Finite Group Databasebeta

← C3×#74939 #11801913

Subgroups — C3×#74939 #11801913

Order 1152.

1125 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#892C211yesmaximal, characteristic
2C32×#387C211yesmaximal, characteristic, complemented
3C3×#4990C211yesmaximal, characteristic
4C3×#4980C211yesmaximal, characteristic, complemented
5C3×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
6C3×#4940C211yesmaximal, characteristic
7C3×C42×Dic3C211yesmaximal, characteristic, complemented
8C3×#4670C211yesmaximal, characteristic
9C3×#4669C211yesmaximal, characteristic
10C3×#4666C211yesmaximal, characteristic
11C3×#4666C211yesmaximal, characteristic
12C3×#4654C211yesmaximal, characteristic, complemented
13C3×#4653C211yesmaximal, characteristic, complemented
14C3×#4649C211yesmaximal, characteristic, complemented
15C3×#4648C211yesmaximal, characteristic, complemented
16C3×#2298—31nomaximal
17#74939C311yesmaximal, characteristic, direct product factor
18C22×C3×C4×D3C2211yescharacteristic
19C2×C32×C4⋊C4C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21C2×C32×C42C2211yescharacteristic
22C2×C3×(C2×D3)⋊C4C2211yescharacteristic
23C2×C3×(C2×D3)⋊C4C2211yescharacteristic
24C2×C3×(C2×D3)⋊C4C2211yescharacteristic
25C2×C3×(C2×D3)⋊C4C2211yescharacteristic
26C2×C3×(C2×D3)⋊C4C2211yescharacteristic
27C2×C3×(C2×D3)⋊C4C2211yescharacteristic
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×Dic3⋊C4C2211yescharacteristic
31C2×C3×Dic3⋊C4C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33C2×C3×C4×Dic3C2211yescharacteristic
34C2×C3×C4×Dic3C2211yescharacteristic
35C2×C3×C4×Dic3C2211yescharacteristic
36C2×C3×C4×Dic3C2211yescharacteristic
37C2×C3×C4×Dic3C2211yescharacteristic
38C2×C3×C4×Dic3C2211yescharacteristic
39C2×C3×C4×Dic3C2211yescharacteristic
40C2×C3×C4×Dic3C2211yescharacteristic
41C3×#892C418yescomplemented
42C32×#95C2211yescharacteristic
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
54C2×C3×#117—31no—
55C2×#892C2×C311yescharacteristic
56C3×#388—31no—
57C3×#388—31no—
58C3×#388—31no—
59C3×#388—31no—
60C3×#387—21no—
61C3×#387—31no—
62C3×#387—31no—
63C3×#387—31no—
64C3×#387D311yescharacteristic, complemented
65C3×#387C2×C311yescharacteristic, complemented
66C3×C4×C4⋊C4—31no—
67C3×C4×C4⋊C4—31no—
68C3×C4×C22⋊C4—31no—
69C3×C4×C22⋊C4—31no—
70C3×#376—31no—
71C3×C43—31no—
72#4990C2×C311yescharacteristic
73#4980C2×C311yescharacteristic, complemented
74Dic3×C4⋊C4C2×C311yescharacteristic, complemented
75#4940C2×C311yescharacteristic
76C42×Dic3C2×C311yescharacteristic, complemented
77#4670C2×C311yescharacteristic
78#4669C2×C311yescharacteristic
79#4666C2×C311yescharacteristic
80#4666C2×C311yescharacteristic
81#4654C2×C311yescharacteristic, complemented
82#4653C2×C311yescharacteristic, complemented
83#4649C2×C311yescharacteristic, complemented
84#4648C2×C311yescharacteristic, complemented
85C23×C3×D3C2311yescharacteristic
86C22×C32×C4C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C3×Dic3C2311yescharacteristic
94C22×C3×Dic3C2311yescharacteristic
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C2×C3×C4×D3—22no—
101C2×C3×C4×D3—22no—
102C2×C3×C4×D3C2×C414yes—
103C32×C4⋊C4—22no—
104C32×C4⋊C4C2×C414yes—
105C32×C42—22no—
106C3×(C2×D3)⋊C4—22no—
107C3×(C2×D3)⋊C4—22no—
108C3×(C2×D3)⋊C4—22no—
109C3×(C2×D3)⋊C4—22no—
110C3×(C2×D3)⋊C4C2×C414yes—
111C3×(C2×D3)⋊C4C2×C414yes—
112C3×C4⋊Dic3—22no—
113C3×C4⋊Dic3C2×C414yes—
114C3×Dic3⋊C4—22no—
115C3×Dic3⋊C4—22no—
116C3×C4×Dic3—22no—
117C3×C4×Dic3—22no—
118C3×C4×Dic3—22no—
119C3×C4×Dic3—22no—
120C3×C4×Dic3—22no—
121C3×C4×Dic3—22no—
122C3×C4×Dic3—22no—
123C3×C4×Dic3C2×C414yes—
124C3×C4×Dic3C2×C414yes—
125#2298—31noSylow
126C23×C3×C4—31no—
127C22×C4×D3C22×C311yescharacteristic
128C3×#117—38no—
129C2×C3×C4⋊C4—21no—
130C2×C3×C4⋊C4—21no—
131C2×C3×C4⋊C4—31no—
132C2×C3×C4⋊C4—31no—
133C2×C3×C4⋊C4—31no—
134C2×C3×C4⋊C4—31no—
135C2×C3×C4⋊C4C2×D311yescharacteristic
136C2×C3×C4⋊C4C2×D311yescharacteristic
137C2×C3×C4⋊C4C22×C311yescharacteristic
138C2×C3×C4⋊C4C22×C311yescharacteristic
139C2×C3×C22⋊C4—31no—
140C2×C3×C22⋊C4—31no—
141C2×C3×C22⋊C4—31no—
142C2×C3×C22⋊C4—31no—
143C2×C3×C22⋊C4—31no—
144C2×C3×C22⋊C4—31no—
145C2×C3×C42—21no—
146C2×C3×C42—31no—
147C2×C3×C42—31no—
148C2×C3×C42—31no—
149C2×C3×C42—31no—
150C2×C3×C42—31no—
151C2×C3×C42—31no—
152C2×C3×C42—31no—
153C2×C3×C42—31no—
154C2×C3×C42—31no—
155C2×C3×C42C2×D311yescharacteristic
156C2×C3×C42C22×C311yescharacteristic
157C2×(C2×D3)⋊C4C22×C311yescharacteristic
158C2×(C2×D3)⋊C4C22×C311yescharacteristic
159C2×(C2×D3)⋊C4C22×C311yescharacteristic
160C2×(C2×D3)⋊C4C22×C311yescharacteristic
161C2×(C2×D3)⋊C4C22×C311yescharacteristic
162C2×(C2×D3)⋊C4C22×C311yescharacteristic
163C2×C4⋊Dic3C22×C311yescharacteristic
164C2×C4⋊Dic3C22×C311yescharacteristic
165C2×Dic3⋊C4C22×C311yescharacteristic
166C2×Dic3⋊C4C22×C311yescharacteristic
167C2×C4×Dic3C22×C311yescharacteristic
168C2×C4×Dic3C22×C311yescharacteristic
169C2×C4×Dic3C22×C311yescharacteristic
170C2×C4×Dic3C22×C311yescharacteristic
171C2×C4×Dic3C22×C311yescharacteristic
172C2×C4×Dic3C22×C311yescharacteristic
173C2×C4×Dic3C22×C311yescharacteristic
174C2×C4×Dic3C22×C311yescharacteristic
175C2×C4×Dic3C22×C311yescharacteristic
176#892C3×C418yescomplemented
177C3×#95—21no—
178C3×#95—21no—
179C3×#95—21no—
180C3×#95—21no—
181C3×#95—31no—
182C3×#95—31no—
183C3×#95—31no—
184C3×#95—31no—
185C3×#95—31no—
186C3×#95—31no—
187C3×#95—31no—
188C3×#95—31no—
189C3×#95C2×D311yescharacteristic
190C3×#95C2×D311yescharacteristic
191C3×#95C2×D311yescharacteristic
192C3×#95C2×D311yescharacteristic
193C3×#95C22×C311yescharacteristic
194C3×#95C22×C311yescharacteristic
195C3×#95C22×C311yescharacteristic
196C3×#95C22×C311yescharacteristic
197C3⋊#95C22×C311yescharacteristic
198C3⋊#95C22×C311yescharacteristic
199C3⋊#95C22×C311yescharacteristic
200C3⋊#95C22×C311yescharacteristic
201C3⋊#95C22×C311yescharacteristic
202C3⋊#95C22×C311yescharacteristic
203C3⋊#95C22×C311yescharacteristic
204C3⋊#95C22×C311yescharacteristic
205C23×C32C2411yescharacteristic
206C22×C3×D3—21no—
207C22×C3×D3—21no—
208C22×C3×D3—21no—
209C22×C3×D3—21no—
210C22×C3×D3—21no—
211C22×C3×D3—21no—
212C22×C3×D3C22×C412yes—
213C2×C32×C4—21no—
214C2×C32×C4—21no—
215C2×C32×C4—21no—
216C2×C32×C4—21no—
217C2×C32×C4—21no—
218C2×C32×C4—21no—
219C2×C32×C4—21no—
220C2×C32×C4—21no—
221C2×C32×C4—21no—
222C2×C32×C4—21no—
223C2×C32×C4—21no—
224C2×C32×C4—21no—
225C2×C32×C4—21no—
226C2×C32×C4—21no—
227C2×C32×C4—21no—
228C2×C32×C4—21no—
229C2×C32×C4C22×C412yes—
230C2×C32×C4C22×C412yes—
231C2×C32×C4C22×C412yes—
232C2×C32×C4#4112yes—
233C2×C32×C4#4112yes—
234C2×C3×Dic3—21no—
235C2×C3×Dic3—21no—
236C2×C3×Dic3—21no—
237C2×C3×Dic3—21no—
238C2×C3×Dic3—21no—
239C2×C3×Dic3—21no—
240C2×C3×Dic3—21no—
241C2×C3×Dic3—21no—
242C2×C3×Dic3—21no—
243C2×C3×Dic3—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3C22×C412yes—
249C2×C3×Dic3C22×C412yes—
250C2×C3×Dic3C22×C412yes—
251C2×C3×Dic3#4112yes—
252C2×C3×Dic3#4112yes—
253C2×C3×Dic3#4112yes—
254C2×C3×Dic3#4112yes—
255C3×C4×D3—28no—
256C2×#117—31no—
257#388—31no—
258#388—31no—
259#388—31no—
260#388—31no—
261#387—31no—
262#387—31no—
263#387—31no—
264#387C3×D311yescharacteristic, complemented
265C4×C4⋊C4—31no—
266C4×C4⋊C4—31no—
267C4×C22⋊C4—31no—
268C4×C22⋊C4—31no—
269#376—31no—
270C43—31no—
271C24×C3—31no—
272C23×D3C23×C311yescharacteristic
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—31no—
281C22×C3×C4—31no—
282C22×C3×C4—31no—
283C22×C3×C4—31no—
284C22×C3×C4—31no—
285C22×C3×C4—34no—
286C22×C3×C4—31no—
287C22×C3×C4—31no—
288C22×C3×C4—62no—
289C22×C3×C4—62no—
290C22×C3×C4C22×D311yescharacteristic
291C22×C3×C4C22×D311yescharacteristic
292C22×C3×C4C22×D311yescharacteristic
293C22×C3×C4C22×D311yescharacteristic
294C22×C3×C4C22×D311yescharacteristic
295C22×C3×C4C22×D311yescharacteristic
296C22×C3×C4C22×D311yescharacteristic
297C22×C3×C4C23×C311yescharacteristic
298C22×C3×C4C23×C311yescharacteristic
299C22×C3×C4C23×C311yescharacteristic
300C22×C3×C4C23×C311yescharacteristic
301C22×C3×C4C23×C311yescharacteristic
302C22×C3×C4C23×C311yescharacteristic
303C22×C3×C4C23×C311yescharacteristic
304C22×Dic3C23×C311yescharacteristic
305C22×Dic3C23×C311yescharacteristic
306C22×Dic3C23×C311yescharacteristic
307C22×Dic3C23×C311yescharacteristic
308C22×Dic3C23×C311yescharacteristic
309C22×Dic3C23×C311yescharacteristic
310C22×Dic3C23×C311yescharacteristic
311C2×C4×D3—22no—
312C2×C4×D3—22no—
313C2×C4×D3C2×C3×C414yes—
314C3×C4⋊C4—22no—
315C3×C4⋊C4—22no—
316C3×C4⋊C4—24no—
317C3×C4⋊C4—34no—
318C3×C4⋊C4—42no—
319C3×C4⋊C4—62no—
320C3×C4⋊C4—62no—
321C3×C4⋊C4—62no—
322C3×C4⋊C4C4×D314yes—
323C3×C4⋊C4C2×C3×C414yes—
324C3×C22⋊C4—34no—
325C3×C22⋊C4—34no—
326C3×C22⋊C4—62no—
327C3×C22⋊C4—62no—
328C3×C22⋊C4—62no—
329C3×C22⋊C4—62no—
330C3×C42—22no—
331C3×C42—22no—
332C3×C42—34no—
333C3×C42—34no—
334C3×C42—42no—
335C3×C42—62no—
336C3×C42—62no—
337C3×C42—62no—
338C3×C42—62no—
339C3×C42—62no—
340C3×C42—62no—
341C3×C42—62no—
342(C2×D3)⋊C4—22no—
343(C2×D3)⋊C4—22no—
344(C2×D3)⋊C4—22no—
345(C2×D3)⋊C4—22no—
346(C2×D3)⋊C4C2×C3×C414yes—
347(C2×D3)⋊C4C2×C3×C414yes—
348C4⋊Dic3—22no—
349C4⋊Dic3C2×C3×C414yes—
350Dic3⋊C4—22no—
351Dic3⋊C4—22no—
352C4×Dic3—22no—
353C4×Dic3—22no—
354C4×Dic3—22no—
355C4×Dic3—22no—
356C4×Dic3—22no—
357C4×Dic3—22no—
358C4×Dic3—22no—
359C4×Dic3C2×C3×C414yes—
360C4×Dic3C2×C3×C414yes—
361C22×C32C23×C411yescharacteristic
362C22×C32C2×#4111yescharacteristic
363C22×C32C2×#4111yescharacteristic
364C22×C32C2×#4111yescharacteristic
365C22×C32C2×#4111yescharacteristic
366C22×C32C2×#4111yescharacteristic
367C22×C32C2×#4111yescharacteristic
368C2×C3×D3—22no—
369C2×C3×D3—22no—
370C2×C3×D3—22no—
371C2×C3×D3—41no—
372C2×C3×D3—41no—
373C2×C3×D3—41no—
374C2×C3×D3—41no—
375C32×C4—22no—
376C32×C4—22no—
377C32×C4—22no—
378C32×C4—22no—
379C32×C4—22no—
380C32×C4—41no—
381C32×C4—41no—
382C3×Dic3—22no—
383C3×Dic3—22no—
384C3×Dic3—22no—
385C3×Dic3—22no—
386C3×Dic3—41no—
387C3×Dic3—41no—
388C3×Dic3#11714yes—
389C23×C4—31no—
390#117—38no—
391C2×C4⋊C4—31no—
392C2×C4⋊C4—31no—
393C2×C4⋊C4—31no—
394C2×C4⋊C4—31no—
395C2×C4⋊C4C2×C3×D311yescharacteristic
396C2×C4⋊C4C2×C3×D311yescharacteristic
397C2×C22⋊C4—31no—
398C2×C22⋊C4—31no—
399C2×C22⋊C4—31no—
400C2×C22⋊C4—31no—
401C2×C22⋊C4—31no—
402C2×C22⋊C4—31no—
403C2×C42—31no—
404C2×C42—31no—
405C2×C42—31no—
406C2×C42—31no—
407C2×C42—31no—
408C2×C42—31no—
409C2×C42—31no—
410C2×C42—31no—
411C2×C42—31no—
412C2×C42C2×C3×D311yescharacteristic
413#95—31no—
414#95—31no—
415#95—31no—
416#95—31no—
417#95—31no—
418#95—31no—
419#95—31no—
420#95—31no—
421#95C2×C3×D311yescharacteristic
422#95C2×C3×D311yescharacteristic
423#95C2×C3×D311yescharacteristic
424#95C2×C3×D311yescharacteristic
425C23×C3—21no—
426C23×C3—32no—
427C23×C3—61no—
428C23×C3—61no—
429C23×C3—61no—
430C23×C3—61no—
431C23×C3—61no—
432C23×C3—61no—
433C23×C3C23×D311yescharacteristic
434C23×C3C24×C311yescharacteristic
435C22×D3—21no—
436C22×D3—21no—
437C22×D3—21no—
438C22×D3—21no—
439C22×D3—21no—
440C22×D3—21no—
441C22×D3C22×C3×C412yes—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—21no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—22no—
475C2×C3×C4—22no—
476C2×C3×C4—22no—
477C2×C3×C4—22no—
478C2×C3×C4—22no—
479C2×C3×C4—32no—
480C2×C3×C4—32no—
481C2×C3×C4—32no—
482C2×C3×C4—32no—
483C2×C3×C4—32no—
484C2×C3×C4—32no—
485C2×C3×C4—32no—
486C2×C3×C4—41no—
487C2×C3×C4—41no—
488C2×C3×C4—41no—
489C2×C3×C4—41no—
490C2×C3×C4—41no—
491C2×C3×C4—41no—
492C2×C3×C4—41no—
493C2×C3×C4—41no—
494C2×C3×C4—41no—
495C2×C3×C4—41no—
496C2×C3×C4—41no—
497C2×C3×C4—41no—
498C2×C3×C4—41no—
499C2×C3×C4—41no—
500C2×C3×C4—41no—
501C2×C3×C4—41no—
502C2×C3×C4—68no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4C2×C4×D312yes—
518C2×C3×C4C2×C4×D312yes—
519C2×C3×C4C2×C4×D312yes—
520C2×C3×C4#23712yes—
521C2×C3×C4#23912yes—
522C2×C3×C4C22×C3×C412yes—
523C2×C3×C4C22×C3×C412yes—
524C2×C3×C4C22×C3×C412yes—
525C2×C3×C4C3×#4112yes—
526C2×C3×C4C3×#4112yes—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—21no—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3C22×C3×C412yes—
542C2×Dic3C22×C3×C412yes—
543C2×Dic3C22×C3×C412yes—
544C2×Dic3C3×#4112yes—
545C2×Dic3C3×#4112yes—
546C2×Dic3C3×#4112yes—
547C2×Dic3C3×#4112yes—
548C4×D3—28no—
549C2×C32C2×#11711yescharacteristic
550C2×C32C4×#4111yescharacteristic
551C2×C32C4×#4111yescharacteristic
552C2×C32#52911yescharacteristic
553C2×C32#52911yescharacteristic
554C2×C32#52911yescharacteristic
555C2×C32#52911yescharacteristic
556C3×D3—42no—
557C24—31no—
558C22×C4—31no—
559C22×C4—31no—
560C22×C4—31no—
561C22×C4—31no—
562C22×C4—31no—
563C22×C4—34no—
564C22×C4—31no—
565C22×C4—31no—
566C22×C4—62no—
567C22×C4—62no—
568C22×C4C22×C3×D311yescharacteristic
569C22×C4C22×C3×D311yescharacteristic
570C22×C4C22×C3×D311yescharacteristic
571C22×C4C22×C3×D311yescharacteristic
572C22×C4C22×C3×D311yescharacteristic
573C22×C4C22×C3×D311yescharacteristic
574C22×C4C22×C3×D311yescharacteristic
575C4⋊C4—22no—
576C4⋊C4—34no—
577C4⋊C4—62no—
578C4⋊C4—62no—
579C4⋊C4—62no—
580C4⋊C4C3×C4×D314yes—
581C22⋊C4—34no—
582C22⋊C4—34no—
583C22⋊C4—62no—
584C22⋊C4—62no—
585C22⋊C4—62no—
586C22⋊C4—62no—
587C42—22no—
588C42—34no—
589C42—34no—
590C42—62no—
591C42—62no—
592C42—62no—
593C42—62no—
594C42—62no—
595C42—62no—
596C42—62no—
597C22×C3—21no—
598C22×C3—21no—
599C22×C3—21no—
600C22×C3—21no—
601C22×C3—21no—
602C22×C3—21no—
603C22×C3—21no—
604C22×C3—62no—
605C22×C3—62no—
606C22×C3—62no—
607C22×C3—121no—
608C22×C3—121no—
609C22×C3—121no—
610C22×C3—121no—
611C22×C3C22×C4×D311yescharacteristic
612C22×C3C2×#23711yescharacteristic
613C22×C3C2×#23911yescharacteristic
614C22×C3D3×#4111yescharacteristic
615C22×C3D3×#4111yescharacteristic
616C22×C3D3×#4111yescharacteristic
617C22×C3D3×#4111yescharacteristic
618C22×C3C23×C3×C411yescharacteristic
619C22×C3C2×C3×#4111yescharacteristic
620C22×C3C2×C3×#4111yescharacteristic
621C22×C3C2×C3×#4111yescharacteristic
622C22×C3C2×C3×#4111yescharacteristic
623C22×C3C2×C3×#4111yescharacteristic
624C22×C3C2×C3×#4111yescharacteristic
625C2×D3—22no—
626C2×D3—22no—
627C2×D3—22no—
628C2×D3—41no—
629C2×D3—41no—
630C2×D3—41no—
631C2×D3—41no—
632C3×C4—22no—
633C3×C4—22no—
634C3×C4—22no—
635C3×C4—22no—
636C3×C4—22no—
637C3×C4—22no—
638C3×C4—22no—
639C3×C4—22no—
640C3×C4—22no—
641C3×C4—22no—
642C3×C4—34no—
643C3×C4—42no—
644C3×C4—42no—
645C3×C4—42no—
646C3×C4—42no—
647C3×C4—42no—
648C3×C4—41no—
649C3×C4—41no—
650C3×C4—41no—
651C3×C4—41no—
652C3×C4—62no—
653C3×C4—62no—
654C3×C4—62no—
655C3×C4—62no—
656C3×C4—81no—
657C3×C4—81no—
658C3×C4—121no—
659C3×C4—121no—
660Dic3—22no—
661Dic3—22no—
662Dic3—22no—
663Dic3—22no—
664Dic3—41no—
665Dic3—41no—
666Dic3C3×#11714yes—
667C32#229811yescharacteristic, complemented, Sylow
668C23—32no—
669C23—61no—
670C23—61no—
671C23—61no—
672C23—61no—
673C23—61no—
674C23—61no—
675C23C23×C3×D311yescharacteristic
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—32no—
693C2×C4—32no—
694C2×C4—32no—
695C2×C4—32no—
696C2×C4—32no—
697C2×C4—32no—
698C2×C4—32no—
699C2×C4—68no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4C2×C3×C4×D312yes—
715C2×C4C2×C3×C4×D312yes—
716C2×C4C2×C3×C4×D312yes—
717C2×C4C3×#23712yes—
718C2×C4C3×#23912yes—
719C2×C3—21no—
720C2×C3—21no—
721C2×C3—21no—
722C2×C3—21no—
723C2×C3—21no—
724C2×C3—21no—
725C2×C3—21no—
726C2×C3—122no—
727C2×C3D3×#11711yescharacteristic
728C2×C3C4×#23711yescharacteristic
729C2×C3C4×#23911yescharacteristic
730C2×C3#562411yescharacteristic
731C2×C3#564911yescharacteristic
732C2×C3#569111yescharacteristic
733C2×C3#570611yescharacteristic
734C2×C3C2×C3×#11711yescharacteristic
735C2×C3C3×C4×#4111yescharacteristic
736C2×C3C3×C4×#4111yescharacteristic
737C2×C3C3×#52911yescharacteristic
738C2×C3C3×#52911yescharacteristic
739C2×C3C3×#52911yescharacteristic
740C2×C3C3×#52911yescharacteristic
741D3—42no—
742C22—62no—
743C22—62no—
744C22—62no—
745C22—121no—
746C22—121no—
747C22—121no—
748C22—121no—
749C22C22×C3×C4×D311yescharacteristic
750C22C2×C3×#23711yescharacteristic
751C22C2×C3×#23911yescharacteristic
752C22C3×D3×#4111yescharacteristic
753C22C3×D3×#4111yescharacteristic
754C22C3×D3×#4111yescharacteristic
755C22C3×D3×#4111yescharacteristic
756C4—22no—
757C4—22no—
758C4—22no—
759C4—22no—
760C4—22no—
761C4—34no—
762C4—41no—
763C4—41no—
764C4—62no—
765C4—62no—
766C4—62no—
767C4—62no—
768C4—121no—
769C4—121no—
770C3—21no—
771C3#7493911yescharacteristic, direct product factor
772C3C3×#229811yescharacteristic, complemented
773C2—122no—
774C2C3×D3×#11711yescharacteristic
775C2C3×C4×#23711yescharacteristic
776C2C3×C4×#23911yescharacteristic
777C2C3×#562411yescharacteristic
778C2C3×#564911yescharacteristic
779C2C3×#569111yescharacteristic
780C2C3×#570611yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC32×#387C2
socleC23×C32C24
prime radicalC23×C3×D3C23
cosocleC23×C3C24×C3
hypercenterC3×#387D3
hypocenterC3C3×#2298
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#387

Complements

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

NH ≅ G/Ntype
2. C32×#387C2semidirect
4. C3×#4980C2semidirect
5. C3×Dic3×C4⋊C4C2semidirect
7. C3×C42×Dic3C2semidirect
12. C3×#4654C2semidirect
13. C3×#4653C2semidirect
14. C3×#4649C2semidirect
15. C3×#4648C2semidirect
17. #74939C3direct (N × H)
41. C3×#892C4semidirect
64. C3×#387D3semidirect
65. C3×#387C2×C3semidirect
73. #4980C2×C3semidirect
74. Dic3×C4⋊C4C2×C3semidirect
76. C42×Dic3C2×C3semidirect
81. #4654C2×C3semidirect
82. #4653C2×C3semidirect
83. #4649C2×C3semidirect
84. #4648C2×C3semidirect
176. #892C3×C4semidirect
264. #387C3×D3semidirect
667. C32#2298semidirect
771. C3#74939direct (N × H)
772. C3C3×#2298semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8922
C32×#3872
C3×#49902
C3×#49802
C3×Dic3×C4⋊C42
C3×#49402
C3×C42×Dic32
C3×#46702
C3×#46692
C3×#46662
C3×#46542
C3×#46532
C3×#46492
C3×#46482
C3×#22983
#749393