Finite Group Databasebeta

← #13172035

Subgroups — #13172035

Order 1728.

1354 conjugacy classes of subgroups.

The subgroup lattice has 1216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723725C211yesmaximal, characteristic, complemented
2#11723643C211yesmaximal, characteristic, complemented
3#11723632C211yesmaximal, characteristic, complemented
4#11723592C211yesmaximal, characteristic, complemented
5C3×Dic3×#67C211yesmaximal, characteristic, complemented
6C3×#63971C211yesmaximal, characteristic, complemented
7C3×#63966C211yesmaximal, characteristic, complemented
8#11723027C211yesmaximal, characteristic, complemented
9#11723021C211yesmaximal, characteristic, complemented
10#11723010C211yesmaximal, characteristic, complemented
11#11722999C211yesmaximal, characteristic, complemented
12#11722971C211yesmaximal, characteristic, complemented
13#11722950C211yesmaximal, characteristic, complemented
14#11722927C211yesmaximal, characteristic, complemented
15D3×#3722C211yesmaximal, characteristic, complemented
16#10595221—31nomaximal
17#10595085—31nomaximal
18#10594302—31nomaximal
19C22×D3×C3⋊D3C2211yescharacteristic
20C2×#6312C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic, complemented
23C2×C32×#67C2211yescharacteristic
24C22×C32×Dic3C2211yescharacteristic, complemented
25C2×#6295C2211yescharacteristic
26C2×#6294C2211yescharacteristic, complemented
27C2×#6293C2211yescharacteristic, complemented
28C2×#6292C2211yescharacteristic
29C2×C3×#626C2211yescharacteristic
30C2×C3×D3×Dic3C2211yescharacteristic
31C2×C3×D3×Dic3C2211yescharacteristic
32C3×#3757C2211yescharacteristic, complemented
33C32×#217C2211yescharacteristic, complemented
34#88815C2211yescharacteristic, complemented
35#88814C2211yescharacteristic
36Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
37#88804C2211yescharacteristic
38#88804C2211yescharacteristic
39#88804C2211yescharacteristic
40#88804C2211yescharacteristic
41#88803C2211yescharacteristic
42#88803C2211yescharacteristic, complemented
43(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
44Dic3×C3⋊Dic3C2211yescharacteristic, complemented
45C3×#3724C2211yescharacteristic, complemented
46C3×Dic3⋊Dic3C2211yescharacteristic, complemented
47C3×Dic3⋊Dic3C2211yescharacteristic, complemented
48C3×Dic3⋊Dic3C2211yescharacteristic, complemented
49C3×#3722C2211yescharacteristic
50C3×#3722C2211yescharacteristic
51C3×#3722C2211yescharacteristic, complemented
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×Dic32C2211yescharacteristic, complemented
54#64146—31no—
55#64139—31no—
56#64094—31no—
57C3×#939—31no—
58C3×D4×Dic3—31no—
59C3×#929—31no—
60C3×C4×#67—31no—
61C3×#886—31no—
62C3×#884—31no—
63#63983—31no—
64#63983—31no—
65#63983—61no—
66#63981—31no—
67#63978—31no—
68#63978—31no—
69#63978—61no—
70Dic3×#67—31no—
71Dic3×#67D311yescharacteristic, complemented
72#63971—31no—
73#63971D311yescharacteristic, complemented
74#63970—31no—
75#63966D311yescharacteristic, complemented
76#63964—31no—
77C2×#3722—31no—
78#63958—31no—
79#63953—31no—
80#63953—31no—
81#63953—61no—
82#63923—31no—
83#63922—31no—
84D3×(C2×D3)⋊C4—31no—
85D3×(C2×D3)⋊C4—31no—
86#63913—31no—
87#63904—31no—
88#63898—31no—
89#63897—31no—
90#63893—31no—
91#63890—31no—
92#63890—31no—
93#63868—31no—
94#63868—31no—
95#63862—31no—
96#63861—31no—
97#63857—31no—
98#63852—31no—
99#63852—31no—
100#63848—31no—
101#63848—31no—
102C23×C33C2311yescharacteristic
103C22×C3⋊(C3⋊D3)C2311yescharacteristic
104C22×C3×C3⋊D3C2311yescharacteristic
105C22×C3×C3⋊D3C2311yescharacteristic
106C22×C32×D3C2311yescharacteristic
107C2×D3×C3⋊D3—22no—
108C2×D3×C3⋊D3—41no—
109C2×D3×C3⋊D3—41no—
110#6312—41no—
111C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
112C3×#638—41no—
113C3×#638—41no—
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C3×C3⋊Dic3C2311yescharacteristic
118C32×#67—22no—
119C2×C32×Dic3—41no—
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123C2×C32×Dic3C2311yescharacteristic
124C2×C32×Dic3C2311yescharacteristic
125#6295—41no—
126#6294—41no—
127#6293—41no—
128#6292—41no—
129C3×#626—22no—
130C3×D3×Dic3—41no—
131C3×D3×Dic3—41no—
132#5657—91no—
133#5617—91no—
134#5560—91no—
135C23×C3⋊D3—31no—
136C22×D32—31no—
137C22×D32—31no—
138C22×D32—61no—
139C2×C32×D4—31no—
140C22×C32×C4—31no—
141C2×#638—31no—
142C2×#638—31no—
143C2×#638—31no—
144C2×#638—61no—
145C2×#638—61no—
146C2×#638—61no—
147C2×#638—121no—
148C2×#638C2×D311yescharacteristic
149C2×#638C2×D311yescharacteristic, complemented
150C2×C4⋊(C3⋊D3)—31no—
151C2×#634—31no—
152C2×C3×#67—21no—
153C2×C3×#67—31no—
154C2×C3×#67—31no—
155C2×C3×#67—31no—
156C2×C3×#67—31no—
157C2×C3×#67—31no—
158C2×C3×#67—61no—
159C2×C3×#67—61no—
160C2×C3×#67C2×D311yescharacteristic
161C2×C3×#67C2×D311yescharacteristic
162C22×C3×Dic3—21no—
163C22×C3×Dic3—31no—
164C22×C3×Dic3—31no—
165C22×C3×Dic3C2×D311yescharacteristic, complemented
166C22×C3×Dic3C2×D311yescharacteristic, complemented
167C2×C3×D12—31no—
168C2×C3×C4×D3—31no—
169C2×C3×C4×D3—31no—
170C2×#627—31no—
171C2×#627—31no—
172C2×#627—61no—
173C2×#626—31no—
174C2×#626—31no—
175C2×#626—31no—
176C2×#626—31no—
177C2×#626—61no—
178C2×#626C2×D311yescharacteristic
179C2×#625—31no—
180C2×#624—31no—
181C2×D3×Dic3—31no—
182C2×D3×Dic3—31no—
183C2×D3×Dic3C2×D311yescharacteristic
184C2×D3×Dic3C2×D311yescharacteristic
185C32×C22⋊C4—31no—
186#3757—31no—
187#3757C2×D311yescharacteristic, complemented
188#3752—31no—
189#3752—31no—
190#3752—31no—
191#3752—31no—
192#3752—31no—
193#3752—31no—
194C4⋊(C3⋊Dic3)—31no—
195C4×C3⋊Dic3—31no—
196C3×#217—21no—
197C3×#217—31no—
198C3×#217—31no—
199C3×#217—31no—
200C3×#217—61no—
201C3×#217C2×D311yescharacteristic, complemented
202C3×#217C2×D311yescharacteristic, complemented
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×C4⋊Dic3—31no—
211C3×C4⋊Dic3—31no—
212C3×C4⋊Dic3—31no—
213C3×Dic3⋊C4—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—
220#3724—31no—
221#3724C2×D311yescharacteristic, complemented
222Dic3⋊Dic3—31no—
223Dic3⋊Dic3—31no—
224Dic3⋊Dic3—31no—
225Dic3⋊Dic3—31no—
226Dic3⋊Dic3—61no—
227Dic3⋊Dic3C2×D311yescharacteristic, complemented
228Dic3⋊Dic3C2×D311yescharacteristic, complemented
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—31no—
238#3722—31no—
239#3722—61no—
240#3722—61no—
241#3722—61no—
242#3722—61no—
243#3722C2×D311yescharacteristic
244#3722C2×D311yescharacteristic
245#3722C2×D311yescharacteristic, complemented
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—31no—
253(C2×D3)⋊Dic3—31no—
254(C2×D3)⋊Dic3—61no—
255(C2×D3)⋊Dic3—61no—
256(C2×D3)⋊Dic3—61no—
257(C2×D3)⋊Dic3C2×D311yescharacteristic
258Dic32—31no—
259Dic32—31no—
260Dic32—61no—
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×C32×D3—21no—
276C2×C32×D3—21no—
277C2×C32×D3#4112yes—
278D3×C3⋊D3—44no—
279C3⋊(C3⋊Dic3)—21no—
280C3×C3⋊Dic3—21no—
281C3×C3⋊Dic3—21no—
282C3×C3⋊Dic3—21no—
283C3×C3⋊Dic3—21no—
284C32×Dic3—21no—
285C32×Dic3—21no—
286C32×Dic3—21no—
287C32×Dic3—21no—
288C32×Dic3—21no—
289C3×#123—91no—
290C3×#121—91no—
291C3×C4×D4—91no—
292#939—31no—
293#939—91no—
294#939—91no—
295#938—91no—
296#937—91no—
297#937—91no—
298#937—91no—
299#937—91no—
300#937—181no—
301D4×Dic3—31no—
302D4×Dic3—91no—
303#930—91no—
304#930—91no—
305#930—181no—
306#929—31no—
307C4×#67—31no—
308C4×#67—91no—
309C2×(C2×D3)⋊C4—91no—
310C2×(C2×D3)⋊C4—91no—
311#924—91no—
312#898—91no—
313#898—91no—
314#898—91no—
315#898—91no—
316#897—91no—
317#894—91no—
318#894—91no—
319#893—91no—
320#886—31no—
321#886—91no—
322#885—91no—
323#885—91no—
324#885—91no—
325#885—91no—
326#885—91no—
327#885—181no—
328#884—31no—
329#884—91no—
330#882—91no—
331#882—91no—
332D3×C22⋊C4—91no—
333#879—91no—
334#878—91no—
335#876—91no—
336#875—91no—
337C23×C32—21no—
338C23×C32—21no—
339C23×C32—21no—
340C23×C32—31no—
341C23×C32—41no—
342C23×C32C22×D311yescharacteristic
343C23×C32C22×D311yescharacteristic
344C23×C32C22×D311yescharacteristic
345C22×C3⋊D3—31no—
346C22×C3⋊D3—31no—
347C22×C3⋊D3—31no—
348C22×C3⋊D3—61no—
349C22×C3⋊D3—61no—
350C22×C3⋊D3—61no—
351C22×C3⋊D3—62no—
352C22×C3⋊D3—121no—
353C22×C3⋊D3—121no—
354C22×C3⋊D3—121no—
355C22×C3⋊D3C22×D311yescharacteristic
356C22×C3⋊D3C22×D311yescharacteristic
357C22×C3×D3—21no—
358C22×C3×D3—31no—
359C22×C3×D3—31no—
360C22×C3×D3—31no—
361C22×C3×D3—31no—
362C22×C3×D3—61no—
363C22×C3×D3—61no—
364C22×C3×D3C22×D311yescharacteristic
365C22×C3×D3C22×D311yescharacteristic
366C2×D32—62no—
367C2×D32—62no—
368C2×D32—122no—
369C2×D32—121no—
370C2×D32—121no—
371C2×D32—121no—
372C2×D32—121no—
373C2×D32—122no—
374C2×D32—122no—
375C32×D4—62no—
376C2×C32×C4—31no—
377C2×C32×C4—31no—
378C2×C32×C4—31no—
379C2×C32×C4—31no—
380C2×C32×C4—31no—
381C2×C32×C4—121no—
382#638—41no—
383#638—41no—
384#638—121no—
385#638—121no—
386#638—121no—
387#638—122no—
388#638—122no—
389#638—122no—
390#638—124no—
391C2×C3⋊Dic3—31no—
392C2×C3⋊Dic3—31no—
393C2×C3⋊Dic3—31no—
394C2×C3⋊Dic3—61no—
395C2×C3⋊Dic3—61no—
396C2×C3⋊Dic3—61no—
397C2×C3⋊Dic3—121no—
398C2×C3⋊Dic3C22×D311yescharacteristic
399C2×C3⋊Dic3C22×D311yescharacteristic
400C2×C3⋊Dic3C22×D311yescharacteristic
401C2×C3⋊Dic3C22×D311yescharacteristic
402C4⋊(C3⋊D3)—121no—
403#634—121no—
404C3×#67—22no—
405C3×#67—22no—
406C3×#67—42no—
407C3×#67—62no—
408C3×#67—121no—
409C3×#67—121no—
410C3×#67—121no—
411C3×#67—121no—
412C3×#67—122no—
413C3×#67—122no—
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—31no—
426C2×C3×Dic3—31no—
427C2×C3×Dic3—41no—
428C2×C3×Dic3—41no—
429C2×C3×Dic3—42no—
430C2×C3×Dic3—61no—
431C2×C3×Dic3—61no—
432C2×C3×Dic3—61no—
433C2×C3×Dic3—61no—
434C2×C3×Dic3—121no—
435C2×C3×Dic3—121no—
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
443C2×C3×Dic3C22×D311yescharacteristic
444C2×C3×Dic3C22×D311yescharacteristic
445C2×C3×Dic3C22×D311yescharacteristic
446C3×D12—62no—
447C3×C4×D3—121no—
448C3×C4×D3—121no—
449#627—121no—
450#627—121no—
451#627—122no—
452#626—22no—
453#626—121no—
454#626—121no—
455#626—122no—
456#626—121no—
457#626—121no—
458#625—121no—
459#624—121no—
460D3×Dic3—41no—
461D3×Dic3—41no—
462D3×Dic3—121no—
463D3×Dic3—121no—
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—41no—
471C3×C3⋊D3—41no—
472C32×D3—22no—
473C23×D3—91no—
474C23×D3—91no—
475C23×D3—91no—
476C23×D3—181no—
477C2×C3×D4—31no—
478C2×C3×D4—31no—
479C2×C3×D4—61no—
480C2×C3×D4—91no—
481C2×C3×D4—91no—
482C2×C3×D4—91no—
483C22×C3×C4—31no—
484C22×C3×C4—31no—
485C22×C3×C4—61no—
486C22×C3×C4—91no—
487C22×C3×C4—91no—
488C2×#67—31no—
489C2×#67—31no—
490C2×#67—31no—
491C2×#67—31no—
492C2×#67—31no—
493C2×#67—61no—
494C2×#67—61no—
495C2×#67—91no—
496C2×#67—91no—
497C2×#67—91no—
498C2×#67—91no—
499C2×#67—91no—
500C2×#67—91no—
501C2×#67—181no—
502C2×#67—181no—
503C2×#67—181no—
504C2×#67—361no—
505C2×#67D3211yescharacteristic
506C22×Dic3—31no—
507C22×Dic3—31no—
508C22×Dic3—91no—
509C22×Dic3D3211yescharacteristic, complemented
510C2×D12—31no—
511C2×D12—91no—
512C2×D12—91no—
513C2×D12—91no—
514C2×D12—181no—
515C2×C4×D3—31no—
516C2×C4×D3—31no—
517C2×C4×D3—91no—
518C2×C4×D3—91no—
519C2×Dic6—91no—
520C2×Dic6—91no—
521C2×Dic6—91no—
522C2×Dic6—181no—
523C3×C4⋊C4—91no—
524C3×C4⋊C4—91no—
525C3×C4⋊C4—91no—
526C3×C4⋊C4—91no—
527C3×C22⋊C4—31no—
528C3×C22⋊C4—31no—
529C3×C22⋊C4—61no—
530C3×C22⋊C4—91no—
531C3×C22⋊C4—91no—
532C3×C22⋊C4—91no—
533C3×C22⋊C4—91no—
534C3×C22⋊C4—91no—
535C3×C42—91no—
536#217—31no—
537#217—31no—
538#217—31no—
539#217—61no—
540#217—91no—
541#217—91no—
542#217—91no—
543#217—91no—
544#217—91no—
545#217—181no—
546#217D3211yescharacteristic, complemented
547(C2×D3)⋊C4—31no—
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—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—91no—
571(C2×D3)⋊C4—91no—
572(C2×D3)⋊C4—91no—
573(C2×D3)⋊C4—181no—
574(C2×D3)⋊C4—181no—
575(C2×D3)⋊C4—181no—
576(C2×D3)⋊C4—181no—
577(C2×D3)⋊C4—181no—
578(C2×D3)⋊C4—181no—
579C4⋊Dic3—31no—
580C4⋊Dic3—31no—
581C4⋊Dic3—31no—
582C4⋊Dic3—91no—
583C4⋊Dic3—91no—
584C4⋊Dic3—91no—
585C4⋊Dic3—181no—
586Dic3⋊C4—31no—
587Dic3⋊C4—31no—
588Dic3⋊C4—31no—
589Dic3⋊C4—31no—
590Dic3⋊C4—31no—
591Dic3⋊C4—91no—
592Dic3⋊C4—91no—
593Dic3⋊C4—91no—
594C4×Dic3—31no—
595C4×Dic3—31no—
596C4×Dic3—91no—
597C4×Dic3—91no—
598C4×Dic3—91no—
599C4×Dic3—181no—
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—32no—
614C22×C32—41no—
615C22×C32—41no—
616C22×C32—41no—
617C22×C32—42no—
618C22×C32—41no—
619C22×C32—41no—
620C22×C32—41no—
621C22×C32—41no—
622C22×C32—41no—
623C22×C32—41no—
624C22×C32—61no—
625C22×C32—61no—
626C22×C32—81no—
627C22×C32—81no—
628C22×C32C23×D311yescharacteristic
629C22×C32C23×D311yescharacteristic
630C22×C32C23×D311yescharacteristic
631C2×C3⋊D3—21no—
632C2×C3⋊D3—21no—
633C2×C3⋊D3—21no—
634C2×C3⋊D3—21no—
635C2×C3⋊D3—21no—
636C2×C3⋊D3—21no—
637C2×C3⋊D3—61no—
638C2×C3⋊D3—62no—
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—61no—
647C2×C3⋊D3—121no—
648C2×C3⋊D3—121no—
649C2×C3⋊D3—122no—
650C2×C3⋊D3—121no—
651C2×C3⋊D3—121no—
652C2×C3⋊D3—121no—
653C2×C3⋊D3—121no—
654C2×C3⋊D3—121no—
655C2×C3⋊D3—121no—
656C2×C3⋊D3—124no—
657C2×C3⋊D3—241no—
658C2×C3⋊D3—241no—
659C2×C3×D3—21no—
660C2×C3×D3—21no—
661C2×C3×D3—21no—
662C2×C3×D3—21no—
663C2×C3×D3—22no—
664C2×C3×D3—41no—
665C2×C3×D3—41no—
666C2×C3×D3—62no—
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—61no—
678C2×C3×D3—61no—
679C2×C3×D3—121no—
680C2×C3×D3—121no—
681C2×C3×D3—121no—
682C2×C3×D3—121no—
683C2×C3×D3—121no—
684C2×C3×D3#23512yes—
685C2×C3×D3#23712yes—
686D32—124no—
687D32—124no—
688D32—128no—
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—21no—
698C3⋊Dic3—61no—
699C3⋊Dic3—62no—
700C3⋊Dic3—61no—
701C3⋊Dic3—61no—
702C3⋊Dic3—121no—
703C3⋊Dic3—121no—
704C3⋊Dic3—122no—
705C3×Dic3—22no—
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—41no—
717C3×Dic3—41no—
718C3×Dic3—41no—
719C3×Dic3—41no—
720C3×Dic3—61no—
721C3×Dic3—61no—
722C3×Dic3—61no—
723C3×Dic3—61no—
724C3×Dic3—61no—
725C3×Dic3—61no—
726C3×Dic3—61no—
727C3×Dic3—61no—
728C3×Dic3—121no—
729C3×Dic3—121no—
730C3×Dic3—121no—
731C3×Dic3—121no—
732#126—271no—
733#126—271no—
734#124—271no—
735#124—271no—
736#123—91no—
737#123—271no—
738C22⋊Q8—271no—
739#121—91no—
740#121—271no—
741#121—271no—
742#120—271no—
743#120—271no—
744C4×D4—91no—
745C4×D4—271no—
746C2×C22⋊C4—271no—
747C33#53811yescharacteristic, complemented, Sylow
748C23×C3—21no—
749C23×C3—21no—
750C23×C3—21no—
751C23×C3—31no—
752C23×C3—31no—
753C23×C3—41no—
754C23×C3—61no—
755C23×C3—91no—
756C23×C3—91no—
757C23×C3C2×D3211yescharacteristic
758C23×C3C2×D3211yescharacteristic
759C23×C3C2×D3211yescharacteristic
760C22×D3—31no—
761C22×D3—31no—
762C22×D3—31no—
763C22×D3—31no—
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—362no—
777C22×D3—361no—
778C22×D3—361no—
779C22×D3—361no—
780C22×D3—361no—
781C22×D3—361no—
782C22×D3—361no—
783C22×D3—362no—
784C22×D3—362no—
785C22×D3C2×D3211yescharacteristic
786C3×D4—62no—
787C3×D4—62no—
788C3×D4—122no—
789C3×D4—182no—
790C3×D4—361no—
791C3×D4—361no—
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—31no—
799C2×C3×C4—31no—
800C2×C3×C4—31no—
801C2×C3×C4—31no—
802C2×C3×C4—61no—
803C2×C3×C4—61no—
804C2×C3×C4—61no—
805C2×C3×C4—61no—
806C2×C3×C4—61no—
807C2×C3×C4—91no—
808C2×C3×C4—91no—
809C2×C3×C4—91no—
810C2×C3×C4—91no—
811C2×C3×C4—121no—
812C2×C3×C4—121no—
813C2×C3×C4—122no—
814C2×C3×C4—361no—
815C2×C3×C4—361no—
816#67—22no—
817#67—62no—
818#67—121no—
819#67—121no—
820#67—121no—
821#67—121no—
822#67—122no—
823#67—122no—
824#67—361no—
825#67—361no—
826#67—361no—
827#67—361no—
828#67—361no—
829#67—361no—
830#67—362no—
831#67—362no—
832#67—362no—
833#67—364no—
834C2×Dic3—31no—
835C2×Dic3—31no—
836C2×Dic3—31no—
837C2×Dic3—31no—
838C2×Dic3—31no—
839C2×Dic3—31no—
840C2×Dic3—31no—
841C2×Dic3—31no—
842C2×Dic3—41no—
843C2×Dic3—61no—
844C2×Dic3—61no—
845C2×Dic3—61no—
846C2×Dic3—61no—
847C2×Dic3—91no—
848C2×Dic3—91no—
849C2×Dic3—91no—
850C2×Dic3—121no—
851C2×Dic3—121no—
852C2×Dic3—181no—
853C2×Dic3—181no—
854C2×Dic3—181no—
855C2×Dic3—361no—
856C2×Dic3—361no—
857C2×Dic3C2×D3211yescharacteristic
858C2×Dic3C2×D3211yescharacteristic
859C2×Dic3C2×D3211yescharacteristic
860C2×Dic3C2×D3211yescharacteristic
861C2×Dic3C2×D3211yescharacteristic
862D12—62no—
863D12—361no—
864D12—361no—
865D12—362no—
866D12—361no—
867C4×D3—121no—
868C4×D3—121no—
869C4×D3—361no—
870C4×D3—361no—
871Dic6—361no—
872Dic6—361no—
873Dic6—361no—
874Dic6—362no—
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—21no—
884C2×C32—41no—
885C2×C32—41no—
886C2×C32—41no—
887C2×C32—41no—
888C2×C32—42no—
889C2×C32—41no—
890C2×C32—41no—
891C2×C32—62no—
892C2×C32—81no—
893C2×C32—81no—
894C2×C32—82no—
895C2×C32C2×#23511yescharacteristic
896C2×C32C2×#23711yescharacteristic
897C2×C32#100411yescharacteristic
898C2×C32#100411yescharacteristic
899C2×C32#100411yescharacteristic
900C2×C32D3×#4111yescharacteristic
901C2×C32#100911yescharacteristic
902C2×C32#100911yescharacteristic
903C2×C32#100911yescharacteristic
904C3⋊D3—41no—
905C3⋊D3—41no—
906C3⋊D3—121no—
907C3⋊D3—122no—
908C3⋊D3—121no—
909C3⋊D3—121no—
910C3⋊D3—241no—
911C3⋊D3—241no—
912C3⋊D3—242no—
913C3×D3—22no—
914C3×D3—22no—
915C3×D3—42no—
916C3×D3—122no—
917C3×D3—121no—
918C3×D3—121no—
919C3×D3—121no—
920C3×D3—121no—
921C3×D3—241no—
922C24—271no—
923C2×Q8—271no—
924C2×D4—31no—
925C2×D4—91no—
926C2×D4—91no—
927C2×D4—91no—
928C2×D4—271no—
929C2×D4—271no—
930C2×D4—271no—
931C22×C4—31no—
932C22×C4—91no—
933C22×C4—91no—
934C22×C4—271no—
935C4⋊C4—91no—
936C4⋊C4—91no—
937C4⋊C4—91no—
938C4⋊C4—91no—
939C4⋊C4—271no—
940C4⋊C4—271no—
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—
954C22⋊C4—271no—
955C42—91no—
956C42—271no—
957C22×C3—22no—
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—21no—
970C22×C3—32no—
971C22×C3—32no—
972C22×C3—41no—
973C22×C3—41no—
974C22×C3—41no—
975C22×C3—41no—
976C22×C3—41no—
977C22×C3—41no—
978C22×C3—41no—
979C22×C3—41no—
980C22×C3—42no—
981C22×C3—41no—
982C22×C3—62no—
983C22×C3—61no—
984C22×C3—61no—
985C22×C3—61no—
986C22×C3—61no—
987C22×C3—81no—
988C22×C3—81no—
989C22×C3—121no—
990C22×C3—121no—
991C22×C3—181no—
992C22×C3—181no—
993C22×C3—181no—
994C22×C3—181no—
995C22×C3—181no—
996C22×C3—181no—
997C22×C3C22×D3211yescharacteristic
998C22×C3C22×D3211yescharacteristic
999C22×C3C22×D3211yescharacteristic
1000C2×D3—21no—
1001C2×D3—21no—
1002C2×D3—62no—
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—61no—
1013C2×D3—61no—
1014C2×D3—61no—
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—368no—
1043C2×D3—721no—
1044C2×D3—721no—
1045C2×D3#380412yes—
1046C3×C4—62no—
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—181no—
1062C3×C4—181no—
1063C3×C4—181no—
1064C3×C4—181no—
1065Dic3—21no—
1066Dic3—21no—
1067Dic3—21no—
1068Dic3—21no—
1069Dic3—21no—
1070Dic3—61no—
1071Dic3—61no—
1072Dic3—61no—
1073Dic3—61no—
1074Dic3—61no—
1075Dic3—61no—
1076Dic3—61no—
1077Dic3—61no—
1078Dic3—121no—
1079Dic3—121no—
1080Dic3—121no—
1081Dic3—121no—
1082Dic3—182no—
1083Dic3—181no—
1084Dic3—181no—
1085Dic3—181no—
1086Dic3—361no—
1087Dic3—361no—
1088Dic3—362no—
1089C32—21no—
1090C32—21no—
1091C32—21no—
1092C32—41no—
1093C32#556011yescharacteristic, complemented
1094C32#561711yescharacteristic, complemented
1095C32#565711yescharacteristic, complemented
1096C23—31no—
1097C23—91no—
1098C23—91no—
1099C23—271no—
1100C23—542no—
1101C23—1081no—
1102C23—1081no—
1103C23D3311yescharacteristic
1104Q8—1081no—
1105D4—62no—
1106D4—182no—
1107D4—361no—
1108D4—361no—
1109D4—1081no—
1110D4—1081no—
1111D4—1081no—
1112C2×C4—31no—
1113C2×C4—31no—
1114C2×C4—31no—
1115C2×C4—31no—
1116C2×C4—31no—
1117C2×C4—91no—
1118C2×C4—91no—
1119C2×C4—91no—
1120C2×C4—91no—
1121C2×C4—121no—
1122C2×C4—271no—
1123C2×C4—361no—
1124C2×C4—361no—
1125C2×C4—1081no—
1126C2×C3—21no—
1127C2×C3—21no—
1128C2×C3—21no—
1129C2×C3—21no—
1130C2×C3—21no—
1131C2×C3—21no—
1132C2×C3—21no—
1133C2×C3—21no—
1134C2×C3—21no—
1135C2×C3—42no—
1136C2×C3—41no—
1137C2×C3—41no—
1138C2×C3—41no—
1139C2×C3—41no—
1140C2×C3—41no—
1141C2×C3—41no—
1142C2×C3—62no—
1143C2×C3—62no—
1144C2×C3—81no—
1145C2×C3—81no—
1146C2×C3—82no—
1147C2×C3—122no—
1148C2×C3—361no—
1149C2×C3—361no—
1150C2×C3D3×#23511yescharacteristic
1151C2×C3#6430711yescharacteristic
1152C2×C3#6430811yescharacteristic
1153C2×C3D3×#23711yescharacteristic
1154C2×C3#6431411yescharacteristic
1155C2×C3#6431411yescharacteristic
1156C2×C3#6431411yescharacteristic
1157C2×C3C2×#380411yescharacteristic
1158C2×C3#6433011yescharacteristic
1159D3—22no—
1160D3—122no—
1161D3—121no—
1162D3—121no—
1163D3—121no—
1164D3—121no—
1165D3—241no—
1166D3—362no—
1167D3—361no—
1168D3—361no—
1169D3—361no—
1170D3—721no—
1171D3—721no—
1172D3—722no—
1173C22—21no—
1174C22—21no—
1175C22—21no—
1176C22—32no—
1177C22—61no—
1178C22—61no—
1179C22—181no—
1180C22—181no—
1181C22—181no—
1182C22—181no—
1183C22—181no—
1184C22—181no—
1185C22—541no—
1186C22—541no—
1187C22—541no—
1188C22—1084no—
1189C22C2×D3311yescharacteristic
1190C4—61no—
1191C4—61no—
1192C4—61no—
1193C4—61no—
1194C4—61no—
1195C4—181no—
1196C4—181no—
1197C4—181no—
1198C4—181no—
1199C4—541no—
1200C3—21no—
1201C3—21no—
1202C3—21no—
1203C3—41no—
1204C3#1059430211yescharacteristic, complemented
1205C3#1059508511yescharacteristic, complemented
1206C3#1059522111yescharacteristic, complemented
1207C2—41no—
1208C2—62no—
1209C2—361no—
1210C2—361no—
1211C2—1081no—
1212C2D3×#380411yescharacteristic
1213C2#1172441811yescharacteristic
1214C2#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. #11723725C2semidirect
2. #11723643C2semidirect
3. #11723632C2semidirect
4. #11723592C2semidirect
5. C3×Dic3×#67C2semidirect
6. C3×#63971C2semidirect
7. C3×#63966C2semidirect
8. #11723027C2semidirect
9. #11723021C2semidirect
10. #11723010C2semidirect
11. #11722999C2semidirect
12. #11722971C2semidirect
13. #11722950C2semidirect
14. #11722927C2semidirect
15. D3×#3722C2semidirect
22. C2×C3×#638C22semidirect
24. C22×C32×Dic3C22semidirect
26. C2×#6294C22semidirect
27. C2×#6293C22semidirect
32. C3×#3757C22semidirect
33. C32×#217C22semidirect
34. #88815C22semidirect
36. Dic3⋊(C3⋊Dic3)C22semidirect
42. #88803C22semidirect
44. Dic3×C3⋊Dic3C22semidirect
45. C3×#3724C22semidirect
46. C3×Dic3⋊Dic3C22semidirect
47. C3×Dic3⋊Dic3C22semidirect
48. C3×Dic3⋊Dic3C22semidirect
51. C3×#3722C22semidirect
53. C3×Dic32C22semidirect
71. Dic3×#67D3semidirect
73. #63971D3semidirect
75. #63966D3semidirect
149. C2×#638C2×D3semidirect
165. C22×C3×Dic3C2×D3semidirect
166. C22×C3×Dic3C2×D3semidirect
187. #3757C2×D3semidirect
201. C3×#217C2×D3semidirect
202. C3×#217C2×D3semidirect
221. #3724C2×D3semidirect
227. Dic3⋊Dic3C2×D3semidirect
228. Dic3⋊Dic3C2×D3semidirect
229. Dic3⋊Dic3C2×D3semidirect
245. #3722C2×D3semidirect
261. Dic32C2×D3semidirect
509. C22×Dic3D32semidirect
546. #217D32semidirect
747. C33#538semidirect
1093. C32#5560semidirect
1094. C32#5617semidirect
1095. C32#5657semidirect
1204. C3#10594302semidirect
1205. C3#10595085semidirect
1206. C3#10595221semidirect

Maximal subgroups

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

subgroupindex
#117237252
#117236432
#117236322
#117235922
C3×Dic3×#672
C3×#639712
C3×#639662
#117230272
#117230212
#117230102
#117229992
#117229712
#117229502
#117229272
D3×#37222
#105952213
#105950853
#105943023