Finite Group Databasebeta

← C3×D3×#889 #13173947

Subgroups — C3×D3×#889 #13173947

Order 1728.

1134 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64098C211yesmaximal, characteristic, complemented
2C32×D3×C4⋊C4C211yesmaximal, characteristic
3C32×#889C211yesmaximal, characteristic, complemented
4C3×D3×C4⋊Dic3C211yesmaximal, characteristic
5C3×D3×Dic3⋊C4C211yesmaximal, characteristic
6C3×D3×Dic3⋊C4C211yesmaximal, characteristic
7C3×D3×Dic3⋊C4C211yesmaximal, characteristic
8C3×D3×Dic3⋊C4C211yesmaximal, characteristic
9C3×C4×D3×Dic3C211yesmaximal, characteristic
10C3×#63870C211yesmaximal, characteristic, complemented
11C3×#63867C211yesmaximal, characteristic, complemented
12C3×#63847C211yesmaximal, characteristic, complemented
13C3×#63847C211yesmaximal, characteristic, complemented
14C3×#63846C211yesmaximal, characteristic, complemented
15C3×#63845C211yesmaximal, characteristic, complemented
16C3×D3×#125—31nomaximal
17C2×C3×#889—31nomaximal
18D3×#889C311yesmaximal, characteristic, direct product factor
19C2×C32×C4×D3C2211yescharacteristic
20C2×C32×C4×D3C2211yescharacteristic
21C2×C32×C4×D3C2211yescharacteristic
22C2×C3×D3×Dic3C2211yescharacteristic
23C2×C3×D3×Dic3C2211yescharacteristic
24C2×C3×D3×Dic3C2211yescharacteristic
25C2×C3×D3×Dic3C2211yescharacteristic
26C33×C4⋊C4C2211yescharacteristic
27C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
28C3×#3750C2211yescharacteristic
29C3×#3750C2211yescharacteristic
30C3×#3750C2211yescharacteristic
31C3×#3750C2211yescharacteristic
32C3×C4×C3⋊Dic3C2211yescharacteristic
33C32×C4⋊Dic3C2211yescharacteristic
34C32×C4⋊Dic3C2211yescharacteristic
35C32×Dic3⋊C4C2211yescharacteristic
36C32×Dic3⋊C4C2211yescharacteristic
37C32×Dic3⋊C4C2211yescharacteristic
38C32×Dic3⋊C4C2211yescharacteristic
39C32×Dic3⋊C4C2211yescharacteristic
40C32×Dic3⋊C4C2211yescharacteristic
41C32×C4×Dic3C2211yescharacteristic
42C3×#3724C2211yescharacteristic
43C3×#3724C2211yescharacteristic
44C3×#3724C2211yescharacteristic
45C3×#3724C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×Dic3⋊Dic3C2211yescharacteristic
50C3×Dic3⋊Dic3C2211yescharacteristic
51C3×Dic3⋊Dic3C2211yescharacteristic
52C3×Dic32C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54C32×#125—31no—
55C2×C32×C4⋊C4—31no—
56#64098C2×C311yescharacteristic, complemented
57C2×C3×C4⋊Dic3—31no—
58C2×C3×Dic3⋊C4—31no—
59C2×C3×Dic3⋊C4—31no—
60C2×C3×Dic3⋊C4—31no—
61C2×C3×Dic3⋊C4—31no—
62C2×C3×C4×Dic3—31no—
63C3×D3×C4⋊C4—21no—
64C3×D3×C4⋊C4—31no—
65C3×D3×C4⋊C4—31no—
66C3×D3×C4⋊C4—31no—
67C3×D3×C4⋊C4—31no—
68C3×D3×C4⋊C4—31no—
69C3×D3×C4⋊C4D311yescharacteristic
70C3×D3×C4⋊C4C2×C311yescharacteristic
71C3×#890—31no—
72C3×#890—31no—
73C3×#889—21no—
74C3×#889—31no—
75C3×#889—31no—
76C3×#889—31no—
77C3×#889—31no—
78C3×#889—31no—
79C3×#889—31no—
80C3×#889—31no—
81C3×#889—31no—
82C3×#889—31no—
83C3×#889—31no—
84C3×#889—31no—
85C3×#889—61no—
86C3×#889D311yescharacteristic, direct product factor
87C3×#889C2×C311yescharacteristic, complemented
88C3×C42×D3—31no—
89C3×#870—31no—
90D3×C4⋊Dic3C2×C311yescharacteristic
91D3×Dic3⋊C4C2×C311yescharacteristic
92D3×Dic3⋊C4C2×C311yescharacteristic
93D3×Dic3⋊C4C2×C311yescharacteristic
94D3×Dic3⋊C4C2×C311yescharacteristic
95C4×D3×Dic3C2×C311yescharacteristic
96#63870C2×C311yescharacteristic, complemented
97#63867C2×C311yescharacteristic, complemented
98#63847C2×C311yescharacteristic, complemented
99#63847C2×C311yescharacteristic, complemented
100#63846C2×C311yescharacteristic, complemented
101#63845C2×C311yescharacteristic, complemented
102C22×C32×D3C2311yescharacteristic
103C2×C33×C4C2311yescharacteristic
104C2×C33×C4C2311yescharacteristic
105C2×C33×C4C2311yescharacteristic
106C2×C3×C3⋊Dic3C2311yescharacteristic
107C2×C3×C3⋊Dic3C2311yescharacteristic
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C32×Dic3C2311yescharacteristic
111C2×C32×Dic3C2311yescharacteristic
112C2×C32×Dic3C2311yescharacteristic
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C32×C4×D3—22no—
118C32×C4×D3—22no—
119C32×C4×D3—22no—
120C3×D3×Dic3—22no—
121C3×D3×Dic3—22no—
122C3×D3×Dic3—22no—
123C3×D3×Dic3Q814yes—
124C2×C3×#125—91no—
125D3×#125—31no—
126C2×#889—31no—
127C22×C32×C4—31no—
128C22×C32×C4—31no—
129C22×C32×C4—31no—
130C22×C3×Dic3—31no—
131C22×C3×Dic3—31no—
132C22×C3×Dic3—31no—
133C22×C3×Dic3—31no—
134C2×C3×C4×D3—21no—
135C2×C3×C4×D3—21no—
136C2×C3×C4×D3—21no—
137C2×C3×C4×D3—31no—
138C2×C3×C4×D3—31no—
139C2×C3×C4×D3—31no—
140C2×C3×C4×D3—31no—
141C2×C3×C4×D3C2×D311yescharacteristic
142C2×C3×C4×D3C2×D311yescharacteristic
143C2×C3×C4×D3C2×D311yescharacteristic
144C2×C3×C4×D3C22×C311yescharacteristic
145C2×C3×C4×D3C22×C311yescharacteristic
146C2×C3×C4×D3C22×C311yescharacteristic
147C2×D3×Dic3C22×C311yescharacteristic
148C2×D3×Dic3C22×C311yescharacteristic
149C2×D3×Dic3C22×C311yescharacteristic
150C2×D3×Dic3C22×C311yescharacteristic
151C32×C4⋊C4—21no—
152C32×C4⋊C4—21no—
153C32×C4⋊C4—21no—
154C32×C4⋊C4—31no—
155C32×C4⋊C4—31no—
156C32×C4⋊C4—31no—
157C32×C4⋊C4—31no—
158C32×C4⋊C4—31no—
159C32×C4⋊C4—31no—
160C32×C4⋊C4—31no—
161C32×C4⋊C4—31no—
162C32×C4⋊C4—41no—
163C32×C4⋊C4C2×D311yescharacteristic
164C32×C4⋊C4C2×D311yescharacteristic
165C32×C4⋊C4C22×C311yescharacteristic
166C32×C42—31no—
167C4⋊(C3⋊Dic3)C22×C311yescharacteristic
168#3750C22×C311yescharacteristic
169#3750C22×C311yescharacteristic
170#3750C22×C311yescharacteristic
171#3750C22×C311yescharacteristic
172C4×C3⋊Dic3C22×C311yescharacteristic
173C3×C4⋊Dic3—21no—
174C3×C4⋊Dic3—21no—
175C3×C4⋊Dic3—31no—
176C3×C4⋊Dic3—31no—
177C3×C4⋊Dic3—31no—
178C3×C4⋊Dic3—31no—
179C3×C4⋊Dic3—31no—
180C3×C4⋊Dic3—31no—
181C3×C4⋊Dic3—31no—
182C3×C4⋊Dic3—31no—
183C3×C4⋊Dic3—61no—
184C3×C4⋊Dic3C2×D311yescharacteristic
185C3×C4⋊Dic3C2×D311yescharacteristic
186C3×C4⋊Dic3C22×C311yescharacteristic
187C3×C4⋊Dic3C22×C311yescharacteristic
188C3×Dic3⋊C4—21no—
189C3×Dic3⋊C4—21no—
190C3×Dic3⋊C4—21no—
191C3×Dic3⋊C4—21no—
192C3×Dic3⋊C4—21no—
193C3×Dic3⋊C4—21no—
194C3×Dic3⋊C4—31no—
195C3×Dic3⋊C4—31no—
196C3×Dic3⋊C4—31no—
197C3×Dic3⋊C4—31no—
198C3×Dic3⋊C4—31no—
199C3×Dic3⋊C4—31no—
200C3×Dic3⋊C4—31no—
201C3×Dic3⋊C4—31no—
202C3×Dic3⋊C4—31no—
203C3×Dic3⋊C4—31no—
204C3×Dic3⋊C4—31no—
205C3×Dic3⋊C4—31no—
206C3×Dic3⋊C4—31no—
207C3×Dic3⋊C4—31no—
208C3×Dic3⋊C4—31no—
209C3×Dic3⋊C4—31no—
210C3×Dic3⋊C4—31no—
211C3×Dic3⋊C4—31no—
212C3×Dic3⋊C4—31no—
213C3×Dic3⋊C4—31no—
214C3×Dic3⋊C4—31no—
215C3×Dic3⋊C4—31no—
216C3×Dic3⋊C4—61no—
217C3×Dic3⋊C4—61no—
218C3×Dic3⋊C4—61no—
219C3×Dic3⋊C4—61no—
220C3×Dic3⋊C4C2×D311yescharacteristic
221C3×Dic3⋊C4C2×D311yescharacteristic
222C3×Dic3⋊C4C2×D311yescharacteristic
223C3×Dic3⋊C4C2×D311yescharacteristic
224C3×Dic3⋊C4C2×D311yescharacteristic
225C3×Dic3⋊C4C2×D311yescharacteristic
226C3×Dic3⋊C4C22×C311yescharacteristic
227C3×Dic3⋊C4C22×C311yescharacteristic
228C3×Dic3⋊C4C22×C311yescharacteristic
229C3×Dic3⋊C4C22×C311yescharacteristic
230C3×Dic3⋊C4C22×C311yescharacteristic
231C3×Dic3⋊C4C22×C311yescharacteristic
232C3×C4×Dic3—21no—
233C3×C4×Dic3—31no—
234C3×C4×Dic3—31no—
235C3×C4×Dic3—31no—
236C3×C4×Dic3—31no—
237C3×C4×Dic3—31no—
238C3×C4×Dic3—31no—
239C3×C4×Dic3—61no—
240C3×C4×Dic3C2×D311yescharacteristic
241C3×C4×Dic3C22×C311yescharacteristic
242#3724C22×C311yescharacteristic
243#3724C22×C311yescharacteristic
244#3724C22×C311yescharacteristic
245#3724C22×C311yescharacteristic
246Dic3⋊Dic3C22×C311yescharacteristic
247Dic3⋊Dic3C22×C311yescharacteristic
248Dic3⋊Dic3C22×C311yescharacteristic
249Dic3⋊Dic3C22×C311yescharacteristic
250Dic3⋊Dic3C22×C311yescharacteristic
251Dic3⋊Dic3C22×C311yescharacteristic
252Dic32C22×C311yescharacteristic
253Dic32C22×C311yescharacteristic
254C22×C33C2411yescharacteristic
255C2×C32×D3C2×Q812yes—
256C2×C32×D3#4112yes—
257C2×C32×D3#4112yes—
258C33×C4—21no—
259C33×C4—21no—
260C33×C4—21no—
261C3×C3⋊Dic3—21no—
262C3×C3⋊Dic3—21no—
263C3×C3⋊Dic3—21no—
264C3×C3⋊Dic3C2×Q812yes—
265C32×Dic3—21no—
266C32×Dic3—21no—
267C32×Dic3—21no—
268C32×Dic3—21no—
269C32×Dic3—21no—
270C32×Dic3—21no—
271C32×Dic3C2×Q812yes—
272C3×#125—31no—
273C3×#125—31no—
274C3×#125—61no—
275C3×#125—91no—
276C3×#125—91no—
277C3×#125—91no—
278C3×#125—91no—
279C3×#125—91no—
280C3×#125—91no—
281C3×#125—91no—
282C2×C3×C4⋊C4—31no—
283C2×C3×C4⋊C4—31no—
284C2×C3×C4⋊C4—61no—
285C2×C3×C4⋊C4—91no—
286C2×C3×C4⋊C4—91no—
287C2×C3×C4⋊C4—91no—
288C2×C3×C4⋊C4—91no—
289C2×C3×C4⋊C4—91no—
290C2×C3×C42—91no—
291C2×C4⋊Dic3—31no—
292C2×Dic3⋊C4—31no—
293C2×Dic3⋊C4—31no—
294C2×Dic3⋊C4—31no—
295C2×Dic3⋊C4—31no—
296C2×C4×Dic3—31no—
297D3×C4⋊C4—31no—
298D3×C4⋊C4—31no—
299D3×C4⋊C4—31no—
300D3×C4⋊C4—31no—
301D3×C4⋊C4—31no—
302D3×C4⋊C4C3×D311yescharacteristic
303#890—31no—
304#890—31no—
305#889—31no—
306#889—31no—
307#889—31no—
308#889—31no—
309#889—31no—
310#889—31no—
311#889—31no—
312#889—31no—
313#889—31no—
314#889—31no—
315#889—31no—
316#889—61no—
317#889C3×D311yescharacteristic, direct product factor
318C42×D3—31no—
319#870—31no—
320C23×C32—31no—
321C22×C3×D3—21no—
322C22×C3×D3C22×D311yescharacteristic
323C22×C3×D3C23×C311yescharacteristic
324C2×C32×C4—21no—
325C2×C32×C4—21no—
326C2×C32×C4—21no—
327C2×C32×C4—21no—
328C2×C32×C4—21no—
329C2×C32×C4—21no—
330C2×C32×C4—21no—
331C2×C32×C4—21no—
332C2×C32×C4—21no—
333C2×C32×C4—31no—
334C2×C32×C4—31no—
335C2×C32×C4—31no—
336C2×C32×C4—31no—
337C2×C32×C4—31no—
338C2×C32×C4—31no—
339C2×C32×C4—31no—
340C2×C32×C4—41no—
341C2×C32×C4—41no—
342C2×C32×C4—41no—
343C2×C32×C4—62no—
344C2×C32×C4—62no—
345C2×C32×C4—62no—
346C2×C32×C4C22×D311yescharacteristic
347C2×C32×C4C22×D311yescharacteristic
348C2×C32×C4C22×D311yescharacteristic
349C2×C32×C4C22×D311yescharacteristic
350C2×C32×C4C22×D311yescharacteristic
351C2×C32×C4C22×D311yescharacteristic
352C2×C32×C4C23×C311yescharacteristic
353C2×C32×C4C23×C311yescharacteristic
354C2×C32×C4C23×C311yescharacteristic
355C2×C3⋊Dic3C23×C311yescharacteristic
356C2×C3⋊Dic3C23×C311yescharacteristic
357C2×C3⋊Dic3C23×C311yescharacteristic
358C2×C3⋊Dic3C23×C311yescharacteristic
359C2×C3×Dic3—21no—
360C2×C3×Dic3—21no—
361C2×C3×Dic3—21no—
362C2×C3×Dic3—21no—
363C2×C3×Dic3—21no—
364C2×C3×Dic3—21no—
365C2×C3×Dic3—21no—
366C2×C3×Dic3—31no—
367C2×C3×Dic3—31no—
368C2×C3×Dic3—34no—
369C2×C3×Dic3—31no—
370C2×C3×Dic3—31no—
371C2×C3×Dic3—31no—
372C2×C3×Dic3—31no—
373C2×C3×Dic3—31no—
374C2×C3×Dic3—31no—
375C2×C3×Dic3—61no—
376C2×C3×Dic3—61no—
377C2×C3×Dic3—61no—
378C2×C3×Dic3—61no—
379C2×C3×Dic3—62no—
380C2×C3×Dic3—62no—
381C2×C3×Dic3—62no—
382C2×C3×Dic3C22×D311yescharacteristic
383C2×C3×Dic3C22×D311yescharacteristic
384C2×C3×Dic3C22×D311yescharacteristic
385C2×C3×Dic3C22×D311yescharacteristic
386C2×C3×Dic3C22×D311yescharacteristic
387C2×C3×Dic3C22×D311yescharacteristic
388C2×C3×Dic3C22×D311yescharacteristic
389C2×C3×Dic3C23×C311yescharacteristic
390C2×C3×Dic3C23×C311yescharacteristic
391C2×C3×Dic3C23×C311yescharacteristic
392C2×C3×Dic3C23×C311yescharacteristic
393C2×C3×Dic3C23×C311yescharacteristic
394C2×C3×Dic3C23×C311yescharacteristic
395C2×C3×Dic3C23×C311yescharacteristic
396C3×C4×D3—24no—
397C3×C4×D3—22no—
398C3×C4×D3—22no—
399C3×C4×D3—22no—
400C3×C4×D3—22no—
401C3×C4×D3—22no—
402C3×C4×D3—22no—
403C3×C4×D3—34no—
404C3×C4×D3—42no—
405C3×C4×D3—42no—
406C3×C4×D3—62no—
407C3×C4×D3—62no—
408C3×C4×D3—62no—
409D3×Dic3—22no—
410D3×Dic3—22no—
411D3×Dic3—22no—
412D3×Dic3C3×Q814yes—
413C2×#125—91noSylow
414C2×C33C22×Q811yescharacteristic
415C2×C33C2×#4111yescharacteristic
416C2×C33C2×#4111yescharacteristic
417C32×D3#12514yescomplemented
418C22×C3×C4—31no—
419C22×C3×C4—31no—
420C22×C3×C4—31no—
421C22×C3×C4—31no—
422C22×C3×C4—31no—
423C22×C3×C4—31no—
424C22×C3×C4—61no—
425C22×C3×C4—61no—
426C22×C3×C4—61no—
427C22×C3×C4—91no—
428C22×C3×C4—91no—
429C22×C3×C4—91no—
430C22×C3×C4—91no—
431C22×Dic3—31no—
432C22×Dic3—31no—
433C22×Dic3—31no—
434C22×Dic3—31no—
435C2×C4×D3—31no—
436C2×C4×D3—31no—
437C2×C4×D3—31no—
438C2×C4×D3—31no—
439C2×C4×D3C2×C3×D311yescharacteristic
440C2×C4×D3C2×C3×D311yescharacteristic
441C2×C4×D3C2×C3×D311yescharacteristic
442C3×C4⋊C4—21no—
443C3×C4⋊C4—21no—
444C3×C4⋊C4—21no—
445C3×C4⋊C4—31no—
446C3×C4⋊C4—31no—
447C3×C4⋊C4—31no—
448C3×C4⋊C4—31no—
449C3×C4⋊C4—31no—
450C3×C4⋊C4—31no—
451C3×C4⋊C4—31no—
452C3×C4⋊C4—31no—
453C3×C4⋊C4—31no—
454C3×C4⋊C4—31no—
455C3×C4⋊C4—31no—
456C3×C4⋊C4—31no—
457C3×C4⋊C4—31no—
458C3×C4⋊C4—31no—
459C3×C4⋊C4—31no—
460C3×C4⋊C4—31no—
461C3×C4⋊C4—41no—
462C3×C4⋊C4—61no—
463C3×C4⋊C4—61no—
464C3×C4⋊C4—61no—
465C3×C4⋊C4—61no—
466C3×C4⋊C4—61no—
467C3×C4⋊C4—61no—
468C3×C4⋊C4—61no—
469C3×C4⋊C4—61no—
470C3×C4⋊C4—91no—
471C3×C4⋊C4—91no—
472C3×C4⋊C4—91no—
473C3×C4⋊C4—91no—
474C3×C4⋊C4—91no—
475C3×C4⋊C4—91no—
476C3×C4⋊C4—91no—
477C3×C4⋊C4—91no—
478C3×C4⋊C4—91no—
479C3×C4⋊C4—91no—
480C3×C4⋊C4—91no—
481C3×C4⋊C4—91no—
482C3×C4⋊C4—91no—
483C3×C4⋊C4—91no—
484C3×C4⋊C4—91no—
485C3×C4⋊C4D3211yescharacteristic
486C3×C4⋊C4C2×C3×D311yescharacteristic
487C3×C4⋊C4C2×C3×D311yescharacteristic
488C3×C42—31no—
489C3×C42—31no—
490C3×C42—61no—
491C3×C42—91no—
492C3×C42—91no—
493C3×C42—91no—
494C4⋊Dic3—31no—
495C4⋊Dic3—31no—
496C4⋊Dic3—31no—
497C4⋊Dic3—31no—
498C4⋊Dic3—31no—
499C4⋊Dic3—31no—
500C4⋊Dic3—31no—
501C4⋊Dic3—31no—
502C4⋊Dic3—61no—
503C4⋊Dic3C2×C3×D311yescharacteristic
504C4⋊Dic3C2×C3×D311yescharacteristic
505Dic3⋊C4—31no—
506Dic3⋊C4—31no—
507Dic3⋊C4—31no—
508Dic3⋊C4—31no—
509Dic3⋊C4—31no—
510Dic3⋊C4—31no—
511Dic3⋊C4—31no—
512Dic3⋊C4—31no—
513Dic3⋊C4—31no—
514Dic3⋊C4—31no—
515Dic3⋊C4—31no—
516Dic3⋊C4—31no—
517Dic3⋊C4—31no—
518Dic3⋊C4—31no—
519Dic3⋊C4—31no—
520Dic3⋊C4—31no—
521Dic3⋊C4—31no—
522Dic3⋊C4—31no—
523Dic3⋊C4—31no—
524Dic3⋊C4—31no—
525Dic3⋊C4—31no—
526Dic3⋊C4—31no—
527Dic3⋊C4—61no—
528Dic3⋊C4—61no—
529Dic3⋊C4—61no—
530Dic3⋊C4—61no—
531Dic3⋊C4C2×C3×D311yescharacteristic
532Dic3⋊C4C2×C3×D311yescharacteristic
533Dic3⋊C4C2×C3×D311yescharacteristic
534Dic3⋊C4C2×C3×D311yescharacteristic
535Dic3⋊C4C2×C3×D311yescharacteristic
536Dic3⋊C4C2×C3×D311yescharacteristic
537C4×Dic3—31no—
538C4×Dic3—31no—
539C4×Dic3—31no—
540C4×Dic3—31no—
541C4×Dic3—31no—
542C4×Dic3—31no—
543C4×Dic3—61no—
544C4×Dic3C2×C3×D311yescharacteristic
545C22×C32—21no—
546C22×C32—21no—
547C22×C32—21no—
548C22×C32—32no—
549C22×C32—32no—
550C22×C32—32no—
551C22×C32—41no—
552C22×C32C23×D311yescharacteristic
553C22×C32C23×D311yescharacteristic
554C22×C32C24×C311yescharacteristic
555C2×C3×D3—22no—
556C2×C3×D3—22no—
557C2×C3×D3—22no—
558C2×C3×D3#23512yes—
559C2×C3×D3#23712yes—
560C2×C3×D3D3×Q812yes—
561C2×C3×D3C2×C3×Q812yes—
562C2×C3×D3C3×#4112yes—
563C2×C3×D3C3×#4112yes—
564C32×C4—21no—
565C32×C4—22no—
566C32×C4—21no—
567C32×C4—21no—
568C32×C4—21no—
569C32×C4—21no—
570C32×C4—21no—
571C32×C4—21no—
572C32×C4—21no—
573C32×C4—21no—
574C32×C4—32no—
575C32×C4—41no—
576C32×C4—41no—
577C32×C4—42no—
578C32×C4—41no—
579C32×C4—41no—
580C32×C4—41no—
581C32×C4—41no—
582C32×C4—41no—
583C32×C4—41no—
584C32×C4—61no—
585C32×C4—61no—
586C32×C4—61no—
587C32×C4—61no—
588C32×C4—61no—
589C32×C4—61no—
590C32×C4—81no—
591C32×C4—81no—
592C3⋊Dic3—21no—
593C3⋊Dic3—21no—
594C3⋊Dic3—21no—
595C3⋊Dic3C2×C3×Q812yes—
596C3×Dic3—22no—
597C3×Dic3—21no—
598C3×Dic3—21no—
599C3×Dic3—21no—
600C3×Dic3—21no—
601C3×Dic3—21no—
602C3×Dic3—21no—
603C3×Dic3—21no—
604C3×Dic3—21no—
605C3×Dic3—21no—
606C3×Dic3—21no—
607C3×Dic3—21no—
608C3×Dic3—21no—
609C3×Dic3—22no—
610C3×Dic3—32no—
611C3×Dic3—32no—
612C3×Dic3—41no—
613C3×Dic3—41no—
614C3×Dic3—41no—
615C3×Dic3—41no—
616C3×Dic3—41no—
617C3×Dic3—62no—
618C3×Dic3—61no—
619C3×Dic3—61no—
620C3×Dic3—61no—
621C3×Dic3—61no—
622C3×Dic3—61no—
623C3×Dic3—61no—
624C3×Dic3—121no—
625C3×Dic3—121no—
626C3×Dic3—121no—
627C3×Dic3D3×Q812yes—
628C3×Dic3C2×C3×Q812yes—
629#125—31no—
630#125—91no—
631#125—91no—
632#125—91no—
633#125—91no—
634#125—91no—
635#125—91no—
636#125—91no—
637C2×C4⋊C4—31no—
638C2×C4⋊C4—91no—
639C2×C4⋊C4—91no—
640C2×C4⋊C4—91no—
641C2×C4⋊C4—91no—
642C2×C4⋊C4—91no—
643C2×C42—91no—
644C33C2×#12511yescharacteristic, complemented, Sylow
645C23×C3—31no—
646C23×C3—31no—
647C23×C3—61no—
648C22×D3C22×C3×D311yescharacteristic
649C2×C3×C4—21no—
650C2×C3×C4—21no—
651C2×C3×C4—21no—
652C2×C3×C4—21no—
653C2×C3×C4—21no—
654C2×C3×C4—21no—
655C2×C3×C4—21no—
656C2×C3×C4—21no—
657C2×C3×C4—21no—
658C2×C3×C4—31no—
659C2×C3×C4—31no—
660C2×C3×C4—31no—
661C2×C3×C4—31no—
662C2×C3×C4—31no—
663C2×C3×C4—31no—
664C2×C3×C4—31no—
665C2×C3×C4—31no—
666C2×C3×C4—31no—
667C2×C3×C4—31no—
668C2×C3×C4—31no—
669C2×C3×C4—31no—
670C2×C3×C4—31no—
671C2×C3×C4—31no—
672C2×C3×C4—41no—
673C2×C3×C4—41no—
674C2×C3×C4—41no—
675C2×C3×C4—61no—
676C2×C3×C4—61no—
677C2×C3×C4—61no—
678C2×C3×C4—61no—
679C2×C3×C4—61no—
680C2×C3×C4—61no—
681C2×C3×C4—61no—
682C2×C3×C4—62no—
683C2×C3×C4—62no—
684C2×C3×C4—62no—
685C2×C3×C4—62no—
686C2×C3×C4—62no—
687C2×C3×C4—62no—
688C2×C3×C4—64no—
689C2×C3×C4—94no—
690C2×C3×C4—91no—
691C2×C3×C4—91no—
692C2×C3×C4—91no—
693C2×C3×C4—91no—
694C2×C3×C4—122no—
695C2×C3×C4—122no—
696C2×C3×C4—182no—
697C2×C3×C4—182no—
698C2×C3×C4—182no—
699C2×C3×C4C2×D3211yescharacteristic
700C2×C3×C4C2×D3211yescharacteristic
701C2×C3×C4C2×D3211yescharacteristic
702C2×C3×C4C22×C3×D311yescharacteristic
703C2×C3×C4C22×C3×D311yescharacteristic
704C2×C3×C4C22×C3×D311yescharacteristic
705C2×C3×C4C22×C3×D311yescharacteristic
706C2×C3×C4C22×C3×D311yescharacteristic
707C2×C3×C4C22×C3×D311yescharacteristic
708C2×Dic3—31no—
709C2×Dic3—31no—
710C2×Dic3—34no—
711C2×Dic3—31no—
712C2×Dic3—31no—
713C2×Dic3—31no—
714C2×Dic3—31no—
715C2×Dic3—31no—
716C2×Dic3—31no—
717C2×Dic3—61no—
718C2×Dic3—61no—
719C2×Dic3—61no—
720C2×Dic3—61no—
721C2×Dic3—62no—
722C2×Dic3—62no—
723C2×Dic3—62no—
724C2×Dic3C22×C3×D311yescharacteristic
725C2×Dic3C22×C3×D311yescharacteristic
726C2×Dic3C22×C3×D311yescharacteristic
727C2×Dic3C22×C3×D311yescharacteristic
728C2×Dic3C22×C3×D311yescharacteristic
729C2×Dic3C22×C3×D311yescharacteristic
730C2×Dic3C22×C3×D311yescharacteristic
731C4×D3—22no—
732C4×D3—22no—
733C4×D3—22no—
734C4×D3—34no—
735C4×D3—62no—
736C4×D3—62no—
737C4×D3—62no—
738C2×C32—21no—
739C2×C32—21no—
740C2×C32—21no—
741C2×C32—21no—
742C2×C32—21no—
743C2×C32—21no—
744C2×C32—21no—
745C2×C32—21no—
746C2×C32—21no—
747C2×C32—34no—
748C2×C32—41no—
749C2×C32—41no—
750C2×C32—41no—
751C2×C32C2×#23511yescharacteristic
752C2×C32C2×#23711yescharacteristic
753C2×C32C2×D3×Q811yescharacteristic
754C2×C32C2×D3×Q811yescharacteristic
755C2×C32D3×#4111yescharacteristic
756C2×C32D3×#4111yescharacteristic
757C2×C32C22×C3×Q811yescharacteristic
758C2×C32C2×C3×#4111yescharacteristic
759C2×C32C2×C3×#4111yescharacteristic
760C3×D3—24no—
761C3×D3#88914yesdirect product factor
762C3×D3C3×#12514yescomplemented
763C22×C4—31no—
764C22×C4—31no—
765C22×C4—31no—
766C22×C4—91no—
767C22×C4—91no—
768C22×C4—91no—
769C22×C4—91no—
770C4⋊C4—31no—
771C4⋊C4—31no—
772C4⋊C4—31no—
773C4⋊C4—31no—
774C4⋊C4—31no—
775C4⋊C4—31no—
776C4⋊C4—31no—
777C4⋊C4—31no—
778C4⋊C4—91no—
779C4⋊C4—91no—
780C4⋊C4—91no—
781C4⋊C4—91no—
782C4⋊C4—91no—
783C4⋊C4—91no—
784C4⋊C4—91no—
785C4⋊C4—91no—
786C4⋊C4—91no—
787C4⋊C4—91no—
788C4⋊C4—91no—
789C4⋊C4—91no—
790C4⋊C4—91no—
791C4⋊C4—91no—
792C4⋊C4—91no—
793C4⋊C4C3×D3211yescharacteristic
794C42—31no—
795C42—91no—
796C42—91no—
797C42—91no—
798C22×C3—21no—
799C22×C3—21no—
800C22×C3—21no—
801C22×C3—32no—
802C22×C3—32no—
803C22×C3—32no—
804C22×C3—32no—
805C22×C3—32no—
806C22×C3—32no—
807C22×C3—41no—
808C22×C3—62no—
809C22×C3—62no—
810C22×C3—62no—
811C22×C3C22×D3211yescharacteristic
812C22×C3C23×C3×D311yescharacteristic
813C22×C3C23×C3×D311yescharacteristic
814C2×D3C3×#23512yes—
815C2×D3C3×#23712yes—
816C2×D3C3×D3×Q812yes—
817C3×C4—22no—
818C3×C4—21no—
819C3×C4—21no—
820C3×C4—21no—
821C3×C4—21no—
822C3×C4—21no—
823C3×C4—21no—
824C3×C4—21no—
825C3×C4—21no—
826C3×C4—21no—
827C3×C4—32no—
828C3×C4—32no—
829C3×C4—41no—
830C3×C4—41no—
831C3×C4—41no—
832C3×C4—41no—
833C3×C4—41no—
834C3×C4—41no—
835C3×C4—41no—
836C3×C4—41no—
837C3×C4—42no—
838C3×C4—62no—
839C3×C4—62no—
840C3×C4—61no—
841C3×C4—61no—
842C3×C4—61no—
843C3×C4—61no—
844C3×C4—61no—
845C3×C4—61no—
846C3×C4—61no—
847C3×C4—61no—
848C3×C4—61no—
849C3×C4—61no—
850C3×C4—61no—
851C3×C4—61no—
852C3×C4—81no—
853C3×C4—81no—
854C3×C4—92no—
855C3×C4—121no—
856C3×C4—121no—
857C3×C4—121no—
858C3×C4—121no—
859C3×C4—121no—
860C3×C4—181no—
861C3×C4—181no—
862C3×C4—181no—
863Dic3—21no—
864Dic3—21no—
865Dic3—21no—
866Dic3—21no—
867Dic3—21no—
868Dic3—21no—
869Dic3—32no—
870Dic3—32no—
871Dic3—62no—
872Dic3—61no—
873Dic3—61no—
874Dic3—61no—
875Dic3—61no—
876Dic3—61no—
877Dic3—61no—
878Dic3—121no—
879Dic3—121no—
880Dic3—121no—
881Dic3C3×D3×Q812yes—
882C32—21no—
883C32—21no—
884C32—21no—
885C32—41no—
886C32C2×#88911yescharacteristic, complemented
887C32D3×#12511yescharacteristic, complemented
888C32C2×C3×#12511yescharacteristic, complemented
889C23—31no—
890C2×C4—31no—
891C2×C4—31no—
892C2×C4—31no—
893C2×C4—31no—
894C2×C4—31no—
895C2×C4—31no—
896C2×C4—31no—
897C2×C4—62no—
898C2×C4—62no—
899C2×C4—62no—
900C2×C4—94no—
901C2×C4—91no—
902C2×C4—91no—
903C2×C4—91no—
904C2×C4—91no—
905C2×C4—182no—
906C2×C4—182no—
907C2×C4—182no—
908C2×C4C2×C3×D3211yescharacteristic
909C2×C4C2×C3×D3211yescharacteristic
910C2×C4C2×C3×D3211yescharacteristic
911C2×C3—21no—
912C2×C3—21no—
913C2×C3—21no—
914C2×C3—21no—
915C2×C3—21no—
916C2×C3—21no—
917C2×C3—21no—
918C2×C3—21no—
919C2×C3—21no—
920C2×C3—34no—
921C2×C3—34no—
922C2×C3—41no—
923C2×C3—41no—
924C2×C3—41no—
925C2×C3—64no—
926C2×C3D3×#23511yescharacteristic
927C2×C3D3×#23711yescharacteristic
928C2×C3D32×Q811yescharacteristic
929C2×C3C2×C3×#23511yescharacteristic
930C2×C3C2×C3×#23711yescharacteristic
931C2×C3C2×C3×D3×Q811yescharacteristic
932C2×C3C2×C3×D3×Q811yescharacteristic
933C2×C3C3×D3×#4111yescharacteristic
934C2×C3C3×D3×#4111yescharacteristic
935D3C3×#88914yesdirect product factor
936C22—32no—
937C22—32no—
938C22—32no—
939C22C22×C3×D3211yescharacteristic
940C4—21no—
941C4—21no—
942C4—21no—
943C4—32no—
944C4—61no—
945C4—61no—
946C4—61no—
947C4—61no—
948C4—61no—
949C4—61no—
950C4—92no—
951C4—181no—
952C4—181no—
953C4—181no—
954C3—21no—
955C3—21no—
956C3—21no—
957C3—41no—
958C3D3×#88911yescharacteristic, direct product factor
959C3C2×C3×#88911yescharacteristic, complemented
960C3C3×D3×#12511yescharacteristic, complemented
961C2—34no—
962C2C3×D3×#23511yescharacteristic
963C2C3×D3×#23711yescharacteristic
964C2C3×D32×Q811yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC33×C4⋊C4C22
socleC22×C33C24
prime radicalC22×C32×D3C23
hypercenterC3×C4⋊C4D32
hypocenterC32C2×C3×#125
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×#64098C2semidirect
3. C32×#889C2semidirect
10. C3×#63870C2semidirect
11. C3×#63867C2semidirect
12. C3×#63847C2semidirect
13. C3×#63847C2semidirect
14. C3×#63846C2semidirect
15. C3×#63845C2semidirect
18. D3×#889C3direct (N × H)
56. #64098C2×C3semidirect
86. C3×#889D3direct (N × H)
87. C3×#889C2×C3semidirect
96. #63870C2×C3semidirect
97. #63867C2×C3semidirect
98. #63847C2×C3semidirect
99. #63847C2×C3semidirect
100. #63846C2×C3semidirect
101. #63845C2×C3semidirect
317. #889C3×D3direct (N × H)
417. C32×D3#125semidirect
644. C33C2×#125semidirect
761. C3×D3#889direct (N × H)
762. C3×D3C3×#125semidirect
886. C32C2×#889semidirect
887. C32D3×#125semidirect
888. C32C2×C3×#125semidirect
935. D3C3×#889direct (N × H)
958. C3D3×#889direct (N × H)
959. C3C2×C3×#889semidirect
960. C3C3×D3×#125semidirect

Maximal subgroups

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

subgroupindex
C3×#640982
C32×D3×C4⋊C42
C32×#8892
C3×D3×C4⋊Dic32
C3×D3×Dic3⋊C42
C3×C4×D3×Dic32
C3×#638702
C3×#638672
C3×#638472
C3×#638462
C3×#638452
C3×D3×#1253
C2×C3×#8893
D3×#8893