Finite Group Databasebeta

← C2×#11724407 #13181311

Subgroups — C2×#11724407 #13181311

Order 1728.

4178 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89049C211yesmaximal, characteristic, complemented
2C22×Dic3×C3⋊D3C211yesmaximal, characteristic, complemented
3C2×#89029C212yesmaximal, complemented
4C2×C3×#3811C211yesmaximal, characteristic, complemented
5C2×C3×#3804C212yesmaximal, complemented
6C2×#88964C212yesmaximal, complemented
7C2×#88960C212yesmaximal, complemented
8C2×#88957C211yesmaximal, characteristic, complemented
9C2×#88953C211yesmaximal, characteristic, complemented
10C2×#88949C211yesmaximal, characteristic, complemented
11#11724407C2116yesmaximal, direct product factor
12C2×D32×Dic3C211yesmaximal, characteristic, complemented
13C2×D3×#237—32nomaximal
14C2×#64306—31nomaximal
15C23×C3×C3⋊D3C2211yescharacteristic
16C22×#1113C2211yescharacteristic
17C22×C3×D32C2211yescharacteristic
18C22×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
19C2×C3×#638C2212yescomplemented
20C2×C32×#67C2212yescomplemented
21C22×C32×Dic3C2211yescharacteristic, complemented
22#89049C2218yescomplemented
23C2×#6295C2212yescomplemented
24C2×#6294C2211yescharacteristic
25C2×#6293C2212yescomplemented
26C2×#6290C2212yescomplemented
27C2×Dic3×C3⋊D3C2211yescharacteristic
28C2×Dic3×C3⋊D3C2211yescharacteristic
29C2×Dic3×C3⋊D3C2218yescomplemented
30C2×Dic3×C3⋊D3C2212yescomplemented
31C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
32C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
33#89029C22116yescomplemented
34C2×D3×C3⋊Dic3C2212yescomplemented
35C3×#3811C2218yescomplemented
36C2×C3×#627C2212yescomplemented
37C2×C3×#626C2212yescomplemented
38C2×C3×#626C2212yescomplemented
39C2×C3×#624C2211yescharacteristic
40C2×C3×#624C2212yescomplemented
41C3×#3804C22116yescomplemented
42C2×C3×D3×Dic3C2212yescomplemented
43#88964C22116yescomplemented
44#88960C22116yescomplemented
45#88957C2218yescomplemented
46#88953C2218yescomplemented
47#88949C2218yescomplemented
48D32×Dic3C2218yescomplemented
49C2×#3830—32no—
50C22×C4×C3⋊D3—31no—
51C2×C3×#237—32no—
52C2×C3×D3×D4—32no—
53C2×C3×#235—32no—
54C2×#3811—31no—
55C2×#3811D311yescharacteristic, complemented
56C2×D3×#67—32no—
57C2×D3×#67—32no—
58C2×#3805—32no—
59C2×#3805—32no—
60C2×#3805—32no—
61C2×#3805—62no—
62C2×#3804—32no—
63C2×#3804D312yescomplemented
64C22×D3×Dic3—32no—
65C22×D3×Dic3—32no—
66C22×D3×Dic3—61no—
67D3×#237—332no—
68#64306—316no—
69C2×#3802—31no—
70C2×C4×D32—31no—
71C2×C4×D32—32no—
72C2×C4×D32—31no—
73C2×#3798—32no—
74C2×#3797—31no—
75C2×#3796—32no—
76C2×#3796—32no—
77C2×#3795—32no—
78C2×D3×Dic6—32no—
79C23×C33C2311yescharacteristic
80C22×C3×C3⋊D3—24no—
81C22×C3×C3⋊D3C2312yes—
82C22×C3×C3⋊D3C2311yescharacteristic
83C22×C3×C3⋊D3C2314yes—
84C22×C3×C3⋊D3C2311yescharacteristic
85C22×C32×D3C2312yes—
86C2×#1113—24no—
87C2×#1113C2314yes—
88C2×C3×D32—24no—
89C2×C3×D32C2314yes—
90C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
91C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
92C2×C3⋊(C3⋊Dic3)C2314yescomplemented
93C3×#638C2318yescomplemented
94C2×C3×C3⋊Dic3C2312yes—
95C32×#67C2318yescomplemented
96C2×C32×Dic3C2311yescharacteristic
97C2×C32×Dic3C2312yes—
98C2×C32×Dic3C2311yescharacteristic
99C2×C32×Dic3C2314yescomplemented
100#6295C2318yescomplemented
101#6294C2314yes—
102#6293C2318yescomplemented
103#6290C2318yescomplemented
104Dic3×C3⋊D3C2314yes—
105Dic3×C3⋊D3C2314yes—
106Dic3×C3⋊D3C2318yescomplemented
107Dic3×C3⋊D3C2314yescomplemented
108Dic3×C3⋊D3C2314yescomplemented
109D3×C3⋊Dic3C2318yescomplemented
110C3×#627C2318yescomplemented
111C3×#626C2318yescomplemented
112C3×#626C2318yescomplemented
113C3×#624C2314yes—
114C3×#624C2318yescomplemented
115C3×D3×Dic3C2318yescomplemented
116C2×D3×#41—92no—
117C22×#237—91no—
118C23×C3⋊D3C2×D311yescharacteristic
119C23×C3×D3—32no—
120C23×C3×D3—32no—
121C23×C3×D3—61no—
122C22×D32—31no—
123C22×D32—32no—
124C22×D32C2×D311yescharacteristic
125C2×C32×D4—32no—
126C22×C32×C4—31no—
127C2×#638—32no—
128C2×#638C2×D312yescomplemented
129C22×C3⋊Dic3—32no—
130C22×C3⋊Dic3—31no—
131C22×C3⋊Dic3—32no—
132C22×C3⋊Dic3—61no—
133C22×C3⋊Dic3—62no—
134C22×C3⋊Dic3—121no—
135#3830—316no—
136C2×C4×C3⋊D3—31no—
137C2×C4×C3⋊D3—32no—
138C2×C4×C3⋊D3—31no—
139C2×C4×C3⋊D3—31no—
140C2×C4×C3⋊D3—31no—
141C2×C4×C3⋊D3—38no—
142C2×#634—32no—
143C2×C3×#67—22no—
144C2×C3×#67—32no—
145C2×C3×#67—32no—
146C2×C3×#67—32no—
147C2×C3×#67—32no—
148C2×C3×#67—62no—
149C2×C3×#67C2×D312yescomplemented
150C2×C3×#67C2×D312yescomplemented
151C22×C3×Dic3—21no—
152C22×C3×Dic3—32no—
153C22×C3×Dic3C2×D312yescomplemented
154C3×#237—316no—
155C3×D3×D4—316no—
156C3×#235—316no—
157C2×C3×D12—32no—
158C2×C3×D12—32no—
159C2×C3×C4×D3—32no—
160C2×C3×C4×D3—32no—
161C2×C3×C4×D3—32no—
162C2×C3×C4×D3—32no—
163C2×C3×Dic6—32no—
164C2×C3×Dic6—32no—
165#3811—38no—
166#3811C2×D318yescomplemented
167D3×#67—316no—
168D3×#67—316no—
169C2×#627—32no—
170C2×#627—32no—
171C2×#627—62no—
172C2×#627C2×D312yescomplemented
173C2×#626—32no—
174C2×#626—32no—
175C2×#626C2×D312yescomplemented
176C2×#626C2×D312yescomplemented
177C2×#625—32no—
178C2×#625—32no—
179C2×#625—32no—
180C2×#625—62no—
181C2×#624—31no—
182C2×#624C2×D311yescharacteristic
183C2×#624C2×D312yescomplemented
184#3805—316no—
185#3805—316no—
186#3805—316no—
187#3805—616no—
188#3804—316no—
189#3804C2×D3116yescomplemented
190C2×D3×Dic3—32no—
191C2×D3×Dic3—32no—
192C2×D3×Dic3—32no—
193C2×D3×Dic3—32no—
194C2×D3×Dic3—32no—
195C2×D3×Dic3—32no—
196C2×D3×Dic3—32no—
197C2×D3×Dic3—32no—
198C2×D3×Dic3—32no—
199C2×D3×Dic3—316no—
200C2×D3×Dic3—316no—
201C2×D3×Dic3—61no—
202C2×D3×Dic3—61no—
203C2×D3×Dic3—68no—
204C2×D3×Dic3—61no—
205C2×D3×Dic3—61no—
206C2×D3×Dic3—62no—
207C2×D3×Dic3—62no—
208C2×D3×Dic3C2×D312yescomplemented
209#3802—38no—
210C4×D32—38no—
211C4×D32—38no—
212C4×D32—316no—
213#3798—316no—
214#3797—38no—
215#3796—316no—
216#3796—316no—
217#3795—316no—
218D3×Dic6—316no—
219C22×C33—22no—
220C22×C33C2412yes—
221C22×C33C2411yescharacteristic
222C2×C3×C3⋊D3—22no—
223C2×C3×C3⋊D3—24no—
224C2×C3×C3⋊D3—28no—
225C2×C3×C3⋊D3#4114yescomplemented
226C2×C3×C3⋊D3C2414yes—
227C2×C3×C3⋊D3C2412yes—
228C2×C3×C3⋊D3C2412yes—
229C2×C32×D3—24no—
230C2×C32×D3C2414yes—
231#1113—28no—
232C3×D32—28no—
233C3⋊(C3⋊Dic3)C2412yes—
234C3⋊(C3⋊Dic3)C2412yes—
235C3×C3⋊Dic3C2414yes—
236C32×Dic3C2412yes—
237C32×Dic3C2414yes—
238C32×Dic3C2412yes—
239C2×C3×#41—92no—
240C22×C3×D4—91no—
241C22×#67—91no—
242C22×#67—91no—
243C23×Dic3—91no—
244C23×Dic3—91no—
245D3×#41—932no—
246C2×#239—92no—
247C2×D3×Q8—92no—
248C2×#237—32no—
249C2×#237—92no—
250C2×#237—92no—
251C2×#237—92no—
252C2×#237—916no—
253C2×#237—92no—
254C2×#237—92no—
255C2×#237—92no—
256C2×#237—182no—
257C2×D3×D4—32no—
258C2×D3×D4—92no—
259C2×D3×D4—92no—
260C2×#235—32no—
261C2×#235—92no—
262C2×#235—92no—
263C22×C4×D3—91no—
264C22×C4×D3—92no—
265C22×C4×D3—92no—
266C22×C4×D3—92no—
267C22×C4×D3—181no—
268C22×Dic6—91no—
269C23×C32—21no—
270C23×C32—22no—
271C23×C32—32no—
272C23×C32—41no—
273C23×C32C22×D312yes—
274C23×C32C22×D311yescharacteristic
275C22×C3⋊D3—24no—
276C22×C3⋊D3C22×D312yes—
277C22×C3⋊D3C22×D311yescharacteristic
278C22×C3⋊D3C22×D314yes—
279C22×C3⋊D3C22×D311yescharacteristic
280C22×C3×D3—22no—
281C22×C3×D3—32no—
282C22×C3×D3—32no—
283C22×C3×D3—32no—
284C22×C3×D3—32no—
285C22×C3×D3—38no—
286C22×C3×D3—38no—
287C22×C3×D3—61no—
288C22×C3×D3—61no—
289C22×C3×D3—64no—
290C22×C3×D3—62no—
291C22×C3×D3—68no—
292C22×C3×D3—68no—
293C22×C3×D3—68no—
294C22×C3×D3C22×D312yes—
295C22×C3×D3C22×D312yes—
296C2×D32—24no—
297C2×D32—34no—
298C2×D32—38no—
299C2×D32—68no—
300C2×D32—64no—
301C2×D32C22×D314yes—
302C32×D4—38no—
303C2×C32×C4—31no—
304C2×C32×C4—32no—
305C2×C32×C4—31no—
306C2×C32×C4—34no—
307#638—38no—
308#638C22×D318yescomplemented
309C2×C3⋊Dic3—31no—
310C2×C3⋊Dic3—32no—
311C2×C3⋊Dic3—32no—
312C2×C3⋊Dic3—31no—
313C2×C3⋊Dic3—38no—
314C2×C3⋊Dic3—34no—
315C2×C3⋊Dic3—38no—
316C2×C3⋊Dic3—61no—
317C2×C3⋊Dic3—62no—
318C2×C3⋊Dic3—61no—
319C2×C3⋊Dic3—62no—
320C2×C3⋊Dic3—64no—
321C2×C3⋊Dic3—68no—
322C2×C3⋊Dic3—121no—
323C2×C3⋊Dic3—121no—
324C2×C3⋊Dic3—124no—
325C2×C3⋊Dic3C22×D312yes—
326C4×C3⋊D3—34no—
327C4×C3⋊D3—34no—
328C4×C3⋊D3—34no—
329C4×C3⋊D3—38no—
330C4×C3⋊D3—34no—
331#634—38no—
332C3×#67—28no—
333C3×#67—38no—
334C3×#67—38no—
335C3×#67—38no—
336C3×#67—38no—
337C3×#67—68no—
338C3×#67C22×D318yescomplemented
339C3×#67C22×D318yescomplemented
340C2×C3×Dic3—21no—
341C2×C3×Dic3—21no—
342C2×C3×Dic3—22no—
343C2×C3×Dic3—24no—
344C2×C3×Dic3—32no—
345C2×C3×Dic3—32no—
346C2×C3×Dic3—38no—
347C2×C3×Dic3—62no—
348C2×C3×Dic3C22×D312yes—
349C2×C3×Dic3C22×D312yes—
350C2×C3×Dic3C22×D312yes—
351C2×C3×Dic3C22×D312yes—
352C2×C3×Dic3C22×D318yescomplemented
353C3×D12—38no—
354C3×D12—38no—
355C3×C4×D3—38no—
356C3×C4×D3—38no—
357C3×C4×D3—38no—
358C3×C4×D3—38no—
359C3×Dic6—38no—
360C3×Dic6—38no—
361#627—38no—
362#627—38no—
363#627—68no—
364#627C22×D318yescomplemented
365#626—38no—
366#626—38no—
367#626C22×D318yescomplemented
368#626C22×D318yescomplemented
369#625—38no—
370#625—38no—
371#625—38no—
372#625—68no—
373#624—34no—
374#624C22×D314yes—
375#624C22×D318yescomplemented
376D3×Dic3—38no—
377D3×Dic3—38no—
378D3×Dic3—38no—
379D3×Dic3—38no—
380D3×Dic3—38no—
381D3×Dic3—38no—
382D3×Dic3—38no—
383D3×Dic3—38no—
384D3×Dic3—38no—
385D3×Dic3—68no—
386D3×Dic3—64no—
387D3×Dic3—64no—
388D3×Dic3—64no—
389D3×Dic3—64no—
390D3×Dic3—68no—
391D3×Dic3C22×D318yescomplemented
392C22×#41—271noSylow
393C2×C33—22no—
394C2×C33C2×#4112yescomplemented
395C2×C33C2511yescharacteristic
396C3×C3⋊D3—22no—
397C3×C3⋊D3—24no—
398C3×C3⋊D3C2×#4114yescomplemented
399C32×D3—24no—
400C24×C3—91no—
401C24×C3—91no—
402C23×D3—32no—
403C23×D3—32no—
404C23×D3—61no—
405C23×D3—92no—
406C23×D3—91no—
407C3×#41—916no—
408C2×C3×Q8—92no—
409C2×C3×D4—32no—
410C2×C3×D4—32no—
411C2×C3×D4—62no—
412C2×C3×D4—92no—
413C2×C3×D4—92no—
414C2×C3×D4—98no—
415C2×C3×D4—92no—
416C22×C3×C4—32no—
417C22×C3×C4—61no—
418C22×C3×C4—91no—
419C22×C3×C4—92no—
420C22×C3×C4—92no—
421C2×#67—32no—
422C2×#67—32no—
423C2×#67—32no—
424C2×#67—32no—
425C2×#67—62no—
426C2×#67—92no—
427C2×#67—92no—
428C2×#67—98no—
429C2×#67—98no—
430C2×#67—92no—
431C2×#67—92no—
432C2×#67—92no—
433C2×#67—182no—
434C2×#67D3212yescomplemented
435C22×Dic3—32no—
436C22×Dic3—91no—
437C22×Dic3—98no—
438C22×Dic3—92no—
439C22×Dic3—92no—
440C22×Dic3—92no—
441C22×Dic3—91no—
442C22×Dic3—91no—
443C22×Dic3—92no—
444C22×Dic3—91no—
445C22×Dic3—91no—
446C22×Dic3—91no—
447C22×Dic3—98no—
448C22×Dic3—182no—
449C22×Dic3—181no—
450C22×Dic3—182no—
451C22×Dic3—361no—
452C22×Dic3D3211yescharacteristic, complemented
453#239—916no—
454D3×Q8—916no—
455#237—316no—
456#237—916no—
457#237—916no—
458#237—916no—
459#237—916no—
460#237—916no—
461#237—916no—
462#237—1816no—
463D3×D4—316no—
464D3×D4—916no—
465D3×D4—916no—
466#235—316no—
467#235—916no—
468#235—916no—
469C2×D12—32no—
470C2×D12—32no—
471C2×D12—92no—
472C2×C4×D3—32no—
473C2×C4×D3—32no—
474C2×C4×D3—32no—
475C2×C4×D3—32no—
476C2×C4×D3—98no—
477C2×C4×D3—916no—
478C2×C4×D3—916no—
479C2×C4×D3—92no—
480C2×C4×D3—92no—
481C2×C4×D3—92no—
482C2×C4×D3—92no—
483C2×C4×D3—92no—
484C2×C4×D3—92no—
485C2×C4×D3—92no—
486C2×C4×D3—916no—
487C2×C4×D3—92no—
488C2×C4×D3—181no—
489C2×C4×D3—181no—
490C2×C4×D3—181no—
491C2×C4×D3—181no—
492C2×C4×D3—188no—
493C2×C4×D3—182no—
494C2×Dic6—32no—
495C2×Dic6—32no—
496C2×Dic6—98no—
497C2×Dic6—92no—
498C2×Dic6—92no—
499C2×Dic6—92no—
500C2×Dic6—182no—
501C22×C32—22no—
502C22×C32—24no—
503C22×C32—24no—
504C22×C32—22no—
505C22×C32—21no—
506C22×C32—22no—
507C22×C32—24no—
508C22×C32—34no—
509C22×C32—42no—
510C22×C32—41no—
511C22×C32—44no—
512C22×C32—44no—
513C22×C32—64no—
514C22×C32C23×D314yes—
515C22×C32C23×D312yes—
516C22×C32C23×D311yescharacteristic
517C22×C32C23×D312yes—
518C2×C3⋊D3—22no—
519C2×C3⋊D3—28no—
520C2×C3⋊D3—24no—
521C2×C3⋊D3#23714yescomplemented
522C2×C3⋊D3C23×D314yes—
523C2×C3⋊D3C23×D312yes—
524C2×C3⋊D3C23×D312yes—
525C2×C3×D3—24no—
526C2×C3×D3—24no—
527C2×C3×D3—24no—
528C2×C3×D3—38no—
529C2×C3×D3—34no—
530C2×C3×D3—34no—
531C2×C3×D3—34no—
532C2×C3×D3—34no—
533C2×C3×D3—44no—
534C2×C3×D3—64no—
535C2×C3×D3—62no—
536C2×C3×D3—62no—
537C2×C3×D3—64no—
538C2×C3×D3—616no—
539C2×C3×D3—616no—
540C2×C3×D3—616no—
541C2×C3×D3—64no—
542C2×C3×D3—64no—
543C2×C3×D3—64no—
544C2×C3×D3—64no—
545C2×C3×D3—124no—
546C2×C3×D3C23×D314yes—
547C2×C3×D3C23×D314yes—
548D32—28no—
549D32—616no—
550D32—68no—
551C32×C4—32no—
552C32×C4—34no—
553C32×C4—32no—
554C3⋊Dic3—32no—
555C3⋊Dic3—34no—
556C3⋊Dic3—34no—
557C3⋊Dic3—32no—
558C3⋊Dic3—62no—
559C3⋊Dic3—64no—
560C3⋊Dic3—62no—
561C3⋊Dic3—64no—
562C3⋊Dic3—122no—
563C3⋊Dic3—122no—
564C3⋊Dic3C23×D314yes—
565C3×Dic3—22no—
566C3×Dic3—22no—
567C3×Dic3—24no—
568C3×Dic3—34no—
569C3×Dic3—34no—
570C3×Dic3—64no—
571C3×Dic3C23×D314yes—
572C3×Dic3C23×D314yes—
573C3×Dic3C23×D314yes—
574C3×Dic3C23×D314yes—
575C2×#41—92no—
576C2×#41—272no—
577C2×#41—272no—
578C2×#41—272no—
579C2×#41—2716no—
580C22×Q8—271no—
581C22×D4—91no—
582C22×D4—271no—
583C22×D4—271no—
584C23×C4—271no—
585C23×C4—271no—
586C23×C4—271no—
587C33C22×#4111yescharacteristic, complemented, Sylow
588C23×C3—21no—
589C23×C3—22no—
590C23×C3—32no—
591C23×C3—32no—
592C23×C3—41no—
593C23×C3—62no—
594C23×C3—94no—
595C23×C3—91no—
596C23×C3—94no—
597C23×C3—91no—
598C23×C3—92no—
599C23×C3—184no—
600C23×C3—184no—
601C23×C3C2×D3211yescharacteristic
602C23×C3C2×D3212yes—
603C22×D3—32no—
604C22×D3—32no—
605C22×D3—32no—
606C22×D3—32no—
607C22×D3—38no—
608C22×D3—38no—
609C22×D3—61no—
610C22×D3—64no—
611C22×D3—61no—
612C22×D3—62no—
613C22×D3—68no—
614C22×D3—68no—
615C22×D3—68no—
616C22×D3—98no—
617C22×D3—94no—
618C22×D3—188no—
619C22×D3—184no—
620C22×D3C2×D3212yes—
621C3×Q8—98no—
622C3×D4—38no—
623C3×D4—38no—
624C3×D4—68no—
625C3×D4—98no—
626C3×D4—98no—
627C3×D4—98no—
628C2×C3×C4—32no—
629C2×C3×C4—32no—
630C2×C3×C4—32no—
631C2×C3×C4—32no—
632C2×C3×C4—38no—
633C2×C3×C4—62no—
634C2×C3×C4—64no—
635C2×C3×C4—61no—
636C2×C3×C4—61no—
637C2×C3×C4—94no—
638C2×C3×C4—98no—
639C2×C3×C4—98no—
640C2×C3×C4—92no—
641#67—38no—
642#67—38no—
643#67—38no—
644#67—38no—
645#67—68no—
646#67—98no—
647#67—98no—
648#67—98no—
649#67—98no—
650#67—98no—
651#67—188no—
652#67C2×D3218yescomplemented
653C2×Dic3—32no—
654C2×Dic3—32no—
655C2×Dic3—38no—
656C2×Dic3—62no—
657C2×Dic3—94no—
658C2×Dic3—98no—
659C2×Dic3—98no—
660C2×Dic3—92no—
661C2×Dic3—91no—
662C2×Dic3—92no—
663C2×Dic3—98no—
664C2×Dic3—91no—
665C2×Dic3—94no—
666C2×Dic3—94no—
667C2×Dic3—98no—
668C2×Dic3—94no—
669C2×Dic3—94no—
670C2×Dic3—94no—
671C2×Dic3—188no—
672C2×Dic3—182no—
673C2×Dic3—184no—
674C2×Dic3—181no—
675C2×Dic3—181no—
676C2×Dic3—182no—
677C2×Dic3—188no—
678C2×Dic3—364no—
679C2×Dic3—361no—
680C2×Dic3—361no—
681C2×Dic3C2×D3211yescharacteristic
682C2×Dic3C2×D3212yes—
683C2×Dic3C2×D3211yescharacteristic
684C2×Dic3C2×D3214yescomplemented
685D12—38no—
686D12—38no—
687D12—98no—
688C4×D3—38no—
689C4×D3—38no—
690C4×D3—38no—
691C4×D3—38no—
692C4×D3—98no—
693C4×D3—98no—
694C4×D3—98no—
695C4×D3—98no—
696C4×D3—98no—
697C4×D3—98no—
698C4×D3—98no—
699C4×D3—98no—
700C4×D3—184no—
701C4×D3—184no—
702C4×D3—184no—
703C4×D3—184no—
704C4×D3—188no—
705Dic6—38no—
706Dic6—38no—
707Dic6—98no—
708Dic6—98no—
709Dic6—98no—
710Dic6—188no—
711C2×C32—22no—
712C2×C32—24no—
713C2×C32—24no—
714C2×C32—22no—
715C2×C32—24no—
716C2×C32—21no—
717C2×C32—22no—
718C2×C32—42no—
719C2×C32—41no—
720C2×C32—44no—
721C2×C32—44no—
722C2×C32—64no—
723C2×C32C2×#23712yescomplemented
724C2×C32D3×#4114yescomplemented
725C2×C32C24×D311yescharacteristic
726C2×C32C24×D312yes—
727C3⋊D3—22no—
728C3⋊D3—24no—
729C3⋊D3C2×#23714yescomplemented
730C3×D3—24no—
731C3×D3—24no—
732C3×D3—38no—
733C3×D3—44no—
734C3×D3—64no—
735C3×D3—64no—
736C3×D3—64no—
737C3×D3—64no—
738C3×D3—64no—
739C3×D3—124no—
740C24—91no—
741C24—91no—
742C24—271no—
743#41—916no—
744#41—2716no—
745#41—2716no—
746#41—2716no—
747C2×Q8—92no—
748C2×Q8—272no—
749C2×Q8—278no—
750C2×D4—32no—
751C2×D4—92no—
752C2×D4—92no—
753C2×D4—98no—
754C2×D4—92no—
755C2×D4—272no—
756C2×D4—278no—
757C2×D4—278no—
758C2×D4—272no—
759C22×C4—31no—
760C22×C4—91no—
761C22×C4—92no—
762C22×C4—92no—
763C22×C4—271no—
764C22×C4—271no—
765C22×C4—278no—
766C22×C4—271no—
767C22×C4—271no—
768C22×C4—272no—
769C22×C4—278no—
770C22×C4—271no—
771C22×C4—278no—
772C22×C4—272no—
773C22×C4—271no—
774C22×C3—24no—
775C22×C3—22no—
776C22×C3—24no—
777C22×C3—22no—
778C22×C3—24no—
779C22×C3—22no—
780C22×C3—21no—
781C22×C3—34no—
782C22×C3—34no—
783C22×C3—44no—
784C22×C3—44no—
785C22×C3—42no—
786C22×C3—41no—
787C22×C3—64no—
788C22×C3—64no—
789C22×C3—64no—
790C22×C3—94no—
791C22×C3—92no—
792C22×C3—92no—
793C22×C3—94no—
794C22×C3—124no—
795C22×C3—188no—
796C22×C3—188no—
797C22×C3—182no—
798C22×C3—184no—
799C22×C3C22×D3212yes—
800C22×C3C22×D3214yes—
801C22×C3C22×D3211yescharacteristic
802C22×C3C22×D3212yes—
803C2×D3—24no—
804C2×D3—38no—
805C2×D3—34no—
806C2×D3—34no—
807C2×D3—34no—
808C2×D3—34no—
809C2×D3—62no—
810C2×D3—62no—
811C2×D3—64no—
812C2×D3—64no—
813C2×D3—616no—
814C2×D3—616no—
815C2×D3—616no—
816C2×D3—64no—
817C2×D3—64no—
818C2×D3—64no—
819C2×D3—64no—
820C2×D3—124no—
821C2×D3—1816no—
822C2×D3—188no—
823C2×D3C22×D3214yes—
824C3×C4—34no—
825C3×C4—34no—
826C3×C4—34no—
827C3×C4—34no—
828C3×C4—64no—
829C3×C4—62no—
830C3×C4—62no—
831C3×C4—94no—
832Dic3—34no—
833Dic3—34no—
834Dic3—64no—
835Dic3—94no—
836Dic3—92no—
837Dic3—94no—
838Dic3—92no—
839Dic3—184no—
840Dic3—182no—
841Dic3—182no—
842Dic3—184no—
843Dic3—362no—
844Dic3—362no—
845Dic3C22×D3212yes—
846Dic3C22×D3214yes—
847Dic3C22×D3212yes—
848C32—21no—
849C32—22no—
850C32—41no—
851C32C22×#23711yescharacteristic, complemented
852C32C2×D3×#4112yescomplemented
853C23—32no—
854C23—94no—
855C23—91no—
856C23—94no—
857C23—92no—
858C23—91no—
859C23—184no—
860C23—184no—
861C23—274no—
862C23—544no—
863C23D3311yescharacteristic
864Q8—98no—
865Q8—278no—
866D4—38no—
867D4—98no—
868D4—98no—
869D4—98no—
870D4—278no—
871D4—278no—
872C2×C4—34no—
873C2×C4—31no—
874C2×C4—31no—
875C2×C4—32no—
876C2×C4—94no—
877C2×C4—98no—
878C2×C4—98no—
879C2×C4—92no—
880C2×C4—274no—
881C2×C4—274no—
882C2×C4—274no—
883C2×C4—274no—
884C2×C4—278no—
885C2×C4—274no—
886C2×C4—278no—
887C2×C4—274no—
888C2×C4—271no—
889C2×C4—271no—
890C2×C3—24no—
891C2×C3—22no—
892C2×C3—24no—
893C2×C3—22no—
894C2×C3—24no—
895C2×C3—22no—
896C2×C3—21no—
897C2×C3—44no—
898C2×C3—44no—
899C2×C3—42no—
900C2×C3—41no—
901C2×C3—64no—
902C2×C3—64no—
903C2×C3—94no—
904C2×C3—124no—
905C2×C3—182no—
906C2×C3—184no—
907C2×C3#6430612yescomplemented
908C2×C3D3×#23714yescomplemented
909C2×C3C23×D3211yescharacteristic
910C2×C3C23×D3212yes—
911D3—24no—
912D3—38no—
913D3—64no—
914D3—64no—
915D3—64no—
916D3—64no—
917D3—64no—
918D3—124no—
919C22—22no—
920C22—34no—
921C22—64no—
922C22—94no—
923C22—92no—
924C22—94no—
925C22—92no—
926C22—188no—
927C22—188no—
928C22—182no—
929C22—184no—
930C22—548no—
931C22C2×D3312yes—
932C22C2×D3311yescharacteristic
933C4—32no—
934C4—32no—
935C4—34no—
936C4—94no—
937C4—272no—
938C4—272no—
939C3—21no—
940C3—22no—
941C3—41no—
942C3C2×#6430611yescharacteristic, complemented
943C3C2×D3×#23712yescomplemented
944C2—22no—
945C2—64no—
946C2—94no—
947C2—182no—
948C2—184no—
949C2#1172440712yesdirect product factor
950C2C22×D3311yescharacteristic
subgroupG/H
centerC22C2×D33
commutator, cosocleC2×C33C25
FrattiniC2C22×D33
FittingC23×C33C23
socleC22×C33C24
hypercenterC23D33
hypocenterC33C22×#41
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C2×#89049C2semidirect
2. C22×Dic3×C3⋊D3C2semidirect
3. C2×#89029C2semidirect
4. C2×C3×#3811C2semidirect
5. C2×C3×#3804C2semidirect
6. C2×#88964C2semidirect
7. C2×#88960C2semidirect
8. C2×#88957C2semidirect
9. C2×#88953C2semidirect
10. C2×#88949C2semidirect
11. #11724407C2direct (N × H)
12. C2×D32×Dic3C2semidirect
18. C22×C3⋊(C3⋊Dic3)C22semidirect
19. C2×C3×#638C22semidirect
20. C2×C32×#67C22semidirect
21. C22×C32×Dic3C22semidirect
22. #89049C22semidirect
23. C2×#6295C22semidirect
25. C2×#6293C22semidirect
26. C2×#6290C22semidirect
29. C2×Dic3×C3⋊D3C22semidirect
30. C2×Dic3×C3⋊D3C22semidirect
31. C2×Dic3×C3⋊D3C22semidirect
32. C2×Dic3×C3⋊D3C22semidirect
33. #89029C22semidirect
34. C2×D3×C3⋊Dic3C22semidirect
35. C3×#3811C22semidirect
36. C2×C3×#627C22semidirect
37. C2×C3×#626C22semidirect
38. C2×C3×#626C22semidirect
40. C2×C3×#624C22semidirect
41. C3×#3804C22semidirect
42. C2×C3×D3×Dic3C22semidirect
43. #88964C22semidirect
44. #88960C22semidirect
45. #88957C22semidirect
46. #88953C22semidirect
47. #88949C22semidirect
48. D32×Dic3C22semidirect
55. C2×#3811D3semidirect
63. C2×#3804D3semidirect
92. C2×C3⋊(C3⋊Dic3)C23semidirect
93. C3×#638C23semidirect
95. C32×#67C23semidirect
99. C2×C32×Dic3C23semidirect
100. #6295C23semidirect
102. #6293C23semidirect
103. #6290C23semidirect
106. Dic3×C3⋊D3C23semidirect
107. Dic3×C3⋊D3C23semidirect
108. Dic3×C3⋊D3C23semidirect
109. D3×C3⋊Dic3C23semidirect
110. C3×#627C23semidirect
111. C3×#626C23semidirect
112. C3×#626C23semidirect
114. C3×#624C23semidirect
115. C3×D3×Dic3C23semidirect
128. C2×#638C2×D3semidirect
149. C2×C3×#67C2×D3semidirect
150. C2×C3×#67C2×D3semidirect
153. C22×C3×Dic3C2×D3semidirect
166. #3811C2×D3semidirect
172. C2×#627C2×D3semidirect
175. C2×#626C2×D3semidirect
176. C2×#626C2×D3semidirect
183. C2×#624C2×D3semidirect
189. #3804C2×D3semidirect
208. C2×D3×Dic3C2×D3semidirect
225. C2×C3×C3⋊D3#41semidirect
308. #638C22×D3semidirect
338. C3×#67C22×D3semidirect
339. C3×#67C22×D3semidirect
352. C2×C3×Dic3C22×D3semidirect
364. #627C22×D3semidirect
367. #626C22×D3semidirect
368. #626C22×D3semidirect
375. #624C22×D3semidirect
391. D3×Dic3C22×D3semidirect
394. C2×C33C2×#41semidirect
398. C3×C3⋊D3C2×#41semidirect
434. C2×#67D32semidirect
452. C22×Dic3D32semidirect
521. C2×C3⋊D3#237semidirect
587. C33C22×#41semidirect
652. #67C2×D32semidirect
684. C2×Dic3C2×D32semidirect
723. C2×C32C2×#237semidirect
724. C2×C32D3×#41semidirect
729. C3⋊D3C2×#237semidirect
851. C32C22×#237semidirect
852. C32C2×D3×#41semidirect
907. C2×C3#64306semidirect
908. C2×C3D3×#237semidirect
942. C3C2×#64306semidirect
943. C3C2×D3×#237semidirect
949. C2#11724407direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#890492
C22×Dic3×C3⋊D32
C2×#890292
C2×C3×#38112
C2×C3×#38042
C2×#889642
C2×#889602
C2×#889572
C2×#889532
C2×#889492
#117244072
C2×D32×Dic32
C2×D3×#2373
C2×#643063