Finite Group Databasebeta

← C3×#10595088 #13174685

Subgroups — C3×#10595088 #13174685

Order 1728.

1312 conjugacy classes of subgroups.

The subgroup lattice has 1134 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×#638C211yesmaximal, characteristic, complemented
2C32×#929C211yesmaximal, characteristic, complemented
3C32×C4×#67C211yesmaximal, characteristic, complemented
4C3×#63983C211yesmaximal, characteristic
5C3×#63975C211yesmaximal, characteristic, complemented
6C3×#63969C211yesmaximal, characteristic, complemented
7C3×#63959C211yesmaximal, characteristic, complemented
8C3×#63921C211yesmaximal, characteristic, complemented
9C3×D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10C3×#63878C211yesmaximal, characteristic, complemented
11C3×#63865C211yesmaximal, characteristic, complemented
12C3×#63862C211yesmaximal, characteristic, complemented
13C3×#63859C211yesmaximal, characteristic, complemented
14C3×#63851C211yesmaximal, characteristic, complemented
15C3×#63836C211yesmaximal, characteristic, complemented
16C3×#5659—31nomaximal
17C3×#5556—31nomaximal
18#10595088C311yesmaximal, characteristic, direct product factor
19C22×C3×D32C2211yescharacteristic
20C22×C33×C4C2211yescharacteristic, complemented
21C2×C3×#638C2211yescharacteristic
22C2×C3×C4×C3⋊D3C2211yescharacteristic
23C2×C32×#67C2211yescharacteristic
24C2×C32×#67C2211yescharacteristic
25C2×C32×C4×D3C2211yescharacteristic
26C2×C3×#627C2211yescharacteristic, complemented
27C2×C3×#624C2211yescharacteristic
28C2×C3×D3×Dic3C2211yescharacteristic
29C3×#3757C2211yescharacteristic, complemented
30C3×#3752C2211yescharacteristic
31C3×#3750C2211yescharacteristic, complemented
32C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
33C32×#217C2211yescharacteristic, complemented
34C32×#217C2211yescharacteristic, complemented
35C32×(C2×D3)⋊C4C2211yescharacteristic
36C32×(C2×D3)⋊C4C2211yescharacteristic
37C32×(C2×D3)⋊C4C2211yescharacteristic
38C32×Dic3⋊C4C2211yescharacteristic, complemented
39C32×Dic3⋊C4C2211yescharacteristic, complemented
40C32×Dic3⋊C4C2211yescharacteristic, complemented
41C32×C4×Dic3C2211yescharacteristic, complemented
42C3×#3724C2211yescharacteristic, complemented
43C3×Dic3⋊Dic3C2211yescharacteristic, complemented
44C3×Dic3⋊Dic3C2211yescharacteristic, complemented
45C3×Dic3⋊Dic3C2211yescharacteristic, complemented
46C3×#3722C2211yescharacteristic
47C3×#3722C2211yescharacteristic
48C3×(C2×D3)⋊Dic3C2211yescharacteristic
49C3×(C2×D3)⋊Dic3C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×Dic32C2211yescharacteristic, complemented
54C32×#123—31no—
55C32×C4×D4—31no—
56C4×#638C2×C311yescharacteristic, complemented
57C3×#937—31no—
58C3×#937—31no—
59C3×#936—31no—
60C3×#935—31no—
61C3×#929—21no—
62C3×#929D311yescharacteristic, complemented
63C3×#929C2×C311yescharacteristic, complemented
64C3×C4×#67—21no—
65C3×C4×#67—31no—
66C3×C4×#67—31no—
67C3×C4×#67—61no—
68C3×C4×#67D311yescharacteristic, complemented
69C3×C4×#67C2×C311yescharacteristic, complemented
70C2×C3×(C2×D3)⋊C4—31no—
71C3×#924—31no—
72C3×#898—31no—
73C3×#896—31no—
74C3×#896—31no—
75C3×#896—31no—
76C3×#892—31no—
77C3×#892—31no—
78C3×#885—31no—
79C3×#883—31no—
80C3×#883—31no—
81C3×#883—31no—
82C3×D3×C22⋊C4—31no—
83C3×D3×C22⋊C4—31no—
84C3×D3×C22⋊C4—31no—
85C3×#879—31no—
86C3×#879—31no—
87C3×#877—31no—
88C3×#876—31no—
89C3×#872—31no—
90#63983C2×C311yescharacteristic
91#63975C2×C311yescharacteristic, complemented
92#63969C2×C311yescharacteristic, complemented
93#63959C2×C311yescharacteristic, complemented
94#63921C2×C311yescharacteristic, complemented
95D3×(C2×D3)⋊C4C2×C311yescharacteristic, complemented
96#63878C2×C311yescharacteristic, complemented
97#63865C2×C311yescharacteristic, complemented
98#63862C2×C311yescharacteristic, complemented
99#63859C2×C311yescharacteristic, complemented
100#63851C2×C311yescharacteristic, complemented
101#63836C2×C311yescharacteristic, complemented
102C23×C33C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C32×D3C2311yescharacteristic
105C22×C32×D3C2311yescharacteristic
106C2×C3×D32—22no—
107C2×C3×D32—22no—
108C2×C3×D32—41no—
109C2×C33×C4—41no—
110C2×C33×C4C2311yescharacteristic
111C2×C33×C4C2311yescharacteristic
112C3×#638—22no—
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C3×C4×C3⋊D3—41no—
117C32×#67—22no—
118C32×#67—41no—
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123C2×C32×Dic3C2311yescharacteristic
124C2×C32×Dic3C2311yescharacteristic
125C32×C4×D3—41no—
126C3×#627—41no—
127C3×#624—22no—
128C3×D3×Dic3—22no—
129C3×#551—91no—
130#5659—31no—
131#5556—31no—
132C23×C3×D3—31no—
133C23×C3×D3—31no—
134C22×D32C22×C311yescharacteristic
135C2×C32×D4—31no—
136C2×C32×D4—31no—
137C22×C32×C4—21no—
138C22×C32×C4—21no—
139C22×C32×C4—21no—
140C22×C32×C4—31no—
141C22×C32×C4—41no—
142C22×C32×C4C2×D311yescharacteristic, complemented
143C22×C32×C4C2×D311yescharacteristic, complemented
144C22×C32×C4C22×C311yescharacteristic, complemented
145C2×#638C22×C311yescharacteristic
146C2×C4×C3⋊D3C22×C311yescharacteristic
147C2×C3×#67—21no—
148C2×C3×#67—21no—
149C2×C3×#67—31no—
150C2×C3×#67—31no—
151C2×C3×#67—61no—
152C2×C3×#67C2×D311yescharacteristic
153C2×C3×#67C2×D311yescharacteristic
154C2×C3×#67C22×C311yescharacteristic
155C2×C3×#67C22×C311yescharacteristic
156C22×C3×Dic3—31no—
157C2×C3×C4×D3—21no—
158C2×C3×C4×D3—31no—
159C2×C3×C4×D3—31no—
160C2×C3×C4×D3—31no—
161C2×C3×C4×D3—31no—
162C2×C3×C4×D3—31no—
163C2×C3×C4×D3—61no—
164C2×C3×C4×D3C2×D311yescharacteristic
165C2×C3×C4×D3C22×C311yescharacteristic
166C2×C3×Dic6—31no—
167C2×C3×Dic6—31no—
168C2×#627C22×C311yescharacteristic, complemented
169C2×#624C22×C311yescharacteristic
170C2×D3×Dic3C22×C311yescharacteristic
171C32×C4⋊C4—31no—
172C32×C4⋊C4—31no—
173C32×C4⋊C4—31no—
174C32×C22⋊C4—31no—
175C32×C22⋊C4—31no—
176C32×C22⋊C4—31no—
177C32×C22⋊C4—31no—
178C32×C22⋊C4—31no—
179C32×C42—31no—
180#3757C22×C311yescharacteristic, complemented
181#3752C22×C311yescharacteristic
182#3750C22×C311yescharacteristic, complemented
183C4×C3⋊Dic3C22×C311yescharacteristic, complemented
184C3×#217—21no—
185C3×#217—21no—
186C3×#217—31no—
187C3×#217—31no—
188C3×#217—31no—
189C3×#217—31no—
190C3×#217—31no—
191C3×#217—31no—
192C3×#217—31no—
193C3×#217—61no—
194C3×#217C2×D311yescharacteristic, complemented
195C3×#217C2×D311yescharacteristic, complemented
196C3×#217C22×C311yescharacteristic, complemented
197C3×#217C22×C311yescharacteristic, complemented
198C3×(C2×D3)⋊C4—21no—
199C3×(C2×D3)⋊C4—21no—
200C3×(C2×D3)⋊C4—21no—
201C3×(C2×D3)⋊C4—31no—
202C3×(C2×D3)⋊C4—31no—
203C3×(C2×D3)⋊C4—31no—
204C3×(C2×D3)⋊C4—31no—
205C3×(C2×D3)⋊C4—31no—
206C3×(C2×D3)⋊C4—31no—
207C3×(C2×D3)⋊C4—31no—
208C3×(C2×D3)⋊C4—31no—
209C3×(C2×D3)⋊C4—31no—
210C3×(C2×D3)⋊C4—31no—
211C3×(C2×D3)⋊C4—31no—
212C3×(C2×D3)⋊C4—61no—
213C3×(C2×D3)⋊C4C2×D311yescharacteristic
214C3×(C2×D3)⋊C4C2×D311yescharacteristic
215C3×(C2×D3)⋊C4C2×D311yescharacteristic
216C3×(C2×D3)⋊C4C22×C311yescharacteristic
217C3×(C2×D3)⋊C4C22×C311yescharacteristic
218C3×(C2×D3)⋊C4C22×C311yescharacteristic
219C3×C4⋊Dic3—31no—
220C3×C4⋊Dic3—31no—
221C3×C4⋊Dic3—31no—
222C3×Dic3⋊C4—21no—
223C3×Dic3⋊C4—21no—
224C3×Dic3⋊C4—21no—
225C3×Dic3⋊C4—31no—
226C3×Dic3⋊C4—31no—
227C3×Dic3⋊C4—31no—
228C3×Dic3⋊C4—31no—
229C3×Dic3⋊C4—31no—
230C3×Dic3⋊C4—31no—
231C3×Dic3⋊C4—31no—
232C3×Dic3⋊C4—61no—
233C3×Dic3⋊C4C2×D311yescharacteristic, complemented
234C3×Dic3⋊C4C2×D311yescharacteristic, complemented
235C3×Dic3⋊C4C2×D311yescharacteristic, complemented
236C3×Dic3⋊C4C22×C311yescharacteristic, complemented
237C3×Dic3⋊C4C22×C311yescharacteristic, complemented
238C3×Dic3⋊C4C22×C311yescharacteristic, complemented
239C3×C4×Dic3—21no—
240C3×C4×Dic3—31no—
241C3×C4×Dic3—31no—
242C3×C4×Dic3—31no—
243C3×C4×Dic3—31no—
244C3×C4×Dic3—61no—
245C3×C4×Dic3C2×D311yescharacteristic, complemented
246C3×C4×Dic3C22×C311yescharacteristic, complemented
247#3724C22×C311yescharacteristic, complemented
248Dic3⋊Dic3C22×C311yescharacteristic, complemented
249Dic3⋊Dic3C22×C311yescharacteristic, complemented
250Dic3⋊Dic3C22×C311yescharacteristic, complemented
251#3722C22×C311yescharacteristic
252#3722C22×C311yescharacteristic
253(C2×D3)⋊Dic3C22×C311yescharacteristic
254(C2×D3)⋊Dic3C22×C311yescharacteristic
255(C2×D3)⋊Dic3C22×C311yescharacteristic
256(C2×D3)⋊Dic3C22×C311yescharacteristic
257(C2×D3)⋊Dic3C22×C311yescharacteristic
258Dic32C22×C311yescharacteristic, complemented
259C22×C33—21no—
260C22×C33—21no—
261C22×C33—21no—
262C22×C33C2411yescharacteristic
263C2×C3×C3⋊D3—21no—
264C2×C3×C3⋊D3—21no—
265C2×C3×C3⋊D3#4112yes—
266C2×C32×D3—21no—
267C2×C32×D3—21no—
268C2×C32×D3—21no—
269C2×C32×D3—21no—
270C2×C32×D3—21no—
271C2×C32×D3#4112yes—
272C3×D32—44no—
273C33×C4—21no—
274C33×C4—21no—
275C3×C3⋊Dic3—21no—
276C3×C3⋊Dic3—21no—
277C3×C3⋊Dic3—21no—
278C32×Dic3—21no—
279C32×Dic3—21no—
280C32×Dic3—21no—
281C32×Dic3—21no—
282C32×Dic3—21no—
283C32×Dic3—21no—
284C3×#126—91no—
285C3×#126—91no—
286C3×#124—91no—
287C3×#123—31no—
288C3×#123—31no—
289C3×#123—61no—
290C3×#123—91no—
291C3×#123—91no—
292C3×C22⋊Q8—91no—
293C3×C22⋊Q8—91no—
294C3×#120—91no—
295C3×C4×D4—31no—
296C3×C4×D4—31no—
297C3×C4×D4—61no—
298C3×C4×D4—91no—
299C3×#117—91no—
300C3×#117—91no—
301C2×C3×C22⋊C4—91no—
302C2×C3×C22⋊C4—91no—
303#937—31no—
304#937—31no—
305#936—31no—
306#935—31no—
307#929C3×D311yescharacteristic, complemented
308C4×#67—31no—
309C4×#67—31no—
310C4×#67—61no—
311C4×#67C3×D311yescharacteristic, complemented
312C2×(C2×D3)⋊C4—31no—
313#924—31no—
314#898—31no—
315#896—31no—
316#896—31no—
317#896—31no—
318#892—31no—
319#892—31no—
320#885—31no—
321#883—31no—
322#883—31no—
323#883—31no—
324D3×C22⋊C4—31no—
325D3×C22⋊C4—31no—
326D3×C22⋊C4—31no—
327#879—31no—
328#879—31no—
329#877—31no—
330#876—31no—
331#872—31no—
332C23×C32—21no—
333C23×C32—21no—
334C23×C32—21no—
335C23×C32—31no—
336C23×C32—31no—
337C23×C32—41no—
338C23×C32C22×D311yescharacteristic
339C23×C32C22×D311yescharacteristic
340C23×C32C23×C311yescharacteristic
341C22×C3⋊D3C23×C311yescharacteristic
342C22×C3×D3—21no—
343C22×C3×D3—21no—
344C22×C3×D3—31no—
345C22×C3×D3—31no—
346C22×C3×D3—61no—
347C22×C3×D3—62no—
348C22×C3×D3—62no—
349C22×C3×D3—62no—
350C22×C3×D3—62no—
351C22×C3×D3—121no—
352C22×C3×D3—121no—
353C22×C3×D3C22×D311yescharacteristic
354C22×C3×D3C22×D311yescharacteristic
355C22×C3×D3C23×C311yescharacteristic
356C22×C3×D3C23×C311yescharacteristic
357C2×D32—22no—
358C2×D32—22no—
359C2×D32—41no—
360C32×D4—62no—
361C32×D4—121no—
362C2×C32×C4—21no—
363C2×C32×C4—21no—
364C2×C32×C4—21no—
365C2×C32×C4—21no—
366C2×C32×C4—21no—
367C2×C32×C4—21no—
368C2×C32×C4—31no—
369C2×C32×C4—31no—
370C2×C32×C4—31no—
371C2×C32×C4—31no—
372C2×C32×C4—31no—
373C2×C32×C4—31no—
374C2×C32×C4—41no—
375C2×C32×C4—41no—
376C2×C32×C4—41no—
377C2×C32×C4—41no—
378C2×C32×C4—41no—
379C2×C32×C4—42no—
380C2×C32×C4—42no—
381C2×C32×C4—42no—
382C2×C32×C4—44no—
383C2×C32×C4—121no—
384C2×C32×C4C22×D311yescharacteristic
385C2×C32×C4C22×D311yescharacteristic
386C2×C32×C4C22×D311yescharacteristic
387C2×C32×C4C22×D311yescharacteristic
388C2×C32×C4C23×C311yescharacteristic
389C2×C32×C4C23×C311yescharacteristic
390#638—22no—
391C2×C3⋊Dic3C23×C311yescharacteristic
392C2×C3⋊Dic3C23×C311yescharacteristic
393C2×C3⋊Dic3C23×C311yescharacteristic
394C4×C3⋊D3—41no—
395C3×#67—24no—
396C3×#67—22no—
397C3×#67—22no—
398C3×#67—41no—
399C3×#67—41no—
400C3×#67—42no—
401C3×#67—62no—
402C3×#67—62no—
403C3×#67—64no—
404C2×C3×Dic3—21no—
405C2×C3×Dic3—21no—
406C2×C3×Dic3—21no—
407C2×C3×Dic3—21no—
408C2×C3×Dic3—21no—
409C2×C3×Dic3—21no—
410C2×C3×Dic3—31no—
411C2×C3×Dic3—31no—
412C2×C3×Dic3—31no—
413C2×C3×Dic3—31no—
414C2×C3×Dic3—31no—
415C2×C3×Dic3—31no—
416C2×C3×Dic3—61no—
417C2×C3×Dic3—61no—
418C2×C3×Dic3—61no—
419C2×C3×Dic3—62no—
420C2×C3×Dic3C22×D311yescharacteristic
421C2×C3×Dic3C22×D311yescharacteristic
422C2×C3×Dic3C22×D311yescharacteristic
423C2×C3×Dic3C22×D311yescharacteristic
424C2×C3×Dic3C22×D311yescharacteristic
425C2×C3×Dic3C22×D311yescharacteristic
426C2×C3×Dic3C23×C311yescharacteristic
427C2×C3×Dic3C23×C311yescharacteristic
428C2×C3×Dic3C23×C311yescharacteristic
429C2×C3×Dic3C23×C311yescharacteristic
430C2×C3×Dic3C23×C311yescharacteristic
431C2×C3×Dic3C23×C311yescharacteristic
432C3×C4×D3—41no—
433C3×C4×D3—41no—
434C3×C4×D3—42no—
435C3×C4×D3—62no—
436C3×C4×D3—62no—
437C3×C4×D3—62no—
438C3×C4×D3—121no—
439C3×C4×D3—121no—
440C3×C4×D3—122no—
441C3×Dic6—121no—
442C3×Dic6—121no—
443#627—41no—
444#624—22no—
445D3×Dic3—22no—
446#551—91noSylow
447C2×C33—41no—
448C2×C33C2×#4111yescharacteristic
449C2×C33C2×#4111yescharacteristic
450C2×C33H(5,𝔽2)11yescharacteristic
451C3×C3⋊D3—22no—
452C32×D3—22no—
453C32×D3—41no—
454C24×C3—91no—
455C23×D3—31no—
456C23×D3—31no—
457C2×C3×Q8—91no—
458C2×C3×D4—31no—
459C2×C3×D4—31no—
460C2×C3×D4—31no—
461C2×C3×D4—31no—
462C2×C3×D4—61no—
463C2×C3×D4—61no—
464C2×C3×D4—91no—
465C22×C3×C4—21no—
466C22×C3×C4—21no—
467C22×C3×C4—21no—
468C22×C3×C4—31no—
469C22×C3×C4—31no—
470C22×C3×C4—41no—
471C22×C3×C4—61no—
472C22×C3×C4—91no—
473C22×C3×C4—91no—
474C22×C3×C4—91no—
475C22×C3×C4D3211yescharacteristic, complemented
476C22×C3×C4C2×C3×D311yescharacteristic, complemented
477C22×C3×C4C2×C3×D311yescharacteristic, complemented
478C2×#67—31no—
479C2×#67—31no—
480C2×#67—61no—
481C2×#67C2×C3×D311yescharacteristic
482C2×#67C2×C3×D311yescharacteristic
483C22×Dic3—31no—
484C2×C4×D3—31no—
485C2×C4×D3—31no—
486C2×C4×D3—31no—
487C2×C4×D3—31no—
488C2×C4×D3—31no—
489C2×C4×D3—61no—
490C2×C4×D3C2×C3×D311yescharacteristic
491C2×Dic6—31no—
492C2×Dic6—31no—
493C3×C4⋊C4—31no—
494C3×C4⋊C4—31no—
495C3×C4⋊C4—31no—
496C3×C4⋊C4—31no—
497C3×C4⋊C4—31no—
498C3×C4⋊C4—31no—
499C3×C4⋊C4—61no—
500C3×C4⋊C4—61no—
501C3×C4⋊C4—61no—
502C3×C4⋊C4—91no—
503C3×C4⋊C4—91no—
504C3×C4⋊C4—91no—
505C3×C4⋊C4—91no—
506C3×C4⋊C4—91no—
507C3×C22⋊C4—31no—
508C3×C22⋊C4—31no—
509C3×C22⋊C4—31no—
510C3×C22⋊C4—31no—
511C3×C22⋊C4—31no—
512C3×C22⋊C4—31no—
513C3×C22⋊C4—31no—
514C3×C22⋊C4—31no—
515C3×C22⋊C4—31no—
516C3×C22⋊C4—31no—
517C3×C22⋊C4—61no—
518C3×C22⋊C4—61no—
519C3×C22⋊C4—61no—
520C3×C22⋊C4—61no—
521C3×C22⋊C4—61no—
522C3×C22⋊C4—91no—
523C3×C22⋊C4—91no—
524C3×C22⋊C4—91no—
525C3×C22⋊C4—91no—
526C3×C22⋊C4—91no—
527C3×C22⋊C4—91no—
528C3×C22⋊C4—91no—
529C3×C22⋊C4—91no—
530C3×C22⋊C4—91no—
531C3×C42—31no—
532C3×C42—31no—
533C3×C42—61no—
534C3×C42—91no—
535C3×C42—91no—
536#217—31no—
537#217—31no—
538#217—31no—
539#217—31no—
540#217—31no—
541#217—31no—
542#217—31no—
543#217—61no—
544#217C2×C3×D311yescharacteristic, complemented
545#217C2×C3×D311yescharacteristic, complemented
546(C2×D3)⋊C4—31no—
547(C2×D3)⋊C4—31no—
548(C2×D3)⋊C4—31no—
549(C2×D3)⋊C4—31no—
550(C2×D3)⋊C4—31no—
551(C2×D3)⋊C4—31no—
552(C2×D3)⋊C4—31no—
553(C2×D3)⋊C4—31no—
554(C2×D3)⋊C4—31no—
555(C2×D3)⋊C4—31no—
556(C2×D3)⋊C4—31no—
557(C2×D3)⋊C4—61no—
558(C2×D3)⋊C4C2×C3×D311yescharacteristic
559(C2×D3)⋊C4C2×C3×D311yescharacteristic
560(C2×D3)⋊C4C2×C3×D311yescharacteristic
561C4⋊Dic3—31no—
562C4⋊Dic3—31no—
563C4⋊Dic3—31no—
564Dic3⋊C4—31no—
565Dic3⋊C4—31no—
566Dic3⋊C4—31no—
567Dic3⋊C4—31no—
568Dic3⋊C4—31no—
569Dic3⋊C4—31no—
570Dic3⋊C4—31no—
571Dic3⋊C4—61no—
572Dic3⋊C4C2×C3×D311yescharacteristic, complemented
573Dic3⋊C4C2×C3×D311yescharacteristic, complemented
574Dic3⋊C4C2×C3×D311yescharacteristic, complemented
575C4×Dic3—31no—
576C4×Dic3—31no—
577C4×Dic3—31no—
578C4×Dic3—31no—
579C4×Dic3—61no—
580C4×Dic3C2×C3×D311yescharacteristic, complemented
581C22×C32—21no—
582C22×C32—21no—
583C22×C32—21no—
584C22×C32—22no—
585C22×C32—22no—
586C22×C32—22no—
587C22×C32—21no—
588C22×C32—21no—
589C22×C32—21no—
590C22×C32—21no—
591C22×C32—21no—
592C22×C32—21no—
593C22×C32—21no—
594C22×C32—21no—
595C22×C32—21no—
596C22×C32—32no—
597C22×C32—41no—
598C22×C32—41no—
599C22×C32—41no—
600C22×C32—41no—
601C22×C32—41no—
602C22×C32—41no—
603C22×C32—41no—
604C22×C32—42no—
605C22×C32—42no—
606C22×C32—42no—
607C22×C32—61no—
608C22×C32—61no—
609C22×C32—61no—
610C22×C32—61no—
611C22×C32—61no—
612C22×C32C23×D311yescharacteristic
613C22×C32C23×D311yescharacteristic
614C22×C32C24×C311yescharacteristic
615C2×C3⋊D3—21no—
616C2×C3⋊D3—21no—
617C2×C3⋊D3C3×#4112yes—
618C2×C3×D3—21no—
619C2×C3×D3—21no—
620C2×C3×D3—21no—
621C2×C3×D3—21no—
622C2×C3×D3—21no—
623C2×C3×D3—21no—
624C2×C3×D3—21no—
625C2×C3×D3—21no—
626C2×C3×D3—21no—
627C2×C3×D3—21no—
628C2×C3×D3—22no—
629C2×C3×D3—32no—
630C2×C3×D3—32no—
631C2×C3×D3—41no—
632C2×C3×D3—41no—
633C2×C3×D3—41no—
634C2×C3×D3—41no—
635C2×C3×D3—41no—
636C2×C3×D3—62no—
637C2×C3×D3—61no—
638C2×C3×D3—61no—
639C2×C3×D3—61no—
640C2×C3×D3—61no—
641C2×C3×D3—121no—
642C2×C3×D3—121no—
643C2×C3×D3—124no—
644C2×C3×D3—124no—
645C2×C3×D3#23512yes—
646C2×C3×D3C3×#4112yes—
647D32—44no—
648C32×C4—21no—
649C32×C4—21no—
650C32×C4—22no—
651C32×C4—22no—
652C32×C4—21no—
653C32×C4—21no—
654C32×C4—21no—
655C32×C4—21no—
656C32×C4—41no—
657C32×C4—41no—
658C32×C4—41no—
659C32×C4—41no—
660C32×C4—42no—
661C32×C4—42no—
662C32×C4—61no—
663C32×C4—61no—
664C32×C4—61no—
665C32×C4—61no—
666C32×C4—61no—
667C32×C4—61no—
668C3⋊Dic3—21no—
669C3⋊Dic3—21no—
670C3⋊Dic3—21no—
671C3×Dic3—22no—
672C3×Dic3—21no—
673C3×Dic3—21no—
674C3×Dic3—21no—
675C3×Dic3—21no—
676C3×Dic3—21no—
677C3×Dic3—21no—
678C3×Dic3—21no—
679C3×Dic3—21no—
680C3×Dic3—21no—
681C3×Dic3—21no—
682C3×Dic3—21no—
683C3×Dic3—21no—
684C3×Dic3—41no—
685C3×Dic3—41no—
686C3×Dic3—41no—
687C3×Dic3—41no—
688C3×Dic3—41no—
689C3×Dic3—62no—
690C3×Dic3—61no—
691C3×Dic3—61no—
692C3×Dic3—61no—
693C3×Dic3—61no—
694C3×Dic3—61no—
695C3×Dic3—61no—
696C3×Dic3—121no—
697C3×Dic3—121no—
698#126—91no—
699#126—91no—
700#124—91no—
701#123—31no—
702#123—91no—
703#123—91no—
704C22⋊Q8—91no—
705C22⋊Q8—91no—
706#120—91no—
707C4×D4—31no—
708C4×D4—91no—
709#117—91no—
710#117—91no—
711C2×C22⋊C4—91no—
712C2×C22⋊C4—91no—
713C33#55111yescharacteristic, complemented, Sylow
714C23×C3—21no—
715C23×C3—21no—
716C23×C3—21no—
717C23×C3—31no—
718C23×C3—31no—
719C23×C3—31no—
720C23×C3—31no—
721C23×C3—41no—
722C23×C3—61no—
723C23×C3—61no—
724C23×C3—91no—
725C23×C3—182no—
726C23×C3—182no—
727C23×C3—361no—
728C23×C3C2×D3211yescharacteristic
729C23×C3C22×C3×D311yescharacteristic
730C23×C3C22×C3×D311yescharacteristic
731C22×D3—31no—
732C22×D3—31no—
733C22×D3—61no—
734C22×D3—62no—
735C22×D3—62no—
736C22×D3—62no—
737C22×D3—62no—
738C22×D3—121no—
739C22×D3—121no—
740C22×D3C22×C3×D311yescharacteristic
741C22×D3C22×C3×D311yescharacteristic
742C3×Q8—361no—
743C3×D4—62no—
744C3×D4—62no—
745C3×D4—64no—
746C3×D4—121no—
747C3×D4—121no—
748C3×D4—122no—
749C3×D4—182no—
750C2×C3×C4—21no—
751C2×C3×C4—21no—
752C2×C3×C4—21no—
753C2×C3×C4—21no—
754C2×C3×C4—21no—
755C2×C3×C4—21no—
756C2×C3×C4—31no—
757C2×C3×C4—31no—
758C2×C3×C4—31no—
759C2×C3×C4—31no—
760C2×C3×C4—31no—
761C2×C3×C4—31no—
762C2×C3×C4—31no—
763C2×C3×C4—31no—
764C2×C3×C4—31no—
765C2×C3×C4—31no—
766C2×C3×C4—31no—
767C2×C3×C4—31no—
768C2×C3×C4—41no—
769C2×C3×C4—41no—
770C2×C3×C4—41no—
771C2×C3×C4—42no—
772C2×C3×C4—42no—
773C2×C3×C4—42no—
774C2×C3×C4—44no—
775C2×C3×C4—41no—
776C2×C3×C4—41no—
777C2×C3×C4—61no—
778C2×C3×C4—61no—
779C2×C3×C4—61no—
780C2×C3×C4—61no—
781C2×C3×C4—61no—
782C2×C3×C4—61no—
783C2×C3×C4—91no—
784C2×C3×C4—91no—
785C2×C3×C4—91no—
786C2×C3×C4—121no—
787C2×C3×C4—121no—
788C2×C3×C4—122no—
789C2×C3×C4—182no—
790C2×C3×C4—182no—
791C2×C3×C4—361no—
792C2×C3×C4C2×D3211yescharacteristic
793C2×C3×C4C2×D3211yescharacteristic
794C2×C3×C4C22×C3×D311yescharacteristic
795C2×C3×C4C22×C3×D311yescharacteristic
796C2×C3×C4C22×C3×D311yescharacteristic
797C2×C3×C4C22×C3×D311yescharacteristic
798#67—22no—
799#67—41no—
800#67—62no—
801#67—62no—
802#67—64no—
803C2×Dic3—31no—
804C2×Dic3—31no—
805C2×Dic3—31no—
806C2×Dic3—31no—
807C2×Dic3—31no—
808C2×Dic3—31no—
809C2×Dic3—61no—
810C2×Dic3—61no—
811C2×Dic3—61no—
812C2×Dic3—62no—
813C2×Dic3C22×C3×D311yescharacteristic
814C2×Dic3C22×C3×D311yescharacteristic
815C2×Dic3C22×C3×D311yescharacteristic
816C2×Dic3C22×C3×D311yescharacteristic
817C2×Dic3C22×C3×D311yescharacteristic
818C2×Dic3C22×C3×D311yescharacteristic
819C4×D3—41no—
820C4×D3—62no—
821C4×D3—62no—
822C4×D3—62no—
823C4×D3—121no—
824C4×D3—121no—
825C4×D3—122no—
826Dic6—121no—
827Dic6—121no—
828C2×C32—21no—
829C2×C32—21no—
830C2×C32—21no—
831C2×C32—21no—
832C2×C32—21no—
833C2×C32—21no—
834C2×C32—21no—
835C2×C32—21no—
836C2×C32—21no—
837C2×C32—41no—
838C2×C32—41no—
839C2×C32—41no—
840C2×C32—42no—
841C2×C32—42no—
842C2×C32—42no—
843C2×C32—44no—
844C2×C32—41no—
845C2×C32—41no—
846C2×C32—41no—
847C2×C32—62no—
848C2×C32—121no—
849C2×C32C2×#23511yescharacteristic
850C2×C32#100411yescharacteristic
851C2×C32#100411yescharacteristic
852C2×C32D3×#4111yescharacteristic
853C2×C32D3×#4111yescharacteristic
854C2×C32D3×#4111yescharacteristic
855C2×C32C2×C3×#4111yescharacteristic
856C2×C32C2×C3×#4111yescharacteristic
857C2×C32C3×H(5,𝔽2)11yescharacteristic
858C3⋊D3—22no—
859C3×D3—22no—
860C3×D3—22no—
861C3×D3—42no—
862C3×D3—41no—
863C3×D3—41no—
864C3×D3—62no—
865C3×D3—62no—
866C3×D3—81no—
867C3×D3—122no—
868C24—91no—
869C2×Q8—91no—
870C2×D4—31no—
871C2×D4—31no—
872C2×D4—91no—
873C22×C4—31no—
874C22×C4—91no—
875C22×C4—91no—
876C22×C4—91no—
877C22×C4C3×D3211yescharacteristic, complemented
878C4⋊C4—31no—
879C4⋊C4—31no—
880C4⋊C4—31no—
881C4⋊C4—91no—
882C4⋊C4—91no—
883C4⋊C4—91no—
884C4⋊C4—91no—
885C4⋊C4—91no—
886C22⋊C4—31no—
887C22⋊C4—31no—
888C22⋊C4—31no—
889C22⋊C4—31no—
890C22⋊C4—31no—
891C22⋊C4—91no—
892C22⋊C4—91no—
893C22⋊C4—91no—
894C22⋊C4—91no—
895C22⋊C4—91no—
896C22⋊C4—91no—
897C22⋊C4—91no—
898C22⋊C4—91no—
899C22⋊C4—91no—
900C42—31no—
901C42—91no—
902C42—91no—
903C22×C3—22no—
904C22×C3—22no—
905C22×C3—22no—
906C22×C3—21no—
907C22×C3—21no—
908C22×C3—21no—
909C22×C3—21no—
910C22×C3—21no—
911C22×C3—21no—
912C22×C3—21no—
913C22×C3—21no—
914C22×C3—21no—
915C22×C3—21no—
916C22×C3—21no—
917C22×C3—21no—
918C22×C3—32no—
919C22×C3—32no—
920C22×C3—41no—
921C22×C3—41no—
922C22×C3—41no—
923C22×C3—41no—
924C22×C3—41no—
925C22×C3—41no—
926C22×C3—42no—
927C22×C3—42no—
928C22×C3—42no—
929C22×C3—41no—
930C22×C3—62no—
931C22×C3—61no—
932C22×C3—61no—
933C22×C3—61no—
934C22×C3—61no—
935C22×C3—61no—
936C22×C3—61no—
937C22×C3—61no—
938C22×C3—61no—
939C22×C3—61no—
940C22×C3—61no—
941C22×C3—92no—
942C22×C3—121no—
943C22×C3—121no—
944C22×C3—121no—
945C22×C3—121no—
946C22×C3—121no—
947C22×C3—181no—
948C22×C3—181no—
949C22×C3—364no—
950C22×C3C22×D3211yescharacteristic
951C22×C3C23×C3×D311yescharacteristic
952C22×C3C23×C3×D311yescharacteristic
953C2×D3—21no—
954C2×D3—21no—
955C2×D3—21no—
956C2×D3—21no—
957C2×D3—21no—
958C2×D3—32no—
959C2×D3—32no—
960C2×D3—62no—
961C2×D3—61no—
962C2×D3—61no—
963C2×D3—61no—
964C2×D3—61no—
965C2×D3—121no—
966C2×D3—121no—
967C2×D3—124no—
968C2×D3—124no—
969C2×D3C3×#23512yes—
970C3×C4—22no—
971C3×C4—22no—
972C3×C4—21no—
973C3×C4—21no—
974C3×C4—21no—
975C3×C4—21no—
976C3×C4—21no—
977C3×C4—21no—
978C3×C4—41no—
979C3×C4—41no—
980C3×C4—41no—
981C3×C4—41no—
982C3×C4—42no—
983C3×C4—42no—
984C3×C4—62no—
985C3×C4—61no—
986C3×C4—61no—
987C3×C4—61no—
988C3×C4—61no—
989C3×C4—61no—
990C3×C4—61no—
991C3×C4—61no—
992C3×C4—61no—
993C3×C4—61no—
994C3×C4—61no—
995C3×C4—61no—
996C3×C4—61no—
997C3×C4—121no—
998C3×C4—121no—
999C3×C4—121no—
1000C3×C4—121no—
1001C3×C4—121no—
1002C3×C4—181no—
1003C3×C4—181no—
1004C3×C4—181no—
1005Dic3—21no—
1006Dic3—21no—
1007Dic3—21no—
1008Dic3—21no—
1009Dic3—21no—
1010Dic3—21no—
1011Dic3—62no—
1012Dic3—61no—
1013Dic3—61no—
1014Dic3—61no—
1015Dic3—61no—
1016Dic3—61no—
1017Dic3—61no—
1018Dic3—121no—
1019Dic3—121no—
1020C32—21no—
1021C32—21no—
1022C32—21no—
1023C32—41no—
1024C32#555611yescharacteristic, complemented
1025C32#565911yescharacteristic, complemented
1026C32C3×#55111yescharacteristic, complemented
1027C23—31no—
1028C23—31no—
1029C23—91no—
1030C23—182no—
1031C23—182no—
1032C23—361no—
1033C23C2×C3×D3211yescharacteristic
1034Q8—361no—
1035D4—62no—
1036D4—121no—
1037D4—182no—
1038C2×C4—31no—
1039C2×C4—31no—
1040C2×C4—31no—
1041C2×C4—31no—
1042C2×C4—31no—
1043C2×C4—31no—
1044C2×C4—41no—
1045C2×C4—91no—
1046C2×C4—91no—
1047C2×C4—91no—
1048C2×C4—121no—
1049C2×C4—182no—
1050C2×C4—182no—
1051C2×C4—361no—
1052C2×C4C2×C3×D3211yescharacteristic
1053C2×C4C2×C3×D3211yescharacteristic
1054C2×C3—21no—
1055C2×C3—21no—
1056C2×C3—21no—
1057C2×C3—21no—
1058C2×C3—21no—
1059C2×C3—21no—
1060C2×C3—21no—
1061C2×C3—21no—
1062C2×C3—21no—
1063C2×C3—42no—
1064C2×C3—42no—
1065C2×C3—42no—
1066C2×C3—44no—
1067C2×C3—41no—
1068C2×C3—41no—
1069C2×C3—41no—
1070C2×C3—41no—
1071C2×C3—41no—
1072C2×C3—41no—
1073C2×C3—62no—
1074C2×C3—62no—
1075C2×C3—122no—
1076C2×C3—121no—
1077C2×C3—121no—
1078C2×C3—182no—
1079C2×C3—241no—
1080C2×C3D3×#23511yescharacteristic
1081C2×C3#6430611yescharacteristic
1082C2×C3#6433011yescharacteristic
1083C2×C3C2×C3×#23511yescharacteristic
1084C2×C3C3×#100411yescharacteristic
1085C2×C3C3×#100411yescharacteristic
1086C2×C3C3×D3×#4111yescharacteristic
1087C2×C3C3×D3×#4111yescharacteristic
1088C2×C3C3×D3×#4111yescharacteristic
1089D3—22no—
1090D3—41no—
1091D3—62no—
1092D3—62no—
1093D3—122no—
1094C22—21no—
1095C22—21no—
1096C22—21no—
1097C22—32no—
1098C22—61no—
1099C22—61no—
1100C22—61no—
1101C22—61no—
1102C22—61no—
1103C22—92no—
1104C22—181no—
1105C22—181no—
1106C22—364no—
1107C22C22×C3×D3211yescharacteristic
1108C4—21no—
1109C4—21no—
1110C4—61no—
1111C4—61no—
1112C4—61no—
1113C4—61no—
1114C4—61no—
1115C4—61no—
1116C4—181no—
1117C4—181no—
1118C4—181no—
1119C3—21no—
1120C3—21no—
1121C3—21no—
1122C3—41no—
1123C3#1059508811yescharacteristic, direct product factor
1124C3C3×#555611yescharacteristic, complemented
1125C3C3×#565911yescharacteristic, complemented
1126C2—41no—
1127C2—62no—
1128C2—121no—
1129C2—182no—
1130C2C3×D3×#23511yescharacteristic
1131C2C3×#6430611yescharacteristic
1132C2C3×#6433011yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC22×C33×C4C22
socleC22×C33C24
prime radicalC3×#63983C2
hypercenterC22×C3×C4D32
hypocenterC32C3×#551
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
1. C3×C4×#638C2semidirect
2. C32×#929C2semidirect
3. C32×C4×#67C2semidirect
5. C3×#63975C2semidirect
6. C3×#63969C2semidirect
7. C3×#63959C2semidirect
8. C3×#63921C2semidirect
9. C3×D3×(C2×D3)⋊C4C2semidirect
10. C3×#63878C2semidirect
11. C3×#63865C2semidirect
12. C3×#63862C2semidirect
13. C3×#63859C2semidirect
14. C3×#63851C2semidirect
15. C3×#63836C2semidirect
18. #10595088C3direct (N × H)
20. C22×C33×C4C22semidirect
26. C2×C3×#627C22semidirect
29. C3×#3757C22semidirect
31. C3×#3750C22semidirect
32. C3×C4×C3⋊Dic3C22semidirect
33. C32×#217C22semidirect
34. C32×#217C22semidirect
38. C32×Dic3⋊C4C22semidirect
39. C32×Dic3⋊C4C22semidirect
40. C32×Dic3⋊C4C22semidirect
41. C32×C4×Dic3C22semidirect
42. C3×#3724C22semidirect
43. C3×Dic3⋊Dic3C22semidirect
44. C3×Dic3⋊Dic3C22semidirect
45. C3×Dic3⋊Dic3C22semidirect
53. C3×Dic32C22semidirect
56. C4×#638C2×C3semidirect
62. C3×#929D3semidirect
63. C3×#929C2×C3semidirect
68. C3×C4×#67D3semidirect
69. C3×C4×#67C2×C3semidirect
91. #63975C2×C3semidirect
92. #63969C2×C3semidirect
93. #63959C2×C3semidirect
94. #63921C2×C3semidirect
95. D3×(C2×D3)⋊C4C2×C3semidirect
96. #63878C2×C3semidirect
97. #63865C2×C3semidirect
98. #63862C2×C3semidirect
99. #63859C2×C3semidirect
100. #63851C2×C3semidirect
101. #63836C2×C3semidirect
142. C22×C32×C4C2×D3semidirect
143. C22×C32×C4C2×D3semidirect
144. C22×C32×C4C22×C3semidirect
168. C2×#627C22×C3semidirect
180. #3757C22×C3semidirect
182. #3750C22×C3semidirect
183. C4×C3⋊Dic3C22×C3semidirect
194. C3×#217C2×D3semidirect
195. C3×#217C2×D3semidirect
196. C3×#217C22×C3semidirect
197. C3×#217C22×C3semidirect
233. C3×Dic3⋊C4C2×D3semidirect
234. C3×Dic3⋊C4C2×D3semidirect
235. C3×Dic3⋊C4C2×D3semidirect
236. C3×Dic3⋊C4C22×C3semidirect
237. C3×Dic3⋊C4C22×C3semidirect
238. C3×Dic3⋊C4C22×C3semidirect
245. C3×C4×Dic3C2×D3semidirect
246. C3×C4×Dic3C22×C3semidirect
247. #3724C22×C3semidirect
248. Dic3⋊Dic3C22×C3semidirect
249. Dic3⋊Dic3C22×C3semidirect
250. Dic3⋊Dic3C22×C3semidirect
258. Dic32C22×C3semidirect
307. #929C3×D3semidirect
311. C4×#67C3×D3semidirect
475. C22×C3×C4D32semidirect
476. C22×C3×C4C2×C3×D3semidirect
477. C22×C3×C4C2×C3×D3semidirect
544. #217C2×C3×D3semidirect
545. #217C2×C3×D3semidirect
572. Dic3⋊C4C2×C3×D3semidirect
573. Dic3⋊C4C2×C3×D3semidirect
574. Dic3⋊C4C2×C3×D3semidirect
580. C4×Dic3C2×C3×D3semidirect
713. C33#551semidirect
877. C22×C4C3×D32semidirect
1024. C32#5556semidirect
1025. C32#5659semidirect
1026. C32C3×#551semidirect
1123. C3#10595088direct (N × H)
1124. C3C3×#5556semidirect
1125. C3C3×#5659semidirect

Maximal subgroups

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

subgroupindex
C3×C4×#6382
C32×#9292
C32×C4×#672
C3×#639832
C3×#639752
C3×#639692
C3×#639592
C3×#639212
C3×D3×(C2×D3)⋊C42
C3×#638782
C3×#638652
C3×#638622
C3×#638592
C3×#638512
C3×#638362
C3×#56593
C3×#55563
#105950883