Finite Group Databasebeta

← #13170779

Subgroups — #13170779

Order 1728.

1778 conjugacy classes of subgroups.

The subgroup lattice has 1258 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88954C211yesmaximal, characteristic
2C2×D3×#624C211yesmaximal, characteristic, complemented
3#11723690C211yesmaximal, characteristic, complemented
4#11723539C211yesmaximal, characteristic, complemented
5#11723539C211yesmaximal, characteristic, complemented
6#11723503C211yesmaximal, characteristic, complemented
7C3×#63891C211yesmaximal, characteristic, complemented
8C3×#63890C211yesmaximal, characteristic, complemented
9C3×#63854C211yesmaximal, characteristic, complemented
10#11722995C211yesmaximal, characteristic, complemented
11#11722994C211yesmaximal, characteristic, complemented
12#11722986C211yesmaximal, characteristic, complemented
13#11722985C211yesmaximal, characteristic, complemented
14#11722912C211yesmaximal, characteristic, complemented
15#11722906C211yesmaximal, characteristic, complemented
16#10594608—31nomaximal
17#10594295—31nomaximal
18#10594260—31nomaximal
19C22×D3×C3⋊D3C2211yescharacteristic
20C22×D3×C3⋊D3C2211yescharacteristic
21C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
22C2×#6295C2211yescharacteristic
23C2×#6294C2211yescharacteristic, complemented
24C2×#6289C2211yescharacteristic
25C2×#6289C2211yescharacteristic
26C2×#6289C2211yescharacteristic
27C2×#6289C2211yescharacteristic
28C2×C3×#626C2211yescharacteristic
29C2×C3×#626C2211yescharacteristic
30C2×C3×#625C2211yescharacteristic
31C2×C3×#624C2211yescharacteristic, complemented
32C2×C3×D3×Dic3C2211yescharacteristic, complemented
33C2×C3×D3×Dic3C2211yescharacteristic, complemented
34#88954—24no—
35D3×#624—24no—
36C3×#3752C2211yescharacteristic, complemented
37C3×#3752C2211yescharacteristic, complemented
38C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
39C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
40C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
41C32×C4⋊Dic3C2211yescharacteristic, complemented
42#88815C2211yescharacteristic, complemented
43#88814C2211yescharacteristic, complemented
44#88806C2211yescharacteristic, complemented
45#88806C2211yescharacteristic, complemented
46#88803C2211yescharacteristic, complemented
47#88803C2211yescharacteristic, complemented
48(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
49(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
50C3×#3724C2211yescharacteristic, complemented
51C3×Dic3⋊Dic3C2211yescharacteristic, complemented
52C3×Dic3⋊Dic3C2211yescharacteristic, complemented
53C3×#3722C2211yescharacteristic, complemented
54C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
55C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
56C2×#3811—31no—
57C2×#3811—31no—
58C22×#624—31no—
59C2×#3802—31no—
60C2×C4×D32—31no—
61C2×C4×D32—31no—
62C4⋊C4×C3⋊D3—31no—
63C22⋊C4×C3⋊D3—31no—
64C22⋊C4×C3⋊D3—31no—
65C3×#894—31no—
66C3×#894—31no—
67C3×#886—31no—
68C3×#886—31no—
69C3×#883—31no—
70C3×#883—31no—
71#63974—31no—
72#63969—31no—
73#63969—31no—
74#63961—31no—
75#63961—31no—
76#63921—31no—
77#63921—31no—
78#63921—31no—
79#63921—31no—
80#63921—31no—
81#63921—31no—
82#63921—61no—
83#63921—61no—
84#63905—31no—
85#63905—31no—
86#63900—31no—
87#63900—31no—
88#63900—31no—
89#63900—61no—
90#63891—31no—
91#63891D311yescharacteristic, complemented
92#63890—31no—
93#63890D311yescharacteristic, complemented
94#63884—31no—
95#63884—31no—
96#63883—31no—
97#63883—31no—
98#63854—31no—
99#63854—31no—
100#63854—31no—
101#63854D311yescharacteristic, complemented
102#63850—31no—
103#63850—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×D3×C3⋊D3—22no—
113C2×D3×C3⋊D3—22no—
114C2×D3×C3⋊D3D414yes—
115C2×C33×C4C2311yescharacteristic
116C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
117C4×C3⋊(C3⋊D3)—22no—
118C2×C3×C3⋊Dic3C2311yescharacteristic
119C2×C3×C3⋊Dic3C2311yescharacteristic
120C2×C3×C3⋊Dic3C2311yescharacteristic
121C2×C3×C3⋊Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123C2×C32×Dic3C2311yescharacteristic
124C2×C32×Dic3C2311yescharacteristic
125C2×C32×Dic3C2311yescharacteristic
126#6295—22no—
127#6294—22no—
128#6289—22no—
129#6289—22no—
130#6289—22no—
131#6289—22no—
132C3×#626—22no—
133C3×#626—22no—
134C3×#625—22no—
135C3×#624—22no—
136C3×D3×Dic3—22no—
137C3×D3×Dic3—22no—
138D3×#123—91no—
139D3×#123—91no—
140D3×#123—91no—
141C23×C3⋊D3—31no—
142C23×C3⋊D3—31no—
143C22×D32—31no—
144C22×D32—31no—
145C22×D32—31no—
146C22×D32—31no—
147C22×D32—61no—
148C22×D32—61no—
149C2×C4×C3⋊D3—31no—
150C2×C4×C3⋊D3—31no—
151C2×C4×C3⋊D3—31no—
152C2×C4×C3⋊D3—31no—
153C2×C4×C3⋊D3—31no—
154C2×C4×C3⋊D3—31no—
155C2×C4×C3⋊D3—31no—
156C2×C4×C3⋊D3—61no—
157C2×C4×C3⋊D3—61no—
158C2×C4×C3⋊D3—61no—
159C2×C4×C3⋊D3—121no—
160C2×C3×#67—31no—
161C2×C3×#67—31no—
162C2×C3×#67—31no—
163C2×C3×#67—31no—
164C22×C3×Dic3—31no—
165C22×C3×Dic3—31no—
166C2×C3×D12—31no—
167C2×C3×D12—31no—
168C2×C3×C4×D3—31no—
169C2×C3×C4×D3—31no—
170C2×C3×C4×D3—31no—
171C2×C3×C4×D3—31no—
172#3811—64no—
173#3811—64no—
174C2×#626—31no—
175C2×#626—31no—
176C2×#626C2×D311yescharacteristic
177C2×#626C2×D311yescharacteristic
178C2×#625—31no—
179C2×#625C2×D311yescharacteristic
180C2×#624—31no—
181C2×#624—31no—
182C2×#624—31no—
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×#624—61no—
193C2×#624—61no—
194C2×#624C2×D311yescharacteristic, complemented
195C2×D3×Dic3—31no—
196C2×D3×Dic3—31no—
197C2×D3×Dic3C2×D311yescharacteristic, complemented
198C2×D3×Dic3C2×D311yescharacteristic, complemented
199#3802—64no—
200C4×D32—64no—
201C4×D32—64no—
202C32×C4⋊C4—31no—
203C32×C22⋊C4—31no—
204C32×C22⋊C4—31no—
205#3757—31no—
206#3757—31no—
207#3752—31no—
208#3752—31no—
209#3752C2×D311yescharacteristic, complemented
210#3752C2×D311yescharacteristic, complemented
211C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
212#3750—31no—
213#3750—31no—
214C3×#217—31no—
215C3×#217—31no—
216C3×(C2×D3)⋊C4—21no—
217C3×(C2×D3)⋊C4—21no—
218C3×(C2×D3)⋊C4—31no—
219C3×(C2×D3)⋊C4—31no—
220C3×(C2×D3)⋊C4—31no—
221C3×(C2×D3)⋊C4—31no—
222C3×(C2×D3)⋊C4—31no—
223C3×(C2×D3)⋊C4—31no—
224C3×(C2×D3)⋊C4—31no—
225C3×(C2×D3)⋊C4—31no—
226C3×(C2×D3)⋊C4—61no—
227C3×(C2×D3)⋊C4—61no—
228C3×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
229C3×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
230C3×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
231C3×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
232C3×C4⋊Dic3—21no—
233C3×C4⋊Dic3—31no—
234C3×C4⋊Dic3—31no—
235C3×C4⋊Dic3—31no—
236C3×C4⋊Dic3—31no—
237C3×C4⋊Dic3—61no—
238C3×C4⋊Dic3C2×D311yescharacteristic, complemented
239C3×C4⋊Dic3C2×D311yescharacteristic, complemented
240C3×Dic3⋊C4—31no—
241C3×Dic3⋊C4—31no—
242C3×Dic3⋊C4—31no—
243C3×Dic3⋊C4—31no—
244#3724—31no—
245#3724—31no—
246#3724—31no—
247#3724—31no—
248#3724—31no—
249#3724—61no—
250#3724—61no—
251#3724C2×D311yescharacteristic, complemented
252Dic3⋊Dic3—31no—
253Dic3⋊Dic3—31no—
254Dic3⋊Dic3C2×D311yescharacteristic, complemented
255Dic3⋊Dic3C2×D311yescharacteristic, complemented
256#3722—31no—
257#3722C2×D311yescharacteristic, complemented
258(C2×D3)⋊Dic3—31no—
259(C2×D3)⋊Dic3—31no—
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—31no—
267(C2×D3)⋊Dic3—31no—
268(C2×D3)⋊Dic3—61no—
269(C2×D3)⋊Dic3—61no—
270(C2×D3)⋊Dic3—61no—
271(C2×D3)⋊Dic3—61no—
272(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
273(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
274C22×C33C2411yescharacteristic
275C2×C3⋊(C3⋊D3)C2×D412yes—
276C2×C3⋊(C3⋊D3)#4112yes—
277C2×C3⋊(C3⋊D3)#4112yes—
278C2×C3×C3⋊D3—21no—
279C2×C3×C3⋊D3—21no—
280C2×C3×C3⋊D3—21no—
281C2×C3×C3⋊D3—21no—
282C2×C3×C3⋊D3—21no—
283C2×C3×C3⋊D3C2×D412yes—
284C2×C32×D3—21no—
285C2×C32×D3—21no—
286C2×C32×D3—21no—
287C2×C32×D3—21no—
288C2×C32×D3—21no—
289C2×C32×D3C2×D412yes—
290D3×C3⋊D3—28no—
291D3×C3⋊D3—44no—
292C33×C4—21no—
293C3⋊(C3⋊Dic3)—21no—
294C3×C3⋊Dic3—21no—
295C3×C3⋊Dic3—21no—
296C3×C3⋊Dic3—21no—
297C3×C3⋊Dic3—21no—
298C32×Dic3—21no—
299C32×Dic3—21no—
300C32×Dic3—21no—
301C32×Dic3—21no—
302C2×D3×D4—91no—
303C2×D3×D4—91no—
304C2×D3×D4—91no—
305C22×C4×D3—91no—
306C22×C4×D3—91no—
307C22×C4×D3—91no—
308C3×#123—91no—
309C3×#123—91no—
310C3×#123—91no—
311#935—91no—
312#935—91no—
313#935—91no—
314#929—91no—
315#929—91no—
316#929—91no—
317#894—31no—
318#894—31no—
319#894—91no—
320#894—91no—
321#894—91no—
322#894—91no—
323D3×C4⋊C4—91no—
324D3×C4⋊C4—91no—
325D3×C4⋊C4—91no—
326D3×C4⋊C4—91no—
327D3×C4⋊C4—91no—
328D3×C4⋊C4—91no—
329D3×C4⋊C4—181no—
330#886—31no—
331#886—31no—
332#886—91no—
333#883—31no—
334#883—31no—
335#883—91no—
336#883—91no—
337#883—91no—
338#883—91no—
339D3×C22⋊C4—91no—
340D3×C22⋊C4—91no—
341D3×C22⋊C4—91no—
342D3×C22⋊C4—91no—
343D3×C22⋊C4—91no—
344D3×C22⋊C4—91no—
345D3×C22⋊C4—91no—
346D3×C22⋊C4—91no—
347D3×C22⋊C4—91no—
348D3×C22⋊C4—181no—
349D3×C22⋊C4—181no—
350C23×C32—31no—
351C23×C32—31no—
352C22×C3⋊D3—31no—
353C22×C3⋊D3—31no—
354C22×C3⋊D3—31no—
355C22×C3⋊D3—34no—
356C22×C3⋊D3—61no—
357C22×C3⋊D3—61no—
358C22×C3⋊D3—61no—
359C22×C3⋊D3—62no—
360C22×C3⋊D3—62no—
361C22×C3⋊D3—62no—
362C22×C3⋊D3—62no—
363C22×C3⋊D3—62no—
364C22×C3⋊D3—121no—
365C22×C3⋊D3C22×D311yescharacteristic
366C22×C3⋊D3C22×D311yescharacteristic
367C22×C3×D3—21no—
368C22×C3×D3—21no—
369C22×C3×D3—31no—
370C22×C3×D3—31no—
371C22×C3×D3—31no—
372C22×C3×D3—31no—
373C22×C3×D3—61no—
374C22×C3×D3—61no—
375C22×C3×D3C22×D311yescharacteristic
376C22×C3×D3C22×D311yescharacteristic
377C22×C3×D3C22×D311yescharacteristic
378C22×C3×D3C22×D311yescharacteristic
379C2×D32—34no—
380C2×D32—34no—
381C2×D32—64no—
382C2×D32—62no—
383C2×D32—62no—
384C2×D32—62no—
385C2×D32—62no—
386C2×D32—62no—
387C2×D32—62no—
388C2×D32—62no—
389C2×D32—62no—
390C2×D32—62no—
391C2×D32—62no—
392C2×D32—64no—
393C2×D32—122no—
394C2×D32—122no—
395C2×D32—122no—
396C2×D32—122no—
397C2×C32×C4—21no—
398C2×C32×C4—21no—
399C2×C32×C4—21no—
400C2×C32×C4—31no—
401C2×C32×C4—31no—
402C2×C32×C4—31no—
403C2×C32×C4—31no—
404C2×C32×C4—41no—
405C2×C32×C4C22×D311yescharacteristic
406C2×C32×C4C22×D311yescharacteristic
407C2×C32×C4C22×D311yescharacteristic
408C2×C3⋊Dic3—31no—
409C2×C3⋊Dic3—31no—
410C2×C3⋊Dic3—31no—
411C2×C3⋊Dic3—61no—
412C2×C3⋊Dic3—61no—
413C2×C3⋊Dic3—61no—
414C2×C3⋊Dic3—121no—
415C2×C3⋊Dic3C22×D311yescharacteristic
416C2×C3⋊Dic3C22×D311yescharacteristic
417C2×C3⋊Dic3C22×D311yescharacteristic
418C2×C3⋊Dic3C22×D311yescharacteristic
419C4×C3⋊D3—62no—
420C4×C3⋊D3—62no—
421C4×C3⋊D3—62no—
422C4×C3⋊D3—62no—
423C4×C3⋊D3—62no—
424C4×C3⋊D3—62no—
425C4×C3⋊D3—62no—
426C4×C3⋊D3—64no—
427C4×C3⋊D3—122no—
428C4×C3⋊D3—122no—
429C4×C3⋊D3—124no—
430C3×#67—62no—
431C3×#67—62no—
432C3×#67—62no—
433C3×#67—62no—
434C2×C3×Dic3—21no—
435C2×C3×Dic3—21no—
436C2×C3×Dic3—21no—
437C2×C3×Dic3—21no—
438C2×C3×Dic3—31no—
439C2×C3×Dic3—31no—
440C2×C3×Dic3—31no—
441C2×C3×Dic3—31no—
442C2×C3×Dic3—31no—
443C2×C3×Dic3—31no—
444C2×C3×Dic3—31no—
445C2×C3×Dic3—31no—
446C2×C3×Dic3—61no—
447C2×C3×Dic3—61no—
448C2×C3×Dic3—61no—
449C2×C3×Dic3—61no—
450C2×C3×Dic3—62no—
451C2×C3×Dic3—62no—
452C2×C3×Dic3C22×D311yescharacteristic
453C2×C3×Dic3C22×D311yescharacteristic
454C2×C3×Dic3C22×D311yescharacteristic
455C2×C3×Dic3C22×D311yescharacteristic
456C2×C3×Dic3C22×D311yescharacteristic
457C2×C3×Dic3C22×D311yescharacteristic
458C2×C3×Dic3C22×D311yescharacteristic
459C2×C3×Dic3C22×D311yescharacteristic
460C3×D12—62no—
461C3×D12—62no—
462C3×C4×D3—62no—
463C3×C4×D3—62no—
464C3×C4×D3—62no—
465C3×C4×D3—62no—
466#626—22no—
467#626—22no—
468#626—62no—
469#626—62no—
470#625—22no—
471#625—62no—
472#624—22no—
473#624—62no—
474#624—62no—
475#624—62no—
476#624—62no—
477#624—62no—
478#624—62no—
479#624—62no—
480#624—62no—
481#624—62no—
482#624—122no—
483#624—122no—
484#624—122no—
485#624—122no—
486D3×Dic3—22no—
487D3×Dic3—22no—
488D3×Dic3—62no—
489D3×Dic3—62no—
490C2×#123—271noSylow
491C2×C33C22×D411yescharacteristic
492C2×C33C2×#4111yescharacteristic
493C2×C33C2×#4111yescharacteristic
494C3⋊(C3⋊D3)#12314yescomplemented
495C3×C3⋊D3—22no—
496C3×C3⋊D3—41no—
497C32×D3—22no—
498C32×D3—41no—
499C23×D3—91no—
500C23×D3—91no—
501C23×D3—91no—
502C23×D3—91no—
503C23×D3—91no—
504C23×D3—91no—
505C23×D3—181no—
506C23×D3—181no—
507C2×C3×D4—91no—
508C2×C3×D4—91no—
509C2×C3×D4—91no—
510C22×C3×C4—91no—
511C22×C3×C4—91no—
512C22×C3×C4—91no—
513C2×#67—31no—
514C2×#67—31no—
515C2×#67—31no—
516C2×#67—31no—
517C2×#67—91no—
518C2×#67—91no—
519C22×Dic3—31no—
520C22×Dic3—31no—
521C22×Dic3—91no—
522D3×D4—184no—
523D3×D4—184no—
524D3×D4—184no—
525C2×D12—31no—
526C2×D12—31no—
527C2×D12—91no—
528C2×C4×D3—31no—
529C2×C4×D3—31no—
530C2×C4×D3—31no—
531C2×C4×D3—31no—
532C2×C4×D3—91no—
533C2×C4×D3—91no—
534C2×C4×D3—91no—
535C2×C4×D3—91no—
536C2×C4×D3—91no—
537C2×C4×D3—91no—
538C2×C4×D3—91no—
539C2×C4×D3—91no—
540C2×C4×D3—91no—
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—181no—
552C2×C4×D3—181no—
553C2×C4×D3—181no—
554C2×C4×D3—181no—
555C2×C4×D3—181no—
556C2×C4×D3—184no—
557C2×C4×D3—184no—
558C2×C4×D3—184no—
559C2×C4×D3—361no—
560C3×C4⋊C4—31no—
561C3×C4⋊C4—31no—
562C3×C4⋊C4—61no—
563C3×C4⋊C4—91no—
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×C22⋊C4—91no—
577C3×C22⋊C4—91no—
578#217—31no—
579#217—31no—
580#217—91no—
581#217—91no—
582#217—91no—
583#217—91no—
584#217—91no—
585#217—91no—
586#217—91no—
587#217—181no—
588#217—181no—
589(C2×D3)⋊C4—31no—
590(C2×D3)⋊C4—31no—
591(C2×D3)⋊C4—31no—
592(C2×D3)⋊C4—31no—
593(C2×D3)⋊C4—31no—
594(C2×D3)⋊C4—31no—
595(C2×D3)⋊C4—31no—
596(C2×D3)⋊C4—31no—
597(C2×D3)⋊C4—61no—
598(C2×D3)⋊C4—61no—
599(C2×D3)⋊C4—91no—
600(C2×D3)⋊C4—91no—
601(C2×D3)⋊C4—91no—
602(C2×D3)⋊C4—91no—
603(C2×D3)⋊C4—91no—
604(C2×D3)⋊C4—91no—
605(C2×D3)⋊C4—91no—
606(C2×D3)⋊C4—91no—
607(C2×D3)⋊C4—181no—
608(C2×D3)⋊C4—181no—
609(C2×D3)⋊C4D3211yescharacteristic, complemented
610(C2×D3)⋊C4D3211yescharacteristic, complemented
611C4⋊Dic3—31no—
612C4⋊Dic3—31no—
613C4⋊Dic3—31no—
614C4⋊Dic3—31no—
615C4⋊Dic3—61no—
616C4⋊Dic3—91no—
617C4⋊Dic3D3211yescharacteristic, complemented
618Dic3⋊C4—31no—
619Dic3⋊C4—31no—
620Dic3⋊C4—31no—
621Dic3⋊C4—31no—
622Dic3⋊C4—91no—
623Dic3⋊C4—91no—
624Dic3⋊C4—91no—
625Dic3⋊C4—91no—
626Dic3⋊C4—91no—
627Dic3⋊C4—91no—
628Dic3⋊C4—91no—
629Dic3⋊C4—91no—
630Dic3⋊C4—181no—
631Dic3⋊C4—181no—
632C22×C32—21no—
633C22×C32—21no—
634C22×C32—21no—
635C22×C32—32no—
636C22×C32—41no—
637C22×C32—61no—
638C22×C32—61no—
639C22×C32—61no—
640C22×C32—61no—
641C22×C32—61no—
642C22×C32C23×D311yescharacteristic
643C22×C32C23×D311yescharacteristic
644C22×C32C23×D311yescharacteristic
645C2×C3⋊D3—21no—
646C2×C3⋊D3—21no—
647C2×C3⋊D3—21no—
648C2×C3⋊D3—21no—
649C2×C3⋊D3—21no—
650C2×C3⋊D3—32no—
651C2×C3⋊D3—32no—
652C2×C3⋊D3—32no—
653C2×C3⋊D3—32no—
654C2×C3⋊D3—32no—
655C2×C3⋊D3—32no—
656C2×C3⋊D3—32no—
657C2×C3⋊D3—32no—
658C2×C3⋊D3—32no—
659C2×C3⋊D3—62no—
660C2×C3⋊D3—62no—
661C2×C3⋊D3—62no—
662C2×C3⋊D3—62no—
663C2×C3⋊D3—62no—
664C2×C3⋊D3—62no—
665C2×C3⋊D3—62no—
666C2×C3⋊D3—62no—
667C2×C3⋊D3—62no—
668C2×C3⋊D3—68no—
669C2×C3⋊D3—122no—
670C2×C3⋊D3—122no—
671C2×C3⋊D3—122no—
672C2×C3⋊D3—124no—
673C2×C3⋊D3D3×D412yes—
674C2×C3×D3—21no—
675C2×C3×D3—21no—
676C2×C3×D3—21no—
677C2×C3×D3—21no—
678C2×C3×D3—22no—
679C2×C3×D3—21no—
680C2×C3×D3—21no—
681C2×C3×D3—21no—
682C2×C3×D3—21no—
683C2×C3×D3—21no—
684C2×C3×D3—21no—
685C2×C3×D3—22no—
686C2×C3×D3—32no—
687C2×C3×D3—32no—
688C2×C3×D3—41no—
689C2×C3×D3—41no—
690C2×C3×D3—41no—
691C2×C3×D3—41no—
692C2×C3×D3—62no—
693C2×C3×D3—61no—
694C2×C3×D3—61no—
695C2×C3×D3—61no—
696C2×C3×D3—61no—
697C2×C3×D3—62no—
698C2×C3×D3—61no—
699C2×C3×D3—61no—
700C2×C3×D3—61no—
701C2×C3×D3—61no—
702C2×C3×D3—61no—
703C2×C3×D3—61no—
704C2×C3×D3—121no—
705C2×C3×D3—121no—
706C2×C3×D3—121no—
707C2×C3×D3—121no—
708C2×C3×D3D3×D412yes—
709C2×C3×D3D3×D412yes—
710D32—68no—
711D32—68no—
712D32—128no—
713D32—124no—
714D32—124no—
715D32—128no—
716C32×C4—21no—
717C32×C4—22no—
718C32×C4—21no—
719C32×C4—21no—
720C32×C4—41no—
721C32×C4—41no—
722C32×C4—42no—
723C32×C4—61no—
724C32×C4—61no—
725C32×C4—61no—
726C32×C4—61no—
727C3⋊Dic3—21no—
728C3⋊Dic3—21no—
729C3⋊Dic3—21no—
730C3⋊Dic3—21no—
731C3⋊Dic3—61no—
732C3⋊Dic3—62no—
733C3⋊Dic3—61no—
734C3⋊Dic3—61no—
735C3⋊Dic3—121no—
736C3⋊Dic3—121no—
737C3⋊Dic3—122no—
738C3×Dic3—21no—
739C3×Dic3—21no—
740C3×Dic3—21no—
741C3×Dic3—21no—
742C3×Dic3—21no—
743C3×Dic3—21no—
744C3×Dic3—21no—
745C3×Dic3—21no—
746C3×Dic3—41no—
747C3×Dic3—41no—
748C3×Dic3—41no—
749C3×Dic3—41no—
750C3×Dic3—61no—
751C3×Dic3—61no—
752C3×Dic3—61no—
753C3×Dic3—61no—
754C3×Dic3—61no—
755C3×Dic3—61no—
756C3×Dic3—61no—
757C3×Dic3—61no—
758C3×Dic3—121no—
759C3×Dic3—121no—
760C3×Dic3—121no—
761C3×Dic3—121no—
762C22×D4—271no—
763C23×C4—271no—
764#123—91no—
765#123—91no—
766#123—91no—
767#123—271no—
768#123—271no—
769#123—271no—
770#123—271no—
771#123—271no—
772C2×C4⋊C4—271no—
773C2×C4⋊C4—271no—
774C2×C22⋊C4—271no—
775C2×C22⋊C4—271no—
776C2×C22⋊C4—271no—
777C33C2×#12311yescharacteristic, complemented, Sylow
778C23×C3—31no—
779C23×C3—31no—
780C23×C3—31no—
781C23×C3—31no—
782C23×C3—61no—
783C23×C3—61no—
784C23×C3—91no—
785C23×C3—91no—
786C22×D3—31no—
787C22×D3—31no—
788C22×D3—31no—
789C22×D3—31no—
790C22×D3—61no—
791C22×D3—61no—
792C22×D3—94no—
793C22×D3—94no—
794C22×D3—91no—
795C22×D3—91no—
796C22×D3—91no—
797C22×D3—94no—
798C22×D3—184no—
799C22×D3—181no—
800C22×D3—181no—
801C22×D3—181no—
802C22×D3—182no—
803C22×D3—182no—
804C22×D3—182no—
805C22×D3—182no—
806C22×D3—182no—
807C22×D3—182no—
808C22×D3—182no—
809C22×D3—182no—
810C22×D3—182no—
811C22×D3—182no—
812C22×D3—182no—
813C22×D3—182no—
814C22×D3—182no—
815C22×D3—182no—
816C22×D3—182no—
817C22×D3—184no—
818C22×D3—361no—
819C22×D3—362no—
820C22×D3—362no—
821C22×D3—362no—
822C22×D3—362no—
823C22×D3C2×D3211yescharacteristic
824C22×D3C2×D3211yescharacteristic
825C3×D4—182no—
826C3×D4—182no—
827C3×D4—182no—
828C2×C3×C4—21no—
829C2×C3×C4—21no—
830C2×C3×C4—21no—
831C2×C3×C4—31no—
832C2×C3×C4—31no—
833C2×C3×C4—31no—
834C2×C3×C4—31no—
835C2×C3×C4—31no—
836C2×C3×C4—31no—
837C2×C3×C4—31no—
838C2×C3×C4—31no—
839C2×C3×C4—41no—
840C2×C3×C4—61no—
841C2×C3×C4—61no—
842C2×C3×C4—61no—
843C2×C3×C4—61no—
844C2×C3×C4—91no—
845C2×C3×C4—91no—
846C2×C3×C4—91no—
847C2×C3×C4—91no—
848C2×C3×C4—182no—
849C2×C3×C4—182no—
850C2×C3×C4—182no—
851C2×C3×C4C2×D3211yescharacteristic
852C2×C3×C4C2×D3211yescharacteristic
853C2×C3×C4C2×D3211yescharacteristic
854#67—62no—
855#67—62no—
856#67—62no—
857#67—62no—
858#67—182no—
859#67—182no—
860C2×Dic3—31no—
861C2×Dic3—31no—
862C2×Dic3—31no—
863C2×Dic3—31no—
864C2×Dic3—31no—
865C2×Dic3—31no—
866C2×Dic3—31no—
867C2×Dic3—31no—
868C2×Dic3—61no—
869C2×Dic3—61no—
870C2×Dic3—61no—
871C2×Dic3—61no—
872C2×Dic3—62no—
873C2×Dic3—62no—
874C2×Dic3—91no—
875C2×Dic3—91no—
876C2×Dic3—91no—
877C2×Dic3—181no—
878C2×Dic3—181no—
879C2×Dic3—181no—
880C2×Dic3—182no—
881C2×Dic3—361no—
882C2×Dic3C2×D3211yescharacteristic
883C2×Dic3C2×D3211yescharacteristic
884C2×Dic3C2×D3211yescharacteristic
885C2×Dic3C2×D3211yescharacteristic
886D12—62no—
887D12—62no—
888D12—182no—
889C4×D3—62no—
890C4×D3—62no—
891C4×D3—62no—
892C4×D3—62no—
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—182no—
902C4×D3—182no—
903C4×D3—182no—
904C4×D3—182no—
905C4×D3—182no—
906C4×D3—182no—
907C4×D3—182no—
908C4×D3—182no—
909C4×D3—182no—
910C4×D3—184no—
911C4×D3—362no—
912C4×D3—362no—
913C4×D3—362no—
914C4×D3—362no—
915C4×D3—362no—
916C4×D3—362no—
917C4×D3—364no—
918C2×C32—21no—
919C2×C32—21no—
920C2×C32—21no—
921C2×C32—21no—
922C2×C32—21no—
923C2×C32—21no—
924C2×C32—21no—
925C2×C32—21no—
926C2×C32—21no—
927C2×C32—41no—
928C2×C32—41no—
929C2×C32—41no—
930C2×C32—62no—
931C2×C32—121no—
932C2×C32C2×D3×D411yescharacteristic
933C2×C32C2×D3×D411yescharacteristic
934C2×C32C2×D3×D411yescharacteristic
935C2×C32D3×#4111yescharacteristic
936C2×C32D3×#4111yescharacteristic
937C2×C32D3×#4111yescharacteristic
938C2×C32D3×#4111yescharacteristic
939C2×C32D3×#4111yescharacteristic
940C2×C32D3×#4111yescharacteristic
941C3⋊D3—22no—
942C3⋊D3—34no—
943C3⋊D3—34no—
944C3⋊D3—34no—
945C3⋊D3—41no—
946C3⋊D3—64no—
947C3⋊D3—64no—
948C3⋊D3—64no—
949C3⋊D3—124no—
950C3×D3—22no—
951C3×D3—22no—
952C3×D3—42no—
953C3×D3—42no—
954C3×D3—41no—
955C3×D3—41no—
956C3×D3—62no—
957C3×D3—62no—
958C3×D3—122no—
959C3×D3—122no—
960C3×D3—121no—
961C3×D3—121no—
962C24—271no—
963C24—271no—
964C2×D4—91no—
965C2×D4—91no—
966C2×D4—91no—
967C2×D4—271no—
968C2×D4—544no—
969C22×C4—91no—
970C22×C4—91no—
971C22×C4—91no—
972C22×C4—271no—
973C22×C4—271no—
974C22×C4—271no—
975C22×C4—271no—
976C22×C4—271no—
977C22×C4—271no—
978C22×C4—544no—
979C4⋊C4—31no—
980C4⋊C4—91no—
981C4⋊C4—91no—
982C4⋊C4—91no—
983C4⋊C4—91no—
984C4⋊C4—271no—
985C4⋊C4—271no—
986C4⋊C4—271no—
987C22⋊C4—31no—
988C22⋊C4—31no—
989C22⋊C4—91no—
990C22⋊C4—91no—
991C22⋊C4—91no—
992C22⋊C4—91no—
993C22⋊C4—91no—
994C22⋊C4—271no—
995C22⋊C4—271no—
996C22⋊C4—271no—
997C22⋊C4—271no—
998C22⋊C4—271no—
999C22×C3—21no—
1000C22×C3—21no—
1001C22×C3—21no—
1002C22×C3—32no—
1003C22×C3—32no—
1004C22×C3—41no—
1005C22×C3—62no—
1006C22×C3—62no—
1007C22×C3—61no—
1008C22×C3—61no—
1009C22×C3—61no—
1010C22×C3—61no—
1011C22×C3—61no—
1012C22×C3—61no—
1013C22×C3—61no—
1014C22×C3—61no—
1015C22×C3—61no—
1016C22×C3—61no—
1017C22×C3—92no—
1018C22×C3—121no—
1019C22×C3—121no—
1020C22×C3—121no—
1021C22×C3—121no—
1022C22×C3—181no—
1023C22×C3—181no—
1024C22×C3—181no—
1025C22×C3—181no—
1026C22×C3—181no—
1027C22×C3C22×D3211yescharacteristic
1028C22×C3C22×D3211yescharacteristic
1029C22×C3C22×D3211yescharacteristic
1030C2×D3—21no—
1031C2×D3—21no—
1032C2×D3—21no—
1033C2×D3—21no—
1034C2×D3—21no—
1035C2×D3—32no—
1036C2×D3—32no—
1037C2×D3—62no—
1038C2×D3—61no—
1039C2×D3—61no—
1040C2×D3—61no—
1041C2×D3—61no—
1042C2×D3—62no—
1043C2×D3—61no—
1044C2×D3—61no—
1045C2×D3—61no—
1046C2×D3—61no—
1047C2×D3—61no—
1048C2×D3—61no—
1049C2×D3—92no—
1050C2×D3—92no—
1051C2×D3—92no—
1052C2×D3—92no—
1053C2×D3—92no—
1054C2×D3—92no—
1055C2×D3—92no—
1056C2×D3—92no—
1057C2×D3—92no—
1058C2×D3—121no—
1059C2×D3—121no—
1060C2×D3—121no—
1061C2×D3—121no—
1062C2×D3—182no—
1063C2×D3—182no—
1064C2×D3—182no—
1065C2×D3—182no—
1066C2×D3—182no—
1067C2×D3—182no—
1068C2×D3—182no—
1069C2×D3—182no—
1070C2×D3—182no—
1071C2×D3—188no—
1072C2×D3—188no—
1073C2×D3—188no—
1074C2×D3—362no—
1075C2×D3—362no—
1076C2×D3—362no—
1077C2×D3—368no—
1078C2×D3—364no—
1079C2×D3—364no—
1080C2×D3—364no—
1081C2×D3—368no—
1082C2×D3#380212yes—
1083C3×C4—22no—
1084C3×C4—21no—
1085C3×C4—21no—
1086C3×C4—21no—
1087C3×C4—41no—
1088C3×C4—41no—
1089C3×C4—42no—
1090C3×C4—61no—
1091C3×C4—61no—
1092C3×C4—61no—
1093C3×C4—61no—
1094C3×C4—61no—
1095C3×C4—61no—
1096C3×C4—61no—
1097C3×C4—61no—
1098C3×C4—121no—
1099C3×C4—121no—
1100C3×C4—121no—
1101C3×C4—121no—
1102C3×C4—181no—
1103C3×C4—181no—
1104C3×C4—181no—
1105C3×C4—181no—
1106Dic3—21no—
1107Dic3—21no—
1108Dic3—21no—
1109Dic3—21no—
1110Dic3—61no—
1111Dic3—61no—
1112Dic3—61no—
1113Dic3—61no—
1114Dic3—61no—
1115Dic3—61no—
1116Dic3—61no—
1117Dic3—61no—
1118Dic3—121no—
1119Dic3—121no—
1120Dic3—121no—
1121Dic3—121no—
1122Dic3—182no—
1123Dic3—181no—
1124Dic3—181no—
1125Dic3—181no—
1126Dic3—361no—
1127Dic3—361no—
1128Dic3—362no—
1129C32—21no—
1130C32—21no—
1131C32—21no—
1132C32—41no—
1133C32D3×#12311yescharacteristic, complemented
1134C32D3×#12311yescharacteristic, complemented
1135C32D3×#12311yescharacteristic, complemented
1136C23—31no—
1137C23—31no—
1138C23—91no—
1139C23—91no—
1140C23—274no—
1141C23—271no—
1142C23—542no—
1143C23—542no—
1144C23—542no—
1145C23—542no—
1146C23—542no—
1147D4—182no—
1148D4—182no—
1149D4—182no—
1150D4—542no—
1151C2×C4—31no—
1152C2×C4—31no—
1153C2×C4—31no—
1154C2×C4—31no—
1155C2×C4—91no—
1156C2×C4—91no—
1157C2×C4—91no—
1158C2×C4—91no—
1159C2×C4—182no—
1160C2×C4—182no—
1161C2×C4—182no—
1162C2×C4—271no—
1163C2×C4—542no—
1164C2×C4—542no—
1165C2×C4—542no—
1166C2×C4—542no—
1167C2×C4—542no—
1168C2×C4—542no—
1169C2×C4D3311yescharacteristic
1170C2×C3—21no—
1171C2×C3—21no—
1172C2×C3—21no—
1173C2×C3—21no—
1174C2×C3—21no—
1175C2×C3—21no—
1176C2×C3—21no—
1177C2×C3—21no—
1178C2×C3—21no—
1179C2×C3—41no—
1180C2×C3—41no—
1181C2×C3—41no—
1182C2×C3—62no—
1183C2×C3—62no—
1184C2×C3—122no—
1185C2×C3—122no—
1186C2×C3—121no—
1187C2×C3—121no—
1188C2×C3—182no—
1189C2×C3—361no—
1190C2×C3C2×#380211yescharacteristic
1191C2×C3#6430611yescharacteristic
1192C2×C3#6430611yescharacteristic
1193C2×C3D32×D411yescharacteristic
1194C2×C3D32×D411yescharacteristic
1195C2×C3#6431211yescharacteristic
1196C2×C3#6431211yescharacteristic
1197C2×C3#6431211yescharacteristic
1198C2×C3#6431911yescharacteristic
1199D3—22no—
1200D3—41no—
1201D3—62no—
1202D3—62no—
1203D3—94no—
1204D3—94no—
1205D3—94no—
1206D3—122no—
1207D3—122no—
1208D3—121no—
1209D3—121no—
1210D3—184no—
1211D3—184no—
1212D3—184no—
1213D3—364no—
1214C22—32no—
1215C22—61no—
1216C22—61no—
1217C22—61no—
1218C22—61no—
1219C22—61no—
1220C22—92no—
1221C22—181no—
1222C22—181no—
1223C22—181no—
1224C22—181no—
1225C22—181no—
1226C22—272no—
1227C22—272no—
1228C22—272no—
1229C22—548no—
1230C22—1084no—
1231C22C2×D3311yescharacteristic
1232C4—21no—
1233C4—61no—
1234C4—61no—
1235C4—61no—
1236C4—61no—
1237C4—181no—
1238C4—181no—
1239C4—181no—
1240C4—181no—
1241C4—541no—
1242C3—21no—
1243C3—21no—
1244C3—21no—
1245C3—41no—
1246C3#1059426011yescharacteristic, complemented
1247C3#1059429511yescharacteristic, complemented
1248C3#1059460811yescharacteristic, complemented
1249C2—62no—
1250C2—121no—
1251C2—182no—
1252C2—274no—
1253C2—361no—
1254C2#1172437611yescharacteristic
1255C2D3×#380211yescharacteristic
1256C2#1172441111yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC2×#88954C2
hypercenterC2×C4D33
hypocenterC33C2×#123
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C2×D3×#624C2semidirect
3. #11723690C2semidirect
4. #11723539C2semidirect
5. #11723539C2semidirect
6. #11723503C2semidirect
7. C3×#63891C2semidirect
8. C3×#63890C2semidirect
9. C3×#63854C2semidirect
10. #11722995C2semidirect
11. #11722994C2semidirect
12. #11722986C2semidirect
13. #11722985C2semidirect
14. #11722912C2semidirect
15. #11722906C2semidirect
23. C2×#6294C22semidirect
31. C2×C3×#624C22semidirect
32. C2×C3×D3×Dic3C22semidirect
33. C2×C3×D3×Dic3C22semidirect
36. C3×#3752C22semidirect
37. C3×#3752C22semidirect
38. C3×C4⋊(C3⋊Dic3)C22semidirect
39. C32×(C2×D3)⋊C4C22semidirect
40. C32×(C2×D3)⋊C4C22semidirect
41. C32×C4⋊Dic3C22semidirect
42. #88815C22semidirect
43. #88814C22semidirect
44. #88806C22semidirect
45. #88806C22semidirect
46. #88803C22semidirect
47. #88803C22semidirect
48. (C2×D3)⋊(C3⋊Dic3)C22semidirect
49. (C2×D3)⋊(C3⋊Dic3)C22semidirect
50. C3×#3724C22semidirect
51. C3×Dic3⋊Dic3C22semidirect
52. C3×Dic3⋊Dic3C22semidirect
53. C3×#3722C22semidirect
54. C3×(C2×D3)⋊Dic3C22semidirect
55. C3×(C2×D3)⋊Dic3C22semidirect
91. #63891D3semidirect
93. #63890D3semidirect
101. #63854D3semidirect
194. C2×#624C2×D3semidirect
197. C2×D3×Dic3C2×D3semidirect
198. C2×D3×Dic3C2×D3semidirect
209. #3752C2×D3semidirect
210. #3752C2×D3semidirect
211. C4⋊(C3⋊Dic3)C2×D3semidirect
228. C3×(C2×D3)⋊C4C2×D3semidirect
229. C3×(C2×D3)⋊C4C2×D3semidirect
230. C3×(C2×D3)⋊C4C2×D3semidirect
231. C3×(C2×D3)⋊C4C2×D3semidirect
238. C3×C4⋊Dic3C2×D3semidirect
239. C3×C4⋊Dic3C2×D3semidirect
251. #3724C2×D3semidirect
254. Dic3⋊Dic3C2×D3semidirect
255. Dic3⋊Dic3C2×D3semidirect
257. #3722C2×D3semidirect
272. (C2×D3)⋊Dic3C2×D3semidirect
273. (C2×D3)⋊Dic3C2×D3semidirect
494. C3⋊(C3⋊D3)#123semidirect
609. (C2×D3)⋊C4D32semidirect
610. (C2×D3)⋊C4D32semidirect
617. C4⋊Dic3D32semidirect
777. C33C2×#123semidirect
1133. C32D3×#123semidirect
1134. C32D3×#123semidirect
1135. C32D3×#123semidirect
1246. C3#10594260semidirect
1247. C3#10594295semidirect
1248. C3#10594608semidirect

Maximal subgroups

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

subgroupindex
C2×#889542
C2×D3×#6242
#117236902
#117235392
#117235032
C3×#638912
C3×#638902
C3×#638542
#117229952
#117229942
#117229862
#117229852
#117229122
#117229062
#105946083
#105942953
#105942603