Finite Group Databasebeta

← #13168073

Subgroups — #13168073

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#11723675C211yesmaximal, characteristic, complemented
2#11723531C211yesmaximal, characteristic, complemented
3#11723462C211yesmaximal, characteristic, complemented
4#11723421C211yesmaximal, characteristic, complemented
5C3×#63922C211yesmaximal, characteristic, complemented
6C3×#63893C211yesmaximal, characteristic, complemented
7C3×#63884C211yesmaximal, characteristic, complemented
8#11723019C211yesmaximal, characteristic, complemented
9#11723005C211yesmaximal, characteristic, complemented
10#11723001C211yesmaximal, characteristic, complemented
11#11722959C211yesmaximal, characteristic, complemented
12#11722958C211yesmaximal, characteristic, complemented
13#11722948C211yesmaximal, characteristic, complemented
14#11722924C211yesmaximal, characteristic, complemented
15D3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
16#10595185—31nomaximal
17#10594650—31nomaximal
18#10594173—31nomaximal
19C22×C3×D32C2211yescharacteristic
20C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
21C2×C32×D12C2211yescharacteristic
22C2×#6292C2211yescharacteristic
23C2×#6291C2211yescharacteristic
24C2×#6291C2211yescharacteristic
25C2×#6291C2211yescharacteristic, complemented
26C2×D3×C3⋊Dic3C2211yescharacteristic
27C2×C3×#627C2211yescharacteristic, complemented
28C2×C3×#626C2211yescharacteristic
29C2×C3×#625C2211yescharacteristic
30C2×C3×D3×Dic3C2211yescharacteristic
31C2×C3×D3×Dic3C2211yescharacteristic, complemented
32C3×#3752C2211yescharacteristic
33C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
34C3×#3750C2211yescharacteristic, complemented
35C32×(C2×D3)⋊C4C2211yescharacteristic
36C32×Dic3⋊C4C2211yescharacteristic, complemented
37#88815C2211yescharacteristic, complemented
38#88814C2211yescharacteristic
39#88814C2211yescharacteristic
40#88813C2211yescharacteristic, complemented
41#88807C2211yescharacteristic, complemented
42#88804C2211yescharacteristic, complemented
43#88804C2211yescharacteristic, complemented
44#88803C2211yescharacteristic
45(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
46(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
47Dic3×C3⋊Dic3C2211yescharacteristic, complemented
48C3×Dic3⋊Dic3C2211yescharacteristic, complemented
49C3×(C2×D3)⋊Dic3C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
54#64147—31no—
55#64103—31no—
56#64090—31no—
57C3×#937—31no—
58C3×#935—31no—
59C3×#897—31no—
60C3×#894—31no—
61C3×#882—31no—
62C3×#878—31no—
63#63978—31no—
64#63978—31no—
65#63977—31no—
66#63977—31no—
67#67⋊Dic3—31no—
68Dic3×#67—31no—
69#63971—31no—
70D3×#217—31no—
71C2×(C2×D3)⋊Dic3—31no—
72#63959—31no—
73#63956—31no—
74#63953—31no—
75#63923—31no—
76#63922D311yescharacteristic, complemented
77D3×(C2×D3)⋊C4—31no—
78#63916—31no—
79#63916—31no—
80#63916—61no—
81#63909—31no—
82#63907—31no—
83#63907—31no—
84#63907—31no—
85#63906—31no—
86#63893D311yescharacteristic, complemented
87#63886—31no—
88#63884D311yescharacteristic, complemented
89#63881—31no—
90#63881—31no—
91#63881—61no—
92#63879—31no—
93#63863—31no—
94#63862—31no—
95#63861—31no—
96#63858—31no—
97#63858—31no—
98#63853—31no—
99#63853—31no—
100#63853—61no—
101#63848—31no—
102C22×C3⋊(C3⋊D3)C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C32×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
117C2×C3×C3⋊Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C32×D12—41no—
122#6292—41no—
123#6291—22no—
124#6291—41no—
125#6291—41no—
126D3×C3⋊Dic3—41no—
127C3×#627—41no—
128C3×#626—41no—
129C3×#625—22no—
130C3×D3×Dic3—41no—
131C3×D3×Dic3—41no—
132#5657—91no—
133#5644—91no—
134#5593—91no—
135C23×C3×D3—31no—
136C23×C3×D3—31no—
137C22×D32C2×D311yescharacteristic
138C2×C32×D4—31no—
139C2×#638—31no—
140C2×#638—31no—
141C2×#638—31no—
142C22×C3⋊Dic3—31no—
143C2×C4⋊(C3⋊D3)—31no—
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—
153C2×C3×#67—31no—
154C22×C3×Dic3—31no—
155C22×C3×Dic3—31no—
156C2×C3×D12—21no—
157C2×C3×D12—31no—
158C2×C3×D12C2×D311yescharacteristic
159C2×C3×D12C2×D311yescharacteristic
160C2×C3×C4×D3—31no—
161C2×C3×C4×D3—31no—
162C2×C3×Dic6—31no—
163C2×C3×Dic6—31no—
164C2×#627C2×D311yescharacteristic, complemented
165C2×#626—31no—
166C2×#626—31no—
167C2×#626—31no—
168C2×#626—31no—
169C2×#626—31no—
170C2×#626—31no—
171C2×#626—31no—
172C2×#626—31no—
173C2×#626—61no—
174C2×#626—61no—
175C2×#626—61no—
176C2×#626—61no—
177C2×#626C2×D311yescharacteristic
178C2×#625C2×D311yescharacteristic
179C2×D3×Dic3—31no—
180C2×D3×Dic3—31no—
181C2×D3×Dic3—61no—
182C2×D3×Dic3C2×D311yescharacteristic
183C2×D3×Dic3C2×D311yescharacteristic, complemented
184C32×C4⋊C4—31no—
185C32×C22⋊C4—31no—
186#3757—31no—
187#3757—31no—
188#3752—31no—
189#3752—31no—
190#3752—31no—
191#3752C2×D311yescharacteristic
192C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
193#3750—31no—
194#3750C2×D311yescharacteristic, complemented
195C4×C3⋊Dic3—31no—
196C3×#217—31no—
197C3×#217—31no—
198C3×#217—31no—
199C3×#217—31no—
200C3×#217—31no—
201C3×(C2×D3)⋊C4—21no—
202C3×(C2×D3)⋊C4—31no—
203C3×(C2×D3)⋊C4—31no—
204C3×(C2×D3)⋊C4—31no—
205C3×(C2×D3)⋊C4—31no—
206C3×(C2×D3)⋊C4—31no—
207C3×(C2×D3)⋊C4—31no—
208C3×(C2×D3)⋊C4—31no—
209C3×(C2×D3)⋊C4—61no—
210C3×(C2×D3)⋊C4C2×D311yescharacteristic
211C3×(C2×D3)⋊C4C2×D311yescharacteristic
212C3×C4⋊Dic3—31no—
213C3×C4⋊Dic3—31no—
214C3×C4⋊Dic3—31no—
215C3×C4⋊Dic3—61no—
216C3×Dic3⋊C4—21no—
217C3×Dic3⋊C4—31no—
218C3×Dic3⋊C4—31no—
219C3×Dic3⋊C4—31no—
220C3×Dic3⋊C4—61no—
221C3×Dic3⋊C4C2×D311yescharacteristic, complemented
222C3×Dic3⋊C4C2×D311yescharacteristic, complemented
223#3724—31no—
224Dic3⋊Dic3—31no—
225Dic3⋊Dic3—31no—
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—61no—
237#3722—61no—
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—31no—
248(C2×D3)⋊Dic3—61no—
249(C2×D3)⋊Dic3—61no—
250(C2×D3)⋊Dic3—61no—
251(C2×D3)⋊Dic3C2×D311yescharacteristic
252(C2×D3)⋊Dic3C2×D311yescharacteristic
253(C2×D3)⋊Dic3C2×D311yescharacteristic
254(C2×D3)⋊Dic3C2×D311yescharacteristic
255(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
256Dic32—31no—
257Dic32—31no—
258Dic32—31no—
259Dic32—31no—
260Dic32—31no—
261Dic32—61no—
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×C32×D3—21no—
270C2×C32×D3—21no—
271C2×C32×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—
285C3×C3⋊Dic3—21no—
286C32×Dic3—21no—
287C32×Dic3—21no—
288C32×Dic3—21no—
289C3×#123—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#938—91no—
300#938—181no—
301#937—31no—
302#936—91no—
303#935—31no—
304D4×Dic3—91no—
305#930—91no—
306#930—91no—
307C4×#67—91no—
308C2×(C2×D3)⋊C4—91no—
309#898—91no—
310#898—91no—
311#898—91no—
312#897—31no—
313#895—91no—
314#895—91no—
315#894—31no—
316#894—91no—
317#894—91no—
318#894—181no—
319#893—91no—
320#885—91no—
321#885—91no—
322#885—91no—
323#884—91no—
324#883—91no—
325#882—31no—
326#882—91no—
327#882—91no—
328#67⋊C4—91no—
329#67⋊C4—91no—
330#67⋊C4—91no—
331#67⋊C4—181no—
332D3×C22⋊C4—91no—
333#879—91no—
334#879—91no—
335#879—91no—
336#878—31no—
337C23×C32—31no—
338C23×C32—31no—
339C23×C32—31no—
340C22×C3⋊D3—31no—
341C22×C3⋊D3—31no—
342C22×C3⋊D3—31no—
343C22×C3⋊D3—61no—
344C22×C3⋊D3—61no—
345C22×C3⋊D3—61no—
346C22×C3⋊D3—121no—
347C22×C3⋊D3C22×D311yescharacteristic
348C22×C3×D3—21no—
349C22×C3×D3—21no—
350C22×C3×D3—21no—
351C22×C3×D3—31no—
352C22×C3×D3—31no—
353C22×C3×D3—61no—
354C22×C3×D3—62no—
355C22×C3×D3—62no—
356C22×C3×D3—121no—
357C22×C3×D3—121no—
358C22×C3×D3—121no—
359C22×C3×D3—121no—
360C22×C3×D3C22×D311yescharacteristic
361C22×C3×D3C22×D311yescharacteristic
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—
369C32×D4—121no—
370C2×C32×C4—21no—
371C2×C32×C4—21no—
372C2×C32×C4—21no—
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—
382#638—121no—
383C2×C3⋊Dic3—31no—
384C2×C3⋊Dic3—31no—
385C2×C3⋊Dic3—31no—
386C2×C3⋊Dic3—61no—
387C2×C3⋊Dic3—61no—
388C2×C3⋊Dic3—61no—
389C2×C3⋊Dic3—121no—
390C2×C3⋊Dic3—121no—
391C2×C3⋊Dic3C22×D311yescharacteristic
392C2×C3⋊Dic3C22×D311yescharacteristic
393C2×C3⋊Dic3C22×D311yescharacteristic
394C2×C3⋊Dic3C22×D311yescharacteristic
395C2×C3⋊Dic3C22×D311yescharacteristic
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—62no—
406C3×#67—121no—
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—31no—
419C2×C3×Dic3—31no—
420C2×C3×Dic3—61no—
421C2×C3×Dic3—61no—
422C2×C3×Dic3—61no—
423C2×C3×Dic3—61no—
424C2×C3×Dic3—61no—
425C2×C3×Dic3—121no—
426C2×C3×Dic3—121no—
427C2×C3×Dic3C22×D311yescharacteristic
428C2×C3×Dic3C22×D311yescharacteristic
429C2×C3×Dic3C22×D311yescharacteristic
430C2×C3×Dic3C22×D311yescharacteristic
431C2×C3×Dic3C22×D311yescharacteristic
432C2×C3×Dic3C22×D311yescharacteristic
433C3×D12—41no—
434C3×D12—41no—
435C3×D12—42no—
436C3×D12—121no—
437C3×C4×D3—121no—
438C3×C4×D3—121no—
439C3×Dic6—121no—
440C3×Dic6—121no—
441#627—41no—
442#626—41no—
443#626—64no—
444#626—62no—
445#626—62no—
446#626—121no—
447#626—121no—
448#626—122no—
449#626—121no—
450#626—121no—
451#626—121no—
452#626—121no—
453#626—122no—
454#626—122no—
455#625—22no—
456D3×Dic3—41no—
457D3×Dic3—41no—
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—
467C32×D3—22no—
468C32×D3—41no—
469C32×D3—41no—
470C24×C3—91no—
471C23×D3—31no—
472C23×D3—31no—
473C2×C3×Q8—91no—
474C2×C3×D4—31no—
475C2×C3×D4—31no—
476C2×C3×D4—61no—
477C2×C3×D4—91no—
478C2×C3×D4—91no—
479C22×C3×C4—91no—
480C22×C3×C4—91no—
481C2×#67—31no—
482C2×#67—31no—
483C2×#67—31no—
484C2×#67—91no—
485C2×#67—91no—
486C2×#67—91no—
487C2×#67—91no—
488C2×#67—91no—
489C2×#67—91no—
490C2×#67—91no—
491C2×#67—181no—
492C2×#67—181no—
493C2×#67—181no—
494C22×Dic3—31no—
495C22×Dic3—31no—
496C22×Dic3—91no—
497C22×Dic3—91no—
498C22×Dic3—181no—
499C2×D12—31no—
500C2×D12—91no—
501C2×D12—91no—
502C2×D12—91no—
503C2×D12—91no—
504C2×D12—91no—
505C2×D12—181no—
506C2×D12D3211yescharacteristic
507C2×C4×D3—31no—
508C2×C4×D3—31no—
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×C22⋊C4—31no—
526C3×C22⋊C4—31no—
527C3×C22⋊C4—61no—
528C3×C22⋊C4—91no—
529C3×C22⋊C4—91no—
530C3×C22⋊C4—91no—
531C3×C22⋊C4—91no—
532C3×C22⋊C4—91no—
533C3×C22⋊C4—91no—
534#217—31no—
535#217—31no—
536#217—31no—
537#217—31no—
538#217—31no—
539#217—91no—
540#217—91no—
541#217—91no—
542#217—91no—
543#217—91no—
544#217—91no—
545#217—91no—
546#217—181no—
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—31no—
554(C2×D3)⋊C4—31no—
555(C2×D3)⋊C4—61no—
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)⋊C4D3211yescharacteristic
574C4⋊Dic3—31no—
575C4⋊Dic3—31no—
576C4⋊Dic3—31no—
577C4⋊Dic3—61no—
578C4⋊Dic3—91no—
579C4⋊Dic3—91no—
580Dic3⋊C4—31no—
581Dic3⋊C4—31no—
582Dic3⋊C4—31no—
583Dic3⋊C4—61no—
584Dic3⋊C4—91no—
585Dic3⋊C4—91no—
586Dic3⋊C4—91no—
587Dic3⋊C4—91no—
588Dic3⋊C4—181no—
589Dic3⋊C4D3211yescharacteristic, complemented
590C4×Dic3—91no—
591C4×Dic3—91no—
592C4×Dic3—91no—
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×C32—61no—
608C22×C32—61no—
609C22×C32—61no—
610C22×C32C23×D311yescharacteristic
611C22×C32C23×D311yescharacteristic
612C22×C32C23×D311yescharacteristic
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—21no—
648C2×C3×D3—21no—
649C2×C3×D3—21no—
650C2×C3×D3—21no—
651C2×C3×D3—21no—
652C2×C3×D3—21no—
653C2×C3×D3—22no—
654C2×C3×D3—41no—
655C2×C3×D3—41no—
656C2×C3×D3—41no—
657C2×C3×D3—41no—
658C2×C3×D3—41no—
659C2×C3×D3—41no—
660C2×C3×D3—41no—
661C2×C3×D3—41no—
662C2×C3×D3—61no—
663C2×C3×D3—61no—
664C2×C3×D3—61no—
665C2×C3×D3—61no—
666C2×C3×D3—61no—
667C2×C3×D3—61no—
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—
686C3⋊Dic3—21no—
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—41no—
705C3×Dic3—41no—
706C3×Dic3—41no—
707C3×Dic3—62no—
708C3×Dic3—61no—
709C3×Dic3—61no—
710C3×Dic3—61no—
711C3×Dic3—61no—
712C3×Dic3—61no—
713C3×Dic3—61no—
714C3×Dic3—61no—
715C3×Dic3—61no—
716C3×Dic3—61no—
717C3×Dic3—61no—
718C3×Dic3—121no—
719C3×Dic3—121no—
720C3×Dic3—121no—
721C3×Dic3—121no—
722#126—271no—
723#126—271no—
724#124—271no—
725#124—271no—
726#123—91no—
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—31no—
743C23×C3—31no—
744C23×C3—61no—
745C23×C3—61no—
746C23×C3—61no—
747C23×C3—91no—
748C23×C3—182no—
749C23×C3—361no—
750C23×C3—361no—
751C22×D3—31no—
752C22×D3—31no—
753C22×D3—61no—
754C22×D3—62no—
755C22×D3—62no—
756C22×D3—91no—
757C22×D3—91no—
758C22×D3—91no—
759C22×D3—121no—
760C22×D3—121no—
761C22×D3—121no—
762C22×D3—121no—
763C22×D3—181no—
764C22×D3—181no—
765C22×D3—181no—
766C22×D3—361no—
767C22×D3C2×D3211yescharacteristic
768C22×D3C2×D3211yescharacteristic
769C22×D3C2×D3211yescharacteristic
770C3×Q8—361no—
771C3×D4—121no—
772C3×D4—121no—
773C3×D4—122no—
774C3×D4—182no—
775C3×D4—361no—
776C2×C3×C4—21no—
777C2×C3×C4—21no—
778C2×C3×C4—21no—
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—91no—
790C2×C3×C4—91no—
791C2×C3×C4—91no—
792C2×C3×C4—91no—
793C2×C3×C4—91no—
794C2×C3×C4—361no—
795C2×C3×C4—361no—
796C2×C3×C4C2×D3211yescharacteristic
797C2×C3×C4C2×D3211yescharacteristic
798C2×C3×C4C2×D3211yescharacteristic
799#67—62no—
800#67—62no—
801#67—121no—
802#67—182no—
803#67—182no—
804#67—184no—
805#67—361no—
806#67—361no—
807#67—361no—
808#67—361no—
809#67—361no—
810#67—362no—
811#67—362no—
812C2×Dic3—31no—
813C2×Dic3—31no—
814C2×Dic3—31no—
815C2×Dic3—31no—
816C2×Dic3—31no—
817C2×Dic3—31no—
818C2×Dic3—31no—
819C2×Dic3—31no—
820C2×Dic3—31no—
821C2×Dic3—31no—
822C2×Dic3—61no—
823C2×Dic3—61no—
824C2×Dic3—61no—
825C2×Dic3—61no—
826C2×Dic3—61no—
827C2×Dic3—91no—
828C2×Dic3—91no—
829C2×Dic3—91no—
830C2×Dic3—121no—
831C2×Dic3—121no—
832C2×Dic3—181no—
833C2×Dic3—181no—
834C2×Dic3—181no—
835C2×Dic3—361no—
836C2×Dic3—361no—
837C2×Dic3—361no—
838C2×Dic3—362no—
839C2×Dic3C2×D3211yescharacteristic
840C2×Dic3C2×D3211yescharacteristic
841C2×Dic3C2×D3211yescharacteristic
842D12—41no—
843D12—121no—
844D12—182no—
845D12—361no—
846D12—361no—
847D12—362no—
848D12—361no—
849D12—361no—
850C4×D3—121no—
851C4×D3—121no—
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×C32—121no—
877C2×C32C2×#23711yescharacteristic
878C2×C32#100411yescharacteristic
879C2×C32#100411yescharacteristic
880C2×C32#100411yescharacteristic
881C2×C32#100411yescharacteristic
882C2×C32C2×#23911yescharacteristic
883C2×C32D3×#4111yescharacteristic
884C2×C32#100911yescharacteristic
885C2×C32#100911yescharacteristic
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—41no—
900C3×D3—41no—
901C3×D3—81no—
902C3×D3—81no—
903C3×D3—121no—
904C3×D3—121no—
905C3×D3—241no—
906C24—91no—
907C2×Q8—91no—
908C2×D4—31no—
909C2×D4—91no—
910C2×D4—91no—
911C2×D4—271no—
912C2×D4—271no—
913C2×D4—271no—
914C2×D4—271no—
915C22×C4—91no—
916C22×C4—91no—
917C22×C4—271no—
918C22×C4—271no—
919C4⋊C4—31no—
920C4⋊C4—91no—
921C4⋊C4—91no—
922C4⋊C4—91no—
923C4⋊C4—271no—
924C4⋊C4—271no—
925C22⋊C4—31no—
926C22⋊C4—91no—
927C22⋊C4—91no—
928C22⋊C4—91no—
929C22⋊C4—91no—
930C22⋊C4—91no—
931C22⋊C4—91no—
932C22⋊C4—271no—
933C22⋊C4—271no—
934C22⋊C4—271no—
935C22⋊C4—271no—
936C22⋊C4—271no—
937C22⋊C4—271no—
938C22⋊C4—271no—
939C42—271no—
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—61no—
959C22×C3—61no—
960C22×C3—61no—
961C22×C3—61no—
962C22×C3—61no—
963C22×C3—61no—
964C22×C3—121no—
965C22×C3—121no—
966C22×C3—121no—
967C22×C3—121no—
968C22×C3—121no—
969C22×C3—121no—
970C22×C3—121no—
971C22×C3—121no—
972C22×C3—181no—
973C22×C3—181no—
974C22×C3—181no—
975C22×C3—364no—
976C22×C3C22×D3211yescharacteristic
977C22×C3C22×D3211yescharacteristic
978C22×C3C22×D3211yescharacteristic
979C2×D3—21no—
980C2×D3—21no—
981C2×D3—21no—
982C2×D3—21no—
983C2×D3—21no—
984C2×D3—21no—
985C2×D3—21no—
986C2×D3—21no—
987C2×D3—61no—
988C2×D3—61no—
989C2×D3—61no—
990C2×D3—61no—
991C2×D3—61no—
992C2×D3—61no—
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—121no—
1034C3×C4—121no—
1035C3×C4—121no—
1036C3×C4—181no—
1037C3×C4—181no—
1038C3×C4—181no—
1039C3×C4—181no—
1040C3×C4—181no—
1041Dic3—21no—
1042Dic3—21no—
1043Dic3—21no—
1044Dic3—62no—
1045Dic3—61no—
1046Dic3—61no—
1047Dic3—61no—
1048Dic3—61no—
1049Dic3—61no—
1050Dic3—61no—
1051Dic3—61no—
1052Dic3—61no—
1053Dic3—61no—
1054Dic3—61no—
1055Dic3—121no—
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#565711yescharacteristic, complemented
1073C23—31no—
1074C23—31no—
1075C23—31no—
1076C23—91no—
1077C23—182no—
1078C23—271no—
1079C23—361no—
1080C23—361no—
1081Q8—361no—
1082D4—121no—
1083D4—182no—
1084D4—361no—
1085D4—542no—
1086D4—1081no—
1087D4—1081no—
1088D4—1081no—
1089C2×C4—31no—
1090C2×C4—31no—
1091C2×C4—31no—
1092C2×C4—91no—
1093C2×C4—91no—
1094C2×C4—91no—
1095C2×C4—91no—
1096C2×C4—91no—
1097C2×C4—271no—
1098C2×C4—361no—
1099C2×C4—361no—
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—121no—
1121C2×C3—121no—
1122C2×C3—241no—
1123C2×C3—241no—
1124C2×C3—361no—
1125C2×C3C2×#379611yescharacteristic
1126C2×C3#6430711yescharacteristic
1127C2×C3D3×#23711yescharacteristic
1128C2×C3#6431311yescharacteristic
1129C2×C3#6431411yescharacteristic
1130C2×C3#6431411yescharacteristic
1131C2×C3#6431411yescharacteristic
1132C2×C3D3×#23911yescharacteristic
1133C2×C3#6433011yescharacteristic
1134D3—22no—
1135D3—41no—
1136D3—41no—
1137D3—121no—
1138D3—121no—
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—61no—
1154C22—61no—
1155C22—61no—
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—181no—
1169C4—181no—
1170C4—181no—
1171C4—181no—
1172C4—181no—
1173C4—541no—
1174C3—21no—
1175C3—21no—
1176C3—21no—
1177C3—41no—
1178C3#1059417311yescharacteristic, complemented
1179C3#1059465011yescharacteristic, complemented
1180C3#1059518511yescharacteristic, complemented
1181C2—62no—
1182C2—121no—
1183C2—121no—
1184C2—361no—
1185C2—1081no—
1186C2D3×#379611yescharacteristic
1187C2#1172438111yescharacteristic
1188C2#1172441911yescharacteristic
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. #11723675C2semidirect
2. #11723531C2semidirect
3. #11723462C2semidirect
4. #11723421C2semidirect
5. C3×#63922C2semidirect
6. C3×#63893C2semidirect
7. C3×#63884C2semidirect
8. #11723019C2semidirect
9. #11723005C2semidirect
10. #11723001C2semidirect
11. #11722959C2semidirect
12. #11722958C2semidirect
13. #11722948C2semidirect
14. #11722924C2semidirect
15. D3×(C2×D3)⋊Dic3C2semidirect
20. C2×C4×C3⋊(C3⋊D3)C22semidirect
25. C2×#6291C22semidirect
27. C2×C3×#627C22semidirect
31. C2×C3×D3×Dic3C22semidirect
33. C3×C4⋊(C3⋊Dic3)C22semidirect
34. C3×#3750C22semidirect
36. C32×Dic3⋊C4C22semidirect
37. #88815C22semidirect
40. #88813C22semidirect
41. #88807C22semidirect
42. #88804C22semidirect
43. #88804C22semidirect
46. (C2×D3)⋊(C3⋊Dic3)C22semidirect
47. Dic3×C3⋊Dic3C22semidirect
48. C3×Dic3⋊Dic3C22semidirect
53. C3×(C2×D3)⋊Dic3C22semidirect
76. #63922D3semidirect
86. #63893D3semidirect
88. #63884D3semidirect
164. C2×#627C2×D3semidirect
183. C2×D3×Dic3C2×D3semidirect
192. C4⋊(C3⋊Dic3)C2×D3semidirect
194. #3750C2×D3semidirect
221. C3×Dic3⋊C4C2×D3semidirect
222. C3×Dic3⋊C4C2×D3semidirect
229. Dic3⋊Dic3C2×D3semidirect
255. (C2×D3)⋊Dic3C2×D3semidirect
589. Dic3⋊C4D32semidirect
737. C33#538semidirect
1070. C32#5593semidirect
1071. C32#5644semidirect
1072. C32#5657semidirect
1178. C3#10594173semidirect
1179. C3#10594650semidirect
1180. C3#10595185semidirect

Maximal subgroups

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

subgroupindex
#117236752
#117235312
#117234622
#117234212
C3×#639222
C3×#638932
C3×#638842
#117230192
#117230052
#117230012
#117229592
#117229582
#117229482
#117229242
D3×(C2×D3)⋊Dic32
#105951853
#105946503
#105941733