Finite Group Databasebeta

← C3×#10594968 #13174614

Subgroups — C3×#10594968 #13174614

Order 1728.

1172 conjugacy classes of subgroups.

The subgroup lattice has 1070 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×#924C211yesmaximal, characteristic, complemented
4C3×#63975C211yesmaximal, characteristic, complemented
5C3×#63969C211yesmaximal, characteristic, complemented
6C3×#63958C211yesmaximal, characteristic
7C3×#63956C211yesmaximal, characteristic, complemented
8C3×#63888C211yesmaximal, characteristic, complemented
9C3×#63887C211yesmaximal, characteristic, complemented
10C3×#63883C211yesmaximal, characteristic, complemented
11C3×#63881C211yesmaximal, characteristic, complemented
12C3×#63870C211yesmaximal, characteristic, complemented
13C3×#63862C211yesmaximal, characteristic, complemented
14C3×#63854C211yesmaximal, characteristic, complemented
15C3×#63846C211yesmaximal, characteristic, complemented
16C3×#5660—31nomaximal
17C3×#5638—31nomaximal
18#10594968C311yesmaximal, characteristic, direct product factor
19C22×C33×C4C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C2×C3×C4×C3⋊D3C2211yescharacteristic
22C2×C32×#67C2211yescharacteristic
23C2×C32×Dic6C2211yescharacteristic
24C2×C3×#626C2211yescharacteristic
25C2×C3×#624C2211yescharacteristic
26C2×C3×#624C2211yescharacteristic
27C2×C3×D3×Dic3C2211yescharacteristic
28C3×#3757C2211yescharacteristic
29C3×#3752C2211yescharacteristic
30C3×#3750C2211yescharacteristic
31C3×C4×C3⋊Dic3C2211yescharacteristic
32C32×#217C2211yescharacteristic
33C32×#217C2211yescharacteristic
34C32×#217C2211yescharacteristic
35C32×(C2×D3)⋊C4C2211yescharacteristic
36C32×(C2×D3)⋊C4C2211yescharacteristic
37C32×C4⋊Dic3C2211yescharacteristic
38C32×Dic3⋊C4C2211yescharacteristic
39C32×Dic3⋊C4C2211yescharacteristic
40C32×Dic3⋊C4C2211yescharacteristic
41C32×Dic3⋊C4C2211yescharacteristic
42C3×#3724C2211yescharacteristic
43C3×#3724C2211yescharacteristic
44C3×Dic3⋊Dic3C2211yescharacteristic
45C3×Dic3⋊Dic3C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×Dic3⋊Dic3C2211yescharacteristic
50C3×#3722C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54C32×#123—31no—
55C32×C22⋊Q8—31no—
56C4×#638C2×C311yescharacteristic, complemented
57C3×#946—31no—
58C3×#946—31no—
59C3×#938—31no—
60C3×#935—31no—
61C3×#929—21no—
62C3×#929D311yescharacteristic, complemented
63C3×#929C2×C311yescharacteristic, complemented
64C3×C4×#67—31no—
65C3×C4×#67—31no—
66C3×C4×#67—61no—
67C3×#924—21no—
68C3×#924D311yescharacteristic, complemented
69C3×#924C2×C311yescharacteristic, complemented
70C3×#898—31no—
71C3×#896—31no—
72C3×#894—31no—
73C3×#893—31no—
74C3×D3×C4⋊C4—31no—
75C3×D3×C4⋊C4—31no—
76C3×#890—31no—
77C3×#889—31no—
78C3×#889—31no—
79C3×#889—31no—
80C3×#884—31no—
81C3×#883—31no—
82C3×#883—31no—
83C3×#883—31no—
84C3×#883—31no—
85C3×#67⋊C4—31no—
86C3×#879—31no—
87C3×#879—31no—
88C3×#879—31no—
89C3×#878—31no—
90#63975C2×C311yescharacteristic, complemented
91#63969C2×C311yescharacteristic, complemented
92#63958C2×C311yescharacteristic
93#63956C2×C311yescharacteristic, complemented
94#63888C2×C311yescharacteristic, complemented
95#63887C2×C311yescharacteristic, complemented
96#63883C2×C311yescharacteristic, complemented
97#63881C2×C311yescharacteristic, complemented
98#63870C2×C311yescharacteristic, complemented
99#63862C2×C311yescharacteristic, complemented
100#63854C2×C311yescharacteristic, complemented
101#63846C2×C311yescharacteristic, complemented
102C23×C33C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C32×D3C2311yescharacteristic
105C2×C33×C4—41no—
106C2×C33×C4C2311yescharacteristic
107C2×C33×C4C2311yescharacteristic
108C3×#638—22no—
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C3×C4×C3⋊D3—41no—
113C32×#67—41no—
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C32×Dic6—41no—
122C3×#626—22no—
123C3×#624—22no—
124C3×#624—41no—
125C3×D3×Dic3—41no—
126C3×#539—91no—
127#5660—31no—
128#5638—31no—
129C2×C32×Q8—31no—
130C2×C32×D4—31no—
131C22×C32×C4—21no—
132C22×C32×C4—21no—
133C22×C32×C4—21no—
134C22×C32×C4—41no—
135C22×C32×C4C2×D311yescharacteristic
136C22×C32×C4C2×D311yescharacteristic
137C22×C32×C4C22×C311yescharacteristic
138C2×#638C22×C311yescharacteristic
139C2×C4×C3⋊D3C22×C311yescharacteristic
140C2×C3×#67—21no—
141C2×C3×#67—31no—
142C2×C3×#67—31no—
143C2×C3×#67—31no—
144C2×C3×#67—61no—
145C2×C3×#67C2×D311yescharacteristic
146C2×C3×#67C22×C311yescharacteristic
147C22×C3×Dic3—31no—
148C2×C3×D12—31no—
149C2×C3×C4×D3—31no—
150C2×C3×C4×D3—31no—
151C2×C3×C4×D3—31no—
152C2×C3×C4×D3—31no—
153C2×C3×C4×D3—31no—
154C2×C3×C4×D3—31no—
155C2×C3×C4×D3—31no—
156C2×C3×C4×D3—61no—
157C2×C3×Dic6—21no—
158C2×C3×Dic6C2×D311yescharacteristic
159C2×C3×Dic6C22×C311yescharacteristic
160C2×#626C22×C311yescharacteristic
161C2×#624C22×C311yescharacteristic
162C2×#624C22×C311yescharacteristic
163C2×D3×Dic3C22×C311yescharacteristic
164C32×C4⋊C4—31no—
165C32×C4⋊C4—31no—
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—
174#3757C22×C311yescharacteristic
175#3752C22×C311yescharacteristic
176#3750C22×C311yescharacteristic
177C4×C3⋊Dic3C22×C311yescharacteristic
178C3×#217—21no—
179C3×#217—21no—
180C3×#217—21no—
181C3×#217—31no—
182C3×#217—31no—
183C3×#217—31no—
184C3×#217—31no—
185C3×#217—61no—
186C3×#217C2×D311yescharacteristic
187C3×#217C2×D311yescharacteristic
188C3×#217C2×D311yescharacteristic
189C3×#217C22×C311yescharacteristic
190C3×#217C22×C311yescharacteristic
191C3×#217C22×C311yescharacteristic
192C3×(C2×D3)⋊C4—21no—
193C3×(C2×D3)⋊C4—21no—
194C3×(C2×D3)⋊C4—31no—
195C3×(C2×D3)⋊C4—31no—
196C3×(C2×D3)⋊C4—31no—
197C3×(C2×D3)⋊C4—31no—
198C3×(C2×D3)⋊C4—31no—
199C3×(C2×D3)⋊C4—31no—
200C3×(C2×D3)⋊C4—61no—
201C3×(C2×D3)⋊C4C2×D311yescharacteristic
202C3×(C2×D3)⋊C4C2×D311yescharacteristic
203C3×(C2×D3)⋊C4C22×C311yescharacteristic
204C3×(C2×D3)⋊C4C22×C311yescharacteristic
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⋊Dic3C2×D311yescharacteristic
213C3×C4⋊Dic3C22×C311yescharacteristic
214C3×Dic3⋊C4—21no—
215C3×Dic3⋊C4—21no—
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—61no—
231C3×Dic3⋊C4C2×D311yescharacteristic
232C3×Dic3⋊C4C2×D311yescharacteristic
233C3×Dic3⋊C4C2×D311yescharacteristic
234C3×Dic3⋊C4C2×D311yescharacteristic
235C3×Dic3⋊C4C22×C311yescharacteristic
236C3×Dic3⋊C4C22×C311yescharacteristic
237C3×Dic3⋊C4C22×C311yescharacteristic
238C3×Dic3⋊C4C22×C311yescharacteristic
239C3×C4×Dic3—31no—
240C3×C4×Dic3—31no—
241C3×C4×Dic3—31no—
242C3×C4×Dic3—31no—
243C3×C4×Dic3—61no—
244#3724C22×C311yescharacteristic
245#3724C22×C311yescharacteristic
246Dic3⋊Dic3C22×C311yescharacteristic
247Dic3⋊Dic3C22×C311yescharacteristic
248Dic3⋊Dic3C22×C311yescharacteristic
249Dic3⋊Dic3C22×C311yescharacteristic
250Dic3⋊Dic3C22×C311yescharacteristic
251Dic3⋊Dic3C22×C311yescharacteristic
252#3722C22×C311yescharacteristic
253(C2×D3)⋊Dic3C22×C311yescharacteristic
254(C2×D3)⋊Dic3C22×C311yescharacteristic
255Dic32C22×C311yescharacteristic
256C22×C33—21no—
257C22×C33—21no—
258C22×C33—21no—
259C22×C33C2411yescharacteristic
260C2×C3×C3⋊D3—21no—
261C2×C3×C3⋊D3—21no—
262C2×C3×C3⋊D3#4112yes—
263C2×C32×D3—21no—
264C2×C32×D3—21no—
265C2×C32×D3—21no—
266C33×C4—21no—
267C33×C4—21no—
268C3×C3⋊Dic3—21no—
269C3×C3⋊Dic3—21no—
270C3×C3⋊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—31no—
289C3×C22⋊Q8—31no—
290C3×C22⋊Q8—61no—
291C3×C22⋊Q8—91no—
292C3×C22⋊Q8—91no—
293C3×#121—91no—
294C3×C4×D4—91no—
295C3×C4×D4—91no—
296C2×C3×C4⋊C4—91no—
297#946—31no—
298#946—31no—
299#938—31no—
300#935—31no—
301#929C3×D311yescharacteristic, complemented
302C4×#67—31no—
303C4×#67—31no—
304C4×#67—61no—
305#924C3×D311yescharacteristic, complemented
306#898—31no—
307#896—31no—
308#894—31no—
309#893—31no—
310D3×C4⋊C4—31no—
311D3×C4⋊C4—31no—
312#890—31no—
313#889—31no—
314#889—31no—
315#889—31no—
316#884—31no—
317#883—31no—
318#883—31no—
319#883—31no—
320#883—31no—
321#67⋊C4—31no—
322#879—31no—
323#879—31no—
324#879—31no—
325#878—31no—
326C23×C32—21no—
327C23×C32—21no—
328C23×C32—21no—
329C23×C32—31no—
330C23×C32—41no—
331C23×C32C22×D311yescharacteristic
332C23×C32C22×D311yescharacteristic
333C23×C32C23×C311yescharacteristic
334C22×C3⋊D3C23×C311yescharacteristic
335C22×C3×D3—21no—
336C22×C3×D3—31no—
337C22×C3×D3—31no—
338C22×C3×D3—61no—
339C22×C3×D3C22×D311yescharacteristic
340C22×C3×D3C23×C311yescharacteristic
341C32×Q8—121no—
342C32×D4—121no—
343C2×C32×C4—21no—
344C2×C32×C4—21no—
345C2×C32×C4—21no—
346C2×C32×C4—21no—
347C2×C32×C4—21no—
348C2×C32×C4—21no—
349C2×C32×C4—31no—
350C2×C32×C4—31no—
351C2×C32×C4—31no—
352C2×C32×C4—31no—
353C2×C32×C4—31no—
354C2×C32×C4—31no—
355C2×C32×C4—31no—
356C2×C32×C4—41no—
357C2×C32×C4—41no—
358C2×C32×C4—41no—
359C2×C32×C4—41no—
360C2×C32×C4—41no—
361C2×C32×C4—42no—
362C2×C32×C4—42no—
363C2×C32×C4—42no—
364C2×C32×C4—44no—
365C2×C32×C4C22×D311yescharacteristic
366C2×C32×C4C22×D311yescharacteristic
367C2×C32×C4C22×D311yescharacteristic
368C2×C32×C4C22×D311yescharacteristic
369C2×C32×C4C23×C311yescharacteristic
370C2×C32×C4C23×C311yescharacteristic
371#638—22no—
372C2×C3⋊Dic3C23×C311yescharacteristic
373C2×C3⋊Dic3C23×C311yescharacteristic
374C2×C3⋊Dic3C23×C311yescharacteristic
375C4×C3⋊D3—41no—
376C3×#67—41no—
377C3×#67—41no—
378C3×#67—42no—
379C3×#67—62no—
380C3×#67—62no—
381C3×#67—62no—
382C3×#67—64no—
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—31no—
391C2×C3×Dic3—31no—
392C2×C3×Dic3—31no—
393C2×C3×Dic3—31no—
394C2×C3×Dic3—31no—
395C2×C3×Dic3—31no—
396C2×C3×Dic3—61no—
397C2×C3×Dic3—61no—
398C2×C3×Dic3—61no—
399C2×C3×Dic3—121no—
400C2×C3×Dic3C22×D311yescharacteristic
401C2×C3×Dic3C22×D311yescharacteristic
402C2×C3×Dic3C22×D311yescharacteristic
403C2×C3×Dic3C22×D311yescharacteristic
404C2×C3×Dic3C22×D311yescharacteristic
405C2×C3×Dic3C22×D311yescharacteristic
406C2×C3×Dic3C22×D311yescharacteristic
407C2×C3×Dic3C23×C311yescharacteristic
408C2×C3×Dic3C23×C311yescharacteristic
409C2×C3×Dic3C23×C311yescharacteristic
410C2×C3×Dic3C23×C311yescharacteristic
411C2×C3×Dic3C23×C311yescharacteristic
412C2×C3×Dic3C23×C311yescharacteristic
413C2×C3×Dic3C23×C311yescharacteristic
414C3×D12—62no—
415C3×C4×D3—62no—
416C3×C4×D3—62no—
417C3×C4×D3—121no—
418C3×C4×D3—121no—
419C3×C4×D3—121no—
420C3×C4×D3—121no—
421C3×C4×D3—121no—
422C3×C4×D3—122no—
423C3×Dic6—41no—
424C3×Dic6—41no—
425C3×Dic6—42no—
426#626—22no—
427#624—22no—
428#624—41no—
429D3×Dic3—41no—
430#539—91noSylow
431C2×C33—41no—
432C2×C33C2×#4111yescharacteristic
433C2×C33H(5,𝔽2)11yescharacteristic
434C2×C332−1+411yescharacteristic
435C3×C3⋊D3—22no—
436C32×D3—41no—
437C2×C3×Q8—31no—
438C2×C3×Q8—31no—
439C2×C3×Q8—61no—
440C2×C3×D4—31no—
441C2×C3×D4—31no—
442C2×C3×D4—61no—
443C2×C3×D4—91no—
444C2×C3×D4—91no—
445C22×C3×C4—21no—
446C22×C3×C4—21no—
447C22×C3×C4—21no—
448C22×C3×C4—41no—
449C22×C3×C4—91no—
450C22×C3×C4—91no—
451C22×C3×C4—91no—
452C22×C3×C4—91no—
453C22×C3×C4D3211yescharacteristic
454C22×C3×C4C2×C3×D311yescharacteristic
455C22×C3×C4C2×C3×D311yescharacteristic
456C2×#67—31no—
457C2×#67—31no—
458C2×#67—31no—
459C2×#67—61no—
460C2×#67C2×C3×D311yescharacteristic
461C22×Dic3—31no—
462C2×D12—31no—
463C2×C4×D3—31no—
464C2×C4×D3—31no—
465C2×C4×D3—31no—
466C2×C4×D3—31no—
467C2×C4×D3—31no—
468C2×C4×D3—31no—
469C2×C4×D3—31no—
470C2×C4×D3—61no—
471C2×Dic6C2×C3×D311yescharacteristic
472C3×C4⋊C4—31no—
473C3×C4⋊C4—31no—
474C3×C4⋊C4—31no—
475C3×C4⋊C4—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—61no—
486C3×C4⋊C4—61no—
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—91no—
517C3×C42—91no—
518#217—31no—
519#217—31no—
520#217—31no—
521#217—31no—
522#217—61no—
523#217C2×C3×D311yescharacteristic
524#217C2×C3×D311yescharacteristic
525#217C2×C3×D311yescharacteristic
526(C2×D3)⋊C4—31no—
527(C2×D3)⋊C4—31no—
528(C2×D3)⋊C4—31no—
529(C2×D3)⋊C4—31no—
530(C2×D3)⋊C4—31no—
531(C2×D3)⋊C4—31no—
532(C2×D3)⋊C4—61no—
533(C2×D3)⋊C4C2×C3×D311yescharacteristic
534(C2×D3)⋊C4C2×C3×D311yescharacteristic
535C4⋊Dic3—31no—
536C4⋊Dic3—31no—
537C4⋊Dic3—31no—
538C4⋊Dic3—31no—
539C4⋊Dic3—31no—
540C4⋊Dic3—31no—
541C4⋊Dic3C2×C3×D311yescharacteristic
542Dic3⋊C4—31no—
543Dic3⋊C4—31no—
544Dic3⋊C4—31no—
545Dic3⋊C4—31no—
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—61no—
555Dic3⋊C4C2×C3×D311yescharacteristic
556Dic3⋊C4C2×C3×D311yescharacteristic
557Dic3⋊C4C2×C3×D311yescharacteristic
558Dic3⋊C4C2×C3×D311yescharacteristic
559C4×Dic3—31no—
560C4×Dic3—31no—
561C4×Dic3—31no—
562C4×Dic3—31no—
563C4×Dic3—61no—
564C22×C32—21no—
565C22×C32—21no—
566C22×C32—21no—
567C22×C32—22no—
568C22×C32—22no—
569C22×C32—22no—
570C22×C32—21no—
571C22×C32—21no—
572C22×C32—21no—
573C22×C32—21no—
574C22×C32—21no—
575C22×C32—21no—
576C22×C32—21no—
577C22×C32—21no—
578C22×C32—21no—
579C22×C32—41no—
580C22×C32—41no—
581C22×C32—41no—
582C22×C32—41no—
583C22×C32—41no—
584C22×C32—41no—
585C22×C32—41no—
586C22×C32—42no—
587C22×C32—42no—
588C22×C32—42no—
589C22×C32—61no—
590C22×C32—61no—
591C22×C32—61no—
592C22×C32C23×D311yescharacteristic
593C22×C32C23×D311yescharacteristic
594C22×C32C24×C311yescharacteristic
595C2×C3⋊D3—21no—
596C2×C3⋊D3—21no—
597C2×C3⋊D3C3×#4112yes—
598C2×C3×D3—21no—
599C2×C3×D3—21no—
600C2×C3×D3—21no—
601C2×C3×D3—21no—
602C2×C3×D3—21no—
603C2×C3×D3—21no—
604C2×C3×D3—32no—
605C2×C3×D3—32no—
606C2×C3×D3—41no—
607C2×C3×D3—41no—
608C2×C3×D3—41no—
609C2×C3×D3—62no—
610C2×C3×D3—61no—
611C2×C3×D3—61no—
612C2×C3×D3—61no—
613C2×C3×D3—61no—
614C2×C3×D3—121no—
615C2×C3×D3—121no—
616C32×C4—21no—
617C32×C4—21no—
618C32×C4—22no—
619C32×C4—22no—
620C32×C4—21no—
621C32×C4—21no—
622C32×C4—21no—
623C32×C4—21no—
624C32×C4—41no—
625C32×C4—41no—
626C32×C4—41no—
627C32×C4—41no—
628C32×C4—42no—
629C32×C4—42no—
630C32×C4—61no—
631C32×C4—61no—
632C32×C4—61no—
633C32×C4—61no—
634C32×C4—61no—
635C32×C4—61no—
636C32×C4—61no—
637C3⋊Dic3—21no—
638C3⋊Dic3—21no—
639C3⋊Dic3—21no—
640C3×Dic3—21no—
641C3×Dic3—21no—
642C3×Dic3—21no—
643C3×Dic3—21no—
644C3×Dic3—21no—
645C3×Dic3—21no—
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—41no—
655C3×Dic3—41no—
656C3×Dic3—41no—
657C3×Dic3—41no—
658C3×Dic3—41no—
659C3×Dic3—41no—
660C3×Dic3—41no—
661C3×Dic3—62no—
662C3×Dic3—61no—
663C3×Dic3—61no—
664C3×Dic3—61no—
665C3×Dic3—61no—
666C3×Dic3—61no—
667C3×Dic3—61no—
668C3×Dic3—121no—
669C3×Dic3—121no—
670#126—91no—
671#126—91no—
672#125—91no—
673#125—91no—
674#123—31no—
675#123—91no—
676#123—91no—
677#123—91no—
678C22⋊Q8—31no—
679C22⋊Q8—91no—
680C22⋊Q8—91no—
681#121—91no—
682C4×D4—91no—
683C4×D4—91no—
684C2×C4⋊C4—91no—
685C33#53911yescharacteristic, complemented, Sylow
686C23×C3—21no—
687C23×C3—21no—
688C23×C3—21no—
689C23×C3—31no—
690C23×C3—31no—
691C23×C3—41no—
692C23×C3—61no—
693C23×C3—91no—
694C23×C3C2×D3211yescharacteristic
695C23×C3C22×C3×D311yescharacteristic
696C23×C3C22×C3×D311yescharacteristic
697C22×D3—31no—
698C22×D3—31no—
699C22×D3—61no—
700C22×D3C22×C3×D311yescharacteristic
701C3×Q8—121no—
702C3×Q8—121no—
703C3×Q8—122no—
704C3×D4—121no—
705C3×D4—121no—
706C3×D4—122no—
707C3×D4—182no—
708C3×D4—182no—
709C2×C3×C4—21no—
710C2×C3×C4—21no—
711C2×C3×C4—21no—
712C2×C3×C4—21no—
713C2×C3×C4—21no—
714C2×C3×C4—21no—
715C2×C3×C4—31no—
716C2×C3×C4—31no—
717C2×C3×C4—31no—
718C2×C3×C4—31no—
719C2×C3×C4—31no—
720C2×C3×C4—31no—
721C2×C3×C4—31no—
722C2×C3×C4—31no—
723C2×C3×C4—31no—
724C2×C3×C4—31no—
725C2×C3×C4—31no—
726C2×C3×C4—31no—
727C2×C3×C4—31no—
728C2×C3×C4—31no—
729C2×C3×C4—41no—
730C2×C3×C4—41no—
731C2×C3×C4—41no—
732C2×C3×C4—42no—
733C2×C3×C4—42no—
734C2×C3×C4—42no—
735C2×C3×C4—44no—
736C2×C3×C4—41no—
737C2×C3×C4—41no—
738C2×C3×C4—61no—
739C2×C3×C4—61no—
740C2×C3×C4—61no—
741C2×C3×C4—61no—
742C2×C3×C4—61no—
743C2×C3×C4—61no—
744C2×C3×C4—61no—
745C2×C3×C4—91no—
746C2×C3×C4—91no—
747C2×C3×C4—91no—
748C2×C3×C4—182no—
749C2×C3×C4—361no—
750C2×C3×C4—361no—
751C2×C3×C4—361no—
752C2×C3×C4C2×D3211yescharacteristic
753C2×C3×C4C2×D3211yescharacteristic
754C2×C3×C4C22×C3×D311yescharacteristic
755C2×C3×C4C22×C3×D311yescharacteristic
756C2×C3×C4C22×C3×D311yescharacteristic
757C2×C3×C4C22×C3×D311yescharacteristic
758#67—41no—
759#67—62no—
760#67—62no—
761#67—62no—
762#67—64no—
763C2×Dic3—31no—
764C2×Dic3—31no—
765C2×Dic3—31no—
766C2×Dic3—31no—
767C2×Dic3—31no—
768C2×Dic3—31no—
769C2×Dic3—61no—
770C2×Dic3—61no—
771C2×Dic3—61no—
772C2×Dic3—121no—
773C2×Dic3C22×C3×D311yescharacteristic
774C2×Dic3C22×C3×D311yescharacteristic
775C2×Dic3C22×C3×D311yescharacteristic
776C2×Dic3C22×C3×D311yescharacteristic
777C2×Dic3C22×C3×D311yescharacteristic
778C2×Dic3C22×C3×D311yescharacteristic
779C2×Dic3C22×C3×D311yescharacteristic
780D12—62no—
781C4×D3—62no—
782C4×D3—62no—
783C4×D3—121no—
784C4×D3—121no—
785C4×D3—121no—
786C4×D3—121no—
787C4×D3—121no—
788C4×D3—122no—
789Dic6—41no—
790C2×C32—21no—
791C2×C32—21no—
792C2×C32—21no—
793C2×C32—21no—
794C2×C32—21no—
795C2×C32—21no—
796C2×C32—21no—
797C2×C32—21no—
798C2×C32—21no—
799C2×C32—41no—
800C2×C32—41no—
801C2×C32—41no—
802C2×C32—42no—
803C2×C32—42no—
804C2×C32—42no—
805C2×C32—44no—
806C2×C32—41no—
807C2×C32—41no—
808C2×C32—41no—
809C2×C32—121no—
810C2×C32#100411yescharacteristic
811C2×C32#100411yescharacteristic
812C2×C32#100711yescharacteristic
813C2×C32D3×#4111yescharacteristic
814C2×C32D3×#4111yescharacteristic
815C2×C32#101011yescharacteristic
816C2×C32C2×C3×#4111yescharacteristic
817C2×C32C3×H(5,𝔽2)11yescharacteristic
818C2×C32C3×2−1+411yescharacteristic
819C3⋊D3—22no—
820C3×D3—41no—
821C3×D3—41no—
822C3×D3—62no—
823C3×D3—62no—
824C3×D3—81no—
825C3×D3—122no—
826C2×Q8—31no—
827C2×D4—31no—
828C2×D4—91no—
829C2×D4—91no—
830C22×C4—91no—
831C22×C4—91no—
832C22×C4—91no—
833C22×C4—91no—
834C22×C4C3×D3211yescharacteristic
835C4⋊C4—31no—
836C4⋊C4—31no—
837C4⋊C4—31no—
838C4⋊C4—31no—
839C4⋊C4—31no—
840C4⋊C4—91no—
841C4⋊C4—91no—
842C4⋊C4—91no—
843C4⋊C4—91no—
844C4⋊C4—91no—
845C4⋊C4—91no—
846C4⋊C4—91no—
847C4⋊C4—91no—
848C4⋊C4—91no—
849C22⋊C4—31no—
850C22⋊C4—31no—
851C22⋊C4—31no—
852C22⋊C4—31no—
853C22⋊C4—31no—
854C22⋊C4—91no—
855C22⋊C4—91no—
856C22⋊C4—91no—
857C22⋊C4—91no—
858C22⋊C4—91no—
859C42—91no—
860C42—91no—
861C22×C3—22no—
862C22×C3—22no—
863C22×C3—22no—
864C22×C3—21no—
865C22×C3—21no—
866C22×C3—21no—
867C22×C3—21no—
868C22×C3—21no—
869C22×C3—21no—
870C22×C3—21no—
871C22×C3—21no—
872C22×C3—21no—
873C22×C3—21no—
874C22×C3—21no—
875C22×C3—21no—
876C22×C3—41no—
877C22×C3—41no—
878C22×C3—41no—
879C22×C3—41no—
880C22×C3—41no—
881C22×C3—41no—
882C22×C3—42no—
883C22×C3—42no—
884C22×C3—42no—
885C22×C3—41no—
886C22×C3—61no—
887C22×C3—61no—
888C22×C3—61no—
889C22×C3—61no—
890C22×C3—61no—
891C22×C3—61no—
892C22×C3—92no—
893C22×C3—121no—
894C22×C3—121no—
895C22×C3—121no—
896C22×C3—181no—
897C22×C3—181no—
898C22×C3C22×D3211yescharacteristic
899C22×C3C23×C3×D311yescharacteristic
900C22×C3C23×C3×D311yescharacteristic
901C2×D3—21no—
902C2×D3—21no—
903C2×D3—21no—
904C2×D3—32no—
905C2×D3—32no—
906C2×D3—62no—
907C2×D3—61no—
908C2×D3—61no—
909C2×D3—61no—
910C2×D3—61no—
911C2×D3—121no—
912C2×D3—121no—
913C3×C4—22no—
914C3×C4—22no—
915C3×C4—21no—
916C3×C4—21no—
917C3×C4—21no—
918C3×C4—21no—
919C3×C4—21no—
920C3×C4—21no—
921C3×C4—41no—
922C3×C4—41no—
923C3×C4—41no—
924C3×C4—41no—
925C3×C4—42no—
926C3×C4—42no—
927C3×C4—61no—
928C3×C4—61no—
929C3×C4—61no—
930C3×C4—61no—
931C3×C4—61no—
932C3×C4—61no—
933C3×C4—61no—
934C3×C4—61no—
935C3×C4—61no—
936C3×C4—61no—
937C3×C4—61no—
938C3×C4—61no—
939C3×C4—61no—
940C3×C4—61no—
941C3×C4—121no—
942C3×C4—121no—
943C3×C4—121no—
944C3×C4—121no—
945C3×C4—121no—
946C3×C4—121no—
947C3×C4—121no—
948C3×C4—181no—
949C3×C4—181no—
950C3×C4—181no—
951Dic3—21no—
952Dic3—21no—
953Dic3—21no—
954Dic3—21no—
955Dic3—21no—
956Dic3—21no—
957Dic3—21no—
958Dic3—62no—
959Dic3—61no—
960Dic3—61no—
961Dic3—61no—
962Dic3—61no—
963Dic3—61no—
964Dic3—61no—
965Dic3—121no—
966Dic3—121no—
967C32—21no—
968C32—21no—
969C32—21no—
970C32—41no—
971C32#563811yescharacteristic, complemented
972C32#566011yescharacteristic, complemented
973C32C3×#53911yescharacteristic, complemented
974C23—31no—
975C23—91no—
976C23C2×C3×D3211yescharacteristic
977Q8—121no—
978D4—121no—
979D4—182no—
980D4—182no—
981C2×C4—31no—
982C2×C4—31no—
983C2×C4—31no—
984C2×C4—31no—
985C2×C4—31no—
986C2×C4—31no—
987C2×C4—31no—
988C2×C4—41no—
989C2×C4—91no—
990C2×C4—91no—
991C2×C4—91no—
992C2×C4—182no—
993C2×C4—361no—
994C2×C4—361no—
995C2×C4—361no—
996C2×C4C2×C3×D3211yescharacteristic
997C2×C4C2×C3×D3211yescharacteristic
998C2×C3—21no—
999C2×C3—21no—
1000C2×C3—21no—
1001C2×C3—21no—
1002C2×C3—21no—
1003C2×C3—21no—
1004C2×C3—21no—
1005C2×C3—21no—
1006C2×C3—21no—
1007C2×C3—42no—
1008C2×C3—42no—
1009C2×C3—42no—
1010C2×C3—44no—
1011C2×C3—41no—
1012C2×C3—41no—
1013C2×C3—41no—
1014C2×C3—41no—
1015C2×C3—41no—
1016C2×C3—41no—
1017C2×C3—121no—
1018C2×C3—121no—
1019C2×C3—182no—
1020C2×C3—241no—
1021C2×C3#6429711yescharacteristic
1022C2×C3#6430611yescharacteristic
1023C2×C3#6433011yescharacteristic
1024C2×C3C3×#100411yescharacteristic
1025C2×C3C3×#100411yescharacteristic
1026C2×C3C3×#100711yescharacteristic
1027C2×C3C3×D3×#4111yescharacteristic
1028C2×C3C3×D3×#4111yescharacteristic
1029C2×C3C3×#101011yescharacteristic
1030D3—41no—
1031D3—62no—
1032D3—62no—
1033D3—122no—
1034C22—21no—
1035C22—21no—
1036C22—21no—
1037C22—61no—
1038C22—61no—
1039C22—61no—
1040C22—92no—
1041C22—181no—
1042C22—181no—
1043C22C22×C3×D3211yescharacteristic
1044C4—21no—
1045C4—21no—
1046C4—61no—
1047C4—61no—
1048C4—61no—
1049C4—61no—
1050C4—61no—
1051C4—61no—
1052C4—61no—
1053C4—181no—
1054C4—181no—
1055C4—181no—
1056C3—21no—
1057C3—21no—
1058C3—21no—
1059C3—41no—
1060C3#1059496811yescharacteristic, direct product factor
1061C3C3×#563811yescharacteristic, complemented
1062C3C3×#566011yescharacteristic, complemented
1063C2—41no—
1064C2—121no—
1065C2—182no—
1066C2C3×#6429711yescharacteristic
1067C2C3×#6430611yescharacteristic
1068C2C3×#6433011yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC22×C33×C4C22
socleC22×C33C24
prime radicalC3×#63958C2
hypercenterC22×C3×C4D32
hypocenterC32C3×#539
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×#924C2semidirect
4. C3×#63975C2semidirect
5. C3×#63969C2semidirect
7. C3×#63956C2semidirect
8. C3×#63888C2semidirect
9. C3×#63887C2semidirect
10. C3×#63883C2semidirect
11. C3×#63881C2semidirect
12. C3×#63870C2semidirect
13. C3×#63862C2semidirect
14. C3×#63854C2semidirect
15. C3×#63846C2semidirect
18. #10594968C3direct (N × H)
56. C4×#638C2×C3semidirect
62. C3×#929D3semidirect
63. C3×#929C2×C3semidirect
68. C3×#924D3semidirect
69. C3×#924C2×C3semidirect
90. #63975C2×C3semidirect
91. #63969C2×C3semidirect
93. #63956C2×C3semidirect
94. #63888C2×C3semidirect
95. #63887C2×C3semidirect
96. #63883C2×C3semidirect
97. #63881C2×C3semidirect
98. #63870C2×C3semidirect
99. #63862C2×C3semidirect
100. #63854C2×C3semidirect
101. #63846C2×C3semidirect
301. #929C3×D3semidirect
305. #924C3×D3semidirect
685. C33#539semidirect
971. C32#5638semidirect
972. C32#5660semidirect
973. C32C3×#539semidirect
1060. C3#10594968direct (N × H)
1061. C3C3×#5638semidirect
1062. C3C3×#5660semidirect

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×#9242
C3×#639752
C3×#639692
C3×#639582
C3×#639562
C3×#638882
C3×#638872
C3×#638832
C3×#638812
C3×#638702
C3×#638622
C3×#638542
C3×#638462
C3×#56603
C3×#56383
#105949683