Finite Group Databasebeta

← C3×#10594624 #13173932

Subgroups — C3×#10594624 #13173932

Order 1728.

1554 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×D32C211yesmaximal, characteristic
2C2×C3×#3797C211yesmaximal, characteristic, complemented
3C3×C4⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
4C32×#896C212yesmaximal, complemented
5C3×#63921C211yesmaximal, characteristic
6C3×#63921C211yesmaximal, characteristic
7C3×#63893C212yesmaximal, complemented
8C3×#63887C212yesmaximal, complemented
9C3×#63883C211yesmaximal, characteristic, complemented
10C3×#63883C211yesmaximal, characteristic, complemented
11C3×#63851C212yesmaximal, complemented
12C3×D3×C22⋊Q8—32nomaximal
13#10594624C311yesmaximal, characteristic, direct product factor
14C22×C3×D32C2211yescharacteristic
15C2×C3×C4×C3⋊D3C2211yescharacteristic
16C2×C3×C4×C3⋊D3C2211yescharacteristic
17C2×C3×C4×C3⋊D3C2211yescharacteristic
18C2×C32×C4×D3C2212yes—
19C2×C32×Dic6C2212yescomplemented
20C2×C3×#627C2212yescomplemented
21C2×C3×#624C2211yescharacteristic
22C2×C3×#624C2211yescharacteristic
23C2×C3×#624C2211yescharacteristic
24C2×C3×D3×Dic3C2212yes—
25C3×C4×D32—24no—
26C3×#3797—24no—
27C33×C4⋊C4C2211yescharacteristic, complemented
28C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
29C3×#3750C2211yescharacteristic, complemented
30C3×#3750C2211yescharacteristic, complemented
31C32×(C2×D3)⋊C4C2212yes—
32C32×(C2×D3)⋊C4C2212yes—
33C32×Dic3⋊C4C2212yescomplemented
34C32×Dic3⋊C4C2212yescomplemented
35C3×Dic3⋊Dic3C2212yescomplemented
36C3×Dic3⋊Dic3C2212yescomplemented
37C3×(C2×D3)⋊Dic3C2212yes—
38C3×(C2×D3)⋊Dic3C2212yes—
39C2×C3×D3×Q8—32no—
40C22×C3×C4×D3—32no—
41C2×C4×D32C2×C311yescharacteristic
42C2×#3797C2×C311yescharacteristic, complemented
43C32×C22⋊Q8—32no—
44C4⋊C4×C3⋊D3C2×C311yescharacteristic, complemented
45C3×#946—32no—
46C3×#924—32no—
47C3×#897—32no—
48C3×#896—22no—
49C3×#896—32no—
50C3×#896D312yescomplemented
51C3×#896C2×C312yescomplemented
52C3×D3×C4⋊C4—32no—
53C3×D3×C4⋊C4—32no—
54C3×D3×C4⋊C4—32no—
55C3×D3×C4⋊C4—61no—
56C3×D3×C22⋊C4—32no—
57C3×D3×C22⋊C4—32no—
58C3×#878—32no—
59C3×#878—32no—
60#63921C2×C311yescharacteristic
61#63921C2×C311yescharacteristic
62#63893C2×C312yescomplemented
63#63887C2×C312yescomplemented
64#63883C2×C311yescharacteristic, complemented
65#63883C2×C311yescharacteristic, complemented
66#63851C2×C312yescomplemented
67C22×C3×C3⋊D3C2311yescharacteristic
68C22×C32×D3C2312yes—
69C2×C3×D32—22no—
70C2×C3×D32—22no—
71C2×C3×D32Q814yescomplemented
72C2×C33×C4C2311yescharacteristic
73C2×C33×C4C2311yescharacteristic
74C2×C33×C4C2311yescharacteristic
75C2×C3×C3⋊Dic3C2311yescharacteristic
76C2×C3×C3⋊Dic3C2311yescharacteristic
77C2×C3×C3⋊Dic3C2311yescharacteristic
78C3×C4×C3⋊D3—22no—
79C3×C4×C3⋊D3—22no—
80C3×C4×C3⋊D3—22no—
81C2×C32×Dic3C2312yes—
82C2×C32×Dic3C2312yes—
83C2×C32×Dic3C2312yes—
84C32×C4×D3—24no—
85C32×Dic6—24no—
86C3×#627—24no—
87C3×#624—22no—
88C3×#624—22no—
89C3×#624D414yes—
90C3×D3×Dic3—24no—
91C2×C3×C22⋊Q8—91no—
92D3×C22⋊Q8—32no—
93C23×C3×D3—32no—
94C22×D32C22×C311yescharacteristic
95C2×C32×Q8—32no—
96C22×C32×C4—32no—
97C2×C4×C3⋊D3C22×C311yescharacteristic
98C2×C4×C3⋊D3C22×C311yescharacteristic
99C2×C4×C3⋊D3C22×C311yescharacteristic
100C22×C3×Dic3—32no—
101C3×D3×Q8—68no—
102C2×C3×C4×D3—22no—
103C2×C3×C4×D3—32no—
104C2×C3×C4×D3—32no—
105C2×C3×C4×D3—32no—
106C2×C3×C4×D3—32no—
107C2×C3×C4×D3—32no—
108C2×C3×C4×D3—32no—
109C2×C3×C4×D3—32no—
110C2×C3×C4×D3—68no—
111C2×C3×C4×D3—61no—
112C2×C3×C4×D3—61no—
113C2×C3×C4×D3—61no—
114C2×C3×C4×D3C2×D312yes—
115C2×C3×C4×D3C22×C312yes—
116C2×C3×Dic6—22no—
117C2×C3×Dic6—32no—
118C2×C3×Dic6—32no—
119C2×C3×Dic6C2×D312yescomplemented
120C2×C3×Dic6C22×C312yescomplemented
121C2×#627C22×C312yescomplemented
122C2×#624C22×C311yescharacteristic
123C2×#624C22×C311yescharacteristic
124C2×#624C22×C311yescharacteristic
125C2×D3×Dic3C22×C312yes—
126C4×D32—24no—
127#3797—24no—
128C32×C4⋊C4—21no—
129C32×C4⋊C4—22no—
130C32×C4⋊C4—32no—
131C32×C4⋊C4—32no—
132C32×C4⋊C4—41no—
133C32×C4⋊C4C2×D312yescomplemented
134C32×C4⋊C4C22×C311yescharacteristic, complemented
135C32×C22⋊C4—32no—
136C32×C22⋊C4—32no—
137C4⋊(C3⋊Dic3)C22×C311yescharacteristic, complemented
138#3750C22×C311yescharacteristic, complemented
139#3750C22×C311yescharacteristic, complemented
140C3×#217—32no—
141C3×#217—32no—
142C3×(C2×D3)⋊C4—22no—
143C3×(C2×D3)⋊C4—22no—
144C3×(C2×D3)⋊C4—32no—
145C3×(C2×D3)⋊C4—32no—
146C3×(C2×D3)⋊C4C2×D312yes—
147C3×(C2×D3)⋊C4C2×D312yes—
148C3×(C2×D3)⋊C4C22×C312yes—
149C3×(C2×D3)⋊C4C22×C312yes—
150C3×C4⋊Dic3—32no—
151C3×C4⋊Dic3—32no—
152C3×C4⋊Dic3—32no—
153C3×C4⋊Dic3—61no—
154C3×Dic3⋊C4—22no—
155C3×Dic3⋊C4—22no—
156C3×Dic3⋊C4—32no—
157C3×Dic3⋊C4—32no—
158C3×Dic3⋊C4—32no—
159C3×Dic3⋊C4—32no—
160C3×Dic3⋊C4—61no—
161C3×Dic3⋊C4—61no—
162C3×Dic3⋊C4C2×D312yescomplemented
163C3×Dic3⋊C4C2×D312yescomplemented
164C3×Dic3⋊C4C22×C312yescomplemented
165C3×Dic3⋊C4C22×C312yescomplemented
166Dic3⋊Dic3C22×C312yescomplemented
167Dic3⋊Dic3C22×C312yescomplemented
168(C2×D3)⋊Dic3C22×C312yes—
169(C2×D3)⋊Dic3C22×C312yes—
170C22×C33C2411yescharacteristic
171C2×C3×C3⋊D3C2×D412yes—
172C2×C3×C3⋊D3C2×Q812yes—
173C2×C3×C3⋊D3#4112yes—
174C2×C32×D3—22no—
175C2×C32×D3—22no—
176C2×C32×D3C2×Q814yescomplemented
177C3×D32—28no—
178C33×C4—21no—
179C33×C4—21no—
180C33×C4—21no—
181C3×C3⋊Dic3—21no—
182C3×C3⋊Dic3—21no—
183C3×C3⋊Dic3—21no—
184C32×Dic3—22no—
185C32×Dic3—22no—
186C32×Dic3C2×D414yes—
187C22×C3×Q8—91no—
188C23×C3×C4—91no—
189C2×D3×Q8—32no—
190C22×C4×D3—32no—
191C3×C22⋊Q8—32no—
192C3×C22⋊Q8—32no—
193C3×C22⋊Q8—62no—
194C3×C22⋊Q8—92no—
195C3×C22⋊Q8—92no—
196C3×C22⋊Q8—92no—
197C2×C3×C4⋊C4—91no—
198C2×C3×C4⋊C4—91no—
199C2×C3×C4⋊C4—91no—
200C2×C3×C22⋊C4—91no—
201C2×C3×C22⋊C4—91no—
202#946—32no—
203#924—32no—
204#897—32no—
205#896—32no—
206#896C3×D312yescomplemented
207D3×C4⋊C4—32no—
208D3×C4⋊C4—32no—
209D3×C4⋊C4—32no—
210D3×C4⋊C4—61no—
211D3×C22⋊C4—32no—
212D3×C22⋊C4—32no—
213#878—32no—
214#878—32no—
215C23×C32—32no—
216C22×C3⋊D3C23×C311yescharacteristic
217C22×C3×D3—22no—
218C22×C3×D3—32no—
219C22×C3×D3—38no—
220C22×C3×D3—61no—
221C22×C3×D3—64no—
222C22×C3×D3—64no—
223C22×C3×D3C22×D312yes—
224C22×C3×D3C23×C312yes—
225C2×D32—22no—
226C2×D32—22no—
227C2×D32C3×Q814yescomplemented
228C32×Q8—64no—
229C2×C32×C4—21no—
230C2×C32×C4—21no—
231C2×C32×C4—21no—
232C2×C32×C4—22no—
233C2×C32×C4—22no—
234C2×C32×C4—22no—
235C2×C32×C4—32no—
236C2×C32×C4—32no—
237C2×C32×C4—32no—
238C2×C32×C4—41no—
239C2×C32×C4—41no—
240C2×C32×C4—41no—
241C2×C32×C4—64no—
242C2×C32×C4C22×D312yes—
243C2×C32×C4C22×D312yes—
244C2×C32×C4C22×D312yes—
245C2×C32×C4C23×C311yescharacteristic
246C2×C32×C4C23×C311yescharacteristic
247C2×C32×C4C23×C311yescharacteristic
248C2×C3⋊Dic3C23×C311yescharacteristic
249C2×C3⋊Dic3C23×C311yescharacteristic
250C2×C3⋊Dic3C23×C311yescharacteristic
251C4×C3⋊D3—22no—
252C4×C3⋊D3—22no—
253C4×C3⋊D3—22no—
254C2×C3×Dic3—22no—
255C2×C3×Dic3—22no—
256C2×C3×Dic3—22no—
257C2×C3×Dic3—32no—
258C2×C3×Dic3—32no—
259C2×C3×Dic3—32no—
260C2×C3×Dic3—61no—
261C2×C3×Dic3—61no—
262C2×C3×Dic3—61no—
263C2×C3×Dic3—64no—
264C2×C3×Dic3C22×D312yes—
265C2×C3×Dic3C22×D312yes—
266C2×C3×Dic3C22×D312yes—
267C2×C3×Dic3C23×C312yes—
268C2×C3×Dic3C23×C312yes—
269C2×C3×Dic3C23×C312yes—
270C3×C4×D3—24no—
271C3×C4×D3—24no—
272C3×C4×D3—38no—
273C3×C4×D3—44no—
274C3×C4×D3—64no—
275C3×C4×D3—64no—
276C3×C4×D3—64no—
277C3×C4×D3—64no—
278C3×C4×D3—64no—
279C3×C4×D3—64no—
280C3×C4×D3—64no—
281C3×C4×D3—122no—
282C3×C4×D3—122no—
283C3×Dic6—24no—
284C3×Dic6—24no—
285C3×Dic6—44no—
286C3×Dic6—64no—
287C3×Dic6—64no—
288#627—24no—
289#624—22no—
290#624—22no—
291#624C3×D414yes—
292D3×Dic3—24no—
293C2×C22⋊Q8—91noSylow
294C2×C33C22×D411yescharacteristic
295C2×C33C22×Q811yescharacteristic
296C2×C33C2×#4111yescharacteristic
297C3×C3⋊D3C22⋊Q814yescomplemented
298C32×D3—24no—
299C24×C3—91no—
300C23×D3—32no—
301C2×C3×Q8—32no—
302C2×C3×Q8—32no—
303C2×C3×Q8—62no—
304C2×C3×Q8—92no—
305C2×C3×Q8—184no—
306C22×C3×C4—32no—
307C22×C3×C4—32no—
308C22×C3×C4—62no—
309C22×C3×C4—91no—
310C22×C3×C4—91no—
311C22×C3×C4—91no—
312C22×C3×C4—92no—
313C22×C3×C4—91no—
314C22×C3×C4—91no—
315C22×C3×C4—91no—
316C22×C3×C4—184no—
317C22×Dic3—32no—
318D3×Q8—68no—
319C2×C4×D3—32no—
320C2×C4×D3—32no—
321C2×C4×D3—32no—
322C2×C4×D3—32no—
323C2×C4×D3—32no—
324C2×C4×D3—32no—
325C2×C4×D3—32no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—68no—
330C2×C4×D3C2×C3×D312yes—
331C2×Dic6—32no—
332C2×Dic6—32no—
333C2×Dic6C2×C3×D312yescomplemented
334C3×C4⋊C4—21no—
335C3×C4⋊C4—22no—
336C3×C4⋊C4—32no—
337C3×C4⋊C4—32no—
338C3×C4⋊C4—32no—
339C3×C4⋊C4—32no—
340C3×C4⋊C4—41no—
341C3×C4⋊C4—62no—
342C3×C4⋊C4—62no—
343C3×C4⋊C4—92no—
344C3×C4⋊C4—92no—
345C3×C4⋊C4—91no—
346C3×C4⋊C4—91no—
347C3×C4⋊C4—91no—
348C3×C4⋊C4D3211yescharacteristic, complemented
349C3×C4⋊C4C2×C3×D312yescomplemented
350C3×C22⋊C4—32no—
351C3×C22⋊C4—32no—
352C3×C22⋊C4—32no—
353C3×C22⋊C4—32no—
354C3×C22⋊C4—62no—
355C3×C22⋊C4—62no—
356C3×C22⋊C4—92no—
357C3×C22⋊C4—92no—
358#217—32no—
359#217—32no—
360(C2×D3)⋊C4—32no—
361(C2×D3)⋊C4—32no—
362(C2×D3)⋊C4C2×C3×D312yes—
363(C2×D3)⋊C4C2×C3×D312yes—
364C4⋊Dic3—32no—
365C4⋊Dic3—32no—
366C4⋊Dic3—32no—
367C4⋊Dic3—61no—
368Dic3⋊C4—32no—
369Dic3⋊C4—32no—
370Dic3⋊C4—32no—
371Dic3⋊C4—32no—
372Dic3⋊C4—61no—
373Dic3⋊C4—61no—
374Dic3⋊C4C2×C3×D312yescomplemented
375Dic3⋊C4C2×C3×D312yescomplemented
376C22×C32—21no—
377C22×C32—22no—
378C22×C32—34no—
379C22×C32—41no—
380C22×C32—62no—
381C22×C32—62no—
382C22×C32C23×D312yes—
383C22×C32C24×C311yescharacteristic
384C2×C3⋊D3C2×C3×D412yes—
385C2×C3⋊D3C2×C3×Q812yes—
386C2×C3⋊D3C3×#4112yes—
387C2×C3×D3—22no—
388C2×C3×D3—22no—
389C2×C3×D3—22no—
390C2×C3×D3—22no—
391C2×C3×D3—24no—
392C2×C3×D3—34no—
393C2×C3×D3—34no—
394C2×C3×D3—34no—
395C2×C3×D3—42no—
396C2×C3×D3—42no—
397C2×C3×D3—62no—
398C2×C3×D3—62no—
399C2×C3×D3—62no—
400C2×C3×D3—616no—
401C2×C3×D3D3×Q814yescomplemented
402C2×C3×D3C2×C3×Q814yescomplemented
403D32—28no—
404C32×C4—21no—
405C32×C4—22no—
406C32×C4—22no—
407C32×C4—22no—
408C32×C4—22no—
409C32×C4—21no—
410C32×C4—21no—
411C32×C4—34no—
412C32×C4—42no—
413C32×C4—42no—
414C32×C4—42no—
415C32×C4—42no—
416C32×C4—41no—
417C32×C4—41no—
418C32×C4—62no—
419C32×C4—62no—
420C32×C4—81no—
421C32×C4—81no—
422C3⋊Dic3—21no—
423C3⋊Dic3—21no—
424C3⋊Dic3—21no—
425C3×Dic3—22no—
426C3×Dic3—22no—
427C3×Dic3—22no—
428C3×Dic3—22no—
429C3×Dic3—24no—
430C3×Dic3—42no—
431C3×Dic3—42no—
432C3×Dic3—62no—
433C3×Dic3—62no—
434C3×Dic3—62no—
435C3×Dic3—62no—
436C3×Dic3—121no—
437C3×Dic3—121no—
438C3×Dic3D3×D414yes—
439C3×Dic3C2×C3×D414yes—
440C22×Q8—91no—
441C23×C4—91no—
442C22⋊Q8—32no—
443C22⋊Q8—92no—
444C22⋊Q8—92no—
445C22⋊Q8—92no—
446C2×C4⋊C4—91no—
447C2×C4⋊C4—91no—
448C2×C4⋊C4—91no—
449C2×C22⋊C4—91no—
450C2×C22⋊C4—91no—
451C33C2×C22⋊Q811yescharacteristic, complemented, Sylow
452C23×C3—32no—
453C23×C3—32no—
454C23×C3—62no—
455C23×C3—94no—
456C23×C3—91no—
457C23×C3—182no—
458C23×C3—182no—
459C22×D3—32no—
460C22×D3—38no—
461C22×D3—61no—
462C22×D3—64no—
463C22×D3—64no—
464C22×D3C22×C3×D312yes—
465C3×Q8—64no—
466C3×Q8—64no—
467C3×Q8—124no—
468C3×Q8—184no—
469C2×C3×C4—21no—
470C2×C3×C4—22no—
471C2×C3×C4—22no—
472C2×C3×C4—22no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—32no—
476C2×C3×C4—32no—
477C2×C3×C4—32no—
478C2×C3×C4—32no—
479C2×C3×C4—32no—
480C2×C3×C4—32no—
481C2×C3×C4—41no—
482C2×C3×C4—41no—
483C2×C3×C4—41no—
484C2×C3×C4—62no—
485C2×C3×C4—62no—
486C2×C3×C4—62no—
487C2×C3×C4—64no—
488C2×C3×C4—64no—
489C2×C3×C4—94no—
490C2×C3×C4—91no—
491C2×C3×C4—91no—
492C2×C3×C4—91no—
493C2×C3×C4—124no—
494C2×C3×C4—182no—
495C2×C3×C4—182no—
496C2×C3×C4—182no—
497C2×C3×C4—184no—
498C2×C3×C4—182no—
499C2×C3×C4—182no—
500C2×C3×C4C2×D3211yescharacteristic
501C2×C3×C4C2×D3211yescharacteristic
502C2×C3×C4C2×D3211yescharacteristic
503C2×C3×C4C22×C3×D312yes—
504C2×C3×C4C22×C3×D312yes—
505C2×C3×C4C22×C3×D312yes—
506C2×Dic3—32no—
507C2×Dic3—32no—
508C2×Dic3—32no—
509C2×Dic3—61no—
510C2×Dic3—61no—
511C2×Dic3—61no—
512C2×Dic3—64no—
513C2×Dic3C22×C3×D312yes—
514C2×Dic3C22×C3×D312yes—
515C2×Dic3C22×C3×D312yes—
516C4×D3—24no—
517C4×D3—38no—
518C4×D3—64no—
519C4×D3—64no—
520C4×D3—64no—
521C4×D3—64no—
522C4×D3—64no—
523C4×D3—64no—
524C4×D3—64no—
525C4×D3—122no—
526C4×D3—122no—
527Dic6—24no—
528Dic6—64no—
529Dic6—64no—
530C2×C32—21no—
531C2×C32—21no—
532C2×C32—21no—
533C2×C32—22no—
534C2×C32—22no—
535C2×C32—22no—
536C2×C32—41no—
537C2×C32—41no—
538C2×C32—41no—
539C2×C32—64no—
540C2×C32C2×D3×D412yes—
541C2×C32C2×D3×Q812yes—
542C2×C32D3×#4112yes—
543C2×C32C22×C3×D411yescharacteristic
544C2×C32C22×C3×Q811yescharacteristic
545C2×C32C2×C3×#4111yescharacteristic
546C3⋊D3C3×C22⋊Q814yescomplemented
547C3×D3—24no—
548C3×D3—24no—
549C3×D3—38no—
550C3×D3—44no—
551C3×D3—64no—
552C24—91no—
553C2×Q8—32no—
554C2×Q8—92no—
555C2×Q8—184no—
556C22×C4—32no—
557C22×C4—91no—
558C22×C4—91no—
559C22×C4—91no—
560C22×C4—92no—
561C22×C4—91no—
562C22×C4—91no—
563C22×C4—91no—
564C22×C4—184no—
565C4⋊C4—32no—
566C4⋊C4—32no—
567C4⋊C4—92no—
568C4⋊C4—92no—
569C4⋊C4—91no—
570C4⋊C4—91no—
571C4⋊C4—91no—
572C4⋊C4C3×D3211yescharacteristic, complemented
573C22⋊C4—32no—
574C22⋊C4—32no—
575C22⋊C4—92no—
576C22⋊C4—92no—
577C22×C3—21no—
578C22×C3—22no—
579C22×C3—34no—
580C22×C3—34no—
581C22×C3—41no—
582C22×C3—64no—
583C22×C3—62no—
584C22×C3—62no—
585C22×C3—62no—
586C22×C3—62no—
587C22×C3—92no—
588C22×C3—92no—
589C22×C3—92no—
590C22×C3—122no—
591C22×C3—122no—
592C22×C3—188no—
593C22×C3C22×D3211yescharacteristic
594C22×C3C23×C3×D312yes—
595C2×D3—22no—
596C2×D3—22no—
597C2×D3—34no—
598C2×D3—34no—
599C2×D3—34no—
600C2×D3—62no—
601C2×D3—62no—
602C2×D3—62no—
603C2×D3—616no—
604C2×D3C3×D3×Q814yescomplemented
605C3×C4—22no—
606C3×C4—21no—
607C3×C4—21no—
608C3×C4—21no—
609C3×C4—22no—
610C3×C4—22no—
611C3×C4—22no—
612C3×C4—34no—
613C3×C4—34no—
614C3×C4—41no—
615C3×C4—41no—
616C3×C4—42no—
617C3×C4—42no—
618C3×C4—42no—
619C3×C4—42no—
620C3×C4—64no—
621C3×C4—62no—
622C3×C4—62no—
623C3×C4—62no—
624C3×C4—62no—
625C3×C4—81no—
626C3×C4—81no—
627C3×C4—122no—
628C3×C4—122no—
629C3×C4—181no—
630C3×C4—181no—
631C3×C4—181no—
632Dic3—22no—
633Dic3—22no—
634Dic3—62no—
635Dic3—62no—
636Dic3—62no—
637Dic3—62no—
638Dic3—121no—
639Dic3—121no—
640Dic3C3×D3×D414yes—
641C32—21no—
642C32—22no—
643C32—41no—
644C32D3×C22⋊Q812yescomplemented
645C32C2×C3×C22⋊Q811yescharacteristic, complemented
646C23—32no—
647C23—94no—
648C23—91no—
649C23—182no—
650C23—182no—
651Q8—64no—
652Q8—184no—
653C2×C4—32no—
654C2×C4—32no—
655C2×C4—32no—
656C2×C4—64no—
657C2×C4—94no—
658C2×C4—91no—
659C2×C4—91no—
660C2×C4—91no—
661C2×C4—182no—
662C2×C4—182no—
663C2×C4—182no—
664C2×C4—184no—
665C2×C4—182no—
666C2×C4—182no—
667C2×C4C2×C3×D3211yescharacteristic
668C2×C4C2×C3×D3211yescharacteristic
669C2×C4C2×C3×D3211yescharacteristic
670C2×C3—21no—
671C2×C3—22no—
672C2×C3—21no—
673C2×C3—22no—
674C2×C3—21no—
675C2×C3—22no—
676C2×C3—41no—
677C2×C3—41no—
678C2×C3—41no—
679C2×C3—64no—
680C2×C3—64no—
681C2×C3—94no—
682C2×C3—124no—
683C2×C3#6430611yescharacteristic
684C2×C3D32×D411yescharacteristic
685C2×C3D32×Q811yescharacteristic
686C2×C3C2×C3×D3×D412yes—
687C2×C3C2×C3×D3×Q812yes—
688C2×C3C3×D3×#4112yes—
689D3—24no—
690D3—38no—
691D3—64no—
692C22—34no—
693C22—62no—
694C22—62no—
695C22—92no—
696C22—92no—
697C22—92no—
698C22—188no—
699C22C22×C3×D3211yescharacteristic
700C4—21no—
701C4—21no—
702C4—21no—
703C4—34no—
704C4—62no—
705C4—62no—
706C4—181no—
707C4—181no—
708C4—181no—
709C3—21no—
710C3—22no—
711C3—41no—
712C3#1059462411yescharacteristic, direct product factor
713C3C3×D3×C22⋊Q812yescomplemented
714C2—64no—
715C2—94no—
716C2C3×#6430611yescharacteristic
717C2C3×D32×D411yescharacteristic
718C2C3×D32×Q811yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC33×C4⋊C4C22
socleC22×C33C24
prime radicalC22×C3×D32C22
hypercenterC3×C4⋊C4D32
hypocenterC32C2×C3×C22⋊Q8
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#3797C2semidirect
3. C3×C4⋊C4×C3⋊D3C2semidirect
4. C32×#896C2semidirect
7. C3×#63893C2semidirect
8. C3×#63887C2semidirect
9. C3×#63883C2semidirect
10. C3×#63883C2semidirect
11. C3×#63851C2semidirect
13. #10594624C3direct (N × H)
19. C2×C32×Dic6C22semidirect
20. C2×C3×#627C22semidirect
27. C33×C4⋊C4C22semidirect
28. C3×C4⋊(C3⋊Dic3)C22semidirect
29. C3×#3750C22semidirect
30. C3×#3750C22semidirect
33. C32×Dic3⋊C4C22semidirect
34. C32×Dic3⋊C4C22semidirect
35. C3×Dic3⋊Dic3C22semidirect
36. C3×Dic3⋊Dic3C22semidirect
42. C2×#3797C2×C3semidirect
44. C4⋊C4×C3⋊D3C2×C3semidirect
50. C3×#896D3semidirect
51. C3×#896C2×C3semidirect
62. #63893C2×C3semidirect
63. #63887C2×C3semidirect
64. #63883C2×C3semidirect
65. #63883C2×C3semidirect
66. #63851C2×C3semidirect
71. C2×C3×D32Q8semidirect
119. C2×C3×Dic6C2×D3semidirect
120. C2×C3×Dic6C22×C3semidirect
121. C2×#627C22×C3semidirect
133. C32×C4⋊C4C2×D3semidirect
134. C32×C4⋊C4C22×C3semidirect
137. C4⋊(C3⋊Dic3)C22×C3semidirect
138. #3750C22×C3semidirect
139. #3750C22×C3semidirect
162. C3×Dic3⋊C4C2×D3semidirect
163. C3×Dic3⋊C4C2×D3semidirect
164. C3×Dic3⋊C4C22×C3semidirect
165. C3×Dic3⋊C4C22×C3semidirect
166. Dic3⋊Dic3C22×C3semidirect
167. Dic3⋊Dic3C22×C3semidirect
176. C2×C32×D3C2×Q8semidirect
206. #896C3×D3semidirect
227. C2×D32C3×Q8semidirect
297. C3×C3⋊D3C22⋊Q8semidirect
333. C2×Dic6C2×C3×D3semidirect
348. C3×C4⋊C4D32semidirect
349. C3×C4⋊C4C2×C3×D3semidirect
374. Dic3⋊C4C2×C3×D3semidirect
375. Dic3⋊C4C2×C3×D3semidirect
401. C2×C3×D3D3×Q8semidirect
402. C2×C3×D3C2×C3×Q8semidirect
451. C33C2×C22⋊Q8semidirect
546. C3⋊D3C3×C22⋊Q8semidirect
572. C4⋊C4C3×D32semidirect
604. C2×D3C3×D3×Q8semidirect
644. C32D3×C22⋊Q8semidirect
645. C32C2×C3×C22⋊Q8semidirect
712. C3#10594624direct (N × H)
713. C3C3×D3×C22⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×D322
C2×C3×#37972
C3×C4⋊C4×C3⋊D32
C32×#8962
C3×#639212
C3×#638932
C3×#638872
C3×#638832
C3×#638512
C3×D3×C22⋊Q83
#105946243