Finite Group Databasebeta

← #13168457

Subgroups — #13168457

Order 1728.

1188 conjugacy classes of subgroups.

The subgroup lattice has 1098 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723686C211yesmaximal, characteristic, complemented
2#11723515C211yesmaximal, characteristic, complemented
3#11723430C211yesmaximal, characteristic, complemented
4#11723400C211yesmaximal, characteristic, complemented
5C3×#63910C211yesmaximal, characteristic, complemented
6C3×#63879C211yesmaximal, characteristic, complemented
7C3×D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
8#11723023C211yesmaximal, characteristic, complemented
9#11722986C211yesmaximal, characteristic, complemented
10#11722956C211yesmaximal, characteristic, complemented
11#11722956C211yesmaximal, characteristic, complemented
12#11722936C211yesmaximal, characteristic, complemented
13#11722930C211yesmaximal, characteristic, complemented
14#11722927C211yesmaximal, characteristic, complemented
15#11722915C211yesmaximal, characteristic, complemented
16#10595028—31nomaximal
17#10594560—31nomaximal
18#10594198—31nomaximal
19C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
20C2×C32×C4×D3C2211yescharacteristic
21C2×#6294C2211yescharacteristic
22C2×#6290C2211yescharacteristic
23C2×#6290C2211yescharacteristic
24C2×C3×#626C2211yescharacteristic
25C2×C3×#626C2211yescharacteristic
26C2×C3×#625C2211yescharacteristic
27C2×C3×#624C2211yescharacteristic
28C2×C3×D3×Dic3C2211yescharacteristic
29C2×C3×D3×Dic3C2211yescharacteristic
30C2×C3×D3×Dic3C2211yescharacteristic
31C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic
32C3×#3750C2211yescharacteristic
33C3×#3750C2211yescharacteristic
34C32×(C2×D3)⋊C4C2211yescharacteristic
35C32×Dic3⋊C4C2211yescharacteristic
36#88814C2211yescharacteristic
37#88814C2211yescharacteristic
38#88814C2211yescharacteristic
39#88806C2211yescharacteristic
40#88806C2211yescharacteristic
41Dic3⋊(C3⋊Dic3)C2211yescharacteristic
42Dic3⋊(C3⋊Dic3)C2211yescharacteristic
43#88803C2211yescharacteristic
44#88803C2211yescharacteristic
45(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
46(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
47Dic3×C3⋊Dic3C2211yescharacteristic
48Dic3×C3⋊Dic3C2211yescharacteristic
49C3×#3724C2211yescharacteristic
50C3×Dic3⋊Dic3C2211yescharacteristic
51C3×#3722C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64139—31no—
55#64099—31no—
56#64088—31no—
57C3×C4×#67—31no—
58C2×C3×Dic3⋊C4—31no—
59C3×#895—31no—
60C3×D3×C4⋊C4—31no—
61C3×#884—31no—
62C3×#67⋊C4—31no—
63#63978—31no—
64#63978—31no—
65Dic3×#67—31no—
66#63970—31no—
67#63970—31no—
68#63961—31no—
69#63952—31no—
70#63952—31no—
71#63910D311yescharacteristic, complemented
72#63908—31no—
73#63908—31no—
74#63908—31no—
75#63908—31no—
76#63908—61no—
77#63904—31no—
78#63902—31no—
79C4×#625—31no—
80#63898—31no—
81#63897—31no—
82#63884—31no—
83#63884—31no—
84#63884—31no—
85#63879—31no—
86#63879—31no—
87#63879D311yescharacteristic, complemented
88D3×Dic3⋊C4D311yescharacteristic, complemented
89#63868—31no—
90#63861—31no—
91#63861—31no—
92#63861—31no—
93#63861—61no—
94#63859—31no—
95#63855—31no—
96#63850—31no—
97#63845—31no—
98#63845—31no—
99#63845—61no—
100#63841—31no—
101#63836—31no—
102C22×C3×C3⋊D3C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C32×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
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C3×C4⋊(C3⋊D3)—41no—
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C32×C4×D3—41no—
119#6294—41no—
120#6290—22no—
121#6290—22no—
122C3×#626—22no—
123C3×#626—41no—
124C3×#625—22no—
125C3×#624—22no—
126C3×D3×Dic3—22no—
127C3×D3×Dic3—41no—
128C3×D3×Dic3—41no—
129#5614—91no—
130#5540—91no—
131#5514—91no—
132C22×C32×C4—31no—
133C2×#638—31no—
134C2×#638—31no—
135C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
136C2×C3×#67—31no—
137C2×C3×#67—31no—
138C2×C3×#67—31no—
139C2×C3×#67—31no—
140C22×C3×Dic3—31no—
141C22×C3×Dic3—31no—
142C22×C3×Dic3—31no—
143C2×C3×D12—31no—
144C2×C3×D12—31no—
145C2×C3×D12—31no—
146C2×C3×D12—31no—
147C2×C3×D12—61no—
148C2×C3×C4×D3—21no—
149C2×C3×C4×D3—31no—
150C2×C3×C4×D3—31no—
151C2×C3×C4×D3—31no—
152C2×C3×C4×D3—31no—
153C2×C3×C4×D3—31no—
154C2×C3×C4×D3C2×D311yescharacteristic
155C2×C3×C4×D3C2×D311yescharacteristic
156C2×#626C2×D311yescharacteristic
157C2×#626C2×D311yescharacteristic
158C2×#625—31no—
159C2×#625—31no—
160C2×#625—31no—
161C2×#625—31no—
162C2×#625—61no—
163C2×#625—61no—
164C2×#625C2×D311yescharacteristic
165C2×#624—31no—
166C2×#624C2×D311yescharacteristic
167C2×D3×Dic3—31no—
168C2×D3×Dic3—31no—
169C2×D3×Dic3C2×D311yescharacteristic
170C2×D3×Dic3C2×D311yescharacteristic
171C2×D3×Dic3C2×D311yescharacteristic
172C32×C4⋊C4—31no—
173C32×C22⋊C4—31no—
174#3757—31no—
175#3757—31no—
176#3752—31no—
177#3752—31no—
178C4⋊(C3⋊Dic3)—31no—
179C4⋊(C3⋊Dic3)—31no—
180C4⋊(C3⋊Dic3)—31no—
181C4⋊(C3⋊Dic3)—31no—
182C4⋊(C3⋊Dic3)—31no—
183C4⋊(C3⋊Dic3)—61no—
184C4⋊(C3⋊Dic3)—61no—
185C4⋊(C3⋊Dic3)—61no—
186C4⋊(C3⋊Dic3)—121no—
187#3750—31no—
188#3750—31no—
189#3750C2×D311yescharacteristic
190#3750C2×D311yescharacteristic
191C4×C3⋊Dic3—31no—
192C4×C3⋊Dic3—31no—
193C3×#217—31no—
194C3×(C2×D3)⋊C4—21no—
195C3×(C2×D3)⋊C4—31no—
196C3×(C2×D3)⋊C4—31no—
197C3×(C2×D3)⋊C4—31no—
198C3×(C2×D3)⋊C4C2×D311yescharacteristic
199C3×(C2×D3)⋊C4C2×D311yescharacteristic
200C3×C4⋊Dic3—31no—
201C3×Dic3⋊C4—21no—
202C3×Dic3⋊C4—31no—
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—61no—
210C3×Dic3⋊C4—61no—
211C3×Dic3⋊C4C2×D311yescharacteristic
212C3×Dic3⋊C4C2×D311yescharacteristic
213C3×C4×Dic3—31no—
214C3×C4×Dic3—31no—
215#3724—31no—
216#3724—31no—
217#3724—31no—
218#3724—31no—
219#3724—61no—
220#3724—61no—
221#3724C2×D311yescharacteristic
222Dic3⋊Dic3—31no—
223Dic3⋊Dic3—31no—
224Dic3⋊Dic3—31no—
225Dic3⋊Dic3—31no—
226Dic3⋊Dic3—61no—
227Dic3⋊Dic3—61no—
228Dic3⋊Dic3C2×D311yescharacteristic
229#3722—31no—
230#3722—31no—
231#3722—31no—
232#3722C2×D311yescharacteristic
233(C2×D3)⋊Dic3—31no—
234(C2×D3)⋊Dic3—31no—
235(C2×D3)⋊Dic3—31no—
236(C2×D3)⋊Dic3—31no—
237(C2×D3)⋊Dic3—31no—
238(C2×D3)⋊Dic3—31no—
239(C2×D3)⋊Dic3—31no—
240(C2×D3)⋊Dic3—31no—
241(C2×D3)⋊Dic3—31no—
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—61no—
248(C2×D3)⋊Dic3—61no—
249(C2×D3)⋊Dic3—61no—
250(C2×D3)⋊Dic3—61no—
251(C2×D3)⋊Dic3C2×D311yescharacteristic
252Dic32—31no—
253Dic32—31no—
254Dic32—31no—
255Dic32—31no—
256Dic32—61no—
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×C32×D3—21no—
267C2×C32×D3—21no—
268C2×C32×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—
278C3×C3⋊Dic3—21no—
279C32×Dic3—21no—
280C32×Dic3—21no—
281C32×Dic3—21no—
282C32×Dic3#4112yes—
283C3×#121—91no—
284C3×C4×D4—91no—
285C2×C3×C4⋊C4—91no—
286#939—91no—
287#939—91no—
288#938—91no—
289#938—91no—
290#938—91no—
291#935—91no—
292#935—91no—
293D4×Dic3—91no—
294#930—91no—
295#930—91no—
296#930—91no—
297#930—91no—
298#930—181no—
299#929—91no—
300C4×#67—31no—
301C4×#67—91no—
302C4×#67—91no—
303C4×#67—91no—
304C4×#67—91no—
305#926—91no—
306C2×Dic3⋊C4—31no—
307#898—91no—
308#898—91no—
309#895—31no—
310#894—91no—
311#894—91no—
312#894—91no—
313#893—91no—
314#892—91no—
315D3×C4⋊C4—31no—
316#890—91no—
317#890—91no—
318#890—181no—
319#889—91no—
320#884—31no—
321#67⋊C4—31no—
322#67⋊C4—91no—
323#67⋊C4—91no—
324#67⋊C4—91no—
325#879—91no—
326#879—91no—
327#879—91no—
328#879—181no—
329#876—91no—
330#872—91no—
331C23×C32—31no—
332C23×C32—31no—
333C22×C3⋊D3C22×D311yescharacteristic
334C22×C3⋊D3C22×D311yescharacteristic
335C22×C3×D3—21no—
336C22×C3×D3—21no—
337C22×C3×D3—31no—
338C22×C3×D3—31no—
339C22×C3×D3—31no—
340C22×C3×D3—31no—
341C22×C3×D3—61no—
342C22×C3×D3—61no—
343C22×C3×D3C22×D311yescharacteristic
344C22×C3×D3C22×D311yescharacteristic
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—41no—
355C2×C32×C4—121no—
356C2×C32×C4C22×D311yescharacteristic
357C2×C32×C4C22×D311yescharacteristic
358C2×C32×C4C22×D311yescharacteristic
359#638—62no—
360#638—62no—
361C2×C3⋊Dic3—31no—
362C2×C3⋊Dic3—31no—
363C2×C3⋊Dic3—31no—
364C2×C3⋊Dic3—31no—
365C2×C3⋊Dic3—31no—
366C2×C3⋊Dic3—31no—
367C2×C3⋊Dic3—61no—
368C2×C3⋊Dic3—61no—
369C2×C3⋊Dic3—61no—
370C2×C3⋊Dic3—61no—
371C2×C3⋊Dic3—61no—
372C2×C3⋊Dic3—61no—
373C2×C3⋊Dic3—121no—
374C2×C3⋊Dic3—121no—
375C2×C3⋊Dic3C22×D311yescharacteristic
376C2×C3⋊Dic3C22×D311yescharacteristic
377C2×C3⋊Dic3C22×D311yescharacteristic
378C2×C3⋊Dic3C22×D311yescharacteristic
379C4⋊(C3⋊D3)—41no—
380C3×#67—62no—
381C3×#67—62no—
382C3×#67—62no—
383C3×#67—121no—
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—31no—
395C2×C3×Dic3—31no—
396C2×C3×Dic3—61no—
397C2×C3×Dic3—61no—
398C2×C3×Dic3—61no—
399C2×C3×Dic3—61no—
400C2×C3×Dic3—62no—
401C2×C3×Dic3—121no—
402C2×C3×Dic3—121no—
403C2×C3×Dic3C22×D311yescharacteristic
404C2×C3×Dic3C22×D311yescharacteristic
405C2×C3×Dic3C22×D311yescharacteristic
406C2×C3×Dic3C22×D311yescharacteristic
407C2×C3×Dic3C22×D311yescharacteristic
408C2×C3×Dic3C22×D311yescharacteristic
409C2×C3×Dic3C22×D311yescharacteristic
410C2×C3×Dic3C22×D311yescharacteristic
411C3×D12—62no—
412C3×D12—121no—
413C3×D12—121no—
414C3×D12—122no—
415C3×D12—121no—
416C3×C4×D3—41no—
417C3×C4×D3—41no—
418C3×C4×D3—42no—
419C3×C4×D3—62no—
420C3×C4×D3—62no—
421C3×C4×D3—62no—
422C3×C4×D3—121no—
423C3×C4×D3—121no—
424#626—22no—
425#626—41no—
426#625—22no—
427#625—62no—
428#625—62no—
429#625—62no—
430#625—62no—
431#625—122no—
432#625—122no—
433#624—22no—
434#624—121no—
435D3×Dic3—22no—
436D3×Dic3—41no—
437D3×Dic3—41no—
438D3×Dic3—121no—
439D3×Dic3—121no—
440#553—271noSylow
441C2×C33C2×#4111yescharacteristic
442C2×C33C2×#4111yescharacteristic
443C2×C33H(5,𝔽2)11yescharacteristic
444C3×C3⋊D3—41no—
445C3×C3⋊D3—41no—
446C32×D3—22no—
447C32×D3—41no—
448C2×C3×D4—91no—
449C2×C3×D4—91no—
450C2×C3×D4—91no—
451C2×C3×D4—91no—
452C22×C3×C4—31no—
453C22×C3×C4—31no—
454C22×C3×C4—61no—
455C22×C3×C4—91no—
456C22×C3×C4—91no—
457C22×C3×C4—91no—
458C22×C3×C4—91no—
459C2×#67—31no—
460C2×#67—31no—
461C2×#67—31no—
462C2×#67—31no—
463C2×#67—91no—
464C2×#67—91no—
465C2×#67—91no—
466C2×#67—91no—
467C2×#67—91no—
468C2×#67—91no—
469C2×#67—181no—
470C2×#67—181no—
471C22×Dic3—31no—
472C22×Dic3—31no—
473C22×Dic3—31no—
474C22×Dic3—91no—
475C2×D12—31no—
476C2×D12—31no—
477C2×D12—31no—
478C2×D12—31no—
479C2×D12—61no—
480C2×C4×D3—31no—
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×D3D3211yescharacteristic
488C3×C4⋊C4—31no—
489C3×C4⋊C4—31no—
490C3×C4⋊C4—61no—
491C3×C4⋊C4—91no—
492C3×C4⋊C4—91no—
493C3×C4⋊C4—91no—
494C3×C4⋊C4—91no—
495C3×C22⋊C4—31no—
496C3×C22⋊C4—31no—
497C3×C22⋊C4—61no—
498C3×C22⋊C4—91no—
499C3×C22⋊C4—91no—
500C3×C42—91no—
501#217—31no—
502#217—91no—
503#217—91no—
504#217—91no—
505#217—91no—
506#217—91no—
507#217—91no—
508#217—91no—
509#217—91no—
510#217—91no—
511#217—181no—
512#217—181no—
513(C2×D3)⋊C4—31no—
514(C2×D3)⋊C4—31no—
515(C2×D3)⋊C4—31no—
516(C2×D3)⋊C4—91no—
517(C2×D3)⋊C4—91no—
518(C2×D3)⋊C4—91no—
519(C2×D3)⋊C4—91no—
520(C2×D3)⋊C4—91no—
521(C2×D3)⋊C4—91no—
522(C2×D3)⋊C4—91no—
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—181no—
529(C2×D3)⋊C4—181no—
530(C2×D3)⋊C4D3211yescharacteristic
531C4⋊Dic3—31no—
532C4⋊Dic3—91no—
533C4⋊Dic3—91no—
534C4⋊Dic3—91no—
535C4⋊Dic3—91no—
536C4⋊Dic3—91no—
537C4⋊Dic3—91no—
538C4⋊Dic3—91no—
539C4⋊Dic3—181no—
540C4⋊Dic3—181no—
541C4⋊Dic3—181no—
542C4⋊Dic3—181no—
543C4⋊Dic3—181no—
544C4⋊Dic3—361no—
545Dic3⋊C4—31no—
546Dic3⋊C4—31no—
547Dic3⋊C4—31no—
548Dic3⋊C4—31no—
549Dic3⋊C4—31no—
550Dic3⋊C4—31no—
551Dic3⋊C4—31no—
552Dic3⋊C4—61no—
553Dic3⋊C4—61no—
554Dic3⋊C4—91no—
555Dic3⋊C4—91no—
556Dic3⋊C4—91no—
557Dic3⋊C4—91no—
558Dic3⋊C4—91no—
559Dic3⋊C4—91no—
560Dic3⋊C4—91no—
561Dic3⋊C4—91no—
562Dic3⋊C4—181no—
563Dic3⋊C4—181no—
564Dic3⋊C4D3211yescharacteristic
565C4×Dic3—31no—
566C4×Dic3—31no—
567C4×Dic3—91no—
568C4×Dic3—91no—
569C4×Dic3—91no—
570C4×Dic3—91no—
571C4×Dic3—91no—
572C4×Dic3—91no—
573C4×Dic3—181no—
574C4×Dic3—181no—
575C22×C32—21no—
576C22×C32—21no—
577C22×C32—21no—
578C22×C32—32no—
579C22×C32—41no—
580C22×C32—61no—
581C22×C32—61no—
582C22×C32—61no—
583C22×C32—61no—
584C22×C32—61no—
585C22×C32C23×D311yescharacteristic
586C22×C32C23×D311yescharacteristic
587C22×C32C23×D311yescharacteristic
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—21no—
595C2×C3×D3—21no—
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—21no—
603C2×C3×D3—21no—
604C2×C3×D3—22no—
605C2×C3×D3—41no—
606C2×C3×D3—41no—
607C2×C3×D3—41no—
608C2×C3×D3—41no—
609C2×C3×D3—41no—
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—121no—
623C2×C3×D3—121no—
624C2×C3×D3—121no—
625C2×C3×D3—121no—
626C2×C3×D3—121no—
627C2×C3×D3—121no—
628C2×C3×D3#23512yes—
629C2×C3×D3#23912yes—
630C32×C4—21no—
631C32×C4—22no—
632C32×C4—21no—
633C32×C4—21no—
634C32×C4—32no—
635C32×C4—41no—
636C32×C4—41no—
637C32×C4—42no—
638C32×C4—61no—
639C32×C4—61no—
640C32×C4—61no—
641C3⋊Dic3—21no—
642C3⋊Dic3—21no—
643C3⋊Dic3—21no—
644C3⋊Dic3—21no—
645C3⋊Dic3—61no—
646C3⋊Dic3—61no—
647C3⋊Dic3—61no—
648C3⋊Dic3—61no—
649C3⋊Dic3—61no—
650C3⋊Dic3—61no—
651C3⋊Dic3—121no—
652C3⋊Dic3—121no—
653C3⋊Dic3—121no—
654C3⋊Dic3—121no—
655C3⋊Dic3—121no—
656C3⋊Dic3—121no—
657C3⋊Dic3—241no—
658C3⋊Dic3—241no—
659C3×Dic3—21no—
660C3×Dic3—21no—
661C3×Dic3—21no—
662C3×Dic3—21no—
663C3×Dic3—21no—
664C3×Dic3—21no—
665C3×Dic3—22no—
666C3×Dic3—41no—
667C3×Dic3—41no—
668C3×Dic3—41no—
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#23512yes—
682C3×Dic3#23712yes—
683#126—271no—
684#126—271no—
685#125—271no—
686#123—271no—
687#123—271no—
688#121—91no—
689#121—271no—
690#121—271no—
691#121—271no—
692C4×D4—91no—
693C4×D4—271no—
694C4×D4—271no—
695C4×D4—271no—
696#117—271no—
697C2×C4⋊C4—91no—
698C33#55311yescharacteristic, complemented, Sylow
699C23×C3—31no—
700C23×C3—31no—
701C23×C3—31no—
702C23×C3—31no—
703C23×C3—61no—
704C23×C3—61no—
705C23×C3—91no—
706C23×C3—91no—
707C22×D3—31no—
708C22×D3—31no—
709C22×D3—31no—
710C22×D3—31no—
711C22×D3—61no—
712C22×D3—61no—
713C22×D3C2×D3211yescharacteristic
714C22×D3C2×D3211yescharacteristic
715C3×D4—182no—
716C3×D4—182no—
717C3×D4—361no—
718C3×D4—361no—
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—41no—
731C2×C3×C4—61no—
732C2×C3×C4—61no—
733C2×C3×C4—61no—
734C2×C3×C4—61no—
735C2×C3×C4—91no—
736C2×C3×C4—91no—
737C2×C3×C4—91no—
738C2×C3×C4—91no—
739C2×C3×C4—121no—
740C2×C3×C4—121no—
741C2×C3×C4—122no—
742C2×C3×C4—182no—
743C2×C3×C4—182no—
744C2×C3×C4—361no—
745C2×C3×C4—361no—
746C2×C3×C4C2×D3211yescharacteristic
747C2×C3×C4C2×D3211yescharacteristic
748C2×C3×C4C2×D3211yescharacteristic
749#67—62no—
750#67—62no—
751#67—62no—
752#67—121no—
753#67—182no—
754#67—182no—
755#67—182no—
756#67—182no—
757#67—182no—
758#67—182no—
759#67—362no—
760#67—362no—
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—61no—
770C2×Dic3—61no—
771C2×Dic3—61no—
772C2×Dic3—61no—
773C2×Dic3—62no—
774C2×Dic3—91no—
775C2×Dic3—91no—
776C2×Dic3—91no—
777C2×Dic3—91no—
778C2×Dic3—91no—
779C2×Dic3—91no—
780C2×Dic3—121no—
781C2×Dic3—121no—
782C2×Dic3—181no—
783C2×Dic3—181no—
784C2×Dic3—181no—
785C2×Dic3—181no—
786C2×Dic3—181no—
787C2×Dic3—181no—
788C2×Dic3—361no—
789C2×Dic3—361no—
790C2×Dic3—361no—
791C2×Dic3C2×D3211yescharacteristic
792C2×Dic3C2×D3211yescharacteristic
793C2×Dic3C2×D3211yescharacteristic
794C2×Dic3C2×D3211yescharacteristic
795D12—62no—
796D12—121no—
797D12—121no—
798D12—122no—
799D12—121no—
800C4×D3—41no—
801C4×D3—62no—
802C4×D3—62no—
803C4×D3—62no—
804C4×D3—121no—
805C4×D3—121no—
806C4×D3—361no—
807C4×D3—361no—
808C2×C32—21no—
809C2×C32—21no—
810C2×C32—21no—
811C2×C32—21no—
812C2×C32—21no—
813C2×C32—21no—
814C2×C32—21no—
815C2×C32—21no—
816C2×C32—21no—
817C2×C32—41no—
818C2×C32—41no—
819C2×C32—41no—
820C2×C32—62no—
821C2×C32—121no—
822C2×C32C2×#23511yescharacteristic
823C2×C32C2×#23511yescharacteristic
824C2×C32C2×#23711yescharacteristic
825C2×C32#100411yescharacteristic
826C2×C32#100411yescharacteristic
827C2×C32#100411yescharacteristic
828C2×C32C2×#23911yescharacteristic
829C2×C32D3×#4111yescharacteristic
830C2×C32D3×#4111yescharacteristic
831C3⋊D3—41no—
832C3⋊D3—41no—
833C3×D3—22no—
834C3×D3—22no—
835C3×D3—42no—
836C3×D3—41no—
837C3×D3—41no—
838C3×D3—81no—
839C3×D3—121no—
840C3×D3—121no—
841C3×D3—121no—
842C3×D3—121no—
843C3×D3—241no—
844C3×D3—241no—
845C2×D4—91no—
846C2×D4—91no—
847C2×D4—91no—
848C2×D4—91no—
849C2×D4—271no—
850C2×D4—271no—
851C22×C4—31no—
852C22×C4—91no—
853C22×C4—91no—
854C22×C4—91no—
855C22×C4—91no—
856C22×C4—271no—
857C4⋊C4—31no—
858C4⋊C4—91no—
859C4⋊C4—91no—
860C4⋊C4—91no—
861C4⋊C4—91no—
862C4⋊C4—271no—
863C4⋊C4—271no—
864C4⋊C4—271no—
865C4⋊C4—271no—
866C4⋊C4—271no—
867C22⋊C4—31no—
868C22⋊C4—91no—
869C22⋊C4—91no—
870C22⋊C4—271no—
871C22⋊C4—271no—
872C22⋊C4—271no—
873C22⋊C4—271no—
874C22⋊C4—271no—
875C22⋊C4—271no—
876C22⋊C4—271no—
877C42—91no—
878C42—271no—
879C42—271no—
880C22×C3—21no—
881C22×C3—21no—
882C22×C3—21no—
883C22×C3—32no—
884C22×C3—32no—
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—61no—
894C22×C3—61no—
895C22×C3—61no—
896C22×C3—61no—
897C22×C3—121no—
898C22×C3—121no—
899C22×C3—121no—
900C22×C3—121no—
901C22×C3—121no—
902C22×C3—181no—
903C22×C3—181no—
904C22×C3—181no—
905C22×C3—181no—
906C22×C3—181no—
907C22×C3—181no—
908C22×C3C22×D3211yescharacteristic
909C22×C3C22×D3211yescharacteristic
910C22×C3C22×D3211yescharacteristic
911C2×D3—21no—
912C2×D3—21no—
913C2×D3—21no—
914C2×D3—21no—
915C2×D3—21no—
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—121no—
929C2×D3—121no—
930C2×D3—121no—
931C2×D3—121no—
932C2×D3—121no—
933C2×D3—121no—
934C2×D3#379912yes—
935C3×C4—22no—
936C3×C4—21no—
937C3×C4—21no—
938C3×C4—21no—
939C3×C4—32no—
940C3×C4—32no—
941C3×C4—41no—
942C3×C4—41no—
943C3×C4—42no—
944C3×C4—62no—
945C3×C4—61no—
946C3×C4—61no—
947C3×C4—61no—
948C3×C4—61no—
949C3×C4—61no—
950C3×C4—61no—
951C3×C4—121no—
952C3×C4—121no—
953C3×C4—121no—
954C3×C4—181no—
955C3×C4—181no—
956C3×C4—181no—
957C3×C4—181no—
958Dic3—21no—
959Dic3—21no—
960Dic3—21no—
961Dic3—61no—
962Dic3—61no—
963Dic3—61no—
964Dic3—61no—
965Dic3—61no—
966Dic3—61no—
967Dic3—61no—
968Dic3—61no—
969Dic3—121no—
970Dic3—121no—
971Dic3—121no—
972Dic3—121no—
973Dic3—181no—
974Dic3—181no—
975Dic3—181no—
976Dic3—181no—
977Dic3—181no—
978Dic3—181no—
979Dic3—361no—
980Dic3—361no—
981Dic3—361no—
982Dic3—361no—
983Dic3—361no—
984Dic3—361no—
985Dic3—721no—
986Dic3—721no—
987Dic3#379512yes—
988C32—21no—
989C32—21no—
990C32—21no—
991C32—41no—
992C32#551411yescharacteristic, complemented
993C32#554011yescharacteristic, complemented
994C32#561411yescharacteristic, complemented
995C23—31no—
996C23—31no—
997C23—91no—
998C23—91no—
999D4—182no—
1000D4—182no—
1001D4—361no—
1002D4—361no—
1003D4—542no—
1004D4—542no—
1005C2×C4—31no—
1006C2×C4—31no—
1007C2×C4—31no—
1008C2×C4—31no—
1009C2×C4—91no—
1010C2×C4—91no—
1011C2×C4—91no—
1012C2×C4—91no—
1013C2×C4—121no—
1014C2×C4—182no—
1015C2×C4—182no—
1016C2×C4—271no—
1017C2×C4—271no—
1018C2×C4—361no—
1019C2×C4—361no—
1020C2×C4—1081no—
1021C2×C4D3311yescharacteristic
1022C2×C3—21no—
1023C2×C3—21no—
1024C2×C3—21no—
1025C2×C3—21no—
1026C2×C3—21no—
1027C2×C3—21no—
1028C2×C3—21no—
1029C2×C3—21no—
1030C2×C3—21no—
1031C2×C3—41no—
1032C2×C3—41no—
1033C2×C3—41no—
1034C2×C3—62no—
1035C2×C3—62no—
1036C2×C3—122no—
1037C2×C3—121no—
1038C2×C3—121no—
1039C2×C3—241no—
1040C2×C3—361no—
1041C2×C3—361no—
1042C2×C3C2×#379511yescharacteristic
1043C2×C3C2×#379911yescharacteristic
1044C2×C3D3×#23511yescharacteristic
1045C2×C3D3×#23511yescharacteristic
1046C2×C3D3×#23711yescharacteristic
1047C2×C3#6431311yescharacteristic
1048C2×C3#6431311yescharacteristic
1049C2×C3D3×#23911yescharacteristic
1050C2×C3#6433011yescharacteristic
1051D3—22no—
1052D3—41no—
1053D3—121no—
1054D3—121no—
1055D3—121no—
1056D3—121no—
1057D3—241no—
1058D3—241no—
1059C22—32no—
1060C22—61no—
1061C22—61no—
1062C22—61no—
1063C22—61no—
1064C22—61no—
1065C22—181no—
1066C22—181no—
1067C22—181no—
1068C22—181no—
1069C22—181no—
1070C22—181no—
1071C22C2×D3311yescharacteristic
1072C4—21no—
1073C4—32no—
1074C4—61no—
1075C4—61no—
1076C4—61no—
1077C4—181no—
1078C4—181no—
1079C4—181no—
1080C4—181no—
1081C4—541no—
1082C4—541no—
1083C3—21no—
1084C3—21no—
1085C3—21no—
1086C3—41no—
1087C3#1059419811yescharacteristic, complemented
1088C3#1059456011yescharacteristic, complemented
1089C3#1059502811yescharacteristic, complemented
1090C2—62no—
1091C2—121no—
1092C2—361no—
1093C2—361no—
1094C2D3×#379511yescharacteristic
1095C2D3×#379911yescharacteristic
1096C2#1172441511yescharacteristic
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. #11723686C2semidirect
2. #11723515C2semidirect
3. #11723430C2semidirect
4. #11723400C2semidirect
5. C3×#63910C2semidirect
6. C3×#63879C2semidirect
7. C3×D3×Dic3⋊C4C2semidirect
8. #11723023C2semidirect
9. #11722986C2semidirect
10. #11722956C2semidirect
11. #11722956C2semidirect
12. #11722936C2semidirect
13. #11722930C2semidirect
14. #11722927C2semidirect
15. #11722915C2semidirect
71. #63910D3semidirect
87. #63879D3semidirect
88. D3×Dic3⋊C4D3semidirect
698. C33#553semidirect
992. C32#5514semidirect
993. C32#5540semidirect
994. C32#5614semidirect
1087. C3#10594198semidirect
1088. C3#10594560semidirect
1089. C3#10595028semidirect

Maximal subgroups

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

subgroupindex
#117236862
#117235152
#117234302
#117234002
C3×#639102
C3×#638792
C3×D3×Dic3⋊C42
#117230232
#117229862
#117229562
#117229362
#117229302
#117229272
#117229152
#105950283
#105945603
#105941983