Finite Group Databasebeta

← C3×#82253 #11817702

Subgroups — C3×#82253 #11817702

Order 1152.

1201 conjugacy classes of subgroups.

The subgroup lattice has 877 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#117C211yesmaximal, characteristic, complemented
2C2×C3×#898C211yesmaximal, characteristic, complemented
3C3×#5213C211yesmaximal, characteristic
4C3×#5210C211yesmaximal, characteristic, complemented
5C3×#4993C211yesmaximal, characteristic, complemented
6C3×#4983C211yesmaximal, characteristic, complemented
7C3×#4980C211yesmaximal, characteristic, complemented
8C3×#4961C211yesmaximal, characteristic
9C3×#4957C211yesmaximal, characteristic
10C3×#4949C211yesmaximal, characteristic, complemented
11C3×#4944C211yesmaximal, characteristic, complemented
12C3×#4940C211yesmaximal, characteristic, complemented
13C3×#4940C211yesmaximal, characteristic, complemented
14C3×C4×Dic3⋊C4C211yesmaximal, characteristic, complemented
15C3×#4928C211yesmaximal, characteristic, complemented
16C3×#2479—31nomaximal
17#82253C311yesmaximal, characteristic, direct product factor
18C23×C32×C4C2211yescharacteristic
19C22×C3×#67C2211yescharacteristic
20C32×#117—24no—
21C2×C32×C4⋊C4C2211yescharacteristic
22C2×C32×C4⋊C4C2211yescharacteristic
23C2×C32×C22⋊C4C2211yescharacteristic
24C2×C32×C22⋊C4C2211yescharacteristic
25C2×C32×C42C2211yescharacteristic
26C2×C32×C42C2211yescharacteristic
27C2×C3×#217C2211yescharacteristic
28C2×C3×#217C2211yescharacteristic
29C2×C3×#217C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×C4⋊Dic3C2211yescharacteristic
37C2×C3×C4⋊Dic3C2211yescharacteristic
38C2×C3×Dic3⋊C4C2211yescharacteristic
39C2×C3×Dic3⋊C4C2211yescharacteristic
40C2×C3×Dic3⋊C4C2211yescharacteristic
41C2×C3×Dic3⋊C4C2211yescharacteristic
42C2×C3×Dic3⋊C4C2211yescharacteristic
43C2×C3×Dic3⋊C4C2211yescharacteristic
44C2×C3×C4×Dic3C2211yescharacteristic
45C2×C3×C4×Dic3C2211yescharacteristic
46C3×#898—24no—
47C3×C3⋊#95C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53C3×C3⋊#95C2211yescharacteristic
54C3×C3⋊#95C2211yescharacteristic
55C2×C3×#126—31no—
56C2×C3×#117—21no—
57C2×C3×#117D311yescharacteristic, complemented
58C2×C3×#117C2×C311yescharacteristic, complemented
59C2×#898C2×C311yescharacteristic, complemented
60C3×#399—31no—
61C3×#399—31no—
62C3×#398—31no—
63C3×#394—31no—
64C3×#390—31no—
65C3×#389—31no—
66C3×#388—31no—
67C3×#388—31no—
68C3×#388—31no—
69C3×#387—31no—
70C3×#386—31no—
71C3×#385—31no—
72C3×C4×C4⋊C4—31no—
73#5213C2×C311yescharacteristic
74#5210C2×C311yescharacteristic, complemented
75#4993C2×C311yescharacteristic, complemented
76#4983C2×C311yescharacteristic, complemented
77#4980C2×C311yescharacteristic, complemented
78#4961C2×C311yescharacteristic
79#4957C2×C311yescharacteristic
80#4949C2×C311yescharacteristic, complemented
81#4944C2×C311yescharacteristic, complemented
82#4940C2×C311yescharacteristic, complemented
83#4940C2×C311yescharacteristic, complemented
84C4×Dic3⋊C4C2×C311yescharacteristic, complemented
85#4928C2×C311yescharacteristic, complemented
86C24×C32C2311yescharacteristic
87C23×C3×D3C2311yescharacteristic
88C22×C32×C4—22no—
89C22×C32×C4—22no—
90C22×C32×C4—22no—
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C2×C3×#67—22no—
98C2×C3×#67—22no—
99C2×C3×#67—41no—
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C32×C4⋊C4—22no—
108C32×C4⋊C4D414yescomplemented
109C32×C22⋊C4—22no—
110C32×C22⋊C4—22no—
111C32×C42—22no—
112C32×C42—22no—
113C3×#217—22no—
114C3×#217—22no—
115C3×#217—41no—
116C3×(C2×D3)⋊C4—22no—
117C3×(C2×D3)⋊C4—22no—
118C3×(C2×D3)⋊C4—22no—
119C3×(C2×D3)⋊C4—22no—
120C3×(C2×D3)⋊C4—22no—
121C3×(C2×D3)⋊C4—41no—
122C3×C4⋊Dic3—22no—
123C3×C4⋊Dic3—22no—
124C3×Dic3⋊C4—22no—
125C3×Dic3⋊C4—22no—
126C3×Dic3⋊C4—22no—
127C3×Dic3⋊C4—41no—
128C3×Dic3⋊C4—41no—
129C3×Dic3⋊C4—41no—
130C3×C4×Dic3—22no—
131C3×C4×Dic3—22no—
132#2479—31noSylow
133C22×C3×D4—31no—
134C23×C3×C4—21no—
135C23×C3×C4C2×D311yescharacteristic
136C23×C3×C4C22×C311yescharacteristic
137C22×#67C22×C311yescharacteristic
138C3×#126—64no—
139C3×#117—28no—
140C3×#117—24no—
141C3×#117—24no—
142C2×C3×C4⋊C4—21no—
143C2×C3×C4⋊C4—21no—
144C2×C3×C4⋊C4—31no—
145C2×C3×C4⋊C4—31no—
146C2×C3×C4⋊C4—31no—
147C2×C3×C4⋊C4—31no—
148C2×C3×C4⋊C4—31no—
149C2×C3×C4⋊C4—31no—
150C2×C3×C4⋊C4—31no—
151C2×C3×C4⋊C4—31no—
152C2×C3×C4⋊C4C2×D311yescharacteristic
153C2×C3×C4⋊C4C2×D311yescharacteristic
154C2×C3×C4⋊C4C22×C311yescharacteristic
155C2×C3×C4⋊C4C22×C311yescharacteristic
156C2×C3×C22⋊C4—21no—
157C2×C3×C22⋊C4—21no—
158C2×C3×C22⋊C4—31no—
159C2×C3×C22⋊C4—31no—
160C2×C3×C22⋊C4—31no—
161C2×C3×C22⋊C4—31no—
162C2×C3×C22⋊C4—31no—
163C2×C3×C22⋊C4—31no—
164C2×C3×C22⋊C4—31no—
165C2×C3×C22⋊C4—31no—
166C2×C3×C22⋊C4—31no—
167C2×C3×C22⋊C4C2×D311yescharacteristic
168C2×C3×C22⋊C4C2×D311yescharacteristic
169C2×C3×C22⋊C4C22×C311yescharacteristic
170C2×C3×C22⋊C4C22×C311yescharacteristic
171C2×C3×C42—21no—
172C2×C3×C42—21no—
173C2×C3×C42—31no—
174C2×C3×C42—31no—
175C2×C3×C42C2×D311yescharacteristic
176C2×C3×C42C2×D311yescharacteristic
177C2×C3×C42C22×C311yescharacteristic
178C2×C3×C42C22×C311yescharacteristic
179C2×#217C22×C311yescharacteristic
180C2×#217C22×C311yescharacteristic
181C2×#217C22×C311yescharacteristic
182C2×(C2×D3)⋊C4C22×C311yescharacteristic
183C2×(C2×D3)⋊C4C22×C311yescharacteristic
184C2×(C2×D3)⋊C4C22×C311yescharacteristic
185C2×(C2×D3)⋊C4C22×C311yescharacteristic
186C2×(C2×D3)⋊C4C22×C311yescharacteristic
187C2×(C2×D3)⋊C4C22×C311yescharacteristic
188C2×C4⋊Dic3C22×C311yescharacteristic
189C2×C4⋊Dic3C22×C311yescharacteristic
190C2×Dic3⋊C4C22×C311yescharacteristic
191C2×Dic3⋊C4C22×C311yescharacteristic
192C2×Dic3⋊C4C22×C311yescharacteristic
193C2×Dic3⋊C4C22×C311yescharacteristic
194C2×Dic3⋊C4C22×C311yescharacteristic
195C2×Dic3⋊C4C22×C311yescharacteristic
196C2×C4×Dic3C22×C311yescharacteristic
197C2×C4×Dic3C22×C311yescharacteristic
198#898—24no—
199C3×#95—31no—
200C3×#95—31no—
201C3×#95—31no—
202C3×#95—31no—
203C3×#95—31no—
204C3×#95—31no—
205C3×#95—31no—
206C3×#95—31no—
207C3⋊#95C22×C311yescharacteristic
208C3⋊#95C22×C311yescharacteristic
209C3⋊#95C22×C311yescharacteristic
210C3⋊#95C22×C311yescharacteristic
211C3⋊#95C22×C311yescharacteristic
212C3⋊#95C22×C311yescharacteristic
213C3⋊#95C22×C311yescharacteristic
214C3⋊#95C22×C311yescharacteristic
215C23×C32—21no—
216C23×C32—21no—
217C23×C32—21no—
218C23×C32—21no—
219C23×C32—21no—
220C23×C32—21no—
221C23×C32#4112yes—
222C23×C32C2411yescharacteristic
223C22×C3×D3—21no—
224C22×C3×D3—21no—
225C22×C3×D3—21no—
226C22×C3×D3—21no—
227C22×C3×D3—21no—
228C22×C3×D3—21no—
229C22×C3×D3—21no—
230C2×C32×C4—28no—
231C2×C32×C4—21no—
232C2×C32×C4—21no—
233C2×C32×C4—21no—
234C2×C32×C4—21no—
235C2×C32×C4—21no—
236C2×C32×C4—21no—
237C2×C32×C4—21no—
238C2×C32×C4—21no—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4C2×D412yes—
246C2×C32×C4C2×D412yes—
247C2×C32×C4C2×D412yes—
248C2×C32×C4#4112yes—
249C3×#67—44no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3#4112yes—
270C2×C3×Dic3#4112yes—
271C2×#126—31no—
272C2×#117C3×D311yescharacteristic, complemented
273#399—31no—
274#399—31no—
275#398—31no—
276#394—31no—
277#390—31no—
278#389—31no—
279#388—31no—
280#388—31no—
281#388—31no—
282#387—31no—
283#386—31no—
284#385—31no—
285C4×C4⋊C4—31no—
286C24×C3—21no—
287C24×C3—31no—
288C24×C3C22×D311yescharacteristic
289C24×C3C23×C311yescharacteristic
290C23×D3C23×C311yescharacteristic
291C2×C3×D4—62no—
292C2×C3×D4—62no—
293C2×C3×D4—121no—
294C22×C3×C4—24no—
295C22×C3×C4—24no—
296C22×C3×C4—24no—
297C22×C3×C4—22no—
298C22×C3×C4—22no—
299C22×C3×C4—22no—
300C22×C3×C4—22no—
301C22×C3×C4—22no—
302C22×C3×C4—22no—
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4—31no—
310C22×C3×C4—31no—
311C22×C3×C4—31no—
312C22×C3×C4—31no—
313C22×C3×C4—31no—
314C22×C3×C4—31no—
315C22×C3×C4—31no—
316C22×C3×C4C22×D311yescharacteristic
317C22×C3×C4C22×D311yescharacteristic
318C22×C3×C4C22×D311yescharacteristic
319C22×C3×C4C22×D311yescharacteristic
320C22×C3×C4C22×D311yescharacteristic
321C22×C3×C4C22×D311yescharacteristic
322C22×C3×C4C23×C311yescharacteristic
323C22×C3×C4C23×C311yescharacteristic
324C22×C3×C4C23×C311yescharacteristic
325C22×C3×C4C23×C311yescharacteristic
326C22×C3×C4C23×C311yescharacteristic
327C22×C3×C4C23×C311yescharacteristic
328C2×#67—22no—
329C2×#67—22no—
330C2×#67—41no—
331C22×Dic3C23×C311yescharacteristic
332C22×Dic3C23×C311yescharacteristic
333C22×Dic3C23×C311yescharacteristic
334C22×Dic3C23×C311yescharacteristic
335C22×Dic3C23×C311yescharacteristic
336C22×Dic3C23×C311yescharacteristic
337C22×Dic3C23×C311yescharacteristic
338C3×C4⋊C4—24no—
339C3×C4⋊C4—22no—
340C3×C4⋊C4—22no—
341C3×C4⋊C4—24no—
342C3×C4⋊C4—62no—
343C3×C4⋊C4—62no—
344C3×C4⋊C4—62no—
345C3×C4⋊C4—62no—
346C3×C4⋊C4—62no—
347C3×C4⋊C4—121no—
348C3×C4⋊C4—121no—
349C3×C4⋊C4—121no—
350C3×C4⋊C4#6714yescomplemented
351C3×C4⋊C4C3×D414yescomplemented
352C3×C22⋊C4—24no—
353C3×C22⋊C4—24no—
354C3×C22⋊C4—22no—
355C3×C22⋊C4—22no—
356C3×C22⋊C4—22no—
357C3×C22⋊C4—22no—
358C3×C22⋊C4—62no—
359C3×C22⋊C4—62no—
360C3×C22⋊C4—62no—
361C3×C22⋊C4—62no—
362C3×C22⋊C4—62no—
363C3×C22⋊C4—62no—
364C3×C22⋊C4—62no—
365C3×C22⋊C4—121no—
366C3×C22⋊C4—121no—
367C3×C42—24no—
368C3×C42—24no—
369C3×C42—22no—
370C3×C42—22no—
371C3×C42—22no—
372C3×C42—22no—
373C3×C42—62no—
374C3×C42—62no—
375#217—22no—
376#217—22no—
377#217—41no—
378(C2×D3)⋊C4—22no—
379(C2×D3)⋊C4—22no—
380(C2×D3)⋊C4—22no—
381(C2×D3)⋊C4—22no—
382(C2×D3)⋊C4—22no—
383(C2×D3)⋊C4—41no—
384C4⋊Dic3—22no—
385C4⋊Dic3—22no—
386Dic3⋊C4—22no—
387Dic3⋊C4—22no—
388Dic3⋊C4—22no—
389Dic3⋊C4—41no—
390Dic3⋊C4—41no—
391Dic3⋊C4—41no—
392C4×Dic3—22no—
393C4×Dic3—22no—
394C22×C32—22no—
395C22×C32—22no—
396C22×C32—22no—
397C22×C32—41no—
398C22×C32—41no—
399C22×C32—41no—
400C22×C32—41no—
401C22×C32C22×D411yescharacteristic
402C22×C32C2×#4111yescharacteristic
403C22×C32C2×#4111yescharacteristic
404C22×C32C2×#4111yescharacteristic
405C22×C32C2×#4111yescharacteristic
406C22×C32H(5,𝔽2)11yescharacteristic
407C22×C322−1+411yescharacteristic
408C2×C3×D3—41no—
409C2×C3×D3—41no—
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412C2×C3×D3—41no—
413C2×C3×D3—41no—
414C2×C3×D3—41no—
415C32×C4—22no—
416C32×C4—22no—
417C32×C4—22no—
418C32×C4—22no—
419C32×C4—41no—
420C32×C4—41no—
421C3×Dic3—22no—
422C3×Dic3—22no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C22×D4—31no—
429C23×C4C2×C3×D311yescharacteristic
430#126—64no—
431#117—24no—
432C2×C4⋊C4—31no—
433C2×C4⋊C4—31no—
434C2×C4⋊C4—31no—
435C2×C4⋊C4—31no—
436C2×C4⋊C4—31no—
437C2×C4⋊C4—31no—
438C2×C4⋊C4—31no—
439C2×C4⋊C4—31no—
440C2×C4⋊C4C2×C3×D311yescharacteristic
441C2×C4⋊C4C2×C3×D311yescharacteristic
442C2×C22⋊C4—31no—
443C2×C22⋊C4—31no—
444C2×C22⋊C4—31no—
445C2×C22⋊C4—31no—
446C2×C22⋊C4—31no—
447C2×C22⋊C4—31no—
448C2×C22⋊C4—31no—
449C2×C22⋊C4—31no—
450C2×C22⋊C4—31no—
451C2×C22⋊C4C2×C3×D311yescharacteristic
452C2×C22⋊C4C2×C3×D311yescharacteristic
453C2×C42—31no—
454C2×C42—31no—
455C2×C42C2×C3×D311yescharacteristic
456C2×C42C2×C3×D311yescharacteristic
457#95—31no—
458#95—31no—
459#95—31no—
460#95—31no—
461#95—31no—
462#95—31no—
463#95—31no—
464#95—31no—
465C23×C3—22no—
466C23×C3—22no—
467C23×C3—21no—
468C23×C3—21no—
469C23×C3—21no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—21no—
474C23×C3—21no—
475C23×C3—21no—
476C23×C3—21no—
477C23×C3—21no—
478C23×C3—21no—
479C23×C3—21no—
480C23×C3—22no—
481C23×C3—41no—
482C23×C3—41no—
483C23×C3—41no—
484C23×C3—41no—
485C23×C3—61no—
486C23×C3—61no—
487C23×C3—61no—
488C23×C3—61no—
489C23×C3—61no—
490C23×C3—61no—
491C23×C3—61no—
492C23×C3#23512yes—
493C23×C3C3×#4112yes—
494C23×C3C23×D311yescharacteristic
495C23×C3C24×C311yescharacteristic
496C22×D3—21no—
497C22×D3—21no—
498C22×D3—21no—
499C22×D3—21no—
500C22×D3—21no—
501C22×D3—21no—
502C22×D3—21no—
503C3×D4—124no—
504C2×C3×C4—22no—
505C2×C3×C4—216no—
506C2×C3×C4—28no—
507C2×C3×C4—28no—
508C2×C3×C4—22no—
509C2×C3×C4—22no—
510C2×C3×C4—22no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—22no—
528C2×C3×C4—22no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—22no—
542C2×C3×C4—22no—
543C2×C3×C4—22no—
544C2×C3×C4—22no—
545C2×C3×C4—32no—
546C2×C3×C4—32no—
547C2×C3×C4—41no—
548C2×C3×C4—41no—
549C2×C3×C4—41no—
550C2×C3×C4—41no—
551C2×C3×C4—41no—
552C2×C3×C4—41no—
553C2×C3×C4—41no—
554C2×C3×C4—41no—
555C2×C3×C4—61no—
556C2×C3×C4—61no—
557C2×C3×C4—61no—
558C2×C3×C4—61no—
559C2×C3×C4—61no—
560C2×C3×C4—61no—
561C2×C3×C4—61no—
562C2×C3×C4—61no—
563C2×C3×C4—61no—
564C2×C3×C4—61no—
565C2×C3×C4—61no—
566C2×C3×C4—61no—
567C2×C3×C4—61no—
568C2×C3×C4—61no—
569C2×C3×C4—61no—
570C2×C3×C4—61no—
571C2×C3×C4—61no—
572C2×C3×C4—61no—
573C2×C3×C4—61no—
574C2×C3×C4#23512yes—
575C2×C3×C4C2×#6712yes—
576C2×C3×C4C2×#6712yes—
577C2×C3×C4C2×#6712yes—
578C2×C3×C4C2×C3×D412yes—
579C2×C3×C4C2×C3×D412yes—
580C2×C3×C4C2×C3×D412yes—
581C2×C3×C4C3×#4112yes—
582#67—44no—
583C2×Dic3—21no—
584C2×Dic3—21no—
585C2×Dic3—21no—
586C2×Dic3—21no—
587C2×Dic3—21no—
588C2×Dic3—21no—
589C2×Dic3—21no—
590C2×Dic3—21no—
591C2×Dic3—21no—
592C2×Dic3—21no—
593C2×Dic3—21no—
594C2×Dic3—21no—
595C2×Dic3—21no—
596C2×Dic3—21no—
597C2×Dic3—21no—
598C2×Dic3—21no—
599C2×Dic3—21no—
600C2×Dic3—21no—
601C2×Dic3—21no—
602C2×Dic3C3×#4112yes—
603C2×Dic3C3×#4112yes—
604C2×C32—42no—
605C2×C32#52511yescharacteristic
606C2×C32#52911yescharacteristic
607C2×C32#54211yescharacteristic
608C2×C32#54711yescharacteristic
609C2×C32#55011yescharacteristic
610C2×C32#55111yescharacteristic
611C2×C32#55211yescharacteristic
612C3×D3—81no—
613C24—31no—
614C24C22×C3×D311yescharacteristic
615C2×D4—62no—
616C2×D4—62no—
617C2×D4—121no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—31no—
622C22×C4—31no—
623C22×C4—31no—
624C22×C4—31no—
625C22×C4—31no—
626C22×C4—31no—
627C22×C4—31no—
628C22×C4C22×C3×D311yescharacteristic
629C22×C4C22×C3×D311yescharacteristic
630C22×C4C22×C3×D311yescharacteristic
631C22×C4C22×C3×D311yescharacteristic
632C22×C4C22×C3×D311yescharacteristic
633C22×C4C22×C3×D311yescharacteristic
634C4⋊C4—22no—
635C4⋊C4—62no—
636C4⋊C4—62no—
637C4⋊C4—62no—
638C4⋊C4—62no—
639C4⋊C4—62no—
640C4⋊C4—121no—
641C4⋊C4—121no—
642C4⋊C4—121no—
643C4⋊C4C3×#6714yescomplemented
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—62no—
647C22⋊C4—62no—
648C22⋊C4—62no—
649C22⋊C4—62no—
650C22⋊C4—62no—
651C22⋊C4—62no—
652C22⋊C4—62no—
653C22⋊C4—121no—
654C22⋊C4—121no—
655C42—22no—
656C42—22no—
657C42—62no—
658C42—62no—
659C22×C3—24no—
660C22×C3—22no—
661C22×C3—22no—
662C22×C3—22no—
663C22×C3—22no—
664C22×C3—22no—
665C22×C3—22no—
666C22×C3—21no—
667C22×C3—21no—
668C22×C3—21no—
669C22×C3—21no—
670C22×C3—21no—
671C22×C3—21no—
672C22×C3—21no—
673C22×C3—42no—
674C22×C3—42no—
675C22×C3—42no—
676C22×C3—42no—
677C22×C3—42no—
678C22×C3—42no—
679C22×C3—41no—
680C22×C3—41no—
681C22×C3—41no—
682C22×C3—41no—
683C22×C3—41no—
684C22×C3—41no—
685C22×C3—41no—
686C22×C3—41no—
687C22×C3—121no—
688C22×C3—121no—
689C22×C3—121no—
690C22×C3—121no—
691C22×C3—121no—
692C22×C3—121no—
693C22×C3—121no—
694C22×C3C2×#23511yescharacteristic
695C22×C3C2×#23511yescharacteristic
696C22×C3D3×#4111yescharacteristic
697C22×C3D3×#4111yescharacteristic
698C22×C3#100911yescharacteristic
699C22×C3#101011yescharacteristic
700C22×C3C22×#6711yescharacteristic
701C22×C3C22×C3×D411yescharacteristic
702C22×C3C2×C3×#4111yescharacteristic
703C22×C3C2×C3×#4111yescharacteristic
704C22×C3C2×C3×#4111yescharacteristic
705C22×C3C2×C3×#4111yescharacteristic
706C22×C3C3×H(5,𝔽2)11yescharacteristic
707C22×C3C3×2−1+411yescharacteristic
708C2×D3—41no—
709C2×D3—41no—
710C2×D3—41no—
711C2×D3—41no—
712C2×D3—41no—
713C2×D3—41no—
714C2×D3—41no—
715C3×C4—24no—
716C3×C4—24no—
717C3×C4—22no—
718C3×C4—22no—
719C3×C4—22no—
720C3×C4—22no—
721C3×C4—22no—
722C3×C4—22no—
723C3×C4—22no—
724C3×C4—22no—
725C3×C4—42no—
726C3×C4—42no—
727C3×C4—42no—
728C3×C4—42no—
729C3×C4—41no—
730C3×C4—41no—
731C3×C4—41no—
732C3×C4—41no—
733C3×C4—62no—
734C3×C4—62no—
735C3×C4—121no—
736C3×C4—121no—
737C3×C4—121no—
738C3×C4—121no—
739C3×C4—121no—
740Dic3—22no—
741Dic3—22no—
742Dic3—41no—
743Dic3—41no—
744Dic3—41no—
745Dic3—41no—
746Dic3—41no—
747C32#247911yescharacteristic, complemented, Sylow
748C23—21no—
749C23—21no—
750C23—21no—
751C23—21no—
752C23—21no—
753C23—21no—
754C23—61no—
755C23—61no—
756C23—61no—
757C23—61no—
758C23—61no—
759C23—61no—
760C23—61no—
761C23C3×#23512yes—
762C23C23×C3×D311yescharacteristic
763D4—124no—
764C2×C4—28no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—32no—
780C2×C4—32no—
781C2×C4—61no—
782C2×C4—61no—
783C2×C4—61no—
784C2×C4—61no—
785C2×C4—61no—
786C2×C4—61no—
787C2×C4—61no—
788C2×C4—61no—
789C2×C4—61no—
790C2×C4—61no—
791C2×C4—61no—
792C2×C4—61no—
793C2×C4—61no—
794C2×C4—61no—
795C2×C4—61no—
796C2×C4—61no—
797C2×C4—61no—
798C2×C4—61no—
799C2×C4—61no—
800C2×C4C3×#23512yes—
801C2×C4C2×C3×#6712yes—
802C2×C4C2×C3×#6712yes—
803C2×C4C2×C3×#6712yes—
804C2×C3—21no—
805C2×C3—21no—
806C2×C3—21no—
807C2×C3—21no—
808C2×C3—21no—
809C2×C3—21no—
810C2×C3—21no—
811C2×C3—44no—
812C2×C3—42no—
813C2×C3—42no—
814C2×C3—241no—
815C2×C3#552711yescharacteristic
816C2×C3#552811yescharacteristic
817C2×C3#553111yescharacteristic
818C2×C3#553411yescharacteristic
819C2×C3#579111yescharacteristic
820C2×C3#582411yescharacteristic
821C2×C3#583411yescharacteristic
822C2×C3C3×#52511yescharacteristic
823C2×C3C3×#52911yescharacteristic
824C2×C3C3×#54211yescharacteristic
825C2×C3C3×#54711yescharacteristic
826C2×C3C3×#55011yescharacteristic
827C2×C3C3×#55111yescharacteristic
828C2×C3C3×#55211yescharacteristic
829D3—81no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—121no—
838C22—121no—
839C22—121no—
840C22—121no—
841C22—121no—
842C22—121no—
843C22—121no—
844C22C2×C3×#23511yescharacteristic
845C22C2×C3×#23511yescharacteristic
846C22C3×D3×#4111yescharacteristic
847C22C3×D3×#4111yescharacteristic
848C22C3×#100911yescharacteristic
849C22C3×#101011yescharacteristic
850C22C22×C3×#6711yescharacteristic
851C4—22no—
852C4—22no—
853C4—22no—
854C4—22no—
855C4—41no—
856C4—41no—
857C4—62no—
858C4—62no—
859C4—121no—
860C4—121no—
861C4—121no—
862C4—121no—
863C4—121no—
864C3—21no—
865C3#8225311yescharacteristic, direct product factor
866C3C3×#247911yescharacteristic, complemented
867C2—42no—
868C2—241no—
869C2C3×#552711yescharacteristic
870C2C3×#552811yescharacteristic
871C2C3×#553111yescharacteristic
872C2C3×#553411yescharacteristic
873C2C3×#579111yescharacteristic
874C2C3×#582411yescharacteristic
875C2C3×#583411yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC2×C32×#117C2
socleC23×C32C24
prime radicalC22×C3×#67C22
hypercenterC2×C3×#117D3
hypocenterC3C3×#2479
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×#117

Complements

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

NH ≅ G/Ntype
1. C2×C32×#117C2semidirect
2. C2×C3×#898C2semidirect
4. C3×#5210C2semidirect
5. C3×#4993C2semidirect
6. C3×#4983C2semidirect
7. C3×#4980C2semidirect
10. C3×#4949C2semidirect
11. C3×#4944C2semidirect
12. C3×#4940C2semidirect
13. C3×#4940C2semidirect
14. C3×C4×Dic3⋊C4C2semidirect
15. C3×#4928C2semidirect
17. #82253C3direct (N × H)
57. C2×C3×#117D3semidirect
58. C2×C3×#117C2×C3semidirect
59. C2×#898C2×C3semidirect
74. #5210C2×C3semidirect
75. #4993C2×C3semidirect
76. #4983C2×C3semidirect
77. #4980C2×C3semidirect
80. #4949C2×C3semidirect
81. #4944C2×C3semidirect
82. #4940C2×C3semidirect
83. #4940C2×C3semidirect
84. C4×Dic3⋊C4C2×C3semidirect
85. #4928C2×C3semidirect
108. C32×C4⋊C4D4semidirect
272. C2×#117C3×D3semidirect
350. C3×C4⋊C4#67semidirect
351. C3×C4⋊C4C3×D4semidirect
643. C4⋊C4C3×#67semidirect
747. C32#2479semidirect
865. C3#82253direct (N × H)
866. C3C3×#2479semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1172
C2×C3×#8982
C3×#52132
C3×#52102
C3×#49932
C3×#49832
C3×#49802
C3×#49612
C3×#49572
C3×#49492
C3×#49442
C3×#49402
C3×C4×Dic3⋊C42
C3×#49282
C3×#24793
#822533