Finite Group Databasebeta

← C2×#11724411 #13181318

Subgroups — C2×#11724411 #13181318

Order 1728.

4402 conjugacy classes of subgroups.

The subgroup lattice has 972 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89046C211yesmaximal, characteristic, complemented
2C2×#89039C212yesmaximal, complemented
3C22×#6289C211yesmaximal, characteristic, complemented
4C2×C3×#3805C211yesmaximal, characteristic, complemented
5C2×C3×#3804C212yesmaximal, complemented
6C2×#88965C211yesmaximal, characteristic, complemented
7C2×#88962C212yesmaximal, complemented
8C2×#88959C211yesmaximal, characteristic, complemented
9C2×#88958C211yesmaximal, characteristic, complemented
10C2×#88954C211yesmaximal, characteristic, complemented
11#11724411C2116yesmaximal, direct product factor
12C2×D3×#624C212yesmaximal, complemented
13C2×#64312—32nomaximal
14C2×#64306—31nomaximal
15C23×C3⋊(C3⋊D3)C2211yescharacteristic
16C22×D3×C3⋊D3C2212yes—
17C2×C3×#638C2212yescomplemented
18C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
19C2×C32×#67C2212yescomplemented
20C22×C32×Dic3C2211yescharacteristic, complemented
21C2×#6296C2211yescharacteristic, complemented
22C2×#6295C2211yescharacteristic, complemented
23#89046C2218yescomplemented
24C2×#6294C2212yescomplemented
25#89039C22116yescomplemented
26C2×#6292C2212yescomplemented
27C2×#6291C2212yescomplemented
28C2×#6289C2211yescharacteristic
29C2×#6289C2211yescharacteristic
30C2×#6289C2212yes—
31C2×#6289C2218yescomplemented
32C2×#6289C2211yescharacteristic, complemented
33C2×#6289C2211yescharacteristic, complemented
34C2×C3×#627C2212yescomplemented
35C2×C3×#627C2211yescharacteristic, complemented
36C2×C3×#626C2212yescomplemented
37C2×C3×#625C2211yescharacteristic, complemented
38C2×C3×#624C2212yescomplemented
39C3×#3805C2218yescomplemented
40C3×#3804C22116yescomplemented
41C2×C3×D3×Dic3C2212yescomplemented
42C2×C3×D3×Dic3C2212yescomplemented
43#88965C2218yescomplemented
44#88962C22116yescomplemented
45#88959C2218yescomplemented
46#88958C2218yescomplemented
47#88954C2218yescomplemented
48D3×#624C22116yescomplemented
49C2×D4×C3⋊D3—32no—
50C22×C4×C3⋊D3—31no—
51C2×C3×#237—32no—
52C2×C3×#237—32no—
53C2×C3×#235—32no—
54C2×#3811—32no—
55C2×#3811—32no—
56C2×#3811—32no—
57C2×#3811—62no—
58C22×#624—32no—
59C22×#624—32no—
60C22×#624—61no—
61C2×#3805—31no—
62C2×#3805D311yescharacteristic, complemented
63C2×#3804—32no—
64C2×#3804—32no—
65C2×#3804—32no—
66C2×#3804D312yescomplemented
67#64312—332no—
68#64306—316no—
69C2×#3802—31no—
70C2×C4×D32—32no—
71C2×C4×D32—32no—
72C2×#3799—32no—
73C2×#3799—32no—
74C2×#3798—31no—
75C2×#3798—31no—
76C2×#3797—31no—
77C2×#3797—32no—
78C2×#3796—32no—
79C23×C33C2311yescharacteristic
80C22×C3⋊(C3⋊D3)—24no—
81C22×C3⋊(C3⋊D3)C2311yescharacteristic
82C22×C3⋊(C3⋊D3)C2314yes—
83C22×C3⋊(C3⋊D3)C2311yescharacteristic
84C22×C3×C3⋊D3C2312yes—
85C22×C32×D3C2312yes—
86C2×D3×C3⋊D3—28no—
87C2×D3×C3⋊D3C2318yes—
88C3×#638C2318yescomplemented
89C2×C3×C3⋊Dic3C2311yescharacteristic
90C2×C3×C3⋊Dic3C2312yes—
91C2×C3×C3⋊Dic3C2311yescharacteristic
92C2×C3×C3⋊Dic3C2314yescomplemented
93C32×#67C2318yescomplemented
94C2×C32×Dic3C2311yescharacteristic
95C2×C32×Dic3C2312yes—
96C2×C32×Dic3C2311yescharacteristic
97C2×C32×Dic3C2314yescomplemented
98#6296C2314yescomplemented
99#6295C2314yescomplemented
100#6294C2318yescomplemented
101#6292C2318yescomplemented
102#6291C2318yescomplemented
103#6289C2314yes—
104#6289C2318yes—
105#6289C2314yes—
106#6289C2314yescomplemented
107#6289C2314yescomplemented
108C3×#627C2318yescomplemented
109C3×#627C2314yescomplemented
110C3×#626C2318yescomplemented
111C3×#625C2314yescomplemented
112C3×#624C2318yescomplemented
113C3×D3×Dic3C2318yescomplemented
114C3×D3×Dic3C2318yescomplemented
115C2×D3×#41—92no—
116C2×D3×#41—91no—
117C23×C3⋊D3—32no—
118C23×C3⋊D3—31no—
119C23×C3⋊D3—32no—
120C23×C3⋊D3—61no—
121C23×C3⋊D3—62no—
122C23×C3⋊D3—121no—
123C22×D32—32no—
124C22×D32—32no—
125C22×D32—62no—
126C2×C32×D4—32no—
127C22×C32×C4—31no—
128C2×#638—32no—
129C2×#638C2×D312yescomplemented
130C22×C3⋊Dic3C2×D311yescharacteristic, complemented
131D4×C3⋊D3—316no—
132C2×C4⋊(C3⋊D3)—32no—
133C2×C4×C3⋊D3—31no—
134C2×C4×C3⋊D3—32no—
135C2×C4×C3⋊D3—31no—
136C2×C4×C3⋊D3—31no—
137C2×C4×C3⋊D3—31no—
138C2×C4×C3⋊D3—38no—
139C2×C3×#67—22no—
140C2×C3×#67—32no—
141C2×C3×#67—32no—
142C2×C3×#67—32no—
143C2×C3×#67—32no—
144C2×C3×#67—62no—
145C2×C3×#67C2×D312yescomplemented
146C2×C3×#67C2×D312yescomplemented
147C22×C3×Dic3—21no—
148C22×C3×Dic3—32no—
149C22×C3×Dic3—32no—
150C22×C3×Dic3—32no—
151C22×C3×Dic3—61no—
152C22×C3×Dic3C2×D312yescomplemented
153C3×#237—316no—
154C3×#237—316no—
155C3×#235—316no—
156C2×C3×D12—32no—
157C2×C3×C4×D3—32no—
158C2×C3×C4×D3—32no—
159C2×C3×C4×D3—32no—
160C2×C3×C4×D3—32no—
161C2×C3×Dic6—32no—
162C2×C3×Dic6—32no—
163C2×C3×Dic6—32no—
164#3811—316no—
165#3811—316no—
166#3811—316no—
167#3811—616no—
168C2×#627—31no—
169C2×#627—32no—
170C2×#627C2×D311yescharacteristic, complemented
171C2×#627C2×D312yescomplemented
172C2×#626—32no—
173C2×#626—32no—
174C2×#626—32no—
175C2×#626—32no—
176C2×#626—32no—
177C2×#626—62no—
178C2×#626—62no—
179C2×#626C2×D312yescomplemented
180C2×#625—31no—
181C2×#625C2×D311yescharacteristic, complemented
182C2×#624—32no—
183C2×#624—32no—
184C2×#624—32no—
185C2×#624—32no—
186C2×#624—32no—
187C2×#624—32no—
188C2×#624—32no—
189C2×#624—316no—
190C2×#624—316no—
191C2×#624—61no—
192C2×#624—61no—
193C2×#624—68no—
194C2×#624—61no—
195C2×#624—61no—
196C2×#624—62no—
197C2×#624C2×D312yescomplemented
198#3805—38no—
199#3805C2×D318yescomplemented
200#3804—316no—
201#3804—316no—
202#3804—316no—
203#3804C2×D3116yescomplemented
204C2×D3×Dic3—32no—
205C2×D3×Dic3—32no—
206C2×D3×Dic3C2×D312yescomplemented
207C2×D3×Dic3C2×D312yescomplemented
208#3802—38no—
209C4×D32—316no—
210C4×D32—316no—
211#3799—316no—
212#3799—316no—
213#3798—38no—
214#3798—38no—
215#3797—38no—
216#3797—316no—
217#3796—316no—
218C22×C33—22no—
219C22×C33C2412yes—
220C22×C33C2411yescharacteristic
221C2×C3⋊(C3⋊D3)—22no—
222C2×C3⋊(C3⋊D3)—28no—
223C2×C3⋊(C3⋊D3)#4114yescomplemented
224C2×C3⋊(C3⋊D3)C2412yes—
225C2×C3⋊(C3⋊D3)C2412yes—
226C2×C3×C3⋊D3—24no—
227C2×C3×C3⋊D3C2414yes—
228C2×C32×D3—24no—
229C2×C32×D3C2414yes—
230D3×C3⋊D3—216no—
231C3×C3⋊Dic3C2412yes—
232C3×C3⋊Dic3C2414yes—
233C3×C3⋊Dic3C2412yes—
234C32×Dic3C2412yes—
235C32×Dic3C2414yes—
236C32×Dic3C2412yes—
237C2×C3×#41—92no—
238C2×C3×#41—91no—
239D3×#41—932no—
240D3×#41—916no—
241C2×#239—91no—
242C2×#239—92no—
243C2×D3×Q8—92no—
244C2×D3×Q8—91no—
245C2×#237—32no—
246C2×#237—32no—
247C2×#237—92no—
248C2×#237—91no—
249C2×#237—92no—
250C2×D3×D4—92no—
251C2×D3×D4—91no—
252C2×D3×D4—92no—
253C2×D3×D4—92no—
254C2×D3×D4—92no—
255C2×D3×D4—182no—
256C2×#235—32no—
257C2×#235—92no—
258C2×#235—92no—
259C2×#235—92no—
260C2×#235—91no—
261C22×C4×D3—92no—
262C22×C4×D3—92no—
263C22×C4×D3—92no—
264C22×C4×D3—92no—
265C22×C4×D3—91no—
266C22×C4×D3—181no—
267C23×C32—21no—
268C23×C32—22no—
269C23×C32—32no—
270C23×C32—41no—
271C23×C32C22×D312yes—
272C23×C32C22×D311yescharacteristic
273C22×C3⋊D3—31no—
274C22×C3⋊D3—32no—
275C22×C3⋊D3—32no—
276C22×C3⋊D3—38no—
277C22×C3⋊D3—31no—
278C22×C3⋊D3—34no—
279C22×C3⋊D3—38no—
280C22×C3⋊D3—62no—
281C22×C3⋊D3—61no—
282C22×C3⋊D3—61no—
283C22×C3⋊D3—64no—
284C22×C3⋊D3—62no—
285C22×C3⋊D3—68no—
286C22×C3⋊D3—64no—
287C22×C3⋊D3—68no—
288C22×C3⋊D3—68no—
289C22×C3⋊D3—68no—
290C22×C3⋊D3—121no—
291C22×C3⋊D3—121no—
292C22×C3⋊D3—124no—
293C22×C3⋊D3—128no—
294C22×C3⋊D3—128no—
295C22×C3⋊D3C22×D312yes—
296C22×C3×D3—22no—
297C22×C3×D3—32no—
298C22×C3×D3—32no—
299C22×C3×D3—62no—
300C22×C3×D3C22×D312yes—
301C22×C3×D3C22×D312yes—
302C2×D32—38no—
303C2×D32—38no—
304C2×D32—68no—
305C2×D32—68no—
306C2×D32—68no—
307C2×D32—128no—
308C32×D4—38no—
309C2×C32×C4—32no—
310C2×C32×C4—31no—
311C2×C32×C4—31no—
312C2×C32×C4—34no—
313#638—38no—
314#638C22×D318yescomplemented
315C2×C3⋊Dic3C22×D311yescharacteristic
316C2×C3⋊Dic3C22×D312yes—
317C2×C3⋊Dic3C22×D311yescharacteristic
318C2×C3⋊Dic3C22×D314yescomplemented
319C4⋊(C3⋊D3)—38no—
320C4×C3⋊D3—38no—
321C4×C3⋊D3—34no—
322C4×C3⋊D3—34no—
323C4×C3⋊D3—34no—
324C4×C3⋊D3—34no—
325C3×#67—28no—
326C3×#67—38no—
327C3×#67—38no—
328C3×#67—38no—
329C3×#67—38no—
330C3×#67—68no—
331C3×#67C22×D318yescomplemented
332C3×#67C22×D318yescomplemented
333C2×C3×Dic3—21no—
334C2×C3×Dic3—21no—
335C2×C3×Dic3—22no—
336C2×C3×Dic3—24no—
337C2×C3×Dic3—32no—
338C2×C3×Dic3—32no—
339C2×C3×Dic3—32no—
340C2×C3×Dic3—32no—
341C2×C3×Dic3—38no—
342C2×C3×Dic3—38no—
343C2×C3×Dic3—38no—
344C2×C3×Dic3—61no—
345C2×C3×Dic3—61no—
346C2×C3×Dic3—62no—
347C2×C3×Dic3—64no—
348C2×C3×Dic3C22×D312yes—
349C2×C3×Dic3C22×D312yes—
350C2×C3×Dic3C22×D312yes—
351C2×C3×Dic3C22×D312yes—
352C2×C3×Dic3C22×D318yescomplemented
353C3×D12—38no—
354C3×C4×D3—38no—
355C3×C4×D3—38no—
356C3×C4×D3—38no—
357C3×C4×D3—38no—
358C3×Dic6—38no—
359C3×Dic6—38no—
360C3×Dic6—38no—
361#627—34no—
362#627—38no—
363#627C22×D314yescomplemented
364#627C22×D318yescomplemented
365#626—38no—
366#626—38no—
367#626—38no—
368#626—38no—
369#626—38no—
370#626—68no—
371#626—68no—
372#626C22×D318yescomplemented
373#625—34no—
374#625C22×D314yescomplemented
375#624—38no—
376#624—38no—
377#624—38no—
378#624—38no—
379#624—38no—
380#624—38no—
381#624—38no—
382#624—64no—
383#624—64no—
384#624—68no—
385#624—64no—
386#624—64no—
387#624C22×D318yescomplemented
388D3×Dic3—38no—
389D3×Dic3—38no—
390D3×Dic3C22×D318yescomplemented
391D3×Dic3C22×D318yescomplemented
392C22×#41—271noSylow
393C2×C33—22no—
394C2×C33C2×#4112yescomplemented
395C2×C33C2511yescharacteristic
396C3⋊(C3⋊D3)—22no—
397C3⋊(C3⋊D3)C2×#4114yescomplemented
398C3×C3⋊D3—24no—
399C32×D3—24no—
400C23×D3—92no—
401C23×D3—92no—
402C23×D3—91no—
403C23×D3—92no—
404C23×D3—92no—
405C23×D3—182no—
406C23×D3—181no—
407C23×D3—182no—
408C23×D3—361no—
409C3×#41—916no—
410C3×#41—98no—
411C2×C3×Q8—91no—
412C2×C3×Q8—92no—
413C2×C3×D4—32no—
414C2×C3×D4—32no—
415C2×C3×D4—62no—
416C2×C3×D4—92no—
417C2×C3×D4—91no—
418C2×C3×D4—92no—
419C22×C3×C4—32no—
420C22×C3×C4—61no—
421C22×C3×C4—92no—
422C22×C3×C4—92no—
423C22×C3×C4—92no—
424C22×C3×C4—91no—
425C2×#67—32no—
426C2×#67—32no—
427C2×#67—32no—
428C2×#67—32no—
429C2×#67—62no—
430C2×#67—92no—
431C2×#67—92no—
432C2×#67—92no—
433C2×#67—92no—
434C2×#67—182no—
435C2×#67D3212yescomplemented
436C22×Dic3—32no—
437C22×Dic3—32no—
438C22×Dic3—32no—
439C22×Dic3—61no—
440C22×Dic3—92no—
441C22×Dic3D3211yescharacteristic, complemented
442#239—98no—
443#239—916no—
444D3×Q8—916no—
445D3×Q8—98no—
446#237—316no—
447#237—316no—
448#237—916no—
449#237—98no—
450#237—916no—
451D3×D4—916no—
452D3×D4—98no—
453D3×D4—916no—
454D3×D4—916no—
455D3×D4—916no—
456D3×D4—1816no—
457#235—316no—
458#235—916no—
459#235—916no—
460#235—916no—
461#235—98no—
462C2×D12—32no—
463C2×D12—92no—
464C2×D12—92no—
465C2×D12—91no—
466C2×D12—92no—
467C2×D12—182no—
468C2×C4×D3—32no—
469C2×C4×D3—32no—
470C2×C4×D3—32no—
471C2×C4×D3—32no—
472C2×C4×D3—916no—
473C2×C4×D3—916no—
474C2×C4×D3—916no—
475C2×C4×D3—92no—
476C2×C4×D3—92no—
477C2×C4×D3—92no—
478C2×C4×D3—92no—
479C2×C4×D3—92no—
480C2×C4×D3—92no—
481C2×C4×D3—916no—
482C2×C4×D3—92no—
483C2×C4×D3—92no—
484C2×C4×D3—91no—
485C2×C4×D3—91no—
486C2×C4×D3—92no—
487C2×C4×D3—91no—
488C2×C4×D3—91no—
489C2×C4×D3—98no—
490C2×C4×D3—181no—
491C2×C4×D3—181no—
492C2×C4×D3—181no—
493C2×C4×D3—181no—
494C2×C4×D3—188no—
495C2×C4×D3—182no—
496C2×Dic6—32no—
497C2×Dic6—32no—
498C2×Dic6—32no—
499C2×Dic6—92no—
500C2×Dic6—91no—
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×D312yes—
517C22×C32C23×D311yescharacteristic
518C2×C3⋊D3—24no—
519C2×C3⋊D3—34no—
520C2×C3⋊D3—38no—
521C2×C3⋊D3—34no—
522C2×C3⋊D3—32no—
523C2×C3⋊D3—34no—
524C2×C3⋊D3—32no—
525C2×C3⋊D3—68no—
526C2×C3⋊D3—64no—
527C2×C3⋊D3—62no—
528C2×C3⋊D3—62no—
529C2×C3⋊D3—64no—
530C2×C3⋊D3—64no—
531C2×C3⋊D3—68no—
532C2×C3⋊D3—62no—
533C2×C3⋊D3—616no—
534C2×C3⋊D3—616no—
535C2×C3⋊D3—616no—
536C2×C3⋊D3—64no—
537C2×C3⋊D3—64no—
538C2×C3⋊D3—124no—
539C2×C3⋊D3—122no—
540C2×C3⋊D3—122no—
541C2×C3⋊D3—1216no—
542C2×C3⋊D3—124no—
543C2×C3⋊D3—1216no—
544C2×C3⋊D3—124no—
545C2×C3⋊D3C23×D314yes—
546C2×C3×D3—24no—
547C2×C3×D3—24no—
548C2×C3×D3—24no—
549C2×C3×D3—34no—
550C2×C3×D3—34no—
551C2×C3×D3—44no—
552C2×C3×D3—64no—
553C2×C3×D3—64no—
554C2×C3×D3—64no—
555C2×C3×D3—124no—
556C2×C3×D3C23×D314yes—
557C2×C3×D3C23×D314yes—
558D32—616no—
559D32—616no—
560D32—1216no—
561C32×C4—34no—
562C32×C4—32no—
563C32×C4—32no—
564C3⋊Dic3C23×D312yes—
565C3⋊Dic3C23×D314yes—
566C3⋊Dic3C23×D312yes—
567C3×Dic3—22no—
568C3×Dic3—22no—
569C3×Dic3—24no—
570C3×Dic3—34no—
571C3×Dic3—34no—
572C3×Dic3—34no—
573C3×Dic3—34no—
574C3×Dic3—62no—
575C3×Dic3—62no—
576C3×Dic3—64no—
577C3×Dic3C23×D314yes—
578C3×Dic3C23×D314yes—
579C3×Dic3C23×D314yes—
580C3×Dic3C23×D314yes—
581C2×#41—92no—
582C2×#41—91no—
583C2×#41—271no—
584C2×#41—271no—
585C2×#41—271no—
586C2×#41—272no—
587C2×#41—2716no—
588C22×Q8—271no—
589C22×D4—272no—
590C22×D4—271no—
591C23×C4—271no—
592C23×C4—272no—
593C33C22×#4111yescharacteristic, complemented, Sylow
594C23×C3—21no—
595C23×C3—22no—
596C23×C3—32no—
597C23×C3—32no—
598C23×C3—41no—
599C23×C3—62no—
600C23×C3—92no—
601C23×C3C2×D3212yes—
602C23×C3C2×D3211yescharacteristic
603C22×D3—32no—
604C22×D3—32no—
605C22×D3—62no—
606C22×D3—98no—
607C22×D3—98no—
608C22×D3—91no—
609C22×D3—92no—
610C22×D3—91no—
611C22×D3—92no—
612C22×D3—94no—
613C22×D3—98no—
614C22×D3—98no—
615C22×D3—188no—
616C22×D3—181no—
617C22×D3—184no—
618C22×D3—181no—
619C22×D3—182no—
620C22×D3—182no—
621C22×D3—188no—
622C22×D3—188no—
623C22×D3—188no—
624C22×D3—188no—
625C22×D3—184no—
626C22×D3—188no—
627C22×D3—188no—
628C22×D3—361no—
629C22×D3—364no—
630C22×D3—361no—
631C22×D3—368no—
632C22×D3—368no—
633C22×D3—368no—
634C22×D3C2×D3212yes—
635C3×Q8—94no—
636C3×Q8—98no—
637C3×D4—38no—
638C3×D4—38no—
639C3×D4—68no—
640C3×D4—98no—
641C3×D4—94no—
642C3×D4—98no—
643C2×C3×C4—32no—
644C2×C3×C4—32no—
645C2×C3×C4—32no—
646C2×C3×C4—32no—
647C2×C3×C4—38no—
648C2×C3×C4—64no—
649C2×C3×C4—61no—
650C2×C3×C4—61no—
651C2×C3×C4—62no—
652C2×C3×C4—98no—
653C2×C3×C4—98no—
654C2×C3×C4—98no—
655C2×C3×C4—91no—
656C2×C3×C4—92no—
657C2×C3×C4—91no—
658C2×C3×C4—94no—
659#67—38no—
660#67—38no—
661#67—38no—
662#67—38no—
663#67—68no—
664#67—98no—
665#67—98no—
666#67—98no—
667#67—98no—
668#67—188no—
669#67C2×D3218yescomplemented
670C2×Dic3—32no—
671C2×Dic3—32no—
672C2×Dic3—32no—
673C2×Dic3—32no—
674C2×Dic3—38no—
675C2×Dic3—38no—
676C2×Dic3—38no—
677C2×Dic3—61no—
678C2×Dic3—61no—
679C2×Dic3—62no—
680C2×Dic3—64no—
681C2×Dic3—98no—
682C2×Dic3C2×D3212yes—
683C2×Dic3C2×D3211yescharacteristic
684C2×Dic3C2×D3211yescharacteristic
685C2×Dic3C2×D3214yescomplemented
686D12—38no—
687D12—98no—
688D12—98no—
689D12—94no—
690D12—98no—
691D12—188no—
692C4×D3—38no—
693C4×D3—38no—
694C4×D3—38no—
695C4×D3—38no—
696C4×D3—98no—
697C4×D3—98no—
698C4×D3—98no—
699C4×D3—98no—
700C4×D3—98no—
701C4×D3—98no—
702C4×D3—98no—
703C4×D3—98no—
704C4×D3—94no—
705C4×D3—94no—
706C4×D3—98no—
707C4×D3—94no—
708C4×D3—94no—
709C4×D3—184no—
710C4×D3—184no—
711C4×D3—184no—
712C4×D3—184no—
713C4×D3—188no—
714Dic6—38no—
715Dic6—38no—
716Dic6—38no—
717Dic6—98no—
718Dic6—94no—
719C2×C32—22no—
720C2×C32—24no—
721C2×C32—24no—
722C2×C32—22no—
723C2×C32—24no—
724C2×C32—21no—
725C2×C32—22no—
726C2×C32—42no—
727C2×C32—41no—
728C2×C32—44no—
729C2×C32—44no—
730C2×C32—64no—
731C2×C32D3×#4114yescomplemented
732C2×C32D3×#4112yescomplemented
733C2×C32C24×D312yes—
734C2×C32C24×D311yescharacteristic
735C3⋊D3—24no—
736C3⋊D3—34no—
737C3⋊D3—38no—
738C3⋊D3—68no—
739C3⋊D3—64no—
740C3⋊D3—62no—
741C3⋊D3—64no—
742C3⋊D3—64no—
743C3⋊D3—124no—
744C3⋊D3—124no—
745C3⋊D3—124no—
746C3×D3—24no—
747C3×D3—24no—
748C3×D3—44no—
749C3×D3—64no—
750C3×D3—64no—
751C3×D3—124no—
752C24—272no—
753C24—271no—
754#41—916no—
755#41—98no—
756#41—278no—
757#41—278no—
758#41—278no—
759#41—2716no—
760C2×Q8—92no—
761C2×Q8—91no—
762C2×Q8—271no—
763C2×Q8—278no—
764C2×D4—32no—
765C2×D4—92no—
766C2×D4—91no—
767C2×D4—92no—
768C2×D4—272no—
769C2×D4—272no—
770C2×D4—271no—
771C2×D4—2716no—
772C2×D4—278no—
773C22×C4—31no—
774C22×C4—92no—
775C22×C4—92no—
776C22×C4—92no—
777C22×C4—91no—
778C22×C4—271no—
779C22×C4—271no—
780C22×C4—272no—
781C22×C4—278no—
782C22×C4—271no—
783C22×C4—271no—
784C22×C4—2716no—
785C22×C4—272no—
786C22×C3—24no—
787C22×C3—22no—
788C22×C3—24no—
789C22×C3—22no—
790C22×C3—24no—
791C22×C3—21no—
792C22×C3—22no—
793C22×C3—34no—
794C22×C3—34no—
795C22×C3—44no—
796C22×C3—44no—
797C22×C3—42no—
798C22×C3—41no—
799C22×C3—64no—
800C22×C3—64no—
801C22×C3—64no—
802C22×C3—94no—
803C22×C3—124no—
804C22×C3—184no—
805C22×C3C22×D3214yes—
806C22×C3C22×D3212yes—
807C22×C3C22×D3211yescharacteristic
808C22×C3C22×D3212yes—
809C2×D3—24no—
810C2×D3—34no—
811C2×D3—34no—
812C2×D3—64no—
813C2×D3—64no—
814C2×D3—64no—
815C2×D3—94no—
816C2×D3—98no—
817C2×D3—92no—
818C2×D3—94no—
819C2×D3—92no—
820C2×D3—94no—
821C2×D3—124no—
822C2×D3—182no—
823C2×D3—182no—
824C2×D3—184no—
825C2×D3—184no—
826C2×D3—188no—
827C2×D3—184no—
828C2×D3—1816no—
829C2×D3—1816no—
830C2×D3—1816no—
831C2×D3—188no—
832C2×D3—1816no—
833C2×D3—1816no—
834C2×D3—184no—
835C2×D3—182no—
836C2×D3—184no—
837C2×D3—364no—
838C2×D3—362no—
839C2×D3—362no—
840C2×D3—3616no—
841C2×D3—3616no—
842C2×D3—364no—
843C2×D3—3616no—
844C2×D3—364no—
845C2×D3C22×D3214yes—
846C3×C4—34no—
847C3×C4—34no—
848C3×C4—34no—
849C3×C4—34no—
850C3×C4—62no—
851C3×C4—62no—
852C3×C4—64no—
853C3×C4—92no—
854C3×C4—94no—
855C3×C4—92no—
856Dic3—34no—
857Dic3—34no—
858Dic3—34no—
859Dic3—34no—
860Dic3—62no—
861Dic3—62no—
862Dic3—64no—
863Dic3C22×D3214yes—
864Dic3C22×D3212yes—
865Dic3C22×D3212yes—
866C32—21no—
867C32—22no—
868C32—41no—
869C32C2×D3×#4112yescomplemented
870C32C2×D3×#4111yescharacteristic, complemented
871C23—32no—
872C23—92no—
873C23—278no—
874C23—271no—
875C23—274no—
876C23—271no—
877C23—544no—
878C23—548no—
879C23D3311yescharacteristic
880Q8—98no—
881Q8—94no—
882Q8—274no—
883D4—38no—
884D4—98no—
885D4—94no—
886D4—98no—
887D4—278no—
888D4—278no—
889D4—274no—
890C2×C4—34no—
891C2×C4—31no—
892C2×C4—31no—
893C2×C4—32no—
894C2×C4—98no—
895C2×C4—98no—
896C2×C4—98no—
897C2×C4—94no—
898C2×C4—91no—
899C2×C4—92no—
900C2×C4—91no—
901C2×C4—274no—
902C2×C4—274no—
903C2×C4—278no—
904C2×C4—274no—
905C2×C4—274no—
906C2×C4—278no—
907C2×C3—24no—
908C2×C3—22no—
909C2×C3—24no—
910C2×C3—24no—
911C2×C3—22no—
912C2×C3—21no—
913C2×C3—22no—
914C2×C3—44no—
915C2×C3—44no—
916C2×C3—42no—
917C2×C3—41no—
918C2×C3—64no—
919C2×C3—64no—
920C2×C3—124no—
921C2×C3—184no—
922C2×C3#6430612yescomplemented
923C2×C3#6431214yescomplemented
924C2×C3C23×D3211yescharacteristic
925C2×C3C23×D3212yes—
926D3—24no—
927D3—64no—
928D3—64no—
929D3—94no—
930D3—98no—
931D3—124no—
932D3—184no—
933D3—188no—
934D3—184no—
935D3—182no—
936D3—184no—
937D3—364no—
938D3—364no—
939D3—364no—
940C22—22no—
941C22—34no—
942C22—64no—
943C22—94no—
944C22—184no—
945C22—274no—
946C22—272no—
947C22—272no—
948C22—548no—
949C22—5416no—
950C22—542no—
951C22C2×D3312yes—
952C22C2×D3311yescharacteristic
953C4—32no—
954C4—32no—
955C4—34no—
956C4—92no—
957C4—94no—
958C4—92no—
959C3—22no—
960C3—21no—
961C3—41no—
962C3C2×#6430611yescharacteristic, complemented
963C3C2×#6431212yescomplemented
964C2—22no—
965C2—64no—
966C2—184no—
967C2—274no—
968C2—542no—
969C2#1172441112yesdirect product factor
970C2C22×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×#89046C2semidirect
2. C2×#89039C2semidirect
3. C22×#6289C2semidirect
4. C2×C3×#3805C2semidirect
5. C2×C3×#3804C2semidirect
6. C2×#88965C2semidirect
7. C2×#88962C2semidirect
8. C2×#88959C2semidirect
9. C2×#88958C2semidirect
10. C2×#88954C2semidirect
11. #11724411C2direct (N × H)
12. C2×D3×#624C2semidirect
17. C2×C3×#638C22semidirect
18. C22×C3×C3⋊Dic3C22semidirect
19. C2×C32×#67C22semidirect
20. C22×C32×Dic3C22semidirect
21. C2×#6296C22semidirect
22. C2×#6295C22semidirect
23. #89046C22semidirect
24. C2×#6294C22semidirect
25. #89039C22semidirect
26. C2×#6292C22semidirect
27. C2×#6291C22semidirect
31. C2×#6289C22semidirect
32. C2×#6289C22semidirect
33. C2×#6289C22semidirect
34. C2×C3×#627C22semidirect
35. C2×C3×#627C22semidirect
36. C2×C3×#626C22semidirect
37. C2×C3×#625C22semidirect
38. C2×C3×#624C22semidirect
39. C3×#3805C22semidirect
40. C3×#3804C22semidirect
41. C2×C3×D3×Dic3C22semidirect
42. C2×C3×D3×Dic3C22semidirect
43. #88965C22semidirect
44. #88962C22semidirect
45. #88959C22semidirect
46. #88958C22semidirect
47. #88954C22semidirect
48. D3×#624C22semidirect
62. C2×#3805D3semidirect
66. C2×#3804D3semidirect
88. C3×#638C23semidirect
92. C2×C3×C3⋊Dic3C23semidirect
93. C32×#67C23semidirect
97. C2×C32×Dic3C23semidirect
98. #6296C23semidirect
99. #6295C23semidirect
100. #6294C23semidirect
101. #6292C23semidirect
102. #6291C23semidirect
106. #6289C23semidirect
107. #6289C23semidirect
108. C3×#627C23semidirect
109. C3×#627C23semidirect
110. C3×#626C23semidirect
111. C3×#625C23semidirect
112. C3×#624C23semidirect
113. C3×D3×Dic3C23semidirect
114. C3×D3×Dic3C23semidirect
129. C2×#638C2×D3semidirect
130. C22×C3⋊Dic3C2×D3semidirect
145. C2×C3×#67C2×D3semidirect
146. C2×C3×#67C2×D3semidirect
152. C22×C3×Dic3C2×D3semidirect
170. C2×#627C2×D3semidirect
171. C2×#627C2×D3semidirect
179. C2×#626C2×D3semidirect
181. C2×#625C2×D3semidirect
197. C2×#624C2×D3semidirect
199. #3805C2×D3semidirect
203. #3804C2×D3semidirect
206. C2×D3×Dic3C2×D3semidirect
207. C2×D3×Dic3C2×D3semidirect
223. C2×C3⋊(C3⋊D3)#41semidirect
314. #638C22×D3semidirect
318. C2×C3⋊Dic3C22×D3semidirect
331. C3×#67C22×D3semidirect
332. C3×#67C22×D3semidirect
352. C2×C3×Dic3C22×D3semidirect
363. #627C22×D3semidirect
364. #627C22×D3semidirect
372. #626C22×D3semidirect
374. #625C22×D3semidirect
387. #624C22×D3semidirect
390. D3×Dic3C22×D3semidirect
391. D3×Dic3C22×D3semidirect
394. C2×C33C2×#41semidirect
397. C3⋊(C3⋊D3)C2×#41semidirect
435. C2×#67D32semidirect
441. C22×Dic3D32semidirect
593. C33C22×#41semidirect
669. #67C2×D32semidirect
685. C2×Dic3C2×D32semidirect
731. C2×C32D3×#41semidirect
732. C2×C32D3×#41semidirect
869. C32C2×D3×#41semidirect
870. C32C2×D3×#41semidirect
922. C2×C3#64306semidirect
923. C2×C3#64312semidirect
962. C3C2×#64306semidirect
963. C3C2×#64312semidirect
969. C2#11724411direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#890462
C2×#890392
C22×#62892
C2×C3×#38052
C2×C3×#38042
C2×#889652
C2×#889622
C2×#889592
C2×#889582
C2×#889542
#117244112
C2×D3×#6242
C2×#643123
C2×#643063