Finite Group Databasebeta

← C3×#82398 #11806089

Subgroups — C3×#82398 #11806089

Order 1152.

2069 conjugacy classes of subgroups.

The subgroup lattice has 1130 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4×D4C211yesmaximal, characteristic, complemented
2C2×C3×#937C211yesmaximal, characteristic
3C2×C3×C4×#67C211yesmaximal, characteristic, complemented
4C22×C3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
5C2×C3×D3×C22⋊C4C211yesmaximal, characteristic, complemented
6C3×#5220C211yesmaximal, characteristic, complemented
7C3×#5213C211yesmaximal, characteristic, complemented
8C3×#5210C211yesmaximal, characteristic, complemented
9C3×#4990C211yesmaximal, characteristic, complemented
10C3×#4989C211yesmaximal, characteristic, complemented
11C3×#4957C211yesmaximal, characteristic, complemented
12C3×#4956C211yesmaximal, characteristic, complemented
13C3×Dic3×C22⋊C4C211yesmaximal, characteristic, complemented
14C3×#4940C211yesmaximal, characteristic, complemented
15C3×C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
16C3×#2358—31nomaximal
17#82398C311yesmaximal, characteristic, direct product factor
18C24×C3×D3C2211yescharacteristic
19C22×C32×D4C2211yescharacteristic
20C23×C32×C4C2211yescharacteristic
21C23×C32×C4C2211yescharacteristic, complemented
22C22×C3×#67C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic
24C23×C3×Dic3C2211yescharacteristic
25C22×C3×C4×D3C2211yescharacteristic
26C22×C3×C4×D3C2211yescharacteristic
27C32×C4×D4—24no—
28C2×C32×C4⋊C4C2211yescharacteristic, complemented
29C2×C32×C22⋊C4C2211yescharacteristic
30C2×C32×C22⋊C4C2211yescharacteristic, complemented
31C2×C32×C42C2211yescharacteristic, complemented
32C2×C3×#217C2211yescharacteristic
33C2×C3×#217C2211yescharacteristic
34C2×C3×#217C2211yescharacteristic, complemented
35C2×C3×#217C2211yescharacteristic, complemented
36C3×#937C418yescomplemented
37C3×C4×#67—24no—
38C2×C3×(C2×D3)⋊C4—24no—
39C2×C3×(C2×D3)⋊C4C2211yescharacteristic
40C2×C3×(C2×D3)⋊C4C2211yescharacteristic
41C2×C3×(C2×D3)⋊C4C2211yescharacteristic
42C2×C3×(C2×D3)⋊C4C2211yescharacteristic
43C2×C3×(C2×D3)⋊C4C2211yescharacteristic
44C2×C3×(C2×D3)⋊C4C2211yescharacteristic
45C2×C3×(C2×D3)⋊C4C2211yescharacteristic
46C2×C3×(C2×D3)⋊C4C2211yescharacteristic
47C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
48C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
49C2×C3×C4×Dic3C2211yescharacteristic, complemented
50C2×C3×C4×Dic3C2211yescharacteristic, complemented
51C3×D3×C22⋊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—21no—
60C2×C3×C4×D4—31no—
61C2×C3×C4×D4D311yescharacteristic, complemented
62C2×C3×C4×D4C2×C311yescharacteristic, complemented
63C22×C3×C22⋊C4—31no—
64C22×C3×C22⋊C4—31no—
65C2×#937C2×C311yescharacteristic
66C2×C4×#67C2×C311yescharacteristic, complemented
67C22×(C2×D3)⋊C4C2×C311yescharacteristic, complemented
68C2×D3×C22⋊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#5220C2×C311yescharacteristic, complemented
80#5213C2×C311yescharacteristic, complemented
81#5210C2×C311yescharacteristic, complemented
82#4990C2×C311yescharacteristic, complemented
83#4989C2×C311yescharacteristic, complemented
84#4957C2×C311yescharacteristic, complemented
85#4956C2×C311yescharacteristic, complemented
86Dic3×C22⋊C4C2×C311yescharacteristic, complemented
87#4940C2×C311yescharacteristic, complemented
88C4×(C2×D3)⋊C4C2×C311yescharacteristic, complemented
89C24×C32C2311yescharacteristic
90C24×C32C2311yescharacteristic
91C23×C3×D3—22no—
92C23×C3×D3—22no—
93C23×C3×D3—22no—
94C23×C3×D3—22no—
95C23×C3×D3—41no—
96C23×C3×D3—41no—
97C23×C3×D3C2×C414yescomplemented
98C23×C3×D3C2311yescharacteristic
99C23×C3×D3C2311yescharacteristic
100C2×C32×D4—22no—
101C2×C32×D4—22no—
102C2×C32×D4C2×C414yescomplemented
103C22×C32×C4—22no—
104C22×C32×C4—22no—
105C22×C32×C4—22no—
106C22×C32×C4—22no—
107C22×C32×C4—41no—
108C22×C32×C4—41no—
109C22×C32×C4C2311yescharacteristic
110C22×C32×C4C2311yescharacteristic
111C22×C32×C4C2311yescharacteristic
112C22×C32×C4C2311yescharacteristic
113C22×C32×C4C2311yescharacteristic
114C2×C3×#67—22no—
115C2×C3×#67—22no—
116C2×C3×#67—41no—
117C2×C3×#67—41no—
118C2×C3×#67C2×C414yescomplemented
119C2×C3×#67C2×C414yescomplemented
120C22×C3×Dic3—22no—
121C22×C3×Dic3—22no—
122C22×C3×Dic3—41no—
123C22×C3×Dic3C2311yescharacteristic
124C22×C3×Dic3C2311yescharacteristic
125C22×C3×Dic3C2311yescharacteristic
126C22×C3×Dic3C2311yescharacteristic
127C22×C3×Dic3C2311yescharacteristic
128C22×C3×Dic3C2311yescharacteristic
129C2×C3×C4×D3—22no—
130C2×C3×C4×D3—22no—
131C2×C3×C4×D3—22no—
132C2×C3×C4×D3—22no—
133C2×C3×C4×D3—41no—
134C2×C3×C4×D3—41no—
135C32×C4⋊C4—22no—
136C32×C22⋊C4—22no—
137C32×C22⋊C4D414yescomplemented
138C32×C42—22no—
139C3×#217—22no—
140C3×#217—22no—
141C3×#217—41no—
142C3×#217C2×C414yescomplemented
143C3×(C2×D3)⋊C4—22no—
144C3×(C2×D3)⋊C4—22no—
145C3×(C2×D3)⋊C4—22no—
146C3×(C2×D3)⋊C4—22no—
147C3×(C2×D3)⋊C4—22no—
148C3×(C2×D3)⋊C4C2×C414yescomplemented
149C3×(C2×D3)⋊C4C2×C414yescomplemented
150C3×(C2×D3)⋊C4D414yescomplemented
151C3×Dic3⋊C4—22no—
152C3×Dic3⋊C4—41no—
153C3×C4×Dic3—22no—
154C3×C4×Dic3—41no—
155#2358—31noSylow
156C25×C3—31no—
157C24×D3C22×C311yescharacteristic
158C22×C3×D4—21no—
159C22×C3×D4—31no—
160C22×C3×D4—31no—
161C22×C3×D4C2×D311yescharacteristic
162C22×C3×D4C22×C311yescharacteristic
163C23×C3×C4—21no—
164C23×C3×C4—21no—
165C23×C3×C4—31no—
166C23×C3×C4—31no—
167C23×C3×C4—31no—
168C23×C3×C4C2×D311yescharacteristic
169C23×C3×C4C2×D311yescharacteristic, complemented
170C23×C3×C4C22×C311yescharacteristic
171C23×C3×C4C22×C311yescharacteristic, complemented
172C22×#67C22×C311yescharacteristic
173C22×#67C22×C311yescharacteristic
174C23×Dic3C22×C311yescharacteristic
175C22×C4×D3C22×C311yescharacteristic
176C22×C4×D3C22×C311yescharacteristic
177C3×#120—38no—
178C3×C4×D4—28no—
179C3×C4×D4—24no—
180C3×C4×D4—24no—
181C3×C4×D4—64no—
182C2×C3×C4⋊C4—21no—
183C2×C3×C4⋊C4—31no—
184C2×C3×C4⋊C4—31no—
185C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
186C2×C3×C4⋊C4C22×C311yescharacteristic, complemented
187C2×C3×C22⋊C4—21no—
188C2×C3×C22⋊C4—21no—
189C2×C3×C22⋊C4—31no—
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—31no—
201C2×C3×C22⋊C4—64no—
202C2×C3×C22⋊C4—64no—
203C2×C3×C22⋊C4C2×D311yescharacteristic
204C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
205C2×C3×C22⋊C4C22×C311yescharacteristic
206C2×C3×C22⋊C4C22×C311yescharacteristic, complemented
207C2×C3×C42—21no—
208C2×C3×C42—31no—
209C2×C3×C42—31no—
210C2×C3×C42C2×D311yescharacteristic, complemented
211C2×C3×C42C22×C311yescharacteristic, complemented
212C2×#217C22×C311yescharacteristic
213C2×#217C22×C311yescharacteristic
214C2×#217C22×C311yescharacteristic, complemented
215C2×#217C22×C311yescharacteristic, complemented
216#937C3×C418yescomplemented
217C4×#67—24no—
218C2×(C2×D3)⋊C4—24no—
219C2×(C2×D3)⋊C4C22×C311yescharacteristic
220C2×(C2×D3)⋊C4C22×C311yescharacteristic
221C2×(C2×D3)⋊C4C22×C311yescharacteristic
222C2×(C2×D3)⋊C4C22×C311yescharacteristic
223C2×(C2×D3)⋊C4C22×C311yescharacteristic
224C2×(C2×D3)⋊C4C22×C311yescharacteristic
225C2×(C2×D3)⋊C4C22×C311yescharacteristic
226C2×(C2×D3)⋊C4C22×C311yescharacteristic
227C2×Dic3⋊C4C22×C311yescharacteristic, complemented
228C2×Dic3⋊C4C22×C311yescharacteristic, complemented
229C2×C4×Dic3C22×C311yescharacteristic, complemented
230C2×C4×Dic3C22×C311yescharacteristic, complemented
231D3×C22⋊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—21no—
249C23×C32—21no—
250C23×C32—21no—
251C23×C32—21no—
252C23×C32—21no—
253C23×C32—21no—
254C23×C32C22×C412yes—
255C23×C32C22×C412yes—
256C23×C32C2×D412yes—
257C23×C32#4112yes—
258C23×C32C2411yescharacteristic
259C22×C3×D3—21no—
260C22×C3×D3—21no—
261C22×C3×D3—21no—
262C22×C3×D3—21no—
263C22×C3×D3—28no—
264C22×C3×D3—21no—
265C22×C3×D3—21no—
266C22×C3×D3—21no—
267C22×C3×D3—21no—
268C22×C3×D3—21no—
269C22×C3×D3—21no—
270C22×C3×D3—28no—
271C22×C3×D3—44no—
272C22×C3×D3—44no—
273C22×C3×D3—44no—
274C22×C3×D3—44no—
275C22×C3×D3—44no—
276C22×C3×D3C22×C412yes—
277C22×C3×D3C22×C412yes—
278C22×C3×D3C2×D412yes—
279C22×C3×D3#4112yes—
280C32×D4—28no—
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—21no—
291C2×C32×C4—21no—
292C2×C32×C4—44no—
293C2×C32×C4—44no—
294C2×C32×C4C22×C412yes—
295C2×C32×C4C2×D412yes—
296C2×C32×C4C2×D412yes—
297C2×C32×C4C2×D412yes—
298C3×#67—28no—
299C3×#67—44no—
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—21no—
314C2×C3×Dic3—21no—
315C2×C3×Dic3—44no—
316C2×C3×Dic3C22×C412yes—
317C2×C3×Dic3C22×C412yes—
318C2×C3×Dic3C2×D412yes—
319C3×C4×D3—44no—
320C3×C4×D3—44no—
321C2×#120—31no—
322C2×C4×D4—31no—
323C2×C4×D4C3×D311yescharacteristic, complemented
324C22×C22⋊C4—31no—
325C22×C22⋊C4—31no—
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—21no—
337C24×C3—21no—
338C24×C3—31no—
339C24×C3—31no—
340C24×C3—34no—
341C24×C3—62no—
342C24×C3—62no—
343C24×C3—62no—
344C24×C3—62no—
345C24×C3—121no—
346C24×C3—121no—
347C24×C3C22×D311yescharacteristic
348C24×C3C22×D311yescharacteristic
349C24×C3C23×C311yescharacteristic
350C24×C3C23×C311yescharacteristic
351C23×D3—22no—
352C23×D3—22no—
353C23×D3—22no—
354C23×D3—22no—
355C23×D3—41no—
356C23×D3—41no—
357C23×D3C2×C3×C414yescomplemented
358C23×D3C23×C311yescharacteristic
359C23×D3C23×C311yescharacteristic
360C2×C3×D4—24no—
361C2×C3×D4—24no—
362C2×C3×D4—22no—
363C2×C3×D4—22no—
364C2×C3×D4—22no—
365C2×C3×D4—22no—
366C2×C3×D4—24no—
367C2×C3×D4—34no—
368C2×C3×D4—34no—
369C2×C3×D4—62no—
370C2×C3×D4—62no—
371C2×C3×D4—121no—
372C2×C3×D4—121no—
373C2×C3×D4C4×D314yescomplemented
374C2×C3×D4C2×C3×C414yescomplemented
375C22×C3×C4—24no—
376C22×C3×C4—24no—
377C22×C3×C4—22no—
378C22×C3×C4—22no—
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—21no—
386C22×C3×C4—21no—
387C22×C3×C4—21no—
388C22×C3×C4—21no—
389C22×C3×C4—21no—
390C22×C3×C4—31no—
391C22×C3×C4—31no—
392C22×C3×C4—31no—
393C22×C3×C4—31no—
394C22×C3×C4—31no—
395C22×C3×C4—31no—
396C22×C3×C4—42no—
397C22×C3×C4—42no—
398C22×C3×C4—41no—
399C22×C3×C4—41no—
400C22×C3×C4—41no—
401C22×C3×C4—41no—
402C22×C3×C4—42no—
403C22×C3×C4—42no—
404C22×C3×C4—62no—
405C22×C3×C4—62no—
406C22×C3×C4—62no—
407C22×C3×C4—62no—
408C22×C3×C4—62no—
409C22×C3×C4—62no—
410C22×C3×C4—121no—
411C22×C3×C4—121no—
412C22×C3×C4—121no—
413C22×C3×C4C22×D311yescharacteristic
414C22×C3×C4C22×D311yescharacteristic
415C22×C3×C4C22×D311yescharacteristic
416C22×C3×C4C22×D311yescharacteristic
417C22×C3×C4C22×D311yescharacteristic
418C22×C3×C4C23×C311yescharacteristic
419C22×C3×C4C23×C311yescharacteristic
420C22×C3×C4C23×C311yescharacteristic
421C22×C3×C4C23×C311yescharacteristic
422C22×C3×C4C23×C311yescharacteristic
423C2×#67—22no—
424C2×#67—22no—
425C2×#67—41no—
426C2×#67—41no—
427C2×#67C2×C3×C414yescomplemented
428C2×#67C2×C3×C414yescomplemented
429C22×Dic3—22no—
430C22×Dic3—22no—
431C22×Dic3—41no—
432C22×Dic3C23×C311yescharacteristic
433C22×Dic3C23×C311yescharacteristic
434C22×Dic3C23×C311yescharacteristic
435C22×Dic3C23×C311yescharacteristic
436C22×Dic3C23×C311yescharacteristic
437C22×Dic3C23×C311yescharacteristic
438C2×C4×D3—22no—
439C2×C4×D3—22no—
440C2×C4×D3—22no—
441C2×C4×D3—22no—
442C2×C4×D3—41no—
443C2×C4×D3—41no—
444C3×C4⋊C4—24no—
445C3×C4⋊C4—22no—
446C3×C4⋊C4—22no—
447C3×C4⋊C4—62no—
448C3×C4⋊C4—121no—
449C3×C22⋊C4—24no—
450C3×C22⋊C4—22no—
451C3×C22⋊C4—22no—
452C3×C22⋊C4—24no—
453C3×C22⋊C4—34no—
454C3×C22⋊C4—34no—
455C3×C22⋊C4—34no—
456C3×C22⋊C4—34no—
457C3×C22⋊C4—62no—
458C3×C22⋊C4—62no—
459C3×C22⋊C4—62no—
460C3×C22⋊C4—62no—
461C3×C22⋊C4—62no—
462C3×C22⋊C4—62no—
463C3×C22⋊C4—62no—
464C3×C22⋊C4—121no—
465C3×C22⋊C4#6714yescomplemented
466C3×C22⋊C4C3×D414yescomplemented
467C3×C42—24no—
468C3×C42—22no—
469C3×C42—22no—
470C3×C42—62no—
471C3×C42—121no—
472#217—22no—
473#217—22no—
474#217—41no—
475#217C2×C3×C414yescomplemented
476(C2×D3)⋊C4—22no—
477(C2×D3)⋊C4—22no—
478(C2×D3)⋊C4—22no—
479(C2×D3)⋊C4—22no—
480(C2×D3)⋊C4—22no—
481(C2×D3)⋊C4C2×C3×C414yescomplemented
482(C2×D3)⋊C4C2×C3×C414yescomplemented
483(C2×D3)⋊C4C3×D414yescomplemented
484Dic3⋊C4—22no—
485Dic3⋊C4—41no—
486C4×Dic3—22no—
487C4×Dic3—41no—
488C22×C32—22no—
489C22×C32—22no—
490C22×C32—22no—
491C22×C32—22no—
492C22×C32—22no—
493C22×C32—22no—
494C22×C32—22no—
495C22×C32—22no—
496C22×C32—22no—
497C22×C32—41no—
498C22×C32—41no—
499C22×C32—41no—
500C22×C32—41no—
501C22×C32C4×D414yescomplemented
502C22×C32C23×C411yescharacteristic
503C22×C32C22×D411yescharacteristic
504C22×C32C22×D411yescharacteristic
505C22×C32C2×#4111yescharacteristic
506C22×C32C2×#4111yescharacteristic
507C22×C32H(5,𝔽2)11yescharacteristic
508C22×C32H(5,𝔽2)11yescharacteristic
509C2×C3×D3—22no—
510C2×C3×D3—22no—
511C2×C3×D3—22no—
512C2×C3×D3—22no—
513C2×C3×D3—22no—
514C2×C3×D3—22no—
515C2×C3×D3—22no—
516C2×C3×D3—22no—
517C2×C3×D3—22no—
518C2×C3×D3—416no—
519C2×C3×D3—41no—
520C2×C3×D3—41no—
521C2×C3×D3—41no—
522C2×C3×D3—41no—
523C2×C3×D3C4×D414yescomplemented
524C32×C4—22no—
525C32×C4—22no—
526C32×C4—22no—
527C32×C4—22no—
528C32×C4—41no—
529C3×Dic3—22no—
530C3×Dic3—22no—
531C3×Dic3—22no—
532C3×Dic3—41no—
533C3×Dic3—41no—
534C3×Dic3—41no—
535C25—31no—
536C22×D4—31no—
537C22×D4—31no—
538C22×D4C2×C3×D311yescharacteristic
539C23×C4—31no—
540C23×C4—31no—
541C23×C4—31no—
542C23×C4C2×C3×D311yescharacteristic
543C23×C4C2×C3×D311yescharacteristic, complemented
544#120—38no—
545C4×D4—24no—
546C4×D4—64no—
547C2×C4⋊C4—31no—
548C2×C4⋊C4—31no—
549C2×C4⋊C4C2×C3×D311yescharacteristic, complemented
550C2×C22⋊C4—31no—
551C2×C22⋊C4—31no—
552C2×C22⋊C4—31no—
553C2×C22⋊C4—31no—
554C2×C22⋊C4—31no—
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—64no—
563C2×C22⋊C4—64no—
564C2×C22⋊C4C2×C3×D311yescharacteristic
565C2×C22⋊C4C2×C3×D311yescharacteristic, complemented
566C2×C42—31no—
567C2×C42—31no—
568C2×C42C2×C3×D311yescharacteristic, complemented
569#95—31no—
570#95—31no—
571#95—31no—
572#95—31no—
573#95—31no—
574#95—31no—
575C23×C3—21no—
576C23×C3—21no—
577C23×C3—21no—
578C23×C3—21no—
579C23×C3—21no—
580C23×C3—21no—
581C23×C3—21no—
582C23×C3—21no—
583C23×C3—22no—
584C23×C3—22no—
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—22no—
599C23×C3—22no—
600C23×C3—22no—
601C23×C3—22no—
602C23×C3—32no—
603C23×C3—32no—
604C23×C3—32no—
605C23×C3—32no—
606C23×C3—41no—
607C23×C3—41no—
608C23×C3—41no—
609C23×C3—41no—
610C23×C3—41no—
611C23×C3—41no—
612C23×C3—41no—
613C23×C3—41no—
614C23×C3—68no—
615C23×C3—61no—
616C23×C3—61no—
617C23×C3—61no—
618C23×C3—61no—
619C23×C3—68no—
620C23×C3—61no—
621C23×C3—61no—
622C23×C3—61no—
623C23×C3—61no—
624C23×C3—61no—
625C23×C3—61no—
626C23×C3—124no—
627C23×C3—124no—
628C23×C3—124no—
629C23×C3—124no—
630C23×C3—124no—
631C23×C3C2×C4×D312yes—
632C23×C3C2×C4×D312yes—
633C23×C3#23512yes—
634C23×C3C2×#6712yes—
635C23×C3C22×C3×C412yes—
636C23×C3C22×C3×C412yes—
637C23×C3C2×C3×D412yes—
638C23×C3C3×#4112yes—
639C23×C3C23×D311yescharacteristic
640C23×C3C24×C311yescharacteristic
641C22×D3—21no—
642C22×D3—21no—
643C22×D3—21no—
644C22×D3—21no—
645C22×D3—28no—
646C22×D3—21no—
647C22×D3—21no—
648C22×D3—21no—
649C22×D3—21no—
650C22×D3—21no—
651C22×D3—21no—
652C22×D3—28no—
653C22×D3—44no—
654C22×D3—44no—
655C22×D3—44no—
656C22×D3—44no—
657C22×D3—44no—
658C22×D3C22×C3×C412yes—
659C22×D3C22×C3×C412yes—
660C22×D3C2×C3×D412yes—
661C22×D3C3×#4112yes—
662C3×D4—216no—
663C3×D4—28no—
664C3×D4—28no—
665C3×D4—68no—
666C3×D4—124no—
667C2×C3×C4—22no—
668C2×C3×C4—22no—
669C2×C3×C4—22no—
670C2×C3×C4—22no—
671C2×C3×C4—21no—
672C2×C3×C4—21no—
673C2×C3×C4—21no—
674C2×C3×C4—21no—
675C2×C3×C4—21no—
676C2×C3×C4—21no—
677C2×C3×C4—21no—
678C2×C3×C4—21no—
679C2×C3×C4—21no—
680C2×C3×C4—21no—
681C2×C3×C4—21no—
682C2×C3×C4—21no—
683C2×C3×C4—21no—
684C2×C3×C4—21no—
685C2×C3×C4—21no—
686C2×C3×C4—21no—
687C2×C3×C4—22no—
688C2×C3×C4—21no—
689C2×C3×C4—21no—
690C2×C3×C4—21no—
691C2×C3×C4—21no—
692C2×C3×C4—21no—
693C2×C3×C4—21no—
694C2×C3×C4—22no—
695C2×C3×C4—22no—
696C2×C3×C4—22no—
697C2×C3×C4—22no—
698C2×C3×C4—32no—
699C2×C3×C4—32no—
700C2×C3×C4—32no—
701C2×C3×C4—41no—
702C2×C3×C4—41no—
703C2×C3×C4—41no—
704C2×C3×C4—41no—
705C2×C3×C4—41no—
706C2×C3×C4—41no—
707C2×C3×C4—44no—
708C2×C3×C4—44no—
709C2×C3×C4—44no—
710C2×C3×C4—44no—
711C2×C3×C4—48no—
712C2×C3×C4—48no—
713C2×C3×C4—61no—
714C2×C3×C4—61no—
715C2×C3×C4—61no—
716C2×C3×C4—61no—
717C2×C3×C4—61no—
718C2×C3×C4—61no—
719C2×C3×C4—61no—
720C2×C3×C4—61no—
721C2×C3×C4—61no—
722C2×C3×C4—61no—
723C2×C3×C4—61no—
724C2×C3×C4—61no—
725C2×C3×C4—61no—
726C2×C3×C4—61no—
727C2×C3×C4—61no—
728C2×C3×C4—124no—
729C2×C3×C4—124no—
730C2×C3×C4—124no—
731C2×C3×C4C2×C4×D312yes—
732C2×C3×C4D3×D412yes—
733C2×C3×C4C2×#6712yes—
734C2×C3×C4C2×#6712yes—
735C2×C3×C4C22×C3×C412yes—
736C2×C3×C4C2×C3×D412yes—
737C2×C3×C4C2×C3×D412yes—
738C2×C3×C4C2×C3×D412yes—
739#67—28no—
740#67—44no—
741C2×Dic3—21no—
742C2×Dic3—21no—
743C2×Dic3—21no—
744C2×Dic3—21no—
745C2×Dic3—21no—
746C2×Dic3—21no—
747C2×Dic3—21no—
748C2×Dic3—21no—
749C2×Dic3—21no—
750C2×Dic3—21no—
751C2×Dic3—21no—
752C2×Dic3—21no—
753C2×Dic3—21no—
754C2×Dic3—21no—
755C2×Dic3—21no—
756C2×Dic3—44no—
757C2×Dic3C22×C3×C412yes—
758C2×Dic3C22×C3×C412yes—
759C2×Dic3C2×C3×D412yes—
760C4×D3—44no—
761C4×D3—44no—
762C2×C32—24no—
763C2×C32—42no—
764C2×C32C2×C4×D411yescharacteristic
765C2×C32C2×C4×D411yescharacteristic
766C2×C32#51811yescharacteristic
767C2×C32D4211yescharacteristic
768C2×C32#54611yescharacteristic
769C2×C32#54611yescharacteristic
770C2×C32#55111yescharacteristic
771C3×D3—24no—
772C3×D3—42no—
773C24—31no—
774C24—31no—
775C24—34no—
776C24—62no—
777C24—62no—
778C24—62no—
779C24—62no—
780C24—121no—
781C24—121no—
782C24C22×C3×D311yescharacteristic
783C24C22×C3×D311yescharacteristic
784C2×D4—22no—
785C2×D4—22no—
786C2×D4—34no—
787C2×D4—34no—
788C2×D4—62no—
789C2×D4—62no—
790C2×D4—121no—
791C2×D4—121no—
792C2×D4C3×C4×D314yescomplemented
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—31no—
798C22×C4—31no—
799C22×C4—31no—
800C22×C4—31no—
801C22×C4—31no—
802C22×C4—31no—
803C22×C4—41no—
804C22×C4—41no—
805C22×C4—62no—
806C22×C4—62no—
807C22×C4—62no—
808C22×C4—62no—
809C22×C4—62no—
810C22×C4—62no—
811C22×C4—121no—
812C22×C4—121no—
813C22×C4—121no—
814C22×C4C22×C3×D311yescharacteristic
815C22×C4C22×C3×D311yescharacteristic
816C22×C4C22×C3×D311yescharacteristic
817C22×C4C22×C3×D311yescharacteristic
818C22×C4C22×C3×D311yescharacteristic
819C4⋊C4—22no—
820C4⋊C4—62no—
821C4⋊C4—121no—
822C22⋊C4—22no—
823C22⋊C4—34no—
824C22⋊C4—34no—
825C22⋊C4—34no—
826C22⋊C4—34no—
827C22⋊C4—62no—
828C22⋊C4—62no—
829C22⋊C4—62no—
830C22⋊C4—62no—
831C22⋊C4—62no—
832C22⋊C4—62no—
833C22⋊C4—62no—
834C22⋊C4—121no—
835C22⋊C4C3×#6714yescomplemented
836C42—22no—
837C42—62no—
838C42—121no—
839C22×C3—22no—
840C22×C3—22no—
841C22×C3—22no—
842C22×C3—22no—
843C22×C3—22no—
844C22×C3—22no—
845C22×C3—22no—
846C22×C3—22no—
847C22×C3—22no—
848C22×C3—22no—
849C22×C3—22no—
850C22×C3—22no—
851C22×C3—24no—
852C22×C3—22no—
853C22×C3—22no—
854C22×C3—22no—
855C22×C3—22no—
856C22×C3—22no—
857C22×C3—22no—
858C22×C3—24no—
859C22×C3—21no—
860C22×C3—21no—
861C22×C3—21no—
862C22×C3—21no—
863C22×C3—21no—
864C22×C3—21no—
865C22×C3—21no—
866C22×C3—34no—
867C22×C3—42no—
868C22×C3—42no—
869C22×C3—42no—
870C22×C3—42no—
871C22×C3—42no—
872C22×C3—42no—
873C22×C3—42no—
874C22×C3—42no—
875C22×C3—42no—
876C22×C3—42no—
877C22×C3—42no—
878C22×C3—42no—
879C22×C3—41no—
880C22×C3—41no—
881C22×C3—41no—
882C22×C3—41no—
883C22×C3—41no—
884C22×C3—41no—
885C22×C3—41no—
886C22×C3—41no—
887C22×C3—62no—
888C22×C3—62no—
889C22×C3—62no—
890C22×C3—62no—
891C22×C3—62no—
892C22×C3—62no—
893C22×C3—62no—
894C22×C3—62no—
895C22×C3—62no—
896C22×C3—1216no—
897C22×C3—121no—
898C22×C3—121no—
899C22×C3—121no—
900C22×C3—121no—
901C22×C3C4×#6714yescomplemented
902C22×C3C3×C4×D414yescomplemented
903C22×C3C22×C4×D311yescharacteristic
904C22×C3C2×#23511yescharacteristic
905C22×C3C2×D3×D411yescharacteristic
906C22×C3#100411yescharacteristic
907C22×C3D3×#4111yescharacteristic
908C22×C3#100911yescharacteristic
909C22×C3C22×#6711yescharacteristic
910C22×C3C23×C3×C411yescharacteristic
911C22×C3C22×C3×D411yescharacteristic
912C22×C3C22×C3×D411yescharacteristic
913C22×C3C2×C3×#4111yescharacteristic
914C22×C3C2×C3×#4111yescharacteristic
915C22×C3C3×H(5,𝔽2)11yescharacteristic
916C22×C3C3×H(5,𝔽2)11yescharacteristic
917C2×D3—22no—
918C2×D3—22no—
919C2×D3—22no—
920C2×D3—22no—
921C2×D3—22no—
922C2×D3—22no—
923C2×D3—22no—
924C2×D3—22no—
925C2×D3—22no—
926C2×D3—416no—
927C2×D3—41no—
928C2×D3—41no—
929C2×D3—41no—
930C2×D3—41no—
931C2×D3C3×C4×D414yescomplemented
932C3×C4—24no—
933C3×C4—24no—
934C3×C4—22no—
935C3×C4—22no—
936C3×C4—22no—
937C3×C4—22no—
938C3×C4—22no—
939C3×C4—22no—
940C3×C4—22no—
941C3×C4—22no—
942C3×C4—42no—
943C3×C4—42no—
944C3×C4—42no—
945C3×C4—41no—
946C3×C4—41no—
947C3×C4—62no—
948C3×C4—62no—
949C3×C4—62no—
950C3×C4—121no—
951C3×C4—121no—
952C3×C4—121no—
953Dic3—22no—
954Dic3—22no—
955Dic3—22no—
956Dic3—41no—
957Dic3—41no—
958Dic3—41no—
959C32#235811yescharacteristic, complemented, Sylow
960C23—21no—
961C23—21no—
962C23—21no—
963C23—21no—
964C23—21no—
965C23—21no—
966C23—21no—
967C23—21no—
968C23—21no—
969C23—21no—
970C23—32no—
971C23—32no—
972C23—32no—
973C23—32no—
974C23—68no—
975C23—61no—
976C23—61no—
977C23—61no—
978C23—61no—
979C23—68no—
980C23—61no—
981C23—61no—
982C23—61no—
983C23—61no—
984C23—61no—
985C23—61no—
986C23—124no—
987C23—124no—
988C23—124no—
989C23—124no—
990C23—124no—
991C23C2×C3×C4×D312yes—
992C23C2×C3×C4×D312yes—
993C23C3×#23512yes—
994C23C2×C3×#6712yes—
995C23C23×C3×D311yescharacteristic
996D4—28no—
997D4—68no—
998D4—124no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—32no—
1011C2×C4—32no—
1012C2×C4—32no—
1013C2×C4—44no—
1014C2×C4—44no—
1015C2×C4—61no—
1016C2×C4—61no—
1017C2×C4—61no—
1018C2×C4—61no—
1019C2×C4—61no—
1020C2×C4—61no—
1021C2×C4—61no—
1022C2×C4—61no—
1023C2×C4—61no—
1024C2×C4—61no—
1025C2×C4—61no—
1026C2×C4—61no—
1027C2×C4—61no—
1028C2×C4—61no—
1029C2×C4—61no—
1030C2×C4—124no—
1031C2×C4—124no—
1032C2×C4—124no—
1033C2×C4C2×C3×C4×D312yes—
1034C2×C4C3×D3×D412yes—
1035C2×C4C2×C3×#6712yes—
1036C2×C4C2×C3×#6712yes—
1037C2×C3—24no—
1038C2×C3—24no—
1039C2×C3—21no—
1040C2×C3—21no—
1041C2×C3—21no—
1042C2×C3—21no—
1043C2×C3—21no—
1044C2×C3—21no—
1045C2×C3—21no—
1046C2×C3—44no—
1047C2×C3—44no—
1048C2×C3—42no—
1049C2×C3—42no—
1050C2×C3—64no—
1051C2×C3—122no—
1052C2×C3C4×D3×D411yescharacteristic
1053C2×C3#554511yescharacteristic
1054C2×C3#555011yescharacteristic
1055C2×C3#555611yescharacteristic
1056C2×C3C2×C4×#6711yescharacteristic
1057C2×C3D4×#6711yescharacteristic
1058C2×C3#582911yescharacteristic
1059C2×C3C2×C3×C4×D411yescharacteristic
1060C2×C3C2×C3×C4×D411yescharacteristic
1061C2×C3C3×#51811yescharacteristic
1062C2×C3C3×D4211yescharacteristic
1063C2×C3C3×#54611yescharacteristic
1064C2×C3C3×#54611yescharacteristic
1065C2×C3C3×#55111yescharacteristic
1066D3—24no—
1067D3—42no—
1068C22—22no—
1069C22—22no—
1070C22—22no—
1071C22—22no—
1072C22—22no—
1073C22—22no—
1074C22—22no—
1075C22—22no—
1076C22—22no—
1077C22—34no—
1078C22—41no—
1079C22—41no—
1080C22—41no—
1081C22—41no—
1082C22—62no—
1083C22—62no—
1084C22—62no—
1085C22—62no—
1086C22—62no—
1087C22—62no—
1088C22—62no—
1089C22—62no—
1090C22—62no—
1091C22—1216no—
1092C22—121no—
1093C22—121no—
1094C22—121no—
1095C22—121no—
1096C22C3×C4×#6714yescomplemented
1097C22C22×C3×C4×D311yescharacteristic
1098C22C2×C3×#23511yescharacteristic
1099C22C2×C3×D3×D411yescharacteristic
1100C22C3×#100411yescharacteristic
1101C22C3×D3×#4111yescharacteristic
1102C22C3×#100911yescharacteristic
1103C22C22×C3×#6711yescharacteristic
1104C4—22no—
1105C4—22no—
1106C4—22no—
1107C4—22no—
1108C4—41no—
1109C4—62no—
1110C4—62no—
1111C4—62no—
1112C4—121no—
1113C4—121no—
1114C4—121no—
1115C3—21no—
1116C3#8239811yescharacteristic, direct product factor
1117C3C3×#235811yescharacteristic, complemented
1118C2—24no—
1119C2—42no—
1120C2—64no—
1121C2—122no—
1122C2C3×C4×D3×D411yescharacteristic
1123C2C3×#554511yescharacteristic
1124C2C3×#555011yescharacteristic
1125C2C3×#555611yescharacteristic
1126C2C2×C3×C4×#6711yescharacteristic
1127C2C3×D4×#6711yescharacteristic
1128C2C3×#582911yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC2×C32×C4×D4C2
socleC23×C32C24
prime radicalC2×C3×#937C2
cosocleC23×C3C24×C3
hypercenterC2×C3×C4×D4D3
hypocenterC3C3×#2358
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×C32×C4×D4C2semidirect
3. C2×C3×C4×#67C2semidirect
4. C22×C3×(C2×D3)⋊C4C2semidirect
5. C2×C3×D3×C22⋊C4C2semidirect
6. C3×#5220C2semidirect
7. C3×#5213C2semidirect
8. C3×#5210C2semidirect
9. C3×#4990C2semidirect
10. C3×#4989C2semidirect
11. C3×#4957C2semidirect
12. C3×#4956C2semidirect
13. C3×Dic3×C22⋊C4C2semidirect
14. C3×#4940C2semidirect
15. C3×C4×(C2×D3)⋊C4C2semidirect
17. #82398C3direct (N × H)
21. C23×C32×C4C22semidirect
28. C2×C32×C4⋊C4C22semidirect
30. C2×C32×C22⋊C4C22semidirect
31. C2×C32×C42C22semidirect
34. C2×C3×#217C22semidirect
35. C2×C3×#217C22semidirect
36. C3×#937C4semidirect
47. C2×C3×Dic3⋊C4C22semidirect
48. C2×C3×Dic3⋊C4C22semidirect
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
61. C2×C3×C4×D4D3semidirect
62. C2×C3×C4×D4C2×C3semidirect
66. C2×C4×#67C2×C3semidirect
67. C22×(C2×D3)⋊C4C2×C3semidirect
68. C2×D3×C22⋊C4C2×C3semidirect
79. #5220C2×C3semidirect
80. #5213C2×C3semidirect
81. #5210C2×C3semidirect
82. #4990C2×C3semidirect
83. #4989C2×C3semidirect
84. #4957C2×C3semidirect
85. #4956C2×C3semidirect
86. Dic3×C22⋊C4C2×C3semidirect
87. #4940C2×C3semidirect
88. C4×(C2×D3)⋊C4C2×C3semidirect
97. C23×C3×D3C2×C4semidirect
102. C2×C32×D4C2×C4semidirect
118. C2×C3×#67C2×C4semidirect
119. C2×C3×#67C2×C4semidirect
137. C32×C22⋊C4D4semidirect
142. C3×#217C2×C4semidirect
148. C3×(C2×D3)⋊C4C2×C4semidirect
149. C3×(C2×D3)⋊C4C2×C4semidirect
150. C3×(C2×D3)⋊C4D4semidirect
169. C23×C3×C4C2×D3semidirect
171. C23×C3×C4C22×C3semidirect
185. C2×C3×C4⋊C4C2×D3semidirect
186. C2×C3×C4⋊C4C22×C3semidirect
204. C2×C3×C22⋊C4C2×D3semidirect
206. C2×C3×C22⋊C4C22×C3semidirect
210. C2×C3×C42C2×D3semidirect
211. C2×C3×C42C22×C3semidirect
214. C2×#217C22×C3semidirect
215. C2×#217C22×C3semidirect
216. #937C3×C4semidirect
227. C2×Dic3⋊C4C22×C3semidirect
228. C2×Dic3⋊C4C22×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
323. C2×C4×D4C3×D3semidirect
357. C23×D3C2×C3×C4semidirect
373. C2×C3×D4C4×D3semidirect
374. C2×C3×D4C2×C3×C4semidirect
427. C2×#67C2×C3×C4semidirect
428. C2×#67C2×C3×C4semidirect
465. C3×C22⋊C4#67semidirect
466. C3×C22⋊C4C3×D4semidirect
475. #217C2×C3×C4semidirect
481. (C2×D3)⋊C4C2×C3×C4semidirect
482. (C2×D3)⋊C4C2×C3×C4semidirect
483. (C2×D3)⋊C4C3×D4semidirect
501. C22×C32C4×D4semidirect
523. C2×C3×D3C4×D4semidirect
543. C23×C4C2×C3×D3semidirect
549. C2×C4⋊C4C2×C3×D3semidirect
565. C2×C22⋊C4C2×C3×D3semidirect
568. C2×C42C2×C3×D3semidirect
792. C2×D4C3×C4×D3semidirect
835. C22⋊C4C3×#67semidirect
901. C22×C3C4×#67semidirect
902. C22×C3C3×C4×D4semidirect
931. C2×D3C3×C4×D4semidirect
959. C32#2358semidirect
1096. C22C3×C4×#67semidirect
1116. C3#82398direct (N × H)
1117. C3C3×#2358semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4×D42
C2×C3×#9372
C2×C3×C4×#672
C22×C3×(C2×D3)⋊C42
C2×C3×D3×C22⋊C42
C3×#52202
C3×#52132
C3×#52102
C3×#49902
C3×#49892
C3×#49572
C3×#49562
C3×Dic3×C22⋊C42
C3×#49402
C3×C4×(C2×D3)⋊C42
C3×#23583
#823983