Finite Group Databasebeta

← #13172866

Subgroups — #13172866

Order 1728.

1810 conjugacy classes of subgroups.

The subgroup lattice has 1398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#638C211yesmaximal, characteristic, complemented
2C2×#88961C211yesmaximal, characteristic, complemented
3#11723725C211yesmaximal, characteristic, complemented
4#11723633C211yesmaximal, characteristic, complemented
5#11723592C211yesmaximal, characteristic, complemented
6C3×#63977C211yesmaximal, characteristic, complemented
7C3×#63976C211yesmaximal, characteristic, complemented
8C3×#63971C211yesmaximal, characteristic, complemented
9#11723029C211yesmaximal, characteristic, complemented
10#11723009C211yesmaximal, characteristic, complemented
11#11722966C211yesmaximal, characteristic, complemented
12#11722958C211yesmaximal, characteristic, complemented
13#11722950C211yesmaximal, characteristic, complemented
14#11722949C211yesmaximal, characteristic, complemented
15#11722917C211yesmaximal, characteristic, complemented
16#10595502—31nomaximal
17#10595285—31nomaximal
18#10594269—31nomaximal
19C23×C32×D3C2211yescharacteristic
20C22×D3×C3⋊D3C2211yescharacteristic
21C2×#6312C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic
23C2×C3×#638C2211yescharacteristic, complemented
24C2×C32×#67C2211yescharacteristic, complemented
25C2×#6295C2211yescharacteristic, complemented
26C2×#6294C2211yescharacteristic, complemented
27D3×#638—24no—
28C2×#6293C2211yescharacteristic, complemented
29C2×#6292C2211yescharacteristic, complemented
30C2×#6291C2211yescharacteristic
31C2×#6291C2211yescharacteristic, complemented
32C2×#6290C2211yescharacteristic
33C2×#6290C2211yescharacteristic, complemented
34C2×D3×C3⋊Dic3C2211yescharacteristic
35C2×C3×#626C2211yescharacteristic
36C2×C3×#626C2211yescharacteristic, complemented
37C2×C3×#626C2211yescharacteristic, complemented
38C2×C3×#625C2211yescharacteristic
39C2×C3×#625C2211yescharacteristic, complemented
40C2×C3×D3×Dic3C2211yescharacteristic, complemented
41#88961—24no—
42C3×#3757C2211yescharacteristic, complemented
43C32×#217C2211yescharacteristic, complemented
44#88815C2211yescharacteristic, complemented
45#88814C2211yescharacteristic, complemented
46#88804C2211yescharacteristic, complemented
47#88804C2211yescharacteristic, complemented
48Dic3×C3⋊Dic3C2211yescharacteristic, complemented
49Dic3×C3⋊Dic3C2211yescharacteristic, complemented
50C3×#3724C2211yescharacteristic, complemented
51C3×#3722C2211yescharacteristic, complemented
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×(C2×D3)⋊Dic3C2211yescharacteristic
54C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
55C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
56C22×#638—31no—
57C2×D3×#67—31no—
58C2×D3×#67—31no—
59C2×D3×#67—61no—
60C2×#3805—31no—
61C2×#3804—31no—
62C2×#3795—31no—
63#64149—31no—
64#64094—31no—
65C3×#953—31no—
66C3×#953—31no—
67C3×#939—31no—
68C3×#937—31no—
69C3×#884—31no—
70C3×#882—31no—
71#63983—31no—
72#63981—31no—
73#63981—31no—
74#63979—31no—
75#63979—31no—
76#63979—31no—
77#63979—31no—
78#63979—61no—
79#63978—31no—
80#63977D311yescharacteristic, complemented
81#63976D311yescharacteristic, complemented
82#63971—31no—
83#63971—31no—
84#63971—31no—
85#63971D311yescharacteristic, complemented
86#63970—31no—
87#63958—31no—
88#63957—31no—
89#63953—31no—
90#63953—31no—
91#63953—31no—
92#63953—61no—
93#63923—31no—
94#63922—31no—
95#63922—31no—
96#63915—31no—
97#63914—31no—
98#63913—31no—
99#63910—31no—
100#63906—31no—
101#63886—31no—
102#63878—31no—
103#63878—31no—
104C23×C33C2311yescharacteristic
105C22×C3⋊(C3⋊D3)C2311yescharacteristic
106C22×C3×C3⋊D3C2311yescharacteristic
107C22×C3×C3⋊D3C2311yescharacteristic
108C22×C32×D3—22no—
109C22×C32×D3—41no—
110C22×C32×D3—41no—
111C22×C32×D3C2311yescharacteristic
112C22×C32×D3C2311yescharacteristic
113C22×C32×D3C2311yescharacteristic
114C2×D3×C3⋊D3—22no—
115C2×D3×C3⋊D3—41no—
116C2×D3×C3⋊D3—41no—
117#6312—22no—
118C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
119C3×#638—22no—
120C3×#638—41no—
121C2×C3×C3⋊Dic3C2311yescharacteristic
122C2×C3×C3⋊Dic3C2311yescharacteristic
123C2×C3×C3⋊Dic3C2311yescharacteristic
124C2×C3×C3⋊Dic3C2311yescharacteristic
125C32×#67—41no—
126C2×C32×Dic3C2311yescharacteristic
127C2×C32×Dic3C2311yescharacteristic
128C2×C32×Dic3C2311yescharacteristic
129#6295—41no—
130#6294—22no—
131#6293—22no—
132#6292—41no—
133#6291—22no—
134#6291—41no—
135#6290—22no—
136#6290—22no—
137D3×C3⋊Dic3D414yescomplemented
138C3×#626—22no—
139C3×#626—41no—
140C3×#626—41no—
141C3×#625—22no—
142C3×#625—41no—
143C3×D3×Dic3—22no—
144#5607—91no—
145#5592—91no—
146#5592—91no—
147C24×C32—31no—
148C23×C3⋊D3—31no—
149C23×C3×D3—21no—
150C23×C3×D3C2×D311yescharacteristic
151C23×C3×D3C2×D311yescharacteristic
152C22×D32—31no—
153C22×D32—31no—
154C22×D32—61no—
155C2×C32×D4—31no—
156C2×#638—31no—
157C2×#638—31no—
158C2×#638—31no—
159C2×#638—31no—
160C2×#638—31no—
161C2×#638—31no—
162C2×#638—31no—
163C2×#638—64no—
164C2×#638—61no—
165C2×#638—61no—
166C2×#638—61no—
167C2×#638—121no—
168C2×#638C2×D311yescharacteristic
169C2×#638C2×D311yescharacteristic, complemented
170C22×C3⋊Dic3—31no—
171C2×C4⋊(C3⋊D3)—31no—
172C2×#634—31no—
173C2×C3×#67—21no—
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—31no—
182C2×C3×#67—31no—
183C2×C3×#67—31no—
184C2×C3×#67—31no—
185C2×C3×#67—61no—
186C2×C3×#67—61no—
187C2×C3×#67C2×D311yescharacteristic, complemented
188C2×C3×#67C2×D311yescharacteristic, complemented
189C22×C3×Dic3—31no—
190C2×C3×D12—31no—
191C2×C3×D12—31no—
192C2×C3×D12—31no—
193C2×C3×C4×D3—31no—
194D3×#67—64no—
195D3×#67—64no—
196D3×#67—68no—
197C2×#627—31no—
198C2×#627—31no—
199C2×#627—61no—
200C2×#626—31no—
201C2×#626—31no—
202C2×#626—31no—
203C2×#626—31no—
204C2×#626—31no—
205C2×#626—31no—
206C2×#626—31no—
207C2×#626—31no—
208C2×#626—61no—
209C2×#626—61no—
210C2×#626—61no—
211C2×#626C2×D311yescharacteristic
212C2×#626C2×D311yescharacteristic, complemented
213C2×#626C2×D311yescharacteristic, complemented
214C2×#625—31no—
215C2×#625—31no—
216C2×#625—31no—
217C2×#625—31no—
218C2×#625—31no—
219C2×#625—61no—
220C2×#625—61no—
221C2×#625C2×D311yescharacteristic
222C2×#625C2×D311yescharacteristic, complemented
223C2×#624—31no—
224#3805—64no—
225#3804—64no—
226C2×D3×Dic3—31no—
227C2×D3×Dic3—31no—
228C2×D3×Dic3—31no—
229C2×D3×Dic3—31no—
230C2×D3×Dic3—61no—
231C2×D3×Dic3C2×D311yescharacteristic, complemented
232#3795—64no—
233C32×C22⋊C4—31no—
234#3757C2×D311yescharacteristic, complemented
235#3752—31no—
236#3752—31no—
237C4×C3⋊Dic3—31no—
238C4×C3⋊Dic3—31no—
239C3×#217—21no—
240C3×#217—31no—
241C3×#217—31no—
242C3×#217—31no—
243C3×#217—31no—
244C3×#217—31no—
245C3×#217—31no—
246C3×#217—61no—
247C3×#217C2×D311yescharacteristic, complemented
248C3×#217C2×D311yescharacteristic, complemented
249C3×(C2×D3)⋊C4—31no—
250C3×(C2×D3)⋊C4—31no—
251C3×(C2×D3)⋊C4—31no—
252C3×(C2×D3)⋊C4—31no—
253C3×(C2×D3)⋊C4—31no—
254C3×(C2×D3)⋊C4—31no—
255C3×Dic3⋊C4—31no—
256C3×Dic3⋊C4—31no—
257#3724—31no—
258#3724C2×D311yescharacteristic, complemented
259Dic3⋊Dic3—31no—
260Dic3⋊Dic3—31no—
261#3722—31no—
262#3722—31no—
263#3722—31no—
264#3722—31no—
265#3722—31no—
266#3722—61no—
267#3722—61no—
268#3722C2×D311yescharacteristic, complemented
269(C2×D3)⋊Dic3—31no—
270(C2×D3)⋊Dic3—31no—
271(C2×D3)⋊Dic3C2×D311yescharacteristic
272(C2×D3)⋊Dic3C2×D311yescharacteristic
273(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
274(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
275Dic32—31no—
276Dic32—31no—
277Dic32—31no—
278Dic32—31no—
279Dic32—61no—
280Dic32—61no—
281C22×C33—21no—
282C22×C33—21no—
283C22×C33—21no—
284C22×C33C2411yescharacteristic
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×C32×D3—21no—
295C2×C32×D3—21no—
296C2×C32×D3—21no—
297C2×C32×D3—21no—
298C2×C32×D3—21no—
299C2×C32×D3—21no—
300C2×C32×D3—21no—
301C2×C32×D3—21no—
302C2×C32×D3—44no—
303C2×C32×D3C2×D412yes—
304D3×C3⋊D3—44no—
305C3⋊(C3⋊Dic3)C2×D412yes—
306C3×C3⋊Dic3—21no—
307C3×C3⋊Dic3—21no—
308C3×C3⋊Dic3—21no—
309C3×C3⋊Dic3C2×D412yes—
310C32×Dic3—21no—
311C32×Dic3—21no—
312C32×Dic3—21no—
313C22×#67—91no—
314C22×#67—91no—
315C22×#67—181no—
316C2×#237—91no—
317C2×#237—91no—
318C2×D3×D4—91no—
319C2×#235—91no—
320C3×#121—91no—
321C3×#120—91no—
322C3×#120—91no—
323#953—31no—
324#953—31no—
325#940—91no—
326#940—91no—
327#940—91no—
328#940—91no—
329#940—91no—
330#940—91no—
331#940—181no—
332#939—31no—
333#939—91no—
334#939—91no—
335#939—91no—
336#938—91no—
337#937—31no—
338#937—91no—
339#937—91no—
340#937—91no—
341#930—91no—
342#895—91no—
343#892—91no—
344#885—91no—
345#885—91no—
346#885—91no—
347#885—91no—
348#885—91no—
349#885—91no—
350#885—181no—
351#884—31no—
352#884—91no—
353#884—91no—
354#884—91no—
355#882—31no—
356#882—91no—
357#882—91no—
358#882—91no—
359#877—91no—
360#877—91no—
361C23×C32—21no—
362C23×C32—21no—
363C23×C32—21no—
364C23×C32—31no—
365C23×C32—31no—
366C23×C32—31no—
367C23×C32—41no—
368C23×C32—62no—
369C23×C32—121no—
370C23×C32—121no—
371C23×C32C22×D311yescharacteristic
372C23×C32C22×D311yescharacteristic
373C23×C32C22×D311yescharacteristic
374C22×C3⋊D3—31no—
375C22×C3⋊D3—31no—
376C22×C3⋊D3—31no—
377C22×C3⋊D3—61no—
378C22×C3⋊D3—61no—
379C22×C3⋊D3—61no—
380C22×C3⋊D3—62no—
381C22×C3⋊D3—121no—
382C22×C3⋊D3—121no—
383C22×C3⋊D3—121no—
384C22×C3⋊D3C22×D311yescharacteristic
385C22×C3⋊D3C22×D311yescharacteristic
386C22×C3×D3—24no—
387C22×C3×D3—22no—
388C22×C3×D3—22no—
389C22×C3×D3—21no—
390C22×C3×D3—21no—
391C22×C3×D3—21no—
392C22×C3×D3—31no—
393C22×C3×D3—31no—
394C22×C3×D3—31no—
395C22×C3×D3—31no—
396C22×C3×D3—41no—
397C22×C3×D3—41no—
398C22×C3×D3—41no—
399C22×C3×D3—41no—
400C22×C3×D3—42no—
401C22×C3×D3—42no—
402C22×C3×D3—61no—
403C22×C3×D3—61no—
404C22×C3×D3C22×D311yescharacteristic
405C22×C3×D3C22×D311yescharacteristic
406C22×C3×D3C22×D311yescharacteristic
407C22×C3×D3C22×D311yescharacteristic
408C22×C3×D3C22×D311yescharacteristic
409C22×C3×D3C22×D311yescharacteristic
410C2×D32—64no—
411C2×D32—62no—
412C2×D32—62no—
413C2×D32—121no—
414C2×D32—121no—
415C2×D32—121no—
416C2×D32—121no—
417C2×D32—122no—
418C2×D32—122no—
419C32×D4—121no—
420C2×C32×C4—31no—
421C2×C32×C4—31no—
422C2×C32×C4—31no—
423#638—22no—
424#638—41no—
425#638—62no—
426#638—62no—
427#638—62no—
428#638—62no—
429#638—62no—
430#638—62no—
431#638—64no—
432#638—122no—
433#638—122no—
434#638—124no—
435#638—121no—
436C2×C3⋊Dic3—31no—
437C2×C3⋊Dic3—31no—
438C2×C3⋊Dic3—31no—
439C2×C3⋊Dic3—34no—
440C2×C3⋊Dic3—61no—
441C2×C3⋊Dic3—61no—
442C2×C3⋊Dic3—61no—
443C2×C3⋊Dic3—121no—
444C2×C3⋊Dic3C22×D311yescharacteristic
445C2×C3⋊Dic3C22×D311yescharacteristic
446C2×C3⋊Dic3C22×D311yescharacteristic
447C2×C3⋊Dic3C22×D311yescharacteristic
448C4⋊(C3⋊D3)—121no—
449#634—62no—
450C3×#67—41no—
451C3×#67—41no—
452C3×#67—42no—
453C3×#67—62no—
454C3×#67—62no—
455C3×#67—62no—
456C3×#67—62no—
457C3×#67—64no—
458C3×#67—62no—
459C3×#67—121no—
460C3×#67—121no—
461C3×#67—121no—
462C3×#67—121no—
463C3×#67—121no—
464C3×#67—121no—
465C3×#67—122no—
466C2×C3×Dic3—21no—
467C2×C3×Dic3—21no—
468C2×C3×Dic3—21no—
469C2×C3×Dic3—31no—
470C2×C3×Dic3—31no—
471C2×C3×Dic3—31no—
472C2×C3×Dic3—31no—
473C2×C3×Dic3—31no—
474C2×C3×Dic3—31no—
475C2×C3×Dic3—31no—
476C2×C3×Dic3—31no—
477C2×C3×Dic3—61no—
478C2×C3×Dic3—61no—
479C2×C3×Dic3—61no—
480C2×C3×Dic3—61no—
481C2×C3×Dic3—62no—
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—121no—
490C3×D12—121no—
491C3×C4×D3—62no—
492#627—62no—
493#627—62no—
494#627—122no—
495#626—22no—
496#626—41no—
497#626—41no—
498#626—62no—
499#626—62no—
500#626—64no—
501#626—121no—
502#626—121no—
503#626—122no—
504#626—121no—
505#626—121no—
506#626—122no—
507#626—121no—
508#626—121no—
509#625—22no—
510#625—41no—
511#625—62no—
512#625—62no—
513#625—62no—
514#625—62no—
515#625—64no—
516#625—122no—
517#625—121no—
518#624—62no—
519D3×Dic3—22no—
520D3×Dic3—34no—
521D3×Dic3—34no—
522D3×Dic3—64no—
523D3×Dic3—62no—
524D3×Dic3—62no—
525#535—271noSylow
526C2×C33—41no—
527C2×C33C22×D411yescharacteristic
528C2×C33H(5,𝔽2)11yescharacteristic
529C2×C33H(5,𝔽2)11yescharacteristic
530C3⋊(C3⋊D3)—41no—
531C3×C3⋊D3—41no—
532C3×C3⋊D3—41no—
533C32×D3—22no—
534C32×D3—41no—
535C32×D3—41no—
536C24×C3—31no—
537C24×C3—31no—
538C24×C3—61no—
539C23×D3—91no—
540C23×D3—91no—
541C23×D3—91no—
542C23×D3—181no—
543C23×D3D3211yescharacteristic
544C2×C3×D4—31no—
545C2×C3×D4—31no—
546C2×C3×D4—61no—
547C2×C3×D4—91no—
548C2×C3×D4—91no—
549C2×C3×D4—91no—
550C2×C3×D4—91no—
551C2×C3×D4—91no—
552C2×C3×D4—91no—
553C2×C3×D4—91no—
554C22×C3×C4—91no—
555C2×#67—31no—
556C2×#67—31no—
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—31no—
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—181no—
590C2×#67—181no—
591C2×#67—184no—
592C2×#67—184no—
593C2×#67—188no—
594C2×#67—361no—
595C2×#67D3211yescharacteristic, complemented
596C22×Dic3—31no—
597C22×Dic3—91no—
598C22×Dic3—91no—
599C22×Dic3—91no—
600C22×Dic3—181no—
601#237—184no—
602#237—184no—
603D3×D4—184no—
604#235—184no—
605C2×D12—31no—
606C2×D12—31no—
607C2×D12—31no—
608C2×D12—91no—
609C2×D12—91no—
610C2×D12—91no—
611C2×D12—91no—
612C2×D12—91no—
613C2×D12—181no—
614C2×C4×D3—31no—
615C2×C4×D3—91no—
616C2×C4×D3—91no—
617C2×C4×D3—91no—
618C2×Dic6—91no—
619C2×Dic6—91no—
620C2×Dic6—91no—
621C2×Dic6—181no—
622C3×C4⋊C4—91no—
623C3×C22⋊C4—31no—
624C3×C22⋊C4—31no—
625C3×C22⋊C4—61no—
626C3×C22⋊C4—91no—
627C3×C22⋊C4—91no—
628C3×C22⋊C4—91no—
629C3×C22⋊C4—91no—
630C3×C22⋊C4—91no—
631C3×C22⋊C4—91no—
632#217—31no—
633#217—31no—
634#217—31no—
635#217—31no—
636#217—31no—
637#217—31no—
638#217—61no—
639#217—91no—
640#217D3211yescharacteristic, complemented
641(C2×D3)⋊C4—31no—
642(C2×D3)⋊C4—31no—
643(C2×D3)⋊C4—31no—
644(C2×D3)⋊C4—31no—
645(C2×D3)⋊C4—31no—
646(C2×D3)⋊C4—31no—
647(C2×D3)⋊C4—91no—
648(C2×D3)⋊C4—91no—
649(C2×D3)⋊C4—91no—
650(C2×D3)⋊C4—91no—
651(C2×D3)⋊C4—91no—
652(C2×D3)⋊C4—91no—
653(C2×D3)⋊C4—91no—
654(C2×D3)⋊C4—91no—
655(C2×D3)⋊C4—181no—
656(C2×D3)⋊C4—181no—
657C4⋊Dic3—91no—
658Dic3⋊C4—31no—
659Dic3⋊C4—31no—
660Dic3⋊C4—91no—
661Dic3⋊C4—91no—
662C4×Dic3—91no—
663C4×Dic3—91no—
664C4×Dic3—91no—
665C4×Dic3—91no—
666C4×Dic3—91no—
667C4×Dic3—91no—
668C4×Dic3—181no—
669C4×Dic3—181no—
670C22×C32—21no—
671C22×C32—22no—
672C22×C32—21no—
673C22×C32—21no—
674C22×C32—21no—
675C22×C32—21no—
676C22×C32—21no—
677C22×C32—21no—
678C22×C32—21no—
679C22×C32—21no—
680C22×C32—21no—
681C22×C32—21no—
682C22×C32—21no—
683C22×C32—32no—
684C22×C32—41no—
685C22×C32—41no—
686C22×C32—41no—
687C22×C32—42no—
688C22×C32—41no—
689C22×C32—41no—
690C22×C32—41no—
691C22×C32—41no—
692C22×C32—41no—
693C22×C32—41no—
694C22×C32—61no—
695C22×C32—61no—
696C22×C32—61no—
697C22×C32—61no—
698C22×C32—61no—
699C22×C32—61no—
700C22×C32—61no—
701C22×C32—61no—
702C22×C32—81no—
703C22×C32—81no—
704C22×C32—124no—
705C22×C32C23×D311yescharacteristic
706C22×C32C23×D311yescharacteristic
707C22×C32C23×D311yescharacteristic
708C2×C3⋊D3—21no—
709C2×C3⋊D3—21no—
710C2×C3⋊D3—21no—
711C2×C3⋊D3—21no—
712C2×C3⋊D3—21no—
713C2×C3⋊D3—21no—
714C2×C3⋊D3—61no—
715C2×C3⋊D3—62no—
716C2×C3⋊D3—61no—
717C2×C3⋊D3—61no—
718C2×C3⋊D3—61no—
719C2×C3⋊D3—61no—
720C2×C3⋊D3—61no—
721C2×C3⋊D3—61no—
722C2×C3⋊D3—61no—
723C2×C3⋊D3—61no—
724C2×C3⋊D3—121no—
725C2×C3⋊D3—121no—
726C2×C3⋊D3—122no—
727C2×C3⋊D3—121no—
728C2×C3⋊D3—121no—
729C2×C3⋊D3—121no—
730C2×C3⋊D3—121no—
731C2×C3⋊D3—121no—
732C2×C3⋊D3—121no—
733C2×C3⋊D3—124no—
734C2×C3⋊D3—241no—
735C2×C3⋊D3—241no—
736C2×C3×D3—22no—
737C2×C3×D3—22no—
738C2×C3×D3—21no—
739C2×C3×D3—21no—
740C2×C3×D3—21no—
741C2×C3×D3—21no—
742C2×C3×D3—22no—
743C2×C3×D3—21no—
744C2×C3×D3—21no—
745C2×C3×D3—21no—
746C2×C3×D3—21no—
747C2×C3×D3—21no—
748C2×C3×D3—21no—
749C2×C3×D3—21no—
750C2×C3×D3—21no—
751C2×C3×D3—21no—
752C2×C3×D3—21no—
753C2×C3×D3—21no—
754C2×C3×D3—21no—
755C2×C3×D3—22no—
756C2×C3×D3—41no—
757C2×C3×D3—41no—
758C2×C3×D3—41no—
759C2×C3×D3—41no—
760C2×C3×D3—41no—
761C2×C3×D3—48no—
762C2×C3×D3—44no—
763C2×C3×D3—44no—
764C2×C3×D3—62no—
765C2×C3×D3—61no—
766C2×C3×D3—61no—
767C2×C3×D3—61no—
768C2×C3×D3—61no—
769C2×C3×D3—61no—
770C2×C3×D3—61no—
771C2×C3×D3—61no—
772C2×C3×D3—61no—
773C2×C3×D3—61no—
774C2×C3×D3—61no—
775C2×C3×D3—61no—
776C2×C3×D3—61no—
777C2×C3×D3—121no—
778C2×C3×D3—121no—
779C2×C3×D3—121no—
780C2×C3×D3—121no—
781C2×C3×D3—121no—
782C2×C3×D3D3×D412yes—
783C2×C3×D3D3×D412yes—
784D32—128no—
785D32—124no—
786D32—124no—
787C32×C4—61no—
788C32×C4—61no—
789C32×C4—61no—
790C3⋊Dic3—21no—
791C3⋊Dic3—21no—
792C3⋊Dic3—21no—
793C3⋊Dic3—32no—
794C3⋊Dic3—32no—
795C3⋊Dic3—32no—
796C3⋊Dic3—62no—
797C3⋊Dic3—62no—
798C3⋊Dic3—62no—
799C3⋊Dic3—122no—
800C3⋊Dic3D3×D412yes—
801C3×Dic3—22no—
802C3×Dic3—21no—
803C3×Dic3—21no—
804C3×Dic3—21no—
805C3×Dic3—21no—
806C3×Dic3—21no—
807C3×Dic3—21no—
808C3×Dic3—32no—
809C3×Dic3—32no—
810C3×Dic3—41no—
811C3×Dic3—41no—
812C3×Dic3—62no—
813C3×Dic3—62no—
814C3×Dic3—61no—
815C3×Dic3—61no—
816C3×Dic3—61no—
817C3×Dic3—61no—
818C3×Dic3—61no—
819C3×Dic3—61no—
820C3×Dic3—121no—
821C3×Dic3—121no—
822C2×#41—271no—
823C22×D4—271no—
824#127—271no—
825#127—271no—
826#124—271no—
827#124—271no—
828#121—91no—
829#121—271no—
830#121—271no—
831#121—271no—
832#120—91no—
833#120—91no—
834#120—271no—
835#120—271no—
836#117—271no—
837C33#53511yescharacteristic, complemented, Sylow
838C23×C3—21no—
839C23×C3—21no—
840C23×C3—21no—
841C23×C3—31no—
842C23×C3—31no—
843C23×C3—31no—
844C23×C3—31no—
845C23×C3—31no—
846C23×C3—31no—
847C23×C3—41no—
848C23×C3—61no—
849C23×C3—61no—
850C23×C3—61no—
851C23×C3—62no—
852C23×C3—62no—
853C23×C3—64no—
854C23×C3—91no—
855C23×C3—91no—
856C23×C3—121no—
857C23×C3—121no—
858C23×C3—121no—
859C23×C3—121no—
860C23×C3—122no—
861C23×C3—122no—
862C23×C3C2×D3211yescharacteristic
863C23×C3C2×D3211yescharacteristic
864C23×C3C2×D3211yescharacteristic
865C22×D3—22no—
866C22×D3—31no—
867C22×D3—31no—
868C22×D3—31no—
869C22×D3—31no—
870C22×D3—41no—
871C22×D3—41no—
872C22×D3—61no—
873C22×D3—61no—
874C22×D3—91no—
875C22×D3—91no—
876C22×D3—91no—
877C22×D3—181no—
878C22×D3—181no—
879C22×D3—181no—
880C22×D3—182no—
881C22×D3—182no—
882C22×D3—184no—
883C22×D3—182no—
884C22×D3—361no—
885C22×D3—361no—
886C22×D3—361no—
887C22×D3—361no—
888C22×D3—361no—
889C22×D3—361no—
890C22×D3—361no—
891C22×D3—362no—
892C22×D3—362no—
893C22×D3C2×D3211yescharacteristic
894C22×D3C2×D3211yescharacteristic
895C22×D3C2×D3211yescharacteristic
896C3×D4—121no—
897C3×D4—121no—
898C3×D4—122no—
899C3×D4—182no—
900C3×D4—182no—
901C3×D4—182no—
902C3×D4—361no—
903C3×D4—361no—
904C3×D4—361no—
905C3×D4—361no—
906C2×C3×C4—31no—
907C2×C3×C4—31no—
908C2×C3×C4—31no—
909C2×C3×C4—31no—
910C2×C3×C4—31no—
911C2×C3×C4—31no—
912C2×C3×C4—61no—
913C2×C3×C4—61no—
914C2×C3×C4—61no—
915C2×C3×C4—91no—
916C2×C3×C4—91no—
917C2×C3×C4—91no—
918C2×C3×C4—91no—
919C2×C3×C4—182no—
920#67—41no—
921#67—62no—
922#67—62no—
923#67—62no—
924#67—62no—
925#67—64no—
926#67—62no—
927#67—121no—
928#67—121no—
929#67—121no—
930#67—121no—
931#67—121no—
932#67—121no—
933#67—122no—
934#67—182no—
935#67—182no—
936#67—184no—
937#67—182no—
938#67—182no—
939#67—182no—
940#67—182no—
941#67—182no—
942#67—182no—
943#67—182no—
944#67—182no—
945#67—182no—
946#67—184no—
947#67—184no—
948#67—362no—
949#67—362no—
950#67—362no—
951#67—364no—
952#67—361no—
953#67—361no—
954#67—361no—
955#67—361no—
956#67—361no—
957#67—362no—
958C2×Dic3—31no—
959C2×Dic3—31no—
960C2×Dic3—31no—
961C2×Dic3—31no—
962C2×Dic3—31no—
963C2×Dic3—31no—
964C2×Dic3—31no—
965C2×Dic3—31no—
966C2×Dic3—61no—
967C2×Dic3—61no—
968C2×Dic3—61no—
969C2×Dic3—61no—
970C2×Dic3—62no—
971C2×Dic3—94no—
972C2×Dic3—94no—
973C2×Dic3—91no—
974C2×Dic3—91no—
975C2×Dic3—91no—
976C2×Dic3—184no—
977C2×Dic3—181no—
978C2×Dic3—181no—
979C2×Dic3—181no—
980C2×Dic3—182no—
981C2×Dic3—361no—
982C2×Dic3C2×D3211yescharacteristic
983C2×Dic3C2×D3211yescharacteristic
984C2×Dic3C2×D3211yescharacteristic
985D12—62no—
986D12—121no—
987D12—121no—
988D12—182no—
989D12—361no—
990D12—361no—
991D12—362no—
992D12—361no—
993D12—361no—
994C4×D3—62no—
995C4×D3—94no—
996C4×D3—182no—
997C4×D3—182no—
998Dic6—182no—
999Dic6—182no—
1000Dic6—182no—
1001Dic6—362no—
1002C2×C32—21no—
1003C2×C32—21no—
1004C2×C32—21no—
1005C2×C32—21no—
1006C2×C32—21no—
1007C2×C32—21no—
1008C2×C32—21no—
1009C2×C32—21no—
1010C2×C32—21no—
1011C2×C32—41no—
1012C2×C32—41no—
1013C2×C32—41no—
1014C2×C32—41no—
1015C2×C32—42no—
1016C2×C32—41no—
1017C2×C32—41no—
1018C2×C32—62no—
1019C2×C32—81no—
1020C2×C32—81no—
1021C2×C32—82no—
1022C2×C32—121no—
1023C2×C32—121no—
1024C2×C32C2×D3×D411yescharacteristic
1025C2×C32C2×D3×D411yescharacteristic
1026C2×C32C2×D3×D411yescharacteristic
1027C2×C32#100411yescharacteristic
1028C2×C32#100411yescharacteristic
1029C2×C32#100411yescharacteristic
1030C2×C32#100411yescharacteristic
1031C2×C32#100411yescharacteristic
1032C2×C32#100911yescharacteristic
1033C3⋊D3—41no—
1034C3⋊D3—41no—
1035C3⋊D3—121no—
1036C3⋊D3—122no—
1037C3⋊D3—121no—
1038C3⋊D3—121no—
1039C3⋊D3—241no—
1040C3⋊D3—241no—
1041C3⋊D3—242no—
1042C3×D3—24no—
1043C3×D3—22no—
1044C3×D3—22no—
1045C3×D3—42no—
1046C3×D3—41no—
1047C3×D3—41no—
1048C3×D3—41no—
1049C3×D3—41no—
1050C3×D3—81no—
1051C3×D3—122no—
1052C3×D3—121no—
1053C3×D3—121no—
1054C3×D3—121no—
1055C3×D3—121no—
1056C3×D3—241no—
1057C24—31no—
1058C24—271no—
1059#41—544no—
1060C2×Q8—271no—
1061C2×D4—31no—
1062C2×D4—91no—
1063C2×D4—91no—
1064C2×D4—91no—
1065C2×D4—91no—
1066C2×D4—91no—
1067C2×D4—91no—
1068C2×D4—91no—
1069C2×D4—271no—
1070C2×D4—271no—
1071C2×D4—271no—
1072C2×D4—271no—
1073C2×D4—271no—
1074C2×D4—271no—
1075C2×D4—271no—
1076C2×D4—544no—
1077C22×C4—91no—
1078C22×C4—271no—
1079C22×C4—271no—
1080C4⋊C4—91no—
1081C4⋊C4—271no—
1082C22⋊C4—31no—
1083C22⋊C4—91no—
1084C22⋊C4—91no—
1085C22⋊C4—91no—
1086C22⋊C4—91no—
1087C22⋊C4—91no—
1088C22⋊C4—91no—
1089C22⋊C4—271no—
1090C22⋊C4—271no—
1091C22⋊C4—271no—
1092C42—271no—
1093C42—271no—
1094C22×C3—22no—
1095C22×C3—21no—
1096C22×C3—21no—
1097C22×C3—21no—
1098C22×C3—21no—
1099C22×C3—21no—
1100C22×C3—21no—
1101C22×C3—21no—
1102C22×C3—21no—
1103C22×C3—21no—
1104C22×C3—21no—
1105C22×C3—21no—
1106C22×C3—21no—
1107C22×C3—32no—
1108C22×C3—32no—
1109C22×C3—41no—
1110C22×C3—41no—
1111C22×C3—41no—
1112C22×C3—41no—
1113C22×C3—41no—
1114C22×C3—41no—
1115C22×C3—41no—
1116C22×C3—41no—
1117C22×C3—42no—
1118C22×C3—41no—
1119C22×C3—62no—
1120C22×C3—62no—
1121C22×C3—62no—
1122C22×C3—62no—
1123C22×C3—61no—
1124C22×C3—61no—
1125C22×C3—61no—
1126C22×C3—61no—
1127C22×C3—61no—
1128C22×C3—61no—
1129C22×C3—61no—
1130C22×C3—61no—
1131C22×C3—61no—
1132C22×C3—61no—
1133C22×C3—61no—
1134C22×C3—61no—
1135C22×C3—61no—
1136C22×C3—61no—
1137C22×C3—61no—
1138C22×C3—61no—
1139C22×C3—81no—
1140C22×C3—81no—
1141C22×C3—121no—
1142C22×C3—121no—
1143C22×C3—121no—
1144C22×C3—121no—
1145C22×C3—121no—
1146C22×C3—128no—
1147C22×C3—124no—
1148C22×C3—124no—
1149C22×C3—181no—
1150C22×C3—181no—
1151C22×C3—181no—
1152C22×C3—181no—
1153C22×C3—181no—
1154C22×C3—181no—
1155C22×C3C22×D3211yescharacteristic
1156C22×C3C22×D3211yescharacteristic
1157C22×C3C22×D3211yescharacteristic
1158C2×D3—21no—
1159C2×D3—21no—
1160C2×D3—21no—
1161C2×D3—21no—
1162C2×D3—21no—
1163C2×D3—21no—
1164C2×D3—21no—
1165C2×D3—21no—
1166C2×D3—44no—
1167C2×D3—62no—
1168C2×D3—61no—
1169C2×D3—61no—
1170C2×D3—61no—
1171C2×D3—61no—
1172C2×D3—61no—
1173C2×D3—61no—
1174C2×D3—61no—
1175C2×D3—61no—
1176C2×D3—61no—
1177C2×D3—61no—
1178C2×D3—61no—
1179C2×D3—61no—
1180C2×D3—121no—
1181C2×D3—121no—
1182C2×D3—121no—
1183C2×D3—121no—
1184C2×D3—121no—
1185C2×D3—182no—
1186C2×D3—181no—
1187C2×D3—181no—
1188C2×D3—181no—
1189C2×D3—181no—
1190C2×D3—181no—
1191C2×D3—181no—
1192C2×D3—181no—
1193C2×D3—181no—
1194C2×D3—181no—
1195C2×D3—361no—
1196C2×D3—361no—
1197C2×D3—361no—
1198C2×D3—361no—
1199C2×D3—361no—
1200C2×D3—361no—
1201C2×D3—361no—
1202C2×D3—361no—
1203C2×D3—362no—
1204C2×D3—364no—
1205C2×D3—368no—
1206C2×D3—364no—
1207C2×D3—364no—
1208C2×D3—721no—
1209C2×D3—721no—
1210C2×D3#381112yes—
1211C3×C4—62no—
1212C3×C4—61no—
1213C3×C4—61no—
1214C3×C4—61no—
1215C3×C4—61no—
1216C3×C4—61no—
1217C3×C4—61no—
1218C3×C4—92no—
1219C3×C4—121no—
1220C3×C4—121no—
1221C3×C4—181no—
1222C3×C4—181no—
1223C3×C4—181no—
1224Dic3—21no—
1225Dic3—21no—
1226Dic3—21no—
1227Dic3—32no—
1228Dic3—32no—
1229Dic3—62no—
1230Dic3—62no—
1231Dic3—61no—
1232Dic3—61no—
1233Dic3—61no—
1234Dic3—61no—
1235Dic3—61no—
1236Dic3—61no—
1237Dic3—92no—
1238Dic3—92no—
1239Dic3—92no—
1240Dic3—121no—
1241Dic3—121no—
1242Dic3—182no—
1243Dic3—182no—
1244Dic3—182no—
1245Dic3—362no—
1246C32—21no—
1247C32—21no—
1248C32—21no—
1249C32—41no—
1250C32#559211yescharacteristic, complemented
1251C32#559211yescharacteristic, complemented
1252C32#560711yescharacteristic, complemented
1253C23—31no—
1254C23—31no—
1255C23—31no—
1256C23—62no—
1257C23—91no—
1258C23—91no—
1259C23—121no—
1260C23—121no—
1261C23—271no—
1262C23—542no—
1263C23—1081no—
1264C23—1081no—
1265C23D3311yescharacteristic
1266Q8—542no—
1267D4—121no—
1268D4—182no—
1269D4—182no—
1270D4—182no—
1271D4—361no—
1272D4—361no—
1273D4—361no—
1274D4—361no—
1275D4—542no—
1276D4—542no—
1277D4—542no—
1278D4—542no—
1279D4—1081no—
1280D4—1081no—
1281D4—1081no—
1282C2×C4—31no—
1283C2×C4—31no—
1284C2×C4—31no—
1285C2×C4—91no—
1286C2×C4—91no—
1287C2×C4—91no—
1288C2×C4—91no—
1289C2×C4—182no—
1290C2×C4—274no—
1291C2×C4—271no—
1292C2×C4—542no—
1293C2×C3—21no—
1294C2×C3—21no—
1295C2×C3—21no—
1296C2×C3—21no—
1297C2×C3—21no—
1298C2×C3—21no—
1299C2×C3—21no—
1300C2×C3—21no—
1301C2×C3—21no—
1302C2×C3—42no—
1303C2×C3—41no—
1304C2×C3—41no—
1305C2×C3—41no—
1306C2×C3—41no—
1307C2×C3—41no—
1308C2×C3—41no—
1309C2×C3—64no—
1310C2×C3—62no—
1311C2×C3—62no—
1312C2×C3—81no—
1313C2×C3—81no—
1314C2×C3—82no—
1315C2×C3—122no—
1316C2×C3—121no—
1317C2×C3—121no—
1318C2×C3—121no—
1319C2×C3—121no—
1320C2×C3—241no—
1321C2×C3—361no—
1322C2×C3—361no—
1323C2×C3#6430711yescharacteristic
1324C2×C3D32×D411yescharacteristic
1325C2×C3D32×D411yescharacteristic
1326C2×C3#6431311yescharacteristic
1327C2×C3#6431411yescharacteristic
1328C2×C3C2×#381111yescharacteristic
1329C2×C3#6433011yescharacteristic
1330C2×C3#6433011yescharacteristic
1331C2×C3#6433011yescharacteristic
1332D3—22no—
1333D3—41no—
1334D3—41no—
1335D3—122no—
1336D3—121no—
1337D3—121no—
1338D3—121no—
1339D3—121no—
1340D3—241no—
1341D3—362no—
1342D3—361no—
1343D3—361no—
1344D3—361no—
1345D3—721no—
1346D3—721no—
1347D3—722no—
1348C22—21no—
1349C22—21no—
1350C22—21no—
1351C22—32no—
1352C22—61no—
1353C22—61no—
1354C22—61no—
1355C22—61no—
1356C22—61no—
1357C22—61no—
1358C22—61no—
1359C22—61no—
1360C22—124no—
1361C22—181no—
1362C22—181no—
1363C22—181no—
1364C22—181no—
1365C22—181no—
1366C22—181no—
1367C22—541no—
1368C22—541no—
1369C22—541no—
1370C22—1084no—
1371C22C2×D3311yescharacteristic
1372C4—61no—
1373C4—61no—
1374C4—61no—
1375C4—92no—
1376C4—181no—
1377C4—181no—
1378C4—181no—
1379C4—272no—
1380C3—21no—
1381C3—21no—
1382C3—21no—
1383C3—41no—
1384C3#1059426911yescharacteristic, complemented
1385C3#1059528511yescharacteristic, complemented
1386C3#1059550211yescharacteristic, complemented
1387C2—41no—
1388C2—62no—
1389C2—121no—
1390C2—121no—
1391C2—361no—
1392C2—361no—
1393C2—1081no—
1394C2#1172441411yescharacteristic
1395C2#1172441811yescharacteristic
1396C2D3×#381111yescharacteristic
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×D3×#638C2semidirect
2. C2×#88961C2semidirect
3. #11723725C2semidirect
4. #11723633C2semidirect
5. #11723592C2semidirect
6. C3×#63977C2semidirect
7. C3×#63976C2semidirect
8. C3×#63971C2semidirect
9. #11723029C2semidirect
10. #11723009C2semidirect
11. #11722966C2semidirect
12. #11722958C2semidirect
13. #11722950C2semidirect
14. #11722949C2semidirect
15. #11722917C2semidirect
23. C2×C3×#638C22semidirect
24. C2×C32×#67C22semidirect
25. C2×#6295C22semidirect
26. C2×#6294C22semidirect
28. C2×#6293C22semidirect
29. C2×#6292C22semidirect
31. C2×#6291C22semidirect
33. C2×#6290C22semidirect
36. C2×C3×#626C22semidirect
37. C2×C3×#626C22semidirect
39. C2×C3×#625C22semidirect
40. C2×C3×D3×Dic3C22semidirect
42. C3×#3757C22semidirect
43. C32×#217C22semidirect
44. #88815C22semidirect
45. #88814C22semidirect
46. #88804C22semidirect
47. #88804C22semidirect
48. Dic3×C3⋊Dic3C22semidirect
49. Dic3×C3⋊Dic3C22semidirect
50. C3×#3724C22semidirect
51. C3×#3722C22semidirect
54. C3×(C2×D3)⋊Dic3C22semidirect
55. C3×(C2×D3)⋊Dic3C22semidirect
80. #63977D3semidirect
81. #63976D3semidirect
85. #63971D3semidirect
137. D3×C3⋊Dic3D4semidirect
169. C2×#638C2×D3semidirect
187. C2×C3×#67C2×D3semidirect
188. C2×C3×#67C2×D3semidirect
212. C2×#626C2×D3semidirect
213. C2×#626C2×D3semidirect
222. C2×#625C2×D3semidirect
231. C2×D3×Dic3C2×D3semidirect
234. #3757C2×D3semidirect
247. C3×#217C2×D3semidirect
248. C3×#217C2×D3semidirect
258. #3724C2×D3semidirect
268. #3722C2×D3semidirect
273. (C2×D3)⋊Dic3C2×D3semidirect
274. (C2×D3)⋊Dic3C2×D3semidirect
595. C2×#67D32semidirect
640. #217D32semidirect
837. C33#535semidirect
1250. C32#5592semidirect
1251. C32#5592semidirect
1252. C32#5607semidirect
1384. C3#10594269semidirect
1385. C3#10595285semidirect
1386. C3#10595502semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#6382
C2×#889612
#117237252
#117236332
#117235922
C3×#639772
C3×#639762
C3×#639712
#117230292
#117230092
#117229662
#117229582
#117229502
#117229492
#117229172
#105955023
#105952853
#105942693