Finite Group Databasebeta

← #13169152

Subgroups — #13169152

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#11723687C211yesmaximal, characteristic
2#11723488C211yesmaximal, characteristic, complemented
3#11723438C211yesmaximal, characteristic, complemented
4#11723405C211yesmaximal, characteristic, complemented
5C3×#63895C211yesmaximal, characteristic, complemented
6C3×#63894C211yesmaximal, characteristic, complemented
7C3×#63867C211yesmaximal, characteristic, complemented
8#11723025C211yesmaximal, characteristic, complemented
9#11722997C211yesmaximal, characteristic, complemented
10#11722995C211yesmaximal, characteristic, complemented
11#11722995C211yesmaximal, characteristic, complemented
12#11722979C211yesmaximal, characteristic, complemented
13#11722970C211yesmaximal, characteristic, complemented
14#11722931C211yesmaximal, characteristic, complemented
15#11722911C211yesmaximal, characteristic, complemented
16#10594406—31nomaximal
17#10594338—31nomaximal
18#10593913—31nomaximal
19C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
20C2×#6295C2211yescharacteristic
21C2×#6295C2211yescharacteristic
22C2×#6294C2211yescharacteristic
23C2×Dic3×C3⋊D3C2211yescharacteristic
24C2×C3×#627C2211yescharacteristic
25C2×C3×#624C2211yescharacteristic
26C2×C3×#624C2211yescharacteristic
27C2×C3×#624C2211yescharacteristic
28#88857C2211yescharacteristic
29C3×#3752C2211yescharacteristic
30C3×#3750C2211yescharacteristic
31C32×C4⋊Dic3C2211yescharacteristic
32C32×Dic3⋊C4C2211yescharacteristic
33C32×C4×Dic3C2211yescharacteristic
34#88814C2211yescharacteristic
35#88807C2211yescharacteristic
36#88806C2211yescharacteristic
37#88806C2211yescharacteristic
38#88806C2211yescharacteristic
39Dic3⋊(C3⋊Dic3)C2211yescharacteristic
40#88803C2211yescharacteristic
41#88803C2211yescharacteristic
42#88803C2211yescharacteristic
43#88803C2211yescharacteristic
44#88803C2211yescharacteristic
45Dic3×C3⋊Dic3C2211yescharacteristic
46C3×#3724C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×Dic3⋊Dic3C2211yescharacteristic
50C3×Dic3⋊Dic3C2211yescharacteristic
51C3×#3722C2211yescharacteristic
52C3×#3722C2211yescharacteristic
53C3×#3722C2211yescharacteristic
54#64103—31no—
55#64098—31no—
56#64085—31no—
57C3×#897—31no—
58C3×#896—31no—
59C3×#893—31no—
60C3×#889—31no—
61C3×C4×D12—31no—
62C3×#870—31no—
63#63910—31no—
64#63905—31no—
65#63905—31no—
66#63904—31no—
67#63904—31no—
68C4×#625—31no—
69#63900—31no—
70#63899—31no—
71#63895D311yescharacteristic, complemented
72#63894D311yescharacteristic, complemented
73#63891—31no—
74#63890—31no—
75#63888—31no—
76#63888—31no—
77#63887—31no—
78#63886—31no—
79#63885—31no—
80#63884—31no—
81#63884—31no—
82#63884—61no—
83D3×Dic3⋊C4—31no—
84D3×Dic3⋊C4—31no—
85#63867D311yescharacteristic, complemented
86#63862—31no—
87#63859—31no—
88#63859—31no—
89#63859—61no—
90#63858—31no—
91#63856—31no—
92#63854—31no—
93#63854—31no—
94#63853—31no—
95#63851—31no—
96#63850—31no—
97#63850—31no—
98#63848—31no—
99#63847—31no—
100#63847—31no—
101#63847—61no—
102C22×C3×C3⋊D3C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C3×C3⋊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
111C3×C4⋊(C3⋊D3)—22no—
112C2×C32×Dic3C2311yescharacteristic
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118#6295—22no—
119#6295—41no—
120#6294—41no—
121Dic3×C3⋊D3—22no—
122C3×#627—41no—
123C3×#624—41no—
124C3×#624—41no—
125C3×#624—41no—
126#5692—91no—
127#5638—91no—
128#5564—91no—
129C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
130C2×C4×C3⋊D3—31no—
131C2×C3×D12—31no—
132C2×C3×D12—31no—
133C2×C3×D12—61no—
134C2×C3×C4×D3—31no—
135C2×C3×C4×D3—31no—
136C2×C3×C4×D3—31no—
137C2×C3×C4×D3—31no—
138C2×C3×C4×D3—31no—
139C2×C3×C4×D3—31no—
140C2×C3×Dic6—31no—
141C2×C3×Dic6—31no—
142C2×#627C2×D311yescharacteristic
143C2×#626—31no—
144C2×#626—31no—
145C2×#626—31no—
146C2×#626—31no—
147C2×#625—31no—
148C2×#625—31no—
149C2×#624—31no—
150C2×#624C2×D311yescharacteristic
151C2×#624C2×D311yescharacteristic
152C2×#624C2×D311yescharacteristic
153C2×D3×Dic3—31no—
154C2×D3×Dic3—31no—
155C2×D3×Dic3—31no—
156C2×D3×Dic3—31no—
157C2×D3×Dic3—61no—
158C32×C4⋊C4—31no—
159C32×C4⋊C4—31no—
160C32×C42—31no—
161#3752—31no—
162#3752—31no—
163#3752—31no—
164#3752—31no—
165#3752—31no—
166#3752C2×D311yescharacteristic
167C4⋊(C3⋊Dic3)—31no—
168#3750—31no—
169#3750—31no—
170#3750—31no—
171#3750—31no—
172#3750—31no—
173#3750—31no—
174#3750—31no—
175#3750—61no—
176#3750—61no—
177#3750—61no—
178#3750—121no—
179#3750C2×D311yescharacteristic
180C4×C3⋊Dic3—31no—
181C3×(C2×D3)⋊C4—31no—
182C3×(C2×D3)⋊C4—31no—
183C3×(C2×D3)⋊C4—31no—
184C3×(C2×D3)⋊C4—31no—
185C3×(C2×D3)⋊C4—31no—
186C3×(C2×D3)⋊C4—31no—
187C3×(C2×D3)⋊C4—31no—
188C3×(C2×D3)⋊C4—31no—
189C3×(C2×D3)⋊C4—61no—
190C3×C4⋊Dic3—21no—
191C3×C4⋊Dic3—31no—
192C3×C4⋊Dic3—31no—
193C3×C4⋊Dic3—31no—
194C3×C4⋊Dic3—31no—
195C3×C4⋊Dic3C2×D311yescharacteristic
196C3×C4⋊Dic3C2×D311yescharacteristic
197C3×Dic3⋊C4—21no—
198C3×Dic3⋊C4—31no—
199C3×Dic3⋊C4—31no—
200C3×Dic3⋊C4—31no—
201C3×Dic3⋊C4—31no—
202C3×Dic3⋊C4—31no—
203C3×Dic3⋊C4—31no—
204C3×Dic3⋊C4—31no—
205C3×Dic3⋊C4—31no—
206C3×Dic3⋊C4—61no—
207C3×Dic3⋊C4C2×D311yescharacteristic
208C3×Dic3⋊C4C2×D311yescharacteristic
209C3×C4×Dic3—21no—
210C3×C4×Dic3C2×D311yescharacteristic
211C3×C4×Dic3C2×D311yescharacteristic
212#3724—31no—
213#3724—31no—
214#3724—31no—
215#3724—31no—
216#3724—31no—
217#3724—31no—
218#3724—61no—
219#3724—61no—
220#3724—61no—
221#3724C2×D311yescharacteristic
222Dic3⋊Dic3—31no—
223Dic3⋊Dic3—31no—
224Dic3⋊Dic3—31no—
225Dic3⋊Dic3—31no—
226Dic3⋊Dic3—61no—
227Dic3⋊Dic3—61no—
228Dic3⋊Dic3C2×D311yescharacteristic
229Dic3⋊Dic3C2×D311yescharacteristic
230Dic3⋊Dic3C2×D311yescharacteristic
231Dic3⋊Dic3C2×D311yescharacteristic
232#3722—31no—
233#3722C2×D311yescharacteristic
234#3722C2×D311yescharacteristic
235#3722C2×D311yescharacteristic
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—31no—
245(C2×D3)⋊Dic3—31no—
246(C2×D3)⋊Dic3—31no—
247(C2×D3)⋊Dic3—31no—
248(C2×D3)⋊Dic3—61no—
249(C2×D3)⋊Dic3—61no—
250(C2×D3)⋊Dic3—61no—
251(C2×D3)⋊Dic3—61no—
252(C2×D3)⋊Dic3—61no—
253Dic32—31no—
254Dic32—31no—
255Dic32—61no—
256C22×C33C2411yescharacteristic
257C2×C3×C3⋊D3—21no—
258C2×C3×C3⋊D3—21no—
259C2×C3×C3⋊D3—21no—
260C2×C3×C3⋊D3—21no—
261C2×C3×C3⋊D3—21no—
262C2×C3×C3⋊D3—21no—
263C2×C3×C3⋊D3—21no—
264C2×C3×C3⋊D3—21no—
265C2×C3×C3⋊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—
272C32×Dic3—21no—
273C32×Dic3—21no—
274C32×Dic3—21no—
275C32×Dic3—21no—
276C32×Dic3—21no—
277C32×Dic3—21no—
278C3×#125—91no—
279C3×C22⋊Q8—91no—
280C3×C4×D4—91no—
281#946—91no—
282#946—91no—
283#939—91no—
284#935—91no—
285#929—91no—
286#929—91no—
287C4×#67—91no—
288C4×#67—91no—
289#924—91no—
290C2×Dic3⋊C4—91no—
291#898—91no—
292#898—91no—
293#897—31no—
294#896—31no—
295#896—91no—
296#896—91no—
297#895—91no—
298#894—91no—
299#894—91no—
300#894—91no—
301#894—91no—
302#894—91no—
303#894—181no—
304#893—31no—
305#893—91no—
306D3×C4⋊C4—91no—
307D3×C4⋊C4—91no—
308#889—31no—
309#889—91no—
310#889—91no—
311#889—91no—
312#889—181no—
313#886—91no—
314#884—91no—
315#883—91no—
316#883—91no—
317#883—91no—
318#879—91no—
319#879—91no—
320#878—91no—
321#876—91no—
322#876—91no—
323#876—181no—
324C4×D12—31no—
325#870—31no—
326C22×C3⋊D3C22×D311yescharacteristic
327C22×C3⋊D3C22×D311yescharacteristic
328C22×C3⋊D3C22×D311yescharacteristic
329C22×C3×D3—31no—
330C22×C3×D3—31no—
331C22×C3×D3—31no—
332C22×C3×D3—31no—
333C22×C3×D3—31no—
334C22×C3×D3—31no—
335C22×C3×D3—61no—
336C22×C3×D3—61no—
337C22×C3×D3—61no—
338C2×C32×C4—21no—
339C2×C32×C4—21no—
340C2×C32×C4—21no—
341C2×C32×C4—31no—
342C2×C32×C4—31no—
343C2×C32×C4—31no—
344C2×C32×C4—31no—
345C2×C32×C4—31no—
346C2×C32×C4—31no—
347C2×C32×C4—41no—
348C2×C32×C4C22×D311yescharacteristic
349C2×C32×C4C22×D311yescharacteristic
350C2×C32×C4C22×D311yescharacteristic
351C2×C3⋊Dic3—31no—
352C2×C3⋊Dic3—31no—
353C2×C3⋊Dic3—31no—
354C2×C3⋊Dic3—31no—
355C2×C3⋊Dic3—31no—
356C2×C3⋊Dic3—31no—
357C2×C3⋊Dic3—61no—
358C2×C3⋊Dic3—61no—
359C2×C3⋊Dic3—61no—
360C2×C3⋊Dic3—61no—
361C2×C3⋊Dic3—61no—
362C2×C3⋊Dic3—61no—
363C2×C3⋊Dic3—121no—
364C2×C3⋊Dic3—121no—
365C2×C3⋊Dic3C22×D311yescharacteristic
366C2×C3⋊Dic3C22×D311yescharacteristic
367C2×C3⋊Dic3C22×D311yescharacteristic
368C4⋊(C3⋊D3)—22no—
369C4×C3⋊D3—62no—
370C2×C3×Dic3—21no—
371C2×C3×Dic3—21no—
372C2×C3×Dic3—21no—
373C2×C3×Dic3—21no—
374C2×C3×Dic3—21no—
375C2×C3×Dic3—21no—
376C2×C3×Dic3—31no—
377C2×C3×Dic3—31no—
378C2×C3×Dic3—31no—
379C2×C3×Dic3—31no—
380C2×C3×Dic3—31no—
381C2×C3×Dic3—31no—
382C2×C3×Dic3—61no—
383C2×C3×Dic3—61no—
384C2×C3×Dic3—61no—
385C2×C3×Dic3C22×D311yescharacteristic
386C2×C3×Dic3C22×D311yescharacteristic
387C2×C3×Dic3C22×D311yescharacteristic
388C2×C3×Dic3C22×D311yescharacteristic
389C2×C3×Dic3C22×D311yescharacteristic
390C2×C3×Dic3C22×D311yescharacteristic
391C2×C3×Dic3C22×D311yescharacteristic
392C2×C3×Dic3C22×D311yescharacteristic
393C2×C3×Dic3C22×D311yescharacteristic
394C2×C3×Dic3C22×D311yescharacteristic
395C2×C3×Dic3C22×D311yescharacteristic
396C2×C3×Dic3C22×D311yescharacteristic
397C3×D12—62no—
398C3×D12—62no—
399C3×D12—122no—
400C3×C4×D3—121no—
401C3×C4×D3—121no—
402C3×C4×D3—121no—
403C3×C4×D3—121no—
404C3×C4×D3—121no—
405C3×C4×D3—121no—
406C3×Dic6—121no—
407C3×Dic6—121no—
408#627—41no—
409#626—62no—
410#626—62no—
411#626—121no—
412#626—121no—
413#625—62no—
414#625—121no—
415#624—41no—
416#624—41no—
417#624—41no—
418#624—121no—
419D3×Dic3—62no—
420D3×Dic3—62no—
421D3×Dic3—122no—
422D3×Dic3—121no—
423D3×Dic3—121no—
424#539—271noSylow
425C2×C33C2×#4111yescharacteristic
426C2×C33H(5,𝔽2)11yescharacteristic
427C2×C332−1+411yescharacteristic
428C3×C3⋊D3—22no—
429C3×C3⋊D3—41no—
430C3×C3⋊D3—41no—
431C2×C3×Q8—91no—
432C2×C3×D4—91no—
433C22×C3×C4—91no—
434C22×C3×C4—91no—
435C22×C3×C4—91no—
436C2×#67—91no—
437C2×#67—91no—
438C2×#67—91no—
439C2×#67—91no—
440C22×Dic3—91no—
441C22×Dic3—91no—
442C2×D12—31no—
443C2×D12—31no—
444C2×D12—61no—
445C2×D12—91no—
446C2×D12—91no—
447C2×C4×D3—31no—
448C2×C4×D3—31no—
449C2×C4×D3—31no—
450C2×C4×D3—31no—
451C2×C4×D3—31no—
452C2×C4×D3—31no—
453C2×C4×D3—91no—
454C2×C4×D3—91no—
455C2×C4×D3—91no—
456C2×C4×D3—91no—
457C2×C4×D3—181no—
458C2×Dic6—31no—
459C2×Dic6—31no—
460C3×C4⋊C4—31no—
461C3×C4⋊C4—31no—
462C3×C4⋊C4—31no—
463C3×C4⋊C4—31no—
464C3×C4⋊C4—61no—
465C3×C4⋊C4—61no—
466C3×C4⋊C4—91no—
467C3×C4⋊C4—91no—
468C3×C4⋊C4—91no—
469C3×C4⋊C4—91no—
470C3×C4⋊C4—91no—
471C3×C4⋊C4—91no—
472C3×C22⋊C4—91no—
473C3×C22⋊C4—91no—
474C3×C22⋊C4—91no—
475C3×C22⋊C4—91no—
476C3×C42—31no—
477C3×C42—31no—
478C3×C42—61no—
479#217—91no—
480#217—91no—
481#217—91no—
482#217—91no—
483#217—91no—
484#217—91no—
485(C2×D3)⋊C4—31no—
486(C2×D3)⋊C4—31no—
487(C2×D3)⋊C4—31no—
488(C2×D3)⋊C4—31no—
489(C2×D3)⋊C4—31no—
490(C2×D3)⋊C4—31no—
491(C2×D3)⋊C4—31no—
492(C2×D3)⋊C4—31no—
493(C2×D3)⋊C4—61no—
494(C2×D3)⋊C4—91no—
495(C2×D3)⋊C4—91no—
496(C2×D3)⋊C4—91no—
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)⋊C4—91no—
503(C2×D3)⋊C4—91no—
504(C2×D3)⋊C4—91no—
505(C2×D3)⋊C4—91no—
506(C2×D3)⋊C4—181no—
507(C2×D3)⋊C4—181no—
508(C2×D3)⋊C4—181no—
509(C2×D3)⋊C4—181no—
510(C2×D3)⋊C4—181no—
511C4⋊Dic3—31no—
512C4⋊Dic3—31no—
513C4⋊Dic3—31no—
514C4⋊Dic3—31no—
515C4⋊Dic3—91no—
516C4⋊Dic3—91no—
517C4⋊Dic3—91no—
518C4⋊Dic3—181no—
519C4⋊Dic3D3211yescharacteristic
520Dic3⋊C4—31no—
521Dic3⋊C4—31no—
522Dic3⋊C4—31no—
523Dic3⋊C4—31no—
524Dic3⋊C4—31no—
525Dic3⋊C4—31no—
526Dic3⋊C4—31no—
527Dic3⋊C4—31no—
528Dic3⋊C4—61no—
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—181no—
551Dic3⋊C4—361no—
552Dic3⋊C4D3211yescharacteristic
553C4×Dic3—91no—
554C4×Dic3—91no—
555C4×Dic3—91no—
556C4×Dic3—181no—
557C4×Dic3D3211yescharacteristic
558C22×C32—21no—
559C22×C32—21no—
560C22×C32—21no—
561C22×C32—41no—
562C22×C32C23×D311yescharacteristic
563C22×C32C23×D311yescharacteristic
564C22×C32C23×D311yescharacteristic
565C2×C3⋊D3—21no—
566C2×C3⋊D3—21no—
567C2×C3⋊D3—21no—
568C2×C3⋊D3—21no—
569C2×C3⋊D3—21no—
570C2×C3⋊D3—21no—
571C2×C3⋊D3—21no—
572C2×C3⋊D3—21no—
573C2×C3⋊D3#23512yes—
574C2×C3×D3—32no—
575C2×C3×D3—32no—
576C2×C3×D3—62no—
577C2×C3×D3—61no—
578C2×C3×D3—61no—
579C2×C3×D3—61no—
580C2×C3×D3—61no—
581C2×C3×D3—61no—
582C2×C3×D3—61no—
583C2×C3×D3—61no—
584C2×C3×D3—61no—
585C2×C3×D3—61no—
586C2×C3×D3—61no—
587C2×C3×D3—61no—
588C2×C3×D3—61no—
589C2×C3×D3—61no—
590C2×C3×D3—61no—
591C2×C3×D3—61no—
592C2×C3×D3—61no—
593C2×C3×D3—121no—
594C2×C3×D3—121no—
595C2×C3×D3—121no—
596C2×C3×D3—121no—
597C2×C3×D3—121no—
598C2×C3×D3—121no—
599C2×C3×D3—121no—
600C2×C3×D3—121no—
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—61no—
611C32×C4—61no—
612C32×C4—61no—
613C32×C4—81no—
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—21no—
638C3×Dic3—21no—
639C3×Dic3—21no—
640C3×Dic3—21no—
641C3×Dic3—21no—
642C3×Dic3—21no—
643C3×Dic3—41no—
644C3×Dic3—41no—
645C3×Dic3—41no—
646C3×Dic3—41no—
647C3×Dic3—41no—
648C3×Dic3—41no—
649C3×Dic3—61no—
650C3×Dic3—61no—
651C3×Dic3—61no—
652C3×Dic3—61no—
653C3×Dic3—61no—
654C3×Dic3—61no—
655C3×Dic3—121no—
656C3×Dic3—121no—
657C3×Dic3—121no—
658#126—271no—
659#126—271no—
660#125—91no—
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—271no—
670C4×D4—91no—
671C4×D4—271no—
672C2×C4⋊C4—271no—
673C33#53911yescharacteristic, complemented, Sylow
674C23×C3—91no—
675C23×C3—91no—
676C23×C3—91no—
677C22×D3—31no—
678C22×D3—31no—
679C22×D3—31no—
680C22×D3—31no—
681C22×D3—31no—
682C22×D3—31no—
683C22×D3—61no—
684C22×D3—61no—
685C22×D3—61no—
686C3×Q8—361no—
687C3×D4—182no—
688C2×C3×C4—21no—
689C2×C3×C4—21no—
690C2×C3×C4—21no—
691C2×C3×C4—31no—
692C2×C3×C4—31no—
693C2×C3×C4—31no—
694C2×C3×C4—31no—
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—31no—
702C2×C3×C4—31no—
703C2×C3×C4—41no—
704C2×C3×C4—61no—
705C2×C3×C4—61no—
706C2×C3×C4—61no—
707C2×C3×C4—61no—
708C2×C3×C4—61no—
709C2×C3×C4—61no—
710C2×C3×C4—91no—
711C2×C3×C4—91no—
712C2×C3×C4—91no—
713C2×C3×C4—361no—
714C2×C3×C4—361no—
715C2×C3×C4—361no—
716C2×C3×C4C2×D3211yescharacteristic
717C2×C3×C4C2×D3211yescharacteristic
718C2×C3×C4C2×D3211yescharacteristic
719#67—182no—
720#67—182no—
721#67—361no—
722#67—361no—
723C2×Dic3—31no—
724C2×Dic3—31no—
725C2×Dic3—31no—
726C2×Dic3—31no—
727C2×Dic3—31no—
728C2×Dic3—31no—
729C2×Dic3—61no—
730C2×Dic3—61no—
731C2×Dic3—61no—
732C2×Dic3—91no—
733C2×Dic3—91no—
734C2×Dic3—91no—
735C2×Dic3—91no—
736C2×Dic3—91no—
737C2×Dic3—91no—
738C2×Dic3—181no—
739C2×Dic3—181no—
740C2×Dic3—181no—
741C2×Dic3—181no—
742C2×Dic3—181no—
743C2×Dic3—181no—
744C2×Dic3—182no—
745C2×Dic3—361no—
746C2×Dic3—361no—
747C2×Dic3—361no—
748C2×Dic3C2×D3211yescharacteristic
749C2×Dic3C2×D3211yescharacteristic
750C2×Dic3C2×D3211yescharacteristic
751C2×Dic3C2×D3211yescharacteristic
752C2×Dic3C2×D3211yescharacteristic
753C2×Dic3C2×D3211yescharacteristic
754D12—62no—
755D12—62no—
756D12—122no—
757D12—182no—
758D12—361no—
759C4×D3—121no—
760C4×D3—121no—
761C4×D3—121no—
762C4×D3—121no—
763C4×D3—121no—
764C4×D3—121no—
765C4×D3—182no—
766C4×D3—182no—
767C4×D3—362no—
768C4×D3—361no—
769C4×D3—361no—
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×C32C2×#23511yescharacteristic
785C2×C32#100411yescharacteristic
786C2×C32#100411yescharacteristic
787C2×C32#100711yescharacteristic
788C2×C32#100711yescharacteristic
789C2×C32D3×#4111yescharacteristic
790C2×C32D3×#4111yescharacteristic
791C2×C32#100911yescharacteristic
792C2×C32#101011yescharacteristic
793C3⋊D3—22no—
794C3⋊D3—41no—
795C3⋊D3—41no—
796C3×D3—62no—
797C3×D3—62no—
798C3×D3—122no—
799C3×D3—121no—
800C3×D3—121no—
801C3×D3—121no—
802C3×D3—121no—
803C3×D3—241no—
804C3×D3—241no—
805C2×Q8—91no—
806C2×D4—91no—
807C2×D4—271no—
808C2×D4—271no—
809C22×C4—91no—
810C22×C4—91no—
811C22×C4—91no—
812C22×C4—271no—
813C22×C4—271no—
814C4⋊C4—31no—
815C4⋊C4—31no—
816C4⋊C4—91no—
817C4⋊C4—91no—
818C4⋊C4—91no—
819C4⋊C4—91no—
820C4⋊C4—91no—
821C4⋊C4—91no—
822C4⋊C4—271no—
823C4⋊C4—271no—
824C4⋊C4—271no—
825C4⋊C4—271no—
826C4⋊C4—271no—
827C4⋊C4—271no—
828C22⋊C4—91no—
829C22⋊C4—91no—
830C22⋊C4—91no—
831C22⋊C4—91no—
832C22⋊C4—271no—
833C22⋊C4—271no—
834C22⋊C4—271no—
835C22⋊C4—271no—
836C22⋊C4—271no—
837C22⋊C4—271no—
838C42—31no—
839C42—271no—
840C22×C3—21no—
841C22×C3—21no—
842C22×C3—21no—
843C22×C3—41no—
844C22×C3—92no—
845C22×C3—181no—
846C22×C3—181no—
847C22×C3—181no—
848C22×C3—181no—
849C22×C3—181no—
850C22×C3—181no—
851C22×C3—181no—
852C22×C3—181no—
853C22×C3C22×D3211yescharacteristic
854C22×C3C22×D3211yescharacteristic
855C22×C3C22×D3211yescharacteristic
856C2×D3—32no—
857C2×D3—32no—
858C2×D3—62no—
859C2×D3—61no—
860C2×D3—61no—
861C2×D3—61no—
862C2×D3—61no—
863C2×D3—61no—
864C2×D3—61no—
865C2×D3—61no—
866C2×D3—61no—
867C2×D3—61no—
868C2×D3—61no—
869C2×D3—61no—
870C2×D3—61no—
871C2×D3—61no—
872C2×D3—61no—
873C2×D3—61no—
874C2×D3—61no—
875C2×D3—121no—
876C2×D3—121no—
877C2×D3—121no—
878C2×D3—121no—
879C2×D3—121no—
880C2×D3—121no—
881C2×D3—121no—
882C2×D3—121no—
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—61no—
896C3×C4—61no—
897C3×C4—61no—
898C3×C4—61no—
899C3×C4—61no—
900C3×C4—61no—
901C3×C4—81no—
902C3×C4—121no—
903C3×C4—121no—
904C3×C4—121no—
905C3×C4—121no—
906C3×C4—121no—
907C3×C4—121no—
908C3×C4—181no—
909C3×C4—181no—
910C3×C4—181no—
911Dic3—21no—
912Dic3—21no—
913Dic3—21no—
914Dic3—21no—
915Dic3—21no—
916Dic3—21no—
917Dic3—61no—
918Dic3—61no—
919Dic3—61no—
920Dic3—61no—
921Dic3—61no—
922Dic3—61no—
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#563811yescharacteristic, complemented
946C32#569211yescharacteristic, complemented
947C23—91no—
948C23—91no—
949C23—91no—
950Q8—361no—
951D4—182no—
952D4—542no—
953D4—1081no—
954C2×C4—31no—
955C2×C4—31no—
956C2×C4—31no—
957C2×C4—31no—
958C2×C4—31no—
959C2×C4—31no—
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—542no—
969C2×C4—1081no—
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—182no—
984C2×C3—361no—
985C2×C3—361no—
986C2×C3#6429711yescharacteristic
987C2×C3D3×#23511yescharacteristic
988C2×C3D3×#23511yescharacteristic
989C2×C3#6430711yescharacteristic
990C2×C3#6430711yescharacteristic
991C2×C3#6431211yescharacteristic
992C2×C3#6431311yescharacteristic
993C2×C3#6431511yescharacteristic
994C2×C3#6431611yescharacteristic
995D3—62no—
996D3—62no—
997D3—122no—
998D3—121no—
999D3—121no—
1000D3—121no—
1001D3—121no—
1002D3—241no—
1003D3—241no—
1004C22—92no—
1005C22—181no—
1006C22—181no—
1007C22—181no—
1008C22—181no—
1009C22—181no—
1010C22—181no—
1011C22—181no—
1012C22—181no—
1013C22C2×D3311yescharacteristic
1014C4—21no—
1015C4—61no—
1016C4—61no—
1017C4—61no—
1018C4—61no—
1019C4—61no—
1020C4—61no—
1021C4—181no—
1022C4—181no—
1023C4—181no—
1024C4—541no—
1025C4—541no—
1026C3—21no—
1027C3—21no—
1028C3—21no—
1029C3—41no—
1030C3#1059391311yescharacteristic, complemented
1031C3#1059433811yescharacteristic, complemented
1032C3#1059440611yescharacteristic, complemented
1033C2—182no—
1034C2—361no—
1035C2—361no—
1036C2#1172438011yescharacteristic
1037C2#1172439711yescharacteristic
1038C2#1172441011yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radical#11723687C2
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
2. #11723488C2semidirect
3. #11723438C2semidirect
4. #11723405C2semidirect
5. C3×#63895C2semidirect
6. C3×#63894C2semidirect
7. C3×#63867C2semidirect
8. #11723025C2semidirect
9. #11722997C2semidirect
10. #11722995C2semidirect
11. #11722995C2semidirect
12. #11722979C2semidirect
13. #11722970C2semidirect
14. #11722931C2semidirect
15. #11722911C2semidirect
71. #63895D3semidirect
72. #63894D3semidirect
85. #63867D3semidirect
673. C33#539semidirect
944. C32#5564semidirect
945. C32#5638semidirect
946. C32#5692semidirect
1030. C3#10593913semidirect
1031. C3#10594338semidirect
1032. C3#10594406semidirect

Maximal subgroups

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

subgroupindex
#117236872
#117234882
#117234382
#117234052
C3×#638952
C3×#638942
C3×#638672
#117230252
#117229972
#117229952
#117229792
#117229702
#117229312
#117229112
#105944063
#105943383
#105939133