Finite Group Databasebeta

← #13168205

Subgroups — #13168205

Order 1728.

1206 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
1#11723687C211yesmaximal, characteristic, complemented
2Dic3×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
3#11723480C211yesmaximal, characteristic, complemented
4#11723400C211yesmaximal, characteristic, complemented
5C3×#63910C211yesmaximal, characteristic, complemented
6C3×#63859C211yesmaximal, characteristic, complemented
7C3×#63836C211yesmaximal, characteristic, complemented
8#11723023C211yesmaximal, characteristic, complemented
9#11722997C211yesmaximal, characteristic, complemented
10#11722967C211yesmaximal, characteristic, complemented
11#11722957C211yesmaximal, characteristic, complemented
12#11722931C211yesmaximal, characteristic, complemented
13#11722929C211yesmaximal, characteristic, complemented
14#11722928C211yesmaximal, characteristic, complemented
15#11722908C211yesmaximal, characteristic, complemented
16#10594433—31nomaximal
17#10594125—31nomaximal
18#10593937—31nomaximal
19C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
20C2×#6295C2211yescharacteristic
21C2×#6295C2211yescharacteristic
22C2×#6294C2211yescharacteristic
23C2×#6290C2211yescharacteristic
24C2×Dic3×C3⋊D3C2211yescharacteristic
25C2×Dic3×C3⋊D3C2211yescharacteristic
26C2×D3×C3⋊Dic3C2211yescharacteristic
27C2×C3×#626C2211yescharacteristic
28C2×C3×#626C2211yescharacteristic
29C2×C3×#624C2211yescharacteristic
30C2×C3×#624C2211yescharacteristic
31C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic
32C3×#3752C2211yescharacteristic
33C3×#3750C2211yescharacteristic
34C32×(C2×D3)⋊C4C2211yescharacteristic
35C32×Dic3⋊C4C2211yescharacteristic
36C32×C4×Dic3C2211yescharacteristic
37#88814C2211yescharacteristic
38#88806C2211yescharacteristic
39Dic3⋊(C3⋊Dic3)C2211yescharacteristic
40Dic3⋊(C3⋊Dic3)C2211yescharacteristic
41Dic3⋊(C3⋊Dic3)C2211yescharacteristic
42#88803C2211yescharacteristic
43#88803C2211yescharacteristic
44#88803C2211yescharacteristic
45Dic3×C3⋊Dic3C2211yescharacteristic
46C3×#3724C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×#3722C2211yescharacteristic
50C3×#3722C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64099—31no—
55#64095—31no—
56C4×C4⋊(C3⋊D3)—31no—
57C3×#895—31no—
58C3×#892—31no—
59C3×#884—31no—
60C3×#879—31no—
61C3×#876—31no—
62C3×#872—31no—
63#67⋊Dic3—31no—
64#67⋊Dic3—31no—
65#63971—31no—
66#63958—31no—
67#63912—31no—
68#63910—31no—
69#63910D311yescharacteristic, complemented
70#63908—31no—
71#63906—31no—
72#63904—31no—
73#63904—31no—
74C4×#625—31no—
75#63898—31no—
76Dic3×D12—31no—
77Dic3×D12—31no—
78Dic3×D12—31no—
79Dic3×D12—61no—
80#63891—31no—
81#63891—31no—
82#63891—31no—
83#63891—61no—
84#63890—31no—
85D3×C4⋊Dic3—31no—
86D3×C4⋊Dic3—31no—
87#63886—31no—
88#63885—31no—
89#63885—31no—
90#63883—31no—
91#63881—31no—
92#63880—31no—
93#63868—31no—
94#63861—31no—
95#63859—31no—
96#63859D311yescharacteristic, complemented
97#63853—31no—
98#63845—31no—
99#63845—31no—
100#63845—61no—
101#63836D311yescharacteristic, complemented
102C22×C3×C3⋊D3C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C3×C3⋊D3C2311yescharacteristic
105C22×C32×D3C2311yescharacteristic
106C2×C33×C4C2311yescharacteristic
107C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
108C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C3×C4⋊(C3⋊D3)—22no—
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118#6295—22no—
119#6295—41no—
120#6294—41no—
121#6290—41no—
122Dic3×C3⋊D3—41no—
123Dic3×C3⋊D3—41no—
124D3×C3⋊Dic3—41no—
125C3×#626—22no—
126C3×#626—22no—
127C3×#624—22no—
128C3×#624—22no—
129#5709—91no—
130#5618—91no—
131#5530—91no—
132C2×#638—31no—
133C22×C3⋊Dic3—31no—
134C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
135C2×C4×C3⋊D3—31no—
136C2×C4×C3⋊D3—31no—
137C2×C3×#67—31no—
138C2×C3×#67—31no—
139C2×C3×D12—31no—
140C2×C3×D12—31no—
141C2×C3×D12—31no—
142C2×C3×D12—31no—
143C2×C3×D12—61no—
144C2×C3×C4×D3—31no—
145C2×C3×C4×D3—31no—
146C2×C3×C4×D3—31no—
147C2×C3×C4×D3—31no—
148C2×#626—31no—
149C2×#626—31no—
150C2×#626—31no—
151C2×#626—31no—
152C2×#626C2×D311yescharacteristic
153C2×#626C2×D311yescharacteristic
154C2×#625—31no—
155C2×#625—31no—
156C2×#625—31no—
157C2×#625—31no—
158C2×#625—61no—
159C2×#624—31no—
160C2×#624C2×D311yescharacteristic
161C2×#624C2×D311yescharacteristic
162C2×D3×Dic3—31no—
163C2×D3×Dic3—31no—
164C2×D3×Dic3—31no—
165C2×D3×Dic3—31no—
166C2×D3×Dic3—31no—
167C2×D3×Dic3—31no—
168C2×D3×Dic3—31no—
169C2×D3×Dic3—31no—
170C2×D3×Dic3—61no—
171C2×D3×Dic3—61no—
172C2×D3×Dic3—61no—
173C32×C4⋊C4—31no—
174C32×C22⋊C4—31no—
175C32×C42—31no—
176#3752—31no—
177#3752—31no—
178#3752—31no—
179#3752C2×D311yescharacteristic
180C4⋊(C3⋊Dic3)—31no—
181C4⋊(C3⋊Dic3)—31no—
182C4⋊(C3⋊Dic3)—31no—
183C4⋊(C3⋊Dic3)—31no—
184C4⋊(C3⋊Dic3)—31no—
185C4⋊(C3⋊Dic3)—31no—
186C4⋊(C3⋊Dic3)—61no—
187C4⋊(C3⋊Dic3)—61no—
188C4⋊(C3⋊Dic3)—61no—
189C4⋊(C3⋊Dic3)—121no—
190#3750—31no—
191#3750C2×D311yescharacteristic
192C4×C3⋊Dic3—31no—
193C3×#217—31no—
194C3×#217—31no—
195C3×(C2×D3)⋊C4—21no—
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—61no—
205C3×(C2×D3)⋊C4C2×D311yescharacteristic
206C3×(C2×D3)⋊C4C2×D311yescharacteristic
207C3×C4⋊Dic3—31no—
208C3×C4⋊Dic3—31no—
209C3×Dic3⋊C4—21no—
210C3×Dic3⋊C4—31no—
211C3×Dic3⋊C4—31no—
212C3×Dic3⋊C4—31no—
213C3×Dic3⋊C4—31no—
214C3×Dic3⋊C4—31no—
215C3×Dic3⋊C4—31no—
216C3×Dic3⋊C4—61no—
217C3×Dic3⋊C4C2×D311yescharacteristic
218C3×Dic3⋊C4C2×D311yescharacteristic
219C3×C4×Dic3—21no—
220C3×C4×Dic3—31no—
221C3×C4×Dic3—31no—
222C3×C4×Dic3C2×D311yescharacteristic
223C3×C4×Dic3C2×D311yescharacteristic
224#3724—31no—
225#3724—31no—
226#3724—61no—
227#3724C2×D311yescharacteristic
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⋊Dic3—61no—
237Dic3⋊Dic3C2×D311yescharacteristic
238Dic3⋊Dic3C2×D311yescharacteristic
239#3722—31no—
240#3722C2×D311yescharacteristic
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—31no—
249(C2×D3)⋊Dic3—31no—
250(C2×D3)⋊Dic3—61no—
251(C2×D3)⋊Dic3—61no—
252(C2×D3)⋊Dic3—61no—
253(C2×D3)⋊Dic3C2×D311yescharacteristic
254(C2×D3)⋊Dic3C2×D311yescharacteristic
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#4112yes—
269C2×C32×D3—21no—
270C2×C32×D3—21no—
271C2×C32×D3—21no—
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×#121—91no—
285C3×#117—91no—
286#939—91no—
287#939—91no—
288#938—91no—
289D4×Dic3—91no—
290D4×Dic3—91no—
291D4×Dic3—91no—
292#930—91no—
293C4×#67—91no—
294C4×#67—91no—
295C2×C4⋊Dic3—91no—
296#898—91no—
297#895—31no—
298#895—91no—
299#894—91no—
300#893—91no—
301#893—91no—
302#892—31no—
303D3×C4⋊C4—91no—
304D3×C4⋊C4—91no—
305#890—91no—
306#890—91no—
307#890—181no—
308#889—91no—
309#886—91no—
310#886—91no—
311#886—91no—
312#886—181no—
313#884—31no—
314#884—91no—
315#884—91no—
316#884—91no—
317#884—91no—
318#883—91no—
319#883—91no—
320#67⋊C4—91no—
321#67⋊C4—91no—
322#879—31no—
323#879—91no—
324#876—31no—
325#876—91no—
326C4×D12—91no—
327C4×D12—91no—
328C4×D12—91no—
329C4×D12—181no—
330#872—31no—
331C23×C32—31no—
332C22×C3⋊D3C22×D311yescharacteristic
333C22×C3⋊D3C22×D311yescharacteristic
334C22×C3⋊D3C22×D311yescharacteristic
335C22×C3×D3—21no—
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—61no—
343C22×C3×D3—61no—
344C22×C3×D3—61no—
345C22×C3×D3C22×D311yescharacteristic
346C22×C3×D3C22×D311yescharacteristic
347C2×C32×C4—21no—
348C2×C32×C4—21no—
349C2×C32×C4—21no—
350C2×C32×C4—31no—
351C2×C32×C4—31no—
352C2×C32×C4—31no—
353C2×C32×C4—31no—
354C2×C32×C4—31no—
355C2×C32×C4—41no—
356C2×C32×C4C22×D311yescharacteristic
357C2×C32×C4C22×D311yescharacteristic
358C2×C32×C4C22×D311yescharacteristic
359#638—121no—
360C2×C3⋊Dic3—31no—
361C2×C3⋊Dic3—31no—
362C2×C3⋊Dic3—31no—
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—61no—
370C2×C3⋊Dic3—61no—
371C2×C3⋊Dic3—61no—
372C2×C3⋊Dic3—121no—
373C2×C3⋊Dic3—121no—
374C2×C3⋊Dic3—121no—
375C2×C3⋊Dic3C22×D311yescharacteristic
376C2×C3⋊Dic3C22×D311yescharacteristic
377C2×C3⋊Dic3C22×D311yescharacteristic
378C4⋊(C3⋊D3)—22no—
379C4×C3⋊D3—121no—
380C4×C3⋊D3—121no—
381C3×#67—62no—
382C3×#67—62no—
383C2×C3×Dic3—21no—
384C2×C3×Dic3—21no—
385C2×C3×Dic3—21no—
386C2×C3×Dic3—21no—
387C2×C3×Dic3—21no—
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—61no—
395C2×C3×Dic3—61no—
396C2×C3×Dic3—61no—
397C2×C3×Dic3C22×D311yescharacteristic
398C2×C3×Dic3C22×D311yescharacteristic
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
407C3×D12—62no—
408C3×D12—62no—
409C3×D12—64no—
410C3×D12—62no—
411C3×D12—62no—
412C3×C4×D3—62no—
413C3×C4×D3—62no—
414C3×C4×D3—62no—
415C3×C4×D3—62no—
416#626—22no—
417#626—22no—
418#626—62no—
419#626—62no—
420#626—121no—
421#626—121no—
422#625—62no—
423#625—121no—
424#625—121no—
425#625—121no—
426#625—122no—
427#624—22no—
428#624—22no—
429#624—121no—
430D3×Dic3—121no—
431D3×Dic3—121no—
432D3×Dic3—121no—
433D3×Dic3—121no—
434D3×Dic3—122no—
435D3×Dic3—122no—
436D3×Dic3—121no—
437D3×Dic3—121no—
438D3×Dic3—121no—
439D3×Dic3—121no—
440D3×Dic3—122no—
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—
448C32×D3—41no—
449C2×C3×D4—91no—
450C2×C3×D4—91no—
451C2×C3×D4—91no—
452C22×C3×C4—91no—
453C22×C3×C4—91no—
454C2×#67—31no—
455C2×#67—31no—
456C2×#67—91no—
457C2×#67—91no—
458C2×#67—91no—
459C2×#67—91no—
460C2×#67—91no—
461C2×#67—91no—
462C2×#67—91no—
463C2×#67—181no—
464C22×Dic3—91no—
465C22×Dic3—91no—
466C22×Dic3—91no—
467C22×Dic3—91no—
468C22×Dic3—91no—
469C22×Dic3—181no—
470C2×D12—31no—
471C2×D12—31no—
472C2×D12—31no—
473C2×D12—31no—
474C2×D12—61no—
475C2×D12—91no—
476C2×D12—91no—
477C2×C4×D3—31no—
478C2×C4×D3—31no—
479C2×C4×D3—31no—
480C2×C4×D3—31no—
481C2×C4×D3—91no—
482C2×C4×D3—91no—
483C2×C4×D3—91no—
484C2×C4×D3—91no—
485C2×C4×D3—91no—
486C2×C4×D3—91no—
487C2×C4×D3—91no—
488C2×C4×D3—181no—
489C2×C4×D3—181no—
490C3×C4⋊C4—31no—
491C3×C4⋊C4—31no—
492C3×C4⋊C4—61no—
493C3×C4⋊C4—91no—
494C3×C4⋊C4—91no—
495C3×C4⋊C4—91no—
496C3×C4⋊C4—91no—
497C3×C22⋊C4—31no—
498C3×C22⋊C4—31no—
499C3×C22⋊C4—61no—
500C3×C22⋊C4—91no—
501C3×C22⋊C4—91no—
502C3×C22⋊C4—91no—
503C3×C22⋊C4—91no—
504C3×C22⋊C4—91no—
505C3×C42—31no—
506C3×C42—31no—
507C3×C42—61no—
508C3×C42—91no—
509#217—31no—
510#217—31no—
511#217—91no—
512#217—91no—
513#217—91no—
514#217—91no—
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—61no—
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—181no—
533(C2×D3)⋊C4—181no—
534(C2×D3)⋊C4—181no—
535(C2×D3)⋊C4D3211yescharacteristic
536C4⋊Dic3—31no—
537C4⋊Dic3—31no—
538C4⋊Dic3—91no—
539C4⋊Dic3—91no—
540C4⋊Dic3—91no—
541C4⋊Dic3—91no—
542C4⋊Dic3—91no—
543C4⋊Dic3—91no—
544C4⋊Dic3—91no—
545C4⋊Dic3—91no—
546C4⋊Dic3—91no—
547C4⋊Dic3—181no—
548C4⋊Dic3—181no—
549C4⋊Dic3—181no—
550C4⋊Dic3—181no—
551C4⋊Dic3—181no—
552C4⋊Dic3—181no—
553C4⋊Dic3—361no—
554Dic3⋊C4—31no—
555Dic3⋊C4—31no—
556Dic3⋊C4—31no—
557Dic3⋊C4—31no—
558Dic3⋊C4—31no—
559Dic3⋊C4—31no—
560Dic3⋊C4—61no—
561Dic3⋊C4—91no—
562Dic3⋊C4—91no—
563Dic3⋊C4—91no—
564Dic3⋊C4—91no—
565Dic3⋊C4—91no—
566Dic3⋊C4—91no—
567Dic3⋊C4—181no—
568Dic3⋊C4D3211yescharacteristic
569C4×Dic3—31no—
570C4×Dic3—31no—
571C4×Dic3—91no—
572C4×Dic3—91no—
573C4×Dic3—91no—
574C4×Dic3—181no—
575C4×Dic3D3211yescharacteristic
576C22×C32—21no—
577C22×C32—21no—
578C22×C32—21no—
579C22×C32—41no—
580C22×C32—61no—
581C22×C32—61no—
582C22×C32—61no—
583C22×C32C23×D311yescharacteristic
584C22×C32C23×D311yescharacteristic
585C22×C32C23×D311yescharacteristic
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#23712yes—
595C2×C3×D3—22no—
596C2×C3×D3—21no—
597C2×C3×D3—21no—
598C2×C3×D3—21no—
599C2×C3×D3—21no—
600C2×C3×D3—21no—
601C2×C3×D3—21no—
602C2×C3×D3—32no—
603C2×C3×D3—32no—
604C2×C3×D3—41no—
605C2×C3×D3—41no—
606C2×C3×D3—62no—
607C2×C3×D3—61no—
608C2×C3×D3—61no—
609C2×C3×D3—61no—
610C2×C3×D3—61no—
611C2×C3×D3—62no—
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—61no—
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—32no—
636C32×C4—41no—
637C32×C4—41no—
638C32×C4—42no—
639C32×C4—61no—
640C32×C4—61no—
641C32×C4—61no—
642C32×C4—61no—
643C3⋊Dic3—21no—
644C3⋊Dic3—21no—
645C3⋊Dic3—21no—
646C3⋊Dic3—61no—
647C3⋊Dic3—61no—
648C3⋊Dic3—61no—
649C3⋊Dic3—61no—
650C3⋊Dic3—61no—
651C3⋊Dic3—61no—
652C3⋊Dic3—121no—
653C3⋊Dic3—121no—
654C3⋊Dic3—121no—
655C3⋊Dic3—121no—
656C3⋊Dic3—121no—
657C3⋊Dic3—121no—
658C3⋊Dic3—241no—
659C3⋊Dic3—241no—
660C3×Dic3—22no—
661C3×Dic3—21no—
662C3×Dic3—21no—
663C3×Dic3—21no—
664C3×Dic3—21no—
665C3×Dic3—21no—
666C3×Dic3—21no—
667C3×Dic3—21no—
668C3×Dic3—21no—
669C3×Dic3—22no—
670C3×Dic3—41no—
671C3×Dic3—41no—
672C3×Dic3—41no—
673C3×Dic3—61no—
674C3×Dic3—61no—
675C3×Dic3—61no—
676C3×Dic3—61no—
677C3×Dic3—61no—
678C3×Dic3—61no—
679C3×Dic3—121no—
680C3×Dic3—121no—
681C3×Dic3—121no—
682C3×Dic3#23512yes—
683C3×Dic3#23712yes—
684#126—91no—
685#126—271no—
686#125—271no—
687#123—271no—
688#123—271no—
689#121—91no—
690#121—271no—
691#121—271no—
692#121—271no—
693C4×D4—271no—
694C4×D4—271no—
695C4×D4—271no—
696C4×D4—271no—
697#117—91no—
698C2×C4⋊C4—271no—
699C33#55311yescharacteristic, complemented, Sylow
700C23×C3—31no—
701C23×C3—31no—
702C23×C3—61no—
703C23×C3—91no—
704C23×C3—91no—
705C23×C3—91no—
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×D3C2×D3211yescharacteristic
716C3×D4—182no—
717C3×D4—182no—
718C3×D4—182no—
719C2×C3×C4—21no—
720C2×C3×C4—21no—
721C2×C3×C4—21no—
722C2×C3×C4—31no—
723C2×C3×C4—31no—
724C2×C3×C4—31no—
725C2×C3×C4—31no—
726C2×C3×C4—31no—
727C2×C3×C4—31no—
728C2×C3×C4—31no—
729C2×C3×C4—31no—
730C2×C3×C4—31no—
731C2×C3×C4—31no—
732C2×C3×C4—41no—
733C2×C3×C4—61no—
734C2×C3×C4—61no—
735C2×C3×C4—61no—
736C2×C3×C4—61no—
737C2×C3×C4—61no—
738C2×C3×C4—91no—
739C2×C3×C4—91no—
740C2×C3×C4—91no—
741C2×C3×C4—182no—
742C2×C3×C4—182no—
743C2×C3×C4C2×D3211yescharacteristic
744C2×C3×C4C2×D3211yescharacteristic
745C2×C3×C4C2×D3211yescharacteristic
746#67—62no—
747#67—62no—
748#67—182no—
749#67—182no—
750#67—361no—
751#67—361no—
752#67—361no—
753#67—361no—
754#67—361no—
755#67—362no—
756C2×Dic3—31no—
757C2×Dic3—31no—
758C2×Dic3—31no—
759C2×Dic3—31no—
760C2×Dic3—31no—
761C2×Dic3—31no—
762C2×Dic3—61no—
763C2×Dic3—61no—
764C2×Dic3—61no—
765C2×Dic3—91no—
766C2×Dic3—91no—
767C2×Dic3—91no—
768C2×Dic3—91no—
769C2×Dic3—91no—
770C2×Dic3—91no—
771C2×Dic3—181no—
772C2×Dic3—181no—
773C2×Dic3—181no—
774C2×Dic3—181no—
775C2×Dic3—181no—
776C2×Dic3—181no—
777C2×Dic3—361no—
778C2×Dic3—361no—
779C2×Dic3—361no—
780C2×Dic3—361no—
781C2×Dic3—361no—
782C2×Dic3—361no—
783C2×Dic3—361no—
784C2×Dic3—362no—
785C2×Dic3C2×D3211yescharacteristic
786C2×Dic3C2×D3211yescharacteristic
787C2×Dic3C2×D3211yescharacteristic
788C2×Dic3C2×D3211yescharacteristic
789C2×Dic3C2×D3211yescharacteristic
790D12—62no—
791D12—62no—
792D12—64no—
793D12—62no—
794D12—62no—
795D12—182no—
796D12—361no—
797C4×D3—62no—
798C4×D3—62no—
799C4×D3—62no—
800C4×D3—62no—
801C4×D3—361no—
802C4×D3—361no—
803C4×D3—361no—
804C4×D3—361no—
805C4×D3—361no—
806C4×D3—361no—
807C4×D3—361no—
808C4×D3—362no—
809C4×D3—362no—
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×C32—121no—
823C2×C32C2×#23511yescharacteristic
824C2×C32C2×#23711yescharacteristic
825C2×C32C2×#23711yescharacteristic
826C2×C32D3×#4111yescharacteristic
827C2×C32D3×#4111yescharacteristic
828C2×C32D3×#4111yescharacteristic
829C2×C32#100911yescharacteristic
830C2×C32#100911yescharacteristic
831C2×C32#100911yescharacteristic
832C3⋊D3—22no—
833C3⋊D3—41no—
834C3⋊D3—41no—
835C3×D3—42no—
836C3×D3—41no—
837C3×D3—41no—
838C3×D3—62no—
839C3×D3—62no—
840C3×D3—122no—
841C3×D3—122no—
842C3×D3—121no—
843C3×D3—121no—
844C3×D3—121no—
845C3×D3—121no—
846C3×D3—241no—
847C2×D4—91no—
848C2×D4—91no—
849C2×D4—91no—
850C2×D4—271no—
851C2×D4—271no—
852C2×D4—271no—
853C22×C4—91no—
854C22×C4—91no—
855C22×C4—271no—
856C22×C4—271no—
857C22×C4—271no—
858C22×C4—271no—
859C4⋊C4—31no—
860C4⋊C4—91no—
861C4⋊C4—91no—
862C4⋊C4—91no—
863C4⋊C4—91no—
864C4⋊C4—271no—
865C4⋊C4—271no—
866C4⋊C4—271no—
867C4⋊C4—271no—
868C4⋊C4—271no—
869C22⋊C4—31no—
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—31no—
880C42—91no—
881C42—271no—
882C22×C3—21no—
883C22×C3—21no—
884C22×C3—21no—
885C22×C3—41no—
886C22×C3—62no—
887C22×C3—61no—
888C22×C3—61no—
889C22×C3—61no—
890C22×C3—61no—
891C22×C3—61no—
892C22×C3—61no—
893C22×C3—92no—
894C22×C3—121no—
895C22×C3—121no—
896C22×C3—181no—
897C22×C3—181no—
898C22×C3—181no—
899C22×C3—181no—
900C22×C3—181no—
901C22×C3—181no—
902C22×C3—181no—
903C22×C3—181no—
904C22×C3C22×D3211yescharacteristic
905C22×C3C22×D3211yescharacteristic
906C22×C3C22×D3211yescharacteristic
907C2×D3—21no—
908C2×D3—21no—
909C2×D3—21no—
910C2×D3—32no—
911C2×D3—32no—
912C2×D3—62no—
913C2×D3—61no—
914C2×D3—61no—
915C2×D3—61no—
916C2×D3—61no—
917C2×D3—62no—
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—61no—
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—32no—
942C3×C4—32no—
943C3×C4—41no—
944C3×C4—41no—
945C3×C4—42no—
946C3×C4—62no—
947C3×C4—62no—
948C3×C4—61no—
949C3×C4—61no—
950C3×C4—61no—
951C3×C4—61no—
952C3×C4—61no—
953C3×C4—61no—
954C3×C4—61no—
955C3×C4—61no—
956C3×C4—121no—
957C3×C4—121no—
958C3×C4—121no—
959C3×C4—181no—
960C3×C4—181no—
961C3×C4—181no—
962Dic3—21no—
963Dic3—21no—
964Dic3—21no—
965Dic3—21no—
966Dic3—61no—
967Dic3—61no—
968Dic3—61no—
969Dic3—61no—
970Dic3—61no—
971Dic3—61no—
972Dic3—121no—
973Dic3—121no—
974Dic3—121no—
975Dic3—181no—
976Dic3—181no—
977Dic3—181no—
978Dic3—181no—
979Dic3—181no—
980Dic3—181no—
981Dic3—361no—
982Dic3—361no—
983Dic3—361no—
984Dic3—361no—
985Dic3—361no—
986Dic3—361no—
987Dic3—721no—
988Dic3—721no—
989Dic3#379512yes—
990C32—21no—
991C32—21no—
992C32—21no—
993C32—41no—
994C32#553011yescharacteristic, complemented
995C32#561811yescharacteristic, complemented
996C32#570911yescharacteristic, complemented
997C23—31no—
998C23—91no—
999C23—91no—
1000C23—91no—
1001D4—182no—
1002D4—182no—
1003D4—182no—
1004D4—542no—
1005D4—1081no—
1006D4—1081no—
1007C2×C4—31no—
1008C2×C4—31no—
1009C2×C4—31no—
1010C2×C4—31no—
1011C2×C4—31no—
1012C2×C4—91no—
1013C2×C4—91no—
1014C2×C4—91no—
1015C2×C4—182no—
1016C2×C4—182no—
1017C2×C4—271no—
1018C2×C4—271no—
1019C2×C4—1081no—
1020C2×C4—1081no—
1021C2×C4—1081no—
1022C2×C4—1081no—
1023C2×C4D3311yescharacteristic
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—122no—
1037C2×C3—121no—
1038C2×C3—121no—
1039C2×C3—182no—
1040C2×C3—361no—
1041C2×C3—361no—
1042C2×C3C2×#379511yescharacteristic
1043C2×C3D3×#23511yescharacteristic
1044C2×C3#6430611yescharacteristic
1045C2×C3#6430811yescharacteristic
1046C2×C3#6430811yescharacteristic
1047C2×C3D3×#23711yescharacteristic
1048C2×C3D3×#23711yescharacteristic
1049C2×C3D3×#23711yescharacteristic
1050C2×C3#6432011yescharacteristic
1051D3—41no—
1052D3—62no—
1053D3—62no—
1054D3—122no—
1055D3—122no—
1056D3—121no—
1057D3—121no—
1058D3—121no—
1059D3—121no—
1060D3—241no—
1061C22—61no—
1062C22—61no—
1063C22—61no—
1064C22—92no—
1065C22—181no—
1066C22—181no—
1067C22—181no—
1068C22—181no—
1069C22—181no—
1070C22—181no—
1071C22—181no—
1072C22—181no—
1073C22C2×D3311yescharacteristic
1074C4—21no—
1075C4—32no—
1076C4—61no—
1077C4—61no—
1078C4—61no—
1079C4—61no—
1080C4—181no—
1081C4—181no—
1082C4—181no—
1083C4—541no—
1084C4—541no—
1085C3—21no—
1086C3—21no—
1087C3—21no—
1088C3—41no—
1089C3#1059393711yescharacteristic, complemented
1090C3#1059412511yescharacteristic, complemented
1091C3#1059443311yescharacteristic, complemented
1092C2—121no—
1093C2—182no—
1094C2—361no—
1095C2—361no—
1096C2D3×#379511yescharacteristic
1097C2#1172439011yescharacteristic
1098C2#1172440711yescharacteristic
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. #11723687C2semidirect
2. Dic3×C4⋊(C3⋊D3)C2semidirect
3. #11723480C2semidirect
4. #11723400C2semidirect
5. C3×#63910C2semidirect
6. C3×#63859C2semidirect
7. C3×#63836C2semidirect
8. #11723023C2semidirect
9. #11722997C2semidirect
10. #11722967C2semidirect
11. #11722957C2semidirect
12. #11722931C2semidirect
13. #11722929C2semidirect
14. #11722928C2semidirect
15. #11722908C2semidirect
69. #63910D3semidirect
96. #63859D3semidirect
101. #63836D3semidirect
699. C33#553semidirect
994. C32#5530semidirect
995. C32#5618semidirect
996. C32#5709semidirect
1089. C3#10593937semidirect
1090. C3#10594125semidirect
1091. C3#10594433semidirect

Maximal subgroups

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

subgroupindex
#117236872
Dic3×C4⋊(C3⋊D3)2
#117234802
#117234002
C3×#639102
C3×#638592
C3×#638362
#117230232
#117229972
#117229672
#117229572
#117229312
#117229292
#117229282
#117229082
#105944333
#105941253
#105939373