Finite Group Databasebeta

← #13168751

Subgroups — #13168751

Order 1728.

1092 conjugacy classes of subgroups.

The subgroup lattice has 1040 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723679C211yesmaximal, characteristic, complemented
2#11723473C211yesmaximal, characteristic, complemented
3#11723428C211yesmaximal, characteristic, complemented
4#11723405C211yesmaximal, characteristic, complemented
5C3×#63899C211yesmaximal, characteristic, complemented
6C3×#63898C211yesmaximal, characteristic, complemented
7C3×#63885C211yesmaximal, characteristic
8#11723022C211yesmaximal, characteristic, complemented
9#11722989C211yesmaximal, characteristic, complemented
10#11722985C211yesmaximal, characteristic, complemented
11#11722985C211yesmaximal, characteristic, complemented
12#11722969C211yesmaximal, characteristic, complemented
13#11722969C211yesmaximal, characteristic, complemented
14Dic3×#625C211yesmaximal, characteristic, complemented
15D3×#3724C211yesmaximal, characteristic, complemented
16#10595216—31nomaximal
17#10594406—31nomaximal
18#10594114—31nomaximal
19C2×C32×D12C2211yescharacteristic
20C2×D3×C3⋊Dic3C2211yescharacteristic
21C2×C3×#627C2211yescharacteristic
22C2×C3×#625C2211yescharacteristic
23C2×C3×#625C2211yescharacteristic
24C2×C3×D3×Dic3C2211yescharacteristic
25C2×C3×D3×Dic3C2211yescharacteristic
26C2×C3×D3×Dic3C2211yescharacteristic
27C2×C3×D3×Dic3C2211yescharacteristic
28#88857C2211yescharacteristic
29C3×#3750C2211yescharacteristic
30C3×#3750C2211yescharacteristic
31C3×C4×C3⋊Dic3C2211yescharacteristic
32C32×(C2×D3)⋊C4C2211yescharacteristic
33C32×C4⋊Dic3C2211yescharacteristic
34#88815C2211yescharacteristic
35#88815C2211yescharacteristic
36#88815C2211yescharacteristic
37#88815C2211yescharacteristic
38#88806C2211yescharacteristic
39#88806C2211yescharacteristic
40#88806C2211yescharacteristic
41Dic3⋊(C3⋊Dic3)C2211yescharacteristic
42Dic3⋊(C3⋊Dic3)C2211yescharacteristic
43(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
44(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
45(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
46(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
47(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
48Dic3×C3⋊Dic3C2211yescharacteristic
49C3×#3724C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×(C2×D3)⋊Dic3C2211yescharacteristic
54#64144—31no—
55#64098—31no—
56#64088—31no—
57C3×#939—31no—
58C3×D4×Dic3—31no—
59C3×#896—31no—
60C3×#893—31no—
61C3×#884—31no—
62C3×#878—31no—
63Dic3×#67—31no—
64Dic3×#67—31no—
65#63969—31no—
66#63969—31no—
67#63969—31no—
68C2×#3724—31no—
69#63964—31no—
70#63964—31no—
71#63962—31no—
72#63961—31no—
73#63961—31no—
74#63956—31no—
75#63905—31no—
76#63905—31no—
77C4×#625—31no—
78#63899D311yescharacteristic, complemented
79#63898D311yescharacteristic, complemented
80#63891—31no—
81#63887—31no—
82#63887—31no—
83#63885D311yescharacteristic
84#63884—31no—
85#63884—31no—
86#63884—61no—
87D3×Dic3⋊C4—31no—
88D3×Dic3⋊C4—31no—
89#63870—31no—
90#63867—31no—
91#63867—31no—
92#63862—31no—
93#63861—31no—
94#63859—31no—
95#63859—31no—
96#63859—61no—
97#63856—31no—
98#63856—31no—
99#63847—31no—
100#63847—31no—
101#63847—61no—
102C22×C32×D3C2311yescharacteristic
103C22×C32×D3C2311yescharacteristic
104C22×C32×D3C2311yescharacteristic
105C2×C33×C4C2311yescharacteristic
106C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
107C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C32×D12—22no—
118D3×C3⋊Dic3—22no—
119C3×#627—41no—
120C3×#625—22no—
121C3×#625—41no—
122C3×D3×Dic3—41no—
123C3×D3×Dic3—41no—
124C3×D3×Dic3—41no—
125C3×D3×Dic3—41no—
126#5638—91no—
127#5602—91no—
128#5564—91no—
129C2×C32×D4—31no—
130C22×C3⋊Dic3—31no—
131C2×C3×#67—31no—
132C2×C3×#67—31no—
133C2×C3×#67—31no—
134C2×C3×#67—31no—
135C22×C3×Dic3—31no—
136C22×C3×Dic3—31no—
137C22×C3×Dic3—31no—
138C22×C3×Dic3—31no—
139C2×C3×D12—21no—
140C2×C3×D12C2×D311yescharacteristic
141C2×C3×D12C2×D311yescharacteristic
142C2×C3×C4×D3—31no—
143C2×C3×C4×D3—31no—
144C2×C3×C4×D3—31no—
145C2×C3×C4×D3—31no—
146C2×C3×Dic6—31no—
147C2×C3×Dic6—31no—
148C2×#627C2×D311yescharacteristic
149C2×#625C2×D311yescharacteristic
150C2×#625C2×D311yescharacteristic
151C2×D3×Dic3—31no—
152C2×D3×Dic3—31no—
153C2×D3×Dic3—61no—
154C2×D3×Dic3C2×D311yescharacteristic
155C2×D3×Dic3C2×D311yescharacteristic
156C2×D3×Dic3C2×D311yescharacteristic
157C2×D3×Dic3C2×D311yescharacteristic
158C32×C4⋊C4—31no—
159C32×C22⋊C4—31no—
160#3757—31no—
161#3757—31no—
162#3757—31no—
163#3757—31no—
164#3757—31no—
165C4⋊(C3⋊Dic3)—31no—
166C4⋊(C3⋊Dic3)—31no—
167#3750—31no—
168#3750—31no—
169#3750—31no—
170#3750—31no—
171#3750—31no—
172#3750—31no—
173#3750—61no—
174#3750—61no—
175#3750—61no—
176#3750—121no—
177#3750C2×D311yescharacteristic
178#3750C2×D311yescharacteristic
179C4×C3⋊Dic3—31no—
180C4×C3⋊Dic3C2×D311yescharacteristic
181C3×#217—31no—
182C3×#217—31no—
183C3×#217—31no—
184C3×#217—31no—
185C3×(C2×D3)⋊C4—21no—
186C3×(C2×D3)⋊C4—31no—
187C3×(C2×D3)⋊C4—31no—
188C3×(C2×D3)⋊C4—31no—
189C3×(C2×D3)⋊C4—31no—
190C3×(C2×D3)⋊C4C2×D311yescharacteristic
191C3×(C2×D3)⋊C4C2×D311yescharacteristic
192C3×C4⋊Dic3—21no—
193C3×C4⋊Dic3C2×D311yescharacteristic
194C3×C4⋊Dic3C2×D311yescharacteristic
195C3×Dic3⋊C4—31no—
196C3×Dic3⋊C4—31no—
197C3×Dic3⋊C4—31no—
198C3×Dic3⋊C4—31no—
199C3×Dic3⋊C4—31no—
200C3×Dic3⋊C4—31no—
201C3×Dic3⋊C4—61no—
202C3×Dic3⋊C4—61no—
203C3×C4×Dic3—31no—
204C3×C4×Dic3—31no—
205C3×C4×Dic3—61no—
206#3724—31no—
207#3724—31no—
208#3724—31no—
209#3724—31no—
210#3724—31no—
211#3724—31no—
212#3724—31no—
213#3724—31no—
214#3724—31no—
215#3724—31no—
216#3724—61no—
217#3724—61no—
218#3724—61no—
219#3724C2×D311yescharacteristic
220Dic3⋊Dic3—31no—
221Dic3⋊Dic3—31no—
222Dic3⋊Dic3—31no—
223Dic3⋊Dic3—31no—
224Dic3⋊Dic3—31no—
225Dic3⋊Dic3—31no—
226Dic3⋊Dic3—31no—
227Dic3⋊Dic3—31no—
228Dic3⋊Dic3—31no—
229Dic3⋊Dic3—31no—
230Dic3⋊Dic3—31no—
231Dic3⋊Dic3—31no—
232Dic3⋊Dic3—61no—
233Dic3⋊Dic3—61no—
234(C2×D3)⋊Dic3—31no—
235(C2×D3)⋊Dic3—31no—
236(C2×D3)⋊Dic3—31no—
237(C2×D3)⋊Dic3—31no—
238(C2×D3)⋊Dic3—31no—
239(C2×D3)⋊Dic3—31no—
240(C2×D3)⋊Dic3—31no—
241(C2×D3)⋊Dic3—31no—
242(C2×D3)⋊Dic3—31no—
243(C2×D3)⋊Dic3—31no—
244(C2×D3)⋊Dic3—61no—
245(C2×D3)⋊Dic3—61no—
246(C2×D3)⋊Dic3—61no—
247(C2×D3)⋊Dic3—61no—
248(C2×D3)⋊Dic3—61no—
249(C2×D3)⋊Dic3C2×D311yescharacteristic
250(C2×D3)⋊Dic3C2×D311yescharacteristic
251(C2×D3)⋊Dic3C2×D311yescharacteristic
252(C2×D3)⋊Dic3C2×D311yescharacteristic
253Dic32—31no—
254Dic32—31no—
255Dic32—61no—
256C22×C33C2411yescharacteristic
257C2×C32×D3—21no—
258C2×C32×D3—21no—
259C2×C32×D3—21no—
260C2×C32×D3—21no—
261C2×C32×D3—21no—
262C2×C32×D3—21no—
263C2×C32×D3—21no—
264C2×C32×D3—21no—
265C2×C32×D3#4112yes—
266C33×C4—21no—
267C3⋊(C3⋊Dic3)—21no—
268C3⋊(C3⋊Dic3)—21no—
269C3×C3⋊Dic3—21no—
270C3×C3⋊Dic3—21no—
271C3×C3⋊Dic3—21no—
272C3×C3⋊Dic3—21no—
273C3×C3⋊Dic3—21no—
274C3×C3⋊Dic3—21no—
275C32×Dic3—21no—
276C32×Dic3—21no—
277C32×Dic3—21no—
278C3×C22⋊Q8—91no—
279C3×#121—91no—
280C3×C4×D4—91no—
281#946—91no—
282#946—91no—
283#939—31no—
284#935—91no—
285#935—91no—
286#935—91no—
287#935—91no—
288#935—91no—
289#935—181no—
290D4×Dic3—31no—
291D4×Dic3—91no—
292#929—91no—
293#929—91no—
294C4×#67—91no—
295C4×#67—91no—
296#924—91no—
297#924—91no—
298C2×Dic3⋊C4—91no—
299C2×Dic3⋊C4—91no—
300#898—91no—
301#896—31no—
302#894—91no—
303#893—31no—
304D3×C4⋊C4—91no—
305#889—91no—
306#889—91no—
307#889—91no—
308#889—91no—
309#889—91no—
310#889—181no—
311#886—91no—
312#884—31no—
313#883—91no—
314#883—91no—
315#883—91no—
316#879—91no—
317#879—91no—
318#879—91no—
319#879—91no—
320#879—181no—
321#878—31no—
322#878—91no—
323#878—91no—
324#876—91no—
325#870—91no—
326C23×C32—31no—
327C23×C32—31no—
328C23×C32—31no—
329C22×C3×D3—21no—
330C22×C3×D3—21no—
331C22×C3×D3—21no—
332C22×C3×D3C22×D311yescharacteristic
333C22×C3×D3C22×D311yescharacteristic
334C22×C3×D3C22×D311yescharacteristic
335C22×C3×D3C22×D311yescharacteristic
336C22×C3×D3C22×D311yescharacteristic
337C22×C3×D3C22×D311yescharacteristic
338C32×D4—62no—
339C2×C32×C4—21no—
340C2×C32×C4—21no—
341C2×C32×C4—21no—
342C2×C32×C4—31no—
343C2×C32×C4—31no—
344C2×C32×C4—31no—
345C2×C32×C4—41no—
346C2×C32×C4C22×D311yescharacteristic
347C2×C32×C4C22×D311yescharacteristic
348C2×C32×C4C22×D311yescharacteristic
349C2×C3⋊Dic3—31no—
350C2×C3⋊Dic3—31no—
351C2×C3⋊Dic3—31no—
352C2×C3⋊Dic3—31no—
353C2×C3⋊Dic3—31no—
354C2×C3⋊Dic3—31no—
355C2×C3⋊Dic3—61no—
356C2×C3⋊Dic3—61no—
357C2×C3⋊Dic3—61no—
358C2×C3⋊Dic3—61no—
359C2×C3⋊Dic3—61no—
360C2×C3⋊Dic3—61no—
361C2×C3⋊Dic3—62no—
362C2×C3⋊Dic3—121no—
363C2×C3⋊Dic3—121no—
364C2×C3⋊Dic3C22×D311yescharacteristic
365C2×C3⋊Dic3C22×D311yescharacteristic
366C2×C3⋊Dic3C22×D311yescharacteristic
367C2×C3⋊Dic3C22×D311yescharacteristic
368C2×C3⋊Dic3C22×D311yescharacteristic
369C2×C3⋊Dic3C22×D311yescharacteristic
370C3×#67—62no—
371C3×#67—62no—
372C3×#67—121no—
373C3×#67—121no—
374C2×C3×Dic3—21no—
375C2×C3×Dic3—21no—
376C2×C3×Dic3—21no—
377C2×C3×Dic3—31no—
378C2×C3×Dic3—31no—
379C2×C3×Dic3—31no—
380C2×C3×Dic3—31no—
381C2×C3×Dic3—31no—
382C2×C3×Dic3—31no—
383C2×C3×Dic3—31no—
384C2×C3×Dic3—31no—
385C2×C3×Dic3—31no—
386C2×C3×Dic3—31no—
387C2×C3×Dic3—31no—
388C2×C3×Dic3—31no—
389C2×C3×Dic3—61no—
390C2×C3×Dic3—61no—
391C2×C3×Dic3—61no—
392C2×C3×Dic3—61no—
393C2×C3×Dic3—61no—
394C2×C3×Dic3—61no—
395C2×C3×Dic3—121no—
396C2×C3×Dic3—121no—
397C2×C3×Dic3—121no—
398C2×C3×Dic3—121no—
399C2×C3×Dic3C22×D311yescharacteristic
400C2×C3×Dic3C22×D311yescharacteristic
401C2×C3×Dic3C22×D311yescharacteristic
402C2×C3×Dic3C22×D311yescharacteristic
403C2×C3×Dic3C22×D311yescharacteristic
404C2×C3×Dic3C22×D311yescharacteristic
405C3×D12—22no—
406C3×D12—22no—
407C3×D12—42no—
408C3×C4×D3—121no—
409C3×C4×D3—121no—
410C3×C4×D3—121no—
411C3×C4×D3—121no—
412C3×Dic6—121no—
413C3×Dic6—121no—
414#627—41no—
415#625—22no—
416#625—41no—
417D3×Dic3—41no—
418D3×Dic3—41no—
419D3×Dic3—41no—
420D3×Dic3—41no—
421D3×Dic3—62no—
422D3×Dic3—62no—
423D3×Dic3—122no—
424#539—271noSylow
425C2×C33C2×#4111yescharacteristic
426C2×C33H(5,𝔽2)11yescharacteristic
427C2×C332−1+411yescharacteristic
428C32×D3—22no—
429C32×D3—41no—
430C32×D3—41no—
431C2×C3×Q8—91no—
432C2×C3×D4—31no—
433C2×C3×D4—31no—
434C2×C3×D4—61no—
435C2×C3×D4—91no—
436C2×C3×D4—91no—
437C22×C3×C4—91no—
438C22×C3×C4—91no—
439C22×C3×C4—91no—
440C22×C3×C4—91no—
441C2×#67—31no—
442C2×#67—31no—
443C2×#67—31no—
444C2×#67—31no—
445C22×Dic3—31no—
446C22×Dic3—31no—
447C22×Dic3—31no—
448C22×Dic3—31no—
449C22×Dic3—91no—
450C22×Dic3—91no—
451C22×Dic3—181no—
452C2×D12D3211yescharacteristic
453C2×C4×D3—31no—
454C2×C4×D3—31no—
455C2×C4×D3—31no—
456C2×C4×D3—31no—
457C2×C4×D3—91no—
458C2×Dic6—31no—
459C2×Dic6—31no—
460C3×C4⋊C4—31no—
461C3×C4⋊C4—31no—
462C3×C4⋊C4—61no—
463C3×C4⋊C4—91no—
464C3×C4⋊C4—91no—
465C3×C4⋊C4—91no—
466C3×C22⋊C4—31no—
467C3×C22⋊C4—31no—
468C3×C22⋊C4—61no—
469C3×C22⋊C4—91no—
470C3×C22⋊C4—91no—
471C3×C22⋊C4—91no—
472C3×C22⋊C4—91no—
473C3×C42—91no—
474#217—31no—
475#217—31no—
476#217—31no—
477#217—31no—
478#217—91no—
479#217—91no—
480#217—91no—
481#217—91no—
482#217—91no—
483#217—91no—
484#217—91no—
485#217—91no—
486#217—91no—
487#217—91no—
488#217—181no—
489#217—181no—
490#217—181no—
491#217—181no—
492#217—181no—
493(C2×D3)⋊C4—31no—
494(C2×D3)⋊C4—31no—
495(C2×D3)⋊C4—31no—
496(C2×D3)⋊C4—31no—
497(C2×D3)⋊C4—91no—
498(C2×D3)⋊C4—91no—
499(C2×D3)⋊C4—91no—
500(C2×D3)⋊C4—91no—
501(C2×D3)⋊C4—91no—
502(C2×D3)⋊C4D3211yescharacteristic
503C4⋊Dic3—91no—
504C4⋊Dic3—91no—
505C4⋊Dic3—91no—
506C4⋊Dic3—91no—
507C4⋊Dic3—91no—
508C4⋊Dic3—91no—
509C4⋊Dic3—91no—
510C4⋊Dic3—91no—
511C4⋊Dic3—181no—
512C4⋊Dic3—181no—
513C4⋊Dic3D3211yescharacteristic
514Dic3⋊C4—31no—
515Dic3⋊C4—31no—
516Dic3⋊C4—31no—
517Dic3⋊C4—31no—
518Dic3⋊C4—31no—
519Dic3⋊C4—31no—
520Dic3⋊C4—61no—
521Dic3⋊C4—61no—
522Dic3⋊C4—91no—
523Dic3⋊C4—91no—
524Dic3⋊C4—91no—
525Dic3⋊C4—91no—
526Dic3⋊C4—91no—
527Dic3⋊C4—91no—
528Dic3⋊C4—91no—
529Dic3⋊C4—91no—
530Dic3⋊C4—91no—
531Dic3⋊C4—91no—
532Dic3⋊C4—91no—
533Dic3⋊C4—91no—
534Dic3⋊C4—91no—
535Dic3⋊C4—91no—
536Dic3⋊C4—91no—
537Dic3⋊C4—91no—
538Dic3⋊C4—91no—
539Dic3⋊C4—91no—
540Dic3⋊C4—91no—
541Dic3⋊C4—91no—
542Dic3⋊C4—91no—
543Dic3⋊C4—91no—
544Dic3⋊C4—181no—
545Dic3⋊C4—181no—
546Dic3⋊C4—181no—
547Dic3⋊C4—181no—
548Dic3⋊C4—181no—
549Dic3⋊C4—181no—
550Dic3⋊C4—361no—
551C4×Dic3—31no—
552C4×Dic3—31no—
553C4×Dic3—61no—
554C4×Dic3—91no—
555C4×Dic3—91no—
556C4×Dic3—91no—
557C4×Dic3—181no—
558C22×C32—21no—
559C22×C32—21no—
560C22×C32—21no—
561C22×C32—32no—
562C22×C32—41no—
563C22×C32—61no—
564C22×C32—61no—
565C22×C32—61no—
566C22×C32—61no—
567C22×C32—61no—
568C22×C32—61no—
569C22×C32—61no—
570C22×C32—61no—
571C22×C32C23×D311yescharacteristic
572C22×C32C23×D311yescharacteristic
573C22×C32C23×D311yescharacteristic
574C2×C3×D3—21no—
575C2×C3×D3—21no—
576C2×C3×D3—21no—
577C2×C3×D3—21no—
578C2×C3×D3—21no—
579C2×C3×D3—21no—
580C2×C3×D3—21no—
581C2×C3×D3—21no—
582C2×C3×D3—21no—
583C2×C3×D3—21no—
584C2×C3×D3—21no—
585C2×C3×D3—21no—
586C2×C3×D3—21no—
587C2×C3×D3—21no—
588C2×C3×D3—21no—
589C2×C3×D3—21no—
590C2×C3×D3—22no—
591C2×C3×D3—41no—
592C2×C3×D3—41no—
593C2×C3×D3—41no—
594C2×C3×D3—41no—
595C2×C3×D3—41no—
596C2×C3×D3—41no—
597C2×C3×D3—41no—
598C2×C3×D3—41no—
599C2×C3×D3#23512yes—
600C2×C3×D3#23712yes—
601C32×C4—21no—
602C32×C4—21no—
603C32×C4—21no—
604C32×C4—41no—
605C32×C4—41no—
606C32×C4—41no—
607C32×C4—61no—
608C32×C4—61no—
609C32×C4—61no—
610C32×C4—81no—
611C3⋊Dic3—21no—
612C3⋊Dic3—21no—
613C3⋊Dic3—21no—
614C3⋊Dic3—21no—
615C3⋊Dic3—21no—
616C3⋊Dic3—21no—
617C3⋊Dic3—61no—
618C3⋊Dic3—62no—
619C3⋊Dic3—61no—
620C3⋊Dic3—61no—
621C3⋊Dic3—61no—
622C3⋊Dic3—61no—
623C3⋊Dic3—61no—
624C3⋊Dic3—121no—
625C3⋊Dic3—121no—
626C3⋊Dic3—122no—
627C3⋊Dic3—121no—
628C3⋊Dic3—121no—
629C3⋊Dic3—121no—
630C3⋊Dic3—241no—
631C3×Dic3—21no—
632C3×Dic3—21no—
633C3×Dic3—21no—
634C3×Dic3—21no—
635C3×Dic3—21no—
636C3×Dic3—21no—
637C3×Dic3—41no—
638C3×Dic3—41no—
639C3×Dic3—41no—
640C3×Dic3—61no—
641C3×Dic3—61no—
642C3×Dic3—61no—
643C3×Dic3—61no—
644C3×Dic3—61no—
645C3×Dic3—61no—
646C3×Dic3—61no—
647C3×Dic3—61no—
648C3×Dic3—61no—
649C3×Dic3—61no—
650C3×Dic3—61no—
651C3×Dic3—61no—
652C3×Dic3—121no—
653C3×Dic3—121no—
654C3×Dic3—121no—
655C3×Dic3—121no—
656C3×Dic3—121no—
657C3×Dic3—121no—
658#126—271no—
659#126—271no—
660#125—271no—
661#125—271no—
662#123—271no—
663#123—271no—
664#123—271no—
665#123—271no—
666C22⋊Q8—91no—
667C22⋊Q8—271no—
668C22⋊Q8—271no—
669#121—91no—
670C4×D4—91no—
671C4×D4—271no—
672C2×C4⋊C4—271no—
673C33#53911yescharacteristic, complemented, Sylow
674C23×C3—31no—
675C23×C3—31no—
676C23×C3—31no—
677C23×C3—31no—
678C23×C3—31no—
679C23×C3—31no—
680C23×C3—61no—
681C23×C3—61no—
682C23×C3—61no—
683C22×D3C2×D3211yescharacteristic
684C22×D3C2×D3211yescharacteristic
685C22×D3C2×D3211yescharacteristic
686C3×Q8—361no—
687C3×D4—62no—
688C3×D4—62no—
689C3×D4—122no—
690C3×D4—182no—
691C3×D4—361no—
692C2×C3×C4—21no—
693C2×C3×C4—21no—
694C2×C3×C4—21no—
695C2×C3×C4—31no—
696C2×C3×C4—31no—
697C2×C3×C4—31no—
698C2×C3×C4—31no—
699C2×C3×C4—31no—
700C2×C3×C4—31no—
701C2×C3×C4—41no—
702C2×C3×C4—61no—
703C2×C3×C4—61no—
704C2×C3×C4—61no—
705C2×C3×C4—91no—
706C2×C3×C4—91no—
707C2×C3×C4—91no—
708C2×C3×C4—91no—
709C2×C3×C4—91no—
710C2×C3×C4—91no—
711C2×C3×C4—361no—
712C2×C3×C4—361no—
713C2×C3×C4—361no—
714C2×C3×C4—361no—
715C2×C3×C4C2×D3211yescharacteristic
716C2×C3×C4C2×D3211yescharacteristic
717C2×C3×C4C2×D3211yescharacteristic
718#67—62no—
719#67—62no—
720#67—121no—
721#67—121no—
722C2×Dic3—31no—
723C2×Dic3—31no—
724C2×Dic3—31no—
725C2×Dic3—31no—
726C2×Dic3—31no—
727C2×Dic3—31no—
728C2×Dic3—31no—
729C2×Dic3—31no—
730C2×Dic3—31no—
731C2×Dic3—31no—
732C2×Dic3—31no—
733C2×Dic3—31no—
734C2×Dic3—61no—
735C2×Dic3—61no—
736C2×Dic3—61no—
737C2×Dic3—61no—
738C2×Dic3—61no—
739C2×Dic3—61no—
740C2×Dic3—91no—
741C2×Dic3—91no—
742C2×Dic3—91no—
743C2×Dic3—91no—
744C2×Dic3—91no—
745C2×Dic3—91no—
746C2×Dic3—121no—
747C2×Dic3—121no—
748C2×Dic3—121no—
749C2×Dic3—121no—
750C2×Dic3—181no—
751C2×Dic3—181no—
752C2×Dic3—181no—
753C2×Dic3—181no—
754C2×Dic3—181no—
755C2×Dic3—181no—
756C2×Dic3—182no—
757C2×Dic3—182no—
758C2×Dic3—361no—
759C2×Dic3—361no—
760C2×Dic3—362no—
761C2×Dic3C2×D3211yescharacteristic
762C2×Dic3C2×D3211yescharacteristic
763C2×Dic3C2×D3211yescharacteristic
764D12—22no—
765C4×D3—121no—
766C4×D3—121no—
767C4×D3—121no—
768C4×D3—121no—
769C4×D3—182no—
770Dic6—121no—
771Dic6—121no—
772C2×C32—21no—
773C2×C32—21no—
774C2×C32—21no—
775C2×C32—21no—
776C2×C32—21no—
777C2×C32—21no—
778C2×C32—21no—
779C2×C32—21no—
780C2×C32—21no—
781C2×C32—41no—
782C2×C32—41no—
783C2×C32—41no—
784C2×C32—62no—
785C2×C32—121no—
786C2×C32—121no—
787C2×C32C2×#23511yescharacteristic
788C2×C32C2×#23711yescharacteristic
789C2×C32#100411yescharacteristic
790C2×C32#100411yescharacteristic
791C2×C32#100411yescharacteristic
792C2×C32#100711yescharacteristic
793C2×C32D3×#4111yescharacteristic
794C2×C32#101011yescharacteristic
795C2×C32#101011yescharacteristic
796C3×D3—22no—
797C3×D3—22no—
798C3×D3—42no—
799C3×D3—41no—
800C3×D3—41no—
801C3×D3—41no—
802C3×D3—41no—
803C3×D3—81no—
804C3×D3—81no—
805C2×Q8—91no—
806C2×D4—31no—
807C2×D4—91no—
808C2×D4—91no—
809C22×C4—91no—
810C22×C4—91no—
811C22×C4—91no—
812C22×C4—91no—
813C22×C4—271no—
814C4⋊C4—31no—
815C4⋊C4—91no—
816C4⋊C4—91no—
817C4⋊C4—91no—
818C4⋊C4—271no—
819C4⋊C4—271no—
820C4⋊C4—271no—
821C4⋊C4—271no—
822C4⋊C4—271no—
823C4⋊C4—271no—
824C4⋊C4—271no—
825C4⋊C4—271no—
826C4⋊C4—271no—
827C4⋊C4—271no—
828C22⋊C4—31no—
829C22⋊C4—91no—
830C22⋊C4—91no—
831C22⋊C4—91no—
832C22⋊C4—91no—
833C22⋊C4—271no—
834C22⋊C4—271no—
835C22⋊C4—271no—
836C22⋊C4—271no—
837C22⋊C4—271no—
838C42—91no—
839C42—271no—
840C22×C3—21no—
841C22×C3—21no—
842C22×C3—21no—
843C22×C3—32no—
844C22×C3—32no—
845C22×C3—41no—
846C22×C3—62no—
847C22×C3—61no—
848C22×C3—61no—
849C22×C3—61no—
850C22×C3—61no—
851C22×C3—61no—
852C22×C3—61no—
853C22×C3—61no—
854C22×C3—61no—
855C22×C3—61no—
856C22×C3—61no—
857C22×C3—61no—
858C22×C3—61no—
859C22×C3—61no—
860C22×C3—61no—
861C22×C3—61no—
862C22×C3—61no—
863C22×C3—121no—
864C22×C3—121no—
865C22×C3—121no—
866C22×C3—121no—
867C22×C3—121no—
868C22×C3—121no—
869C22×C3—121no—
870C22×C3—121no—
871C22×C3C22×D3211yescharacteristic
872C22×C3C22×D3211yescharacteristic
873C22×C3C22×D3211yescharacteristic
874C2×D3—21no—
875C2×D3—21no—
876C2×D3—21no—
877C2×D3—21no—
878C2×D3—21no—
879C2×D3—21no—
880C2×D3—21no—
881C2×D3—21no—
882C2×D3#380412yes—
883C3×C4—21no—
884C3×C4—21no—
885C3×C4—21no—
886C3×C4—41no—
887C3×C4—41no—
888C3×C4—41no—
889C3×C4—61no—
890C3×C4—61no—
891C3×C4—61no—
892C3×C4—61no—
893C3×C4—61no—
894C3×C4—61no—
895C3×C4—81no—
896C3×C4—121no—
897C3×C4—121no—
898C3×C4—121no—
899C3×C4—181no—
900C3×C4—181no—
901C3×C4—181no—
902C3×C4—181no—
903C3×C4—181no—
904C3×C4—181no—
905Dic3—21no—
906Dic3—21no—
907Dic3—21no—
908Dic3—61no—
909Dic3—61no—
910Dic3—61no—
911Dic3—61no—
912Dic3—61no—
913Dic3—61no—
914Dic3—61no—
915Dic3—61no—
916Dic3—61no—
917Dic3—61no—
918Dic3—61no—
919Dic3—61no—
920Dic3—121no—
921Dic3—121no—
922Dic3—121no—
923Dic3—121no—
924Dic3—121no—
925Dic3—121no—
926Dic3—182no—
927Dic3—181no—
928Dic3—181no—
929Dic3—181no—
930Dic3—181no—
931Dic3—181no—
932Dic3—181no—
933Dic3—361no—
934Dic3—361no—
935Dic3—361no—
936Dic3—361no—
937Dic3—361no—
938Dic3—362no—
939Dic3—721no—
940C32—21no—
941C32—21no—
942C32—21no—
943C32—41no—
944C32#556411yescharacteristic, complemented
945C32#560211yescharacteristic, complemented
946C32#563811yescharacteristic, complemented
947C23—31no—
948C23—31no—
949C23—31no—
950Q8—361no—
951D4—62no—
952D4—182no—
953D4—361no—
954C2×C4—31no—
955C2×C4—31no—
956C2×C4—31no—
957C2×C4—91no—
958C2×C4—91no—
959C2×C4—91no—
960C2×C4—91no—
961C2×C4—91no—
962C2×C4—91no—
963C2×C4—271no—
964C2×C4—271no—
965C2×C4—361no—
966C2×C4—361no—
967C2×C4—361no—
968C2×C4—361no—
969C2×C4—542no—
970C2×C4D3311yescharacteristic
971C2×C3—21no—
972C2×C3—21no—
973C2×C3—21no—
974C2×C3—21no—
975C2×C3—21no—
976C2×C3—21no—
977C2×C3—21no—
978C2×C3—21no—
979C2×C3—21no—
980C2×C3—41no—
981C2×C3—41no—
982C2×C3—41no—
983C2×C3—62no—
984C2×C3—62no—
985C2×C3—122no—
986C2×C3—121no—
987C2×C3—121no—
988C2×C3—121no—
989C2×C3—121no—
990C2×C3—241no—
991C2×C3—241no—
992C2×C3#6429711yescharacteristic
993C2×C3D3×#23511yescharacteristic
994C2×C3#6430911yescharacteristic
995C2×C3D3×#23711yescharacteristic
996C2×C3#6431311yescharacteristic
997C2×C3#6431311yescharacteristic
998C2×C3#6431311yescharacteristic
999C2×C3#6431511yescharacteristic
1000C2×C3C2×#380411yescharacteristic
1001D3—22no—
1002D3—41no—
1003D3—41no—
1004C22—32no—
1005C22—61no—
1006C22—61no—
1007C22—61no—
1008C22—61no—
1009C22—61no—
1010C22—61no—
1011C22—61no—
1012C22—61no—
1013C22C2×D3311yescharacteristic
1014C4—21no—
1015C4—61no—
1016C4—61no—
1017C4—61no—
1018C4—181no—
1019C4—181no—
1020C4—181no—
1021C4—181no—
1022C4—181no—
1023C4—181no—
1024C4—541no—
1025C4—541no—
1026C3—21no—
1027C3—21no—
1028C3—21no—
1029C3—41no—
1030C3#1059411411yescharacteristic, complemented
1031C3#1059440611yescharacteristic, complemented
1032C3#1059521611yescharacteristic, complemented
1033C2—62no—
1034C2—121no—
1035C2—121no—
1036C2#1172438211yescharacteristic
1037C2#1172439311yescharacteristic
1038C2D3×#380411yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC3×#63885C2
hypercenterC2×C4D33
hypocenterC33#539
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. #11723679C2semidirect
2. #11723473C2semidirect
3. #11723428C2semidirect
4. #11723405C2semidirect
5. C3×#63899C2semidirect
6. C3×#63898C2semidirect
8. #11723022C2semidirect
9. #11722989C2semidirect
10. #11722985C2semidirect
11. #11722985C2semidirect
12. #11722969C2semidirect
13. #11722969C2semidirect
14. Dic3×#625C2semidirect
15. D3×#3724C2semidirect
78. #63899D3semidirect
79. #63898D3semidirect
673. C33#539semidirect
944. C32#5564semidirect
945. C32#5602semidirect
946. C32#5638semidirect
1030. C3#10594114semidirect
1031. C3#10594406semidirect
1032. C3#10595216semidirect

Maximal subgroups

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

subgroupindex
#117236792
#117234732
#117234282
#117234052
C3×#638992
C3×#638982
C3×#638852
#117230222
#117229892
#117229852
#117229692
Dic3×#6252
D3×#37242
#105952163
#105944063
#105941143