Finite Group Databasebeta

← #13170747

Subgroups — #13170747

Order 1728.

1652 conjugacy classes of subgroups.

The subgroup lattice has 1242 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88960C211yesmaximal, characteristic, complemented
2C2×D3×#624C211yesmaximal, characteristic, complemented
3#11723690C211yesmaximal, characteristic, complemented
4#11723540C211yesmaximal, characteristic, complemented
5#11723485C211yesmaximal, characteristic, complemented
6#11723471C211yesmaximal, characteristic, complemented
7C3×Dic3×D12C211yesmaximal, characteristic, complemented
8C3×#63886C211yesmaximal, characteristic, complemented
9C3×#63836C211yesmaximal, characteristic, complemented
10#11722998C211yesmaximal, characteristic, complemented
11#11722971C211yesmaximal, characteristic, complemented
12#11722963C211yesmaximal, characteristic, complemented
13#11722950C211yesmaximal, characteristic, complemented
14#11722932C211yesmaximal, characteristic, complemented
15Dic3×#626C211yesmaximal, characteristic, complemented
16#10595138—31nomaximal
17#10594626—31nomaximal
18#10593997—31nomaximal
19C22×D3×C3⋊D3C2211yescharacteristic
20C2×C32×D12C2211yescharacteristic
21C2×#6295C2211yescharacteristic
22C2×#6294C2211yescharacteristic
23C2×#6293C2211yescharacteristic, complemented
24C2×#6292C2211yescharacteristic
25C2×#6291C2211yescharacteristic
26C2×#6290C2211yescharacteristic
27C2×#6289C2211yescharacteristic
28C2×#6289C2211yescharacteristic
29C2×Dic3×C3⋊D3C2211yescharacteristic, 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#88960—24no—
37D3×#624—24no—
38#88859C2211yescharacteristic
39C3×#3752C2211yescharacteristic
40C3×#3752C2211yescharacteristic, complemented
41C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
42C32×Dic3⋊C4C2211yescharacteristic, complemented
43C32×C4×Dic3C2211yescharacteristic, complemented
44#88815C2211yescharacteristic, complemented
45#88814C2211yescharacteristic, complemented
46Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
47Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
48#88804C2211yescharacteristic
49(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
50C3×Dic3⋊Dic3C2211yescharacteristic, complemented
51C3×#3722C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
54C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
55C3×Dic32C2211yescharacteristic, complemented
56C22×#624—31no—
57C2×#3804—31no—
58C2×C4×D32—31no—
59C2×C4×D32—31no—
60C2×#3798—31no—
61C2×#3795—31no—
62#64146—31no—
63#64106—31no—
64C4×C4⋊(C3⋊D3)—31no—
65C3×#939—31no—
66C3×D4×Dic3—31no—
67C3×#895—31no—
68C3×#892—31no—
69C3×C4×D12—31no—
70C3×#872—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#63916—31no—
83#63910—31no—
84C4×#626—31no—
85C4×#626—31no—
86#63895—31no—
87#63895—31no—
88#63895—61no—
89#63893—31no—
90Dic3×D12—31no—
91Dic3×D12D311yescharacteristic, complemented
92#63891—31no—
93#63891—31no—
94#63891—31no—
95#63890—31no—
96#63886D311yescharacteristic, complemented
97#63880—31no—
98#63880—31no—
99#63880—31no—
100#63880—61no—
101#63857—31no—
102#63854—31no—
103#63836D311yescharacteristic, complemented
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#6293—22no—
126#6292—22no—
127#6291—22no—
128#6290—22no—
129#6289—22no—
130#6289—22no—
131Dic3×C3⋊D3—22no—
132C3×#626—22no—
133C3×#626—22no—
134C3×#624D414yescomplemented
135C3×D3×Dic3—22no—
136C3×D3×Dic3—22no—
137C3×D3×Dic3—22no—
138#5606—91no—
139#5547—91no—
140#5524—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×C4×C3⋊D3—31no—
152C2×#634—31no—
153C2×C3×#67—31no—
154C2×C3×#67—31no—
155C22×C3×Dic3—31no—
156C22×C3×Dic3—31no—
157C22×C3×Dic3—31no—
158C2×C3×D12—21no—
159C2×C3×D12—31no—
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×C4×D3—31no—
167C2×C3×C4×D3—31no—
168C2×#627—31no—
169C2×#627—31no—
170C2×#627—61no—
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×#626C2×D311yescharacteristic
180C2×#626C2×D311yescharacteristic, complemented
181C2×#625—31no—
182C2×#625—31no—
183C2×#625—31no—
184C2×#625—61no—
185C2×#624—31no—
186C2×#624—31no—
187C2×#624—31no—
188C2×#624—31no—
189C2×#624—31no—
190C2×#624—64no—
191C2×#624—61no—
192C2×#624—61no—
193C2×#624C2×D311yescharacteristic
194#3804—64no—
195C2×D3×Dic3—31no—
196C2×D3×Dic3—31no—
197C2×D3×Dic3—31no—
198C2×D3×Dic3—31no—
199C2×D3×Dic3—61no—
200C2×D3×Dic3C2×D311yescharacteristic
201C2×D3×Dic3C2×D311yescharacteristic
202C2×D3×Dic3C2×D311yescharacteristic, complemented
203C4×D32—64no—
204C4×D32—64no—
205#3798—64no—
206#3795—64no—
207C32×C4⋊C4—31no—
208C32×C42—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#3752C2×D311yescharacteristic, complemented
220C4⋊(C3⋊Dic3)—31no—
221C4⋊(C3⋊Dic3)—31no—
222C4⋊(C3⋊Dic3)C2×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—31no—
238C3×C4⋊Dic3—31no—
239C3×C4⋊Dic3—31no—
240C3×C4⋊Dic3—61no—
241C3×Dic3⋊C4—21no—
242C3×Dic3⋊C4—31no—
243C3×Dic3⋊C4C2×D311yescharacteristic, complemented
244C3×Dic3⋊C4C2×D311yescharacteristic, complemented
245C3×C4×Dic3—21no—
246C3×C4×Dic3—31no—
247C3×C4×Dic3—31no—
248C3×C4×Dic3C2×D311yescharacteristic, complemented
249C3×C4×Dic3C2×D311yescharacteristic, complemented
250#3724—31no—
251Dic3⋊Dic3—31no—
252Dic3⋊Dic3—31no—
253Dic3⋊Dic3—31no—
254Dic3⋊Dic3—31no—
255Dic3⋊Dic3—31no—
256Dic3⋊Dic3—31no—
257Dic3⋊Dic3—61no—
258Dic3⋊Dic3—61no—
259Dic3⋊Dic3C2×D311yescharacteristic, complemented
260#3722—31no—
261#3722—31no—
262#3722—31no—
263#3722—61no—
264#3722C2×D311yescharacteristic
265(C2×D3)⋊Dic3—31no—
266(C2×D3)⋊Dic3—31no—
267(C2×D3)⋊Dic3—31no—
268(C2×D3)⋊Dic3—31no—
269(C2×D3)⋊Dic3—61no—
270(C2×D3)⋊Dic3C2×D311yescharacteristic
271(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
272(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
273Dic32C2×D311yescharacteristic, complemented
274C22×C33C2411yescharacteristic
275C2×C3⋊(C3⋊D3)—21no—
276C2×C3⋊(C3⋊D3)—21no—
277C2×C3⋊(C3⋊D3)#4112yescomplemented
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⋊D3C2×D412yes—
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⋊Dic3—21no—
297C32×Dic3—21no—
298C32×Dic3—21no—
299C32×Dic3C2×D412yes—
300C32×Dic3C2×D412yes—
301C2×#237—91no—
302C2×#235—91no—
303C2×#235—91no—
304C22×C4×D3—91no—
305C22×C4×D3—91no—
306C22×C4×D3—91no—
307C3×#121—91no—
308C3×C4×D4—91no—
309C3×#117—91no—
310#939—31no—
311#938—91no—
312#937—91no—
313#937—91no—
314#937—91no—
315#937—181no—
316D4×Dic3—31no—
317D4×Dic3—91no—
318C4×#67—91no—
319C4×#67—91no—
320#924—91no—
321#897—91no—
322#897—91no—
323#897—91no—
324#897—181no—
325#896—91no—
326#895—31no—
327#895—91no—
328#894—91no—
329#892—31no—
330#886—91no—
331#886—91no—
332#884—91no—
333#883—91no—
334#883—91no—
335#883—91no—
336#882—91no—
337#882—91no—
338#882—91no—
339#67⋊C4—91no—
340#67⋊C4—91no—
341#878—91no—
342C4×D12—31no—
343C4×D12—91no—
344C4×D12—91no—
345C4×D12—91no—
346C4×D12—91no—
347C4×D12—181no—
348#872—31no—
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—62no—
411C4×C3⋊D3—62no—
412C4×C3⋊D3—62no—
413#634—62no—
414C3×#67—62no—
415C3×#67—62no—
416C2×C3×Dic3—21no—
417C2×C3×Dic3—21no—
418C2×C3×Dic3—21no—
419C2×C3×Dic3—21no—
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—62no—
433C2×C3×Dic3—62no—
434C2×C3×Dic3—62no—
435C2×C3×Dic3C22×D311yescharacteristic
436C2×C3×Dic3C22×D311yescharacteristic
437C2×C3×Dic3C22×D311yescharacteristic
438C2×C3×Dic3C22×D311yescharacteristic
439C2×C3×Dic3C22×D311yescharacteristic
440C2×C3×Dic3C22×D311yescharacteristic
441C2×C3×Dic3C22×D311yescharacteristic
442C2×C3×Dic3C22×D311yescharacteristic
443C3×D12—22no—
444C3×D12—22no—
445C3×D12—42no—
446C3×D12—62no—
447C3×D12—62no—
448C3×C4×D3—34no—
449C3×C4×D3—34no—
450C3×C4×D3—62no—
451C3×C4×D3—62no—
452C3×C4×D3—62no—
453#627—62no—
454#627—62no—
455#627—122no—
456#626—22no—
457#626—22no—
458#626—62no—
459#626—62no—
460#626—64no—
461#626—62no—
462#626—62no—
463#626—62no—
464#626—62no—
465#626—122no—
466#625—62no—
467#625—62no—
468#625—62no—
469#625—122no—
470#624—62no—
471#624—62no—
472#624—62no—
473#624—62no—
474#624—62no—
475#624—122no—
476#624—122no—
477#624D1214yescomplemented
478D3×Dic3—22no—
479D3×Dic3—22no—
480D3×Dic3—22no—
481D3×Dic3—62no—
482D3×Dic3—62no—
483D3×Dic3—62no—
484D3×Dic3—62no—
485D3×Dic3—122no—
486#525—271noSylow
487C2×C33C22×D411yescharacteristic
488C2×C33C2×#4111yescharacteristic
489C2×C33C2×#4111yescharacteristic
490C3⋊(C3⋊D3)—22no—
491C3×C3⋊D3—22no—
492C3×C3⋊D3—41no—
493C32×D3—22no—
494C32×D3—41no—
495C23×D3—91no—
496C23×D3—91no—
497C23×D3—91no—
498C23×D3—181no—
499C2×C3×D4—31no—
500C2×C3×D4—31no—
501C2×C3×D4—61no—
502C2×C3×D4—91no—
503C2×C3×D4—91no—
504C22×C3×C4—91no—
505C22×C3×C4—91no—
506C22×C3×C4—91no—
507C22×C3×C4—91no—
508C2×#67—31no—
509C2×#67—31no—
510C2×#67—91no—
511C2×#67—91no—
512C2×#67—91no—
513C2×#67—91no—
514C2×#67—91no—
515C2×#67—91no—
516C2×#67—91no—
517C2×#67—91no—
518C2×#67—181no—
519C2×#67—181no—
520C22×Dic3—31no—
521C22×Dic3—31no—
522C22×Dic3—31no—
523C22×Dic3—91no—
524C22×Dic3—91no—
525#237—184no—
526#235—184no—
527#235—184no—
528C2×D12—31no—
529C2×D12—31no—
530C2×D12—91no—
531C2×D12—91no—
532C2×D12—91no—
533C2×D12—91no—
534C2×D12—181no—
535C2×D12D3211yescharacteristic
536C2×C4×D3—31no—
537C2×C4×D3—31no—
538C2×C4×D3—31no—
539C2×C4×D3—31no—
540C2×C4×D3—31no—
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—91no—
551C2×C4×D3—181no—
552C2×C4×D3—181no—
553C2×C4×D3—181no—
554C2×C4×D3—184no—
555C2×C4×D3—184no—
556C2×C4×D3—184no—
557C2×Dic6—91no—
558C2×Dic6—91no—
559C2×Dic6—91no—
560C2×Dic6—181no—
561C3×C4⋊C4—31no—
562C3×C4⋊C4—31no—
563C3×C4⋊C4—61no—
564C3×C4⋊C4—91no—
565C3×C4⋊C4—91no—
566C3×C22⋊C4—91no—
567C3×C22⋊C4—91no—
568C3×C22⋊C4—91no—
569C3×C22⋊C4—91no—
570C3×C22⋊C4—91no—
571C3×C22⋊C4—91no—
572C3×C42—31no—
573C3×C42—31no—
574C3×C42—61no—
575C3×C42—91no—
576#217—31no—
577#217—31no—
578#217—31no—
579#217—91no—
580#217—91no—
581#217—91no—
582#217—181no—
583(C2×D3)⋊C4—31no—
584(C2×D3)⋊C4—31no—
585(C2×D3)⋊C4—31no—
586(C2×D3)⋊C4—31no—
587(C2×D3)⋊C4—31no—
588(C2×D3)⋊C4—31no—
589(C2×D3)⋊C4—31no—
590(C2×D3)⋊C4—31no—
591(C2×D3)⋊C4—31no—
592(C2×D3)⋊C4—61no—
593(C2×D3)⋊C4—61no—
594(C2×D3)⋊C4—91no—
595(C2×D3)⋊C4—91no—
596(C2×D3)⋊C4—91no—
597(C2×D3)⋊C4—91no—
598(C2×D3)⋊C4—91no—
599(C2×D3)⋊C4—91no—
600(C2×D3)⋊C4—91no—
601(C2×D3)⋊C4—91no—
602(C2×D3)⋊C4—91no—
603(C2×D3)⋊C4—181no—
604(C2×D3)⋊C4—181no—
605(C2×D3)⋊C4—181no—
606(C2×D3)⋊C4—181no—
607(C2×D3)⋊C4—361no—
608C4⋊Dic3—31no—
609C4⋊Dic3—31no—
610C4⋊Dic3—31no—
611C4⋊Dic3—61no—
612C4⋊Dic3—91no—
613C4⋊Dic3—91no—
614C4⋊Dic3—91no—
615C4⋊Dic3—91no—
616C4⋊Dic3—91no—
617C4⋊Dic3—181no—
618C4⋊Dic3—181no—
619Dic3⋊C4—31no—
620Dic3⋊C4—91no—
621Dic3⋊C4—91no—
622Dic3⋊C4—91no—
623Dic3⋊C4—91no—
624Dic3⋊C4D3211yescharacteristic, complemented
625C4×Dic3—31no—
626C4×Dic3—31no—
627C4×Dic3D3211yescharacteristic, complemented
628C22×C32—21no—
629C22×C32—21no—
630C22×C32—21no—
631C22×C32—32no—
632C22×C32—41no—
633C22×C32—61no—
634C22×C32—61no—
635C22×C32—61no—
636C22×C32—61no—
637C22×C32—61no—
638C22×C32C23×D311yescharacteristic
639C22×C32C23×D311yescharacteristic
640C22×C32C23×D311yescharacteristic
641C2×C3⋊D3—21no—
642C2×C3⋊D3—21no—
643C2×C3⋊D3—21no—
644C2×C3⋊D3—21no—
645C2×C3⋊D3—21no—
646C2×C3⋊D3—32no—
647C2×C3⋊D3—32no—
648C2×C3⋊D3—32no—
649C2×C3⋊D3—62no—
650C2×C3⋊D3—62no—
651C2×C3⋊D3—62no—
652C2×C3⋊D3—68no—
653C2×C3⋊D3—61no—
654C2×C3⋊D3—61no—
655C2×C3⋊D3—61no—
656C2×C3⋊D3—61no—
657C2×C3⋊D3—61no—
658C2×C3⋊D3—61no—
659C2×C3⋊D3—122no—
660C2×C3⋊D3—121no—
661C2×C3⋊D3—121no—
662C2×C3⋊D3—121no—
663C2×C3⋊D3—121no—
664C2×C3⋊D3—121no—
665C2×C3⋊D3—121no—
666C2×C3⋊D3—241no—
667C2×C3⋊D3—241no—
668C2×C3⋊D3C2×D1212yes—
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—22no—
680C2×C3×D3—32no—
681C2×C3×D3—32no—
682C2×C3×D3—41no—
683C2×C3×D3—41no—
684C2×C3×D3—41no—
685C2×C3×D3—41no—
686C2×C3×D3—41no—
687C2×C3×D3—62no—
688C2×C3×D3—61no—
689C2×C3×D3—61no—
690C2×C3×D3—61no—
691C2×C3×D3—61no—
692C2×C3×D3—62no—
693C2×C3×D3—61no—
694C2×C3×D3—61no—
695C2×C3×D3—61no—
696C2×C3×D3—61no—
697C2×C3×D3—61no—
698C2×C3×D3—61no—
699C2×C3×D3—121no—
700C2×C3×D3—121no—
701C2×C3×D3—121no—
702C2×C3×D3—121no—
703C2×C3×D3#23512yescomplemented
704C2×C3×D3#23712yescomplemented
705D32—68no—
706D32—68no—
707D32—128no—
708C32×C4—21no—
709C32×C4—21no—
710C32×C4—21no—
711C32×C4—32no—
712C32×C4—32no—
713C32×C4—41no—
714C32×C4—41no—
715C32×C4—41no—
716C32×C4—61no—
717C32×C4—61no—
718C32×C4—81no—
719C3⋊Dic3—21no—
720C3⋊Dic3—21no—
721C3⋊Dic3—21no—
722C3⋊Dic3—21no—
723C3⋊Dic3—61no—
724C3⋊Dic3—61no—
725C3⋊Dic3—61no—
726C3⋊Dic3—121no—
727C3⋊Dic3—121no—
728C3⋊Dic3—121no—
729C3⋊Dic3—241no—
730C3×Dic3—22no—
731C3×Dic3—21no—
732C3×Dic3—21no—
733C3×Dic3—21no—
734C3×Dic3—21no—
735C3×Dic3—22no—
736C3×Dic3—22no—
737C3×Dic3—41no—
738C3×Dic3—61no—
739C3×Dic3—61no—
740C3×Dic3—61no—
741C3×Dic3—61no—
742C3×Dic3—61no—
743C3×Dic3—61no—
744C3×Dic3—61no—
745C3×Dic3—61no—
746C3×Dic3—121no—
747C3×Dic3—121no—
748C3×Dic3—121no—
749C3×Dic3—121no—
750C3×Dic3C2×D1212yes—
751C3×Dic3C2×D1212yes—
752C3×Dic3D3×D412yes—
753C3×Dic3D3×D412yes—
754C2×#41—271no—
755C23×C4—271no—
756#123—271no—
757#123—271no—
758C22⋊Q8—271no—
759C22⋊Q8—271no—
760#121—91no—
761#121—271no—
762#120—271no—
763#120—271no—
764C4×D4—91no—
765C4×D4—271no—
766C4×D4—271no—
767C4×D4—271no—
768#117—91no—
769C33#52511yescharacteristic, complemented, Sylow
770C23×C3—31no—
771C23×C3—31no—
772C23×C3—31no—
773C23×C3—31no—
774C23×C3—61no—
775C23×C3—61no—
776C23×C3—91no—
777C23×C3—91no—
778C22×D3—31no—
779C22×D3—31no—
780C22×D3—31no—
781C22×D3—31no—
782C22×D3—61no—
783C22×D3—61no—
784C22×D3—91no—
785C22×D3—91no—
786C22×D3—91no—
787C22×D3—181no—
788C22×D3—181no—
789C22×D3—181no—
790C22×D3—182no—
791C22×D3—182no—
792C22×D3—182no—
793C22×D3—182no—
794C22×D3—182no—
795C22×D3—182no—
796C22×D3—182no—
797C22×D3—182no—
798C22×D3—182no—
799C22×D3—361no—
800C22×D3—362no—
801C22×D3—362no—
802C22×D3—362no—
803C22×D3C2×D3211yescharacteristic
804C22×D3C2×D3211yescharacteristic
805C3×D4—62no—
806C3×D4—62no—
807C3×D4—122no—
808C3×D4—182no—
809C3×D4—182no—
810C2×C3×C4—21no—
811C2×C3×C4—21no—
812C2×C3×C4—21no—
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—31no—
821C2×C3×C4—41no—
822C2×C3×C4—61no—
823C2×C3×C4—61no—
824C2×C3×C4—61no—
825C2×C3×C4—61no—
826C2×C3×C4—94no—
827C2×C3×C4—91no—
828C2×C3×C4—91no—
829C2×C3×C4—91no—
830C2×C3×C4—91no—
831C2×C3×C4—182no—
832C2×C3×C4—182no—
833C2×C3×C4—182no—
834C2×C3×C4C2×D3211yescharacteristic
835C2×C3×C4C2×D3211yescharacteristic
836C2×C3×C4C2×D3211yescharacteristic
837#67—62no—
838#67—62no—
839#67—182no—
840#67—182no—
841#67—182no—
842#67—182no—
843#67—182no—
844#67—182no—
845#67—182no—
846#67—182no—
847#67—362no—
848#67—362no—
849C2×Dic3—31no—
850C2×Dic3—31no—
851C2×Dic3—31no—
852C2×Dic3—31no—
853C2×Dic3—31no—
854C2×Dic3—31no—
855C2×Dic3—31no—
856C2×Dic3—31no—
857C2×Dic3—61no—
858C2×Dic3—61no—
859C2×Dic3—61no—
860C2×Dic3—61no—
861C2×Dic3—62no—
862C2×Dic3—62no—
863C2×Dic3—62no—
864C2×Dic3—91no—
865C2×Dic3—91no—
866C2×Dic3—91no—
867C2×Dic3—181no—
868C2×Dic3—181no—
869C2×Dic3—181no—
870C2×Dic3—182no—
871C2×Dic3—182no—
872C2×Dic3—361no—
873C2×Dic3C2×D3211yescharacteristic
874C2×Dic3C2×D3211yescharacteristic
875C2×Dic3C2×D3211yescharacteristic
876C2×Dic3C2×D3211yescharacteristic
877D12—22no—
878D12—62no—
879D12—62no—
880D12—182no—
881D12—182no—
882D12—184no—
883D12—182no—
884D12—182no—
885C4×D3—34no—
886C4×D3—34no—
887C4×D3—62no—
888C4×D3—62no—
889C4×D3—62no—
890C4×D3—182no—
891C4×D3—182no—
892C4×D3—182no—
893C4×D3—182no—
894C4×D3—182no—
895C4×D3—182no—
896C4×D3—182no—
897C4×D3—182no—
898C4×D3—182no—
899C4×D3—182no—
900C4×D3—362no—
901C4×D3—362no—
902C4×D3—362no—
903Dic6—182no—
904Dic6—182no—
905Dic6—182no—
906Dic6—362no—
907C2×C32—21no—
908C2×C32—21no—
909C2×C32—21no—
910C2×C32—21no—
911C2×C32—21no—
912C2×C32—21no—
913C2×C32—21no—
914C2×C32—21no—
915C2×C32—21no—
916C2×C32—41no—
917C2×C32—41no—
918C2×C32—41no—
919C2×C32—62no—
920C2×C32—121no—
921C2×C32C22×D1211yescharacteristic
922C2×C32C2×#23511yescharacteristic
923C2×C32C2×D3×D411yescharacteristic
924C2×C32C2×D3×D411yescharacteristic
925C2×C32C2×#23711yescharacteristic
926C2×C32D3×#4111yescharacteristic
927C2×C32D3×#4111yescharacteristic
928C2×C32D3×#4111yescharacteristic
929C2×C32D3×#4111yescharacteristic
930C3⋊D3—22no—
931C3⋊D3—41no—
932C3⋊D3—62no—
933C3⋊D3—62no—
934C3⋊D3—62no—
935C3⋊D3—122no—
936C3⋊D3—122no—
937C3⋊D3—122no—
938C3⋊D3—242no—
939C3×D3—22no—
940C3×D3—22no—
941C3×D3—42no—
942C3×D3—41no—
943C3×D3—41no—
944C3×D3—62no—
945C3×D3—62no—
946C3×D3—81no—
947C3×D3—122no—
948C3×D3—122no—
949C3×D3—121no—
950C3×D3—121no—
951C24—271no—
952#41—544no—
953C2×Q8—271no—
954C2×D4—31no—
955C2×D4—91no—
956C2×D4—91no—
957C2×D4—271no—
958C2×D4—271no—
959C2×D4—271no—
960C2×D4—271no—
961C22×C4—91no—
962C22×C4—91no—
963C22×C4—91no—
964C22×C4—91no—
965C22×C4—271no—
966C22×C4—271no—
967C22×C4—271no—
968C22×C4—271no—
969C22×C4—544no—
970C4⋊C4—31no—
971C4⋊C4—91no—
972C4⋊C4—91no—
973C4⋊C4—271no—
974C4⋊C4—271no—
975C4⋊C4—271no—
976C22⋊C4—91no—
977C22⋊C4—91no—
978C22⋊C4—91no—
979C22⋊C4—91no—
980C22⋊C4—91no—
981C22⋊C4—91no—
982C22⋊C4—271no—
983C22⋊C4—271no—
984C22⋊C4—271no—
985C22⋊C4—271no—
986C42—31no—
987C42—91no—
988C22×C3—21no—
989C22×C3—21no—
990C22×C3—21no—
991C22×C3—32no—
992C22×C3—32no—
993C22×C3—41no—
994C22×C3—62no—
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—92no—
1006C22×C3—121no—
1007C22×C3—121no—
1008C22×C3—121no—
1009C22×C3—121no—
1010C22×C3—121no—
1011C22×C3—181no—
1012C22×C3—181no—
1013C22×C3—181no—
1014C22×C3—181no—
1015C22×C3—181no—
1016C22×C3C22×D3211yescharacteristic
1017C22×C3C22×D3211yescharacteristic
1018C22×C3C22×D3211yescharacteristic
1019C2×D3—21no—
1020C2×D3—21no—
1021C2×D3—21no—
1022C2×D3—21no—
1023C2×D3—21no—
1024C2×D3—32no—
1025C2×D3—32no—
1026C2×D3—62no—
1027C2×D3—61no—
1028C2×D3—61no—
1029C2×D3—61no—
1030C2×D3—61no—
1031C2×D3—62no—
1032C2×D3—61no—
1033C2×D3—61no—
1034C2×D3—61no—
1035C2×D3—61no—
1036C2×D3—61no—
1037C2×D3—61no—
1038C2×D3—92no—
1039C2×D3—92no—
1040C2×D3—92no—
1041C2×D3—121no—
1042C2×D3—121no—
1043C2×D3—121no—
1044C2×D3—121no—
1045C2×D3—182no—
1046C2×D3—182no—
1047C2×D3—182no—
1048C2×D3—188no—
1049C2×D3—188no—
1050C2×D3—188no—
1051C2×D3—181no—
1052C2×D3—181no—
1053C2×D3—181no—
1054C2×D3—181no—
1055C2×D3—181no—
1056C2×D3—181no—
1057C2×D3—362no—
1058C2×D3—368no—
1059C2×D3—361no—
1060C2×D3—361no—
1061C2×D3—361no—
1062C2×D3—361no—
1063C2×D3—361no—
1064C2×D3—361no—
1065C2×D3—721no—
1066C2×D3—721no—
1067C2×D3#380412yescomplemented
1068C3×C4—21no—
1069C3×C4—21no—
1070C3×C4—21no—
1071C3×C4—32no—
1072C3×C4—32no—
1073C3×C4—32no—
1074C3×C4—32no—
1075C3×C4—41no—
1076C3×C4—41no—
1077C3×C4—41no—
1078C3×C4—62no—
1079C3×C4—62no—
1080C3×C4—62no—
1081C3×C4—61no—
1082C3×C4—61no—
1083C3×C4—61no—
1084C3×C4—61no—
1085C3×C4—81no—
1086C3×C4—121no—
1087C3×C4—181no—
1088C3×C4—181no—
1089C3×C4—181no—
1090C3×C4—181no—
1091Dic3—21no—
1092Dic3—21no—
1093Dic3—61no—
1094Dic3—61no—
1095Dic3—61no—
1096Dic3—61no—
1097Dic3—61no—
1098Dic3—61no—
1099Dic3—61no—
1100Dic3—61no—
1101Dic3—121no—
1102Dic3—121no—
1103Dic3—121no—
1104Dic3—121no—
1105Dic3—181no—
1106Dic3—181no—
1107Dic3—181no—
1108Dic3—361no—
1109Dic3—361no—
1110Dic3—361no—
1111Dic3—721no—
1112Dic3D3×D1212yes—
1113Dic3D3×D1212yes—
1114C32—21no—
1115C32—21no—
1116C32—21no—
1117C32—41no—
1118C32#552411yescharacteristic, complemented
1119C32#554711yescharacteristic, complemented
1120C32#560611yescharacteristic, complemented
1121C23—31no—
1122C23—31no—
1123C23—91no—
1124C23—91no—
1125C23—271no—
1126C23—542no—
1127C23—542no—
1128C23—542no—
1129Q8—542no—
1130D4—62no—
1131D4—182no—
1132D4—182no—
1133D4—542no—
1134D4—542no—
1135D4—542no—
1136D4—542no—
1137C2×C4—31no—
1138C2×C4—31no—
1139C2×C4—31no—
1140C2×C4—31no—
1141C2×C4—94no—
1142C2×C4—91no—
1143C2×C4—91no—
1144C2×C4—91no—
1145C2×C4—91no—
1146C2×C4—182no—
1147C2×C4—182no—
1148C2×C4—182no—
1149C2×C4—271no—
1150C2×C4—542no—
1151C2×C4—542no—
1152C2×C4—542no—
1153C2×C4—542no—
1154C2×C4D3311yescharacteristic
1155C2×C3—21no—
1156C2×C3—21no—
1157C2×C3—21no—
1158C2×C3—21no—
1159C2×C3—21no—
1160C2×C3—21no—
1161C2×C3—21no—
1162C2×C3—21no—
1163C2×C3—21no—
1164C2×C3—41no—
1165C2×C3—41no—
1166C2×C3—41no—
1167C2×C3—62no—
1168C2×C3—62no—
1169C2×C3—122no—
1170C2×C3—121no—
1171C2×C3—121no—
1172C2×C3—182no—
1173C2×C3—241no—
1174C2×C3—361no—
1175C2×C3C2×D3×D1211yescharacteristic
1176C2×C3C2×D3×D1211yescharacteristic
1177C2×C3D3×#23511yescharacteristic
1178C2×C3#6430611yescharacteristic
1179C2×C3D32×D411yescharacteristic
1180C2×C3D3×#23711yescharacteristic
1181C2×C3#6431211yescharacteristic
1182C2×C3#6431911yescharacteristic
1183C2×C3C2×#380411yescharacteristic
1184D3—22no—
1185D3—41no—
1186D3—62no—
1187D3—62no—
1188D3—122no—
1189D3—122no—
1190D3—121no—
1191D3—121no—
1192D3—182no—
1193D3—182no—
1194D3—182no—
1195D3—362no—
1196D3—362no—
1197D3—362no—
1198D3—722no—
1199C22—32no—
1200C22—61no—
1201C22—61no—
1202C22—61no—
1203C22—61no—
1204C22—61no—
1205C22—92no—
1206C22—181no—
1207C22—181no—
1208C22—181no—
1209C22—181no—
1210C22—181no—
1211C22—272no—
1212C22—548no—
1213C22—541no—
1214C22—541no—
1215C22C2×D3311yescharacteristic
1216C4—21no—
1217C4—32no—
1218C4—32no—
1219C4—61no—
1220C4—61no—
1221C4—181no—
1222C4—181no—
1223C4—181no—
1224C4—181no—
1225C4—541no—
1226C3—21no—
1227C3—21no—
1228C3—21no—
1229C3—41no—
1230C3#1059399711yescharacteristic, complemented
1231C3#1059462611yescharacteristic, complemented
1232C3#1059513811yescharacteristic, complemented
1233C2—62no—
1234C2—121no—
1235C2—182no—
1236C2—361no—
1237C2—542no—
1238C2#1172437611yescharacteristic
1239C2D32×D1211yescharacteristic
1240C2D3×#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×#88960C2semidirect
2. C2×D3×#624C2semidirect
3. #11723690C2semidirect
4. #11723540C2semidirect
5. #11723485C2semidirect
6. #11723471C2semidirect
7. C3×Dic3×D12C2semidirect
8. C3×#63886C2semidirect
9. C3×#63836C2semidirect
10. #11722998C2semidirect
11. #11722971C2semidirect
12. #11722963C2semidirect
13. #11722950C2semidirect
14. #11722932C2semidirect
15. Dic3×#626C2semidirect
23. C2×#6293C22semidirect
29. C2×Dic3×C3⋊D3C22semidirect
31. C2×C3×#626C22semidirect
35. C2×C3×D3×Dic3C22semidirect
40. C3×#3752C22semidirect
41. C3×C4⋊(C3⋊Dic3)C22semidirect
42. C32×Dic3⋊C4C22semidirect
43. C32×C4×Dic3C22semidirect
44. #88815C22semidirect
45. #88814C22semidirect
46. Dic3⋊(C3⋊Dic3)C22semidirect
47. Dic3⋊(C3⋊Dic3)C22semidirect
50. C3×Dic3⋊Dic3C22semidirect
53. C3×(C2×D3)⋊Dic3C22semidirect
54. C3×(C2×D3)⋊Dic3C22semidirect
55. C3×Dic32C22semidirect
91. Dic3×D12D3semidirect
96. #63886D3semidirect
103. #63836D3semidirect
134. C3×#624D4semidirect
180. C2×#626C2×D3semidirect
202. C2×D3×Dic3C2×D3semidirect
219. #3752C2×D3semidirect
222. C4⋊(C3⋊Dic3)C2×D3semidirect
243. C3×Dic3⋊C4C2×D3semidirect
244. C3×Dic3⋊C4C2×D3semidirect
248. C3×C4×Dic3C2×D3semidirect
249. C3×C4×Dic3C2×D3semidirect
259. Dic3⋊Dic3C2×D3semidirect
271. (C2×D3)⋊Dic3C2×D3semidirect
272. (C2×D3)⋊Dic3C2×D3semidirect
273. Dic32C2×D3semidirect
277. C2×C3⋊(C3⋊D3)#41semidirect
289. C2×C32×D3#41semidirect
477. #624D12semidirect
624. Dic3⋊C4D32semidirect
627. C4×Dic3D32semidirect
703. C2×C3×D3#235semidirect
704. C2×C3×D3#237semidirect
769. C33#525semidirect
1067. C2×D3#3804semidirect
1118. C32#5524semidirect
1119. C32#5547semidirect
1120. C32#5606semidirect
1230. C3#10593997semidirect
1231. C3#10594626semidirect
1232. C3#10595138semidirect

Maximal subgroups

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

subgroupindex
C2×#889602
C2×D3×#6242
#117236902
#117235402
#117234852
#117234712
C3×Dic3×D122
C3×#638862
C3×#638362
#117229982
#117229712
#117229632
#117229502
#117229322
Dic3×#6262
#105951383
#105946263
#105939973