Finite Group Databasebeta

← #13172151

Subgroups — #13172151

Order 1728.

1830 conjugacy classes of subgroups.

The subgroup lattice has 1278 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#638C211yesmaximal, characteristic
2#11723726C211yesmaximal, characteristic, complemented
3#11723622C211yesmaximal, characteristic, complemented
4#11723618C211yesmaximal, characteristic, complemented
5C3×D3×#217C211yesmaximal, characteristic, complemented
6C2×C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
7C3×#63952C211yesmaximal, characteristic, complemented
8#11722936C211yesmaximal, characteristic, complemented
9#11722935C211yesmaximal, characteristic, complemented
10#11722932C211yesmaximal, characteristic, complemented
11#11722930C211yesmaximal, characteristic, complemented
12#11722917C211yesmaximal, characteristic, complemented
13#11722916C211yesmaximal, characteristic, complemented
14#11722906C211yesmaximal, characteristic, complemented
15#11722904C211yesmaximal, characteristic, complemented
16#10595510—31nomaximal
17#10595056—31nomaximal
18#10594254—31nomaximal
19C23×C32×D3C2211yescharacteristic
20C22×D3×C3⋊D3C2211yescharacteristic
21C2×#6312C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic
23C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
24C22×C32×Dic3C2211yescharacteristic, complemented
25C2×#6294C2211yescharacteristic, complemented
26D3×#638C418yescomplemented
27C2×#6291C2211yescharacteristic
28C2×#6290C2211yescharacteristic
29C2×#6289C2211yescharacteristic, complemented
30C2×#6289C2211yescharacteristic, complemented
31C2×D3×C3⋊Dic3C2211yescharacteristic
32C2×C3×#624C2211yescharacteristic, complemented
33C2×C3×D3×Dic3C2211yescharacteristic, complemented
34C2×C3×D3×Dic3C2211yescharacteristic, complemented
35C3×#3757C2211yescharacteristic, complemented
36C32×#217C2211yescharacteristic, complemented
37#88815C2211yescharacteristic, complemented
38#88814C2211yescharacteristic, complemented
39#88813C2211yescharacteristic, complemented
40#88806C2211yescharacteristic, complemented
41#88806C2211yescharacteristic, complemented
42#88804C2211yescharacteristic, complemented
43#88804C2211yescharacteristic, complemented
44Dic3×C3⋊Dic3C2211yescharacteristic, complemented
45Dic3×C3⋊Dic3C2211yescharacteristic, complemented
46C3×#3724C2211yescharacteristic, complemented
47C3×#3722C2211yescharacteristic, complemented
48C3×(C2×D3)⋊Dic3C2211yescharacteristic
49C3×(C2×D3)⋊Dic3C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
53C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
54C3×Dic32C2211yescharacteristic, complemented
55C22×#638—31no—
56C2×D3×#67—31no—
57C2×D3×#67—31no—
58C2×D3×#67—61no—
59C4×#638—31no—
60#64090—31no—
61C2×C3×#217—31no—
62C2×C3×#217—31no—
63C3×C4×#67—31no—
64C2×C3×(C2×D3)⋊C4—31no—
65C3×#67⋊C4—31no—
66C3×D3×C22⋊C4—31no—
67#63974—31no—
68#63974—31no—
69#67⋊Dic3—31no—
70Dic3×#67—31no—
71D3×#217D311yescharacteristic, complemented
72C2×(C2×D3)⋊Dic3D311yescharacteristic, complemented
73#63957—31no—
74#63957—31no—
75#63952—31no—
76#63952—31no—
77#63952—31no—
78#63952—31no—
79#63952—31no—
80#63952—31no—
81#63952—31no—
82#63952—31no—
83#63952—31no—
84#63952—61no—
85#63952—61no—
86#63952D311yescharacteristic, complemented
87#63921—31no—
88#63921—31no—
89D3×(C2×D3)⋊C4—31no—
90D3×(C2×D3)⋊C4—31no—
91#63904—31no—
92C4×#626—31no—
93#63902—31no—
94C4×#625—31no—
95#63881—31no—
96#63880—31no—
97#63879—31no—
98#63879—31no—
99#63878—31no—
100#63878—31no—
101#63877—31no—
102#63877—31no—
103C23×C33C2311yescharacteristic
104C22×C3⋊(C3⋊D3)C2311yescharacteristic
105C22×C3×C3⋊D3C2311yescharacteristic
106C22×C32×D3—41no—
107C22×C32×D3—41no—
108C22×C32×D3C2×C414yescomplemented
109C22×C32×D3C2311yescharacteristic
110C22×C32×D3C2311yescharacteristic
111C2×D3×C3⋊D3—41no—
112C2×D3×C3⋊D3—41no—
113C2×D3×C3⋊D3C2×C414yescomplemented
114#6312C2×C414yescomplemented
115C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
116C3×#638C2×C414yescomplemented
117C2×C3×C3⋊Dic3—41no—
118C2×C3×C3⋊Dic3C2311yescharacteristic
119C2×C3×C3⋊Dic3C2311yescharacteristic
120C2×C3×C3⋊Dic3C2311yescharacteristic
121C2×C3×C3⋊Dic3C2311yescharacteristic
122C2×C3×C3⋊Dic3C2311yescharacteristic
123C2×C32×Dic3—41no—
124C2×C32×Dic3C2311yescharacteristic
125C2×C32×Dic3C2311yescharacteristic
126C2×C32×Dic3C2311yescharacteristic
127C2×C32×Dic3C2311yescharacteristic
128#6294—41no—
129#6291C2×C414yescomplemented
130#6290C2×C414yescomplemented
131#6289—41no—
132#6289—41no—
133D3×C3⋊Dic3C2×C414yescomplemented
134C3×#624—41no—
135C3×D3×Dic3—41no—
136C3×D3×Dic3—41no—
137#5545—91no—
138#5486—91no—
139#5486—91no—
140C24×C32—31no—
141C23×C3⋊D3—31no—
142C23×C3×D3—21no—
143C23×C3×D3C2×D311yescharacteristic
144C23×C3×D3C2×D311yescharacteristic
145C22×D32—31no—
146C22×D32—31no—
147C22×D32—61no—
148C22×C32×C4—31no—
149C2×#638—31no—
150C2×#638—31no—
151C2×#638—31no—
152C2×#638—31no—
153C2×#638—38no—
154C2×#638—31no—
155C2×#638—61no—
156C2×#638—61no—
157C2×#638—61no—
158C2×#638—121no—
159C2×#638C2×D311yescharacteristic
160C22×C3⋊Dic3—31no—
161C22×C3⋊Dic3C2×D311yescharacteristic, complemented
162C2×C4×C3⋊D3—31no—
163C2×C4×C3⋊D3—31no—
164C2×C3×#67—31no—
165C2×C3×#67—31no—
166C2×C3×#67—61no—
167C22×C3×Dic3—21no—
168C22×C3×Dic3—31no—
169C22×C3×Dic3—31no—
170C22×C3×Dic3—31no—
171C22×C3×Dic3—31no—
172C22×C3×Dic3—61no—
173C22×C3×Dic3C2×D311yescharacteristic, complemented
174C22×C3×Dic3C2×D311yescharacteristic, complemented
175C2×C3×C4×D3—31no—
176C2×C3×C4×D3—31no—
177C2×C3×C4×D3—31no—
178C2×C3×C4×D3—31no—
179D3×#67—38no—
180D3×#67—38no—
181D3×#67—68no—
182C2×#626—31no—
183C2×#626—31no—
184C2×#626—61no—
185C2×#625—31no—
186C2×#625—31no—
187C2×#625—61no—
188C2×#624—31no—
189C2×#624—31no—
190C2×#624—31no—
191C2×#624—31no—
192C2×#624—31no—
193C2×#624—61no—
194C2×#624—61no—
195C2×#624C2×D311yescharacteristic, complemented
196C2×D3×Dic3—31no—
197C2×D3×Dic3—31no—
198C2×D3×Dic3—31no—
199C2×D3×Dic3—31no—
200C2×D3×Dic3—61no—
201C2×D3×Dic3C2×D311yescharacteristic, complemented
202C2×D3×Dic3C2×D311yescharacteristic, complemented
203C32×C22⋊C4—31no—
204#3757C2×D311yescharacteristic, complemented
205#3752—31no—
206#3752—31no—
207#3750—31no—
208#3750—31no—
209C4×C3⋊Dic3—31no—
210C4×C3⋊Dic3—31no—
211C3×#217—21no—
212C3×#217—31no—
213C3×#217—31no—
214C3×#217—31no—
215C3×#217—31no—
216C3×#217—31no—
217C3×#217—31no—
218C3×#217—31no—
219C3×#217—31no—
220C3×#217—61no—
221C3×#217C2×D311yescharacteristic, complemented
222C3×#217C2×D311yescharacteristic, complemented
223C3×(C2×D3)⋊C4—31no—
224C3×(C2×D3)⋊C4—31no—
225C3×(C2×D3)⋊C4—31no—
226C3×(C2×D3)⋊C4—31no—
227C3×(C2×D3)⋊C4—31no—
228C3×(C2×D3)⋊C4—31no—
229C3×(C2×D3)⋊C4—31no—
230C3×(C2×D3)⋊C4—31no—
231C3×Dic3⋊C4—31no—
232C3×Dic3⋊C4—31no—
233C3×C4×Dic3—31no—
234C3×C4×Dic3—31no—
235#3724—31no—
236#3724—31no—
237#3724—31no—
238#3724—31no—
239#3724—31no—
240#3724—61no—
241#3724—61no—
242#3724C2×D311yescharacteristic, complemented
243Dic3⋊Dic3—31no—
244Dic3⋊Dic3—31no—
245#3722—31no—
246#3722—31no—
247#3722—31no—
248#3722—31no—
249#3722—31no—
250#3722—61no—
251#3722—61no—
252#3722C2×D311yescharacteristic, complemented
253(C2×D3)⋊Dic3—31no—
254(C2×D3)⋊Dic3—31no—
255(C2×D3)⋊Dic3C2×D311yescharacteristic
256(C2×D3)⋊Dic3C2×D311yescharacteristic
257(C2×D3)⋊Dic3C2×D311yescharacteristic
258(C2×D3)⋊Dic3C2×D311yescharacteristic
259(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
260(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
261Dic32—31no—
262Dic32—31no—
263Dic32—31no—
264Dic32—31no—
265Dic32—31no—
266Dic32—31no—
267Dic32—31no—
268Dic32—61no—
269Dic32—61no—
270Dic32C2×D311yescharacteristic, complemented
271C22×C33—21no—
272C22×C33—21no—
273C22×C33C22×C412yes—
274C22×C33C2411yescharacteristic
275C2×C3⋊(C3⋊D3)—21no—
276C2×C3⋊(C3⋊D3)—21no—
277C2×C3⋊(C3⋊D3)C22×C412yes—
278C2×C3×C3⋊D3—21no—
279C2×C3×C3⋊D3—21no—
280C2×C3×C3⋊D3C22×C412yes—
281C2×C32×D3—21no—
282C2×C32×D3—21no—
283C2×C32×D3—21no—
284C2×C32×D3—21no—
285C2×C32×D3—44no—
286C2×C32×D3C22×C412yes—
287C2×C32×D3C22×C412yes—
288D3×C3⋊D3—44no—
289C3⋊(C3⋊Dic3)C22×C412yes—
290C3×C3⋊Dic3—21no—
291C3×C3⋊Dic3—21no—
292C3×C3⋊Dic3—21no—
293C3×C3⋊Dic3—21no—
294C3×C3⋊Dic3C22×C412yes—
295C32×Dic3—21no—
296C32×Dic3—21no—
297C32×Dic3—21no—
298C32×Dic3—21no—
299C22×#67—91no—
300C22×#67—91no—
301C22×#67—181no—
302C2×D3×D4—91no—
303C3×C4×D4—91no—
304C2×C3×C22⋊C4—91no—
305C2×C3×C22⋊C4—91no—
306C2×#217—31no—
307C2×#217—31no—
308D4×Dic3—91no—
309C4×#67—31no—
310C4×#67—91no—
311C4×#67—91no—
312C4×#67—91no—
313C4×#67—91no—
314C4×#67—91no—
315C4×#67—91no—
316C4×#67—91no—
317C4×#67—91no—
318C4×#67—91no—
319C4×#67—181no—
320C2×(C2×D3)⋊C4—31no—
321C2×(C2×D3)⋊C4—91no—
322#893—91no—
323#892—91no—
324#67⋊C4—31no—
325#67⋊C4—91no—
326#67⋊C4—91no—
327#67⋊C4—91no—
328#67⋊C4—91no—
329#67⋊C4—91no—
330#67⋊C4—91no—
331#67⋊C4—91no—
332#67⋊C4—91no—
333#67⋊C4—91no—
334#67⋊C4—181no—
335D3×C22⋊C4—31no—
336D3×C22⋊C4—91no—
337D3×C22⋊C4—91no—
338D3×C22⋊C4—91no—
339D3×C22⋊C4—91no—
340D3×C22⋊C4—91no—
341#877—91no—
342#877—91no—
343#877—91no—
344#877—91no—
345C4×D12—91no—
346#872—91no—
347C23×C32—21no—
348C23×C32—21no—
349C23×C32—21no—
350C23×C32—31no—
351C23×C32—31no—
352C23×C32—34no—
353C23×C32—41no—
354C23×C32—121no—
355C23×C32—121no—
356C23×C32C22×D311yescharacteristic
357C23×C32C22×D311yescharacteristic
358C23×C32C22×D311yescharacteristic
359C22×C3⋊D3—31no—
360C22×C3⋊D3—31no—
361C22×C3⋊D3—31no—
362C22×C3⋊D3—34no—
363C22×C3⋊D3—61no—
364C22×C3⋊D3—61no—
365C22×C3⋊D3—61no—
366C22×C3⋊D3—121no—
367C22×C3⋊D3—121no—
368C22×C3⋊D3—121no—
369C22×C3⋊D3C22×D311yescharacteristic
370C22×C3×D3—24no—
371C22×C3×D3—21no—
372C22×C3×D3—21no—
373C22×C3×D3—31no—
374C22×C3×D3—31no—
375C22×C3×D3—41no—
376C22×C3×D3—41no—
377C22×C3×D3—41no—
378C22×C3×D3—41no—
379C22×C3×D3—42no—
380C22×C3×D3—42no—
381C22×C3×D3—61no—
382C22×C3×D3C4×D314yescomplemented
383C22×C3×D3C4×D314yescomplemented
384C22×C3×D3C22×D311yescharacteristic
385C22×C3×D3C22×D311yescharacteristic
386C22×C3×D3C22×D311yescharacteristic
387C22×C3×D3C22×D311yescharacteristic
388C2×D32—34no—
389C2×D32—34no—
390C2×D32—64no—
391C2×D32—121no—
392C2×D32—121no—
393C2×D32—121no—
394C2×D32—121no—
395C2×D32—122no—
396C2×D32—122no—
397C2×C32×C4—31no—
398C2×C32×C4—31no—
399C2×C32×C4—31no—
400C2×C32×C4—31no—
401C2×C32×C4—121no—
402#638—34no—
403#638—34no—
404#638—34no—
405#638—34no—
406#638—34no—
407#638—64no—
408#638—64no—
409#638—64no—
410#638—124no—
411#638C4×D314yescomplemented
412C2×C3⋊Dic3—31no—
413C2×C3⋊Dic3—31no—
414C2×C3⋊Dic3—31no—
415C2×C3⋊Dic3—34no—
416C2×C3⋊Dic3—41no—
417C2×C3⋊Dic3—61no—
418C2×C3⋊Dic3—61no—
419C2×C3⋊Dic3—61no—
420C2×C3⋊Dic3—121no—
421C2×C3⋊Dic3C22×D311yescharacteristic
422C2×C3⋊Dic3C22×D311yescharacteristic
423C2×C3⋊Dic3C22×D311yescharacteristic
424C2×C3⋊Dic3C22×D311yescharacteristic
425C2×C3⋊Dic3C22×D311yescharacteristic
426C4×C3⋊D3—121no—
427C4×C3⋊D3—121no—
428C3×#67—34no—
429C3×#67—34no—
430C3×#67—64no—
431C2×C3×Dic3—21no—
432C2×C3×Dic3—21no—
433C2×C3×Dic3—21no—
434C2×C3×Dic3—21no—
435C2×C3×Dic3—31no—
436C2×C3×Dic3—31no—
437C2×C3×Dic3—31no—
438C2×C3×Dic3—31no—
439C2×C3×Dic3—31no—
440C2×C3×Dic3—31no—
441C2×C3×Dic3—31no—
442C2×C3×Dic3—31no—
443C2×C3×Dic3—31no—
444C2×C3×Dic3—31no—
445C2×C3×Dic3—41no—
446C2×C3×Dic3—41no—
447C2×C3×Dic3—42no—
448C2×C3×Dic3—61no—
449C2×C3×Dic3—61no—
450C2×C3×Dic3—61no—
451C2×C3×Dic3—61no—
452C2×C3×Dic3—61no—
453C2×C3×Dic3—121no—
454C2×C3×Dic3—121no—
455C2×C3×Dic3—121no—
456C2×C3×Dic3—121no—
457C2×C3×Dic3—122no—
458C2×C3×Dic3C22×D311yescharacteristic
459C2×C3×Dic3C22×D311yescharacteristic
460C2×C3×Dic3C22×D311yescharacteristic
461C2×C3×Dic3C22×D311yescharacteristic
462C2×C3×Dic3C22×D311yescharacteristic
463C2×C3×Dic3C22×D311yescharacteristic
464C2×C3×Dic3C22×D311yescharacteristic
465C2×C3×Dic3C22×D311yescharacteristic
466C3×C4×D3—121no—
467C3×C4×D3—121no—
468C3×C4×D3—121no—
469C3×C4×D3—121no—
470#626—34no—
471#626—34no—
472#626—64no—
473#625—34no—
474#625—34no—
475#625—64no—
476#624—41no—
477#624—121no—
478#624—121no—
479#624—121no—
480#624—121no—
481#624—122no—
482#624—122no—
483#624—121no—
484D3×Dic3—34no—
485D3×Dic3—34no—
486D3×Dic3—41no—
487D3×Dic3—41no—
488D3×Dic3—64no—
489D3×Dic3—121no—
490D3×Dic3—121no—
491#518—271noSylow
492C2×C33—22no—
493C2×C33C23×C411yescharacteristic
494C2×C33H(5,𝔽2)11yescharacteristic
495C2×C33H(5,𝔽2)11yescharacteristic
496C3⋊(C3⋊D3)—22no—
497C3×C3⋊D3—22no—
498C32×D3—22no—
499C32×D3—22no—
500C24×C3—31no—
501C24×C3—31no—
502C24×C3—61no—
503C23×D3—91no—
504C23×D3—91no—
505C23×D3—91no—
506C23×D3—181no—
507C23×D3D3211yescharacteristic
508C2×C3×D4—91no—
509C22×C3×C4—31no—
510C22×C3×C4—31no—
511C22×C3×C4—61no—
512C22×C3×C4—91no—
513C22×C3×C4—91no—
514C22×C3×C4—91no—
515C22×C3×C4—91no—
516C2×#67—31no—
517C2×#67—31no—
518C2×#67—61no—
519C2×#67—91no—
520C2×#67—91no—
521C2×#67—98no—
522C2×#67—98no—
523C2×#67—91no—
524C2×#67—91no—
525C2×#67—91no—
526C2×#67—91no—
527C2×#67—91no—
528C2×#67—91no—
529C2×#67—181no—
530C2×#67—188no—
531C2×#67—181no—
532C2×#67—181no—
533C2×#67—181no—
534C2×#67—181no—
535C2×#67—361no—
536C22×Dic3—31no—
537C22×Dic3—31no—
538C22×Dic3—31no—
539C22×Dic3—31no—
540C22×Dic3—61no—
541C22×Dic3—91no—
542C22×Dic3—91no—
543C22×Dic3—91no—
544C22×Dic3—181no—
545C22×Dic3D3211yescharacteristic, complemented
546D3×D4—98no—
547C2×D12—91no—
548C2×C4×D3—31no—
549C2×C4×D3—31no—
550C2×C4×D3—31no—
551C2×C4×D3—31no—
552C2×C4×D3—91no—
553C2×C4×D3—91no—
554C2×C4×D3—91no—
555C2×C4×D3—91no—
556C2×C4×D3—91no—
557C2×C4×D3—91no—
558C2×C4×D3—91no—
559C2×C4×D3—91no—
560C2×C4×D3—91no—
561C2×C4×D3—181no—
562C2×C4×D3—181no—
563C3×C4⋊C4—91no—
564C3×C22⋊C4—31no—
565C3×C22⋊C4—31no—
566C3×C22⋊C4—61no—
567C3×C22⋊C4—91no—
568C3×C22⋊C4—91no—
569C3×C22⋊C4—91no—
570C3×C22⋊C4—91no—
571C3×C22⋊C4—91no—
572C3×C22⋊C4—91no—
573C3×C22⋊C4—91no—
574C3×C22⋊C4—91no—
575C3×C42—91no—
576#217—31no—
577#217—31no—
578#217—31no—
579#217—31no—
580#217—31no—
581#217—31no—
582#217—31no—
583#217—31no—
584#217—61no—
585#217—91no—
586#217D3211yescharacteristic, complemented
587(C2×D3)⋊C4—31no—
588(C2×D3)⋊C4—31no—
589(C2×D3)⋊C4—31no—
590(C2×D3)⋊C4—31no—
591(C2×D3)⋊C4—31no—
592(C2×D3)⋊C4—31no—
593(C2×D3)⋊C4—31no—
594(C2×D3)⋊C4—31no—
595(C2×D3)⋊C4—91no—
596(C2×D3)⋊C4—91no—
597(C2×D3)⋊C4—91no—
598(C2×D3)⋊C4—91no—
599(C2×D3)⋊C4—91no—
600(C2×D3)⋊C4—91no—
601(C2×D3)⋊C4—91no—
602(C2×D3)⋊C4—91no—
603(C2×D3)⋊C4—181no—
604(C2×D3)⋊C4—181no—
605C4⋊Dic3—91no—
606Dic3⋊C4—31no—
607Dic3⋊C4—31no—
608Dic3⋊C4—91no—
609Dic3⋊C4—91no—
610Dic3⋊C4—91no—
611Dic3⋊C4—91no—
612Dic3⋊C4—91no—
613Dic3⋊C4—91no—
614Dic3⋊C4—91no—
615Dic3⋊C4—91no—
616Dic3⋊C4—181no—
617Dic3⋊C4—181no—
618C4×Dic3—31no—
619C4×Dic3—31no—
620C4×Dic3—91no—
621C4×Dic3—91no—
622C4×Dic3—91no—
623C4×Dic3—91no—
624C4×Dic3—91no—
625C4×Dic3—91no—
626C4×Dic3—91no—
627C4×Dic3—91no—
628C4×Dic3—91no—
629C4×Dic3—181no—
630C4×Dic3—181no—
631C22×C32—21no—
632C22×C32—21no—
633C22×C32—21no—
634C22×C32—21no—
635C22×C32—21no—
636C22×C32—21no—
637C22×C32—21no—
638C22×C32—21no—
639C22×C32—21no—
640C22×C32—22no—
641C22×C32—22no—
642C22×C32—22no—
643C22×C32—32no—
644C22×C32—32no—
645C22×C32—41no—
646C22×C32—42no—
647C22×C32—41no—
648C22×C32—41no—
649C22×C32—41no—
650C22×C32—41no—
651C22×C32—41no—
652C22×C32—41no—
653C22×C32—61no—
654C22×C32—61no—
655C22×C32—61no—
656C22×C32—61no—
657C22×C32—81no—
658C22×C32—81no—
659C22×C32—124no—
660C22×C32C2×C4×D312yes—
661C22×C32C2×C4×D312yes—
662C22×C32C2×C4×D312yes—
663C22×C32C23×D311yescharacteristic
664C22×C32C23×D311yescharacteristic
665C22×C32C23×D311yescharacteristic
666C2×C3⋊D3—21no—
667C2×C3⋊D3—21no—
668C2×C3⋊D3—32no—
669C2×C3⋊D3—32no—
670C2×C3⋊D3—32no—
671C2×C3⋊D3—62no—
672C2×C3⋊D3—62no—
673C2×C3⋊D3—62no—
674C2×C3⋊D3—61no—
675C2×C3⋊D3—61no—
676C2×C3⋊D3—61no—
677C2×C3⋊D3—61no—
678C2×C3⋊D3—61no—
679C2×C3⋊D3—61no—
680C2×C3⋊D3—122no—
681C2×C3⋊D3—121no—
682C2×C3⋊D3—121no—
683C2×C3⋊D3—121no—
684C2×C3⋊D3—121no—
685C2×C3⋊D3—121no—
686C2×C3⋊D3—121no—
687C2×C3⋊D3—124no—
688C2×C3⋊D3—241no—
689C2×C3⋊D3—241no—
690C2×C3⋊D3C2×C4×D312yes—
691C2×C3×D3—22no—
692C2×C3×D3—22no—
693C2×C3×D3—21no—
694C2×C3×D3—21no—
695C2×C3×D3—21no—
696C2×C3×D3—21no—
697C2×C3×D3—21no—
698C2×C3×D3—21no—
699C2×C3×D3—21no—
700C2×C3×D3—21no—
701C2×C3×D3—22no—
702C2×C3×D3—22no—
703C2×C3×D3—32no—
704C2×C3×D3—32no—
705C2×C3×D3—41no—
706C2×C3×D3—41no—
707C2×C3×D3—44no—
708C2×C3×D3—44no—
709C2×C3×D3—48no—
710C2×C3×D3—62no—
711C2×C3×D3—61no—
712C2×C3×D3—61no—
713C2×C3×D3—61no—
714C2×C3×D3—61no—
715C2×C3×D3—121no—
716C2×C3×D3—121no—
717C2×C3×D3C2×C4×D312yes—
718C2×C3×D3C2×C4×D312yes—
719C2×C3×D3C2×C4×D312yes—
720C2×C3×D3C2×C4×D312yes—
721D32—124no—
722D32—124no—
723D32—128no—
724C32×C4—61no—
725C32×C4—61no—
726C32×C4—61no—
727C32×C4—61no—
728C3⋊Dic3—21no—
729C3⋊Dic3—21no—
730C3⋊Dic3—21no—
731C3⋊Dic3—21no—
732C3⋊Dic3—32no—
733C3⋊Dic3—32no—
734C3⋊Dic3—32no—
735C3⋊Dic3—62no—
736C3⋊Dic3—62no—
737C3⋊Dic3—62no—
738C3⋊Dic3—122no—
739C3⋊Dic3C2×C4×D312yes—
740C3×Dic3—22no—
741C3×Dic3—21no—
742C3×Dic3—21no—
743C3×Dic3—21no—
744C3×Dic3—21no—
745C3×Dic3—21no—
746C3×Dic3—21no—
747C3×Dic3—21no—
748C3×Dic3—21no—
749C3×Dic3—32no—
750C3×Dic3—32no—
751C3×Dic3—41no—
752C3×Dic3—41no—
753C3×Dic3—41no—
754C3×Dic3—62no—
755C3×Dic3—62no—
756C3×Dic3—61no—
757C3×Dic3—61no—
758C3×Dic3—61no—
759C3×Dic3—61no—
760C3×Dic3—61no—
761C3×Dic3—61no—
762C3×Dic3—61no—
763C3×Dic3—61no—
764C3×Dic3—121no—
765C3×Dic3—121no—
766C3×Dic3—121no—
767C22×D4—271no—
768C4×D4—91no—
769C4×D4—271no—
770C4×D4—271no—
771C4×D4—271no—
772C4×D4—271no—
773C4×D4—271no—
774C4×D4—271no—
775C4×D4—271no—
776#117—271no—
777#117—271no—
778C2×C22⋊C4—91no—
779C2×C22⋊C4—91no—
780C2×C22⋊C4—271no—
781C2×C22⋊C4—271no—
782C33#51811yescharacteristic, complemented, Sylow
783C23×C3—21no—
784C23×C3—21no—
785C23×C3—21no—
786C23×C3—31no—
787C23×C3—31no—
788C23×C3—31no—
789C23×C3—31no—
790C23×C3—34no—
791C23×C3—34no—
792C23×C3—41no—
793C23×C3—61no—
794C23×C3—61no—
795C23×C3—64no—
796C23×C3—91no—
797C23×C3—121no—
798C23×C3—121no—
799C23×C3—121no—
800C23×C3—121no—
801C23×C3—122no—
802C23×C3—122no—
803C23×C3C2×D3211yescharacteristic
804C23×C3C2×D3211yescharacteristic
805C23×C3C2×D3211yescharacteristic
806C22×D3—31no—
807C22×D3—31no—
808C22×D3—41no—
809C22×D3—41no—
810C22×D3—61no—
811C22×D3—94no—
812C22×D3—94no—
813C22×D3—91no—
814C22×D3—91no—
815C22×D3—91no—
816C22×D3—94no—
817C22×D3—184no—
818C22×D3—181no—
819C22×D3—181no—
820C22×D3—181no—
821C22×D3—361no—
822C22×D3—361no—
823C22×D3—361no—
824C22×D3—361no—
825C22×D3—361no—
826C22×D3—361no—
827C22×D3—361no—
828C22×D3—362no—
829C22×D3—362no—
830C22×D3#62414yescomplemented
831C22×D3C2×D3211yescharacteristic
832C22×D3C2×D3211yescharacteristic
833C3×D4—94no—
834C2×C3×C4—31no—
835C2×C3×C4—31no—
836C2×C3×C4—31no—
837C2×C3×C4—31no—
838C2×C3×C4—31no—
839C2×C3×C4—31no—
840C2×C3×C4—31no—
841C2×C3×C4—31no—
842C2×C3×C4—61no—
843C2×C3×C4—61no—
844C2×C3×C4—61no—
845C2×C3×C4—61no—
846C2×C3×C4—91no—
847C2×C3×C4—91no—
848C2×C3×C4—91no—
849C2×C3×C4—91no—
850C2×C3×C4—91no—
851C2×C3×C4—121no—
852C2×C3×C4—121no—
853C2×C3×C4—122no—
854C2×C3×C4—361no—
855C2×C3×C4—361no—
856C2×C3×C4—361no—
857C2×C3×C4—361no—
858#67—34no—
859#67—34no—
860#67—64no—
861#67—94no—
862#67—94no—
863#67—94no—
864#67—94no—
865#67—94no—
866#67—94no—
867#67—94no—
868#67—94no—
869#67—184no—
870#67—184no—
871#67—184no—
872#67—184no—
873#67—184no—
874#67—364no—
875C2×Dic3—31no—
876C2×Dic3—31no—
877C2×Dic3—31no—
878C2×Dic3—31no—
879C2×Dic3—31no—
880C2×Dic3—31no—
881C2×Dic3—31no—
882C2×Dic3—31no—
883C2×Dic3—31no—
884C2×Dic3—31no—
885C2×Dic3—41no—
886C2×Dic3—61no—
887C2×Dic3—61no—
888C2×Dic3—61no—
889C2×Dic3—61no—
890C2×Dic3—61no—
891C2×Dic3—94no—
892C2×Dic3—94no—
893C2×Dic3—91no—
894C2×Dic3—91no—
895C2×Dic3—91no—
896C2×Dic3—121no—
897C2×Dic3—121no—
898C2×Dic3—121no—
899C2×Dic3—121no—
900C2×Dic3—122no—
901C2×Dic3—184no—
902C2×Dic3—181no—
903C2×Dic3—181no—
904C2×Dic3—181no—
905C2×Dic3—361no—
906C2×Dic3—361no—
907C2×Dic3C2×D3211yescharacteristic
908C2×Dic3C2×D3211yescharacteristic
909C2×Dic3C2×D3211yescharacteristic
910C2×Dic3C2×D3211yescharacteristic
911D12—94no—
912C4×D3—94no—
913C4×D3—121no—
914C4×D3—121no—
915C4×D3—121no—
916C4×D3—121no—
917C4×D3—361no—
918C4×D3—361no—
919C4×D3—361no—
920C4×D3—361no—
921C4×D3—361no—
922C4×D3—361no—
923C4×D3—362no—
924C4×D3—361no—
925C4×D3—361no—
926C4×D3—362no—
927C2×C32—22no—
928C2×C32—22no—
929C2×C32—22no—
930C2×C32—21no—
931C2×C32—21no—
932C2×C32—21no—
933C2×C32—21no—
934C2×C32—21no—
935C2×C32—21no—
936C2×C32—21no—
937C2×C32—21no—
938C2×C32—21no—
939C2×C32—41no—
940C2×C32—41no—
941C2×C32—41no—
942C2×C32—42no—
943C2×C32—42no—
944C2×C32—42no—
945C2×C32—62no—
946C2×C32—62no—
947C2×C32—82no—
948C2×C32C22×C4×D311yescharacteristic
949C2×C32C22×C4×D311yescharacteristic
950C2×C32C22×C4×D311yescharacteristic
951C2×C32#100411yescharacteristic
952C2×C32#100411yescharacteristic
953C2×C32#100411yescharacteristic
954C2×C32#100411yescharacteristic
955C2×C32#100411yescharacteristic
956C2×C32#100911yescharacteristic
957C3⋊D3—22no—
958C3⋊D3—62no—
959C3⋊D3—62no—
960C3⋊D3—62no—
961C3⋊D3—122no—
962C3⋊D3—122no—
963C3⋊D3—122no—
964C3⋊D3—242no—
965C3×D3—24no—
966C3×D3—22no—
967C3×D3—22no—
968C3×D3—22no—
969C3×D3—22no—
970C3×D3—42no—
971C3×D3—62no—
972C3×D3—62no—
973C3×D3—122no—
974C24—31no—
975C24—271no—
976C2×D4—91no—
977C2×D4—271no—
978C2×D4—278no—
979C2×D4—271no—
980C2×D4—271no—
981C22×C4—31no—
982C22×C4—91no—
983C22×C4—91no—
984C22×C4—91no—
985C22×C4—91no—
986C22×C4—271no—
987C22×C4—271no—
988C22×C4—271no—
989C22×C4—271no—
990C4⋊C4—91no—
991C4⋊C4—271no—
992C4⋊C4—271no—
993C4⋊C4—271no—
994C22⋊C4—31no—
995C22⋊C4—91no—
996C22⋊C4—91no—
997C22⋊C4—91no—
998C22⋊C4—91no—
999C22⋊C4—91no—
1000C22⋊C4—91no—
1001C22⋊C4—91no—
1002C22⋊C4—91no—
1003C22⋊C4—271no—
1004C22⋊C4—271no—
1005C22⋊C4—271no—
1006C42—91no—
1007C42—271no—
1008C42—271no—
1009C42—271no—
1010C22×C3—21no—
1011C22×C3—21no—
1012C22×C3—21no—
1013C22×C3—21no—
1014C22×C3—21no—
1015C22×C3—21no—
1016C22×C3—21no—
1017C22×C3—21no—
1018C22×C3—21no—
1019C22×C3—22no—
1020C22×C3—22no—
1021C22×C3—22no—
1022C22×C3—32no—
1023C22×C3—32no—
1024C22×C3—32no—
1025C22×C3—32no—
1026C22×C3—41no—
1027C22×C3—41no—
1028C22×C3—41no—
1029C22×C3—41no—
1030C22×C3—41no—
1031C22×C3—41no—
1032C22×C3—41no—
1033C22×C3—42no—
1034C22×C3—62no—
1035C22×C3—62no—
1036C22×C3—62no—
1037C22×C3—62no—
1038C22×C3—61no—
1039C22×C3—61no—
1040C22×C3—61no—
1041C22×C3—61no—
1042C22×C3—61no—
1043C22×C3—61no—
1044C22×C3—61no—
1045C22×C3—61no—
1046C22×C3—81no—
1047C22×C3—81no—
1048C22×C3—92no—
1049C22×C3—121no—
1050C22×C3—121no—
1051C22×C3—124no—
1052C22×C3—124no—
1053C22×C3—128no—
1054C22×C3—181no—
1055C22×C3—181no—
1056C22×C3C4×D3212yes—
1057C22×C3C4×D3212yes—
1058C22×C3C2×#62412yes—
1059C22×C3C22×D3211yescharacteristic
1060C22×C3C22×D3211yescharacteristic
1061C22×C3C22×D3211yescharacteristic
1062C2×D3—21no—
1063C2×D3—21no—
1064C2×D3—21no—
1065C2×D3—21no—
1066C2×D3—32no—
1067C2×D3—32no—
1068C2×D3—44no—
1069C2×D3—62no—
1070C2×D3—61no—
1071C2×D3—61no—
1072C2×D3—61no—
1073C2×D3—61no—
1074C2×D3—92no—
1075C2×D3—92no—
1076C2×D3—92no—
1077C2×D3—121no—
1078C2×D3—121no—
1079C2×D3—182no—
1080C2×D3—182no—
1081C2×D3—182no—
1082C2×D3—181no—
1083C2×D3—181no—
1084C2×D3—181no—
1085C2×D3—181no—
1086C2×D3—181no—
1087C2×D3—181no—
1088C2×D3—362no—
1089C2×D3—361no—
1090C2×D3—361no—
1091C2×D3—361no—
1092C2×D3—361no—
1093C2×D3—361no—
1094C2×D3—361no—
1095C2×D3—364no—
1096C2×D3—364no—
1097C2×D3—364no—
1098C2×D3—368no—
1099C2×D3—721no—
1100C2×D3—721no—
1101C2×D3C2×#62412yes—
1102C2×D3C2×#62412yes—
1103C3×C4—62no—
1104C3×C4—61no—
1105C3×C4—61no—
1106C3×C4—61no—
1107C3×C4—61no—
1108C3×C4—61no—
1109C3×C4—61no—
1110C3×C4—61no—
1111C3×C4—61no—
1112C3×C4—92no—
1113C3×C4—121no—
1114C3×C4—121no—
1115C3×C4—121no—
1116C3×C4—181no—
1117C3×C4—181no—
1118C3×C4—181no—
1119C3×C4—181no—
1120Dic3—21no—
1121Dic3—21no—
1122Dic3—21no—
1123Dic3—21no—
1124Dic3—32no—
1125Dic3—32no—
1126Dic3—62no—
1127Dic3—62no—
1128Dic3—61no—
1129Dic3—61no—
1130Dic3—61no—
1131Dic3—61no—
1132Dic3—61no—
1133Dic3—61no—
1134Dic3—61no—
1135Dic3—61no—
1136Dic3—92no—
1137Dic3—92no—
1138Dic3—92no—
1139Dic3—121no—
1140Dic3—121no—
1141Dic3—121no—
1142Dic3—182no—
1143Dic3—182no—
1144Dic3—182no—
1145Dic3—362no—
1146C32—21no—
1147C32—21no—
1148C32—21no—
1149C32—41no—
1150C32#548611yescharacteristic, complemented
1151C32#548611yescharacteristic, complemented
1152C32#554511yescharacteristic, complemented
1153C23—31no—
1154C23—31no—
1155C23—34no—
1156C23—91no—
1157C23—121no—
1158C23—121no—
1159C23—274no—
1160C23—271no—
1161C23—1081no—
1162C23—1081no—
1163C23D3311yescharacteristic
1164D4—94no—
1165D4—274no—
1166D4—274no—
1167D4—274no—
1168C2×C4—31no—
1169C2×C4—31no—
1170C2×C4—31no—
1171C2×C4—31no—
1172C2×C4—91no—
1173C2×C4—91no—
1174C2×C4—91no—
1175C2×C4—91no—
1176C2×C4—91no—
1177C2×C4—121no—
1178C2×C4—274no—
1179C2×C4—271no—
1180C2×C4—361no—
1181C2×C4—361no—
1182C2×C4—361no—
1183C2×C4—361no—
1184C2×C4—1081no—
1185C2×C4—1081no—
1186C2×C4—1081no—
1187C2×C3—22no—
1188C2×C3—22no—
1189C2×C3—22no—
1190C2×C3—21no—
1191C2×C3—21no—
1192C2×C3—21no—
1193C2×C3—21no—
1194C2×C3—21no—
1195C2×C3—21no—
1196C2×C3—21no—
1197C2×C3—21no—
1198C2×C3—21no—
1199C2×C3—42no—
1200C2×C3—42no—
1201C2×C3—42no—
1202C2×C3—41no—
1203C2×C3—41no—
1204C2×C3—41no—
1205C2×C3—64no—
1206C2×C3—62no—
1207C2×C3—62no—
1208C2×C3—62no—
1209C2×C3—62no—
1210C2×C3—82no—
1211C2×C3—122no—
1212C2×C3—182no—
1213C2×C3C2×C4×D3211yescharacteristic
1214C2×C3C2×C4×D3211yescharacteristic
1215C2×C3#6430711yescharacteristic
1216C2×C3#6431311yescharacteristic
1217C2×C3#6431411yescharacteristic
1218C2×C3C22×#62411yescharacteristic
1219C2×C3#6433011yescharacteristic
1220C2×C3#6433011yescharacteristic
1221C2×C3#6433011yescharacteristic
1222D3—22no—
1223D3—22no—
1224D3—62no—
1225D3—62no—
1226D3—122no—
1227D3—182no—
1228D3—182no—
1229D3—182no—
1230D3—362no—
1231D3—362no—
1232D3—362no—
1233D3—722no—
1234C22—21no—
1235C22—21no—
1236C22—32no—
1237C22—32no—
1238C22—61no—
1239C22—61no—
1240C22—61no—
1241C22—61no—
1242C22—92no—
1243C22—124no—
1244C22—181no—
1245C22—181no—
1246C22—272no—
1247C22—541no—
1248C22—541no—
1249C22—1084no—
1250C22D3×#62412yes—
1251C22C2×D3311yescharacteristic
1252C4—61no—
1253C4—61no—
1254C4—61no—
1255C4—61no—
1256C4—92no—
1257C4—181no—
1258C4—181no—
1259C4—181no—
1260C4—181no—
1261C4—272no—
1262C3—21no—
1263C3—21no—
1264C3—21no—
1265C3—41no—
1266C3#1059425411yescharacteristic, complemented
1267C3#1059505611yescharacteristic, complemented
1268C3#1059551011yescharacteristic, complemented
1269C2—22no—
1270C2—62no—
1271C2—62no—
1272C2—182no—
1273C2—542no—
1274C2C2×D3×#62411yescharacteristic
1275C2#1172441411yescharacteristic
1276C2#1172441811yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutatorC2×C33C23×C4
FittingC23×C33C23
socle, cosocleC22×C33C24
prime radicalC2×D3×#638C2
hypercenterC23D33
hypocenterC33#518
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
2. #11723726C2semidirect
3. #11723622C2semidirect
4. #11723618C2semidirect
5. C3×D3×#217C2semidirect
6. C2×C3×(C2×D3)⋊Dic3C2semidirect
7. C3×#63952C2semidirect
8. #11722936C2semidirect
9. #11722935C2semidirect
10. #11722932C2semidirect
11. #11722930C2semidirect
12. #11722917C2semidirect
13. #11722916C2semidirect
14. #11722906C2semidirect
15. #11722904C2semidirect
23. C22×C3×C3⋊Dic3C22semidirect
24. C22×C32×Dic3C22semidirect
25. C2×#6294C22semidirect
26. D3×#638C4semidirect
29. C2×#6289C22semidirect
30. C2×#6289C22semidirect
32. C2×C3×#624C22semidirect
33. C2×C3×D3×Dic3C22semidirect
34. C2×C3×D3×Dic3C22semidirect
35. C3×#3757C22semidirect
36. C32×#217C22semidirect
37. #88815C22semidirect
38. #88814C22semidirect
39. #88813C22semidirect
40. #88806C22semidirect
41. #88806C22semidirect
42. #88804C22semidirect
43. #88804C22semidirect
44. Dic3×C3⋊Dic3C22semidirect
45. Dic3×C3⋊Dic3C22semidirect
46. C3×#3724C22semidirect
47. C3×#3722C22semidirect
52. C3×(C2×D3)⋊Dic3C22semidirect
53. C3×(C2×D3)⋊Dic3C22semidirect
54. C3×Dic32C22semidirect
71. D3×#217D3semidirect
72. C2×(C2×D3)⋊Dic3D3semidirect
86. #63952D3semidirect
108. C22×C32×D3C2×C4semidirect
113. C2×D3×C3⋊D3C2×C4semidirect
114. #6312C2×C4semidirect
116. C3×#638C2×C4semidirect
129. #6291C2×C4semidirect
130. #6290C2×C4semidirect
133. D3×C3⋊Dic3C2×C4semidirect
161. C22×C3⋊Dic3C2×D3semidirect
173. C22×C3×Dic3C2×D3semidirect
174. C22×C3×Dic3C2×D3semidirect
195. C2×#624C2×D3semidirect
201. C2×D3×Dic3C2×D3semidirect
202. C2×D3×Dic3C2×D3semidirect
204. #3757C2×D3semidirect
221. C3×#217C2×D3semidirect
222. C3×#217C2×D3semidirect
242. #3724C2×D3semidirect
252. #3722C2×D3semidirect
259. (C2×D3)⋊Dic3C2×D3semidirect
260. (C2×D3)⋊Dic3C2×D3semidirect
270. Dic32C2×D3semidirect
382. C22×C3×D3C4×D3semidirect
383. C22×C3×D3C4×D3semidirect
411. #638C4×D3semidirect
545. C22×Dic3D32semidirect
586. #217D32semidirect
782. C33#518semidirect
830. C22×D3#624semidirect
1150. C32#5486semidirect
1151. C32#5486semidirect
1152. C32#5545semidirect
1266. C3#10594254semidirect
1267. C3#10595056semidirect
1268. C3#10595510semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#6382
#117237262
#117236222
#117236182
C3×D3×#2172
C2×C3×(C2×D3)⋊Dic32
C3×#639522
#117229362
#117229352
#117229322
#117229302
#117229172
#117229162
#117229062
#117229042
#105955103
#105950563
#105942543