Finite Group Databasebeta

← #13169171

Subgroups — #13169171

Order 1728.

1794 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89026C211yesmaximal, characteristic
2#11723691C211yesmaximal, characteristic, complemented
3#11723452C211yesmaximal, characteristic, complemented
4#11723413C211yesmaximal, characteristic, complemented
5C3×#63898C211yesmaximal, characteristic, complemented
6C3×#63894C211yesmaximal, characteristic, complemented
7C3×Dic3×D12C211yesmaximal, characteristic, complemented
8#11722936C212yesmaximal, complemented
9#11722930C212yesmaximal, complemented
10#11722904C212yesmaximal, complemented
11D3×#3722C212yesmaximal, complemented
12#10595223—31nomaximal
13#10594606—31nomaximal
14#10593996—31nomaximal
15C22×D3×C3⋊D3C2212yes—
16C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
17C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
18C2×C32×D12C2211yescharacteristic
19C2×#6294C2212yescomplemented
20C2×#6290C2212yes—
21#89026C418yescomplemented
22C2×C3×#624C2212yescomplemented
23C2×C3×D3×Dic3C2212yescomplemented
24C2×C3×D3×Dic3C2212yescomplemented
25C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
26C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
27C32×C4⋊Dic3C2211yescharacteristic, complemented
28C32×C4×Dic3C2211yescharacteristic, complemented
29#88814C2212yescomplemented
30#88806C2211yescharacteristic, complemented
31#88806C2211yescharacteristic, complemented
32#88804C2212yes—
33#88804C2211yescharacteristic
34#88804C2211yescharacteristic
35Dic3×C3⋊Dic3C2212yescomplemented
36C3×#3722C2212yescomplemented
37C3×(C2×D3)⋊Dic3C2212yescomplemented
38C3×(C2×D3)⋊Dic3C2212yescomplemented
39C2×D4×C3⋊D3—31no—
40C2×#3802—31no—
41C2×#3802—31no—
42C2×#3802—61no—
43#64101—31no—
44#64081—31no—
45C3×D4×Dic3—31no—
46C3×D4×Dic3—31no—
47C3×#893—31no—
48C3×#893—31no—
49C3×C4×D12—31no—
50C3×C4×D12—31no—
51#63974—32no—
52C2×#3722—32no—
53#63952—32no—
54#63952—32no—
55D3×(C2×D3)⋊C4—32no—
56D3×(C2×D3)⋊C4—32no—
57D3×(C2×D3)⋊C4—32no—
58D3×(C2×D3)⋊C4—32no—
59#63902—32no—
60C4×#625—32no—
61#63898—31no—
62#63898D311yescharacteristic, complemented
63#63894—31no—
64#63894D311yescharacteristic, complemented
65Dic3×D12—31no—
66Dic3×D12D311yescharacteristic, complemented
67#63879—32no—
68#63879—32no—
69#63874—31no—
70#63874—31no—
71#63874—61no—
72#63849—31no—
73#63849—31no—
74#63849—61no—
75C22×C3⋊(C3⋊D3)C2311yescharacteristic
76C22×C3×C3⋊D3C2312yes—
77C22×C32×D3C2312yes—
78C2×D3×C3⋊D3—42no—
79C2×D3×C3⋊D3—42no—
80C2×D3×C3⋊D3C2×C418yescomplemented
81C2×C33×C4C2311yescharacteristic
82C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
83C4×C3⋊(C3⋊D3)C2×C414yescomplemented
84C2×C3×C3⋊Dic3C2311yescharacteristic
85C2×C3×C3⋊Dic3C2311yescharacteristic
86C2×C3×C3⋊Dic3C2312yes—
87C3×C4⋊(C3⋊D3)C2×C414yescomplemented
88C2×C32×Dic3C2311yescharacteristic
89C2×C32×Dic3C2312yes—
90C2×C32×Dic3C2311yescharacteristic
91C32×D12C2×C414yescomplemented
92#6294—42no—
93#6290C2×C418yescomplemented
94C3×#624—42no—
95C3×D3×Dic3—42no—
96C3×D3×Dic3—42no—
97#5545—91no—
98#5545—91no—
99#5545—91no—
100C23×C3⋊D3—32no—
101C22×D32—32no—
102C22×D32—32no—
103C22×D32—62no—
104C2×C32×D4—31no—
105C2×#638—32no—
106D4×C3⋊D3—38no—
107C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
108C2×C4×C3⋊D3—31no—
109C2×C4×C3⋊D3—31no—
110C2×C4×C3⋊D3—31no—
111C2×C4×C3⋊D3—61no—
112C2×C4×C3⋊D3—61no—
113C2×C4×C3⋊D3—61no—
114C2×C4×C3⋊D3—121no—
115C22×C3×Dic3—32no—
116C22×C3×Dic3—32no—
117C2×C3×D12—21no—
118C2×C3×D12—31no—
119C2×C3×D12—31no—
120C2×C3×D12—61no—
121C2×C3×D12C2×D311yescharacteristic
122C2×C3×D12C2×D311yescharacteristic
123C2×C3×C4×D3—32no—
124C2×C3×C4×D3—32no—
125C2×C3×C4×D3—32no—
126C2×C3×C4×D3—32no—
127C2×#625—32no—
128C2×#625—32no—
129C2×#625—62no—
130C2×#624—32no—
131C2×#624C2×D312yescomplemented
132C2×D3×Dic3—32no—
133C2×D3×Dic3—32no—
134C2×D3×Dic3C2×D312yescomplemented
135C2×D3×Dic3C2×D312yescomplemented
136#3802—38no—
137#3802—38no—
138#3802—68no—
139C32×C4⋊C4—31no—
140C32×C42—31no—
141#3752—31no—
142#3752—31no—
143#3752—32no—
144C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
145#3750—31no—
146#3750—31no—
147C4×C3⋊Dic3—32no—
148C4×C3⋊Dic3C2×D311yescharacteristic, complemented
149C3×#217—32no—
150C3×#217—32no—
151C3×(C2×D3)⋊C4—32no—
152C3×(C2×D3)⋊C4—32no—
153C3×(C2×D3)⋊C4—32no—
154C3×(C2×D3)⋊C4—32no—
155C3×C4⋊Dic3—21no—
156C3×C4⋊Dic3—31no—
157C3×C4⋊Dic3—31no—
158C3×C4⋊Dic3—61no—
159C3×C4⋊Dic3C2×D311yescharacteristic, complemented
160C3×C4⋊Dic3C2×D311yescharacteristic, complemented
161C3×C4×Dic3—21no—
162C3×C4×Dic3—31no—
163C3×C4×Dic3—31no—
164C3×C4×Dic3—61no—
165C3×C4×Dic3C2×D311yescharacteristic, complemented
166C3×C4×Dic3C2×D311yescharacteristic, complemented
167#3724—31no—
168#3724—31no—
169#3724—31no—
170#3724—31no—
171#3724—61no—
172#3724—61no—
173#3722—32no—
174#3722—32no—
175#3722—32no—
176#3722—31no—
177#3722—31no—
178#3722—31no—
179#3722—31no—
180#3722—62no—
181#3722—61no—
182#3722—61no—
183#3722C2×D312yescomplemented
184(C2×D3)⋊Dic3—32no—
185(C2×D3)⋊Dic3—32no—
186(C2×D3)⋊Dic3C2×D312yescomplemented
187(C2×D3)⋊Dic3C2×D312yescomplemented
188Dic32—32no—
189Dic32—32no—
190Dic32—62no—
191C22×C33C2411yescharacteristic
192C2×C3⋊(C3⋊D3)—21no—
193C2×C3⋊(C3⋊D3)—21no—
194C2×C3⋊(C3⋊D3)C22×C412yes—
195C2×C3×C3⋊D3—22no—
196C2×C3×C3⋊D3—22no—
197C2×C3×C3⋊D3C22×C414yes—
198C2×C32×D3—22no—
199C2×C32×D3—22no—
200C2×C32×D3C22×C414yes—
201D3×C3⋊D3—48no—
202C33×C4C22×C412yes—
203C3⋊(C3⋊Dic3)C22×C412yes—
204C3×C3⋊Dic3—21no—
205C3×C3⋊Dic3—22no—
206C3×C3⋊Dic3—21no—
207C32×Dic3—21no—
208C32×Dic3—22no—
209C32×Dic3—21no—
210C2×D3×D4—91no—
211C2×D3×D4—91no—
212C2×D3×D4—91no—
213C2×D3×D4—181no—
214C3×C4×D4—91no—
215C3×C4×D4—91no—
216C3×C4×D4—91no—
217D4×Dic3—31no—
218D4×Dic3—31no—
219D4×Dic3—91no—
220C4×#67—92no—
221C4×#67—92no—
222C4×#67—92no—
223C2×(C2×D3)⋊C4—92no—
224C2×(C2×D3)⋊C4—92no—
225C2×(C2×D3)⋊C4—92no—
226#893—31no—
227#893—31no—
228#893—91no—
229#892—91no—
230#892—91no—
231#892—91no—
232#892—181no—
233#67⋊C4—92no—
234#67⋊C4—92no—
235#67⋊C4—92no—
236D3×C22⋊C4—92no—
237D3×C22⋊C4—92no—
238D3×C22⋊C4—92no—
239C4×D12—31no—
240C4×D12—31no—
241C4×D12—91no—
242#872—91no—
243#872—91no—
244#872—91no—
245#872—181no—
246C23×C32—32no—
247C22×C3⋊D3—31no—
248C22×C3⋊D3—31no—
249C22×C3⋊D3—31no—
250C22×C3⋊D3—38no—
251C22×C3⋊D3—61no—
252C22×C3⋊D3—61no—
253C22×C3⋊D3—61no—
254C22×C3⋊D3—121no—
255C22×C3⋊D3—122no—
256C22×C3⋊D3—122no—
257C22×C3⋊D3C22×D312yes—
258C22×C3×D3—22no—
259C22×C3×D3—32no—
260C22×C3×D3—32no—
261C22×C3×D3—62no—
262C22×C3×D3C22×D312yes—
263C22×C3×D3C22×D312yes—
264C2×D32—38no—
265C2×D32—38no—
266C2×D32—68no—
267C2×D32—122no—
268C2×D32—122no—
269C2×D32—122no—
270C2×D32—122no—
271C2×D32—124no—
272C2×D32—124no—
273C32×D4—34no—
274C2×C32×C4—21no—
275C2×C32×C4—21no—
276C2×C32×C4—21no—
277C2×C32×C4—32no—
278C2×C32×C4—31no—
279C2×C32×C4—31no—
280C2×C32×C4—41no—
281C2×C32×C4C22×D311yescharacteristic
282C2×C32×C4C22×D311yescharacteristic
283C2×C32×C4C22×D311yescharacteristic
284#638—38no—
285C2×C3⋊Dic3—31no—
286C2×C3⋊Dic3—31no—
287C2×C3⋊Dic3—31no—
288C2×C3⋊Dic3—61no—
289C2×C3⋊Dic3—61no—
290C2×C3⋊Dic3—61no—
291C2×C3⋊Dic3—121no—
292C2×C3⋊Dic3C22×D311yescharacteristic
293C2×C3⋊Dic3C22×D312yes—
294C2×C3⋊Dic3C22×D311yescharacteristic
295C4⋊(C3⋊D3)C4×D314yescomplemented
296C4×C3⋊D3—34no—
297C4×C3⋊D3—34no—
298C4×C3⋊D3—34no—
299C4×C3⋊D3—64no—
300C4×C3⋊D3—64no—
301C4×C3⋊D3—64no—
302C4×C3⋊D3—124no—
303C2×C3×Dic3—22no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3—32no—
307C2×C3×Dic3—32no—
308C2×C3×Dic3—31no—
309C2×C3×Dic3—31no—
310C2×C3×Dic3—31no—
311C2×C3×Dic3—31no—
312C2×C3×Dic3—62no—
313C2×C3×Dic3—61no—
314C2×C3×Dic3—61no—
315C2×C3×Dic3—122no—
316C2×C3×Dic3—122no—
317C2×C3×Dic3C22×D312yes—
318C2×C3×Dic3C22×D312yes—
319C2×C3×Dic3C22×D311yescharacteristic
320C2×C3×Dic3C22×D311yescharacteristic
321C2×C3×Dic3C22×D311yescharacteristic
322C2×C3×Dic3C22×D311yescharacteristic
323C3×D12—24no—
324C3×D12—34no—
325C3×D12—34no—
326C3×D12—64no—
327C3×D12C4×D314yescomplemented
328C3×D12C4×D314yescomplemented
329C3×C4×D3—122no—
330C3×C4×D3—122no—
331C3×C4×D3—122no—
332C3×C4×D3—122no—
333#625—38no—
334#625—38no—
335#625—68no—
336#624—42no—
337#624—122no—
338D3×Dic3—42no—
339D3×Dic3—42no—
340D3×Dic3—122no—
341D3×Dic3—122no—
342#518—271noSylow
343C2×C33C23×C411yescharacteristic
344C2×C33H(5,𝔽2)11yescharacteristic
345C2×C33H(5,𝔽2)11yescharacteristic
346C3⋊(C3⋊D3)—22no—
347C3×C3⋊D3—24no—
348C32×D3—24no—
349C23×D3—92no—
350C23×D3—92no—
351C23×D3—92no—
352C23×D3—182no—
353C2×C3×D4—31no—
354C2×C3×D4—31no—
355C2×C3×D4—61no—
356C2×C3×D4—91no—
357C22×C3×C4—92no—
358C22×C3×C4—92no—
359C22×C3×C4—92no—
360C2×#67—92no—
361C2×#67—92no—
362C2×#67—92no—
363C2×#67—182no—
364C22×Dic3—32no—
365C22×Dic3—32no—
366C22×Dic3—92no—
367D3×D4—98no—
368D3×D4—98no—
369D3×D4—98no—
370D3×D4—188no—
371C2×D12—31no—
372C2×D12—31no—
373C2×D12—61no—
374C2×D12D3211yescharacteristic
375C2×C4×D3—32no—
376C2×C4×D3—32no—
377C2×C4×D3—32no—
378C2×C4×D3—32no—
379C2×C4×D3—91no—
380C2×C4×D3—91no—
381C2×C4×D3—91no—
382C2×C4×D3—92no—
383C2×C4×D3—92no—
384C2×C4×D3—181no—
385C2×C4×D3—181no—
386C2×C4×D3—181no—
387C2×C4×D3—361no—
388C3×C4⋊C4—31no—
389C3×C4⋊C4—31no—
390C3×C4⋊C4—61no—
391C3×C4⋊C4—91no—
392C3×C22⋊C4—92no—
393C3×C22⋊C4—92no—
394C3×C22⋊C4—92no—
395C3×C42—31no—
396C3×C42—31no—
397C3×C42—61no—
398C3×C42—91no—
399#217—32no—
400#217—32no—
401#217—92no—
402(C2×D3)⋊C4—32no—
403(C2×D3)⋊C4—32no—
404(C2×D3)⋊C4—32no—
405(C2×D3)⋊C4—32no—
406(C2×D3)⋊C4—91no—
407(C2×D3)⋊C4—91no—
408(C2×D3)⋊C4—91no—
409(C2×D3)⋊C4—91no—
410(C2×D3)⋊C4—92no—
411(C2×D3)⋊C4—92no—
412(C2×D3)⋊C4—92no—
413(C2×D3)⋊C4—92no—
414(C2×D3)⋊C4—91no—
415(C2×D3)⋊C4—91no—
416(C2×D3)⋊C4—92no—
417(C2×D3)⋊C4—181no—
418(C2×D3)⋊C4—181no—
419(C2×D3)⋊C4—182no—
420C4⋊Dic3—31no—
421C4⋊Dic3—31no—
422C4⋊Dic3—61no—
423C4⋊Dic3D3211yescharacteristic, complemented
424Dic3⋊C4—91no—
425Dic3⋊C4—91no—
426Dic3⋊C4—91no—
427Dic3⋊C4—91no—
428Dic3⋊C4—91no—
429Dic3⋊C4—91no—
430Dic3⋊C4—181no—
431Dic3⋊C4—181no—
432C4×Dic3—31no—
433C4×Dic3—31no—
434C4×Dic3—61no—
435C4×Dic3—92no—
436C4×Dic3—92no—
437C4×Dic3—92no—
438C4×Dic3—182no—
439C4×Dic3D3211yescharacteristic, complemented
440C22×C32—21no—
441C22×C32—21no—
442C22×C32—21no—
443C22×C32—34no—
444C22×C32—41no—
445C22×C32—62no—
446C22×C32—62no—
447C22×C32C23×D311yescharacteristic
448C22×C32C23×D311yescharacteristic
449C22×C32C23×D311yescharacteristic
450C2×C3⋊D3—22no—
451C2×C3⋊D3—22no—
452C2×C3⋊D3—32no—
453C2×C3⋊D3—32no—
454C2×C3⋊D3—32no—
455C2×C3⋊D3—62no—
456C2×C3⋊D3—62no—
457C2×C3⋊D3—62no—
458C2×C3⋊D3—61no—
459C2×C3⋊D3—61no—
460C2×C3⋊D3—62no—
461C2×C3⋊D3—62no—
462C2×C3⋊D3—61no—
463C2×C3⋊D3—61no—
464C2×C3⋊D3—61no—
465C2×C3⋊D3—61no—
466C2×C3⋊D3—122no—
467C2×C3⋊D3—121no—
468C2×C3⋊D3—121no—
469C2×C3⋊D3—121no—
470C2×C3⋊D3—121no—
471C2×C3⋊D3—122no—
472C2×C3⋊D3—122no—
473C2×C3⋊D3—128no—
474C2×C3⋊D3C2×C4×D314yes—
475C2×C3×D3—22no—
476C2×C3×D3—22no—
477C2×C3×D3—22no—
478C2×C3×D3—22no—
479C2×C3×D3—24no—
480C2×C3×D3—34no—
481C2×C3×D3—34no—
482C2×C3×D3—42no—
483C2×C3×D3—42no—
484C2×C3×D3—64no—
485C2×C3×D3—62no—
486C2×C3×D3—62no—
487C2×C3×D3—62no—
488C2×C3×D3—62no—
489C2×C3×D3—122no—
490C2×C3×D3—122no—
491C2×C3×D3C2×C4×D314yes—
492C2×C3×D3C2×C4×D314yes—
493D32—128no—
494D32—128no—
495D32—1216no—
496C32×C4—22no—
497C32×C4—22no—
498C32×C4—22no—
499C32×C4—42no—
500C32×C4—61no—
501C32×C4—62no—
502C32×C4—61no—
503C32×C4C2×C4×D312yes—
504C32×C4C2×C4×D312yes—
505C32×C4C2×C4×D312yes—
506C3⋊Dic3—21no—
507C3⋊Dic3—22no—
508C3⋊Dic3—21no—
509C3⋊Dic3—32no—
510C3⋊Dic3—32no—
511C3⋊Dic3—32no—
512C3⋊Dic3—62no—
513C3⋊Dic3—62no—
514C3⋊Dic3—62no—
515C3⋊Dic3—122no—
516C3×Dic3—21no—
517C3×Dic3—22no—
518C3×Dic3—21no—
519C3×Dic3—22no—
520C3×Dic3—21no—
521C3×Dic3—21no—
522C3×Dic3—41no—
523C3×Dic3—41no—
524C3×Dic3—42no—
525C3×Dic3—61no—
526C3×Dic3—61no—
527C3×Dic3—62no—
528C3×Dic3—61no—
529C3×Dic3—62no—
530C3×Dic3—61no—
531C3×Dic3—121no—
532C3×Dic3—121no—
533C3×Dic3—122no—
534C22×D4—271no—
535C4×D4—91no—
536C4×D4—91no—
537C4×D4—91no—
538C4×D4—271no—
539C4×D4—272no—
540C4×D4—272no—
541#117—271no—
542#117—271no—
543C2×C22⋊C4—272no—
544C2×C22⋊C4—272no—
545C33#51811yescharacteristic, complemented, Sylow
546C23×C3—32no—
547C23×C3—32no—
548C23×C3—62no—
549C23×C3—92no—
550C22×D3—32no—
551C22×D3—32no—
552C22×D3—62no—
553C22×D3—98no—
554C22×D3—98no—
555C22×D3—91no—
556C22×D3—91no—
557C22×D3—91no—
558C22×D3—98no—
559C22×D3—188no—
560C22×D3—181no—
561C22×D3—181no—
562C22×D3—181no—
563C22×D3—361no—
564C22×D3—362no—
565C22×D3—362no—
566C22×D3—362no—
567C22×D3—362no—
568C22×D3—362no—
569C22×D3—362no—
570C22×D3—364no—
571C22×D3—364no—
572C22×D3C2×D3212yes—
573C3×D4—34no—
574C3×D4—34no—
575C3×D4—64no—
576C3×D4—94no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—32no—
581C2×C3×C4—32no—
582C2×C3×C4—31no—
583C2×C3×C4—31no—
584C2×C3×C4—31no—
585C2×C3×C4—31no—
586C2×C3×C4—41no—
587C2×C3×C4—62no—
588C2×C3×C4—61no—
589C2×C3×C4—61no—
590C2×C3×C4—92no—
591C2×C3×C4—91no—
592C2×C3×C4—91no—
593C2×C3×C4—362no—
594C2×C3×C4—362no—
595C2×C3×C4—362no—
596C2×C3×C4C2×D3211yescharacteristic
597C2×C3×C4C2×D3211yescharacteristic
598C2×C3×C4C2×D3211yescharacteristic
599#67—98no—
600#67—98no—
601#67—98no—
602#67—188no—
603C2×Dic3—31no—
604C2×Dic3—31no—
605C2×Dic3—31no—
606C2×Dic3—31no—
607C2×Dic3—32no—
608C2×Dic3—32no—
609C2×Dic3—61no—
610C2×Dic3—61no—
611C2×Dic3—62no—
612C2×Dic3—91no—
613C2×Dic3—91no—
614C2×Dic3—91no—
615C2×Dic3—122no—
616C2×Dic3—122no—
617C2×Dic3—181no—
618C2×Dic3—181no—
619C2×Dic3—181no—
620C2×Dic3—361no—
621C2×Dic3—362no—
622C2×Dic3C2×D3212yes—
623C2×Dic3C2×D3211yescharacteristic
624C2×Dic3C2×D3211yescharacteristic
625D12—34no—
626D12—34no—
627D12—64no—
628D12#62414yescomplemented
629C4×D3—94no—
630C4×D3—94no—
631C4×D3—94no—
632C4×D3—122no—
633C4×D3—122no—
634C4×D3—122no—
635C4×D3—122no—
636C4×D3—184no—
637C4×D3—184no—
638C4×D3—184no—
639C4×D3—364no—
640C4×D3—362no—
641C4×D3—362no—
642C2×C32—21no—
643C2×C32—21no—
644C2×C32—21no—
645C2×C32—21no—
646C2×C32—21no—
647C2×C32—21no—
648C2×C32—21no—
649C2×C32—21no—
650C2×C32—21no—
651C2×C32—41no—
652C2×C32—41no—
653C2×C32—41no—
654C2×C32—64no—
655C2×C32C22×C4×D311yescharacteristic
656C2×C32C22×C4×D311yescharacteristic
657C2×C32C22×C4×D311yescharacteristic
658C2×C32#100411yescharacteristic
659C2×C32#100411yescharacteristic
660C2×C32#100411yescharacteristic
661C2×C32#100911yescharacteristic
662C2×C32#100911yescharacteristic
663C2×C32#100911yescharacteristic
664C3⋊D3—24no—
665C3⋊D3—62no—
666C3⋊D3—64no—
667C3⋊D3—62no—
668C3⋊D3—62no—
669C3⋊D3—122no—
670C3⋊D3—122no—
671C3⋊D3—124no—
672C3×D3—24no—
673C3×D3—24no—
674C3×D3—44no—
675C3×D3—64no—
676C3×D3—64no—
677C3×D3—124no—
678C24—272no—
679C2×D4—31no—
680C2×D4—91no—
681C2×D4—278no—
682C2×D4—272no—
683C22×C4—92no—
684C22×C4—92no—
685C22×C4—92no—
686C22×C4—272no—
687C22×C4—271no—
688C4⋊C4—31no—
689C4⋊C4—91no—
690C4⋊C4—271no—
691C4⋊C4—271no—
692C22⋊C4—92no—
693C22⋊C4—92no—
694C22⋊C4—92no—
695C22⋊C4—271no—
696C22⋊C4—271no—
697C22⋊C4—272no—
698C22⋊C4—272no—
699C42—31no—
700C42—91no—
701C42—272no—
702C22×C3—21no—
703C22×C3—21no—
704C22×C3—21no—
705C22×C3—34no—
706C22×C3—34no—
707C22×C3—41no—
708C22×C3—64no—
709C22×C3—62no—
710C22×C3—62no—
711C22×C3—62no—
712C22×C3—62no—
713C22×C3—94no—
714C22×C3—122no—
715C22×C3—122no—
716C22×C3—182no—
717C22×C3—182no—
718C22×C3C22×D3211yescharacteristic
719C22×C3C22×D3211yescharacteristic
720C22×C3C22×D3211yescharacteristic
721C2×D3—22no—
722C2×D3—22no—
723C2×D3—34no—
724C2×D3—34no—
725C2×D3—64no—
726C2×D3—62no—
727C2×D3—62no—
728C2×D3—62no—
729C2×D3—62no—
730C2×D3—92no—
731C2×D3—92no—
732C2×D3—92no—
733C2×D3—122no—
734C2×D3—122no—
735C2×D3—182no—
736C2×D3—182no—
737C2×D3—182no—
738C2×D3—182no—
739C2×D3—182no—
740C2×D3—181no—
741C2×D3—181no—
742C2×D3—181no—
743C2×D3—181no—
744C2×D3—181no—
745C2×D3—181no—
746C2×D3—362no—
747C2×D3—361no—
748C2×D3—361no—
749C2×D3—361no—
750C2×D3—361no—
751C2×D3—362no—
752C2×D3—362no—
753C2×D3—368no—
754C2×D3—368no—
755C2×D3—368no—
756C2×D3—3616no—
757C2×D3C2×#62414yes—
758C3×C4—22no—
759C3×C4—22no—
760C3×C4—22no—
761C3×C4—42no—
762C3×C4—62no—
763C3×C4—61no—
764C3×C4—61no—
765C3×C4—62no—
766C3×C4—61no—
767C3×C4—61no—
768C3×C4—121no—
769C3×C4—122no—
770C3×C4—121no—
771C3×C4—181no—
772C3×C4—181no—
773C3×C4—182no—
774C3×C4C4×D3212yes—
775C3×C4C4×D3212yes—
776C3×C4C2×#62412yes—
777Dic3—21no—
778Dic3—21no—
779Dic3—22no—
780Dic3—62no—
781Dic3—61no—
782Dic3—61no—
783Dic3—62no—
784Dic3—61no—
785Dic3—61no—
786Dic3—92no—
787Dic3—92no—
788Dic3—92no—
789Dic3—121no—
790Dic3—122no—
791Dic3—121no—
792Dic3—182no—
793Dic3—182no—
794Dic3—182no—
795Dic3—362no—
796C32—21no—
797C32—21no—
798C32—21no—
799C32—41no—
800C32#554511yescharacteristic, complemented
801C32#554511yescharacteristic, complemented
802C32#554511yescharacteristic, complemented
803C23—32no—
804C23—92no—
805C23—278no—
806C23—271no—
807C23—1082no—
808C23—1082no—
809D4—34no—
810D4—94no—
811D4—278no—
812C2×C4—31no—
813C2×C4—31no—
814C2×C4—32no—
815C2×C4—91no—
816C2×C4—91no—
817C2×C4—92no—
818C2×C4—271no—
819C2×C4—274no—
820C2×C4—362no—
821C2×C4—362no—
822C2×C4—362no—
823C2×C4—1082no—
824C2×C4D3311yescharacteristic
825C2×C3—21no—
826C2×C3—21no—
827C2×C3—21no—
828C2×C3—21no—
829C2×C3—21no—
830C2×C3—21no—
831C2×C3—21no—
832C2×C3—21no—
833C2×C3—21no—
834C2×C3—41no—
835C2×C3—41no—
836C2×C3—41no—
837C2×C3—64no—
838C2×C3—64no—
839C2×C3—124no—
840C2×C3—184no—
841C2×C3C2×C4×D3211yescharacteristic
842C2×C3C2×C4×D3211yescharacteristic
843C2×C3#6430711yescharacteristic
844C2×C3#6430711yescharacteristic
845C2×C3#6431311yescharacteristic
846C2×C3#6431411yescharacteristic
847C2×C3#6431411yescharacteristic
848C2×C3#6432011yescharacteristic
849C2×C3C22×#62411yescharacteristic
850D3—24no—
851D3—64no—
852D3—64no—
853D3—124no—
854D3—184no—
855D3—182no—
856D3—182no—
857D3—182no—
858D3—362no—
859D3—362no—
860D3—364no—
861C22—34no—
862C22—62no—
863C22—62no—
864C22—94no—
865C22—182no—
866C22—182no—
867C22—272no—
868C22—541no—
869C22—541no—
870C22—1088no—
871C22C2×D3311yescharacteristic
872C4—61no—
873C4—62no—
874C4—61no—
875C4—181no—
876C4—182no—
877C4—181no—
878C4—272no—
879C4D3×#62412yes—
880C3—21no—
881C3—21no—
882C3—21no—
883C3—41no—
884C3#1059399611yescharacteristic, complemented
885C3#1059460611yescharacteristic, complemented
886C3#1059522311yescharacteristic, complemented
887C2—64no—
888C2—184no—
889C2—542no—
890C2#1172438111yescharacteristic
891C2#1172438511yescharacteristic
892C2C2×D3×#62411yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutatorC2×C33C23×C4
FittingC2×C33×C4C23
socle, cosocleC22×C33C24
prime radicalC2×#89026C2
hypercenterC2×C4D33
hypocenterC33#518
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. #11723691C2semidirect
3. #11723452C2semidirect
4. #11723413C2semidirect
5. C3×#63898C2semidirect
6. C3×#63894C2semidirect
7. C3×Dic3×D12C2semidirect
8. #11722936C2semidirect
9. #11722930C2semidirect
10. #11722904C2semidirect
11. D3×#3722C2semidirect
19. C2×#6294C22semidirect
21. #89026C4semidirect
22. C2×C3×#624C22semidirect
23. C2×C3×D3×Dic3C22semidirect
24. C2×C3×D3×Dic3C22semidirect
25. C3×C4⋊(C3⋊Dic3)C22semidirect
26. C3×C4×C3⋊Dic3C22semidirect
27. C32×C4⋊Dic3C22semidirect
28. C32×C4×Dic3C22semidirect
29. #88814C22semidirect
30. #88806C22semidirect
31. #88806C22semidirect
35. Dic3×C3⋊Dic3C22semidirect
36. C3×#3722C22semidirect
37. C3×(C2×D3)⋊Dic3C22semidirect
38. C3×(C2×D3)⋊Dic3C22semidirect
62. #63898D3semidirect
64. #63894D3semidirect
66. Dic3×D12D3semidirect
80. C2×D3×C3⋊D3C2×C4semidirect
83. C4×C3⋊(C3⋊D3)C2×C4semidirect
87. C3×C4⋊(C3⋊D3)C2×C4semidirect
91. C32×D12C2×C4semidirect
93. #6290C2×C4semidirect
131. C2×#624C2×D3semidirect
134. C2×D3×Dic3C2×D3semidirect
135. C2×D3×Dic3C2×D3semidirect
144. C4⋊(C3⋊Dic3)C2×D3semidirect
148. C4×C3⋊Dic3C2×D3semidirect
159. C3×C4⋊Dic3C2×D3semidirect
160. C3×C4⋊Dic3C2×D3semidirect
165. C3×C4×Dic3C2×D3semidirect
166. C3×C4×Dic3C2×D3semidirect
183. #3722C2×D3semidirect
186. (C2×D3)⋊Dic3C2×D3semidirect
187. (C2×D3)⋊Dic3C2×D3semidirect
295. C4⋊(C3⋊D3)C4×D3semidirect
327. C3×D12C4×D3semidirect
328. C3×D12C4×D3semidirect
423. C4⋊Dic3D32semidirect
439. C4×Dic3D32semidirect
545. C33#518semidirect
628. D12#624semidirect
800. C32#5545semidirect
801. C32#5545semidirect
802. C32#5545semidirect
884. C3#10593996semidirect
885. C3#10594606semidirect
886. C3#10595223semidirect

Maximal subgroups

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

subgroupindex
C2×#890262
#117236912
#117234522
#117234132
C3×#638982
C3×#638942
C3×Dic3×D122
#117229362
#117229302
#117229042
D3×#37222
#105952233
#105946063
#105939963