Finite Group Databasebeta

← #13170787

Subgroups — #13170787

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×#88965C211yesmaximal, characteristic, complemented
2C2×D3×#624C211yesmaximal, characteristic, complemented
3#11723687C211yesmaximal, characteristic, complemented
4#11723541C211yesmaximal, characteristic, complemented
5#11723504C211yesmaximal, characteristic, complemented
6#11723468C211yesmaximal, characteristic, complemented
7C3×#63899C211yesmaximal, characteristic, complemented
8C3×#63894C211yesmaximal, characteristic, complemented
9C3×#63880C211yesmaximal, characteristic, complemented
10#11723000C211yesmaximal, characteristic, complemented
11#11722979C211yesmaximal, characteristic, complemented
12#11722960C211yesmaximal, characteristic, complemented
13#11722950C211yesmaximal, characteristic, complemented
14#11722931C211yesmaximal, characteristic, complemented
15#11722930C211yesmaximal, characteristic, complemented
16#10594623—31nomaximal
17#10594066—31nomaximal
18#10594006—31nomaximal
19C22×D3×C3⋊D3C2211yescharacteristic
20C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
21C2×#6295C2211yescharacteristic
22C2×#6295C2211yescharacteristic, complemented
23C2×#6294C2211yescharacteristic
24C2×#6292C2211yescharacteristic
25C2×#6292C2211yescharacteristic
26C2×#6290C2211yescharacteristic
27C2×#6289C2211yescharacteristic
28C2×#6289C2211yescharacteristic
29C2×C3×#627C2211yescharacteristic, complemented
30C2×C3×#626C2211yescharacteristic
31C2×C3×#624C2211yescharacteristic
32C2×C3×#624C2211yescharacteristic, complemented
33C2×C3×#624C2211yescharacteristic, complemented
34C2×C3×D3×Dic3C2211yescharacteristic
35C2×C3×D3×Dic3C2211yescharacteristic
36#88965—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
46#88806C2211yescharacteristic, complemented
47#88804C2211yescharacteristic
48#88803C2211yescharacteristic
49#88803C2211yescharacteristic, complemented
50Dic3×C3⋊Dic3C2211yescharacteristic, complemented
51C3×#3724C2211yescharacteristic, complemented
52C3×Dic3⋊Dic3C2211yescharacteristic, complemented
53C3×#3722C2211yescharacteristic
54C3×#3722C2211yescharacteristic, complemented
55C3×(C2×D3)⋊Dic3C2211yescharacteristic
56C22×#624—31no—
57C2×C4×D32—31no—
58C2×C4×D32—31no—
59C2×#3799—31no—
60C2×#3799—31no—
61C2×#3798—31no—
62#64103—31no—
63#64091—31no—
64#64081—31no—
65C3×#896—31no—
66C3×#893—31no—
67C3×#67⋊C4—31no—
68C3×#878—31no—
69C3×C4×D12—31no—
70C3×C4×D12—31no—
71#63981—31no—
72#63978—31no—
73#63952—31no—
74#63923—31no—
75#63922—31no—
76#63922—31no—
77#63922—31no—
78#63922—61no—
79#63910—31no—
80#63906—31no—
81#63904—31no—
82#63904—31no—
83C4×#625—31no—
84C4×#625—31no—
85#63899—31no—
86#63899D311yescharacteristic, complemented
87#63897—31no—
88#63894D311yescharacteristic, complemented
89#63888—31no—
90#63887—31no—
91#63886—31no—
92#63885—31no—
93#63885—31no—
94#63880D311yescharacteristic, complemented
95#63879—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×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#6292—22no—
127#6292—22no—
128#6290—22no—
129#6289—22no—
130#6289D414yescomplemented
131C3×#627—22no—
132C3×#626—22no—
133C3×#624—22no—
134C3×#624—22no—
135C3×#624—22no—
136C3×D3×Dic3—22no—
137C3×D3×Dic3—22no—
138#5627—91no—
139#5547—91no—
140#5547—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×C3×#67—31no—
152C22×C3×Dic3—31no—
153C22×C3×Dic3—31no—
154C2×C3×D12—31no—
155C2×C3×D12—31no—
156C2×C3×D12—31no—
157C2×C3×D12—61no—
158C2×C3×C4×D3—31no—
159C2×C3×C4×D3—31no—
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×C3×Dic6—31no—
167C2×C3×Dic6—31no—
168C2×#627C2×D311yescharacteristic, complemented
169C2×#626—31no—
170C2×#626—31no—
171C2×#626—31no—
172C2×#626—31no—
173C2×#626—31no—
174C2×#626—31no—
175C2×#626—31no—
176C2×#626—31no—
177C2×#626—61no—
178C2×#626—61no—
179C2×#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
195C2×#624C2×D311yescharacteristic, complemented
196C2×D3×Dic3—31no—
197C2×D3×Dic3—31no—
198C2×D3×Dic3C2×D311yescharacteristic
199C2×D3×Dic3C2×D311yescharacteristic
200C4×D32—64no—
201C4×D32—64no—
202#3799—64no—
203#3799—64no—
204#3798—64no—
205C32×C4⋊C4—31no—
206C32×C22⋊C4—31no—
207C32×C42—31no—
208#3752—31no—
209#3752—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, complemented
219#3750—31no—
220#3750—31no—
221#3750C2×D311yescharacteristic, complemented
222C4×C3⋊Dic3—31no—
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—61no—
233C3×(C2×D3)⋊C4C2×D311yescharacteristic
234C3×(C2×D3)⋊C4C2×D311yescharacteristic
235C3×C4⋊Dic3—21no—
236C3×C4⋊Dic3—31no—
237C3×C4⋊Dic3C2×D311yescharacteristic, complemented
238C3×C4⋊Dic3C2×D311yescharacteristic, complemented
239C3×Dic3⋊C4—31no—
240C3×Dic3⋊C4—31no—
241C3×Dic3⋊C4—31no—
242C3×Dic3⋊C4—31no—
243C3×Dic3⋊C4—31no—
244C3×Dic3⋊C4—61no—
245C3×C4×Dic3—21no—
246C3×C4×Dic3C2×D311yescharacteristic, complemented
247C3×C4×Dic3C2×D311yescharacteristic, complemented
248#3724—31no—
249#3724—31no—
250#3724—61no—
251#3724C2×D311yescharacteristic, complemented
252Dic3⋊Dic3—31no—
253Dic3⋊Dic3—31no—
254Dic3⋊Dic3—61no—
255Dic3⋊Dic3C2×D311yescharacteristic, complemented
256#3722—31no—
257#3722—31no—
258#3722—31no—
259#3722—61no—
260#3722C2×D311yescharacteristic
261#3722C2×D311yescharacteristic, complemented
262(C2×D3)⋊Dic3—31no—
263(C2×D3)⋊Dic3—31no—
264(C2×D3)⋊Dic3—31no—
265(C2×D3)⋊Dic3—31no—
266(C2×D3)⋊Dic3—31no—
267(C2×D3)⋊Dic3—31no—
268(C2×D3)⋊Dic3—61no—
269(C2×D3)⋊Dic3—61no—
270(C2×D3)⋊Dic3C2×D311yescharacteristic
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—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×D3#4112yescomplemented
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×#239—91no—
302C2×#235—91no—
303C2×#235—91no—
304C22×C4×D3—91no—
305C22×C4×D3—91no—
306C22×C4×D3—91no—
307C3×C22⋊Q8—91no—
308C3×C4×D4—91no—
309C3×C4×D4—91no—
310#946—91no—
311#939—91no—
312#939—91no—
313#937—91no—
314#937—91no—
315#930—91no—
316C4×#67—91no—
317C4×#67—91no—
318C4×#67—91no—
319C4×#67—91no—
320#896—31no—
321#896—91no—
322#895—91no—
323#894—91no—
324#894—91no—
325#894—91no—
326#894—91no—
327#894—181no—
328#893—31no—
329#893—91no—
330#892—91no—
331#884—91no—
332#884—91no—
333#883—91no—
334#883—91no—
335#882—91no—
336#882—91no—
337#882—91no—
338#882—91no—
339#882—181no—
340#67⋊C4—31no—
341#67⋊C4—91no—
342#878—31no—
343#878—91no—
344C4×D12—31no—
345C4×D12—31no—
346#872—91no—
347#872—91no—
348#872—181no—
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—34no—
411C4×C3⋊D3—62no—
412C3×#67—62no—
413C2×C3×Dic3—21no—
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—61no—
425C2×C3×Dic3—61no—
426C2×C3×Dic3—61no—
427C2×C3×Dic3—62no—
428C2×C3×Dic3—62no—
429C2×C3×Dic3C22×D311yescharacteristic
430C2×C3×Dic3C22×D311yescharacteristic
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
439C3×D12—62no—
440C3×D12—62no—
441C3×D12—62no—
442C3×D12—122no—
443C3×C4×D3—62no—
444C3×C4×D3—62no—
445C3×C4×D3—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—62no—
456#626—62no—
457#626—62no—
458#626—62no—
459#626—62no—
460#626—62no—
461#626—62no—
462#626—62no—
463#626—122no—
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—22no—
473#624—34no—
474#624—34no—
475#624—64no—
476#624—62no—
477#624—62no—
478#624—62no—
479#624—122no—
480D3×Dic3—22no—
481D3×Dic3—22no—
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—
491C3×C3⋊D3—41no—
492C32×D3—22no—
493C23×D3—91no—
494C23×D3—91no—
495C23×D3—91no—
496C23×D3—181no—
497C2×C3×Q8—91no—
498C2×C3×D4—91no—
499C2×C3×D4—91no—
500C22×C3×C4—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—
519#239—184no—
520#235—184no—
521#235—184no—
522C2×D12—31no—
523C2×D12—31no—
524C2×D12—31no—
525C2×D12—61no—
526C2×D12—91no—
527C2×D12—91no—
528C2×D12—91no—
529C2×D12—91no—
530C2×D12—91no—
531C2×D12—91no—
532C2×D12—181no—
533C2×D12—181no—
534C2×C4×D3—31no—
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—31no—
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—61no—
560C3×C4⋊C4—91no—
561C3×C4⋊C4—91no—
562C3×C4⋊C4—91no—
563C3×C22⋊C4—31no—
564C3×C22⋊C4—31no—
565C3×C22⋊C4—61no—
566C3×C22⋊C4—91no—
567C3×C22⋊C4—91no—
568C3×C22⋊C4—91no—
569C3×C22⋊C4—91no—
570C3×C42—31no—
571C3×C42—31no—
572C3×C42—61no—
573#217—31no—
574#217—91no—
575#217—91no—
576#217—91no—
577(C2×D3)⋊C4—31no—
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—61no—
585(C2×D3)⋊C4—91no—
586(C2×D3)⋊C4—91no—
587(C2×D3)⋊C4—91no—
588(C2×D3)⋊C4—91no—
589(C2×D3)⋊C4—91no—
590(C2×D3)⋊C4—91no—
591(C2×D3)⋊C4—91no—
592(C2×D3)⋊C4—91no—
593(C2×D3)⋊C4—91no—
594(C2×D3)⋊C4—91no—
595(C2×D3)⋊C4—91no—
596(C2×D3)⋊C4—91no—
597(C2×D3)⋊C4—181no—
598(C2×D3)⋊C4—181no—
599(C2×D3)⋊C4—181no—
600(C2×D3)⋊C4—181no—
601(C2×D3)⋊C4—181no—
602(C2×D3)⋊C4—181no—
603(C2×D3)⋊C4—361no—
604(C2×D3)⋊C4D3211yescharacteristic
605C4⋊Dic3—31no—
606C4⋊Dic3—91no—
607C4⋊Dic3D3211yescharacteristic, complemented
608Dic3⋊C4—31no—
609Dic3⋊C4—31no—
610Dic3⋊C4—31no—
611Dic3⋊C4—31no—
612Dic3⋊C4—31no—
613Dic3⋊C4—61no—
614Dic3⋊C4—91no—
615Dic3⋊C4—91no—
616Dic3⋊C4—91no—
617Dic3⋊C4—91no—
618Dic3⋊C4—91no—
619Dic3⋊C4—181no—
620Dic3⋊C4—181no—
621C4×Dic3—91no—
622C4×Dic3—91no—
623C4×Dic3—91no—
624C4×Dic3—181no—
625C4×Dic3D3211yescharacteristic, complemented
626C22×C32—21no—
627C22×C32—21no—
628C22×C32—21no—
629C22×C32—32no—
630C22×C32—41no—
631C22×C32—61no—
632C22×C32—61no—
633C22×C32C23×D311yescharacteristic
634C22×C32C23×D311yescharacteristic
635C22×C32C23×D311yescharacteristic
636C2×C3⋊D3—21no—
637C2×C3⋊D3—21no—
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—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#23512yescomplemented
667C2×C3×D3—21no—
668C2×C3×D3—21no—
669C2×C3×D3—21no—
670C2×C3×D3—21no—
671C2×C3×D3—22no—
672C2×C3×D3—32no—
673C2×C3×D3—32no—
674C2×C3×D3—41no—
675C2×C3×D3—41no—
676C2×C3×D3—62no—
677C2×C3×D3—61no—
678C2×C3×D3—61no—
679C2×C3×D3—61no—
680C2×C3×D3—61no—
681C2×C3×D3—61no—
682C2×C3×D3—61no—
683C2×C3×D3—61no—
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—121no—
694C2×C3×D3—121no—
695C2×C3×D3—121no—
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#23912yescomplemented
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—61no—
717C32×C4—81no—
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—21no—
735C3×Dic3—21no—
736C3×Dic3—22no—
737C3×Dic3—32no—
738C3×Dic3—32no—
739C3×Dic3—41no—
740C3×Dic3—41no—
741C3×Dic3—41no—
742C3×Dic3—41no—
743C3×Dic3—62no—
744C3×Dic3—61no—
745C3×Dic3—61no—
746C3×Dic3—61no—
747C3×Dic3—61no—
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—271no—
759#121—271no—
760#120—271no—
761#120—271no—
762C4×D4—91no—
763C4×D4—91no—
764C4×D4—271no—
765C4×D4—271no—
766#117—271no—
767C33#52511yescharacteristic, complemented, Sylow
768C23×C3—31no—
769C23×C3—31no—
770C23×C3—61no—
771C23×C3—91no—
772C23×C3—91no—
773C23×C3—91no—
774C22×D3—31no—
775C22×D3—31no—
776C22×D3—31no—
777C22×D3—31no—
778C22×D3—31no—
779C22×D3—31no—
780C22×D3—61no—
781C22×D3—61no—
782C22×D3—61no—
783C22×D3—91no—
784C22×D3—91no—
785C22×D3—91no—
786C22×D3—181no—
787C22×D3—181no—
788C22×D3—181no—
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—182no—
798C22×D3—361no—
799C22×D3—362no—
800C22×D3—362no—
801C22×D3—362no—
802C22×D3C2×D3211yescharacteristic
803C3×Q8—182no—
804C3×D4—182no—
805C3×D4—182no—
806C2×C3×C4—21no—
807C2×C3×C4—21no—
808C2×C3×C4—21no—
809C2×C3×C4—31no—
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—41no—
820C2×C3×C4—61no—
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—182no—
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—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—31no—
850C2×Dic3—31no—
851C2×Dic3—31no—
852C2×Dic3—31no—
853C2×Dic3—61no—
854C2×Dic3—61no—
855C2×Dic3—61no—
856C2×Dic3—62no—
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—361no—
866C2×Dic3C2×D3211yescharacteristic
867C2×Dic3C2×D3211yescharacteristic
868C2×Dic3C2×D3211yescharacteristic
869C2×Dic3C2×D3211yescharacteristic
870C2×Dic3C2×D3211yescharacteristic
871D12—62no—
872D12—62no—
873D12—62no—
874D12—122no—
875D12—182no—
876D12—182no—
877D12—182no—
878D12—182no—
879D12—182no—
880D12—182no—
881D12—362no—
882D12—362no—
883C4×D3—62no—
884C4×D3—62no—
885C4×D3—62no—
886C4×D3—62no—
887C4×D3—62no—
888C4×D3—62no—
889C4×D3—62no—
890C4×D3—62no—
891C4×D3—94no—
892C4×D3—94no—
893C4×D3—94no—
894C4×D3—184no—
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×C32C2×#23511yescharacteristic
917C2×C32C2×#23511yescharacteristic
918C2×C32C2×D3×D411yescharacteristic
919C2×C32C2×D3×D411yescharacteristic
920C2×C32C2×D3×D411yescharacteristic
921C2×C32C2×#23911yescharacteristic
922C2×C32D3×#4111yescharacteristic
923C2×C32D3×#4111yescharacteristic
924C2×C32D3×#4111yescharacteristic
925C3⋊D3—22no—
926C3⋊D3—41no—
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—62no—
939C3×D3—62no—
940C3×D3—122no—
941C3×D3—121no—
942C3×D3—121no—
943C3×D3—121no—
944C3×D3—121no—
945C3×D3—241no—
946C3×D3—241no—
947C24—271no—
948#41—544no—
949C2×Q8—91no—
950C2×D4—91no—
951C2×D4—91no—
952C2×D4—271no—
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—91no—
962C22×C4—271no—
963C22×C4—271no—
964C22×C4—271no—
965C22×C4—544no—
966C4⋊C4—31no—
967C4⋊C4—91no—
968C4⋊C4—91no—
969C4⋊C4—91no—
970C4⋊C4—271no—
971C4⋊C4—271no—
972C22⋊C4—31no—
973C22⋊C4—91no—
974C22⋊C4—91no—
975C22⋊C4—91no—
976C22⋊C4—91no—
977C22⋊C4—271no—
978C22⋊C4—271no—
979C22⋊C4—271no—
980C22⋊C4—271no—
981C22⋊C4—271no—
982C42—31no—
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—92no—
996C22×C3—121no—
997C22×C3—121no—
998C22×C3—181no—
999C22×C3—181no—
1000C22×C3—181no—
1001C22×C3—181no—
1002C22×C3—181no—
1003C22×C3—181no—
1004C22×C3—181no—
1005C22×C3—181no—
1006C22×C3C22×D3211yescharacteristic
1007C22×C3C22×D3211yescharacteristic
1008C22×C3C22×D3211yescharacteristic
1009C2×D3—21no—
1010C2×D3—21no—
1011C2×D3—32no—
1012C2×D3—32no—
1013C2×D3—62no—
1014C2×D3—61no—
1015C2×D3—61no—
1016C2×D3—61no—
1017C2×D3—61no—
1018C2×D3—61no—
1019C2×D3—61no—
1020C2×D3—61no—
1021C2×D3—61no—
1022C2×D3—61no—
1023C2×D3—61no—
1024C2×D3—61no—
1025C2×D3—61no—
1026C2×D3—61no—
1027C2×D3—61no—
1028C2×D3—61no—
1029C2×D3—61no—
1030C2×D3—92no—
1031C2×D3—92no—
1032C2×D3—92no—
1033C2×D3—121no—
1034C2×D3—121no—
1035C2×D3—121no—
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#379912yescomplemented
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—61no—
1080C3×C4—61no—
1081C3×C4—81no—
1082C3×C4—92no—
1083C3×C4—121no—
1084C3×C4—121no—
1085C3×C4—121no—
1086C3×C4—121no—
1087C3×C4—181no—
1088C3×C4—181no—
1089Dic3—21no—
1090Dic3—21no—
1091Dic3—21no—
1092Dic3—21no—
1093Dic3—32no—
1094Dic3—32no—
1095Dic3—62no—
1096Dic3—61no—
1097Dic3—61no—
1098Dic3—61no—
1099Dic3—61no—
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#554711yescharacteristic, complemented
1116C32#562711yescharacteristic, complemented
1117C23—31no—
1118C23—91no—
1119C23—91no—
1120C23—91no—
1121C23—271no—
1122C23—542no—
1123C23—542no—
1124C23—542no—
1125Q8—182no—
1126D4—182no—
1127D4—182no—
1128D4—542no—
1129D4—542no—
1130D4—542no—
1131D4—542no—
1132D4—542no—
1133C2×C4—31no—
1134C2×C4—31no—
1135C2×C4—31no—
1136C2×C4—31no—
1137C2×C4—31no—
1138C2×C4—91no—
1139C2×C4—91no—
1140C2×C4—91no—
1141C2×C4—182no—
1142C2×C4—182no—
1143C2×C4—182no—
1144C2×C4—182no—
1145C2×C4—182no—
1146C2×C4—274no—
1147C2×C4—271no—
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—182no—
1167C2×C3—361no—
1168C2×C3—361no—
1169C2×C3C2×#379911yescharacteristic
1170C2×C3C2×#380211yescharacteristic
1171C2×C3D3×#23511yescharacteristic
1172C2×C3D3×#23511yescharacteristic
1173C2×C3D3×#23511yescharacteristic
1174C2×C3D32×D411yescharacteristic
1175C2×C3D32×D411yescharacteristic
1176C2×C3#6431211yescharacteristic
1177C2×C3D3×#23911yescharacteristic
1178D3—22no—
1179D3—62no—
1180D3—62no—
1181D3—122no—
1182D3—121no—
1183D3—121no—
1184D3—121no—
1185D3—121no—
1186D3—182no—
1187D3—182no—
1188D3—182no—
1189D3—241no—
1190D3—241no—
1191D3—362no—
1192D3—362no—
1193D3—362no—
1194D3—722no—
1195C22—32no—
1196C22—61no—
1197C22—61no—
1198C22—92no—
1199C22—181no—
1200C22—181no—
1201C22—181no—
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—61no—
1218C4—92no—
1219C4—181no—
1220C4—181no—
1221C4—541no—
1222C3—21no—
1223C3—21no—
1224C3—21no—
1225C3—41no—
1226C3#1059400611yescharacteristic, complemented
1227C3#1059406611yescharacteristic, complemented
1228C3#1059462311yescharacteristic, complemented
1229C2—62no—
1230C2—182no—
1231C2—361no—
1232C2—361no—
1233C2—542no—
1234C2D3×#379911yescharacteristic
1235C2D3×#380211yescharacteristic
1236C2#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×#88965C2semidirect
2. C2×D3×#624C2semidirect
3. #11723687C2semidirect
4. #11723541C2semidirect
5. #11723504C2semidirect
6. #11723468C2semidirect
7. C3×#63899C2semidirect
8. C3×#63894C2semidirect
9. C3×#63880C2semidirect
10. #11723000C2semidirect
11. #11722979C2semidirect
12. #11722960C2semidirect
13. #11722950C2semidirect
14. #11722931C2semidirect
15. #11722930C2semidirect
22. C2×#6295C22semidirect
29. C2×C3×#627C22semidirect
32. C2×C3×#624C22semidirect
33. C2×C3×#624C22semidirect
39. C3×#3752C22semidirect
40. C3×#3750C22semidirect
42. C32×C4⋊Dic3C22semidirect
43. C32×C4×Dic3C22semidirect
44. #88814C22semidirect
45. #88807C22semidirect
46. #88806C22semidirect
49. #88803C22semidirect
50. Dic3×C3⋊Dic3C22semidirect
51. C3×#3724C22semidirect
52. C3×Dic3⋊Dic3C22semidirect
54. C3×#3722C22semidirect
86. #63899D3semidirect
88. #63894D3semidirect
94. #63880D3semidirect
130. #6289D4semidirect
168. C2×#627C2×D3semidirect
194. C2×#624C2×D3semidirect
195. C2×#624C2×D3semidirect
218. #3752C2×D3semidirect
221. #3750C2×D3semidirect
237. C3×C4⋊Dic3C2×D3semidirect
238. C3×C4⋊Dic3C2×D3semidirect
246. C3×C4×Dic3C2×D3semidirect
247. C3×C4×Dic3C2×D3semidirect
251. #3724C2×D3semidirect
255. Dic3⋊Dic3C2×D3semidirect
261. #3722C2×D3semidirect
286. C2×C3×C3⋊D3#41semidirect
289. C2×C32×D3#41semidirect
607. C4⋊Dic3D32semidirect
625. C4×Dic3D32semidirect
666. C2×C3⋊D3#235semidirect
701. C2×C3×D3#235semidirect
702. C2×C3×D3#239semidirect
767. C33#525semidirect
1063. C2×D3#3799semidirect
1114. C32#5547semidirect
1115. C32#5547semidirect
1116. C32#5627semidirect
1226. C3#10594006semidirect
1227. C3#10594066semidirect
1228. C3#10594623semidirect

Maximal subgroups

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

subgroupindex
C2×#889652
C2×D3×#6242
#117236872
#117235412
#117235042
#117234682
C3×#638992
C3×#638942
C3×#638802
#117230002
#117229792
#117229602
#117229502
#117229312
#117229302
#105946233
#105940663
#105940063