Finite Group Databasebeta

← #13155316

Subgroups — #13155316

Order 1728.

830 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3798C211yesmaximal, characteristic
2C2×D3×C3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
3C2×C3×#3711C211yesmaximal, characteristic, complemented
4#11722072C211yesmaximal, characteristic, complemented
5#11722023C211yesmaximal, characteristic, complemented
6(C2×D3)⋊(C3⋊(C3⋊C8))C211yesmaximal, characteristic, complemented
7C3×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8#10591145—31nomaximal
9#10591071—31nomaximal
10#10590955—31nomaximal
11C2×C3×C4×C3⋊D3C2211yescharacteristic
12C2×C32×C4×D3C2211yescharacteristic
13C2×C32×C4×D3C2211yescharacteristic
14C2×C3×#627C411yescharacteristic
15C2×C3×#626C411yescharacteristic
16C2×C3×#626C411yescharacteristic
17C2×C3×#625C411yescharacteristic
18C3×#3798—22no—
19C3×#3798—22no—
20C2×C3⋊(C3⋊(C3⋊C8))C2211yescharacteristic
21C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic
22C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic
23C2×C32×C3⋊C8C2211yescharacteristic
24D3×C3⋊(C3⋊C8)—22no—
25C3×#3711—22no—
26C2×C3×#235—31no—
27C2×C3×#235—31no—
28C2×#3798D311yescharacteristic
29C22×C3⋊(C3⋊C8)—31no—
30C2×C3×#208—31no—
31C2×C3×ΓL(1,𝔽25)—31no—
32C2×#3711D311yescharacteristic, complemented
33C2×D3×C3⋊C8—31no—
34C2×D3×C3⋊C8—31no—
35C2×D3×C3⋊C8—61no—
36#63657—31no—
37#63647—31no—
38C3×#830—31no—
39C3×(C2×D3)⋊C8—31no—
40#63557—31no—
41(C2×D3)⋊(C3⋊C8)—31no—
42(C2×D3)⋊(C3⋊C8)—31no—
43(C2×D3)⋊(C3⋊C8)—31no—
44(C2×D3)⋊(C3⋊C8)—31no—
45(C2×D3)⋊(C3⋊C8)—31no—
46(C2×D3)⋊(C3⋊C8)—31no—
47(C2×D3)⋊(C3⋊C8)—61no—
48(C2×D3)⋊(C3⋊C8)—61no—
49(C2×D3)⋊(C3⋊C8)D311yescharacteristic, complemented
50C22×C3×C3⋊D3C2×C411yescharacteristic
51C22×C32×D3C2×C411yescharacteristic
52C22×C32×D3C2×C411yescharacteristic
53C2×C33×C4C2311yescharacteristic
54C2×C3×C3⋊Dic3C2×C411yescharacteristic
55C3×C4×C3⋊D3—21no—
56C3×C4×C3⋊D3—21no—
57C2×C32×Dic3C2×C411yescharacteristic
58C2×C32×Dic3C2×C411yescharacteristic
59C32×C4×D3—21no—
60C32×C4×D3—21no—
61C32×C4×D3D412yes—
62C32×C4×D3D412yes—
63C3×#627—22no—
64C3×#626—22no—
65C3×#626—22no—
66C3×#625—22no—
67C3⋊(C3⋊(C3⋊C8))—21no—
68C3×C3⋊(C3⋊C8)—21no—
69C3×C3⋊(C3⋊C8)—21no—
70C32×C3⋊C8—21no—
71#5234—91no—
72#5129—91no—
73#4727—91no—
74C22×C32×C4—31no—
75C22×C32×C4—31no—
76C2×C4×C3⋊D3C2×D311yescharacteristic
77C2×C3×#67—31no—
78C2×C3×#67—31no—
79C2×C3×#67—31no—
80C2×C3×#67—31no—
81C3×#235—62no—
82C3×#235—62no—
83C3×#235—62no—
84C3×#235—62no—
85C2×C3×D12—31no—
86C2×C3×D12—31no—
87C2×C3×C4×D3—21no—
88C2×C3×C4×D3—21no—
89C2×C3×C4×D3—31no—
90C2×C3×C4×D3—31no—
91C2×C3×C4×D3—61no—
92C2×C3×C4×D3C2×D311yescharacteristic
93C2×C3×C4×D3C2×D311yescharacteristic
94C2×C3×C4×D3C2×D311yescharacteristic
95C2×C3×C4×D3C2×D311yescharacteristic
96C2×C3×Dic6—31no—
97C2×C3×Dic6—31no—
98C2×#627Dic311yescharacteristic
99C2×#626Dic311yescharacteristic
100C2×#626Dic311yescharacteristic
101C2×#625Dic311yescharacteristic
102#3798—22no—
103#3798—22no—
104C2×C32×C8—31no—
105C2×C3⋊(C3⋊C8)—31no—
106C2×C3⋊(C3⋊C8)—31no—
107C2×C3⋊(C3⋊C8)—31no—
108C2×C3⋊(C3⋊C8)—62no—
109C2×C3⋊(C3⋊C8)—61no—
110C2×C3⋊(C3⋊C8)—61no—
111C2×C3⋊(C3⋊C8)—61no—
112C2×C3⋊(C3⋊C8)—121no—
113C2×C3⋊(C3⋊C8)C2×D311yescharacteristic
114C2×C3⋊(C3⋊C8)C2×D311yescharacteristic
115C3×#208—62no—
116C2×C3×C3⋊C8—21no—
117C2×C3×C3⋊C8—31no—
118C2×C3×C3⋊C8—31no—
119C2×C3×C3⋊C8—31no—
120C2×C3×C3⋊C8—31no—
121C2×C3×C3⋊C8—61no—
122C2×C3×C3⋊C8—61no—
123C2×C3×C3⋊C8C2×D311yescharacteristic
124C2×C3×C3⋊C8C2×D311yescharacteristic
125C3×ΓL(1,𝔽25)—62no—
126#3711—22no—
127D3×C3⋊C8—64no—
128D3×C3⋊C8—62no—
129D3×C3⋊C8—62no—
130C22×C33C22×C411yescharacteristic
131C2×C3×C3⋊D3—21no—
132C2×C3×C3⋊D3—21no—
133C2×C3×C3⋊D3—21no—
134C2×C32×D3—21no—
135C2×C32×D3—21no—
136C2×C32×D3—21no—
137C2×C32×D3—21no—
138C2×C32×D3—21no—
139C2×C32×D3C22⋊C412yes—
140C33×C4C2×D411yescharacteristic
141C33×C4C2×D411yescharacteristic
142C3×C3⋊Dic3—21no—
143C32×Dic3—21no—
144C32×Dic3C22⋊C412yes—
145C2×C3×#41—91no—
146C2×#235—31no—
147C2×#235—31no—
148C2×C3×M16—91no—
149C2×#208—31no—
150C22×C3⋊C8—91no—
151C22×C3⋊C8—91no—
152C22×C3⋊C8—181no—
153C2×ΓL(1,𝔽25)—31no—
154C2×D3×C8—91no—
155C3×C22⋊C8—91no—
156#830—31no—
157#830—91no—
158#830—91no—
159#830—91no—
160#830—91no—
161#830—181no—
162(C2×D3)⋊C8—31no—
163(C2×D3)⋊C8—91no—
164(C2×D3)⋊C8—91no—
165(C2×D3)⋊C8—91no—
166(C2×D3)⋊C8—91no—
167(C2×D3)⋊C8—91no—
168(C2×D3)⋊C8—181no—
169C23×C32—31no—
170C23×C32—31no—
171C22×C3⋊D3C2×Dic311yescharacteristic
172C22×C3×D3—21no—
173C22×C3×D3—21no—
174C22×C3×D3—31no—
175C22×C3×D3—31no—
176C22×C3×D3—61no—
177C22×C3×D3C4×D311yescharacteristic
178C22×C3×D3C4×D311yescharacteristic
179C22×C3×D3C2×Dic311yescharacteristic
180C22×C3×D3C2×Dic311yescharacteristic
181C2×C32×C4—21no—
182C2×C32×C4—21no—
183C2×C32×C4—21no—
184C2×C32×C4—31no—
185C2×C32×C4—32no—
186C2×C32×C4—32no—
187C2×C32×C4—31no—
188C2×C32×C4—41no—
189C2×C32×C4—61no—
190C2×C32×C4—61no—
191C2×C32×C4C22×D311yescharacteristic
192C2×C32×C4C22×D311yescharacteristic
193C2×C32×C4C22×D311yescharacteristic
194C2×C3⋊Dic3C2×Dic311yescharacteristic
195C4×C3⋊D3—21no—
196C4×C3⋊D3—21no—
197C3×#67—62no—
198C3×#67—62no—
199C3×#67—62no—
200C3×#67—62no—
201C2×C3×Dic3—21no—
202C2×C3×Dic3—21no—
203C2×C3×Dic3—31no—
204C2×C3×Dic3—31no—
205C2×C3×Dic3—61no—
206C2×C3×Dic3C4×D311yescharacteristic
207C2×C3×Dic3C4×D311yescharacteristic
208C2×C3×Dic3C2×Dic311yescharacteristic
209C2×C3×Dic3C2×Dic311yescharacteristic
210C3×D12—62no—
211C3×D12—62no—
212C3×C4×D3—21no—
213C3×C4×D3—21no—
214C3×C4×D3—21no—
215C3×C4×D3—21no—
216C3×C4×D3—22no—
217C3×C4×D3—22no—
218C3×C4×D3—41no—
219C3×C4×D3—41no—
220C3×C4×D3—61no—
221C3×C4×D3—61no—
222C3×C4×D3—61no—
223C3×C4×D3—61no—
224C3×C4×D3—121no—
225C3×C4×D3—121no—
226C3×C4×D3D1212yes—
227C3×C4×D3#6712yes—
228C3×C4×D3#6712yes—
229C3×C4×D3#6712yes—
230C3×Dic6—62no—
231C3×Dic6—62no—
232#627—22no—
233#626—22no—
234#626—22no—
235#625—22no—
236C32×C8—61no—
237C3⋊(C3⋊C8)—21no—
238C3⋊(C3⋊C8)—21no—
239C3⋊(C3⋊C8)—61no—
240C3⋊(C3⋊C8)—62no—
241C3⋊(C3⋊C8)—61no—
242C3⋊(C3⋊C8)—61no—
243C3⋊(C3⋊C8)—121no—
244C3⋊(C3⋊C8)—121no—
245C3⋊(C3⋊C8)—122no—
246C3×C3⋊C8—21no—
247C3×C3⋊C8—21no—
248C3×C3⋊C8—41no—
249C3×C3⋊C8—62no—
250C3×C3⋊C8—61no—
251C3×C3⋊C8—61no—
252C3×C3⋊C8—61no—
253C3×C3⋊C8—61no—
254C3×C3⋊C8—121no—
255#408—271noSylow
256C2×C33C2×C22⋊C411yescharacteristic
257C2×C33#13111yescharacteristic
258C2×C33#13111yescharacteristic
259C3×C3⋊D3—41no—
260C32×D3—22no—
261C32×D3—41no—
262C3×#41—182no—
263C3×#41—182no—
264C2×C3×Q8—91no—
265C2×C3×D4—91no—
266C2×C3×D4—91no—
267C2×C3×D4—91no—
268C22×C3×C4—31no—
269C22×C3×C4—31no—
270C22×C3×C4—31no—
271C22×C3×C4—31no—
272C22×C3×C4—61no—
273C22×C3×C4—61no—
274C22×C3×C4—91no—
275C2×#67—31no—
276C2×#67—31no—
277C2×#67—31no—
278C2×#67—31no—
279#235—62no—
280#235—62no—
281#235—62no—
282#235—62no—
283C2×D12—31no—
284C2×D12—31no—
285C2×C4×D3—31no—
286C2×C4×D3—31no—
287C2×C4×D3—61no—
288C2×C4×D3D3211yescharacteristic
289C2×C4×D3D3211yescharacteristic
290C2×Dic6—31no—
291C2×Dic6—31no—
292C3×M16—182no—
293C2×C3×C8—31no—
294C2×C3×C8—31no—
295C2×C3×C8—61no—
296C2×C3×C8—91no—
297C2×C3×C8—91no—
298#208—62no—
299C2×C3⋊C8—31no—
300C2×C3⋊C8—31no—
301C2×C3⋊C8—31no—
302C2×C3⋊C8—31no—
303C2×C3⋊C8—61no—
304C2×C3⋊C8—61no—
305C2×C3⋊C8—91no—
306C2×C3⋊C8—91no—
307C2×C3⋊C8—91no—
308C2×C3⋊C8—181no—
309C2×C3⋊C8—181no—
310C2×C3⋊C8—181no—
311C2×C3⋊C8—182no—
312C2×C3⋊C8—182no—
313C2×C3⋊C8—184no—
314C2×C3⋊C8—361no—
315C2×C3⋊C8D3211yescharacteristic
316ΓL(1,𝔽25)—62no—
317D3×C8—182no—
318C22×C32—21no—
319C22×C32—21no—
320C22×C32—21no—
321C22×C32—32no—
322C22×C32—41no—
323C22×C32—61no—
324C22×C32—61no—
325C22×C32—61no—
326C22×C32—61no—
327C22×C32—61no—
328C22×C32C2×C4×D311yescharacteristic
329C22×C32C2×C4×D311yescharacteristic
330C22×C32C22×Dic311yescharacteristic
331C2×C3⋊D3—21no—
332C2×C3⋊D3—21no—
333C2×C3⋊D3—21no—
334C2×C3×D3—22no—
335C2×C3×D3—22no—
336C2×C3×D3—21no—
337C2×C3×D3—21no—
338C2×C3×D3—21no—
339C2×C3×D3—21no—
340C2×C3×D3—22no—
341C2×C3×D3—21no—
342C2×C3×D3—21no—
343C2×C3×D3—21no—
344C2×C3×D3—21no—
345C2×C3×D3—21no—
346C2×C3×D3—21no—
347C2×C3×D3—22no—
348C2×C3×D3—41no—
349C2×C3×D3—41no—
350C2×C3×D3—62no—
351C2×C3×D3—61no—
352C2×C3×D3—61no—
353C2×C3×D3—61no—
354C2×C3×D3—61no—
355C2×C3×D3—61no—
356C2×C3×D3—61no—
357C2×C3×D3—121no—
358C2×C3×D3—121no—
359C2×C3×D3(C2×D3)⋊C412yes—
360C2×C3×D3#21712yes—
361C32×C4—21no—
362C32×C4—21no—
363C32×C4—21no—
364C32×C4—21no—
365C32×C4—21no—
366C32×C4—21no—
367C32×C4—32no—
368C32×C4—41no—
369C32×C4—41no—
370C32×C4—61no—
371C32×C4C2×D1211yescharacteristic
372C32×C4D3×D411yescharacteristic
373C32×C4D3×D411yescharacteristic
374C32×C4C2×#6711yescharacteristic
375C32×C4C2×#6711yescharacteristic
376C32×C4C2×#6711yescharacteristic
377C3⋊Dic3—21no—
378C3×Dic3—21no—
379C3×Dic3—21no—
380C3×Dic3—22no—
381C3×Dic3—41no—
382C3×Dic3—61no—
383C3×Dic3—61no—
384C3×Dic3—121no—
385C3×Dic3(C2×D3)⋊C412yes—
386C3×Dic3#21712yes—
387C2×#41—91no—
388C2×M16—91no—
389C22×C8—271no—
390C22⋊C8—91no—
391C22⋊C8—271no—
392C22⋊C8—271no—
393C22⋊C8—271no—
394C33#40811yescharacteristic, complemented, Sylow
395C23×C3—31no—
396C23×C3—31no—
397C23×C3—31no—
398C23×C3—31no—
399C23×C3—61no—
400C23×C3—61no—
401C23×C3—91no—
402C22×D3—31no—
403C22×D3—31no—
404C22×D3—61no—
405C22×D3D3×Dic311yescharacteristic
406C22×D3D3×Dic311yescharacteristic
407C3×Q8—182no—
408C3×D4—182no—
409C3×D4—182no—
410C3×D4—182no—
411C2×C3×C4—21no—
412C2×C3×C4—21no—
413C2×C3×C4—21no—
414C2×C3×C4—31no—
415C2×C3×C4—31no—
416C2×C3×C4—32no—
417C2×C3×C4—32no—
418C2×C3×C4—32no—
419C2×C3×C4—32no—
420C2×C3×C4—31no—
421C2×C3×C4—31no—
422C2×C3×C4—41no—
423C2×C3×C4—62no—
424C2×C3×C4—62no—
425C2×C3×C4—61no—
426C2×C3×C4—61no—
427C2×C3×C4—61no—
428C2×C3×C4—61no—
429C2×C3×C4—61no—
430C2×C3×C4—61no—
431C2×C3×C4—91no—
432C2×C3×C4—121no—
433C2×C3×C4—121no—
434C2×C3×C4—181no—
435C2×C3×C4—181no—
436C2×C3×C4C2×D3211yescharacteristic
437C2×C3×C4C2×D3211yescharacteristic
438C2×C3×C4C2×D3211yescharacteristic
439#67—62no—
440#67—62no—
441#67—62no—
442#67—62no—
443C2×Dic3—31no—
444C2×Dic3—31no—
445C2×Dic3—61no—
446C2×Dic3D3×Dic311yescharacteristic
447C2×Dic3D3×Dic311yescharacteristic
448D12—62no—
449D12—62no—
450C4×D3—21no—
451C4×D3—21no—
452C4×D3—61no—
453C4×D3—61no—
454C4×D3—61no—
455C4×D3—61no—
456C4×D3—121no—
457C4×D3—121no—
458C4×D3#62512yes—
459C4×D3#62612yes—
460Dic6—62no—
461Dic6—62no—
462C3×C8—61no—
463C3×C8—61no—
464C3×C8—121no—
465C3×C8—181no—
466C3×C8—181no—
467C3⋊C8—21no—
468C3⋊C8—62no—
469C3⋊C8—61no—
470C3⋊C8—61no—
471C3⋊C8—61no—
472C3⋊C8—61no—
473C3⋊C8—121no—
474C3⋊C8—182no—
475C3⋊C8—181no—
476C3⋊C8—181no—
477C3⋊C8—181no—
478C3⋊C8—361no—
479C3⋊C8—361no—
480C3⋊C8—362no—
481C2×C32—21no—
482C2×C32—21no—
483C2×C32—21no—
484C2×C32—21no—
485C2×C32—21no—
486C2×C32—21no—
487C2×C32—21no—
488C2×C32—21no—
489C2×C32—21no—
490C2×C32—41no—
491C2×C32—41no—
492C2×C32—41no—
493C2×C32—62no—
494C2×C32—121no—
495C2×C32D3×C22⋊C411yescharacteristic
496C2×C32#90111yescharacteristic
497C2×C32#90711yescharacteristic
498C2×C32#90711yescharacteristic
499C2×C32#90711yescharacteristic
500C2×C32C2×(C2×D3)⋊C411yescharacteristic
501C2×C32#94811yescharacteristic
502C2×C32#94811yescharacteristic
503C2×C32C2×#21711yescharacteristic
504C3⋊D3—41no—
505C3×D3—24no—
506C3×D3—22no—
507C3×D3—22no—
508C3×D3—42no—
509C3×D3—41no—
510C3×D3—41no—
511C3×D3—122no—
512C3×D3—121no—
513C3×D3—121no—
514#41—182no—
515#41—182no—
516C2×Q8—91no—
517C2×D4—91no—
518C2×D4—91no—
519C2×D4—91no—
520C22×C4—31no—
521C22×C4—31no—
522C22×C4—91no—
523M16—182no—
524C2×C8—31no—
525C2×C8—91no—
526C2×C8—91no—
527C2×C8—271no—
528C2×C8—542no—
529C22×C3—21no—
530C22×C3—21no—
531C22×C3—21no—
532C22×C3—32no—
533C22×C3—32no—
534C22×C3—41no—
535C22×C3—62no—
536C22×C3—62no—
537C22×C3—62no—
538C22×C3—62no—
539C22×C3—61no—
540C22×C3—61no—
541C22×C3—61no—
542C22×C3—61no—
543C22×C3—61no—
544C22×C3—61no—
545C22×C3—61no—
546C22×C3—61no—
547C22×C3—61no—
548C22×C3—61no—
549C22×C3—121no—
550C22×C3—121no—
551C22×C3—181no—
552C22×C3—181no—
553C22×C3—181no—
554C22×C3C4×D3211yescharacteristic
555C22×C3C2×D3×Dic311yescharacteristic
556C22×C3C2×D3×Dic311yescharacteristic
557C2×D3—21no—
558C2×D3—21no—
559C2×D3—21no—
560C2×D3—21no—
561C2×D3—21no—
562C2×D3—62no—
563C2×D3—61no—
564C2×D3—61no—
565C2×D3—61no—
566C2×D3—61no—
567C2×D3—61no—
568C2×D3—61no—
569C2×D3—121no—
570C2×D3—121no—
571C2×D3(C2×D3)⋊Dic312yes—
572C3×C4—21no—
573C3×C4—21no—
574C3×C4—21no—
575C3×C4—21no—
576C3×C4—21no—
577C3×C4—21no—
578C3×C4—32no—
579C3×C4—32no—
580C3×C4—41no—
581C3×C4—41no—
582C3×C4—62no—
583C3×C4—61no—
584C3×C4—61no—
585C3×C4—121no—
586C3×C4—181no—
587C3×C4D3×D1211yescharacteristic
588C3×C4C2×#62511yescharacteristic
589C3×C4C2×#62611yescharacteristic
590C3×C4D3×#6711yescharacteristic
591C3×C4D3×#6711yescharacteristic
592C3×C4D3×#6711yescharacteristic
593Dic3—21no—
594Dic3—61no—
595Dic3—61no—
596Dic3—121no—
597Dic3(C2×D3)⋊Dic312yes—
598C32—21no—
599C32—21no—
600C32—21no—
601C32—41no—
602C32#472711yescharacteristic, complemented
603C32#512911yescharacteristic, complemented
604C32#523411yescharacteristic, complemented
605C23—31no—
606C23—31no—
607C23—91no—
608Q8—182no—
609D4—182no—
610D4—182no—
611D4—182no—
612C2×C4—31no—
613C2×C4—32no—
614C2×C4—32no—
615C2×C4—31no—
616C2×C4—61no—
617C2×C4—61no—
618C2×C4—91no—
619C2×C4—181no—
620C2×C4—181no—
621C2×C4D3311yescharacteristic
622C8—61no—
623C8—181no—
624C8—181no—
625C8—541no—
626C2×C3—21no—
627C2×C3—21no—
628C2×C3—21no—
629C2×C3—21no—
630C2×C3—21no—
631C2×C3—21no—
632C2×C3—21no—
633C2×C3—21no—
634C2×C3—21no—
635C2×C3—41no—
636C2×C3—41no—
637C2×C3—41no—
638C2×C3—64no—
639C2×C3—62no—
640C2×C3—62no—
641C2×C3—122no—
642C2×C3—121no—
643C2×C3—121no—
644C2×C3—361no—
645C2×C3#6380411yescharacteristic
646C2×C3#6380511yescharacteristic
647C2×C3#6381411yescharacteristic
648C2×C3#6381511yescharacteristic
649C2×C3#6381511yescharacteristic
650C2×C3#6381511yescharacteristic
651C2×C3D3×(C2×D3)⋊C411yescharacteristic
652C2×C3C2×(C2×D3)⋊Dic311yescharacteristic
653C2×C3D3×#21711yescharacteristic
654D3—22no—
655D3—41no—
656D3—122no—
657D3—121no—
658D3—121no—
659C22—32no—
660C22—61no—
661C22—61no—
662C22—61no—
663C22—61no—
664C22—61no—
665C22—181no—
666C22—181no—
667C22—181no—
668C22D32×Dic311yescharacteristic
669C4—32no—
670C4—61no—
671C4—181no—
672C4D3×#62511yescharacteristic
673C4D3×#62611yescharacteristic
674C3—21no—
675C3—21no—
676C3—21no—
677C3—41no—
678C3#1059095511yescharacteristic, complemented
679C3#1059107111yescharacteristic, complemented
680C3#1059114511yescharacteristic, complemented
681C2—62no—
682C2—121no—
683C2—361no—
684C2#1172282211yescharacteristic
685C2#1172282311yescharacteristic
686C2D3×(C2×D3)⋊Dic311yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2×C4D33
commutator, socleC22×C33C22×C4
Fitting, cosocleC2×C33×C4C23
prime radicalC2×C3×#3798C2
hypocenterC33#408
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C2×D3×C3⋊(C3⋊C8)C2semidirect
3. C2×C3×#3711C2semidirect
4. #11722072C2semidirect
5. #11722023C2semidirect
6. (C2×D3)⋊(C3⋊(C3⋊C8))C2semidirect
7. C3×(C2×D3)⋊(C3⋊C8)C2semidirect
32. C2×#3711D3semidirect
49. (C2×D3)⋊(C3⋊C8)D3semidirect
394. C33#408semidirect
602. C32#4727semidirect
603. C32#5129semidirect
604. C32#5234semidirect
678. C3#10590955semidirect
679. C3#10591071semidirect
680. C3#10591145semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#37982
C2×D3×C3⋊(C3⋊C8)2
C2×C3×#37112
#117220722
#117220232
(C2×D3)⋊(C3⋊(C3⋊C8))2
C3×(C2×D3)⋊(C3⋊C8)2
#105911453
#105910713
#105909553