Finite Group Databasebeta

← C2×C3×#64297 #13181532

Subgroups — C2×C3×#64297 #13181532

Order 1728.

3714 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3828C211yesmaximal, characteristic, complemented
2C2×C32×#235C211yesmaximal, characteristic, complemented
3C22×C32×Dic6C211yesmaximal, characteristic, complemented
4C2×C3×#3804C214yesmaximal, complemented
5C2×C3×#3799C212yesmaximal, complemented
6C2×C3×#3797C212yesmaximal, complemented
7C3×#64297C2116yesmaximal, direct product factor
8C2×C3×#3796C212yesmaximal, complemented
9C2×C3×D3×Dic6C212yesmaximal, complemented
10C2×C3×#1010—31nomaximal
11C2×C3×#1007—31nomaximal
12C2×#64297C311yesmaximal, characteristic, direct product factor
13C22×C33×C4C2211yescharacteristic
14C2×C3×#638C2212yes—
15C3×#3828C2218yescomplemented
16C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
17C2×C3×C4×C3⋊D3C2212yes—
18C2×C3×#634C2211yescharacteristic
19C2×C32×#67C2212yes—
20C22×C32×Dic3C2212yes—
21C32×#235C2218yescomplemented
22C2×C32×D12C2211yescharacteristic
23C2×C32×C4×D3C2212yes—
24C2×C32×Dic6C2212yes—
25C2×C32×Dic6C2212yes—
26C2×C32×Dic6C2211yescharacteristic
27C2×C32×Dic6C2218yescomplemented
28C2×C3×#627C2214yes—
29C2×C3×#626C2214yes—
30C2×C3×#624C2214yes—
31C3×#3804C22132yescomplemented
32C2×C3×D3×Dic3C2214yes—
33C3×#3799C22116yescomplemented
34C3×#3797C22116yescomplemented
35C3×#3796C22116yescomplemented
36C3×D3×Dic6C22116yescomplemented
37C2×C32×#41—31no—
38C22×C32×Q8—31no—
39C2×#3828C2×C311yescharacteristic, complemented
40C3×#1010—316no—
41C3×#1007—316no—
42C2×C3×#239—32no—
43C2×C3×#239—32no—
44C2×C3×D3×Q8—32no—
45C2×C3×D3×Q8—32no—
46C2×C3×D3×Q8—32no—
47C2×C3×#237—34no—
48C2×C3×#237—32no—
49C2×C3×#235—21no—
50C2×C3×#235—31no—
51C2×C3×#235—31no—
52C2×C3×#235—34no—
53C2×C3×#235—32no—
54C2×C3×#235—61no—
55C2×C3×#235D311yescharacteristic, complemented
56C2×C3×#235C2×C311yescharacteristic, complemented
57C22×C3×Dic6—21no—
58C22×C3×Dic6—32no—
59C22×C3×Dic6D311yescharacteristic, complemented
60C22×C3×Dic6C2×C311yescharacteristic, complemented
61C2×#3804C2×C314yescomplemented
62C2×#3799C2×C312yescomplemented
63C2×#3797C2×C312yescomplemented
64#64297C2×C3116yesdirect product factor
65C2×#3796C2×C312yescomplemented
66C2×D3×Dic6C2×C312yescomplemented
67C23×C33C2311yescharacteristic
68C22×C3×C3⋊D3C2312yes—
69C22×C32×D3C2312yes—
70C2×C33×C4C2311yescharacteristic
71C2×C33×C4C2311yescharacteristic
72C2×C33×C4C2314yes—
73C3×#638C2318yes—
74C2×C3×C3⋊Dic3C2312yes—
75C3×C4⋊(C3⋊D3)C2314yes—
76C3×C4×C3⋊D3C2318yes—
77C3×#634C2314yes—
78C32×#67C2318yes—
79C2×C32×Dic3C2314yes—
80C2×C32×Dic3C2318yes—
81C2×C32×Dic3C2312yes—
82C32×D12C2314yes—
83C32×C4×D3C2318yes—
84C32×Dic6C2318yes—
85C32×Dic6C2318yes—
86C32×Dic6C2314yes—
87C3×#627C23116yes—
88C3×#626C23116yes—
89C3×#624C23116yes—
90C3×D3×Dic3C23116yes—
91C2×C3×2−1+4—91no—
92C2×#1010—31no—
93C2×#1007—31no—
94C32×#41—38no—
95C2×C32×Q8—31no—
96C2×C32×Q8—32no—
97C2×C32×Q8—32no—
98C2×C32×Q8—38no—
99C2×C32×D4—32no—
100C2×C32×D4—31no—
101C22×C32×C4—21no—
102C22×C32×C4—21no—
103C22×C32×C4—21no—
104C22×C32×C4—32no—
105C22×C32×C4—32no—
106C22×C32×C4—41no—
107C22×C32×C4C2×D311yescharacteristic
108C22×C32×C4C2×D311yescharacteristic
109C22×C32×C4C22×C311yescharacteristic
110C2×#638C22×C312yes—
111#3828C22×C318yescomplemented
112C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
113C2×C4×C3⋊D3C22×C312yes—
114C2×#634C22×C311yescharacteristic
115C2×C3×#67—22no—
116C2×C3×#67—32no—
117C2×C3×#67—32no—
118C2×C3×#67—34no—
119C2×C3×#67—62no—
120C2×C3×#67C2×D312yes—
121C2×C3×#67C22×C312yes—
122C22×C3×Dic3—22no—
123C22×C3×Dic3—34no—
124C22×C3×Dic3C2×D312yes—
125C22×C3×Dic3C22×C312yes—
126C3×#239—316no—
127C3×#239—316no—
128C3×D3×Q8—316no—
129C3×D3×Q8—316no—
130C3×D3×Q8—316no—
131C3×#237—332no—
132C3×#237—316no—
133C3×#235—28no—
134C3×#235—38no—
135C3×#235—38no—
136C3×#235—332no—
137C3×#235—316no—
138C3×#235—68no—
139C3×#235C2×D318yescomplemented
140C3×#235C22×C318yescomplemented
141C2×C3×D12—21no—
142C2×C3×D12—34no—
143C2×C3×D12—31no—
144C2×C3×D12—31no—
145C2×C3×D12—61no—
146C2×C3×D12C2×D311yescharacteristic
147C2×C3×D12C22×C311yescharacteristic
148C2×C3×C4×D3—22no—
149C2×C3×C4×D3—34no—
150C2×C3×C4×D3—32no—
151C2×C3×C4×D3—32no—
152C2×C3×C4×D3—34no—
153C2×C3×C4×D3—34no—
154C2×C3×C4×D3—62no—
155C2×C3×C4×D3C2×D312yes—
156C2×C3×C4×D3C22×C312yes—
157C2×C3×Dic6—22no—
158C2×C3×Dic6—22no—
159C2×C3×Dic6—21no—
160C2×C3×Dic6—28no—
161C2×C3×Dic6—31no—
162C2×C3×Dic6—31no—
163C2×C3×Dic6—34no—
164C2×C3×Dic6—34no—
165C2×C3×Dic6—316no—
166C2×C3×Dic6—61no—
167C2×C3×Dic6C2×D312yes—
168C2×C3×Dic6C2×D312yes—
169C2×C3×Dic6C2×D311yescharacteristic
170C2×C3×Dic6C2×D318yescomplemented
171C2×C3×Dic6C22×C312yes—
172C2×C3×Dic6C22×C312yes—
173C2×C3×Dic6C22×C311yescharacteristic
174C2×C3×Dic6C22×C318yescomplemented
175C2×#627C22×C314yes—
176C2×#626C22×C314yes—
177C2×#624C22×C314yes—
178#3804C22×C3132yescomplemented
179C2×D3×Dic3C22×C314yes—
180#3799C22×C3116yescomplemented
181#3797C22×C3116yescomplemented
182#3796C22×C3116yescomplemented
183D3×Dic6C22×C3116yescomplemented
184C22×C33—22no—
185C22×C33C2412yes—
186C22×C33C2411yescharacteristic
187C2×C3×C3⋊D3—24no—
188C2×C3×C3⋊D3C2414yes—
189C2×C32×D3—24no—
190C2×C32×D3C2414yes—
191C33×C4C2412yes—
192C33×C4C2412yes—
193C3×C3⋊Dic3C2414yes—
194C32×Dic3C2418yes—
195C32×Dic3C2414yes—
196C3×2−1+4—916no—
197C2×C3×#41—31no—
198C2×C3×#41—31no—
199C2×C3×#41—61no—
200C2×C3×#41—94no—
201C2×C3×#41—92no—
202C2×C3×#41—92no—
203C2×C3×#41—91no—
204C22×C3×Q8—31no—
205C22×C3×Q8—31no—
206C22×C3×Q8—61no—
207C22×C3×Q8—92no—
208C22×C3×Q8—92no—
209#1010—316no—
210#1007—316no—
211C2×#239—32no—
212C2×#239—32no—
213C2×D3×Q8—32no—
214C2×D3×Q8—32no—
215C2×D3×Q8—32no—
216C2×#237—34no—
217C2×#237—32no—
218C2×#235—31no—
219C2×#235—31no—
220C2×#235—34no—
221C2×#235—32no—
222C2×#235—61no—
223C2×#235C3×D311yescharacteristic, complemented
224C22×Dic6—32no—
225C22×Dic6C3×D311yescharacteristic, complemented
226C23×C32—21no—
227C23×C32—21no—
228C23×C32—21no—
229C23×C32—32no—
230C23×C32—41no—
231C23×C32C22×D311yescharacteristic
232C23×C32C22×D311yescharacteristic
233C23×C32C23×C311yescharacteristic
234C22×C3⋊D3C23×C312yes—
235C22×C3×D3—22no—
236C22×C3×D3—32no—
237C22×C3×D3—32no—
238C22×C3×D3—62no—
239C22×C3×D3C22×D312yes—
240C22×C3×D3C23×C312yes—
241C32×Q8—34no—
242C32×Q8—38no—
243C32×Q8—38no—
244C32×D4—38no—
245C32×D4—34no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—24no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—24no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—24no—
255C2×C32×C4—32no—
256C2×C32×C4—34no—
257C2×C32×C4—38no—
258C2×C32×C4—38no—
259C2×C32×C4—41no—
260C2×C32×C4—41no—
261C2×C32×C4—44no—
262C2×C32×C4C22×D311yescharacteristic
263C2×C32×C4C22×D311yescharacteristic
264C2×C32×C4C22×D311yescharacteristic
265C2×C32×C4C22×D311yescharacteristic
266C2×C32×C4C22×D314yes—
267C2×C32×C4C22×D314yes—
268C2×C32×C4C23×C311yescharacteristic
269C2×C32×C4C23×C311yescharacteristic
270C2×C32×C4C23×C314yes—
271#638C23×C318yes—
272C2×C3⋊Dic3C23×C312yes—
273C4⋊(C3⋊D3)C23×C314yes—
274C4×C3⋊D3C23×C318yes—
275#634C23×C314yes—
276C3×#67—28no—
277C3×#67—38no—
278C3×#67—38no—
279C3×#67—316no—
280C3×#67—68no—
281C3×#67C22×D318yes—
282C3×#67C23×C318yes—
283C2×C3×Dic3—24no—
284C2×C3×Dic3—28no—
285C2×C3×Dic3—22no—
286C2×C3×Dic3—32no—
287C2×C3×Dic3—32no—
288C2×C3×Dic3—316no—
289C2×C3×Dic3—62no—
290C2×C3×Dic3C22×D312yes—
291C2×C3×Dic3C22×D314yes—
292C2×C3×Dic3C22×D318yes—
293C2×C3×Dic3C23×C314yes—
294C2×C3×Dic3C23×C318yes—
295C2×C3×Dic3C23×C312yes—
296C3×D12—24no—
297C3×D12—316no—
298C3×D12—34no—
299C3×D12—34no—
300C3×D12—64no—
301C3×D12C22×D314yes—
302C3×D12C23×C314yes—
303C3×C4×D3—28no—
304C3×C4×D3—316no—
305C3×C4×D3—38no—
306C3×C4×D3—38no—
307C3×C4×D3—316no—
308C3×C4×D3—316no—
309C3×C4×D3—68no—
310C3×C4×D3C22×D318yes—
311C3×C4×D3C23×C318yes—
312C3×Dic6—28no—
313C3×Dic6—28no—
314C3×Dic6—24no—
315C3×Dic6—34no—
316C3×Dic6—34no—
317C3×Dic6—316no—
318C3×Dic6—316no—
319C3×Dic6—64no—
320C3×Dic6C22×D318yes—
321C3×Dic6C22×D318yes—
322C3×Dic6C22×D314yes—
323C3×Dic6C23×C318yes—
324C3×Dic6C23×C318yes—
325C3×Dic6C23×C314yes—
326#627C23×C3116yes—
327#626C23×C3116yes—
328#624C23×C3116yes—
329D3×Dic3C23×C3116yes—
330C2×2−1+4—91noSylow
331C2×C33—22no—
332C2×C332−1+412yescomplemented
333C2×C33C2511yescharacteristic
334C3×C3⋊D3—24no—
335C32×D3—24no—
336C3×#41—38no—
337C3×#41—38no—
338C3×#41—68no—
339C3×#41—932no—
340C3×#41—916no—
341C3×#41—916no—
342C3×#41—98no—
343C2×C3×Q8—32no—
344C2×C3×Q8—32no—
345C2×C3×Q8—31no—
346C2×C3×Q8—38no—
347C2×C3×Q8—31no—
348C2×C3×Q8—32no—
349C2×C3×Q8—32no—
350C2×C3×Q8—38no—
351C2×C3×Q8—62no—
352C2×C3×Q8—62no—
353C2×C3×Q8—68no—
354C2×C3×Q8—61no—
355C2×C3×Q8—94no—
356C2×C3×Q8—916no—
357C2×C3×Q8—916no—
358C2×C3×Q8—91no—
359C2×C3×D4—32no—
360C2×C3×D4—32no—
361C2×C3×D4—31no—
362C2×C3×D4—31no—
363C2×C3×D4—61no—
364C2×C3×D4—62no—
365C2×C3×D4—94no—
366C2×C3×D4—92no—
367C2×C3×D4—91no—
368C22×C3×C4—21no—
369C22×C3×C4—21no—
370C22×C3×C4—21no—
371C22×C3×C4—32no—
372C22×C3×C4—32no—
373C22×C3×C4—32no—
374C22×C3×C4—32no—
375C22×C3×C4—41no—
376C22×C3×C4—62no—
377C22×C3×C4—62no—
378C22×C3×C4—94no—
379C22×C3×C4—94no—
380C22×C3×C4—92no—
381C22×C3×C4D3211yescharacteristic
382C22×C3×C4C2×C3×D311yescharacteristic
383C22×C3×C4C2×C3×D311yescharacteristic
384C2×#67—32no—
385C2×#67—32no—
386C2×#67—34no—
387C2×#67—62no—
388C2×#67C2×C3×D312yes—
389C22×Dic3—34no—
390C22×Dic3C2×C3×D312yes—
391#239—316no—
392#239—316no—
393D3×Q8—316no—
394D3×Q8—316no—
395D3×Q8—316no—
396#237—332no—
397#237—316no—
398#235—38no—
399#235—38no—
400#235—332no—
401#235—316no—
402#235—68no—
403#235C2×C3×D318yescomplemented
404C2×D12—34no—
405C2×D12—31no—
406C2×D12—31no—
407C2×D12—61no—
408C2×D12C2×C3×D311yescharacteristic
409C2×C4×D3—34no—
410C2×C4×D3—32no—
411C2×C4×D3—32no—
412C2×C4×D3—34no—
413C2×C4×D3—34no—
414C2×C4×D3—62no—
415C2×C4×D3C2×C3×D312yes—
416C2×Dic6—31no—
417C2×Dic6—31no—
418C2×Dic6—34no—
419C2×Dic6—34no—
420C2×Dic6—316no—
421C2×Dic6—61no—
422C2×Dic6C2×C3×D312yes—
423C2×Dic6C2×C3×D312yes—
424C2×Dic6C2×C3×D311yescharacteristic
425C2×Dic6C2×C3×D318yescomplemented
426C22×C32—22no—
427C22×C32—24no—
428C22×C32—22no—
429C22×C32—22no—
430C22×C32—22no—
431C22×C32—21no—
432C22×C32—22no—
433C22×C32—21no—
434C22×C32—21no—
435C22×C32—22no—
436C22×C32—34no—
437C22×C32—41no—
438C22×C32—42no—
439C22×C32—42no—
440C22×C32—42no—
441C22×C32—44no—
442C22×C32—64no—
443C22×C32C23×D312yes—
444C22×C32C23×D312yes—
445C22×C32C23×D311yescharacteristic
446C22×C32C23×D311yescharacteristic
447C22×C32C24×C312yes—
448C22×C32C24×C311yescharacteristic
449C2×C3⋊D3—24no—
450C2×C3⋊D3C24×C314yes—
451C2×C3×D3—24no—
452C2×C3×D3—24no—
453C2×C3×D3—24no—
454C2×C3×D3—34no—
455C2×C3×D3—34no—
456C2×C3×D3—44no—
457C2×C3×D3—64no—
458C2×C3×D3—64no—
459C2×C3×D3—64no—
460C2×C3×D3—124no—
461C2×C3×D3C23×D314yes—
462C2×C3×D3C24×C314yes—
463C32×C4—22no—
464C32×C4—22no—
465C32×C4—22no—
466C32×C4—22no—
467C32×C4—22no—
468C32×C4—22no—
469C32×C4—34no—
470C32×C4—38no—
471C32×C4—42no—
472C32×C4—42no—
473C32×C4C23×D312yes—
474C32×C4C23×D312yes—
475C32×C4C23×D312yes—
476C32×C4C23×D312yes—
477C32×C4C24×C312yes—
478C32×C4C24×C312yes—
479C3⋊Dic3C24×C314yes—
480C3×Dic3—28no—
481C3×Dic3—24no—
482C3×Dic3—34no—
483C3×Dic3—34no—
484C3×Dic3—64no—
485C3×Dic3C23×D314yes—
486C3×Dic3C23×D318yes—
487C3×Dic3C24×C318yes—
488C3×Dic3C24×C314yes—
4892−1+4—916no—
490C2×#41—31no—
491C2×#41—94no—
492C2×#41—92no—
493C2×#41—92no—
494C2×#41—91no—
495C22×Q8—31no—
496C22×Q8—92no—
497C22×Q8—92no—
498C33C2×2−1+411yescharacteristic, complemented, Sylow
499C23×C3—21no—
500C23×C3—21no—
501C23×C3—21no—
502C23×C3—32no—
503C23×C3—32no—
504C23×C3—41no—
505C23×C3—62no—
506C23×C3—92no—
507C23×C3C2×D3211yescharacteristic
508C23×C3C22×C3×D311yescharacteristic
509C23×C3C22×C3×D311yescharacteristic
510C22×D3—32no—
511C22×D3—32no—
512C22×D3—62no—
513C22×D3C22×C3×D312yes—
514C3×Q8—38no—
515C3×Q8—38no—
516C3×Q8—34no—
517C3×Q8—34no—
518C3×Q8—38no—
519C3×Q8—38no—
520C3×Q8—68no—
521C3×Q8—68no—
522C3×Q8—64no—
523C3×Q8—916no—
524C3×Q8—94no—
525C3×D4—38no—
526C3×D4—38no—
527C3×D4—34no—
528C3×D4—34no—
529C3×D4—64no—
530C3×D4—68no—
531C3×D4—916no—
532C3×D4—98no—
533C3×D4—94no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—24no—
539C2×C3×C4—24no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—24no—
543C2×C3×C4—38no—
544C2×C3×C4—32no—
545C2×C3×C4—34no—
546C2×C3×C4—32no—
547C2×C3×C4—34no—
548C2×C3×C4—38no—
549C2×C3×C4—38no—
550C2×C3×C4—38no—
551C2×C3×C4—41no—
552C2×C3×C4—41no—
553C2×C3×C4—44no—
554C2×C3×C4—68no—
555C2×C3×C4—62no—
556C2×C3×C4—64no—
557C2×C3×C4—68no—
558C2×C3×C4—916no—
559C2×C3×C4—916no—
560C2×C3×C4—92no—
561C2×C3×C4—98no—
562C2×C3×C4C2×D3214yes—
563C2×C3×C4C2×D3211yescharacteristic
564C2×C3×C4C2×D3211yescharacteristic
565C2×C3×C4C22×C3×D311yescharacteristic
566C2×C3×C4C22×C3×D311yescharacteristic
567C2×C3×C4C22×C3×D311yescharacteristic
568C2×C3×C4C22×C3×D311yescharacteristic
569C2×C3×C4C22×C3×D314yes—
570C2×C3×C4C22×C3×D314yes—
571#67—38no—
572#67—38no—
573#67—316no—
574#67—68no—
575#67C22×C3×D318yes—
576C2×Dic3—32no—
577C2×Dic3—32no—
578C2×Dic3—316no—
579C2×Dic3—62no—
580C2×Dic3C22×C3×D312yes—
581C2×Dic3C22×C3×D314yes—
582C2×Dic3C22×C3×D318yes—
583D12—316no—
584D12—34no—
585D12—34no—
586D12—64no—
587D12C22×C3×D314yes—
588C4×D3—316no—
589C4×D3—38no—
590C4×D3—38no—
591C4×D3—316no—
592C4×D3—316no—
593C4×D3—68no—
594C4×D3C22×C3×D318yes—
595Dic6—34no—
596Dic6—34no—
597Dic6—316no—
598Dic6—316no—
599Dic6—64no—
600Dic6C22×C3×D318yes—
601Dic6C22×C3×D318yes—
602Dic6C22×C3×D314yes—
603C2×C32—22no—
604C2×C32—24no—
605C2×C32—22no—
606C2×C32—22no—
607C2×C32—22no—
608C2×C32—22no—
609C2×C32—22no—
610C2×C32—21no—
611C2×C32—21no—
612C2×C32—21no—
613C2×C32—42no—
614C2×C32—41no—
615C2×C32—42no—
616C2×C32—42no—
617C2×C32—44no—
618C2×C32—64no—
619C2×C32#100712yescomplemented
620C2×C32#101012yescomplemented
621C2×C32C3×2−1+412yescomplemented
622C2×C32C24×D311yescharacteristic
623C2×C32C24×D311yescharacteristic
624C2×C32C25×C311yescharacteristic
625C3⋊D3—24no—
626C3×D3—24no—
627C3×D3—24no—
628C3×D3—44no—
629C3×D3—64no—
630C3×D3—64no—
631C3×D3—124no—
632#41—38no—
633#41—932no—
634#41—916no—
635#41—916no—
636#41—98no—
637C2×Q8—32no—
638C2×Q8—32no—
639C2×Q8—38no—
640C2×Q8—31no—
641C2×Q8—94no—
642C2×Q8—916no—
643C2×Q8—916no—
644C2×Q8—91no—
645C2×D4—32no—
646C2×D4—31no—
647C2×D4—94no—
648C2×D4—92no—
649C2×D4—91no—
650C22×C4—32no—
651C22×C4—32no—
652C22×C4—94no—
653C22×C4—94no—
654C22×C4—92no—
655C22×C4C3×D3211yescharacteristic
656C22×C3—24no—
657C22×C3—22no—
658C22×C3—22no—
659C22×C3—22no—
660C22×C3—21no—
661C22×C3—22no—
662C22×C3—21no—
663C22×C3—21no—
664C22×C3—22no—
665C22×C3—22no—
666C22×C3—34no—
667C22×C3—34no—
668C22×C3—42no—
669C22×C3—42no—
670C22×C3—44no—
671C22×C3—42no—
672C22×C3—41no—
673C22×C3—64no—
674C22×C3—64no—
675C22×C3—64no—
676C22×C3—94no—
677C22×C3—124no—
678C22×C3—184no—
679C22×C3C22×D3212yes—
680C22×C3C22×D3211yescharacteristic
681C22×C3C23×C3×D312yes—
682C22×C3C23×C3×D312yes—
683C22×C3C23×C3×D311yescharacteristic
684C22×C3C23×C3×D311yescharacteristic
685C2×D3—24no—
686C2×D3—34no—
687C2×D3—34no—
688C2×D3—64no—
689C2×D3—64no—
690C2×D3—64no—
691C2×D3—124no—
692C2×D3C23×C3×D314yes—
693C3×C4—22no—
694C3×C4—22no—
695C3×C4—22no—
696C3×C4—22no—
697C3×C4—22no—
698C3×C4—22no—
699C3×C4—34no—
700C3×C4—38no—
701C3×C4—34no—
702C3×C4—38no—
703C3×C4—42no—
704C3×C4—42no—
705C3×C4—64no—
706C3×C4—68no—
707C3×C4—94no—
708C3×C4C22×D3212yes—
709C3×C4C22×D3212yes—
710C3×C4C23×C3×D312yes—
711C3×C4C23×C3×D312yes—
712C3×C4C23×C3×D312yes—
713C3×C4C23×C3×D312yes—
714Dic3—34no—
715Dic3—34no—
716Dic3—64no—
717Dic3C23×C3×D314yes—
718Dic3C23×C3×D318yes—
719C32—21no—
720C32—21no—
721C32—21no—
722C32—41no—
723C32C2×#100711yescharacteristic, complemented
724C32C2×#101011yescharacteristic, complemented
725C32C2×C3×2−1+411yescharacteristic, complemented
726C23—32no—
727C23—92no—
728C23C2×C3×D3211yescharacteristic
729Q8—38no—
730Q8—38no—
731Q8—34no—
732Q8—916no—
733Q8—94no—
734D4—38no—
735D4—34no—
736D4—916no—
737D4—98no—
738D4—94no—
739C2×C4—32no—
740C2×C4—34no—
741C2×C4—38no—
742C2×C4—38no—
743C2×C4—916no—
744C2×C4—916no—
745C2×C4—92no—
746C2×C4—98no—
747C2×C4C2×C3×D3211yescharacteristic
748C2×C4C2×C3×D3211yescharacteristic
749C2×C4C2×C3×D3214yes—
750C2×C3—24no—
751C2×C3—22no—
752C2×C3—22no—
753C2×C3—22no—
754C2×C3—21no—
755C2×C3—21no—
756C2×C3—21no—
757C2×C3—22no—
758C2×C3—22no—
759C2×C3—22no—
760C2×C3—42no—
761C2×C3—42no—
762C2×C3—44no—
763C2×C3—41no—
764C2×C3—42no—
765C2×C3—64no—
766C2×C3—64no—
767C2×C3—124no—
768C2×C3—184no—
769C2×C3#6429712yesdirect product factor
770C2×C3C3×#100712yescomplemented
771C2×C3C3×#101012yescomplemented
772C2×C3C23×D3211yescharacteristic
773C2×C3C24×C3×D311yescharacteristic
774C2×C3C24×C3×D311yescharacteristic
775D3—24no—
776D3—64no—
777D3—64no—
778D3—124no—
779C22—22no—
780C22—34no—
781C22—64no—
782C22—94no—
783C22—184no—
784C22C22×C3×D3212yes—
785C22C22×C3×D3211yescharacteristic
786C4—34no—
787C4—38no—
788C4—94no—
789C4C22×C3×D3212yes—
790C4C22×C3×D3212yes—
791C3—21no—
792C3—21no—
793C3—21no—
794C3—41no—
795C3C2×#6429711yescharacteristic, direct product factor
796C3C2×C3×#100711yescharacteristic, complemented
797C3C2×C3×#101011yescharacteristic, complemented
798C2—22no—
799C2—64no—
800C2—184no—
801C2C3×#6429712yesdirect product factor
802C2C23×C3×D3211yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC2×C32C25×C3
FrattiniC2C23×C3×D32
FittingC22×C33×C4C22
socleC22×C33C24
hypercenterC22×C3×C4D32
hypocenterC32C2×C3×2−1+4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#3828C2semidirect
2. C2×C32×#235C2semidirect
3. C22×C32×Dic6C2semidirect
4. C2×C3×#3804C2semidirect
5. C2×C3×#3799C2semidirect
6. C2×C3×#3797C2semidirect
7. C3×#64297C2direct (N × H)
8. C2×C3×#3796C2semidirect
9. C2×C3×D3×Dic6C2semidirect
12. C2×#64297C3direct (N × H)
15. C3×#3828C22semidirect
21. C32×#235C22semidirect
27. C2×C32×Dic6C22semidirect
31. C3×#3804C22semidirect
33. C3×#3799C22semidirect
34. C3×#3797C22semidirect
35. C3×#3796C22semidirect
36. C3×D3×Dic6C22semidirect
39. C2×#3828C2×C3semidirect
55. C2×C3×#235D3semidirect
56. C2×C3×#235C2×C3semidirect
59. C22×C3×Dic6D3semidirect
60. C22×C3×Dic6C2×C3semidirect
61. C2×#3804C2×C3semidirect
62. C2×#3799C2×C3semidirect
63. C2×#3797C2×C3semidirect
64. #64297C2×C3direct (N × H)
65. C2×#3796C2×C3semidirect
66. C2×D3×Dic6C2×C3semidirect
111. #3828C22×C3semidirect
139. C3×#235C2×D3semidirect
140. C3×#235C22×C3semidirect
170. C2×C3×Dic6C2×D3semidirect
174. C2×C3×Dic6C22×C3semidirect
178. #3804C22×C3semidirect
180. #3799C22×C3semidirect
181. #3797C22×C3semidirect
182. #3796C22×C3semidirect
183. D3×Dic6C22×C3semidirect
223. C2×#235C3×D3semidirect
225. C22×Dic6C3×D3semidirect
332. C2×C332−1+4semidirect
403. #235C2×C3×D3semidirect
425. C2×Dic6C2×C3×D3semidirect
498. C33C2×2−1+4semidirect
619. C2×C32#1007semidirect
620. C2×C32#1010semidirect
621. C2×C32C3×2−1+4semidirect
723. C32C2×#1007semidirect
724. C32C2×#1010semidirect
725. C32C2×C3×2−1+4semidirect
769. C2×C3#64297direct (N × H)
770. C2×C3C3×#1007semidirect
771. C2×C3C3×#1010semidirect
795. C3C2×#64297direct (N × H)
796. C3C2×C3×#1007semidirect
797. C3C2×C3×#1010semidirect
801. C2C3×#64297direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#38282
C2×C32×#2352
C22×C32×Dic62
C2×C3×#38042
C2×C3×#37992
C2×C3×#37972
C3×#642972
C2×C3×#37962
C2×C3×D3×Dic62
C2×C3×#10103
C2×C3×#10073
C2×#642973