Finite Group Databasebeta

← C3×#75319 #11812828

Subgroups — C3×#75319 #11812828

Order 1152.

1425 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#895C211yesmaximal, characteristic
2C2×C3×#894C211yesmaximal, characteristic, complemented
3C2×C3×D3×C4⋊C4C211yesmaximal, characteristic, complemented
4C2×C3×C4×D12C211yesmaximal, characteristic, complemented
5C32×#387C211yesmaximal, characteristic, complemented
6C3×#4981C211yesmaximal, characteristic, complemented
7C3×#4940C211yesmaximal, characteristic, complemented
8C3×#4677C211yesmaximal, characteristic, complemented
9C3×#4674C211yesmaximal, characteristic, complemented
10C3×#4672C211yesmaximal, characteristic, complemented
11C3×#4668C211yesmaximal, characteristic, complemented
12C3×#4668C211yesmaximal, characteristic, complemented
13C3×#4665C211yesmaximal, characteristic, complemented
14C3×#4665C211yesmaximal, characteristic, complemented
15C3×#4665C211yesmaximal, characteristic, complemented
16C3×#2443—31nomaximal
17#75319C311yesmaximal, characteristic, direct product factor
18C22×C3×D12C2211yescharacteristic
19C22×C3×D12C2211yescharacteristic
20C22×C3×D12C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×C3×C4×D3C2211yescharacteristic
24C22×C3×C4×D3C2211yescharacteristic
25C2×C32×C4⋊C4C2211yescharacteristic
26C2×C32×C4⋊C4C2211yescharacteristic
27C2×C32×C42C2211yescharacteristic
28C2×C3×(C2×D3)⋊C4C2211yescharacteristic
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×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×(C2×D3)⋊C4C2211yescharacteristic
39C2×C3×C4⋊Dic3C2211yescharacteristic
40C2×C3×C4⋊Dic3C2211yescharacteristic
41C2×C3×C4⋊Dic3C2211yescharacteristic
42C2×C3×Dic3⋊C4C2211yescharacteristic
43C2×C3×Dic3⋊C4C2211yescharacteristic
44C2×C3×Dic3⋊C4C2211yescharacteristic
45C3×#895—24no—
46C3×#894—24no—
47C3×D3×C4⋊C4—24no—
48C3×C4×D12—24no—
49C32×#95C2211yescharacteristic
50C32×#95C2211yescharacteristic
51C32×#95C2211yescharacteristic
52C32×#95C2211yescharacteristic
53C3×C3⋊#95C2211yescharacteristic
54C3×C3⋊#95C2211yescharacteristic
55C3×C3⋊#95C2211yescharacteristic
56C3×C3⋊#95C2211yescharacteristic
57C2×C3×#123—31no—
58C2×C3×#121—31no—
59C2×C3×C4×D4—31no—
60C22×C3×C4⋊C4—31no—
61C2×#895C2×C311yescharacteristic
62C2×#894C2×C311yescharacteristic, complemented
63C2×D3×C4⋊C4C2×C311yescharacteristic, complemented
64C2×C4×D12C2×C311yescharacteristic, complemented
65C3×#399—31no—
66C3×#398—31no—
67C3×#397—31no—
68C3×#394—31no—
69C3×#388—31no—
70C3×#387—21no—
71C3×#387D311yescharacteristic, complemented
72C3×#387C2×C311yescharacteristic, complemented
73C3×#386—31no—
74C3×#386—31no—
75C3×#386—31no—
76C3×#385—31no—
77C3×#385—31no—
78#4981C2×C311yescharacteristic, complemented
79#4940C2×C311yescharacteristic, complemented
80#4677C2×C311yescharacteristic, complemented
81#4674C2×C311yescharacteristic, complemented
82#4672C2×C311yescharacteristic, complemented
83#4668C2×C311yescharacteristic, complemented
84#4668C2×C311yescharacteristic, complemented
85#4665C2×C311yescharacteristic, complemented
86#4665C2×C311yescharacteristic, complemented
87#4665C2×C311yescharacteristic, complemented
88C23×C3×D3C2311yescharacteristic
89C23×C3×D3C2311yescharacteristic
90C23×C3×D3C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C22×C32×C4C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C2×C3×D12—22no—
104C2×C3×D12—22no—
105C2×C3×D12—22no—
106C2×C3×D12—22no—
107C2×C3×D12—22no—
108C2×C3×D12—22no—
109C2×C3×D12—22no—
110C2×C3×D12—41no—
111C2×C3×D12D414yes—
112C2×C3×C4×D3—22no—
113C2×C3×C4×D3—22no—
114C2×C3×C4×D3—22no—
115C2×C3×C4×D3—22no—
116C2×C3×C4×D3—22no—
117C2×C3×C4×D3—22no—
118C2×C3×C4×D3—22no—
119C2×C3×C4×D3—22no—
120C2×C3×C4×D3—22no—
121C2×C3×C4×D3—41no—
122C2×C3×C4×D3—41no—
123C2×C3×C4×D3—41no—
124C32×C4⋊C4—22no—
125C32×C4⋊C4D414yescomplemented
126C32×C42—22no—
127C3×(C2×D3)⋊C4—22no—
128C3×(C2×D3)⋊C4—22no—
129C3×(C2×D3)⋊C4—22no—
130C3×(C2×D3)⋊C4—22no—
131C3×(C2×D3)⋊C4—22no—
132C3×(C2×D3)⋊C4—22no—
133C3×(C2×D3)⋊C4—22no—
134C3×(C2×D3)⋊C4—22no—
135C3×(C2×D3)⋊C4—22no—
136C3×(C2×D3)⋊C4—22no—
137C3×(C2×D3)⋊C4—41no—
138C3×C4⋊Dic3—22no—
139C3×C4⋊Dic3—22no—
140C3×C4⋊Dic3—41no—
141C3×Dic3⋊C4—22no—
142C3×Dic3⋊C4—22no—
143C3×Dic3⋊C4—22no—
144#2443—31noSylow
145C22×C3×D4—31no—
146C22×C3×D4—31no—
147C22×C3×D4—31no—
148C23×C3×C4—31no—
149C23×C3×C4—31no—
150C23×C3×C4—31no—
151C23×C3×C4—31no—
152C22×D12C22×C311yescharacteristic
153C22×D12C22×C311yescharacteristic
154C22×D12C22×C311yescharacteristic
155C22×C4×D3C22×C311yescharacteristic
156C22×C4×D3C22×C311yescharacteristic
157C22×C4×D3C22×C311yescharacteristic
158C22×C4×D3C22×C311yescharacteristic
159C3×#123—64no—
160C3×#121—64no—
161C3×C4×D4—64no—
162C2×C3×C4⋊C4—21no—
163C2×C3×C4⋊C4—21no—
164C2×C3×C4⋊C4—31no—
165C2×C3×C4⋊C4—31no—
166C2×C3×C4⋊C4—31no—
167C2×C3×C4⋊C4—31no—
168C2×C3×C4⋊C4—31no—
169C2×C3×C4⋊C4—31no—
170C2×C3×C4⋊C4—64no—
171C2×C3×C4⋊C4C2×D311yescharacteristic
172C2×C3×C4⋊C4C2×D311yescharacteristic
173C2×C3×C4⋊C4C22×C311yescharacteristic
174C2×C3×C4⋊C4C22×C311yescharacteristic
175C2×C3×C22⋊C4—31no—
176C2×C3×C22⋊C4—31no—
177C2×C3×C22⋊C4—31no—
178C2×C3×C22⋊C4—31no—
179C2×C3×C22⋊C4—31no—
180C2×C3×C22⋊C4—31no—
181C2×C3×C22⋊C4—31no—
182C2×C3×C22⋊C4—31no—
183C2×C3×C22⋊C4—31no—
184C2×C3×C22⋊C4—31no—
185C2×C3×C22⋊C4—31no—
186C2×C3×C42—21no—
187C2×C3×C42C2×D311yescharacteristic
188C2×C3×C42C22×C311yescharacteristic
189C2×(C2×D3)⋊C4C22×C311yescharacteristic
190C2×(C2×D3)⋊C4C22×C311yescharacteristic
191C2×(C2×D3)⋊C4C22×C311yescharacteristic
192C2×(C2×D3)⋊C4C22×C311yescharacteristic
193C2×(C2×D3)⋊C4C22×C311yescharacteristic
194C2×(C2×D3)⋊C4C22×C311yescharacteristic
195C2×(C2×D3)⋊C4C22×C311yescharacteristic
196C2×(C2×D3)⋊C4C22×C311yescharacteristic
197C2×(C2×D3)⋊C4C22×C311yescharacteristic
198C2×(C2×D3)⋊C4C22×C311yescharacteristic
199C2×(C2×D3)⋊C4C22×C311yescharacteristic
200C2×C4⋊Dic3C22×C311yescharacteristic
201C2×C4⋊Dic3C22×C311yescharacteristic
202C2×C4⋊Dic3C22×C311yescharacteristic
203C2×Dic3⋊C4C22×C311yescharacteristic
204C2×Dic3⋊C4C22×C311yescharacteristic
205C2×Dic3⋊C4C22×C311yescharacteristic
206#895—24no—
207#894—24no—
208D3×C4⋊C4—24no—
209C4×D12—24no—
210C3×#95—21no—
211C3×#95—21no—
212C3×#95—21no—
213C3×#95—21no—
214C3×#95—31no—
215C3×#95—31no—
216C3×#95—31no—
217C3×#95—31no—
218C3×#95C2×D311yescharacteristic
219C3×#95C2×D311yescharacteristic
220C3×#95C2×D311yescharacteristic
221C3×#95C2×D311yescharacteristic
222C3×#95C22×C311yescharacteristic
223C3×#95C22×C311yescharacteristic
224C3×#95C22×C311yescharacteristic
225C3×#95C22×C311yescharacteristic
226C3⋊#95C22×C311yescharacteristic
227C3⋊#95C22×C311yescharacteristic
228C3⋊#95C22×C311yescharacteristic
229C3⋊#95C22×C311yescharacteristic
230C23×C32C2411yescharacteristic
231C22×C3×D3—21no—
232C22×C3×D3—21no—
233C22×C3×D3—21no—
234C22×C3×D3—21no—
235C22×C3×D3—21no—
236C22×C3×D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3—21no—
239C22×C3×D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3—21no—
243C22×C3×D3—21no—
244C22×C3×D3—21no—
245C22×C3×D3—21no—
246C22×C3×D3—21no—
247C22×C3×D3—21no—
248C22×C3×D3C2×D412yes—
249C22×C3×D3C2×D412yes—
250C22×C3×D3#4112yes—
251C22×C3×D3#4112yes—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4—21no—
258C2×C32×C4—21no—
259C2×C32×C4—21no—
260C2×C32×C4—21no—
261C2×C32×C4—21no—
262C2×C32×C4—21no—
263C2×C32×C4—21no—
264C2×C32×C4—21no—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4—21no—
268C2×C32×C4—21no—
269C2×C32×C4C2×D412yes—
270C2×C32×C4C2×D412yes—
271C2×C32×C4C2×D412yes—
272C2×C32×C4C2×D412yes—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3—21no—
287C2×C3×Dic3#4112yes—
288C3×D12—28no—
289C3×D12—44no—
290C3×D12—44no—
291C3×C4×D3—28no—
292C3×C4×D3—44no—
293C3×C4×D3—44no—
294C3×C4×D3—44no—
295C2×#123—31no—
296C2×#121—31no—
297C2×C4×D4—31no—
298C22×C4⋊C4—31no—
299#399—31no—
300#398—31no—
301#397—31no—
302#394—31no—
303#388—31no—
304#387C3×D311yescharacteristic, complemented
305#386—31no—
306#386—31no—
307#386—31no—
308#385—31no—
309#385—31no—
310C24×C3—31no—
311C24×C3—31no—
312C24×C3—31no—
313C23×D3C23×C311yescharacteristic
314C23×D3C23×C311yescharacteristic
315C23×D3C23×C311yescharacteristic
316C2×C3×D4—34no—
317C2×C3×D4—62no—
318C2×C3×D4—62no—
319C2×C3×D4—62no—
320C2×C3×D4—62no—
321C2×C3×D4—62no—
322C2×C3×D4—62no—
323C2×C3×D4—62no—
324C2×C3×D4—121no—
325C22×C3×C4—21no—
326C22×C3×C4—21no—
327C22×C3×C4—21no—
328C22×C3×C4—21no—
329C22×C3×C4—21no—
330C22×C3×C4—21no—
331C22×C3×C4—21no—
332C22×C3×C4—31no—
333C22×C3×C4—31no—
334C22×C3×C4—31no—
335C22×C3×C4—31no—
336C22×C3×C4—31no—
337C22×C3×C4—62no—
338C22×C3×C4—62no—
339C22×C3×C4—62no—
340C22×C3×C4—62no—
341C22×C3×C4—62no—
342C22×C3×C4—62no—
343C22×C3×C4—62no—
344C22×C3×C4—62no—
345C22×C3×C4—62no—
346C22×C3×C4—121no—
347C22×C3×C4—121no—
348C22×C3×C4—121no—
349C22×C3×C4C22×D311yescharacteristic
350C22×C3×C4C22×D311yescharacteristic
351C22×C3×C4C22×D311yescharacteristic
352C22×C3×C4C22×D311yescharacteristic
353C22×C3×C4C22×D311yescharacteristic
354C22×C3×C4C22×D311yescharacteristic
355C22×C3×C4C22×D311yescharacteristic
356C22×C3×C4C23×C311yescharacteristic
357C22×C3×C4C23×C311yescharacteristic
358C22×C3×C4C23×C311yescharacteristic
359C22×C3×C4C23×C311yescharacteristic
360C22×C3×C4C23×C311yescharacteristic
361C22×C3×C4C23×C311yescharacteristic
362C22×C3×C4C23×C311yescharacteristic
363C22×Dic3C23×C311yescharacteristic
364C22×Dic3C23×C311yescharacteristic
365C22×Dic3C23×C311yescharacteristic
366C22×Dic3C23×C311yescharacteristic
367C22×Dic3C23×C311yescharacteristic
368C2×D12—22no—
369C2×D12—22no—
370C2×D12—22no—
371C2×D12—22no—
372C2×D12—22no—
373C2×D12—22no—
374C2×D12—22no—
375C2×D12—41no—
376C2×D12C3×D414yes—
377C2×C4×D3—22no—
378C2×C4×D3—22no—
379C2×C4×D3—22no—
380C2×C4×D3—22no—
381C2×C4×D3—22no—
382C2×C4×D3—22no—
383C2×C4×D3—22no—
384C2×C4×D3—22no—
385C2×C4×D3—22no—
386C2×C4×D3—41no—
387C2×C4×D3—41no—
388C2×C4×D3—41no—
389C3×C4⋊C4—22no—
390C3×C4⋊C4—22no—
391C3×C4⋊C4—24no—
392C3×C4⋊C4—42no—
393C3×C4⋊C4—62no—
394C3×C4⋊C4—62no—
395C3×C4⋊C4—62no—
396C3×C4⋊C4—62no—
397C3×C4⋊C4—62no—
398C3×C4⋊C4—121no—
399C3×C4⋊C4D1214yescomplemented
400C3×C4⋊C4C3×D414yescomplemented
401C3×C22⋊C4—62no—
402C3×C22⋊C4—62no—
403C3×C22⋊C4—62no—
404C3×C22⋊C4—62no—
405C3×C22⋊C4—62no—
406C3×C22⋊C4—62no—
407C3×C22⋊C4—62no—
408C3×C22⋊C4—62no—
409C3×C22⋊C4—62no—
410C3×C22⋊C4—62no—
411C3×C22⋊C4—121no—
412C3×C42—22no—
413C3×C42—22no—
414C3×C42—42no—
415(C2×D3)⋊C4—22no—
416(C2×D3)⋊C4—22no—
417(C2×D3)⋊C4—22no—
418(C2×D3)⋊C4—22no—
419(C2×D3)⋊C4—22no—
420(C2×D3)⋊C4—22no—
421(C2×D3)⋊C4—22no—
422(C2×D3)⋊C4—22no—
423(C2×D3)⋊C4—22no—
424(C2×D3)⋊C4—22no—
425(C2×D3)⋊C4—41no—
426C4⋊Dic3—22no—
427C4⋊Dic3—22no—
428C4⋊Dic3—41no—
429Dic3⋊C4—22no—
430Dic3⋊C4—22no—
431Dic3⋊C4—22no—
432C22×C32C22×D411yescharacteristic
433C22×C32C22×D411yescharacteristic
434C22×C32C2×#4111yescharacteristic
435C22×C32C2×#4111yescharacteristic
436C22×C32C2×#4111yescharacteristic
437C22×C32H(5,𝔽2)11yescharacteristic
438C22×C322−1+411yescharacteristic
439C2×C3×D3—22no—
440C2×C3×D3—22no—
441C2×C3×D3—22no—
442C2×C3×D3—22no—
443C2×C3×D3—22no—
444C2×C3×D3—22no—
445C2×C3×D3—22no—
446C2×C3×D3—22no—
447C2×C3×D3—22no—
448C2×C3×D3—41no—
449C2×C3×D3—41no—
450C2×C3×D3—41no—
451C2×C3×D3—41no—
452C2×C3×D3—41no—
453C2×C3×D3—41no—
454C2×C3×D3—41no—
455C2×C3×D3—41no—
456C2×C3×D3—41no—
457C2×C3×D3—41no—
458C2×C3×D3—41no—
459C2×C3×D3#12314yescomplemented
460C32×C4—22no—
461C32×C4—22no—
462C32×C4—22no—
463C32×C4—22no—
464C32×C4—41no—
465C32×C4—41no—
466C32×C4—41no—
467C3×Dic3—22no—
468C3×Dic3—41no—
469C3×Dic3—41no—
470C3×Dic3—41no—
471C3×Dic3—41no—
472C22×D4—31no—
473C22×D4—31no—
474C22×D4—31no—
475C23×C4—31no—
476C23×C4—31no—
477C23×C4—31no—
478C23×C4—31no—
479#123—64no—
480#121—64no—
481C4×D4—64no—
482C2×C4⋊C4—31no—
483C2×C4⋊C4—31no—
484C2×C4⋊C4—31no—
485C2×C4⋊C4—31no—
486C2×C4⋊C4—31no—
487C2×C4⋊C4—31no—
488C2×C4⋊C4—64no—
489C2×C4⋊C4C2×C3×D311yescharacteristic
490C2×C4⋊C4C2×C3×D311yescharacteristic
491C2×C22⋊C4—31no—
492C2×C22⋊C4—31no—
493C2×C22⋊C4—31no—
494C2×C22⋊C4—31no—
495C2×C22⋊C4—31no—
496C2×C22⋊C4—31no—
497C2×C22⋊C4—31no—
498C2×C22⋊C4—31no—
499C2×C22⋊C4—31no—
500C2×C22⋊C4—31no—
501C2×C22⋊C4—31no—
502C2×C42C2×C3×D311yescharacteristic
503#95—31no—
504#95—31no—
505#95—31no—
506#95—31no—
507#95C2×C3×D311yescharacteristic
508#95C2×C3×D311yescharacteristic
509#95C2×C3×D311yescharacteristic
510#95C2×C3×D311yescharacteristic
511C23×C3—21no—
512C23×C3—32no—
513C23×C3—32no—
514C23×C3—32no—
515C23×C3—32no—
516C23×C3—61no—
517C23×C3—61no—
518C23×C3—61no—
519C23×C3—61no—
520C23×C3—61no—
521C23×C3—61no—
522C23×C3—61no—
523C23×C3—61no—
524C23×C3—61no—
525C23×C3—61no—
526C23×C3—61no—
527C23×C3—61no—
528C23×C3—61no—
529C23×C3—61no—
530C23×C3—61no—
531C23×C3—61no—
532C23×C3—61no—
533C23×C3C23×D311yescharacteristic
534C23×C3C24×C311yescharacteristic
535C22×D3—21no—
536C22×D3—21no—
537C22×D3—21no—
538C22×D3—21no—
539C22×D3—21no—
540C22×D3—21no—
541C22×D3—21no—
542C22×D3—21no—
543C22×D3—21no—
544C22×D3—21no—
545C22×D3—21no—
546C22×D3—21no—
547C22×D3—21no—
548C22×D3—21no—
549C22×D3—21no—
550C22×D3—21no—
551C22×D3—21no—
552C22×D3C2×C3×D412yes—
553C22×D3C2×C3×D412yes—
554C22×D3C3×#4112yes—
555C22×D3C3×#4112yes—
556C3×D4—68no—
557C3×D4—124no—
558C3×D4—124no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—21no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—22no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—21no—
594C2×C3×C4—22no—
595C2×C3×C4—22no—
596C2×C3×C4—22no—
597C2×C3×C4—22no—
598C2×C3×C4—32no—
599C2×C3×C4—41no—
600C2×C3×C4—41no—
601C2×C3×C4—41no—
602C2×C3×C4—41no—
603C2×C3×C4—41no—
604C2×C3×C4—41no—
605C2×C3×C4—41no—
606C2×C3×C4—41no—
607C2×C3×C4—41no—
608C2×C3×C4—41no—
609C2×C3×C4—41no—
610C2×C3×C4—41no—
611C2×C3×C4—41no—
612C2×C3×C4—41no—
613C2×C3×C4—41no—
614C2×C3×C4—41no—
615C2×C3×C4—68no—
616C2×C3×C4—61no—
617C2×C3×C4—61no—
618C2×C3×C4—61no—
619C2×C3×C4—61no—
620C2×C3×C4—61no—
621C2×C3×C4—61no—
622C2×C3×C4—61no—
623C2×C3×C4—61no—
624C2×C3×C4—61no—
625C2×C3×C4—61no—
626C2×C3×C4—61no—
627C2×C3×C4—61no—
628C2×C3×C4—61no—
629C2×C3×C4—61no—
630C2×C3×C4—124no—
631C2×C3×C4—124no—
632C2×C3×C4—124no—
633C2×C3×C4C2×D1212yes—
634C2×C3×C4C2×D1212yes—
635C2×C3×C4C2×D1212yes—
636C2×C3×C4D3×D412yes—
637C2×C3×C4C2×C3×D412yes—
638C2×C3×C4C2×C3×D412yes—
639C2×C3×C4C2×C3×D412yes—
640C2×C3×C4C2×C3×D412yes—
641C2×Dic3—21no—
642C2×Dic3—21no—
643C2×Dic3—21no—
644C2×Dic3—21no—
645C2×Dic3—21no—
646C2×Dic3—21no—
647C2×Dic3—21no—
648C2×Dic3—21no—
649C2×Dic3—21no—
650C2×Dic3—21no—
651C2×Dic3—21no—
652C2×Dic3—21no—
653C2×Dic3—21no—
654C2×Dic3—21no—
655C2×Dic3C3×#4112yes—
656D12—28no—
657D12—44no—
658D12—44no—
659C4×D3—28no—
660C4×D3—44no—
661C4×D3—44no—
662C4×D3—44no—
663C2×C32C2×#12311yescharacteristic
664C2×C32#52511yescharacteristic
665C2×C32#53911yescharacteristic
666C2×C32D4211yescharacteristic
667C2×C32#54711yescharacteristic
668C2×C32#54811yescharacteristic
669C2×C32#55311yescharacteristic
670C3×D3—24no—
671C3×D3—42no—
672C3×D3—81no—
673C24—31no—
674C24—31no—
675C24—31no—
676C2×D4—34no—
677C2×D4—62no—
678C2×D4—62no—
679C2×D4—62no—
680C2×D4—62no—
681C2×D4—62no—
682C2×D4—62no—
683C2×D4—62no—
684C2×D4—121no—
685C22×C4—31no—
686C22×C4—31no—
687C22×C4—31no—
688C22×C4—31no—
689C22×C4—31no—
690C22×C4—62no—
691C22×C4—62no—
692C22×C4—62no—
693C22×C4—62no—
694C22×C4—62no—
695C22×C4—62no—
696C22×C4—62no—
697C22×C4—62no—
698C22×C4—62no—
699C22×C4—121no—
700C22×C4—121no—
701C22×C4—121no—
702C22×C4C22×C3×D311yescharacteristic
703C22×C4C22×C3×D311yescharacteristic
704C22×C4C22×C3×D311yescharacteristic
705C22×C4C22×C3×D311yescharacteristic
706C22×C4C22×C3×D311yescharacteristic
707C22×C4C22×C3×D311yescharacteristic
708C22×C4C22×C3×D311yescharacteristic
709C4⋊C4—22no—
710C4⋊C4—62no—
711C4⋊C4—62no—
712C4⋊C4—62no—
713C4⋊C4—62no—
714C4⋊C4—62no—
715C4⋊C4—121no—
716C4⋊C4C3×D1214yescomplemented
717C22⋊C4—62no—
718C22⋊C4—62no—
719C22⋊C4—62no—
720C22⋊C4—62no—
721C22⋊C4—62no—
722C22⋊C4—62no—
723C22⋊C4—62no—
724C22⋊C4—62no—
725C22⋊C4—62no—
726C22⋊C4—62no—
727C22⋊C4—121no—
728C42—22no—
729C22×C3—21no—
730C22×C3—21no—
731C22×C3—21no—
732C22×C3—21no—
733C22×C3—21no—
734C22×C3—21no—
735C22×C3—21no—
736C22×C3—34no—
737C22×C3—62no—
738C22×C3—62no—
739C22×C3—62no—
740C22×C3—62no—
741C22×C3—62no—
742C22×C3—62no—
743C22×C3—62no—
744C22×C3—62no—
745C22×C3—62no—
746C22×C3—121no—
747C22×C3—121no—
748C22×C3—121no—
749C22×C3—121no—
750C22×C3—121no—
751C22×C3—121no—
752C22×C3—121no—
753C22×C3—121no—
754C22×C3—121no—
755C22×C3—121no—
756C22×C3—121no—
757C22×C3C22×D1211yescharacteristic
758C22×C3C2×D3×D411yescharacteristic
759C22×C3#100711yescharacteristic
760C22×C3D3×#4111yescharacteristic
761C22×C3D3×#4111yescharacteristic
762C22×C3D3×#4111yescharacteristic
763C22×C3#100911yescharacteristic
764C22×C3C22×C3×D411yescharacteristic
765C22×C3C22×C3×D411yescharacteristic
766C22×C3C2×C3×#4111yescharacteristic
767C22×C3C2×C3×#4111yescharacteristic
768C22×C3C2×C3×#4111yescharacteristic
769C22×C3C3×H(5,𝔽2)11yescharacteristic
770C22×C3C3×2−1+411yescharacteristic
771C2×D3—22no—
772C2×D3—22no—
773C2×D3—22no—
774C2×D3—22no—
775C2×D3—22no—
776C2×D3—22no—
777C2×D3—22no—
778C2×D3—22no—
779C2×D3—22no—
780C2×D3—41no—
781C2×D3—41no—
782C2×D3—41no—
783C2×D3—41no—
784C2×D3—41no—
785C2×D3—41no—
786C2×D3—41no—
787C2×D3—41no—
788C2×D3—41no—
789C2×D3—41no—
790C2×D3—41no—
791C2×D3C3×#12314yescomplemented
792C3×C4—22no—
793C3×C4—22no—
794C3×C4—22no—
795C3×C4—22no—
796C3×C4—22no—
797C3×C4—22no—
798C3×C4—22no—
799C3×C4—22no—
800C3×C4—42no—
801C3×C4—42no—
802C3×C4—42no—
803C3×C4—42no—
804C3×C4—42no—
805C3×C4—41no—
806C3×C4—41no—
807C3×C4—41no—
808C3×C4—41no—
809C3×C4—41no—
810C3×C4—41no—
811C3×C4—62no—
812C3×C4—81no—
813C3×C4—81no—
814C3×C4—121no—
815C3×C4—121no—
816C3×C4—121no—
817C3×C4—121no—
818Dic3—22no—
819Dic3—41no—
820Dic3—41no—
821Dic3—41no—
822Dic3—41no—
823C32#244311yescharacteristic, complemented, Sylow
824C23—32no—
825C23—32no—
826C23—32no—
827C23—32no—
828C23—61no—
829C23—61no—
830C23—61no—
831C23—61no—
832C23—61no—
833C23—61no—
834C23—61no—
835C23—61no—
836C23—61no—
837C23—61no—
838C23—61no—
839C23—61no—
840C23—61no—
841C23—61no—
842C23—61no—
843C23—61no—
844C23—61no—
845C23C23×C3×D311yescharacteristic
846D4—68no—
847D4—124no—
848D4—124no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—32no—
867C2×C4—68no—
868C2×C4—61no—
869C2×C4—61no—
870C2×C4—61no—
871C2×C4—61no—
872C2×C4—61no—
873C2×C4—61no—
874C2×C4—61no—
875C2×C4—61no—
876C2×C4—61no—
877C2×C4—61no—
878C2×C4—61no—
879C2×C4—61no—
880C2×C4—61no—
881C2×C4—61no—
882C2×C4—124no—
883C2×C4—124no—
884C2×C4—124no—
885C2×C4C2×C3×D1212yes—
886C2×C4C2×C3×D1212yes—
887C2×C4C2×C3×D1212yes—
888C2×C4C3×D3×D412yes—
889C2×C3—21no—
890C2×C3—21no—
891C2×C3—21no—
892C2×C3—21no—
893C2×C3—21no—
894C2×C3—21no—
895C2×C3—21no—
896C2×C3—64no—
897C2×C3—122no—
898C2×C3—241no—
899C2×C3#552411yescharacteristic
900C2×C3D4×D1211yescharacteristic
901C2×C3#557611yescharacteristic
902C2×C3#563111yescharacteristic
903C2×C3D3×#12311yescharacteristic
904C2×C3#569211yescharacteristic
905C2×C3#570911yescharacteristic
906C2×C3C2×C3×#12311yescharacteristic
907C2×C3C3×#52511yescharacteristic
908C2×C3C3×#53911yescharacteristic
909C2×C3C3×D4211yescharacteristic
910C2×C3C3×#54711yescharacteristic
911C2×C3C3×#54811yescharacteristic
912C2×C3C3×#55311yescharacteristic
913D3—24no—
914D3—42no—
915D3—81no—
916C22—34no—
917C22—62no—
918C22—62no—
919C22—62no—
920C22—62no—
921C22—62no—
922C22—62no—
923C22—62no—
924C22—62no—
925C22—62no—
926C22—121no—
927C22—121no—
928C22—121no—
929C22—121no—
930C22—121no—
931C22—121no—
932C22—121no—
933C22—121no—
934C22—121no—
935C22—121no—
936C22—121no—
937C22C22×C3×D1211yescharacteristic
938C22C2×C3×D3×D411yescharacteristic
939C22C3×#100711yescharacteristic
940C22C3×D3×#4111yescharacteristic
941C22C3×D3×#4111yescharacteristic
942C22C3×D3×#4111yescharacteristic
943C22C3×#100911yescharacteristic
944C4—22no—
945C4—22no—
946C4—22no—
947C4—22no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—62no—
952C4—121no—
953C4—121no—
954C4—121no—
955C4—121no—
956C3—21no—
957C3#7531911yescharacteristic, direct product factor
958C3C3×#244311yescharacteristic, complemented
959C2—64no—
960C2—122no—
961C2—241no—
962C2C3×#552411yescharacteristic
963C2C3×D4×D1211yescharacteristic
964C2C3×#557611yescharacteristic
965C2C3×#563111yescharacteristic
966C2C3×D3×#12311yescharacteristic
967C2C3×#569211yescharacteristic
968C2C3×#570911yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC32×#387C2
socleC23×C32C24
prime radicalC2×C3×#895C2
hypercenterC3×#387D3
hypocenterC3C3×#2443
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#387

Complements

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

NH ≅ G/Ntype
2. C2×C3×#894C2semidirect
3. C2×C3×D3×C4⋊C4C2semidirect
4. C2×C3×C4×D12C2semidirect
5. C32×#387C2semidirect
6. C3×#4981C2semidirect
7. C3×#4940C2semidirect
8. C3×#4677C2semidirect
9. C3×#4674C2semidirect
10. C3×#4672C2semidirect
11. C3×#4668C2semidirect
12. C3×#4668C2semidirect
13. C3×#4665C2semidirect
14. C3×#4665C2semidirect
15. C3×#4665C2semidirect
17. #75319C3direct (N × H)
62. C2×#894C2×C3semidirect
63. C2×D3×C4⋊C4C2×C3semidirect
64. C2×C4×D12C2×C3semidirect
71. C3×#387D3semidirect
72. C3×#387C2×C3semidirect
78. #4981C2×C3semidirect
79. #4940C2×C3semidirect
80. #4677C2×C3semidirect
81. #4674C2×C3semidirect
82. #4672C2×C3semidirect
83. #4668C2×C3semidirect
84. #4668C2×C3semidirect
85. #4665C2×C3semidirect
86. #4665C2×C3semidirect
87. #4665C2×C3semidirect
125. C32×C4⋊C4D4semidirect
304. #387C3×D3semidirect
399. C3×C4⋊C4D12semidirect
400. C3×C4⋊C4C3×D4semidirect
459. C2×C3×D3#123semidirect
716. C4⋊C4C3×D12semidirect
791. C2×D3C3×#123semidirect
823. C32#2443semidirect
957. C3#75319direct (N × H)
958. C3C3×#2443semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8952
C2×C3×#8942
C2×C3×D3×C4⋊C42
C2×C3×C4×D122
C32×#3872
C3×#49812
C3×#49402
C3×#46772
C3×#46742
C3×#46722
C3×#46682
C3×#46652
C3×#24433
#753193