Finite Group Databasebeta

← C3×#82896 #11810288

Subgroups — C3×#82896 #11810288

Order 1152.

1771 conjugacy classes of subgroups.

The subgroup lattice has 1099 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#123C211yesmaximal, characteristic, complemented
2C2×C3×#937C211yesmaximal, characteristic
3C2×C3×C4×#67C211yesmaximal, characteristic, complemented
4C2×C3×D3×C22⋊C4C211yesmaximal, characteristic, complemented
5C3×#5222C211yesmaximal, characteristic, complemented
6C3×#5213C211yesmaximal, characteristic, complemented
7C3×#4993C211yesmaximal, characteristic, complemented
8C3×#4990C211yesmaximal, characteristic, complemented
9C3×#4989C211yesmaximal, characteristic, complemented
10C3×#4987C211yesmaximal, characteristic, complemented
11C3×#4961C211yesmaximal, characteristic, complemented
12C3×#4956C211yesmaximal, characteristic, complemented
13C3×#4955C211yesmaximal, characteristic, complemented
14C3×#4952C211yesmaximal, characteristic, complemented
15C3×#4951C211yesmaximal, characteristic, complemented
16C3×#2418—31nomaximal
17#82896C311yesmaximal, characteristic, direct product factor
18C24×C3×D3C2211yescharacteristic
19C22×C32×D4C2211yescharacteristic
20C23×C32×C4C2211yescharacteristic, complemented
21C22×C3×#67C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C22×C3×C4×D3C2211yescharacteristic
24C22×C3×C4×D3C2211yescharacteristic
25C32×#123—24no—
26C2×C32×C4⋊C4C2211yescharacteristic, complemented
27C2×C32×C4⋊C4C2211yescharacteristic, complemented
28C2×C32×C22⋊C4C2211yescharacteristic
29C2×C32×C22⋊C4C2211yescharacteristic
30C2×C32×C22⋊C4C2211yescharacteristic, complemented
31C2×C3×#217C2211yescharacteristic
32C2×C3×#217C2211yescharacteristic
33C2×C3×#217C2211yescharacteristic
34C2×C3×#217C2211yescharacteristic, complemented
35C2×C3×#217C2211yescharacteristic, complemented
36C3×#937—24no—
37C3×C4×#67—24no—
38C2×C3×(C2×D3)⋊C4C2211yescharacteristic
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×C4⋊Dic3C2211yescharacteristic, complemented
47C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
48C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
49C2×C3×C4×Dic3C2211yescharacteristic, complemented
50C3×D3×C22⋊C4—24no—
51C3×C3⋊#95C2211yescharacteristic, complemented
52C3×C3⋊#95C2211yescharacteristic, complemented
53C3×C3⋊#95C2211yescharacteristic, complemented
54C3×C3⋊#95C2211yescharacteristic, complemented
55C3×C3⋊#95C2211yescharacteristic, complemented
56C3×C3⋊#95C2211yescharacteristic, complemented
57C2×C3×#123—21no—
58C2×C3×#123D311yescharacteristic, complemented
59C2×C3×#123C2×C311yescharacteristic, complemented
60C2×C3×#120—31no—
61C2×C3×C4×D4—31no—
62C22×C3×C22⋊C4—31no—
63C2×#937C2×C311yescharacteristic
64C2×C4×#67C2×C311yescharacteristic, complemented
65C2×D3×C22⋊C4C2×C311yescharacteristic, complemented
66C3×#399—31no—
67C3×#397—31no—
68C3×#394—31no—
69C3×#394—31no—
70C3×#388—31no—
71C3×#388—31no—
72C3×#386—31no—
73C3×#386—31no—
74C3×#385—31no—
75C3×#380—31no—
76C3×#379—31no—
77#5222C2×C311yescharacteristic, complemented
78#5213C2×C311yescharacteristic, complemented
79#4993C2×C311yescharacteristic, complemented
80#4990C2×C311yescharacteristic, complemented
81#4989C2×C311yescharacteristic, complemented
82#4987C2×C311yescharacteristic, complemented
83#4961C2×C311yescharacteristic, complemented
84#4956C2×C311yescharacteristic, complemented
85#4955C2×C311yescharacteristic, complemented
86#4952C2×C311yescharacteristic, complemented
87#4951C2×C311yescharacteristic, complemented
88C24×C32C2311yescharacteristic
89C24×C32C2311yescharacteristic
90C23×C3×D3—22no—
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×D3C2311yescharacteristic
98C23×C3×D3C2311yescharacteristic
99C2×C32×D4—22no—
100C2×C32×D4—22no—
101C2×C32×D4—41no—
102C22×C32×C4—22no—
103C22×C32×C4—22no—
104C22×C32×C4—41no—
105C22×C32×C4C2311yescharacteristic
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×#67D414yes—
116C22×C3×Dic3C2311yescharacteristic
117C22×C3×Dic3C2311yescharacteristic
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C22×C3×Dic3C2311yescharacteristic
122C2×C3×C4×D3—22no—
123C2×C3×C4×D3—22no—
124C2×C3×C4×D3—22no—
125C2×C3×C4×D3—22no—
126C2×C3×C4×D3—41no—
127C2×C3×C4×D3—41no—
128C32×C4⋊C4—22no—
129C32×C4⋊C4—22no—
130C32×C22⋊C4—22no—
131C32×C22⋊C4—22no—
132C32×C22⋊C4D414yescomplemented
133C3×#217—22no—
134C3×#217—22no—
135C3×#217—22no—
136C3×#217—41no—
137C3×#217—41no—
138C3×(C2×D3)⋊C4—22no—
139C3×(C2×D3)⋊C4—22no—
140C3×(C2×D3)⋊C4—22no—
141C3×(C2×D3)⋊C4—22no—
142C3×(C2×D3)⋊C4—22no—
143C3×(C2×D3)⋊C4—22no—
144C3×(C2×D3)⋊C4—22no—
145C3×(C2×D3)⋊C4—41no—
146C3×C4⋊Dic3—41no—
147C3×Dic3⋊C4—22no—
148C3×Dic3⋊C4—41no—
149C3×C4×Dic3—22no—
150#2418—31noSylow
151C25×C3—31no—
152C24×D3C22×C311yescharacteristic
153C22×C3×D4—21no—
154C22×C3×D4—31no—
155C22×C3×D4—31no—
156C22×C3×D4C2×D311yescharacteristic
157C22×C3×D4C22×C311yescharacteristic
158C23×C3×C4—21no—
159C23×C3×C4—31no—
160C23×C3×C4—31no—
161C23×C3×C4C2×D311yescharacteristic, complemented
162C23×C3×C4C22×C311yescharacteristic, complemented
163C22×#67C22×C311yescharacteristic
164C22×#67C22×C311yescharacteristic
165C22×C4×D3C22×C311yescharacteristic
166C22×C4×D3C22×C311yescharacteristic
167C3×#123—28no—
168C3×#123—24no—
169C3×#123—24no—
170C3×#120—64no—
171C3×C4×D4—64no—
172C2×C3×C4⋊C4—21no—
173C2×C3×C4⋊C4—21no—
174C2×C3×C4⋊C4—31no—
175C2×C3×C4⋊C4—31no—
176C2×C3×C4⋊C4—31no—
177C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
178C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
179C2×C3×C4⋊C4C22×C311yescharacteristic, complemented
180C2×C3×C4⋊C4C22×C311yescharacteristic, complemented
181C2×C3×C22⋊C4—21no—
182C2×C3×C22⋊C4—21no—
183C2×C3×C22⋊C4—21no—
184C2×C3×C22⋊C4—31no—
185C2×C3×C22⋊C4—31no—
186C2×C3×C22⋊C4—31no—
187C2×C3×C22⋊C4—31no—
188C2×C3×C22⋊C4—31no—
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—64no—
198C2×C3×C22⋊C4C2×D311yescharacteristic
199C2×C3×C22⋊C4C2×D311yescharacteristic
200C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
201C2×C3×C22⋊C4C22×C311yescharacteristic
202C2×C3×C22⋊C4C22×C311yescharacteristic
203C2×C3×C22⋊C4C22×C311yescharacteristic, complemented
204C2×C3×C42—31no—
205C2×#217C22×C311yescharacteristic
206C2×#217C22×C311yescharacteristic
207C2×#217C22×C311yescharacteristic
208C2×#217C22×C311yescharacteristic, complemented
209C2×#217C22×C311yescharacteristic, complemented
210#937—24no—
211C4×#67—24no—
212C2×(C2×D3)⋊C4C22×C311yescharacteristic
213C2×(C2×D3)⋊C4C22×C311yescharacteristic
214C2×(C2×D3)⋊C4C22×C311yescharacteristic
215C2×(C2×D3)⋊C4C22×C311yescharacteristic
216C2×(C2×D3)⋊C4C22×C311yescharacteristic
217C2×(C2×D3)⋊C4C22×C311yescharacteristic
218C2×(C2×D3)⋊C4C22×C311yescharacteristic
219C2×(C2×D3)⋊C4C22×C311yescharacteristic
220C2×C4⋊Dic3C22×C311yescharacteristic, complemented
221C2×Dic3⋊C4C22×C311yescharacteristic, complemented
222C2×Dic3⋊C4C22×C311yescharacteristic, complemented
223C2×C4×Dic3C22×C311yescharacteristic, complemented
224D3×C22⋊C4—24no—
225C3×#95—31no—
226C3×#95—31no—
227C3×#95—31no—
228C3×#95—31no—
229C3×#95—31no—
230C3×#95—31no—
231C3⋊#95C22×C311yescharacteristic, complemented
232C3⋊#95C22×C311yescharacteristic, complemented
233C3⋊#95C22×C311yescharacteristic, complemented
234C3⋊#95C22×C311yescharacteristic, complemented
235C3⋊#95C22×C311yescharacteristic, complemented
236C3⋊#95C22×C311yescharacteristic, complemented
237C23×C32—21no—
238C23×C32—21no—
239C23×C32—21no—
240C23×C32—21no—
241C23×C32—21no—
242C23×C32—21no—
243C23×C32—21no—
244C23×C32—21no—
245C23×C32—21no—
246C23×C32—21no—
247C23×C32—21no—
248C23×C32—21no—
249C23×C32C2×D412yes—
250C23×C32C2×D412yes—
251C23×C32C2411yescharacteristic
252C22×C3×D3—21no—
253C22×C3×D3—21no—
254C22×C3×D3—21no—
255C22×C3×D3—21no—
256C22×C3×D3—28no—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3—21no—
261C22×C3×D3—21no—
262C22×C3×D3—21no—
263C22×C3×D3—44no—
264C22×C3×D3—44no—
265C22×C3×D3—44no—
266C22×C3×D3—44no—
267C22×C3×D3—44no—
268C22×C3×D3—44no—
269C22×C3×D3C2×D412yes—
270C22×C3×D3#4112yes—
271C22×C3×D3#4112yes—
272C22×C3×D3#4112yes—
273C32×D4—44no—
274C2×C32×C4—21no—
275C2×C32×C4—21no—
276C2×C32×C4—21no—
277C2×C32×C4—21no—
278C2×C32×C4—21no—
279C2×C32×C4—21no—
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—44no—
288C2×C32×C4C2×D412yes—
289C2×C32×C4C2×D412yes—
290C3×#67—28no—
291C3×#67—44no—
292C2×C3×Dic3—21no—
293C2×C3×Dic3—21no—
294C2×C3×Dic3—21no—
295C2×C3×Dic3—21no—
296C2×C3×Dic3—21no—
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×Dic3C2×D412yes—
310C3×C4×D3—44no—
311C3×C4×D3—44no—
312C2×#123C3×D311yescharacteristic, complemented
313C2×#120—31no—
314C2×C4×D4—31no—
315C22×C22⋊C4—31no—
316#399—31no—
317#397—31no—
318#394—31no—
319#394—31no—
320#388—31no—
321#388—31no—
322#386—31no—
323#386—31no—
324#385—31no—
325#380—31no—
326#379—31no—
327C24×C3—21no—
328C24×C3—21no—
329C24×C3—31no—
330C24×C3—31no—
331C24×C3—62no—
332C24×C3—62no—
333C24×C3—62no—
334C24×C3—62no—
335C24×C3—62no—
336C24×C3—121no—
337C24×C3—121no—
338C24×C3C22×D311yescharacteristic
339C24×C3C22×D311yescharacteristic
340C24×C3C23×C311yescharacteristic
341C24×C3C23×C311yescharacteristic
342C23×D3—22no—
343C23×D3—22no—
344C23×D3—22no—
345C23×D3—22no—
346C23×D3—22no—
347C23×D3—41no—
348C23×D3—41no—
349C23×D3C23×C311yescharacteristic
350C23×D3C23×C311yescharacteristic
351C2×C3×D4—24no—
352C2×C3×D4—22no—
353C2×C3×D4—22no—
354C2×C3×D4—22no—
355C2×C3×D4—22no—
356C2×C3×D4—34no—
357C2×C3×D4—42no—
358C2×C3×D4—41no—
359C2×C3×D4—41no—
360C2×C3×D4—42no—
361C2×C3×D4—62no—
362C2×C3×D4—62no—
363C2×C3×D4—62no—
364C2×C3×D4—62no—
365C2×C3×D4—121no—
366C22×C3×C4—24no—
367C22×C3×C4—22no—
368C22×C3×C4—22no—
369C22×C3×C4—22no—
370C22×C3×C4—22no—
371C22×C3×C4—21no—
372C22×C3×C4—21no—
373C22×C3×C4—21no—
374C22×C3×C4—21no—
375C22×C3×C4—21no—
376C22×C3×C4—31no—
377C22×C3×C4—31no—
378C22×C3×C4—31no—
379C22×C3×C4—31no—
380C22×C3×C4—31no—
381C22×C3×C4—31no—
382C22×C3×C4—42no—
383C22×C3×C4—41no—
384C22×C3×C4—41no—
385C22×C3×C4—42no—
386C22×C3×C4—62no—
387C22×C3×C4—62no—
388C22×C3×C4—62no—
389C22×C3×C4—62no—
390C22×C3×C4—121no—
391C22×C3×C4—121no—
392C22×C3×C4C22×D311yescharacteristic
393C22×C3×C4C22×D311yescharacteristic
394C22×C3×C4C22×D311yescharacteristic
395C22×C3×C4C22×D311yescharacteristic
396C22×C3×C4C22×D311yescharacteristic
397C22×C3×C4C23×C311yescharacteristic
398C22×C3×C4C23×C311yescharacteristic
399C22×C3×C4C23×C311yescharacteristic
400C22×C3×C4C23×C311yescharacteristic
401C22×C3×C4C23×C311yescharacteristic
402C2×#67—22no—
403C2×#67—22no—
404C2×#67—22no—
405C2×#67—22no—
406C2×#67—41no—
407C2×#67C3×D414yes—
408C22×Dic3C23×C311yescharacteristic
409C22×Dic3C23×C311yescharacteristic
410C22×Dic3C23×C311yescharacteristic
411C22×Dic3C23×C311yescharacteristic
412C22×Dic3C23×C311yescharacteristic
413C22×Dic3C23×C311yescharacteristic
414C2×C4×D3—22no—
415C2×C4×D3—22no—
416C2×C4×D3—22no—
417C2×C4×D3—22no—
418C2×C4×D3—41no—
419C2×C4×D3—41no—
420C3×C4⋊C4—24no—
421C3×C4⋊C4—24no—
422C3×C4⋊C4—22no—
423C3×C4⋊C4—22no—
424C3×C4⋊C4—22no—
425C3×C4⋊C4—22no—
426C3×C4⋊C4—62no—
427C3×C4⋊C4—121no—
428C3×C4⋊C4—121no—
429C3×C22⋊C4—24no—
430C3×C22⋊C4—24no—
431C3×C22⋊C4—22no—
432C3×C22⋊C4—22no—
433C3×C22⋊C4—22no—
434C3×C22⋊C4—22no—
435C3×C22⋊C4—24no—
436C3×C22⋊C4—62no—
437C3×C22⋊C4—62no—
438C3×C22⋊C4—62no—
439C3×C22⋊C4—62no—
440C3×C22⋊C4—62no—
441C3×C22⋊C4—62no—
442C3×C22⋊C4—62no—
443C3×C22⋊C4—62no—
444C3×C22⋊C4—62no—
445C3×C22⋊C4—62no—
446C3×C22⋊C4—121no—
447C3×C22⋊C4—121no—
448C3×C22⋊C4—121no—
449C3×C22⋊C4#6714yescomplemented
450C3×C22⋊C4C3×D414yescomplemented
451C3×C42—62no—
452#217—22no—
453#217—22no—
454#217—22no—
455#217—41no—
456#217—41no—
457(C2×D3)⋊C4—22no—
458(C2×D3)⋊C4—22no—
459(C2×D3)⋊C4—22no—
460(C2×D3)⋊C4—22no—
461(C2×D3)⋊C4—22no—
462(C2×D3)⋊C4—22no—
463(C2×D3)⋊C4—22no—
464(C2×D3)⋊C4—41no—
465C4⋊Dic3—41no—
466Dic3⋊C4—22no—
467Dic3⋊C4—41no—
468C4×Dic3—22no—
469C22×C32—22no—
470C22×C32—22no—
471C22×C32—22no—
472C22×C32—22no—
473C22×C32—22no—
474C22×C32—22no—
475C22×C32—41no—
476C22×C32—41no—
477C22×C32—41no—
478C22×C32—41no—
479C22×C32—41no—
480C22×C32—41no—
481C22×C32—41no—
482C22×C32—41no—
483C22×C32C22×D411yescharacteristic
484C22×C32C22×D411yescharacteristic
485C22×C32C2×#4111yescharacteristic
486C22×C32C2×#4111yescharacteristic
487C22×C32C2×#4111yescharacteristic
488C22×C32H(5,𝔽2)11yescharacteristic
489C22×C32H(5,𝔽2)11yescharacteristic
490C2×C3×D3—22no—
491C2×C3×D3—22no—
492C2×C3×D3—22no—
493C2×C3×D3—22no—
494C2×C3×D3—22no—
495C2×C3×D3—22no—
496C2×C3×D3—22no—
497C2×C3×D3—22no—
498C2×C3×D3—22no—
499C2×C3×D3—416no—
500C2×C3×D3—41no—
501C2×C3×D3—41no—
502C2×C3×D3—41no—
503C2×C3×D3—41no—
504C2×C3×D3#12314yescomplemented
505C32×C4—22no—
506C32×C4—22no—
507C32×C4—41no—
508C32×C4—41no—
509C32×C4—41no—
510C3×Dic3—22no—
511C3×Dic3—41no—
512C3×Dic3—41no—
513C3×Dic3—41no—
514C3×Dic3—41no—
515C3×Dic3—41no—
516C25—31no—
517C22×D4—31no—
518C22×D4—31no—
519C22×D4C2×C3×D311yescharacteristic
520C23×C4—31no—
521C23×C4—31no—
522C23×C4C2×C3×D311yescharacteristic, complemented
523#123—24no—
524#120—64no—
525C4×D4—64no—
526C2×C4⋊C4—31no—
527C2×C4⋊C4—31no—
528C2×C4⋊C4—31no—
529C2×C4⋊C4C2×C3×D311yescharacteristic, complemented
530C2×C4⋊C4C2×C3×D311yescharacteristic, complemented
531C2×C22⋊C4—31no—
532C2×C22⋊C4—31no—
533C2×C22⋊C4—31no—
534C2×C22⋊C4—31no—
535C2×C22⋊C4—31no—
536C2×C22⋊C4—31no—
537C2×C22⋊C4—31no—
538C2×C22⋊C4—31no—
539C2×C22⋊C4—31no—
540C2×C22⋊C4—31no—
541C2×C22⋊C4—31no—
542C2×C22⋊C4—31no—
543C2×C22⋊C4—31no—
544C2×C22⋊C4—64no—
545C2×C22⋊C4C2×C3×D311yescharacteristic
546C2×C22⋊C4C2×C3×D311yescharacteristic
547C2×C22⋊C4C2×C3×D311yescharacteristic, complemented
548C2×C42—31no—
549#95—31no—
550#95—31no—
551#95—31no—
552#95—31no—
553#95—31no—
554#95—31no—
555C23×C3—22no—
556C23×C3—22no—
557C23×C3—21no—
558C23×C3—21no—
559C23×C3—21no—
560C23×C3—21no—
561C23×C3—21no—
562C23×C3—21no—
563C23×C3—21no—
564C23×C3—21no—
565C23×C3—21no—
566C23×C3—21no—
567C23×C3—21no—
568C23×C3—21no—
569C23×C3—21no—
570C23×C3—21no—
571C23×C3—21no—
572C23×C3—21no—
573C23×C3—21no—
574C23×C3—21no—
575C23×C3—21no—
576C23×C3—21no—
577C23×C3—21no—
578C23×C3—21no—
579C23×C3—21no—
580C23×C3—21no—
581C23×C3—21no—
582C23×C3—22no—
583C23×C3—22no—
584C23×C3—32no—
585C23×C3—32no—
586C23×C3—32no—
587C23×C3—32no—
588C23×C3—41no—
589C23×C3—41no—
590C23×C3—41no—
591C23×C3—41no—
592C23×C3—41no—
593C23×C3—41no—
594C23×C3—41no—
595C23×C3—41no—
596C23×C3—41no—
597C23×C3—41no—
598C23×C3—68no—
599C23×C3—61no—
600C23×C3—61no—
601C23×C3—61no—
602C23×C3—61no—
603C23×C3—61no—
604C23×C3—61no—
605C23×C3—61no—
606C23×C3—61no—
607C23×C3—61no—
608C23×C3—61no—
609C23×C3—124no—
610C23×C3—124no—
611C23×C3—124no—
612C23×C3—124no—
613C23×C3—124no—
614C23×C3—124no—
615C23×C3D3×D412yes—
616C23×C3C2×#6712yes—
617C23×C3C2×C3×D412yes—
618C23×C3C2×C3×D412yes—
619C23×C3C23×D311yescharacteristic
620C23×C3C24×C311yescharacteristic
621C22×D3—21no—
622C22×D3—21no—
623C22×D3—21no—
624C22×D3—21no—
625C22×D3—28no—
626C22×D3—21no—
627C22×D3—21no—
628C22×D3—21no—
629C22×D3—21no—
630C22×D3—21no—
631C22×D3—21no—
632C22×D3—44no—
633C22×D3—44no—
634C22×D3—44no—
635C22×D3—44no—
636C22×D3—44no—
637C22×D3—44no—
638C22×D3C2×C3×D412yes—
639C22×D3C3×#4112yes—
640C22×D3C3×#4112yes—
641C22×D3C3×#4112yes—
642C3×D4—44no—
643C3×D4—44no—
644C3×D4—48no—
645C3×D4—68no—
646C3×D4—124no—
647C2×C3×C4—21no—
648C2×C3×C4—21no—
649C2×C3×C4—21no—
650C2×C3×C4—21no—
651C2×C3×C4—21no—
652C2×C3×C4—21no—
653C2×C3×C4—21no—
654C2×C3×C4—21no—
655C2×C3×C4—22no—
656C2×C3×C4—22no—
657C2×C3×C4—22no—
658C2×C3×C4—21no—
659C2×C3×C4—21no—
660C2×C3×C4—21no—
661C2×C3×C4—21no—
662C2×C3×C4—21no—
663C2×C3×C4—21no—
664C2×C3×C4—21no—
665C2×C3×C4—21no—
666C2×C3×C4—21no—
667C2×C3×C4—21no—
668C2×C3×C4—21no—
669C2×C3×C4—21no—
670C2×C3×C4—21no—
671C2×C3×C4—21no—
672C2×C3×C4—21no—
673C2×C3×C4—21no—
674C2×C3×C4—21no—
675C2×C3×C4—21no—
676C2×C3×C4—22no—
677C2×C3×C4—22no—
678C2×C3×C4—32no—
679C2×C3×C4—41no—
680C2×C3×C4—41no—
681C2×C3×C4—41no—
682C2×C3×C4—41no—
683C2×C3×C4—41no—
684C2×C3×C4—41no—
685C2×C3×C4—41no—
686C2×C3×C4—41no—
687C2×C3×C4—41no—
688C2×C3×C4—41no—
689C2×C3×C4—44no—
690C2×C3×C4—44no—
691C2×C3×C4—48no—
692C2×C3×C4—61no—
693C2×C3×C4—61no—
694C2×C3×C4—61no—
695C2×C3×C4—61no—
696C2×C3×C4—61no—
697C2×C3×C4—61no—
698C2×C3×C4—61no—
699C2×C3×C4—61no—
700C2×C3×C4—61no—
701C2×C3×C4—61no—
702C2×C3×C4—61no—
703C2×C3×C4—61no—
704C2×C3×C4—61no—
705C2×C3×C4—61no—
706C2×C3×C4—61no—
707C2×C3×C4—61no—
708C2×C3×C4—61no—
709C2×C3×C4—124no—
710C2×C3×C4—124no—
711C2×C3×C4C2×#6712yes—
712C2×C3×C4C2×#6712yes—
713C2×C3×C4C2×C3×D412yes—
714C2×C3×C4C2×C3×D412yes—
715#67—28no—
716#67—44no—
717C2×Dic3—21no—
718C2×Dic3—21no—
719C2×Dic3—21no—
720C2×Dic3—21no—
721C2×Dic3—21no—
722C2×Dic3—21no—
723C2×Dic3—21no—
724C2×Dic3—21no—
725C2×Dic3—21no—
726C2×Dic3—21no—
727C2×Dic3—21no—
728C2×Dic3—21no—
729C2×Dic3—21no—
730C2×Dic3—21no—
731C2×Dic3—21no—
732C2×Dic3—21no—
733C2×Dic3—21no—
734C2×Dic3C2×C3×D412yes—
735C4×D3—44no—
736C4×D3—44no—
737C2×C32—42no—
738C2×C32—42no—
739C2×C32C2×#12311yescharacteristic
740C2×C32#52511yescharacteristic
741C2×C32#53811yescharacteristic
742C2×C32D4211yescharacteristic
743C2×C32#54611yescharacteristic
744C2×C32#54611yescharacteristic
745C2×C32#55111yescharacteristic
746C3×D3—24no—
747C3×D3—42no—
748C24—31no—
749C24—31no—
750C24—62no—
751C24—62no—
752C24—62no—
753C24—62no—
754C24—62no—
755C24—121no—
756C24—121no—
757C24C22×C3×D311yescharacteristic
758C24C22×C3×D311yescharacteristic
759C2×D4—22no—
760C2×D4—22no—
761C2×D4—34no—
762C2×D4—41no—
763C2×D4—62no—
764C2×D4—62no—
765C2×D4—62no—
766C2×D4—62no—
767C2×D4—121no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—31no—
771C22×C4—31no—
772C22×C4—31no—
773C22×C4—31no—
774C22×C4—31no—
775C22×C4—31no—
776C22×C4—41no—
777C22×C4—62no—
778C22×C4—62no—
779C22×C4—62no—
780C22×C4—62no—
781C22×C4—121no—
782C22×C4—121no—
783C22×C4C22×C3×D311yescharacteristic
784C22×C4C22×C3×D311yescharacteristic
785C22×C4C22×C3×D311yescharacteristic
786C22×C4C22×C3×D311yescharacteristic
787C22×C4C22×C3×D311yescharacteristic
788C4⋊C4—22no—
789C4⋊C4—22no—
790C4⋊C4—62no—
791C4⋊C4—121no—
792C4⋊C4—121no—
793C22⋊C4—22no—
794C22⋊C4—22no—
795C22⋊C4—62no—
796C22⋊C4—62no—
797C22⋊C4—62no—
798C22⋊C4—62no—
799C22⋊C4—62no—
800C22⋊C4—62no—
801C22⋊C4—62no—
802C22⋊C4—62no—
803C22⋊C4—62no—
804C22⋊C4—62no—
805C22⋊C4—121no—
806C22⋊C4—121no—
807C22⋊C4—121no—
808C22⋊C4C3×#6714yescomplemented
809C42—62no—
810C22×C3—24no—
811C22×C3—22no—
812C22×C3—22no—
813C22×C3—22no—
814C22×C3—22no—
815C22×C3—22no—
816C22×C3—22no—
817C22×C3—22no—
818C22×C3—22no—
819C22×C3—22no—
820C22×C3—22no—
821C22×C3—22no—
822C22×C3—22no—
823C22×C3—21no—
824C22×C3—21no—
825C22×C3—21no—
826C22×C3—21no—
827C22×C3—21no—
828C22×C3—21no—
829C22×C3—21no—
830C22×C3—34no—
831C22×C3—42no—
832C22×C3—42no—
833C22×C3—42no—
834C22×C3—42no—
835C22×C3—42no—
836C22×C3—42no—
837C22×C3—42no—
838C22×C3—42no—
839C22×C3—42no—
840C22×C3—41no—
841C22×C3—41no—
842C22×C3—41no—
843C22×C3—41no—
844C22×C3—41no—
845C22×C3—41no—
846C22×C3—41no—
847C22×C3—41no—
848C22×C3—41no—
849C22×C3—41no—
850C22×C3—41no—
851C22×C3—41no—
852C22×C3—41no—
853C22×C3—41no—
854C22×C3—41no—
855C22×C3—41no—
856C22×C3—62no—
857C22×C3—62no—
858C22×C3—62no—
859C22×C3—62no—
860C22×C3—62no—
861C22×C3—62no—
862C22×C3—62no—
863C22×C3—62no—
864C22×C3—62no—
865C22×C3—81no—
866C22×C3—81no—
867C22×C3—81no—
868C22×C3—81no—
869C22×C3—1216no—
870C22×C3—121no—
871C22×C3—121no—
872C22×C3—121no—
873C22×C3—121no—
874C22×C3C2×D3×D411yescharacteristic
875C22×C3#100411yescharacteristic
876C22×C3D3×#4111yescharacteristic
877C22×C3D3×#4111yescharacteristic
878C22×C3D3×#4111yescharacteristic
879C22×C3#100911yescharacteristic
880C22×C3C22×#6711yescharacteristic
881C22×C3C22×C3×D411yescharacteristic
882C22×C3C22×C3×D411yescharacteristic
883C22×C3C2×C3×#4111yescharacteristic
884C22×C3C2×C3×#4111yescharacteristic
885C22×C3C2×C3×#4111yescharacteristic
886C22×C3C3×H(5,𝔽2)11yescharacteristic
887C22×C3C3×H(5,𝔽2)11yescharacteristic
888C2×D3—22no—
889C2×D3—22no—
890C2×D3—22no—
891C2×D3—22no—
892C2×D3—22no—
893C2×D3—22no—
894C2×D3—22no—
895C2×D3—22no—
896C2×D3—22no—
897C2×D3—416no—
898C2×D3—41no—
899C2×D3—41no—
900C2×D3—41no—
901C2×D3—41no—
902C2×D3C3×#12314yescomplemented
903C3×C4—22no—
904C3×C4—22no—
905C3×C4—22no—
906C3×C4—22no—
907C3×C4—42no—
908C3×C4—42no—
909C3×C4—42no—
910C3×C4—42no—
911C3×C4—42no—
912C3×C4—41no—
913C3×C4—41no—
914C3×C4—41no—
915C3×C4—41no—
916C3×C4—41no—
917C3×C4—41no—
918C3×C4—62no—
919C3×C4—121no—
920C3×C4—121no—
921C3×C4—121no—
922C3×C4—121no—
923C3×C4—121no—
924Dic3—22no—
925Dic3—41no—
926Dic3—41no—
927Dic3—41no—
928Dic3—41no—
929Dic3—41no—
930C32#241811yescharacteristic, complemented, Sylow
931C23—21no—
932C23—21no—
933C23—21no—
934C23—21no—
935C23—21no—
936C23—21no—
937C23—21no—
938C23—21no—
939C23—21no—
940C23—21no—
941C23—21no—
942C23—21no—
943C23—32no—
944C23—32no—
945C23—32no—
946C23—32no—
947C23—68no—
948C23—61no—
949C23—61no—
950C23—61no—
951C23—61no—
952C23—61no—
953C23—61no—
954C23—61no—
955C23—61no—
956C23—61no—
957C23—61no—
958C23—124no—
959C23—124no—
960C23—124no—
961C23—124no—
962C23—124no—
963C23—124no—
964C23C3×D3×D412yes—
965C23C2×C3×#6712yes—
966C23C23×C3×D311yescharacteristic
967D4—44no—
968D4—68no—
969D4—124no—
970C2×C4—21no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—21no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—21no—
979C2×C4—21no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—32no—
984C2×C4—44no—
985C2×C4—61no—
986C2×C4—61no—
987C2×C4—61no—
988C2×C4—61no—
989C2×C4—61no—
990C2×C4—61no—
991C2×C4—61no—
992C2×C4—61no—
993C2×C4—61no—
994C2×C4—61no—
995C2×C4—61no—
996C2×C4—61no—
997C2×C4—61no—
998C2×C4—61no—
999C2×C4—61no—
1000C2×C4—61no—
1001C2×C4—61no—
1002C2×C4—124no—
1003C2×C4—124no—
1004C2×C4C2×C3×#6712yes—
1005C2×C4C2×C3×#6712yes—
1006C2×C3—21no—
1007C2×C3—21no—
1008C2×C3—21no—
1009C2×C3—21no—
1010C2×C3—21no—
1011C2×C3—21no—
1012C2×C3—21no—
1013C2×C3—44no—
1014C2×C3—42no—
1015C2×C3—42no—
1016C2×C3—42no—
1017C2×C3—42no—
1018C2×C3—64no—
1019C2×C3—82no—
1020C2×C3—122no—
1021C2×C3D3×#12311yescharacteristic
1022C2×C3#565411yescharacteristic
1023C2×C3#565711yescharacteristic
1024C2×C3#565911yescharacteristic
1025C2×C3D4×#6711yescharacteristic
1026C2×C3#582811yescharacteristic
1027C2×C3#582911yescharacteristic
1028C2×C3C2×C3×#12311yescharacteristic
1029C2×C3C3×#52511yescharacteristic
1030C2×C3C3×#53811yescharacteristic
1031C2×C3C3×D4211yescharacteristic
1032C2×C3C3×#54611yescharacteristic
1033C2×C3C3×#54611yescharacteristic
1034C2×C3C3×#55111yescharacteristic
1035D3—24no—
1036D3—42no—
1037C22—22no—
1038C22—22no—
1039C22—22no—
1040C22—22no—
1041C22—22no—
1042C22—22no—
1043C22—34no—
1044C22—41no—
1045C22—41no—
1046C22—41no—
1047C22—41no—
1048C22—41no—
1049C22—41no—
1050C22—41no—
1051C22—41no—
1052C22—62no—
1053C22—62no—
1054C22—62no—
1055C22—62no—
1056C22—62no—
1057C22—62no—
1058C22—62no—
1059C22—62no—
1060C22—62no—
1061C22—1216no—
1062C22—121no—
1063C22—121no—
1064C22—121no—
1065C22—121no—
1066C22C2×C3×D3×D411yescharacteristic
1067C22C3×#100411yescharacteristic
1068C22C3×D3×#4111yescharacteristic
1069C22C3×D3×#4111yescharacteristic
1070C22C3×D3×#4111yescharacteristic
1071C22C3×#100911yescharacteristic
1072C22C22×C3×#6711yescharacteristic
1073C4—22no—
1074C4—22no—
1075C4—41no—
1076C4—41no—
1077C4—41no—
1078C4—62no—
1079C4—121no—
1080C4—121no—
1081C4—121no—
1082C4—121no—
1083C4—121no—
1084C3—21no—
1085C3#8289611yescharacteristic, direct product factor
1086C3C3×#241811yescharacteristic, complemented
1087C2—42no—
1088C2—42no—
1089C2—64no—
1090C2—122no—
1091C2C3×D3×#12311yescharacteristic
1092C2C3×#565411yescharacteristic
1093C2C3×#565711yescharacteristic
1094C2C3×#565911yescharacteristic
1095C2C3×D4×#6711yescharacteristic
1096C2C3×#582811yescharacteristic
1097C2C3×#582911yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC2×C32×#123C2
socleC23×C32C24
prime radicalC2×C3×#937C2
hypercenterC2×C3×#123D3
hypocenterC3C3×#2418
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×#123

Complements

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

NH ≅ G/Ntype
1. C2×C32×#123C2semidirect
3. C2×C3×C4×#67C2semidirect
4. C2×C3×D3×C22⋊C4C2semidirect
5. C3×#5222C2semidirect
6. C3×#5213C2semidirect
7. C3×#4993C2semidirect
8. C3×#4990C2semidirect
9. C3×#4989C2semidirect
10. C3×#4987C2semidirect
11. C3×#4961C2semidirect
12. C3×#4956C2semidirect
13. C3×#4955C2semidirect
14. C3×#4952C2semidirect
15. C3×#4951C2semidirect
17. #82896C3direct (N × H)
20. C23×C32×C4C22semidirect
26. C2×C32×C4⋊C4C22semidirect
27. C2×C32×C4⋊C4C22semidirect
30. C2×C32×C22⋊C4C22semidirect
34. C2×C3×#217C22semidirect
35. C2×C3×#217C22semidirect
46. C2×C3×C4⋊Dic3C22semidirect
47. C2×C3×Dic3⋊C4C22semidirect
48. C2×C3×Dic3⋊C4C22semidirect
49. C2×C3×C4×Dic3C22semidirect
51. C3×C3⋊#95C22semidirect
52. C3×C3⋊#95C22semidirect
53. C3×C3⋊#95C22semidirect
54. C3×C3⋊#95C22semidirect
55. C3×C3⋊#95C22semidirect
56. C3×C3⋊#95C22semidirect
58. C2×C3×#123D3semidirect
59. C2×C3×#123C2×C3semidirect
64. C2×C4×#67C2×C3semidirect
65. C2×D3×C22⋊C4C2×C3semidirect
77. #5222C2×C3semidirect
78. #5213C2×C3semidirect
79. #4993C2×C3semidirect
80. #4990C2×C3semidirect
81. #4989C2×C3semidirect
82. #4987C2×C3semidirect
83. #4961C2×C3semidirect
84. #4956C2×C3semidirect
85. #4955C2×C3semidirect
86. #4952C2×C3semidirect
87. #4951C2×C3semidirect
132. C32×C22⋊C4D4semidirect
161. C23×C3×C4C2×D3semidirect
162. C23×C3×C4C22×C3semidirect
177. C2×C3×C4⋊C4C2×D3semidirect
178. C2×C3×C4⋊C4C2×D3semidirect
179. C2×C3×C4⋊C4C22×C3semidirect
180. C2×C3×C4⋊C4C22×C3semidirect
200. C2×C3×C22⋊C4C2×D3semidirect
203. C2×C3×C22⋊C4C22×C3semidirect
208. C2×#217C22×C3semidirect
209. C2×#217C22×C3semidirect
220. C2×C4⋊Dic3C22×C3semidirect
221. C2×Dic3⋊C4C22×C3semidirect
222. C2×Dic3⋊C4C22×C3semidirect
223. C2×C4×Dic3C22×C3semidirect
231. C3⋊#95C22×C3semidirect
232. C3⋊#95C22×C3semidirect
233. C3⋊#95C22×C3semidirect
234. C3⋊#95C22×C3semidirect
235. C3⋊#95C22×C3semidirect
236. C3⋊#95C22×C3semidirect
312. C2×#123C3×D3semidirect
449. C3×C22⋊C4#67semidirect
450. C3×C22⋊C4C3×D4semidirect
504. C2×C3×D3#123semidirect
522. C23×C4C2×C3×D3semidirect
529. C2×C4⋊C4C2×C3×D3semidirect
530. C2×C4⋊C4C2×C3×D3semidirect
547. C2×C22⋊C4C2×C3×D3semidirect
808. C22⋊C4C3×#67semidirect
902. C2×D3C3×#123semidirect
930. C32#2418semidirect
1085. C3#82896direct (N × H)
1086. C3C3×#2418semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1232
C2×C3×#9372
C2×C3×C4×#672
C2×C3×D3×C22⋊C42
C3×#52222
C3×#52132
C3×#49932
C3×#49902
C3×#49892
C3×#49872
C3×#49612
C3×#49562
C3×#49552
C3×#49522
C3×#49512
C3×#24183
#828963