Finite Group Databasebeta

← C2×#11724588 #13181618

Subgroups — C2×#11724588 #13181618

Order 1728.

6332 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C3⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
2C2×C3×#3830C211yesmaximal, characteristic, complemented
3C2×C32×D3×D4C211yesmaximal, characteristic, complemented
4C2×#89039C212yesmaximal, complemented
5C2×D3×#638C212yesmaximal, complemented
6C22×#6291C212yesmaximal, complemented
7C2×#89028C212yesmaximal, complemented
8#11724588C2116yesmaximal, direct product factor
9C2×C3⋊D3×D12C211yesmaximal, characteristic, complemented
10C2×#89022C211yesmaximal, characteristic, complemented
11C2×#89020C211yesmaximal, characteristic, complemented
12C2×#89015C211yesmaximal, characteristic, complemented
13C2×#64361—31nomaximal
14C2×#64314—34nomaximal
15C23×C3⋊(C3⋊D3)C2212yescomplemented
16C23×C32×D3C2212yescomplemented
17C22×D3×C3⋊D3C2212yescomplemented
18C2×C33×D4C2211yescharacteristic, complemented
19C2×#6312C2212yescomplemented
20D4×C3⋊(C3⋊D3)C2218yescomplemented
21C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic, complemented
22C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
23C2×C3×#638C2212yescomplemented
24C22×C3×C3⋊Dic3C2212yescomplemented
25C3×#3830C2218yescomplemented
26C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
27C2×C3×#634C2211yescharacteristic, complemented
28C2×C32×#67C2212yescomplemented
29C32×D3×D4C2218yescomplemented
30C2×C32×D12C2211yescharacteristic, complemented
31C2×C32×C4×D3C2211yescharacteristic, complemented
32#89039C22116yescomplemented
33D3×#638C22116yescomplemented
34C2×#6293C2211yescharacteristic, complemented
35C2×#6292C2211yescharacteristic, complemented
36C2×#6291C2212yescomplemented
37C2×#6291C2211yescharacteristic, complemented
38C2×#6291C2212yescomplemented
39C2×#6291C2212yescomplemented
40C2×#6291C22116yescomplemented
41C2×#6290C2211yescharacteristic, complemented
42C2×#6289C2212yescomplemented
43#89028C22116yescomplemented
44C2×D3×C3⋊Dic3C2212yescomplemented
45C3⋊D3×D12C2218yescomplemented
46#89022C2218yescomplemented
47#89020C2218yescomplemented
48#89015C2218yescomplemented
49C22×C32×D4—31no—
50C22×#638—32no—
51C22×#638—32no—
52#64361—316no—
53C2×#3830—32no—
54C2×#3830—31no—
55C2×#3830D311yescharacteristic, complemented
56C2×D4×C3⋊D3—31no—
57C2×D4×C3⋊D3—32no—
58C2×D4×C3⋊D3—31no—
59C2×D4×C3⋊D3—34no—
60C2×D4×C3⋊D3—64no—
61C2×#3828—31no—
62C2×#3828—31no—
63C2×C3×#237—34no—
64C2×C3×D3×D4D314yescomplemented
65C2×#3811—38no—
66C2×D3×#67—38no—
67C22×#626—38no—
68C2×#3804—38no—
69#64314—364no—
70C2×D3×D12—34no—
71C2×#3799—34no—
72C2×#3798—34no—
73C2×#3796—34no—
74C23×C33C2312yes—
75C22×C3⋊(C3⋊D3)—44no—
76C22×C3⋊(C3⋊D3)C2312yes—
77C22×C3⋊(C3⋊D3)C2311yescharacteristic
78C22×C3⋊(C3⋊D3)C2318yescomplemented
79C22×C3×C3⋊D3C2311yescharacteristic
80C22×C32×D3—44no—
81C22×C32×D3C2312yes—
82C22×C32×D3C2311yescharacteristic
83C22×C32×D3C2318yescomplemented
84C2×D3×C3⋊D3—44no—
85C2×D3×C3⋊D3C2318yescomplemented
86C33×D4C2314yescomplemented
87C2×C33×C4C2311yescharacteristic
88#6312C2318yescomplemented
89C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
90C4⋊(C3⋊(C3⋊D3))C2314yescomplemented
91C4×C3⋊(C3⋊D3)C2314yescomplemented
92C3×#638C2318yescomplemented
93C2×C3×C3⋊Dic3C2312yes—
94C2×C3×C3⋊Dic3C2311yescharacteristic
95C2×C3×C3⋊Dic3C2318yescomplemented
96C3×C4×C3⋊D3C2314yescomplemented
97C3×#634C2314yescomplemented
98C32×#67C2318yescomplemented
99C2×C32×Dic3C2311yescharacteristic
100C32×D12C2314yescomplemented
101C32×C4×D3C2314yescomplemented
102#6293C2314yescomplemented
103#6292C2314yescomplemented
104#6291C2318yescomplemented
105#6291C2314yescomplemented
106#6291C2318yescomplemented
107#6291C2318yescomplemented
108#6290C2314yescomplemented
109#6289C2318yescomplemented
110D3×C3⋊Dic3C2318yescomplemented
111C2×#1009—91no—
112C2×#1004—94no—
113C24×C32—32no—
114C23×C3⋊D3—32no—
115C23×C3⋊D3—38no—
116C23×C3⋊D3—32no—
117C23×C3⋊D3—68no—
118C23×C3×D3C2×D318yescomplemented
119C22×D32—38no—
120C2×C32×D4—24no—
121C2×C32×D4—32no—
122C2×C32×D4—38no—
123C2×C32×D4—31no—
124C2×C32×D4C2×D314yescomplemented
125C2×C32×D4C2×D311yescharacteristic, complemented
126C22×C32×C4—31no—
127C2×#638—32no—
128C2×#638—38no—
129C2×#638—31no—
130C2×#638—316no—
131C2×#638—31no—
132C2×#638—32no—
133C2×#638—32no—
134C2×#638—32no—
135C2×#638—316no—
136C2×#638—68no—
137C2×#638C2×D312yescomplemented
138C22×C3⋊Dic3—32no—
139C22×C3⋊Dic3C2×D312yescomplemented
140#3830—316no—
141#3830—38no—
142#3830C2×D318yescomplemented
143D4×C3⋊D3—38no—
144D4×C3⋊D3—332no—
145D4×C3⋊D3—316no—
146D4×C3⋊D3—38no—
147D4×C3⋊D3—632no—
148#3828—38no—
149#3828—38no—
150C2×C4⋊(C3⋊D3)—31no—
151C2×C4⋊(C3⋊D3)—31no—
152C2×C4⋊(C3⋊D3)—34no—
153C2×C4⋊(C3⋊D3)—64no—
154C2×C4×C3⋊D3—31no—
155C2×C4×C3⋊D3—34no—
156C2×C4×C3⋊D3—32no—
157C2×C4×C3⋊D3—64no—
158C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
159C2×#634—31no—
160C2×#634C2×D311yescharacteristic, complemented
161C2×C3×#67—38no—
162C2×C3×#67C2×D318yescomplemented
163C22×C3×Dic3—38no—
164C3×#237—332no—
165C3×D3×D4C2×D3132yescomplemented
166C2×C3×D12C2×D314yescomplemented
167C2×C3×C4×D3—34no—
168C2×C3×C4×D3C2×D314yescomplemented
169C2×C3×Dic6—34no—
170#3811—364no—
171D3×#67—364no—
172C2×#627—34no—
173C2×#626—38no—
174C2×#626—34no—
175C2×#626—38no—
176C2×#626—38no—
177C2×#626—364no—
178C2×#626—34no—
179C2×#625—34no—
180C2×#624—38no—
181#3804—364no—
182C2×D3×Dic3—38no—
183D3×D12—332no—
184#3799—332no—
185#3798—332no—
186#3796—332no—
187C22×C33—24no—
188C22×C33C2414yes—
189C22×C33C2411yescharacteristic
190C2×C3⋊(C3⋊D3)—22no—
191C2×C3⋊(C3⋊D3)—24no—
192C2×C3⋊(C3⋊D3)—48no—
193C2×C3⋊(C3⋊D3)C2414yes—
194C2×C3⋊(C3⋊D3)C2412yes—
195C2×C3×C3⋊D3—22no—
196C2×C3×C3⋊D3C2412yes—
197C2×C32×D3—24no—
198C2×C32×D3—22no—
199C2×C32×D3—48no—
200C2×C32×D3C2414yes—
201C2×C32×D3C2412yes—
202D3×C3⋊D3—48no—
203C33×C4C2412yes—
204C3⋊(C3⋊Dic3)C2412yes—
205C3×C3⋊Dic3C2414yes—
206C3×C3⋊Dic3C2412yes—
207C32×Dic3C2412yes—
208C2×C3×#41—91no—
209C22×C3×D4—34no—
210C22×#67—98no—
211C22×#67—98no—
212#1009—916no—
213C2×#239—91no—
214C2×#239—91no—
215#1004—964no—
216C2×#237—34no—
217C2×#237—94no—
218C2×#237—98no—
219C2×D3×D4—94no—
220C2×D3×D4—98no—
221C2×D3×D4—92no—
222C2×D3×D4—94no—
223C2×D3×D4—91no—
224C2×D3×D4—92no—
225C2×D3×D4—184no—
226C2×D3×D4C3⋊D311yescharacteristic, complemented
227C2×#235—94no—
228C2×#235—94no—
229C2×#235—92no—
230C2×#235—91no—
231C22×D12—92no—
232C22×D12—91no—
233C23×C32—28no—
234C23×C32—32no—
235C23×C32—31no—
236C23×C32—38no—
237C23×C32—124no—
238C23×C32C22×D318yes—
239C23×C32C22×D312yes—
240C22×C3⋊D3—31no—
241C22×C3⋊D3—32no—
242C22×C3⋊D3—38no—
243C22×C3⋊D3—38no—
244C22×C3⋊D3—38no—
245C22×C3⋊D3—34no—
246C22×C3⋊D3—332no—
247C22×C3⋊D3—64no—
248C22×C3⋊D3—68no—
249C22×C3⋊D3—632no—
250C22×C3⋊D3—124no—
251C22×C3⋊D3—124no—
252C22×C3⋊D3—1216no—
253C22×C3⋊D3—1232no—
254C22×C3⋊D3C22×D311yescharacteristic
255C22×C3×D3—34no—
256C22×C3×D3—416no—
257C22×C3×D3C22×D318yes—
258C22×C3×D3C22×D314yes—
259C22×C3×D3C22×D3132yescomplemented
260C2×D32—332no—
261C2×D32—1216no—
262C32×D4—216no—
263C32×D4—38no—
264C32×D4—34no—
265C32×D4C22×D3116yescomplemented
266C32×D4C22×D314yescomplemented
267C2×C32×C4—24no—
268C2×C32×C4—31no—
269C2×C32×C4—34no—
270C2×C32×C4C22×D314yes—
271C2×C32×C4C22×D311yescharacteristic
272#638—38no—
273#638—34no—
274#638—34no—
275#638—38no—
276#638—38no—
277#638—38no—
278#638—332no—
279#638—632no—
280#638C22×D318yescomplemented
281C2×C3⋊Dic3—31no—
282C2×C3⋊Dic3—38no—
283C2×C3⋊Dic3—34no—
284C2×C3⋊Dic3—64no—
285C2×C3⋊Dic3C22×D311yescharacteristic
286C2×C3⋊Dic3C22×D312yes—
287C2×C3⋊Dic3C22×D318yescomplemented
288C4⋊(C3⋊D3)—34no—
289C4⋊(C3⋊D3)—34no—
290C4⋊(C3⋊D3)—316no—
291C4⋊(C3⋊D3)—616no—
292C4×C3⋊D3—34no—
293C4×C3⋊D3—38no—
294C4×C3⋊D3—316no—
295C4×C3⋊D3—616no—
296C4×C3⋊D3C22×D314yescomplemented
297#634—34no—
298#634C22×D314yescomplemented
299C3×#67—332no—
300C3×#67C22×D3132yescomplemented
301C2×C3×Dic3—38no—
302C2×C3×Dic3—34no—
303C2×C3×Dic3—332no—
304C2×C3×Dic3C22×D314yes—
305C3×D12C22×D3116yescomplemented
306C3×C4×D3—316no—
307C3×C4×D3C22×D3116yescomplemented
308C3×Dic6—316no—
309#627—316no—
310#626—332no—
311#626—316no—
312#626—332no—
313#626—332no—
314#626—316no—
315#625—316no—
316#624—332no—
317D3×Dic3—332no—
318C2×H(5,𝔽2)—271noSylow
319C2×C33—24no—
320C2×C33H(5,𝔽2)12yescomplemented
321C2×C33C2511yescharacteristic
322C3⋊(C3⋊D3)—22no—
323C3⋊(C3⋊D3)—24no—
324C3×C3⋊D3—22no—
325C32×D3—24no—
326C32×D3—22no—
327C24×C3—38no—
328C23×D3—98no—
329C23×D3—98no—
330C23×D3—92no—
331C23×D3—92no—
332C23×D3—188no—
333C23×D3C2×C3⋊D312yescomplemented
334C3×#41—98no—
335C2×C3×Q8—91no—
336C2×C3×D4—24no—
337C2×C3×D4—38no—
338C2×C3×D4—332no—
339C2×C3×D4—34no—
340C2×C3×D4—92no—
341C2×C3×D4D3214yescomplemented
342C2×C3×D4C2×C3⋊D311yescharacteristic, complemented
343C22×C3×C4—34no—
344C22×C3×C4—92no—
345C22×C3×C4—91no—
346C2×#67—38no—
347C2×#67—98no—
348C2×#67—94no—
349C2×#67—98no—
350C2×#67—98no—
351C2×#67—964no—
352C2×#67—964no—
353C2×#67—94no—
354C2×#67—98no—
355C2×#67—92no—
356C2×#67—91no—
357C2×#67—91no—
358C2×#67—188no—
359C2×#67C2×C3⋊D312yescomplemented
360C22×Dic3—38no—
361C22×Dic3—98no—
362#239—98no—
363#239—98no—
364#237—332no—
365#237—932no—
366#237—964no—
367D3×D4—932no—
368D3×D4—964no—
369D3×D4—916no—
370D3×D4—932no—
371D3×D4—98no—
372D3×D4—916no—
373D3×D4—1832no—
374D3×D4C2×C3⋊D318yescomplemented
375#235—932no—
376#235—932no—
377#235—916no—
378#235—98no—
379C2×D12—94no—
380C2×D12—92no—
381C2×D12—91no—
382C2×D12—92no—
383C2×D12—92no—
384C2×D12—916no—
385C2×D12—94no—
386C2×D12—91no—
387C2×D12—98no—
388C2×D12—184no—
389C2×D12C2×C3⋊D311yescharacteristic, complemented
390C2×C4×D3—34no—
391C2×C4×D3—98no—
392C2×C4×D3—92no—
393C2×C4×D3—94no—
394C2×C4×D3—91no—
395C2×C4×D3—92no—
396C2×C4×D3—184no—
397C2×C4×D3C2×C3⋊D311yescharacteristic, complemented
398C2×Dic6—34no—
399C2×Dic6—94no—
400C2×Dic6—91no—
401C22×C32—24no—
402C22×C32—24no—
403C22×C32—216no—
404C22×C32—216no—
405C22×C32—34no—
406C22×C32—32no—
407C22×C32—416no—
408C22×C32—64no—
409C22×C32—62no—
410C22×C32—128no—
411C22×C32C23×D3116yes—
412C22×C32C23×D314yes—
413C22×C32C23×D314yes—
414C22×C32C23×D311yescharacteristic
415C2×C3⋊D3—22no—
416C2×C3⋊D3—34no—
417C2×C3⋊D3—32no—
418C2×C3⋊D3—316no—
419C2×C3⋊D3—38no—
420C2×C3⋊D3—68no—
421C2×C3⋊D3—616no—
422C2×C3⋊D3—616no—
423C2×C3⋊D3—68no—
424C2×C3⋊D3—62no—
425C2×C3⋊D3—64no—
426C2×C3⋊D3—616no—
427C2×C3⋊D3—1216no—
428C2×C3⋊D3—128no—
429C2×C3⋊D3—128no—
430C2×C3⋊D3—1232no—
431C2×C3⋊D3—1264no—
432C2×C3⋊D3C23×D312yes—
433C2×C3×D3—216no—
434C2×C3×D3—28no—
435C2×C3×D3—38no—
436C2×C3×D3—432no—
437C2×C3×D3—68no—
438C2×C3×D3C23×D3116yes—
439C2×C3×D3C23×D318yes—
440D32—1232no—
441C32×C4—28no—
442C32×C4—32no—
443C32×C4C23×D318yes—
444C32×C4C23×D312yes—
445C3⋊Dic3—32no—
446C3⋊Dic3—38no—
447C3⋊Dic3—68no—
448C3⋊Dic3C23×D312yes—
449C3⋊Dic3C23×D314yes—
450C3×Dic3—316no—
451C3×Dic3—38no—
452C3×Dic3C23×D318yes—
453H(5,𝔽2)—2716no—
454C2×#41—91no—
455C2×#41—271no—
456C2×#41—271no—
457C2×#41—272no—
458C2×#41—271no—
459C22×D4—31no—
460C22×D4—271no—
461C22×D4—272no—
462C22×D4—272no—
463C22×D4—272no—
464C22×D4—271no—
465C33C2×H(5,𝔽2)11yescharacteristic, complemented, Sylow
466C23×C3—28no—
467C23×C3—38no—
468C23×C3—34no—
469C23×C3—332no—
470C23×C3—91no—
471C23×C3—1216no—
472C23×C3C2×D3218yes—
473C23×C3C22×C3⋊D312yes—
474C22×D3—34no—
475C22×D3—44no—
476C22×D3—932no—
477C22×D3—94no—
478C22×D3—98no—
479C22×D3—92no—
480C22×D3—91no—
481C22×D3—932no—
482C22×D3—98no—
483C22×D3—98no—
484C22×D3—184no—
485C22×D3—188no—
486C22×D3—1832no—
487C22×D3—364no—
488C22×D3—3616no—
489C22×D3—3616no—
490C22×D3—364no—
491C22×D3—3632no—
492C22×D3C22×C3⋊D312yes—
493C22×D3C22×C3⋊D311yescharacteristic
494C22×D3C22×C3⋊D318yescomplemented
495C3×Q8—94no—
496C3×D4—216no—
497C3×D4—332no—
498C3×D4—316no—
499C3×D4—98no—
500C3×D4C2×D32116yescomplemented
501C3×D4C22×C3⋊D314yescomplemented
502C2×C3×C4—24no—
503C2×C3×C4—34no—
504C2×C3×C4—316no—
505C2×C3×C4—91no—
506C2×C3×C4—92no—
507C2×C3×C4—98no—
508C2×C3×C4—94no—
509C2×C3×C4C2×D3214yes—
510C2×C3×C4C22×C3⋊D311yescharacteristic
511#67—332no—
512#67—932no—
513#67—916no—
514#67—932no—
515#67—932no—
516#67—916no—
517#67—932no—
518#67—98no—
519#67—94no—
520#67—94no—
521#67—1832no—
522#67C22×C3⋊D318yescomplemented
523C2×Dic3—38no—
524C2×Dic3—34no—
525C2×Dic3—332no—
526C2×Dic3—932no—
527C2×Dic3—94no—
528C2×Dic3—91no—
529C2×Dic3—184no—
530C2×Dic3C22×C3⋊D311yescharacteristic
531D12—916no—
532D12—98no—
533D12—94no—
534D12—98no—
535D12—98no—
536D12—916no—
537D12—94no—
538D12—1816no—
539D12C22×C3⋊D314yescomplemented
540C4×D3—316no—
541C4×D3—932no—
542C4×D3—98no—
543C4×D3—916no—
544C4×D3—94no—
545C4×D3—98no—
546C4×D3—1816no—
547C4×D3C22×C3⋊D314yescomplemented
548Dic6—316no—
549Dic6—916no—
550Dic6—94no—
551C2×C32—24no—
552C2×C32—28no—
553C2×C32—24no—
554C2×C32—216no—
555C2×C32—416no—
556C2×C32—64no—
557C2×C32—62no—
558C2×C32#100418yescomplemented
559C2×C32#100912yescomplemented
560C2×C32C24×D314yes—
561C2×C32C24×D311yescharacteristic
562C3⋊D3—22no—
563C3⋊D3—616no—
564C3⋊D3—68no—
565C3⋊D3—62no—
566C3⋊D3—64no—
567C3⋊D3—616no—
568C3⋊D3—1216no—
569C3×D3—216no—
570C3×D3—28no—
571C3×D3—68no—
572C24—32no—
573C24—272no—
574C24—272no—
575#41—98no—
576#41—278no—
577#41—278no—
578#41—2716no—
579#41—278no—
580C2×Q8—91no—
581C2×Q8—271no—
582C2×D4—32no—
583C2×D4—38no—
584C2×D4—31no—
585C2×D4—92no—
586C2×D4—271no—
587C2×D4—278no—
588C2×D4—271no—
589C2×D4—272no—
590C2×D4—272no—
591C2×D4—272no—
592C2×D4—2716no—
593C2×D4—2716no—
594C2×D4—2716no—
595C2×D4—271no—
596C2×D4—272no—
597C2×D4—278no—
598C2×D4—271no—
599C2×D4D3×C3⋊D311yescharacteristic, complemented
600C22×C4—31no—
601C22×C4—92no—
602C22×C4—91no—
603C22×C4—272no—
604C22×C4—272no—
605C22×C4—271no—
606C22×C3—216no—
607C22×C3—24no—
608C22×C3—216no—
609C22×C3—24no—
610C22×C3—316no—
611C22×C3—38no—
612C22×C3—416no—
613C22×C3—616no—
614C22×C3—68no—
615C22×C3—92no—
616C22×C3—1232no—
617C22×C3—182no—
618C22×C3C22×D32116yes—
619C22×C3C22×D3214yes—
620C22×C3C23×C3⋊D314yes—
621C22×C3C23×C3⋊D311yescharacteristic
622C2×D3—22no—
623C2×D3—24no—
624C2×D3—38no—
625C2×D3—48no—
626C2×D3—68no—
627C2×D3—98no—
628C2×D3—916no—
629C2×D3—92no—
630C2×D3—94no—
631C2×D3—188no—
632C2×D3—1816no—
633C2×D3—1816no—
634C2×D3—188no—
635C2×D3—1816no—
636C2×D3—182no—
637C2×D3—184no—
638C2×D3—3616no—
639C2×D3—368no—
640C2×D3—3632no—
641C2×D3—3632no—
642C2×D3—368no—
643C2×D3—3664no—
644C2×D3C23×C3⋊D314yes—
645C2×D3C23×C3⋊D312yes—
646C3×C4—28no—
647C3×C4—38no—
648C3×C4—92no—
649C3×C4—94no—
650C3×C4C22×D3218yes—
651C3×C4C23×C3⋊D312yes—
652Dic3—316no—
653Dic3—38no—
654Dic3—98no—
655Dic3—92no—
656Dic3—188no—
657Dic3C23×C3⋊D312yes—
658C32—24no—
659C32C2×#100414yescomplemented
660C32C2×#100911yescharacteristic, complemented
661C23—31no—
662C23—32no—
663C23—38no—
664C23—91no—
665C23—124no—
666C23—278no—
667C23—271no—
668C23—272no—
669C23—278no—
670C23—1084no—
671C23—1084no—
672C23C2×D3×C3⋊D312yes—
673Q8—94no—
674Q8—274no—
675D4—38no—
676D4—34no—
677D4—98no—
678D4—274no—
679D4—274no—
680D4—278no—
681D4—278no—
682D4—278no—
683D4—274no—
684D4—278no—
685D4—274no—
686D4C2×D3×C3⋊D314yescomplemented
687C2×C4—31no—
688C2×C4—34no—
689C2×C4—98no—
690C2×C4—91no—
691C2×C4—92no—
692C2×C4—94no—
693C2×C4—278no—
694C2×C4—278no—
695C2×C4—271no—
696C2×C4—274no—
697C2×C4C2×D3×C3⋊D311yescharacteristic
698C2×C3—216no—
699C2×C3—24no—
700C2×C3—28no—
701C2×C3—24no—
702C2×C3—416no—
703C2×C3—616no—
704C2×C3—68no—
705C2×C3—182no—
706C2×C3#6431418yescomplemented
707C2×C3#6436112yescomplemented
708C2×C3C23×D3214yes—
709C2×C3C24×C3⋊D311yescharacteristic
710D3—22no—
711D3—24no—
712D3—68no—
713D3—1816no—
714D3—188no—
715D3—1816no—
716D3—182no—
717D3—184no—
718D3—3616no—
719C22—24no—
720C22—32no—
721C22—34no—
722C22—62no—
723C22—64no—
724C22—92no—
725C22—128no—
726C22—182no—
727C22—272no—
728C22—274no—
729C22—542no—
730C22—544no—
731C22—1088no—
732C22—1088no—
733C22C22×D3×C3⋊D314yes—
734C22C22×D3×C3⋊D311yescharacteristic
735C4—32no—
736C4—92no—
737C4—94no—
738C4—272no—
739C4C22×D3×C3⋊D312yes—
740C3—24no—
741C3C2×#6431414yescomplemented
742C3C2×#6436111yescharacteristic, complemented
743C2—24no—
744C2—62no—
745C2—64no—
746C2—182no—
747C2—542no—
748C2—544no—
749C2#1172458812yesdirect product factor
750C2C23×D3×C3⋊D311yescharacteristic
subgroupG/H
centerC22C22×D3×C3⋊D3
commutator, cosocleC2×C33C25
FrattiniC2C23×D3×C3⋊D3
FittingC2×C33×D4C22
socleC22×C33C24
hypercenterC2×D4D3×C3⋊D3
hypocenterC33C2×H(5,𝔽2)
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×D4×C3⋊(C3⋊D3)C2semidirect
2. C2×C3×#3830C2semidirect
3. C2×C32×D3×D4C2semidirect
4. C2×#89039C2semidirect
5. C2×D3×#638C2semidirect
6. C22×#6291C2semidirect
7. C2×#89028C2semidirect
8. #11724588C2direct (N × H)
9. C2×C3⋊D3×D12C2semidirect
10. C2×#89022C2semidirect
11. C2×#89020C2semidirect
12. C2×#89015C2semidirect
15. C23×C3⋊(C3⋊D3)C22semidirect
16. C23×C32×D3C22semidirect
17. C22×D3×C3⋊D3C22semidirect
18. C2×C33×D4C22semidirect
19. C2×#6312C22semidirect
20. D4×C3⋊(C3⋊D3)C22semidirect
21. C2×C4⋊(C3⋊(C3⋊D3))C22semidirect
22. C2×C4×C3⋊(C3⋊D3)C22semidirect
23. C2×C3×#638C22semidirect
24. C22×C3×C3⋊Dic3C22semidirect
25. C3×#3830C22semidirect
26. C2×C3×C4×C3⋊D3C22semidirect
27. C2×C3×#634C22semidirect
28. C2×C32×#67C22semidirect
29. C32×D3×D4C22semidirect
30. C2×C32×D12C22semidirect
31. C2×C32×C4×D3C22semidirect
32. #89039C22semidirect
33. D3×#638C22semidirect
34. C2×#6293C22semidirect
35. C2×#6292C22semidirect
36. C2×#6291C22semidirect
37. C2×#6291C22semidirect
38. C2×#6291C22semidirect
39. C2×#6291C22semidirect
40. C2×#6291C22semidirect
41. C2×#6290C22semidirect
42. C2×#6289C22semidirect
43. #89028C22semidirect
44. C2×D3×C3⋊Dic3C22semidirect
45. C3⋊D3×D12C22semidirect
46. #89022C22semidirect
47. #89020C22semidirect
48. #89015C22semidirect
55. C2×#3830D3semidirect
64. C2×C3×D3×D4D3semidirect
78. C22×C3⋊(C3⋊D3)C23semidirect
83. C22×C32×D3C23semidirect
85. C2×D3×C3⋊D3C23semidirect
86. C33×D4C23semidirect
88. #6312C23semidirect
90. C4⋊(C3⋊(C3⋊D3))C23semidirect
91. C4×C3⋊(C3⋊D3)C23semidirect
92. C3×#638C23semidirect
95. C2×C3×C3⋊Dic3C23semidirect
96. C3×C4×C3⋊D3C23semidirect
97. C3×#634C23semidirect
98. C32×#67C23semidirect
100. C32×D12C23semidirect
101. C32×C4×D3C23semidirect
102. #6293C23semidirect
103. #6292C23semidirect
104. #6291C23semidirect
105. #6291C23semidirect
106. #6291C23semidirect
107. #6291C23semidirect
108. #6290C23semidirect
109. #6289C23semidirect
110. D3×C3⋊Dic3C23semidirect
118. C23×C3×D3C2×D3semidirect
124. C2×C32×D4C2×D3semidirect
125. C2×C32×D4C2×D3semidirect
137. C2×#638C2×D3semidirect
139. C22×C3⋊Dic3C2×D3semidirect
142. #3830C2×D3semidirect
158. C2×C4×C3⋊D3C2×D3semidirect
160. C2×#634C2×D3semidirect
162. C2×C3×#67C2×D3semidirect
165. C3×D3×D4C2×D3semidirect
166. C2×C3×D12C2×D3semidirect
168. C2×C3×C4×D3C2×D3semidirect
226. C2×D3×D4C3⋊D3semidirect
259. C22×C3×D3C22×D3semidirect
265. C32×D4C22×D3semidirect
266. C32×D4C22×D3semidirect
280. #638C22×D3semidirect
287. C2×C3⋊Dic3C22×D3semidirect
296. C4×C3⋊D3C22×D3semidirect
298. #634C22×D3semidirect
300. C3×#67C22×D3semidirect
305. C3×D12C22×D3semidirect
307. C3×C4×D3C22×D3semidirect
320. C2×C33H(5,𝔽2)semidirect
333. C23×D3C2×C3⋊D3semidirect
341. C2×C3×D4D32semidirect
342. C2×C3×D4C2×C3⋊D3semidirect
359. C2×#67C2×C3⋊D3semidirect
374. D3×D4C2×C3⋊D3semidirect
389. C2×D12C2×C3⋊D3semidirect
397. C2×C4×D3C2×C3⋊D3semidirect
465. C33C2×H(5,𝔽2)semidirect
494. C22×D3C22×C3⋊D3semidirect
500. C3×D4C2×D32semidirect
501. C3×D4C22×C3⋊D3semidirect
522. #67C22×C3⋊D3semidirect
539. D12C22×C3⋊D3semidirect
547. C4×D3C22×C3⋊D3semidirect
558. C2×C32#1004semidirect
559. C2×C32#1009semidirect
599. C2×D4D3×C3⋊D3semidirect
659. C32C2×#1004semidirect
660. C32C2×#1009semidirect
686. D4C2×D3×C3⋊D3semidirect
706. C2×C3#64314semidirect
707. C2×C3#64361semidirect
741. C3C2×#64314semidirect
742. C3C2×#64361semidirect
749. C2#11724588direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×C3⋊(C3⋊D3)2
C2×C3×#38302
C2×C32×D3×D42
C2×#890392
C2×D3×#6382
C22×#62912
C2×#890282
#117245882
C2×C3⋊D3×D122
C2×#890222
C2×#890202
C2×#890152
C2×#643613
C2×#643143