Finite Group Databasebeta

← C2×C3×#5779 #11918916

Subgroups — C2×C3×#5779 #11918916

Order 1152.

2945 conjugacy classes of subgroups.

The subgroup lattice has 841 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1010C211yesmaximal, characteristic, complemented
2C2×C3×#1007C211yesmaximal, characteristic, complemented
3C2×C32×#137C211yesmaximal, characteristic, complemented
4C2×C3×#950C211yesmaximal, characteristic, complemented
5C22×C3×#216C211yesmaximal, characteristic, complemented
6C3×#5779C2116yesmaximal, direct product factor
7C2×C3×#918C212yesmaximal, complemented
8C2×C3×D3×Q16C212yesmaximal, complemented
9C2×C3×#916C212yesmaximal, complemented
10C2×C3×#915C212yesmaximal, complemented
11C2×C3×#909C211yesmaximal, characteristic, complemented
12C2×C3×#907C211yesmaximal, characteristic, complemented
13C2×C3×#578—31nomaximal
14C2×#5779C311yesmaximal, characteristic, direct product factor
15C2×C32×#41C2211yescharacteristic
16C22×C32×Q8C2211yescharacteristic
17C3×#1010—24no—
18C3×#1010C2218yescomplemented
19C3×#1007—24no—
20C3×#1007C2218yescomplemented
21C2×C3×#239—21no—
22C2×C3×#239C2212yes—
23C2×C3×D3×Q8—21no—
24C2×C3×D3×Q8C2212yes—
25C2×C3×D3×Q8C2212yes—
26C2×C3×#237—22no—
27C2×C3×#237C2212yes—
28C2×C3×#235—22no—
29C2×C3×#235—21no—
30C2×C3×#235C2211yescharacteristic
31C2×C3×#235C2211yescharacteristic
32C22×C3×Dic6—21no—
33C22×C3×Dic6C2211yescharacteristic
34C32×#137C2218yescomplemented
35C2×C32×Q16C2212yes—
36C2×C32×SD16C2212yes—
37C2×C32×M16C2211yescharacteristic
38C3×#950C2218yescomplemented
39C2×C3×#216C2212yes—
40C2×C3×#216C2212yes—
41C2×C3×#216C2211yescharacteristic
42C2×C3×#216C2218yescomplemented
43C2×C3×#215C2211yescharacteristic
44C2×C3×#214C2211yescharacteristic
45C2×C3×#213C2211yescharacteristic
46C22×C3×C3⋊C8C2211yescharacteristic
47C3×#918C22116yescomplemented
48C3×D3×Q16C22116yescomplemented
49C3×#916C22116yescomplemented
50C3×#915C22116yescomplemented
51C3×#909C2218yescomplemented
52C3×#907C2218yescomplemented
53C2×C3×Dic12C2212yes—
54C2×C3×#204C2212yes—
55C2×C3×ΓL(1,𝔽25)C2212yes—
56C2×C3×D3×C8C2212yes—
57C2×C3×2−1+4—31no—
58C2×C3×2−1+4—31no—
59C2×#1010C2×C311yescharacteristic, complemented
60C2×#1007C2×C311yescharacteristic, complemented
61C3×#578—316no—
62C2×C3×#137—21no—
63C2×C3×#137—32no—
64C2×C3×#137—32no—
65C2×C3×#137—31no—
66C2×C3×#137D311yescharacteristic, complemented
67C2×C3×#137C2×C311yescharacteristic, complemented
68C2×C3×#135—31no—
69C2×C3×#135—32no—
70C22×C3×Q16—31no—
71C22×C3×Q16—32no—
72C2×C3×#131—31no—
73C2×#950C2×C311yescharacteristic, complemented
74C22×#216C2×C311yescharacteristic, complemented
75#5779C2×C3116yesdirect product factor
76C2×#918C2×C312yescomplemented
77C2×D3×Q16C2×C312yescomplemented
78C2×#916C2×C312yescomplemented
79C2×#915C2×C312yescomplemented
80C2×#909C2×C311yescharacteristic, complemented
81C2×#907C2×C311yescharacteristic, complemented
82C32×#41—22no—
83C32×#41C2314yes—
84C2×C32×Q8—21no—
85C2×C32×Q8—22no—
86C2×C32×Q8C2311yescharacteristic
87C2×C32×Q8C2312yes—
88C2×C32×Q8C2314yes—
89C2×C32×D4—21no—
90C2×C32×D4C2311yescharacteristic
91C22×C32×C4—21no—
92C22×C32×C4—21no—
93C22×C32×C4C2311yescharacteristic
94C2×C3×#67—21no—
95C2×C3×#67—22no—
96C2×C3×#67D412yes—
97C22×C3×Dic3—21no—
98C22×C3×Dic3—22no—
99C3×#239—28no—
100C3×#239—24no—
101C3×#239C2318yes—
102C3×D3×Q8—24no—
103C3×D3×Q8—24no—
104C3×D3×Q8—28no—
105C3×D3×Q8C2318yes—
106C3×D3×Q8C2318yes—
107C3×#237—216no—
108C3×#237—24no—
109C3×#237C2318yes—
110C3×#235—22no—
111C3×#235—216no—
112C3×#235—28no—
113C3×#235D414yes—
114C3×#235C2314yes—
115C3×#235C2314yes—
116C2×C3×D12—22no—
117C2×C3×D12D411yescharacteristic
118C2×C3×D12C2311yescharacteristic
119C2×C3×C4×D3—22no—
120C2×C3×C4×D3—22no—
121C2×C3×C4×D3—21no—
122C2×C3×C4×D3—22no—
123C2×C3×C4×D3C2312yes—
124C2×C3×Dic6—21no—
125C2×C3×Dic6—22no—
126C2×C3×Dic6—22no—
127C2×C3×Dic6—22no—
128C2×C3×Dic6—28no—
129C2×C3×Dic6D411yescharacteristic
130C2×C3×Dic6C2312yes—
131C2×C3×Dic6C2311yescharacteristic
132C2×C3×Dic6C2314yes—
133C32×Q16C2318yes—
134C32×SD16C2318yes—
135C32×M16C2314yes—
136C2×C32×C8C2312yes—
137C3×#216C2318yes—
138C3×#216C2318yes—
139C3×#216C2314yes—
140C3×#215C2314yes—
141C3×#214C2314yes—
142C3×#213C2314yes—
143C2×C3×C3⋊C8C2311yescharacteristic
144C2×C3×C3⋊C8C2311yescharacteristic
145C2×C3×C3⋊C8C2314yes—
146C3×Dic12C2318yes—
147C3×#204C2318yes—
148C3×ΓL(1,𝔽25)C2318yes—
149C3×D3×C8C2318yes—
150C2×#578—31noSylow
151C3×2−1+4—38no—
152C3×2−1+4—38no—
153C3×2−1+4—64no—
154C3×2−1+4—64no—
155C2×C3×#41—21no—
156C2×C3×#41—31no—
157C2×C3×#41—32no—
158C2×C3×#41—32no—
159C2×C3×#41—31no—
160C2×C3×#41—62no—
161C2×C3×#41—61no—
162C2×C3×#41—62no—
163C2×C3×#41—61no—
164C2×C3×#41C2×D311yescharacteristic
165C2×C3×#41C22×C311yescharacteristic
166C22×C3×Q8—21no—
167C22×C3×Q8—32no—
168C22×C3×Q8—32no—
169C22×C3×Q8—31no—
170C22×C3×Q8—61no—
171C22×C3×Q8—61no—
172C22×C3×Q8C2×D311yescharacteristic
173C22×C3×Q8C22×C311yescharacteristic
174#1010—24no—
175#1010C22×C318yescomplemented
176#1007—24no—
177#1007C22×C318yescomplemented
178C2×#239—21no—
179C2×#239C22×C312yes—
180C2×D3×Q8—21no—
181C2×D3×Q8C22×C312yes—
182C2×D3×Q8C22×C312yes—
183C2×#237—22no—
184C2×#237C22×C312yes—
185C2×#235—22no—
186C2×#235—21no—
187C2×#235C22×C311yescharacteristic
188C2×#235C22×C311yescharacteristic
189C22×Dic6—21no—
190C22×Dic6C22×C311yescharacteristic
191C3×#137—28no—
192C3×#137—316no—
193C3×#137—316no—
194C3×#137—38no—
195C3×#137C2×D318yescomplemented
196C3×#137C22×C318yescomplemented
197C3×#135—38no—
198C3×#135—316no—
199C2×C3×Q16—22no—
200C2×C3×Q16—31no—
201C2×C3×Q16—32no—
202C2×C3×Q16—32no—
203C2×C3×Q16—38no—
204C2×C3×Q16—316no—
205C2×C3×Q16—32no—
206C2×C3×Q16C2×D312yes—
207C2×C3×Q16C22×C312yes—
208C2×C3×SD16—22no—
209C2×C3×SD16—31no—
210C2×C3×SD16—31no—
211C2×C3×SD16—32no—
212C2×C3×SD16C2×D312yes—
213C2×C3×SD16C22×C312yes—
214C2×C3×D8—31no—
215C3×#131—38no—
216C2×C3×M16—21no—
217C2×C3×M16—32no—
218C2×C3×M16C2×D311yescharacteristic
219C2×C3×M16C22×C311yescharacteristic
220C22×C3×C8—31no—
221C22×C3×C8—32no—
222#950C22×C318yescomplemented
223C2×#216C22×C312yes—
224C2×#216C22×C312yes—
225C2×#216C22×C311yescharacteristic
226C2×#216C22×C318yescomplemented
227C2×#215C22×C311yescharacteristic
228C2×#214C22×C311yescharacteristic
229C2×#213C22×C311yescharacteristic
230C22×C3⋊C8C22×C311yescharacteristic
231#918C22×C3116yescomplemented
232D3×Q16C22×C3116yescomplemented
233#916C22×C3116yescomplemented
234#915C22×C3116yescomplemented
235#909C22×C318yescomplemented
236#907C22×C318yescomplemented
237C2×Dic12C22×C312yes—
238C2×#204C22×C312yes—
239C2×ΓL(1,𝔽25)C22×C312yes—
240C2×D3×C8C22×C312yes—
241C23×C32—21no—
242C23×C32C2×D411yescharacteristic
243C22×C3×D3—21no—
244C22×C3×D3C2×D412yes—
245C32×Q8—21no—
246C32×Q8—22no—
247C32×Q8—24no—
248C32×Q8C2412yes—
249C32×Q8C2414yes—
250C32×D4—24no—
251C32×D4—21no—
252C32×D4C2412yes—
253C2×C32×C4—21no—
254C2×C32×C4—22no—
255C2×C32×C4—24no—
256C2×C32×C4—24no—
257C2×C32×C4C2×D411yescharacteristic
258C2×C32×C4C2×D412yes—
259C2×C32×C4C2411yescharacteristic
260C2×C32×C4C2412yes—
261C3×#67—24no—
262C3×#67—28no—
263C3×#67C2×D418yes—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—22no—
266C2×C3×Dic3—24no—
267C2×C3×Dic3—28no—
268C2×C3×Dic3C2×D412yes—
269C3×D12—28no—
270C3×D12—21no—
271C3×D12C2×D414yes—
272C3×D12C2412yes—
273C3×C4×D3—28no—
274C3×C4×D3—28no—
275C3×C4×D3—24no—
276C3×C4×D3—28no—
277C3×C4×D3C2×D414yes—
278C3×C4×D3C2414yes—
279C3×Dic6—24no—
280C3×Dic6—22no—
281C3×Dic6—21no—
282C3×Dic6—28no—
283C3×Dic6—28no—
284C3×Dic6C2×D414yes—
285C3×Dic6C2414yes—
286C3×Dic6C2412yes—
287C32×C8C2414yes—
288C3×C3⋊C8C2412yes—
289C3×C3⋊C8C2412yes—
290C2×2−1+4—31no—
291C2×2−1+4—31no—
292#578—316no—
293C2×#137—32no—
294C2×#137—32no—
295C2×#137—31no—
296C2×#137C3×D311yescharacteristic, complemented
297C2×#135—31no—
298C2×#135—32no—
299C22×Q16—31no—
300C22×Q16—32no—
301C2×#131—31no—
302C3×#41—22no—
303C3×#41—22no—
304C3×#41—24no—
305C3×#41—34no—
306C3×#41—34no—
307C3×#41—38no—
308C3×#41—38no—
309C3×#41—34no—
310C3×#41—42no—
311C3×#41—616no—
312C3×#41—68no—
313C3×#41—64no—
314C3×#41—64no—
315C3×#41—616no—
316C3×#41—68no—
317C3×#41—62no—
318C3×#41C22×D314yes—
319C3×#41C23×C314yes—
320C2×C3×Q8—21no—
321C2×C3×Q8—22no—
322C2×C3×Q8—21no—
323C2×C3×Q8—22no—
324C2×C3×Q8—22no—
325C2×C3×Q8—21no—
326C2×C3×Q8—24no—
327C2×C3×Q8—31no—
328C2×C3×Q8—38no—
329C2×C3×Q8—38no—
330C2×C3×Q8—31no—
331C2×C3×Q8—32no—
332C2×C3×Q8—34no—
333C2×C3×Q8—41no—
334C2×C3×Q8—42no—
335C2×C3×Q8—62no—
336C2×C3×Q8—62no—
337C2×C3×Q8—68no—
338C2×C3×Q8—64no—
339C2×C3×Q8—64no—
340C2×C3×Q8—68no—
341C2×C3×Q8—61no—
342C2×C3×Q8—62no—
343C2×C3×Q8C22×D311yescharacteristic
344C2×C3×Q8C22×D312yes—
345C2×C3×Q8C22×D314yes—
346C2×C3×Q8C23×C311yescharacteristic
347C2×C3×Q8C23×C312yes—
348C2×C3×Q8C23×C314yes—
349C2×C3×D4—21no—
350C2×C3×D4—21no—
351C2×C3×D4—21no—
352C2×C3×D4—32no—
353C2×C3×D4—31no—
354C2×C3×D4—31no—
355C2×C3×D4—41no—
356C2×C3×D4—62no—
357C2×C3×D4—62no—
358C2×C3×D4—61no—
359C2×C3×D4C22×D311yescharacteristic
360C2×C3×D4C23×C311yescharacteristic
361C22×C3×C4—21no—
362C22×C3×C4—21no—
363C22×C3×C4—21no—
364C22×C3×C4—21no—
365C22×C3×C4—21no—
366C22×C3×C4—32no—
367C22×C3×C4—41no—
368C22×C3×C4—41no—
369C22×C3×C4—62no—
370C22×C3×C4—62no—
371C22×C3×C4—62no—
372C22×C3×C4—62no—
373C22×C3×C4—61no—
374C22×C3×C4—61no—
375C22×C3×C4C22×D311yescharacteristic
376C22×C3×C4C23×C311yescharacteristic
377C2×#67—21no—
378C2×#67—22no—
379C2×#67C3×D412yes—
380C22×Dic3—21no—
381C22×Dic3—22no—
382#239—28no—
383#239—24no—
384#239C23×C318yes—
385D3×Q8—24no—
386D3×Q8—24no—
387D3×Q8—28no—
388D3×Q8C23×C318yes—
389D3×Q8C23×C318yes—
390#237—216no—
391#237—24no—
392#237C23×C318yes—
393#235—22no—
394#235—216no—
395#235—28no—
396#235C3×D414yes—
397#235C23×C314yes—
398#235C23×C314yes—
399C2×D12—22no—
400C2×D12C3×D411yescharacteristic
401C2×D12C23×C311yescharacteristic
402C2×C4×D3—22no—
403C2×C4×D3—22no—
404C2×C4×D3—21no—
405C2×C4×D3—22no—
406C2×C4×D3C23×C312yes—
407C2×Dic6—21no—
408C2×Dic6—22no—
409C2×Dic6—22no—
410C2×Dic6—22no—
411C2×Dic6—28no—
412C2×Dic6C3×D411yescharacteristic
413C2×Dic6C23×C312yes—
414C2×Dic6C23×C311yescharacteristic
415C2×Dic6C23×C314yes—
416C3×Q16—28no—
417C3×Q16—34no—
418C3×Q16—38no—
419C3×Q16—38no—
420C3×Q16—38no—
421C3×Q16C22×D318yes—
422C3×Q16C23×C318yes—
423C3×SD16—28no—
424C3×SD16—34no—
425C3×SD16—34no—
426C3×SD16—38no—
427C3×SD16C22×D318yes—
428C3×SD16C23×C318yes—
429C3×D8—34no—
430C3×M16—24no—
431C3×M16—38no—
432C3×M16C22×D314yes—
433C3×M16C23×C314yes—
434C2×C3×C8—22no—
435C2×C3×C8—31no—
436C2×C3×C8—31no—
437C2×C3×C8—34no—
438C2×C3×C8—38no—
439C2×C3×C8C22×D312yes—
440C2×C3×C8C23×C312yes—
441#216C23×C318yes—
442#216C23×C318yes—
443#216C23×C314yes—
444#215C23×C314yes—
445#214C23×C314yes—
446#213C23×C314yes—
447C2×C3⋊C8C23×C311yescharacteristic
448C2×C3⋊C8C23×C311yescharacteristic
449C2×C3⋊C8C23×C314yes—
450Dic12C23×C318yes—
451#204C23×C318yes—
452ΓL(1,𝔽25)C23×C318yes—
453D3×C8C23×C318yes—
454C22×C32—22no—
455C22×C32—22no—
456C22×C32—42no—
457C22×C32C22×D412yes—
458C22×C32C22×D411yescharacteristic
459C2×C3×D3—24no—
460C2×C3×D3—22no—
461C2×C3×D3—42no—
462C2×C3×D3C22×D414yes—
463C32×C4—22no—
464C32×C4—24no—
465C32×C4C22×D411yescharacteristic
466C32×C4C22×D412yes—
467C32×C4C2511yescharacteristic
468C3×Dic3—22no—
469C3×Dic3—24no—
470C3×Dic3C22×D414yes—
4712−1+4—38no—
4722−1+4—38no—
4732−1+4—64no—
4742−1+4—64no—
475C2×#41—31no—
476C2×#41—32no—
477C2×#41—32no—
478C2×#41—31no—
479C2×#41—62no—
480C2×#41—61no—
481C2×#41—62no—
482C2×#41—61no—
483C2×#41C2×C3×D311yescharacteristic
484C22×Q8—32no—
485C22×Q8—32no—
486C22×Q8—31no—
487C22×Q8—61no—
488C22×Q8—61no—
489C22×Q8C2×C3×D311yescharacteristic
490#137—316no—
491#137—316no—
492#137—38no—
493#137C2×C3×D318yescomplemented
494#135—38no—
495#135—316no—
496C2×Q16—31no—
497C2×Q16—32no—
498C2×Q16—32no—
499C2×Q16—38no—
500C2×Q16—316no—
501C2×Q16—32no—
502C2×Q16C2×C3×D312yes—
503C2×SD16—31no—
504C2×SD16—31no—
505C2×SD16—32no—
506C2×SD16C2×C3×D312yes—
507C2×D8—31no—
508#131—38no—
509C2×M16—32no—
510C2×M16C2×C3×D311yescharacteristic
511C22×C8—31no—
512C22×C8—32no—
513C23×C3—21no—
514C23×C3—21no—
515C23×C3—21no—
516C23×C3—32no—
517C23×C3—41no—
518C23×C3—61no—
519C23×C3D3×D411yescharacteristic
520C23×C3C2×C3×D411yescharacteristic
521C22×D3—21no—
522C22×D3C2×C3×D412yes—
523C3×Q8—24no—
524C3×Q8—22no—
525C3×Q8—21no—
526C3×Q8—21no—
527C3×Q8—22no—
528C3×Q8—24no—
529C3×Q8—24no—
530C3×Q8—22no—
531C3×Q8—34no—
532C3×Q8—34no—
533C3×Q8—32no—
534C3×Q8—44no—
535C3×Q8—42no—
536C3×Q8—41no—
537C3×Q8—68no—
538C3×Q8—68no—
539C3×Q8—64no—
540C3×Q8—62no—
541C3×Q8—61no—
542C3×Q8C23×D312yes—
543C3×Q8C23×D314yes—
544C3×Q8C24×C312yes—
545C3×Q8C24×C314yes—
546C3×D4—24no—
547C3×D4—24no—
548C3×D4—21no—
549C3×D4—21no—
550C3×D4—22no—
551C3×D4—38no—
552C3×D4—34no—
553C3×D4—32no—
554C3×D4—41no—
555C3×D4—44no—
556C3×D4—68no—
557C3×D4—68no—
558C3×D4—64no—
559C3×D4—61no—
560C3×D4C23×D312yes—
561C3×D4C24×C312yes—
562C2×C3×C4—24no—
563C2×C3×C4—21no—
564C2×C3×C4—22no—
565C2×C3×C4—21no—
566C2×C3×C4—22no—
567C2×C3×C4—24no—
568C2×C3×C4—24no—
569C2×C3×C4—24no—
570C2×C3×C4—21no—
571C2×C3×C4—22no—
572C2×C3×C4—21no—
573C2×C3×C4—22no—
574C2×C3×C4—32no—
575C2×C3×C4—34no—
576C2×C3×C4—34no—
577C2×C3×C4—44no—
578C2×C3×C4—41no—
579C2×C3×C4—42no—
580C2×C3×C4—44no—
581C2×C3×C4—68no—
582C2×C3×C4—68no—
583C2×C3×C4—68no—
584C2×C3×C4—68no—
585C2×C3×C4—64no—
586C2×C3×C4—61no—
587C2×C3×C4—62no—
588C2×C3×C4—64no—
589C2×C3×C4D3×D412yes—
590C2×C3×C4D3×D411yescharacteristic
591C2×C3×C4C2×C3×D411yescharacteristic
592C2×C3×C4C2×C3×D412yes—
593C2×C3×C4C23×D312yes—
594C2×C3×C4C23×D311yescharacteristic
595C2×C3×C4C24×C311yescharacteristic
596C2×C3×C4C24×C312yes—
597#67—24no—
598#67—28no—
599#67C2×C3×D418yes—
600C2×Dic3—21no—
601C2×Dic3—22no—
602C2×Dic3—24no—
603C2×Dic3—28no—
604C2×Dic3C2×C3×D412yes—
605D12—28no—
606D12—21no—
607D12C2×C3×D414yes—
608D12C24×C312yes—
609C4×D3—28no—
610C4×D3—28no—
611C4×D3—24no—
612C4×D3—28no—
613C4×D3C2×C3×D414yes—
614C4×D3C24×C314yes—
615Dic6—24no—
616Dic6—22no—
617Dic6—21no—
618Dic6—28no—
619Dic6—28no—
620Dic6C2×C3×D414yes—
621Dic6C24×C314yes—
622Dic6C24×C312yes—
623C3×C8—24no—
624C3×C8—32no—
625C3×C8—32no—
626C3×C8C23×D314yes—
627C3×C8C24×C314yes—
628C3⋊C8C24×C312yes—
629C3⋊C8C24×C312yes—
630C2×C32—22no—
631C2×C32—42no—
632C2×C32#57812yescomplemented
633C2×C32C23×D411yescharacteristic
634C3×D3—24no—
635C3×D3—42no—
636#41—22no—
637#41—34no—
638#41—34no—
639#41—38no—
640#41—38no—
641#41—34no—
642#41—616no—
643#41—68no—
644#41—64no—
645#41—64no—
646#41—616no—
647#41—68no—
648#41—62no—
649#41C22×C3×D314yes—
650C2×Q8—21no—
651C2×Q8—22no—
652C2×Q8—31no—
653C2×Q8—38no—
654C2×Q8—38no—
655C2×Q8—31no—
656C2×Q8—32no—
657C2×Q8—34no—
658C2×Q8—62no—
659C2×Q8—62no—
660C2×Q8—68no—
661C2×Q8—64no—
662C2×Q8—64no—
663C2×Q8—68no—
664C2×Q8—61no—
665C2×Q8—62no—
666C2×Q8C22×C3×D311yescharacteristic
667C2×Q8C22×C3×D312yes—
668C2×Q8C22×C3×D314yes—
669C2×D4—21no—
670C2×D4—32no—
671C2×D4—31no—
672C2×D4—31no—
673C2×D4—62no—
674C2×D4—62no—
675C2×D4—61no—
676C2×D4C22×C3×D311yescharacteristic
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—32no—
680C22×C4—62no—
681C22×C4—62no—
682C22×C4—62no—
683C22×C4—62no—
684C22×C4—61no—
685C22×C4—61no—
686C22×C4C22×C3×D311yescharacteristic
687Q16—34no—
688Q16—38no—
689Q16—38no—
690Q16—38no—
691Q16C22×C3×D318yes—
692SD16—34no—
693SD16—34no—
694SD16—38no—
695SD16C22×C3×D318yes—
696D8—34no—
697M16—38no—
698M16C22×C3×D314yes—
699C2×C8—31no—
700C2×C8—31no—
701C2×C8—34no—
702C2×C8—38no—
703C2×C8C22×C3×D312yes—
704C22×C3—22no—
705C22×C3—22no—
706C22×C3—22no—
707C22×C3—22no—
708C22×C3—21no—
709C22×C3—22no—
710C22×C3—34no—
711C22×C3—42no—
712C22×C3—42no—
713C22×C3—42no—
714C22×C3—42no—
715C22×C3—64no—
716C22×C3—62no—
717C22×C3—82no—
718C22×C3—122no—
719C22×C3C2×D3×D412yes—
720C22×C3C2×D3×D411yescharacteristic
721C22×C3C22×C3×D412yes—
722C22×C3C22×C3×D411yescharacteristic
723C2×D3—24no—
724C2×D3—22no—
725C2×D3—42no—
726C2×D3C22×C3×D414yes—
727C3×C4—22no—
728C3×C4—24no—
729C3×C4—22no—
730C3×C4—24no—
731C3×C4—22no—
732C3×C4—21no—
733C3×C4—21no—
734C3×C4—34no—
735C3×C4—42no—
736C3×C4—44no—
737C3×C4—62no—
738C3×C4—64no—
739C3×C4C2×D3×D412yes—
740C3×C4C2×D3×D411yescharacteristic
741C3×C4C22×C3×D411yescharacteristic
742C3×C4C22×C3×D412yes—
743C3×C4C24×D311yescharacteristic
744C3×C4C25×C311yescharacteristic
745Dic3—22no—
746Dic3—24no—
747Dic3C22×C3×D414yes—
748C32C2×#57811yescharacteristic, complemented, Sylow
749C23—21no—
750C23—32no—
751C23—61no—
752C23C3×D3×D411yescharacteristic
753Q8—24no—
754Q8—22no—
755Q8—21no—
756Q8—34no—
757Q8—32no—
758Q8—34no—
759Q8—68no—
760Q8—68no—
761Q8—64no—
762Q8—61no—
763Q8—62no—
764Q8C23×C3×D312yes—
765Q8C23×C3×D314yes—
766D4—24no—
767D4—21no—
768D4—38no—
769D4—34no—
770D4—32no—
771D4—68no—
772D4—68no—
773D4—64no—
774D4—61no—
775D4C23×C3×D312yes—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—32no—
781C2×C4—34no—
782C2×C4—34no—
783C2×C4—68no—
784C2×C4—68no—
785C2×C4—68no—
786C2×C4—68no—
787C2×C4—61no—
788C2×C4—62no—
789C2×C4—64no—
790C2×C4—64no—
791C2×C4C3×D3×D411yescharacteristic
792C2×C4C3×D3×D412yes—
793C2×C4C23×C3×D311yescharacteristic
794C2×C4C23×C3×D312yes—
795C8—32no—
796C8—32no—
797C8C23×C3×D314yes—
798C2×C3—22no—
799C2×C3—22no—
800C2×C3—22no—
801C2×C3—21no—
802C2×C3—42no—
803C2×C3—42no—
804C2×C3—42no—
805C2×C3—64no—
806C2×C3—82no—
807C2×C3—122no—
808C2×C3#577912yesdirect product factor
809C2×C3C3×#57812yescomplemented
810C2×C3C22×D3×D411yescharacteristic
811C2×C3C23×C3×D411yescharacteristic
812D3—24no—
813D3—42no—
814C22—22no—
815C22—22no—
816C22—34no—
817C22—42no—
818C22—64no—
819C22—62no—
820C22—122no—
821C22C2×C3×D3×D412yes—
822C22C2×C3×D3×D411yescharacteristic
823C4—22no—
824C4—24no—
825C4—34no—
826C4—62no—
827C4—64no—
828C4C2×C3×D3×D412yes—
829C4C2×C3×D3×D411yescharacteristic
830C4C24×C3×D311yescharacteristic
831C3—21no—
832C3C2×#577911yescharacteristic, direct product factor
833C3C2×C3×#57811yescharacteristic, complemented
834C2—22no—
835C2—42no—
836C2—64no—
837C2—122no—
838C2C3×#577912yesdirect product factor
839C2C22×C3×D3×D411yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC3×C4C25×C3
FrattiniC4C24×C3×D3
FittingC2×C32×#137C2
socleC22×C32C22×D4
hypercenterC2×C3×#137D3
hypocenterC3C2×C3×#578
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×#137

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1010C2semidirect
2. C2×C3×#1007C2semidirect
3. C2×C32×#137C2semidirect
4. C2×C3×#950C2semidirect
5. C22×C3×#216C2semidirect
6. C3×#5779C2direct (N × H)
7. C2×C3×#918C2semidirect
8. C2×C3×D3×Q16C2semidirect
9. C2×C3×#916C2semidirect
10. C2×C3×#915C2semidirect
11. C2×C3×#909C2semidirect
12. C2×C3×#907C2semidirect
14. C2×#5779C3direct (N × H)
18. C3×#1010C22semidirect
20. C3×#1007C22semidirect
34. C32×#137C22semidirect
38. C3×#950C22semidirect
42. C2×C3×#216C22semidirect
47. C3×#918C22semidirect
48. C3×D3×Q16C22semidirect
49. C3×#916C22semidirect
50. C3×#915C22semidirect
51. C3×#909C22semidirect
52. C3×#907C22semidirect
59. C2×#1010C2×C3semidirect
60. C2×#1007C2×C3semidirect
66. C2×C3×#137D3semidirect
67. C2×C3×#137C2×C3semidirect
73. C2×#950C2×C3semidirect
74. C22×#216C2×C3semidirect
75. #5779C2×C3direct (N × H)
76. C2×#918C2×C3semidirect
77. C2×D3×Q16C2×C3semidirect
78. C2×#916C2×C3semidirect
79. C2×#915C2×C3semidirect
80. C2×#909C2×C3semidirect
81. C2×#907C2×C3semidirect
175. #1010C22×C3semidirect
177. #1007C22×C3semidirect
195. C3×#137C2×D3semidirect
196. C3×#137C22×C3semidirect
222. #950C22×C3semidirect
226. C2×#216C22×C3semidirect
231. #918C22×C3semidirect
232. D3×Q16C22×C3semidirect
233. #916C22×C3semidirect
234. #915C22×C3semidirect
235. #909C22×C3semidirect
236. #907C22×C3semidirect
296. C2×#137C3×D3semidirect
493. #137C2×C3×D3semidirect
632. C2×C32#578semidirect
748. C32C2×#578semidirect
808. C2×C3#5779direct (N × H)
809. C2×C3C3×#578semidirect
832. C3C2×#5779direct (N × H)
833. C3C2×C3×#578semidirect
838. C2C3×#5779direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#10102
C2×C3×#10072
C2×C32×#1372
C2×C3×#9502
C22×C3×#2162
C3×#57792
C2×C3×#9182
C2×C3×D3×Q162
C2×C3×#9162
C2×C3×#9152
C2×C3×#9092
C2×C3×#9072
C2×C3×#5783
C2×#57793