Finite Group Databasebeta

← #13172177

Subgroups — #13172177

Order 1728.

1336 conjugacy classes of subgroups.

The subgroup lattice has 1214 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723729C211yesmaximal, characteristic, complemented
2#11723632C211yesmaximal, characteristic, complemented
3#11723624C211yesmaximal, characteristic, complemented
4#11723623C211yesmaximal, characteristic, complemented
5C3×#63966C211yesmaximal, characteristic, complemented
6C3×#63953C211yesmaximal, characteristic, complemented
7C3×#63952C211yesmaximal, characteristic, complemented
8#11723024C211yesmaximal, characteristic, complemented
9#11723023C211yesmaximal, characteristic, complemented
10#11723003C211yesmaximal, characteristic, complemented
11#11723000C211yesmaximal, characteristic, complemented
12#11722974C211yesmaximal, characteristic, complemented
13#11722952C211yesmaximal, characteristic, complemented
14#11722933C211yesmaximal, characteristic, complemented
15#11722905C211yesmaximal, characteristic, complemented
16#10595085—31nomaximal
17#10594307—31nomaximal
18#10594298—31nomaximal
19C22×#1113C2211yescharacteristic
20C2×#6312C2211yescharacteristic, complemented
21C2×C3×#638C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic
23C2×C3×#638C2211yescharacteristic
24C22×C32×Dic3C2211yescharacteristic, complemented
25C2×#6292C2211yescharacteristic
26C2×#6292C2211yescharacteristic
27C2×#6292C2211yescharacteristic
28C2×#6289C2211yescharacteristic, complemented
29C2×Dic3×C3⋊D3C2211yescharacteristic
30C2×C3×#627C2211yescharacteristic, complemented
31C2×C3×#624C2211yescharacteristic
32C32×#217C2211yescharacteristic, complemented
33C32×#217C2211yescharacteristic, complemented
34#88814C2211yescharacteristic
35#88814C2211yescharacteristic
36#88814C2211yescharacteristic
37#88807C2211yescharacteristic, complemented
38#88806C2211yescharacteristic, complemented
39Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
40#88804C2211yescharacteristic, complemented
41#88804C2211yescharacteristic, complemented
42#88803C2211yescharacteristic
43#88803C2211yescharacteristic
44C3×#3724C2211yescharacteristic, complemented
45C3×Dic3⋊Dic3C2211yescharacteristic, complemented
46C3×Dic3⋊Dic3C2211yescharacteristic, complemented
47C3×#3722C2211yescharacteristic
48C3×#3722C2211yescharacteristic
49C3×#3722C2211yescharacteristic
50C3×#3722C2211yescharacteristic
51C3×#3722C2211yescharacteristic
52C3×Dic32C2211yescharacteristic, complemented
53C3×Dic32C2211yescharacteristic, complemented
54#64139—31no—
55#64093—31no—
56#64093—31no—
57C3×#929—31no—
58C3×C4×#67—31no—
59C3×#886—31no—
60C3×#885—31no—
61C3×#885—31no—
62C3×#67⋊C4—31no—
63#63983—31no—
64#63983—31no—
65#63983—31no—
66#63978—31no—
67#63978—31no—
68#63978—61no—
69#63971—31no—
70#63971—31no—
71#63971—61no—
72#63966D311yescharacteristic, complemented
73#63958—31no—
74#63958—31no—
75#63958—61no—
76#63953D311yescharacteristic, complemented
77#63952D311yescharacteristic, complemented
78#63923—31no—
79#63923—31no—
80#63923—31no—
81#63921—31no—
82D3×(C2×D3)⋊C4—31no—
83D3×(C2×D3)⋊C4—31no—
84#63907—31no—
85#63904—31no—
86C4×#626—31no—
87#63897—31no—
88#63894—31no—
89#63893—31no—
90#63887—31no—
91#63871—31no—
92#63868—31no—
93#63868—31no—
94#63864—31no—
95#63861—31no—
96#63859—31no—
97#63859—31no—
98#63858—31no—
99#63854—31no—
100#63853—31no—
101#63852—31no—
102C23×C33C2311yescharacteristic
103C22×C3⋊(C3⋊D3)C2311yescharacteristic
104C22×C3×C3⋊D3C2311yescharacteristic
105C22×C3×C3⋊D3C2311yescharacteristic
106C22×C3×C3⋊D3C2311yescharacteristic
107C2×#1113—22no—
108C2×#1113—41no—
109C2×#1113—41no—
110#6312—41no—
111C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
112C3×#638—22no—
113C3×#638—41no—
114C3×#638—41no—
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C3×C3⋊Dic3C2311yescharacteristic
118C2×C32×Dic3—41no—
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123C2×C32×Dic3C2311yescharacteristic
124C2×C32×Dic3C2311yescharacteristic
125#6292—22no—
126#6292—41no—
127#6292—41no—
128#6289—41no—
129Dic3×C3⋊D3—41no—
130C3×#627—41no—
131C3×#624—41no—
132#5678—91no—
133#5657—91no—
134#5560—91no—
135C22×D32—31no—
136C22×D32—31no—
137C22×D32—31no—
138C22×C32×C4—31no—
139C2×#638—31no—
140C2×#638—31no—
141C2×#638—31no—
142C2×#638—61no—
143C2×#638—61no—
144C2×#638—61no—
145C2×#638—121no—
146C2×#638C2×D311yescharacteristic
147C2×#638C2×D311yescharacteristic
148C2×#638C2×D311yescharacteristic
149C2×C4⋊(C3⋊D3)—31no—
150C2×C4⋊(C3⋊D3)—31no—
151C2×C4⋊(C3⋊D3)—31no—
152C2×C4×C3⋊D3—31no—
153C2×C4×C3⋊D3—31no—
154C2×C3×#67—31no—
155C2×C3×#67—31no—
156C2×C3×#67—31no—
157C2×C3×#67—31no—
158C2×C3×#67—31no—
159C2×C3×#67—31no—
160C2×C3×#67—61no—
161C2×C3×#67—61no—
162C2×C3×#67—61no—
163C22×C3×Dic3—21no—
164C22×C3×Dic3C2×D311yescharacteristic, complemented
165C22×C3×Dic3C2×D311yescharacteristic, complemented
166C2×C3×C4×D3—31no—
167C2×C3×C4×D3—31no—
168C2×C3×Dic6—31no—
169C2×C3×Dic6—31no—
170C2×#627C2×D311yescharacteristic, complemented
171C2×#626—31no—
172C2×#626—31no—
173C2×#626—31no—
174C2×#626—31no—
175C2×#626—31no—
176C2×#626—31no—
177C2×#626—61no—
178C2×#626—61no—
179C2×#626—61no—
180C2×#624—31no—
181C2×#624—31no—
182C2×#624—61no—
183C2×#624C2×D311yescharacteristic
184C2×D3×Dic3—31no—
185C2×D3×Dic3—31no—
186C2×D3×Dic3—61no—
187C32×C22⋊C4—31no—
188C32×C22⋊C4—31no—
189#3752—31no—
190#3752—31no—
191#3752—31no—
192#3752—31no—
193C4⋊(C3⋊Dic3)—31no—
194#3750—31no—
195#3750—31no—
196C3×#217—21no—
197C3×#217—21no—
198C3×#217C2×D311yescharacteristic, complemented
199C3×#217C2×D311yescharacteristic, complemented
200C3×#217C2×D311yescharacteristic, complemented
201C3×#217C2×D311yescharacteristic, complemented
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—31no—
210C3×(C2×D3)⋊C4—31no—
211C3×(C2×D3)⋊C4—31no—
212C3×C4⋊Dic3—31no—
213C3×C4⋊Dic3—31no—
214C3×Dic3⋊C4—31no—
215C3×Dic3⋊C4—31no—
216C3×Dic3⋊C4—31no—
217C3×Dic3⋊C4—31no—
218C3×C4×Dic3—31no—
219C3×C4×Dic3—31no—
220C3×C4×Dic3—31no—
221C3×C4×Dic3—31no—
222#3724—31no—
223#3724—31no—
224#3724—61no—
225#3724C2×D311yescharacteristic, complemented
226Dic3⋊Dic3—31no—
227Dic3⋊Dic3—31no—
228Dic3⋊Dic3—31no—
229Dic3⋊Dic3—31no—
230Dic3⋊Dic3—61no—
231Dic3⋊Dic3—61no—
232Dic3⋊Dic3C2×D311yescharacteristic, complemented
233Dic3⋊Dic3C2×D311yescharacteristic, complemented
234#3722—31no—
235#3722—31no—
236#3722—31no—
237#3722—31no—
238#3722—31no—
239#3722—31no—
240#3722—31no—
241#3722—61no—
242#3722—61no—
243#3722C2×D311yescharacteristic
244#3722C2×D311yescharacteristic
245#3722C2×D311yescharacteristic
246#3722C2×D311yescharacteristic
247#3722C2×D311yescharacteristic
248(C2×D3)⋊Dic3—31no—
249(C2×D3)⋊Dic3—31no—
250(C2×D3)⋊Dic3—31no—
251(C2×D3)⋊Dic3—31no—
252(C2×D3)⋊Dic3—31no—
253(C2×D3)⋊Dic3—31no—
254(C2×D3)⋊Dic3—31no—
255(C2×D3)⋊Dic3—31no—
256(C2×D3)⋊Dic3—31no—
257(C2×D3)⋊Dic3—31no—
258(C2×D3)⋊Dic3—61no—
259(C2×D3)⋊Dic3—61no—
260Dic32C2×D311yescharacteristic, complemented
261Dic32C2×D311yescharacteristic, complemented
262C22×C33—21no—
263C22×C33—21no—
264C22×C33—21no—
265C22×C33C2411yescharacteristic
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×C3×C3⋊D3—21no—
273C2×C3×C3⋊D3—21no—
274C2×C3×C3⋊D3—21no—
275C2×C3×C3⋊D3—21no—
276C2×C3×C3⋊D3—21no—
277C2×C3×C3⋊D3#4112yes—
278#1113—44no—
279C3⋊(C3⋊Dic3)—21no—
280C3×C3⋊Dic3—21no—
281C3×C3⋊Dic3—21no—
282C3×C3⋊Dic3—21no—
283C32×Dic3—21no—
284C32×Dic3—21no—
285C32×Dic3—21no—
286C32×Dic3—21no—
287C32×Dic3—21no—
288C32×Dic3—21no—
289C3×#124—91no—
290C3×#123—91no—
291C3×C4×D4—91no—
292#947—91no—
293#946—91no—
294#939—91no—
295#939—91no—
296#938—91no—
297#937—91no—
298#937—91no—
299#937—91no—
300#930—91no—
301#930—91no—
302#930—181no—
303#929—31no—
304C4×#67—31no—
305C4×#67—91no—
306C2×(C2×D3)⋊C4—91no—
307#898—91no—
308#898—91no—
309#897—91no—
310#894—91no—
311#894—91no—
312#893—91no—
313#886—31no—
314#885—31no—
315#885—31no—
316#885—91no—
317#884—91no—
318#884—91no—
319#884—91no—
320#884—91no—
321#884—181no—
322#884—181no—
323#883—91no—
324#882—91no—
325#882—91no—
326#882—91no—
327#67⋊C4—31no—
328D3×C22⋊C4—91no—
329D3×C22⋊C4—91no—
330#879—91no—
331#879—91no—
332#878—91no—
333#876—91no—
334#876—91no—
335#875—91no—
336C4×D12—91no—
337C23×C32—21no—
338C23×C32—21no—
339C23×C32—21no—
340C23×C32—41no—
341C23×C32C22×D311yescharacteristic
342C23×C32C22×D311yescharacteristic
343C23×C32C22×D311yescharacteristic
344C22×C3⋊D3—31no—
345C22×C3⋊D3—31no—
346C22×C3⋊D3—31no—
347C22×C3⋊D3—61no—
348C22×C3⋊D3—61no—
349C22×C3⋊D3—61no—
350C22×C3⋊D3—121no—
351C22×C3⋊D3C22×D311yescharacteristic
352C22×C3⋊D3C22×D311yescharacteristic
353C22×C3⋊D3C22×D311yescharacteristic
354C22×C3×D3—31no—
355C22×C3×D3—31no—
356C22×C3×D3—31no—
357C22×C3×D3—31no—
358C22×C3×D3—31no—
359C22×C3×D3—31no—
360C22×C3×D3—61no—
361C22×C3×D3—61no—
362C22×C3×D3—61no—
363C2×D32—62no—
364C2×D32—62no—
365C2×D32—62no—
366C2×D32—121no—
367C2×D32—121no—
368C2×D32—121no—
369C2×D32—121no—
370C2×D32—121no—
371C2×D32—121no—
372C2×C32×C4—31no—
373C2×C32×C4—31no—
374C2×C32×C4—31no—
375C2×C32×C4—31no—
376C2×C32×C4—31no—
377C2×C32×C4—31no—
378C2×C32×C4—121no—
379#638—22no—
380#638—41no—
381#638—41no—
382#638—121no—
383#638—121no—
384#638—121no—
385#638—122no—
386#638—122no—
387#638—122no—
388#638—124no—
389C2×C3⋊Dic3—31no—
390C2×C3⋊Dic3—31no—
391C2×C3⋊Dic3—31no—
392C2×C3⋊Dic3—61no—
393C2×C3⋊Dic3—61no—
394C2×C3⋊Dic3—61no—
395C2×C3⋊Dic3—121no—
396C2×C3⋊Dic3C22×D311yescharacteristic
397C2×C3⋊Dic3C22×D311yescharacteristic
398C2×C3⋊Dic3C22×D311yescharacteristic
399C4⋊(C3⋊D3)—62no—
400C4⋊(C3⋊D3)—121no—
401C4⋊(C3⋊D3)—121no—
402C4×C3⋊D3—121no—
403C4×C3⋊D3—121no—
404C3×#67—62no—
405C3×#67—62no—
406C3×#67—122no—
407C3×#67—121no—
408C3×#67—121no—
409C3×#67—121no—
410C3×#67—121no—
411C3×#67—122no—
412C3×#67—122no—
413C2×C3×Dic3—21no—
414C2×C3×Dic3—21no—
415C2×C3×Dic3—21no—
416C2×C3×Dic3—21no—
417C2×C3×Dic3—21no—
418C2×C3×Dic3—21no—
419C2×C3×Dic3—31no—
420C2×C3×Dic3—31no—
421C2×C3×Dic3—31no—
422C2×C3×Dic3—31no—
423C2×C3×Dic3—31no—
424C2×C3×Dic3—31no—
425C2×C3×Dic3—41no—
426C2×C3×Dic3—41no—
427C2×C3×Dic3—42no—
428C2×C3×Dic3—61no—
429C2×C3×Dic3—61no—
430C2×C3×Dic3—61no—
431C2×C3×Dic3C22×D311yescharacteristic
432C2×C3×Dic3C22×D311yescharacteristic
433C2×C3×Dic3C22×D311yescharacteristic
434C2×C3×Dic3C22×D311yescharacteristic
435C2×C3×Dic3C22×D311yescharacteristic
436C2×C3×Dic3C22×D311yescharacteristic
437C2×C3×Dic3C22×D311yescharacteristic
438C2×C3×Dic3C22×D311yescharacteristic
439C2×C3×Dic3C22×D311yescharacteristic
440C2×C3×Dic3C22×D311yescharacteristic
441C2×C3×Dic3C22×D311yescharacteristic
442C2×C3×Dic3C22×D311yescharacteristic
443C3×C4×D3—121no—
444C3×C4×D3—121no—
445C3×Dic6—121no—
446C3×Dic6—121no—
447#627—41no—
448#626—62no—
449#626—62no—
450#626—122no—
451#626—121no—
452#626—121no—
453#626—121no—
454#626—121no—
455#626—122no—
456#626—122no—
457#624—41no—
458#624—121no—
459#624—121no—
460#624—122no—
461D3×Dic3—121no—
462D3×Dic3—121no—
463D3×Dic3—122no—
464#538—271noSylow
465C2×C33—41no—
466C2×C33C2×#4111yescharacteristic
467C2×C33H(5,𝔽2)11yescharacteristic
468C2×C33H(5,𝔽2)11yescharacteristic
469C3⋊(C3⋊D3)—41no—
470C3×C3⋊D3—22no—
471C3×C3⋊D3—41no—
472C3×C3⋊D3—41no—
473C23×D3—91no—
474C23×D3—91no—
475C23×D3—91no—
476C2×C3×Q8—91no—
477C2×C3×D4—91no—
478C2×C3×D4—91no—
479C2×C3×D4—91no—
480C22×C3×C4—31no—
481C22×C3×C4—31no—
482C22×C3×C4—61no—
483C22×C3×C4—91no—
484C2×#67—31no—
485C2×#67—31no—
486C2×#67—31no—
487C2×#67—31no—
488C2×#67—31no—
489C2×#67—31no—
490C2×#67—61no—
491C2×#67—61no—
492C2×#67—61no—
493C2×#67—91no—
494C2×#67—91no—
495C2×#67—91no—
496C2×#67—91no—
497C2×#67—91no—
498C2×#67—91no—
499C2×#67—181no—
500C2×#67—181no—
501C2×#67—181no—
502C2×#67—361no—
503C22×Dic3—91no—
504C22×Dic3D3211yescharacteristic, complemented
505C2×D12—91no—
506C2×D12—91no—
507C2×D12—91no—
508C2×D12—91no—
509C2×D12—91no—
510C2×D12—91no—
511C2×D12—181no—
512C2×D12—181no—
513C2×D12—181no—
514C2×C4×D3—31no—
515C2×C4×D3—31no—
516C2×C4×D3—91no—
517C2×C4×D3—91no—
518C2×C4×D3—91no—
519C2×C4×D3—91no—
520C2×C4×D3—91no—
521C2×C4×D3—181no—
522C2×C4×D3—181no—
523C2×Dic6—31no—
524C2×Dic6—31no—
525C3×C4⋊C4—91no—
526C3×C4⋊C4—91no—
527C3×C4⋊C4—91no—
528C3×C22⋊C4—31no—
529C3×C22⋊C4—31no—
530C3×C22⋊C4—31no—
531C3×C22⋊C4—31no—
532C3×C22⋊C4—61no—
533C3×C22⋊C4—61no—
534C3×C22⋊C4—91no—
535C3×C22⋊C4—91no—
536C3×C22⋊C4—91no—
537C3×C22⋊C4—91no—
538C3×C22⋊C4—91no—
539C3×C42—91no—
540C3×C42—91no—
541#217—91no—
542#217—91no—
543#217—91no—
544#217—91no—
545#217—91no—
546#217D3211yescharacteristic, complemented
547#217D3211yescharacteristic, complemented
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—31no—
556(C2×D3)⋊C4—31no—
557(C2×D3)⋊C4—31no—
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—91no—
571(C2×D3)⋊C4—91no—
572(C2×D3)⋊C4—91no—
573(C2×D3)⋊C4—91no—
574(C2×D3)⋊C4—181no—
575(C2×D3)⋊C4—181no—
576(C2×D3)⋊C4—181no—
577(C2×D3)⋊C4—181no—
578C4⋊Dic3—31no—
579C4⋊Dic3—31no—
580C4⋊Dic3—91no—
581C4⋊Dic3—91no—
582C4⋊Dic3—91no—
583C4⋊Dic3—181no—
584Dic3⋊C4—31no—
585Dic3⋊C4—31no—
586Dic3⋊C4—31no—
587Dic3⋊C4—31no—
588Dic3⋊C4—91no—
589Dic3⋊C4—91no—
590Dic3⋊C4—91no—
591Dic3⋊C4—91no—
592Dic3⋊C4—91no—
593Dic3⋊C4—91no—
594Dic3⋊C4—181no—
595Dic3⋊C4—181no—
596C4×Dic3—31no—
597C4×Dic3—31no—
598C4×Dic3—31no—
599C4×Dic3—31no—
600C22×C32—21no—
601C22×C32—22no—
602C22×C32—21no—
603C22×C32—21no—
604C22×C32—21no—
605C22×C32—21no—
606C22×C32—21no—
607C22×C32—21no—
608C22×C32—21no—
609C22×C32—21no—
610C22×C32—21no—
611C22×C32—21no—
612C22×C32—21no—
613C22×C32—41no—
614C22×C32—41no—
615C22×C32—41no—
616C22×C32—42no—
617C22×C32—41no—
618C22×C32—41no—
619C22×C32—41no—
620C22×C32—41no—
621C22×C32—41no—
622C22×C32—41no—
623C22×C32—81no—
624C22×C32—81no—
625C22×C32C23×D311yescharacteristic
626C22×C32C23×D311yescharacteristic
627C22×C32C23×D311yescharacteristic
628C2×C3⋊D3—21no—
629C2×C3⋊D3—21no—
630C2×C3⋊D3—21no—
631C2×C3⋊D3—21no—
632C2×C3⋊D3—21no—
633C2×C3⋊D3—21no—
634C2×C3⋊D3—21no—
635C2×C3⋊D3—21no—
636C2×C3⋊D3—61no—
637C2×C3⋊D3—62no—
638C2×C3⋊D3—61no—
639C2×C3⋊D3—61no—
640C2×C3⋊D3—61no—
641C2×C3⋊D3—61no—
642C2×C3⋊D3—61no—
643C2×C3⋊D3—61no—
644C2×C3⋊D3—61no—
645C2×C3⋊D3—61no—
646C2×C3⋊D3—121no—
647C2×C3⋊D3—121no—
648C2×C3⋊D3—122no—
649C2×C3⋊D3—121no—
650C2×C3⋊D3—121no—
651C2×C3⋊D3—121no—
652C2×C3⋊D3—121no—
653C2×C3⋊D3—121no—
654C2×C3⋊D3—121no—
655C2×C3⋊D3—241no—
656C2×C3⋊D3—241no—
657C2×C3⋊D3#23512yes—
658C2×C3×D3—32no—
659C2×C3×D3—32no—
660C2×C3×D3—62no—
661C2×C3×D3—61no—
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—61no—
669C2×C3×D3—61no—
670C2×C3×D3—61no—
671C2×C3×D3—61no—
672C2×C3×D3—61no—
673C2×C3×D3—61no—
674C2×C3×D3—61no—
675C2×C3×D3—61no—
676C2×C3×D3—61no—
677C2×C3×D3—121no—
678C2×C3×D3—121no—
679C2×C3×D3—121no—
680C2×C3×D3—121no—
681C2×C3×D3—121no—
682C2×C3×D3—121no—
683C2×C3×D3—121no—
684C2×C3×D3—121no—
685D32—124no—
686D32—124no—
687D32—124no—
688C32×C4—61no—
689C32×C4—61no—
690C32×C4—61no—
691C32×C4—61no—
692C32×C4—61no—
693C32×C4—61no—
694C3⋊Dic3—21no—
695C3⋊Dic3—21no—
696C3⋊Dic3—21no—
697C3⋊Dic3—61no—
698C3⋊Dic3—62no—
699C3⋊Dic3—61no—
700C3⋊Dic3—61no—
701C3⋊Dic3—121no—
702C3⋊Dic3—121no—
703C3⋊Dic3—122no—
704C3×Dic3—22no—
705C3×Dic3—21no—
706C3×Dic3—21no—
707C3×Dic3—21no—
708C3×Dic3—21no—
709C3×Dic3—21no—
710C3×Dic3—21no—
711C3×Dic3—21no—
712C3×Dic3—21no—
713C3×Dic3—21no—
714C3×Dic3—21no—
715C3×Dic3—21no—
716C3×Dic3—21no—
717C3×Dic3—41no—
718C3×Dic3—41no—
719C3×Dic3—41no—
720C3×Dic3—41no—
721C3×Dic3—41no—
722C3×Dic3—62no—
723C3×Dic3—61no—
724C3×Dic3—61no—
725C3×Dic3—61no—
726C3×Dic3—61no—
727C3×Dic3—61no—
728C3×Dic3—61no—
729C3×Dic3—121no—
730C3×Dic3—121no—
731#126—271no—
732#126—271no—
733#124—91no—
734#124—271no—
735#123—91no—
736#123—271no—
737C22⋊Q8—271no—
738#121—271no—
739#121—271no—
740#121—271no—
741#120—271no—
742#120—271no—
743C4×D4—91no—
744C4×D4—271no—
745C2×C22⋊C4—271no—
746C33#53811yescharacteristic, complemented, Sylow
747C23×C3—21no—
748C23×C3—21no—
749C23×C3—21no—
750C23×C3—41no—
751C23×C3—91no—
752C23×C3—91no—
753C23×C3—91no—
754C23×C3C2×D3211yescharacteristic
755C23×C3C2×D3211yescharacteristic
756C23×C3C2×D3211yescharacteristic
757C22×D3—31no—
758C22×D3—31no—
759C22×D3—31no—
760C22×D3—31no—
761C22×D3—31no—
762C22×D3—31no—
763C22×D3—61no—
764C22×D3—61no—
765C22×D3—61no—
766C22×D3—91no—
767C22×D3—91no—
768C22×D3—91no—
769C22×D3—181no—
770C22×D3—181no—
771C22×D3—181no—
772C22×D3—182no—
773C22×D3—182no—
774C22×D3—182no—
775C22×D3—361no—
776C22×D3—361no—
777C22×D3—361no—
778C22×D3—361no—
779C22×D3—361no—
780C22×D3—361no—
781C22×D3—361no—
782C3×Q8—361no—
783C3×D4—182no—
784C3×D4—361no—
785C3×D4—361no—
786C2×C3×C4—31no—
787C2×C3×C4—31no—
788C2×C3×C4—31no—
789C2×C3×C4—31no—
790C2×C3×C4—31no—
791C2×C3×C4—31no—
792C2×C3×C4—31no—
793C2×C3×C4—31no—
794C2×C3×C4—31no—
795C2×C3×C4—31no—
796C2×C3×C4—31no—
797C2×C3×C4—31no—
798C2×C3×C4—61no—
799C2×C3×C4—61no—
800C2×C3×C4—61no—
801C2×C3×C4—61no—
802C2×C3×C4—61no—
803C2×C3×C4—61no—
804C2×C3×C4—91no—
805C2×C3×C4—91no—
806C2×C3×C4—91no—
807C2×C3×C4—121no—
808C2×C3×C4—121no—
809C2×C3×C4—122no—
810C2×C3×C4—361no—
811#67—62no—
812#67—62no—
813#67—122no—
814#67—121no—
815#67—121no—
816#67—121no—
817#67—121no—
818#67—122no—
819#67—122no—
820#67—182no—
821#67—361no—
822#67—361no—
823#67—361no—
824#67—361no—
825#67—361no—
826#67—362no—
827#67—362no—
828#67—362no—
829#67—364no—
830C2×Dic3—31no—
831C2×Dic3—31no—
832C2×Dic3—31no—
833C2×Dic3—31no—
834C2×Dic3—31no—
835C2×Dic3—31no—
836C2×Dic3—41no—
837C2×Dic3—61no—
838C2×Dic3—61no—
839C2×Dic3—61no—
840C2×Dic3—91no—
841C2×Dic3—91no—
842C2×Dic3—91no—
843C2×Dic3—181no—
844C2×Dic3—181no—
845C2×Dic3—181no—
846C2×Dic3—361no—
847C2×Dic3—361no—
848C2×Dic3C2×D3211yescharacteristic
849C2×Dic3C2×D3211yescharacteristic
850C2×Dic3C2×D3211yescharacteristic
851C2×Dic3C2×D3211yescharacteristic
852C2×Dic3C2×D3211yescharacteristic
853C2×Dic3C2×D3211yescharacteristic
854D12—182no—
855D12—182no—
856D12—362no—
857D12—361no—
858D12—361no—
859D12—361no—
860D12—361no—
861D12—362no—
862D12—362no—
863C4×D3—121no—
864C4×D3—121no—
865C4×D3—361no—
866C4×D3—361no—
867C4×D3—361no—
868C4×D3—362no—
869C4×D3—361no—
870C4×D3—361no—
871C4×D3—362no—
872Dic6—121no—
873Dic6—121no—
874C2×C32—21no—
875C2×C32—21no—
876C2×C32—21no—
877C2×C32—21no—
878C2×C32—21no—
879C2×C32—21no—
880C2×C32—21no—
881C2×C32—21no—
882C2×C32—21no—
883C2×C32—41no—
884C2×C32—41no—
885C2×C32—41no—
886C2×C32—41no—
887C2×C32—42no—
888C2×C32—41no—
889C2×C32—41no—
890C2×C32—81no—
891C2×C32—81no—
892C2×C32—82no—
893C2×C32C2×#23511yescharacteristic
894C2×C32#100411yescharacteristic
895C2×C32#100411yescharacteristic
896C2×C32#100411yescharacteristic
897C2×C32D3×#4111yescharacteristic
898C2×C32D3×#4111yescharacteristic
899C2×C32#100911yescharacteristic
900C2×C32#100911yescharacteristic
901C2×C32#100911yescharacteristic
902C3⋊D3—22no—
903C3⋊D3—41no—
904C3⋊D3—41no—
905C3⋊D3—121no—
906C3⋊D3—122no—
907C3⋊D3—121no—
908C3⋊D3—121no—
909C3⋊D3—241no—
910C3⋊D3—241no—
911C3⋊D3—242no—
912C3×D3—62no—
913C3×D3—62no—
914C3×D3—122no—
915C3×D3—121no—
916C3×D3—121no—
917C3×D3—121no—
918C3×D3—121no—
919C3×D3—241no—
920C3×D3—241no—
921C24—271no—
922C2×Q8—91no—
923C2×D4—91no—
924C2×D4—91no—
925C2×D4—91no—
926C2×D4—271no—
927C2×D4—271no—
928C2×D4—271no—
929C2×D4—271no—
930C22×C4—31no—
931C22×C4—91no—
932C22×C4—271no—
933C22×C4—271no—
934C4⋊C4—91no—
935C4⋊C4—91no—
936C4⋊C4—91no—
937C4⋊C4—271no—
938C4⋊C4—271no—
939C4⋊C4—271no—
940C22⋊C4—31no—
941C22⋊C4—31no—
942C22⋊C4—91no—
943C22⋊C4—91no—
944C22⋊C4—91no—
945C22⋊C4—91no—
946C22⋊C4—91no—
947C22⋊C4—271no—
948C22⋊C4—271no—
949C22⋊C4—271no—
950C22⋊C4—271no—
951C22⋊C4—271no—
952C22⋊C4—271no—
953C22⋊C4—271no—
954C42—91no—
955C42—91no—
956C22×C3—22no—
957C22×C3—21no—
958C22×C3—21no—
959C22×C3—21no—
960C22×C3—21no—
961C22×C3—21no—
962C22×C3—21no—
963C22×C3—21no—
964C22×C3—21no—
965C22×C3—21no—
966C22×C3—21no—
967C22×C3—21no—
968C22×C3—21no—
969C22×C3—41no—
970C22×C3—41no—
971C22×C3—41no—
972C22×C3—41no—
973C22×C3—41no—
974C22×C3—41no—
975C22×C3—41no—
976C22×C3—41no—
977C22×C3—42no—
978C22×C3—41no—
979C22×C3—81no—
980C22×C3—81no—
981C22×C3—92no—
982C22×C3—181no—
983C22×C3—181no—
984C22×C3—181no—
985C22×C3—181no—
986C22×C3—181no—
987C22×C3—181no—
988C22×C3—181no—
989C22×C3—181no—
990C22×C3C22×D3211yescharacteristic
991C22×C3C22×D3211yescharacteristic
992C22×C3C22×D3211yescharacteristic
993C2×D3—32no—
994C2×D3—32no—
995C2×D3—62no—
996C2×D3—61no—
997C2×D3—61no—
998C2×D3—61no—
999C2×D3—61no—
1000C2×D3—61no—
1001C2×D3—61no—
1002C2×D3—61no—
1003C2×D3—61no—
1004C2×D3—61no—
1005C2×D3—61no—
1006C2×D3—61no—
1007C2×D3—61no—
1008C2×D3—61no—
1009C2×D3—61no—
1010C2×D3—61no—
1011C2×D3—61no—
1012C2×D3—121no—
1013C2×D3—121no—
1014C2×D3—121no—
1015C2×D3—121no—
1016C2×D3—121no—
1017C2×D3—121no—
1018C2×D3—121no—
1019C2×D3—121no—
1020C2×D3—182no—
1021C2×D3—181no—
1022C2×D3—181no—
1023C2×D3—181no—
1024C2×D3—181no—
1025C2×D3—181no—
1026C2×D3—181no—
1027C2×D3—181no—
1028C2×D3—181no—
1029C2×D3—181no—
1030C2×D3—361no—
1031C2×D3—361no—
1032C2×D3—361no—
1033C2×D3—361no—
1034C2×D3—361no—
1035C2×D3—361no—
1036C2×D3—361no—
1037C2×D3—361no—
1038C2×D3—362no—
1039C2×D3—364no—
1040C2×D3—364no—
1041C2×D3—364no—
1042C2×D3—721no—
1043C2×D3—721no—
1044C3×C4—62no—
1045C3×C4—61no—
1046C3×C4—61no—
1047C3×C4—61no—
1048C3×C4—61no—
1049C3×C4—61no—
1050C3×C4—61no—
1051C3×C4—61no—
1052C3×C4—61no—
1053C3×C4—61no—
1054C3×C4—61no—
1055C3×C4—61no—
1056C3×C4—61no—
1057C3×C4—121no—
1058C3×C4—121no—
1059C3×C4—121no—
1060C3×C4—121no—
1061C3×C4—121no—
1062C3×C4—181no—
1063C3×C4—181no—
1064C3×C4—181no—
1065Dic3—21no—
1066Dic3—21no—
1067Dic3—21no—
1068Dic3—21no—
1069Dic3—21no—
1070Dic3—21no—
1071Dic3—62no—
1072Dic3—61no—
1073Dic3—61no—
1074Dic3—61no—
1075Dic3—61no—
1076Dic3—61no—
1077Dic3—61no—
1078Dic3—121no—
1079Dic3—121no—
1080Dic3—182no—
1081Dic3—181no—
1082Dic3—181no—
1083Dic3—181no—
1084Dic3—361no—
1085Dic3—361no—
1086Dic3—362no—
1087C32—21no—
1088C32—21no—
1089C32—21no—
1090C32—41no—
1091C32#556011yescharacteristic, complemented
1092C32#565711yescharacteristic, complemented
1093C32#567811yescharacteristic, complemented
1094C23—91no—
1095C23—91no—
1096C23—91no—
1097C23—271no—
1098C23—542no—
1099C23—1081no—
1100C23—1081no—
1101C23D3311yescharacteristic
1102Q8—361no—
1103D4—182no—
1104D4—361no—
1105D4—361no—
1106D4—542no—
1107D4—1081no—
1108D4—1081no—
1109D4—1081no—
1110C2×C4—31no—
1111C2×C4—31no—
1112C2×C4—31no—
1113C2×C4—31no—
1114C2×C4—31no—
1115C2×C4—31no—
1116C2×C4—91no—
1117C2×C4—91no—
1118C2×C4—91no—
1119C2×C4—121no—
1120C2×C4—271no—
1121C2×C4—361no—
1122C2×C4—1081no—
1123C2×C4—1081no—
1124C2×C3—21no—
1125C2×C3—21no—
1126C2×C3—21no—
1127C2×C3—21no—
1128C2×C3—21no—
1129C2×C3—21no—
1130C2×C3—21no—
1131C2×C3—21no—
1132C2×C3—21no—
1133C2×C3—42no—
1134C2×C3—41no—
1135C2×C3—41no—
1136C2×C3—41no—
1137C2×C3—41no—
1138C2×C3—41no—
1139C2×C3—41no—
1140C2×C3—81no—
1141C2×C3—81no—
1142C2×C3—82no—
1143C2×C3—182no—
1144C2×C3—361no—
1145C2×C3—361no—
1146C2×C3D3×#23511yescharacteristic
1147C2×C3D3×#23511yescharacteristic
1148C2×C3#6430711yescharacteristic
1149C2×C3#6430811yescharacteristic
1150C2×C3#6431211yescharacteristic
1151C2×C3#6431411yescharacteristic
1152C2×C3#6431411yescharacteristic
1153C2×C3#6431411yescharacteristic
1154C2×C3#6433011yescharacteristic
1155D3—62no—
1156D3—62no—
1157D3—122no—
1158D3—121no—
1159D3—121no—
1160D3—121no—
1161D3—121no—
1162D3—241no—
1163D3—241no—
1164D3—362no—
1165D3—361no—
1166D3—361no—
1167D3—361no—
1168D3—721no—
1169D3—721no—
1170D3—722no—
1171C22—21no—
1172C22—21no—
1173C22—21no—
1174C22—92no—
1175C22—181no—
1176C22—181no—
1177C22—181no—
1178C22—181no—
1179C22—181no—
1180C22—181no—
1181C22—181no—
1182C22—181no—
1183C22—541no—
1184C22—541no—
1185C22—541no—
1186C22—1084no—
1187C22C2×D3311yescharacteristic
1188C4—61no—
1189C4—61no—
1190C4—61no—
1191C4—61no—
1192C4—61no—
1193C4—61no—
1194C4—181no—
1195C4—181no—
1196C4—181no—
1197C4—541no—
1198C3—21no—
1199C3—21no—
1200C3—21no—
1201C3—41no—
1202C3#1059429811yescharacteristic, complemented
1203C3#1059430711yescharacteristic, complemented
1204C3#1059508511yescharacteristic, complemented
1205C2—41no—
1206C2—182no—
1207C2—361no—
1208C2—361no—
1209C2—1081no—
1210C2#1172441011yescharacteristic
1211C2#1172441811yescharacteristic
1212C2#1172442011yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
hypercenterC23D33
hypocenterC33#538
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #11723729C2semidirect
2. #11723632C2semidirect
3. #11723624C2semidirect
4. #11723623C2semidirect
5. C3×#63966C2semidirect
6. C3×#63953C2semidirect
7. C3×#63952C2semidirect
8. #11723024C2semidirect
9. #11723023C2semidirect
10. #11723003C2semidirect
11. #11723000C2semidirect
12. #11722974C2semidirect
13. #11722952C2semidirect
14. #11722933C2semidirect
15. #11722905C2semidirect
20. C2×#6312C22semidirect
24. C22×C32×Dic3C22semidirect
28. C2×#6289C22semidirect
30. C2×C3×#627C22semidirect
32. C32×#217C22semidirect
33. C32×#217C22semidirect
37. #88807C22semidirect
38. #88806C22semidirect
39. Dic3⋊(C3⋊Dic3)C22semidirect
40. #88804C22semidirect
41. #88804C22semidirect
44. C3×#3724C22semidirect
45. C3×Dic3⋊Dic3C22semidirect
46. C3×Dic3⋊Dic3C22semidirect
52. C3×Dic32C22semidirect
53. C3×Dic32C22semidirect
72. #63966D3semidirect
76. #63953D3semidirect
77. #63952D3semidirect
164. C22×C3×Dic3C2×D3semidirect
165. C22×C3×Dic3C2×D3semidirect
170. C2×#627C2×D3semidirect
198. C3×#217C2×D3semidirect
199. C3×#217C2×D3semidirect
200. C3×#217C2×D3semidirect
201. C3×#217C2×D3semidirect
225. #3724C2×D3semidirect
232. Dic3⋊Dic3C2×D3semidirect
233. Dic3⋊Dic3C2×D3semidirect
260. Dic32C2×D3semidirect
261. Dic32C2×D3semidirect
504. C22×Dic3D32semidirect
546. #217D32semidirect
547. #217D32semidirect
746. C33#538semidirect
1091. C32#5560semidirect
1092. C32#5657semidirect
1093. C32#5678semidirect
1202. C3#10594298semidirect
1203. C3#10594307semidirect
1204. C3#10595085semidirect

Maximal subgroups

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

subgroupindex
#117237292
#117236322
#117236242
#117236232
C3×#639662
C3×#639532
C3×#639522
#117230242
#117230232
#117230032
#117230002
#117229742
#117229522
#117229332
#117229052
#105950853
#105943073
#105942983