Finite Group Databasebeta

← C3×#82670 #11824532

Subgroups — C3×#82670 #11824532

Order 1152.

1661 conjugacy classes of subgroups.

The subgroup lattice has 1100 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#121C211yesmaximal, characteristic, complemented
2C2×C3×#939C211yesmaximal, characteristic, complemented
3C2×C3×#939C211yesmaximal, characteristic, complemented
4C2×C3×D4×Dic3C211yesmaximal, characteristic, complemented
5C3×#5223C211yesmaximal, characteristic, complemented
6C3×#5220C211yesmaximal, characteristic, complemented
7C3×#5220C211yesmaximal, characteristic, complemented
8C3×#5213C211yesmaximal, characteristic, complemented
9C2×C3×C3⋊#95C211yesmaximal, characteristic, complemented
10C3×#4990C211yesmaximal, characteristic, complemented
11C3×#4982C211yesmaximal, characteristic, complemented
12C3×#4961C211yesmaximal, characteristic, complemented
13C3×#4958C211yesmaximal, characteristic, complemented
14C3×#4952C211yesmaximal, characteristic, complemented
15C3×#4945C211yesmaximal, characteristic, complemented
16C3×#2543—31nomaximal
17#82670C311yesmaximal, characteristic, direct product factor
18C22×C32×D4C2211yescharacteristic
19C22×C32×D4C2211yescharacteristic
20C22×C32×D4C2211yescharacteristic
21C23×C32×C4C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic
24C22×C3×#67C2211yescharacteristic
25C23×C3×Dic3C2211yescharacteristic
26C23×C3×Dic3C2211yescharacteristic
27C23×C3×Dic3C2211yescharacteristic
28C32×#121—24no—
29C2×C32×C4⋊C4C2211yescharacteristic
30C2×C32×C22⋊C4C2211yescharacteristic
31C2×C32×C22⋊C4C2211yescharacteristic
32C2×C3×#217C2211yescharacteristic
33C2×C3×#217C2211yescharacteristic
34C2×C3×#217C2211yescharacteristic
35C2×C3×#217C2211yescharacteristic
36C2×C3×#217C2211yescharacteristic
37C2×C3×#217C2211yescharacteristic
38C3×#939—24no—
39C3×#939—24no—
40C3×D4×Dic3—24no—
41C2×C3×(C2×D3)⋊C4C2211yescharacteristic
42C2×C3×(C2×D3)⋊C4C2211yescharacteristic
43C2×C3×(C2×D3)⋊C4C2211yescharacteristic
44C2×C3×(C2×D3)⋊C4C2211yescharacteristic
45C2×C3×C4⋊Dic3C2211yescharacteristic
46C2×C3×Dic3⋊C4C2211yescharacteristic
47C2×C3×Dic3⋊C4C2211yescharacteristic
48C2×C3×C4×Dic3C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53C3×C3⋊#95C2211yescharacteristic
54C3×C3⋊#95C2211yescharacteristic
55C3×C3⋊#95C2211yescharacteristic
56C3×C3⋊#95C2211yescharacteristic
57C2×C3×#121—21no—
58C2×C3×#121—31no—
59C2×C3×#121—31no—
60C2×C3×#121D311yescharacteristic, complemented
61C2×C3×#121C2×C311yescharacteristic, complemented
62C2×C3×C4×D4—31no—
63C2×#939C2×C311yescharacteristic, complemented
64C2×#939C2×C311yescharacteristic, complemented
65C2×D4×Dic3C2×C311yescharacteristic, complemented
66C3×#398—31no—
67C3×#397—31no—
68C3×#394—31no—
69C3×#392—31no—
70C3×#388—31no—
71C3×#388—31no—
72C3×#386—31no—
73C3×#386—31no—
74C3×#386—31no—
75C3×#386—31no—
76C2×C3×#95—31no—
77#5223C2×C311yescharacteristic, complemented
78#5220C2×C311yescharacteristic, complemented
79#5220C2×C311yescharacteristic, complemented
80#5213C2×C311yescharacteristic, complemented
81C2×C3⋊#95C2×C311yescharacteristic, complemented
82#4990C2×C311yescharacteristic, complemented
83#4982C2×C311yescharacteristic, complemented
84#4961C2×C311yescharacteristic, complemented
85#4958C2×C311yescharacteristic, complemented
86#4952C2×C311yescharacteristic, complemented
87#4945C2×C311yescharacteristic, complemented
88C24×C32C2311yescharacteristic
89C24×C32C2311yescharacteristic
90C24×C32C2311yescharacteristic
91C23×C3×D3C2311yescharacteristic
92C2×C32×D4—22no—
93C2×C32×D4—22no—
94C2×C32×D4—22no—
95C2×C32×D4—22no—
96C2×C32×D4—22no—
97C2×C32×D4—22no—
98C2×C32×D4—22no—
99C2×C32×D4—41no—
100C2×C32×D4D414yescomplemented
101C22×C32×C4—22no—
102C22×C32×C4—22no—
103C22×C32×C4—41no—
104C22×C32×C4C2311yescharacteristic
105C22×C32×C4C2311yescharacteristic
106C22×C32×C4C2311yescharacteristic
107C22×C32×C4C2311yescharacteristic
108C2×C3×#67—22no—
109C2×C3×#67—22no—
110C2×C3×#67—22no—
111C2×C3×#67—22no—
112C2×C3×#67—22no—
113C2×C3×#67—22no—
114C2×C3×#67—41no—
115C2×C3×#67—41no—
116C2×C3×#67—41no—
117C22×C3×Dic3—22no—
118C22×C3×Dic3—22no—
119C22×C3×Dic3—22no—
120C22×C3×Dic3—41no—
121C22×C3×Dic3—41no—
122C22×C3×Dic3—41no—
123C22×C3×Dic3—41no—
124C22×C3×Dic3—41no—
125C22×C3×Dic3D414yescomplemented
126C22×C3×Dic3C2311yescharacteristic
127C22×C3×Dic3C2311yescharacteristic
128C22×C3×Dic3C2311yescharacteristic
129C22×C3×Dic3C2311yescharacteristic
130C22×C3×Dic3C2311yescharacteristic
131C22×C3×Dic3C2311yescharacteristic
132C22×C3×Dic3C2311yescharacteristic
133C32×C4⋊C4—22no—
134C32×C22⋊C4—22no—
135C32×C22⋊C4—22no—
136C3×#217—22no—
137C3×#217—22no—
138C3×#217—22no—
139C3×#217—22no—
140C3×#217—22no—
141C3×#217—41no—
142C3×(C2×D3)⋊C4—22no—
143C3×(C2×D3)⋊C4—22no—
144C3×(C2×D3)⋊C4—22no—
145C3×(C2×D3)⋊C4—41no—
146C3×C4⋊Dic3—22no—
147C3×Dic3⋊C4—22no—
148C3×Dic3⋊C4—22no—
149C3×C4×Dic3—22no—
150#2543—31noSylow
151C22×C3×D4—21no—
152C22×C3×D4—21no—
153C22×C3×D4—21no—
154C22×C3×D4—31no—
155C22×C3×D4—31no—
156C22×C3×D4—31no—
157C22×C3×D4C2×D311yescharacteristic
158C22×C3×D4C2×D311yescharacteristic
159C22×C3×D4C2×D311yescharacteristic
160C22×C3×D4C22×C311yescharacteristic
161C22×C3×D4C22×C311yescharacteristic
162C22×C3×D4C22×C311yescharacteristic
163C23×C3×C4—21no—
164C23×C3×C4—31no—
165C23×C3×C4—31no—
166C23×C3×C4—31no—
167C23×C3×C4C2×D311yescharacteristic
168C23×C3×C4C22×C311yescharacteristic
169C22×#67C22×C311yescharacteristic
170C22×#67C22×C311yescharacteristic
171C22×#67C22×C311yescharacteristic
172C23×Dic3C22×C311yescharacteristic
173C23×Dic3C22×C311yescharacteristic
174C23×Dic3C22×C311yescharacteristic
175C3×#121—28no—
176C3×#121—24no—
177C3×#121—24no—
178C3×#121—64no—
179C3×#121—64no—
180C3×C4×D4—64no—
181C2×C3×C4⋊C4—21no—
182C2×C3×C4⋊C4—31no—
183C2×C3×C4⋊C4—31no—
184C2×C3×C4⋊C4—31no—
185C2×C3×C4⋊C4C2×D311yescharacteristic
186C2×C3×C4⋊C4C22×C311yescharacteristic
187C2×C3×C22⋊C4—21no—
188C2×C3×C22⋊C4—21no—
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⋊C4—31no—
196C2×C3×C22⋊C4—31no—
197C2×C3×C22⋊C4—31no—
198C2×C3×C22⋊C4—31no—
199C2×C3×C22⋊C4C2×D311yescharacteristic
200C2×C3×C22⋊C4C2×D311yescharacteristic
201C2×C3×C22⋊C4C22×C311yescharacteristic
202C2×C3×C22⋊C4C22×C311yescharacteristic
203C2×C3×C42—31no—
204C2×#217C22×C311yescharacteristic
205C2×#217C22×C311yescharacteristic
206C2×#217C22×C311yescharacteristic
207C2×#217C22×C311yescharacteristic
208C2×#217C22×C311yescharacteristic
209C2×#217C22×C311yescharacteristic
210#939—24no—
211#939—24no—
212D4×Dic3—24no—
213C2×(C2×D3)⋊C4C22×C311yescharacteristic
214C2×(C2×D3)⋊C4C22×C311yescharacteristic
215C2×(C2×D3)⋊C4C22×C311yescharacteristic
216C2×(C2×D3)⋊C4C22×C311yescharacteristic
217C2×C4⋊Dic3C22×C311yescharacteristic
218C2×Dic3⋊C4C22×C311yescharacteristic
219C2×Dic3⋊C4C22×C311yescharacteristic
220C2×C4×Dic3C22×C311yescharacteristic
221C3×#95—31no—
222C3×#95—31no—
223C3×#95—31no—
224C3×#95—31no—
225C3×#95—31no—
226C3×#95—31no—
227C3×#95—31no—
228C3×#95—31no—
229C3⋊#95C22×C311yescharacteristic
230C3⋊#95C22×C311yescharacteristic
231C3⋊#95C22×C311yescharacteristic
232C3⋊#95C22×C311yescharacteristic
233C3⋊#95C22×C311yescharacteristic
234C3⋊#95C22×C311yescharacteristic
235C3⋊#95C22×C311yescharacteristic
236C3⋊#95C22×C311yescharacteristic
237C23×C32—21no—
238C23×C32—21no—
239C23×C32—21no—
240C23×C32—21no—
241C23×C32—21no—
242C23×C32—21no—
243C23×C32—21no—
244C23×C32—21no—
245C23×C32—21no—
246C23×C32—21no—
247C23×C32—21no—
248C23×C32—21no—
249C23×C32—21no—
250C23×C32—21no—
251C23×C32—21no—
252C23×C32—21no—
253C23×C32—21no—
254C23×C32C2×D412yes—
255C23×C32C2×D412yes—
256C23×C32C2×D412yes—
257C23×C32#4112yes—
258C23×C32C2411yescharacteristic
259C22×C3×D3—21no—
260C22×C3×D3—21no—
261C22×C3×D3—21no—
262C22×C3×D3—21no—
263C22×C3×D3—21no—
264C22×C3×D3—21no—
265C22×C3×D3—21no—
266C32×D4—28no—
267C32×D4—44no—
268C32×D4—44no—
269C2×C32×C4—21no—
270C2×C32×C4—21no—
271C2×C32×C4—21no—
272C2×C32×C4—21no—
273C2×C32×C4—21no—
274C2×C32×C4—21no—
275C2×C32×C4—21no—
276C2×C32×C4—21no—
277C2×C32×C4—21no—
278C2×C32×C4—21no—
279C2×C32×C4—44no—
280C2×C32×C4C2×D412yes—
281C2×C32×C4#4112yes—
282C3×#67—44no—
283C3×#67—44no—
284C3×#67—44no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3—21no—
287C2×C3×Dic3—21no—
288C2×C3×Dic3—21no—
289C2×C3×Dic3—21no—
290C2×C3×Dic3—21no—
291C2×C3×Dic3—21no—
292C2×C3×Dic3—21no—
293C2×C3×Dic3—21no—
294C2×C3×Dic3—21no—
295C2×C3×Dic3—21no—
296C2×C3×Dic3—21no—
297C2×C3×Dic3—21no—
298C2×C3×Dic3—21no—
299C2×C3×Dic3—21no—
300C2×C3×Dic3—21no—
301C2×C3×Dic3—21no—
302C2×C3×Dic3—21no—
303C2×C3×Dic3—44no—
304C2×C3×Dic3—44no—
305C2×C3×Dic3—44no—
306C2×C3×Dic3C2×D412yes—
307C2×C3×Dic3C2×D412yes—
308C2×C3×Dic3#4112yes—
309C2×#121—31no—
310C2×#121—31no—
311C2×#121C3×D311yescharacteristic, complemented
312C2×C4×D4—31no—
313#398—31no—
314#397—31no—
315#394—31no—
316#392—31no—
317#388—31no—
318#388—31no—
319#386—31no—
320#386—31no—
321#386—31no—
322#386—31no—
323C2×#95—31no—
324C24×C3—21no—
325C24×C3—21no—
326C24×C3—21no—
327C24×C3—31no—
328C24×C3C22×D311yescharacteristic
329C24×C3C22×D311yescharacteristic
330C24×C3C22×D311yescharacteristic
331C24×C3C23×C311yescharacteristic
332C24×C3C23×C311yescharacteristic
333C24×C3C23×C311yescharacteristic
334C23×D3C23×C311yescharacteristic
335C2×C3×D4—22no—
336C2×C3×D4—22no—
337C2×C3×D4—22no—
338C2×C3×D4—22no—
339C2×C3×D4—24no—
340C2×C3×D4—24no—
341C2×C3×D4—22no—
342C2×C3×D4—22no—
343C2×C3×D4—22no—
344C2×C3×D4—22no—
345C2×C3×D4—22no—
346C2×C3×D4—22no—
347C2×C3×D4—22no—
348C2×C3×D4—22no—
349C2×C3×D4—22no—
350C2×C3×D4—22no—
351C2×C3×D4—24no—
352C2×C3×D4—42no—
353C2×C3×D4—42no—
354C2×C3×D4—42no—
355C2×C3×D4—42no—
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—62no—
365C2×C3×D4—62no—
366C2×C3×D4—121no—
367C2×C3×D4—121no—
368C2×C3×D4—121no—
369C2×C3×D4#6714yescomplemented
370C2×C3×D4C3×D414yescomplemented
371C22×C3×C4—24no—
372C22×C3×C4—22no—
373C22×C3×C4—22no—
374C22×C3×C4—22no—
375C22×C3×C4—22no—
376C22×C3×C4—21no—
377C22×C3×C4—21no—
378C22×C3×C4—21no—
379C22×C3×C4—21no—
380C22×C3×C4—31no—
381C22×C3×C4—31no—
382C22×C3×C4—31no—
383C22×C3×C4—34no—
384C22×C3×C4—31no—
385C22×C3×C4—31no—
386C22×C3×C4—31no—
387C22×C3×C4—31no—
388C22×C3×C4—42no—
389C22×C3×C4—41no—
390C22×C3×C4—41no—
391C22×C3×C4—42no—
392C22×C3×C4—62no—
393C22×C3×C4—62no—
394C22×C3×C4—62no—
395C22×C3×C4—121no—
396C22×C3×C4—121no—
397C22×C3×C4—121no—
398C22×C3×C4—121no—
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×#67—41no—
417C22×Dic3—22no—
418C22×Dic3—22no—
419C22×Dic3—22no—
420C22×Dic3—41no—
421C22×Dic3—41no—
422C22×Dic3—41no—
423C22×Dic3—41no—
424C22×Dic3—41no—
425C22×Dic3C3×D414yescomplemented
426C22×Dic3C23×C311yescharacteristic
427C22×Dic3C23×C311yescharacteristic
428C22×Dic3C23×C311yescharacteristic
429C22×Dic3C23×C311yescharacteristic
430C22×Dic3C23×C311yescharacteristic
431C22×Dic3C23×C311yescharacteristic
432C22×Dic3C23×C311yescharacteristic
433C3×C4⋊C4—24no—
434C3×C4⋊C4—22no—
435C3×C4⋊C4—22no—
436C3×C4⋊C4—62no—
437C3×C4⋊C4—62no—
438C3×C4⋊C4—62no—
439C3×C22⋊C4—24no—
440C3×C22⋊C4—24no—
441C3×C22⋊C4—22no—
442C3×C22⋊C4—22no—
443C3×C22⋊C4—22no—
444C3×C22⋊C4—22no—
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—62no—
453C3×C22⋊C4—121no—
454C3×C22⋊C4—121no—
455C3×C42—62no—
456#217—22no—
457#217—22no—
458#217—22no—
459#217—22no—
460#217—22no—
461#217—41no—
462(C2×D3)⋊C4—22no—
463(C2×D3)⋊C4—22no—
464(C2×D3)⋊C4—22no—
465(C2×D3)⋊C4—41no—
466C4⋊Dic3—22no—
467Dic3⋊C4—22no—
468Dic3⋊C4—22no—
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—41no—
480C22×C32—41no—
481C22×C32—41no—
482C22×C32—41no—
483C22×C32—41no—
484C22×C32—41no—
485C22×C32—41no—
486C22×C32—41no—
487C22×C32—41no—
488C22×C32—41no—
489C22×C32—41no—
490C22×C32#12114yes—
491C22×C32C22×D411yescharacteristic
492C22×C32C22×D411yescharacteristic
493C22×C32C2×#4111yescharacteristic
494C22×C32C2×#4111yescharacteristic
495C22×C32C2×#4111yescharacteristic
496C22×C32H(5,𝔽2)11yescharacteristic
497C22×C32H(5,𝔽2)11yescharacteristic
498C2×C3×D3—41no—
499C2×C3×D3—41no—
500C2×C3×D3—41no—
501C2×C3×D3—41no—
502C2×C3×D3—41no—
503C2×C3×D3—41no—
504C2×C3×D3—41no—
505C32×C4—22no—
506C32×C4—22no—
507C32×C4—41no—
508C32×C4—41no—
509C3×Dic3—22no—
510C3×Dic3—22no—
511C3×Dic3—22no—
512C3×Dic3—41no—
513C3×Dic3—41no—
514C3×Dic3—41no—
515C3×Dic3—41no—
516C22×D4—31no—
517C22×D4—31no—
518C22×D4—31no—
519C22×D4C2×C3×D311yescharacteristic
520C22×D4C2×C3×D311yescharacteristic
521C22×D4C2×C3×D311yescharacteristic
522C23×C4—31no—
523C23×C4—31no—
524C23×C4—31no—
525C23×C4C2×C3×D311yescharacteristic
526#121—24no—
527#121—64no—
528#121—64no—
529C4×D4—64no—
530C2×C4⋊C4—31no—
531C2×C4⋊C4—31no—
532C2×C4⋊C4—31no—
533C2×C4⋊C4C2×C3×D311yescharacteristic
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—31no—
543C2×C22⋊C4—31no—
544C2×C22⋊C4C2×C3×D311yescharacteristic
545C2×C22⋊C4C2×C3×D311yescharacteristic
546C2×C42—31no—
547#95—31no—
548#95—31no—
549#95—31no—
550#95—31no—
551#95—31no—
552#95—31no—
553#95—31no—
554#95—31no—
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—22no—
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—22no—
592C23×C3—22no—
593C23×C3—22no—
594C23×C3—22no—
595C23×C3—41no—
596C23×C3—41no—
597C23×C3—41no—
598C23×C3—41no—
599C23×C3—41no—
600C23×C3—41no—
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—61no—
612C23×C3—61no—
613C23×C3—61no—
614C23×C3—61no—
615C23×C3—61no—
616C23×C3—61no—
617C23×C3—61no—
618C23×C3D3×D412yes—
619C23×C3#23712yes—
620C23×C3C2×#6712yes—
621C23×C3C2×#6712yes—
622C23×C3C2×C3×D412yes—
623C23×C3C2×C3×D412yes—
624C23×C3C2×C3×D412yes—
625C23×C3C3×#4112yes—
626C23×C3C23×D311yescharacteristic
627C23×C3C24×C311yescharacteristic
628C22×D3—21no—
629C22×D3—21no—
630C22×D3—21no—
631C22×D3—21no—
632C22×D3—21no—
633C22×D3—21no—
634C22×D3—21no—
635C3×D4—28no—
636C3×D4—28no—
637C3×D4—48no—
638C3×D4—44no—
639C3×D4—44no—
640C3×D4—48no—
641C3×D4—48no—
642C3×D4—44no—
643C3×D4—44no—
644C3×D4—124no—
645C3×D4—124no—
646C3×D4—124no—
647C2×C3×C4—22no—
648C2×C3×C4—22no—
649C2×C3×C4—21no—
650C2×C3×C4—21no—
651C2×C3×C4—21no—
652C2×C3×C4—21no—
653C2×C3×C4—21no—
654C2×C3×C4—21no—
655C2×C3×C4—21no—
656C2×C3×C4—21no—
657C2×C3×C4—22no—
658C2×C3×C4—22no—
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—22no—
672C2×C3×C4—22no—
673C2×C3×C4—32no—
674C2×C3×C4—32no—
675C2×C3×C4—32no—
676C2×C3×C4—41no—
677C2×C3×C4—41no—
678C2×C3×C4—41no—
679C2×C3×C4—41no—
680C2×C3×C4—41no—
681C2×C3×C4—41no—
682C2×C3×C4—44no—
683C2×C3×C4—44no—
684C2×C3×C4—48no—
685C2×C3×C4—61no—
686C2×C3×C4—61no—
687C2×C3×C4—61no—
688C2×C3×C4—61no—
689C2×C3×C4—61no—
690C2×C3×C4—61no—
691C2×C3×C4—61no—
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—124no—
704C2×C3×C4—124no—
705C2×C3×C4—124no—
706C2×C3×C4#23712yes—
707C2×C3×C4C2×#6712yes—
708C2×C3×C4C2×C3×D412yes—
709C2×C3×C4C3×#4112yes—
710#67—44no—
711#67—44no—
712#67—44no—
713C2×Dic3—21no—
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×Dic3—21no—
731C2×Dic3—44no—
732C2×Dic3—44no—
733C2×Dic3—44no—
734C2×Dic3C2×C3×D412yes—
735C2×Dic3C2×C3×D412yes—
736C2×Dic3C3×#4112yes—
737C2×C32—24no—
738C2×C32—42no—
739C2×C32—81no—
740C2×C32C2×#12111yescharacteristic
741C2×C32#53211yescharacteristic
742C2×C32#53411yescharacteristic
743C2×C32#54611yescharacteristic
744C2×C32#54611yescharacteristic
745C2×C32#55311yescharacteristic
746C2×C32#55311yescharacteristic
747C3×D3—81no—
748C24—31no—
749C24C22×C3×D311yescharacteristic
750C24C22×C3×D311yescharacteristic
751C24C22×C3×D311yescharacteristic
752C2×D4—22no—
753C2×D4—22no—
754C2×D4—22no—
755C2×D4—22no—
756C2×D4—22no—
757C2×D4—22no—
758C2×D4—22no—
759C2×D4—41no—
760C2×D4—62no—
761C2×D4—62no—
762C2×D4—62no—
763C2×D4—62no—
764C2×D4—62no—
765C2×D4—62no—
766C2×D4—121no—
767C2×D4—121no—
768C2×D4—121no—
769C2×D4C3×#6714yescomplemented
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—31no—
773C22×C4—31no—
774C22×C4—31no—
775C22×C4—34no—
776C22×C4—31no—
777C22×C4—31no—
778C22×C4—31no—
779C22×C4—31no—
780C22×C4—41no—
781C22×C4—62no—
782C22×C4—62no—
783C22×C4—62no—
784C22×C4—121no—
785C22×C4—121no—
786C22×C4—121no—
787C22×C4—121no—
788C22×C4—121no—
789C22×C4C22×C3×D311yescharacteristic
790C22×C4C22×C3×D311yescharacteristic
791C22×C4C22×C3×D311yescharacteristic
792C22×C4C22×C3×D311yescharacteristic
793C4⋊C4—22no—
794C4⋊C4—62no—
795C4⋊C4—62no—
796C4⋊C4—62no—
797C22⋊C4—22no—
798C22⋊C4—22no—
799C22⋊C4—62no—
800C22⋊C4—62no—
801C22⋊C4—62no—
802C22⋊C4—62no—
803C22⋊C4—62no—
804C22⋊C4—62no—
805C22⋊C4—62no—
806C22⋊C4—62no—
807C22⋊C4—121no—
808C22⋊C4—121no—
809C42—62no—
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—22no—
821C22×C3—22no—
822C22×C3—22no—
823C22×C3—22no—
824C22×C3—22no—
825C22×C3—22no—
826C22×C3—22no—
827C22×C3—22no—
828C22×C3—24no—
829C22×C3—21no—
830C22×C3—21no—
831C22×C3—21no—
832C22×C3—21no—
833C22×C3—21no—
834C22×C3—21no—
835C22×C3—21no—
836C22×C3—42no—
837C22×C3—42no—
838C22×C3—42no—
839C22×C3—42no—
840C22×C3—42no—
841C22×C3—42no—
842C22×C3—42no—
843C22×C3—42no—
844C22×C3—42no—
845C22×C3—42no—
846C22×C3—42no—
847C22×C3—42no—
848C22×C3—41no—
849C22×C3—41no—
850C22×C3—41no—
851C22×C3—41no—
852C22×C3—41no—
853C22×C3—41no—
854C22×C3—41no—
855C22×C3—41no—
856C22×C3—41no—
857C22×C3—41no—
858C22×C3—41no—
859C22×C3—41no—
860C22×C3—41no—
861C22×C3—41no—
862C22×C3—41no—
863C22×C3—41no—
864C22×C3—41no—
865C22×C3—41no—
866C22×C3—41no—
867C22×C3—41no—
868C22×C3—41no—
869C22×C3—41no—
870C22×C3—81no—
871C22×C3—81no—
872C22×C3—81no—
873C22×C3—81no—
874C22×C3—81no—
875C22×C3—81no—
876C22×C3—81no—
877C22×C3—81no—
878C22×C3—121no—
879C22×C3—121no—
880C22×C3—121no—
881C22×C3—121no—
882C22×C3—121no—
883C22×C3—121no—
884C22×C3—121no—
885C22×C3#93914yes—
886C22×C3C3×#12114yes—
887C22×C3C2×D3×D411yescharacteristic
888C22×C3C2×#23711yescharacteristic
889C22×C3C2×#23711yescharacteristic
890C22×C3#100411yescharacteristic
891C22×C3D3×#4111yescharacteristic
892C22×C3#100911yescharacteristic
893C22×C3C22×#6711yescharacteristic
894C22×C3C22×C3×D411yescharacteristic
895C22×C3C22×C3×D411yescharacteristic
896C22×C3C2×C3×#4111yescharacteristic
897C22×C3C2×C3×#4111yescharacteristic
898C22×C3C2×C3×#4111yescharacteristic
899C22×C3C3×H(5,𝔽2)11yescharacteristic
900C22×C3C3×H(5,𝔽2)11yescharacteristic
901C2×D3—41no—
902C2×D3—41no—
903C2×D3—41no—
904C2×D3—41no—
905C2×D3—41no—
906C2×D3—41no—
907C2×D3—41no—
908C3×C4—24no—
909C3×C4—22no—
910C3×C4—22no—
911C3×C4—22no—
912C3×C4—22no—
913C3×C4—42no—
914C3×C4—42no—
915C3×C4—42no—
916C3×C4—41no—
917C3×C4—41no—
918C3×C4—41no—
919C3×C4—41no—
920C3×C4—62no—
921C3×C4—62no—
922C3×C4—62no—
923C3×C4—121no—
924C3×C4—121no—
925C3×C4—121no—
926C3×C4—121no—
927Dic3—22no—
928Dic3—22no—
929Dic3—22no—
930Dic3—41no—
931Dic3—41no—
932Dic3—41no—
933Dic3—41no—
934C32#254311yescharacteristic, complemented, Sylow
935C23—21no—
936C23—21no—
937C23—21no—
938C23—21no—
939C23—21no—
940C23—21no—
941C23—21no—
942C23—21no—
943C23—21no—
944C23—21no—
945C23—21no—
946C23—21no—
947C23—21no—
948C23—21no—
949C23—21no—
950C23—21no—
951C23—21no—
952C23—61no—
953C23—61no—
954C23—61no—
955C23—61no—
956C23—61no—
957C23—61no—
958C23—61no—
959C23C3×D3×D412yes—
960C23C3×#23712yes—
961C23C2×C3×#6712yes—
962C23C2×C3×#6712yes—
963C23C23×C3×D311yescharacteristic
964D4—28no—
965D4—44no—
966D4—44no—
967D4—124no—
968D4—124no—
969D4—124no—
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—32no—
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—61no—
1001C2×C4—61no—
1002C2×C4—124no—
1003C2×C4—124no—
1004C2×C4—124no—
1005C2×C4C3×#23712yes—
1006C2×C4C2×C3×#6712yes—
1007C2×C3—24no—
1008C2×C3—24no—
1009C2×C3—21no—
1010C2×C3—21no—
1011C2×C3—21no—
1012C2×C3—21no—
1013C2×C3—21no—
1014C2×C3—21no—
1015C2×C3—21no—
1016C2×C3—44no—
1017C2×C3—42no—
1018C2×C3—42no—
1019C2×C3—82no—
1020C2×C3—82no—
1021C2×C3—81no—
1022C2×C3—81no—
1023C2×C3—241no—
1024C2×C3#559611yescharacteristic
1025C2×C3#560111yescharacteristic
1026C2×C3#560511yescharacteristic
1027C2×C3#561811yescharacteristic
1028C2×C3C2×#93911yescharacteristic
1029C2×C3#580611yescharacteristic
1030C2×C3#582911yescharacteristic
1031C2×C3C2×C3×#12111yescharacteristic
1032C2×C3C3×#53211yescharacteristic
1033C2×C3C3×#53411yescharacteristic
1034C2×C3C3×#54611yescharacteristic
1035C2×C3C3×#54611yescharacteristic
1036C2×C3C3×#55311yescharacteristic
1037C2×C3C3×#55311yescharacteristic
1038D3—81no—
1039C22—22no—
1040C22—22no—
1041C22—22no—
1042C22—22no—
1043C22—22no—
1044C22—22no—
1045C22—22no—
1046C22—22no—
1047C22—22no—
1048C22—41no—
1049C22—41no—
1050C22—41no—
1051C22—41no—
1052C22—41no—
1053C22—41no—
1054C22—41no—
1055C22—41no—
1056C22—41no—
1057C22—41no—
1058C22—41no—
1059C22—121no—
1060C22—121no—
1061C22—121no—
1062C22—121no—
1063C22—121no—
1064C22—121no—
1065C22—121no—
1066C22C3×#93914yes—
1067C22C2×C3×D3×D411yescharacteristic
1068C22C2×C3×#23711yescharacteristic
1069C22C2×C3×#23711yescharacteristic
1070C22C3×#100411yescharacteristic
1071C22C3×D3×#4111yescharacteristic
1072C22C3×#100911yescharacteristic
1073C22C22×C3×#6711yescharacteristic
1074C4—22no—
1075C4—22no—
1076C4—41no—
1077C4—41no—
1078C4—62no—
1079C4—62no—
1080C4—62no—
1081C4—121no—
1082C4—121no—
1083C4—121no—
1084C4—121no—
1085C3—21no—
1086C3#8267011yescharacteristic, direct product factor
1087C3C3×#254311yescharacteristic, complemented
1088C2—24no—
1089C2—42no—
1090C2—81no—
1091C2—241no—
1092C2C3×#559611yescharacteristic
1093C2C3×#560111yescharacteristic
1094C2C3×#560511yescharacteristic
1095C2C3×#561811yescharacteristic
1096C2C2×C3×#93911yescharacteristic
1097C2C3×#580611yescharacteristic
1098C2C3×#582911yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC2×C32×#121C2
socleC23×C32C24
hypercenterC2×C3×#121D3
hypocenterC3C3×#2543
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×#121

Complements

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

NH ≅ G/Ntype
1. C2×C32×#121C2semidirect
2. C2×C3×#939C2semidirect
3. C2×C3×#939C2semidirect
4. C2×C3×D4×Dic3C2semidirect
5. C3×#5223C2semidirect
6. C3×#5220C2semidirect
7. C3×#5220C2semidirect
8. C3×#5213C2semidirect
9. C2×C3×C3⋊#95C2semidirect
10. C3×#4990C2semidirect
11. C3×#4982C2semidirect
12. C3×#4961C2semidirect
13. C3×#4958C2semidirect
14. C3×#4952C2semidirect
15. C3×#4945C2semidirect
17. #82670C3direct (N × H)
60. C2×C3×#121D3semidirect
61. C2×C3×#121C2×C3semidirect
63. C2×#939C2×C3semidirect
64. C2×#939C2×C3semidirect
65. C2×D4×Dic3C2×C3semidirect
77. #5223C2×C3semidirect
78. #5220C2×C3semidirect
79. #5220C2×C3semidirect
80. #5213C2×C3semidirect
81. C2×C3⋊#95C2×C3semidirect
82. #4990C2×C3semidirect
83. #4982C2×C3semidirect
84. #4961C2×C3semidirect
85. #4958C2×C3semidirect
86. #4952C2×C3semidirect
87. #4945C2×C3semidirect
100. C2×C32×D4D4semidirect
125. C22×C3×Dic3D4semidirect
311. C2×#121C3×D3semidirect
369. C2×C3×D4#67semidirect
370. C2×C3×D4C3×D4semidirect
425. C22×Dic3C3×D4semidirect
769. C2×D4C3×#67semidirect
934. C32#2543semidirect
1086. C3#82670direct (N × H)
1087. C3C3×#2543semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1212
C2×C3×#9392
C2×C3×D4×Dic32
C3×#52232
C3×#52202
C3×#52132
C2×C3×C3⋊#952
C3×#49902
C3×#49822
C3×#49612
C3×#49582
C3×#49522
C3×#49452
C3×#25433
#826703