Finite Group Databasebeta

← C3×#74667 #11803840

Subgroups — C3×#74667 #11803840

Order 1152.

1623 conjugacy classes of subgroups.

The subgroup lattice has 1076 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#940C211yesmaximal, characteristic
2C2×C3×C4×#67C211yesmaximal, characteristic, complemented
3C2×C3×#67⋊C4C211yesmaximal, characteristic, complemented
4C32×#386C211yesmaximal, characteristic, complemented
5C3×#5220C211yesmaximal, characteristic, complemented
6C3×#5213C211yesmaximal, characteristic, complemented
7C3×#4958C211yesmaximal, characteristic, complemented
8C3×#4957C211yesmaximal, characteristic, complemented
9C3×#4957C211yesmaximal, characteristic, complemented
10C3×#4956C211yesmaximal, characteristic, complemented
11C3×#4956C211yesmaximal, characteristic, complemented
12C3×#4665C211yesmaximal, characteristic, complemented
13C3×#4665C211yesmaximal, characteristic, complemented
14C3×#4650C211yesmaximal, characteristic, complemented
15C3×#4648C211yesmaximal, characteristic, complemented
16C3×#2328—31nomaximal
17#74667C311yesmaximal, characteristic, direct product factor
18C22×C32×D4C2211yescharacteristic
19C23×C32×C4C2211yescharacteristic
20C22×C3×#67C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic
24C23×C3×Dic3C2211yescharacteristic
25C22×C3×D12C2211yescharacteristic
26C22×C3×C4×D3C2211yescharacteristic
27C22×C3×C4×D3C2211yescharacteristic
28C2×C32×C22⋊C4C2211yescharacteristic
29C2×C32×C22⋊C4C2211yescharacteristic
30C2×C32×C22⋊C4C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×#217C2211yescharacteristic
33C2×C3×#217C2211yescharacteristic
34C3×#940C418yescomplemented
35C3×C4×#67—24no—
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×(C2×D3)⋊C4C2211yescharacteristic
39C2×C3×(C2×D3)⋊C4C2211yescharacteristic
40C2×C3×(C2×D3)⋊C4C2211yescharacteristic
41C2×C3×(C2×D3)⋊C4C2211yescharacteristic
42C2×C3×Dic3⋊C4C2211yescharacteristic
43C2×C3×Dic3⋊C4C2211yescharacteristic
44C2×C3×C4×Dic3C2211yescharacteristic
45C2×C3×C4×Dic3C2211yescharacteristic
46C2×C3×C4×Dic3C2211yescharacteristic
47C3×#67⋊C4—24no—
48C32×#95C2211yescharacteristic
49C32×#95C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53C3×C3⋊#95C2211yescharacteristic
54C3×C3⋊#95C2211yescharacteristic
55C3×C3⋊#95C2211yescharacteristic
56C2×C3×#127—31no—
57C2×C3×C4×D4—31no—
58C2×C3×C4×D4—31no—
59C2×#940C2×C311yescharacteristic
60C2×C4×#67C2×C311yescharacteristic, complemented
61C2×#67⋊C4C2×C311yescharacteristic, complemented
62C3×#390—31no—
63C3×#390—31no—
64C3×#386—21no—
65C3×#386—31no—
66C3×#386—31no—
67C3×#386—31no—
68C3×#386—31no—
69C3×#386—31no—
70C3×#386—31no—
71C3×#386—31no—
72C3×#386D311yescharacteristic, complemented
73C3×#386C2×C311yescharacteristic, complemented
74C3×#382—31no—
75C3×#376—31no—
76#5220C2×C311yescharacteristic, complemented
77#5213C2×C311yescharacteristic, complemented
78#4958C2×C311yescharacteristic, complemented
79#4957C2×C311yescharacteristic, complemented
80#4957C2×C311yescharacteristic, complemented
81#4956C2×C311yescharacteristic, complemented
82#4956C2×C311yescharacteristic, complemented
83#4665C2×C311yescharacteristic, complemented
84#4665C2×C311yescharacteristic, complemented
85#4650C2×C311yescharacteristic, complemented
86#4648C2×C311yescharacteristic, complemented
87C24×C32C2311yescharacteristic
88C24×C32C2311yescharacteristic
89C23×C3×D3C2311yescharacteristic
90C23×C3×D3C2311yescharacteristic
91C2×C32×D4—41no—
92C2×C32×D4—41no—
93C2×C32×D4C2×C414yescomplemented
94C22×C32×C4—22no—
95C22×C32×C4—41no—
96C22×C32×C4—41no—
97C22×C32×C4C2311yescharacteristic
98C22×C32×C4C2311yescharacteristic
99C22×C32×C4C2311yescharacteristic
100C22×C32×C4C2311yescharacteristic
101C22×C32×C4C2311yescharacteristic
102C2×C3×#67—22no—
103C2×C3×#67—22no—
104C2×C3×#67—22no—
105C2×C3×#67—22no—
106C2×C3×#67—41no—
107C2×C3×#67—41no—
108C2×C3×#67—41no—
109C2×C3×#67—41no—
110C2×C3×#67C2×C414yescomplemented
111C2×C3×#67C2×C414yescomplemented
112C2×C3×#67C2×C414yescomplemented
113C2×C3×#67C2×C414yescomplemented
114C22×C3×Dic3—22no—
115C22×C3×Dic3—41no—
116C22×C3×Dic3—41no—
117C22×C3×Dic3C2311yescharacteristic
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C22×C3×Dic3C2311yescharacteristic
122C22×C3×Dic3C2311yescharacteristic
123C2×C3×D12—41no—
124C2×C3×D12—41no—
125C2×C3×D12C2×C414yescomplemented
126C2×C3×C4×D3—22no—
127C2×C3×C4×D3—22no—
128C2×C3×C4×D3—41no—
129C2×C3×C4×D3—41no—
130C2×C3×C4×D3—41no—
131C2×C3×C4×D3—41no—
132C32×C22⋊C4—22no—
133C32×C22⋊C4—41no—
134C32×C22⋊C4—41no—
135C3×#217—22no—
136C3×#217—41no—
137C3×#217—41no—
138C3×(C2×D3)⋊C4—22no—
139C3×(C2×D3)⋊C4—22no—
140C3×(C2×D3)⋊C4—41no—
141C3×(C2×D3)⋊C4—41no—
142C3×(C2×D3)⋊C4—41no—
143C3×(C2×D3)⋊C4—41no—
144C3×Dic3⋊C4—22no—
145C3×Dic3⋊C4—22no—
146C3×C4×Dic3—22no—
147C3×C4×Dic3C2×C414yescomplemented
148C3×C4×Dic3D414yescomplemented
149#2328—31noSylow
150C22×C3×D4—21no—
151C22×C3×D4—31no—
152C22×C3×D4—31no—
153C22×C3×D4—31no—
154C22×C3×D4—31no—
155C22×C3×D4—31no—
156C22×C3×D4C2×D311yescharacteristic
157C22×C3×D4C22×C311yescharacteristic
158C23×C3×C4—21no—
159C23×C3×C4—31no—
160C23×C3×C4—31no—
161C23×C3×C4—31no—
162C23×C3×C4C2×D311yescharacteristic
163C23×C3×C4C22×C311yescharacteristic
164C22×#67C22×C311yescharacteristic
165C22×#67C22×C311yescharacteristic
166C22×#67C22×C311yescharacteristic
167C22×#67C22×C311yescharacteristic
168C23×Dic3C22×C311yescharacteristic
169C22×D12C22×C311yescharacteristic
170C22×C4×D3C22×C311yescharacteristic
171C22×C4×D3C22×C311yescharacteristic
172C3×#127—38no—
173C3×C4×D4—64no—
174C3×C4×D4—64no—
175C2×C3×C4⋊C4—31no—
176C2×C3×C4⋊C4—31no—
177C2×C3×C22⋊C4—21no—
178C2×C3×C22⋊C4—21no—
179C2×C3×C22⋊C4—21no—
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×C22⋊C4—31no—
187C2×C3×C22⋊C4—31no—
188C2×C3×C22⋊C4—31no—
189C2×C3×C22⋊C4C2×D311yescharacteristic
190C2×C3×C22⋊C4C2×D311yescharacteristic
191C2×C3×C22⋊C4C2×D311yescharacteristic
192C2×C3×C22⋊C4C22×C311yescharacteristic
193C2×C3×C22⋊C4C22×C311yescharacteristic
194C2×C3×C22⋊C4C22×C311yescharacteristic
195C2×C3×C42—31no—
196C2×C3×C42—31no—
197C2×C3×C42—31no—
198C2×#217C22×C311yescharacteristic
199C2×#217C22×C311yescharacteristic
200C2×#217C22×C311yescharacteristic
201#940C3×C418yescomplemented
202C4×#67—24no—
203C2×(C2×D3)⋊C4C22×C311yescharacteristic
204C2×(C2×D3)⋊C4C22×C311yescharacteristic
205C2×(C2×D3)⋊C4C22×C311yescharacteristic
206C2×(C2×D3)⋊C4C22×C311yescharacteristic
207C2×(C2×D3)⋊C4C22×C311yescharacteristic
208C2×(C2×D3)⋊C4C22×C311yescharacteristic
209C2×Dic3⋊C4C22×C311yescharacteristic
210C2×Dic3⋊C4C22×C311yescharacteristic
211C2×C4×Dic3C22×C311yescharacteristic
212C2×C4×Dic3C22×C311yescharacteristic
213C2×C4×Dic3C22×C311yescharacteristic
214#67⋊C4—24no—
215C3×#95—21no—
216C3×#95—21no—
217C3×#95—31no—
218C3×#95—31no—
219C3×#95—31no—
220C3×#95—31no—
221C3×#95—31no—
222C3×#95—31no—
223C3×#95C2×D311yescharacteristic
224C3×#95C2×D311yescharacteristic
225C3×#95C22×C311yescharacteristic
226C3×#95C22×C311yescharacteristic
227C3⋊#95C22×C311yescharacteristic
228C3⋊#95C22×C311yescharacteristic
229C3⋊#95C22×C311yescharacteristic
230C3⋊#95C22×C311yescharacteristic
231C3⋊#95C22×C311yescharacteristic
232C3⋊#95C22×C311yescharacteristic
233C23×C32—21no—
234C23×C32—21no—
235C23×C32—21no—
236C23×C32—21no—
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×C32C22×C412yes—
246C23×C32C22×C412yes—
247C23×C32C2411yescharacteristic
248C22×C3×D3—21no—
249C22×C3×D3—21no—
250C22×C3×D3—21no—
251C22×C3×D3—21no—
252C22×C3×D3—21no—
253C22×C3×D3—21no—
254C22×C3×D3—21no—
255C22×C3×D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3C22×C412yes—
261C22×C3×D3C22×C412yes—
262C32×D4—44no—
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×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—44no—
277C2×C32×C4C22×C412yes—
278C2×C32×C4C2×D412yes—
279C3×#67—28no—
280C3×#67—28no—
281C3×#67—44no—
282C3×#67—44no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—21no—
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—44no—
297C2×C3×Dic3C22×C412yes—
298C2×C3×Dic3C22×C412yes—
299C2×C3×Dic3C2×D412yes—
300C2×C3×Dic3C2×D412yes—
301C2×C3×Dic3#4112yes—
302C3×D12—44no—
303C3×C4×D3—44no—
304C3×C4×D3—44no—
305C2×#127—31no—
306C2×C4×D4—31no—
307C2×C4×D4—31no—
308#390—31no—
309#390—31no—
310#386—31no—
311#386—31no—
312#386—31no—
313#386—31no—
314#386—31no—
315#386—31no—
316#386—31no—
317#386C3×D311yescharacteristic, complemented
318#382—31no—
319#376—31no—
320C24×C3—21no—
321C24×C3—21no—
322C24×C3—31no—
323C24×C3—31no—
324C24×C3C22×D311yescharacteristic
325C24×C3C22×D311yescharacteristic
326C24×C3C23×C311yescharacteristic
327C24×C3C23×C311yescharacteristic
328C23×D3C23×C311yescharacteristic
329C23×D3C23×C311yescharacteristic
330C2×C3×D4—24no—
331C2×C3×D4—34no—
332C2×C3×D4—34no—
333C2×C3×D4—34no—
334C2×C3×D4—34no—
335C2×C3×D4—34no—
336C2×C3×D4—41no—
337C2×C3×D4—41no—
338C2×C3×D4—41no—
339C2×C3×D4—41no—
340C2×C3×D4—42no—
341C2×C3×D4—42no—
342C2×C3×D4—62no—
343C2×C3×D4—62no—
344C2×C3×D4—62no—
345C2×C3×D4—62no—
346C2×C3×D4—121no—
347C2×C3×D4—121no—
348C2×C3×D4—121no—
349C2×C3×D4—121no—
350C2×C3×D4—121no—
351C2×C3×D4—121no—
352C2×C3×D4C4×D314yescomplemented
353C2×C3×D4C2×C3×C414yescomplemented
354C22×C3×C4—22no—
355C22×C3×C4—22no—
356C22×C3×C4—21no—
357C22×C3×C4—21no—
358C22×C3×C4—21no—
359C22×C3×C4—21no—
360C22×C3×C4—21no—
361C22×C3×C4—31no—
362C22×C3×C4—31no—
363C22×C3×C4—31no—
364C22×C3×C4—31no—
365C22×C3×C4—31no—
366C22×C3×C4—31no—
367C22×C3×C4—42no—
368C22×C3×C4—41no—
369C22×C3×C4—41no—
370C22×C3×C4—41no—
371C22×C3×C4—41no—
372C22×C3×C4—42no—
373C22×C3×C4—42no—
374C22×C3×C4—62no—
375C22×C3×C4—62no—
376C22×C3×C4—62no—
377C22×C3×C4—121no—
378C22×C3×C4—121no—
379C22×C3×C4—121no—
380C22×C3×C4—121no—
381C22×C3×C4—121no—
382C22×C3×C4—121no—
383C22×C3×C4C22×D311yescharacteristic
384C22×C3×C4C22×D311yescharacteristic
385C22×C3×C4C22×D311yescharacteristic
386C22×C3×C4C22×D311yescharacteristic
387C22×C3×C4C22×D311yescharacteristic
388C22×C3×C4C23×C311yescharacteristic
389C22×C3×C4C23×C311yescharacteristic
390C22×C3×C4C23×C311yescharacteristic
391C22×C3×C4C23×C311yescharacteristic
392C22×C3×C4C23×C311yescharacteristic
393C2×#67—22no—
394C2×#67—22no—
395C2×#67—22no—
396C2×#67—22no—
397C2×#67—41no—
398C2×#67—41no—
399C2×#67—41no—
400C2×#67—41no—
401C2×#67C2×C3×C414yescomplemented
402C2×#67C2×C3×C414yescomplemented
403C2×#67C2×C3×C414yescomplemented
404C2×#67C2×C3×C414yescomplemented
405C22×Dic3—22no—
406C22×Dic3—41no—
407C22×Dic3—41no—
408C22×Dic3C23×C311yescharacteristic
409C22×Dic3C23×C311yescharacteristic
410C22×Dic3C23×C311yescharacteristic
411C22×Dic3C23×C311yescharacteristic
412C22×Dic3C23×C311yescharacteristic
413C22×Dic3C23×C311yescharacteristic
414C2×D12—41no—
415C2×D12—41no—
416C2×D12C2×C3×C414yescomplemented
417C2×C4×D3—22no—
418C2×C4×D3—22no—
419C2×C4×D3—41no—
420C2×C4×D3—41no—
421C2×C4×D3—41no—
422C2×C4×D3—41no—
423C3×C4⋊C4—62no—
424C3×C4⋊C4—62no—
425C3×C22⋊C4—22no—
426C3×C22⋊C4—22no—
427C3×C22⋊C4—42no—
428C3×C22⋊C4—41no—
429C3×C22⋊C4—41no—
430C3×C22⋊C4—41no—
431C3×C22⋊C4—41no—
432C3×C22⋊C4—42no—
433C3×C22⋊C4—42no—
434C3×C22⋊C4—62no—
435C3×C22⋊C4—62no—
436C3×C22⋊C4—62no—
437C3×C22⋊C4—121no—
438C3×C22⋊C4—121no—
439C3×C22⋊C4—121no—
440C3×C22⋊C4—121no—
441C3×C22⋊C4—121no—
442C3×C22⋊C4—121no—
443C3×C42—34no—
444C3×C42—34no—
445C3×C42—62no—
446#217—22no—
447#217—41no—
448#217—41no—
449(C2×D3)⋊C4—22no—
450(C2×D3)⋊C4—22no—
451(C2×D3)⋊C4—41no—
452(C2×D3)⋊C4—41no—
453(C2×D3)⋊C4—41no—
454(C2×D3)⋊C4—41no—
455Dic3⋊C4—22no—
456Dic3⋊C4—22no—
457C4×Dic3—22no—
458C4×Dic3C2×C3×C414yescomplemented
459C4×Dic3C3×D414yescomplemented
460C22×C32—22no—
461C22×C32—22no—
462C22×C32—22no—
463C22×C32—22no—
464C22×C32—22no—
465C22×C32—22no—
466C22×C32—41no—
467C22×C32—41no—
468C22×C32—41no—
469C22×C32—41no—
470C22×C32—41no—
471C22×C32—41no—
472C22×C32—41no—
473C22×C32—41no—
474C22×C32C23×C411yescharacteristic
475C22×C32C22×D411yescharacteristic
476C22×C32C2×#4111yescharacteristic
477C22×C32H(5,𝔽2)11yescharacteristic
478C22×C32H(5,𝔽2)11yescharacteristic
479C22×C32H(5,𝔽2)11yescharacteristic
480C22×C32H(5,𝔽2)11yescharacteristic
481C2×C3×D3—22no—
482C2×C3×D3—22no—
483C2×C3×D3—22no—
484C2×C3×D3—22no—
485C2×C3×D3—22no—
486C2×C3×D3—22no—
487C2×C3×D3—41no—
488C2×C3×D3—41no—
489C2×C3×D3—41no—
490C2×C3×D3—41no—
491C2×C3×D3—41no—
492C2×C3×D3—41no—
493C2×C3×D3—41no—
494C2×C3×D3—41no—
495C32×C4—22no—
496C32×C4—22no—
497C32×C4—41no—
498C32×C4—41no—
499C32×C4—41no—
500C3×Dic3—22no—
501C3×Dic3—22no—
502C3×Dic3—41no—
503C3×Dic3—41no—
504C3×Dic3—41no—
505C3×Dic3C4×D414yes—
506C22×D4—31no—
507C22×D4—31no—
508C22×D4—31no—
509C22×D4—31no—
510C22×D4—31no—
511C22×D4C2×C3×D311yescharacteristic
512C23×C4—31no—
513C23×C4—31no—
514C23×C4—31no—
515C23×C4C2×C3×D311yescharacteristic
516#127—38no—
517C4×D4—64no—
518C4×D4—64no—
519C2×C4⋊C4—31no—
520C2×C4⋊C4—31no—
521C2×C22⋊C4—31no—
522C2×C22⋊C4—31no—
523C2×C22⋊C4—31no—
524C2×C22⋊C4—31no—
525C2×C22⋊C4—31no—
526C2×C22⋊C4—31no—
527C2×C22⋊C4—31no—
528C2×C22⋊C4—31no—
529C2×C22⋊C4—31no—
530C2×C22⋊C4C2×C3×D311yescharacteristic
531C2×C22⋊C4C2×C3×D311yescharacteristic
532C2×C22⋊C4C2×C3×D311yescharacteristic
533C2×C42—31no—
534C2×C42—31no—
535C2×C42—31no—
536#95—31no—
537#95—31no—
538#95—31no—
539#95—31no—
540#95—31no—
541#95—31no—
542#95C2×C3×D311yescharacteristic
543#95C2×C3×D311yescharacteristic
544C23×C3—22no—
545C23×C3—22no—
546C23×C3—21no—
547C23×C3—21no—
548C23×C3—21no—
549C23×C3—21no—
550C23×C3—21no—
551C23×C3—21no—
552C23×C3—21no—
553C23×C3—21no—
554C23×C3—21no—
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—22no—
572C23×C3—22no—
573C23×C3—32no—
574C23×C3—32no—
575C23×C3—41no—
576C23×C3—41no—
577C23×C3—41no—
578C23×C3—41no—
579C23×C3—41no—
580C23×C3—41no—
581C23×C3—41no—
582C23×C3—41no—
583C23×C3—41no—
584C23×C3—41no—
585C23×C3—61no—
586C23×C3—61no—
587C23×C3—61no—
588C23×C3—61no—
589C23×C3—61no—
590C23×C3—61no—
591C23×C3—61no—
592C23×C3—61no—
593C23×C3—61no—
594C23×C3—61no—
595C23×C3—61no—
596C23×C3—61no—
597C23×C3C2×C4×D312yes—
598C23×C3C2×C4×D312yes—
599C23×C3C22×C3×C412yes—
600C23×C3C22×C3×C412yes—
601C23×C3C23×D311yescharacteristic
602C23×C3C24×C311yescharacteristic
603C22×D3—21no—
604C22×D3—21no—
605C22×D3—21no—
606C22×D3—21no—
607C22×D3—21no—
608C22×D3—21no—
609C22×D3—21no—
610C22×D3—21no—
611C22×D3—21no—
612C22×D3—21no—
613C22×D3—21no—
614C22×D3—21no—
615C22×D3C22×C3×C412yes—
616C22×D3C22×C3×C412yes—
617C3×D4—44no—
618C3×D4—44no—
619C3×D4—48no—
620C3×D4—68no—
621C3×D4—68no—
622C3×D4—124no—
623C3×D4—124no—
624C3×D4—124no—
625C2×C3×C4—21no—
626C2×C3×C4—21no—
627C2×C3×C4—21no—
628C2×C3×C4—21no—
629C2×C3×C4—21no—
630C2×C3×C4—21no—
631C2×C3×C4—21no—
632C2×C3×C4—21no—
633C2×C3×C4—22no—
634C2×C3×C4—21no—
635C2×C3×C4—21no—
636C2×C3×C4—21no—
637C2×C3×C4—21no—
638C2×C3×C4—21no—
639C2×C3×C4—21no—
640C2×C3×C4—21no—
641C2×C3×C4—21no—
642C2×C3×C4—21no—
643C2×C3×C4—21no—
644C2×C3×C4—21no—
645C2×C3×C4—21no—
646C2×C3×C4—21no—
647C2×C3×C4—21no—
648C2×C3×C4—21no—
649C2×C3×C4—21no—
650C2×C3×C4—21no—
651C2×C3×C4—21no—
652C2×C3×C4—22no—
653C2×C3×C4—22no—
654C2×C3×C4—32no—
655C2×C3×C4—32no—
656C2×C3×C4—32no—
657C2×C3×C4—32no—
658C2×C3×C4—32no—
659C2×C3×C4—41no—
660C2×C3×C4—41no—
661C2×C3×C4—41no—
662C2×C3×C4—41no—
663C2×C3×C4—41no—
664C2×C3×C4—41no—
665C2×C3×C4—41no—
666C2×C3×C4—41no—
667C2×C3×C4—41no—
668C2×C3×C4—41no—
669C2×C3×C4—41no—
670C2×C3×C4—41no—
671C2×C3×C4—44no—
672C2×C3×C4—44no—
673C2×C3×C4—48no—
674C2×C3×C4—61no—
675C2×C3×C4—61no—
676C2×C3×C4—61no—
677C2×C3×C4—61no—
678C2×C3×C4—61no—
679C2×C3×C4—61no—
680C2×C3×C4—61no—
681C2×C3×C4—61no—
682C2×C3×C4—61no—
683C2×C3×C4—61no—
684C2×C3×C4—61no—
685C2×C3×C4—61no—
686C2×C3×C4—61no—
687C2×C3×C4—124no—
688C2×C3×C4—124no—
689C2×C3×C4—124no—
690C2×C3×C4C2×C4×D312yes—
691C2×C3×C4D3×D412yes—
692C2×C3×C4C22×C3×C412yes—
693C2×C3×C4C2×C3×D412yes—
694#67—28no—
695#67—28no—
696#67—44no—
697#67—44no—
698C2×Dic3—21no—
699C2×Dic3—21no—
700C2×Dic3—21no—
701C2×Dic3—21no—
702C2×Dic3—21no—
703C2×Dic3—21no—
704C2×Dic3—21no—
705C2×Dic3—21no—
706C2×Dic3—21no—
707C2×Dic3—21no—
708C2×Dic3—21no—
709C2×Dic3—21no—
710C2×Dic3—21no—
711C2×Dic3—44no—
712C2×Dic3C22×C3×C412yes—
713C2×Dic3C22×C3×C412yes—
714C2×Dic3C2×C3×D412yes—
715C2×Dic3C2×C3×D412yes—
716C2×Dic3C3×#4112yes—
717D12—44no—
718C4×D3—44no—
719C4×D3—44no—
720C2×C32—42no—
721C2×C32—42no—
722C2×C32C2×C4×D411yescharacteristic
723C2×C32#51811yescharacteristic
724C2×C32#51811yescharacteristic
725C2×C32#53511yescharacteristic
726C2×C32#53511yescharacteristic
727C2×C32#54011yescharacteristic
728C2×C32#54011yescharacteristic
729C3×D3—42no—
730C3×D3—42no—
731C24—31no—
732C24—31no—
733C24C22×C3×D311yescharacteristic
734C24C22×C3×D311yescharacteristic
735C2×D4—34no—
736C2×D4—34no—
737C2×D4—34no—
738C2×D4—34no—
739C2×D4—34no—
740C2×D4—41no—
741C2×D4—41no—
742C2×D4—62no—
743C2×D4—62no—
744C2×D4—62no—
745C2×D4—62no—
746C2×D4—121no—
747C2×D4—121no—
748C2×D4—121no—
749C2×D4—121no—
750C2×D4—121no—
751C2×D4—121no—
752C2×D4C3×C4×D314yescomplemented
753C22×C4—22no—
754C22×C4—31no—
755C22×C4—31no—
756C22×C4—31no—
757C22×C4—31no—
758C22×C4—31no—
759C22×C4—31no—
760C22×C4—41no—
761C22×C4—41no—
762C22×C4—62no—
763C22×C4—62no—
764C22×C4—62no—
765C22×C4—121no—
766C22×C4—121no—
767C22×C4—121no—
768C22×C4—121no—
769C22×C4—121no—
770C22×C4—121no—
771C22×C4C22×C3×D311yescharacteristic
772C22×C4C22×C3×D311yescharacteristic
773C22×C4C22×C3×D311yescharacteristic
774C22×C4C22×C3×D311yescharacteristic
775C22×C4C22×C3×D311yescharacteristic
776C4⋊C4—62no—
777C4⋊C4—62no—
778C22⋊C4—22no—
779C22⋊C4—41no—
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⋊C4—121no—
790C42—34no—
791C42—34no—
792C42—62no—
793C22×C3—24no—
794C22×C3—22no—
795C22×C3—22no—
796C22×C3—22no—
797C22×C3—22no—
798C22×C3—22no—
799C22×C3—22no—
800C22×C3—22no—
801C22×C3—22no—
802C22×C3—22no—
803C22×C3—22no—
804C22×C3—22no—
805C22×C3—22no—
806C22×C3—21no—
807C22×C3—21no—
808C22×C3—21no—
809C22×C3—21no—
810C22×C3—21no—
811C22×C3—21no—
812C22×C3—21no—
813C22×C3—42no—
814C22×C3—42no—
815C22×C3—42no—
816C22×C3—42no—
817C22×C3—42no—
818C22×C3—42no—
819C22×C3—42no—
820C22×C3—42no—
821C22×C3—42no—
822C22×C3—41no—
823C22×C3—41no—
824C22×C3—41no—
825C22×C3—41no—
826C22×C3—41no—
827C22×C3—41no—
828C22×C3—41no—
829C22×C3—41no—
830C22×C3—41no—
831C22×C3—41no—
832C22×C3—41no—
833C22×C3—41no—
834C22×C3—41no—
835C22×C3—41no—
836C22×C3—41no—
837C22×C3—41no—
838C22×C3—62no—
839C22×C3—62no—
840C22×C3—62no—
841C22×C3—62no—
842C22×C3—62no—
843C22×C3—62no—
844C22×C3—81no—
845C22×C3—81no—
846C22×C3—81no—
847C22×C3—81no—
848C22×C3—121no—
849C22×C3—121no—
850C22×C3—121no—
851C22×C3—121no—
852C22×C3—121no—
853C22×C3—121no—
854C22×C3—121no—
855C22×C3—121no—
856C22×C3C22×C4×D311yescharacteristic
857C22×C3C2×D3×D411yescharacteristic
858C22×C3#100411yescharacteristic
859C22×C3#100411yescharacteristic
860C22×C3#100411yescharacteristic
861C22×C3D3×#4111yescharacteristic
862C22×C3#100911yescharacteristic
863C22×C3C23×C3×C411yescharacteristic
864C22×C3C22×C3×D411yescharacteristic
865C22×C3C2×C3×#4111yescharacteristic
866C22×C3C3×H(5,𝔽2)11yescharacteristic
867C22×C3C3×H(5,𝔽2)11yescharacteristic
868C22×C3C3×H(5,𝔽2)11yescharacteristic
869C22×C3C3×H(5,𝔽2)11yescharacteristic
870C2×D3—22no—
871C2×D3—22no—
872C2×D3—22no—
873C2×D3—22no—
874C2×D3—22no—
875C2×D3—22no—
876C2×D3—41no—
877C2×D3—41no—
878C2×D3—41no—
879C2×D3—41no—
880C2×D3—41no—
881C2×D3—41no—
882C2×D3—41no—
883C2×D3—41no—
884C3×C4—22no—
885C3×C4—22no—
886C3×C4—22no—
887C3×C4—22no—
888C3×C4—34no—
889C3×C4—42no—
890C3×C4—42no—
891C3×C4—42no—
892C3×C4—41no—
893C3×C4—41no—
894C3×C4—41no—
895C3×C4—41no—
896C3×C4—41no—
897C3×C4—41no—
898C3×C4—62no—
899C3×C4—62no—
900C3×C4—81no—
901C3×C4—81no—
902C3×C4—121no—
903C3×C4—121no—
904C3×C4—121no—
905Dic3—22no—
906Dic3—22no—
907Dic3—41no—
908Dic3—41no—
909Dic3—41no—
910Dic3C3×C4×D414yes—
911C32#232811yescharacteristic, complemented, Sylow
912C23—21no—
913C23—21no—
914C23—21no—
915C23—21no—
916C23—21no—
917C23—21no—
918C23—21no—
919C23—21no—
920C23—21no—
921C23—21no—
922C23—21no—
923C23—21no—
924C23—32no—
925C23—32no—
926C23—61no—
927C23—61no—
928C23—61no—
929C23—61no—
930C23—61no—
931C23—61no—
932C23—61no—
933C23—61no—
934C23—61no—
935C23—61no—
936C23—61no—
937C23—61no—
938C23C2×C3×C4×D312yes—
939C23C2×C3×C4×D312yes—
940C23C23×C3×D311yescharacteristic
941D4—44no—
942D4—68no—
943D4—68no—
944D4—124no—
945D4—124no—
946D4—124no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—32no—
961C2×C4—32no—
962C2×C4—32no—
963C2×C4—32no—
964C2×C4—32no—
965C2×C4—44no—
966C2×C4—61no—
967C2×C4—61no—
968C2×C4—61no—
969C2×C4—61no—
970C2×C4—61no—
971C2×C4—61no—
972C2×C4—61no—
973C2×C4—61no—
974C2×C4—61no—
975C2×C4—61no—
976C2×C4—61no—
977C2×C4—61no—
978C2×C4—61no—
979C2×C4—124no—
980C2×C4—124no—
981C2×C4—124no—
982C2×C4C2×C3×C4×D312yes—
983C2×C4C3×D3×D412yes—
984C2×C3—21no—
985C2×C3—21no—
986C2×C3—21no—
987C2×C3—21no—
988C2×C3—21no—
989C2×C3—21no—
990C2×C3—21no—
991C2×C3—44no—
992C2×C3—42no—
993C2×C3—42no—
994C2×C3—42no—
995C2×C3—42no—
996C2×C3—82no—
997C2×C3—122no—
998C2×C3—122no—
999C2×C3#548611yescharacteristic
1000C2×C3C4×D3×D411yescharacteristic
1001C2×C3#554511yescharacteristic
1002C2×C3#559211yescharacteristic
1003C2×C3#560711yescharacteristic
1004C2×C3#561511yescharacteristic
1005C2×C3#566311yescharacteristic
1006C2×C3C2×C3×C4×D411yescharacteristic
1007C2×C3C3×#51811yescharacteristic
1008C2×C3C3×#51811yescharacteristic
1009C2×C3C3×#53511yescharacteristic
1010C2×C3C3×#53511yescharacteristic
1011C2×C3C3×#54011yescharacteristic
1012C2×C3C3×#54011yescharacteristic
1013D3—42no—
1014D3—42no—
1015C22—22no—
1016C22—22no—
1017C22—22no—
1018C22—22no—
1019C22—22no—
1020C22—22no—
1021C22—41no—
1022C22—41no—
1023C22—41no—
1024C22—41no—
1025C22—41no—
1026C22—41no—
1027C22—41no—
1028C22—41no—
1029C22—62no—
1030C22—62no—
1031C22—62no—
1032C22—62no—
1033C22—62no—
1034C22—62no—
1035C22—121no—
1036C22—121no—
1037C22—121no—
1038C22—121no—
1039C22—121no—
1040C22—121no—
1041C22—121no—
1042C22—121no—
1043C22C22×C3×C4×D311yescharacteristic
1044C22C2×C3×D3×D411yescharacteristic
1045C22C3×#100411yescharacteristic
1046C22C3×#100411yescharacteristic
1047C22C3×#100411yescharacteristic
1048C22C3×D3×#4111yescharacteristic
1049C22C3×#100911yescharacteristic
1050C4—22no—
1051C4—22no—
1052C4—34no—
1053C4—41no—
1054C4—41no—
1055C4—41no—
1056C4—62no—
1057C4—62no—
1058C4—121no—
1059C4—121no—
1060C4—121no—
1061C3—21no—
1062C3#7466711yescharacteristic, direct product factor
1063C3C3×#232811yescharacteristic, complemented
1064C2—42no—
1065C2—42no—
1066C2—122no—
1067C2—122no—
1068C2C3×#548611yescharacteristic
1069C2C3×C4×D3×D411yescharacteristic
1070C2C3×#554511yescharacteristic
1071C2C3×#559211yescharacteristic
1072C2C3×#560711yescharacteristic
1073C2C3×#561511yescharacteristic
1074C2C3×#566311yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC32×#386C2
socleC23×C32C24
prime radicalC2×C3×#940C2
cosocleC23×C3C24×C3
hypercenterC3×#386D3
hypocenterC3C3×#2328
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#386

Complements

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

NH ≅ G/Ntype
2. C2×C3×C4×#67C2semidirect
3. C2×C3×#67⋊C4C2semidirect
4. C32×#386C2semidirect
5. C3×#5220C2semidirect
6. C3×#5213C2semidirect
7. C3×#4958C2semidirect
8. C3×#4957C2semidirect
9. C3×#4957C2semidirect
10. C3×#4956C2semidirect
11. C3×#4956C2semidirect
12. C3×#4665C2semidirect
13. C3×#4665C2semidirect
14. C3×#4650C2semidirect
15. C3×#4648C2semidirect
17. #74667C3direct (N × H)
34. C3×#940C4semidirect
60. C2×C4×#67C2×C3semidirect
61. C2×#67⋊C4C2×C3semidirect
72. C3×#386D3semidirect
73. C3×#386C2×C3semidirect
76. #5220C2×C3semidirect
77. #5213C2×C3semidirect
78. #4958C2×C3semidirect
79. #4957C2×C3semidirect
80. #4957C2×C3semidirect
81. #4956C2×C3semidirect
82. #4956C2×C3semidirect
83. #4665C2×C3semidirect
84. #4665C2×C3semidirect
85. #4650C2×C3semidirect
86. #4648C2×C3semidirect
93. C2×C32×D4C2×C4semidirect
110. C2×C3×#67C2×C4semidirect
111. C2×C3×#67C2×C4semidirect
112. C2×C3×#67C2×C4semidirect
113. C2×C3×#67C2×C4semidirect
125. C2×C3×D12C2×C4semidirect
147. C3×C4×Dic3C2×C4semidirect
148. C3×C4×Dic3D4semidirect
201. #940C3×C4semidirect
317. #386C3×D3semidirect
352. C2×C3×D4C4×D3semidirect
353. C2×C3×D4C2×C3×C4semidirect
401. C2×#67C2×C3×C4semidirect
402. C2×#67C2×C3×C4semidirect
403. C2×#67C2×C3×C4semidirect
404. C2×#67C2×C3×C4semidirect
416. C2×D12C2×C3×C4semidirect
458. C4×Dic3C2×C3×C4semidirect
459. C4×Dic3C3×D4semidirect
752. C2×D4C3×C4×D3semidirect
911. C32#2328semidirect
1062. C3#74667direct (N × H)
1063. C3C3×#2328semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9402
C2×C3×C4×#672
C2×C3×#67⋊C42
C32×#3862
C3×#52202
C3×#52132
C3×#49582
C3×#49572
C3×#49562
C3×#46652
C3×#46502
C3×#46482
C3×#23283
#746673