Finite Group Databasebeta

← #13170788

Subgroups — #13170788

Order 1728.

1638 conjugacy classes of subgroups.

The subgroup lattice has 1238 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88962C211yesmaximal, characteristic, complemented
2C2×D3×#624C211yesmaximal, characteristic, complemented
3#11723685C211yesmaximal, characteristic, complemented
4#11723540C211yesmaximal, characteristic, complemented
5#11723504C211yesmaximal, characteristic, complemented
6#11723469C211yesmaximal, characteristic, complemented
7C3×#63898C211yesmaximal, characteristic, complemented
8C3×#63895C211yesmaximal, characteristic, complemented
9C3×#63886C211yesmaximal, characteristic, complemented
10#11722996C211yesmaximal, characteristic, complemented
11#11722969C211yesmaximal, characteristic, complemented
12#11722957C211yesmaximal, characteristic, complemented
13#11722950C211yesmaximal, characteristic, complemented
14#11722936C211yesmaximal, characteristic, complemented
15#11722927C211yesmaximal, characteristic, complemented
16#10595138—31nomaximal
17#10594632—31nomaximal
18#10594623—31nomaximal
19C22×D3×C3⋊D3C2211yescharacteristic
20C2×C32×D12C2211yescharacteristic
21C2×#6295C2211yescharacteristic
22C2×#6294C2211yescharacteristic
23C2×#6294C2211yescharacteristic, complemented
24C2×#6292C2211yescharacteristic
25C2×#6291C2211yescharacteristic
26C2×#6290C2211yescharacteristic
27C2×#6289C2211yescharacteristic
28C2×#6289C2211yescharacteristic
29C2×C3×#627C2211yescharacteristic, complemented
30C2×C3×#626C2211yescharacteristic
31C2×C3×#626C2211yescharacteristic, complemented
32C2×C3×#624C2211yescharacteristic
33C2×C3×D3×Dic3C2211yescharacteristic
34C2×C3×D3×Dic3C2211yescharacteristic
35C2×C3×D3×Dic3C2211yescharacteristic, complemented
36#88962—24no—
37D3×#624—24no—
38#88859C2211yescharacteristic
39C3×#3752C2211yescharacteristic
40C3×#3752C2211yescharacteristic, complemented
41C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
42C32×C4⋊Dic3C2211yescharacteristic, complemented
43C32×Dic3⋊C4C2211yescharacteristic, complemented
44#88815C2211yescharacteristic, complemented
45#88806C2211yescharacteristic, complemented
46Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
47#88804C2211yescharacteristic
48#88803C2211yescharacteristic, complemented
49(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
50Dic3×C3⋊Dic3C2211yescharacteristic, complemented
51C3×Dic3⋊Dic3C2211yescharacteristic, complemented
52C3×#3722C2211yescharacteristic
53C3×(C2×D3)⋊Dic3C2211yescharacteristic
54C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
55C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
56C22×#624—31no—
57C2×#3804—31no—
58C2×C4×D32—31no—
59C2×C4×D32—31no—
60C2×#3799—31no—
61C2×#3796—31no—
62#64146—31no—
63#64103—31no—
64#64101—31no—
65C3×#939—31no—
66C3×D4×Dic3—31no—
67C3×#897—31no—
68C3×#896—31no—
69C3×#895—31no—
70C3×#893—31no—
71#63981—31no—
72#63975—31no—
73Dic3×#67—31no—
74#63964—31no—
75#63958—31no—
76#63952—31no—
77#63923—31no—
78#63922—31no—
79#63922—31no—
80#63922—31no—
81#63922—61no—
82#63908—31no—
83#63906—31no—
84#63904—31no—
85#63902—31no—
86#63902—31no—
87#63898—31no—
88#63898D311yescharacteristic, complemented
89#63895D311yescharacteristic, complemented
90#63887—31no—
91#63886D311yescharacteristic, complemented
92#63880—31no—
93#63880—31no—
94#63879—31no—
95#63856—31no—
96#63854—31no—
97#63854—31no—
98#63854—31no—
99#63854—61no—
100#63853—31no—
101#63836—31no—
102#63836—31no—
103#63836—61no—
104C22×C3⋊(C3⋊D3)C2311yescharacteristic
105C22×C3×C3⋊D3C2311yescharacteristic
106C22×C3×C3⋊D3C2311yescharacteristic
107C22×C32×D3C2311yescharacteristic
108C22×C32×D3C2311yescharacteristic
109C2×D3×C3⋊D3—22no—
110C2×D3×C3⋊D3—22no—
111C2×D3×C3⋊D3—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×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122C32×D12—22no—
123#6295—22no—
124#6294—22no—
125#6294—22no—
126#6292—22no—
127#6291—22no—
128#6290—22no—
129#6289—22no—
130#6289D414yescomplemented
131C3×#627—22no—
132C3×#626—22no—
133C3×#626—22no—
134C3×#624—22no—
135C3×D3×Dic3—22no—
136C3×D3×Dic3—22no—
137C3×D3×Dic3—22no—
138#5627—91no—
139#5606—91no—
140#5547—91no—
141C23×C3⋊D3—31no—
142C22×D32—31no—
143C22×D32—31no—
144C22×D32—61no—
145C2×C32×D4—31no—
146C2×#638—31no—
147C2×#638—31no—
148C2×C4⋊(C3⋊D3)—31no—
149C2×C4×C3⋊D3—31no—
150C2×C4×C3⋊D3—31no—
151C2×C3×#67—31no—
152C2×C3×#67—31no—
153C22×C3×Dic3—31no—
154C22×C3×Dic3—31no—
155C22×C3×Dic3—31no—
156C2×C3×D12—21no—
157C2×C3×D12—31no—
158C2×C3×D12—31no—
159C2×C3×D12C2×D311yescharacteristic
160C2×C3×D12C2×D311yescharacteristic
161C2×C3×C4×D3—31no—
162C2×C3×C4×D3—31no—
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—61no—
176C2×#626—61no—
177C2×#626C2×D311yescharacteristic
178C2×#626C2×D311yescharacteristic, complemented
179C2×#625—31no—
180C2×#625—31no—
181C2×#625—31no—
182C2×#625—61no—
183C2×#624—31no—
184C2×#624—31no—
185C2×#624—31no—
186C2×#624—31no—
187C2×#624—31no—
188C2×#624—31no—
189C2×#624—64no—
190C2×#624—61no—
191C2×#624—61no—
192C2×#624C2×D311yescharacteristic
193#3804—64no—
194C2×D3×Dic3—31no—
195C2×D3×Dic3—31no—
196C2×D3×Dic3—31no—
197C2×D3×Dic3—31no—
198C2×D3×Dic3C2×D311yescharacteristic
199C2×D3×Dic3C2×D311yescharacteristic
200C2×D3×Dic3C2×D311yescharacteristic, complemented
201C4×D32—64no—
202C4×D32—64no—
203#3799—64no—
204#3796—64no—
205C32×C4⋊C4—31no—
206C32×C4⋊C4—31no—
207#3757—31no—
208#3752—31no—
209#3752—31no—
210#3752—31no—
211#3752—31no—
212#3752—31no—
213#3752—61no—
214#3752—61no—
215#3752—61no—
216#3752—121no—
217#3752C2×D311yescharacteristic
218#3752C2×D311yescharacteristic, complemented
219C4⋊(C3⋊Dic3)—31no—
220#3750—31no—
221C4×C3⋊Dic3—31no—
222C4×C3⋊Dic3C2×D311yescharacteristic, complemented
223C3×#217—31no—
224C3×#217—31no—
225C3×#217—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×(C2×D3)⋊C4—31no—
232C3×(C2×D3)⋊C4—31no—
233C3×(C2×D3)⋊C4—31no—
234C3×(C2×D3)⋊C4—31no—
235C3×(C2×D3)⋊C4—61no—
236C3×(C2×D3)⋊C4—61no—
237C3×C4⋊Dic3—21no—
238C3×C4⋊Dic3—31no—
239C3×C4⋊Dic3C2×D311yescharacteristic, complemented
240C3×C4⋊Dic3C2×D311yescharacteristic, complemented
241C3×Dic3⋊C4—21no—
242C3×Dic3⋊C4—31no—
243C3×Dic3⋊C4C2×D311yescharacteristic, complemented
244C3×Dic3⋊C4C2×D311yescharacteristic, complemented
245C3×C4×Dic3—31no—
246C3×C4×Dic3—31no—
247C3×C4×Dic3—61no—
248#3724—31no—
249#3724—31no—
250#3724—31no—
251#3724—61no—
252Dic3⋊Dic3—31no—
253Dic3⋊Dic3—31no—
254Dic3⋊Dic3—31no—
255Dic3⋊Dic3—31no—
256Dic3⋊Dic3—61no—
257Dic3⋊Dic3C2×D311yescharacteristic, complemented
258#3722—31no—
259#3722—31no—
260#3722—61no—
261#3722C2×D311yescharacteristic
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)⋊Dic3—61no—
268(C2×D3)⋊Dic3C2×D311yescharacteristic
269(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
270(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
271Dic32—31no—
272Dic32—31no—
273Dic32—61no—
274C22×C33C2411yescharacteristic
275C2×C3⋊(C3⋊D3)—21no—
276C2×C3⋊(C3⋊D3)—21no—
277C2×C3⋊(C3⋊D3)C2×D412yes—
278C2×C3×C3⋊D3—21no—
279C2×C3×C3⋊D3—21no—
280C2×C3×C3⋊D3—21no—
281C2×C3×C3⋊D3—21no—
282C2×C3×C3⋊D3—21no—
283C2×C3×C3⋊D3#4112yescomplemented
284C2×C32×D3—21no—
285C2×C32×D3—21no—
286C2×C32×D3—21no—
287C2×C32×D3—21no—
288C2×C32×D3—21no—
289C2×C32×D3#4112yescomplemented
290D3×C3⋊D3—28no—
291C33×C4—21no—
292C3⋊(C3⋊Dic3)—21no—
293C3×C3⋊Dic3—21no—
294C3×C3⋊Dic3—21no—
295C3×C3⋊Dic3—21no—
296C3×C3⋊Dic3C2×D412yes—
297C32×Dic3—21no—
298C32×Dic3—21no—
299C32×Dic3—21no—
300C32×Dic3C2×D412yes—
301C2×#239—91no—
302C2×#237—91no—
303C2×#235—91no—
304C22×C4×D3—91no—
305C22×C4×D3—91no—
306C22×C4×D3—91no—
307C3×C22⋊Q8—91no—
308C3×#121—91no—
309C3×C4×D4—91no—
310#946—91no—
311#939—31no—
312#938—91no—
313#937—91no—
314#937—91no—
315#937—91no—
316#937—181no—
317D4×Dic3—31no—
318D4×Dic3—91no—
319#930—91no—
320C4×#67—91no—
321C4×#67—91no—
322#924—91no—
323#897—31no—
324#896—31no—
325#895—31no—
326#894—91no—
327#894—91no—
328#894—91no—
329#894—181no—
330#893—31no—
331#893—91no—
332#892—91no—
333#892—91no—
334#892—181no—
335#884—91no—
336#883—91no—
337#883—91no—
338#883—91no—
339#882—91no—
340#882—91no—
341#882—91no—
342#67⋊C4—91no—
343#67⋊C4—91no—
344#67⋊C4—91no—
345#67⋊C4—91no—
346#878—91no—
347C4×D12—91no—
348#872—91no—
349C23×C32—31no—
350C23×C32—31no—
351C22×C3⋊D3—31no—
352C22×C3⋊D3—31no—
353C22×C3⋊D3—31no—
354C22×C3⋊D3—61no—
355C22×C3⋊D3—61no—
356C22×C3⋊D3—61no—
357C22×C3⋊D3—62no—
358C22×C3⋊D3—62no—
359C22×C3⋊D3—62no—
360C22×C3⋊D3—121no—
361C22×C3⋊D3C22×D311yescharacteristic
362C22×C3⋊D3C22×D311yescharacteristic
363C22×C3×D3—21no—
364C22×C3×D3—21no—
365C22×C3×D3—31no—
366C22×C3×D3—31no—
367C22×C3×D3—31no—
368C22×C3×D3—31no—
369C22×C3×D3—61no—
370C22×C3×D3—61no—
371C22×C3×D3C22×D311yescharacteristic
372C22×C3×D3C22×D311yescharacteristic
373C22×C3×D3C22×D311yescharacteristic
374C22×C3×D3C22×D311yescharacteristic
375C2×D32—62no—
376C2×D32—62no—
377C2×D32—62no—
378C2×D32—62no—
379C2×D32—62no—
380C2×D32—62no—
381C2×D32—122no—
382C2×D32—122no—
383C2×D32—122no—
384C32×D4—62no—
385C2×C32×C4—21no—
386C2×C32×C4—21no—
387C2×C32×C4—21no—
388C2×C32×C4—31no—
389C2×C32×C4—31no—
390C2×C32×C4—31no—
391C2×C32×C4—31no—
392C2×C32×C4—41no—
393C2×C32×C4C22×D311yescharacteristic
394C2×C32×C4C22×D311yescharacteristic
395C2×C32×C4C22×D311yescharacteristic
396#638—62no—
397#638—62no—
398C2×C3⋊Dic3—31no—
399C2×C3⋊Dic3—31no—
400C2×C3⋊Dic3—31no—
401C2×C3⋊Dic3—61no—
402C2×C3⋊Dic3—61no—
403C2×C3⋊Dic3—61no—
404C2×C3⋊Dic3—121no—
405C2×C3⋊Dic3C22×D311yescharacteristic
406C2×C3⋊Dic3C22×D311yescharacteristic
407C2×C3⋊Dic3C22×D311yescharacteristic
408C2×C3⋊Dic3C22×D311yescharacteristic
409C4⋊(C3⋊D3)—62no—
410C4×C3⋊D3—34no—
411C4×C3⋊D3—62no—
412C3×#67—62no—
413C3×#67—62no—
414C2×C3×Dic3—21no—
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—61no—
427C2×C3×Dic3—61no—
428C2×C3×Dic3—61no—
429C2×C3×Dic3—61no—
430C2×C3×Dic3—62no—
431C2×C3×Dic3—62no—
432C2×C3×Dic3—62no—
433C2×C3×Dic3C22×D311yescharacteristic
434C2×C3×Dic3C22×D311yescharacteristic
435C2×C3×Dic3C22×D311yescharacteristic
436C2×C3×Dic3C22×D311yescharacteristic
437C2×C3×Dic3C22×D311yescharacteristic
438C2×C3×Dic3C22×D311yescharacteristic
439C2×C3×Dic3C22×D311yescharacteristic
440C2×C3×Dic3C22×D311yescharacteristic
441C3×D12—22no—
442C3×D12—22no—
443C3×D12—42no—
444C3×D12—62no—
445C3×D12—62no—
446C3×C4×D3—62no—
447C3×C4×D3—62no—
448C3×C4×D3—62no—
449C3×C4×D3—62no—
450C3×C4×D3—62no—
451C3×Dic6—62no—
452C3×Dic6—62no—
453#627—22no—
454#626—22no—
455#626—22no—
456#626—62no—
457#626—62no—
458#626—62no—
459#626—62no—
460#626—62no—
461#626—62no—
462#626—122no—
463#626—122no—
464#625—62no—
465#625—62no—
466#625—62no—
467#625—122no—
468#624—22no—
469#624—34no—
470#624—34no—
471#624—64no—
472#624—62no—
473#624—62no—
474#624—62no—
475#624—62no—
476#624—122no—
477D3×Dic3—22no—
478D3×Dic3—22no—
479D3×Dic3—22no—
480D3×Dic3—62no—
481D3×Dic3—62no—
482D3×Dic3—62no—
483D3×Dic3—62no—
484#525—271noSylow
485C2×C33C22×D411yescharacteristic
486C2×C33C2×#4111yescharacteristic
487C2×C33C2×#4111yescharacteristic
488C3⋊(C3⋊D3)—22no—
489C3×C3⋊D3—22no—
490C3×C3⋊D3—41no—
491C32×D3—22no—
492C32×D3—41no—
493C23×D3—91no—
494C23×D3—91no—
495C23×D3—91no—
496C23×D3—181no—
497C2×C3×Q8—91no—
498C2×C3×D4—31no—
499C2×C3×D4—31no—
500C2×C3×D4—61no—
501C2×C3×D4—91no—
502C2×C3×D4—91no—
503C22×C3×C4—91no—
504C22×C3×C4—91no—
505C22×C3×C4—91no—
506C22×C3×C4—91no—
507C2×#67—31no—
508C2×#67—31no—
509C2×#67—91no—
510C2×#67—91no—
511C2×#67—91no—
512C2×#67—91no—
513C2×#67—91no—
514C2×#67—91no—
515C2×#67—91no—
516C2×#67—91no—
517C2×#67—181no—
518C2×#67—181no—
519C22×Dic3—31no—
520C22×Dic3—31no—
521C22×Dic3—31no—
522C22×Dic3—91no—
523C22×Dic3—91no—
524#239—184no—
525#237—184no—
526#235—184no—
527C2×D12—31no—
528C2×D12—31no—
529C2×D12—91no—
530C2×D12—91no—
531C2×D12—91no—
532C2×D12—91no—
533C2×D12—181no—
534C2×D12D3211yescharacteristic
535C2×C4×D3—31no—
536C2×C4×D3—31no—
537C2×C4×D3—31no—
538C2×C4×D3—31no—
539C2×C4×D3—31no—
540C2×C4×D3—91no—
541C2×C4×D3—91no—
542C2×C4×D3—91no—
543C2×C4×D3—91no—
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—181no—
551C2×C4×D3—181no—
552C2×C4×D3—184no—
553C2×C4×D3—184no—
554C2×C4×D3—184no—
555C2×Dic6—31no—
556C2×Dic6—31no—
557C3×C4⋊C4—31no—
558C3×C4⋊C4—31no—
559C3×C4⋊C4—31no—
560C3×C4⋊C4—31no—
561C3×C4⋊C4—61no—
562C3×C4⋊C4—61no—
563C3×C4⋊C4—91no—
564C3×C22⋊C4—91no—
565C3×C22⋊C4—91no—
566C3×C22⋊C4—91no—
567C3×C22⋊C4—91no—
568C3×C22⋊C4—91no—
569C3×C22⋊C4—91no—
570C3×C42—91no—
571#217—31no—
572#217—31no—
573#217—31no—
574#217—91no—
575#217—91no—
576#217—91no—
577#217—181no—
578(C2×D3)⋊C4—31no—
579(C2×D3)⋊C4—31no—
580(C2×D3)⋊C4—31no—
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—61no—
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—91no—
598(C2×D3)⋊C4—181no—
599(C2×D3)⋊C4—181no—
600(C2×D3)⋊C4—181no—
601(C2×D3)⋊C4—181no—
602(C2×D3)⋊C4—181no—
603(C2×D3)⋊C4—361no—
604C4⋊Dic3—31no—
605C4⋊Dic3—91no—
606C4⋊Dic3—91no—
607C4⋊Dic3—91no—
608C4⋊Dic3—181no—
609C4⋊Dic3D3211yescharacteristic, complemented
610Dic3⋊C4—31no—
611Dic3⋊C4—91no—
612Dic3⋊C4—91no—
613Dic3⋊C4—91no—
614Dic3⋊C4—91no—
615Dic3⋊C4—91no—
616Dic3⋊C4—91no—
617Dic3⋊C4—181no—
618Dic3⋊C4D3211yescharacteristic, complemented
619C4×Dic3—31no—
620C4×Dic3—31no—
621C4×Dic3—61no—
622C4×Dic3—91no—
623C4×Dic3—91no—
624C4×Dic3—91no—
625C4×Dic3—181no—
626C22×C32—21no—
627C22×C32—21no—
628C22×C32—21no—
629C22×C32—32no—
630C22×C32—41no—
631C22×C32—61no—
632C22×C32—61no—
633C22×C32—61no—
634C22×C32—61no—
635C22×C32—61no—
636C22×C32C23×D311yescharacteristic
637C22×C32C23×D311yescharacteristic
638C22×C32C23×D311yescharacteristic
639C2×C3⋊D3—21no—
640C2×C3⋊D3—21no—
641C2×C3⋊D3—21no—
642C2×C3⋊D3—21no—
643C2×C3⋊D3—21no—
644C2×C3⋊D3—32no—
645C2×C3⋊D3—32no—
646C2×C3⋊D3—32no—
647C2×C3⋊D3—62no—
648C2×C3⋊D3—62no—
649C2×C3⋊D3—62no—
650C2×C3⋊D3—68no—
651C2×C3⋊D3—61no—
652C2×C3⋊D3—61no—
653C2×C3⋊D3—61no—
654C2×C3⋊D3—61no—
655C2×C3⋊D3—61no—
656C2×C3⋊D3—61no—
657C2×C3⋊D3—122no—
658C2×C3⋊D3—121no—
659C2×C3⋊D3—121no—
660C2×C3⋊D3—121no—
661C2×C3⋊D3—121no—
662C2×C3⋊D3—121no—
663C2×C3⋊D3—121no—
664C2×C3⋊D3—241no—
665C2×C3⋊D3—241no—
666C2×C3⋊D3#23912yescomplemented
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—22no—
678C2×C3×D3—32no—
679C2×C3×D3—32no—
680C2×C3×D3—41no—
681C2×C3×D3—41no—
682C2×C3×D3—41no—
683C2×C3×D3—41no—
684C2×C3×D3—41no—
685C2×C3×D3—62no—
686C2×C3×D3—61no—
687C2×C3×D3—61no—
688C2×C3×D3—61no—
689C2×C3×D3—61no—
690C2×C3×D3—61no—
691C2×C3×D3—61no—
692C2×C3×D3—61no—
693C2×C3×D3—61no—
694C2×C3×D3—61no—
695C2×C3×D3—61no—
696C2×C3×D3—121no—
697C2×C3×D3—121no—
698C2×C3×D3—121no—
699C2×C3×D3—121no—
700C2×C3×D3—121no—
701C2×C3×D3#23512yescomplemented
702C2×C3×D3#23712yescomplemented
703D32—68no—
704D32—68no—
705D32—128no—
706C32×C4—21no—
707C32×C4—21no—
708C32×C4—21no—
709C32×C4—32no—
710C32×C4—41no—
711C32×C4—41no—
712C32×C4—41no—
713C32×C4—61no—
714C32×C4—61no—
715C32×C4—61no—
716C32×C4—81no—
717C3⋊Dic3—21no—
718C3⋊Dic3—21no—
719C3⋊Dic3—21no—
720C3⋊Dic3—61no—
721C3⋊Dic3—61no—
722C3⋊Dic3—61no—
723C3⋊Dic3—121no—
724C3⋊Dic3—121no—
725C3⋊Dic3—121no—
726C3⋊Dic3—241no—
727C3⋊Dic3D3×D412yes—
728C3×Dic3—21no—
729C3×Dic3—21no—
730C3×Dic3—21no—
731C3×Dic3—21no—
732C3×Dic3—21no—
733C3×Dic3—21no—
734C3×Dic3—22no—
735C3×Dic3—32no—
736C3×Dic3—32no—
737C3×Dic3—41no—
738C3×Dic3—41no—
739C3×Dic3—41no—
740C3×Dic3—62no—
741C3×Dic3—61no—
742C3×Dic3—61no—
743C3×Dic3—61no—
744C3×Dic3—61no—
745C3×Dic3—61no—
746C3×Dic3—61no—
747C3×Dic3—121no—
748C3×Dic3—121no—
749C3×Dic3—121no—
750C3×Dic3D3×D412yes—
751C3×Dic3D3×D412yes—
752C2×#41—271no—
753C23×C4—271no—
754#123—271no—
755#123—271no—
756C22⋊Q8—91no—
757C22⋊Q8—271no—
758#121—91no—
759#121—271no—
760#120—271no—
761#120—271no—
762C4×D4—91no—
763C4×D4—271no—
764C4×D4—271no—
765C4×D4—271no—
766#117—271no—
767C33#52511yescharacteristic, complemented, Sylow
768C23×C3—31no—
769C23×C3—31no—
770C23×C3—31no—
771C23×C3—31no—
772C23×C3—61no—
773C23×C3—61no—
774C23×C3—91no—
775C23×C3—91no—
776C22×D3—31no—
777C22×D3—31no—
778C22×D3—31no—
779C22×D3—31no—
780C22×D3—61no—
781C22×D3—61no—
782C22×D3—91no—
783C22×D3—91no—
784C22×D3—91no—
785C22×D3—181no—
786C22×D3—181no—
787C22×D3—181no—
788C22×D3—182no—
789C22×D3—182no—
790C22×D3—182no—
791C22×D3—182no—
792C22×D3—182no—
793C22×D3—182no—
794C22×D3—182no—
795C22×D3—182no—
796C22×D3—182no—
797C22×D3—361no—
798C22×D3—362no—
799C22×D3—362no—
800C22×D3—362no—
801C22×D3C2×D3211yescharacteristic
802C22×D3C2×D3211yescharacteristic
803C3×Q8—182no—
804C3×D4—62no—
805C3×D4—62no—
806C3×D4—122no—
807C3×D4—182no—
808C3×D4—182no—
809C2×C3×C4—21no—
810C2×C3×C4—21no—
811C2×C3×C4—21no—
812C2×C3×C4—31no—
813C2×C3×C4—31no—
814C2×C3×C4—31no—
815C2×C3×C4—31no—
816C2×C3×C4—31no—
817C2×C3×C4—31no—
818C2×C3×C4—31no—
819C2×C3×C4—31no—
820C2×C3×C4—41no—
821C2×C3×C4—61no—
822C2×C3×C4—61no—
823C2×C3×C4—61no—
824C2×C3×C4—61no—
825C2×C3×C4—91no—
826C2×C3×C4—91no—
827C2×C3×C4—91no—
828C2×C3×C4—91no—
829C2×C3×C4—182no—
830C2×C3×C4—182no—
831C2×C3×C4—182no—
832C2×C3×C4—182no—
833C2×C3×C4C2×D3211yescharacteristic
834C2×C3×C4C2×D3211yescharacteristic
835C2×C3×C4C2×D3211yescharacteristic
836#67—62no—
837#67—62no—
838#67—182no—
839#67—182no—
840#67—182no—
841#67—182no—
842#67—182no—
843#67—182no—
844#67—182no—
845#67—182no—
846#67—362no—
847#67—362no—
848C2×Dic3—31no—
849C2×Dic3—31no—
850C2×Dic3—31no—
851C2×Dic3—31no—
852C2×Dic3—31no—
853C2×Dic3—31no—
854C2×Dic3—31no—
855C2×Dic3—31no—
856C2×Dic3—61no—
857C2×Dic3—61no—
858C2×Dic3—61no—
859C2×Dic3—61no—
860C2×Dic3—62no—
861C2×Dic3—62no—
862C2×Dic3—62no—
863C2×Dic3—91no—
864C2×Dic3—91no—
865C2×Dic3—91no—
866C2×Dic3—181no—
867C2×Dic3—181no—
868C2×Dic3—181no—
869C2×Dic3—182no—
870C2×Dic3—182no—
871C2×Dic3—361no—
872C2×Dic3C2×D3211yescharacteristic
873C2×Dic3C2×D3211yescharacteristic
874C2×Dic3C2×D3211yescharacteristic
875C2×Dic3C2×D3211yescharacteristic
876D12—22no—
877D12—62no—
878D12—62no—
879D12—182no—
880D12—182no—
881D12—182no—
882D12—182no—
883D12—362no—
884C4×D3—62no—
885C4×D3—62no—
886C4×D3—62no—
887C4×D3—62no—
888C4×D3—62no—
889C4×D3—94no—
890C4×D3—94no—
891C4×D3—94no—
892C4×D3—184no—
893C4×D3—182no—
894C4×D3—182no—
895C4×D3—182no—
896C4×D3—182no—
897C4×D3—182no—
898C4×D3—182no—
899C4×D3—182no—
900C4×D3—362no—
901Dic6—62no—
902Dic6—62no—
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—21no—
912C2×C32—41no—
913C2×C32—41no—
914C2×C32—41no—
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×#23911yescharacteristic
923C2×C32D3×#4111yescharacteristic
924C2×C32D3×#4111yescharacteristic
925C2×C32D3×#4111yescharacteristic
926C3⋊D3—22no—
927C3⋊D3—41no—
928C3⋊D3—62no—
929C3⋊D3—62no—
930C3⋊D3—62no—
931C3⋊D3—122no—
932C3⋊D3—122no—
933C3⋊D3—122no—
934C3⋊D3—242no—
935C3×D3—22no—
936C3×D3—22no—
937C3×D3—42no—
938C3×D3—41no—
939C3×D3—41no—
940C3×D3—62no—
941C3×D3—62no—
942C3×D3—81no—
943C3×D3—122no—
944C3×D3—121no—
945C3×D3—121no—
946C3×D3—241no—
947C24—271no—
948#41—544no—
949C2×Q8—91no—
950C2×D4—31no—
951C2×D4—91no—
952C2×D4—91no—
953C2×D4—271no—
954C2×D4—271no—
955C2×D4—271no—
956C2×D4—271no—
957C22×C4—91no—
958C22×C4—91no—
959C22×C4—91no—
960C22×C4—91no—
961C22×C4—271no—
962C22×C4—271no—
963C22×C4—271no—
964C22×C4—271no—
965C22×C4—544no—
966C4⋊C4—31no—
967C4⋊C4—31no—
968C4⋊C4—91no—
969C4⋊C4—271no—
970C4⋊C4—271no—
971C4⋊C4—271no—
972C22⋊C4—91no—
973C22⋊C4—91no—
974C22⋊C4—91no—
975C22⋊C4—91no—
976C22⋊C4—91no—
977C22⋊C4—91no—
978C22⋊C4—271no—
979C22⋊C4—271no—
980C22⋊C4—271no—
981C22⋊C4—271no—
982C42—91no—
983C42—271no—
984C22×C3—21no—
985C22×C3—21no—
986C22×C3—21no—
987C22×C3—32no—
988C22×C3—32no—
989C22×C3—41no—
990C22×C3—62no—
991C22×C3—61no—
992C22×C3—61no—
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—92no—
1002C22×C3—121no—
1003C22×C3—121no—
1004C22×C3—121no—
1005C22×C3—121no—
1006C22×C3—121no—
1007C22×C3—181no—
1008C22×C3—181no—
1009C22×C3—181no—
1010C22×C3—181no—
1011C22×C3—181no—
1012C22×C3C22×D3211yescharacteristic
1013C22×C3C22×D3211yescharacteristic
1014C22×C3C22×D3211yescharacteristic
1015C2×D3—21no—
1016C2×D3—21no—
1017C2×D3—21no—
1018C2×D3—21no—
1019C2×D3—21no—
1020C2×D3—32no—
1021C2×D3—32no—
1022C2×D3—62no—
1023C2×D3—61no—
1024C2×D3—61no—
1025C2×D3—61no—
1026C2×D3—61no—
1027C2×D3—61no—
1028C2×D3—61no—
1029C2×D3—61no—
1030C2×D3—61no—
1031C2×D3—61no—
1032C2×D3—61no—
1033C2×D3—92no—
1034C2×D3—92no—
1035C2×D3—92no—
1036C2×D3—121no—
1037C2×D3—121no—
1038C2×D3—121no—
1039C2×D3—121no—
1040C2×D3—121no—
1041C2×D3—182no—
1042C2×D3—182no—
1043C2×D3—182no—
1044C2×D3—188no—
1045C2×D3—188no—
1046C2×D3—188no—
1047C2×D3—181no—
1048C2×D3—181no—
1049C2×D3—181no—
1050C2×D3—181no—
1051C2×D3—181no—
1052C2×D3—181no—
1053C2×D3—362no—
1054C2×D3—368no—
1055C2×D3—361no—
1056C2×D3—361no—
1057C2×D3—361no—
1058C2×D3—361no—
1059C2×D3—361no—
1060C2×D3—361no—
1061C2×D3—721no—
1062C2×D3—721no—
1063C2×D3#380412yescomplemented
1064C3×C4—21no—
1065C3×C4—21no—
1066C3×C4—21no—
1067C3×C4—32no—
1068C3×C4—32no—
1069C3×C4—41no—
1070C3×C4—41no—
1071C3×C4—41no—
1072C3×C4—62no—
1073C3×C4—61no—
1074C3×C4—61no—
1075C3×C4—61no—
1076C3×C4—61no—
1077C3×C4—61no—
1078C3×C4—61no—
1079C3×C4—81no—
1080C3×C4—92no—
1081C3×C4—121no—
1082C3×C4—121no—
1083C3×C4—121no—
1084C3×C4—181no—
1085C3×C4—181no—
1086C3×C4—181no—
1087Dic3—21no—
1088Dic3—21no—
1089Dic3—21no—
1090Dic3—32no—
1091Dic3—32no—
1092Dic3—62no—
1093Dic3—61no—
1094Dic3—61no—
1095Dic3—61no—
1096Dic3—61no—
1097Dic3—61no—
1098Dic3—61no—
1099Dic3—121no—
1100Dic3—121no—
1101Dic3—121no—
1102Dic3—181no—
1103Dic3—181no—
1104Dic3—181no—
1105Dic3—361no—
1106Dic3—361no—
1107Dic3—361no—
1108Dic3—721no—
1109Dic3#380212yes—
1110C32—21no—
1111C32—21no—
1112C32—21no—
1113C32—41no—
1114C32#554711yescharacteristic, complemented
1115C32#560611yescharacteristic, complemented
1116C32#562711yescharacteristic, complemented
1117C23—31no—
1118C23—31no—
1119C23—91no—
1120C23—91no—
1121C23—271no—
1122C23—542no—
1123C23—542no—
1124C23—542no—
1125Q8—182no—
1126D4—62no—
1127D4—182no—
1128D4—182no—
1129D4—542no—
1130D4—542no—
1131D4—542no—
1132D4—542no—
1133C2×C4—31no—
1134C2×C4—31no—
1135C2×C4—31no—
1136C2×C4—31no—
1137C2×C4—91no—
1138C2×C4—91no—
1139C2×C4—91no—
1140C2×C4—91no—
1141C2×C4—182no—
1142C2×C4—182no—
1143C2×C4—182no—
1144C2×C4—182no—
1145C2×C4—274no—
1146C2×C4—271no—
1147C2×C4—542no—
1148C2×C4—542no—
1149C2×C4—542no—
1150C2×C4D3311yescharacteristic
1151C2×C3—21no—
1152C2×C3—21no—
1153C2×C3—21no—
1154C2×C3—21no—
1155C2×C3—21no—
1156C2×C3—21no—
1157C2×C3—21no—
1158C2×C3—21no—
1159C2×C3—21no—
1160C2×C3—41no—
1161C2×C3—41no—
1162C2×C3—41no—
1163C2×C3—62no—
1164C2×C3—62no—
1165C2×C3—122no—
1166C2×C3—121no—
1167C2×C3—121no—
1168C2×C3—182no—
1169C2×C3—241no—
1170C2×C3—361no—
1171C2×C3C2×#380211yescharacteristic
1172C2×C3D3×#23511yescharacteristic
1173C2×C3D32×D411yescharacteristic
1174C2×C3D32×D411yescharacteristic
1175C2×C3D3×#23711yescharacteristic
1176C2×C3#6431211yescharacteristic
1177C2×C3D3×#23911yescharacteristic
1178C2×C3D3×#23911yescharacteristic
1179C2×C3C2×#380411yescharacteristic
1180D3—22no—
1181D3—41no—
1182D3—62no—
1183D3—62no—
1184D3—122no—
1185D3—121no—
1186D3—121no—
1187D3—182no—
1188D3—182no—
1189D3—182no—
1190D3—241no—
1191D3—362no—
1192D3—362no—
1193D3—362no—
1194D3—722no—
1195C22—32no—
1196C22—61no—
1197C22—61no—
1198C22—61no—
1199C22—61no—
1200C22—61no—
1201C22—92no—
1202C22—181no—
1203C22—181no—
1204C22—181no—
1205C22—181no—
1206C22—181no—
1207C22—272no—
1208C22—548no—
1209C22—541no—
1210C22—541no—
1211C22C2×D3311yescharacteristic
1212C4—21no—
1213C4—32no—
1214C4—61no—
1215C4—61no—
1216C4—61no—
1217C4—92no—
1218C4—181no—
1219C4—181no—
1220C4—181no—
1221C4—541no—
1222C3—21no—
1223C3—21no—
1224C3—21no—
1225C3—41no—
1226C3#1059462311yescharacteristic, complemented
1227C3#1059463211yescharacteristic, complemented
1228C3#1059513811yescharacteristic, complemented
1229C2—62no—
1230C2—121no—
1231C2—182no—
1232C2—361no—
1233C2—542no—
1234C2#1172437711yescharacteristic
1235C2D3×#380211yescharacteristic
1236C2D3×#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×D3×#624C2semidirect
3. #11723685C2semidirect
4. #11723540C2semidirect
5. #11723504C2semidirect
6. #11723469C2semidirect
7. C3×#63898C2semidirect
8. C3×#63895C2semidirect
9. C3×#63886C2semidirect
10. #11722996C2semidirect
11. #11722969C2semidirect
12. #11722957C2semidirect
13. #11722950C2semidirect
14. #11722936C2semidirect
15. #11722927C2semidirect
23. C2×#6294C22semidirect
29. C2×C3×#627C22semidirect
31. C2×C3×#626C22semidirect
35. C2×C3×D3×Dic3C22semidirect
40. C3×#3752C22semidirect
41. C3×C4×C3⋊Dic3C22semidirect
42. C32×C4⋊Dic3C22semidirect
43. C32×Dic3⋊C4C22semidirect
44. #88815C22semidirect
45. #88806C22semidirect
46. Dic3⋊(C3⋊Dic3)C22semidirect
48. #88803C22semidirect
50. Dic3×C3⋊Dic3C22semidirect
51. C3×Dic3⋊Dic3C22semidirect
54. C3×(C2×D3)⋊Dic3C22semidirect
55. C3×(C2×D3)⋊Dic3C22semidirect
88. #63898D3semidirect
89. #63895D3semidirect
91. #63886D3semidirect
130. #6289D4semidirect
168. C2×#627C2×D3semidirect
178. C2×#626C2×D3semidirect
200. C2×D3×Dic3C2×D3semidirect
218. #3752C2×D3semidirect
222. C4×C3⋊Dic3C2×D3semidirect
239. C3×C4⋊Dic3C2×D3semidirect
240. C3×C4⋊Dic3C2×D3semidirect
243. C3×Dic3⋊C4C2×D3semidirect
244. C3×Dic3⋊C4C2×D3semidirect
257. Dic3⋊Dic3C2×D3semidirect
269. (C2×D3)⋊Dic3C2×D3semidirect
270. (C2×D3)⋊Dic3C2×D3semidirect
283. C2×C3×C3⋊D3#41semidirect
289. C2×C32×D3#41semidirect
609. C4⋊Dic3D32semidirect
618. Dic3⋊C4D32semidirect
666. C2×C3⋊D3#239semidirect
701. C2×C3×D3#235semidirect
702. C2×C3×D3#237semidirect
767. C33#525semidirect
1063. C2×D3#3804semidirect
1114. C32#5547semidirect
1115. C32#5606semidirect
1116. C32#5627semidirect
1226. C3#10594623semidirect
1227. C3#10594632semidirect
1228. C3#10595138semidirect

Maximal subgroups

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

subgroupindex
C2×#889622
C2×D3×#6242
#117236852
#117235402
#117235042
#117234692
C3×#638982
C3×#638952
C3×#638862
#117229962
#117229692
#117229572
#117229502
#117229362
#117229272
#105951383
#105946323
#105946233