Finite Group Databasebeta

← #13170742

Subgroups — #13170742

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#11723687C211yesmaximal, characteristic, complemented
4#11723541C211yesmaximal, characteristic, complemented
5#11723495C211yesmaximal, characteristic, complemented
6#11723471C211yesmaximal, characteristic, complemented
7C3×#63894C211yesmaximal, characteristic, complemented
8C3×#63890C211yesmaximal, characteristic, complemented
9C3×#63877C211yesmaximal, characteristic, complemented
10#11722988C211yesmaximal, characteristic, complemented
11#11722984C211yesmaximal, characteristic, complemented
12#11722968C211yesmaximal, characteristic, complemented
13#11722950C211yesmaximal, characteristic, complemented
14#11722934C211yesmaximal, characteristic, complemented
15#11722933C211yesmaximal, characteristic, complemented
16#10594614—31nomaximal
17#10594079—31nomaximal
18#10593997—31nomaximal
19C22×D3×C3⋊D3C2211yescharacteristic
20C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
21C2×#6295C2211yescharacteristic
22C2×#6295C2211yescharacteristic, complemented
23C2×#6294C2211yescharacteristic
24C2×#6293C2211yescharacteristic, complemented
25C2×#6292C2211yescharacteristic
26C2×#6292C2211yescharacteristic
27C2×#6290C2211yescharacteristic
28C2×#6289C2211yescharacteristic
29C2×#6289C2211yescharacteristic
30C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
31C2×C3×#626C2211yescharacteristic
32C2×C3×#624C2211yescharacteristic
33C2×C3×#624C2211yescharacteristic, complemented
34C2×C3×D3×Dic3C2211yescharacteristic
35C2×C3×D3×Dic3C2211yescharacteristic
36#88960—24no—
37D3×#624—24no—
38#88859C2211yescharacteristic
39C3×#3752C2211yescharacteristic, complemented
40C3×#3750C2211yescharacteristic, complemented
41C32×(C2×D3)⋊C4C2211yescharacteristic
42C32×C4⋊Dic3C2211yescharacteristic, complemented
43C32×C4×Dic3C2211yescharacteristic, complemented
44#88814C2211yescharacteristic, complemented
45#88807C2211yescharacteristic, complemented
46Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
47#88804C2211yescharacteristic
48#88803C2211yescharacteristic
49C3×#3724C2211yescharacteristic, complemented
50C3×Dic3⋊Dic3C2211yescharacteristic, complemented
51C3×#3722C2211yescharacteristic
52C3×#3722C2211yescharacteristic, complemented
53C3×#3722C2211yescharacteristic, complemented
54C3×(C2×D3)⋊Dic3C2211yescharacteristic
55C3×Dic32C2211yescharacteristic, complemented
56C22×#624—31no—
57C2×#3804—31no—
58C2×C4×D32—31no—
59C2×C4×D32—31no—
60C2×#3798—31no—
61C2×#3795—31no—
62#64105—31no—
63#64091—31no—
64C4×C4⋊(C3⋊D3)—31no—
65C3×#894—31no—
66C3×#893—31no—
67C3×#886—31no—
68C3×#877—31no—
69C3×C4×D12—31no—
70C3×#872—31no—
71#63981—31no—
72#63966—31no—
73#63923—31no—
74#63922—31no—
75#63922—31no—
76#63922—31no—
77#63922—61no—
78#63912—31no—
79#63910—31no—
80#63910—31no—
81#63910—31no—
82#63905—31no—
83#63904—31no—
84C4×#626—31no—
85C4×#626—31no—
86#63896—31no—
87#63895—31no—
88#63895—31no—
89#63895—31no—
90#63895—61no—
91#63894—31no—
92#63894D311yescharacteristic, complemented
93#63893—31no—
94#63891—31no—
95#63890D311yescharacteristic, complemented
96#63886—31no—
97#63885—31no—
98#63880—31no—
99#63880—31no—
100#63880—31no—
101#63880—61no—
102#63879—31no—
103#63877D311yescharacteristic, complemented
104C22×C3⋊(C3⋊D3)C2311yescharacteristic
105C22×C3×C3⋊D3C2311yescharacteristic
106C22×C3×C3⋊D3C2311yescharacteristic
107C22×C3×C3⋊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
117C3×C4⋊(C3⋊D3)—22no—
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123#6295—22no—
124#6295—22no—
125#6294—22no—
126#6293—22no—
127#6292—22no—
128#6292—22no—
129#6290—22no—
130#6289—22no—
131#6289—22no—
132Dic3×C3⋊D3—22no—
133C3×#626—22no—
134C3×#624—22no—
135C3×#624—22no—
136C3×D3×Dic3—22no—
137C3×D3×Dic3D414yescomplemented
138#5656—91no—
139#5547—91no—
140#5524—91no—
141C23×C3⋊D3—31no—
142C22×D32—31no—
143C22×D32—31no—
144C22×D32—61no—
145C2×#638—31no—
146C2×C4⋊(C3⋊D3)—31no—
147C2×C4⋊(C3⋊D3)—31no—
148C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
149C2×C4×C3⋊D3—31no—
150C2×C4×C3⋊D3—31no—
151C2×C4×C3⋊D3—31no—
152C2×#634—31no—
153C2×C3×#67—31no—
154C22×C3×Dic3—31no—
155C22×C3×Dic3—31no—
156C2×C3×D12—31no—
157C2×C3×D12—31no—
158C2×C3×D12—31no—
159C2×C3×D12—61no—
160C2×C3×C4×D3—31no—
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×#627—31no—
167C2×#627—31no—
168C2×#627—61no—
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×#626C2×D311yescharacteristic
180C2×#625—31no—
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
194C2×#624C2×D311yescharacteristic, complemented
195#3804—64no—
196C2×D3×Dic3—31no—
197C2×D3×Dic3—31no—
198C2×D3×Dic3—31no—
199C2×D3×Dic3—31no—
200C2×D3×Dic3—61no—
201C2×D3×Dic3C2×D311yescharacteristic
202C2×D3×Dic3C2×D311yescharacteristic
203C4×D32—64no—
204C4×D32—64no—
205#3798—64no—
206#3795—64no—
207C32×C4⋊C4—31no—
208C32×C22⋊C4—31no—
209C32×C42—31no—
210#3752—31no—
211#3752—31no—
212#3752—31no—
213#3752—31no—
214#3752—31no—
215#3752—61no—
216#3752—61no—
217#3752—61no—
218#3752—121no—
219#3752C2×D311yescharacteristic, complemented
220C4⋊(C3⋊Dic3)—31no—
221#3750—31no—
222#3750C2×D311yescharacteristic, complemented
223C3×#217—31no—
224C3×(C2×D3)⋊C4—21no—
225C3×(C2×D3)⋊C4—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—61no—
235C3×(C2×D3)⋊C4C2×D311yescharacteristic
236C3×(C2×D3)⋊C4C2×D311yescharacteristic
237C3×C4⋊Dic3—21no—
238C3×C4⋊Dic3—31no—
239C3×C4⋊Dic3C2×D311yescharacteristic, complemented
240C3×C4⋊Dic3C2×D311yescharacteristic, complemented
241C3×Dic3⋊C4—31no—
242C3×Dic3⋊C4—31no—
243C3×Dic3⋊C4—31no—
244C3×Dic3⋊C4—31no—
245C3×Dic3⋊C4—31no—
246C3×Dic3⋊C4—61no—
247C3×C4×Dic3—21no—
248C3×C4×Dic3—31no—
249C3×C4×Dic3—31no—
250C3×C4×Dic3C2×D311yescharacteristic, complemented
251C3×C4×Dic3C2×D311yescharacteristic, complemented
252#3724C2×D311yescharacteristic, complemented
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#3722C2×D311yescharacteristic, complemented
266#3722C2×D311yescharacteristic, complemented
267(C2×D3)⋊Dic3—31no—
268(C2×D3)⋊Dic3—31no—
269(C2×D3)⋊Dic3—31no—
270(C2×D3)⋊Dic3—31no—
271(C2×D3)⋊Dic3—61no—
272(C2×D3)⋊Dic3C2×D311yescharacteristic
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⋊D3—21no—
284C2×C3×C3⋊D3—21no—
285C2×C3×C3⋊D3—21no—
286C2×C3×C3⋊D3#4112yescomplemented
287C2×C32×D3—21no—
288C2×C32×D3—21no—
289C2×C32×D3C2×D412yes—
290D3×C3⋊D3—28no—
291C33×C4—21no—
292C3⋊(C3⋊Dic3)—21no—
293C3×C3⋊Dic3—21no—
294C3×C3⋊Dic3—21no—
295C3×C3⋊Dic3C2×D412yes—
296C32×Dic3—21no—
297C32×Dic3—21no—
298C32×Dic3—21no—
299C32×Dic3—21no—
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×#123—91no—
308C3×C4×D4—91no—
309C3×#117—91no—
310#939—91no—
311#937—91no—
312#937—91no—
313#929—91no—
314C4×#67—91no—
315C4×#67—91no—
316#897—91no—
317#897—91no—
318#896—91no—
319#896—91no—
320#896—91no—
321#896—181no—
322#895—91no—
323#895—91no—
324#894—31no—
325#893—31no—
326#893—91no—
327#886—31no—
328#886—91no—
329#884—91no—
330#884—91no—
331#884—91no—
332#883—91no—
333#882—91no—
334#882—91no—
335#882—91no—
336#882—91no—
337#882—181no—
338#67⋊C4—91no—
339#67⋊C4—91no—
340#878—91no—
341#877—31no—
342C4×D12—31no—
343C4×D12—91no—
344C4×D12—91no—
345C4×D12—91no—
346C4×D12—91no—
347C4×D12—181no—
348#872—31no—
349C23×C32—31no—
350C22×C3⋊D3—31no—
351C22×C3⋊D3—31no—
352C22×C3⋊D3—31no—
353C22×C3⋊D3—61no—
354C22×C3⋊D3—61no—
355C22×C3⋊D3—61no—
356C22×C3⋊D3—62no—
357C22×C3⋊D3—62no—
358C22×C3⋊D3—62no—
359C22×C3⋊D3—121no—
360C22×C3⋊D3C22×D311yescharacteristic
361C22×C3⋊D3C22×D311yescharacteristic
362C22×C3⋊D3C22×D311yescharacteristic
363C22×C3×D3—21no—
364C22×C3×D3—31no—
365C22×C3×D3—31no—
366C22×C3×D3—31no—
367C22×C3×D3—31no—
368C22×C3×D3—31no—
369C22×C3×D3—31no—
370C22×C3×D3—61no—
371C22×C3×D3—61no—
372C22×C3×D3—61no—
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—
384C2×C32×C4—21no—
385C2×C32×C4—21no—
386C2×C32×C4—21no—
387C2×C32×C4—31no—
388C2×C32×C4—31no—
389C2×C32×C4—31no—
390C2×C32×C4—31no—
391C2×C32×C4—31no—
392C2×C32×C4—41no—
393C2×C32×C4C22×D311yescharacteristic
394C2×C32×C4C22×D311yescharacteristic
395C2×C32×C4C22×D311yescharacteristic
396#638—62no—
397C2×C3⋊Dic3—31no—
398C2×C3⋊Dic3—31no—
399C2×C3⋊Dic3—31no—
400C2×C3⋊Dic3—61no—
401C2×C3⋊Dic3—61no—
402C2×C3⋊Dic3—61no—
403C2×C3⋊Dic3—121no—
404C2×C3⋊Dic3C22×D311yescharacteristic
405C2×C3⋊Dic3C22×D311yescharacteristic
406C2×C3⋊Dic3C22×D311yescharacteristic
407C4⋊(C3⋊D3)—22no—
408C4⋊(C3⋊D3)—62no—
409C4⋊(C3⋊D3)—62no—
410C4×C3⋊D3—62no—
411C4×C3⋊D3—62no—
412C4×C3⋊D3—62no—
413#634—62no—
414C3×#67—62no—
415C2×C3×Dic3—21no—
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—34no—
423C2×C3×Dic3—31no—
424C2×C3×Dic3—31no—
425C2×C3×Dic3—31no—
426C2×C3×Dic3—31no—
427C2×C3×Dic3—61no—
428C2×C3×Dic3—61no—
429C2×C3×Dic3—61no—
430C2×C3×Dic3—62no—
431C2×C3×Dic3C22×D311yescharacteristic
432C2×C3×Dic3C22×D311yescharacteristic
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—62no—
442C3×D12—62no—
443C3×D12—62no—
444C3×D12—122no—
445C3×C4×D3—34no—
446C3×C4×D3—62no—
447C3×C4×D3—62no—
448C3×C4×D3—62no—
449C3×C4×D3—62no—
450C3×C4×D3—62no—
451#627—62no—
452#627—62no—
453#627—122no—
454#626—22no—
455#626—62no—
456#626—62no—
457#626—62no—
458#626—62no—
459#626—64no—
460#626—62no—
461#626—62no—
462#626—62no—
463#626—62no—
464#626—122no—
465#625—62no—
466#625—62no—
467#625—62no—
468#625—62no—
469#625—122no—
470#624—22no—
471#624—22no—
472#624—62no—
473#624—62no—
474#624—62no—
475#624—62no—
476#624—62no—
477#624—122no—
478#624—122no—
479D3×Dic3—22no—
480D3×Dic3—62no—
481D3×Dic3—62no—
482D3×Dic3—62no—
483D3×Dic3—62no—
484D3×Dic3—122no—
485D3×Dic3D1214yescomplemented
486#525—271noSylow
487C2×C33C22×D411yescharacteristic
488C2×C33C2×#4111yescharacteristic
489C2×C33C2×#4111yescharacteristic
490C3⋊(C3⋊D3)—22no—
491C3×C3⋊D3—22no—
492C3×C3⋊D3—41no—
493C3×C3⋊D3—41no—
494C32×D3—22no—
495C23×D3—91no—
496C23×D3—91no—
497C23×D3—91no—
498C23×D3—181no—
499C2×C3×D4—91no—
500C2×C3×D4—91no—
501C22×C3×C4—91no—
502C22×C3×C4—91no—
503C22×C3×C4—91no—
504C22×C3×C4—91no—
505C2×#67—31no—
506C2×#67—91no—
507C2×#67—91no—
508C2×#67—91no—
509C2×#67—91no—
510C2×#67—91no—
511C2×#67—91no—
512C2×#67—91no—
513C2×#67—91no—
514C2×#67—91no—
515C2×#67—181no—
516C22×Dic3—31no—
517C22×Dic3—31no—
518C22×Dic3—91no—
519C22×Dic3—91no—
520#237—184no—
521#235—184no—
522#235—184no—
523C2×D12—31no—
524C2×D12—31no—
525C2×D12—31no—
526C2×D12—61no—
527C2×D12—91no—
528C2×D12—91no—
529C2×D12—91no—
530C2×D12—91no—
531C2×D12—91no—
532C2×D12—91no—
533C2×D12—181no—
534C2×D12—181no—
535C2×C4×D3—31no—
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×C4⋊C4—91no—
567C3×C22⋊C4—31no—
568C3×C22⋊C4—31no—
569C3×C22⋊C4—61no—
570C3×C22⋊C4—91no—
571C3×C22⋊C4—91no—
572C3×C22⋊C4—91no—
573C3×C22⋊C4—91no—
574C3×C22⋊C4—91no—
575C3×C42—31no—
576C3×C42—31no—
577C3×C42—61no—
578C3×C42—91no—
579#217—31no—
580#217—91no—
581#217—91no—
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—31no—
588(C2×D3)⋊C4—31no—
589(C2×D3)⋊C4—31no—
590(C2×D3)⋊C4—31no—
591(C2×D3)⋊C4—61no—
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—91no—
599(C2×D3)⋊C4—91no—
600(C2×D3)⋊C4—91no—
601(C2×D3)⋊C4—91no—
602(C2×D3)⋊C4—181no—
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—
608(C2×D3)⋊C4D3211yescharacteristic
609C4⋊Dic3—31no—
610C4⋊Dic3—91no—
611C4⋊Dic3—91no—
612C4⋊Dic3—91no—
613C4⋊Dic3—181no—
614C4⋊Dic3D3211yescharacteristic, complemented
615Dic3⋊C4—31no—
616Dic3⋊C4—31no—
617Dic3⋊C4—31no—
618Dic3⋊C4—31no—
619Dic3⋊C4—31no—
620Dic3⋊C4—61no—
621Dic3⋊C4—91no—
622Dic3⋊C4—91no—
623Dic3⋊C4—91no—
624Dic3⋊C4—181no—
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×C32C23×D311yescharacteristic
636C22×C32C23×D311yescharacteristic
637C22×C32C23×D311yescharacteristic
638C2×C3⋊D3—21no—
639C2×C3⋊D3—21no—
640C2×C3⋊D3—21no—
641C2×C3⋊D3—21no—
642C2×C3⋊D3—21no—
643C2×C3⋊D3—21no—
644C2×C3⋊D3—21no—
645C2×C3⋊D3—21no—
646C2×C3⋊D3—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⋊D3#23512yescomplemented
669C2×C3×D3—21no—
670C2×C3×D3—21no—
671C2×C3×D3—21no—
672C2×C3×D3—21no—
673C2×C3×D3—22no—
674C2×C3×D3—32no—
675C2×C3×D3—32no—
676C2×C3×D3—41no—
677C2×C3×D3—41no—
678C2×C3×D3—62no—
679C2×C3×D3—61no—
680C2×C3×D3—61no—
681C2×C3×D3—61no—
682C2×C3×D3—61no—
683C2×C3×D3—62no—
684C2×C3×D3—61no—
685C2×C3×D3—61no—
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—121no—
702C2×C3×D3—121no—
703C2×C3×D3C2×D1212yes—
704C2×C3×D3D3×D412yes—
705D32—68no—
706D32—68no—
707D32—128no—
708C32×C4—21no—
709C32×C4—21no—
710C32×C4—21no—
711C32×C4—32no—
712C32×C4—41no—
713C32×C4—41no—
714C32×C4—41no—
715C32×C4—61no—
716C32×C4—61no—
717C32×C4—61no—
718C32×C4—61no—
719C32×C4—81no—
720C3⋊Dic3—21no—
721C3⋊Dic3—21no—
722C3⋊Dic3—61no—
723C3⋊Dic3—61no—
724C3⋊Dic3—61no—
725C3⋊Dic3—121no—
726C3⋊Dic3—121no—
727C3⋊Dic3—121no—
728C3⋊Dic3—241no—
729C3⋊Dic3C2×D1212yes—
730C3×Dic3—22no—
731C3×Dic3—21no—
732C3×Dic3—21no—
733C3×Dic3—21no—
734C3×Dic3—21no—
735C3×Dic3—21no—
736C3×Dic3—21no—
737C3×Dic3—21no—
738C3×Dic3—21no—
739C3×Dic3—22no—
740C3×Dic3—32no—
741C3×Dic3—32no—
742C3×Dic3—41no—
743C3×Dic3—41no—
744C3×Dic3—41no—
745C3×Dic3—62no—
746C3×Dic3—61no—
747C3×Dic3—61no—
748C3×Dic3—61no—
749C3×Dic3—61no—
750C3×Dic3—121no—
751C3×Dic3—121no—
752C3×Dic3C2×D1212yes—
753C3×Dic3D3×D412yes—
754C2×#41—271no—
755C23×C4—271no—
756#123—91no—
757#123—271no—
758C22⋊Q8—271no—
759C22⋊Q8—271no—
760#121—271no—
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—61no—
773C23×C3—91no—
774C23×C3—91no—
775C23×C3—91no—
776C22×D3—31no—
777C22×D3—31no—
778C22×D3—31no—
779C22×D3—31no—
780C22×D3—31no—
781C22×D3—31no—
782C22×D3—61no—
783C22×D3—61no—
784C22×D3—61no—
785C22×D3—91no—
786C22×D3—91no—
787C22×D3—91no—
788C22×D3—181no—
789C22×D3—181no—
790C22×D3—181no—
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—182no—
800C22×D3—361no—
801C22×D3—362no—
802C22×D3—362no—
803C22×D3—362no—
804C22×D3C2×D3211yescharacteristic
805C3×D4—182no—
806C3×D4—182no—
807C2×C3×C4—21no—
808C2×C3×C4—21no—
809C2×C3×C4—21no—
810C2×C3×C4—31no—
811C2×C3×C4—31no—
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—61no—
826C2×C3×C4—94no—
827C2×C3×C4—91no—
828C2×C3×C4—91no—
829C2×C3×C4—91no—
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—182no—
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—
847C2×Dic3—31no—
848C2×Dic3—31no—
849C2×Dic3—34no—
850C2×Dic3—31no—
851C2×Dic3—31no—
852C2×Dic3—31no—
853C2×Dic3—31no—
854C2×Dic3—61no—
855C2×Dic3—61no—
856C2×Dic3—61no—
857C2×Dic3—62no—
858C2×Dic3—91no—
859C2×Dic3—91no—
860C2×Dic3—91no—
861C2×Dic3—181no—
862C2×Dic3—181no—
863C2×Dic3—181no—
864C2×Dic3—182no—
865C2×Dic3—182no—
866C2×Dic3—361no—
867C2×Dic3C2×D3211yescharacteristic
868C2×Dic3C2×D3211yescharacteristic
869C2×Dic3C2×D3211yescharacteristic
870C2×Dic3C2×D3211yescharacteristic
871C2×Dic3C2×D3211yescharacteristic
872D12—62no—
873D12—62no—
874D12—62no—
875D12—122no—
876D12—182no—
877D12—182no—
878D12—182no—
879D12—182no—
880D12—184no—
881D12—182no—
882D12—182no—
883D12—362no—
884C4×D3—34no—
885C4×D3—62no—
886C4×D3—62no—
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×C32C22×D1211yescharacteristic
921C2×C32C2×#23511yescharacteristic
922C2×C32C2×D3×D411yescharacteristic
923C2×C32C2×D3×D411yescharacteristic
924C2×C32D3×#4111yescharacteristic
925C2×C32D3×#4111yescharacteristic
926C2×C32D3×#4111yescharacteristic
927C2×C32D3×#4111yescharacteristic
928C2×C32D3×#4111yescharacteristic
929C3⋊D3—22no—
930C3⋊D3—41no—
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—62no—
943C3×D3—62no—
944C3×D3—122no—
945C3×D3—122no—
946C3×D3—121no—
947C3×D3—121no—
948C3×D3—121no—
949C3×D3—121no—
950C3×D3—241no—
951C24—271no—
952#41—544no—
953C2×Q8—271no—
954C2×D4—91no—
955C2×D4—91no—
956C2×D4—271no—
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—91no—
974C4⋊C4—271no—
975C4⋊C4—271no—
976C22⋊C4—31no—
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—92no—
1000C22×C3—121no—
1001C22×C3—121no—
1002C22×C3—181no—
1003C22×C3—181no—
1004C22×C3—181no—
1005C22×C3—181no—
1006C22×C3—181no—
1007C22×C3—181no—
1008C22×C3—181no—
1009C22×C3—181no—
1010C22×C3C22×D3211yescharacteristic
1011C22×C3C22×D3211yescharacteristic
1012C22×C3C22×D3211yescharacteristic
1013C2×D3—21no—
1014C2×D3—21no—
1015C2×D3—32no—
1016C2×D3—32no—
1017C2×D3—62no—
1018C2×D3—61no—
1019C2×D3—61no—
1020C2×D3—61no—
1021C2×D3—61no—
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—61no—
1034C2×D3—61no—
1035C2×D3—92no—
1036C2×D3—92no—
1037C2×D3—92no—
1038C2×D3—121no—
1039C2×D3—121no—
1040C2×D3—121no—
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×D3D3×D1212yes—
1068C3×C4—21no—
1069C3×C4—21no—
1070C3×C4—21no—
1071C3×C4—32no—
1072C3×C4—32no—
1073C3×C4—41no—
1074C3×C4—41no—
1075C3×C4—41no—
1076C3×C4—62no—
1077C3×C4—62no—
1078C3×C4—61no—
1079C3×C4—61no—
1080C3×C4—61no—
1081C3×C4—61no—
1082C3×C4—61no—
1083C3×C4—61no—
1084C3×C4—61no—
1085C3×C4—61no—
1086C3×C4—81no—
1087C3×C4—92no—
1088C3×C4—121no—
1089C3×C4—121no—
1090C3×C4—121no—
1091C3×C4—181no—
1092C3×C4—181no—
1093Dic3—21no—
1094Dic3—21no—
1095Dic3—21no—
1096Dic3—21no—
1097Dic3—32no—
1098Dic3—32no—
1099Dic3—62no—
1100Dic3—61no—
1101Dic3—61no—
1102Dic3—61no—
1103Dic3—61no—
1104Dic3—121no—
1105Dic3—121no—
1106Dic3—181no—
1107Dic3—181no—
1108Dic3—181no—
1109Dic3—361no—
1110Dic3—361no—
1111Dic3—361no—
1112Dic3—721no—
1113Dic3D3×D1212yes—
1114C32—21no—
1115C32—21no—
1116C32—21no—
1117C32—41no—
1118C32#552411yescharacteristic, complemented
1119C32#554711yescharacteristic, complemented
1120C32#565611yescharacteristic, complemented
1121C23—31no—
1122C23—91no—
1123C23—91no—
1124C23—91no—
1125C23—271no—
1126C23—542no—
1127C23—542no—
1128C23—542no—
1129Q8—542no—
1130D4—182no—
1131D4—182no—
1132D4—542no—
1133D4—542no—
1134D4—542no—
1135D4—542no—
1136D4—542no—
1137C2×C4—31no—
1138C2×C4—31no—
1139C2×C4—31no—
1140C2×C4—31no—
1141C2×C4—31no—
1142C2×C4—94no—
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—182no—
1171C2×C3—361no—
1172C2×C3—361no—
1173C2×C3C2×D3×D1211yescharacteristic
1174C2×C3C2×D3×D1211yescharacteristic
1175C2×C3D3×#23511yescharacteristic
1176C2×C3D3×#23511yescharacteristic
1177C2×C3#6430611yescharacteristic
1178C2×C3D32×D411yescharacteristic
1179C2×C3#6431211yescharacteristic
1180C2×C3#6431211yescharacteristic
1181C2×C3#6431911yescharacteristic
1182D3—22no—
1183D3—62no—
1184D3—62no—
1185D3—122no—
1186D3—122no—
1187D3—121no—
1188D3—121no—
1189D3—121no—
1190D3—121no—
1191D3—182no—
1192D3—182no—
1193D3—182no—
1194D3—241no—
1195D3—362no—
1196D3—362no—
1197D3—362no—
1198D3—722no—
1199C22—32no—
1200C22—61no—
1201C22—61no—
1202C22—92no—
1203C22—181no—
1204C22—181no—
1205C22—181no—
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—61no—
1219C4—61no—
1220C4—61no—
1221C4—61no—
1222C4—92no—
1223C4—181no—
1224C4—181no—
1225C4—541no—
1226C3—21no—
1227C3—21no—
1228C3—21no—
1229C3—41no—
1230C3#1059399711yescharacteristic, complemented
1231C3#1059407911yescharacteristic, complemented
1232C3#1059461411yescharacteristic, complemented
1233C2—62no—
1234C2—182no—
1235C2—361no—
1236C2—361no—
1237C2—542no—
1238C2#1172437611yescharacteristic
1239C2D32×D1211yescharacteristic
1240C2#1172441011yescharacteristic
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. #11723687C2semidirect
4. #11723541C2semidirect
5. #11723495C2semidirect
6. #11723471C2semidirect
7. C3×#63894C2semidirect
8. C3×#63890C2semidirect
9. C3×#63877C2semidirect
10. #11722988C2semidirect
11. #11722984C2semidirect
12. #11722968C2semidirect
13. #11722950C2semidirect
14. #11722934C2semidirect
15. #11722933C2semidirect
22. C2×#6295C22semidirect
24. C2×#6293C22semidirect
30. C2×Dic3×C3⋊D3C22semidirect
33. C2×C3×#624C22semidirect
39. C3×#3752C22semidirect
40. C3×#3750C22semidirect
42. C32×C4⋊Dic3C22semidirect
43. C32×C4×Dic3C22semidirect
44. #88814C22semidirect
45. #88807C22semidirect
46. Dic3⋊(C3⋊Dic3)C22semidirect
49. C3×#3724C22semidirect
50. C3×Dic3⋊Dic3C22semidirect
52. C3×#3722C22semidirect
53. C3×#3722C22semidirect
55. C3×Dic32C22semidirect
92. #63894D3semidirect
95. #63890D3semidirect
103. #63877D3semidirect
137. C3×D3×Dic3D4semidirect
194. C2×#624C2×D3semidirect
219. #3752C2×D3semidirect
222. #3750C2×D3semidirect
239. C3×C4⋊Dic3C2×D3semidirect
240. C3×C4⋊Dic3C2×D3semidirect
250. C3×C4×Dic3C2×D3semidirect
251. C3×C4×Dic3C2×D3semidirect
252. #3724C2×D3semidirect
259. Dic3⋊Dic3C2×D3semidirect
265. #3722C2×D3semidirect
266. #3722C2×D3semidirect
273. Dic32C2×D3semidirect
277. C2×C3⋊(C3⋊D3)#41semidirect
286. C2×C3×C3⋊D3#41semidirect
485. D3×Dic3D12semidirect
614. C4⋊Dic3D32semidirect
627. C4×Dic3D32semidirect
668. C2×C3⋊D3#235semidirect
769. C33#525semidirect
1118. C32#5524semidirect
1119. C32#5547semidirect
1120. C32#5656semidirect
1230. C3#10593997semidirect
1231. C3#10594079semidirect
1232. C3#10594614semidirect

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
#117236872
#117235412
#117234952
#117234712
C3×#638942
C3×#638902
C3×#638772
#117229882
#117229842
#117229682
#117229502
#117229342
#117229332
#105946143
#105940793
#105939973