Finite Group Databasebeta

← C3×#74892 #11810294

Subgroups — C3×#74892 #11810294

Order 1152.

1743 conjugacy classes of subgroups.

The subgroup lattice has 1096 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#937C211yesmaximal, characteristic
2C2×C3×#929C211yesmaximal, characteristic, complemented
3C2×C3×C4×#67C211yesmaximal, characteristic, complemented
4C2×C3×D3×C22⋊C4C211yesmaximal, characteristic, complemented
5C32×#386C211yesmaximal, characteristic, complemented
6C3×#5222C211yesmaximal, characteristic, complemented
7C3×#4961C211yesmaximal, characteristic, complemented
8C3×#4956C211yesmaximal, characteristic, complemented
9C3×#4955C211yesmaximal, characteristic, complemented
10C3×#4949C211yesmaximal, characteristic, complemented
11C3×#4945C211yesmaximal, characteristic, complemented
12C3×#4675C211yesmaximal, characteristic, complemented
13C3×#4669C211yesmaximal, characteristic, complemented
14C3×#4668C211yesmaximal, characteristic, complemented
15C3×#4667C211yesmaximal, characteristic, complemented
16C3×#2418—31nomaximal
17#74892C311yesmaximal, characteristic, direct product factor
18C24×C3×D3C2211yescharacteristic
19C22×C32×D4C2211yescharacteristic
20C23×C32×C4C2211yescharacteristic, complemented
21C22×C3×#67C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C22×C3×C4×D3C2211yescharacteristic
24C22×C3×C4×D3C2211yescharacteristic
25C2×C32×C22⋊C4C2211yescharacteristic
26C2×C32×C22⋊C4C2211yescharacteristic
27C2×C32×C22⋊C4C2211yescharacteristic, complemented
28C2×C3×#217C2211yescharacteristic
29C2×C3×#217C2211yescharacteristic
30C2×C3×#217C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic, complemented
32C2×C3×#217C2211yescharacteristic, complemented
33C3×#937—24no—
34C3×#929—24no—
35C3×C4×#67—24no—
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×(C2×D3)⋊C4C2211yescharacteristic
43C2×C3×(C2×D3)⋊C4C2211yescharacteristic
44C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
45C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
46C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
47C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
48C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
49C2×C3×C4×Dic3C2211yescharacteristic, complemented
50C3×D3×C22⋊C4—24no—
51C32×#95C2211yescharacteristic, complemented
52C32×#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×#937C2×C311yescharacteristic
62C2×#929C2×C311yescharacteristic, complemented
63C2×C4×#67C2×C311yescharacteristic, complemented
64C2×D3×C22⋊C4C2×C311yescharacteristic, complemented
65C3×#399—31no—
66C3×#397—31no—
67C3×#394—31no—
68C3×#394—31no—
69C3×#388—31no—
70C3×#388—31no—
71C3×#386—21no—
72C3×#386—31no—
73C3×#386D311yescharacteristic, complemented
74C3×#386C2×C311yescharacteristic, complemented
75C3×#385—31no—
76C3×#380—31no—
77C3×#379—31no—
78#5222C2×C311yescharacteristic, complemented
79#4961C2×C311yescharacteristic, complemented
80#4956C2×C311yescharacteristic, complemented
81#4955C2×C311yescharacteristic, complemented
82#4949C2×C311yescharacteristic, complemented
83#4945C2×C311yescharacteristic, complemented
84#4675C2×C311yescharacteristic, complemented
85#4669C2×C311yescharacteristic, complemented
86#4668C2×C311yescharacteristic, complemented
87#4667C2×C311yescharacteristic, complemented
88C24×C32C2311yescharacteristic
89C24×C32C2311yescharacteristic
90C23×C3×D3—22no—
91C23×C3×D3—22no—
92C23×C3×D3—22no—
93C23×C3×D3—22no—
94C23×C3×D3—22no—
95C23×C3×D3—41no—
96C23×C3×D3—41no—
97C23×C3×D3C2311yescharacteristic
98C23×C3×D3C2311yescharacteristic
99C2×C32×D4—22no—
100C2×C32×D4—22no—
101C2×C32×D4—41no—
102C22×C32×C4—22no—
103C22×C32×C4—22no—
104C22×C32×C4—41no—
105C22×C32×C4C2311yescharacteristic
106C22×C32×C4C2311yescharacteristic
107C22×C32×C4C2311yescharacteristic
108C22×C32×C4C2311yescharacteristic
109C22×C32×C4C2311yescharacteristic
110C2×C3×#67—22no—
111C2×C3×#67—22no—
112C2×C3×#67—22no—
113C2×C3×#67—22no—
114C2×C3×#67—41no—
115C2×C3×#67D414yes—
116C22×C3×Dic3C2311yescharacteristic
117C22×C3×Dic3C2311yescharacteristic
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C22×C3×Dic3C2311yescharacteristic
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—
128C32×C22⋊C4—22no—
129C32×C22⋊C4—41no—
130C32×C22⋊C4—41no—
131C3×#217—22no—
132C3×#217—22no—
133C3×#217—22no—
134C3×#217—22no—
135C3×#217—22no—
136C3×(C2×D3)⋊C4—22no—
137C3×(C2×D3)⋊C4—22no—
138C3×(C2×D3)⋊C4—22no—
139C3×(C2×D3)⋊C4—22no—
140C3×(C2×D3)⋊C4—22no—
141C3×(C2×D3)⋊C4—22no—
142C3×(C2×D3)⋊C4—41no—
143C3×(C2×D3)⋊C4D414yescomplemented
144C3×C4⋊Dic3—41no—
145C3×Dic3⋊C4—22no—
146C3×Dic3⋊C4—22no—
147C3×Dic3⋊C4—22no—
148C3×Dic3⋊C4—41no—
149C3×C4×Dic3—22no—
150#2418—31noSylow
151C25×C3—31no—
152C24×D3C22×C311yescharacteristic
153C22×C3×D4—21no—
154C22×C3×D4—31no—
155C22×C3×D4—31no—
156C22×C3×D4C2×D311yescharacteristic
157C22×C3×D4C22×C311yescharacteristic
158C23×C3×C4—21no—
159C23×C3×C4—31no—
160C23×C3×C4—31no—
161C23×C3×C4C2×D311yescharacteristic, complemented
162C23×C3×C4C22×C311yescharacteristic, complemented
163C22×#67C22×C311yescharacteristic
164C22×#67C22×C311yescharacteristic
165C22×C4×D3C22×C311yescharacteristic
166C22×C4×D3C22×C311yescharacteristic
167C3×#123—64no—
168C3×#120—64no—
169C3×C4×D4—64no—
170C2×C3×C4⋊C4—31no—
171C2×C3×C4⋊C4—31no—
172C2×C3×C4⋊C4—31no—
173C2×C3×C4⋊C4—31no—
174C2×C3×C4⋊C4—31no—
175C2×C3×C22⋊C4—21no—
176C2×C3×C22⋊C4—21no—
177C2×C3×C22⋊C4—21no—
178C2×C3×C22⋊C4—31no—
179C2×C3×C22⋊C4—31no—
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—31no—
191C2×C3×C22⋊C4—64no—
192C2×C3×C22⋊C4C2×D311yescharacteristic
193C2×C3×C22⋊C4C2×D311yescharacteristic
194C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
195C2×C3×C22⋊C4C22×C311yescharacteristic
196C2×C3×C22⋊C4C22×C311yescharacteristic
197C2×C3×C22⋊C4C22×C311yescharacteristic, complemented
198C2×C3×C42—31no—
199C2×#217C22×C311yescharacteristic
200C2×#217C22×C311yescharacteristic
201C2×#217C22×C311yescharacteristic
202C2×#217C22×C311yescharacteristic, complemented
203C2×#217C22×C311yescharacteristic, complemented
204#937—24no—
205#929—24no—
206C4×#67—24no—
207C2×(C2×D3)⋊C4C22×C311yescharacteristic
208C2×(C2×D3)⋊C4C22×C311yescharacteristic
209C2×(C2×D3)⋊C4C22×C311yescharacteristic
210C2×(C2×D3)⋊C4C22×C311yescharacteristic
211C2×(C2×D3)⋊C4C22×C311yescharacteristic
212C2×(C2×D3)⋊C4C22×C311yescharacteristic
213C2×(C2×D3)⋊C4C22×C311yescharacteristic
214C2×(C2×D3)⋊C4C22×C311yescharacteristic
215C2×C4⋊Dic3C22×C311yescharacteristic, complemented
216C2×Dic3⋊C4C22×C311yescharacteristic, complemented
217C2×Dic3⋊C4C22×C311yescharacteristic, complemented
218C2×Dic3⋊C4C22×C311yescharacteristic, complemented
219C2×Dic3⋊C4C22×C311yescharacteristic, complemented
220C2×C4×Dic3C22×C311yescharacteristic, complemented
221D3×C22⋊C4—24no—
222C3×#95—21no—
223C3×#95—21no—
224C3×#95—31no—
225C3×#95—31no—
226C3×#95—31no—
227C3×#95—31no—
228C3×#95C2×D311yescharacteristic, complemented
229C3×#95C2×D311yescharacteristic, complemented
230C3×#95C22×C311yescharacteristic, complemented
231C3×#95C22×C311yescharacteristic, complemented
232C3⋊#95C22×C311yescharacteristic, complemented
233C3⋊#95C22×C311yescharacteristic, complemented
234C3⋊#95C22×C311yescharacteristic, complemented
235C3⋊#95C22×C311yescharacteristic, complemented
236C23×C32—21no—
237C23×C32—21no—
238C23×C32—21no—
239C23×C32—21no—
240C23×C32—21no—
241C23×C32—21no—
242C23×C32—21no—
243C23×C32—21no—
244C23×C32—21no—
245C23×C32—21no—
246C23×C32—21no—
247C23×C32—21no—
248C23×C32C2×D412yes—
249C23×C32#4112yes—
250C23×C32C2411yescharacteristic
251C22×C3×D3—21no—
252C22×C3×D3—21no—
253C22×C3×D3—21no—
254C22×C3×D3—21no—
255C22×C3×D3—28no—
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×D3—44no—
263C22×C3×D3—44no—
264C22×C3×D3—44no—
265C22×C3×D3—44no—
266C22×C3×D3—44no—
267C22×C3×D3—44no—
268C22×C3×D3C2×D412yes—
269C22×C3×D3C2×D412yes—
270C22×C3×D3#4112yes—
271C22×C3×D3#4112yes—
272C32×D4—44no—
273C2×C32×C4—21no—
274C2×C32×C4—21no—
275C2×C32×C4—21no—
276C2×C32×C4—21no—
277C2×C32×C4—21no—
278C2×C32×C4—21no—
279C2×C32×C4—21no—
280C2×C32×C4—21no—
281C2×C32×C4—21no—
282C2×C32×C4—21no—
283C2×C32×C4—21no—
284C2×C32×C4—21no—
285C2×C32×C4—21no—
286C2×C32×C4—21no—
287C2×C32×C4—44no—
288C2×C32×C4C2×D412yes—
289C3×#67—28no—
290C3×#67—44no—
291C2×C3×Dic3—21no—
292C2×C3×Dic3—21no—
293C2×C3×Dic3—21no—
294C2×C3×Dic3—21no—
295C2×C3×Dic3—21no—
296C2×C3×Dic3—21no—
297C2×C3×Dic3—21no—
298C2×C3×Dic3—21no—
299C2×C3×Dic3—21no—
300C2×C3×Dic3—21no—
301C2×C3×Dic3—21no—
302C2×C3×Dic3—21no—
303C2×C3×Dic3—21no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3—21no—
307C2×C3×Dic3C2×D412yes—
308C2×C3×Dic3C2×D412yes—
309C3×C4×D3—44no—
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#386C3×D311yescharacteristic, complemented
323#385—31no—
324#380—31no—
325#379—31no—
326C24×C3—21no—
327C24×C3—21no—
328C24×C3—31no—
329C24×C3—31no—
330C24×C3—62no—
331C24×C3—62no—
332C24×C3—62no—
333C24×C3—62no—
334C24×C3—62no—
335C24×C3—121no—
336C24×C3—121no—
337C24×C3C22×D311yescharacteristic
338C24×C3C22×D311yescharacteristic
339C24×C3C23×C311yescharacteristic
340C24×C3C23×C311yescharacteristic
341C23×D3—22no—
342C23×D3—22no—
343C23×D3—22no—
344C23×D3—22no—
345C23×D3—22no—
346C23×D3—41no—
347C23×D3—41no—
348C23×D3C23×C311yescharacteristic
349C23×D3C23×C311yescharacteristic
350C2×C3×D4—24no—
351C2×C3×D4—22no—
352C2×C3×D4—22no—
353C2×C3×D4—22no—
354C2×C3×D4—22no—
355C2×C3×D4—34no—
356C2×C3×D4—42no—
357C2×C3×D4—41no—
358C2×C3×D4—41no—
359C2×C3×D4—42no—
360C2×C3×D4—62no—
361C2×C3×D4—62no—
362C2×C3×D4—62no—
363C2×C3×D4—62no—
364C2×C3×D4—121no—
365C22×C3×C4—22no—
366C22×C3×C4—22no—
367C22×C3×C4—22no—
368C22×C3×C4—22no—
369C22×C3×C4—21no—
370C22×C3×C4—21no—
371C22×C3×C4—21no—
372C22×C3×C4—21no—
373C22×C3×C4—21no—
374C22×C3×C4—31no—
375C22×C3×C4—31no—
376C22×C3×C4—31no—
377C22×C3×C4—31no—
378C22×C3×C4—31no—
379C22×C3×C4—31no—
380C22×C3×C4—42no—
381C22×C3×C4—42no—
382C22×C3×C4—41no—
383C22×C3×C4—41no—
384C22×C3×C4—42no—
385C22×C3×C4—62no—
386C22×C3×C4—62no—
387C22×C3×C4—62no—
388C22×C3×C4—62no—
389C22×C3×C4—121no—
390C22×C3×C4—121no—
391C22×C3×C4C22×D311yescharacteristic
392C22×C3×C4C22×D311yescharacteristic
393C22×C3×C4C22×D311yescharacteristic
394C22×C3×C4C22×D311yescharacteristic
395C22×C3×C4C22×D311yescharacteristic
396C22×C3×C4C23×C311yescharacteristic
397C22×C3×C4C23×C311yescharacteristic
398C22×C3×C4C23×C311yescharacteristic
399C22×C3×C4C23×C311yescharacteristic
400C22×C3×C4C23×C311yescharacteristic
401C2×#67—22no—
402C2×#67—22no—
403C2×#67—22no—
404C2×#67—22no—
405C2×#67—41no—
406C2×#67C3×D414yes—
407C22×Dic3C23×C311yescharacteristic
408C22×Dic3C23×C311yescharacteristic
409C22×Dic3C23×C311yescharacteristic
410C22×Dic3C23×C311yescharacteristic
411C22×Dic3C23×C311yescharacteristic
412C22×Dic3C23×C311yescharacteristic
413C2×C4×D3—22no—
414C2×C4×D3—22no—
415C2×C4×D3—22no—
416C2×C4×D3—22no—
417C2×C4×D3—41no—
418C2×C4×D3—41no—
419C3×C4⋊C4—62no—
420C3×C4⋊C4—62no—
421C3×C4⋊C4—62no—
422C3×C4⋊C4—121no—
423C3×C4⋊C4—121no—
424C3×C22⋊C4—22no—
425C3×C22⋊C4—22no—
426C3×C22⋊C4—34no—
427C3×C22⋊C4—42no—
428C3×C22⋊C4—41no—
429C3×C22⋊C4—41no—
430C3×C22⋊C4—41no—
431C3×C22⋊C4—41no—
432C3×C22⋊C4—42no—
433C3×C22⋊C4—42no—
434C3×C22⋊C4—62no—
435C3×C22⋊C4—62no—
436C3×C22⋊C4—62no—
437C3×C22⋊C4—62no—
438C3×C22⋊C4—62no—
439C3×C22⋊C4—62no—
440C3×C22⋊C4—62no—
441C3×C22⋊C4—62no—
442C3×C22⋊C4—62no—
443C3×C22⋊C4—62no—
444C3×C22⋊C4—62no—
445C3×C22⋊C4—121no—
446C3×C42—62no—
447#217—22no—
448#217—22no—
449#217—22no—
450#217—22no—
451#217—22no—
452(C2×D3)⋊C4—22no—
453(C2×D3)⋊C4—22no—
454(C2×D3)⋊C4—22no—
455(C2×D3)⋊C4—22no—
456(C2×D3)⋊C4—22no—
457(C2×D3)⋊C4—22no—
458(C2×D3)⋊C4—41no—
459(C2×D3)⋊C4C3×D414yescomplemented
460C4⋊Dic3—41no—
461Dic3⋊C4—22no—
462Dic3⋊C4—22no—
463Dic3⋊C4—22no—
464Dic3⋊C4—41no—
465C4×Dic3—22no—
466C22×C32—22no—
467C22×C32—22no—
468C22×C32—22no—
469C22×C32—22no—
470C22×C32—22no—
471C22×C32—22no—
472C22×C32—41no—
473C22×C32—41no—
474C22×C32—41no—
475C22×C32—41no—
476C22×C32—41no—
477C22×C32—41no—
478C22×C32—41no—
479C22×C32—41no—
480C22×C32C22×D411yescharacteristic
481C22×C32C22×D411yescharacteristic
482C22×C32C2×#4111yescharacteristic
483C22×C32C2×#4111yescharacteristic
484C22×C32C2×#4111yescharacteristic
485C22×C32H(5,𝔽2)11yescharacteristic
486C22×C32H(5,𝔽2)11yescharacteristic
487C2×C3×D3—22no—
488C2×C3×D3—22no—
489C2×C3×D3—22no—
490C2×C3×D3—22no—
491C2×C3×D3—22no—
492C2×C3×D3—22no—
493C2×C3×D3—22no—
494C2×C3×D3—22no—
495C2×C3×D3—22no—
496C2×C3×D3—416no—
497C2×C3×D3—41no—
498C2×C3×D3—41no—
499C2×C3×D3—41no—
500C2×C3×D3—41no—
501C2×C3×D3#12314yescomplemented
502C32×C4—22no—
503C32×C4—41no—
504C32×C4—41no—
505C32×C4—41no—
506C32×C4—41no—
507C3×Dic3—22no—
508C3×Dic3—22no—
509C3×Dic3—41no—
510C3×Dic3—41no—
511C3×Dic3—41no—
512C3×Dic3—41no—
513C25—31no—
514C22×D4—31no—
515C22×D4—31no—
516C22×D4C2×C3×D311yescharacteristic
517C23×C4—31no—
518C23×C4—31no—
519C23×C4C2×C3×D311yescharacteristic, complemented
520#123—64no—
521#120—64no—
522C4×D4—64no—
523C2×C4⋊C4—31no—
524C2×C4⋊C4—31no—
525C2×C4⋊C4—31no—
526C2×C4⋊C4—31no—
527C2×C4⋊C4—31no—
528C2×C22⋊C4—31no—
529C2×C22⋊C4—31no—
530C2×C22⋊C4—31no—
531C2×C22⋊C4—31no—
532C2×C22⋊C4—31no—
533C2×C22⋊C4—31no—
534C2×C22⋊C4—31no—
535C2×C22⋊C4—31no—
536C2×C22⋊C4—31no—
537C2×C22⋊C4—31no—
538C2×C22⋊C4—31no—
539C2×C22⋊C4—31no—
540C2×C22⋊C4—31no—
541C2×C22⋊C4—64no—
542C2×C22⋊C4C2×C3×D311yescharacteristic
543C2×C22⋊C4C2×C3×D311yescharacteristic
544C2×C22⋊C4C2×C3×D311yescharacteristic, complemented
545C2×C42—31no—
546#95—31no—
547#95—31no—
548#95—31no—
549#95—31no—
550#95C2×C3×D311yescharacteristic, complemented
551#95C2×C3×D311yescharacteristic, complemented
552C23×C3—22no—
553C23×C3—22no—
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—21no—
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—21no—
579C23×C3—22no—
580C23×C3—22no—
581C23×C3—32no—
582C23×C3—32no—
583C23×C3—32no—
584C23×C3—32no—
585C23×C3—41no—
586C23×C3—41no—
587C23×C3—41no—
588C23×C3—41no—
589C23×C3—41no—
590C23×C3—41no—
591C23×C3—41no—
592C23×C3—41no—
593C23×C3—41no—
594C23×C3—41no—
595C23×C3—68no—
596C23×C3—61no—
597C23×C3—61no—
598C23×C3—61no—
599C23×C3—61no—
600C23×C3—61no—
601C23×C3—61no—
602C23×C3—61no—
603C23×C3—61no—
604C23×C3—61no—
605C23×C3—61no—
606C23×C3—124no—
607C23×C3—124no—
608C23×C3—124no—
609C23×C3—124no—
610C23×C3—124no—
611C23×C3—124no—
612C23×C3#23512yes—
613C23×C3D3×D412yes—
614C23×C3C2×C3×D412yes—
615C23×C3C3×#4112yes—
616C23×C3C23×D311yescharacteristic
617C23×C3C24×C311yescharacteristic
618C22×D3—21no—
619C22×D3—21no—
620C22×D3—21no—
621C22×D3—21no—
622C22×D3—28no—
623C22×D3—21no—
624C22×D3—21no—
625C22×D3—21no—
626C22×D3—21no—
627C22×D3—21no—
628C22×D3—21no—
629C22×D3—44no—
630C22×D3—44no—
631C22×D3—44no—
632C22×D3—44no—
633C22×D3—44no—
634C22×D3—44no—
635C22×D3C2×C3×D412yes—
636C22×D3C2×C3×D412yes—
637C22×D3C3×#4112yes—
638C22×D3C3×#4112yes—
639C3×D4—44no—
640C3×D4—44no—
641C3×D4—48no—
642C3×D4—68no—
643C3×D4—124no—
644C2×C3×C4—21no—
645C2×C3×C4—21no—
646C2×C3×C4—21no—
647C2×C3×C4—21no—
648C2×C3×C4—22no—
649C2×C3×C4—22no—
650C2×C3×C4—21no—
651C2×C3×C4—21no—
652C2×C3×C4—21no—
653C2×C3×C4—21no—
654C2×C3×C4—21no—
655C2×C3×C4—21no—
656C2×C3×C4—21no—
657C2×C3×C4—21no—
658C2×C3×C4—21no—
659C2×C3×C4—21no—
660C2×C3×C4—21no—
661C2×C3×C4—21no—
662C2×C3×C4—21no—
663C2×C3×C4—21no—
664C2×C3×C4—21no—
665C2×C3×C4—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—22no—
675C2×C3×C4—32no—
676C2×C3×C4—32no—
677C2×C3×C4—41no—
678C2×C3×C4—41no—
679C2×C3×C4—41no—
680C2×C3×C4—41no—
681C2×C3×C4—41no—
682C2×C3×C4—41no—
683C2×C3×C4—41no—
684C2×C3×C4—41no—
685C2×C3×C4—41no—
686C2×C3×C4—41no—
687C2×C3×C4—41no—
688C2×C3×C4—41no—
689C2×C3×C4—44no—
690C2×C3×C4—44no—
691C2×C3×C4—48no—
692C2×C3×C4—61no—
693C2×C3×C4—61no—
694C2×C3×C4—61no—
695C2×C3×C4—61no—
696C2×C3×C4—61no—
697C2×C3×C4—61no—
698C2×C3×C4—61no—
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—124no—
709C2×C3×C4—124no—
710C2×C3×C4D3×D412yes—
711C2×C3×C4C2×C3×D412yes—
712#67—28no—
713#67—44no—
714C2×Dic3—21no—
715C2×Dic3—21no—
716C2×Dic3—21no—
717C2×Dic3—21no—
718C2×Dic3—21no—
719C2×Dic3—21no—
720C2×Dic3—21no—
721C2×Dic3—21no—
722C2×Dic3—21no—
723C2×Dic3—21no—
724C2×Dic3—21no—
725C2×Dic3—21no—
726C2×Dic3—21no—
727C2×Dic3—21no—
728C2×Dic3—21no—
729C2×Dic3—21no—
730C2×Dic3C2×C3×D412yes—
731C2×Dic3C2×C3×D412yes—
732C4×D3—44no—
733C4×D3—44no—
734C2×C32—42no—
735C2×C32—42no—
736C2×C32C2×#12311yescharacteristic
737C2×C32#52511yescharacteristic
738C2×C32#53811yescharacteristic
739C2×C32D4211yescharacteristic
740C2×C32#54611yescharacteristic
741C2×C32#54611yescharacteristic
742C2×C32#55111yescharacteristic
743C3×D3—24no—
744C3×D3—42no—
745C24—31no—
746C24—31no—
747C24—62no—
748C24—62no—
749C24—62no—
750C24—62no—
751C24—62no—
752C24—121no—
753C24—121no—
754C24C22×C3×D311yescharacteristic
755C24C22×C3×D311yescharacteristic
756C2×D4—22no—
757C2×D4—22no—
758C2×D4—34no—
759C2×D4—41no—
760C2×D4—62no—
761C2×D4—62no—
762C2×D4—62no—
763C2×D4—62no—
764C2×D4—121no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—31no—
768C22×C4—31no—
769C22×C4—31no—
770C22×C4—31no—
771C22×C4—31no—
772C22×C4—31no—
773C22×C4—41no—
774C22×C4—62no—
775C22×C4—62no—
776C22×C4—62no—
777C22×C4—62no—
778C22×C4—121no—
779C22×C4—121no—
780C22×C4C22×C3×D311yescharacteristic
781C22×C4C22×C3×D311yescharacteristic
782C22×C4C22×C3×D311yescharacteristic
783C22×C4C22×C3×D311yescharacteristic
784C22×C4C22×C3×D311yescharacteristic
785C4⋊C4—62no—
786C4⋊C4—62no—
787C4⋊C4—62no—
788C4⋊C4—121no—
789C4⋊C4—121no—
790C22⋊C4—22no—
791C22⋊C4—34no—
792C22⋊C4—41no—
793C22⋊C4—41no—
794C22⋊C4—62no—
795C22⋊C4—62no—
796C22⋊C4—62no—
797C22⋊C4—62no—
798C22⋊C4—62no—
799C22⋊C4—62no—
800C22⋊C4—62no—
801C22⋊C4—62no—
802C22⋊C4—62no—
803C22⋊C4—62no—
804C22⋊C4—62no—
805C22⋊C4—121no—
806C42—62no—
807C22×C3—24no—
808C22×C3—22no—
809C22×C3—22no—
810C22×C3—22no—
811C22×C3—22no—
812C22×C3—22no—
813C22×C3—22no—
814C22×C3—22no—
815C22×C3—22no—
816C22×C3—22no—
817C22×C3—22no—
818C22×C3—22no—
819C22×C3—22no—
820C22×C3—21no—
821C22×C3—21no—
822C22×C3—21no—
823C22×C3—21no—
824C22×C3—21no—
825C22×C3—21no—
826C22×C3—21no—
827C22×C3—34no—
828C22×C3—42no—
829C22×C3—42no—
830C22×C3—42no—
831C22×C3—42no—
832C22×C3—42no—
833C22×C3—42no—
834C22×C3—42no—
835C22×C3—42no—
836C22×C3—42no—
837C22×C3—41no—
838C22×C3—41no—
839C22×C3—41no—
840C22×C3—41no—
841C22×C3—41no—
842C22×C3—41no—
843C22×C3—41no—
844C22×C3—41no—
845C22×C3—41no—
846C22×C3—41no—
847C22×C3—41no—
848C22×C3—41no—
849C22×C3—41no—
850C22×C3—41no—
851C22×C3—41no—
852C22×C3—41no—
853C22×C3—62no—
854C22×C3—62no—
855C22×C3—62no—
856C22×C3—62no—
857C22×C3—62no—
858C22×C3—62no—
859C22×C3—62no—
860C22×C3—62no—
861C22×C3—62no—
862C22×C3—81no—
863C22×C3—81no—
864C22×C3—81no—
865C22×C3—81no—
866C22×C3—1216no—
867C22×C3—121no—
868C22×C3—121no—
869C22×C3—121no—
870C22×C3—121no—
871C22×C3C2×#23511yescharacteristic
872C22×C3C2×D3×D411yescharacteristic
873C22×C3C2×D3×D411yescharacteristic
874C22×C3#100411yescharacteristic
875C22×C3#100411yescharacteristic
876C22×C3D3×#4111yescharacteristic
877C22×C3D3×#4111yescharacteristic
878C22×C3C22×C3×D411yescharacteristic
879C22×C3C22×C3×D411yescharacteristic
880C22×C3C2×C3×#4111yescharacteristic
881C22×C3C2×C3×#4111yescharacteristic
882C22×C3C2×C3×#4111yescharacteristic
883C22×C3C3×H(5,𝔽2)11yescharacteristic
884C22×C3C3×H(5,𝔽2)11yescharacteristic
885C2×D3—22no—
886C2×D3—22no—
887C2×D3—22no—
888C2×D3—22no—
889C2×D3—22no—
890C2×D3—22no—
891C2×D3—22no—
892C2×D3—22no—
893C2×D3—22no—
894C2×D3—416no—
895C2×D3—41no—
896C2×D3—41no—
897C2×D3—41no—
898C2×D3—41no—
899C2×D3C3×#12314yescomplemented
900C3×C4—22no—
901C3×C4—22no—
902C3×C4—42no—
903C3×C4—42no—
904C3×C4—42no—
905C3×C4—41no—
906C3×C4—41no—
907C3×C4—41no—
908C3×C4—41no—
909C3×C4—41no—
910C3×C4—41no—
911C3×C4—41no—
912C3×C4—41no—
913C3×C4—62no—
914C3×C4—62no—
915C3×C4—81no—
916C3×C4—81no—
917C3×C4—121no—
918C3×C4—121no—
919C3×C4—121no—
920C3×C4—121no—
921Dic3—22no—
922Dic3—22no—
923Dic3—41no—
924Dic3—41no—
925Dic3—41no—
926Dic3—41no—
927C32#241811yescharacteristic, complemented, Sylow
928C23—21no—
929C23—21no—
930C23—21no—
931C23—21no—
932C23—21no—
933C23—21no—
934C23—21no—
935C23—21no—
936C23—21no—
937C23—21no—
938C23—21no—
939C23—21no—
940C23—32no—
941C23—32no—
942C23—32no—
943C23—32no—
944C23—68no—
945C23—61no—
946C23—61no—
947C23—61no—
948C23—61no—
949C23—61no—
950C23—61no—
951C23—61no—
952C23—61no—
953C23—61no—
954C23—61no—
955C23—124no—
956C23—124no—
957C23—124no—
958C23—124no—
959C23—124no—
960C23—124no—
961C23C3×#23512yes—
962C23C3×D3×D412yes—
963C23C23×C3×D311yescharacteristic
964D4—44no—
965D4—68no—
966D4—124no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—21no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—21no—
979C2×C4—21no—
980C2×C4—21no—
981C2×C4—32no—
982C2×C4—32no—
983C2×C4—44no—
984C2×C4—61no—
985C2×C4—61no—
986C2×C4—61no—
987C2×C4—61no—
988C2×C4—61no—
989C2×C4—61no—
990C2×C4—61no—
991C2×C4—61no—
992C2×C4—61no—
993C2×C4—61no—
994C2×C4—61no—
995C2×C4—61no—
996C2×C4—61no—
997C2×C4—61no—
998C2×C4—61no—
999C2×C4—61no—
1000C2×C4—124no—
1001C2×C4—124no—
1002C2×C4C3×D3×D412yes—
1003C2×C3—21no—
1004C2×C3—21no—
1005C2×C3—21no—
1006C2×C3—21no—
1007C2×C3—21no—
1008C2×C3—21no—
1009C2×C3—21no—
1010C2×C3—44no—
1011C2×C3—42no—
1012C2×C3—42no—
1013C2×C3—42no—
1014C2×C3—42no—
1015C2×C3—64no—
1016C2×C3—82no—
1017C2×C3—122no—
1018C2×C3#549011yescharacteristic
1019C2×C3#554711yescharacteristic
1020C2×C3#555611yescharacteristic
1021C2×C3#559011yescharacteristic
1022C2×C3#561211yescharacteristic
1023C2×C3#561311yescharacteristic
1024C2×C3D3×#12311yescharacteristic
1025C2×C3C2×C3×#12311yescharacteristic
1026C2×C3C3×#52511yescharacteristic
1027C2×C3C3×#53811yescharacteristic
1028C2×C3C3×D4211yescharacteristic
1029C2×C3C3×#54611yescharacteristic
1030C2×C3C3×#54611yescharacteristic
1031C2×C3C3×#55111yescharacteristic
1032D3—24no—
1033D3—42no—
1034C22—22no—
1035C22—22no—
1036C22—22no—
1037C22—22no—
1038C22—22no—
1039C22—22no—
1040C22—34no—
1041C22—41no—
1042C22—41no—
1043C22—41no—
1044C22—41no—
1045C22—41no—
1046C22—41no—
1047C22—41no—
1048C22—41no—
1049C22—62no—
1050C22—62no—
1051C22—62no—
1052C22—62no—
1053C22—62no—
1054C22—62no—
1055C22—62no—
1056C22—62no—
1057C22—62no—
1058C22—1216no—
1059C22—121no—
1060C22—121no—
1061C22—121no—
1062C22—121no—
1063C22C2×C3×#23511yescharacteristic
1064C22C2×C3×D3×D411yescharacteristic
1065C22C2×C3×D3×D411yescharacteristic
1066C22C3×#100411yescharacteristic
1067C22C3×#100411yescharacteristic
1068C22C3×D3×#4111yescharacteristic
1069C22C3×D3×#4111yescharacteristic
1070C4—22no—
1071C4—41no—
1072C4—41no—
1073C4—41no—
1074C4—41no—
1075C4—62no—
1076C4—62no—
1077C4—121no—
1078C4—121no—
1079C4—121no—
1080C4—121no—
1081C3—21no—
1082C3#7489211yescharacteristic, direct product factor
1083C3C3×#241811yescharacteristic, complemented
1084C2—42no—
1085C2—42no—
1086C2—64no—
1087C2—122no—
1088C2C3×#549011yescharacteristic
1089C2C3×#554711yescharacteristic
1090C2C3×#555611yescharacteristic
1091C2C3×#559011yescharacteristic
1092C2C3×#561211yescharacteristic
1093C2C3×#561311yescharacteristic
1094C2C3×D3×#12311yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC32×#386C2
socleC23×C32C24
prime radicalC2×C3×#937C2
hypercenterC3×#386D3
hypocenterC3C3×#2418
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×#929C2semidirect
3. C2×C3×C4×#67C2semidirect
4. C2×C3×D3×C22⋊C4C2semidirect
5. C32×#386C2semidirect
6. C3×#5222C2semidirect
7. C3×#4961C2semidirect
8. C3×#4956C2semidirect
9. C3×#4955C2semidirect
10. C3×#4949C2semidirect
11. C3×#4945C2semidirect
12. C3×#4675C2semidirect
13. C3×#4669C2semidirect
14. C3×#4668C2semidirect
15. C3×#4667C2semidirect
17. #74892C3direct (N × H)
20. C23×C32×C4C22semidirect
27. C2×C32×C22⋊C4C22semidirect
31. C2×C3×#217C22semidirect
32. C2×C3×#217C22semidirect
44. C2×C3×C4⋊Dic3C22semidirect
45. C2×C3×Dic3⋊C4C22semidirect
46. C2×C3×Dic3⋊C4C22semidirect
47. C2×C3×Dic3⋊C4C22semidirect
48. C2×C3×Dic3⋊C4C22semidirect
49. C2×C3×C4×Dic3C22semidirect
51. C32×#95C22semidirect
52. C32×#95C22semidirect
53. C3×C3⋊#95C22semidirect
54. C3×C3⋊#95C22semidirect
55. C3×C3⋊#95C22semidirect
56. C3×C3⋊#95C22semidirect
62. C2×#929C2×C3semidirect
63. C2×C4×#67C2×C3semidirect
64. C2×D3×C22⋊C4C2×C3semidirect
73. C3×#386D3semidirect
74. C3×#386C2×C3semidirect
78. #5222C2×C3semidirect
79. #4961C2×C3semidirect
80. #4956C2×C3semidirect
81. #4955C2×C3semidirect
82. #4949C2×C3semidirect
83. #4945C2×C3semidirect
84. #4675C2×C3semidirect
85. #4669C2×C3semidirect
86. #4668C2×C3semidirect
87. #4667C2×C3semidirect
143. C3×(C2×D3)⋊C4D4semidirect
161. C23×C3×C4C2×D3semidirect
162. C23×C3×C4C22×C3semidirect
194. C2×C3×C22⋊C4C2×D3semidirect
197. C2×C3×C22⋊C4C22×C3semidirect
202. C2×#217C22×C3semidirect
203. C2×#217C22×C3semidirect
215. C2×C4⋊Dic3C22×C3semidirect
216. C2×Dic3⋊C4C22×C3semidirect
217. C2×Dic3⋊C4C22×C3semidirect
218. C2×Dic3⋊C4C22×C3semidirect
219. C2×Dic3⋊C4C22×C3semidirect
220. C2×C4×Dic3C22×C3semidirect
228. C3×#95C2×D3semidirect
229. C3×#95C2×D3semidirect
230. C3×#95C22×C3semidirect
231. C3×#95C22×C3semidirect
232. C3⋊#95C22×C3semidirect
233. C3⋊#95C22×C3semidirect
234. C3⋊#95C22×C3semidirect
235. C3⋊#95C22×C3semidirect
322. #386C3×D3semidirect
459. (C2×D3)⋊C4C3×D4semidirect
501. C2×C3×D3#123semidirect
519. C23×C4C2×C3×D3semidirect
544. C2×C22⋊C4C2×C3×D3semidirect
550. #95C2×C3×D3semidirect
551. #95C2×C3×D3semidirect
899. C2×D3C3×#123semidirect
927. C32#2418semidirect
1082. C3#74892direct (N × H)
1083. C3C3×#2418semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9372
C2×C3×#9292
C2×C3×C4×#672
C2×C3×D3×C22⋊C42
C32×#3862
C3×#52222
C3×#49612
C3×#49562
C3×#49552
C3×#49492
C3×#49452
C3×#46752
C3×#46692
C3×#46682
C3×#46672
C3×#24183
#748923