Finite Group Databasebeta

← #13172678

Subgroups — #13172678

Order 1728.

1652 conjugacy classes of subgroups.

The subgroup lattice has 1302 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3804C211yesmaximal, characteristic, complemented
2C2×#88953C211yesmaximal, characteristic, complemented
3#11723729C211yesmaximal, characteristic, complemented
4#11723631C211yesmaximal, characteristic, complemented
5Dic3×#638C211yesmaximal, characteristic, complemented
6#11723615C211yesmaximal, characteristic, complemented
7C3×#63983C211yesmaximal, characteristic, complemented
8C3×#63978C211yesmaximal, characteristic, complemented
9#11723001C211yesmaximal, characteristic, complemented
10#11722992C211yesmaximal, characteristic, complemented
11#11722988C211yesmaximal, characteristic, complemented
12#11722974C211yesmaximal, characteristic, complemented
13#11722929C211yesmaximal, characteristic, complemented
14#11722905C211yesmaximal, characteristic, complemented
15D3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
16#10595304—31nomaximal
17#10595294—31nomaximal
18#10595070—31nomaximal
19C22×#1113C2211yescharacteristic
20C22×C3×D32C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic, complemented
23C2×C3×#638C2211yescharacteristic, complemented
24C2×C32×#67C2211yescharacteristic, complemented
25C2×C32×#67C2211yescharacteristic, complemented
26C22×C32×Dic3C2211yescharacteristic, complemented
27C2×#6290C2211yescharacteristic
28C2×#6290C2211yescharacteristic
29C2×Dic3×C3⋊D3C2211yescharacteristic
30C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
31C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
32C2×C3×#627C2211yescharacteristic, complemented
33C2×C3×#626C2211yescharacteristic
34C2×C3×#626C2211yescharacteristic
35C2×C3×#624C2211yescharacteristic, complemented
36C3×#3804—24no—
37C2×C3×D3×Dic3C2211yescharacteristic, complemented
38#88953—24no—
39#88864C2211yescharacteristic, complemented
40#88814C2211yescharacteristic
41#88814C2211yescharacteristic, complemented
42#88814C2211yescharacteristic, complemented
43#88807C2211yescharacteristic, complemented
44#88807C2211yescharacteristic, complemented
45Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
46#88803C2211yescharacteristic
47#88803C2211yescharacteristic, complemented
48(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
49Dic3×C3⋊Dic3C2211yescharacteristic, complemented
50C3×Dic3⋊Dic3C2211yescharacteristic, complemented
51C3×#3722C2211yescharacteristic
52C3×#3722C2211yescharacteristic, complemented
53C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
54C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
55C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
56C2×C3×#237—31no—
57C2×C3×#235—31no—
58C2×D3×#67—31no—
59C2×D3×#67—31no—
60C2×#3804D311yescharacteristic, complemented
61C2×#3802—31no—
62#64148—31no—
63#64147—31no—
64C4×#638—31no—
65C3×#939—31no—
66C3×#937—31no—
67C3×#937—31no—
68C3×#930—31no—
69#63983—31no—
70#63983—31no—
71#63983—31no—
72#63983D311yescharacteristic, complemented
73#63978D311yescharacteristic, complemented
74#63975—31no—
75#67⋊Dic3—31no—
76Dic3×#67—31no—
77Dic3×#67—31no—
78Dic3×#67—61no—
79#63970—31no—
80#63970—31no—
81#63970—31no—
82#63970—31no—
83#63970—61no—
84#63970—61no—
85D3×#217—31no—
86#63966—31no—
87C2×(C2×D3)⋊Dic3—31no—
88#63959—31no—
89#63921—31no—
90D3×(C2×D3)⋊C4—31no—
91D3×(C2×D3)⋊C4—31no—
92D3×(C2×D3)⋊C4—31no—
93#63907—31no—
94#63905—31no—
95#63905—31no—
96#63905—31no—
97#63898—31no—
98#63893—31no—
99#63891—31no—
100#63887—31no—
101#63881—31no—
102#63871—31no—
103#63863—31no—
104C23×C33C2311yescharacteristic
105C22×C3×C3⋊D3C2311yescharacteristic
106C22×C3×C3⋊D3C2311yescharacteristic
107C22×C3×C3⋊D3C2311yescharacteristic
108C22×C32×D3C2311yescharacteristic
109C22×C32×D3C2311yescharacteristic
110C2×#1113—22no—
111C2×#1113—22no—
112C2×#1113—41no—
113C2×C3×D32—22no—
114C2×C3×D32—22no—
115C2×C3×D32—41no—
116C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
117C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
118C3×#638—22no—
119C3×#638—22no—
120C3×#638—41no—
121C2×C3×C3⋊Dic3C2311yescharacteristic
122C2×C3×C3⋊Dic3C2311yescharacteristic
123C2×C3×C3⋊Dic3C2311yescharacteristic
124C32×#67—22no—
125C32×#67—41no—
126C2×C32×Dic3—22no—
127C2×C32×Dic3C2311yescharacteristic
128C2×C32×Dic3C2311yescharacteristic
129C2×C32×Dic3C2311yescharacteristic
130C2×C32×Dic3C2311yescharacteristic
131#6290—22no—
132#6290—22no—
133Dic3×C3⋊D3—22no—
134Dic3×C3⋊D3—41no—
135D3×C3⋊Dic3—41no—
136C3×#627—22no—
137C3×#626—22no—
138C3×#626D414yescomplemented
139C3×#624—22no—
140C3×D3×Dic3—22no—
141#5829—91no—
142#5612—91no—
143#5591—91no—
144C23×C3×D3—31no—
145C23×C3×D3—31no—
146C22×D32—31no—
147C22×D32—31no—
148C22×D32—31no—
149C22×D32C2×D311yescharacteristic
150C2×C32×D4—31no—
151C2×C32×D4—31no—
152C22×C32×C4—31no—
153C2×#638—31no—
154C2×#638—31no—
155C2×#638C2×D311yescharacteristic
156C2×#638C2×D311yescharacteristic, complemented
157C2×#638C2×D311yescharacteristic, complemented
158C22×C3⋊Dic3—31no—
159C2×C4×C3⋊D3—31no—
160C2×C4×C3⋊D3—31no—
161C2×C3×#67—21no—
162C2×C3×#67—21no—
163C2×C3×#67—31no—
164C2×C3×#67—31no—
165C2×C3×#67—31no—
166C2×C3×#67—31no—
167C2×C3×#67—31no—
168C2×C3×#67—31no—
169C2×C3×#67—31no—
170C2×C3×#67—31no—
171C2×C3×#67—61no—
172C2×C3×#67—61no—
173C2×C3×#67—61no—
174C2×C3×#67C2×D311yescharacteristic, complemented
175C2×C3×#67C2×D311yescharacteristic, complemented
176C2×C3×#67C2×D311yescharacteristic, complemented
177C2×C3×#67C2×D311yescharacteristic, complemented
178C22×C3×Dic3—21no—
179C22×C3×Dic3—31no—
180C22×C3×Dic3C2×D311yescharacteristic, complemented
181C22×C3×Dic3C2×D311yescharacteristic, complemented
182C3×#237—64no—
183C3×#235—64no—
184C2×C3×D12—31no—
185C2×C3×D12—31no—
186C2×C3×C4×D3—31no—
187C2×C3×C4×D3—31no—
188C2×C3×C4×D3—31no—
189C2×C3×Dic6—31no—
190C2×C3×Dic6—31no—
191D3×#67—64no—
192D3×#67—64no—
193C2×#627C2×D311yescharacteristic, complemented
194C2×#626C2×D311yescharacteristic
195C2×#626C2×D311yescharacteristic
196C2×#625—31no—
197C2×#625—31no—
198C2×#625—31no—
199C2×#625—31no—
200C2×#625—61no—
201C2×#625—61no—
202C2×#624C2×D311yescharacteristic, complemented
203#3804—24no—
204C2×D3×Dic3—31no—
205C2×D3×Dic3—31no—
206C2×D3×Dic3—31no—
207C2×D3×Dic3—31no—
208C2×D3×Dic3—31no—
209C2×D3×Dic3—31no—
210C2×D3×Dic3—61no—
211C2×D3×Dic3—61no—
212C2×D3×Dic3—61no—
213C2×D3×Dic3C2×D311yescharacteristic, complemented
214#3802—64no—
215#3757—31no—
216#3757—31no—
217#3757—31no—
218#3757—31no—
219#3757—61no—
220#3757—61no—
221#3757—61no—
222#3757—121no—
223#3752—31no—
224#3752—31no—
225C4⋊(C3⋊Dic3)—31no—
226#3750—31no—
227#3750—31no—
228C4×C3⋊Dic3—31no—
229C3×#217—31no—
230C3×#217—31no—
231C3×#217—31no—
232C3×(C2×D3)⋊C4—31no—
233C3×(C2×D3)⋊C4—31no—
234C3×(C2×D3)⋊C4—31no—
235C3×(C2×D3)⋊C4—31no—
236C3×(C2×D3)⋊C4—31no—
237C3×(C2×D3)⋊C4—31no—
238C3×(C2×D3)⋊C4—31no—
239C3×C4⋊Dic3—31no—
240C3×Dic3⋊C4—31no—
241Dic3⋊Dic3—31no—
242Dic3⋊Dic3—31no—
243Dic3⋊Dic3—31no—
244Dic3⋊Dic3—31no—
245Dic3⋊Dic3—31no—
246Dic3⋊Dic3—31no—
247Dic3⋊Dic3—61no—
248Dic3⋊Dic3—61no—
249Dic3⋊Dic3—61no—
250Dic3⋊Dic3C2×D311yescharacteristic, complemented
251#3722—31no—
252#3722—31no—
253#3722—31no—
254#3722C2×D311yescharacteristic
255#3722C2×D311yescharacteristic, complemented
256(C2×D3)⋊Dic3—31no—
257(C2×D3)⋊Dic3—31no—
258(C2×D3)⋊Dic3—31no—
259(C2×D3)⋊Dic3—31no—
260(C2×D3)⋊Dic3—31no—
261(C2×D3)⋊Dic3—31no—
262(C2×D3)⋊Dic3—31no—
263(C2×D3)⋊Dic3—31no—
264(C2×D3)⋊Dic3—31no—
265(C2×D3)⋊Dic3—31no—
266(C2×D3)⋊Dic3—31no—
267(C2×D3)⋊Dic3—31no—
268(C2×D3)⋊Dic3—61no—
269(C2×D3)⋊Dic3—61no—
270(C2×D3)⋊Dic3—61no—
271(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
272(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
273(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
274Dic32—31no—
275Dic32—31no—
276Dic32—61no—
277C22×C33—21no—
278C22×C33—21no—
279C22×C33—21no—
280C22×C33C2411yescharacteristic
281C2×C3×C3⋊D3—21no—
282C2×C3×C3⋊D3—21no—
283C2×C3×C3⋊D3—21no—
284C2×C3×C3⋊D3—21no—
285C2×C3×C3⋊D3—21no—
286C2×C3×C3⋊D3—21no—
287C2×C3×C3⋊D3—21no—
288C2×C3×C3⋊D3C2×D412yes—
289C2×C3×C3⋊D3#4112yescomplemented
290C2×C32×D3—21no—
291C2×C32×D3—21no—
292C2×C32×D3—21no—
293C2×C32×D3—21no—
294C2×C32×D3—21no—
295C2×C32×D3C2×D412yes—
296#1113—44no—
297C3×D32—44no—
298C3⋊(C3⋊Dic3)—21no—
299C3⋊(C3⋊Dic3)—21no—
300C3×C3⋊Dic3—21no—
301C3×C3⋊Dic3—21no—
302C3×C3⋊Dic3—21no—
303C32×Dic3—21no—
304C32×Dic3—21no—
305C32×Dic3—21no—
306C32×Dic3C2×D412yes—
307C2×C3×#41—91no—
308C22×#67—91no—
309C2×#237—31no—
310C2×D3×D4—91no—
311C2×D3×D4—91no—
312C2×#235—31no—
313C3×#121—91no—
314C3×#120—91no—
315C2×#217—91no—
316#947—91no—
317#946—91no—
318#939—31no—
319#939—91no—
320#939—91no—
321#939—91no—
322#939—181no—
323#938—91no—
324#938—91no—
325#938—91no—
326#938—181no—
327#937—31no—
328#937—31no—
329#937—91no—
330#937—91no—
331#937—91no—
332#936—91no—
333D4×Dic3—91no—
334D4×Dic3—91no—
335#930—31no—
336#929—91no—
337#929—91no—
338C4×#67—91no—
339C4×#67—91no—
340C4×#67—181no—
341C2×(C2×D3)⋊C4—91no—
342C2×(C2×D3)⋊C4—91no—
343#897—91no—
344#893—91no—
345#886—91no—
346#885—91no—
347#883—91no—
348#883—91no—
349#883—91no—
350#67⋊C4—91no—
351D3×C22⋊C4—91no—
352D3×C22⋊C4—91no—
353D3×C22⋊C4—91no—
354#878—91no—
355C23×C32—21no—
356C23×C32—21no—
357C23×C32—21no—
358C23×C32—31no—
359C23×C32—31no—
360C23×C32—41no—
361C23×C32C22×D311yescharacteristic
362C23×C32C22×D311yescharacteristic
363C23×C32C22×D311yescharacteristic
364C22×C3⋊D3C22×D311yescharacteristic
365C22×C3⋊D3C22×D311yescharacteristic
366C22×C3⋊D3C22×D311yescharacteristic
367C22×C3×D3—21no—
368C22×C3×D3—21no—
369C22×C3×D3—31no—
370C22×C3×D3—31no—
371C22×C3×D3—31no—
372C22×C3×D3—31no—
373C22×C3×D3—31no—
374C22×C3×D3—31no—
375C22×C3×D3—61no—
376C22×C3×D3—61no—
377C22×C3×D3—61no—
378C22×C3×D3—62no—
379C22×C3×D3—62no—
380C22×C3×D3—62no—
381C22×C3×D3—62no—
382C22×C3×D3—121no—
383C22×C3×D3—121no—
384C22×C3×D3C22×D311yescharacteristic
385C22×C3×D3C22×D311yescharacteristic
386C22×C3×D3C22×D311yescharacteristic
387C22×C3×D3C22×D311yescharacteristic
388C2×D32—22no—
389C2×D32—22no—
390C2×D32—41no—
391C2×D32—62no—
392C2×D32—62no—
393C2×D32—62no—
394C2×D32—62no—
395C2×D32—62no—
396C2×D32—62no—
397C2×D32—121no—
398C2×D32—121no—
399C2×D32—121no—
400C32×D4—62no—
401C32×D4—121no—
402C2×C32×C4—31no—
403C2×C32×C4—31no—
404C2×C32×C4—31no—
405C2×C32×C4—31no—
406C2×C32×C4—62no—
407#638—22no—
408#638—22no—
409#638—41no—
410#638—62no—
411#638—62no—
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—61no—
423C2×C3⋊Dic3—61no—
424C2×C3⋊Dic3—121no—
425C2×C3⋊Dic3—121no—
426C2×C3⋊Dic3—121no—
427C2×C3⋊Dic3C22×D311yescharacteristic
428C2×C3⋊Dic3C22×D311yescharacteristic
429C2×C3⋊Dic3C22×D311yescharacteristic
430C4×C3⋊D3—62no—
431C4×C3⋊D3—121no—
432C3×#67—22no—
433C3×#67—22no—
434C3×#67—34no—
435C3×#67—42no—
436C3×#67—41no—
437C3×#67—41no—
438C3×#67—42no—
439C3×#67—62no—
440C3×#67—62no—
441C3×#67—62no—
442C3×#67—62no—
443C3×#67—64no—
444C3×#67—62no—
445C3×#67—122no—
446C3×#67—121no—
447C3×#67—121no—
448C3×#67—122no—
449C2×C3×Dic3—22no—
450C2×C3×Dic3—22no—
451C2×C3×Dic3—21no—
452C2×C3×Dic3—21no—
453C2×C3×Dic3—21no—
454C2×C3×Dic3—21no—
455C2×C3×Dic3—31no—
456C2×C3×Dic3—31no—
457C2×C3×Dic3—31no—
458C2×C3×Dic3—31no—
459C2×C3×Dic3—31no—
460C2×C3×Dic3—31no—
461C2×C3×Dic3—42no—
462C2×C3×Dic3—61no—
463C2×C3×Dic3—61no—
464C2×C3×Dic3—61no—
465C2×C3×Dic3—62no—
466C2×C3×Dic3C22×D311yescharacteristic
467C2×C3×Dic3C22×D311yescharacteristic
468C2×C3×Dic3C22×D311yescharacteristic
469C2×C3×Dic3C22×D311yescharacteristic
470C2×C3×Dic3C22×D311yescharacteristic
471C2×C3×Dic3C22×D311yescharacteristic
472C2×C3×Dic3C22×D311yescharacteristic
473C2×C3×Dic3C22×D311yescharacteristic
474C3×D12—34no—
475C3×D12—62no—
476C3×C4×D3—62no—
477C3×C4×D3—62no—
478C3×C4×D3—62no—
479C3×Dic6—62no—
480C3×Dic6—62no—
481#627—22no—
482#626—22no—
483#626#6714yescomplemented
484#625—62no—
485#625—62no—
486#625—62no—
487#625—62no—
488#625—122no—
489#625—122no—
490#624—22no—
491D3×Dic3—22no—
492D3×Dic3—62no—
493D3×Dic3—62no—
494D3×Dic3—122no—
495D3×Dic3—121no—
496D3×Dic3—121no—
497D3×Dic3—122no—
498D3×Dic3—121no—
499D3×Dic3—121no—
500D3×Dic3—122no—
501#546—271noSylow
502C2×C33—41no—
503C2×C33C22×D411yescharacteristic
504C2×C33C2×#4111yescharacteristic
505C2×C33H(5,𝔽2)11yescharacteristic
506C3×C3⋊D3—22no—
507C3×C3⋊D3—22no—
508C3×C3⋊D3—41no—
509C32×D3—22no—
510C32×D3—41no—
511C24×C3—91no—
512C23×D3—31no—
513C23×D3—31no—
514C23×D3—91no—
515C23×D3—91no—
516C23×D3—91no—
517C3×#41—184no—
518C2×C3×Q8—91no—
519C2×C3×D4—31no—
520C2×C3×D4—31no—
521C2×C3×D4—31no—
522C2×C3×D4—31no—
523C2×C3×D4—61no—
524C2×C3×D4—61no—
525C2×C3×D4—91no—
526C2×C3×D4—91no—
527C2×C3×D4—91no—
528C2×C3×D4—91no—
529C2×C3×D4—91no—
530C22×C3×C4—31no—
531C22×C3×C4—31no—
532C22×C3×C4—61no—
533C22×C3×C4—91no—
534C22×C3×C4—91no—
535C2×#67—31no—
536C2×#67—31no—
537C2×#67—31no—
538C2×#67—31no—
539C2×#67—31no—
540C2×#67—31no—
541C2×#67—31no—
542C2×#67—31no—
543C2×#67—61no—
544C2×#67—61no—
545C2×#67—61no—
546C2×#67—91no—
547C2×#67—91no—
548C2×#67—91no—
549C2×#67—91no—
550C2×#67—91no—
551C2×#67—91no—
552C2×#67—181no—
553C2×#67—181no—
554C2×#67—184no—
555C2×#67D3211yescharacteristic, complemented
556C2×#67D3211yescharacteristic, complemented
557C22×Dic3—31no—
558C22×Dic3—91no—
559C22×Dic3—91no—
560C22×Dic3—91no—
561C22×Dic3—91no—
562C22×Dic3—181no—
563C22×Dic3D3211yescharacteristic, complemented
564#237—64no—
565D3×D4—184no—
566D3×D4—184no—
567#235—64no—
568C2×D12—31no—
569C2×D12—31no—
570C2×C4×D3—31no—
571C2×C4×D3—31no—
572C2×C4×D3—31no—
573C2×C4×D3—91no—
574C2×C4×D3—91no—
575C2×C4×D3—91no—
576C2×C4×D3—91no—
577C2×C4×D3—91no—
578C2×C4×D3—181no—
579C2×C4×D3—181no—
580C2×Dic6—31no—
581C2×Dic6—31no—
582C3×C4⋊C4—91no—
583C3×C22⋊C4—91no—
584C3×C22⋊C4—91no—
585C3×C22⋊C4—91no—
586C3×C22⋊C4—91no—
587C3×C22⋊C4—91no—
588#217—31no—
589#217—31no—
590#217—31no—
591#217—91no—
592#217—91no—
593#217—91no—
594#217—91no—
595#217—91no—
596#217—91no—
597#217—91no—
598#217—91no—
599#217—91no—
600#217—91no—
601#217—181no—
602#217—181no—
603#217—181no—
604#217—181no—
605#217—361no—
606(C2×D3)⋊C4—31no—
607(C2×D3)⋊C4—31no—
608(C2×D3)⋊C4—31no—
609(C2×D3)⋊C4—31no—
610(C2×D3)⋊C4—31no—
611(C2×D3)⋊C4—31no—
612(C2×D3)⋊C4—31no—
613(C2×D3)⋊C4—91no—
614(C2×D3)⋊C4—91no—
615(C2×D3)⋊C4—91no—
616(C2×D3)⋊C4—91no—
617(C2×D3)⋊C4—91no—
618(C2×D3)⋊C4—91no—
619(C2×D3)⋊C4—91no—
620(C2×D3)⋊C4—91no—
621(C2×D3)⋊C4—91no—
622(C2×D3)⋊C4—91no—
623(C2×D3)⋊C4—91no—
624(C2×D3)⋊C4—181no—
625(C2×D3)⋊C4—181no—
626C4⋊Dic3—31no—
627C4⋊Dic3—91no—
628C4⋊Dic3—91no—
629C4⋊Dic3—91no—
630C4⋊Dic3—91no—
631C4⋊Dic3—181no—
632Dic3⋊C4—31no—
633Dic3⋊C4—91no—
634Dic3⋊C4—91no—
635Dic3⋊C4—91no—
636Dic3⋊C4—91no—
637Dic3⋊C4—91no—
638Dic3⋊C4—181no—
639Dic3⋊C4—181no—
640C4×Dic3—91no—
641C4×Dic3—91no—
642C4×Dic3—91no—
643C4×Dic3—181no—
644C22×C32—21no—
645C22×C32—22no—
646C22×C32—21no—
647C22×C32—21no—
648C22×C32—21no—
649C22×C32—21no—
650C22×C32—21no—
651C22×C32—21no—
652C22×C32—21no—
653C22×C32—21no—
654C22×C32—21no—
655C22×C32—21no—
656C22×C32—21no—
657C22×C32—32no—
658C22×C32—41no—
659C22×C32—41no—
660C22×C32—41no—
661C22×C32—42no—
662C22×C32—41no—
663C22×C32—41no—
664C22×C32—41no—
665C22×C32—41no—
666C22×C32—41no—
667C22×C32—41no—
668C22×C32—61no—
669C22×C32—61no—
670C22×C32—61no—
671C22×C32—61no—
672C22×C32—61no—
673C22×C32—81no—
674C22×C32—81no—
675C22×C32C23×D311yescharacteristic
676C22×C32C23×D311yescharacteristic
677C22×C32C23×D311yescharacteristic
678C2×C3⋊D3—21no—
679C2×C3⋊D3—21no—
680C2×C3⋊D3—21no—
681C2×C3⋊D3—21no—
682C2×C3⋊D3—21no—
683C2×C3⋊D3—21no—
684C2×C3⋊D3—21no—
685C2×C3⋊D3#23712yescomplemented
686C2×C3⋊D3C2×#6712yes—
687C2×C3×D3—21no—
688C2×C3×D3—21no—
689C2×C3×D3—21no—
690C2×C3×D3—21no—
691C2×C3×D3—21no—
692C2×C3×D3—21no—
693C2×C3×D3—21no—
694C2×C3×D3—21no—
695C2×C3×D3—21no—
696C2×C3×D3—21no—
697C2×C3×D3—22no—
698C2×C3×D3—32no—
699C2×C3×D3—32no—
700C2×C3×D3—32no—
701C2×C3×D3—32no—
702C2×C3×D3—41no—
703C2×C3×D3—41no—
704C2×C3×D3—41no—
705C2×C3×D3—41no—
706C2×C3×D3—41no—
707C2×C3×D3—62no—
708C2×C3×D3—62no—
709C2×C3×D3—61no—
710C2×C3×D3—61no—
711C2×C3×D3—61no—
712C2×C3×D3—61no—
713C2×C3×D3—61no—
714C2×C3×D3—61no—
715C2×C3×D3—61no—
716C2×C3×D3—61no—
717C2×C3×D3—61no—
718C2×C3×D3—61no—
719C2×C3×D3—61no—
720C2×C3×D3—61no—
721C2×C3×D3—61no—
722C2×C3×D3—61no—
723C2×C3×D3—121no—
724C2×C3×D3—121no—
725C2×C3×D3—121no—
726C2×C3×D3—121no—
727C2×C3×D3—121no—
728C2×C3×D3—121no—
729C2×C3×D3—121no—
730C2×C3×D3—124no—
731C2×C3×D3—124no—
732C2×C3×D3D3×D412yes—
733C2×C3×D3C2×#6712yes—
734D32—44no—
735D32—124no—
736D32—124no—
737D32—124no—
738C32×C4—32no—
739C32×C4—61no—
740C32×C4—61no—
741C32×C4—61no—
742C3⋊Dic3—21no—
743C3⋊Dic3—21no—
744C3⋊Dic3—21no—
745C3⋊Dic3—61no—
746C3⋊Dic3—61no—
747C3⋊Dic3—61no—
748C3⋊Dic3—61no—
749C3⋊Dic3—61no—
750C3⋊Dic3—61no—
751C3⋊Dic3—121no—
752C3⋊Dic3—121no—
753C3⋊Dic3—121no—
754C3⋊Dic3—121no—
755C3⋊Dic3—121no—
756C3⋊Dic3—121no—
757C3⋊Dic3—241no—
758C3⋊Dic3—241no—
759C3×Dic3—22no—
760C3×Dic3—21no—
761C3×Dic3—21no—
762C3×Dic3—21no—
763C3×Dic3—21no—
764C3×Dic3—21no—
765C3×Dic3—21no—
766C3×Dic3—22no—
767C3×Dic3—41no—
768C3×Dic3—41no—
769C3×Dic3—62no—
770C3×Dic3—62no—
771C3×Dic3—61no—
772C3×Dic3—61no—
773C3×Dic3—61no—
774C3×Dic3—61no—
775C3×Dic3—61no—
776C3×Dic3—61no—
777C3×Dic3—121no—
778C3×Dic3D3×D412yes—
779C3×Dic3C2×#6712yes—
780C2×#41—91no—
781C22×D4—271no—
782#124—271no—
783#123—271no—
784#123—271no—
785C22⋊Q8—271no—
786#121—91no—
787#121—271no—
788#121—271no—
789#120—91no—
790#120—271no—
791C4×D4—271no—
792C4×D4—271no—
793C2×C22⋊C4—271no—
794C2×C22⋊C4—271no—
795C33#54611yescharacteristic, complemented, Sylow
796C23×C3—21no—
797C23×C3—21no—
798C23×C3—21no—
799C23×C3—31no—
800C23×C3—31no—
801C23×C3—31no—
802C23×C3—31no—
803C23×C3—41no—
804C23×C3—61no—
805C23×C3—61no—
806C23×C3—91no—
807C23×C3—91no—
808C23×C3—91no—
809C23×C3—182no—
810C23×C3—182no—
811C23×C3—361no—
812C23×C3C2×D3211yescharacteristic
813C23×C3C2×D3211yescharacteristic
814C23×C3C2×D3211yescharacteristic
815C22×D3—31no—
816C22×D3—31no—
817C22×D3—31no—
818C22×D3—31no—
819C22×D3—31no—
820C22×D3—31no—
821C22×D3—61no—
822C22×D3—61no—
823C22×D3—61no—
824C22×D3—62no—
825C22×D3—62no—
826C22×D3—62no—
827C22×D3—62no—
828C22×D3—121no—
829C22×D3—121no—
830C22×D3—182no—
831C22×D3—182no—
832C22×D3—182no—
833C22×D3—182no—
834C22×D3—182no—
835C22×D3—182no—
836C22×D3—361no—
837C22×D3—361no—
838C22×D3—361no—
839C22×D3C2×D3211yescharacteristic
840C22×D3C2×D3211yescharacteristic
841C3×Q8—182no—
842C3×D4—62no—
843C3×D4—62no—
844C3×D4—94no—
845C3×D4—122no—
846C3×D4—121no—
847C3×D4—121no—
848C3×D4—122no—
849C3×D4—182no—
850C3×D4—182no—
851C3×D4—182no—
852C3×D4—361no—
853C2×C3×C4—31no—
854C2×C3×C4—31no—
855C2×C3×C4—31no—
856C2×C3×C4—31no—
857C2×C3×C4—31no—
858C2×C3×C4—31no—
859C2×C3×C4—31no—
860C2×C3×C4—31no—
861C2×C3×C4—61no—
862C2×C3×C4—61no—
863C2×C3×C4—61no—
864C2×C3×C4—61no—
865C2×C3×C4—62no—
866C2×C3×C4—62no—
867C2×C3×C4—91no—
868C2×C3×C4—91no—
869C2×C3×C4—91no—
870C2×C3×C4—122no—
871C2×C3×C4—182no—
872C2×C3×C4—182no—
873#67—22no—
874#67—34no—
875#67—41no—
876#67—62no—
877#67—62no—
878#67—62no—
879#67—62no—
880#67—64no—
881#67—62no—
882#67—122no—
883#67—121no—
884#67—121no—
885#67—122no—
886#67—182no—
887#67—182no—
888#67—182no—
889#67—182no—
890#67—182no—
891#67—182no—
892#67—362no—
893#67—362no—
894C2×Dic3—22no—
895C2×Dic3—31no—
896C2×Dic3—31no—
897C2×Dic3—31no—
898C2×Dic3—31no—
899C2×Dic3—31no—
900C2×Dic3—31no—
901C2×Dic3—61no—
902C2×Dic3—61no—
903C2×Dic3—61no—
904C2×Dic3—62no—
905C2×Dic3—91no—
906C2×Dic3—91no—
907C2×Dic3—91no—
908C2×Dic3—91no—
909C2×Dic3—91no—
910C2×Dic3—91no—
911C2×Dic3—181no—
912C2×Dic3—181no—
913C2×Dic3—181no—
914C2×Dic3—181no—
915C2×Dic3—181no—
916C2×Dic3—181no—
917C2×Dic3—182no—
918C2×Dic3—361no—
919C2×Dic3—361no—
920C2×Dic3—361no—
921C2×Dic3—361no—
922C2×Dic3—361no—
923C2×Dic3—362no—
924C2×Dic3C2×D3211yescharacteristic
925C2×Dic3C2×D3211yescharacteristic
926C2×Dic3C2×D3211yescharacteristic
927C2×Dic3C2×D3211yescharacteristic
928D12—34no—
929D12—62no—
930C4×D3—62no—
931C4×D3—62no—
932C4×D3—62no—
933C4×D3—182no—
934C4×D3—182no—
935C4×D3—362no—
936C4×D3—361no—
937C4×D3—361no—
938C4×D3—361no—
939C4×D3—362no—
940Dic6—62no—
941Dic6—62no—
942C2×C32—21no—
943C2×C32—21no—
944C2×C32—21no—
945C2×C32—21no—
946C2×C32—21no—
947C2×C32—21no—
948C2×C32—21no—
949C2×C32—21no—
950C2×C32—21no—
951C2×C32—41no—
952C2×C32—41no—
953C2×C32—41no—
954C2×C32—41no—
955C2×C32—42no—
956C2×C32—41no—
957C2×C32—41no—
958C2×C32—62no—
959C2×C32—81no—
960C2×C32—81no—
961C2×C32—82no—
962C2×C32—121no—
963C2×C32C2×D3×D411yescharacteristic
964C2×C32C2×D3×D411yescharacteristic
965C2×C32C2×#23711yescharacteristic
966C2×C32#100411yescharacteristic
967C2×C32#100411yescharacteristic
968C2×C32D3×#4111yescharacteristic
969C2×C32D3×#4111yescharacteristic
970C2×C32#100911yescharacteristic
971C2×C32C22×#6711yescharacteristic
972C3⋊D3—22no—
973C3⋊D3—22no—
974C3⋊D3—41no—
975C3×D3—22no—
976C3×D3—22no—
977C3×D3—42no—
978C3×D3—41no—
979C3×D3—41no—
980C3×D3—62no—
981C3×D3—62no—
982C3×D3—62no—
983C3×D3—62no—
984C3×D3—81no—
985C3×D3—122no—
986C3×D3—122no—
987C3×D3—121no—
988C3×D3—121no—
989C3×D3—241no—
990C24—91no—
991C24—271no—
992#41—184no—
993C2×Q8—91no—
994C2×D4—31no—
995C2×D4—31no—
996C2×D4—91no—
997C2×D4—91no—
998C2×D4—91no—
999C2×D4—91no—
1000C2×D4—91no—
1001C2×D4—271no—
1002C2×D4—271no—
1003C2×D4—544no—
1004C22×C4—31no—
1005C22×C4—91no—
1006C22×C4—91no—
1007C22×C4—271no—
1008C22×C4—271no—
1009C22×C4—271no—
1010C4⋊C4—91no—
1011C4⋊C4—271no—
1012C4⋊C4—271no—
1013C4⋊C4—271no—
1014C22⋊C4—91no—
1015C22⋊C4—91no—
1016C22⋊C4—91no—
1017C22⋊C4—91no—
1018C22⋊C4—91no—
1019C22⋊C4—271no—
1020C22⋊C4—271no—
1021C22⋊C4—271no—
1022C22⋊C4—271no—
1023C22⋊C4—271no—
1024C22⋊C4—271no—
1025C22⋊C4—271no—
1026C42—271no—
1027C22×C3—22no—
1028C22×C3—21no—
1029C22×C3—21no—
1030C22×C3—21no—
1031C22×C3—21no—
1032C22×C3—21no—
1033C22×C3—21no—
1034C22×C3—21no—
1035C22×C3—21no—
1036C22×C3—21no—
1037C22×C3—21no—
1038C22×C3—21no—
1039C22×C3—21no—
1040C22×C3—32no—
1041C22×C3—32no—
1042C22×C3—41no—
1043C22×C3—41no—
1044C22×C3—41no—
1045C22×C3—41no—
1046C22×C3—41no—
1047C22×C3—41no—
1048C22×C3—41no—
1049C22×C3—41no—
1050C22×C3—42no—
1051C22×C3—41no—
1052C22×C3—62no—
1053C22×C3—61no—
1054C22×C3—61no—
1055C22×C3—61no—
1056C22×C3—61no—
1057C22×C3—61no—
1058C22×C3—61no—
1059C22×C3—61no—
1060C22×C3—61no—
1061C22×C3—61no—
1062C22×C3—61no—
1063C22×C3—81no—
1064C22×C3—81no—
1065C22×C3—92no—
1066C22×C3—92no—
1067C22×C3—121no—
1068C22×C3—121no—
1069C22×C3—121no—
1070C22×C3—121no—
1071C22×C3—121no—
1072C22×C3—181no—
1073C22×C3—181no—
1074C22×C3—181no—
1075C22×C3—181no—
1076C22×C3—181no—
1077C22×C3—181no—
1078C22×C3—181no—
1079C22×C3—364no—
1080C22×C3C22×D3211yescharacteristic
1081C22×C3C22×D3211yescharacteristic
1082C22×C3C22×D3211yescharacteristic
1083C2×D3—21no—
1084C2×D3—21no—
1085C2×D3—21no—
1086C2×D3—21no—
1087C2×D3—21no—
1088C2×D3—32no—
1089C2×D3—32no—
1090C2×D3—32no—
1091C2×D3—32no—
1092C2×D3—62no—
1093C2×D3—62no—
1094C2×D3—61no—
1095C2×D3—61no—
1096C2×D3—61no—
1097C2×D3—61no—
1098C2×D3—61no—
1099C2×D3—61no—
1100C2×D3—61no—
1101C2×D3—61no—
1102C2×D3—61no—
1103C2×D3—61no—
1104C2×D3—61no—
1105C2×D3—61no—
1106C2×D3—61no—
1107C2×D3—61no—
1108C2×D3—121no—
1109C2×D3—121no—
1110C2×D3—121no—
1111C2×D3—121no—
1112C2×D3—121no—
1113C2×D3—121no—
1114C2×D3—121no—
1115C2×D3—124no—
1116C2×D3—124no—
1117C2×D3—364no—
1118C2×D3—364no—
1119C2×D3—364no—
1120C2×D3D3×#6712yes—
1121C3×C4—32no—
1122C3×C4—32no—
1123C3×C4—62no—
1124C3×C4—62no—
1125C3×C4—61no—
1126C3×C4—61no—
1127C3×C4—61no—
1128C3×C4—61no—
1129C3×C4—61no—
1130C3×C4—61no—
1131C3×C4—121no—
1132C3×C4—121no—
1133C3×C4—181no—
1134C3×C4—181no—
1135C3×C4—181no—
1136Dic3—21no—
1137Dic3—21no—
1138Dic3—21no—
1139Dic3—62no—
1140Dic3—62no—
1141Dic3—61no—
1142Dic3—61no—
1143Dic3—61no—
1144Dic3—61no—
1145Dic3—61no—
1146Dic3—61no—
1147Dic3—121no—
1148Dic3—181no—
1149Dic3—181no—
1150Dic3—181no—
1151Dic3—181no—
1152Dic3—181no—
1153Dic3—181no—
1154Dic3—361no—
1155Dic3—361no—
1156Dic3—361no—
1157Dic3—361no—
1158Dic3—361no—
1159Dic3—361no—
1160Dic3—721no—
1161Dic3—721no—
1162Dic3D3×#6712yes—
1163C32—21no—
1164C32—21no—
1165C32—21no—
1166C32—41no—
1167C32#559111yescharacteristic, complemented
1168C32#561211yescharacteristic, complemented
1169C32#582911yescharacteristic, complemented
1170C23—31no—
1171C23—31no—
1172C23—91no—
1173C23—91no—
1174C23—91no—
1175C23—182no—
1176C23—182no—
1177C23—361no—
1178C23—542no—
1179C23—542no—
1180C23—1081no—
1181C23D3311yescharacteristic
1182Q8—182no—
1183D4—62no—
1184D4—94no—
1185D4—121no—
1186D4—182no—
1187D4—182no—
1188D4—182no—
1189D4—361no—
1190D4—542no—
1191D4—542no—
1192C2×C4—31no—
1193C2×C4—31no—
1194C2×C4—31no—
1195C2×C4—31no—
1196C2×C4—62no—
1197C2×C4—91no—
1198C2×C4—91no—
1199C2×C4—91no—
1200C2×C4—182no—
1201C2×C4—182no—
1202C2×C4—271no—
1203C2×C4—271no—
1204C2×C4—542no—
1205C2×C4—1081no—
1206C2×C4—1081no—
1207C2×C3—21no—
1208C2×C3—21no—
1209C2×C3—21no—
1210C2×C3—21no—
1211C2×C3—21no—
1212C2×C3—21no—
1213C2×C3—21no—
1214C2×C3—21no—
1215C2×C3—21no—
1216C2×C3—42no—
1217C2×C3—41no—
1218C2×C3—41no—
1219C2×C3—41no—
1220C2×C3—41no—
1221C2×C3—41no—
1222C2×C3—41no—
1223C2×C3—62no—
1224C2×C3—62no—
1225C2×C3—81no—
1226C2×C3—81no—
1227C2×C3—82no—
1228C2×C3—122no—
1229C2×C3—121no—
1230C2×C3—121no—
1231C2×C3—182no—
1232C2×C3—182no—
1233C2×C3—241no—
1234C2×C3—361no—
1235C2×C3#6430611yescharacteristic
1236C2×C3#6430711yescharacteristic
1237C2×C3D32×D411yescharacteristic
1238C2×C3D3×#23711yescharacteristic
1239C2×C3D3×#23711yescharacteristic
1240C2×C3#6431411yescharacteristic
1241C2×C3C2×D3×#6711yescharacteristic
1242C2×C3C2×D3×#6711yescharacteristic
1243C2×C3#6433011yescharacteristic
1244D3—22no—
1245D3—41no—
1246D3—62no—
1247D3—62no—
1248D3—62no—
1249D3—62no—
1250D3—122no—
1251D3—122no—
1252D3—121no—
1253D3—121no—
1254D3—241no—
1255C22—21no—
1256C22—21no—
1257C22—21no—
1258C22—32no—
1259C22—61no—
1260C22—61no—
1261C22—61no—
1262C22—61no—
1263C22—61no—
1264C22—92no—
1265C22—92no—
1266C22—181no—
1267C22—181no—
1268C22—181no—
1269C22—181no—
1270C22—181no—
1271C22—181no—
1272C22—181no—
1273C22—364no—
1274C22—1084no—
1275C22C2×D3311yescharacteristic
1276C4—32no—
1277C4—61no—
1278C4—61no—
1279C4—61no—
1280C4—181no—
1281C4—181no—
1282C4—181no—
1283C4—541no—
1284C4—541no—
1285C3—21no—
1286C3—21no—
1287C3—21no—
1288C3—41no—
1289C3#1059507011yescharacteristic, complemented
1290C3#1059529411yescharacteristic, complemented
1291C3#1059530411yescharacteristic, complemented
1292C2—41no—
1293C2—62no—
1294C2—121no—
1295C2—182no—
1296C2—182no—
1297C2—361no—
1298C2#1172440711yescharacteristic
1299C2#1172441811yescharacteristic
1300C2D32×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
hypercenterC23D33
hypocenterC33#546
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C2×C3×#3804C2semidirect
2. C2×#88953C2semidirect
3. #11723729C2semidirect
4. #11723631C2semidirect
5. Dic3×#638C2semidirect
6. #11723615C2semidirect
7. C3×#63983C2semidirect
8. C3×#63978C2semidirect
9. #11723001C2semidirect
10. #11722992C2semidirect
11. #11722988C2semidirect
12. #11722974C2semidirect
13. #11722929C2semidirect
14. #11722905C2semidirect
15. D3×(C2×D3)⋊Dic3C2semidirect
22. C2×C3×#638C22semidirect
23. C2×C3×#638C22semidirect
24. C2×C32×#67C22semidirect
25. C2×C32×#67C22semidirect
26. C22×C32×Dic3C22semidirect
30. C2×Dic3×C3⋊D3C22semidirect
31. C2×D3×C3⋊Dic3C22semidirect
32. C2×C3×#627C22semidirect
35. C2×C3×#624C22semidirect
37. C2×C3×D3×Dic3C22semidirect
39. #88864C22semidirect
41. #88814C22semidirect
42. #88814C22semidirect
43. #88807C22semidirect
44. #88807C22semidirect
45. Dic3⋊(C3⋊Dic3)C22semidirect
47. #88803C22semidirect
48. (C2×D3)⋊(C3⋊Dic3)C22semidirect
49. Dic3×C3⋊Dic3C22semidirect
50. C3×Dic3⋊Dic3C22semidirect
52. C3×#3722C22semidirect
53. C3×(C2×D3)⋊Dic3C22semidirect
54. C3×(C2×D3)⋊Dic3C22semidirect
55. C3×(C2×D3)⋊Dic3C22semidirect
60. C2×#3804D3semidirect
72. #63983D3semidirect
73. #63978D3semidirect
138. C3×#626D4semidirect
156. C2×#638C2×D3semidirect
157. C2×#638C2×D3semidirect
174. C2×C3×#67C2×D3semidirect
175. C2×C3×#67C2×D3semidirect
176. C2×C3×#67C2×D3semidirect
177. C2×C3×#67C2×D3semidirect
180. C22×C3×Dic3C2×D3semidirect
181. C22×C3×Dic3C2×D3semidirect
193. C2×#627C2×D3semidirect
202. C2×#624C2×D3semidirect
213. C2×D3×Dic3C2×D3semidirect
250. Dic3⋊Dic3C2×D3semidirect
255. #3722C2×D3semidirect
271. (C2×D3)⋊Dic3C2×D3semidirect
272. (C2×D3)⋊Dic3C2×D3semidirect
273. (C2×D3)⋊Dic3C2×D3semidirect
289. C2×C3×C3⋊D3#41semidirect
483. #626#67semidirect
555. C2×#67D32semidirect
556. C2×#67D32semidirect
563. C22×Dic3D32semidirect
685. C2×C3⋊D3#237semidirect
795. C33#546semidirect
1167. C32#5591semidirect
1168. C32#5612semidirect
1169. C32#5829semidirect
1289. C3#10595070semidirect
1290. C3#10595294semidirect
1291. C3#10595304semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#38042
C2×#889532
#117237292
#117236312
Dic3×#6382
#117236152
C3×#639832
C3×#639782
#117230012
#117229922
#117229882
#117229742
#117229292
#117229052
D3×(C2×D3)⋊Dic32
#105953043
#105952943
#105950703