Finite Group Databasebeta

← C3×#78101 #11810306

Subgroups — C3×#78101 #11810306

Order 1152.

1693 conjugacy classes of subgroups.

The subgroup lattice has 1080 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#894C211yesmaximal, characteristic, complemented
2C2×C3×#893C211yesmaximal, characteristic, complemented
3C2×C3×#882C211yesmaximal, characteristic
4C2×C3×D3×C22⋊C4C211yesmaximal, characteristic, complemented
5C32×#399C211yesmaximal, characteristic, complemented
6C3×#4992C211yesmaximal, characteristic, complemented
7C3×#4991C211yesmaximal, characteristic, complemented
8C3×#4989C211yesmaximal, characteristic, complemented
9C3×#4987C211yesmaximal, characteristic, complemented
10C3×#4961C211yesmaximal, characteristic, complemented
11C3×#4956C211yesmaximal, characteristic, complemented
12C3×#4955C211yesmaximal, characteristic, complemented
13C3×#4944C211yesmaximal, characteristic, complemented
14C3×#4670C211yesmaximal, characteristic, complemented
15C3×#4665C211yesmaximal, characteristic, complemented
16C3×#2418—31nomaximal
17#78101C311yesmaximal, characteristic, direct product factor
18C24×C3×D3C2211yescharacteristic
19C22×C3×#67C2211yescharacteristic
20C22×C3×D12C2211yescharacteristic
21C22×C3×D12C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×C3×C4×D3C2211yescharacteristic
24C22×C3×C4×D3C2211yescharacteristic, complemented
25C2×C32×C4⋊C4C2211yescharacteristic, complemented
26C2×C32×C4⋊C4C2211yescharacteristic, complemented
27C2×C32×C4⋊C4C2211yescharacteristic, complemented
28C2×C32×C22⋊C4C2211yescharacteristic
29C2×C32×C22⋊C4C2211yescharacteristic
30C2×C32×C22⋊C4C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×#217C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×(C2×D3)⋊C4C2211yescharacteristic
39C2×C3×(C2×D3)⋊C4C2211yescharacteristic
40C2×C3×(C2×D3)⋊C4C2211yescharacteristic
41C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
42C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
43C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
44C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
45C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
46C2×C3×C4×Dic3C2211yescharacteristic, complemented
47C3×#894—24no—
48C3×#893—24no—
49C3×#882—24no—
50C3×D3×C22⋊C4—24no—
51C32×#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—31no—
58C2×C3×#120—31no—
59C2×C3×C4×D4—31no—
60C22×C3×C22⋊C4—31no—
61C2×#894C2×C311yescharacteristic, complemented
62C2×#893C2×C311yescharacteristic, complemented
63C2×#882C2×C311yescharacteristic
64C2×D3×C22⋊C4C2×C311yescharacteristic, complemented
65C3×#399—21no—
66C3×#399D311yescharacteristic, complemented
67C3×#399C2×C311yescharacteristic, complemented
68C3×#397—31no—
69C3×#394—31no—
70C3×#394—31no—
71C3×#388—31no—
72C3×#388—31no—
73C3×#386—31no—
74C3×#386—31no—
75C3×#385—31no—
76C3×#380—31no—
77C3×#379—31no—
78#4992C2×C311yescharacteristic, complemented
79#4991C2×C311yescharacteristic, complemented
80#4989C2×C311yescharacteristic, complemented
81#4987C2×C311yescharacteristic, complemented
82#4961C2×C311yescharacteristic, complemented
83#4956C2×C311yescharacteristic, complemented
84#4955C2×C311yescharacteristic, complemented
85#4944C2×C311yescharacteristic, complemented
86#4670C2×C311yescharacteristic, complemented
87#4665C2×C311yescharacteristic, complemented
88C24×C32C2311yescharacteristic
89C23×C3×D3—22no—
90C23×C3×D3—22no—
91C23×C3×D3—22no—
92C23×C3×D3—22no—
93C23×C3×D3—22no—
94C23×C3×D3—41no—
95C23×C3×D3—41no—
96C23×C3×D3C2311yescharacteristic
97C23×C3×D3C2311yescharacteristic
98C23×C3×D3C2311yescharacteristic
99C22×C32×C4C2311yescharacteristic
100C22×C32×C4C2311yescharacteristic
101C22×C32×C4C2311yescharacteristic
102C22×C32×C4C2311yescharacteristic
103C22×C32×C4C2311yescharacteristic
104C22×C32×C4C2311yescharacteristic
105C2×C3×#67—22no—
106C2×C3×#67—22no—
107C2×C3×#67—41no—
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C2×C3×D12—22no—
114C2×C3×D12—22no—
115C2×C3×D12—22no—
116C2×C3×D12—22no—
117C2×C3×D12—41no—
118C2×C3×D12D414yes—
119C2×C3×C4×D3—22no—
120C2×C3×C4×D3—22no—
121C2×C3×C4×D3—22no—
122C2×C3×C4×D3—22no—
123C2×C3×C4×D3—22no—
124C2×C3×C4×D3—22no—
125C2×C3×C4×D3—41no—
126C2×C3×C4×D3—41no—
127C2×C3×C4×D3—41no—
128C32×C4⋊C4—22no—
129C32×C4⋊C4—22no—
130C32×C4⋊C4—41no—
131C32×C22⋊C4—22no—
132C32×C22⋊C4—22no—
133C32×C22⋊C4—41no—
134C3×#217—22no—
135C3×#217—22no—
136C3×(C2×D3)⋊C4—22no—
137C3×(C2×D3)⋊C4—22no—
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—41no—
145C3×(C2×D3)⋊C4—41no—
146C3×(C2×D3)⋊C4D414yescomplemented
147C3×C4⋊Dic3—41no—
148C3×Dic3⋊C4—22no—
149C3×C4×Dic3—22no—
150#2418—31noSylow
151C25×C3—31no—
152C24×D3C22×C311yescharacteristic
153C22×C3×D4—31no—
154C22×C3×D4—31no—
155C22×C3×D4—31no—
156C23×C3×C4—31no—
157C23×C3×C4—31no—
158C23×C3×C4—31no—
159C22×#67C22×C311yescharacteristic
160C22×D12C22×C311yescharacteristic
161C22×D12C22×C311yescharacteristic
162C22×C4×D3C22×C311yescharacteristic
163C22×C4×D3C22×C311yescharacteristic
164C22×C4×D3C22×C311yescharacteristic, complemented
165C3×#123—64no—
166C3×#120—64no—
167C3×C4×D4—64no—
168C2×C3×C4⋊C4—21no—
169C2×C3×C4⋊C4—21no—
170C2×C3×C4⋊C4—21no—
171C2×C3×C4⋊C4—31no—
172C2×C3×C4⋊C4—31no—
173C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
174C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
175C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
176C2×C3×C4⋊C4C22×C311yescharacteristic, complemented
177C2×C3×C4⋊C4C22×C311yescharacteristic, complemented
178C2×C3×C4⋊C4C22×C311yescharacteristic, complemented
179C2×C3×C22⋊C4—21no—
180C2×C3×C22⋊C4—21no—
181C2×C3×C22⋊C4—21no—
182C2×C3×C22⋊C4—31no—
183C2×C3×C22⋊C4—31no—
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—64no—
196C2×C3×C22⋊C4C2×D311yescharacteristic
197C2×C3×C22⋊C4C2×D311yescharacteristic
198C2×C3×C22⋊C4C2×D311yescharacteristic
199C2×C3×C22⋊C4C22×C311yescharacteristic
200C2×C3×C22⋊C4C22×C311yescharacteristic
201C2×C3×C22⋊C4C22×C311yescharacteristic
202C2×C3×C42—31no—
203C2×#217C22×C311yescharacteristic
204C2×#217C22×C311yescharacteristic
205C2×(C2×D3)⋊C4C22×C311yescharacteristic
206C2×(C2×D3)⋊C4C22×C311yescharacteristic
207C2×(C2×D3)⋊C4C22×C311yescharacteristic
208C2×(C2×D3)⋊C4C22×C311yescharacteristic
209C2×(C2×D3)⋊C4C22×C311yescharacteristic
210C2×(C2×D3)⋊C4C22×C311yescharacteristic
211C2×(C2×D3)⋊C4C22×C311yescharacteristic
212C2×(C2×D3)⋊C4C22×C311yescharacteristic
213C2×(C2×D3)⋊C4C22×C311yescharacteristic, complemented
214C2×(C2×D3)⋊C4C22×C311yescharacteristic, complemented
215C2×(C2×D3)⋊C4C22×C311yescharacteristic, complemented
216C2×C4⋊Dic3C22×C311yescharacteristic, complemented
217C2×Dic3⋊C4C22×C311yescharacteristic, complemented
218C2×C4×Dic3C22×C311yescharacteristic, complemented
219#894—24no—
220#893—24no—
221#882—24no—
222D3×C22⋊C4—24no—
223C3×#95—21no—
224C3×#95—31no—
225C3×#95—31no—
226C3×#95—31no—
227C3×#95—31no—
228C3×#95—31no—
229C3×#95C2×D311yescharacteristic, complemented
230C3×#95C22×C311yescharacteristic, complemented
231C3⋊#95C22×C311yescharacteristic, complemented
232C3⋊#95C22×C311yescharacteristic, complemented
233C3⋊#95C22×C311yescharacteristic, complemented
234C3⋊#95C22×C311yescharacteristic, complemented
235C3⋊#95C22×C311yescharacteristic, complemented
236C23×C32—21no—
237C23×C32—21no—
238C23×C32—21no—
239C23×C32—21no—
240C23×C32—21no—
241C23×C32—21no—
242C23×C32#4112yes—
243C23×C32C2411yescharacteristic
244C22×C3×D3—21no—
245C22×C3×D3—21no—
246C22×C3×D3—21no—
247C22×C3×D3—21no—
248C22×C3×D3—28no—
249C22×C3×D3—21no—
250C22×C3×D3—21no—
251C22×C3×D3—21no—
252C22×C3×D3—21no—
253C22×C3×D3—21no—
254C22×C3×D3—21no—
255C22×C3×D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3—21no—
261C22×C3×D3—44no—
262C22×C3×D3—44no—
263C22×C3×D3—44no—
264C22×C3×D3—44no—
265C22×C3×D3—44no—
266C22×C3×D3—44no—
267C22×C3×D3C2×D412yes—
268C22×C3×D3C2×D412yes—
269C22×C3×D3C2×D412yes—
270C22×C3×D3#4112yes—
271C22×C3×D3#4112yes—
272C2×C32×C4—21no—
273C2×C32×C4—21no—
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—21no—
288C2×C32×C4C2×D412yes—
289C2×C32×C4C2×D412yes—
290C3×#67—44no—
291C2×C3×Dic3—21no—
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×Dic3C2×D412yes—
306C3×D12—28no—
307C3×D12—44no—
308C3×C4×D3—44no—
309C3×C4×D3—44no—
310C3×C4×D3—44no—
311C2×#123—31no—
312C2×#120—31no—
313C2×C4×D4—31no—
314C22×C22⋊C4—31no—
315#399C3×D311yescharacteristic, complemented
316#397—31no—
317#394—31no—
318#394—31no—
319#388—31no—
320#388—31no—
321#386—31no—
322#386—31no—
323#385—31no—
324#380—31no—
325#379—31no—
326C24×C3—21no—
327C24×C3—31no—
328C24×C3—31no—
329C24×C3—31no—
330C24×C3—62no—
331C24×C3—62no—
332C24×C3—62no—
333C24×C3—62no—
334C24×C3—62no—
335C24×C3—121no—
336C24×C3—121no—
337C24×C3C22×D311yescharacteristic
338C24×C3C23×C311yescharacteristic
339C23×D3—22no—
340C23×D3—22no—
341C23×D3—22no—
342C23×D3—22no—
343C23×D3—22no—
344C23×D3—41no—
345C23×D3—41no—
346C23×D3C23×C311yescharacteristic
347C23×D3C23×C311yescharacteristic
348C23×D3C23×C311yescharacteristic
349C2×C3×D4—34no—
350C2×C3×D4—62no—
351C2×C3×D4—62no—
352C2×C3×D4—62no—
353C2×C3×D4—62no—
354C2×C3×D4—62no—
355C2×C3×D4—62no—
356C2×C3×D4—121no—
357C2×C3×D4—121no—
358C22×C3×C4—21no—
359C22×C3×C4—21no—
360C22×C3×C4—21no—
361C22×C3×C4—21no—
362C22×C3×C4—21no—
363C22×C3×C4—21no—
364C22×C3×C4—31no—
365C22×C3×C4—31no—
366C22×C3×C4—31no—
367C22×C3×C4—31no—
368C22×C3×C4—31no—
369C22×C3×C4—62no—
370C22×C3×C4—62no—
371C22×C3×C4—62no—
372C22×C3×C4—62no—
373C22×C3×C4—62no—
374C22×C3×C4—62no—
375C22×C3×C4—121no—
376C22×C3×C4—121no—
377C22×C3×C4—121no—
378C22×C3×C4C22×D311yescharacteristic
379C22×C3×C4C22×D311yescharacteristic
380C22×C3×C4C22×D311yescharacteristic
381C22×C3×C4C22×D311yescharacteristic
382C22×C3×C4C22×D311yescharacteristic
383C22×C3×C4C22×D311yescharacteristic
384C22×C3×C4C23×C311yescharacteristic
385C22×C3×C4C23×C311yescharacteristic
386C22×C3×C4C23×C311yescharacteristic
387C22×C3×C4C23×C311yescharacteristic
388C22×C3×C4C23×C311yescharacteristic
389C22×C3×C4C23×C311yescharacteristic
390C2×#67—22no—
391C2×#67—22no—
392C2×#67—41no—
393C22×Dic3C23×C311yescharacteristic
394C22×Dic3C23×C311yescharacteristic
395C22×Dic3C23×C311yescharacteristic
396C22×Dic3C23×C311yescharacteristic
397C22×Dic3C23×C311yescharacteristic
398C2×D12—22no—
399C2×D12—22no—
400C2×D12—22no—
401C2×D12—22no—
402C2×D12—41no—
403C2×D12C3×D414yes—
404C2×C4×D3—22no—
405C2×C4×D3—22no—
406C2×C4×D3—22no—
407C2×C4×D3—22no—
408C2×C4×D3—22no—
409C2×C4×D3—22no—
410C2×C4×D3—41no—
411C2×C4×D3—41no—
412C2×C4×D3—41no—
413C3×C4⋊C4—22no—
414C3×C4⋊C4—22no—
415C3×C4⋊C4—22no—
416C3×C4⋊C4—22no—
417C3×C4⋊C4—42no—
418C3×C4⋊C4—42no—
419C3×C4⋊C4—41no—
420C3×C4⋊C4—41no—
421C3×C4⋊C4—42no—
422C3×C4⋊C4—62no—
423C3×C4⋊C4—121no—
424C3×C22⋊C4—22no—
425C3×C22⋊C4—22no—
426C3×C22⋊C4—22no—
427C3×C22⋊C4—22no—
428C3×C22⋊C4—34no—
429C3×C22⋊C4—42no—
430C3×C22⋊C4—42no—
431C3×C22⋊C4—41no—
432C3×C22⋊C4—41no—
433C3×C22⋊C4—42no—
434C3×C22⋊C4—62no—
435C3×C22⋊C4—62no—
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—121no—
445C3×C22⋊C4—121no—
446C3×C42—62no—
447#217—22no—
448#217—22no—
449(C2×D3)⋊C4—22no—
450(C2×D3)⋊C4—22no—
451(C2×D3)⋊C4—22no—
452(C2×D3)⋊C4—22no—
453(C2×D3)⋊C4—22no—
454(C2×D3)⋊C4—22no—
455(C2×D3)⋊C4—22no—
456(C2×D3)⋊C4—22no—
457(C2×D3)⋊C4—41no—
458(C2×D3)⋊C4—41no—
459(C2×D3)⋊C4C3×D414yescomplemented
460C4⋊Dic3—41no—
461Dic3⋊C4—22no—
462C4×Dic3—22no—
463C22×C32—22no—
464C22×C32—22no—
465C22×C32—22no—
466C22×C32—41no—
467C22×C32—41no—
468C22×C32—41no—
469C22×C32—41no—
470C22×C32C22×D411yescharacteristic
471C22×C32C22×D411yescharacteristic
472C22×C32C2×#4111yescharacteristic
473C22×C32C2×#4111yescharacteristic
474C22×C32C2×#4111yescharacteristic
475C22×C32H(5,𝔽2)11yescharacteristic
476C22×C32H(5,𝔽2)11yescharacteristic
477C2×C3×D3—22no—
478C2×C3×D3—22no—
479C2×C3×D3—22no—
480C2×C3×D3—22no—
481C2×C3×D3—22no—
482C2×C3×D3—22no—
483C2×C3×D3—22no—
484C2×C3×D3—22no—
485C2×C3×D3—22no—
486C2×C3×D3—22no—
487C2×C3×D3—22no—
488C2×C3×D3—22no—
489C2×C3×D3—416no—
490C2×C3×D3—41no—
491C2×C3×D3—41no—
492C2×C3×D3—41no—
493C2×C3×D3—41no—
494C2×C3×D3—41no—
495C2×C3×D3—41no—
496C2×C3×D3—41no—
497C2×C3×D3—41no—
498C2×C3×D3#12314yescomplemented
499C32×C4—22no—
500C32×C4—22no—
501C32×C4—41no—
502C32×C4—41no—
503C32×C4—41no—
504C32×C4—41no—
505C3×Dic3—22no—
506C3×Dic3—41no—
507C3×Dic3—41no—
508C3×Dic3—41no—
509C3×Dic3—41no—
510C25—31no—
511C22×D4—31no—
512C22×D4—31no—
513C22×D4—31no—
514C23×C4—31no—
515C23×C4—31no—
516C23×C4—31no—
517#123—64no—
518#120—64no—
519C4×D4—64no—
520C2×C4⋊C4—31no—
521C2×C4⋊C4—31no—
522C2×C4⋊C4C2×C3×D311yescharacteristic, complemented
523C2×C4⋊C4C2×C3×D311yescharacteristic, complemented
524C2×C4⋊C4C2×C3×D311yescharacteristic, complemented
525C2×C22⋊C4—31no—
526C2×C22⋊C4—31no—
527C2×C22⋊C4—31no—
528C2×C22⋊C4—31no—
529C2×C22⋊C4—31no—
530C2×C22⋊C4—31no—
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—64no—
539C2×C22⋊C4C2×C3×D311yescharacteristic
540C2×C22⋊C4C2×C3×D311yescharacteristic
541C2×C22⋊C4C2×C3×D311yescharacteristic
542C2×C42—31no—
543#95—31no—
544#95—31no—
545#95—31no—
546#95—31no—
547#95—31no—
548#95C2×C3×D311yescharacteristic, complemented
549C23×C3—21no—
550C23×C3—21no—
551C23×C3—21no—
552C23×C3—21no—
553C23×C3—21no—
554C23×C3—21no—
555C23×C3—21no—
556C23×C3—21no—
557C23×C3—21no—
558C23×C3—21no—
559C23×C3—21no—
560C23×C3—21no—
561C23×C3—21no—
562C23×C3—22no—
563C23×C3—32no—
564C23×C3—32no—
565C23×C3—32no—
566C23×C3—32no—
567C23×C3—32no—
568C23×C3—41no—
569C23×C3—41no—
570C23×C3—41no—
571C23×C3—41no—
572C23×C3—41no—
573C23×C3—41no—
574C23×C3—68no—
575C23×C3—61no—
576C23×C3—61no—
577C23×C3—61no—
578C23×C3—61no—
579C23×C3—61no—
580C23×C3—61no—
581C23×C3—61no—
582C23×C3—61no—
583C23×C3—61no—
584C23×C3—61no—
585C23×C3—61no—
586C23×C3—61no—
587C23×C3—61no—
588C23×C3—61no—
589C23×C3—61no—
590C23×C3—61no—
591C23×C3—124no—
592C23×C3—124no—
593C23×C3—124no—
594C23×C3—124no—
595C23×C3—124no—
596C23×C3—124no—
597C23×C3#23912yes—
598C23×C3C3×#4112yes—
599C23×C3C23×D311yescharacteristic
600C23×C3C24×C311yescharacteristic
601C22×D3—21no—
602C22×D3—21no—
603C22×D3—21no—
604C22×D3—21no—
605C22×D3—28no—
606C22×D3—21no—
607C22×D3—21no—
608C22×D3—21no—
609C22×D3—21no—
610C22×D3—21no—
611C22×D3—21no—
612C22×D3—21no—
613C22×D3—21no—
614C22×D3—21no—
615C22×D3—21no—
616C22×D3—21no—
617C22×D3—21no—
618C22×D3—44no—
619C22×D3—44no—
620C22×D3—44no—
621C22×D3—44no—
622C22×D3—44no—
623C22×D3—44no—
624C22×D3C2×C3×D412yes—
625C22×D3C2×C3×D412yes—
626C22×D3C2×C3×D412yes—
627C22×D3C3×#4112yes—
628C22×D3C3×#4112yes—
629C3×D4—68no—
630C3×D4—124no—
631C3×D4—124no—
632C2×C3×C4—21no—
633C2×C3×C4—21no—
634C2×C3×C4—21no—
635C2×C3×C4—21no—
636C2×C3×C4—21no—
637C2×C3×C4—21no—
638C2×C3×C4—21no—
639C2×C3×C4—21no—
640C2×C3×C4—22no—
641C2×C3×C4—21no—
642C2×C3×C4—21no—
643C2×C3×C4—21no—
644C2×C3×C4—21no—
645C2×C3×C4—21no—
646C2×C3×C4—21no—
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—21no—
656C2×C3×C4—21no—
657C2×C3×C4—21no—
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—22no—
666C2×C3×C4—22no—
667C2×C3×C4—32no—
668C2×C3×C4—41no—
669C2×C3×C4—41no—
670C2×C3×C4—41no—
671C2×C3×C4—41no—
672C2×C3×C4—41no—
673C2×C3×C4—41no—
674C2×C3×C4—41no—
675C2×C3×C4—41no—
676C2×C3×C4—41no—
677C2×C3×C4—41no—
678C2×C3×C4—41no—
679C2×C3×C4—41no—
680C2×C3×C4—41no—
681C2×C3×C4—41no—
682C2×C3×C4—41no—
683C2×C3×C4—61no—
684C2×C3×C4—61no—
685C2×C3×C4—61no—
686C2×C3×C4—61no—
687C2×C3×C4—61no—
688C2×C3×C4—61no—
689C2×C3×C4—61no—
690C2×C3×C4—61no—
691C2×C3×C4—61no—
692C2×C3×C4—61no—
693C2×C3×C4—61no—
694C2×C3×C4—61no—
695C2×C3×C4—61no—
696C2×C3×C4—61no—
697C2×C3×C4—124no—
698C2×C3×C4—124no—
699C2×C3×C4—124no—
700C2×C3×C4D3×D412yes—
701C2×C3×C4D3×D412yes—
702C2×C3×C4C2×C3×D412yes—
703C2×C3×C4C2×C3×D412yes—
704#67—44no—
705C2×Dic3—21no—
706C2×Dic3—21no—
707C2×Dic3—21no—
708C2×Dic3—21no—
709C2×Dic3—21no—
710C2×Dic3—21no—
711C2×Dic3—21no—
712C2×Dic3—21no—
713C2×Dic3—21no—
714C2×Dic3—21no—
715C2×Dic3—21no—
716C2×Dic3—21no—
717C2×Dic3—21no—
718C2×Dic3—21no—
719C2×Dic3C2×C3×D412yes—
720D12—28no—
721D12—44no—
722C4×D3—44no—
723C4×D3—44no—
724C4×D3—44no—
725C2×C32—42no—
726C2×C32C2×#12311yescharacteristic
727C2×C32#52511yescharacteristic
728C2×C32#53811yescharacteristic
729C2×C32D4211yescharacteristic
730C2×C32#54611yescharacteristic
731C2×C32#54611yescharacteristic
732C2×C32#55111yescharacteristic
733C3×D3—24no—
734C3×D3—42no—
735C3×D3—42no—
736C24—31no—
737C24—31no—
738C24—31no—
739C24—62no—
740C24—62no—
741C24—62no—
742C24—62no—
743C24—62no—
744C24—121no—
745C24—121no—
746C24C22×C3×D311yescharacteristic
747C2×D4—34no—
748C2×D4—62no—
749C2×D4—62no—
750C2×D4—62no—
751C2×D4—62no—
752C2×D4—62no—
753C2×D4—62no—
754C2×D4—121no—
755C2×D4—121no—
756C22×C4—31no—
757C22×C4—31no—
758C22×C4—31no—
759C22×C4—31no—
760C22×C4—31no—
761C22×C4—62no—
762C22×C4—62no—
763C22×C4—62no—
764C22×C4—62no—
765C22×C4—62no—
766C22×C4—62no—
767C22×C4—121no—
768C22×C4—121no—
769C22×C4—121no—
770C22×C4C22×C3×D311yescharacteristic
771C22×C4C22×C3×D311yescharacteristic
772C22×C4C22×C3×D311yescharacteristic
773C22×C4C22×C3×D311yescharacteristic
774C22×C4C22×C3×D311yescharacteristic
775C22×C4C22×C3×D311yescharacteristic
776C4⋊C4—22no—
777C4⋊C4—22no—
778C4⋊C4—41no—
779C4⋊C4—62no—
780C4⋊C4—121no—
781C22⋊C4—22no—
782C22⋊C4—22no—
783C22⋊C4—34no—
784C22⋊C4—41no—
785C22⋊C4—62no—
786C22⋊C4—62no—
787C22⋊C4—62no—
788C22⋊C4—62no—
789C22⋊C4—62no—
790C22⋊C4—62no—
791C22⋊C4—62no—
792C22⋊C4—62no—
793C22⋊C4—62no—
794C22⋊C4—62no—
795C22⋊C4—121no—
796C22⋊C4—121no—
797C42—62no—
798C22×C3—22no—
799C22×C3—22no—
800C22×C3—22no—
801C22×C3—22no—
802C22×C3—22no—
803C22×C3—22no—
804C22×C3—21no—
805C22×C3—21no—
806C22×C3—21no—
807C22×C3—21no—
808C22×C3—21no—
809C22×C3—21no—
810C22×C3—21no—
811C22×C3—34no—
812C22×C3—42no—
813C22×C3—42no—
814C22×C3—42no—
815C22×C3—41no—
816C22×C3—41no—
817C22×C3—41no—
818C22×C3—41no—
819C22×C3—41no—
820C22×C3—41no—
821C22×C3—41no—
822C22×C3—41no—
823C22×C3—62no—
824C22×C3—62no—
825C22×C3—62no—
826C22×C3—62no—
827C22×C3—62no—
828C22×C3—62no—
829C22×C3—62no—
830C22×C3—62no—
831C22×C3—62no—
832C22×C3—62no—
833C22×C3—62no—
834C22×C3—62no—
835C22×C3—81no—
836C22×C3—81no—
837C22×C3—81no—
838C22×C3—81no—
839C22×C3—1216no—
840C22×C3—121no—
841C22×C3—121no—
842C22×C3—121no—
843C22×C3—121no—
844C22×C3—121no—
845C22×C3—121no—
846C22×C3—121no—
847C22×C3—121no—
848C22×C3C2×D3×D411yescharacteristic
849C22×C3C2×D3×D411yescharacteristic
850C22×C3#100411yescharacteristic
851C22×C3C2×#23911yescharacteristic
852C22×C3D3×#4111yescharacteristic
853C22×C3D3×#4111yescharacteristic
854C22×C3#100911yescharacteristic
855C22×C3C22×C3×D411yescharacteristic
856C22×C3C22×C3×D411yescharacteristic
857C22×C3C2×C3×#4111yescharacteristic
858C22×C3C2×C3×#4111yescharacteristic
859C22×C3C2×C3×#4111yescharacteristic
860C22×C3C3×H(5,𝔽2)11yescharacteristic
861C22×C3C3×H(5,𝔽2)11yescharacteristic
862C2×D3—22no—
863C2×D3—22no—
864C2×D3—22no—
865C2×D3—22no—
866C2×D3—22no—
867C2×D3—22no—
868C2×D3—22no—
869C2×D3—22no—
870C2×D3—22no—
871C2×D3—22no—
872C2×D3—22no—
873C2×D3—22no—
874C2×D3—416no—
875C2×D3—41no—
876C2×D3—41no—
877C2×D3—41no—
878C2×D3—41no—
879C2×D3—41no—
880C2×D3—41no—
881C2×D3—41no—
882C2×D3—41no—
883C2×D3C3×#12314yescomplemented
884C3×C4—22no—
885C3×C4—22no—
886C3×C4—22no—
887C3×C4—22no—
888C3×C4—42no—
889C3×C4—42no—
890C3×C4—42no—
891C3×C4—41no—
892C3×C4—41no—
893C3×C4—41no—
894C3×C4—41no—
895C3×C4—41no—
896C3×C4—41no—
897C3×C4—41no—
898C3×C4—41no—
899C3×C4—62no—
900C3×C4—81no—
901C3×C4—81no—
902C3×C4—81no—
903C3×C4—121no—
904C3×C4—121no—
905C3×C4—121no—
906C3×C4—121no—
907Dic3—22no—
908Dic3—41no—
909Dic3—41no—
910Dic3—41no—
911Dic3—41no—
912C32#241811yescharacteristic, complemented, Sylow
913C23—21no—
914C23—21no—
915C23—21no—
916C23—21no—
917C23—21no—
918C23—21no—
919C23—32no—
920C23—32no—
921C23—32no—
922C23—32no—
923C23—32no—
924C23—68no—
925C23—61no—
926C23—61no—
927C23—61no—
928C23—61no—
929C23—61no—
930C23—61no—
931C23—61no—
932C23—61no—
933C23—61no—
934C23—61no—
935C23—61no—
936C23—61no—
937C23—61no—
938C23—61no—
939C23—61no—
940C23—61no—
941C23—124no—
942C23—124no—
943C23—124no—
944C23—124no—
945C23—124no—
946C23—124no—
947C23C3×#23912yes—
948C23C23×C3×D311yescharacteristic
949D4—68no—
950D4—124no—
951D4—124no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—32no—
969C2×C4—61no—
970C2×C4—61no—
971C2×C4—61no—
972C2×C4—61no—
973C2×C4—61no—
974C2×C4—61no—
975C2×C4—61no—
976C2×C4—61no—
977C2×C4—61no—
978C2×C4—61no—
979C2×C4—61no—
980C2×C4—61no—
981C2×C4—61no—
982C2×C4—61no—
983C2×C4—124no—
984C2×C4—124no—
985C2×C4—124no—
986C2×C4C3×D3×D412yes—
987C2×C4C3×D3×D412yes—
988C2×C3—21no—
989C2×C3—21no—
990C2×C3—21no—
991C2×C3—21no—
992C2×C3—21no—
993C2×C3—21no—
994C2×C3—21no—
995C2×C3—42no—
996C2×C3—42no—
997C2×C3—64no—
998C2×C3—82no—
999C2×C3—122no—
1000C2×C3—122no—
1001C2×C3#562711yescharacteristic
1002C2×C3#563011yescharacteristic
1003C2×C3#563711yescharacteristic
1004C2×C3D3×#12311yescharacteristic
1005C2×C3#565411yescharacteristic
1006C2×C3#565711yescharacteristic
1007C2×C3#571711yescharacteristic
1008C2×C3C2×C3×#12311yescharacteristic
1009C2×C3C3×#52511yescharacteristic
1010C2×C3C3×#53811yescharacteristic
1011C2×C3C3×D4211yescharacteristic
1012C2×C3C3×#54611yescharacteristic
1013C2×C3C3×#54611yescharacteristic
1014C2×C3C3×#55111yescharacteristic
1015D3—24no—
1016D3—42no—
1017D3—42no—
1018C22—22no—
1019C22—22no—
1020C22—22no—
1021C22—34no—
1022C22—41no—
1023C22—41no—
1024C22—41no—
1025C22—41no—
1026C22—62no—
1027C22—62no—
1028C22—62no—
1029C22—62no—
1030C22—62no—
1031C22—62no—
1032C22—62no—
1033C22—62no—
1034C22—62no—
1035C22—62no—
1036C22—62no—
1037C22—62no—
1038C22—1216no—
1039C22—121no—
1040C22—121no—
1041C22—121no—
1042C22—121no—
1043C22—121no—
1044C22—121no—
1045C22—121no—
1046C22—121no—
1047C22C2×C3×D3×D411yescharacteristic
1048C22C2×C3×D3×D411yescharacteristic
1049C22C3×#100411yescharacteristic
1050C22C2×C3×#23911yescharacteristic
1051C22C3×D3×#4111yescharacteristic
1052C22C3×D3×#4111yescharacteristic
1053C22C3×#100911yescharacteristic
1054C4—22no—
1055C4—22no—
1056C4—41no—
1057C4—41no—
1058C4—41no—
1059C4—41no—
1060C4—62no—
1061C4—121no—
1062C4—121no—
1063C4—121no—
1064C4—121no—
1065C3—21no—
1066C3#7810111yescharacteristic, direct product factor
1067C3C3×#241811yescharacteristic, complemented
1068C2—42no—
1069C2—64no—
1070C2—122no—
1071C2—122no—
1072C2C3×#562711yescharacteristic
1073C2C3×#563011yescharacteristic
1074C2C3×#563711yescharacteristic
1075C2C3×D3×#12311yescharacteristic
1076C2C3×#565411yescharacteristic
1077C2C3×#565711yescharacteristic
1078C2C3×#571711yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC32×#399C2
socleC23×C32C24
prime radicalC2×C3×#882C2
hypercenterC3×#399D3
hypocenterC3C3×#2418
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#399

Complements

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

NH ≅ G/Ntype
1. C2×C3×#894C2semidirect
2. C2×C3×#893C2semidirect
4. C2×C3×D3×C22⋊C4C2semidirect
5. C32×#399C2semidirect
6. C3×#4992C2semidirect
7. C3×#4991C2semidirect
8. C3×#4989C2semidirect
9. C3×#4987C2semidirect
10. C3×#4961C2semidirect
11. C3×#4956C2semidirect
12. C3×#4955C2semidirect
13. C3×#4944C2semidirect
14. C3×#4670C2semidirect
15. C3×#4665C2semidirect
17. #78101C3direct (N × H)
24. C22×C3×C4×D3C22semidirect
25. C2×C32×C4⋊C4C22semidirect
26. C2×C32×C4⋊C4C22semidirect
27. C2×C32×C4⋊C4C22semidirect
41. C2×C3×(C2×D3)⋊C4C22semidirect
42. C2×C3×(C2×D3)⋊C4C22semidirect
43. C2×C3×(C2×D3)⋊C4C22semidirect
44. C2×C3×C4⋊Dic3C22semidirect
45. C2×C3×Dic3⋊C4C22semidirect
46. C2×C3×C4×Dic3C22semidirect
51. C32×#95C22semidirect
52. C3×C3⋊#95C22semidirect
53. C3×C3⋊#95C22semidirect
54. C3×C3⋊#95C22semidirect
55. C3×C3⋊#95C22semidirect
56. C3×C3⋊#95C22semidirect
61. C2×#894C2×C3semidirect
62. C2×#893C2×C3semidirect
64. C2×D3×C22⋊C4C2×C3semidirect
66. C3×#399D3semidirect
67. C3×#399C2×C3semidirect
78. #4992C2×C3semidirect
79. #4991C2×C3semidirect
80. #4989C2×C3semidirect
81. #4987C2×C3semidirect
82. #4961C2×C3semidirect
83. #4956C2×C3semidirect
84. #4955C2×C3semidirect
85. #4944C2×C3semidirect
86. #4670C2×C3semidirect
87. #4665C2×C3semidirect
146. C3×(C2×D3)⋊C4D4semidirect
164. C22×C4×D3C22×C3semidirect
173. C2×C3×C4⋊C4C2×D3semidirect
174. C2×C3×C4⋊C4C2×D3semidirect
175. C2×C3×C4⋊C4C2×D3semidirect
176. C2×C3×C4⋊C4C22×C3semidirect
177. C2×C3×C4⋊C4C22×C3semidirect
178. C2×C3×C4⋊C4C22×C3semidirect
213. C2×(C2×D3)⋊C4C22×C3semidirect
214. C2×(C2×D3)⋊C4C22×C3semidirect
215. C2×(C2×D3)⋊C4C22×C3semidirect
216. C2×C4⋊Dic3C22×C3semidirect
217. C2×Dic3⋊C4C22×C3semidirect
218. C2×C4×Dic3C22×C3semidirect
229. C3×#95C2×D3semidirect
230. C3×#95C22×C3semidirect
231. C3⋊#95C22×C3semidirect
232. C3⋊#95C22×C3semidirect
233. C3⋊#95C22×C3semidirect
234. C3⋊#95C22×C3semidirect
235. C3⋊#95C22×C3semidirect
315. #399C3×D3semidirect
459. (C2×D3)⋊C4C3×D4semidirect
498. C2×C3×D3#123semidirect
522. C2×C4⋊C4C2×C3×D3semidirect
523. C2×C4⋊C4C2×C3×D3semidirect
524. C2×C4⋊C4C2×C3×D3semidirect
548. #95C2×C3×D3semidirect
883. C2×D3C3×#123semidirect
912. C32#2418semidirect
1066. C3#78101direct (N × H)
1067. C3C3×#2418semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8942
C2×C3×#8932
C2×C3×#8822
C2×C3×D3×C22⋊C42
C32×#3992
C3×#49922
C3×#49912
C3×#49892
C3×#49872
C3×#49612
C3×#49562
C3×#49552
C3×#49442
C3×#46702
C3×#46652
C3×#24183
#781013