Finite Group Databasebeta

← #72241990

Subgroups — #72241990

Order 5616.

580 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 580 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#72241982C211yesmaximal, characteristic, complemented
2#72241982C211yesmaximal, characteristic, complemented
3C3×#64625⋊C3C211yesmaximal, characteristic, complemented
4C3×#64625⋊C3C211yesmaximal, characteristic, complemented
5C2×(C3⋊(D13⋊C3))⋊D3C211yesmaximal, characteristic, complemented
6#72241939C211yesmaximal, characteristic, complemented
7C22×C3⋊D3×C13⋊C3C211yesmaximal, characteristic, complemented
8#14273312C311yesmaximal, characteristic, complemented
9D3×(C22⋊D13)⋊C3—31nomaximal
10D3×(C22⋊D13)⋊C3—31nomaximal
11C22×C32×C13⋊C3C2211yescharacteristic, complemented
12C2×C3⋊D3×C13⋊C3—22no—
13C2×C3⋊D3×C13⋊C3C2211yescharacteristic
14C2×C3⋊D3×C13⋊C3C2211yescharacteristic, complemented
15C2×C3×C3⋊(D13⋊C3)C2211yescharacteristic, complemented
16C2×C3×C3⋊(D13⋊C3)C2211yescharacteristic, complemented
17(C3⋊(D13⋊C3))⋊D3—22no—
18C3×C3⋊(Dic13⋊C3)C2211yescharacteristic, complemented
19C3×C3⋊(Dic13⋊C3)C2211yescharacteristic, complemented
20C22×C13×C3⋊D3C2×C311yescharacteristic, complemented
21C2×(C3⋊D3)⋊D13C2×C311yescharacteristic, complemented
22C22×D3×C13⋊C3—31no—
23C22×D3×C13⋊C3—31no—
24C22×D3×C13⋊C3—61no—
25C2×D3×D13⋊C3—31no—
26C2×D3×D13⋊C3—31no—
27C3×#64625C2×C311yescharacteristic, complemented
28C3×#64625C2×C311yescharacteristic, complemented
29#11745538C2×C311yescharacteristic, complemented
30#11745538C2×C311yescharacteristic, complemented
31#11745537C2×C311yescharacteristic, complemented
32#64625⋊C3—21no—
33#64625⋊C3—21no—
34#64625⋊C3D311yescharacteristic, complemented
35#64625⋊C3D311yescharacteristic, complemented
36C3×(C22⋊D13)⋊C3—31no—
37C3×(C22⋊D13)⋊C3—31no—
38#64604⋊C3—31no—
39#64604⋊C3—31no—
40#64602⋊C3—31no—
41#64602⋊C3—31no—
42D3×Dic13⋊C3—31no—
43D3×Dic13⋊C3—31no—
44C2×C32×C13⋊C3—21no—
45C2×C32×C13⋊C3C2311yescharacteristic
46C3⋊D3×C13⋊C3—21no—
47C3⋊D3×C13⋊C3D412yescomplemented
48C3×C3⋊(D13⋊C3)—21no—
49C3×C3⋊(D13⋊C3)—21no—
50D3×C22⋊D13—31no—
51D3×C22⋊D13—31no—
52C2×(C22⋊D13)⋊C3—91no—
53C22×C32×C13C22×C311yescharacteristic, complemented
54C2×C13×C3⋊D3—22no—
55C2×C13×C3⋊D3C22×C311yescharacteristic
56C2×C13×C3⋊D3C22×C311yescharacteristic, complemented
57C2×C3×D39C22×C311yescharacteristic, complemented
58C2×C3×D39C22×C311yescharacteristic, complemented
59C22×C3×C13⋊C3—21no—
60C22×C3×C13⋊C3—21no—
61C22×C3×C13⋊C3—21no—
62C22×C3×C13⋊C3—41no—
63C22×C3×C13⋊C3C2×D311yescharacteristic, complemented
64C22×C3×C13⋊C3C2×D311yescharacteristic, complemented
65(C3⋊D3)⋊D13—22no—
66C2×C3⋊(D13⋊C3)—21no—
67C2×C3⋊(D13⋊C3)—21no—
68C2×C3⋊(D13⋊C3)C2×D311yescharacteristic, complemented
69C2×C3⋊(D13⋊C3)C2×D311yescharacteristic, complemented
70C2×D3×C13⋊C3—31no—
71C2×D3×C13⋊C3—31no—
72C2×D3×C13⋊C3—31no—
73C2×D3×C13⋊C3—31no—
74C2×D3×C13⋊C3—61no—
75C2×D3×C13⋊C3—61no—
76C2×D3×C13⋊C3—62no—
77C2×D3×C13⋊C3—62no—
78C2×D3×C13⋊C3—62no—
79C2×D3×C13⋊C3—62no—
80C2×C3×D13⋊C3—31no—
81C2×C3×D13⋊C3—31no—
82D3×D13⋊C3—62no—
83D3×D13⋊C3—62no—
84C3×Dic39C22×C311yescharacteristic, complemented
85C3×Dic39C22×C311yescharacteristic, complemented
86C3⋊(Dic13⋊C3)—21no—
87C3⋊(Dic13⋊C3)—21no—
88C3⋊(Dic13⋊C3)C2×D311yescharacteristic, complemented
89C3⋊(Dic13⋊C3)C2×D311yescharacteristic, complemented
90C3×Dic13⋊C3—31no—
91C3×Dic13⋊C3—31no—
92C3×#3811—131nomaximal, Hall
93C32×C13⋊C3C2×D411yescharacteristic, complemented, Hall
94C22×D3×C13—31no—
95C22×D3×C13—31no—
96C22×D3×C13—61no—
97C23×C13⋊C3—91no—
98C2×D3×D13—31no—
99C2×D3×D13—31no—
100C22×D13⋊C3—91no—
101#64625C3×D311yescharacteristic, complemented
102#64625C3×D311yescharacteristic, complemented
103C3×C22⋊D13—31no—
104C3×C22⋊D13—31no—
105#64604—31no—
106#64604—31no—
107#64602—31no—
108#64602—31no—
109D3×Dic13—31no—
110D3×Dic13—31no—
111(C22⋊D13)⋊C3—31no—
112(C22⋊D13)⋊C3—31no—
113(C22⋊D13)⋊C3—61no—
114(C22⋊D13)⋊C3—61no—
115(C22⋊D13)⋊C3—91no—
116(C22⋊D13)⋊C3—91no—
117C2×Dic13⋊C3—91no—
118C2×C32×C13—21no—
119C2×C32×C13C23×C311yescharacteristic
120C13×C3⋊D3—21no—
121C13×C3⋊D3C3×D412yescomplemented
122C3×D39—21no—
123C3×D39—21no—
124C2×C3×C13⋊C3—21no—
125C2×C3×C13⋊C3—21no—
126C2×C3×C13⋊C3—21no—
127C2×C3×C13⋊C3—21no—
128C2×C3×C13⋊C3—21no—
129C2×C3×C13⋊C3—21no—
130C2×C3×C13⋊C3—21no—
131C2×C3×C13⋊C3—41no—
132C2×C3×C13⋊C3—41no—
133C2×C3×C13⋊C3—41no—
134C2×C3×C13⋊C3—41no—
135C2×C3×C13⋊C3—41no—
136C2×C3×C13⋊C3C22×D311yescharacteristic
137C2×C3×C13⋊C3C22×D311yescharacteristic
138C3⋊(D13⋊C3)—21no—
139C3⋊(D13⋊C3)—21no—
140C3⋊(D13⋊C3)—41no—
141C3⋊(D13⋊C3)—41no—
142D3×C13⋊C3—32no—
143D3×C13⋊C3—32no—
144D3×C13⋊C3—62no—
145D3×C13⋊C3—61no—
146D3×C13⋊C3—61no—
147D3×C13⋊C3—61no—
148D3×C13⋊C3—61no—
149C3×D13⋊C3—61no—
150C3×D13⋊C3—61no—
151C22×C3×C3⋊D3—261no—
152C2×C3×D32—131no—
153C32×#67—131no—
154C32×#67—131no—
155C3×#626—131no—
156C3×#626—131no—
157C3×#624—131no—
158C2×C22⋊D13—91noHall
159C22×C3×C13—21no—
160C22×C3×C13C2×C3×D311yescharacteristic, complemented
161C22×C3×C13C2×C3×D311yescharacteristic, complemented
162C2×D39C2×C3×D311yescharacteristic, complemented
163C2×D39C2×C3×D311yescharacteristic, complemented
164C2×D3×C13—31no—
165C2×D3×C13—31no—
166C2×D3×C13—31no—
167C2×D3×C13—31no—
168C2×D3×C13—61no—
169C2×D3×C13—61no—
170C2×D3×C13—62no—
171C2×D3×C13—62no—
172C2×D3×C13—62no—
173C2×D3×C13—62no—
174C2×C3×D13—31no—
175C2×C3×D13—31no—
176C22×C13⋊C3—21no—
177C22×C13⋊C3—21no—
178C22×C13⋊C3—41no—
179C22×C13⋊C3—91no—
180C22×C13⋊C3—91no—
181C22×C13⋊C3—182no—
182C22×C13⋊C3D3211yescharacteristic, complemented
183D3×D13—62no—
184D3×D13—62no—
185C2×D13⋊C3—31no—
186C2×D13⋊C3—31no—
187C2×D13⋊C3—61no—
188C2×D13⋊C3—61no—
189C2×D13⋊C3—182no—
190Dic39C2×C3×D311yescharacteristic, complemented
191Dic39C2×C3×D311yescharacteristic, complemented
192C3×Dic13—31no—
193C3×Dic13—31no—
194Dic13⋊C3—31no—
195Dic13⋊C3—31no—
196Dic13⋊C3—61no—
197Dic13⋊C3—61no—
198C3×D3×D4—391no—
199C3×D3×D4—391no—
200#3811—131no—
201C32×C13C2×C3×D411yescharacteristic, complemented
202C3×C13⋊C3—21no—
203C3×C13⋊C3—21no—
204C3×C13⋊C3—21no—
205C3×C13⋊C3—41no—
206C3×C13⋊C3D3×D411yescharacteristic, complemented
207C3×C13⋊C3D3×D411yescharacteristic, complemented
208C22×C33—261no—
209C2×C3×C3⋊D3—262no—
210C2×C3×C3⋊D3—261no—
211C2×C3×C3⋊D3—261no—
212C2×C32×D3—131no—
213C2×C32×D3—131no—
214C3×D32—262no—
215C32×Dic3—131no—
216C32×Dic3—131no—
217C23×C13—91no—
218C22×D13—91no—
219C22⋊D13—31no—
220C22⋊D13—31no—
221C22⋊D13—91no—
222C22⋊D13—91no—
223C2×Dic13—91no—
224C2×C3×C13—21no—
225C2×C3×C13—21no—
226C2×C3×C13—21no—
227C2×C3×C13—21no—
228C2×C3×C13—21no—
229C2×C3×C13C22×C3×D311yescharacteristic
230C2×C3×C13C22×C3×D311yescharacteristic
231D39—21no—
232D39—21no—
233C3×D13—61no—
234C3×D13—61no—
235D3×C13—32no—
236D3×C13—32no—
237D3×C13—62no—
238D3×C13—61no—
239D3×C13—61no—
240D3×C13—61no—
241D3×C13—61no—
242C2×C13⋊C3—21no—
243C2×C13⋊C3—21no—
244C2×C13⋊C3—21no—
245C2×C13⋊C3—41no—
246C2×C13⋊C3—41no—
247C2×C13⋊C3—41no—
248C2×C13⋊C3—41no—
249C2×C13⋊C3—41no—
250C2×C13⋊C3—92no—
251C2×C13⋊C3—181no—
252C2×C13⋊C3C2×D3211yescharacteristic
253D13⋊C3—61no—
254D13⋊C3—61no—
255D13⋊C3—121no—
256D13⋊C3—121no—
257C22×C3⋊D3D13⋊C311yescharacteristic, complemented
258C22×C3×D3—391no—
259C22×C3×D3—391no—
260C22×C3×D3—781no—
261C22×C3×D3—781no—
262C22×C3×D3—781no—
263C2×D32—131no—
264C32×D4—391no—
265C32×D4—391no—
266C3×#67—131no—
267C3×#67—131no—
268C3×#67—131no—
269C3×#67—131no—
270C3×#67—261no—
271C3×#67—261no—
272C3×#67—391no—
273C3×#67—391no—
274C3×D12—391no—
275C3×D12—391no—
276C3×C4×D3—391no—
277C3×C4×D3—391no—
278#626—131no—
279#626—131no—
280#624—131no—
281C2×C33—261no—
282C2×C33—261no—
283C3×C3⋊D3—261no—
284C3×C3⋊D3—262no—
285C32×D3—261no—
286C32×D3—261no—
287C22×C13—91no—
288C22×C13—91no—
289C22×C13—182no—
290C22×C13C3×D3211yescharacteristic, complemented
291C2×D13—31no—
292C2×D13—31no—
293C2×D13—182no—
294Dic13—31no—
295Dic13—31no—
296C2×C3×D4—1171no—
297D3×D4—391no—
298D3×D4—391no—
299C3×C13—21no—
300C3×C13C3×D3×D411yescharacteristic, complemented
301C3×C13C3×D3×D411yescharacteristic, complemented
302C13⋊C3—21no—
303C13⋊C3—21no—
304C13⋊C3—41no—
305C13⋊C3#381111yescharacteristic, complemented
306C22×C32—261no—
307C22×C32—261no—
308C22×C32—261no—
309C22×C32—261no—
310C22×C32—391no—
311C22×C32—391no—
312C22×C32—521no—
313C22×C32—521no—
314C22×C32C2×D13⋊C311yescharacteristic, complemented
315C2×C3⋊D3—22no—
316C2×C3⋊D3C2×D13⋊C311yescharacteristic
317C2×C3⋊D3C2×D13⋊C311yescharacteristic, complemented
318C2×C3×D3—131no—
319C2×C3×D3—131no—
320C2×C3×D3—131no—
321C2×C3×D3—131no—
322C2×C3×D3—261no—
323C2×C3×D3—261no—
324C2×C3×D3—781no—
325C2×C3×D3—781no—
326C2×C3×D3—781no—
327C2×C3×D3—781no—
328C2×C3×D3—781no—
329C2×C3×D3—782no—
330C2×C3×D3—782no—
331C2×C3×D3—782no—
332C2×C3×D3—782no—
333C2×C3×D3—781no—
334C2×C3×D3—782no—
335C2×C3×D3—782no—
336D32—262no—
337C32×C4—391no—
338C32×C4—391no—
339C3×Dic3—131no—
340C3×Dic3—131no—
341C3×Dic3—131no—
342C3×Dic3—131no—
343C3×Dic3—261no—
344C3×Dic3—261no—
345C33—261noSylow
346C2×C13—21no—
347C2×C13—92no—
348C2×C13—181no—
349C2×C13C2×C3×D3211yescharacteristic
350D13—61no—
351D13—61no—
352C23×C3—1171no—
353C23×C3—2341no—
354C22×D3—31no—
355C22×D3—31no—
356C22×D3—61no—
357C22×D3—391no—
358C22×D3—391no—
359C3×D4—391no—
360C3×D4—391no—
361C3×D4—391no—
362C3×D4—391no—
363C3×D4—781no—
364C3×D4—781no—
365C3×D4—1171no—
366C3×D4—1171no—
367C2×C3×C4—1171no—
368#67—131no—
369#67—131no—
370#67—391no—
371#67—391no—
372D12—391no—
373D12—391no—
374C4×D3—391no—
375C4×D3—391no—
376C2×C32—21no—
377C2×C32—261no—
378C2×C32—261no—
379C2×C32—261no—
380C2×C32—261no—
381C2×C32—261no—
382C2×C32—261no—
383C2×C32—261no—
384C2×C32—261no—
385C2×C32—521no—
386C2×C32—521no—
387C2×C32—521no—
388C2×C32—521no—
389C2×C32—521no—
390C2×C32—521no—
391C2×C32—781no—
392C2×C32—781no—
393C2×C32C22×D13⋊C311yescharacteristic
394C3⋊D3—21no—
395C3⋊D3(C22⋊D13)⋊C312yescomplemented
396C3×D3—261no—
397C3×D3—261no—
398C3×D3—261no—
399C3×D3—261no—
400C3×D3—521no—
401C3×D3—521no—
402C3×D3—782no—
403C3×D3—782no—
404C3×D3—782no—
405C3×D3—781no—
406C3×D3—781no—
407C3×D3—781no—
408C3×D3—781no—
409C2×D4—1171noSylow
410C13C3×#381111yescharacteristic, complemented, Sylow
411C22×C3—21no—
412C22×C3—261no—
413C22×C3—391no—
414C22×C3—391no—
415C22×C3—391no—
416C22×C3—391no—
417C22×C3—521no—
418C22×C3—521no—
419C22×C3—521no—
420C22×C3—781no—
421C22×C3—781no—
422C22×C3—2341no—
423C22×C3—2341no—
424C22×C3—2342no—
425C22×C3—2342no—
426C22×C3D3×D13⋊C311yescharacteristic, complemented
427C22×C3D3×D13⋊C311yescharacteristic, complemented
428C2×D3—31no—
429C2×D3—31no—
430C2×D3—31no—
431C2×D3—31no—
432C2×D3—61no—
433C2×D3—61no—
434C2×D3—62no—
435C2×D3—62no—
436C2×D3—62no—
437C2×D3—62no—
438C2×D3—131no—
439C2×D3—131no—
440C2×D3—782no—
441C2×D3—782no—
442C3×C4—391no—
443C3×C4—391no—
444C3×C4—391no—
445C3×C4—391no—
446C3×C4—781no—
447C3×C4—781no—
448Dic3—131no—
449Dic3—131no—
450C32—261no—
451C32—261no—
452C32—261no—
453C32—261no—
454C32—521no—
455C32—521no—
456C32C2×(C22⋊D13)⋊C311yescharacteristic, complemented
457C23—91no—
458C23—1171no—
459D4—391no—
460D4—391no—
461D4—1171no—
462D4—1171no—
463C2×C4—1171no—
464C2×C3—21no—
465C2×C3—21no—
466C2×C3—21no—
467C2×C3—21no—
468C2×C3—21no—
469C2×C3—261no—
470C2×C3—261no—
471C2×C3—521no—
472C2×C3—521no—
473C2×C3—521no—
474C2×C3—521no—
475C2×C3—521no—
476C2×C3—521no—
477C2×C3—521no—
478C2×C3—781no—
479C2×C3—781no—
480C2×C3—781no—
481C2×C3—781no—
482C2×C3—1561no—
483C2×C3—1561no—
484C2×C3—2342no—
485C2×C3—2341no—
486C2×C3C2×D3×D13⋊C311yescharacteristic
487C2×C3C2×D3×D13⋊C311yescharacteristic
488D3—32no—
489D3—32no—
490D3—62no—
491D3—61no—
492D3—61no—
493D3—61no—
494D3—61no—
495D3—261no—
496D3—261no—
497C22—91no—
498C22—91no—
499C22—182no—
500C22—391no—
501C22—391no—
502C22—2342no—
503C22(C3⋊(D13⋊C3))⋊D311yescharacteristic, complemented
504C4—391no—
505C4—391no—
506C3—21no—
507C3—261no—
508C3—521no—
509C3—521no—
510C3—521no—
511C3D3×(C22⋊D13)⋊C311yescharacteristic, complemented
512C3D3×(C22⋊D13)⋊C311yescharacteristic, complemented
513C2—21no—
514C2—92no—
515C2—181no—
516C2—781no—
517C2—781no—
518C2C2×(C3⋊(D13⋊C3))⋊D311yescharacteristic
subgroupG/H
center, FrattiniC2C2×(C3⋊(D13⋊C3))⋊D3
commutator, socle, cosocleC2×C32×C13C23×C3
FittingC22×C32×C13C22×C3
hypercenterC22(C3⋊(D13⋊C3))⋊D3
hypocenterC32×C13C2×C3×D4
LCSG ▷ C2×C32×C13 ▷ C32×C13
UCSC1 ◁ C2 ◁ C22

Complements

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

NH ≅ G/Ntype
1. #72241982C2semidirect
2. #72241982C2semidirect
3. C3×#64625⋊C3C2semidirect
4. C3×#64625⋊C3C2semidirect
5. C2×(C3⋊(D13⋊C3))⋊D3C2semidirect
6. #72241939C2semidirect
7. C22×C3⋊D3×C13⋊C3C2semidirect
8. #14273312C3semidirect
11. C22×C32×C13⋊C3C22semidirect
14. C2×C3⋊D3×C13⋊C3C22semidirect
15. C2×C3×C3⋊(D13⋊C3)C22semidirect
16. C2×C3×C3⋊(D13⋊C3)C22semidirect
18. C3×C3⋊(Dic13⋊C3)C22semidirect
19. C3×C3⋊(Dic13⋊C3)C22semidirect
20. C22×C13×C3⋊D3C2×C3semidirect
21. C2×(C3⋊D3)⋊D13C2×C3semidirect
27. C3×#64625C2×C3semidirect
28. C3×#64625C2×C3semidirect
29. #11745538C2×C3semidirect
30. #11745538C2×C3semidirect
31. #11745537C2×C3semidirect
34. #64625⋊C3D3semidirect
35. #64625⋊C3D3semidirect
47. C3⋊D3×C13⋊C3D4semidirect
53. C22×C32×C13C22×C3semidirect
56. C2×C13×C3⋊D3C22×C3semidirect
57. C2×C3×D39C22×C3semidirect
58. C2×C3×D39C22×C3semidirect
63. C22×C3×C13⋊C3C2×D3semidirect
64. C22×C3×C13⋊C3C2×D3semidirect
68. C2×C3⋊(D13⋊C3)C2×D3semidirect
69. C2×C3⋊(D13⋊C3)C2×D3semidirect
84. C3×Dic39C22×C3semidirect
85. C3×Dic39C22×C3semidirect
88. C3⋊(Dic13⋊C3)C2×D3semidirect
89. C3⋊(Dic13⋊C3)C2×D3semidirect
93. C32×C13⋊C3C2×D4semidirect
101. #64625C3×D3semidirect
102. #64625C3×D3semidirect
121. C13×C3⋊D3C3×D4semidirect
160. C22×C3×C13C2×C3×D3semidirect
161. C22×C3×C13C2×C3×D3semidirect
162. C2×D39C2×C3×D3semidirect
163. C2×D39C2×C3×D3semidirect
182. C22×C13⋊C3D32semidirect
190. Dic39C2×C3×D3semidirect
191. Dic39C2×C3×D3semidirect
201. C32×C13C2×C3×D4semidirect
206. C3×C13⋊C3D3×D4semidirect
207. C3×C13⋊C3D3×D4semidirect
257. C22×C3⋊D3D13⋊C3semidirect
290. C22×C13C3×D32semidirect
300. C3×C13C3×D3×D4semidirect
301. C3×C13C3×D3×D4semidirect
305. C13⋊C3#3811semidirect
314. C22×C32C2×D13⋊C3semidirect
317. C2×C3⋊D3C2×D13⋊C3semidirect
395. C3⋊D3(C22⋊D13)⋊C3semidirect
410. C13C3×#3811semidirect
426. C22×C3D3×D13⋊C3semidirect
427. C22×C3D3×D13⋊C3semidirect
456. C32C2×(C22⋊D13)⋊C3semidirect
503. C22(C3⋊(D13⋊C3))⋊D3semidirect
511. C3D3×(C22⋊D13)⋊C3semidirect
512. C3D3×(C22⋊D13)⋊C3semidirect

Maximal subgroups

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

subgroupindex
#722419822
C3×#64625⋊C32
C2×(C3⋊(D13⋊C3))⋊D32
#722419392
C22×C3⋊D3×C13⋊C32
#142733123
D3×(C22⋊D13)⋊C33
C3×#381113