Finite Group Databasebeta

← #13168398

Subgroups — #13168398

Order 1728.

1218 conjugacy classes of subgroups.

The subgroup lattice has 1120 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723690C211yesmaximal, characteristic, complemented
2#11723514C211yesmaximal, characteristic, complemented
3#11723504C211yesmaximal, characteristic, complemented
4#11723403C211yesmaximal, characteristic, complemented
5C3×#63904C211yesmaximal, characteristic, complemented
6C3×D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
7C3×#63848C211yesmaximal, characteristic, complemented
8#11723012C211yesmaximal, characteristic, complemented
9#11722961C211yesmaximal, characteristic, complemented
10#11722960C211yesmaximal, characteristic, complemented
11#11722959C211yesmaximal, characteristic, complemented
12#11722937C211yesmaximal, characteristic, complemented
13#11722936C211yesmaximal, characteristic, complemented
14#11722932C211yesmaximal, characteristic, complemented
15#11722915C211yesmaximal, characteristic, complemented
16#10594843—31nomaximal
17#10594545—31nomaximal
18#10594414—31nomaximal
19C2×C32×C4×D3C2211yescharacteristic
20C2×#6295C2211yescharacteristic
21C2×#6294C2211yescharacteristic
22C2×#6292C2211yescharacteristic
23C2×#6292C2211yescharacteristic
24C2×#6291C2211yescharacteristic
25C2×#6290C2211yescharacteristic
26C2×#6289C2211yescharacteristic
27C2×C3×#626C2211yescharacteristic
28C2×C3×#624C2211yescharacteristic
29C2×C3×D3×Dic3C2211yescharacteristic
30C2×C3×D3×Dic3C2211yescharacteristic
31#88859C2211yescharacteristic
32C3×#3752C2211yescharacteristic
33C3×#3752C2211yescharacteristic
34C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
35C32×C4⋊Dic3C2211yescharacteristic
36C32×Dic3⋊C4C2211yescharacteristic
37#88815C2211yescharacteristic
38#88814C2211yescharacteristic
39#88807C2211yescharacteristic
40#88806C2211yescharacteristic
41Dic3⋊(C3⋊Dic3)C2211yescharacteristic
42#88804C2211yescharacteristic
43#88804C2211yescharacteristic
44#88803C2211yescharacteristic
45Dic3×C3⋊Dic3C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×#3722C2211yescharacteristic
50C3×#3722C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×Dic32C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64139—31no—
55#64107—31no—
56#64103—31no—
57C3×C4×#67—31no—
58C2×C3×C4⋊Dic3—31no—
59C3×#898—31no—
60C3×#898—31no—
61C3×#893—31no—
62C3×D3×C4⋊C4—31no—
63#63978—31no—
64#63978—31no—
65#63952—31no—
66#63952—31no—
67#63910—31no—
68#63909—31no—
69#63909—31no—
70#63906—31no—
71#63906—31no—
72#63906—31no—
73#63906—31no—
74#63906—61no—
75#63904D311yescharacteristic, complemented
76C4×#626—31no—
77#63902—31no—
78#63894—31no—
79#63891—31no—
80#63890—31no—
81D3×C4⋊Dic3D311yescharacteristic, complemented
82#63886—31no—
83#63885—31no—
84#63881—31no—
85#63880—31no—
86#63880—31no—
87#63879—31no—
88#63869—31no—
89#63867—31no—
90#63855—31no—
91#63854—31no—
92#63854—31no—
93#63854—31no—
94#63854—61no—
95#63848—31no—
96#63848—31no—
97#63848—61no—
98#63848D311yescharacteristic, complemented
99#63846—31no—
100#63841—31no—
101#63836—31no—
102C22×C3⋊(C3⋊D3)C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C3×C3⋊D3C2311yescharacteristic
105C22×C32×D3C2311yescharacteristic
106C2×C33×C4C2311yescharacteristic
107C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C32×Dic3C2311yescharacteristic
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C32×C4×D3—22no—
118#6295—41no—
119#6294—41no—
120#6292—22no—
121#6292—41no—
122#6291—22no—
123#6290—22no—
124#6289—41no—
125C3×#626—22no—
126C3×#624—22no—
127C3×D3×Dic3—41no—
128C3×D3×Dic3—41no—
129#5709—91no—
130#5565—91no—
131#5514—91no—
132C22×C32×C4—31no—
133C2×#638—31no—
134C2×#638—31no—
135C2×C4⋊(C3⋊D3)—31no—
136C2×C4⋊(C3⋊D3)—31no—
137C2×C4×C3⋊D3—31no—
138C2×C3×#67—31no—
139C22×C3×Dic3—31no—
140C22×C3×Dic3—31no—
141C2×C3×D12—31no—
142C2×C3×C4×D3—21no—
143C2×C3×C4×D3—31no—
144C2×C3×C4×D3—31no—
145C2×C3×C4×D3—31no—
146C2×C3×C4×D3—31no—
147C2×C3×C4×D3C2×D311yescharacteristic
148C2×C3×C4×D3C2×D311yescharacteristic
149C2×#626—31no—
150C2×#626—31no—
151C2×#626—31no—
152C2×#626—31no—
153C2×#626—31no—
154C2×#626—31no—
155C2×#626—31no—
156C2×#626—31no—
157C2×#626—61no—
158C2×#626—61no—
159C2×#626—61no—
160C2×#626C2×D311yescharacteristic
161C2×#625—31no—
162C2×#625—31no—
163C2×#625—31no—
164C2×#625—61no—
165C2×#624—31no—
166C2×#624—31no—
167C2×#624—31no—
168C2×#624—61no—
169C2×#624C2×D311yescharacteristic
170C2×D3×Dic3—31no—
171C2×D3×Dic3—31no—
172C2×D3×Dic3C2×D311yescharacteristic
173C2×D3×Dic3C2×D311yescharacteristic
174C32×C4⋊C4—31no—
175C32×C4⋊C4—31no—
176#3752—31no—
177#3752—31no—
178#3752—31no—
179#3752—31no—
180#3752—31no—
181#3752—31no—
182#3752—61no—
183#3752—61no—
184#3752—61no—
185#3752—121no—
186#3752C2×D311yescharacteristic
187#3752C2×D311yescharacteristic
188C4⋊(C3⋊Dic3)—31no—
189C4⋊(C3⋊Dic3)C2×D311yescharacteristic
190#3750—31no—
191#3750—31no—
192C4×C3⋊Dic3—31no—
193C3×#217—31no—
194C3×(C2×D3)⋊C4—31no—
195C3×(C2×D3)⋊C4—31no—
196C3×(C2×D3)⋊C4—31no—
197C3×(C2×D3)⋊C4—31no—
198C3×(C2×D3)⋊C4—31no—
199C3×(C2×D3)⋊C4—31no—
200C3×(C2×D3)⋊C4—31no—
201C3×(C2×D3)⋊C4—31no—
202C3×(C2×D3)⋊C4—31no—
203C3×(C2×D3)⋊C4—61no—
204C3×(C2×D3)⋊C4—61no—
205C3×C4⋊Dic3—21no—
206C3×C4⋊Dic3—31no—
207C3×C4⋊Dic3—31no—
208C3×C4⋊Dic3—31no—
209C3×C4⋊Dic3—31no—
210C3×C4⋊Dic3—31no—
211C3×C4⋊Dic3—61no—
212C3×C4⋊Dic3C2×D311yescharacteristic
213C3×C4⋊Dic3C2×D311yescharacteristic
214C3×Dic3⋊C4—21no—
215C3×Dic3⋊C4—31no—
216C3×Dic3⋊C4—31no—
217C3×Dic3⋊C4—31no—
218C3×Dic3⋊C4C2×D311yescharacteristic
219C3×Dic3⋊C4C2×D311yescharacteristic
220C3×C4×Dic3—31no—
221C3×C4×Dic3—31no—
222C3×C4×Dic3—31no—
223C3×C4×Dic3—31no—
224#3724—31no—
225#3724—31no—
226#3724—31no—
227#3724—61no—
228Dic3⋊Dic3—31no—
229Dic3⋊Dic3—31no—
230Dic3⋊Dic3—31no—
231Dic3⋊Dic3—31no—
232Dic3⋊Dic3—31no—
233Dic3⋊Dic3—31no—
234Dic3⋊Dic3—61no—
235Dic3⋊Dic3—61no—
236Dic3⋊Dic3C2×D311yescharacteristic
237Dic3⋊Dic3C2×D311yescharacteristic
238Dic3⋊Dic3C2×D311yescharacteristic
239#3722—31no—
240#3722—31no—
241#3722—31no—
242#3722—31no—
243#3722—31no—
244#3722—61no—
245#3722—61no—
246#3722C2×D311yescharacteristic
247#3722C2×D311yescharacteristic
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)⋊Dic3C2×D311yescharacteristic
254Dic32—31no—
255Dic32—31no—
256Dic32—61no—
257Dic32C2×D311yescharacteristic
258Dic32C2×D311yescharacteristic
259C22×C33C2411yescharacteristic
260C2×C3⋊(C3⋊D3)—21no—
261C2×C3⋊(C3⋊D3)—21no—
262C2×C3⋊(C3⋊D3)—21no—
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#4112yes—
272C33×C4—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×#126—91no—
284C3×C4×D4—91no—
285C2×C3×C4⋊C4—91no—
286#939—91no—
287#939—91no—
288#930—91no—
289#930—91no—
290#930—91no—
291#930—91no—
292#930—91no—
293#930—181no—
294C4×#67—31no—
295C4×#67—91no—
296C4×#67—91no—
297#926—91no—
298C2×C4⋊Dic3—31no—
299#898—31no—
300#898—31no—
301#898—91no—
302#898—91no—
303#898—91no—
304#898—181no—
305#895—91no—
306#895—91no—
307#894—91no—
308#894—91no—
309#894—91no—
310#894—181no—
311#893—31no—
312#893—91no—
313#892—91no—
314D3×C4⋊C4—31no—
315#890—91no—
316#889—91no—
317#886—91no—
318#884—91no—
319#884—91no—
320#884—91no—
321#883—91no—
322#883—91no—
323#67⋊C4—91no—
324#67⋊C4—91no—
325#67⋊C4—91no—
326#67⋊C4—91no—
327C4×D12—91no—
328C4×D12—91no—
329#872—91no—
330#870—91no—
331C23×C32—31no—
332C22×C3⋊D3—31no—
333C22×C3⋊D3—31no—
334C22×C3⋊D3—31no—
335C22×C3⋊D3—61no—
336C22×C3⋊D3—61no—
337C22×C3⋊D3—61no—
338C22×C3⋊D3—121no—
339C22×C3⋊D3C22×D311yescharacteristic
340C22×C3⋊D3C22×D311yescharacteristic
341C22×C3×D3—21no—
342C22×C3×D3—31no—
343C22×C3×D3—31no—
344C22×C3×D3—31no—
345C22×C3×D3—31no—
346C22×C3×D3—61no—
347C22×C3×D3—61no—
348C22×C3×D3C22×D311yescharacteristic
349C22×C3×D3C22×D311yescharacteristic
350C2×C32×C4—21no—
351C2×C32×C4—21no—
352C2×C32×C4—21no—
353C2×C32×C4—31no—
354C2×C32×C4—31no—
355C2×C32×C4—31no—
356C2×C32×C4—31no—
357C2×C32×C4—31no—
358C2×C32×C4—41no—
359C2×C32×C4—62no—
360C2×C32×C4C22×D311yescharacteristic
361C2×C32×C4C22×D311yescharacteristic
362C2×C32×C4C22×D311yescharacteristic
363#638—62no—
364#638—62no—
365C2×C3⋊Dic3—31no—
366C2×C3⋊Dic3—31no—
367C2×C3⋊Dic3—31no—
368C2×C3⋊Dic3—61no—
369C2×C3⋊Dic3—61no—
370C2×C3⋊Dic3—61no—
371C2×C3⋊Dic3—121no—
372C2×C3⋊Dic3C22×D311yescharacteristic
373C2×C3⋊Dic3C22×D311yescharacteristic
374C2×C3⋊Dic3C22×D311yescharacteristic
375C2×C3⋊Dic3C22×D311yescharacteristic
376C4⋊(C3⋊D3)—62no—
377C4⋊(C3⋊D3)—121no—
378C4×C3⋊D3—121no—
379C3×#67—62no—
380C2×C3×Dic3—21no—
381C2×C3×Dic3—21no—
382C2×C3×Dic3—21no—
383C2×C3×Dic3—21no—
384C2×C3×Dic3—21no—
385C2×C3×Dic3—31no—
386C2×C3×Dic3—31no—
387C2×C3×Dic3—31no—
388C2×C3×Dic3—31no—
389C2×C3×Dic3—31no—
390C2×C3×Dic3—31no—
391C2×C3×Dic3—31no—
392C2×C3×Dic3—31no—
393C2×C3×Dic3—61no—
394C2×C3×Dic3—61no—
395C2×C3×Dic3—61no—
396C2×C3×Dic3—61no—
397C2×C3×Dic3—121no—
398C2×C3×Dic3—121no—
399C2×C3×Dic3C22×D311yescharacteristic
400C2×C3×Dic3C22×D311yescharacteristic
401C2×C3×Dic3C22×D311yescharacteristic
402C2×C3×Dic3C22×D311yescharacteristic
403C2×C3×Dic3C22×D311yescharacteristic
404C2×C3×Dic3C22×D311yescharacteristic
405C2×C3×Dic3C22×D311yescharacteristic
406C2×C3×Dic3C22×D311yescharacteristic
407C2×C3×Dic3C22×D311yescharacteristic
408C2×C3×Dic3C22×D311yescharacteristic
409C3×D12—62no—
410C3×C4×D3—22no—
411C3×C4×D3—22no—
412C3×C4×D3—42no—
413C3×C4×D3—62no—
414C3×C4×D3—62no—
415C3×C4×D3—121no—
416C3×C4×D3—121no—
417#626—22no—
418#626—62no—
419#626—62no—
420#626—62no—
421#626—62no—
422#626—122no—
423#626—122no—
424#626—121no—
425#626—121no—
426#626—122no—
427#626—121no—
428#626—121no—
429#625—62no—
430#625—62no—
431#625—122no—
432#625—121no—
433#624—22no—
434#624—121no—
435#624—121no—
436#624—122no—
437#624—121no—
438D3×Dic3—41no—
439D3×Dic3—41no—
440D3×Dic3—121no—
441D3×Dic3—121no—
442#553—271noSylow
443C2×C33C2×#4111yescharacteristic
444C2×C33C2×#4111yescharacteristic
445C2×C33H(5,𝔽2)11yescharacteristic
446C3⋊(C3⋊D3)—41no—
447C3×C3⋊D3—41no—
448C3×C3⋊D3—41no—
449C32×D3—22no—
450C2×C3×D4—91no—
451C22×C3×C4—31no—
452C22×C3×C4—31no—
453C22×C3×C4—61no—
454C22×C3×C4—91no—
455C22×C3×C4—91no—
456C22×C3×C4—91no—
457C2×#67—31no—
458C2×#67—91no—
459C2×#67—91no—
460C2×#67—91no—
461C2×#67—91no—
462C2×#67—91no—
463C2×#67—91no—
464C2×#67—91no—
465C2×#67—91no—
466C2×#67—91no—
467C2×#67—181no—
468C2×#67—181no—
469C22×Dic3—31no—
470C22×Dic3—31no—
471C22×Dic3—91no—
472C2×D12—31no—
473C2×D12—91no—
474C2×D12—91no—
475C2×D12—91no—
476C2×D12—91no—
477C2×D12—91no—
478C2×D12—91no—
479C2×D12—181no—
480C2×D12—181no—
481C2×C4×D3—31no—
482C2×C4×D3—31no—
483C2×C4×D3—31no—
484C2×C4×D3—31no—
485C2×C4×D3—91no—
486C2×C4×D3—91no—
487C2×C4×D3—91no—
488C2×C4×D3—91no—
489C2×C4×D3—91no—
490C2×C4×D3—181no—
491C2×C4×D3D3211yescharacteristic
492C3×C4⋊C4—31no—
493C3×C4⋊C4—31no—
494C3×C4⋊C4—31no—
495C3×C4⋊C4—31no—
496C3×C4⋊C4—61no—
497C3×C4⋊C4—61no—
498C3×C4⋊C4—91no—
499C3×C4⋊C4—91no—
500C3×C4⋊C4—91no—
501C3×C4⋊C4—91no—
502C3×C22⋊C4—91no—
503C3×C22⋊C4—91no—
504C3×C22⋊C4—91no—
505C3×C22⋊C4—91no—
506C3×C22⋊C4—91no—
507C3×C42—91no—
508C3×C42—91no—
509#217—31no—
510#217—91no—
511#217—91no—
512(C2×D3)⋊C4—31no—
513(C2×D3)⋊C4—31no—
514(C2×D3)⋊C4—31no—
515(C2×D3)⋊C4—31no—
516(C2×D3)⋊C4—31no—
517(C2×D3)⋊C4—31no—
518(C2×D3)⋊C4—31no—
519(C2×D3)⋊C4—31no—
520(C2×D3)⋊C4—31no—
521(C2×D3)⋊C4—61no—
522(C2×D3)⋊C4—61no—
523(C2×D3)⋊C4—91no—
524(C2×D3)⋊C4—91no—
525(C2×D3)⋊C4—91no—
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)⋊C4—181no—
539(C2×D3)⋊C4—181no—
540(C2×D3)⋊C4—181no—
541(C2×D3)⋊C4—181no—
542(C2×D3)⋊C4—361no—
543C4⋊Dic3—31no—
544C4⋊Dic3—31no—
545C4⋊Dic3—31no—
546C4⋊Dic3—31no—
547C4⋊Dic3—31no—
548C4⋊Dic3—61no—
549C4⋊Dic3—91no—
550C4⋊Dic3—91no—
551C4⋊Dic3—91no—
552C4⋊Dic3—91no—
553C4⋊Dic3—181no—
554C4⋊Dic3D3211yescharacteristic
555Dic3⋊C4—31no—
556Dic3⋊C4—31no—
557Dic3⋊C4—31no—
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—181no—
567Dic3⋊C4—181no—
568Dic3⋊C4D3211yescharacteristic
569C4×Dic3—31no—
570C4×Dic3—31no—
571C4×Dic3—31no—
572C4×Dic3—31no—
573C4×Dic3—91no—
574C4×Dic3—91no—
575C4×Dic3—91no—
576C4×Dic3—181no—
577C22×C32—21no—
578C22×C32—21no—
579C22×C32—21no—
580C22×C32—32no—
581C22×C32—41no—
582C22×C32—61no—
583C22×C32—61no—
584C22×C32C23×D311yescharacteristic
585C22×C32C23×D311yescharacteristic
586C22×C32C23×D311yescharacteristic
587C2×C3⋊D3—21no—
588C2×C3⋊D3—21no—
589C2×C3⋊D3—21no—
590C2×C3⋊D3—21no—
591C2×C3⋊D3—21no—
592C2×C3⋊D3—21no—
593C2×C3⋊D3—61no—
594C2×C3⋊D3—62no—
595C2×C3⋊D3—61no—
596C2×C3⋊D3—61no—
597C2×C3⋊D3—61no—
598C2×C3⋊D3—61no—
599C2×C3⋊D3—61no—
600C2×C3⋊D3—61no—
601C2×C3⋊D3—61no—
602C2×C3⋊D3—61no—
603C2×C3⋊D3—121no—
604C2×C3⋊D3—121no—
605C2×C3⋊D3—122no—
606C2×C3⋊D3—121no—
607C2×C3⋊D3—121no—
608C2×C3⋊D3—121no—
609C2×C3⋊D3—121no—
610C2×C3⋊D3—121no—
611C2×C3⋊D3—121no—
612C2×C3⋊D3—241no—
613C2×C3⋊D3—241no—
614C2×C3×D3—21no—
615C2×C3×D3—21no—
616C2×C3×D3—21no—
617C2×C3×D3—21no—
618C2×C3×D3—22no—
619C2×C3×D3—41no—
620C2×C3×D3—41no—
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—61no—
628C2×C3×D3—61no—
629C2×C3×D3—61no—
630C2×C3×D3—61no—
631C2×C3×D3—61no—
632C2×C3×D3—61no—
633C2×C3×D3—121no—
634C2×C3×D3—121no—
635C2×C3×D3—121no—
636C2×C3×D3—121no—
637C2×C3×D3—121no—
638C2×C3×D3—121no—
639C2×C3×D3#23512yes—
640C2×C3×D3#23912yes—
641C32×C4—21no—
642C32×C4—21no—
643C32×C4—21no—
644C32×C4—32no—
645C32×C4—41no—
646C32×C4—41no—
647C32×C4—41no—
648C32×C4—61no—
649C32×C4—61no—
650C32×C4—61no—
651C32×C4—61no—
652C32×C4—81no—
653C3⋊Dic3—21no—
654C3⋊Dic3—21no—
655C3⋊Dic3—21no—
656C3⋊Dic3—21no—
657C3⋊Dic3—61no—
658C3⋊Dic3—61no—
659C3⋊Dic3—61no—
660C3⋊Dic3—121no—
661C3⋊Dic3—121no—
662C3⋊Dic3—121no—
663C3⋊Dic3—241no—
664C3×Dic3—21no—
665C3×Dic3—21no—
666C3×Dic3—21no—
667C3×Dic3—21no—
668C3×Dic3—21no—
669C3×Dic3—21no—
670C3×Dic3—21no—
671C3×Dic3—21no—
672C3×Dic3—22no—
673C3×Dic3—41no—
674C3×Dic3—41no—
675C3×Dic3—41no—
676C3×Dic3—41no—
677C3×Dic3—61no—
678C3×Dic3—61no—
679C3×Dic3—61no—
680C3×Dic3—61no—
681C3×Dic3—61no—
682C3×Dic3—61no—
683C3×Dic3—61no—
684C3×Dic3—61no—
685C3×Dic3—121no—
686C3×Dic3—121no—
687C3×Dic3—121no—
688C3×Dic3—121no—
689C3×Dic3#23512yes—
690C3×Dic3#23712yes—
691#126—91no—
692#126—271no—
693#125—271no—
694#123—271no—
695#123—271no—
696#121—271no—
697#121—271no—
698#121—271no—
699#121—271no—
700C4×D4—91no—
701C4×D4—271no—
702C4×D4—271no—
703C4×D4—271no—
704#117—271no—
705C2×C4⋊C4—91no—
706C33#55311yescharacteristic, complemented, Sylow
707C23×C3—31no—
708C23×C3—31no—
709C23×C3—61no—
710C23×C3—91no—
711C23×C3—91no—
712C22×D3—31no—
713C22×D3—31no—
714C22×D3—31no—
715C22×D3—31no—
716C22×D3—61no—
717C22×D3—61no—
718C22×D3—91no—
719C22×D3—91no—
720C22×D3—91no—
721C22×D3—181no—
722C22×D3—181no—
723C22×D3—181no—
724C22×D3—361no—
725C22×D3C2×D3211yescharacteristic
726C3×D4—182no—
727C2×C3×C4—21no—
728C2×C3×C4—21no—
729C2×C3×C4—21no—
730C2×C3×C4—31no—
731C2×C3×C4—31no—
732C2×C3×C4—31no—
733C2×C3×C4—31no—
734C2×C3×C4—31no—
735C2×C3×C4—31no—
736C2×C3×C4—31no—
737C2×C3×C4—31no—
738C2×C3×C4—31no—
739C2×C3×C4—31no—
740C2×C3×C4—41no—
741C2×C3×C4—61no—
742C2×C3×C4—61no—
743C2×C3×C4—61no—
744C2×C3×C4—61no—
745C2×C3×C4—61no—
746C2×C3×C4—62no—
747C2×C3×C4—62no—
748C2×C3×C4—91no—
749C2×C3×C4—91no—
750C2×C3×C4—91no—
751C2×C3×C4—91no—
752C2×C3×C4—122no—
753C2×C3×C4—182no—
754C2×C3×C4—361no—
755C2×C3×C4—361no—
756C2×C3×C4C2×D3211yescharacteristic
757C2×C3×C4C2×D3211yescharacteristic
758C2×C3×C4C2×D3211yescharacteristic
759#67—62no—
760#67—182no—
761#67—182no—
762#67—182no—
763#67—182no—
764#67—182no—
765#67—182no—
766#67—362no—
767#67—362no—
768#67—361no—
769#67—361no—
770#67—361no—
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—61no—
780C2×Dic3—61no—
781C2×Dic3—61no—
782C2×Dic3—61no—
783C2×Dic3—91no—
784C2×Dic3—91no—
785C2×Dic3—91no—
786C2×Dic3—121no—
787C2×Dic3—121no—
788C2×Dic3—181no—
789C2×Dic3—181no—
790C2×Dic3—181no—
791C2×Dic3—361no—
792C2×Dic3—361no—
793C2×Dic3C2×D3211yescharacteristic
794C2×Dic3C2×D3211yescharacteristic
795C2×Dic3C2×D3211yescharacteristic
796C2×Dic3C2×D3211yescharacteristic
797C2×Dic3C2×D3211yescharacteristic
798D12—62no—
799D12—182no—
800D12—182no—
801D12—182no—
802D12—362no—
803D12—361no—
804D12—361no—
805D12—362no—
806D12—361no—
807C4×D3—22no—
808C4×D3—62no—
809C4×D3—62no—
810C4×D3—121no—
811C4×D3—121no—
812C4×D3—361no—
813C4×D3—361no—
814C4×D3—361no—
815C4×D3—361no—
816C4×D3—361no—
817C4×D3—362no—
818C2×C32—21no—
819C2×C32—21no—
820C2×C32—21no—
821C2×C32—21no—
822C2×C32—21no—
823C2×C32—21no—
824C2×C32—21no—
825C2×C32—21no—
826C2×C32—21no—
827C2×C32—41no—
828C2×C32—41no—
829C2×C32—41no—
830C2×C32—62no—
831C2×C32C2×#23511yescharacteristic
832C2×C32C2×#23511yescharacteristic
833C2×C32C2×#23711yescharacteristic
834C2×C32#100411yescharacteristic
835C2×C32C2×#23911yescharacteristic
836C2×C32D3×#4111yescharacteristic
837C2×C32D3×#4111yescharacteristic
838C2×C32#100911yescharacteristic
839C2×C32#100911yescharacteristic
840C3⋊D3—41no—
841C3⋊D3—41no—
842C3⋊D3—121no—
843C3⋊D3—122no—
844C3⋊D3—121no—
845C3⋊D3—121no—
846C3⋊D3—241no—
847C3⋊D3—241no—
848C3⋊D3—242no—
849C3×D3—22no—
850C3×D3—22no—
851C3×D3—42no—
852C3×D3—121no—
853C3×D3—121no—
854C3×D3—121no—
855C3×D3—121no—
856C3×D3—241no—
857C3×D3—241no—
858C2×D4—91no—
859C2×D4—271no—
860C2×D4—271no—
861C2×D4—271no—
862C2×D4—271no—
863C2×D4—271no—
864C22×C4—31no—
865C22×C4—91no—
866C22×C4—91no—
867C22×C4—91no—
868C22×C4—271no—
869C22×C4—271no—
870C4⋊C4—31no—
871C4⋊C4—31no—
872C4⋊C4—91no—
873C4⋊C4—91no—
874C4⋊C4—91no—
875C4⋊C4—91no—
876C4⋊C4—271no—
877C4⋊C4—271no—
878C4⋊C4—271no—
879C4⋊C4—271no—
880C22⋊C4—91no—
881C22⋊C4—91no—
882C22⋊C4—91no—
883C22⋊C4—91no—
884C22⋊C4—91no—
885C22⋊C4—271no—
886C22⋊C4—271no—
887C22⋊C4—271no—
888C22⋊C4—271no—
889C22⋊C4—271no—
890C42—91no—
891C42—91no—
892C42—271no—
893C22×C3—21no—
894C22×C3—21no—
895C22×C3—21no—
896C22×C3—32no—
897C22×C3—32no—
898C22×C3—41no—
899C22×C3—62no—
900C22×C3—61no—
901C22×C3—61no—
902C22×C3—61no—
903C22×C3—61no—
904C22×C3—121no—
905C22×C3—121no—
906C22×C3—181no—
907C22×C3—181no—
908C22×C3—181no—
909C22×C3—181no—
910C22×C3—181no—
911C22×C3—181no—
912C22×C3C22×D3211yescharacteristic
913C22×C3C22×D3211yescharacteristic
914C22×C3C22×D3211yescharacteristic
915C2×D3—21no—
916C2×D3—21no—
917C2×D3—61no—
918C2×D3—61no—
919C2×D3—61no—
920C2×D3—61no—
921C2×D3—61no—
922C2×D3—61no—
923C2×D3—61no—
924C2×D3—61no—
925C2×D3—61no—
926C2×D3—61no—
927C2×D3—61no—
928C2×D3—61no—
929C2×D3—121no—
930C2×D3—121no—
931C2×D3—121no—
932C2×D3—121no—
933C2×D3—121no—
934C2×D3—121no—
935C2×D3—182no—
936C2×D3—181no—
937C2×D3—181no—
938C2×D3—181no—
939C2×D3—181no—
940C2×D3—181no—
941C2×D3—181no—
942C2×D3—181no—
943C2×D3—181no—
944C2×D3—181no—
945C2×D3—361no—
946C2×D3—361no—
947C2×D3—361no—
948C2×D3—361no—
949C2×D3—361no—
950C2×D3—361no—
951C2×D3—361no—
952C2×D3—361no—
953C2×D3—362no—
954C2×D3—721no—
955C2×D3—721no—
956C2×D3#379912yes—
957C3×C4—21no—
958C3×C4—21no—
959C3×C4—21no—
960C3×C4—32no—
961C3×C4—32no—
962C3×C4—41no—
963C3×C4—41no—
964C3×C4—41no—
965C3×C4—62no—
966C3×C4—61no—
967C3×C4—61no—
968C3×C4—61no—
969C3×C4—61no—
970C3×C4—61no—
971C3×C4—61no—
972C3×C4—61no—
973C3×C4—61no—
974C3×C4—81no—
975C3×C4—121no—
976C3×C4—121no—
977C3×C4—121no—
978C3×C4—121no—
979C3×C4—181no—
980C3×C4—181no—
981C3×C4—181no—
982C3×C4—181no—
983Dic3—21no—
984Dic3—21no—
985Dic3—21no—
986Dic3—21no—
987Dic3—61no—
988Dic3—61no—
989Dic3—61no—
990Dic3—61no—
991Dic3—61no—
992Dic3—61no—
993Dic3—61no—
994Dic3—61no—
995Dic3—121no—
996Dic3—121no—
997Dic3—121no—
998Dic3—121no—
999Dic3—181no—
1000Dic3—181no—
1001Dic3—181no—
1002Dic3—361no—
1003Dic3—361no—
1004Dic3—361no—
1005Dic3—721no—
1006Dic3#380412yes—
1007C32—21no—
1008C32—21no—
1009C32—21no—
1010C32—41no—
1011C32#551411yescharacteristic, complemented
1012C32#556511yescharacteristic, complemented
1013C32#570911yescharacteristic, complemented
1014C23—31no—
1015C23—91no—
1016C23—91no—
1017C23—271no—
1018D4—182no—
1019D4—542no—
1020D4—542no—
1021D4—542no—
1022D4—1081no—
1023D4—1081no—
1024C2×C4—31no—
1025C2×C4—31no—
1026C2×C4—31no—
1027C2×C4—31no—
1028C2×C4—31no—
1029C2×C4—62no—
1030C2×C4—91no—
1031C2×C4—91no—
1032C2×C4—91no—
1033C2×C4—91no—
1034C2×C4—182no—
1035C2×C4—271no—
1036C2×C4—361no—
1037C2×C4—361no—
1038C2×C4—1081no—
1039C2×C4—1081no—
1040C2×C4D3311yescharacteristic
1041C2×C3—21no—
1042C2×C3—21no—
1043C2×C3—21no—
1044C2×C3—21no—
1045C2×C3—21no—
1046C2×C3—21no—
1047C2×C3—21no—
1048C2×C3—21no—
1049C2×C3—21no—
1050C2×C3—41no—
1051C2×C3—41no—
1052C2×C3—41no—
1053C2×C3—62no—
1054C2×C3—62no—
1055C2×C3—122no—
1056C2×C3—361no—
1057C2×C3—361no—
1058C2×C3C2×#379911yescharacteristic
1059C2×C3D3×#23511yescharacteristic
1060C2×C3D3×#23511yescharacteristic
1061C2×C3#6430711yescharacteristic
1062C2×C3D3×#23711yescharacteristic
1063C2×C3#6431411yescharacteristic
1064C2×C3D3×#23911yescharacteristic
1065C2×C3#6432011yescharacteristic
1066C2×C3C2×#380411yescharacteristic
1067D3—22no—
1068D3—121no—
1069D3—121no—
1070D3—121no—
1071D3—121no—
1072D3—241no—
1073D3—241no—
1074D3—362no—
1075D3—361no—
1076D3—361no—
1077D3—361no—
1078D3—721no—
1079D3—721no—
1080D3—722no—
1081C22—32no—
1082C22—61no—
1083C22—61no—
1084C22—181no—
1085C22—181no—
1086C22—181no—
1087C22—181no—
1088C22—181no—
1089C22—181no—
1090C22—541no—
1091C22—541no—
1092C22—541no—
1093C22C2×D3311yescharacteristic
1094C4—21no—
1095C4—32no—
1096C4—61no—
1097C4—61no—
1098C4—61no—
1099C4—61no—
1100C4—181no—
1101C4—181no—
1102C4—181no—
1103C4—181no—
1104C4—541no—
1105C3—21no—
1106C3—21no—
1107C3—21no—
1108C3—41no—
1109C3#1059441411yescharacteristic, complemented
1110C3#1059454511yescharacteristic, complemented
1111C3#1059484311yescharacteristic, complemented
1112C2—62no—
1113C2—361no—
1114C2—361no—
1115C2—1081no—
1116C2D3×#379911yescharacteristic
1117C2#1172438511yescharacteristic
1118C2D3×#380411yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
hypercenterC2×C4D33
hypocenterC33#553
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. #11723690C2semidirect
2. #11723514C2semidirect
3. #11723504C2semidirect
4. #11723403C2semidirect
5. C3×#63904C2semidirect
6. C3×D3×C4⋊Dic3C2semidirect
7. C3×#63848C2semidirect
8. #11723012C2semidirect
9. #11722961C2semidirect
10. #11722960C2semidirect
11. #11722959C2semidirect
12. #11722937C2semidirect
13. #11722936C2semidirect
14. #11722932C2semidirect
15. #11722915C2semidirect
75. #63904D3semidirect
81. D3×C4⋊Dic3D3semidirect
98. #63848D3semidirect
706. C33#553semidirect
1011. C32#5514semidirect
1012. C32#5565semidirect
1013. C32#5709semidirect
1109. C3#10594414semidirect
1110. C3#10594545semidirect
1111. C3#10594843semidirect

Maximal subgroups

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

subgroupindex
#117236902
#117235142
#117235042
#117234032
C3×#639042
C3×D3×C4⋊Dic32
C3×#638482
#117230122
#117229612
#117229602
#117229592
#117229372
#117229362
#117229322
#117229152
#105948433
#105945453
#105944143