Finite Group Databasebeta

← D3×#41×C3⋊D3 #13181636

Subgroups — D3×#41×C3⋊D3 #13181636

Order 1728.

5996 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×C3⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
2C3×#41×C3⋊D3C211yesmaximal, characteristic, complemented
3C32×D3×#41C211yesmaximal, characteristic, complemented
4#11724596C211yesmaximal, characteristic, complemented
5C3⋊D3×#239C211yesmaximal, characteristic, complemented
6D3×#3832C211yesmaximal, characteristic, complemented
7D3×Q8×C3⋊D3C211yesmaximal, characteristic, complemented
8#11724586C213yesmaximal, complemented
9C3⋊D3×#237C213yesmaximal, complemented
10D3×#3830C213yesmaximal, complemented
11D3×D4×C3⋊D3C213yesmaximal, complemented
12#11724578C213yesmaximal, complemented
13C3⋊D3×#235C213yesmaximal, complemented
14D3×#3828C213yesmaximal, complemented
15C2×C4×D3×C3⋊D3C213yesmaximal, complemented
16C2×#41×C3⋊D3—31nomaximal
17D32×#41—34nomaximal
18C22×D3×C3⋊D3C2213yes—
19C33×#41C2211yescharacteristic, complemented
20#89080C2211yescharacteristic, complemented
21Q8×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
22#89078C2213yescomplemented
23D4×C3⋊(C3⋊D3)C2213yescomplemented
24#89076C2213yescomplemented
25C2×C4×C3⋊(C3⋊D3)C2213yescomplemented
26C3×#3832C2211yescharacteristic, complemented
27C3×Q8×C3⋊D3C2211yescharacteristic, complemented
28C3×#3830C2213yescomplemented
29C3×D4×C3⋊D3C2213yescomplemented
30C3×#3828C2213yescomplemented
31C2×C3×C4×C3⋊D3C2213yescomplemented
32C32×#239C2211yescharacteristic, complemented
33C32×D3×Q8C2211yescharacteristic, complemented
34C32×#237C2213yescomplemented
35C32×D3×D4C2213yescomplemented
36C32×#235C2213yescomplemented
37C2×C32×C4×D3C2213yescomplemented
38#89039C2216yescomplemented
39C3⋊D3×#67C2216yescomplemented
40D3×#638C2216yescomplemented
41C2×#6289C2213yescomplemented
42#89031C2216yescomplemented
43C2×Dic3×C3⋊D3C2213yescomplemented
44#89029C2216yescomplemented
45#89028C2216yescomplemented
46C2×D3×C3⋊Dic3C2213yescomplemented
47#89026C2213yescomplemented
48C3⋊D3×D12C2213yescomplemented
49D3×C4⋊(C3⋊D3)C2213yescomplemented
50C4×D3×C3⋊D3C2211yescharacteristic
51C4×D3×C3⋊D3C2213yes—
52C4×D3×C3⋊D3C2213yescomplemented
53C4×D3×C3⋊D3C2213yescomplemented
54C4×D3×C3⋊D3C2213yescomplemented
55C4×D3×C3⋊D3C2213yescomplemented
56C4×D3×C3⋊D3C2213yescomplemented
57C4×D3×C3⋊D3C2213yescomplemented
58#89022C2213yescomplemented
59#89021C2213yescomplemented
60#89020C2216yescomplemented
61#89019C2213yescomplemented
62#89018C2213yescomplemented
63#89017C2213yescomplemented
64C3⋊D3×Dic6C2213yescomplemented
65#89015C2213yescomplemented
66#89014C2213yescomplemented
67D3×#634C2213yescomplemented
68C2×C32×#41—31no—
69#41×C3⋊D3—31no—
70#41×C3⋊D3—31no—
71#41×C3⋊D3—31no—
72#41×C3⋊D3—33no—
73#41×C3⋊D3—33no—
74#41×C3⋊D3—33no—
75#41×C3⋊D3—33no—
76#41×C3⋊D3—34no—
77#41×C3⋊D3—64no—
78#41×C3⋊D3D311yescharacteristic, direct product factor
79C2×#3832—31no—
80C2×Q8×C3⋊D3—31no—
81C2×#3830—33no—
82C2×D4×C3⋊D3—33no—
83C2×#3828—33no—
84C22×C4×C3⋊D3—33no—
85C3×D3×#41—34no—
86C3×D3×#41D314yescomplemented
87#64319—34no—
88D3×#239—34no—
89D3×#239—34no—
90D32×Q8—34no—
91#64312—312no—
92D3×#237—312no—
93D3×#237—312no—
94D32×D4—312no—
95#64306—312no—
96D3×#235—312no—
97D3×#235—312no—
98C2×C4×D32—312no—
99C22×C3⋊(C3⋊D3)C2313yes—
100C22×C3×C3⋊D3C2313yes—
101C22×C32×D3C2313yes—
102C2×D3×C3⋊D3—212no—
103C2×D3×C3⋊D3C2313yes—
104C2×D3×C3⋊D3C2313yes—
105C2×D3×C3⋊D3C2313yes—
106C2×D3×C3⋊D3C2311yescharacteristic
107C33×Q8C2311yescharacteristic, complemented
108C33×D4C2313yescomplemented
109C2×C33×C4C2313yescomplemented
110#6312C2316yescomplemented
111C2×C3⋊(C3⋊Dic3)C2313yescomplemented
112C4⋊(C3⋊(C3⋊D3))C2313yescomplemented
113C4×C3⋊(C3⋊D3)C2313yes—
114C4×C3⋊(C3⋊D3)C2311yescharacteristic
115C4×C3⋊(C3⋊D3)C2313yescomplemented
116C4×C3⋊(C3⋊D3)C2313yescomplemented
117#6308C2313yescomplemented
118C3×#638C2316yescomplemented
119C2×C3×C3⋊Dic3C2313yescomplemented
120C3×C4⋊(C3⋊D3)C2313yescomplemented
121C3×C4×C3⋊D3C2313yes—
122C3×C4×C3⋊D3C2311yescharacteristic
123C3×C4×C3⋊D3C2313yescomplemented
124C3×C4×C3⋊D3C2313yescomplemented
125C3×#634C2313yescomplemented
126C32×#67C2316yescomplemented
127C2×C32×Dic3C2313yescomplemented
128C32×D12C2313yescomplemented
129C32×C4×D3C2313yes—
130C32×C4×D3C2311yescharacteristic
131C32×C4×D3C2313yescomplemented
132C32×C4×D3C2313yescomplemented
133C32×Dic6C2313yescomplemented
134#6293C2316yescomplemented
135#6292C2316yescomplemented
136#6291C2316yescomplemented
137#6290C2316yescomplemented
138#6289C2313yes—
139#6289C2311yescharacteristic
140#6289C2313yescomplemented
141#6289C2313yescomplemented
142Dic3×C3⋊D3C2313yes—
143Dic3×C3⋊D3C2311yescharacteristic
144Dic3×C3⋊D3C2313yescomplemented
145Dic3×C3⋊D3C2313yescomplemented
146D3×C3⋊Dic3C2313yes—
147D3×C3⋊Dic3C2311yescharacteristic
148D3×C3⋊Dic3C2313yescomplemented
149D3×C3⋊Dic3C2313yescomplemented
150C2×D3×#41—94no—
151C2×D3×#41—91no—
152C23×C3⋊D3—33no—
153C22×D32—312no—
154C32×#41—24no—
155C32×#41—31no—
156C32×#41—33no—
157C32×#41—33no—
158C32×#41C2×D314yescomplemented
159C32×#41C2×D311yescharacteristic, complemented
160C2×C32×Q8—31no—
161C2×C32×D4—33no—
162C22×C32×C4—33no—
163C2×#638—36no—
164C22×C3⋊Dic3—33no—
165#3832—31no—
166#3832—34no—
167#3832—33no—
168#3832—33no—
169#3832—64no—
170#3832C2×D311yescharacteristic, complemented
171Q8×C3⋊D3—31no—
172Q8×C3⋊D3—34no—
173Q8×C3⋊D3—33no—
174Q8×C3⋊D3—33no—
175Q8×C3⋊D3—64no—
176Q8×C3⋊D3C2×D311yescharacteristic, complemented
177#3830—33no—
178#3830—312no—
179#3830—36no—
180#3830—36no—
181#3830—33no—
182#3830—33no—
183#3830—612no—
184#3830C2×D313yescomplemented
185D4×C3⋊D3—36no—
186D4×C3⋊D3—33no—
187D4×C3⋊D3—312no—
188D4×C3⋊D3—36no—
189D4×C3⋊D3—33no—
190D4×C3⋊D3—33no—
191D4×C3⋊D3—612no—
192D4×C3⋊D3C2×D313yescomplemented
193#3828—33no—
194#3828—312no—
195#3828—36no—
196#3828—33no—
197#3828—36no—
198#3828—33no—
199#3828—612no—
200#3828C2×D313yescomplemented
201C2×C4⋊(C3⋊D3)—33no—
202C2×C4×C3⋊D3—33no—
203C2×C4×C3⋊D3—33no—
204C2×C4×C3⋊D3—312no—
205C2×C4×C3⋊D3—33no—
206C2×C4×C3⋊D3—31no—
207C2×C4×C3⋊D3—33no—
208C2×C4×C3⋊D3—33no—
209C2×C4×C3⋊D3—33no—
210C2×C4×C3⋊D3—33no—
211C2×C4×C3⋊D3—33no—
212C2×C4×C3⋊D3—33no—
213C2×C4×C3⋊D3—33no—
214C2×C4×C3⋊D3—612no—
215C2×C4×C3⋊D3C2×D313yescomplemented
216C2×#634—33no—
217C3×#239—34no—
218C3×#239C2×D314yescomplemented
219C3×D3×Q8—34no—
220C3×D3×Q8C2×D314yescomplemented
221C3×#237—312no—
222C3×#237C2×D3112yescomplemented
223C3×D3×D4—312no—
224C3×D3×D4C2×D3112yescomplemented
225C3×#235—312no—
226C3×#235C2×D3112yescomplemented
227C2×C3×C4×D3—312no—
228C2×C3×C4×D3C2×D3112yescomplemented
229#3811—324no—
230D3×#67—324no—
231D3×#67—324no—
232C2×#624—312no—
233#3805—324no—
234#3804—324no—
235#3804—324no—
236C2×D3×Dic3—312no—
237C2×D3×Dic3—312no—
238#3802—312no—
239D3×D12—312no—
240D3×D12—312no—
241C4×D32—34no—
242C4×D32—312no—
243C4×D32—312no—
244C4×D32—312no—
245C4×D32—312no—
246C4×D32—312no—
247C4×D32—312no—
248C4×D32—312no—
249#3799—312no—
250#3799—312no—
251#3798—324no—
252#3797—312no—
253#3796—312no—
254#3796—312no—
255#3795—312no—
256#3795—312no—
257D3×Dic6—312no—
258D3×Dic6—312no—
259C22×C33C2413yes—
260C2×C3⋊(C3⋊D3)—26no—
261C2×C3⋊(C3⋊D3)C2413yes—
262C2×C3⋊(C3⋊D3)C2411yescharacteristic
263C2×C3×C3⋊D3—26no—
264C2×C3×C3⋊D3C2413yes—
265C2×C3×C3⋊D3C2411yescharacteristic
266C2×C32×D3—26no—
267C2×C32×D3C2413yes—
268C2×C32×D3C2411yescharacteristic
269D3×C3⋊D3—26no—
270D3×C3⋊D3—26no—
271D3×C3⋊D3—26no—
272D3×C3⋊D3#4114yesdirect product factor
273C33×C4C2413yes—
274C33×C4C2411yescharacteristic
275C3⋊(C3⋊Dic3)C2411yescharacteristic
276C3⋊(C3⋊Dic3)C2413yes—
277C3×C3⋊Dic3C2411yescharacteristic
278C3×C3⋊Dic3C2413yes—
279C32×Dic3C2411yescharacteristic
280C32×Dic3C2413yes—
281C2×C3×#41—34no—
282C2×C3×#41—91no—
283D3×#41—34no—
284D3×#41—912no—
285D3×#41—912no—
286D3×#41—912no—
287D3×#41—912no—
288D3×#41—94no—
289D3×#41—94no—
290D3×#41—94no—
291D3×#41—91no—
292D3×#41—91no—
293D3×#41—91no—
294D3×#41—93no—
295D3×#41—93no—
296D3×#41—93no—
297D3×#41—93no—
298D3×#41—184no—
299D3×#41C3⋊D311yescharacteristic, direct product factor
300C2×#239—94no—
301C2×#239—91no—
302C2×D3×Q8—94no—
303C2×D3×Q8—91no—
304C2×#237—912no—
305C2×#237—93no—
306C2×D3×D4—912no—
307C2×D3×D4—93no—
308C2×#235—912no—
309C2×#235—93no—
310C22×C4×D3—912no—
311C22×C4×D3—93no—
312C23×C32—33no—
313C22×C3⋊D3—31no—
314C22×C3⋊D3—33no—
315C22×C3⋊D3—33no—
316C22×C3⋊D3—33no—
317C22×C3⋊D3—33no—
318C22×C3⋊D3—312no—
319C22×C3⋊D3—612no—
320C22×C3⋊D3—612no—
321C22×C3⋊D3C22×D313yes—
322C22×C3×D3—312no—
323C22×C3×D3C22×D3112yes—
324C2×D32—34no—
325C2×D32—312no—
326C2×D32—312no—
327C2×D32—312no—
328C2×D32—648no—
329C32×Q8—24no—
330C32×Q8—33no—
331C32×Q8C22×D314yescomplemented
332C32×Q8C22×D311yescharacteristic, complemented
333C32×D4—212no—
334C32×D4—36no—
335C32×D4—33no—
336C32×D4C22×D3112yescomplemented
337C32×D4C22×D313yescomplemented
338C2×C32×C4—212no—
339C2×C32×C4—33no—
340C2×C32×C4—33no—
341C2×C32×C4—31no—
342C2×C32×C4—33no—
343C2×C32×C4—33no—
344C2×C32×C4C22×D3112yescomplemented
345C2×C32×C4C22×D313yescomplemented
346#638—36no—
347#638—36no—
348#638—36no—
349#638—324no—
350#638—624no—
351#638C22×D316yescomplemented
352C2×C3⋊Dic3—33no—
353C2×C3⋊Dic3—33no—
354C2×C3⋊Dic3—31no—
355C2×C3⋊Dic3—33no—
356C2×C3⋊Dic3—33no—
357C2×C3⋊Dic3—312no—
358C2×C3⋊Dic3—612no—
359C2×C3⋊Dic3C22×D313yescomplemented
360C4⋊(C3⋊D3)—36no—
361C4⋊(C3⋊D3)—33no—
362C4⋊(C3⋊D3)—312no—
363C4⋊(C3⋊D3)—612no—
364C4⋊(C3⋊D3)C22×D313yescomplemented
365C4×C3⋊D3—31no—
366C4×C3⋊D3—33no—
367C4×C3⋊D3—33no—
368C4×C3⋊D3—33no—
369C4×C3⋊D3—31no—
370C4×C3⋊D3—33no—
371C4×C3⋊D3—33no—
372C4×C3⋊D3—33no—
373C4×C3⋊D3—31no—
374C4×C3⋊D3—33no—
375C4×C3⋊D3—33no—
376C4×C3⋊D3—33no—
377C4×C3⋊D3—312no—
378C4×C3⋊D3—34no—
379C4×C3⋊D3—312no—
380C4×C3⋊D3—312no—
381C4×C3⋊D3—64no—
382C4×C3⋊D3—612no—
383C4×C3⋊D3—612no—
384C4×C3⋊D3—612no—
385C4×C3⋊D3C22×D311yescharacteristic
386C4×C3⋊D3C22×D313yes—
387C4×C3⋊D3C22×D313yescomplemented
388C4×C3⋊D3C22×D313yescomplemented
389#634—33no—
390#634—36no—
391#634—312no—
392#634—612no—
393#634C22×D313yescomplemented
394C3×#67—324no—
395C3×#67C22×D3124yescomplemented
396C2×C3×Dic3—312no—
397C2×C3×Dic3C22×D3112yescomplemented
398C3×D12—312no—
399C3×D12C22×D3112yescomplemented
400C3×C4×D3—312no—
401C3×C4×D3—34no—
402C3×C4×D3—312no—
403C3×C4×D3—312no—
404C3×C4×D3C22×D3112yes—
405C3×C4×D3C22×D314yes—
406C3×C4×D3C22×D3112yescomplemented
407C3×C4×D3C22×D3112yescomplemented
408C3×Dic6—312no—
409C3×Dic6C22×D3112yescomplemented
410#627—324no—
411#626—324no—
412#626—324no—
413#625—324no—
414#624—312no—
415#624—34no—
416#624—312no—
417#624—312no—
418D3×Dic3—312no—
419D3×Dic3—34no—
420D3×Dic3—312no—
421D3×Dic3—312no—
422D3×Dic3—312no—
423D3×Dic3—34no—
424D3×Dic3—312no—
425D3×Dic3—312no—
426C22×#41—271noSylow
427C2×C33—23no—
428C2×C33C2511yescharacteristic
429C3⋊(C3⋊D3)—23no—
430C3⋊(C3⋊D3)C2×#4112yescomplemented
431C3×C3⋊D3—23no—
432C3×C3⋊D3C2×#4112yescomplemented
433C32×D3—23no—
434C32×D3C2×#4112yescomplemented
435C23×D3—912no—
436C23×D3—93no—
437C3×#41—24no—
438C3×#41—34no—
439C3×#41—312no—
440C3×#41—312no—
441C3×#41—91no—
442C3×#41—93no—
443C3×#41—93no—
444C3×#41D3214yescomplemented
445C3×#41C2×C3⋊D311yescharacteristic, complemented
446C2×C3×Q8—34no—
447C2×C3×Q8—91no—
448C2×C3×D4—312no—
449C2×C3×D4—93no—
450C22×C3×C4—312no—
451C22×C3×C4—93no—
452C2×#67—924no—
453C2×#67—96no—
454C22×Dic3—912no—
455C22×Dic3—93no—
456#239—34no—
457#239—912no—
458#239—912no—
459#239—94no—
460#239—91no—
461#239—93no—
462#239—93no—
463#239—184no—
464#239C2×C3⋊D311yescharacteristic, complemented
465D3×Q8—34no—
466D3×Q8—912no—
467D3×Q8—912no—
468D3×Q8—94no—
469D3×Q8—91no—
470D3×Q8—93no—
471D3×Q8—93no—
472D3×Q8—184no—
473D3×Q8C2×C3⋊D311yescharacteristic, complemented
474#237—312no—
475#237—912no—
476#237—912no—
477#237—924no—
478#237—924no—
479#237—912no—
480#237—93no—
481#237—96no—
482#237—96no—
483#237—93no—
484#237—93no—
485#237—1812no—
486#237C2×C3⋊D313yescomplemented
487D3×D4—312no—
488D3×D4—912no—
489D3×D4—912no—
490D3×D4—924no—
491D3×D4—924no—
492D3×D4—96no—
493D3×D4—912no—
494D3×D4—93no—
495D3×D4—96no—
496D3×D4—93no—
497D3×D4—93no—
498D3×D4—1812no—
499D3×D4C2×C3⋊D313yescomplemented
500#235—312no—
501#235—912no—
502#235—924no—
503#235—912no—
504#235—924no—
505#235—912no—
506#235—93no—
507#235—96no—
508#235—93no—
509#235—96no—
510#235—93no—
511#235—1812no—
512#235C2×C3⋊D313yescomplemented
513C2×D12—912no—
514C2×D12—93no—
515C2×C4×D3—312no—
516C2×C4×D3—94no—
517C2×C4×D3—912no—
518C2×C4×D3—912no—
519C2×C4×D3—912no—
520C2×C4×D3—912no—
521C2×C4×D3—912no—
522C2×C4×D3—912no—
523C2×C4×D3—912no—
524C2×C4×D3—912no—
525C2×C4×D3—912no—
526C2×C4×D3—93no—
527C2×C4×D3—912no—
528C2×C4×D3—93no—
529C2×C4×D3—93no—
530C2×C4×D3—91no—
531C2×C4×D3—93no—
532C2×C4×D3—93no—
533C2×C4×D3—93no—
534C2×C4×D3—93no—
535C2×C4×D3—93no—
536C2×C4×D3—93no—
537C2×C4×D3—93no—
538C2×C4×D3—1812no—
539C2×C4×D3C2×C3⋊D313yescomplemented
540C2×Dic6—912no—
541C2×Dic6—93no—
542C22×C32—212no—
543C22×C32—31no—
544C22×C32—33no—
545C22×C32—66no—
546C22×C32C23×D3112yes—
547C22×C32C23×D313yes—
548C2×C3⋊D3—26no—
549C2×C3⋊D3—31no—
550C2×C3⋊D3—34no—
551C2×C3⋊D3—33no—
552C2×C3⋊D3—34no—
553C2×C3⋊D3—312no—
554C2×C3⋊D3—64no—
555C2×C3⋊D3—612no—
556C2×C3⋊D3—66no—
557C2×C3⋊D3—66no—
558C2×C3⋊D3—66no—
559C2×C3⋊D3—66no—
560C2×C3⋊D3—624no—
561C2×C3⋊D3—1224no—
562C2×C3⋊D3C23×D313yes—
563C2×C3⋊D3C23×D311yescharacteristic
564C2×C3×D3—224no—
565C2×C3×D3—34no—
566C2×C3×D3—312no—
567C2×C3×D3—624no—
568C2×C3×D3C23×D3112yes—
569C2×C3×D3C23×D314yes—
570D32—316no—
571D32—624no—
572D32—624no—
573D32—624no—
574C32×C4—212no—
575C32×C4—24no—
576C32×C4—33no—
577C32×C4—31no—
578C32×C4C23×D3112yes—
579C32×C4C23×D314yes—
580C32×C4C23×D313yes—
581C32×C4C23×D311yescharacteristic
582C3⋊Dic3—33no—
583C3⋊Dic3—31no—
584C3⋊Dic3—34no—
585C3⋊Dic3—312no—
586C3⋊Dic3—612no—
587C3⋊Dic3—64no—
588C3⋊Dic3C23×D313yes—
589C3⋊Dic3C23×D311yescharacteristic
590C3×Dic3—34no—
591C3×Dic3—312no—
592C3×Dic3C23×D314yes—
593C3×Dic3C23×D3112yes—
594C2×#41—31no—
595C2×#41—91no—
596C2×#41—273no—
597C2×#41—273no—
598C2×#41—273no—
599C2×#41—273no—
600C2×#41—271no—
601C2×#41—271no—
602C2×#41—271no—
603C2×#41—273no—
604C2×#41—273no—
605C2×#41—271no—
606C22×Q8—271no—
607C22×D4—273no—
608C23×C4—273no—
609C33C22×#4111yescharacteristic, complemented, Sylow
610C23×C3—312no—
611C23×C3—93no—
612C22×D3—312no—
613C22×D3—94no—
614C22×D3—912no—
615C22×D3—912no—
616C22×D3—912no—
617C22×D3—91no—
618C22×D3—912no—
619C22×D3—93no—
620C22×D3—93no—
621C22×D3—93no—
622C22×D3—93no—
623C22×D3—1812no—
624C22×D3—1812no—
625C22×D3—1848no—
626C22×D3C22×C3⋊D313yes—
627C3×Q8—24no—
628C3×Q8—312no—
629C3×Q8—93no—
630C3×Q8C2×D3214yescomplemented
631C3×Q8C22×C3⋊D311yescharacteristic, complemented
632C3×D4—212no—
633C3×D4—324no—
634C3×D4—312no—
635C3×D4—96no—
636C3×D4—93no—
637C3×D4C2×D32112yescomplemented
638C3×D4C22×C3⋊D313yescomplemented
639C2×C3×C4—212no—
640C2×C3×C4—312no—
641C2×C3×C4—312no—
642C2×C3×C4—34no—
643C2×C3×C4—312no—
644C2×C3×C4—312no—
645C2×C3×C4—93no—
646C2×C3×C4—93no—
647C2×C3×C4—91no—
648C2×C3×C4—93no—
649C2×C3×C4—93no—
650C2×C3×C4C2×D32112yescomplemented
651C2×C3×C4C22×C3⋊D313yescomplemented
652#67—324no—
653#67—924no—
654#67—924no—
655#67—924no—
656#67—96no—
657#67—96no—
658#67—96no—
659#67—1824no—
660#67C22×C3⋊D316yescomplemented
661C2×Dic3—312no—
662C2×Dic3—912no—
663C2×Dic3—94no—
664C2×Dic3—912no—
665C2×Dic3—912no—
666C2×Dic3—912no—
667C2×Dic3—93no—
668C2×Dic3—93no—
669C2×Dic3—91no—
670C2×Dic3—93no—
671C2×Dic3—93no—
672C2×Dic3—1812no—
673C2×Dic3C22×C3⋊D313yescomplemented
674D12—312no—
675D12—924no—
676D12—96no—
677D12—912no—
678D12—93no—
679D12—1812no—
680D12C22×C3⋊D313yescomplemented
681C4×D3—34no—
682C4×D3—312no—
683C4×D3—312no—
684C4×D3—312no—
685C4×D3—94no—
686C4×D3—912no—
687C4×D3—912no—
688C4×D3—912no—
689C4×D3—94no—
690C4×D3—912no—
691C4×D3—912no—
692C4×D3—912no—
693C4×D3—91no—
694C4×D3—93no—
695C4×D3—93no—
696C4×D3—93no—
697C4×D3—94no—
698C4×D3—912no—
699C4×D3—912no—
700C4×D3—912no—
701C4×D3—91no—
702C4×D3—93no—
703C4×D3—93no—
704C4×D3—93no—
705C4×D3—91no—
706C4×D3—93no—
707C4×D3—93no—
708C4×D3—93no—
709C4×D3—184no—
710C4×D3—1812no—
711C4×D3—1812no—
712C4×D3—1812no—
713C4×D3C22×C3⋊D311yescharacteristic
714C4×D3C22×C3⋊D313yes—
715C4×D3C22×C3⋊D313yescomplemented
716C4×D3C22×C3⋊D313yescomplemented
717Dic6—312no—
718Dic6—924no—
719Dic6—912no—
720Dic6—93no—
721Dic6—96no—
722Dic6—1812no—
723Dic6C22×C3⋊D313yescomplemented
724C2×C32—23no—
725C2×C32—24no—
726C2×C32—212no—
727C2×C32—32no—
728C2×C32—412no—
729C2×C32—63no—
730C2×C32C24×D314yes—
731C2×C32C24×D311yescharacteristic
732C3⋊D3—23no—
733C3⋊D3—32no—
734C3⋊D3—38no—
735C3⋊D3—68no—
736C3⋊D3—63no—
737C3⋊D3—612no—
738C3⋊D3—1212no—
739C3⋊D3D3×#4112yesdirect product factor
740C3×D3—212no—
741C3×D3—38no—
742C3×D3—612no—
743C3×D3D3×#4118yescomplemented
744C24—273no—
745#41—31no—
746#41—33no—
747#41—33no—
748#41—91no—
749#41—93no—
750#41—93no—
751#41—276no—
752#41—276no—
753#41—273no—
754#41—273no—
755#41—276no—
756#41—273no—
757#41—273no—
758#41—276no—
759#41—273no—
760#41—273no—
761#41—271no—
762#41—273no—
763#41—273no—
764#41D3×C3⋊D311yescharacteristic, direct product factor
765C2×Q8—31no—
766C2×Q8—91no—
767C2×Q8—273no—
768C2×Q8—273no—
769C2×Q8—273no—
770C2×Q8—271no—
771C2×D4—33no—
772C2×D4—93no—
773C2×D4—273no—
774C2×D4—273no—
775C2×D4—276no—
776C2×D4—273no—
777C2×D4—276no—
778C2×D4—276no—
779C2×D4—273no—
780C22×C4—33no—
781C22×C4—93no—
782C22×C4—271no—
783C22×C4—273no—
784C22×C4—273no—
785C22×C4—273no—
786C22×C4—273no—
787C22×C4—273no—
788C22×C4—273no—
789C22×C4—273no—
790C22×C4—273no—
791C22×C4—273no—
792C22×C4—273no—
793C22×C4—273no—
794C22×C3—212no—
795C22×C3—34no—
796C22×C3—312no—
797C22×C3—624no—
798C22×C3—91no—
799C22×C3—93no—
800C22×C3—186no—
801C22×C3C22×D32112yes—
802C22×C3C23×C3⋊D313yes—
803C2×D3—26no—
804C2×D3—34no—
805C2×D3—312no—
806C2×D3—624no—
807C2×D3—916no—
808C2×D3—94no—
809C2×D3—91no—
810C2×D3—94no—
811C2×D3—912no—
812C2×D3—93no—
813C2×D3—184no—
814C2×D3—1812no—
815C2×D3—186no—
816C2×D3—186no—
817C2×D3—1824no—
818C2×D3—1824no—
819C2×D3—1824no—
820C2×D3—186no—
821C2×D3—1824no—
822C2×D3—186no—
823C2×D3—3624no—
824C2×D3C23×C3⋊D313yes—
825C2×D3C23×C3⋊D311yescharacteristic
826C3×C4—212no—
827C3×C4—24no—
828C3×C4—312no—
829C3×C4—34no—
830C3×C4—93no—
831C3×C4—91no—
832C3×C4C22×D32112yes—
833C3×C4C22×D3214yes—
834C3×C4C23×C3⋊D313yes—
835C3×C4C23×C3⋊D311yescharacteristic
836Dic3—312no—
837Dic3—34no—
838Dic3—912no—
839Dic3—94no—
840Dic3—93no—
841Dic3—91no—
842Dic3—1812no—
843Dic3—184no—
844Dic3C23×C3⋊D313yes—
845Dic3C23×C3⋊D311yescharacteristic
846C32—24no—
847C32C2×D3×#4114yescomplemented
848C32C2×D3×#4111yescharacteristic, complemented
849C23—33no—
850C23—93no—
851C23—271no—
852C23—273no—
853C23—273no—
854C23—273no—
855C23—273no—
856C23—5412no—
857Q8—33no—
858Q8—93no—
859Q8—276no—
860Q8—273no—
861Q8C2×D3×C3⋊D311yescharacteristic, complemented
862D4—36no—
863D4—33no—
864D4—96no—
865D4—93no—
866D4—276no—
867D4—276no—
868D4—276no—
869D4—276no—
870D4—273no—
871D4C2×D3×C3⋊D313yescomplemented
872C2×C4—33no—
873C2×C4—33no—
874C2×C4—33no—
875C2×C4—31no—
876C2×C4—33no—
877C2×C4—93no—
878C2×C4—93no—
879C2×C4—93no—
880C2×C4—91no—
881C2×C4—93no—
882C2×C4—271no—
883C2×C4—273no—
884C2×C4—273no—
885C2×C4—273no—
886C2×C4—271no—
887C2×C4—273no—
888C2×C4—273no—
889C2×C4—273no—
890C2×C4—271no—
891C2×C4—273no—
892C2×C4—273no—
893C2×C4—273no—
894C2×C4—273no—
895C2×C4—273no—
896C2×C4—273no—
897C2×C4—271no—
898C2×C4—273no—
899C2×C4C2×D3×C3⋊D313yescomplemented
900C2×C3—212no—
901C2×C3—23no—
902C2×C3—24no—
903C2×C3—38no—
904C2×C3—412no—
905C2×C3—612no—
906C2×C3—92no—
907C2×C3—183no—
908C2×C3C23×D3214yes—
909C2×C3C24×C3⋊D311yescharacteristic
910D3—23no—
911D3—38no—
912D3—612no—
913D3—98no—
914D3—92no—
915D3—188no—
916D3—1812no—
917D3—183no—
918D3—3612no—
919D3#41×C3⋊D312yesdirect product factor
920C22—31no—
921C22—33no—
922C22—66no—
923C22—91no—
924C22—93no—
925C22—186no—
926C22—274no—
927C22—271no—
928C22—273no—
929C22—546no—
930C22—546no—
931C22—546no—
932C22—546no—
933C22C22×D3×C3⋊D313yes—
934C4—31no—
935C4—33no—
936C4—91no—
937C4—93no—
938C4—271no—
939C4—273no—
940C4C22×D3×C3⋊D313yes—
941C4C22×D3×C3⋊D311yescharacteristic
942C3—24no—
943C3D32×#4114yescomplemented
944C3C2×#41×C3⋊D311yescharacteristic, complemented
945C2—23no—
946C2—32no—
947C2—63no—
948C2—92no—
949C2—183no—
950C2—272no—
951C2—543no—
952C2C23×D3×C3⋊D311yescharacteristic
subgroupG/H
centerC4C22×D3×C3⋊D3
commutator, socle, cosocleC2×C33C25
FrattiniC2C23×D3×C3⋊D3
FittingC33×#41C22
hypercenter#41D3×C3⋊D3
hypocenterC33C22×#41
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C4 ◁ #41

Complements

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

NH ≅ G/Ntype
1. #41×C3⋊(C3⋊D3)C2semidirect
2. C3×#41×C3⋊D3C2semidirect
3. C32×D3×#41C2semidirect
4. #11724596C2semidirect
5. C3⋊D3×#239C2semidirect
6. D3×#3832C2semidirect
7. D3×Q8×C3⋊D3C2semidirect
8. #11724586C2semidirect
9. C3⋊D3×#237C2semidirect
10. D3×#3830C2semidirect
11. D3×D4×C3⋊D3C2semidirect
12. #11724578C2semidirect
13. C3⋊D3×#235C2semidirect
14. D3×#3828C2semidirect
15. C2×C4×D3×C3⋊D3C2semidirect
19. C33×#41C22semidirect
20. #89080C22semidirect
21. Q8×C3⋊(C3⋊D3)C22semidirect
22. #89078C22semidirect
23. D4×C3⋊(C3⋊D3)C22semidirect
24. #89076C22semidirect
25. C2×C4×C3⋊(C3⋊D3)C22semidirect
26. C3×#3832C22semidirect
27. C3×Q8×C3⋊D3C22semidirect
28. C3×#3830C22semidirect
29. C3×D4×C3⋊D3C22semidirect
30. C3×#3828C22semidirect
31. C2×C3×C4×C3⋊D3C22semidirect
32. C32×#239C22semidirect
33. C32×D3×Q8C22semidirect
34. C32×#237C22semidirect
35. C32×D3×D4C22semidirect
36. C32×#235C22semidirect
37. C2×C32×C4×D3C22semidirect
38. #89039C22semidirect
39. C3⋊D3×#67C22semidirect
40. D3×#638C22semidirect
41. C2×#6289C22semidirect
42. #89031C22semidirect
43. C2×Dic3×C3⋊D3C22semidirect
44. #89029C22semidirect
45. #89028C22semidirect
46. C2×D3×C3⋊Dic3C22semidirect
47. #89026C22semidirect
48. C3⋊D3×D12C22semidirect
49. D3×C4⋊(C3⋊D3)C22semidirect
52. C4×D3×C3⋊D3C22semidirect
53. C4×D3×C3⋊D3C22semidirect
54. C4×D3×C3⋊D3C22semidirect
55. C4×D3×C3⋊D3C22semidirect
56. C4×D3×C3⋊D3C22semidirect
57. C4×D3×C3⋊D3C22semidirect
58. #89022C22semidirect
59. #89021C22semidirect
60. #89020C22semidirect
61. #89019C22semidirect
62. #89018C22semidirect
63. #89017C22semidirect
64. C3⋊D3×Dic6C22semidirect
65. #89015C22semidirect
66. #89014C22semidirect
67. D3×#634C22semidirect
78. #41×C3⋊D3D3direct (N × H)
86. C3×D3×#41D3semidirect
107. C33×Q8C23semidirect
108. C33×D4C23semidirect
109. C2×C33×C4C23semidirect
110. #6312C23semidirect
111. C2×C3⋊(C3⋊Dic3)C23semidirect
112. C4⋊(C3⋊(C3⋊D3))C23semidirect
115. C4×C3⋊(C3⋊D3)C23semidirect
116. C4×C3⋊(C3⋊D3)C23semidirect
117. #6308C23semidirect
118. C3×#638C23semidirect
119. C2×C3×C3⋊Dic3C23semidirect
120. C3×C4⋊(C3⋊D3)C23semidirect
123. C3×C4×C3⋊D3C23semidirect
124. C3×C4×C3⋊D3C23semidirect
125. C3×#634C23semidirect
126. C32×#67C23semidirect
127. C2×C32×Dic3C23semidirect
128. C32×D12C23semidirect
131. C32×C4×D3C23semidirect
132. C32×C4×D3C23semidirect
133. C32×Dic6C23semidirect
134. #6293C23semidirect
135. #6292C23semidirect
136. #6291C23semidirect
137. #6290C23semidirect
140. #6289C23semidirect
141. #6289C23semidirect
144. Dic3×C3⋊D3C23semidirect
145. Dic3×C3⋊D3C23semidirect
148. D3×C3⋊Dic3C23semidirect
149. D3×C3⋊Dic3C23semidirect
158. C32×#41C2×D3semidirect
159. C32×#41C2×D3semidirect
170. #3832C2×D3semidirect
176. Q8×C3⋊D3C2×D3semidirect
184. #3830C2×D3semidirect
192. D4×C3⋊D3C2×D3semidirect
200. #3828C2×D3semidirect
215. C2×C4×C3⋊D3C2×D3semidirect
218. C3×#239C2×D3semidirect
220. C3×D3×Q8C2×D3semidirect
222. C3×#237C2×D3semidirect
224. C3×D3×D4C2×D3semidirect
226. C3×#235C2×D3semidirect
228. C2×C3×C4×D3C2×D3semidirect
272. D3×C3⋊D3#41direct (N × H)
299. D3×#41C3⋊D3direct (N × H)
331. C32×Q8C22×D3semidirect
332. C32×Q8C22×D3semidirect
336. C32×D4C22×D3semidirect
337. C32×D4C22×D3semidirect
344. C2×C32×C4C22×D3semidirect
345. C2×C32×C4C22×D3semidirect
351. #638C22×D3semidirect
359. C2×C3⋊Dic3C22×D3semidirect
364. C4⋊(C3⋊D3)C22×D3semidirect
387. C4×C3⋊D3C22×D3semidirect
388. C4×C3⋊D3C22×D3semidirect
393. #634C22×D3semidirect
395. C3×#67C22×D3semidirect
397. C2×C3×Dic3C22×D3semidirect
399. C3×D12C22×D3semidirect
406. C3×C4×D3C22×D3semidirect
407. C3×C4×D3C22×D3semidirect
409. C3×Dic6C22×D3semidirect
430. C3⋊(C3⋊D3)C2×#41semidirect
432. C3×C3⋊D3C2×#41semidirect
434. C32×D3C2×#41semidirect
444. C3×#41D32semidirect
445. C3×#41C2×C3⋊D3semidirect
464. #239C2×C3⋊D3semidirect
473. D3×Q8C2×C3⋊D3semidirect
486. #237C2×C3⋊D3semidirect
499. D3×D4C2×C3⋊D3semidirect
512. #235C2×C3⋊D3semidirect
539. C2×C4×D3C2×C3⋊D3semidirect
609. C33C22×#41semidirect
630. C3×Q8C2×D32semidirect
631. C3×Q8C22×C3⋊D3semidirect
637. C3×D4C2×D32semidirect
638. C3×D4C22×C3⋊D3semidirect
650. C2×C3×C4C2×D32semidirect
651. C2×C3×C4C22×C3⋊D3semidirect
660. #67C22×C3⋊D3semidirect
673. C2×Dic3C22×C3⋊D3semidirect
680. D12C22×C3⋊D3semidirect
715. C4×D3C22×C3⋊D3semidirect
716. C4×D3C22×C3⋊D3semidirect
723. Dic6C22×C3⋊D3semidirect
739. C3⋊D3D3×#41direct (N × H)
743. C3×D3D3×#41semidirect
764. #41D3×C3⋊D3direct (N × H)
847. C32C2×D3×#41semidirect
848. C32C2×D3×#41semidirect
861. Q8C2×D3×C3⋊D3semidirect
871. D4C2×D3×C3⋊D3semidirect
899. C2×C4C2×D3×C3⋊D3semidirect
919. D3#41×C3⋊D3direct (N × H)
943. C3D32×#41semidirect
944. C3C2×#41×C3⋊D3semidirect

Maximal subgroups

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

subgroupindex
#41×C3⋊(C3⋊D3)2
C3×#41×C3⋊D32
C32×D3×#412
#117245962
C3⋊D3×#2392
D3×#38322
D3×Q8×C3⋊D32
#117245862
C3⋊D3×#2372
D3×#38302
D3×D4×C3⋊D32
#117245782
C3⋊D3×#2352
D3×#38282
C2×C4×D3×C3⋊D32
C2×#41×C3⋊D33
D32×#413