Finite Group Databasebeta

← #13170801

Subgroups — #13170801

Order 1728.

1620 conjugacy classes of subgroups.

The subgroup lattice has 1236 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88962C211yesmaximal, characteristic, complemented
2C2×D32×Dic3C211yesmaximal, characteristic, complemented
3#11723683C211yesmaximal, characteristic, complemented
4#11723493C211yesmaximal, characteristic, complemented
5#11723475C211yesmaximal, characteristic, complemented
6#11723461C211yesmaximal, characteristic, complemented
7C3×#63922C211yesmaximal, characteristic, complemented
8C3×#63899C211yesmaximal, characteristic, complemented
9C3×#63898C211yesmaximal, characteristic, complemented
10#11722991C211yesmaximal, characteristic, complemented
11#11722976C211yesmaximal, characteristic, complemented
12#11722958C211yesmaximal, characteristic, complemented
13#11722948C211yesmaximal, characteristic, complemented
14#11722935C211yesmaximal, characteristic, complemented
15#11722924C211yesmaximal, characteristic, complemented
16#10595129—31nomaximal
17#10594623—31nomaximal
18#10594055—31nomaximal
19C22×C3×D32C2211yescharacteristic
20C2×C32×D12C2211yescharacteristic
21C2×#6294C2211yescharacteristic
22C2×#6292C2211yescharacteristic
23C2×#6291C2211yescharacteristic
24C2×#6291C2211yescharacteristic
25C2×#6291C2211yescharacteristic, complemented
26C2×#6289C2211yescharacteristic, complemented
27C2×Dic3×C3⋊D3C2211yescharacteristic
28C2×D3×C3⋊Dic3C2211yescharacteristic
29C2×D3×C3⋊Dic3C2211yescharacteristic
30C2×C3×#627C2211yescharacteristic, complemented
31C2×C3×#626C2211yescharacteristic
32C2×C3×#625C2211yescharacteristic
33C2×C3×D3×Dic3C2211yescharacteristic
34C2×C3×D3×Dic3C2211yescharacteristic
35C2×C3×D3×Dic3C2211yescharacteristic, complemented
36#88962—24no—
37D32×Dic3—24no—
38#88859C2211yescharacteristic, complemented
39C3×#3752C2211yescharacteristic
40C3×#3750C2211yescharacteristic, complemented
41C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
42C32×(C2×D3)⋊C4C2211yescharacteristic
43C32×C4⋊Dic3C2211yescharacteristic, complemented
44#88815C2211yescharacteristic, complemented
45#88814C2211yescharacteristic
46#88813C2211yescharacteristic, complemented
47#88807C2211yescharacteristic, complemented
48#88807C2211yescharacteristic, complemented
49#88804C2211yescharacteristic, complemented
50(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
51C3×#3724C2211yescharacteristic, complemented
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×(C2×D3)⋊Dic3C2211yescharacteristic
54C3×(C2×D3)⋊Dic3C2211yescharacteristic
55C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
56C2×#3804—31no—
57C22×D3×Dic3—31no—
58C22×D3×Dic3—31no—
59C2×C4×D32—31no—
60C2×#3799—31no—
61C2×#3796—31no—
62#64148—31no—
63#64103—31no—
64#64090—31no—
65C3×#937—31no—
66C3×D4×Dic3—31no—
67C3×#896—31no—
68C3×#893—31no—
69C3×#882—31no—
70C3×#878—31no—
71#63982—31no—
72#63978—31no—
73#63977—31no—
74#63977—31no—
75#67⋊Dic3—31no—
76Dic3×#67—31no—
77#63971—31no—
78#63969—31no—
79#63952—31no—
80#63923—31no—
81#63922D311yescharacteristic, complemented
82#63906—31no—
83#63904—31no—
84#63899D311yescharacteristic, complemented
85#63898D311yescharacteristic, complemented
86#63890—31no—
87#63890—31no—
88#63890—61no—
89#63887—31no—
90#63887—31no—
91#63886—31no—
92#63886—31no—
93#63886—61no—
94#63884—31no—
95#63881—31no—
96#63880—31no—
97#63880—31no—
98#63880—61no—
99#63879—31no—
100#63878—31no—
101#63877—31no—
102#63853—31no—
103#63836—31no—
104C22×C3⋊(C3⋊D3)C2311yescharacteristic
105C22×C3×C3⋊D3C2311yescharacteristic
106C22×C32×D3C2311yescharacteristic
107C22×C32×D3C2311yescharacteristic
108C22×C32×D3C2311yescharacteristic
109C2×C3×D32—22no—
110C2×C3×D32—22no—
111C2×C3×D32—22no—
112C2×C33×C4C2311yescharacteristic
113C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C3×C3⋊Dic3C2311yescharacteristic
118C2×C3×C3⋊Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122C32×D12—22no—
123#6294D414yescomplemented
124#6292—22no—
125#6291—22no—
126#6291—22no—
127#6291—22no—
128#6289—22no—
129Dic3×C3⋊D3—22no—
130D3×C3⋊Dic3—22no—
131D3×C3⋊Dic3—22no—
132C3×#627—22no—
133C3×#626—22no—
134C3×#625—22no—
135C3×D3×Dic3—22no—
136C3×D3×Dic3—22no—
137C3×D3×Dic3—22no—
138#5627—91no—
139#5586—91no—
140#5547—91no—
141C23×C3×D3—31no—
142C23×C3×D3—31no—
143C22×D32C2×D311yescharacteristic
144C2×C32×D4—31no—
145C2×#638—31no—
146C2×#638—31no—
147C2×#638—31no—
148C22×C3⋊Dic3—31no—
149C22×C3⋊Dic3—31no—
150C2×C4⋊(C3⋊D3)—31no—
151C2×C4×C3⋊D3—31no—
152C2×C4×C3⋊D3—31no—
153C2×C3×#67—31no—
154C2×C3×#67—31no—
155C2×C3×#67—31no—
156C22×C3×Dic3—31no—
157C22×C3×Dic3—31no—
158C22×C3×Dic3—31no—
159C2×C3×D12—21no—
160C2×C3×D12—31no—
161C2×C3×D12C2×D311yescharacteristic
162C2×C3×D12C2×D311yescharacteristic
163C2×C3×C4×D3—31no—
164C2×C3×C4×D3—31no—
165C2×C3×C4×D3—31no—
166C2×C3×Dic6—31no—
167C2×C3×Dic6—31no—
168C2×#627C2×D311yescharacteristic, complemented
169C2×#626—31no—
170C2×#626—31no—
171C2×#626—31no—
172C2×#626—31no—
173C2×#626—31no—
174C2×#626—31no—
175C2×#626—31no—
176C2×#626—31no—
177C2×#626—61no—
178C2×#626—61no—
179C2×#626—61no—
180C2×#626—61no—
181C2×#626C2×D311yescharacteristic
182C2×#625C2×D311yescharacteristic
183C2×#624—31no—
184C2×#624—31no—
185C2×#624—31no—
186C2×#624—61no—
187#3804—64no—
188C2×D3×Dic3—31no—
189C2×D3×Dic3—31no—
190C2×D3×Dic3—31no—
191C2×D3×Dic3—31no—
192C2×D3×Dic3—31no—
193C2×D3×Dic3—31no—
194C2×D3×Dic3—31no—
195C2×D3×Dic3—31no—
196C2×D3×Dic3—64no—
197C2×D3×Dic3—64no—
198C2×D3×Dic3—61no—
199C2×D3×Dic3—61no—
200C2×D3×Dic3—61no—
201C2×D3×Dic3C2×D311yescharacteristic
202C2×D3×Dic3C2×D311yescharacteristic
203C2×D3×Dic3C2×D311yescharacteristic, complemented
204C4×D32—64no—
205#3799—64no—
206#3796—64no—
207C32×C4⋊C4—31no—
208C32×C22⋊C4—31no—
209#3757—31no—
210#3752—31no—
211#3752—31no—
212#3752—31no—
213#3752—31no—
214#3752—61no—
215#3752—61no—
216#3752—61no—
217#3752—121no—
218#3752C2×D311yescharacteristic
219#3750—31no—
220#3750—31no—
221#3750C2×D311yescharacteristic, complemented
222C4×C3⋊Dic3C2×D311yescharacteristic, complemented
223C3×#217—31no—
224C3×#217—31no—
225C3×#217—31no—
226C3×#217—31no—
227C3×(C2×D3)⋊C4—21no—
228C3×(C2×D3)⋊C4—31no—
229C3×(C2×D3)⋊C4—31no—
230C3×(C2×D3)⋊C4—31no—
231C3×(C2×D3)⋊C4—31no—
232C3×(C2×D3)⋊C4—31no—
233C3×(C2×D3)⋊C4—31no—
234C3×(C2×D3)⋊C4—61no—
235C3×(C2×D3)⋊C4C2×D311yescharacteristic
236C3×(C2×D3)⋊C4C2×D311yescharacteristic
237C3×C4⋊Dic3—21no—
238C3×C4⋊Dic3C2×D311yescharacteristic, complemented
239C3×C4⋊Dic3C2×D311yescharacteristic, complemented
240C3×Dic3⋊C4—31no—
241C3×Dic3⋊C4—31no—
242C3×Dic3⋊C4—31no—
243C3×Dic3⋊C4—31no—
244C3×Dic3⋊C4—61no—
245C3×C4×Dic3—31no—
246C3×C4×Dic3—31no—
247C3×C4×Dic3—61no—
248#3724—31no—
249#3724C2×D311yescharacteristic, complemented
250Dic3⋊Dic3—31no—
251Dic3⋊Dic3—31no—
252Dic3⋊Dic3—31no—
253Dic3⋊Dic3—31no—
254Dic3⋊Dic3—31no—
255Dic3⋊Dic3—31no—
256Dic3⋊Dic3—61no—
257Dic3⋊Dic3—61no—
258#3722—31no—
259#3722—31no—
260#3722—31no—
261#3722—61no—
262(C2×D3)⋊Dic3—31no—
263(C2×D3)⋊Dic3—31no—
264(C2×D3)⋊Dic3—31no—
265(C2×D3)⋊Dic3—31no—
266(C2×D3)⋊Dic3—61no—
267(C2×D3)⋊Dic3C2×D311yescharacteristic
268(C2×D3)⋊Dic3C2×D311yescharacteristic
269(C2×D3)⋊Dic3C2×D311yescharacteristic
270(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
271Dic32—31no—
272Dic32—31no—
273Dic32—31no—
274C22×C33C2411yescharacteristic
275C2×C3⋊(C3⋊D3)—21no—
276C2×C3⋊(C3⋊D3)—21no—
277C2×C3⋊(C3⋊D3)—21no—
278C2×C3×C3⋊D3—21no—
279C2×C3×C3⋊D3—21no—
280C2×C3×C3⋊D3C2×D412yes—
281C2×C32×D3—21no—
282C2×C32×D3—21no—
283C2×C32×D3—21no—
284C2×C32×D3—21no—
285C2×C32×D3—21no—
286C2×C32×D3—21no—
287C2×C32×D3—21no—
288C2×C32×D3#4112yescomplemented
289C2×C32×D3#4112yescomplemented
290C3×D32—28no—
291C33×C4—21no—
292C3⋊(C3⋊Dic3)—21no—
293C3×C3⋊Dic3—21no—
294C3×C3⋊Dic3—21no—
295C3×C3⋊Dic3—21no—
296C3×C3⋊Dic3C2×D412yes—
297C3×C3⋊Dic3C2×D412yes—
298C32×Dic3—21no—
299C32×Dic3—21no—
300C32×Dic3—21no—
301C23×Dic3—91no—
302C2×#239—91no—
303C2×#237—91no—
304C2×#235—91no—
305C22×C4×D3—91no—
306C22×C4×D3—91no—
307C3×C22⋊Q8—91no—
308C3×#120—91no—
309C3×C4×D4—91no—
310#953—91no—
311#946—91no—
312#939—91no—
313#939—91no—
314#939—91no—
315#939—181no—
316#937—31no—
317#935—91no—
318D4×Dic3—31no—
319D4×Dic3—91no—
320#930—91no—
321C4×#67—91no—
322C4×#67—91no—
323#896—31no—
324#895—91no—
325#894—91no—
326#894—91no—
327#894—91no—
328#894—181no—
329#893—31no—
330#893—91no—
331#892—91no—
332#886—91no—
333#884—91no—
334#883—91no—
335#882—31no—
336#882—91no—
337#882—91no—
338#67⋊C4—91no—
339#67⋊C4—91no—
340#67⋊C4—91no—
341#67⋊C4—91no—
342#67⋊C4—181no—
343#878—31no—
344#878—91no—
345#878—91no—
346#877—91no—
347C4×D12—91no—
348#872—91no—
349C23×C32—31no—
350C23×C32—31no—
351C23×C32—31no—
352C22×C3⋊D3—31no—
353C22×C3⋊D3—31no—
354C22×C3⋊D3—31no—
355C22×C3⋊D3—61no—
356C22×C3⋊D3—61no—
357C22×C3⋊D3—61no—
358C22×C3⋊D3—121no—
359C22×C3⋊D3C22×D311yescharacteristic
360C22×C3×D3—21no—
361C22×C3×D3—21no—
362C22×C3×D3—21no—
363C22×C3×D3—31no—
364C22×C3×D3—31no—
365C22×C3×D3—61no—
366C22×C3×D3—62no—
367C22×C3×D3—62no—
368C22×C3×D3—62no—
369C22×C3×D3—62no—
370C22×C3×D3—62no—
371C22×C3×D3—62no—
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—22no—
379C2×D32—22no—
380C2×D32—22no—
381C32×D4—62no—
382C2×C32×C4—21no—
383C2×C32×C4—21no—
384C2×C32×C4—21no—
385C2×C32×C4—31no—
386C2×C32×C4—31no—
387C2×C32×C4—31no—
388C2×C32×C4—41no—
389C2×C32×C4C22×D311yescharacteristic
390C2×C32×C4C22×D311yescharacteristic
391C2×C32×C4C22×D311yescharacteristic
392#638—62no—
393#638—62no—
394#638—62no—
395C2×C3⋊Dic3—31no—
396C2×C3⋊Dic3—31no—
397C2×C3⋊Dic3—31no—
398C2×C3⋊Dic3—61no—
399C2×C3⋊Dic3—61no—
400C2×C3⋊Dic3—61no—
401C2×C3⋊Dic3—62no—
402C2×C3⋊Dic3—62no—
403C2×C3⋊Dic3—121no—
404C2×C3⋊Dic3C22×D311yescharacteristic
405C2×C3⋊Dic3C22×D311yescharacteristic
406C2×C3⋊Dic3C22×D311yescharacteristic
407C2×C3⋊Dic3C22×D311yescharacteristic
408C2×C3⋊Dic3C22×D311yescharacteristic
409C4⋊(C3⋊D3)—62no—
410C4×C3⋊D3—62no—
411C4×C3⋊D3—62no—
412C3×#67—62no—
413C3×#67—62no—
414C3×#67—62no—
415C2×C3×Dic3—21no—
416C2×C3×Dic3—21no—
417C2×C3×Dic3—21no—
418C2×C3×Dic3—31no—
419C2×C3×Dic3—31no—
420C2×C3×Dic3—31no—
421C2×C3×Dic3—31no—
422C2×C3×Dic3—31no—
423C2×C3×Dic3—31no—
424C2×C3×Dic3—31no—
425C2×C3×Dic3—31no—
426C2×C3×Dic3—31no—
427C2×C3×Dic3—31no—
428C2×C3×Dic3—61no—
429C2×C3×Dic3—61no—
430C2×C3×Dic3—61no—
431C2×C3×Dic3—61no—
432C2×C3×Dic3—61no—
433C2×C3×Dic3—62no—
434C2×C3×Dic3—62no—
435C2×C3×Dic3—62no—
436C2×C3×Dic3C22×D311yescharacteristic
437C2×C3×Dic3C22×D311yescharacteristic
438C2×C3×Dic3C22×D311yescharacteristic
439C2×C3×Dic3C22×D311yescharacteristic
440C2×C3×Dic3C22×D311yescharacteristic
441C2×C3×Dic3C22×D311yescharacteristic
442C3×D12—22no—
443C3×D12—22no—
444C3×D12—42no—
445C3×D12—62no—
446C3×C4×D3—62no—
447C3×C4×D3—62no—
448C3×C4×D3—62no—
449C3×Dic6—62no—
450C3×Dic6—62no—
451#627—22no—
452#626—22no—
453#626—62no—
454#626—62no—
455#626—62no—
456#626—62no—
457#626—64no—
458#626—62no—
459#626—62no—
460#626—62no—
461#626—62no—
462#626—122no—
463#626—122no—
464#626—122no—
465#625—22no—
466#624—34no—
467#624—62no—
468#624—62no—
469#624—122no—
470D3×Dic3—22no—
471D3×Dic3—22no—
472D3×Dic3—22no—
473D3×Dic3—34no—
474D3×Dic3—34no—
475D3×Dic3—62no—
476D3×Dic3—62no—
477D3×Dic3—62no—
478D3×Dic3—62no—
479D3×Dic3—62no—
480D3×Dic3—62no—
481D3×Dic3—122no—
482D3×Dic3—122no—
483D3×Dic3—122no—
484#525—271noSylow
485C2×C33C22×D411yescharacteristic
486C2×C33C2×#4111yescharacteristic
487C2×C33C2×#4111yescharacteristic
488C3⋊(C3⋊D3)—41no—
489C3×C3⋊D3—22no—
490C32×D3—22no—
491C32×D3—22no—
492C32×D3—41no—
493C24×C3—91no—
494C23×D3—31no—
495C23×D3—31no—
496C2×C3×Q8—91no—
497C2×C3×D4—31no—
498C2×C3×D4—31no—
499C2×C3×D4—61no—
500C2×C3×D4—91no—
501C2×C3×D4—91no—
502C22×C3×C4—91no—
503C22×C3×C4—91no—
504C22×C3×C4—91no—
505C2×#67—31no—
506C2×#67—31no—
507C2×#67—31no—
508C2×#67—91no—
509C2×#67—91no—
510C2×#67—91no—
511C2×#67—91no—
512C2×#67—91no—
513C2×#67—91no—
514C2×#67—91no—
515C2×#67—181no—
516C2×#67—181no—
517C2×#67—181no—
518C22×Dic3—31no—
519C22×Dic3—31no—
520C22×Dic3—31no—
521C22×Dic3—91no—
522C22×Dic3—91no—
523C22×Dic3—91no—
524C22×Dic3—91no—
525C22×Dic3—91no—
526C22×Dic3—91no—
527C22×Dic3—181no—
528C22×Dic3—181no—
529C22×Dic3—184no—
530#239—184no—
531#237—184no—
532#235—184no—
533C2×D12—31no—
534C2×D12—91no—
535C2×D12—91no—
536C2×D12—91no—
537C2×D12—91no—
538C2×D12—91no—
539C2×D12—181no—
540C2×D12D3211yescharacteristic
541C2×C4×D3—31no—
542C2×C4×D3—31no—
543C2×C4×D3—31no—
544C2×C4×D3—91no—
545C2×C4×D3—91no—
546C2×C4×D3—91no—
547C2×C4×D3—91no—
548C2×C4×D3—91no—
549C2×C4×D3—91no—
550C2×C4×D3—91no—
551C2×C4×D3—91no—
552C2×C4×D3—91no—
553C2×C4×D3—181no—
554C2×C4×D3—181no—
555C2×C4×D3—184no—
556C2×C4×D3—184no—
557C2×Dic6—31no—
558C2×Dic6—31no—
559C3×C4⋊C4—31no—
560C3×C4⋊C4—31no—
561C3×C4⋊C4—61no—
562C3×C4⋊C4—91no—
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×C42—91no—
573#217—31no—
574#217—31no—
575#217—31no—
576#217—31no—
577#217—91no—
578#217—91no—
579#217—91no—
580#217—181no—
581(C2×D3)⋊C4—31no—
582(C2×D3)⋊C4—31no—
583(C2×D3)⋊C4—31no—
584(C2×D3)⋊C4—31no—
585(C2×D3)⋊C4—31no—
586(C2×D3)⋊C4—31no—
587(C2×D3)⋊C4—61no—
588(C2×D3)⋊C4—91no—
589(C2×D3)⋊C4—91no—
590(C2×D3)⋊C4—91no—
591(C2×D3)⋊C4—91no—
592(C2×D3)⋊C4—91no—
593(C2×D3)⋊C4—91no—
594(C2×D3)⋊C4—91no—
595(C2×D3)⋊C4—91no—
596(C2×D3)⋊C4—91no—
597(C2×D3)⋊C4—181no—
598(C2×D3)⋊C4—181no—
599(C2×D3)⋊C4—181no—
600(C2×D3)⋊C4—181no—
601(C2×D3)⋊C4—361no—
602(C2×D3)⋊C4D3211yescharacteristic
603C4⋊Dic3—91no—
604C4⋊Dic3—91no—
605C4⋊Dic3—91no—
606C4⋊Dic3D3211yescharacteristic, complemented
607Dic3⋊C4—31no—
608Dic3⋊C4—31no—
609Dic3⋊C4—31no—
610Dic3⋊C4—31no—
611Dic3⋊C4—61no—
612Dic3⋊C4—91no—
613Dic3⋊C4—91no—
614Dic3⋊C4—91no—
615Dic3⋊C4—91no—
616Dic3⋊C4—91no—
617Dic3⋊C4—91no—
618Dic3⋊C4—181no—
619Dic3⋊C4—181no—
620C4×Dic3—31no—
621C4×Dic3—31no—
622C4×Dic3—61no—
623C4×Dic3—91no—
624C4×Dic3—91no—
625C4×Dic3—91no—
626C22×C32—21no—
627C22×C32—21no—
628C22×C32—21no—
629C22×C32—32no—
630C22×C32—32no—
631C22×C32—41no—
632C22×C32—61no—
633C22×C32—61no—
634C22×C32—61no—
635C22×C32—61no—
636C22×C32—61no—
637C22×C32—61no—
638C22×C32—61no—
639C22×C32C23×D311yescharacteristic
640C22×C32C23×D311yescharacteristic
641C22×C32C23×D311yescharacteristic
642C2×C3⋊D3—21no—
643C2×C3⋊D3—21no—
644C2×C3⋊D3—61no—
645C2×C3⋊D3—62no—
646C2×C3⋊D3—61no—
647C2×C3⋊D3—61no—
648C2×C3⋊D3—61no—
649C2×C3⋊D3—61no—
650C2×C3⋊D3—61no—
651C2×C3⋊D3—61no—
652C2×C3⋊D3—61no—
653C2×C3⋊D3—61no—
654C2×C3⋊D3—121no—
655C2×C3⋊D3—121no—
656C2×C3⋊D3—122no—
657C2×C3⋊D3—121no—
658C2×C3⋊D3—121no—
659C2×C3⋊D3—121no—
660C2×C3⋊D3—121no—
661C2×C3⋊D3—121no—
662C2×C3⋊D3—121no—
663C2×C3⋊D3—241no—
664C2×C3⋊D3—241no—
665C2×C3⋊D3D3×D412yes—
666C2×C3×D3—21no—
667C2×C3×D3—21no—
668C2×C3×D3—21no—
669C2×C3×D3—21no—
670C2×C3×D3—21no—
671C2×C3×D3—21no—
672C2×C3×D3—21no—
673C2×C3×D3—21no—
674C2×C3×D3—21no—
675C2×C3×D3—21no—
676C2×C3×D3—21no—
677C2×C3×D3—21no—
678C2×C3×D3—21no—
679C2×C3×D3—21no—
680C2×C3×D3—22no—
681C2×C3×D3—22no—
682C2×C3×D3—32no—
683C2×C3×D3—32no—
684C2×C3×D3—41no—
685C2×C3×D3—41no—
686C2×C3×D3—41no—
687C2×C3×D3—41no—
688C2×C3×D3—41no—
689C2×C3×D3—41no—
690C2×C3×D3—41no—
691C2×C3×D3—62no—
692C2×C3×D3—68no—
693C2×C3×D3—68no—
694C2×C3×D3—61no—
695C2×C3×D3—61no—
696C2×C3×D3—61no—
697C2×C3×D3—61no—
698C2×C3×D3—121no—
699C2×C3×D3—121no—
700C2×C3×D3#23512yescomplemented
701C2×C3×D3#23712yescomplemented
702C2×C3×D3#23712yescomplemented
703C2×C3×D3#23912yescomplemented
704D32—28no—
705C32×C4—21no—
706C32×C4—21no—
707C32×C4—21no—
708C32×C4—41no—
709C32×C4—41no—
710C32×C4—41no—
711C32×C4—61no—
712C32×C4—61no—
713C32×C4—61no—
714C32×C4—81no—
715C3⋊Dic3—21no—
716C3⋊Dic3—21no—
717C3⋊Dic3—21no—
718C3⋊Dic3—61no—
719C3⋊Dic3—61no—
720C3⋊Dic3—61no—
721C3⋊Dic3—121no—
722C3⋊Dic3—121no—
723C3⋊Dic3—121no—
724C3⋊Dic3—241no—
725C3⋊Dic3D3×D412yes—
726C3⋊Dic3D3×D412yes—
727C3×Dic3—21no—
728C3×Dic3—21no—
729C3×Dic3—21no—
730C3×Dic3—21no—
731C3×Dic3—21no—
732C3×Dic3—21no—
733C3×Dic3—32no—
734C3×Dic3—32no—
735C3×Dic3—32no—
736C3×Dic3—32no—
737C3×Dic3—41no—
738C3×Dic3—41no—
739C3×Dic3—41no—
740C3×Dic3—62no—
741C3×Dic3—62no—
742C3×Dic3—62no—
743C3×Dic3—61no—
744C3×Dic3—61no—
745C3×Dic3—61no—
746C3×Dic3—61no—
747C3×Dic3—61no—
748C3×Dic3—61no—
749C3×Dic3—121no—
750C3×Dic3—121no—
751C2×#41—271no—
752C23×C4—271no—
753#123—271no—
754#123—271no—
755C22⋊Q8—91no—
756C22⋊Q8—271no—
757#121—271no—
758#121—271no—
759#120—91no—
760#120—271no—
761C4×D4—91no—
762C4×D4—271no—
763C4×D4—271no—
764C4×D4—271no—
765#117—271no—
766C33#52511yescharacteristic, complemented, Sylow
767C23×C3—31no—
768C23×C3—31no—
769C23×C3—31no—
770C23×C3—31no—
771C23×C3—31no—
772C23×C3—31no—
773C23×C3—61no—
774C23×C3—61no—
775C23×C3—61no—
776C23×C3—91no—
777C23×C3—182no—
778C23×C3—182no—
779C23×C3—182no—
780C22×D3—31no—
781C22×D3—31no—
782C22×D3—61no—
783C22×D3—62no—
784C22×D3—62no—
785C22×D3—62no—
786C22×D3—62no—
787C22×D3—62no—
788C22×D3—62no—
789C22×D3—91no—
790C22×D3—91no—
791C22×D3—91no—
792C22×D3—181no—
793C22×D3—181no—
794C22×D3—181no—
795C22×D3—361no—
796C22×D3C2×D3211yescharacteristic
797C22×D3C2×D3211yescharacteristic
798C22×D3C2×D3211yescharacteristic
799C3×Q8—182no—
800C3×D4—62no—
801C3×D4—62no—
802C3×D4—122no—
803C3×D4—182no—
804C3×D4—182no—
805C2×C3×C4—21no—
806C2×C3×C4—21no—
807C2×C3×C4—21no—
808C2×C3×C4—31no—
809C2×C3×C4—31no—
810C2×C3×C4—31no—
811C2×C3×C4—31no—
812C2×C3×C4—31no—
813C2×C3×C4—31no—
814C2×C3×C4—41no—
815C2×C3×C4—61no—
816C2×C3×C4—61no—
817C2×C3×C4—61no—
818C2×C3×C4—91no—
819C2×C3×C4—91no—
820C2×C3×C4—91no—
821C2×C3×C4—91no—
822C2×C3×C4—91no—
823C2×C3×C4—182no—
824C2×C3×C4—182no—
825C2×C3×C4—182no—
826C2×C3×C4C2×D3211yescharacteristic
827C2×C3×C4C2×D3211yescharacteristic
828C2×C3×C4C2×D3211yescharacteristic
829#67—62no—
830#67—62no—
831#67—62no—
832#67—182no—
833#67—182no—
834#67—182no—
835#67—182no—
836#67—182no—
837#67—182no—
838#67—182no—
839#67—184no—
840#67—362no—
841#67—362no—
842C2×Dic3—31no—
843C2×Dic3—31no—
844C2×Dic3—31no—
845C2×Dic3—31no—
846C2×Dic3—31no—
847C2×Dic3—31no—
848C2×Dic3—31no—
849C2×Dic3—31no—
850C2×Dic3—31no—
851C2×Dic3—31no—
852C2×Dic3—61no—
853C2×Dic3—61no—
854C2×Dic3—61no—
855C2×Dic3—61no—
856C2×Dic3—61no—
857C2×Dic3—62no—
858C2×Dic3—62no—
859C2×Dic3—62no—
860C2×Dic3—94no—
861C2×Dic3—91no—
862C2×Dic3—91no—
863C2×Dic3—91no—
864C2×Dic3—181no—
865C2×Dic3—181no—
866C2×Dic3—181no—
867C2×Dic3—182no—
868C2×Dic3—182no—
869C2×Dic3—182no—
870C2×Dic3—182no—
871C2×Dic3—182no—
872C2×Dic3—361no—
873C2×Dic3—362no—
874C2×Dic3—362no—
875C2×Dic3C2×D3211yescharacteristic
876C2×Dic3C2×D3211yescharacteristic
877C2×Dic3C2×D3211yescharacteristic
878D12—22no—
879D12—62no—
880D12—182no—
881D12—182no—
882D12—182no—
883D12—182no—
884D12—182no—
885D12—362no—
886C4×D3—62no—
887C4×D3—62no—
888C4×D3—62no—
889C4×D3—94no—
890C4×D3—94no—
891C4×D3—182no—
892C4×D3—182no—
893C4×D3—182no—
894C4×D3—182no—
895C4×D3—182no—
896C4×D3—182no—
897C4×D3—182no—
898C4×D3—362no—
899C4×D3—362no—
900Dic6—62no—
901Dic6—62no—
902C2×C32—21no—
903C2×C32—21no—
904C2×C32—21no—
905C2×C32—21no—
906C2×C32—21no—
907C2×C32—21no—
908C2×C32—21no—
909C2×C32—21no—
910C2×C32—21no—
911C2×C32—41no—
912C2×C32—41no—
913C2×C32—41no—
914C2×C32—62no—
915C2×C32—62no—
916C2×C32—121no—
917C2×C32C2×#23511yescharacteristic
918C2×C32C2×D3×D411yescharacteristic
919C2×C32C2×D3×D411yescharacteristic
920C2×C32C2×D3×D411yescharacteristic
921C2×C32C2×#23711yescharacteristic
922C2×C32C2×#23711yescharacteristic
923C2×C32C2×#23911yescharacteristic
924C2×C32D3×#4111yescharacteristic
925C2×C32D3×#4111yescharacteristic
926C3⋊D3—22no—
927C3⋊D3—121no—
928C3⋊D3—122no—
929C3⋊D3—121no—
930C3⋊D3—121no—
931C3⋊D3—241no—
932C3⋊D3—241no—
933C3⋊D3—242no—
934C3×D3—22no—
935C3×D3—22no—
936C3×D3—22no—
937C3×D3—22no—
938C3×D3—42no—
939C3×D3—42no—
940C3×D3—41no—
941C3×D3—41no—
942C3×D3—62no—
943C3×D3—62no—
944C3×D3—81no—
945C3×D3—122no—
946C24—91no—
947#41—544no—
948C2×Q8—91no—
949C2×D4—31no—
950C2×D4—91no—
951C2×D4—91no—
952C2×D4—271no—
953C2×D4—271no—
954C2×D4—271no—
955C2×D4—271no—
956C22×C4—91no—
957C22×C4—91no—
958C22×C4—91no—
959C22×C4—271no—
960C22×C4—271no—
961C22×C4—271no—
962C22×C4—271no—
963C22×C4—271no—
964C22×C4—544no—
965C4⋊C4—31no—
966C4⋊C4—91no—
967C4⋊C4—91no—
968C4⋊C4—271no—
969C4⋊C4—271no—
970C4⋊C4—271no—
971C22⋊C4—31no—
972C22⋊C4—91no—
973C22⋊C4—91no—
974C22⋊C4—91no—
975C22⋊C4—91no—
976C22⋊C4—91no—
977C22⋊C4—271no—
978C22⋊C4—271no—
979C22⋊C4—271no—
980C22⋊C4—271no—
981C42—91no—
982C42—271no—
983C22×C3—21no—
984C22×C3—21no—
985C22×C3—21no—
986C22×C3—32no—
987C22×C3—32no—
988C22×C3—32no—
989C22×C3—32no—
990C22×C3—41no—
991C22×C3—62no—
992C22×C3—62no—
993C22×C3—61no—
994C22×C3—61no—
995C22×C3—61no—
996C22×C3—61no—
997C22×C3—61no—
998C22×C3—61no—
999C22×C3—61no—
1000C22×C3—61no—
1001C22×C3—61no—
1002C22×C3—61no—
1003C22×C3—61no—
1004C22×C3—61no—
1005C22×C3—61no—
1006C22×C3—61no—
1007C22×C3—92no—
1008C22×C3—121no—
1009C22×C3—121no—
1010C22×C3—121no—
1011C22×C3—121no—
1012C22×C3—121no—
1013C22×C3—121no—
1014C22×C3—121no—
1015C22×C3—188no—
1016C22×C3—181no—
1017C22×C3—181no—
1018C22×C3C22×D3211yescharacteristic
1019C22×C3C22×D3211yescharacteristic
1020C22×C3C22×D3211yescharacteristic
1021C2×D3—21no—
1022C2×D3—21no—
1023C2×D3—21no—
1024C2×D3—21no—
1025C2×D3—21no—
1026C2×D3—21no—
1027C2×D3—21no—
1028C2×D3—32no—
1029C2×D3—32no—
1030C2×D3—62no—
1031C2×D3—68no—
1032C2×D3—68no—
1033C2×D3—61no—
1034C2×D3—61no—
1035C2×D3—61no—
1036C2×D3—61no—
1037C2×D3—121no—
1038C2×D3—121no—
1039C2×D3—182no—
1040C2×D3—181no—
1041C2×D3—181no—
1042C2×D3—181no—
1043C2×D3—181no—
1044C2×D3—181no—
1045C2×D3—181no—
1046C2×D3—181no—
1047C2×D3—181no—
1048C2×D3—181no—
1049C2×D3—361no—
1050C2×D3—361no—
1051C2×D3—361no—
1052C2×D3—361no—
1053C2×D3—361no—
1054C2×D3—361no—
1055C2×D3—361no—
1056C2×D3—361no—
1057C2×D3—362no—
1058C2×D3—721no—
1059C2×D3—721no—
1060C2×D3#379612yescomplemented
1061C2×D3#380412yescomplemented
1062C3×C4—21no—
1063C3×C4—21no—
1064C3×C4—21no—
1065C3×C4—41no—
1066C3×C4—41no—
1067C3×C4—41no—
1068C3×C4—61no—
1069C3×C4—61no—
1070C3×C4—61no—
1071C3×C4—61no—
1072C3×C4—61no—
1073C3×C4—61no—
1074C3×C4—81no—
1075C3×C4—92no—
1076C3×C4—92no—
1077C3×C4—121no—
1078C3×C4—121no—
1079C3×C4—121no—
1080C3×C4—181no—
1081C3×C4—181no—
1082C3×C4—181no—
1083Dic3—21no—
1084Dic3—21no—
1085Dic3—21no—
1086Dic3—32no—
1087Dic3—32no—
1088Dic3—32no—
1089Dic3—32no—
1090Dic3—62no—
1091Dic3—62no—
1092Dic3—62no—
1093Dic3—61no—
1094Dic3—61no—
1095Dic3—61no—
1096Dic3—61no—
1097Dic3—61no—
1098Dic3—61no—
1099Dic3—121no—
1100Dic3—121no—
1101Dic3—181no—
1102Dic3—181no—
1103Dic3—181no—
1104Dic3—361no—
1105Dic3—361no—
1106Dic3—361no—
1107Dic3—721no—
1108C32—21no—
1109C32—21no—
1110C32—21no—
1111C32—41no—
1112C32#554711yescharacteristic, complemented
1113C32#558611yescharacteristic, complemented
1114C32#562711yescharacteristic, complemented
1115C23—31no—
1116C23—31no—
1117C23—31no—
1118C23—91no—
1119C23—182no—
1120C23—182no—
1121C23—182no—
1122C23—271no—
1123Q8—182no—
1124D4—62no—
1125D4—182no—
1126D4—182no—
1127D4—542no—
1128D4—542no—
1129D4—542no—
1130D4—542no—
1131C2×C4—31no—
1132C2×C4—31no—
1133C2×C4—31no—
1134C2×C4—91no—
1135C2×C4—91no—
1136C2×C4—91no—
1137C2×C4—91no—
1138C2×C4—91no—
1139C2×C4—182no—
1140C2×C4—182no—
1141C2×C4—182no—
1142C2×C4—274no—
1143C2×C4—271no—
1144C2×C4—542no—
1145C2×C4—542no—
1146C2×C4—542no—
1147C2×C4—542no—
1148C2×C4D3311yescharacteristic
1149C2×C3—21no—
1150C2×C3—21no—
1151C2×C3—21no—
1152C2×C3—21no—
1153C2×C3—21no—
1154C2×C3—21no—
1155C2×C3—21no—
1156C2×C3—21no—
1157C2×C3—21no—
1158C2×C3—41no—
1159C2×C3—41no—
1160C2×C3—41no—
1161C2×C3—62no—
1162C2×C3—62no—
1163C2×C3—62no—
1164C2×C3—62no—
1165C2×C3—122no—
1166C2×C3—122no—
1167C2×C3—121no—
1168C2×C3—121no—
1169C2×C3—182no—
1170C2×C3—241no—
1171C2×C3C2×#379611yescharacteristic
1172C2×C3D3×#23511yescharacteristic
1173C2×C3D32×D411yescharacteristic
1174C2×C3D32×D411yescharacteristic
1175C2×C3D32×D411yescharacteristic
1176C2×C3D3×#23711yescharacteristic
1177C2×C3D3×#23711yescharacteristic
1178C2×C3D3×#23911yescharacteristic
1179C2×C3C2×#380411yescharacteristic
1180D3—22no—
1181D3—22no—
1182D3—41no—
1183D3—62no—
1184D3—62no—
1185D3—122no—
1186D3—362no—
1187D3—361no—
1188D3—361no—
1189D3—361no—
1190D3—721no—
1191D3—721no—
1192D3—722no—
1193C22—32no—
1194C22—32no—
1195C22—61no—
1196C22—61no—
1197C22—61no—
1198C22—61no—
1199C22—61no—
1200C22—61no—
1201C22—61no—
1202C22—92no—
1203C22—188no—
1204C22—181no—
1205C22—181no—
1206C22—541no—
1207C22—541no—
1208C22—541no—
1209C22C2×D3311yescharacteristic
1210C4—21no—
1211C4—61no—
1212C4—61no—
1213C4—61no—
1214C4—92no—
1215C4—92no—
1216C4—181no—
1217C4—181no—
1218C4—181no—
1219C4—541no—
1220C3—21no—
1221C3—21no—
1222C3—21no—
1223C3—41no—
1224C3#1059405511yescharacteristic, complemented
1225C3#1059462311yescharacteristic, complemented
1226C3#1059512911yescharacteristic, complemented
1227C2—62no—
1228C2—62no—
1229C2—121no—
1230C2—182no—
1231C2—1081no—
1232C2D3×#379611yescharacteristic
1233C2#1172440311yescharacteristic
1234C2D3×#380411yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
hypercenterC2×C4D33
hypocenterC33#525
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C2×#88962C2semidirect
2. C2×D32×Dic3C2semidirect
3. #11723683C2semidirect
4. #11723493C2semidirect
5. #11723475C2semidirect
6. #11723461C2semidirect
7. C3×#63922C2semidirect
8. C3×#63899C2semidirect
9. C3×#63898C2semidirect
10. #11722991C2semidirect
11. #11722976C2semidirect
12. #11722958C2semidirect
13. #11722948C2semidirect
14. #11722935C2semidirect
15. #11722924C2semidirect
25. C2×#6291C22semidirect
26. C2×#6289C22semidirect
30. C2×C3×#627C22semidirect
35. C2×C3×D3×Dic3C22semidirect
38. #88859C22semidirect
40. C3×#3750C22semidirect
41. C3×C4×C3⋊Dic3C22semidirect
43. C32×C4⋊Dic3C22semidirect
44. #88815C22semidirect
46. #88813C22semidirect
47. #88807C22semidirect
48. #88807C22semidirect
49. #88804C22semidirect
50. (C2×D3)⋊(C3⋊Dic3)C22semidirect
51. C3×#3724C22semidirect
55. C3×(C2×D3)⋊Dic3C22semidirect
81. #63922D3semidirect
84. #63899D3semidirect
85. #63898D3semidirect
123. #6294D4semidirect
168. C2×#627C2×D3semidirect
203. C2×D3×Dic3C2×D3semidirect
221. #3750C2×D3semidirect
222. C4×C3⋊Dic3C2×D3semidirect
238. C3×C4⋊Dic3C2×D3semidirect
239. C3×C4⋊Dic3C2×D3semidirect
249. #3724C2×D3semidirect
270. (C2×D3)⋊Dic3C2×D3semidirect
288. C2×C32×D3#41semidirect
289. C2×C32×D3#41semidirect
606. C4⋊Dic3D32semidirect
700. C2×C3×D3#235semidirect
701. C2×C3×D3#237semidirect
702. C2×C3×D3#237semidirect
703. C2×C3×D3#239semidirect
766. C33#525semidirect
1060. C2×D3#3796semidirect
1061. C2×D3#3804semidirect
1112. C32#5547semidirect
1113. C32#5586semidirect
1114. C32#5627semidirect
1224. C3#10594055semidirect
1225. C3#10594623semidirect
1226. C3#10595129semidirect

Maximal subgroups

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

subgroupindex
C2×#889622
C2×D32×Dic32
#117236832
#117234932
#117234752
#117234612
C3×#639222
C3×#638992
C3×#638982
#117229912
#117229762
#117229582
#117229482
#117229352
#117229242
#105951293
#105946233
#105940553