Finite Group Databasebeta

← C2×C3⋊D3×#237 #13181610

Subgroups — C2×C3⋊D3×#237 #13181610

Order 1728.

5996 conjugacy classes of subgroups.

The subgroup lattice has 720 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×#237C211yesmaximal, characteristic, complemented
4C2×C3⋊D3×#67C212yesmaximal, complemented
5C2×#89031C212yesmaximal, complemented
6C22×Dic3×C3⋊D3C212yesmaximal, complemented
7C2×#89029C212yesmaximal, complemented
8C3⋊D3×#237C2116yesmaximal, direct product factor
9C2×C4×D3×C3⋊D3C211yesmaximal, characteristic, complemented
10C2×#89021C211yesmaximal, characteristic, complemented
11C2×#89017C211yesmaximal, characteristic, complemented
12C2×C3⋊D3×Dic6C211yesmaximal, characteristic, complemented
13C2×#41×C3⋊D3—31nomaximal
14C2×D3×#237—34nomaximal
15C23×C3×C3⋊D3C2212yes—
16C22×D3×C3⋊D3C2211yescharacteristic
17C2×C33×D4C2211yescharacteristic, complemented
18C2×#6312C2212yescomplemented
19C22×C3⋊(C3⋊Dic3)C2212yescomplemented
20#89078C2218yescomplemented
21C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
22C2×#6308C2211yescharacteristic, complemented
23C2×C3×#638C2212yescomplemented
24C3×D4×C3⋊D3C2218yescomplemented
25C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
26C2×C3×C4×C3⋊D3C2211yescharacteristic
27C2×C32×#67C2212yescomplemented
28C22×C32×Dic3C2212yescomplemented
29C32×#237C2218yescomplemented
30C2×C32×C4×D3C2211yescharacteristic, complemented
31C2×C32×Dic6C2211yescharacteristic, complemented
32C3⋊D3×#67C22116yescomplemented
33C2×#6293C2212yescomplemented
34C2×#6292C2212yescomplemented
35C2×#6290C2212yescomplemented
36C2×#6289C2211yescharacteristic, complemented
37#89031C22116yescomplemented
38C2×Dic3×C3⋊D3C2212yes—
39C2×Dic3×C3⋊D3C2211yescharacteristic
40C2×Dic3×C3⋊D3C22116yescomplemented
41C2×Dic3×C3⋊D3C2212yescomplemented
42C2×Dic3×C3⋊D3C2212yescomplemented
43#89029C22116yescomplemented
44C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
45C4×D3×C3⋊D3C2218yescomplemented
46#89021C2218yescomplemented
47#89017C2218yescomplemented
48C3⋊D3×Dic6C2218yescomplemented
49C2×C32×#41—31no—
50#41×C3⋊D3—316no—
51C2×#3832—31no—
52C2×Q8×C3⋊D3—31no—
53C2×#3830—31no—
54C2×#3830—32no—
55C2×#3830—34no—
56C2×#3830—64no—
57C2×D4×C3⋊D3—32no—
58C2×D4×C3⋊D3D311yescharacteristic, complemented
59C2×#3828—32no—
60C2×#3828—31no—
61C22×C4×C3⋊D3—31no—
62C22×C4×C3⋊D3—32no—
63C2×C3×#237D314yescomplemented
64C2×C3×D3×D4—34no—
65C2×D3×#67—38no—
66C2×#3805—38no—
67C2×#3804—38no—
68C22×D3×Dic3—38no—
69D3×#237—364no—
70C2×C4×D32—34no—
71C2×#3796—34no—
72C2×#3795—34no—
73C2×D3×Dic6—34no—
74C23×C33C2312yes—
75C22×C3⋊(C3⋊D3)C2311yescharacteristic
76C22×C3×C3⋊D3—28no—
77C22×C3×C3⋊D3C2312yes—
78C22×C3×C3⋊D3C2318yes—
79C22×C3×C3⋊D3C2311yescharacteristic
80C22×C32×D3C2311yescharacteristic
81C2×D3×C3⋊D3—24no—
82C2×D3×C3⋊D3C2314yes—
83C33×D4C2314yescomplemented
84C2×C33×C4C2311yescharacteristic
85#6312C2318yescomplemented
86C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
87C2×C3⋊(C3⋊Dic3)C2312yes—
88C2×C3⋊(C3⋊Dic3)C2318yescomplemented
89C4×C3⋊(C3⋊D3)C2314yescomplemented
90#6308C2314yescomplemented
91C3×#638C2318yescomplemented
92C2×C3×C3⋊Dic3C2311yescharacteristic
93C3×C4⋊(C3⋊D3)C2314yescomplemented
94C3×C4×C3⋊D3C2314yes—
95C32×#67C2318yescomplemented
96C2×C32×Dic3C2311yescharacteristic
97C2×C32×Dic3C2312yes—
98C2×C32×Dic3C2318yescomplemented
99C32×C4×D3C2314yescomplemented
100C32×Dic6C2314yescomplemented
101#6293C2318yescomplemented
102#6292C2318yescomplemented
103#6290C2318yescomplemented
104#6289C2314yescomplemented
105Dic3×C3⋊D3C2318yes—
106Dic3×C3⋊D3C2314yes—
107Dic3×C3⋊D3C2318yescomplemented
108Dic3×C3⋊D3C2318yescomplemented
109D3×C3⋊Dic3C2314yescomplemented
110C2×D3×#41—94no—
111C22×#237—91no—
112C23×C3⋊D3—31no—
113C23×C3⋊D3C2×D312yes—
114C23×C3×D3—38no—
115C22×D32—34no—
116C32×#41—38no—
117C2×C32×Q8—31no—
118C2×C32×D4—24no—
119C2×C32×D4—32no—
120C2×C32×D4C2×D314yescomplemented
121C2×C32×D4C2×D311yescharacteristic, complemented
122C22×C32×C4—32no—
123C22×C32×C4—31no—
124C2×#638—32no—
125C2×#638—38no—
126C2×#638—32no—
127C2×#638—68no—
128C2×#638C2×D312yescomplemented
129C22×C3⋊Dic3—32no—
130C22×C3⋊Dic3—38no—
131C22×C3⋊Dic3—31no—
132C22×C3⋊Dic3—68no—
133#3832—38no—
134Q8×C3⋊D3—38no—
135#3830—38no—
136#3830—332no—
137#3830—316no—
138#3830—632no—
139D4×C3⋊D3—316no—
140D4×C3⋊D3C2×D318yescomplemented
141#3828—316no—
142#3828—38no—
143C2×C4⋊(C3⋊D3)—32no—
144C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
145C2×C4×C3⋊D3—31no—
146C2×C4×C3⋊D3—32no—
147C2×C4×C3⋊D3—32no—
148C2×C4×C3⋊D3—32no—
149C2×C4×C3⋊D3—316no—
150C2×C4×C3⋊D3—31no—
151C2×C4×C3⋊D3—34no—
152C2×C4×C3⋊D3—31no—
153C2×C4×C3⋊D3—38no—
154C2×C4×C3⋊D3—64no—
155C2×C4×C3⋊D3C2×D311yescharacteristic
156C2×#634—31no—
157C2×#634—34no—
158C2×#634—32no—
159C2×#634—64no—
160C2×C3×#67—38no—
161C2×C3×#67C2×D318yescomplemented
162C22×C3×Dic3C2×D318yescomplemented
163C3×#237C2×D3132yescomplemented
164C3×D3×D4—332no—
165C2×C3×D12—34no—
166C2×C3×C4×D3—34no—
167C2×C3×C4×D3C2×D314yescomplemented
168C2×C3×Dic6C2×D314yescomplemented
169D3×#67—364no—
170C2×#627—38no—
171C2×#626—38no—
172C2×#625—38no—
173C2×#624—34no—
174#3805—364no—
175#3804—364no—
176C2×D3×Dic3—34no—
177C2×D3×Dic3—38no—
178C2×D3×Dic3—38no—
179C2×D3×Dic3—38no—
180C2×D3×Dic3—34no—
181C2×D3×Dic3—364no—
182C4×D32—332no—
183#3796—332no—
184#3795—332no—
185D3×Dic6—332no—
186C22×C33—24no—
187C22×C33C2414yes—
188C22×C33C2411yescharacteristic
189C2×C3⋊(C3⋊D3)—22no—
190C2×C3⋊(C3⋊D3)C2412yes—
191C2×C3×C3⋊D3—24no—
192C2×C3×C3⋊D3—216no—
193C2×C3×C3⋊D3#4114yescomplemented
194C2×C3×C3⋊D3C2414yes—
195C2×C3×C3⋊D3C2412yes—
196C2×C32×D3—22no—
197C2×C32×D3C2412yes—
198D3×C3⋊D3—28no—
199C33×C4C2412yes—
200C3⋊(C3⋊Dic3)C2412yes—
201C3⋊(C3⋊Dic3)C2414yes—
202C3×C3⋊Dic3C2412yes—
203C32×Dic3C2412yes—
204C32×Dic3C2414yes—
205C2×C3×#41—34no—
206C22×C3×D4—91no—
207C22×#67—92no—
208C23×Dic3—92no—
209D3×#41—964no—
210C2×#239—94no—
211C2×D3×Q8—94no—
212C2×#237—98no—
213C2×#237—94no—
214C2×#237—91no—
215C2×#237—92no—
216C2×#237—92no—
217C2×#237—916no—
218C2×#237—91no—
219C2×#237—91no—
220C2×#237—184no—
221C2×#237C3⋊D311yescharacteristic, direct product factor
222C2×D3×D4—34no—
223C2×D3×D4—98no—
224C2×#235—94no—
225C2×#235—98no—
226C22×C4×D3—94no—
227C22×C4×D3—98no—
228C22×C4×D3—91no—
229C22×Dic6—91no—
230C23×C32—28no—
231C23×C32—31no—
232C23×C32C22×D318yes—
233C23×C32C22×D312yes—
234C22×C3⋊D3—28no—
235C22×C3⋊D3—31no—
236C22×C3⋊D3—34no—
237C22×C3⋊D3—34no—
238C22×C3⋊D3—64no—
239C22×C3⋊D3—64no—
240C22×C3⋊D3C22×D312yes—
241C22×C3⋊D3C22×D318yes—
242C22×C3⋊D3C22×D311yescharacteristic
243C22×C3×D3—34no—
244C22×C3×D3—38no—
245C22×C3×D3—332no—
246C22×C3×D3—632no—
247C22×C3×D3C22×D314yes—
248C2×D32—316no—
249C2×D32—616no—
250C32×Q8—34no—
251C32×D4—216no—
252C32×D4—38no—
253C32×D4C22×D3116yescomplemented
254C32×D4C22×D314yescomplemented
255C2×C32×C4—24no—
256C2×C32×C4—32no—
257C2×C32×C4—31no—
258C2×C32×C4—38no—
259C2×C32×C4—34no—
260C2×C32×C4C22×D314yes—
261C2×C32×C4C22×D311yescharacteristic
262#638—38no—
263#638—38no—
264#638—332no—
265#638—632no—
266#638C22×D318yescomplemented
267C2×C3⋊Dic3—32no—
268C2×C3⋊Dic3—31no—
269C2×C3⋊Dic3—38no—
270C2×C3⋊Dic3—34no—
271C2×C3⋊Dic3—34no—
272C2×C3⋊Dic3—38no—
273C2×C3⋊Dic3—332no—
274C2×C3⋊Dic3—68no—
275C2×C3⋊Dic3—64no—
276C2×C3⋊Dic3—632no—
277C2×C3⋊Dic3C22×D311yescharacteristic
278C4⋊(C3⋊D3)—38no—
279C4⋊(C3⋊D3)C22×D314yescomplemented
280C4×C3⋊D3—34no—
281C4×C3⋊D3—38no—
282C4×C3⋊D3—38no—
283C4×C3⋊D3—38no—
284C4×C3⋊D3—34no—
285C4×C3⋊D3—34no—
286C4×C3⋊D3—316no—
287C4×C3⋊D3—616no—
288C4×C3⋊D3C22×D314yes—
289#634—34no—
290#634—38no—
291#634—316no—
292#634—616no—
293C3×#67—332no—
294C3×#67C22×D3132yescomplemented
295C2×C3×Dic3—34no—
296C2×C3×Dic3C22×D314yes—
297C2×C3×Dic3C22×D318yes—
298C2×C3×Dic3C22×D3132yescomplemented
299C3×D12—316no—
300C3×C4×D3—316no—
301C3×C4×D3C22×D3116yescomplemented
302C3×Dic6C22×D3116yescomplemented
303#627—332no—
304#626—332no—
305#625—332no—
306#624—316no—
307D3×Dic3—316no—
308D3×Dic3—332no—
309D3×Dic3—316no—
310D3×Dic3—332no—
311D3×Dic3—332no—
312C22×#41—271noSylow
313C2×C33—24no—
314C2×C33C2×#4112yescomplemented
315C2×C33C2511yescharacteristic
316C3⋊(C3⋊D3)—22no—
317C3×C3⋊D3—24no—
318C3×C3⋊D3C2×#4114yescomplemented
319C32×D3—22no—
320C24×C3—92no—
321C23×D3—38no—
322C23×D3—94no—
323C23×D3—91no—
324C3×#41—332no—
325C2×C3×Q8—34no—
326C2×C3×D4—24no—
327C2×C3×D4—38no—
328C2×C3×D4—92no—
329C2×C3×D4—98no—
330C2×C3×D4—91no—
331C2×C3×D4D3214yescomplemented
332C2×C3×D4C2×C3⋊D311yescharacteristic, complemented
333C22×C3×C4—38no—
334C22×C3×C4—34no—
335C22×C3×C4—91no—
336C2×#67—38no—
337C2×#67—98no—
338C2×#67—98no—
339C2×#67—92no—
340C2×#67—92no—
341C2×#67—916no—
342C2×#67—92no—
343C2×#67—188no—
344C2×#67C2×C3⋊D312yescomplemented
345C22×Dic3—94no—
346C22×Dic3—98no—
347C22×Dic3—92no—
348C22×Dic3—92no—
349C22×Dic3—91no—
350C22×Dic3—92no—
351C22×Dic3—92no—
352C22×Dic3—916no—
353C22×Dic3—188no—
354C22×Dic3C2×C3⋊D312yescomplemented
355#239—932no—
356D3×Q8—932no—
357#237—964no—
358#237—932no—
359#237—98no—
360#237—916no—
361#237—916no—
362#237—98no—
363#237—98no—
364#237—1832no—
365#237C2×C3⋊D318yesdirect product factor
366D3×D4—332no—
367D3×D4—964no—
368#235—932no—
369#235—964no—
370C2×D12—34no—
371C2×D12—98no—
372C2×C4×D3—34no—
373C2×C4×D3—932no—
374C2×C4×D3—94no—
375C2×C4×D3—94no—
376C2×C4×D3—98no—
377C2×C4×D3—98no—
378C2×C4×D3—98no—
379C2×C4×D3—964no—
380C2×C4×D3—91no—
381C2×C4×D3—94no—
382C2×C4×D3—91no—
383C2×C4×D3—91no—
384C2×C4×D3—98no—
385C2×C4×D3—184no—
386C2×C4×D3C2×C3⋊D311yescharacteristic, complemented
387C2×Dic6—98no—
388C2×Dic6—94no—
389C2×Dic6—91no—
390C2×Dic6—92no—
391C2×Dic6—98no—
392C2×Dic6—184no—
393C2×Dic6C2×C3⋊D311yescharacteristic, complemented
394C22×C32—24no—
395C22×C32—24no—
396C22×C32—216no—
397C22×C32—216no—
398C22×C32—32no—
399C22×C32—416no—
400C22×C32—62no—
401C22×C32C23×D3116yes—
402C22×C32C23×D314yes—
403C22×C32C23×D314yes—
404C22×C32C23×D311yescharacteristic
405C2×C3⋊D3—24no—
406C2×C3⋊D3—216no—
407C2×C3⋊D3—32no—
408C2×C3⋊D3—38no—
409C2×C3⋊D3—68no—
410C2×C3⋊D3—62no—
411C2×C3⋊D3—68no—
412C2×C3⋊D3—68no—
413C2×C3⋊D3—128no—
414C2×C3⋊D3#23714yesdirect product factor
415C2×C3⋊D3C23×D314yes—
416C2×C3⋊D3C23×D312yes—
417C2×C3×D3—28no—
418C2×C3×D3—316no—
419C2×C3×D3—38no—
420C2×C3×D3—316no—
421C2×C3×D3—664no—
422C2×C3×D3—616no—
423C2×C3×D3C23×D318yes—
424D32—632no—
425C32×C4—28no—
426C32×C4—34no—
427C32×C4—32no—
428C32×C4C23×D318yes—
429C32×C4C23×D312yes—
430C3⋊Dic3—34no—
431C3⋊Dic3—32no—
432C3⋊Dic3—38no—
433C3⋊Dic3—316no—
434C3⋊Dic3—616no—
435C3⋊Dic3—68no—
436C3⋊Dic3C23×D312yes—
437C3×Dic3—38no—
438C3×Dic3C23×D318yes—
439C3×Dic3C23×D3116yes—
440C2×#41—31no—
441C2×#41—272no—
442C2×#41—271no—
443C2×#41—272no—
444C2×#41—271no—
445C2×#41—2716no—
446C2×#41—271no—
447C22×Q8—271no—
448C22×D4—91no—
449C22×D4—272no—
450C23×C4—271no—
451C23×C4—272no—
452C33C22×#4111yescharacteristic, complemented, Sylow
453C23×C3—28no—
454C23×C3—34no—
455C23×C3—91no—
456C23×C3—98no—
457C23×C3—92no—
458C23×C3—188no—
459C23×C3C2×D3218yes—
460C23×C3C22×C3⋊D312yes—
461C22×D3—34no—
462C22×D3—38no—
463C22×D3—332no—
464C22×D3—632no—
465C22×D3—916no—
466C22×D3—94no—
467C22×D3—91no—
468C22×D3—94no—
469C22×D3—184no—
470C22×D3—184no—
471C22×D3—1816no—
472C22×D3C22×C3⋊D311yescharacteristic
473C3×Q8—316no—
474C3×D4—216no—
475C3×D4—332no—
476C3×D4—98no—
477C3×D4—94no—
478C3×D4C2×D32116yescomplemented
479C3×D4C22×C3⋊D314yescomplemented
480C2×C3×C4—24no—
481C2×C3×C4—38no—
482C2×C3×C4—34no—
483C2×C3×C4—332no—
484C2×C3×C4—316no—
485C2×C3×C4—91no—
486C2×C3×C4—94no—
487C2×C3×C4C2×D3214yes—
488C2×C3×C4C22×C3⋊D311yescharacteristic
489#67—332no—
490#67—932no—
491#67—932no—
492#67—98no—
493#67—98no—
494#67—98no—
495#67—1832no—
496#67C22×C3⋊D318yescomplemented
497C2×Dic3—34no—
498C2×Dic3—916no—
499C2×Dic3—98no—
500C2×Dic3—94no—
501C2×Dic3—932no—
502C2×Dic3—92no—
503C2×Dic3—91no—
504C2×Dic3—98no—
505C2×Dic3—98no—
506C2×Dic3—94no—
507C2×Dic3—98no—
508C2×Dic3—98no—
509C2×Dic3—188no—
510C2×Dic3—184no—
511C2×Dic3—1832no—
512C2×Dic3C22×C3⋊D312yes—
513C2×Dic3C22×C3⋊D311yescharacteristic
514C2×Dic3C22×C3⋊D318yescomplemented
515D12—316no—
516D12—932no—
517C4×D3—316no—
518C4×D3—916no—
519C4×D3—916no—
520C4×D3—932no—
521C4×D3—932no—
522C4×D3—932no—
523C4×D3—94no—
524C4×D3—916no—
525C4×D3—94no—
526C4×D3—94no—
527C4×D3—1816no—
528C4×D3C22×C3⋊D314yescomplemented
529Dic6—932no—
530Dic6—916no—
531Dic6—94no—
532Dic6—98no—
533Dic6—1816no—
534Dic6C22×C3⋊D314yescomplemented
535C2×C32—24no—
536C2×C32—28no—
537C2×C32—24no—
538C2×C32—216no—
539C2×C32—416no—
540C2×C32—62no—
541C2×C32C2×#23712yescomplemented
542C2×C32D3×#4118yescomplemented
543C2×C32C24×D314yes—
544C2×C32C24×D311yescharacteristic
545C3⋊D3—24no—
546C3⋊D3—62no—
547C3⋊D3—68no—
548C3⋊D3—128no—
549C3⋊D3C2×#23714yesdirect product factor
550C3×D3—28no—
551C3×D3—316no—
552C3×D3—616no—
553C24—92no—
554C24—271no—
555#41—38no—
556#41—2716no—
557#41—278no—
558#41—2716no—
559#41—278no—
560#41—278no—
561C2×Q8—31no—
562C2×Q8—272no—
563C2×Q8—278no—
564C2×Q8—271no—
565C2×D4—32no—
566C2×D4—92no—
567C2×D4—98no—
568C2×D4—91no—
569C2×D4—272no—
570C2×D4—2716no—
571C2×D4—272no—
572C2×D4—272no—
573C2×D4D3×C3⋊D311yescharacteristic, complemented
574C22×C4—32no—
575C22×C4—31no—
576C22×C4—91no—
577C22×C4—271no—
578C22×C4—278no—
579C22×C4—271no—
580C22×C4—272no—
581C22×C4—2716no—
582C22×C4—272no—
583C22×C4—272no—
584C22×C4—271no—
585C22×C4—272no—
586C22×C4—271no—
587C22×C3—216no—
588C22×C3—24no—
589C22×C3—216no—
590C22×C3—24no—
591C22×C3—38no—
592C22×C3—416no—
593C22×C3—68no—
594C22×C3—94no—
595C22×C3—92no—
596C22×C3—94no—
597C22×C3—1816no—
598C22×C3—184no—
599C22×C3C22×D32116yes—
600C22×C3C22×D3214yes—
601C22×C3C23×C3⋊D314yes—
602C22×C3C23×C3⋊D311yescharacteristic
603C2×D3—22no—
604C2×D3—316no—
605C2×D3—38no—
606C2×D3—316no—
607C2×D3—664no—
608C2×D3—616no—
609C2×D3—98no—
610C2×D3—92no—
611C2×D3—188no—
612C2×D3—188no—
613C2×D3—1832no—
614C2×D3—188no—
615C2×D3—182no—
616C2×D3—368no—
617C2×D3C23×C3⋊D312yes—
618C3×C4—28no—
619C3×C4—316no—
620C3×C4—38no—
621C3×C4—92no—
622C3×C4C22×D3218yes—
623C3×C4C23×C3⋊D312yes—
624Dic3—38no—
625Dic3—916no—
626Dic3—98no—
627Dic3—94no—
628Dic3—92no—
629Dic3—1816no—
630Dic3—188no—
631Dic3C23×C3⋊D314yes—
632Dic3C23×C3⋊D312yes—
633C32—24no—
634C32C22×#23711yescharacteristic, complemented
635C32C2×D3×#4114yescomplemented
636C23—31no—
637C23—91no—
638C23—98no—
639C23—92no—
640C23—188no—
641C23—274no—
642C23—271no—
643C23—544no—
644C23C2×D3×C3⋊D312yes—
645Q8—34no—
646Q8—278no—
647Q8—274no—
648D4—38no—
649D4—98no—
650D4—94no—
651D4—278no—
652D4—278no—
653D4—278no—
654D4C2×D3×C3⋊D314yescomplemented
655C2×C4—38no—
656C2×C4—31no—
657C2×C4—32no—
658C2×C4—34no—
659C2×C4—91no—
660C2×C4—94no—
661C2×C4—274no—
662C2×C4—274no—
663C2×C4—278no—
664C2×C4—278no—
665C2×C4—278no—
666C2×C4—274no—
667C2×C4—278no—
668C2×C4—271no—
669C2×C4—272no—
670C2×C4—274no—
671C2×C4C2×D3×C3⋊D311yescharacteristic
672C2×C3—216no—
673C2×C3—24no—
674C2×C3—28no—
675C2×C3—24no—
676C2×C3—416no—
677C2×C3—68no—
678C2×C3—94no—
679C2×C3—184no—
680C2×C3D3×#23718yescomplemented
681C2×C3#41×C3⋊D312yescomplemented
682C2×C3C23×D3214yes—
683C2×C3C24×C3⋊D311yescharacteristic
684D3—22no—
685D3—316no—
686D3—616no—
687D3—188no—
688D3—182no—
689D3—368no—
690C22—24no—
691C22—32no—
692C22—62no—
693C22—94no—
694C22—92no—
695C22—94no—
696C22—1816no—
697C22—184no—
698C22—272no—
699C22—548no—
700C22—542no—
701C22C22×D3×C3⋊D314yes—
702C22C22×D3×C3⋊D311yescharacteristic
703C4—32no—
704C4—34no—
705C4—92no—
706C4—272no—
707C4—274no—
708C4C22×D3×C3⋊D312yes—
709C3—24no—
710C3C2×D3×#23714yescomplemented
711C3C2×#41×C3⋊D311yescharacteristic, complemented
712C2—24no—
713C2—62no—
714C2—94no—
715C2—184no—
716C2—542no—
717C2C3⋊D3×#23712yesdirect product factor
718C2C23×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
hypocenterC33C22×#41
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×#237C2semidirect
4. C2×C3⋊D3×#67C2semidirect
5. C2×#89031C2semidirect
6. C22×Dic3×C3⋊D3C2semidirect
7. C2×#89029C2semidirect
8. C3⋊D3×#237C2direct (N × H)
9. C2×C4×D3×C3⋊D3C2semidirect
10. C2×#89021C2semidirect
11. C2×#89017C2semidirect
12. C2×C3⋊D3×Dic6C2semidirect
17. C2×C33×D4C22semidirect
18. C2×#6312C22semidirect
19. C22×C3⋊(C3⋊Dic3)C22semidirect
20. #89078C22semidirect
21. C2×C4×C3⋊(C3⋊D3)C22semidirect
22. C2×#6308C22semidirect
23. C2×C3×#638C22semidirect
24. C3×D4×C3⋊D3C22semidirect
25. C2×C3×C4⋊(C3⋊D3)C22semidirect
27. C2×C32×#67C22semidirect
28. C22×C32×Dic3C22semidirect
29. C32×#237C22semidirect
30. C2×C32×C4×D3C22semidirect
31. C2×C32×Dic6C22semidirect
32. C3⋊D3×#67C22semidirect
33. C2×#6293C22semidirect
34. C2×#6292C22semidirect
35. C2×#6290C22semidirect
36. C2×#6289C22semidirect
37. #89031C22semidirect
40. C2×Dic3×C3⋊D3C22semidirect
41. C2×Dic3×C3⋊D3C22semidirect
42. C2×Dic3×C3⋊D3C22semidirect
43. #89029C22semidirect
44. C2×D3×C3⋊Dic3C22semidirect
45. C4×D3×C3⋊D3C22semidirect
46. #89021C22semidirect
47. #89017C22semidirect
48. C3⋊D3×Dic6C22semidirect
58. C2×D4×C3⋊D3D3semidirect
63. C2×C3×#237D3semidirect
83. C33×D4C23semidirect
85. #6312C23semidirect
88. C2×C3⋊(C3⋊Dic3)C23semidirect
89. C4×C3⋊(C3⋊D3)C23semidirect
90. #6308C23semidirect
91. C3×#638C23semidirect
93. C3×C4⋊(C3⋊D3)C23semidirect
95. C32×#67C23semidirect
98. C2×C32×Dic3C23semidirect
99. C32×C4×D3C23semidirect
100. C32×Dic6C23semidirect
101. #6293C23semidirect
102. #6292C23semidirect
103. #6290C23semidirect
104. #6289C23semidirect
107. Dic3×C3⋊D3C23semidirect
108. Dic3×C3⋊D3C23semidirect
109. D3×C3⋊Dic3C23semidirect
120. C2×C32×D4C2×D3semidirect
121. C2×C32×D4C2×D3semidirect
128. C2×#638C2×D3semidirect
140. D4×C3⋊D3C2×D3semidirect
144. C2×C4⋊(C3⋊D3)C2×D3semidirect
161. C2×C3×#67C2×D3semidirect
162. C22×C3×Dic3C2×D3semidirect
163. C3×#237C2×D3semidirect
167. C2×C3×C4×D3C2×D3semidirect
168. C2×C3×Dic6C2×D3semidirect
193. C2×C3×C3⋊D3#41semidirect
221. C2×#237C3⋊D3direct (N × H)
253. C32×D4C22×D3semidirect
254. C32×D4C22×D3semidirect
266. #638C22×D3semidirect
279. C4⋊(C3⋊D3)C22×D3semidirect
294. C3×#67C22×D3semidirect
298. C2×C3×Dic3C22×D3semidirect
301. C3×C4×D3C22×D3semidirect
302. C3×Dic6C22×D3semidirect
314. C2×C33C2×#41semidirect
318. C3×C3⋊D3C2×#41semidirect
331. C2×C3×D4D32semidirect
332. C2×C3×D4C2×C3⋊D3semidirect
344. C2×#67C2×C3⋊D3semidirect
354. C22×Dic3C2×C3⋊D3semidirect
365. #237C2×C3⋊D3direct (N × H)
386. C2×C4×D3C2×C3⋊D3semidirect
393. C2×Dic6C2×C3⋊D3semidirect
414. C2×C3⋊D3#237direct (N × H)
452. C33C22×#41semidirect
478. C3×D4C2×D32semidirect
479. C3×D4C22×C3⋊D3semidirect
496. #67C22×C3⋊D3semidirect
514. C2×Dic3C22×C3⋊D3semidirect
528. C4×D3C22×C3⋊D3semidirect
534. Dic6C22×C3⋊D3semidirect
541. C2×C32C2×#237semidirect
542. C2×C32D3×#41semidirect
549. C3⋊D3C2×#237direct (N × H)
573. C2×D4D3×C3⋊D3semidirect
634. C32C22×#237semidirect
635. C32C2×D3×#41semidirect
654. D4C2×D3×C3⋊D3semidirect
680. C2×C3D3×#237semidirect
681. C2×C3#41×C3⋊D3semidirect
710. C3C2×D3×#237semidirect
711. C3C2×#41×C3⋊D3semidirect
717. C2C3⋊D3×#237direct (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×#2372
C2×C3⋊D3×#672
C2×#890312
C22×Dic3×C3⋊D32
C2×#890292
C3⋊D3×#2372
C2×C4×D3×C3⋊D32
C2×#890212
C2×#890172
C2×C3⋊D3×Dic62
C2×#41×C3⋊D33
C2×D3×#2373