Finite Group Databasebeta

← #13167998

Subgroups — #13167998

Order 1728.

1216 conjugacy classes of subgroups.

The subgroup lattice has 1088 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723674C211yesmaximal, characteristic, complemented
2#11723500C211yesmaximal, characteristic, complemented
3#11723487C211yesmaximal, characteristic, complemented
4#11723418C211yesmaximal, characteristic, complemented
5C3×#63921C211yesmaximal, characteristic
6C3×#63896C211yesmaximal, characteristic, complemented
7C3×#63893C211yesmaximal, characteristic, complemented
8#11722980C211yesmaximal, characteristic, complemented
9#11722976C211yesmaximal, characteristic, complemented
10#11722975C211yesmaximal, characteristic, complemented
11#11722972C211yesmaximal, characteristic, complemented
12#11722971C211yesmaximal, characteristic, complemented
13#11722970C211yesmaximal, characteristic, complemented
14D3×(C2×D3)⋊Dic3C211yesmaximal, characteristic
15D3×(C2×D3)⋊Dic3C211yesmaximal, characteristic
16#10594635—31nomaximal
17#10594170—31nomaximal
18#10594170—31nomaximal
19C22×C3×D32C2211yescharacteristic
20C2×C3×C4×C3⋊D3C2211yescharacteristic
21C2×C3×#634C2211yescharacteristic, complemented
22C2×#6293C2211yescharacteristic, complemented
23C2×#6293C2211yescharacteristic, complemented
24C2×D3×C3⋊Dic3C2211yescharacteristic
25C2×D3×C3⋊Dic3C2211yescharacteristic
26C2×C3×#627C2211yescharacteristic, complemented
27C2×C3×#624C2211yescharacteristic
28C2×C3×D3×Dic3C2211yescharacteristic
29C2×C3×D3×Dic3C2211yescharacteristic
30#88857C2211yescharacteristic, complemented
31C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
32C32×(C2×D3)⋊C4C2211yescharacteristic
33C32×(C2×D3)⋊C4C2211yescharacteristic
34C32×Dic3⋊C4C2211yescharacteristic, complemented
35#88815C2211yescharacteristic, complemented
36#88815C2211yescharacteristic, complemented
37#88814C2211yescharacteristic
38#88814C2211yescharacteristic
39#88807C2211yescharacteristic, complemented
40#88807C2211yescharacteristic, complemented
41#88806C2211yescharacteristic, complemented
42Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
43#88803C2211yescharacteristic
44#88803C2211yescharacteristic
45(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
46(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
47C3×#3724C2211yescharacteristic, complemented
48C3×Dic3⋊Dic3C2211yescharacteristic, complemented
49C3×Dic3⋊Dic3C2211yescharacteristic, complemented
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×(C2×D3)⋊Dic3C2211yescharacteristic
54#64105—31no—
55#64087—31no—
56#64087—31no—
57C3×#897—31no—
58C3×#896—31no—
59C3×D3×C22⋊C4—31no—
60C3×D3×C22⋊C4—31no—
61C3×#878—31no—
62C3×#878—31no—
63#63982—31no—
64#63982—31no—
65D3×#217—31no—
66D3×#217—31no—
67#63964—31no—
68#63964—31no—
69C2×(C2×D3)⋊Dic3—31no—
70C2×(C2×D3)⋊Dic3—31no—
71#63921D311yescharacteristic
72D3×(C2×D3)⋊C4—31no—
73D3×(C2×D3)⋊C4—31no—
74#63899—31no—
75#63899—31no—
76#63899—31no—
77#63899—61no—
78#63896—31no—
79#63896—31no—
80#63896D311yescharacteristic, complemented
81#63895—31no—
82#63893—31no—
83#63893D311yescharacteristic, complemented
84#63888—31no—
85#63887—31no—
86#63887—31no—
87#63887—31no—
88#63887—31no—
89#63887—61no—
90#63871—31no—
91#63857—31no—
92#63857—31no—
93#63857—31no—
94#63856—31no—
95#63856—31no—
96#63851—31no—
97#63851—31no—
98#63851—31no—
99#63851—31no—
100#63851—31no—
101#63851—61no—
102C22×C3×C3⋊D3C2311yescharacteristic
103C22×C32×D3C2311yescharacteristic
104C22×C32×D3C2311yescharacteristic
105C2×C3×D32—41no—
106C2×C3×D32—41no—
107C2×C3×D32Q814yescomplemented
108C2×C33×C4C2311yescharacteristic
109C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
110C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C3×C4×C3⋊D3—41no—
117C3×#634—41no—
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122#6293—41no—
123#6293—41no—
124D3×C3⋊Dic3—41no—
125D3×C3⋊Dic3—41no—
126C3×#627—41no—
127C3×#624—41no—
128C3×D3×Dic3—41no—
129C3×D3×Dic3—41no—
130#5634—91no—
131#5634—91no—
132#5483—91no—
133C23×C3×D3—31no—
134C23×C3×D3—31no—
135C22×D32C2×D311yescharacteristic
136C22×C3⋊Dic3—31no—
137C22×C3⋊Dic3—31no—
138C2×C4×C3⋊D3C2×D311yescharacteristic
139C2×#634—31no—
140C2×#634—31no—
141C2×#634C2×D311yescharacteristic, complemented
142C22×C3×Dic3—31no—
143C22×C3×Dic3—31no—
144C2×C3×C4×D3—31no—
145C2×C3×C4×D3—31no—
146C2×C3×C4×D3—31no—
147C2×C3×C4×D3—31no—
148C2×C3×C4×D3—31no—
149C2×C3×C4×D3—31no—
150C2×C3×C4×D3—61no—
151C2×C3×Dic6—31no—
152C2×C3×Dic6—31no—
153C2×C3×Dic6—31no—
154C2×C3×Dic6—31no—
155C2×C3×Dic6—61no—
156C2×#627—31no—
157C2×#627—31no—
158C2×#627—31no—
159C2×#627—31no—
160C2×#627—61no—
161C2×#627—61no—
162C2×#627C2×D311yescharacteristic, complemented
163C2×#624C2×D311yescharacteristic
164C2×D3×Dic3—31no—
165C2×D3×Dic3—31no—
166C2×D3×Dic3—31no—
167C2×D3×Dic3—31no—
168C2×D3×Dic3—61no—
169C2×D3×Dic3—61no—
170C2×D3×Dic3C2×D311yescharacteristic
171C2×D3×Dic3C2×D311yescharacteristic
172C32×C4⋊C4—31no—
173C32×C22⋊C4—31no—
174C32×C22⋊C4—31no—
175#3757—31no—
176#3757—31no—
177#3752—31no—
178#3752—31no—
179C4⋊(C3⋊Dic3)—31no—
180C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
181#3750—31no—
182#3750—31no—
183#3750—31no—
184#3750—31no—
185#3750—31no—
186#3750—31no—
187#3750—61no—
188#3750—61no—
189#3750—61no—
190#3750—121no—
191C3×#217—31no—
192C3×#217—31no—
193C3×#217—31no—
194C3×#217—31no—
195C3×(C2×D3)⋊C4—21no—
196C3×(C2×D3)⋊C4—21no—
197C3×(C2×D3)⋊C4—31no—
198C3×(C2×D3)⋊C4—31no—
199C3×(C2×D3)⋊C4—31no—
200C3×(C2×D3)⋊C4—31no—
201C3×(C2×D3)⋊C4C2×D311yescharacteristic
202C3×(C2×D3)⋊C4C2×D311yescharacteristic
203C3×(C2×D3)⋊C4C2×D311yescharacteristic
204C3×(C2×D3)⋊C4C2×D311yescharacteristic
205C3×C4⋊Dic3—31no—
206C3×C4⋊Dic3—31no—
207C3×C4⋊Dic3—31no—
208C3×C4⋊Dic3—31no—
209C3×C4⋊Dic3—61no—
210C3×Dic3⋊C4—21no—
211C3×Dic3⋊C4—31no—
212C3×Dic3⋊C4—31no—
213C3×Dic3⋊C4—31no—
214C3×Dic3⋊C4—31no—
215C3×Dic3⋊C4C2×D311yescharacteristic, complemented
216C3×Dic3⋊C4C2×D311yescharacteristic, complemented
217#3724—31no—
218#3724—31no—
219#3724—31no—
220#3724—31no—
221#3724—61no—
222#3724C2×D311yescharacteristic, complemented
223Dic3⋊Dic3—31no—
224Dic3⋊Dic3—31no—
225Dic3⋊Dic3—31no—
226Dic3⋊Dic3—31no—
227Dic3⋊Dic3—31no—
228Dic3⋊Dic3—31no—
229Dic3⋊Dic3—31no—
230Dic3⋊Dic3—31no—
231Dic3⋊Dic3—31no—
232Dic3⋊Dic3—31no—
233Dic3⋊Dic3—61no—
234Dic3⋊Dic3—61no—
235Dic3⋊Dic3—61no—
236Dic3⋊Dic3C2×D311yescharacteristic, complemented
237Dic3⋊Dic3C2×D311yescharacteristic, complemented
238#3722—31no—
239#3722—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—31no—
250(C2×D3)⋊Dic3—31no—
251(C2×D3)⋊Dic3—31no—
252(C2×D3)⋊Dic3—61no—
253(C2×D3)⋊Dic3—61no—
254(C2×D3)⋊Dic3—61no—
255(C2×D3)⋊Dic3—61no—
256(C2×D3)⋊Dic3C2×D311yescharacteristic
257(C2×D3)⋊Dic3C2×D311yescharacteristic
258(C2×D3)⋊Dic3C2×D311yescharacteristic
259(C2×D3)⋊Dic3C2×D311yescharacteristic
260C22×C33C2411yescharacteristic
261C2×C3×C3⋊D3—21no—
262C2×C3×C3⋊D3—21no—
263C2×C3×C3⋊D3C2×Q812yes—
264C2×C32×D3—21no—
265C2×C32×D3—21no—
266C2×C32×D3—21no—
267C2×C32×D3—21no—
268C2×C32×D3C2×Q812yes—
269C2×C32×D3C2×Q812yes—
270C3×D32—44no—
271C33×C4—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—
278C3×C3⋊Dic3—21no—
279C32×Dic3—21no—
280C32×Dic3—21no—
281C32×Dic3—21no—
282C32×Dic3—21no—
283C3×C22⋊Q8—91no—
284C3×C22⋊Q8—91no—
285C2×C3×C22⋊C4—91no—
286C2×#217—91no—
287C2×#217—91no—
288#946—91no—
289#946—91no—
290#946—91no—
291#946—91no—
292C2×(C2×D3)⋊C4—91no—
293C2×(C2×D3)⋊C4—91no—
294#924—91no—
295#924—91no—
296#924—91no—
297#924—91no—
298#924—91no—
299#924—91no—
300#897—31no—
301#897—91no—
302#897—91no—
303#897—91no—
304#896—31no—
305#896—91no—
306#896—91no—
307#896—91no—
308#896—91no—
309#896—91no—
310#896—91no—
311#896—91no—
312#896—181no—
313D3×C22⋊C4—31no—
314D3×C22⋊C4—31no—
315D3×C22⋊C4—91no—
316D3×C22⋊C4—91no—
317#878—31no—
318#878—31no—
319#878—91no—
320#878—91no—
321#878—91no—
322#878—91no—
323#878—91no—
324#878—91no—
325#878—91no—
326#878—91no—
327#878—91no—
328#878—91no—
329#878—181no—
330#878—181no—
331C23×C32—31no—
332C23×C32—31no—
333C22×C3⋊D3C22×D311yescharacteristic
334C22×C3×D3—21no—
335C22×C3×D3—21no—
336C22×C3×D3—31no—
337C22×C3×D3—31no—
338C22×C3×D3—34no—
339C22×C3×D3—34no—
340C22×C3×D3—61no—
341C22×C3×D3—121no—
342C22×C3×D3—121no—
343C22×C3×D3—121no—
344C22×C3×D3—121no—
345C22×C3×D3C22×D311yescharacteristic
346C22×C3×D3C22×D311yescharacteristic
347C22×C3×D3C22×D311yescharacteristic
348C22×C3×D3C22×D311yescharacteristic
349C2×D32—41no—
350C2×D32—41no—
351C2×D32Dic614yescomplemented
352C2×C32×C4—21no—
353C2×C32×C4—21no—
354C2×C32×C4—21no—
355C2×C32×C4—31no—
356C2×C32×C4—31no—
357C2×C32×C4—31no—
358C2×C32×C4—31no—
359C2×C32×C4—41no—
360C2×C32×C4C22×D311yescharacteristic
361C2×C32×C4C22×D311yescharacteristic
362C2×C32×C4C22×D311yescharacteristic
363C2×C3⋊Dic3—31no—
364C2×C3⋊Dic3—31no—
365C2×C3⋊Dic3—31no—
366C2×C3⋊Dic3—31no—
367C2×C3⋊Dic3—31no—
368C2×C3⋊Dic3—31no—
369C2×C3⋊Dic3—61no—
370C2×C3⋊Dic3—61no—
371C2×C3⋊Dic3—61no—
372C2×C3⋊Dic3—61no—
373C2×C3⋊Dic3—61no—
374C2×C3⋊Dic3—61no—
375C2×C3⋊Dic3—121no—
376C2×C3⋊Dic3—121no—
377C2×C3⋊Dic3—121no—
378C2×C3⋊Dic3—121no—
379C2×C3⋊Dic3C22×D311yescharacteristic
380C2×C3⋊Dic3C22×D311yescharacteristic
381C2×C3⋊Dic3C22×D311yescharacteristic
382C2×C3⋊Dic3C22×D311yescharacteristic
383C2×C3⋊Dic3C22×D311yescharacteristic
384C4×C3⋊D3—41no—
385#634—41no—
386#634—121no—
387#634—121no—
388C2×C3×Dic3—21no—
389C2×C3×Dic3—21no—
390C2×C3×Dic3—21no—
391C2×C3×Dic3—21no—
392C2×C3×Dic3—31no—
393C2×C3×Dic3—31no—
394C2×C3×Dic3—31no—
395C2×C3×Dic3—31no—
396C2×C3×Dic3—31no—
397C2×C3×Dic3—31no—
398C2×C3×Dic3—31no—
399C2×C3×Dic3—31no—
400C2×C3×Dic3—31no—
401C2×C3×Dic3—31no—
402C2×C3×Dic3—61no—
403C2×C3×Dic3—61no—
404C2×C3×Dic3—61no—
405C2×C3×Dic3—61no—
406C2×C3×Dic3—61no—
407C2×C3×Dic3—121no—
408C2×C3×Dic3—121no—
409C2×C3×Dic3C22×D311yescharacteristic
410C2×C3×Dic3C22×D311yescharacteristic
411C2×C3×Dic3C22×D311yescharacteristic
412C2×C3×Dic3C22×D311yescharacteristic
413C2×C3×Dic3C22×D311yescharacteristic
414C2×C3×Dic3C22×D311yescharacteristic
415C2×C3×Dic3C22×D311yescharacteristic
416C2×C3×Dic3C22×D311yescharacteristic
417C3×C4×D3—121no—
418C3×C4×D3—121no—
419C3×C4×D3—121no—
420C3×C4×D3—121no—
421C3×C4×D3—122no—
422C3×C4×D3—121no—
423C3×C4×D3—121no—
424C3×Dic6—121no—
425C3×Dic6—121no—
426C3×Dic6—121no—
427C3×Dic6—121no—
428C3×Dic6—122no—
429#627—41no—
430#627—121no—
431#627—121no—
432#627—121no—
433#627—121no—
434#627—122no—
435#627—122no—
436#624—41no—
437D3×Dic3—41no—
438D3×Dic3—41no—
439D3×Dic3—121no—
440D3×Dic3—121no—
441D3×Dic3—121no—
442D3×Dic3—121no—
443D3×Dic3—122no—
444D3×Dic3—122no—
445#543—271noSylow
446C2×C33C22×Q811yescharacteristic
447C2×C33H(5,𝔽2)11yescharacteristic
448C2×C33H(5,𝔽2)11yescharacteristic
449C3×C3⋊D3—22no—
450C32×D3—22no—
451C32×D3—22no—
452C24×C3—91no—
453C23×D3—31no—
454C23×D3—31no—
455C2×C3×Q8—91no—
456C2×C3×Q8—91no—
457C22×C3×C4—91no—
458C22×C3×C4—91no—
459C22×C3×C4—91no—
460C22×C3×C4—91no—
461C22×Dic3—31no—
462C22×Dic3—31no—
463C22×Dic3—91no—
464C22×Dic3—91no—
465C22×Dic3—91no—
466C22×Dic3—91no—
467C22×Dic3—181no—
468C22×Dic3—181no—
469C2×C4×D3—31no—
470C2×C4×D3—31no—
471C2×C4×D3—31no—
472C2×C4×D3—31no—
473C2×C4×D3—31no—
474C2×C4×D3—31no—
475C2×C4×D3—61no—
476C2×C4×D3—91no—
477C2×C4×D3—91no—
478C2×Dic6—31no—
479C2×Dic6—31no—
480C2×Dic6—31no—
481C2×Dic6—31no—
482C2×Dic6—61no—
483C2×Dic6—91no—
484C2×Dic6—91no—
485C2×Dic6—91no—
486C2×Dic6—91no—
487C2×Dic6—91no—
488C2×Dic6—91no—
489C2×Dic6—181no—
490C2×Dic6—181no—
491C3×C4⋊C4—31no—
492C3×C4⋊C4—31no—
493C3×C4⋊C4—61no—
494C3×C4⋊C4—91no—
495C3×C4⋊C4—91no—
496C3×C4⋊C4—91no—
497C3×C4⋊C4—91no—
498C3×C22⋊C4—31no—
499C3×C22⋊C4—31no—
500C3×C22⋊C4—31no—
501C3×C22⋊C4—31no—
502C3×C22⋊C4—61no—
503C3×C22⋊C4—61no—
504C3×C22⋊C4—91no—
505C3×C22⋊C4—91no—
506C3×C22⋊C4—91no—
507C3×C22⋊C4—91no—
508#217—31no—
509#217—31no—
510#217—31no—
511#217—31no—
512#217—91no—
513#217—91no—
514#217—91no—
515#217—91no—
516#217—91no—
517#217—91no—
518#217—91no—
519#217—91no—
520#217—181no—
521#217—181no—
522(C2×D3)⋊C4—31no—
523(C2×D3)⋊C4—31no—
524(C2×D3)⋊C4—31no—
525(C2×D3)⋊C4—31no—
526(C2×D3)⋊C4—91no—
527(C2×D3)⋊C4—91no—
528(C2×D3)⋊C4—91no—
529(C2×D3)⋊C4—91no—
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—181no—
537(C2×D3)⋊C4—181no—
538(C2×D3)⋊C4D3211yescharacteristic
539(C2×D3)⋊C4D3211yescharacteristic
540C4⋊Dic3—31no—
541C4⋊Dic3—31no—
542C4⋊Dic3—31no—
543C4⋊Dic3—31no—
544C4⋊Dic3—61no—
545C4⋊Dic3—91no—
546C4⋊Dic3—91no—
547C4⋊Dic3—91no—
548C4⋊Dic3—91no—
549C4⋊Dic3—91no—
550C4⋊Dic3—91no—
551C4⋊Dic3—181no—
552Dic3⋊C4—31no—
553Dic3⋊C4—31no—
554Dic3⋊C4—31no—
555Dic3⋊C4—31no—
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—91no—
570Dic3⋊C4—91no—
571Dic3⋊C4—181no—
572Dic3⋊C4—181no—
573Dic3⋊C4—181no—
574Dic3⋊C4—181no—
575Dic3⋊C4—181no—
576Dic3⋊C4—181no—
577Dic3⋊C4—361no—
578Dic3⋊C4D3211yescharacteristic, complemented
579C22×C32—21no—
580C22×C32—21no—
581C22×C32—21no—
582C22×C32—32no—
583C22×C32—32no—
584C22×C32—41no—
585C22×C32—61no—
586C22×C32—61no—
587C22×C32—61no—
588C22×C32—61no—
589C22×C32C23×D311yescharacteristic
590C22×C32C23×D311yescharacteristic
591C22×C32C23×D311yescharacteristic
592C2×C3⋊D3—21no—
593C2×C3⋊D3—21no—
594C2×C3⋊D3C2×Dic612yes—
595C2×C3×D3—21no—
596C2×C3×D3—21no—
597C2×C3×D3—21no—
598C2×C3×D3—21no—
599C2×C3×D3—21no—
600C2×C3×D3—21no—
601C2×C3×D3—21no—
602C2×C3×D3—21no—
603C2×C3×D3—22no—
604C2×C3×D3—22no—
605C2×C3×D3—32no—
606C2×C3×D3—32no—
607C2×C3×D3—41no—
608C2×C3×D3—41no—
609C2×C3×D3—41no—
610C2×C3×D3—41no—
611C2×C3×D3—62no—
612C2×C3×D3—61no—
613C2×C3×D3—61no—
614C2×C3×D3—61no—
615C2×C3×D3—61no—
616C2×C3×D3—121no—
617C2×C3×D3—121no—
618C2×C3×D3—124no—
619C2×C3×D3—124no—
620C2×C3×D3C2×Dic612yes—
621C2×C3×D3C2×Dic612yes—
622C2×C3×D3D3×Q812yes—
623C2×C3×D3D3×Q812yes—
624D32—44no—
625C32×C4—21no—
626C32×C4—21no—
627C32×C4—21no—
628C32×C4—41no—
629C32×C4—41no—
630C32×C4—41no—
631C32×C4—61no—
632C32×C4—61no—
633C32×C4—61no—
634C32×C4—61no—
635C32×C4—81no—
636C3⋊Dic3—21no—
637C3⋊Dic3—21no—
638C3⋊Dic3—21no—
639C3⋊Dic3—21no—
640C3⋊Dic3—21no—
641C3⋊Dic3—61no—
642C3⋊Dic3—62no—
643C3⋊Dic3—61no—
644C3⋊Dic3—61no—
645C3⋊Dic3—61no—
646C3⋊Dic3—61no—
647C3⋊Dic3—61no—
648C3⋊Dic3—121no—
649C3⋊Dic3—121no—
650C3⋊Dic3—122no—
651C3⋊Dic3—121no—
652C3⋊Dic3—121no—
653C3⋊Dic3—121no—
654C3⋊Dic3—241no—
655C3×Dic3—21no—
656C3×Dic3—21no—
657C3×Dic3—21no—
658C3×Dic3—21no—
659C3×Dic3—21no—
660C3×Dic3—21no—
661C3×Dic3—21no—
662C3×Dic3—21no—
663C3×Dic3—41no—
664C3×Dic3—41no—
665C3×Dic3—41no—
666C3×Dic3—41no—
667C3×Dic3—62no—
668C3×Dic3—62no—
669C3×Dic3—61no—
670C3×Dic3—61no—
671C3×Dic3—61no—
672C3×Dic3—61no—
673C3×Dic3—61no—
674C3×Dic3—61no—
675C3×Dic3—61no—
676C3×Dic3—61no—
677C3×Dic3—61no—
678C3×Dic3—61no—
679C3×Dic3—121no—
680C3×Dic3—121no—
681C3×Dic3—121no—
682C22⋊Q8—91no—
683C22⋊Q8—91no—
684C22⋊Q8—271no—
685C22⋊Q8—271no—
686C22⋊Q8—271no—
687C22⋊Q8—271no—
688C22⋊Q8—271no—
689C22⋊Q8—271no—
690C22⋊Q8—271no—
691C22⋊Q8—271no—
692C22⋊Q8—271no—
693C22⋊Q8—271no—
694C2×C22⋊C4—91no—
695C2×C22⋊C4—271no—
696C2×C22⋊C4—271no—
697C33#54311yescharacteristic, complemented, Sylow
698C23×C3—31no—
699C23×C3—31no—
700C23×C3—31no—
701C23×C3—31no—
702C23×C3—61no—
703C23×C3—61no—
704C23×C3—94no—
705C23×C3—91no—
706C23×C3—361no—
707C23×C3—361no—
708C22×D3—31no—
709C22×D3—31no—
710C22×D3—34no—
711C22×D3—34no—
712C22×D3—61no—
713C22×D3—121no—
714C22×D3—121no—
715C22×D3—121no—
716C22×D3—121no—
717C22×D3C2×D3211yescharacteristic
718C22×D3C2×D3211yescharacteristic
719C3×Q8—361no—
720C3×Q8—361no—
721C2×C3×C4—21no—
722C2×C3×C4—21no—
723C2×C3×C4—21no—
724C2×C3×C4—31no—
725C2×C3×C4—31no—
726C2×C3×C4—31no—
727C2×C3×C4—31no—
728C2×C3×C4—31no—
729C2×C3×C4—31no—
730C2×C3×C4—31no—
731C2×C3×C4—31no—
732C2×C3×C4—41no—
733C2×C3×C4—61no—
734C2×C3×C4—61no—
735C2×C3×C4—61no—
736C2×C3×C4—61no—
737C2×C3×C4—91no—
738C2×C3×C4—91no—
739C2×C3×C4—91no—
740C2×C3×C4—91no—
741C2×C3×C4—91no—
742C2×C3×C4—361no—
743C2×C3×C4—361no—
744C2×C3×C4—361no—
745C2×C3×C4—361no—
746C2×C3×C4C2×D3211yescharacteristic
747C2×C3×C4C2×D3211yescharacteristic
748C2×C3×C4C2×D3211yescharacteristic
749C2×Dic3—31no—
750C2×Dic3—31no—
751C2×Dic3—31no—
752C2×Dic3—31no—
753C2×Dic3—31no—
754C2×Dic3—31no—
755C2×Dic3—31no—
756C2×Dic3—31no—
757C2×Dic3—31no—
758C2×Dic3—31no—
759C2×Dic3—61no—
760C2×Dic3—61no—
761C2×Dic3—61no—
762C2×Dic3—61no—
763C2×Dic3—61no—
764C2×Dic3—91no—
765C2×Dic3—91no—
766C2×Dic3—91no—
767C2×Dic3—91no—
768C2×Dic3—91no—
769C2×Dic3—91no—
770C2×Dic3—121no—
771C2×Dic3—121no—
772C2×Dic3—181no—
773C2×Dic3—181no—
774C2×Dic3—181no—
775C2×Dic3—181no—
776C2×Dic3—181no—
777C2×Dic3—181no—
778C2×Dic3—361no—
779C2×Dic3—361no—
780C2×Dic3—361no—
781C2×Dic3—361no—
782C2×Dic3—361no—
783C2×Dic3—361no—
784C2×Dic3—362no—
785C2×Dic3—362no—
786C2×Dic3C2×D3211yescharacteristic
787C2×Dic3C2×D3211yescharacteristic
788C2×Dic3C2×D3211yescharacteristic
789C2×Dic3C2×D3211yescharacteristic
790C4×D3—121no—
791C4×D3—121no—
792C4×D3—121no—
793C4×D3—121no—
794C4×D3—122no—
795C4×D3—121no—
796C4×D3—121no—
797C4×D3—361no—
798C4×D3—361no—
799Dic6—121no—
800Dic6—121no—
801Dic6—121no—
802Dic6—121no—
803Dic6—122no—
804Dic6—361no—
805Dic6—361no—
806Dic6—361no—
807Dic6—361no—
808Dic6—361no—
809Dic6—361no—
810Dic6—362no—
811Dic6—362no—
812C2×C32—21no—
813C2×C32—21no—
814C2×C32—21no—
815C2×C32—21no—
816C2×C32—21no—
817C2×C32—21no—
818C2×C32—21no—
819C2×C32—21no—
820C2×C32—21no—
821C2×C32—41no—
822C2×C32—41no—
823C2×C32—41no—
824C2×C32—62no—
825C2×C32—62no—
826C2×C32C22×Dic611yescharacteristic
827C2×C32#100411yescharacteristic
828C2×C32#100411yescharacteristic
829C2×C32#100411yescharacteristic
830C2×C32#100411yescharacteristic
831C2×C32C2×D3×Q811yescharacteristic
832C2×C32C2×D3×Q811yescharacteristic
833C2×C32#100911yescharacteristic
834C2×C32#100911yescharacteristic
835C3⋊D3—22no—
836C3×D3—22no—
837C3×D3—22no—
838C3×D3—22no—
839C3×D3—22no—
840C3×D3—42no—
841C3×D3—42no—
842C3×D3—62no—
843C3×D3—62no—
844C3×D3—122no—
845C24—91no—
846C2×Q8—91no—
847C2×Q8—91no—
848C2×Q8—271no—
849C2×Q8—271no—
850C22×C4—91no—
851C22×C4—91no—
852C22×C4—91no—
853C22×C4—91no—
854C22×C4—271no—
855C22×C4—271no—
856C4⋊C4—31no—
857C4⋊C4—91no—
858C4⋊C4—91no—
859C4⋊C4—91no—
860C4⋊C4—91no—
861C4⋊C4—271no—
862C4⋊C4—271no—
863C4⋊C4—271no—
864C4⋊C4—271no—
865C4⋊C4—271no—
866C4⋊C4—271no—
867C4⋊C4—271no—
868C22⋊C4—31no—
869C22⋊C4—31no—
870C22⋊C4—91no—
871C22⋊C4—91no—
872C22⋊C4—91no—
873C22⋊C4—91no—
874C22⋊C4—271no—
875C22⋊C4—271no—
876C22⋊C4—271no—
877C22⋊C4—271no—
878C22⋊C4—271no—
879C22⋊C4—271no—
880C22×C3—21no—
881C22×C3—21no—
882C22×C3—21no—
883C22×C3—32no—
884C22×C3—32no—
885C22×C3—32no—
886C22×C3—32no—
887C22×C3—41no—
888C22×C3—62no—
889C22×C3—62no—
890C22×C3—61no—
891C22×C3—61no—
892C22×C3—61no—
893C22×C3—61no—
894C22×C3—61no—
895C22×C3—61no—
896C22×C3—61no—
897C22×C3—61no—
898C22×C3—92no—
899C22×C3—121no—
900C22×C3—121no—
901C22×C3—121no—
902C22×C3—121no—
903C22×C3—181no—
904C22×C3—181no—
905C22×C3—364no—
906C22×C3C22×D3211yescharacteristic
907C22×C3C22×D3211yescharacteristic
908C22×C3C22×D3211yescharacteristic
909C2×D3—21no—
910C2×D3—21no—
911C2×D3—21no—
912C2×D3—21no—
913C2×D3—32no—
914C2×D3—32no—
915C2×D3—62no—
916C2×D3—61no—
917C2×D3—61no—
918C2×D3—61no—
919C2×D3—61no—
920C2×D3—121no—
921C2×D3—121no—
922C2×D3—124no—
923C2×D3—124no—
924C2×D3D3×Dic612yes—
925C2×D3D3×Dic612yes—
926C3×C4—21no—
927C3×C4—21no—
928C3×C4—21no—
929C3×C4—41no—
930C3×C4—41no—
931C3×C4—41no—
932C3×C4—61no—
933C3×C4—61no—
934C3×C4—61no—
935C3×C4—61no—
936C3×C4—61no—
937C3×C4—61no—
938C3×C4—61no—
939C3×C4—61no—
940C3×C4—81no—
941C3×C4—121no—
942C3×C4—121no—
943C3×C4—121no—
944C3×C4—121no—
945C3×C4—181no—
946C3×C4—181no—
947C3×C4—181no—
948C3×C4—181no—
949C3×C4—181no—
950Dic3—21no—
951Dic3—21no—
952Dic3—21no—
953Dic3—21no—
954Dic3—62no—
955Dic3—62no—
956Dic3—61no—
957Dic3—61no—
958Dic3—61no—
959Dic3—61no—
960Dic3—61no—
961Dic3—61no—
962Dic3—61no—
963Dic3—61no—
964Dic3—61no—
965Dic3—61no—
966Dic3—121no—
967Dic3—121no—
968Dic3—121no—
969Dic3—182no—
970Dic3—181no—
971Dic3—181no—
972Dic3—181no—
973Dic3—181no—
974Dic3—181no—
975Dic3—181no—
976Dic3—361no—
977Dic3—361no—
978Dic3—361no—
979Dic3—361no—
980Dic3—361no—
981Dic3—362no—
982Dic3—721no—
983C32—21no—
984C32—21no—
985C32—21no—
986C32—41no—
987C32#548311yescharacteristic, complemented
988C32#563411yescharacteristic, complemented
989C32#563411yescharacteristic, complemented
990C23—31no—
991C23—31no—
992C23—94no—
993C23—91no—
994C23—361no—
995C23—361no—
996Q8—361no—
997Q8—361no—
998Q8—1081no—
999Q8—1081no—
1000C2×C4—31no—
1001C2×C4—31no—
1002C2×C4—31no—
1003C2×C4—31no—
1004C2×C4—91no—
1005C2×C4—91no—
1006C2×C4—91no—
1007C2×C4—91no—
1008C2×C4—91no—
1009C2×C4—271no—
1010C2×C4—271no—
1011C2×C4—361no—
1012C2×C4—361no—
1013C2×C4—361no—
1014C2×C4—361no—
1015C2×C4—1081no—
1016C2×C4—1081no—
1017C2×C4D3311yescharacteristic
1018C2×C3—21no—
1019C2×C3—21no—
1020C2×C3—21no—
1021C2×C3—21no—
1022C2×C3—21no—
1023C2×C3—21no—
1024C2×C3—21no—
1025C2×C3—21no—
1026C2×C3—21no—
1027C2×C3—41no—
1028C2×C3—41no—
1029C2×C3—41no—
1030C2×C3—62no—
1031C2×C3—62no—
1032C2×C3—62no—
1033C2×C3—62no—
1034C2×C3—122no—
1035C2×C3—122no—
1036C2×C3—182no—
1037C2×C3C2×D3×Dic611yescharacteristic
1038C2×C3C2×D3×Dic611yescharacteristic
1039C2×C3#6430711yescharacteristic
1040C2×C3#6431311yescharacteristic
1041C2×C3#6431311yescharacteristic
1042C2×C3#6431411yescharacteristic
1043C2×C3#6431411yescharacteristic
1044C2×C3#6431411yescharacteristic
1045C2×C3D32×Q811yescharacteristic
1046D3—22no—
1047D3—22no—
1048D3—62no—
1049D3—62no—
1050D3—122no—
1051C22—32no—
1052C22—32no—
1053C22—61no—
1054C22—61no—
1055C22—61no—
1056C22—61no—
1057C22—92no—
1058C22—181no—
1059C22—181no—
1060C22—364no—
1061C22C2×D3311yescharacteristic
1062C4—21no—
1063C4—61no—
1064C4—61no—
1065C4—61no—
1066C4—61no—
1067C4—181no—
1068C4—181no—
1069C4—181no—
1070C4—181no—
1071C4—181no—
1072C4—541no—
1073C4—541no—
1074C3—21no—
1075C3—21no—
1076C3—21no—
1077C3—41no—
1078C3#1059417011yescharacteristic, complemented
1079C3#1059417011yescharacteristic, complemented
1080C3#1059463511yescharacteristic, complemented
1081C2—62no—
1082C2—62no—
1083C2—182no—
1084C2D32×Dic611yescharacteristic
1085C2#1172438111yescharacteristic
1086C2#1172441611yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC22×C3×D32C22
hypercenterC2×C4D33
hypocenterC33#543
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. #11723674C2semidirect
2. #11723500C2semidirect
3. #11723487C2semidirect
4. #11723418C2semidirect
6. C3×#63896C2semidirect
7. C3×#63893C2semidirect
8. #11722980C2semidirect
9. #11722976C2semidirect
10. #11722975C2semidirect
11. #11722972C2semidirect
12. #11722971C2semidirect
13. #11722970C2semidirect
21. C2×C3×#634C22semidirect
22. C2×#6293C22semidirect
23. C2×#6293C22semidirect
26. C2×C3×#627C22semidirect
30. #88857C22semidirect
31. C3×C4⋊(C3⋊Dic3)C22semidirect
34. C32×Dic3⋊C4C22semidirect
35. #88815C22semidirect
36. #88815C22semidirect
39. #88807C22semidirect
40. #88807C22semidirect
41. #88806C22semidirect
42. Dic3⋊(C3⋊Dic3)C22semidirect
47. C3×#3724C22semidirect
48. C3×Dic3⋊Dic3C22semidirect
49. C3×Dic3⋊Dic3C22semidirect
80. #63896D3semidirect
83. #63893D3semidirect
107. C2×C3×D32Q8semidirect
141. C2×#634C2×D3semidirect
162. C2×#627C2×D3semidirect
180. C4⋊(C3⋊Dic3)C2×D3semidirect
215. C3×Dic3⋊C4C2×D3semidirect
216. C3×Dic3⋊C4C2×D3semidirect
222. #3724C2×D3semidirect
236. Dic3⋊Dic3C2×D3semidirect
237. Dic3⋊Dic3C2×D3semidirect
351. C2×D32Dic6semidirect
578. Dic3⋊C4D32semidirect
697. C33#543semidirect
987. C32#5483semidirect
988. C32#5634semidirect
989. C32#5634semidirect
1078. C3#10594170semidirect
1079. C3#10594170semidirect
1080. C3#10594635semidirect

Maximal subgroups

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

subgroupindex
#117236742
#117235002
#117234872
#117234182
C3×#639212
C3×#638962
C3×#638932
#117229802
#117229762
#117229752
#117229722
#117229712
#117229702
D3×(C2×D3)⋊Dic32
#105946353
#105941703