Finite Group Databasebeta

← #13171901

Subgroups — #13171901

Order 1728.

1288 conjugacy classes of subgroups.

The subgroup lattice has 1150 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723726C211yesmaximal, characteristic, complemented
2#11723635C211yesmaximal, characteristic, complemented
3#11723632C211yesmaximal, characteristic, complemented
4#11723618C211yesmaximal, characteristic, complemented
5C3×#63978C211yesmaximal, characteristic, complemented
6C3×Dic3×#67C211yesmaximal, characteristic, complemented
7C2×C3×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
8#11723028C211yesmaximal, characteristic, complemented
9#11723025C211yesmaximal, characteristic, complemented
10#11723012C211yesmaximal, characteristic, complemented
11#11722996C211yesmaximal, characteristic, complemented
12#11722994C211yesmaximal, characteristic, complemented
13#11722959C211yesmaximal, characteristic, complemented
14#11722937C211yesmaximal, characteristic, complemented
15#11722914C211yesmaximal, characteristic, complemented
16#10595196—31nomaximal
17#10594953—31nomaximal
18#10594843—31nomaximal
19C2×#6312C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C22×C3×C3⋊Dic3C2211yescharacteristic
22C2×C32×#67C2211yescharacteristic
23C22×C32×Dic3C2211yescharacteristic
24C22×C32×Dic3C2211yescharacteristic
25C2×#6294C2211yescharacteristic
26C2×#6292C2211yescharacteristic
27C2×#6291C2211yescharacteristic
28C2×#6289C2211yescharacteristic
29C2×C3×#626C2211yescharacteristic
30C2×C3×D3×Dic3C2211yescharacteristic
31C3×#3757C2211yescharacteristic
32#88815C2211yescharacteristic
33#88814C2211yescharacteristic
34#88813C2211yescharacteristic
35#88807C2211yescharacteristic
36#88806C2211yescharacteristic
37Dic3⋊(C3⋊Dic3)C2211yescharacteristic
38#88804C2211yescharacteristic
39#88804C2211yescharacteristic
40#88804C2211yescharacteristic
41#88803C2211yescharacteristic
42(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
43Dic3×C3⋊Dic3C2211yescharacteristic
44C3×Dic3⋊Dic3C2211yescharacteristic
45C3×Dic3⋊Dic3C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×Dic3⋊Dic3C2211yescharacteristic
50C3×#3722C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64148—31no—
55#64139—31no—
56C4×#638—31no—
57C3×#939—31no—
58C3×D4×Dic3—31no—
59C3×#930—31no—
60C3×C4×#67—31no—
61C2×C3×C4⋊Dic3—31no—
62C2×C3×Dic3⋊C4—31no—
63#63978—31no—
64#63978—31no—
65#63978—31no—
66#63978—31no—
67#63978—31no—
68#63978—61no—
69#63978—61no—
70#63978D311yescharacteristic, complemented
71#63975—31no—
72#67⋊Dic3—31no—
73Dic3×#67—31no—
74Dic3×#67D311yescharacteristic, complemented
75#63969—31no—
76C2×Dic3⋊Dic3D311yescharacteristic, complemented
77#63955—31no—
78#63952—31no—
79#63952—31no—
80#63952—31no—
81#63952—61no—
82#63909—31no—
83#63894—31no—
84#63886—31no—
85#63884—31no—
86#63881—31no—
87#63880—31no—
88#63878—31no—
89#63869—31no—
90#63867—31no—
91#63862—31no—
92#63858—31no—
93#63854—31no—
94#63854—31no—
95#63853—31no—
96#63848—31no—
97#63848—31no—
98#63848—31no—
99#63848—31no—
100#63846—31no—
101#63841—31no—
102C23×C33C2311yescharacteristic
103C22×C3⋊(C3⋊D3)C2311yescharacteristic
104C22×C3×C3⋊D3C2311yescharacteristic
105C22×C32×D3C2311yescharacteristic
106#6312—22no—
107C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
108C3×#638—22no—
109C2×C3×C3⋊Dic3—41no—
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C32×#67—22no—
116C2×C32×Dic3—22no—
117C2×C32×Dic3—41no—
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123#6294—41no—
124#6292—22no—
125#6291—41no—
126#6289—41no—
127C3×#626—41no—
128C3×D3×Dic3—22no—
129#5601—91no—
130#5565—91no—
131#5514—91no—
132C2×C32×D4—31no—
133C22×C32×C4—31no—
134C22×C32×C4—31no—
135C2×#638—31no—
136C2×#638—31no—
137C2×#638—31no—
138C2×#638—31no—
139C2×#638—61no—
140C2×#638—61no—
141C2×#638—61no—
142C2×#638—121no—
143C2×#638C2×D311yescharacteristic
144C22×C3⋊Dic3C2×D311yescharacteristic
145C2×C4⋊(C3⋊D3)—31no—
146C2×C4×C3⋊D3—31no—
147C2×C3×#67—21no—
148C2×C3×#67—31no—
149C2×C3×#67—31no—
150C2×C3×#67—31no—
151C2×C3×#67—61no—
152C2×C3×#67C2×D311yescharacteristic
153C2×C3×#67C2×D311yescharacteristic
154C22×C3×Dic3—21no—
155C22×C3×Dic3—21no—
156C22×C3×Dic3—31no—
157C22×C3×Dic3—31no—
158C22×C3×Dic3—31no—
159C22×C3×Dic3—61no—
160C22×C3×Dic3C2×D311yescharacteristic
161C22×C3×Dic3C2×D311yescharacteristic
162C22×C3×Dic3C2×D311yescharacteristic
163C22×C3×Dic3C2×D311yescharacteristic
164C2×C3×D12—31no—
165C2×C3×C4×D3—31no—
166C2×#626—31no—
167C2×#626—31no—
168C2×#626—31no—
169C2×#626—31no—
170C2×#626—61no—
171C2×#626—61no—
172C2×#626C2×D311yescharacteristic
173C2×#624—31no—
174C2×#624—31no—
175C2×#624—31no—
176C2×#624—61no—
177C2×D3×Dic3—31no—
178C2×D3×Dic3—31no—
179C2×D3×Dic3C2×D311yescharacteristic
180#3757—31no—
181#3757C2×D311yescharacteristic
182#3752—31no—
183#3752—31no—
184#3752—31no—
185#3752—31no—
186C4⋊(C3⋊Dic3)—31no—
187#3750—31no—
188#3750—31no—
189C4×C3⋊Dic3—31no—
190C3×#217—31no—
191C3×#217—31no—
192C3×#217—31no—
193C3×#217—31no—
194C3×#217—61no—
195C3×(C2×D3)⋊C4—31no—
196C3×(C2×D3)⋊C4—31no—
197C3×(C2×D3)⋊C4—31no—
198C3×(C2×D3)⋊C4—31no—
199C3×C4⋊Dic3—31no—
200C3×C4⋊Dic3—31no—
201C3×C4⋊Dic3—31no—
202C3×C4⋊Dic3—31no—
203C3×C4⋊Dic3—31no—
204C3×C4⋊Dic3—31no—
205C3×Dic3⋊C4—31no—
206C3×Dic3⋊C4—31no—
207C3×Dic3⋊C4—31no—
208C3×Dic3⋊C4—31no—
209C3×Dic3⋊C4—31no—
210C3×Dic3⋊C4—31no—
211C3×C4×Dic3—31no—
212C3×C4×Dic3—31no—
213#3724—31no—
214#3724—31no—
215#3724—31no—
216#3724—61no—
217Dic3⋊Dic3—31no—
218Dic3⋊Dic3—31no—
219Dic3⋊Dic3—31no—
220Dic3⋊Dic3—31no—
221Dic3⋊Dic3—31no—
222Dic3⋊Dic3—31no—
223Dic3⋊Dic3—61no—
224Dic3⋊Dic3—61no—
225Dic3⋊Dic3C2×D311yescharacteristic
226Dic3⋊Dic3C2×D311yescharacteristic
227Dic3⋊Dic3C2×D311yescharacteristic
228Dic3⋊Dic3C2×D311yescharacteristic
229Dic3⋊Dic3C2×D311yescharacteristic
230Dic3⋊Dic3C2×D311yescharacteristic
231#3722—31no—
232#3722—31no—
233#3722—31no—
234#3722—31no—
235#3722—31no—
236#3722—31no—
237#3722—31no—
238#3722—61no—
239#3722—61no—
240#3722—61no—
241#3722C2×D311yescharacteristic
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—61no—
249(C2×D3)⋊Dic3—61no—
250(C2×D3)⋊Dic3C2×D311yescharacteristic
251(C2×D3)⋊Dic3C2×D311yescharacteristic
252Dic32—31no—
253Dic32—31no—
254Dic32—31no—
255Dic32—31no—
256Dic32—31no—
257Dic32—61no—
258Dic32C2×D311yescharacteristic
259C22×C33—21no—
260C22×C33—21no—
261C22×C33#4112yes—
262C22×C33C2411yescharacteristic
263C2×C3⋊(C3⋊D3)—21no—
264C2×C3⋊(C3⋊D3)—21no—
265C2×C3⋊(C3⋊D3)—21no—
266C2×C3×C3⋊D3—21no—
267C2×C3×C3⋊D3—21no—
268C2×C3×C3⋊D3—21no—
269C2×C32×D3—21no—
270C2×C32×D3—21no—
271C2×C32×D3—21no—
272C3⋊(C3⋊Dic3)—21no—
273C3×C3⋊Dic3—21no—
274C3×C3⋊Dic3—21no—
275C3×C3⋊Dic3—21no—
276C3×C3⋊Dic3—21no—
277C3×C3⋊Dic3—21no—
278C32×Dic3—21no—
279C32×Dic3—21no—
280C32×Dic3—21no—
281C32×Dic3—21no—
282C32×Dic3#4112yes—
283C3×#121—91no—
284C3×C4×D4—91no—
285C2×C3×C4⋊C4—91no—
286#939—31no—
287#939—91no—
288#939—91no—
289#939—91no—
290#939—91no—
291#939—181no—
292#935—91no—
293D4×Dic3—31no—
294D4×Dic3—91no—
295#930—31no—
296#930—91no—
297#930—91no—
298#930—91no—
299#930—91no—
300#930—181no—
301C4×#67—31no—
302C4×#67—91no—
303C4×#67—91no—
304C4×#67—91no—
305C4×#67—181no—
306#926—91no—
307C2×C4⋊Dic3—31no—
308C2×Dic3⋊C4—31no—
309#898—91no—
310#898—91no—
311#898—91no—
312#898—91no—
313#898—91no—
314#895—91no—
315#894—91no—
316#894—91no—
317#893—91no—
318#892—91no—
319#890—91no—
320#889—91no—
321#883—91no—
322#883—91no—
323#883—91no—
324#67⋊C4—91no—
325#67⋊C4—91no—
326#67⋊C4—91no—
327#879—91no—
328#877—91no—
329C4×D12—91no—
330#870—91no—
331C23×C32—21no—
332C23×C32—21no—
333C23×C32—21no—
334C23×C32—31no—
335C23×C32—41no—
336C23×C32C22×D311yescharacteristic
337C23×C32C22×D311yescharacteristic
338C23×C32C22×D311yescharacteristic
339C22×C3⋊D3—31no—
340C22×C3⋊D3—31no—
341C22×C3⋊D3—31no—
342C22×C3⋊D3—61no—
343C22×C3⋊D3—61no—
344C22×C3⋊D3—61no—
345C22×C3⋊D3—121no—
346C22×C3⋊D3C22×D311yescharacteristic
347C22×C3×D3—21no—
348C22×C3×D3—31no—
349C22×C3×D3—31no—
350C22×C3×D3—61no—
351C22×C3×D3C22×D311yescharacteristic
352C22×C3×D3C22×D311yescharacteristic
353C32×D4—62no—
354C2×C32×C4—31no—
355C2×C32×C4—31no—
356C2×C32×C4—31no—
357C2×C32×C4—31no—
358C2×C32×C4—31no—
359C2×C32×C4—62no—
360C2×C32×C4—121no—
361#638—22no—
362#638—62no—
363#638—64no—
364#638—62no—
365#638—62no—
366#638—122no—
367#638—122no—
368#638—124no—
369#638—121no—
370C2×C3⋊Dic3—31no—
371C2×C3⋊Dic3—31no—
372C2×C3⋊Dic3—31no—
373C2×C3⋊Dic3—41no—
374C2×C3⋊Dic3—61no—
375C2×C3⋊Dic3—61no—
376C2×C3⋊Dic3—61no—
377C2×C3⋊Dic3—121no—
378C2×C3⋊Dic3C22×D311yescharacteristic
379C2×C3⋊Dic3C22×D311yescharacteristic
380C2×C3⋊Dic3C22×D311yescharacteristic
381C2×C3⋊Dic3C22×D311yescharacteristic
382C2×C3⋊Dic3C22×D311yescharacteristic
383C4⋊(C3⋊D3)—62no—
384C4×C3⋊D3—121no—
385C3×#67—22no—
386C3×#67—22no—
387C3×#67—42no—
388C3×#67—62no—
389C3×#67—62no—
390C3×#67—122no—
391C3×#67—121no—
392C2×C3×Dic3—22no—
393C2×C3×Dic3—22no—
394C2×C3×Dic3—21no—
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—42no—
410C2×C3×Dic3—41no—
411C2×C3×Dic3—41no—
412C2×C3×Dic3—42no—
413C2×C3×Dic3—61no—
414C2×C3×Dic3—61no—
415C2×C3×Dic3—61no—
416C2×C3×Dic3—61no—
417C2×C3×Dic3—61no—
418C2×C3×Dic3—62no—
419C2×C3×Dic3—121no—
420C2×C3×Dic3—121no—
421C2×C3×Dic3—122no—
422C2×C3×Dic3C22×D311yescharacteristic
423C2×C3×Dic3C22×D311yescharacteristic
424C2×C3×Dic3C22×D311yescharacteristic
425C2×C3×Dic3C22×D311yescharacteristic
426C2×C3×Dic3C22×D311yescharacteristic
427C2×C3×Dic3C22×D311yescharacteristic
428C2×C3×Dic3C22×D311yescharacteristic
429C2×C3×Dic3C22×D311yescharacteristic
430C2×C3×Dic3C22×D311yescharacteristic
431C2×C3×Dic3C22×D311yescharacteristic
432C3×D12—121no—
433C3×C4×D3—62no—
434#626—41no—
435#626—62no—
436#626—62no—
437#626—122no—
438#626—121no—
439#626—121no—
440#626—122no—
441#624—121no—
442#624—121no—
443#624—122no—
444#624—121no—
445D3×Dic3—22no—
446D3×Dic3—121no—
447D3×Dic3—121no—
448#553—271noSylow
449C2×C33—22no—
450C2×C33C2×#4111yescharacteristic
451C2×C33C2×#4111yescharacteristic
452C2×C33H(5,𝔽2)11yescharacteristic
453C3⋊(C3⋊D3)—41no—
454C3×C3⋊D3—41no—
455C32×D3—41no—
456C2×C3×D4—31no—
457C2×C3×D4—31no—
458C2×C3×D4—61no—
459C2×C3×D4—91no—
460C2×C3×D4—91no—
461C22×C3×C4—31no—
462C22×C3×C4—31no—
463C22×C3×C4—31no—
464C22×C3×C4—31no—
465C22×C3×C4—61no—
466C22×C3×C4—61no—
467C22×C3×C4—91no—
468C22×C3×C4—91no—
469C2×#67—31no—
470C2×#67—31no—
471C2×#67—31no—
472C2×#67—61no—
473C2×#67—91no—
474C2×#67—91no—
475C2×#67—91no—
476C2×#67—91no—
477C2×#67—91no—
478C2×#67—91no—
479C2×#67—181no—
480C2×#67—181no—
481C2×#67—181no—
482C2×#67—181no—
483C2×#67—361no—
484C2×#67D3211yescharacteristic
485C22×Dic3—31no—
486C22×Dic3—31no—
487C22×Dic3—31no—
488C22×Dic3—61no—
489C22×Dic3—91no—
490C22×Dic3D3211yescharacteristic
491C22×Dic3D3211yescharacteristic
492C2×D12—31no—
493C2×D12—91no—
494C2×D12—91no—
495C2×D12—91no—
496C2×D12—181no—
497C2×C4×D3—31no—
498C2×C4×D3—91no—
499C2×C4×D3—91no—
500C2×C4×D3—91no—
501C2×C4×D3—91no—
502C2×C4×D3—91no—
503C2×C4×D3—181no—
504C3×C4⋊C4—91no—
505C3×C4⋊C4—91no—
506C3×C4⋊C4—91no—
507C3×C4⋊C4—91no—
508C3×C4⋊C4—91no—
509C3×C4⋊C4—91no—
510C3×C22⋊C4—91no—
511C3×C22⋊C4—91no—
512C3×C22⋊C4—91no—
513C3×C22⋊C4—91no—
514C3×C42—91no—
515#217—31no—
516#217—31no—
517#217—31no—
518#217—31no—
519#217—61no—
520#217—91no—
521#217—91no—
522#217—91no—
523#217—91no—
524#217—181no—
525(C2×D3)⋊C4—31no—
526(C2×D3)⋊C4—31no—
527(C2×D3)⋊C4—31no—
528(C2×D3)⋊C4—31no—
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—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—
544(C2×D3)⋊C4—181no—
545(C2×D3)⋊C4—181no—
546(C2×D3)⋊C4—181no—
547C4⋊Dic3—31no—
548C4⋊Dic3—31no—
549C4⋊Dic3—31no—
550C4⋊Dic3—31no—
551C4⋊Dic3—31no—
552C4⋊Dic3—31no—
553C4⋊Dic3—91no—
554C4⋊Dic3—91no—
555C4⋊Dic3—91no—
556C4⋊Dic3—91no—
557C4⋊Dic3—181no—
558Dic3⋊C4—31no—
559Dic3⋊C4—31no—
560Dic3⋊C4—31no—
561Dic3⋊C4—31no—
562Dic3⋊C4—31no—
563Dic3⋊C4—31no—
564Dic3⋊C4—91no—
565Dic3⋊C4—91no—
566Dic3⋊C4—91no—
567Dic3⋊C4—91no—
568Dic3⋊C4—91no—
569Dic3⋊C4—91no—
570Dic3⋊C4—91no—
571Dic3⋊C4—91no—
572Dic3⋊C4—181no—
573Dic3⋊C4—181no—
574C4×Dic3—31no—
575C4×Dic3—31no—
576C4×Dic3—91no—
577C4×Dic3—91no—
578C4×Dic3—91no—
579C4×Dic3—91no—
580C4×Dic3—91no—
581C4×Dic3—91no—
582C4×Dic3—181no—
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—22no—
593C22×C32—22no—
594C22×C32—22no—
595C22×C32—41no—
596C22×C32—42no—
597C22×C32—41no—
598C22×C32—41no—
599C22×C32—41no—
600C22×C32—41no—
601C22×C32—41no—
602C22×C32—41no—
603C22×C32—61no—
604C22×C32—61no—
605C22×C32—61no—
606C22×C32—81no—
607C22×C32—81no—
608C22×C32#23512yes—
609C22×C32#23712yes—
610C22×C32#23912yes—
611C22×C32C23×D311yescharacteristic
612C22×C32C23×D311yescharacteristic
613C22×C32C23×D311yescharacteristic
614C2×C3⋊D3—21no—
615C2×C3⋊D3—21no—
616C2×C3⋊D3—21no—
617C2×C3⋊D3—61no—
618C2×C3⋊D3—62no—
619C2×C3⋊D3—61no—
620C2×C3⋊D3—61no—
621C2×C3⋊D3—61no—
622C2×C3⋊D3—61no—
623C2×C3⋊D3—61no—
624C2×C3⋊D3—61no—
625C2×C3⋊D3—61no—
626C2×C3⋊D3—61no—
627C2×C3⋊D3—121no—
628C2×C3⋊D3—121no—
629C2×C3⋊D3—122no—
630C2×C3⋊D3—121no—
631C2×C3⋊D3—121no—
632C2×C3⋊D3—121no—
633C2×C3⋊D3—121no—
634C2×C3⋊D3—121no—
635C2×C3⋊D3—121no—
636C2×C3⋊D3—241no—
637C2×C3⋊D3—241no—
638C2×C3×D3—21no—
639C2×C3×D3—21no—
640C2×C3×D3—21no—
641C2×C3×D3—21no—
642C2×C3×D3—21no—
643C2×C3×D3—21no—
644C2×C3×D3—41no—
645C2×C3×D3—41no—
646C2×C3×D3—41no—
647C2×C3×D3—61no—
648C2×C3×D3—61no—
649C2×C3×D3—61no—
650C2×C3×D3—61no—
651C2×C3×D3—61no—
652C2×C3×D3—61no—
653C2×C3×D3—121no—
654C2×C3×D3—121no—
655C2×C3×D3—121no—
656C32×C4—32no—
657C32×C4—61no—
658C32×C4—61no—
659C32×C4—61no—
660C32×C4—61no—
661C3⋊Dic3—21no—
662C3⋊Dic3—21no—
663C3⋊Dic3—21no—
664C3⋊Dic3—21no—
665C3⋊Dic3—21no—
666C3⋊Dic3—61no—
667C3⋊Dic3—62no—
668C3⋊Dic3—61no—
669C3⋊Dic3—61no—
670C3⋊Dic3—121no—
671C3⋊Dic3—121no—
672C3⋊Dic3—122no—
673C3×Dic3—22no—
674C3×Dic3—21no—
675C3×Dic3—21no—
676C3×Dic3—21no—
677C3×Dic3—21no—
678C3×Dic3—21no—
679C3×Dic3—21no—
680C3×Dic3—21no—
681C3×Dic3—21no—
682C3×Dic3—22no—
683C3×Dic3—41no—
684C3×Dic3—41no—
685C3×Dic3—41no—
686C3×Dic3—62no—
687C3×Dic3—61no—
688C3×Dic3—61no—
689C3×Dic3—61no—
690C3×Dic3—61no—
691C3×Dic3—61no—
692C3×Dic3—61no—
693C3×Dic3—61no—
694C3×Dic3—61no—
695C3×Dic3—61no—
696C3×Dic3—61no—
697C3×Dic3—121no—
698C3×Dic3—121no—
699C3×Dic3—121no—
700C3×Dic3—121no—
701C3×Dic3#23512yes—
702C3×Dic3#23712yes—
703#126—271no—
704#126—271no—
705#125—271no—
706#123—271no—
707#123—271no—
708#121—91no—
709#121—271no—
710#121—271no—
711#121—271no—
712C4×D4—91no—
713C4×D4—271no—
714C4×D4—271no—
715C4×D4—271no—
716#117—271no—
717C2×C4⋊C4—91no—
718C33#55311yescharacteristic, complemented, Sylow
719C23×C3—21no—
720C23×C3—21no—
721C23×C3—21no—
722C23×C3—31no—
723C23×C3—31no—
724C23×C3—41no—
725C23×C3—61no—
726C23×C3—91no—
727C23×C3C2×D3211yescharacteristic
728C23×C3C2×D3211yescharacteristic
729C23×C3C2×D3211yescharacteristic
730C22×D3—31no—
731C22×D3—31no—
732C22×D3—61no—
733C22×D3—91no—
734C22×D3—91no—
735C22×D3—91no—
736C22×D3—181no—
737C22×D3—181no—
738C22×D3—181no—
739C22×D3—361no—
740C22×D3C2×D3211yescharacteristic
741C3×D4—62no—
742C3×D4—62no—
743C3×D4—122no—
744C3×D4—182no—
745C3×D4—361no—
746C2×C3×C4—31no—
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—31no—
756C2×C3×C4—61no—
757C2×C3×C4—61no—
758C2×C3×C4—61no—
759C2×C3×C4—61no—
760C2×C3×C4—61no—
761C2×C3×C4—62no—
762C2×C3×C4—62no—
763C2×C3×C4—91no—
764C2×C3×C4—91no—
765C2×C3×C4—91no—
766C2×C3×C4—91no—
767C2×C3×C4—91no—
768C2×C3×C4—122no—
769C2×C3×C4—121no—
770C2×C3×C4—121no—
771C2×C3×C4—122no—
772C2×C3×C4—182no—
773C2×C3×C4—361no—
774#67—22no—
775#67—62no—
776#67—62no—
777#67—122no—
778#67—121no—
779#67—184no—
780#67—182no—
781#67—182no—
782#67—182no—
783#67—182no—
784#67—362no—
785#67—362no—
786#67—364no—
787#67—361no—
788#67—361no—
789#67—362no—
790C2×Dic3—22no—
791C2×Dic3—31no—
792C2×Dic3—31no—
793C2×Dic3—31no—
794C2×Dic3—31no—
795C2×Dic3—31no—
796C2×Dic3—31no—
797C2×Dic3—31no—
798C2×Dic3—31no—
799C2×Dic3—31no—
800C2×Dic3—31no—
801C2×Dic3—41no—
802C2×Dic3—61no—
803C2×Dic3—61no—
804C2×Dic3—61no—
805C2×Dic3—61no—
806C2×Dic3—61no—
807C2×Dic3—62no—
808C2×Dic3—91no—
809C2×Dic3—91no—
810C2×Dic3—91no—
811C2×Dic3—121no—
812C2×Dic3—121no—
813C2×Dic3—122no—
814C2×Dic3—181no—
815C2×Dic3—181no—
816C2×Dic3—181no—
817C2×Dic3—361no—
818C2×Dic3—361no—
819C2×Dic3C2×D3211yescharacteristic
820C2×Dic3C2×D3211yescharacteristic
821C2×Dic3C2×D3211yescharacteristic
822C2×Dic3C2×D3211yescharacteristic
823C2×Dic3C2×D3211yescharacteristic
824D12—121no—
825D12—182no—
826D12—182no—
827D12—362no—
828D12—361no—
829C4×D3—62no—
830C4×D3—361no—
831C4×D3—361no—
832C4×D3—361no—
833C4×D3—361no—
834C4×D3—361no—
835C4×D3—362no—
836C2×C32—22no—
837C2×C32—22no—
838C2×C32—22no—
839C2×C32—21no—
840C2×C32—21no—
841C2×C32—21no—
842C2×C32—21no—
843C2×C32—21no—
844C2×C32—21no—
845C2×C32—21no—
846C2×C32—21no—
847C2×C32—21no—
848C2×C32—41no—
849C2×C32—41no—
850C2×C32—41no—
851C2×C32—42no—
852C2×C32—42no—
853C2×C32—42no—
854C2×C32—82no—
855C2×C32—121no—
856C2×C32C2×#23511yescharacteristic
857C2×C32C2×#23511yescharacteristic
858C2×C32C2×#23711yescharacteristic
859C2×C32C2×#23711yescharacteristic
860C2×C32#100411yescharacteristic
861C2×C32#100411yescharacteristic
862C2×C32C2×#23911yescharacteristic
863C2×C32D3×#4111yescharacteristic
864C2×C32#100911yescharacteristic
865C3⋊D3—41no—
866C3⋊D3—121no—
867C3⋊D3—122no—
868C3⋊D3—121no—
869C3⋊D3—121no—
870C3⋊D3—241no—
871C3⋊D3—241no—
872C3⋊D3—242no—
873C3×D3—41no—
874C3×D3—41no—
875C3×D3—81no—
876C3×D3—121no—
877C3×D3—121no—
878C3×D3—241no—
879C2×D4—31no—
880C2×D4—91no—
881C2×D4—91no—
882C2×D4—271no—
883C2×D4—271no—
884C2×D4—271no—
885C22×C4—31no—
886C22×C4—31no—
887C22×C4—91no—
888C22×C4—91no—
889C22×C4—271no—
890C22×C4—271no—
891C4⋊C4—91no—
892C4⋊C4—91no—
893C4⋊C4—91no—
894C4⋊C4—91no—
895C4⋊C4—91no—
896C4⋊C4—91no—
897C4⋊C4—271no—
898C4⋊C4—271no—
899C4⋊C4—271no—
900C4⋊C4—271no—
901C22⋊C4—91no—
902C22⋊C4—91no—
903C22⋊C4—91no—
904C22⋊C4—91no—
905C22⋊C4—271no—
906C22⋊C4—271no—
907C22⋊C4—271no—
908C22⋊C4—271no—
909C22⋊C4—271no—
910C22⋊C4—271no—
911C42—91no—
912C42—271no—
913C42—271no—
914C22×C3—21no—
915C22×C3—21no—
916C22×C3—21no—
917C22×C3—21no—
918C22×C3—21no—
919C22×C3—21no—
920C22×C3—21no—
921C22×C3—21no—
922C22×C3—21no—
923C22×C3—22no—
924C22×C3—22no—
925C22×C3—22no—
926C22×C3—41no—
927C22×C3—41no—
928C22×C3—41no—
929C22×C3—41no—
930C22×C3—41no—
931C22×C3—41no—
932C22×C3—41no—
933C22×C3—42no—
934C22×C3—61no—
935C22×C3—61no—
936C22×C3—61no—
937C22×C3—61no—
938C22×C3—61no—
939C22×C3—61no—
940C22×C3—81no—
941C22×C3—81no—
942C22×C3—121no—
943C22×C3—121no—
944C22×C3—121no—
945C22×C3—181no—
946C22×C3—181no—
947C22×C3—181no—
948C22×C3#379612yes—
949C22×C3#379912yes—
950C22×C3#380412yes—
951C22×C3C22×D3211yescharacteristic
952C22×C3C22×D3211yescharacteristic
953C22×C3C22×D3211yescharacteristic
954C2×D3—21no—
955C2×D3—21no—
956C2×D3—21no—
957C2×D3—61no—
958C2×D3—61no—
959C2×D3—61no—
960C2×D3—61no—
961C2×D3—61no—
962C2×D3—61no—
963C2×D3—121no—
964C2×D3—121no—
965C2×D3—121no—
966C2×D3—182no—
967C2×D3—181no—
968C2×D3—181no—
969C2×D3—181no—
970C2×D3—181no—
971C2×D3—181no—
972C2×D3—181no—
973C2×D3—181no—
974C2×D3—181no—
975C2×D3—181no—
976C2×D3—361no—
977C2×D3—361no—
978C2×D3—361no—
979C2×D3—361no—
980C2×D3—361no—
981C2×D3—361no—
982C2×D3—361no—
983C2×D3—361no—
984C2×D3—362no—
985C2×D3—721no—
986C2×D3—721no—
987C3×C4—32no—
988C3×C4—32no—
989C3×C4—62no—
990C3×C4—62no—
991C3×C4—61no—
992C3×C4—61no—
993C3×C4—61no—
994C3×C4—61no—
995C3×C4—61no—
996C3×C4—61no—
997C3×C4—61no—
998C3×C4—61no—
999C3×C4—121no—
1000C3×C4—121no—
1001C3×C4—121no—
1002C3×C4—181no—
1003C3×C4—181no—
1004C3×C4—181no—
1005C3×C4—181no—
1006C3×C4—181no—
1007Dic3—21no—
1008Dic3—21no—
1009Dic3—21no—
1010Dic3—21no—
1011Dic3—62no—
1012Dic3—61no—
1013Dic3—61no—
1014Dic3—61no—
1015Dic3—61no—
1016Dic3—61no—
1017Dic3—61no—
1018Dic3—61no—
1019Dic3—61no—
1020Dic3—61no—
1021Dic3—61no—
1022Dic3—121no—
1023Dic3—121no—
1024Dic3—121no—
1025Dic3—121no—
1026Dic3—182no—
1027Dic3—181no—
1028Dic3—181no—
1029Dic3—181no—
1030Dic3—361no—
1031Dic3—361no—
1032Dic3—362no—
1033Dic3#380412yes—
1034C32—21no—
1035C32—21no—
1036C32—21no—
1037C32—41no—
1038C32#551411yescharacteristic, complemented
1039C32#556511yescharacteristic, complemented
1040C32#560111yescharacteristic, complemented
1041C23—31no—
1042C23—91no—
1043C23—271no—
1044C23D3311yescharacteristic
1045D4—62no—
1046D4—182no—
1047D4—361no—
1048D4—542no—
1049D4—542no—
1050D4—1081no—
1051C2×C4—31no—
1052C2×C4—31no—
1053C2×C4—31no—
1054C2×C4—31no—
1055C2×C4—31no—
1056C2×C4—62no—
1057C2×C4—91no—
1058C2×C4—91no—
1059C2×C4—91no—
1060C2×C4—91no—
1061C2×C4—91no—
1062C2×C4—121no—
1063C2×C4—182no—
1064C2×C4—271no—
1065C2×C4—361no—
1066C2×C4—1081no—
1067C2×C4—1081no—
1068C2×C3—22no—
1069C2×C3—22no—
1070C2×C3—22no—
1071C2×C3—21no—
1072C2×C3—21no—
1073C2×C3—21no—
1074C2×C3—21no—
1075C2×C3—21no—
1076C2×C3—21no—
1077C2×C3—21no—
1078C2×C3—21no—
1079C2×C3—21no—
1080C2×C3—42no—
1081C2×C3—42no—
1082C2×C3—42no—
1083C2×C3—41no—
1084C2×C3—41no—
1085C2×C3—41no—
1086C2×C3—82no—
1087C2×C3—121no—
1088C2×C3—121no—
1089C2×C3—241no—
1090C2×C3—361no—
1091C2×C3C2×#379611yescharacteristic
1092C2×C3C2×#379911yescharacteristic
1093C2×C3D3×#23511yescharacteristic
1094C2×C3#6430711yescharacteristic
1095C2×C3D3×#23711yescharacteristic
1096C2×C3#6431411yescharacteristic
1097C2×C3C2×#380411yescharacteristic
1098C2×C3C2×#380411yescharacteristic
1099C2×C3#6433011yescharacteristic
1100D3—41no—
1101D3—121no—
1102D3—121no—
1103D3—241no—
1104D3—362no—
1105D3—361no—
1106D3—361no—
1107D3—361no—
1108D3—721no—
1109D3—721no—
1110D3—722no—
1111C22—21no—
1112C22—21no—
1113C22—61no—
1114C22—61no—
1115C22—61no—
1116C22—181no—
1117C22—181no—
1118C22—181no—
1119C22—541no—
1120C22—541no—
1121C22—541no—
1122C22#8896212yes—
1123C22C2×D3311yescharacteristic
1124C4—32no—
1125C4—61no—
1126C4—61no—
1127C4—61no—
1128C4—61no—
1129C4—181no—
1130C4—181no—
1131C4—181no—
1132C4—181no—
1133C4—181no—
1134C4—541no—
1135C3—21no—
1136C3—21no—
1137C3—21no—
1138C3—41no—
1139C3#1059484311yescharacteristic, complemented
1140C3#1059495311yescharacteristic, complemented
1141C3#1059519611yescharacteristic, complemented
1142C2—22no—
1143C2—121no—
1144C2—361no—
1145C2—1081no—
1146C2D3×#380411yescharacteristic
1147C2#1172441811yescharacteristic
1148C2C2×#8896211yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
hypercenterC23D33
hypocenterC33#553
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. #11723726C2semidirect
2. #11723635C2semidirect
3. #11723632C2semidirect
4. #11723618C2semidirect
5. C3×#63978C2semidirect
6. C3×Dic3×#67C2semidirect
7. C2×C3×Dic3⋊Dic3C2semidirect
8. #11723028C2semidirect
9. #11723025C2semidirect
10. #11723012C2semidirect
11. #11722996C2semidirect
12. #11722994C2semidirect
13. #11722959C2semidirect
14. #11722937C2semidirect
15. #11722914C2semidirect
70. #63978D3semidirect
74. Dic3×#67D3semidirect
76. C2×Dic3⋊Dic3D3semidirect
718. C33#553semidirect
1038. C32#5514semidirect
1039. C32#5565semidirect
1040. C32#5601semidirect
1139. C3#10594843semidirect
1140. C3#10594953semidirect
1141. C3#10595196semidirect

Maximal subgroups

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

subgroupindex
#117237262
#117236352
#117236322
#117236182
C3×#639782
C3×Dic3×#672
C2×C3×Dic3⋊Dic32
#117230282
#117230252
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