Finite Group Databasebeta

← C2×#11722962 #13172367

Subgroups — C2×#11722962 #13172367

Order 1728.

2258 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×#6295C211yesmaximal, characteristic, complemented
2C22×Dic3×C3⋊D3C211yesmaximal, characteristic, complemented
3C22×C3×#626C211yesmaximal, characteristic, complemented
4C22×C3×#626C211yesmaximal, characteristic, complemented
5C2×#88803C211yesmaximal, characteristic, complemented
6C2×(C2×D3)⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
7C2×C3×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
8#11722962C218yesmaximal, direct product factor
9C2×#63970—31nomaximal
10C2×#63916—31nomaximal
11C2×#63886—31nomaximal
12C23×C3×C3⋊D3C2211yescharacteristic
13C23×C3×C3⋊D3C2211yescharacteristic
14C23×C32×D3C2211yescharacteristic
15C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
16C22×C3×C3⋊Dic3C2211yescharacteristic
17C22×C32×Dic3C2211yescharacteristic
18C22×C32×Dic3C2211yescharacteristic
19C2×#6295—24no—
20C2×#6295C2214yescomplemented
21C2×Dic3×C3⋊D3—24no—
22C2×Dic3×C3⋊D3C2214yescomplemented
23C2×C3×#626—24no—
24C2×C3×#626—24no—
25C2×C3×#626C2214yescomplemented
26C2×C3×#626C2214yescomplemented
27#88803C2214yescomplemented
28(C2×D3)⋊(C3⋊Dic3)C2214yescomplemented
29C3×Dic3⋊Dic3C2214yescomplemented
30C22×C4×C3⋊D3—31no—
31C22×C3×#67—31no—
32C22×C3×#67—31no—
33C22×C3×D12—31no—
34C22×C3×D12—31no—
35C22×#626—31no—
36C22×#626—31no—
37C22×#626D311yescharacteristic, complemented
38C22×#626D311yescharacteristic, complemented
39C22×#625—31no—
40C22×D3×Dic3—31no—
41C22×D3×Dic3—31no—
42C22×D3×Dic3—61no—
43C2×#3757—31no—
44C2×#3752—31no—
45C2×C3×C4⋊Dic3—31no—
46C2×C3×Dic3⋊C4—31no—
47#63970—38no—
48C2×Dic3⋊Dic3D311yescharacteristic, complemented
49C2×(C2×D3)⋊Dic3—31no—
50C2×(C2×D3)⋊Dic3—31no—
51C2×(C2×D3)⋊Dic3—31no—
52C2×(C2×D3)⋊Dic3—31no—
53C2×(C2×D3)⋊Dic3—61no—
54C2×(C2×D3)⋊Dic3—61no—
55#63916—38no—
56#63886—38no—
57C23×C33C2311yescharacteristic
58C22×C3×C3⋊D3—22no—
59C22×C3×C3⋊D3—22no—
60C22×C3×C3⋊D3—22no—
61C22×C3×C3⋊D3—22no—
62C22×C3×C3⋊D3—22no—
63C22×C3×C3⋊D3D414yescomplemented
64C22×C3×C3⋊D3C2312yes—
65C22×C3×C3⋊D3C2312yes—
66C22×C32×D3—22no—
67C22×C32×D3—22no—
68C22×C32×D3—22no—
69C22×C32×D3C2312yes—
70C2×C3⋊(C3⋊Dic3)—22no—
71C2×C3⋊(C3⋊Dic3)C2312yes—
72C2×C3×C3⋊Dic3—22no—
73C2×C3×C3⋊Dic3C2312yes—
74C2×C32×Dic3—22no—
75C2×C32×Dic3D414yescomplemented
76C2×C32×Dic3C2312yes—
77C2×C32×Dic3C2312yes—
78#6295—28no—
79Dic3×C3⋊D3—28no—
80C3×#626—28no—
81C3×#626—28no—
82C2×#939—91no—
83C2×#938—91no—
84C2×#895—91no—
85C24×C32—31no—
86C23×C3⋊D3C2×D311yescharacteristic
87C23×C3⋊D3C2×D311yescharacteristic
88C23×C3×D3—21no—
89C23×C3×D3—31no—
90C23×C3×D3—31no—
91C23×C3×D3—31no—
92C23×C3×D3—31no—
93C23×C3×D3—61no—
94C23×C3×D3—61no—
95C23×C3×D3C2×D311yescharacteristic
96C23×C3×D3C2×D311yescharacteristic
97C22×C32×C4—31no—
98C22×C32×C4—31no—
99C22×C3⋊Dic3—31no—
100C22×C3⋊Dic3—31no—
101C22×C3⋊Dic3—31no—
102C22×C3⋊Dic3—61no—
103C22×C3⋊Dic3—61no—
104C22×C3⋊Dic3—61no—
105C22×C3⋊Dic3—121no—
106C22×C3⋊Dic3C2×D311yescharacteristic
107C2×C4×C3⋊D3—34no—
108C2×C4×C3⋊D3—64no—
109C2×C3×#67—34no—
110C2×C3×#67—34no—
111C2×C3×#67—64no—
112C2×C3×#67—64no—
113C22×C3×Dic3—21no—
114C22×C3×Dic3—21no—
115C22×C3×Dic3—31no—
116C22×C3×Dic3—31no—
117C22×C3×Dic3—61no—
118C22×C3×Dic3C2×D311yescharacteristic
119C22×C3×Dic3C2×D311yescharacteristic
120C22×C3×Dic3C2×D311yescharacteristic
121C22×C3×Dic3C2×D311yescharacteristic
122C2×C3×D12—34no—
123C2×C3×D12—34no—
124C2×C3×D12—64no—
125C2×C3×D12—64no—
126C2×#626—24no—
127C2×#626—24no—
128C2×#626—34no—
129C2×#626—34no—
130C2×#626—64no—
131C2×#626—64no—
132C2×#626C2×D314yescomplemented
133C2×#626C2×D314yescomplemented
134C2×#625—34no—
135C2×#625—64no—
136C2×D3×Dic3—34no—
137C2×D3×Dic3—34no—
138C2×D3×Dic3—64no—
139C2×D3×Dic3—68no—
140C2×D3×Dic3—64no—
141C2×D3×Dic3—64no—
142#3757—34no—
143#3752—34no—
144C3×C4⋊Dic3—34no—
145C3×Dic3⋊C4—34no—
146Dic3⋊Dic3C2×D314yescomplemented
147(C2×D3)⋊Dic3—34no—
148(C2×D3)⋊Dic3—34no—
149(C2×D3)⋊Dic3—34no—
150(C2×D3)⋊Dic3—34no—
151(C2×D3)⋊Dic3—64no—
152(C2×D3)⋊Dic3—64no—
153C22×C33C2×D412yes—
154C22×C33C2×D412yes—
155C22×C33#4112yes—
156C22×C33C2411yescharacteristic
157C2×C3×C3⋊D3—28no—
158C2×C3×C3⋊D3—22no—
159C2×C3×C3⋊D3—22no—
160C2×C3×C3⋊D3—22no—
161C2×C3×C3⋊D3—22no—
162C2×C3×C3⋊D3—22no—
163C2×C3×C3⋊D3—44no—
164C2×C3×C3⋊D3C2×D414yescomplemented
165C2×C32×D3—22no—
166C2×C32×D3—22no—
167C2×C32×D3—22no—
168C2×C32×D3—44no—
169C3⋊(C3⋊Dic3)—22no—
170C3×C3⋊Dic3—22no—
171C32×Dic3—22no—
172C32×Dic3C2×D414yescomplemented
173C22×C3×D4—91no—
174C22×C3×D4—91no—
175C22×#67—31no—
176C22×#67—31no—
177C22×#67—91no—
178C22×#67—91no—
179C23×Dic3—91no—
180C22×D12—31no—
181C22×D12—31no—
182C22×D12—91no—
183C22×C4×D3—91no—
184C22×C4×D3—91no—
185C22×C4×D3—181no—
186C2×C3×C4⋊C4—91no—
187C2×#217—91no—
188C2×#217—91no—
189C2×#217—91no—
190C2×#217—181no—
191#939—98no—
192#938—98no—
193C2×(C2×D3)⋊C4—91no—
194C2×(C2×D3)⋊C4—91no—
195C2×(C2×D3)⋊C4—91no—
196C2×(C2×D3)⋊C4—181no—
197C2×C4⋊Dic3—31no—
198C2×Dic3⋊C4—31no—
199#895—98no—
200C23×C32—21no—
201C23×C32—21no—
202C23×C32—21no—
203C23×C32—32no—
204C23×C32—41no—
205C23×C32—62no—
206C23×C32—62no—
207C23×C32—62no—
208C23×C32C22×D311yescharacteristic
209C23×C32C22×D311yescharacteristic
210C23×C32C22×D311yescharacteristic
211C22×C3⋊D3—22no—
212C22×C3⋊D3—22no—
213C22×C3⋊D3—22no—
214C22×C3⋊D3—22no—
215C22×C3⋊D3—22no—
216C22×C3⋊D3#6714yescomplemented
217C22×C3⋊D3C22×D312yes—
218C22×C3⋊D3C22×D312yes—
219C22×C3×D3—24no—
220C22×C3×D3—22no—
221C22×C3×D3—22no—
222C22×C3×D3—22no—
223C22×C3×D3—22no—
224C22×C3×D3—22no—
225C22×C3×D3—22no—
226C22×C3×D3—22no—
227C22×C3×D3—34no—
228C22×C3×D3—34no—
229C22×C3×D3—32no—
230C22×C3×D3—32no—
231C22×C3×D3—32no—
232C22×C3×D3—32no—
233C22×C3×D3—42no—
234C22×C3×D3—42no—
235C22×C3×D3—64no—
236C22×C3×D3—62no—
237C22×C3×D3—62no—
238C22×C3×D3—64no—
239C22×C3×D3—64no—
240C22×C3×D3—62no—
241C22×C3×D3—62no—
242C22×C3×D3—62no—
243C22×C3×D3—62no—
244C22×C3×D3—64no—
245C22×C3×D3—62no—
246C22×C3×D3—62no—
247C22×C3×D3—62no—
248C22×C3×D3—62no—
249C22×C3×D3—62no—
250C22×C3×D3—62no—
251C22×C3×D3—122no—
252C22×C3×D3—122no—
253C22×C3×D3C22×D312yes—
254C22×C3×D3C22×D312yes—
255C2×C32×C4—34no—
256C2×C32×C4—32no—
257C2×C32×C4—32no—
258C2×C32×C4—62no—
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—
275C4×C3⋊D3—68no—
276C3×#67—68no—
277C3×#67—68no—
278C2×C3×Dic3—22no—
279C2×C3×Dic3—22no—
280C2×C3×Dic3—24no—
281C2×C3×Dic3—22no—
282C2×C3×Dic3—22no—
283C2×C3×Dic3—32no—
284C2×C3×Dic3—32no—
285C2×C3×Dic3—42no—
286C2×C3×Dic3—62no—
287C2×C3×Dic3—62no—
288C2×C3×Dic3—62no—
289C2×C3×Dic3—122no—
290C2×C3×Dic3D1214yescomplemented
291C2×C3×Dic3#6714yescomplemented
292C2×C3×Dic3C22×D312yes—
293C2×C3×Dic3C22×D312yes—
294C2×C3×Dic3C22×D312yes—
295C2×C3×Dic3C22×D312yes—
296C3×D12—68no—
297C3×D12—68no—
298#626—28no—
299#626—28no—
300#626—68no—
301#626—68no—
302#625—68no—
303D3×Dic3—616no—
304D3×Dic3—68no—
305D3×Dic3—68no—
306C2×#121—271noSylow
307C2×C33#12114yescomplemented
308C2×C33C22×D411yescharacteristic
309C2×C33C22×D411yescharacteristic
310C2×C33C2×#4111yescharacteristic
311C3×C3⋊D3—24no—
312C3×C3⋊D3—42no—
313C32×D3—42no—
314C24×C3—31no—
315C24×C3—31no—
316C24×C3—61no—
317C24×C3—91no—
318C24×C3—91no—
319C23×D3—31no—
320C23×D3—31no—
321C23×D3—31no—
322C23×D3—31no—
323C23×D3—61no—
324C23×D3—61no—
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—31no—
333C22×C3×C4—31no—
334C22×C3×C4—61no—
335C22×C3×C4—61no—
336C22×C3×C4—91no—
337C2×#67—34no—
338C2×#67—34no—
339C2×#67—64no—
340C2×#67—64no—
341C2×#67—94no—
342C2×#67—94no—
343C2×#67—184no—
344C2×#67—184no—
345C22×Dic3—31no—
346C22×Dic3—31no—
347C22×Dic3—61no—
348C22×Dic3—91no—
349C22×Dic3—91no—
350C22×Dic3—91no—
351C22×Dic3—94no—
352C22×Dic3—181no—
353C22×Dic3—181no—
354C22×Dic3—181no—
355C22×Dic3—184no—
356C22×Dic3—361no—
357C22×Dic3D3211yescharacteristic
358C22×Dic3D3211yescharacteristic
359C2×D12—34no—
360C2×D12—34no—
361C2×D12—64no—
362C2×D12—64no—
363C2×D12—94no—
364C2×D12—184no—
365C2×C4×D3—94no—
366C2×C4×D3—94no—
367C2×C4×D3—184no—
368C2×C4×D3—184no—
369C2×C4×D3—184no—
370C2×C4×D3—188no—
371C3×C4⋊C4—94no—
372#217—94no—
373#217—94no—
374#217—94no—
375#217—184no—
376(C2×D3)⋊C4—94no—
377(C2×D3)⋊C4—94no—
378(C2×D3)⋊C4—94no—
379(C2×D3)⋊C4—184no—
380C4⋊Dic3—34no—
381Dic3⋊C4—34no—
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—42no—
395C22×C32—42no—
396C22×C32—42no—
397C22×C32—41no—
398C22×C32—62no—
399C22×C32—62no—
400C22×C32—62no—
401C22×C32—124no—
402C22×C32C2×D1212yes—
403C22×C32D3×D412yes—
404C22×C32D3×D412yes—
405C22×C32D3×D412yes—
406C22×C32#23712yes—
407C22×C32#23712yes—
408C22×C32#23912yes—
409C22×C32C2×#6712yes—
410C22×C32C2×#6712yes—
411C22×C32C23×D311yescharacteristic
412C22×C32C23×D311yescharacteristic
413C22×C32C23×D311yescharacteristic
414C2×C3⋊D3—28no—
415C2×C3⋊D3—22no—
416C2×C3⋊D3—22no—
417C2×C3⋊D3—22no—
418C2×C3⋊D3—22no—
419C2×C3⋊D3—22no—
420C2×C3⋊D3—44no—
421C2×C3⋊D3C2×#6714yescomplemented
422C2×C3×D3—24no—
423C2×C3×D3—22no—
424C2×C3×D3—22no—
425C2×C3×D3—22no—
426C2×C3×D3—22no—
427C2×C3×D3—22no—
428C2×C3×D3—22no—
429C2×C3×D3—34no—
430C2×C3×D3—34no—
431C2×C3×D3—42no—
432C2×C3×D3—42no—
433C2×C3×D3—48no—
434C2×C3×D3—44no—
435C2×C3×D3—44no—
436C2×C3×D3—64no—
437C2×C3×D3—64no—
438C2×C3×D3—64no—
439C2×C3×D3—616no—
440C2×C3×D3—68no—
441C2×C3×D3—68no—
442C2×C3×D3—62no—
443C2×C3×D3—62no—
444C2×C3×D3—62no—
445C2×C3×D3—62no—
446C2×C3×D3—64no—
447C2×C3×D3—62no—
448C2×C3×D3—62no—
449C2×C3×D3—62no—
450C2×C3×D3—62no—
451C2×C3×D3—62no—
452C2×C3×D3—62no—
453C2×C3×D3—122no—
454C2×C3×D3—122no—
455C2×C3×D3—128no—
456C2×C3×D3—124no—
457C2×C3×D3—124no—
458C32×C4—34no—
459C32×C4—62no—
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—22no—
469C3×Dic3—22no—
470C3×Dic3—24no—
471C3×Dic3—42no—
472C3×Dic3—62no—
473C3×Dic3—62no—
474C3×Dic3—122no—
475C3×Dic3C2×D1214yescomplemented
476C3×Dic3C2×#6714yescomplemented
477C22×D4—91no—
478C22×D4—91no—
479C22×D4—271no—
480C23×C4—271no—
481#121—278no—
482C2×C4⋊C4—91no—
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—41no—
492C23×C3—62no—
493C23×C3—64no—
494C23×C3—62no—
495C23×C3—62no—
496C23×C3—62no—
497C23×C3—62no—
498C23×C3—62no—
499C23×C3—62no—
500C23×C3—92no—
501C23×C3—94no—
502C23×C3—92no—
503C23×C3—122no—
504C23×C3—122no—
505C23×C3—182no—
506C23×C3—182no—
507C23×C3—182no—
508C23×C3—182no—
509C23×C3—182no—
510C23×C3C2×D3211yescharacteristic
511C23×C3C2×D3211yescharacteristic
512C23×C3C2×D3211yescharacteristic
513C22×D3—22no—
514C22×D3—22no—
515C22×D3—22no—
516C22×D3—32no—
517C22×D3—32no—
518C22×D3—34no—
519C22×D3—34no—
520C22×D3—32no—
521C22×D3—32no—
522C22×D3—64no—
523C22×D3—62no—
524C22×D3—62no—
525C22×D3—64no—
526C22×D3—64no—
527C22×D3—62no—
528C22×D3—62no—
529C22×D3—62no—
530C22×D3—62no—
531C22×D3—64no—
532C22×D3—62no—
533C22×D3—62no—
534C22×D3—62no—
535C22×D3—62no—
536C22×D3—62no—
537C22×D3—62no—
538C22×D3—122no—
539C22×D3—122no—
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—32no—
548C2×C3×C4—32no—
549C2×C3×C4—62no—
550C2×C3×C4—64no—
551C2×C3×C4—62no—
552C2×C3×C4—62no—
553C2×C3×C4—62no—
554C2×C3×C4—92no—
555C2×C3×C4—122no—
556C2×C3×C4—182no—
557#67—68no—
558#67—68no—
559#67—188no—
560#67—188no—
561C2×Dic3—22no—
562C2×Dic3—32no—
563C2×Dic3—32no—
564C2×Dic3—62no—
565C2×Dic3—62no—
566C2×Dic3—62no—
567C2×Dic3—92no—
568C2×Dic3—92no—
569C2×Dic3—92no—
570C2×Dic3—122no—
571C2×Dic3—182no—
572C2×Dic3—182no—
573C2×Dic3—182no—
574C2×Dic3—184no—
575C2×Dic3—182no—
576C2×Dic3—182no—
577C2×Dic3—182no—
578C2×Dic3—188no—
579C2×Dic3—362no—
580C2×Dic3—362no—
581C2×Dic3—362no—
582C2×Dic3—364no—
583C2×Dic3#62614yescomplemented
584C2×Dic3C2×D3212yes—
585C2×Dic3C2×D3212yes—
586D12—68no—
587D12—68no—
588D12—188no—
589C4×D3—188no—
590C4×D3—188no—
591C4×D3—1816no—
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—122no—
609C2×C32#89514yescomplemented
610C2×C32#93814yescomplemented
611C2×C32#93914yescomplemented
612C2×C32C22×D1211yescharacteristic
613C2×C32C2×D3×D411yescharacteristic
614C2×C32C2×D3×D411yescharacteristic
615C2×C32C2×D3×D411yescharacteristic
616C2×C32C2×#23711yescharacteristic
617C2×C32C2×#23711yescharacteristic
618C2×C32C2×#23911yescharacteristic
619C2×C32C22×#6711yescharacteristic
620C2×C32C22×#6711yescharacteristic
621C3⋊D3—24no—
622C3⋊D3—42no—
623C3×D3—44no—
624C3×D3—42no—
625C3×D3—42no—
626C3×D3—68no—
627C3×D3—64no—
628C3×D3—64no—
629C3×D3—124no—
630C3×D3—122no—
631C3×D3—122no—
632C24—31no—
633C24—91no—
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—31no—
643C22×C4—91no—
644C22×C4—274no—
645C22×C4—271no—
646C22×C4—544no—
647C4⋊C4—94no—
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—41no—
663C22×C3—42no—
664C22×C3—42no—
665C22×C3—42no—
666C22×C3—64no—
667C22×C3—62no—
668C22×C3—62no—
669C22×C3—62no—
670C22×C3—62no—
671C22×C3—62no—
672C22×C3—62no—
673C22×C3—94no—
674C22×C3—122no—
675C22×C3—122no—
676C22×C3—128no—
677C22×C3—124no—
678C22×C3—124no—
679C22×C3—182no—
680C22×C3—182no—
681C22×C3—188no—
682C22×C3—182no—
683C22×C3—182no—
684C22×C3—182no—
685C22×C3—364no—
686C22×C3#379612yes—
687C22×C3#379612yes—
688C22×C3D3×D1212yes—
689C22×C3#380212yes—
690C22×C3#380512yes—
691C22×C3C2×#62612yes—
692C22×C3D3×#6712yes—
693C22×C3D3×#6712yes—
694C22×C3D3×#6712yes—
695C22×C3C22×D3211yescharacteristic
696C22×C3C22×D3211yescharacteristic
697C22×C3C22×D3211yescharacteristic
698C2×D3—22no—
699C2×D3—22no—
700C2×D3—22no—
701C2×D3—34no—
702C2×D3—34no—
703C2×D3—44no—
704C2×D3—64no—
705C2×D3—64no—
706C2×D3—64no—
707C2×D3—616no—
708C2×D3—62no—
709C2×D3—62no—
710C2×D3—62no—
711C2×D3—62no—
712C2×D3—68no—
713C2×D3—68no—
714C2×D3—64no—
715C2×D3—62no—
716C2×D3—62no—
717C2×D3—62no—
718C2×D3—62no—
719C2×D3—62no—
720C2×D3—62no—
721C2×D3—122no—
722C2×D3—122no—
723C2×D3—128no—
724C2×D3—124no—
725C2×D3—124no—
726C3×C4—34no—
727C3×C4—34no—
728C3×C4—64no—
729C3×C4—62no—
730C3×C4—62no—
731C3×C4—122no—
732C3×C4—182no—
733Dic3—22no—
734Dic3—62no—
735Dic3—62no—
736Dic3—122no—
737Dic3—184no—
738Dic3—182no—
739Dic3—182no—
740Dic3—182no—
741Dic3—362no—
742Dic3—362no—
743Dic3—364no—
744Dic3C2×#62614yescomplemented
745C32—21no—
746C32—21no—
747C32—21no—
748C32—41no—
749C32C2×#89511yescharacteristic, complemented
750C32C2×#93811yescharacteristic, complemented
751C32C2×#93911yescharacteristic, complemented
752C23—32no—
753C23—62no—
754C23—62no—
755C23—62no—
756C23—92no—
757C23—94no—
758C23—92no—
759C23—182no—
760C23—182no—
761C23—182no—
762C23—182no—
763C23—182no—
764C23D3311yescharacteristic
765D4—188no—
766D4—188no—
767D4—548no—
768C2×C4—32no—
769C2×C4—34no—
770C2×C4—32no—
771C2×C4—62no—
772C2×C4—92no—
773C2×C4—182no—
774C2×C4—272no—
775C2×C4—548no—
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—124no—
794C2×C3—122no—
795C2×C3—122no—
796C2×C3—184no—
797C2×C3—362no—
798C2×C3#6388614yescomplemented
799C2×C3#6391614yescomplemented
800C2×C3#6397014yescomplemented
801C2×C3C2×#379611yescharacteristic
802C2×C3C2×#379611yescharacteristic
803C2×C3C2×D3×D1211yescharacteristic
804C2×C3C2×#380211yescharacteristic
805C2×C3C2×#380511yescharacteristic
806C2×C3C22×#62611yescharacteristic
807C2×C3C2×D3×#6711yescharacteristic
808C2×C3C2×D3×#6711yescharacteristic
809C2×C3C2×D3×#6711yescharacteristic
810D3—42no—
811D3—68no—
812D3—64no—
813D3—64no—
814D3—124no—
815D3—122no—
816D3—122no—
817C22—62no—
818C22—62no—
819C22—62no—
820C22—94no—
821C22—124no—
822C22—182no—
823C22—182no—
824C22—188no—
825C22—182no—
826C22—182no—
827C22—182no—
828C22—364no—
829C22D3×#62612yes—
830C22#8895312yes—
831C22#8896412yes—
832C22C2×D3311yescharacteristic
833C4—34no—
834C4—62no—
835C4—182no—
836C4—542no—
837C3—21no—
838C3—21no—
839C3—21no—
840C3—41no—
841C3C2×#6388611yescharacteristic, complemented
842C3C2×#6391611yescharacteristic, complemented
843C3C2×#6397011yescharacteristic, complemented
844C2—122no—
845C2—184no—
846C2—362no—
847C2#1172296214yesdirect product factor
848C2C2×D3×#62611yescharacteristic
849C2C2×#8895311yescharacteristic
850C2C2×#8896411yescharacteristic
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×#6295C2semidirect
2. C22×Dic3×C3⋊D3C2semidirect
3. C22×C3×#626C2semidirect
4. C22×C3×#626C2semidirect
5. C2×#88803C2semidirect
6. C2×(C2×D3)⋊(C3⋊Dic3)C2semidirect
7. C2×C3×Dic3⋊Dic3C2semidirect
8. #11722962C2direct (N × H)
20. C2×#6295C22semidirect
22. C2×Dic3×C3⋊D3C22semidirect
25. C2×C3×#626C22semidirect
26. C2×C3×#626C22semidirect
27. #88803C22semidirect
28. (C2×D3)⋊(C3⋊Dic3)C22semidirect
29. C3×Dic3⋊Dic3C22semidirect
37. C22×#626D3semidirect
38. C22×#626D3semidirect
48. C2×Dic3⋊Dic3D3semidirect
63. C22×C3×C3⋊D3D4semidirect
75. C2×C32×Dic3D4semidirect
132. C2×#626C2×D3semidirect
133. C2×#626C2×D3semidirect
146. Dic3⋊Dic3C2×D3semidirect
164. C2×C3×C3⋊D3C2×D4semidirect
172. C32×Dic3C2×D4semidirect
216. C22×C3⋊D3#67semidirect
290. C2×C3×Dic3D12semidirect
291. C2×C3×Dic3#67semidirect
307. C2×C33#121semidirect
421. C2×C3⋊D3C2×#67semidirect
475. C3×Dic3C2×D12semidirect
476. C3×Dic3C2×#67semidirect
485. C33C2×#121semidirect
583. C2×Dic3#626semidirect
609. C2×C32#895semidirect
610. C2×C32#938semidirect
611. C2×C32#939semidirect
744. Dic3C2×#626semidirect
749. C32C2×#895semidirect
750. C32C2×#938semidirect
751. C32C2×#939semidirect
798. C2×C3#63886semidirect
799. C2×C3#63916semidirect
800. C2×C3#63970semidirect
841. C3C2×#63886semidirect
842. C3C2×#63916semidirect
843. C3C2×#63970semidirect
847. C2#11722962direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#62952
C22×Dic3×C3⋊D32
C22×C3×#6262
C2×#888032
C2×(C2×D3)⋊(C3⋊Dic3)2
C2×C3×Dic3⋊Dic32
#117229622
C2×#639703
C2×#639163
C2×#638863