Finite Group Databasebeta

← #13172686

Subgroups — #13172686

Order 1728.

1744 conjugacy classes of subgroups.

The subgroup lattice has 1334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3804C211yesmaximal, characteristic, complemented
2C2×#88954C211yesmaximal, characteristic, complemented
3#11723725C211yesmaximal, characteristic, complemented
4#11723643C211yesmaximal, characteristic, complemented
5#11723643C211yesmaximal, characteristic, complemented
6#11723618C211yesmaximal, characteristic, complemented
7C3×#63978C211yesmaximal, characteristic, complemented
8C3×#63970C211yesmaximal, characteristic, complemented
9#11723001C211yesmaximal, characteristic, complemented
10#11722995C211yesmaximal, characteristic, complemented
11#11722985C211yesmaximal, characteristic, complemented
12#11722973C211yesmaximal, characteristic, complemented
13#11722927C211yesmaximal, characteristic, complemented
14#11722904C211yesmaximal, characteristic, complemented
15D3×#3722C211yesmaximal, characteristic, complemented
16#10595305—31nomaximal
17#10595296—31nomaximal
18#10595070—31nomaximal
19C22×D3×C3⋊D3C2211yescharacteristic
20C22×D3×C3⋊D3C2211yescharacteristic
21C2×#6312C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic, complemented
23C2×C3×#638C2211yescharacteristic, complemented
24C2×C32×#67C2211yescharacteristic, complemented
25C2×C32×#67C2211yescharacteristic, complemented
26C22×C32×Dic3C2211yescharacteristic, complemented
27C2×#6295C2211yescharacteristic
28C2×#6294C2211yescharacteristic, complemented
29C2×#6289C2211yescharacteristic
30C2×C3×#627C2211yescharacteristic, complemented
31C2×C3×#626C2211yescharacteristic
32C2×C3×#626C2211yescharacteristic
33C2×C3×#625C2211yescharacteristic
34C2×C3×#624C2211yescharacteristic, complemented
35C3×#3804—24no—
36C2×C3×D3×Dic3C2211yescharacteristic, complemented
37C2×C3×D3×Dic3C2211yescharacteristic, complemented
38#88954—24no—
39C3×#3757C2211yescharacteristic, complemented
40#88815C2211yescharacteristic, complemented
41#88814C2211yescharacteristic, complemented
42#88806C2211yescharacteristic, complemented
43#88804C2211yescharacteristic
44#88804C2211yescharacteristic
45#88804C2211yescharacteristic
46#88803C2211yescharacteristic, complemented
47#88803C2211yescharacteristic, complemented
48(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
49(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
50Dic3×C3⋊Dic3C2211yescharacteristic, complemented
51C3×Dic3⋊Dic3C2211yescharacteristic, complemented
52C3×Dic3⋊Dic3C2211yescharacteristic, complemented
53C3×#3722C2211yescharacteristic, complemented
54C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
55C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
56C2×C3×#237—31no—
57C2×C3×#235—31no—
58C2×#3811—31no—
59C2×#3811—31no—
60C2×#3804D311yescharacteristic, complemented
61C2×#3802—31no—
62#64146—31no—
63#64146—31no—
64C4×#638—31no—
65C3×#939—31no—
66C3×#939—31no—
67C3×#938—31no—
68C3×#930—31no—
69#63983—31no—
70#63983—31no—
71#63983—31no—
72#63983—31no—
73#63983—61no—
74#63983—61no—
75#63978D311yescharacteristic, complemented
76#63974—31no—
77Dic3×#67—31no—
78#63971—31no—
79#63970—31no—
80#63970D311yescharacteristic, complemented
81#63969—31no—
82C2×#3722—31no—
83#63961—31no—
84#63959—31no—
85#63958—31no—
86#63952—31no—
87#63952—31no—
88#63952—61no—
89D3×(C2×D3)⋊C4—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#63904—31no—
97#63898—31no—
98#63895—31no—
99#63888—31no—
100#63871—31no—
101#63863—31no—
102#63854—31no—
103#63850—31no—
104C23×C33C2311yescharacteristic
105C22×C3⋊(C3⋊D3)C2311yescharacteristic
106C22×C3×C3⋊D3C2311yescharacteristic
107C22×C3×C3⋊D3C2311yescharacteristic
108C22×C32×D3C2311yescharacteristic
109C22×C32×D3C2311yescharacteristic
110C2×D3×C3⋊D3—22no—
111C2×D3×C3⋊D3—22no—
112C2×D3×C3⋊D3—22no—
113C2×D3×C3⋊D3—22no—
114C2×D3×C3⋊D3—41no—
115C2×D3×C3⋊D3—41no—
116#6312—22no—
117C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
118C3×#638—22no—
119C3×#638—41no—
120C2×C3×C3⋊Dic3C2311yescharacteristic
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#6295—22no—
132#6294—41no—
133#6289—22no—
134C3×#627—22no—
135C3×#626—22no—
136C3×#626D414yescomplemented
137C3×#625—22no—
138C3×#624—22no—
139C3×D3×Dic3—22no—
140C3×D3×Dic3—41no—
141#5829—91no—
142#5612—91no—
143#5610—91no—
144C23×C3⋊D3—31no—
145C23×C3⋊D3—31no—
146C22×D32—31no—
147C22×D32—31no—
148C22×D32—31no—
149C22×D32—31no—
150C22×D32—61no—
151C22×D32—61no—
152C2×C32×D4—31no—
153C2×C32×D4—31no—
154C22×C32×C4—31no—
155C2×#638—31no—
156C2×#638—31no—
157C2×#638—31no—
158C2×#638—61no—
159C2×#638—61no—
160C2×#638—61no—
161C2×#638—121no—
162C2×#638C2×D311yescharacteristic, complemented
163C2×#638C2×D311yescharacteristic, complemented
164C2×C4×C3⋊D3—31no—
165C2×C3×#67—21no—
166C2×C3×#67—21no—
167C2×C3×#67—31no—
168C2×C3×#67—31no—
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—61no—
176C2×C3×#67—61no—
177C2×C3×#67C2×D311yescharacteristic, complemented
178C2×C3×#67C2×D311yescharacteristic, complemented
179C2×C3×#67C2×D311yescharacteristic, complemented
180C2×C3×#67C2×D311yescharacteristic, complemented
181C22×C3×Dic3—21no—
182C22×C3×Dic3—31no—
183C22×C3×Dic3—31no—
184C22×C3×Dic3C2×D311yescharacteristic, complemented
185C22×C3×Dic3C2×D311yescharacteristic, complemented
186C3×#237—64no—
187C3×#235—64no—
188C2×C3×D12—31no—
189C2×C3×D12—31no—
190C2×C3×C4×D3—31no—
191C2×C3×C4×D3—31no—
192C2×C3×C4×D3—31no—
193C2×C3×C4×D3—31no—
194C2×C3×Dic6—31no—
195C2×C3×Dic6—31no—
196#3811—64no—
197#3811—64no—
198C2×#627C2×D311yescharacteristic, complemented
199C2×#626—31no—
200C2×#626—31no—
201C2×#626C2×D311yescharacteristic
202C2×#626C2×D311yescharacteristic
203C2×#625—31no—
204C2×#625C2×D311yescharacteristic
205C2×#624—31no—
206C2×#624—31no—
207C2×#624—31no—
208C2×#624—61no—
209C2×#624C2×D311yescharacteristic, complemented
210#3804—24no—
211C2×D3×Dic3—31no—
212C2×D3×Dic3—31no—
213C2×D3×Dic3C2×D311yescharacteristic, complemented
214C2×D3×Dic3C2×D311yescharacteristic, complemented
215#3802—64no—
216#3757—31no—
217#3757—31no—
218#3757C2×D311yescharacteristic, complemented
219#3752—31no—
220#3752—31no—
221#3752—31no—
222#3752—31no—
223#3752—31no—
224#3750—31no—
225C4×C3⋊Dic3—31no—
226C3×#217—31no—
227C3×#217—31no—
228C3×#217—31no—
229C3×#217—31no—
230C3×#217—61no—
231C3×(C2×D3)⋊C4—31no—
232C3×(C2×D3)⋊C4—31no—
233C3×(C2×D3)⋊C4—31no—
234C3×(C2×D3)⋊C4—31no—
235C3×C4⋊Dic3—31no—
236C3×C4⋊Dic3—31no—
237C3×Dic3⋊C4—31no—
238C3×Dic3⋊C4—31no—
239#3724—31no—
240#3724—31no—
241#3724—31no—
242#3724—61no—
243Dic3⋊Dic3—31no—
244Dic3⋊Dic3—31no—
245Dic3⋊Dic3C2×D311yescharacteristic, complemented
246Dic3⋊Dic3C2×D311yescharacteristic, complemented
247#3722—31no—
248#3722—31no—
249#3722—31no—
250#3722—31no—
251#3722—31no—
252#3722—31no—
253#3722—31no—
254#3722—61no—
255#3722—61no—
256#3722—61no—
257#3722C2×D311yescharacteristic, complemented
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)⋊Dic3—61no—
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)#4112yescomplemented
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×D3C2×D412yes—
296D3×C3⋊D3—44no—
297D3×C3⋊D3—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—
308C2×#237—31no—
309C2×D3×D4—91no—
310C2×D3×D4—91no—
311C2×D3×D4—91no—
312C2×#235—31no—
313C3×#121—91no—
314C3×#121—91no—
315#947—91no—
316#946—91no—
317#939—31no—
318#939—31no—
319#939—91no—
320#938—31no—
321#938—91no—
322#937—91no—
323#937—91no—
324#937—91no—
325#937—91no—
326#937—91no—
327#937—91no—
328#937—181no—
329#937—181no—
330#936—91no—
331#935—91no—
332D4×Dic3—91no—
333#930—31no—
334#929—91no—
335#929—91no—
336C4×#67—91no—
337C4×#67—91no—
338C4×#67—91no—
339C4×#67—181no—
340C2×(C2×D3)⋊C4—91no—
341C2×(C2×D3)⋊C4—91no—
342C2×(C2×D3)⋊C4—91no—
343#897—91no—
344#896—91no—
345#894—91no—
346#893—91no—
347#885—91no—
348#884—91no—
349#883—91no—
350#883—91no—
351#67⋊C4—91no—
352D3×C22⋊C4—91no—
353D3×C22⋊C4—91no—
354D3×C22⋊C4—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⋊D3—31no—
365C22×C3⋊D3—31no—
366C22×C3⋊D3—31no—
367C22×C3⋊D3—61no—
368C22×C3⋊D3—61no—
369C22×C3⋊D3—61no—
370C22×C3⋊D3—62no—
371C22×C3⋊D3—62no—
372C22×C3⋊D3—62no—
373C22×C3⋊D3—62no—
374C22×C3⋊D3—121no—
375C22×C3⋊D3—121no—
376C22×C3⋊D3—121no—
377C22×C3⋊D3C22×D311yescharacteristic
378C22×C3⋊D3C22×D311yescharacteristic
379C22×C3×D3—21no—
380C22×C3×D3—21no—
381C22×C3×D3—31no—
382C22×C3×D3—31no—
383C22×C3×D3—31no—
384C22×C3×D3—31no—
385C22×C3×D3—61no—
386C22×C3×D3—61no—
387C22×C3×D3C22×D311yescharacteristic
388C22×C3×D3C22×D311yescharacteristic
389C22×C3×D3C22×D311yescharacteristic
390C22×C3×D3C22×D311yescharacteristic
391C2×D32—62no—
392C2×D32—62no—
393C2×D32—62no—
394C2×D32—62no—
395C2×D32—62no—
396C2×D32—62no—
397C2×D32—62no—
398C2×D32—62no—
399C2×D32—122no—
400C2×D32—122no—
401C2×D32—122no—
402C2×D32—122no—
403C2×D32—121no—
404C2×D32—121no—
405C2×D32—121no—
406C2×D32—121no—
407C2×D32—122no—
408C2×D32—122no—
409C32×D4—62no—
410C32×D4—121no—
411C2×C32×C4—31no—
412C2×C32×C4—31no—
413C2×C32×C4—31no—
414C2×C32×C4—31no—
415C2×C32×C4—62no—
416#638—22no—
417#638—41no—
418#638—62no—
419#638—62no—
420#638—62no—
421#638—64no—
422#638—122no—
423#638—122no—
424#638—124no—
425C2×C3⋊Dic3—31no—
426C2×C3⋊Dic3—31no—
427C2×C3⋊Dic3—31no—
428C2×C3⋊Dic3—61no—
429C2×C3⋊Dic3—61no—
430C2×C3⋊Dic3—61no—
431C2×C3⋊Dic3—121no—
432C2×C3⋊Dic3C22×D311yescharacteristic
433C2×C3⋊Dic3C22×D311yescharacteristic
434C2×C3⋊Dic3C22×D311yescharacteristic
435C2×C3⋊Dic3C22×D311yescharacteristic
436C4×C3⋊D3—62no—
437C3×#67—22no—
438C3×#67—22no—
439C3×#67—34no—
440C3×#67—42no—
441C3×#67—41no—
442C3×#67—41no—
443C3×#67—42no—
444C3×#67—62no—
445C3×#67—62no—
446C3×#67—62no—
447C3×#67—62no—
448C3×#67—62no—
449C3×#67—122no—
450C3×#67—121no—
451C3×#67—121no—
452C3×#67—122no—
453C2×C3×Dic3—22no—
454C2×C3×Dic3—22no—
455C2×C3×Dic3—21no—
456C2×C3×Dic3—21no—
457C2×C3×Dic3—21no—
458C2×C3×Dic3—21no—
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—31no—
467C2×C3×Dic3—42no—
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×Dic3C22×D311yescharacteristic
475C2×C3×Dic3C22×D311yescharacteristic
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—34no—
483C3×D12—62no—
484C3×C4×D3—62no—
485C3×C4×D3—62no—
486C3×C4×D3—62no—
487C3×C4×D3—121no—
488C3×Dic6—62no—
489C3×Dic6—62no—
490#627—22no—
491#626—22no—
492#626—62no—
493#626—62no—
494#626#6714yescomplemented
495#625—22no—
496#625—62no—
497#624—22no—
498#624—62no—
499#624—62no—
500#624—122no—
501#624—121no—
502D3×Dic3—22no—
503D3×Dic3—41no—
504D3×Dic3—121no—
505D3×Dic3—121no—
506#546—271noSylow
507C2×C33—41no—
508C2×C33C22×D411yescharacteristic
509C2×C33C2×#4111yescharacteristic
510C2×C33H(5,𝔽2)11yescharacteristic
511C3⋊(C3⋊D3)—22no—
512C3×C3⋊D3—22no—
513C3×C3⋊D3—41no—
514C32×D3—22no—
515C32×D3—41no—
516C23×D3—91no—
517C23×D3—91no—
518C23×D3—91no—
519C23×D3—91no—
520C23×D3—91no—
521C23×D3—91no—
522C23×D3—181no—
523C23×D3—181no—
524C3×#41—184no—
525C2×C3×Q8—91no—
526C2×C3×D4—31no—
527C2×C3×D4—31no—
528C2×C3×D4—31no—
529C2×C3×D4—31no—
530C2×C3×D4—61no—
531C2×C3×D4—61no—
532C2×C3×D4—91no—
533C2×C3×D4—91no—
534C2×C3×D4—91no—
535C2×C3×D4—91no—
536C2×C3×D4—91no—
537C22×C3×C4—31no—
538C22×C3×C4—31no—
539C22×C3×C4—61no—
540C22×C3×C4—91no—
541C22×C3×C4—91no—
542C22×C3×C4—91no—
543C2×#67—31no—
544C2×#67—31no—
545C2×#67—31no—
546C2×#67—31no—
547C2×#67—31no—
548C2×#67—31no—
549C2×#67—31no—
550C2×#67—31no—
551C2×#67—61no—
552C2×#67—61no—
553C2×#67—91no—
554C2×#67—91no—
555C2×#67—91no—
556C2×#67—91no—
557C2×#67—91no—
558C2×#67—181no—
559C2×#67—181no—
560C2×#67—181no—
561C2×#67—361no—
562C2×#67D3211yescharacteristic, complemented
563C2×#67D3211yescharacteristic, complemented
564C22×Dic3—31no—
565C22×Dic3—31no—
566C22×Dic3—91no—
567C22×Dic3D3211yescharacteristic, complemented
568#237—64no—
569D3×D4—184no—
570D3×D4—184no—
571D3×D4—184no—
572#235—64no—
573C2×D12—31no—
574C2×D12—31no—
575C2×D12—91no—
576C2×C4×D3—31no—
577C2×C4×D3—31no—
578C2×C4×D3—31no—
579C2×C4×D3—31no—
580C2×C4×D3—91no—
581C2×C4×D3—91no—
582C2×C4×D3—91no—
583C2×C4×D3—91no—
584C2×C4×D3—91no—
585C2×C4×D3—181no—
586C2×Dic6—31no—
587C2×Dic6—31no—
588C3×C4⋊C4—91no—
589C3×C4⋊C4—91no—
590C3×C22⋊C4—91no—
591C3×C22⋊C4—91no—
592C3×C22⋊C4—91no—
593C3×C22⋊C4—91no—
594#217—31no—
595#217—31no—
596#217—31no—
597#217—31no—
598#217—61no—
599#217—91no—
600#217—91no—
601#217—91no—
602#217—91no—
603#217—91no—
604#217—91no—
605#217—91no—
606#217—181no—
607#217—181no—
608(C2×D3)⋊C4—31no—
609(C2×D3)⋊C4—31no—
610(C2×D3)⋊C4—31no—
611(C2×D3)⋊C4—31no—
612(C2×D3)⋊C4—91no—
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—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—181no—
630(C2×D3)⋊C4—181no—
631(C2×D3)⋊C4—181no—
632(C2×D3)⋊C4—181no—
633(C2×D3)⋊C4—181no—
634C4⋊Dic3—31no—
635C4⋊Dic3—31no—
636C4⋊Dic3—91no—
637Dic3⋊C4—31no—
638Dic3⋊C4—31no—
639Dic3⋊C4—91no—
640Dic3⋊C4—91no—
641Dic3⋊C4—91no—
642Dic3⋊C4—91no—
643Dic3⋊C4—91no—
644Dic3⋊C4—181no—
645C4×Dic3—91no—
646C4×Dic3—91no—
647C4×Dic3—91no—
648C4×Dic3—181no—
649C22×C32—21no—
650C22×C32—22no—
651C22×C32—21no—
652C22×C32—21no—
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—32no—
663C22×C32—41no—
664C22×C32—41no—
665C22×C32—41no—
666C22×C32—42no—
667C22×C32—41no—
668C22×C32—41no—
669C22×C32—41no—
670C22×C32—41no—
671C22×C32—41no—
672C22×C32—41no—
673C22×C32—61no—
674C22×C32—61no—
675C22×C32—61no—
676C22×C32—61no—
677C22×C32—61no—
678C22×C32—81no—
679C22×C32—81no—
680C22×C32C23×D311yescharacteristic
681C22×C32C23×D311yescharacteristic
682C22×C32C23×D311yescharacteristic
683C2×C3⋊D3—21no—
684C2×C3⋊D3—21no—
685C2×C3⋊D3—21no—
686C2×C3⋊D3—21no—
687C2×C3⋊D3—21no—
688C2×C3⋊D3—32no—
689C2×C3⋊D3—32no—
690C2×C3⋊D3—32no—
691C2×C3⋊D3—62no—
692C2×C3⋊D3—62no—
693C2×C3⋊D3—62no—
694C2×C3⋊D3—61no—
695C2×C3⋊D3—61no—
696C2×C3⋊D3—61no—
697C2×C3⋊D3—61no—
698C2×C3⋊D3—61no—
699C2×C3⋊D3—61no—
700C2×C3⋊D3—122no—
701C2×C3⋊D3—121no—
702C2×C3⋊D3—121no—
703C2×C3⋊D3—121no—
704C2×C3⋊D3—121no—
705C2×C3⋊D3—121no—
706C2×C3⋊D3—121no—
707C2×C3⋊D3—124no—
708C2×C3⋊D3—124no—
709C2×C3⋊D3—241no—
710C2×C3⋊D3—241no—
711C2×C3⋊D3C2×#6712yes—
712C2×C3×D3—21no—
713C2×C3×D3—21no—
714C2×C3×D3—21no—
715C2×C3×D3—21no—
716C2×C3×D3—22no—
717C2×C3×D3—21no—
718C2×C3×D3—21no—
719C2×C3×D3—21no—
720C2×C3×D3—21no—
721C2×C3×D3—21no—
722C2×C3×D3—21no—
723C2×C3×D3—22no—
724C2×C3×D3—32no—
725C2×C3×D3—32no—
726C2×C3×D3—41no—
727C2×C3×D3—41no—
728C2×C3×D3—41no—
729C2×C3×D3—41no—
730C2×C3×D3—62no—
731C2×C3×D3—61no—
732C2×C3×D3—61no—
733C2×C3×D3—61no—
734C2×C3×D3—61no—
735C2×C3×D3—62no—
736C2×C3×D3—61no—
737C2×C3×D3—61no—
738C2×C3×D3—61no—
739C2×C3×D3—61no—
740C2×C3×D3—61no—
741C2×C3×D3—61no—
742C2×C3×D3—121no—
743C2×C3×D3—121no—
744C2×C3×D3—121no—
745C2×C3×D3—121no—
746C2×C3×D3D3×D412yes—
747C2×C3×D3C2×#6712yes—
748D32—124no—
749D32—124no—
750D32—124no—
751D32—124no—
752D32—128no—
753D32—128no—
754C32×C4—32no—
755C32×C4—61no—
756C32×C4—61no—
757C32×C4—61no—
758C3⋊Dic3—21no—
759C3⋊Dic3—21no—
760C3⋊Dic3—21no—
761C3⋊Dic3—21no—
762C3⋊Dic3—61no—
763C3⋊Dic3—62no—
764C3⋊Dic3—61no—
765C3⋊Dic3—61no—
766C3⋊Dic3—121no—
767C3⋊Dic3—121no—
768C3⋊Dic3—122no—
769C3×Dic3—21no—
770C3×Dic3—21no—
771C3×Dic3—21no—
772C3×Dic3—21no—
773C3×Dic3—21no—
774C3×Dic3—21no—
775C3×Dic3—22no—
776C3×Dic3—41no—
777C3×Dic3—41no—
778C3×Dic3—41no—
779C3×Dic3—61no—
780C3×Dic3—61no—
781C3×Dic3—61no—
782C3×Dic3—61no—
783C3×Dic3—61no—
784C3×Dic3—61no—
785C3×Dic3—61no—
786C3×Dic3—61no—
787C3×Dic3—121no—
788C3×Dic3—121no—
789C3×Dic3—121no—
790C3×Dic3—121no—
791C3×Dic3D3×D412yes—
792C3×Dic3C2×#6712yes—
793C2×#41—91no—
794C22×D4—271no—
795#124—271no—
796#123—271no—
797#123—271no—
798C22⋊Q8—271no—
799#121—91no—
800#121—91no—
801#121—271no—
802#120—271no—
803#120—271no—
804C4×D4—271no—
805C4×D4—271no—
806C2×C22⋊C4—271no—
807C2×C22⋊C4—271no—
808C33#54611yescharacteristic, complemented, Sylow
809C23×C3—21no—
810C23×C3—21no—
811C23×C3—21no—
812C23×C3—31no—
813C23×C3—31no—
814C23×C3—31no—
815C23×C3—31no—
816C23×C3—41no—
817C23×C3—61no—
818C23×C3—61no—
819C23×C3—91no—
820C23×C3—91no—
821C23×C3C2×D3211yescharacteristic
822C23×C3C2×D3211yescharacteristic
823C23×C3C2×D3211yescharacteristic
824C22×D3—31no—
825C22×D3—31no—
826C22×D3—31no—
827C22×D3—31no—
828C22×D3—61no—
829C22×D3—61no—
830C22×D3—91no—
831C22×D3—91no—
832C22×D3—91no—
833C22×D3—181no—
834C22×D3—181no—
835C22×D3—181no—
836C22×D3—182no—
837C22×D3—182no—
838C22×D3—182no—
839C22×D3—182no—
840C22×D3—182no—
841C22×D3—182no—
842C22×D3—182no—
843C22×D3—182no—
844C22×D3—182no—
845C22×D3—182no—
846C22×D3—182no—
847C22×D3—182no—
848C22×D3—361no—
849C22×D3—362no—
850C22×D3—362no—
851C22×D3—362no—
852C22×D3—362no—
853C22×D3—361no—
854C22×D3—361no—
855C22×D3—361no—
856C22×D3—361no—
857C22×D3—361no—
858C22×D3—361no—
859C22×D3—362no—
860C22×D3—362no—
861C22×D3C2×D3211yescharacteristic
862C22×D3C2×D3211yescharacteristic
863C3×Q8—182no—
864C3×D4—62no—
865C3×D4—62no—
866C3×D4—94no—
867C3×D4—122no—
868C3×D4—121no—
869C3×D4—121no—
870C3×D4—122no—
871C3×D4—182no—
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—31no—
882C2×C3×C4—31no—
883C2×C3×C4—61no—
884C2×C3×C4—61no—
885C2×C3×C4—61no—
886C2×C3×C4—61no—
887C2×C3×C4—62no—
888C2×C3×C4—62no—
889C2×C3×C4—91no—
890C2×C3×C4—91no—
891C2×C3×C4—91no—
892C2×C3×C4—91no—
893C2×C3×C4—122no—
894C2×C3×C4—182no—
895C2×C3×C4—182no—
896C2×C3×C4—361no—
897#67—22no—
898#67—34no—
899#67—41no—
900#67—62no—
901#67—62no—
902#67—62no—
903#67—62no—
904#67—62no—
905#67—122no—
906#67—121no—
907#67—121no—
908#67—122no—
909#67—182no—
910#67—182no—
911#67—182no—
912#67—182no—
913#67—182no—
914#67—184no—
915#67—362no—
916#67—362no—
917#67—364no—
918C2×Dic3—22no—
919C2×Dic3—31no—
920C2×Dic3—31no—
921C2×Dic3—31no—
922C2×Dic3—31no—
923C2×Dic3—31no—
924C2×Dic3—31no—
925C2×Dic3—31no—
926C2×Dic3—31no—
927C2×Dic3—61no—
928C2×Dic3—61no—
929C2×Dic3—61no—
930C2×Dic3—61no—
931C2×Dic3—62no—
932C2×Dic3—91no—
933C2×Dic3—91no—
934C2×Dic3—91no—
935C2×Dic3—121no—
936C2×Dic3—181no—
937C2×Dic3—181no—
938C2×Dic3—181no—
939C2×Dic3—361no—
940C2×Dic3—361no—
941C2×Dic3C2×D3211yescharacteristic
942C2×Dic3C2×D3211yescharacteristic
943C2×Dic3C2×D3211yescharacteristic
944C2×Dic3C2×D3211yescharacteristic
945D12—34no—
946D12—62no—
947D12—182no—
948C4×D3—62no—
949C4×D3—62no—
950C4×D3—62no—
951C4×D3—121no—
952C4×D3—182no—
953C4×D3—182no—
954C4×D3—182no—
955C4×D3—362no—
956C4×D3—361no—
957C4×D3—361no—
958Dic6—62no—
959Dic6—62no—
960C2×C32—21no—
961C2×C32—21no—
962C2×C32—21no—
963C2×C32—21no—
964C2×C32—21no—
965C2×C32—21no—
966C2×C32—21no—
967C2×C32—21no—
968C2×C32—21no—
969C2×C32—41no—
970C2×C32—41no—
971C2×C32—41no—
972C2×C32—41no—
973C2×C32—42no—
974C2×C32—41no—
975C2×C32—41no—
976C2×C32—62no—
977C2×C32—81no—
978C2×C32—81no—
979C2×C32—82no—
980C2×C32—121no—
981C2×C32C2×D3×D411yescharacteristic
982C2×C32C2×D3×D411yescharacteristic
983C2×C32#100411yescharacteristic
984C2×C32#100411yescharacteristic
985C2×C32D3×#4111yescharacteristic
986C2×C32D3×#4111yescharacteristic
987C2×C32D3×#4111yescharacteristic
988C2×C32#100911yescharacteristic
989C2×C32C22×#6711yescharacteristic
990C3⋊D3—22no—
991C3⋊D3—41no—
992C3⋊D3—62no—
993C3⋊D3—62no—
994C3⋊D3—62no—
995C3⋊D3—122no—
996C3⋊D3—122no—
997C3⋊D3—122no—
998C3⋊D3—242no—
999C3×D3—22no—
1000C3×D3—22no—
1001C3×D3—42no—
1002C3×D3—42no—
1003C3×D3—41no—
1004C3×D3—41no—
1005C3×D3—62no—
1006C3×D3—62no—
1007C3×D3—122no—
1008C3×D3—122no—
1009C3×D3—121no—
1010C3×D3—121no—
1011C24—271no—
1012C24—271no—
1013#41—184no—
1014C2×Q8—91no—
1015C2×D4—31no—
1016C2×D4—31no—
1017C2×D4—91no—
1018C2×D4—91no—
1019C2×D4—91no—
1020C2×D4—91no—
1021C2×D4—91no—
1022C2×D4—271no—
1023C2×D4—271no—
1024C2×D4—544no—
1025C22×C4—31no—
1026C22×C4—91no—
1027C22×C4—91no—
1028C22×C4—91no—
1029C22×C4—271no—
1030C22×C4—271no—
1031C4⋊C4—91no—
1032C4⋊C4—91no—
1033C4⋊C4—271no—
1034C4⋊C4—271no—
1035C22⋊C4—91no—
1036C22⋊C4—91no—
1037C22⋊C4—91no—
1038C22⋊C4—91no—
1039C22⋊C4—271no—
1040C22⋊C4—271no—
1041C22⋊C4—271no—
1042C22⋊C4—271no—
1043C22⋊C4—271no—
1044C22⋊C4—271no—
1045C22⋊C4—271no—
1046C22⋊C4—271no—
1047C42—271no—
1048C22×C3—22no—
1049C22×C3—21no—
1050C22×C3—21no—
1051C22×C3—21no—
1052C22×C3—21no—
1053C22×C3—21no—
1054C22×C3—21no—
1055C22×C3—21no—
1056C22×C3—21no—
1057C22×C3—21no—
1058C22×C3—21no—
1059C22×C3—21no—
1060C22×C3—21no—
1061C22×C3—32no—
1062C22×C3—32no—
1063C22×C3—41no—
1064C22×C3—41no—
1065C22×C3—41no—
1066C22×C3—41no—
1067C22×C3—41no—
1068C22×C3—41no—
1069C22×C3—41no—
1070C22×C3—41no—
1071C22×C3—42no—
1072C22×C3—41no—
1073C22×C3—62no—
1074C22×C3—62no—
1075C22×C3—61no—
1076C22×C3—61no—
1077C22×C3—61no—
1078C22×C3—61no—
1079C22×C3—61no—
1080C22×C3—61no—
1081C22×C3—61no—
1082C22×C3—61no—
1083C22×C3—61no—
1084C22×C3—61no—
1085C22×C3—81no—
1086C22×C3—81no—
1087C22×C3—92no—
1088C22×C3—121no—
1089C22×C3—121no—
1090C22×C3—121no—
1091C22×C3—121no—
1092C22×C3—181no—
1093C22×C3—181no—
1094C22×C3—181no—
1095C22×C3—181no—
1096C22×C3—181no—
1097C22×C3C22×D3211yescharacteristic
1098C22×C3C22×D3211yescharacteristic
1099C22×C3C22×D3211yescharacteristic
1100C2×D3—21no—
1101C2×D3—21no—
1102C2×D3—21no—
1103C2×D3—21no—
1104C2×D3—21no—
1105C2×D3—32no—
1106C2×D3—32no—
1107C2×D3—62no—
1108C2×D3—61no—
1109C2×D3—61no—
1110C2×D3—61no—
1111C2×D3—61no—
1112C2×D3—62no—
1113C2×D3—61no—
1114C2×D3—61no—
1115C2×D3—61no—
1116C2×D3—61no—
1117C2×D3—61no—
1118C2×D3—61no—
1119C2×D3—92no—
1120C2×D3—92no—
1121C2×D3—92no—
1122C2×D3—121no—
1123C2×D3—121no—
1124C2×D3—121no—
1125C2×D3—121no—
1126C2×D3—182no—
1127C2×D3—182no—
1128C2×D3—182no—
1129C2×D3—181no—
1130C2×D3—181no—
1131C2×D3—181no—
1132C2×D3—181no—
1133C2×D3—181no—
1134C2×D3—181no—
1135C2×D3—362no—
1136C2×D3—361no—
1137C2×D3—361no—
1138C2×D3—361no—
1139C2×D3—361no—
1140C2×D3—361no—
1141C2×D3—361no—
1142C2×D3—364no—
1143C2×D3—364no—
1144C2×D3—364no—
1145C2×D3—364no—
1146C2×D3—364no—
1147C2×D3—364no—
1148C2×D3—368no—
1149C2×D3—368no—
1150C2×D3—721no—
1151C2×D3—721no—
1152C2×D3D3×#6712yes—
1153C3×C4—32no—
1154C3×C4—32no—
1155C3×C4—62no—
1156C3×C4—61no—
1157C3×C4—61no—
1158C3×C4—61no—
1159C3×C4—61no—
1160C3×C4—61no—
1161C3×C4—61no—
1162C3×C4—121no—
1163C3×C4—121no—
1164C3×C4—121no—
1165C3×C4—181no—
1166C3×C4—181no—
1167C3×C4—181no—
1168C3×C4—181no—
1169Dic3—21no—
1170Dic3—21no—
1171Dic3—21no—
1172Dic3—61no—
1173Dic3—61no—
1174Dic3—61no—
1175Dic3—61no—
1176Dic3—61no—
1177Dic3—61no—
1178Dic3—61no—
1179Dic3—61no—
1180Dic3—121no—
1181Dic3—121no—
1182Dic3—121no—
1183Dic3—121no—
1184Dic3—182no—
1185Dic3—181no—
1186Dic3—181no—
1187Dic3—181no—
1188Dic3—361no—
1189Dic3—361no—
1190Dic3—362no—
1191Dic3D3×#6712yes—
1192C32—21no—
1193C32—21no—
1194C32—21no—
1195C32—41no—
1196C32#561011yescharacteristic, complemented
1197C32#561211yescharacteristic, complemented
1198C32#582911yescharacteristic, complemented
1199C23—31no—
1200C23—31no—
1201C23—91no—
1202C23—91no—
1203C23—271no—
1204C23—542no—
1205C23—542no—
1206C23—542no—
1207C23—542no—
1208C23—1081no—
1209C23—1081no—
1210C23D3311yescharacteristic
1211Q8—182no—
1212D4—62no—
1213D4—94no—
1214D4—121no—
1215D4—182no—
1216D4—182no—
1217D4—182no—
1218D4—361no—
1219D4—542no—
1220D4—542no—
1221C2×C4—31no—
1222C2×C4—31no—
1223C2×C4—31no—
1224C2×C4—31no—
1225C2×C4—62no—
1226C2×C4—91no—
1227C2×C4—91no—
1228C2×C4—91no—
1229C2×C4—91no—
1230C2×C4—182no—
1231C2×C4—182no—
1232C2×C4—271no—
1233C2×C4—361no—
1234C2×C4—542no—
1235C2×C4—1081no—
1236C2×C3—21no—
1237C2×C3—21no—
1238C2×C3—21no—
1239C2×C3—21no—
1240C2×C3—21no—
1241C2×C3—21no—
1242C2×C3—21no—
1243C2×C3—21no—
1244C2×C3—21no—
1245C2×C3—42no—
1246C2×C3—41no—
1247C2×C3—41no—
1248C2×C3—41no—
1249C2×C3—41no—
1250C2×C3—41no—
1251C2×C3—41no—
1252C2×C3—62no—
1253C2×C3—62no—
1254C2×C3—81no—
1255C2×C3—81no—
1256C2×C3—82no—
1257C2×C3—122no—
1258C2×C3—122no—
1259C2×C3—121no—
1260C2×C3—121no—
1261C2×C3—182no—
1262C2×C3—361no—
1263C2×C3#6430611yescharacteristic
1264C2×C3#6430711yescharacteristic
1265C2×C3D32×D411yescharacteristic
1266C2×C3#6431211yescharacteristic
1267C2×C3#6431211yescharacteristic
1268C2×C3#6431411yescharacteristic
1269C2×C3C2×D3×#6711yescharacteristic
1270C2×C3C2×D3×#6711yescharacteristic
1271C2×C3#6433011yescharacteristic
1272D3—22no—
1273D3—41no—
1274D3—62no—
1275D3—62no—
1276D3—122no—
1277D3—122no—
1278D3—121no—
1279D3—121no—
1280D3—182no—
1281D3—182no—
1282D3—182no—
1283D3—362no—
1284D3—362no—
1285D3—362no—
1286D3—722no—
1287C22—21no—
1288C22—21no—
1289C22—21no—
1290C22—32no—
1291C22—61no—
1292C22—61no—
1293C22—61no—
1294C22—61no—
1295C22—61no—
1296C22—92no—
1297C22—181no—
1298C22—181no—
1299C22—181no—
1300C22—181no—
1301C22—181no—
1302C22—272no—
1303C22—541no—
1304C22—541no—
1305C22—1084no—
1306C22—1084no—
1307C22C2×D3311yescharacteristic
1308C4—32no—
1309C4—61no—
1310C4—61no—
1311C4—61no—
1312C4—181no—
1313C4—181no—
1314C4—181no—
1315C4—181no—
1316C4—541no—
1317C3—21no—
1318C3—21no—
1319C3—21no—
1320C3—41no—
1321C3#1059507011yescharacteristic, complemented
1322C3#1059529611yescharacteristic, complemented
1323C3#1059530511yescharacteristic, complemented
1324C2—41no—
1325C2—62no—
1326C2—121no—
1327C2—182no—
1328C2—361no—
1329C2—542no—
1330C2#1172441111yescharacteristic
1331C2#1172441811yescharacteristic
1332C2D32×#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×#88954C2semidirect
3. #11723725C2semidirect
4. #11723643C2semidirect
5. #11723643C2semidirect
6. #11723618C2semidirect
7. C3×#63978C2semidirect
8. C3×#63970C2semidirect
9. #11723001C2semidirect
10. #11722995C2semidirect
11. #11722985C2semidirect
12. #11722973C2semidirect
13. #11722927C2semidirect
14. #11722904C2semidirect
15. D3×#3722C2semidirect
22. C2×C3×#638C22semidirect
23. C2×C3×#638C22semidirect
24. C2×C32×#67C22semidirect
25. C2×C32×#67C22semidirect
26. C22×C32×Dic3C22semidirect
28. C2×#6294C22semidirect
30. C2×C3×#627C22semidirect
34. C2×C3×#624C22semidirect
36. C2×C3×D3×Dic3C22semidirect
37. C2×C3×D3×Dic3C22semidirect
39. C3×#3757C22semidirect
40. #88815C22semidirect
41. #88814C22semidirect
42. #88806C22semidirect
46. #88803C22semidirect
47. #88803C22semidirect
48. (C2×D3)⋊(C3⋊Dic3)C22semidirect
49. (C2×D3)⋊(C3⋊Dic3)C22semidirect
50. Dic3×C3⋊Dic3C22semidirect
51. C3×Dic3⋊Dic3C22semidirect
52. C3×Dic3⋊Dic3C22semidirect
53. C3×#3722C22semidirect
54. C3×(C2×D3)⋊Dic3C22semidirect
55. C3×(C2×D3)⋊Dic3C22semidirect
60. C2×#3804D3semidirect
75. #63978D3semidirect
80. #63970D3semidirect
136. C3×#626D4semidirect
162. C2×#638C2×D3semidirect
163. C2×#638C2×D3semidirect
177. C2×C3×#67C2×D3semidirect
178. C2×C3×#67C2×D3semidirect
179. C2×C3×#67C2×D3semidirect
180. C2×C3×#67C2×D3semidirect
184. C22×C3×Dic3C2×D3semidirect
185. C22×C3×Dic3C2×D3semidirect
198. C2×#627C2×D3semidirect
209. C2×#624C2×D3semidirect
213. C2×D3×Dic3C2×D3semidirect
214. C2×D3×Dic3C2×D3semidirect
218. #3757C2×D3semidirect
245. Dic3⋊Dic3C2×D3semidirect
246. Dic3⋊Dic3C2×D3semidirect
257. #3722C2×D3semidirect
272. (C2×D3)⋊Dic3C2×D3semidirect
273. (C2×D3)⋊Dic3C2×D3semidirect
283. C2×C3⋊(C3⋊D3)#41semidirect
494. #626#67semidirect
562. C2×#67D32semidirect
563. C2×#67D32semidirect
567. C22×Dic3D32semidirect
808. C33#546semidirect
1196. C32#5610semidirect
1197. C32#5612semidirect
1198. C32#5829semidirect
1321. C3#10595070semidirect
1322. C3#10595296semidirect
1323. C3#10595305semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#38042
C2×#889542
#117237252
#117236432
#117236182
C3×#639782
C3×#639702
#117230012
#117229952
#117229852
#117229732
#117229272
#117229042
D3×#37222
#105953053
#105952963
#105950703