Finite Group Databasebeta

← C3×#73826 #11810309

Subgroups — C3×#73826 #11810309

Order 1152.

1853 conjugacy classes of subgroups.

The subgroup lattice has 1117 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#953C211yesmaximal, characteristic
2C22×C3×#217C211yesmaximal, characteristic, complemented
3C2×C3×#883C211yesmaximal, characteristic, complemented
4C2×C3×#67⋊C4C211yesmaximal, characteristic, complemented
5C32×#379C211yesmaximal, characteristic, complemented
6C3×#4961C211yesmaximal, characteristic, complemented
7C3×#4959C211yesmaximal, characteristic, complemented
8C3×#4958C211yesmaximal, characteristic, complemented
9C3×#4956C211yesmaximal, characteristic, complemented
10C3×#4952C211yesmaximal, characteristic, complemented
11C3×#4951C211yesmaximal, characteristic, complemented
12C3×#4950C211yesmaximal, characteristic, complemented
13C3×#4949C211yesmaximal, characteristic, complemented
14C3×#4945C211yesmaximal, characteristic, complemented
15C3×#4942C211yesmaximal, characteristic, complemented
16C3×#2418—31nomaximal
17#73826C311yesmaximal, characteristic, direct product factor
18C25×C32C2211yescharacteristic
19C22×C3×#67C2211yescharacteristic
20C22×C3×#67C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C23×C3×Dic3C2211yescharacteristic
23C23×C3×Dic3C2211yescharacteristic
24C22×C3×C4×D3C2211yescharacteristic, complemented
25C2×C32×C22⋊C4C2211yescharacteristic
26C2×C32×C22⋊C4C2211yescharacteristic
27C2×C32×C22⋊C4C2211yescharacteristic
28C2×C32×C22⋊C4C2211yescharacteristic
29C2×C32×C22⋊C4C2211yescharacteristic
30C2×C32×C22⋊C4C2211yescharacteristic
31C3×#953—24no—
32C2×C3×#217—24no—
33C2×C3×#217C2211yescharacteristic
34C2×C3×#217C2211yescharacteristic
35C2×C3×#217C2211yescharacteristic
36C2×C3×#217C2211yescharacteristic
37C2×C3×#217C2211yescharacteristic
38C2×C3×#217C2211yescharacteristic
39C2×C3×#217C2211yescharacteristic
40C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
41C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
42C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
43C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
44C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
45C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
46C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
47C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
48C2×C3×C4×Dic3C2211yescharacteristic, complemented
49C3×#883—24no—
50C3×#67⋊C4—24no—
51C3×C3⋊#95C2211yescharacteristic, complemented
52C3×C3⋊#95C2211yescharacteristic, complemented
53C3×C3⋊#95C2211yescharacteristic, complemented
54C3×C3⋊#95C2211yescharacteristic, complemented
55C3×C3⋊#95C2211yescharacteristic, complemented
56C3×C3⋊#95C2211yescharacteristic, complemented
57C2×C3×#123—31no—
58C2×C3×#120—31no—
59C2×C3×C4×D4—31no—
60C22×C3×C22⋊C4—31no—
61C2×#953C2×C311yescharacteristic
62C22×#217C2×C311yescharacteristic, complemented
63C2×#883C2×C311yescharacteristic, complemented
64C2×#67⋊C4C2×C311yescharacteristic, complemented
65C3×#399—31no—
66C3×#397—31no—
67C3×#394—31no—
68C3×#394—31no—
69C3×#388—31no—
70C3×#388—31no—
71C3×#386—31no—
72C3×#386—31no—
73C3×#385—31no—
74C3×#380—31no—
75C3×#379—21no—
76C3×#379D311yescharacteristic, complemented
77C3×#379C2×C311yescharacteristic, complemented
78#4961C2×C311yescharacteristic, complemented
79#4959C2×C311yescharacteristic, complemented
80#4958C2×C311yescharacteristic, complemented
81#4956C2×C311yescharacteristic, complemented
82#4952C2×C311yescharacteristic, complemented
83#4951C2×C311yescharacteristic, complemented
84#4950C2×C311yescharacteristic, complemented
85#4949C2×C311yescharacteristic, complemented
86#4945C2×C311yescharacteristic, complemented
87#4942C2×C311yescharacteristic, complemented
88C24×C32—22no—
89C24×C32—22no—
90C24×C32—22no—
91C24×C32—22no—
92C24×C32—22no—
93C24×C32—41no—
94C24×C32—41no—
95C24×C32C2311yescharacteristic
96C24×C32C2311yescharacteristic
97C24×C32C2311yescharacteristic
98C23×C3×D3C2311yescharacteristic
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—41no—
110C2×C3×#67—41no—
111C2×C3×#67D414yes—
112C22×C3×Dic3—22no—
113C22×C3×Dic3—22no—
114C22×C3×Dic3—22no—
115C22×C3×Dic3—22no—
116C22×C3×Dic3—41no—
117C22×C3×Dic3—41no—
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C22×C3×Dic3C2311yescharacteristic
122C22×C3×Dic3C2311yescharacteristic
123C22×C3×Dic3C2311yescharacteristic
124C22×C3×Dic3C2311yescharacteristic
125C2×C3×C4×D3—22no—
126C2×C3×C4×D3—22no—
127C2×C3×C4×D3—41no—
128C32×C22⋊C4—22no—
129C32×C22⋊C4—22no—
130C32×C22⋊C4—22no—
131C32×C22⋊C4—22no—
132C32×C22⋊C4—41no—
133C32×C22⋊C4—41no—
134C3×#217—22no—
135C3×#217—22no—
136C3×#217—22no—
137C3×#217—22no—
138C3×#217—22no—
139C3×#217—22no—
140C3×#217D414yescomplemented
141C3×(C2×D3)⋊C4—22no—
142C3×(C2×D3)⋊C4—22no—
143C3×(C2×D3)⋊C4—41no—
144C3×C4⋊Dic3—22no—
145C3×C4⋊Dic3—41no—
146C3×Dic3⋊C4—22no—
147C3×Dic3⋊C4—22no—
148C3×Dic3⋊C4—41no—
149C3×C4×Dic3—22no—
150#2418—31noSylow
151C25×C3—21no—
152C25×C3C2×D311yescharacteristic
153C25×C3C22×C311yescharacteristic
154C22×C3×D4—31no—
155C22×C3×D4—31no—
156C22×C3×D4—31no—
157C23×C3×C4—31no—
158C23×C3×C4—31no—
159C23×C3×C4—31no—
160C22×#67C22×C311yescharacteristic
161C22×#67C22×C311yescharacteristic
162C22×#67C22×C311yescharacteristic
163C23×Dic3C22×C311yescharacteristic
164C23×Dic3C22×C311yescharacteristic
165C22×C4×D3C22×C311yescharacteristic, complemented
166C3×#123—64no—
167C3×#120—64no—
168C3×C4×D4—64no—
169C2×C3×C4⋊C4—31no—
170C2×C3×C4⋊C4—31no—
171C2×C3×C4⋊C4—31no—
172C2×C3×C4⋊C4—31no—
173C2×C3×C4⋊C4—31no—
174C2×C3×C22⋊C4—21no—
175C2×C3×C22⋊C4—21no—
176C2×C3×C22⋊C4—21no—
177C2×C3×C22⋊C4—21no—
178C2×C3×C22⋊C4—21no—
179C2×C3×C22⋊C4—21no—
180C2×C3×C22⋊C4—31no—
181C2×C3×C22⋊C4—31no—
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—64no—
191C2×C3×C22⋊C4C2×D311yescharacteristic
192C2×C3×C22⋊C4C2×D311yescharacteristic
193C2×C3×C22⋊C4C2×D311yescharacteristic
194C2×C3×C22⋊C4C2×D311yescharacteristic
195C2×C3×C22⋊C4C2×D311yescharacteristic
196C2×C3×C22⋊C4C2×D311yescharacteristic
197C2×C3×C22⋊C4C22×C311yescharacteristic
198C2×C3×C22⋊C4C22×C311yescharacteristic
199C2×C3×C22⋊C4C22×C311yescharacteristic
200C2×C3×C22⋊C4C22×C311yescharacteristic
201C2×C3×C22⋊C4C22×C311yescharacteristic
202C2×C3×C22⋊C4C22×C311yescharacteristic
203C2×C3×C42—31no—
204#953—24no—
205C2×#217—24no—
206C2×#217C22×C311yescharacteristic
207C2×#217C22×C311yescharacteristic
208C2×#217C22×C311yescharacteristic
209C2×#217C22×C311yescharacteristic
210C2×#217C22×C311yescharacteristic
211C2×#217C22×C311yescharacteristic
212C2×#217C22×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×C4⋊Dic3C22×C311yescharacteristic, complemented
218C2×Dic3⋊C4C22×C311yescharacteristic, complemented
219C2×Dic3⋊C4C22×C311yescharacteristic, complemented
220C2×Dic3⋊C4C22×C311yescharacteristic, complemented
221C2×C4×Dic3C22×C311yescharacteristic, complemented
222#883—24no—
223#67⋊C4—24no—
224C3×#95—31no—
225C3×#95—31no—
226C3×#95—31no—
227C3×#95—31no—
228C3×#95—31no—
229C3×#95—31no—
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—21no—
243C23×C32—21no—
244C23×C32—28no—
245C23×C32—21no—
246C23×C32—21no—
247C23×C32—21no—
248C23×C32—21no—
249C23×C32—21no—
250C23×C32—21no—
251C23×C32—21no—
252C23×C32—21no—
253C23×C32—44no—
254C23×C32—44no—
255C23×C32—44no—
256C23×C32—44no—
257C23×C32—44no—
258C23×C32—44no—
259C23×C32C2×D412yes—
260C23×C32C2×D412yes—
261C23×C32#4112yes—
262C23×C32#4112yes—
263C23×C32#4112yes—
264C23×C32C2411yescharacteristic
265C22×C3×D3—21no—
266C22×C3×D3—21no—
267C22×C3×D3—21no—
268C22×C3×D3—21no—
269C22×C3×D3—21no—
270C22×C3×D3—21no—
271C22×C3×D3C2×D412yes—
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—
284C3×#67—28no—
285C3×#67—44no—
286C3×#67—44no—
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×Dic3—21no—
302C2×C3×Dic3—21no—
303C2×C3×Dic3—21no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3—44no—
306C2×C3×Dic3—44no—
307C2×C3×Dic3C2×D412yes—
308C2×C3×Dic3C2×D412yes—
309C2×C3×Dic3C2×D412yes—
310C3×C4×D3—44no—
311C2×#123—31no—
312C2×#120—31no—
313C2×C4×D4—31no—
314C22×C22⋊C4—31no—
315#399—31no—
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#379C3×D311yescharacteristic, complemented
326C24×C3—22no—
327C24×C3—22no—
328C24×C3—22no—
329C24×C3—22no—
330C24×C3—22no—
331C24×C3—22no—
332C24×C3—24no—
333C24×C3—22no—
334C24×C3—22no—
335C24×C3—22no—
336C24×C3—22no—
337C24×C3—21no—
338C24×C3—21no—
339C24×C3—21no—
340C24×C3—31no—
341C24×C3—42no—
342C24×C3—42no—
343C24×C3—42no—
344C24×C3—42no—
345C24×C3—41no—
346C24×C3—41no—
347C24×C3—41no—
348C24×C3—41no—
349C24×C3—42no—
350C24×C3—42no—
351C24×C3C22×D311yescharacteristic
352C24×C3C22×D311yescharacteristic
353C24×C3C22×D311yescharacteristic
354C24×C3C23×C311yescharacteristic
355C24×C3C23×C311yescharacteristic
356C24×C3C23×C311yescharacteristic
357C23×D3C23×C311yescharacteristic
358C2×C3×D4—34no—
359C2×C3×D4—62no—
360C2×C3×D4—62no—
361C2×C3×D4—62no—
362C2×C3×D4—62no—
363C2×C3×D4—62no—
364C2×C3×D4—62no—
365C2×C3×D4—121no—
366C2×C3×D4—121no—
367C22×C3×C4—21no—
368C22×C3×C4—21no—
369C22×C3×C4—21no—
370C22×C3×C4—21no—
371C22×C3×C4—31no—
372C22×C3×C4—31no—
373C22×C3×C4—31no—
374C22×C3×C4—31no—
375C22×C3×C4—31no—
376C22×C3×C4—31no—
377C22×C3×C4—31no—
378C22×C3×C4—62no—
379C22×C3×C4—62no—
380C22×C3×C4—62no—
381C22×C3×C4—62no—
382C22×C3×C4—62no—
383C22×C3×C4—62no—
384C22×C3×C4—121no—
385C22×C3×C4—121no—
386C22×C3×C4—121no—
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
395C2×#67—22no—
396C2×#67—22no—
397C2×#67—22no—
398C2×#67—22no—
399C2×#67—22no—
400C2×#67—22no—
401C2×#67—41no—
402C2×#67—41no—
403C2×#67C3×D414yes—
404C22×Dic3—22no—
405C22×Dic3—22no—
406C22×Dic3—22no—
407C22×Dic3—22no—
408C22×Dic3—41no—
409C22×Dic3—41no—
410C22×Dic3C23×C311yescharacteristic
411C22×Dic3C23×C311yescharacteristic
412C22×Dic3C23×C311yescharacteristic
413C22×Dic3C23×C311yescharacteristic
414C22×Dic3C23×C311yescharacteristic
415C22×Dic3C23×C311yescharacteristic
416C22×Dic3C23×C311yescharacteristic
417C2×C4×D3—22no—
418C2×C4×D3—22no—
419C2×C4×D3—41no—
420C3×C4⋊C4—62no—
421C3×C4⋊C4—62no—
422C3×C4⋊C4—62no—
423C3×C4⋊C4—121no—
424C3×C4⋊C4—121no—
425C3×C22⋊C4—22no—
426C3×C22⋊C4—22no—
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—34no—
434C3×C22⋊C4—42no—
435C3×C22⋊C4—42no—
436C3×C22⋊C4—42no—
437C3×C22⋊C4—42no—
438C3×C22⋊C4—41no—
439C3×C22⋊C4—41no—
440C3×C22⋊C4—41no—
441C3×C22⋊C4—41no—
442C3×C22⋊C4—42no—
443C3×C22⋊C4—42no—
444C3×C22⋊C4—62no—
445C3×C22⋊C4—62no—
446C3×C22⋊C4—62no—
447C3×C22⋊C4—62no—
448C3×C22⋊C4—62no—
449C3×C22⋊C4—62no—
450C3×C22⋊C4—62no—
451C3×C22⋊C4—62no—
452C3×C22⋊C4—121no—
453C3×C42—62no—
454#217—22no—
455#217—22no—
456#217—22no—
457#217—22no—
458#217—22no—
459#217—22no—
460#217C3×D414yescomplemented
461(C2×D3)⋊C4—22no—
462(C2×D3)⋊C4—22no—
463(C2×D3)⋊C4—41no—
464C4⋊Dic3—22no—
465C4⋊Dic3—41no—
466Dic3⋊C4—22no—
467Dic3⋊C4—22no—
468Dic3⋊C4—41no—
469C4×Dic3—22no—
470C22×C32—22no—
471C22×C32—22no—
472C22×C32—22no—
473C22×C32—22no—
474C22×C32—22no—
475C22×C32—22no—
476C22×C32—22no—
477C22×C32—22no—
478C22×C32—22no—
479C22×C32—22no—
480C22×C32—22no—
481C22×C32—22no—
482C22×C32—416no—
483C22×C32—41no—
484C22×C32—41no—
485C22×C32—41no—
486C22×C32—41no—
487C22×C32—41no—
488C22×C32—41no—
489C22×C32—41no—
490C22×C32—41no—
491C22×C32#12314yescomplemented
492C22×C32C22×D411yescharacteristic
493C22×C32C22×D411yescharacteristic
494C22×C32C2×#4111yescharacteristic
495C22×C32C2×#4111yescharacteristic
496C22×C32C2×#4111yescharacteristic
497C22×C32H(5,𝔽2)11yescharacteristic
498C22×C32H(5,𝔽2)11yescharacteristic
499C2×C3×D3—22no—
500C2×C3×D3—22no—
501C2×C3×D3—22no—
502C2×C3×D3—41no—
503C2×C3×D3—41no—
504C2×C3×D3—41no—
505C2×C3×D3—41no—
506C32×C4—41no—
507C32×C4—41no—
508C32×C4—41no—
509C32×C4—41no—
510C3×Dic3—22no—
511C3×Dic3—22no—
512C3×Dic3—22no—
513C3×Dic3—41no—
514C3×Dic3—41no—
515C3×Dic3—41no—
516C3×Dic3—41no—
517C25C2×C3×D311yescharacteristic
518C22×D4—31no—
519C22×D4—31no—
520C22×D4—31no—
521C23×C4—31no—
522C23×C4—31no—
523C23×C4—31no—
524#123—64no—
525#120—64no—
526C4×D4—64no—
527C2×C4⋊C4—31no—
528C2×C4⋊C4—31no—
529C2×C4⋊C4—31no—
530C2×C4⋊C4—31no—
531C2×C4⋊C4—31no—
532C2×C22⋊C4—31no—
533C2×C22⋊C4—31no—
534C2×C22⋊C4—31no—
535C2×C22⋊C4—31no—
536C2×C22⋊C4—31no—
537C2×C22⋊C4—31no—
538C2×C22⋊C4—31no—
539C2×C22⋊C4—31no—
540C2×C22⋊C4—31no—
541C2×C22⋊C4—31no—
542C2×C22⋊C4—64no—
543C2×C22⋊C4C2×C3×D311yescharacteristic
544C2×C22⋊C4C2×C3×D311yescharacteristic
545C2×C22⋊C4C2×C3×D311yescharacteristic
546C2×C22⋊C4C2×C3×D311yescharacteristic
547C2×C22⋊C4C2×C3×D311yescharacteristic
548C2×C22⋊C4C2×C3×D311yescharacteristic
549C2×C42—31no—
550#95—31no—
551#95—31no—
552#95—31no—
553#95—31no—
554#95—31no—
555#95—31no—
556C23×C3—21no—
557C23×C3—21no—
558C23×C3—21no—
559C23×C3—21no—
560C23×C3—21no—
561C23×C3—21no—
562C23×C3—21no—
563C23×C3—21no—
564C23×C3—22no—
565C23×C3—22no—
566C23×C3—28no—
567C23×C3—28no—
568C23×C3—22no—
569C23×C3—22no—
570C23×C3—21no—
571C23×C3—21no—
572C23×C3—21no—
573C23×C3—21no—
574C23×C3—21no—
575C23×C3—21no—
576C23×C3—21no—
577C23×C3—21no—
578C23×C3—21no—
579C23×C3—21no—
580C23×C3—21no—
581C23×C3—21no—
582C23×C3—21no—
583C23×C3—21no—
584C23×C3—21no—
585C23×C3—21no—
586C23×C3—21no—
587C23×C3—21no—
588C23×C3—21no—
589C23×C3—21no—
590C23×C3—21no—
591C23×C3—21no—
592C23×C3—21no—
593C23×C3—21no—
594C23×C3—21no—
595C23×C3—22no—
596C23×C3—22no—
597C23×C3—22no—
598C23×C3—22no—
599C23×C3—22no—
600C23×C3—32no—
601C23×C3—41no—
602C23×C3—41no—
603C23×C3—41no—
604C23×C3—41no—
605C23×C3—41no—
606C23×C3—41no—
607C23×C3—41no—
608C23×C3—41no—
609C23×C3—41no—
610C23×C3—41no—
611C23×C3—41no—
612C23×C3—41no—
613C23×C3—48no—
614C23×C3—44no—
615C23×C3—44no—
616C23×C3—44no—
617C23×C3—44no—
618C23×C3—44no—
619C23×C3—44no—
620C23×C3—44no—
621C23×C3—44no—
622C23×C3—48no—
623C23×C3—48no—
624C23×C3—44no—
625C23×C3—44no—
626C23×C3—48no—
627C23×C3—48no—
628C23×C3—48no—
629C23×C3—48no—
630C23×C3—44no—
631C23×C3—44no—
632C23×C3—61no—
633C23×C3—61no—
634C23×C3—61no—
635C23×C3—61no—
636C23×C3—61no—
637C23×C3—61no—
638C23×C3#23512yes—
639C23×C3D3×D412yes—
640C23×C3D3×D412yes—
641C23×C3#23712yes—
642C23×C3#23712yes—
643C23×C3C2×C3×D412yes—
644C23×C3C2×C3×D412yes—
645C23×C3C3×#4112yes—
646C23×C3C3×#4112yes—
647C23×C3C3×#4112yes—
648C23×C3C23×D311yescharacteristic
649C23×C3C24×C311yescharacteristic
650C22×D3—21no—
651C22×D3—21no—
652C22×D3—21no—
653C22×D3—21no—
654C22×D3—21no—
655C22×D3—21no—
656C22×D3C2×C3×D412yes—
657C3×D4—68no—
658C3×D4—124no—
659C3×D4—124no—
660C2×C3×C4—21no—
661C2×C3×C4—21no—
662C2×C3×C4—21no—
663C2×C3×C4—21no—
664C2×C3×C4—21no—
665C2×C3×C4—21no—
666C2×C3×C4—21no—
667C2×C3×C4—21no—
668C2×C3×C4—21no—
669C2×C3×C4—21no—
670C2×C3×C4—21no—
671C2×C3×C4—21no—
672C2×C3×C4—21no—
673C2×C3×C4—21no—
674C2×C3×C4—21no—
675C2×C3×C4—21no—
676C2×C3×C4—21no—
677C2×C3×C4—21no—
678C2×C3×C4—21no—
679C2×C3×C4—21no—
680C2×C3×C4—21no—
681C2×C3×C4—21no—
682C2×C3×C4—21no—
683C2×C3×C4—21no—
684C2×C3×C4—32no—
685C2×C3×C4—32no—
686C2×C3×C4—32no—
687C2×C3×C4—41no—
688C2×C3×C4—41no—
689C2×C3×C4—41no—
690C2×C3×C4—41no—
691C2×C3×C4—41no—
692C2×C3×C4—41no—
693C2×C3×C4—41no—
694C2×C3×C4—41no—
695C2×C3×C4—41no—
696C2×C3×C4—41no—
697C2×C3×C4—41no—
698C2×C3×C4—41no—
699C2×C3×C4—61no—
700C2×C3×C4—61no—
701C2×C3×C4—61no—
702C2×C3×C4—61no—
703C2×C3×C4—61no—
704C2×C3×C4—61no—
705C2×C3×C4—61no—
706C2×C3×C4—61no—
707C2×C3×C4—61no—
708C2×C3×C4—61no—
709C2×C3×C4—61no—
710C2×C3×C4—61no—
711C2×C3×C4—61no—
712C2×C3×C4—61no—
713C2×C3×C4—61no—
714C2×C3×C4—61no—
715C2×C3×C4—61no—
716C2×C3×C4—61no—
717C2×C3×C4—124no—
718C2×C3×C4—124no—
719C2×C3×C4—124no—
720#67—28no—
721#67—44no—
722#67—44no—
723C2×Dic3—21no—
724C2×Dic3—21no—
725C2×Dic3—21no—
726C2×Dic3—21no—
727C2×Dic3—21no—
728C2×Dic3—21no—
729C2×Dic3—21no—
730C2×Dic3—21no—
731C2×Dic3—21no—
732C2×Dic3—21no—
733C2×Dic3—21no—
734C2×Dic3—21no—
735C2×Dic3—21no—
736C2×Dic3—21no—
737C2×Dic3—21no—
738C2×Dic3—21no—
739C2×Dic3—21no—
740C2×Dic3—21no—
741C2×Dic3—44no—
742C2×Dic3—44no—
743C2×Dic3C2×C3×D412yes—
744C2×Dic3C2×C3×D412yes—
745C2×Dic3C2×C3×D412yes—
746C4×D3—44no—
747C2×C32—24no—
748C2×C32—42no—
749C2×C32—42no—
750C2×C32C2×#12311yescharacteristic
751C2×C32#52511yescharacteristic
752C2×C32#53811yescharacteristic
753C2×C32D4211yescharacteristic
754C2×C32#54611yescharacteristic
755C2×C32#54611yescharacteristic
756C2×C32#55111yescharacteristic
757C3×D3—42no—
758C24—22no—
759C24—22no—
760C24—22no—
761C24—22no—
762C24—22no—
763C24—31no—
764C24—41no—
765C24—41no—
766C24C22×C3×D311yescharacteristic
767C24C22×C3×D311yescharacteristic
768C24C22×C3×D311yescharacteristic
769C2×D4—34no—
770C2×D4—62no—
771C2×D4—62no—
772C2×D4—62no—
773C2×D4—62no—
774C2×D4—62no—
775C2×D4—62no—
776C2×D4—121no—
777C2×D4—121no—
778C22×C4—31no—
779C22×C4—31no—
780C22×C4—31no—
781C22×C4—31no—
782C22×C4—31no—
783C22×C4—31no—
784C22×C4—31no—
785C22×C4—62no—
786C22×C4—62no—
787C22×C4—62no—
788C22×C4—62no—
789C22×C4—62no—
790C22×C4—62no—
791C22×C4—121no—
792C22×C4—121no—
793C22×C4—121no—
794C22×C4C22×C3×D311yescharacteristic
795C22×C4C22×C3×D311yescharacteristic
796C22×C4C22×C3×D311yescharacteristic
797C22×C4C22×C3×D311yescharacteristic
798C4⋊C4—62no—
799C4⋊C4—62no—
800C4⋊C4—62no—
801C4⋊C4—121no—
802C4⋊C4—121no—
803C22⋊C4—22no—
804C22⋊C4—22no—
805C22⋊C4—22no—
806C22⋊C4—22no—
807C22⋊C4—34no—
808C22⋊C4—41no—
809C22⋊C4—41no—
810C22⋊C4—62no—
811C22⋊C4—62no—
812C22⋊C4—62no—
813C22⋊C4—62no—
814C22⋊C4—62no—
815C22⋊C4—62no—
816C22⋊C4—62no—
817C22⋊C4—62no—
818C22⋊C4—121no—
819C42—62no—
820C22×C3—22no—
821C22×C3—22no—
822C22×C3—22no—
823C22×C3—22no—
824C22×C3—22no—
825C22×C3—22no—
826C22×C3—22no—
827C22×C3—22no—
828C22×C3—22no—
829C22×C3—22no—
830C22×C3—22no—
831C22×C3—22no—
832C22×C3—24no—
833C22×C3—24no—
834C22×C3—22no—
835C22×C3—22no—
836C22×C3—22no—
837C22×C3—22no—
838C22×C3—22no—
839C22×C3—22no—
840C22×C3—22no—
841C22×C3—22no—
842C22×C3—22no—
843C22×C3—22no—
844C22×C3—22no—
845C22×C3—22no—
846C22×C3—24no—
847C22×C3—21no—
848C22×C3—21no—
849C22×C3—21no—
850C22×C3—21no—
851C22×C3—21no—
852C22×C3—21no—
853C22×C3—21no—
854C22×C3—42no—
855C22×C3—42no—
856C22×C3—42no—
857C22×C3—42no—
858C22×C3—42no—
859C22×C3—42no—
860C22×C3—42no—
861C22×C3—42no—
862C22×C3—42no—
863C22×C3—42no—
864C22×C3—416no—
865C22×C3—416no—
866C22×C3—42no—
867C22×C3—42no—
868C22×C3—42no—
869C22×C3—42no—
870C22×C3—42no—
871C22×C3—42no—
872C22×C3—42no—
873C22×C3—42no—
874C22×C3—432no—
875C22×C3—41no—
876C22×C3—41no—
877C22×C3—41no—
878C22×C3—41no—
879C22×C3—41no—
880C22×C3—41no—
881C22×C3—41no—
882C22×C3—41no—
883C22×C3—41no—
884C22×C3—41no—
885C22×C3—41no—
886C22×C3—41no—
887C22×C3—41no—
888C22×C3—41no—
889C22×C3—41no—
890C22×C3—41no—
891C22×C3—62no—
892C22×C3—62no—
893C22×C3—62no—
894C22×C3—121no—
895C22×C3—121no—
896C22×C3—121no—
897C22×C3—121no—
898C22×C3#88314yescomplemented
899C22×C3C3×#12314yescomplemented
900C22×C3C2×#23511yescharacteristic
901C22×C3C2×D3×D411yescharacteristic
902C22×C3C2×D3×D411yescharacteristic
903C22×C3C2×#23711yescharacteristic
904C22×C3C2×#23711yescharacteristic
905C22×C3#100411yescharacteristic
906C22×C3#100411yescharacteristic
907C22×C3C22×C3×D411yescharacteristic
908C22×C3C22×C3×D411yescharacteristic
909C22×C3C2×C3×#4111yescharacteristic
910C22×C3C2×C3×#4111yescharacteristic
911C22×C3C2×C3×#4111yescharacteristic
912C22×C3C3×H(5,𝔽2)11yescharacteristic
913C22×C3C3×H(5,𝔽2)11yescharacteristic
914C2×D3—22no—
915C2×D3—22no—
916C2×D3—22no—
917C2×D3—41no—
918C2×D3—41no—
919C2×D3—41no—
920C2×D3—41no—
921C3×C4—41no—
922C3×C4—41no—
923C3×C4—41no—
924C3×C4—41no—
925C3×C4—41no—
926C3×C4—41no—
927C3×C4—41no—
928C3×C4—41no—
929C3×C4—62no—
930C3×C4—62no—
931C3×C4—62no—
932C3×C4—81no—
933C3×C4—81no—
934C3×C4—81no—
935C3×C4—81no—
936C3×C4—121no—
937C3×C4—121no—
938C3×C4—121no—
939C3×C4—121no—
940Dic3—22no—
941Dic3—22no—
942Dic3—22no—
943Dic3—41no—
944Dic3—41no—
945Dic3—41no—
946Dic3—41no—
947C32#241811yescharacteristic, complemented, Sylow
948C23—21no—
949C23—21no—
950C23—21no—
951C23—21no—
952C23—28no—
953C23—21no—
954C23—21no—
955C23—21no—
956C23—21no—
957C23—21no—
958C23—21no—
959C23—21no—
960C23—21no—
961C23—21no—
962C23—21no—
963C23—21no—
964C23—21no—
965C23—32no—
966C23—44no—
967C23—44no—
968C23—44no—
969C23—44no—
970C23—44no—
971C23—44no—
972C23—61no—
973C23—61no—
974C23—61no—
975C23—61no—
976C23—61no—
977C23—61no—
978C23C3×#23512yes—
979C23C3×D3×D412yes—
980C23C3×D3×D412yes—
981C23C3×#23712yes—
982C23C3×#23712yes—
983C23C23×C3×D311yescharacteristic
984D4—68no—
985D4—124no—
986D4—124no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—32no—
1000C2×C4—32no—
1001C2×C4—32no—
1002C2×C4—61no—
1003C2×C4—61no—
1004C2×C4—61no—
1005C2×C4—61no—
1006C2×C4—61no—
1007C2×C4—61no—
1008C2×C4—61no—
1009C2×C4—61no—
1010C2×C4—61no—
1011C2×C4—61no—
1012C2×C4—61no—
1013C2×C4—61no—
1014C2×C4—61no—
1015C2×C4—61no—
1016C2×C4—61no—
1017C2×C4—61no—
1018C2×C4—61no—
1019C2×C4—61no—
1020C2×C4—124no—
1021C2×C4—124no—
1022C2×C4—124no—
1023C2×C3—24no—
1024C2×C3—24no—
1025C2×C3—21no—
1026C2×C3—21no—
1027C2×C3—21no—
1028C2×C3—21no—
1029C2×C3—21no—
1030C2×C3—21no—
1031C2×C3—21no—
1032C2×C3—44no—
1033C2×C3—44no—
1034C2×C3—44no—
1035C2×C3—42no—
1036C2×C3—42no—
1037C2×C3—42no—
1038C2×C3—42no—
1039C2×C3—122no—
1040C2×C3C2×#88311yescharacteristic
1041C2×C3#549011yescharacteristic
1042C2×C3#549511yescharacteristic
1043C2×C3#558611yescharacteristic
1044C2×C3#559011yescharacteristic
1045C2×C3#559111yescharacteristic
1046C2×C3#559311yescharacteristic
1047C2×C3C2×C3×#12311yescharacteristic
1048C2×C3C3×#52511yescharacteristic
1049C2×C3C3×#53811yescharacteristic
1050C2×C3C3×D4211yescharacteristic
1051C2×C3C3×#54611yescharacteristic
1052C2×C3C3×#54611yescharacteristic
1053C2×C3C3×#55111yescharacteristic
1054D3—42no—
1055C22—22no—
1056C22—22no—
1057C22—22no—
1058C22—22no—
1059C22—22no—
1060C22—22no—
1061C22—22no—
1062C22—22no—
1063C22—22no—
1064C22—22no—
1065C22—22no—
1066C22—22no—
1067C22—416no—
1068C22—41no—
1069C22—41no—
1070C22—41no—
1071C22—41no—
1072C22—41no—
1073C22—41no—
1074C22—41no—
1075C22—41no—
1076C22—62no—
1077C22—62no—
1078C22—62no—
1079C22—121no—
1080C22—121no—
1081C22—121no—
1082C22—121no—
1083C22C3×#88314yescomplemented
1084C22C2×C3×#23511yescharacteristic
1085C22C2×C3×D3×D411yescharacteristic
1086C22C2×C3×D3×D411yescharacteristic
1087C22C2×C3×#23711yescharacteristic
1088C22C2×C3×#23711yescharacteristic
1089C22C3×#100411yescharacteristic
1090C22C3×#100411yescharacteristic
1091C4—41no—
1092C4—41no—
1093C4—41no—
1094C4—41no—
1095C4—62no—
1096C4—62no—
1097C4—62no—
1098C4—121no—
1099C4—121no—
1100C4—121no—
1101C4—121no—
1102C3—21no—
1103C3#7382611yescharacteristic, direct product factor
1104C3C3×#241811yescharacteristic, complemented
1105C2—24no—
1106C2—42no—
1107C2—42no—
1108C2—122no—
1109C2C2×C3×#88311yescharacteristic
1110C2C3×#549011yescharacteristic
1111C2C3×#549511yescharacteristic
1112C2C3×#558611yescharacteristic
1113C2C3×#559011yescharacteristic
1114C2C3×#559111yescharacteristic
1115C2C3×#559311yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC32×#379C2
socleC23×C32C24
prime radicalC2×C3×#953C2
hypercenterC3×#379D3
hypocenterC3C3×#2418
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#379

Complements

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

NH ≅ G/Ntype
2. C22×C3×#217C2semidirect
3. C2×C3×#883C2semidirect
4. C2×C3×#67⋊C4C2semidirect
5. C32×#379C2semidirect
6. C3×#4961C2semidirect
7. C3×#4959C2semidirect
8. C3×#4958C2semidirect
9. C3×#4956C2semidirect
10. C3×#4952C2semidirect
11. C3×#4951C2semidirect
12. C3×#4950C2semidirect
13. C3×#4949C2semidirect
14. C3×#4945C2semidirect
15. C3×#4942C2semidirect
17. #73826C3direct (N × H)
24. C22×C3×C4×D3C22semidirect
40. C2×C3×(C2×D3)⋊C4C22semidirect
41. C2×C3×(C2×D3)⋊C4C22semidirect
42. C2×C3×(C2×D3)⋊C4C22semidirect
43. C2×C3×C4⋊Dic3C22semidirect
44. C2×C3×C4⋊Dic3C22semidirect
45. C2×C3×Dic3⋊C4C22semidirect
46. C2×C3×Dic3⋊C4C22semidirect
47. C2×C3×Dic3⋊C4C22semidirect
48. C2×C3×C4×Dic3C22semidirect
51. C3×C3⋊#95C22semidirect
52. C3×C3⋊#95C22semidirect
53. C3×C3⋊#95C22semidirect
54. C3×C3⋊#95C22semidirect
55. C3×C3⋊#95C22semidirect
56. C3×C3⋊#95C22semidirect
62. C22×#217C2×C3semidirect
63. C2×#883C2×C3semidirect
64. C2×#67⋊C4C2×C3semidirect
76. C3×#379D3semidirect
77. C3×#379C2×C3semidirect
78. #4961C2×C3semidirect
79. #4959C2×C3semidirect
80. #4958C2×C3semidirect
81. #4956C2×C3semidirect
82. #4952C2×C3semidirect
83. #4951C2×C3semidirect
84. #4950C2×C3semidirect
85. #4949C2×C3semidirect
86. #4945C2×C3semidirect
87. #4942C2×C3semidirect
140. C3×#217D4semidirect
165. C22×C4×D3C22×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×C4⋊Dic3C22×C3semidirect
218. C2×Dic3⋊C4C22×C3semidirect
219. C2×Dic3⋊C4C22×C3semidirect
220. C2×Dic3⋊C4C22×C3semidirect
221. C2×C4×Dic3C22×C3semidirect
230. C3⋊#95C22×C3semidirect
231. C3⋊#95C22×C3semidirect
232. C3⋊#95C22×C3semidirect
233. C3⋊#95C22×C3semidirect
234. C3⋊#95C22×C3semidirect
235. C3⋊#95C22×C3semidirect
325. #379C3×D3semidirect
460. #217C3×D4semidirect
491. C22×C32#123semidirect
898. C22×C3#883semidirect
899. C22×C3C3×#123semidirect
947. C32#2418semidirect
1083. C22C3×#883semidirect
1103. C3#73826direct (N × H)
1104. C3C3×#2418semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9532
C22×C3×#2172
C2×C3×#8832
C2×C3×#67⋊C42
C32×#3792
C3×#49612
C3×#49592
C3×#49582
C3×#49562
C3×#49522
C3×#49512
C3×#49502
C3×#49492
C3×#49452
C3×#49422
C3×#24183
#738263