Finite Group Databasebeta

← #13170745

Subgroups — #13170745

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×#88961C211yesmaximal, characteristic, complemented
2C2×D3×#624C211yesmaximal, characteristic, complemented
3#11723691C211yesmaximal, characteristic, complemented
4#11723541C211yesmaximal, characteristic, complemented
5#11723485C211yesmaximal, characteristic, complemented
6#11723461C211yesmaximal, characteristic, complemented
7C3×#63910C211yesmaximal, characteristic, complemented
8C3×#63891C211yesmaximal, characteristic, complemented
9C3×#63878C211yesmaximal, characteristic, complemented
10#11722988C211yesmaximal, characteristic, complemented
11#11722972C211yesmaximal, characteristic, complemented
12#11722963C211yesmaximal, characteristic, complemented
13#11722949C211yesmaximal, characteristic, complemented
14#11722937C211yesmaximal, characteristic, complemented
15#11722928C211yesmaximal, characteristic, complemented
16#10594626—31nomaximal
17#10594267—31nomaximal
18#10594079—31nomaximal
19C22×D3×C3⋊D3C2211yescharacteristic
20C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
21C2×#6294C2211yescharacteristic
22C2×#6294C2211yescharacteristic, complemented
23C2×#6293C2211yescharacteristic, complemented
24C2×#6292C2211yescharacteristic
25C2×#6291C2211yescharacteristic
26C2×#6290C2211yescharacteristic
27C2×#6289C2211yescharacteristic
28C2×#6289C2211yescharacteristic
29C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
30C2×C3×#626C2211yescharacteristic
31C2×C3×#626C2211yescharacteristic, complemented
32C2×C3×#625C2211yescharacteristic
33C2×C3×#624C2211yescharacteristic
34C2×C3×D3×Dic3C2211yescharacteristic
35C2×C3×D3×Dic3C2211yescharacteristic
36#88961—24no—
37D3×#624—24no—
38#88859C2211yescharacteristic
39C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
40C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
41C32×(C2×D3)⋊C4C2211yescharacteristic
42C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
43C32×Dic3⋊C4C2211yescharacteristic, complemented
44#88814C2211yescharacteristic
45#88814C2211yescharacteristic, complemented
46#88807C2211yescharacteristic, complemented
47Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
48#88804C2211yescharacteristic
49#88803C2211yescharacteristic
50C3×Dic3⋊Dic3C2211yescharacteristic, complemented
51C3×Dic3⋊Dic3C2211yescharacteristic, complemented
52C3×#3722C2211yescharacteristic, complemented
53C3×(C2×D3)⋊Dic3C2211yescharacteristic
54C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
55C3×Dic32C2211yescharacteristic, complemented
56C22×#624—31no—
57C2×#3805—31no—
58C2×#3804—31no—
59C2×C4×D32—31no—
60C2×C4×D32—31no—
61C2×#3795—31no—
62#64106—31no—
63#64091—31no—
64#64090—31no—
65C3×#895—31no—
66C3×#892—31no—
67C3×#886—31no—
68C3×#884—31no—
69C3×#883—31no—
70C3×#877—31no—
71#63983—31no—
72#63981—31no—
73#67⋊Dic3—31no—
74#63966—31no—
75#63958—31no—
76#63922—31no—
77#63922—31no—
78#63922—31no—
79#63922—61no—
80#63916—31no—
81#63910—31no—
82#63910D311yescharacteristic, complemented
83#63905—31no—
84#63898—31no—
85#63895—31no—
86#63895—31no—
87#63895—31no—
88#63895—61no—
89#63894—31no—
90#63894—31no—
91Dic3×D12—31no—
92Dic3×D12—31no—
93#63891—31no—
94#63891D311yescharacteristic, complemented
95#63881—31no—
96#63880—31no—
97#63880—31no—
98#63880—31no—
99#63880—31no—
100#63880—61no—
101#63878D311yescharacteristic, complemented
102#63857—31no—
103#63851—31no—
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
118C3×C4⋊(C3⋊D3)—22no—
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123#6294—22no—
124#6294—22no—
125#6293—22no—
126#6292—22no—
127#6291—22no—
128#6290—22no—
129#6289—22no—
130#6289—22no—
131D3×C3⋊Dic3—22no—
132C3×#626—22no—
133C3×#626—22no—
134C3×#625—22no—
135C3×#624—22no—
136C3×D3×Dic3—22no—
137C3×D3×Dic3D414yescomplemented
138#5656—91no—
139#5606—91no—
140#5524—91no—
141C23×C3⋊D3—31no—
142C22×D32—31no—
143C22×D32—31no—
144C22×D32—61no—
145C2×#638—31no—
146C2×#638—31no—
147C22×C3⋊Dic3—31no—
148C2×C4⋊(C3⋊D3)—31no—
149C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
150C2×C4×C3⋊D3—31no—
151C2×C4×C3⋊D3—31no—
152C2×#634—31no—
153C2×C3×#67—31no—
154C2×C3×#67—31no—
155C2×C3×#67—31no—
156C2×C3×#67—31no—
157C22×C3×Dic3—31no—
158C22×C3×Dic3—31no—
159C2×C3×D12—31no—
160C2×C3×D12—31no—
161C2×C3×D12—31no—
162C2×C3×D12—31no—
163C2×C3×D12—61no—
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—61no—
176C2×#626—61no—
177C2×#626C2×D311yescharacteristic
178C2×#626C2×D311yescharacteristic, complemented
179C2×#625—31no—
180C2×#625—31no—
181C2×#625—61no—
182C2×#625C2×D311yescharacteristic
183C2×#624—31no—
184C2×#624—31no—
185C2×#624—31no—
186C2×#624—31no—
187C2×#624—31no—
188C2×#624—31no—
189C2×#624—64no—
190C2×#624—61no—
191C2×#624—61no—
192C2×#624C2×D311yescharacteristic
193#3805—64no—
194#3804—64no—
195C2×D3×Dic3—31no—
196C2×D3×Dic3—31no—
197C2×D3×Dic3—31no—
198C2×D3×Dic3—31no—
199C2×D3×Dic3—31no—
200C2×D3×Dic3—31no—
201C2×D3×Dic3—61no—
202C2×D3×Dic3C2×D311yescharacteristic
203C2×D3×Dic3C2×D311yescharacteristic
204C4×D32—64no—
205C4×D32—64no—
206#3795—64no—
207C32×C4⋊C4—31no—
208C32×C22⋊C4—31no—
209C32×C22⋊C4—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—
219C4⋊(C3⋊Dic3)—31no—
220C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
221#3750—31no—
222C4×C3⋊Dic3C2×D311yescharacteristic, complemented
223C3×#217—31no—
224C3×#217—31no—
225C3×(C2×D3)⋊C4—21no—
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)⋊C4C2×D311yescharacteristic
232C3×(C2×D3)⋊C4C2×D311yescharacteristic
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—31no—
239C3×C4⋊Dic3—61no—
240C3×Dic3⋊C4—21no—
241C3×Dic3⋊C4—31no—
242C3×Dic3⋊C4—31no—
243C3×Dic3⋊C4C2×D311yescharacteristic, complemented
244C3×Dic3⋊C4C2×D311yescharacteristic, complemented
245C3×C4×Dic3—31no—
246C3×C4×Dic3—31no—
247C3×C4×Dic3—31no—
248C3×C4×Dic3—31no—
249C3×C4×Dic3—61no—
250Dic3⋊Dic3—31no—
251Dic3⋊Dic3—31no—
252Dic3⋊Dic3—31no—
253Dic3⋊Dic3—31no—
254Dic3⋊Dic3—61no—
255Dic3⋊Dic3—61no—
256Dic3⋊Dic3C2×D311yescharacteristic, complemented
257Dic3⋊Dic3C2×D311yescharacteristic, complemented
258#3722—31no—
259#3722—31no—
260#3722—31no—
261#3722—31no—
262#3722—61no—
263#3722C2×D311yescharacteristic, complemented
264(C2×D3)⋊Dic3—31no—
265(C2×D3)⋊Dic3—31no—
266(C2×D3)⋊Dic3—31no—
267(C2×D3)⋊Dic3—31no—
268(C2×D3)⋊Dic3—31no—
269(C2×D3)⋊Dic3—31no—
270(C2×D3)⋊Dic3—61no—
271(C2×D3)⋊Dic3C2×D311yescharacteristic
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⋊D3#4112yescomplemented
284C2×C32×D3—21no—
285C2×C32×D3—21no—
286C2×C32×D3—21no—
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⋊Dic3—21no—
296C3×C3⋊Dic3C2×D412yes—
297C32×Dic3—21no—
298C32×Dic3—21no—
299C32×Dic3—21no—
300C32×Dic3C2×D412yes—
301C2×#237—91no—
302C2×#237—91no—
303C2×#235—91no—
304C22×C4×D3—91no—
305C22×C4×D3—91no—
306C22×C4×D3—91no—
307C3×#123—91no—
308C3×#121—91no—
309C3×#117—91no—
310#938—91no—
311#937—91no—
312#937—91no—
313#937—91no—
314D4×Dic3—91no—
315D4×Dic3—91no—
316#929—91no—
317#924—91no—
318#897—91no—
319#897—91no—
320#897—91no—
321#897—181no—
322#896—91no—
323#896—91no—
324#895—31no—
325#895—91no—
326#893—91no—
327#893—91no—
328#892—31no—
329#886—31no—
330#886—91no—
331#884—31no—
332#884—91no—
333#883—31no—
334#883—91no—
335#882—91no—
336#882—91no—
337#882—91no—
338#882—181no—
339#67⋊C4—91no—
340#67⋊C4—91no—
341#67⋊C4—91no—
342#67⋊C4—91no—
343#67⋊C4—181no—
344#877—31no—
345C4×D12—91no—
346C4×D12—91no—
347C4×D12—91no—
348C4×D12—91no—
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—
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—41no—
392C2×C32×C4C22×D311yescharacteristic
393C2×C32×C4C22×D311yescharacteristic
394C2×C32×C4C22×D311yescharacteristic
395#638—62no—
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—62no—
404C2×C3⋊Dic3—121no—
405C2×C3⋊Dic3C22×D311yescharacteristic
406C2×C3⋊Dic3C22×D311yescharacteristic
407C2×C3⋊Dic3C22×D311yescharacteristic
408C2×C3⋊Dic3C22×D311yescharacteristic
409C4⋊(C3⋊D3)—22no—
410C4⋊(C3⋊D3)—62no—
411C4×C3⋊D3—62no—
412C4×C3⋊D3—62no—
413#634—62no—
414C3×#67—62no—
415C3×#67—62no—
416C3×#67—62no—
417C3×#67—62no—
418C2×C3×Dic3—21no—
419C2×C3×Dic3—21no—
420C2×C3×Dic3—21no—
421C2×C3×Dic3—21no—
422C2×C3×Dic3—31no—
423C2×C3×Dic3—31no—
424C2×C3×Dic3—34no—
425C2×C3×Dic3—31no—
426C2×C3×Dic3—31no—
427C2×C3×Dic3—31no—
428C2×C3×Dic3—31no—
429C2×C3×Dic3—31no—
430C2×C3×Dic3—31no—
431C2×C3×Dic3—61no—
432C2×C3×Dic3—61no—
433C2×C3×Dic3—61no—
434C2×C3×Dic3—61no—
435C2×C3×Dic3—62no—
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
443C2×C3×Dic3C22×D311yescharacteristic
444C3×D12—62no—
445C3×D12—62no—
446C3×D12—62no—
447C3×D12—62no—
448C3×D12—122no—
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—62no—
461#626—62no—
462#626—64no—
463#626—122no—
464#625—22no—
465#625—62no—
466#625—62no—
467#625—122no—
468#624—22no—
469#624—62no—
470#624—62no—
471#624—62no—
472#624—62no—
473#624—62no—
474#624—62no—
475#624—122no—
476#624—122no—
477D3×Dic3—22no—
478D3×Dic3—62no—
479D3×Dic3—62no—
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—
493C32×D3—22no—
494C32×D3—41no—
495C23×D3—91no—
496C23×D3—91no—
497C23×D3—91no—
498C23×D3—181no—
499C2×C3×D4—91no—
500C2×C3×D4—91no—
501C2×C3×D4—91no—
502C2×C3×D4—91no—
503C22×C3×C4—91no—
504C22×C3×C4—91no—
505C22×C3×C4—91no—
506C2×#67—31no—
507C2×#67—31no—
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—181no—
517C2×#67—181no—
518C22×Dic3—31no—
519C22×Dic3—31no—
520C22×Dic3—91no—
521C22×Dic3—91no—
522C22×Dic3—91no—
523C22×Dic3—91no—
524C22×Dic3—181no—
525#237—184no—
526#237—184no—
527#235—184no—
528C2×D12—31no—
529C2×D12—31no—
530C2×D12—31no—
531C2×D12—31no—
532C2×D12—61no—
533C2×D12—91no—
534C2×D12—91no—
535C2×D12—91no—
536C2×D12—181no—
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—91no—
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—31no—
570C3×C22⋊C4—31no—
571C3×C22⋊C4—61no—
572C3×C22⋊C4—61no—
573C3×C22⋊C4—91no—
574C3×C22⋊C4—91no—
575C3×C22⋊C4—91no—
576C3×C42—91no—
577C3×C42—91no—
578#217—31no—
579#217—31no—
580#217—91no—
581#217—91no—
582#217—91no—
583(C2×D3)⋊C4—31no—
584(C2×D3)⋊C4—31no—
585(C2×D3)⋊C4—31no—
586(C2×D3)⋊C4—31no—
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—91no—
598(C2×D3)⋊C4—91no—
599(C2×D3)⋊C4—181no—
600(C2×D3)⋊C4—181no—
601(C2×D3)⋊C4—181no—
602(C2×D3)⋊C4—181no—
603(C2×D3)⋊C4—181no—
604(C2×D3)⋊C4—361no—
605(C2×D3)⋊C4D3211yescharacteristic
606(C2×D3)⋊C4D3211yescharacteristic, complemented
607C4⋊Dic3—31no—
608C4⋊Dic3—31no—
609C4⋊Dic3—31no—
610C4⋊Dic3—31no—
611C4⋊Dic3—61no—
612C4⋊Dic3—91no—
613C4⋊Dic3—91no—
614C4⋊Dic3—91no—
615C4⋊Dic3—181no—
616Dic3⋊C4—31no—
617Dic3⋊C4—31no—
618Dic3⋊C4—91no—
619Dic3⋊C4—91no—
620Dic3⋊C4—91no—
621Dic3⋊C4—181no—
622Dic3⋊C4D3211yescharacteristic, complemented
623C4×Dic3—31no—
624C4×Dic3—31no—
625C4×Dic3—31no—
626C4×Dic3—31no—
627C4×Dic3—61no—
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⋊D3#23712yescomplemented
669C2×C3×D3—21no—
670C2×C3×D3—21no—
671C2×C3×D3—21no—
672C2×C3×D3—21no—
673C2×C3×D3—22no—
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—22no—
681C2×C3×D3—32no—
682C2×C3×D3—32no—
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—61no—
693C2×C3×D3—61no—
694C2×C3×D3—61no—
695C2×C3×D3—61no—
696C2×C3×D3—61no—
697C2×C3×D3—61no—
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—81no—
719C3⋊Dic3—21no—
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—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—62no—
743C3×Dic3—62no—
744C3×Dic3—61no—
745C3×Dic3—61no—
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—91no—
761#121—271no—
762#120—271no—
763#120—271no—
764C4×D4—271no—
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—182no—
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—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—94no—
826C2×C3×C4—91no—
827C2×C3×C4—91no—
828C2×C3×C4—91no—
829C2×C3×C4—91no—
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—182no—
840#67—182no—
841#67—182no—
842#67—184no—
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—31no—
855C2×Dic3—31no—
856C2×Dic3—61no—
857C2×Dic3—61no—
858C2×Dic3—61no—
859C2×Dic3—61no—
860C2×Dic3—62no—
861C2×Dic3—91no—
862C2×Dic3—91no—
863C2×Dic3—91no—
864C2×Dic3—181no—
865C2×Dic3—181no—
866C2×Dic3—181no—
867C2×Dic3—182no—
868C2×Dic3—182no—
869C2×Dic3—182no—
870C2×Dic3—182no—
871C2×Dic3—361no—
872C2×Dic3—362no—
873C2×Dic3C2×D3211yescharacteristic
874C2×Dic3C2×D3211yescharacteristic
875C2×Dic3C2×D3211yescharacteristic
876C2×Dic3C2×D3211yescharacteristic
877D12—62no—
878D12—62no—
879D12—62no—
880D12—62no—
881D12—122no—
882D12—182no—
883D12—182no—
884D12—182no—
885D12—362no—
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—182no—
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×D3×D411yescharacteristic
923C2×C32C2×D3×D411yescharacteristic
924C2×C32C2×#23711yescharacteristic
925C2×C32D3×#4111yescharacteristic
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—42no—
943C3×D3—41no—
944C3×D3—41no—
945C3×D3—62no—
946C3×D3—62no—
947C3×D3—122no—
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—91no—
957C2×D4—91no—
958C2×D4—271no—
959C2×D4—271no—
960C2×D4—271no—
961C22×C4—91no—
962C22×C4—91no—
963C22×C4—91no—
964C22×C4—271no—
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—31no—
978C22⋊C4—91no—
979C22⋊C4—91no—
980C22⋊C4—91no—
981C22⋊C4—271no—
982C22⋊C4—271no—
983C22⋊C4—271no—
984C22⋊C4—271no—
985C22⋊C4—271no—
986C42—91no—
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—62no—
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—92no—
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—61no—
1032C2×D3—61no—
1033C2×D3—61no—
1034C2×D3—61no—
1035C2×D3—61no—
1036C2×D3—61no—
1037C2×D3—92no—
1038C2×D3—92no—
1039C2×D3—92no—
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—61no—
1078C3×C4—61no—
1079C3×C4—61no—
1080C3×C4—61no—
1081C3×C4—61no—
1082C3×C4—61no—
1083C3×C4—81no—
1084C3×C4—92no—
1085C3×C4—121no—
1086C3×C4—121no—
1087C3×C4—121no—
1088C3×C4—181no—
1089C3×C4—181no—
1090C3×C4—181no—
1091Dic3—21no—
1092Dic3—21no—
1093Dic3—21no—
1094Dic3—32no—
1095Dic3—32no—
1096Dic3—62no—
1097Dic3—62no—
1098Dic3—61no—
1099Dic3—61no—
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#560611yescharacteristic, complemented
1120C32#565611yescharacteristic, complemented
1121C23—31no—
1122C23—31no—
1123C23—91no—
1124C23—91no—
1125C23—271no—
1126C23—542no—
1127C23—542no—
1128C23—542no—
1129Q8—542no—
1130D4—182no—
1131D4—182no—
1132D4—182no—
1133D4—182no—
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—271no—
1149C2×C4—542no—
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—122no—
1171C2×C3—121no—
1172C2×C3—121no—
1173C2×C3—182no—
1174C2×C3—361no—
1175C2×C3C2×D3×D1211yescharacteristic
1176C2×C3C2×D3×D1211yescharacteristic
1177C2×C3#6430611yescharacteristic
1178C2×C3D32×D411yescharacteristic
1179C2×C3D3×#23711yescharacteristic
1180C2×C3D3×#23711yescharacteristic
1181C2×C3#6431211yescharacteristic
1182C2×C3#6431211yescharacteristic
1183C2×C3#6431911yescharacteristic
1184D3—22no—
1185D3—41no—
1186D3—62no—
1187D3—62no—
1188D3—122no—
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—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—61no—
1219C4—61no—
1220C4—61no—
1221C4—92no—
1222C4—181no—
1223C4—181no—
1224C4—181no—
1225C4—541no—
1226C3—21no—
1227C3—21no—
1228C3—21no—
1229C3—41no—
1230C3#1059407911yescharacteristic, complemented
1231C3#1059426711yescharacteristic, complemented
1232C3#1059462611yescharacteristic, complemented
1233C2—62no—
1234C2—121no—
1235C2—182no—
1236C2—361no—
1237C2—542no—
1238C2#1172437611yescharacteristic
1239C2D32×D1211yescharacteristic
1240C2#1172440811yescharacteristic
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×#88961C2semidirect
2. C2×D3×#624C2semidirect
3. #11723691C2semidirect
4. #11723541C2semidirect
5. #11723485C2semidirect
6. #11723461C2semidirect
7. C3×#63910C2semidirect
8. C3×#63891C2semidirect
9. C3×#63878C2semidirect
10. #11722988C2semidirect
11. #11722972C2semidirect
12. #11722963C2semidirect
13. #11722949C2semidirect
14. #11722937C2semidirect
15. #11722928C2semidirect
22. C2×#6294C22semidirect
23. C2×#6293C22semidirect
29. C2×D3×C3⋊Dic3C22semidirect
31. C2×C3×#626C22semidirect
39. C3×C4⋊(C3⋊Dic3)C22semidirect
40. C3×C4×C3⋊Dic3C22semidirect
42. C32×(C2×D3)⋊C4C22semidirect
43. C32×Dic3⋊C4C22semidirect
45. #88814C22semidirect
46. #88807C22semidirect
47. Dic3⋊(C3⋊Dic3)C22semidirect
50. C3×Dic3⋊Dic3C22semidirect
51. C3×Dic3⋊Dic3C22semidirect
52. C3×#3722C22semidirect
54. C3×(C2×D3)⋊Dic3C22semidirect
55. C3×Dic32C22semidirect
82. #63910D3semidirect
94. #63891D3semidirect
101. #63878D3semidirect
137. C3×D3×Dic3D4semidirect
178. C2×#626C2×D3semidirect
220. C4⋊(C3⋊Dic3)C2×D3semidirect
222. C4×C3⋊Dic3C2×D3semidirect
233. C3×(C2×D3)⋊C4C2×D3semidirect
234. C3×(C2×D3)⋊C4C2×D3semidirect
243. C3×Dic3⋊C4C2×D3semidirect
244. C3×Dic3⋊C4C2×D3semidirect
256. Dic3⋊Dic3C2×D3semidirect
257. Dic3⋊Dic3C2×D3semidirect
263. #3722C2×D3semidirect
272. (C2×D3)⋊Dic3C2×D3semidirect
273. Dic32C2×D3semidirect
277. C2×C3⋊(C3⋊D3)#41semidirect
283. C2×C3×C3⋊D3#41semidirect
485. D3×Dic3D12semidirect
606. (C2×D3)⋊C4D32semidirect
622. Dic3⋊C4D32semidirect
668. C2×C3⋊D3#237semidirect
769. C33#525semidirect
1118. C32#5524semidirect
1119. C32#5606semidirect
1120. C32#5656semidirect
1230. C3#10594079semidirect
1231. C3#10594267semidirect
1232. C3#10594626semidirect

Maximal subgroups

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

subgroupindex
C2×#889612
C2×D3×#6242
#117236912
#117235412
#117234852
#117234612
C3×#639102
C3×#638912
C3×#638782
#117229882
#117229722
#117229632
#117229492
#117229372
#117229282
#105946263
#105942673
#105940793