Finite Group Databasebeta

← C3×#10594428 #13173987

Subgroups — C3×#10594428 #13173987

Order 1728.

1104 conjugacy classes of subgroups.

The subgroup lattice has 1044 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64098C211yesmaximal, characteristic, complemented
2C32×#895C211yesmaximal, characteristic
3C32×#889C211yesmaximal, characteristic, complemented
4C3×#63899C211yesmaximal, characteristic, complemented
5C3×#63898C211yesmaximal, characteristic, complemented
6C3×#63893C211yesmaximal, characteristic, complemented
7C3×Dic3×D12C211yesmaximal, characteristic, complemented
8C3×#63884C211yesmaximal, characteristic, complemented
9C3×#63884C211yesmaximal, characteristic, complemented
10C3×#63884C211yesmaximal, characteristic, complemented
11C3×#63884C211yesmaximal, characteristic, complemented
12C3×D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
13C3×#63862C211yesmaximal, characteristic, complemented
14C3×#63859C211yesmaximal, characteristic, complemented
15C3×#63851C211yesmaximal, characteristic, complemented
16C3×#5692—31nomaximal
17C3×#5602—31nomaximal
18#10594428C311yesmaximal, characteristic, direct product factor
19C2×C32×D12C2211yescharacteristic
20C2×C32×D12C2211yescharacteristic
21C2×C32×D12C2211yescharacteristic
22C2×C32×C4×D3C2211yescharacteristic
23C2×C3×#627C2211yescharacteristic
24C2×C3×D3×Dic3C2211yescharacteristic
25C2×C3×D3×Dic3C2211yescharacteristic
26C2×C3×D3×Dic3C2211yescharacteristic
27C2×C3×D3×Dic3C2211yescharacteristic
28C33×C4⋊C4C2211yescharacteristic
29C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
30C3×#3750C2211yescharacteristic
31C3×#3750C2211yescharacteristic
32C3×#3750C2211yescharacteristic
33C3×#3750C2211yescharacteristic
34C3×C4×C3⋊Dic3C2211yescharacteristic
35C32×(C2×D3)⋊C4C2211yescharacteristic
36C32×(C2×D3)⋊C4C2211yescharacteristic
37C32×C4⋊Dic3C2211yescharacteristic
38C32×Dic3⋊C4C2211yescharacteristic
39C32×Dic3⋊C4C2211yescharacteristic
40C32×Dic3⋊C4C2211yescharacteristic
41C32×Dic3⋊C4C2211yescharacteristic
42C32×C4×Dic3C2211yescharacteristic
43C3×#3724C2211yescharacteristic
44C3×Dic3⋊Dic3C2211yescharacteristic
45C3×Dic3⋊Dic3C2211yescharacteristic
46C3×(C2×D3)⋊Dic3C2211yescharacteristic
47C3×(C2×D3)⋊Dic3C2211yescharacteristic
48C3×(C2×D3)⋊Dic3C2211yescharacteristic
49C3×(C2×D3)⋊Dic3C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×(C2×D3)⋊Dic3C2211yescharacteristic
54C32×#125—31no—
55C32×#121—31no—
56#64098C2×C311yescharacteristic, complemented
57C3×#935—31no—
58C3×#935—31no—
59C3×#935—31no—
60C3×#935—31no—
61C3×D4×Dic3—31no—
62C3×D4×Dic3—31no—
63C3×#924—31no—
64C2×C3×Dic3⋊C4—31no—
65C3×#898—31no—
66C3×#897—31no—
67C3×#896—31no—
68C3×#896—31no—
69C3×#895—21no—
70C3×#895D311yescharacteristic
71C3×#895C2×C311yescharacteristic
72C3×#894—31no—
73C3×#894—31no—
74C3×#894—31no—
75C3×#894—31no—
76C3×#893—31no—
77C3×D3×C4⋊C4—31no—
78C3×#889—21no—
79C3×#889—31no—
80C3×#889—31no—
81C3×#889—61no—
82C3×#889D311yescharacteristic, complemented
83C3×#889C2×C311yescharacteristic, complemented
84C3×#879—31no—
85C3×#879—31no—
86C3×#878—31no—
87C3×#878—31no—
88C3×#876—31no—
89C3×C4×D12—31no—
90#63899C2×C311yescharacteristic, complemented
91#63898C2×C311yescharacteristic, complemented
92#63893C2×C311yescharacteristic, complemented
93Dic3×D12C2×C311yescharacteristic, complemented
94#63884C2×C311yescharacteristic, complemented
95#63884C2×C311yescharacteristic, complemented
96#63884C2×C311yescharacteristic, complemented
97#63884C2×C311yescharacteristic, complemented
98D3×Dic3⋊C4C2×C311yescharacteristic, complemented
99#63862C2×C311yescharacteristic, complemented
100#63859C2×C311yescharacteristic, complemented
101#63851C2×C311yescharacteristic, complemented
102C22×C32×D3C2311yescharacteristic
103C22×C32×D3C2311yescharacteristic
104C22×C32×D3C2311yescharacteristic
105C2×C33×C4C2311yescharacteristic
106C2×C33×C4C2311yescharacteristic
107C2×C33×C4C2311yescharacteristic
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C32×Dic3C2311yescharacteristic
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C32×D12—22no—
118C32×D12—22no—
119C32×D12—41no—
120C32×C4×D3—41no—
121C3×#627—41no—
122C3×D3×Dic3—22no—
123C3×D3×Dic3—41no—
124C3×D3×Dic3—41no—
125C3×D3×Dic3—41no—
126C3×#539—91no—
127#5692—31no—
128#5602—31no—
129C2×C32×D4—31no—
130C2×C32×D4—31no—
131C2×C32×D4—31no—
132C22×C32×C4—31no—
133C22×C3×Dic3—31no—
134C22×C3×Dic3—31no—
135C22×C3×Dic3—31no—
136C22×C3×Dic3—31no—
137C2×C3×D12—21no—
138C2×C3×D12—21no—
139C2×C3×D12—21no—
140C2×C3×D12C2×D311yescharacteristic
141C2×C3×D12C2×D311yescharacteristic
142C2×C3×D12C2×D311yescharacteristic
143C2×C3×D12C22×C311yescharacteristic
144C2×C3×D12C22×C311yescharacteristic
145C2×C3×D12C22×C311yescharacteristic
146C2×C3×C4×D3—21no—
147C2×C3×C4×D3—31no—
148C2×C3×C4×D3—31no—
149C2×C3×C4×D3—31no—
150C2×C3×C4×D3—31no—
151C2×C3×C4×D3C2×D311yescharacteristic
152C2×C3×C4×D3C22×C311yescharacteristic
153C2×C3×Dic6—31no—
154C2×C3×Dic6—31no—
155C2×#627C22×C311yescharacteristic
156C2×D3×Dic3C22×C311yescharacteristic
157C2×D3×Dic3C22×C311yescharacteristic
158C2×D3×Dic3C22×C311yescharacteristic
159C2×D3×Dic3C22×C311yescharacteristic
160C32×C4⋊C4—21no—
161C32×C4⋊C4—21no—
162C32×C4⋊C4—21no—
163C32×C4⋊C4—31no—
164C32×C4⋊C4—31no—
165C32×C4⋊C4—31no—
166C32×C4⋊C4—31no—
167C32×C4⋊C4—31no—
168C32×C4⋊C4—41no—
169C32×C4⋊C4C2×D311yescharacteristic
170C32×C4⋊C4C2×D311yescharacteristic
171C32×C4⋊C4C22×C311yescharacteristic
172C32×C22⋊C4—31no—
173C32×C22⋊C4—31no—
174C32×C42—31no—
175C4⋊(C3⋊Dic3)C22×C311yescharacteristic
176#3750C22×C311yescharacteristic
177#3750C22×C311yescharacteristic
178#3750C22×C311yescharacteristic
179#3750C22×C311yescharacteristic
180C4×C3⋊Dic3C22×C311yescharacteristic
181C3×#217—31no—
182C3×#217—31no—
183C3×#217—31no—
184C3×#217—31no—
185C3×#217—31no—
186C3×#217—31no—
187C3×#217—31no—
188C3×#217—31no—
189C3×(C2×D3)⋊C4—21no—
190C3×(C2×D3)⋊C4—21no—
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)⋊C4C2×D311yescharacteristic
200C3×(C2×D3)⋊C4C2×D311yescharacteristic
201C3×(C2×D3)⋊C4C22×C311yescharacteristic
202C3×(C2×D3)⋊C4C22×C311yescharacteristic
203C3×C4⋊Dic3—21no—
204C3×C4⋊Dic3—31no—
205C3×C4⋊Dic3—31no—
206C3×C4⋊Dic3—31no—
207C3×C4⋊Dic3—31no—
208C3×C4⋊Dic3—61no—
209C3×C4⋊Dic3C2×D311yescharacteristic
210C3×C4⋊Dic3C22×C311yescharacteristic
211C3×Dic3⋊C4—21no—
212C3×Dic3⋊C4—21no—
213C3×Dic3⋊C4—21no—
214C3×Dic3⋊C4—21no—
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—31no—
226C3×Dic3⋊C4—31no—
227C3×Dic3⋊C4—61no—
228C3×Dic3⋊C4—61no—
229C3×Dic3⋊C4—61no—
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—21no—
240C3×C4×Dic3—31no—
241C3×C4×Dic3—31no—
242C3×C4×Dic3—61no—
243C3×C4×Dic3C2×D311yescharacteristic
244C3×C4×Dic3C22×C311yescharacteristic
245#3724C22×C311yescharacteristic
246Dic3⋊Dic3C22×C311yescharacteristic
247Dic3⋊Dic3C22×C311yescharacteristic
248(C2×D3)⋊Dic3C22×C311yescharacteristic
249(C2×D3)⋊Dic3C22×C311yescharacteristic
250(C2×D3)⋊Dic3C22×C311yescharacteristic
251(C2×D3)⋊Dic3C22×C311yescharacteristic
252(C2×D3)⋊Dic3C22×C311yescharacteristic
253(C2×D3)⋊Dic3C22×C311yescharacteristic
254(C2×D3)⋊Dic3C22×C311yescharacteristic
255(C2×D3)⋊Dic3C22×C311yescharacteristic
256C22×C33C2411yescharacteristic
257C2×C32×D3—21no—
258C2×C32×D3—21no—
259C2×C32×D3—21no—
260C2×C32×D3—21no—
261C2×C32×D3—21no—
262C2×C32×D3—21no—
263C2×C32×D3—21no—
264C2×C32×D3—21no—
265C2×C32×D3#4112yes—
266C33×C4—21no—
267C33×C4—21no—
268C33×C4—21no—
269C3×C3⋊Dic3—21no—
270C3×C3⋊Dic3—21no—
271C3×C3⋊Dic3—21no—
272C3×C3⋊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—31no—
281C3×#125—31no—
282C3×#125—61no—
283C3×#125—91no—
284C3×#123—91no—
285C3×#123—91no—
286C3×#123—91no—
287C3×#123—91no—
288C3×C22⋊Q8—91no—
289C3×C22⋊Q8—91no—
290C3×C22⋊Q8—91no—
291C3×#121—31no—
292C3×#121—31no—
293C3×#121—61no—
294C3×C4×D4—91no—
295C3×C4×D4—91no—
296C2×C3×C4⋊C4—91no—
297#935—31no—
298#935—31no—
299#935—31no—
300#935—31no—
301D4×Dic3—31no—
302D4×Dic3—31no—
303#924—31no—
304C2×Dic3⋊C4—31no—
305#898—31no—
306#897—31no—
307#896—31no—
308#896—31no—
309#895C3×D311yescharacteristic
310#894—31no—
311#894—31no—
312#894—31no—
313#894—31no—
314#893—31no—
315D3×C4⋊C4—31no—
316#889—31no—
317#889—31no—
318#889—61no—
319#889C3×D311yescharacteristic, complemented
320#879—31no—
321#879—31no—
322#878—31no—
323#878—31no—
324#876—31no—
325C4×D12—31no—
326C23×C32—31no—
327C23×C32—31no—
328C23×C32—31no—
329C22×C3×D3—21no—
330C22×C3×D3—21no—
331C22×C3×D3—21no—
332C22×C3×D3C22×D311yescharacteristic
333C22×C3×D3C22×D311yescharacteristic
334C22×C3×D3C22×D311yescharacteristic
335C22×C3×D3C23×C311yescharacteristic
336C22×C3×D3C23×C311yescharacteristic
337C22×C3×D3C23×C311yescharacteristic
338C32×D4—62no—
339C32×D4—62no—
340C32×D4—121no—
341C2×C32×C4—21no—
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—21no—
349C2×C32×C4—21no—
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—121no—
359C2×C32×C4C22×D311yescharacteristic
360C2×C32×C4C22×D311yescharacteristic
361C2×C32×C4C22×D311yescharacteristic
362C2×C32×C4C22×D311yescharacteristic
363C2×C32×C4C22×D311yescharacteristic
364C2×C32×C4C22×D311yescharacteristic
365C2×C32×C4C23×C311yescharacteristic
366C2×C32×C4C23×C311yescharacteristic
367C2×C32×C4C23×C311yescharacteristic
368C2×C3⋊Dic3C23×C311yescharacteristic
369C2×C3⋊Dic3C23×C311yescharacteristic
370C2×C3⋊Dic3C23×C311yescharacteristic
371C2×C3⋊Dic3C23×C311yescharacteristic
372C2×C3×Dic3—21no—
373C2×C3×Dic3—21no—
374C2×C3×Dic3—21no—
375C2×C3×Dic3—21no—
376C2×C3×Dic3—21no—
377C2×C3×Dic3—31no—
378C2×C3×Dic3—31no—
379C2×C3×Dic3—31no—
380C2×C3×Dic3—31no—
381C2×C3×Dic3—31no—
382C2×C3×Dic3—31no—
383C2×C3×Dic3—31no—
384C2×C3×Dic3—31no—
385C2×C3×Dic3—61no—
386C2×C3×Dic3—61no—
387C2×C3×Dic3—61no—
388C2×C3×Dic3—61no—
389C2×C3×Dic3—62no—
390C2×C3×Dic3—121no—
391C2×C3×Dic3—121no—
392C2×C3×Dic3—121no—
393C2×C3×Dic3C22×D311yescharacteristic
394C2×C3×Dic3C22×D311yescharacteristic
395C2×C3×Dic3C22×D311yescharacteristic
396C2×C3×Dic3C22×D311yescharacteristic
397C2×C3×Dic3C22×D311yescharacteristic
398C2×C3×Dic3C23×C311yescharacteristic
399C2×C3×Dic3C23×C311yescharacteristic
400C2×C3×Dic3C23×C311yescharacteristic
401C2×C3×Dic3C23×C311yescharacteristic
402C2×C3×Dic3C23×C311yescharacteristic
403C3×D12—22no—
404C3×D12—22no—
405C3×D12—22no—
406C3×D12—22no—
407C3×D12—42no—
408C3×D12—42no—
409C3×D12—41no—
410C3×D12—41no—
411C3×D12—42no—
412C3×C4×D3—41no—
413C3×C4×D3—41no—
414C3×C4×D3—42no—
415C3×C4×D3—62no—
416C3×C4×D3—121no—
417C3×C4×D3—121no—
418C3×C4×D3—121no—
419C3×Dic6—121no—
420C3×Dic6—121no—
421#627—41no—
422D3×Dic3—22no—
423D3×Dic3—41no—
424D3×Dic3—41no—
425D3×Dic3—41no—
426#539—91noSylow
427C2×C33C2×#4111yescharacteristic
428C2×C33H(5,𝔽2)11yescharacteristic
429C2×C332−1+411yescharacteristic
430C32×D3—22no—
431C32×D3—41no—
432C32×D3—41no—
433C2×C3×Q8—91no—
434C2×C3×D4—31no—
435C2×C3×D4—31no—
436C2×C3×D4—31no—
437C2×C3×D4—31no—
438C2×C3×D4—31no—
439C2×C3×D4—31no—
440C2×C3×D4—61no—
441C2×C3×D4—61no—
442C2×C3×D4—61no—
443C22×C3×C4—31no—
444C22×C3×C4—31no—
445C22×C3×C4—61no—
446C22×C3×C4—91no—
447C22×C3×C4—91no—
448C22×C3×C4—91no—
449C22×C3×C4—91no—
450C22×Dic3—31no—
451C22×Dic3—31no—
452C22×Dic3—31no—
453C22×Dic3—31no—
454C2×D12C2×C3×D311yescharacteristic
455C2×D12C2×C3×D311yescharacteristic
456C2×D12C2×C3×D311yescharacteristic
457C2×C4×D3—31no—
458C2×C4×D3—31no—
459C2×C4×D3—31no—
460C2×C4×D3—31no—
461C2×C4×D3C2×C3×D311yescharacteristic
462C2×Dic6—31no—
463C2×Dic6—31no—
464C3×C4⋊C4—21no—
465C3×C4⋊C4—21no—
466C3×C4⋊C4—21no—
467C3×C4⋊C4—31no—
468C3×C4⋊C4—31no—
469C3×C4⋊C4—31no—
470C3×C4⋊C4—31no—
471C3×C4⋊C4—31no—
472C3×C4⋊C4—31no—
473C3×C4⋊C4—31no—
474C3×C4⋊C4—31no—
475C3×C4⋊C4—31no—
476C3×C4⋊C4—31no—
477C3×C4⋊C4—41no—
478C3×C4⋊C4—61no—
479C3×C4⋊C4—61no—
480C3×C4⋊C4—61no—
481C3×C4⋊C4—61no—
482C3×C4⋊C4—61no—
483C3×C4⋊C4—91no—
484C3×C4⋊C4—91no—
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⋊C4D3211yescharacteristic
492C3×C4⋊C4C2×C3×D311yescharacteristic
493C3×C4⋊C4C2×C3×D311yescharacteristic
494C3×C22⋊C4—31no—
495C3×C22⋊C4—31no—
496C3×C22⋊C4—31no—
497C3×C22⋊C4—31no—
498C3×C22⋊C4—61no—
499C3×C22⋊C4—61no—
500C3×C22⋊C4—91no—
501C3×C22⋊C4—91no—
502C3×C22⋊C4—91no—
503C3×C22⋊C4—91no—
504C3×C22⋊C4—91no—
505C3×C22⋊C4—91no—
506C3×C22⋊C4—91no—
507C3×C22⋊C4—91no—
508C3×C42—31no—
509C3×C42—31no—
510C3×C42—61no—
511C3×C42—91no—
512#217—31no—
513#217—31no—
514#217—31no—
515#217—31no—
516#217—31no—
517#217—31no—
518#217—31no—
519#217—31no—
520(C2×D3)⋊C4—31no—
521(C2×D3)⋊C4—31no—
522(C2×D3)⋊C4—31no—
523(C2×D3)⋊C4—31no—
524(C2×D3)⋊C4—31no—
525(C2×D3)⋊C4—31no—
526(C2×D3)⋊C4—31no—
527(C2×D3)⋊C4—31no—
528(C2×D3)⋊C4C2×C3×D311yescharacteristic
529(C2×D3)⋊C4C2×C3×D311yescharacteristic
530C4⋊Dic3—31no—
531C4⋊Dic3—31no—
532C4⋊Dic3—31no—
533C4⋊Dic3—31no—
534C4⋊Dic3—61no—
535C4⋊Dic3C2×C3×D311yescharacteristic
536Dic3⋊C4—31no—
537Dic3⋊C4—31no—
538Dic3⋊C4—31no—
539Dic3⋊C4—31no—
540Dic3⋊C4—31no—
541Dic3⋊C4—31no—
542Dic3⋊C4—31no—
543Dic3⋊C4—31no—
544Dic3⋊C4—31no—
545Dic3⋊C4—31no—
546Dic3⋊C4—31no—
547Dic3⋊C4—31no—
548Dic3⋊C4—61no—
549Dic3⋊C4—61no—
550Dic3⋊C4—61no—
551Dic3⋊C4—61no—
552Dic3⋊C4C2×C3×D311yescharacteristic
553Dic3⋊C4C2×C3×D311yescharacteristic
554Dic3⋊C4C2×C3×D311yescharacteristic
555Dic3⋊C4C2×C3×D311yescharacteristic
556C4×Dic3—31no—
557C4×Dic3—31no—
558C4×Dic3—61no—
559C4×Dic3C2×C3×D311yescharacteristic
560C22×C32—21no—
561C22×C32—21no—
562C22×C32—21no—
563C22×C32—32no—
564C22×C32—41no—
565C22×C32—61no—
566C22×C32—61no—
567C22×C32—61no—
568C22×C32—61no—
569C22×C32—61no—
570C22×C32—61no—
571C22×C32—61no—
572C22×C32—61no—
573C22×C32C23×D311yescharacteristic
574C22×C32C23×D311yescharacteristic
575C22×C32C24×C311yescharacteristic
576C2×C3×D3—21no—
577C2×C3×D3—21no—
578C2×C3×D3—21no—
579C2×C3×D3—21no—
580C2×C3×D3—21no—
581C2×C3×D3—21no—
582C2×C3×D3—21no—
583C2×C3×D3—21no—
584C2×C3×D3—21no—
585C2×C3×D3—21no—
586C2×C3×D3—21no—
587C2×C3×D3—21no—
588C2×C3×D3—21no—
589C2×C3×D3—21no—
590C2×C3×D3—21no—
591C2×C3×D3—21no—
592C2×C3×D3—22no—
593C2×C3×D3—41no—
594C2×C3×D3—41no—
595C2×C3×D3—41no—
596C2×C3×D3—41no—
597C2×C3×D3—41no—
598C2×C3×D3—41no—
599C2×C3×D3—41no—
600C2×C3×D3—41no—
601C2×C3×D3#23712yes—
602C2×C3×D3C3×#4112yes—
603C32×C4—21no—
604C32×C4—22no—
605C32×C4—21no—
606C32×C4—21no—
607C32×C4—21no—
608C32×C4—21no—
609C32×C4—21no—
610C32×C4—21no—
611C32×C4—21no—
612C32×C4—21no—
613C32×C4—41no—
614C32×C4—41no—
615C32×C4—42no—
616C32×C4—41no—
617C32×C4—41no—
618C32×C4—41no—
619C32×C4—41no—
620C32×C4—41no—
621C32×C4—41no—
622C32×C4—61no—
623C32×C4—61no—
624C32×C4—61no—
625C32×C4—61no—
626C32×C4—61no—
627C32×C4—81no—
628C32×C4—81no—
629C3⋊Dic3—21no—
630C3⋊Dic3—21no—
631C3⋊Dic3—21no—
632C3⋊Dic3—21no—
633C3×Dic3—22no—
634C3×Dic3—21no—
635C3×Dic3—21no—
636C3×Dic3—21no—
637C3×Dic3—21no—
638C3×Dic3—21no—
639C3×Dic3—21no—
640C3×Dic3—21no—
641C3×Dic3—21no—
642C3×Dic3—21no—
643C3×Dic3—21no—
644C3×Dic3—41no—
645C3×Dic3—41no—
646C3×Dic3—41no—
647C3×Dic3—41no—
648C3×Dic3—62no—
649C3×Dic3—61no—
650C3×Dic3—61no—
651C3×Dic3—61no—
652C3×Dic3—61no—
653C3×Dic3—61no—
654C3×Dic3—61no—
655C3×Dic3—61no—
656C3×Dic3—61no—
657C3×Dic3—121no—
658C3×Dic3—121no—
659C3×Dic3—121no—
660#126—91no—
661#126—91no—
662#125—31no—
663#125—91no—
664#123—91no—
665#123—91no—
666#123—91no—
667#123—91no—
668C22⋊Q8—91no—
669C22⋊Q8—91no—
670C22⋊Q8—91no—
671#121—31no—
672C4×D4—91no—
673C4×D4—91no—
674C2×C4⋊C4—91no—
675C33#53911yescharacteristic, complemented, Sylow
676C23×C3—31no—
677C23×C3—31no—
678C23×C3—31no—
679C23×C3—31no—
680C23×C3—31no—
681C23×C3—31no—
682C23×C3—61no—
683C23×C3—61no—
684C23×C3—61no—
685C22×D3C22×C3×D311yescharacteristic
686C22×D3C22×C3×D311yescharacteristic
687C22×D3C22×C3×D311yescharacteristic
688C3×Q8—361no—
689C3×D4—62no—
690C3×D4—62no—
691C3×D4—62no—
692C3×D4—62no—
693C3×D4—122no—
694C3×D4—122no—
695C3×D4—121no—
696C3×D4—121no—
697C3×D4—122no—
698C2×C3×C4—21no—
699C2×C3×C4—21no—
700C2×C3×C4—21no—
701C2×C3×C4—21no—
702C2×C3×C4—21no—
703C2×C3×C4—21no—
704C2×C3×C4—21no—
705C2×C3×C4—21no—
706C2×C3×C4—21no—
707C2×C3×C4—31no—
708C2×C3×C4—31no—
709C2×C3×C4—31no—
710C2×C3×C4—31no—
711C2×C3×C4—31no—
712C2×C3×C4—31no—
713C2×C3×C4—31no—
714C2×C3×C4—31no—
715C2×C3×C4—31no—
716C2×C3×C4—31no—
717C2×C3×C4—41no—
718C2×C3×C4—41no—
719C2×C3×C4—41no—
720C2×C3×C4—61no—
721C2×C3×C4—61no—
722C2×C3×C4—61no—
723C2×C3×C4—61no—
724C2×C3×C4—61no—
725C2×C3×C4—91no—
726C2×C3×C4—91no—
727C2×C3×C4—91no—
728C2×C3×C4—91no—
729C2×C3×C4—121no—
730C2×C3×C4—121no—
731C2×C3×C4—122no—
732C2×C3×C4—182no—
733C2×C3×C4—361no—
734C2×C3×C4—361no—
735C2×C3×C4—361no—
736C2×C3×C4C2×D3211yescharacteristic
737C2×C3×C4C2×D3211yescharacteristic
738C2×C3×C4C2×D3211yescharacteristic
739C2×C3×C4C22×C3×D311yescharacteristic
740C2×C3×C4C22×C3×D311yescharacteristic
741C2×C3×C4C22×C3×D311yescharacteristic
742C2×C3×C4C22×C3×D311yescharacteristic
743C2×C3×C4C22×C3×D311yescharacteristic
744C2×C3×C4C22×C3×D311yescharacteristic
745C2×Dic3—31no—
746C2×Dic3—31no—
747C2×Dic3—31no—
748C2×Dic3—31no—
749C2×Dic3—31no—
750C2×Dic3—31no—
751C2×Dic3—31no—
752C2×Dic3—31no—
753C2×Dic3—61no—
754C2×Dic3—61no—
755C2×Dic3—61no—
756C2×Dic3—61no—
757C2×Dic3—62no—
758C2×Dic3—121no—
759C2×Dic3—121no—
760C2×Dic3—121no—
761C2×Dic3C22×C3×D311yescharacteristic
762C2×Dic3C22×C3×D311yescharacteristic
763C2×Dic3C22×C3×D311yescharacteristic
764C2×Dic3C22×C3×D311yescharacteristic
765C2×Dic3C22×C3×D311yescharacteristic
766D12—22no—
767D12—22no—
768D12—41no—
769C4×D3—41no—
770C4×D3—62no—
771C4×D3—121no—
772C4×D3—121no—
773C4×D3—121no—
774Dic6—121no—
775Dic6—121no—
776C2×C32—21no—
777C2×C32—21no—
778C2×C32—21no—
779C2×C32—21no—
780C2×C32—21no—
781C2×C32—21no—
782C2×C32—21no—
783C2×C32—21no—
784C2×C32—21no—
785C2×C32—41no—
786C2×C32—41no—
787C2×C32—41no—
788C2×C32—62no—
789C2×C32—121no—
790C2×C32—121no—
791C2×C32C2×#23711yescharacteristic
792C2×C32#100411yescharacteristic
793C2×C32#100711yescharacteristic
794C2×C32D3×#4111yescharacteristic
795C2×C32#100911yescharacteristic
796C2×C32#101011yescharacteristic
797C2×C32C2×C3×#4111yescharacteristic
798C2×C32C3×H(5,𝔽2)11yescharacteristic
799C2×C32C3×2−1+411yescharacteristic
800C3×D3—22no—
801C3×D3—22no—
802C3×D3—42no—
803C3×D3—41no—
804C3×D3—41no—
805C3×D3—41no—
806C3×D3—41no—
807C3×D3—81no—
808C3×D3—81no—
809C2×Q8—91no—
810C2×D4—31no—
811C2×D4—31no—
812C2×D4—31no—
813C22×C4—31no—
814C22×C4—91no—
815C22×C4—91no—
816C22×C4—91no—
817C22×C4—91no—
818C4⋊C4—31no—
819C4⋊C4—31no—
820C4⋊C4—31no—
821C4⋊C4—31no—
822C4⋊C4—31no—
823C4⋊C4—91no—
824C4⋊C4—91no—
825C4⋊C4—91no—
826C4⋊C4—91no—
827C4⋊C4—91no—
828C4⋊C4—91no—
829C4⋊C4—91no—
830C4⋊C4—91no—
831C4⋊C4C3×D3211yescharacteristic
832C22⋊C4—31no—
833C22⋊C4—31no—
834C22⋊C4—91no—
835C22⋊C4—91no—
836C22⋊C4—91no—
837C22⋊C4—91no—
838C22⋊C4—91no—
839C22⋊C4—91no—
840C22⋊C4—91no—
841C22⋊C4—91no—
842C42—31no—
843C42—91no—
844C22×C3—21no—
845C22×C3—21no—
846C22×C3—21no—
847C22×C3—32no—
848C22×C3—32no—
849C22×C3—41no—
850C22×C3—62no—
851C22×C3—61no—
852C22×C3—61no—
853C22×C3—61no—
854C22×C3—61no—
855C22×C3—61no—
856C22×C3—61no—
857C22×C3—61no—
858C22×C3—61no—
859C22×C3—61no—
860C22×C3—61no—
861C22×C3—61no—
862C22×C3—61no—
863C22×C3—61no—
864C22×C3—61no—
865C22×C3—61no—
866C22×C3—61no—
867C22×C3—121no—
868C22×C3—121no—
869C22×C3—121no—
870C22×C3—121no—
871C22×C3—121no—
872C22×C3—121no—
873C22×C3—121no—
874C22×C3—121no—
875C22×C3C22×D3211yescharacteristic
876C22×C3C23×C3×D311yescharacteristic
877C22×C3C23×C3×D311yescharacteristic
878C2×D3—21no—
879C2×D3—21no—
880C2×D3—21no—
881C2×D3—21no—
882C2×D3—21no—
883C2×D3—21no—
884C2×D3—21no—
885C2×D3—21no—
886C2×D3C3×#23712yes—
887C3×C4—22no—
888C3×C4—21no—
889C3×C4—21no—
890C3×C4—21no—
891C3×C4—21no—
892C3×C4—21no—
893C3×C4—21no—
894C3×C4—21no—
895C3×C4—21no—
896C3×C4—21no—
897C3×C4—41no—
898C3×C4—41no—
899C3×C4—41no—
900C3×C4—41no—
901C3×C4—41no—
902C3×C4—41no—
903C3×C4—41no—
904C3×C4—41no—
905C3×C4—42no—
906C3×C4—62no—
907C3×C4—61no—
908C3×C4—61no—
909C3×C4—61no—
910C3×C4—61no—
911C3×C4—61no—
912C3×C4—61no—
913C3×C4—61no—
914C3×C4—61no—
915C3×C4—61no—
916C3×C4—61no—
917C3×C4—81no—
918C3×C4—81no—
919C3×C4—121no—
920C3×C4—121no—
921C3×C4—121no—
922C3×C4—121no—
923C3×C4—181no—
924C3×C4—181no—
925C3×C4—181no—
926C3×C4—181no—
927Dic3—21no—
928Dic3—21no—
929Dic3—21no—
930Dic3—21no—
931Dic3—21no—
932Dic3—62no—
933Dic3—61no—
934Dic3—61no—
935Dic3—61no—
936Dic3—61no—
937Dic3—61no—
938Dic3—61no—
939Dic3—61no—
940Dic3—61no—
941Dic3—121no—
942Dic3—121no—
943Dic3—121no—
944C32—21no—
945C32—21no—
946C32—21no—
947C32—41no—
948C32#560211yescharacteristic, complemented
949C32#569211yescharacteristic, complemented
950C32C3×#53911yescharacteristic, complemented
951C23—31no—
952C23—31no—
953C23—31no—
954Q8—361no—
955D4—62no—
956D4—62no—
957D4—121no—
958C2×C4—31no—
959C2×C4—31no—
960C2×C4—31no—
961C2×C4—31no—
962C2×C4—31no—
963C2×C4—91no—
964C2×C4—91no—
965C2×C4—91no—
966C2×C4—91no—
967C2×C4—121no—
968C2×C4—182no—
969C2×C4—361no—
970C2×C4—361no—
971C2×C4—361no—
972C2×C4C2×C3×D3211yescharacteristic
973C2×C4C2×C3×D3211yescharacteristic
974C2×C4C2×C3×D3211yescharacteristic
975C2×C3—21no—
976C2×C3—21no—
977C2×C3—21no—
978C2×C3—21no—
979C2×C3—21no—
980C2×C3—21no—
981C2×C3—21no—
982C2×C3—21no—
983C2×C3—21no—
984C2×C3—41no—
985C2×C3—41no—
986C2×C3—41no—
987C2×C3—62no—
988C2×C3—62no—
989C2×C3—122no—
990C2×C3—121no—
991C2×C3—121no—
992C2×C3—121no—
993C2×C3—121no—
994C2×C3—241no—
995C2×C3—241no—
996C2×C3#6430711yescharacteristic
997C2×C3D3×#23711yescharacteristic
998C2×C3#6431511yescharacteristic
999C2×C3C2×C3×#23711yescharacteristic
1000C2×C3C3×#100411yescharacteristic
1001C2×C3C3×#100711yescharacteristic
1002C2×C3C3×D3×#4111yescharacteristic
1003C2×C3C3×#100911yescharacteristic
1004C2×C3C3×#101011yescharacteristic
1005D3—22no—
1006D3—41no—
1007D3—41no—
1008C22—32no—
1009C22—61no—
1010C22—61no—
1011C22—61no—
1012C22—61no—
1013C22—61no—
1014C22—61no—
1015C22—61no—
1016C22—61no—
1017C22C22×C3×D3211yescharacteristic
1018C4—21no—
1019C4—21no—
1020C4—21no—
1021C4—61no—
1022C4—61no—
1023C4—61no—
1024C4—61no—
1025C4—61no—
1026C4—181no—
1027C4—181no—
1028C4—181no—
1029C4—181no—
1030C3—21no—
1031C3—21no—
1032C3—21no—
1033C3—41no—
1034C3#1059442811yescharacteristic, direct product factor
1035C3C3×#560211yescharacteristic, complemented
1036C3C3×#569211yescharacteristic, complemented
1037C2—62no—
1038C2—121no—
1039C2—121no—
1040C2C3×#6430711yescharacteristic
1041C2C3×D3×#23711yescharacteristic
1042C2C3×#6431511yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC33×C4⋊C4C22
socleC22×C33C24
prime radicalC32×#895C2
hypercenterC3×C4⋊C4D32
hypocenterC32C3×#539
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×#64098C2semidirect
3. C32×#889C2semidirect
4. C3×#63899C2semidirect
5. C3×#63898C2semidirect
6. C3×#63893C2semidirect
7. C3×Dic3×D12C2semidirect
8. C3×#63884C2semidirect
9. C3×#63884C2semidirect
10. C3×#63884C2semidirect
11. C3×#63884C2semidirect
12. C3×D3×Dic3⋊C4C2semidirect
13. C3×#63862C2semidirect
14. C3×#63859C2semidirect
15. C3×#63851C2semidirect
18. #10594428C3direct (N × H)
56. #64098C2×C3semidirect
82. C3×#889D3semidirect
83. C3×#889C2×C3semidirect
90. #63899C2×C3semidirect
91. #63898C2×C3semidirect
92. #63893C2×C3semidirect
93. Dic3×D12C2×C3semidirect
94. #63884C2×C3semidirect
95. #63884C2×C3semidirect
96. #63884C2×C3semidirect
97. #63884C2×C3semidirect
98. D3×Dic3⋊C4C2×C3semidirect
99. #63862C2×C3semidirect
100. #63859C2×C3semidirect
101. #63851C2×C3semidirect
319. #889C3×D3semidirect
675. C33#539semidirect
948. C32#5602semidirect
949. C32#5692semidirect
950. C32C3×#539semidirect
1034. C3#10594428direct (N × H)
1035. C3C3×#5602semidirect
1036. C3C3×#5692semidirect

Maximal subgroups

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

subgroupindex
C3×#640982
C32×#8952
C32×#8892
C3×#638992
C3×#638982
C3×#638932
C3×Dic3×D122
C3×#638842
C3×D3×Dic3⋊C42
C3×#638622
C3×#638592
C3×#638512
C3×#56923
C3×#56023
#105944283