Finite Group Databasebeta

← C2×#11722933 #13172171

Subgroups — C2×#11722933 #13172171

Order 1728.

2442 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6292C211yesmaximal, characteristic
2C22×#6289C211yesmaximal, characteristic, complemented
3C22×C3×#624C211yesmaximal, characteristic, complemented
4C2×#88814C211yesmaximal, characteristic, complemented
5C2×#88804C211yesmaximal, characteristic, complemented
6C2×C3×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
7C2×C3×Dic32C211yesmaximal, characteristic, complemented
8#11722933C218yesmaximal, direct product factor
9C2×#63904—31nomaximal
10C2×C4×#626—31nomaximal
11C2×#63894—31nomaximal
12C23×C3⋊(C3⋊D3)C2211yescharacteristic
13C23×C3×C3⋊D3C2211yescharacteristic
14C22×C3×C3⋊Dic3C2211yescharacteristic
15C22×C3×C3⋊Dic3C2211yescharacteristic
16C22×C32×Dic3C2211yescharacteristic
17C22×C32×Dic3C2211yescharacteristic
18C22×C32×Dic3C2211yescharacteristic
19C2×#6292C418yescomplemented
20C2×#6292C2214yes—
21C2×#6289—24no—
22C2×#6289C2214yescomplemented
23C2×C3×#624—24no—
24C2×C3×#624C2214yescomplemented
25#88814C2214yescomplemented
26#88804C2214yescomplemented
27C3×Dic3⋊Dic3C2214yescomplemented
28C3×Dic32C2214yescomplemented
29C22×C4⋊(C3⋊D3)—31no—
30C22×C4×C3⋊D3—31no—
31C22×C3×C4×D3—31no—
32C22×C3×C4×D3—31no—
33C22×#626—31no—
34C22×#626—31no—
35C22×#626—61no—
36C22×#624—31no—
37C22×#624—31no—
38C22×#624—61no—
39C22×#624D311yescharacteristic, complemented
40C2×#3752—31no—
41C2×C3×C4⋊Dic3—31no—
42C2×C3×Dic3⋊C4—31no—
43C2×C3×C4×Dic3—31no—
44C2×C3×C4×Dic3—31no—
45C2×Dic3⋊Dic3D311yescharacteristic, complemented
46C2×#3722—31no—
47C2×#3722—31no—
48C2×#3722—31no—
49C2×#3722—61no—
50C2×(C2×D3)⋊Dic3—31no—
51C2×(C2×D3)⋊Dic3—31no—
52C2×Dic32D311yescharacteristic, complemented
53#63904—38no—
54C4×#626—38no—
55#63894—38no—
56C23×C33C2311yescharacteristic
57C22×C3⋊(C3⋊D3)—22no—
58C22×C3⋊(C3⋊D3)—22no—
59C22×C3⋊(C3⋊D3)C2×C414yescomplemented
60C22×C3⋊(C3⋊D3)C2312yes—
61C22×C3×C3⋊D3—22no—
62C22×C3×C3⋊D3—22no—
63C22×C3×C3⋊D3C2×C414yescomplemented
64C22×C3×C3⋊D3C2312yes—
65C2×C3×C3⋊Dic3—22no—
66C2×C3×C3⋊Dic3—22no—
67C2×C3×C3⋊Dic3C2312yes—
68C2×C3×C3⋊Dic3C2312yes—
69C2×C32×Dic3—22no—
70C2×C32×Dic3C2×C414yescomplemented
71C2×C32×Dic3D414yescomplemented
72C2×C32×Dic3C2312yes—
73C2×C32×Dic3C2312yes—
74C2×C32×Dic3C2312yes—
75#6292C2×C4116yescomplemented
76#6289—28no—
77C3×#624—28no—
78C2×C4×#67—91no—
79C2×#893—91no—
80C2×C4×D12—91no—
81C23×C3⋊D3—31no—
82C23×C3⋊D3—31no—
83C23×C3⋊D3—31no—
84C23×C3⋊D3—61no—
85C23×C3⋊D3—61no—
86C23×C3⋊D3—61no—
87C23×C3⋊D3—121no—
88C23×C3⋊D3C2×D311yescharacteristic
89C23×C3×D3—31no—
90C23×C3×D3—31no—
91C23×C3×D3—61no—
92C22×C32×C4—31no—
93C22×C32×C4—31no—
94C22×C32×C4—31no—
95C22×C3⋊Dic3C2×D311yescharacteristic
96C22×C3⋊Dic3C2×D311yescharacteristic
97C2×C4⋊(C3⋊D3)—38no—
98C2×C4⋊(C3⋊D3)—34no—
99C2×C4×C3⋊D3—34no—
100C2×C4×C3⋊D3—64no—
101C22×C3×Dic3—21no—
102C22×C3×Dic3—21no—
103C22×C3×Dic3—21no—
104C22×C3×Dic3—31no—
105C22×C3×Dic3—31no—
106C22×C3×Dic3—31no—
107C22×C3×Dic3—31no—
108C22×C3×Dic3—61no—
109C22×C3×Dic3—61no—
110C22×C3×Dic3C2×D311yescharacteristic
111C22×C3×Dic3C2×D311yescharacteristic
112C22×C3×Dic3C2×D311yescharacteristic
113C22×C3×Dic3C2×D311yescharacteristic
114C22×C3×Dic3C2×D311yescharacteristic
115C22×C3×Dic3C2×D311yescharacteristic
116C2×C3×C4×D3—34no—
117C2×C3×C4×D3—34no—
118C2×C3×C4×D3—64no—
119C2×C3×C4×D3—64no—
120C2×#626—38no—
121C2×#626—38no—
122C2×#626—34no—
123C2×#626—34no—
124C2×#626—68no—
125C2×#626—64no—
126C2×#624—24no—
127C2×#624—34no—
128C2×#624—34no—
129C2×#624—64no—
130C2×#624—68no—
131C2×#624—64no—
132C2×#624—64no—
133C2×#624C2×D314yescomplemented
134#3752—34no—
135C3×C4⋊Dic3—34no—
136C3×Dic3⋊C4—34no—
137C3×C4×Dic3—34no—
138C3×C4×Dic3—34no—
139Dic3⋊Dic3C2×D314yescomplemented
140#3722—34no—
141#3722—34no—
142#3722—34no—
143#3722—64no—
144(C2×D3)⋊Dic3—34no—
145(C2×D3)⋊Dic3—34no—
146Dic32C2×D314yescomplemented
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⋊D3)C22×C414yescomplemented
155C2×C3×C3⋊D3—28no—
156C2×C3×C3⋊D3—22no—
157C2×C3×C3⋊D3—22no—
158C2×C3×C3⋊D3C22×C414yescomplemented
159C3×C3⋊Dic3—22no—
160C3×C3⋊Dic3—22no—
161C32×Dic3—22no—
162C32×Dic3C22×C414yescomplemented
163C32×Dic3C2×D414yescomplemented
164C23×C3×C4—91no—
165C22×#67—91no—
166C22×D12—91no—
167C22×D12—91no—
168C22×D12—181no—
169C22×C4×D3—31no—
170C22×C4×D3—31no—
171C22×C4×D3—91no—
172C22×C4×D3—91no—
173C22×C4×D3—91no—
174C22×C4×D3—181no—
175C2×C3×C4⋊C4—91no—
176C2×C3×C42—91no—
177C2×#217—91no—
178C4×#67—98no—
179C2×(C2×D3)⋊C4—91no—
180C2×(C2×D3)⋊C4—91no—
181C2×(C2×D3)⋊C4—91no—
182C2×(C2×D3)⋊C4—91no—
183C2×(C2×D3)⋊C4—91no—
184C2×(C2×D3)⋊C4—181no—
185C2×C4⋊Dic3—31no—
186C2×Dic3⋊C4—31no—
187C2×C4×Dic3—31no—
188C2×C4×Dic3—31no—
189#893—98no—
190C4×D12—98no—
191C23×C32—21no—
192C23×C32—21no—
193C23×C32—21no—
194C23×C32—41no—
195C23×C32C22×D311yescharacteristic
196C23×C32C22×D311yescharacteristic
197C23×C32C22×D311yescharacteristic
198C22×C3⋊D3—22no—
199C22×C3⋊D3—22no—
200C22×C3⋊D3—34no—
201C22×C3⋊D3—34no—
202C22×C3⋊D3—34no—
203C22×C3⋊D3—32no—
204C22×C3⋊D3—32no—
205C22×C3⋊D3—32no—
206C22×C3⋊D3—64no—
207C22×C3⋊D3—62no—
208C22×C3⋊D3—62no—
209C22×C3⋊D3—64no—
210C22×C3⋊D3—64no—
211C22×C3⋊D3—62no—
212C22×C3⋊D3—62no—
213C22×C3⋊D3—62no—
214C22×C3⋊D3—64no—
215C22×C3⋊D3—64no—
216C22×C3⋊D3—62no—
217C22×C3⋊D3—62no—
218C22×C3⋊D3—62no—
219C22×C3⋊D3—62no—
220C22×C3⋊D3—124no—
221C22×C3⋊D3—122no—
222C22×C3⋊D3—122no—
223C22×C3⋊D3—122no—
224C22×C3⋊D3—122no—
225C22×C3⋊D3—122no—
226C22×C3⋊D3—124no—
227C22×C3⋊D3—124no—
228C22×C3⋊D3C4×D314yescomplemented
229C22×C3⋊D3C22×D312yes—
230C22×C3×D3—34no—
231C22×C3×D3—34no—
232C22×C3×D3—32no—
233C22×C3×D3—32no—
234C22×C3×D3—64no—
235C22×C3×D3—62no—
236C22×C3×D3—62no—
237C22×C3×D3—62no—
238C22×C3×D3—62no—
239C22×C3×D3—62no—
240C22×C3×D3—122no—
241C22×C3×D3—122no—
242C2×C32×C4—34no—
243C2×C32×C4—34no—
244C2×C32×C4—32no—
245C2×C32×C4—32no—
246C2×C32×C4—32no—
247C2×C32×C4—62no—
248C2×C3⋊Dic3—22no—
249C2×C3⋊Dic3—22no—
250C2×C3⋊Dic3C22×D312yes—
251C2×C3⋊Dic3C22×D312yes—
252C4⋊(C3⋊D3)—316no—
253C4×C3⋊D3—68no—
254C2×C3×Dic3—22no—
255C2×C3×Dic3—22no—
256C2×C3×Dic3—24no—
257C2×C3×Dic3—24no—
258C2×C3×Dic3—22no—
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—42no—
266C2×C3×Dic3—62no—
267C2×C3×Dic3—62no—
268C2×C3×Dic3—64no—
269C2×C3×Dic3—62no—
270C2×C3×Dic3—62no—
271C2×C3×Dic3—62no—
272C2×C3×Dic3—62no—
273C2×C3×Dic3—122no—
274C2×C3×Dic3C4×D314yescomplemented
275C2×C3×Dic3C4×D314yescomplemented
276C2×C3×Dic3D1214yescomplemented
277C2×C3×Dic3#6714yescomplemented
278C2×C3×Dic3C22×D312yes—
279C2×C3×Dic3C22×D312yes—
280C2×C3×Dic3C22×D312yes—
281C2×C3×Dic3C22×D312yes—
282C2×C3×Dic3C22×D312yes—
283C2×C3×Dic3C22×D312yes—
284C3×C4×D3—68no—
285C3×C4×D3—68no—
286#626—316no—
287#626—316no—
288#626—616no—
289#624—28no—
290#624—616no—
291#624—68no—
292#624—68no—
293C2×C4×D4—271noSylow
294C2×C33C4×D414yescomplemented
295C2×C33C23×C411yescharacteristic
296C2×C33C22×D411yescharacteristic
297C2×C33C2×#4111yescharacteristic
298C3⋊(C3⋊D3)—24no—
299C3×C3⋊D3—24no—
300C24×C3—91no—
301C23×D3—31no—
302C23×D3—31no—
303C23×D3—61no—
304C23×D3—91no—
305C23×D3—91no—
306C23×D3—91no—
307C23×D3—181no—
308C23×D3—181no—
309C23×D3—181no—
310C23×D3—361no—
311C22×C3×C4—31no—
312C22×C3×C4—31no—
313C22×C3×C4—31no—
314C22×C3×C4—31no—
315C22×C3×C4—31no—
316C22×C3×C4—31no—
317C22×C3×C4—61no—
318C22×C3×C4—61no—
319C22×C3×C4—61no—
320C22×C3×C4—94no—
321C22×C3×C4—91no—
322C22×C3×C4—91no—
323C22×C3×C4—184no—
324C2×#67—98no—
325C2×#67—94no—
326C22×Dic3—31no—
327C22×Dic3—31no—
328C22×Dic3—31no—
329C22×Dic3—31no—
330C22×Dic3—61no—
331C22×Dic3—61no—
332C22×Dic3D3211yescharacteristic
333C22×Dic3D3211yescharacteristic
334C22×Dic3D3211yescharacteristic
335C2×D12—94no—
336C2×D12—94no—
337C2×D12—98no—
338C2×D12—98no—
339C2×D12—184no—
340C2×D12—188no—
341C2×C4×D3—34no—
342C2×C4×D3—34no—
343C2×C4×D3—64no—
344C2×C4×D3—64no—
345C2×C4×D3—94no—
346C2×C4×D3—94no—
347C2×C4×D3—94no—
348C2×C4×D3—184no—
349C2×C4×D3—184no—
350C2×C4×D3—184no—
351C2×C4×D3—188no—
352C2×C4×D3—184no—
353C3×C4⋊C4—94no—
354C3×C42—94no—
355#217—94no—
356(C2×D3)⋊C4—94no—
357(C2×D3)⋊C4—94no—
358(C2×D3)⋊C4—94no—
359(C2×D3)⋊C4—94no—
360(C2×D3)⋊C4—94no—
361(C2×D3)⋊C4—184no—
362C4⋊Dic3—34no—
363Dic3⋊C4—34no—
364C4×Dic3—34no—
365C4×Dic3—34no—
366C22×C32—21no—
367C22×C32—21no—
368C22×C32—21no—
369C22×C32—22no—
370C22×C32—22no—
371C22×C32—22no—
372C22×C32—22no—
373C22×C32—22no—
374C22×C32—22no—
375C22×C32—22no—
376C22×C32—22no—
377C22×C32—22no—
378C22×C32—42no—
379C22×C32—42no—
380C22×C32—42no—
381C22×C32—41no—
382C22×C32C2×C4×D312yes—
383C22×C32C2×C4×D312yes—
384C22×C32C2×C4×D312yes—
385C22×C32C2×D1212yes—
386C22×C32#23512yes—
387C22×C32#23512yes—
388C22×C32D3×D412yes—
389C22×C32#23912yes—
390C22×C32C2×#6712yes—
391C22×C32C23×D311yescharacteristic
392C22×C32C23×D311yescharacteristic
393C22×C32C23×D311yescharacteristic
394C2×C3⋊D3—28no—
395C2×C3⋊D3—22no—
396C2×C3⋊D3—22no—
397C2×C3⋊D3—34no—
398C2×C3⋊D3—34no—
399C2×C3⋊D3—34no—
400C2×C3⋊D3—64no—
401C2×C3⋊D3—64no—
402C2×C3⋊D3—64no—
403C2×C3⋊D3—68no—
404C2×C3⋊D3—62no—
405C2×C3⋊D3—62no—
406C2×C3⋊D3—64no—
407C2×C3⋊D3—64no—
408C2×C3⋊D3—616no—
409C2×C3⋊D3—68no—
410C2×C3⋊D3—68no—
411C2×C3⋊D3—62no—
412C2×C3⋊D3—62no—
413C2×C3⋊D3—62no—
414C2×C3⋊D3—62no—
415C2×C3⋊D3—124no—
416C2×C3⋊D3—122no—
417C2×C3⋊D3—122no—
418C2×C3⋊D3—122no—
419C2×C3⋊D3—122no—
420C2×C3⋊D3—128no—
421C2×C3⋊D3—128no—
422C2×C3⋊D3—124no—
423C2×C3⋊D3—1216no—
424C2×C3⋊D3—124no—
425C2×C3⋊D3C2×C4×D314yescomplemented
426C2×C3×D3—34no—
427C2×C3×D3—34no—
428C2×C3×D3—64no—
429C2×C3×D3—68no—
430C2×C3×D3—68no—
431C2×C3×D3—62no—
432C2×C3×D3—62no—
433C2×C3×D3—62no—
434C2×C3×D3—62no—
435C2×C3×D3—122no—
436C2×C3×D3—122no—
437C2×C3×D3—128no—
438C32×C4—34no—
439C32×C4—34no—
440C32×C4—62no—
441C3⋊Dic3—22no—
442C3⋊Dic3—22no—
443C3×Dic3—22no—
444C3×Dic3—22no—
445C3×Dic3—24no—
446C3×Dic3—24no—
447C3×Dic3—42no—
448C3×Dic3—64no—
449C3×Dic3—62no—
450C3×Dic3—62no—
451C3×Dic3—62no—
452C3×Dic3—62no—
453C3×Dic3—122no—
454C3×Dic3C2×C4×D314yescomplemented
455C3×Dic3C2×C4×D314yescomplemented
456C3×Dic3C2×D1214yescomplemented
457C3×Dic3C2×#6714yescomplemented
458C22×D4—271no—
459C23×C4—91no—
460C23×C4—271no—
461C4×D4—278no—
462C2×C4⋊C4—91no—
463C2×C22⋊C4—271no—
464C2×C22⋊C4—271no—
465C2×C42—91no—
466C33C2×C4×D411yescharacteristic, complemented, Sylow
467C23×C3—21no—
468C23×C3—21no—
469C23×C3—21no—
470C23×C3—41no—
471C23×C3—92no—
472C23×C3—94no—
473C23×C3—182no—
474C23×C3—182no—
475C23×C3C2×D3211yescharacteristic
476C23×C3C2×D3211yescharacteristic
477C23×C3C2×D3211yescharacteristic
478C22×D3—32no—
479C22×D3—32no—
480C22×D3—34no—
481C22×D3—34no—
482C22×D3—64no—
483C22×D3—62no—
484C22×D3—62no—
485C22×D3—62no—
486C22×D3—62no—
487C22×D3—62no—
488C22×D3—92no—
489C22×D3—92no—
490C22×D3—92no—
491C22×D3—94no—
492C22×D3—94no—
493C22×D3—94no—
494C22×D3—122no—
495C22×D3—122no—
496C22×D3—182no—
497C22×D3—184no—
498C22×D3—182no—
499C22×D3—182no—
500C22×D3—184no—
501C22×D3—184no—
502C22×D3—184no—
503C22×D3—184no—
504C22×D3—182no—
505C22×D3—182no—
506C22×D3—182no—
507C22×D3—182no—
508C22×D3—182no—
509C22×D3—182no—
510C22×D3—362no—
511C22×D3—364no—
512C22×D3—362no—
513C22×D3—362no—
514C22×D3—362no—
515C22×D3—362no—
516C22×D3—364no—
517C22×D3—364no—
518C2×C3×C4—32no—
519C2×C3×C4—32no—
520C2×C3×C4—32no—
521C2×C3×C4—32no—
522C2×C3×C4—34no—
523C2×C3×C4—34no—
524C2×C3×C4—34no—
525C2×C3×C4—34no—
526C2×C3×C4—32no—
527C2×C3×C4—32no—
528C2×C3×C4—62no—
529C2×C3×C4—64no—
530C2×C3×C4—62no—
531C2×C3×C4—64no—
532C2×C3×C4—62no—
533C2×C3×C4—62no—
534C2×C3×C4—62no—
535C2×C3×C4—92no—
536C2×C3×C4—92no—
537C2×C3×C4—122no—
538C2×C3×C4—188no—
539C2×C3×C4—182no—
540C2×C3×C4—182no—
541#67—916no—
542C2×Dic3—22no—
543C2×Dic3—32no—
544C2×Dic3—32no—
545C2×Dic3—32no—
546C2×Dic3—32no—
547C2×Dic3—62no—
548C2×Dic3—62no—
549C2×Dic3—64no—
550C2×Dic3—62no—
551C2×Dic3—62no—
552C2×Dic3—62no—
553C2×Dic3—62no—
554C2×Dic3—122no—
555C2×Dic3#62414yescomplemented
556C2×Dic3#62614yescomplemented
557C2×Dic3C2×D3212yes—
558C2×Dic3C2×D3212yes—
559C2×Dic3C2×D3212yes—
560D12—916no—
561D12—916no—
562D12—1816no—
563C4×D3—68no—
564C4×D3—68no—
565C4×D3—188no—
566C4×D3—188no—
567C4×D3—1816no—
568C4×D3—188no—
569C2×C32—21no—
570C2×C32—21no—
571C2×C32—21no—
572C2×C32—21no—
573C2×C32—21no—
574C2×C32—21no—
575C2×C32—21no—
576C2×C32—21no—
577C2×C32—21no—
578C2×C32—24no—
579C2×C32—24no—
580C2×C32—24no—
581C2×C32—44no—
582C2×C32—41no—
583C2×C32—41no—
584C2×C32—41no—
585C2×C32C4×D1214yescomplemented
586C2×C32#89314yescomplemented
587C2×C32C4×#6714yescomplemented
588C2×C32C22×C4×D311yescharacteristic
589C2×C32C22×C4×D311yescharacteristic
590C2×C32C22×C4×D311yescharacteristic
591C2×C32C22×D1211yescharacteristic
592C2×C32C2×#23511yescharacteristic
593C2×C32C2×#23511yescharacteristic
594C2×C32C2×D3×D411yescharacteristic
595C2×C32C2×#23911yescharacteristic
596C2×C32C22×#6711yescharacteristic
597C3⋊D3—24no—
598C3⋊D3—64no—
599C3⋊D3—68no—
600C3⋊D3—64no—
601C3⋊D3—64no—
602C3⋊D3—124no—
603C3⋊D3—124no—
604C3⋊D3—128no—
605C3×D3—64no—
606C3×D3—64no—
607C3×D3—124no—
608C24—91no—
609C24—271no—
610C2×D4—274no—
611C2×D4—278no—
612C22×C4—31no—
613C22×C4—31no—
614C22×C4—31no—
615C22×C4—94no—
616C22×C4—91no—
617C22×C4—91no—
618C22×C4—184no—
619C22×C4—274no—
620C22×C4—544no—
621C4⋊C4—94no—
622C22⋊C4—274no—
623C22⋊C4—274no—
624C42—94no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—22no—
629C22×C3—22no—
630C22×C3—22no—
631C22×C3—22no—
632C22×C3—22no—
633C22×C3—22no—
634C22×C3—22no—
635C22×C3—22no—
636C22×C3—22no—
637C22×C3—41no—
638C22×C3—42no—
639C22×C3—42no—
640C22×C3—42no—
641C22×C3—94no—
642C22×C3—182no—
643C22×C3—182no—
644C22×C3—188no—
645C22×C3#379812yes—
646C22×C3#379912yes—
647C22×C3#379912yes—
648C22×C3C4×D3212yes—
649C22×C3C4×D3212yes—
650C22×C3D3×D1212yes—
651C22×C3C2×#62412yes—
652C22×C3C2×#62612yes—
653C22×C3D3×#6712yes—
654C22×C3C22×D3211yescharacteristic
655C22×C3C22×D3211yescharacteristic
656C22×C3C22×D3211yescharacteristic
657C2×D3—34no—
658C2×D3—34no—
659C2×D3—64no—
660C2×D3—62no—
661C2×D3—62no—
662C2×D3—62no—
663C2×D3—62no—
664C2×D3—68no—
665C2×D3—68no—
666C2×D3—94no—
667C2×D3—94no—
668C2×D3—94no—
669C2×D3—122no—
670C2×D3—122no—
671C2×D3—128no—
672C2×D3—184no—
673C2×D3—184no—
674C2×D3—184no—
675C2×D3—184no—
676C2×D3—184no—
677C2×D3—1816no—
678C2×D3—182no—
679C2×D3—182no—
680C2×D3—182no—
681C2×D3—182no—
682C2×D3—182no—
683C2×D3—182no—
684C2×D3—188no—
685C2×D3—188no—
686C2×D3—188no—
687C2×D3—364no—
688C2×D3—362no—
689C2×D3—362no—
690C2×D3—362no—
691C2×D3—362no—
692C2×D3—368no—
693C2×D3—368no—
694C2×D3—364no—
695C2×D3—364no—
696C2×D3—3616no—
697C3×C4—34no—
698C3×C4—34no—
699C3×C4—34no—
700C3×C4—34no—
701C3×C4—64no—
702C3×C4—64no—
703C3×C4—62no—
704C3×C4—62no—
705C3×C4—122no—
706C3×C4—182no—
707C3×C4—182no—
708Dic3—22no—
709Dic3—64no—
710Dic3—62no—
711Dic3—62no—
712Dic3—62no—
713Dic3—62no—
714Dic3—122no—
715Dic3C2×#62414yescomplemented
716Dic3C2×#62614yescomplemented
717C32—21no—
718C32—21no—
719C32—21no—
720C32—41no—
721C32C2×C4×D1211yescharacteristic, complemented
722C32C2×#89311yescharacteristic, complemented
723C32C2×C4×#6711yescharacteristic, complemented
724C23—92no—
725C23—94no—
726C23—182no—
727C23—182no—
728C23—272no—
729C23—274no—
730C23—542no—
731C23—542no—
732C23D3311yescharacteristic
733D4—2716no—
734C2×C4—32no—
735C2×C4—32no—
736C2×C4—34no—
737C2×C4—34no—
738C2×C4—32no—
739C2×C4—62no—
740C2×C4—92no—
741C2×C4—92no—
742C2×C4—188no—
743C2×C4—182no—
744C2×C4—182no—
745C2×C4—548no—
746C2×C3—21no—
747C2×C3—21no—
748C2×C3—21no—
749C2×C3—21no—
750C2×C3—21no—
751C2×C3—21no—
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—21no—
755C2×C3—24no—
756C2×C3—24no—
757C2×C3—24no—
758C2×C3—41no—
759C2×C3—41no—
760C2×C3—41no—
761C2×C3—44no—
762C2×C3—184no—
763C2×C3#6389414yescomplemented
764C2×C3C4×#62614yescomplemented
765C2×C3#6390414yescomplemented
766C2×C3C2×#379811yescharacteristic
767C2×C3C2×#379911yescharacteristic
768C2×C3C2×#379911yescharacteristic
769C2×C3C2×C4×D3211yescharacteristic
770C2×C3C2×C4×D3211yescharacteristic
771C2×C3C2×D3×D1211yescharacteristic
772C2×C3C22×#62411yescharacteristic
773C2×C3C22×#62611yescharacteristic
774C2×C3C2×D3×#6711yescharacteristic
775D3—64no—
776D3—64no—
777D3—124no—
778D3—188no—
779D3—184no—
780D3—184no—
781D3—184no—
782D3—364no—
783D3—364no—
784D3—368no—
785C22—94no—
786C22—182no—
787C22—182no—
788C22—188no—
789C22—274no—
790C22—542no—
791C22—542no—
792C22—548no—
793C22D3×#62412yes—
794C22D3×#62612yes—
795C22#8896512yes—
796C22C2×D3311yescharacteristic
797C4—34no—
798C4—34no—
799C4—62no—
800C4—182no—
801C4—182no—
802C3—21no—
803C3—21no—
804C3—21no—
805C3—41no—
806C3C2×#6389411yescharacteristic, complemented
807C3C2×C4×#62611yescharacteristic, complemented
808C3C2×#6390411yescharacteristic, complemented
809C2—184no—
810C2—544no—
811C2#1172293314yesdirect product factor
812C2C2×D3×#62411yescharacteristic
813C2C2×D3×#62611yescharacteristic
814C2C2×#8896511yescharacteristic
subgroupG/H
center, hypercenterC23D33
commutatorC2×C33C23×C4
FrattiniC22C2×D33
Fitting, socleC23×C33C23
prime radicalC22×#6292C2
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
2. C22×#6289C2semidirect
3. C22×C3×#624C2semidirect
4. C2×#88814C2semidirect
5. C2×#88804C2semidirect
6. C2×C3×Dic3⋊Dic3C2semidirect
7. C2×C3×Dic32C2semidirect
8. #11722933C2direct (N × H)
19. C2×#6292C4semidirect
22. C2×#6289C22semidirect
24. C2×C3×#624C22semidirect
25. #88814C22semidirect
26. #88804C22semidirect
27. C3×Dic3⋊Dic3C22semidirect
28. C3×Dic32C22semidirect
39. C22×#624D3semidirect
45. C2×Dic3⋊Dic3D3semidirect
52. C2×Dic32D3semidirect
59. C22×C3⋊(C3⋊D3)C2×C4semidirect
63. C22×C3×C3⋊D3C2×C4semidirect
70. C2×C32×Dic3C2×C4semidirect
71. C2×C32×Dic3D4semidirect
75. #6292C2×C4semidirect
133. C2×#624C2×D3semidirect
139. Dic3⋊Dic3C2×D3semidirect
146. Dic32C2×D3semidirect
154. C2×C3⋊(C3⋊D3)C22×C4semidirect
158. C2×C3×C3⋊D3C22×C4semidirect
162. C32×Dic3C22×C4semidirect
163. C32×Dic3C2×D4semidirect
228. C22×C3⋊D3C4×D3semidirect
274. C2×C3×Dic3C4×D3semidirect
275. C2×C3×Dic3C4×D3semidirect
276. C2×C3×Dic3D12semidirect
277. C2×C3×Dic3#67semidirect
294. C2×C33C4×D4semidirect
425. C2×C3⋊D3C2×C4×D3semidirect
454. C3×Dic3C2×C4×D3semidirect
455. C3×Dic3C2×C4×D3semidirect
456. C3×Dic3C2×D12semidirect
457. C3×Dic3C2×#67semidirect
466. C33C2×C4×D4semidirect
555. C2×Dic3#624semidirect
556. C2×Dic3#626semidirect
585. C2×C32C4×D12semidirect
586. C2×C32#893semidirect
587. C2×C32C4×#67semidirect
715. Dic3C2×#624semidirect
716. Dic3C2×#626semidirect
721. C32C2×C4×D12semidirect
722. C32C2×#893semidirect
723. C32C2×C4×#67semidirect
763. C2×C3#63894semidirect
764. C2×C3C4×#626semidirect
765. C2×C3#63904semidirect
806. C3C2×#63894semidirect
807. C3C2×C4×#626semidirect
808. C3C2×#63904semidirect
811. C2#11722933direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#62922
C22×#62892
C22×C3×#6242
C2×#888142
C2×#888042
C2×C3×Dic3⋊Dic32
C2×C3×Dic322
#117229332
C2×#639043
C2×C4×#6263
C2×#638943