Finite Group Databasebeta

← #13172016

Subgroups — #13172016

Order 1728.

1798 conjugacy classes of subgroups.

The subgroup lattice has 1340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#638C211yesmaximal, characteristic, complemented
2C2×C3×#3804C211yesmaximal, characteristic, complemented
3#11723726C211yesmaximal, characteristic, complemented
4#11723635C211yesmaximal, characteristic, complemented
5#11723612C211yesmaximal, characteristic, complemented
6C3×#63976C211yesmaximal, characteristic, complemented
7C2×C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
8#11723005C211yesmaximal, characteristic, complemented
9#11722992C211yesmaximal, characteristic, complemented
10#11722976C211yesmaximal, characteristic, complemented
11#11722965C211yesmaximal, characteristic, complemented
12#11722958C211yesmaximal, characteristic, complemented
13#11722949C211yesmaximal, characteristic, complemented
14#11722924C211yesmaximal, characteristic, complemented
15#11722904C211yesmaximal, characteristic, complemented
16#10595500—31nomaximal
17#10595304—31nomaximal
18#10595065—31nomaximal
19C23×C32×D3C2211yescharacteristic
20C22×D3×C3⋊D3C2211yescharacteristic
21C2×#6312C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic
23C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
24C2×C32×#67C2211yescharacteristic, complemented
25C22×C32×Dic3C2211yescharacteristic, complemented
26C2×#6294C2211yescharacteristic, complemented
27D3×#638—24no—
28C2×#6291C2211yescharacteristic
29C2×#6291C2211yescharacteristic, complemented
30C2×#6290C2211yescharacteristic
31C2×D3×C3⋊Dic3C2211yescharacteristic
32C2×C3×#627C2211yescharacteristic, complemented
33C2×C3×#626C2211yescharacteristic, complemented
34C2×C3×#625C2211yescharacteristic
35C2×C3×#625C2211yescharacteristic, complemented
36C2×C3×#624C2211yescharacteristic, complemented
37C3×#3804—24no—
38C2×C3×D3×Dic3C2211yescharacteristic, complemented
39C3×#3757C2211yescharacteristic, complemented
40#88815C2211yescharacteristic, complemented
41#88814C2211yescharacteristic, complemented
42#88813C2211yescharacteristic, complemented
43#88807C2211yescharacteristic, complemented
44#88807C2211yescharacteristic, complemented
45#88807C2211yescharacteristic, complemented
46#88804C2211yescharacteristic, complemented
47#88804C2211yescharacteristic, complemented
48#88804C2211yescharacteristic, complemented
49(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
54C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
55C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
56C22×#638—31no—
57C2×C3×#237—31no—
58C2×C3×#235—31no—
59C2×D3×#67—31no—
60C2×D3×#67—31no—
61C2×D3×#67—61no—
62C2×#3804D311yescharacteristic, complemented
63#64148—31no—
64#64138—31no—
65C3×#953—31no—
66C2×C3×#217—31no—
67C3×#937—31no—
68C2×C3×(C2×D3)⋊C4—31no—
69#63983—31no—
70#63982—31no—
71#63981—31no—
72#63978—31no—
73#63978—31no—
74#63978—31no—
75#63978—61no—
76#63976D311yescharacteristic, complemented
77#63975—31no—
78#63974—31no—
79#67⋊Dic3—31no—
80#67⋊Dic3—31no—
81Dic3×#67—31no—
82Dic3×#67—31no—
83#63971—31no—
84#63970—31no—
85#63966—31no—
86#63966—31no—
87#63966—61no—
88C2×(C2×D3)⋊Dic3D311yescharacteristic, complemented
89#63958—31no—
90#63953—31no—
91#63952—31no—
92#63922—31no—
93D3×(C2×D3)⋊C4—31no—
94D3×(C2×D3)⋊C4—31no—
95#63907—31no—
96#63907—31no—
97#63906—31no—
98#63905—31no—
99#63905—31no—
100#63887—31no—
101#63887—31no—
102#63885—31no—
103#63879—31no—
104C23×C33C2311yescharacteristic
105C22×C3⋊(C3⋊D3)C2311yescharacteristic
106C22×C3×C3⋊D3C2311yescharacteristic
107C22×C32×D3—22no—
108C22×C32×D3—22no—
109C22×C32×D3—41no—
110C22×C32×D3C2311yescharacteristic
111C22×C32×D3C2311yescharacteristic
112C22×C32×D3C2311yescharacteristic
113C2×D3×C3⋊D3—22no—
114C2×D3×C3⋊D3—22no—
115C2×D3×C3⋊D3—41no—
116#6312—22no—
117C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
118C3×#638D414yescomplemented
119C2×C3×C3⋊Dic3—41no—
120C2×C3×C3⋊Dic3C2311yescharacteristic
121C2×C3×C3⋊Dic3C2311yescharacteristic
122C2×C3×C3⋊Dic3C2311yescharacteristic
123C2×C3×C3⋊Dic3C2311yescharacteristic
124C2×C3×C3⋊Dic3C2311yescharacteristic
125C32×#67—22no—
126C2×C32×Dic3—22no—
127C2×C32×Dic3C2311yescharacteristic
128C2×C32×Dic3C2311yescharacteristic
129C2×C32×Dic3C2311yescharacteristic
130#6294—41no—
131#6291—22no—
132#6291—41no—
133#6290—22no—
134D3×C3⋊Dic3—22no—
135C3×#627—22no—
136C3×#626—22no—
137C3×#625—22no—
138C3×#625—41no—
139C3×#624—22no—
140C3×D3×Dic3—22no—
141#5829—91no—
142#5591—91no—
143#5490—91no—
144C24×C32—31no—
145C23×C3⋊D3—31no—
146C23×C3×D3—21no—
147C23×C3×D3C2×D311yescharacteristic
148C23×C3×D3C2×D311yescharacteristic
149C22×D32—31no—
150C22×D32—31no—
151C22×D32—61no—
152C2×C32×D4—31no—
153C22×C32×C4—31no—
154C2×#638—31no—
155C2×#638—31no—
156C2×#638—31no—
157C2×#638—31no—
158C2×#638—31no—
159C2×#638—31no—
160C2×#638—61no—
161C2×#638—64no—
162C2×#638—61no—
163C2×#638—61no—
164C2×#638—121no—
165C2×#638C2×D311yescharacteristic
166C22×C3⋊Dic3—31no—
167C22×C3⋊Dic3C2×D311yescharacteristic, complemented
168C2×C3×#67—21no—
169C2×C3×#67—31no—
170C2×C3×#67—31no—
171C2×C3×#67—31no—
172C2×C3×#67—31no—
173C2×C3×#67—31no—
174C2×C3×#67—31no—
175C2×C3×#67—31no—
176C2×C3×#67—61no—
177C2×C3×#67C2×D311yescharacteristic, complemented
178C2×C3×#67C2×D311yescharacteristic, complemented
179C22×C3×Dic3—21no—
180C22×C3×Dic3—31no—
181C22×C3×Dic3—31no—
182C22×C3×Dic3—31no—
183C22×C3×Dic3—61no—
184C22×C3×Dic3C2×D311yescharacteristic, complemented
185C22×C3×Dic3C2×D311yescharacteristic, complemented
186C3×#237—64no—
187C3×#235—64no—
188C2×C3×D12—31no—
189C2×C3×C4×D3—31no—
190C2×C3×C4×D3—31no—
191C2×C3×C4×D3—31no—
192C2×C3×Dic6—31no—
193C2×C3×Dic6—31no—
194D3×#67—64no—
195D3×#67—64no—
196D3×#67—68no—
197C2×#627C2×D311yescharacteristic, complemented
198C2×#626—31no—
199C2×#626—31no—
200C2×#626—31no—
201C2×#626—31no—
202C2×#626—61no—
203C2×#626—61no—
204C2×#626C2×D311yescharacteristic, complemented
205C2×#625—31no—
206C2×#625—31no—
207C2×#625—61no—
208C2×#625C2×D311yescharacteristic
209C2×#625C2×D311yescharacteristic, complemented
210C2×#624—31no—
211C2×#624C2×D311yescharacteristic, complemented
212#3804—24no—
213C2×D3×Dic3—31no—
214C2×D3×Dic3—31no—
215C2×D3×Dic3—31no—
216C2×D3×Dic3—31no—
217C2×D3×Dic3—61no—
218C2×D3×Dic3C2×D311yescharacteristic, complemented
219#3757—31no—
220#3757C2×D311yescharacteristic, complemented
221#3752—31no—
222#3752—31no—
223#3752—31no—
224#3750—31no—
225#3750—31no—
226#3750—31no—
227C3×#217—31no—
228C3×#217—31no—
229C3×#217—31no—
230C3×#217—31no—
231C3×#217—31no—
232C3×#217—31no—
233C3×#217—31no—
234C3×#217—31no—
235C3×#217—61no—
236C3×(C2×D3)⋊C4—31no—
237C3×(C2×D3)⋊C4—31no—
238C3×(C2×D3)⋊C4—31no—
239C3×(C2×D3)⋊C4—31no—
240C3×(C2×D3)⋊C4—31no—
241C3×(C2×D3)⋊C4—31no—
242#3724—31no—
243Dic3⋊Dic3—31no—
244Dic3⋊Dic3—31no—
245Dic3⋊Dic3—31no—
246Dic3⋊Dic3—31no—
247Dic3⋊Dic3—31no—
248Dic3⋊Dic3—31no—
249Dic3⋊Dic3—31no—
250Dic3⋊Dic3—31no—
251Dic3⋊Dic3—61no—
252Dic3⋊Dic3—61no—
253Dic3⋊Dic3—61no—
254#3722—31no—
255#3722—31no—
256#3722—31no—
257#3722—31no—
258#3722—31no—
259#3722—31no—
260#3722—31no—
261#3722—61no—
262#3722—61no—
263#3722—61no—
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)⋊Dic3C2×D311yescharacteristic
270(C2×D3)⋊Dic3C2×D311yescharacteristic
271(C2×D3)⋊Dic3C2×D311yescharacteristic
272(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
273(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
274(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
275Dic32—31no—
276Dic32—31no—
277Dic32—31no—
278C22×C33—21no—
279C22×C33—21no—
280C22×C33C2×D412yes—
281C22×C33C2411yescharacteristic
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⋊D3C2×D412yes—
288C2×C32×D3—21no—
289C2×C32×D3—21no—
290C2×C32×D3—21no—
291C2×C32×D3—21no—
292C2×C32×D3—21no—
293C2×C32×D3—21no—
294C2×C32×D3—21no—
295C2×C32×D3—21no—
296C2×C32×D3—44no—
297C2×C32×D3#4112yescomplemented
298D3×C3⋊D3—44no—
299C3⋊(C3⋊Dic3)—21no—
300C3×C3⋊Dic3—21no—
301C3×C3⋊Dic3—21no—
302C3×C3⋊Dic3—21no—
303C3×C3⋊Dic3—21no—
304C3×C3⋊Dic3C2×D412yes—
305C32×Dic3—21no—
306C32×Dic3—21no—
307C32×Dic3—21no—
308C2×C3×#41—91no—
309C22×#67—91no—
310C22×#67—91no—
311C22×#67—181no—
312C2×#237—31no—
313C2×D3×D4—91no—
314C2×#235—31no—
315C3×#120—91no—
316C2×C3×C22⋊C4—91no—
317#953—31no—
318C2×#217—31no—
319#947—91no—
320#946—91no—
321#939—91no—
322#939—91no—
323#939—91no—
324#939—91no—
325#939—181no—
326#938—91no—
327#937—31no—
328#937—91no—
329#937—91no—
330D4×Dic3—91no—
331D4×Dic3—91no—
332#930—91no—
333#930—91no—
334#929—91no—
335#929—91no—
336#929—91no—
337#929—181no—
338C4×#67—91no—
339C4×#67—91no—
340C2×(C2×D3)⋊C4—31no—
341C2×(C2×D3)⋊C4—91no—
342#886—91no—
343#885—91no—
344#885—91no—
345#884—91no—
346#884—91no—
347#883—91no—
348#883—91no—
349#882—91no—
350#67⋊C4—91no—
351#67⋊C4—91no—
352D3×C22⋊C4—91no—
353D3×C22⋊C4—91no—
354#878—91no—
355#878—91no—
356C23×C32—21no—
357C23×C32—21no—
358C23×C32—21no—
359C23×C32—31no—
360C23×C32—31no—
361C23×C32—31no—
362C23×C32—41no—
363C23×C32—62no—
364C23×C32—62no—
365C23×C32—121no—
366C23×C32C22×D311yescharacteristic
367C23×C32C22×D311yescharacteristic
368C23×C32C22×D311yescharacteristic
369C22×C3⋊D3—31no—
370C22×C3⋊D3—31no—
371C22×C3⋊D3—31no—
372C22×C3⋊D3—61no—
373C22×C3⋊D3—61no—
374C22×C3⋊D3—61no—
375C22×C3⋊D3—62no—
376C22×C3⋊D3—62no—
377C22×C3⋊D3—121no—
378C22×C3⋊D3—121no—
379C22×C3⋊D3C22×D311yescharacteristic
380C22×C3×D3—24no—
381C22×C3×D3—22no—
382C22×C3×D3—22no—
383C22×C3×D3—22no—
384C22×C3×D3—22no—
385C22×C3×D3—21no—
386C22×C3×D3—21no—
387C22×C3×D3—21no—
388C22×C3×D3—31no—
389C22×C3×D3—31no—
390C22×C3×D3—42no—
391C22×C3×D3—41no—
392C22×C3×D3—41no—
393C22×C3×D3—42no—
394C22×C3×D3—61no—
395C22×C3×D3C22×D311yescharacteristic
396C22×C3×D3C22×D311yescharacteristic
397C22×C3×D3C22×D311yescharacteristic
398C22×C3×D3C22×D311yescharacteristic
399C22×C3×D3C22×D311yescharacteristic
400C22×C3×D3C22×D311yescharacteristic
401C2×D32—62no—
402C2×D32—62no—
403C2×D32—64no—
404C2×D32—62no—
405C2×D32—62no—
406C2×D32—122no—
407C2×D32—121no—
408C2×D32—121no—
409C2×D32—122no—
410C32×D4—62no—
411C2×C32×C4—31no—
412C2×C32×C4—31no—
413C2×C32×C4—31no—
414C2×C32×C4—62no—
415#638—62no—
416#638—62no—
417#638—62no—
418#638—64no—
419#638—62no—
420#638—62no—
421#638—122no—
422#638—122no—
423#638—124no—
424#638—121no—
425#638#6714yescomplemented
426C2×C3⋊Dic3—31no—
427C2×C3⋊Dic3—31no—
428C2×C3⋊Dic3—31no—
429C2×C3⋊Dic3—41no—
430C2×C3⋊Dic3—61no—
431C2×C3⋊Dic3—61no—
432C2×C3⋊Dic3—61no—
433C2×C3⋊Dic3—62no—
434C2×C3⋊Dic3—121no—
435C2×C3⋊Dic3C22×D311yescharacteristic
436C2×C3⋊Dic3C22×D311yescharacteristic
437C2×C3⋊Dic3C22×D311yescharacteristic
438C2×C3⋊Dic3C22×D311yescharacteristic
439C2×C3⋊Dic3C22×D311yescharacteristic
440C3×#67—22no—
441C3×#67—22no—
442C3×#67—34no—
443C3×#67—34no—
444C3×#67—42no—
445C3×#67—64no—
446C3×#67—62no—
447C3×#67—62no—
448C3×#67—62no—
449C3×#67—121no—
450C3×#67—121no—
451C2×C3×Dic3—22no—
452C2×C3×Dic3—22no—
453C2×C3×Dic3—21no—
454C2×C3×Dic3—21no—
455C2×C3×Dic3—21no—
456C2×C3×Dic3—31no—
457C2×C3×Dic3—31no—
458C2×C3×Dic3—31no—
459C2×C3×Dic3—31no—
460C2×C3×Dic3—31no—
461C2×C3×Dic3—31no—
462C2×C3×Dic3—31no—
463C2×C3×Dic3—31no—
464C2×C3×Dic3—31no—
465C2×C3×Dic3—31no—
466C2×C3×Dic3—42no—
467C2×C3×Dic3—61no—
468C2×C3×Dic3—61no—
469C2×C3×Dic3—61no—
470C2×C3×Dic3—61no—
471C2×C3×Dic3—61no—
472C2×C3×Dic3—62no—
473C2×C3×Dic3—121no—
474C2×C3×Dic3—121no—
475C2×C3×Dic3—122no—
476C2×C3×Dic3C22×D311yescharacteristic
477C2×C3×Dic3C22×D311yescharacteristic
478C2×C3×Dic3C22×D311yescharacteristic
479C2×C3×Dic3C22×D311yescharacteristic
480C2×C3×Dic3C22×D311yescharacteristic
481C2×C3×Dic3C22×D311yescharacteristic
482C3×D12—62no—
483C3×C4×D3—62no—
484C3×C4×D3—62no—
485C3×C4×D3—62no—
486C3×Dic6—62no—
487C3×Dic6—62no—
488#627—22no—
489#626—22no—
490#626—62no—
491#626—62no—
492#626—64no—
493#626—121no—
494#626—121no—
495#626—122no—
496#625—22no—
497#625—41no—
498#625—62no—
499#625—62no—
500#625—64no—
501#624—22no—
502#624—121no—
503D3×Dic3—22no—
504D3×Dic3—62no—
505D3×Dic3—62no—
506D3×Dic3—64no—
507D3×Dic3—121no—
508D3×Dic3—121no—
509#546—271noSylow
510C2×C33—22no—
511C2×C33C22×D411yescharacteristic
512C2×C33C2×#4111yescharacteristic
513C2×C33H(5,𝔽2)11yescharacteristic
514C3⋊(C3⋊D3)—41no—
515C3×C3⋊D3—22no—
516C32×D3—22no—
517C32×D3—41no—
518C32×D3—41no—
519C24×C3—31no—
520C24×C3—31no—
521C24×C3—61no—
522C23×D3—91no—
523C23×D3—91no—
524C23×D3—91no—
525C23×D3—181no—
526C23×D3D3211yescharacteristic
527C3×#41—184no—
528C2×C3×Q8—91no—
529C2×C3×D4—31no—
530C2×C3×D4—31no—
531C2×C3×D4—61no—
532C2×C3×D4—91no—
533C2×C3×D4—91no—
534C2×C3×D4—91no—
535C2×C3×D4—91no—
536C22×C3×C4—31no—
537C22×C3×C4—31no—
538C22×C3×C4—61no—
539C22×C3×C4—91no—
540C22×C3×C4—91no—
541C22×C3×C4—91no—
542C2×#67—31no—
543C2×#67—31no—
544C2×#67—31no—
545C2×#67—31no—
546C2×#67—31no—
547C2×#67—31no—
548C2×#67—31no—
549C2×#67—61no—
550C2×#67—91no—
551C2×#67—91no—
552C2×#67—91no—
553C2×#67—91no—
554C2×#67—91no—
555C2×#67—91no—
556C2×#67—91no—
557C2×#67—91no—
558C2×#67—91no—
559C2×#67—91no—
560C2×#67—181no—
561C2×#67—181no—
562C2×#67—181no—
563C2×#67—181no—
564C2×#67—181no—
565C2×#67—181no—
566C2×#67—184no—
567C2×#67—184no—
568C2×#67—188no—
569C2×#67—361no—
570C2×#67D3211yescharacteristic, complemented
571C22×Dic3—31no—
572C22×Dic3—31no—
573C22×Dic3—31no—
574C22×Dic3—61no—
575C22×Dic3—91no—
576C22×Dic3—91no—
577C22×Dic3—91no—
578C22×Dic3—181no—
579C22×Dic3D3211yescharacteristic, complemented
580#237—64no—
581D3×D4—184no—
582#235—64no—
583C2×D12—31no—
584C2×D12—91no—
585C2×D12—91no—
586C2×C4×D3—31no—
587C2×C4×D3—31no—
588C2×C4×D3—31no—
589C2×C4×D3—91no—
590C2×C4×D3—91no—
591C2×C4×D3—91no—
592C2×Dic6—31no—
593C2×Dic6—31no—
594C3×C22⋊C4—91no—
595C3×C22⋊C4—91no—
596C3×C22⋊C4—91no—
597C3×C22⋊C4—91no—
598C3×C22⋊C4—91no—
599C3×C22⋊C4—91no—
600C3×C22⋊C4—91no—
601#217—31no—
602#217—31no—
603#217—31no—
604#217—31no—
605#217—31no—
606#217—31no—
607#217—31no—
608#217—31no—
609#217—61no—
610#217—91no—
611#217—91no—
612#217—91no—
613#217—181no—
614(C2×D3)⋊C4—31no—
615(C2×D3)⋊C4—31no—
616(C2×D3)⋊C4—31no—
617(C2×D3)⋊C4—31no—
618(C2×D3)⋊C4—31no—
619(C2×D3)⋊C4—31no—
620(C2×D3)⋊C4—91no—
621(C2×D3)⋊C4—91no—
622(C2×D3)⋊C4—91no—
623(C2×D3)⋊C4—91no—
624(C2×D3)⋊C4—91no—
625(C2×D3)⋊C4—91no—
626(C2×D3)⋊C4—91no—
627(C2×D3)⋊C4—91no—
628(C2×D3)⋊C4—91no—
629(C2×D3)⋊C4—91no—
630(C2×D3)⋊C4—91no—
631(C2×D3)⋊C4—91no—
632(C2×D3)⋊C4—181no—
633(C2×D3)⋊C4—181no—
634(C2×D3)⋊C4—181no—
635C4⋊Dic3—91no—
636C4⋊Dic3—91no—
637C4⋊Dic3—91no—
638C4⋊Dic3—91no—
639Dic3⋊C4—91no—
640Dic3⋊C4—91no—
641Dic3⋊C4—91no—
642Dic3⋊C4—91no—
643Dic3⋊C4—91no—
644Dic3⋊C4—91no—
645Dic3⋊C4—91no—
646Dic3⋊C4—91no—
647Dic3⋊C4—181no—
648Dic3⋊C4—181no—
649Dic3⋊C4—181no—
650C4×Dic3—91no—
651C4×Dic3—91no—
652C4×Dic3—91no—
653C22×C32—21no—
654C22×C32—21no—
655C22×C32—21no—
656C22×C32—21no—
657C22×C32—21no—
658C22×C32—21no—
659C22×C32—21no—
660C22×C32—21no—
661C22×C32—21no—
662C22×C32—22no—
663C22×C32—22no—
664C22×C32—22no—
665C22×C32—32no—
666C22×C32—41no—
667C22×C32—42no—
668C22×C32—41no—
669C22×C32—41no—
670C22×C32—41no—
671C22×C32—41no—
672C22×C32—41no—
673C22×C32—41no—
674C22×C32—61no—
675C22×C32—61no—
676C22×C32—61no—
677C22×C32—61no—
678C22×C32—61no—
679C22×C32—61no—
680C22×C32—61no—
681C22×C32—61no—
682C22×C32—81no—
683C22×C32—81no—
684C22×C32—124no—
685C22×C32D3×D412yes—
686C22×C32D3×D412yes—
687C22×C32C2×#6712yes—
688C22×C32C23×D311yescharacteristic
689C22×C32C23×D311yescharacteristic
690C22×C32C23×D311yescharacteristic
691C2×C3⋊D3—21no—
692C2×C3⋊D3—21no—
693C2×C3⋊D3—61no—
694C2×C3⋊D3—62no—
695C2×C3⋊D3—61no—
696C2×C3⋊D3—61no—
697C2×C3⋊D3—61no—
698C2×C3⋊D3—61no—
699C2×C3⋊D3—61no—
700C2×C3⋊D3—61no—
701C2×C3⋊D3—61no—
702C2×C3⋊D3—61no—
703C2×C3⋊D3—121no—
704C2×C3⋊D3—121no—
705C2×C3⋊D3—122no—
706C2×C3⋊D3—121no—
707C2×C3⋊D3—121no—
708C2×C3⋊D3—121no—
709C2×C3⋊D3—121no—
710C2×C3⋊D3—121no—
711C2×C3⋊D3—121no—
712C2×C3⋊D3—124no—
713C2×C3⋊D3—241no—
714C2×C3⋊D3—241no—
715C2×C3⋊D3C2×#6712yes—
716C2×C3×D3—22no—
717C2×C3×D3—22no—
718C2×C3×D3—21no—
719C2×C3×D3—21no—
720C2×C3×D3—21no—
721C2×C3×D3—21no—
722C2×C3×D3—22no—
723C2×C3×D3—21no—
724C2×C3×D3—21no—
725C2×C3×D3—21no—
726C2×C3×D3—21no—
727C2×C3×D3—21no—
728C2×C3×D3—21no—
729C2×C3×D3—21no—
730C2×C3×D3—21no—
731C2×C3×D3—21no—
732C2×C3×D3—21no—
733C2×C3×D3—21no—
734C2×C3×D3—21no—
735C2×C3×D3—22no—
736C2×C3×D3—32no—
737C2×C3×D3—32no—
738C2×C3×D3—41no—
739C2×C3×D3—41no—
740C2×C3×D3—41no—
741C2×C3×D3—41no—
742C2×C3×D3—41no—
743C2×C3×D3—44no—
744C2×C3×D3—44no—
745C2×C3×D3—48no—
746C2×C3×D3—62no—
747C2×C3×D3—61no—
748C2×C3×D3—61no—
749C2×C3×D3—61no—
750C2×C3×D3—61no—
751C2×C3×D3—121no—
752C2×C3×D3—121no—
753C2×C3×D3#23512yescomplemented
754C2×C3×D3#23712yescomplemented
755D32—124no—
756D32—124no—
757D32—128no—
758C32×C4—61no—
759C32×C4—61no—
760C32×C4—61no—
761C3⋊Dic3—21no—
762C3⋊Dic3—21no—
763C3⋊Dic3—21no—
764C3⋊Dic3—21no—
765C3⋊Dic3—61no—
766C3⋊Dic3—62no—
767C3⋊Dic3—61no—
768C3⋊Dic3—61no—
769C3⋊Dic3—121no—
770C3⋊Dic3—121no—
771C3⋊Dic3—122no—
772C3⋊Dic3C2×#6712yes—
773C3×Dic3—21no—
774C3×Dic3—21no—
775C3×Dic3—21no—
776C3×Dic3—21no—
777C3×Dic3—21no—
778C3×Dic3—21no—
779C3×Dic3—32no—
780C3×Dic3—32no—
781C3×Dic3—41no—
782C3×Dic3—41no—
783C3×Dic3—41no—
784C3×Dic3—62no—
785C3×Dic3—62no—
786C3×Dic3—61no—
787C3×Dic3—61no—
788C3×Dic3—61no—
789C3×Dic3—61no—
790C3×Dic3—61no—
791C3×Dic3—61no—
792C3×Dic3—61no—
793C3×Dic3—61no—
794C3×Dic3—121no—
795C3×Dic3—121no—
796C3×Dic3—121no—
797C2×#41—91no—
798C22×D4—271no—
799#124—271no—
800#123—271no—
801#123—271no—
802C22⋊Q8—271no—
803#121—271no—
804#121—271no—
805#121—271no—
806#120—91no—
807#120—271no—
808C4×D4—271no—
809C4×D4—271no—
810C2×C22⋊C4—91no—
811C2×C22⋊C4—271no—
812C33#54611yescharacteristic, complemented, Sylow
813C23×C3—21no—
814C23×C3—21no—
815C23×C3—21no—
816C23×C3—31no—
817C23×C3—31no—
818C23×C3—31no—
819C23×C3—31no—
820C23×C3—31no—
821C23×C3—31no—
822C23×C3—41no—
823C23×C3—61no—
824C23×C3—61no—
825C23×C3—61no—
826C23×C3—62no—
827C23×C3—62no—
828C23×C3—64no—
829C23×C3—62no—
830C23×C3—62no—
831C23×C3—91no—
832C23×C3—122no—
833C23×C3—121no—
834C23×C3—121no—
835C23×C3—122no—
836C23×C3C2×D3211yescharacteristic
837C23×C3C2×D3211yescharacteristic
838C23×C3C2×D3211yescharacteristic
839C22×D3—22no—
840C22×D3—22no—
841C22×D3—31no—
842C22×D3—31no—
843C22×D3—41no—
844C22×D3—61no—
845C22×D3—91no—
846C22×D3—91no—
847C22×D3—91no—
848C22×D3—181no—
849C22×D3—181no—
850C22×D3—181no—
851C22×D3—182no—
852C22×D3—182no—
853C22×D3—182no—
854C22×D3—182no—
855C22×D3—182no—
856C22×D3—184no—
857C22×D3—182no—
858C22×D3—361no—
859C22×D3—362no—
860C22×D3—361no—
861C22×D3—361no—
862C22×D3—361no—
863C22×D3—362no—
864C22×D3C2×D3211yescharacteristic
865C22×D3C2×D3211yescharacteristic
866C22×D3C2×D3211yescharacteristic
867C3×Q8—182no—
868C3×D4—62no—
869C3×D4—62no—
870C3×D4—94no—
871C3×D4—122no—
872C3×D4—182no—
873C3×D4—182no—
874C3×D4—361no—
875C2×C3×C4—31no—
876C2×C3×C4—31no—
877C2×C3×C4—31no—
878C2×C3×C4—31no—
879C2×C3×C4—31no—
880C2×C3×C4—31no—
881C2×C3×C4—61no—
882C2×C3×C4—61no—
883C2×C3×C4—61no—
884C2×C3×C4—62no—
885C2×C3×C4—62no—
886C2×C3×C4—91no—
887C2×C3×C4—91no—
888C2×C3×C4—91no—
889C2×C3×C4—91no—
890C2×C3×C4—91no—
891C2×C3×C4—122no—
892C2×C3×C4—182no—
893C2×C3×C4—182no—
894C2×C3×C4—361no—
895#67—22no—
896#67—34no—
897#67—34no—
898#67—64no—
899#67—62no—
900#67—62no—
901#67—62no—
902#67—121no—
903#67—121no—
904#67—182no—
905#67—182no—
906#67—184no—
907#67—182no—
908#67—182no—
909#67—182no—
910#67—184no—
911#67—184no—
912#67—182no—
913#67—182no—
914#67—182no—
915#67—362no—
916#67—362no—
917#67—364no—
918#67—361no—
919#67—361no—
920#67—362no—
921C2×Dic3—22no—
922C2×Dic3—31no—
923C2×Dic3—31no—
924C2×Dic3—31no—
925C2×Dic3—31no—
926C2×Dic3—31no—
927C2×Dic3—31no—
928C2×Dic3—31no—
929C2×Dic3—31no—
930C2×Dic3—31no—
931C2×Dic3—31no—
932C2×Dic3—61no—
933C2×Dic3—61no—
934C2×Dic3—61no—
935C2×Dic3—61no—
936C2×Dic3—61no—
937C2×Dic3—62no—
938C2×Dic3—91no—
939C2×Dic3—91no—
940C2×Dic3—91no—
941C2×Dic3—121no—
942C2×Dic3—121no—
943C2×Dic3—122no—
944C2×Dic3—181no—
945C2×Dic3—181no—
946C2×Dic3—181no—
947C2×Dic3—182no—
948C2×Dic3—182no—
949C2×Dic3—184no—
950C2×Dic3—361no—
951C2×Dic3—361no—
952C2×Dic3C2×D3211yescharacteristic
953C2×Dic3C2×D3211yescharacteristic
954C2×Dic3C2×D3211yescharacteristic
955D12—62no—
956D12—182no—
957D12—361no—
958C4×D3—62no—
959C4×D3—62no—
960C4×D3—62no—
961C4×D3—182no—
962C4×D3—361no—
963C4×D3—361no—
964Dic6—62no—
965Dic6—62no—
966C2×C32—22no—
967C2×C32—22no—
968C2×C32—22no—
969C2×C32—21no—
970C2×C32—21no—
971C2×C32—21no—
972C2×C32—21no—
973C2×C32—21no—
974C2×C32—21no—
975C2×C32—21no—
976C2×C32—21no—
977C2×C32—21no—
978C2×C32—41no—
979C2×C32—41no—
980C2×C32—41no—
981C2×C32—42no—
982C2×C32—42no—
983C2×C32—42no—
984C2×C32—62no—
985C2×C32—82no—
986C2×C32—121no—
987C2×C32—121no—
988C2×C32C2×#23511yescharacteristic
989C2×C32C2×D3×D411yescharacteristic
990C2×C32C2×D3×D411yescharacteristic
991C2×C32C2×#23711yescharacteristic
992C2×C32#100411yescharacteristic
993C2×C32#100411yescharacteristic
994C2×C32D3×#4111yescharacteristic
995C2×C32#100911yescharacteristic
996C2×C32C22×#6711yescharacteristic
997C3⋊D3—22no—
998C3⋊D3—121no—
999C3⋊D3—122no—
1000C3⋊D3—121no—
1001C3⋊D3—121no—
1002C3⋊D3—241no—
1003C3⋊D3—241no—
1004C3⋊D3—242no—
1005C3×D3—24no—
1006C3×D3—22no—
1007C3×D3—22no—
1008C3×D3—42no—
1009C3×D3—41no—
1010C3×D3—41no—
1011C3×D3—41no—
1012C3×D3—41no—
1013C3×D3—62no—
1014C3×D3—62no—
1015C3×D3—81no—
1016C3×D3—122no—
1017C24—31no—
1018C24—271no—
1019#41—184no—
1020C2×Q8—91no—
1021C2×D4—31no—
1022C2×D4—91no—
1023C2×D4—91no—
1024C2×D4—91no—
1025C2×D4—91no—
1026C2×D4—271no—
1027C2×D4—271no—
1028C2×D4—271no—
1029C2×D4—271no—
1030C2×D4—544no—
1031C22×C4—31no—
1032C22×C4—91no—
1033C22×C4—91no—
1034C22×C4—91no—
1035C22×C4—271no—
1036C22×C4—271no—
1037C4⋊C4—271no—
1038C4⋊C4—271no—
1039C4⋊C4—271no—
1040C4⋊C4—271no—
1041C22⋊C4—91no—
1042C22⋊C4—91no—
1043C22⋊C4—91no—
1044C22⋊C4—91no—
1045C22⋊C4—91no—
1046C22⋊C4—91no—
1047C22⋊C4—91no—
1048C22⋊C4—271no—
1049C22⋊C4—271no—
1050C22⋊C4—271no—
1051C22⋊C4—271no—
1052C22⋊C4—271no—
1053C42—271no—
1054C22×C3—21no—
1055C22×C3—21no—
1056C22×C3—21no—
1057C22×C3—21no—
1058C22×C3—21no—
1059C22×C3—21no—
1060C22×C3—21no—
1061C22×C3—21no—
1062C22×C3—21no—
1063C22×C3—22no—
1064C22×C3—22no—
1065C22×C3—22no—
1066C22×C3—32no—
1067C22×C3—32no—
1068C22×C3—41no—
1069C22×C3—41no—
1070C22×C3—41no—
1071C22×C3—41no—
1072C22×C3—41no—
1073C22×C3—41no—
1074C22×C3—41no—
1075C22×C3—42no—
1076C22×C3—62no—
1077C22×C3—62no—
1078C22×C3—62no—
1079C22×C3—62no—
1080C22×C3—61no—
1081C22×C3—61no—
1082C22×C3—61no—
1083C22×C3—61no—
1084C22×C3—61no—
1085C22×C3—61no—
1086C22×C3—61no—
1087C22×C3—61no—
1088C22×C3—61no—
1089C22×C3—61no—
1090C22×C3—61no—
1091C22×C3—61no—
1092C22×C3—61no—
1093C22×C3—61no—
1094C22×C3—61no—
1095C22×C3—61no—
1096C22×C3—81no—
1097C22×C3—81no—
1098C22×C3—92no—
1099C22×C3—121no—
1100C22×C3—121no—
1101C22×C3—121no—
1102C22×C3—121no—
1103C22×C3—121no—
1104C22×C3—124no—
1105C22×C3—124no—
1106C22×C3—128no—
1107C22×C3—181no—
1108C22×C3—181no—
1109C22×C3D3×#6712yes—
1110C22×C3D3×#6712yes—
1111C22×C3#381112yes—
1112C22×C3C22×D3211yescharacteristic
1113C22×C3C22×D3211yescharacteristic
1114C22×C3C22×D3211yescharacteristic
1115C2×D3—21no—
1116C2×D3—21no—
1117C2×D3—21no—
1118C2×D3—21no—
1119C2×D3—21no—
1120C2×D3—21no—
1121C2×D3—21no—
1122C2×D3—21no—
1123C2×D3—32no—
1124C2×D3—32no—
1125C2×D3—44no—
1126C2×D3—62no—
1127C2×D3—61no—
1128C2×D3—61no—
1129C2×D3—61no—
1130C2×D3—61no—
1131C2×D3—121no—
1132C2×D3—121no—
1133C2×D3—182no—
1134C2×D3—181no—
1135C2×D3—181no—
1136C2×D3—181no—
1137C2×D3—181no—
1138C2×D3—181no—
1139C2×D3—181no—
1140C2×D3—181no—
1141C2×D3—181no—
1142C2×D3—181no—
1143C2×D3—361no—
1144C2×D3—361no—
1145C2×D3—361no—
1146C2×D3—361no—
1147C2×D3—361no—
1148C2×D3—361no—
1149C2×D3—361no—
1150C2×D3—361no—
1151C2×D3—362no—
1152C2×D3—364no—
1153C2×D3—364no—
1154C2×D3—364no—
1155C2×D3—368no—
1156C2×D3—721no—
1157C2×D3—721no—
1158C2×D3#380412yescomplemented
1159C3×C4—61no—
1160C3×C4—61no—
1161C3×C4—61no—
1162C3×C4—61no—
1163C3×C4—61no—
1164C3×C4—61no—
1165C3×C4—92no—
1166C3×C4—121no—
1167C3×C4—121no—
1168C3×C4—121no—
1169C3×C4—181no—
1170C3×C4—181no—
1171C3×C4—181no—
1172C3×C4—181no—
1173Dic3—21no—
1174Dic3—21no—
1175Dic3—21no—
1176Dic3—32no—
1177Dic3—32no—
1178Dic3—62no—
1179Dic3—62no—
1180Dic3—61no—
1181Dic3—61no—
1182Dic3—61no—
1183Dic3—61no—
1184Dic3—61no—
1185Dic3—61no—
1186Dic3—61no—
1187Dic3—61no—
1188Dic3—121no—
1189Dic3—121no—
1190Dic3—121no—
1191Dic3—182no—
1192Dic3—181no—
1193Dic3—181no—
1194Dic3—181no—
1195Dic3—361no—
1196Dic3—361no—
1197Dic3—362no—
1198C32—21no—
1199C32—21no—
1200C32—21no—
1201C32—41no—
1202C32#549011yescharacteristic, complemented
1203C32#559111yescharacteristic, complemented
1204C32#582911yescharacteristic, complemented
1205C23—31no—
1206C23—31no—
1207C23—31no—
1208C23—62no—
1209C23—62no—
1210C23—91no—
1211C23—121no—
1212C23—271no—
1213C23—542no—
1214C23—542no—
1215C23—1081no—
1216C23D3311yescharacteristic
1217Q8—182no—
1218D4—62no—
1219D4—94no—
1220D4—182no—
1221D4—182no—
1222D4—361no—
1223D4—542no—
1224D4—542no—
1225D4—542no—
1226D4—1081no—
1227C2×C4—31no—
1228C2×C4—31no—
1229C2×C4—31no—
1230C2×C4—62no—
1231C2×C4—91no—
1232C2×C4—91no—
1233C2×C4—91no—
1234C2×C4—91no—
1235C2×C4—91no—
1236C2×C4—182no—
1237C2×C4—182no—
1238C2×C4—271no—
1239C2×C4—361no—
1240C2×C4—542no—
1241C2×C4—1081no—
1242C2×C3—22no—
1243C2×C3—22no—
1244C2×C3—22no—
1245C2×C3—21no—
1246C2×C3—21no—
1247C2×C3—21no—
1248C2×C3—21no—
1249C2×C3—21no—
1250C2×C3—21no—
1251C2×C3—21no—
1252C2×C3—21no—
1253C2×C3—21no—
1254C2×C3—42no—
1255C2×C3—42no—
1256C2×C3—42no—
1257C2×C3—41no—
1258C2×C3—41no—
1259C2×C3—41no—
1260C2×C3—64no—
1261C2×C3—62no—
1262C2×C3—62no—
1263C2×C3—82no—
1264C2×C3—122no—
1265C2×C3—121no—
1266C2×C3—121no—
1267C2×C3—121no—
1268C2×C3—121no—
1269C2×C3—182no—
1270C2×C3—241no—
1271C2×C3D3×#23511yescharacteristic
1272C2×C3#6430711yescharacteristic
1273C2×C3D3×#23711yescharacteristic
1274C2×C3#6431411yescharacteristic
1275C2×C3C2×#380411yescharacteristic
1276C2×C3C2×D3×#6711yescharacteristic
1277C2×C3C2×D3×#6711yescharacteristic
1278C2×C3C2×#381111yescharacteristic
1279C2×C3#6433011yescharacteristic
1280D3—22no—
1281D3—41no—
1282D3—41no—
1283D3—62no—
1284D3—62no—
1285D3—122no—
1286D3—362no—
1287D3—361no—
1288D3—361no—
1289D3—361no—
1290D3—721no—
1291D3—721no—
1292D3—722no—
1293C22—21no—
1294C22—21no—
1295C22—32no—
1296C22—61no—
1297C22—61no—
1298C22—61no—
1299C22—61no—
1300C22—61no—
1301C22—61no—
1302C22—61no—
1303C22—61no—
1304C22—92no—
1305C22—124no—
1306C22—181no—
1307C22—181no—
1308C22—541no—
1309C22—541no—
1310C22—541no—
1311C22—1084no—
1312C22#8895212yes—
1313C22C2×D3311yescharacteristic
1314C4—61no—
1315C4—61no—
1316C4—61no—
1317C4—92no—
1318C4—181no—
1319C4—181no—
1320C4—181no—
1321C4—181no—
1322C4—541no—
1323C3—21no—
1324C3—21no—
1325C3—21no—
1326C3—41no—
1327C3#1059506511yescharacteristic, complemented
1328C3#1059530411yescharacteristic, complemented
1329C3#1059550011yescharacteristic, complemented
1330C2—22no—
1331C2—62no—
1332C2—121no—
1333C2—121no—
1334C2—182no—
1335C2—1081no—
1336C2D3×#380411yescharacteristic
1337C2#1172441811yescharacteristic
1338C2C2×#8895211yescharacteristic
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×D3×#638C2semidirect
2. C2×C3×#3804C2semidirect
3. #11723726C2semidirect
4. #11723635C2semidirect
5. #11723612C2semidirect
6. C3×#63976C2semidirect
7. C2×C3×(C2×D3)⋊Dic3C2semidirect
8. #11723005C2semidirect
9. #11722992C2semidirect
10. #11722976C2semidirect
11. #11722965C2semidirect
12. #11722958C2semidirect
13. #11722949C2semidirect
14. #11722924C2semidirect
15. #11722904C2semidirect
23. C22×C3×C3⋊Dic3C22semidirect
24. C2×C32×#67C22semidirect
25. C22×C32×Dic3C22semidirect
26. C2×#6294C22semidirect
29. C2×#6291C22semidirect
32. C2×C3×#627C22semidirect
33. C2×C3×#626C22semidirect
35. C2×C3×#625C22semidirect
36. C2×C3×#624C22semidirect
38. C2×C3×D3×Dic3C22semidirect
39. C3×#3757C22semidirect
40. #88815C22semidirect
41. #88814C22semidirect
42. #88813C22semidirect
43. #88807C22semidirect
44. #88807C22semidirect
45. #88807C22semidirect
46. #88804C22semidirect
47. #88804C22semidirect
48. #88804C22semidirect
49. (C2×D3)⋊(C3⋊Dic3)C22semidirect
53. C3×(C2×D3)⋊Dic3C22semidirect
54. C3×(C2×D3)⋊Dic3C22semidirect
55. C3×(C2×D3)⋊Dic3C22semidirect
62. C2×#3804D3semidirect
76. #63976D3semidirect
88. C2×(C2×D3)⋊Dic3D3semidirect
118. C3×#638D4semidirect
167. C22×C3⋊Dic3C2×D3semidirect
177. C2×C3×#67C2×D3semidirect
178. C2×C3×#67C2×D3semidirect
184. C22×C3×Dic3C2×D3semidirect
185. C22×C3×Dic3C2×D3semidirect
197. C2×#627C2×D3semidirect
204. C2×#626C2×D3semidirect
209. C2×#625C2×D3semidirect
211. C2×#624C2×D3semidirect
218. C2×D3×Dic3C2×D3semidirect
220. #3757C2×D3semidirect
272. (C2×D3)⋊Dic3C2×D3semidirect
273. (C2×D3)⋊Dic3C2×D3semidirect
274. (C2×D3)⋊Dic3C2×D3semidirect
297. C2×C32×D3#41semidirect
425. #638#67semidirect
570. C2×#67D32semidirect
579. C22×Dic3D32semidirect
753. C2×C3×D3#235semidirect
754. C2×C3×D3#237semidirect
812. C33#546semidirect
1158. C2×D3#3804semidirect
1202. C32#5490semidirect
1203. C32#5591semidirect
1204. C32#5829semidirect
1327. C3#10595065semidirect
1328. C3#10595304semidirect
1329. C3#10595500semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#6382
C2×C3×#38042
#117237262
#117236352
#117236122
C3×#639762
C2×C3×(C2×D3)⋊Dic32
#117230052
#117229922
#117229762
#117229652
#117229582
#117229492
#117229242
#117229042
#105955003
#105953043
#105950653