Finite Group Databasebeta

← C3×#78027 #11817705

Subgroups — C3×#78027 #11817705

Order 1152.

1129 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#892C211yesmaximal, characteristic, complemented
2C2×C3×#879C211yesmaximal, characteristic, complemented
3C32×#399C211yesmaximal, characteristic, complemented
4C3×#4993C211yesmaximal, characteristic, complemented
5C3×#4990C211yesmaximal, characteristic, complemented
6C3×#4983C211yesmaximal, characteristic, complemented
7C3×#4976C211yesmaximal, characteristic, complemented
8C3×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
9C3×#4959C211yesmaximal, characteristic
10C3×#4957C211yesmaximal, characteristic
11C3×#4956C211yesmaximal, characteristic
12C3×#4951C211yesmaximal, characteristic, complemented
13C3×#4945C211yesmaximal, characteristic, complemented
14C3×#4668C211yesmaximal, characteristic, complemented
15C3×#4654C211yesmaximal, characteristic, complemented
16C3×#2479—31nomaximal
17#78027C311yesmaximal, characteristic, direct product factor
18C22×C3×#67C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21C2×C32×C4⋊C4C2211yescharacteristic
22C2×C32×C4⋊C4C2211yescharacteristic
23C2×C32×C22⋊C4C2211yescharacteristic
24C2×C32×C22⋊C4C2211yescharacteristic
25C2×C32×C22⋊C4C2211yescharacteristic
26C2×C3×#217C2211yescharacteristic
27C2×C3×#217C2211yescharacteristic
28C2×C3×#217C2211yescharacteristic
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×C4⋊Dic3C2211yescharacteristic
35C2×C3×C4⋊Dic3C2211yescharacteristic
36C2×C3×Dic3⋊C4C2211yescharacteristic
37C2×C3×Dic3⋊C4C2211yescharacteristic
38C2×C3×Dic3⋊C4C2211yescharacteristic
39C2×C3×Dic3⋊C4C2211yescharacteristic
40C2×C3×Dic3⋊C4C2211yescharacteristic
41C2×C3×C4×Dic3C2211yescharacteristic
42C2×C3×C4×Dic3C2211yescharacteristic
43C2×C3×C4×Dic3C2211yescharacteristic
44C2×C3×C4×Dic3C2211yescharacteristic
45C3×#892—24no—
46C3×#879—24no—
47C32×#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—31no—
57C2×#892C2×C311yescharacteristic, complemented
58C2×#879C2×C311yescharacteristic, complemented
59C3×#399—21no—
60C3×#399—31no—
61C3×#399D311yescharacteristic, complemented
62C3×#399C2×C311yescharacteristic, complemented
63C3×#398—31no—
64C3×#394—31no—
65C3×#390—31no—
66C3×#389—31no—
67C3×#388—31no—
68C3×#388—31no—
69C3×#388—31no—
70C3×#387—31no—
71C3×#386—31no—
72C3×#385—31no—
73C3×C4×C4⋊C4—31no—
74#4993C2×C311yescharacteristic, complemented
75#4990C2×C311yescharacteristic, complemented
76#4983C2×C311yescharacteristic, complemented
77#4976C2×C311yescharacteristic, complemented
78Dic3×C4⋊C4C2×C311yescharacteristic, complemented
79#4959C2×C311yescharacteristic
80#4957C2×C311yescharacteristic
81#4956C2×C311yescharacteristic
82#4951C2×C311yescharacteristic, complemented
83#4945C2×C311yescharacteristic, complemented
84#4668C2×C311yescharacteristic, complemented
85#4654C2×C311yescharacteristic, complemented
86C24×C32C2311yescharacteristic
87C23×C3×D3C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C2×C3×#67—22no—
95C2×C3×#67—22no—
96C2×C3×#67—41no—
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C2×C3×C4×D3—22no—
105C2×C3×C4×D3—22no—
106C2×C3×C4×D3—22no—
107C32×C4⋊C4—22no—
108C32×C4⋊C4—22no—
109C32×C4⋊C4—41no—
110C32×C22⋊C4—22no—
111C32×C22⋊C4—22no—
112C32×C22⋊C4—41no—
113C3×#217—22no—
114C3×#217—22no—
115C3×#217—22no—
116C3×(C2×D3)⋊C4—22no—
117C3×(C2×D3)⋊C4—22no—
118C3×(C2×D3)⋊C4—22no—
119C3×(C2×D3)⋊C4—22no—
120C3×(C2×D3)⋊C4—41no—
121C3×C4⋊Dic3—22no—
122C3×C4⋊Dic3D414yescomplemented
123C3×Dic3⋊C4—22no—
124C3×Dic3⋊C4—22no—
125C3×Dic3⋊C4—22no—
126C3×Dic3⋊C4—41no—
127C3×Dic3⋊C4—41no—
128C3×C4×Dic3—22no—
129C3×C4×Dic3—22no—
130C3×C4×Dic3—22no—
131C3×C4×Dic3—22no—
132#2479—31noSylow
133C22×C3×D4—31no—
134C23×C3×C4—31no—
135C22×#67C22×C311yescharacteristic
136C22×C4×D3C22×C311yescharacteristic
137C3×#126—64no—
138C3×#117—64no—
139C2×C3×C4⋊C4—21no—
140C2×C3×C4⋊C4—21no—
141C2×C3×C4⋊C4—21no—
142C2×C3×C4⋊C4—31no—
143C2×C3×C4⋊C4—31no—
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⋊C4C2×D311yescharacteristic
150C2×C3×C4⋊C4C2×D311yescharacteristic
151C2×C3×C4⋊C4C2×D311yescharacteristic
152C2×C3×C4⋊C4C22×C311yescharacteristic
153C2×C3×C4⋊C4C22×C311yescharacteristic
154C2×C3×C4⋊C4C22×C311yescharacteristic
155C2×C3×C22⋊C4—21no—
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⋊C4C2×D311yescharacteristic
167C2×C3×C22⋊C4C2×D311yescharacteristic
168C2×C3×C22⋊C4C2×D311yescharacteristic
169C2×C3×C22⋊C4C22×C311yescharacteristic
170C2×C3×C22⋊C4C22×C311yescharacteristic
171C2×C3×C22⋊C4C22×C311yescharacteristic
172C2×C3×C42—31no—
173C2×C3×C42—31no—
174C2×C3×C42—31no—
175C2×C3×C42—31no—
176C2×#217C22×C311yescharacteristic
177C2×#217C22×C311yescharacteristic
178C2×#217C22×C311yescharacteristic
179C2×(C2×D3)⋊C4C22×C311yescharacteristic
180C2×(C2×D3)⋊C4C22×C311yescharacteristic
181C2×(C2×D3)⋊C4C22×C311yescharacteristic
182C2×(C2×D3)⋊C4C22×C311yescharacteristic
183C2×(C2×D3)⋊C4C22×C311yescharacteristic
184C2×C4⋊Dic3C22×C311yescharacteristic
185C2×C4⋊Dic3C22×C311yescharacteristic
186C2×Dic3⋊C4C22×C311yescharacteristic
187C2×Dic3⋊C4C22×C311yescharacteristic
188C2×Dic3⋊C4C22×C311yescharacteristic
189C2×Dic3⋊C4C22×C311yescharacteristic
190C2×Dic3⋊C4C22×C311yescharacteristic
191C2×C4×Dic3C22×C311yescharacteristic
192C2×C4×Dic3C22×C311yescharacteristic
193C2×C4×Dic3C22×C311yescharacteristic
194C2×C4×Dic3C22×C311yescharacteristic
195#892—24no—
196#879—24no—
197C3×#95—21no—
198C3×#95—31no—
199C3×#95—31no—
200C3×#95—31no—
201C3×#95—31no—
202C3×#95—31no—
203C3×#95—31no—
204C3×#95—31no—
205C3×#95C2×D311yescharacteristic
206C3×#95C22×C311yescharacteristic
207C3⋊#95C22×C311yescharacteristic
208C3⋊#95C22×C311yescharacteristic
209C3⋊#95C22×C311yescharacteristic
210C3⋊#95C22×C311yescharacteristic
211C3⋊#95C22×C311yescharacteristic
212C3⋊#95C22×C311yescharacteristic
213C3⋊#95C22×C311yescharacteristic
214C23×C32—21no—
215C23×C32—21no—
216C23×C32—21no—
217C23×C32—21no—
218C23×C32—21no—
219C23×C32—21no—
220C23×C32—21no—
221C23×C32C2411yescharacteristic
222C22×C3×D3—21no—
223C22×C3×D3—21no—
224C22×C3×D3—21no—
225C22×C3×D3—21no—
226C22×C3×D3—21no—
227C22×C3×D3—21no—
228C22×C3×D3#4112yes—
229C2×C32×C4—21no—
230C2×C32×C4—21no—
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×C4#4112yes—
247C3×#67—44no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
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×Dic3C2×D412yes—
266C2×C3×Dic3C2×D412yes—
267C2×C3×Dic3#4112yes—
268C2×C3×Dic3#4112yes—
269C3×C4×D3—28no—
270C2×#126—31no—
271C2×#117—31no—
272#399—31no—
273#399C3×D311yescharacteristic, complemented
274#398—31no—
275#394—31no—
276#390—31no—
277#389—31no—
278#388—31no—
279#388—31no—
280#388—31no—
281#387—31no—
282#386—31no—
283#385—31no—
284C4×C4⋊C4—31no—
285C24×C3—21no—
286C24×C3—31no—
287C24×C3C22×D311yescharacteristic
288C24×C3C23×C311yescharacteristic
289C23×D3C23×C311yescharacteristic
290C2×C3×D4—62no—
291C2×C3×D4—62no—
292C2×C3×D4—121no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—31no—
300C22×C3×C4—31no—
301C22×C3×C4—31no—
302C22×C3×C4—31no—
303C22×C3×C4—31no—
304C22×C3×C4—31no—
305C22×C3×C4—31no—
306C22×C3×C4—62no—
307C22×C3×C4—62no—
308C22×C3×C4—62no—
309C22×C3×C4C22×D311yescharacteristic
310C22×C3×C4C22×D311yescharacteristic
311C22×C3×C4C22×D311yescharacteristic
312C22×C3×C4C22×D311yescharacteristic
313C22×C3×C4C22×D311yescharacteristic
314C22×C3×C4C22×D311yescharacteristic
315C22×C3×C4C23×C311yescharacteristic
316C22×C3×C4C23×C311yescharacteristic
317C22×C3×C4C23×C311yescharacteristic
318C22×C3×C4C23×C311yescharacteristic
319C22×C3×C4C23×C311yescharacteristic
320C22×C3×C4C23×C311yescharacteristic
321C2×#67—22no—
322C2×#67—22no—
323C2×#67—41no—
324C22×Dic3C23×C311yescharacteristic
325C22×Dic3C23×C311yescharacteristic
326C22×Dic3C23×C311yescharacteristic
327C22×Dic3C23×C311yescharacteristic
328C22×Dic3C23×C311yescharacteristic
329C22×Dic3C23×C311yescharacteristic
330C22×Dic3C23×C311yescharacteristic
331C2×C4×D3—22no—
332C2×C4×D3—22no—
333C2×C4×D3—22no—
334C3×C4⋊C4—22no—
335C3×C4⋊C4—22no—
336C3×C4⋊C4—22no—
337C3×C4⋊C4—22no—
338C3×C4⋊C4—34no—
339C3×C4⋊C4—42no—
340C3×C4⋊C4—42no—
341C3×C4⋊C4—41no—
342C3×C4⋊C4—41no—
343C3×C4⋊C4—42no—
344C3×C4⋊C4—62no—
345C3×C4⋊C4—62no—
346C3×C4⋊C4—62no—
347C3×C4⋊C4—62no—
348C3×C4⋊C4—121no—
349C3×C4⋊C4—121no—
350C3×C22⋊C4—22no—
351C3×C22⋊C4—22no—
352C3×C22⋊C4—22no—
353C3×C22⋊C4—22no—
354C3×C22⋊C4—42no—
355C3×C22⋊C4—42no—
356C3×C22⋊C4—41no—
357C3×C22⋊C4—41no—
358C3×C22⋊C4—42no—
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—62no—
366C3×C22⋊C4—121no—
367C3×C42—62no—
368C3×C42—62no—
369C3×C42—62no—
370C3×C42—62no—
371#217—22no—
372#217—22no—
373#217—22no—
374(C2×D3)⋊C4—22no—
375(C2×D3)⋊C4—22no—
376(C2×D3)⋊C4—22no—
377(C2×D3)⋊C4—22no—
378(C2×D3)⋊C4—41no—
379C4⋊Dic3—22no—
380C4⋊Dic3C3×D414yescomplemented
381Dic3⋊C4—22no—
382Dic3⋊C4—22no—
383Dic3⋊C4—22no—
384Dic3⋊C4—41no—
385Dic3⋊C4—41no—
386C4×Dic3—22no—
387C4×Dic3—22no—
388C4×Dic3—22no—
389C4×Dic3—22no—
390C22×C32—41no—
391C22×C32—41no—
392C22×C32—41no—
393C22×C32—41no—
394C22×C32—41no—
395C22×C32—41no—
396C22×C32—41no—
397C22×C32C22×D411yescharacteristic
398C22×C32C2×#4111yescharacteristic
399C22×C32C2×#4111yescharacteristic
400C22×C32C2×#4111yescharacteristic
401C22×C32C2×#4111yescharacteristic
402C22×C32H(5,𝔽2)11yescharacteristic
403C22×C322−1+411yescharacteristic
404C2×C3×D3—22no—
405C2×C3×D3—22no—
406C2×C3×D3—22no—
407C2×C3×D3—41no—
408C2×C3×D3—41no—
409C2×C3×D3—41no—
410C2×C3×D3—41no—
411C32×C4—22no—
412C32×C4—22no—
413C32×C4—41no—
414C32×C4—41no—
415C32×C4—41no—
416C32×C4—41no—
417C3×Dic3—22no—
418C3×Dic3—22no—
419C3×Dic3—22no—
420C3×Dic3—22no—
421C3×Dic3—41no—
422C3×Dic3—41no—
423C3×Dic3—41no—
424C22×D4—31no—
425C23×C4—31no—
426#126—64no—
427#117—64no—
428C2×C4⋊C4—31no—
429C2×C4⋊C4—31no—
430C2×C4⋊C4—31no—
431C2×C4⋊C4—31no—
432C2×C4⋊C4—31no—
433C2×C4⋊C4—31no—
434C2×C4⋊C4—31no—
435C2×C4⋊C4C2×C3×D311yescharacteristic
436C2×C4⋊C4C2×C3×D311yescharacteristic
437C2×C4⋊C4C2×C3×D311yescharacteristic
438C2×C22⋊C4—31no—
439C2×C22⋊C4—31no—
440C2×C22⋊C4—31no—
441C2×C22⋊C4—31no—
442C2×C22⋊C4—31no—
443C2×C22⋊C4—31no—
444C2×C22⋊C4—31no—
445C2×C22⋊C4—31no—
446C2×C22⋊C4C2×C3×D311yescharacteristic
447C2×C22⋊C4C2×C3×D311yescharacteristic
448C2×C22⋊C4C2×C3×D311yescharacteristic
449C2×C42—31no—
450C2×C42—31no—
451C2×C42—31no—
452C2×C42—31no—
453#95—31no—
454#95—31no—
455#95—31no—
456#95—31no—
457#95—31no—
458#95—31no—
459#95—31no—
460#95C2×C3×D311yescharacteristic
461C23×C3—22no—
462C23×C3—21no—
463C23×C3—21no—
464C23×C3—21no—
465C23×C3—21no—
466C23×C3—21no—
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—32no—
478C23×C3—41no—
479C23×C3—41no—
480C23×C3—41no—
481C23×C3—41no—
482C23×C3—41no—
483C23×C3—41no—
484C23×C3—61no—
485C23×C3—61no—
486C23×C3—61no—
487C23×C3—61no—
488C23×C3—61no—
489C23×C3—61no—
490C23×C3C23×D311yescharacteristic
491C23×C3C24×C311yescharacteristic
492C22×D3—21no—
493C22×D3—21no—
494C22×D3—21no—
495C22×D3—21no—
496C22×D3—21no—
497C22×D3—21no—
498C22×D3C3×#4112yes—
499C3×D4—124no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—22no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
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—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—22no—
534C2×C3×C4—22no—
535C2×C3×C4—32no—
536C2×C3×C4—32no—
537C2×C3×C4—32no—
538C2×C3×C4—32no—
539C2×C3×C4—41no—
540C2×C3×C4—41no—
541C2×C3×C4—41no—
542C2×C3×C4—41no—
543C2×C3×C4—41no—
544C2×C3×C4—41no—
545C2×C3×C4—41no—
546C2×C3×C4—41no—
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—68no—
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×C4D3×D412yes—
573C2×C3×C4#23712yes—
574C2×C3×C4C2×C3×D412yes—
575C2×C3×C4C3×#4112yes—
576#67—44no—
577C2×Dic3—21no—
578C2×Dic3—21no—
579C2×Dic3—21no—
580C2×Dic3—21no—
581C2×Dic3—21no—
582C2×Dic3—21no—
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×Dic3C2×C3×D412yes—
595C2×Dic3C2×C3×D412yes—
596C2×Dic3C3×#4112yes—
597C2×Dic3C3×#4112yes—
598C4×D3—28no—
599C2×C32—81no—
600C2×C32#52511yescharacteristic
601C2×C32#52911yescharacteristic
602C2×C32#54211yescharacteristic
603C2×C32#54711yescharacteristic
604C2×C32#55011yescharacteristic
605C2×C32#55111yescharacteristic
606C2×C32#55211yescharacteristic
607C3×D3—42no—
608C24—31no—
609C24C22×C3×D311yescharacteristic
610C2×D4—62no—
611C2×D4—62no—
612C2×D4—121no—
613C22×C4—31no—
614C22×C4—31no—
615C22×C4—31no—
616C22×C4—31no—
617C22×C4—31no—
618C22×C4—31no—
619C22×C4—31no—
620C22×C4—62no—
621C22×C4—62no—
622C22×C4—62no—
623C22×C4C22×C3×D311yescharacteristic
624C22×C4C22×C3×D311yescharacteristic
625C22×C4C22×C3×D311yescharacteristic
626C22×C4C22×C3×D311yescharacteristic
627C22×C4C22×C3×D311yescharacteristic
628C22×C4C22×C3×D311yescharacteristic
629C4⋊C4—22no—
630C4⋊C4—22no—
631C4⋊C4—34no—
632C4⋊C4—41no—
633C4⋊C4—62no—
634C4⋊C4—62no—
635C4⋊C4—62no—
636C4⋊C4—62no—
637C4⋊C4—121no—
638C4⋊C4—121no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—41no—
642C22⋊C4—62no—
643C22⋊C4—62no—
644C22⋊C4—62no—
645C22⋊C4—62no—
646C22⋊C4—62no—
647C22⋊C4—62no—
648C22⋊C4—62no—
649C22⋊C4—121no—
650C42—62no—
651C42—62no—
652C42—62no—
653C42—62no—
654C22×C3—21no—
655C22×C3—21no—
656C22×C3—21no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—21no—
660C22×C3—21no—
661C22×C3—42no—
662C22×C3—42no—
663C22×C3—42no—
664C22×C3—41no—
665C22×C3—41no—
666C22×C3—41no—
667C22×C3—41no—
668C22×C3—41no—
669C22×C3—41no—
670C22×C3—41no—
671C22×C3—41no—
672C22×C3—41no—
673C22×C3—41no—
674C22×C3—41no—
675C22×C3—41no—
676C22×C3—41no—
677C22×C3—41no—
678C22×C3—62no—
679C22×C3—62no—
680C22×C3—62no—
681C22×C3—81no—
682C22×C3—81no—
683C22×C3—81no—
684C22×C3—81no—
685C22×C3—121no—
686C22×C3—121no—
687C22×C3—121no—
688C22×C3—121no—
689C22×C3C2×D3×D411yescharacteristic
690C22×C3C2×#23711yescharacteristic
691C22×C3#100411yescharacteristic
692C22×C3#100711yescharacteristic
693C22×C3D3×#4111yescharacteristic
694C22×C3D3×#4111yescharacteristic
695C22×C3D3×#4111yescharacteristic
696C22×C3C22×C3×D411yescharacteristic
697C22×C3C2×C3×#4111yescharacteristic
698C22×C3C2×C3×#4111yescharacteristic
699C22×C3C2×C3×#4111yescharacteristic
700C22×C3C2×C3×#4111yescharacteristic
701C22×C3C3×H(5,𝔽2)11yescharacteristic
702C22×C3C3×2−1+411yescharacteristic
703C2×D3—22no—
704C2×D3—22no—
705C2×D3—22no—
706C2×D3—41no—
707C2×D3—41no—
708C2×D3—41no—
709C2×D3—41no—
710C3×C4—22no—
711C3×C4—22no—
712C3×C4—22no—
713C3×C4—22no—
714C3×C4—42no—
715C3×C4—42no—
716C3×C4—42no—
717C3×C4—41no—
718C3×C4—41no—
719C3×C4—41no—
720C3×C4—41no—
721C3×C4—41no—
722C3×C4—41no—
723C3×C4—41no—
724C3×C4—41no—
725C3×C4—62no—
726C3×C4—62no—
727C3×C4—62no—
728C3×C4—62no—
729C3×C4—81no—
730C3×C4—81no—
731C3×C4—81no—
732C3×C4—121no—
733C3×C4—121no—
734C3×C4—121no—
735Dic3—22no—
736Dic3—22no—
737Dic3—22no—
738Dic3—22no—
739Dic3—41no—
740Dic3—41no—
741Dic3—41no—
742C32#247911yescharacteristic, complemented, Sylow
743C23—21no—
744C23—21no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—21no—
749C23—21no—
750C23—32no—
751C23—61no—
752C23—61no—
753C23—61no—
754C23—61no—
755C23—61no—
756C23—61no—
757C23C23×C3×D311yescharacteristic
758D4—124no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
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—32no—
776C2×C4—32no—
777C2×C4—32no—
778C2×C4—32no—
779C2×C4—68no—
780C2×C4—61no—
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×C4C3×D3×D412yes—
798C2×C4C3×#23712yes—
799C2×C3—21no—
800C2×C3—21no—
801C2×C3—21no—
802C2×C3—21no—
803C2×C3—21no—
804C2×C3—21no—
805C2×C3—21no—
806C2×C3—82no—
807C2×C3—81no—
808C2×C3—81no—
809C2×C3—122no—
810C2×C3#563111yescharacteristic
811C2×C3#563911yescharacteristic
812C2×C3#564011yescharacteristic
813C2×C3#564911yescharacteristic
814C2×C3#565611yescharacteristic
815C2×C3#565911yescharacteristic
816C2×C3#571811yescharacteristic
817C2×C3C3×#52511yescharacteristic
818C2×C3C3×#52911yescharacteristic
819C2×C3C3×#54211yescharacteristic
820C2×C3C3×#54711yescharacteristic
821C2×C3C3×#55011yescharacteristic
822C2×C3C3×#55111yescharacteristic
823C2×C3C3×#55211yescharacteristic
824D3—42no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—62no—
833C22—62no—
834C22—62no—
835C22—121no—
836C22—121no—
837C22—121no—
838C22—121no—
839C22C2×C3×D3×D411yescharacteristic
840C22C2×C3×#23711yescharacteristic
841C22C3×#100411yescharacteristic
842C22C3×#100711yescharacteristic
843C22C3×D3×#4111yescharacteristic
844C22C3×D3×#4111yescharacteristic
845C22C3×D3×#4111yescharacteristic
846C4—22no—
847C4—22no—
848C4—41no—
849C4—41no—
850C4—41no—
851C4—41no—
852C4—62no—
853C4—62no—
854C4—62no—
855C4—62no—
856C4—121no—
857C4—121no—
858C4—121no—
859C3—21no—
860C3#7802711yescharacteristic, direct product factor
861C3C3×#247911yescharacteristic, complemented
862C2—81no—
863C2—122no—
864C2C3×#563111yescharacteristic
865C2C3×#563911yescharacteristic
866C2C3×#564011yescharacteristic
867C2C3×#564911yescharacteristic
868C2C3×#565611yescharacteristic
869C2C3×#565911yescharacteristic
870C2C3×#571811yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC32×#399C2
socleC23×C32C24
prime radicalC22×C3×#67C22
hypercenterC3×#399D3
hypocenterC3C3×#2479
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#399

Complements

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

NH ≅ G/Ntype
1. C2×C3×#892C2semidirect
2. C2×C3×#879C2semidirect
3. C32×#399C2semidirect
4. C3×#4993C2semidirect
5. C3×#4990C2semidirect
6. C3×#4983C2semidirect
7. C3×#4976C2semidirect
8. C3×Dic3×C4⋊C4C2semidirect
12. C3×#4951C2semidirect
13. C3×#4945C2semidirect
14. C3×#4668C2semidirect
15. C3×#4654C2semidirect
17. #78027C3direct (N × H)
57. C2×#892C2×C3semidirect
58. C2×#879C2×C3semidirect
61. C3×#399D3semidirect
62. C3×#399C2×C3semidirect
74. #4993C2×C3semidirect
75. #4990C2×C3semidirect
76. #4983C2×C3semidirect
77. #4976C2×C3semidirect
78. Dic3×C4⋊C4C2×C3semidirect
82. #4951C2×C3semidirect
83. #4945C2×C3semidirect
84. #4668C2×C3semidirect
85. #4654C2×C3semidirect
122. C3×C4⋊Dic3D4semidirect
273. #399C3×D3semidirect
380. C4⋊Dic3C3×D4semidirect
742. C32#2479semidirect
860. C3#78027direct (N × H)
861. C3C3×#2479semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8922
C2×C3×#8792
C32×#3992
C3×#49932
C3×#49902
C3×#49832
C3×#49762
C3×Dic3×C4⋊C42
C3×#49592
C3×#49572
C3×#49562
C3×#49512
C3×#49452
C3×#46682
C3×#46542
C3×#24793
#780273