Finite Group Databasebeta

← C3×#86315 #11904532

Subgroups — C3×#86315 #11904532

Order 1152.

3239 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1010C211yesmaximal, characteristic, complemented
2C22×C3×#237C211yesmaximal, characteristic, complemented
3C32×#535C211yesmaximal, characteristic, complemented
4C3×#5828C211yesmaximal, characteristic, complemented
5C3×#5805C211yesmaximal, characteristic, complemented
6C3×#5718C214yesmaximal, complemented
7C3×#5677C214yesmaximal, complemented
8C3×#5599C214yesmaximal, complemented
9C3×#5598C214yesmaximal, complemented
10C3×#5592C214yesmaximal, complemented
11C3×#5586C214yesmaximal, complemented
12C3×#5524C211yesmaximal, characteristic, complemented
13C3×#5516C211yesmaximal, characteristic, complemented
14C3×#3487—31nomaximal
15#86315C311yesmaximal, characteristic, direct product factor
16C2×C32×#41C2211yescharacteristic
17C22×C32×D4C2211yescharacteristic
18C22×C3×#67C2212yes—
19C23×C3×Dic3C2212yes—
20C3×#1010—28no—
21C2×C3×D3×Q8C2212yescomplemented
22C2×C3×#237—28no—
23C2×C3×#237C2214yes—
24C2×C3×#237C2214yes—
25C2×C3×#237C2214yes—
26C2×C3×#237C2212yescomplemented
27C2×C3×#235C2211yescharacteristic
28C2×C3×#235C2212yescomplemented
29C22×C3×C4×D3C2211yescharacteristic
30C22×C3×Dic6C2211yescharacteristic
31C22×C3×Dic6C2212yescomplemented
32C32×#127C2212yescomplemented
33C32×#124C2212yescomplemented
34C32×#121C2214yescomplemented
35C32×#120C2214yes—
36C32×#117C2211yescharacteristic
37C3×#953C2214yes—
38C3×#946C2212yescomplemented
39C3×#940C2212yescomplemented
40C3×#940C2218yescomplemented
41C3×#939C2218yescomplemented
42C3×#939C2218yescomplemented
43C3×#938C2214yescomplemented
44C3×#938C2212yescomplemented
45C3×#937C2212yes—
46C3×#936C2212yescomplemented
47C3×#935C2212yes—
48C3×D4×Dic3C2218yescomplemented
49C3×C4×#67C2214yescomplemented
50C3×#926C2211yescharacteristic
51C3×#897C2212yescomplemented
52C3×#895C2212yescomplemented
53C3×#887C2214yescomplemented
54C3×#886C2212yes—
55C3×#885C2218yescomplemented
56C3×#884C2218yescomplemented
57C3×#882C2212yes—
58C3×#67⋊C4C2218yescomplemented
59C3×#878C2218yescomplemented
60C3×#877C2214yes—
61C3×C4×D12C2214yescomplemented
62C3×C4×Dic6C2214yescomplemented
63C2×C3×2−1+4—31no—
64C22×C3×#41—31no—
65C2×#1010C2×C311yescharacteristic, complemented
66C22×#237C2×C311yescharacteristic, complemented
67C3×#550—34no—
68C3×#550—34no—
69C3×#548—34no—
70C3×#548—34no—
71C3×#535—21no—
72C3×#535—31no—
73C3×#535—34no—
74C3×#535D311yescharacteristic, complemented
75C3×#535C2×C311yescharacteristic, complemented
76C3×#525—31no—
77C3×#525—34no—
78C3×#525—31no—
79C3×#519—31no—
80#5828C2×C311yescharacteristic, complemented
81#5805C2×C311yescharacteristic, complemented
82#5718C2×C314yescomplemented
83#5677C2×C314yescomplemented
84#5599C2×C314yescomplemented
85#5598C2×C314yescomplemented
86#5592C2×C314yescomplemented
87#5586C2×C314yescomplemented
88#5524C2×C311yescharacteristic, complemented
89#5516C2×C311yescharacteristic, complemented
90C24×C32C2312yes—
91C23×C3×D3C2311yescharacteristic
92C32×#41—24no—
93C2×C32×Q8C2311yescharacteristic
94C2×C32×D4—24no—
95C2×C32×D4C2312yes—
96C2×C32×D4C2312yes—
97C2×C32×D4C2312yes—
98C2×C32×D4C2311yescharacteristic
99C2×C32×D4C2318yes—
100C22×C32×C4C2312yes—
101C22×C32×C4C2311yescharacteristic
102C2×C3×#67—28no—
103C2×C3×#67C2312yes—
104C2×C3×#67C2318yes—
105C2×C3×#67C2314yes—
106C2×C3×#67C2318yes—
107C2×C3×#67C2314yes—
108C22×C3×Dic3—28no—
109C22×C3×Dic3C2318yes—
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2314yes—
112C22×C3×Dic3C2312yes—
113C3×D3×Q8—28no—
114C3×#237—216no—
115C3×#237—216no—
116C3×#237—216no—
117C3×#237—28no—
118C3×#235—24no—
119C3×#235—28no—
120C2×C3×D12C2311yescharacteristic
121C2×C3×D12C2314yes—
122C2×C3×C4×D3—24no—
123C2×C3×C4×D3C2314yes—
124C2×C3×C4×D3C2312yes—
125C2×C3×C4×D3C2312yes—
126C2×C3×C4×D3C2312yes—
127C2×C3×Dic6—28no—
128C2×C3×Dic6D418yescomplemented
129C2×C3×Dic6C2314yes—
130C2×C3×Dic6C2311yescharacteristic
131C2×C3×Dic6C2312yes—
132C2×C3×Dic6C2312yes—
133C32×C4⋊C4C2312yes—
134C32×C22⋊C4C2312yes—
135C32×C22⋊C4C2318yes—
136C32×C42C2312yes—
137C3×#217C2312yes—
138C3×#217C2318yes—
139C3×#217C2314yes—
140C3×(C2×D3)⋊C4C2314yes—
141C3×(C2×D3)⋊C4C2314yes—
142C3×(C2×D3)⋊C4C2314yes—
143C3×C4⋊Dic3C2314yes—
144C3×C4⋊Dic3C2312yes—
145C3×Dic3⋊C4C2318yes—
146C3×Dic3⋊C4C2314yes—
147C3×C4×Dic3C2318yes—
148C3×C4×Dic3C2312yes—
149#3487—31noSylow
150C3×2−1+4—68no—
151C2×C3×#41—21no—
152C2×C3×#41—34no—
153C2×C3×#41—34no—
154C2×C3×#41—34no—
155C2×C3×#41—32no—
156C2×C3×#41—31no—
157C2×C3×#41—32no—
158C2×C3×#41—68no—
159C2×C3×#41C2×D311yescharacteristic
160C2×C3×#41C22×C311yescharacteristic
161C22×C3×Q8—32no—
162C22×C3×Q8—31no—
163C22×C3×Q8—32no—
164C22×C3×D4—21no—
165C22×C3×D4—32no—
166C22×C3×D4C2×D311yescharacteristic
167C22×C3×D4C22×C311yescharacteristic
168C23×C3×C4—32no—
169C23×C3×C4—31no—
170C22×#67C22×C312yes—
171C23×Dic3C22×C312yes—
172#1010—28no—
173C2×D3×Q8C22×C312yescomplemented
174C2×#237—28no—
175C2×#237C22×C314yes—
176C2×#237C22×C314yes—
177C2×#237C22×C314yes—
178C2×#237C22×C312yescomplemented
179C2×#235C22×C311yescharacteristic
180C2×#235C22×C312yescomplemented
181C22×C4×D3C22×C311yescharacteristic
182C22×Dic6C22×C311yescharacteristic
183C22×Dic6C22×C312yescomplemented
184C3×#127—22no—
185C3×#127—38no—
186C3×#127—32no—
187C3×#127C2×D312yescomplemented
188C3×#127C22×C312yescomplemented
189C3×#124—22no—
190C3×#124—32no—
191C3×#124—38no—
192C3×#124C2×D312yescomplemented
193C3×#124C22×C312yescomplemented
194C3×#123—32no—
195C3×#123—32no—
196C3×C22⋊Q8—32no—
197C3×C22⋊Q8—32no—
198C3×C22⋊Q8—38no—
199C3×#121—24no—
200C3×#121—32no—
201C3×#121—34no—
202C3×#121—38no—
203C3×#121—38no—
204C3×#121—32no—
205C3×#121—38no—
206C3×#121C2×D314yescomplemented
207C3×#121C22×C314yescomplemented
208C3×#120—24no—
209C3×#120—34no—
210C3×#120—32no—
211C3×#120—32no—
212C3×#120C2×D314yes—
213C3×#120C22×C314yes—
214C3×C4×Q8—34no—
215C3×C4×Q8—34no—
216C3×C4×D4—38no—
217C3×C4×D4—34no—
218C3×C4×D4—38no—
219C3×C4×D4—34no—
220C3×#117—21no—
221C3×#117—31no—
222C3×#117—34no—
223C3×#117C2×D311yescharacteristic
224C3×#117C22×C311yescharacteristic
225#953C22×C314yes—
226#946C22×C312yescomplemented
227#940C22×C318yescomplemented
228#940C22×C312yescomplemented
229#939C22×C318yescomplemented
230#939C22×C318yescomplemented
231#938C22×C314yescomplemented
232#938C22×C312yescomplemented
233#937C22×C312yes—
234#936C22×C312yescomplemented
235#935C22×C312yes—
236D4×Dic3C22×C318yescomplemented
237C4×#67C22×C314yescomplemented
238#926C22×C311yescharacteristic
239#897C22×C312yescomplemented
240#895C22×C312yescomplemented
241#887C22×C314yescomplemented
242#886C22×C312yes—
243#885C22×C318yescomplemented
244#884C22×C318yescomplemented
245#882C22×C312yes—
246#67⋊C4C22×C318yescomplemented
247#878C22×C318yescomplemented
248#877C22×C314yes—
249C4×D12C22×C314yescomplemented
250C4×Dic6C22×C314yescomplemented
251C23×C32—24no—
252C23×C32—44no—
253C23×C32C2414yes—
254C23×C32C2412yes—
255C23×C32C2411yescharacteristic
256C22×C3×D3—22no—
257C22×C3×D3—42no—
258C22×C3×D3C2412yes—
259C22×C3×D3C2412yes—
260C32×Q8—22no—
261C32×D4—24no—
262C32×D4—24no—
263C32×D4—24no—
264C32×D4—22no—
265C32×D4—48no—
266C2×C32×C4—24no—
267C2×C32×C4C2×D414yes—
268C2×C32×C4C2414yes—
269C2×C32×C4C2412yes—
270C2×C32×C4C2411yescharacteristic
271C2×C32×C4C2411yescharacteristic
272C3×#67—24no—
273C3×#67—28no—
274C3×#67—216no—
275C3×#67—48no—
276C3×#67—44no—
277C2×C3×Dic3—22no—
278C2×C3×Dic3—28no—
279C2×C3×Dic3—216no—
280C2×C3×Dic3C2×D418yes—
281C2×C3×Dic3C2414yes—
282C2×C3×Dic3C2412yes—
283C2×C3×Dic3C2412yes—
284C2×C3×Dic3C2414yes—
285C3×D12—22no—
286C3×D12—44no—
287C3×C4×D3—24no—
288C3×C4×D3—24no—
289C3×C4×D3—24no—
290C3×C4×D3—28no—
291C3×Dic6—22no—
292C3×Dic6—28no—
293C3×Dic6C2×D418yes—
294C3×Dic6C2×D418yes—
295C2×2−1+4—31no—
296C22×#41—31no—
297#550—34no—
298#550—34no—
299#548—34no—
300#548—34no—
301#535—31no—
302#535—34no—
303#535C3×D311yescharacteristic, complemented
304#525—31no—
305#525—34no—
306#525—31no—
307#519—31no—
308C24×C3—22no—
309C24×C3—31no—
310C24×C3C22×D312yes—
311C24×C3C23×C312yes—
312C23×D3C23×C311yescharacteristic
313C3×#41—24no—
314C3×#41—24no—
315C3×#41—44no—
316C3×#41—68no—
317C3×#41—616no—
318C3×#41—616no—
319C3×#41—616no—
320C3×#41—68no—
321C3×#41—64no—
322C2×C3×Q8—21no—
323C2×C3×Q8—38no—
324C2×C3×Q8—32no—
325C2×C3×Q8—32no—
326C2×C3×Q8—34no—
327C2×C3×Q8—31no—
328C2×C3×Q8—68no—
329C2×C3×Q8—68no—
330C2×C3×Q8C22×D311yescharacteristic
331C2×C3×Q8C23×C311yescharacteristic
332C2×C3×D4—24no—
333C2×C3×D4—24no—
334C2×C3×D4—22no—
335C2×C3×D4—22no—
336C2×C3×D4—22no—
337C2×C3×D4—21no—
338C2×C3×D4—28no—
339C2×C3×D4—32no—
340C2×C3×D4—38no—
341C2×C3×D4—34no—
342C2×C3×D4—34no—
343C2×C3×D4—38no—
344C2×C3×D4—31no—
345C2×C3×D4—34no—
346C2×C3×D4—44no—
347C2×C3×D4—68no—
348C2×C3×D4C22×D312yes—
349C2×C3×D4C22×D312yes—
350C2×C3×D4C22×D311yescharacteristic
351C2×C3×D4C22×D312yes—
352C2×C3×D4C22×D318yes—
353C2×C3×D4C23×C312yes—
354C2×C3×D4C23×C312yes—
355C2×C3×D4C23×C312yes—
356C2×C3×D4C23×C311yescharacteristic
357C2×C3×D4C23×C318yes—
358C22×C3×C4—21no—
359C22×C3×C4—22no—
360C22×C3×C4—32no—
361C22×C3×C4—34no—
362C22×C3×C4—38no—
363C22×C3×C4—31no—
364C22×C3×C4—34no—
365C22×C3×C4—32no—
366C22×C3×C4—32no—
367C22×C3×C4—32no—
368C22×C3×C4—68no—
369C22×C3×C4—64no—
370C22×C3×C4C22×D312yes—
371C22×C3×C4C22×D311yescharacteristic
372C22×C3×C4C23×C312yes—
373C22×C3×C4C23×C311yescharacteristic
374C2×#67—28no—
375C2×#67C23×C312yes—
376C2×#67C23×C318yes—
377C2×#67C23×C314yes—
378C2×#67C23×C318yes—
379C2×#67C23×C314yes—
380C22×Dic3—28no—
381C22×Dic3C23×C318yes—
382C22×Dic3C23×C311yescharacteristic
383C22×Dic3C23×C314yes—
384C22×Dic3C23×C312yes—
385D3×Q8—28no—
386#237—216no—
387#237—216no—
388#237—216no—
389#237—28no—
390#235—24no—
391#235—28no—
392C2×D12C23×C311yescharacteristic
393C2×D12C23×C314yes—
394C2×C4×D3—24no—
395C2×C4×D3C23×C312yes—
396C2×C4×D3C23×C312yes—
397C2×C4×D3C23×C314yes—
398C2×C4×D3C23×C312yes—
399C2×Dic6—28no—
400C2×Dic6C3×D418yescomplemented
401C2×Dic6C23×C314yes—
402C2×Dic6C23×C311yescharacteristic
403C2×Dic6C23×C312yes—
404C2×Dic6C23×C312yes—
405C3×C4⋊C4—22no—
406C3×C4⋊C4—38no—
407C3×C4⋊C4—34no—
408C3×C4⋊C4—32no—
409C3×C4⋊C4—34no—
410C3×C4⋊C4C22×D312yes—
411C3×C4⋊C4C23×C312yes—
412C3×C22⋊C4—22no—
413C3×C22⋊C4—28no—
414C3×C22⋊C4—32no—
415C3×C22⋊C4—34no—
416C3×C22⋊C4—38no—
417C3×C22⋊C4—34no—
418C3×C22⋊C4—34no—
419C3×C22⋊C4—34no—
420C3×C22⋊C4C22×D312yes—
421C3×C22⋊C4C22×D318yes—
422C3×C22⋊C4C23×C312yes—
423C3×C22⋊C4C23×C318yes—
424C3×C42—22no—
425C3×C42—38no—
426C3×C42—32no—
427C3×C42C22×D312yes—
428C3×C42C23×C312yes—
429#217C23×C312yes—
430#217C23×C318yes—
431#217C23×C314yes—
432(C2×D3)⋊C4C23×C314yes—
433(C2×D3)⋊C4C23×C314yes—
434(C2×D3)⋊C4C23×C314yes—
435C4⋊Dic3C23×C312yes—
436C4⋊Dic3C23×C314yes—
437Dic3⋊C4C23×C318yes—
438Dic3⋊C4C23×C314yes—
439C4×Dic3C23×C318yes—
440C4×Dic3C23×C312yes—
441C22×C32—22no—
442C22×C32—22no—
443C22×C32—24no—
444C22×C32—24no—
445C22×C32—28no—
446C22×C32—48no—
447C22×C32C22×D412yes—
448C22×C32C2511yescharacteristic
449C2×C3×D3—22no—
450C2×C3×D3—22no—
451C2×C3×D3—22no—
452C2×C3×D3—24no—
453C2×C3×D3—22no—
454C2×C3×D3—44no—
455C32×C4—22no—
456C32×C4—24no—
457C32×C4C22×D412yes—
458C32×C4C22×D412yes—
459C3×Dic3—22no—
460C3×Dic3—22no—
461C3×Dic3—24no—
462C3×Dic3C22×D418yes—
4632−1+4—68no—
464C2×#41—34no—
465C2×#41—34no—
466C2×#41—34no—
467C2×#41—32no—
468C2×#41—31no—
469C2×#41—32no—
470C2×#41—68no—
471C2×#41C2×C3×D311yescharacteristic
472C22×Q8—32no—
473C22×Q8—31no—
474C22×Q8—32no—
475C22×D4—32no—
476C22×D4C2×C3×D311yescharacteristic
477C23×C4—32no—
478C23×C4—31no—
479#127—38no—
480#127—32no—
481#127C2×C3×D312yescomplemented
482#124—32no—
483#124—38no—
484#124C2×C3×D312yescomplemented
485#123—32no—
486#123—32no—
487C22⋊Q8—32no—
488C22⋊Q8—32no—
489C22⋊Q8—38no—
490#121—32no—
491#121—38no—
492#121—34no—
493#121—38no—
494#121—32no—
495#121—38no—
496#121C2×C3×D314yescomplemented
497#120—34no—
498#120—32no—
499#120—32no—
500#120C2×C3×D314yes—
501C4×Q8—34no—
502C4×Q8—34no—
503C4×D4—38no—
504C4×D4—34no—
505C4×D4—38no—
506C4×D4—34no—
507#117—31no—
508#117—34no—
509#117C2×C3×D311yescharacteristic
510C23×C3—24no—
511C23×C3—24no—
512C23×C3—21no—
513C23×C3—24no—
514C23×C3—22no—
515C23×C3—32no—
516C23×C3—32no—
517C23×C3—44no—
518C23×C3—44no—
519C23×C3—44no—
520C23×C3—62no—
521C23×C3—84no—
522C23×C3—122no—
523C23×C3C23×D314yes—
524C23×C3C23×D312yes—
525C23×C3C23×D311yescharacteristic
526C23×C3C24×C314yes—
527C23×C3C24×C312yes—
528C23×C3C24×C311yescharacteristic
529C22×D3—22no—
530C22×D3—42no—
531C22×D3C24×C312yes—
532C22×D3C24×C312yes—
533C3×Q8—22no—
534C3×Q8—22no—
535C3×Q8—38no—
536C3×Q8—38no—
537C3×Q8—42no—
538C3×Q8—68no—
539C3×Q8—62no—
540C3×D4—24no—
541C3×D4—24no—
542C3×D4—24no—
543C3×D4—24no—
544C3×D4—22no—
545C3×D4—24no—
546C3×D4—24no—
547C3×D4—22no—
548C3×D4—44no—
549C3×D4—44no—
550C3×D4—42no—
551C3×D4—44no—
552C3×D4—48no—
553C3×D4—48no—
554C3×D4—616no—
555C3×D4—68no—
556C3×D4—64no—
557C3×D4—62no—
558C3×D4—88no—
559C3×D4—124no—
560C3×D4—124no—
561C3×D4—128no—
562C2×C3×C4—24no—
563C2×C3×C4—24no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—24no—
567C2×C3×C4—22no—
568C2×C3×C4—24no—
569C2×C3×C4—38no—
570C2×C3×C4—34no—
571C2×C3×C4—34no—
572C2×C3×C4—32no—
573C2×C3×C4—32no—
574C2×C3×C4—44no—
575C2×C3×C4—68no—
576C2×C3×C4—616no—
577C2×C3×C4—68no—
578C2×C3×C4—62no—
579C2×C3×C4—64no—
580C2×C3×C4—64no—
581C2×C3×C4—64no—
582C2×C3×C4D3×D414yes—
583C2×C3×C4C2×C3×D414yes—
584C2×C3×C4C23×D314yes—
585C2×C3×C4C23×D312yes—
586C2×C3×C4C23×D311yescharacteristic
587C2×C3×C4C23×D311yescharacteristic
588C2×C3×C4C24×C314yes—
589C2×C3×C4C24×C312yes—
590C2×C3×C4C24×C311yescharacteristic
591C2×C3×C4C24×C311yescharacteristic
592#67—24no—
593#67—28no—
594#67—216no—
595#67—48no—
596#67—44no—
597C2×Dic3—22no—
598C2×Dic3—28no—
599C2×Dic3—216no—
600C2×Dic3C2×C3×D418yes—
601C2×Dic3C24×C314yes—
602C2×Dic3C24×C312yes—
603C2×Dic3C24×C312yes—
604C2×Dic3C24×C314yes—
605D12—22no—
606D12—44no—
607C4×D3—24no—
608C4×D3—24no—
609C4×D3—24no—
610C4×D3—28no—
611Dic6—22no—
612Dic6—28no—
613Dic6C2×C3×D418yes—
614Dic6C2×C3×D418yes—
615C2×C32—22no—
616C2×C32—42no—
617C2×C32—44no—
618C2×C32C23×D411yescharacteristic
619C2×C32#58512yes—
620C3×D3—42no—
621C3×D3—42no—
622C24—31no—
623C24C22×C3×D312yes—
624#41—24no—
625#41—68no—
626#41—616no—
627#41—616no—
628#41—616no—
629#41—68no—
630#41—64no—
631C2×Q8—32no—
632C2×Q8—32no—
633C2×Q8—34no—
634C2×Q8—31no—
635C2×Q8—38no—
636C2×Q8—68no—
637C2×Q8—68no—
638C2×Q8C22×C3×D311yescharacteristic
639C2×D4—24no—
640C2×D4—32no—
641C2×D4—38no—
642C2×D4—34no—
643C2×D4—34no—
644C2×D4—38no—
645C2×D4—31no—
646C2×D4—34no—
647C2×D4—68no—
648C2×D4C22×C3×D312yes—
649C2×D4C22×C3×D312yes—
650C2×D4C22×C3×D311yescharacteristic
651C2×D4C22×C3×D312yes—
652C2×D4C22×C3×D318yes—
653C22×C4—32no—
654C22×C4—34no—
655C22×C4—38no—
656C22×C4—31no—
657C22×C4—34no—
658C22×C4—32no—
659C22×C4—32no—
660C22×C4—32no—
661C22×C4—68no—
662C22×C4—64no—
663C22×C4C22×C3×D312yes—
664C22×C4C22×C3×D311yescharacteristic
665C4⋊C4—38no—
666C4⋊C4—32no—
667C4⋊C4—34no—
668C4⋊C4—34no—
669C4⋊C4C22×C3×D312yes—
670C22⋊C4—32no—
671C22⋊C4—34no—
672C22⋊C4—38no—
673C22⋊C4—34no—
674C22⋊C4—34no—
675C22⋊C4—34no—
676C22⋊C4C22×C3×D312yes—
677C22⋊C4C22×C3×D318yes—
678C42—38no—
679C42—32no—
680C42C22×C3×D312yes—
681C22×C3—22no—
682C22×C3—22no—
683C22×C3—22no—
684C22×C3—24no—
685C22×C3—24no—
686C22×C3—28no—
687C22×C3—22no—
688C22×C3—24no—
689C22×C3—24no—
690C22×C3—28no—
691C22×C3—22no—
692C22×C3—21no—
693C22×C3—42no—
694C22×C3—42no—
695C22×C3—44no—
696C22×C3—44no—
697C22×C3—48no—
698C22×C3—48no—
699C22×C3—48no—
700C22×C3—62no—
701C22×C3—62no—
702C22×C3—64no—
703C22×C3—62no—
704C22×C3—62no—
705C22×C3—88no—
706C22×C3—124no—
707C22×C3C2×D3×D412yes—
708C22×C3C22×C3×D412yes—
709C22×C3C24×D311yescharacteristic
710C22×C3C25×C311yescharacteristic
711C2×D3—22no—
712C2×D3—22no—
713C2×D3—22no—
714C2×D3—24no—
715C2×D3—22no—
716C2×D3—44no—
717C3×C4—22no—
718C3×C4—24no—
719C3×C4—22no—
720C3×C4—24no—
721C3×C4—22no—
722C3×C4—22no—
723C3×C4—38no—
724C3×C4—42no—
725C3×C4—44no—
726C3×C4—62no—
727C3×C4—62no—
728C3×C4—64no—
729C3×C4C2×D3×D412yes—
730C3×C4C2×D3×D412yes—
731C3×C4C22×C3×D412yes—
732C3×C4C22×C3×D412yes—
733Dic3—22no—
734Dic3—22no—
735Dic3—24no—
736Dic3C22×C3×D418yes—
737C32#348711yescharacteristic, complemented, Sylow
738C23—24no—
739C23—32no—
740C23—32no—
741C23—44no—
742C23—62no—
743C23—122no—
744C23C23×C3×D314yes—
745C23C23×C3×D312yes—
746C23C23×C3×D311yescharacteristic
747Q8—22no—
748Q8—38no—
749Q8—38no—
750Q8—68no—
751Q8—62no—
752D4—24no—
753D4—24no—
754D4—24no—
755D4—22no—
756D4—48no—
757D4—616no—
758D4—68no—
759D4—64no—
760D4—62no—
761D4—124no—
762D4—124no—
763D4—128no—
764C2×C4—24no—
765C2×C4—38no—
766C2×C4—34no—
767C2×C4—34no—
768C2×C4—32no—
769C2×C4—32no—
770C2×C4—68no—
771C2×C4—616no—
772C2×C4—68no—
773C2×C4—62no—
774C2×C4—64no—
775C2×C4—64no—
776C2×C4—64no—
777C2×C4C3×D3×D414yes—
778C2×C4C23×C3×D314yes—
779C2×C4C23×C3×D312yes—
780C2×C4C23×C3×D311yescharacteristic
781C2×C4C23×C3×D311yescharacteristic
782C2×C3—22no—
783C2×C3—22no—
784C2×C3—21no—
785C2×C3—22no—
786C2×C3—42no—
787C2×C3—44no—
788C2×C3—42no—
789C2×C3—44no—
790C2×C3—42no—
791C2×C3—84no—
792C2×C3—82no—
793C2×C3—122no—
794C2×C3—122no—
795C2×C3C22×D3×D411yescharacteristic
796C2×C3#596612yes—
797C2×C3C23×C3×D411yescharacteristic
798C2×C3C3×#58512yes—
799D3—42no—
800D3—42no—
801C22—22no—
802C22—22no—
803C22—24no—
804C22—24no—
805C22—28no—
806C22—48no—
807C22—62no—
808C22—62no—
809C22—64no—
810C22—62no—
811C22—62no—
812C22—124no—
813C22C2×C3×D3×D412yes—
814C22C24×C3×D311yescharacteristic
815C4—22no—
816C4—24no—
817C4—38no—
818C4—62no—
819C4—62no—
820C4—64no—
821C4C2×C3×D3×D412yes—
822C4C2×C3×D3×D412yes—
823C3—21no—
824C3#8631511yescharacteristic, direct product factor
825C3C3×#348711yescharacteristic, complemented
826C2—22no—
827C2—44no—
828C2—42no—
829C2—122no—
830C2—122no—
831C2C22×C3×D3×D411yescharacteristic
832C2C3×#596612yes—
subgroupG/H
centerC22×C3C24×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC32×#535C2
socleC22×C32C25
hypercenterC3×#535D3
hypocenterC3C3×#3487
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×#535

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1010C2semidirect
2. C22×C3×#237C2semidirect
3. C32×#535C2semidirect
4. C3×#5828C2semidirect
5. C3×#5805C2semidirect
6. C3×#5718C2semidirect
7. C3×#5677C2semidirect
8. C3×#5599C2semidirect
9. C3×#5598C2semidirect
10. C3×#5592C2semidirect
11. C3×#5586C2semidirect
12. C3×#5524C2semidirect
13. C3×#5516C2semidirect
15. #86315C3direct (N × H)
21. C2×C3×D3×Q8C22semidirect
26. C2×C3×#237C22semidirect
28. C2×C3×#235C22semidirect
31. C22×C3×Dic6C22semidirect
32. C32×#127C22semidirect
33. C32×#124C22semidirect
34. C32×#121C22semidirect
38. C3×#946C22semidirect
39. C3×#940C22semidirect
40. C3×#940C22semidirect
41. C3×#939C22semidirect
42. C3×#939C22semidirect
43. C3×#938C22semidirect
44. C3×#938C22semidirect
46. C3×#936C22semidirect
48. C3×D4×Dic3C22semidirect
49. C3×C4×#67C22semidirect
51. C3×#897C22semidirect
52. C3×#895C22semidirect
53. C3×#887C22semidirect
55. C3×#885C22semidirect
56. C3×#884C22semidirect
58. C3×#67⋊C4C22semidirect
59. C3×#878C22semidirect
61. C3×C4×D12C22semidirect
62. C3×C4×Dic6C22semidirect
65. C2×#1010C2×C3semidirect
66. C22×#237C2×C3semidirect
74. C3×#535D3semidirect
75. C3×#535C2×C3semidirect
80. #5828C2×C3semidirect
81. #5805C2×C3semidirect
82. #5718C2×C3semidirect
83. #5677C2×C3semidirect
84. #5599C2×C3semidirect
85. #5598C2×C3semidirect
86. #5592C2×C3semidirect
87. #5586C2×C3semidirect
88. #5524C2×C3semidirect
89. #5516C2×C3semidirect
128. C2×C3×Dic6D4semidirect
173. C2×D3×Q8C22×C3semidirect
178. C2×#237C22×C3semidirect
180. C2×#235C22×C3semidirect
183. C22×Dic6C22×C3semidirect
187. C3×#127C2×D3semidirect
188. C3×#127C22×C3semidirect
192. C3×#124C2×D3semidirect
193. C3×#124C22×C3semidirect
206. C3×#121C2×D3semidirect
207. C3×#121C22×C3semidirect
226. #946C22×C3semidirect
227. #940C22×C3semidirect
228. #940C22×C3semidirect
229. #939C22×C3semidirect
230. #939C22×C3semidirect
231. #938C22×C3semidirect
232. #938C22×C3semidirect
234. #936C22×C3semidirect
236. D4×Dic3C22×C3semidirect
237. C4×#67C22×C3semidirect
239. #897C22×C3semidirect
240. #895C22×C3semidirect
241. #887C22×C3semidirect
243. #885C22×C3semidirect
244. #884C22×C3semidirect
246. #67⋊C4C22×C3semidirect
247. #878C22×C3semidirect
249. C4×D12C22×C3semidirect
250. C4×Dic6C22×C3semidirect
303. #535C3×D3semidirect
400. C2×Dic6C3×D4semidirect
481. #127C2×C3×D3semidirect
484. #124C2×C3×D3semidirect
496. #121C2×C3×D3semidirect
737. C32#3487semidirect
824. C3#86315direct (N × H)
825. C3C3×#3487semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10102
C22×C3×#2372
C32×#5352
C3×#58282
C3×#58052
C3×#57182
C3×#56772
C3×#55992
C3×#55982
C3×#55922
C3×#55862
C3×#55242
C3×#55162
C3×#34873
#863153