Finite Group Databasebeta

← C3×#74897 #11812956

Subgroups — C3×#74897 #11812956

Order 1152.

1363 conjugacy classes of subgroups.

The subgroup lattice has 976 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#938C211yesmaximal, characteristic
2C2×C3×C4×#67C211yesmaximal, characteristic, complemented
3C32×#386C211yesmaximal, characteristic, complemented
4C3×#5222C211yesmaximal, characteristic, complemented
5C3×#5211C211yesmaximal, characteristic, complemented
6C3×#4956C211yesmaximal, characteristic, complemented
7C3×#4956C211yesmaximal, characteristic, complemented
8C3×#4956C211yesmaximal, characteristic, complemented
9C3×#4953C211yesmaximal, characteristic, complemented
10C3×#4952C211yesmaximal, characteristic, complemented
11C3×#4951C211yesmaximal, characteristic, complemented
12C3×#4668C211yesmaximal, characteristic, complemented
13C3×D3×#95C211yesmaximal, characteristic, complemented
14C3×#4660C211yesmaximal, characteristic, complemented
15C3×#4655C211yesmaximal, characteristic, complemented
16C3×#2444—31nomaximal
17#74897C311yesmaximal, characteristic, direct product factor
18C22×C32×D4C2211yescharacteristic
19C23×C32×C4C2211yescharacteristic
20C22×C3×#67C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×C3×C4×D3C2211yescharacteristic
24C22×C3×C4×D3C2211yescharacteristic
25C2×C32×C22⋊C4C2211yescharacteristic
26C2×C32×C22⋊C4C2211yescharacteristic
27C2×C32×C22⋊C4C2211yescharacteristic
28C2×C3×#217C2211yescharacteristic
29C2×C3×#217C2211yescharacteristic
30C2×C3×#217C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×#217C2211yescharacteristic
33C2×C3×#217C2211yescharacteristic
34C3×#938—24no—
35C3×C4×#67—24no—
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×C4⋊Dic3C2211yescharacteristic
39C2×C3×C4⋊Dic3C2211yescharacteristic
40C2×C3×Dic3⋊C4C2211yescharacteristic
41C2×C3×Dic3⋊C4C2211yescharacteristic
42C2×C3×C4×Dic3C2211yescharacteristic
43C32×#95C2211yescharacteristic
44C32×#95C2211yescharacteristic
45C3×C3⋊#95C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53C3×C3⋊#95C2211yescharacteristic
54C3×C3⋊#95C2211yescharacteristic
55C2×C3×#121—31no—
56C2×C3×C4×D4—31no—
57C2×#938C2×C311yescharacteristic
58C2×C4×#67C2×C311yescharacteristic, complemented
59C3×#400—31no—
60C3×#397—31no—
61C3×#397—31no—
62C3×#394—31no—
63C3×#388—31no—
64C3×#387—31no—
65C3×#386—21no—
66C3×#386—31no—
67C3×#386—31no—
68C3×#386—31no—
69C3×#386D311yescharacteristic, complemented
70C3×#386C2×C311yescharacteristic, complemented
71C3×#385—31no—
72C3×#381—31no—
73C2×C3×#95—31no—
74#5222C2×C311yescharacteristic, complemented
75#5211C2×C311yescharacteristic, complemented
76#4956C2×C311yescharacteristic, complemented
77#4956C2×C311yescharacteristic, complemented
78#4956C2×C311yescharacteristic, complemented
79#4953C2×C311yescharacteristic, complemented
80#4952C2×C311yescharacteristic, complemented
81#4951C2×C311yescharacteristic, complemented
82#4668C2×C311yescharacteristic, complemented
83D3×#95C2×C311yescharacteristic, complemented
84#4660C2×C311yescharacteristic, complemented
85#4655C2×C311yescharacteristic, complemented
86C24×C32C2311yescharacteristic
87C24×C32C2311yescharacteristic
88C23×C3×D3C2311yescharacteristic
89C2×C32×D4—22no—
90C2×C32×D4—22no—
91C2×C32×D4—41no—
92C22×C32×C4—22no—
93C22×C32×C4—22no—
94C22×C32×C4—41no—
95C22×C32×C4C2311yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C22×C32×C4C2311yescharacteristic
98C22×C32×C4C2311yescharacteristic
99C22×C32×C4C2311yescharacteristic
100C2×C3×#67—22no—
101C2×C3×#67—22no—
102C2×C3×#67—22no—
103C2×C3×#67—22no—
104C2×C3×#67—22no—
105C2×C3×#67D414yes—
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C2×C3×C4×D3—22no—
114C2×C3×C4×D3—22no—
115C2×C3×C4×D3—22no—
116C2×C3×C4×D3—22no—
117C2×C3×C4×D3—22no—
118C2×C3×C4×D3—41no—
119C2×C3×C4×D3—41no—
120C2×C3×C4×D3—41no—
121C2×C3×C4×D3—41no—
122C32×C22⋊C4—22no—
123C32×C22⋊C4—41no—
124C32×C22⋊C4—41no—
125C3×#217—22no—
126C3×#217—22no—
127C3×#217—22no—
128C3×#217—41no—
129C3×#217—41no—
130C3×#217—41no—
131C3×(C2×D3)⋊C4—22no—
132C3×(C2×D3)⋊C4—22no—
133C3×C4⋊Dic3—22no—
134C3×C4⋊Dic3—41no—
135C3×Dic3⋊C4—22no—
136C3×Dic3⋊C4—22no—
137C3×C4×Dic3—22no—
138#2444—31noSylow
139C22×C3×D4—21no—
140C22×C3×D4—31no—
141C22×C3×D4—31no—
142C22×C3×D4C2×D311yescharacteristic
143C22×C3×D4C22×C311yescharacteristic
144C23×C3×C4—21no—
145C23×C3×C4—31no—
146C23×C3×C4—31no—
147C23×C3×C4—31no—
148C23×C3×C4C2×D311yescharacteristic
149C23×C3×C4C22×C311yescharacteristic
150C22×#67C22×C311yescharacteristic
151C22×#67C22×C311yescharacteristic
152C22×C4×D3C22×C311yescharacteristic
153C22×C4×D3C22×C311yescharacteristic
154C22×C4×D3C22×C311yescharacteristic
155C3×#121—64no—
156C3×C4×D4—64no—
157C2×C3×C4⋊C4—31no—
158C2×C3×C4⋊C4—31no—
159C2×C3×C4⋊C4—31no—
160C2×C3×C4⋊C4—31no—
161C2×C3×C22⋊C4—21no—
162C2×C3×C22⋊C4—21no—
163C2×C3×C22⋊C4—21no—
164C2×C3×C22⋊C4—31no—
165C2×C3×C22⋊C4—31no—
166C2×C3×C22⋊C4—31no—
167C2×C3×C22⋊C4—31no—
168C2×C3×C22⋊C4—31no—
169C2×C3×C22⋊C4—31no—
170C2×C3×C22⋊C4—31no—
171C2×C3×C22⋊C4—31no—
172C2×C3×C22⋊C4C2×D311yescharacteristic
173C2×C3×C22⋊C4C2×D311yescharacteristic
174C2×C3×C22⋊C4C2×D311yescharacteristic
175C2×C3×C22⋊C4C22×C311yescharacteristic
176C2×C3×C22⋊C4C22×C311yescharacteristic
177C2×C3×C22⋊C4C22×C311yescharacteristic
178C2×C3×C42—31no—
179C2×#217C22×C311yescharacteristic
180C2×#217C22×C311yescharacteristic
181C2×#217C22×C311yescharacteristic
182C2×#217C22×C311yescharacteristic
183C2×#217C22×C311yescharacteristic
184C2×#217C22×C311yescharacteristic
185#938—24no—
186C4×#67—24no—
187C2×(C2×D3)⋊C4C22×C311yescharacteristic
188C2×(C2×D3)⋊C4C22×C311yescharacteristic
189C2×C4⋊Dic3C22×C311yescharacteristic
190C2×C4⋊Dic3C22×C311yescharacteristic
191C2×Dic3⋊C4C22×C311yescharacteristic
192C2×Dic3⋊C4C22×C311yescharacteristic
193C2×C4×Dic3C22×C311yescharacteristic
194C3×#95—21no—
195C3×#95—21no—
196C3×#95—31no—
197C3×#95—31no—
198C3×#95—31no—
199C3×#95—31no—
200C3×#95—31no—
201C3×#95—31no—
202C3×#95—31no—
203C3×#95—31no—
204C3×#95—31no—
205C3×#95—31no—
206C3×#95C2×D311yescharacteristic
207C3×#95C2×D311yescharacteristic
208C3×#95C22×C311yescharacteristic
209C3×#95C22×C311yescharacteristic
210C3⋊#95C22×C311yescharacteristic
211C3⋊#95C22×C311yescharacteristic
212C3⋊#95C22×C311yescharacteristic
213C3⋊#95C22×C311yescharacteristic
214C3⋊#95C22×C311yescharacteristic
215C3⋊#95C22×C311yescharacteristic
216C3⋊#95C22×C311yescharacteristic
217C3⋊#95C22×C311yescharacteristic
218C3⋊#95C22×C311yescharacteristic
219C3⋊#95C22×C311yescharacteristic
220C23×C32—21no—
221C23×C32—21no—
222C23×C32—21no—
223C23×C32—21no—
224C23×C32—21no—
225C23×C32—21no—
226C23×C32—21no—
227C23×C32—21no—
228C23×C32—21no—
229C23×C32—21no—
230C23×C32—21no—
231C23×C32—21no—
232C23×C32—21no—
233C23×C32C2×D412yes—
234C23×C32C2411yescharacteristic
235C22×C3×D3—21no—
236C22×C3×D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3—21no—
239C22×C3×D3C2×D412yes—
240C22×C3×D3#4112yes—
241C22×C3×D3#4112yes—
242C32×D4—44no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—44no—
257C2×C32×C4#4112yes—
258C2×C32×C4#4112yes—
259C3×#67—28no—
260C3×#67—44no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3C2×D412yes—
282C3×C4×D3—44no—
283C3×C4×D3—44no—
284C3×C4×D3—44no—
285C2×#121—31no—
286C2×C4×D4—31no—
287#400—31no—
288#397—31no—
289#397—31no—
290#394—31no—
291#388—31no—
292#387—31no—
293#386—31no—
294#386—31no—
295#386—31no—
296#386C3×D311yescharacteristic, complemented
297#385—31no—
298#381—31no—
299C2×#95—31no—
300C24×C3—21no—
301C24×C3—21no—
302C24×C3—31no—
303C24×C3C22×D311yescharacteristic
304C24×C3C22×D311yescharacteristic
305C24×C3C23×C311yescharacteristic
306C24×C3C23×C311yescharacteristic
307C23×D3C23×C311yescharacteristic
308C2×C3×D4—24no—
309C2×C3×D4—22no—
310C2×C3×D4—22no—
311C2×C3×D4—22no—
312C2×C3×D4—22no—
313C2×C3×D4—34no—
314C2×C3×D4—42no—
315C2×C3×D4—41no—
316C2×C3×D4—41no—
317C2×C3×D4—42no—
318C2×C3×D4—62no—
319C2×C3×D4—62no—
320C2×C3×D4—62no—
321C2×C3×D4—62no—
322C2×C3×D4—62no—
323C22×C3×C4—22no—
324C22×C3×C4—22no—
325C22×C3×C4—22no—
326C22×C3×C4—22no—
327C22×C3×C4—21no—
328C22×C3×C4—21no—
329C22×C3×C4—21no—
330C22×C3×C4—21no—
331C22×C3×C4—21no—
332C22×C3×C4—31no—
333C22×C3×C4—31no—
334C22×C3×C4—31no—
335C22×C3×C4—31no—
336C22×C3×C4—31no—
337C22×C3×C4—31no—
338C22×C3×C4—31no—
339C22×C3×C4—42no—
340C22×C3×C4—42no—
341C22×C3×C4—41no—
342C22×C3×C4—41no—
343C22×C3×C4—42no—
344C22×C3×C4—62no—
345C22×C3×C4—62no—
346C22×C3×C4—62no—
347C22×C3×C4—62no—
348C22×C3×C4—62no—
349C22×C3×C4—121no—
350C22×C3×C4—121no—
351C22×C3×C4—121no—
352C22×C3×C4—121no—
353C22×C3×C4C22×D311yescharacteristic
354C22×C3×C4C22×D311yescharacteristic
355C22×C3×C4C22×D311yescharacteristic
356C22×C3×C4C22×D311yescharacteristic
357C22×C3×C4C22×D311yescharacteristic
358C22×C3×C4C23×C311yescharacteristic
359C22×C3×C4C23×C311yescharacteristic
360C22×C3×C4C23×C311yescharacteristic
361C22×C3×C4C23×C311yescharacteristic
362C22×C3×C4C23×C311yescharacteristic
363C2×#67—22no—
364C2×#67—22no—
365C2×#67—22no—
366C2×#67—22no—
367C2×#67—22no—
368C2×#67C3×D414yes—
369C22×Dic3C23×C311yescharacteristic
370C22×Dic3C23×C311yescharacteristic
371C22×Dic3C23×C311yescharacteristic
372C22×Dic3C23×C311yescharacteristic
373C22×Dic3C23×C311yescharacteristic
374C22×Dic3C23×C311yescharacteristic
375C22×Dic3C23×C311yescharacteristic
376C2×C4×D3—22no—
377C2×C4×D3—22no—
378C2×C4×D3—22no—
379C2×C4×D3—22no—
380C2×C4×D3—22no—
381C2×C4×D3—41no—
382C2×C4×D3—41no—
383C2×C4×D3—41no—
384C2×C4×D3—41no—
385C3×C4⋊C4—62no—
386C3×C4⋊C4—62no—
387C3×C4⋊C4—62no—
388C3×C4⋊C4—121no—
389C3×C22⋊C4—22no—
390C3×C22⋊C4—22no—
391C3×C22⋊C4—42no—
392C3×C22⋊C4—41no—
393C3×C22⋊C4—41no—
394C3×C22⋊C4—41no—
395C3×C22⋊C4—41no—
396C3×C22⋊C4—42no—
397C3×C22⋊C4—42no—
398C3×C22⋊C4—62no—
399C3×C22⋊C4—62no—
400C3×C22⋊C4—62no—
401C3×C22⋊C4—62no—
402C3×C22⋊C4—62no—
403C3×C22⋊C4—121no—
404C3×C22⋊C4—121no—
405C3×C22⋊C4—121no—
406C3×C42—62no—
407#217—22no—
408#217—22no—
409#217—22no—
410#217—41no—
411#217—41no—
412#217—41no—
413(C2×D3)⋊C4—22no—
414(C2×D3)⋊C4—22no—
415C4⋊Dic3—22no—
416C4⋊Dic3—41no—
417Dic3⋊C4—22no—
418Dic3⋊C4—22no—
419C4×Dic3—22no—
420C22×C32—22no—
421C22×C32—22no—
422C22×C32—22no—
423C22×C32—41no—
424C22×C32—41no—
425C22×C32—41no—
426C22×C32—41no—
427C22×C32—41no—
428C22×C32—41no—
429C22×C32—41no—
430C22×C32—41no—
431C22×C32—41no—
432C22×C32—41no—
433C22×C32—41no—
434C22×C32C22×D411yescharacteristic
435C22×C32C2×#4111yescharacteristic
436C22×C32C2×#4111yescharacteristic
437C22×C32C2×#4111yescharacteristic
438C22×C32C2×#4111yescharacteristic
439C22×C32H(5,𝔽2)11yescharacteristic
440C22×C32H(5,𝔽2)11yescharacteristic
441C2×C3×D3—22no—
442C2×C3×D3—22no—
443C2×C3×D3—22no—
444C2×C3×D3—22no—
445C2×C3×D3—22no—
446C2×C3×D3—22no—
447C2×C3×D3#12314yes—
448C32×C4—22no—
449C32×C4—22no—
450C32×C4—41no—
451C32×C4—41no—
452C32×C4—41no—
453C3×Dic3—22no—
454C3×Dic3—41no—
455C3×Dic3—41no—
456C3×Dic3—41no—
457C3×Dic3—41no—
458C3×Dic3—41no—
459C3×Dic3—41no—
460C22×D4—31no—
461C22×D4—31no—
462C22×D4C2×C3×D311yescharacteristic
463C23×C4—31no—
464C23×C4—31no—
465C23×C4—31no—
466C23×C4C2×C3×D311yescharacteristic
467#121—64no—
468C4×D4—64no—
469C2×C4⋊C4—31no—
470C2×C4⋊C4—31no—
471C2×C4⋊C4—31no—
472C2×C4⋊C4—31no—
473C2×C22⋊C4—31no—
474C2×C22⋊C4—31no—
475C2×C22⋊C4—31no—
476C2×C22⋊C4—31no—
477C2×C22⋊C4—31no—
478C2×C22⋊C4—31no—
479C2×C22⋊C4—31no—
480C2×C22⋊C4—31no—
481C2×C22⋊C4C2×C3×D311yescharacteristic
482C2×C22⋊C4C2×C3×D311yescharacteristic
483C2×C22⋊C4C2×C3×D311yescharacteristic
484C2×C42—31no—
485#95—31no—
486#95—31no—
487#95—31no—
488#95—31no—
489#95—31no—
490#95—31no—
491#95—31no—
492#95—31no—
493#95—31no—
494#95—31no—
495#95C2×C3×D311yescharacteristic
496#95C2×C3×D311yescharacteristic
497C23×C3—22no—
498C23×C3—22no—
499C23×C3—21no—
500C23×C3—21no—
501C23×C3—21no—
502C23×C3—21no—
503C23×C3—21no—
504C23×C3—21no—
505C23×C3—21no—
506C23×C3—21no—
507C23×C3—21no—
508C23×C3—21no—
509C23×C3—21no—
510C23×C3—21no—
511C23×C3—22no—
512C23×C3—21no—
513C23×C3—21no—
514C23×C3—21no—
515C23×C3—21no—
516C23×C3—21no—
517C23×C3—21no—
518C23×C3—21no—
519C23×C3—21no—
520C23×C3—21no—
521C23×C3—21no—
522C23×C3—21no—
523C23×C3—21no—
524C23×C3—21no—
525C23×C3—21no—
526C23×C3—21no—
527C23×C3—22no—
528C23×C3—32no—
529C23×C3—32no—
530C23×C3—32no—
531C23×C3—41no—
532C23×C3—41no—
533C23×C3—41no—
534C23×C3—41no—
535C23×C3—41no—
536C23×C3—41no—
537C23×C3—41no—
538C23×C3—41no—
539C23×C3—41no—
540C23×C3—41no—
541C23×C3—61no—
542C23×C3—61no—
543C23×C3—61no—
544C23×C3—61no—
545C23×C3D3×D412yes—
546C23×C3C2×C3×D412yes—
547C23×C3C23×D311yescharacteristic
548C23×C3C24×C311yescharacteristic
549C22×D3—21no—
550C22×D3—21no—
551C22×D3—21no—
552C22×D3—21no—
553C22×D3C2×C3×D412yes—
554C22×D3C3×#4112yes—
555C22×D3C3×#4112yes—
556C3×D4—44no—
557C3×D4—44no—
558C3×D4—48no—
559C3×D4—68no—
560C3×D4—124no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—22no—
570C2×C3×C4—21no—
571C2×C3×C4—21no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—22no—
589C2×C3×C4—22no—
590C2×C3×C4—32no—
591C2×C3×C4—41no—
592C2×C3×C4—41no—
593C2×C3×C4—41no—
594C2×C3×C4—41no—
595C2×C3×C4—41no—
596C2×C3×C4—41no—
597C2×C3×C4—41no—
598C2×C3×C4—41no—
599C2×C3×C4—41no—
600C2×C3×C4—41no—
601C2×C3×C4—41no—
602C2×C3×C4—41no—
603C2×C3×C4—44no—
604C2×C3×C4—44no—
605C2×C3×C4—48no—
606C2×C3×C4—61no—
607C2×C3×C4—61no—
608C2×C3×C4—61no—
609C2×C3×C4—61no—
610C2×C3×C4—61no—
611C2×C3×C4—61no—
612C2×C3×C4—61no—
613C2×C3×C4—61no—
614C2×C3×C4—61no—
615C2×C3×C4—61no—
616C2×C3×C4—61no—
617C2×C3×C4—61no—
618C2×C3×C4—61no—
619C2×C3×C4—61no—
620C2×C3×C4—61no—
621C2×C3×C4—61no—
622C2×C3×C4—61no—
623C2×C3×C4—61no—
624C2×C3×C4—61no—
625C2×C3×C4—61no—
626C2×C3×C4—124no—
627C2×C3×C4—124no—
628C2×C3×C4—124no—
629C2×C3×C4#23512yes—
630C2×C3×C4#23712yes—
631C2×C3×C4C3×#4112yes—
632C2×C3×C4C3×#4112yes—
633#67—28no—
634#67—44no—
635C2×Dic3—21no—
636C2×Dic3—21no—
637C2×Dic3—21no—
638C2×Dic3—21no—
639C2×Dic3—21no—
640C2×Dic3—21no—
641C2×Dic3—21no—
642C2×Dic3—21no—
643C2×Dic3—21no—
644C2×Dic3—21no—
645C2×Dic3—21no—
646C2×Dic3—21no—
647C2×Dic3—21no—
648C2×Dic3—21no—
649C2×Dic3—21no—
650C2×Dic3—21no—
651C2×Dic3—21no—
652C2×Dic3—21no—
653C2×Dic3—21no—
654C2×Dic3—21no—
655C2×Dic3C2×C3×D412yes—
656C4×D3—44no—
657C4×D3—44no—
658C4×D3—44no—
659C2×C32—42no—
660C2×C32—81no—
661C2×C32C2×#12311yescharacteristic
662C2×C32#52911yescharacteristic
663C2×C32#53811yescharacteristic
664C2×C32#54611yescharacteristic
665C2×C32#54611yescharacteristic
666C2×C32#55311yescharacteristic
667C2×C32#55311yescharacteristic
668C3×D3—24no—
669C24—31no—
670C24C22×C3×D311yescharacteristic
671C24C22×C3×D311yescharacteristic
672C2×D4—22no—
673C2×D4—22no—
674C2×D4—34no—
675C2×D4—41no—
676C2×D4—62no—
677C2×D4—62no—
678C2×D4—62no—
679C2×D4—62no—
680C2×D4—62no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—31no—
684C22×C4—31no—
685C22×C4—31no—
686C22×C4—31no—
687C22×C4—31no—
688C22×C4—31no—
689C22×C4—31no—
690C22×C4—41no—
691C22×C4—62no—
692C22×C4—62no—
693C22×C4—62no—
694C22×C4—62no—
695C22×C4—62no—
696C22×C4—121no—
697C22×C4—121no—
698C22×C4—121no—
699C22×C4—121no—
700C22×C4C22×C3×D311yescharacteristic
701C22×C4C22×C3×D311yescharacteristic
702C22×C4C22×C3×D311yescharacteristic
703C22×C4C22×C3×D311yescharacteristic
704C22×C4C22×C3×D311yescharacteristic
705C4⋊C4—62no—
706C4⋊C4—62no—
707C4⋊C4—62no—
708C4⋊C4—121no—
709C22⋊C4—22no—
710C22⋊C4—41no—
711C22⋊C4—41no—
712C22⋊C4—62no—
713C22⋊C4—62no—
714C22⋊C4—62no—
715C22⋊C4—62no—
716C22⋊C4—62no—
717C22⋊C4—121no—
718C22⋊C4—121no—
719C22⋊C4—121no—
720C42—62no—
721C22×C3—24no—
722C22×C3—22no—
723C22×C3—22no—
724C22×C3—22no—
725C22×C3—22no—
726C22×C3—22no—
727C22×C3—22no—
728C22×C3—21no—
729C22×C3—21no—
730C22×C3—21no—
731C22×C3—21no—
732C22×C3—21no—
733C22×C3—21no—
734C22×C3—21no—
735C22×C3—34no—
736C22×C3—42no—
737C22×C3—42no—
738C22×C3—42no—
739C22×C3—42no—
740C22×C3—42no—
741C22×C3—42no—
742C22×C3—42no—
743C22×C3—42no—
744C22×C3—42no—
745C22×C3—41no—
746C22×C3—41no—
747C22×C3—41no—
748C22×C3—41no—
749C22×C3—41no—
750C22×C3—41no—
751C22×C3—41no—
752C22×C3—41no—
753C22×C3—41no—
754C22×C3—41no—
755C22×C3—41no—
756C22×C3—41no—
757C22×C3—41no—
758C22×C3—41no—
759C22×C3—41no—
760C22×C3—41no—
761C22×C3—41no—
762C22×C3—41no—
763C22×C3—41no—
764C22×C3—41no—
765C22×C3—41no—
766C22×C3—41no—
767C22×C3—62no—
768C22×C3—62no—
769C22×C3—62no—
770C22×C3—62no—
771C22×C3—62no—
772C22×C3—62no—
773C22×C3—81no—
774C22×C3—81no—
775C22×C3—81no—
776C22×C3—81no—
777C22×C3C2×#23511yescharacteristic
778C22×C3C2×D3×D411yescharacteristic
779C22×C3C2×#23711yescharacteristic
780C22×C3#100411yescharacteristic
781C22×C3#100411yescharacteristic
782C22×C3D3×#4111yescharacteristic
783C22×C3D3×#4111yescharacteristic
784C22×C3C22×C3×D411yescharacteristic
785C22×C3C2×C3×#4111yescharacteristic
786C22×C3C2×C3×#4111yescharacteristic
787C22×C3C2×C3×#4111yescharacteristic
788C22×C3C2×C3×#4111yescharacteristic
789C22×C3C3×H(5,𝔽2)11yescharacteristic
790C22×C3C3×H(5,𝔽2)11yescharacteristic
791C2×D3—22no—
792C2×D3—22no—
793C2×D3—22no—
794C2×D3—22no—
795C2×D3—22no—
796C2×D3—22no—
797C2×D3C3×#12314yes—
798C3×C4—22no—
799C3×C4—22no—
800C3×C4—22no—
801C3×C4—22no—
802C3×C4—42no—
803C3×C4—42no—
804C3×C4—42no—
805C3×C4—41no—
806C3×C4—41no—
807C3×C4—41no—
808C3×C4—41no—
809C3×C4—41no—
810C3×C4—41no—
811C3×C4—62no—
812C3×C4—81no—
813C3×C4—81no—
814C3×C4—121no—
815C3×C4—121no—
816C3×C4—121no—
817C3×C4—121no—
818C3×C4—121no—
819C3×C4—121no—
820Dic3—22no—
821Dic3—41no—
822Dic3—41no—
823Dic3—41no—
824Dic3—41no—
825Dic3—41no—
826Dic3—41no—
827C32#244411yescharacteristic, complemented, Sylow
828C23—21no—
829C23—21no—
830C23—21no—
831C23—21no—
832C23—21no—
833C23—21no—
834C23—21no—
835C23—21no—
836C23—21no—
837C23—21no—
838C23—21no—
839C23—21no—
840C23—21no—
841C23—32no—
842C23—32no—
843C23—32no—
844C23—61no—
845C23—61no—
846C23—61no—
847C23—61no—
848C23C3×D3×D412yes—
849C23C23×C3×D311yescharacteristic
850D4—44no—
851D4—68no—
852D4—124no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—32no—
867C2×C4—44no—
868C2×C4—61no—
869C2×C4—61no—
870C2×C4—61no—
871C2×C4—61no—
872C2×C4—61no—
873C2×C4—61no—
874C2×C4—61no—
875C2×C4—61no—
876C2×C4—61no—
877C2×C4—61no—
878C2×C4—61no—
879C2×C4—61no—
880C2×C4—61no—
881C2×C4—61no—
882C2×C4—61no—
883C2×C4—61no—
884C2×C4—61no—
885C2×C4—61no—
886C2×C4—61no—
887C2×C4—61no—
888C2×C4—124no—
889C2×C4—124no—
890C2×C4—124no—
891C2×C4C3×#23512yes—
892C2×C4C3×#23712yes—
893C2×C3—21no—
894C2×C3—21no—
895C2×C3—21no—
896C2×C3—21no—
897C2×C3—21no—
898C2×C3—21no—
899C2×C3—21no—
900C2×C3—44no—
901C2×C3—42no—
902C2×C3—42no—
903C2×C3—64no—
904C2×C3—82no—
905C2×C3—81no—
906C2×C3—81no—
907C2×C3#549011yescharacteristic
908C2×C3#555711yescharacteristic
909C2×C3#555811yescharacteristic
910C2×C3#559111yescharacteristic
911C2×C3#561311yescharacteristic
912C2×C3#561411yescharacteristic
913C2×C3D3×#12311yescharacteristic
914C2×C3C2×C3×#12311yescharacteristic
915C2×C3C3×#52911yescharacteristic
916C2×C3C3×#53811yescharacteristic
917C2×C3C3×#54611yescharacteristic
918C2×C3C3×#54611yescharacteristic
919C2×C3C3×#55311yescharacteristic
920C2×C3C3×#55311yescharacteristic
921D3—24no—
922C22—22no—
923C22—22no—
924C22—22no—
925C22—34no—
926C22—41no—
927C22—41no—
928C22—41no—
929C22—41no—
930C22—41no—
931C22—41no—
932C22—41no—
933C22—41no—
934C22—41no—
935C22—41no—
936C22—41no—
937C22—62no—
938C22—62no—
939C22—62no—
940C22—62no—
941C22—62no—
942C22—62no—
943C22C2×C3×#23511yescharacteristic
944C22C2×C3×D3×D411yescharacteristic
945C22C2×C3×#23711yescharacteristic
946C22C3×#100411yescharacteristic
947C22C3×#100411yescharacteristic
948C22C3×D3×#4111yescharacteristic
949C22C3×D3×#4111yescharacteristic
950C4—22no—
951C4—22no—
952C4—41no—
953C4—41no—
954C4—41no—
955C4—62no—
956C4—121no—
957C4—121no—
958C4—121no—
959C4—121no—
960C4—121no—
961C4—121no—
962C3—21no—
963C3#7489711yescharacteristic, direct product factor
964C3C3×#244411yescharacteristic, complemented
965C2—42no—
966C2—64no—
967C2—81no—
968C2C3×#549011yescharacteristic
969C2C3×#555711yescharacteristic
970C2C3×#555811yescharacteristic
971C2C3×#559111yescharacteristic
972C2C3×#561311yescharacteristic
973C2C3×#561411yescharacteristic
974C2C3×D3×#12311yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC32×#386C2
socleC23×C32C24
prime radicalC2×C3×#938C2
hypercenterC3×#386D3
hypocenterC3C3×#2444
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#386

Complements

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

NH ≅ G/Ntype
2. C2×C3×C4×#67C2semidirect
3. C32×#386C2semidirect
4. C3×#5222C2semidirect
5. C3×#5211C2semidirect
6. C3×#4956C2semidirect
7. C3×#4956C2semidirect
8. C3×#4956C2semidirect
9. C3×#4953C2semidirect
10. C3×#4952C2semidirect
11. C3×#4951C2semidirect
12. C3×#4668C2semidirect
13. C3×D3×#95C2semidirect
14. C3×#4660C2semidirect
15. C3×#4655C2semidirect
17. #74897C3direct (N × H)
58. C2×C4×#67C2×C3semidirect
69. C3×#386D3semidirect
70. C3×#386C2×C3semidirect
74. #5222C2×C3semidirect
75. #5211C2×C3semidirect
76. #4956C2×C3semidirect
77. #4956C2×C3semidirect
78. #4956C2×C3semidirect
79. #4953C2×C3semidirect
80. #4952C2×C3semidirect
81. #4951C2×C3semidirect
82. #4668C2×C3semidirect
83. D3×#95C2×C3semidirect
84. #4660C2×C3semidirect
85. #4655C2×C3semidirect
296. #386C3×D3semidirect
827. C32#2444semidirect
963. C3#74897direct (N × H)
964. C3C3×#2444semidirect

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
C32×#3862
C3×#52222
C3×#52112
C3×#49562
C3×#49532
C3×#49522
C3×#49512
C3×#46682
C3×D3×#952
C3×#46602
C3×#46552
C3×#24443
#748973