Finite Group Databasebeta

← C3×#10594842 #13174619

Subgroups — C3×#10594842 #13174619

Order 1728.

1206 conjugacy classes of subgroups.

The subgroup lattice has 1074 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×#638C211yesmaximal, characteristic, complemented
2C32×C4×#67C211yesmaximal, characteristic, complemented
3C2×C32×Dic3⋊C4C211yesmaximal, characteristic, complemented
4C3×#63978C211yesmaximal, characteristic
5C3×#63966C211yesmaximal, characteristic, complemented
6C3×#63964C211yesmaximal, characteristic, complemented
7C3×#63961C211yesmaximal, characteristic, complemented
8C3×#63870C211yesmaximal, characteristic, complemented
9C3×#63868C211yesmaximal, characteristic, complemented
10C3×#63867C211yesmaximal, characteristic, complemented
11C3×#63865C211yesmaximal, characteristic, complemented
12C3×#63862C211yesmaximal, characteristic, complemented
13C3×#63853C211yesmaximal, characteristic, complemented
14C3×#63851C211yesmaximal, characteristic, complemented
15C3×#63850C211yesmaximal, characteristic, complemented
16C3×#5564—31nomaximal
17C3×#5515—31nomaximal
18#10594842C311yesmaximal, characteristic, direct product factor
19C22×C33×C4C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C2×C3×C4×C3⋊D3C2211yescharacteristic
22C2×C32×#67C2211yescharacteristic
23C22×C32×Dic3C2211yescharacteristic
24C22×C32×Dic3C2211yescharacteristic
25C2×C32×C4×D3C2211yescharacteristic
26C2×C3×#627C2211yescharacteristic
27C2×C3×#626C2211yescharacteristic
28C3×#3757C2211yescharacteristic
29C3×#3752C2211yescharacteristic
30C3×#3750C2211yescharacteristic
31C3×C4×C3⋊Dic3C2211yescharacteristic
32C32×#217C2211yescharacteristic
33C32×(C2×D3)⋊C4C2211yescharacteristic
34C32×Dic3⋊C4C2211yescharacteristic
35C32×Dic3⋊C4C2211yescharacteristic
36C32×Dic3⋊C4C2211yescharacteristic
37C32×Dic3⋊C4C2211yescharacteristic
38C32×Dic3⋊C4C2211yescharacteristic
39C32×C4×Dic3C2211yescharacteristic
40C3×#3724C2211yescharacteristic
41C3×#3724C2211yescharacteristic
42C3×#3724C2211yescharacteristic
43C3×Dic3⋊Dic3C2211yescharacteristic
44C3×Dic3⋊Dic3C2211yescharacteristic
45C3×Dic3⋊Dic3C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×#3722C2211yescharacteristic
49C3×#3722C2211yescharacteristic
50C3×#3722C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×(C2×D3)⋊Dic3C2211yescharacteristic
54C32×C4×D4—31no—
55C2×C32×C4⋊C4—31no—
56C4×#638C2×C311yescharacteristic, complemented
57C3×#939—31no—
58C3×#935—31no—
59C3×#930—31no—
60C3×#929—31no—
61C3×#929—31no—
62C3×#929—31no—
63C3×C4×#67—21no—
64C3×C4×#67—31no—
65C3×C4×#67—31no—
66C3×C4×#67—61no—
67C3×C4×#67D311yescharacteristic, complemented
68C3×C4×#67C2×C311yescharacteristic, complemented
69C3×#924—31no—
70C3×#924—31no—
71C2×C3×Dic3⋊C4—21no—
72C2×C3×Dic3⋊C4D311yescharacteristic, complemented
73C2×C3×Dic3⋊C4C2×C311yescharacteristic, complemented
74C3×#898—31no—
75C3×#898—31no—
76C3×#896—31no—
77C3×#896—31no—
78C3×#896—31no—
79C3×#894—31no—
80C3×#894—31no—
81C3×#889—31no—
82C3×#889—31no—
83C3×#889—31no—
84C3×#886—31no—
85C3×#883—31no—
86C3×#879—31no—
87C3×#878—31no—
88C3×#876—31no—
89C3×#870—31no—
90#63978C2×C311yescharacteristic
91#63966C2×C311yescharacteristic, complemented
92#63964C2×C311yescharacteristic, complemented
93#63961C2×C311yescharacteristic, complemented
94#63870C2×C311yescharacteristic, complemented
95#63868C2×C311yescharacteristic, complemented
96#63867C2×C311yescharacteristic, complemented
97#63865C2×C311yescharacteristic, complemented
98#63862C2×C311yescharacteristic, complemented
99#63853C2×C311yescharacteristic, complemented
100#63851C2×C311yescharacteristic, complemented
101#63850C2×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—22no—
114C2×C32×Dic3—22no—
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
123C32×C4×D3—41no—
124C3×#627—41no—
125C3×#626—41no—
126C3×#539—91no—
127#5564—31no—
128#5515—31no—
129C2×C32×D4—31no—
130C22×C32×C4—21no—
131C22×C32×C4—21no—
132C22×C32×C4—21no—
133C22×C32×C4—31no—
134C22×C32×C4—31no—
135C22×C32×C4—31no—
136C22×C32×C4—41no—
137C22×C32×C4C2×D311yescharacteristic
138C22×C32×C4C2×D311yescharacteristic
139C22×C32×C4C22×C311yescharacteristic
140C2×#638C22×C311yescharacteristic
141C2×C4×C3⋊D3C22×C311yescharacteristic
142C2×C3×#67—21no—
143C2×C3×#67—31no—
144C2×C3×#67—31no—
145C2×C3×#67—31no—
146C2×C3×#67—61no—
147C2×C3×#67C2×D311yescharacteristic
148C2×C3×#67C22×C311yescharacteristic
149C22×C3×Dic3—21no—
150C22×C3×Dic3—21no—
151C22×C3×Dic3C2×D311yescharacteristic
152C22×C3×Dic3C2×D311yescharacteristic
153C22×C3×Dic3C22×C311yescharacteristic
154C22×C3×Dic3C22×C311yescharacteristic
155C2×C3×D12—31no—
156C2×C3×C4×D3—21no—
157C2×C3×C4×D3—31no—
158C2×C3×C4×D3—31no—
159C2×C3×C4×D3—61no—
160C2×C3×C4×D3C2×D311yescharacteristic
161C2×C3×C4×D3C22×C311yescharacteristic
162C2×C3×Dic6—31no—
163C2×C3×Dic6—31no—
164C2×#627C22×C311yescharacteristic
165C2×#626C22×C311yescharacteristic
166C32×C4⋊C4—31no—
167C32×C4⋊C4—31no—
168C32×C4⋊C4—31no—
169C32×C4⋊C4—31no—
170C32×C4⋊C4—31no—
171C32×C22⋊C4—31no—
172C32×C22⋊C4—31no—
173C32×C42—31no—
174#3757C22×C311yescharacteristic
175#3752C22×C311yescharacteristic
176#3750C22×C311yescharacteristic
177C4×C3⋊Dic3C22×C311yescharacteristic
178C3×#217—21no—
179C3×#217—31no—
180C3×#217—31no—
181C3×#217—31no—
182C3×#217—31no—
183C3×#217—31no—
184C3×#217—61no—
185C3×#217C2×D311yescharacteristic
186C3×#217C22×C311yescharacteristic
187C3×(C2×D3)⋊C4—21no—
188C3×(C2×D3)⋊C4—31no—
189C3×(C2×D3)⋊C4—31no—
190C3×(C2×D3)⋊C4—31no—
191C3×(C2×D3)⋊C4—31no—
192C3×(C2×D3)⋊C4—31no—
193C3×(C2×D3)⋊C4—31no—
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—61no—
200C3×(C2×D3)⋊C4C2×D311yescharacteristic
201C3×(C2×D3)⋊C4C22×C311yescharacteristic
202C3×C4⋊Dic3—31no—
203C3×C4⋊Dic3—31no—
204C3×C4⋊Dic3—31no—
205C3×C4⋊Dic3—31no—
206C3×C4⋊Dic3—31no—
207C3×Dic3⋊C4—21no—
208C3×Dic3⋊C4—21no—
209C3×Dic3⋊C4—21no—
210C3×Dic3⋊C4—21no—
211C3×Dic3⋊C4—21no—
212C3×Dic3⋊C4—31no—
213C3×Dic3⋊C4—31no—
214C3×Dic3⋊C4—31no—
215C3×Dic3⋊C4—31no—
216C3×Dic3⋊C4—31no—
217C3×Dic3⋊C4—31no—
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—61no—
226C3×Dic3⋊C4C2×D311yescharacteristic
227C3×Dic3⋊C4C2×D311yescharacteristic
228C3×Dic3⋊C4C2×D311yescharacteristic
229C3×Dic3⋊C4C2×D311yescharacteristic
230C3×Dic3⋊C4C2×D311yescharacteristic
231C3×Dic3⋊C4C22×C311yescharacteristic
232C3×Dic3⋊C4C22×C311yescharacteristic
233C3×Dic3⋊C4C22×C311yescharacteristic
234C3×Dic3⋊C4C22×C311yescharacteristic
235C3×Dic3⋊C4C22×C311yescharacteristic
236C3×C4×Dic3—21no—
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
245Dic3⋊Dic3C22×C311yescharacteristic
246Dic3⋊Dic3C22×C311yescharacteristic
247Dic3⋊Dic3C22×C311yescharacteristic
248Dic3⋊Dic3C22×C311yescharacteristic
249Dic3⋊Dic3C22×C311yescharacteristic
250#3722C22×C311yescharacteristic
251#3722C22×C311yescharacteristic
252#3722C22×C311yescharacteristic
253(C2×D3)⋊Dic3C22×C311yescharacteristic
254(C2×D3)⋊Dic3C22×C311yescharacteristic
255(C2×D3)⋊Dic3C22×C311yescharacteristic
256C22×C33—21no—
257C22×C33—21no—
258C22×C33#4112yes—
259C22×C33C2411yescharacteristic
260C2×C3×C3⋊D3—21no—
261C2×C3×C3⋊D3—21no—
262C2×C3×C3⋊D3—21no—
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—91no—
283C3×#123—91no—
284C3×#123—91no—
285C3×#123—91no—
286C3×C22⋊Q8—91no—
287C3×C22⋊Q8—91no—
288C3×C22⋊Q8—91no—
289C3×#121—91no—
290C3×C4×D4—31no—
291C3×C4×D4—31no—
292C3×C4×D4—61no—
293C3×C4×D4—91no—
294C2×C3×C4⋊C4—31no—
295C2×C3×C4⋊C4—31no—
296C2×C3×C4⋊C4—61no—
297#939—31no—
298#935—31no—
299#930—31no—
300#929—31no—
301#929—31no—
302#929—31no—
303C4×#67—31no—
304C4×#67—31no—
305C4×#67—61no—
306C4×#67C3×D311yescharacteristic, complemented
307#924—31no—
308#924—31no—
309C2×Dic3⋊C4C3×D311yescharacteristic, complemented
310#898—31no—
311#898—31no—
312#896—31no—
313#896—31no—
314#896—31no—
315#894—31no—
316#894—31no—
317#889—31no—
318#889—31no—
319#889—31no—
320#886—31no—
321#883—31no—
322#879—31no—
323#878—31no—
324#876—31no—
325#870—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×D4—62no—
342C2×C32×C4—21no—
343C2×C32×C4—21no—
344C2×C32×C4—21no—
345C2×C32×C4—21no—
346C2×C32×C4—21no—
347C2×C32×C4—21no—
348C2×C32×C4—31no—
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—41no—
356C2×C32×C4—41no—
357C2×C32×C4—41no—
358C2×C32×C4—41no—
359C2×C32×C4—41no—
360C2×C32×C4—42no—
361C2×C32×C4—42no—
362C2×C32×C4—42no—
363C2×C32×C4—44no—
364C2×C32×C4—62no—
365C2×C32×C4—121no—
366C2×C32×C4—121no—
367C2×C32×C4C22×D311yescharacteristic
368C2×C32×C4C22×D311yescharacteristic
369C2×C32×C4C22×D311yescharacteristic
370C2×C32×C4C22×D311yescharacteristic
371C2×C32×C4C23×C311yescharacteristic
372C2×C32×C4C23×C311yescharacteristic
373#638—22no—
374C2×C3⋊Dic3C23×C311yescharacteristic
375C2×C3⋊Dic3C23×C311yescharacteristic
376C2×C3⋊Dic3C23×C311yescharacteristic
377C4×C3⋊D3—41no—
378C3×#67—24no—
379C3×#67—22no—
380C3×#67—22no—
381C3×#67—64no—
382C3×#67—62no—
383C3×#67—62no—
384C3×#67—121no—
385C2×C3×Dic3—24no—
386C2×C3×Dic3—22no—
387C2×C3×Dic3—22no—
388C2×C3×Dic3—21no—
389C2×C3×Dic3—21no—
390C2×C3×Dic3—21no—
391C2×C3×Dic3—21no—
392C2×C3×Dic3—21no—
393C2×C3×Dic3—21no—
394C2×C3×Dic3—21no—
395C2×C3×Dic3—31no—
396C2×C3×Dic3—31no—
397C2×C3×Dic3—31no—
398C2×C3×Dic3—31no—
399C2×C3×Dic3—31no—
400C2×C3×Dic3—31no—
401C2×C3×Dic3—41no—
402C2×C3×Dic3—41no—
403C2×C3×Dic3—42no—
404C2×C3×Dic3—61no—
405C2×C3×Dic3—61no—
406C2×C3×Dic3—61no—
407C2×C3×Dic3C22×D311yescharacteristic
408C2×C3×Dic3C22×D311yescharacteristic
409C2×C3×Dic3C22×D311yescharacteristic
410C2×C3×Dic3C22×D311yescharacteristic
411C2×C3×Dic3C22×D311yescharacteristic
412C2×C3×Dic3C22×D311yescharacteristic
413C2×C3×Dic3C22×D311yescharacteristic
414C2×C3×Dic3C23×C311yescharacteristic
415C2×C3×Dic3C23×C311yescharacteristic
416C2×C3×Dic3C23×C311yescharacteristic
417C2×C3×Dic3C23×C311yescharacteristic
418C2×C3×Dic3C23×C311yescharacteristic
419C2×C3×Dic3C23×C311yescharacteristic
420C2×C3×Dic3C23×C311yescharacteristic
421C3×D12—121no—
422C3×C4×D3—41no—
423C3×C4×D3—41no—
424C3×C4×D3—42no—
425C3×C4×D3—121no—
426C3×C4×D3—121no—
427C3×C4×D3—122no—
428C3×Dic6—121no—
429C3×Dic6—121no—
430#627—41no—
431#626—41no—
432#539—91noSylow
433C2×C33—22no—
434C2×C33C2×#4111yescharacteristic
435C2×C33H(5,𝔽2)11yescharacteristic
436C2×C332−1+411yescharacteristic
437C3×C3⋊D3—41no—
438C32×D3—41no—
439C2×C3×Q8—91no—
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—31no—
449C22×C3×C4—31no—
450C22×C3×C4—31no—
451C22×C3×C4—31no—
452C22×C3×C4—31no—
453C22×C3×C4—31no—
454C22×C3×C4—41no—
455C22×C3×C4—61no—
456C22×C3×C4—61no—
457C22×C3×C4—61no—
458C22×C3×C4—91no—
459C22×C3×C4D3211yescharacteristic
460C22×C3×C4C2×C3×D311yescharacteristic
461C22×C3×C4C2×C3×D311yescharacteristic
462C2×#67—31no—
463C2×#67—31no—
464C2×#67—31no—
465C2×#67—61no—
466C2×#67C2×C3×D311yescharacteristic
467C22×Dic3C2×C3×D311yescharacteristic
468C22×Dic3C2×C3×D311yescharacteristic
469C2×D12—31no—
470C2×C4×D3—31no—
471C2×C4×D3—31no—
472C2×C4×D3—61no—
473C2×C4×D3C2×C3×D311yescharacteristic
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—31no—
483C3×C4⋊C4—31no—
484C3×C4⋊C4—31no—
485C3×C4⋊C4—31no—
486C3×C4⋊C4—61no—
487C3×C4⋊C4—61no—
488C3×C4⋊C4—61no—
489C3×C4⋊C4—61no—
490C3×C4⋊C4—61no—
491C3×C4⋊C4—91no—
492C3×C4⋊C4—91no—
493C3×C4⋊C4—91no—
494C3×C4⋊C4—91no—
495C3×C4⋊C4—91no—
496C3×C4⋊C4—91no—
497C3×C4⋊C4—91no—
498C3×C4⋊C4—91no—
499C3×C4⋊C4—91no—
500C3×C22⋊C4—31no—
501C3×C22⋊C4—31no—
502C3×C22⋊C4—31no—
503C3×C22⋊C4—31no—
504C3×C22⋊C4—61no—
505C3×C22⋊C4—61no—
506C3×C22⋊C4—91no—
507C3×C22⋊C4—91no—
508C3×C22⋊C4—91no—
509C3×C22⋊C4—91no—
510C3×C22⋊C4—91no—
511C3×C22⋊C4—91no—
512C3×C22⋊C4—91no—
513C3×C22⋊C4—91no—
514C3×C42—31no—
515C3×C42—31no—
516C3×C42—61no—
517C3×C42—91no—
518#217—31no—
519#217—31no—
520#217—31no—
521#217—31no—
522#217—31no—
523#217—61no—
524#217C2×C3×D311yescharacteristic
525(C2×D3)⋊C4—31no—
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—31no—
533(C2×D3)⋊C4—31no—
534(C2×D3)⋊C4—31no—
535(C2×D3)⋊C4—31no—
536(C2×D3)⋊C4—61no—
537(C2×D3)⋊C4C2×C3×D311yescharacteristic
538C4⋊Dic3—31no—
539C4⋊Dic3—31no—
540C4⋊Dic3—31no—
541C4⋊Dic3—31no—
542C4⋊Dic3—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—31no—
555Dic3⋊C4—31no—
556Dic3⋊C4—61no—
557Dic3⋊C4C2×C3×D311yescharacteristic
558Dic3⋊C4C2×C3×D311yescharacteristic
559Dic3⋊C4C2×C3×D311yescharacteristic
560Dic3⋊C4C2×C3×D311yescharacteristic
561Dic3⋊C4C2×C3×D311yescharacteristic
562C4×Dic3—31no—
563C4×Dic3—31no—
564C4×Dic3—61no—
565C4×Dic3C2×C3×D311yescharacteristic
566C22×C32—21no—
567C22×C32—21no—
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—22no—
578C22×C32—22no—
579C22×C32—22no—
580C22×C32—42no—
581C22×C32—41no—
582C22×C32—41no—
583C22×C32—41no—
584C22×C32—41no—
585C22×C32—41no—
586C22×C32—42no—
587C22×C32—42no—
588C22×C32—61no—
589C22×C32—61no—
590C22×C32—61no—
591C22×C32#23512yes—
592C22×C32#23512yes—
593C22×C32C3×#4112yes—
594C22×C32C23×D311yescharacteristic
595C22×C32C23×D311yescharacteristic
596C22×C32C24×C311yescharacteristic
597C2×C3⋊D3—21no—
598C2×C3⋊D3—21no—
599C2×C3⋊D3—21no—
600C2×C3×D3—22no—
601C2×C3×D3—21no—
602C2×C3×D3—21no—
603C2×C3×D3—21no—
604C2×C3×D3—21no—
605C2×C3×D3—21no—
606C2×C3×D3—21no—
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—61no—
615C2×C3×D3—61no—
616C2×C3×D3—121no—
617C2×C3×D3—121no—
618C32×C4—21no—
619C32×C4—21no—
620C32×C4—22no—
621C32×C4—22no—
622C32×C4—21no—
623C32×C4—21no—
624C32×C4—21no—
625C32×C4—21no—
626C32×C4—41no—
627C32×C4—41no—
628C32×C4—41no—
629C32×C4—41no—
630C32×C4—42no—
631C32×C4—42no—
632C32×C4—61no—
633C32×C4—61no—
634C32×C4—61no—
635C32×C4—61no—
636C32×C4—61no—
637C32×C4—61no—
638C32×C4—61no—
639C3⋊Dic3—21no—
640C3⋊Dic3—21no—
641C3⋊Dic3—21no—
642C3×Dic3—22no—
643C3×Dic3—22no—
644C3×Dic3—22no—
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—21no—
655C3×Dic3—21no—
656C3×Dic3—21no—
657C3×Dic3—21no—
658C3×Dic3—21no—
659C3×Dic3—41no—
660C3×Dic3—41no—
661C3×Dic3—41no—
662C3×Dic3—41no—
663C3×Dic3—62no—
664C3×Dic3—61no—
665C3×Dic3—61no—
666C3×Dic3—61no—
667C3×Dic3—61no—
668C3×Dic3—61no—
669C3×Dic3—61no—
670C3×Dic3—121no—
671C3×Dic3—121no—
672#126—91no—
673#126—91no—
674#125—91no—
675#125—91no—
676#123—91no—
677#123—91no—
678#123—91no—
679#123—91no—
680C22⋊Q8—91no—
681C22⋊Q8—91no—
682C22⋊Q8—91no—
683#121—91no—
684C4×D4—31no—
685C4×D4—91no—
686C2×C4⋊C4—31no—
687C33#53911yescharacteristic, complemented, Sylow
688C23×C3—21no—
689C23×C3—21no—
690C23×C3—21no—
691C23×C3—31no—
692C23×C3—31no—
693C23×C3—41no—
694C23×C3—61no—
695C23×C3—91no—
696C23×C3C2×D3211yescharacteristic
697C23×C3C22×C3×D311yescharacteristic
698C23×C3C22×C3×D311yescharacteristic
699C22×D3—31no—
700C22×D3—31no—
701C22×D3—61no—
702C22×D3C22×C3×D311yescharacteristic
703C3×Q8—361no—
704C3×D4—64no—
705C3×D4—62no—
706C3×D4—62no—
707C3×D4—182no—
708C3×D4—361no—
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—64no—
746C2×C3×C4—62no—
747C2×C3×C4—62no—
748C2×C3×C4—91no—
749C2×C3×C4—91no—
750C2×C3×C4—91no—
751C2×C3×C4—121no—
752C2×C3×C4—121no—
753C2×C3×C4—122no—
754C2×C3×C4—121no—
755C2×C3×C4—121no—
756C2×C3×C4—122no—
757C2×C3×C4—361no—
758C2×C3×C4C2×D3211yescharacteristic
759C2×C3×C4C2×D3211yescharacteristic
760C2×C3×C4C22×C3×D311yescharacteristic
761C2×C3×C4C22×C3×D311yescharacteristic
762C2×C3×C4C22×C3×D311yescharacteristic
763C2×C3×C4C22×C3×D311yescharacteristic
764#67—22no—
765#67—64no—
766#67—62no—
767#67—62no—
768#67—121no—
769C2×Dic3—22no—
770C2×Dic3—31no—
771C2×Dic3—31no—
772C2×Dic3—31no—
773C2×Dic3—31no—
774C2×Dic3—31no—
775C2×Dic3—31no—
776C2×Dic3—41no—
777C2×Dic3—61no—
778C2×Dic3—61no—
779C2×Dic3—61no—
780C2×Dic3C22×C3×D311yescharacteristic
781C2×Dic3C22×C3×D311yescharacteristic
782C2×Dic3C22×C3×D311yescharacteristic
783C2×Dic3C22×C3×D311yescharacteristic
784C2×Dic3C22×C3×D311yescharacteristic
785C2×Dic3C22×C3×D311yescharacteristic
786C2×Dic3C22×C3×D311yescharacteristic
787D12—121no—
788C4×D3—41no—
789C4×D3—121no—
790C4×D3—121no—
791C4×D3—122no—
792Dic6—121no—
793Dic6—121no—
794C2×C32—22no—
795C2×C32—24no—
796C2×C32—22no—
797C2×C32—22no—
798C2×C32—21no—
799C2×C32—21no—
800C2×C32—21no—
801C2×C32—21no—
802C2×C32—21no—
803C2×C32—21no—
804C2×C32—21no—
805C2×C32—21no—
806C2×C32—21no—
807C2×C32—41no—
808C2×C32—41no—
809C2×C32—41no—
810C2×C32—42no—
811C2×C32—42no—
812C2×C32—44no—
813C2×C32—121no—
814C2×C32C2×#23511yescharacteristic
815C2×C32C2×#23511yescharacteristic
816C2×C32#100411yescharacteristic
817C2×C32#100411yescharacteristic
818C2×C32#100711yescharacteristic
819C2×C32#101011yescharacteristic
820C2×C32C2×C3×#4111yescharacteristic
821C2×C32C3×H(5,𝔽2)11yescharacteristic
822C2×C32C3×2−1+411yescharacteristic
823C3⋊D3—41no—
824C3×D3—42no—
825C3×D3—41no—
826C3×D3—41no—
827C3×D3—122no—
828C3×D3—121no—
829C3×D3—121no—
830C2×Q8—91no—
831C2×D4—31no—
832C2×D4—91no—
833C2×D4—91no—
834C22×C4—31no—
835C22×C4—31no—
836C22×C4—31no—
837C22×C4—91no—
838C22×C4C3×D3211yescharacteristic
839C4⋊C4—31no—
840C4⋊C4—31no—
841C4⋊C4—31no—
842C4⋊C4—31no—
843C4⋊C4—31no—
844C4⋊C4—91no—
845C4⋊C4—91no—
846C4⋊C4—91no—
847C4⋊C4—91no—
848C4⋊C4—91no—
849C4⋊C4—91no—
850C4⋊C4—91no—
851C4⋊C4—91no—
852C4⋊C4—91no—
853C22⋊C4—31no—
854C22⋊C4—31no—
855C22⋊C4—91no—
856C22⋊C4—91no—
857C22⋊C4—91no—
858C22⋊C4—91no—
859C22⋊C4—91no—
860C22⋊C4—91no—
861C22⋊C4—91no—
862C22⋊C4—91no—
863C42—31no—
864C42—91no—
865C22×C3—22no—
866C22×C3—22no—
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—22no—
877C22×C3—22no—
878C22×C3—22no—
879C22×C3—41no—
880C22×C3—41no—
881C22×C3—41no—
882C22×C3—41no—
883C22×C3—42no—
884C22×C3—42no—
885C22×C3—41no—
886C22×C3—42no—
887C22×C3—62no—
888C22×C3—61no—
889C22×C3—61no—
890C22×C3—61no—
891C22×C3—61no—
892C22×C3—61no—
893C22×C3—61no—
894C22×C3—121no—
895C22×C3—121no—
896C22×C3—181no—
897C22×C3—181no—
898C22×C3—181no—
899C22×C3#379812yes—
900C22×C3C3×#23512yes—
901C22×C3C3×#23512yes—
902C22×C3C22×D3211yescharacteristic
903C22×C3C23×C3×D311yescharacteristic
904C22×C3C23×C3×D311yescharacteristic
905C2×D3—21no—
906C2×D3—21no—
907C2×D3—21no—
908C2×D3—62no—
909C2×D3—61no—
910C2×D3—61no—
911C2×D3—61no—
912C2×D3—61no—
913C2×D3—61no—
914C2×D3—61no—
915C2×D3—121no—
916C2×D3—121no—
917C3×C4—22no—
918C3×C4—22no—
919C3×C4—21no—
920C3×C4—21no—
921C3×C4—21no—
922C3×C4—21no—
923C3×C4—21no—
924C3×C4—21no—
925C3×C4—41no—
926C3×C4—41no—
927C3×C4—41no—
928C3×C4—41no—
929C3×C4—42no—
930C3×C4—42no—
931C3×C4—62no—
932C3×C4—62no—
933C3×C4—62no—
934C3×C4—61no—
935C3×C4—61no—
936C3×C4—61no—
937C3×C4—61no—
938C3×C4—61no—
939C3×C4—61no—
940C3×C4—61no—
941C3×C4—61no—
942C3×C4—61no—
943C3×C4—61no—
944C3×C4—61no—
945C3×C4—61no—
946C3×C4—61no—
947C3×C4—61no—
948C3×C4—121no—
949C3×C4—121no—
950C3×C4—121no—
951C3×C4—121no—
952C3×C4—181no—
953C3×C4—181no—
954C3×C4—181no—
955Dic3—21no—
956Dic3—21no—
957Dic3—21no—
958Dic3—21no—
959Dic3—21no—
960Dic3—21no—
961Dic3—21no—
962Dic3—62no—
963Dic3—61no—
964Dic3—61no—
965Dic3—61no—
966Dic3—61no—
967Dic3—61no—
968Dic3—61no—
969Dic3—121no—
970Dic3—121no—
971C32—21no—
972C32—21no—
973C32—21no—
974C32—41no—
975C32#551511yescharacteristic, complemented
976C32#556411yescharacteristic, complemented
977C32C3×#53911yescharacteristic, complemented
978C23—31no—
979C23—91no—
980C23C2×C3×D3211yescharacteristic
981Q8—361no—
982D4—62no—
983D4—182no—
984D4—361no—
985C2×C4—31no—
986C2×C4—31no—
987C2×C4—31no—
988C2×C4—31no—
989C2×C4—31no—
990C2×C4—31no—
991C2×C4—31no—
992C2×C4—41no—
993C2×C4—62no—
994C2×C4—91no—
995C2×C4—91no—
996C2×C4—91no—
997C2×C4—121no—
998C2×C4—121no—
999C2×C4—361no—
1000C2×C4C2×C3×D3211yescharacteristic
1001C2×C4C2×C3×D3211yescharacteristic
1002C2×C3—24no—
1003C2×C3—22no—
1004C2×C3—22no—
1005C2×C3—22no—
1006C2×C3—21no—
1007C2×C3—21no—
1008C2×C3—21no—
1009C2×C3—21no—
1010C2×C3—21no—
1011C2×C3—21no—
1012C2×C3—21no—
1013C2×C3—21no—
1014C2×C3—21no—
1015C2×C3—42no—
1016C2×C3—42no—
1017C2×C3—44no—
1018C2×C3—41no—
1019C2×C3—41no—
1020C2×C3—41no—
1021C2×C3—122no—
1022C2×C3—121no—
1023C2×C3—121no—
1024C2×C3—361no—
1025C2×C3#6429711yescharacteristic
1026C2×C3C2×#379811yescharacteristic
1027C2×C3#6433011yescharacteristic
1028C2×C3C2×C3×#23511yescharacteristic
1029C2×C3C2×C3×#23511yescharacteristic
1030C2×C3C3×#100411yescharacteristic
1031C2×C3C3×#100411yescharacteristic
1032C2×C3C3×#100711yescharacteristic
1033C2×C3C3×#101011yescharacteristic
1034D3—41no—
1035D3—122no—
1036D3—121no—
1037D3—121no—
1038C22—21no—
1039C22—21no—
1040C22—61no—
1041C22—61no—
1042C22—61no—
1043C22—181no—
1044C22—181no—
1045C22—181no—
1046C22C3×#379812yes—
1047C22C22×C3×D3211yescharacteristic
1048C4—21no—
1049C4—21no—
1050C4—61no—
1051C4—61no—
1052C4—61no—
1053C4—61no—
1054C4—61no—
1055C4—61no—
1056C4—61no—
1057C4—181no—
1058C4—181no—
1059C4—181no—
1060C3—21no—
1061C3—21no—
1062C3—21no—
1063C3—41no—
1064C3#1059484211yescharacteristic, direct product factor
1065C3C3×#551511yescharacteristic, complemented
1066C3C3×#556411yescharacteristic, complemented
1067C2—22no—
1068C2—121no—
1069C2—361no—
1070C2C3×#6429711yescharacteristic
1071C2C2×C3×#379811yescharacteristic
1072C2C3×#6433011yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC22×C33×C4C22
socleC22×C33C24
prime radicalC3×#63978C2
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×C4×#67C2semidirect
3. C2×C32×Dic3⋊C4C2semidirect
5. C3×#63966C2semidirect
6. C3×#63964C2semidirect
7. C3×#63961C2semidirect
8. C3×#63870C2semidirect
9. C3×#63868C2semidirect
10. C3×#63867C2semidirect
11. C3×#63865C2semidirect
12. C3×#63862C2semidirect
13. C3×#63853C2semidirect
14. C3×#63851C2semidirect
15. C3×#63850C2semidirect
18. #10594842C3direct (N × H)
56. C4×#638C2×C3semidirect
67. C3×C4×#67D3semidirect
68. C3×C4×#67C2×C3semidirect
72. C2×C3×Dic3⋊C4D3semidirect
73. C2×C3×Dic3⋊C4C2×C3semidirect
91. #63966C2×C3semidirect
92. #63964C2×C3semidirect
93. #63961C2×C3semidirect
94. #63870C2×C3semidirect
95. #63868C2×C3semidirect
96. #63867C2×C3semidirect
97. #63865C2×C3semidirect
98. #63862C2×C3semidirect
99. #63853C2×C3semidirect
100. #63851C2×C3semidirect
101. #63850C2×C3semidirect
306. C4×#67C3×D3semidirect
309. C2×Dic3⋊C4C3×D3semidirect
687. C33#539semidirect
975. C32#5515semidirect
976. C32#5564semidirect
977. C32C3×#539semidirect
1064. C3#10594842direct (N × H)
1065. C3C3×#5515semidirect
1066. C3C3×#5564semidirect

Maximal subgroups

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

subgroupindex
C3×C4×#6382
C32×C4×#672
C2×C32×Dic3⋊C42
C3×#639782
C3×#639662
C3×#639642
C3×#639612
C3×#638702
C3×#638682
C3×#638672
C3×#638652
C3×#638622
C3×#638532
C3×#638512
C3×#638502
C3×#55643
C3×#55153
#105948423