Finite Group Databasebeta

← #13178104

Subgroups — #13178104

Order 1728.

3512 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6312C211yesmaximal, characteristic, complemented
2C22×C3×#638C211yesmaximal, characteristic, complemented
3C2×#89039C211yesmaximal, characteristic, complemented
4C2×C3⋊D3×#67C211yesmaximal, characteristic, complemented
5C32×#953C211yesmaximal, characteristic, complemented
6#11723643C211yesmaximal, characteristic, complemented
7#11723639C211yesmaximal, characteristic, complemented
8#11723637C211yesmaximal, characteristic, complemented
9#11723636C211yesmaximal, characteristic, complemented
10#11723635C211yesmaximal, characteristic, complemented
11#11723633C211yesmaximal, characteristic, complemented
12#11723626C211yesmaximal, characteristic, complemented
13#11723624C211yesmaximal, characteristic, complemented
14#11723623C211yesmaximal, characteristic, complemented
15#11723622C211yesmaximal, characteristic, complemented
16#10596061—31nomaximal
17#10595526—34nomaximal
18C24×C33C2211yescharacteristic, complemented
19C23×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
20C23×C3×C3⋊D3C2211yescharacteristic, complemented
21C22×D3×C3⋊D3C2211yescharacteristic, complemented
22C2×#6312—24no—
23C2×#6312C2211yescharacteristic
24C2×#6312C2211yescharacteristic, complemented
25C2×#6312C2211yescharacteristic, complemented
26C2×#6312C2211yescharacteristic, complemented
27C22×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
28C2×C3×#638—24no—
29C2×C3×#638C2211yescharacteristic
30C2×C3×#638C2211yescharacteristic, complemented
31C2×C3×#638C2211yescharacteristic, complemented
32C2×C3×#638C2211yescharacteristic, complemented
33C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
34C2×C32×#67C2211yescharacteristic, complemented
35C2×C32×#67C2211yescharacteristic, complemented
36C2×C32×#67C2211yescharacteristic, complemented
37#89039—24no—
38C3⋊D3×#67—24no—
39C2×#6292C2211yescharacteristic, complemented
40C2×#6292C2211yescharacteristic, complemented
41C2×#6292C2211yescharacteristic, complemented
42C2×#6291C2211yescharacteristic, complemented
43C2×#6290C2211yescharacteristic, complemented
44C2×#6289C2211yescharacteristic, complemented
45C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
46C32×#217C2211yescharacteristic, complemented
47C32×#217C2211yescharacteristic, complemented
48C32×#217C2211yescharacteristic, complemented
49#88807C2211yescharacteristic, complemented
50#88806C2211yescharacteristic, complemented
51#88804C2211yescharacteristic, complemented
52#88804C2211yescharacteristic, complemented
53#88803C2211yescharacteristic, complemented
54#88803C2211yescharacteristic, complemented
55(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
56Dic3×C3⋊Dic3C2211yescharacteristic, complemented
57C22×#638—31no—
58C22×#638—34no—
59C22×#638—64no—
60C22×#638D311yescharacteristic, complemented
61C2×D4×C3⋊D3—31no—
62C2×D4×C3⋊D3—31no—
63C22×C3×#67—34no—
64C2×#3811—34no—
65C2×D3×#67—34no—
66C32×#120—31no—
67#64149—31no—
68#64148—31no—
69#64148—31no—
70#64146—31no—
71#64093—31no—
72#64093—31no—
73#64091—31no—
74#64091—31no—
75#64090—31no—
76#64090—31no—
77C3×#953D314yescomplemented
78#63983—34no—
79#63981—34no—
80#63980—34no—
81#63979—34no—
82#63978—34no—
83#63977—34no—
84#67⋊Dic3—34no—
85#63971—34no—
86#63958—34no—
87#63952—34no—
88C23×C33—22no—
89C23×C33—22no—
90C23×C33—41no—
91C23×C33C2311yescharacteristic
92C23×C33C2311yescharacteristic
93C23×C33C2311yescharacteristic
94C22×C3⋊(C3⋊D3)—22no—
95C22×C3⋊(C3⋊D3)—22no—
96C22×C3⋊(C3⋊D3)—41no—
97C22×C3⋊(C3⋊D3)C2311yescharacteristic
98C22×C3⋊(C3⋊D3)C2311yescharacteristic
99C22×C3×C3⋊D3—22no—
100C22×C3×C3⋊D3—22no—
101C22×C3×C3⋊D3—41no—
102C22×C3×C3⋊D3C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C32×D3C2311yescharacteristic
105C2×D3×C3⋊D3—22no—
106C2×D3×C3⋊D3—22no—
107C2×D3×C3⋊D3—41no—
108#6312—22no—
109#6312—22no—
110#6312—22no—
111#6312D414yescomplemented
112C2×C3⋊(C3⋊Dic3)—22no—
113C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
114C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
115C3×#638—22no—
116C3×#638—22no—
117C3×#638—22no—
118C3×#638D414yescomplemented
119C2×C3×C3⋊Dic3—22no—
120C2×C3×C3⋊Dic3C2311yescharacteristic
121C2×C3×C3⋊Dic3C2311yescharacteristic
122C32×#67—22no—
123C32×#67—22no—
124C32×#67—41no—
125C2×C32×Dic3C2311yescharacteristic
126C2×C32×Dic3C2311yescharacteristic
127C2×C32×Dic3C2311yescharacteristic
128#6292—22no—
129#6292—22no—
130#6292—41no—
131#6291—22no—
132#6290—22no—
133#6289—22no—
134Dic3×C3⋊D3—22no—
135D4×#67—91no—
136#5590—94no—
137C24×C32—24no—
138C24×C32C2×D314yescomplemented
139C24×C32C2×D311yescharacteristic, complemented
140C23×C3⋊D3—31no—
141C23×C3⋊D3—34no—
142C23×C3⋊D3—31no—
143C23×C3⋊D3—64no—
144C23×C3⋊D3C2×D311yescharacteristic, complemented
145C23×C3×D3—34no—
146C22×D32—34no—
147C2×C32×D4—31no—
148C2×C32×D4—31no—
149C2×C32×D4—31no—
150C2×#638—24no—
151C2×#638—31no—
152C2×#638—34no—
153C2×#638—31no—
154C2×#638—31no—
155C2×#638—31no—
156C2×#638—34no—
157C2×#638—34no—
158C2×#638—34no—
159C2×#638—31no—
160C2×#638—31no—
161C2×#638—64no—
162C2×#638—616no—
163C2×#638—64no—
164C2×#638—64no—
165C2×#638—64no—
166C2×#638—64no—
167C2×#638—632no—
168C2×#638C2×D311yescharacteristic
169C2×#638C2×D311yescharacteristic, complemented
170C2×#638C2×D311yescharacteristic, complemented
171C2×#638C2×D311yescharacteristic, complemented
172C22×C3⋊Dic3—31no—
173C22×C3⋊Dic3—34no—
174C22×C3⋊Dic3—64no—
175C22×C3⋊Dic3C2×D311yescharacteristic, complemented
176D4×C3⋊D3—64no—
177D4×C3⋊D3—64no—
178C2×C4⋊(C3⋊D3)—31no—
179C2×C4⋊(C3⋊D3)—31no—
180C2×C4⋊(C3⋊D3)—31no—
181C2×C4×C3⋊D3—31no—
182C2×C4×C3⋊D3—31no—
183C2×C3×#67—34no—
184C2×C3×#67—34no—
185C2×C3×#67—34no—
186C2×C3×#67—34no—
187C2×C3×#67—616no—
188C2×C3×#67C2×D314yescomplemented
189C2×C3×#67C2×D314yescomplemented
190C2×C3×#67C2×D314yescomplemented
191C22×C3×Dic3—34no—
192#3811—616no—
193D3×#67—616no—
194C2×#626—34no—
195C2×#626—34no—
196C2×#626—34no—
197C2×#626—34no—
198C2×#625—34no—
199C2×#624—34no—
200C2×D3×Dic3—34no—
201C32×C22⋊C4—31no—
202C32×C22⋊C4—31no—
203C32×C22⋊C4—31no—
204#3757—31no—
205#3752—31no—
206#3752—31no—
207#3752—31no—
208#3752—31no—
209#3750—31no—
210#3750—31no—
211C4×C3⋊Dic3—31no—
212C3×#217C2×D314yescomplemented
213C3×#217C2×D314yescomplemented
214C3×#217C2×D314yescomplemented
215#3724—34no—
216Dic3⋊Dic3—34no—
217#3722—34no—
218#3722—34no—
219(C2×D3)⋊Dic3—34no—
220(C2×D3)⋊Dic3—34no—
221(C2×D3)⋊Dic3—34no—
222Dic32—34no—
223C22×C33—21no—
224C22×C33—21no—
225C22×C33—21no—
226C22×C33—21no—
227C22×C33—21no—
228C22×C33—21no—
229C22×C33—21no—
230C22×C33—44no—
231C22×C33C2×D412yescomplemented
232C22×C33C2×D412yescomplemented
233C22×C33C2411yescharacteristic
234C2×C3⋊(C3⋊D3)—21no—
235C2×C3⋊(C3⋊D3)—21no—
236C2×C3⋊(C3⋊D3)—21no—
237C2×C3⋊(C3⋊D3)—21no—
238C2×C3⋊(C3⋊D3)—21no—
239C2×C3⋊(C3⋊D3)—44no—
240C2×C3⋊(C3⋊D3)C2×D412yescomplemented
241C2×C3×C3⋊D3—21no—
242C2×C3×C3⋊D3—21no—
243C2×C3×C3⋊D3—21no—
244C2×C3×C3⋊D3—21no—
245C2×C3×C3⋊D3—21no—
246C2×C3×C3⋊D3—44no—
247C2×C3×C3⋊D3C2×D412yescomplemented
248C2×C32×D3—21no—
249C2×C32×D3—21no—
250C2×C32×D3—21no—
251D3×C3⋊D3—44no—
252C3⋊(C3⋊Dic3)—21no—
253C3⋊(C3⋊Dic3)C2×D412yescomplemented
254C3×C3⋊Dic3—21no—
255C3×C3⋊Dic3C2×D412yescomplemented
256C32×Dic3—21no—
257C32×Dic3—21no—
258C32×Dic3—21no—
259C22×C3×D4—91no—
260C22×#67—34no—
261C22×#67—94no—
262C22×#67—91no—
263C22×#67—91no—
264C22×#67—184no—
265C2×D3×D4—94no—
266C2×D3×D4—94no—
267C2×D3×D4—91no—
268C3×#120—34no—
269#953—91no—
270#953C3⋊D311yescharacteristic, complemented
271#940—94no—
272#940—91no—
273#939—94no—
274#939—94no—
275#939—91no—
276#939—91no—
277#938—91no—
278#937—94no—
279#937—91no—
280#937—91no—
281D4×Dic3—91no—
282#930—91no—
283C4×#67—91no—
284#884—94no—
285#884—94no—
286#882—94no—
287#882—94no—
288#67⋊C4—94no—
289#67⋊C4—94no—
290C23×C32—216no—
291C23×C32—28no—
292C23×C32—22no—
293C23×C32—22no—
294C23×C32—24no—
295C23×C32—24no—
296C23×C32—24no—
297C23×C32—28no—
298C23×C32—31no—
299C23×C32—48no—
300C23×C32—41no—
301C23×C32—44no—
302C23×C32—48no—
303C23×C32C22×D314yes—
304C23×C32C22×D314yes—
305C23×C32C22×D314yes—
306C23×C32C22×D311yescharacteristic
307C23×C32C22×D311yescharacteristic
308C23×C32C22×D311yescharacteristic
309C22×C3⋊D3—22no—
310C22×C3⋊D3—22no—
311C22×C3⋊D3—31no—
312C22×C3⋊D3—31no—
313C22×C3⋊D3—34no—
314C22×C3⋊D3—34no—
315C22×C3⋊D3—41no—
316C22×C3⋊D3—64no—
317C22×C3⋊D3—64no—
318C22×C3⋊D3—62no—
319C22×C3⋊D3—62no—
320C22×C3⋊D3—68no—
321C22×C3⋊D3—616no—
322C22×C3⋊D3—62no—
323C22×C3⋊D3—62no—
324C22×C3⋊D3—68no—
325C22×C3⋊D3—128no—
326C22×C3⋊D3—121no—
327C22×C3⋊D3—121no—
328C22×C3⋊D3—124no—
329C22×C3⋊D3—128no—
330C22×C3⋊D3C22×D311yescharacteristic
331C22×C3⋊D3C22×D311yescharacteristic
332C22×C3×D3—34no—
333C22×C3×D3—34no—
334C22×C3×D3—68no—
335C22×C3×D3—68no—
336C22×C3×D3—124no—
337C22×C3×D3C22×D314yes—
338C2×D32—68no—
339C2×D32—68no—
340C2×D32—124no—
341C32×D4—62no—
342C32×D4—62no—
343C32×D4—121no—
344C2×C32×C4—31no—
345C2×C32×C4—31no—
346C2×C32×C4—31no—
347#638—22no—
348#638—22no—
349#638—22no—
350#638—34no—
351#638—316no—
352#638—616no—
353#638—62no—
354#638—62no—
355#638—68no—
356#638—62no—
357#638—68no—
358#638—616no—
359#638—616no—
360#638—616no—
361#638—68no—
362#638—62no—
363#638—62no—
364#638#6714yescomplemented
365C2×C3⋊Dic3—22no—
366C2×C3⋊Dic3—31no—
367C2×C3⋊Dic3—31no—
368C2×C3⋊Dic3—34no—
369C2×C3⋊Dic3—34no—
370C2×C3⋊Dic3—64no—
371C2×C3⋊Dic3—64no—
372C2×C3⋊Dic3—62no—
373C2×C3⋊Dic3—68no—
374C2×C3⋊Dic3—616no—
375C2×C3⋊Dic3C22×D311yescharacteristic
376C2×C3⋊Dic3C22×D311yescharacteristic
377C4⋊(C3⋊D3)—62no—
378C4⋊(C3⋊D3)—62no—
379C4⋊(C3⋊D3)—121no—
380C4×C3⋊D3—62no—
381C4×C3⋊D3—62no—
382C3×#67—28no—
383C3×#67—28no—
384C3×#67—316no—
385C3×#67—44no—
386C3×#67—68no—
387C3×#67—68no—
388C3×#67—68no—
389C2×C3×Dic3—34no—
390C2×C3×Dic3—34no—
391C2×C3×Dic3—68no—
392C2×C3×Dic3C22×D314yes—
393C2×C3×Dic3C22×D314yes—
394C2×C3×Dic3C22×D314yes—
395#626—68no—
396#626—68no—
397#626—68no—
398#626—124no—
399#625—68no—
400#624—68no—
401D3×Dic3—68no—
402D42—271noSylow
403C2×C33—22no—
404C2×C33—22no—
405C2×C33—41no—
406C2×C33C22×D411yescharacteristic
407C2×C33C22×D411yescharacteristic
408C2×C33H(5,𝔽2)11yescharacteristic
409C3⋊(C3⋊D3)—22no—
410C3⋊(C3⋊D3)—41no—
411C3×C3⋊D3—22no—
412C3×C3⋊D3—41no—
413C32×D3—41no—
414C24×C3—24no—
415C24×C3—91no—
416C24×C3D3214yescomplemented
417C24×C3C2×C3⋊D311yescharacteristic, complemented
418C23×D3—34no—
419C23×D3—94no—
420C23×D3—94no—
421C23×D3—91no—
422C23×D3—91no—
423C23×D3—184no—
424C2×C3×D4—34no—
425C2×C3×D4—34no—
426C2×C3×D4—34no—
427C2×C3×D4—91no—
428C2×C3×D4—91no—
429C2×C3×D4—91no—
430C2×C3×D4—91no—
431C2×C3×D4—184no—
432C22×C3×C4—91no—
433C2×#67—34no—
434C2×#67—34no—
435C2×#67—34no—
436C2×#67—34no—
437C2×#67—616no—
438C2×#67—94no—
439C2×#67—94no—
440C2×#67—91no—
441C2×#67—94no—
442C2×#67—94no—
443C2×#67—94no—
444C2×#67—94no—
445C2×#67—91no—
446C2×#67—91no—
447C2×#67—91no—
448C2×#67—91no—
449C2×#67—91no—
450C2×#67—91no—
451C2×#67—91no—
452C2×#67—184no—
453C2×#67—184no—
454C2×#67—184no—
455C2×#67—184no—
456C2×#67—184no—
457C2×#67—1816no—
458C2×#67—184no—
459C2×#67—1832no—
460C2×#67C2×C3⋊D311yescharacteristic, complemented
461C2×#67C2×C3⋊D311yescharacteristic, complemented
462C2×#67C2×C3⋊D311yescharacteristic, complemented
463C22×Dic3—34no—
464C22×Dic3—94no—
465C22×Dic3—91no—
466C22×Dic3—91no—
467C22×Dic3—184no—
468D3×D4—184no—
469D3×D4—1816no—
470D3×D4—1816no—
471C2×D12—94no—
472C2×D12—94no—
473C2×D12—91no—
474C2×D12—94no—
475C2×C4×D3—94no—
476C2×C4×D3—94no—
477C2×C4×D3—91no—
478C3×C22⋊C4—34no—
479C3×C22⋊C4—34no—
480C3×C22⋊C4—34no—
481#217—94no—
482#217—91no—
483#217—91no—
484#217C2×C3⋊D311yescharacteristic, complemented
485#217C2×C3⋊D311yescharacteristic, complemented
486#217C2×C3⋊D311yescharacteristic, complemented
487(C2×D3)⋊C4—94no—
488(C2×D3)⋊C4—94no—
489(C2×D3)⋊C4—94no—
490(C2×D3)⋊C4—94no—
491(C2×D3)⋊C4—91no—
492(C2×D3)⋊C4—91no—
493(C2×D3)⋊C4—91no—
494C4⋊Dic3—91no—
495Dic3⋊C4—94no—
496Dic3⋊C4—94no—
497Dic3⋊C4—91no—
498C4×Dic3—94no—
499C4×Dic3—91no—
500C22×C32—28no—
501C22×C32—28no—
502C22×C32—24no—
503C22×C32—21no—
504C22×C32—21no—
505C22×C32—24no—
506C22×C32—21no—
507C22×C32—21no—
508C22×C32—28no—
509C22×C32—24no—
510C22×C32—21no—
511C22×C32—21no—
512C22×C32—21no—
513C22×C32—24no—
514C22×C32—28no—
515C22×C32—28no—
516C22×C32—24no—
517C22×C32—24no—
518C22×C32—24no—
519C22×C32—24no—
520C22×C32—44no—
521C22×C32—44no—
522C22×C32—44no—
523C22×C32—44no—
524C22×C32—44no—
525C22×C32—416no—
526C22×C32—432no—
527C22×C32—61no—
528C22×C32—61no—
529C22×C32—61no—
530C22×C32D3×D418yescomplemented
531C22×C32D3×D418yescomplemented
532C22×C32D3×D412yescomplemented
533C22×C32C2×#6712yescomplemented
534C22×C32C23×D314yes—
535C22×C32C23×D311yescharacteristic
536C2×C3⋊D3—21no—
537C2×C3⋊D3—21no—
538C2×C3⋊D3—21no—
539C2×C3⋊D3—21no—
540C2×C3⋊D3—21no—
541C2×C3⋊D3—32no—
542C2×C3⋊D3—38no—
543C2×C3⋊D3—44no—
544C2×C3⋊D3—68no—
545C2×C3⋊D3—61no—
546C2×C3⋊D3—61no—
547C2×C3⋊D3—68no—
548C2×C3⋊D3—64no—
549C2×C3⋊D3—61no—
550C2×C3⋊D3—61no—
551C2×C3⋊D3—61no—
552C2×C3⋊D3—64no—
553C2×C3⋊D3—64no—
554C2×C3⋊D3—64no—
555C2×C3⋊D3—64no—
556C2×C3⋊D3—124no—
557C2×C3⋊D3—124no—
558C2×C3⋊D3—124no—
559C2×C3⋊D3—124no—
560C2×C3⋊D3—124no—
561C2×C3⋊D3—124no—
562C2×C3⋊D3—1216no—
563C2×C3⋊D3—1232no—
564C2×C3⋊D3C2×#6712yescomplemented
565C2×C3×D3—24no—
566C2×C3×D3—24no—
567C2×C3×D3—24no—
568C2×C3×D3—38no—
569C2×C3×D3—64no—
570C2×C3×D3—64no—
571C2×C3×D3—64no—
572C2×C3×D3—64no—
573C2×C3×D3—64no—
574C2×C3×D3—1216no—
575D32—1216no—
576C32×C4—61no—
577C32×C4—61no—
578C32×C4—61no—
579C3⋊Dic3—21no—
580C3⋊Dic3—32no—
581C3⋊Dic3—38no—
582C3⋊Dic3—68no—
583C3⋊Dic3—68no—
584C3⋊Dic3—64no—
585C3⋊Dic3—61no—
586C3⋊Dic3C2×#6712yescomplemented
587C3×Dic3—24no—
588C3×Dic3—24no—
589C3×Dic3—24no—
590C3×Dic3—38no—
591C3×Dic3—64no—
592C22×D4—91no—
593C22×D4—271no—
594C22×D4—271no—
595C22×D4—271no—
596#127—271no—
597#121—271no—
598#121—271no—
599#121—271no—
600#121—271no—
601#120—31no—
602#120—271no—
603#120—271no—
604#120—271no—
605C4×D4—271no—
606C4×D4—271no—
607C33D4211yescharacteristic, complemented, Sylow
608C23×C3—216no—
609C23×C3—28no—
610C23×C3—28no—
611C23×C3—22no—
612C23×C3—22no—
613C23×C3—24no—
614C23×C3—24no—
615C23×C3—24no—
616C23×C3—34no—
617C23×C3—48no—
618C23×C3—44no—
619C23×C3—41no—
620C23×C3—48no—
621C23×C3—91no—
622C23×C3—91no—
623C23×C3—182no—
624C23×C3—182no—
625C23×C3—361no—
626C23×C3C2×D3214yes—
627C23×C3C2×D3214yes—
628C23×C3C2×D3214yes—
629C23×C3C22×C3⋊D311yescharacteristic
630C23×C3C22×C3⋊D311yescharacteristic
631C23×C3C22×C3⋊D311yescharacteristic
632C22×D3—34no—
633C22×D3—34no—
634C22×D3—68no—
635C22×D3—68no—
636C22×D3—94no—
637C22×D3—91no—
638C22×D3—94no—
639C22×D3—91no—
640C22×D3—124no—
641C22×D3—184no—
642C22×D3—184no—
643C22×D3—182no—
644C22×D3—182no—
645C22×D3—188no—
646C22×D3—188no—
647C22×D3—188no—
648C22×D3—182no—
649C22×D3—1816no—
650C22×D3—188no—
651C22×D3—182no—
652C22×D3—368no—
653C22×D3—361no—
654C22×D3—364no—
655C22×D3—364no—
656C22×D3—361no—
657C22×D3—368no—
658C22×D3C22×C3⋊D311yescharacteristic
659C3×D4—68no—
660C3×D4—68no—
661C3×D4—94no—
662C3×D4—124no—
663C3×D4—182no—
664C3×D4—182no—
665C3×D4—182no—
666C2×C3×C4—34no—
667C2×C3×C4—34no—
668C2×C3×C4—34no—
669C2×C3×C4—91no—
670C2×C3×C4—91no—
671C2×C3×C4—182no—
672#67—22no—
673#67—22no—
674#67—316no—
675#67—41no—
676#67—68no—
677#67—68no—
678#67—68no—
679#67—916no—
680#67—94no—
681#67—1816no—
682#67—182no—
683#67—182no—
684#67—188no—
685#67—182no—
686#67—188no—
687#67—188no—
688#67—182no—
689#67—188no—
690#67—182no—
691#67—1816no—
692#67—1816no—
693#67—1816no—
694#67—188no—
695#67—182no—
696#67—361no—
697C2×Dic3—34no—
698C2×Dic3—34no—
699C2×Dic3—68no—
700C2×Dic3—94no—
701C2×Dic3—91no—
702C2×Dic3—94no—
703C2×Dic3—91no—
704C2×Dic3—184no—
705C2×Dic3—184no—
706C2×Dic3—182no—
707C2×Dic3—188no—
708C2×Dic3—182no—
709C2×Dic3—1816no—
710C2×Dic3C22×C3⋊D311yescharacteristic
711C2×Dic3C22×C3⋊D311yescharacteristic
712C2×Dic3C22×C3⋊D311yescharacteristic
713D12—188no—
714D12—188no—
715D12—182no—
716D12—364no—
717C4×D3—182no—
718C4×D3—188no—
719C4×D3—188no—
720C2×C32—216no—
721C2×C32—22no—
722C2×C32—22no—
723C2×C32—28no—
724C2×C32—24no—
725C2×C32—24no—
726C2×C32—24no—
727C2×C32—28no—
728C2×C32—48no—
729C2×C32—48no—
730C2×C32—41no—
731C2×C32—44no—
732C2×C32—121no—
733C2×C32C2×D3×D414yes—
734C2×C32C2×D3×D414yes—
735C2×C32C2×D3×D411yescharacteristic
736C2×C32#100414yes—
737C2×C32#100411yescharacteristic
738C2×C32C22×#6711yescharacteristic
739C3⋊D3—22no—
740C3⋊D3—41no—
741C3⋊D3—62no—
742C3⋊D3—68no—
743C3⋊D3—128no—
744C3⋊D3—128no—
745C3⋊D3—121no—
746C3⋊D3—124no—
747C3×D3—44no—
748C3×D3—68no—
749C3×D3—124no—
750C24—91no—
751C24—271no—
752C24—271no—
753C24D3×C3⋊D311yescharacteristic, complemented
754C2×D4—31no—
755C2×D4—31no—
756C2×D4—31no—
757C2×D4—91no—
758C2×D4—91no—
759C2×D4—91no—
760C2×D4—91no—
761C2×D4—184no—
762C2×D4—271no—
763C2×D4—271no—
764C2×D4—271no—
765C2×D4—271no—
766C2×D4—271no—
767C2×D4—271no—
768C2×D4—271no—
769C2×D4—271no—
770C2×D4—271no—
771C2×D4—544no—
772C2×D4—544no—
773C2×D4—544no—
774C22×C4—91no—
775C22×C4—271no—
776C22×C4—271no—
777C22×C4—271no—
778C4⋊C4—271no—
779C4⋊C4—271no—
780C22⋊C4—31no—
781C22⋊C4—31no—
782C22⋊C4—31no—
783C22⋊C4—271no—
784C22⋊C4—271no—
785C22⋊C4—271no—
786C22⋊C4—271no—
787C22⋊C4—271no—
788C42—271no—
789C22×C3—28no—
790C22×C3—28no—
791C22×C3—24no—
792C22×C3—24no—
793C22×C3—24no—
794C22×C3—24no—
795C22×C3—21no—
796C22×C3—21no—
797C22×C3—21no—
798C22×C3—21no—
799C22×C3—28no—
800C22×C3—24no—
801C22×C3—24no—
802C22×C3—24no—
803C22×C3—21no—
804C22×C3—21no—
805C22×C3—21no—
806C22×C3—24no—
807C22×C3—28no—
808C22×C3—28no—
809C22×C3—44no—
810C22×C3—44no—
811C22×C3—44no—
812C22×C3—44no—
813C22×C3—416no—
814C22×C3—44no—
815C22×C3—432no—
816C22×C3—64no—
817C22×C3—64no—
818C22×C3—64no—
819C22×C3—92no—
820C22×C3—181no—
821C22×C3—181no—
822C22×C3—181no—
823C22×C3—181no—
824C22×C3—181no—
825C22×C3—364no—
826C22×C3D3×#6718yescomplemented
827C22×C3#381118yescomplemented
828C22×C3D4×C3⋊D312yescomplemented
829C22×C3D4×C3⋊D312yescomplemented
830C22×C3C22×D3214yes—
831C22×C3C23×C3⋊D311yescharacteristic
832C2×D3—21no—
833C2×D3—21no—
834C2×D3—21no—
835C2×D3—38no—
836C2×D3—64no—
837C2×D3—64no—
838C2×D3—64no—
839C2×D3—64no—
840C2×D3—64no—
841C2×D3—98no—
842C2×D3—92no—
843C2×D3—1216no—
844C2×D3—188no—
845C2×D3—184no—
846C2×D3—184no—
847C2×D3—181no—
848C2×D3—181no—
849C2×D3—188no—
850C2×D3—184no—
851C2×D3—184no—
852C2×D3—184no—
853C2×D3—181no—
854C2×D3—181no—
855C2×D3—181no—
856C2×D3—364no—
857C2×D3—364no—
858C2×D3—364no—
859C2×D3—364no—
860C2×D3—364no—
861C2×D3—3616no—
862C2×D3—3616no—
863C2×D3—364no—
864C2×D3—3632no—
865C3×C4—64no—
866C3×C4—64no—
867C3×C4—64no—
868C3×C4—92no—
869C3×C4—181no—
870Dic3—21no—
871Dic3—21no—
872Dic3—21no—
873Dic3—38no—
874Dic3—64no—
875Dic3—98no—
876Dic3—92no—
877Dic3—188no—
878Dic3—188no—
879Dic3—184no—
880Dic3—181no—
881C32—24no—
882C32#559014yescomplemented
883C32D4×#6711yescharacteristic, complemented
884C23—22no—
885C23—22no—
886C23—31no—
887C23—41no—
888C23—91no—
889C23—91no—
890C23—182no—
891C23—182no—
892C23—271no—
893C23—271no—
894C23—361no—
895C23—542no—
896C23—542no—
897C23—542no—
898C23—542no—
899C23—1081no—
900C23—1081no—
901C23C2×D3×C3⋊D311yescharacteristic
902C23C2×D3×C3⋊D311yescharacteristic
903C23C2×D3×C3⋊D311yescharacteristic
904D4—62no—
905D4—62no—
906D4—94no—
907D4—121no—
908D4—182no—
909D4—182no—
910D4—182no—
911D4—274no—
912D4—542no—
913D4—542no—
914D4—542no—
915D4—542no—
916D4—542no—
917D4—542no—
918D4—542no—
919D4—1081no—
920C2×C4—31no—
921C2×C4—31no—
922C2×C4—31no—
923C2×C4—91no—
924C2×C4—91no—
925C2×C4—182no—
926C2×C4—271no—
927C2×C4—271no—
928C2×C4—542no—
929C2×C4—542no—
930C2×C4—542no—
931C2×C3—216no—
932C2×C3—28no—
933C2×C3—28no—
934C2×C3—22no—
935C2×C3—22no—
936C2×C3—24no—
937C2×C3—24no—
938C2×C3—24no—
939C2×C3—48no—
940C2×C3—48no—
941C2×C3—44no—
942C2×C3—41no—
943C2×C3—124no—
944C2×C3—182no—
945C2×C3—361no—
946C2×C3C2×D3×#6714yes—
947C2×C3C2×#381114yes—
948C2×C3#6433014yes—
949C2×C3C2×D4×C3⋊D311yescharacteristic
950C2×C3C2×D4×C3⋊D311yescharacteristic
951C2×C3#6436111yescharacteristic
952D3—41no—
953D3—68no—
954D3—124no—
955D3—188no—
956D3—182no—
957D3—368no—
958D3—368no—
959D3—364no—
960D3—361no—
961C22—21no—
962C22—21no—
963C22—21no—
964C22—21no—
965C22—21no—
966C22—21no—
967C22—21no—
968C22—44no—
969C22—61no—
970C22—61no—
971C22—61no—
972C22—92no—
973C22—181no—
974C22—181no—
975C22—181no—
976C22—181no—
977C22—181no—
978C22—272no—
979C22—364no—
980C22—541no—
981C22—541no—
982C22—541no—
983C22—541no—
984C22—541no—
985C22—1084no—
986C22—1084no—
987C22C3⋊D3×#6712yescomplemented
988C22#8903912yescomplemented
989C22C22×D3×C3⋊D311yescharacteristic
990C4—61no—
991C4—61no—
992C4—61no—
993C4—92no—
994C4—181no—
995C4—272no—
996C4—541no—
997C3—24no—
998C3#1059552614yescomplemented
999C3#1059606111yescharacteristic, complemented
1000C2—22no—
1001C2—22no—
1002C2—41no—
1003C2—121no—
1004C2—182no—
1005C2—361no—
1006C2—542no—
1007C2—1081no—
1008C2C2×C3⋊D3×#6711yescharacteristic
1009C2C2×#8903911yescharacteristic
1010C2#1172461111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC24×C33C22
hypercenterC24D3×C3⋊D3
hypocenterC33D42
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C24

Complements

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

NH ≅ G/Ntype
1. C22×#6312C2semidirect
2. C22×C3×#638C2semidirect
3. C2×#89039C2semidirect
4. C2×C3⋊D3×#67C2semidirect
5. C32×#953C2semidirect
6. #11723643C2semidirect
7. #11723639C2semidirect
8. #11723637C2semidirect
9. #11723636C2semidirect
10. #11723635C2semidirect
11. #11723633C2semidirect
12. #11723626C2semidirect
13. #11723624C2semidirect
14. #11723623C2semidirect
15. #11723622C2semidirect
18. C24×C33C22semidirect
19. C23×C3⋊(C3⋊D3)C22semidirect
20. C23×C3×C3⋊D3C22semidirect
21. C22×D3×C3⋊D3C22semidirect
24. C2×#6312C22semidirect
25. C2×#6312C22semidirect
26. C2×#6312C22semidirect
27. C22×C3⋊(C3⋊Dic3)C22semidirect
30. C2×C3×#638C22semidirect
31. C2×C3×#638C22semidirect
32. C2×C3×#638C22semidirect
33. C22×C3×C3⋊Dic3C22semidirect
34. C2×C32×#67C22semidirect
35. C2×C32×#67C22semidirect
36. C2×C32×#67C22semidirect
39. C2×#6292C22semidirect
40. C2×#6292C22semidirect
41. C2×#6292C22semidirect
42. C2×#6291C22semidirect
43. C2×#6290C22semidirect
44. C2×#6289C22semidirect
45. C2×Dic3×C3⋊D3C22semidirect
46. C32×#217C22semidirect
47. C32×#217C22semidirect
48. C32×#217C22semidirect
49. #88807C22semidirect
50. #88806C22semidirect
51. #88804C22semidirect
52. #88804C22semidirect
53. #88803C22semidirect
54. #88803C22semidirect
55. (C2×D3)⋊(C3⋊Dic3)C22semidirect
56. Dic3×C3⋊Dic3C22semidirect
60. C22×#638D3semidirect
77. C3×#953D3semidirect
111. #6312D4semidirect
118. C3×#638D4semidirect
138. C24×C32C2×D3semidirect
139. C24×C32C2×D3semidirect
144. C23×C3⋊D3C2×D3semidirect
169. C2×#638C2×D3semidirect
170. C2×#638C2×D3semidirect
171. C2×#638C2×D3semidirect
175. C22×C3⋊Dic3C2×D3semidirect
188. C2×C3×#67C2×D3semidirect
189. C2×C3×#67C2×D3semidirect
190. C2×C3×#67C2×D3semidirect
212. C3×#217C2×D3semidirect
213. C3×#217C2×D3semidirect
214. C3×#217C2×D3semidirect
231. C22×C33C2×D4semidirect
232. C22×C33C2×D4semidirect
240. C2×C3⋊(C3⋊D3)C2×D4semidirect
247. C2×C3×C3⋊D3C2×D4semidirect
253. C3⋊(C3⋊Dic3)C2×D4semidirect
255. C3×C3⋊Dic3C2×D4semidirect
270. #953C3⋊D3semidirect
364. #638#67semidirect
416. C24×C3D32semidirect
417. C24×C3C2×C3⋊D3semidirect
460. C2×#67C2×C3⋊D3semidirect
461. C2×#67C2×C3⋊D3semidirect
462. C2×#67C2×C3⋊D3semidirect
484. #217C2×C3⋊D3semidirect
485. #217C2×C3⋊D3semidirect
486. #217C2×C3⋊D3semidirect
530. C22×C32D3×D4semidirect
531. C22×C32D3×D4semidirect
532. C22×C32D3×D4semidirect
533. C22×C32C2×#67semidirect
564. C2×C3⋊D3C2×#67semidirect
586. C3⋊Dic3C2×#67semidirect
607. C33D42semidirect
753. C24D3×C3⋊D3semidirect
826. C22×C3D3×#67semidirect
827. C22×C3#3811semidirect
828. C22×C3D4×C3⋊D3semidirect
829. C22×C3D4×C3⋊D3semidirect
882. C32#5590semidirect
883. C32D4×#67semidirect
987. C22C3⋊D3×#67semidirect
988. C22#89039semidirect
998. C3#10595526semidirect
999. C3#10596061semidirect

Maximal subgroups

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

subgroupindex
C22×#63122
C22×C3×#6382
C2×#890392
C2×C3⋊D3×#672
C32×#9532
#117236432
#117236392
#117236372
#117236362
#117236352
#117236332
#117236262
#117236242
#117236232
#117236222
#105960613
#105955263