Finite Group Databasebeta

← C3×#82128 #11810297

Subgroups — C3×#82128 #11810297

Order 1152.

1937 conjugacy classes of subgroups.

The subgroup lattice has 1124 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×C22⋊C4C211yesmaximal, characteristic, complemented
2C2×C3×#953C211yesmaximal, characteristic
3C2×C3×C4×#67C211yesmaximal, characteristic, complemented
4C2×C3×#883C211yesmaximal, characteristic, complemented
5C3×#5247C211yesmaximal, characteristic, complemented
6C3×#5213C211yesmaximal, characteristic, complemented
7C3×#5212C211yesmaximal, characteristic, complemented
8C3×#5210C211yesmaximal, characteristic, complemented
9C3×#4961C211yesmaximal, characteristic, complemented
10C3×#4959C211yesmaximal, characteristic, complemented
11C3×#4956C211yesmaximal, characteristic, complemented
12C3×#4952C211yesmaximal, characteristic, complemented
13C3×#4951C211yesmaximal, characteristic, complemented
14C3×#4949C211yesmaximal, characteristic, complemented
15C3×#4945C211yesmaximal, characteristic, complemented
16C3×#2418—31nomaximal
17#82128C311yesmaximal, characteristic, direct product factor
18C25×C32C2211yescharacteristic
19C23×C32×C4C2211yescharacteristic
20C23×C32×C4C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic
24C22×C3×C4×D3C2211yescharacteristic, complemented
25C2×C32×C22⋊C4—24no—
26C2×C32×C22⋊C4C2211yescharacteristic
27C2×C32×C22⋊C4C2211yescharacteristic
28C2×C32×C22⋊C4C2211yescharacteristic
29C2×C32×C22⋊C4C2211yescharacteristic
30C3×#953—24no—
31C2×C3×#217C2211yescharacteristic
32C2×C3×#217C2211yescharacteristic
33C2×C3×#217C2211yescharacteristic
34C2×C3×#217C2211yescharacteristic
35C2×C3×#217C2211yescharacteristic
36C2×C3×#217C2211yescharacteristic
37C2×C3×#217C2211yescharacteristic
38C2×C3×#217C2211yescharacteristic
39C2×C3×#217C2211yescharacteristic
40C3×C4×#67—24no—
41C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
42C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
43C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
44C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
45C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
46C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
47C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
48C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
49C2×C3×C4×Dic3C2211yescharacteristic, complemented
50C3×#883—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—21no—
61C22×C3×C22⋊C4D311yescharacteristic, complemented
62C22×C3×C22⋊C4C2×C311yescharacteristic, complemented
63C2×#953C2×C311yescharacteristic
64C2×C4×#67C2×C311yescharacteristic, complemented
65C2×#883C2×C311yescharacteristic, complemented
66C3×#399—31no—
67C3×#397—31no—
68C3×#394—31no—
69C3×#394—31no—
70C3×#388—31no—
71C3×#388—31no—
72C3×#386—31no—
73C3×#386—31no—
74C3×#385—31no—
75C3×#380—31no—
76C3×#379—31no—
77#5247C2×C311yescharacteristic, complemented
78#5213C2×C311yescharacteristic, complemented
79#5212C2×C311yescharacteristic, complemented
80#5210C2×C311yescharacteristic, complemented
81#4961C2×C311yescharacteristic, complemented
82#4959C2×C311yescharacteristic, complemented
83#4956C2×C311yescharacteristic, complemented
84#4952C2×C311yescharacteristic, complemented
85#4951C2×C311yescharacteristic, complemented
86#4949C2×C311yescharacteristic, complemented
87#4945C2×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×C4—22no—
100C22×C32×C4—22no—
101C22×C32×C4—22no—
102C22×C32×C4—22no—
103C22×C32×C4—41no—
104C22×C32×C4—41no—
105C22×C32×C4C2311yescharacteristic
106C22×C32×C4C2311yescharacteristic
107C22×C32×C4C2311yescharacteristic
108C22×C32×C4C2311yescharacteristic
109C2×C3×#67—22no—
110C2×C3×#67—22no—
111C2×C3×#67—22no—
112C2×C3×#67—22no—
113C2×C3×#67—22no—
114C2×C3×#67—22no—
115C2×C3×#67—41no—
116C2×C3×#67—41no—
117C2×C3×#67D414yes—
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⋊C4D414yescomplemented
132C3×#217—22no—
133C3×#217—22no—
134C3×#217—22no—
135C3×#217—22no—
136C3×#217—22no—
137C3×#217—22no—
138C3×#217—22no—
139C3×#217—41no—
140C3×#217—41no—
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—21no—
158C23×C3×C4—21no—
159C23×C3×C4—31no—
160C23×C3×C4C2×D311yescharacteristic
161C23×C3×C4C2×D311yescharacteristic
162C23×C3×C4C22×C311yescharacteristic
163C23×C3×C4C22×C311yescharacteristic
164C22×#67C22×C311yescharacteristic
165C22×#67C22×C311yescharacteristic
166C22×#67C22×C311yescharacteristic
167C22×C4×D3C22×C311yescharacteristic, complemented
168C3×#123—64no—
169C3×#120—64no—
170C3×C4×D4—64no—
171C2×C3×C4⋊C4—31no—
172C2×C3×C4⋊C4—31no—
173C2×C3×C4⋊C4—31no—
174C2×C3×C4⋊C4—31no—
175C2×C3×C4⋊C4—31no—
176C2×C3×C22⋊C4—28no—
177C2×C3×C22⋊C4—24no—
178C2×C3×C22⋊C4—24no—
179C2×C3×C22⋊C4—21no—
180C2×C3×C22⋊C4—21no—
181C2×C3×C22⋊C4—21no—
182C2×C3×C22⋊C4—21no—
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—31no—
192C2×C3×C22⋊C4—31no—
193C2×C3×C22⋊C4—31no—
194C2×C3×C22⋊C4—31no—
195C2×C3×C22⋊C4C2×D311yescharacteristic
196C2×C3×C22⋊C4C2×D311yescharacteristic
197C2×C3×C22⋊C4C2×D311yescharacteristic
198C2×C3×C22⋊C4C2×D311yescharacteristic
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×#217C22×C311yescharacteristic
206C2×#217C22×C311yescharacteristic
207C2×#217C22×C311yescharacteristic
208C2×#217C22×C311yescharacteristic
209C2×#217C22×C311yescharacteristic
210C2×#217C22×C311yescharacteristic
211C2×#217C22×C311yescharacteristic
212C2×#217C22×C311yescharacteristic
213C2×#217C22×C311yescharacteristic
214C4×#67—24no—
215C2×(C2×D3)⋊C4C22×C311yescharacteristic, complemented
216C2×(C2×D3)⋊C4C22×C311yescharacteristic, complemented
217C2×(C2×D3)⋊C4C22×C311yescharacteristic, complemented
218C2×C4⋊Dic3C22×C311yescharacteristic, complemented
219C2×C4⋊Dic3C22×C311yescharacteristic, complemented
220C2×Dic3⋊C4C22×C311yescharacteristic, complemented
221C2×Dic3⋊C4C22×C311yescharacteristic, complemented
222C2×Dic3⋊C4C22×C311yescharacteristic, complemented
223C2×C4×Dic3C22×C311yescharacteristic, complemented
224#883—24no—
225C3×#95—31no—
226C3×#95—31no—
227C3×#95—31no—
228C3×#95—31no—
229C3×#95—31no—
230C3×#95—31no—
231C3⋊#95C22×C311yescharacteristic, complemented
232C3⋊#95C22×C311yescharacteristic, complemented
233C3⋊#95C22×C311yescharacteristic, complemented
234C3⋊#95C22×C311yescharacteristic, complemented
235C3⋊#95C22×C311yescharacteristic, complemented
236C3⋊#95C22×C311yescharacteristic, complemented
237C23×C32—21no—
238C23×C32—21no—
239C23×C32—21no—
240C23×C32—21no—
241C23×C32—28no—
242C23×C32—21no—
243C23×C32—21no—
244C23×C32—21no—
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—21no—
254C23×C32—44no—
255C23×C32—44no—
256C23×C32—44no—
257C23×C32—44no—
258C23×C32—44no—
259C23×C32—44no—
260C23×C32C2×D412yes—
261C23×C32C2×D412yes—
262C23×C32#4112yes—
263C23×C32#4112yes—
264C23×C32#4112yes—
265C23×C32C2411yescharacteristic
266C22×C3×D3—21no—
267C22×C3×D3—21no—
268C22×C3×D3—21no—
269C22×C3×D3—21no—
270C22×C3×D3—21no—
271C22×C3×D3—21no—
272C22×C3×D3C2×D412yes—
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—44no—
284C2×C32×C4—44no—
285C2×C32×C4C2×D412yes—
286C2×C32×C4C2×D412yes—
287C3×#67—28no—
288C3×#67—44no—
289C3×#67—44no—
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—21no—
306C2×C3×Dic3—21no—
307C2×C3×Dic3—21no—
308C2×C3×Dic3—21no—
309C2×C3×Dic3—21no—
310C2×C3×Dic3C2×D412yes—
311C3×C4×D3—44no—
312C2×#123—31no—
313C2×#120—31no—
314C2×C4×D4—31no—
315C22×C22⋊C4C3×D311yescharacteristic, complemented
316#399—31no—
317#397—31no—
318#394—31no—
319#394—31no—
320#388—31no—
321#388—31no—
322#386—31no—
323#386—31no—
324#385—31no—
325#380—31no—
326#379—31no—
327C24×C3—24no—
328C24×C3—24no—
329C24×C3—24no—
330C24×C3—22no—
331C24×C3—22no—
332C24×C3—22no—
333C24×C3—22no—
334C24×C3—22no—
335C24×C3—22no—
336C24×C3—22no—
337C24×C3—22no—
338C24×C3—22no—
339C24×C3—22no—
340C24×C3—21no—
341C24×C3—21no—
342C24×C3—21no—
343C24×C3—31no—
344C24×C3—42no—
345C24×C3—42no—
346C24×C3—41no—
347C24×C3—41no—
348C24×C3—41no—
349C24×C3—41no—
350C24×C3—42no—
351C24×C3—42no—
352C24×C3C22×D311yescharacteristic
353C24×C3C22×D311yescharacteristic
354C24×C3C22×D311yescharacteristic
355C24×C3C23×C311yescharacteristic
356C24×C3C23×C311yescharacteristic
357C24×C3C23×C311yescharacteristic
358C23×D3C23×C311yescharacteristic
359C2×C3×D4—34no—
360C2×C3×D4—62no—
361C2×C3×D4—62no—
362C2×C3×D4—62no—
363C2×C3×D4—62no—
364C2×C3×D4—62no—
365C2×C3×D4—62no—
366C2×C3×D4—121no—
367C2×C3×D4—121no—
368C22×C3×C4—24no—
369C22×C3×C4—24no—
370C22×C3×C4—22no—
371C22×C3×C4—22no—
372C22×C3×C4—22no—
373C22×C3×C4—22no—
374C22×C3×C4—22no—
375C22×C3×C4—22no—
376C22×C3×C4—22no—
377C22×C3×C4—22no—
378C22×C3×C4—21no—
379C22×C3×C4—21no—
380C22×C3×C4—21no—
381C22×C3×C4—21no—
382C22×C3×C4—31no—
383C22×C3×C4—31no—
384C22×C3×C4—31no—
385C22×C3×C4—31no—
386C22×C3×C4—31no—
387C22×C3×C4—31no—
388C22×C3×C4—31no—
389C22×C3×C4—42no—
390C22×C3×C4—42no—
391C22×C3×C4—41no—
392C22×C3×C4—41no—
393C22×C3×C4—41no—
394C22×C3×C4—41no—
395C22×C3×C4—42no—
396C22×C3×C4—42no—
397C22×C3×C4—62no—
398C22×C3×C4—62no—
399C22×C3×C4—121no—
400C22×C3×C4C22×D311yescharacteristic
401C22×C3×C4C22×D311yescharacteristic
402C22×C3×C4C22×D311yescharacteristic
403C22×C3×C4C22×D311yescharacteristic
404C22×C3×C4C23×C311yescharacteristic
405C22×C3×C4C23×C311yescharacteristic
406C22×C3×C4C23×C311yescharacteristic
407C22×C3×C4C23×C311yescharacteristic
408C2×#67—22no—
409C2×#67—22no—
410C2×#67—22no—
411C2×#67—22no—
412C2×#67—22no—
413C2×#67—22no—
414C2×#67—41no—
415C2×#67—41no—
416C2×#67C3×D414yes—
417C22×Dic3C23×C311yescharacteristic
418C22×Dic3C23×C311yescharacteristic
419C22×Dic3C23×C311yescharacteristic
420C22×Dic3C23×C311yescharacteristic
421C22×Dic3C23×C311yescharacteristic
422C22×Dic3C23×C311yescharacteristic
423C22×Dic3C23×C311yescharacteristic
424C2×C4×D3—22no—
425C2×C4×D3—22no—
426C2×C4×D3—41no—
427C3×C4⋊C4—62no—
428C3×C4⋊C4—62no—
429C3×C4⋊C4—62no—
430C3×C4⋊C4—121no—
431C3×C4⋊C4—121no—
432C3×C22⋊C4—24no—
433C3×C22⋊C4—24no—
434C3×C22⋊C4—24no—
435C3×C22⋊C4—22no—
436C3×C22⋊C4—22no—
437C3×C22⋊C4—22no—
438C3×C22⋊C4—22no—
439C3×C22⋊C4—22no—
440C3×C22⋊C4—22no—
441C3×C22⋊C4—24no—
442C3×C22⋊C4—62no—
443C3×C22⋊C4—62no—
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—121no—
452C3×C22⋊C4—121no—
453C3×C22⋊C4—121no—
454C3×C22⋊C4#6714yescomplemented
455C3×C22⋊C4C3×D414yescomplemented
456C3×C42—62no—
457#217—22no—
458#217—22no—
459#217—22no—
460#217—22no—
461#217—22no—
462#217—22no—
463#217—22no—
464#217—41no—
465#217—41no—
466(C2×D3)⋊C4—22no—
467(C2×D3)⋊C4—22no—
468(C2×D3)⋊C4—41no—
469C4⋊Dic3—22no—
470C4⋊Dic3—41no—
471Dic3⋊C4—22no—
472Dic3⋊C4—22no—
473Dic3⋊C4—41no—
474C4×Dic3—22no—
475C22×C32—22no—
476C22×C32—22no—
477C22×C32—22no—
478C22×C32—22no—
479C22×C32—22no—
480C22×C32—22no—
481C22×C32—22no—
482C22×C32—22no—
483C22×C32—22no—
484C22×C32—22no—
485C22×C32—22no—
486C22×C32—22no—
487C22×C32—416no—
488C22×C32—41no—
489C22×C32—41no—
490C22×C32—41no—
491C22×C32—41no—
492C22×C32—41no—
493C22×C32—41no—
494C22×C32—41no—
495C22×C32—41no—
496C22×C32#12314yescomplemented
497C22×C32C22×D411yescharacteristic
498C22×C32C22×D411yescharacteristic
499C22×C32C2×#4111yescharacteristic
500C22×C32C2×#4111yescharacteristic
501C22×C32C2×#4111yescharacteristic
502C22×C32H(5,𝔽2)11yescharacteristic
503C22×C32H(5,𝔽2)11yescharacteristic
504C2×C3×D3—22no—
505C2×C3×D3—22no—
506C2×C3×D3—22no—
507C2×C3×D3—41no—
508C2×C3×D3—41no—
509C2×C3×D3—41no—
510C2×C3×D3—41no—
511C32×C4—22no—
512C32×C4—22no—
513C32×C4—41no—
514C32×C4—41no—
515C3×Dic3—22no—
516C3×Dic3—41no—
517C3×Dic3—41no—
518C3×Dic3—41no—
519C3×Dic3—41no—
520C3×Dic3—41no—
521C3×Dic3—41no—
522C25C2×C3×D311yescharacteristic
523C22×D4—31no—
524C22×D4—31no—
525C22×D4—31no—
526C23×C4—31no—
527C23×C4C2×C3×D311yescharacteristic
528C23×C4C2×C3×D311yescharacteristic
529#123—64no—
530#120—64no—
531C4×D4—64no—
532C2×C4⋊C4—31no—
533C2×C4⋊C4—31no—
534C2×C4⋊C4—31no—
535C2×C4⋊C4—31no—
536C2×C4⋊C4—31no—
537C2×C22⋊C4—24no—
538C2×C22⋊C4—31no—
539C2×C22⋊C4—31no—
540C2×C22⋊C4—31no—
541C2×C22⋊C4—31no—
542C2×C22⋊C4—31no—
543C2×C22⋊C4—31no—
544C2×C22⋊C4—31no—
545C2×C22⋊C4—31no—
546C2×C22⋊C4—31no—
547C2×C22⋊C4—31no—
548C2×C22⋊C4—31no—
549C2×C22⋊C4—31no—
550C2×C22⋊C4C2×C3×D311yescharacteristic
551C2×C22⋊C4C2×C3×D311yescharacteristic
552C2×C22⋊C4C2×C3×D311yescharacteristic
553C2×C22⋊C4C2×C3×D311yescharacteristic
554C2×C42—31no—
555#95—31no—
556#95—31no—
557#95—31no—
558#95—31no—
559#95—31no—
560#95—31no—
561C23×C3—22no—
562C23×C3—22no—
563C23×C3—22no—
564C23×C3—22no—
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—22no—
574C23×C3—216no—
575C23×C3—28no—
576C23×C3—28no—
577C23×C3—22no—
578C23×C3—22no—
579C23×C3—22no—
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—21no—
596C23×C3—21no—
597C23×C3—21no—
598C23×C3—21no—
599C23×C3—21no—
600C23×C3—21no—
601C23×C3—21no—
602C23×C3—21no—
603C23×C3—21no—
604C23×C3—21no—
605C23×C3—22no—
606C23×C3—22no—
607C23×C3—22no—
608C23×C3—22no—
609C23×C3—22no—
610C23×C3—32no—
611C23×C3—41no—
612C23×C3—41no—
613C23×C3—41no—
614C23×C3—41no—
615C23×C3—41no—
616C23×C3—41no—
617C23×C3—41no—
618C23×C3—41no—
619C23×C3—44no—
620C23×C3—44no—
621C23×C3—44no—
622C23×C3—44no—
623C23×C3—44no—
624C23×C3—44no—
625C23×C3—44no—
626C23×C3—44no—
627C23×C3—48no—
628C23×C3—48no—
629C23×C3—48no—
630C23×C3—48no—
631C23×C3—48no—
632C23×C3—44no—
633C23×C3—44no—
634C23×C3—48no—
635C23×C3—44no—
636C23×C3—44no—
637C23×C3—61no—
638C23×C3—61no—
639C23×C3—61no—
640C23×C3—61no—
641C23×C3—61no—
642C23×C3—61no—
643C23×C3#23512yes—
644C23×C3#23512yes—
645C23×C3D3×D412yes—
646C23×C3#23712yes—
647C23×C3C2×#6712yes—
648C23×C3C2×C3×D412yes—
649C23×C3C2×C3×D412yes—
650C23×C3C3×#4112yes—
651C23×C3C3×#4112yes—
652C23×C3C3×#4112yes—
653C23×C3C23×D311yescharacteristic
654C23×C3C24×C311yescharacteristic
655C22×D3—21no—
656C22×D3—21no—
657C22×D3—21no—
658C22×D3—21no—
659C22×D3—21no—
660C22×D3—21no—
661C22×D3C2×C3×D412yes—
662C3×D4—68no—
663C3×D4—124no—
664C3×D4—124no—
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—22no—
674C2×C3×C4—22no—
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—21no—
685C2×C3×C4—21no—
686C2×C3×C4—21no—
687C2×C3×C4—22no—
688C2×C3×C4—22no—
689C2×C3×C4—32no—
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—44no—
699C2×C3×C4—44no—
700C2×C3×C4—44no—
701C2×C3×C4—44no—
702C2×C3×C4—48no—
703C2×C3×C4—48no—
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—61no—
718C2×C3×C4—61no—
719C2×C3×C4—61no—
720C2×C3×C4—61no—
721C2×C3×C4—61no—
722C2×C3×C4—61no—
723C2×C3×C4—61no—
724C2×C3×C4—124no—
725C2×C3×C4C2×#6712yes—
726C2×C3×C4C2×#6712yes—
727C2×C3×C4C2×C3×D412yes—
728C2×C3×C4C2×C3×D412yes—
729#67—28no—
730#67—44no—
731#67—44no—
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—21no—
742C2×Dic3—21no—
743C2×Dic3—21no—
744C2×Dic3—21no—
745C2×Dic3—21no—
746C2×Dic3—21no—
747C2×Dic3—21no—
748C2×Dic3—21no—
749C2×Dic3—21no—
750C2×Dic3—21no—
751C2×Dic3—21no—
752C2×Dic3C2×C3×D412yes—
753C4×D3—44no—
754C2×C32—24no—
755C2×C32—42no—
756C2×C32—42no—
757C2×C32C2×#12311yescharacteristic
758C2×C32#52511yescharacteristic
759C2×C32#53811yescharacteristic
760C2×C32D4211yescharacteristic
761C2×C32#54611yescharacteristic
762C2×C32#54611yescharacteristic
763C2×C32#55111yescharacteristic
764C3×D3—42no—
765C24—22no—
766C24—22no—
767C24—22no—
768C24—22no—
769C24—22no—
770C24—31no—
771C24—41no—
772C24—41no—
773C24C22×C3×D311yescharacteristic
774C24C22×C3×D311yescharacteristic
775C24C22×C3×D311yescharacteristic
776C2×D4—34no—
777C2×D4—62no—
778C2×D4—62no—
779C2×D4—62no—
780C2×D4—62no—
781C2×D4—62no—
782C2×D4—62no—
783C2×D4—121no—
784C2×D4—121no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—31no—
790C22×C4—31no—
791C22×C4—31no—
792C22×C4—31no—
793C22×C4—31no—
794C22×C4—31no—
795C22×C4—31no—
796C22×C4—41no—
797C22×C4—41no—
798C22×C4—62no—
799C22×C4—62no—
800C22×C4—121no—
801C22×C4C22×C3×D311yescharacteristic
802C22×C4C22×C3×D311yescharacteristic
803C22×C4C22×C3×D311yescharacteristic
804C22×C4C22×C3×D311yescharacteristic
805C4⋊C4—62no—
806C4⋊C4—62no—
807C4⋊C4—62no—
808C4⋊C4—121no—
809C4⋊C4—121no—
810C22⋊C4—22no—
811C22⋊C4—22no—
812C22⋊C4—22no—
813C22⋊C4—62no—
814C22⋊C4—62no—
815C22⋊C4—62no—
816C22⋊C4—62no—
817C22⋊C4—62no—
818C22⋊C4—62no—
819C22⋊C4—62no—
820C22⋊C4—62no—
821C22⋊C4—62no—
822C22⋊C4—121no—
823C22⋊C4—121no—
824C22⋊C4—121no—
825C22⋊C4C3×#6714yescomplemented
826C42—62no—
827C22×C3—24no—
828C22×C3—24no—
829C22×C3—24no—
830C22×C3—24no—
831C22×C3—24no—
832C22×C3—24no—
833C22×C3—22no—
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—24no—
846C22×C3—24no—
847C22×C3—22no—
848C22×C3—22no—
849C22×C3—22no—
850C22×C3—22no—
851C22×C3—22no—
852C22×C3—22no—
853C22×C3—22no—
854C22×C3—22no—
855C22×C3—22no—
856C22×C3—22no—
857C22×C3—22no—
858C22×C3—22no—
859C22×C3—24no—
860C22×C3—21no—
861C22×C3—21no—
862C22×C3—21no—
863C22×C3—21no—
864C22×C3—21no—
865C22×C3—21no—
866C22×C3—21no—
867C22×C3—42no—
868C22×C3—42no—
869C22×C3—42no—
870C22×C3—42no—
871C22×C3—432no—
872C22×C3—416no—
873C22×C3—416no—
874C22×C3—42no—
875C22×C3—42no—
876C22×C3—42no—
877C22×C3—42no—
878C22×C3—42no—
879C22×C3—42no—
880C22×C3—42no—
881C22×C3—42no—
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—41no—
892C22×C3—41no—
893C22×C3—41no—
894C22×C3—41no—
895C22×C3—41no—
896C22×C3—41no—
897C22×C3—41no—
898C22×C3—62no—
899C22×C3—62no—
900C22×C3—62no—
901C22×C3—121no—
902C22×C3—121no—
903C22×C3—121no—
904C22×C3—121no—
905C22×C3#88314yescomplemented
906C22×C3C3×#12314yescomplemented
907C22×C3C2×#23511yescharacteristic
908C22×C3C2×#23511yescharacteristic
909C22×C3C2×D3×D411yescharacteristic
910C22×C3C2×#23711yescharacteristic
911C22×C3#100411yescharacteristic
912C22×C3#100411yescharacteristic
913C22×C3C22×#6711yescharacteristic
914C22×C3C22×C3×D411yescharacteristic
915C22×C3C22×C3×D411yescharacteristic
916C22×C3C2×C3×#4111yescharacteristic
917C22×C3C2×C3×#4111yescharacteristic
918C22×C3C2×C3×#4111yescharacteristic
919C22×C3C3×H(5,𝔽2)11yescharacteristic
920C22×C3C3×H(5,𝔽2)11yescharacteristic
921C2×D3—22no—
922C2×D3—22no—
923C2×D3—22no—
924C2×D3—41no—
925C2×D3—41no—
926C2×D3—41no—
927C2×D3—41no—
928C3×C4—22no—
929C3×C4—22no—
930C3×C4—22no—
931C3×C4—22no—
932C3×C4—42no—
933C3×C4—42no—
934C3×C4—42no—
935C3×C4—42no—
936C3×C4—41no—
937C3×C4—41no—
938C3×C4—41no—
939C3×C4—41no—
940C3×C4—62no—
941C3×C4—121no—
942C3×C4—121no—
943C3×C4—121no—
944C3×C4—121no—
945C3×C4—121no—
946C3×C4—121no—
947Dic3—22no—
948Dic3—41no—
949Dic3—41no—
950Dic3—41no—
951Dic3—41no—
952Dic3—41no—
953Dic3—41no—
954C32#241811yescharacteristic, complemented, Sylow
955C23—21no—
956C23—21no—
957C23—21no—
958C23—21no—
959C23—28no—
960C23—21no—
961C23—21no—
962C23—21no—
963C23—21no—
964C23—21no—
965C23—21no—
966C23—21no—
967C23—21no—
968C23—21no—
969C23—21no—
970C23—21no—
971C23—21no—
972C23—32no—
973C23—44no—
974C23—44no—
975C23—44no—
976C23—44no—
977C23—44no—
978C23—44no—
979C23—61no—
980C23—61no—
981C23—61no—
982C23—61no—
983C23—61no—
984C23—61no—
985C23C3×#23512yes—
986C23C3×#23512yes—
987C23C3×D3×D412yes—
988C23C3×#23712yes—
989C23C2×C3×#6712yes—
990C23C23×C3×D311yescharacteristic
991D4—68no—
992D4—124no—
993D4—124no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—32no—
1005C2×C4—44no—
1006C2×C4—44no—
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—61no—
1021C2×C4—61no—
1022C2×C4—61no—
1023C2×C4—61no—
1024C2×C4—61no—
1025C2×C4—61no—
1026C2×C4—61no—
1027C2×C4—124no—
1028C2×C4C2×C3×#6712yes—
1029C2×C4C2×C3×#6712yes—
1030C2×C3—28no—
1031C2×C3—24no—
1032C2×C3—24no—
1033C2×C3—21no—
1034C2×C3—21no—
1035C2×C3—21no—
1036C2×C3—21no—
1037C2×C3—21no—
1038C2×C3—21no—
1039C2×C3—21no—
1040C2×C3—44no—
1041C2×C3—44no—
1042C2×C3—42no—
1043C2×C3—42no—
1044C2×C3—42no—
1045C2×C3—42no—
1046C2×C3—122no—
1047C2×C3C2×#88311yescharacteristic
1048C2×C3#549011yescharacteristic
1049C2×C3#549411yescharacteristic
1050C2×C3#549511yescharacteristic
1051C2×C3#579111yescharacteristic
1052C2×C3D4×#6711yescharacteristic
1053C2×C3#580611yescharacteristic
1054C2×C3C2×C3×#12311yescharacteristic
1055C2×C3C3×#52511yescharacteristic
1056C2×C3C3×#53811yescharacteristic
1057C2×C3C3×D4211yescharacteristic
1058C2×C3C3×#54611yescharacteristic
1059C2×C3C3×#54611yescharacteristic
1060C2×C3C3×#55111yescharacteristic
1061D3—42no—
1062C22—22no—
1063C22—22no—
1064C22—22no—
1065C22—22no—
1066C22—22no—
1067C22—22no—
1068C22—22no—
1069C22—22no—
1070C22—22no—
1071C22—22no—
1072C22—22no—
1073C22—22no—
1074C22—416no—
1075C22—41no—
1076C22—41no—
1077C22—41no—
1078C22—41no—
1079C22—41no—
1080C22—41no—
1081C22—41no—
1082C22—41no—
1083C22—62no—
1084C22—62no—
1085C22—62no—
1086C22—121no—
1087C22—121no—
1088C22—121no—
1089C22—121no—
1090C22C3×#88314yescomplemented
1091C22C2×C3×#23511yescharacteristic
1092C22C2×C3×#23511yescharacteristic
1093C22C2×C3×D3×D411yescharacteristic
1094C22C2×C3×#23711yescharacteristic
1095C22C3×#100411yescharacteristic
1096C22C3×#100411yescharacteristic
1097C22C22×C3×#6711yescharacteristic
1098C4—22no—
1099C4—22no—
1100C4—41no—
1101C4—41no—
1102C4—62no—
1103C4—121no—
1104C4—121no—
1105C4—121no—
1106C4—121no—
1107C4—121no—
1108C4—121no—
1109C3—21no—
1110C3#8212811yescharacteristic, direct product factor
1111C3C3×#241811yescharacteristic, complemented
1112C2—24no—
1113C2—42no—
1114C2—42no—
1115C2—122no—
1116C2C2×C3×#88311yescharacteristic
1117C2C3×#549011yescharacteristic
1118C2C3×#549411yescharacteristic
1119C2C3×#549511yescharacteristic
1120C2C3×#579111yescharacteristic
1121C2C3×D4×#6711yescharacteristic
1122C2C3×#580611yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC22×C32×C22⋊C4C2
socleC23×C32C24
prime radicalC2×C3×#953C2
hypercenterC22×C3×C22⋊C4D3
hypocenterC3C3×#2418
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C22×C3×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×C32×C22⋊C4C2semidirect
3. C2×C3×C4×#67C2semidirect
4. C2×C3×#883C2semidirect
5. C3×#5247C2semidirect
6. C3×#5213C2semidirect
7. C3×#5212C2semidirect
8. C3×#5210C2semidirect
9. C3×#4961C2semidirect
10. C3×#4959C2semidirect
11. C3×#4956C2semidirect
12. C3×#4952C2semidirect
13. C3×#4951C2semidirect
14. C3×#4949C2semidirect
15. C3×#4945C2semidirect
17. #82128C3direct (N × H)
24. C22×C3×C4×D3C22semidirect
41. C2×C3×(C2×D3)⋊C4C22semidirect
42. C2×C3×(C2×D3)⋊C4C22semidirect
43. C2×C3×(C2×D3)⋊C4C22semidirect
44. C2×C3×C4⋊Dic3C22semidirect
45. C2×C3×C4⋊Dic3C22semidirect
46. C2×C3×Dic3⋊C4C22semidirect
47. C2×C3×Dic3⋊C4C22semidirect
48. C2×C3×Dic3⋊C4C22semidirect
49. 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
61. C22×C3×C22⋊C4D3semidirect
62. C22×C3×C22⋊C4C2×C3semidirect
64. C2×C4×#67C2×C3semidirect
65. C2×#883C2×C3semidirect
77. #5247C2×C3semidirect
78. #5213C2×C3semidirect
79. #5212C2×C3semidirect
80. #5210C2×C3semidirect
81. #4961C2×C3semidirect
82. #4959C2×C3semidirect
83. #4956C2×C3semidirect
84. #4952C2×C3semidirect
85. #4951C2×C3semidirect
86. #4949C2×C3semidirect
87. #4945C2×C3semidirect
131. C32×C22⋊C4D4semidirect
167. C22×C4×D3C22×C3semidirect
215. C2×(C2×D3)⋊C4C22×C3semidirect
216. C2×(C2×D3)⋊C4C22×C3semidirect
217. C2×(C2×D3)⋊C4C22×C3semidirect
218. C2×C4⋊Dic3C22×C3semidirect
219. C2×C4⋊Dic3C22×C3semidirect
220. C2×Dic3⋊C4C22×C3semidirect
221. C2×Dic3⋊C4C22×C3semidirect
222. C2×Dic3⋊C4C22×C3semidirect
223. C2×C4×Dic3C22×C3semidirect
231. C3⋊#95C22×C3semidirect
232. C3⋊#95C22×C3semidirect
233. C3⋊#95C22×C3semidirect
234. C3⋊#95C22×C3semidirect
235. C3⋊#95C22×C3semidirect
236. C3⋊#95C22×C3semidirect
315. C22×C22⋊C4C3×D3semidirect
454. C3×C22⋊C4#67semidirect
455. C3×C22⋊C4C3×D4semidirect
496. C22×C32#123semidirect
825. C22⋊C4C3×#67semidirect
905. C22×C3#883semidirect
906. C22×C3C3×#123semidirect
954. C32#2418semidirect
1090. C22C3×#883semidirect
1110. C3#82128direct (N × H)
1111. C3C3×#2418semidirect

Maximal subgroups

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

subgroupindex
C22×C32×C22⋊C42
C2×C3×#9532
C2×C3×C4×#672
C2×C3×#8832
C3×#52472
C3×#52132
C3×#52122
C3×#52102
C3×#49612
C3×#49592
C3×#49562
C3×#49522
C3×#49512
C3×#49492
C3×#49452
C3×#24183
#821283