Finite Group Databasebeta

← C2×#11722929 #13172003

Subgroups — C2×#11722929 #13172003

Order 1728.

2338 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Dic3×C3⋊D3C211yesmaximal, characteristic, complemented
2C22×D3×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C22×C3×#626C211yesmaximal, characteristic
4C2×#88814C211yesmaximal, characteristic, complemented
5C2×Dic3×C3⋊Dic3C211yesmaximal, characteristic, complemented
6C2×C3×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
7C2×C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
8#11722929C218yesmaximal, direct product factor
9C2×#67⋊Dic3—31nomaximal
10C2×#63898—31nomaximal
11C2×#63881—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×Dic3×C3⋊D3—24no—
20C2×Dic3×C3⋊D3C2214yescomplemented
21C2×D3×C3⋊Dic3—24no—
22C2×D3×C3⋊Dic3C2214yescomplemented
23C2×C3×#626C418yescomplemented
24C2×C3×#626C2214yes—
25#88814C2214yescomplemented
26Dic3×C3⋊Dic3C2214yescomplemented
27C3×Dic3⋊Dic3C2214yescomplemented
28C3×(C2×D3)⋊Dic3C2214yescomplemented
29C23×C3⋊Dic3—31no—
30C22×C4×C3⋊D3—31no—
31C22×C3×#67—31no—
32C22×C3×D12—31no—
33C22×#626D311yescharacteristic
34C22×D3×Dic3—31no—
35C22×D3×Dic3—31no—
36C22×D3×Dic3—31no—
37C22×D3×Dic3—31no—
38C22×D3×Dic3—61no—
39C22×D3×Dic3—61no—
40C2×C4×C3⋊Dic3—31no—
41C2×C3×#217—31no—
42C2×C3×(C2×D3)⋊C4—31no—
43C2×C3×C4⋊Dic3—31no—
44C2×C3×Dic3⋊C4—31no—
45#67⋊Dic3—38no—
46C2×Dic3⋊Dic3D311yescharacteristic, complemented
47C2×#3722—31no—
48C2×(C2×D3)⋊Dic3—31no—
49C2×(C2×D3)⋊Dic3—31no—
50C2×(C2×D3)⋊Dic3D311yescharacteristic, complemented
51C2×Dic32—31no—
52C2×Dic32—31no—
53C2×Dic32—61no—
54#63898—38no—
55#63881—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)D414yescomplemented
66C2×C3⋊(C3⋊Dic3)C2312yes—
67C2×C3×C3⋊Dic3—22no—
68C2×C3×C3⋊Dic3—22no—
69C2×C3×C3⋊Dic3C2312yes—
70C2×C3×C3⋊Dic3C2312yes—
71C2×C32×Dic3—22no—
72C2×C32×Dic3C2×C414yescomplemented
73C2×C32×Dic3C2312yes—
74C2×C32×Dic3C2312yes—
75Dic3×C3⋊D3—28no—
76D3×C3⋊Dic3—28no—
77C3×#626C2×C4116yescomplemented
78C2×D4×Dic3—91no—
79C2×#893—91no—
80C2×#67⋊C4—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—64no—
96C22×C3⋊Dic3—61no—
97C22×C3⋊Dic3—61no—
98C22×C3⋊Dic3—61no—
99C22×C3⋊Dic3—121no—
100C22×C3⋊Dic3C2×D311yescharacteristic
101C22×C3⋊Dic3C2×D311yescharacteristic
102C2×C4×C3⋊D3—34no—
103C2×C4×C3⋊D3—64no—
104C2×C3×#67—38no—
105C2×C3×#67—34no—
106C22×C3×Dic3—21no—
107C22×C3×Dic3—21no—
108C22×C3×Dic3—31no—
109C22×C3×Dic3—31no—
110C22×C3×Dic3—31no—
111C22×C3×Dic3—31no—
112C22×C3×Dic3—61no—
113C22×C3×Dic3—61no—
114C22×C3×Dic3C2×D311yescharacteristic
115C22×C3×Dic3C2×D311yescharacteristic
116C22×C3×Dic3C2×D311yescharacteristic
117C22×C3×Dic3C2×D311yescharacteristic
118C2×C3×D12—38no—
119C2×C3×D12—34no—
120C2×#626Dic318yescomplemented
121C2×#626C2×D314yes—
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—68no—
130C2×D3×Dic3—64no—
131C2×D3×Dic3—64no—
132C2×D3×Dic3—64no—
133C2×D3×Dic3—68no—
134C4×C3⋊Dic3—34no—
135C3×#217—34no—
136C3×(C2×D3)⋊C4—34no—
137C3×C4⋊Dic3—34no—
138C3×Dic3⋊C4—34no—
139Dic3⋊Dic3C2×D314yescomplemented
140#3722—34no—
141(C2×D3)⋊Dic3—34no—
142(C2×D3)⋊Dic3—34no—
143(C2×D3)⋊Dic3C2×D314yescomplemented
144Dic32—34no—
145Dic32—34no—
146Dic32—64no—
147C22×C33C22×C412yes—
148C22×C33C2×D412yes—
149C22×C33#4112yes—
150C22×C33C2411yescharacteristic
151C2×C3×C3⋊D3—28no—
152C2×C3×C3⋊D3—22no—
153C2×C3×C3⋊D3—22no—
154C2×C3×C3⋊D3C22×C414yescomplemented
155C2×C32×D3—28no—
156C2×C32×D3—22no—
157C2×C32×D3—22no—
158C2×C32×D3C22×C414yescomplemented
159C3⋊(C3⋊Dic3)C2×D414yescomplemented
160C3×C3⋊Dic3—22no—
161C3×C3⋊Dic3—22no—
162C32×Dic3—22no—
163C32×Dic3C22×C414yescomplemented
164C22×C3×D4—91no—
165C22×#67—31no—
166C23×Dic3—91no—
167C23×Dic3—91no—
168C23×Dic3—91no—
169C23×Dic3—181no—
170C22×D12—31no—
171C22×C4×D3—91no—
172C22×C4×D3—91no—
173C22×C4×D3—91no—
174C22×C4×D3—181no—
175C2×C3×C4⋊C4—91no—
176C2×C3×C22⋊C4—91no—
177C2×#217—31no—
178C2×#217—91no—
179D4×Dic3—98no—
180C2×(C2×D3)⋊C4—31no—
181C2×(C2×D3)⋊C4—91no—
182C2×(C2×D3)⋊C4—91no—
183C2×C4⋊Dic3—31no—
184C2×Dic3⋊C4—31no—
185C2×C4×Dic3—91no—
186C2×C4×Dic3—91no—
187C2×C4×Dic3—91no—
188C2×C4×Dic3—181no—
189#893—98no—
190#67⋊C4—98no—
191C23×C32—21no—
192C23×C32—21no—
193C23×C32—21no—
194C23×C32—34no—
195C23×C32—32no—
196C23×C32—41no—
197C23×C32—62no—
198C23×C32—62no—
199C23×C32C22×D311yescharacteristic
200C23×C32C22×D311yescharacteristic
201C23×C32C22×D311yescharacteristic
202C22×C3⋊D3—22no—
203C22×C3⋊D3—22no—
204C22×C3⋊D3C2×Dic314yescomplemented
205C22×C3⋊D3C22×D312yes—
206C22×C3×D3—24no—
207C22×C3×D3—24no—
208C22×C3×D3—22no—
209C22×C3×D3—22no—
210C22×C3×D3—22no—
211C22×C3×D3—22no—
212C22×C3×D3—24no—
213C22×C3×D3—22no—
214C22×C3×D3—34no—
215C22×C3×D3—34no—
216C22×C3×D3—32no—
217C22×C3×D3—32no—
218C22×C3×D3—64no—
219C22×C3×D3—62no—
220C22×C3×D3—64no—
221C22×C3×D3—64no—
222C22×C3×D3—62no—
223C22×C3×D3—62no—
224C22×C3×D3—62no—
225C22×C3×D3—62no—
226C22×C3×D3C4×D314yescomplemented
227C22×C3×D3C2×Dic314yescomplemented
228C22×C3×D3C22×D312yes—
229C22×C3×D3C22×D312yes—
230C2×C32×C4—34no—
231C2×C32×C4—32no—
232C2×C32×C4—32no—
233C2×C32×C4—62no—
234C2×C3⋊Dic3—22no—
235C2×C3⋊Dic3—22no—
236C2×C3⋊Dic3—34no—
237C2×C3⋊Dic3—34no—
238C2×C3⋊Dic3—34no—
239C2×C3⋊Dic3—32no—
240C2×C3⋊Dic3—32no—
241C2×C3⋊Dic3—32no—
242C2×C3⋊Dic3—62no—
243C2×C3⋊Dic3—64no—
244C2×C3⋊Dic3—64no—
245C2×C3⋊Dic3—64no—
246C2×C3⋊Dic3—62no—
247C2×C3⋊Dic3—62no—
248C2×C3⋊Dic3—68no—
249C2×C3⋊Dic3—124no—
250C2×C3⋊Dic3—122no—
251C2×C3⋊Dic3C22×D312yes—
252C2×C3⋊Dic3C22×D312yes—
253C4×C3⋊D3—68no—
254C3×#67—316no—
255C2×C3×Dic3—24no—
256C2×C3×Dic3—22no—
257C2×C3×Dic3—22no—
258C2×C3×Dic3—24no—
259C2×C3×Dic3—22no—
260C2×C3×Dic3—22no—
261C2×C3×Dic3—32no—
262C2×C3×Dic3—32no—
263C2×C3×Dic3—32no—
264C2×C3×Dic3—32no—
265C2×C3×Dic3—62no—
266C2×C3×Dic3—62no—
267C2×C3×Dic3—64no—
268C2×C3×Dic3—64no—
269C2×C3×Dic3—62no—
270C2×C3×Dic3—62no—
271C2×C3×Dic3—62no—
272C2×C3×Dic3—62no—
273C2×C3×Dic3C4×D314yescomplemented
274C2×C3×Dic3C2×Dic314yescomplemented
275C2×C3×Dic3C22×D312yes—
276C2×C3×Dic3C22×D312yes—
277C2×C3×Dic3C22×D312yes—
278C2×C3×Dic3C22×D312yes—
279C3×D12—316no—
280#626C2×Dic3116yescomplemented
281D3×Dic3—68no—
282D3×Dic3—68no—
283D3×Dic3—616no—
284D3×Dic3—68no—
285D3×Dic3—68no—
286D3×Dic3—616no—
287C2×C4×D4—271noSylow
288C2×C33C4×D414yescomplemented
289C2×C33C23×C411yescharacteristic
290C2×C33C22×D411yescharacteristic
291C2×C33C2×#4111yescharacteristic
292C3×C3⋊D3—24no—
293C32×D3—24no—
294C24×C3—31no—
295C24×C3—31no—
296C24×C3—61no—
297C24×C3—91no—
298C23×D3—31no—
299C23×D3—31no—
300C23×D3—61no—
301C23×D3D3211yescharacteristic
302C2×C3×D4—94no—
303C2×C3×D4—98no—
304C22×C3×C4—31no—
305C22×C3×C4—31no—
306C22×C3×C4—31no—
307C22×C3×C4—31no—
308C22×C3×C4—61no—
309C22×C3×C4—61no—
310C22×C3×C4—91no—
311C22×C3×C4—91no—
312C2×#67—38no—
313C2×#67—34no—
314C22×Dic3—31no—
315C22×Dic3—31no—
316C22×Dic3—31no—
317C22×Dic3—31no—
318C22×Dic3—61no—
319C22×Dic3—61no—
320C22×Dic3—94no—
321C22×Dic3—94no—
322C22×Dic3—91no—
323C22×Dic3—91no—
324C22×Dic3—91no—
325C22×Dic3—94no—
326C22×Dic3—184no—
327C22×Dic3—181no—
328C22×Dic3—181no—
329C22×Dic3—181no—
330C22×Dic3—184no—
331C22×Dic3—184no—
332C22×Dic3—184no—
333C22×Dic3—188no—
334C22×Dic3—361no—
335C22×Dic3D3211yescharacteristic
336C22×Dic3D3211yescharacteristic
337C2×D12—38no—
338C2×D12—34no—
339C2×C4×D3—94no—
340C2×C4×D3—94no—
341C2×C4×D3—94no—
342C2×C4×D3—184no—
343C2×C4×D3—184no—
344C2×C4×D3—184no—
345C2×C4×D3—184no—
346C2×C4×D3—188no—
347C3×C4⋊C4—94no—
348C3×C22⋊C4—94no—
349#217—34no—
350#217—94no—
351(C2×D3)⋊C4—34no—
352(C2×D3)⋊C4—94no—
353(C2×D3)⋊C4—94no—
354C4⋊Dic3—34no—
355Dic3⋊C4—34no—
356C4×Dic3—94no—
357C4×Dic3—94no—
358C4×Dic3—94no—
359C4×Dic3—184no—
360C22×C32—21no—
361C22×C32—21no—
362C22×C32—21no—
363C22×C32—22no—
364C22×C32—22no—
365C22×C32—22no—
366C22×C32—22no—
367C22×C32—22no—
368C22×C32—22no—
369C22×C32—22no—
370C22×C32—22no—
371C22×C32—22no—
372C22×C32—34no—
373C22×C32—42no—
374C22×C32—42no—
375C22×C32—42no—
376C22×C32—41no—
377C22×C32—68no—
378C22×C32—62no—
379C22×C32—62no—
380C22×C32C2×C4×D312yes—
381C22×C32C2×C4×D312yes—
382C22×C32D3×D412yes—
383C22×C32D3×D412yes—
384C22×C32D3×D412yes—
385C22×C32#23712yes—
386C22×C32#23712yes—
387C22×C32#23912yes—
388C22×C32C22×Dic312yes—
389C22×C32C23×D311yescharacteristic
390C22×C32C23×D311yescharacteristic
391C22×C32C23×D311yescharacteristic
392C2×C3⋊D3—28no—
393C2×C3⋊D3—22no—
394C2×C3⋊D3—22no—
395C2×C3⋊D3C22×Dic314yescomplemented
396C2×C3×D3—24no—
397C2×C3×D3—24no—
398C2×C3×D3—216no—
399C2×C3×D3—28no—
400C2×C3×D3—28no—
401C2×C3×D3—22no—
402C2×C3×D3—22no—
403C2×C3×D3—22no—
404C2×C3×D3—22no—
405C2×C3×D3—24no—
406C2×C3×D3—34no—
407C2×C3×D3—34no—
408C2×C3×D3—64no—
409C2×C3×D3—64no—
410C2×C3×D3—64no—
411C2×C3×D3—616no—
412C2×C3×D3—68no—
413C2×C3×D3—68no—
414C2×C3×D3—62no—
415C2×C3×D3—62no—
416C2×C3×D3—62no—
417C2×C3×D3—62no—
418C2×C3×D3C2×C4×D314yescomplemented
419C2×C3×D3C22×Dic314yescomplemented
420C32×C4—34no—
421C32×C4—62no—
422C3⋊Dic3—22no—
423C3⋊Dic3—22no—
424C3⋊Dic3—34no—
425C3⋊Dic3—34no—
426C3⋊Dic3—34no—
427C3⋊Dic3—64no—
428C3⋊Dic3—64no—
429C3⋊Dic3—64no—
430C3⋊Dic3—124no—
431C3×Dic3—24no—
432C3×Dic3—22no—
433C3×Dic3—22no—
434C3×Dic3—24no—
435C3×Dic3—64no—
436C3×Dic3—64no—
437C3×Dic3—62no—
438C3×Dic3—62no—
439C3×Dic3—62no—
440C3×Dic3—62no—
441C3×Dic3C2×C4×D314yescomplemented
442C3×Dic3C22×Dic314yescomplemented
443C22×D4—91no—
444C23×C4—271no—
445C23×C4—271no—
446C4×D4—278no—
447C2×C4⋊C4—91no—
448C2×C22⋊C4—91no—
449C2×C22⋊C4—271no—
450C2×C42—271no—
451C33C2×C4×D411yescharacteristic, complemented, Sylow
452C23×C3—21no—
453C23×C3—21no—
454C23×C3—21no—
455C23×C3—32no—
456C23×C3—32no—
457C23×C3—34no—
458C23×C3—34no—
459C23×C3—41no—
460C23×C3—62no—
461C23×C3—64no—
462C23×C3—64no—
463C23×C3—64no—
464C23×C3—62no—
465C23×C3—62no—
466C23×C3—62no—
467C23×C3—62no—
468C23×C3—92no—
469C23×C3—94no—
470C23×C3—182no—
471C23×C3—182no—
472C23×C3C2×D3211yescharacteristic
473C23×C3C2×D3211yescharacteristic
474C23×C3C2×D3211yescharacteristic
475C22×D3—22no—
476C22×D3—22no—
477C22×D3—32no—
478C22×D3—32no—
479C22×D3—34no—
480C22×D3—34no—
481C22×D3—64no—
482C22×D3—62no—
483C22×D3—64no—
484C22×D3—64no—
485C22×D3—62no—
486C22×D3—62no—
487C22×D3—62no—
488C22×D3—62no—
489C22×D3D3×Dic314yescomplemented
490C22×D3C2×D3212yes—
491C3×D4—916no—
492C2×C3×C4—32no—
493C2×C3×C4—32no—
494C2×C3×C4—34no—
495C2×C3×C4—34no—
496C2×C3×C4—32no—
497C2×C3×C4—32no—
498C2×C3×C4—62no—
499C2×C3×C4—62no—
500C2×C3×C4—64no—
501C2×C3×C4—64no—
502C2×C3×C4—62no—
503C2×C3×C4—62no—
504C2×C3×C4—92no—
505C2×C3×C4—92no—
506C2×C3×C4—182no—
507C2×C3×C4—182no—
508#67—316no—
509C2×Dic3—22no—
510C2×Dic3—32no—
511C2×Dic3—32no—
512C2×Dic3—32no—
513C2×Dic3—32no—
514C2×Dic3—62no—
515C2×Dic3—62no—
516C2×Dic3—64no—
517C2×Dic3—64no—
518C2×Dic3—62no—
519C2×Dic3—62no—
520C2×Dic3—62no—
521C2×Dic3—62no—
522C2×Dic3—92no—
523C2×Dic3—92no—
524C2×Dic3—92no—
525C2×Dic3—94no—
526C2×Dic3—94no—
527C2×Dic3—94no—
528C2×Dic3—182no—
529C2×Dic3—182no—
530C2×Dic3—184no—
531C2×Dic3—184no—
532C2×Dic3—182no—
533C2×Dic3—184no—
534C2×Dic3—188no—
535C2×Dic3—188no—
536C2×Dic3—188no—
537C2×Dic3—1816no—
538C2×Dic3—362no—
539C2×Dic3—364no—
540C2×Dic3D3×Dic314yescomplemented
541C2×Dic3C2×D3212yes—
542C2×Dic3C2×D3212yes—
543D12—316no—
544C4×D3—188no—
545C4×D3—188no—
546C4×D3—188no—
547C4×D3—1816no—
548C2×C32—21no—
549C2×C32—21no—
550C2×C32—21no—
551C2×C32—21no—
552C2×C32—21no—
553C2×C32—21no—
554C2×C32—21no—
555C2×C32—21no—
556C2×C32—21no—
557C2×C32—24no—
558C2×C32—24no—
559C2×C32—24no—
560C2×C32—44no—
561C2×C32—41no—
562C2×C32—41no—
563C2×C32—41no—
564C2×C32—64no—
565C2×C32#67⋊C414yescomplemented
566C2×C32#89314yescomplemented
567C2×C32D4×Dic314yescomplemented
568C2×C32C22×C4×D311yescharacteristic
569C2×C32C22×C4×D311yescharacteristic
570C2×C32C2×D3×D411yescharacteristic
571C2×C32C2×D3×D411yescharacteristic
572C2×C32C2×D3×D411yescharacteristic
573C2×C32C2×#23711yescharacteristic
574C2×C32C2×#23711yescharacteristic
575C2×C32C2×#23911yescharacteristic
576C2×C32C23×Dic311yescharacteristic
577C3⋊D3—24no—
578C3×D3—28no—
579C3×D3—24no—
580C3×D3—24no—
581C3×D3—68no—
582C3×D3—64no—
583C3×D3—64no—
584C24—31no—
585C24—91no—
586C2×D4—94no—
587C2×D4—98no—
588C22×C4—31no—
589C22×C4—31no—
590C22×C4—91no—
591C22×C4—91no—
592C22×C4—274no—
593C22×C4—274no—
594C22×C4—271no—
595C22×C4—544no—
596C22×C4—544no—
597C4⋊C4—94no—
598C22⋊C4—94no—
599C22⋊C4—274no—
600C42—274no—
601C22×C3—21no—
602C22×C3—21no—
603C22×C3—21no—
604C22×C3—22no—
605C22×C3—22no—
606C22×C3—22no—
607C22×C3—22no—
608C22×C3—22no—
609C22×C3—22no—
610C22×C3—22no—
611C22×C3—22no—
612C22×C3—22no—
613C22×C3—34no—
614C22×C3—34no—
615C22×C3—41no—
616C22×C3—42no—
617C22×C3—42no—
618C22×C3—42no—
619C22×C3—64no—
620C22×C3—64no—
621C22×C3—64no—
622C22×C3—616no—
623C22×C3—62no—
624C22×C3—62no—
625C22×C3—62no—
626C22×C3—62no—
627C22×C3—68no—
628C22×C3—68no—
629C22×C3—94no—
630C22×C3—182no—
631C22×C3—182no—
632C22×C3—188no—
633C22×C3#379612yes—
634C22×C3#379612yes—
635C22×C3C4×D3212yes—
636C22×C3#380212yes—
637C22×C3C2×D3×Dic312yes—
638C22×C3C2×D3×Dic312yes—
639C22×C3#380512yes—
640C22×C3#381112yes—
641C22×C3#381112yes—
642C22×C3C22×D3211yescharacteristic
643C22×C3C22×D3211yescharacteristic
644C22×C3C22×D3211yescharacteristic
645C2×D3—22no—
646C2×D3—22no—
647C2×D3—28no—
648C2×D3—34no—
649C2×D3—34no—
650C2×D3—64no—
651C2×D3—64no—
652C2×D3—64no—
653C2×D3—616no—
654C2×D3—62no—
655C2×D3—62no—
656C2×D3—62no—
657C2×D3—62no—
658C2×D3—68no—
659C2×D3—68no—
660C2×D3C2×D3×Dic314yescomplemented
661C3×C4—34no—
662C3×C4—34no—
663C3×C4—64no—
664C3×C4—64no—
665C3×C4—62no—
666C3×C4—62no—
667C3×C4—182no—
668C3×C4—182no—
669Dic3—22no—
670Dic3—64no—
671Dic3—64no—
672Dic3—62no—
673Dic3—62no—
674Dic3—62no—
675Dic3—62no—
676Dic3—94no—
677Dic3—94no—
678Dic3—94no—
679Dic3—184no—
680Dic3—184no—
681Dic3—184no—
682Dic3—364no—
683Dic3C2×D3×Dic314yescomplemented
684C32—21no—
685C32—21no—
686C32—21no—
687C32—41no—
688C32C2×#67⋊C411yescharacteristic, complemented
689C32C2×#89311yescharacteristic, complemented
690C32C2×D4×Dic311yescharacteristic, complemented
691C23—32no—
692C23—34no—
693C23—62no—
694C23—62no—
695C23—92no—
696C23—94no—
697C23—182no—
698C23—182no—
699C23D3311yescharacteristic
700D4—916no—
701C2×C4—32no—
702C2×C4—34no—
703C2×C4—32no—
704C2×C4—62no—
705C2×C4—92no—
706C2×C4—92no—
707C2×C4—182no—
708C2×C4—182no—
709C2×C4—272no—
710C2×C4—274no—
711C2×C4—548no—
712C2×C4—548no—
713C2×C3—21no—
714C2×C3—21no—
715C2×C3—21no—
716C2×C3—21no—
717C2×C3—21no—
718C2×C3—21no—
719C2×C3—21no—
720C2×C3—21no—
721C2×C3—21no—
722C2×C3—24no—
723C2×C3—24no—
724C2×C3—24no—
725C2×C3—41no—
726C2×C3—41no—
727C2×C3—41no—
728C2×C3—44no—
729C2×C3—68no—
730C2×C3—64no—
731C2×C3—64no—
732C2×C3—184no—
733C2×C3#6388114yescomplemented
734C2×C3#6389814yescomplemented
735C2×C3#67⋊Dic314yescomplemented
736C2×C3C2×#379611yescharacteristic
737C2×C3C2×#379611yescharacteristic
738C2×C3C2×C4×D3211yescharacteristic
739C2×C3C2×#380211yescharacteristic
740C2×C3C22×D3×Dic311yescharacteristic
741C2×C3C22×D3×Dic311yescharacteristic
742C2×C3C2×#380511yescharacteristic
743C2×C3C2×#381111yescharacteristic
744C2×C3C2×#381111yescharacteristic
745D3—24no—
746D3—68no—
747D3—64no—
748D3—64no—
749C22—34no—
750C22—62no—
751C22—62no—
752C22—68no—
753C22—94no—
754C22—182no—
755C22—182no—
756C22—188no—
757C22D32×Dic312yes—
758C22#8895412yes—
759C22#8896412yes—
760C22C2×D3311yescharacteristic
761C4—34no—
762C4—62no—
763C4—182no—
764C4—182no—
765C4—274no—
766C3—21no—
767C3—21no—
768C3—21no—
769C3—41no—
770C3C2×#6388111yescharacteristic, complemented
771C3C2×#6389811yescharacteristic, complemented
772C3C2×#67⋊Dic311yescharacteristic, complemented
773C2—64no—
774C2—184no—
775C2#1172292914yesdirect product factor
776C2C2×D32×Dic311yescharacteristic
777C2C2×#8895411yescharacteristic
778C2C2×#8896411yescharacteristic
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×Dic3×C3⋊D3C2semidirect
2. C22×D3×C3⋊Dic3C2semidirect
4. C2×#88814C2semidirect
5. C2×Dic3×C3⋊Dic3C2semidirect
6. C2×C3×Dic3⋊Dic3C2semidirect
7. C2×C3×(C2×D3)⋊Dic3C2semidirect
8. #11722929C2direct (N × H)
20. C2×Dic3×C3⋊D3C22semidirect
22. C2×D3×C3⋊Dic3C22semidirect
23. C2×C3×#626C4semidirect
25. #88814C22semidirect
26. Dic3×C3⋊Dic3C22semidirect
27. C3×Dic3⋊Dic3C22semidirect
28. C3×(C2×D3)⋊Dic3C22semidirect
46. C2×Dic3⋊Dic3D3semidirect
50. C2×(C2×D3)⋊Dic3D3semidirect
59. C22×C3×C3⋊D3C2×C4semidirect
63. C22×C32×D3C2×C4semidirect
65. C2×C3⋊(C3⋊Dic3)D4semidirect
72. C2×C32×Dic3C2×C4semidirect
77. C3×#626C2×C4semidirect
120. C2×#626Dic3semidirect
139. Dic3⋊Dic3C2×D3semidirect
143. (C2×D3)⋊Dic3C2×D3semidirect
154. C2×C3×C3⋊D3C22×C4semidirect
158. C2×C32×D3C22×C4semidirect
159. C3⋊(C3⋊Dic3)C2×D4semidirect
163. C32×Dic3C22×C4semidirect
204. C22×C3⋊D3C2×Dic3semidirect
226. C22×C3×D3C4×D3semidirect
227. C22×C3×D3C2×Dic3semidirect
273. C2×C3×Dic3C4×D3semidirect
274. C2×C3×Dic3C2×Dic3semidirect
280. #626C2×Dic3semidirect
288. C2×C33C4×D4semidirect
395. C2×C3⋊D3C22×Dic3semidirect
418. C2×C3×D3C2×C4×D3semidirect
419. C2×C3×D3C22×Dic3semidirect
441. C3×Dic3C2×C4×D3semidirect
442. C3×Dic3C22×Dic3semidirect
451. C33C2×C4×D4semidirect
489. C22×D3D3×Dic3semidirect
540. C2×Dic3D3×Dic3semidirect
565. C2×C32#67⋊C4semidirect
566. C2×C32#893semidirect
567. C2×C32D4×Dic3semidirect
660. C2×D3C2×D3×Dic3semidirect
683. Dic3C2×D3×Dic3semidirect
688. C32C2×#67⋊C4semidirect
689. C32C2×#893semidirect
690. C32C2×D4×Dic3semidirect
733. C2×C3#63881semidirect
734. C2×C3#63898semidirect
735. C2×C3#67⋊Dic3semidirect
770. C3C2×#63881semidirect
771. C3C2×#63898semidirect
772. C3C2×#67⋊Dic3semidirect
775. C2#11722929direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Dic3×C3⋊D32
C22×D3×C3⋊Dic32
C22×C3×#6262
C2×#888142
C2×Dic3×C3⋊Dic32
C2×C3×Dic3⋊Dic32
C2×C3×(C2×D3)⋊Dic32
#117229292
C2×#67⋊Dic33
C2×#638983
C2×#638813