Finite Group Databasebeta

← C2×#11722956 #13172323

Subgroups — C2×#11722956 #13172323

Order 1728.

2218 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6290C211yesmaximal, characteristic, complemented
2C22×C3×#626C211yesmaximal, characteristic, complemented
3C22×C3×#625C211yesmaximal, characteristic, complemented
4C22×C3×D3×Dic3C211yesmaximal, characteristic, complemented
5C2×#88814C211yesmaximal, characteristic, complemented
6C2×Dic3⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
7C2×(C2×D3)⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
8#11722956C218yesmaximal, direct product factor
9C2×#63978—31nomaximal
10C2×#63970—31nomaximal
11C2×#63908—31nomaximal
12C23×C3×C3⋊D3C2211yescharacteristic
13C23×C32×D3C2211yescharacteristic
14C23×C32×D3C2211yescharacteristic
15C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
16C22×C3×C3⋊Dic3C2211yescharacteristic
17C22×C3×C3⋊Dic3C2211yescharacteristic
18C22×C32×Dic3C2211yescharacteristic
19C2×#6290—24no—
20C2×#6290C2214yescomplemented
21C2×C3×#626—24no—
22C2×C3×#626C2214yescomplemented
23C2×C3×#625—24no—
24C2×C3×#625C2214yescomplemented
25C2×C3×D3×Dic3—24no—
26C2×C3×D3×Dic3C2214yescomplemented
27#88814C2214yescomplemented
28Dic3⋊(C3⋊Dic3)C2214yescomplemented
29(C2×D3)⋊(C3⋊Dic3)C2214yescomplemented
30C22×#638—31no—
31C22×C3×#67—31no—
32C22×C3×#67—31no—
33C22×C3×#67—31no—
34C23×C3×Dic3—31no—
35C22×C3×D12—31no—
36C22×C3×C4×D3—31no—
37C22×#626D311yescharacteristic, complemented
38C22×#625—31no—
39C22×#625—31no—
40C22×#625—61no—
41C22×#625D311yescharacteristic, complemented
42C22×D3×Dic3D311yescharacteristic, complemented
43C2×#3757—31no—
44C2×C4⋊(C3⋊Dic3)—31no—
45#63978—38no—
46#63970—38no—
47C2×Dic3⋊Dic3—31no—
48C2×Dic3⋊Dic3—31no—
49C2×Dic3⋊Dic3—61no—
50C2×#3722—31no—
51C2×(C2×D3)⋊Dic3—31no—
52C2×(C2×D3)⋊Dic3—31no—
53C2×(C2×D3)⋊Dic3—31no—
54C2×(C2×D3)⋊Dic3—31no—
55C2×(C2×D3)⋊Dic3—61no—
56#63908—38no—
57C23×C33C2311yescharacteristic
58C22×C3×C3⋊D3—22no—
59C22×C3×C3⋊D3—22no—
60C22×C3×C3⋊D3—22no—
61C22×C3×C3⋊D3C2312yes—
62C22×C32×D3—22no—
63C22×C32×D3—22no—
64C22×C32×D3—22no—
65C22×C32×D3—22no—
66C22×C32×D3—22no—
67C22×C32×D3D414yescomplemented
68C22×C32×D3C2312yes—
69C22×C32×D3C2312yes—
70C2×C3⋊(C3⋊Dic3)—22no—
71C2×C3⋊(C3⋊Dic3)C2312yes—
72C2×C3×C3⋊Dic3—22no—
73C2×C3×C3⋊Dic3—22no—
74C2×C3×C3⋊Dic3C2312yes—
75C2×C3×C3⋊Dic3C2312yes—
76C2×C32×Dic3D414yescomplemented
77C2×C32×Dic3C2312yes—
78#6290—28no—
79C3×#626—28no—
80C3×#625—28no—
81C3×D3×Dic3—28no—
82C2×#939—91no—
83C2×#938—91no—
84C2×#930—91no—
85C24×C32—31no—
86C24×C32—31no—
87C23×C3⋊D3C2×D311yescharacteristic
88C23×C3×D3—21no—
89C23×C3×D3—21no—
90C23×C3×D3—31no—
91C23×C3×D3—31no—
92C23×C3×D3—61no—
93C23×C3×D3C2×D311yescharacteristic
94C23×C3×D3C2×D311yescharacteristic
95C23×C3×D3C2×D311yescharacteristic
96C23×C3×D3C2×D311yescharacteristic
97C22×C32×C4—31no—
98C2×#638—34no—
99C2×#638—64no—
100C22×C3⋊Dic3—31no—
101C22×C3⋊Dic3—31no—
102C22×C3⋊Dic3—31no—
103C22×C3⋊Dic3—61no—
104C22×C3⋊Dic3—61no—
105C22×C3⋊Dic3—61no—
106C22×C3⋊Dic3—121no—
107C22×C3⋊Dic3C2×D311yescharacteristic
108C22×C3⋊Dic3C2×D311yescharacteristic
109C2×C3×#67—34no—
110C2×C3×#67—34no—
111C2×C3×#67—34no—
112C2×C3×#67—64no—
113C2×C3×#67—64no—
114C2×C3×#67—64no—
115C22×C3×Dic3—21no—
116C22×C3×Dic3—31no—
117C22×C3×Dic3—31no—
118C22×C3×Dic3—31no—
119C22×C3×Dic3—31no—
120C22×C3×Dic3—34no—
121C22×C3×Dic3—64no—
122C22×C3×Dic3—61no—
123C22×C3×Dic3—61no—
124C22×C3×Dic3C2×D311yescharacteristic
125C22×C3×Dic3C2×D311yescharacteristic
126C2×C3×D12—34no—
127C2×C3×D12—64no—
128C2×C3×C4×D3—34no—
129C2×C3×C4×D3—64no—
130C2×#626—24no—
131C2×#626C2×D314yescomplemented
132C2×#625—24no—
133C2×#625—34no—
134C2×#625—34no—
135C2×#625—64no—
136C2×#625—68no—
137C2×#625—64no—
138C2×#625—64no—
139C2×#625C2×D314yescomplemented
140C2×D3×Dic3—24no—
141C2×D3×Dic3C2×D314yescomplemented
142#3757—34no—
143C4⋊(C3⋊Dic3)—34no—
144Dic3⋊Dic3—34no—
145Dic3⋊Dic3—34no—
146Dic3⋊Dic3—64no—
147#3722—34no—
148(C2×D3)⋊Dic3—34no—
149(C2×D3)⋊Dic3—34no—
150(C2×D3)⋊Dic3—34no—
151(C2×D3)⋊Dic3—34no—
152(C2×D3)⋊Dic3—64no—
153C22×C33C2×D412yes—
154C22×C33C2×D412yes—
155C22×C33#4112yes—
156C22×C33C2411yescharacteristic
157C2×C3×C3⋊D3—22no—
158C2×C3×C3⋊D3—22no—
159C2×C3×C3⋊D3—22no—
160C2×C3×C3⋊D3—44no—
161C2×C32×D3—28no—
162C2×C32×D3—22no—
163C2×C32×D3—22no—
164C2×C32×D3—22no—
165C2×C32×D3—22no—
166C2×C32×D3—22no—
167C2×C32×D3—44no—
168C2×C32×D3C2×D414yescomplemented
169C3⋊(C3⋊Dic3)—22no—
170C3×C3⋊Dic3—22no—
171C3×C3⋊Dic3—22no—
172C32×Dic3C2×D414yescomplemented
173C22×C3×D4—91no—
174C22×C3×D4—91no—
175C23×C3×C4—91no—
176C22×#67—31no—
177C22×#67—31no—
178C22×#67—31no—
179C22×#67—91no—
180C22×#67—91no—
181C22×#67—91no—
182C22×#67—181no—
183C23×Dic3—31no—
184C22×D12—31no—
185C22×C4×D3—31no—
186C2×#217—91no—
187C2×#217—91no—
188C2×#217—91no—
189C2×#217—181no—
190#939—98no—
191#938—98no—
192#930—98no—
193C2×(C2×D3)⋊C4—91no—
194C2×(C2×D3)⋊C4—91no—
195C2×(C2×D3)⋊C4—91no—
196C2×C4⋊Dic3—91no—
197C2×C4⋊Dic3—91no—
198C2×C4⋊Dic3—181no—
199C2×Dic3⋊C4—91no—
200C23×C32—21no—
201C23×C32—21no—
202C23×C32—21no—
203C23×C32—34no—
204C23×C32—32no—
205C23×C32—32no—
206C23×C32—41no—
207C23×C32—62no—
208C23×C32—62no—
209C23×C32—62no—
210C23×C32—62no—
211C23×C32—62no—
212C23×C32C22×D311yescharacteristic
213C23×C32C22×D311yescharacteristic
214C23×C32C22×D311yescharacteristic
215C22×C3⋊D3—22no—
216C22×C3⋊D3—22no—
217C22×C3⋊D3—22no—
218C22×C3⋊D3C22×D312yes—
219C22×C3×D3—22no—
220C22×C3×D3—22no—
221C22×C3×D3—22no—
222C22×C3×D3—22no—
223C22×C3×D3—24no—
224C22×C3×D3—22no—
225C22×C3×D3—22no—
226C22×C3×D3—22no—
227C22×C3×D3—22no—
228C22×C3×D3—22no—
229C22×C3×D3—22no—
230C22×C3×D3—24no—
231C22×C3×D3—22no—
232C22×C3×D3—22no—
233C22×C3×D3—32no—
234C22×C3×D3—32no—
235C22×C3×D3—42no—
236C22×C3×D3—42no—
237C22×C3×D3—42no—
238C22×C3×D3—42no—
239C22×C3×D3—62no—
240C22×C3×D3—64no—
241C22×C3×D3—62no—
242C22×C3×D3—62no—
243C22×C3×D3—62no—
244C22×C3×D3—62no—
245C22×C3×D3—62no—
246C22×C3×D3—62no—
247C22×C3×D3—122no—
248C22×C3×D3—122no—
249C22×C3×D3D1214yescomplemented
250C22×C3×D3#6714yescomplemented
251C22×C3×D3C22×D312yes—
252C22×C3×D3C22×D312yes—
253C22×C3×D3C22×D312yes—
254C22×C3×D3C22×D312yes—
255C2×C32×C4—34no—
256C2×C32×C4—32no—
257#638—68no—
258C2×C3⋊Dic3—22no—
259C2×C3⋊Dic3—22no—
260C2×C3⋊Dic3—32no—
261C2×C3⋊Dic3—32no—
262C2×C3⋊Dic3—32no—
263C2×C3⋊Dic3—62no—
264C2×C3⋊Dic3—62no—
265C2×C3⋊Dic3—62no—
266C2×C3⋊Dic3—62no—
267C2×C3⋊Dic3—64no—
268C2×C3⋊Dic3—62no—
269C2×C3⋊Dic3—62no—
270C2×C3⋊Dic3—122no—
271C2×C3⋊Dic3—122no—
272C2×C3⋊Dic3—122no—
273C2×C3⋊Dic3—124no—
274C2×C3⋊Dic3C22×D312yes—
275C2×C3⋊Dic3C22×D312yes—
276C3×#67—68no—
277C3×#67—68no—
278C3×#67—68no—
279C2×C3×Dic3—24no—
280C2×C3×Dic3—22no—
281C2×C3×Dic3—32no—
282C2×C3×Dic3—32no—
283C2×C3×Dic3—32no—
284C2×C3×Dic3—32no—
285C2×C3×Dic3—62no—
286C2×C3×Dic3—62no—
287C2×C3×Dic3—62no—
288C2×C3×Dic3—62no—
289C2×C3×Dic3—62no—
290C2×C3×Dic3—62no—
291C2×C3×Dic3—68no—
292C2×C3×Dic3—122no—
293C2×C3×Dic3—122no—
294C2×C3×Dic3#6714yescomplemented
295C2×C3×Dic3#6714yescomplemented
296C2×C3×Dic3C22×D312yes—
297C2×C3×Dic3C22×D312yes—
298C3×D12—68no—
299C3×C4×D3—68no—
300#626—28no—
301#625—28no—
302#625—616no—
303#625—68no—
304#625—68no—
305D3×Dic3—28no—
306C2×#121—271noSylow
307C2×C33#12114yescomplemented
308C2×C33C22×D411yescharacteristic
309C2×C33C22×D411yescharacteristic
310C2×C33C2×#4111yescharacteristic
311C3×C3⋊D3—42no—
312C32×D3—24no—
313C32×D3—42no—
314C24×C3—31no—
315C24×C3—31no—
316C24×C3—31no—
317C24×C3—31no—
318C24×C3—61no—
319C24×C3—61no—
320C24×C3—91no—
321C23×D3—31no—
322C23×D3—31no—
323C23×D3—61no—
324C23×D3D3211yescharacteristic
325C23×D3D3211yescharacteristic
326C2×C3×D4—94no—
327C2×C3×D4—94no—
328C2×C3×D4—184no—
329C2×C3×D4—184no—
330C22×C3×C4—31no—
331C22×C3×C4—31no—
332C22×C3×C4—61no—
333C22×C3×C4—94no—
334C22×C3×C4—91no—
335C22×C3×C4—91no—
336C22×C3×C4—184no—
337C2×#67—34no—
338C2×#67—34no—
339C2×#67—34no—
340C2×#67—64no—
341C2×#67—64no—
342C2×#67—64no—
343C2×#67—94no—
344C2×#67—94no—
345C2×#67—94no—
346C2×#67—184no—
347C2×#67—184no—
348C2×#67—184no—
349C2×#67—188no—
350C2×#67—184no—
351C22×Dic3—31no—
352C22×Dic3—31no—
353C22×Dic3—31no—
354C22×Dic3—31no—
355C22×Dic3—34no—
356C22×Dic3—61no—
357C22×Dic3—61no—
358C22×Dic3—64no—
359C22×Dic3—91no—
360C22×Dic3—91no—
361C22×Dic3—91no—
362C22×Dic3—181no—
363C22×Dic3—181no—
364C22×Dic3—181no—
365C22×Dic3—361no—
366C22×Dic3D3211yescharacteristic
367C2×D12—34no—
368C2×D12—64no—
369C2×C4×D3—34no—
370C2×C4×D3—64no—
371#217—94no—
372#217—94no—
373#217—94no—
374#217—184no—
375(C2×D3)⋊C4—94no—
376(C2×D3)⋊C4—94no—
377(C2×D3)⋊C4—94no—
378C4⋊Dic3—94no—
379C4⋊Dic3—94no—
380C4⋊Dic3—184no—
381Dic3⋊C4—94no—
382C22×C32—21no—
383C22×C32—21no—
384C22×C32—21no—
385C22×C32—22no—
386C22×C32—22no—
387C22×C32—22no—
388C22×C32—22no—
389C22×C32—22no—
390C22×C32—22no—
391C22×C32—22no—
392C22×C32—22no—
393C22×C32—22no—
394C22×C32—34no—
395C22×C32—42no—
396C22×C32—42no—
397C22×C32—42no—
398C22×C32—41no—
399C22×C32—62no—
400C22×C32—68no—
401C22×C32—62no—
402C22×C32—62no—
403C22×C32—62no—
404C22×C32—62no—
405C22×C32—124no—
406C22×C32C2×D1212yes—
407C22×C32#23512yes—
408C22×C32D3×D412yes—
409C22×C32D3×D412yes—
410C22×C32#23712yes—
411C22×C32#23712yes—
412C22×C32C2×#6712yes—
413C22×C32C2×#6712yes—
414C22×C32C2×#6712yes—
415C22×C32C23×D311yescharacteristic
416C22×C32C23×D311yescharacteristic
417C22×C32C23×D311yescharacteristic
418C2×C3⋊D3—22no—
419C2×C3⋊D3—22no—
420C2×C3⋊D3—22no—
421C2×C3⋊D3—44no—
422C2×C3×D3—28no—
423C2×C3×D3—28no—
424C2×C3×D3—22no—
425C2×C3×D3—22no—
426C2×C3×D3—22no—
427C2×C3×D3—22no—
428C2×C3×D3—24no—
429C2×C3×D3—22no—
430C2×C3×D3—22no—
431C2×C3×D3—22no—
432C2×C3×D3—22no—
433C2×C3×D3—22no—
434C2×C3×D3—22no—
435C2×C3×D3—24no—
436C2×C3×D3—42no—
437C2×C3×D3—42no—
438C2×C3×D3—48no—
439C2×C3×D3—42no—
440C2×C3×D3—42no—
441C2×C3×D3—48no—
442C2×C3×D3—44no—
443C2×C3×D3—44no—
444C2×C3×D3—64no—
445C2×C3×D3—62no—
446C2×C3×D3—62no—
447C2×C3×D3—62no—
448C2×C3×D3—62no—
449C2×C3×D3—62no—
450C2×C3×D3—62no—
451C2×C3×D3—122no—
452C2×C3×D3—122no—
453C2×C3×D3—128no—
454C2×C3×D3—124no—
455C2×C3×D3—124no—
456C2×C3×D3C2×D1214yescomplemented
457C2×C3×D3C2×#6714yescomplemented
458C32×C4—34no—
459C3⋊Dic3—22no—
460C3⋊Dic3—22no—
461C3⋊Dic3—62no—
462C3⋊Dic3—64no—
463C3⋊Dic3—62no—
464C3⋊Dic3—62no—
465C3⋊Dic3—122no—
466C3⋊Dic3—122no—
467C3⋊Dic3—124no—
468C3×Dic3—24no—
469C3×Dic3—62no—
470C3×Dic3—62no—
471C3×Dic3—62no—
472C3×Dic3—62no—
473C3×Dic3—122no—
474C3×Dic3—122no—
475C3×Dic3C2×#6714yescomplemented
476C3×Dic3C2×#6714yescomplemented
477C22×D4—91no—
478C22×D4—91no—
479C22×D4—271no—
480C23×C4—91no—
481#121—278no—
482C2×C4⋊C4—271no—
483C2×C22⋊C4—271no—
484C2×C22⋊C4—271no—
485C33C2×#12111yescharacteristic, complemented, Sylow
486C23×C3—21no—
487C23×C3—21no—
488C23×C3—21no—
489C23×C3—32no—
490C23×C3—32no—
491C23×C3—34no—
492C23×C3—34no—
493C23×C3—32no—
494C23×C3—32no—
495C23×C3—41no—
496C23×C3—62no—
497C23×C3—62no—
498C23×C3—64no—
499C23×C3—64no—
500C23×C3—62no—
501C23×C3—62no—
502C23×C3—62no—
503C23×C3—62no—
504C23×C3—62no—
505C23×C3—62no—
506C23×C3—62no—
507C23×C3—62no—
508C23×C3—62no—
509C23×C3—62no—
510C23×C3—92no—
511C23×C3—122no—
512C23×C3—122no—
513C23×C3—122no—
514C23×C3—122no—
515C23×C3—182no—
516C23×C3—182no—
517C23×C3—182no—
518C23×C3C2×D3211yescharacteristic
519C23×C3C2×D3211yescharacteristic
520C23×C3C2×D3211yescharacteristic
521C22×D3—22no—
522C22×D3—22no—
523C22×D3—22no—
524C22×D3—22no—
525C22×D3—22no—
526C22×D3—32no—
527C22×D3—32no—
528C22×D3—62no—
529C22×D3—64no—
530C22×D3—62no—
531C22×D3—62no—
532C22×D3—62no—
533C22×D3—62no—
534C22×D3—62no—
535C22×D3—62no—
536C22×D3—122no—
537C22×D3—122no—
538C22×D3#62614yescomplemented
539C22×D3C2×D3212yes—
540C22×D3C2×D3212yes—
541C3×D4—188no—
542C3×D4—188no—
543C2×C3×C4—32no—
544C2×C3×C4—32no—
545C2×C3×C4—34no—
546C2×C3×C4—34no—
547C2×C3×C4—62no—
548C2×C3×C4—64no—
549C2×C3×C4—92no—
550C2×C3×C4—92no—
551C2×C3×C4—188no—
552C2×C3×C4—182no—
553C2×C3×C4—182no—
554#67—68no—
555#67—68no—
556#67—68no—
557#67—188no—
558#67—188no—
559#67—1816no—
560#67—188no—
561C2×Dic3—32no—
562C2×Dic3—32no—
563C2×Dic3—32no—
564C2×Dic3—32no—
565C2×Dic3—62no—
566C2×Dic3—62no—
567C2×Dic3—62no—
568C2×Dic3—62no—
569C2×Dic3—62no—
570C2×Dic3—62no—
571C2×Dic3—68no—
572C2×Dic3—92no—
573C2×Dic3—92no—
574C2×Dic3—92no—
575C2×Dic3—122no—
576C2×Dic3—122no—
577C2×Dic3—182no—
578C2×Dic3—182no—
579C2×Dic3—182no—
580C2×Dic3—184no—
581C2×Dic3—182no—
582C2×Dic3—182no—
583C2×Dic3—182no—
584C2×Dic3—362no—
585C2×Dic3—362no—
586C2×Dic3—362no—
587C2×Dic3—364no—
588C2×Dic3#62514yescomplemented
589C2×Dic3C2×D3212yes—
590D12—68no—
591C4×D3—68no—
592C2×C32—21no—
593C2×C32—21no—
594C2×C32—21no—
595C2×C32—21no—
596C2×C32—21no—
597C2×C32—21no—
598C2×C32—21no—
599C2×C32—21no—
600C2×C32—21no—
601C2×C32—24no—
602C2×C32—24no—
603C2×C32—24no—
604C2×C32—44no—
605C2×C32—41no—
606C2×C32—41no—
607C2×C32—41no—
608C2×C32—64no—
609C2×C32—122no—
610C2×C32#93014yescomplemented
611C2×C32#93814yescomplemented
612C2×C32#93914yescomplemented
613C2×C32C22×D1211yescharacteristic
614C2×C32C2×#23511yescharacteristic
615C2×C32C2×D3×D411yescharacteristic
616C2×C32C2×D3×D411yescharacteristic
617C2×C32C2×#23711yescharacteristic
618C2×C32C2×#23711yescharacteristic
619C2×C32C22×#6711yescharacteristic
620C2×C32C22×#6711yescharacteristic
621C2×C32C22×#6711yescharacteristic
622C3⋊D3—42no—
623C3×D3—24no—
624C3×D3—24no—
625C3×D3—44no—
626C3×D3—44no—
627C3×D3—42no—
628C3×D3—42no—
629C3×D3—124no—
630C3×D3—122no—
631C3×D3—122no—
632C24—31no—
633C24—31no—
634C24—91no—
635C2×D4—94no—
636C2×D4—94no—
637C2×D4—184no—
638C2×D4—184no—
639C2×D4—274no—
640C2×D4—544no—
641C22×C4—31no—
642C22×C4—94no—
643C22×C4—91no—
644C22×C4—91no—
645C22×C4—184no—
646C22×C4—271no—
647C4⋊C4—274no—
648C22⋊C4—274no—
649C22⋊C4—274no—
650C22×C3—21no—
651C22×C3—21no—
652C22×C3—21no—
653C22×C3—22no—
654C22×C3—22no—
655C22×C3—22no—
656C22×C3—22no—
657C22×C3—22no—
658C22×C3—22no—
659C22×C3—22no—
660C22×C3—22no—
661C22×C3—22no—
662C22×C3—34no—
663C22×C3—34no—
664C22×C3—41no—
665C22×C3—42no—
666C22×C3—42no—
667C22×C3—42no—
668C22×C3—64no—
669C22×C3—64no—
670C22×C3—62no—
671C22×C3—62no—
672C22×C3—62no—
673C22×C3—62no—
674C22×C3—68no—
675C22×C3—68no—
676C22×C3—62no—
677C22×C3—62no—
678C22×C3—62no—
679C22×C3—62no—
680C22×C3—62no—
681C22×C3—62no—
682C22×C3—122no—
683C22×C3—122no—
684C22×C3—128no—
685C22×C3—122no—
686C22×C3—122no—
687C22×C3—128no—
688C22×C3—124no—
689C22×C3—124no—
690C22×C3—182no—
691C22×C3—182no—
692C22×C3—182no—
693C22×C3—364no—
694C22×C3#379512yes—
695C22×C3D3×D1212yes—
696C22×C3#380412yes—
697C22×C3#380512yes—
698C22×C3C2×#62512yes—
699C22×C3C2×#62612yes—
700C22×C3D3×#6712yes—
701C22×C3D3×#6712yes—
702C22×C3D3×#6712yes—
703C22×C3C22×D3211yescharacteristic
704C22×C3C22×D3211yescharacteristic
705C22×C3C22×D3211yescharacteristic
706C2×D3—22no—
707C2×D3—22no—
708C2×D3—28no—
709C2×D3—22no—
710C2×D3—22no—
711C2×D3—22no—
712C2×D3—44no—
713C2×D3—64no—
714C2×D3—62no—
715C2×D3—62no—
716C2×D3—62no—
717C2×D3—62no—
718C2×D3—62no—
719C2×D3—62no—
720C2×D3—122no—
721C2×D3—122no—
722C2×D3—128no—
723C2×D3—124no—
724C2×D3—124no—
725C2×D3C2×#62614yescomplemented
726C3×C4—34no—
727C3×C4—34no—
728C3×C4—64no—
729C3×C4—182no—
730C3×C4—182no—
731Dic3—62no—
732Dic3—62no—
733Dic3—62no—
734Dic3—62no—
735Dic3—122no—
736Dic3—122no—
737Dic3—184no—
738Dic3—182no—
739Dic3—182no—
740Dic3—182no—
741Dic3—362no—
742Dic3—362no—
743Dic3—364no—
744Dic3C2×#62514yescomplemented
745C32—21no—
746C32—21no—
747C32—21no—
748C32—41no—
749C32C2×#93011yescharacteristic, complemented
750C32C2×#93811yescharacteristic, complemented
751C32C2×#93911yescharacteristic, complemented
752C23—32no—
753C23—34no—
754C23—32no—
755C23—62no—
756C23—62no—
757C23—62no—
758C23—62no—
759C23—62no—
760C23—92no—
761C23—182no—
762C23—182no—
763C23—182no—
764C23D3311yescharacteristic
765D4—188no—
766D4—188no—
767D4—548no—
768C2×C4—32no—
769C2×C4—34no—
770C2×C4—92no—
771C2×C4—92no—
772C2×C4—188no—
773C2×C4—182no—
774C2×C4—182no—
775C2×C4—272no—
776C2×C4—542no—
777C2×C3—21no—
778C2×C3—21no—
779C2×C3—21no—
780C2×C3—21no—
781C2×C3—21no—
782C2×C3—21no—
783C2×C3—21no—
784C2×C3—21no—
785C2×C3—21no—
786C2×C3—24no—
787C2×C3—24no—
788C2×C3—24no—
789C2×C3—41no—
790C2×C3—41no—
791C2×C3—41no—
792C2×C3—44no—
793C2×C3—64no—
794C2×C3—64no—
795C2×C3—124no—
796C2×C3—124no—
797C2×C3—122no—
798C2×C3—122no—
799C2×C3—362no—
800C2×C3#6390814yescomplemented
801C2×C3#6397014yescomplemented
802C2×C3#6397814yescomplemented
803C2×C3C2×#379511yescharacteristic
804C2×C3C2×D3×D1211yescharacteristic
805C2×C3C2×#380411yescharacteristic
806C2×C3C2×#380511yescharacteristic
807C2×C3C22×#62511yescharacteristic
808C2×C3C22×#62611yescharacteristic
809C2×C3C2×D3×#6711yescharacteristic
810C2×C3C2×D3×#6711yescharacteristic
811C2×C3C2×D3×#6711yescharacteristic
812D3—24no—
813D3—42no—
814D3—124no—
815D3—122no—
816D3—122no—
817C22—34no—
818C22—62no—
819C22—62no—
820C22—68no—
821C22—62no—
822C22—62no—
823C22—62no—
824C22—124no—
825C22—182no—
826C22—182no—
827C22—182no—
828C22—364no—
829C22D3×#62512yes—
830C22D3×#62612yes—
831C22#8896112yes—
832C22C2×D3311yescharacteristic
833C4—34no—
834C4—182no—
835C4—182no—
836C4—542no—
837C3—21no—
838C3—21no—
839C3—21no—
840C3—41no—
841C3C2×#6390811yescharacteristic, complemented
842C3C2×#6397011yescharacteristic, complemented
843C3C2×#6397811yescharacteristic, complemented
844C2—64no—
845C2—122no—
846C2—362no—
847C2#1172295614yesdirect product factor
848C2C2×D3×#62511yescharacteristic
849C2C2×D3×#62611yescharacteristic
850C2C2×#8896111yescharacteristic
subgroupG/H
center, hypercenterC23D33
commutator, cosocleC22×C33C24
FrattiniC22C2×D33
Fitting, socleC23×C33C23
hypocenterC33C2×#121
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C22×#6290C2semidirect
2. C22×C3×#626C2semidirect
3. C22×C3×#625C2semidirect
4. C22×C3×D3×Dic3C2semidirect
5. C2×#88814C2semidirect
6. C2×Dic3⋊(C3⋊Dic3)C2semidirect
7. C2×(C2×D3)⋊(C3⋊Dic3)C2semidirect
8. #11722956C2direct (N × H)
20. C2×#6290C22semidirect
22. C2×C3×#626C22semidirect
24. C2×C3×#625C22semidirect
26. C2×C3×D3×Dic3C22semidirect
27. #88814C22semidirect
28. Dic3⋊(C3⋊Dic3)C22semidirect
29. (C2×D3)⋊(C3⋊Dic3)C22semidirect
37. C22×#626D3semidirect
41. C22×#625D3semidirect
42. C22×D3×Dic3D3semidirect
67. C22×C32×D3D4semidirect
76. C2×C32×Dic3D4semidirect
131. C2×#626C2×D3semidirect
139. C2×#625C2×D3semidirect
141. C2×D3×Dic3C2×D3semidirect
168. C2×C32×D3C2×D4semidirect
172. C32×Dic3C2×D4semidirect
249. C22×C3×D3D12semidirect
250. C22×C3×D3#67semidirect
294. C2×C3×Dic3#67semidirect
295. C2×C3×Dic3#67semidirect
307. C2×C33#121semidirect
456. C2×C3×D3C2×D12semidirect
457. C2×C3×D3C2×#67semidirect
475. C3×Dic3C2×#67semidirect
476. C3×Dic3C2×#67semidirect
485. C33C2×#121semidirect
538. C22×D3#626semidirect
588. C2×Dic3#625semidirect
610. C2×C32#930semidirect
611. C2×C32#938semidirect
612. C2×C32#939semidirect
725. C2×D3C2×#626semidirect
744. Dic3C2×#625semidirect
749. C32C2×#930semidirect
750. C32C2×#938semidirect
751. C32C2×#939semidirect
800. C2×C3#63908semidirect
801. C2×C3#63970semidirect
802. C2×C3#63978semidirect
841. C3C2×#63908semidirect
842. C3C2×#63970semidirect
843. C3C2×#63978semidirect
847. C2#11722956direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#62902
C22×C3×#6262
C22×C3×#6252
C22×C3×D3×Dic32
C2×#888142
C2×Dic3⋊(C3⋊Dic3)2
C2×(C2×D3)⋊(C3⋊Dic3)2
#117229562
C2×#639783
C2×#639703
C2×#639083