Finite Group Databasebeta

← C3×#77674 #11812950

Subgroups — C3×#77674 #11812950

Order 1152.

1305 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#884C211yesmaximal, characteristic
2C2×C3×#67⋊C4C211yesmaximal, characteristic, complemented
3C32×#397C211yesmaximal, characteristic, complemented
4C3×#4990C211yesmaximal, characteristic, complemented
5C3×#4989C211yesmaximal, characteristic, complemented
6C3×#4959C211yesmaximal, characteristic, complemented
7C3×#4958C211yesmaximal, characteristic, complemented
8C3×#4956C211yesmaximal, characteristic, complemented
9C3×#4943C211yesmaximal, characteristic, complemented
10C3×#4675C211yesmaximal, characteristic, complemented
11C3×#4665C211yesmaximal, characteristic, complemented
12C3×#4665C211yesmaximal, characteristic, complemented
13C3×D3×#95C211yesmaximal, characteristic, complemented
14C3×#4658C211yesmaximal, characteristic, complemented
15C3×#4652C211yesmaximal, characteristic, complemented
16C3×#2444—31nomaximal
17#77674C311yesmaximal, characteristic, direct product factor
18C22×C3×#67C2211yescharacteristic
19C22×C3×#67C2211yescharacteristic
20C23×C3×Dic3C2211yescharacteristic
21C22×C3×D12C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×C3×C4×D3C2211yescharacteristic
24C22×C3×C4×D3C2211yescharacteristic
25C2×C32×C4⋊C4C2211yescharacteristic
26C2×C32×C22⋊C4C2211yescharacteristic
27C2×C32×C22⋊C4C2211yescharacteristic
28C2×C32×C22⋊C4C2211yescharacteristic
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×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×Dic3⋊C4C2211yescharacteristic
38C2×C3×Dic3⋊C4C2211yescharacteristic
39C2×C3×Dic3⋊C4C2211yescharacteristic
40C2×C3×C4×Dic3C2211yescharacteristic
41C3×#884—24no—
42C3×#67⋊C4—24no—
43C32×#95C2211yescharacteristic
44C32×#95C2211yescharacteristic
45C32×#95C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
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×#121—31no—
56C2×C3×C4×D4—31no—
57C2×#884C2×C311yescharacteristic
58C2×#67⋊C4C2×C311yescharacteristic, complemented
59C3×#400—31no—
60C3×#397—21no—
61C3×#397—31no—
62C3×#397D311yescharacteristic, complemented
63C3×#397C2×C311yescharacteristic, complemented
64C3×#394—31no—
65C3×#388—31no—
66C3×#387—31no—
67C3×#386—31no—
68C3×#386—31no—
69C3×#386—31no—
70C3×#386—31no—
71C3×#385—31no—
72C3×#381—31no—
73C2×C3×#95—31no—
74#4990C2×C311yescharacteristic, complemented
75#4989C2×C311yescharacteristic, complemented
76#4959C2×C311yescharacteristic, complemented
77#4958C2×C311yescharacteristic, complemented
78#4956C2×C311yescharacteristic, complemented
79#4943C2×C311yescharacteristic, complemented
80#4675C2×C311yescharacteristic, complemented
81#4665C2×C311yescharacteristic, complemented
82#4665C2×C311yescharacteristic, complemented
83D3×#95C2×C311yescharacteristic, complemented
84#4658C2×C311yescharacteristic, complemented
85#4652C2×C311yescharacteristic, complemented
86C24×C32C2311yescharacteristic
87C23×C3×D3C2311yescharacteristic
88C23×C3×D3C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C2×C3×#67—22no—
96C2×C3×#67—22no—
97C2×C3×#67—22no—
98C2×C3×#67—22no—
99C2×C3×#67—41no—
100C2×C3×#67D414yes—
101C22×C3×Dic3—22no—
102C22×C3×Dic3—22no—
103C22×C3×Dic3—41no—
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C2×C3×D12—22no—
111C2×C3×D12—22no—
112C2×C3×D12—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—41no—
119C2×C3×C4×D3—41no—
120C2×C3×C4×D3—41no—
121C2×C3×C4×D3—41no—
122C32×C4⋊C4—41no—
123C32×C22⋊C4—22no—
124C32×C22⋊C4—22no—
125C32×C22⋊C4—41no—
126C3×#217—41no—
127C3×(C2×D3)⋊C4—22no—
128C3×(C2×D3)⋊C4—22no—
129C3×(C2×D3)⋊C4—22no—
130C3×(C2×D3)⋊C4—22no—
131C3×(C2×D3)⋊C4—41no—
132C3×(C2×D3)⋊C4—41no—
133C3×(C2×D3)⋊C4—41no—
134C3×Dic3⋊C4—22no—
135C3×Dic3⋊C4—22no—
136C3×Dic3⋊C4—22no—
137C3×C4×Dic3—22no—
138#2444—31noSylow
139C22×C3×D4—31no—
140C22×C3×D4—31no—
141C22×C3×D4—31no—
142C23×C3×C4—31no—
143C23×C3×C4—31no—
144C23×C3×C4—31no—
145C23×C3×C4—31no—
146C22×#67C22×C311yescharacteristic
147C22×#67C22×C311yescharacteristic
148C23×Dic3C22×C311yescharacteristic
149C22×D12C22×C311yescharacteristic
150C22×C4×D3C22×C311yescharacteristic
151C22×C4×D3C22×C311yescharacteristic
152C22×C4×D3C22×C311yescharacteristic
153C3×#121—64no—
154C3×C4×D4—64no—
155C2×C3×C4⋊C4—21no—
156C2×C3×C4⋊C4—31no—
157C2×C3×C4⋊C4—31no—
158C2×C3×C4⋊C4—31no—
159C2×C3×C4⋊C4C2×D311yescharacteristic
160C2×C3×C4⋊C4C22×C311yescharacteristic
161C2×C3×C22⋊C4—21no—
162C2×C3×C22⋊C4—21no—
163C2×C3×C22⋊C4—21no—
164C2×C3×C22⋊C4—31no—
165C2×C3×C22⋊C4—31no—
166C2×C3×C22⋊C4—31no—
167C2×C3×C22⋊C4—31no—
168C2×C3×C22⋊C4—31no—
169C2×C3×C22⋊C4—31no—
170C2×C3×C22⋊C4—31no—
171C2×C3×C22⋊C4—31no—
172C2×C3×C22⋊C4C2×D311yescharacteristic
173C2×C3×C22⋊C4C2×D311yescharacteristic
174C2×C3×C22⋊C4C2×D311yescharacteristic
175C2×C3×C22⋊C4C22×C311yescharacteristic
176C2×C3×C22⋊C4C22×C311yescharacteristic
177C2×C3×C22⋊C4C22×C311yescharacteristic
178C2×C3×C42—31no—
179C2×#217C22×C311yescharacteristic
180C2×(C2×D3)⋊C4C22×C311yescharacteristic
181C2×(C2×D3)⋊C4C22×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×Dic3⋊C4C22×C311yescharacteristic
188C2×Dic3⋊C4C22×C311yescharacteristic
189C2×Dic3⋊C4C22×C311yescharacteristic
190C2×C4×Dic3C22×C311yescharacteristic
191#884—24no—
192#67⋊C4—24no—
193C3×#95—21no—
194C3×#95—21no—
195C3×#95—21no—
196C3×#95—31no—
197C3×#95—31no—
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×#95C2×D311yescharacteristic
207C3×#95C2×D311yescharacteristic
208C3×#95C22×C311yescharacteristic
209C3×#95C22×C311yescharacteristic
210C3×#95C22×C311yescharacteristic
211C3⋊#95C22×C311yescharacteristic
212C3⋊#95C22×C311yescharacteristic
213C3⋊#95C22×C311yescharacteristic
214C3⋊#95C22×C311yescharacteristic
215C3⋊#95C22×C311yescharacteristic
216C3⋊#95C22×C311yescharacteristic
217C3⋊#95C22×C311yescharacteristic
218C3⋊#95C22×C311yescharacteristic
219C3⋊#95C22×C311yescharacteristic
220C23×C32—21no—
221C23×C32—21no—
222C23×C32—21no—
223C23×C32—21no—
224C23×C32—21no—
225C23×C32—21no—
226C23×C32C2×D412yes—
227C23×C32C2411yescharacteristic
228C22×C3×D3—21no—
229C22×C3×D3—21no—
230C22×C3×D3—21no—
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×D3C2×D412yes—
240C22×C3×D3#4112yes—
241C22×C3×D3#4112yes—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
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—
260C3×#67—28no—
261C3×#67—44no—
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—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—44no—
278C2×C3×Dic3C2×D412yes—
279C2×C3×Dic3#4112yes—
280C2×C3×Dic3#4112yes—
281C3×D12—44no—
282C3×C4×D3—44no—
283C3×C4×D3—44no—
284C3×C4×D3—44no—
285C2×#121—31no—
286C2×C4×D4—31no—
287#400—31no—
288#397—31no—
289#397C3×D311yescharacteristic, complemented
290#394—31no—
291#388—31no—
292#387—31no—
293#386—31no—
294#386—31no—
295#386—31no—
296#386—31no—
297#385—31no—
298#381—31no—
299C2×#95—31no—
300C24×C3—21no—
301C24×C3—31no—
302C24×C3—31no—
303C24×C3C22×D311yescharacteristic
304C24×C3C23×C311yescharacteristic
305C23×D3C23×C311yescharacteristic
306C23×D3C23×C311yescharacteristic
307C2×C3×D4—34no—
308C2×C3×D4—62no—
309C2×C3×D4—62no—
310C2×C3×D4—62no—
311C2×C3×D4—62no—
312C2×C3×D4—62no—
313C2×C3×D4—62no—
314C2×C3×D4—62no—
315C2×C3×D4—121no—
316C22×C3×C4—21no—
317C22×C3×C4—21no—
318C22×C3×C4—21no—
319C22×C3×C4—21no—
320C22×C3×C4—21no—
321C22×C3×C4—21no—
322C22×C3×C4—31no—
323C22×C3×C4—31no—
324C22×C3×C4—31no—
325C22×C3×C4—31no—
326C22×C3×C4—31no—
327C22×C3×C4—31no—
328C22×C3×C4—62no—
329C22×C3×C4—62no—
330C22×C3×C4—62no—
331C22×C3×C4—62no—
332C22×C3×C4—62no—
333C22×C3×C4—62no—
334C22×C3×C4—62no—
335C22×C3×C4—121no—
336C22×C3×C4—121no—
337C22×C3×C4—121no—
338C22×C3×C4—121no—
339C22×C3×C4—121no—
340C22×C3×C4C22×D311yescharacteristic
341C22×C3×C4C22×D311yescharacteristic
342C22×C3×C4C22×D311yescharacteristic
343C22×C3×C4C22×D311yescharacteristic
344C22×C3×C4C22×D311yescharacteristic
345C22×C3×C4C22×D311yescharacteristic
346C22×C3×C4C23×C311yescharacteristic
347C22×C3×C4C23×C311yescharacteristic
348C22×C3×C4C23×C311yescharacteristic
349C22×C3×C4C23×C311yescharacteristic
350C22×C3×C4C23×C311yescharacteristic
351C22×C3×C4C23×C311yescharacteristic
352C2×#67—22no—
353C2×#67—22no—
354C2×#67—22no—
355C2×#67—22no—
356C2×#67—41no—
357C2×#67C3×D414yes—
358C22×Dic3—22no—
359C22×Dic3—22no—
360C22×Dic3—41no—
361C22×Dic3C23×C311yescharacteristic
362C22×Dic3C23×C311yescharacteristic
363C22×Dic3C23×C311yescharacteristic
364C22×Dic3C23×C311yescharacteristic
365C22×Dic3C23×C311yescharacteristic
366C22×Dic3C23×C311yescharacteristic
367C2×D12—22no—
368C2×D12—22no—
369C2×D12—22no—
370C2×C4×D3—22no—
371C2×C4×D3—22no—
372C2×C4×D3—22no—
373C2×C4×D3—22no—
374C2×C4×D3—22no—
375C2×C4×D3—41no—
376C2×C4×D3—41no—
377C2×C4×D3—41no—
378C2×C4×D3—41no—
379C3×C4⋊C4—41no—
380C3×C4⋊C4—41no—
381C3×C4⋊C4—42no—
382C3×C4⋊C4—62no—
383C3×C4⋊C4—62no—
384C3×C4⋊C4—62no—
385C3×C22⋊C4—22no—
386C3×C22⋊C4—22no—
387C3×C22⋊C4—22no—
388C3×C22⋊C4—22no—
389C3×C22⋊C4—42no—
390C3×C22⋊C4—42no—
391C3×C22⋊C4—41no—
392C3×C22⋊C4—41no—
393C3×C22⋊C4—42no—
394C3×C22⋊C4—62no—
395C3×C22⋊C4—62no—
396C3×C22⋊C4—62no—
397C3×C22⋊C4—62no—
398C3×C22⋊C4—121no—
399C3×C22⋊C4—121no—
400C3×C22⋊C4—121no—
401C3×C22⋊C4—121no—
402C3×C42—62no—
403#217—41no—
404(C2×D3)⋊C4—22no—
405(C2×D3)⋊C4—22no—
406(C2×D3)⋊C4—22no—
407(C2×D3)⋊C4—22no—
408(C2×D3)⋊C4—41no—
409(C2×D3)⋊C4—41no—
410(C2×D3)⋊C4—41no—
411Dic3⋊C4—22no—
412Dic3⋊C4—22no—
413Dic3⋊C4—22no—
414C4×Dic3—22no—
415C22×C32—22no—
416C22×C32—22no—
417C22×C32—22no—
418C22×C32—41no—
419C22×C32—41no—
420C22×C32—41no—
421C22×C32—41no—
422C22×C32C22×D411yescharacteristic
423C22×C32C2×#4111yescharacteristic
424C22×C32C2×#4111yescharacteristic
425C22×C32C2×#4111yescharacteristic
426C22×C32C2×#4111yescharacteristic
427C22×C32H(5,𝔽2)11yescharacteristic
428C22×C32H(5,𝔽2)11yescharacteristic
429C2×C3×D3—22no—
430C2×C3×D3—22no—
431C2×C3×D3—22no—
432C2×C3×D3—22no—
433C2×C3×D3—22no—
434C2×C3×D3—22no—
435C2×C3×D3—41no—
436C2×C3×D3—41no—
437C2×C3×D3—41no—
438C2×C3×D3—41no—
439C2×C3×D3—41no—
440C2×C3×D3—41no—
441C2×C3×D3—41no—
442C2×C3×D3#12314yes—
443C32×C4—41no—
444C32×C4—41no—
445C32×C4—41no—
446C32×C4—41no—
447C32×C4—41no—
448C32×C4—41no—
449C3×Dic3—22no—
450C3×Dic3—22no—
451C3×Dic3—22no—
452C3×Dic3—41no—
453C3×Dic3—41no—
454C3×Dic3—41no—
455C22×D4—31no—
456C22×D4—31no—
457C22×D4—31no—
458C23×C4—31no—
459C23×C4—31no—
460C23×C4—31no—
461C23×C4—31no—
462#121—64no—
463C4×D4—64no—
464C2×C4⋊C4—31no—
465C2×C4⋊C4—31no—
466C2×C4⋊C4—31no—
467C2×C4⋊C4C2×C3×D311yescharacteristic
468C2×C22⋊C4—31no—
469C2×C22⋊C4—31no—
470C2×C22⋊C4—31no—
471C2×C22⋊C4—31no—
472C2×C22⋊C4—31no—
473C2×C22⋊C4—31no—
474C2×C22⋊C4—31no—
475C2×C22⋊C4—31no—
476C2×C22⋊C4C2×C3×D311yescharacteristic
477C2×C22⋊C4C2×C3×D311yescharacteristic
478C2×C22⋊C4C2×C3×D311yescharacteristic
479C2×C42—31no—
480#95—31no—
481#95—31no—
482#95—31no—
483#95—31no—
484#95—31no—
485#95—31no—
486#95—31no—
487#95—31no—
488#95—31no—
489#95C2×C3×D311yescharacteristic
490#95C2×C3×D311yescharacteristic
491#95C2×C3×D311yescharacteristic
492C23×C3—21no—
493C23×C3—21no—
494C23×C3—21no—
495C23×C3—21no—
496C23×C3—21no—
497C23×C3—21no—
498C23×C3—21no—
499C23×C3—21no—
500C23×C3—21no—
501C23×C3—21no—
502C23×C3—21no—
503C23×C3—21no—
504C23×C3—21no—
505C23×C3—22no—
506C23×C3—32no—
507C23×C3—32no—
508C23×C3—32no—
509C23×C3—41no—
510C23×C3—41no—
511C23×C3—41no—
512C23×C3—41no—
513C23×C3—41no—
514C23×C3—41no—
515C23×C3—61no—
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×C3D3×D412yes—
527C23×C3C2×C3×D412yes—
528C23×C3C23×D311yescharacteristic
529C23×C3C24×C311yescharacteristic
530C22×D3—21no—
531C22×D3—21no—
532C22×D3—21no—
533C22×D3—21no—
534C22×D3—21no—
535C22×D3—21no—
536C22×D3—21no—
537C22×D3—21no—
538C22×D3—21no—
539C22×D3—21no—
540C22×D3—21no—
541C22×D3C2×C3×D412yes—
542C22×D3C3×#4112yes—
543C22×D3C3×#4112yes—
544C3×D4—68no—
545C3×D4—124no—
546C3×D4—124no—
547C2×C3×C4—22no—
548C2×C3×C4—21no—
549C2×C3×C4—21no—
550C2×C3×C4—21no—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
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—21no—
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—32no—
585C2×C3×C4—32no—
586C2×C3×C4—32no—
587C2×C3×C4—41no—
588C2×C3×C4—41no—
589C2×C3×C4—41no—
590C2×C3×C4—41no—
591C2×C3×C4—41no—
592C2×C3×C4—41no—
593C2×C3×C4—41no—
594C2×C3×C4—41no—
595C2×C3×C4—41no—
596C2×C3×C4—41no—
597C2×C3×C4—41no—
598C2×C3×C4—41no—
599C2×C3×C4—41no—
600C2×C3×C4—41no—
601C2×C3×C4—41no—
602C2×C3×C4—41no—
603C2×C3×C4—41no—
604C2×C3×C4—61no—
605C2×C3×C4—61no—
606C2×C3×C4—61no—
607C2×C3×C4—61no—
608C2×C3×C4—61no—
609C2×C3×C4—61no—
610C2×C3×C4—61no—
611C2×C3×C4—61no—
612C2×C3×C4—61no—
613C2×C3×C4—61no—
614C2×C3×C4—61no—
615C2×C3×C4—61no—
616C2×C3×C4—61no—
617C2×C3×C4—61no—
618C2×C3×C4—61no—
619C2×C3×C4—124no—
620C2×C3×C4—124no—
621C2×C3×C4—124no—
622C2×C3×C4—124no—
623#67—28no—
624#67—44no—
625C2×Dic3—21no—
626C2×Dic3—21no—
627C2×Dic3—21no—
628C2×Dic3—21no—
629C2×Dic3—21no—
630C2×Dic3—21no—
631C2×Dic3—21no—
632C2×Dic3—21no—
633C2×Dic3—21no—
634C2×Dic3—21no—
635C2×Dic3—21no—
636C2×Dic3—21no—
637C2×Dic3—21no—
638C2×Dic3—21no—
639C2×Dic3—21no—
640C2×Dic3—44no—
641C2×Dic3C2×C3×D412yes—
642C2×Dic3C3×#4112yes—
643C2×Dic3C3×#4112yes—
644D12—44no—
645C4×D3—44no—
646C4×D3—44no—
647C4×D3—44no—
648C2×C32—42no—
649C2×C32C2×#12311yescharacteristic
650C2×C32#52911yescharacteristic
651C2×C32#53811yescharacteristic
652C2×C32#54611yescharacteristic
653C2×C32#54611yescharacteristic
654C2×C32#55311yescharacteristic
655C2×C32#55311yescharacteristic
656C3×D3—24no—
657C3×D3—81no—
658C24—31no—
659C24—31no—
660C24C22×C3×D311yescharacteristic
661C2×D4—34no—
662C2×D4—62no—
663C2×D4—62no—
664C2×D4—62no—
665C2×D4—62no—
666C2×D4—62no—
667C2×D4—62no—
668C2×D4—62no—
669C2×D4—121no—
670C22×C4—31no—
671C22×C4—31no—
672C22×C4—31no—
673C22×C4—31no—
674C22×C4—31no—
675C22×C4—31no—
676C22×C4—62no—
677C22×C4—62no—
678C22×C4—62no—
679C22×C4—62no—
680C22×C4—62no—
681C22×C4—62no—
682C22×C4—62no—
683C22×C4—121no—
684C22×C4—121no—
685C22×C4—121no—
686C22×C4—121no—
687C22×C4—121no—
688C22×C4C22×C3×D311yescharacteristic
689C22×C4C22×C3×D311yescharacteristic
690C22×C4C22×C3×D311yescharacteristic
691C22×C4C22×C3×D311yescharacteristic
692C22×C4C22×C3×D311yescharacteristic
693C22×C4C22×C3×D311yescharacteristic
694C4⋊C4—41no—
695C4⋊C4—62no—
696C4⋊C4—62no—
697C4⋊C4—62no—
698C22⋊C4—22no—
699C22⋊C4—22no—
700C22⋊C4—41no—
701C22⋊C4—62no—
702C22⋊C4—62no—
703C22⋊C4—62no—
704C22⋊C4—62no—
705C22⋊C4—121no—
706C22⋊C4—121no—
707C22⋊C4—121no—
708C22⋊C4—121no—
709C42—62no—
710C22×C3—22no—
711C22×C3—22no—
712C22×C3—22no—
713C22×C3—22no—
714C22×C3—22no—
715C22×C3—22no—
716C22×C3—21no—
717C22×C3—21no—
718C22×C3—21no—
719C22×C3—21no—
720C22×C3—21no—
721C22×C3—21no—
722C22×C3—21no—
723C22×C3—34no—
724C22×C3—42no—
725C22×C3—42no—
726C22×C3—42no—
727C22×C3—41no—
728C22×C3—41no—
729C22×C3—41no—
730C22×C3—41no—
731C22×C3—41no—
732C22×C3—41no—
733C22×C3—41no—
734C22×C3—41no—
735C22×C3—62no—
736C22×C3—62no—
737C22×C3—62no—
738C22×C3—62no—
739C22×C3—62no—
740C22×C3—62no—
741C22×C3—81no—
742C22×C3—81no—
743C22×C3—81no—
744C22×C3—81no—
745C22×C3—121no—
746C22×C3—121no—
747C22×C3—121no—
748C22×C3—121no—
749C22×C3—121no—
750C22×C3—121no—
751C22×C3—121no—
752C22×C3C2×D3×D411yescharacteristic
753C22×C3#100411yescharacteristic
754C22×C3D3×#4111yescharacteristic
755C22×C3D3×#4111yescharacteristic
756C22×C3D3×#4111yescharacteristic
757C22×C3D3×#4111yescharacteristic
758C22×C3#100911yescharacteristic
759C22×C3C22×C3×D411yescharacteristic
760C22×C3C2×C3×#4111yescharacteristic
761C22×C3C2×C3×#4111yescharacteristic
762C22×C3C2×C3×#4111yescharacteristic
763C22×C3C2×C3×#4111yescharacteristic
764C22×C3C3×H(5,𝔽2)11yescharacteristic
765C22×C3C3×H(5,𝔽2)11yescharacteristic
766C2×D3—22no—
767C2×D3—22no—
768C2×D3—22no—
769C2×D3—22no—
770C2×D3—22no—
771C2×D3—22no—
772C2×D3—41no—
773C2×D3—41no—
774C2×D3—41no—
775C2×D3—41no—
776C2×D3—41no—
777C2×D3—41no—
778C2×D3—41no—
779C2×D3C3×#12314yes—
780C3×C4—42no—
781C3×C4—41no—
782C3×C4—41no—
783C3×C4—41no—
784C3×C4—41no—
785C3×C4—41no—
786C3×C4—41no—
787C3×C4—41no—
788C3×C4—41no—
789C3×C4—41no—
790C3×C4—41no—
791C3×C4—41no—
792C3×C4—41no—
793C3×C4—62no—
794C3×C4—62no—
795C3×C4—62no—
796C3×C4—81no—
797C3×C4—81no—
798C3×C4—81no—
799C3×C4—81no—
800C3×C4—81no—
801C3×C4—121no—
802C3×C4—121no—
803C3×C4—121no—
804Dic3—22no—
805Dic3—22no—
806Dic3—22no—
807Dic3—41no—
808Dic3—41no—
809Dic3—41no—
810C32#244411yescharacteristic, complemented, Sylow
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—21no—
817C23—32no—
818C23—32no—
819C23—32no—
820C23—61no—
821C23—61no—
822C23—61no—
823C23—61no—
824C23—61no—
825C23—61no—
826C23—61no—
827C23—61no—
828C23—61no—
829C23—61no—
830C23—61no—
831C23C3×D3×D412yes—
832C23C23×C3×D311yescharacteristic
833D4—68no—
834D4—124no—
835D4—124no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—32no—
855C2×C4—32no—
856C2×C4—32no—
857C2×C4—61no—
858C2×C4—61no—
859C2×C4—61no—
860C2×C4—61no—
861C2×C4—61no—
862C2×C4—61no—
863C2×C4—61no—
864C2×C4—61no—
865C2×C4—61no—
866C2×C4—61no—
867C2×C4—61no—
868C2×C4—61no—
869C2×C4—61no—
870C2×C4—61no—
871C2×C4—61no—
872C2×C4—124no—
873C2×C4—124no—
874C2×C4—124no—
875C2×C4—124no—
876C2×C3—21no—
877C2×C3—21no—
878C2×C3—21no—
879C2×C3—21no—
880C2×C3—21no—
881C2×C3—21no—
882C2×C3—21no—
883C2×C3—42no—
884C2×C3—42no—
885C2×C3—64no—
886C2×C3—82no—
887C2×C3—241no—
888C2×C3#561011yescharacteristic
889C2×C3D3×#12311yescharacteristic
890C2×C3#565411yescharacteristic
891C2×C3#566111yescharacteristic
892C2×C3#567811yescharacteristic
893C2×C3#570611yescharacteristic
894C2×C3#570911yescharacteristic
895C2×C3C2×C3×#12311yescharacteristic
896C2×C3C3×#52911yescharacteristic
897C2×C3C3×#53811yescharacteristic
898C2×C3C3×#54611yescharacteristic
899C2×C3C3×#54611yescharacteristic
900C2×C3C3×#55311yescharacteristic
901C2×C3C3×#55311yescharacteristic
902D3—24no—
903D3—81no—
904C22—22no—
905C22—22no—
906C22—22no—
907C22—34no—
908C22—41no—
909C22—41no—
910C22—41no—
911C22—41no—
912C22—62no—
913C22—62no—
914C22—62no—
915C22—62no—
916C22—62no—
917C22—62no—
918C22—121no—
919C22—121no—
920C22—121no—
921C22—121no—
922C22—121no—
923C22—121no—
924C22—121no—
925C22C2×C3×D3×D411yescharacteristic
926C22C3×#100411yescharacteristic
927C22C3×D3×#4111yescharacteristic
928C22C3×D3×#4111yescharacteristic
929C22C3×D3×#4111yescharacteristic
930C22C3×D3×#4111yescharacteristic
931C22C3×#100911yescharacteristic
932C4—41no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—41no—
937C4—41no—
938C4—62no—
939C4—62no—
940C4—62no—
941C4—121no—
942C4—121no—
943C4—121no—
944C3—21no—
945C3#7767411yescharacteristic, direct product factor
946C3C3×#244411yescharacteristic, complemented
947C2—42no—
948C2—64no—
949C2—241no—
950C2C3×#561011yescharacteristic
951C2C3×D3×#12311yescharacteristic
952C2C3×#565411yescharacteristic
953C2C3×#566111yescharacteristic
954C2C3×#567811yescharacteristic
955C2C3×#570611yescharacteristic
956C2C3×#570911yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC32×#397C2
socleC23×C32C24
prime radicalC2×C3×#884C2
hypercenterC3×#397D3
hypocenterC3C3×#2444
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#397

Complements

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

NH ≅ G/Ntype
2. C2×C3×#67⋊C4C2semidirect
3. C32×#397C2semidirect
4. C3×#4990C2semidirect
5. C3×#4989C2semidirect
6. C3×#4959C2semidirect
7. C3×#4958C2semidirect
8. C3×#4956C2semidirect
9. C3×#4943C2semidirect
10. C3×#4675C2semidirect
11. C3×#4665C2semidirect
12. C3×#4665C2semidirect
13. C3×D3×#95C2semidirect
14. C3×#4658C2semidirect
15. C3×#4652C2semidirect
17. #77674C3direct (N × H)
58. C2×#67⋊C4C2×C3semidirect
62. C3×#397D3semidirect
63. C3×#397C2×C3semidirect
74. #4990C2×C3semidirect
75. #4989C2×C3semidirect
76. #4959C2×C3semidirect
77. #4958C2×C3semidirect
78. #4956C2×C3semidirect
79. #4943C2×C3semidirect
80. #4675C2×C3semidirect
81. #4665C2×C3semidirect
82. #4665C2×C3semidirect
83. D3×#95C2×C3semidirect
84. #4658C2×C3semidirect
85. #4652C2×C3semidirect
289. #397C3×D3semidirect
810. C32#2444semidirect
945. C3#77674direct (N × H)
946. C3C3×#2444semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8842
C2×C3×#67⋊C42
C32×#3972
C3×#49902
C3×#49892
C3×#49592
C3×#49582
C3×#49562
C3×#49432
C3×#46752
C3×#46652
C3×D3×#952
C3×#46582
C3×#46522
C3×#24443
#776743