Finite Group Databasebeta

← C2×#11722957 #13172326

Subgroups — C2×#11722957 #13172326

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×#6295C211yesmaximal, characteristic, complemented
2C22×#6290C211yesmaximal, characteristic, complemented
3C22×C3×#626C211yesmaximal, characteristic, complemented
4C22×C3×#624C211yesmaximal, characteristic, complemented
5C2×Dic3⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
6C2×#88803C211yesmaximal, characteristic, complemented
7C2×C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
8#11722957C218yesmaximal, direct product factor
9C2×#63958—31nomaximal
10C2×#63908—31nomaximal
11C2×#63906—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×#6290—24no—
22C2×#6290C2214yescomplemented
23C2×C3×#626—24no—
24C2×C3×#626C2214yescomplemented
25C2×C3×#624—24no—
26C2×C3×#624C2214yescomplemented
27Dic3⋊(C3⋊Dic3)C2214yescomplemented
28#88803C2214yescomplemented
29C3×(C2×D3)⋊Dic3C2214yescomplemented
30C22×#638—31no—
31C22×C3×#67—31no—
32C22×C3×D12—31no—
33C22×C3×C4×D3—31no—
34C22×C3×C4×D3—31no—
35C22×#626—31no—
36C22×#626—31no—
37C22×#626D311yescharacteristic, complemented
38C22×#625—31no—
39C22×#625—31no—
40C22×#625—31no—
41C22×#625—61no—
42C22×#624D311yescharacteristic, complemented
43C2×#3752—31no—
44C2×C4⋊(C3⋊Dic3)—31no—
45C2×C3×#217—31no—
46C2×C3×(C2×D3)⋊C4—31no—
47C2×Dic3⋊Dic3—31no—
48C2×Dic3⋊Dic3—31no—
49C2×Dic3⋊Dic3—61no—
50C2×(C2×D3)⋊Dic3—31no—
51C2×(C2×D3)⋊Dic3—31no—
52C2×(C2×D3)⋊Dic3—61no—
53C2×(C2×D3)⋊Dic3D311yescharacteristic, complemented
54#63958—38no—
55#63908—38no—
56#63906—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—
79#6290—28no—
80C3×#626—28no—
81C3×#624—28no—
82C2×#938—91no—
83C2×#930—91no—
84C2×#884—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—
99C2×#638—34no—
100C2×#638—64no—
101C22×C3⋊Dic3—31no—
102C22×C3⋊Dic3—31no—
103C22×C3⋊Dic3—31no—
104C22×C3⋊Dic3—61no—
105C22×C3⋊Dic3—61no—
106C22×C3⋊Dic3—61no—
107C22×C3⋊Dic3—121no—
108C22×C3⋊Dic3C2×D311yescharacteristic
109C2×C3×#67—34no—
110C2×C3×#67—64no—
111C22×C3×Dic3—21no—
112C22×C3×Dic3—21no—
113C22×C3×Dic3—31no—
114C22×C3×Dic3—31no—
115C22×C3×Dic3—61no—
116C22×C3×Dic3C2×D311yescharacteristic
117C22×C3×Dic3C2×D311yescharacteristic
118C22×C3×Dic3C2×D311yescharacteristic
119C22×C3×Dic3C2×D311yescharacteristic
120C2×C3×D12—34no—
121C2×C3×D12—64no—
122C2×C3×C4×D3—34no—
123C2×C3×C4×D3—34no—
124C2×C3×C4×D3—64no—
125C2×C3×C4×D3—64no—
126C2×#626—24no—
127C2×#626—34no—
128C2×#626—34no—
129C2×#626—64no—
130C2×#626—64no—
131C2×#626C2×D314yescomplemented
132C2×#625—34no—
133C2×#625—34no—
134C2×#625—34no—
135C2×#625—64no—
136C2×#625—64no—
137C2×#625—64no—
138C2×#625—64no—
139C2×#625—68no—
140C2×#624—24no—
141C2×#624C2×D314yescomplemented
142#3752—34no—
143C4⋊(C3⋊Dic3)—34no—
144C3×#217—34no—
145C3×(C2×D3)⋊C4—34no—
146Dic3⋊Dic3—34no—
147Dic3⋊Dic3—34no—
148Dic3⋊Dic3—64no—
149(C2×D3)⋊Dic3—34no—
150(C2×D3)⋊Dic3—34no—
151(C2×D3)⋊Dic3—64no—
152(C2×D3)⋊Dic3C2×D314yescomplemented
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—
174C23×C3×C4—91no—
175C22×#67—31no—
176C22×#67—91no—
177C22×#67—91no—
178C22×#67—91no—
179C22×#67—91no—
180C22×#67—91no—
181C22×#67—181no—
182C22×D12—31no—
183C22×D12—91no—
184C22×C4×D3—31no—
185C22×C4×D3—31no—
186C2×C3×C22⋊C4—91no—
187C2×#217—31no—
188C2×#217—91no—
189#938—98no—
190#930—98no—
191C2×(C2×D3)⋊C4—31no—
192C2×(C2×D3)⋊C4—91no—
193C2×(C2×D3)⋊C4—91no—
194C2×(C2×D3)⋊C4—181no—
195C2×C4⋊Dic3—91no—
196C2×C4⋊Dic3—91no—
197C2×C4⋊Dic3—181no—
198C2×Dic3⋊C4—91no—
199#884—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⋊D3D1214yescomplemented
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—62no—
236C22×C3×D3—64no—
237C22×C3×D3—62no—
238C22×C3×D3—62no—
239C22×C3×D3—62no—
240C22×C3×D3—62no—
241C22×C3×D3—62no—
242C22×C3×D3—64no—
243C22×C3×D3—62no—
244C22×C3×D3—62no—
245C22×C3×D3—62no—
246C22×C3×D3—62no—
247C22×C3×D3—62no—
248C22×C3×D3—62no—
249C22×C3×D3—122no—
250C22×C3×D3—122no—
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—
259#638—68no—
260C2×C3⋊Dic3—22no—
261C2×C3⋊Dic3—32no—
262C2×C3⋊Dic3—32no—
263C2×C3⋊Dic3—32no—
264C2×C3⋊Dic3—62no—
265C2×C3⋊Dic3—62no—
266C2×C3⋊Dic3—62no—
267C2×C3⋊Dic3—62no—
268C2×C3⋊Dic3—64no—
269C2×C3⋊Dic3—62no—
270C2×C3⋊Dic3—62no—
271C2×C3⋊Dic3—122no—
272C2×C3⋊Dic3—122no—
273C2×C3⋊Dic3—122no—
274C2×C3⋊Dic3—124no—
275C2×C3⋊Dic3C22×D312yes—
276C3×#67—68no—
277C2×C3×Dic3—22no—
278C2×C3×Dic3—22no—
279C2×C3×Dic3—24no—
280C2×C3×Dic3—22no—
281C2×C3×Dic3—22no—
282C2×C3×Dic3—32no—
283C2×C3×Dic3—32no—
284C2×C3×Dic3—42no—
285C2×C3×Dic3—62no—
286C2×C3×Dic3—62no—
287C2×C3×Dic3—62no—
288C2×C3×Dic3—122no—
289C2×C3×Dic3#6714yescomplemented
290C2×C3×Dic3#6714yescomplemented
291C2×C3×Dic3C22×D312yes—
292C2×C3×Dic3C22×D312yes—
293C2×C3×Dic3C22×D312yes—
294C2×C3×Dic3C22×D312yes—
295C3×D12—68no—
296C3×C4×D3—68no—
297C3×C4×D3—68no—
298#626—28no—
299#626—68no—
300#626—68no—
301#625—68no—
302#625—68no—
303#625—68no—
304#625—616no—
305#624—28no—
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—184no—
328C22×C3×C4—31no—
329C22×C3×C4—31no—
330C22×C3×C4—31no—
331C22×C3×C4—31no—
332C22×C3×C4—61no—
333C22×C3×C4—61no—
334C22×C3×C4—94no—
335C22×C3×C4—91no—
336C22×C3×C4—184no—
337C2×#67—34no—
338C2×#67—64no—
339C2×#67—94no—
340C2×#67—94no—
341C2×#67—94no—
342C2×#67—94no—
343C2×#67—94no—
344C2×#67—184no—
345C2×#67—184no—
346C2×#67—184no—
347C2×#67—184no—
348C2×#67—184no—
349C2×#67—184no—
350C2×#67—188no—
351C22×Dic3—31no—
352C22×Dic3—31no—
353C22×Dic3—61no—
354C22×Dic3—91no—
355C22×Dic3—91no—
356C22×Dic3—91no—
357C22×Dic3—181no—
358C22×Dic3—181no—
359C22×Dic3—181no—
360C22×Dic3—361no—
361C22×Dic3D3211yescharacteristic
362C22×Dic3D3211yescharacteristic
363C2×D12—34no—
364C2×D12—64no—
365C2×D12—94no—
366C2×D12—184no—
367C2×C4×D3—34no—
368C2×C4×D3—34no—
369C2×C4×D3—64no—
370C2×C4×D3—64no—
371C3×C22⋊C4—94no—
372#217—34no—
373#217—94no—
374(C2×D3)⋊C4—34no—
375(C2×D3)⋊C4—94no—
376(C2×D3)⋊C4—94no—
377(C2×D3)⋊C4—184no—
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—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×C32#23512yes—
404C22×C32#23512yes—
405C22×C32D3×D412yes—
406C22×C32D3×D412yes—
407C22×C32D3×D412yes—
408C22×C32#23712yes—
409C22×C32C2×#6712yes—
410C22×C32C2×#6712yes—
411C22×C32C23×D311yescharacteristic
412C22×C32C23×D311yescharacteristic
413C22×C32C23×D311yescharacteristic
414C2×C3⋊D3—22no—
415C2×C3⋊D3—28no—
416C2×C3⋊D3—22no—
417C2×C3⋊D3—22no—
418C2×C3⋊D3—22no—
419C2×C3⋊D3—22no—
420C2×C3⋊D3—44no—
421C2×C3⋊D3C2×D1214yescomplemented
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—68no—
438C2×C3×D3—68no—
439C2×C3×D3—62no—
440C2×C3×D3—62no—
441C2×C3×D3—62no—
442C2×C3×D3—62no—
443C2×C3×D3—64no—
444C2×C3×D3—62no—
445C2×C3×D3—62no—
446C2×C3×D3—62no—
447C2×C3×D3—62no—
448C2×C3×D3—62no—
449C2×C3×D3—62no—
450C2×C3×D3—122no—
451C2×C3×D3—122no—
452C2×C3×D3—128no—
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×#6714yescomplemented
476C3×Dic3C2×#6714yescomplemented
477C22×D4—91no—
478C22×D4—271no—
479C22×D4—271no—
480C23×C4—91no—
481#121—278no—
482C2×C4⋊C4—271no—
483C2×C22⋊C4—91no—
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—62no—
526C22×D3—62no—
527C22×D3—62no—
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—122no—
539C22×D3—122no—
540C22×D3C2×D3212yes—
541C3×D4—188no—
542C2×C3×C4—32no—
543C2×C3×C4—32no—
544C2×C3×C4—34no—
545C2×C3×C4—34no—
546C2×C3×C4—32no—
547C2×C3×C4—32no—
548C2×C3×C4—62no—
549C2×C3×C4—64no—
550C2×C3×C4—62no—
551C2×C3×C4—62no—
552C2×C3×C4—62no—
553C2×C3×C4—92no—
554C2×C3×C4—122no—
555C2×C3×C4—188no—
556C2×C3×C4—182no—
557#67—68no—
558#67—188no—
559#67—188no—
560#67—188no—
561#67—188no—
562#67—188no—
563#67—1816no—
564C2×Dic3—22no—
565C2×Dic3—32no—
566C2×Dic3—32no—
567C2×Dic3—62no—
568C2×Dic3—62no—
569C2×Dic3—62no—
570C2×Dic3—92no—
571C2×Dic3—92no—
572C2×Dic3—92no—
573C2×Dic3—122no—
574C2×Dic3—182no—
575C2×Dic3—182no—
576C2×Dic3—182no—
577C2×Dic3—184no—
578C2×Dic3—182no—
579C2×Dic3—182no—
580C2×Dic3—182no—
581C2×Dic3—362no—
582C2×Dic3—362no—
583C2×Dic3—362no—
584C2×Dic3—364no—
585C2×Dic3#62514yescomplemented
586C2×Dic3C2×D3212yes—
587C2×Dic3C2×D3212yes—
588D12—68no—
589D12—188no—
590C4×D3—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—122no—
609C2×C32#88414yescomplemented
610C2×C32#93014yescomplemented
611C2×C32#93814yescomplemented
612C2×C32C22×D1211yescharacteristic
613C2×C32C2×#23511yescharacteristic
614C2×C32C2×#23511yescharacteristic
615C2×C32C2×D3×D411yescharacteristic
616C2×C32C2×D3×D411yescharacteristic
617C2×C32C2×D3×D411yescharacteristic
618C2×C32C2×#23711yescharacteristic
619C2×C32C22×#6711yescharacteristic
620C2×C32C22×#6711yescharacteristic
621C3⋊D3—24no—
622C3⋊D3—42no—
623C3×D3—44no—
624C3×D3—42no—
625C3×D3—42no—
626C3×D3—64no—
627C3×D3—64no—
628C3×D3—124no—
629C3×D3—124no—
630C3×D3—122no—
631C3×D3—122no—
632C24—31no—
633C24—91no—
634C24—91no—
635C2×D4—94no—
636C2×D4—184no—
637C2×D4—274no—
638C2×D4—274no—
639C2×D4—544no—
640C2×D4—544no—
641C22×C4—31no—
642C22×C4—31no—
643C22×C4—94no—
644C22×C4—91no—
645C22×C4—184no—
646C22×C4—271no—
647C4⋊C4—274no—
648C22⋊C4—94no—
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#379512yes—
687C22×C3#379812yes—
688C22×C3D3×D1212yes—
689C22×C3D3×D1212yes—
690C22×C3#380412yes—
691C22×C3C2×#62512yes—
692C22×C3D3×#6712yes—
693C22×C3D3×#6712yes—
694C22×C3#381112yes—
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—62no—
706C2×D3—62no—
707C2×D3—62no—
708C2×D3—62no—
709C2×D3—68no—
710C2×D3—68no—
711C2×D3—64no—
712C2×D3—62no—
713C2×D3—62no—
714C2×D3—62no—
715C2×D3—62no—
716C2×D3—62no—
717C2×D3—62no—
718C2×D3—122no—
719C2×D3—122no—
720C2×D3—128no—
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×#62514yescomplemented
745C32—21no—
746C32—21no—
747C32—21no—
748C32—41no—
749C32C2×#88411yescharacteristic, complemented
750C32C2×#93011yescharacteristic, complemented
751C32C2×#93811yescharacteristic, 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—548no—
767D4—548no—
768C2×C4—32no—
769C2×C4—34no—
770C2×C4—32no—
771C2×C4—62no—
772C2×C4—92no—
773C2×C4—188no—
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—124no—
794C2×C3—122no—
795C2×C3—122no—
796C2×C3—184no—
797C2×C3—362no—
798C2×C3#6390614yescomplemented
799C2×C3#6390814yescomplemented
800C2×C3#6395814yescomplemented
801C2×C3C2×#379511yescharacteristic
802C2×C3C2×#379811yescharacteristic
803C2×C3C2×D3×D1211yescharacteristic
804C2×C3C2×D3×D1211yescharacteristic
805C2×C3C2×#380411yescharacteristic
806C2×C3C22×#62511yescharacteristic
807C2×C3C2×D3×#6711yescharacteristic
808C2×C3C2×D3×#6711yescharacteristic
809C2×C3C2×#381111yescharacteristic
810D3—42no—
811D3—64no—
812D3—64no—
813D3—124no—
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×#62512yes—
830C22#8895512yes—
831C22#8896012yes—
832C22C2×D3311yescharacteristic
833C4—34no—
834C4—62no—
835C4—182no—
836C4—542no—
837C3—21no—
838C3—21no—
839C3—21no—
840C3—41no—
841C3C2×#6390611yescharacteristic, complemented
842C3C2×#6390811yescharacteristic, complemented
843C3C2×#6395811yescharacteristic, complemented
844C2—122no—
845C2—184no—
846C2—362no—
847C2#1172295714yesdirect product factor
848C2C2×D3×#62511yescharacteristic
849C2C2×#8895511yescharacteristic
850C2C2×#8896011yescharacteristic
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×#6290C2semidirect
3. C22×C3×#626C2semidirect
4. C22×C3×#624C2semidirect
5. C2×Dic3⋊(C3⋊Dic3)C2semidirect
6. C2×#88803C2semidirect
7. C2×C3×(C2×D3)⋊Dic3C2semidirect
8. #11722957C2direct (N × H)
20. C2×#6295C22semidirect
22. C2×#6290C22semidirect
24. C2×C3×#626C22semidirect
26. C2×C3×#624C22semidirect
27. Dic3⋊(C3⋊Dic3)C22semidirect
28. #88803C22semidirect
29. C3×(C2×D3)⋊Dic3C22semidirect
37. C22×#626D3semidirect
42. C22×#624D3semidirect
53. C2×(C2×D3)⋊Dic3D3semidirect
63. C22×C3×C3⋊D3D4semidirect
75. C2×C32×Dic3D4semidirect
131. C2×#626C2×D3semidirect
141. C2×#624C2×D3semidirect
152. (C2×D3)⋊Dic3C2×D3semidirect
164. C2×C3×C3⋊D3C2×D4semidirect
172. C32×Dic3C2×D4semidirect
216. C22×C3⋊D3D12semidirect
289. C2×C3×Dic3#67semidirect
290. C2×C3×Dic3#67semidirect
307. C2×C33#121semidirect
421. C2×C3⋊D3C2×D12semidirect
475. C3×Dic3C2×#67semidirect
476. C3×Dic3C2×#67semidirect
485. C33C2×#121semidirect
585. C2×Dic3#625semidirect
609. C2×C32#884semidirect
610. C2×C32#930semidirect
611. C2×C32#938semidirect
744. Dic3C2×#625semidirect
749. C32C2×#884semidirect
750. C32C2×#930semidirect
751. C32C2×#938semidirect
798. C2×C3#63906semidirect
799. C2×C3#63908semidirect
800. C2×C3#63958semidirect
841. C3C2×#63906semidirect
842. C3C2×#63908semidirect
843. C3C2×#63958semidirect
847. C2#11722957direct (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×#62902
C22×C3×#6262
C22×C3×#6242
C2×Dic3⋊(C3⋊Dic3)2
C2×#888032
C2×C3×(C2×D3)⋊Dic32
#117229572
C2×#639583
C2×#639083
C2×#639063