Finite Group Databasebeta

← #13177315

Subgroups — #13177315

Order 1728.

2532 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89039C211yesmaximal, characteristic, complemented
2C2×#89029C211yesmaximal, characteristic, complemented
3C2×#88859C211yesmaximal, characteristic, complemented
4C3×C4×#638C211yesmaximal, characteristic, complemented
5C32×#930C211yesmaximal, characteristic, complemented
6#11723638C211yesmaximal, characteristic, complemented
7#11723603C211yesmaximal, characteristic, complemented
8#11723540C211yesmaximal, characteristic, complemented
9C3⋊D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10#11723520C211yesmaximal, characteristic, complemented
11#11723495C211yesmaximal, characteristic, complemented
12#11723493C211yesmaximal, characteristic, complemented
13#11723475C211yesmaximal, characteristic, complemented
14#11723461C211yesmaximal, characteristic, complemented
15#11723419C211yesmaximal, characteristic, complemented
16#10596081—31nomaximal
17#10595075—34nomaximal
18C23×C3⋊(C3⋊D3)C2211yescharacteristic
19C22×D3×C3⋊D3C2211yescharacteristic
20C22×C33×C4C2211yescharacteristic, complemented
21C22×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
22C2×C3×#638C2211yescharacteristic
23C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
24C2×C32×#67C2211yescharacteristic
25C2×C32×#67C2211yescharacteristic, complemented
26C2×C32×D12C2211yescharacteristic, complemented
27#89039—24no—
28C2×#6293C2211yescharacteristic, complemented
29C2×#6292C2211yescharacteristic
30C2×#6291C2211yescharacteristic
31C2×#6291C2211yescharacteristic
32C2×#6291C2211yescharacteristic, complemented
33C2×#6290C2211yescharacteristic, complemented
34C2×#6289C2211yescharacteristic
35C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
36#89029—24no—
37C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
38#88859C2211yescharacteristic
39#88859C2211yescharacteristic
40#88859C2211yescharacteristic, complemented
41#88859C2211yescharacteristic, complemented
42C3×#3757C2211yescharacteristic, complemented
43C3×#3752C2211yescharacteristic, complemented
44C3×#3750C2211yescharacteristic, complemented
45C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
46C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
47C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
48C32×C4⋊Dic3C2211yescharacteristic, complemented
49#88807C2211yescharacteristic, complemented
50#88807C2211yescharacteristic, complemented
51#88804C2211yescharacteristic
52#88804C2211yescharacteristic, complemented
53(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
54(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
55C2×#3830—31no—
56C2×D4×C3⋊D3—31no—
57C2×#3811—34no—
58C2×#3805—34no—
59C32×#121—31no—
60#64148—31no—
61#64146—31no—
62#64146—31no—
63#64144—31no—
64C4×#638D311yescharacteristic, complemented
65C2×#3752—31no—
66C2×#3752—34no—
67C2×#3752—64no—
68#64105—31no—
69#64103—31no—
70#64094—31no—
71#64093—31no—
72#64090—31no—
73C22⋊C4×C3⋊D3—31no—
74C3×#930D314yescomplemented
75C3×C4×#67—34no—
76#63981—34no—
77#63962—34no—
78#63922—34no—
79D3×(C2×D3)⋊C4—34no—
80#63906—34no—
81#63895—34no—
82#63890—34no—
83#63886—34no—
84#63880—34no—
85#63852—34no—
86C23×C33C2311yescharacteristic
87C22×C3⋊(C3⋊D3)—22no—
88C22×C3⋊(C3⋊D3)—22no—
89C22×C3⋊(C3⋊D3)—41no—
90C22×C3⋊(C3⋊D3)C2311yescharacteristic
91C22×C3⋊(C3⋊D3)C2311yescharacteristic
92C22×C3×C3⋊D3C2311yescharacteristic
93C22×C32×D3C2311yescharacteristic
94C22×C32×D3C2311yescharacteristic
95C2×D3×C3⋊D3—22no—
96C2×D3×C3⋊D3—22no—
97C2×D3×C3⋊D3—41no—
98C2×C33×C4—41no—
99C2×C33×C4C2311yescharacteristic
100C2×C33×C4C2311yescharacteristic
101C2×C3⋊(C3⋊Dic3)—22no—
102C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
103C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
104C3×#638D414yescomplemented
105C2×C3×C3⋊Dic3C2311yescharacteristic
106C2×C3×C3⋊Dic3C2311yescharacteristic
107C2×C3×C3⋊Dic3C2311yescharacteristic
108C3×C4×C3⋊D3—41no—
109C32×#67—22no—
110C32×#67—22no—
111C2×C32×Dic3C2311yescharacteristic
112C2×C32×Dic3C2311yescharacteristic
113C32×D12—41no—
114#6293—22no—
115#6292—22no—
116#6291—22no—
117#6291—22no—
118#6291—41no—
119#6290—22no—
120#6289—22no—
121Dic3×C3⋊D3—22no—
122D3×C3⋊Dic3—22no—
123#5610—94no—
124#5554—91no—
125C23×C3⋊D3—31no—
126C23×C3⋊D3—34no—
127C23×C3⋊D3—31no—
128C23×C3⋊D3—64no—
129C22×D32—34no—
130C2×C32×D4—31no—
131C2×C32×D4—31no—
132C2×C32×D4—31no—
133C22×C32×C4—24no—
134C22×C32×C4C2×D314yescomplemented
135C22×C32×C4C2×D311yescharacteristic, complemented
136C2×#638—31no—
137C2×#638—31no—
138C2×#638—31no—
139C2×#638—31no—
140C2×#638C2×D311yescharacteristic
141C22×C3⋊Dic3—31no—
142C22×C3⋊Dic3—34no—
143C22×C3⋊Dic3—31no—
144C22×C3⋊Dic3—64no—
145#3830—64no—
146D4×C3⋊D3—64no—
147C2×C4⋊(C3⋊D3)—31no—
148C2×C4×C3⋊D3—31no—
149C2×C4×C3⋊D3—31no—
150C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
151C2×#634—31no—
152C2×C3×#67—34no—
153C2×C3×#67C2×D314yes—
154C2×C3×#67C2×D314yescomplemented
155C2×C3×D12C2×D314yescomplemented
156C2×C3×C4×D3—34no—
157#3811—616no—
158C2×#627—34no—
159C2×#626—34no—
160C2×#626—34no—
161C2×#626—34no—
162C2×#626—34no—
163C2×#625—34no—
164C2×#624—34no—
165#3805—616no—
166C2×D3×Dic3—34no—
167C2×D3×Dic3—34no—
168C32×C4⋊C4—31no—
169C32×C22⋊C4—31no—
170C32×C22⋊C4—31no—
171#3757—31no—
172#3757—31no—
173#3757C2×D311yescharacteristic, complemented
174#3752—31no—
175#3752—31no—
176#3752—31no—
177#3752—31no—
178#3752—34no—
179#3752—34no—
180#3752—34no—
181#3752—34no—
182#3752—31no—
183#3752—31no—
184#3752—64no—
185#3752—64no—
186#3752—64no—
187#3752—64no—
188#3752C2×D311yescharacteristic, complemented
189#3750—31no—
190#3750—31no—
191#3750C2×D311yescharacteristic, complemented
192C4×C3⋊Dic3C2×D311yescharacteristic, complemented
193C3×#217—34no—
194C3×(C2×D3)⋊C4—34no—
195C3×(C2×D3)⋊C4C2×D314yescomplemented
196C3×(C2×D3)⋊C4C2×D314yescomplemented
197C3×C4⋊Dic3C2×D314yescomplemented
198C3×Dic3⋊C4—34no—
199C3×C4×Dic3—34no—
200Dic3⋊Dic3—34no—
201Dic3⋊Dic3—34no—
202#3722—34no—
203#3722—34no—
204(C2×D3)⋊Dic3—34no—
205(C2×D3)⋊Dic3—34no—
206C22×C33—21no—
207C22×C33—21no—
208C22×C33C2×D412yes—
209C22×C33C2411yescharacteristic
210C2×C3⋊(C3⋊D3)—21no—
211C2×C3⋊(C3⋊D3)—21no—
212C2×C3⋊(C3⋊D3)—21no—
213C2×C3⋊(C3⋊D3)—21no—
214C2×C3⋊(C3⋊D3)—21no—
215C2×C3⋊(C3⋊D3)—44no—
216C2×C3⋊(C3⋊D3)#4112yescomplemented
217C2×C3×C3⋊D3—21no—
218C2×C3×C3⋊D3—21no—
219C2×C3×C3⋊D3C2×D412yes—
220C2×C32×D3—21no—
221C2×C32×D3—21no—
222C2×C32×D3—21no—
223C2×C32×D3—21no—
224C2×C32×D3—21no—
225C2×C32×D3—21no—
226D3×C3⋊D3—44no—
227C33×C4—21no—
228C33×C4—21no—
229C3⋊(C3⋊Dic3)—21no—
230C3⋊(C3⋊Dic3)—21no—
231C3×C3⋊Dic3—21no—
232C3×C3⋊Dic3—21no—
233C3×C3⋊Dic3C2×D412yes—
234C32×Dic3—21no—
235C32×Dic3—21no—
236C2×#237—94no—
237C2×#237—91no—
238C2×D3×D4—94no—
239C2×D3×D4—91no—
240C3×#121—34no—
241C3×C4×D4—91no—
242#939—94no—
243#937—94no—
244#937—94no—
245#935—94no—
246#930—91no—
247#930C3⋊D311yescharacteristic, complemented
248C4×#67—34no—
249C2×(C2×D3)⋊C4—94no—
250C2×(C2×D3)⋊C4—91no—
251C2×(C2×D3)⋊C4—91no—
252C2×(C2×D3)⋊C4—184no—
253#897—91no—
254#896—94no—
255#895—91no—
256#894—94no—
257#886—91no—
258#886—91no—
259#885—94no—
260#884—94no—
261#882—91no—
262#882—91no—
263#67⋊C4—94no—
264D3×C22⋊C4—94no—
265#875—91no—
266C4×D12—91no—
267C23×C32—24no—
268C23×C32—31no—
269C23×C32—31no—
270C23×C32C22×D314yes—
271C23×C32C22×D311yescharacteristic
272C22×C3⋊D3—31no—
273C22×C3⋊D3—31no—
274C22×C3⋊D3—34no—
275C22×C3⋊D3—34no—
276C22×C3⋊D3—64no—
277C22×C3⋊D3—64no—
278C22×C3⋊D3—62no—
279C22×C3⋊D3—62no—
280C22×C3⋊D3—68no—
281C22×C3⋊D3—616no—
282C22×C3⋊D3—62no—
283C22×C3⋊D3—62no—
284C22×C3⋊D3—68no—
285C22×C3⋊D3—128no—
286C22×C3⋊D3—121no—
287C22×C3⋊D3—121no—
288C22×C3⋊D3—124no—
289C22×C3⋊D3—128no—
290C22×C3⋊D3C22×D311yescharacteristic
291C22×C3×D3—34no—
292C22×C3×D3C22×D314yes—
293C22×C3×D3C22×D314yes—
294C2×D32—68no—
295C2×D32—68no—
296C2×D32—124no—
297C32×D4—62no—
298C32×D4—62no—
299C32×D4—121no—
300C2×C32×C4—24no—
301C2×C32×C4—24no—
302C2×C32×C4—31no—
303C2×C32×C4—31no—
304C2×C32×C4—41no—
305C2×C32×C4—44no—
306C2×C32×C4—48no—
307C2×C32×C4C22×D314yes—
308C2×C32×C4C22×D314yes—
309C2×C32×C4C22×D311yescharacteristic
310C2×C32×C4C22×D311yescharacteristic
311#638—62no—
312#638—62no—
313#638—62no—
314#638—121no—
315#638D1214yescomplemented
316C2×C3⋊Dic3—31no—
317C2×C3⋊Dic3—31no—
318C2×C3⋊Dic3—34no—
319C2×C3⋊Dic3—34no—
320C2×C3⋊Dic3—64no—
321C2×C3⋊Dic3—64no—
322C2×C3⋊Dic3—62no—
323C2×C3⋊Dic3—62no—
324C2×C3⋊Dic3—68no—
325C2×C3⋊Dic3—128no—
326C2×C3⋊Dic3C22×D311yescharacteristic
327C2×C3⋊Dic3C22×D311yescharacteristic
328C2×C3⋊Dic3C22×D311yescharacteristic
329C4⋊(C3⋊D3)—62no—
330C4×C3⋊D3—41no—
331C4×C3⋊D3—62no—
332C4×C3⋊D3—62no—
333#634—62no—
334C3×#67—28no—
335C3×#67—28no—
336C3×#67—316no—
337C2×C3×Dic3—34no—
338C2×C3×Dic3—34no—
339C2×C3×Dic3—34no—
340C2×C3×Dic3C22×D314yes—
341C2×C3×Dic3C22×D314yes—
342C3×D12—44no—
343C3×C4×D3—124no—
344#627—68no—
345#626—68no—
346#626—68no—
347#626—68no—
348#626—124no—
349#625—68no—
350#624—68no—
351D3×Dic3—68no—
352D3×Dic3—68no—
353#546—271noSylow
354C2×C33—22no—
355C2×C33C22×D411yescharacteristic
356C2×C33C2×#4111yescharacteristic
357C2×C33H(5,𝔽2)11yescharacteristic
358C3⋊(C3⋊D3)—22no—
359C3⋊(C3⋊D3)—41no—
360C3×C3⋊D3—22no—
361C32×D3—41no—
362C32×D3—41no—
363C23×D3—94no—
364C23×D3—94no—
365C23×D3—91no—
366C23×D3—91no—
367C23×D3—184no—
368C2×C3×D4—34no—
369C2×C3×D4—34no—
370C2×C3×D4—34no—
371C2×C3×D4—91no—
372C22×C3×C4—24no—
373C22×C3×C4—91no—
374C22×C3×C4D3214yescomplemented
375C22×C3×C4C2×C3⋊D311yescharacteristic, complemented
376C2×#67—34no—
377C2×#67—94no—
378C2×#67—94no—
379C2×#67—94no—
380C2×#67—94no—
381C2×#67—91no—
382C2×#67—91no—
383C2×#67C2×C3⋊D311yescharacteristic
384C2×#67C2×C3⋊D311yescharacteristic, complemented
385C22×Dic3—94no—
386C22×Dic3—94no—
387C22×Dic3—91no—
388C22×Dic3—91no—
389C22×Dic3—184no—
390#237—184no—
391#237—1816no—
392D3×D4—184no—
393D3×D4—1816no—
394C2×D12—94no—
395C2×D12—91no—
396C2×D12—91no—
397C2×D12—91no—
398C2×D12C2×C3⋊D311yescharacteristic, complemented
399C2×C4×D3—34no—
400C2×C4×D3—94no—
401C2×C4×D3—94no—
402C2×C4×D3—91no—
403C2×C4×D3—91no—
404C2×Dic6—94no—
405C2×Dic6—91no—
406C3×C4⋊C4—34no—
407C3×C4⋊C4—91no—
408C3×C22⋊C4—34no—
409C3×C22⋊C4—34no—
410C3×C22⋊C4—91no—
411C3×C22⋊C4—91no—
412C3×C42—91no—
413#217—34no—
414#217—94no—
415#217—94no—
416(C2×D3)⋊C4—34no—
417(C2×D3)⋊C4—94no—
418(C2×D3)⋊C4—94no—
419(C2×D3)⋊C4—91no—
420(C2×D3)⋊C4—91no—
421(C2×D3)⋊C4—94no—
422(C2×D3)⋊C4—94no—
423(C2×D3)⋊C4—94no—
424(C2×D3)⋊C4—94no—
425(C2×D3)⋊C4—91no—
426(C2×D3)⋊C4—91no—
427(C2×D3)⋊C4—91no—
428(C2×D3)⋊C4—91no—
429(C2×D3)⋊C4—91no—
430(C2×D3)⋊C4—91no—
431(C2×D3)⋊C4—184no—
432(C2×D3)⋊C4—184no—
433(C2×D3)⋊C4—184no—
434(C2×D3)⋊C4—184no—
435(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
436(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
437C4⋊Dic3—91no—
438C4⋊Dic3—91no—
439C4⋊Dic3C2×C3⋊D311yescharacteristic, complemented
440Dic3⋊C4—34no—
441Dic3⋊C4—94no—
442Dic3⋊C4—94no—
443C4×Dic3—34no—
444C22×C32—28no—
445C22×C32—28no—
446C22×C32—24no—
447C22×C32—21no—
448C22×C32—24no—
449C22×C32—21no—
450C22×C32—24no—
451C22×C32—28no—
452C22×C32—61no—
453C22×C32—61no—
454C22×C32—61no—
455C22×C32—61no—
456C22×C32—61no—
457C22×C32—61no—
458C22×C32C2×D1212yes—
459C22×C32D3×D418yes—
460C22×C32C23×D314yes—
461C22×C32C23×D311yescharacteristic
462C2×C3⋊D3—21no—
463C2×C3⋊D3—21no—
464C2×C3⋊D3—32no—
465C2×C3⋊D3—38no—
466C2×C3⋊D3—68no—
467C2×C3⋊D3—61no—
468C2×C3⋊D3—61no—
469C2×C3⋊D3—68no—
470C2×C3⋊D3—61no—
471C2×C3⋊D3—61no—
472C2×C3⋊D3—64no—
473C2×C3⋊D3—61no—
474C2×C3⋊D3—64no—
475C2×C3⋊D3—64no—
476C2×C3⋊D3—64no—
477C2×C3⋊D3—64no—
478C2×C3⋊D3—124no—
479C2×C3⋊D3—124no—
480C2×C3⋊D3—124no—
481C2×C3⋊D3—124no—
482C2×C3⋊D3—124no—
483C2×C3⋊D3—124no—
484C2×C3⋊D3—1216no—
485C2×C3⋊D3—1232no—
486C2×C3⋊D3C2×D1212yes—
487C2×C3×D3—24no—
488C2×C3×D3—24no—
489C2×C3×D3—24no—
490C2×C3×D3—24no—
491C2×C3×D3—24no—
492C2×C3×D3—24no—
493C2×C3×D3—38no—
494C2×C3×D3—64no—
495C2×C3×D3—64no—
496D32—1216no—
497C32×C4—21no—
498C32×C4—21no—
499C32×C4—24no—
500C32×C4—24no—
501C32×C4—44no—
502C32×C4—44no—
503C32×C4—61no—
504C32×C4—61no—
505C3⋊Dic3—21no—
506C3⋊Dic3—21no—
507C3⋊Dic3—61no—
508C3⋊Dic3—61no—
509C3⋊Dic3—64no—
510C3⋊Dic3—64no—
511C3⋊Dic3—124no—
512C3⋊Dic3—124no—
513C3⋊Dic3C2×D1212yes—
514C3×Dic3—24no—
515C3×Dic3—24no—
516C3×Dic3—38no—
517C3×Dic3—64no—
518C3×Dic3—64no—
519C2×#41—271no—
520C22×D4—271no—
521#124—271no—
522#123—271no—
523#123—271no—
524C22⋊Q8—271no—
525#121—31no—
526#121—271no—
527#121—271no—
528#120—271no—
529#120—271no—
530C4×D4—91no—
531C4×D4—271no—
532C2×C22⋊C4—271no—
533C2×C22⋊C4—271no—
534C33#54611yescharacteristic, complemented, Sylow
535C23×C3—24no—
536C23×C3—34no—
537C23×C3—34no—
538C23×C3—91no—
539C23×C3C2×D3214yes—
540C23×C3C22×C3⋊D311yescharacteristic
541C22×D3—34no—
542C22×D3—94no—
543C22×D3—91no—
544C22×D3—94no—
545C22×D3—91no—
546C22×D3—184no—
547C22×D3—184no—
548C22×D3—182no—
549C22×D3—182no—
550C22×D3—188no—
551C22×D3—188no—
552C22×D3—188no—
553C22×D3—182no—
554C22×D3—1816no—
555C22×D3—188no—
556C22×D3—182no—
557C22×D3—368no—
558C22×D3—361no—
559C22×D3—364no—
560C22×D3—364no—
561C22×D3—361no—
562C22×D3—368no—
563C22×D3C22×C3⋊D311yescharacteristic
564C22×D3C22×C3⋊D311yescharacteristic
565C3×D4—68no—
566C3×D4—68no—
567C3×D4—94no—
568C3×D4—124no—
569C2×C3×C4—24no—
570C2×C3×C4—24no—
571C2×C3×C4—34no—
572C2×C3×C4—34no—
573C2×C3×C4—44no—
574C2×C3×C4—41no—
575C2×C3×C4—48no—
576C2×C3×C4—91no—
577C2×C3×C4—91no—
578C2×C3×C4—91no—
579C2×C3×C4—361no—
580C2×C3×C4C2×D3214yes—
581C2×C3×C4C2×D3214yes—
582C2×C3×C4C22×C3⋊D311yescharacteristic
583C2×C3×C4C22×C3⋊D311yescharacteristic
584#67—22no—
585#67—22no—
586#67—316no—
587#67—182no—
588#67—188no—
589#67—188no—
590#67—182no—
591#67—188no—
592#67—364no—
593C2×Dic3—34no—
594C2×Dic3—34no—
595C2×Dic3—34no—
596C2×Dic3—94no—
597C2×Dic3—94no—
598C2×Dic3—91no—
599C2×Dic3—91no—
600C2×Dic3—184no—
601C2×Dic3—184no—
602C2×Dic3—182no—
603C2×Dic3—188no—
604C2×Dic3—188no—
605C2×Dic3—182no—
606C2×Dic3—368no—
607C2×Dic3C22×C3⋊D311yescharacteristic
608C2×Dic3C22×C3⋊D311yescharacteristic
609D12—41no—
610D12—188no—
611D12—182no—
612D12—182no—
613D12—361no—
614C4×D3—124no—
615C4×D3—182no—
616C4×D3—188no—
617C4×D3—188no—
618C4×D3—182no—
619Dic6—182no—
620Dic6—188no—
621C2×C32—216no—
622C2×C32—22no—
623C2×C32—28no—
624C2×C32—24no—
625C2×C32—24no—
626C2×C32—24no—
627C2×C32—121no—
628C2×C32—121no—
629C2×C32C22×D1211yescharacteristic
630C2×C32C2×D3×D414yes—
631C2×C32#100414yes—
632C2×C32#100411yescharacteristic
633C2×C32D3×#4114yes—
634C2×C32D3×#4111yescharacteristic
635C3⋊D3—22no—
636C3⋊D3—62no—
637C3⋊D3—68no—
638C3⋊D3—128no—
639C3⋊D3—128no—
640C3⋊D3—121no—
641C3⋊D3—124no—
642C3×D3—44no—
643C3×D3—44no—
644C3×D3—68no—
645C24—271no—
646C24—271no—
647#41—544no—
648C2×Q8—271no—
649C2×D4—31no—
650C2×D4—31no—
651C2×D4—31no—
652C2×D4—91no—
653C2×D4—271no—
654C2×D4—271no—
655C2×D4—271no—
656C2×D4—271no—
657C2×D4—271no—
658C2×D4—544no—
659C22×C4—91no—
660C22×C4—271no—
661C22×C4—271no—
662C22×C4—271no—
663C22×C4—271no—
664C22×C4D3×C3⋊D311yescharacteristic, complemented
665C4⋊C4—31no—
666C4⋊C4—91no—
667C4⋊C4—271no—
668C4⋊C4—271no—
669C22⋊C4—31no—
670C22⋊C4—31no—
671C22⋊C4—91no—
672C22⋊C4—91no—
673C22⋊C4—271no—
674C22⋊C4—271no—
675C22⋊C4—271no—
676C22⋊C4—271no—
677C22⋊C4—271no—
678C22⋊C4—271no—
679C22⋊C4—271no—
680C22⋊C4—271no—
681C42—91no—
682C22×C3—28no—
683C22×C3—28no—
684C22×C3—24no—
685C22×C3—24no—
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—24no—
689C22×C3—28no—
690C22×C3—64no—
691C22×C3—64no—
692C22×C3—64no—
693C22×C3—64no—
694C22×C3—64no—
695C22×C3—64no—
696C22×C3—92no—
697C22×C3—181no—
698C22×C3—181no—
699C22×C3D3×D1218yes—
700C22×C3D4×C3⋊D312yes—
701C22×C3C22×D3214yes—
702C22×C3C23×C3⋊D311yescharacteristic
703C2×D3—21no—
704C2×D3—21no—
705C2×D3—21no—
706C2×D3—21no—
707C2×D3—21no—
708C2×D3—21no—
709C2×D3—38no—
710C2×D3—64no—
711C2×D3—64no—
712C2×D3—98no—
713C2×D3—92no—
714C2×D3—188no—
715C2×D3—184no—
716C2×D3—184no—
717C2×D3—181no—
718C2×D3—181no—
719C2×D3—188no—
720C2×D3—184no—
721C2×D3—184no—
722C2×D3—184no—
723C2×D3—181no—
724C2×D3—181no—
725C2×D3—181no—
726C2×D3—364no—
727C2×D3—364no—
728C2×D3—364no—
729C2×D3—364no—
730C2×D3—364no—
731C2×D3—3616no—
732C2×D3—3616no—
733C2×D3—364no—
734C2×D3—3632no—
735C3×C4—24no—
736C3×C4—24no—
737C3×C4—21no—
738C3×C4—21no—
739C3×C4—44no—
740C3×C4—44no—
741C3×C4—64no—
742C3×C4—64no—
743C3×C4—92no—
744C3×C4—181no—
745C3×C4—181no—
746Dic3—21no—
747Dic3—21no—
748Dic3—38no—
749Dic3—64no—
750Dic3—64no—
751Dic3—184no—
752Dic3—184no—
753Dic3—181no—
754Dic3—181no—
755Dic3—364no—
756Dic3—364no—
757C32—24no—
758C32#555411yescharacteristic, complemented
759C32#561014yescomplemented
760C23—31no—
761C23—31no—
762C23—91no—
763C23—271no—
764C23—271no—
765C23—542no—
766C23—542no—
767C23—542no—
768C23—542no—
769C23—1081no—
770C23—1081no—
771C23C2×D3×C3⋊D311yescharacteristic
772Q8—542no—
773D4—62no—
774D4—62no—
775D4—94no—
776D4—121no—
777D4—542no—
778D4—542no—
779D4—542no—
780D4—542no—
781D4—1081no—
782C2×C4—31no—
783C2×C4—31no—
784C2×C4—41no—
785C2×C4—91no—
786C2×C4—91no—
787C2×C4—91no—
788C2×C4—271no—
789C2×C4—271no—
790C2×C4—361no—
791C2×C4—542no—
792C2×C4—542no—
793C2×C4—542no—
794C2×C4—542no—
795C2×C4C2×D3×C3⋊D311yescharacteristic
796C2×C4C2×D3×C3⋊D311yescharacteristic
797C2×C3—216no—
798C2×C3—28no—
799C2×C3—22no—
800C2×C3—24no—
801C2×C3—24no—
802C2×C3—24no—
803C2×C3—124no—
804C2×C3—124no—
805C2×C3—182no—
806C2×C3C2×D3×D1214yes—
807C2×C3#6430614yes—
808C2×C3#6433014yes—
809C2×C3C2×D4×C3⋊D311yescharacteristic
810C2×C3#6436111yescharacteristic
811C2×C3#41×C3⋊D311yescharacteristic
812D3—41no—
813D3—41no—
814D3—68no—
815D3—188no—
816D3—182no—
817D3—368no—
818D3—368no—
819D3—364no—
820D3—361no—
821C22—21no—
822C22—21no—
823C22—61no—
824C22—61no—
825C22—61no—
826C22—61no—
827C22—61no—
828C22—61no—
829C22—92no—
830C22—181no—
831C22—181no—
832C22—272no—
833C22—541no—
834C22—541no—
835C22—541no—
836C22—541no—
837C22—541no—
838C22—1084no—
839C22—1084no—
840C22C3⋊D3×D1212yes—
841C22C22×D3×C3⋊D311yescharacteristic
842C4—21no—
843C4—21no—
844C4—61no—
845C4—61no—
846C4—92no—
847C4—181no—
848C4—181no—
849C4—541no—
850C4—541no—
851C3—24no—
852C3#1059507514yescomplemented
853C3#1059608111yescharacteristic, complemented
854C2—22no—
855C2—121no—
856C2—121no—
857C2—182no—
858C2—542no—
859C2—1081no—
860C2C2×C3⋊D3×D1211yescharacteristic
861C2#1172457811yescharacteristic
862C2#1172461111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC22×C33×C4C22
hypercenterC22×C4D3×C3⋊D3
hypocenterC33#546
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C2×#89039C2semidirect
2. C2×#89029C2semidirect
3. C2×#88859C2semidirect
4. C3×C4×#638C2semidirect
5. C32×#930C2semidirect
6. #11723638C2semidirect
7. #11723603C2semidirect
8. #11723540C2semidirect
9. C3⋊D3×(C2×D3)⋊C4C2semidirect
10. #11723520C2semidirect
11. #11723495C2semidirect
12. #11723493C2semidirect
13. #11723475C2semidirect
14. #11723461C2semidirect
15. #11723419C2semidirect
20. C22×C33×C4C22semidirect
21. C22×C3⋊(C3⋊Dic3)C22semidirect
23. C2×C3×C4×C3⋊D3C22semidirect
25. C2×C32×#67C22semidirect
26. C2×C32×D12C22semidirect
28. C2×#6293C22semidirect
32. C2×#6291C22semidirect
33. C2×#6290C22semidirect
35. C2×Dic3×C3⋊D3C22semidirect
37. C2×D3×C3⋊Dic3C22semidirect
40. #88859C22semidirect
41. #88859C22semidirect
42. C3×#3757C22semidirect
43. C3×#3752C22semidirect
44. C3×#3750C22semidirect
45. C3×C4×C3⋊Dic3C22semidirect
46. C32×(C2×D3)⋊C4C22semidirect
47. C32×(C2×D3)⋊C4C22semidirect
48. C32×C4⋊Dic3C22semidirect
49. #88807C22semidirect
50. #88807C22semidirect
52. #88804C22semidirect
53. (C2×D3)⋊(C3⋊Dic3)C22semidirect
54. (C2×D3)⋊(C3⋊Dic3)C22semidirect
64. C4×#638D3semidirect
74. C3×#930D3semidirect
104. C3×#638D4semidirect
134. C22×C32×C4C2×D3semidirect
135. C22×C32×C4C2×D3semidirect
150. C2×C4×C3⋊D3C2×D3semidirect
154. C2×C3×#67C2×D3semidirect
155. C2×C3×D12C2×D3semidirect
173. #3757C2×D3semidirect
188. #3752C2×D3semidirect
191. #3750C2×D3semidirect
192. C4×C3⋊Dic3C2×D3semidirect
195. C3×(C2×D3)⋊C4C2×D3semidirect
196. C3×(C2×D3)⋊C4C2×D3semidirect
197. C3×C4⋊Dic3C2×D3semidirect
216. C2×C3⋊(C3⋊D3)#41semidirect
247. #930C3⋊D3semidirect
315. #638D12semidirect
374. C22×C3×C4D32semidirect
375. C22×C3×C4C2×C3⋊D3semidirect
384. C2×#67C2×C3⋊D3semidirect
398. C2×D12C2×C3⋊D3semidirect
435. (C2×D3)⋊C4C2×C3⋊D3semidirect
436. (C2×D3)⋊C4C2×C3⋊D3semidirect
439. C4⋊Dic3C2×C3⋊D3semidirect
534. C33#546semidirect
664. C22×C4D3×C3⋊D3semidirect
758. C32#5554semidirect
759. C32#5610semidirect
852. C3#10595075semidirect
853. C3#10596081semidirect

Maximal subgroups

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

subgroupindex
C2×#890392
C2×#890292
C2×#888592
C3×C4×#6382
C32×#9302
#117236382
#117236032
#117235402
C3⋊D3×(C2×D3)⋊C42
#117235202
#117234952
#117234932
#117234752
#117234612
#117234192
#105960813
#105950753