Finite Group Databasebeta

← C3×#10595127 #13174768

Subgroups — C3×#10595127 #13174768

Order 1728.

1192 conjugacy classes of subgroups.

The subgroup lattice has 1092 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64148C211yesmaximal, characteristic
2C32×#935C211yesmaximal, characteristic, complemented
3C32×D4×Dic3C211yesmaximal, characteristic, complemented
4C3×#63982C211yesmaximal, characteristic, complemented
5C3×#63975C211yesmaximal, characteristic, complemented
6C3×#63966C211yesmaximal, characteristic, complemented
7C3×#63966C211yesmaximal, characteristic, complemented
8C2×C3×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
9C3×#63964C211yesmaximal, characteristic, complemented
10C3×#63956C211yesmaximal, characteristic, complemented
11C3×#63952C211yesmaximal, characteristic, complemented
12C3×#63895C211yesmaximal, characteristic, complemented
13C3×#63868C211yesmaximal, characteristic, complemented
14C3×#63867C211yesmaximal, characteristic, complemented
15C3×#63846C211yesmaximal, characteristic, complemented
16C3×#5665—31nomaximal
17C3×#5564—31nomaximal
18#10595127C311yesmaximal, characteristic, direct product factor
19C2×C33×D4C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C22×C3×C3⋊Dic3C2211yescharacteristic
23C22×C32×Dic3C2211yescharacteristic
24C22×C32×Dic3C2211yescharacteristic
25C22×C32×Dic3C2211yescharacteristic
26C2×C3×#627C2211yescharacteristic
27C2×C3×#624C2211yescharacteristic
28C3×#3757C2211yescharacteristic
29C3×#3752C2211yescharacteristic
30C3×#3750C2211yescharacteristic
31C32×#217C2211yescharacteristic
32C32×#217C2211yescharacteristic
33C32×#217C2211yescharacteristic
34C32×#217C2211yescharacteristic
35C32×#217C2211yescharacteristic
36C32×C4⋊Dic3C2211yescharacteristic
37C32×Dic3⋊C4C2211yescharacteristic
38C32×Dic3⋊C4C2211yescharacteristic
39C32×C4×Dic3C2211yescharacteristic
40C3×#3724C2211yescharacteristic
41C3×#3724C2211yescharacteristic
42C3×Dic3⋊Dic3C2211yescharacteristic
43C3×Dic3⋊Dic3C2211yescharacteristic
44C3×Dic3⋊Dic3C2211yescharacteristic
45C3×Dic3⋊Dic3C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×Dic3⋊Dic3C2211yescharacteristic
50C3×#3722C2211yescharacteristic
51C3×#3722C2211yescharacteristic
52C3×#3722C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54C32×#123—31no—
55C32×C4×D4—31no—
56#64148C2×C311yescharacteristic
57C3×#939—31no—
58C3×#939—31no—
59C3×#939—61no—
60C3×#935—21no—
61C3×#935D311yescharacteristic, complemented
62C3×#935C2×C311yescharacteristic, complemented
63C3×D4×Dic3—21no—
64C3×D4×Dic3D311yescharacteristic, complemented
65C3×D4×Dic3C2×C311yescharacteristic, complemented
66C3×#929—31no—
67C3×#929—31no—
68C3×C4×#67—31no—
69C2×C3×C4⋊Dic3—31no—
70C3×#924—31no—
71C2×C3×Dic3⋊C4—31no—
72C3×#898—31no—
73C3×#897—31no—
74C3×#896—31no—
75C3×#890—31no—
76C3×#889—31no—
77C3×#889—31no—
78C3×#886—31no—
79C3×#886—31no—
80C3×#883—31no—
81C3×#883—31no—
82C3×#67⋊C4—31no—
83C3×#879—31no—
84C3×#879—31no—
85C3×#878—31no—
86C3×#878—31no—
87C3×#878—31no—
88C3×#876—31no—
89C3×#870—31no—
90#63982C2×C311yescharacteristic, complemented
91#63975C2×C311yescharacteristic, complemented
92#63966C2×C311yescharacteristic, complemented
93#63966C2×C311yescharacteristic, complemented
94C2×Dic3⋊Dic3C2×C311yescharacteristic, complemented
95#63964C2×C311yescharacteristic, complemented
96#63956C2×C311yescharacteristic, complemented
97#63952C2×C311yescharacteristic, complemented
98#63895C2×C311yescharacteristic, complemented
99#63868C2×C311yescharacteristic, complemented
100#63867C2×C311yescharacteristic, complemented
101#63846C2×C311yescharacteristic, complemented
102C23×C33C2311yescharacteristic
103C23×C33C2311yescharacteristic
104C22×C3×C3⋊D3C2311yescharacteristic
105C33×D4—22no—
106C2×C33×C4C2311yescharacteristic
107C3×#638—22no—
108C3×#638—41no—
109C2×C3×C3⋊Dic3—41no—
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C32×Dic3—22no—
114C2×C32×Dic3—41no—
115C2×C32×Dic3—41no—
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123C2×C32×Dic3C2311yescharacteristic
124C3×#627—41no—
125C3×#624—41no—
126C3×#539—91no—
127#5665—31no—
128#5564—31no—
129C2×C32×D4—21no—
130C2×C32×D4—21no—
131C2×C32×D4—21no—
132C2×C32×D4—41no—
133C2×C32×D4C2×D311yescharacteristic
134C2×C32×D4C2×D311yescharacteristic
135C2×C32×D4C22×C311yescharacteristic
136C22×C32×C4—31no—
137C22×C32×C4—31no—
138C22×C32×C4—31no—
139C2×#638C22×C311yescharacteristic
140C2×#638C22×C311yescharacteristic
141C22×C3⋊Dic3C22×C311yescharacteristic
142C2×C3×#67—31no—
143C2×C3×#67—31no—
144C2×C3×#67—31no—
145C2×C3×#67—31no—
146C2×C3×#67—61no—
147C2×C3×#67—61no—
148C22×C3×Dic3—21no—
149C22×C3×Dic3—21no—
150C22×C3×Dic3—21no—
151C22×C3×Dic3—31no—
152C22×C3×Dic3—31no—
153C22×C3×Dic3—61no—
154C22×C3×Dic3C2×D311yescharacteristic
155C22×C3×Dic3C2×D311yescharacteristic
156C22×C3×Dic3C2×D311yescharacteristic
157C22×C3×Dic3C22×C311yescharacteristic
158C22×C3×Dic3C22×C311yescharacteristic
159C22×C3×Dic3C22×C311yescharacteristic
160C2×C3×C4×D3—31no—
161C2×C3×C4×D3—31no—
162C2×C3×Dic6—31no—
163C2×C3×Dic6—31no—
164C2×#627C22×C311yescharacteristic
165C2×#624C22×C311yescharacteristic
166C32×C4⋊C4—31no—
167C32×C4⋊C4—31no—
168C32×C4⋊C4—31no—
169C32×C22⋊C4—31no—
170C32×C22⋊C4—31no—
171C32×C22⋊C4—31no—
172C32×C22⋊C4—31no—
173C32×C22⋊C4—31no—
174C32×C42—31no—
175#3757C22×C311yescharacteristic
176#3752C22×C311yescharacteristic
177#3750C22×C311yescharacteristic
178C3×#217—21no—
179C3×#217—21no—
180C3×#217—21no—
181C3×#217—21no—
182C3×#217—21no—
183C3×#217—31no—
184C3×#217—31no—
185C3×#217—61no—
186C3×#217C2×D311yescharacteristic
187C3×#217C2×D311yescharacteristic
188C3×#217C2×D311yescharacteristic
189C3×#217C2×D311yescharacteristic
190C3×#217C2×D311yescharacteristic
191C3×#217C22×C311yescharacteristic
192C3×#217C22×C311yescharacteristic
193C3×#217C22×C311yescharacteristic
194C3×#217C22×C311yescharacteristic
195C3×#217C22×C311yescharacteristic
196C3×(C2×D3)⋊C4—31no—
197C3×(C2×D3)⋊C4—31no—
198C3×(C2×D3)⋊C4—31no—
199C3×(C2×D3)⋊C4—31no—
200C3×(C2×D3)⋊C4—31no—
201C3×(C2×D3)⋊C4—31no—
202C3×(C2×D3)⋊C4—31no—
203C3×(C2×D3)⋊C4—31no—
204C3×(C2×D3)⋊C4—61no—
205C3×C4⋊Dic3—21no—
206C3×C4⋊Dic3—31no—
207C3×C4⋊Dic3—31no—
208C3×C4⋊Dic3—31no—
209C3×C4⋊Dic3—31no—
210C3×C4⋊Dic3—31no—
211C3×C4⋊Dic3—31no—
212C3×C4⋊Dic3—31no—
213C3×C4⋊Dic3—31no—
214C3×C4⋊Dic3C2×D311yescharacteristic
215C3×C4⋊Dic3C22×C311yescharacteristic
216C3×Dic3⋊C4—21no—
217C3×Dic3⋊C4—21no—
218C3×Dic3⋊C4—31no—
219C3×Dic3⋊C4—31no—
220C3×Dic3⋊C4—31no—
221C3×Dic3⋊C4—31no—
222C3×Dic3⋊C4—31no—
223C3×Dic3⋊C4—31no—
224C3×Dic3⋊C4—31no—
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
234C3×Dic3⋊C4C2×D311yescharacteristic
235C3×Dic3⋊C4C22×C311yescharacteristic
236C3×Dic3⋊C4C22×C311yescharacteristic
237C3×C4×Dic3—21no—
238C3×C4×Dic3—31no—
239C3×C4×Dic3—31no—
240C3×C4×Dic3C2×D311yescharacteristic
241C3×C4×Dic3C22×C311yescharacteristic
242#3724C22×C311yescharacteristic
243#3724C22×C311yescharacteristic
244Dic3⋊Dic3C22×C311yescharacteristic
245Dic3⋊Dic3C22×C311yescharacteristic
246Dic3⋊Dic3C22×C311yescharacteristic
247Dic3⋊Dic3C22×C311yescharacteristic
248Dic3⋊Dic3C22×C311yescharacteristic
249Dic3⋊Dic3C22×C311yescharacteristic
250Dic3⋊Dic3C22×C311yescharacteristic
251Dic3⋊Dic3C22×C311yescharacteristic
252#3722C22×C311yescharacteristic
253#3722C22×C311yescharacteristic
254#3722C22×C311yescharacteristic
255Dic32C22×C311yescharacteristic
256C22×C33—21no—
257C22×C33—21no—
258C22×C33—21no—
259C22×C33—21no—
260C22×C33—21no—
261C22×C33#4112yes—
262C22×C33C2411yescharacteristic
263C2×C3×C3⋊D3—21no—
264C2×C3×C3⋊D3—21no—
265C2×C3×C3⋊D3—21no—
266C33×C4—21no—
267C3×C3⋊Dic3—21no—
268C3×C3⋊Dic3—21no—
269C3×C3⋊Dic3—21no—
270C32×Dic3—21no—
271C32×Dic3—21no—
272C32×Dic3—21no—
273C32×Dic3—21no—
274C32×Dic3—21no—
275C32×Dic3—21no—
276C32×Dic3—21no—
277C32×Dic3—21no—
278C3×#126—91no—
279C3×#126—91no—
280C3×#125—91no—
281C3×#125—91no—
282C3×#123—31no—
283C3×#123—31no—
284C3×#123—61no—
285C3×#123—91no—
286C3×#123—91no—
287C3×#123—91no—
288C3×C22⋊Q8—91no—
289C3×C22⋊Q8—91no—
290C3×C22⋊Q8—91no—
291C3×#121—91no—
292C3×C4×D4—31no—
293C3×C4×D4—31no—
294C3×C4×D4—61no—
295C3×C4×D4—91no—
296C2×C3×C4⋊C4—91no—
297#939—31no—
298#939—31no—
299#939—61no—
300#935C3×D311yescharacteristic, complemented
301D4×Dic3C3×D311yescharacteristic, complemented
302#929—31no—
303#929—31no—
304C4×#67—31no—
305C2×C4⋊Dic3—31no—
306#924—31no—
307C2×Dic3⋊C4—31no—
308#898—31no—
309#897—31no—
310#896—31no—
311#890—31no—
312#889—31no—
313#889—31no—
314#886—31no—
315#886—31no—
316#883—31no—
317#883—31no—
318#67⋊C4—31no—
319#879—31no—
320#879—31no—
321#878—31no—
322#878—31no—
323#878—31no—
324#876—31no—
325#870—31no—
326C23×C32—21no—
327C23×C32—21no—
328C23×C32—21no—
329C23×C32—21no—
330C23×C32—21no—
331C23×C32—21no—
332C23×C32—41no—
333C23×C32—41no—
334C23×C32C22×D311yescharacteristic
335C23×C32C22×D311yescharacteristic
336C23×C32C22×D311yescharacteristic
337C23×C32C22×D311yescharacteristic
338C23×C32C23×C311yescharacteristic
339C23×C32C23×C311yescharacteristic
340C22×C3⋊D3C23×C311yescharacteristic
341C22×C3×D3—31no—
342C22×C3×D3—31no—
343C22×C3×D3—61no—
344C32×D4—22no—
345C32×D4—24no—
346C32×D4—22no—
347C32×D4—22no—
348C32×D4—42no—
349C32×D4—42no—
350C32×D4—44no—
351C2×C32×C4—21no—
352C2×C32×C4—21no—
353C2×C32×C4—21no—
354C2×C32×C4—31no—
355C2×C32×C4—31no—
356C2×C32×C4—31no—
357C2×C32×C4—31no—
358C2×C32×C4—31no—
359C2×C32×C4—31no—
360C2×C32×C4—31no—
361C2×C32×C4—31no—
362C2×C32×C4—41no—
363C2×C32×C4—62no—
364C2×C32×C4—121no—
365C2×C32×C4—121no—
366C2×C32×C4C22×D311yescharacteristic
367C2×C32×C4C22×D311yescharacteristic
368C2×C32×C4C23×C311yescharacteristic
369#638—22no—
370#638—41no—
371C2×C3⋊Dic3—41no—
372C2×C3⋊Dic3C23×C311yescharacteristic
373C2×C3⋊Dic3C23×C311yescharacteristic
374C2×C3⋊Dic3C23×C311yescharacteristic
375C3×#67—62no—
376C3×#67—62no—
377C3×#67—122no—
378C3×#67—121no—
379C3×#67—121no—
380C3×#67—122no—
381C2×C3×Dic3—22no—
382C2×C3×Dic3—22no—
383C2×C3×Dic3—21no—
384C2×C3×Dic3—21no—
385C2×C3×Dic3—21no—
386C2×C3×Dic3—21no—
387C2×C3×Dic3—21no—
388C2×C3×Dic3—21no—
389C2×C3×Dic3—21no—
390C2×C3×Dic3—21no—
391C2×C3×Dic3—31no—
392C2×C3×Dic3—31no—
393C2×C3×Dic3—31no—
394C2×C3×Dic3—31no—
395C2×C3×Dic3—31no—
396C2×C3×Dic3—31no—
397C2×C3×Dic3—42no—
398C2×C3×Dic3—41no—
399C2×C3×Dic3—41no—
400C2×C3×Dic3—41no—
401C2×C3×Dic3—41no—
402C2×C3×Dic3—42no—
403C2×C3×Dic3—42no—
404C2×C3×Dic3—61no—
405C2×C3×Dic3—61no—
406C2×C3×Dic3—61no—
407C2×C3×Dic3—121no—
408C2×C3×Dic3—121no—
409C2×C3×Dic3—122no—
410C2×C3×Dic3C22×D311yescharacteristic
411C2×C3×Dic3C22×D311yescharacteristic
412C2×C3×Dic3C22×D311yescharacteristic
413C2×C3×Dic3C22×D311yescharacteristic
414C2×C3×Dic3C22×D311yescharacteristic
415C2×C3×Dic3C22×D311yescharacteristic
416C2×C3×Dic3C22×D311yescharacteristic
417C2×C3×Dic3C22×D311yescharacteristic
418C2×C3×Dic3C23×C311yescharacteristic
419C2×C3×Dic3C23×C311yescharacteristic
420C2×C3×Dic3C23×C311yescharacteristic
421C2×C3×Dic3C23×C311yescharacteristic
422C2×C3×Dic3C23×C311yescharacteristic
423C2×C3×Dic3C23×C311yescharacteristic
424C2×C3×Dic3C23×C311yescharacteristic
425C2×C3×Dic3C23×C311yescharacteristic
426C3×C4×D3—121no—
427C3×C4×D3—121no—
428C3×Dic6—121no—
429C3×Dic6—121no—
430#627—41no—
431#624—41no—
432#539—91noSylow
433C2×C33—22no—
434C2×C33—41no—
435C2×C33C2×#4111yescharacteristic
436C2×C33H(5,𝔽2)11yescharacteristic
437C2×C332−1+411yescharacteristic
438C3×C3⋊D3—41no—
439C2×C3×Q8—91no—
440C2×C3×D4—21no—
441C2×C3×D4—21no—
442C2×C3×D4—21no—
443C2×C3×D4—41no—
444C2×C3×D4—91no—
445C2×C3×D4—91no—
446C2×C3×D4D3211yescharacteristic
447C2×C3×D4C2×C3×D311yescharacteristic
448C2×C3×D4C2×C3×D311yescharacteristic
449C22×C3×C4—31no—
450C22×C3×C4—31no—
451C22×C3×C4—31no—
452C22×C3×C4—31no—
453C22×C3×C4—31no—
454C22×C3×C4—31no—
455C22×C3×C4—61no—
456C22×C3×C4—61no—
457C22×C3×C4—61no—
458C22×C3×C4—91no—
459C22×C3×C4—91no—
460C2×#67—31no—
461C2×#67—31no—
462C2×#67—31no—
463C2×#67—31no—
464C2×#67—61no—
465C2×#67—61no—
466C22×Dic3—31no—
467C22×Dic3—31no—
468C22×Dic3—61no—
469C22×Dic3C2×C3×D311yescharacteristic
470C22×Dic3C2×C3×D311yescharacteristic
471C22×Dic3C2×C3×D311yescharacteristic
472C2×C4×D3—31no—
473C2×C4×D3—31no—
474C2×Dic6—31no—
475C2×Dic6—31no—
476C3×C4⋊C4—31no—
477C3×C4⋊C4—31no—
478C3×C4⋊C4—31no—
479C3×C4⋊C4—31no—
480C3×C4⋊C4—31no—
481C3×C4⋊C4—31no—
482C3×C4⋊C4—61no—
483C3×C4⋊C4—61no—
484C3×C4⋊C4—61no—
485C3×C4⋊C4—91no—
486C3×C4⋊C4—91no—
487C3×C4⋊C4—91no—
488C3×C4⋊C4—91no—
489C3×C4⋊C4—91no—
490C3×C4⋊C4—91no—
491C3×C4⋊C4—91no—
492C3×C4⋊C4—91no—
493C3×C4⋊C4—91no—
494C3×C4⋊C4—91no—
495C3×C4⋊C4—91no—
496C3×C22⋊C4—31no—
497C3×C22⋊C4—31no—
498C3×C22⋊C4—31no—
499C3×C22⋊C4—31no—
500C3×C22⋊C4—31no—
501C3×C22⋊C4—31no—
502C3×C22⋊C4—31no—
503C3×C22⋊C4—31no—
504C3×C22⋊C4—31no—
505C3×C22⋊C4—31no—
506C3×C22⋊C4—61no—
507C3×C22⋊C4—61no—
508C3×C22⋊C4—61no—
509C3×C22⋊C4—61no—
510C3×C22⋊C4—61no—
511C3×C22⋊C4—91no—
512C3×C22⋊C4—91no—
513C3×C22⋊C4—91no—
514C3×C22⋊C4—91no—
515C3×C22⋊C4—91no—
516C3×C42—31no—
517C3×C42—31no—
518C3×C42—61no—
519C3×C42—91no—
520#217—31no—
521#217—31no—
522#217—61no—
523#217C2×C3×D311yescharacteristic
524#217C2×C3×D311yescharacteristic
525#217C2×C3×D311yescharacteristic
526#217C2×C3×D311yescharacteristic
527#217C2×C3×D311yescharacteristic
528(C2×D3)⋊C4—31no—
529(C2×D3)⋊C4—31no—
530(C2×D3)⋊C4—31no—
531(C2×D3)⋊C4—31no—
532(C2×D3)⋊C4—31no—
533(C2×D3)⋊C4—31no—
534(C2×D3)⋊C4—31no—
535(C2×D3)⋊C4—31no—
536(C2×D3)⋊C4—61no—
537C4⋊Dic3—31no—
538C4⋊Dic3—31no—
539C4⋊Dic3—31no—
540C4⋊Dic3—31no—
541C4⋊Dic3—31no—
542C4⋊Dic3—31no—
543C4⋊Dic3—31no—
544C4⋊Dic3—31no—
545C4⋊Dic3C2×C3×D311yescharacteristic
546Dic3⋊C4—31no—
547Dic3⋊C4—31no—
548Dic3⋊C4—31no—
549Dic3⋊C4—31no—
550Dic3⋊C4—31no—
551Dic3⋊C4—31no—
552Dic3⋊C4—31no—
553Dic3⋊C4—31no—
554Dic3⋊C4—31no—
555Dic3⋊C4—31no—
556Dic3⋊C4—31no—
557Dic3⋊C4—31no—
558Dic3⋊C4—31no—
559Dic3⋊C4—31no—
560Dic3⋊C4—61no—
561Dic3⋊C4C2×C3×D311yescharacteristic
562Dic3⋊C4C2×C3×D311yescharacteristic
563C4×Dic3—31no—
564C4×Dic3—31no—
565C4×Dic3C2×C3×D311yescharacteristic
566C22×C32—21no—
567C22×C32—21no—
568C22×C32—21no—
569C22×C32—21no—
570C22×C32—21no—
571C22×C32—21no—
572C22×C32—21no—
573C22×C32—22no—
574C22×C32—21no—
575C22×C32—21no—
576C22×C32—21no—
577C22×C32—21no—
578C22×C32—21no—
579C22×C32—21no—
580C22×C32—21no—
581C22×C32—21no—
582C22×C32—21no—
583C22×C32—21no—
584C22×C32—21no—
585C22×C32—22no—
586C22×C32—22no—
587C22×C32—22no—
588C22×C32—41no—
589C22×C32—42no—
590C22×C32—41no—
591C22×C32—41no—
592C22×C32—42no—
593C22×C32—41no—
594C22×C32—41no—
595C22×C32—41no—
596C22×C32—41no—
597C22×C32—41no—
598C22×C32—41no—
599C22×C32—41no—
600C22×C32—41no—
601C22×C32—41no—
602C22×C32—41no—
603C22×C32—41no—
604C22×C32—41no—
605C22×C32—81no—
606C22×C32—81no—
607C22×C32—81no—
608C22×C32—81no—
609C22×C32#23512yes—
610C22×C32#23712yes—
611C22×C32C3×#4112yes—
612C22×C32C23×D311yescharacteristic
613C22×C32C23×D311yescharacteristic
614C22×C32C24×C311yescharacteristic
615C2×C3⋊D3—21no—
616C2×C3⋊D3—21no—
617C2×C3⋊D3—21no—
618C2×C3×D3—61no—
619C2×C3×D3—61no—
620C2×C3×D3—61no—
621C2×C3×D3—61no—
622C2×C3×D3—61no—
623C2×C3×D3—61no—
624C2×C3×D3—121no—
625C2×C3×D3—121no—
626C2×C3×D3—121no—
627C32×C4—21no—
628C32×C4—22no—
629C32×C4—21no—
630C32×C4—21no—
631C32×C4—41no—
632C32×C4—41no—
633C32×C4—42no—
634C32×C4—61no—
635C32×C4—61no—
636C32×C4—61no—
637C32×C4—61no—
638C32×C4—61no—
639C32×C4—61no—
640C32×C4—61no—
641C32×C4—61no—
642C3⋊Dic3—21no—
643C3⋊Dic3—21no—
644C3⋊Dic3—21no—
645C3×Dic3—22no—
646C3×Dic3—21no—
647C3×Dic3—21no—
648C3×Dic3—21no—
649C3×Dic3—21no—
650C3×Dic3—21no—
651C3×Dic3—21no—
652C3×Dic3—21no—
653C3×Dic3—21no—
654C3×Dic3—21no—
655C3×Dic3—21no—
656C3×Dic3—21no—
657C3×Dic3—21no—
658C3×Dic3—21no—
659C3×Dic3—21no—
660C3×Dic3—21no—
661C3×Dic3—21no—
662C3×Dic3—41no—
663C3×Dic3—41no—
664C3×Dic3—41no—
665C3×Dic3—41no—
666C3×Dic3—41no—
667C3×Dic3—41no—
668C3×Dic3—41no—
669C3×Dic3—62no—
670C3×Dic3—61no—
671C3×Dic3—61no—
672C3×Dic3—61no—
673C3×Dic3—61no—
674C3×Dic3—61no—
675C3×Dic3—61no—
676C3×Dic3—121no—
677C3×Dic3—121no—
678#126—91no—
679#126—91no—
680#125—91no—
681#125—91no—
682#123—31no—
683#123—91no—
684#123—91no—
685#123—91no—
686C22⋊Q8—91no—
687C22⋊Q8—91no—
688C22⋊Q8—91no—
689#121—91no—
690C4×D4—31no—
691C4×D4—91no—
692C2×C4⋊C4—91no—
693C33#53911yescharacteristic, complemented, Sylow
694C23×C3—21no—
695C23×C3—21no—
696C23×C3—21no—
697C23×C3—21no—
698C23×C3—21no—
699C23×C3—21no—
700C23×C3—41no—
701C23×C3—41no—
702C23×C3—91no—
703C23×C3C2×D3211yescharacteristic
704C23×C3C2×D3211yescharacteristic
705C23×C3C22×C3×D311yescharacteristic
706C23×C3C22×C3×D311yescharacteristic
707C23×C3C22×C3×D311yescharacteristic
708C23×C3C22×C3×D311yescharacteristic
709C22×D3—31no—
710C22×D3—31no—
711C22×D3—61no—
712C3×Q8—361no—
713C3×D4—24no—
714C3×D4—22no—
715C3×D4—22no—
716C3×D4—22no—
717C3×D4—42no—
718C3×D4—42no—
719C3×D4—44no—
720C3×D4—182no—
721C3×D4—361no—
722C2×C3×C4—21no—
723C2×C3×C4—21no—
724C2×C3×C4—21no—
725C2×C3×C4—31no—
726C2×C3×C4—31no—
727C2×C3×C4—31no—
728C2×C3×C4—31no—
729C2×C3×C4—31no—
730C2×C3×C4—31no—
731C2×C3×C4—31no—
732C2×C3×C4—31no—
733C2×C3×C4—31no—
734C2×C3×C4—31no—
735C2×C3×C4—31no—
736C2×C3×C4—31no—
737C2×C3×C4—31no—
738C2×C3×C4—31no—
739C2×C3×C4—31no—
740C2×C3×C4—31no—
741C2×C3×C4—41no—
742C2×C3×C4—61no—
743C2×C3×C4—61no—
744C2×C3×C4—61no—
745C2×C3×C4—61no—
746C2×C3×C4—61no—
747C2×C3×C4—61no—
748C2×C3×C4—61no—
749C2×C3×C4—61no—
750C2×C3×C4—62no—
751C2×C3×C4—62no—
752C2×C3×C4—91no—
753C2×C3×C4—91no—
754C2×C3×C4—91no—
755C2×C3×C4—122no—
756C2×C3×C4—121no—
757C2×C3×C4—121no—
758C2×C3×C4—121no—
759C2×C3×C4—121no—
760C2×C3×C4—122no—
761C2×C3×C4—122no—
762C2×C3×C4—361no—
763C2×C3×C4—361no—
764C2×C3×C4C2×D3211yescharacteristic
765C2×C3×C4C22×C3×D311yescharacteristic
766C2×C3×C4C22×C3×D311yescharacteristic
767#67—62no—
768#67—62no—
769#67—122no—
770#67—121no—
771#67—121no—
772#67—122no—
773C2×Dic3—22no—
774C2×Dic3—31no—
775C2×Dic3—31no—
776C2×Dic3—31no—
777C2×Dic3—31no—
778C2×Dic3—31no—
779C2×Dic3—31no—
780C2×Dic3—41no—
781C2×Dic3—41no—
782C2×Dic3—61no—
783C2×Dic3—61no—
784C2×Dic3—61no—
785C2×Dic3—121no—
786C2×Dic3—121no—
787C2×Dic3—122no—
788C2×Dic3C22×C3×D311yescharacteristic
789C2×Dic3C22×C3×D311yescharacteristic
790C2×Dic3C22×C3×D311yescharacteristic
791C2×Dic3C22×C3×D311yescharacteristic
792C2×Dic3C22×C3×D311yescharacteristic
793C2×Dic3C22×C3×D311yescharacteristic
794C2×Dic3C22×C3×D311yescharacteristic
795C2×Dic3C22×C3×D311yescharacteristic
796C4×D3—121no—
797C4×D3—121no—
798Dic6—121no—
799Dic6—121no—
800C2×C32—22no—
801C2×C32—22no—
802C2×C32—22no—
803C2×C32—21no—
804C2×C32—21no—
805C2×C32—21no—
806C2×C32—21no—
807C2×C32—21no—
808C2×C32—21no—
809C2×C32—21no—
810C2×C32—21no—
811C2×C32—21no—
812C2×C32—41no—
813C2×C32—41no—
814C2×C32—41no—
815C2×C32—42no—
816C2×C32—42no—
817C2×C32—42no—
818C2×C32—41no—
819C2×C32—42no—
820C2×C32—41no—
821C2×C32—41no—
822C2×C32—82no—
823C2×C32—81no—
824C2×C32—81no—
825C2×C32—82no—
826C2×C32C2×#23511yescharacteristic
827C2×C32C2×#23711yescharacteristic
828C2×C32#100411yescharacteristic
829C2×C32#100911yescharacteristic
830C2×C32#101011yescharacteristic
831C2×C32#101011yescharacteristic
832C2×C32C2×C3×#4111yescharacteristic
833C2×C32C3×H(5,𝔽2)11yescharacteristic
834C2×C32C3×2−1+411yescharacteristic
835C3⋊D3—41no—
836C3×D3—121no—
837C3×D3—121no—
838C3×D3—241no—
839C2×Q8—91no—
840C2×D4—91no—
841C2×D4—91no—
842C2×D4C3×D3211yescharacteristic
843C22×C4—31no—
844C22×C4—31no—
845C22×C4—31no—
846C22×C4—91no—
847C22×C4—91no—
848C4⋊C4—31no—
849C4⋊C4—31no—
850C4⋊C4—31no—
851C4⋊C4—91no—
852C4⋊C4—91no—
853C4⋊C4—91no—
854C4⋊C4—91no—
855C4⋊C4—91no—
856C4⋊C4—91no—
857C4⋊C4—91no—
858C4⋊C4—91no—
859C4⋊C4—91no—
860C4⋊C4—91no—
861C4⋊C4—91no—
862C22⋊C4—31no—
863C22⋊C4—31no—
864C22⋊C4—31no—
865C22⋊C4—31no—
866C22⋊C4—31no—
867C22⋊C4—91no—
868C22⋊C4—91no—
869C22⋊C4—91no—
870C22⋊C4—91no—
871C22⋊C4—91no—
872C42—31no—
873C42—91no—
874C22×C3—21no—
875C22×C3—21no—
876C22×C3—21no—
877C22×C3—21no—
878C22×C3—21no—
879C22×C3—21no—
880C22×C3—22no—
881C22×C3—21no—
882C22×C3—21no—
883C22×C3—21no—
884C22×C3—21no—
885C22×C3—21no—
886C22×C3—21no—
887C22×C3—21no—
888C22×C3—21no—
889C22×C3—21no—
890C22×C3—21no—
891C22×C3—21no—
892C22×C3—21no—
893C22×C3—22no—
894C22×C3—22no—
895C22×C3—22no—
896C22×C3—41no—
897C22×C3—41no—
898C22×C3—41no—
899C22×C3—41no—
900C22×C3—41no—
901C22×C3—41no—
902C22×C3—41no—
903C22×C3—41no—
904C22×C3—41no—
905C22×C3—41no—
906C22×C3—41no—
907C22×C3—41no—
908C22×C3—41no—
909C22×C3—41no—
910C22×C3—42no—
911C22×C3—41no—
912C22×C3—42no—
913C22×C3—81no—
914C22×C3—81no—
915C22×C3—81no—
916C22×C3—81no—
917C22×C3—181no—
918C22×C3—181no—
919C22×C3—181no—
920C22×C3#380412yes—
921C22×C3C3×#23512yes—
922C22×C3C3×#23712yes—
923C22×C3C22×D3211yescharacteristic
924C22×C3C23×C3×D311yescharacteristic
925C22×C3C23×C3×D311yescharacteristic
926C2×D3—61no—
927C2×D3—61no—
928C2×D3—61no—
929C2×D3—61no—
930C2×D3—61no—
931C2×D3—61no—
932C2×D3—121no—
933C2×D3—121no—
934C2×D3—121no—
935C3×C4—22no—
936C3×C4—21no—
937C3×C4—21no—
938C3×C4—21no—
939C3×C4—41no—
940C3×C4—41no—
941C3×C4—42no—
942C3×C4—62no—
943C3×C4—61no—
944C3×C4—61no—
945C3×C4—61no—
946C3×C4—61no—
947C3×C4—61no—
948C3×C4—61no—
949C3×C4—61no—
950C3×C4—61no—
951C3×C4—61no—
952C3×C4—61no—
953C3×C4—61no—
954C3×C4—61no—
955C3×C4—61no—
956C3×C4—61no—
957C3×C4—61no—
958C3×C4—61no—
959C3×C4—121no—
960C3×C4—121no—
961C3×C4—121no—
962C3×C4—121no—
963C3×C4—121no—
964C3×C4—121no—
965C3×C4—121no—
966C3×C4—181no—
967C3×C4—181no—
968C3×C4—181no—
969Dic3—21no—
970Dic3—21no—
971Dic3—21no—
972Dic3—21no—
973Dic3—21no—
974Dic3—21no—
975Dic3—21no—
976Dic3—21no—
977Dic3—62no—
978Dic3—61no—
979Dic3—61no—
980Dic3—61no—
981Dic3—61no—
982Dic3—61no—
983Dic3—61no—
984Dic3—121no—
985Dic3—121no—
986C32—21no—
987C32—21no—
988C32—21no—
989C32—41no—
990C32#556411yescharacteristic, complemented
991C32#566511yescharacteristic, complemented
992C32C3×#53911yescharacteristic, complemented
993C23—91no—
994C23C2×C3×D3211yescharacteristic
995C23C2×C3×D3211yescharacteristic
996Q8—361no—
997D4—22no—
998D4—182no—
999D4—361no—
1000C2×C4—31no—
1001C2×C4—31no—
1002C2×C4—31no—
1003C2×C4—31no—
1004C2×C4—31no—
1005C2×C4—31no—
1006C2×C4—31no—
1007C2×C4—31no—
1008C2×C4—62no—
1009C2×C4—91no—
1010C2×C4—91no—
1011C2×C4—91no—
1012C2×C4—121no—
1013C2×C4—121no—
1014C2×C4—361no—
1015C2×C4—361no—
1016C2×C4C2×C3×D3211yescharacteristic
1017C2×C3—22no—
1018C2×C3—22no—
1019C2×C3—22no—
1020C2×C3—21no—
1021C2×C3—21no—
1022C2×C3—21no—
1023C2×C3—21no—
1024C2×C3—21no—
1025C2×C3—21no—
1026C2×C3—21no—
1027C2×C3—21no—
1028C2×C3—21no—
1029C2×C3—42no—
1030C2×C3—42no—
1031C2×C3—42no—
1032C2×C3—42no—
1033C2×C3—41no—
1034C2×C3—41no—
1035C2×C3—41no—
1036C2×C3—41no—
1037C2×C3—41no—
1038C2×C3—41no—
1039C2×C3—82no—
1040C2×C3—81no—
1041C2×C3—81no—
1042C2×C3—82no—
1043C2×C3—361no—
1044C2×C3#6430911yescharacteristic
1045C2×C3#6431411yescharacteristic
1046C2×C3C2×#380411yescharacteristic
1047C2×C3C2×C3×#23511yescharacteristic
1048C2×C3C2×C3×#23711yescharacteristic
1049C2×C3C3×#100411yescharacteristic
1050C2×C3C3×#100911yescharacteristic
1051C2×C3C3×#101011yescharacteristic
1052C2×C3C3×#101011yescharacteristic
1053D3—121no—
1054D3—121no—
1055D3—241no—
1056C22—21no—
1057C22—21no—
1058C22—21no—
1059C22—21no—
1060C22—21no—
1061C22—181no—
1062C22—181no—
1063C22—181no—
1064C22C3×#380412yes—
1065C22C22×C3×D3211yescharacteristic
1066C4—21no—
1067C4—61no—
1068C4—61no—
1069C4—61no—
1070C4—61no—
1071C4—61no—
1072C4—61no—
1073C4—61no—
1074C4—61no—
1075C4—181no—
1076C4—181no—
1077C4—181no—
1078C3—21no—
1079C3—21no—
1080C3—21no—
1081C3—41no—
1082C3#1059512711yescharacteristic, direct product factor
1083C3C3×#556411yescharacteristic, complemented
1084C3C3×#566511yescharacteristic, complemented
1085C2—22no—
1086C2—41no—
1087C2—361no—
1088C2C3×#6430911yescharacteristic
1089C2C3×#6431411yescharacteristic
1090C2C2×C3×#380411yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC2×C33×D4C22
socleC22×C33C24
prime radicalC3×#64148C2
hypercenterC2×C3×D4D32
hypocenterC32C3×#539
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
2. C32×#935C2semidirect
3. C32×D4×Dic3C2semidirect
4. C3×#63982C2semidirect
5. C3×#63975C2semidirect
6. C3×#63966C2semidirect
7. C3×#63966C2semidirect
8. C2×C3×Dic3⋊Dic3C2semidirect
9. C3×#63964C2semidirect
10. C3×#63956C2semidirect
11. C3×#63952C2semidirect
12. C3×#63895C2semidirect
13. C3×#63868C2semidirect
14. C3×#63867C2semidirect
15. C3×#63846C2semidirect
18. #10595127C3direct (N × H)
61. C3×#935D3semidirect
62. C3×#935C2×C3semidirect
64. C3×D4×Dic3D3semidirect
65. C3×D4×Dic3C2×C3semidirect
90. #63982C2×C3semidirect
91. #63975C2×C3semidirect
92. #63966C2×C3semidirect
93. #63966C2×C3semidirect
94. C2×Dic3⋊Dic3C2×C3semidirect
95. #63964C2×C3semidirect
96. #63956C2×C3semidirect
97. #63952C2×C3semidirect
98. #63895C2×C3semidirect
99. #63868C2×C3semidirect
100. #63867C2×C3semidirect
101. #63846C2×C3semidirect
300. #935C3×D3semidirect
301. D4×Dic3C3×D3semidirect
693. C33#539semidirect
990. C32#5564semidirect
991. C32#5665semidirect
992. C32C3×#539semidirect
1082. C3#10595127direct (N × H)
1083. C3C3×#5564semidirect
1084. C3C3×#5665semidirect

Maximal subgroups

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

subgroupindex
C3×#641482
C32×#9352
C32×D4×Dic32
C3×#639822
C3×#639752
C3×#639662
C2×C3×Dic3⋊Dic32
C3×#639642
C3×#639562
C3×#639522
C3×#638952
C3×#638682
C3×#638672
C3×#638462
C3×#56653
C3×#55643
#105951273