Finite Group Databasebeta

← #13172654

Subgroups — #13172654

Order 1728.

1792 conjugacy classes of subgroups.

The subgroup lattice has 1398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×#67C211yesmaximal, characteristic, complemented
2C2×#88952C211yesmaximal, characteristic, complemented
3#11723724C211yesmaximal, characteristic, complemented
4#11723643C211yesmaximal, characteristic, complemented
5#11723630C211yesmaximal, characteristic, complemented
6#11723616C211yesmaximal, characteristic, complemented
7C3×#63976C211yesmaximal, characteristic, complemented
8C3×#63970C211yesmaximal, characteristic, complemented
9#11722994C211yesmaximal, characteristic, complemented
10#11722987C211yesmaximal, characteristic, complemented
11#11722985C211yesmaximal, characteristic, complemented
12#11722958C211yesmaximal, characteristic, complemented
13#11722953C211yesmaximal, characteristic, complemented
14#11722949C211yesmaximal, characteristic, complemented
15D3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
16#10595524—31nomaximal
17#10595302—31nomaximal
18#10595281—31nomaximal
19C23×C32×D3C2211yescharacteristic, complemented
20C22×D3×C3⋊D3C2211yescharacteristic, complemented
21C22×C3×D32C2211yescharacteristic
22C2×#6312C2211yescharacteristic, complemented
23C2×C3×#638C2211yescharacteristic
24C2×C32×#67C2211yescharacteristic, complemented
25C2×C32×#67C2211yescharacteristic, complemented
26C2×#6294C2211yescharacteristic, complemented
27C2×#6291C2211yescharacteristic
28C2×#6291C2211yescharacteristic, complemented
29C2×#6291C2211yescharacteristic, complemented
30C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
31C3×D3×#67—24no—
32C2×C3×#626C2211yescharacteristic
33C2×C3×#625C2211yescharacteristic
34C2×C3×#625C2211yescharacteristic, complemented
35C2×C3×#625C2211yescharacteristic, complemented
36C2×C3×#625C2211yescharacteristic, complemented
37C2×C3×D3×Dic3C2211yescharacteristic, complemented
38C2×C3×D3×Dic3C2211yescharacteristic, complemented
39#88952—24no—
40C3×#3757C2211yescharacteristic, complemented
41C3×#3757C2211yescharacteristic, complemented
42#88815C2211yescharacteristic, complemented
43#88815C2211yescharacteristic, complemented
44#88814C2211yescharacteristic, complemented
45#88806C2211yescharacteristic, complemented
46#88804C2211yescharacteristic, complemented
47#88804C2211yescharacteristic, complemented
48#88803C2211yescharacteristic, complemented
49(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
50(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
51(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
52C3×Dic3⋊Dic3C2211yescharacteristic, complemented
53C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
54C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
55C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
56C22×C3×#67—31no—
57C2×C3×D3×D4—31no—
58C2×#3811—31no—
59C2×D3×#67—31no—
60C2×D3×#67—31no—
61C2×D3×#67D311yescharacteristic, complemented
62#64162—31no—
63#64148—31no—
64#64146—31no—
65C3×#953—31no—
66C3×#939—31no—
67C3×#938—31no—
68C3×#937—31no—
69#63983—31no—
70#63983—31no—
71#63983—31no—
72#63983—61no—
73#63981—31no—
74#63980—31no—
75#63978—31no—
76#63977—31no—
77#63977—31no—
78#63977—61no—
79#63976D311yescharacteristic, complemented
80#63975—31no—
81#63971—31no—
82#63971—31no—
83#63971—31no—
84#63971—61no—
85#63970—31no—
86#63970—31no—
87#63970D311yescharacteristic, complemented
88#63969—31no—
89#63969—31no—
90#63969—31no—
91#63969—31no—
92D3×#217—31no—
93#63966—31no—
94#63961—31no—
95C2×(C2×D3)⋊Dic3—31no—
96#63922—31no—
97D3×(C2×D3)⋊C4—31no—
98#63906—31no—
99#63905—31no—
100#63890—31no—
101#63884—31no—
102#63854—31no—
103#63850—31no—
104C23×C33C2311yescharacteristic
105C22×C3⋊(C3⋊D3)C2311yescharacteristic
106C22×C3×C3⋊D3C2311yescharacteristic
107C22×C32×D3—22no—
108C22×C32×D3—41no—
109C22×C32×D3—41no—
110C22×C32×D3C2311yescharacteristic
111C22×C32×D3C2311yescharacteristic
112C22×C32×D3C2311yescharacteristic
113C22×C32×D3C2311yescharacteristic
114C2×D3×C3⋊D3—22no—
115C2×D3×C3⋊D3—41no—
116C2×D3×C3⋊D3—41no—
117C2×C3×D32—41no—
118C2×C3×D32—41no—
119C2×C3×D32D414yescomplemented
120#6312—41no—
121C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
122C3×#638—22no—
123C2×C3×C3⋊Dic3C2311yescharacteristic
124C2×C3×C3⋊Dic3C2311yescharacteristic
125C2×C3×C3⋊Dic3C2311yescharacteristic
126C2×C3×C3⋊Dic3C2311yescharacteristic
127C2×C3×C3⋊Dic3C2311yescharacteristic
128C32×#67—22no—
129C32×#67—41no—
130C2×C32×Dic3C2311yescharacteristic
131C2×C32×Dic3C2311yescharacteristic
132#6294—22no—
133#6291—22no—
134#6291—22no—
135#6291—41no—
136D3×C3⋊Dic3—41no—
137C3×#626—22no—
138C3×#625—22no—
139C3×#625—22no—
140C3×#625—22no—
141C3×#625—41no—
142C3×D3×Dic3—22no—
143C3×D3×Dic3—41no—
144#5804—91no—
145#5605—91no—
146#5589—91no—
147C24×C32—31no—
148C23×C3⋊D3—31no—
149C23×C3×D3—21no—
150C23×C3×D3—31no—
151C23×C3×D3—31no—
152C23×C3×D3C2×D311yescharacteristic, complemented
153C23×C3×D3C2×D311yescharacteristic, complemented
154C22×D32—31no—
155C22×D32—31no—
156C22×D32—61no—
157C22×D32C2×D311yescharacteristic
158C2×C32×D4—31no—
159C2×C32×D4—31no—
160C2×#638—31no—
161C2×#638—31no—
162C2×#638—31no—
163C2×#638—31no—
164C2×#638—31no—
165C2×#638—31no—
166C2×#638—61no—
167C2×#638—61no—
168C2×#638—61no—
169C2×#638—121no—
170C2×#638C2×D311yescharacteristic
171C22×C3⋊Dic3—31no—
172C2×C3×#67—21no—
173C2×C3×#67—21no—
174C2×C3×#67—31no—
175C2×C3×#67—31no—
176C2×C3×#67—31no—
177C2×C3×#67—31no—
178C2×C3×#67—31no—
179C2×C3×#67—31no—
180C2×C3×#67—31no—
181C2×C3×#67—31no—
182C2×C3×#67—31no—
183C2×C3×#67—31no—
184C2×C3×#67—31no—
185C2×C3×#67—64no—
186C2×C3×#67—61no—
187C2×C3×#67C2×D311yescharacteristic, complemented
188C2×C3×#67C2×D311yescharacteristic, complemented
189C2×C3×#67C2×D311yescharacteristic, complemented
190C2×C3×#67C2×D311yescharacteristic, complemented
191C22×C3×Dic3—31no—
192C22×C3×Dic3—31no—
193C3×D3×D4—64no—
194C2×C3×D12—31no—
195C2×C3×C4×D3—31no—
196C2×C3×C4×D3—31no—
197#3811—64no—
198D3×#67—24no—
199D3×#67—64no—
200D3×#67—64no—
201C2×#626—31no—
202C2×#626—31no—
203C2×#626—31no—
204C2×#626—31no—
205C2×#626—31no—
206C2×#626—31no—
207C2×#626—61no—
208C2×#626—61no—
209C2×#626—61no—
210C2×#626C2×D311yescharacteristic
211C2×#625C2×D311yescharacteristic
212C2×#625C2×D311yescharacteristic, complemented
213C2×#625C2×D311yescharacteristic, complemented
214C2×#625C2×D311yescharacteristic, complemented
215C2×#624—31no—
216C2×D3×Dic3—31no—
217C2×D3×Dic3—31no—
218C2×D3×Dic3—31no—
219C2×D3×Dic3—31no—
220C2×D3×Dic3—61no—
221C2×D3×Dic3C2×D311yescharacteristic, complemented
222C2×D3×Dic3C2×D311yescharacteristic, complemented
223#3757—31no—
224#3757—31no—
225#3757—31no—
226#3757C2×D311yescharacteristic, complemented
227#3757C2×D311yescharacteristic, complemented
228#3752—31no—
229#3752—31no—
230#3752—31no—
231#3750—31no—
232C3×#217—31no—
233C3×#217—31no—
234C3×#217—31no—
235C3×#217—31no—
236C3×#217—31no—
237C3×#217—31no—
238C3×#217—31no—
239C3×#217—61no—
240C3×#217—61no—
241C3×(C2×D3)⋊C4—31no—
242C3×(C2×D3)⋊C4—31no—
243C3×(C2×D3)⋊C4—31no—
244C3×C4⋊Dic3—31no—
245C3×Dic3⋊C4—31no—
246#3724—31no—
247#3724—31no—
248#3724—31no—
249#3724—31no—
250#3724—61no—
251Dic3⋊Dic3—31no—
252Dic3⋊Dic3—31no—
253Dic3⋊Dic3—31no—
254Dic3⋊Dic3—31no—
255Dic3⋊Dic3C2×D311yescharacteristic, complemented
256#3722—31no—
257#3722—31no—
258#3722—31no—
259#3722—31no—
260#3722—31no—
261#3722—61no—
262#3722—61no—
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—31no—
269(C2×D3)⋊Dic3—31no—
270(C2×D3)⋊Dic3—31no—
271(C2×D3)⋊Dic3—31no—
272(C2×D3)⋊Dic3—31no—
273(C2×D3)⋊Dic3—61no—
274(C2×D3)⋊Dic3—61no—
275(C2×D3)⋊Dic3—61no—
276(C2×D3)⋊Dic3—61no—
277(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
278(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
279(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
280C22×C33—21no—
281C22×C33—21no—
282C22×C33—21no—
283C22×C33C2411yescharacteristic
284C2×C3⋊(C3⋊D3)—21no—
285C2×C3⋊(C3⋊D3)—21no—
286C2×C3⋊(C3⋊D3)—21no—
287C2×C3×C3⋊D3—21no—
288C2×C3×C3⋊D3—21no—
289C2×C3×C3⋊D3C2×D412yes—
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—21no—
297C2×C32×D3—21no—
298C2×C32×D3—21no—
299C2×C32×D3—21no—
300C2×C32×D3—44no—
301C2×C32×D3C2×D412yes—
302C2×C32×D3C2×D412yes—
303D3×C3⋊D3—44no—
304C3×D32—44no—
305C3⋊(C3⋊Dic3)—21no—
306C3×C3⋊Dic3—21no—
307C3×C3⋊Dic3—21no—
308C3×C3⋊Dic3—21no—
309C3×C3⋊Dic3—21no—
310C3×C3⋊Dic3—21no—
311C32×Dic3—21no—
312C32×Dic3—21no—
313C22×C3×D4—91no—
314C22×#67—31no—
315C22×#67—91no—
316C2×D3×D4—31no—
317C2×D3×D4—91no—
318C2×D3×D4—91no—
319C3×#121—91no—
320C3×#120—91no—
321#953—31no—
322#953—91no—
323#953—91no—
324#953—181no—
325C2×#217—91no—
326#939—31no—
327#939—91no—
328#939—91no—
329#939—91no—
330#939—91no—
331#939—91no—
332#939—181no—
333#938—31no—
334#938—91no—
335#937—31no—
336#937—91no—
337#937—91no—
338#937—91no—
339#937—91no—
340#937—91no—
341#937—181no—
342#935—91no—
343#935—91no—
344#935—91no—
345#930—91no—
346#929—91no—
347#929—91no—
348C2×(C2×D3)⋊C4—91no—
349#894—91no—
350#894—91no—
351#886—91no—
352#884—91no—
353#884—91no—
354#883—91no—
355#883—91no—
356#883—91no—
357#883—91no—
358#882—91no—
359#882—91no—
360D3×C22⋊C4—91no—
361C23×C32—21no—
362C23×C32—21no—
363C23×C32—21no—
364C23×C32—31no—
365C23×C32—31no—
366C23×C32—31no—
367C23×C32—31no—
368C23×C32—41no—
369C23×C32—62no—
370C23×C32—121no—
371C23×C32—121no—
372C23×C32C22×D311yescharacteristic
373C23×C32C22×D311yescharacteristic
374C23×C32C22×D311yescharacteristic
375C22×C3⋊D3—31no—
376C22×C3⋊D3—31no—
377C22×C3⋊D3—31no—
378C22×C3⋊D3—61no—
379C22×C3⋊D3—61no—
380C22×C3⋊D3—61no—
381C22×C3⋊D3—62no—
382C22×C3⋊D3—121no—
383C22×C3⋊D3—121no—
384C22×C3⋊D3—121no—
385C22×C3⋊D3C22×D311yescharacteristic
386C22×C3×D3—22no—
387C22×C3×D3—22no—
388C22×C3×D3—21no—
389C22×C3×D3—21no—
390C22×C3×D3—21no—
391C22×C3×D3—21no—
392C22×C3×D3—31no—
393C22×C3×D3—31no—
394C22×C3×D3—34no—
395C22×C3×D3—34no—
396C22×C3×D3—42no—
397C22×C3×D3—41no—
398C22×C3×D3—41no—
399C22×C3×D3—41no—
400C22×C3×D3—41no—
401C22×C3×D3—42no—
402C22×C3×D3—42no—
403C22×C3×D3—61no—
404C22×C3×D3—121no—
405C22×C3×D3—121no—
406C22×C3×D3—121no—
407C22×C3×D3—121no—
408C22×C3×D3C22×D311yescharacteristic
409C22×C3×D3C22×D311yescharacteristic
410C22×C3×D3C22×D311yescharacteristic
411C22×C3×D3C22×D311yescharacteristic
412C22×C3×D3C22×D311yescharacteristic
413C22×C3×D3C22×D311yescharacteristic
414C22×C3×D3C22×D311yescharacteristic
415C22×C3×D3C22×D311yescharacteristic
416C2×D32—41no—
417C2×D32—41no—
418C2×D32—62no—
419C2×D32—62no—
420C2×D32—122no—
421C2×D32—121no—
422C2×D32—121no—
423C2×D32—121no—
424C2×D32—121no—
425C2×D32—122no—
426C2×D32—122no—
427C2×D32#6714yescomplemented
428C32×D4—62no—
429C32×D4—121no—
430C2×C32×C4—31no—
431C2×C32×C4—31no—
432#638—22no—
433#638—62no—
434#638—62no—
435#638—121no—
436#638—121no—
437#638—121no—
438#638—121no—
439#638—122no—
440#638—122no—
441#638—122no—
442#638—124no—
443C2×C3⋊Dic3—31no—
444C2×C3⋊Dic3—31no—
445C2×C3⋊Dic3—31no—
446C2×C3⋊Dic3—61no—
447C2×C3⋊Dic3—61no—
448C2×C3⋊Dic3—61no—
449C2×C3⋊Dic3—121no—
450C2×C3⋊Dic3—121no—
451C2×C3⋊Dic3C22×D311yescharacteristic
452C2×C3⋊Dic3C22×D311yescharacteristic
453C2×C3⋊Dic3C22×D311yescharacteristic
454C2×C3⋊Dic3C22×D311yescharacteristic
455C2×C3⋊Dic3C22×D311yescharacteristic
456C3×#67—22no—
457C3×#67—22no—
458C3×#67—42no—
459C3×#67—41no—
460C3×#67—41no—
461C3×#67—42no—
462C3×#67—62no—
463C3×#67—62no—
464C3×#67—62no—
465C3×#67—62no—
466C3×#67—62no—
467C3×#67—62no—
468C3×#67—62no—
469C3×#67—62no—
470C3×#67—62no—
471C3×#67—122no—
472C3×#67—121no—
473C3×#67—121no—
474C2×C3×Dic3—21no—
475C2×C3×Dic3—21no—
476C2×C3×Dic3—31no—
477C2×C3×Dic3—31no—
478C2×C3×Dic3—31no—
479C2×C3×Dic3—31no—
480C2×C3×Dic3—31no—
481C2×C3×Dic3—31no—
482C2×C3×Dic3—31no—
483C2×C3×Dic3—31no—
484C2×C3×Dic3—31no—
485C2×C3×Dic3—31no—
486C2×C3×Dic3—61no—
487C2×C3×Dic3—61no—
488C2×C3×Dic3—61no—
489C2×C3×Dic3—61no—
490C2×C3×Dic3—61no—
491C2×C3×Dic3—62no—
492C2×C3×Dic3—121no—
493C2×C3×Dic3C22×D311yescharacteristic
494C2×C3×Dic3C22×D311yescharacteristic
495C2×C3×Dic3C22×D311yescharacteristic
496C2×C3×Dic3C22×D311yescharacteristic
497C3×D12—62no—
498C3×C4×D3—62no—
499C3×C4×D3—121no—
500#626—22no—
501#626—62no—
502#626—62no—
503#626—62no—
504#626—62no—
505#626—122no—
506#626—122no—
507#626—121no—
508#626—121no—
509#626—122no—
510#625—22no—
511#625—22no—
512#625—22no—
513#625—41no—
514#624—62no—
515D3×Dic3—22no—
516D3×Dic3—41no—
517D3×Dic3—62no—
518D3×Dic3—62no—
519D3×Dic3—121no—
520D3×Dic3—121no—
521D3×Dic3—122no—
522#534—271noSylow
523C2×C33—41no—
524C2×C33C22×D411yescharacteristic
525C2×C33H(5,𝔽2)11yescharacteristic
526C2×C33H(5,𝔽2)11yescharacteristic
527C3⋊(C3⋊D3)—41no—
528C3×C3⋊D3—22no—
529C32×D3—22no—
530C32×D3—22no—
531C32×D3—41no—
532C32×D3—41no—
533C24×C3—31no—
534C24×C3—31no—
535C24×C3—61no—
536C24×C3—91no—
537C23×D3—31no—
538C23×D3—31no—
539C23×D3—91no—
540C23×D3—91no—
541C23×D3—91no—
542C23×D3—181no—
543C23×D3D3211yescharacteristic, complemented
544C2×C3×D4—31no—
545C2×C3×D4—31no—
546C2×C3×D4—31no—
547C2×C3×D4—31no—
548C2×C3×D4—61no—
549C2×C3×D4—61no—
550C2×C3×D4—91no—
551C2×C3×D4—91no—
552C2×C3×D4—91no—
553C2×C3×D4—91no—
554C2×C3×D4—91no—
555C2×C3×D4—91no—
556C2×C3×D4—184no—
557C22×C3×C4—91no—
558C22×C3×C4—91no—
559C2×#67—31no—
560C2×#67—31no—
561C2×#67—31no—
562C2×#67—31no—
563C2×#67—31no—
564C2×#67—31no—
565C2×#67—31no—
566C2×#67—31no—
567C2×#67—31no—
568C2×#67—31no—
569C2×#67—31no—
570C2×#67—61no—
571C2×#67—64no—
572C2×#67—91no—
573C2×#67—91no—
574C2×#67—91no—
575C2×#67—91no—
576C2×#67—91no—
577C2×#67—91no—
578C2×#67—91no—
579C2×#67—91no—
580C2×#67—91no—
581C2×#67—181no—
582C2×#67—181no—
583C2×#67—181no—
584C2×#67—181no—
585C2×#67—181no—
586C2×#67—181no—
587C2×#67—184no—
588C2×#67—361no—
589C2×#67D3211yescharacteristic, complemented
590C2×#67D3211yescharacteristic, complemented
591C22×Dic3—31no—
592C22×Dic3—31no—
593C22×Dic3—91no—
594C22×Dic3—91no—
595C22×Dic3—91no—
596C22×Dic3—181no—
597D3×D4—64no—
598D3×D4—184no—
599D3×D4—184no—
600C2×D12—31no—
601C2×D12—91no—
602C2×D12—91no—
603C2×D12—91no—
604C2×C4×D3—31no—
605C2×C4×D3—31no—
606C2×C4×D3—91no—
607C2×C4×D3—91no—
608C2×C4×D3—91no—
609C3×C4⋊C4—91no—
610C3×C22⋊C4—91no—
611C3×C22⋊C4—91no—
612C3×C22⋊C4—91no—
613C3×C22⋊C4—91no—
614C3×C22⋊C4—91no—
615#217—31no—
616#217—31no—
617#217—31no—
618#217—31no—
619#217—31no—
620#217—31no—
621#217—31no—
622#217—61no—
623#217—61no—
624#217—91no—
625#217—91no—
626#217—91no—
627#217—91no—
628#217—91no—
629#217—91no—
630#217—91no—
631#217—91no—
632#217—181no—
633#217—181no—
634#217—181no—
635(C2×D3)⋊C4—31no—
636(C2×D3)⋊C4—31no—
637(C2×D3)⋊C4—31no—
638(C2×D3)⋊C4—91no—
639(C2×D3)⋊C4—91no—
640(C2×D3)⋊C4—91no—
641(C2×D3)⋊C4—91no—
642(C2×D3)⋊C4—91no—
643(C2×D3)⋊C4—91no—
644(C2×D3)⋊C4—91no—
645(C2×D3)⋊C4—91no—
646(C2×D3)⋊C4—91no—
647(C2×D3)⋊C4—91no—
648(C2×D3)⋊C4—91no—
649(C2×D3)⋊C4—91no—
650(C2×D3)⋊C4—91no—
651(C2×D3)⋊C4—181no—
652(C2×D3)⋊C4—181no—
653(C2×D3)⋊C4—181no—
654C4⋊Dic3—31no—
655C4⋊Dic3—91no—
656C4⋊Dic3—91no—
657Dic3⋊C4—31no—
658Dic3⋊C4—91no—
659Dic3⋊C4—91no—
660Dic3⋊C4—91no—
661Dic3⋊C4—91no—
662Dic3⋊C4—91no—
663Dic3⋊C4—91no—
664Dic3⋊C4—91no—
665Dic3⋊C4—181no—
666C22×C32—21no—
667C22×C32—22no—
668C22×C32—21no—
669C22×C32—21no—
670C22×C32—21no—
671C22×C32—21no—
672C22×C32—21no—
673C22×C32—21no—
674C22×C32—21no—
675C22×C32—21no—
676C22×C32—21no—
677C22×C32—21no—
678C22×C32—21no—
679C22×C32—32no—
680C22×C32—32no—
681C22×C32—41no—
682C22×C32—41no—
683C22×C32—41no—
684C22×C32—42no—
685C22×C32—41no—
686C22×C32—41no—
687C22×C32—41no—
688C22×C32—41no—
689C22×C32—41no—
690C22×C32—41no—
691C22×C32—61no—
692C22×C32—61no—
693C22×C32—61no—
694C22×C32—61no—
695C22×C32—61no—
696C22×C32—61no—
697C22×C32—61no—
698C22×C32—61no—
699C22×C32—61no—
700C22×C32—61no—
701C22×C32—81no—
702C22×C32—81no—
703C22×C32—124no—
704C22×C32C23×D311yescharacteristic
705C22×C32C23×D311yescharacteristic
706C22×C32C23×D311yescharacteristic
707C2×C3⋊D3—21no—
708C2×C3⋊D3—21no—
709C2×C3⋊D3—61no—
710C2×C3⋊D3—62no—
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—121no—
720C2×C3⋊D3—121no—
721C2×C3⋊D3—122no—
722C2×C3⋊D3—121no—
723C2×C3⋊D3—121no—
724C2×C3⋊D3—121no—
725C2×C3⋊D3—121no—
726C2×C3⋊D3—121no—
727C2×C3⋊D3—121no—
728C2×C3⋊D3—124no—
729C2×C3⋊D3—241no—
730C2×C3⋊D3—241no—
731C2×C3⋊D3C2×#6712yes—
732C2×C3×D3—21no—
733C2×C3×D3—21no—
734C2×C3×D3—21no—
735C2×C3×D3—21no—
736C2×C3×D3—21no—
737C2×C3×D3—21no—
738C2×C3×D3—21no—
739C2×C3×D3—21no—
740C2×C3×D3—22no—
741C2×C3×D3—22no—
742C2×C3×D3—21no—
743C2×C3×D3—21no—
744C2×C3×D3—21no—
745C2×C3×D3—21no—
746C2×C3×D3—21no—
747C2×C3×D3—21no—
748C2×C3×D3—21no—
749C2×C3×D3—21no—
750C2×C3×D3—21no—
751C2×C3×D3—21no—
752C2×C3×D3—21no—
753C2×C3×D3—21no—
754C2×C3×D3—22no—
755C2×C3×D3—22no—
756C2×C3×D3—32no—
757C2×C3×D3—32no—
758C2×C3×D3—41no—
759C2×C3×D3—41no—
760C2×C3×D3—41no—
761C2×C3×D3—41no—
762C2×C3×D3—41no—
763C2×C3×D3—41no—
764C2×C3×D3—41no—
765C2×C3×D3—41no—
766C2×C3×D3—44no—
767C2×C3×D3—44no—
768C2×C3×D3—48no—
769C2×C3×D3—62no—
770C2×C3×D3—61no—
771C2×C3×D3—61no—
772C2×C3×D3—61no—
773C2×C3×D3—61no—
774C2×C3×D3—121no—
775C2×C3×D3—121no—
776C2×C3×D3—124no—
777C2×C3×D3—124no—
778C2×C3×D3D3×D412yes—
779C2×C3×D3D3×D412yes—
780C2×C3×D3C2×#6712yes—
781C2×C3×D3C2×#6712yes—
782D32—44no—
783D32—124no—
784D32—124no—
785D32—128no—
786C32×C4—61no—
787C32×C4—61no—
788C3⋊Dic3—21no—
789C3⋊Dic3—21no—
790C3⋊Dic3—21no—
791C3⋊Dic3—21no—
792C3⋊Dic3—21no—
793C3⋊Dic3—61no—
794C3⋊Dic3—62no—
795C3⋊Dic3—61no—
796C3⋊Dic3—61no—
797C3⋊Dic3—121no—
798C3⋊Dic3—121no—
799C3⋊Dic3—122no—
800C3×Dic3—21no—
801C3×Dic3—21no—
802C3×Dic3—21no—
803C3×Dic3—21no—
804C3×Dic3—41no—
805C3×Dic3—41no—
806C3×Dic3—61no—
807C3×Dic3—61no—
808C3×Dic3—61no—
809C3×Dic3—61no—
810C3×Dic3—61no—
811C3×Dic3—61no—
812C3×Dic3—61no—
813C3×Dic3—61no—
814C3×Dic3—61no—
815C3×Dic3—61no—
816C3×Dic3—121no—
817C3×Dic3—121no—
818C3×Dic3—121no—
819C3×Dic3—121no—
820C3×Dic3—121no—
821C22×D4—91no—
822C22×D4—271no—
823#123—271no—
824#123—271no—
825#123—271no—
826#123—271no—
827#121—91no—
828#121—271no—
829#121—271no—
830#121—271no—
831#120—91no—
832#120—271no—
833#120—271no—
834#120—271no—
835C2×C22⋊C4—271no—
836C33#53411yescharacteristic, complemented, Sylow
837C23×C3—21no—
838C23×C3—21no—
839C23×C3—21no—
840C23×C3—31no—
841C23×C3—31no—
842C23×C3—31no—
843C23×C3—31no—
844C23×C3—31no—
845C23×C3—31no—
846C23×C3—31no—
847C23×C3—31no—
848C23×C3—41no—
849C23×C3—61no—
850C23×C3—61no—
851C23×C3—61no—
852C23×C3—61no—
853C23×C3—62no—
854C23×C3—62no—
855C23×C3—94no—
856C23×C3—91no—
857C23×C3—122no—
858C23×C3—121no—
859C23×C3—121no—
860C23×C3—121no—
861C23×C3—121no—
862C23×C3—122no—
863C23×C3—122no—
864C23×C3—361no—
865C23×C3—361no—
866C23×C3C2×D3211yescharacteristic
867C23×C3C2×D3211yescharacteristic
868C23×C3C2×D3211yescharacteristic
869C22×D3—22no—
870C22×D3—31no—
871C22×D3—31no—
872C22×D3—34no—
873C22×D3—34no—
874C22×D3—41no—
875C22×D3—41no—
876C22×D3—61no—
877C22×D3—91no—
878C22×D3—91no—
879C22×D3—91no—
880C22×D3—121no—
881C22×D3—121no—
882C22×D3—121no—
883C22×D3—121no—
884C22×D3—181no—
885C22×D3—181no—
886C22×D3—181no—
887C22×D3—182no—
888C22×D3—182no—
889C22×D3—182no—
890C22×D3—361no—
891C22×D3—362no—
892C22×D3—361no—
893C22×D3—361no—
894C22×D3—361no—
895C22×D3—361no—
896C22×D3—361no—
897C22×D3—361no—
898C22×D3—362no—
899C22×D3—362no—
900C22×D3C2×D3211yescharacteristic
901C22×D3C2×D3211yescharacteristic
902C22×D3C2×D3211yescharacteristic
903C22×D3C2×D3211yescharacteristic
904C3×D4—62no—
905C3×D4—62no—
906C3×D4—122no—
907C3×D4—121no—
908C3×D4—121no—
909C3×D4—122no—
910C3×D4—182no—
911C3×D4—182no—
912C3×D4—182no—
913C3×D4—182no—
914C3×D4—182no—
915C3×D4—361no—
916C2×C3×C4—31no—
917C2×C3×C4—31no—
918C2×C3×C4—31no—
919C2×C3×C4—31no—
920C2×C3×C4—61no—
921C2×C3×C4—61no—
922C2×C3×C4—91no—
923C2×C3×C4—91no—
924C2×C3×C4—91no—
925C2×C3×C4—91no—
926C2×C3×C4—91no—
927C2×C3×C4—182no—
928C2×C3×C4—361no—
929#67—22no—
930#67—41no—
931#67—62no—
932#67—62no—
933#67—62no—
934#67—62no—
935#67—62no—
936#67—62no—
937#67—62no—
938#67—62no—
939#67—62no—
940#67—122no—
941#67—121no—
942#67—121no—
943#67—182no—
944#67—182no—
945#67—182no—
946#67—182no—
947#67—362no—
948#67—362no—
949#67—361no—
950#67—361no—
951#67—362no—
952#67—361no—
953#67—361no—
954#67—361no—
955#67—362no—
956#67—362no—
957#67—362no—
958#67—364no—
959C2×Dic3—31no—
960C2×Dic3—31no—
961C2×Dic3—31no—
962C2×Dic3—31no—
963C2×Dic3—31no—
964C2×Dic3—31no—
965C2×Dic3—31no—
966C2×Dic3—31no—
967C2×Dic3—31no—
968C2×Dic3—31no—
969C2×Dic3—61no—
970C2×Dic3—61no—
971C2×Dic3—61no—
972C2×Dic3—61no—
973C2×Dic3—61no—
974C2×Dic3—62no—
975C2×Dic3—91no—
976C2×Dic3—91no—
977C2×Dic3—91no—
978C2×Dic3—121no—
979C2×Dic3—181no—
980C2×Dic3—181no—
981C2×Dic3—181no—
982C2×Dic3—182no—
983C2×Dic3—361no—
984C2×Dic3—361no—
985C2×Dic3—361no—
986C2×Dic3—362no—
987C2×Dic3C2×D3211yescharacteristic
988C2×Dic3C2×D3211yescharacteristic
989D12—62no—
990D12—182no—
991D12—182no—
992D12—361no—
993C4×D3—62no—
994C4×D3—121no—
995C4×D3—182no—
996C4×D3—182no—
997C4×D3—361no—
998C2×C32—21no—
999C2×C32—21no—
1000C2×C32—21no—
1001C2×C32—21no—
1002C2×C32—21no—
1003C2×C32—21no—
1004C2×C32—21no—
1005C2×C32—21no—
1006C2×C32—21no—
1007C2×C32—41no—
1008C2×C32—41no—
1009C2×C32—41no—
1010C2×C32—41no—
1011C2×C32—42no—
1012C2×C32—41no—
1013C2×C32—41no—
1014C2×C32—62no—
1015C2×C32—62no—
1016C2×C32—81no—
1017C2×C32—81no—
1018C2×C32—82no—
1019C2×C32—121no—
1020C2×C32—121no—
1021C2×C32C2×D3×D411yescharacteristic
1022C2×C32C2×D3×D411yescharacteristic
1023C2×C32#100411yescharacteristic
1024C2×C32#100411yescharacteristic
1025C2×C32#100411yescharacteristic
1026C2×C32#100411yescharacteristic
1027C2×C32#100411yescharacteristic
1028C2×C32#100911yescharacteristic
1029C2×C32C22×#6711yescharacteristic
1030C3⋊D3—22no—
1031C3⋊D3—121no—
1032C3⋊D3—122no—
1033C3⋊D3—121no—
1034C3⋊D3—121no—
1035C3⋊D3—241no—
1036C3⋊D3—241no—
1037C3⋊D3—242no—
1038C3×D3—22no—
1039C3×D3—22no—
1040C3×D3—22no—
1041C3×D3—22no—
1042C3×D3—42no—
1043C3×D3—42no—
1044C3×D3—42no—
1045C3×D3—42no—
1046C3×D3—41no—
1047C3×D3—41no—
1048C3×D3—41no—
1049C3×D3—41no—
1050C3×D3—62no—
1051C3×D3—62no—
1052C3×D3—122no—
1053C24—31no—
1054C24—91no—
1055C24—271no—
1056C2×D4—31no—
1057C2×D4—31no—
1058C2×D4—91no—
1059C2×D4—91no—
1060C2×D4—91no—
1061C2×D4—91no—
1062C2×D4—91no—
1063C2×D4—91no—
1064C2×D4—184no—
1065C2×D4—271no—
1066C2×D4—271no—
1067C2×D4—271no—
1068C2×D4—271no—
1069C2×D4—544no—
1070C22×C4—91no—
1071C22×C4—91no—
1072C22×C4—271no—
1073C22×C4—271no—
1074C4⋊C4—91no—
1075C4⋊C4—271no—
1076C4⋊C4—271no—
1077C4⋊C4—271no—
1078C22⋊C4—91no—
1079C22⋊C4—91no—
1080C22⋊C4—91no—
1081C22⋊C4—91no—
1082C22⋊C4—91no—
1083C22⋊C4—271no—
1084C22⋊C4—271no—
1085C22⋊C4—271no—
1086C22⋊C4—271no—
1087C22⋊C4—271no—
1088C22⋊C4—271no—
1089C22⋊C4—271no—
1090C22×C3—22no—
1091C22×C3—21no—
1092C22×C3—21no—
1093C22×C3—21no—
1094C22×C3—21no—
1095C22×C3—21no—
1096C22×C3—21no—
1097C22×C3—21no—
1098C22×C3—21no—
1099C22×C3—21no—
1100C22×C3—21no—
1101C22×C3—21no—
1102C22×C3—21no—
1103C22×C3—32no—
1104C22×C3—32no—
1105C22×C3—32no—
1106C22×C3—32no—
1107C22×C3—41no—
1108C22×C3—41no—
1109C22×C3—41no—
1110C22×C3—41no—
1111C22×C3—41no—
1112C22×C3—41no—
1113C22×C3—41no—
1114C22×C3—41no—
1115C22×C3—42no—
1116C22×C3—41no—
1117C22×C3—62no—
1118C22×C3—62no—
1119C22×C3—62no—
1120C22×C3—62no—
1121C22×C3—61no—
1122C22×C3—61no—
1123C22×C3—61no—
1124C22×C3—61no—
1125C22×C3—61no—
1126C22×C3—61no—
1127C22×C3—61no—
1128C22×C3—61no—
1129C22×C3—61no—
1130C22×C3—61no—
1131C22×C3—61no—
1132C22×C3—61no—
1133C22×C3—61no—
1134C22×C3—61no—
1135C22×C3—61no—
1136C22×C3—61no—
1137C22×C3—61no—
1138C22×C3—61no—
1139C22×C3—61no—
1140C22×C3—61no—
1141C22×C3—81no—
1142C22×C3—81no—
1143C22×C3—92no—
1144C22×C3—121no—
1145C22×C3—121no—
1146C22×C3—121no—
1147C22×C3—121no—
1148C22×C3—121no—
1149C22×C3—121no—
1150C22×C3—121no—
1151C22×C3—121no—
1152C22×C3—124no—
1153C22×C3—124no—
1154C22×C3—128no—
1155C22×C3—181no—
1156C22×C3—181no—
1157C22×C3—364no—
1158C22×C3C22×D3211yescharacteristic
1159C22×C3C22×D3211yescharacteristic
1160C22×C3C22×D3211yescharacteristic
1161C2×D3—21no—
1162C2×D3—21no—
1163C2×D3—21no—
1164C2×D3—21no—
1165C2×D3—21no—
1166C2×D3—21no—
1167C2×D3—21no—
1168C2×D3—21no—
1169C2×D3—21no—
1170C2×D3—21no—
1171C2×D3—32no—
1172C2×D3—32no—
1173C2×D3—44no—
1174C2×D3—62no—
1175C2×D3—61no—
1176C2×D3—61no—
1177C2×D3—61no—
1178C2×D3—61no—
1179C2×D3—121no—
1180C2×D3—121no—
1181C2×D3—124no—
1182C2×D3—124no—
1183C2×D3—182no—
1184C2×D3—181no—
1185C2×D3—181no—
1186C2×D3—181no—
1187C2×D3—181no—
1188C2×D3—181no—
1189C2×D3—181no—
1190C2×D3—181no—
1191C2×D3—181no—
1192C2×D3—181no—
1193C2×D3—361no—
1194C2×D3—361no—
1195C2×D3—361no—
1196C2×D3—361no—
1197C2×D3—361no—
1198C2×D3—361no—
1199C2×D3—361no—
1200C2×D3—361no—
1201C2×D3—362no—
1202C2×D3—364no—
1203C2×D3—364no—
1204C2×D3—364no—
1205C2×D3—368no—
1206C2×D3—721no—
1207C2×D3—721no—
1208C2×D3D3×#6712yes—
1209C2×D3D3×#6712yes—
1210C3×C4—61no—
1211C3×C4—61no—
1212C3×C4—61no—
1213C3×C4—61no—
1214C3×C4—121no—
1215C3×C4—121no—
1216C3×C4—181no—
1217C3×C4—181no—
1218C3×C4—181no—
1219C3×C4—181no—
1220C3×C4—181no—
1221Dic3—21no—
1222Dic3—21no—
1223Dic3—61no—
1224Dic3—61no—
1225Dic3—61no—
1226Dic3—61no—
1227Dic3—61no—
1228Dic3—61no—
1229Dic3—61no—
1230Dic3—61no—
1231Dic3—61no—
1232Dic3—61no—
1233Dic3—121no—
1234Dic3—121no—
1235Dic3—121no—
1236Dic3—121no—
1237Dic3—121no—
1238Dic3—182no—
1239Dic3—181no—
1240Dic3—181no—
1241Dic3—181no—
1242Dic3—361no—
1243Dic3—361no—
1244Dic3—362no—
1245C32—21no—
1246C32—21no—
1247C32—21no—
1248C32—41no—
1249C32#558911yescharacteristic, complemented
1250C32#560511yescharacteristic, complemented
1251C32#580411yescharacteristic, complemented
1252C23—31no—
1253C23—31no—
1254C23—31no—
1255C23—31no—
1256C23—62no—
1257C23—94no—
1258C23—91no—
1259C23—121no—
1260C23—121no—
1261C23—271no—
1262C23—361no—
1263C23—361no—
1264C23—542no—
1265C23—1081no—
1266C23—1081no—
1267C23D3311yescharacteristic
1268D4—62no—
1269D4—121no—
1270D4—182no—
1271D4—182no—
1272D4—182no—
1273D4—182no—
1274D4—182no—
1275D4—361no—
1276D4—542no—
1277D4—542no—
1278D4—1081no—
1279D4—1081no—
1280C2×C4—31no—
1281C2×C4—31no—
1282C2×C4—91no—
1283C2×C4—91no—
1284C2×C4—91no—
1285C2×C4—91no—
1286C2×C4—91no—
1287C2×C4—182no—
1288C2×C4—271no—
1289C2×C4—361no—
1290C2×C4—542no—
1291C2×C4—1081no—
1292C2×C3—21no—
1293C2×C3—21no—
1294C2×C3—21no—
1295C2×C3—21no—
1296C2×C3—21no—
1297C2×C3—21no—
1298C2×C3—21no—
1299C2×C3—21no—
1300C2×C3—21no—
1301C2×C3—42no—
1302C2×C3—41no—
1303C2×C3—41no—
1304C2×C3—41no—
1305C2×C3—41no—
1306C2×C3—41no—
1307C2×C3—41no—
1308C2×C3—62no—
1309C2×C3—62no—
1310C2×C3—62no—
1311C2×C3—62no—
1312C2×C3—81no—
1313C2×C3—81no—
1314C2×C3—82no—
1315C2×C3—122no—
1316C2×C3—122no—
1317C2×C3—122no—
1318C2×C3—122no—
1319C2×C3—121no—
1320C2×C3—121no—
1321C2×C3—121no—
1322C2×C3—121no—
1323C2×C3—182no—
1324C2×C3D32×D411yescharacteristic
1325C2×C3#6431311yescharacteristic
1326C2×C3#6431411yescharacteristic
1327C2×C3#6431411yescharacteristic
1328C2×C3C2×D3×#6711yescharacteristic
1329C2×C3C2×D3×#6711yescharacteristic
1330C2×C3#6433011yescharacteristic
1331C2×C3#6433011yescharacteristic
1332C2×C3#6433011yescharacteristic
1333D3—22no—
1334D3—22no—
1335D3—41no—
1336D3—41no—
1337D3—62no—
1338D3—62no—
1339D3—122no—
1340D3—362no—
1341D3—361no—
1342D3—361no—
1343D3—361no—
1344D3—721no—
1345D3—721no—
1346D3—722no—
1347C22—21no—
1348C22—21no—
1349C22—21no—
1350C22—32no—
1351C22—32no—
1352C22—61no—
1353C22—61no—
1354C22—61no—
1355C22—61no—
1356C22—61no—
1357C22—61no—
1358C22—61no—
1359C22—61no—
1360C22—61no—
1361C22—61no—
1362C22—92no—
1363C22—124no—
1364C22—181no—
1365C22—181no—
1366C22—364no—
1367C22—541no—
1368C22—541no—
1369C22—541no—
1370C22—1084no—
1371C22C2×D3311yescharacteristic
1372C4—61no—
1373C4—61no—
1374C4—181no—
1375C4—181no—
1376C4—181no—
1377C4—181no—
1378C4—181no—
1379C4—541no—
1380C3—21no—
1381C3—21no—
1382C3—21no—
1383C3—41no—
1384C3#1059528111yescharacteristic, complemented
1385C3#1059530211yescharacteristic, complemented
1386C3#1059552411yescharacteristic, complemented
1387C2—41no—
1388C2—62no—
1389C2—62no—
1390C2—121no—
1391C2—121no—
1392C2—182no—
1393C2—1081no—
1394C2#1172441411yescharacteristic
1395C2#1172441911yescharacteristic
1396C2D32×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
hypercenterC23D33
hypocenterC33#534
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×#67C2semidirect
2. C2×#88952C2semidirect
3. #11723724C2semidirect
4. #11723643C2semidirect
5. #11723630C2semidirect
6. #11723616C2semidirect
7. C3×#63976C2semidirect
8. C3×#63970C2semidirect
9. #11722994C2semidirect
10. #11722987C2semidirect
11. #11722985C2semidirect
12. #11722958C2semidirect
13. #11722953C2semidirect
14. #11722949C2semidirect
15. D3×(C2×D3)⋊Dic3C2semidirect
19. C23×C32×D3C22semidirect
20. C22×D3×C3⋊D3C22semidirect
22. C2×#6312C22semidirect
24. C2×C32×#67C22semidirect
25. C2×C32×#67C22semidirect
26. C2×#6294C22semidirect
28. C2×#6291C22semidirect
29. C2×#6291C22semidirect
30. C2×D3×C3⋊Dic3C22semidirect
34. C2×C3×#625C22semidirect
35. C2×C3×#625C22semidirect
36. C2×C3×#625C22semidirect
37. C2×C3×D3×Dic3C22semidirect
38. C2×C3×D3×Dic3C22semidirect
40. C3×#3757C22semidirect
41. C3×#3757C22semidirect
42. #88815C22semidirect
43. #88815C22semidirect
44. #88814C22semidirect
45. #88806C22semidirect
46. #88804C22semidirect
47. #88804C22semidirect
48. #88803C22semidirect
49. (C2×D3)⋊(C3⋊Dic3)C22semidirect
50. (C2×D3)⋊(C3⋊Dic3)C22semidirect
51. (C2×D3)⋊(C3⋊Dic3)C22semidirect
52. C3×Dic3⋊Dic3C22semidirect
53. C3×(C2×D3)⋊Dic3C22semidirect
54. C3×(C2×D3)⋊Dic3C22semidirect
55. C3×(C2×D3)⋊Dic3C22semidirect
61. C2×D3×#67D3semidirect
79. #63976D3semidirect
87. #63970D3semidirect
119. C2×C3×D32D4semidirect
152. C23×C3×D3C2×D3semidirect
153. C23×C3×D3C2×D3semidirect
187. C2×C3×#67C2×D3semidirect
188. C2×C3×#67C2×D3semidirect
189. C2×C3×#67C2×D3semidirect
190. C2×C3×#67C2×D3semidirect
212. C2×#625C2×D3semidirect
213. C2×#625C2×D3semidirect
214. C2×#625C2×D3semidirect
221. C2×D3×Dic3C2×D3semidirect
222. C2×D3×Dic3C2×D3semidirect
226. #3757C2×D3semidirect
227. #3757C2×D3semidirect
255. Dic3⋊Dic3C2×D3semidirect
277. (C2×D3)⋊Dic3C2×D3semidirect
278. (C2×D3)⋊Dic3C2×D3semidirect
279. (C2×D3)⋊Dic3C2×D3semidirect
427. C2×D32#67semidirect
543. C23×D3D32semidirect
589. C2×#67D32semidirect
590. C2×#67D32semidirect
836. C33#534semidirect
1249. C32#5589semidirect
1250. C32#5605semidirect
1251. C32#5804semidirect
1384. C3#10595281semidirect
1385. C3#10595302semidirect
1386. C3#10595524semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×#672
C2×#889522
#117237242
#117236432
#117236302
#117236162
C3×#639762
C3×#639702
#117229942
#117229872
#117229852
#117229582
#117229532
#117229492
D3×(C2×D3)⋊Dic32
#105955243
#105953023
#105952813