Finite Group Databasebeta

← C2×#11722958 #13172360

Subgroups — C2×#11722958 #13172360

Order 1728.

2442 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6291C211yesmaximal, characteristic, complemented
2C22×#6291C211yesmaximal, characteristic, complemented
3C22×C3×#625C211yesmaximal, characteristic, complemented
4C22×C3×D3×Dic3C211yesmaximal, characteristic, complemented
5C2×#88815C211yesmaximal, characteristic, complemented
6C2×#88804C211yesmaximal, characteristic, complemented
7C2×C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
8#11722958C218yesmaximal, direct product factor
9C2×#63978—31nomaximal
10C2×#63971—31nomaximal
11C2×#63906—31nomaximal
12C23×C3⋊(C3⋊D3)C2211yescharacteristic
13C23×C32×D3C2211yescharacteristic
14C23×C32×D3C2211yescharacteristic
15C22×C3×C3⋊Dic3C2211yescharacteristic
16C22×C3×C3⋊Dic3C2211yescharacteristic
17C22×C3×C3⋊Dic3C2211yescharacteristic
18C22×C32×Dic3C2211yescharacteristic
19C2×#6291—24no—
20C2×#6291—24no—
21C2×#6291C2214yescomplemented
22C2×#6291C2214yescomplemented
23C2×C3×#625—24no—
24C2×C3×#625C2214yescomplemented
25C2×C3×D3×Dic3—24no—
26C2×C3×D3×Dic3C2214yescomplemented
27#88815C2214yescomplemented
28#88804C2214yescomplemented
29C3×(C2×D3)⋊Dic3C2214yescomplemented
30C22×#638—31no—
31C22×#638—31no—
32C22×C3×#67—31no—
33C22×C3×#67—31no—
34C23×C3×Dic3—31no—
35C22×C3×C4×D3—31no—
36C22×#626—31no—
37C22×#626—31no—
38C22×#626—31no—
39C22×#626—31no—
40C22×#626—61no—
41C22×#626—61no—
42C22×#625D311yescharacteristic, complemented
43C22×D3×Dic3D311yescharacteristic, complemented
44C2×#3752—31no—
45C2×C3×#217—31no—
46C2×C3×(C2×D3)⋊C4—31no—
47#63978—38no—
48#63971—38no—
49C2×#3724—31no—
50C2×Dic3⋊Dic3—31no—
51C2×Dic3⋊Dic3—31no—
52C2×#3722—31no—
53C2×#3722—31no—
54C2×#3722—61no—
55C2×(C2×D3)⋊Dic3D311yescharacteristic, complemented
56#63906—38no—
57C23×C33C2311yescharacteristic
58C22×C3⋊(C3⋊D3)—22no—
59C22×C3⋊(C3⋊D3)—22no—
60C22×C3⋊(C3⋊D3)—22no—
61C22×C3⋊(C3⋊D3)C2312yes—
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—22no—
72C2×C3×C3⋊Dic3D414yescomplemented
73C2×C3×C3⋊Dic3C2312yes—
74C2×C3×C3⋊Dic3C2312yes—
75C2×C3×C3⋊Dic3C2312yes—
76C2×C32×Dic3—22no—
77C2×C32×Dic3C2312yes—
78#6291—28no—
79#6291—28no—
80C3×#625—28no—
81C3×D3×Dic3—28no—
82C2×#939—91no—
83C2×#930—91no—
84C2×#884—91no—
85C24×C32—31no—
86C24×C32—31no—
87C23×C3⋊D3—31no—
88C23×C3⋊D3—31no—
89C23×C3⋊D3—31no—
90C23×C3⋊D3—61no—
91C23×C3⋊D3—61no—
92C23×C3⋊D3—61no—
93C23×C3⋊D3—121no—
94C23×C3×D3—21no—
95C23×C3×D3—21no—
96C23×C3×D3C2×D311yescharacteristic
97C23×C3×D3C2×D311yescharacteristic
98C23×C3×D3C2×D311yescharacteristic
99C23×C3×D3C2×D311yescharacteristic
100C22×C32×C4—31no—
101C2×#638—34no—
102C2×#638—34no—
103C2×#638—64no—
104C2×#638—64no—
105C22×C3⋊Dic3C2×D311yescharacteristic
106C22×C3⋊Dic3C2×D311yescharacteristic
107C22×C3⋊Dic3C2×D311yescharacteristic
108C2×C3×#67—34no—
109C2×C3×#67—34no—
110C2×C3×#67—64no—
111C2×C3×#67—64no—
112C22×C3×Dic3—21no—
113C22×C3×Dic3—31no—
114C22×C3×Dic3—31no—
115C22×C3×Dic3—31no—
116C22×C3×Dic3—31no—
117C22×C3×Dic3—31no—
118C22×C3×Dic3—31no—
119C22×C3×Dic3—34no—
120C22×C3×Dic3—64no—
121C22×C3×Dic3—61no—
122C22×C3×Dic3—61no—
123C22×C3×Dic3—61no—
124C22×C3×Dic3C2×D311yescharacteristic
125C22×C3×Dic3C2×D311yescharacteristic
126C2×C3×C4×D3—34no—
127C2×C3×C4×D3—64no—
128C2×#626—34no—
129C2×#626—34no—
130C2×#626—34no—
131C2×#626—34no—
132C2×#626—64no—
133C2×#626—64no—
134C2×#626—64no—
135C2×#626—64no—
136C2×#626—68no—
137C2×#626—68no—
138C2×#626—64no—
139C2×#626—64no—
140C2×#625—24no—
141C2×#625C2×D314yescomplemented
142C2×D3×Dic3—24no—
143C2×D3×Dic3C2×D314yescomplemented
144#3752—34no—
145C3×#217—34no—
146C3×(C2×D3)⋊C4—34no—
147#3724—34no—
148Dic3⋊Dic3—34no—
149Dic3⋊Dic3—34no—
150#3722—34no—
151#3722—34no—
152#3722—64no—
153(C2×D3)⋊Dic3C2×D314yescomplemented
154C22×C33C2×D412yes—
155C22×C33C2×D412yes—
156C22×C33#4112yes—
157C22×C33C2411yescharacteristic
158C2×C3⋊(C3⋊D3)—22no—
159C2×C3⋊(C3⋊D3)—22no—
160C2×C3⋊(C3⋊D3)—22no—
161C2×C3⋊(C3⋊D3)—44no—
162C2×C32×D3—28no—
163C2×C32×D3—22no—
164C2×C32×D3—22no—
165C2×C32×D3—22no—
166C2×C32×D3—22no—
167C2×C32×D3—22no—
168C2×C32×D3—44no—
169C2×C32×D3C2×D414yescomplemented
170C3×C3⋊Dic3—22no—
171C3×C3⋊Dic3—22no—
172C3×C3⋊Dic3C2×D414yescomplemented
173C32×Dic3—22no—
174C22×C3×D4—91no—
175C23×C3×C4—91no—
176C22×#67—31no—
177C22×#67—31no—
178C22×#67—91no—
179C22×#67—91no—
180C22×#67—91no—
181C22×#67—91no—
182C22×#67—181no—
183C22×#67—181no—
184C23×Dic3—31no—
185C22×D12—91no—
186C22×D12—91no—
187C22×C4×D3—31no—
188C2×C3×C22⋊C4—91no—
189C2×#217—31no—
190#939—98no—
191#930—98no—
192C2×(C2×D3)⋊C4—31no—
193C2×(C2×D3)⋊C4—91no—
194C2×(C2×D3)⋊C4—91no—
195C2×(C2×D3)⋊C4—91no—
196C2×(C2×D3)⋊C4—181no—
197C2×C4⋊Dic3—91no—
198C2×Dic3⋊C4—91no—
199C2×Dic3⋊C4—91no—
200#884—98no—
201C23×C32—21no—
202C23×C32—21no—
203C23×C32—21no—
204C23×C32—34no—
205C23×C32—32no—
206C23×C32—32no—
207C23×C32—41no—
208C23×C32—62no—
209C23×C32—62no—
210C23×C32—62no—
211C23×C32—62no—
212C23×C32—62no—
213C23×C32C22×D311yescharacteristic
214C23×C32C22×D311yescharacteristic
215C23×C32C22×D311yescharacteristic
216C22×C3⋊D3—32no—
217C22×C3⋊D3—32no—
218C22×C3⋊D3—32no—
219C22×C3⋊D3—62no—
220C22×C3⋊D3—62no—
221C22×C3⋊D3—62no—
222C22×C3⋊D3—62no—
223C22×C3⋊D3—62no—
224C22×C3⋊D3—62no—
225C22×C3⋊D3—64no—
226C22×C3⋊D3—64no—
227C22×C3⋊D3—64no—
228C22×C3⋊D3—62no—
229C22×C3⋊D3—62no—
230C22×C3⋊D3—62no—
231C22×C3⋊D3—62no—
232C22×C3⋊D3—62no—
233C22×C3⋊D3—62no—
234C22×C3⋊D3—122no—
235C22×C3⋊D3—122no—
236C22×C3⋊D3—122no—
237C22×C3⋊D3—122no—
238C22×C3⋊D3—122no—
239C22×C3⋊D3—122no—
240C22×C3⋊D3—122no—
241C22×C3⋊D3—124no—
242C22×C3⋊D3—124no—
243C22×C3⋊D3—124no—
244C22×C3×D3—22no—
245C22×C3×D3—22no—
246C22×C3×D3—22no—
247C22×C3×D3—22no—
248C22×C3×D3—24no—
249C22×C3×D3—22no—
250C22×C3×D3—22no—
251C22×C3×D3—22no—
252C22×C3×D3—22no—
253C22×C3×D3—22no—
254C22×C3×D3—22no—
255C22×C3×D3—24no—
256C22×C3×D3—22no—
257C22×C3×D3—22no—
258C22×C3×D3—42no—
259C22×C3×D3—42no—
260C22×C3×D3—42no—
261C22×C3×D3—42no—
262C22×C3×D3D1214yescomplemented
263C22×C3×D3#6714yescomplemented
264C22×C3×D3C22×D312yes—
265C22×C3×D3C22×D312yes—
266C22×C3×D3C22×D312yes—
267C22×C3×D3C22×D312yes—
268C2×C32×C4—32no—
269C2×C32×C4—62no—
270#638—68no—
271#638—68no—
272C2×C3⋊Dic3—22no—
273C2×C3⋊Dic3—22no—
274C2×C3⋊Dic3#6714yescomplemented
275C2×C3⋊Dic3C22×D312yes—
276C2×C3⋊Dic3C22×D312yes—
277C2×C3⋊Dic3C22×D312yes—
278C3×#67—68no—
279C3×#67—68no—
280C2×C3×Dic3—22no—
281C2×C3×Dic3—22no—
282C2×C3×Dic3—22no—
283C2×C3×Dic3—34no—
284C2×C3×Dic3—34no—
285C2×C3×Dic3—32no—
286C2×C3×Dic3—32no—
287C2×C3×Dic3—32no—
288C2×C3×Dic3—32no—
289C2×C3×Dic3—32no—
290C2×C3×Dic3—32no—
291C2×C3×Dic3—42no—
292C2×C3×Dic3—64no—
293C2×C3×Dic3—62no—
294C2×C3×Dic3—62no—
295C2×C3×Dic3—62no—
296C2×C3×Dic3—68no—
297C2×C3×Dic3—64no—
298C2×C3×Dic3—62no—
299C2×C3×Dic3—62no—
300C2×C3×Dic3—62no—
301C2×C3×Dic3—62no—
302C2×C3×Dic3—122no—
303C2×C3×Dic3C22×D312yes—
304C2×C3×Dic3C22×D312yes—
305C3×C4×D3—68no—
306#626—68no—
307#626—68no—
308#626—616no—
309#626—616no—
310#626—68no—
311#626—68no—
312#625—28no—
313D3×Dic3—28no—
314C2×#121—271noSylow
315C2×C33#12114yescomplemented
316C2×C33C22×D411yescharacteristic
317C2×C33C22×D411yescharacteristic
318C2×C33C2×#4111yescharacteristic
319C3⋊(C3⋊D3)—42no—
320C32×D3—24no—
321C32×D3—42no—
322C24×C3—31no—
323C24×C3—31no—
324C24×C3—31no—
325C24×C3—31no—
326C24×C3—61no—
327C24×C3—61no—
328C23×D3—91no—
329C23×D3—91no—
330C23×D3—91no—
331C23×D3—181no—
332C23×D3—181no—
333C23×D3—181no—
334C23×D3—361no—
335C23×D3D3211yescharacteristic
336C23×D3D3211yescharacteristic
337C2×C3×D4—94no—
338C2×C3×D4—184no—
339C22×C3×C4—31no—
340C22×C3×C4—31no—
341C22×C3×C4—61no—
342C22×C3×C4—94no—
343C22×C3×C4—91no—
344C22×C3×C4—91no—
345C22×C3×C4—91no—
346C22×C3×C4—184no—
347C2×#67—34no—
348C2×#67—34no—
349C2×#67—64no—
350C2×#67—64no—
351C2×#67—94no—
352C2×#67—94no—
353C2×#67—94no—
354C2×#67—94no—
355C2×#67—184no—
356C2×#67—184no—
357C2×#67—184no—
358C2×#67—184no—
359C2×#67—184no—
360C2×#67—184no—
361C2×#67—188no—
362C2×#67—188no—
363C22×Dic3—31no—
364C22×Dic3—31no—
365C22×Dic3—31no—
366C22×Dic3—31no—
367C22×Dic3—31no—
368C22×Dic3—31no—
369C22×Dic3—34no—
370C22×Dic3—61no—
371C22×Dic3—61no—
372C22×Dic3—61no—
373C22×Dic3—64no—
374C22×Dic3D3211yescharacteristic
375C2×D12—94no—
376C2×D12—94no—
377C2×D12—184no—
378C2×D12—184no—
379C2×C4×D3—34no—
380C2×C4×D3—64no—
381C3×C22⋊C4—94no—
382#217—34no—
383(C2×D3)⋊C4—34no—
384(C2×D3)⋊C4—94no—
385(C2×D3)⋊C4—94no—
386(C2×D3)⋊C4—94no—
387(C2×D3)⋊C4—184no—
388C4⋊Dic3—94no—
389Dic3⋊C4—94no—
390Dic3⋊C4—94no—
391C22×C32—21no—
392C22×C32—21no—
393C22×C32—21no—
394C22×C32—22no—
395C22×C32—22no—
396C22×C32—22no—
397C22×C32—22no—
398C22×C32—22no—
399C22×C32—22no—
400C22×C32—22no—
401C22×C32—22no—
402C22×C32—22no—
403C22×C32—34no—
404C22×C32—42no—
405C22×C32—42no—
406C22×C32—42no—
407C22×C32—41no—
408C22×C32—62no—
409C22×C32—68no—
410C22×C32—62no—
411C22×C32—62no—
412C22×C32—62no—
413C22×C32—62no—
414C22×C32—124no—
415C22×C32C2×D1212yes—
416C22×C32#23512yes—
417C22×C32#23512yes—
418C22×C32D3×D412yes—
419C22×C32D3×D412yes—
420C22×C32D3×D412yes—
421C22×C32#23712yes—
422C22×C32C2×#6712yes—
423C22×C32C2×#6712yes—
424C22×C32C23×D311yescharacteristic
425C22×C32C23×D311yescharacteristic
426C22×C32C23×D311yescharacteristic
427C2×C3⋊D3—62no—
428C2×C3⋊D3—62no—
429C2×C3⋊D3—62no—
430C2×C3⋊D3—64no—
431C2×C3⋊D3—64no—
432C2×C3⋊D3—64no—
433C2×C3⋊D3—62no—
434C2×C3⋊D3—62no—
435C2×C3⋊D3—62no—
436C2×C3⋊D3—62no—
437C2×C3⋊D3—62no—
438C2×C3⋊D3—62no—
439C2×C3⋊D3—122no—
440C2×C3⋊D3—122no—
441C2×C3⋊D3—122no—
442C2×C3⋊D3—122no—
443C2×C3⋊D3—122no—
444C2×C3⋊D3—122no—
445C2×C3⋊D3—124no—
446C2×C3⋊D3—124no—
447C2×C3⋊D3—124no—
448C2×C3⋊D3—128no—
449C2×C3⋊D3—128no—
450C2×C3⋊D3—128no—
451C2×C3⋊D3—1216no—
452C2×C3⋊D3—124no—
453C2×C3⋊D3—124no—
454C2×C3⋊D3—124no—
455C2×C3×D3—28no—
456C2×C3×D3—28no—
457C2×C3×D3—22no—
458C2×C3×D3—22no—
459C2×C3×D3—22no—
460C2×C3×D3—22no—
461C2×C3×D3—24no—
462C2×C3×D3—22no—
463C2×C3×D3—22no—
464C2×C3×D3—22no—
465C2×C3×D3—22no—
466C2×C3×D3—22no—
467C2×C3×D3—22no—
468C2×C3×D3—24no—
469C2×C3×D3—42no—
470C2×C3×D3—42no—
471C2×C3×D3—48no—
472C2×C3×D3—42no—
473C2×C3×D3—42no—
474C2×C3×D3—48no—
475C2×C3×D3—44no—
476C2×C3×D3—44no—
477C2×C3×D3C2×D1214yescomplemented
478C2×C3×D3C2×#6714yescomplemented
479C32×C4—62no—
480C3⋊Dic3—22no—
481C3⋊Dic3—22no—
482C3⋊Dic3C2×#6714yescomplemented
483C3×Dic3—22no—
484C3×Dic3—22no—
485C3×Dic3—34no—
486C3×Dic3—34no—
487C3×Dic3—42no—
488C3×Dic3—64no—
489C3×Dic3—64no—
490C3×Dic3—62no—
491C3×Dic3—62no—
492C3×Dic3—62no—
493C3×Dic3—62no—
494C3×Dic3—122no—
495C22×D4—91no—
496C22×D4—271no—
497C22×D4—271no—
498C23×C4—91no—
499#121—278no—
500C2×C4⋊C4—271no—
501C2×C22⋊C4—91no—
502C2×C22⋊C4—271no—
503C33C2×#12111yescharacteristic, complemented, Sylow
504C23×C3—21no—
505C23×C3—21no—
506C23×C3—21no—
507C23×C3—32no—
508C23×C3—32no—
509C23×C3—34no—
510C23×C3—34no—
511C23×C3—32no—
512C23×C3—32no—
513C23×C3—41no—
514C23×C3—62no—
515C23×C3—64no—
516C23×C3—62no—
517C23×C3—64no—
518C23×C3—62no—
519C23×C3—62no—
520C23×C3—62no—
521C23×C3—62no—
522C23×C3—62no—
523C23×C3—62no—
524C23×C3—62no—
525C23×C3—62no—
526C23×C3—62no—
527C23×C3—62no—
528C23×C3—122no—
529C23×C3—122no—
530C23×C3—122no—
531C23×C3—122no—
532C23×C3C2×D3211yescharacteristic
533C23×C3C2×D3211yescharacteristic
534C23×C3C2×D3211yescharacteristic
535C22×D3—22no—
536C22×D3—22no—
537C22×D3—22no—
538C22×D3—22no—
539C22×D3—22no—
540C22×D3—92no—
541C22×D3—92no—
542C22×D3—92no—
543C22×D3—182no—
544C22×D3—182no—
545C22×D3—182no—
546C22×D3—184no—
547C22×D3—184no—
548C22×D3—184no—
549C22×D3—182no—
550C22×D3—182no—
551C22×D3—182no—
552C22×D3—182no—
553C22×D3—182no—
554C22×D3—182no—
555C22×D3—182no—
556C22×D3—182no—
557C22×D3—182no—
558C22×D3—362no—
559C22×D3—362no—
560C22×D3—362no—
561C22×D3—362no—
562C22×D3—362no—
563C22×D3—362no—
564C22×D3—362no—
565C22×D3—364no—
566C22×D3—364no—
567C22×D3—364no—
568C22×D3#62614yescomplemented
569C22×D3C2×D3212yes—
570C22×D3C2×D3212yes—
571C3×D4—188no—
572C2×C3×C4—32no—
573C2×C3×C4—32no—
574C2×C3×C4—62no—
575C2×C3×C4—62no—
576C2×C3×C4—62no—
577C2×C3×C4—92no—
578C2×C3×C4—94no—
579C2×C3×C4—92no—
580C2×C3×C4—92no—
581C2×C3×C4—122no—
582C2×C3×C4—188no—
583C2×C3×C4—182no—
584C2×C3×C4—182no—
585#67—68no—
586#67—68no—
587#67—188no—
588#67—188no—
589#67—188no—
590#67—188no—
591#67—1816no—
592#67—1816no—
593C2×Dic3—22no—
594C2×Dic3—32no—
595C2×Dic3—32no—
596C2×Dic3—34no—
597C2×Dic3—34no—
598C2×Dic3—32no—
599C2×Dic3—32no—
600C2×Dic3—32no—
601C2×Dic3—32no—
602C2×Dic3—64no—
603C2×Dic3—62no—
604C2×Dic3—62no—
605C2×Dic3—62no—
606C2×Dic3—68no—
607C2×Dic3—64no—
608C2×Dic3—62no—
609C2×Dic3—62no—
610C2×Dic3—62no—
611C2×Dic3—62no—
612C2×Dic3—122no—
613C2×Dic3C2×D3212yes—
614D12—188no—
615D12—188no—
616C4×D3—68no—
617C2×C32—21no—
618C2×C32—21no—
619C2×C32—21no—
620C2×C32—21no—
621C2×C32—21no—
622C2×C32—21no—
623C2×C32—21no—
624C2×C32—21no—
625C2×C32—21no—
626C2×C32—24no—
627C2×C32—24no—
628C2×C32—24no—
629C2×C32—44no—
630C2×C32—41no—
631C2×C32—41no—
632C2×C32—41no—
633C2×C32—64no—
634C2×C32—122no—
635C2×C32#88414yescomplemented
636C2×C32#93014yescomplemented
637C2×C32#93914yescomplemented
638C2×C32C22×D1211yescharacteristic
639C2×C32C2×#23511yescharacteristic
640C2×C32C2×#23511yescharacteristic
641C2×C32C2×D3×D411yescharacteristic
642C2×C32C2×D3×D411yescharacteristic
643C2×C32C2×D3×D411yescharacteristic
644C2×C32C2×#23711yescharacteristic
645C2×C32C22×#6711yescharacteristic
646C2×C32C22×#6711yescharacteristic
647C3⋊D3—124no—
648C3⋊D3—124no—
649C3⋊D3—124no—
650C3⋊D3—128no—
651C3⋊D3—122no—
652C3⋊D3—122no—
653C3⋊D3—122no—
654C3×D3—24no—
655C3×D3—24no—
656C3×D3—44no—
657C3×D3—44no—
658C3×D3—42no—
659C3×D3—42no—
660C24—31no—
661C24—31no—
662C24—271no—
663C2×D4—94no—
664C2×D4—184no—
665C2×D4—274no—
666C2×D4—274no—
667C2×D4—544no—
668C2×D4—544no—
669C22×C4—31no—
670C22×C4—94no—
671C22×C4—91no—
672C22×C4—91no—
673C22×C4—91no—
674C22×C4—184no—
675C4⋊C4—274no—
676C22⋊C4—94no—
677C22⋊C4—274no—
678C22×C3—21no—
679C22×C3—21no—
680C22×C3—21no—
681C22×C3—22no—
682C22×C3—22no—
683C22×C3—22no—
684C22×C3—22no—
685C22×C3—22no—
686C22×C3—22no—
687C22×C3—22no—
688C22×C3—22no—
689C22×C3—22no—
690C22×C3—34no—
691C22×C3—34no—
692C22×C3—41no—
693C22×C3—42no—
694C22×C3—42no—
695C22×C3—42no—
696C22×C3—64no—
697C22×C3—64no—
698C22×C3—62no—
699C22×C3—62no—
700C22×C3—62no—
701C22×C3—62no—
702C22×C3—68no—
703C22×C3—68no—
704C22×C3—62no—
705C22×C3—62no—
706C22×C3—62no—
707C22×C3—62no—
708C22×C3—62no—
709C22×C3—62no—
710C22×C3—122no—
711C22×C3—122no—
712C22×C3—128no—
713C22×C3—122no—
714C22×C3—122no—
715C22×C3—128no—
716C22×C3—124no—
717C22×C3—124no—
718C22×C3#379812yes—
719C22×C3D3×D1212yes—
720C22×C3#380412yes—
721C22×C3#380412yes—
722C22×C3C2×#62612yes—
723C22×C3D3×#6712yes—
724C22×C3D3×#6712yes—
725C22×C3D3×#6712yes—
726C22×C3#381112yes—
727C22×C3C22×D3211yescharacteristic
728C22×C3C22×D3211yescharacteristic
729C22×C3C22×D3211yescharacteristic
730C2×D3—22no—
731C2×D3—22no—
732C2×D3—28no—
733C2×D3—22no—
734C2×D3—22no—
735C2×D3—22no—
736C2×D3—44no—
737C2×D3—184no—
738C2×D3—184no—
739C2×D3—184no—
740C2×D3—182no—
741C2×D3—182no—
742C2×D3—182no—
743C2×D3—182no—
744C2×D3—182no—
745C2×D3—182no—
746C2×D3—182no—
747C2×D3—182no—
748C2×D3—182no—
749C2×D3—362no—
750C2×D3—362no—
751C2×D3—362no—
752C2×D3—362no—
753C2×D3—362no—
754C2×D3—362no—
755C2×D3—364no—
756C2×D3—364no—
757C2×D3—364no—
758C2×D3—368no—
759C2×D3—368no—
760C2×D3—368no—
761C2×D3—3616no—
762C2×D3—364no—
763C2×D3—364no—
764C2×D3—364no—
765C2×D3C2×#62614yescomplemented
766C3×C4—62no—
767C3×C4—62no—
768C3×C4—94no—
769C3×C4—122no—
770C3×C4—182no—
771C3×C4—182no—
772Dic3—22no—
773Dic3—34no—
774Dic3—34no—
775Dic3—64no—
776Dic3—64no—
777Dic3—62no—
778Dic3—62no—
779Dic3—62no—
780Dic3—62no—
781Dic3—122no—
782C32—21no—
783C32—21no—
784C32—21no—
785C32—41no—
786C32C2×#88411yescharacteristic, complemented
787C32C2×#93011yescharacteristic, complemented
788C32C2×#93911yescharacteristic, complemented
789C23—32no—
790C23—34no—
791C23—32no—
792C23—62no—
793C23—62no—
794C23—62no—
795C23—62no—
796C23—62no—
797C23—272no—
798C23—542no—
799C23—542no—
800C23—542no—
801C23D3311yescharacteristic
802D4—188no—
803D4—548no—
804D4—548no—
805C2×C4—32no—
806C2×C4—62no—
807C2×C4—92no—
808C2×C4—94no—
809C2×C4—92no—
810C2×C4—92no—
811C2×C4—188no—
812C2×C4—182no—
813C2×C4—182no—
814C2×C3—21no—
815C2×C3—21no—
816C2×C3—21no—
817C2×C3—21no—
818C2×C3—21no—
819C2×C3—21no—
820C2×C3—21no—
821C2×C3—21no—
822C2×C3—21no—
823C2×C3—24no—
824C2×C3—24no—
825C2×C3—24no—
826C2×C3—41no—
827C2×C3—41no—
828C2×C3—41no—
829C2×C3—44no—
830C2×C3—64no—
831C2×C3—64no—
832C2×C3—124no—
833C2×C3—124no—
834C2×C3—122no—
835C2×C3—122no—
836C2×C3#6390614yescomplemented
837C2×C3#6397114yescomplemented
838C2×C3#6397814yescomplemented
839C2×C3C2×#379811yescharacteristic
840C2×C3C2×D3×D1211yescharacteristic
841C2×C3C2×#380411yescharacteristic
842C2×C3C2×#380411yescharacteristic
843C2×C3C22×#62611yescharacteristic
844C2×C3C2×D3×#6711yescharacteristic
845C2×C3C2×D3×#6711yescharacteristic
846C2×C3C2×D3×#6711yescharacteristic
847C2×C3C2×#381111yescharacteristic
848D3—24no—
849D3—42no—
850D3—364no—
851D3—364no—
852D3—364no—
853D3—368no—
854D3—362no—
855D3—362no—
856D3—362no—
857C22—34no—
858C22—62no—
859C22—62no—
860C22—68no—
861C22—62no—
862C22—62no—
863C22—62no—
864C22—124no—
865C22—542no—
866C22—542no—
867C22—542no—
868C22—1084no—
869C22D3×#62612yes—
870C22#8895212yes—
871C22#8895912yes—
872C22C2×D3311yescharacteristic
873C4—62no—
874C4—94no—
875C4—182no—
876C4—182no—
877C3—21no—
878C3—21no—
879C3—21no—
880C3—41no—
881C3C2×#6390611yescharacteristic, complemented
882C3C2×#6397111yescharacteristic, complemented
883C3C2×#6397811yescharacteristic, complemented
884C2—64no—
885C2—122no—
886C2—1082no—
887C2#1172295814yesdirect product factor
888C2C2×D3×#62611yescharacteristic
889C2C2×#8895211yescharacteristic
890C2C2×#8895911yescharacteristic
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×#6291C2semidirect
2. C22×#6291C2semidirect
3. C22×C3×#625C2semidirect
4. C22×C3×D3×Dic3C2semidirect
5. C2×#88815C2semidirect
6. C2×#88804C2semidirect
7. C2×C3×(C2×D3)⋊Dic3C2semidirect
8. #11722958C2direct (N × H)
21. C2×#6291C22semidirect
22. C2×#6291C22semidirect
24. C2×C3×#625C22semidirect
26. C2×C3×D3×Dic3C22semidirect
27. #88815C22semidirect
28. #88804C22semidirect
29. C3×(C2×D3)⋊Dic3C22semidirect
42. C22×#625D3semidirect
43. C22×D3×Dic3D3semidirect
55. C2×(C2×D3)⋊Dic3D3semidirect
67. C22×C32×D3D4semidirect
72. C2×C3×C3⋊Dic3D4semidirect
141. C2×#625C2×D3semidirect
143. C2×D3×Dic3C2×D3semidirect
153. (C2×D3)⋊Dic3C2×D3semidirect
169. C2×C32×D3C2×D4semidirect
172. C3×C3⋊Dic3C2×D4semidirect
262. C22×C3×D3D12semidirect
263. C22×C3×D3#67semidirect
274. C2×C3⋊Dic3#67semidirect
315. C2×C33#121semidirect
477. C2×C3×D3C2×D12semidirect
478. C2×C3×D3C2×#67semidirect
482. C3⋊Dic3C2×#67semidirect
503. C33C2×#121semidirect
568. C22×D3#626semidirect
635. C2×C32#884semidirect
636. C2×C32#930semidirect
637. C2×C32#939semidirect
765. C2×D3C2×#626semidirect
786. C32C2×#884semidirect
787. C32C2×#930semidirect
788. C32C2×#939semidirect
836. C2×C3#63906semidirect
837. C2×C3#63971semidirect
838. C2×C3#63978semidirect
881. C3C2×#63906semidirect
882. C3C2×#63971semidirect
883. C3C2×#63978semidirect
887. C2#11722958direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#62912
C22×C3×#6252
C22×C3×D3×Dic32
C2×#888152
C2×#888042
C2×C3×(C2×D3)⋊Dic32
#117229582
C2×#639783
C2×#639713
C2×#639063