Finite Group Databasebeta

← #13178329

Subgroups — #13178329

Order 1728.

1208 conjugacy classes of subgroups.

The subgroup lattice has 1100 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64107C211yesmaximal, characteristic, complemented
2C3×#64103C211yesmaximal, characteristic, complemented
3C3×C4⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
4#11723696C211yesmaximal, characteristic, complemented
5#11723695C211yesmaximal, characteristic, complemented
6#11723695C211yesmaximal, characteristic, complemented
7C4×#6295C211yesmaximal, characteristic, complemented
8#11723690C211yesmaximal, characteristic, complemented
9#11723687C211yesmaximal, characteristic, complemented
10#11723684C211yesmaximal, characteristic, complemented
11#11723684C211yesmaximal, characteristic, complemented
12#11723684C211yesmaximal, characteristic, complemented
13#11723683C211yesmaximal, characteristic, complemented
14#11723675C211yesmaximal, characteristic, complemented
15#11723669C211yesmaximal, characteristic, complemented
16#10594545—31nomaximal
17#10594544—31nomaximal
18#10594473—31nomaximal
19C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
20C2×C3×C4×C3⋊D3C2211yescharacteristic
21C2×C3×C4×C3⋊D3C2211yescharacteristic
22C2×C3×C4×C3⋊D3C2211yescharacteristic
23C2×C3×C4×C3⋊D3C2211yescharacteristic
24C2×#6295C2211yescharacteristic
25C2×#6295C2211yescharacteristic
26C2×#6295C2211yescharacteristic
27C2×#6295C2211yescharacteristic
28C2×#6295C2211yescharacteristic
29C2×#6294C2211yescharacteristic
30C2×#6294C2211yescharacteristic
31C33×C4⋊C4C2211yescharacteristic
32C3×#3752C2211yescharacteristic
33C3×#3752C2211yescharacteristic
34C3×#3752C2211yescharacteristic
35C3×#3752C2211yescharacteristic
36C3×#3752C2211yescharacteristic
37C3×#3752C2211yescharacteristic
38C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
39C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
40C3×#3750C2211yescharacteristic
41C3×#3750C2211yescharacteristic
42C3×#3750C2211yescharacteristic
43C3×#3750C2211yescharacteristic
44C3×C4×C3⋊Dic3C2211yescharacteristic
45#88815C2211yescharacteristic
46#88815C2211yescharacteristic
47#88815C2211yescharacteristic
48#88814C2211yescharacteristic
49#88814C2211yescharacteristic
50#88814C2211yescharacteristic
51#88814C2211yescharacteristic
52#88813C2211yescharacteristic
53#88813C2211yescharacteristic
54#64107D311yescharacteristic, complemented
55#64103D311yescharacteristic, complemented
56C4⋊C4×C3⋊D3D311yescharacteristic, complemented
57C3×#898—31no—
58C3×#898—31no—
59C3×#898—61no—
60C3×#894—31no—
61C3×#894—31no—
62C3×#894—61no—
63C3×D3×C4⋊C4—31no—
64C3×D3×C4⋊C4—31no—
65C3×D3×C4⋊C4—61no—
66#63916—31no—
67#63912—31no—
68#63912—31no—
69#63910—31no—
70#63909—31no—
71#63908—31no—
72#63906—31no—
73#63906—31no—
74#63906—31no—
75#63906—31no—
76#63904—31no—
77#63904—31no—
78#63904—31no—
79C4×#626—31no—
80C4×#626—31no—
81C4×#625—31no—
82#63891—31no—
83#63890—31no—
84#63886—31no—
85#63885—31no—
86#63881—31no—
87#63881—31no—
88#63881—31no—
89#63879—31no—
90#63879—31no—
91#63879—31no—
92#63878—31no—
93#63877—31no—
94#63861—31no—
95#63858—31no—
96#63854—31no—
97#63848—31no—
98#63847—31no—
99#63846—31no—
100#63845—31no—
101#63836—31no—
102C22×C3×C3⋊D3C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C3×C3⋊D3C2311yescharacteristic
105C22×C3×C3⋊D3C2311yescharacteristic
106C2×C33×C4C2311yescharacteristic
107C2×C33×C4C2311yescharacteristic
108C2×C33×C4C2311yescharacteristic
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C3×C4⋊(C3⋊D3)—41no—
118C3×C4×C3⋊D3—22no—
119C3×C4×C3⋊D3—41no—
120C3×C4×C3⋊D3—41no—
121C3×C4×C3⋊D3—41no—
122#6295—22no—
123#6295—22no—
124#6295—22no—
125#6295—22no—
126#6295—41no—
127#6294—22no—
128#6294—41no—
129#5709—91no—
130#5661—91no—
131#5514—91no—
132C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
133C2×C4×C3⋊D3C2×D311yescharacteristic
134C2×C4×C3⋊D3C2×D311yescharacteristic
135C2×C4×C3⋊D3C2×D311yescharacteristic
136C2×C4×C3⋊D3C2×D311yescharacteristic
137C2×C3×D12—31no—
138C2×C3×D12—31no—
139C2×C3×D12—61no—
140C2×C3×C4×D3—31no—
141C2×C3×C4×D3—31no—
142C2×C3×C4×D3—31no—
143C2×C3×C4×D3—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—61no—
149C2×C3×C4×D3—61no—
150C2×C3×C4×D3—61no—
151C2×C3×C4×D3—61no—
152C2×#626—31no—
153C2×#626—31no—
154C2×#626—31no—
155C2×#626—31no—
156C2×#626—31no—
157C2×#626—31no—
158C2×#626—31no—
159C2×#626—31no—
160C2×#626—31no—
161C2×#626—31no—
162C2×#625—31no—
163C2×#625—31no—
164C2×#625—31no—
165C2×#625—31no—
166C2×#625—31no—
167C2×#624—31no—
168C2×#624—31no—
169C2×D3×Dic3—31no—
170C2×D3×Dic3—31no—
171C2×D3×Dic3—31no—
172C2×D3×Dic3—31no—
173C32×C4⋊C4—21no—
174C32×C4⋊C4—21no—
175C32×C4⋊C4—21no—
176C32×C4⋊C4—41no—
177C32×C4⋊C4C2×D311yescharacteristic
178C32×C4⋊C4C2×D311yescharacteristic
179C32×C4⋊C4C2×D311yescharacteristic
180#3752C2×D311yescharacteristic
181#3752C2×D311yescharacteristic
182#3752C2×D311yescharacteristic
183#3752C2×D311yescharacteristic
184#3752C2×D311yescharacteristic
185#3752C2×D311yescharacteristic
186C4⋊(C3⋊Dic3)C2×D311yescharacteristic
187C4⋊(C3⋊Dic3)C2×D311yescharacteristic
188#3750C2×D311yescharacteristic
189#3750C2×D311yescharacteristic
190#3750C2×D311yescharacteristic
191#3750C2×D311yescharacteristic
192C4×C3⋊Dic3C2×D311yescharacteristic
193C3×(C2×D3)⋊C4—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—31no—
204C3×(C2×D3)⋊C4—31no—
205C3×(C2×D3)⋊C4—61no—
206C3×(C2×D3)⋊C4—61no—
207C3×(C2×D3)⋊C4—61no—
208C3×(C2×D3)⋊C4—61no—
209C3×(C2×D3)⋊C4—61no—
210C3×(C2×D3)⋊C4—61no—
211C3×C4⋊Dic3—31no—
212C3×C4⋊Dic3—31no—
213C3×C4⋊Dic3—31no—
214C3×C4⋊Dic3—31no—
215C3×C4⋊Dic3—61no—
216C3×C4⋊Dic3—61no—
217C3×Dic3⋊C4—31no—
218C3×Dic3⋊C4—31no—
219C3×Dic3⋊C4—31no—
220C3×Dic3⋊C4—31no—
221C3×Dic3⋊C4—31no—
222C3×Dic3⋊C4—31no—
223C3×Dic3⋊C4—31no—
224C3×Dic3⋊C4—31no—
225C3×Dic3⋊C4—61no—
226C3×Dic3⋊C4—61no—
227C3×Dic3⋊C4—61no—
228C3×Dic3⋊C4—61no—
229C3×C4×Dic3—31no—
230C3×C4×Dic3—31no—
231C3×C4×Dic3—61no—
232#3724—31no—
233#3724—31no—
234#3724—31no—
235Dic3⋊Dic3—31no—
236Dic3⋊Dic3—31no—
237Dic3⋊Dic3—31no—
238Dic3⋊Dic3—31no—
239Dic3⋊Dic3—31no—
240Dic3⋊Dic3—31no—
241#3722—31no—
242#3722—31no—
243#3722—31no—
244#3722—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—31no—
253Dic32—31no—
254Dic32—31no—
255Dic32—31no—
256Dic32—31no—
257Dic32—31no—
258Dic32—31no—
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×C3×C3⋊D3—21no—
270C2×C3×C3⋊D3—21no—
271C2×C3×C3⋊D3#4112yes—
272C33×C4—21no—
273C33×C4—21no—
274C33×C4—21no—
275C3×C3⋊Dic3—21no—
276C3×C3⋊Dic3—21no—
277C3×C3⋊Dic3—21no—
278C3×C3⋊Dic3—21no—
279C3×C3⋊Dic3—21no—
280C3×C3⋊Dic3—21no—
281C3×C3⋊Dic3—21no—
282C3×C3⋊Dic3#4112yes—
283C3×#126—91no—
284C3×#123—91no—
285C2×C3×C4⋊C4—91no—
286#939—91no—
287#938—91no—
288#930—91no—
289#930—91no—
290#930—91no—
291C4×#67—91no—
292C4×#67—91no—
293C4×#67—91no—
294C4×#67—91no—
295C4×#67—91no—
296#898—31no—
297#898—31no—
298#898—61no—
299#898—91no—
300#898—91no—
301#895—91no—
302#895—91no—
303#894—31no—
304#894—31no—
305#894—61no—
306#894—91no—
307#893—91no—
308#893—91no—
309#893—91no—
310#892—91no—
311D3×C4⋊C4—31no—
312D3×C4⋊C4—31no—
313D3×C4⋊C4—61no—
314#890—91no—
315#889—91no—
316#889—91no—
317#886—91no—
318#884—91no—
319#884—91no—
320#884—91no—
321#884—91no—
322#884—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#872—91no—
331C22×C3⋊D3C22×D311yescharacteristic
332C22×C3⋊D3C22×D311yescharacteristic
333C22×C3⋊D3C22×D311yescharacteristic
334C22×C3⋊D3C22×D311yescharacteristic
335C22×C3×D3—31no—
336C22×C3×D3—31no—
337C22×C3×D3—31no—
338C22×C3×D3—31no—
339C22×C3×D3—31no—
340C22×C3×D3—31no—
341C22×C3×D3—31no—
342C22×C3×D3—31no—
343C22×C3×D3—61no—
344C22×C3×D3—61no—
345C22×C3×D3—61no—
346C22×C3×D3—61no—
347C2×C32×C4—21no—
348C2×C32×C4—21no—
349C2×C32×C4—21no—
350C2×C32×C4—21no—
351C2×C32×C4—21no—
352C2×C32×C4—21no—
353C2×C32×C4—21no—
354C2×C32×C4—21no—
355C2×C32×C4—21no—
356C2×C32×C4—41no—
357C2×C32×C4—41no—
358C2×C32×C4—41no—
359C2×C32×C4C22×D311yescharacteristic
360C2×C32×C4C22×D311yescharacteristic
361C2×C32×C4C22×D311yescharacteristic
362C2×C32×C4C22×D311yescharacteristic
363C2×C32×C4C22×D311yescharacteristic
364C2×C32×C4C22×D311yescharacteristic
365C2×C32×C4C22×D311yescharacteristic
366C2×C32×C4C22×D311yescharacteristic
367C2×C32×C4C22×D311yescharacteristic
368C2×C3⋊Dic3C22×D311yescharacteristic
369C2×C3⋊Dic3C22×D311yescharacteristic
370C2×C3⋊Dic3C22×D311yescharacteristic
371C2×C3⋊Dic3C22×D311yescharacteristic
372C2×C3⋊Dic3C22×D311yescharacteristic
373C2×C3⋊Dic3C22×D311yescharacteristic
374C2×C3⋊Dic3C22×D311yescharacteristic
375C2×C3⋊Dic3C22×D311yescharacteristic
376C4⋊(C3⋊D3)—41no—
377C4×C3⋊D3—22no—
378C4×C3⋊D3—41no—
379C4×C3⋊D3—41no—
380C4×C3⋊D3—41no—
381C2×C3×Dic3—31no—
382C2×C3×Dic3—31no—
383C2×C3×Dic3—31no—
384C2×C3×Dic3—31no—
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—31no—
394C2×C3×Dic3—31no—
395C2×C3×Dic3—31no—
396C2×C3×Dic3—31no—
397C2×C3×Dic3—61no—
398C2×C3×Dic3—61no—
399C2×C3×Dic3—61no—
400C2×C3×Dic3—61no—
401C2×C3×Dic3—61no—
402C2×C3×Dic3—61no—
403C2×C3×Dic3—61no—
404C2×C3×Dic3—61no—
405C3×D12—121no—
406C3×D12—121no—
407C3×D12—122no—
408C3×C4×D3—62no—
409C3×C4×D3—62no—
410C3×C4×D3—64no—
411C3×C4×D3—121no—
412C3×C4×D3—121no—
413C3×C4×D3—121no—
414C3×C4×D3—121no—
415C3×C4×D3—121no—
416C3×C4×D3—121no—
417C3×C4×D3—122no—
418C3×C4×D3—122no—
419C3×C4×D3—122no—
420#626—62no—
421#626—62no—
422#626—62no—
423#626—62no—
424#626—62no—
425#626—62no—
426#626—62no—
427#626—62no—
428#626—121no—
429#626—121no—
430#625—62no—
431#625—62no—
432#625—62no—
433#625—62no—
434#625—121no—
435#624—62no—
436#624—121no—
437D3×Dic3—62no—
438D3×Dic3—62no—
439D3×Dic3—121no—
440D3×Dic3—121no—
441#553—271noSylow
442C2×C33C2×#4111yescharacteristic
443C2×C33C2×#4111yescharacteristic
444C2×C33H(5,𝔽2)11yescharacteristic
445C3×C3⋊D3—22no—
446C3×C3⋊D3—41no—
447C3×C3⋊D3—41no—
448C3×C3⋊D3—41no—
449C2×C3×D4—91no—
450C22×C3×C4—91no—
451C22×C3×C4—91no—
452C22×C3×C4—91no—
453C22×C3×C4—91no—
454C2×#67—91no—
455C2×#67—91no—
456C2×#67—91no—
457C2×#67—91no—
458C2×#67—91no—
459C2×#67—91no—
460C2×#67—91no—
461C2×#67—91no—
462C2×#67—91no—
463C2×#67—91no—
464C22×Dic3—91no—
465C22×Dic3—91no—
466C2×D12—31no—
467C2×D12—31no—
468C2×D12—61no—
469C2×D12—91no—
470C2×D12—91no—
471C2×D12—91no—
472C2×D12—91no—
473C2×D12—91no—
474C2×C4×D3—31no—
475C2×C4×D3—31no—
476C2×C4×D3—31no—
477C2×C4×D3—31no—
478C2×C4×D3—31no—
479C2×C4×D3—31no—
480C2×C4×D3—31no—
481C2×C4×D3—31no—
482C2×C4×D3—61no—
483C2×C4×D3—61no—
484C2×C4×D3—61no—
485C2×C4×D3—61no—
486C2×C4×D3—91no—
487C2×C4×D3—91no—
488C2×C4×D3—91no—
489C2×C4×D3—91no—
490C3×C4⋊C4—21no—
491C3×C4⋊C4—21no—
492C3×C4⋊C4—21no—
493C3×C4⋊C4—41no—
494C3×C4⋊C4—91no—
495C3×C4⋊C4—91no—
496C3×C4⋊C4—91no—
497C3×C4⋊C4—91no—
498C3×C4⋊C4—91no—
499C3×C4⋊C4—91no—
500C3×C4⋊C4D3211yescharacteristic
501C3×C4⋊C4D3211yescharacteristic
502C3×C4⋊C4D3211yescharacteristic
503C3×C22⋊C4—91no—
504C3×C22⋊C4—91no—
505C3×C22⋊C4—91no—
506C3×C22⋊C4—91no—
507C3×C22⋊C4—91no—
508C3×C22⋊C4—91no—
509C3×C42—91no—
510#217—91no—
511#217—91no—
512#217—91no—
513#217—91no—
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—31no—
522(C2×D3)⋊C4—31no—
523(C2×D3)⋊C4—31no—
524(C2×D3)⋊C4—31no—
525(C2×D3)⋊C4—31no—
526(C2×D3)⋊C4—61no—
527(C2×D3)⋊C4—61no—
528(C2×D3)⋊C4—61no—
529(C2×D3)⋊C4—61no—
530(C2×D3)⋊C4—61no—
531(C2×D3)⋊C4—61no—
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—
540C4⋊Dic3—31no—
541C4⋊Dic3—31no—
542C4⋊Dic3—31no—
543C4⋊Dic3—31no—
544C4⋊Dic3—61no—
545C4⋊Dic3—61no—
546C4⋊Dic3—91no—
547C4⋊Dic3—91no—
548C4⋊Dic3—91no—
549Dic3⋊C4—31no—
550Dic3⋊C4—31no—
551Dic3⋊C4—31no—
552Dic3⋊C4—31no—
553Dic3⋊C4—31no—
554Dic3⋊C4—31no—
555Dic3⋊C4—31no—
556Dic3⋊C4—31no—
557Dic3⋊C4—61no—
558Dic3⋊C4—61no—
559Dic3⋊C4—61no—
560Dic3⋊C4—61no—
561Dic3⋊C4—91no—
562Dic3⋊C4—91no—
563Dic3⋊C4—91no—
564Dic3⋊C4—91no—
565Dic3⋊C4—91no—
566Dic3⋊C4—91no—
567C4×Dic3—31no—
568C4×Dic3—31no—
569C4×Dic3—61no—
570C4×Dic3—91no—
571C4×Dic3—91no—
572C4×Dic3—91no—
573C4×Dic3—91no—
574C4×Dic3—91no—
575C4×Dic3—91no—
576C22×C32—21no—
577C22×C32—21no—
578C22×C32—21no—
579C22×C32—41no—
580C22×C32C23×D311yescharacteristic
581C22×C32C23×D311yescharacteristic
582C22×C32C23×D311yescharacteristic
583C2×C3⋊D3—21no—
584C2×C3⋊D3—21no—
585C2×C3⋊D3—21no—
586C2×C3⋊D3—21no—
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—21no—
594C2×C3⋊D3#23912yes—
595C2×C3×D3—32no—
596C2×C3×D3—32no—
597C2×C3×D3—62no—
598C2×C3×D3—62no—
599C2×C3×D3—62no—
600C2×C3×D3—61no—
601C2×C3×D3—61no—
602C2×C3×D3—61no—
603C2×C3×D3—61no—
604C2×C3×D3—62no—
605C2×C3×D3—61no—
606C2×C3×D3—61no—
607C2×C3×D3—61no—
608C2×C3×D3—61no—
609C2×C3×D3—61no—
610C2×C3×D3—61no—
611C2×C3×D3—61no—
612C2×C3×D3—61no—
613C2×C3×D3—61no—
614C2×C3×D3—61no—
615C2×C3×D3—61no—
616C2×C3×D3—61no—
617C2×C3×D3—61no—
618C2×C3×D3—61no—
619C2×C3×D3—61no—
620C2×C3×D3—61no—
621C2×C3×D3—61no—
622C2×C3×D3—61no—
623C2×C3×D3—121no—
624C2×C3×D3—121no—
625C2×C3×D3—121no—
626C2×C3×D3—121no—
627C2×C3×D3—121no—
628C2×C3×D3—121no—
629C2×C3×D3—121no—
630C2×C3×D3—121no—
631C32×C4—21no—
632C32×C4—22no—
633C32×C4—21no—
634C32×C4—21no—
635C32×C4—21no—
636C32×C4—21no—
637C32×C4—21no—
638C32×C4—21no—
639C32×C4—21no—
640C32×C4—21no—
641C32×C4—41no—
642C32×C4—41no—
643C32×C4—42no—
644C32×C4—41no—
645C32×C4—41no—
646C32×C4—41no—
647C32×C4—41no—
648C32×C4—41no—
649C32×C4—41no—
650C32×C4—81no—
651C32×C4—81no—
652C3⋊Dic3—21no—
653C3⋊Dic3—21no—
654C3⋊Dic3—21no—
655C3⋊Dic3—21no—
656C3⋊Dic3—21no—
657C3⋊Dic3—21no—
658C3⋊Dic3—21no—
659C3⋊Dic3#23512yes—
660C3×Dic3—32no—
661C3×Dic3—32no—
662C3×Dic3—62no—
663C3×Dic3—61no—
664C3×Dic3—61no—
665C3×Dic3—61no—
666C3×Dic3—61no—
667C3×Dic3—61no—
668C3×Dic3—61no—
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—121no—
678C3×Dic3—121no—
679C3×Dic3—121no—
680C3×Dic3—121no—
681C3×Dic3—121no—
682C3×Dic3—121no—
683C3×Dic3—121no—
684#126—91no—
685#126—271no—
686#125—271no—
687#123—91no—
688#123—271no—
689#121—271no—
690#121—271no—
691#121—271no—
692#121—271no—
693C4×D4—271no—
694C4×D4—271no—
695C4×D4—271no—
696C4×D4—271no—
697#117—271no—
698C2×C4⋊C4—91no—
699C33#55311yescharacteristic, complemented, Sylow
700C23×C3—91no—
701C23×C3—91no—
702C23×C3—91no—
703C23×C3—91no—
704C22×D3—31no—
705C22×D3—31no—
706C22×D3—31no—
707C22×D3—31no—
708C22×D3—31no—
709C22×D3—31no—
710C22×D3—31no—
711C22×D3—31no—
712C22×D3—61no—
713C22×D3—61no—
714C22×D3—61no—
715C22×D3—61no—
716C3×D4—361no—
717C2×C3×C4—21no—
718C2×C3×C4—21no—
719C2×C3×C4—21no—
720C2×C3×C4—21no—
721C2×C3×C4—21no—
722C2×C3×C4—21no—
723C2×C3×C4—21no—
724C2×C3×C4—21no—
725C2×C3×C4—21no—
726C2×C3×C4—41no—
727C2×C3×C4—41no—
728C2×C3×C4—41no—
729C2×C3×C4—91no—
730C2×C3×C4—91no—
731C2×C3×C4—91no—
732C2×C3×C4—91no—
733C2×C3×C4—91no—
734C2×C3×C4—91no—
735C2×C3×C4—91no—
736C2×C3×C4—91no—
737C2×C3×C4—182no—
738C2×C3×C4—361no—
739C2×C3×C4—361no—
740C2×C3×C4—361no—
741C2×C3×C4C2×D3211yescharacteristic
742C2×C3×C4C2×D3211yescharacteristic
743C2×C3×C4C2×D3211yescharacteristic
744C2×C3×C4C2×D3211yescharacteristic
745C2×C3×C4C2×D3211yescharacteristic
746C2×C3×C4C2×D3211yescharacteristic
747C2×C3×C4C2×D3211yescharacteristic
748C2×C3×C4C2×D3211yescharacteristic
749C2×C3×C4C2×D3211yescharacteristic
750#67—182no—
751#67—182no—
752#67—182no—
753#67—182no—
754#67—182no—
755#67—182no—
756#67—182no—
757#67—182no—
758#67—361no—
759#67—361no—
760C2×Dic3—31no—
761C2×Dic3—31no—
762C2×Dic3—31no—
763C2×Dic3—31no—
764C2×Dic3—31no—
765C2×Dic3—31no—
766C2×Dic3—31no—
767C2×Dic3—31no—
768C2×Dic3—31no—
769C2×Dic3—31no—
770C2×Dic3—31no—
771C2×Dic3—31no—
772C2×Dic3—31no—
773C2×Dic3—31no—
774C2×Dic3—31no—
775C2×Dic3—31no—
776C2×Dic3—61no—
777C2×Dic3—61no—
778C2×Dic3—61no—
779C2×Dic3—61no—
780C2×Dic3—61no—
781C2×Dic3—61no—
782C2×Dic3—61no—
783C2×Dic3—61no—
784C2×Dic3—182no—
785C2×Dic3—361no—
786D12—121no—
787D12—121no—
788D12—122no—
789D12—182no—
790D12—182no—
791D12—182no—
792D12—182no—
793D12—361no—
794C4×D3—62no—
795C4×D3—62no—
796C4×D3—64no—
797C4×D3—121no—
798C4×D3—121no—
799C4×D3—121no—
800C4×D3—121no—
801C4×D3—121no—
802C4×D3—121no—
803C4×D3—122no—
804C4×D3—122no—
805C4×D3—122no—
806C4×D3—182no—
807C4×D3—182no—
808C4×D3—361no—
809C4×D3—361no—
810C2×C32—21no—
811C2×C32—21no—
812C2×C32—21no—
813C2×C32—21no—
814C2×C32—21no—
815C2×C32—21no—
816C2×C32—21no—
817C2×C32—21no—
818C2×C32—21no—
819C2×C32—41no—
820C2×C32—41no—
821C2×C32—41no—
822C2×C32C2×#23511yescharacteristic
823C2×C32#100411yescharacteristic
824C2×C32#100411yescharacteristic
825C2×C32C2×#23911yescharacteristic
826C2×C32D3×#4111yescharacteristic
827C2×C32D3×#4111yescharacteristic
828C2×C32D3×#4111yescharacteristic
829C2×C32D3×#4111yescharacteristic
830C2×C32#100911yescharacteristic
831C3⋊D3—22no—
832C3⋊D3—41no—
833C3⋊D3—41no—
834C3⋊D3—41no—
835C3×D3—64no—
836C3×D3—62no—
837C3×D3—62no—
838C3×D3—122no—
839C3×D3—121no—
840C3×D3—121no—
841C3×D3—121no—
842C3×D3—121no—
843C3×D3—121no—
844C3×D3—121no—
845C3×D3—241no—
846C3×D3—241no—
847C2×D4—91no—
848C2×D4—271no—
849C2×D4—271no—
850C2×D4—271no—
851C2×D4—271no—
852C2×D4—271no—
853C22×C4—91no—
854C22×C4—91no—
855C22×C4—91no—
856C22×C4—91no—
857C22×C4—271no—
858C22×C4—271no—
859C4⋊C4—91no—
860C4⋊C4—91no—
861C4⋊C4—91no—
862C4⋊C4—91no—
863C4⋊C4—91no—
864C4⋊C4—91no—
865C4⋊C4—271no—
866C4⋊C4—271no—
867C4⋊C4—271no—
868C4⋊C4#111311yescharacteristic
869C22⋊C4—91no—
870C22⋊C4—91no—
871C22⋊C4—91no—
872C22⋊C4—91no—
873C22⋊C4—91no—
874C22⋊C4—91no—
875C22⋊C4—271no—
876C22⋊C4—271no—
877C22⋊C4—271no—
878C22⋊C4—271no—
879C42—91no—
880C42—271no—
881C42—271no—
882C22×C3—21no—
883C22×C3—21no—
884C22×C3—21no—
885C22×C3—41no—
886C22×C3—92no—
887C22×C3—181no—
888C22×C3—181no—
889C22×C3—181no—
890C22×C3—181no—
891C22×C3—181no—
892C22×C3—181no—
893C22×C3—181no—
894C22×C3—181no—
895C22×C3—181no—
896C22×C3—181no—
897C22×C3—181no—
898C22×C3C22×D3211yescharacteristic
899C22×C3C22×D3211yescharacteristic
900C22×C3C22×D3211yescharacteristic
901C2×D3—32no—
902C2×D3—32no—
903C2×D3—62no—
904C2×D3—62no—
905C2×D3—62no—
906C2×D3—61no—
907C2×D3—61no—
908C2×D3—61no—
909C2×D3—61no—
910C2×D3—62no—
911C2×D3—61no—
912C2×D3—61no—
913C2×D3—61no—
914C2×D3—61no—
915C2×D3—61no—
916C2×D3—61no—
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—121no—
936C2×D3—121no—
937C3×C4—22no—
938C3×C4—21no—
939C3×C4—21no—
940C3×C4—21no—
941C3×C4—21no—
942C3×C4—21no—
943C3×C4—21no—
944C3×C4—21no—
945C3×C4—21no—
946C3×C4—21no—
947C3×C4—41no—
948C3×C4—41no—
949C3×C4—41no—
950C3×C4—41no—
951C3×C4—41no—
952C3×C4—41no—
953C3×C4—41no—
954C3×C4—41no—
955C3×C4—42no—
956C3×C4—81no—
957C3×C4—81no—
958C3×C4—92no—
959C3×C4—181no—
960C3×C4—181no—
961C3×C4—181no—
962C3×C4—181no—
963C3×C4—181no—
964C3×C4—181no—
965C3×C4—181no—
966Dic3—32no—
967Dic3—32no—
968Dic3—62no—
969Dic3—61no—
970Dic3—61no—
971Dic3—61no—
972Dic3—61no—
973Dic3—61no—
974Dic3—61no—
975Dic3—61no—
976Dic3—61no—
977Dic3—61no—
978Dic3—61no—
979Dic3—61no—
980Dic3—61no—
981Dic3—61no—
982Dic3—61no—
983Dic3—121no—
984Dic3—121no—
985Dic3—121no—
986Dic3—121no—
987Dic3—121no—
988Dic3—121no—
989Dic3—121no—
990C32—21no—
991C32—21no—
992C32—21no—
993C32—41no—
994C32#551411yescharacteristic, complemented
995C32#566111yescharacteristic, complemented
996C32#570911yescharacteristic, complemented
997C23—91no—
998C23—91no—
999C23—91no—
1000C23—91no—
1001D4—361no—
1002D4—542no—
1003D4—542no—
1004D4—542no—
1005D4—542no—
1006D4—1081no—
1007C2×C4—91no—
1008C2×C4—91no—
1009C2×C4—91no—
1010C2×C4—91no—
1011C2×C4—91no—
1012C2×C4—91no—
1013C2×C4—91no—
1014C2×C4—91no—
1015C2×C4—182no—
1016C2×C4—361no—
1017C2×C4—361no—
1018C2×C4—361no—
1019C2×C4—542no—
1020C2×C4—1081no—
1021C2×C4C2×#111311yescharacteristic
1022C2×C4C2×#111311yescharacteristic
1023C2×C4C2×#111311yescharacteristic
1024C2×C3—21no—
1025C2×C3—21no—
1026C2×C3—21no—
1027C2×C3—21no—
1028C2×C3—21no—
1029C2×C3—21no—
1030C2×C3—21no—
1031C2×C3—21no—
1032C2×C3—21no—
1033C2×C3—41no—
1034C2×C3—41no—
1035C2×C3—41no—
1036C2×C3—182no—
1037C2×C3—361no—
1038C2×C3—361no—
1039C2×C3—361no—
1040C2×C3D3×#23511yescharacteristic
1041C2×C3D3×#23511yescharacteristic
1042C2×C3#6430611yescharacteristic
1043C2×C3#6431311yescharacteristic
1044C2×C3#6431411yescharacteristic
1045C2×C3#6431411yescharacteristic
1046C2×C3D3×#23911yescharacteristic
1047C2×C3D3×#23911yescharacteristic
1048C2×C3#6431911yescharacteristic
1049D3—64no—
1050D3—62no—
1051D3—62no—
1052D3—122no—
1053D3—121no—
1054D3—121no—
1055D3—121no—
1056D3—121no—
1057D3—121no—
1058D3—121no—
1059D3—241no—
1060D3—241no—
1061C22—92no—
1062C22—181no—
1063C22—181no—
1064C22—181no—
1065C22—181no—
1066C22—181no—
1067C22—181no—
1068C22—181no—
1069C22—181no—
1070C22—181no—
1071C22—181no—
1072C22—181no—
1073C22C22×#111311yescharacteristic
1074C4—21no—
1075C4—21no—
1076C4—21no—
1077C4—92no—
1078C4—181no—
1079C4—181no—
1080C4—181no—
1081C4—181no—
1082C4—181no—
1083C4—181no—
1084C4—181no—
1085C3—21no—
1086C3—21no—
1087C3—21no—
1088C3—41no—
1089C3#1059447311yescharacteristic, complemented
1090C3#1059454411yescharacteristic, complemented
1091C3#1059454511yescharacteristic, complemented
1092C2—182no—
1093C2—361no—
1094C2—361no—
1095C2—361no—
1096C2#1172461811yescharacteristic
1097C2#1172462311yescharacteristic
1098C2#1172462611yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC33×C4⋊C4C22
hypercenterC4⋊C4#1113
hypocenterC33#553
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×#64107C2semidirect
2. C3×#64103C2semidirect
3. C3×C4⋊C4×C3⋊D3C2semidirect
4. #11723696C2semidirect
5. #11723695C2semidirect
6. #11723695C2semidirect
7. C4×#6295C2semidirect
8. #11723690C2semidirect
9. #11723687C2semidirect
10. #11723684C2semidirect
11. #11723684C2semidirect
12. #11723684C2semidirect
13. #11723683C2semidirect
14. #11723675C2semidirect
15. #11723669C2semidirect
54. #64107D3semidirect
55. #64103D3semidirect
56. C4⋊C4×C3⋊D3D3semidirect
699. C33#553semidirect
994. C32#5514semidirect
995. C32#5661semidirect
996. C32#5709semidirect
1089. C3#10594473semidirect
1090. C3#10594544semidirect
1091. C3#10594545semidirect

Maximal subgroups

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

subgroupindex
C3×#641072
C3×#641032
C3×C4⋊C4×C3⋊D32
#117236962
#117236952
C4×#62952
#117236902
#117236872
#117236842
#117236832
#117236752
#117236692
#105945453
#105945443
#105944733