Finite Group Databasebeta

← C3×#10595222 #13174766

Subgroups — C3×#10595222 #13174766

Order 1728.

1582 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#237C211yesmaximal, characteristic
2C3×D4×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C32×D4×Dic3C211yesmaximal, characteristic, complemented
4C3×#67⋊Dic3C212yesmaximal, complemented
5C3×Dic3×#67C212yesmaximal, complemented
6C2×C3×Dic3⋊Dic3C212yesmaximal, complemented
7C3×#63955C212yesmaximal, complemented
8C3×D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
9C3×#63855C211yesmaximal, characteristic, complemented
10C3×#63843C211yesmaximal, characteristic, complemented
11C3×Dic3×Dic6C211yesmaximal, characteristic, complemented
12C3×#5827—31nomaximal
13C3×#5546—31nomaximal
14#10595222C311yesmaximal, characteristic, direct product factor
15C2×C33×D4C2211yescharacteristic
16C22×C3×C3⋊Dic3C2212yes—
17C2×C32×#67C2212yes—
18C22×C32×Dic3C2212yes—
19C22×C32×Dic3C2212yes—
20C32×#237C418yescomplemented
21C2×C32×C4×D3C2211yescharacteristic
22C2×C32×Dic6C2211yescharacteristic
23C2×C3×D3×Dic3C2212yes—
24C3×#3757C2212yes—
25C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
26C3×C4×C3⋊Dic3C2211yescharacteristic
27C32×#217C2212yes—
28C32×C4⋊Dic3C2211yescharacteristic
29C32×C4×Dic3C2211yescharacteristic
30C3×Dic3⋊Dic3C2211yescharacteristic
31C3×Dic3⋊Dic3C2212yes—
32C3×Dic3⋊Dic3C2211yescharacteristic
33C3×Dic3⋊Dic3C2212yes—
34C3×Dic3⋊Dic3C2212yes—
35C3×(C2×D3)⋊Dic3C2211yescharacteristic
36C3×(C2×D3)⋊Dic3C2211yescharacteristic
37C3×Dic32C2212yes—
38C3×Dic32C2212yes—
39C2×C32×#41—31no—
40C2×C3×#237—21no—
41C2×C3×#237D311yescharacteristic
42C2×C3×#237C2×C311yescharacteristic
43C32×C4×D4—31no—
44D4×C3⋊Dic3C2×C311yescharacteristic, complemented
45C3×Q8×Dic3—31no—
46C3×Q8×Dic3—31no—
47C3×D4×Dic3—21no—
48C3×D4×Dic3—31no—
49C3×D4×Dic3—31no—
50C3×D4×Dic3—32no—
51C3×D4×Dic3—32no—
52C3×D4×Dic3—61no—
53C3×D4×Dic3D311yescharacteristic, complemented
54C3×D4×Dic3C2×C311yescharacteristic, complemented
55C3×C4×#67—32no—
56C3×#926—32no—
57C3×#926—31no—
58C2×C3×C4⋊Dic3—32no—
59C2×C3×C4⋊Dic3—31no—
60C2×C3×Dic3⋊C4—32no—
61C3×D3×C4⋊C4—31no—
62C3×#887—31no—
63C3×#67⋊C4—32no—
64C3×#877—32no—
65C3×#872—31no—
66C3×C4×Dic6—31no—
67#67⋊Dic3C2×C312yescomplemented
68Dic3×#67C2×C312yescomplemented
69C2×Dic3⋊Dic3C2×C312yescomplemented
70#63955C2×C312yescomplemented
71D3×C4⋊Dic3C2×C311yescharacteristic, complemented
72#63855C2×C311yescharacteristic, complemented
73#63843C2×C311yescharacteristic, complemented
74Dic3×Dic6C2×C311yescharacteristic, complemented
75C23×C33C2312yes—
76C22×C32×D3C2311yescharacteristic
77C33×D4C2×C414yescomplemented
78C2×C33×C4C2311yescharacteristic
79C2×C3×C3⋊Dic3—42no—
80C2×C3×C3⋊Dic3C2311yescharacteristic
81C2×C3×C3⋊Dic3C2311yescharacteristic
82C2×C3×C3⋊Dic3C2312yes—
83C32×#67C2×C418yescomplemented
84C2×C32×Dic3—42no—
85C2×C32×Dic3C2×C418yescomplemented
86C2×C32×Dic3C2311yescharacteristic
87C2×C32×Dic3C2312yes—
88C2×C32×Dic3C2311yescharacteristic
89C2×C32×Dic3C2312yes—
90C2×C32×Dic3C2311yescharacteristic
91C32×C4×D3C2×C414yescomplemented
92C32×Dic6C2×C414yescomplemented
93C3×D3×Dic3—42no—
94C3×#520—91no—
95#5827—31no—
96#5546—31no—
97C32×#41—38no—
98C2×C32×Q8—31no—
99C2×C32×D4—21no—
100C2×C32×D4—21no—
101C2×C32×D4—21no—
102C2×C32×D4—32no—
103C2×C32×D4—41no—
104C2×C32×D4C2×D311yescharacteristic
105C2×C32×D4C2×D311yescharacteristic
106C2×C32×D4C22×C311yescharacteristic
107C22×C32×C4—32no—
108C22×C32×C4—31no—
109C22×C32×C4—32no—
110C22×C3⋊Dic3C22×C312yes—
111C2×C3×#67—22no—
112C2×C3×#67C2×D312yes—
113C2×C3×#67C22×C312yes—
114C22×C3×Dic3—22no—
115C22×C3×Dic3—22no—
116C22×C3×Dic3—32no—
117C22×C3×Dic3—32no—
118C22×C3×Dic3—32no—
119C22×C3×Dic3—62no—
120C22×C3×Dic3C2×D312yes—
121C22×C3×Dic3C2×D312yes—
122C22×C3×Dic3C22×C312yes—
123C22×C3×Dic3C22×C312yes—
124C3×#237—28no—
125C3×#237Dic318yescomplemented
126C3×#237C3×C418yescomplemented
127C2×C3×C4×D3—21no—
128C2×C3×C4×D3—32no—
129C2×C3×C4×D3C2×D311yescharacteristic
130C2×C3×C4×D3C22×C311yescharacteristic
131C2×C3×Dic6—21no—
132C2×C3×Dic6C2×D311yescharacteristic
133C2×C3×Dic6C22×C311yescharacteristic
134C2×D3×Dic3C22×C312yes—
135C32×C4⋊C4—31no—
136C32×C22⋊C4—32no—
137C32×C42—31no—
138#3757C22×C312yes—
139C4⋊(C3⋊Dic3)C22×C311yescharacteristic
140C4×C3⋊Dic3C22×C311yescharacteristic
141C3×#217—22no—
142C3×#217—32no—
143C3×#217—32no—
144C3×#217—31no—
145C3×#217—31no—
146C3×#217—62no—
147C3×#217C2×D312yes—
148C3×#217C22×C312yes—
149C3×(C2×D3)⋊C4—31no—
150C3×(C2×D3)⋊C4—31no—
151C3×C4⋊Dic3—21no—
152C3×C4⋊Dic3—31no—
153C3×C4⋊Dic3—31no—
154C3×C4⋊Dic3—32no—
155C3×C4⋊Dic3—31no—
156C3×C4⋊Dic3—32no—
157C3×C4⋊Dic3—32no—
158C3×C4⋊Dic3—31no—
159C3×C4⋊Dic3—61no—
160C3×C4⋊Dic3C2×D311yescharacteristic
161C3×C4⋊Dic3C22×C311yescharacteristic
162C3×Dic3⋊C4—31no—
163C3×Dic3⋊C4—32no—
164C3×Dic3⋊C4—32no—
165C3×Dic3⋊C4—31no—
166C3×Dic3⋊C4—32no—
167C3×C4×Dic3—21no—
168C3×C4×Dic3—31no—
169C3×C4×Dic3—31no—
170C3×C4×Dic3—32no—
171C3×C4×Dic3—32no—
172C3×C4×Dic3—32no—
173C3×C4×Dic3—32no—
174C3×C4×Dic3—61no—
175C3×C4×Dic3C2×D311yescharacteristic
176C3×C4×Dic3C22×C311yescharacteristic
177Dic3⋊Dic3C22×C312yes—
178Dic3⋊Dic3C22×C312yes—
179Dic3⋊Dic3C22×C311yescharacteristic
180Dic3⋊Dic3C22×C311yescharacteristic
181Dic3⋊Dic3C22×C312yes—
182(C2×D3)⋊Dic3C22×C311yescharacteristic
183(C2×D3)⋊Dic3C22×C311yescharacteristic
184Dic32C22×C312yes—
185Dic32C22×C312yes—
186C22×C33—22no—
187C22×C33—22no—
188C22×C33C22×C414yes—
189C22×C33C2411yescharacteristic
190C2×C32×D3—21no—
191C2×C32×D3—21no—
192C2×C32×D3C22×C412yes—
193C33×C4C22×C412yes—
194C3×C3⋊Dic3—21no—
195C3×C3⋊Dic3—22no—
196C3×C3⋊Dic3—21no—
197C32×Dic3—21no—
198C32×Dic3—22no—
199C32×Dic3—21no—
200C32×Dic3C22×C414yes—
201C32×Dic3C22×C412yes—
202C2×C3×#41—31no—
203C2×C3×#41—31no—
204C2×C3×#41—61no—
205C2×#237C3×D311yescharacteristic
206C3×C4×Q8—91no—
207C3×C4×Q8—91no—
208C3×C4×D4—31no—
209C3×C4×D4—31no—
210C3×C4×D4—61no—
211C3×C4×D4—92no—
212C3×C4×D4—92no—
213C3×C4×D4—91no—
214C3×#117—91no—
215C3×#117—92no—
216C2×C3×C4⋊C4—91no—
217C2×C3×C4⋊C4—92no—
218Q8×Dic3—31no—
219Q8×Dic3—31no—
220D4×Dic3—31no—
221D4×Dic3—31no—
222D4×Dic3—32no—
223D4×Dic3—32no—
224D4×Dic3—61no—
225D4×Dic3C3×D311yescharacteristic, complemented
226C4×#67—32no—
227#926—32no—
228#926—31no—
229C2×C4⋊Dic3—32no—
230C2×C4⋊Dic3—31no—
231C2×Dic3⋊C4—32no—
232D3×C4⋊C4—31no—
233#887—31no—
234#67⋊C4—32no—
235#877—32no—
236#872—31no—
237C4×Dic6—31no—
238C23×C32—22no—
239C23×C32—22no—
240C23×C32—22no—
241C23×C32—31no—
242C23×C32—42no—
243C23×C32C22×D312yes—
244C23×C32C22×D312yes—
245C23×C32C23×C312yes—
246C22×C3×D3—21no—
247C22×C3×D3C22×D311yescharacteristic
248C22×C3×D3C23×C311yescharacteristic
249C32×Q8—34no—
250C32×D4—24no—
251C32×D4—24no—
252C32×D4—24no—
253C32×D4—38no—
254C32×D4—44no—
255C32×D4C4×D314yescomplemented
256C32×D4C2×Dic314yescomplemented
257C32×D4C2×C3×C414yescomplemented
258C2×C32×C4—21no—
259C2×C32×C4—21no—
260C2×C32×C4—21no—
261C2×C32×C4—38no—
262C2×C32×C4—32no—
263C2×C32×C4—31no—
264C2×C32×C4—34no—
265C2×C32×C4—31no—
266C2×C32×C4—32no—
267C2×C32×C4—31no—
268C2×C32×C4—41no—
269C2×C32×C4—122no—
270C2×C32×C4C22×D311yescharacteristic
271C2×C32×C4C22×D311yescharacteristic
272C2×C32×C4C23×C311yescharacteristic
273C2×C3⋊Dic3—42no—
274C2×C3⋊Dic3C23×C311yescharacteristic
275C2×C3⋊Dic3C23×C312yes—
276C2×C3⋊Dic3C23×C311yescharacteristic
277C3×#67—28no—
278C3×#67C2×Dic318yescomplemented
279C3×#67C2×C3×C418yescomplemented
280C2×C3×Dic3—28no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—22no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3—22no—
286C2×C3×Dic3—31no—
287C2×C3×Dic3—31no—
288C2×C3×Dic3—31no—
289C2×C3×Dic3—32no—
290C2×C3×Dic3—31no—
291C2×C3×Dic3—32no—
292C2×C3×Dic3—42no—
293C2×C3×Dic3—42no—
294C2×C3×Dic3—44no—
295C2×C3×Dic3—61no—
296C2×C3×Dic3—61no—
297C2×C3×Dic3—62no—
298C2×C3×Dic3—122no—
299C2×C3×Dic3—122no—
300C2×C3×Dic3—122no—
301C2×C3×Dic3—124no—
302C2×C3×Dic3C2×Dic318yescomplemented
303C2×C3×Dic3C2×C3×C418yescomplemented
304C2×C3×Dic3C22×D311yescharacteristic
305C2×C3×Dic3C22×D312yes—
306C2×C3×Dic3C22×D311yescharacteristic
307C2×C3×Dic3C22×D312yes—
308C2×C3×Dic3C22×D311yescharacteristic
309C2×C3×Dic3C23×C311yescharacteristic
310C2×C3×Dic3C23×C312yes—
311C2×C3×Dic3C23×C311yescharacteristic
312C2×C3×Dic3C23×C312yes—
313C2×C3×Dic3C23×C311yescharacteristic
314C3×C4×D3—24no—
315C3×C4×D3—122no—
316C3×C4×D3C2×Dic314yescomplemented
317C3×C4×D3C2×C3×C414yescomplemented
318C3×Dic6—24no—
319C3×Dic6C2×Dic314yescomplemented
320C3×Dic6C2×C3×C414yescomplemented
321D3×Dic3—42no—
322#520—91noSylow
323C2×C33—24no—
324C2×C33C23×C411yescharacteristic
325C2×C33H(5,𝔽2)11yescharacteristic
326C2×C332−1+411yescharacteristic
327C32×D3—22no—
328C3×#41—38no—
329C3×#41—38no—
330C3×#41—68no—
331C2×C3×Q8—31no—
332C2×C3×Q8—31no—
333C2×C3×Q8—61no—
334C2×C3×D4—21no—
335C2×C3×D4—21no—
336C2×C3×D4—21no—
337C2×C3×D4—32no—
338C2×C3×D4—32no—
339C2×C3×D4—41no—
340C2×C3×D4—62no—
341C2×C3×D4D3211yescharacteristic
342C2×C3×D4C2×C3×D311yescharacteristic
343C2×C3×D4C2×C3×D311yescharacteristic
344C22×C3×C4—32no—
345C22×C3×C4—32no—
346C22×C3×C4—31no—
347C22×C3×C4—31no—
348C22×C3×C4—32no—
349C22×C3×C4—32no—
350C22×C3×C4—61no—
351C22×C3×C4—62no—
352C22×C3×C4—62no—
353C22×C3×C4—92no—
354C22×C3×C4—92no—
355C2×#67C2×C3×D312yes—
356C22×Dic3—32no—
357C22×Dic3—32no—
358C22×Dic3—32no—
359C22×Dic3—62no—
360C22×Dic3C2×C3×D312yes—
361C22×Dic3C2×C3×D312yes—
362#237C3×Dic318yescomplemented
363C2×C4×D3—32no—
364C2×C4×D3C2×C3×D311yescharacteristic
365C2×Dic6C2×C3×D311yescharacteristic
366C3×C4⋊C4—31no—
367C3×C4⋊C4—31no—
368C3×C4⋊C4—61no—
369C3×C4⋊C4—91no—
370C3×C4⋊C4—92no—
371C3×C4⋊C4—92no—
372C3×C4⋊C4—92no—
373C3×C4⋊C4—91no—
374C3×C4⋊C4—91no—
375C3×C22⋊C4—32no—
376C3×C22⋊C4—32no—
377C3×C22⋊C4—62no—
378C3×C22⋊C4—91no—
379C3×C22⋊C4—91no—
380C3×C22⋊C4—92no—
381C3×C42—31no—
382C3×C42—31no—
383C3×C42—61no—
384C3×C42—92no—
385C3×C42—92no—
386C3×C42—91no—
387#217—32no—
388#217—32no—
389#217—31no—
390#217—31no—
391#217—62no—
392#217C2×C3×D312yes—
393(C2×D3)⋊C4—31no—
394(C2×D3)⋊C4—31no—
395C4⋊Dic3—31no—
396C4⋊Dic3—31no—
397C4⋊Dic3—32no—
398C4⋊Dic3—31no—
399C4⋊Dic3—32no—
400C4⋊Dic3—32no—
401C4⋊Dic3—31no—
402C4⋊Dic3—61no—
403C4⋊Dic3C2×C3×D311yescharacteristic
404Dic3⋊C4—32no—
405Dic3⋊C4—31no—
406Dic3⋊C4—31no—
407Dic3⋊C4—32no—
408Dic3⋊C4—32no—
409C4×Dic3—31no—
410C4×Dic3—31no—
411C4×Dic3—32no—
412C4×Dic3—32no—
413C4×Dic3—32no—
414C4×Dic3—32no—
415C4×Dic3—61no—
416C4×Dic3C2×C3×D311yescharacteristic
417C22×C32—22no—
418C22×C32—22no—
419C22×C32—22no—
420C22×C32—22no—
421C22×C32—22no—
422C22×C32—22no—
423C22×C32—21no—
424C22×C32—21no—
425C22×C32—21no—
426C22×C32—24no—
427C22×C32—24no—
428C22×C32—24no—
429C22×C32—32no—
430C22×C32—41no—
431C22×C32—44no—
432C22×C32—42no—
433C22×C32—42no—
434C22×C32—42no—
435C22×C32—42no—
436C22×C32—42no—
437C22×C32—42no—
438C22×C32—61no—
439C22×C32—61no—
440C22×C32—82no—
441C22×C32—82no—
442C22×C32C2×C4×D314yes—
443C22×C32C22×Dic314yes—
444C22×C32C22×C3×C414yes—
445C22×C32C23×D311yescharacteristic
446C22×C32C23×D311yescharacteristic
447C22×C32C24×C311yescharacteristic
448C2×C3×D3—21no—
449C2×C3×D3—21no—
450C2×C3×D3—21no—
451C2×C3×D3—21no—
452C2×C3×D3—22no—
453C2×C3×D3—41no—
454C2×C3×D3—41no—
455C2×C3×D3C22×Dic312yes—
456C2×C3×D3C22×C3×C412yes—
457C32×C4—22no—
458C32×C4—22no—
459C32×C4—22no—
460C32×C4—32no—
461C32×C4—34no—
462C32×C4—42no—
463C32×C4—61no—
464C32×C4—62no—
465C32×C4—61no—
466C32×C4C2×C4×D312yes—
467C32×C4C22×Dic312yes—
468C32×C4C22×C3×C412yes—
469C3⋊Dic3—21no—
470C3⋊Dic3—22no—
471C3⋊Dic3—21no—
472C3×Dic3—22no—
473C3×Dic3—21no—
474C3×Dic3—22no—
475C3×Dic3—21no—
476C3×Dic3—22no—
477C3×Dic3—21no—
478C3×Dic3—21no—
479C3×Dic3—24no—
480C3×Dic3—22no—
481C3×Dic3—41no—
482C3×Dic3—42no—
483C3×Dic3—62no—
484C3×Dic3—61no—
485C3×Dic3—62no—
486C3×Dic3—62no—
487C3×Dic3—61no—
488C3×Dic3—61no—
489C3×Dic3—61no—
490C3×Dic3—121no—
491C3×Dic3—122no—
492C3×Dic3C22×Dic314yes—
493C3×Dic3C22×Dic312yes—
494C3×Dic3C22×C3×C414yes—
495C3×Dic3C22×C3×C412yes—
496C2×#41—31no—
497C4×Q8—91no—
498C4×Q8—91no—
499C4×D4—31no—
500C4×D4—92no—
501C4×D4—92no—
502C4×D4—91no—
503#117—91no—
504#117—92no—
505C2×C4⋊C4—91no—
506C2×C4⋊C4—92no—
507C33#52011yescharacteristic, complemented, Sylow
508C23×C3—22no—
509C23×C3—22no—
510C23×C3—22no—
511C23×C3—31no—
512C23×C3—31no—
513C23×C3—42no—
514C23×C3—61no—
515C23×C3C2×D3212yes—
516C23×C3C22×C3×D312yes—
517C23×C3C22×C3×D312yes—
518C22×D3C22×C3×D311yescharacteristic
519C3×Q8—34no—
520C3×Q8—34no—
521C3×Q8—64no—
522C3×D4—24no—
523C3×D4—24no—
524C3×D4—24no—
525C3×D4—38no—
526C3×D4—38no—
527C3×D4—44no—
528C3×D4—68no—
529C3×D4D3×Dic314yescomplemented
530C3×D4C3×C4×D314yescomplemented
531C3×D4C2×C3×Dic314yescomplemented
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—32no—
536C2×C3×C4—31no—
537C2×C3×C4—32no—
538C2×C3×C4—31no—
539C2×C3×C4—38no—
540C2×C3×C4—38no—
541C2×C3×C4—34no—
542C2×C3×C4—34no—
543C2×C3×C4—31no—
544C2×C3×C4—31no—
545C2×C3×C4—32no—
546C2×C3×C4—31no—
547C2×C3×C4—32no—
548C2×C3×C4—31no—
549C2×C3×C4—41no—
550C2×C3×C4—64no—
551C2×C3×C4—61no—
552C2×C3×C4—61no—
553C2×C3×C4—62no—
554C2×C3×C4—68no—
555C2×C3×C4—61no—
556C2×C3×C4—62no—
557C2×C3×C4—91no—
558C2×C3×C4—91no—
559C2×C3×C4—92no—
560C2×C3×C4—122no—
561C2×C3×C4—122no—
562C2×C3×C4—124no—
563C2×C3×C4—362no—
564C2×C3×C4—362no—
565C2×C3×C4C2×D3211yescharacteristic
566C2×C3×C4C22×C3×D311yescharacteristic
567C2×C3×C4C22×C3×D311yescharacteristic
568#67C2×C3×Dic318yescomplemented
569C2×Dic3—31no—
570C2×Dic3—31no—
571C2×Dic3—31no—
572C2×Dic3—32no—
573C2×Dic3—32no—
574C2×Dic3—31no—
575C2×Dic3—42no—
576C2×Dic3—61no—
577C2×Dic3—61no—
578C2×Dic3—62no—
579C2×Dic3—122no—
580C2×Dic3—122no—
581C2×Dic3—122no—
582C2×Dic3—124no—
583C2×Dic3C2×C3×Dic318yescomplemented
584C2×Dic3C22×C3×D311yescharacteristic
585C2×Dic3C22×C3×D312yes—
586C2×Dic3C22×C3×D311yescharacteristic
587C2×Dic3C22×C3×D312yes—
588C2×Dic3C22×C3×D311yescharacteristic
589C4×D3—122no—
590C4×D3C2×C3×Dic314yescomplemented
591Dic6C2×C3×Dic314yescomplemented
592C2×C32—24no—
593C2×C32—24no—
594C2×C32—24no—
595C2×C32—21no—
596C2×C32—21no—
597C2×C32—21no—
598C2×C32—21no—
599C2×C32—21no—
600C2×C32—21no—
601C2×C32—21no—
602C2×C32—21no—
603C2×C32—21no—
604C2×C32—41no—
605C2×C32—41no—
606C2×C32—41no—
607C2×C32—44no—
608C2×C32—44no—
609C2×C32—44no—
610C2×C32—62no—
611C2×C32—84no—
612C2×C32C22×C4×D311yescharacteristic
613C2×C32#100411yescharacteristic
614C2×C32#100911yescharacteristic
615C2×C32#101011yescharacteristic
616C2×C32#101011yescharacteristic
617C2×C32C23×Dic311yescharacteristic
618C2×C32C23×C3×C411yescharacteristic
619C2×C32C3×H(5,𝔽2)11yescharacteristic
620C2×C32C3×2−1+411yescharacteristic
621C3×D3—22no—
622C3×D3—22no—
623C3×D3—42no—
624#41—38no—
625C2×Q8—31no—
626C2×D4—32no—
627C2×D4C3×D3211yescharacteristic
628C22×C4—32no—
629C22×C4—31no—
630C22×C4—32no—
631C22×C4—92no—
632C22×C4—92no—
633C4⋊C4—31no—
634C4⋊C4—91no—
635C4⋊C4—92no—
636C4⋊C4—92no—
637C4⋊C4—92no—
638C4⋊C4—91no—
639C4⋊C4—91no—
640C22⋊C4—32no—
641C22⋊C4—91no—
642C22⋊C4—91no—
643C22⋊C4—92no—
644C42—31no—
645C42—92no—
646C42—92no—
647C42—91no—
648C22×C3—22no—
649C22×C3—22no—
650C22×C3—22no—
651C22×C3—22no—
652C22×C3—22no—
653C22×C3—22no—
654C22×C3—21no—
655C22×C3—21no—
656C22×C3—21no—
657C22×C3—24no—
658C22×C3—24no—
659C22×C3—24no—
660C22×C3—32no—
661C22×C3—32no—
662C22×C3—42no—
663C22×C3—42no—
664C22×C3—42no—
665C22×C3—42no—
666C22×C3—42no—
667C22×C3—42no—
668C22×C3—41no—
669C22×C3—44no—
670C22×C3—62no—
671C22×C3—61no—
672C22×C3—61no—
673C22×C3—61no—
674C22×C3—61no—
675C22×C3—82no—
676C22×C3—82no—
677C22×C3—121no—
678C22×C3—121no—
679C22×C3C2×D3×Dic314yes—
680C22×C3C2×C3×C4×D314yes—
681C22×C3C22×C3×Dic314yes—
682C22×C3C22×D3211yescharacteristic
683C22×C3C23×C3×D311yescharacteristic
684C22×C3C23×C3×D311yescharacteristic
685C2×D3—21no—
686C2×D3—21no—
687C2×D3C22×C3×Dic312yes—
688C3×C4—22no—
689C3×C4—22no—
690C3×C4—22no—
691C3×C4—32no—
692C3×C4—34no—
693C3×C4—32no—
694C3×C4—34no—
695C3×C4—42no—
696C3×C4—62no—
697C3×C4—64no—
698C3×C4—62no—
699C3×C4—61no—
700C3×C4—61no—
701C3×C4—62no—
702C3×C4—62no—
703C3×C4—61no—
704C3×C4—61no—
705C3×C4—122no—
706C3×C4—121no—
707C3×C4—181no—
708C3×C4—181no—
709C3×C4—182no—
710C3×C4C2×D3×Dic312yes—
711C3×C4C2×C3×C4×D312yes—
712C3×C4C22×C3×Dic312yes—
713Dic3—21no—
714Dic3—22no—
715Dic3—21no—
716Dic3—62no—
717Dic3—61no—
718Dic3—62no—
719Dic3—62no—
720Dic3—61no—
721Dic3—61no—
722Dic3—61no—
723Dic3—122no—
724Dic3—121no—
725Dic3C22×C3×Dic314yes—
726Dic3C22×C3×Dic312yes—
727C32—21no—
728C32—21no—
729C32—21no—
730C32—41no—
731C32#554611yescharacteristic, complemented
732C32#582711yescharacteristic, complemented
733C32C3×#52011yescharacteristic, complemented
734C23—31no—
735C23C2×C3×D3212yes—
736Q8—34no—
737D4—38no—
738D4C3×D3×Dic314yescomplemented
739C2×C4—32no—
740C2×C4—31no—
741C2×C4—38no—
742C2×C4—34no—
743C2×C4—31no—
744C2×C4—31no—
745C2×C4—32no—
746C2×C4—91no—
747C2×C4—91no—
748C2×C4—92no—
749C2×C4—122no—
750C2×C4—362no—
751C2×C4—362no—
752C2×C4C2×C3×D3211yescharacteristic
753C2×C3—24no—
754C2×C3—24no—
755C2×C3—24no—
756C2×C3—21no—
757C2×C3—21no—
758C2×C3—21no—
759C2×C3—21no—
760C2×C3—21no—
761C2×C3—21no—
762C2×C3—21no—
763C2×C3—21no—
764C2×C3—21no—
765C2×C3—44no—
766C2×C3—44no—
767C2×C3—44no—
768C2×C3—41no—
769C2×C3—41no—
770C2×C3—41no—
771C2×C3—62no—
772C2×C3—62no—
773C2×C3—84no—
774C2×C3—122no—
775C2×C3#6430911yescharacteristic
776C2×C3#6431411yescharacteristic
777C2×C3C22×D3×Dic311yescharacteristic
778C2×C3C22×C3×C4×D311yescharacteristic
779C2×C3C3×#100411yescharacteristic
780C2×C3C3×#100911yescharacteristic
781C2×C3C3×#101011yescharacteristic
782C2×C3C3×#101011yescharacteristic
783C2×C3C23×C3×Dic311yescharacteristic
784D3—22no—
785C22—22no—
786C22—22no—
787C22—32no—
788C22—61no—
789C22—61no—
790C22C2×C3×D3×Dic314yes—
791C22C22×C3×D3211yescharacteristic
792C4—32no—
793C4—34no—
794C4—61no—
795C4—61no—
796C4—62no—
797C4—181no—
798C4—181no—
799C4—182no—
800C4C2×C3×D3×Dic312yes—
801C3—21no—
802C3—21no—
803C3—21no—
804C3—41no—
805C3#1059522211yescharacteristic, direct product factor
806C3C3×#554611yescharacteristic, complemented
807C3C3×#582711yescharacteristic, complemented
808C2—24no—
809C2—62no—
810C2C3×#6430911yescharacteristic
811C2C3×#6431411yescharacteristic
812C2C22×C3×D3×Dic311yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutatorC2×C32C23×C3×C4
FrattiniC22C22×C3×D32
FittingC2×C33×D4C22
socleC22×C33C24
prime radicalC2×C32×#237C2
cosocleC22×C32C24×C3
hypercenterC2×C3×D4D32
hypocenterC32C3×#520
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
2. C3×D4×C3⋊Dic3C2semidirect
3. C32×D4×Dic3C2semidirect
4. C3×#67⋊Dic3C2semidirect
5. C3×Dic3×#67C2semidirect
6. C2×C3×Dic3⋊Dic3C2semidirect
7. C3×#63955C2semidirect
8. C3×D3×C4⋊Dic3C2semidirect
9. C3×#63855C2semidirect
10. C3×#63843C2semidirect
11. C3×Dic3×Dic6C2semidirect
14. #10595222C3direct (N × H)
20. C32×#237C4semidirect
44. D4×C3⋊Dic3C2×C3semidirect
53. C3×D4×Dic3D3semidirect
54. C3×D4×Dic3C2×C3semidirect
67. #67⋊Dic3C2×C3semidirect
68. Dic3×#67C2×C3semidirect
69. C2×Dic3⋊Dic3C2×C3semidirect
70. #63955C2×C3semidirect
71. D3×C4⋊Dic3C2×C3semidirect
72. #63855C2×C3semidirect
73. #63843C2×C3semidirect
74. Dic3×Dic6C2×C3semidirect
77. C33×D4C2×C4semidirect
83. C32×#67C2×C4semidirect
85. C2×C32×Dic3C2×C4semidirect
91. C32×C4×D3C2×C4semidirect
92. C32×Dic6C2×C4semidirect
125. C3×#237Dic3semidirect
126. C3×#237C3×C4semidirect
225. D4×Dic3C3×D3semidirect
255. C32×D4C4×D3semidirect
256. C32×D4C2×Dic3semidirect
257. C32×D4C2×C3×C4semidirect
278. C3×#67C2×Dic3semidirect
279. C3×#67C2×C3×C4semidirect
302. C2×C3×Dic3C2×Dic3semidirect
303. C2×C3×Dic3C2×C3×C4semidirect
316. C3×C4×D3C2×Dic3semidirect
317. C3×C4×D3C2×C3×C4semidirect
319. C3×Dic6C2×Dic3semidirect
320. C3×Dic6C2×C3×C4semidirect
362. #237C3×Dic3semidirect
507. C33#520semidirect
529. C3×D4D3×Dic3semidirect
530. C3×D4C3×C4×D3semidirect
531. C3×D4C2×C3×Dic3semidirect
568. #67C2×C3×Dic3semidirect
583. C2×Dic3C2×C3×Dic3semidirect
590. C4×D3C2×C3×Dic3semidirect
591. Dic6C2×C3×Dic3semidirect
731. C32#5546semidirect
732. C32#5827semidirect
733. C32C3×#520semidirect
738. D4C3×D3×Dic3semidirect
805. C3#10595222direct (N × H)
806. C3C3×#5546semidirect
807. C3C3×#5827semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#2372
C3×D4×C3⋊Dic32
C32×D4×Dic32
C3×#67⋊Dic32
C3×Dic3×#672
C2×C3×Dic3⋊Dic32
C3×#639552
C3×D3×C4⋊Dic32
C3×#638552
C3×#638432
C3×Dic3×Dic62
C3×#58273
C3×#55463
#105952223