Finite Group Databasebeta

← #13168231

Subgroups — #13168231

Order 1728.

1272 conjugacy classes of subgroups.

The subgroup lattice has 1126 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723694C211yesmaximal, characteristic, complemented
2C4×#6292C211yesmaximal, characteristic, complemented
3#11723462C211yesmaximal, characteristic, complemented
4#11723421C211yesmaximal, characteristic, complemented
5C3×#63881C211yesmaximal, characteristic, complemented
6C3×#63880C211yesmaximal, characteristic, complemented
7C3×#63867C211yesmaximal, characteristic, complemented
8#11723025C211yesmaximal, characteristic, complemented
9#11723021C211yesmaximal, characteristic, complemented
10#11722961C211yesmaximal, characteristic, complemented
11#11722959C211yesmaximal, characteristic, complemented
12#11722959C211yesmaximal, characteristic, complemented
13#11722955C211yesmaximal, characteristic, complemented
14#11722915C211yesmaximal, characteristic, complemented
15D3×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
16#10594415—31nomaximal
17#10594218—31nomaximal
18#10593925—31nomaximal
19C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
20C2×C3×C4×C3⋊D3C2211yescharacteristic
21C2×#6295C2211yescharacteristic
22C2×#6292C2211yescharacteristic
23C2×#6292C2211yescharacteristic
24C2×#6291C2211yescharacteristic
25C2×D3×C3⋊Dic3C2211yescharacteristic
26C2×C3×#626C2211yescharacteristic
27C2×C3×#626C2211yescharacteristic
28C2×C3×#624C2211yescharacteristic
29C2×C3×D3×Dic3C2211yescharacteristic
30C2×C3×D3×Dic3C2211yescharacteristic
31C3×#3752C2211yescharacteristic
32C3×#3750C2211yescharacteristic
33C32×(C2×D3)⋊C4C2211yescharacteristic
34C32×Dic3⋊C4C2211yescharacteristic
35C32×C4×Dic3C2211yescharacteristic
36#88815C2211yescharacteristic
37#88814C2211yescharacteristic
38#88814C2211yescharacteristic
39#88807C2211yescharacteristic
40Dic3⋊(C3⋊Dic3)C2211yescharacteristic
41#88804C2211yescharacteristic
42#88804C2211yescharacteristic
43#88804C2211yescharacteristic
44#88803C2211yescharacteristic
45#88803C2211yescharacteristic
46Dic3×C3⋊Dic3C2211yescharacteristic
47C3×#3724C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×Dic3⋊Dic3C2211yescharacteristic
50C3×Dic3⋊Dic3C2211yescharacteristic
51C3×Dic3⋊Dic3C2211yescharacteristic
52C3×#3722C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64103—31no—
55#64090—31no—
56C4×C4⋊(C3⋊D3)—31no—
57C3×#893—31no—
58C3×#889—31no—
59C3×#67⋊C4—31no—
60C3×#67⋊C4—31no—
61C3×C4×D12—31no—
62C3×#870—31no—
63#63980—31no—
64#63978—31no—
65#63978—31no—
66C2×Dic3⋊Dic3—31no—
67#63910—31no—
68#63909—31no—
69#63909—31no—
70#63909—31no—
71#63906—31no—
72#63905—31no—
73C4×#626—31no—
74C4×#626—31no—
75C4×#626—61no—
76D3×C4⋊Dic3—31no—
77#63886—31no—
78#63886—31no—
79#63886—31no—
80#63886—31no—
81#63881—31no—
82#63881—31no—
83#63881—61no—
84#63881D311yescharacteristic, complemented
85#63880D311yescharacteristic, complemented
86D3×Dic3⋊C4—31no—
87#63868—31no—
88#63868—31no—
89#63867D311yescharacteristic, complemented
90#63862—31no—
91#63858—31no—
92#63855—31no—
93#63853—31no—
94#63853—31no—
95#63853—31no—
96#63853—61no—
97#63850—31no—
98#63848—31no—
99#63848—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
108C4×C3⋊(C3⋊D3)—41no—
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C3×C4×C3⋊D3—41no—
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119#6295—41no—
120#6292—22no—
121#6292—41no—
122#6291—22no—
123D3×C3⋊Dic3—41no—
124C3×#626—22no—
125C3×#626—22no—
126C3×#624—22no—
127C3×D3×Dic3—22no—
128C3×D3×Dic3—41no—
129#5695—91no—
130#5565—91no—
131#5540—91no—
132C2×#638—31no—
133C22×C3⋊Dic3—31no—
134C2×C4⋊(C3⋊D3)—31no—
135C2×C4⋊(C3⋊D3)—31no—
136C2×C4×C3⋊D3—31no—
137C2×C4×C3⋊D3—31no—
138C2×C4×C3⋊D3—31no—
139C2×C4×C3⋊D3—61no—
140C2×C4×C3⋊D3—61no—
141C2×C4×C3⋊D3—61no—
142C2×C4×C3⋊D3—121no—
143C2×C4×C3⋊D3C2×D311yescharacteristic
144C2×C3×#67—31no—
145C2×C3×#67—31no—
146C22×C3×Dic3—31no—
147C22×C3×Dic3—31no—
148C2×C3×D12—31no—
149C2×C3×D12—31no—
150C2×C3×C4×D3—31no—
151C2×C3×C4×D3—31no—
152C2×C3×C4×D3—31no—
153C2×C3×C4×D3—31no—
154C2×C3×C4×D3—31no—
155C2×C3×C4×D3—31no—
156C2×C3×C4×D3—61no—
157C2×#626—31no—
158C2×#626—31no—
159C2×#626—31no—
160C2×#626—31no—
161C2×#626—31no—
162C2×#626—31no—
163C2×#626—31no—
164C2×#626—31no—
165C2×#626—61no—
166C2×#626—61no—
167C2×#626—61no—
168C2×#626C2×D311yescharacteristic
169C2×#626C2×D311yescharacteristic
170C2×#625—31no—
171C2×#624C2×D311yescharacteristic
172C2×D3×Dic3—31no—
173C2×D3×Dic3—31no—
174C2×D3×Dic3—61no—
175C2×D3×Dic3C2×D311yescharacteristic
176C2×D3×Dic3C2×D311yescharacteristic
177C32×C4⋊C4—31no—
178C32×C22⋊C4—31no—
179C32×C42—31no—
180#3752—31no—
181#3752—31no—
182#3752—31no—
183#3752—31no—
184#3752—31no—
185#3752C2×D311yescharacteristic
186C4⋊(C3⋊Dic3)—31no—
187#3750—31no—
188#3750C2×D311yescharacteristic
189C4×C3⋊Dic3—31no—
190C3×(C2×D3)⋊C4—21no—
191C3×(C2×D3)⋊C4—31no—
192C3×(C2×D3)⋊C4—31no—
193C3×(C2×D3)⋊C4—31no—
194C3×(C2×D3)⋊C4—31no—
195C3×(C2×D3)⋊C4—61no—
196C3×(C2×D3)⋊C4C2×D311yescharacteristic
197C3×(C2×D3)⋊C4C2×D311yescharacteristic
198C3×C4⋊Dic3—31no—
199C3×C4⋊Dic3—31no—
200C3×C4⋊Dic3—31no—
201C3×C4⋊Dic3—31no—
202C3×Dic3⋊C4—21no—
203C3×Dic3⋊C4—31no—
204C3×Dic3⋊C4—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×Dic3⋊C4—61no—
212C3×Dic3⋊C4C2×D311yescharacteristic
213C3×Dic3⋊C4C2×D311yescharacteristic
214C3×C4×Dic3—21no—
215C3×C4×Dic3—31no—
216C3×C4×Dic3—31no—
217C3×C4×Dic3C2×D311yescharacteristic
218C3×C4×Dic3C2×D311yescharacteristic
219#3724—31no—
220#3724C2×D311yescharacteristic
221Dic3⋊Dic3—31no—
222Dic3⋊Dic3—31no—
223Dic3⋊Dic3—31no—
224Dic3⋊Dic3—31no—
225Dic3⋊Dic3—31no—
226Dic3⋊Dic3—31no—
227Dic3⋊Dic3—61no—
228Dic3⋊Dic3—61no—
229Dic3⋊Dic3C2×D311yescharacteristic
230Dic3⋊Dic3C2×D311yescharacteristic
231Dic3⋊Dic3C2×D311yescharacteristic
232Dic3⋊Dic3C2×D311yescharacteristic
233#3722—31no—
234#3722—31no—
235#3722—31no—
236#3722—31no—
237#3722—31no—
238#3722—31no—
239#3722—31no—
240#3722—31no—
241#3722—61no—
242#3722—61no—
243#3722—61no—
244#3722C2×D311yescharacteristic
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—
253(C2×D3)⋊Dic3—61no—
254(C2×D3)⋊Dic3—61no—
255Dic32—31no—
256Dic32—31no—
257Dic32—61no—
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×#125—91no—
284C3×C4×D4—91no—
285C3×C4×D4—91no—
286#939—91no—
287#939—91no—
288#939—91no—
289#939—91no—
290#930—91no—
291#930—91no—
292#930—91no—
293#929—91no—
294C4×#67—91no—
295#926—91no—
296C2×C4⋊Dic3—91no—
297C2×Dic3⋊C4—91no—
298#898—91no—
299#898—91no—
300#898—91no—
301#898—91no—
302#895—91no—
303#895—91no—
304#895—91no—
305#895—91no—
306#894—91no—
307#894—91no—
308#894—91no—
309#894—181no—
310#893—31no—
311#893—91no—
312#892—91no—
313D3×C4⋊C4—91no—
314#889—31no—
315#884—91no—
316#883—91no—
317#883—91no—
318#67⋊C4—31no—
319#67⋊C4—31no—
320#67⋊C4—91no—
321#67⋊C4—91no—
322#67⋊C4—181no—
323#879—91no—
324#876—91no—
325C4×D12—31no—
326C4×D12—91no—
327C4×D12—91no—
328C4×D12—181no—
329#872—91no—
330#870—31no—
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×C4C22×D311yescharacteristic
360C2×C32×C4C22×D311yescharacteristic
361C2×C32×C4C22×D311yescharacteristic
362#638—62no—
363C2×C3⋊Dic3—31no—
364C2×C3⋊Dic3—31no—
365C2×C3⋊Dic3—31no—
366C2×C3⋊Dic3—61no—
367C2×C3⋊Dic3—61no—
368C2×C3⋊Dic3—61no—
369C2×C3⋊Dic3—121no—
370C2×C3⋊Dic3—121no—
371C2×C3⋊Dic3C22×D311yescharacteristic
372C2×C3⋊Dic3C22×D311yescharacteristic
373C2×C3⋊Dic3C22×D311yescharacteristic
374C2×C3⋊Dic3C22×D311yescharacteristic
375C4⋊(C3⋊D3)—62no—
376C4⋊(C3⋊D3)—121no—
377C4×C3⋊D3—41no—
378C4×C3⋊D3—121no—
379C4×C3⋊D3—121no—
380C4×C3⋊D3—121no—
381C4×C3⋊D3—122no—
382C4×C3⋊D3—122no—
383C4×C3⋊D3—122no—
384C4×C3⋊D3—124no—
385C3×#67—62no—
386C3×#67—62no—
387C2×C3×Dic3—21no—
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—61no—
401C2×C3×Dic3—61no—
402C2×C3×Dic3—61no—
403C2×C3×Dic3—61no—
404C2×C3×Dic3—62no—
405C2×C3×Dic3—121no—
406C2×C3×Dic3C22×D311yescharacteristic
407C2×C3×Dic3C22×D311yescharacteristic
408C2×C3×Dic3C22×D311yescharacteristic
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
416C3×D12—62no—
417C3×D12—62no—
418C3×C4×D3—62no—
419C3×C4×D3—62no—
420C3×C4×D3—62no—
421C3×C4×D3—121no—
422C3×C4×D3—121no—
423C3×C4×D3—121no—
424C3×C4×D3—122no—
425#626—22no—
426#626—22no—
427#626—64no—
428#626—64no—
429#626—62no—
430#626—62no—
431#626—62no—
432#626—62no—
433#626—121no—
434#626—121no—
435#626—122no—
436#626—121no—
437#626—121no—
438#625—121no—
439#624—22no—
440D3×Dic3—22no—
441D3×Dic3—41no—
442D3×Dic3—121no—
443D3×Dic3—121no—
444D3×Dic3—122no—
445#553—271noSylow
446C2×C33C2×#4111yescharacteristic
447C2×C33C2×#4111yescharacteristic
448C2×C33H(5,𝔽2)11yescharacteristic
449C3⋊(C3⋊D3)—41no—
450C3×C3⋊D3—41no—
451C3×C3⋊D3—41no—
452C32×D3—22no—
453C2×C3×D4—91no—
454C2×C3×D4—91no—
455C22×C3×C4—91no—
456C22×C3×C4—91no—
457C22×C3×C4—91no—
458C22×C3×C4—91no—
459C2×#67—31no—
460C2×#67—31no—
461C2×#67—91no—
462C2×#67—91no—
463C2×#67—91no—
464C2×#67—91no—
465C2×#67—91no—
466C2×#67—91no—
467C2×#67—181no—
468C22×Dic3—31no—
469C22×Dic3—31no—
470C22×Dic3—91no—
471C22×Dic3—91no—
472C22×Dic3—181no—
473C2×D12—31no—
474C2×D12—31no—
475C2×D12—91no—
476C2×D12—91no—
477C2×D12—91no—
478C2×D12—91no—
479C2×D12—91no—
480C2×D12—91no—
481C2×D12—181no—
482C2×D12—181no—
483C2×C4×D3—31no—
484C2×C4×D3—31no—
485C2×C4×D3—31no—
486C2×C4×D3—31no—
487C2×C4×D3—31no—
488C2×C4×D3—31no—
489C2×C4×D3—61no—
490C2×C4×D3—91no—
491C2×C4×D3—91no—
492C2×C4×D3—91no—
493C2×C4×D3—91no—
494C2×C4×D3—181no—
495C2×C4×D3—181no—
496C2×C4×D3—181no—
497C2×C4×D3—361no—
498C3×C4⋊C4—31no—
499C3×C4⋊C4—31no—
500C3×C4⋊C4—61no—
501C3×C4⋊C4—91no—
502C3×C4⋊C4—91no—
503C3×C4⋊C4—91no—
504C3×C4⋊C4—91no—
505C3×C4⋊C4—91no—
506C3×C4⋊C4—91no—
507C3×C22⋊C4—31no—
508C3×C22⋊C4—31no—
509C3×C22⋊C4—61no—
510C3×C22⋊C4—91no—
511C3×C22⋊C4—91no—
512C3×C42—31no—
513C3×C42—31no—
514C3×C42—61no—
515C3×C42—91no—
516#217—91no—
517#217—91no—
518#217—91no—
519#217—91no—
520(C2×D3)⋊C4—31no—
521(C2×D3)⋊C4—31no—
522(C2×D3)⋊C4—31no—
523(C2×D3)⋊C4—31no—
524(C2×D3)⋊C4—61no—
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—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—181no—
543(C2×D3)⋊C4—181no—
544(C2×D3)⋊C4—181no—
545(C2×D3)⋊C4—181no—
546(C2×D3)⋊C4—181no—
547(C2×D3)⋊C4D3211yescharacteristic
548C4⋊Dic3—31no—
549C4⋊Dic3—31no—
550C4⋊Dic3—31no—
551C4⋊Dic3—31no—
552C4⋊Dic3—91no—
553C4⋊Dic3—91no—
554C4⋊Dic3—91no—
555C4⋊Dic3—91no—
556C4⋊Dic3—181no—
557Dic3⋊C4—31no—
558Dic3⋊C4—31no—
559Dic3⋊C4—31no—
560Dic3⋊C4—31no—
561Dic3⋊C4—31no—
562Dic3⋊C4—31no—
563Dic3⋊C4—31no—
564Dic3⋊C4—31no—
565Dic3⋊C4—61no—
566Dic3⋊C4—91no—
567Dic3⋊C4—91no—
568Dic3⋊C4—91no—
569Dic3⋊C4—91no—
570Dic3⋊C4—91no—
571Dic3⋊C4—181no—
572Dic3⋊C4D3211yescharacteristic
573C4×Dic3—31no—
574C4×Dic3—31no—
575C4×Dic3—91no—
576C4×Dic3—91no—
577C4×Dic3—91no—
578C4×Dic3—181no—
579C4×Dic3D3211yescharacteristic
580C22×C32—21no—
581C22×C32—21no—
582C22×C32—21no—
583C22×C32—32no—
584C22×C32—41no—
585C22×C32—61no—
586C22×C32—61no—
587C22×C32C23×D311yescharacteristic
588C22×C32C23×D311yescharacteristic
589C22×C32C23×D311yescharacteristic
590C2×C3⋊D3—21no—
591C2×C3⋊D3—21no—
592C2×C3⋊D3—21no—
593C2×C3⋊D3—21no—
594C2×C3⋊D3—21no—
595C2×C3⋊D3—21no—
596C2×C3⋊D3—61no—
597C2×C3⋊D3—61no—
598C2×C3⋊D3—61no—
599C2×C3⋊D3—62no—
600C2×C3⋊D3—62no—
601C2×C3⋊D3—62no—
602C2×C3⋊D3—61no—
603C2×C3⋊D3—61no—
604C2×C3⋊D3—61no—
605C2×C3⋊D3—61no—
606C2×C3⋊D3—61no—
607C2×C3⋊D3—61no—
608C2×C3⋊D3—121no—
609C2×C3⋊D3—121no—
610C2×C3⋊D3—121no—
611C2×C3⋊D3—121no—
612C2×C3⋊D3—121no—
613C2×C3⋊D3—121no—
614C2×C3⋊D3—122no—
615C2×C3⋊D3—122no—
616C2×C3⋊D3—122no—
617C2×C3×D3—21no—
618C2×C3×D3—21no—
619C2×C3×D3—21no—
620C2×C3×D3—21no—
621C2×C3×D3—22no—
622C2×C3×D3—41no—
623C2×C3×D3—41no—
624C2×C3×D3—62no—
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—61no—
634C2×C3×D3—61no—
635C2×C3×D3—61no—
636C2×C3×D3—61no—
637C2×C3×D3—121no—
638C2×C3×D3—121no—
639C2×C3×D3—121no—
640C2×C3×D3—121no—
641C2×C3×D3—121no—
642C2×C3×D3#23512yes—
643C2×C3×D3#23512yes—
644C32×C4—21no—
645C32×C4—22no—
646C32×C4—21no—
647C32×C4—21no—
648C32×C4—32no—
649C32×C4—41no—
650C32×C4—41no—
651C32×C4—42no—
652C32×C4—61no—
653C32×C4—61no—
654C32×C4—61no—
655C32×C4—61no—
656C3⋊Dic3—21no—
657C3⋊Dic3—21no—
658C3⋊Dic3—21no—
659C3⋊Dic3—21no—
660C3⋊Dic3—61no—
661C3⋊Dic3—62no—
662C3⋊Dic3—61no—
663C3⋊Dic3—61no—
664C3⋊Dic3—121no—
665C3⋊Dic3—121no—
666C3⋊Dic3—122no—
667C3×Dic3—21no—
668C3×Dic3—21no—
669C3×Dic3—21no—
670C3×Dic3—21no—
671C3×Dic3—21no—
672C3×Dic3—21no—
673C3×Dic3—21no—
674C3×Dic3—21no—
675C3×Dic3—22no—
676C3×Dic3—41no—
677C3×Dic3—41no—
678C3×Dic3—41no—
679C3×Dic3—41no—
680C3×Dic3—62no—
681C3×Dic3—61no—
682C3×Dic3—61no—
683C3×Dic3—61no—
684C3×Dic3—61no—
685C3×Dic3—61no—
686C3×Dic3—61no—
687C3×Dic3—61no—
688C3×Dic3—61no—
689C3×Dic3—121no—
690C3×Dic3—121no—
691C3×Dic3—121no—
692C3×Dic3#23712yes—
693C3×Dic3#23912yes—
694#126—271no—
695#126—271no—
696#125—91no—
697#123—271no—
698#123—271no—
699#121—271no—
700#121—271no—
701#121—271no—
702#121—271no—
703C4×D4—91no—
704C4×D4—91no—
705C4×D4—271no—
706C4×D4—271no—
707#117—271no—
708C2×C4⋊C4—271no—
709C33#55311yescharacteristic, complemented, Sylow
710C23×C3—31no—
711C23×C3—31no—
712C23×C3—61no—
713C23×C3—91no—
714C23×C3—91no—
715C22×D3—31no—
716C22×D3—31no—
717C22×D3—31no—
718C22×D3—31no—
719C22×D3—61no—
720C22×D3—61no—
721C22×D3—91no—
722C22×D3—91no—
723C22×D3—91no—
724C22×D3—181no—
725C22×D3—181no—
726C22×D3—181no—
727C22×D3—361no—
728C22×D3C2×D3211yescharacteristic
729C3×D4—182no—
730C3×D4—182no—
731C2×C3×C4—21no—
732C2×C3×C4—21no—
733C2×C3×C4—21no—
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—31no—
741C2×C3×C4—31no—
742C2×C3×C4—31no—
743C2×C3×C4—31no—
744C2×C3×C4—41no—
745C2×C3×C4—61no—
746C2×C3×C4—61no—
747C2×C3×C4—61no—
748C2×C3×C4—61no—
749C2×C3×C4—61no—
750C2×C3×C4—91no—
751C2×C3×C4—91no—
752C2×C3×C4—91no—
753C2×C3×C4—91no—
754C2×C3×C4—182no—
755C2×C3×C4—182no—
756C2×C3×C4—361no—
757C2×C3×C4—361no—
758C2×C3×C4C2×D3211yescharacteristic
759C2×C3×C4C2×D3211yescharacteristic
760C2×C3×C4C2×D3211yescharacteristic
761#67—62no—
762#67—62no—
763#67—182no—
764#67—182no—
765#67—184no—
766#67—182no—
767#67—361no—
768#67—361no—
769#67—361no—
770C2×Dic3—31no—
771C2×Dic3—31no—
772C2×Dic3—31no—
773C2×Dic3—31no—
774C2×Dic3—31no—
775C2×Dic3—31no—
776C2×Dic3—31no—
777C2×Dic3—31no—
778C2×Dic3—61no—
779C2×Dic3—61no—
780C2×Dic3—61no—
781C2×Dic3—61no—
782C2×Dic3—62no—
783C2×Dic3—91no—
784C2×Dic3—91no—
785C2×Dic3—91no—
786C2×Dic3—121no—
787C2×Dic3—181no—
788C2×Dic3—181no—
789C2×Dic3—181no—
790C2×Dic3—361no—
791C2×Dic3—361no—
792C2×Dic3—361no—
793C2×Dic3—362no—
794C2×Dic3C2×D3211yescharacteristic
795C2×Dic3C2×D3211yescharacteristic
796C2×Dic3C2×D3211yescharacteristic
797C2×Dic3C2×D3211yescharacteristic
798C2×Dic3C2×D3211yescharacteristic
799D12—62no—
800D12—62no—
801D12—182no—
802D12—182no—
803D12—184no—
804D12—182no—
805D12—361no—
806D12—361no—
807D12—362no—
808D12—361no—
809C4×D3—62no—
810C4×D3—62no—
811C4×D3—62no—
812C4×D3—121no—
813C4×D3—121no—
814C4×D3—121no—
815C4×D3—122no—
816C4×D3—361no—
817C4×D3—361no—
818C4×D3—361no—
819C4×D3—362no—
820C4×D3—361no—
821C4×D3—362no—
822C4×D3—362no—
823C4×D3—364no—
824C2×C32—21no—
825C2×C32—21no—
826C2×C32—21no—
827C2×C32—21no—
828C2×C32—21no—
829C2×C32—21no—
830C2×C32—21no—
831C2×C32—21no—
832C2×C32—21no—
833C2×C32—41no—
834C2×C32—41no—
835C2×C32—41no—
836C2×C32—62no—
837C2×C32C2×#23511yescharacteristic
838C2×C32C2×#23511yescharacteristic
839C2×C32C2×#23711yescharacteristic
840C2×C32#100411yescharacteristic
841C2×C32C2×#23911yescharacteristic
842C2×C32D3×#4111yescharacteristic
843C2×C32D3×#4111yescharacteristic
844C2×C32#100911yescharacteristic
845C2×C32#100911yescharacteristic
846C3⋊D3—41no—
847C3⋊D3—41no—
848C3⋊D3—122no—
849C3⋊D3—122no—
850C3⋊D3—122no—
851C3⋊D3—124no—
852C3⋊D3—121no—
853C3⋊D3—121no—
854C3⋊D3—121no—
855C3×D3—22no—
856C3×D3—22no—
857C3×D3—42no—
858C3×D3—122no—
859C3×D3—121no—
860C3×D3—121no—
861C3×D3—121no—
862C3×D3—121no—
863C3×D3—241no—
864C2×D4—91no—
865C2×D4—91no—
866C2×D4—271no—
867C2×D4—271no—
868C2×D4—271no—
869C2×D4—271no—
870C22×C4—91no—
871C22×C4—91no—
872C22×C4—91no—
873C22×C4—91no—
874C22×C4—271no—
875C22×C4—271no—
876C4⋊C4—31no—
877C4⋊C4—91no—
878C4⋊C4—91no—
879C4⋊C4—91no—
880C4⋊C4—91no—
881C4⋊C4—91no—
882C4⋊C4—91no—
883C4⋊C4—271no—
884C4⋊C4—271no—
885C4⋊C4—271no—
886C22⋊C4—31no—
887C22⋊C4—91no—
888C22⋊C4—91no—
889C22⋊C4—271no—
890C22⋊C4—271no—
891C22⋊C4—271no—
892C22⋊C4—271no—
893C22⋊C4—271no—
894C22⋊C4—271no—
895C22⋊C4—271no—
896C42—31no—
897C42—91no—
898C42—271no—
899C22×C3—21no—
900C22×C3—21no—
901C22×C3—21no—
902C22×C3—32no—
903C22×C3—32no—
904C22×C3—41no—
905C22×C3—62no—
906C22×C3—61no—
907C22×C3—61no—
908C22×C3—61no—
909C22×C3—61no—
910C22×C3—121no—
911C22×C3—121no—
912C22×C3—181no—
913C22×C3—181no—
914C22×C3—181no—
915C22×C3—181no—
916C22×C3—181no—
917C22×C3—181no—
918C22×C3C22×D3211yescharacteristic
919C22×C3C22×D3211yescharacteristic
920C22×C3C22×D3211yescharacteristic
921C2×D3—21no—
922C2×D3—21no—
923C2×D3—62no—
924C2×D3—61no—
925C2×D3—61no—
926C2×D3—61no—
927C2×D3—61no—
928C2×D3—61no—
929C2×D3—61no—
930C2×D3—61no—
931C2×D3—61no—
932C2×D3—61no—
933C2×D3—61no—
934C2×D3—61no—
935C2×D3—61no—
936C2×D3—121no—
937C2×D3—121no—
938C2×D3—121no—
939C2×D3—121no—
940C2×D3—121no—
941C2×D3—182no—
942C2×D3—182no—
943C2×D3—182no—
944C2×D3—181no—
945C2×D3—181no—
946C2×D3—181no—
947C2×D3—181no—
948C2×D3—181no—
949C2×D3—181no—
950C2×D3—181no—
951C2×D3—181no—
952C2×D3—181no—
953C2×D3—361no—
954C2×D3—361no—
955C2×D3—361no—
956C2×D3—361no—
957C2×D3—361no—
958C2×D3—361no—
959C2×D3—362no—
960C2×D3—362no—
961C2×D3—362no—
962C2×D3#379812yes—
963C3×C4—22no—
964C3×C4—21no—
965C3×C4—21no—
966C3×C4—21no—
967C3×C4—32no—
968C3×C4—32no—
969C3×C4—41no—
970C3×C4—41no—
971C3×C4—42no—
972C3×C4—62no—
973C3×C4—61no—
974C3×C4—61no—
975C3×C4—61no—
976C3×C4—61no—
977C3×C4—61no—
978C3×C4—61no—
979C3×C4—61no—
980C3×C4—61no—
981C3×C4—121no—
982C3×C4—121no—
983C3×C4—121no—
984C3×C4—121no—
985C3×C4—181no—
986C3×C4—181no—
987C3×C4—181no—
988C3×C4—181no—
989Dic3—21no—
990Dic3—21no—
991Dic3—21no—
992Dic3—21no—
993Dic3—62no—
994Dic3—61no—
995Dic3—61no—
996Dic3—61no—
997Dic3—61no—
998Dic3—61no—
999Dic3—61no—
1000Dic3—61no—
1001Dic3—61no—
1002Dic3—121no—
1003Dic3—121no—
1004Dic3—121no—
1005Dic3—182no—
1006Dic3—181no—
1007Dic3—181no—
1008Dic3—181no—
1009Dic3—361no—
1010Dic3—361no—
1011Dic3—362no—
1012Dic3#379612yes—
1013C32—21no—
1014C32—21no—
1015C32—21no—
1016C32—41no—
1017C32#554011yescharacteristic, complemented
1018C32#556511yescharacteristic, complemented
1019C32#569511yescharacteristic, complemented
1020C23—31no—
1021C23—91no—
1022C23—91no—
1023C23—271no—
1024D4—182no—
1025D4—182no—
1026D4—542no—
1027D4—542no—
1028D4—1081no—
1029D4—1081no—
1030C2×C4—31no—
1031C2×C4—31no—
1032C2×C4—31no—
1033C2×C4—31no—
1034C2×C4—31no—
1035C2×C4—91no—
1036C2×C4—91no—
1037C2×C4—91no—
1038C2×C4—91no—
1039C2×C4—182no—
1040C2×C4—182no—
1041C2×C4—271no—
1042C2×C4—361no—
1043C2×C4—361no—
1044C2×C4—1081no—
1045C2×C4—1081no—
1046C2×C4D3311yescharacteristic
1047C2×C3—21no—
1048C2×C3—21no—
1049C2×C3—21no—
1050C2×C3—21no—
1051C2×C3—21no—
1052C2×C3—21no—
1053C2×C3—21no—
1054C2×C3—21no—
1055C2×C3—21no—
1056C2×C3—41no—
1057C2×C3—41no—
1058C2×C3—41no—
1059C2×C3—62no—
1060C2×C3—62no—
1061C2×C3—122no—
1062C2×C3—361no—
1063C2×C3—361no—
1064C2×C3C2×#379611yescharacteristic
1065C2×C3C2×#379811yescharacteristic
1066C2×C3D3×#23511yescharacteristic
1067C2×C3D3×#23511yescharacteristic
1068C2×C3#6430811yescharacteristic
1069C2×C3D3×#23711yescharacteristic
1070C2×C3#6431411yescharacteristic
1071C2×C3#6431411yescharacteristic
1072C2×C3D3×#23911yescharacteristic
1073D3—22no—
1074D3—122no—
1075D3—121no—
1076D3—121no—
1077D3—121no—
1078D3—121no—
1079D3—241no—
1080D3—362no—
1081D3—362no—
1082D3—362no—
1083D3—364no—
1084D3—361no—
1085D3—361no—
1086D3—361no—
1087C22—32no—
1088C22—61no—
1089C22—61no—
1090C22—181no—
1091C22—181no—
1092C22—181no—
1093C22—181no—
1094C22—181no—
1095C22—181no—
1096C22—541no—
1097C22—541no—
1098C22—541no—
1099C22C2×D3311yescharacteristic
1100C4—21no—
1101C4—32no—
1102C4—61no—
1103C4—61no—
1104C4—61no—
1105C4—61no—
1106C4—181no—
1107C4—181no—
1108C4—181no—
1109C4—181no—
1110C4—541no—
1111C3—21no—
1112C3—21no—
1113C3—21no—
1114C3—41no—
1115C3#1059392511yescharacteristic, complemented
1116C3#1059421811yescharacteristic, complemented
1117C3#1059441511yescharacteristic, complemented
1118C2—62no—
1119C2—361no—
1120C2—361no—
1121C2—1081no—
1122C2D3×#379611yescharacteristic
1123C2D3×#379811yescharacteristic
1124C2#1172442011yescharacteristic
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. #11723694C2semidirect
2. C4×#6292C2semidirect
3. #11723462C2semidirect
4. #11723421C2semidirect
5. C3×#63881C2semidirect
6. C3×#63880C2semidirect
7. C3×#63867C2semidirect
8. #11723025C2semidirect
9. #11723021C2semidirect
10. #11722961C2semidirect
11. #11722959C2semidirect
12. #11722959C2semidirect
13. #11722955C2semidirect
14. #11722915C2semidirect
15. D3×Dic3⋊Dic3C2semidirect
84. #63881D3semidirect
85. #63880D3semidirect
89. #63867D3semidirect
709. C33#553semidirect
1017. C32#5540semidirect
1018. C32#5565semidirect
1019. C32#5695semidirect
1115. C3#10593925semidirect
1116. C3#10594218semidirect
1117. C3#10594415semidirect

Maximal subgroups

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

subgroupindex
#117236942
C4×#62922
#117234622
#117234212
C3×#638812
C3×#638802
C3×#638672
#117230252
#117230212
#117229612
#117229592
#117229552
#117229152
D3×Dic3⋊Dic32
#105944153
#105942183
#105939253