Finite Group Databasebeta

← #13177337

Subgroups — #13177337

Order 1728.

3500 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C3⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
2C2×#89039C212yesmaximal, complemented
3C2×#89026C211yesmaximal, characteristic, complemented
4C3×#64139C211yesmaximal, characteristic, complemented
5C32×#930C211yesmaximal, characteristic, complemented
6#11723637C212yesmaximal, complemented
7#11723539C212yesmaximal, complemented
8#11723532C211yesmaximal, characteristic, complemented
9#11723531C211yesmaximal, characteristic, complemented
10#11723527C212yesmaximal, complemented
11#11723503C211yesmaximal, characteristic, complemented
12C3⋊D3×#121—31nomaximal
13#10595081—34nomaximal
14C23×C3⋊(C3⋊D3)C2211yescharacteristic
15C22×D3×C3⋊D3C2212yes—
16C22×C33×C4C2211yescharacteristic, complemented
17C22×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
18C2×C4×C3⋊(C3⋊D3)—24no—
19C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
20C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
21C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
22C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
23C2×C3×#638C2212yescomplemented
24C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
25C2×C32×#67C2212yescomplemented
26C2×C32×D12C2211yescharacteristic, complemented
27#89039—28no—
28C2×#6292C2212yescomplemented
29C2×#6291C2212yescomplemented
30C2×#6290C2212yescomplemented
31C2×#6289C2212yes—
32#89026—24no—
33C3×#3752C2212yescomplemented
34C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
35C32×(C2×D3)⋊C4C2212yescomplemented
36C32×C4⋊Dic3C2211yescharacteristic, complemented
37#88806C2212yescomplemented
38#88803C2212yescomplemented
39(C2×D3)⋊(C3⋊Dic3)C2212yescomplemented
40C2×D4×C3⋊D3—32no—
41C2×D4×C3⋊D3—31no—
42C22×C4×C3⋊D3—31no—
43C22×C4×C3⋊D3—34no—
44C22×C4×C3⋊D3—64no—
45C2×#3811—38no—
46C2×#3802—34no—
47C32×#121—31no—
48#64148—32no—
49#64147—31no—
50#64139D311yescharacteristic, complemented
51#64104—31no—
52C4⋊C4×C3⋊D3—31no—
53#64093—32no—
54C22⋊C4×C3⋊D3—32no—
55C3×#930—34no—
56C3×#930D314yescomplemented
57#63980—38no—
58#63921—38no—
59#63916—34no—
60#63916—34no—
61#63912—38no—
62#63900—34no—
63C23×C33C2311yescharacteristic
64C22×C3⋊(C3⋊D3)—22no—
65C22×C3⋊(C3⋊D3)—22no—
66C22×C3⋊(C3⋊D3)D414yescomplemented
67C22×C3⋊(C3⋊D3)C2311yescharacteristic
68C22×C3⋊(C3⋊D3)C2311yescharacteristic
69C22×C3×C3⋊D3C2312yes—
70C22×C32×D3C2312yes—
71C2×D3×C3⋊D3—24no—
72C2×D3×C3⋊D3—24no—
73C2×D3×C3⋊D3—24no—
74C2×C33×C4—22no—
75C2×C33×C4C2311yescharacteristic
76C2×C33×C4C2311yescharacteristic
77C2×C3⋊(C3⋊Dic3)—22no—
78C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
79C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
80C4×C3⋊(C3⋊D3)—22no—
81C4×C3⋊(C3⋊D3)—22no—
82C4×C3⋊(C3⋊D3)—22no—
83C4×C3⋊(C3⋊D3)D414yescomplemented
84C3×#638—24no—
85C2×C3×C3⋊Dic3C2312yes—
86C3×C4⋊(C3⋊D3)—22no—
87C32×#67—24no—
88C2×C32×Dic3C2312yes—
89C32×D12—22no—
90#6292—24no—
91#6291—24no—
92#6290—24no—
93#6289—24no—
94D3×#121—94no—
95D3×#121—91no—
96C23×C3⋊D3—31no—
97C23×C3⋊D3—34no—
98C23×C3⋊D3—32no—
99C23×C3⋊D3—64no—
100C22×D32—38no—
101C2×C32×D4—32no—
102C2×C32×D4—31no—
103C22×C32×C4—24no—
104C22×C32×C4C2×D314yescomplemented
105C22×C32×C4C2×D311yescharacteristic, complemented
106C2×#638—32no—
107C2×#638—32no—
108C2×#638C2×D312yescomplemented
109C22×C3⋊Dic3—31no—
110C22×C3⋊Dic3—34no—
111C22×C3⋊Dic3—64no—
112D4×C3⋊D3—64no—
113D4×C3⋊D3—68no—
114C2×C4⋊(C3⋊D3)—32no—
115C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
116C2×C4×C3⋊D3—31no—
117C2×C4×C3⋊D3—34no—
118C2×C4×C3⋊D3—31no—
119C2×C4×C3⋊D3—31no—
120C2×C4×C3⋊D3—31no—
121C2×C4×C3⋊D3—34no—
122C2×C4×C3⋊D3—34no—
123C2×C4×C3⋊D3—34no—
124C2×C4×C3⋊D3—32no—
125C2×C4×C3⋊D3—64no—
126C2×C4×C3⋊D3—616no—
127C2×C4×C3⋊D3—64no—
128C2×C4×C3⋊D3—64no—
129C2×C4×C3⋊D3—64no—
130C2×C4×C3⋊D3—64no—
131C2×C4×C3⋊D3—632no—
132C2×C3×#67—38no—
133C2×C3×#67C2×D318yescomplemented
134C2×C3×D12—34no—
135C2×C3×D12C2×D314yescomplemented
136#3811—632no—
137C2×#626—38no—
138C2×#626—38no—
139C2×#625—38no—
140C2×#624—38no—
141#3802—616no—
142C32×C4⋊C4—31no—
143C32×C22⋊C4—32no—
144#3757—32no—
145#3752—32no—
146#3752C2×D312yescomplemented
147C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
148#3750—32no—
149C3×(C2×D3)⋊C4—38no—
150C3×(C2×D3)⋊C4C2×D318yescomplemented
151C3×C4⋊Dic3—34no—
152C3×C4⋊Dic3C2×D314yescomplemented
153#3724—38no—
154(C2×D3)⋊Dic3—38no—
155(C2×D3)⋊Dic3—38no—
156C22×C33—21no—
157C22×C33—21no—
158C22×C33C2×D412yescomplemented
159C22×C33C2411yescharacteristic
160C2×C3⋊(C3⋊D3)—21no—
161C2×C3⋊(C3⋊D3)—21no—
162C2×C3⋊(C3⋊D3)—28no—
163C2×C3⋊(C3⋊D3)C2×D412yes—
164C2×C3⋊(C3⋊D3)C2×D412yes—
165C2×C3⋊(C3⋊D3)C2×D412yescomplemented
166C2×C3⋊(C3⋊D3)#4112yes—
167C2×C3×C3⋊D3—22no—
168C2×C3×C3⋊D3—22no—
169C2×C3×C3⋊D3—22no—
170C2×C32×D3—22no—
171C2×C32×D3—22no—
172C2×C32×D3—22no—
173D3×C3⋊D3—48no—
174C33×C4—21no—
175C33×C4C2×D412yescomplemented
176C3⋊(C3⋊Dic3)—21no—
177C3⋊(C3⋊Dic3)C2×D412yescomplemented
178C3×C3⋊Dic3—22no—
179C32×Dic3—22no—
180C2×D3×D4—94no—
181C2×D3×D4—98no—
182C2×D3×D4—92no—
183C2×D3×D4—91no—
184C22×C4×D3—94no—
185C22×C4×D3—91no—
186C22×C4×D3—184no—
187C3×#121—34no—
188C3×#121—91no—
189#939—98no—
190#939—92no—
191#938—94no—
192#938—91no—
193#930—34no—
194#930C3⋊D311yescharacteristic, complemented
195#895—94no—
196#895—91no—
197D3×C4⋊C4—94no—
198D3×C4⋊C4—91no—
199#884—98no—
200#884—92no—
201D3×C22⋊C4—98no—
202D3×C22⋊C4—92no—
203C23×C32—24no—
204C23×C32—32no—
205C23×C32C22×D314yes—
206C23×C32C22×D311yescharacteristic
207C22×C3⋊D3—31no—
208C22×C3⋊D3—34no—
209C22×C3⋊D3—31no—
210C22×C3⋊D3—34no—
211C22×C3⋊D3—316no—
212C22×C3⋊D3—34no—
213C22×C3⋊D3—616no—
214C22×C3⋊D3—64no—
215C22×C3⋊D3—64no—
216C22×C3⋊D3—64no—
217C22×C3⋊D3—64no—
218C22×C3⋊D3—64no—
219C22×C3⋊D3—62no—
220C22×C3⋊D3—68no—
221C22×C3⋊D3—62no—
222C22×C3⋊D3—68no—
223C22×C3⋊D3—616no—
224C22×C3⋊D3—616no—
225C22×C3⋊D3C22×D312yes—
226C22×C3×D3—38no—
227C22×C3×D3C22×D318yes—
228C2×D32—616no—
229C2×D32—616no—
230C2×D32—616no—
231C32×D4—64no—
232C32×D4—62no—
233C2×C32×C4—216no—
234C2×C32×C4—28no—
235C2×C32×C4—22no—
236C2×C32×C4—24no—
237C2×C32×C4—24no—
238C2×C32×C4—32no—
239C2×C32×C4C22×D314yes—
240C2×C32×C4C22×D314yes—
241C2×C32×C4C22×D311yescharacteristic
242C2×C32×C4C22×D311yescharacteristic
243#638—24no—
244#638—64no—
245#638—64no—
246C2×C3⋊Dic3—31no—
247C2×C3⋊Dic3—31no—
248C2×C3⋊Dic3—34no—
249C2×C3⋊Dic3—34no—
250C2×C3⋊Dic3—64no—
251C2×C3⋊Dic3—64no—
252C2×C3⋊Dic3—62no—
253C2×C3⋊Dic3—68no—
254C2×C3⋊Dic3—616no—
255C2×C3⋊Dic3C22×D312yes—
256C4⋊(C3⋊D3)—22no—
257C4⋊(C3⋊D3)—64no—
258C4×C3⋊D3—34no—
259C4×C3⋊D3—316no—
260C4×C3⋊D3—616no—
261C4×C3⋊D3—64no—
262C4×C3⋊D3—62no—
263C4×C3⋊D3—68no—
264C4×C3⋊D3—62no—
265C4×C3⋊D3—68no—
266C4×C3⋊D3—616no—
267C4×C3⋊D3—616no—
268C4×C3⋊D3—616no—
269C4×C3⋊D3—68no—
270C4×C3⋊D3—62no—
271C3×#67—216no—
272C3×#67—616no—
273C2×C3×Dic3—38no—
274C2×C3×Dic3C22×D318yes—
275C3×D12—28no—
276C3×D12—68no—
277#626—616no—
278#626—616no—
279#625—616no—
280#624—616no—
281C2×#121—271noSylow
282C2×C33—22no—
283C2×C33C22×D411yescharacteristic
284C2×C33C22×D411yescharacteristic
285C2×C33C2×#4111yescharacteristic
286C3⋊(C3⋊D3)—22no—
287C3⋊(C3⋊D3)#12114yescomplemented
288C3×C3⋊D3—42no—
289C32×D3—42no—
290C23×D3—98no—
291C23×D3—94no—
292C23×D3—91no—
293C23×D3—92no—
294C23×D3—184no—
295C2×C3×D4—38no—
296C2×C3×D4—34no—
297C2×C3×D4—92no—
298C2×C3×D4—91no—
299C22×C3×C4—24no—
300C22×C3×C4D3214yescomplemented
301C22×C3×C4C2×C3⋊D311yescharacteristic, complemented
302C2×#67—38no—
303C2×#67—98no—
304C2×#67—98no—
305C2×#67—92no—
306C2×#67—92no—
307C2×#67C2×C3⋊D312yescomplemented
308C22×Dic3—94no—
309C22×Dic3—91no—
310C22×Dic3—184no—
311D3×D4—184no—
312D3×D4—1816no—
313D3×D4—188no—
314D3×D4—1832no—
315C2×D12—34no—
316C2×D12—98no—
317C2×D12—92no—
318C2×D12C2×C3⋊D311yescharacteristic, complemented
319C2×C4×D3—94no—
320C2×C4×D3—91no—
321C2×C4×D3—98no—
322C2×C4×D3—94no—
323C2×C4×D3—94no—
324C2×C4×D3—94no—
325C2×C4×D3—91no—
326C2×C4×D3—91no—
327C2×C4×D3—91no—
328C2×C4×D3—92no—
329C2×C4×D3—184no—
330C2×C4×D3—184no—
331C2×C4×D3—184no—
332C2×C4×D3—184no—
333C2×C4×D3—1816no—
334C2×C4×D3—184no—
335C2×C4×D3—1832no—
336C3×C4⋊C4—34no—
337C3×C4⋊C4—91no—
338C3×C22⋊C4—38no—
339C3×C22⋊C4—92no—
340#217—98no—
341#217—92no—
342(C2×D3)⋊C4—38no—
343(C2×D3)⋊C4—98no—
344(C2×D3)⋊C4—92no—
345(C2×D3)⋊C4C2×C3⋊D312yescomplemented
346C4⋊Dic3—34no—
347C4⋊Dic3C2×C3⋊D311yescharacteristic, complemented
348Dic3⋊C4—98no—
349Dic3⋊C4—92no—
350C22×C32—28no—
351C22×C32—28no—
352C22×C32—24no—
353C22×C32—21no—
354C22×C32—24no—
355C22×C32—21no—
356C22×C32—24no—
357C22×C32—28no—
358C22×C32—62no—
359C22×C32—62no—
360C22×C32—62no—
361C22×C32D3×D418yescomplemented
362C22×C32D3×D412yescomplemented
363C22×C32C23×D314yes—
364C22×C32C23×D311yescharacteristic
365C2×C3⋊D3—22no—
366C2×C3⋊D3—22no—
367C2×C3⋊D3—22no—
368C2×C3⋊D3—32no—
369C2×C3⋊D3—32no—
370C2×C3⋊D3—32no—
371C2×C3⋊D3—32no—
372C2×C3⋊D3—38no—
373C2×C3⋊D3—38no—
374C2×C3⋊D3—38no—
375C2×C3⋊D3—38no—
376C2×C3⋊D3—68no—
377C2×C3⋊D3—68no—
378C2×C3⋊D3—68no—
379C2×C3⋊D3—68no—
380C2×C3⋊D3—68no—
381C2×C3⋊D3—632no—
382C2×C3⋊D3—68no—
383C2×C3⋊D3—664no—
384C2×C3⋊D3—68no—
385C2×C3⋊D3—64no—
386C2×C3⋊D3—61no—
387C2×C3⋊D3—64no—
388C2×C3⋊D3—61no—
389C2×C3⋊D3—128no—
390C2×C3×D3—28no—
391C2×C3×D3—28no—
392C2×C3×D3—28no—
393C2×C3×D3—68no—
394C2×C3×D3—68no—
395C2×C3×D3—68no—
396D32—1232no—
397C32×C4—28no—
398C32×C4—24no—
399C32×C4—21no—
400C32×C4—28no—
401C32×C4—62no—
402C32×C4D3×D418yescomplemented
403C32×C4D3×D412yescomplemented
404C3⋊Dic3—22no—
405C3⋊Dic3—32no—
406C3⋊Dic3—38no—
407C3⋊Dic3—68no—
408C3⋊Dic3—68no—
409C3⋊Dic3—64no—
410C3⋊Dic3—61no—
411C3×Dic3—28no—
412C3×Dic3—68no—
413C22×D4—272no—
414C22×D4—271no—
415C23×C4—271no—
416#121—31no—
417#121—91no—
418#121—272no—
419#121—271no—
420#121—271no—
421#121—272no—
422C2×C4⋊C4—271no—
423C2×C22⋊C4—272no—
424C33C2×#12111yescharacteristic, complemented, Sylow
425C23×C3—24no—
426C23×C3—38no—
427C23×C3—92no—
428C23×C3C2×D3214yes—
429C23×C3C22×C3⋊D311yescharacteristic
430C22×D3—38no—
431C22×D3—94no—
432C22×D3—91no—
433C22×D3—94no—
434C22×D3—91no—
435C22×D3—916no—
436C22×D3—94no—
437C22×D3—184no—
438C22×D3—184no—
439C22×D3—1816no—
440C22×D3—184no—
441C22×D3—184no—
442C22×D3—184no—
443C22×D3—1816no—
444C22×D3—1816no—
445C22×D3—1816no—
446C22×D3—188no—
447C22×D3—182no—
448C22×D3—188no—
449C22×D3—182no—
450C22×D3—1816no—
451C22×D3—1816no—
452C22×D3C22×C3⋊D312yes—
453C3×D4—616no—
454C3×D4—68no—
455C3×D4—184no—
456C3×D4—182no—
457C2×C3×C4—216no—
458C2×C3×C4—28no—
459C2×C3×C4—22no—
460C2×C3×C4—24no—
461C2×C3×C4—24no—
462C2×C3×C4—38no—
463C2×C3×C4—92no—
464C2×C3×C4C2×D3214yes—
465C2×C3×C4C2×D3214yes—
466C2×C3×C4C22×C3⋊D311yescharacteristic
467C2×C3×C4C22×C3⋊D311yescharacteristic
468#67—24no—
469#67—616no—
470#67—184no—
471#67—1816no—
472#67—184no—
473#67—1816no—
474C2×Dic3—38no—
475C2×Dic3—94no—
476C2×Dic3—91no—
477C2×Dic3—94no—
478C2×Dic3—91no—
479C2×Dic3—184no—
480C2×Dic3—184no—
481C2×Dic3—188no—
482C2×Dic3—182no—
483C2×Dic3—1816no—
484C2×Dic3C22×C3⋊D312yes—
485D12—22no—
486D12—68no—
487D12—1816no—
488D12—184no—
489C4×D3—916no—
490C4×D3—94no—
491C4×D3—1816no—
492C4×D3—184no—
493C4×D3—1816no—
494C4×D3—188no—
495C4×D3—182no—
496C4×D3—188no—
497C4×D3—182no—
498C4×D3—1816no—
499C4×D3—1816no—
500C4×D3—1816no—
501C4×D3—188no—
502C4×D3—182no—
503C2×C32—216no—
504C2×C32—28no—
505C2×C32—22no—
506C2×C32—24no—
507C2×C32—24no—
508C2×C32—24no—
509C2×C32—122no—
510C2×C32C2×D3×D414yes—
511C2×C32C2×D3×D414yes—
512C2×C32C2×D3×D411yescharacteristic
513C2×C32C2×D3×D411yescharacteristic
514C2×C32D3×#4114yes—
515C2×C32D3×#4111yescharacteristic
516C3⋊D3—34no—
517C3⋊D3—316no—
518C3⋊D3—42no—
519C3⋊D3—616no—
520C3⋊D3—616no—
521C3⋊D3—68no—
522C3⋊D3—62no—
523C3×D3—48no—
524C3×D3—128no—
525C24—272no—
526C24—271no—
527C2×D4—32no—
528C2×D4—31no—
529C2×D4—92no—
530C2×D4—91no—
531C2×D4—272no—
532C2×D4—272no—
533C2×D4—272no—
534C2×D4—544no—
535C2×D4—548no—
536C22×C4—272no—
537C22×C4—271no—
538C22×C4—271no—
539C22×C4—271no—
540C22×C4—271no—
541C22×C4—271no—
542C22×C4—544no—
543C22×C4D3×C3⋊D311yescharacteristic, complemented
544C4⋊C4—31no—
545C4⋊C4—91no—
546C4⋊C4—272no—
547C22⋊C4—32no—
548C22⋊C4—92no—
549C22⋊C4—272no—
550C22⋊C4—272no—
551C22×C3—28no—
552C22×C3—28no—
553C22×C3—24no—
554C22×C3—24no—
555C22×C3—21no—
556C22×C3—21no—
557C22×C3—24no—
558C22×C3—28no—
559C22×C3—68no—
560C22×C3—68no—
561C22×C3—68no—
562C22×C3—182no—
563C22×C3—182no—
564C22×C3—182no—
565C22×C3#380218yescomplemented
566C22×C3D4×C3⋊D312yescomplemented
567C22×C3C22×D3214yes—
568C22×C3C23×C3⋊D311yescharacteristic
569C2×D3—22no—
570C2×D3—22no—
571C2×D3—22no—
572C2×D3—68no—
573C2×D3—68no—
574C2×D3—68no—
575C2×D3—98no—
576C2×D3—98no—
577C2×D3—98no—
578C2×D3—92no—
579C2×D3—92no—
580C2×D3—92no—
581C2×D3—98no—
582C2×D3—92no—
583C2×D3—188no—
584C2×D3—188no—
585C2×D3—188no—
586C2×D3—188no—
587C2×D3—1832no—
588C2×D3—188no—
589C2×D3—188no—
590C2×D3—1864no—
591C2×D3—188no—
592C2×D3—184no—
593C2×D3—184no—
594C2×D3—181no—
595C2×D3—181no—
596C2×D3—368no—
597C2×D3—3632no—
598C3×C4—28no—
599C3×C4—24no—
600C3×C4—21no—
601C3×C4—28no—
602C3×C4—68no—
603C3×C4—182no—
604C3×C4#381118yescomplemented
605C3×C4D4×C3⋊D312yescomplemented
606Dic3—22no—
607Dic3—68no—
608Dic3—98no—
609Dic3—92no—
610Dic3—188no—
611Dic3—188no—
612Dic3—184no—
613Dic3—181no—
614C32—24no—
615C32D3×#12114yescomplemented
616C32D3×#12111yescharacteristic, complemented
617C23—32no—
618C23—92no—
619C23—271no—
620C23—271no—
621C23—274no—
622C23—542no—
623C23—542no—
624C23—544no—
625C23—544no—
626C23—544no—
627C23C2×D3×C3⋊D311yescharacteristic
628D4—64no—
629D4—62no—
630D4—184no—
631D4—182no—
632D4—544no—
633D4—544no—
634D4—544no—
635C2×C4—22no—
636C2×C4—32no—
637C2×C4—92no—
638C2×C4—271no—
639C2×C4—274no—
640C2×C4—271no—
641C2×C4—542no—
642C2×C4—542no—
643C2×C4—544no—
644C2×C4—542no—
645C2×C4—542no—
646C2×C4C2×D3×C3⋊D311yescharacteristic
647C2×C4C2×D3×C3⋊D311yescharacteristic
648C2×C3—216no—
649C2×C3—28no—
650C2×C3—22no—
651C2×C3—24no—
652C2×C3—24no—
653C2×C3—24no—
654C2×C3—128no—
655C2×C3—362no—
656C2×C3C2×#380214yes—
657C2×C3#6430614yes—
658C2×C3C2×#381114yes—
659C2×C3C2×D4×C3⋊D311yescharacteristic
660C2×C3C2×D4×C3⋊D311yescharacteristic
661C2×C3#41×C3⋊D311yescharacteristic
662D3—42no—
663D3—916no—
664D3—94no—
665D3—128no—
666D3—1816no—
667D3—1816no—
668D3—188no—
669D3—182no—
670C22—21no—
671C22—21no—
672C22—62no—
673C22—62no—
674C22—62no—
675C22—182no—
676C22—182no—
677C22—182no—
678C22—272no—
679C22—272no—
680C22—272no—
681C22—272no—
682C22—548no—
683C22—541no—
684C22—541no—
685C22—1088no—
686C22#8902612yescomplemented
687C22C22×D3×C3⋊D311yescharacteristic
688C4—21no—
689C4—62no—
690C4—182no—
691C4—272no—
692C4—541no—
693C4#8903912yescomplemented
694C3—24no—
695C3#1059508114yescomplemented
696C3C3⋊D3×#12111yescharacteristic, complemented
697C2—22no—
698C2—122no—
699C2—274no—
700C2—362no—
701C2—542no—
702C2C2×#8902611yescharacteristic
703C2#1172457811yescharacteristic
704C2C2×#8903911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC22×C33×C4C22
hypercenterC22×C4D3×C3⋊D3
hypocenterC33C2×#121
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C22×C4×C3⋊(C3⋊D3)C2semidirect
2. C2×#89039C2semidirect
3. C2×#89026C2semidirect
4. C3×#64139C2semidirect
5. C32×#930C2semidirect
6. #11723637C2semidirect
7. #11723539C2semidirect
8. #11723532C2semidirect
9. #11723531C2semidirect
10. #11723527C2semidirect
11. #11723503C2semidirect
16. C22×C33×C4C22semidirect
17. C22×C3⋊(C3⋊Dic3)C22semidirect
21. C2×C4×C3⋊(C3⋊D3)C22semidirect
22. C2×C4×C3⋊(C3⋊D3)C22semidirect
23. C2×C3×#638C22semidirect
24. C2×C3×C4⋊(C3⋊D3)C22semidirect
25. C2×C32×#67C22semidirect
26. C2×C32×D12C22semidirect
28. C2×#6292C22semidirect
29. C2×#6291C22semidirect
30. C2×#6290C22semidirect
33. C3×#3752C22semidirect
34. C3×C4⋊(C3⋊Dic3)C22semidirect
35. C32×(C2×D3)⋊C4C22semidirect
36. C32×C4⋊Dic3C22semidirect
37. #88806C22semidirect
38. #88803C22semidirect
39. (C2×D3)⋊(C3⋊Dic3)C22semidirect
50. #64139D3semidirect
56. C3×#930D3semidirect
66. C22×C3⋊(C3⋊D3)D4semidirect
83. C4×C3⋊(C3⋊D3)D4semidirect
104. C22×C32×C4C2×D3semidirect
105. C22×C32×C4C2×D3semidirect
108. C2×#638C2×D3semidirect
115. C2×C4⋊(C3⋊D3)C2×D3semidirect
133. C2×C3×#67C2×D3semidirect
135. C2×C3×D12C2×D3semidirect
146. #3752C2×D3semidirect
147. C4⋊(C3⋊Dic3)C2×D3semidirect
150. C3×(C2×D3)⋊C4C2×D3semidirect
152. C3×C4⋊Dic3C2×D3semidirect
158. C22×C33C2×D4semidirect
165. C2×C3⋊(C3⋊D3)C2×D4semidirect
175. C33×C4C2×D4semidirect
177. C3⋊(C3⋊Dic3)C2×D4semidirect
194. #930C3⋊D3semidirect
287. C3⋊(C3⋊D3)#121semidirect
300. C22×C3×C4D32semidirect
301. C22×C3×C4C2×C3⋊D3semidirect
307. C2×#67C2×C3⋊D3semidirect
318. C2×D12C2×C3⋊D3semidirect
345. (C2×D3)⋊C4C2×C3⋊D3semidirect
347. C4⋊Dic3C2×C3⋊D3semidirect
361. C22×C32D3×D4semidirect
362. C22×C32D3×D4semidirect
402. C32×C4D3×D4semidirect
403. C32×C4D3×D4semidirect
424. C33C2×#121semidirect
543. C22×C4D3×C3⋊D3semidirect
565. C22×C3#3802semidirect
566. C22×C3D4×C3⋊D3semidirect
604. C3×C4#3811semidirect
605. C3×C4D4×C3⋊D3semidirect
615. C32D3×#121semidirect
616. C32D3×#121semidirect
686. C22#89026semidirect
693. C4#89039semidirect
695. C3#10595081semidirect
696. C3C3⋊D3×#121semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C3⋊(C3⋊D3)2
C2×#890392
C2×#890262
C3×#641392
C32×#9302
#117236372
#117235392
#117235322
#117235312
#117235272
#117235032
C3⋊D3×#1213
#105950813