Finite Group Databasebeta

← #13170786

Subgroups — #13170786

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×#88959C211yesmaximal, characteristic, complemented
2C2×D3×#624C211yesmaximal, characteristic, complemented
3#11723692C211yesmaximal, characteristic, complemented
4#11723540C211yesmaximal, characteristic, complemented
5#11723468C211yesmaximal, characteristic, complemented
6#11723422C211yesmaximal, characteristic, complemented
7C3×Dic3×D12C211yesmaximal, characteristic, complemented
8C3×#63885C211yesmaximal, characteristic, complemented
9C3×#63880C211yesmaximal, characteristic, complemented
10#11722996C211yesmaximal, characteristic, complemented
11#11722978C211yesmaximal, characteristic, complemented
12#11722965C211yesmaximal, characteristic, complemented
13#11722949C211yesmaximal, characteristic, complemented
14#11722930C211yesmaximal, characteristic, complemented
15Dic3×#625C211yesmaximal, characteristic, complemented
16#10595138—31nomaximal
17#10594286—31nomaximal
18#10594006—31nomaximal
19C22×D3×C3⋊D3C2211yescharacteristic
20C2×C32×D12C2211yescharacteristic
21C2×#6296C2211yescharacteristic, complemented
22C2×#6294C2211yescharacteristic
23C2×#6291C2211yescharacteristic
24C2×#6291C2211yescharacteristic
25C2×#6290C2211yescharacteristic
26C2×#6289C2211yescharacteristic
27C2×#6289C2211yescharacteristic
28C2×C3×#626C2211yescharacteristic
29C2×C3×#625C2211yescharacteristic
30C2×C3×#625C2211yescharacteristic, complemented
31C2×C3×#624C2211yescharacteristic
32C2×C3×D3×Dic3C2211yescharacteristic
33C2×C3×D3×Dic3C2211yescharacteristic
34C2×C3×D3×Dic3C2211yescharacteristic, complemented
35C2×C3×D3×Dic3C2211yescharacteristic, complemented
36#88959—24no—
37D3×#624—24no—
38#88859C2211yescharacteristic
39C3×#3752C2211yescharacteristic
40C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
41C3×#3750C2211yescharacteristic, complemented
42C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
43C32×C4×Dic3C2211yescharacteristic, complemented
44#88815C2211yescharacteristic, complemented
45#88814C2211yescharacteristic
46#88807C2211yescharacteristic, complemented
47#88806C2211yescharacteristic, complemented
48#88804C2211yescharacteristic
49(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
50(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
51Dic3×C3⋊Dic3C2211yescharacteristic, complemented
52C3×Dic3⋊Dic3C2211yescharacteristic, complemented
53C3×(C2×D3)⋊Dic3C2211yescharacteristic
54C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
55C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
56C22×#624—31no—
57C2×#3804—31no—
58C2×#3804—31no—
59C2×C4×D32—31no—
60C2×C4×D32—31no—
61C2×#3798—31no—
62#64146—31no—
63#64092—31no—
64#64081—31no—
65C3×#939—31no—
66C3×D4×Dic3—31no—
67C3×#884—31no—
68C3×#67⋊C4—31no—
69C3×C4×D12—31no—
70C3×C4×D12—31no—
71#63983—31no—
72#63981—31no—
73#63975—31no—
74Dic3×#67—31no—
75Dic3×#67—31no—
76#63970—31no—
77#63964—31no—
78#63958—31no—
79#63952—31no—
80#63922—31no—
81#63922—31no—
82#63922—31no—
83#63922—61no—
84C4×#625—31no—
85C4×#625—31no—
86#63899—31no—
87#63899—31no—
88#63895—31no—
89#63893—31no—
90Dic3×D12D311yescharacteristic, complemented
91#63885—31no—
92#63885D311yescharacteristic, complemented
93#63880D311yescharacteristic, complemented
94#63879—31no—
95#63854—31no—
96#63854—31no—
97#63854—31no—
98#63854—61no—
99#63853—31no—
100#63851—31no—
101#63836—31no—
102#63836—31no—
103#63836—61no—
104C22×C3⋊(C3⋊D3)C2311yescharacteristic
105C22×C3×C3⋊D3C2311yescharacteristic
106C22×C32×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×C3×C3⋊Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122C32×D12—22no—
123#6296—22no—
124#6294—22no—
125#6291—22no—
126#6291—22no—
127#6290—22no—
128#6289—22no—
129#6289D414yescomplemented
130C3×#626—22no—
131C3×#625—22no—
132C3×#625—22no—
133C3×#624—22no—
134C3×D3×Dic3—22no—
135C3×D3×Dic3—22no—
136C3×D3×Dic3—22no—
137C3×D3×Dic3—22no—
138#5606—91no—
139#5547—91no—
140#5547—91no—
141C23×C3⋊D3—31no—
142C22×D32—31no—
143C22×D32—31no—
144C22×D32—61no—
145C2×C32×D4—31no—
146C2×#638—31no—
147C2×#638—31no—
148C2×#638—31no—
149C2×C4×C3⋊D3—31no—
150C2×C4×C3⋊D3—31no—
151C2×C3×#67—31no—
152C2×C3×#67—31no—
153C2×C3×#67—31no—
154C2×C3×#67—31no—
155C2×C3×#67—31no—
156C22×C3×Dic3—31no—
157C22×C3×Dic3—31no—
158C22×C3×Dic3—31no—
159C22×C3×Dic3—31no—
160C2×C3×D12—21no—
161C2×C3×D12—31no—
162C2×C3×D12C2×D311yescharacteristic
163C2×C3×D12C2×D311yescharacteristic
164C2×C3×C4×D3—31no—
165C2×C3×C4×D3—31no—
166C2×C3×C4×D3—31no—
167C2×C3×C4×D3—31no—
168C2×C3×C4×D3—31no—
169C2×C3×C4×D3—31no—
170C2×#627—31no—
171C2×#627—31no—
172C2×#627—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—61no—
183C2×#625C2×D311yescharacteristic
184C2×#625C2×D311yescharacteristic, complemented
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—
195#3804—64no—
196C2×D3×Dic3—31no—
197C2×D3×Dic3—31no—
198C2×D3×Dic3C2×D311yescharacteristic
199C2×D3×Dic3C2×D311yescharacteristic
200C2×D3×Dic3C2×D311yescharacteristic, complemented
201C2×D3×Dic3C2×D311yescharacteristic, complemented
202C4×D32—64no—
203C4×D32—64no—
204#3798—64no—
205C32×C22⋊C4—31no—
206C32×C42—31no—
207#3757—31no—
208#3757—31no—
209#3752—31no—
210#3752—31no—
211#3752—31no—
212#3752—31no—
213#3752—61no—
214#3752—61no—
215#3752—61no—
216#3752—121no—
217#3752C2×D311yescharacteristic
218C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
219#3750—31no—
220#3750—31no—
221#3750C2×D311yescharacteristic, complemented
222C4×C3⋊Dic3—31no—
223C3×#217—31no—
224C3×#217—31no—
225C3×#217—31no—
226C3×(C2×D3)⋊C4—21no—
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, complemented
234C3×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
235C3×C4⋊Dic3—31no—
236C3×C4⋊Dic3—31no—
237C3×C4⋊Dic3—31no—
238C3×C4⋊Dic3—61no—
239C3×Dic3⋊C4—31no—
240C3×Dic3⋊C4—31no—
241C3×Dic3⋊C4—31no—
242C3×Dic3⋊C4—61no—
243C3×C4×Dic3—21no—
244C3×C4×Dic3C2×D311yescharacteristic, complemented
245C3×C4×Dic3C2×D311yescharacteristic, complemented
246#3724—31no—
247#3724—31no—
248#3724—31no—
249#3724—61no—
250Dic3⋊Dic3—31no—
251Dic3⋊Dic3—31no—
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(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
269(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
270(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
271Dic32—31no—
272Dic32—31no—
273Dic32—61no—
274C22×C33C2411yescharacteristic
275C2×C3⋊(C3⋊D3)—21no—
276C2×C3⋊(C3⋊D3)—21no—
277C2×C3⋊(C3⋊D3)C2×D412yes—
278C2×C3×C3⋊D3—21no—
279C2×C3×C3⋊D3—21no—
280C2×C3×C3⋊D3#4112yescomplemented
281C2×C32×D3—21no—
282C2×C32×D3—21no—
283C2×C32×D3—21no—
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—
297C3×C3⋊Dic3C2×D412yes—
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×#121—91no—
308C3×C4×D4—91no—
309C3×C4×D4—91no—
310#939—31no—
311#939—91no—
312#938—91no—
313#937—91no—
314#937—91no—
315#937—91no—
316#937—91no—
317#937—181no—
318D4×Dic3—31no—
319D4×Dic3—91no—
320C4×#67—91no—
321C4×#67—91no—
322C4×#67—91no—
323C4×#67—91no—
324#924—91no—
325#897—91no—
326#896—91no—
327#896—91no—
328#894—91no—
329#894—91no—
330#892—91no—
331#884—31no—
332#884—91no—
333#883—91no—
334#883—91no—
335#883—91no—
336#883—91no—
337#883—181no—
338#882—91no—
339#882—91no—
340#67⋊C4—31no—
341#67⋊C4—91no—
342#878—91no—
343#878—91no—
344C4×D12—31no—
345C4×D12—31no—
346#872—91no—
347#872—91no—
348#872—181no—
349C23×C32—31no—
350C23×C32—31no—
351C23×C32—31no—
352C22×C3⋊D3—31no—
353C22×C3⋊D3—31no—
354C22×C3⋊D3—31no—
355C22×C3⋊D3—61no—
356C22×C3⋊D3—61no—
357C22×C3⋊D3—61no—
358C22×C3⋊D3—62no—
359C22×C3⋊D3—62no—
360C22×C3⋊D3—62no—
361C22×C3⋊D3—121no—
362C22×C3⋊D3C22×D311yescharacteristic
363C22×C3×D3—21no—
364C22×C3×D3—21no—
365C22×C3×D3—21no—
366C22×C3×D3—31no—
367C22×C3×D3—31no—
368C22×C3×D3—61no—
369C22×C3×D3C22×D311yescharacteristic
370C22×C3×D3C22×D311yescharacteristic
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—41no—
392C2×C32×C4C22×D311yescharacteristic
393C2×C32×C4C22×D311yescharacteristic
394C2×C32×C4C22×D311yescharacteristic
395#638—62no—
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
409C2×C3⋊Dic3C22×D311yescharacteristic
410C4×C3⋊D3—34no—
411C4×C3⋊D3—62no—
412C3×#67—62no—
413C3×#67—62no—
414C3×#67—62no—
415C3×#67—62no—
416C3×#67—62no—
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—31no—
429C2×C3×Dic3—31no—
430C2×C3×Dic3—61no—
431C2×C3×Dic3—61no—
432C2×C3×Dic3—61no—
433C2×C3×Dic3—61no—
434C2×C3×Dic3—61no—
435C2×C3×Dic3—62no—
436C2×C3×Dic3—62no—
437C2×C3×Dic3—62no—
438C2×C3×Dic3—62no—
439C2×C3×Dic3C22×D311yescharacteristic
440C2×C3×Dic3C22×D311yescharacteristic
441C2×C3×Dic3C22×D311yescharacteristic
442C2×C3×Dic3C22×D311yescharacteristic
443C2×C3×Dic3C22×D311yescharacteristic
444C2×C3×Dic3C22×D311yescharacteristic
445C3×D12—22no—
446C3×D12—22no—
447C3×D12—42no—
448C3×D12—62no—
449C3×C4×D3—62no—
450C3×C4×D3—62no—
451C3×C4×D3—62no—
452C3×C4×D3—62no—
453C3×C4×D3—62no—
454C3×C4×D3—62no—
455#627—62no—
456#627—62no—
457#627—62no—
458#626—22no—
459#626—62no—
460#626—62no—
461#626—62no—
462#626—62no—
463#626—122no—
464#626—122no—
465#625—22no—
466#625—22no—
467#625—62no—
468#625—62no—
469#625—122no—
470#624—22no—
471#624—34no—
472#624—34no—
473#624—64no—
474#624—62no—
475#624—62no—
476#624—62no—
477#624—122no—
478D3×Dic3—22no—
479D3×Dic3—22no—
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—
490C32×D3—22no—
491C32×D3—41no—
492C32×D3—41no—
493C23×D3—91no—
494C23×D3—91no—
495C23×D3—91no—
496C23×D3—181no—
497C2×C3×D4—31no—
498C2×C3×D4—31no—
499C2×C3×D4—61no—
500C2×C3×D4—91no—
501C2×C3×D4—91no—
502C2×C3×D4—91no—
503C22×C3×C4—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—31no—
511C2×#67—31no—
512C2×#67—31no—
513C2×#67—91no—
514C2×#67—91no—
515C2×#67—91no—
516C2×#67—91no—
517C2×#67—91no—
518C2×#67—91no—
519C2×#67—91no—
520C2×#67—181no—
521C2×#67—181no—
522C2×#67—181no—
523C22×Dic3—31no—
524C22×Dic3—31no—
525C22×Dic3—31no—
526C22×Dic3—31no—
527C22×Dic3—91no—
528#237—184no—
529#235—184no—
530#235—184no—
531C2×D12—31no—
532C2×D12—91no—
533C2×D12—91no—
534C2×D12D3211yescharacteristic
535C2×C4×D3—31no—
536C2×C4×D3—31no—
537C2×C4×D3—31no—
538C2×C4×D3—31no—
539C2×C4×D3—31no—
540C2×C4×D3—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—181no—
550C2×C4×D3—181no—
551C2×C4×D3—184no—
552C2×C4×D3—184no—
553C2×C4×D3—184no—
554C2×Dic6—91no—
555C2×Dic6—91no—
556C2×Dic6—91no—
557C3×C4⋊C4—91no—
558C3×C4⋊C4—91no—
559C3×C4⋊C4—91no—
560C3×C22⋊C4—31no—
561C3×C22⋊C4—31no—
562C3×C22⋊C4—61no—
563C3×C22⋊C4—91no—
564C3×C22⋊C4—91no—
565C3×C22⋊C4—91no—
566C3×C22⋊C4—91no—
567C3×C42—31no—
568C3×C42—31no—
569C3×C42—61no—
570#217—31no—
571#217—31no—
572#217—31no—
573#217—91no—
574#217—91no—
575#217—91no—
576#217—91no—
577#217—91no—
578#217—181no—
579#217—181no—
580(C2×D3)⋊C4—31no—
581(C2×D3)⋊C4—31no—
582(C2×D3)⋊C4—31no—
583(C2×D3)⋊C4—31no—
584(C2×D3)⋊C4—31no—
585(C2×D3)⋊C4—61no—
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—181no—
597(C2×D3)⋊C4—181no—
598(C2×D3)⋊C4—181no—
599(C2×D3)⋊C4—181no—
600(C2×D3)⋊C4—361no—
601(C2×D3)⋊C4D3211yescharacteristic, complemented
602C4⋊Dic3—31no—
603C4⋊Dic3—31no—
604C4⋊Dic3—31no—
605C4⋊Dic3—61no—
606C4⋊Dic3—91no—
607C4⋊Dic3—91no—
608Dic3⋊C4—31no—
609Dic3⋊C4—31no—
610Dic3⋊C4—31no—
611Dic3⋊C4—61no—
612Dic3⋊C4—91no—
613Dic3⋊C4—91no—
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×C32—61no—
634C22×C32—61no—
635C22×C32—61no—
636C22×C32—61no—
637C22×C32—61no—
638C22×C32—61no—
639C22×C32C23×D311yescharacteristic
640C22×C32C23×D311yescharacteristic
641C22×C32C23×D311yescharacteristic
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—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—21no—
680C2×C3×D3—21no—
681C2×C3×D3—21no—
682C2×C3×D3—21no—
683C2×C3×D3—22no—
684C2×C3×D3—32no—
685C2×C3×D3—32no—
686C2×C3×D3—41no—
687C2×C3×D3—41no—
688C2×C3×D3—41no—
689C2×C3×D3—41no—
690C2×C3×D3—41no—
691C2×C3×D3—41no—
692C2×C3×D3—41no—
693C2×C3×D3—41no—
694C2×C3×D3—62no—
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#23512yescomplemented
702C2×C3×D3#23712yescomplemented
703D32—68no—
704D32—68no—
705D32—128no—
706C32×C4—21no—
707C32×C4—21no—
708C32×C4—21no—
709C32×C4—32no—
710C32×C4—41no—
711C32×C4—41no—
712C32×C4—41no—
713C32×C4—61no—
714C32×C4—61no—
715C32×C4—81no—
716C3⋊Dic3—21no—
717C3⋊Dic3—21no—
718C3⋊Dic3—21no—
719C3⋊Dic3—21no—
720C3⋊Dic3—61no—
721C3⋊Dic3—61no—
722C3⋊Dic3—61no—
723C3⋊Dic3—121no—
724C3⋊Dic3—121no—
725C3⋊Dic3—121no—
726C3⋊Dic3—241no—
727C3⋊Dic3D3×D412yes—
728C3×Dic3—21no—
729C3×Dic3—21no—
730C3×Dic3—21no—
731C3×Dic3—21no—
732C3×Dic3—22no—
733C3×Dic3—32no—
734C3×Dic3—32no—
735C3×Dic3—41no—
736C3×Dic3—41no—
737C3×Dic3—62no—
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×Dic3D3×D412yes—
751C3×Dic3D3×D412yes—
752C2×#41—271no—
753C23×C4—271no—
754#123—271no—
755#123—271no—
756C22⋊Q8—271no—
757C22⋊Q8—271no—
758#121—91no—
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—31no—
771C23×C3—31no—
772C23×C3—31no—
773C23×C3—31no—
774C23×C3—61no—
775C23×C3—61no—
776C23×C3—61no—
777C23×C3—91no—
778C22×D3—31no—
779C22×D3—31no—
780C22×D3—61no—
781C22×D3—91no—
782C22×D3—91no—
783C22×D3—91no—
784C22×D3—181no—
785C22×D3—181no—
786C22×D3—181no—
787C22×D3—182no—
788C22×D3—182no—
789C22×D3—182no—
790C22×D3—182no—
791C22×D3—182no—
792C22×D3—182no—
793C22×D3—182no—
794C22×D3—182no—
795C22×D3—182no—
796C22×D3—361no—
797C22×D3—362no—
798C22×D3—362no—
799C22×D3—362no—
800C22×D3C2×D3211yescharacteristic
801C22×D3C2×D3211yescharacteristic
802C22×D3C2×D3211yescharacteristic
803C3×D4—62no—
804C3×D4—62no—
805C3×D4—122no—
806C3×D4—182no—
807C3×D4—182no—
808C3×D4—182no—
809C2×C3×C4—21no—
810C2×C3×C4—21no—
811C2×C3×C4—21no—
812C2×C3×C4—31no—
813C2×C3×C4—31no—
814C2×C3×C4—31no—
815C2×C3×C4—31no—
816C2×C3×C4—31no—
817C2×C3×C4—31no—
818C2×C3×C4—41no—
819C2×C3×C4—61no—
820C2×C3×C4—61no—
821C2×C3×C4—61no—
822C2×C3×C4—91no—
823C2×C3×C4—91no—
824C2×C3×C4—91no—
825C2×C3×C4—91no—
826C2×C3×C4—91no—
827C2×C3×C4—182no—
828C2×C3×C4—182no—
829C2×C3×C4—182no—
830C2×C3×C4—182no—
831C2×C3×C4—182no—
832C2×C3×C4C2×D3211yescharacteristic
833C2×C3×C4C2×D3211yescharacteristic
834C2×C3×C4C2×D3211yescharacteristic
835#67—62no—
836#67—62no—
837#67—62no—
838#67—62no—
839#67—62no—
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—
849#67—362no—
850C2×Dic3—31no—
851C2×Dic3—31no—
852C2×Dic3—31no—
853C2×Dic3—31no—
854C2×Dic3—31no—
855C2×Dic3—31no—
856C2×Dic3—31no—
857C2×Dic3—31no—
858C2×Dic3—31no—
859C2×Dic3—31no—
860C2×Dic3—61no—
861C2×Dic3—61no—
862C2×Dic3—61no—
863C2×Dic3—61no—
864C2×Dic3—61no—
865C2×Dic3—62no—
866C2×Dic3—62no—
867C2×Dic3—62no—
868C2×Dic3—62no—
869C2×Dic3—91no—
870C2×Dic3—91no—
871C2×Dic3—91no—
872C2×Dic3—181no—
873C2×Dic3—181no—
874C2×Dic3—181no—
875C2×Dic3—182no—
876C2×Dic3—361no—
877C2×Dic3C2×D3211yescharacteristic
878C2×Dic3C2×D3211yescharacteristic
879C2×Dic3C2×D3211yescharacteristic
880D12—22no—
881D12—62no—
882D12—182no—
883D12—182no—
884C4×D3—62no—
885C4×D3—62no—
886C4×D3—62no—
887C4×D3—62no—
888C4×D3—62no—
889C4×D3—62no—
890C4×D3—94no—
891C4×D3—94no—
892C4×D3—94no—
893C4×D3—184no—
894C4×D3—182no—
895C4×D3—182no—
896C4×D3—182no—
897C4×D3—182no—
898C4×D3—182no—
899C4×D3—362no—
900Dic6—182no—
901Dic6—182no—
902Dic6—182no—
903C2×C32—21no—
904C2×C32—21no—
905C2×C32—21no—
906C2×C32—21no—
907C2×C32—21no—
908C2×C32—21no—
909C2×C32—21no—
910C2×C32—21no—
911C2×C32—21no—
912C2×C32—41no—
913C2×C32—41no—
914C2×C32—41no—
915C2×C32—62no—
916C2×C32—121no—
917C2×C32—121no—
918C2×C32C2×#23511yescharacteristic
919C2×C32C2×#23511yescharacteristic
920C2×C32C2×D3×D411yescharacteristic
921C2×C32C2×D3×D411yescharacteristic
922C2×C32C2×D3×D411yescharacteristic
923C2×C32C2×#23711yescharacteristic
924C2×C32D3×#4111yescharacteristic
925C2×C32D3×#4111yescharacteristic
926C2×C32D3×#4111yescharacteristic
927C3⋊D3—22no—
928C3⋊D3—62no—
929C3⋊D3—62no—
930C3⋊D3—62no—
931C3⋊D3—122no—
932C3⋊D3—122no—
933C3⋊D3—122no—
934C3⋊D3—242no—
935C3×D3—22no—
936C3×D3—22no—
937C3×D3—42no—
938C3×D3—41no—
939C3×D3—41no—
940C3×D3—41no—
941C3×D3—41no—
942C3×D3—62no—
943C3×D3—62no—
944C3×D3—81no—
945C3×D3—81no—
946C3×D3—122no—
947C24—271no—
948#41—544no—
949C2×Q8—271no—
950C2×D4—31no—
951C2×D4—91no—
952C2×D4—91no—
953C2×D4—91no—
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—91no—
967C4⋊C4—91no—
968C4⋊C4—91no—
969C4⋊C4—271no—
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—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—61no—
1006C22×C3—61no—
1007C22×C3—92no—
1008C22×C3—121no—
1009C22×C3—121no—
1010C22×C3—121no—
1011C22×C3—121no—
1012C22×C3—121no—
1013C22×C3—121no—
1014C22×C3—121no—
1015C22×C3—121no—
1016C22×C3—181no—
1017C22×C3—181no—
1018C22×C3C22×D3211yescharacteristic
1019C22×C3C22×D3211yescharacteristic
1020C22×C3C22×D3211yescharacteristic
1021C2×D3—21no—
1022C2×D3—21no—
1023C2×D3—21no—
1024C2×D3—21no—
1025C2×D3—21no—
1026C2×D3—21no—
1027C2×D3—21no—
1028C2×D3—21no—
1029C2×D3—32no—
1030C2×D3—32no—
1031C2×D3—62no—
1032C2×D3—61no—
1033C2×D3—61no—
1034C2×D3—61no—
1035C2×D3—61no—
1036C2×D3—92no—
1037C2×D3—92no—
1038C2×D3—92no—
1039C2×D3—121no—
1040C2×D3—121no—
1041C2×D3—182no—
1042C2×D3—182no—
1043C2×D3—182no—
1044C2×D3—188no—
1045C2×D3—188no—
1046C2×D3—188no—
1047C2×D3—181no—
1048C2×D3—181no—
1049C2×D3—181no—
1050C2×D3—181no—
1051C2×D3—181no—
1052C2×D3—181no—
1053C2×D3—362no—
1054C2×D3—368no—
1055C2×D3—361no—
1056C2×D3—361no—
1057C2×D3—361no—
1058C2×D3—361no—
1059C2×D3—361no—
1060C2×D3—361no—
1061C2×D3—721no—
1062C2×D3—721no—
1063C2×D3#380412yescomplemented
1064C3×C4—21no—
1065C3×C4—21no—
1066C3×C4—21no—
1067C3×C4—32no—
1068C3×C4—32no—
1069C3×C4—41no—
1070C3×C4—41no—
1071C3×C4—41no—
1072C3×C4—62no—
1073C3×C4—61no—
1074C3×C4—61no—
1075C3×C4—61no—
1076C3×C4—61no—
1077C3×C4—81no—
1078C3×C4—92no—
1079C3×C4—121no—
1080C3×C4—121no—
1081C3×C4—181no—
1082C3×C4—181no—
1083C3×C4—181no—
1084C3×C4—181no—
1085Dic3—21no—
1086Dic3—21no—
1087Dic3—32no—
1088Dic3—32no—
1089Dic3—62no—
1090Dic3—61no—
1091Dic3—61no—
1092Dic3—61no—
1093Dic3—61no—
1094Dic3—61no—
1095Dic3—61no—
1096Dic3—61no—
1097Dic3—61no—
1098Dic3—121no—
1099Dic3—121no—
1100Dic3—121no—
1101Dic3—121no—
1102Dic3—181no—
1103Dic3—181no—
1104Dic3—181no—
1105Dic3—361no—
1106Dic3—361no—
1107Dic3—361no—
1108Dic3—721no—
1109Dic3#380212yes—
1110C32—21no—
1111C32—21no—
1112C32—21no—
1113C32—41no—
1114C32#554711yescharacteristic, complemented
1115C32#554711yescharacteristic, complemented
1116C32#560611yescharacteristic, complemented
1117C23—31no—
1118C23—31no—
1119C23—31no—
1120C23—91no—
1121C23—271no—
1122C23—542no—
1123C23—542no—
1124C23—542no—
1125Q8—542no—
1126D4—62no—
1127D4—182no—
1128D4—182no—
1129D4—182no—
1130D4—542no—
1131D4—542no—
1132D4—542no—
1133C2×C4—31no—
1134C2×C4—31no—
1135C2×C4—31no—
1136C2×C4—91no—
1137C2×C4—91no—
1138C2×C4—91no—
1139C2×C4—91no—
1140C2×C4—91no—
1141C2×C4—182no—
1142C2×C4—182no—
1143C2×C4—182no—
1144C2×C4—182no—
1145C2×C4—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—121no—
1167C2×C3—121no—
1168C2×C3—121no—
1169C2×C3—121no—
1170C2×C3—182no—
1171C2×C3—241no—
1172C2×C3—241no—
1173C2×C3C2×#380211yescharacteristic
1174C2×C3D3×#23511yescharacteristic
1175C2×C3D3×#23511yescharacteristic
1176C2×C3D3×#23511yescharacteristic
1177C2×C3D32×D411yescharacteristic
1178C2×C3D32×D411yescharacteristic
1179C2×C3D3×#23711yescharacteristic
1180C2×C3#6431211yescharacteristic
1181C2×C3C2×#380411yescharacteristic
1182D3—22no—
1183D3—41no—
1184D3—41no—
1185D3—62no—
1186D3—62no—
1187D3—122no—
1188D3—182no—
1189D3—182no—
1190D3—182no—
1191D3—362no—
1192D3—362no—
1193D3—362no—
1194D3—722no—
1195C22—32no—
1196C22—61no—
1197C22—61no—
1198C22—61no—
1199C22—61no—
1200C22—61no—
1201C22—61no—
1202C22—61no—
1203C22—61no—
1204C22—92no—
1205C22—181no—
1206C22—181no—
1207C22—272no—
1208C22—548no—
1209C22—541no—
1210C22—541no—
1211C22C2×D3311yescharacteristic
1212C4—21no—
1213C4—32no—
1214C4—61no—
1215C4—61no—
1216C4—92no—
1217C4—181no—
1218C4—181no—
1219C4—181no—
1220C4—181no—
1221C4—541no—
1222C3—21no—
1223C3—21no—
1224C3—21no—
1225C3—41no—
1226C3#1059400611yescharacteristic, complemented
1227C3#1059428611yescharacteristic, complemented
1228C3#1059513811yescharacteristic, complemented
1229C2—62no—
1230C2—121no—
1231C2—121no—
1232C2—182no—
1233C2—542no—
1234C2#1172438811yescharacteristic
1235C2D3×#380211yescharacteristic
1236C2D3×#380411yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
hypercenterC2×C4D33
hypocenterC33#525
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C2×#88959C2semidirect
2. C2×D3×#624C2semidirect
3. #11723692C2semidirect
4. #11723540C2semidirect
5. #11723468C2semidirect
6. #11723422C2semidirect
7. C3×Dic3×D12C2semidirect
8. C3×#63885C2semidirect
9. C3×#63880C2semidirect
10. #11722996C2semidirect
11. #11722978C2semidirect
12. #11722965C2semidirect
13. #11722949C2semidirect
14. #11722930C2semidirect
15. Dic3×#625C2semidirect
21. C2×#6296C22semidirect
30. C2×C3×#625C22semidirect
34. C2×C3×D3×Dic3C22semidirect
35. C2×C3×D3×Dic3C22semidirect
40. C3×C4⋊(C3⋊Dic3)C22semidirect
41. C3×#3750C22semidirect
42. C32×(C2×D3)⋊C4C22semidirect
43. C32×C4×Dic3C22semidirect
44. #88815C22semidirect
46. #88807C22semidirect
47. #88806C22semidirect
50. (C2×D3)⋊(C3⋊Dic3)C22semidirect
51. Dic3×C3⋊Dic3C22semidirect
52. C3×Dic3⋊Dic3C22semidirect
54. C3×(C2×D3)⋊Dic3C22semidirect
55. C3×(C2×D3)⋊Dic3C22semidirect
90. Dic3×D12D3semidirect
92. #63885D3semidirect
93. #63880D3semidirect
129. #6289D4semidirect
184. C2×#625C2×D3semidirect
200. C2×D3×Dic3C2×D3semidirect
201. C2×D3×Dic3C2×D3semidirect
218. C4⋊(C3⋊Dic3)C2×D3semidirect
221. #3750C2×D3semidirect
233. C3×(C2×D3)⋊C4C2×D3semidirect
234. C3×(C2×D3)⋊C4C2×D3semidirect
244. C3×C4×Dic3C2×D3semidirect
245. C3×C4×Dic3C2×D3semidirect
255. Dic3⋊Dic3C2×D3semidirect
269. (C2×D3)⋊Dic3C2×D3semidirect
270. (C2×D3)⋊Dic3C2×D3semidirect
280. C2×C3×C3⋊D3#41semidirect
289. C2×C32×D3#41semidirect
601. (C2×D3)⋊C4D32semidirect
625. C4×Dic3D32semidirect
666. C2×C3⋊D3#235semidirect
701. C2×C3×D3#235semidirect
702. C2×C3×D3#237semidirect
767. C33#525semidirect
1063. C2×D3#3804semidirect
1114. C32#5547semidirect
1115. C32#5547semidirect
1116. C32#5606semidirect
1226. C3#10594006semidirect
1227. C3#10594286semidirect
1228. C3#10595138semidirect

Maximal subgroups

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

subgroupindex
C2×#889592
C2×D3×#6242
#117236922
#117235402
#117234682
#117234222
C3×Dic3×D122
C3×#638852
C3×#638802
#117229962
#117229782
#117229652
#117229492
#117229302
Dic3×#6252
#105951383
#105942863
#105940063