Finite Group Databasebeta

← #13168050

Subgroups — #13168050

Order 1728.

1246 conjugacy classes of subgroups.

The subgroup lattice has 1108 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723688C211yesmaximal, characteristic, complemented
2#11723487C211yesmaximal, characteristic, complemented
3#11723473C211yesmaximal, characteristic, complemented
4#11723464C211yesmaximal, characteristic, complemented
5C3×#63922C211yesmaximal, characteristic
6C3×#63877C211yesmaximal, characteristic, complemented
7C3×#63860C211yesmaximal, characteristic, complemented
8#11723022C211yesmaximal, characteristic, complemented
9#11723020C211yesmaximal, characteristic, complemented
10#11722991C211yesmaximal, characteristic, complemented
11#11722985C211yesmaximal, characteristic, complemented
12#11722928C211yesmaximal, characteristic, complemented
13#11722925C211yesmaximal, characteristic, complemented
14#11722902C211yesmaximal, characteristic, complemented
15D3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
16#10595176—31nomaximal
17#10594117—31nomaximal
18#10594016—31nomaximal
19C22×C3×D32C2211yescharacteristic
20C2×C3×#634C2211yescharacteristic, complemented
21C2×C32×D12C2211yescharacteristic
22C2×#6294C2211yescharacteristic
23C2×Dic3×C3⋊D3C2211yescharacteristic
24C2×D3×C3⋊Dic3C2211yescharacteristic
25C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
26C2×C3×#626C2211yescharacteristic
27C2×C3×#625C2211yescharacteristic
28C2×C3×D3×Dic3C2211yescharacteristic
29#88857C2211yescharacteristic, complemented
30C3×#3752C2211yescharacteristic
31C3×#3750C2211yescharacteristic, complemented
32C32×(C2×D3)⋊C4C2211yescharacteristic
33C32×C4×Dic3C2211yescharacteristic, complemented
34#88815C2211yescharacteristic, complemented
35#88815C2211yescharacteristic, complemented
36#88814C2211yescharacteristic
37#88807C2211yescharacteristic, complemented
38#88806C2211yescharacteristic, complemented
39Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
40#88803C2211yescharacteristic
41(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
42(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
43(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
44(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
45Dic3×C3⋊Dic3C2211yescharacteristic, complemented
46C3×#3724C2211yescharacteristic, complemented
47C3×(C2×D3)⋊Dic3C2211yescharacteristic
48C3×(C2×D3)⋊Dic3C2211yescharacteristic
49C3×(C2×D3)⋊Dic3C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
52C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
53C3×Dic32C2211yescharacteristic, complemented
54#64144—31no—
55#64087—31no—
56#64081—31no—
57C3×#937—31no—
58C3×#936—31no—
59C3×#882—31no—
60C3×#877—31no—
61C3×#875—31no—
62C3×#872—31no—
63#67⋊Dic3—31no—
64#67⋊Dic3—31no—
65#67⋊Dic3—31no—
66#63969—31no—
67#63969—31no—
68D3×#217—31no—
69D3×#217—31no—
70D3×#217—31no—
71#63961—31no—
72C2×(C2×D3)⋊Dic3—31no—
73#63956—31no—
74#63956—31no—
75#63922D311yescharacteristic
76#63921—31no—
77D3×(C2×D3)⋊C4—31no—
78#63905—31no—
79#63902—31no—
80#63896—31no—
81Dic3×D12—31no—
82#63888—31no—
83#63887—31no—
84#63887—31no—
85#63887—31no—
86#63887—61no—
87#63884—31no—
88#63884—31no—
89#63884—31no—
90#63884—61no—
91#63880—31no—
92#63877—31no—
93#63877—31no—
94#63877—61no—
95#63877D311yescharacteristic, complemented
96#63862—31no—
97#63861—31no—
98#63860D311yescharacteristic, complemented
99#63859—31no—
100#63859—31no—
101#63853—31no—
102C22×C3×C3⋊D3C2311yescharacteristic
103C22×C32×D3C2311yescharacteristic
104C22×C32×D3C2311yescharacteristic
105C22×C32×D3C2311yescharacteristic
106C2×C3×D32—22no—
107C2×C3×D32—22no—
108C2×C3×D32—41no—
109C2×C33×C4C2311yescharacteristic
110C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
111C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C3×#634—41no—
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C32×D12—41no—
122#6294—41no—
123Dic3×C3⋊D3—22no—
124D3×C3⋊Dic3—41no—
125D3×C3⋊Dic3—41no—
126C3×#626—22no—
127C3×#625—22no—
128C3×D3×Dic3—22no—
129#5679—91no—
130#5587—91no—
131#5527—91no—
132C23×C3×D3—31no—
133C23×C3×D3—31no—
134C22×D32C2×D311yescharacteristic
135C2×C32×D4—31no—
136C22×C3⋊Dic3—31no—
137C22×C3⋊Dic3—31no—
138C2×C4×C3⋊D3—31no—
139C2×#634C2×D311yescharacteristic, complemented
140C2×C3×#67—31no—
141C2×C3×#67—31no—
142C2×C3×#67—31no—
143C22×C3×Dic3—31no—
144C2×C3×D12—21no—
145C2×C3×D12—31no—
146C2×C3×D12C2×D311yescharacteristic
147C2×C3×D12C2×D311yescharacteristic
148C2×C3×C4×D3—31no—
149C2×C3×Dic6—31no—
150C2×C3×Dic6—31no—
151C2×C3×Dic6—61no—
152C2×#626C2×D311yescharacteristic
153C2×#625C2×D311yescharacteristic
154C2×#624—31no—
155C2×D3×Dic3—31no—
156C2×D3×Dic3—31no—
157C2×D3×Dic3—31no—
158C2×D3×Dic3—31no—
159C2×D3×Dic3—31no—
160C2×D3×Dic3—31no—
161C2×D3×Dic3—31no—
162C2×D3×Dic3—31no—
163C2×D3×Dic3—61no—
164C2×D3×Dic3—61no—
165C2×D3×Dic3—61no—
166C2×D3×Dic3C2×D311yescharacteristic
167C32×C22⋊C4—31no—
168C32×C42—31no—
169#3757—31no—
170#3757—31no—
171#3757—31no—
172#3757—31no—
173#3752—31no—
174#3752C2×D311yescharacteristic
175C4⋊(C3⋊Dic3)—31no—
176#3750—31no—
177#3750—31no—
178#3750—31no—
179#3750—31no—
180#3750—31no—
181#3750—61no—
182#3750—61no—
183#3750—61no—
184#3750—121no—
185#3750C2×D311yescharacteristic, complemented
186C4×C3⋊Dic3—31no—
187C3×#217—31no—
188C3×#217—31no—
189C3×#217—31no—
190C3×#217—31no—
191C3×#217—31no—
192C3×#217—31no—
193C3×(C2×D3)⋊C4—21no—
194C3×(C2×D3)⋊C4—31no—
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×(C2×D3)⋊C4—31no—
202C3×(C2×D3)⋊C4—61no—
203C3×(C2×D3)⋊C4C2×D311yescharacteristic
204C3×(C2×D3)⋊C4C2×D311yescharacteristic
205C3×Dic3⋊C4—31no—
206C3×Dic3⋊C4—31no—
207C3×Dic3⋊C4—31no—
208C3×Dic3⋊C4—31no—
209C3×Dic3⋊C4—61no—
210C3×C4×Dic3—21no—
211C3×C4×Dic3—31no—
212C3×C4×Dic3—31no—
213C3×C4×Dic3C2×D311yescharacteristic, complemented
214C3×C4×Dic3C2×D311yescharacteristic, complemented
215#3724—31no—
216#3724—31no—
217#3724—31no—
218#3724—31no—
219#3724—61no—
220#3724C2×D311yescharacteristic, complemented
221Dic3⋊Dic3—31no—
222Dic3⋊Dic3—31no—
223Dic3⋊Dic3—31no—
224Dic3⋊Dic3—31no—
225Dic3⋊Dic3—31no—
226Dic3⋊Dic3—31no—
227Dic3⋊Dic3—31no—
228Dic3⋊Dic3—31no—
229Dic3⋊Dic3—61no—
230Dic3⋊Dic3—61no—
231#3722—31no—
232(C2×D3)⋊Dic3—31no—
233(C2×D3)⋊Dic3—31no—
234(C2×D3)⋊Dic3—31no—
235(C2×D3)⋊Dic3—31no—
236(C2×D3)⋊Dic3—31no—
237(C2×D3)⋊Dic3—31no—
238(C2×D3)⋊Dic3—31no—
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—61no—
245(C2×D3)⋊Dic3—61no—
246(C2×D3)⋊Dic3—61no—
247(C2×D3)⋊Dic3—61no—
248(C2×D3)⋊Dic3—61no—
249(C2×D3)⋊Dic3C2×D311yescharacteristic
250(C2×D3)⋊Dic3C2×D311yescharacteristic
251(C2×D3)⋊Dic3C2×D311yescharacteristic
252(C2×D3)⋊Dic3C2×D311yescharacteristic
253(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
254(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
255Dic32—31no—
256Dic32—31no—
257Dic32—61no—
258Dic32C2×D311yescharacteristic, complemented
259C22×C33C2411yescharacteristic
260C2×C3×C3⋊D3—21no—
261C2×C3×C3⋊D3—21no—
262C2×C3×C3⋊D3#4112yes—
263C2×C32×D3—21no—
264C2×C32×D3—21no—
265C2×C32×D3—21no—
266C2×C32×D3—21no—
267C2×C32×D3—21no—
268C2×C32×D3—21no—
269C2×C32×D3—21no—
270C2×C32×D3—21no—
271C2×C32×D3#4112yes—
272C3×D32—44no—
273C33×C4—21no—
274C3⋊(C3⋊Dic3)—21no—
275C3⋊(C3⋊Dic3)—21no—
276C3×C3⋊Dic3—21no—
277C3×C3⋊Dic3—21no—
278C3×C3⋊Dic3—21no—
279C3×C3⋊Dic3—21no—
280C3×C3⋊Dic3—21no—
281C32×Dic3—21no—
282C32×Dic3—21no—
283C32×Dic3—21no—
284C3×#124—91no—
285C3×#120—91no—
286C3×#117—91no—
287C2×#217—91no—
288C2×#217—91no—
289#946—91no—
290#946—91no—
291#937—31no—
292#936—31no—
293#935—91no—
294#935—91no—
295#935—91no—
296#935—91no—
297#935—181no—
298D4×Dic3—91no—
299D4×Dic3—91no—
300#929—91no—
301C2×(C2×D3)⋊C4—91no—
302#898—91no—
303#896—91no—
304#894—91no—
305#894—91no—
306#883—91no—
307#883—91no—
308#882—31no—
309#67⋊C4—91no—
310#67⋊C4—91no—
311#67⋊C4—91no—
312D3×C22⋊C4—91no—
313D3×C22⋊C4—91no—
314D3×C22⋊C4—91no—
315#879—91no—
316#879—91no—
317#879—91no—
318#879—91no—
319#878—91no—
320#878—91no—
321#878—91no—
322#878—181no—
323#877—31no—
324#877—91no—
325#876—91no—
326#875—31no—
327C4×D12—91no—
328#872—31no—
329#872—91no—
330#872—91no—
331#872—181no—
332C23×C32—31no—
333C23×C32—31no—
334C23×C32—31no—
335C22×C3⋊D3C22×D311yescharacteristic
336C22×C3×D3—21no—
337C22×C3×D3—21no—
338C22×C3×D3—21no—
339C22×C3×D3—31no—
340C22×C3×D3—31no—
341C22×C3×D3—61no—
342C22×C3×D3—62no—
343C22×C3×D3—62no—
344C22×C3×D3—62no—
345C22×C3×D3—62no—
346C22×C3×D3—121no—
347C22×C3×D3—121no—
348C22×C3×D3C22×D311yescharacteristic
349C22×C3×D3C22×D311yescharacteristic
350C22×C3×D3C22×D311yescharacteristic
351C22×C3×D3C22×D311yescharacteristic
352C22×C3×D3C22×D311yescharacteristic
353C22×C3×D3C22×D311yescharacteristic
354C2×D32—22no—
355C2×D32—22no—
356C2×D32—41no—
357C32×D4—121no—
358C2×C32×C4—21no—
359C2×C32×C4—21no—
360C2×C32×C4—21no—
361C2×C32×C4—31no—
362C2×C32×C4—31no—
363C2×C32×C4—31no—
364C2×C32×C4—41no—
365C2×C32×C4C22×D311yescharacteristic
366C2×C32×C4C22×D311yescharacteristic
367C2×C32×C4C22×D311yescharacteristic
368C2×C3⋊Dic3—31no—
369C2×C3⋊Dic3—31no—
370C2×C3⋊Dic3—31no—
371C2×C3⋊Dic3—31no—
372C2×C3⋊Dic3—31no—
373C2×C3⋊Dic3—31no—
374C2×C3⋊Dic3—61no—
375C2×C3⋊Dic3—61no—
376C2×C3⋊Dic3—61no—
377C2×C3⋊Dic3—61no—
378C2×C3⋊Dic3—61no—
379C2×C3⋊Dic3—61no—
380C2×C3⋊Dic3—121no—
381C2×C3⋊Dic3—121no—
382C2×C3⋊Dic3—121no—
383C2×C3⋊Dic3—121no—
384C2×C3⋊Dic3C22×D311yescharacteristic
385C2×C3⋊Dic3C22×D311yescharacteristic
386C2×C3⋊Dic3C22×D311yescharacteristic
387C2×C3⋊Dic3C22×D311yescharacteristic
388C2×C3⋊Dic3C22×D311yescharacteristic
389C4×C3⋊D3—62no—
390#634—41no—
391C3×#67—62no—
392C3×#67—62no—
393C3×#67—62no—
394C2×C3×Dic3—21no—
395C2×C3×Dic3—21no—
396C2×C3×Dic3—21no—
397C2×C3×Dic3—31no—
398C2×C3×Dic3—31no—
399C2×C3×Dic3—31no—
400C2×C3×Dic3—31no—
401C2×C3×Dic3—31no—
402C2×C3×Dic3—31no—
403C2×C3×Dic3—31no—
404C2×C3×Dic3—31no—
405C2×C3×Dic3—31no—
406C2×C3×Dic3—31no—
407C2×C3×Dic3—61no—
408C2×C3×Dic3—61no—
409C2×C3×Dic3—61no—
410C2×C3×Dic3—61no—
411C2×C3×Dic3—61no—
412C2×C3×Dic3—62no—
413C2×C3×Dic3C22×D311yescharacteristic
414C2×C3×Dic3C22×D311yescharacteristic
415C2×C3×Dic3C22×D311yescharacteristic
416C2×C3×Dic3C22×D311yescharacteristic
417C2×C3×Dic3C22×D311yescharacteristic
418C2×C3×Dic3C22×D311yescharacteristic
419C3×D12—41no—
420C3×D12—41no—
421C3×D12—42no—
422C3×D12—62no—
423C3×C4×D3—62no—
424C3×Dic6—121no—
425C3×Dic6—121no—
426C3×Dic6—122no—
427#626—22no—
428#625—22no—
429#624—121no—
430D3×Dic3—22no—
431D3×Dic3—62no—
432D3×Dic3—62no—
433D3×Dic3—64no—
434D3×Dic3—121no—
435D3×Dic3—121no—
436D3×Dic3—121no—
437D3×Dic3—121no—
438D3×Dic3—121no—
439D3×Dic3—121no—
440D3×Dic3—122no—
441D3×Dic3—122no—
442#551—271noSylow
443C2×C33C2×#4111yescharacteristic
444C2×C33C2×#4111yescharacteristic
445C2×C33H(5,𝔽2)11yescharacteristic
446C3×C3⋊D3—22no—
447C32×D3—22no—
448C32×D3—41no—
449C32×D3—41no—
450C24×C3—91no—
451C23×D3—31no—
452C23×D3—31no—
453C2×C3×Q8—91no—
454C2×C3×D4—31no—
455C2×C3×D4—31no—
456C2×C3×D4—61no—
457C2×C3×D4—91no—
458C2×C3×D4—91no—
459C22×C3×C4—91no—
460C2×#67—31no—
461C2×#67—31no—
462C2×#67—31no—
463C22×Dic3—31no—
464C22×Dic3—91no—
465C22×Dic3—91no—
466C22×Dic3—91no—
467C22×Dic3—91no—
468C22×Dic3—91no—
469C22×Dic3—91no—
470C22×Dic3—181no—
471C22×Dic3—181no—
472C2×D12—31no—
473C2×D12D3211yescharacteristic
474C2×C4×D3—31no—
475C2×C4×D3—91no—
476C2×C4×D3—91no—
477C2×C4×D3—91no—
478C2×C4×D3—91no—
479C2×C4×D3—91no—
480C2×C4×D3—91no—
481C2×C4×D3—181no—
482C2×Dic6—31no—
483C2×Dic6—31no—
484C2×Dic6—61no—
485C3×C4⋊C4—91no—
486C3×C4⋊C4—91no—
487C3×C22⋊C4—31no—
488C3×C22⋊C4—31no—
489C3×C22⋊C4—61no—
490C3×C22⋊C4—91no—
491C3×C22⋊C4—91no—
492C3×C22⋊C4—91no—
493C3×C22⋊C4—91no—
494C3×C22⋊C4—91no—
495C3×C22⋊C4—91no—
496C3×C22⋊C4—91no—
497C3×C42—31no—
498C3×C42—31no—
499C3×C42—61no—
500C3×C42—91no—
501#217—31no—
502#217—31no—
503#217—31no—
504#217—31no—
505#217—31no—
506#217—31no—
507#217—91no—
508#217—91no—
509#217—91no—
510#217—91no—
511#217—91no—
512#217—91no—
513#217—91no—
514#217—91no—
515#217—91no—
516#217—91no—
517#217—181no—
518#217—181no—
519#217—181no—
520#217—181no—
521(C2×D3)⋊C4—31no—
522(C2×D3)⋊C4—31no—
523(C2×D3)⋊C4—31no—
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—61no—
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—181no—
539(C2×D3)⋊C4D3211yescharacteristic
540C4⋊Dic3—91no—
541C4⋊Dic3—91no—
542C4⋊Dic3—91no—
543C4⋊Dic3—91no—
544C4⋊Dic3—91no—
545C4⋊Dic3—181no—
546Dic3⋊C4—31no—
547Dic3⋊C4—31no—
548Dic3⋊C4—31no—
549Dic3⋊C4—31no—
550Dic3⋊C4—61no—
551Dic3⋊C4—91no—
552Dic3⋊C4—91no—
553Dic3⋊C4—91no—
554Dic3⋊C4—91no—
555Dic3⋊C4—91no—
556Dic3⋊C4—91no—
557Dic3⋊C4—91no—
558Dic3⋊C4—91no—
559Dic3⋊C4—91no—
560Dic3⋊C4—91no—
561Dic3⋊C4—91no—
562Dic3⋊C4—91no—
563Dic3⋊C4—91no—
564Dic3⋊C4—181no—
565Dic3⋊C4—181no—
566Dic3⋊C4—181no—
567Dic3⋊C4—181no—
568Dic3⋊C4—181no—
569Dic3⋊C4—361no—
570C4×Dic3—31no—
571C4×Dic3—31no—
572C4×Dic3—91no—
573C4×Dic3—91no—
574C4×Dic3—91no—
575C4×Dic3—181no—
576C4×Dic3D3211yescharacteristic, complemented
577C22×C32—21no—
578C22×C32—21no—
579C22×C32—21no—
580C22×C32—32no—
581C22×C32—41no—
582C22×C32—61no—
583C22×C32—61no—
584C22×C32—61no—
585C22×C32—61no—
586C22×C32—61no—
587C22×C32—61no—
588C22×C32—61no—
589C22×C32—61no—
590C22×C32C23×D311yescharacteristic
591C22×C32C23×D311yescharacteristic
592C22×C32C23×D311yescharacteristic
593C2×C3⋊D3—21no—
594C2×C3⋊D3—21no—
595C2×C3⋊D3#23712yes—
596C2×C3×D3—21no—
597C2×C3×D3—21no—
598C2×C3×D3—21no—
599C2×C3×D3—21no—
600C2×C3×D3—22no—
601C2×C3×D3—21no—
602C2×C3×D3—21no—
603C2×C3×D3—21no—
604C2×C3×D3—21no—
605C2×C3×D3—21no—
606C2×C3×D3—21no—
607C2×C3×D3—21no—
608C2×C3×D3—21no—
609C2×C3×D3—21no—
610C2×C3×D3—21no—
611C2×C3×D3—21no—
612C2×C3×D3—21no—
613C2×C3×D3—22no—
614C2×C3×D3—32no—
615C2×C3×D3—32no—
616C2×C3×D3—41no—
617C2×C3×D3—41no—
618C2×C3×D3—41no—
619C2×C3×D3—41no—
620C2×C3×D3—41no—
621C2×C3×D3—41no—
622C2×C3×D3—41no—
623C2×C3×D3—62no—
624C2×C3×D3—61no—
625C2×C3×D3—61no—
626C2×C3×D3—61no—
627C2×C3×D3—61no—
628C2×C3×D3—121no—
629C2×C3×D3—121no—
630C2×C3×D3—124no—
631C2×C3×D3—124no—
632C2×C3×D3#23512yes—
633C2×C3×D3#23712yes—
634D32—44no—
635C32×C4—21no—
636C32×C4—21no—
637C32×C4—21no—
638C32×C4—41no—
639C32×C4—41no—
640C32×C4—41no—
641C32×C4—61no—
642C32×C4—61no—
643C32×C4—61no—
644C32×C4—81no—
645C3⋊Dic3—21no—
646C3⋊Dic3—21no—
647C3⋊Dic3—21no—
648C3⋊Dic3—21no—
649C3⋊Dic3—21no—
650C3⋊Dic3—61no—
651C3⋊Dic3—62no—
652C3⋊Dic3—61no—
653C3⋊Dic3—61no—
654C3⋊Dic3—61no—
655C3⋊Dic3—61no—
656C3⋊Dic3—61no—
657C3⋊Dic3—121no—
658C3⋊Dic3—121no—
659C3⋊Dic3—122no—
660C3⋊Dic3—121no—
661C3⋊Dic3—121no—
662C3⋊Dic3—121no—
663C3⋊Dic3—241no—
664C3×Dic3—22no—
665C3×Dic3—21no—
666C3×Dic3—21no—
667C3×Dic3—21no—
668C3×Dic3—21no—
669C3×Dic3—21no—
670C3×Dic3—21no—
671C3×Dic3—41no—
672C3×Dic3—41no—
673C3×Dic3—62no—
674C3×Dic3—61no—
675C3×Dic3—61no—
676C3×Dic3—61no—
677C3×Dic3—61no—
678C3×Dic3—61no—
679C3×Dic3—61no—
680C3×Dic3—61no—
681C3×Dic3—61no—
682C3×Dic3—61no—
683C3×Dic3—61no—
684C3×Dic3—121no—
685C3×Dic3—121no—
686C3×Dic3—121no—
687C3×Dic3—121no—
688#126—271no—
689#126—271no—
690#124—91no—
691#123—271no—
692#123—271no—
693#123—271no—
694C22⋊Q8—271no—
695C22⋊Q8—271no—
696#120—91no—
697C4×D4—271no—
698C4×D4—271no—
699#117—91no—
700#117—271no—
701C2×C22⋊C4—271no—
702C2×C22⋊C4—271no—
703C33#55111yescharacteristic, complemented, Sylow
704C23×C3—31no—
705C23×C3—31no—
706C23×C3—31no—
707C23×C3—31no—
708C23×C3—31no—
709C23×C3—31no—
710C23×C3—61no—
711C23×C3—61no—
712C23×C3—61no—
713C23×C3—91no—
714C23×C3—182no—
715C23×C3—182no—
716C23×C3—361no—
717C22×D3—31no—
718C22×D3—31no—
719C22×D3—61no—
720C22×D3—62no—
721C22×D3—62no—
722C22×D3—62no—
723C22×D3—62no—
724C22×D3—121no—
725C22×D3—121no—
726C22×D3C2×D3211yescharacteristic
727C22×D3C2×D3211yescharacteristic
728C22×D3C2×D3211yescharacteristic
729C3×Q8—361no—
730C3×D4—121no—
731C3×D4—121no—
732C3×D4—122no—
733C3×D4—182no—
734C3×D4—182no—
735C2×C3×C4—21no—
736C2×C3×C4—21no—
737C2×C3×C4—21no—
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—41no—
745C2×C3×C4—61no—
746C2×C3×C4—61no—
747C2×C3×C4—61no—
748C2×C3×C4—91no—
749C2×C3×C4—91no—
750C2×C3×C4—91no—
751C2×C3×C4—91no—
752C2×C3×C4—91no—
753C2×C3×C4—182no—
754C2×C3×C4C2×D3211yescharacteristic
755C2×C3×C4C2×D3211yescharacteristic
756C2×C3×C4C2×D3211yescharacteristic
757#67—62no—
758#67—62no—
759#67—62no—
760C2×Dic3—31no—
761C2×Dic3—31no—
762C2×Dic3—31no—
763C2×Dic3—31no—
764C2×Dic3—31no—
765C2×Dic3—31no—
766C2×Dic3—31no—
767C2×Dic3—31no—
768C2×Dic3—31no—
769C2×Dic3—31no—
770C2×Dic3—61no—
771C2×Dic3—61no—
772C2×Dic3—61no—
773C2×Dic3—61no—
774C2×Dic3—61no—
775C2×Dic3—62no—
776C2×Dic3—91no—
777C2×Dic3—91no—
778C2×Dic3—91no—
779C2×Dic3—91no—
780C2×Dic3—91no—
781C2×Dic3—91no—
782C2×Dic3—181no—
783C2×Dic3—181no—
784C2×Dic3—181no—
785C2×Dic3—181no—
786C2×Dic3—181no—
787C2×Dic3—181no—
788C2×Dic3—182no—
789C2×Dic3—361no—
790C2×Dic3—361no—
791C2×Dic3—361no—
792C2×Dic3—361no—
793C2×Dic3—361no—
794C2×Dic3—361no—
795C2×Dic3—361no—
796C2×Dic3—362no—
797C2×Dic3—362no—
798C2×Dic3C2×D3211yescharacteristic
799C2×Dic3C2×D3211yescharacteristic
800C2×Dic3C2×D3211yescharacteristic
801D12—41no—
802D12—62no—
803C4×D3—62no—
804C4×D3—182no—
805C4×D3—182no—
806C4×D3—184no—
807C4×D3—361no—
808C4×D3—361no—
809C4×D3—361no—
810C4×D3—361no—
811Dic6—121no—
812Dic6—121no—
813Dic6—122no—
814C2×C32—21no—
815C2×C32—21no—
816C2×C32—21no—
817C2×C32—21no—
818C2×C32—21no—
819C2×C32—21no—
820C2×C32—21no—
821C2×C32—21no—
822C2×C32—21no—
823C2×C32—41no—
824C2×C32—41no—
825C2×C32—41no—
826C2×C32—62no—
827C2×C32—121no—
828C2×C32—121no—
829C2×C32C2×#23511yescharacteristic
830C2×C32C2×#23711yescharacteristic
831C2×C32C2×#23711yescharacteristic
832C2×C32#100411yescharacteristic
833C2×C32#100411yescharacteristic
834C2×C32D3×#4111yescharacteristic
835C2×C32D3×#4111yescharacteristic
836C2×C32D3×#4111yescharacteristic
837C2×C32#100911yescharacteristic
838C3⋊D3—22no—
839C3×D3—22no—
840C3×D3—22no—
841C3×D3—42no—
842C3×D3—42no—
843C3×D3—41no—
844C3×D3—41no—
845C3×D3—41no—
846C3×D3—41no—
847C3×D3—62no—
848C3×D3—62no—
849C3×D3—81no—
850C3×D3—122no—
851C24—91no—
852C2×Q8—91no—
853C2×D4—31no—
854C2×D4—91no—
855C2×D4—91no—
856C22×C4—91no—
857C22×C4—271no—
858C22×C4—271no—
859C22×C4—271no—
860C22×C4—271no—
861C4⋊C4—91no—
862C4⋊C4—91no—
863C4⋊C4—271no—
864C4⋊C4—271no—
865C4⋊C4—271no—
866C4⋊C4—271no—
867C4⋊C4—271no—
868C4⋊C4—271no—
869C22⋊C4—31no—
870C22⋊C4—91no—
871C22⋊C4—91no—
872C22⋊C4—91no—
873C22⋊C4—91no—
874C22⋊C4—91no—
875C22⋊C4—91no—
876C22⋊C4—91no—
877C22⋊C4—271no—
878C22⋊C4—271no—
879C22⋊C4—271no—
880C22⋊C4—271no—
881C22⋊C4—271no—
882C22⋊C4—271no—
883C42—31no—
884C42—91no—
885C42—271no—
886C22×C3—21no—
887C22×C3—21no—
888C22×C3—21no—
889C22×C3—32no—
890C22×C3—32no—
891C22×C3—41no—
892C22×C3—62no—
893C22×C3—62no—
894C22×C3—61no—
895C22×C3—61no—
896C22×C3—61no—
897C22×C3—61no—
898C22×C3—61no—
899C22×C3—61no—
900C22×C3—61no—
901C22×C3—61no—
902C22×C3—61no—
903C22×C3—61no—
904C22×C3—61no—
905C22×C3—61no—
906C22×C3—61no—
907C22×C3—61no—
908C22×C3—61no—
909C22×C3—61no—
910C22×C3—92no—
911C22×C3—121no—
912C22×C3—121no—
913C22×C3—121no—
914C22×C3—121no—
915C22×C3—121no—
916C22×C3—121no—
917C22×C3—121no—
918C22×C3—181no—
919C22×C3—181no—
920C22×C3—364no—
921C22×C3C22×D3211yescharacteristic
922C22×C3C22×D3211yescharacteristic
923C22×C3C22×D3211yescharacteristic
924C2×D3—21no—
925C2×D3—21no—
926C2×D3—21no—
927C2×D3—21no—
928C2×D3—21no—
929C2×D3—21no—
930C2×D3—21no—
931C2×D3—21no—
932C2×D3—32no—
933C2×D3—32no—
934C2×D3—62no—
935C2×D3—61no—
936C2×D3—61no—
937C2×D3—61no—
938C2×D3—61no—
939C2×D3—121no—
940C2×D3—121no—
941C2×D3—124no—
942C2×D3—124no—
943C2×D3#379512yes—
944C3×C4—21no—
945C3×C4—21no—
946C3×C4—21no—
947C3×C4—41no—
948C3×C4—41no—
949C3×C4—41no—
950C3×C4—62no—
951C3×C4—61no—
952C3×C4—61no—
953C3×C4—61no—
954C3×C4—61no—
955C3×C4—61no—
956C3×C4—61no—
957C3×C4—81no—
958C3×C4—121no—
959C3×C4—121no—
960C3×C4—181no—
961C3×C4—181no—
962C3×C4—181no—
963C3×C4—181no—
964C3×C4—181no—
965Dic3—21no—
966Dic3—21no—
967Dic3—21no—
968Dic3—62no—
969Dic3—61no—
970Dic3—61no—
971Dic3—61no—
972Dic3—61no—
973Dic3—61no—
974Dic3—61no—
975Dic3—61no—
976Dic3—61no—
977Dic3—61no—
978Dic3—61no—
979Dic3—121no—
980Dic3—121no—
981Dic3—121no—
982Dic3—121no—
983Dic3—182no—
984Dic3—181no—
985Dic3—181no—
986Dic3—181no—
987Dic3—181no—
988Dic3—181no—
989Dic3—181no—
990Dic3—361no—
991Dic3—361no—
992Dic3—361no—
993Dic3—361no—
994Dic3—361no—
995Dic3—362no—
996Dic3—721no—
997C32—21no—
998C32—21no—
999C32—21no—
1000C32—41no—
1001C32#552711yescharacteristic, complemented
1002C32#558711yescharacteristic, complemented
1003C32#567911yescharacteristic, complemented
1004C23—31no—
1005C23—31no—
1006C23—31no—
1007C23—91no—
1008C23—182no—
1009C23—182no—
1010C23—361no—
1011Q8—361no—
1012D4—121no—
1013D4—182no—
1014D4—182no—
1015C2×C4—31no—
1016C2×C4—31no—
1017C2×C4—31no—
1018C2×C4—91no—
1019C2×C4—91no—
1020C2×C4—91no—
1021C2×C4—91no—
1022C2×C4—91no—
1023C2×C4—182no—
1024C2×C4—271no—
1025C2×C4—271no—
1026C2×C4—542no—
1027C2×C4—1081no—
1028C2×C4—1081no—
1029C2×C4—1081no—
1030C2×C4D3311yescharacteristic
1031C2×C3—21no—
1032C2×C3—21no—
1033C2×C3—21no—
1034C2×C3—21no—
1035C2×C3—21no—
1036C2×C3—21no—
1037C2×C3—21no—
1038C2×C3—21no—
1039C2×C3—21no—
1040C2×C3—41no—
1041C2×C3—41no—
1042C2×C3—41no—
1043C2×C3—62no—
1044C2×C3—62no—
1045C2×C3—122no—
1046C2×C3—122no—
1047C2×C3—121no—
1048C2×C3—121no—
1049C2×C3—121no—
1050C2×C3—121no—
1051C2×C3—182no—
1052C2×C3—241no—
1053C2×C3C2×#379511yescharacteristic
1054C2×C3D3×#23511yescharacteristic
1055C2×C3#6430611yescharacteristic
1056C2×C3#6430711yescharacteristic
1057C2×C3D3×#23711yescharacteristic
1058C2×C3D3×#23711yescharacteristic
1059C2×C3D3×#23711yescharacteristic
1060C2×C3#6431411yescharacteristic
1061C2×C3#6433011yescharacteristic
1062D3—22no—
1063D3—41no—
1064D3—41no—
1065D3—62no—
1066D3—62no—
1067D3—122no—
1068C22—32no—
1069C22—61no—
1070C22—61no—
1071C22—61no—
1072C22—61no—
1073C22—61no—
1074C22—61no—
1075C22—61no—
1076C22—61no—
1077C22—92no—
1078C22—181no—
1079C22—181no—
1080C22—364no—
1081C22C2×D3311yescharacteristic
1082C4—21no—
1083C4—61no—
1084C4—61no—
1085C4—61no—
1086C4—181no—
1087C4—181no—
1088C4—181no—
1089C4—181no—
1090C4—181no—
1091C4—541no—
1092C4—541no—
1093C3—21no—
1094C3—21no—
1095C3—21no—
1096C3—41no—
1097C3#1059401611yescharacteristic, complemented
1098C3#1059411711yescharacteristic, complemented
1099C3#1059517611yescharacteristic, complemented
1100C2—62no—
1101C2—121no—
1102C2—121no—
1103C2—182no—
1104C2D3×#379511yescharacteristic
1105C2#1172437311yescharacteristic
1106C2#1172441811yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC3×#63922C2
hypercenterC2×C4D33
hypocenterC33#551
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. #11723688C2semidirect
2. #11723487C2semidirect
3. #11723473C2semidirect
4. #11723464C2semidirect
6. C3×#63877C2semidirect
7. C3×#63860C2semidirect
8. #11723022C2semidirect
9. #11723020C2semidirect
10. #11722991C2semidirect
11. #11722985C2semidirect
12. #11722928C2semidirect
13. #11722925C2semidirect
14. #11722902C2semidirect
15. D3×(C2×D3)⋊Dic3C2semidirect
20. C2×C3×#634C22semidirect
25. C2×D3×C3⋊Dic3C22semidirect
29. #88857C22semidirect
31. C3×#3750C22semidirect
33. C32×C4×Dic3C22semidirect
34. #88815C22semidirect
35. #88815C22semidirect
37. #88807C22semidirect
38. #88806C22semidirect
39. Dic3⋊(C3⋊Dic3)C22semidirect
44. (C2×D3)⋊(C3⋊Dic3)C22semidirect
45. Dic3×C3⋊Dic3C22semidirect
46. C3×#3724C22semidirect
51. C3×(C2×D3)⋊Dic3C22semidirect
52. C3×(C2×D3)⋊Dic3C22semidirect
53. C3×Dic32C22semidirect
95. #63877D3semidirect
98. #63860D3semidirect
139. C2×#634C2×D3semidirect
185. #3750C2×D3semidirect
213. C3×C4×Dic3C2×D3semidirect
214. C3×C4×Dic3C2×D3semidirect
220. #3724C2×D3semidirect
253. (C2×D3)⋊Dic3C2×D3semidirect
254. (C2×D3)⋊Dic3C2×D3semidirect
258. Dic32C2×D3semidirect
576. C4×Dic3D32semidirect
703. C33#551semidirect
1001. C32#5527semidirect
1002. C32#5587semidirect
1003. C32#5679semidirect
1097. C3#10594016semidirect
1098. C3#10594117semidirect
1099. C3#10595176semidirect

Maximal subgroups

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

subgroupindex
#117236882
#117234872
#117234732
#117234642
C3×#639222
C3×#638772
C3×#638602
#117230222
#117230202
#117229912
#117229852
#117229282
#117229252
#117229022
D3×(C2×D3)⋊Dic32
#105951763
#105941173
#105940163