Finite Group Databasebeta

← #13170813

Subgroups — #13170813

Order 1728.

1646 conjugacy classes of subgroups.

The subgroup lattice has 1214 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#625C211yesmaximal, characteristic
2#11723684C211yesmaximal, characteristic, complemented
3#11723508C211yesmaximal, characteristic, complemented
4C4×#6290C211yesmaximal, characteristic, complemented
5#11723460C211yesmaximal, characteristic, complemented
6C3×#63921C211yesmaximal, characteristic, complemented
7C3×D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
8C3×#63879C211yesmaximal, characteristic, complemented
9#11722936C211yesmaximal, characteristic, complemented
10#11722934C211yesmaximal, characteristic, complemented
11#11722930C211yesmaximal, characteristic, complemented
12#11722924C211yesmaximal, characteristic, complemented
13#11722916C211yesmaximal, characteristic, complemented
14#11722902C211yesmaximal, characteristic, complemented
15D3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
16#10595056—31nomaximal
17#10594254—31nomaximal
18#10594181—31nomaximal
19C22×C3×D32C2211yescharacteristic
20C22×C3×D32C2211yescharacteristic
21C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
22C2×C32×C4×D3C2211yescharacteristic, complemented
23C2×#6295C2211yescharacteristic
24C2×#6294C2211yescharacteristic, complemented
25C2×#6290C2211yescharacteristic
26C2×#6290C2211yescharacteristic
27C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
28C2×D3×C3⋊Dic3C2211yescharacteristic
29C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
30C2×C3×#625C2211yescharacteristic
31C2×C3×#624C2211yescharacteristic, complemented
32C2×C3×D3×Dic3C2211yescharacteristic, complemented
33C2×C3×D3×Dic3C2211yescharacteristic, complemented
34D3×#625C418yescomplemented
35C4×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
36C3×#3752C2211yescharacteristic, complemented
37C3×#3750C2211yescharacteristic, complemented
38C32×(C2×D3)⋊C4C2211yescharacteristic
39C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
40#88814C2211yescharacteristic, complemented
41#88813C2211yescharacteristic, complemented
42#88807C2211yescharacteristic, complemented
43#88806C2211yescharacteristic, complemented
44#88806C2211yescharacteristic, complemented
45#88803C2211yescharacteristic, complemented
46(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
47(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
48Dic3×C3⋊Dic3C2211yescharacteristic, complemented
49C3×#3722C2211yescharacteristic, complemented
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
53C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
54C3×Dic32C2211yescharacteristic, complemented
55C2×D3×#67—31no—
56C2×D3×#67—31no—
57C22×#625—31no—
58C4×#638—31no—
59#64090—31no—
60#64086—31no—
61C3×C4×#67—31no—
62C2×C3×(C2×D3)⋊C4—31no—
63C3×#67⋊C4—31no—
64C3×D3×C22⋊C4—31no—
65C3×D3×C22⋊C4—31no—
66C3×D3×C22⋊C4—31no—
67#67⋊Dic3—31no—
68Dic3×#67—31no—
69D3×#217—31no—
70D3×#217—31no—
71D3×#217—31no—
72C2×(C2×D3)⋊Dic3—31no—
73#63957—31no—
74#63952—31no—
75#63952—31no—
76#63921—31no—
77#63921D311yescharacteristic, complemented
78D3×(C2×D3)⋊C4—31no—
79D3×(C2×D3)⋊C4D311yescharacteristic, complemented
80#63904—31no—
81C4×#626—31no—
82#63902—31no—
83#63902—31no—
84#63902—31no—
85#63902—61no—
86C4×#625—31no—
87C4×#625—31no—
88C4×#625—31no—
89C4×#625—61no—
90#63881—31no—
91#63880—31no—
92#63879—31no—
93#63879—31no—
94#63879—31no—
95#63879—31no—
96#63879—31no—
97#63879D311yescharacteristic, complemented
98#63878—31no—
99#63878—31no—
100#63878—61no—
101#63877—31no—
102#63877—31no—
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C3×C3⋊D3C2311yescharacteristic
105C22×C32×D3C2311yescharacteristic
106C22×C32×D3C2311yescharacteristic
107C22×C32×D3C2311yescharacteristic
108C2×C3×D32—41no—
109C2×C3×D32—41no—
110C2×C3×D32—41no—
111C2×C3×D32—41no—
112C2×C3×D32C2×C414yescomplemented
113C2×C3×D32C2×C414yescomplemented
114C2×C33×C4C2311yescharacteristic
115C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
116C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
117C2×C3×C3⋊Dic3C2311yescharacteristic
118C2×C3×C3⋊Dic3C2311yescharacteristic
119C2×C3×C3⋊Dic3C2311yescharacteristic
120C2×C3×C3⋊Dic3C2311yescharacteristic
121C3×C4×C3⋊D3—41no—
122C2×C32×Dic3C2311yescharacteristic
123C2×C32×Dic3C2311yescharacteristic
124C2×C32×Dic3C2311yescharacteristic
125C32×C4×D3—41no—
126#6295C2×C414yescomplemented
127#6294—41no—
128#6290C2×C414yescomplemented
129#6290C2×C414yescomplemented
130Dic3×C3⋊D3—41no—
131D3×C3⋊Dic3—41no—
132D3×C3⋊Dic3C2×C414yescomplemented
133C3×#625C2×C414yescomplemented
134C3×#624—41no—
135C3×D3×Dic3—41no—
136C3×D3×Dic3—41no—
137#5545—91no—
138#5486—91no—
139#5486—91no—
140C23×C3×D3—31no—
141C23×C3×D3—31no—
142C23×C3×D3—31no—
143C23×C3×D3—31no—
144C22×D32C2×D311yescharacteristic
145C22×D32C2×D311yescharacteristic
146C22×C32×C4—31no—
147C2×#638—31no—
148C2×#638—31no—
149C22×C3⋊Dic3—31no—
150C22×C3⋊Dic3—31no—
151C2×C4×C3⋊D3—31no—
152C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
153C2×C3×#67—31no—
154C2×C3×#67—31no—
155C22×C3×Dic3—31no—
156C22×C3×Dic3—31no—
157C2×C3×C4×D3—21no—
158C2×C3×C4×D3—31no—
159C2×C3×C4×D3—31no—
160C2×C3×C4×D3—31no—
161C2×C3×C4×D3—31no—
162C2×C3×C4×D3—31no—
163C2×C3×C4×D3—31no—
164C2×C3×C4×D3—61no—
165C2×C3×C4×D3C2×D311yescharacteristic, complemented
166C2×C3×C4×D3C2×D311yescharacteristic, complemented
167D3×#67—38no—
168D3×#67—38no—
169C2×#626—31no—
170C2×#626—31no—
171C2×#625—31no—
172C2×#625—31no—
173C2×#625—31no—
174C2×#625—31no—
175C2×#625—31no—
176C2×#625—38no—
177C2×#625—61no—
178C2×#625—61no—
179C2×#625C2×D311yescharacteristic
180C2×#624—31no—
181C2×#624C2×D311yescharacteristic, complemented
182C2×D3×Dic3—31no—
183C2×D3×Dic3—31no—
184C2×D3×Dic3—31no—
185C2×D3×Dic3—31no—
186C2×D3×Dic3—31no—
187C2×D3×Dic3—31no—
188C2×D3×Dic3—31no—
189C2×D3×Dic3—31no—
190C2×D3×Dic3—61no—
191C2×D3×Dic3—61no—
192C2×D3×Dic3—61no—
193C2×D3×Dic3C2×D311yescharacteristic, complemented
194C2×D3×Dic3C2×D311yescharacteristic, complemented
195C32×C22⋊C4—31no—
196C32×C22⋊C4—31no—
197#3757—31no—
198#3757—31no—
199#3752—31no—
200#3752C2×D311yescharacteristic, complemented
201#3750—31no—
202#3750—31no—
203#3750—31no—
204#3750C2×D311yescharacteristic, complemented
205C4×C3⋊Dic3—31no—
206C4×C3⋊Dic3—31no—
207C4×C3⋊Dic3—31no—
208C4×C3⋊Dic3—31no—
209C4×C3⋊Dic3—61no—
210C4×C3⋊Dic3—61no—
211C4×C3⋊Dic3—61no—
212C4×C3⋊Dic3—121no—
213C3×#217—31no—
214C3×#217—31no—
215C3×#217—31no—
216C3×#217—31no—
217C3×(C2×D3)⋊C4—21no—
218C3×(C2×D3)⋊C4—21no—
219C3×(C2×D3)⋊C4—31no—
220C3×(C2×D3)⋊C4—31no—
221C3×(C2×D3)⋊C4—31no—
222C3×(C2×D3)⋊C4—31no—
223C3×(C2×D3)⋊C4—31no—
224C3×(C2×D3)⋊C4—31no—
225C3×(C2×D3)⋊C4—31no—
226C3×(C2×D3)⋊C4—31no—
227C3×(C2×D3)⋊C4—61no—
228C3×(C2×D3)⋊C4C2×D311yescharacteristic
229C3×(C2×D3)⋊C4C2×D311yescharacteristic
230C3×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
231C3×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
232C3×Dic3⋊C4—31no—
233C3×Dic3⋊C4—31no—
234C3×Dic3⋊C4—61no—
235C3×C4×Dic3—31no—
236C3×C4×Dic3—31no—
237#3724—31no—
238#3724—31no—
239#3724—31no—
240#3724—31no—
241#3724—61no—
242#3724—61no—
243Dic3⋊Dic3—31no—
244Dic3⋊Dic3—31no—
245Dic3⋊Dic3—61no—
246#3722—31no—
247#3722C2×D311yescharacteristic, complemented
248(C2×D3)⋊Dic3—31no—
249(C2×D3)⋊Dic3—31no—
250(C2×D3)⋊Dic3—31no—
251(C2×D3)⋊Dic3—31no—
252(C2×D3)⋊Dic3—31no—
253(C2×D3)⋊Dic3—31no—
254(C2×D3)⋊Dic3—31no—
255(C2×D3)⋊Dic3—31no—
256(C2×D3)⋊Dic3—61no—
257(C2×D3)⋊Dic3—61no—
258(C2×D3)⋊Dic3—61no—
259(C2×D3)⋊Dic3C2×D311yescharacteristic
260(C2×D3)⋊Dic3C2×D311yescharacteristic
261(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
262(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
263Dic32—31no—
264Dic32—31no—
265Dic32—31no—
266Dic32—31no—
267Dic32—31no—
268Dic32—61no—
269Dic32C2×D311yescharacteristic, complemented
270C22×C33C2411yescharacteristic
271C2×C3×C3⋊D3—21no—
272C2×C3×C3⋊D3—21no—
273C2×C3×C3⋊D3—21no—
274C2×C3×C3⋊D3—21no—
275C2×C3×C3⋊D3C22×C412yes—
276C2×C3×C3⋊D3C22×C412yes—
277C2×C32×D3—21no—
278C2×C32×D3—21no—
279C2×C32×D3—21no—
280C2×C32×D3—21no—
281C2×C32×D3—21no—
282C2×C32×D3—21no—
283C2×C32×D3C22×C412yes—
284C2×C32×D3C22×C412yes—
285C2×C32×D3C22×C412yes—
286C3×D32—44no—
287C3×D32—44no—
288C33×C4—21no—
289C3⋊(C3⋊Dic3)—21no—
290C3⋊(C3⋊Dic3)C22×C412yes—
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—
298C22×#67—91no—
299C22×#67—91no—
300C2×D3×D4—91no—
301C3×C4×D4—91no—
302C2×C3×C22⋊C4—91no—
303C2×C3×C22⋊C4—91no—
304C2×#217—91no—
305C2×#217—91no—
306D4×Dic3—91no—
307C4×#67—31no—
308C4×#67—91no—
309C4×#67—91no—
310C4×#67—91no—
311C4×#67—91no—
312C4×#67—91no—
313C4×#67—91no—
314C4×#67—91no—
315C4×#67—91no—
316C4×#67—91no—
317C4×#67—181no—
318C2×(C2×D3)⋊C4—31no—
319C2×(C2×D3)⋊C4—91no—
320#893—91no—
321#892—91no—
322#67⋊C4—31no—
323#67⋊C4—91no—
324#67⋊C4—91no—
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—181no—
333D3×C22⋊C4—31no—
334D3×C22⋊C4—31no—
335D3×C22⋊C4—31no—
336D3×C22⋊C4—91no—
337D3×C22⋊C4—91no—
338D3×C22⋊C4—91no—
339#877—91no—
340#877—91no—
341#877—91no—
342#877—91no—
343#877—181no—
344C4×D12—91no—
345#872—91no—
346C23×C32—31no—
347C23×C32—31no—
348C23×C32—31no—
349C22×C3⋊D3C22×D311yescharacteristic
350C22×C3⋊D3C22×D311yescharacteristic
351C22×C3×D3—21no—
352C22×C3×D3—21no—
353C22×C3×D3—21no—
354C22×C3×D3—31no—
355C22×C3×D3—31no—
356C22×C3×D3—31no—
357C22×C3×D3—31no—
358C22×C3×D3—34no—
359C22×C3×D3—34no—
360C22×C3×D3—34no—
361C22×C3×D3—34no—
362C22×C3×D3—61no—
363C22×C3×D3—61no—
364C22×C3×D3—121no—
365C22×C3×D3—121no—
366C22×C3×D3—121no—
367C22×C3×D3—121no—
368C22×C3×D3—121no—
369C22×C3×D3—121no—
370C22×C3×D3—121no—
371C22×C3×D3—121no—
372C22×C3×D3C22×D311yescharacteristic
373C22×C3×D3C22×D311yescharacteristic
374C22×C3×D3C22×D311yescharacteristic
375C22×C3×D3C22×D311yescharacteristic
376C22×C3×D3C22×D311yescharacteristic
377C22×C3×D3C22×D311yescharacteristic
378C2×D32—41no—
379C2×D32—41no—
380C2×D32—41no—
381C2×D32—41no—
382C2×D32C4×D314yescomplemented
383C2×D32C4×D314yescomplemented
384C2×C32×C4—21no—
385C2×C32×C4—21no—
386C2×C32×C4—21no—
387C2×C32×C4—31no—
388C2×C32×C4—31no—
389C2×C32×C4—31no—
390C2×C32×C4—41no—
391C2×C32×C4—121no—
392C2×C32×C4C22×D311yescharacteristic
393C2×C32×C4C22×D311yescharacteristic
394C2×C32×C4C22×D311yescharacteristic
395#638—34no—
396#638—34no—
397C2×C3⋊Dic3—31no—
398C2×C3⋊Dic3—31no—
399C2×C3⋊Dic3—31no—
400C2×C3⋊Dic3—34no—
401C2×C3⋊Dic3—31no—
402C2×C3⋊Dic3—31no—
403C2×C3⋊Dic3—31no—
404C2×C3⋊Dic3—61no—
405C2×C3⋊Dic3—61no—
406C2×C3⋊Dic3—61no—
407C2×C3⋊Dic3—61no—
408C2×C3⋊Dic3—61no—
409C2×C3⋊Dic3—61no—
410C2×C3⋊Dic3—121no—
411C2×C3⋊Dic3—121no—
412C2×C3⋊Dic3—121no—
413C2×C3⋊Dic3C22×D311yescharacteristic
414C2×C3⋊Dic3C22×D311yescharacteristic
415C2×C3⋊Dic3C22×D311yescharacteristic
416C2×C3⋊Dic3C22×D311yescharacteristic
417C4×C3⋊D3—41no—
418C4×C3⋊D3—121no—
419C3×#67—34no—
420C3×#67—34no—
421C2×C3×Dic3—21no—
422C2×C3×Dic3—21no—
423C2×C3×Dic3—21no—
424C2×C3×Dic3—31no—
425C2×C3×Dic3—31no—
426C2×C3×Dic3—31no—
427C2×C3×Dic3—31no—
428C2×C3×Dic3—31no—
429C2×C3×Dic3—31no—
430C2×C3×Dic3—31no—
431C2×C3×Dic3—31no—
432C2×C3×Dic3—61no—
433C2×C3×Dic3—61no—
434C2×C3×Dic3—61no—
435C2×C3×Dic3—61no—
436C2×C3×Dic3—121no—
437C2×C3×Dic3—121no—
438C2×C3×Dic3C22×D311yescharacteristic
439C2×C3×Dic3C22×D311yescharacteristic
440C2×C3×Dic3C22×D311yescharacteristic
441C2×C3×Dic3C22×D311yescharacteristic
442C2×C3×Dic3C22×D311yescharacteristic
443C2×C3×Dic3C22×D311yescharacteristic
444C3×C4×D3—41no—
445C3×C4×D3—41no—
446C3×C4×D3—42no—
447C3×C4×D3—121no—
448C3×C4×D3—121no—
449C3×C4×D3—121no—
450C3×C4×D3—121no—
451C3×C4×D3—121no—
452C3×C4×D3—121no—
453C3×C4×D3—122no—
454#626—34no—
455#626—34no—
456#625—34no—
457#625—34no—
458#625—34no—
459#625—34no—
460#625—34no—
461#625—64no—
462#625—64no—
463#625C4×D314yescomplemented
464#624—41no—
465#624—121no—
466D3×Dic3—34no—
467D3×Dic3—34no—
468D3×Dic3—41no—
469D3×Dic3—41no—
470D3×Dic3—64no—
471D3×Dic3—121no—
472D3×Dic3—121no—
473D3×Dic3—122no—
474D3×Dic3—121no—
475D3×Dic3—121no—
476D3×Dic3—121no—
477D3×Dic3—121no—
478D3×Dic3—122no—
479#518—271noSylow
480C2×C33C23×C411yescharacteristic
481C2×C33H(5,𝔽2)11yescharacteristic
482C2×C33H(5,𝔽2)11yescharacteristic
483C3×C3⋊D3—22no—
484C3×C3⋊D3—22no—
485C32×D3—22no—
486C32×D3—22no—
487C32×D3—22no—
488C24×C3—91no—
489C24×C3—91no—
490C23×D3—31no—
491C23×D3—31no—
492C23×D3—31no—
493C23×D3—31no—
494C2×C3×D4—91no—
495C22×C3×C4—31no—
496C22×C3×C4—31no—
497C22×C3×C4—61no—
498C22×C3×C4—91no—
499C22×C3×C4—91no—
500C22×C3×C4—91no—
501C22×C3×C4—91no—
502C2×#67—31no—
503C2×#67—31no—
504C2×#67—91no—
505C2×#67—91no—
506C2×#67—98no—
507C2×#67—98no—
508C2×#67—91no—
509C2×#67—91no—
510C2×#67—91no—
511C2×#67—91no—
512C2×#67—91no—
513C2×#67—91no—
514C2×#67—181no—
515C2×#67—181no—
516C22×Dic3—31no—
517C22×Dic3—31no—
518C22×Dic3—91no—
519C22×Dic3—91no—
520C22×Dic3—91no—
521C22×Dic3—91no—
522C22×Dic3—91no—
523C22×Dic3—91no—
524C22×Dic3—181no—
525C22×Dic3—181no—
526D3×D4—98no—
527C2×D12—91no—
528C2×C4×D3—31no—
529C2×C4×D3—31no—
530C2×C4×D3—31no—
531C2×C4×D3—31no—
532C2×C4×D3—31no—
533C2×C4×D3—31no—
534C2×C4×D3—61no—
535C2×C4×D3—91no—
536C2×C4×D3—91no—
537C2×C4×D3—91no—
538C2×C4×D3—91no—
539C2×C4×D3—91no—
540C2×C4×D3—91no—
541C2×C4×D3—181no—
542C2×C4×D3D3211yescharacteristic, complemented
543C3×C4⋊C4—91no—
544C3×C22⋊C4—31no—
545C3×C22⋊C4—31no—
546C3×C22⋊C4—31no—
547C3×C22⋊C4—31no—
548C3×C22⋊C4—61no—
549C3×C22⋊C4—61no—
550C3×C22⋊C4—91no—
551C3×C22⋊C4—91no—
552C3×C22⋊C4—91no—
553C3×C22⋊C4—91no—
554C3×C22⋊C4—91no—
555C3×C22⋊C4—91no—
556C3×C42—91no—
557#217—31no—
558#217—31no—
559#217—31no—
560#217—31no—
561#217—91no—
562#217—91no—
563#217—91no—
564#217—91no—
565#217—91no—
566#217—91no—
567#217—181no—
568#217—181no—
569(C2×D3)⋊C4—31no—
570(C2×D3)⋊C4—31no—
571(C2×D3)⋊C4—31no—
572(C2×D3)⋊C4—31no—
573(C2×D3)⋊C4—31no—
574(C2×D3)⋊C4—31no—
575(C2×D3)⋊C4—31no—
576(C2×D3)⋊C4—31no—
577(C2×D3)⋊C4—61no—
578(C2×D3)⋊C4—91no—
579(C2×D3)⋊C4—91no—
580(C2×D3)⋊C4—91no—
581(C2×D3)⋊C4—91no—
582(C2×D3)⋊C4—91no—
583(C2×D3)⋊C4—91no—
584(C2×D3)⋊C4—181no—
585(C2×D3)⋊C4D3211yescharacteristic
586(C2×D3)⋊C4D3211yescharacteristic, complemented
587C4⋊Dic3—91no—
588Dic3⋊C4—31no—
589Dic3⋊C4—31no—
590Dic3⋊C4—61no—
591Dic3⋊C4—91no—
592Dic3⋊C4—91no—
593Dic3⋊C4—91no—
594Dic3⋊C4—91no—
595Dic3⋊C4—91no—
596Dic3⋊C4—91no—
597Dic3⋊C4—91no—
598Dic3⋊C4—91no—
599Dic3⋊C4—181no—
600Dic3⋊C4—181no—
601Dic3⋊C4—181no—
602C4×Dic3—31no—
603C4×Dic3—31no—
604C4×Dic3—91no—
605C4×Dic3—91no—
606C4×Dic3—91no—
607C4×Dic3—91no—
608C4×Dic3—91no—
609C4×Dic3—91no—
610C4×Dic3—91no—
611C4×Dic3—91no—
612C4×Dic3—91no—
613C4×Dic3—181no—
614C4×Dic3—181no—
615C4×Dic3—181no—
616C4×Dic3—181no—
617C4×Dic3—361no—
618C22×C32—21no—
619C22×C32—21no—
620C22×C32—21no—
621C22×C32—32no—
622C22×C32—32no—
623C22×C32—32no—
624C22×C32—41no—
625C22×C32—61no—
626C22×C32—61no—
627C22×C32—61no—
628C22×C32—61no—
629C22×C32—61no—
630C22×C32—61no—
631C22×C32C23×D311yescharacteristic
632C22×C32C23×D311yescharacteristic
633C22×C32C23×D311yescharacteristic
634C2×C3⋊D3—21no—
635C2×C3⋊D3—21no—
636C2×C3⋊D3—21no—
637C2×C3⋊D3—21no—
638C2×C3⋊D3C2×C4×D312yes—
639C2×C3⋊D3C2×C4×D312yes—
640C2×C3×D3—21no—
641C2×C3×D3—21no—
642C2×C3×D3—21no—
643C2×C3×D3—21no—
644C2×C3×D3—21no—
645C2×C3×D3—21no—
646C2×C3×D3—21no—
647C2×C3×D3—21no—
648C2×C3×D3—21no—
649C2×C3×D3—21no—
650C2×C3×D3—21no—
651C2×C3×D3—21no—
652C2×C3×D3—22no—
653C2×C3×D3—22no—
654C2×C3×D3—22no—
655C2×C3×D3—32no—
656C2×C3×D3—32no—
657C2×C3×D3—32no—
658C2×C3×D3—32no—
659C2×C3×D3—41no—
660C2×C3×D3—41no—
661C2×C3×D3—41no—
662C2×C3×D3—41no—
663C2×C3×D3—41no—
664C2×C3×D3—41no—
665C2×C3×D3—62no—
666C2×C3×D3—62no—
667C2×C3×D3—61no—
668C2×C3×D3—61no—
669C2×C3×D3—61no—
670C2×C3×D3—61no—
671C2×C3×D3—61no—
672C2×C3×D3—61no—
673C2×C3×D3—61no—
674C2×C3×D3—61no—
675C2×C3×D3—121no—
676C2×C3×D3—121no—
677C2×C3×D3—121no—
678C2×C3×D3—121no—
679C2×C3×D3—124no—
680C2×C3×D3—124no—
681C2×C3×D3—124no—
682C2×C3×D3—124no—
683C2×C3×D3C2×C4×D312yes—
684C2×C3×D3C2×C4×D312yes—
685C2×C3×D3C2×C4×D312yes—
686C2×C3×D3C2×C4×D312yes—
687C2×C3×D3C2×C4×D312yes—
688C2×C3×D3C2×C4×D312yes—
689D32—44no—
690D32—44no—
691C32×C4—21no—
692C32×C4—22no—
693C32×C4—21no—
694C32×C4—21no—
695C32×C4—41no—
696C32×C4—41no—
697C32×C4—42no—
698C32×C4—61no—
699C32×C4—61no—
700C32×C4—61no—
701C3⋊Dic3—21no—
702C3⋊Dic3—21no—
703C3⋊Dic3—21no—
704C3⋊Dic3—32no—
705C3⋊Dic3—32no—
706C3⋊Dic3—32no—
707C3⋊Dic3—62no—
708C3⋊Dic3—62no—
709C3⋊Dic3—62no—
710C3⋊Dic3—61no—
711C3⋊Dic3—62no—
712C3⋊Dic3—61no—
713C3⋊Dic3—61no—
714C3⋊Dic3—122no—
715C3⋊Dic3—121no—
716C3⋊Dic3—121no—
717C3⋊Dic3—122no—
718C3⋊Dic3C2×C4×D312yes—
719C3×Dic3—21no—
720C3×Dic3—21no—
721C3×Dic3—21no—
722C3×Dic3—21no—
723C3×Dic3—21no—
724C3×Dic3—21no—
725C3×Dic3—32no—
726C3×Dic3—32no—
727C3×Dic3—41no—
728C3×Dic3—41no—
729C3×Dic3—41no—
730C3×Dic3—62no—
731C3×Dic3—61no—
732C3×Dic3—61no—
733C3×Dic3—61no—
734C3×Dic3—61no—
735C3×Dic3—61no—
736C3×Dic3—61no—
737C3×Dic3—121no—
738C3×Dic3—121no—
739C3×Dic3—121no—
740C22×D4—271no—
741C4×D4—91no—
742C4×D4—271no—
743C4×D4—271no—
744C4×D4—271no—
745C4×D4—271no—
746C4×D4—271no—
747C4×D4—271no—
748C4×D4—271no—
749#117—271no—
750#117—271no—
751C2×C22⋊C4—91no—
752C2×C22⋊C4—91no—
753C2×C22⋊C4—271no—
754C2×C22⋊C4—271no—
755C33#51811yescharacteristic, complemented, Sylow
756C23×C3—31no—
757C23×C3—31no—
758C23×C3—31no—
759C23×C3—31no—
760C23×C3—31no—
761C23×C3—31no—
762C23×C3—61no—
763C23×C3—61no—
764C23×C3—61no—
765C23×C3—94no—
766C23×C3—94no—
767C23×C3—91no—
768C23×C3—91no—
769C23×C3—361no—
770C23×C3—361no—
771C23×C3—361no—
772C23×C3—361no—
773C22×D3—31no—
774C22×D3—31no—
775C22×D3—31no—
776C22×D3—31no—
777C22×D3—34no—
778C22×D3—34no—
779C22×D3—34no—
780C22×D3—34no—
781C22×D3—61no—
782C22×D3—61no—
783C22×D3—121no—
784C22×D3—121no—
785C22×D3—121no—
786C22×D3—121no—
787C22×D3—121no—
788C22×D3—121no—
789C22×D3—121no—
790C22×D3—121no—
791C22×D3C2×D3211yescharacteristic
792C22×D3C2×D3211yescharacteristic
793C22×D3C2×D3211yescharacteristic
794C3×D4—94no—
795C2×C3×C4—21no—
796C2×C3×C4—21no—
797C2×C3×C4—21no—
798C2×C3×C4—31no—
799C2×C3×C4—31no—
800C2×C3×C4—31no—
801C2×C3×C4—31no—
802C2×C3×C4—31no—
803C2×C3×C4—31no—
804C2×C3×C4—41no—
805C2×C3×C4—61no—
806C2×C3×C4—61no—
807C2×C3×C4—61no—
808C2×C3×C4—91no—
809C2×C3×C4—91no—
810C2×C3×C4—91no—
811C2×C3×C4—91no—
812C2×C3×C4—121no—
813C2×C3×C4—121no—
814C2×C3×C4—122no—
815C2×C3×C4—361no—
816C2×C3×C4—361no—
817C2×C3×C4—361no—
818C2×C3×C4—361no—
819C2×C3×C4C2×D3211yescharacteristic
820C2×C3×C4C2×D3211yescharacteristic
821C2×C3×C4C2×D3211yescharacteristic
822#67—34no—
823#67—34no—
824#67—94no—
825#67—94no—
826#67—94no—
827#67—94no—
828#67—94no—
829#67—94no—
830#67—94no—
831#67—94no—
832#67—184no—
833#67—184no—
834C2×Dic3—31no—
835C2×Dic3—31no—
836C2×Dic3—31no—
837C2×Dic3—31no—
838C2×Dic3—31no—
839C2×Dic3—31no—
840C2×Dic3—31no—
841C2×Dic3—31no—
842C2×Dic3—61no—
843C2×Dic3—61no—
844C2×Dic3—61no—
845C2×Dic3—61no—
846C2×Dic3—94no—
847C2×Dic3—94no—
848C2×Dic3—91no—
849C2×Dic3—91no—
850C2×Dic3—91no—
851C2×Dic3—91no—
852C2×Dic3—91no—
853C2×Dic3—91no—
854C2×Dic3—121no—
855C2×Dic3—121no—
856C2×Dic3—184no—
857C2×Dic3—181no—
858C2×Dic3—181no—
859C2×Dic3—181no—
860C2×Dic3—181no—
861C2×Dic3—181no—
862C2×Dic3—181no—
863C2×Dic3—361no—
864C2×Dic3—361no—
865C2×Dic3—361no—
866C2×Dic3—361no—
867C2×Dic3—361no—
868C2×Dic3—361no—
869C2×Dic3—362no—
870C2×Dic3C2×D3211yescharacteristic
871C2×Dic3C2×D3211yescharacteristic
872C2×Dic3C2×D3211yescharacteristic
873D12—94no—
874C4×D3—41no—
875C4×D3—94no—
876C4×D3—121no—
877C4×D3—121no—
878C4×D3—121no—
879C4×D3—121no—
880C4×D3—121no—
881C4×D3—121no—
882C4×D3—122no—
883C4×D3—361no—
884C4×D3—361no—
885C4×D3—361no—
886C4×D3—361no—
887C4×D3—362no—
888C4×D3—361no—
889C2×C32—21no—
890C2×C32—21no—
891C2×C32—21no—
892C2×C32—21no—
893C2×C32—21no—
894C2×C32—21no—
895C2×C32—21no—
896C2×C32—21no—
897C2×C32—21no—
898C2×C32—41no—
899C2×C32—41no—
900C2×C32—41no—
901C2×C32—62no—
902C2×C32—62no—
903C2×C32—62no—
904C2×C32C22×C4×D311yescharacteristic
905C2×C32C22×C4×D311yescharacteristic
906C2×C32C22×C4×D311yescharacteristic
907C2×C32#100411yescharacteristic
908C2×C32#100411yescharacteristic
909C2×C32#100411yescharacteristic
910C2×C32#100411yescharacteristic
911C2×C32#100411yescharacteristic
912C2×C32#100911yescharacteristic
913C3⋊D3—22no—
914C3⋊D3—22no—
915C3×D3—22no—
916C3×D3—22no—
917C3×D3—22no—
918C3×D3—22no—
919C3×D3—22no—
920C3×D3—22no—
921C3×D3—42no—
922C3×D3—42no—
923C3×D3—42no—
924C3×D3—62no—
925C3×D3—62no—
926C3×D3—62no—
927C3×D3—62no—
928C3×D3—122no—
929C3×D3—122no—
930C24—91no—
931C24—91no—
932C2×D4—91no—
933C2×D4—271no—
934C2×D4—278no—
935C2×D4—271no—
936C2×D4—271no—
937C22×C4—31no—
938C22×C4—91no—
939C22×C4—91no—
940C22×C4—91no—
941C22×C4—91no—
942C22×C4—271no—
943C22×C4—271no—
944C22×C4—271no—
945C22×C4—271no—
946C4⋊C4—91no—
947C4⋊C4—271no—
948C4⋊C4—271no—
949C4⋊C4—271no—
950C22⋊C4—31no—
951C22⋊C4—31no—
952C22⋊C4—91no—
953C22⋊C4—91no—
954C22⋊C4—91no—
955C22⋊C4—91no—
956C22⋊C4—91no—
957C22⋊C4—91no—
958C22⋊C4—271no—
959C22⋊C4—271no—
960C22⋊C4—271no—
961C22⋊C4—271no—
962C42—91no—
963C42—271no—
964C42—271no—
965C42—271no—
966C22×C3—21no—
967C22×C3—21no—
968C22×C3—21no—
969C22×C3—32no—
970C22×C3—32no—
971C22×C3—32no—
972C22×C3—32no—
973C22×C3—32no—
974C22×C3—32no—
975C22×C3—41no—
976C22×C3—62no—
977C22×C3—62no—
978C22×C3—62no—
979C22×C3—61no—
980C22×C3—61no—
981C22×C3—61no—
982C22×C3—61no—
983C22×C3—61no—
984C22×C3—61no—
985C22×C3—61no—
986C22×C3—61no—
987C22×C3—61no—
988C22×C3—61no—
989C22×C3—61no—
990C22×C3—61no—
991C22×C3—92no—
992C22×C3—92no—
993C22×C3—121no—
994C22×C3—121no—
995C22×C3—121no—
996C22×C3—121no—
997C22×C3—121no—
998C22×C3—121no—
999C22×C3—181no—
1000C22×C3—181no—
1001C22×C3—181no—
1002C22×C3—181no—
1003C22×C3—364no—
1004C22×C3—364no—
1005C22×C3C22×D3211yescharacteristic
1006C22×C3C22×D3211yescharacteristic
1007C22×C3C22×D3211yescharacteristic
1008C2×D3—21no—
1009C2×D3—21no—
1010C2×D3—21no—
1011C2×D3—21no—
1012C2×D3—21no—
1013C2×D3—21no—
1014C2×D3—32no—
1015C2×D3—32no—
1016C2×D3—32no—
1017C2×D3—32no—
1018C2×D3—62no—
1019C2×D3—62no—
1020C2×D3—61no—
1021C2×D3—61no—
1022C2×D3—61no—
1023C2×D3—61no—
1024C2×D3—61no—
1025C2×D3—61no—
1026C2×D3—61no—
1027C2×D3—61no—
1028C2×D3—121no—
1029C2×D3—121no—
1030C2×D3—121no—
1031C2×D3—121no—
1032C2×D3—124no—
1033C2×D3—124no—
1034C2×D3—124no—
1035C2×D3—124no—
1036C2×D3C4×D3212yes—
1037C2×D3C4×D3212yes—
1038C2×D3C4×D3212yes—
1039C3×C4—22no—
1040C3×C4—21no—
1041C3×C4—21no—
1042C3×C4—21no—
1043C3×C4—41no—
1044C3×C4—41no—
1045C3×C4—42no—
1046C3×C4—61no—
1047C3×C4—61no—
1048C3×C4—61no—
1049C3×C4—61no—
1050C3×C4—61no—
1051C3×C4—61no—
1052C3×C4—92no—
1053C3×C4—121no—
1054C3×C4—121no—
1055C3×C4—121no—
1056C3×C4—181no—
1057C3×C4—181no—
1058C3×C4—181no—
1059Dic3—21no—
1060Dic3—21no—
1061Dic3—21no—
1062Dic3—32no—
1063Dic3—32no—
1064Dic3—62no—
1065Dic3—61no—
1066Dic3—61no—
1067Dic3—61no—
1068Dic3—61no—
1069Dic3—61no—
1070Dic3—61no—
1071Dic3—92no—
1072Dic3—92no—
1073Dic3—92no—
1074Dic3—121no—
1075Dic3—121no—
1076Dic3—121no—
1077Dic3—182no—
1078Dic3—182no—
1079Dic3—182no—
1080Dic3—182no—
1081Dic3—181no—
1082Dic3—181no—
1083Dic3—181no—
1084Dic3—362no—
1085Dic3—361no—
1086Dic3—361no—
1087Dic3—362no—
1088C32—21no—
1089C32—21no—
1090C32—21no—
1091C32—41no—
1092C32#548611yescharacteristic, complemented
1093C32#548611yescharacteristic, complemented
1094C32#554511yescharacteristic, complemented
1095C23—31no—
1096C23—31no—
1097C23—31no—
1098C23—94no—
1099C23—94no—
1100C23—91no—
1101C23—91no—
1102C23—361no—
1103C23—361no—
1104C23—361no—
1105C23—361no—
1106D4—94no—
1107D4—274no—
1108D4—274no—
1109D4—274no—
1110C2×C4—31no—
1111C2×C4—31no—
1112C2×C4—31no—
1113C2×C4—91no—
1114C2×C4—91no—
1115C2×C4—91no—
1116C2×C4—91no—
1117C2×C4—121no—
1118C2×C4—274no—
1119C2×C4—271no—
1120C2×C4—271no—
1121C2×C4—361no—
1122C2×C4—361no—
1123C2×C4—361no—
1124C2×C4—361no—
1125C2×C4—1081no—
1126C2×C4—1081no—
1127C2×C4—1081no—
1128C2×C4D3311yescharacteristic
1129C2×C3—21no—
1130C2×C3—21no—
1131C2×C3—21no—
1132C2×C3—21no—
1133C2×C3—21no—
1134C2×C3—21no—
1135C2×C3—21no—
1136C2×C3—21no—
1137C2×C3—21no—
1138C2×C3—41no—
1139C2×C3—41no—
1140C2×C3—41no—
1141C2×C3—62no—
1142C2×C3—62no—
1143C2×C3—62no—
1144C2×C3—62no—
1145C2×C3—62no—
1146C2×C3—62no—
1147C2×C3—122no—
1148C2×C3—122no—
1149C2×C3—122no—
1150C2×C3—182no—
1151C2×C3—182no—
1152C2×C3C2×C4×D3211yescharacteristic
1153C2×C3C2×C4×D3211yescharacteristic
1154C2×C3C2×C4×D3211yescharacteristic
1155C2×C3#6430711yescharacteristic
1156C2×C3#6431311yescharacteristic
1157C2×C3#6431311yescharacteristic
1158C2×C3#6431311yescharacteristic
1159C2×C3#6431411yescharacteristic
1160C2×C3#6433011yescharacteristic
1161D3—22no—
1162D3—22no—
1163D3—22no—
1164D3—62no—
1165D3—62no—
1166D3—62no—
1167D3—62no—
1168D3—122no—
1169D3—122no—
1170C22—32no—
1171C22—32no—
1172C22—32no—
1173C22—61no—
1174C22—61no—
1175C22—61no—
1176C22—61no—
1177C22—61no—
1178C22—61no—
1179C22—92no—
1180C22—92no—
1181C22—181no—
1182C22—181no—
1183C22—181no—
1184C22—181no—
1185C22—364no—
1186C22—364no—
1187C22C2×D3311yescharacteristic
1188C4—21no—
1189C4—61no—
1190C4—61no—
1191C4—61no—
1192C4—92no—
1193C4—181no—
1194C4—181no—
1195C4—181no—
1196C4—272no—
1197C4—541no—
1198C3—21no—
1199C3—21no—
1200C3—21no—
1201C3—41no—
1202C3#1059418111yescharacteristic, complemented
1203C3#1059425411yescharacteristic, complemented
1204C3#1059505611yescharacteristic, complemented
1205C2—62no—
1206C2—62no—
1207C2—62no—
1208C2—182no—
1209C2—182no—
1210C2#1172438111yescharacteristic
1211C2C4×D3311yescharacteristic
1212C2#1172441511yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutatorC2×C33C23×C4
FittingC2×C33×C4C23
socle, cosocleC22×C33C24
prime radicalC2×D3×#625C2
hypercenterC2×C4D33
hypocenterC33#518
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. #11723684C2semidirect
3. #11723508C2semidirect
4. C4×#6290C2semidirect
5. #11723460C2semidirect
6. C3×#63921C2semidirect
7. C3×D3×(C2×D3)⋊C4C2semidirect
8. C3×#63879C2semidirect
9. #11722936C2semidirect
10. #11722934C2semidirect
11. #11722930C2semidirect
12. #11722924C2semidirect
13. #11722916C2semidirect
14. #11722902C2semidirect
15. D3×(C2×D3)⋊Dic3C2semidirect
21. C2×C3×C4×C3⋊D3C22semidirect
22. C2×C32×C4×D3C22semidirect
24. C2×#6294C22semidirect
27. C2×Dic3×C3⋊D3C22semidirect
29. C2×D3×C3⋊Dic3C22semidirect
31. C2×C3×#624C22semidirect
32. C2×C3×D3×Dic3C22semidirect
33. C2×C3×D3×Dic3C22semidirect
34. D3×#625C4semidirect
35. C4×C3⋊(C3⋊Dic3)C22semidirect
36. C3×#3752C22semidirect
37. C3×#3750C22semidirect
39. C32×(C2×D3)⋊C4C22semidirect
40. #88814C22semidirect
41. #88813C22semidirect
42. #88807C22semidirect
43. #88806C22semidirect
44. #88806C22semidirect
45. #88803C22semidirect
47. (C2×D3)⋊(C3⋊Dic3)C22semidirect
48. Dic3×C3⋊Dic3C22semidirect
49. C3×#3722C22semidirect
52. C3×(C2×D3)⋊Dic3C22semidirect
53. C3×(C2×D3)⋊Dic3C22semidirect
54. C3×Dic32C22semidirect
77. #63921D3semidirect
79. D3×(C2×D3)⋊C4D3semidirect
97. #63879D3semidirect
112. C2×C3×D32C2×C4semidirect
113. C2×C3×D32C2×C4semidirect
126. #6295C2×C4semidirect
128. #6290C2×C4semidirect
129. #6290C2×C4semidirect
132. D3×C3⋊Dic3C2×C4semidirect
133. C3×#625C2×C4semidirect
152. C2×C4×C3⋊D3C2×D3semidirect
165. C2×C3×C4×D3C2×D3semidirect
166. C2×C3×C4×D3C2×D3semidirect
181. C2×#624C2×D3semidirect
193. C2×D3×Dic3C2×D3semidirect
194. C2×D3×Dic3C2×D3semidirect
200. #3752C2×D3semidirect
204. #3750C2×D3semidirect
230. C3×(C2×D3)⋊C4C2×D3semidirect
231. C3×(C2×D3)⋊C4C2×D3semidirect
247. #3722C2×D3semidirect
261. (C2×D3)⋊Dic3C2×D3semidirect
262. (C2×D3)⋊Dic3C2×D3semidirect
269. Dic32C2×D3semidirect
382. C2×D32C4×D3semidirect
383. C2×D32C4×D3semidirect
463. #625C4×D3semidirect
542. C2×C4×D3D32semidirect
586. (C2×D3)⋊C4D32semidirect
755. C33#518semidirect
1092. C32#5486semidirect
1093. C32#5486semidirect
1094. C32#5545semidirect
1202. C3#10594181semidirect
1203. C3#10594254semidirect
1204. C3#10595056semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#6252
#117236842
#117235082
C4×#62902
#117234602
C3×#639212
C3×D3×(C2×D3)⋊C42
C3×#638792
#117229362
#117229342
#117229302
#117229242
#117229162
#117229022
D3×(C2×D3)⋊Dic32
#105950563
#105942543
#105941813