Finite Group Databasebeta

← #13172909

Subgroups — #13172909

Order 1728.

1798 conjugacy classes of subgroups.

The subgroup lattice has 1254 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Dic3×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×#88964C211yesmaximal, characteristic, complemented
3#11723727C211yesmaximal, characteristic, complemented
4#11723626C211yesmaximal, characteristic, complemented
5#67⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
6C3×#63981C211yesmaximal, characteristic, complemented
7C3×#63978C211yesmaximal, characteristic, complemented
8C3×#63964C211yesmaximal, characteristic, complemented
9#11722997C211yesmaximal, characteristic, complemented
10#11722991C211yesmaximal, characteristic, complemented
11#11722974C211yesmaximal, characteristic, complemented
12#11722962C211yesmaximal, characteristic, complemented
13#11722938C211yesmaximal, characteristic, complemented
14#11722929C211yesmaximal, characteristic, complemented
15#11722921C211yesmaximal, characteristic, complemented
16#10595130—31nomaximal
17#10594922—31nomaximal
18#10594055—31nomaximal
19C23×C3×C3⋊D3C2211yescharacteristic
20C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C2×C32×#67C2211yescharacteristic
23C22×C32×Dic3C2211yescharacteristic
24C2×#6295C2211yescharacteristic
25C2×#6295C2211yescharacteristic
26C2×Dic3×C3⋊D3—24no—
27C2×Dic3×C3⋊D3C2211yescharacteristic
28C2×Dic3×C3⋊D3C2211yescharacteristic
29C2×Dic3×C3⋊D3C2211yescharacteristic
30C2×Dic3×C3⋊D3C2211yescharacteristic
31C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
32C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
33C2×C3×#627C2211yescharacteristic, complemented
34C2×C3×#626C2211yescharacteristic
35C2×C3×#626C2211yescharacteristic
36C2×C3×#626C2211yescharacteristic, complemented
37#88964—24no—
38C3×#3757C2211yescharacteristic
39C32×#217C2211yescharacteristic
40#88814C2211yescharacteristic
41#88814C2211yescharacteristic
42#88807C2211yescharacteristic, complemented
43Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
44#88803C2211yescharacteristic, complemented
45(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
46Dic3×C3⋊Dic3C2211yescharacteristic, complemented
47Dic3×C3⋊Dic3C2211yescharacteristic, complemented
48C3×#3724C2211yescharacteristic, complemented
49C3×Dic3⋊Dic3C2211yescharacteristic, complemented
50C3×Dic3⋊Dic3C2211yescharacteristic, complemented
51C3×Dic3⋊Dic3C2211yescharacteristic, complemented
52C3×#3722C2211yescharacteristic
53C3×#3722C2211yescharacteristic
54C3×#3722C2211yescharacteristic, complemented
55C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
56C22×C4×C3⋊D3—31no—
57C2×#3805—31no—
58C22×D3×Dic3—31no—
59C22×D3×Dic3—31no—
60C22×D3×Dic3—61no—
61C2×#3796—31no—
62C2×#3796—31no—
63D4×C3⋊Dic3—31no—
64#64090—31no—
65C3×#939—31no—
66C3×#937—31no—
67C3×#930—31no—
68C3×#924—31no—
69C3×#882—31no—
70C3×#878—31no—
71#63981—31no—
72#63981D311yescharacteristic, complemented
73#63978D311yescharacteristic, complemented
74#63977—31no—
75#63976—31no—
76#67⋊Dic3—31no—
77#67⋊Dic3—31no—
78#67⋊Dic3—31no—
79#67⋊Dic3—31no—
80#67⋊Dic3—31no—
81#67⋊Dic3—61no—
82#67⋊Dic3—61no—
83#63970—31no—
84#63969—31no—
85#63964D311yescharacteristic, complemented
86#63916—31no—
87#63902—31no—
88#63898—31no—
89#63893—31no—
90#63891—31no—
91#63890—31no—
92#63887—31no—
93#63886—31no—
94#63884—31no—
95#63881—31no—
96#63881—31no—
97#63881—31no—
98#63878—31no—
99#63878—31no—
100#63871—31no—
101#63853—31no—
102#63853—31no—
103#63849—31no—
104C23×C33C2311yescharacteristic
105C22×C3×C3⋊D3—22no—
106C22×C3×C3⋊D3—22no—
107C22×C3×C3⋊D3—22no—
108C22×C3×C3⋊D3C2311yescharacteristic
109C22×C3×C3⋊D3C2311yescharacteristic
110C22×C3×C3⋊D3C2311yescharacteristic
111C22×C32×D3C2311yescharacteristic
112C2×C3⋊(C3⋊Dic3)—22no—
113C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
114C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
115C3×#638—22no—
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C3×C3⋊Dic3C2311yescharacteristic
118C2×C3×C3⋊Dic3C2311yescharacteristic
119C32×#67—22no—
120C2×C32×Dic3—22no—
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123C2×C32×Dic3C2311yescharacteristic
124C2×C32×Dic3C2311yescharacteristic
125C2×C32×Dic3C2311yescharacteristic
126#6295—22no—
127#6295—22no—
128Dic3×C3⋊D3—22no—
129Dic3×C3⋊D3—22no—
130Dic3×C3⋊D3—22no—
131Dic3×C3⋊D3—22no—
132Dic3×C3⋊D3D414yescomplemented
133D3×C3⋊Dic3—22no—
134C3×#627—22no—
135C3×#626—22no—
136C3×#626—22no—
137C3×#626—22no—
138#5627—91no—
139#5606—91no—
140#5586—91no—
141C23×C3⋊D3C2×D311yescharacteristic
142C23×C3×D3—31no—
143C23×C3×D3—31no—
144C23×C3×D3—61no—
145C2×C32×D4—31no—
146C22×C32×C4—31no—
147C2×#638C2×D311yescharacteristic
148C22×C3⋊Dic3—31no—
149C22×C3⋊Dic3—31no—
150C22×C3⋊Dic3—31no—
151C22×C3⋊Dic3—31no—
152C22×C3⋊Dic3—61no—
153C22×C3⋊Dic3—61no—
154C22×C3⋊Dic3—61no—
155C22×C3⋊Dic3—121no—
156C2×C4×C3⋊D3—31no—
157C2×C4×C3⋊D3—31no—
158C2×C4×C3⋊D3—31no—
159C2×C4×C3⋊D3—31no—
160C2×C4×C3⋊D3—31no—
161C2×C4×C3⋊D3—64no—
162C2×C3×#67—21no—
163C2×C3×#67—31no—
164C2×C3×#67—31no—
165C2×C3×#67—31no—
166C2×C3×#67—31no—
167C2×C3×#67—31no—
168C2×C3×#67—61no—
169C2×C3×#67C2×D311yescharacteristic
170C2×C3×#67C2×D311yescharacteristic
171C22×C3×Dic3—21no—
172C22×C3×Dic3C2×D311yescharacteristic
173C22×C3×Dic3C2×D311yescharacteristic
174C2×C3×D12—31no—
175C2×C3×D12—31no—
176C2×C3×D12—31no—
177C2×C3×Dic6—31no—
178C2×C3×Dic6—31no—
179C2×#627C2×D311yescharacteristic, complemented
180C2×#626—31no—
181C2×#626—31no—
182C2×#626—31no—
183C2×#626—31no—
184C2×#626C2×D311yescharacteristic
185C2×#626C2×D311yescharacteristic
186C2×#626C2×D311yescharacteristic, complemented
187C2×#625—31no—
188C2×#625—31no—
189#3805—64no—
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—31no—
197C2×D3×Dic3—31no—
198C2×D3×Dic3—31no—
199C2×D3×Dic3—31no—
200C2×D3×Dic3—31no—
201C2×D3×Dic3—31no—
202C2×D3×Dic3—64no—
203C2×D3×Dic3—64no—
204C2×D3×Dic3—61no—
205C2×D3×Dic3—61no—
206C2×D3×Dic3—61no—
207C2×D3×Dic3—61no—
208C2×D3×Dic3—68no—
209C2×D3×Dic3—61no—
210C2×D3×Dic3—61no—
211#3796—64no—
212#3796—64no—
213C32×C22⋊C4—31no—
214#3757—31no—
215#3757C2×D311yescharacteristic
216#3752—31no—
217C4⋊(C3⋊Dic3)—31no—
218#3750—31no—
219C4×C3⋊Dic3—31no—
220C4×C3⋊Dic3—31no—
221C3×#217—21no—
222C3×#217—31no—
223C3×#217—31no—
224C3×#217—31no—
225C3×#217—61no—
226C3×#217C2×D311yescharacteristic
227C3×#217C2×D311yescharacteristic
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×C4⋊Dic3—31no—
236C3×C4⋊Dic3—31no—
237C3×C4⋊Dic3—31no—
238C3×Dic3⋊C4—31no—
239C3×Dic3⋊C4—31no—
240C3×Dic3⋊C4—31no—
241C3×Dic3⋊C4—31no—
242C3×Dic3⋊C4—31no—
243#3724C2×D311yescharacteristic, complemented
244Dic3⋊Dic3—31no—
245Dic3⋊Dic3—31no—
246Dic3⋊Dic3—31no—
247Dic3⋊Dic3—31no—
248Dic3⋊Dic3—61no—
249Dic3⋊Dic3—61no—
250Dic3⋊Dic3C2×D311yescharacteristic, complemented
251Dic3⋊Dic3C2×D311yescharacteristic, complemented
252Dic3⋊Dic3C2×D311yescharacteristic, complemented
253#3722—31no—
254#3722—31no—
255#3722C2×D311yescharacteristic
256#3722C2×D311yescharacteristic
257#3722C2×D311yescharacteristic, complemented
258(C2×D3)⋊Dic3—31no—
259(C2×D3)⋊Dic3—31no—
260(C2×D3)⋊Dic3—31no—
261(C2×D3)⋊Dic3—31no—
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, complemented
269Dic32—31no—
270Dic32—31no—
271Dic32—31no—
272Dic32—31no—
273Dic32—61no—
274Dic32—61no—
275C22×C33—21no—
276C22×C33—21no—
277C22×C33#4112yescomplemented
278C22×C33C2411yescharacteristic
279C2×C3×C3⋊D3—28no—
280C2×C3×C3⋊D3—21no—
281C2×C3×C3⋊D3—21no—
282C2×C3×C3⋊D3—21no—
283C2×C3×C3⋊D3—21no—
284C2×C3×C3⋊D3—21no—
285C2×C3×C3⋊D3—21no—
286C2×C3×C3⋊D3—21no—
287C2×C3×C3⋊D3C2×D412yes—
288C2×C3×C3⋊D3#4112yescomplemented
289C2×C32×D3—21no—
290C2×C32×D3—21no—
291C2×C32×D3—21no—
292C3⋊(C3⋊Dic3)—21no—
293C3⋊(C3⋊Dic3)C2×D412yes—
294C3×C3⋊Dic3—21no—
295C3×C3⋊Dic3—21no—
296C3×C3⋊Dic3—21no—
297C32×Dic3—21no—
298C32×Dic3—21no—
299C32×Dic3—21no—
300C32×Dic3—21no—
301C32×Dic3C2×D412yes—
302C23×Dic3—91no—
303C2×#239—91no—
304C2×#237—91no—
305C2×#237—91no—
306C22×C4×D3—91no—
307C22×C4×D3—91no—
308C22×C4×D3—181no—
309C3×C22⋊Q8—91no—
310C3×#121—91no—
311C3×#120—91no—
312#953—91no—
313#946—91no—
314#939—31no—
315#939—91no—
316#938—91no—
317#937—31no—
318#937—91no—
319#935—91no—
320D4×Dic3—91no—
321D4×Dic3—91no—
322D4×Dic3—91no—
323D4×Dic3—91no—
324D4×Dic3—181no—
325#930—31no—
326#924—31no—
327#897—91no—
328#895—91no—
329#894—91no—
330#894—91no—
331#893—91no—
332#893—91no—
333#892—91no—
334#892—91no—
335#886—91no—
336#883—91no—
337#883—91no—
338#882—31no—
339#882—91no—
340#67⋊C4—91no—
341#67⋊C4—91no—
342#67⋊C4—91no—
343#67⋊C4—91no—
344#67⋊C4—91no—
345#67⋊C4—91no—
346#67⋊C4—181no—
347#878—31no—
348#878—91no—
349#877—91no—
350C23×C32—21no—
351C23×C32—21no—
352C23×C32—21no—
353C23×C32—31no—
354C23×C32—41no—
355C23×C32C22×D311yescharacteristic
356C23×C32C22×D311yescharacteristic
357C23×C32C22×D311yescharacteristic
358C22×C3⋊D3—22no—
359C22×C3⋊D3—22no—
360C22×C3⋊D3—22no—
361C22×C3⋊D3C22×D311yescharacteristic
362C22×C3⋊D3C22×D311yescharacteristic
363C22×C3⋊D3C22×D311yescharacteristic
364C22×C3×D3—21no—
365C22×C3×D3—31no—
366C22×C3×D3—31no—
367C22×C3×D3—31no—
368C22×C3×D3—31no—
369C22×C3×D3—31no—
370C22×C3×D3—31no—
371C22×C3×D3—61no—
372C22×C3×D3—61no—
373C22×C3×D3—61no—
374C22×C3×D3—62no—
375C22×C3×D3—62no—
376C22×C3×D3—62no—
377C22×C3×D3—62no—
378C22×C3×D3—64no—
379C22×C3×D3—64no—
380C22×C3×D3—64no—
381C22×C3×D3—62no—
382C22×C3×D3—62no—
383C22×C3×D3C22×D311yescharacteristic
384C22×C3×D3C22×D311yescharacteristic
385C32×D4—62no—
386C2×C32×C4—31no—
387C2×C32×C4—31no—
388C2×C32×C4—31no—
389C2×C32×C4—31no—
390C2×C32×C4—31no—
391C2×C32×C4—62no—
392#638—22no—
393C2×C3⋊Dic3—31no—
394C2×C3⋊Dic3—31no—
395C2×C3⋊Dic3—31no—
396C2×C3⋊Dic3—31no—
397C2×C3⋊Dic3—31no—
398C2×C3⋊Dic3—31no—
399C2×C3⋊Dic3—61no—
400C2×C3⋊Dic3—61no—
401C2×C3⋊Dic3—61no—
402C2×C3⋊Dic3—61no—
403C2×C3⋊Dic3—61no—
404C2×C3⋊Dic3—61no—
405C2×C3⋊Dic3—62no—
406C2×C3⋊Dic3—62no—
407C2×C3⋊Dic3—62no—
408C2×C3⋊Dic3—62no—
409C2×C3⋊Dic3—64no—
410C2×C3⋊Dic3—121no—
411C2×C3⋊Dic3—121no—
412C2×C3⋊Dic3—122no—
413C2×C3⋊Dic3—122no—
414C2×C3⋊Dic3—124no—
415C2×C3⋊Dic3C22×D311yescharacteristic
416C2×C3⋊Dic3C22×D311yescharacteristic
417C2×C3⋊Dic3C22×D311yescharacteristic
418C4×C3⋊D3—34no—
419C4×C3⋊D3—62no—
420C4×C3⋊D3—62no—
421C4×C3⋊D3—62no—
422C4×C3⋊D3—62no—
423C3×#67—24no—
424C3×#67—22no—
425C3×#67—22no—
426C3×#67—62no—
427C3×#67—62no—
428C3×#67—64no—
429C3×#67—62no—
430C3×#67—62no—
431C3×#67—62no—
432C2×C3×Dic3—24no—
433C2×C3×Dic3—22no—
434C2×C3×Dic3—22no—
435C2×C3×Dic3—21no—
436C2×C3×Dic3—21no—
437C2×C3×Dic3—21no—
438C2×C3×Dic3—21no—
439C2×C3×Dic3—21no—
440C2×C3×Dic3—31no—
441C2×C3×Dic3—31no—
442C2×C3×Dic3—31no—
443C2×C3×Dic3—31no—
444C2×C3×Dic3—31no—
445C2×C3×Dic3—31no—
446C2×C3×Dic3—61no—
447C2×C3×Dic3—61no—
448C2×C3×Dic3—61no—
449C2×C3×Dic3C22×D311yescharacteristic
450C2×C3×Dic3C22×D311yescharacteristic
451C2×C3×Dic3C22×D311yescharacteristic
452C2×C3×Dic3C22×D311yescharacteristic
453C2×C3×Dic3C22×D311yescharacteristic
454C2×C3×Dic3C22×D311yescharacteristic
455C2×C3×Dic3C22×D311yescharacteristic
456C2×C3×Dic3C22×D311yescharacteristic
457C2×C3×Dic3C22×D311yescharacteristic
458C2×C3×Dic3C22×D311yescharacteristic
459C3×D12—62no—
460C3×D12—62no—
461C3×D12—62no—
462C3×Dic6—62no—
463C3×Dic6—62no—
464#627—22no—
465#626—22no—
466#626—22no—
467#626—22no—
468#626—62no—
469#626—62no—
470#626—62no—
471#626—62no—
472#625—62no—
473#625—62no—
474D3×Dic3—34no—
475D3×Dic3—34no—
476D3×Dic3—64no—
477D3×Dic3—62no—
478D3×Dic3—62no—
479D3×Dic3—62no—
480D3×Dic3—62no—
481D3×Dic3—62no—
482D3×Dic3—62no—
483D3×Dic3—64no—
484D3×Dic3—64no—
485D3×Dic3—64no—
486D3×Dic3—62no—
487D3×Dic3—62no—
488D3×Dic3—62no—
489D3×Dic3—62no—
490D3×Dic3—122no—
491D3×Dic3—122no—
492#525—271noSylow
493C2×C33—22no—
494C2×C33C22×D411yescharacteristic
495C2×C33C2×#4111yescharacteristic
496C2×C33C2×#4111yescharacteristic
497C3×C3⋊D3—22no—
498C3×C3⋊D3—22no—
499C3×C3⋊D3—41no—
500C32×D3—41no—
501C24×C3—91no—
502C23×D3—31no—
503C23×D3—31no—
504C23×D3—61no—
505C2×C3×Q8—91no—
506C2×C3×D4—31no—
507C2×C3×D4—31no—
508C2×C3×D4—61no—
509C2×C3×D4—91no—
510C2×C3×D4—91no—
511C2×C3×D4—91no—
512C2×C3×D4—91no—
513C22×C3×C4—31no—
514C22×C3×C4—31no—
515C22×C3×C4—61no—
516C2×#67—31no—
517C2×#67—31no—
518C2×#67—31no—
519C2×#67—31no—
520C2×#67—31no—
521C2×#67—61no—
522C2×#67—91no—
523C2×#67—91no—
524C2×#67—91no—
525C2×#67—91no—
526C2×#67D3211yescharacteristic
527C22×Dic3—91no—
528C22×Dic3—91no—
529C22×Dic3—91no—
530C22×Dic3—91no—
531C22×Dic3—91no—
532C22×Dic3—91no—
533C22×Dic3—91no—
534C22×Dic3—91no—
535C22×Dic3—91no—
536C22×Dic3—91no—
537C22×Dic3—181no—
538C22×Dic3—181no—
539C22×Dic3—181no—
540C22×Dic3—181no—
541C22×Dic3—184no—
542C22×Dic3—361no—
543C22×Dic3D3211yescharacteristic
544#239—184no—
545#237—184no—
546#237—184no—
547C2×D12—31no—
548C2×D12—31no—
549C2×D12—31no—
550C2×D12—91no—
551C2×D12—91no—
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—91no—
562C2×C4×D3—91no—
563C2×C4×D3—181no—
564C2×C4×D3—181no—
565C2×C4×D3—181no—
566C2×C4×D3—181no—
567C2×C4×D3—181no—
568C2×C4×D3—184no—
569C2×C4×D3—184no—
570C2×C4×D3—188no—
571C2×Dic6—31no—
572C2×Dic6—31no—
573C3×C4⋊C4—91no—
574C3×C4⋊C4—91no—
575C3×C4⋊C4—91no—
576C3×C4⋊C4—91no—
577C3×C22⋊C4—31no—
578C3×C22⋊C4—31no—
579C3×C22⋊C4—61no—
580C3×C22⋊C4—91no—
581C3×C22⋊C4—91no—
582C3×C22⋊C4—91no—
583C3×C22⋊C4—91no—
584C3×C22⋊C4—91no—
585#217—31no—
586#217—31no—
587#217—31no—
588#217—61no—
589#217—91no—
590#217—91no—
591#217—91no—
592#217—91no—
593#217—91no—
594#217—181no—
595#217D3211yescharacteristic
596(C2×D3)⋊C4—31no—
597(C2×D3)⋊C4—31no—
598(C2×D3)⋊C4—31no—
599(C2×D3)⋊C4—31no—
600(C2×D3)⋊C4—31no—
601(C2×D3)⋊C4—31no—
602(C2×D3)⋊C4—31no—
603(C2×D3)⋊C4—91no—
604(C2×D3)⋊C4—91no—
605(C2×D3)⋊C4—91no—
606(C2×D3)⋊C4—91no—
607(C2×D3)⋊C4—91no—
608(C2×D3)⋊C4—91no—
609(C2×D3)⋊C4—91no—
610(C2×D3)⋊C4—181no—
611C4⋊Dic3—31no—
612C4⋊Dic3—31no—
613C4⋊Dic3—31no—
614C4⋊Dic3—91no—
615C4⋊Dic3—91no—
616C4⋊Dic3—91no—
617C4⋊Dic3—181no—
618Dic3⋊C4—31no—
619Dic3⋊C4—31no—
620Dic3⋊C4—31no—
621Dic3⋊C4—31no—
622Dic3⋊C4—31no—
623Dic3⋊C4—91no—
624Dic3⋊C4—91no—
625Dic3⋊C4—91no—
626Dic3⋊C4—181no—
627C4×Dic3—91no—
628C4×Dic3—91no—
629C4×Dic3—91no—
630C4×Dic3—91no—
631C4×Dic3—91no—
632C4×Dic3—91no—
633C4×Dic3—181no—
634C4×Dic3—181no—
635C22×C32—21no—
636C22×C32—21no—
637C22×C32—22no—
638C22×C32—22no—
639C22×C32—21no—
640C22×C32—21no—
641C22×C32—21no—
642C22×C32—21no—
643C22×C32—21no—
644C22×C32—21no—
645C22×C32—21no—
646C22×C32—22no—
647C22×C32—22no—
648C22×C32—22no—
649C22×C32—42no—
650C22×C32—41no—
651C22×C32—41no—
652C22×C32—41no—
653C22×C32—41no—
654C22×C32—41no—
655C22×C32—42no—
656C22×C32—42no—
657C22×C32—61no—
658C22×C32—61no—
659C22×C32—61no—
660C22×C32#23712yescomplemented
661C22×C32#23712yescomplemented
662C22×C32#23912yescomplemented
663C22×C32C23×D311yescharacteristic
664C22×C32C23×D311yescharacteristic
665C22×C32C23×D311yescharacteristic
666C2×C3⋊D3—28no—
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⋊D3D3×D412yes—
675C2×C3⋊D3#23712yescomplemented
676C2×C3×D3—22no—
677C2×C3×D3—21no—
678C2×C3×D3—21no—
679C2×C3×D3—21no—
680C2×C3×D3—21no—
681C2×C3×D3—21no—
682C2×C3×D3—21no—
683C2×C3×D3—32no—
684C2×C3×D3—32no—
685C2×C3×D3—32no—
686C2×C3×D3—32no—
687C2×C3×D3—41no—
688C2×C3×D3—41no—
689C2×C3×D3—62no—
690C2×C3×D3—62no—
691C2×C3×D3—62no—
692C2×C3×D3—616no—
693C2×C3×D3—68no—
694C2×C3×D3—68no—
695C2×C3×D3—62no—
696C2×C3×D3—62no—
697C2×C3×D3—62no—
698C2×C3×D3—61no—
699C2×C3×D3—61no—
700C2×C3×D3—61no—
701C2×C3×D3—61no—
702C2×C3×D3—61no—
703C2×C3×D3—61no—
704C2×C3×D3—61no—
705C2×C3×D3—61no—
706C2×C3×D3—62no—
707C2×C3×D3—61no—
708C2×C3×D3—61no—
709C2×C3×D3—61no—
710C2×C3×D3—61no—
711C2×C3×D3—61no—
712C2×C3×D3—61no—
713C2×C3×D3—121no—
714C2×C3×D3—121no—
715C32×C4—32no—
716C32×C4—61no—
717C32×C4—61no—
718C32×C4—61no—
719C32×C4—61no—
720C3⋊Dic3—21no—
721C3⋊Dic3—21no—
722C3⋊Dic3—21no—
723C3⋊Dic3—32no—
724C3⋊Dic3—32no—
725C3⋊Dic3—32no—
726C3⋊Dic3—62no—
727C3⋊Dic3—62no—
728C3⋊Dic3—62no—
729C3⋊Dic3—61no—
730C3⋊Dic3—62no—
731C3⋊Dic3—61no—
732C3⋊Dic3—61no—
733C3⋊Dic3—122no—
734C3⋊Dic3—121no—
735C3⋊Dic3—121no—
736C3⋊Dic3—122no—
737C3×Dic3—22no—
738C3×Dic3—22no—
739C3×Dic3—21no—
740C3×Dic3—21no—
741C3×Dic3—21no—
742C3×Dic3—21no—
743C3×Dic3—21no—
744C3×Dic3—21no—
745C3×Dic3—21no—
746C3×Dic3—21no—
747C3×Dic3—22no—
748C3×Dic3—41no—
749C3×Dic3—41no—
750C3×Dic3—62no—
751C3×Dic3—61no—
752C3×Dic3—61no—
753C3×Dic3—61no—
754C3×Dic3—61no—
755C3×Dic3—61no—
756C3×Dic3—61no—
757C3×Dic3—121no—
758C3×Dic3—121no—
759C3×Dic3D3×D412yes—
760C3×Dic3D3×D412yes—
761C2×#41—271no—
762C23×C4—271no—
763#123—271no—
764#123—271no—
765C22⋊Q8—91no—
766C22⋊Q8—271no—
767#121—91no—
768#121—271no—
769#120—91no—
770#120—271no—
771C4×D4—271no—
772C4×D4—271no—
773C4×D4—271no—
774C4×D4—271no—
775#117—271no—
776C33#52511yescharacteristic, complemented, Sylow
777C23×C3—21no—
778C23×C3—21no—
779C23×C3—21no—
780C23×C3—31no—
781C23×C3—31no—
782C23×C3—41no—
783C23×C3—61no—
784C23×C3—91no—
785C23×C3—91no—
786C23×C3—91no—
787C23×C3—182no—
788C23×C3—182no—
789C23×C3—182no—
790C23×C3C2×D3211yescharacteristic
791C23×C3C2×D3211yescharacteristic
792C23×C3C2×D3211yescharacteristic
793C22×D3—31no—
794C22×D3—31no—
795C22×D3—31no—
796C22×D3—31no—
797C22×D3—31no—
798C22×D3—31no—
799C22×D3—61no—
800C22×D3—61no—
801C22×D3—61no—
802C22×D3—62no—
803C22×D3—62no—
804C22×D3—62no—
805C22×D3—62no—
806C22×D3—64no—
807C22×D3—64no—
808C22×D3—64no—
809C22×D3—62no—
810C22×D3—62no—
811C22×D3C2×D3211yescharacteristic
812C3×Q8—182no—
813C3×D4—64no—
814C3×D4—62no—
815C3×D4—62no—
816C3×D4—182no—
817C3×D4—182no—
818C3×D4—182no—
819C3×D4—182no—
820C2×C3×C4—31no—
821C2×C3×C4—31no—
822C2×C3×C4—31no—
823C2×C3×C4—31no—
824C2×C3×C4—31no—
825C2×C3×C4—31no—
826C2×C3×C4—31no—
827C2×C3×C4—31no—
828C2×C3×C4—31no—
829C2×C3×C4—31no—
830C2×C3×C4—61no—
831C2×C3×C4—61no—
832C2×C3×C4—61no—
833C2×C3×C4—61no—
834C2×C3×C4—61no—
835C2×C3×C4—62no—
836C2×C3×C4—62no—
837C2×C3×C4—64no—
838C2×C3×C4—91no—
839C2×C3×C4—91no—
840C2×C3×C4—91no—
841#67—22no—
842#67—62no—
843#67—62no—
844#67—64no—
845#67—62no—
846#67—62no—
847#67—62no—
848#67—182no—
849#67—182no—
850#67—182no—
851#67—182no—
852C2×Dic3—22no—
853C2×Dic3—31no—
854C2×Dic3—31no—
855C2×Dic3—31no—
856C2×Dic3—31no—
857C2×Dic3—31no—
858C2×Dic3—31no—
859C2×Dic3—61no—
860C2×Dic3—61no—
861C2×Dic3—61no—
862C2×Dic3—91no—
863C2×Dic3—91no—
864C2×Dic3—91no—
865C2×Dic3—94no—
866C2×Dic3—91no—
867C2×Dic3—91no—
868C2×Dic3—91no—
869C2×Dic3—181no—
870C2×Dic3—181no—
871C2×Dic3—181no—
872C2×Dic3—181no—
873C2×Dic3—181no—
874C2×Dic3—181no—
875C2×Dic3—182no—
876C2×Dic3—182no—
877C2×Dic3—182no—
878C2×Dic3—182no—
879C2×Dic3—182no—
880C2×Dic3—182no—
881C2×Dic3—182no—
882C2×Dic3—182no—
883C2×Dic3—184no—
884C2×Dic3—182no—
885C2×Dic3—361no—
886C2×Dic3—361no—
887C2×Dic3—362no—
888C2×Dic3—362no—
889C2×Dic3—362no—
890C2×Dic3—364no—
891C2×Dic3C2×D3211yescharacteristic
892C2×Dic3C2×D3211yescharacteristic
893C2×Dic3C2×D3211yescharacteristic
894C2×Dic3C2×D3211yescharacteristic
895C2×Dic3C2×D3211yescharacteristic
896D12—62no—
897D12—62no—
898D12—62no—
899D12—182no—
900D12—182no—
901C4×D3—94no—
902C4×D3—94no—
903C4×D3—184no—
904C4×D3—182no—
905C4×D3—182no—
906C4×D3—182no—
907C4×D3—182no—
908C4×D3—182no—
909C4×D3—182no—
910C4×D3—182no—
911C4×D3—182no—
912C4×D3—182no—
913C4×D3—184no—
914C4×D3—184no—
915C4×D3—184no—
916C4×D3—362no—
917Dic6—62no—
918Dic6—62no—
919C2×C32—22no—
920C2×C32—24no—
921C2×C32—22no—
922C2×C32—22no—
923C2×C32—21no—
924C2×C32—21no—
925C2×C32—21no—
926C2×C32—21no—
927C2×C32—21no—
928C2×C32—21no—
929C2×C32—21no—
930C2×C32—21no—
931C2×C32—21no—
932C2×C32—41no—
933C2×C32—41no—
934C2×C32—41no—
935C2×C32—42no—
936C2×C32—42no—
937C2×C32—44no—
938C2×C32—121no—
939C2×C32C2×D3×D411yescharacteristic
940C2×C32C2×D3×D411yescharacteristic
941C2×C32C2×D3×D411yescharacteristic
942C2×C32C2×#23711yescharacteristic
943C2×C32C2×#23711yescharacteristic
944C2×C32C2×#23711yescharacteristic
945C2×C32C2×#23911yescharacteristic
946C2×C32D3×#4111yescharacteristic
947C2×C32D3×#4111yescharacteristic
948C3⋊D3—22no—
949C3⋊D3—22no—
950C3⋊D3—41no—
951C3×D3—42no—
952C3×D3—41no—
953C3×D3—41no—
954C3×D3—64no—
955C3×D3—64no—
956C3×D3—62no—
957C3×D3—62no—
958C3×D3—62no—
959C3×D3—62no—
960C3×D3—122no—
961C3×D3—121no—
962C3×D3—121no—
963C24—91no—
964#41—544no—
965C2×Q8—91no—
966C2×D4—31no—
967C2×D4—91no—
968C2×D4—91no—
969C2×D4—91no—
970C2×D4—91no—
971C2×D4—271no—
972C2×D4—271no—
973C22×C4—31no—
974C22×C4—271no—
975C22×C4—271no—
976C22×C4—271no—
977C22×C4—271no—
978C22×C4—271no—
979C22×C4—271no—
980C22×C4—271no—
981C22×C4—544no—
982C4⋊C4—91no—
983C4⋊C4—91no—
984C4⋊C4—91no—
985C4⋊C4—91no—
986C4⋊C4—271no—
987C4⋊C4—271no—
988C22⋊C4—31no—
989C22⋊C4—91no—
990C22⋊C4—91no—
991C22⋊C4—91no—
992C22⋊C4—91no—
993C22⋊C4—91no—
994C22⋊C4—271no—
995C22⋊C4—271no—
996C22⋊C4—271no—
997C22⋊C4—271no—
998C42—271no—
999C42—271no—
1000C22×C3—22no—
1001C22×C3—22no—
1002C22×C3—21no—
1003C22×C3—21no—
1004C22×C3—21no—
1005C22×C3—21no—
1006C22×C3—21no—
1007C22×C3—21no—
1008C22×C3—21no—
1009C22×C3—21no—
1010C22×C3—21no—
1011C22×C3—22no—
1012C22×C3—22no—
1013C22×C3—22no—
1014C22×C3—41no—
1015C22×C3—41no—
1016C22×C3—41no—
1017C22×C3—41no—
1018C22×C3—42no—
1019C22×C3—42no—
1020C22×C3—41no—
1021C22×C3—42no—
1022C22×C3—62no—
1023C22×C3—61no—
1024C22×C3—61no—
1025C22×C3—61no—
1026C22×C3—61no—
1027C22×C3—61no—
1028C22×C3—61no—
1029C22×C3—92no—
1030C22×C3—92no—
1031C22×C3—121no—
1032C22×C3—121no—
1033C22×C3—188no—
1034C22×C3—181no—
1035C22×C3—181no—
1036C22×C3—181no—
1037C22×C3—181no—
1038C22×C3—181no—
1039C22×C3—181no—
1040C22×C3—181no—
1041C22×C3#379612yescomplemented
1042C22×C3#379612yescomplemented
1043C22×C3#380512yescomplemented
1044C22×C3C22×D3211yescharacteristic
1045C22×C3C22×D3211yescharacteristic
1046C22×C3C22×D3211yescharacteristic
1047C2×D3—21no—
1048C2×D3—21no—
1049C2×D3—21no—
1050C2×D3—32no—
1051C2×D3—32no—
1052C2×D3—32no—
1053C2×D3—32no—
1054C2×D3—62no—
1055C2×D3—62no—
1056C2×D3—62no—
1057C2×D3—616no—
1058C2×D3—68no—
1059C2×D3—68no—
1060C2×D3—62no—
1061C2×D3—62no—
1062C2×D3—62no—
1063C2×D3—61no—
1064C2×D3—61no—
1065C2×D3—61no—
1066C2×D3—61no—
1067C2×D3—61no—
1068C2×D3—61no—
1069C2×D3—61no—
1070C2×D3—61no—
1071C2×D3—62no—
1072C2×D3—61no—
1073C2×D3—61no—
1074C2×D3—61no—
1075C2×D3—61no—
1076C2×D3—61no—
1077C2×D3—61no—
1078C2×D3—121no—
1079C2×D3—121no—
1080C3×C4—32no—
1081C3×C4—32no—
1082C3×C4—62no—
1083C3×C4—62no—
1084C3×C4—62no—
1085C3×C4—61no—
1086C3×C4—61no—
1087C3×C4—61no—
1088C3×C4—61no—
1089C3×C4—61no—
1090C3×C4—61no—
1091C3×C4—61no—
1092C3×C4—61no—
1093C3×C4—121no—
1094C3×C4—121no—
1095C3×C4—181no—
1096C3×C4—181no—
1097C3×C4—181no—
1098Dic3—21no—
1099Dic3—21no—
1100Dic3—21no—
1101Dic3—21no—
1102Dic3—62no—
1103Dic3—61no—
1104Dic3—61no—
1105Dic3—61no—
1106Dic3—61no—
1107Dic3—61no—
1108Dic3—61no—
1109Dic3—92no—
1110Dic3—92no—
1111Dic3—92no—
1112Dic3—121no—
1113Dic3—121no—
1114Dic3—182no—
1115Dic3—182no—
1116Dic3—182no—
1117Dic3—182no—
1118Dic3—181no—
1119Dic3—181no—
1120Dic3—181no—
1121Dic3—362no—
1122Dic3—361no—
1123Dic3—361no—
1124Dic3—362no—
1125Dic3#381112yes—
1126C32—21no—
1127C32—21no—
1128C32—21no—
1129C32—41no—
1130C32#558611yescharacteristic, complemented
1131C32#560611yescharacteristic, complemented
1132C32#562711yescharacteristic, complemented
1133C23—31no—
1134C23—91no—
1135C23—91no—
1136C23—91no—
1137C23—182no—
1138C23—182no—
1139C23—182no—
1140C23D3311yescharacteristic
1141Q8—182no—
1142D4—62no—
1143D4—182no—
1144D4—182no—
1145D4—182no—
1146D4—182no—
1147D4—542no—
1148D4—542no—
1149C2×C4—31no—
1150C2×C4—31no—
1151C2×C4—31no—
1152C2×C4—31no—
1153C2×C4—31no—
1154C2×C4—62no—
1155C2×C4—91no—
1156C2×C4—91no—
1157C2×C4—91no—
1158C2×C4—274no—
1159C2×C4—271no—
1160C2×C4—271no—
1161C2×C4—542no—
1162C2×C4—542no—
1163C2×C4—542no—
1164C2×C4—542no—
1165C2×C4—542no—
1166C2×C4—542no—
1167C2×C3—24no—
1168C2×C3—22no—
1169C2×C3—22no—
1170C2×C3—22no—
1171C2×C3—21no—
1172C2×C3—21no—
1173C2×C3—21no—
1174C2×C3—21no—
1175C2×C3—21no—
1176C2×C3—21no—
1177C2×C3—21no—
1178C2×C3—21no—
1179C2×C3—21no—
1180C2×C3—42no—
1181C2×C3—42no—
1182C2×C3—44no—
1183C2×C3—41no—
1184C2×C3—41no—
1185C2×C3—41no—
1186C2×C3—122no—
1187C2×C3—121no—
1188C2×C3—121no—
1189C2×C3—182no—
1190C2×C3—182no—
1191C2×C3—361no—
1192C2×C3C2×#379611yescharacteristic
1193C2×C3C2×#379611yescharacteristic
1194C2×C3#6430611yescharacteristic
1195C2×C3D32×D411yescharacteristic
1196C2×C3D32×D411yescharacteristic
1197C2×C3D3×#23711yescharacteristic
1198C2×C3D3×#23711yescharacteristic
1199C2×C3C2×#380511yescharacteristic
1200C2×C3C2×#381111yescharacteristic
1201D3—41no—
1202D3—64no—
1203D3—64no—
1204D3—62no—
1205D3—62no—
1206D3—62no—
1207D3—62no—
1208D3—122no—
1209D3—121no—
1210D3—121no—
1211C22—21no—
1212C22—21no—
1213C22—61no—
1214C22—61no—
1215C22—61no—
1216C22—92no—
1217C22—92no—
1218C22—188no—
1219C22—181no—
1220C22—181no—
1221C22—181no—
1222C22—181no—
1223C22—181no—
1224C22—181no—
1225C22—181no—
1226C22#8896412yescomplemented
1227C22C2×D3311yescharacteristic
1228C4—32no—
1229C4—61no—
1230C4—61no—
1231C4—61no—
1232C4—61no—
1233C4—181no—
1234C4—181no—
1235C4—181no—
1236C4—272no—
1237C4—541no—
1238C3—21no—
1239C3—21no—
1240C3—21no—
1241C3—41no—
1242C3#1059405511yescharacteristic, complemented
1243C3#1059492211yescharacteristic, complemented
1244C3#1059513011yescharacteristic, complemented
1245C2—22no—
1246C2—121no—
1247C2—182no—
1248C2—182no—
1249C2—361no—
1250C2#1172440711yescharacteristic
1251C2C2×#8896411yescharacteristic
1252C2D3×#381111yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
hypercenterC23D33
hypocenterC33#525
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C22×Dic3×C3⋊D3C2semidirect
2. C2×#88964C2semidirect
3. #11723727C2semidirect
4. #11723626C2semidirect
5. #67⋊(C3⋊Dic3)C2semidirect
6. C3×#63981C2semidirect
7. C3×#63978C2semidirect
8. C3×#63964C2semidirect
9. #11722997C2semidirect
10. #11722991C2semidirect
11. #11722974C2semidirect
12. #11722962C2semidirect
13. #11722938C2semidirect
14. #11722929C2semidirect
15. #11722921C2semidirect
31. C2×Dic3×C3⋊D3C22semidirect
32. C2×D3×C3⋊Dic3C22semidirect
33. C2×C3×#627C22semidirect
36. C2×C3×#626C22semidirect
42. #88807C22semidirect
43. Dic3⋊(C3⋊Dic3)C22semidirect
44. #88803C22semidirect
45. (C2×D3)⋊(C3⋊Dic3)C22semidirect
46. Dic3×C3⋊Dic3C22semidirect
47. Dic3×C3⋊Dic3C22semidirect
48. C3×#3724C22semidirect
49. C3×Dic3⋊Dic3C22semidirect
50. C3×Dic3⋊Dic3C22semidirect
51. C3×Dic3⋊Dic3C22semidirect
54. C3×#3722C22semidirect
55. C3×(C2×D3)⋊Dic3C22semidirect
72. #63981D3semidirect
73. #63978D3semidirect
85. #63964D3semidirect
132. Dic3×C3⋊D3D4semidirect
179. C2×#627C2×D3semidirect
186. C2×#626C2×D3semidirect
243. #3724C2×D3semidirect
250. Dic3⋊Dic3C2×D3semidirect
251. Dic3⋊Dic3C2×D3semidirect
252. Dic3⋊Dic3C2×D3semidirect
257. #3722C2×D3semidirect
268. (C2×D3)⋊Dic3C2×D3semidirect
277. C22×C33#41semidirect
288. C2×C3×C3⋊D3#41semidirect
660. C22×C32#237semidirect
661. C22×C32#237semidirect
662. C22×C32#239semidirect
675. C2×C3⋊D3#237semidirect
776. C33#525semidirect
1041. C22×C3#3796semidirect
1042. C22×C3#3796semidirect
1043. C22×C3#3805semidirect
1130. C32#5586semidirect
1131. C32#5606semidirect
1132. C32#5627semidirect
1226. C22#88964semidirect
1242. C3#10594055semidirect
1243. C3#10594922semidirect
1244. C3#10595130semidirect

Maximal subgroups

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

subgroupindex
C22×Dic3×C3⋊D32
C2×#889642
#117237272
#117236262
#67⋊(C3⋊Dic3)2
C3×#639812
C3×#639782
C3×#639642
#117229972
#117229912
#117229742
#117229622
#117229382
#117229292
#117229212
#105951303
#105949223
#105940553