Finite Group Databasebeta

← #13172019

Subgroups — #13172019

Order 1728.

1310 conjugacy classes of subgroups.

The subgroup lattice has 1136 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723715C211yesmaximal, characteristic, complemented
2#11723640C211yesmaximal, characteristic, complemented
3D3×#3757C211yesmaximal, characteristic, complemented
4#11723602C211yesmaximal, characteristic, complemented
5C3×#63976C211yesmaximal, characteristic
6C3×Dic3×#67C211yesmaximal, characteristic, complemented
7C2×C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
8#11723026C211yesmaximal, characteristic, complemented
9#11723020C211yesmaximal, characteristic, complemented
10#11723004C211yesmaximal, characteristic, complemented
11#11722989C211yesmaximal, characteristic, complemented
12#11722985C211yesmaximal, characteristic, complemented
13#11722980C211yesmaximal, characteristic, complemented
14#11722924C211yesmaximal, characteristic, complemented
15#11722916C211yesmaximal, characteristic, complemented
16#10595509—31nomaximal
17#10595175—31nomaximal
18#10594938—31nomaximal
19C23×C32×D3C2211yescharacteristic
20C22×C3×C3⋊Dic3C2211yescharacteristic
21C2×C32×#67C2211yescharacteristic
22C22×C32×Dic3C2211yescharacteristic
23C2×#6293C2211yescharacteristic, complemented
24C2×D3×C3⋊Dic3C2211yescharacteristic
25C2×D3×C3⋊Dic3C2211yescharacteristic
26C2×C3×#625C2211yescharacteristic
27C2×C3×#625C2211yescharacteristic
28C2×C3×D3×Dic3C2211yescharacteristic, complemented
29#88864C2211yescharacteristic
30C3×#3757C2211yescharacteristic
31C3×#3757C2211yescharacteristic
32#88815C2211yescharacteristic, complemented
33#88815C2211yescharacteristic, complemented
34#88813C2211yescharacteristic, complemented
35#88813C2211yescharacteristic, complemented
36#88807C2211yescharacteristic, complemented
37#88806C2211yescharacteristic, complemented
38#88806C2211yescharacteristic, complemented
39#88806C2211yescharacteristic, complemented
40Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
41(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
42(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
43(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
44(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
45C3×Dic3⋊Dic3C2211yescharacteristic, complemented
46C3×(C2×D3)⋊Dic3C2211yescharacteristic
47C3×(C2×D3)⋊Dic3C2211yescharacteristic
48C3×(C2×D3)⋊Dic3C2211yescharacteristic
49C3×(C2×D3)⋊Dic3C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
53C3×Dic32C2211yescharacteristic, complemented
54C2×#3757—31no—
55#64144—31no—
56#64133—31no—
57C3×#953—31no—
58C2×C3×#217—31no—
59C3×#937—31no—
60C3×D4×Dic3—31no—
61C3×C4×#67—31no—
62C2×C3×(C2×D3)⋊C4—31no—
63#63982—31no—
64#63976D311yescharacteristic
65#67⋊Dic3—31no—
66Dic3×#67—31no—
67Dic3×#67D311yescharacteristic, complemented
68#63969—31no—
69#63969—31no—
70D3×#217—31no—
71D3×#217—31no—
72D3×#217—61no—
73#63964—31no—
74#63964—31no—
75#63964—61no—
76#63962—31no—
77#63961—31no—
78#63961—31no—
79#63961—31no—
80#63961—61no—
81C2×(C2×D3)⋊Dic3D311yescharacteristic, complemented
82#63959—31no—
83#63959—31no—
84#63957—31no—
85#63957—31no—
86#63956—31no—
87#63956—31no—
88#63955—31no—
89#63955—31no—
90#63913—31no—
91#63905—31no—
92#63899—31no—
93#63896—31no—
94#63891—31no—
95#63879—31no—
96#63877—31no—
97#63877—31no—
98#63861—31no—
99#63859—31no—
100#63859—31no—
101#63858—31no—
102C23×C33C2311yescharacteristic
103C22×C32×D3—22no—
104C22×C32×D3—22no—
105C22×C32×D3—41no—
106C22×C32×D3C2311yescharacteristic
107C22×C32×D3C2311yescharacteristic
108C22×C32×D3C2311yescharacteristic
109C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
110C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
111C2×C3×C3⋊Dic3—22no—
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C3×C3⋊Dic3C2311yescharacteristic
118C32×#67—22no—
119C2×C32×Dic3—41no—
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123#6293—41no—
124D3×C3⋊Dic3—22no—
125D3×C3⋊Dic3—41no—
126C3×#625—22no—
127C3×#625—41no—
128C3×D3×Dic3—41no—
129#5587—91no—
130#5556—91no—
131#5495—91no—
132C24×C32—31no—
133C23×C3×D3—21no—
134C23×C3×D3C2×D311yescharacteristic
135C23×C3×D3C2×D311yescharacteristic
136C2×C32×D4—31no—
137C22×C32×C4—31no—
138C22×C3⋊Dic3—31no—
139C22×C3⋊Dic3—31no—
140C22×C3⋊Dic3C2×D311yescharacteristic
141C2×#634—31no—
142C2×C3×#67—21no—
143C2×C3×#67—31no—
144C2×C3×#67—31no—
145C2×C3×#67—31no—
146C2×C3×#67—31no—
147C2×C3×#67C2×D311yescharacteristic
148C2×C3×#67C2×D311yescharacteristic
149C22×C3×Dic3—21no—
150C22×C3×Dic3—31no—
151C22×C3×Dic3—31no—
152C22×C3×Dic3—31no—
153C22×C3×Dic3—61no—
154C22×C3×Dic3C2×D311yescharacteristic
155C22×C3×Dic3C2×D311yescharacteristic
156C2×C3×C4×D3—31no—
157C2×#627—31no—
158C2×#627—31no—
159C2×#627—61no—
160C2×#625C2×D311yescharacteristic
161C2×#625C2×D311yescharacteristic
162C2×D3×Dic3—31no—
163C2×D3×Dic3—31no—
164C2×D3×Dic3—31no—
165C2×D3×Dic3—31no—
166C2×D3×Dic3—61no—
167C2×D3×Dic3—61no—
168C2×D3×Dic3C2×D311yescharacteristic, complemented
169#3757—31no—
170#3757—31no—
171#3757—31no—
172#3757—31no—
173#3757—31no—
174#3757—31no—
175#3757—31no—
176#3757—61no—
177#3757—61no—
178#3757—61no—
179#3757—121no—
180#3757C2×D311yescharacteristic
181#3757C2×D311yescharacteristic
182C4⋊(C3⋊Dic3)—31no—
183#3750—31no—
184#3750—31no—
185#3750—31no—
186#3750—31no—
187C3×#217—31no—
188C3×#217—31no—
189C3×#217—31no—
190C3×#217—31no—
191C3×#217—31no—
192C3×#217—31no—
193C3×#217—31no—
194C3×#217—31no—
195C3×#217—31no—
196C3×#217—31no—
197C3×#217—31no—
198C3×#217—61no—
199C3×#217—61no—
200C3×(C2×D3)⋊C4—31no—
201C3×(C2×D3)⋊C4—31no—
202C3×(C2×D3)⋊C4—31no—
203C3×(C2×D3)⋊C4—31no—
204C3×(C2×D3)⋊C4—31no—
205C3×(C2×D3)⋊C4—31no—
206C3×(C2×D3)⋊C4—31no—
207C3×C4⋊Dic3—31no—
208C3×Dic3⋊C4—31no—
209C3×C4×Dic3—31no—
210C3×C4×Dic3—31no—
211#3724—31no—
212#3724—31no—
213#3724—31no—
214#3724—31no—
215#3724—31no—
216#3724—31no—
217#3724—31no—
218#3724—31no—
219#3724—61no—
220#3724—61no—
221#3724—61no—
222Dic3⋊Dic3—31no—
223Dic3⋊Dic3—31no—
224Dic3⋊Dic3—31no—
225Dic3⋊Dic3—31no—
226Dic3⋊Dic3—31no—
227Dic3⋊Dic3—31no—
228Dic3⋊Dic3—31no—
229Dic3⋊Dic3—31no—
230Dic3⋊Dic3—61no—
231Dic3⋊Dic3—61no—
232Dic3⋊Dic3C2×D311yescharacteristic, complemented
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—61no—
242(C2×D3)⋊Dic3—61no—
243(C2×D3)⋊Dic3—61no—
244(C2×D3)⋊Dic3—61no—
245(C2×D3)⋊Dic3C2×D311yescharacteristic
246(C2×D3)⋊Dic3C2×D311yescharacteristic
247(C2×D3)⋊Dic3C2×D311yescharacteristic
248(C2×D3)⋊Dic3C2×D311yescharacteristic
249(C2×D3)⋊Dic3C2×D311yescharacteristic
250(C2×D3)⋊Dic3C2×D311yescharacteristic
251(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
252Dic32—31no—
253Dic32—31no—
254Dic32—31no—
255Dic32—31no—
256Dic32—31no—
257Dic32—31no—
258Dic32C2×D311yescharacteristic, complemented
259C22×C33—21no—
260C22×C33—21no—
261C22×C33#4112yes—
262C22×C33C2411yescharacteristic
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—44no—
272C2×C32×D3#4112yes—
273C3⋊(C3⋊Dic3)—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×#120—91no—
285C3×C4×D4—91no—
286C2×C3×C22⋊C4—91no—
287#953—31no—
288C2×#217—31no—
289C2×#217—91no—
290C2×#217—91no—
291C2×#217—181no—
292#937—31no—
293#936—91no—
294#935—91no—
295#935—91no—
296#935—91no—
297#935—91no—
298#935—181no—
299D4×Dic3—31no—
300D4×Dic3—91no—
301#929—91no—
302#929—91no—
303C4×#67—31no—
304C4×#67—91no—
305C2×(C2×D3)⋊C4—31no—
306#926—91no—
307#924—91no—
308#924—91no—
309#924—181no—
310#898—91no—
311#896—91no—
312#886—91no—
313#885—91no—
314#885—91no—
315#883—91no—
316#883—91no—
317#67⋊C4—91no—
318D3×C22⋊C4—91no—
319#879—91no—
320#879—91no—
321#879—91no—
322#879—91no—
323#878—91no—
324#878—91no—
325#878—91no—
326#877—91no—
327#877—91no—
328#877—91no—
329#877—91no—
330#876—91no—
331#872—91no—
332C23×C32—21no—
333C23×C32—21no—
334C23×C32—21no—
335C23×C32—31no—
336C23×C32—31no—
337C23×C32—31no—
338C23×C32—41no—
339C23×C32—62no—
340C23×C32—62no—
341C23×C32—121no—
342C23×C32C22×D311yescharacteristic
343C23×C32C22×D311yescharacteristic
344C23×C32C22×D311yescharacteristic
345C22×C3×D3—24no—
346C22×C3×D3—22no—
347C22×C3×D3—22no—
348C22×C3×D3—22no—
349C22×C3×D3—22no—
350C22×C3×D3—21no—
351C22×C3×D3—21no—
352C22×C3×D3—21no—
353C22×C3×D3—42no—
354C22×C3×D3—41no—
355C22×C3×D3—41no—
356C22×C3×D3—42no—
357C22×C3×D3C22×D311yescharacteristic
358C22×C3×D3C22×D311yescharacteristic
359C22×C3×D3C22×D311yescharacteristic
360C22×C3×D3C22×D311yescharacteristic
361C22×C3×D3C22×D311yescharacteristic
362C22×C3×D3C22×D311yescharacteristic
363C32×D4—62no—
364C2×C32×C4—31no—
365C2×C32×C4—31no—
366C2×C32×C4—31no—
367C2×C32×C4—121no—
368C2×C3⋊Dic3—22no—
369C2×C3⋊Dic3—31no—
370C2×C3⋊Dic3—31no—
371C2×C3⋊Dic3—31no—
372C2×C3⋊Dic3—31no—
373C2×C3⋊Dic3—31no—
374C2×C3⋊Dic3—31no—
375C2×C3⋊Dic3—61no—
376C2×C3⋊Dic3—61no—
377C2×C3⋊Dic3—61no—
378C2×C3⋊Dic3—61no—
379C2×C3⋊Dic3—61no—
380C2×C3⋊Dic3—61no—
381C2×C3⋊Dic3—62no—
382C2×C3⋊Dic3—121no—
383C2×C3⋊Dic3—121no—
384C2×C3⋊Dic3—121no—
385C2×C3⋊Dic3C22×D311yescharacteristic
386C2×C3⋊Dic3C22×D311yescharacteristic
387C2×C3⋊Dic3C22×D311yescharacteristic
388C2×C3⋊Dic3C22×D311yescharacteristic
389C2×C3⋊Dic3C22×D311yescharacteristic
390C2×C3⋊Dic3C22×D311yescharacteristic
391#634—121no—
392C3×#67—22no—
393C3×#67—22no—
394C3×#67—42no—
395C3×#67—62no—
396C3×#67—62no—
397C3×#67—121no—
398C3×#67—121no—
399C2×C3×Dic3—21no—
400C2×C3×Dic3—21no—
401C2×C3×Dic3—21no—
402C2×C3×Dic3—31no—
403C2×C3×Dic3—31no—
404C2×C3×Dic3—31no—
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—31no—
414C2×C3×Dic3—41no—
415C2×C3×Dic3—41no—
416C2×C3×Dic3—42no—
417C2×C3×Dic3—61no—
418C2×C3×Dic3—61no—
419C2×C3×Dic3—61no—
420C2×C3×Dic3—61no—
421C2×C3×Dic3—61no—
422C2×C3×Dic3—61no—
423C2×C3×Dic3—62no—
424C2×C3×Dic3—62no—
425C2×C3×Dic3—122no—
426C2×C3×Dic3—121no—
427C2×C3×Dic3C22×D311yescharacteristic
428C2×C3×Dic3C22×D311yescharacteristic
429C2×C3×Dic3C22×D311yescharacteristic
430C2×C3×Dic3C22×D311yescharacteristic
431C2×C3×Dic3C22×D311yescharacteristic
432C2×C3×Dic3C22×D311yescharacteristic
433C3×C4×D3—121no—
434#627—121no—
435#627—121no—
436#627—122no—
437#625—22no—
438#625—41no—
439D3×Dic3—41no—
440D3×Dic3—62no—
441D3×Dic3—62no—
442D3×Dic3—122no—
443D3×Dic3—121no—
444D3×Dic3—121no—
445D3×Dic3—122no—
446#551—271noSylow
447C2×C33—22no—
448C2×C33C2×#4111yescharacteristic
449C2×C33C2×#4111yescharacteristic
450C2×C33H(5,𝔽2)11yescharacteristic
451C32×D3—22no—
452C32×D3—41no—
453C32×D3—41no—
454C24×C3—31no—
455C24×C3—31no—
456C24×C3—61no—
457C23×D3D3211yescharacteristic
458C2×C3×D4—31no—
459C2×C3×D4—31no—
460C2×C3×D4—61no—
461C2×C3×D4—91no—
462C2×C3×D4—91no—
463C22×C3×C4—31no—
464C22×C3×C4—31no—
465C22×C3×C4—61no—
466C22×C3×C4—91no—
467C22×C3×C4—91no—
468C2×#67—31no—
469C2×#67—31no—
470C2×#67—31no—
471C2×#67—31no—
472C2×#67D3211yescharacteristic
473C22×Dic3—31no—
474C22×Dic3—31no—
475C22×Dic3—31no—
476C22×Dic3—61no—
477C22×Dic3—91no—
478C22×Dic3—91no—
479C22×Dic3—91no—
480C22×Dic3—91no—
481C22×Dic3—181no—
482C22×Dic3—181no—
483C22×Dic3D3211yescharacteristic
484C2×C4×D3—31no—
485C2×C4×D3—91no—
486C2×C4×D3—91no—
487C2×Dic6—91no—
488C2×Dic6—91no—
489C2×Dic6—91no—
490C2×Dic6—181no—
491C3×C4⋊C4—91no—
492C3×C22⋊C4—91no—
493C3×C22⋊C4—91no—
494C3×C22⋊C4—91no—
495C3×C22⋊C4—91no—
496C3×C22⋊C4—91no—
497C3×C22⋊C4—91no—
498C3×C22⋊C4—91no—
499C3×C22⋊C4—91no—
500C3×C22⋊C4—91no—
501C3×C42—91no—
502#217—31no—
503#217—31no—
504#217—31no—
505#217—31no—
506#217—31no—
507#217—31no—
508#217—31no—
509#217—31no—
510#217—31no—
511#217—31no—
512#217—31no—
513#217—61no—
514#217—61no—
515#217—91no—
516#217—91no—
517#217—91no—
518#217—91no—
519#217—91no—
520#217—91no—
521#217—91no—
522#217—91no—
523#217—91no—
524#217—91no—
525#217—91no—
526#217—181no—
527#217—181no—
528#217—181no—
529#217—181no—
530#217—181no—
531#217—181no—
532#217—181no—
533#217—361no—
534(C2×D3)⋊C4—31no—
535(C2×D3)⋊C4—31no—
536(C2×D3)⋊C4—31no—
537(C2×D3)⋊C4—31no—
538(C2×D3)⋊C4—31no—
539(C2×D3)⋊C4—31no—
540(C2×D3)⋊C4—31no—
541(C2×D3)⋊C4—91no—
542(C2×D3)⋊C4—91no—
543(C2×D3)⋊C4—91no—
544(C2×D3)⋊C4—91no—
545C4⋊Dic3—31no—
546C4⋊Dic3—91no—
547C4⋊Dic3—91no—
548C4⋊Dic3—91no—
549C4⋊Dic3—91no—
550C4⋊Dic3—91no—
551C4⋊Dic3—181no—
552Dic3⋊C4—31no—
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—91no—
565Dic3⋊C4—91no—
566Dic3⋊C4—91no—
567Dic3⋊C4—91no—
568Dic3⋊C4—91no—
569Dic3⋊C4—181no—
570Dic3⋊C4—181no—
571Dic3⋊C4—181no—
572Dic3⋊C4—181no—
573C4×Dic3—31no—
574C4×Dic3—31no—
575C4×Dic3—91no—
576C4×Dic3—91no—
577C4×Dic3—91no—
578C4×Dic3—91no—
579C4×Dic3—91no—
580C4×Dic3—91no—
581C22×C32—21no—
582C22×C32—21no—
583C22×C32—21no—
584C22×C32—21no—
585C22×C32—21no—
586C22×C32—21no—
587C22×C32—21no—
588C22×C32—21no—
589C22×C32—21no—
590C22×C32—22no—
591C22×C32—22no—
592C22×C32—22no—
593C22×C32—32no—
594C22×C32—41no—
595C22×C32—42no—
596C22×C32—41no—
597C22×C32—41no—
598C22×C32—41no—
599C22×C32—41no—
600C22×C32—41no—
601C22×C32—41no—
602C22×C32—61no—
603C22×C32—61no—
604C22×C32—61no—
605C22×C32—61no—
606C22×C32—61no—
607C22×C32—61no—
608C22×C32—61no—
609C22×C32—61no—
610C22×C32—81no—
611C22×C32—81no—
612C22×C32—124no—
613C22×C32#23512yes—
614C22×C32#23712yes—
615C22×C32#23712yes—
616C22×C32C23×D311yescharacteristic
617C22×C32C23×D311yescharacteristic
618C22×C32C23×D311yescharacteristic
619C2×C3×D3—22no—
620C2×C3×D3—22no—
621C2×C3×D3—21no—
622C2×C3×D3—21no—
623C2×C3×D3—21no—
624C2×C3×D3—21no—
625C2×C3×D3—22no—
626C2×C3×D3—21no—
627C2×C3×D3—21no—
628C2×C3×D3—21no—
629C2×C3×D3—21no—
630C2×C3×D3—21no—
631C2×C3×D3—21no—
632C2×C3×D3—21no—
633C2×C3×D3—21no—
634C2×C3×D3—21no—
635C2×C3×D3—21no—
636C2×C3×D3—21no—
637C2×C3×D3—21no—
638C2×C3×D3—22no—
639C2×C3×D3—41no—
640C2×C3×D3—41no—
641C2×C3×D3—41no—
642C2×C3×D3—41no—
643C2×C3×D3—41no—
644C2×C3×D3—44no—
645C2×C3×D3—44no—
646C2×C3×D3—48no—
647C2×C3×D3#23512yes—
648C2×C3×D3#23712yes—
649C32×C4—61no—
650C32×C4—61no—
651C32×C4—61no—
652C3⋊Dic3—21no—
653C3⋊Dic3—21no—
654C3⋊Dic3—21no—
655C3⋊Dic3—21no—
656C3⋊Dic3—21no—
657C3⋊Dic3—21no—
658C3⋊Dic3—61no—
659C3⋊Dic3—61no—
660C3⋊Dic3—61no—
661C3⋊Dic3—61no—
662C3⋊Dic3—61no—
663C3⋊Dic3—61no—
664C3⋊Dic3—121no—
665C3⋊Dic3—121no—
666C3⋊Dic3—121no—
667C3⋊Dic3—121no—
668C3⋊Dic3—121no—
669C3⋊Dic3—121no—
670C3⋊Dic3—241no—
671C3⋊Dic3—241no—
672C3×Dic3—22no—
673C3×Dic3—21no—
674C3×Dic3—21no—
675C3×Dic3—21no—
676C3×Dic3—21no—
677C3×Dic3—21no—
678C3×Dic3—21no—
679C3×Dic3—41no—
680C3×Dic3—41no—
681C3×Dic3—61no—
682C3×Dic3—61no—
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—61no—
692C3×Dic3—61no—
693C3×Dic3—121no—
694C3×Dic3—121no—
695C3×Dic3—121no—
696C3×Dic3—121no—
697C3×Dic3—121no—
698C3×Dic3—121no—
699#126—271no—
700#126—271no—
701#124—271no—
702#123—271no—
703#123—271no—
704#123—271no—
705C22⋊Q8—271no—
706C22⋊Q8—271no—
707#120—91no—
708C4×D4—91no—
709C4×D4—271no—
710#117—271no—
711#117—271no—
712C2×C22⋊C4—91no—
713C2×C22⋊C4—271no—
714C33#55111yescharacteristic, complemented, Sylow
715C23×C3—21no—
716C23×C3—21no—
717C23×C3—21no—
718C23×C3—31no—
719C23×C3—31no—
720C23×C3—31no—
721C23×C3—31no—
722C23×C3—31no—
723C23×C3—31no—
724C23×C3—41no—
725C23×C3—61no—
726C23×C3—61no—
727C23×C3—61no—
728C23×C3—62no—
729C23×C3—62no—
730C23×C3—64no—
731C23×C3—62no—
732C23×C3—62no—
733C23×C3—122no—
734C23×C3—121no—
735C23×C3—121no—
736C23×C3—122no—
737C23×C3C2×D3211yescharacteristic
738C23×C3C2×D3211yescharacteristic
739C23×C3C2×D3211yescharacteristic
740C22×D3—22no—
741C22×D3—22no—
742C22×D3—41no—
743C22×D3C2×D3211yescharacteristic
744C22×D3C2×D3211yescharacteristic
745C22×D3C2×D3211yescharacteristic
746C3×D4—62no—
747C3×D4—62no—
748C3×D4—122no—
749C3×D4—182no—
750C3×D4—361no—
751C2×C3×C4—31no—
752C2×C3×C4—31no—
753C2×C3×C4—31no—
754C2×C3×C4—31no—
755C2×C3×C4—31no—
756C2×C3×C4—31no—
757C2×C3×C4—61no—
758C2×C3×C4—61no—
759C2×C3×C4—61no—
760C2×C3×C4—91no—
761C2×C3×C4—91no—
762C2×C3×C4—91no—
763C2×C3×C4—91no—
764C2×C3×C4—91no—
765C2×C3×C4—91no—
766C2×C3×C4—121no—
767C2×C3×C4—121no—
768C2×C3×C4—122no—
769C2×C3×C4—182no—
770C2×C3×C4—361no—
771#67—22no—
772#67—62no—
773#67—62no—
774#67—121no—
775#67—121no—
776C2×Dic3—31no—
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—31no—
786C2×Dic3—31no—
787C2×Dic3—31no—
788C2×Dic3—41no—
789C2×Dic3—61no—
790C2×Dic3—61no—
791C2×Dic3—61no—
792C2×Dic3—61no—
793C2×Dic3—61no—
794C2×Dic3—61no—
795C2×Dic3—62no—
796C2×Dic3—62no—
797C2×Dic3—91no—
798C2×Dic3—91no—
799C2×Dic3—91no—
800C2×Dic3—91no—
801C2×Dic3—91no—
802C2×Dic3—91no—
803C2×Dic3—122no—
804C2×Dic3—121no—
805C2×Dic3—181no—
806C2×Dic3—181no—
807C2×Dic3—181no—
808C2×Dic3—181no—
809C2×Dic3—181no—
810C2×Dic3—181no—
811C2×Dic3—182no—
812C2×Dic3—182no—
813C2×Dic3—361no—
814C2×Dic3—361no—
815C2×Dic3—362no—
816C2×Dic3—361no—
817C2×Dic3—361no—
818C2×Dic3—362no—
819C2×Dic3C2×D3211yescharacteristic
820C2×Dic3C2×D3211yescharacteristic
821C2×Dic3C2×D3211yescharacteristic
822C4×D3—121no—
823C4×D3—182no—
824C4×D3—361no—
825Dic6—361no—
826Dic6—361no—
827Dic6—361no—
828Dic6—362no—
829C2×C32—22no—
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—42no—
847C2×C32—62no—
848C2×C32—82no—
849C2×C32—121no—
850C2×C32—121no—
851C2×C32C2×#23511yescharacteristic
852C2×C32C2×#23511yescharacteristic
853C2×C32C2×#23711yescharacteristic
854C2×C32C2×#23711yescharacteristic
855C2×C32C2×#23711yescharacteristic
856C2×C32#100411yescharacteristic
857C2×C32#100411yescharacteristic
858C2×C32#100411yescharacteristic
859C2×C32D3×#4111yescharacteristic
860C3×D3—24no—
861C3×D3—22no—
862C3×D3—22no—
863C3×D3—42no—
864C3×D3—41no—
865C3×D3—41no—
866C3×D3—41no—
867C3×D3—41no—
868C3×D3—81no—
869C24—31no—
870C2×Q8—271no—
871C2×D4—31no—
872C2×D4—91no—
873C2×D4—91no—
874C22×C4—31no—
875C22×C4—91no—
876C22×C4—91no—
877C22×C4—271no—
878C22×C4—271no—
879C4⋊C4—91no—
880C4⋊C4—271no—
881C4⋊C4—271no—
882C4⋊C4—271no—
883C4⋊C4—271no—
884C4⋊C4—271no—
885C4⋊C4—271no—
886C4⋊C4—271no—
887C22⋊C4—91no—
888C22⋊C4—91no—
889C22⋊C4—91no—
890C22⋊C4—91no—
891C22⋊C4—91no—
892C22⋊C4—91no—
893C22⋊C4—91no—
894C22⋊C4—91no—
895C22⋊C4—91no—
896C22⋊C4—271no—
897C22⋊C4—271no—
898C22⋊C4—271no—
899C22⋊C4—271no—
900C22⋊C4—271no—
901C42—91no—
902C42—271no—
903C42—271no—
904C22×C3—21no—
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—22no—
914C22×C3—22no—
915C22×C3—22no—
916C22×C3—32no—
917C22×C3—32no—
918C22×C3—41no—
919C22×C3—41no—
920C22×C3—41no—
921C22×C3—41no—
922C22×C3—41no—
923C22×C3—41no—
924C22×C3—41no—
925C22×C3—42no—
926C22×C3—62no—
927C22×C3—62no—
928C22×C3—62no—
929C22×C3—62no—
930C22×C3—61no—
931C22×C3—61no—
932C22×C3—61no—
933C22×C3—61no—
934C22×C3—61no—
935C22×C3—61no—
936C22×C3—61no—
937C22×C3—61no—
938C22×C3—61no—
939C22×C3—61no—
940C22×C3—61no—
941C22×C3—61no—
942C22×C3—61no—
943C22×C3—61no—
944C22×C3—61no—
945C22×C3—61no—
946C22×C3—81no—
947C22×C3—81no—
948C22×C3—121no—
949C22×C3—121no—
950C22×C3—121no—
951C22×C3—121no—
952C22×C3—121no—
953C22×C3—124no—
954C22×C3—124no—
955C22×C3—128no—
956C22×C3#379512yes—
957C22×C3#380412yes—
958C22×C3#380512yes—
959C22×C3C22×D3211yescharacteristic
960C22×C3C22×D3211yescharacteristic
961C22×C3C22×D3211yescharacteristic
962C2×D3—21no—
963C2×D3—21no—
964C2×D3—21no—
965C2×D3—21no—
966C2×D3—21no—
967C2×D3—21no—
968C2×D3—21no—
969C2×D3—21no—
970C2×D3—44no—
971C2×D3#380412yes—
972C3×C4—62no—
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—181no—
982C3×C4—181no—
983C3×C4—181no—
984C3×C4—181no—
985C3×C4—181no—
986C3×C4—181no—
987Dic3—21no—
988Dic3—21no—
989Dic3—21no—
990Dic3—61no—
991Dic3—61no—
992Dic3—61no—
993Dic3—61no—
994Dic3—61no—
995Dic3—61no—
996Dic3—61no—
997Dic3—61no—
998Dic3—61no—
999Dic3—61no—
1000Dic3—61no—
1001Dic3—61no—
1002Dic3—121no—
1003Dic3—121no—
1004Dic3—121no—
1005Dic3—121no—
1006Dic3—121no—
1007Dic3—121no—
1008Dic3—181no—
1009Dic3—181no—
1010Dic3—181no—
1011Dic3—181no—
1012Dic3—181no—
1013Dic3—181no—
1014Dic3—361no—
1015Dic3—361no—
1016Dic3—361no—
1017Dic3—361no—
1018Dic3—361no—
1019Dic3—361no—
1020Dic3—721no—
1021Dic3—721no—
1022C32—21no—
1023C32—21no—
1024C32—21no—
1025C32—41no—
1026C32#549511yescharacteristic, complemented
1027C32#555611yescharacteristic, complemented
1028C32#558711yescharacteristic, complemented
1029C23—31no—
1030C23—31no—
1031C23—31no—
1032C23—62no—
1033C23—62no—
1034C23—121no—
1035C23D3311yescharacteristic
1036Q8—1081no—
1037D4—62no—
1038D4—182no—
1039D4—361no—
1040C2×C4—31no—
1041C2×C4—31no—
1042C2×C4—31no—
1043C2×C4—91no—
1044C2×C4—91no—
1045C2×C4—91no—
1046C2×C4—91no—
1047C2×C4—91no—
1048C2×C4—91no—
1049C2×C4—121no—
1050C2×C4—182no—
1051C2×C4—271no—
1052C2×C4—271no—
1053C2×C4—361no—
1054C2×C4—542no—
1055C2×C4—1081no—
1056C2×C3—22no—
1057C2×C3—22no—
1058C2×C3—22no—
1059C2×C3—21no—
1060C2×C3—21no—
1061C2×C3—21no—
1062C2×C3—21no—
1063C2×C3—21no—
1064C2×C3—21no—
1065C2×C3—21no—
1066C2×C3—21no—
1067C2×C3—21no—
1068C2×C3—42no—
1069C2×C3—42no—
1070C2×C3—42no—
1071C2×C3—41no—
1072C2×C3—41no—
1073C2×C3—41no—
1074C2×C3—64no—
1075C2×C3—62no—
1076C2×C3—62no—
1077C2×C3—82no—
1078C2×C3—122no—
1079C2×C3—121no—
1080C2×C3—121no—
1081C2×C3—121no—
1082C2×C3—121no—
1083C2×C3—241no—
1084C2×C3C2×#379511yescharacteristic
1085C2×C3D3×#23511yescharacteristic
1086C2×C3D3×#23711yescharacteristic
1087C2×C3#6431311yescharacteristic
1088C2×C3C2×#380411yescharacteristic
1089C2×C3C2×#380411yescharacteristic
1090C2×C3C2×#380511yescharacteristic
1091C2×C3#6433011yescharacteristic
1092C2×C3#6433011yescharacteristic
1093D3—22no—
1094D3—41no—
1095D3—41no—
1096C22—21no—
1097C22—21no—
1098C22—32no—
1099C22—61no—
1100C22—61no—
1101C22—61no—
1102C22—61no—
1103C22—61no—
1104C22—61no—
1105C22—61no—
1106C22—61no—
1107C22—124no—
1108C22#8896112yes—
1109C22C2×D3311yescharacteristic
1110C4—61no—
1111C4—61no—
1112C4—61no—
1113C4—181no—
1114C4—181no—
1115C4—181no—
1116C4—181no—
1117C4—181no—
1118C4—181no—
1119C4—541no—
1120C4—541no—
1121C3—21no—
1122C3—21no—
1123C3—21no—
1124C3—41no—
1125C3#1059493811yescharacteristic, complemented
1126C3#1059517511yescharacteristic, complemented
1127C3#1059550911yescharacteristic, complemented
1128C2—22no—
1129C2—62no—
1130C2—121no—
1131C2—121no—
1132C2D3×#380411yescharacteristic
1133C2#1172441411yescharacteristic
1134C2C2×#8896111yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
prime radicalC3×#63976C2
hypercenterC23D33
hypocenterC33#551
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. #11723715C2semidirect
2. #11723640C2semidirect
3. D3×#3757C2semidirect
4. #11723602C2semidirect
6. C3×Dic3×#67C2semidirect
7. C2×C3×(C2×D3)⋊Dic3C2semidirect
8. #11723026C2semidirect
9. #11723020C2semidirect
10. #11723004C2semidirect
11. #11722989C2semidirect
12. #11722985C2semidirect
13. #11722980C2semidirect
14. #11722924C2semidirect
15. #11722916C2semidirect
23. C2×#6293C22semidirect
28. C2×C3×D3×Dic3C22semidirect
32. #88815C22semidirect
33. #88815C22semidirect
34. #88813C22semidirect
35. #88813C22semidirect
36. #88807C22semidirect
37. #88806C22semidirect
38. #88806C22semidirect
39. #88806C22semidirect
40. Dic3⋊(C3⋊Dic3)C22semidirect
43. (C2×D3)⋊(C3⋊Dic3)C22semidirect
44. (C2×D3)⋊(C3⋊Dic3)C22semidirect
45. C3×Dic3⋊Dic3C22semidirect
52. C3×(C2×D3)⋊Dic3C22semidirect
53. C3×Dic32C22semidirect
67. Dic3×#67D3semidirect
81. C2×(C2×D3)⋊Dic3D3semidirect
168. C2×D3×Dic3C2×D3semidirect
232. Dic3⋊Dic3C2×D3semidirect
251. (C2×D3)⋊Dic3C2×D3semidirect
258. Dic32C2×D3semidirect
714. C33#551semidirect
1026. C32#5495semidirect
1027. C32#5556semidirect
1028. C32#5587semidirect
1125. C3#10594938semidirect
1126. C3#10595175semidirect
1127. C3#10595509semidirect

Maximal subgroups

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

subgroupindex
#117237152
#117236402
D3×#37572
#117236022
C3×#639762
C3×Dic3×#672
C2×C3×(C2×D3)⋊Dic32
#117230262
#117230202
#117230042
#117229892
#117229852
#117229802
#117229242
#117229162
#105955093
#105951753
#105949383