2×#626C2×D311yescharacteristic
221C2×#625—31no—
222C2×#625—31no—
223C2×#625—31no—
224C2×#625—31no—
225C2×#625—31no—
226C2×#625—61no—
227C2×#624C2×D311yescharacteristic, complemented
228#3804—24no—
229C2×D3×Dic3C2×D311yescharacteristic
230D3×D12—64no—
231#3757—31no—
232#3752—31no—
233#3752—31no—
234#3752—31no—
235#3752—31no—
236C4⋊(C3⋊Dic3)—31no—
237C4×C3⋊Dic3—31no—
238C3×#217—31no—
239C3×#217—31no—
240C3×#217—31no—
241C3×(C2×D3)⋊C4—31no—
242C3×(C2×D3)⋊C4—31no—
243C3×(C2×D3)⋊C4—31no—
244C3×(C2×D3)⋊C4—31no—
245C3×(C2×D3)⋊C4—31no—
246C3×(C2×D3)⋊C4—31no—
247C3×(C2×D3)⋊C4—31no—
248C3×C4⋊Dic3—31no—
249C3×Dic3⋊C4—31no—
250Dic3⋊Dic3—31no—
251Dic3⋊Dic3—31no—
252Dic3⋊Dic3—61no—
253Dic3⋊Dic3C2×D311yescharacteristic, complemented
254#3722—31no—
255#3722—31no—
256#3722—31no—
257#3722—31no—
258#3722—61no—
259#3722—61no—
260#3722C2×D311yescharacteristic, complemented
261#3722C2×D311yescharacteristic, complemented
262(C2×D3)⋊Dic3—31no—
263(C2×D3)⋊Dic3—31no—
264(C2×D3)⋊Dic3—31no—
265(C2×D3)⋊Dic3—31no—
266(C2×D3)⋊Dic3—31no—
267(C2×D3)⋊Dic3—31no—
268(C2×D3)⋊Dic3—61no—
269(C2×D3)⋊Dic3—61no—
270(C2×D3)⋊Dic3—61no—
271(C2×D3)⋊Dic3C2×D311yescharacteristic
272(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
273(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
274Dic32—31no—
275Dic32—31no—
276Dic32—31no—
277Dic32—31no—
278Dic32—31no—
279Dic32—61no—
280C22×C33—21no—
281C22×C33—21no—
282C22×C33—21no—
283C22×C33C2411yescharacteristic
284C2×C3⋊(C3⋊D3)—21no—
285C2×C3⋊(C3⋊D3)—21no—
286C2×C3⋊(C3⋊D3)—21no—
287C2×C3×C3⋊D3—21no—
288C2×C3×C3⋊D3—21no—
289C2×C3×C3⋊D3—21no—
290C2×C3×C3⋊D3—21no—
291C2×C3×C3⋊D3—21no—
292C2×C3×C3⋊D3—21no—
293C2×C3×C3⋊D3—21no—
294C2×C3×C3⋊D3—21no—
295C2×C3×C3⋊D3—21no—
296C2×C32×D3—21no—
297C2×C32×D3—21no—
298C2×C32×D3—21no—
299C2×C32×D3—21no—
300C2×C32×D3—21no—
301C2×C32×D3C2×D412yes—
302D3×C3⋊D3—44no—
303C3×D32—44no—
304C3⋊(C3⋊Dic3)—21no—
305C3×C3⋊Dic3—21no—
306C3×C3⋊Dic3—21no—
307C3×C3⋊Dic3C2×D412yes—
308C32×Dic3—21no—
309C32×Dic3—21no—
310C32×Dic3—21no—
311C32×Dic3C2×D412yes—
312C2×C3×#41—91no—
313C22×#67—91no—
314C2×#237—31no—
315C2×D3×D4—91no—
316C2×#235—31no—
317C22×D12—91no—
318C3×#121—91no—
319C3×#120—91no—
320#953—91no—
321#947—91no—
322#947—91no—
323#940—91no—
324#940—91no—
325#940—91no—
326#940—91no—
327#940—91no—
328#940—91no—
329#940—181no—
330#939—31no—
331#939—91no—
332#938—91no—
333#937—31no—
334#937—31no—
335#937—91no—
336#937—91no—
337#937—91no—
338#937—91no—
339#937—91no—
340#937—181no—
341#930—31no—
342#930—91no—
343#930—91no—
344#930—91no—
345#930—91no—
346#930—181no—
347#926—91no—
348#895—91no—
349#892—91no—
350#885—91no—
351#885—91no—
352#885—91no—
353#885—91no—
354#884—91no—
355#884—91no—
356#882—91no—
357#882—91no—
358#882—91no—
359#877—91no—
360C23×C32—21no—
361C23×C32—21no—
362C23×C32—21no—
363C23×C32—31no—
364C23×C32—31no—
365C23×C32—41no—
366C23×C32C22×D311yescharacteristic
367C23×C32C22×D311yescharacteristic
368C23×C32C22×D311yescharacteristic
369C22×C3⋊D3—31no—
370C22×C3⋊D3—31no—
371C22×C3⋊D3—31no—
372C22×C3⋊D3—61no—
373C22×C3⋊D3—61no—
374C22×C3⋊D3—61no—
375C22×C3⋊D3—62no—
376C22×C3⋊D3—121no—
377C22×C3⋊D3—121no—
378C22×C3⋊D3—121no—
379C22×C3⋊D3C22×D311yescharacteristic
380C22×C3⋊D3C22×D311yescharacteristic
381C22×C3⋊D3C22×D311yescharacteristic
382C22×C3×D3—21no—
383C22×C3×D3—21no—
384C22×C3×D3—31no—
385C22×C3×D3—31no—
386C22×C3×D3—31no—
387C22×C3×D3—31no—
388C22×C3×D3—31no—
389C22×C3×D3—31no—
390C22×C3×D3—61no—
391C22×C3×D3—61no—
392C22×C3×D3—61no—
393C22×C3×D3—62no—
394C22×C3×D3—62no—
395C22×C3×D3—121no—
396C22×C3×D3—121no—
397C22×C3×D3—121no—
398C22×C3×D3—121no—
399C22×C3×D3C22×D311yescharacteristic
400C22×C3×D3C22×D311yescharacteristic
401C22×C3×D3C22×D311yescharacteristic
402C22×C3×D3C22×D311yescharacteristic
403C2×D32—22no—
404C2×D32—41no—
405C2×D32—41no—
406C2×D32—62no—
407C2×D32—62no—
408C2×D32—122no—
409C2×D32—121no—
410C2×D32—121no—
411C2×D32—121no—
412C2×D32—121no—
413C2×D32—122no—
414C2×D32—122no—
415C32×D4—62no—
416C32×D4—121no—
417C2×C32×C4—31no—
418C2×C32×C4—31no—
419C2×C32×C4—31no—
420C2×C32×C4—31no—
421C2×C32×C4—62no—
422#638—22no—
423#638—41no—
424#638—41no—
425#638—62no—
426#638—121no—
427#638—121no—
428#638—121no—
429#638—121no—
430#638—122no—
431#638—122no—
432#638—122no—
433#638—124no—
434C2×C3⋊Dic3—31no—
435C2×C3⋊Dic3—31no—
436C2×C3⋊Dic3—31no—
437C2×C3⋊Dic3—61no—
438C2×C3⋊Dic3—61no—
439C2×C3⋊Dic3—61no—
440C2×C3⋊Dic3—121no—
441C2×C3⋊Dic3C22×D311yescharacteristic
442C2×C3⋊Dic3C22×D311yescharacteristic
443C2×C3⋊Dic3C22×D311yescharacteristic
444C4⋊(C3⋊D3)—62no—
445C4⋊(C3⋊D3)—121no—
446C3×#67—22no—
447C3×#67—22no—
448C3×#67—42no—
449C3×#67—41no—
450C3×#67—41no—
451C3×#67—42no—
452C3×#67—62no—
453C3×#67—62no—
454C3×#67—62no—
455C3×#67—62no—
456C3×#67—122no—
457C3×#67—121no—
458C3×#67—121no—
459C3×#67—121no—
460C3×#67—121no—
461C3×#67—122no—
462C3×#67—122no—
463C2×C3×Dic3—22no—
464C2×C3×Dic3—22no—
465C2×C3×Dic3—21no—
466C2×C3×Dic3—21no—
467C2×C3×Dic3—21no—
468C2×C3×Dic3—21no—
469C2×C3×Dic3—31no—
470C2×C3×Dic3—31no—
471C2×C3×Dic3—34no—
472C2×C3×Dic3—31no—
473C2×C3×Dic3—31no—
474C2×C3×Dic3—31no—
475C2×C3×Dic3—31no—
476C2×C3×Dic3—42no—
477C2×C3×Dic3—61no—
478C2×C3×Dic3—61no—
479C2×C3×Dic3—61no—
480C2×C3×Dic3C22×D311yescharacteristic
481C2×C3×Dic3C22×D311yescharacteristic
482C2×C3×Dic3C22×D311yescharacteristic
483C2×C3×Dic3C22×D311yescharacteristic
484C2×C3×Dic3C22×D311yescharacteristic
485C2×C3×Dic3C22×D311yescharacteristic
486C2×C3×Dic3C22×D311yescharacteristic
487C2×C3×Dic3C22×D311yescharacteristic
488C3×D12—62no—
489C3×D12—62no—
490C3×C4×D3—34no—
491C3×C4×D3—62no—
492C3×C4×D3—62no—
493C3×Dic6—62no—
494C3×Dic6—62no—
495#627—22no—
496#626—22no—
497#626—22no—
498#626—62no—
499#626—62no—
500#626—62no—
501#626—62no—
502#626—62no—
503#626—62no—
504#626—122no—
505#626—122no—
506#626—121no—
507#626—121no—
508#626—122no—
509#626—121no—
510#626—121no—
511#626—121no—
512#626—121no—
513#625—62no—
514#625—121no—
515#625—121no—
516#625—121no—
517#625—121no—
518#625—122no—
519#624—22no—
520D3×Dic3#6714yescomplemented
521#535—271noSylow
522C2×C33—41no—
523C2×C33C22×D411yescharacteristic
524C2×C33H(5,𝔽2)11yescharacteristic
525C2×C33H(5,𝔽2)11yescharacteristic
526C3⋊(C3⋊D3)—41no—
527C3×C3⋊D3—41no—
528C3×C3⋊D3—41no—
529C3×C3⋊D3—41no—
530C32×D3—22no—
531C32×D3—41no—
532C24×C3—91no—
533C23×D3—31no—
534C23×D3—31no—
535C23×D3—91no—
536C23×D3—91no—
537C23×D3—91no—
538C23×D3—181no—
539C3×#41—184no—
540C2×C3×Q8—91no—
541C2×C3×D4—31no—
542C2×C3×D4—31no—
543C2×C3×D4—31no—
544C2×C3×D4—31no—
545C2×C3×D4—61no—
546C2×C3×D4—61no—
547C2×C3×D4—91no—
548C2×C3×D4—91no—
549C2×C3×D4—91no—
550C2×C3×D4—91no—
551C2×C3×D4—91no—
552C22×C3×C4—31no—
553C22×C3×C4—31no—
554C22×C3×C4—61no—
555C22×C3×C4—91no—
556C22×C3×C4—91no—
557C2×#67—31no—
558C2×#67—31no—
559C2×#67—31no—
560C2×#67—31no—
561C2×#67—31no—
562C2×#67—31no—
563C2×#67—31no—
564C2×#67—31no—
565C2×#67—61no—
566C2×#67—61no—
567C2×#67—61no—
568C2×#67—91no—
569C2×#67—91no—
570C2×#67—91no—
571C2×#67—91no—
572C2×#67—91no—
573C2×#67—91no—
574C2×#67—91no—
575C2×#67—91no—
576C2×#67—91no—
577C2×#67—91no—
578C2×#67—91no—
579C2×#67—91no—
580C2×#67—91no—
581C2×#67—91no—
582C2×#67—91no—
583C2×#67—91no—
584C2×#67—181no—
585C2×#67—181no—
586C2×#67—181no—
587C2×#67—181no—
588C2×#67—181no—
589C2×#67—184no—
590C2×#67—361no—
591C2×#67D3211yescharacteristic
592C2×#67D3211yescharacteristic, complemented
593C22×Dic3—31no—
594C22×Dic3D3211yescharacteristic, complemented
595#237—64no—
596D3×D4—184no—
597#235—64no—
598C2×D12—31no—
599C2×D12—31no—
600C2×D12—91no—
601C2×D12—91no—
602C2×D12—91no—
603C2×D12—91no—
604C2×D12—91no—
605C2×D12—91no—
606C2×D12—91no—
607C2×D12—91no—
608C2×D12—181no—
609C2×D12—181no—
610C2×D12—184no—
611C2×C4×D3—31no—
612C2×C4×D3—31no—
613C2×C4×D3—31no—
614C2×Dic6—31no—
615C2×Dic6—31no—
616C3×C4⋊C4—91no—
617C3×C22⋊C4—91no—
618C3×C22⋊C4—91no—
619C3×C22⋊C4—91no—
620C3×C22⋊C4—91no—
621C3×C22⋊C4—91no—
622#217—31no—
623#217—31no—
624#217—31no—
625#217—91no—
626#217—91no—
627#217—91no—
628#217—91no—
629#217—181no—
630(C2×D3)⋊C4—31no—
631(C2×D3)⋊C4—31no—
632(C2×D3)⋊C4—31no—
633(C2×D3)⋊C4—31no—
634(C2×D3)⋊C4—31no—
635(C2×D3)⋊C4—31no—
636(C2×D3)⋊C4—31no—
637(C2×D3)⋊C4—91no—
638(C2×D3)⋊C4—91no—
639(C2×D3)⋊C4—91no—
640(C2×D3)⋊C4—91no—
641(C2×D3)⋊C4—91no—
642(C2×D3)⋊C4—91no—
643(C2×D3)⋊C4—91no—
644(C2×D3)⋊C4—91no—
645(C2×D3)⋊C4—91no—
646(C2×D3)⋊C4—91no—
647(C2×D3)⋊C4—91no—
648(C2×D3)⋊C4—181no—
649(C2×D3)⋊C4—181no—
650(C2×D3)⋊C4—181no—
651(C2×D3)⋊C4—181no—
652C4⋊Dic3—31no—
653C4⋊Dic3—91no—
654C4⋊Dic3—91no—
655C4⋊Dic3—181no—
656Dic3⋊C4—31no—
657Dic3⋊C4—91no—
658C4×Dic3—91no—
659C4×Dic3—91no—
660C4×Dic3—91no—
661C4×Dic3—91no—
662C4×Dic3—91no—
663C4×Dic3—91no—
664C4×Dic3—181no—
665C22×C32—21no—
666C22×C32—22no—
667C22×C32—21no—
668C22×C32—21no—
669C22×C32—21no—
670C22×C32—21no—
671C22×C32—21no—
672C22×C32—21no—
673C22×C32—21no—
674C22×C32—21no—
675C22×C32—21no—
676C22×C32—21no—
677C22×C32—21no—
678C22×C32—32no—
679C22×C32—41no—
680C22×C32—41no—
681C22×C32—41no—
682C22×C32—42no—
683C22×C32—41no—
684C22×C32—41no—
685C22×C32—41no—
686C22×C32—41no—
687C22×C32—41no—
688C22×C32—41no—
689C22×C32—61no—
690C22×C32—61no—
691C22×C32—61no—
692C22×C32—61no—
693C22×C32—61no—
694C22×C32—81no—
695C22×C32—81no—
696C22×C32C23×D311yescharacteristic
697C22×C32C23×D311yescharacteristic
698C22×C32C23×D311yescharacteristic
699C2×C3⋊D3—21no—
700C2×C3⋊D3—21no—
701C2×C3⋊D3—21no—
702C2×C3⋊D3—21no—
703C2×C3⋊D3—21no—
704C2×C3⋊D3—21no—
705C2×C3⋊D3—21no—
706C2×C3⋊D3—21no—
707C2×C3⋊D3—21no—
708C2×C3⋊D3—61no—
709C2×C3⋊D3—62no—
710C2×C3⋊D3—61no—
711C2×C3⋊D3—61no—
712C2×C3⋊D3—61no—
713C2×C3⋊D3—61no—
714C2×C3⋊D3—61no—
715C2×C3⋊D3—61no—
716C2×C3⋊D3—61no—
717C2×C3⋊D3—61no—
718C2×C3⋊D3—121no—
719C2×C3⋊D3—121no—
720C2×C3⋊D3—122no—
721C2×C3⋊D3—121no—
722C2×C3⋊D3—121no—
723C2×C3⋊D3—121no—
724C2×C3⋊D3—121no—
725C2×C3⋊D3—121no—
726C2×C3⋊D3—121no—
727C2×C3⋊D3—124no—
728C2×C3⋊D3—241no—
729C2×C3⋊D3—241no—
730C2×C3×D3—21no—
731C2×C3×D3—21no—
732C2×C3×D3—21no—
733C2×C3×D3—21no—
734C2×C3×D3—21no—
735C2×C3×D3—21no—
736C2×C3×D3—21no—
737C2×C3×D3—21no—
738C2×C3×D3—21no—
739C2×C3×D3—21no—
740C2×C3×D3—22no—
741C2×C3×D3—41no—
742C2×C3×D3—41no—
743C2×C3×D3—41no—
744C2×C3×D3—41no—
745C2×C3×D3—41no—
746C2×C3×D3—62no—
747C2×C3×D3—61no—
748C2×C3×D3—61no—
749C2×C3×D3—61no—
750C2×C3×D3—61no—
751C2×C3×D3—61no—
752C2×C3×D3—61no—
753C2×C3×D3—61no—
754C2×C3×D3—61no—
755C2×C3×D3—61no—
756C2×C3×D3—61no—
757C2×C3×D3—61no—
758C2×C3×D3—61no—
759C2×C3×D3—61no—
760C2×C3×D3—61no—
761C2×C3×D3—61no—
762C2×C3×D3—61no—
763C2×C3×D3—61no—
764C2×C3×D3—61no—
765C2×C3×D3—121no—
766C2×C3×D3—121no—
767C2×C3×D3—121no—
768C2×C3×D3—121no—
769C2×C3×D3—121no—
770C2×C3×D3—121no—
771C2×C3×D3—121no—
772C2×C3×D3—121no—
773C2×C3×D3—124no—
774C2×C3×D3—124no—
775C2×C3×D3D3×D412yes—
776C2×C3×D3C2×#6712yes—
777D32—44no—
778D32—124no—
779D32—124no—
780D32—128no—
781C32×C4—32no—
782C32×C4—61no—
783C32×C4—61no—
784C32×C4—61no—
785C3⋊Dic3—21no—
786C3⋊Dic3—21no—
787C3⋊Dic3—61no—
788C3⋊Dic3—62no—
789C3⋊Dic3—61no—
790C3⋊Dic3—61no—
791C3⋊Dic3—121no—
792C3⋊Dic3—121no—
793C3⋊Dic3—122no—
794C3⋊Dic3C2×#6712yes—
795C3×Dic3—22no—
796C3×Dic3—21no—
797C3×Dic3—21no—
798C3×Dic3—21no—
799C3×Dic3—21no—
800C3×Dic3—21no—
801C3×Dic3—21no—
802C3×Dic3—22no—
803C3×Dic3—32no—
804C3×Dic3—32no—
805C3×Dic3—41no—
806C3×Dic3—41no—
807C3×Dic3—62no—
808C3×Dic3—61no—
809C3×Dic3—61no—
810C3×Dic3—61no—
811C3×Dic3—61no—
812C3×Dic3—121no—
813C3×Dic3—121no—
814C3×Dic3D3×D412yes—
815C3×Dic3C2×#6712yes—
816C2×#41—91no—
817C22×D4—271no—
818#127—271no—
819#127—271no—
820#124—271no—
821#124—271no—
822#121—91no—
823#121—271no—
824#121—271no—
825#121—271no—
826#120—91no—
827#120—271no—
828#120—271no—
829#120—271no—
830#117—271no—
831C33#53511yescharacteristic, complemented, Sylow
832C23×C3—21no—
833C23×C3—21no—
834C23×C3—21no—
835C23×C3—31no—
836C23×C3—31no—
837C23×C3—31no—
838C23×C3—31no—
839C23×C3—41no—
840C23×C3—61no—
841C23×C3—61no—
842C23×C3—91no—
843C23×C3—91no—
844C23×C3—91no—
845C23×C3—182no—
846C23×C3—361no—
847C23×C3—361no—
848C23×C3C2×D3211yescharacteristic
849C23×C3C2×D3211yescharacteristic
850C23×C3C2×D3211yescharacteristic
851C22×D3—31no—
852C22×D3—31no—
853C22×D3—31no—
854C22×D3—31no—
855C22×D3—31no—
856C22×D3—31no—
857C22×D3—61no—
858C22×D3—61no—
859C22×D3—61no—
860C22×D3—62no—
861C22×D3—62no—
862C22×D3—91no—
863C22×D3—91no—
864C22×D3—91no—
865C22×D3—121no—
866C22×D3—121no—
867C22×D3—121no—
868C22×D3—121no—
869C22×D3—181no—
870C22×D3—181no—
871C22×D3—181no—
872C22×D3—182no—
873C22×D3—182no—
874C22×D3—182no—
875C22×D3—361no—
876C22×D3—362no—
877C22×D3—361no—
878C22×D3—361no—
879C22×D3—361no—
880C22×D3—361no—
881C22×D3—361no—
882C22×D3—361no—
883C22×D3—362no—
884C22×D3—362no—
885C22×D3C2×D3211yescharacteristic
886C22×D3C2×D3211yescharacteristic
887C3×Q8—182no—
888C3×D4—62no—
889C3×D4—62no—
890C3×D4—122no—
891C3×D4—121no—
892C3×D4—121no—
893C3×D4—122no—
894C3×D4—182no—
895C3×D4—182no—
896C3×D4—182no—
897C3×D4—361no—
898C3×D4—361no—
899C2×C3×C4—31no—
900C2×C3×C4—31no—
901C2×C3×C4—31no—
902C2×C3×C4—31no—
903C2×C3×C4—31no—
904C2×C3×C4—31no—
905C2×C3×C4—31no—
906C2×C3×C4—31no—
907C2×C3×C4—61no—
908C2×C3×C4—61no—
909C2×C3×C4—61no—
910C2×C3×C4—61no—
911C2×C3×C4—62no—
912C2×C3×C4—62no—
913C2×C3×C4—94no—
914C2×C3×C4—91no—
915C2×C3×C4—91no—
916C2×C3×C4—91no—
917C2×C3×C4—122no—
918C2×C3×C4—182no—
919#67—22no—
920#67—41no—
921#67—62no—
922#67—62no—
923#67—62no—
924#67—62no—
925#67—122no—
926#67—121no—
927#67—121no—
928#67—121no—
929#67—121no—
930#67—122no—
931#67—122no—
932#67—182no—
933#67—182no—
934#67—182no—
935#67—182no—
936#67—182no—
937#67—362no—
938#67—361no—
939#67—361no—
940#67—361no—
941#67—361no—
942#67—361no—
943#67—361no—
944#67—361no—
945#67—361no—
946#67—362no—
947#67—361no—
948#67—361no—
949#67—361no—
950#67—362no—
951#67—362no—
952#67—362no—
953#67—364no—
954C2×Dic3—22no—
955C2×Dic3—31no—
956C2×Dic3—31no—
957C2×Dic3—34no—
958C2×Dic3—31no—
959C2×Dic3—31no—
960C2×Dic3—31no—
961C2×Dic3—31no—
962C2×Dic3—61no—
963C2×Dic3—61no—
964C2×Dic3—61no—
965C2×Dic3—91no—
966C2×Dic3—91no—
967C2×Dic3—91no—
968C2×Dic3—181no—
969C2×Dic3—181no—
970C2×Dic3—181no—
971C2×Dic3—361no—
972C2×Dic3C2×D3211yescharacteristic
973C2×Dic3C2×D3211yescharacteristic
974C2×Dic3C2×D3211yescharacteristic
975C2×Dic3C2×D3211yescharacteristic
976D12—62no—
977D12—62no—
978D12—182no—
979D12—182no—
980D12—182no—
981D12—182no—
982D12—362no—
983D12—361no—
984D12—361no—
985D12—362no—
986D12—361no—
987D12—361no—
988C4×D3—34no—
989C4×D3—62no—
990C4×D3—62no—
991Dic6—62no—
992Dic6—62no—
993C2×C32—21no—
994C2×C32—21no—
995C2×C32—21no—
996C2×C32—21no—
997C2×C32—21no—
998C2×C32—21no—
999C2×C32—21no—
1000C2×C32—21no—
1001C2×C32—21no—
1002C2×C32—41no—
1003C2×C32—41no—
1004C2×C32—41no—
1005C2×C32—41no—
1006C2×C32—42no—
1007C2×C32—41no—
1008C2×C32—41no—
1009C2×C32—62no—
1010C2×C32—81no—
1011C2×C32—81no—
1012C2×C32—82no—
1013C2×C32—121no—
1014C2×C32C2×D3×D411yescharacteristic
1015C2×C32C2×D3×D411yescharacteristic
1016C2×C32#100411yescharacteristic
1017C2×C32#100411yescharacteristic
1018C2×C32#100411yescharacteristic
1019C2×C32#100911yescharacteristic
1020C2×C32#100911yescharacteristic
1021C2×C32#100911yescharacteristic
1022C2×C32C22×#6711yescharacteristic
1023C3⋊D3—41no—
1024C3⋊D3—41no—
1025C3⋊D3—41no—
1026C3⋊D3—121no—
1027C3⋊D3—122no—
1028C3⋊D3—121no—
1029C3⋊D3—121no—
1030C3⋊D3—241no—
1031C3⋊D3—241no—
1032C3⋊D3—242no—
1033C3×D3—22no—
1034C3×D3—22no—
1035C3×D3—42no—
1036C3×D3—41no—
1037C3×D3—41no—
1038C3×D3—81no—
1039C3×D3—122no—
1040C3×D3—121no—
1041C3×D3—121no—
1042C3×D3—121no—
1043C3×D3—121no—
1044C3×D3—121no—
1045C3×D3—121no—
1046C3×D3—241no—
1047C3×D3—241no—
1048C24—91no—
1049C24—271no—
1050#41—184no—
1051C2×Q8—91no—
1052C2×D4—31no—
1053C2×D4—31no—
1054C2×D4—91no—
1055C2×D4—91no—
1056C2×D4—91no—
1057C2×D4—91no—
1058C2×D4—91no—
1059C2×D4—271no—
1060C2×D4—271no—
1061C2×D4—271no—
1062C2×D4—271no—
1063C2×D4—271no—
1064C2×D4—271no—
1065C2×D4—271no—
1066C2×D4—271no—
1067C2×D4—544no—
1068C22×C4—31no—
1069C22×C4—91no—
1070C22×C4—91no—
1071C4⋊C4—91no—
1072C4⋊C4—271no—
1073C22⋊C4—91no—
1074C22⋊C4—91no—
1075C22⋊C4—91no—
1076C22⋊C4—91no—
1077C22⋊C4—91no—
1078C22⋊C4—271no—
1079C22⋊C4—271no—
1080C22⋊C4—271no—
1081C22⋊C4—271no—
1082C22⋊C4—271no—
1083C42—271no—
1084C42—271no—
1085C22×C3—22no—
1086C22×C3—21no—
1087C22×C3—21no—
1088C22×C3—21no—
1089C22×C3—21no—
1090C22×C3—21no—
1091C22×C3—21no—
1092C22×C3—21no—
1093C22×C3—21no—
1094C22×C3—21no—
1095C22×C3—21no—
1096C22×C3—21no—
1097C22×C3—21no—
1098C22×C3—32no—
1099C22×C3—32no—
1100C22×C3—41no—
1101C22×C3—41no—
1102C22×C3—41no—
1103C22×C3—41no—
1104C22×C3—41no—
1105C22×C3—41no—
1106C22×C3—41no—
1107C22×C3—41no—
1108C22×C3—42no—
1109C22×C3—41no—
1110C22×C3—62no—
1111C22×C3—61no—
1112C22×C3—61no—
1113C22×C3—61no—
1114C22×C3—61no—
1115C22×C3—61no—
1116C22×C3—61no—
1117C22×C3—61no—
1118C22×C3—61no—
1119C22×C3—61no—
1120C22×C3—61no—
1121C22×C3—81no—
1122C22×C3—81no—
1123C22×C3—121no—
1124C22×C3—121no—
1125C22×C3—121no—
1126C22×C3—121no—
1127C22×C3—121no—
1128C22×C3—181no—
1129C22×C3—181no—
1130C22×C3—181no—
1131C22×C3—181no—
1132C22×C3—181no—
1133C22×C3—181no—
1134C22×C3—181no—
1135C22×C3—181no—
1136C22×C3—181no—
1137C22×C3—364no—
1138C22×C3C22×D3211yescharacteristic
1139C22×C3C22×D3211yescharacteristic
1140C22×C3C22×D3211yescharacteristic
1141C2×D3—21no—
1142C2×D3—21no—
1143C2×D3—21no—
1144C2×D3—21no—
1145C2×D3—21no—
1146C2×D3—62no—
1147C2×D3—61no—
1148C2×D3—61no—
1149C2×D3—61no—
1150C2×D3—61no—
1151C2×D3—61no—
1152C2×D3—61no—
1153C2×D3—61no—
1154C2×D3—61no—
1155C2×D3—61no—
1156C2×D3—61no—
1157C2×D3—61no—
1158C2×D3—61no—
1159C2×D3—61no—
1160C2×D3—61no—
1161C2×D3—61no—
1162C2×D3—61no—
1163C2×D3—61no—
1164C2×D3—61no—
1165C2×D3—121no—
1166C2×D3—121no—
1167C2×D3—121no—
1168C2×D3—121no—
1169C2×D3—121no—
1170C2×D3—121no—
1171C2×D3—121no—
1172C2×D3—121no—
1173C2×D3—124no—
1174C2×D3—124no—
1175C2×D3—182no—
1176C2×D3—181no—
1177C2×D3—181no—
1178C2×D3—181no—
1179C2×D3—181no—
1180C2×D3—181no—
1181C2×D3—181no—
1182C2×D3—181no—
1183C2×D3—181no—
1184C2×D3—181no—
1185C2×D3—361no—
1186C2×D3—361no—
1187C2×D3—361no—
1188C2×D3—361no—
1189C2×D3—361no—
1190C2×D3—361no—
1191C2×D3—361no—
1192C2×D3—361no—
1193C2×D3—362no—
1194C2×D3—364no—
1195C2×D3—364no—
1196C2×D3—364no—
1197C2×D3—368no—
1198C2×D3—721no—
1199C2×D3—721no—
1200C2×D3D3×#6712yes—
1201C3×C4—32no—
1202C3×C4—32no—
1203C3×C4—62no—
1204C3×C4—62no—
1205C3×C4—61no—
1206C3×C4—61no—
1207C3×C4—61no—
1208C3×C4—61no—
1209C3×C4—61no—
1210C3×C4—61no—
1211C3×C4—92no—
1212C3×C4—121no—
1213C3×C4—121no—
1214C3×C4—181no—
1215C3×C4—181no—
1216Dic3—21no—
1217Dic3—21no—
1218Dic3—21no—
1219Dic3—32no—
1220Dic3—32no—
1221Dic3—62no—
1222Dic3—61no—
1223Dic3—61no—
1224Dic3—61no—
1225Dic3—61no—
1226Dic3—121no—
1227Dic3—121no—
1228Dic3—182no—
1229Dic3—181no—
1230Dic3—181no—
1231Dic3—181no—
1232Dic3—361no—
1233Dic3—361no—
1234Dic3—362no—
1235Dic3D3×#6712yes—
1236C32—21no—
1237C32—21no—
1238C32—21no—
1239C32—41no—
1240C32#559211yescharacteristic, complemented
1241C32#560711yescharacteristic, complemented
1242C32#583011yescharacteristic, complemented
1243C23—31no—
1244C23—31no—
1245C23—91no—
1246C23—91no—
1247C23—91no—
1248C23—182no—
1249C23—271no—
1250C23—361no—
1251C23—361no—
1252C23—542no—
1253C23—1081no—
1254C23—1081no—
1255C23D3311yescharacteristic
1256Q8—182no—
1257D4—62no—
1258D4—121no—
1259D4—182no—
1260D4—182no—
1261D4—182no—
1262D4—361no—
1263D4—361no—
1264D4—542no—
1265D4—542no—
1266D4—542no—
1267D4—1081no—
1268D4—1081no—
1269D4—1081no—
1270D4—1081no—
1271D4—1081no—
1272C2×C4—31no—
1273C2×C4—31no—
1274C2×C4—31no—
1275C2×C4—31no—
1276C2×C4—62no—
1277C2×C4—94no—
1278C2×C4—91no—
1279C2×C4—91no—
1280C2×C4—91no—
1281C2×C4—182no—
1282C2×C4—271no—
1283C2×C3—21no—
1284C2×C3—21no—
1285C2×C3—21no—
1286C2×C3—21no—
1287C2×C3—21no—
1288C2×C3—21no—
1289C2×C3—21no—
1290C2×C3—21no—
1291C2×C3—21no—
1292C2×C3—42no—
1293C2×C3—41no—
1294C2×C3—41no—
1295C2×C3—41no—
1296C2×C3—41no—
1297C2×C3—41no—
1298C2×C3—41no—
1299C2×C3—62no—
1300C2×C3—62no—
1301C2×C3—81no—
1302C2×C3—81no—
1303C2×C3—82no—
1304C2×C3—122no—
1305C2×C3—121no—
1306C2×C3—121no—
1307C2×C3—241no—
1308C2×C3—361no—
1309C2×C3—361no—
1310C2×C3—361no—
1311C2×C3#6430711yescharacteristic
1312C2×C3#6430811yescharacteristic
1313C2×C3D32×D411yescharacteristic
1314C2×C3#6431411yescharacteristic
1315C2×C3#6431411yescharacteristic
1316C2×C3#6431411yescharacteristic
1317C2×C3C2×D3×#6711yescharacteristic
1318C2×C3C2×D3×#6711yescharacteristic
1319C2×C3#6433011yescharacteristic
1320D3—22no—
1321D3—41no—
1322D3—122no—
1323D3—121no—
1324D3—121no—
1325D3—121no—
1326D3—121no—
1327D3—121no—
1328D3—121no—
1329D3—241no—
1330D3—241no—
1331D3—362no—
1332D3—361no—
1333D3—361no—
1334D3—361no—
1335D3—721no—
1336D3—721no—
1337D3—722no—
1338C22—21no—
1339C22—21no—
1340C22—21no—
1341C22—32no—
1342C22—61no—
1343C22—61no—
1344C22—61no—
1345C22—61no—
1346C22—61no—
1347C22—181no—
1348C22—181no—
1349C22—181no—
1350C22—181no—
1351C22—181no—
1352C22—181no—
1353C22—181no—
1354C22—181no—
1355C22—181no—
1356C22—364no—
1357C22—541no—
1358C22—541no—
1359C22—541no—
1360C22—1084no—
1361C22C2×D3311yescharacteristic
1362C4—32no—
1363C4—61no—
1364C4—61no—
1365C4—61no—
1366C4—92no—
1367C4—181no—
1368C4—181no—
1369C4—541no—
1370C3—21no—
1371C3—21no—
1372C3—21no—
1373C3—41no—
1374C3#1059506411yescharacteristic, complemented
1375C3#1059523811yescharacteristic, complemented
1376C3#1059528511yescharacteristic, complemented
1377C2—41no—
1378C2—62no—
1379C2—121no—
1380C2—361no—
1381C2—361no—
1382C2—361no—
1383C2—1081no—
1384C2#1172441811yescharacteristic
1385C2#1172442011yescharacteristic
1386C2D32×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
hypercenterC23D33
hypocenterC33#535
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C2×C3×#3804C2semidirect
2. C2×D3×#626C2semidirect
3. #11723728C2semidirect
4. #11723643C2semidirect
5. #11723633C2semidirect
6. #11723632C2semidirect
7. C3×#63983C2semidirect
8. C3×#63978C2semidirect
9. #11723007C2semidirect
10. #11723005C2semidirect
11. #11722961C2semidirect
12. #11722957C2semidirect
13. #11722950C2semidirect
14. #11722947C2semidirect
15. #11722914C2semidirect
21. C2×#6312C22semidirect
22. C2×C3×#638C22semidirect
23. C2×C3×#638C22semidirect
24. C2×C3×#638C22semidirect
26. C2×C32×#67C22semidirect
27. C22×C32×Dic3C22semidirect
29. C2×#6295C22semidirect
30. C2×#6295C22semidirect
32. C2×#6292C22semidirect
34. C2×#6290C22semidirect
35. C2×C3×#627C22semidirect
38. C2×C3×#624C22semidirect
42. #88813C22semidirect
43. Dic3⋊(C3⋊Dic3)C22semidirect
44. #88804C22semidirect
45. #88804C22semidirect
46. #88803C22semidirect
47. #88803C22semidirect
49. Dic3×C3⋊Dic3C22semidirect
50. C3×Dic3⋊Dic3C22semidirect
51. C3×#3722C22semidirect
52. C3×#3722C22semidirect
54. C3×(C2×D3)⋊Dic3C22semidirect
55. C3×(C2×D3)⋊Dic3C22semidirect
60. C2×#3804D3semidirect
72. #63983D3semidirect
83. #63978D3semidirect
143. C3×D3×Dic3D4semidirect
166. C2×#638C2×D3semidirect
167. C2×#638C2×D3semidirect
168. C2×#638C2×D3semidirect
186. C2×C3×#67C2×D3semidirect
187. C2×C3×#67C2×D3semidirect
190. C22×C3×Dic3C2×D3semidirect
191. C22×C3×Dic3C2×D3semidirect
202. C2×#627C2×D3semidirect
227. C2×#624C2×D3semidirect
253. Dic3⋊Dic3C2×D3semidirect
260. #3722C2×D3semidirect
261. #3722C2×D3semidirect
272. (C2×D3)⋊Dic3C2×D3semidirect
273. (C2×D3)⋊Dic3C2×D3semidirect
520. D3×Dic3#67semidirect
592. C2×#67D32semidirect
594. C22×Dic3D32semidirect
831. C33#535semidirect
1240. C32#5592semidirect
1241. C32#5607semidirect
1242. C32#5830semidirect
1374. C3#10595064semidirect
1375. C3#10595238semidirect
1376. C3#10595285semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#38042
C2×D3×#6262
#117237282
#117236432
#117236332
#117236322
C3×#639832
C3×#639782
#117230072
#117230052
#117229612
#117229572
#117229502
#117229472
#117229142
#105952853
#105952383
#105950643