Finite Group Databasebeta

← #13171943

Subgroups — #13171943

Order 1728.

1286 conjugacy classes of subgroups.

The subgroup lattice has 1130 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723717C211yesmaximal, characteristic, complemented
2#11723637C211yesmaximal, characteristic, complemented
3#11723626C211yesmaximal, characteristic, complemented
4C2×Dic3⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
5C3×#63978C211yesmaximal, characteristic, complemented
6C3×#67⋊Dic3C211yesmaximal, characteristic, complemented
7C3×#63952C211yesmaximal, characteristic, complemented
8#11723023C211yesmaximal, characteristic, complemented
9#11723022C211yesmaximal, characteristic, complemented
10#11723012C211yesmaximal, characteristic, complemented
11#11722997C211yesmaximal, characteristic, complemented
12#11722988C211yesmaximal, characteristic, complemented
13#11722957C211yesmaximal, characteristic, complemented
14Dic3×#626C211yesmaximal, characteristic, complemented
15#11722915C211yesmaximal, characteristic, complemented
16#10595193—31nomaximal
17#10594995—31nomaximal
18#10594218—31nomaximal
19C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C22×C3×C3⋊Dic3C2211yescharacteristic
23C2×C32×#67C2211yescharacteristic
24C22×C32×Dic3C2211yescharacteristic
25C2×#6295C2211yescharacteristic
26C2×#6290C2211yescharacteristic
27C2×Dic3×C3⋊D3C2211yescharacteristic
28C2×C3×#626C2211yescharacteristic
29C2×C3×#624C2211yescharacteristic
30C2×C3×D3×Dic3C2211yescharacteristic
31C32×#217C2211yescharacteristic
32#88815C2211yescharacteristic
33#88814C2211yescharacteristic
34#88814C2211yescharacteristic
35#88807C2211yescharacteristic
36#88806C2211yescharacteristic
37Dic3⋊(C3⋊Dic3)C2211yescharacteristic
38Dic3⋊(C3⋊Dic3)C2211yescharacteristic
39Dic3⋊(C3⋊Dic3)C2211yescharacteristic
40Dic3⋊(C3⋊Dic3)C2211yescharacteristic
41#88803C2211yescharacteristic
42#88803C2211yescharacteristic
43(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
44Dic3×C3⋊Dic3C2211yescharacteristic
45C3×#3724C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×#3722C2211yescharacteristic
49C3×#3722C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×Dic32C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64148—31no—
55C2×C4⋊(C3⋊Dic3)—31no—
56#64090—31no—
57C3×#939—31no—
58C3×D4×Dic3—31no—
59C3×#930—31no—
60C3×C4×#67—31no—
61C3×#67⋊C4—31no—
62C3×#67⋊C4—31no—
63#63980—31no—
64#63980—31no—
65#63980—31no—
66#63980—61no—
67#63978—31no—
68#63978—31no—
69#63978D311yescharacteristic, complemented
70#67⋊Dic3—31no—
71#67⋊Dic3—31no—
72#67⋊Dic3—61no—
73#67⋊Dic3D311yescharacteristic, complemented
74Dic3×#67—31no—
75#63966—31no—
76C2×Dic3⋊Dic3—31no—
77C2×Dic3⋊Dic3—31no—
78C2×Dic3⋊Dic3—61no—
79#63958—31no—
80#63956—31no—
81#63952D311yescharacteristic, complemented
82#63908—31no—
83#63906—31no—
84#63905—31no—
85C4×#626—31no—
86Dic3×D12—31no—
87#63891—31no—
88#63891—31no—
89#63890—31no—
90#63869—31no—
91#63868—31no—
92#63867—31no—
93#63862—31no—
94#63861—31no—
95#63861—31no—
96#63859—31no—
97#63855—31no—
98#63853—31no—
99#63846—31no—
100#63841—31no—
101#63836—31no—
102C23×C33C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C3×C3⋊D3C2311yescharacteristic
105C22×C32×D3C2311yescharacteristic
106C2×C3⋊(C3⋊Dic3)—41no—
107C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
108C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
109C3×#638—22no—
110C3×#638—22no—
111C2×C3×C3⋊Dic3—41no—
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C32×#67—22no—
117C2×C32×Dic3—22no—
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123#6295—41no—
124#6290—41no—
125Dic3×C3⋊D3—41no—
126C3×#626—22no—
127C3×#624—22no—
128C3×D3×Dic3—41no—
129#5618—91no—
130#5565—91no—
131#5540—91no—
132C2×C32×D4—31no—
133C22×C32×C4—31no—
134C2×#638—31no—
135C2×#638C2×D311yescharacteristic
136C2×#638C2×D311yescharacteristic
137C22×C3⋊Dic3—31no—
138C22×C3⋊Dic3—31no—
139C22×C3⋊Dic3—31no—
140C22×C3⋊Dic3—61no—
141C22×C3⋊Dic3—61no—
142C22×C3⋊Dic3—61no—
143C22×C3⋊Dic3—121no—
144C22×C3⋊Dic3C2×D311yescharacteristic
145C2×C4×C3⋊D3—31no—
146C2×C3×#67—21no—
147C2×C3×#67—31no—
148C2×C3×#67—31no—
149C2×C3×#67—31no—
150C2×C3×#67—31no—
151C2×C3×#67—31no—
152C2×C3×#67—61no—
153C2×C3×#67—61no—
154C2×C3×#67C2×D311yescharacteristic
155C2×C3×#67C2×D311yescharacteristic
156C22×C3×Dic3—21no—
157C22×C3×Dic3—31no—
158C22×C3×Dic3—31no—
159C22×C3×Dic3—31no—
160C22×C3×Dic3—61no—
161C22×C3×Dic3C2×D311yescharacteristic
162C22×C3×Dic3C2×D311yescharacteristic
163C2×C3×D12—31no—
164C2×C3×C4×D3—31no—
165C2×C3×C4×D3—31no—
166C2×C3×C4×D3—31no—
167C2×#626—31no—
168C2×#626—31no—
169C2×#626C2×D311yescharacteristic
170C2×#625—31no—
171C2×#625—31no—
172C2×#625—31no—
173C2×#625—61no—
174C2×#624C2×D311yescharacteristic
175C2×D3×Dic3—31no—
176C2×D3×Dic3—31no—
177C2×D3×Dic3—61no—
178C2×D3×Dic3C2×D311yescharacteristic
179C32×C22⋊C4—31no—
180#3757—31no—
181#3752—31no—
182#3752—31no—
183C4⋊(C3⋊Dic3)—31no—
184C4⋊(C3⋊Dic3)—31no—
185C4⋊(C3⋊Dic3)—31no—
186C4⋊(C3⋊Dic3)—31no—
187#3750—31no—
188#3750—31no—
189C4×C3⋊Dic3—31no—
190C3×#217—21no—
191C3×#217—31no—
192C3×#217—31no—
193C3×#217C2×D311yescharacteristic
194C3×#217C2×D311yescharacteristic
195C3×(C2×D3)⋊C4—31no—
196C3×(C2×D3)⋊C4—31no—
197C3×(C2×D3)⋊C4—31no—
198C3×(C2×D3)⋊C4—31no—
199C3×(C2×D3)⋊C4—31no—
200C3×(C2×D3)⋊C4—31no—
201C3×C4⋊Dic3—31no—
202C3×C4⋊Dic3—31no—
203C3×Dic3⋊C4—31no—
204C3×Dic3⋊C4—31no—
205C3×Dic3⋊C4—31no—
206C3×Dic3⋊C4—31no—
207C3×C4×Dic3—31no—
208C3×C4×Dic3—31no—
209C3×C4×Dic3—31no—
210C3×C4×Dic3—31no—
211#3724—31no—
212#3724—31no—
213#3724—31no—
214#3724—61no—
215#3724C2×D311yescharacteristic
216Dic3⋊Dic3—31no—
217Dic3⋊Dic3—31no—
218Dic3⋊Dic3—31no—
219Dic3⋊Dic3—31no—
220Dic3⋊Dic3—31no—
221Dic3⋊Dic3—31no—
222Dic3⋊Dic3—31no—
223Dic3⋊Dic3—31no—
224Dic3⋊Dic3—31no—
225Dic3⋊Dic3—31no—
226Dic3⋊Dic3—31no—
227Dic3⋊Dic3—31no—
228Dic3⋊Dic3—61no—
229Dic3⋊Dic3—61no—
230Dic3⋊Dic3—61no—
231Dic3⋊Dic3—61no—
232Dic3⋊Dic3—61no—
233Dic3⋊Dic3C2×D311yescharacteristic
234Dic3⋊Dic3C2×D311yescharacteristic
235#3722—31no—
236#3722—31no—
237#3722C2×D311yescharacteristic
238#3722C2×D311yescharacteristic
239(C2×D3)⋊Dic3—31no—
240(C2×D3)⋊Dic3—31no—
241(C2×D3)⋊Dic3—31no—
242(C2×D3)⋊Dic3—31no—
243(C2×D3)⋊Dic3—31no—
244(C2×D3)⋊Dic3—31no—
245(C2×D3)⋊Dic3—31no—
246(C2×D3)⋊Dic3—31no—
247(C2×D3)⋊Dic3—31no—
248(C2×D3)⋊Dic3—31no—
249(C2×D3)⋊Dic3—61no—
250(C2×D3)⋊Dic3—61no—
251(C2×D3)⋊Dic3—61no—
252(C2×D3)⋊Dic3C2×D311yescharacteristic
253(C2×D3)⋊Dic3C2×D311yescharacteristic
254Dic32—31no—
255Dic32—31no—
256Dic32—61no—
257Dic32C2×D311yescharacteristic
258Dic32C2×D311yescharacteristic
259C22×C33—21no—
260C22×C33—21no—
261C22×C33#4112yes—
262C22×C33C2411yescharacteristic
263C2×C3×C3⋊D3—21no—
264C2×C3×C3⋊D3—21no—
265C2×C3×C3⋊D3—21no—
266C2×C3×C3⋊D3—21no—
267C2×C3×C3⋊D3—21no—
268C2×C3×C3⋊D3—21no—
269C2×C32×D3—21no—
270C2×C32×D3—21no—
271C2×C32×D3—21no—
272C3⋊(C3⋊Dic3)—21no—
273C3⋊(C3⋊Dic3)—21no—
274C3×C3⋊Dic3—21no—
275C3×C3⋊Dic3—21no—
276C3×C3⋊Dic3—21no—
277C3×C3⋊Dic3—21no—
278C32×Dic3—21no—
279C32×Dic3—21no—
280C32×Dic3—21no—
281C32×Dic3—21no—
282C32×Dic3#4112yes—
283C3×#121—91no—
284C3×C4×D4—91no—
285C3×C4×D4—91no—
286#939—31no—
287#939—91no—
288#939—91no—
289#939—91no—
290#939—91no—
291#939—91no—
292#939—181no—
293#938—91no—
294D4×Dic3—31no—
295D4×Dic3—91no—
296D4×Dic3—91no—
297#930—31no—
298#930—91no—
299#930—91no—
300#929—91no—
301C4×#67—31no—
302C4×#67—91no—
303#926—91no—
304C2×C4⋊Dic3—91no—
305C2×C4⋊Dic3—91no—
306C2×C4⋊Dic3—181no—
307C2×Dic3⋊C4—91no—
308#898—91no—
309#898—91no—
310#894—91no—
311#892—91no—
312#890—91no—
313#889—91no—
314#886—91no—
315#886—91no—
316#884—91no—
317#883—91no—
318#883—91no—
319#67⋊C4—31no—
320#67⋊C4—31no—
321#67⋊C4—91no—
322#67⋊C4—91no—
323#67⋊C4—181no—
324#879—91no—
325#879—91no—
326#879—91no—
327#876—91no—
328C4×D12—91no—
329#872—91no—
330#870—91no—
331C23×C32—21no—
332C23×C32—21no—
333C23×C32—21no—
334C23×C32—31no—
335C23×C32—41no—
336C23×C32C22×D311yescharacteristic
337C23×C32C22×D311yescharacteristic
338C23×C32C22×D311yescharacteristic
339C22×C3⋊D3C22×D311yescharacteristic
340C22×C3⋊D3C22×D311yescharacteristic
341C22×C3×D3—21no—
342C22×C3×D3—31no—
343C22×C3×D3—31no—
344C22×C3×D3—31no—
345C22×C3×D3—31no—
346C22×C3×D3—61no—
347C22×C3×D3—61no—
348C22×C3×D3C22×D311yescharacteristic
349C22×C3×D3C22×D311yescharacteristic
350C32×D4—62no—
351C2×C32×C4—31no—
352C2×C32×C4—31no—
353C2×C32×C4—31no—
354C2×C32×C4—31no—
355C2×C32×C4—31no—
356C2×C32×C4—62no—
357#638—22no—
358#638—22no—
359#638—121no—
360C2×C3⋊Dic3—31no—
361C2×C3⋊Dic3—31no—
362C2×C3⋊Dic3—31no—
363C2×C3⋊Dic3—31no—
364C2×C3⋊Dic3—31no—
365C2×C3⋊Dic3—31no—
366C2×C3⋊Dic3—41no—
367C2×C3⋊Dic3—61no—
368C2×C3⋊Dic3—61no—
369C2×C3⋊Dic3—61no—
370C2×C3⋊Dic3—61no—
371C2×C3⋊Dic3—61no—
372C2×C3⋊Dic3—61no—
373C2×C3⋊Dic3—121no—
374C2×C3⋊Dic3—121no—
375C2×C3⋊Dic3—121no—
376C2×C3⋊Dic3—121no—
377C2×C3⋊Dic3—121no—
378C2×C3⋊Dic3—122no—
379C2×C3⋊Dic3—122no—
380C2×C3⋊Dic3—122no—
381C2×C3⋊Dic3—124no—
382C2×C3⋊Dic3C22×D311yescharacteristic
383C2×C3⋊Dic3C22×D311yescharacteristic
384C2×C3⋊Dic3C22×D311yescharacteristic
385C2×C3⋊Dic3C22×D311yescharacteristic
386C4×C3⋊D3—121no—
387C3×#67—22no—
388C3×#67—22no—
389C3×#67—42no—
390C3×#67—64no—
391C3×#67—62no—
392C3×#67—62no—
393C3×#67—62no—
394C3×#67—62no—
395C3×#67—62no—
396C3×#67—122no—
397C2×C3×Dic3—24no—
398C2×C3×Dic3—22no—
399C2×C3×Dic3—22no—
400C2×C3×Dic3—21no—
401C2×C3×Dic3—21no—
402C2×C3×Dic3—21no—
403C2×C3×Dic3—21no—
404C2×C3×Dic3—21no—
405C2×C3×Dic3—31no—
406C2×C3×Dic3—31no—
407C2×C3×Dic3—31no—
408C2×C3×Dic3—31no—
409C2×C3×Dic3—31no—
410C2×C3×Dic3—31no—
411C2×C3×Dic3—31no—
412C2×C3×Dic3—31no—
413C2×C3×Dic3—61no—
414C2×C3×Dic3—61no—
415C2×C3×Dic3—61no—
416C2×C3×Dic3—61no—
417C2×C3×Dic3—121no—
418C2×C3×Dic3—121no—
419C2×C3×Dic3—121no—
420C2×C3×Dic3—122no—
421C2×C3×Dic3C22×D311yescharacteristic
422C2×C3×Dic3C22×D311yescharacteristic
423C2×C3×Dic3C22×D311yescharacteristic
424C2×C3×Dic3C22×D311yescharacteristic
425C2×C3×Dic3C22×D311yescharacteristic
426C2×C3×Dic3C22×D311yescharacteristic
427C2×C3×Dic3C22×D311yescharacteristic
428C2×C3×Dic3C22×D311yescharacteristic
429C2×C3×Dic3C22×D311yescharacteristic
430C2×C3×Dic3C22×D311yescharacteristic
431C3×D12—62no—
432C3×C4×D3—62no—
433C3×C4×D3—62no—
434C3×C4×D3—121no—
435#626—22no—
436#626—121no—
437#626—121no—
438#625—121no—
439#625—121no—
440#625—121no—
441#625—122no—
442#624—22no—
443D3×Dic3—41no—
444D3×Dic3—121no—
445D3×Dic3—121no—
446D3×Dic3—122no—
447#553—271noSylow
448C2×C33—22no—
449C2×C33C2×#4111yescharacteristic
450C2×C33C2×#4111yescharacteristic
451C2×C33H(5,𝔽2)11yescharacteristic
452C3×C3⋊D3—41no—
453C3×C3⋊D3—41no—
454C32×D3—41no—
455C2×C3×D4—31no—
456C2×C3×D4—31no—
457C2×C3×D4—61no—
458C2×C3×D4—91no—
459C2×C3×D4—91no—
460C2×C3×D4—91no—
461C22×C3×C4—31no—
462C22×C3×C4—31no—
463C22×C3×C4—61no—
464C22×C3×C4—91no—
465C22×C3×C4—91no—
466C22×C3×C4—91no—
467C2×#67—31no—
468C2×#67—31no—
469C2×#67—31no—
470C2×#67—31no—
471C2×#67—31no—
472C2×#67—61no—
473C2×#67—61no—
474C2×#67—91no—
475C2×#67—91no—
476C2×#67—91no—
477C2×#67—91no—
478C2×#67—91no—
479C2×#67—181no—
480C2×#67D3211yescharacteristic
481C22×Dic3—31no—
482C22×Dic3—31no—
483C22×Dic3—31no—
484C22×Dic3—61no—
485C22×Dic3—91no—
486C22×Dic3—91no—
487C22×Dic3—91no—
488C22×Dic3—91no—
489C22×Dic3—181no—
490C22×Dic3—181no—
491C22×Dic3—181no—
492C22×Dic3—361no—
493C22×Dic3D3211yescharacteristic
494C2×D12—31no—
495C2×D12—91no—
496C2×C4×D3—31no—
497C2×C4×D3—31no—
498C2×C4×D3—31no—
499C2×C4×D3—91no—
500C2×C4×D3—91no—
501C2×C4×D3—181no—
502C3×C4⋊C4—91no—
503C3×C4⋊C4—91no—
504C3×C4⋊C4—91no—
505C3×C22⋊C4—31no—
506C3×C22⋊C4—31no—
507C3×C22⋊C4—61no—
508C3×C22⋊C4—91no—
509C3×C22⋊C4—91no—
510C3×C22⋊C4—91no—
511C3×C22⋊C4—91no—
512C3×C42—91no—
513C3×C42—91no—
514#217—31no—
515#217—31no—
516#217—91no—
517#217—91no—
518#217—91no—
519#217—91no—
520#217—91no—
521#217—91no—
522#217—181no—
523#217D3211yescharacteristic
524(C2×D3)⋊C4—31no—
525(C2×D3)⋊C4—31no—
526(C2×D3)⋊C4—31no—
527(C2×D3)⋊C4—31no—
528(C2×D3)⋊C4—31no—
529(C2×D3)⋊C4—31no—
530(C2×D3)⋊C4—91no—
531(C2×D3)⋊C4—91no—
532(C2×D3)⋊C4—91no—
533(C2×D3)⋊C4—91no—
534(C2×D3)⋊C4—91no—
535(C2×D3)⋊C4—91no—
536(C2×D3)⋊C4—91no—
537(C2×D3)⋊C4—91no—
538(C2×D3)⋊C4—91no—
539(C2×D3)⋊C4—181no—
540(C2×D3)⋊C4—181no—
541C4⋊Dic3—31no—
542C4⋊Dic3—31no—
543C4⋊Dic3—91no—
544C4⋊Dic3—91no—
545C4⋊Dic3—91no—
546C4⋊Dic3—91no—
547C4⋊Dic3—91no—
548C4⋊Dic3—91no—
549C4⋊Dic3—91no—
550C4⋊Dic3—91no—
551C4⋊Dic3—91no—
552C4⋊Dic3—91no—
553C4⋊Dic3—181no—
554C4⋊Dic3—181no—
555C4⋊Dic3—181no—
556C4⋊Dic3—181no—
557Dic3⋊C4—31no—
558Dic3⋊C4—31no—
559Dic3⋊C4—31no—
560Dic3⋊C4—31no—
561Dic3⋊C4—91no—
562Dic3⋊C4—91no—
563Dic3⋊C4—91no—
564Dic3⋊C4—91no—
565Dic3⋊C4—91no—
566Dic3⋊C4—91no—
567Dic3⋊C4—91no—
568Dic3⋊C4—91no—
569Dic3⋊C4—91no—
570Dic3⋊C4—91no—
571Dic3⋊C4—91no—
572Dic3⋊C4—181no—
573Dic3⋊C4—181no—
574C4×Dic3—31no—
575C4×Dic3—31no—
576C4×Dic3—31no—
577C4×Dic3—31no—
578C4×Dic3—91no—
579C4×Dic3—91no—
580C4×Dic3—91no—
581C4×Dic3—181no—
582C22×C32—21no—
583C22×C32—21no—
584C22×C32—22no—
585C22×C32—22no—
586C22×C32—21no—
587C22×C32—21no—
588C22×C32—21no—
589C22×C32—21no—
590C22×C32—21no—
591C22×C32—21no—
592C22×C32—21no—
593C22×C32—22no—
594C22×C32—22no—
595C22×C32—22no—
596C22×C32—42no—
597C22×C32—41no—
598C22×C32—41no—
599C22×C32—41no—
600C22×C32—41no—
601C22×C32—41no—
602C22×C32—42no—
603C22×C32—42no—
604C22×C32—61no—
605C22×C32—61no—
606C22×C32—61no—
607C22×C32#23512yes—
608C22×C32#23512yes—
609C22×C32#23712yes—
610C22×C32C23×D311yescharacteristic
611C22×C32C23×D311yescharacteristic
612C22×C32C23×D311yescharacteristic
613C2×C3⋊D3—21no—
614C2×C3⋊D3—21no—
615C2×C3⋊D3—21no—
616C2×C3⋊D3—21no—
617C2×C3⋊D3—21no—
618C2×C3⋊D3—21no—
619C2×C3×D3—21no—
620C2×C3×D3—21no—
621C2×C3×D3—21no—
622C2×C3×D3—21no—
623C2×C3×D3—21no—
624C2×C3×D3—21no—
625C2×C3×D3—41no—
626C2×C3×D3—41no—
627C2×C3×D3—41no—
628C2×C3×D3—62no—
629C2×C3×D3—61no—
630C2×C3×D3—61no—
631C2×C3×D3—61no—
632C2×C3×D3—61no—
633C2×C3×D3—61no—
634C2×C3×D3—61no—
635C2×C3×D3—61no—
636C2×C3×D3—61no—
637C2×C3×D3—61no—
638C2×C3×D3—61no—
639C2×C3×D3—61no—
640C2×C3×D3—61no—
641C2×C3×D3—121no—
642C2×C3×D3—121no—
643C2×C3×D3—121no—
644C2×C3×D3—121no—
645C2×C3×D3—121no—
646C32×C4—32no—
647C32×C4—61no—
648C32×C4—61no—
649C32×C4—61no—
650C32×C4—61no—
651C3⋊Dic3—21no—
652C3⋊Dic3—21no—
653C3⋊Dic3—21no—
654C3⋊Dic3—21no—
655C3⋊Dic3—61no—
656C3⋊Dic3—61no—
657C3⋊Dic3—62no—
658C3⋊Dic3—62no—
659C3⋊Dic3—61no—
660C3⋊Dic3—61no—
661C3⋊Dic3—61no—
662C3⋊Dic3—61no—
663C3⋊Dic3—121no—
664C3⋊Dic3—121no—
665C3⋊Dic3—121no—
666C3⋊Dic3—121no—
667C3⋊Dic3—122no—
668C3⋊Dic3—122no—
669C3×Dic3—22no—
670C3×Dic3—21no—
671C3×Dic3—21no—
672C3×Dic3—21no—
673C3×Dic3—21no—
674C3×Dic3—21no—
675C3×Dic3—21no—
676C3×Dic3—21no—
677C3×Dic3—21no—
678C3×Dic3—22no—
679C3×Dic3—41no—
680C3×Dic3—41no—
681C3×Dic3—41no—
682C3×Dic3—62no—
683C3×Dic3—61no—
684C3×Dic3—61no—
685C3×Dic3—61no—
686C3×Dic3—61no—
687C3×Dic3—61no—
688C3×Dic3—61no—
689C3×Dic3—61no—
690C3×Dic3—61no—
691C3×Dic3—121no—
692C3×Dic3—121no—
693C3×Dic3—121no—
694C3×Dic3#23712yes—
695C3×Dic3#23712yes—
696#126—271no—
697#126—271no—
698#125—271no—
699#123—271no—
700#123—271no—
701#121—91no—
702#121—271no—
703#121—271no—
704#121—271no—
705C4×D4—91no—
706C4×D4—91no—
707C4×D4—271no—
708C4×D4—271no—
709#117—271no—
710C2×C4⋊C4—271no—
711C33#55311yescharacteristic, complemented, Sylow
712C23×C3—21no—
713C23×C3—21no—
714C23×C3—21no—
715C23×C3—31no—
716C23×C3—31no—
717C23×C3—41no—
718C23×C3—61no—
719C23×C3—91no—
720C23×C3—91no—
721C23×C3C2×D3211yescharacteristic
722C23×C3C2×D3211yescharacteristic
723C23×C3C2×D3211yescharacteristic
724C22×D3—31no—
725C22×D3—31no—
726C22×D3—31no—
727C22×D3—31no—
728C22×D3—61no—
729C22×D3—61no—
730C22×D3C2×D3211yescharacteristic
731C3×D4—62no—
732C3×D4—62no—
733C3×D4—122no—
734C3×D4—182no—
735C3×D4—182no—
736C3×D4—182no—
737C2×C3×C4—31no—
738C2×C3×C4—31no—
739C2×C3×C4—31no—
740C2×C3×C4—31no—
741C2×C3×C4—31no—
742C2×C3×C4—31no—
743C2×C3×C4—31no—
744C2×C3×C4—31no—
745C2×C3×C4—31no—
746C2×C3×C4—31no—
747C2×C3×C4—61no—
748C2×C3×C4—61no—
749C2×C3×C4—61no—
750C2×C3×C4—61no—
751C2×C3×C4—61no—
752C2×C3×C4—62no—
753C2×C3×C4—62no—
754C2×C3×C4—64no—
755C2×C3×C4—91no—
756C2×C3×C4—91no—
757C2×C3×C4—91no—
758C2×C3×C4—91no—
759C2×C3×C4—182no—
760C2×C3×C4—361no—
761C2×C3×C4—361no—
762#67—22no—
763#67—64no—
764#67—62no—
765#67—62no—
766#67—62no—
767#67—62no—
768#67—62no—
769#67—122no—
770#67—361no—
771#67—361no—
772#67—361no—
773#67—361no—
774#67—361no—
775#67—362no—
776C2×Dic3—22no—
777C2×Dic3—31no—
778C2×Dic3—31no—
779C2×Dic3—31no—
780C2×Dic3—31no—
781C2×Dic3—31no—
782C2×Dic3—31no—
783C2×Dic3—31no—
784C2×Dic3—31no—
785C2×Dic3—61no—
786C2×Dic3—61no—
787C2×Dic3—61no—
788C2×Dic3—61no—
789C2×Dic3—91no—
790C2×Dic3—91no—
791C2×Dic3—91no—
792C2×Dic3—91no—
793C2×Dic3—91no—
794C2×Dic3—91no—
795C2×Dic3—121no—
796C2×Dic3—121no—
797C2×Dic3—121no—
798C2×Dic3—122no—
799C2×Dic3—181no—
800C2×Dic3—181no—
801C2×Dic3—181no—
802C2×Dic3—181no—
803C2×Dic3—181no—
804C2×Dic3—181no—
805C2×Dic3—361no—
806C2×Dic3—361no—
807C2×Dic3—361no—
808C2×Dic3—361no—
809C2×Dic3—361no—
810C2×Dic3—361no—
811C2×Dic3—362no—
812C2×Dic3—362no—
813C2×Dic3—362no—
814C2×Dic3—364no—
815C2×Dic3C2×D3211yescharacteristic
816C2×Dic3C2×D3211yescharacteristic
817C2×Dic3C2×D3211yescharacteristic
818C2×Dic3C2×D3211yescharacteristic
819C2×Dic3C2×D3211yescharacteristic
820D12—62no—
821D12—361no—
822C4×D3—62no—
823C4×D3—62no—
824C4×D3—121no—
825C4×D3—361no—
826C4×D3—361no—
827C4×D3—362no—
828C2×C32—22no—
829C2×C32—24no—
830C2×C32—22no—
831C2×C32—22no—
832C2×C32—21no—
833C2×C32—21no—
834C2×C32—21no—
835C2×C32—21no—
836C2×C32—21no—
837C2×C32—21no—
838C2×C32—21no—
839C2×C32—21no—
840C2×C32—21no—
841C2×C32—41no—
842C2×C32—41no—
843C2×C32—41no—
844C2×C32—42no—
845C2×C32—42no—
846C2×C32—44no—
847C2×C32—121no—
848C2×C32C2×#23511yescharacteristic
849C2×C32C2×#23511yescharacteristic
850C2×C32C2×#23711yescharacteristic
851C2×C32C2×#23711yescharacteristic
852C2×C32C2×#23711yescharacteristic
853C2×C32#100411yescharacteristic
854C2×C32D3×#4111yescharacteristic
855C2×C32#100911yescharacteristic
856C2×C32#100911yescharacteristic
857C3⋊D3—41no—
858C3⋊D3—41no—
859C3×D3—41no—
860C3×D3—41no—
861C3×D3—81no—
862C3×D3—122no—
863C3×D3—121no—
864C3×D3—121no—
865C3×D3—121no—
866C3×D3—121no—
867C3×D3—241no—
868C2×D4—31no—
869C2×D4—91no—
870C2×D4—91no—
871C2×D4—91no—
872C2×D4—271no—
873C2×D4—271no—
874C22×C4—31no—
875C22×C4—91no—
876C22×C4—91no—
877C22×C4—91no—
878C22×C4—271no—
879C22×C4—271no—
880C4⋊C4—91no—
881C4⋊C4—91no—
882C4⋊C4—91no—
883C4⋊C4—271no—
884C4⋊C4—271no—
885C4⋊C4—271no—
886C4⋊C4—271no—
887C4⋊C4—271no—
888C4⋊C4—271no—
889C4⋊C4—271no—
890C22⋊C4—31no—
891C22⋊C4—91no—
892C22⋊C4—91no—
893C22⋊C4—91no—
894C22⋊C4—91no—
895C22⋊C4—271no—
896C22⋊C4—271no—
897C22⋊C4—271no—
898C22⋊C4—271no—
899C22⋊C4—271no—
900C42—91no—
901C42—91no—
902C42—271no—
903C22×C3—22no—
904C22×C3—22no—
905C22×C3—21no—
906C22×C3—21no—
907C22×C3—21no—
908C22×C3—21no—
909C22×C3—21no—
910C22×C3—21no—
911C22×C3—21no—
912C22×C3—21no—
913C22×C3—21no—
914C22×C3—22no—
915C22×C3—22no—
916C22×C3—22no—
917C22×C3—41no—
918C22×C3—41no—
919C22×C3—41no—
920C22×C3—41no—
921C22×C3—42no—
922C22×C3—42no—
923C22×C3—41no—
924C22×C3—42no—
925C22×C3—61no—
926C22×C3—61no—
927C22×C3—61no—
928C22×C3—61no—
929C22×C3—61no—
930C22×C3—61no—
931C22×C3—121no—
932C22×C3—121no—
933C22×C3—121no—
934C22×C3—181no—
935C22×C3—181no—
936C22×C3—181no—
937C22×C3—181no—
938C22×C3—181no—
939C22×C3—181no—
940C22×C3#379512yes—
941C22×C3#379812yes—
942C22×C3#380412yes—
943C22×C3C22×D3211yescharacteristic
944C22×C3C22×D3211yescharacteristic
945C22×C3C22×D3211yescharacteristic
946C2×D3—21no—
947C2×D3—21no—
948C2×D3—21no—
949C2×D3—62no—
950C2×D3—61no—
951C2×D3—61no—
952C2×D3—61no—
953C2×D3—61no—
954C2×D3—61no—
955C2×D3—61no—
956C2×D3—61no—
957C2×D3—61no—
958C2×D3—61no—
959C2×D3—61no—
960C2×D3—61no—
961C2×D3—61no—
962C2×D3—121no—
963C2×D3—121no—
964C2×D3—121no—
965C2×D3—121no—
966C2×D3—121no—
967C3×C4—32no—
968C3×C4—32no—
969C3×C4—62no—
970C3×C4—62no—
971C3×C4—61no—
972C3×C4—61no—
973C3×C4—61no—
974C3×C4—61no—
975C3×C4—61no—
976C3×C4—61no—
977C3×C4—61no—
978C3×C4—61no—
979C3×C4—121no—
980C3×C4—121no—
981C3×C4—121no—
982C3×C4—181no—
983C3×C4—181no—
984C3×C4—181no—
985C3×C4—181no—
986Dic3—21no—
987Dic3—21no—
988Dic3—21no—
989Dic3—21no—
990Dic3—62no—
991Dic3—61no—
992Dic3—61no—
993Dic3—61no—
994Dic3—61no—
995Dic3—61no—
996Dic3—61no—
997Dic3—61no—
998Dic3—61no—
999Dic3—121no—
1000Dic3—121no—
1001Dic3—121no—
1002Dic3—182no—
1003Dic3—182no—
1004Dic3—181no—
1005Dic3—181no—
1006Dic3—181no—
1007Dic3—181no—
1008Dic3—181no—
1009Dic3—181no—
1010Dic3—361no—
1011Dic3—361no—
1012Dic3—361no—
1013Dic3—361no—
1014Dic3—362no—
1015Dic3—362no—
1016Dic3#380512yes—
1017C32—21no—
1018C32—21no—
1019C32—21no—
1020C32—41no—
1021C32#554011yescharacteristic, complemented
1022C32#556511yescharacteristic, complemented
1023C32#561811yescharacteristic, complemented
1024C23—31no—
1025C23—91no—
1026C23—91no—
1027C23D3311yescharacteristic
1028D4—62no—
1029D4—182no—
1030D4—182no—
1031D4—182no—
1032D4—1081no—
1033D4—1081no—
1034C2×C4—31no—
1035C2×C4—31no—
1036C2×C4—31no—
1037C2×C4—31no—
1038C2×C4—31no—
1039C2×C4—62no—
1040C2×C4—91no—
1041C2×C4—91no—
1042C2×C4—91no—
1043C2×C4—91no—
1044C2×C4—182no—
1045C2×C4—271no—
1046C2×C4—271no—
1047C2×C4—361no—
1048C2×C4—361no—
1049C2×C4—1081no—
1050C2×C4—1081no—
1051C2×C3—24no—
1052C2×C3—22no—
1053C2×C3—22no—
1054C2×C3—22no—
1055C2×C3—21no—
1056C2×C3—21no—
1057C2×C3—21no—
1058C2×C3—21no—
1059C2×C3—21no—
1060C2×C3—21no—
1061C2×C3—21no—
1062C2×C3—21no—
1063C2×C3—21no—
1064C2×C3—42no—
1065C2×C3—42no—
1066C2×C3—44no—
1067C2×C3—41no—
1068C2×C3—41no—
1069C2×C3—41no—
1070C2×C3—121no—
1071C2×C3—121no—
1072C2×C3—241no—
1073C2×C3—361no—
1074C2×C3—361no—
1075C2×C3C2×#379511yescharacteristic
1076C2×C3C2×#379811yescharacteristic
1077C2×C3#6430811yescharacteristic
1078C2×C3D3×#23711yescharacteristic
1079C2×C3D3×#23711yescharacteristic
1080C2×C3#6431411yescharacteristic
1081C2×C3#6431411yescharacteristic
1082C2×C3C2×#380411yescharacteristic
1083C2×C3C2×#380511yescharacteristic
1084D3—41no—
1085D3—122no—
1086D3—121no—
1087D3—121no—
1088D3—121no—
1089D3—121no—
1090D3—241no—
1091C22—21no—
1092C22—21no—
1093C22—61no—
1094C22—61no—
1095C22—61no—
1096C22—181no—
1097C22—181no—
1098C22—181no—
1099C22—181no—
1100C22—181no—
1101C22—181no—
1102C22#8896012yes—
1103C22C2×D3311yescharacteristic
1104C4—32no—
1105C4—61no—
1106C4—61no—
1107C4—61no—
1108C4—61no—
1109C4—181no—
1110C4—181no—
1111C4—181no—
1112C4—181no—
1113C4—541no—
1114C4—541no—
1115C3—21no—
1116C3—21no—
1117C3—21no—
1118C3—41no—
1119C3#1059421811yescharacteristic, complemented
1120C3#1059499511yescharacteristic, complemented
1121C3#1059519311yescharacteristic, complemented
1122C2—22no—
1123C2—121no—
1124C2—361no—
1125C2—361no—
1126C2D3×#380511yescharacteristic
1127C2#1172442011yescharacteristic
1128C2C2×#8896011yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
hypercenterC23D33
hypocenterC33#553
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. #11723717C2semidirect
2. #11723637C2semidirect
3. #11723626C2semidirect
4. C2×Dic3⋊(C3⋊Dic3)C2semidirect
5. C3×#63978C2semidirect
6. C3×#67⋊Dic3C2semidirect
7. C3×#63952C2semidirect
8. #11723023C2semidirect
9. #11723022C2semidirect
10. #11723012C2semidirect
11. #11722997C2semidirect
12. #11722988C2semidirect
13. #11722957C2semidirect
14. Dic3×#626C2semidirect
15. #11722915C2semidirect
69. #63978D3semidirect
73. #67⋊Dic3D3semidirect
81. #63952D3semidirect
711. C33#553semidirect
1021. C32#5540semidirect
1022. C32#5565semidirect
1023. C32#5618semidirect
1119. C3#10594218semidirect
1120. C3#10594995semidirect
1121. C3#10595193semidirect

Maximal subgroups

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

subgroupindex
#117237172
#117236372
#117236262
C2×Dic3⋊(C3⋊Dic3)2
C3×#639782
C3×#67⋊Dic32
C3×#639522
#117230232
#117230222
#117230122
#117229972
#117229882
#117229572
Dic3×#6262
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