Finite Group Databasebeta

← C2×#11722928 #13172002

Subgroups — C2×#11722928 #13172002

Order 1728.

2218 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6294C211yesmaximal, characteristic, complemented
2C22×D3×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C22×C3×#626C211yesmaximal, characteristic
4C2×Dic3⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
5C2×#88803C211yesmaximal, characteristic, complemented
6C2×C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
7C2×C3×Dic32C211yesmaximal, characteristic, complemented
8#11722928C218yesmaximal, direct product factor
9C2×#67⋊Dic3—31nomaximal
10C2×Dic3×D12—31nomaximal
11C2×#63880—31nomaximal
12C23×C3×C3⋊D3C2211yescharacteristic
13C23×C32×D3C2211yescharacteristic
14C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
15C22×C3×C3⋊Dic3C2211yescharacteristic
16C22×C3×C3⋊Dic3C2211yescharacteristic
17C22×C32×Dic3C2211yescharacteristic
18C22×C32×Dic3C2211yescharacteristic
19C2×#6294—24no—
20C2×#6294C2214yescomplemented
21C2×D3×C3⋊Dic3—24no—
22C2×D3×C3⋊Dic3C2214yescomplemented
23C2×C3×#626C418yescomplemented
24C2×C3×#626C2214yes—
25Dic3⋊(C3⋊Dic3)C2214yescomplemented
26#88803C2214yescomplemented
27C3×(C2×D3)⋊Dic3C2214yescomplemented
28C3×Dic32C2214yescomplemented
29C23×C3⋊Dic3—31no—
30C22×C3×#67—31no—
31C22×C3×D12—31no—
32C22×#626D311yescharacteristic
33C22×#624—31no—
34C22×D3×Dic3—31no—
35C22×D3×Dic3—31no—
36C22×D3×Dic3—31no—
37C22×D3×Dic3—31no—
38C22×D3×Dic3—61no—
39C2×#3752—31no—
40C2×C4⋊(C3⋊Dic3)—31no—
41C2×C3×#217—31no—
42C2×C3×(C2×D3)⋊C4—31no—
43C2×C3×C4×Dic3—31no—
44C2×C3×C4×Dic3—31no—
45#67⋊Dic3—38no—
46C2×Dic3⋊Dic3—31no—
47C2×Dic3⋊Dic3—31no—
48C2×Dic3⋊Dic3—61no—
49C2×(C2×D3)⋊Dic3—31no—
50C2×(C2×D3)⋊Dic3—31no—
51C2×(C2×D3)⋊Dic3—61no—
52C2×(C2×D3)⋊Dic3D311yescharacteristic, complemented
53C2×Dic32D311yescharacteristic, complemented
54Dic3×D12—38no—
55#63880—38no—
56C23×C33C2311yescharacteristic
57C22×C3×C3⋊D3—22no—
58C22×C3×C3⋊D3—22no—
59C22×C3×C3⋊D3C2×C414yescomplemented
60C22×C3×C3⋊D3C2312yes—
61C22×C32×D3—22no—
62C22×C32×D3—22no—
63C22×C32×D3C2×C414yescomplemented
64C22×C32×D3C2312yes—
65C2×C3⋊(C3⋊Dic3)—22no—
66C2×C3⋊(C3⋊Dic3)C2312yes—
67C2×C3×C3⋊Dic3—22no—
68C2×C3×C3⋊Dic3D414yescomplemented
69C2×C3×C3⋊Dic3C2312yes—
70C2×C3×C3⋊Dic3C2312yes—
71C2×C32×Dic3—22no—
72C2×C32×Dic3C2×C414yescomplemented
73C2×C32×Dic3C2312yes—
74C2×C32×Dic3C2312yes—
75#6294—28no—
76D3×C3⋊Dic3—28no—
77C3×#626C2×C4116yescomplemented
78C2×D4×Dic3—91no—
79C2×#67⋊C4—91no—
80C2×C4×D12—91no—
81C24×C32—31no—
82C23×C3⋊D3C2×D311yescharacteristic
83C23×C3×D3—21no—
84C23×C3×D3—31no—
85C23×C3×D3—31no—
86C23×C3×D3—61no—
87C23×C3×D3C2×D311yescharacteristic
88C23×C3×D3C2×D311yescharacteristic
89C22×C32×C4—31no—
90C22×C32×C4—31no—
91C22×C3⋊Dic3—31no—
92C22×C3⋊Dic3—31no—
93C22×C3⋊Dic3—31no—
94C22×C3⋊Dic3—34no—
95C22×C3⋊Dic3—61no—
96C22×C3⋊Dic3—64no—
97C22×C3⋊Dic3—61no—
98C22×C3⋊Dic3—61no—
99C22×C3⋊Dic3—121no—
100C22×C3⋊Dic3C2×D311yescharacteristic
101C22×C3⋊Dic3C2×D311yescharacteristic
102C2×C3×#67—38no—
103C2×C3×#67—34no—
104C22×C3×Dic3—21no—
105C22×C3×Dic3—21no—
106C22×C3×Dic3—31no—
107C22×C3×Dic3—31no—
108C22×C3×Dic3—31no—
109C22×C3×Dic3—31no—
110C22×C3×Dic3—61no—
111C22×C3×Dic3—61no—
112C22×C3×Dic3C2×D311yescharacteristic
113C22×C3×Dic3C2×D311yescharacteristic
114C22×C3×Dic3C2×D311yescharacteristic
115C22×C3×Dic3C2×D311yescharacteristic
116C2×C3×D12—38no—
117C2×C3×D12—34no—
118C2×#626Dic318yescomplemented
119C2×#626C2×D314yes—
120C2×#624—34no—
121C2×#624—64no—
122C2×D3×Dic3—34no—
123C2×D3×Dic3—34no—
124C2×D3×Dic3—34no—
125C2×D3×Dic3—34no—
126C2×D3×Dic3—64no—
127C2×D3×Dic3—64no—
128C2×D3×Dic3—64no—
129C2×D3×Dic3—64no—
130C2×D3×Dic3—68no—
131C2×D3×Dic3—64no—
132#3752—34no—
133C4⋊(C3⋊Dic3)—34no—
134C3×#217—34no—
135C3×(C2×D3)⋊C4—34no—
136C3×C4×Dic3—34no—
137C3×C4×Dic3—34no—
138Dic3⋊Dic3—34no—
139Dic3⋊Dic3—34no—
140Dic3⋊Dic3—64no—
141(C2×D3)⋊Dic3—34no—
142(C2×D3)⋊Dic3—34no—
143(C2×D3)⋊Dic3—64no—
144(C2×D3)⋊Dic3C2×D314yescomplemented
145Dic32C2×D314yescomplemented
146C22×C33C22×C412yes—
147C22×C33C2×D412yes—
148C22×C33#4112yes—
149C22×C33C2411yescharacteristic
150C2×C3×C3⋊D3—28no—
151C2×C3×C3⋊D3—22no—
152C2×C3×C3⋊D3—22no—
153C2×C3×C3⋊D3C22×C414yescomplemented
154C2×C32×D3—28no—
155C2×C32×D3—22no—
156C2×C32×D3—22no—
157C2×C32×D3C22×C414yescomplemented
158C3⋊(C3⋊Dic3)—22no—
159C3×C3⋊Dic3—22no—
160C3×C3⋊Dic3C2×D414yescomplemented
161C32×Dic3—22no—
162C32×Dic3C22×C414yescomplemented
163C22×C3×D4—91no—
164C22×#67—31no—
165C23×Dic3—91no—
166C23×Dic3—91no—
167C23×Dic3—91no—
168C23×Dic3—181no—
169C22×D12—31no—
170C22×C4×D3—91no—
171C22×C4×D3—91no—
172C22×C4×D3—91no—
173C2×C3×C22⋊C4—91no—
174C2×C3×C42—91no—
175C2×#217—31no—
176C2×#217—91no—
177D4×Dic3—98no—
178C2×(C2×D3)⋊C4—31no—
179C2×(C2×D3)⋊C4—91no—
180C2×(C2×D3)⋊C4—91no—
181C2×(C2×D3)⋊C4—181no—
182C2×C4⋊Dic3—91no—
183C2×C4⋊Dic3—91no—
184C2×C4⋊Dic3—181no—
185C2×Dic3⋊C4—91no—
186C2×C4×Dic3—31no—
187C2×C4×Dic3—31no—
188#67⋊C4—98no—
189C4×D12—98no—
190C23×C32—21no—
191C23×C32—21no—
192C23×C32—21no—
193C23×C32—34no—
194C23×C32—32no—
195C23×C32—41no—
196C23×C32—62no—
197C23×C32—62no—
198C23×C32C22×D311yescharacteristic
199C23×C32C22×D311yescharacteristic
200C23×C32C22×D311yescharacteristic
201C22×C3⋊D3—22no—
202C22×C3⋊D3—22no—
203C22×C3⋊D3C2×Dic314yescomplemented
204C22×C3⋊D3C22×D312yes—
205C22×C3×D3—24no—
206C22×C3×D3—24no—
207C22×C3×D3—22no—
208C22×C3×D3—22no—
209C22×C3×D3—22no—
210C22×C3×D3—22no—
211C22×C3×D3—24no—
212C22×C3×D3—22no—
213C22×C3×D3—34no—
214C22×C3×D3—34no—
215C22×C3×D3—32no—
216C22×C3×D3—32no—
217C22×C3×D3—62no—
218C22×C3×D3—64no—
219C22×C3×D3—62no—
220C22×C3×D3—62no—
221C22×C3×D3—62no—
222C22×C3×D3—62no—
223C22×C3×D3—122no—
224C22×C3×D3—122no—
225C22×C3×D3C4×D314yescomplemented
226C22×C3×D3C2×Dic314yescomplemented
227C22×C3×D3C22×D312yes—
228C22×C3×D3C22×D312yes—
229C2×C32×C4—34no—
230C2×C32×C4—32no—
231C2×C32×C4—32no—
232C2×C32×C4—62no—
233C2×C3⋊Dic3—22no—
234C2×C3⋊Dic3—32no—
235C2×C3⋊Dic3—32no—
236C2×C3⋊Dic3—32no—
237C2×C3⋊Dic3—62no—
238C2×C3⋊Dic3—62no—
239C2×C3⋊Dic3—62no—
240C2×C3⋊Dic3—62no—
241C2×C3⋊Dic3—68no—
242C2×C3⋊Dic3—64no—
243C2×C3⋊Dic3—62no—
244C2×C3⋊Dic3—62no—
245C2×C3⋊Dic3—122no—
246C2×C3⋊Dic3—122no—
247C2×C3⋊Dic3—122no—
248C2×C3⋊Dic3—124no—
249C2×C3⋊Dic3D1214yescomplemented
250C2×C3⋊Dic3C22×D312yes—
251C2×C3⋊Dic3C22×D312yes—
252C3×#67—316no—
253C2×C3×Dic3—22no—
254C2×C3×Dic3—22no—
255C2×C3×Dic3—24no—
256C2×C3×Dic3—22no—
257C2×C3×Dic3—22no—
258C2×C3×Dic3—34no—
259C2×C3×Dic3—34no—
260C2×C3×Dic3—32no—
261C2×C3×Dic3—32no—
262C2×C3×Dic3—32no—
263C2×C3×Dic3—32no—
264C2×C3×Dic3—42no—
265C2×C3×Dic3—64no—
266C2×C3×Dic3—62no—
267C2×C3×Dic3—62no—
268C2×C3×Dic3—62no—
269C2×C3×Dic3—62no—
270C2×C3×Dic3—122no—
271C2×C3×Dic3C4×D314yescomplemented
272C2×C3×Dic3C2×Dic314yescomplemented
273C2×C3×Dic3C22×D312yes—
274C2×C3×Dic3C22×D312yes—
275C2×C3×Dic3C22×D312yes—
276C2×C3×Dic3C22×D312yes—
277C3×D12—316no—
278#626C2×Dic3116yescomplemented
279#624—68no—
280D3×Dic3—68no—
281D3×Dic3—68no—
282D3×Dic3—68no—
283D3×Dic3—616no—
284D3×Dic3—68no—
285C2×C4×D4—271noSylow
286C2×C33C4×D414yescomplemented
287C2×C33C23×C411yescharacteristic
288C2×C33C22×D411yescharacteristic
289C2×C33C2×#4111yescharacteristic
290C3×C3⋊D3—24no—
291C32×D3—24no—
292C24×C3—31no—
293C24×C3—31no—
294C24×C3—61no—
295C24×C3—91no—
296C23×D3—31no—
297C23×D3—31no—
298C23×D3—61no—
299C23×D3D3211yescharacteristic
300C2×C3×D4—94no—
301C2×C3×D4—98no—
302C22×C3×C4—31no—
303C22×C3×C4—31no—
304C22×C3×C4—31no—
305C22×C3×C4—31no—
306C22×C3×C4—61no—
307C22×C3×C4—61no—
308C22×C3×C4—91no—
309C22×C3×C4—91no—
310C2×#67—38no—
311C2×#67—34no—
312C22×Dic3—31no—
313C22×Dic3—31no—
314C22×Dic3—31no—
315C22×Dic3—31no—
316C22×Dic3—61no—
317C22×Dic3—61no—
318C22×Dic3—94no—
319C22×Dic3—94no—
320C22×Dic3—94no—
321C22×Dic3—91no—
322C22×Dic3—91no—
323C22×Dic3—91no—
324C22×Dic3—184no—
325C22×Dic3—181no—
326C22×Dic3—181no—
327C22×Dic3—181no—
328C22×Dic3—184no—
329C22×Dic3—184no—
330C22×Dic3—184no—
331C22×Dic3—188no—
332C22×Dic3—361no—
333C22×Dic3D3211yescharacteristic
334C22×Dic3D3211yescharacteristic
335C2×D12—38no—
336C2×D12—34no—
337C2×C4×D3—94no—
338C2×C4×D3—94no—
339C2×C4×D3—94no—
340C2×C4×D3—184no—
341C2×C4×D3—184no—
342C2×C4×D3—184no—
343C3×C22⋊C4—94no—
344C3×C42—94no—
345#217—34no—
346#217—94no—
347(C2×D3)⋊C4—34no—
348(C2×D3)⋊C4—94no—
349(C2×D3)⋊C4—94no—
350(C2×D3)⋊C4—184no—
351C4⋊Dic3—94no—
352C4⋊Dic3—94no—
353C4⋊Dic3—184no—
354Dic3⋊C4—94no—
355C4×Dic3—34no—
356C4×Dic3—34no—
357C22×C32—21no—
358C22×C32—21no—
359C22×C32—21no—
360C22×C32—22no—
361C22×C32—22no—
362C22×C32—22no—
363C22×C32—22no—
364C22×C32—22no—
365C22×C32—22no—
366C22×C32—22no—
367C22×C32—22no—
368C22×C32—22no—
369C22×C32—34no—
370C22×C32—42no—
371C22×C32—42no—
372C22×C32—42no—
373C22×C32—41no—
374C22×C32—68no—
375C22×C32—62no—
376C22×C32—62no—
377C22×C32C2×C4×D312yes—
378C22×C32C2×C4×D312yes—
379C22×C32C2×D1212yes—
380C22×C32#23512yes—
381C22×C32D3×D412yes—
382C22×C32D3×D412yes—
383C22×C32#23712yes—
384C22×C32#23712yes—
385C22×C32C22×Dic312yes—
386C22×C32C23×D311yescharacteristic
387C22×C32C23×D311yescharacteristic
388C22×C32C23×D311yescharacteristic
389C2×C3⋊D3—28no—
390C2×C3⋊D3—22no—
391C2×C3⋊D3—22no—
392C2×C3⋊D3C22×Dic314yescomplemented
393C2×C3×D3—24no—
394C2×C3×D3—24no—
395C2×C3×D3—216no—
396C2×C3×D3—28no—
397C2×C3×D3—28no—
398C2×C3×D3—22no—
399C2×C3×D3—22no—
400C2×C3×D3—22no—
401C2×C3×D3—22no—
402C2×C3×D3—24no—
403C2×C3×D3—34no—
404C2×C3×D3—34no—
405C2×C3×D3—64no—
406C2×C3×D3—68no—
407C2×C3×D3—68no—
408C2×C3×D3—62no—
409C2×C3×D3—62no—
410C2×C3×D3—62no—
411C2×C3×D3—62no—
412C2×C3×D3—122no—
413C2×C3×D3—122no—
414C2×C3×D3—128no—
415C2×C3×D3C2×C4×D314yescomplemented
416C2×C3×D3C22×Dic314yescomplemented
417C32×C4—34no—
418C32×C4—62no—
419C3⋊Dic3—22no—
420C3⋊Dic3—62no—
421C3⋊Dic3—64no—
422C3⋊Dic3—62no—
423C3⋊Dic3—62no—
424C3⋊Dic3—122no—
425C3⋊Dic3—122no—
426C3⋊Dic3—124no—
427C3⋊Dic3C2×D1214yescomplemented
428C3×Dic3—22no—
429C3×Dic3—22no—
430C3×Dic3—24no—
431C3×Dic3—34no—
432C3×Dic3—34no—
433C3×Dic3—42no—
434C3×Dic3—64no—
435C3×Dic3—62no—
436C3×Dic3—62no—
437C3×Dic3—122no—
438C3×Dic3C2×C4×D314yescomplemented
439C3×Dic3C22×Dic314yescomplemented
440C22×D4—91no—
441C23×C4—271no—
442C23×C4—271no—
443C4×D4—278no—
444C2×C4⋊C4—271no—
445C2×C22⋊C4—91no—
446C2×C22⋊C4—271no—
447C2×C42—91no—
448C33C2×C4×D411yescharacteristic, complemented, Sylow
449C23×C3—21no—
450C23×C3—21no—
451C23×C3—21no—
452C23×C3—32no—
453C23×C3—32no—
454C23×C3—34no—
455C23×C3—34no—
456C23×C3—41no—
457C23×C3—62no—
458C23×C3—64no—
459C23×C3—64no—
460C23×C3—64no—
461C23×C3—62no—
462C23×C3—62no—
463C23×C3—62no—
464C23×C3—62no—
465C23×C3—92no—
466C23×C3—94no—
467C23×C3—182no—
468C23×C3—182no—
469C23×C3C2×D3211yescharacteristic
470C23×C3C2×D3211yescharacteristic
471C23×C3C2×D3211yescharacteristic
472C22×D3—22no—
473C22×D3—22no—
474C22×D3—32no—
475C22×D3—32no—
476C22×D3—34no—
477C22×D3—34no—
478C22×D3—64no—
479C22×D3—62no—
480C22×D3—62no—
481C22×D3—62no—
482C22×D3—62no—
483C22×D3—62no—
484C22×D3—122no—
485C22×D3—122no—
486C22×D3D3×Dic314yescomplemented
487C22×D3C2×D3212yes—
488C3×D4—916no—
489C2×C3×C4—32no—
490C2×C3×C4—32no—
491C2×C3×C4—34no—
492C2×C3×C4—34no—
493C2×C3×C4—32no—
494C2×C3×C4—32no—
495C2×C3×C4—62no—
496C2×C3×C4—64no—
497C2×C3×C4—62no—
498C2×C3×C4—62no—
499C2×C3×C4—62no—
500C2×C3×C4—92no—
501C2×C3×C4—94no—
502C2×C3×C4—92no—
503C2×C3×C4—122no—
504C2×C3×C4—182no—
505#67—316no—
506C2×Dic3—22no—
507C2×Dic3—32no—
508C2×Dic3—32no—
509C2×Dic3—34no—
510C2×Dic3—34no—
511C2×Dic3—32no—
512C2×Dic3—32no—
513C2×Dic3—64no—
514C2×Dic3—62no—
515C2×Dic3—62no—
516C2×Dic3—62no—
517C2×Dic3—62no—
518C2×Dic3—92no—
519C2×Dic3—92no—
520C2×Dic3—92no—
521C2×Dic3—122no—
522C2×Dic3—182no—
523C2×Dic3—182no—
524C2×Dic3—182no—
525C2×Dic3—188no—
526C2×Dic3—188no—
527C2×Dic3—188no—
528C2×Dic3—1816no—
529C2×Dic3—184no—
530C2×Dic3—182no—
531C2×Dic3—182no—
532C2×Dic3—182no—
533C2×Dic3—362no—
534C2×Dic3—362no—
535C2×Dic3—362no—
536C2×Dic3—364no—
537C2×Dic3D3×Dic314yescomplemented
538C2×Dic3C2×D3212yes—
539C2×Dic3C2×D3212yes—
540D12—316no—
541C4×D3—188no—
542C4×D3—188no—
543C4×D3—188no—
544C2×C32—21no—
545C2×C32—21no—
546C2×C32—21no—
547C2×C32—21no—
548C2×C32—21no—
549C2×C32—21no—
550C2×C32—21no—
551C2×C32—21no—
552C2×C32—21no—
553C2×C32—24no—
554C2×C32—24no—
555C2×C32—24no—
556C2×C32—44no—
557C2×C32—41no—
558C2×C32—41no—
559C2×C32—41no—
560C2×C32—64no—
561C2×C32C4×D1214yescomplemented
562C2×C32#67⋊C414yescomplemented
563C2×C32D4×Dic314yescomplemented
564C2×C32C22×C4×D311yescharacteristic
565C2×C32C22×C4×D311yescharacteristic
566C2×C32C22×D1211yescharacteristic
567C2×C32C2×#23511yescharacteristic
568C2×C32C2×D3×D411yescharacteristic
569C2×C32C2×D3×D411yescharacteristic
570C2×C32C2×#23711yescharacteristic
571C2×C32C2×#23711yescharacteristic
572C2×C32C23×Dic311yescharacteristic
573C3⋊D3—24no—
574C3×D3—28no—
575C3×D3—24no—
576C3×D3—24no—
577C3×D3—64no—
578C3×D3—64no—
579C3×D3—124no—
580C24—31no—
581C24—91no—
582C2×D4—94no—
583C2×D4—98no—
584C22×C4—31no—
585C22×C4—31no—
586C22×C4—91no—
587C22×C4—91no—
588C22×C4—274no—
589C22×C4—274no—
590C22×C4—271no—
591C22×C4—544no—
592C22×C4—544no—
593C4⋊C4—274no—
594C22⋊C4—94no—
595C22⋊C4—274no—
596C42—94no—
597C22×C3—21no—
598C22×C3—21no—
599C22×C3—21no—
600C22×C3—22no—
601C22×C3—22no—
602C22×C3—22no—
603C22×C3—22no—
604C22×C3—22no—
605C22×C3—22no—
606C22×C3—22no—
607C22×C3—22no—
608C22×C3—22no—
609C22×C3—34no—
610C22×C3—34no—
611C22×C3—41no—
612C22×C3—42no—
613C22×C3—42no—
614C22×C3—42no—
615C22×C3—64no—
616C22×C3—64no—
617C22×C3—64no—
618C22×C3—616no—
619C22×C3—62no—
620C22×C3—62no—
621C22×C3—62no—
622C22×C3—62no—
623C22×C3—68no—
624C22×C3—68no—
625C22×C3—94no—
626C22×C3—182no—
627C22×C3—182no—
628C22×C3—188no—
629C22×C3#379512yes—
630C22×C3C4×D3212yes—
631C22×C3D3×D1212yes—
632C22×C3D3×D1212yes—
633C22×C3C2×D3×Dic312yes—
634C22×C3C2×D3×Dic312yes—
635C22×C3#380412yes—
636C22×C3#380512yes—
637C22×C3#381112yes—
638C22×C3C22×D3211yescharacteristic
639C22×C3C22×D3211yescharacteristic
640C22×C3C22×D3211yescharacteristic
641C2×D3—22no—
642C2×D3—22no—
643C2×D3—28no—
644C2×D3—34no—
645C2×D3—34no—
646C2×D3—64no—
647C2×D3—62no—
648C2×D3—62no—
649C2×D3—62no—
650C2×D3—62no—
651C2×D3—68no—
652C2×D3—68no—
653C2×D3—122no—
654C2×D3—122no—
655C2×D3—128no—
656C2×D3C2×D3×Dic314yescomplemented
657C3×C4—34no—
658C3×C4—34no—
659C3×C4—64no—
660C3×C4—62no—
661C3×C4—62no—
662C3×C4—94no—
663C3×C4—122no—
664C3×C4—182no—
665Dic3—22no—
666Dic3—34no—
667Dic3—34no—
668Dic3—64no—
669Dic3—62no—
670Dic3—62no—
671Dic3—122no—
672Dic3—184no—
673Dic3—182no—
674Dic3—182no—
675Dic3—182no—
676Dic3—362no—
677Dic3—362no—
678Dic3—364no—
679Dic3C2×D3×Dic314yescomplemented
680C32—21no—
681C32—21no—
682C32—21no—
683C32—41no—
684C32C2×C4×D1211yescharacteristic, complemented
685C32C2×#67⋊C411yescharacteristic, complemented
686C32C2×D4×Dic311yescharacteristic, complemented
687C23—32no—
688C23—34no—
689C23—62no—
690C23—62no—
691C23—92no—
692C23—94no—
693C23—182no—
694C23—182no—
695C23D3311yescharacteristic
696D4—916no—
697C2×C4—32no—
698C2×C4—34no—
699C2×C4—32no—
700C2×C4—62no—
701C2×C4—92no—
702C2×C4—94no—
703C2×C4—92no—
704C2×C4—182no—
705C2×C4—272no—
706C2×C4—548no—
707C2×C4—548no—
708C2×C4—542no—
709C2×C3—21no—
710C2×C3—21no—
711C2×C3—21no—
712C2×C3—21no—
713C2×C3—21no—
714C2×C3—21no—
715C2×C3—21no—
716C2×C3—21no—
717C2×C3—21no—
718C2×C3—24no—
719C2×C3—24no—
720C2×C3—24no—
721C2×C3—41no—
722C2×C3—41no—
723C2×C3—41no—
724C2×C3—44no—
725C2×C3—68no—
726C2×C3—64no—
727C2×C3—64no—
728C2×C3—184no—
729C2×C3#6388014yescomplemented
730C2×C3Dic3×D1214yescomplemented
731C2×C3#67⋊Dic314yescomplemented
732C2×C3C2×#379511yescharacteristic
733C2×C3C2×C4×D3211yescharacteristic
734C2×C3C2×D3×D1211yescharacteristic
735C2×C3C2×D3×D1211yescharacteristic
736C2×C3C22×D3×Dic311yescharacteristic
737C2×C3C22×D3×Dic311yescharacteristic
738C2×C3C2×#380411yescharacteristic
739C2×C3C2×#380511yescharacteristic
740C2×C3C2×#381111yescharacteristic
741D3—24no—
742D3—64no—
743D3—64no—
744D3—124no—
745C22—34no—
746C22—62no—
747C22—62no—
748C22—68no—
749C22—94no—
750C22—182no—
751C22—182no—
752C22—188no—
753C22D32×Dic312yes—
754C22#8895512yes—
755C22#8896112yes—
756C22C2×D3311yescharacteristic
757C4—34no—
758C4—62no—
759C4—94no—
760C4—182no—
761C4—542no—
762C3—21no—
763C3—21no—
764C3—21no—
765C3—41no—
766C3C2×#6388011yescharacteristic, complemented
767C3C2×Dic3×D1211yescharacteristic, complemented
768C3C2×#67⋊Dic311yescharacteristic, complemented
769C2—64no—
770C2—184no—
771C2#1172292814yesdirect product factor
772C2C2×D32×Dic311yescharacteristic
773C2C2×#8895511yescharacteristic
774C2C2×#8896111yescharacteristic
subgroupG/H
center, hypercenterC23D33
commutatorC2×C33C23×C4
FrattiniC22C2×D33
Fitting, socleC23×C33C23
prime radicalC22×C3×#626C2
cosocleC22×C33C24
hypocenterC33C2×C4×D4
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C22×#6294C2semidirect
2. C22×D3×C3⋊Dic3C2semidirect
4. C2×Dic3⋊(C3⋊Dic3)C2semidirect
5. C2×#88803C2semidirect
6. C2×C3×(C2×D3)⋊Dic3C2semidirect
7. C2×C3×Dic32C2semidirect
8. #11722928C2direct (N × H)
20. C2×#6294C22semidirect
22. C2×D3×C3⋊Dic3C22semidirect
23. C2×C3×#626C4semidirect
25. Dic3⋊(C3⋊Dic3)C22semidirect
26. #88803C22semidirect
27. C3×(C2×D3)⋊Dic3C22semidirect
28. C3×Dic32C22semidirect
52. C2×(C2×D3)⋊Dic3D3semidirect
53. C2×Dic32D3semidirect
59. C22×C3×C3⋊D3C2×C4semidirect
63. C22×C32×D3C2×C4semidirect
68. C2×C3×C3⋊Dic3D4semidirect
72. C2×C32×Dic3C2×C4semidirect
77. C3×#626C2×C4semidirect
118. C2×#626Dic3semidirect
144. (C2×D3)⋊Dic3C2×D3semidirect
145. Dic32C2×D3semidirect
153. C2×C3×C3⋊D3C22×C4semidirect
157. C2×C32×D3C22×C4semidirect
160. C3×C3⋊Dic3C2×D4semidirect
162. C32×Dic3C22×C4semidirect
203. C22×C3⋊D3C2×Dic3semidirect
225. C22×C3×D3C4×D3semidirect
226. C22×C3×D3C2×Dic3semidirect
249. C2×C3⋊Dic3D12semidirect
271. C2×C3×Dic3C4×D3semidirect
272. C2×C3×Dic3C2×Dic3semidirect
278. #626C2×Dic3semidirect
286. C2×C33C4×D4semidirect
392. C2×C3⋊D3C22×Dic3semidirect
415. C2×C3×D3C2×C4×D3semidirect
416. C2×C3×D3C22×Dic3semidirect
427. C3⋊Dic3C2×D12semidirect
438. C3×Dic3C2×C4×D3semidirect
439. C3×Dic3C22×Dic3semidirect
448. C33C2×C4×D4semidirect
486. C22×D3D3×Dic3semidirect
537. C2×Dic3D3×Dic3semidirect
561. C2×C32C4×D12semidirect
562. C2×C32#67⋊C4semidirect
563. C2×C32D4×Dic3semidirect
656. C2×D3C2×D3×Dic3semidirect
679. Dic3C2×D3×Dic3semidirect
684. C32C2×C4×D12semidirect
685. C32C2×#67⋊C4semidirect
686. C32C2×D4×Dic3semidirect
729. C2×C3#63880semidirect
730. C2×C3Dic3×D12semidirect
731. C2×C3#67⋊Dic3semidirect
766. C3C2×#63880semidirect
767. C3C2×Dic3×D12semidirect
768. C3C2×#67⋊Dic3semidirect
771. C2#11722928direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#62942
C22×D3×C3⋊Dic32
C22×C3×#6262
C2×Dic3⋊(C3⋊Dic3)2
C2×#888032
C2×C3×(C2×D3)⋊Dic32
C2×C3×Dic322
#117229282
C2×#67⋊Dic33
C2×Dic3×D123
C2×#638803