Finite Group Databasebeta

← #13172041

Subgroups — #13172041

Order 1728.

1296 conjugacy classes of subgroups.

The subgroup lattice has 1132 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723718C211yesmaximal, characteristic, complemented
2#11723621C211yesmaximal, characteristic, complemented
3D3×#3757C211yesmaximal, characteristic, complemented
4#11723596C211yesmaximal, characteristic, complemented
5C3×#63977C211yesmaximal, characteristic
6C3×D3×#217C211yesmaximal, characteristic, complemented
7C3×#63956C211yesmaximal, characteristic, complemented
8#11722990C211yesmaximal, characteristic, complemented
9#11722986C211yesmaximal, characteristic, complemented
10#11722981C211yesmaximal, characteristic, complemented
11#11722978C211yesmaximal, characteristic, complemented
12#11722929C211yesmaximal, characteristic, complemented
13Dic3×#626C211yesmaximal, characteristic, complemented
14#11722916C211yesmaximal, characteristic, complemented
15#11722914C211yesmaximal, characteristic, complemented
16#10595509—31nomaximal
17#10594115—31nomaximal
18#10594093—31nomaximal
19C23×C32×D3C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C2×#6296C2211yescharacteristic, complemented
22C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
23C2×D3×C3⋊Dic3C2211yescharacteristic
24C2×D3×C3⋊Dic3C2211yescharacteristic
25C2×C3×#626C2211yescharacteristic
26C2×C3×#626C2211yescharacteristic
27C2×C3×D3×Dic3C2211yescharacteristic
28C2×C3×D3×Dic3C2211yescharacteristic
29#88864C2211yescharacteristic
30C3×#3757C2211yescharacteristic
31C3×#3757C2211yescharacteristic
32C32×#217C2211yescharacteristic
33C32×#217C2211yescharacteristic
34#88814C2211yescharacteristic, complemented
35#88814C2211yescharacteristic, complemented
36#88813C2211yescharacteristic, complemented
37#88807C2211yescharacteristic, complemented
38#88806C2211yescharacteristic, complemented
39#88806C2211yescharacteristic, complemented
40Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
41Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
42#88803C2211yescharacteristic, complemented
43(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
44(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
45Dic3×C3⋊Dic3C2211yescharacteristic, complemented
46C3×#3724C2211yescharacteristic, complemented
47C3×Dic3⋊Dic3C2211yescharacteristic, complemented
48C3×Dic3⋊Dic3C2211yescharacteristic, complemented
49C3×(C2×D3)⋊Dic3C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×Dic32C2211yescharacteristic, complemented
54C2×#3757—31no—
55#64092—31no—
56#64088—31no—
57C3×#953—31no—
58C2×C3×#217—31no—
59C3×#882—31no—
60C3×D3×C22⋊C4—31no—
61C3×#879—31no—
62C3×#879—31no—
63#63982—31no—
64#63977D311yescharacteristic
65#67⋊Dic3—31no—
66Dic3×#67—31no—
67#63969—31no—
68#63969—31no—
69#63969—61no—
70D3×#217—31no—
71D3×#217—31no—
72D3×#217—61no—
73D3×#217D311yescharacteristic, complemented
74#63964—31no—
75#63962—31no—
76#63961—31no—
77#63959—31no—
78#63959—31no—
79#63957—31no—
80#63956—31no—
81#63956—31no—
82#63956—61no—
83#63956D311yescharacteristic, complemented
84#63955—31no—
85#63953—31no—
86C4×#626—31no—
87#63899—31no—
88#63898—31no—
89#63893—31no—
90#63893—31no—
91Dic3×D12—31no—
92#63890—31no—
93#63884—31no—
94#63884—31no—
95#63881—31no—
96#63878—31no—
97#63877—31no—
98#63877—31no—
99#63851—31no—
100#63850—31no—
101#63841—31no—
102C23×C33C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C32×D3—22no—
105C22×C32×D3—22no—
106C22×C32×D3—41no—
107C22×C32×D3C2311yescharacteristic
108C22×C32×D3C2311yescharacteristic
109C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
110C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
111C3×#638—41no—
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121#6296—41no—
122Dic3×C3⋊D3—41no—
123D3×C3⋊Dic3—22no—
124D3×C3⋊Dic3—41no—
125C3×#626—22no—
126C3×#626—22no—
127C3×D3×Dic3—22no—
128C3×D3×Dic3—41no—
129#5705—91no—
130#5587—91no—
131#5495—91no—
132C24×C32—31no—
133C23×C3×D3—21no—
134C23×C3×D3C2×D311yescharacteristic
135C23×C3×D3C2×D311yescharacteristic
136C2×#638C2×D311yescharacteristic
137C22×C3⋊Dic3—31no—
138C22×C3⋊Dic3—31no—
139C2×C4×C3⋊D3—31no—
140C2×C3×#67—31no—
141C2×C3×#67—31no—
142C2×C3×#67—31no—
143C2×C3×#67—31no—
144C2×C3×#67—61no—
145C22×C3×Dic3—31no—
146C22×C3×Dic3—31no—
147C2×C3×D12—31no—
148C2×C3×D12—31no—
149C2×C3×C4×D3—31no—
150C2×C3×C4×D3—31no—
151C2×#627—31no—
152C2×#627—31no—
153C2×#627—31no—
154C2×#626C2×D311yescharacteristic
155C2×#626C2×D311yescharacteristic
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—61no—
163C2×D3×Dic3—61no—
164C2×D3×Dic3—61no—
165C2×D3×Dic3C2×D311yescharacteristic
166C2×D3×Dic3C2×D311yescharacteristic
167C32×C22⋊C4—31no—
168C32×C22⋊C4—31no—
169#3757—31no—
170#3757—31no—
171#3757—31no—
172#3757—31no—
173#3757—31no—
174#3757—61no—
175#3757—61no—
176#3757—61no—
177#3757—121no—
178#3757C2×D311yescharacteristic
179#3757C2×D311yescharacteristic
180#3752—31no—
181C4⋊(C3⋊Dic3)—31no—
182C4⋊(C3⋊Dic3)—31no—
183#3750—31no—
184#3750—31no—
185#3750—31no—
186C4×C3⋊Dic3—31no—
187C3×#217—21no—
188C3×#217—21no—
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—61no—
198C3×#217—61no—
199C3×#217C2×D311yescharacteristic
200C3×#217C2×D311yescharacteristic
201C3×#217C2×D311yescharacteristic
202C3×#217C2×D311yescharacteristic
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×C4⋊Dic3—31no—
209C3×Dic3⋊C4—31no—
210C3×Dic3⋊C4—31no—
211C3×Dic3⋊C4—31no—
212C3×Dic3⋊C4—31no—
213C3×C4×Dic3—31no—
214C3×C4×Dic3—31no—
215#3724—31no—
216#3724—31no—
217#3724—31no—
218#3724—31no—
219#3724—61no—
220#3724—61no—
221#3724C2×D311yescharacteristic, complemented
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⋊Dic3C2×D311yescharacteristic, complemented
232Dic3⋊Dic3C2×D311yescharacteristic, complemented
233#3722—31no—
234#3722—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—31no—
245(C2×D3)⋊Dic3—61no—
246(C2×D3)⋊Dic3—61no—
247(C2×D3)⋊Dic3—61no—
248(C2×D3)⋊Dic3C2×D311yescharacteristic
249(C2×D3)⋊Dic3C2×D311yescharacteristic
250(C2×D3)⋊Dic3C2×D311yescharacteristic
251(C2×D3)⋊Dic3C2×D311yescharacteristic
252Dic32—31no—
253Dic32—31no—
254Dic32—31no—
255Dic32—31no—
256Dic32—31no—
257Dic32—61no—
258Dic32C2×D311yescharacteristic, complemented
259C22×C33—21no—
260C22×C33—21no—
261C22×C33—21no—
262C22×C33C2411yescharacteristic
263C2×C3×C3⋊D3—21no—
264C2×C3×C3⋊D3—21no—
265C2×C3×C3⋊D3—21no—
266C2×C32×D3—21no—
267C2×C32×D3—21no—
268C2×C32×D3—21no—
269C2×C32×D3—21no—
270C2×C32×D3—44no—
271C2×C32×D3#4112yes—
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—
280C32×Dic3—21no—
281C32×Dic3—21no—
282C32×Dic3—21no—
283C32×Dic3—21no—
284C3×#126—91no—
285C3×#120—91no—
286C2×C3×C22⋊C4—91no—
287#953—31no—
288C2×#217—31no—
289C2×#217—91no—
290C2×#217—91no—
291C2×#217—181no—
292#936—91no—
293#935—91no—
294#935—91no—
295#935—91no—
296D4×Dic3—91no—
297D4×Dic3—91no—
298#929—91no—
299C4×#67—91no—
300#926—91no—
301#924—91no—
302#897—91no—
303#896—91no—
304#894—91no—
305#894—91no—
306#893—91no—
307#892—91no—
308#886—91no—
309#885—91no—
310#885—91no—
311#883—91no—
312#883—91no—
313#883—181no—
314#882—31no—
315#67⋊C4—91no—
316D3×C22⋊C4—31no—
317D3×C22⋊C4—91no—
318#879—31no—
319#879—31no—
320#879—91no—
321#879—91no—
322#879—91no—
323#879—181no—
324#878—91no—
325#878—91no—
326#878—91no—
327#877—91no—
328#877—91no—
329#877—91no—
330C4×D12—91no—
331#872—91no—
332C23×C32—21no—
333C23×C32—21no—
334C23×C32—21no—
335C23×C32—31no—
336C23×C32—31no—
337C23×C32—41no—
338C23×C32—62no—
339C23×C32—62no—
340C23×C32—121no—
341C23×C32C22×D311yescharacteristic
342C23×C32C22×D311yescharacteristic
343C23×C32C22×D311yescharacteristic
344C22×C3⋊D3C22×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—31no—
353C22×C3×D3—31no—
354C22×C3×D3—42no—
355C22×C3×D3—41no—
356C22×C3×D3—41no—
357C22×C3×D3—42no—
358C22×C3×D3—61no—
359C22×C3×D3C22×D311yescharacteristic
360C22×C3×D3C22×D311yescharacteristic
361C22×C3×D3C22×D311yescharacteristic
362C22×C3×D3C22×D311yescharacteristic
363C2×C32×C4—31no—
364C2×C32×C4—31no—
365C2×C32×C4—31no—
366C2×C32×C4—31no—
367#638—41no—
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—62no—
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—121no—
390C3×#67—62no—
391C3×#67—62no—
392C3×#67—121no—
393C3×#67—121no—
394C3×#67—122no—
395C2×C3×Dic3—21no—
396C2×C3×Dic3—21no—
397C2×C3×Dic3—21no—
398C2×C3×Dic3—21no—
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—31no—
408C2×C3×Dic3—31no—
409C2×C3×Dic3—61no—
410C2×C3×Dic3—61no—
411C2×C3×Dic3—61no—
412C2×C3×Dic3—61no—
413C2×C3×Dic3—61no—
414C2×C3×Dic3—62no—
415C2×C3×Dic3—121no—
416C2×C3×Dic3C22×D311yescharacteristic
417C2×C3×Dic3C22×D311yescharacteristic
418C2×C3×Dic3C22×D311yescharacteristic
419C2×C3×Dic3C22×D311yescharacteristic
420C2×C3×Dic3C22×D311yescharacteristic
421C2×C3×Dic3C22×D311yescharacteristic
422C2×C3×Dic3C22×D311yescharacteristic
423C2×C3×Dic3C22×D311yescharacteristic
424C3×D12—62no—
425C3×D12—62no—
426C3×C4×D3—62no—
427C3×C4×D3—121no—
428#627—121no—
429#627—121no—
430#627—121no—
431#626—22no—
432#626—22no—
433D3×Dic3—22no—
434D3×Dic3—41no—
435D3×Dic3—62no—
436D3×Dic3—62no—
437D3×Dic3—122no—
438D3×Dic3—121no—
439D3×Dic3—121no—
440D3×Dic3—122no—
441D3×Dic3—121no—
442D3×Dic3—121no—
443D3×Dic3—122no—
444#551—271noSylow
445C2×C33—41no—
446C2×C33C2×#4111yescharacteristic
447C2×C33C2×#4111yescharacteristic
448C2×C33H(5,𝔽2)11yescharacteristic
449C3×C3⋊D3—41no—
450C32×D3—22no—
451C32×D3—22no—
452C24×C3—31no—
453C24×C3—31no—
454C24×C3—61no—
455C23×D3D3211yescharacteristic
456C2×C3×D4—91no—
457C2×C3×D4—91no—
458C2×C3×D4—91no—
459C22×C3×C4—91no—
460C22×C3×C4—91no—
461C2×#67—31no—
462C2×#67—31no—
463C2×#67—31no—
464C2×#67—31no—
465C2×#67—61no—
466C22×Dic3—31no—
467C22×Dic3—31no—
468C22×Dic3—91no—
469C22×Dic3—91no—
470C22×Dic3—91no—
471C22×Dic3—91no—
472C22×Dic3—91no—
473C22×Dic3—181no—
474C22×Dic3—181no—
475C2×D12—31no—
476C2×D12—31no—
477C2×C4×D3—31no—
478C2×C4×D3—31no—
479C2×C4×D3—91no—
480C2×C4×D3—91no—
481C2×C4×D3—91no—
482C2×C4×D3—91no—
483C2×C4×D3—181no—
484C2×Dic6—91no—
485C2×Dic6—91no—
486C2×Dic6—91no—
487C3×C4⋊C4—91no—
488C3×C4⋊C4—91no—
489C3×C4⋊C4—91no—
490C3×C22⋊C4—31no—
491C3×C22⋊C4—31no—
492C3×C22⋊C4—31no—
493C3×C22⋊C4—31no—
494C3×C22⋊C4—61no—
495C3×C22⋊C4—61no—
496C3×C22⋊C4—91no—
497C3×C22⋊C4—91no—
498C3×C22⋊C4—91no—
499C3×C22⋊C4—91no—
500C3×C22⋊C4—91no—
501C3×C22⋊C4—91no—
502C3×C42—91no—
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—61no—
512#217—61no—
513#217—91no—
514#217—91no—
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—181no—
524#217—181no—
525#217—181no—
526#217—181no—
527#217—181no—
528#217—361no—
529#217D3211yescharacteristic
530#217D3211yescharacteristic
531(C2×D3)⋊C4—31no—
532(C2×D3)⋊C4—31no—
533(C2×D3)⋊C4—31no—
534(C2×D3)⋊C4—31no—
535(C2×D3)⋊C4—91no—
536(C2×D3)⋊C4—91no—
537(C2×D3)⋊C4—91no—
538(C2×D3)⋊C4—91no—
539(C2×D3)⋊C4—91no—
540(C2×D3)⋊C4—91no—
541(C2×D3)⋊C4—91no—
542(C2×D3)⋊C4—91no—
543(C2×D3)⋊C4—181no—
544C4⋊Dic3—31no—
545C4⋊Dic3—31no—
546C4⋊Dic3—91no—
547C4⋊Dic3—91no—
548C4⋊Dic3—91no—
549C4⋊Dic3—91no—
550C4⋊Dic3—91no—
551C4⋊Dic3—181no—
552C4⋊Dic3—181no—
553Dic3⋊C4—31no—
554Dic3⋊C4—31no—
555Dic3⋊C4—31no—
556Dic3⋊C4—31no—
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—181no—
568Dic3⋊C4—181no—
569Dic3⋊C4—181no—
570C4×Dic3—31no—
571C4×Dic3—31no—
572C4×Dic3—91no—
573C4×Dic3—91no—
574C4×Dic3—91no—
575C4×Dic3—91no—
576C4×Dic3—91no—
577C4×Dic3—91no—
578C4×Dic3—181no—
579C22×C32—21no—
580C22×C32—22no—
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—21no—
591C22×C32—21no—
592C22×C32—32no—
593C22×C32—32no—
594C22×C32—41no—
595C22×C32—41no—
596C22×C32—41no—
597C22×C32—42no—
598C22×C32—41no—
599C22×C32—41no—
600C22×C32—41no—
601C22×C32—41no—
602C22×C32—41no—
603C22×C32—41no—
604C22×C32—61no—
605C22×C32—61no—
606C22×C32—61no—
607C22×C32—61no—
608C22×C32—81no—
609C22×C32—81no—
610C22×C32—124no—
611C22×C32C23×D311yescharacteristic
612C22×C32C23×D311yescharacteristic
613C22×C32C23×D311yescharacteristic
614C2×C3⋊D3—21no—
615C2×C3⋊D3—21no—
616C2×C3⋊D3—21no—
617C2×C3×D3—22no—
618C2×C3×D3—22no—
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—21no—
626C2×C3×D3—21no—
627C2×C3×D3—22no—
628C2×C3×D3—22no—
629C2×C3×D3—41no—
630C2×C3×D3—41no—
631C2×C3×D3—44no—
632C2×C3×D3—44no—
633C2×C3×D3—48no—
634C2×C3×D3—62no—
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#23512yes—
644C2×C3×D3#23712yes—
645C2×C3×D3#23712yes—
646C2×C3×D3#23712yes—
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—21no—
656C3⋊Dic3—61no—
657C3⋊Dic3—61no—
658C3⋊Dic3—61no—
659C3⋊Dic3—61no—
660C3⋊Dic3—61no—
661C3⋊Dic3—61no—
662C3⋊Dic3—121no—
663C3⋊Dic3—121no—
664C3⋊Dic3—121no—
665C3⋊Dic3—121no—
666C3⋊Dic3—121no—
667C3⋊Dic3—121no—
668C3⋊Dic3—241no—
669C3⋊Dic3—241no—
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—41no—
679C3×Dic3—41no—
680C3×Dic3—41no—
681C3×Dic3—41no—
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—121no—
693C3×Dic3—121no—
694C3×Dic3—121no—
695C3×Dic3—121no—
696C3×Dic3—121no—
697#126—91no—
698#126—271no—
699#124—271no—
700#123—271no—
701#123—271no—
702#123—271no—
703C22⋊Q8—271no—
704C22⋊Q8—271no—
705#120—91no—
706C4×D4—271no—
707C4×D4—271no—
708#117—271no—
709#117—271no—
710C2×C22⋊C4—91no—
711C2×C22⋊C4—271no—
712C33#55111yescharacteristic, complemented, Sylow
713C23×C3—21no—
714C23×C3—21no—
715C23×C3—21no—
716C23×C3—31no—
717C23×C3—31no—
718C23×C3—31no—
719C23×C3—31no—
720C23×C3—41no—
721C23×C3—61no—
722C23×C3—61no—
723C23×C3—62no—
724C23×C3—62no—
725C23×C3—62no—
726C23×C3—62no—
727C23×C3—64no—
728C23×C3—91no—
729C23×C3—122no—
730C23×C3—121no—
731C23×C3—121no—
732C23×C3—122no—
733C23×C3C2×D3211yescharacteristic
734C23×C3C2×D3211yescharacteristic
735C23×C3C2×D3211yescharacteristic
736C22×D3—22no—
737C22×D3—22no—
738C22×D3—31no—
739C22×D3—31no—
740C22×D3—41no—
741C22×D3—61no—
742C22×D3C2×D3211yescharacteristic
743C22×D3C2×D3211yescharacteristic
744C3×D4—182no—
745C3×D4—182no—
746C3×D4—361no—
747C2×C3×C4—31no—
748C2×C3×C4—31no—
749C2×C3×C4—31no—
750C2×C3×C4—31no—
751C2×C3×C4—31no—
752C2×C3×C4—31no—
753C2×C3×C4—31no—
754C2×C3×C4—31no—
755C2×C3×C4—61no—
756C2×C3×C4—61no—
757C2×C3×C4—61no—
758C2×C3×C4—61no—
759C2×C3×C4—91no—
760C2×C3×C4—91no—
761C2×C3×C4—91no—
762C2×C3×C4—91no—
763C2×C3×C4—91no—
764C2×C3×C4—182no—
765C2×C3×C4—361no—
766#67—62no—
767#67—62no—
768#67—121no—
769#67—121no—
770#67—122no—
771C2×Dic3—31no—
772C2×Dic3—31no—
773C2×Dic3—31no—
774C2×Dic3—31no—
775C2×Dic3—31no—
776C2×Dic3—31no—
777C2×Dic3—31no—
778C2×Dic3—31no—
779C2×Dic3—31no—
780C2×Dic3—31no—
781C2×Dic3—61no—
782C2×Dic3—61no—
783C2×Dic3—61no—
784C2×Dic3—61no—
785C2×Dic3—61no—
786C2×Dic3—62no—
787C2×Dic3—91no—
788C2×Dic3—91no—
789C2×Dic3—91no—
790C2×Dic3—91no—
791C2×Dic3—91no—
792C2×Dic3—91no—
793C2×Dic3—121no—
794C2×Dic3—181no—
795C2×Dic3—181no—
796C2×Dic3—181no—
797C2×Dic3—181no—
798C2×Dic3—181no—
799C2×Dic3—181no—
800C2×Dic3—182no—
801C2×Dic3—182no—
802C2×Dic3—361no—
803C2×Dic3—361no—
804C2×Dic3—362no—
805C2×Dic3—361no—
806C2×Dic3—361no—
807C2×Dic3—361no—
808C2×Dic3—362no—
809C2×Dic3C2×D3211yescharacteristic
810C2×Dic3C2×D3211yescharacteristic
811C2×Dic3C2×D3211yescharacteristic
812C2×Dic3C2×D3211yescharacteristic
813D12—62no—
814D12—62no—
815C4×D3—62no—
816C4×D3—121no—
817C4×D3—182no—
818C4×D3—361no—
819C4×D3—361no—
820C4×D3—361no—
821C4×D3—362no—
822Dic6—361no—
823Dic6—361no—
824Dic6—361no—
825C2×C32—21no—
826C2×C32—21no—
827C2×C32—21no—
828C2×C32—21no—
829C2×C32—21no—
830C2×C32—21no—
831C2×C32—21no—
832C2×C32—21no—
833C2×C32—21no—
834C2×C32—41no—
835C2×C32—41no—
836C2×C32—41no—
837C2×C32—41no—
838C2×C32—42no—
839C2×C32—41no—
840C2×C32—41no—
841C2×C32—62no—
842C2×C32—62no—
843C2×C32—81no—
844C2×C32—81no—
845C2×C32—82no—
846C2×C32C2×#23511yescharacteristic
847C2×C32C2×#23711yescharacteristic
848C2×C32C2×#23711yescharacteristic
849C2×C32C2×#23711yescharacteristic
850C2×C32#100411yescharacteristic
851C2×C32#100411yescharacteristic
852C2×C32D3×#4111yescharacteristic
853C2×C32D3×#4111yescharacteristic
854C2×C32#100911yescharacteristic
855C3⋊D3—41no—
856C3×D3—24no—
857C3×D3—22no—
858C3×D3—22no—
859C3×D3—22no—
860C3×D3—22no—
861C3×D3—42no—
862C3×D3—122no—
863C3×D3—121no—
864C3×D3—121no—
865C24—31no—
866C2×Q8—271no—
867C2×D4—91no—
868C2×D4—91no—
869C2×D4—91no—
870C22×C4—91no—
871C22×C4—91no—
872C22×C4—271no—
873C22×C4—271no—
874C22×C4—271no—
875C4⋊C4—91no—
876C4⋊C4—91no—
877C4⋊C4—91no—
878C4⋊C4—271no—
879C4⋊C4—271no—
880C4⋊C4—271no—
881C4⋊C4—271no—
882C4⋊C4—271no—
883C22⋊C4—31no—
884C22⋊C4—31no—
885C22⋊C4—91no—
886C22⋊C4—91no—
887C22⋊C4—91no—
888C22⋊C4—91no—
889C22⋊C4—91no—
890C22⋊C4—91no—
891C22⋊C4—271no—
892C22⋊C4—271no—
893C22⋊C4—271no—
894C22⋊C4—271no—
895C22⋊C4—271no—
896C22⋊C4—271no—
897C42—91no—
898C42—271no—
899C42—271no—
900C22×C3—22no—
901C22×C3—21no—
902C22×C3—21no—
903C22×C3—21no—
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—32no—
914C22×C3—32no—
915C22×C3—32no—
916C22×C3—32no—
917C22×C3—41no—
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—41no—
927C22×C3—62no—
928C22×C3—62no—
929C22×C3—62no—
930C22×C3—62no—
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—81no—
940C22×C3—81no—
941C22×C3—121no—
942C22×C3—121no—
943C22×C3—124no—
944C22×C3—124no—
945C22×C3—128no—
946C22×C3—181no—
947C22×C3—181no—
948C22×C3—181no—
949C22×C3C22×D3211yescharacteristic
950C22×C3C22×D3211yescharacteristic
951C22×C3C22×D3211yescharacteristic
952C2×D3—21no—
953C2×D3—21no—
954C2×D3—21no—
955C2×D3—21no—
956C2×D3—44no—
957C2×D3—62no—
958C2×D3—61no—
959C2×D3—61no—
960C2×D3—61no—
961C2×D3—61no—
962C2×D3—61no—
963C2×D3—61no—
964C2×D3—121no—
965C2×D3—121no—
966C2×D3#380412yes—
967C2×D3#380512yes—
968C3×C4—61no—
969C3×C4—61no—
970C3×C4—61no—
971C3×C4—61no—
972C3×C4—61no—
973C3×C4—61no—
974C3×C4—61no—
975C3×C4—61no—
976C3×C4—121no—
977C3×C4—121no—
978C3×C4—121no—
979C3×C4—121no—
980C3×C4—181no—
981C3×C4—181no—
982C3×C4—181no—
983C3×C4—181no—
984C3×C4—181no—
985Dic3—21no—
986Dic3—21no—
987Dic3—21no—
988Dic3—21no—
989Dic3—61no—
990Dic3—61no—
991Dic3—61no—
992Dic3—61no—
993Dic3—61no—
994Dic3—61no—
995Dic3—61no—
996Dic3—61no—
997Dic3—61no—
998Dic3—61no—
999Dic3—121no—
1000Dic3—121no—
1001Dic3—121no—
1002Dic3—121no—
1003Dic3—121no—
1004Dic3—181no—
1005Dic3—181no—
1006Dic3—181no—
1007Dic3—181no—
1008Dic3—181no—
1009Dic3—181no—
1010Dic3—361no—
1011Dic3—361no—
1012Dic3—361no—
1013Dic3—361no—
1014Dic3—361no—
1015Dic3—361no—
1016Dic3—721no—
1017Dic3—721no—
1018C32—21no—
1019C32—21no—
1020C32—21no—
1021C32—41no—
1022C32#549511yescharacteristic, complemented
1023C32#558711yescharacteristic, complemented
1024C32#570511yescharacteristic, complemented
1025C23—31no—
1026C23—31no—
1027C23—62no—
1028C23—62no—
1029C23—91no—
1030C23—121no—
1031C23D3311yescharacteristic
1032Q8—1081no—
1033D4—182no—
1034D4—182no—
1035D4—361no—
1036C2×C4—31no—
1037C2×C4—31no—
1038C2×C4—31no—
1039C2×C4—31no—
1040C2×C4—91no—
1041C2×C4—91no—
1042C2×C4—91no—
1043C2×C4—91no—
1044C2×C4—91no—
1045C2×C4—182no—
1046C2×C4—271no—
1047C2×C4—271no—
1048C2×C4—361no—
1049C2×C4—542no—
1050C2×C4—1081no—
1051C2×C4—1081no—
1052C2×C3—21no—
1053C2×C3—21no—
1054C2×C3—21no—
1055C2×C3—21no—
1056C2×C3—21no—
1057C2×C3—21no—
1058C2×C3—21no—
1059C2×C3—21no—
1060C2×C3—21no—
1061C2×C3—42no—
1062C2×C3—41no—
1063C2×C3—41no—
1064C2×C3—41no—
1065C2×C3—41no—
1066C2×C3—41no—
1067C2×C3—41no—
1068C2×C3—64no—
1069C2×C3—62no—
1070C2×C3—62no—
1071C2×C3—62no—
1072C2×C3—62no—
1073C2×C3—81no—
1074C2×C3—81no—
1075C2×C3—82no—
1076C2×C3—122no—
1077C2×C3—361no—
1078C2×C3D3×#23511yescharacteristic
1079C2×C3#6430711yescharacteristic
1080C2×C3D3×#23711yescharacteristic
1081C2×C3D3×#23711yescharacteristic
1082C2×C3D3×#23711yescharacteristic
1083C2×C3#6431411yescharacteristic
1084C2×C3C2×#380411yescharacteristic
1085C2×C3C2×#380511yescharacteristic
1086C2×C3#6433011yescharacteristic
1087D3—22no—
1088D3—22no—
1089D3—122no—
1090D3—121no—
1091D3—121no—
1092C22—21no—
1093C22—21no—
1094C22—21no—
1095C22—32no—
1096C22—32no—
1097C22—61no—
1098C22—61no—
1099C22—61no—
1100C22—61no—
1101C22—124no—
1102C22—181no—
1103C22—181no—
1104C22—181no—
1105C22C2×D3311yescharacteristic
1106C4—61no—
1107C4—61no—
1108C4—61no—
1109C4—61no—
1110C4—181no—
1111C4—181no—
1112C4—181no—
1113C4—181no—
1114C4—181no—
1115C4—541no—
1116C4—541no—
1117C3—21no—
1118C3—21no—
1119C3—21no—
1120C3—41no—
1121C3#1059409311yescharacteristic, complemented
1122C3#1059411511yescharacteristic, complemented
1123C3#1059550911yescharacteristic, complemented
1124C2—41no—
1125C2—62no—
1126C2—62no—
1127C2—361no—
1128C2D3×#380411yescharacteristic
1129C2D3×#380511yescharacteristic
1130C2#1172441811yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
prime radicalC3×#63977C2
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. #11723718C2semidirect
2. #11723621C2semidirect
3. D3×#3757C2semidirect
4. #11723596C2semidirect
6. C3×D3×#217C2semidirect
7. C3×#63956C2semidirect
8. #11722990C2semidirect
9. #11722986C2semidirect
10. #11722981C2semidirect
11. #11722978C2semidirect
12. #11722929C2semidirect
13. Dic3×#626C2semidirect
14. #11722916C2semidirect
15. #11722914C2semidirect
21. C2×#6296C22semidirect
22. C2×Dic3×C3⋊D3C22semidirect
34. #88814C22semidirect
35. #88814C22semidirect
36. #88813C22semidirect
37. #88807C22semidirect
38. #88806C22semidirect
39. #88806C22semidirect
40. Dic3⋊(C3⋊Dic3)C22semidirect
41. Dic3⋊(C3⋊Dic3)C22semidirect
42. #88803C22semidirect
45. Dic3×C3⋊Dic3C22semidirect
46. C3×#3724C22semidirect
47. C3×Dic3⋊Dic3C22semidirect
48. C3×Dic3⋊Dic3C22semidirect
53. C3×Dic32C22semidirect
73. D3×#217D3semidirect
83. #63956D3semidirect
221. #3724C2×D3semidirect
231. Dic3⋊Dic3C2×D3semidirect
232. Dic3⋊Dic3C2×D3semidirect
258. Dic32C2×D3semidirect
712. C33#551semidirect
1022. C32#5495semidirect
1023. C32#5587semidirect
1024. C32#5705semidirect
1121. C3#10594093semidirect
1122. C3#10594115semidirect
1123. C3#10595509semidirect

Maximal subgroups

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

subgroupindex
#117237182
#117236212
D3×#37572
#117235962
C3×#639772
C3×D3×#2172
C3×#639562
#117229902
#117229862
#117229812
#117229782
#117229292
Dic3×#6262
#117229162
#117229142
#105955093
#105941153
#105940933