Finite Group Databasebeta

← C3×#82099 #11806095

Subgroups — C3×#82099 #11806095

Order 1152.

2193 conjugacy classes of subgroups.

The subgroup lattice has 1152 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×C22⋊C4C211yesmaximal, characteristic, complemented
2C2×C3×#953C211yesmaximal, characteristic
3C22×C3×#217C211yesmaximal, characteristic, complemented
4C2×C3×C4×#67C211yesmaximal, characteristic, complemented
5C2×C3×#67⋊C4C211yesmaximal, characteristic, complemented
6C3×#5213C211yesmaximal, characteristic, complemented
7C3×#5210C211yesmaximal, characteristic, complemented
8C3×C4×#217C211yesmaximal, characteristic, complemented
9C3×#4958C211yesmaximal, characteristic, complemented
10C3×#4957C211yesmaximal, characteristic, complemented
11C3×#4956C211yesmaximal, characteristic, complemented
12C3×#4946C211yesmaximal, characteristic, complemented
13C3×#4945C211yesmaximal, characteristic, complemented
14C3×#4944C211yesmaximal, characteristic, complemented
15C3×Dic3×C22⋊C4C211yesmaximal, characteristic, complemented
16C3×#2358—31nomaximal
17#82099C311yesmaximal, characteristic, direct product factor
18C25×C32C2211yescharacteristic
19C23×C32×C4C2211yescharacteristic
20C23×C32×C4C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic
24C23×C3×Dic3C2211yescharacteristic
25C23×C3×Dic3C2211yescharacteristic
26C22×C3×C4×D3C2211yescharacteristic, complemented
27C2×C32×C22⋊C4—24no—
28C2×C32×C22⋊C4C2211yescharacteristic
29C2×C32×C22⋊C4C2211yescharacteristic
30C2×C32×C22⋊C4C2211yescharacteristic
31C2×C32×C22⋊C4C2211yescharacteristic
32C3×#953C418yescomplemented
33C2×C3×#217—24no—
34C2×C3×#217C2211yescharacteristic
35C2×C3×#217C2211yescharacteristic
36C2×C3×#217C2211yescharacteristic
37C2×C3×#217C2211yescharacteristic
38C2×C3×#217C2211yescharacteristic
39C2×C3×#217C2211yescharacteristic
40C2×C3×#217C2211yescharacteristic
41C3×C4×#67—24no—
42C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
43C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
44C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
45C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
46C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
47C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
48C2×C3×C4×Dic3C2211yescharacteristic, complemented
49C2×C3×C4×Dic3C2211yescharacteristic, complemented
50C2×C3×C4×Dic3C2211yescharacteristic, complemented
51C3×#67⋊C4—24no—
52C3×C3⋊#95C2211yescharacteristic, complemented
53C3×C3⋊#95C2211yescharacteristic, complemented
54C3×C3⋊#95C2211yescharacteristic, complemented
55C3×C3⋊#95C2211yescharacteristic, complemented
56C3×C3⋊#95C2211yescharacteristic, complemented
57C3×C3⋊#95C2211yescharacteristic, complemented
58C2×C3×#120—31no—
59C2×C3×C4×D4—31no—
60C2×C3×C4×D4—31no—
61C22×C3×C22⋊C4—21no—
62C22×C3×C22⋊C4—31no—
63C22×C3×C22⋊C4D311yescharacteristic, complemented
64C22×C3×C22⋊C4C2×C311yescharacteristic, complemented
65C2×#953C2×C311yescharacteristic
66C22×#217C2×C311yescharacteristic, complemented
67C2×C4×#67C2×C311yescharacteristic, complemented
68C2×#67⋊C4C2×C311yescharacteristic, complemented
69C3×#390—31no—
70C3×#388—31no—
71C3×#388—31no—
72C3×#386—31no—
73C3×#386—31no—
74C3×#386—31no—
75C3×#385—31no—
76C3×#385—31no—
77C3×C4×C22⋊C4—31no—
78C3×C4×C22⋊C4—31no—
79#5213C2×C311yescharacteristic, complemented
80#5210C2×C311yescharacteristic, complemented
81C4×#217C2×C311yescharacteristic, complemented
82#4958C2×C311yescharacteristic, complemented
83#4957C2×C311yescharacteristic, complemented
84#4956C2×C311yescharacteristic, complemented
85#4946C2×C311yescharacteristic, complemented
86#4945C2×C311yescharacteristic, complemented
87#4944C2×C311yescharacteristic, complemented
88Dic3×C22⋊C4C2×C311yescharacteristic, complemented
89C24×C32—22no—
90C24×C32—22no—
91C24×C32—22no—
92C24×C32—22no—
93C24×C32—41no—
94C24×C32—41no—
95C24×C32C2×C414yescomplemented
96C24×C32C2311yescharacteristic
97C24×C32C2311yescharacteristic
98C24×C32C2311yescharacteristic
99C23×C3×D3C2311yescharacteristic
100C22×C32×C4—22no—
101C22×C32×C4—22no—
102C22×C32×C4—22no—
103C22×C32×C4—22no—
104C22×C32×C4—41no—
105C22×C32×C4—41no—
106C22×C32×C4C2311yescharacteristic
107C22×C32×C4C2311yescharacteristic
108C22×C32×C4C2311yescharacteristic
109C22×C32×C4C2311yescharacteristic
110C2×C3×#67—22no—
111C2×C3×#67—22no—
112C2×C3×#67—22no—
113C2×C3×#67—22no—
114C2×C3×#67—41no—
115C2×C3×#67—41no—
116C2×C3×#67C2×C414yescomplemented
117C2×C3×#67C2×C414yescomplemented
118C2×C3×#67C2×C414yescomplemented
119C22×C3×Dic3—22no—
120C22×C3×Dic3—22no—
121C22×C3×Dic3—22no—
122C22×C3×Dic3—22no—
123C22×C3×Dic3—41no—
124C22×C3×Dic3—41no—
125C22×C3×Dic3C2311yescharacteristic
126C22×C3×Dic3C2311yescharacteristic
127C22×C3×Dic3C2311yescharacteristic
128C22×C3×Dic3C2311yescharacteristic
129C22×C3×Dic3C2311yescharacteristic
130C22×C3×Dic3C2311yescharacteristic
131C22×C3×Dic3C2311yescharacteristic
132C2×C3×C4×D3—22no—
133C2×C3×C4×D3—22no—
134C2×C3×C4×D3—41no—
135C32×C22⋊C4—22no—
136C32×C22⋊C4—22no—
137C32×C22⋊C4—22no—
138C32×C22⋊C4D414yescomplemented
139C3×#217—22no—
140C3×#217—22no—
141C3×#217—22no—
142C3×#217C2×C414yescomplemented
143C3×#217C2×C414yescomplemented
144C3×#217C2×C414yescomplemented
145C3×#217D414yescomplemented
146C3×(C2×D3)⋊C4—22no—
147C3×(C2×D3)⋊C4—22no—
148C3×(C2×D3)⋊C4—41no—
149C3×Dic3⋊C4—22no—
150C3×Dic3⋊C4—22no—
151C3×Dic3⋊C4—41no—
152C3×C4×Dic3—22no—
153C3×C4×Dic3—22no—
154C3×C4×Dic3—41no—
155#2358—31noSylow
156C25×C3—21no—
157C25×C3C2×D311yescharacteristic
158C25×C3C22×C311yescharacteristic
159C22×C3×D4—31no—
160C22×C3×D4—31no—
161C22×C3×D4—31no—
162C23×C3×C4—21no—
163C23×C3×C4—21no—
164C23×C3×C4—31no—
165C23×C3×C4—31no—
166C23×C3×C4—31no—
167C23×C3×C4C2×D311yescharacteristic
168C23×C3×C4C2×D311yescharacteristic
169C23×C3×C4C22×C311yescharacteristic
170C23×C3×C4C22×C311yescharacteristic
171C22×#67C22×C311yescharacteristic
172C22×#67C22×C311yescharacteristic
173C22×#67C22×C311yescharacteristic
174C23×Dic3C22×C311yescharacteristic
175C23×Dic3C22×C311yescharacteristic
176C22×C4×D3C22×C311yescharacteristic, complemented
177C3×#120—38no—
178C3×C4×D4—64no—
179C3×C4×D4—64no—
180C2×C3×C4⋊C4—31no—
181C2×C3×C4⋊C4—31no—
182C2×C3×C4⋊C4—31no—
183C2×C3×C22⋊C4—28no—
184C2×C3×C22⋊C4—24no—
185C2×C3×C22⋊C4—24no—
186C2×C3×C22⋊C4—21no—
187C2×C3×C22⋊C4—21no—
188C2×C3×C22⋊C4—21no—
189C2×C3×C22⋊C4—21no—
190C2×C3×C22⋊C4—31no—
191C2×C3×C22⋊C4—31no—
192C2×C3×C22⋊C4—31no—
193C2×C3×C22⋊C4—31no—
194C2×C3×C22⋊C4—31no—
195C2×C3×C22⋊C4—31no—
196C2×C3×C22⋊C4—31no—
197C2×C3×C22⋊C4—31no—
198C2×C3×C22⋊C4—31no—
199C2×C3×C22⋊C4—31no—
200C2×C3×C22⋊C4—64no—
201C2×C3×C22⋊C4C2×D311yescharacteristic
202C2×C3×C22⋊C4C2×D311yescharacteristic
203C2×C3×C22⋊C4C2×D311yescharacteristic
204C2×C3×C22⋊C4C2×D311yescharacteristic
205C2×C3×C22⋊C4C22×C311yescharacteristic
206C2×C3×C22⋊C4C22×C311yescharacteristic
207C2×C3×C22⋊C4C22×C311yescharacteristic
208C2×C3×C22⋊C4C22×C311yescharacteristic
209C2×C3×C42—31no—
210C2×C3×C42—31no—
211C2×C3×C42—31no—
212#953C3×C418yescomplemented
213C2×#217—24no—
214C2×#217C22×C311yescharacteristic
215C2×#217C22×C311yescharacteristic
216C2×#217C22×C311yescharacteristic
217C2×#217C22×C311yescharacteristic
218C2×#217C22×C311yescharacteristic
219C2×#217C22×C311yescharacteristic
220C2×#217C22×C311yescharacteristic
221C4×#67—24no—
222C2×(C2×D3)⋊C4C22×C311yescharacteristic, complemented
223C2×(C2×D3)⋊C4C22×C311yescharacteristic, complemented
224C2×(C2×D3)⋊C4C22×C311yescharacteristic, complemented
225C2×Dic3⋊C4C22×C311yescharacteristic, complemented
226C2×Dic3⋊C4C22×C311yescharacteristic, complemented
227C2×Dic3⋊C4C22×C311yescharacteristic, complemented
228C2×C4×Dic3C22×C311yescharacteristic, complemented
229C2×C4×Dic3C22×C311yescharacteristic, complemented
230C2×C4×Dic3C22×C311yescharacteristic, complemented
231#67⋊C4—24no—
232C3×#95—31no—
233C3×#95—31no—
234C3×#95—31no—
235C3×#95—31no—
236C3×#95—31no—
237C3×#95—31no—
238C3⋊#95C22×C311yescharacteristic, complemented
239C3⋊#95C22×C311yescharacteristic, complemented
240C3⋊#95C22×C311yescharacteristic, complemented
241C3⋊#95C22×C311yescharacteristic, complemented
242C3⋊#95C22×C311yescharacteristic, complemented
243C3⋊#95C22×C311yescharacteristic, complemented
244C23×C32—21no—
245C23×C32—21no—
246C23×C32—21no—
247C23×C32—21no—
248C23×C32—28no—
249C23×C32—21no—
250C23×C32—21no—
251C23×C32—21no—
252C23×C32—21no—
253C23×C32—21no—
254C23×C32—21no—
255C23×C32—28no—
256C23×C32—21no—
257C23×C32—21no—
258C23×C32—21no—
259C23×C32—21no—
260C23×C32—44no—
261C23×C32—44no—
262C23×C32—44no—
263C23×C32—44no—
264C23×C32—44no—
265C23×C32C22×C412yes—
266C23×C32C22×C412yes—
267C23×C32C22×C412yes—
268C23×C32C2×D412yes—
269C23×C32C2×D412yes—
270C23×C32#4112yes—
271C23×C32#4112yes—
272C23×C32C2411yescharacteristic
273C22×C3×D3—21no—
274C22×C3×D3—21no—
275C22×C3×D3—21no—
276C22×C3×D3—21no—
277C22×C3×D3—21no—
278C22×C3×D3—21no—
279C22×C3×D3C22×C412yes—
280C2×C32×C4—21no—
281C2×C32×C4—21no—
282C2×C32×C4—21no—
283C2×C32×C4—21no—
284C2×C32×C4—21no—
285C2×C32×C4—21no—
286C2×C32×C4—21no—
287C2×C32×C4—21no—
288C2×C32×C4—21no—
289C2×C32×C4—21no—
290C2×C32×C4—44no—
291C2×C32×C4—44no—
292C2×C32×C4C2×D412yes—
293C2×C32×C4C2×D412yes—
294C3×#67—28no—
295C3×#67—28no—
296C3×#67—44no—
297C2×C3×Dic3—21no—
298C2×C3×Dic3—21no—
299C2×C3×Dic3—21no—
300C2×C3×Dic3—21no—
301C2×C3×Dic3—21no—
302C2×C3×Dic3—21no—
303C2×C3×Dic3—21no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3—21no—
307C2×C3×Dic3—21no—
308C2×C3×Dic3—21no—
309C2×C3×Dic3—21no—
310C2×C3×Dic3—21no—
311C2×C3×Dic3—21no—
312C2×C3×Dic3—21no—
313C2×C3×Dic3—44no—
314C2×C3×Dic3—44no—
315C2×C3×Dic3C22×C412yes—
316C2×C3×Dic3C22×C412yes—
317C2×C3×Dic3C22×C412yes—
318C2×C3×Dic3C2×D412yes—
319C2×C3×Dic3C2×D412yes—
320C3×C4×D3—44no—
321C2×#120—31no—
322C2×C4×D4—31no—
323C2×C4×D4—31no—
324C22×C22⋊C4—31no—
325C22×C22⋊C4C3×D311yescharacteristic, complemented
326#390—31no—
327#388—31no—
328#388—31no—
329#386—31no—
330#386—31no—
331#386—31no—
332#385—31no—
333#385—31no—
334C4×C22⋊C4—31no—
335C4×C22⋊C4—31no—
336C24×C3—24no—
337C24×C3—24no—
338C24×C3—22no—
339C24×C3—22no—
340C24×C3—22no—
341C24×C3—22no—
342C24×C3—22no—
343C24×C3—22no—
344C24×C3—22no—
345C24×C3—22no—
346C24×C3—24no—
347C24×C3—21no—
348C24×C3—21no—
349C24×C3—21no—
350C24×C3—31no—
351C24×C3—42no—
352C24×C3—42no—
353C24×C3—41no—
354C24×C3—41no—
355C24×C3—41no—
356C24×C3—41no—
357C24×C3—42no—
358C24×C3—42no—
359C24×C3C4×D314yescomplemented
360C24×C3C2×C3×C414yescomplemented
361C24×C3C22×D311yescharacteristic
362C24×C3C22×D311yescharacteristic
363C24×C3C22×D311yescharacteristic
364C24×C3C23×C311yescharacteristic
365C24×C3C23×C311yescharacteristic
366C24×C3C23×C311yescharacteristic
367C23×D3C23×C311yescharacteristic
368C2×C3×D4—34no—
369C2×C3×D4—34no—
370C2×C3×D4—34no—
371C2×C3×D4—62no—
372C2×C3×D4—62no—
373C2×C3×D4—62no—
374C2×C3×D4—62no—
375C2×C3×D4—121no—
376C2×C3×D4—121no—
377C22×C3×C4—24no—
378C22×C3×C4—24no—
379C22×C3×C4—22no—
380C22×C3×C4—22no—
381C22×C3×C4—22no—
382C22×C3×C4—22no—
383C22×C3×C4—22no—
384C22×C3×C4—22no—
385C22×C3×C4—22no—
386C22×C3×C4—22no—
387C22×C3×C4—21no—
388C22×C3×C4—21no—
389C22×C3×C4—21no—
390C22×C3×C4—21no—
391C22×C3×C4—31no—
392C22×C3×C4—31no—
393C22×C3×C4—31no—
394C22×C3×C4—31no—
395C22×C3×C4—31no—
396C22×C3×C4—31no—
397C22×C3×C4—31no—
398C22×C3×C4—42no—
399C22×C3×C4—42no—
400C22×C3×C4—41no—
401C22×C3×C4—41no—
402C22×C3×C4—41no—
403C22×C3×C4—41no—
404C22×C3×C4—42no—
405C22×C3×C4—42no—
406C22×C3×C4—62no—
407C22×C3×C4—62no—
408C22×C3×C4—62no—
409C22×C3×C4—62no—
410C22×C3×C4—62no—
411C22×C3×C4—62no—
412C22×C3×C4—121no—
413C22×C3×C4—121no—
414C22×C3×C4—121no—
415C22×C3×C4C22×D311yescharacteristic
416C22×C3×C4C22×D311yescharacteristic
417C22×C3×C4C22×D311yescharacteristic
418C22×C3×C4C22×D311yescharacteristic
419C22×C3×C4C23×C311yescharacteristic
420C22×C3×C4C23×C311yescharacteristic
421C22×C3×C4C23×C311yescharacteristic
422C22×C3×C4C23×C311yescharacteristic
423C2×#67—22no—
424C2×#67—22no—
425C2×#67—22no—
426C2×#67—22no—
427C2×#67—41no—
428C2×#67—41no—
429C2×#67C2×C3×C414yescomplemented
430C2×#67C2×C3×C414yescomplemented
431C2×#67C2×C3×C414yescomplemented
432C22×Dic3—22no—
433C22×Dic3—22no—
434C22×Dic3—22no—
435C22×Dic3—22no—
436C22×Dic3—41no—
437C22×Dic3—41no—
438C22×Dic3C23×C311yescharacteristic
439C22×Dic3C23×C311yescharacteristic
440C22×Dic3C23×C311yescharacteristic
441C22×Dic3C23×C311yescharacteristic
442C22×Dic3C23×C311yescharacteristic
443C22×Dic3C23×C311yescharacteristic
444C22×Dic3C23×C311yescharacteristic
445C2×C4×D3—22no—
446C2×C4×D3—22no—
447C2×C4×D3—41no—
448C3×C4⋊C4—62no—
449C3×C4⋊C4—62no—
450C3×C4⋊C4—121no—
451C3×C22⋊C4—24no—
452C3×C22⋊C4—24no—
453C3×C22⋊C4—24no—
454C3×C22⋊C4—22no—
455C3×C22⋊C4—22no—
456C3×C22⋊C4—22no—
457C3×C22⋊C4—22no—
458C3×C22⋊C4—22no—
459C3×C22⋊C4—22no—
460C3×C22⋊C4—24no—
461C3×C22⋊C4—34no—
462C3×C22⋊C4—34no—
463C3×C22⋊C4—34no—
464C3×C22⋊C4—34no—
465C3×C22⋊C4—62no—
466C3×C22⋊C4—62no—
467C3×C22⋊C4—62no—
468C3×C22⋊C4—62no—
469C3×C22⋊C4—62no—
470C3×C22⋊C4—121no—
471C3×C22⋊C4#6714yescomplemented
472C3×C22⋊C4C3×D414yescomplemented
473C3×C42—62no—
474C3×C42—62no—
475C3×C42—121no—
476#217—22no—
477#217—22no—
478#217—22no—
479#217C2×C3×C414yescomplemented
480#217C2×C3×C414yescomplemented
481#217C2×C3×C414yescomplemented
482#217C3×D414yescomplemented
483(C2×D3)⋊C4—22no—
484(C2×D3)⋊C4—22no—
485(C2×D3)⋊C4—41no—
486Dic3⋊C4—22no—
487Dic3⋊C4—22no—
488Dic3⋊C4—41no—
489C4×Dic3—22no—
490C4×Dic3—22no—
491C4×Dic3—41no—
492C22×C32—22no—
493C22×C32—22no—
494C22×C32—22no—
495C22×C32—22no—
496C22×C32—22no—
497C22×C32—22no—
498C22×C32—22no—
499C22×C32—22no—
500C22×C32—22no—
501C22×C32—22no—
502C22×C32—22no—
503C22×C32—22no—
504C22×C32—22no—
505C22×C32—22no—
506C22×C32—22no—
507C22×C32—416no—
508C22×C32—41no—
509C22×C32—41no—
510C22×C32—41no—
511C22×C32—41no—
512C22×C32C4×D414yescomplemented
513C22×C32C4×D414yescomplemented
514C22×C32C23×C411yescharacteristic
515C22×C32C22×D411yescharacteristic
516C22×C32C22×D411yescharacteristic
517C22×C32C2×#4111yescharacteristic
518C22×C32C2×#4111yescharacteristic
519C22×C32H(5,𝔽2)11yescharacteristic
520C22×C32H(5,𝔽2)11yescharacteristic
521C2×C3×D3—22no—
522C2×C3×D3—22no—
523C2×C3×D3—22no—
524C2×C3×D3—41no—
525C2×C3×D3—41no—
526C2×C3×D3—41no—
527C2×C3×D3—41no—
528C32×C4—22no—
529C32×C4—22no—
530C32×C4—41no—
531C32×C4—41no—
532C3×Dic3—22no—
533C3×Dic3—22no—
534C3×Dic3—22no—
535C3×Dic3—22no—
536C3×Dic3—22no—
537C3×Dic3—41no—
538C3×Dic3—41no—
539C25C2×C3×D311yescharacteristic
540C22×D4—31no—
541C22×D4—31no—
542C22×D4—31no—
543C23×C4—31no—
544C23×C4—31no—
545C23×C4—31no—
546C23×C4C2×C3×D311yescharacteristic
547C23×C4C2×C3×D311yescharacteristic
548#120—38no—
549C4×D4—64no—
550C4×D4—64no—
551C2×C4⋊C4—31no—
552C2×C4⋊C4—31no—
553C2×C4⋊C4—31no—
554C2×C22⋊C4—24no—
555C2×C22⋊C4—31no—
556C2×C22⋊C4—31no—
557C2×C22⋊C4—31no—
558C2×C22⋊C4—31no—
559C2×C22⋊C4—31no—
560C2×C22⋊C4—31no—
561C2×C22⋊C4—31no—
562C2×C22⋊C4—31no—
563C2×C22⋊C4—31no—
564C2×C22⋊C4—31no—
565C2×C22⋊C4—64no—
566C2×C22⋊C4C2×C3×D311yescharacteristic
567C2×C22⋊C4C2×C3×D311yescharacteristic
568C2×C22⋊C4C2×C3×D311yescharacteristic
569C2×C22⋊C4C2×C3×D311yescharacteristic
570C2×C42—31no—
571C2×C42—31no—
572C2×C42—31no—
573#95—31no—
574#95—31no—
575#95—31no—
576#95—31no—
577#95—31no—
578#95—31no—
579C23×C3—22no—
580C23×C3—22no—
581C23×C3—22no—
582C23×C3—22no—
583C23×C3—21no—
584C23×C3—21no—
585C23×C3—21no—
586C23×C3—21no—
587C23×C3—21no—
588C23×C3—21no—
589C23×C3—21no—
590C23×C3—21no—
591C23×C3—21no—
592C23×C3—21no—
593C23×C3—21no—
594C23×C3—21no—
595C23×C3—21no—
596C23×C3—21no—
597C23×C3—21no—
598C23×C3—21no—
599C23×C3—22no—
600C23×C3—216no—
601C23×C3—22no—
602C23×C3—28no—
603C23×C3—28no—
604C23×C3—28no—
605C23×C3—28no—
606C23×C3—21no—
607C23×C3—21no—
608C23×C3—21no—
609C23×C3—21no—
610C23×C3—21no—
611C23×C3—21no—
612C23×C3—21no—
613C23×C3—21no—
614C23×C3—21no—
615C23×C3—21no—
616C23×C3—21no—
617C23×C3—21no—
618C23×C3—21no—
619C23×C3—22no—
620C23×C3—22no—
621C23×C3—22no—
622C23×C3—22no—
623C23×C3—22no—
624C23×C3—22no—
625C23×C3—22no—
626C23×C3—32no—
627C23×C3—41no—
628C23×C3—41no—
629C23×C3—41no—
630C23×C3—41no—
631C23×C3—48no—
632C23×C3—41no—
633C23×C3—41no—
634C23×C3—41no—
635C23×C3—41no—
636C23×C3—44no—
637C23×C3—44no—
638C23×C3—44no—
639C23×C3—44no—
640C23×C3—44no—
641C23×C3—44no—
642C23×C3—44no—
643C23×C3—44no—
644C23×C3—44no—
645C23×C3—44no—
646C23×C3—48no—
647C23×C3—48no—
648C23×C3—48no—
649C23×C3—48no—
650C23×C3—48no—
651C23×C3—61no—
652C23×C3—61no—
653C23×C3—61no—
654C23×C3—61no—
655C23×C3—61no—
656C23×C3—61no—
657C23×C3C2×C4×D312yes—
658C23×C3C2×C4×D312yes—
659C23×C3C2×C4×D312yes—
660C23×C3#23512yes—
661C23×C3D3×D412yes—
662C23×C3#23712yes—
663C23×C3C2×#6712yes—
664C23×C3C22×C3×C412yes—
665C23×C3C22×C3×C412yes—
666C23×C3C22×C3×C412yes—
667C23×C3C2×C3×D412yes—
668C23×C3C2×C3×D412yes—
669C23×C3C3×#4112yes—
670C23×C3C3×#4112yes—
671C23×C3C23×D311yescharacteristic
672C23×C3C24×C311yescharacteristic
673C22×D3—21no—
674C22×D3—21no—
675C22×D3—21no—
676C22×D3—21no—
677C22×D3—21no—
678C22×D3—21no—
679C22×D3C22×C3×C412yes—
680C3×D4—68no—
681C3×D4—68no—
682C3×D4—124no—
683C2×C3×C4—21no—
684C2×C3×C4—21no—
685C2×C3×C4—21no—
686C2×C3×C4—21no—
687C2×C3×C4—21no—
688C2×C3×C4—21no—
689C2×C3×C4—21no—
690C2×C3×C4—21no—
691C2×C3×C4—22no—
692C2×C3×C4—22no—
693C2×C3×C4—21no—
694C2×C3×C4—21no—
695C2×C3×C4—21no—
696C2×C3×C4—21no—
697C2×C3×C4—21no—
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—22no—
706C2×C3×C4—22no—
707C2×C3×C4—32no—
708C2×C3×C4—32no—
709C2×C3×C4—32no—
710C2×C3×C4—32no—
711C2×C3×C4—32no—
712C2×C3×C4—41no—
713C2×C3×C4—41no—
714C2×C3×C4—41no—
715C2×C3×C4—41no—
716C2×C3×C4—41no—
717C2×C3×C4—41no—
718C2×C3×C4—41no—
719C2×C3×C4—41no—
720C2×C3×C4—44no—
721C2×C3×C4—44no—
722C2×C3×C4—44no—
723C2×C3×C4—44no—
724C2×C3×C4—48no—
725C2×C3×C4—48no—
726C2×C3×C4—61no—
727C2×C3×C4—61no—
728C2×C3×C4—61no—
729C2×C3×C4—61no—
730C2×C3×C4—61no—
731C2×C3×C4—61no—
732C2×C3×C4—61no—
733C2×C3×C4—61no—
734C2×C3×C4—61no—
735C2×C3×C4—61no—
736C2×C3×C4—61no—
737C2×C3×C4—61no—
738C2×C3×C4—61no—
739C2×C3×C4—61no—
740C2×C3×C4—61no—
741C2×C3×C4—61no—
742C2×C3×C4—124no—
743C2×C3×C4—124no—
744C2×C3×C4—124no—
745C2×C3×C4C2×#6712yes—
746C2×C3×C4C2×#6712yes—
747C2×C3×C4C2×C3×D412yes—
748C2×C3×C4C2×C3×D412yes—
749#67—28no—
750#67—28no—
751#67—44no—
752C2×Dic3—21no—
753C2×Dic3—21no—
754C2×Dic3—21no—
755C2×Dic3—21no—
756C2×Dic3—21no—
757C2×Dic3—21no—
758C2×Dic3—21no—
759C2×Dic3—21no—
760C2×Dic3—21no—
761C2×Dic3—21no—
762C2×Dic3—21no—
763C2×Dic3—21no—
764C2×Dic3—21no—
765C2×Dic3—21no—
766C2×Dic3—21no—
767C2×Dic3—21no—
768C2×Dic3—44no—
769C2×Dic3—44no—
770C2×Dic3C22×C3×C412yes—
771C2×Dic3C22×C3×C412yes—
772C2×Dic3C22×C3×C412yes—
773C2×Dic3C2×C3×D412yes—
774C2×Dic3C2×C3×D412yes—
775C4×D3—44no—
776C2×C32—24no—
777C2×C32—24no—
778C2×C32—42no—
779C2×C32C2×C4×D411yescharacteristic
780C2×C32C2×C4×D411yescharacteristic
781C2×C32#51811yescharacteristic
782C2×C32D4211yescharacteristic
783C2×C32#54611yescharacteristic
784C2×C32#54611yescharacteristic
785C2×C32#55111yescharacteristic
786C3×D3—42no—
787C24—22no—
788C24—22no—
789C24—22no—
790C24—22no—
791C24—31no—
792C24—41no—
793C24—41no—
794C24C3×C4×D314yescomplemented
795C24C22×C3×D311yescharacteristic
796C24C22×C3×D311yescharacteristic
797C24C22×C3×D311yescharacteristic
798C2×D4—34no—
799C2×D4—34no—
800C2×D4—34no—
801C2×D4—62no—
802C2×D4—62no—
803C2×D4—62no—
804C2×D4—62no—
805C2×D4—121no—
806C2×D4—121no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—31no—
812C22×C4—31no—
813C22×C4—31no—
814C22×C4—31no—
815C22×C4—31no—
816C22×C4—31no—
817C22×C4—31no—
818C22×C4—41no—
819C22×C4—41no—
820C22×C4—62no—
821C22×C4—62no—
822C22×C4—62no—
823C22×C4—62no—
824C22×C4—62no—
825C22×C4—62no—
826C22×C4—121no—
827C22×C4—121no—
828C22×C4—121no—
829C22×C4C22×C3×D311yescharacteristic
830C22×C4C22×C3×D311yescharacteristic
831C22×C4C22×C3×D311yescharacteristic
832C22×C4C22×C3×D311yescharacteristic
833C4⋊C4—62no—
834C4⋊C4—62no—
835C4⋊C4—121no—
836C22⋊C4—22no—
837C22⋊C4—22no—
838C22⋊C4—22no—
839C22⋊C4—34no—
840C22⋊C4—34no—
841C22⋊C4—34no—
842C22⋊C4—34no—
843C22⋊C4—62no—
844C22⋊C4—62no—
845C22⋊C4—62no—
846C22⋊C4—62no—
847C22⋊C4—62no—
848C22⋊C4—121no—
849C22⋊C4C3×#6714yescomplemented
850C42—62no—
851C42—62no—
852C42—121no—
853C22×C3—24no—
854C22×C3—24no—
855C22×C3—24no—
856C22×C3—24no—
857C22×C3—24no—
858C22×C3—24no—
859C22×C3—22no—
860C22×C3—22no—
861C22×C3—22no—
862C22×C3—22no—
863C22×C3—22no—
864C22×C3—22no—
865C22×C3—22no—
866C22×C3—22no—
867C22×C3—22no—
868C22×C3—22no—
869C22×C3—22no—
870C22×C3—22no—
871C22×C3—22no—
872C22×C3—22no—
873C22×C3—22no—
874C22×C3—22no—
875C22×C3—22no—
876C22×C3—22no—
877C22×C3—22no—
878C22×C3—22no—
879C22×C3—22no—
880C22×C3—22no—
881C22×C3—22no—
882C22×C3—22no—
883C22×C3—24no—
884C22×C3—22no—
885C22×C3—22no—
886C22×C3—22no—
887C22×C3—22no—
888C22×C3—22no—
889C22×C3—22no—
890C22×C3—24no—
891C22×C3—24no—
892C22×C3—21no—
893C22×C3—21no—
894C22×C3—21no—
895C22×C3—21no—
896C22×C3—21no—
897C22×C3—21no—
898C22×C3—21no—
899C22×C3—42no—
900C22×C3—42no—
901C22×C3—42no—
902C22×C3—42no—
903C22×C3—42no—
904C22×C3—42no—
905C22×C3—42no—
906C22×C3—42no—
907C22×C3—416no—
908C22×C3—416no—
909C22×C3—432no—
910C22×C3—42no—
911C22×C3—42no—
912C22×C3—42no—
913C22×C3—42no—
914C22×C3—41no—
915C22×C3—41no—
916C22×C3—41no—
917C22×C3—41no—
918C22×C3—41no—
919C22×C3—41no—
920C22×C3—41no—
921C22×C3—41no—
922C22×C3—62no—
923C22×C3—62no—
924C22×C3—62no—
925C22×C3—121no—
926C22×C3—121no—
927C22×C3—121no—
928C22×C3—121no—
929C22×C3#67⋊C414yescomplemented
930C22×C3C4×#6714yescomplemented
931C22×C3C3×C4×D414yescomplemented
932C22×C3C3×C4×D414yescomplemented
933C22×C3C22×C4×D311yescharacteristic
934C22×C3C2×#23511yescharacteristic
935C22×C3C2×D3×D411yescharacteristic
936C22×C3C2×#23711yescharacteristic
937C22×C3#100411yescharacteristic
938C22×C3#100411yescharacteristic
939C22×C3C22×#6711yescharacteristic
940C22×C3C23×C3×C411yescharacteristic
941C22×C3C22×C3×D411yescharacteristic
942C22×C3C22×C3×D411yescharacteristic
943C22×C3C2×C3×#4111yescharacteristic
944C22×C3C2×C3×#4111yescharacteristic
945C22×C3C3×H(5,𝔽2)11yescharacteristic
946C22×C3C3×H(5,𝔽2)11yescharacteristic
947C2×D3—22no—
948C2×D3—22no—
949C2×D3—22no—
950C2×D3—41no—
951C2×D3—41no—
952C2×D3—41no—
953C2×D3—41no—
954C3×C4—22no—
955C3×C4—22no—
956C3×C4—22no—
957C3×C4—22no—
958C3×C4—42no—
959C3×C4—42no—
960C3×C4—42no—
961C3×C4—42no—
962C3×C4—41no—
963C3×C4—41no—
964C3×C4—41no—
965C3×C4—41no—
966C3×C4—62no—
967C3×C4—62no—
968C3×C4—62no—
969C3×C4—62no—
970C3×C4—62no—
971C3×C4—121no—
972C3×C4—121no—
973Dic3—22no—
974Dic3—22no—
975Dic3—22no—
976Dic3—22no—
977Dic3—22no—
978Dic3—41no—
979Dic3—41no—
980C32#235811yescharacteristic, complemented, Sylow
981C23—21no—
982C23—21no—
983C23—21no—
984C23—21no—
985C23—21no—
986C23—21no—
987C23—21no—
988C23—21no—
989C23—28no—
990C23—28no—
991C23—21no—
992C23—21no—
993C23—21no—
994C23—21no—
995C23—21no—
996C23—21no—
997C23—32no—
998C23—44no—
999C23—44no—
1000C23—44no—
1001C23—44no—
1002C23—44no—
1003C23—61no—
1004C23—61no—
1005C23—61no—
1006C23—61no—
1007C23—61no—
1008C23—61no—
1009C23C2×C3×C4×D312yes—
1010C23C2×C3×C4×D312yes—
1011C23C2×C3×C4×D312yes—
1012C23C3×#23512yes—
1013C23C3×D3×D412yes—
1014C23C3×#23712yes—
1015C23C2×C3×#6712yes—
1016C23C23×C3×D311yescharacteristic
1017D4—68no—
1018D4—68no—
1019D4—124no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—32no—
1031C2×C4—32no—
1032C2×C4—32no—
1033C2×C4—32no—
1034C2×C4—32no—
1035C2×C4—44no—
1036C2×C4—44no—
1037C2×C4—61no—
1038C2×C4—61no—
1039C2×C4—61no—
1040C2×C4—61no—
1041C2×C4—61no—
1042C2×C4—61no—
1043C2×C4—61no—
1044C2×C4—61no—
1045C2×C4—61no—
1046C2×C4—61no—
1047C2×C4—61no—
1048C2×C4—61no—
1049C2×C4—61no—
1050C2×C4—61no—
1051C2×C4—61no—
1052C2×C4—61no—
1053C2×C4—124no—
1054C2×C4—124no—
1055C2×C4—124no—
1056C2×C4C2×C3×#6712yes—
1057C2×C4C2×C3×#6712yes—
1058C2×C3—28no—
1059C2×C3—24no—
1060C2×C3—24no—
1061C2×C3—24no—
1062C2×C3—24no—
1063C2×C3—21no—
1064C2×C3—21no—
1065C2×C3—21no—
1066C2×C3—21no—
1067C2×C3—21no—
1068C2×C3—21no—
1069C2×C3—21no—
1070C2×C3—44no—
1071C2×C3—44no—
1072C2×C3—42no—
1073C2×C3—42no—
1074C2×C3—122no—
1075C2×C3C2×#67⋊C411yescharacteristic
1076C2×C3#548611yescharacteristic
1077C2×C3#549011yescharacteristic
1078C2×C3#549511yescharacteristic
1079C2×C3C2×C4×#6711yescharacteristic
1080C2×C3D4×#6711yescharacteristic
1081C2×C3#580611yescharacteristic
1082C2×C3C2×C3×C4×D411yescharacteristic
1083C2×C3C2×C3×C4×D411yescharacteristic
1084C2×C3C3×#51811yescharacteristic
1085C2×C3C3×D4211yescharacteristic
1086C2×C3C3×#54611yescharacteristic
1087C2×C3C3×#54611yescharacteristic
1088C2×C3C3×#55111yescharacteristic
1089D3—42no—
1090C22—22no—
1091C22—22no—
1092C22—22no—
1093C22—22no—
1094C22—22no—
1095C22—22no—
1096C22—22no—
1097C22—22no—
1098C22—22no—
1099C22—22no—
1100C22—22no—
1101C22—22no—
1102C22—22no—
1103C22—22no—
1104C22—22no—
1105C22—416no—
1106C22—41no—
1107C22—41no—
1108C22—41no—
1109C22—41no—
1110C22—62no—
1111C22—62no—
1112C22—62no—
1113C22—121no—
1114C22—121no—
1115C22—121no—
1116C22—121no—
1117C22C3×#67⋊C414yescomplemented
1118C22C3×C4×#6714yescomplemented
1119C22C22×C3×C4×D311yescharacteristic
1120C22C2×C3×#23511yescharacteristic
1121C22C2×C3×D3×D411yescharacteristic
1122C22C2×C3×#23711yescharacteristic
1123C22C3×#100411yescharacteristic
1124C22C3×#100411yescharacteristic
1125C22C22×C3×#6711yescharacteristic
1126C4—22no—
1127C4—22no—
1128C4—41no—
1129C4—41no—
1130C4—62no—
1131C4—62no—
1132C4—62no—
1133C4—62no—
1134C4—62no—
1135C4—121no—
1136C4—121no—
1137C3—21no—
1138C3#8209911yescharacteristic, direct product factor
1139C3C3×#235811yescharacteristic, complemented
1140C2—24no—
1141C2—24no—
1142C2—42no—
1143C2—122no—
1144C2C2×C3×#67⋊C411yescharacteristic
1145C2C3×#548611yescharacteristic
1146C2C3×#549011yescharacteristic
1147C2C3×#549511yescharacteristic
1148C2C2×C3×C4×#6711yescharacteristic
1149C2C3×D4×#6711yescharacteristic
1150C2C3×#580611yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC22×C32×C22⋊C4C2
socleC23×C32C24
prime radicalC2×C3×#953C2
cosocleC23×C3C24×C3
hypercenterC22×C3×C22⋊C4D3
hypocenterC3C3×#2358
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C22×C3×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×C32×C22⋊C4C2semidirect
3. C22×C3×#217C2semidirect
4. C2×C3×C4×#67C2semidirect
5. C2×C3×#67⋊C4C2semidirect
6. C3×#5213C2semidirect
7. C3×#5210C2semidirect
8. C3×C4×#217C2semidirect
9. C3×#4958C2semidirect
10. C3×#4957C2semidirect
11. C3×#4956C2semidirect
12. C3×#4946C2semidirect
13. C3×#4945C2semidirect
14. C3×#4944C2semidirect
15. C3×Dic3×C22⋊C4C2semidirect
17. #82099C3direct (N × H)
26. C22×C3×C4×D3C22semidirect
32. C3×#953C4semidirect
42. C2×C3×(C2×D3)⋊C4C22semidirect
43. C2×C3×(C2×D3)⋊C4C22semidirect
44. C2×C3×(C2×D3)⋊C4C22semidirect
45. C2×C3×Dic3⋊C4C22semidirect
46. C2×C3×Dic3⋊C4C22semidirect
47. C2×C3×Dic3⋊C4C22semidirect
48. C2×C3×C4×Dic3C22semidirect
49. C2×C3×C4×Dic3C22semidirect
50. C2×C3×C4×Dic3C22semidirect
52. C3×C3⋊#95C22semidirect
53. C3×C3⋊#95C22semidirect
54. C3×C3⋊#95C22semidirect
55. C3×C3⋊#95C22semidirect
56. C3×C3⋊#95C22semidirect
57. C3×C3⋊#95C22semidirect
63. C22×C3×C22⋊C4D3semidirect
64. C22×C3×C22⋊C4C2×C3semidirect
66. C22×#217C2×C3semidirect
67. C2×C4×#67C2×C3semidirect
68. C2×#67⋊C4C2×C3semidirect
79. #5213C2×C3semidirect
80. #5210C2×C3semidirect
81. C4×#217C2×C3semidirect
82. #4958C2×C3semidirect
83. #4957C2×C3semidirect
84. #4956C2×C3semidirect
85. #4946C2×C3semidirect
86. #4945C2×C3semidirect
87. #4944C2×C3semidirect
88. Dic3×C22⋊C4C2×C3semidirect
95. C24×C32C2×C4semidirect
116. C2×C3×#67C2×C4semidirect
117. C2×C3×#67C2×C4semidirect
118. C2×C3×#67C2×C4semidirect
138. C32×C22⋊C4D4semidirect
142. C3×#217C2×C4semidirect
143. C3×#217C2×C4semidirect
144. C3×#217C2×C4semidirect
145. C3×#217D4semidirect
176. C22×C4×D3C22×C3semidirect
212. #953C3×C4semidirect
222. C2×(C2×D3)⋊C4C22×C3semidirect
223. C2×(C2×D3)⋊C4C22×C3semidirect
224. C2×(C2×D3)⋊C4C22×C3semidirect
225. C2×Dic3⋊C4C22×C3semidirect
226. C2×Dic3⋊C4C22×C3semidirect
227. C2×Dic3⋊C4C22×C3semidirect
228. C2×C4×Dic3C22×C3semidirect
229. C2×C4×Dic3C22×C3semidirect
230. C2×C4×Dic3C22×C3semidirect
238. C3⋊#95C22×C3semidirect
239. C3⋊#95C22×C3semidirect
240. C3⋊#95C22×C3semidirect
241. C3⋊#95C22×C3semidirect
242. C3⋊#95C22×C3semidirect
243. C3⋊#95C22×C3semidirect
325. C22×C22⋊C4C3×D3semidirect
359. C24×C3C4×D3semidirect
360. C24×C3C2×C3×C4semidirect
429. C2×#67C2×C3×C4semidirect
430. C2×#67C2×C3×C4semidirect
431. C2×#67C2×C3×C4semidirect
471. C3×C22⋊C4#67semidirect
472. C3×C22⋊C4C3×D4semidirect
479. #217C2×C3×C4semidirect
480. #217C2×C3×C4semidirect
481. #217C2×C3×C4semidirect
482. #217C3×D4semidirect
512. C22×C32C4×D4semidirect
513. C22×C32C4×D4semidirect
794. C24C3×C4×D3semidirect
849. C22⋊C4C3×#67semidirect
929. C22×C3#67⋊C4semidirect
930. C22×C3C4×#67semidirect
931. C22×C3C3×C4×D4semidirect
932. C22×C3C3×C4×D4semidirect
980. C32#2358semidirect
1117. C22C3×#67⋊C4semidirect
1118. C22C3×C4×#67semidirect
1138. C3#82099direct (N × H)
1139. C3C3×#2358semidirect

Maximal subgroups

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

subgroupindex
C22×C32×C22⋊C42
C2×C3×#9532
C22×C3×#2172
C2×C3×C4×#672
C2×C3×#67⋊C42
C3×#52132
C3×#52102
C3×C4×#2172
C3×#49582
C3×#49572
C3×#49562
C3×#49462
C3×#49452
C3×#49442
C3×Dic3×C22⋊C42
C3×#23583
#820993