Finite Group Databasebeta

← C3×#74734 #11817717

Subgroups — C3×#74734 #11817717

Order 1152.

1179 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#926C211yesmaximal, characteristic, complemented
2C2×C3×#879C211yesmaximal, characteristic, complemented
3C32×#386C211yesmaximal, characteristic
4C3×#5222C211yesmaximal, characteristic
5C3×#5221C211yesmaximal, characteristic
6C3×#5210C211yesmaximal, characteristic, complemented
7C3×#4951C211yesmaximal, characteristic, complemented
8C3×#4949C211yesmaximal, characteristic, complemented
9C3×#4949C211yesmaximal, characteristic, complemented
10C3×#4945C211yesmaximal, characteristic, complemented
11C3×#4945C211yesmaximal, characteristic, complemented
12C3×#4661C211yesmaximal, characteristic, complemented
13C3×#4653C211yesmaximal, characteristic, complemented
14C3×#4649C211yesmaximal, characteristic, complemented
15C3×#4647C211yesmaximal, characteristic, complemented
16C3×#2479—31nomaximal
17#74734C311yesmaximal, characteristic, direct product factor
18C22×C32×D4C2211yescharacteristic
19C23×C32×C4C2211yescharacteristic
20C2×C32×C22⋊C4C2211yescharacteristic
21C2×C32×C22⋊C4C2211yescharacteristic
22C2×C32×C22⋊C4C2211yescharacteristic
23C2×C3×#217C2211yescharacteristic
24C2×C3×#217C2211yescharacteristic
25C2×C3×#217C2211yescharacteristic
26C2×C3×#217C2211yescharacteristic
27C2×C3×#217C2211yescharacteristic
28C2×C3×#217C2211yescharacteristic
29C2×C3×#217C2211yescharacteristic
30C2×C3×#217C2211yescharacteristic
31C3×#926—24no—
32C2×C3×C4⋊Dic3C2211yescharacteristic
33C2×C3×C4⋊Dic3C2211yescharacteristic
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×Dic3⋊C4C2211yescharacteristic
42C2×C3×C4×Dic3C2211yescharacteristic
43C2×C3×C4×Dic3C2211yescharacteristic
44C2×C3×C4×Dic3C2211yescharacteristic
45C2×C3×C4×Dic3C2211yescharacteristic
46C3×#879—24no—
47C32×#95C2211yescharacteristic
48C32×#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×#926C2×C311yescharacteristic, complemented
58C2×#879C2×C311yescharacteristic, complemented
59C3×#399—31no—
60C3×#399—31no—
61C3×#398—31no—
62C3×#394—31no—
63C3×#390—31no—
64C3×#389—31no—
65C3×#388—31no—
66C3×#388—31no—
67C3×#388—31no—
68C3×#387—31no—
69C3×#386—21no—
70C3×#386D311yescharacteristic
71C3×#386C2×C311yescharacteristic
72C3×#385—31no—
73C3×C4×C4⋊C4—31no—
74#5222C2×C311yescharacteristic
75#5221C2×C311yescharacteristic
76#5210C2×C311yescharacteristic, complemented
77#4951C2×C311yescharacteristic, complemented
78#4949C2×C311yescharacteristic, complemented
79#4949C2×C311yescharacteristic, complemented
80#4945C2×C311yescharacteristic, complemented
81#4945C2×C311yescharacteristic, complemented
82#4661C2×C311yescharacteristic, complemented
83#4653C2×C311yescharacteristic, complemented
84#4649C2×C311yescharacteristic, complemented
85#4647C2×C311yescharacteristic, complemented
86C24×C32C2311yescharacteristic
87C24×C32C2311yescharacteristic
88C2×C32×D4—22no—
89C2×C32×D4—22no—
90C2×C32×D4—41no—
91C22×C32×C4—22no—
92C22×C32×C4—22no—
93C22×C32×C4—22no—
94C22×C32×C4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C22×C32×C4C2311yescharacteristic
98C22×C32×C4C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C32×C22⋊C4—22no—
108C32×C22⋊C4—22no—
109C32×C22⋊C4—41no—
110C3×#217—22no—
111C3×#217—22no—
112C3×#217—22no—
113C3×#217—22no—
114C3×#217—22no—
115C3×#217—22no—
116C3×#217—22no—
117C3×#217—41no—
118C3×C4⋊Dic3—22no—
119C3×C4⋊Dic3—41no—
120C3×C4⋊Dic3—41no—
121C3×C4⋊Dic3D414yescomplemented
122C3×Dic3⋊C4—22no—
123C3×Dic3⋊C4—22no—
124C3×Dic3⋊C4—22no—
125C3×Dic3⋊C4—22no—
126C3×Dic3⋊C4—22no—
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—21no—
134C22×C3×D4C2×D311yescharacteristic
135C22×C3×D4C22×C311yescharacteristic
136C23×C3×C4—21no—
137C23×C3×C4C2×D311yescharacteristic
138C23×C3×C4C22×C311yescharacteristic
139C3×#126—64no—
140C3×#117—64no—
141C2×C3×C4⋊C4—31no—
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⋊C4—31no—
150C2×C3×C4⋊C4—31no—
151C2×C3×C22⋊C4—21no—
152C2×C3×C22⋊C4—21no—
153C2×C3×C22⋊C4—21no—
154C2×C3×C22⋊C4—31no—
155C2×C3×C22⋊C4—31no—
156C2×C3×C22⋊C4—31no—
157C2×C3×C22⋊C4—31no—
158C2×C3×C22⋊C4—31no—
159C2×C3×C22⋊C4—31no—
160C2×C3×C22⋊C4—31no—
161C2×C3×C22⋊C4—31no—
162C2×C3×C22⋊C4C2×D311yescharacteristic
163C2×C3×C22⋊C4C2×D311yescharacteristic
164C2×C3×C22⋊C4C2×D311yescharacteristic
165C2×C3×C22⋊C4C22×C311yescharacteristic
166C2×C3×C22⋊C4C22×C311yescharacteristic
167C2×C3×C22⋊C4C22×C311yescharacteristic
168C2×C3×C42—31no—
169C2×C3×C42—31no—
170C2×C3×C42—31no—
171C2×C3×C42—31no—
172C2×#217C22×C311yescharacteristic
173C2×#217C22×C311yescharacteristic
174C2×#217C22×C311yescharacteristic
175C2×#217C22×C311yescharacteristic
176C2×#217C22×C311yescharacteristic
177C2×#217C22×C311yescharacteristic
178C2×#217C22×C311yescharacteristic
179C2×#217C22×C311yescharacteristic
180#926—24no—
181C2×C4⋊Dic3C22×C311yescharacteristic
182C2×C4⋊Dic3C22×C311yescharacteristic
183C2×C4⋊Dic3C22×C311yescharacteristic
184C2×C4⋊Dic3C22×C311yescharacteristic
185C2×Dic3⋊C4C22×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#879—24no—
196C3×#95—21no—
197C3×#95—21no—
198C3×#95—31no—
199C3×#95—31no—
200C3×#95—31no—
201C3×#95—31no—
202C3×#95—31no—
203C3×#95—31no—
204C3×#95C2×D311yescharacteristic
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×C32—21no—
222C23×C32—21no—
223C23×C32—21no—
224C23×C32—21no—
225C23×C32—21no—
226C23×C32—21no—
227C23×C32#4112yes—
228C23×C32C2411yescharacteristic
229C32×D4—44no—
230C2×C32×C4—28no—
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×C4C2×D412yes—
244C2×C32×C4#4112yes—
245C2×C32×C4#4112yes—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
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×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3C2×D412yes—
268C2×C3×Dic3C2×D412yes—
269C2×C3×Dic3#4112yes—
270C2×#126—31no—
271C2×#117—31no—
272#399—31no—
273#399—31no—
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#386C3×D311yescharacteristic
283#385—31no—
284C4×C4⋊C4—31no—
285C24×C3—21no—
286C24×C3—21no—
287C24×C3C22×D311yescharacteristic
288C24×C3C22×D311yescharacteristic
289C24×C3C23×C311yescharacteristic
290C24×C3C23×C311yescharacteristic
291C2×C3×D4—24no—
292C2×C3×D4—22no—
293C2×C3×D4—22no—
294C2×C3×D4—22no—
295C2×C3×D4—22no—
296C2×C3×D4—42no—
297C2×C3×D4—41no—
298C2×C3×D4—41no—
299C2×C3×D4—42no—
300C22×C3×C4—22no—
301C22×C3×C4—22no—
302C22×C3×C4—22no—
303C22×C3×C4—22no—
304C22×C3×C4—22no—
305C22×C3×C4—22no—
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—31no—
312C22×C3×C4—31no—
313C22×C3×C4—31no—
314C22×C3×C4—31no—
315C22×C3×C4—31no—
316C22×C3×C4—31no—
317C22×C3×C4—31no—
318C22×C3×C4—31no—
319C22×C3×C4—42no—
320C22×C3×C4—42no—
321C22×C3×C4—42no—
322C22×C3×C4C22×D311yescharacteristic
323C22×C3×C4C22×D311yescharacteristic
324C22×C3×C4C22×D311yescharacteristic
325C22×C3×C4C22×D311yescharacteristic
326C22×C3×C4C22×D311yescharacteristic
327C22×C3×C4C23×C311yescharacteristic
328C22×C3×C4C23×C311yescharacteristic
329C22×C3×C4C23×C311yescharacteristic
330C22×C3×C4C23×C311yescharacteristic
331C22×C3×C4C23×C311yescharacteristic
332C22×Dic3C23×C311yescharacteristic
333C22×Dic3C23×C311yescharacteristic
334C22×Dic3C23×C311yescharacteristic
335C22×Dic3C23×C311yescharacteristic
336C22×Dic3C23×C311yescharacteristic
337C22×Dic3C23×C311yescharacteristic
338C22×Dic3C23×C311yescharacteristic
339C22×Dic3C23×C311yescharacteristic
340C3×C4⋊C4—34no—
341C3×C4⋊C4—62no—
342C3×C4⋊C4—62no—
343C3×C4⋊C4—62no—
344C3×C4⋊C4—62no—
345C3×C4⋊C4—62no—
346C3×C4⋊C4—62no—
347C3×C4⋊C4—121no—
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#217—22no—
375#217—22no—
376#217—22no—
377#217—22no—
378#217—41no—
379C4⋊Dic3—22no—
380C4⋊Dic3—41no—
381C4⋊Dic3—41no—
382C4⋊Dic3C3×D414yescomplemented
383Dic3⋊C4—22no—
384Dic3⋊C4—22no—
385Dic3⋊C4—22no—
386Dic3⋊C4—22no—
387Dic3⋊C4—22no—
388Dic3⋊C4—41no—
389C4×Dic3—22no—
390C4×Dic3—22no—
391C4×Dic3—22no—
392C4×Dic3—22no—
393C22×C32—22no—
394C22×C32—22no—
395C22×C32—22no—
396C22×C32—41no—
397C22×C32—41no—
398C22×C32—41no—
399C22×C32—41no—
400C22×C32—41no—
401C22×C32—41no—
402C22×C32—41no—
403C22×C32—41no—
404C22×C32—41no—
405C22×C32—41no—
406C22×C32—41no—
407C22×C32C22×D411yescharacteristic
408C22×C32C2×#4111yescharacteristic
409C22×C32C2×#4111yescharacteristic
410C22×C32C2×#4111yescharacteristic
411C22×C32C2×#4111yescharacteristic
412C22×C32H(5,𝔽2)11yescharacteristic
413C22×C322−1+411yescharacteristic
414C32×C4—22no—
415C32×C4—22no—
416C32×C4—22no—
417C32×C4—41no—
418C32×C4—41no—
419C3×Dic3—22no—
420C3×Dic3—22no—
421C3×Dic3—22no—
422C3×Dic3—41no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C22×D4C2×C3×D311yescharacteristic
428C23×C4C2×C3×D311yescharacteristic
429#126—64no—
430#117—64no—
431C2×C4⋊C4—31no—
432C2×C4⋊C4—31no—
433C2×C4⋊C4—31no—
434C2×C4⋊C4—31no—
435C2×C4⋊C4—31no—
436C2×C4⋊C4—31no—
437C2×C4⋊C4—31no—
438C2×C4⋊C4—31no—
439C2×C4⋊C4—31no—
440C2×C4⋊C4—31no—
441C2×C22⋊C4—31no—
442C2×C22⋊C4—31no—
443C2×C22⋊C4—31no—
444C2×C22⋊C4—31no—
445C2×C22⋊C4—31no—
446C2×C22⋊C4—31no—
447C2×C22⋊C4—31no—
448C2×C22⋊C4—31no—
449C2×C22⋊C4C2×C3×D311yescharacteristic
450C2×C22⋊C4C2×C3×D311yescharacteristic
451C2×C22⋊C4C2×C3×D311yescharacteristic
452C2×C42—31no—
453C2×C42—31no—
454C2×C42—31no—
455C2×C42—31no—
456#95—31no—
457#95—31no—
458#95—31no—
459#95—31no—
460#95—31no—
461#95—31no—
462#95C2×C3×D311yescharacteristic
463#95C2×C3×D311yescharacteristic
464C23×C3—22no—
465C23×C3—22no—
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—21no—
478C23×C3—22no—
479C23×C3—21no—
480C23×C3—21no—
481C23×C3—21no—
482C23×C3—21no—
483C23×C3—21no—
484C23×C3—21no—
485C23×C3—21no—
486C23×C3—21no—
487C23×C3—21no—
488C23×C3—21no—
489C23×C3—21no—
490C23×C3—21no—
491C23×C3—21no—
492C23×C3—21no—
493C23×C3—21no—
494C23×C3—22no—
495C23×C3—41no—
496C23×C3—41no—
497C23×C3—41no—
498C23×C3—41no—
499C23×C3—41no—
500C23×C3—41no—
501C23×C3—41no—
502C23×C3—41no—
503C23×C3—41no—
504C23×C3—41no—
505C23×C3#23712yes—
506C23×C3C3×#4112yes—
507C23×C3C23×D311yescharacteristic
508C23×C3C24×C311yescharacteristic
509C3×D4—44no—
510C3×D4—44no—
511C3×D4—48no—
512C2×C3×C4—28no—
513C2×C3×C4—28no—
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—21no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—22no—
539C2×C3×C4—22no—
540C2×C3×C4—22no—
541C2×C3×C4—32no—
542C2×C3×C4—32no—
543C2×C3×C4—32no—
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—48no—
551C2×C3×C4—41no—
552C2×C3×C4—41no—
553C2×C3×C4—41no—
554C2×C3×C4—41no—
555C2×C3×C4—41no—
556C2×C3×C4—41no—
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×C4—61no—
573C2×C3×C4—61no—
574C2×C3×C4—61no—
575C2×C3×C4—61no—
576C2×C3×C4—61no—
577C2×C3×C4—61no—
578C2×C3×C4#23512yes—
579C2×C3×C4D3×D412yes—
580C2×C3×C4#23712yes—
581C2×C3×C4C2×C3×D412yes—
582C2×C3×C4C3×#4112yes—
583C2×C3×C4C3×#4112yes—
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×Dic3—21no—
595C2×Dic3—21no—
596C2×Dic3—21no—
597C2×Dic3—21no—
598C2×Dic3—21no—
599C2×Dic3—21no—
600C2×Dic3—21no—
601C2×Dic3—21no—
602C2×Dic3—21no—
603C2×Dic3—21no—
604C2×Dic3—21no—
605C2×Dic3C2×C3×D412yes—
606C2×Dic3C2×C3×D412yes—
607C2×Dic3C3×#4112yes—
608C2×C32—42no—
609C2×C32—81no—
610C2×C32#52511yescharacteristic
611C2×C32#52911yescharacteristic
612C2×C32#54211yescharacteristic
613C2×C32#54711yescharacteristic
614C2×C32#55011yescharacteristic
615C2×C32#55111yescharacteristic
616C2×C32#55211yescharacteristic
617C24C22×C3×D311yescharacteristic
618C24C22×C3×D311yescharacteristic
619C2×D4—22no—
620C2×D4—22no—
621C2×D4—41no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—31no—
626C22×C4—31no—
627C22×C4—31no—
628C22×C4—31no—
629C22×C4—31no—
630C22×C4—31no—
631C22×C4—31no—
632C22×C4—31no—
633C22×C4C22×C3×D311yescharacteristic
634C22×C4C22×C3×D311yescharacteristic
635C22×C4C22×C3×D311yescharacteristic
636C22×C4C22×C3×D311yescharacteristic
637C22×C4C22×C3×D311yescharacteristic
638C4⋊C4—34no—
639C4⋊C4—62no—
640C4⋊C4—62no—
641C4⋊C4—62no—
642C4⋊C4—62no—
643C4⋊C4—62no—
644C4⋊C4—62no—
645C4⋊C4—121no—
646C4⋊C4—121no—
647C4⋊C4—121no—
648C22⋊C4—22no—
649C22⋊C4—22no—
650C22⋊C4—41no—
651C22⋊C4—62no—
652C22⋊C4—62no—
653C22⋊C4—62no—
654C22⋊C4—62no—
655C22⋊C4—62no—
656C22⋊C4—62no—
657C22⋊C4—62no—
658C22⋊C4—121no—
659C42—62no—
660C42—62no—
661C42—62no—
662C42—62no—
663C22×C3—24no—
664C22×C3—22no—
665C22×C3—22no—
666C22×C3—22no—
667C22×C3—22no—
668C22×C3—22no—
669C22×C3—22no—
670C22×C3—21no—
671C22×C3—21no—
672C22×C3—21no—
673C22×C3—21no—
674C22×C3—21no—
675C22×C3—21no—
676C22×C3—21no—
677C22×C3—42no—
678C22×C3—42no—
679C22×C3—42no—
680C22×C3—42no—
681C22×C3—42no—
682C22×C3—42no—
683C22×C3—42no—
684C22×C3—42no—
685C22×C3—42no—
686C22×C3—41no—
687C22×C3—41no—
688C22×C3—41no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—41no—
692C22×C3—41no—
693C22×C3—41no—
694C22×C3—41no—
695C22×C3—41no—
696C22×C3—41no—
697C22×C3—41no—
698C22×C3—41no—
699C22×C3—41no—
700C22×C3—41no—
701C22×C3—41no—
702C22×C3—41no—
703C22×C3—41no—
704C22×C3—41no—
705C22×C3—41no—
706C22×C3—41no—
707C22×C3—41no—
708C22×C3—81no—
709C22×C3—81no—
710C22×C3—81no—
711C22×C3—81no—
712C22×C3C2×#23511yescharacteristic
713C22×C3C2×D3×D411yescharacteristic
714C22×C3C2×#23711yescharacteristic
715C22×C3C2×#23711yescharacteristic
716C22×C3#100411yescharacteristic
717C22×C3D3×#4111yescharacteristic
718C22×C3#101011yescharacteristic
719C22×C3C22×C3×D411yescharacteristic
720C22×C3C2×C3×#4111yescharacteristic
721C22×C3C2×C3×#4111yescharacteristic
722C22×C3C2×C3×#4111yescharacteristic
723C22×C3C2×C3×#4111yescharacteristic
724C22×C3C3×H(5,𝔽2)11yescharacteristic
725C22×C3C3×2−1+411yescharacteristic
726C3×C4—22no—
727C3×C4—22no—
728C3×C4—22no—
729C3×C4—22no—
730C3×C4—22no—
731C3×C4—22no—
732C3×C4—42no—
733C3×C4—42no—
734C3×C4—42no—
735C3×C4—41no—
736C3×C4—41no—
737C3×C4—41no—
738C3×C4—41no—
739C3×C4—62no—
740C3×C4—62no—
741C3×C4—62no—
742C3×C4—81no—
743C3×C4—81no—
744C3×C4—121no—
745C3×C4—121no—
746C3×C4—121no—
747C3×C4—121no—
748C3×C4—121no—
749Dic3—22no—
750Dic3—22no—
751Dic3—22no—
752Dic3—41no—
753Dic3—41no—
754Dic3—41no—
755Dic3—41no—
756Dic3—41no—
757C32#247911yescharacteristic, complemented, Sylow
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23C3×#23712yes—
772C23C23×C3×D311yescharacteristic
773D4—44no—
774C2×C4—28no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—32no—
788C2×C4—32no—
789C2×C4—32no—
790C2×C4—61no—
791C2×C4—61no—
792C2×C4—61no—
793C2×C4—61no—
794C2×C4—61no—
795C2×C4—61no—
796C2×C4—61no—
797C2×C4—61no—
798C2×C4—61no—
799C2×C4—61no—
800C2×C4—61no—
801C2×C4—61no—
802C2×C4—61no—
803C2×C4—61no—
804C2×C4—61no—
805C2×C4—61no—
806C2×C4—61no—
807C2×C4—61no—
808C2×C4—61no—
809C2×C4—61no—
810C2×C4—61no—
811C2×C4C3×#23512yes—
812C2×C4C3×D3×D412yes—
813C2×C4C3×#23712yes—
814C2×C3—21no—
815C2×C3—21no—
816C2×C3—21no—
817C2×C3—21no—
818C2×C3—21no—
819C2×C3—21no—
820C2×C3—21no—
821C2×C3—44no—
822C2×C3—42no—
823C2×C3—42no—
824C2×C3—82no—
825C2×C3—81no—
826C2×C3—81no—
827C2×C3#549511yescharacteristic
828C2×C3#555111yescharacteristic
829C2×C3#555711yescharacteristic
830C2×C3#558611yescharacteristic
831C2×C3#559911yescharacteristic
832C2×C3#560311yescharacteristic
833C2×C3#565011yescharacteristic
834C2×C3C3×#52511yescharacteristic
835C2×C3C3×#52911yescharacteristic
836C2×C3C3×#54211yescharacteristic
837C2×C3C3×#54711yescharacteristic
838C2×C3C3×#55011yescharacteristic
839C2×C3C3×#55111yescharacteristic
840C2×C3C3×#55211yescharacteristic
841C22—22no—
842C22—22no—
843C22—22no—
844C22—41no—
845C22—41no—
846C22—41no—
847C22—41no—
848C22—41no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22C2×C3×#23511yescharacteristic
856C22C2×C3×D3×D411yescharacteristic
857C22C2×C3×#23711yescharacteristic
858C22C2×C3×#23711yescharacteristic
859C22C3×#100411yescharacteristic
860C22C3×D3×#4111yescharacteristic
861C22C3×#101011yescharacteristic
862C4—22no—
863C4—22no—
864C4—22no—
865C4—41no—
866C4—41no—
867C4—62no—
868C4—62no—
869C4—62no—
870C4—121no—
871C4—121no—
872C4—121no—
873C4—121no—
874C4—121no—
875C3—21no—
876C3#7473411yescharacteristic, direct product factor
877C3C3×#247911yescharacteristic, complemented
878C2—42no—
879C2—81no—
880C2C3×#549511yescharacteristic
881C2C3×#555111yescharacteristic
882C2C3×#555711yescharacteristic
883C2C3×#558611yescharacteristic
884C2C3×#559911yescharacteristic
885C2C3×#560311yescharacteristic
886C2C3×#565011yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC32×#386C2
socleC23×C32C24
prime radicalC22×C32×D4C22
hypercenterC3×#386D3
hypocenterC3C3×#2479
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#386

Complements

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

NH ≅ G/Ntype
1. C2×C3×#926C2semidirect
2. C2×C3×#879C2semidirect
6. C3×#5210C2semidirect
7. C3×#4951C2semidirect
8. C3×#4949C2semidirect
9. C3×#4949C2semidirect
10. C3×#4945C2semidirect
11. C3×#4945C2semidirect
12. C3×#4661C2semidirect
13. C3×#4653C2semidirect
14. C3×#4649C2semidirect
15. C3×#4647C2semidirect
17. #74734C3direct (N × H)
57. C2×#926C2×C3semidirect
58. C2×#879C2×C3semidirect
76. #5210C2×C3semidirect
77. #4951C2×C3semidirect
78. #4949C2×C3semidirect
79. #4949C2×C3semidirect
80. #4945C2×C3semidirect
81. #4945C2×C3semidirect
82. #4661C2×C3semidirect
83. #4653C2×C3semidirect
84. #4649C2×C3semidirect
85. #4647C2×C3semidirect
121. C3×C4⋊Dic3D4semidirect
382. C4⋊Dic3C3×D4semidirect
757. C32#2479semidirect
876. C3#74734direct (N × H)
877. C3C3×#2479semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9262
C2×C3×#8792
C32×#3862
C3×#52222
C3×#52212
C3×#52102
C3×#49512
C3×#49492
C3×#49452
C3×#46612
C3×#46532
C3×#46492
C3×#46472
C3×#24793
#747343