Finite Group Databasebeta

← C3×#75882 #11824553

Subgroups — C3×#75882 #11824553

Order 1152.

1543 conjugacy classes of subgroups.

The subgroup lattice has 1063 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#895C211yesmaximal, characteristic, complemented
2C2×C3×#884C211yesmaximal, characteristic, complemented
3C2×C3×#884C211yesmaximal, characteristic, complemented
4C2×C3×C4×D12C211yesmaximal, characteristic, complemented
5C32×#388C211yesmaximal, characteristic, complemented
6C3×#4982C211yesmaximal, characteristic, complemented
7C3×#4961C211yesmaximal, characteristic, complemented
8C3×#4960C211yesmaximal, characteristic, complemented
9C3×#4956C211yesmaximal, characteristic, complemented
10C3×#4956C211yesmaximal, characteristic, complemented
11C3×#4940C211yesmaximal, characteristic, complemented
12C3×#4675C211yesmaximal, characteristic, complemented
13C3×#4665C211yesmaximal, characteristic, complemented
14C3×#4665C211yesmaximal, characteristic, complemented
15C3×D3×#95C211yesmaximal, characteristic, complemented
16C3×#2543—31nomaximal
17#75882C311yesmaximal, characteristic, direct product factor
18C22×C3×#67C2211yescharacteristic
19C22×C3×#67C2211yescharacteristic
20C22×C3×#67C2211yescharacteristic
21C22×C3×D12C2211yescharacteristic
22C22×C3×D12C2211yescharacteristic
23C22×C3×D12C2211yescharacteristic
24C22×C3×C4×D3C2211yescharacteristic
25C22×C3×C4×D3C2211yescharacteristic
26C22×C3×C4×D3C2211yescharacteristic
27C22×C3×C4×D3C2211yescharacteristic
28C2×C32×C4⋊C4C2211yescharacteristic
29C2×C32×C22⋊C4C2211yescharacteristic
30C2×C32×C22⋊C4C2211yescharacteristic
31C2×C32×C22⋊C4C2211yescharacteristic
32C2×C32×C42C2211yescharacteristic
33C2×C3×#217C2211yescharacteristic
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
42C2×C3×C4⋊Dic3C2211yescharacteristic
43C2×C3×Dic3⋊C4C2211yescharacteristic
44C2×C3×Dic3⋊C4C2211yescharacteristic
45C3×#895—24no—
46C3×#884—24no—
47C3×#884—24no—
48C3×C4×D12—24no—
49C32×#95C2211yescharacteristic
50C32×#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53C3×C3⋊#95C2211yescharacteristic
54C3×C3⋊#95C2211yescharacteristic
55C3×C3⋊#95C2211yescharacteristic
56C3×C3⋊#95C2211yescharacteristic
57C2×C3×#121—31no—
58C2×C3×#121—31no—
59C2×C3×#121—31no—
60C2×C3×C4×D4—31no—
61C2×#895C2×C311yescharacteristic, complemented
62C2×#884C2×C311yescharacteristic, complemented
63C2×#884C2×C311yescharacteristic, complemented
64C2×C4×D12C2×C311yescharacteristic, complemented
65C3×#398—31no—
66C3×#397—31no—
67C3×#394—31no—
68C3×#392—31no—
69C3×#388—21no—
70C3×#388—31no—
71C3×#388D311yescharacteristic, complemented
72C3×#388C2×C311yescharacteristic, complemented
73C3×#386—31no—
74C3×#386—31no—
75C3×#386—31no—
76C3×#386—31no—
77C2×C3×#95—31no—
78#4982C2×C311yescharacteristic, complemented
79#4961C2×C311yescharacteristic, complemented
80#4960C2×C311yescharacteristic, complemented
81#4956C2×C311yescharacteristic, complemented
82#4956C2×C311yescharacteristic, complemented
83#4940C2×C311yescharacteristic, complemented
84#4675C2×C311yescharacteristic, complemented
85#4665C2×C311yescharacteristic, complemented
86#4665C2×C311yescharacteristic, complemented
87D3×#95C2×C311yescharacteristic, complemented
88C24×C32C2311yescharacteristic
89C23×C3×D3C2311yescharacteristic
90C23×C3×D3C2311yescharacteristic
91C23×C3×D3C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C22×C32×C4C2311yescharacteristic
98C2×C3×#67—22no—
99C2×C3×#67—22no—
100C2×C3×#67—22no—
101C2×C3×#67—22no—
102C2×C3×#67—22no—
103C2×C3×#67—22no—
104C2×C3×#67—41no—
105C2×C3×#67—41no—
106C2×C3×#67—41no—
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C2×C3×D12—22no—
113C2×C3×D12—22no—
114C2×C3×D12—22no—
115C2×C3×D12—22no—
116C2×C3×D12—22no—
117C2×C3×D12—22no—
118C2×C3×D12—22no—
119C2×C3×D12—41no—
120C2×C3×D12D414yescomplemented
121C2×C3×C4×D3—22no—
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—
128C2×C3×C4×D3—41no—
129C2×C3×C4×D3—41no—
130C2×C3×C4×D3—41no—
131C2×C3×C4×D3—41no—
132C2×C3×C4×D3D414yescomplemented
133C32×C4⋊C4—22no—
134C32×C22⋊C4—22no—
135C32×C22⋊C4—22no—
136C32×C22⋊C4—22no—
137C32×C42—22no—
138C3×#217—41no—
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—22no—
146C3×(C2×D3)⋊C4—41no—
147C3×C4⋊Dic3—22no—
148C3×Dic3⋊C4—22no—
149C3×Dic3⋊C4—22no—
150#2543—31noSylow
151C22×C3×D4—31no—
152C22×C3×D4—31no—
153C22×C3×D4—31no—
154C22×C3×D4—31no—
155C22×C3×D4—31no—
156C22×C3×D4—31no—
157C23×C3×C4—31no—
158C23×C3×C4—31no—
159C23×C3×C4—31no—
160C23×C3×C4—31no—
161C22×#67C22×C311yescharacteristic
162C22×#67C22×C311yescharacteristic
163C22×#67C22×C311yescharacteristic
164C22×D12C22×C311yescharacteristic
165C22×D12C22×C311yescharacteristic
166C22×D12C22×C311yescharacteristic
167C22×C4×D3C22×C311yescharacteristic
168C22×C4×D3C22×C311yescharacteristic
169C22×C4×D3C22×C311yescharacteristic
170C22×C4×D3C22×C311yescharacteristic
171C3×#121—64no—
172C3×#121—64no—
173C3×#121—64no—
174C3×C4×D4—64no—
175C2×C3×C4⋊C4—21no—
176C2×C3×C4⋊C4—31no—
177C2×C3×C4⋊C4—31no—
178C2×C3×C4⋊C4—31no—
179C2×C3×C4⋊C4C2×D311yescharacteristic
180C2×C3×C4⋊C4C22×C311yescharacteristic
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⋊C4C2×D311yescharacteristic
194C2×C3×C22⋊C4C2×D311yescharacteristic
195C2×C3×C22⋊C4C2×D311yescharacteristic
196C2×C3×C22⋊C4C22×C311yescharacteristic
197C2×C3×C22⋊C4C22×C311yescharacteristic
198C2×C3×C22⋊C4C22×C311yescharacteristic
199C2×C3×C42—21no—
200C2×C3×C42C2×D311yescharacteristic
201C2×C3×C42C22×C311yescharacteristic
202C2×#217C22×C311yescharacteristic
203C2×(C2×D3)⋊C4C22×C311yescharacteristic
204C2×(C2×D3)⋊C4C22×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×C4⋊Dic3C22×C311yescharacteristic
212C2×Dic3⋊C4C22×C311yescharacteristic
213C2×Dic3⋊C4C22×C311yescharacteristic
214#895—24no—
215#884—24no—
216#884—24no—
217C4×D12—24no—
218C3×#95—21no—
219C3×#95—21no—
220C3×#95—31no—
221C3×#95—31no—
222C3×#95—31no—
223C3×#95—31no—
224C3×#95—31no—
225C3×#95—31no—
226C3×#95C2×D311yescharacteristic
227C3×#95C2×D311yescharacteristic
228C3×#95C22×C311yescharacteristic
229C3×#95C22×C311yescharacteristic
230C3⋊#95C22×C311yescharacteristic
231C3⋊#95C22×C311yescharacteristic
232C3⋊#95C22×C311yescharacteristic
233C3⋊#95C22×C311yescharacteristic
234C3⋊#95C22×C311yescharacteristic
235C3⋊#95C22×C311yescharacteristic
236C23×C32—21no—
237C23×C32—21no—
238C23×C32—21no—
239C23×C32—21no—
240C23×C32—21no—
241C23×C32—21no—
242C23×C32—21no—
243C23×C32C2411yescharacteristic
244C22×C3×D3—21no—
245C22×C3×D3—21no—
246C22×C3×D3—21no—
247C22×C3×D3—21no—
248C22×C3×D3—21no—
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×D3C2×D412yes—
262C22×C3×D3C2×D412yes—
263C22×C3×D3C2×D412yes—
264C22×C3×D3#4112yes—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4—21no—
268C2×C32×C4—21no—
269C2×C32×C4—21no—
270C2×C32×C4—21no—
271C2×C32×C4—21no—
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×C4C2×D412yes—
281C2×C32×C4C2×D412yes—
282C2×C32×C4#4112yes—
283C3×#67—44no—
284C3×#67—44no—
285C3×#67—44no—
286C2×C3×Dic3—21no—
287C2×C3×Dic3—21no—
288C2×C3×Dic3—21no—
289C2×C3×Dic3—21no—
290C2×C3×Dic3—21no—
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×Dic3C2×D412yes—
300C2×C3×Dic3#4112yes—
301C3×D12—28no—
302C3×D12—44no—
303C3×D12—44no—
304C3×C4×D3—44no—
305C3×C4×D3—44no—
306C3×C4×D3—44no—
307C3×C4×D3—44no—
308C2×#121—31no—
309C2×#121—31no—
310C2×#121—31no—
311C2×C4×D4—31no—
312#398—31no—
313#397—31no—
314#394—31no—
315#392—31no—
316#388—31no—
317#388C3×D311yescharacteristic, complemented
318#386—31no—
319#386—31no—
320#386—31no—
321#386—31no—
322C2×#95—31no—
323C24×C3—21no—
324C24×C3—31no—
325C24×C3—31no—
326C24×C3—31no—
327C24×C3C22×D311yescharacteristic
328C24×C3C23×C311yescharacteristic
329C23×D3C23×C311yescharacteristic
330C23×D3C23×C311yescharacteristic
331C23×D3C23×C311yescharacteristic
332C2×C3×D4—34no—
333C2×C3×D4—62no—
334C2×C3×D4—62no—
335C2×C3×D4—62no—
336C2×C3×D4—62no—
337C2×C3×D4—62no—
338C2×C3×D4—62no—
339C2×C3×D4—62no—
340C2×C3×D4—62no—
341C2×C3×D4—62no—
342C2×C3×D4—62no—
343C2×C3×D4—62no—
344C2×C3×D4—62no—
345C2×C3×D4—62no—
346C2×C3×D4—121no—
347C2×C3×D4—121no—
348C2×C3×D4—121no—
349C2×C3×D4—121no—
350C22×C3×C4—21no—
351C22×C3×C4—21no—
352C22×C3×C4—21no—
353C22×C3×C4—21no—
354C22×C3×C4—21no—
355C22×C3×C4—21no—
356C22×C3×C4—31no—
357C22×C3×C4—31no—
358C22×C3×C4—34no—
359C22×C3×C4—31no—
360C22×C3×C4—31no—
361C22×C3×C4—31no—
362C22×C3×C4—62no—
363C22×C3×C4—62no—
364C22×C3×C4—62no—
365C22×C3×C4—62no—
366C22×C3×C4—62no—
367C22×C3×C4—121no—
368C22×C3×C4—121no—
369C22×C3×C4—121no—
370C22×C3×C4—121no—
371C22×C3×C4—121no—
372C22×C3×C4—121no—
373C22×C3×C4C22×D311yescharacteristic
374C22×C3×C4C22×D311yescharacteristic
375C22×C3×C4C22×D311yescharacteristic
376C22×C3×C4C22×D311yescharacteristic
377C22×C3×C4C22×D311yescharacteristic
378C22×C3×C4C22×D311yescharacteristic
379C22×C3×C4C23×C311yescharacteristic
380C22×C3×C4C23×C311yescharacteristic
381C22×C3×C4C23×C311yescharacteristic
382C22×C3×C4C23×C311yescharacteristic
383C22×C3×C4C23×C311yescharacteristic
384C22×C3×C4C23×C311yescharacteristic
385C2×#67—22no—
386C2×#67—22no—
387C2×#67—22no—
388C2×#67—22no—
389C2×#67—22no—
390C2×#67—22no—
391C2×#67—41no—
392C2×#67—41no—
393C2×#67—41no—
394C22×Dic3C23×C311yescharacteristic
395C22×Dic3C23×C311yescharacteristic
396C22×Dic3C23×C311yescharacteristic
397C22×Dic3C23×C311yescharacteristic
398C22×Dic3C23×C311yescharacteristic
399C2×D12—22no—
400C2×D12—22no—
401C2×D12—22no—
402C2×D12—22no—
403C2×D12—22no—
404C2×D12—22no—
405C2×D12—22no—
406C2×D12—41no—
407C2×D12C3×D414yescomplemented
408C2×C4×D3—22no—
409C2×C4×D3—22no—
410C2×C4×D3—22no—
411C2×C4×D3—22no—
412C2×C4×D3—22no—
413C2×C4×D3—41no—
414C2×C4×D3—41no—
415C2×C4×D3—41no—
416C2×C4×D3—41no—
417C2×C4×D3—41no—
418C2×C4×D3—41no—
419C2×C4×D3C3×D414yescomplemented
420C3×C4⋊C4—22no—
421C3×C4⋊C4—22no—
422C3×C4⋊C4—42no—
423C3×C4⋊C4—62no—
424C3×C4⋊C4—62no—
425C3×C4⋊C4—62no—
426C3×C22⋊C4—24no—
427C3×C22⋊C4—22no—
428C3×C22⋊C4—22no—
429C3×C22⋊C4—22no—
430C3×C22⋊C4—22no—
431C3×C22⋊C4—22no—
432C3×C22⋊C4—22no—
433C3×C22⋊C4—42no—
434C3×C22⋊C4—42no—
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—121no—
443C3×C22⋊C4—121no—
444C3×C42—22no—
445C3×C42—22no—
446C3×C42—42no—
447#217—41no—
448(C2×D3)⋊C4—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—41no—
456C4⋊Dic3—22no—
457Dic3⋊C4—22no—
458Dic3⋊C4—22no—
459C22×C32—41no—
460C22×C32—41no—
461C22×C32—41no—
462C22×C32—41no—
463C22×C32—41no—
464C22×C32—41no—
465C22×C32—41no—
466C22×C32C22×D411yescharacteristic
467C22×C32C22×D411yescharacteristic
468C22×C32C2×#4111yescharacteristic
469C22×C32C2×#4111yescharacteristic
470C22×C32C2×#4111yescharacteristic
471C22×C32H(5,𝔽2)11yescharacteristic
472C22×C32H(5,𝔽2)11yescharacteristic
473C2×C3×D3—22no—
474C2×C3×D3—22no—
475C2×C3×D3—22no—
476C2×C3×D3—22no—
477C2×C3×D3—22no—
478C2×C3×D3—22no—
479C2×C3×D3—22no—
480C2×C3×D3—22no—
481C2×C3×D3—22no—
482C2×C3×D3—41no—
483C2×C3×D3—41no—
484C2×C3×D3—41no—
485C2×C3×D3—41no—
486C2×C3×D3—41no—
487C2×C3×D3—41no—
488C2×C3×D3—41no—
489C2×C3×D3—41no—
490C2×C3×D3—41no—
491C2×C3×D3—41no—
492C2×C3×D3—41no—
493C2×C3×D3#12114yes—
494C32×C4—22no—
495C32×C4—22no—
496C32×C4—22no—
497C32×C4—41no—
498C32×C4—41no—
499C32×C4—41no—
500C3×Dic3—22no—
501C3×Dic3—22no—
502C3×Dic3—41no—
503C3×Dic3—41no—
504C3×Dic3—41no—
505C22×D4—31no—
506C22×D4—31no—
507C22×D4—31no—
508C22×D4—31no—
509C22×D4—31no—
510C22×D4—31no—
511C23×C4—31no—
512C23×C4—31no—
513C23×C4—31no—
514C23×C4—31no—
515#121—64no—
516#121—64no—
517#121—64no—
518C4×D4—64no—
519C2×C4⋊C4—31no—
520C2×C4⋊C4—31no—
521C2×C4⋊C4—31no—
522C2×C4⋊C4C2×C3×D311yescharacteristic
523C2×C22⋊C4—31no—
524C2×C22⋊C4—31no—
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⋊C4C2×C3×D311yescharacteristic
533C2×C22⋊C4C2×C3×D311yescharacteristic
534C2×C22⋊C4C2×C3×D311yescharacteristic
535C2×C42C2×C3×D311yescharacteristic
536#95—31no—
537#95—31no—
538#95—31no—
539#95—31no—
540#95—31no—
541#95—31no—
542#95C2×C3×D311yescharacteristic
543#95C2×C3×D311yescharacteristic
544C23×C3—22no—
545C23×C3—21no—
546C23×C3—21no—
547C23×C3—21no—
548C23×C3—21no—
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—32no—
561C23×C3—32no—
562C23×C3—32no—
563C23×C3—32no—
564C23×C3—41no—
565C23×C3—41no—
566C23×C3—41no—
567C23×C3—41no—
568C23×C3—41no—
569C23×C3—41no—
570C23×C3—61no—
571C23×C3—61no—
572C23×C3—61no—
573C23×C3—61no—
574C23×C3—61no—
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×C3C23×D311yescharacteristic
588C23×C3C24×C311yescharacteristic
589C22×D3—21no—
590C22×D3—21no—
591C22×D3—21no—
592C22×D3—21no—
593C22×D3—21no—
594C22×D3—21no—
595C22×D3—21no—
596C22×D3—21no—
597C22×D3—21no—
598C22×D3—21no—
599C22×D3—21no—
600C22×D3—21no—
601C22×D3—21no—
602C22×D3—21no—
603C22×D3—21no—
604C22×D3—21no—
605C22×D3—21no—
606C22×D3C2×C3×D412yes—
607C22×D3C2×C3×D412yes—
608C22×D3C2×C3×D412yes—
609C22×D3C3×#4112yes—
610C3×D4—68no—
611C3×D4—124no—
612C3×D4—124no—
613C3×D4—124no—
614C3×D4—124no—
615C3×D4—124no—
616C2×C3×C4—21no—
617C2×C3×C4—21no—
618C2×C3×C4—21no—
619C2×C3×C4—21no—
620C2×C3×C4—21no—
621C2×C3×C4—21no—
622C2×C3×C4—21no—
623C2×C3×C4—21no—
624C2×C3×C4—21no—
625C2×C3×C4—21no—
626C2×C3×C4—21no—
627C2×C3×C4—21no—
628C2×C3×C4—22no—
629C2×C3×C4—21no—
630C2×C3×C4—21no—
631C2×C3×C4—21no—
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—21no—
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—22no—
648C2×C3×C4—22no—
649C2×C3×C4—22no—
650C2×C3×C4—32no—
651C2×C3×C4—32no—
652C2×C3×C4—41no—
653C2×C3×C4—41no—
654C2×C3×C4—41no—
655C2×C3×C4—41no—
656C2×C3×C4—41no—
657C2×C3×C4—41no—
658C2×C3×C4—41no—
659C2×C3×C4—41no—
660C2×C3×C4—41no—
661C2×C3×C4—41no—
662C2×C3×C4—41no—
663C2×C3×C4—41no—
664C2×C3×C4—41no—
665C2×C3×C4—41no—
666C2×C3×C4—61no—
667C2×C3×C4—61no—
668C2×C3×C4—61no—
669C2×C3×C4—61no—
670C2×C3×C4—61no—
671C2×C3×C4—61no—
672C2×C3×C4—61no—
673C2×C3×C4—61no—
674C2×C3×C4—61no—
675C2×C3×C4—61no—
676C2×C3×C4—61no—
677C2×C3×C4—61no—
678C2×C3×C4—61no—
679C2×C3×C4—124no—
680C2×C3×C4—124no—
681C2×C3×C4—124no—
682C2×C3×C4—124no—
683C2×C3×C4#23512yes—
684C2×C3×C4D3×D412yes—
685C2×C3×C4D3×D412yes—
686C2×C3×C4C2×C3×D412yes—
687C2×C3×C4C2×C3×D412yes—
688C2×C3×C4C3×#4112yes—
689#67—44no—
690#67—44no—
691#67—44no—
692C2×Dic3—21no—
693C2×Dic3—21no—
694C2×Dic3—21no—
695C2×Dic3—21no—
696C2×Dic3—21no—
697C2×Dic3—21no—
698C2×Dic3—21no—
699C2×Dic3—21no—
700C2×Dic3—21no—
701C2×Dic3—21no—
702C2×Dic3—21no—
703C2×Dic3—21no—
704C2×Dic3—21no—
705C2×Dic3C2×C3×D412yes—
706C2×Dic3C3×#4112yes—
707D12—28no—
708D12—44no—
709D12—44no—
710C4×D3—44no—
711C4×D3—44no—
712C4×D3—44no—
713C4×D3—44no—
714C2×C32—81no—
715C2×C32C2×#12111yescharacteristic
716C2×C32#53211yescharacteristic
717C2×C32#53411yescharacteristic
718C2×C32#54611yescharacteristic
719C2×C32#54611yescharacteristic
720C2×C32#55311yescharacteristic
721C2×C32#55311yescharacteristic
722C3×D3—24no—
723C3×D3—42no—
724C3×D3—81no—
725C24—31no—
726C24—31no—
727C24—31no—
728C24C22×C3×D311yescharacteristic
729C2×D4—34no—
730C2×D4—62no—
731C2×D4—62no—
732C2×D4—62no—
733C2×D4—62no—
734C2×D4—62no—
735C2×D4—62no—
736C2×D4—62no—
737C2×D4—62no—
738C2×D4—62no—
739C2×D4—62no—
740C2×D4—62no—
741C2×D4—62no—
742C2×D4—62no—
743C2×D4—121no—
744C2×D4—121no—
745C2×D4—121no—
746C2×D4—121no—
747C22×C4—31no—
748C22×C4—31no—
749C22×C4—34no—
750C22×C4—31no—
751C22×C4—31no—
752C22×C4—31no—
753C22×C4—62no—
754C22×C4—62no—
755C22×C4—62no—
756C22×C4—62no—
757C22×C4—62no—
758C22×C4—121no—
759C22×C4—121no—
760C22×C4—121no—
761C22×C4—121no—
762C22×C4—121no—
763C22×C4—121no—
764C22×C4C22×C3×D311yescharacteristic
765C22×C4C22×C3×D311yescharacteristic
766C22×C4C22×C3×D311yescharacteristic
767C22×C4C22×C3×D311yescharacteristic
768C22×C4C22×C3×D311yescharacteristic
769C22×C4C22×C3×D311yescharacteristic
770C4⋊C4—22no—
771C4⋊C4—62no—
772C4⋊C4—62no—
773C4⋊C4—62no—
774C22⋊C4—22no—
775C22⋊C4—22no—
776C22⋊C4—22no—
777C22⋊C4—62no—
778C22⋊C4—62no—
779C22⋊C4—62no—
780C22⋊C4—62no—
781C22⋊C4—62no—
782C22⋊C4—62no—
783C22⋊C4—62no—
784C22⋊C4—121no—
785C22⋊C4—121no—
786C42—22no—
787C22×C3—21no—
788C22×C3—21no—
789C22×C3—21no—
790C22×C3—21no—
791C22×C3—21no—
792C22×C3—21no—
793C22×C3—21no—
794C22×C3—34no—
795C22×C3—42no—
796C22×C3—42no—
797C22×C3—42no—
798C22×C3—41no—
799C22×C3—41no—
800C22×C3—41no—
801C22×C3—41no—
802C22×C3—41no—
803C22×C3—41no—
804C22×C3—41no—
805C22×C3—41no—
806C22×C3—41no—
807C22×C3—41no—
808C22×C3—41no—
809C22×C3—41no—
810C22×C3—41no—
811C22×C3—41no—
812C22×C3—62no—
813C22×C3—62no—
814C22×C3—62no—
815C22×C3—62no—
816C22×C3—62no—
817C22×C3—62no—
818C22×C3—62no—
819C22×C3—62no—
820C22×C3—62no—
821C22×C3—81no—
822C22×C3—81no—
823C22×C3—81no—
824C22×C3—81no—
825C22×C3—121no—
826C22×C3—121no—
827C22×C3—121no—
828C22×C3—121no—
829C22×C3—121no—
830C22×C3—121no—
831C22×C3—121no—
832C22×C3—121no—
833C22×C3—121no—
834C22×C3—121no—
835C22×C3—121no—
836C22×C3C2×#23511yescharacteristic
837C22×C3C2×D3×D411yescharacteristic
838C22×C3C2×D3×D411yescharacteristic
839C22×C3D3×#4111yescharacteristic
840C22×C3D3×#4111yescharacteristic
841C22×C3#100911yescharacteristic
842C22×C3#100911yescharacteristic
843C22×C3C22×C3×D411yescharacteristic
844C22×C3C22×C3×D411yescharacteristic
845C22×C3C2×C3×#4111yescharacteristic
846C22×C3C2×C3×#4111yescharacteristic
847C22×C3C2×C3×#4111yescharacteristic
848C22×C3C3×H(5,𝔽2)11yescharacteristic
849C22×C3C3×H(5,𝔽2)11yescharacteristic
850C2×D3—22no—
851C2×D3—22no—
852C2×D3—22no—
853C2×D3—22no—
854C2×D3—22no—
855C2×D3—22no—
856C2×D3—22no—
857C2×D3—22no—
858C2×D3—22no—
859C2×D3—41no—
860C2×D3—41no—
861C2×D3—41no—
862C2×D3—41no—
863C2×D3—41no—
864C2×D3—41no—
865C2×D3—41no—
866C2×D3—41no—
867C2×D3—41no—
868C2×D3—41no—
869C2×D3—41no—
870C2×D3C3×#12114yes—
871C3×C4—22no—
872C3×C4—22no—
873C3×C4—22no—
874C3×C4—22no—
875C3×C4—22no—
876C3×C4—22no—
877C3×C4—42no—
878C3×C4—42no—
879C3×C4—42no—
880C3×C4—42no—
881C3×C4—41no—
882C3×C4—41no—
883C3×C4—41no—
884C3×C4—41no—
885C3×C4—41no—
886C3×C4—41no—
887C3×C4—62no—
888C3×C4—62no—
889C3×C4—81no—
890C3×C4—81no—
891C3×C4—121no—
892C3×C4—121no—
893C3×C4—121no—
894Dic3—22no—
895Dic3—22no—
896Dic3—41no—
897Dic3—41no—
898Dic3—41no—
899C32#254311yescharacteristic, complemented, Sylow
900C23—21no—
901C23—21no—
902C23—21no—
903C23—21no—
904C23—21no—
905C23—21no—
906C23—21no—
907C23—32no—
908C23—32no—
909C23—32no—
910C23—32no—
911C23—61no—
912C23—61no—
913C23—61no—
914C23—61no—
915C23—61no—
916C23—61no—
917C23—61no—
918C23—61no—
919C23—61no—
920C23—61no—
921C23—61no—
922C23—61no—
923C23—61no—
924C23—61no—
925C23—61no—
926C23—61no—
927C23—61no—
928C23C23×C3×D311yescharacteristic
929D4—68no—
930D4—124no—
931D4—124no—
932D4—124no—
933D4—124no—
934D4—124no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—21no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—32no—
951C2×C4—32no—
952C2×C4—61no—
953C2×C4—61no—
954C2×C4—61no—
955C2×C4—61no—
956C2×C4—61no—
957C2×C4—61no—
958C2×C4—61no—
959C2×C4—61no—
960C2×C4—61no—
961C2×C4—61no—
962C2×C4—61no—
963C2×C4—61no—
964C2×C4—61no—
965C2×C4—124no—
966C2×C4—124no—
967C2×C4—124no—
968C2×C4—124no—
969C2×C4C3×#23512yes—
970C2×C4C3×D3×D412yes—
971C2×C4C3×D3×D412yes—
972C2×C3—21no—
973C2×C3—21no—
974C2×C3—21no—
975C2×C3—21no—
976C2×C3—21no—
977C2×C3—21no—
978C2×C3—21no—
979C2×C3—64no—
980C2×C3—82no—
981C2×C3—81no—
982C2×C3—81no—
983C2×C3—122no—
984C2×C3—241no—
985C2×C3#553011yescharacteristic
986C2×C3#554811yescharacteristic
987C2×C3#555011yescharacteristic
988C2×C3D3×#12111yescharacteristic
989C2×C3#565311yescharacteristic
990C2×C3#567611yescharacteristic
991C2×C3#570911yescharacteristic
992C2×C3C2×C3×#12111yescharacteristic
993C2×C3C3×#53211yescharacteristic
994C2×C3C3×#53411yescharacteristic
995C2×C3C3×#54611yescharacteristic
996C2×C3C3×#54611yescharacteristic
997C2×C3C3×#55311yescharacteristic
998C2×C3C3×#55311yescharacteristic
999D3—24no—
1000D3—42no—
1001D3—81no—
1002C22—34no—
1003C22—41no—
1004C22—41no—
1005C22—41no—
1006C22—41no—
1007C22—41no—
1008C22—41no—
1009C22—41no—
1010C22—62no—
1011C22—62no—
1012C22—62no—
1013C22—62no—
1014C22—62no—
1015C22—62no—
1016C22—62no—
1017C22—62no—
1018C22—62no—
1019C22—121no—
1020C22—121no—
1021C22—121no—
1022C22—121no—
1023C22—121no—
1024C22—121no—
1025C22—121no—
1026C22—121no—
1027C22—121no—
1028C22—121no—
1029C22—121no—
1030C22C2×C3×#23511yescharacteristic
1031C22C2×C3×D3×D411yescharacteristic
1032C22C2×C3×D3×D411yescharacteristic
1033C22C3×D3×#4111yescharacteristic
1034C22C3×D3×#4111yescharacteristic
1035C22C3×#100911yescharacteristic
1036C22C3×#100911yescharacteristic
1037C4—22no—
1038C4—22no—
1039C4—22no—
1040C4—41no—
1041C4—41no—
1042C4—41no—
1043C4—62no—
1044C4—62no—
1045C4—121no—
1046C4—121no—
1047C4—121no—
1048C3—21no—
1049C3#7588211yescharacteristic, direct product factor
1050C3C3×#254311yescharacteristic, complemented
1051C2—64no—
1052C2—81no—
1053C2—122no—
1054C2—241no—
1055C2C3×#553011yescharacteristic
1056C2C3×#554811yescharacteristic
1057C2C3×#555011yescharacteristic
1058C2C3×D3×#12111yescharacteristic
1059C2C3×#565311yescharacteristic
1060C2C3×#567611yescharacteristic
1061C2C3×#570911yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC32×#388C2
socleC23×C32C24
hypercenterC3×#388D3
hypocenterC3C3×#2543
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#388

Complements

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

NH ≅ G/Ntype
1. C2×C3×#895C2semidirect
2. C2×C3×#884C2semidirect
3. C2×C3×#884C2semidirect
4. C2×C3×C4×D12C2semidirect
5. C32×#388C2semidirect
6. C3×#4982C2semidirect
7. C3×#4961C2semidirect
8. C3×#4960C2semidirect
9. C3×#4956C2semidirect
10. C3×#4956C2semidirect
11. C3×#4940C2semidirect
12. C3×#4675C2semidirect
13. C3×#4665C2semidirect
14. C3×#4665C2semidirect
15. C3×D3×#95C2semidirect
17. #75882C3direct (N × H)
61. C2×#895C2×C3semidirect
62. C2×#884C2×C3semidirect
63. C2×#884C2×C3semidirect
64. C2×C4×D12C2×C3semidirect
71. C3×#388D3semidirect
72. C3×#388C2×C3semidirect
78. #4982C2×C3semidirect
79. #4961C2×C3semidirect
80. #4960C2×C3semidirect
81. #4956C2×C3semidirect
82. #4956C2×C3semidirect
83. #4940C2×C3semidirect
84. #4675C2×C3semidirect
85. #4665C2×C3semidirect
86. #4665C2×C3semidirect
87. D3×#95C2×C3semidirect
120. C2×C3×D12D4semidirect
132. C2×C3×C4×D3D4semidirect
317. #388C3×D3semidirect
407. C2×D12C3×D4semidirect
419. C2×C4×D3C3×D4semidirect
899. C32#2543semidirect
1049. C3#75882direct (N × H)
1050. C3C3×#2543semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8952
C2×C3×#8842
C2×C3×C4×D122
C32×#3882
C3×#49822
C3×#49612
C3×#49602
C3×#49562
C3×#49402
C3×#46752
C3×#46652
C3×D3×#952
C3×#25433
#758823