Finite Group Databasebeta

← C3×#86023 #11904526

Subgroups — C3×#86023 #11904526

Order 1152.

3237 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1010C211yesmaximal, characteristic, complemented
2C22×C3×#235C211yesmaximal, characteristic, complemented
3C32×#525C211yesmaximal, characteristic, complemented
4C3×#5830C211yesmaximal, characteristic, complemented
5C3×#5791C211yesmaximal, characteristic, complemented
6C3×#5656C214yesmaximal, complemented
7C3×#5633C214yesmaximal, complemented
8C3×#5599C214yesmaximal, complemented
9C3×#5592C214yesmaximal, complemented
10C3×#5553C214yesmaximal, complemented
11C3×#5552C214yesmaximal, complemented
12C3×#5525C211yesmaximal, characteristic, complemented
13C3×#5516C211yesmaximal, characteristic, complemented
14C3×#3487—31nomaximal
15#86023C311yesmaximal, characteristic, direct product factor
16C2×C32×#41C2211yescharacteristic
17C23×C32×C4C2211yescharacteristic
18C22×C3×#67C2212yes—
19C3×#1010—28no—
20C2×C3×D3×Q8C2212yescomplemented
21C2×C3×#237C2214yes—
22C2×C3×#237C2212yescomplemented
23C2×C3×#235—28no—
24C2×C3×#235C2211yescharacteristic
25C2×C3×#235C2214yes—
26C2×C3×#235C2214yes—
27C2×C3×#235C2212yescomplemented
28C22×C3×D12C2211yescharacteristic
29C22×C3×C4×D3C2212yes—
30C22×C3×Dic6C2211yescharacteristic
31C22×C3×Dic6C2212yescomplemented
32C32×#123C2212yes—
33C32×C22⋊Q8C2212yescomplemented
34C32×#121C2212yescomplemented
35C32×#120C2212yes—
36C32×C4×D4C2214yescomplemented
37C32×#117C2211yescharacteristic
38C3×#953C2212yes—
39C3×#947C2212yescomplemented
40C3×#940C2218yescomplemented
41C3×#940C2212yescomplemented
42C3×#939C2218yescomplemented
43C3×#937C2214yes—
44C3×#930C2212yescomplemented
45C3×#930C2214yescomplemented
46C3×#929C2212yes—
47C3×C4×#67C2214yescomplemented
48C3×#926C2211yescharacteristic
49C3×#924C2212yescomplemented
50C3×#896C2218yescomplemented
51C3×#895C2214yescomplemented
52C3×#893C2218yescomplemented
53C3×#887C2214yescomplemented
54C3×#885C2218yescomplemented
55C3×#884C2218yescomplemented
56C3×#884C2218yescomplemented
57C3×#882C2214yes—
58C3×#67⋊C4C2218yescomplemented
59C3×#877C2214yes—
60C3×#875C2212yescomplemented
61C3×#874C2212yescomplemented
62C3×C4×Dic6C2214yescomplemented
63C2×C3×2−1+4—31no—
64C22×C3×#41—31no—
65C2×#1010C2×C311yescharacteristic, complemented
66C22×#235C2×C311yescharacteristic, complemented
67C3×#550—34no—
68C3×#550—34no—
69C3×#548—34no—
70C3×#548—34no—
71C3×#535—31no—
72C3×#535—34no—
73C3×#535—31no—
74C3×#525—21no—
75C3×#525—31no—
76C3×#525—34no—
77C3×#525D311yescharacteristic, complemented
78C3×#525C2×C311yescharacteristic, complemented
79C3×#519—31no—
80#5830C2×C311yescharacteristic, complemented
81#5791C2×C311yescharacteristic, complemented
82#5656C2×C314yescomplemented
83#5633C2×C314yescomplemented
84#5599C2×C314yescomplemented
85#5592C2×C314yescomplemented
86#5553C2×C314yescomplemented
87#5552C2×C314yescomplemented
88#5525C2×C311yescharacteristic, complemented
89#5516C2×C311yescharacteristic, complemented
90C24×C32C2311yescharacteristic
91C23×C3×D3C2312yes—
92C32×#41—24no—
93C2×C32×Q8C2311yescharacteristic
94C2×C32×D4C2312yes—
95C2×C32×D4C2311yescharacteristic
96C2×C32×D4C2314yes—
97C22×C32×C4—24no—
98C22×C32×C4C2312yes—
99C22×C32×C4C2312yes—
100C22×C32×C4C2311yescharacteristic
101C22×C32×C4C2312yes—
102C22×C32×C4C2311yescharacteristic
103C2×C3×#67—28no—
104C2×C3×#67C2312yes—
105C2×C3×#67C2314yes—
106C2×C3×#67C2318yes—
107C2×C3×#67C2318yes—
108C2×C3×#67C2314yes—
109C22×C3×Dic3C2314yes—
110C22×C3×Dic3C2312yes—
111C3×D3×Q8—28no—
112C3×#237—216no—
113C3×#237—28no—
114C3×#235—24no—
115C3×#235—216no—
116C3×#235—216no—
117C3×#235—28no—
118C2×C3×D12—24no—
119C2×C3×D12C2312yes—
120C2×C3×D12C2312yes—
121C2×C3×D12C2311yescharacteristic
122C2×C3×D12C2318yes—
123C2×C3×C4×D3—28no—
124C2×C3×C4×D3C2318yes—
125C2×C3×C4×D3C2314yes—
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×C4⋊C4C2314yes—
135C32×C22⋊C4C2312yes—
136C32×C22⋊C4C2314yes—
137C32×C22⋊C4C2314yes—
138C32×C42C2312yes—
139C3×#217C2312yes—
140C3×#217C2314yes—
141C3×(C2×D3)⋊C4C2318yes—
142C3×(C2×D3)⋊C4C2314yes—
143C3×(C2×D3)⋊C4C2318yes—
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—32no—
154C2×C3×#41—34no—
155C2×C3×#41—34no—
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—32no—
165C22×C3×D4—31no—
166C23×C3×C4—21no—
167C23×C3×C4—32no—
168C23×C3×C4C2×D311yescharacteristic
169C23×C3×C4C22×C311yescharacteristic
170C22×#67C22×C312yes—
171#1010—28no—
172C2×D3×Q8C22×C312yescomplemented
173C2×#237C22×C314yes—
174C2×#237C22×C312yescomplemented
175C2×#235—28no—
176C2×#235C22×C314yes—
177C2×#235C22×C314yes—
178C2×#235C22×C311yescharacteristic
179C2×#235C22×C312yescomplemented
180C22×D12C22×C311yescharacteristic
181C22×C4×D3C22×C312yes—
182C22×Dic6C22×C311yescharacteristic
183C22×Dic6C22×C312yescomplemented
184C3×#127—38no—
185C3×#127—32no—
186C3×#127—32no—
187C3×#124—32no—
188C3×#124—38no—
189C3×#124—32no—
190C3×#123—22no—
191C3×#123—32no—
192C3×#123C2×D312yes—
193C3×#123C22×C312yes—
194C3×C22⋊Q8—22no—
195C3×C22⋊Q8—32no—
196C3×C22⋊Q8—38no—
197C3×C22⋊Q8C2×D312yescomplemented
198C3×C22⋊Q8C22×C312yescomplemented
199C3×#121—22no—
200C3×#121—38no—
201C3×#121—32no—
202C3×#121—34no—
203C3×#121—34no—
204C3×#121—38no—
205C3×#121—38no—
206C3×#121C2×D312yescomplemented
207C3×#121C22×C312yescomplemented
208C3×#120—22no—
209C3×#120—32no—
210C3×#120—34no—
211C3×#120—34no—
212C3×#120C2×D312yes—
213C3×#120C22×C312yes—
214C3×C4×Q8—34no—
215C3×C4×Q8—34no—
216C3×C4×D4—24no—
217C3×C4×D4—34no—
218C3×C4×D4—38no—
219C3×C4×D4—38no—
220C3×C4×D4C2×D314yescomplemented
221C3×C4×D4C22×C314yescomplemented
222C3×#117—21no—
223C3×#117—31no—
224C3×#117—34no—
225C3×#117C2×D311yescharacteristic
226C3×#117C22×C311yescharacteristic
227#953C22×C312yes—
228#947C22×C312yescomplemented
229#940C22×C318yescomplemented
230#940C22×C312yescomplemented
231#939C22×C318yescomplemented
232#937C22×C314yes—
233#930C22×C312yescomplemented
234#930C22×C314yescomplemented
235#929C22×C312yes—
236C4×#67C22×C314yescomplemented
237#926C22×C311yescharacteristic
238#924C22×C312yescomplemented
239#896C22×C318yescomplemented
240#895C22×C314yescomplemented
241#893C22×C318yescomplemented
242#887C22×C314yescomplemented
243#885C22×C318yescomplemented
244#884C22×C318yescomplemented
245#884C22×C318yescomplemented
246#882C22×C314yes—
247#67⋊C4C22×C318yescomplemented
248#877C22×C314yes—
249#875C22×C312yescomplemented
250#874C22×C312yescomplemented
251C4×Dic6C22×C314yescomplemented
252C23×C32—22no—
253C23×C32—42no—
254C23×C32C2412yes—
255C23×C32C2412yes—
256C23×C32C2411yescharacteristic
257C22×C3×D3—24no—
258C22×C3×D3—44no—
259C22×C3×D3C2414yes—
260C22×C3×D3C2412yes—
261C32×Q8—22no—
262C32×D4—24no—
263C32×D4—22no—
264C32×D4—44no—
265C2×C32×C4—22no—
266C2×C32×C4—24no—
267C2×C32×C4—24no—
268C2×C32×C4—24no—
269C2×C32×C4C2×D414yes—
270C2×C32×C4C2414yes—
271C2×C32×C4C2412yes—
272C2×C32×C4C2412yes—
273C2×C32×C4C2411yescharacteristic
274C2×C32×C4C2411yescharacteristic
275C3×#67—24no—
276C3×#67—216no—
277C3×#67—28no—
278C3×#67—44no—
279C3×#67—48no—
280C2×C3×Dic3—28no—
281C2×C3×Dic3C2×D418yes—
282C2×C3×Dic3C2414yes—
283C2×C3×Dic3C2412yes—
284C2×C3×Dic3C2414yes—
285C3×D12—24no—
286C3×D12—24no—
287C3×D12—22no—
288C3×D12—48no—
289C3×C4×D3—24no—
290C3×C4×D3—216no—
291C3×C4×D3—28no—
292C3×Dic6—22no—
293C3×Dic6—28no—
294C3×Dic6C2×D418yes—
295C3×Dic6C2×D418yes—
296C2×2−1+4—31no—
297C22×#41—31no—
298#550—34no—
299#550—34no—
300#548—34no—
301#548—34no—
302#535—31no—
303#535—34no—
304#535—31no—
305#525—31no—
306#525—34no—
307#525C3×D311yescharacteristic, complemented
308#519—31no—
309C24×C3—21no—
310C24×C3—32no—
311C24×C3C22×D311yescharacteristic
312C24×C3C23×C311yescharacteristic
313C23×D3C23×C312yes—
314C3×#41—24no—
315C3×#41—24no—
316C3×#41—44no—
317C3×#41—616no—
318C3×#41—616no—
319C3×#41—68no—
320C3×#41—616no—
321C3×#41—68no—
322C3×#41—64no—
323C2×C3×Q8—21no—
324C2×C3×Q8—38no—
325C2×C3×Q8—32no—
326C2×C3×Q8—32no—
327C2×C3×Q8—34no—
328C2×C3×Q8—31no—
329C2×C3×Q8—68no—
330C2×C3×Q8—68no—
331C2×C3×Q8C22×D311yescharacteristic
332C2×C3×Q8C23×C311yescharacteristic
333C2×C3×D4—24no—
334C2×C3×D4—22no—
335C2×C3×D4—21no—
336C2×C3×D4—32no—
337C2×C3×D4—38no—
338C2×C3×D4—34no—
339C2×C3×D4—38no—
340C2×C3×D4—34no—
341C2×C3×D4—32no—
342C2×C3×D4—32no—
343C2×C3×D4—31no—
344C2×C3×D4—38no—
345C2×C3×D4—68no—
346C2×C3×D4—64no—
347C2×C3×D4C22×D312yes—
348C2×C3×D4C22×D311yescharacteristic
349C2×C3×D4C22×D314yes—
350C2×C3×D4C23×C312yes—
351C2×C3×D4C23×C311yescharacteristic
352C2×C3×D4C23×C314yes—
353C22×C3×C4—24no—
354C22×C3×C4—24no—
355C22×C3×C4—21no—
356C22×C3×C4—22no—
357C22×C3×C4—22no—
358C22×C3×C4—22no—
359C22×C3×C4—21no—
360C22×C3×C4—32no—
361C22×C3×C4—34no—
362C22×C3×C4—34no—
363C22×C3×C4—32no—
364C22×C3×C4—38no—
365C22×C3×C4—44no—
366C22×C3×C4—68no—
367C22×C3×C4C22×D312yes—
368C22×C3×C4C22×D312yes—
369C22×C3×C4C22×D312yes—
370C22×C3×C4C22×D311yescharacteristic
371C22×C3×C4C22×D311yescharacteristic
372C22×C3×C4C23×C312yes—
373C22×C3×C4C23×C312yes—
374C22×C3×C4C23×C311yescharacteristic
375C22×C3×C4C23×C312yes—
376C22×C3×C4C23×C311yescharacteristic
377C2×#67—28no—
378C2×#67C23×C312yes—
379C2×#67C23×C314yes—
380C2×#67C23×C318yes—
381C2×#67C23×C318yes—
382C2×#67C23×C314yes—
383C22×Dic3C23×C314yes—
384C22×Dic3C23×C312yes—
385D3×Q8—28no—
386#237—216no—
387#237—28no—
388#235—24no—
389#235—216no—
390#235—216no—
391#235—28no—
392C2×D12—24no—
393C2×D12C23×C311yescharacteristic
394C2×D12C23×C312yes—
395C2×D12C23×C312yes—
396C2×D12C23×C318yes—
397C2×C4×D3—28no—
398C2×C4×D3C23×C318yes—
399C2×C4×D3C23×C314yes—
400C2×C4×D3C23×C312yes—
401C2×Dic6—28no—
402C2×Dic6C3×D418yescomplemented
403C2×Dic6C23×C311yescharacteristic
404C2×Dic6C23×C314yes—
405C2×Dic6C23×C312yes—
406C2×Dic6C23×C312yes—
407C3×C4⋊C4—22no—
408C3×C4⋊C4—24no—
409C3×C4⋊C4—38no—
410C3×C4⋊C4—34no—
411C3×C4⋊C4—32no—
412C3×C4⋊C4C22×D312yes—
413C3×C4⋊C4C22×D314yes—
414C3×C4⋊C4C23×C312yes—
415C3×C4⋊C4C23×C314yes—
416C3×C22⋊C4—22no—
417C3×C22⋊C4—24no—
418C3×C22⋊C4—24no—
419C3×C22⋊C4—32no—
420C3×C22⋊C4—34no—
421C3×C22⋊C4—34no—
422C3×C22⋊C4—38no—
423C3×C22⋊C4—38no—
424C3×C22⋊C4C22×D312yes—
425C3×C22⋊C4C22×D314yes—
426C3×C22⋊C4C22×D314yes—
427C3×C22⋊C4C23×C312yes—
428C3×C22⋊C4C23×C314yes—
429C3×C22⋊C4C23×C314yes—
430C3×C42—22no—
431C3×C42—38no—
432C3×C42—32no—
433C3×C42C22×D312yes—
434C3×C42C23×C312yes—
435#217C23×C312yes—
436#217C23×C314yes—
437(C2×D3)⋊C4C23×C318yes—
438(C2×D3)⋊C4C23×C314yes—
439(C2×D3)⋊C4C23×C318yes—
440C4⋊Dic3C23×C312yes—
441Dic3⋊C4C23×C318yes—
442Dic3⋊C4C23×C314yes—
443C4×Dic3C23×C318yes—
444C4×Dic3C23×C312yes—
445C22×C32—22no—
446C22×C32—22no—
447C22×C32—22no—
448C22×C32—22no—
449C22×C32—24no—
450C22×C32—22no—
451C22×C32—44no—
452C22×C32C22×D412yes—
453C22×C32C2511yescharacteristic
454C2×C3×D3—22no—
455C2×C3×D3—24no—
456C2×C3×D3—24no—
457C2×C3×D3—28no—
458C2×C3×D3—48no—
459C32×C4—22no—
460C32×C4—22no—
461C32×C4—24no—
462C32×C4C22×D412yes—
463C32×C4C22×D412yes—
464C3×Dic3—22no—
465C3×Dic3—24no—
466C3×Dic3C22×D418yes—
4672−1+4—68no—
468C2×#41—34no—
469C2×#41—32no—
470C2×#41—31no—
471C2×#41—34no—
472C2×#41—34no—
473C2×#41—32no—
474C2×#41—68no—
475C2×#41C2×C3×D311yescharacteristic
476C22×Q8—32no—
477C22×Q8—31no—
478C22×Q8—32no—
479C22×D4—32no—
480C22×D4—31no—
481C23×C4—32no—
482C23×C4C2×C3×D311yescharacteristic
483#127—38no—
484#127—32no—
485#127—32no—
486#124—32no—
487#124—38no—
488#124—32no—
489#123—32no—
490#123C2×C3×D312yes—
491C22⋊Q8—32no—
492C22⋊Q8—38no—
493C22⋊Q8C2×C3×D312yescomplemented
494#121—38no—
495#121—32no—
496#121—34no—
497#121—34no—
498#121—38no—
499#121—38no—
500#121C2×C3×D312yescomplemented
501#120—32no—
502#120—34no—
503#120—34no—
504#120C2×C3×D312yes—
505C4×Q8—34no—
506C4×Q8—34no—
507C4×D4—34no—
508C4×D4—38no—
509C4×D4—38no—
510C4×D4C2×C3×D314yescomplemented
511#117—31no—
512#117—34no—
513#117C2×C3×D311yescharacteristic
514C23×C3—22no—
515C23×C3—22no—
516C23×C3—22no—
517C23×C3—21no—
518C23×C3—22no—
519C23×C3—34no—
520C23×C3—32no—
521C23×C3—42no—
522C23×C3—42no—
523C23×C3—42no—
524C23×C3—44no—
525C23×C3—64no—
526C23×C3—124no—
527C23×C3C23×D312yes—
528C23×C3C23×D312yes—
529C23×C3C23×D311yescharacteristic
530C23×C3C24×C312yes—
531C23×C3C24×C312yes—
532C23×C3C24×C311yescharacteristic
533C22×D3—24no—
534C22×D3—44no—
535C22×D3C24×C314yes—
536C22×D3C24×C312yes—
537C3×Q8—22no—
538C3×Q8—22no—
539C3×Q8—38no—
540C3×Q8—38no—
541C3×Q8—42no—
542C3×Q8—68no—
543C3×Q8—62no—
544C3×D4—24no—
545C3×D4—24no—
546C3×D4—22no—
547C3×D4—22no—
548C3×D4—42no—
549C3×D4—44no—
550C3×D4—44no—
551C3×D4—44no—
552C3×D4—48no—
553C3×D4—616no—
554C3×D4—68no—
555C3×D4—64no—
556C3×D4—64no—
557C3×D4—64no—
558C3×D4—62no—
559C3×D4—128no—
560C3×D4—128no—
561C3×D4—124no—
562C2×C3×C4—22no—
563C2×C3×C4—22no—
564C2×C3×C4—24no—
565C2×C3×C4—24no—
566C2×C3×C4—24no—
567C2×C3×C4—24no—
568C2×C3×C4—24no—
569C2×C3×C4—24no—
570C2×C3×C4—21no—
571C2×C3×C4—21no—
572C2×C3×C4—24no—
573C2×C3×C4—22no—
574C2×C3×C4—22no—
575C2×C3×C4—24no—
576C2×C3×C4—38no—
577C2×C3×C4—34no—
578C2×C3×C4—34no—
579C2×C3×C4—32no—
580C2×C3×C4—44no—
581C2×C3×C4—44no—
582C2×C3×C4—44no—
583C2×C3×C4—42no—
584C2×C3×C4—616no—
585C2×C3×C4—68no—
586C2×C3×C4—68no—
587C2×C3×C4—64no—
588C2×C3×C4D3×D414yes—
589C2×C3×C4C2×C3×D414yes—
590C2×C3×C4C23×D314yes—
591C2×C3×C4C23×D312yes—
592C2×C3×C4C23×D312yes—
593C2×C3×C4C23×D311yescharacteristic
594C2×C3×C4C23×D311yescharacteristic
595C2×C3×C4C24×C314yes—
596C2×C3×C4C24×C312yes—
597C2×C3×C4C24×C312yes—
598C2×C3×C4C24×C311yescharacteristic
599C2×C3×C4C24×C311yescharacteristic
600#67—24no—
601#67—216no—
602#67—28no—
603#67—44no—
604#67—48no—
605C2×Dic3—28no—
606C2×Dic3C2×C3×D418yes—
607C2×Dic3C24×C314yes—
608C2×Dic3C24×C312yes—
609C2×Dic3C24×C314yes—
610D12—24no—
611D12—24no—
612D12—22no—
613D12—48no—
614C4×D3—24no—
615C4×D3—216no—
616C4×D3—28no—
617Dic6—22no—
618Dic6—28no—
619Dic6C2×C3×D418yes—
620Dic6C2×C3×D418yes—
621C2×C32—22no—
622C2×C32—42no—
623C2×C32—42no—
624C2×C32C23×D411yescharacteristic
625C2×C32#58512yes—
626C3×D3—42no—
627C3×D3—44no—
628C24—32no—
629C24C22×C3×D311yescharacteristic
630#41—24no—
631#41—616no—
632#41—616no—
633#41—68no—
634#41—616no—
635#41—68no—
636#41—64no—
637C2×Q8—32no—
638C2×Q8—32no—
639C2×Q8—34no—
640C2×Q8—31no—
641C2×Q8—38no—
642C2×Q8—68no—
643C2×Q8—68no—
644C2×Q8C22×C3×D311yescharacteristic
645C2×D4—32no—
646C2×D4—38no—
647C2×D4—34no—
648C2×D4—38no—
649C2×D4—34no—
650C2×D4—32no—
651C2×D4—32no—
652C2×D4—31no—
653C2×D4—38no—
654C2×D4—68no—
655C2×D4—64no—
656C2×D4C22×C3×D312yes—
657C2×D4C22×C3×D311yescharacteristic
658C2×D4C22×C3×D314yes—
659C22×C4—24no—
660C22×C4—32no—
661C22×C4—34no—
662C22×C4—34no—
663C22×C4—32no—
664C22×C4—38no—
665C22×C4—68no—
666C22×C4C22×C3×D312yes—
667C22×C4C22×C3×D312yes—
668C22×C4C22×C3×D312yes—
669C22×C4C22×C3×D311yescharacteristic
670C22×C4C22×C3×D311yescharacteristic
671C4⋊C4—38no—
672C4⋊C4—32no—
673C4⋊C4—34no—
674C4⋊C4C22×C3×D312yes—
675C4⋊C4C22×C3×D314yes—
676C22⋊C4—32no—
677C22⋊C4—34no—
678C22⋊C4—34no—
679C22⋊C4—38no—
680C22⋊C4—38no—
681C22⋊C4C22×C3×D312yes—
682C22⋊C4C22×C3×D314yes—
683C22⋊C4C22×C3×D314yes—
684C42—38no—
685C42—32no—
686C42C22×C3×D312yes—
687C22×C3—22no—
688C22×C3—22no—
689C22×C3—24no—
690C22×C3—22no—
691C22×C3—22no—
692C22×C3—22no—
693C22×C3—24no—
694C22×C3—22no—
695C22×C3—22no—
696C22×C3—22no—
697C22×C3—24no—
698C22×C3—22no—
699C22×C3—22no—
700C22×C3—22no—
701C22×C3—21no—
702C22×C3—42no—
703C22×C3—42no—
704C22×C3—42no—
705C22×C3—42no—
706C22×C3—44no—
707C22×C3—44no—
708C22×C3—44no—
709C22×C3—48no—
710C22×C3—62no—
711C22×C3—64no—
712C22×C3—64no—
713C22×C3—68no—
714C22×C3—128no—
715C22×C3C2×D3×D412yes—
716C22×C3C22×C3×D412yes—
717C22×C3C24×D311yescharacteristic
718C22×C3C25×C311yescharacteristic
719C2×D3—22no—
720C2×D3—24no—
721C2×D3—24no—
722C2×D3—28no—
723C2×D3—48no—
724C3×C4—22no—
725C3×C4—22no—
726C3×C4—24no—
727C3×C4—22no—
728C3×C4—22no—
729C3×C4—24no—
730C3×C4—22no—
731C3×C4—22no—
732C3×C4—38no—
733C3×C4—42no—
734C3×C4—42no—
735C3×C4—44no—
736C3×C4—62no—
737C3×C4—64no—
738C3×C4C2×D3×D412yes—
739C3×C4C2×D3×D412yes—
740C3×C4C22×C3×D412yes—
741C3×C4C22×C3×D412yes—
742Dic3—22no—
743Dic3—24no—
744Dic3C22×C3×D418yes—
745C32#348711yescharacteristic, complemented, Sylow
746C23—22no—
747C23—34no—
748C23—32no—
749C23—42no—
750C23—64no—
751C23—124no—
752C23C23×C3×D312yes—
753C23C23×C3×D312yes—
754C23C23×C3×D311yescharacteristic
755Q8—22no—
756Q8—38no—
757Q8—38no—
758Q8—68no—
759Q8—62no—
760D4—24no—
761D4—22no—
762D4—44no—
763D4—616no—
764D4—68no—
765D4—64no—
766D4—64no—
767D4—64no—
768D4—62no—
769D4—128no—
770D4—128no—
771D4—124no—
772C2×C4—22no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—38no—
777C2×C4—34no—
778C2×C4—34no—
779C2×C4—32no—
780C2×C4—616no—
781C2×C4—68no—
782C2×C4—68no—
783C2×C4—64no—
784C2×C4C3×D3×D414yes—
785C2×C4C23×C3×D314yes—
786C2×C4C23×C3×D312yes—
787C2×C4C23×C3×D312yes—
788C2×C4C23×C3×D311yescharacteristic
789C2×C4C23×C3×D311yescharacteristic
790C2×C3—22no—
791C2×C3—22no—
792C2×C3—21no—
793C2×C3—22no—
794C2×C3—42no—
795C2×C3—44no—
796C2×C3—42no—
797C2×C3—42no—
798C2×C3—42no—
799C2×C3—42no—
800C2×C3—82no—
801C2×C3—124no—
802C2×C3—122no—
803C2×C3C22×D3×D411yescharacteristic
804C2×C3#596412yes—
805C2×C3C23×C3×D411yescharacteristic
806C2×C3C3×#58512yes—
807D3—44no—
808D3—42no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—24no—
814C22—22no—
815C22—44no—
816C22—62no—
817C22—64no—
818C22—64no—
819C22—68no—
820C22—128no—
821C22C2×C3×D3×D412yes—
822C22C24×C3×D311yescharacteristic
823C4—22no—
824C4—22no—
825C4—24no—
826C4—38no—
827C4—62no—
828C4—64no—
829C4C2×C3×D3×D412yes—
830C4C2×C3×D3×D412yes—
831C3—21no—
832C3#8602311yescharacteristic, direct product factor
833C3C3×#348711yescharacteristic, complemented
834C2—22no—
835C2—42no—
836C2—42no—
837C2—124no—
838C2—122no—
839C2C22×C3×D3×D411yescharacteristic
840C2C3×#596412yes—
subgroupG/H
centerC22×C3C24×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC32×#525C2
socleC22×C32C25
hypercenterC3×#525D3
hypocenterC3C3×#3487
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×#525

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1010C2semidirect
2. C22×C3×#235C2semidirect
3. C32×#525C2semidirect
4. C3×#5830C2semidirect
5. C3×#5791C2semidirect
6. C3×#5656C2semidirect
7. C3×#5633C2semidirect
8. C3×#5599C2semidirect
9. C3×#5592C2semidirect
10. C3×#5553C2semidirect
11. C3×#5552C2semidirect
12. C3×#5525C2semidirect
13. C3×#5516C2semidirect
15. #86023C3direct (N × H)
20. C2×C3×D3×Q8C22semidirect
22. C2×C3×#237C22semidirect
27. C2×C3×#235C22semidirect
31. C22×C3×Dic6C22semidirect
33. C32×C22⋊Q8C22semidirect
34. C32×#121C22semidirect
36. C32×C4×D4C22semidirect
39. C3×#947C22semidirect
40. C3×#940C22semidirect
41. C3×#940C22semidirect
42. C3×#939C22semidirect
44. C3×#930C22semidirect
45. C3×#930C22semidirect
47. C3×C4×#67C22semidirect
49. C3×#924C22semidirect
50. C3×#896C22semidirect
51. C3×#895C22semidirect
52. C3×#893C22semidirect
53. C3×#887C22semidirect
54. C3×#885C22semidirect
55. C3×#884C22semidirect
56. C3×#884C22semidirect
58. C3×#67⋊C4C22semidirect
60. C3×#875C22semidirect
61. C3×#874C22semidirect
62. C3×C4×Dic6C22semidirect
65. C2×#1010C2×C3semidirect
66. C22×#235C2×C3semidirect
77. C3×#525D3semidirect
78. C3×#525C2×C3semidirect
80. #5830C2×C3semidirect
81. #5791C2×C3semidirect
82. #5656C2×C3semidirect
83. #5633C2×C3semidirect
84. #5599C2×C3semidirect
85. #5592C2×C3semidirect
86. #5553C2×C3semidirect
87. #5552C2×C3semidirect
88. #5525C2×C3semidirect
89. #5516C2×C3semidirect
128. C2×C3×Dic6D4semidirect
172. C2×D3×Q8C22×C3semidirect
174. C2×#237C22×C3semidirect
179. C2×#235C22×C3semidirect
183. C22×Dic6C22×C3semidirect
197. C3×C22⋊Q8C2×D3semidirect
198. C3×C22⋊Q8C22×C3semidirect
206. C3×#121C2×D3semidirect
207. C3×#121C22×C3semidirect
220. C3×C4×D4C2×D3semidirect
221. C3×C4×D4C22×C3semidirect
228. #947C22×C3semidirect
229. #940C22×C3semidirect
230. #940C22×C3semidirect
231. #939C22×C3semidirect
233. #930C22×C3semidirect
234. #930C22×C3semidirect
236. C4×#67C22×C3semidirect
238. #924C22×C3semidirect
239. #896C22×C3semidirect
240. #895C22×C3semidirect
241. #893C22×C3semidirect
242. #887C22×C3semidirect
243. #885C22×C3semidirect
244. #884C22×C3semidirect
245. #884C22×C3semidirect
247. #67⋊C4C22×C3semidirect
249. #875C22×C3semidirect
250. #874C22×C3semidirect
251. C4×Dic6C22×C3semidirect
307. #525C3×D3semidirect
402. C2×Dic6C3×D4semidirect
493. C22⋊Q8C2×C3×D3semidirect
500. #121C2×C3×D3semidirect
510. C4×D4C2×C3×D3semidirect
745. C32#3487semidirect
832. C3#86023direct (N × H)
833. 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×#2352
C32×#5252
C3×#58302
C3×#57912
C3×#56562
C3×#56332
C3×#55992
C3×#55922
C3×#55532
C3×#55522
C3×#55252
C3×#55162
C3×#34873
#860233