Finite Group Databasebeta

← C3×#74902 #11824535

Subgroups — C3×#74902 #11824535

Order 1152.

1591 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×#938C211yesmaximal, characteristic, complemented
2C2×C3×C4×#67C211yesmaximal, characteristic, complemented
3C2×C3×#884C211yesmaximal, characteristic, complemented
4C2×C3×#884C211yesmaximal, characteristic, complemented
5C32×#386C211yesmaximal, characteristic, complemented
6C3×#5223C211yesmaximal, characteristic, complemented
7C3×#5213C211yesmaximal, characteristic, complemented
8C3×#4959C211yesmaximal, characteristic, complemented
9C3×#4956C211yesmaximal, characteristic, complemented
10C3×#4952C211yesmaximal, characteristic, complemented
11C3×#4944C211yesmaximal, characteristic, complemented
12C3×#4670C211yesmaximal, characteristic, complemented
13C3×#4665C211yesmaximal, characteristic, complemented
14C3×D3×#95C211yesmaximal, characteristic, complemented
15C3×#4657C211yesmaximal, characteristic, complemented
16C3×#2543—31nomaximal
17#74902C311yesmaximal, characteristic, direct product factor
18C22×C32×D4C2211yescharacteristic
19C23×C32×C4C2211yescharacteristic
20C22×C3×#67C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic
24C22×C3×D12C2211yescharacteristic
25C22×C3×C4×D3C2211yescharacteristic
26C22×C3×C4×D3C2211yescharacteristic
27C22×C3×C4×D3C2211yescharacteristic
28C2×C32×C22⋊C4C2211yescharacteristic
29C2×C32×C22⋊C4C2211yescharacteristic
30C2×C32×C22⋊C4C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×#217C2211yescharacteristic
33C2×C3×#217C2211yescharacteristic
34C2×C3×#217C2211yescharacteristic
35C3×#938—24no—
36C3×C4×#67—24no—
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
45C2×C3×Dic3⋊C4C2211yescharacteristic
46C2×C3×C4×Dic3C2211yescharacteristic
47C3×#884—24no—
48C3×#884—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×#938C2×C311yescharacteristic, complemented
62C2×C4×#67C2×C311yescharacteristic, complemented
63C2×#884C2×C311yescharacteristic, complemented
64C2×#884C2×C311yescharacteristic, complemented
65C3×#398—31no—
66C3×#397—31no—
67C3×#394—31no—
68C3×#392—31no—
69C3×#388—31no—
70C3×#388—31no—
71C3×#386—21no—
72C3×#386—31no—
73C3×#386—31no—
74C3×#386—31no—
75C3×#386D311yescharacteristic, complemented
76C3×#386C2×C311yescharacteristic, complemented
77C2×C3×#95—31no—
78#5223C2×C311yescharacteristic, complemented
79#5213C2×C311yescharacteristic, complemented
80#4959C2×C311yescharacteristic, complemented
81#4956C2×C311yescharacteristic, complemented
82#4952C2×C311yescharacteristic, complemented
83#4944C2×C311yescharacteristic, complemented
84#4670C2×C311yescharacteristic, complemented
85#4665C2×C311yescharacteristic, complemented
86D3×#95C2×C311yescharacteristic, complemented
87#4657C2×C311yescharacteristic, complemented
88C24×C32C2311yescharacteristic
89C24×C32C2311yescharacteristic
90C23×C3×D3C2311yescharacteristic
91C23×C3×D3C2311yescharacteristic
92C2×C32×D4—22no—
93C2×C32×D4—22no—
94C2×C32×D4—41no—
95C22×C32×C4—22no—
96C22×C32×C4—41no—
97C22×C32×C4—41no—
98C22×C32×C4C2311yescharacteristic
99C22×C32×C4C2311yescharacteristic
100C22×C32×C4C2311yescharacteristic
101C22×C32×C4C2311yescharacteristic
102C22×C32×C4C2311yescharacteristic
103C2×C3×#67—22no—
104C2×C3×#67—22no—
105C2×C3×#67—22no—
106C2×C3×#67—22no—
107C2×C3×#67—22no—
108C2×C3×#67—22no—
109C2×C3×#67—22no—
110C2×C3×#67—22no—
111C2×C3×#67—41no—
112C2×C3×#67—41no—
113C2×C3×#67—41no—
114C2×C3×#67D414yescomplemented
115C22×C3×Dic3C2311yescharacteristic
116C22×C3×Dic3C2311yescharacteristic
117C22×C3×Dic3C2311yescharacteristic
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C2×C3×D12—22no—
122C2×C3×D12—22no—
123C2×C3×D12—22no—
124C2×C3×C4×D3—22no—
125C2×C3×C4×D3—22no—
126C2×C3×C4×D3—22no—
127C2×C3×C4×D3—22no—
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×C22⋊C4—22no—
134C32×C22⋊C4—22no—
135C32×C22⋊C4—41no—
136C3×#217—22no—
137C3×#217—22no—
138C3×#217—22no—
139C3×#217—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×C4⋊Dic3—22no—
146C3×Dic3⋊C4—22no—
147C3×Dic3⋊C4—22no—
148C3×Dic3⋊C4—22no—
149C3×C4×Dic3—22no—
150#2543—31noSylow
151C22×C3×D4—21no—
152C22×C3×D4—31no—
153C22×C3×D4—31no—
154C22×C3×D4—31no—
155C22×C3×D4—31no—
156C22×C3×D4—31no—
157C22×C3×D4C2×D311yescharacteristic
158C22×C3×D4C22×C311yescharacteristic
159C23×C3×C4—21no—
160C23×C3×C4—31no—
161C23×C3×C4—31no—
162C23×C3×C4—31no—
163C23×C3×C4C2×D311yescharacteristic
164C23×C3×C4C22×C311yescharacteristic
165C22×#67C22×C311yescharacteristic
166C22×#67C22×C311yescharacteristic
167C22×#67C22×C311yescharacteristic
168C22×#67C22×C311yescharacteristic
169C22×D12C22×C311yescharacteristic
170C22×C4×D3C22×C311yescharacteristic
171C22×C4×D3C22×C311yescharacteristic
172C22×C4×D3C22×C311yescharacteristic
173C3×#121—64no—
174C3×#121—64no—
175C3×#121—64no—
176C3×C4×D4—64no—
177C2×C3×C4⋊C4—31no—
178C2×C3×C4⋊C4—31no—
179C2×C3×C4⋊C4—31no—
180C2×C3×C4⋊C4—31no—
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—31no—
200C2×#217C22×C311yescharacteristic
201C2×#217C22×C311yescharacteristic
202C2×#217C22×C311yescharacteristic
203C2×#217C22×C311yescharacteristic
204#938—24no—
205C4×#67—24no—
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
214C2×Dic3⋊C4C22×C311yescharacteristic
215C2×C4×Dic3C22×C311yescharacteristic
216#884—24no—
217#884—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×C32—21no—
244C23×C32—21no—
245C23×C32—21no—
246C23×C32—21no—
247C23×C32—21no—
248C23×C32—21no—
249C23×C32C2×D412yes—
250C23×C32C2411yescharacteristic
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—21no—
262C22×C3×D3C2×D412yes—
263C22×C3×D3C2×D412yes—
264C22×C3×D3#4112yes—
265C32×D4—44no—
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—44no—
280C2×C32×C4C2×D412yes—
281C2×C32×C4#4112yes—
282C3×#67—28no—
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×Dic3—21no—
300C2×C3×Dic3—21no—
301C2×C3×Dic3C2×D412yes—
302C2×C3×Dic3C2×D412yes—
303C2×C3×Dic3#4112yes—
304C3×D12—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#388—31no—
318#386—31no—
319#386—31no—
320#386—31no—
321#386C3×D311yescharacteristic, complemented
322C2×#95—31no—
323C24×C3—21no—
324C24×C3—21no—
325C24×C3—31no—
326C24×C3—31no—
327C24×C3C22×D311yescharacteristic
328C24×C3C22×D311yescharacteristic
329C24×C3C23×C311yescharacteristic
330C24×C3C23×C311yescharacteristic
331C23×D3C23×C311yescharacteristic
332C23×D3C23×C311yescharacteristic
333C2×C3×D4—24no—
334C2×C3×D4—22no—
335C2×C3×D4—22no—
336C2×C3×D4—22no—
337C2×C3×D4—22no—
338C2×C3×D4—34no—
339C2×C3×D4—42no—
340C2×C3×D4—41no—
341C2×C3×D4—41no—
342C2×C3×D4—42no—
343C2×C3×D4—62no—
344C2×C3×D4—62no—
345C2×C3×D4—62no—
346C2×C3×D4—62no—
347C2×C3×D4—62no—
348C2×C3×D4—62no—
349C2×C3×D4—62no—
350C2×C3×D4—62no—
351C2×C3×D4—62no—
352C2×C3×D4—62no—
353C2×C3×D4—62no—
354C2×C3×D4—121no—
355C2×C3×D4—121no—
356C2×C3×D4—121no—
357C22×C3×C4—22no—
358C22×C3×C4—22no—
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—34no—
368C22×C3×C4—31no—
369C22×C3×C4—31no—
370C22×C3×C4—31no—
371C22×C3×C4—42no—
372C22×C3×C4—41no—
373C22×C3×C4—41no—
374C22×C3×C4—41no—
375C22×C3×C4—41no—
376C22×C3×C4—42no—
377C22×C3×C4—42no—
378C22×C3×C4—62no—
379C22×C3×C4—62no—
380C22×C3×C4—62no—
381C22×C3×C4—62no—
382C22×C3×C4—121no—
383C22×C3×C4—121no—
384C22×C3×C4—121no—
385C22×C3×C4—121no—
386C22×C3×C4C22×D311yescharacteristic
387C22×C3×C4C22×D311yescharacteristic
388C22×C3×C4C22×D311yescharacteristic
389C22×C3×C4C22×D311yescharacteristic
390C22×C3×C4C22×D311yescharacteristic
391C22×C3×C4C23×C311yescharacteristic
392C22×C3×C4C23×C311yescharacteristic
393C22×C3×C4C23×C311yescharacteristic
394C22×C3×C4C23×C311yescharacteristic
395C22×C3×C4C23×C311yescharacteristic
396C2×#67—22no—
397C2×#67—22no—
398C2×#67—22no—
399C2×#67—22no—
400C2×#67—22no—
401C2×#67—22no—
402C2×#67—22no—
403C2×#67—22no—
404C2×#67—41no—
405C2×#67—41no—
406C2×#67—41no—
407C2×#67C3×D414yescomplemented
408C22×Dic3C23×C311yescharacteristic
409C22×Dic3C23×C311yescharacteristic
410C22×Dic3C23×C311yescharacteristic
411C22×Dic3C23×C311yescharacteristic
412C22×Dic3C23×C311yescharacteristic
413C22×Dic3C23×C311yescharacteristic
414C2×D12—22no—
415C2×D12—22no—
416C2×D12—22no—
417C2×C4×D3—22no—
418C2×C4×D3—22no—
419C2×C4×D3—22no—
420C2×C4×D3—22no—
421C2×C4×D3—41no—
422C2×C4×D3—41no—
423C2×C4×D3—41no—
424C2×C4×D3—41no—
425C2×C4×D3C3×D414yescomplemented
426C3×C4⋊C4—62no—
427C3×C4⋊C4—62no—
428C3×C4⋊C4—62no—
429C3×C4⋊C4—62no—
430C3×C22⋊C4—22no—
431C3×C22⋊C4—22no—
432C3×C22⋊C4—22no—
433C3×C22⋊C4—22no—
434C3×C22⋊C4—42no—
435C3×C22⋊C4—42no—
436C3×C22⋊C4—41no—
437C3×C22⋊C4—41no—
438C3×C22⋊C4—42no—
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—62no—
447C3×C22⋊C4—121no—
448C3×C42—62no—
449#217—22no—
450#217—22no—
451#217—22no—
452#217—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—
458C4⋊Dic3—22no—
459Dic3⋊C4—22no—
460Dic3⋊C4—22no—
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×C32—41no—
471C22×C32—41no—
472C22×C32—41no—
473C22×C32—41no—
474C22×C32—41no—
475C22×C32—41no—
476C22×C32—41no—
477C22×C32C22×D411yescharacteristic
478C22×C32C22×D411yescharacteristic
479C22×C32C2×#4111yescharacteristic
480C22×C32C2×#4111yescharacteristic
481C22×C32C2×#4111yescharacteristic
482C22×C32H(5,𝔽2)11yescharacteristic
483C22×C32H(5,𝔽2)11yescharacteristic
484C2×C3×D3—22no—
485C2×C3×D3—22no—
486C2×C3×D3—22no—
487C2×C3×D3—22no—
488C2×C3×D3—22no—
489C2×C3×D3—22no—
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#12114yes—
498C32×C4—22no—
499C32×C4—22no—
500C32×C4—41no—
501C32×C4—41no—
502C32×C4—41no—
503C3×Dic3—22no—
504C3×Dic3—22no—
505C3×Dic3—22no—
506C3×Dic3—41no—
507C3×Dic3—41no—
508C3×Dic3—41no—
509C22×D4—31no—
510C22×D4—31no—
511C22×D4—31no—
512C22×D4—31no—
513C22×D4—31no—
514C22×D4C2×C3×D311yescharacteristic
515C23×C4—31no—
516C23×C4—31no—
517C23×C4—31no—
518C23×C4C2×C3×D311yescharacteristic
519#121—64no—
520#121—64no—
521#121—64no—
522C4×D4—64no—
523C2×C4⋊C4—31no—
524C2×C4⋊C4—31no—
525C2×C4⋊C4—31no—
526C2×C4⋊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⋊C4C2×C3×D311yescharacteristic
537C2×C22⋊C4C2×C3×D311yescharacteristic
538C2×C22⋊C4C2×C3×D311yescharacteristic
539C2×C42—31no—
540#95—31no—
541#95—31no—
542#95—31no—
543#95—31no—
544#95—31no—
545#95—31no—
546#95C2×C3×D311yescharacteristic
547#95C2×C3×D311yescharacteristic
548C23×C3—22no—
549C23×C3—22no—
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—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—22no—
579C23×C3—32no—
580C23×C3—32no—
581C23×C3—32no—
582C23×C3—41no—
583C23×C3—41no—
584C23×C3—41no—
585C23×C3—41no—
586C23×C3—41no—
587C23×C3—41no—
588C23×C3—41no—
589C23×C3—41no—
590C23×C3—41no—
591C23×C3—41no—
592C23×C3—61no—
593C23×C3—61no—
594C23×C3—61no—
595C23×C3—61no—
596C23×C3—61no—
597C23×C3—61no—
598C23×C3—61no—
599C23×C3—61no—
600C23×C3—61no—
601C23×C3—61no—
602C23×C3—61no—
603C23×C3D3×D412yes—
604C23×C3C2×C3×D412yes—
605C23×C3C23×D311yescharacteristic
606C23×C3C24×C311yescharacteristic
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×D3C2×C3×D412yes—
619C22×D3C2×C3×D412yes—
620C22×D3C3×#4112yes—
621C3×D4—44no—
622C3×D4—44no—
623C3×D4—48no—
624C3×D4—68no—
625C3×D4—124no—
626C3×D4—124no—
627C3×D4—124no—
628C3×D4—124no—
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—22no—
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—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—22no—
657C2×C3×C4—22no—
658C2×C3×C4—32no—
659C2×C3×C4—32no—
660C2×C3×C4—32no—
661C2×C3×C4—41no—
662C2×C3×C4—41no—
663C2×C3×C4—41no—
664C2×C3×C4—41no—
665C2×C3×C4—41no—
666C2×C3×C4—41no—
667C2×C3×C4—41no—
668C2×C3×C4—41no—
669C2×C3×C4—41no—
670C2×C3×C4—41no—
671C2×C3×C4—41no—
672C2×C3×C4—41no—
673C2×C3×C4—44no—
674C2×C3×C4—44no—
675C2×C3×C4—48no—
676C2×C3×C4—61no—
677C2×C3×C4—61no—
678C2×C3×C4—61no—
679C2×C3×C4—61no—
680C2×C3×C4—61no—
681C2×C3×C4—61no—
682C2×C3×C4—61no—
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—124no—
692C2×C3×C4—124no—
693C2×C3×C4—124no—
694C2×C3×C4#23512yes—
695C2×C3×C4D3×D412yes—
696C2×C3×C4C2×C3×D412yes—
697C2×C3×C4C3×#4112yes—
698#67—28no—
699#67—44no—
700#67—44no—
701#67—44no—
702C2×Dic3—21no—
703C2×Dic3—21no—
704C2×Dic3—21no—
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×Dic3C2×C3×D412yes—
718C2×Dic3C2×C3×D412yes—
719C2×Dic3C3×#4112yes—
720D12—44no—
721C4×D3—44no—
722C4×D3—44no—
723C4×D3—44no—
724C2×C32—42no—
725C2×C32—81no—
726C2×C32C2×#12111yescharacteristic
727C2×C32#53211yescharacteristic
728C2×C32#53411yescharacteristic
729C2×C32#54611yescharacteristic
730C2×C32#54611yescharacteristic
731C2×C32#55311yescharacteristic
732C2×C32#55311yescharacteristic
733C3×D3—24no—
734C3×D3—81no—
735C24—31no—
736C24—31no—
737C24C22×C3×D311yescharacteristic
738C24C22×C3×D311yescharacteristic
739C2×D4—22no—
740C2×D4—22no—
741C2×D4—34no—
742C2×D4—41no—
743C2×D4—62no—
744C2×D4—62no—
745C2×D4—62no—
746C2×D4—62no—
747C2×D4—62no—
748C2×D4—62no—
749C2×D4—62no—
750C2×D4—62no—
751C2×D4—62no—
752C2×D4—62no—
753C2×D4—62no—
754C2×D4—121no—
755C2×D4—121no—
756C2×D4—121no—
757C22×C4—22no—
758C22×C4—31no—
759C22×C4—31no—
760C22×C4—31no—
761C22×C4—34no—
762C22×C4—31no—
763C22×C4—31no—
764C22×C4—31no—
765C22×C4—41no—
766C22×C4—41no—
767C22×C4—62no—
768C22×C4—62no—
769C22×C4—62no—
770C22×C4—62no—
771C22×C4—121no—
772C22×C4—121no—
773C22×C4—121no—
774C22×C4—121no—
775C22×C4C22×C3×D311yescharacteristic
776C22×C4C22×C3×D311yescharacteristic
777C22×C4C22×C3×D311yescharacteristic
778C22×C4C22×C3×D311yescharacteristic
779C22×C4C22×C3×D311yescharacteristic
780C4⋊C4—62no—
781C4⋊C4—62no—
782C4⋊C4—62no—
783C4⋊C4—62no—
784C22⋊C4—22no—
785C22⋊C4—22no—
786C22⋊C4—41no—
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—
796C42—62no—
797C22×C3—24no—
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—42no—
816C22×C3—42no—
817C22×C3—42no—
818C22×C3—42no—
819C22×C3—42no—
820C22×C3—42no—
821C22×C3—41no—
822C22×C3—41no—
823C22×C3—41no—
824C22×C3—41no—
825C22×C3—41no—
826C22×C3—41no—
827C22×C3—41no—
828C22×C3—41no—
829C22×C3—41no—
830C22×C3—41no—
831C22×C3—41no—
832C22×C3—41no—
833C22×C3—41no—
834C22×C3—41no—
835C22×C3—41no—
836C22×C3—41no—
837C22×C3—41no—
838C22×C3—41no—
839C22×C3—41no—
840C22×C3—41no—
841C22×C3—41no—
842C22×C3—41no—
843C22×C3—62no—
844C22×C3—62no—
845C22×C3—62no—
846C22×C3—62no—
847C22×C3—62no—
848C22×C3—62no—
849C22×C3—81no—
850C22×C3—81no—
851C22×C3—81no—
852C22×C3—81no—
853C22×C3—121no—
854C22×C3—121no—
855C22×C3—121no—
856C22×C3—121no—
857C22×C3—121no—
858C22×C3—121no—
859C22×C3—121no—
860C22×C3C2×#23511yescharacteristic
861C22×C3C2×D3×D411yescharacteristic
862C22×C3C2×D3×D411yescharacteristic
863C22×C3#100411yescharacteristic
864C22×C3#100411yescharacteristic
865C22×C3D3×#4111yescharacteristic
866C22×C3D3×#4111yescharacteristic
867C22×C3C22×C3×D411yescharacteristic
868C22×C3C22×C3×D411yescharacteristic
869C22×C3C2×C3×#4111yescharacteristic
870C22×C3C2×C3×#4111yescharacteristic
871C22×C3C2×C3×#4111yescharacteristic
872C22×C3C3×H(5,𝔽2)11yescharacteristic
873C22×C3C3×H(5,𝔽2)11yescharacteristic
874C2×D3—22no—
875C2×D3—22no—
876C2×D3—22no—
877C2×D3—22no—
878C2×D3—22no—
879C2×D3—22no—
880C2×D3—41no—
881C2×D3—41no—
882C2×D3—41no—
883C2×D3—41no—
884C2×D3—41no—
885C2×D3—41no—
886C2×D3—41no—
887C2×D3C3×#12114yes—
888C3×C4—22no—
889C3×C4—22no—
890C3×C4—22no—
891C3×C4—22no—
892C3×C4—42no—
893C3×C4—42no—
894C3×C4—42no—
895C3×C4—41no—
896C3×C4—41no—
897C3×C4—41no—
898C3×C4—41no—
899C3×C4—41no—
900C3×C4—41no—
901C3×C4—62no—
902C3×C4—62no—
903C3×C4—62no—
904C3×C4—81no—
905C3×C4—81no—
906C3×C4—121no—
907C3×C4—121no—
908C3×C4—121no—
909Dic3—22no—
910Dic3—22no—
911Dic3—22no—
912Dic3—41no—
913Dic3—41no—
914Dic3—41no—
915C32#254311yescharacteristic, complemented, Sylow
916C23—21no—
917C23—21no—
918C23—21no—
919C23—21no—
920C23—21no—
921C23—21no—
922C23—21no—
923C23—21no—
924C23—21no—
925C23—21no—
926C23—21no—
927C23—21no—
928C23—21no—
929C23—32no—
930C23—32no—
931C23—32no—
932C23—61no—
933C23—61no—
934C23—61no—
935C23—61no—
936C23—61no—
937C23—61no—
938C23—61no—
939C23—61no—
940C23—61no—
941C23—61no—
942C23—61no—
943C23C3×D3×D412yes—
944C23C23×C3×D311yescharacteristic
945D4—44no—
946D4—68no—
947D4—124no—
948D4—124no—
949D4—124no—
950D4—124no—
951C2×C4—21no—
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—32no—
965C2×C4—32no—
966C2×C4—32no—
967C2×C4—44no—
968C2×C4—61no—
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×#23512yes—
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—44no—
996C2×C3—42no—
997C2×C3—42no—
998C2×C3—64no—
999C2×C3—82no—
1000C2×C3—81no—
1001C2×C3—81no—
1002C2×C3—241no—
1003C2×C3#549011yescharacteristic
1004C2×C3#554811yescharacteristic
1005C2×C3#555811yescharacteristic
1006C2×C3#558911yescharacteristic
1007C2×C3D3×#12111yescharacteristic
1008C2×C3#561011yescharacteristic
1009C2×C3#566111yescharacteristic
1010C2×C3C2×C3×#12111yescharacteristic
1011C2×C3C3×#53211yescharacteristic
1012C2×C3C3×#53411yescharacteristic
1013C2×C3C3×#54611yescharacteristic
1014C2×C3C3×#54611yescharacteristic
1015C2×C3C3×#55311yescharacteristic
1016C2×C3C3×#55311yescharacteristic
1017D3—24no—
1018D3—81no—
1019C22—22no—
1020C22—22no—
1021C22—22no—
1022C22—34no—
1023C22—41no—
1024C22—41no—
1025C22—41no—
1026C22—41no—
1027C22—41no—
1028C22—41no—
1029C22—41no—
1030C22—41no—
1031C22—41no—
1032C22—41no—
1033C22—41no—
1034C22—62no—
1035C22—62no—
1036C22—62no—
1037C22—62no—
1038C22—62no—
1039C22—62no—
1040C22—121no—
1041C22—121no—
1042C22—121no—
1043C22—121no—
1044C22—121no—
1045C22—121no—
1046C22—121no—
1047C22C2×C3×#23511yescharacteristic
1048C22C2×C3×D3×D411yescharacteristic
1049C22C2×C3×D3×D411yescharacteristic
1050C22C3×#100411yescharacteristic
1051C22C3×#100411yescharacteristic
1052C22C3×D3×#4111yescharacteristic
1053C22C3×D3×#4111yescharacteristic
1054C4—22no—
1055C4—22no—
1056C4—41no—
1057C4—41no—
1058C4—41no—
1059C4—62no—
1060C4—62no—
1061C4—62no—
1062C4—121no—
1063C4—121no—
1064C4—121no—
1065C3—21no—
1066C3#7490211yescharacteristic, direct product factor
1067C3C3×#254311yescharacteristic, complemented
1068C2—42no—
1069C2—64no—
1070C2—81no—
1071C2—241no—
1072C2C3×#549011yescharacteristic
1073C2C3×#554811yescharacteristic
1074C2C3×#555811yescharacteristic
1075C2C3×#558911yescharacteristic
1076C2C3×D3×#12111yescharacteristic
1077C2C3×#561011yescharacteristic
1078C2C3×#566111yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC32×#386C2
socleC23×C32C24
hypercenterC3×#386D3
hypocenterC3C3×#2543
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#386

Complements

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

NH ≅ G/Ntype
1. C2×C3×#938C2semidirect
2. C2×C3×C4×#67C2semidirect
3. C2×C3×#884C2semidirect
4. C2×C3×#884C2semidirect
5. C32×#386C2semidirect
6. C3×#5223C2semidirect
7. C3×#5213C2semidirect
8. C3×#4959C2semidirect
9. C3×#4956C2semidirect
10. C3×#4952C2semidirect
11. C3×#4944C2semidirect
12. C3×#4670C2semidirect
13. C3×#4665C2semidirect
14. C3×D3×#95C2semidirect
15. C3×#4657C2semidirect
17. #74902C3direct (N × H)
61. C2×#938C2×C3semidirect
62. C2×C4×#67C2×C3semidirect
63. C2×#884C2×C3semidirect
64. C2×#884C2×C3semidirect
75. C3×#386D3semidirect
76. C3×#386C2×C3semidirect
78. #5223C2×C3semidirect
79. #5213C2×C3semidirect
80. #4959C2×C3semidirect
81. #4956C2×C3semidirect
82. #4952C2×C3semidirect
83. #4944C2×C3semidirect
84. #4670C2×C3semidirect
85. #4665C2×C3semidirect
86. D3×#95C2×C3semidirect
87. #4657C2×C3semidirect
114. C2×C3×#67D4semidirect
132. C2×C3×C4×D3D4semidirect
321. #386C3×D3semidirect
407. C2×#67C3×D4semidirect
425. C2×C4×D3C3×D4semidirect
915. C32#2543semidirect
1066. C3#74902direct (N × H)
1067. C3C3×#2543semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9382
C2×C3×C4×#672
C2×C3×#8842
C32×#3862
C3×#52232
C3×#52132
C3×#49592
C3×#49562
C3×#49522
C3×#49442
C3×#46702
C3×#46652
C3×D3×#952
C3×#46572
C3×#25433
#749023