Finite Group Databasebeta

← C2×C3×D3×#237 #13181547

Subgroups — C2×C3×D3×#237 #13181547

Order 1728.

4178 conjugacy classes of subgroups.

The subgroup lattice has 1092 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3830C211yesmaximal, characteristic, complemented
2C2×C32×#237C211yesmaximal, characteristic, complemented
3C2×C32×D3×D4C211yesmaximal, characteristic, complemented
4C2×C3×D3×#67C212yesmaximal, complemented
5C2×C3×#3805C212yesmaximal, complemented
6C2×C3×#3804C212yesmaximal, complemented
7C22×C3×D3×Dic3C212yesmaximal, complemented
8C3×D3×#237C2116yesmaximal, direct product factor
9C2×C3×C4×D32C211yesmaximal, characteristic, complemented
10C2×C3×#3796C211yesmaximal, characteristic, complemented
11C2×C3×#3795C211yesmaximal, characteristic, complemented
12C2×C3×D3×Dic6C211yesmaximal, characteristic, complemented
13C2×C3×D3×#41—31nomaximal
14C22×C3×#237—31nomaximal
15C2×D3×#237C311yesmaximal, characteristic, direct product factor
16C23×C32×D3C2212yes—
17C22×C3×D32C2211yescharacteristic
18C2×C33×D4C2211yescharacteristic, complemented
19C2×C3×#638C2212yescomplemented
20C22×C3×C3⋊Dic3C2212yescomplemented
21C3×#3830C2218yescomplemented
22C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
23C2×C3×#634C2211yescharacteristic, complemented
24C2×C32×#67C2212yescomplemented
25C2×C32×#67C2212yescomplemented
26C22×C32×Dic3C2212yescomplemented
27C32×#237C2218yescomplemented
28C32×D3×D4C2218yescomplemented
29C2×C32×D12C2211yescharacteristic, complemented
30C2×C32×C4×D3C2211yescharacteristic
31C2×C32×C4×D3C2211yescharacteristic, complemented
32C2×C32×Dic6C2211yescharacteristic, complemented
33C3×D3×#67C22116yescomplemented
34C2×C3×#627C2212yescomplemented
35C2×C3×#626C2212yescomplemented
36C2×C3×#625C2212yescomplemented
37C2×C3×#624C2211yescharacteristic, complemented
38C3×#3805C22116yescomplemented
39C3×#3804C22116yescomplemented
40C2×C3×D3×Dic3C2211yescharacteristic
41C2×C3×D3×Dic3C2212yes—
42C2×C3×D3×Dic3C22116yescomplemented
43C2×C3×D3×Dic3C2212yescomplemented
44C2×C3×D3×Dic3C2212yescomplemented
45C2×C3×D3×Dic3C2211yescharacteristic, complemented
46C3×C4×D32C2218yescomplemented
47C3×#3796C2218yescomplemented
48C3×#3795C2218yescomplemented
49C3×D3×Dic6C2218yescomplemented
50C2×C32×#41—31no—
51C22×C32×D4—31no—
52C2×#3830C2×C311yescharacteristic, complemented
53C22×C3×#67—32no—
54C23×C3×Dic3—32no—
55C3×D3×#41—316no—
56C2×C3×#239—31no—
57C2×C3×D3×Q8—31no—
58C2×C3×#237—21no—
59C2×C3×#237—31no—
60C2×C3×#237—31no—
61C2×C3×#237—32no—
62C2×C3×#237—32no—
63C2×C3×#237—32no—
64C2×C3×#237—316no—
65C2×C3×#237—31no—
66C2×C3×#237—31no—
67C2×C3×#237—61no—
68C2×C3×#237D311yescharacteristic, direct product factor
69C2×C3×#237C2×C311yescharacteristic, complemented
70C2×C3×D3×D4—21no—
71C2×C3×D3×D4—32no—
72C2×C3×D3×D4D311yescharacteristic, complemented
73C2×C3×D3×D4C2×C311yescharacteristic, complemented
74C2×C3×#235—32no—
75C2×C3×#235—31no—
76C22×C3×C4×D3—31no—
77C22×C3×C4×D3—31no—
78C22×C3×C4×D3—32no—
79C22×C3×Dic6—31no—
80C2×D3×#67C2×C312yescomplemented
81C2×#3805C2×C312yescomplemented
82C2×#3804C2×C312yescomplemented
83C22×D3×Dic3C2×C312yescomplemented
84D3×#237C2×C3116yesdirect product factor
85C2×C4×D32C2×C311yescharacteristic, complemented
86C2×#3796C2×C311yescharacteristic, complemented
87C2×#3795C2×C311yescharacteristic, complemented
88C2×D3×Dic6C2×C311yescharacteristic, complemented
89C23×C33C2312yes—
90C22×C3×C3⋊D3C2311yescharacteristic
91C22×C32×D3—28no—
92C22×C32×D3C2311yescharacteristic
93C22×C32×D3C2312yes—
94C22×C32×D3C2318yes—
95C22×C32×D3C2311yescharacteristic
96C2×C3×D32—24no—
97C2×C3×D32C2314yes—
98C33×D4C2314yescomplemented
99C2×C33×C4C2311yescharacteristic
100C3×#638C2318yescomplemented
101C2×C3×C3⋊Dic3C2311yescharacteristic
102C2×C3×C3⋊Dic3C2312yes—
103C2×C3×C3⋊Dic3C2318yescomplemented
104C3×C4×C3⋊D3C2314yescomplemented
105C3×#634C2314yescomplemented
106C32×#67C2318yescomplemented
107C32×#67C2318yescomplemented
108C2×C32×Dic3C2311yescharacteristic
109C2×C32×Dic3C2312yes—
110C2×C32×Dic3C2311yescharacteristic
111C2×C32×Dic3C2318yescomplemented
112C32×D12C2314yescomplemented
113C32×C4×D3C2314yes—
114C32×C4×D3C2314yescomplemented
115C32×Dic6C2314yescomplemented
116C3×#627C2318yescomplemented
117C3×#626C2318yescomplemented
118C3×#625C2318yescomplemented
119C3×#624C2314yescomplemented
120C3×D3×Dic3C2318yes—
121C3×D3×Dic3C2314yes—
122C3×D3×Dic3C2318yescomplemented
123C3×D3×Dic3C2318yescomplemented
124C3×D3×Dic3C2314yescomplemented
125C22×C3×#41—91no—
126C2×D3×#41—31no—
127C22×#237—31no—
128C24×C32—32no—
129C23×C3×D3—22no—
130C23×C3×D3—31no—
131C23×C3×D3—31no—
132C23×C3×D3C2×D312yes—
133C23×C3×D3C22×C312yes—
134C22×D32C22×C311yescharacteristic
135C32×#41—38no—
136C2×C32×Q8—31no—
137C2×C32×D4—21no—
138C2×C32×D4—21no—
139C2×C32×D4—21no—
140C2×C32×D4—32no—
141C2×C32×D4—32no—
142C2×C32×D4—38no—
143C2×C32×D4—31no—
144C2×C32×D4—41no—
145C2×C32×D4C2×D311yescharacteristic, complemented
146C2×C32×D4C2×D311yescharacteristic, complemented
147C2×C32×D4C22×C311yescharacteristic, complemented
148C22×C32×C4—32no—
149C22×C32×C4—31no—
150C22×C32×C4—31no—
151C2×#638C22×C312yescomplemented
152C22×C3⋊Dic3C22×C312yescomplemented
153#3830C22×C318yescomplemented
154C2×C4×C3⋊D3C22×C311yescharacteristic, complemented
155C2×#634C22×C311yescharacteristic, complemented
156C2×C3×#67—22no—
157C2×C3×#67—22no—
158C2×C3×#67—32no—
159C2×C3×#67—32no—
160C2×C3×#67—32no—
161C2×C3×#67—32no—
162C2×C3×#67—316no—
163C2×C3×#67—32no—
164C2×C3×#67—62no—
165C2×C3×#67C2×D312yescomplemented
166C2×C3×#67C2×D312yescomplemented
167C2×C3×#67C22×C312yescomplemented
168C2×C3×#67C22×C312yescomplemented
169C22×C3×Dic3—22no—
170C22×C3×Dic3—32no—
171C22×C3×Dic3—32no—
172C22×C3×Dic3—32no—
173C22×C3×Dic3—31no—
174C22×C3×Dic3—31no—
175C22×C3×Dic3—32no—
176C22×C3×Dic3—32no—
177C22×C3×Dic3—316no—
178C22×C3×Dic3—62no—
179C22×C3×Dic3C2×D312yescomplemented
180C22×C3×Dic3C22×C312yescomplemented
181C3×#239—38no—
182C3×D3×Q8—38no—
183C3×#237—28no—
184C3×#237—38no—
185C3×#237—38no—
186C3×#237—316no—
187C3×#237—316no—
188C3×#237—316no—
189C3×#237—38no—
190C3×#237—38no—
191C3×#237—68no—
192C3×#237C2×D318yesdirect product factor
193C3×#237C22×C318yescomplemented
194C3×D3×D4—28no—
195C3×D3×D4—316no—
196C3×D3×D4C2×D318yescomplemented
197C3×D3×D4C22×C318yescomplemented
198C3×#235—316no—
199C3×#235—38no—
200C2×C3×D12—21no—
201C2×C3×D12—32no—
202C2×C3×D12C2×D311yescharacteristic, complemented
203C2×C3×D12C22×C311yescharacteristic, complemented
204C2×C3×C4×D3—21no—
205C2×C3×C4×D3—21no—
206C2×C3×C4×D3—31no—
207C2×C3×C4×D3—32no—
208C2×C3×C4×D3—32no—
209C2×C3×C4×D3—31no—
210C2×C3×C4×D3—32no—
211C2×C3×C4×D3—316no—
212C2×C3×C4×D3—31no—
213C2×C3×C4×D3—31no—
214C2×C3×C4×D3—31no—
215C2×C3×C4×D3—31no—
216C2×C3×C4×D3—38no—
217C2×C3×C4×D3—38no—
218C2×C3×C4×D3—61no—
219C2×C3×C4×D3C2×D311yescharacteristic
220C2×C3×C4×D3C2×D311yescharacteristic, complemented
221C2×C3×C4×D3C22×C311yescharacteristic
222C2×C3×C4×D3C22×C311yescharacteristic, complemented
223C2×C3×Dic6—21no—
224C2×C3×Dic6—31no—
225C2×C3×Dic6—31no—
226C2×C3×Dic6—32no—
227C2×C3×Dic6—32no—
228C2×C3×Dic6—38no—
229C2×C3×Dic6—61no—
230C2×C3×Dic6C2×D311yescharacteristic, complemented
231C2×C3×Dic6C22×C311yescharacteristic, complemented
232D3×#67C22×C3116yescomplemented
233C2×#627C22×C312yescomplemented
234C2×#626C22×C312yescomplemented
235C2×#625C22×C312yescomplemented
236C2×#624C22×C311yescharacteristic, complemented
237#3805C22×C3116yescomplemented
238#3804C22×C3116yescomplemented
239C2×D3×Dic3C22×C312yes—
240C2×D3×Dic3C22×C311yescharacteristic
241C2×D3×Dic3C22×C3116yescomplemented
242C2×D3×Dic3C22×C312yescomplemented
243C2×D3×Dic3C22×C312yescomplemented
244C2×D3×Dic3C22×C311yescharacteristic, complemented
245C4×D32C22×C318yescomplemented
246#3796C22×C318yescomplemented
247#3795C22×C318yescomplemented
248D3×Dic6C22×C318yescomplemented
249C22×C33—24no—
250C22×C33C2414yes—
251C22×C33C2411yescharacteristic
252C2×C3×C3⋊D3—22no—
253C2×C3×C3⋊D3C2412yes—
254C2×C32×D3—22no—
255C2×C32×D3—24no—
256C2×C32×D3—216no—
257C2×C32×D3#4114yescomplemented
258C2×C32×D3C2414yes—
259C2×C32×D3C2412yes—
260C2×C32×D3C2412yes—
261C3×D32—28no—
262C33×C4C2412yes—
263C3×C3⋊Dic3C2412yes—
264C3×C3⋊Dic3C2414yes—
265C32×Dic3C2412yes—
266C32×Dic3C2414yes—
267C32×Dic3C2412yes—
268C2×C3×#41—31no—
269C2×C3×#41—31no—
270C2×C3×#41—61no—
271C2×C3×#41—92no—
272C2×C3×#41—91no—
273C2×C3×#41—92no—
274C2×C3×#41—91no—
275C2×C3×#41—916no—
276C2×C3×#41—91no—
277C22×C3×Q8—91no—
278C22×C3×D4—31no—
279C22×C3×D4—31no—
280C22×C3×D4—61no—
281C22×C3×D4—92no—
282C23×C3×C4—91no—
283C23×C3×C4—92no—
284C22×#67—32no—
285C23×Dic3—32no—
286D3×#41—316no—
287C2×#239—31no—
288C2×D3×Q8—31no—
289C2×#237—31no—
290C2×#237—31no—
291C2×#237—32no—
292C2×#237—32no—
293C2×#237—32no—
294C2×#237—316no—
295C2×#237—31no—
296C2×#237—31no—
297C2×#237—61no—
298C2×#237C3×D311yescharacteristic, direct product factor
299C2×D3×D4—32no—
300C2×D3×D4C3×D311yescharacteristic, complemented
301C2×#235—32no—
302C2×#235—31no—
303C22×C4×D3—32no—
304C22×C4×D3—31no—
305C22×C4×D3—31no—
306C22×Dic6—31no—
307C23×C32—22no—
308C23×C32—22no—
309C23×C32—22no—
310C23×C32—31no—
311C23×C32—31no—
312C23×C32—38no—
313C23×C32—32no—
314C23×C32—42no—
315C23×C32—68no—
316C23×C32C22×D312yes—
317C23×C32C22×D312yes—
318C23×C32C23×C312yes—
319C22×C3⋊D3C23×C311yescharacteristic
320C22×C3×D3—28no—
321C22×C3×D3—28no—
322C22×C3×D3—21no—
323C22×C3×D3—22no—
324C22×C3×D3—28no—
325C22×C3×D3—21no—
326C22×C3×D3—31no—
327C22×C3×D3—31no—
328C22×C3×D3—34no—
329C22×C3×D3—34no—
330C22×C3×D3—48no—
331C22×C3×D3—61no—
332C22×C3×D3—64no—
333C22×C3×D3—64no—
334C22×C3×D3C22×D311yescharacteristic
335C22×C3×D3C22×D312yes—
336C22×C3×D3C22×D318yes—
337C22×C3×D3C22×D311yescharacteristic
338C22×C3×D3C23×C311yescharacteristic
339C22×C3×D3C23×C312yes—
340C22×C3×D3C23×C318yes—
341C22×C3×D3C23×C311yescharacteristic
342C2×D32—24no—
343C2×D32C23×C314yes—
344C32×Q8—34no—
345C32×D4—24no—
346C32×D4—24no—
347C32×D4—24no—
348C32×D4—38no—
349C32×D4—38no—
350C32×D4—34no—
351C32×D4—44no—
352C32×D4C22×D314yescomplemented
353C32×D4C22×D314yescomplemented
354C32×D4C23×C314yescomplemented
355C2×C32×C4—21no—
356C2×C32×C4—21no—
357C2×C32×C4—21no—
358C2×C32×C4—31no—
359C2×C32×C4—32no—
360C2×C32×C4—31no—
361C2×C32×C4—38no—
362C2×C32×C4—34no—
363C2×C32×C4—34no—
364C2×C32×C4—41no—
365C2×C32×C4C22×D311yescharacteristic
366C2×C32×C4C22×D311yescharacteristic
367C2×C32×C4C23×C311yescharacteristic
368#638C23×C318yescomplemented
369C2×C3⋊Dic3C23×C311yescharacteristic
370C2×C3⋊Dic3C23×C312yes—
371C2×C3⋊Dic3C23×C318yescomplemented
372C4×C3⋊D3C23×C314yescomplemented
373#634C23×C314yescomplemented
374C3×#67—28no—
375C3×#67—28no—
376C3×#67—38no—
377C3×#67—38no—
378C3×#67—38no—
379C3×#67—38no—
380C3×#67—38no—
381C3×#67—68no—
382C3×#67C22×D318yescomplemented
383C3×#67C22×D318yescomplemented
384C3×#67C23×C318yescomplemented
385C3×#67C23×C318yescomplemented
386C2×C3×Dic3—22no—
387C2×C3×Dic3—21no—
388C2×C3×Dic3—21no—
389C2×C3×Dic3—28no—
390C2×C3×Dic3—32no—
391C2×C3×Dic3—32no—
392C2×C3×Dic3—31no—
393C2×C3×Dic3—31no—
394C2×C3×Dic3—38no—
395C2×C3×Dic3—38no—
396C2×C3×Dic3—38no—
397C2×C3×Dic3—34no—
398C2×C3×Dic3—34no—
399C2×C3×Dic3—38no—
400C2×C3×Dic3—38no—
401C2×C3×Dic3—62no—
402C2×C3×Dic3—61no—
403C2×C3×Dic3—68no—
404C2×C3×Dic3C22×D311yescharacteristic
405C2×C3×Dic3C22×D312yes—
406C2×C3×Dic3C22×D311yescharacteristic
407C2×C3×Dic3C22×D318yescomplemented
408C2×C3×Dic3C23×C311yescharacteristic
409C2×C3×Dic3C23×C312yes—
410C2×C3×Dic3C23×C311yescharacteristic
411C2×C3×Dic3C23×C318yescomplemented
412C3×D12—24no—
413C3×D12—38no—
414C3×D12C22×D314yescomplemented
415C3×D12C23×C314yescomplemented
416C3×C4×D3—24no—
417C3×C4×D3—24no—
418C3×C4×D3—34no—
419C3×C4×D3—38no—
420C3×C4×D3—38no—
421C3×C4×D3—34no—
422C3×C4×D3—38no—
423C3×C4×D3—34no—
424C3×C4×D3—34no—
425C3×C4×D3—34no—
426C3×C4×D3—34no—
427C3×C4×D3—64no—
428C3×C4×D3C22×D314yes—
429C3×C4×D3C22×D314yescomplemented
430C3×C4×D3C23×C314yes—
431C3×C4×D3C23×C314yescomplemented
432C3×Dic6—24no—
433C3×Dic6—34no—
434C3×Dic6—34no—
435C3×Dic6—38no—
436C3×Dic6—38no—
437C3×Dic6—64no—
438C3×Dic6C22×D314yescomplemented
439C3×Dic6C23×C314yescomplemented
440#627C23×C318yescomplemented
441#626C23×C318yescomplemented
442#625C23×C318yescomplemented
443#624C23×C314yescomplemented
444D3×Dic3C23×C318yes—
445D3×Dic3C23×C314yes—
446D3×Dic3C23×C318yescomplemented
447D3×Dic3C23×C318yescomplemented
448D3×Dic3C23×C314yescomplemented
449C22×#41—91noSylow
450C2×C33—24no—
451C2×C33C2×#4112yescomplemented
452C2×C33C2511yescharacteristic
453C3×C3⋊D3—22no—
454C32×D3—22no—
455C32×D3—24no—
456C32×D3C2×#4114yescomplemented
457C24×C3—32no—
458C24×C3—32no—
459C24×C3—62no—
460C24×C3—91no—
461C23×D3—31no—
462C23×D3—31no—
463C23×D3C2×C3×D312yes—
464C3×#41—38no—
465C3×#41—38no—
466C3×#41—68no—
467C3×#41—916no—
468C3×#41—98no—
469C3×#41—916no—
470C3×#41—98no—
471C3×#41—98no—
472C2×C3×Q8—31no—
473C2×C3×Q8—31no—
474C2×C3×Q8—61no—
475C2×C3×Q8—92no—
476C2×C3×Q8—98no—
477C2×C3×Q8—91no—
478C2×C3×D4—21no—
479C2×C3×D4—21no—
480C2×C3×D4—21no—
481C2×C3×D4—32no—
482C2×C3×D4—32no—
483C2×C3×D4—32no—
484C2×C3×D4—32no—
485C2×C3×D4—38no—
486C2×C3×D4—38no—
487C2×C3×D4—31no—
488C2×C3×D4—31no—
489C2×C3×D4—41no—
490C2×C3×D4—61no—
491C2×C3×D4—68no—
492C2×C3×D4—62no—
493C2×C3×D4—62no—
494C2×C3×D4—92no—
495C2×C3×D4—916no—
496C2×C3×D4—92no—
497C2×C3×D4—92no—
498C2×C3×D4D3211yescharacteristic, complemented
499C2×C3×D4C2×C3×D311yescharacteristic, complemented
500C2×C3×D4C2×C3×D311yescharacteristic, complemented
501C22×C3×C4—32no—
502C22×C3×C4—32no—
503C22×C3×C4—31no—
504C22×C3×C4—31no—
505C22×C3×C4—31no—
506C22×C3×C4—31no—
507C22×C3×C4—61no—
508C22×C3×C4—61no—
509C22×C3×C4—62no—
510C22×C3×C4—91no—
511C22×C3×C4—98no—
512C22×C3×C4—91no—
513C22×C3×C4—92no—
514C22×C3×C4—916no—
515C22×C3×C4—92no—
516C22×C3×C4—91no—
517C22×C3×C4—92no—
518C22×C3×C4—92no—
519C22×C3×C4—91no—
520C2×#67—32no—
521C2×#67—32no—
522C2×#67—32no—
523C2×#67—32no—
524C2×#67—316no—
525C2×#67—32no—
526C2×#67—62no—
527C2×#67C2×C3×D312yescomplemented
528C2×#67C2×C3×D312yescomplemented
529C22×Dic3—32no—
530C22×Dic3—32no—
531C22×Dic3—32no—
532C22×Dic3—31no—
533C22×Dic3—31no—
534C22×Dic3—32no—
535C22×Dic3—32no—
536C22×Dic3—316no—
537C22×Dic3—62no—
538C22×Dic3C2×C3×D312yescomplemented
539#239—38no—
540D3×Q8—38no—
541#237—38no—
542#237—38no—
543#237—316no—
544#237—316no—
545#237—316no—
546#237—38no—
547#237—38no—
548#237—68no—
549#237C2×C3×D318yesdirect product factor
550D3×D4—316no—
551D3×D4C2×C3×D318yescomplemented
552#235—316no—
553#235—38no—
554C2×D12—32no—
555C2×D12C2×C3×D311yescharacteristic, complemented
556C2×C4×D3—31no—
557C2×C4×D3—32no—
558C2×C4×D3—32no—
559C2×C4×D3—31no—
560C2×C4×D3—32no—
561C2×C4×D3—316no—
562C2×C4×D3—31no—
563C2×C4×D3—31no—
564C2×C4×D3—31no—
565C2×C4×D3—31no—
566C2×C4×D3—38no—
567C2×C4×D3—38no—
568C2×C4×D3—61no—
569C2×C4×D3C2×C3×D311yescharacteristic
570C2×C4×D3C2×C3×D311yescharacteristic, complemented
571C2×Dic6—31no—
572C2×Dic6—31no—
573C2×Dic6—32no—
574C2×Dic6—32no—
575C2×Dic6—38no—
576C2×Dic6—61no—
577C2×Dic6C2×C3×D311yescharacteristic, complemented
578C22×C32—24no—
579C22×C32—24no—
580C22×C32—24no—
581C22×C32—24no—
582C22×C32—21no—
583C22×C32—21no—
584C22×C32—21no—
585C22×C32—24no—
586C22×C32—24no—
587C22×C32—34no—
588C22×C32—32no—
589C22×C32—34no—
590C22×C32—32no—
591C22×C32—41no—
592C22×C32—44no—
593C22×C32—44no—
594C22×C32—44no—
595C22×C32—44no—
596C22×C32—616no—
597C22×C32—62no—
598C22×C32—64no—
599C22×C32—84no—
600C22×C32C23×D314yes—
601C22×C32C23×D314yes—
602C22×C32C23×D311yescharacteristic
603C22×C32C23×D311yescharacteristic
604C22×C32C24×C314yes—
605C22×C32C24×C311yescharacteristic
606C2×C3⋊D3—22no—
607C2×C3⋊D3C24×C312yes—
608C2×C3×D3—24no—
609C2×C3×D3—22no—
610C2×C3×D3—22no—
611C2×C3×D3—24no—
612C2×C3×D3—216no—
613C2×C3×D3—216no—
614C2×C3×D3—22no—
615C2×C3×D3—22no—
616C2×C3×D3—24no—
617C2×C3×D3—24no—
618C2×C3×D3—32no—
619C2×C3×D3—32no—
620C2×C3×D3—416no—
621C2×C3×D3—42no—
622C2×C3×D3—44no—
623C2×C3×D3—62no—
624C2×C3×D3—68no—
625C2×C3×D3—62no—
626C2×C3×D3—62no—
627C2×C3×D3—68no—
628C2×C3×D3—122no—
629C2×C3×D3#23714yesdirect product factor
630C2×C3×D3C3×#4114yescomplemented
631C2×C3×D3C23×D314yes—
632C2×C3×D3C23×D312yes—
633C2×C3×D3C23×D312yes—
634C2×C3×D3C24×C314yes—
635C2×C3×D3C24×C312yes—
636C2×C3×D3C24×C312yes—
637D32—28no—
638C32×C4—22no—
639C32×C4—22no—
640C32×C4—22no—
641C32×C4—32no—
642C32×C4—34no—
643C32×C4—32no—
644C32×C4—42no—
645C32×C4C23×D312yes—
646C32×C4C23×D312yes—
647C32×C4C24×C312yes—
648C3⋊Dic3C24×C312yes—
649C3⋊Dic3C24×C314yes—
650C3×Dic3—24no—
651C3×Dic3—22no—
652C3×Dic3—22no—
653C3×Dic3—34no—
654C3×Dic3—34no—
655C3×Dic3—32no—
656C3×Dic3—32no—
657C3×Dic3—64no—
658C3×Dic3—62no—
659C3×Dic3C23×D312yes—
660C3×Dic3C23×D314yes—
661C3×Dic3C23×D312yes—
662C3×Dic3C24×C312yes—
663C3×Dic3C24×C314yes—
664C3×Dic3C24×C312yes—
665C2×#41—31no—
666C2×#41—92no—
667C2×#41—91no—
668C2×#41—92no—
669C2×#41—91no—
670C2×#41—916no—
671C2×#41—91no—
672C22×Q8—91no—
673C22×D4—31no—
674C22×D4—92no—
675C23×C4—91no—
676C23×C4—92no—
677C33C22×#4111yescharacteristic, complemented, Sylow
678C23×C3—22no—
679C23×C3—22no—
680C23×C3—22no—
681C23×C3—31no—
682C23×C3—31no—
683C23×C3—38no—
684C23×C3—31no—
685C23×C3—32no—
686C23×C3—38no—
687C23×C3—32no—
688C23×C3—31no—
689C23×C3—42no—
690C23×C3—61no—
691C23×C3—61no—
692C23×C3—62no—
693C23×C3—68no—
694C23×C3—68no—
695C23×C3—68no—
696C23×C3—94no—
697C23×C3—91no—
698C23×C3—128no—
699C23×C3—184no—
700C23×C3C2×D3212yes—
701C23×C3C22×C3×D312yes—
702C23×C3C22×C3×D312yes—
703C22×D3—28no—
704C22×D3—31no—
705C22×D3—31no—
706C22×D3—34no—
707C22×D3—34no—
708C22×D3—61no—
709C22×D3—64no—
710C22×D3—64no—
711C22×D3C22×C3×D312yes—
712C22×D3C22×C3×D318yes—
713C22×D3C22×C3×D311yescharacteristic
714C22×D3C22×C3×D311yescharacteristic
715C3×Q8—34no—
716C3×Q8—34no—
717C3×Q8—64no—
718C3×Q8—98no—
719C3×Q8—94no—
720C3×D4—24no—
721C3×D4—24no—
722C3×D4—24no—
723C3×D4—38no—
724C3×D4—38no—
725C3×D4—38no—
726C3×D4—38no—
727C3×D4—34no—
728C3×D4—34no—
729C3×D4—44no—
730C3×D4—64no—
731C3×D4—68no—
732C3×D4—68no—
733C3×D4—98no—
734C3×D4—98no—
735C3×D4—98no—
736C3×D4C2×D3214yescomplemented
737C3×D4C22×C3×D314yescomplemented
738C3×D4C22×C3×D314yescomplemented
739C2×C3×C4—21no—
740C2×C3×C4—21no—
741C2×C3×C4—21no—
742C2×C3×C4—38no—
743C2×C3×C4—31no—
744C2×C3×C4—31no—
745C2×C3×C4—32no—
746C2×C3×C4—31no—
747C2×C3×C4—32no—
748C2×C3×C4—31no—
749C2×C3×C4—38no—
750C2×C3×C4—34no—
751C2×C3×C4—34no—
752C2×C3×C4—34no—
753C2×C3×C4—34no—
754C2×C3×C4—41no—
755C2×C3×C4—64no—
756C2×C3×C4—64no—
757C2×C3×C4—61no—
758C2×C3×C4—61no—
759C2×C3×C4—62no—
760C2×C3×C4—68no—
761C2×C3×C4—94no—
762C2×C3×C4—94no—
763C2×C3×C4—98no—
764C2×C3×C4—98no—
765C2×C3×C4—94no—
766C2×C3×C4—98no—
767C2×C3×C4—98no—
768C2×C3×C4—91no—
769C2×C3×C4—92no—
770C2×C3×C4—94no—
771C2×C3×C4C2×D3211yescharacteristic
772C2×C3×C4C22×C3×D311yescharacteristic
773C2×C3×C4C22×C3×D311yescharacteristic
774#67—38no—
775#67—38no—
776#67—38no—
777#67—38no—
778#67—38no—
779#67—68no—
780#67C22×C3×D318yescomplemented
781#67C22×C3×D318yescomplemented
782C2×Dic3—32no—
783C2×Dic3—32no—
784C2×Dic3—31no—
785C2×Dic3—31no—
786C2×Dic3—38no—
787C2×Dic3—38no—
788C2×Dic3—38no—
789C2×Dic3—34no—
790C2×Dic3—34no—
791C2×Dic3—38no—
792C2×Dic3—38no—
793C2×Dic3—62no—
794C2×Dic3—61no—
795C2×Dic3—68no—
796C2×Dic3C22×C3×D311yescharacteristic
797C2×Dic3C22×C3×D312yes—
798C2×Dic3C22×C3×D311yescharacteristic
799C2×Dic3C22×C3×D318yescomplemented
800D12—38no—
801D12C22×C3×D314yescomplemented
802C4×D3—34no—
803C4×D3—38no—
804C4×D3—38no—
805C4×D3—34no—
806C4×D3—38no—
807C4×D3—34no—
808C4×D3—34no—
809C4×D3—34no—
810C4×D3—34no—
811C4×D3—64no—
812C4×D3C22×C3×D314yes—
813C4×D3C22×C3×D314yescomplemented
814Dic6—34no—
815Dic6—34no—
816Dic6—38no—
817Dic6—38no—
818Dic6—64no—
819Dic6C22×C3×D314yescomplemented
820C2×C32—24no—
821C2×C32—24no—
822C2×C32—24no—
823C2×C32—22no—
824C2×C32—22no—
825C2×C32—22no—
826C2×C32—21no—
827C2×C32—21no—
828C2×C32—21no—
829C2×C32—34no—
830C2×C32—42no—
831C2×C32—41no—
832C2×C32—44no—
833C2×C32—44no—
834C2×C32—44no—
835C2×C32—62no—
836C2×C32—64no—
837C2×C32—84no—
838C2×C32C2×#23712yescomplemented
839C2×C32D3×#4112yescomplemented
840C2×C32C2×C3×#4112yescomplemented
841C2×C32C24×D311yescharacteristic
842C2×C32C24×D311yescharacteristic
843C2×C32C25×C311yescharacteristic
844C3⋊D3—22no—
845C3×D3—24no—
846C3×D3—22no—
847C3×D3—22no—
848C3×D3—24no—
849C3×D3—24no—
850C3×D3—42no—
851C3×D3—44no—
852C3×D3—62no—
853C3×D3—62no—
854C3×D3—122no—
855C3×D3C2×#23714yesdirect product factor
856C3×D3C2×C3×#4114yescomplemented
857C24—32no—
858C24—91no—
859#41—38no—
860#41—916no—
861#41—98no—
862#41—916no—
863#41—98no—
864#41—98no—
865C2×Q8—31no—
866C2×Q8—92no—
867C2×Q8—98no—
868C2×Q8—91no—
869C2×D4—32no—
870C2×D4—32no—
871C2×D4—38no—
872C2×D4—31no—
873C2×D4—92no—
874C2×D4—916no—
875C2×D4—92no—
876C2×D4—92no—
877C2×D4C3×D3211yescharacteristic, complemented
878C22×C4—32no—
879C22×C4—31no—
880C22×C4—31no—
881C22×C4—91no—
882C22×C4—98no—
883C22×C4—91no—
884C22×C4—92no—
885C22×C4—92no—
886C22×C4—91no—
887C22×C4—92no—
888C22×C4—916no—
889C22×C4—92no—
890C22×C4—91no—
891C22×C3—24no—
892C22×C3—24no—
893C22×C3—24no—
894C22×C3—21no—
895C22×C3—21no—
896C22×C3—21no—
897C22×C3—24no—
898C22×C3—24no—
899C22×C3—24no—
900C22×C3—34no—
901C22×C3—34no—
902C22×C3—32no—
903C22×C3—32no—
904C22×C3—32no—
905C22×C3—34no—
906C22×C3—34no—
907C22×C3—32no—
908C22×C3—44no—
909C22×C3—44no—
910C22×C3—44no—
911C22×C3—41no—
912C22×C3—44no—
913C22×C3—62no—
914C22×C3—64no—
915C22×C3—62no—
916C22×C3—64no—
917C22×C3—616no—
918C22×C3—616no—
919C22×C3—64no—
920C22×C3—62no—
921C22×C3—62no—
922C22×C3—64no—
923C22×C3—84no—
924C22×C3—92no—
925C22×C3—124no—
926C22×C3—122no—
927C22×C3—1216no—
928C22×C3—188no—
929C22×C3—182no—
930C22×C3C22×D3214yes—
931C22×C3C22×D3211yescharacteristic
932C22×C3C23×C3×D314yes—
933C22×C3C23×C3×D314yes—
934C22×C3C23×C3×D311yescharacteristic
935C22×C3C23×C3×D311yescharacteristic
936C2×D3—24no—
937C2×D3—22no—
938C2×D3—216no—
939C2×D3—32no—
940C2×D3—32no—
941C2×D3—62no—
942C2×D3—68no—
943C2×D3—62no—
944C2×D3—62no—
945C2×D3—68no—
946C2×D3—122no—
947C2×D3C3×#23714yesdirect product factor
948C2×D3C23×C3×D314yes—
949C2×D3C23×C3×D312yes—
950C2×D3C23×C3×D312yes—
951C3×C4—22no—
952C3×C4—22no—
953C3×C4—22no—
954C3×C4—32no—
955C3×C4—32no—
956C3×C4—34no—
957C3×C4—32no—
958C3×C4—34no—
959C3×C4—32no—
960C3×C4—42no—
961C3×C4—62no—
962C3×C4—62no—
963C3×C4—64no—
964C3×C4—92no—
965C3×C4—94no—
966C3×C4C22×D3212yes—
967C3×C4C23×C3×D312yes—
968C3×C4C23×C3×D312yes—
969Dic3—34no—
970Dic3—34no—
971Dic3—32no—
972Dic3—32no—
973Dic3—64no—
974Dic3—62no—
975Dic3C23×C3×D312yes—
976Dic3C23×C3×D314yes—
977Dic3C23×C3×D312yes—
978C32—21no—
979C32—21no—
980C32—21no—
981C32—41no—
982C32C22×#23711yescharacteristic, complemented
983C32C2×D3×#4111yescharacteristic, complemented
984C32C22×C3×#4111yescharacteristic, complemented
985C23—31no—
986C23—31no—
987C23—38no—
988C23—32no—
989C23—68no—
990C23—94no—
991C23—91no—
992C23—184no—
993C23C2×C3×D3212yes—
994Q8—34no—
995Q8—98no—
996Q8—94no—
997D4—38no—
998D4—38no—
999D4—34no—
1000D4—98no—
1001D4—98no—
1002D4—98no—
1003D4C2×C3×D3214yescomplemented
1004C2×C4—31no—
1005C2×C4—31no—
1006C2×C4—32no—
1007C2×C4—38no—
1008C2×C4—34no—
1009C2×C4—34no—
1010C2×C4—94no—
1011C2×C4—94no—
1012C2×C4—98no—
1013C2×C4—98no—
1014C2×C4—94no—
1015C2×C4—98no—
1016C2×C4—91no—
1017C2×C4—92no—
1018C2×C4—98no—
1019C2×C4—94no—
1020C2×C4C2×C3×D3211yescharacteristic
1021C2×C3—24no—
1022C2×C3—24no—
1023C2×C3—24no—
1024C2×C3—21no—
1025C2×C3—21no—
1026C2×C3—21no—
1027C2×C3—22no—
1028C2×C3—22no—
1029C2×C3—22no—
1030C2×C3—34no—
1031C2×C3—34no—
1032C2×C3—44no—
1033C2×C3—44no—
1034C2×C3—44no—
1035C2×C3—41no—
1036C2×C3—42no—
1037C2×C3—64no—
1038C2×C3—64no—
1039C2×C3—62no—
1040C2×C3—62no—
1041C2×C3—64no—
1042C2×C3—84no—
1043C2×C3—124no—
1044C2×C3—122no—
1045C2×C3—182no—
1046C2×C3D3×#23712yesdirect product factor
1047C2×C3C2×C3×#23712yescomplemented
1048C2×C3C3×D3×#4112yescomplemented
1049C2×C3C23×D3211yescharacteristic
1050C2×C3C24×C3×D311yescharacteristic
1051C2×C3C24×C3×D311yescharacteristic
1052D3—24no—
1053D3—22no—
1054D3—62no—
1055D3—62no—
1056D3—122no—
1057D3C2×C3×#23714yesdirect product factor
1058C22—24no—
1059C22—32no—
1060C22—34no—
1061C22—32no—
1062C22—34no—
1063C22—616no—
1064C22—64no—
1065C22—62no—
1066C22—92no—
1067C22—188no—
1068C22—182no—
1069C22C22×C3×D3214yes—
1070C22C22×C3×D3211yescharacteristic
1071C4—32no—
1072C4—32no—
1073C4—34no—
1074C4—92no—
1075C4—94no—
1076C4C22×C3×D3212yes—
1077C3—21no—
1078C3—21no—
1079C3—21no—
1080C3—41no—
1081C3C2×D3×#23711yescharacteristic, direct product factor
1082C3C22×C3×#23711yescharacteristic, complemented
1083C3C2×C3×D3×#4111yescharacteristic, complemented
1084C2—24no—
1085C2—34no—
1086C2—64no—
1087C2—62no—
1088C2—182no—
1089C2C3×D3×#23712yesdirect product factor
1090C2C23×C3×D3211yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC2×C32C25×C3
FrattiniC2C23×C3×D32
FittingC2×C33×D4C22
socleC22×C33C24
hypercenterC2×C3×D4D32
hypocenterC32C22×C3×#41
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#3830C2semidirect
2. C2×C32×#237C2semidirect
3. C2×C32×D3×D4C2semidirect
4. C2×C3×D3×#67C2semidirect
5. C2×C3×#3805C2semidirect
6. C2×C3×#3804C2semidirect
7. C22×C3×D3×Dic3C2semidirect
8. C3×D3×#237C2direct (N × H)
9. C2×C3×C4×D32C2semidirect
10. C2×C3×#3796C2semidirect
11. C2×C3×#3795C2semidirect
12. C2×C3×D3×Dic6C2semidirect
15. C2×D3×#237C3direct (N × H)
18. C2×C33×D4C22semidirect
19. C2×C3×#638C22semidirect
20. C22×C3×C3⋊Dic3C22semidirect
21. C3×#3830C22semidirect
22. C2×C3×C4×C3⋊D3C22semidirect
23. C2×C3×#634C22semidirect
24. C2×C32×#67C22semidirect
25. C2×C32×#67C22semidirect
26. C22×C32×Dic3C22semidirect
27. C32×#237C22semidirect
28. C32×D3×D4C22semidirect
29. C2×C32×D12C22semidirect
31. C2×C32×C4×D3C22semidirect
32. C2×C32×Dic6C22semidirect
33. C3×D3×#67C22semidirect
34. C2×C3×#627C22semidirect
35. C2×C3×#626C22semidirect
36. C2×C3×#625C22semidirect
37. C2×C3×#624C22semidirect
38. C3×#3805C22semidirect
39. C3×#3804C22semidirect
42. C2×C3×D3×Dic3C22semidirect
43. C2×C3×D3×Dic3C22semidirect
44. C2×C3×D3×Dic3C22semidirect
45. C2×C3×D3×Dic3C22semidirect
46. C3×C4×D32C22semidirect
47. C3×#3796C22semidirect
48. C3×#3795C22semidirect
49. C3×D3×Dic6C22semidirect
52. C2×#3830C2×C3semidirect
68. C2×C3×#237D3direct (N × H)
69. C2×C3×#237C2×C3semidirect
72. C2×C3×D3×D4D3semidirect
73. C2×C3×D3×D4C2×C3semidirect
80. C2×D3×#67C2×C3semidirect
81. C2×#3805C2×C3semidirect
82. C2×#3804C2×C3semidirect
83. C22×D3×Dic3C2×C3semidirect
84. D3×#237C2×C3direct (N × H)
85. C2×C4×D32C2×C3semidirect
86. C2×#3796C2×C3semidirect
87. C2×#3795C2×C3semidirect
88. C2×D3×Dic6C2×C3semidirect
98. C33×D4C23semidirect
100. C3×#638C23semidirect
103. C2×C3×C3⋊Dic3C23semidirect
104. C3×C4×C3⋊D3C23semidirect
105. C3×#634C23semidirect
106. C32×#67C23semidirect
107. C32×#67C23semidirect
111. C2×C32×Dic3C23semidirect
112. C32×D12C23semidirect
114. C32×C4×D3C23semidirect
115. C32×Dic6C23semidirect
116. C3×#627C23semidirect
117. C3×#626C23semidirect
118. C3×#625C23semidirect
119. C3×#624C23semidirect
122. C3×D3×Dic3C23semidirect
123. C3×D3×Dic3C23semidirect
124. C3×D3×Dic3C23semidirect
145. C2×C32×D4C2×D3semidirect
146. C2×C32×D4C2×D3semidirect
147. C2×C32×D4C22×C3semidirect
151. C2×#638C22×C3semidirect
152. C22×C3⋊Dic3C22×C3semidirect
153. #3830C22×C3semidirect
154. C2×C4×C3⋊D3C22×C3semidirect
155. C2×#634C22×C3semidirect
165. C2×C3×#67C2×D3semidirect
166. C2×C3×#67C2×D3semidirect
167. C2×C3×#67C22×C3semidirect
168. C2×C3×#67C22×C3semidirect
179. C22×C3×Dic3C2×D3semidirect
180. C22×C3×Dic3C22×C3semidirect
192. C3×#237C2×D3direct (N × H)
193. C3×#237C22×C3semidirect
196. C3×D3×D4C2×D3semidirect
197. C3×D3×D4C22×C3semidirect
202. C2×C3×D12C2×D3semidirect
203. C2×C3×D12C22×C3semidirect
220. C2×C3×C4×D3C2×D3semidirect
222. C2×C3×C4×D3C22×C3semidirect
230. C2×C3×Dic6C2×D3semidirect
231. C2×C3×Dic6C22×C3semidirect
232. D3×#67C22×C3semidirect
233. C2×#627C22×C3semidirect
234. C2×#626C22×C3semidirect
235. C2×#625C22×C3semidirect
236. C2×#624C22×C3semidirect
237. #3805C22×C3semidirect
238. #3804C22×C3semidirect
241. C2×D3×Dic3C22×C3semidirect
242. C2×D3×Dic3C22×C3semidirect
243. C2×D3×Dic3C22×C3semidirect
244. C2×D3×Dic3C22×C3semidirect
245. C4×D32C22×C3semidirect
246. #3796C22×C3semidirect
247. #3795C22×C3semidirect
248. D3×Dic6C22×C3semidirect
257. C2×C32×D3#41semidirect
298. C2×#237C3×D3direct (N × H)
300. C2×D3×D4C3×D3semidirect
352. C32×D4C22×D3semidirect
353. C32×D4C22×D3semidirect
354. C32×D4C23×C3semidirect
368. #638C23×C3semidirect
371. C2×C3⋊Dic3C23×C3semidirect
372. C4×C3⋊D3C23×C3semidirect
373. #634C23×C3semidirect
382. C3×#67C22×D3semidirect
383. C3×#67C22×D3semidirect
384. C3×#67C23×C3semidirect
385. C3×#67C23×C3semidirect
407. C2×C3×Dic3C22×D3semidirect
411. C2×C3×Dic3C23×C3semidirect
414. C3×D12C22×D3semidirect
415. C3×D12C23×C3semidirect
429. C3×C4×D3C22×D3semidirect
431. C3×C4×D3C23×C3semidirect
438. C3×Dic6C22×D3semidirect
439. C3×Dic6C23×C3semidirect
440. #627C23×C3semidirect
441. #626C23×C3semidirect
442. #625C23×C3semidirect
443. #624C23×C3semidirect
446. D3×Dic3C23×C3semidirect
447. D3×Dic3C23×C3semidirect
448. D3×Dic3C23×C3semidirect
451. C2×C33C2×#41semidirect
456. C32×D3C2×#41semidirect
498. C2×C3×D4D32semidirect
499. C2×C3×D4C2×C3×D3semidirect
500. C2×C3×D4C2×C3×D3semidirect
527. C2×#67C2×C3×D3semidirect
528. C2×#67C2×C3×D3semidirect
538. C22×Dic3C2×C3×D3semidirect
549. #237C2×C3×D3direct (N × H)
551. D3×D4C2×C3×D3semidirect
555. C2×D12C2×C3×D3semidirect
570. C2×C4×D3C2×C3×D3semidirect
577. C2×Dic6C2×C3×D3semidirect
629. C2×C3×D3#237direct (N × H)
630. C2×C3×D3C3×#41semidirect
677. C33C22×#41semidirect
736. C3×D4C2×D32semidirect
737. C3×D4C22×C3×D3semidirect
738. C3×D4C22×C3×D3semidirect
780. #67C22×C3×D3semidirect
781. #67C22×C3×D3semidirect
799. C2×Dic3C22×C3×D3semidirect
801. D12C22×C3×D3semidirect
813. C4×D3C22×C3×D3semidirect
819. Dic6C22×C3×D3semidirect
838. C2×C32C2×#237semidirect
839. C2×C32D3×#41semidirect
840. C2×C32C2×C3×#41semidirect
855. C3×D3C2×#237direct (N × H)
856. C3×D3C2×C3×#41semidirect
877. C2×D4C3×D32semidirect
947. C2×D3C3×#237direct (N × H)
982. C32C22×#237semidirect
983. C32C2×D3×#41semidirect
984. C32C22×C3×#41semidirect
1003. D4C2×C3×D32semidirect
1046. C2×C3D3×#237direct (N × H)
1047. C2×C3C2×C3×#237semidirect
1048. C2×C3C3×D3×#41semidirect
1057. D3C2×C3×#237direct (N × H)
1081. C3C2×D3×#237direct (N × H)
1082. C3C22×C3×#237semidirect
1083. C3C2×C3×D3×#41semidirect
1089. 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×C3×#38302
C2×C32×#2372
C2×C32×D3×D42
C2×C3×D3×#672
C2×C3×#38052
C2×C3×#38042
C22×C3×D3×Dic32
C3×D3×#2372
C2×C3×C4×D322
C2×C3×#37962
C2×C3×#37952
C2×C3×D3×Dic62
C2×C3×D3×#413
C22×C3×#2373
C2×D3×#2373