Finite Group Databasebeta

← #13168074

Subgroups — #13168074

Order 1728.

1320 conjugacy classes of subgroups.

The subgroup lattice has 1190 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723686C211yesmaximal, characteristic, complemented
2#11723532C211yesmaximal, characteristic, complemented
3#11723462C211yesmaximal, characteristic, complemented
4#11723420C211yesmaximal, characteristic, complemented
5C3×#63923C211yesmaximal, characteristic, complemented
6C3×#63899C211yesmaximal, characteristic, complemented
7C3×#63858C211yesmaximal, characteristic, complemented
8#11723027C211yesmaximal, characteristic, complemented
9#11723003C211yesmaximal, characteristic, complemented
10#11723001C211yesmaximal, characteristic, complemented
11#11722966C211yesmaximal, characteristic, complemented
12#11722959C211yesmaximal, characteristic, complemented
13#11722948C211yesmaximal, characteristic, complemented
14#11722928C211yesmaximal, characteristic, complemented
15D3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
16#10594652—31nomaximal
17#10594173—31nomaximal
18#10594127—31nomaximal
19C22×C3×D32C2211yescharacteristic
20C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
21C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
22C2×#6294C2211yescharacteristic, complemented
23C2×#6292C2211yescharacteristic
24C2×#6292C2211yescharacteristic, complemented
25C2×#6291C2211yescharacteristic
26C2×#6291C2211yescharacteristic
27C2×D3×C3⋊Dic3C2211yescharacteristic
28C2×C3×#627C2211yescharacteristic, complemented
29C2×C3×#626C2211yescharacteristic
30C2×C3×#626C2211yescharacteristic
31C2×C3×D3×Dic3C2211yescharacteristic
32C3×#3750C2211yescharacteristic, complemented
33C3×#3750C2211yescharacteristic, complemented
34C32×(C2×D3)⋊C4C2211yescharacteristic
35C32×(C2×D3)⋊C4C2211yescharacteristic
36C32×C4⋊Dic3C2211yescharacteristic, complemented
37#88814C2211yescharacteristic
38#88814C2211yescharacteristic
39#88814C2211yescharacteristic, complemented
40Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
41#88804C2211yescharacteristic, complemented
42#88804C2211yescharacteristic, complemented
43#88803C2211yescharacteristic
44#88803C2211yescharacteristic, complemented
45(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
46Dic3×C3⋊Dic3C2211yescharacteristic, complemented
47C3×#3724C2211yescharacteristic, complemented
48C3×Dic3⋊Dic3C2211yescharacteristic, complemented
49C3×#3722C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×Dic32C2211yescharacteristic, complemented
54#64104—31no—
55#64092—31no—
56#64090—31no—
57C3×#898—31no—
58C3×#896—31no—
59C3×#882—31no—
60C3×#882—31no—
61C3×#879—31no—
62C3×#878—31no—
63#63978—31no—
64#63977—31no—
65#63977—31no—
66#67⋊Dic3—31no—
67#63971—31no—
68D3×#217—31no—
69C2×(C2×D3)⋊Dic3—31no—
70#63959—31no—
71#63923—31no—
72#63923D311yescharacteristic, complemented
73D3×(C2×D3)⋊C4—31no—
74#63916—31no—
75#63916—31no—
76#63916—61no—
77#63910—31no—
78#63909—31no—
79#63907—31no—
80#63907—31no—
81#63899D311yescharacteristic, complemented
82#63897—31no—
83Dic3×D12—31no—
84#63886—31no—
85#63886—31no—
86#63884—31no—
87#63884—31no—
88#63881—31no—
89#63881—31no—
90#63881—61no—
91#63880—31no—
92#63864—31no—
93#63863—31no—
94#63862—31no—
95#63861—31no—
96#63858D311yescharacteristic, complemented
97#63853—31no—
98#63853—31no—
99#63853—61no—
100#63852—31no—
101#63848—31no—
102C22×C3⋊(C3⋊D3)C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C3×C3⋊D3C2311yescharacteristic
105C22×C32×D3C2311yescharacteristic
106C22×C32×D3C2311yescharacteristic
107C2×C3×D32—22no—
108C2×C3×D32—41no—
109C2×C3×D32—41no—
110C2×C33×C4C2311yescharacteristic
111C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
112C4×C3⋊(C3⋊D3)—41no—
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C3×C4⋊(C3⋊D3)—41no—
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122#6294—41no—
123#6292—41no—
124#6292—41no—
125#6291—22no—
126#6291—41no—
127D3×C3⋊Dic3—41no—
128C3×#627—41no—
129C3×#626—22no—
130C3×#626—41no—
131C3×D3×Dic3—41no—
132#5704—91no—
133#5644—91no—
134#5593—91no—
135C23×C3×D3—31no—
136C23×C3×D3—31no—
137C22×D32C2×D311yescharacteristic
138C2×#638—31no—
139C2×#638—31no—
140C22×C3⋊Dic3—31no—
141C2×C4⋊(C3⋊D3)—31no—
142C2×C4⋊(C3⋊D3)—31no—
143C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
144C2×C4×C3⋊D3—31no—
145C2×C4×C3⋊D3—31no—
146C2×C4×C3⋊D3—31no—
147C2×C4×C3⋊D3—61no—
148C2×C4×C3⋊D3—61no—
149C2×C4×C3⋊D3—61no—
150C2×C4×C3⋊D3—121no—
151C2×C3×#67—31no—
152C2×C3×#67—31no—
153C22×C3×Dic3—31no—
154C2×C3×D12—31no—
155C2×C3×D12—31no—
156C2×C3×D12—31no—
157C2×C3×D12—31no—
158C2×C3×D12—61no—
159C2×C3×C4×D3—31no—
160C2×C3×Dic6—31no—
161C2×C3×Dic6—31no—
162C2×#627C2×D311yescharacteristic, complemented
163C2×#626—31no—
164C2×#626—31no—
165C2×#626—31no—
166C2×#626—31no—
167C2×#626—31no—
168C2×#626—31no—
169C2×#626—31no—
170C2×#626—31no—
171C2×#626—61no—
172C2×#626—61no—
173C2×#626—61no—
174C2×#626—61no—
175C2×#626C2×D311yescharacteristic
176C2×#626C2×D311yescharacteristic
177C2×#624—31no—
178C2×D3×Dic3—31no—
179C2×D3×Dic3—31no—
180C2×D3×Dic3—31no—
181C2×D3×Dic3—31no—
182C2×D3×Dic3—61no—
183C2×D3×Dic3C2×D311yescharacteristic
184C32×C4⋊C4—31no—
185C32×C22⋊C4—31no—
186C32×C22⋊C4—31no—
187#3757—31no—
188#3752—31no—
189#3752—31no—
190#3752—31no—
191#3752—31no—
192C4⋊(C3⋊Dic3)—31no—
193#3750C2×D311yescharacteristic, complemented
194#3750C2×D311yescharacteristic, complemented
195C4×C3⋊Dic3—31no—
196C3×#217—31no—
197C3×#217—31no—
198C3×#217—31no—
199C3×(C2×D3)⋊C4—21no—
200C3×(C2×D3)⋊C4—21no—
201C3×(C2×D3)⋊C4—31no—
202C3×(C2×D3)⋊C4—31no—
203C3×(C2×D3)⋊C4—31no—
204C3×(C2×D3)⋊C4—31no—
205C3×(C2×D3)⋊C4—31no—
206C3×(C2×D3)⋊C4C2×D311yescharacteristic
207C3×(C2×D3)⋊C4C2×D311yescharacteristic
208C3×(C2×D3)⋊C4C2×D311yescharacteristic
209C3×(C2×D3)⋊C4C2×D311yescharacteristic
210C3×C4⋊Dic3—21no—
211C3×C4⋊Dic3—31no—
212C3×C4⋊Dic3C2×D311yescharacteristic, complemented
213C3×C4⋊Dic3C2×D311yescharacteristic, complemented
214C3×Dic3⋊C4—31no—
215C3×Dic3⋊C4—31no—
216C3×Dic3⋊C4—31no—
217C3×Dic3⋊C4—31no—
218C3×Dic3⋊C4—31no—
219C3×Dic3⋊C4—31no—
220C3×Dic3⋊C4—31no—
221C3×Dic3⋊C4—61no—
222C3×Dic3⋊C4—61no—
223C3×C4×Dic3—31no—
224C3×C4×Dic3—31no—
225#3724C2×D311yescharacteristic, complemented
226Dic3⋊Dic3—31no—
227Dic3⋊Dic3—31no—
228Dic3⋊Dic3—61no—
229Dic3⋊Dic3C2×D311yescharacteristic, complemented
230#3722—31no—
231#3722—31no—
232#3722—31no—
233#3722—31no—
234#3722—31no—
235#3722—31no—
236#3722—31no—
237#3722—61no—
238#3722—61no—
239#3722C2×D311yescharacteristic
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—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—61no—
253(C2×D3)⋊Dic3—61no—
254(C2×D3)⋊Dic3—61no—
255(C2×D3)⋊Dic3C2×D311yescharacteristic
256(C2×D3)⋊Dic3C2×D311yescharacteristic
257(C2×D3)⋊Dic3C2×D311yescharacteristic
258Dic32—31no—
259Dic32—31no—
260Dic32—61no—
261Dic32C2×D311yescharacteristic, complemented
262C22×C33C2411yescharacteristic
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—21no—
272C2×C32×D3—21no—
273C2×C32×D3—21no—
274C2×C32×D3—21no—
275C2×C32×D3—21no—
276C2×C32×D3—21no—
277C2×C32×D3#4112yes—
278C3×D32—44no—
279C33×C4—21no—
280C3⋊(C3⋊Dic3)—21no—
281C3×C3⋊Dic3—21no—
282C3×C3⋊Dic3—21no—
283C3×C3⋊Dic3—21no—
284C3×C3⋊Dic3—21no—
285C32×Dic3—21no—
286C32×Dic3—21no—
287C32×Dic3—21no—
288C32×Dic3—21no—
289C3×#126—91no—
290C3×C22⋊Q8—91no—
291C3×#120—91no—
292#953—91no—
293C2×#217—91no—
294#947—91no—
295#947—91no—
296#939—91no—
297#939—91no—
298#938—91no—
299#936—91no—
300#935—91no—
301D4×Dic3—91no—
302#930—91no—
303C2×(C2×D3)⋊C4—91no—
304#898—31no—
305#898—91no—
306#898—91no—
307#896—31no—
308#895—91no—
309#895—91no—
310#895—91no—
311#895—91no—
312#895—181no—
313#894—91no—
314#894—91no—
315#894—91no—
316#893—91no—
317#885—91no—
318#885—91no—
319#884—91no—
320#883—91no—
321#883—91no—
322#883—181no—
323#882—31no—
324#882—31no—
325#882—91no—
326#882—91no—
327#67⋊C4—91no—
328#67⋊C4—91no—
329#67⋊C4—91no—
330#67⋊C4—181no—
331D3×C22⋊C4—91no—
332#879—31no—
333#879—91no—
334#878—31no—
335#875—91no—
336C4×D12—91no—
337C23×C32—31no—
338C23×C32—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⋊D3—121no—
346C22×C3⋊D3C22×D311yescharacteristic
347C22×C3⋊D3C22×D311yescharacteristic
348C22×C3×D3—21no—
349C22×C3×D3—21no—
350C22×C3×D3—31no—
351C22×C3×D3—31no—
352C22×C3×D3—31no—
353C22×C3×D3—31no—
354C22×C3×D3—61no—
355C22×C3×D3—61no—
356C22×C3×D3—62no—
357C22×C3×D3—62no—
358C22×C3×D3—121no—
359C22×C3×D3—121no—
360C22×C3×D3—121no—
361C22×C3×D3—121no—
362C22×C3×D3C22×D311yescharacteristic
363C22×C3×D3C22×D311yescharacteristic
364C22×C3×D3C22×D311yescharacteristic
365C22×C3×D3C22×D311yescharacteristic
366C2×D32—22no—
367C2×D32—41no—
368C2×D32—41no—
369C2×C32×C4—21no—
370C2×C32×C4—21no—
371C2×C32×C4—21no—
372C2×C32×C4—31no—
373C2×C32×C4—31no—
374C2×C32×C4—31no—
375C2×C32×C4—31no—
376C2×C32×C4—41no—
377C2×C32×C4C22×D311yescharacteristic
378C2×C32×C4C22×D311yescharacteristic
379C2×C32×C4C22×D311yescharacteristic
380#638—62no—
381#638—121no—
382C2×C3⋊Dic3—31no—
383C2×C3⋊Dic3—31no—
384C2×C3⋊Dic3—31no—
385C2×C3⋊Dic3—61no—
386C2×C3⋊Dic3—61no—
387C2×C3⋊Dic3—61no—
388C2×C3⋊Dic3—121no—
389C2×C3⋊Dic3—121no—
390C2×C3⋊Dic3C22×D311yescharacteristic
391C2×C3⋊Dic3C22×D311yescharacteristic
392C2×C3⋊Dic3C22×D311yescharacteristic
393C2×C3⋊Dic3C22×D311yescharacteristic
394C4⋊(C3⋊D3)—41no—
395C4⋊(C3⋊D3)—121no—
396C4⋊(C3⋊D3)—121no—
397C4×C3⋊D3—121no—
398C4×C3⋊D3—121no—
399C4×C3⋊D3—121no—
400C4×C3⋊D3—122no—
401C4×C3⋊D3—122no—
402C4×C3⋊D3—122no—
403C4×C3⋊D3—124no—
404C3×#67—62no—
405C3×#67—121no—
406C2×C3×Dic3—21no—
407C2×C3×Dic3—21no—
408C2×C3×Dic3—21no—
409C2×C3×Dic3—21no—
410C2×C3×Dic3—31no—
411C2×C3×Dic3—31no—
412C2×C3×Dic3—31no—
413C2×C3×Dic3—31no—
414C2×C3×Dic3—31no—
415C2×C3×Dic3—31no—
416C2×C3×Dic3—31no—
417C2×C3×Dic3—31no—
418C2×C3×Dic3—61no—
419C2×C3×Dic3—61no—
420C2×C3×Dic3—61no—
421C2×C3×Dic3—61no—
422C2×C3×Dic3—121no—
423C2×C3×Dic3C22×D311yescharacteristic
424C2×C3×Dic3C22×D311yescharacteristic
425C2×C3×Dic3C22×D311yescharacteristic
426C2×C3×Dic3C22×D311yescharacteristic
427C2×C3×Dic3C22×D311yescharacteristic
428C2×C3×Dic3C22×D311yescharacteristic
429C2×C3×Dic3C22×D311yescharacteristic
430C2×C3×Dic3C22×D311yescharacteristic
431C3×D12—62no—
432C3×D12—121no—
433C3×D12—121no—
434C3×D12—122no—
435C3×D12—121no—
436C3×C4×D3—121no—
437C3×Dic6—121no—
438C3×Dic6—121no—
439#627—41no—
440#626—22no—
441#626—41no—
442#626—64no—
443#626—62no—
444#626—62no—
445#626—121no—
446#626—121no—
447#626—121no—
448#626—121no—
449#626—122no—
450#626—122no—
451#626—121no—
452#626—121no—
453#626—122no—
454#624—121no—
455D3×Dic3—41no—
456D3×Dic3—121no—
457D3×Dic3—121no—
458D3×Dic3—121no—
459D3×Dic3—121no—
460D3×Dic3—122no—
461#538—271noSylow
462C2×C33C2×#4111yescharacteristic
463C2×C33H(5,𝔽2)11yescharacteristic
464C2×C33H(5,𝔽2)11yescharacteristic
465C3⋊(C3⋊D3)—41no—
466C3×C3⋊D3—41no—
467C3×C3⋊D3—41no—
468C32×D3—22no—
469C32×D3—41no—
470C24×C3—91no—
471C23×D3—31no—
472C23×D3—31no—
473C2×C3×Q8—91no—
474C2×C3×D4—91no—
475C2×C3×D4—91no—
476C2×C3×D4—91no—
477C22×C3×C4—91no—
478C2×#67—31no—
479C2×#67—31no—
480C2×#67—91no—
481C2×#67—91no—
482C2×#67—91no—
483C2×#67—91no—
484C2×#67—91no—
485C2×#67—91no—
486C2×#67—181no—
487C2×#67—181no—
488C22×Dic3—31no—
489C22×Dic3—91no—
490C22×Dic3—91no—
491C22×Dic3—91no—
492C22×Dic3—181no—
493C2×D12—31no—
494C2×D12—31no—
495C2×D12—31no—
496C2×D12—31no—
497C2×D12—61no—
498C2×D12—91no—
499C2×D12—91no—
500C2×D12—91no—
501C2×D12—91no—
502C2×D12—91no—
503C2×D12—91no—
504C2×D12—181no—
505C2×D12—181no—
506C2×C4×D3—31no—
507C2×C4×D3—91no—
508C2×C4×D3—91no—
509C2×C4×D3—91no—
510C2×C4×D3—91no—
511C2×C4×D3—91no—
512C2×C4×D3—91no—
513C2×C4×D3—181no—
514C2×C4×D3—181no—
515C2×C4×D3—181no—
516C2×C4×D3—361no—
517C2×Dic6—31no—
518C2×Dic6—31no—
519C3×C4⋊C4—31no—
520C3×C4⋊C4—31no—
521C3×C4⋊C4—61no—
522C3×C4⋊C4—91no—
523C3×C4⋊C4—91no—
524C3×C4⋊C4—91no—
525C3×C4⋊C4—91no—
526C3×C22⋊C4—31no—
527C3×C22⋊C4—31no—
528C3×C22⋊C4—31no—
529C3×C22⋊C4—31no—
530C3×C22⋊C4—61no—
531C3×C22⋊C4—61no—
532C3×C22⋊C4—91no—
533C3×C22⋊C4—91no—
534C3×C22⋊C4—91no—
535C3×C22⋊C4—91no—
536C3×C42—91no—
537#217—31no—
538#217—31no—
539#217—31no—
540#217—91no—
541#217—91no—
542#217—91no—
543#217—91no—
544#217—91no—
545#217—91no—
546#217—91no—
547#217—181no—
548(C2×D3)⋊C4—31no—
549(C2×D3)⋊C4—31no—
550(C2×D3)⋊C4—31no—
551(C2×D3)⋊C4—31no—
552(C2×D3)⋊C4—31no—
553(C2×D3)⋊C4—91no—
554(C2×D3)⋊C4—91no—
555(C2×D3)⋊C4—91no—
556(C2×D3)⋊C4—91no—
557(C2×D3)⋊C4—91no—
558(C2×D3)⋊C4—91no—
559(C2×D3)⋊C4—91no—
560(C2×D3)⋊C4—91no—
561(C2×D3)⋊C4—91no—
562(C2×D3)⋊C4—91no—
563(C2×D3)⋊C4—91no—
564(C2×D3)⋊C4—91no—
565(C2×D3)⋊C4—91no—
566(C2×D3)⋊C4—91no—
567(C2×D3)⋊C4—91no—
568(C2×D3)⋊C4—91no—
569(C2×D3)⋊C4—91no—
570(C2×D3)⋊C4—181no—
571(C2×D3)⋊C4—181no—
572(C2×D3)⋊C4—181no—
573(C2×D3)⋊C4—181no—
574(C2×D3)⋊C4D3211yescharacteristic
575(C2×D3)⋊C4D3211yescharacteristic
576C4⋊Dic3—31no—
577C4⋊Dic3—91no—
578C4⋊Dic3—91no—
579C4⋊Dic3—181no—
580C4⋊Dic3D3211yescharacteristic, complemented
581Dic3⋊C4—31no—
582Dic3⋊C4—31no—
583Dic3⋊C4—31no—
584Dic3⋊C4—31no—
585Dic3⋊C4—31no—
586Dic3⋊C4—31no—
587Dic3⋊C4—31no—
588Dic3⋊C4—61no—
589Dic3⋊C4—61no—
590Dic3⋊C4—91no—
591C4×Dic3—31no—
592C4×Dic3—31no—
593C4×Dic3—91no—
594C4×Dic3—91no—
595C4×Dic3—91no—
596C4×Dic3—181no—
597C22×C32—21no—
598C22×C32—21no—
599C22×C32—21no—
600C22×C32—32no—
601C22×C32—41no—
602C22×C32—61no—
603C22×C32—61no—
604C22×C32—61no—
605C22×C32—61no—
606C22×C32—61no—
607C22×C32C23×D311yescharacteristic
608C22×C32C23×D311yescharacteristic
609C22×C32C23×D311yescharacteristic
610C2×C3⋊D3—21no—
611C2×C3⋊D3—21no—
612C2×C3⋊D3—21no—
613C2×C3⋊D3—21no—
614C2×C3⋊D3—21no—
615C2×C3⋊D3—21no—
616C2×C3⋊D3—61no—
617C2×C3⋊D3—61no—
618C2×C3⋊D3—61no—
619C2×C3⋊D3—62no—
620C2×C3⋊D3—62no—
621C2×C3⋊D3—62no—
622C2×C3⋊D3—61no—
623C2×C3⋊D3—61no—
624C2×C3⋊D3—61no—
625C2×C3⋊D3—61no—
626C2×C3⋊D3—61no—
627C2×C3⋊D3—61no—
628C2×C3⋊D3—121no—
629C2×C3⋊D3—121no—
630C2×C3⋊D3—121no—
631C2×C3⋊D3—121no—
632C2×C3⋊D3—121no—
633C2×C3⋊D3—121no—
634C2×C3⋊D3—122no—
635C2×C3⋊D3—122no—
636C2×C3⋊D3—122no—
637C2×C3×D3—21no—
638C2×C3×D3—21no—
639C2×C3×D3—21no—
640C2×C3×D3—21no—
641C2×C3×D3—21no—
642C2×C3×D3—21no—
643C2×C3×D3—21no—
644C2×C3×D3—21no—
645C2×C3×D3—21no—
646C2×C3×D3—21no—
647C2×C3×D3—22no—
648C2×C3×D3—41no—
649C2×C3×D3—41no—
650C2×C3×D3—41no—
651C2×C3×D3—41no—
652C2×C3×D3—41no—
653C2×C3×D3—61no—
654C2×C3×D3—61no—
655C2×C3×D3—61no—
656C2×C3×D3—61no—
657C2×C3×D3—61no—
658C2×C3×D3—61no—
659C2×C3×D3—61no—
660C2×C3×D3—61no—
661C2×C3×D3—61no—
662C2×C3×D3—61no—
663C2×C3×D3—61no—
664C2×C3×D3—61no—
665C2×C3×D3—121no—
666C2×C3×D3—121no—
667C2×C3×D3—121no—
668C2×C3×D3—121no—
669C2×C3×D3—121no—
670C2×C3×D3—121no—
671C2×C3×D3—124no—
672C2×C3×D3—124no—
673C2×C3×D3#23712yes—
674C2×C3×D3#23912yes—
675D32—44no—
676C32×C4—21no—
677C32×C4—22no—
678C32×C4—21no—
679C32×C4—21no—
680C32×C4—41no—
681C32×C4—41no—
682C32×C4—42no—
683C32×C4—61no—
684C32×C4—61no—
685C32×C4—61no—
686C32×C4—61no—
687C3⋊Dic3—21no—
688C3⋊Dic3—21no—
689C3⋊Dic3—21no—
690C3⋊Dic3—21no—
691C3⋊Dic3—61no—
692C3⋊Dic3—62no—
693C3⋊Dic3—61no—
694C3⋊Dic3—61no—
695C3⋊Dic3—121no—
696C3⋊Dic3—121no—
697C3⋊Dic3—122no—
698C3×Dic3—21no—
699C3×Dic3—21no—
700C3×Dic3—21no—
701C3×Dic3—21no—
702C3×Dic3—21no—
703C3×Dic3—21no—
704C3×Dic3—21no—
705C3×Dic3—21no—
706C3×Dic3—41no—
707C3×Dic3—41no—
708C3×Dic3—41no—
709C3×Dic3—41no—
710C3×Dic3—62no—
711C3×Dic3—61no—
712C3×Dic3—61no—
713C3×Dic3—61no—
714C3×Dic3—61no—
715C3×Dic3—61no—
716C3×Dic3—61no—
717C3×Dic3—61no—
718C3×Dic3—61no—
719C3×Dic3—121no—
720C3×Dic3—121no—
721C3×Dic3—121no—
722#126—91no—
723#126—271no—
724#124—271no—
725#124—271no—
726#123—271no—
727#123—271no—
728C22⋊Q8—91no—
729#121—271no—
730#121—271no—
731#121—271no—
732#120—91no—
733#120—271no—
734C4×D4—271no—
735C4×D4—271no—
736C2×C22⋊C4—271no—
737C33#53811yescharacteristic, complemented, Sylow
738C23×C3—31no—
739C23×C3—31no—
740C23×C3—31no—
741C23×C3—31no—
742C23×C3—61no—
743C23×C3—61no—
744C23×C3—91no—
745C23×C3—91no—
746C23×C3—182no—
747C23×C3—361no—
748C23×C3—361no—
749C22×D3—31no—
750C22×D3—31no—
751C22×D3—31no—
752C22×D3—31no—
753C22×D3—61no—
754C22×D3—61no—
755C22×D3—62no—
756C22×D3—62no—
757C22×D3—91no—
758C22×D3—91no—
759C22×D3—91no—
760C22×D3—121no—
761C22×D3—121no—
762C22×D3—121no—
763C22×D3—121no—
764C22×D3—181no—
765C22×D3—181no—
766C22×D3—181no—
767C22×D3—361no—
768C22×D3C2×D3211yescharacteristic
769C22×D3C2×D3211yescharacteristic
770C3×Q8—361no—
771C3×D4—182no—
772C3×D4—361no—
773C3×D4—361no—
774C2×C3×C4—21no—
775C2×C3×C4—21no—
776C2×C3×C4—21no—
777C2×C3×C4—31no—
778C2×C3×C4—31no—
779C2×C3×C4—31no—
780C2×C3×C4—31no—
781C2×C3×C4—31no—
782C2×C3×C4—31no—
783C2×C3×C4—31no—
784C2×C3×C4—31no—
785C2×C3×C4—41no—
786C2×C3×C4—61no—
787C2×C3×C4—61no—
788C2×C3×C4—61no—
789C2×C3×C4—61no—
790C2×C3×C4—91no—
791C2×C3×C4—91no—
792C2×C3×C4—91no—
793C2×C3×C4—91no—
794C2×C3×C4—361no—
795C2×C3×C4C2×D3211yescharacteristic
796C2×C3×C4C2×D3211yescharacteristic
797C2×C3×C4C2×D3211yescharacteristic
798#67—62no—
799#67—121no—
800#67—182no—
801#67—182no—
802#67—184no—
803#67—361no—
804#67—361no—
805#67—361no—
806#67—361no—
807#67—362no—
808C2×Dic3—31no—
809C2×Dic3—31no—
810C2×Dic3—31no—
811C2×Dic3—31no—
812C2×Dic3—31no—
813C2×Dic3—31no—
814C2×Dic3—31no—
815C2×Dic3—31no—
816C2×Dic3—61no—
817C2×Dic3—61no—
818C2×Dic3—61no—
819C2×Dic3—61no—
820C2×Dic3—91no—
821C2×Dic3—91no—
822C2×Dic3—91no—
823C2×Dic3—121no—
824C2×Dic3—181no—
825C2×Dic3—181no—
826C2×Dic3—181no—
827C2×Dic3—361no—
828C2×Dic3—361no—
829C2×Dic3—361no—
830C2×Dic3—361no—
831C2×Dic3—362no—
832C2×Dic3C2×D3211yescharacteristic
833C2×Dic3C2×D3211yescharacteristic
834C2×Dic3C2×D3211yescharacteristic
835C2×Dic3C2×D3211yescharacteristic
836D12—62no—
837D12—121no—
838D12—121no—
839D12—122no—
840D12—121no—
841D12—182no—
842D12—361no—
843D12—361no—
844D12—361no—
845D12—361no—
846D12—362no—
847D12—362no—
848D12—361no—
849C4×D3—121no—
850C4×D3—361no—
851C4×D3—361no—
852C4×D3—361no—
853C4×D3—361no—
854C4×D3—361no—
855C4×D3—362no—
856C4×D3—361no—
857C4×D3—362no—
858C4×D3—362no—
859C4×D3—364no—
860Dic6—121no—
861Dic6—121no—
862C2×C32—21no—
863C2×C32—21no—
864C2×C32—21no—
865C2×C32—21no—
866C2×C32—21no—
867C2×C32—21no—
868C2×C32—21no—
869C2×C32—21no—
870C2×C32—21no—
871C2×C32—41no—
872C2×C32—41no—
873C2×C32—41no—
874C2×C32—62no—
875C2×C32—121no—
876C2×C32C2×#23711yescharacteristic
877C2×C32#100411yescharacteristic
878C2×C32#100411yescharacteristic
879C2×C32#100411yescharacteristic
880C2×C32C2×#23911yescharacteristic
881C2×C32D3×#4111yescharacteristic
882C2×C32#100911yescharacteristic
883C2×C32#100911yescharacteristic
884C2×C32#100911yescharacteristic
885C3⋊D3—41no—
886C3⋊D3—41no—
887C3⋊D3—122no—
888C3⋊D3—122no—
889C3⋊D3—122no—
890C3⋊D3—124no—
891C3⋊D3—121no—
892C3⋊D3—121no—
893C3⋊D3—121no—
894C3×D3—22no—
895C3×D3—22no—
896C3×D3—42no—
897C3×D3—41no—
898C3×D3—41no—
899C3×D3—81no—
900C3×D3—121no—
901C3×D3—121no—
902C3×D3—121no—
903C3×D3—121no—
904C3×D3—241no—
905C3×D3—241no—
906C24—91no—
907C2×Q8—91no—
908C2×D4—91no—
909C2×D4—91no—
910C2×D4—91no—
911C2×D4—271no—
912C2×D4—271no—
913C2×D4—271no—
914C2×D4—271no—
915C22×C4—91no—
916C22×C4—271no—
917C22×C4—271no—
918C22×C4—271no—
919C4⋊C4—31no—
920C4⋊C4—91no—
921C4⋊C4—91no—
922C4⋊C4—91no—
923C4⋊C4—91no—
924C4⋊C4—271no—
925C22⋊C4—31no—
926C22⋊C4—31no—
927C22⋊C4—91no—
928C22⋊C4—91no—
929C22⋊C4—91no—
930C22⋊C4—91no—
931C22⋊C4—271no—
932C22⋊C4—271no—
933C22⋊C4—271no—
934C22⋊C4—271no—
935C22⋊C4—271no—
936C22⋊C4—271no—
937C22⋊C4—271no—
938C22⋊C4—271no—
939C42—91no—
940C42—271no—
941C22×C3—21no—
942C22×C3—21no—
943C22×C3—21no—
944C22×C3—32no—
945C22×C3—32no—
946C22×C3—41no—
947C22×C3—62no—
948C22×C3—61no—
949C22×C3—61no—
950C22×C3—61no—
951C22×C3—61no—
952C22×C3—61no—
953C22×C3—61no—
954C22×C3—61no—
955C22×C3—61no—
956C22×C3—61no—
957C22×C3—61no—
958C22×C3—121no—
959C22×C3—121no—
960C22×C3—121no—
961C22×C3—121no—
962C22×C3—121no—
963C22×C3—181no—
964C22×C3—181no—
965C22×C3—181no—
966C22×C3—181no—
967C22×C3—181no—
968C22×C3—181no—
969C22×C3—364no—
970C22×C3C22×D3211yescharacteristic
971C22×C3C22×D3211yescharacteristic
972C22×C3C22×D3211yescharacteristic
973C2×D3—21no—
974C2×D3—21no—
975C2×D3—21no—
976C2×D3—21no—
977C2×D3—21no—
978C2×D3—61no—
979C2×D3—61no—
980C2×D3—61no—
981C2×D3—61no—
982C2×D3—61no—
983C2×D3—61no—
984C2×D3—61no—
985C2×D3—61no—
986C2×D3—61no—
987C2×D3—61no—
988C2×D3—61no—
989C2×D3—61no—
990C2×D3—121no—
991C2×D3—121no—
992C2×D3—121no—
993C2×D3—121no—
994C2×D3—121no—
995C2×D3—121no—
996C2×D3—124no—
997C2×D3—124no—
998C2×D3—182no—
999C2×D3—182no—
1000C2×D3—182no—
1001C2×D3—181no—
1002C2×D3—181no—
1003C2×D3—181no—
1004C2×D3—181no—
1005C2×D3—181no—
1006C2×D3—181no—
1007C2×D3—181no—
1008C2×D3—181no—
1009C2×D3—181no—
1010C2×D3—361no—
1011C2×D3—361no—
1012C2×D3—361no—
1013C2×D3—361no—
1014C2×D3—361no—
1015C2×D3—361no—
1016C2×D3—362no—
1017C2×D3—362no—
1018C2×D3—362no—
1019C2×D3#379612yes—
1020C3×C4—22no—
1021C3×C4—21no—
1022C3×C4—21no—
1023C3×C4—21no—
1024C3×C4—41no—
1025C3×C4—41no—
1026C3×C4—42no—
1027C3×C4—61no—
1028C3×C4—61no—
1029C3×C4—61no—
1030C3×C4—61no—
1031C3×C4—61no—
1032C3×C4—61no—
1033C3×C4—61no—
1034C3×C4—61no—
1035C3×C4—121no—
1036C3×C4—121no—
1037C3×C4—121no—
1038C3×C4—121no—
1039C3×C4—181no—
1040C3×C4—181no—
1041C3×C4—181no—
1042C3×C4—181no—
1043Dic3—21no—
1044Dic3—21no—
1045Dic3—21no—
1046Dic3—21no—
1047Dic3—62no—
1048Dic3—61no—
1049Dic3—61no—
1050Dic3—61no—
1051Dic3—61no—
1052Dic3—61no—
1053Dic3—61no—
1054Dic3—61no—
1055Dic3—61no—
1056Dic3—121no—
1057Dic3—121no—
1058Dic3—121no—
1059Dic3—182no—
1060Dic3—181no—
1061Dic3—181no—
1062Dic3—181no—
1063Dic3—361no—
1064Dic3—361no—
1065Dic3—362no—
1066C32—21no—
1067C32—21no—
1068C32—21no—
1069C32—41no—
1070C32#559311yescharacteristic, complemented
1071C32#564411yescharacteristic, complemented
1072C32#570411yescharacteristic, complemented
1073C23—31no—
1074C23—31no—
1075C23—91no—
1076C23—91no—
1077C23—182no—
1078C23—271no—
1079C23—361no—
1080C23—361no—
1081Q8—361no—
1082D4—182no—
1083D4—361no—
1084D4—361no—
1085D4—542no—
1086D4—1081no—
1087D4—1081no—
1088D4—1081no—
1089C2×C4—31no—
1090C2×C4—31no—
1091C2×C4—31no—
1092C2×C4—31no—
1093C2×C4—91no—
1094C2×C4—91no—
1095C2×C4—91no—
1096C2×C4—91no—
1097C2×C4—271no—
1098C2×C4—361no—
1099C2×C4—1081no—
1100C2×C4—1081no—
1101C2×C4—1081no—
1102C2×C4D3311yescharacteristic
1103C2×C3—21no—
1104C2×C3—21no—
1105C2×C3—21no—
1106C2×C3—21no—
1107C2×C3—21no—
1108C2×C3—21no—
1109C2×C3—21no—
1110C2×C3—21no—
1111C2×C3—21no—
1112C2×C3—41no—
1113C2×C3—41no—
1114C2×C3—41no—
1115C2×C3—62no—
1116C2×C3—62no—
1117C2×C3—122no—
1118C2×C3—121no—
1119C2×C3—121no—
1120C2×C3—241no—
1121C2×C3—361no—
1122C2×C3—361no—
1123C2×C3C2×#379611yescharacteristic
1124C2×C3#6430711yescharacteristic
1125C2×C3#6430811yescharacteristic
1126C2×C3D3×#23711yescharacteristic
1127C2×C3#6431311yescharacteristic
1128C2×C3#6431411yescharacteristic
1129C2×C3#6431411yescharacteristic
1130C2×C3#6431411yescharacteristic
1131C2×C3D3×#23911yescharacteristic
1132D3—22no—
1133D3—41no—
1134D3—121no—
1135D3—121no—
1136D3—121no—
1137D3—121no—
1138D3—241no—
1139D3—241no—
1140D3—362no—
1141D3—362no—
1142D3—362no—
1143D3—364no—
1144D3—361no—
1145D3—361no—
1146D3—361no—
1147C22—32no—
1148C22—61no—
1149C22—61no—
1150C22—61no—
1151C22—61no—
1152C22—61no—
1153C22—181no—
1154C22—181no—
1155C22—181no—
1156C22—181no—
1157C22—181no—
1158C22—181no—
1159C22—364no—
1160C22—541no—
1161C22—541no—
1162C22—541no—
1163C22C2×D3311yescharacteristic
1164C4—21no—
1165C4—61no—
1166C4—61no—
1167C4—61no—
1168C4—61no—
1169C4—181no—
1170C4—181no—
1171C4—181no—
1172C4—181no—
1173C4—541no—
1174C3—21no—
1175C3—21no—
1176C3—21no—
1177C3—41no—
1178C3#1059412711yescharacteristic, complemented
1179C3#1059417311yescharacteristic, complemented
1180C3#1059465211yescharacteristic, complemented
1181C2—62no—
1182C2—121no—
1183C2—361no—
1184C2—361no—
1185C2—1081no—
1186C2D3×#379611yescharacteristic
1187C2#1172438111yescharacteristic
1188C2#1172442011yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
hypercenterC2×C4D33
hypocenterC33#538
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. #11723532C2semidirect
3. #11723462C2semidirect
4. #11723420C2semidirect
5. C3×#63923C2semidirect
6. C3×#63899C2semidirect
7. C3×#63858C2semidirect
8. #11723027C2semidirect
9. #11723003C2semidirect
10. #11723001C2semidirect
11. #11722966C2semidirect
12. #11722959C2semidirect
13. #11722948C2semidirect
14. #11722928C2semidirect
15. D3×(C2×D3)⋊Dic3C2semidirect
20. C2×C4×C3⋊(C3⋊D3)C22semidirect
22. C2×#6294C22semidirect
24. C2×#6292C22semidirect
28. C2×C3×#627C22semidirect
32. C3×#3750C22semidirect
33. C3×#3750C22semidirect
36. C32×C4⋊Dic3C22semidirect
39. #88814C22semidirect
40. Dic3⋊(C3⋊Dic3)C22semidirect
41. #88804C22semidirect
42. #88804C22semidirect
44. #88803C22semidirect
46. Dic3×C3⋊Dic3C22semidirect
47. C3×#3724C22semidirect
48. C3×Dic3⋊Dic3C22semidirect
53. C3×Dic32C22semidirect
72. #63923D3semidirect
81. #63899D3semidirect
96. #63858D3semidirect
162. C2×#627C2×D3semidirect
193. #3750C2×D3semidirect
194. #3750C2×D3semidirect
212. C3×C4⋊Dic3C2×D3semidirect
213. C3×C4⋊Dic3C2×D3semidirect
225. #3724C2×D3semidirect
229. Dic3⋊Dic3C2×D3semidirect
261. Dic32C2×D3semidirect
580. C4⋊Dic3D32semidirect
737. C33#538semidirect
1070. C32#5593semidirect
1071. C32#5644semidirect
1072. C32#5704semidirect
1178. C3#10594127semidirect
1179. C3#10594173semidirect
1180. C3#10594652semidirect

Maximal subgroups

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

subgroupindex
#117236862
#117235322
#117234622
#117234202
C3×#639232
C3×#638992
C3×#638582
#117230272
#117230032
#117230012
#117229662
#117229592
#117229482
#117229282
D3×(C2×D3)⋊Dic32
#105946523
#105941733
#105941273