Finite Group Databasebeta

← C2×#11724587 #13181616

Subgroups — C2×#11724587 #13181616

Order 1728.

6044 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89078C211yesmaximal, characteristic, complemented
2C2×C3×D4×C3⋊D3C211yesmaximal, characteristic, complemented
3C2×C32×D3×D4C211yesmaximal, characteristic, complemented
4C2×C3⋊D3×#67C212yesmaximal, complemented
5C2×D3×#638C212yesmaximal, complemented
6C22×#6290C212yesmaximal, complemented
7C2×#89029C212yesmaximal, complemented
8#11724587C2116yesmaximal, direct product factor
9C2×#89026C211yesmaximal, characteristic, complemented
10C2×#89021C211yesmaximal, characteristic, complemented
11C2×#89020C211yesmaximal, characteristic, complemented
12C2×#89014C211yesmaximal, characteristic, complemented
13C2×#64361—31nomaximal
14C2×#64313—34nomaximal
15C23×C3×C3⋊D3C2212yescomplemented
16C23×C32×D3C2212yescomplemented
17C22×D3×C3⋊D3C2212yescomplemented
18C2×C33×D4C2211yescharacteristic, complemented
19C2×#6312C2212yescomplemented
20C22×C3⋊(C3⋊Dic3)C2212yescomplemented
21#89078C2218yescomplemented
22C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
23C2×#6308C2211yescharacteristic, complemented
24C2×C3×#638C2212yescomplemented
25C3×D4×C3⋊D3C2218yescomplemented
26C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
27C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
28C2×C32×#67C2212yescomplemented
29C32×D3×D4C2218yescomplemented
30C2×C32×D12C2211yescharacteristic, complemented
31C2×C32×C4×D3C2211yescharacteristic, complemented
32C3⋊D3×#67C22116yescomplemented
33D3×#638C22116yescomplemented
34C2×#6293C2211yescharacteristic, complemented
35C2×#6292C2211yescharacteristic, complemented
36C2×#6291C2211yescharacteristic, complemented
37C2×#6290C2212yescomplemented
38C2×#6290C2211yescharacteristic, complemented
39C2×#6290C2212yescomplemented
40C2×#6290C2212yescomplemented
41C2×#6290C22116yescomplemented
42C2×Dic3×C3⋊D3C2212yescomplemented
43#89029C22116yescomplemented
44C2×D3×C3⋊Dic3C2212yescomplemented
45#89026C2218yescomplemented
46#89021C2218yescomplemented
47#89020C2218yescomplemented
48#89014C2218yescomplemented
49C22×C32×D4—31no—
50C22×#638—32no—
51C22×#638—32no—
52#64361—316no—
53C2×#3830—31no—
54C2×#3830—32no—
55C2×#3830—31no—
56C2×#3830—34no—
57C2×#3830—64no—
58C2×D4×C3⋊D3—31no—
59C2×D4×C3⋊D3—32no—
60C2×D4×C3⋊D3D311yescharacteristic, complemented
61C2×#3828—31no—
62C2×#3828—31no—
63C2×C3×D3×D4—34no—
64C2×C3×D3×D4D314yescomplemented
65C2×D3×#67—38no—
66C2×D3×#67—38no—
67C22×#625—38no—
68C2×#3805—38no—
69#64313—364no—
70C2×#3802—34no—
71C2×#3798—34no—
72C2×#3795—34no—
73C2×#3795—34no—
74C23×C33C2312yes—
75C22×C3⋊(C3⋊D3)C2311yescharacteristic
76C22×C3×C3⋊D3—44no—
77C22×C3×C3⋊D3C2312yes—
78C22×C3×C3⋊D3C2311yescharacteristic
79C22×C3×C3⋊D3C2318yescomplemented
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)C2312yes—
90C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
91C2×C3⋊(C3⋊Dic3)C2318yescomplemented
92C4×C3⋊(C3⋊D3)C2314yescomplemented
93#6308C2314yescomplemented
94C3×#638C2318yescomplemented
95C2×C3×C3⋊Dic3C2311yescharacteristic
96C3×C4⋊(C3⋊D3)C2314yescomplemented
97C3×C4×C3⋊D3C2314yescomplemented
98C32×#67C2318yescomplemented
99C2×C32×Dic3C2311yescharacteristic
100C32×D12C2314yescomplemented
101C32×C4×D3C2314yescomplemented
102#6293C2314yescomplemented
103#6292C2314yescomplemented
104#6291C2314yescomplemented
105#6290C2318yescomplemented
106#6290C2314yescomplemented
107#6290C2318yescomplemented
108#6290C2318yescomplemented
109Dic3×C3⋊D3C2318yescomplemented
110D3×C3⋊Dic3C2318yescomplemented
111C2×#1004—94no—
112C2×#1004—91no—
113C24×C32—32no—
114C23×C3⋊D3—32no—
115C23×C3⋊D3C2×D312yescomplemented
116C23×C3×D3—38no—
117C23×C3×D3C2×D318yescomplemented
118C22×D32—38no—
119C2×C32×D4—24no—
120C2×C32×D4—32no—
121C2×C32×D4—38no—
122C2×C32×D4—31no—
123C2×C32×D4C2×D314yescomplemented
124C2×C32×D4C2×D311yescharacteristic, complemented
125C22×C32×C4—31no—
126C2×#638—32no—
127C2×#638—38no—
128C2×#638—32no—
129C2×#638—31no—
130C2×#638—32no—
131C2×#638—32no—
132C2×#638—316no—
133C2×#638—316no—
134C2×#638—31no—
135C2×#638—68no—
136C2×#638C2×D312yescomplemented
137C22×C3⋊Dic3—32no—
138C22×C3⋊Dic3—38no—
139C22×C3⋊Dic3—32no—
140C22×C3⋊Dic3—68no—
141#3830—38no—
142#3830—332no—
143#3830—316no—
144#3830—38no—
145#3830—632no—
146D4×C3⋊D3—316no—
147D4×C3⋊D3—38no—
148D4×C3⋊D3C2×D318yescomplemented
149#3828—38no—
150#3828—38no—
151C2×C4⋊(C3⋊D3)—31no—
152C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
153C2×C4×C3⋊D3—32no—
154C2×C4×C3⋊D3—31no—
155C2×C4×C3⋊D3—34no—
156C2×C4×C3⋊D3—64no—
157C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
158C2×#634—31no—
159C2×#634—34no—
160C2×#634—31no—
161C2×#634—64no—
162C2×C3×#67—38no—
163C2×C3×#67C2×D318yescomplemented
164C3×D3×D4—332no—
165C3×D3×D4C2×D3132yescomplemented
166C2×C3×D12—34no—
167C2×C3×D12C2×D314yescomplemented
168C2×C3×C4×D3—34no—
169C2×C3×C4×D3C2×D314yescomplemented
170D3×#67—364no—
171D3×#67—364no—
172C2×#627—34no—
173C2×#626—34no—
174C2×#626—34no—
175C2×#625—38no—
176C2×#625—38no—
177C2×#625—34no—
178C2×#625—38no—
179C2×#625—364no—
180#3805—364no—
181C2×D3×Dic3—38no—
182C2×D3×Dic3—38no—
183#3802—332no—
184#3798—332no—
185#3795—332no—
186#3795—332no—
187C22×C33—24no—
188C22×C33C2414yes—
189C22×C33C2411yescharacteristic
190C2×C3⋊(C3⋊D3)—22no—
191C2×C3⋊(C3⋊D3)C2412yes—
192C2×C3×C3⋊D3—24no—
193C2×C3×C3⋊D3—22no—
194C2×C3×C3⋊D3—48no—
195C2×C3×C3⋊D3C2414yes—
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)C2414yes—
205C3⋊(C3⋊Dic3)C2412yes—
206C3×C3⋊Dic3C2412yes—
207C32×Dic3C2412yes—
208C22×C3×D4—34no—
209C22×C3×D4—91no—
210C22×#67—98no—
211C22×#67—98no—
212C22×#67—92no—
213C22×#67—92no—
214#1004—964no—
215#1004—916no—
216C2×#237—94no—
217C2×#237—98no—
218C2×#237—94no—
219C2×#237—91no—
220C2×#237—92no—
221C2×#237—91no—
222C2×#237—184no—
223C2×D3×D4—34no—
224C2×D3×D4—94no—
225C2×D3×D4—98no—
226C2×D3×D4—92no—
227C2×D3×D4—91no—
228C2×D3×D4C3⋊D311yescharacteristic, complemented
229C2×#235—94no—
230C2×#235—94no—
231C2×#235—91no—
232C2×#235—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—38no—
242C22×C3⋊D3—34no—
243C22×C3⋊D3—44no—
244C22×C3⋊D3—64no—
245C22×C3⋊D3—124no—
246C22×C3⋊D3C22×D312yes—
247C22×C3⋊D3C22×D311yescharacteristic
248C22×C3⋊D3C22×D318yescomplemented
249C22×C3×D3—38no—
250C22×C3×D3—34no—
251C22×C3×D3—332no—
252C22×C3×D3—416no—
253C22×C3×D3—1216no—
254C22×C3×D3C22×D318yes—
255C22×C3×D3C22×D314yes—
256C22×C3×D3C22×D3132yescomplemented
257C2×D32—332no—
258C2×D32—1216no—
259C32×D4—216no—
260C32×D4—38no—
261C32×D4—34no—
262C32×D4C22×D3116yescomplemented
263C32×D4C22×D314yescomplemented
264C2×C32×C4—24no—
265C2×C32×C4—31no—
266C2×C32×C4—34no—
267C2×C32×C4C22×D314yes—
268C2×C32×C4C22×D311yescharacteristic
269#638—38no—
270#638—38no—
271#638—34no—
272#638—38no—
273#638—38no—
274#638—34no—
275#638—332no—
276#638—632no—
277#638C22×D318yescomplemented
278C2×C3⋊Dic3—32no—
279C2×C3⋊Dic3—31no—
280C2×C3⋊Dic3—38no—
281C2×C3⋊Dic3—38no—
282C2×C3⋊Dic3—38no—
283C2×C3⋊Dic3—34no—
284C2×C3⋊Dic3—332no—
285C2×C3⋊Dic3—68no—
286C2×C3⋊Dic3—64no—
287C2×C3⋊Dic3—632no—
288C2×C3⋊Dic3C22×D311yescharacteristic
289C4⋊(C3⋊D3)—34no—
290C4⋊(C3⋊D3)C22×D314yescomplemented
291C4×C3⋊D3—38no—
292C4×C3⋊D3—34no—
293C4×C3⋊D3—316no—
294C4×C3⋊D3—616no—
295C4×C3⋊D3C22×D314yescomplemented
296#634—34no—
297#634—34no—
298#634—316no—
299#634—616no—
300C3×#67—332no—
301C3×#67C22×D3132yescomplemented
302C2×C3×Dic3—34no—
303C2×C3×Dic3C22×D314yes—
304C3×D12—316no—
305C3×D12C22×D3116yescomplemented
306C3×C4×D3—316no—
307C3×C4×D3C22×D3116yescomplemented
308#627—316no—
309#626—316no—
310#626—316no—
311#625—332no—
312#625—332no—
313#625—316no—
314#625—332no—
315D3×Dic3—332no—
316D3×Dic3—332no—
317C2×H(5,𝔽2)—271noSylow
318C2×C33—24no—
319C2×C33H(5,𝔽2)12yescomplemented
320C2×C33C2511yescharacteristic
321C3⋊(C3⋊D3)—22no—
322C3×C3⋊D3—24no—
323C3×C3⋊D3—22no—
324C32×D3—24no—
325C32×D3—22no—
326C24×C3—38no—
327C24×C3—92no—
328C23×D3—38no—
329C23×D3—98no—
330C23×D3—92no—
331C23×D3C2×C3⋊D312yescomplemented
332C2×C3×D4—24no—
333C2×C3×D4—38no—
334C2×C3×D4—332no—
335C2×C3×D4—34no—
336C2×C3×D4—92no—
337C2×C3×D4—98no—
338C2×C3×D4—91no—
339C2×C3×D4D3214yescomplemented
340C2×C3×D4C2×C3⋊D311yescharacteristic, complemented
341C22×C3×C4—34no—
342C22×C3×C4—91no—
343C2×#67—38no—
344C2×#67—94no—
345C2×#67—964no—
346C2×#67—94no—
347C2×#67—98no—
348C2×#67—98no—
349C2×#67—98no—
350C2×#67—964no—
351C2×#67—98no—
352C2×#67—92no—
353C2×#67—92no—
354C2×#67—91no—
355C2×#67—92no—
356C2×#67—92no—
357C2×#67—916no—
358C2×#67—916no—
359C2×#67—91no—
360C2×#67—188no—
361C2×#67C2×C3⋊D312yescomplemented
362C22×Dic3—98no—
363C22×Dic3—98no—
364C22×Dic3—92no—
365C22×Dic3—92no—
366C22×Dic3—188no—
367#237—932no—
368#237—964no—
369#237—932no—
370#237—98no—
371#237—916no—
372#237—98no—
373#237—1832no—
374D3×D4—332no—
375D3×D4—932no—
376D3×D4—964no—
377D3×D4—916no—
378D3×D4—98no—
379D3×D4C2×C3⋊D318yescomplemented
380#235—932no—
381#235—932no—
382#235—98no—
383#235—98no—
384C2×D12—34no—
385C2×D12—94no—
386C2×D12—91no—
387C2×D12C2×C3⋊D311yescharacteristic, complemented
388C2×C4×D3—34no—
389C2×C4×D3—98no—
390C2×C4×D3—92no—
391C2×C4×D3—94no—
392C2×C4×D3—91no—
393C2×C4×D3—184no—
394C2×C4×D3C2×C3⋊D311yescharacteristic, complemented
395C2×Dic6—94no—
396C2×Dic6—94no—
397C2×Dic6—91no—
398C2×Dic6—91no—
399C2×Dic6—184no—
400C22×C32—24no—
401C22×C32—24no—
402C22×C32—216no—
403C22×C32—216no—
404C22×C32—34no—
405C22×C32—32no—
406C22×C32—416no—
407C22×C32—64no—
408C22×C32—62no—
409C22×C32—128no—
410C22×C32C23×D3116yes—
411C22×C32C23×D314yes—
412C22×C32C23×D314yes—
413C22×C32C23×D311yescharacteristic
414C2×C3⋊D3—22no—
415C2×C3⋊D3—24no—
416C2×C3⋊D3—32no—
417C2×C3⋊D3—38no—
418C2×C3⋊D3—48no—
419C2×C3⋊D3—68no—
420C2×C3⋊D3—62no—
421C2×C3⋊D3—68no—
422C2×C3⋊D3—128no—
423C2×C3⋊D3—128no—
424C2×C3⋊D3C23×D314yes—
425C2×C3⋊D3C23×D312yes—
426C2×C3×D3—216no—
427C2×C3×D3—28no—
428C2×C3×D3—316no—
429C2×C3×D3—38no—
430C2×C3×D3—432no—
431C2×C3×D3—616no—
432C2×C3×D3—68no—
433C2×C3×D3—1232no—
434C2×C3×D3C23×D3116yes—
435C2×C3×D3C23×D318yes—
436D32—1232no—
437C32×C4—28no—
438C32×C4—32no—
439C32×C4C23×D318yes—
440C32×C4C23×D312yes—
441C3⋊Dic3—34no—
442C3⋊Dic3—32no—
443C3⋊Dic3—316no—
444C3⋊Dic3—38no—
445C3⋊Dic3—616no—
446C3⋊Dic3—68no—
447C3⋊Dic3C23×D312yes—
448C3×Dic3—38no—
449C3×Dic3C23×D318yes—
450H(5,𝔽2)—2716no—
451C2×#41—271no—
452C2×#41—271no—
453C2×#41—271no—
454C2×#41—272no—
455C2×#41—271no—
456C22×D4—31no—
457C22×D4—91no—
458C22×D4—271no—
459C22×D4—272no—
460C22×D4—272no—
461C22×D4—272no—
462C33C2×H(5,𝔽2)11yescharacteristic, complemented, Sylow
463C23×C3—28no—
464C23×C3—38no—
465C23×C3—34no—
466C23×C3—332no—
467C23×C3—92no—
468C23×C3—91no—
469C23×C3—98no—
470C23×C3—1216no—
471C23×C3—364no—
472C23×C3C2×D3218yes—
473C23×C3C22×C3⋊D312yes—
474C22×D3—34no—
475C22×D3—38no—
476C22×D3—332no—
477C22×D3—44no—
478C22×D3—932no—
479C22×D3—94no—
480C22×D3—91no—
481C22×D3—98no—
482C22×D3—1216no—
483C22×D3—184no—
484C22×D3—364no—
485C22×D3—3616no—
486C22×D3C22×C3⋊D312yes—
487C22×D3C22×C3⋊D311yescharacteristic
488C22×D3C22×C3⋊D318yescomplemented
489C3×D4—216no—
490C3×D4—332no—
491C3×D4—316no—
492C3×D4—98no—
493C3×D4—94no—
494C3×D4C2×D32116yescomplemented
495C3×D4C22×C3⋊D314yescomplemented
496C2×C3×C4—24no—
497C2×C3×C4—34no—
498C2×C3×C4—316no—
499C2×C3×C4—91no—
500C2×C3×C4—94no—
501C2×C3×C4C2×D3214yes—
502C2×C3×C4C22×C3⋊D311yescharacteristic
503#67—332no—
504#67—916no—
505#67—916no—
506#67—932no—
507#67—932no—
508#67—932no—
509#67—932no—
510#67—98no—
511#67—98no—
512#67—94no—
513#67—98no—
514#67—98no—
515#67—94no—
516#67—1832no—
517#67C22×C3⋊D318yescomplemented
518C2×Dic3—34no—
519C2×Dic3—932no—
520C2×Dic3—98no—
521C2×Dic3—94no—
522C2×Dic3—932no—
523C2×Dic3—92no—
524C2×Dic3—91no—
525C2×Dic3—98no—
526C2×Dic3—98no—
527C2×Dic3—188no—
528C2×Dic3—184no—
529C2×Dic3—1832no—
530C2×Dic3C22×C3⋊D311yescharacteristic
531D12—316no—
532D12—916no—
533D12—94no—
534D12C22×C3⋊D314yescomplemented
535C4×D3—316no—
536C4×D3—932no—
537C4×D3—98no—
538C4×D3—916no—
539C4×D3—94no—
540C4×D3—1816no—
541C4×D3C22×C3⋊D314yescomplemented
542Dic6—916no—
543Dic6—916no—
544Dic6—94no—
545Dic6—94no—
546Dic6—1816no—
547C2×C32—24no—
548C2×C32—28no—
549C2×C32—24no—
550C2×C32—216no—
551C2×C32—416no—
552C2×C32—64no—
553C2×C32—62no—
554C2×C32#100418yescomplemented
555C2×C32#100412yescomplemented
556C2×C32C24×D314yes—
557C2×C32C24×D311yescharacteristic
558C3⋊D3—22no—
559C3⋊D3—24no—
560C3⋊D3—62no—
561C3⋊D3—68no—
562C3⋊D3—128no—
563C3×D3—216no—
564C3×D3—28no—
565C3×D3—616no—
566C3×D3—68no—
567C24—32no—
568C24—92no—
569C24—272no—
570#41—278no—
571#41—278no—
572#41—278no—
573#41—2716no—
574#41—278no—
575C2×Q8—271no—
576C2×Q8—271no—
577C2×D4—32no—
578C2×D4—38no—
579C2×D4—31no—
580C2×D4—92no—
581C2×D4—98no—
582C2×D4—91no—
583C2×D4—271no—
584C2×D4—271no—
585C2×D4—278no—
586C2×D4—2716no—
587C2×D4—2716no—
588C2×D4—271no—
589C2×D4—272no—
590C2×D4—272no—
591C2×D4—272no—
592C2×D4—2716no—
593C2×D4—272no—
594C2×D4D3×C3⋊D311yescharacteristic, complemented
595C22×C4—31no—
596C22×C4—91no—
597C22×C4—272no—
598C22×C4—272no—
599C22×C4—272no—
600C22×C4—271no—
601C22×C3—216no—
602C22×C3—24no—
603C22×C3—216no—
604C22×C3—24no—
605C22×C3—316no—
606C22×C3—38no—
607C22×C3—416no—
608C22×C3—616no—
609C22×C3—68no—
610C22×C3—94no—
611C22×C3—92no—
612C22×C3—1232no—
613C22×C3—184no—
614C22×C3—182no—
615C22×C3—368no—
616C22×C3C22×D32116yes—
617C22×C3C22×D3214yes—
618C22×C3C23×C3⋊D314yes—
619C22×C3C23×C3⋊D311yescharacteristic
620C2×D3—22no—
621C2×D3—24no—
622C2×D3—38no—
623C2×D3—316no—
624C2×D3—48no—
625C2×D3—68no—
626C2×D3—616no—
627C2×D3—98no—
628C2×D3—92no—
629C2×D3—1232no—
630C2×D3—188no—
631C2×D3—188no—
632C2×D3—182no—
633C2×D3—368no—
634C2×D3—368no—
635C2×D3—3632no—
636C2×D3C23×C3⋊D314yes—
637C2×D3C23×C3⋊D312yes—
638C3×C4—28no—
639C3×C4—38no—
640C3×C4—92no—
641C3×C4C22×D3218yes—
642C3×C4C23×C3⋊D312yes—
643Dic3—38no—
644Dic3—98no—
645Dic3—916no—
646Dic3—94no—
647Dic3—92no—
648Dic3—1816no—
649Dic3—188no—
650Dic3C23×C3⋊D312yes—
651C32—24no—
652C32C2×#100414yescomplemented
653C32C2×#100411yescharacteristic, complemented
654C23—31no—
655C23—32no—
656C23—38no—
657C23—91no—
658C23—92no—
659C23—98no—
660C23—124no—
661C23—278no—
662C23—271no—
663C23—364no—
664C23—1084no—
665C23C2×D3×C3⋊D312yes—
666Q8—274no—
667Q8—274no—
668D4—38no—
669D4—34no—
670D4—98no—
671D4—94no—
672D4—274no—
673D4—274no—
674D4—274no—
675D4—278no—
676D4—278no—
677D4—278no—
678D4—278no—
679D4C2×D3×C3⋊D314yescomplemented
680C2×C4—31no—
681C2×C4—34no—
682C2×C4—91no—
683C2×C4—94no—
684C2×C4—278no—
685C2×C4—278no—
686C2×C4—278no—
687C2×C4—272no—
688C2×C4—271no—
689C2×C4—274no—
690C2×C4C2×D3×C3⋊D311yescharacteristic
691C2×C3—216no—
692C2×C3—24no—
693C2×C3—28no—
694C2×C3—24no—
695C2×C3—416no—
696C2×C3—616no—
697C2×C3—68no—
698C2×C3—184no—
699C2×C3—182no—
700C2×C3#6431318yescomplemented
701C2×C3#6436112yescomplemented
702C2×C3C23×D3214yes—
703C2×C3C24×C3⋊D311yescharacteristic
704D3—22no—
705D3—24no—
706D3—68no—
707D3—616no—
708D3—188no—
709D3—182no—
710D3—368no—
711C22—24no—
712C22—32no—
713C22—34no—
714C22—62no—
715C22—64no—
716C22—92no—
717C22—94no—
718C22—128no—
719C22—182no—
720C22—184no—
721C22—272no—
722C22—368no—
723C22—542no—
724C22—1088no—
725C22C22×D3×C3⋊D314yes—
726C22C22×D3×C3⋊D311yescharacteristic
727C4—32no—
728C4—92no—
729C4—274no—
730C4—272no—
731C4C22×D3×C3⋊D312yes—
732C3—24no—
733C3C2×#6431314yescomplemented
734C3C2×#6436111yescharacteristic, complemented
735C2—24no—
736C2—62no—
737C2—64no—
738C2—182no—
739C2—184no—
740C2—542no—
741C2#1172458712yesdirect product factor
742C2C23×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×#89078C2semidirect
2. C2×C3×D4×C3⋊D3C2semidirect
3. C2×C32×D3×D4C2semidirect
4. C2×C3⋊D3×#67C2semidirect
5. C2×D3×#638C2semidirect
6. C22×#6290C2semidirect
7. C2×#89029C2semidirect
8. #11724587C2direct (N × H)
9. C2×#89026C2semidirect
10. C2×#89021C2semidirect
11. C2×#89020C2semidirect
12. C2×#89014C2semidirect
15. C23×C3×C3⋊D3C22semidirect
16. C23×C32×D3C22semidirect
17. C22×D3×C3⋊D3C22semidirect
18. C2×C33×D4C22semidirect
19. C2×#6312C22semidirect
20. C22×C3⋊(C3⋊Dic3)C22semidirect
21. #89078C22semidirect
22. C2×C4×C3⋊(C3⋊D3)C22semidirect
23. C2×#6308C22semidirect
24. C2×C3×#638C22semidirect
25. C3×D4×C3⋊D3C22semidirect
26. C2×C3×C4⋊(C3⋊D3)C22semidirect
27. C2×C3×C4×C3⋊D3C22semidirect
28. C2×C32×#67C22semidirect
29. C32×D3×D4C22semidirect
30. C2×C32×D12C22semidirect
31. C2×C32×C4×D3C22semidirect
32. C3⋊D3×#67C22semidirect
33. D3×#638C22semidirect
34. C2×#6293C22semidirect
35. C2×#6292C22semidirect
36. C2×#6291C22semidirect
37. C2×#6290C22semidirect
38. C2×#6290C22semidirect
39. C2×#6290C22semidirect
40. C2×#6290C22semidirect
41. C2×#6290C22semidirect
42. C2×Dic3×C3⋊D3C22semidirect
43. #89029C22semidirect
44. C2×D3×C3⋊Dic3C22semidirect
45. #89026C22semidirect
46. #89021C22semidirect
47. #89020C22semidirect
48. #89014C22semidirect
60. C2×D4×C3⋊D3D3semidirect
64. C2×C3×D3×D4D3semidirect
79. C22×C3×C3⋊D3C23semidirect
83. C22×C32×D3C23semidirect
85. C2×D3×C3⋊D3C23semidirect
86. C33×D4C23semidirect
88. #6312C23semidirect
91. C2×C3⋊(C3⋊Dic3)C23semidirect
92. C4×C3⋊(C3⋊D3)C23semidirect
93. #6308C23semidirect
94. C3×#638C23semidirect
96. C3×C4⋊(C3⋊D3)C23semidirect
97. C3×C4×C3⋊D3C23semidirect
98. C32×#67C23semidirect
100. C32×D12C23semidirect
101. C32×C4×D3C23semidirect
102. #6293C23semidirect
103. #6292C23semidirect
104. #6291C23semidirect
105. #6290C23semidirect
106. #6290C23semidirect
107. #6290C23semidirect
108. #6290C23semidirect
109. Dic3×C3⋊D3C23semidirect
110. D3×C3⋊Dic3C23semidirect
115. C23×C3⋊D3C2×D3semidirect
117. C23×C3×D3C2×D3semidirect
123. C2×C32×D4C2×D3semidirect
124. C2×C32×D4C2×D3semidirect
136. C2×#638C2×D3semidirect
148. D4×C3⋊D3C2×D3semidirect
152. C2×C4⋊(C3⋊D3)C2×D3semidirect
157. C2×C4×C3⋊D3C2×D3semidirect
163. C2×C3×#67C2×D3semidirect
165. C3×D3×D4C2×D3semidirect
167. C2×C3×D12C2×D3semidirect
169. C2×C3×C4×D3C2×D3semidirect
228. C2×D3×D4C3⋊D3semidirect
248. C22×C3⋊D3C22×D3semidirect
256. C22×C3×D3C22×D3semidirect
262. C32×D4C22×D3semidirect
263. C32×D4C22×D3semidirect
277. #638C22×D3semidirect
290. C4⋊(C3⋊D3)C22×D3semidirect
295. C4×C3⋊D3C22×D3semidirect
301. C3×#67C22×D3semidirect
305. C3×D12C22×D3semidirect
307. C3×C4×D3C22×D3semidirect
319. C2×C33H(5,𝔽2)semidirect
331. C23×D3C2×C3⋊D3semidirect
339. C2×C3×D4D32semidirect
340. C2×C3×D4C2×C3⋊D3semidirect
361. C2×#67C2×C3⋊D3semidirect
379. D3×D4C2×C3⋊D3semidirect
387. C2×D12C2×C3⋊D3semidirect
394. C2×C4×D3C2×C3⋊D3semidirect
462. C33C2×H(5,𝔽2)semidirect
488. C22×D3C22×C3⋊D3semidirect
494. C3×D4C2×D32semidirect
495. C3×D4C22×C3⋊D3semidirect
517. #67C22×C3⋊D3semidirect
534. D12C22×C3⋊D3semidirect
541. C4×D3C22×C3⋊D3semidirect
554. C2×C32#1004semidirect
555. C2×C32#1004semidirect
594. C2×D4D3×C3⋊D3semidirect
652. C32C2×#1004semidirect
653. C32C2×#1004semidirect
679. D4C2×D3×C3⋊D3semidirect
700. C2×C3#64313semidirect
701. C2×C3#64361semidirect
733. C3C2×#64313semidirect
734. C3C2×#64361semidirect
741. C2#11724587direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#890782
C2×C3×D4×C3⋊D32
C2×C32×D3×D42
C2×C3⋊D3×#672
C2×D3×#6382
C22×#62902
C2×#890292
#117245872
C2×#890262
C2×#890212
C2×#890202
C2×#890142
C2×#643613
C2×#643133