Finite Group Databasebeta

← C3×#82656 #11812953

Subgroups — C3×#82656 #11812953

Order 1152.

1433 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#121C211yesmaximal, characteristic
2C2×C3×D4×Dic3C211yesmaximal, characteristic, complemented
3C3×#5222C211yesmaximal, characteristic, complemented
4C3×#5220C211yesmaximal, characteristic, complemented
5C3×#5220C211yesmaximal, characteristic, complemented
6C3×#5220C211yesmaximal, characteristic, complemented
7C3×#5220C211yesmaximal, characteristic, complemented
8C3×#5210C211yesmaximal, characteristic, complemented
9C2×C3×C3⋊#95C211yesmaximal, characteristic, complemented
10C3×#4986C211yesmaximal, characteristic, complemented
11C3×#4978C211yesmaximal, characteristic, complemented
12C3×#4953C211yesmaximal, characteristic, complemented
13C3×#4952C211yesmaximal, characteristic, complemented
14C3×#4944C211yesmaximal, characteristic, complemented
15C3×#4943C211yesmaximal, characteristic, complemented
16C3×#2444—31nomaximal
17#82656C311yesmaximal, characteristic, direct product factor
18C22×C32×D4C2211yescharacteristic
19C22×C32×D4C2211yescharacteristic
20C22×C32×D4C2211yescharacteristic
21C23×C32×C4C2211yescharacteristic
22C23×C3×Dic3C2211yescharacteristic
23C23×C3×Dic3C2211yescharacteristic
24C23×C3×Dic3C2211yescharacteristic
25C32×#121—24no—
26C2×C32×C4⋊C4C2211yescharacteristic
27C2×C32×C22⋊C4C2211yescharacteristic
28C2×C32×C22⋊C4C2211yescharacteristic
29C2×C3×#217C2211yescharacteristic
30C2×C3×#217C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×#217C2211yescharacteristic
33C2×C3×#217C2211yescharacteristic
34C2×C3×#217C2211yescharacteristic
35C2×C3×#217C2211yescharacteristic
36C2×C3×#217C2211yescharacteristic
37C2×C3×#217C2211yescharacteristic
38C3×D4×Dic3—24no—
39C2×C3×C4⋊Dic3C2211yescharacteristic
40C2×C3×Dic3⋊C4C2211yescharacteristic
41C2×C3×Dic3⋊C4C2211yescharacteristic
42C2×C3×C4×Dic3C2211yescharacteristic
43C3×C3⋊#95C2211yescharacteristic
44C3×C3⋊#95C2211yescharacteristic
45C3×C3⋊#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—21no—
56C2×C3×#121D311yescharacteristic
57C2×C3×#121C2×C311yescharacteristic
58C2×C3×C4×D4—31no—
59C2×D4×Dic3C2×C311yescharacteristic, complemented
60C3×#400—31no—
61C3×#397—31no—
62C3×#397—31no—
63C3×#394—31no—
64C3×#388—31no—
65C3×#387—31no—
66C3×#386—31no—
67C3×#386—31no—
68C3×#386—31no—
69C3×#386—31no—
70C3×#385—31no—
71C3×#381—31no—
72C2×C3×#95—31no—
73#5222C2×C311yescharacteristic, complemented
74#5220C2×C311yescharacteristic, complemented
75#5220C2×C311yescharacteristic, complemented
76#5220C2×C311yescharacteristic, complemented
77#5220C2×C311yescharacteristic, complemented
78#5210C2×C311yescharacteristic, complemented
79C2×C3⋊#95C2×C311yescharacteristic, complemented
80#4986C2×C311yescharacteristic, complemented
81#4978C2×C311yescharacteristic, complemented
82#4953C2×C311yescharacteristic, complemented
83#4952C2×C311yescharacteristic, complemented
84#4944C2×C311yescharacteristic, complemented
85#4943C2×C311yescharacteristic, complemented
86C24×C32C2311yescharacteristic
87C24×C32C2311yescharacteristic
88C24×C32C2311yescharacteristic
89C2×C32×D4—22no—
90C2×C32×D4—22no—
91C2×C32×D4—22no—
92C2×C32×D4—22no—
93C2×C32×D4—22no—
94C2×C32×D4—22no—
95C2×C32×D4—22no—
96C2×C32×D4—41no—
97C2×C32×D4D414yes—
98C22×C32×C4—22no—
99C22×C32×C4—22no—
100C22×C32×C4—41no—
101C22×C32×C4C2311yescharacteristic
102C22×C32×C4C2311yescharacteristic
103C22×C32×C4C2311yescharacteristic
104C22×C32×C4C2311yescharacteristic
105C22×C3×Dic3—22no—
106C22×C3×Dic3—22no—
107C22×C3×Dic3—22no—
108C22×C3×Dic3—22no—
109C22×C3×Dic3—22no—
110C22×C3×Dic3—41no—
111C22×C3×Dic3—41no—
112C22×C3×Dic3—41no—
113C22×C3×Dic3—41no—
114C22×C3×Dic3C2311yescharacteristic
115C22×C3×Dic3C2311yescharacteristic
116C22×C3×Dic3C2311yescharacteristic
117C22×C3×Dic3C2311yescharacteristic
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C22×C3×Dic3C2311yescharacteristic
122C32×C4⋊C4—22no—
123C32×C22⋊C4—22no—
124C32×C22⋊C4—22no—
125C3×#217—22no—
126C3×#217—22no—
127C3×#217—22no—
128C3×#217—22no—
129C3×#217—41no—
130C3×#217—41no—
131C3×#217—41no—
132C3×#217—41no—
133C3×#217—41no—
134C3×C4⋊Dic3—22no—
135C3×Dic3⋊C4—22no—
136C3×Dic3⋊C4—41no—
137C3×C4×Dic3—22no—
138#2444—31noSylow
139C22×C3×D4—21no—
140C22×C3×D4—21no—
141C22×C3×D4—21no—
142C22×C3×D4C2×D311yescharacteristic
143C22×C3×D4C2×D311yescharacteristic
144C22×C3×D4C2×D311yescharacteristic
145C22×C3×D4C22×C311yescharacteristic
146C22×C3×D4C22×C311yescharacteristic
147C22×C3×D4C22×C311yescharacteristic
148C23×C3×C4—21no—
149C23×C3×C4—31no—
150C23×C3×C4—31no—
151C23×C3×C4—31no—
152C23×C3×C4C2×D311yescharacteristic
153C23×C3×C4C22×C311yescharacteristic
154C23×Dic3C22×C311yescharacteristic
155C23×Dic3C22×C311yescharacteristic
156C23×Dic3C22×C311yescharacteristic
157C3×#121—28no—
158C3×#121—24no—
159C3×#121—24no—
160C3×C4×D4—64no—
161C2×C3×C4⋊C4—21no—
162C2×C3×C4⋊C4—31no—
163C2×C3×C4⋊C4—31no—
164C2×C3×C4⋊C4—31no—
165C2×C3×C4⋊C4C2×D311yescharacteristic
166C2×C3×C4⋊C4C22×C311yescharacteristic
167C2×C3×C22⋊C4—21no—
168C2×C3×C22⋊C4—21no—
169C2×C3×C22⋊C4—31no—
170C2×C3×C22⋊C4—31no—
171C2×C3×C22⋊C4—31no—
172C2×C3×C22⋊C4—31no—
173C2×C3×C22⋊C4—31no—
174C2×C3×C22⋊C4—31no—
175C2×C3×C22⋊C4—31no—
176C2×C3×C22⋊C4—31no—
177C2×C3×C22⋊C4—31no—
178C2×C3×C22⋊C4C2×D311yescharacteristic
179C2×C3×C22⋊C4C2×D311yescharacteristic
180C2×C3×C22⋊C4C22×C311yescharacteristic
181C2×C3×C22⋊C4C22×C311yescharacteristic
182C2×C3×C42—31no—
183C2×#217C22×C311yescharacteristic
184C2×#217C22×C311yescharacteristic
185C2×#217C22×C311yescharacteristic
186C2×#217C22×C311yescharacteristic
187C2×#217C22×C311yescharacteristic
188C2×#217C22×C311yescharacteristic
189C2×#217C22×C311yescharacteristic
190C2×#217C22×C311yescharacteristic
191C2×#217C22×C311yescharacteristic
192D4×Dic3—24no—
193C2×C4⋊Dic3C22×C311yescharacteristic
194C2×Dic3⋊C4C22×C311yescharacteristic
195C2×Dic3⋊C4C22×C311yescharacteristic
196C2×C4×Dic3C22×C311yescharacteristic
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×#95—31no—
206C3×#95—31no—
207C3×#95—31no—
208C3×#95—31no—
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
220C3⋊#95C22×C311yescharacteristic
221C23×C32—21no—
222C23×C32—21no—
223C23×C32—21no—
224C23×C32—21no—
225C23×C32—21no—
226C23×C32—21no—
227C23×C32—21no—
228C23×C32—21no—
229C23×C32—21no—
230C23×C32—21no—
231C23×C32—21no—
232C23×C32—21no—
233C23×C32—21no—
234C23×C32—21no—
235C23×C32—21no—
236C23×C32—21no—
237C23×C32—21no—
238C23×C32C2×D412yes—
239C23×C32C2×D412yes—
240C23×C32#4112yes—
241C23×C32#4112yes—
242C23×C32C2411yescharacteristic
243C32×D4—28no—
244C32×D4—44no—
245C32×D4—44no—
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—44no—
257C2×C32×C4C2×D412yes—
258C2×C32×C4#4112yes—
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×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—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—44no—
283C2×C3×Dic3—44no—
284C2×C3×Dic3—44no—
285C2×C3×Dic3#4112yes—
286C2×#121C3×D311yescharacteristic
287C2×C4×D4—31no—
288#400—31no—
289#397—31no—
290#397—31no—
291#394—31no—
292#388—31no—
293#387—31no—
294#386—31no—
295#386—31no—
296#386—31no—
297#386—31no—
298#385—31no—
299#381—31no—
300C2×#95—31no—
301C24×C3—21no—
302C24×C3—21no—
303C24×C3—21no—
304C24×C3C22×D311yescharacteristic
305C24×C3C22×D311yescharacteristic
306C24×C3C22×D311yescharacteristic
307C24×C3C23×C311yescharacteristic
308C24×C3C23×C311yescharacteristic
309C24×C3C23×C311yescharacteristic
310C2×C3×D4—22no—
311C2×C3×D4—22no—
312C2×C3×D4—22no—
313C2×C3×D4—22no—
314C2×C3×D4—24no—
315C2×C3×D4—24no—
316C2×C3×D4—22no—
317C2×C3×D4—22no—
318C2×C3×D4—22no—
319C2×C3×D4—22no—
320C2×C3×D4—22no—
321C2×C3×D4—22no—
322C2×C3×D4—22no—
323C2×C3×D4—22no—
324C2×C3×D4—22no—
325C2×C3×D4—22no—
326C2×C3×D4—24no—
327C2×C3×D4—42no—
328C2×C3×D4—42no—
329C2×C3×D4—42no—
330C2×C3×D4—42no—
331C2×C3×D4—42no—
332C2×C3×D4—41no—
333C2×C3×D4—41no—
334C2×C3×D4—42no—
335C2×C3×D4#6714yes—
336C2×C3×D4C3×D414yes—
337C22×C3×C4—24no—
338C22×C3×C4—22no—
339C22×C3×C4—22no—
340C22×C3×C4—22no—
341C22×C3×C4—22no—
342C22×C3×C4—21no—
343C22×C3×C4—21no—
344C22×C3×C4—21no—
345C22×C3×C4—21no—
346C22×C3×C4—31no—
347C22×C3×C4—31no—
348C22×C3×C4—31no—
349C22×C3×C4—31no—
350C22×C3×C4—31no—
351C22×C3×C4—31no—
352C22×C3×C4—31no—
353C22×C3×C4—31no—
354C22×C3×C4—42no—
355C22×C3×C4—41no—
356C22×C3×C4—41no—
357C22×C3×C4—42no—
358C22×C3×C4—62no—
359C22×C3×C4—62no—
360C22×C3×C4—62no—
361C22×C3×C4—62no—
362C22×C3×C4—62no—
363C22×C3×C4—121no—
364C22×C3×C4—121no—
365C22×C3×C4—121no—
366C22×C3×C4—121no—
367C22×C3×C4C22×D311yescharacteristic
368C22×C3×C4C22×D311yescharacteristic
369C22×C3×C4C22×D311yescharacteristic
370C22×C3×C4C22×D311yescharacteristic
371C22×C3×C4C23×C311yescharacteristic
372C22×C3×C4C23×C311yescharacteristic
373C22×C3×C4C23×C311yescharacteristic
374C22×C3×C4C23×C311yescharacteristic
375C22×Dic3—22no—
376C22×Dic3—22no—
377C22×Dic3—22no—
378C22×Dic3—22no—
379C22×Dic3—22no—
380C22×Dic3—41no—
381C22×Dic3—41no—
382C22×Dic3—41no—
383C22×Dic3—41no—
384C22×Dic3C23×C311yescharacteristic
385C22×Dic3C23×C311yescharacteristic
386C22×Dic3C23×C311yescharacteristic
387C22×Dic3C23×C311yescharacteristic
388C22×Dic3C23×C311yescharacteristic
389C22×Dic3C23×C311yescharacteristic
390C22×Dic3C23×C311yescharacteristic
391C22×Dic3C23×C311yescharacteristic
392C3×C4⋊C4—24no—
393C3×C4⋊C4—22no—
394C3×C4⋊C4—22no—
395C3×C4⋊C4—62no—
396C3×C4⋊C4—62no—
397C3×C4⋊C4—121no—
398C3×C22⋊C4—24no—
399C3×C22⋊C4—24no—
400C3×C22⋊C4—22no—
401C3×C22⋊C4—22no—
402C3×C22⋊C4—22no—
403C3×C22⋊C4—22no—
404C3×C22⋊C4—62no—
405C3×C22⋊C4—62no—
406C3×C22⋊C4—62no—
407C3×C22⋊C4—62no—
408C3×C22⋊C4—121no—
409C3×C22⋊C4—121no—
410C3×C22⋊C4—121no—
411C3×C22⋊C4—121no—
412C3×C22⋊C4—121no—
413C3×C42—62no—
414#217—22no—
415#217—22no—
416#217—22no—
417#217—22no—
418#217—41no—
419#217—41no—
420#217—41no—
421#217—41no—
422#217—41no—
423C4⋊Dic3—22no—
424Dic3⋊C4—22no—
425Dic3⋊C4—41no—
426C4×Dic3—22no—
427C22×C32—22no—
428C22×C32—22no—
429C22×C32—22no—
430C22×C32—22no—
431C22×C32—22no—
432C22×C32—22no—
433C22×C32—22no—
434C22×C32—22no—
435C22×C32—22no—
436C22×C32—41no—
437C22×C32—41no—
438C22×C32—41no—
439C22×C32—41no—
440C22×C32—41no—
441C22×C32—41no—
442C22×C32—41no—
443C22×C32—41no—
444C22×C32—41no—
445C22×C32—41no—
446C22×C32—41no—
447C22×C32#12314yes—
448C22×C32C22×D411yescharacteristic
449C22×C32C2×#4111yescharacteristic
450C22×C32C2×#4111yescharacteristic
451C22×C32C2×#4111yescharacteristic
452C22×C32C2×#4111yescharacteristic
453C22×C32H(5,𝔽2)11yescharacteristic
454C22×C32H(5,𝔽2)11yescharacteristic
455C32×C4—22no—
456C32×C4—22no—
457C32×C4—41no—
458C32×C4—41no—
459C3×Dic3—22no—
460C3×Dic3—41no—
461C3×Dic3—41no—
462C3×Dic3—41no—
463C3×Dic3—41no—
464C3×Dic3—41no—
465C3×Dic3—41no—
466C3×Dic3—41no—
467C22×D4C2×C3×D311yescharacteristic
468C22×D4C2×C3×D311yescharacteristic
469C22×D4C2×C3×D311yescharacteristic
470C23×C4—31no—
471C23×C4—31no—
472C23×C4—31no—
473C23×C4C2×C3×D311yescharacteristic
474#121—24no—
475C4×D4—64no—
476C2×C4⋊C4—31no—
477C2×C4⋊C4—31no—
478C2×C4⋊C4—31no—
479C2×C4⋊C4C2×C3×D311yescharacteristic
480C2×C22⋊C4—31no—
481C2×C22⋊C4—31no—
482C2×C22⋊C4—31no—
483C2×C22⋊C4—31no—
484C2×C22⋊C4—31no—
485C2×C22⋊C4—31no—
486C2×C22⋊C4—31no—
487C2×C22⋊C4—31no—
488C2×C22⋊C4—31no—
489C2×C22⋊C4C2×C3×D311yescharacteristic
490C2×C22⋊C4C2×C3×D311yescharacteristic
491C2×C42—31no—
492#95—31no—
493#95—31no—
494#95—31no—
495#95—31no—
496#95—31no—
497#95—31no—
498#95—31no—
499#95—31no—
500#95—31no—
501#95—31no—
502#95—31no—
503#95—31no—
504C23×C3—21no—
505C23×C3—21no—
506C23×C3—21no—
507C23×C3—21no—
508C23×C3—21no—
509C23×C3—21no—
510C23×C3—21no—
511C23×C3—21no—
512C23×C3—21no—
513C23×C3—21no—
514C23×C3—21no—
515C23×C3—21no—
516C23×C3—21no—
517C23×C3—21no—
518C23×C3—21no—
519C23×C3—21no—
520C23×C3—21no—
521C23×C3—21no—
522C23×C3—21no—
523C23×C3—21no—
524C23×C3—22no—
525C23×C3—21no—
526C23×C3—21no—
527C23×C3—21no—
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—21no—
531C23×C3—21no—
532C23×C3—21no—
533C23×C3—21no—
534C23×C3—21no—
535C23×C3—21no—
536C23×C3—21no—
537C23×C3—21no—
538C23×C3—21no—
539C23×C3—21no—
540C23×C3—22no—
541C23×C3—22no—
542C23×C3—22no—
543C23×C3—22no—
544C23×C3—41no—
545C23×C3—41no—
546C23×C3—41no—
547C23×C3—41no—
548C23×C3—41no—
549C23×C3—41no—
550C23×C3—41no—
551C23×C3—41no—
552C23×C3—41no—
553C23×C3—41no—
554C23×C3—41no—
555C23×C3—41no—
556C23×C3—41no—
557C23×C3—41no—
558C23×C3—41no—
559C23×C3—41no—
560C23×C3#23712yes—
561C23×C3#23712yes—
562C23×C3C2×#6712yes—
563C23×C3C2×#6712yes—
564C23×C3C2×C3×D412yes—
565C23×C3C2×C3×D412yes—
566C23×C3C3×#4112yes—
567C23×C3C3×#4112yes—
568C23×C3C23×D311yescharacteristic
569C23×C3C24×C311yescharacteristic
570C3×D4—28no—
571C3×D4—28no—
572C3×D4—48no—
573C3×D4—44no—
574C3×D4—44no—
575C3×D4—48no—
576C3×D4—48no—
577C3×D4—44no—
578C3×D4—44no—
579C2×C3×C4—22no—
580C2×C3×C4—22no—
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—22no—
590C2×C3×C4—22no—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—21no—
594C2×C3×C4—21no—
595C2×C3×C4—21no—
596C2×C3×C4—21no—
597C2×C3×C4—21no—
598C2×C3×C4—21no—
599C2×C3×C4—21no—
600C2×C3×C4—21no—
601C2×C3×C4—21no—
602C2×C3×C4—21no—
603C2×C3×C4—22no—
604C2×C3×C4—22no—
605C2×C3×C4—32no—
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—44no—
613C2×C3×C4—44no—
614C2×C3×C4—48no—
615C2×C3×C4—61no—
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—61no—
631C2×C3×C4—61no—
632C2×C3×C4—61no—
633C2×C3×C4—61no—
634C2×C3×C4—61no—
635C2×C3×C4—61no—
636C2×C3×C4—61no—
637C2×C3×C4—61no—
638C2×C3×C4—124no—
639C2×C3×C4—124no—
640C2×C3×C4—124no—
641C2×C3×C4#23712yes—
642C2×C3×C4C2×#6712yes—
643C2×C3×C4C2×C3×D412yes—
644C2×C3×C4C3×#4112yes—
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×Dic3—21no—
656C2×Dic3—21no—
657C2×Dic3—21no—
658C2×Dic3—21no—
659C2×Dic3—21no—
660C2×Dic3—21no—
661C2×Dic3—21no—
662C2×Dic3—21no—
663C2×Dic3—21no—
664C2×Dic3—21no—
665C2×Dic3—21no—
666C2×Dic3—21no—
667C2×Dic3—21no—
668C2×Dic3—44no—
669C2×Dic3—44no—
670C2×Dic3—44no—
671C2×Dic3C3×#4112yes—
672C2×C32—24no—
673C2×C32—42no—
674C2×C32—81no—
675C2×C32C2×#12311yescharacteristic
676C2×C32#52911yescharacteristic
677C2×C32#53811yescharacteristic
678C2×C32#54611yescharacteristic
679C2×C32#54611yescharacteristic
680C2×C32#55311yescharacteristic
681C2×C32#55311yescharacteristic
682C24C22×C3×D311yescharacteristic
683C24C22×C3×D311yescharacteristic
684C24C22×C3×D311yescharacteristic
685C2×D4—22no—
686C2×D4—22no—
687C2×D4—22no—
688C2×D4—22no—
689C2×D4—22no—
690C2×D4—22no—
691C2×D4—22no—
692C2×D4—41no—
693C2×D4C3×#6714yes—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—31no—
697C22×C4—31no—
698C22×C4—31no—
699C22×C4—31no—
700C22×C4—31no—
701C22×C4—31no—
702C22×C4—31no—
703C22×C4—31no—
704C22×C4—41no—
705C22×C4—62no—
706C22×C4—62no—
707C22×C4—62no—
708C22×C4—62no—
709C22×C4—62no—
710C22×C4—121no—
711C22×C4—121no—
712C22×C4—121no—
713C22×C4—121no—
714C22×C4C22×C3×D311yescharacteristic
715C22×C4C22×C3×D311yescharacteristic
716C22×C4C22×C3×D311yescharacteristic
717C22×C4C22×C3×D311yescharacteristic
718C4⋊C4—22no—
719C4⋊C4—62no—
720C4⋊C4—62no—
721C4⋊C4—121no—
722C22⋊C4—22no—
723C22⋊C4—22no—
724C22⋊C4—62no—
725C22⋊C4—62no—
726C22⋊C4—62no—
727C22⋊C4—62no—
728C22⋊C4—121no—
729C22⋊C4—121no—
730C22⋊C4—121no—
731C22⋊C4—121no—
732C22⋊C4—121no—
733C42—62no—
734C22×C3—22no—
735C22×C3—22no—
736C22×C3—22no—
737C22×C3—22no—
738C22×C3—22no—
739C22×C3—22no—
740C22×C3—22no—
741C22×C3—22no—
742C22×C3—22no—
743C22×C3—22no—
744C22×C3—22no—
745C22×C3—22no—
746C22×C3—22no—
747C22×C3—22no—
748C22×C3—22no—
749C22×C3—22no—
750C22×C3—22no—
751C22×C3—22no—
752C22×C3—24no—
753C22×C3—21no—
754C22×C3—21no—
755C22×C3—21no—
756C22×C3—21no—
757C22×C3—21no—
758C22×C3—21no—
759C22×C3—21no—
760C22×C3—42no—
761C22×C3—42no—
762C22×C3—42no—
763C22×C3—42no—
764C22×C3—42no—
765C22×C3—42no—
766C22×C3—42no—
767C22×C3—42no—
768C22×C3—42no—
769C22×C3—42no—
770C22×C3—42no—
771C22×C3—42no—
772C22×C3—41no—
773C22×C3—41no—
774C22×C3—41no—
775C22×C3—41no—
776C22×C3—41no—
777C22×C3—41no—
778C22×C3—41no—
779C22×C3—41no—
780C22×C3—41no—
781C22×C3—41no—
782C22×C3—41no—
783C22×C3—41no—
784C22×C3—41no—
785C22×C3—41no—
786C22×C3—41no—
787C22×C3—41no—
788C22×C3—41no—
789C22×C3—41no—
790C22×C3—41no—
791C22×C3—41no—
792C22×C3—41no—
793C22×C3—41no—
794C22×C3—81no—
795C22×C3—81no—
796C22×C3—81no—
797C22×C3—81no—
798C22×C3—81no—
799C22×C3—81no—
800C22×C3—81no—
801C22×C3—81no—
802C22×C3#93514yes—
803C22×C3C3×#12314yes—
804C22×C3C2×#23711yescharacteristic
805C22×C3C2×#23711yescharacteristic
806C22×C3C2×#23711yescharacteristic
807C22×C3#100411yescharacteristic
808C22×C3D3×#4111yescharacteristic
809C22×C3#100911yescharacteristic
810C22×C3C22×#6711yescharacteristic
811C22×C3C22×C3×D411yescharacteristic
812C22×C3C2×C3×#4111yescharacteristic
813C22×C3C2×C3×#4111yescharacteristic
814C22×C3C2×C3×#4111yescharacteristic
815C22×C3C2×C3×#4111yescharacteristic
816C22×C3C3×H(5,𝔽2)11yescharacteristic
817C22×C3C3×H(5,𝔽2)11yescharacteristic
818C3×C4—24no—
819C3×C4—22no—
820C3×C4—22no—
821C3×C4—22no—
822C3×C4—22no—
823C3×C4—42no—
824C3×C4—42no—
825C3×C4—42no—
826C3×C4—41no—
827C3×C4—41no—
828C3×C4—41no—
829C3×C4—41no—
830C3×C4—62no—
831C3×C4—121no—
832C3×C4—121no—
833C3×C4—121no—
834C3×C4—121no—
835C3×C4—121no—
836C3×C4—121no—
837C3×C4—121no—
838Dic3—22no—
839Dic3—41no—
840Dic3—41no—
841Dic3—41no—
842Dic3—41no—
843Dic3—41no—
844Dic3—41no—
845Dic3—41no—
846C32#244411yescharacteristic, complemented, Sylow
847C23—21no—
848C23—21no—
849C23—21no—
850C23—21no—
851C23—21no—
852C23—21no—
853C23—21no—
854C23—21no—
855C23—21no—
856C23—21no—
857C23—21no—
858C23—21no—
859C23—21no—
860C23—21no—
861C23—21no—
862C23—21no—
863C23—21no—
864C23C3×#23712yes—
865C23C3×#23712yes—
866C23C2×C3×#6712yes—
867C23C2×C3×#6712yes—
868C23C23×C3×D311yescharacteristic
869D4—28no—
870D4—44no—
871D4—44no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—32no—
883C2×C4—44no—
884C2×C4—61no—
885C2×C4—61no—
886C2×C4—61no—
887C2×C4—61no—
888C2×C4—61no—
889C2×C4—61no—
890C2×C4—61no—
891C2×C4—61no—
892C2×C4—61no—
893C2×C4—61no—
894C2×C4—61no—
895C2×C4—61no—
896C2×C4—61no—
897C2×C4—61no—
898C2×C4—61no—
899C2×C4—61no—
900C2×C4—61no—
901C2×C4—61no—
902C2×C4—61no—
903C2×C4—61no—
904C2×C4—61no—
905C2×C4—61no—
906C2×C4—61no—
907C2×C4—124no—
908C2×C4—124no—
909C2×C4—124no—
910C2×C4C3×#23712yes—
911C2×C4C2×C3×#6712yes—
912C2×C3—24no—
913C2×C3—24no—
914C2×C3—21no—
915C2×C3—21no—
916C2×C3—21no—
917C2×C3—21no—
918C2×C3—21no—
919C2×C3—21no—
920C2×C3—21no—
921C2×C3—44no—
922C2×C3—42no—
923C2×C3—42no—
924C2×C3—82no—
925C2×C3—82no—
926C2×C3—81no—
927C2×C3—81no—
928C2×C3#560011yescharacteristic
929C2×C3#560111yescharacteristic
930C2×C3#561711yescharacteristic
931C2×C3#561811yescharacteristic
932C2×C3C2×#93511yescharacteristic
933C2×C3#580611yescharacteristic
934C2×C3#582911yescharacteristic
935C2×C3C2×C3×#12311yescharacteristic
936C2×C3C3×#52911yescharacteristic
937C2×C3C3×#53811yescharacteristic
938C2×C3C3×#54611yescharacteristic
939C2×C3C3×#54611yescharacteristic
940C2×C3C3×#55311yescharacteristic
941C2×C3C3×#55311yescharacteristic
942C22—22no—
943C22—22no—
944C22—22no—
945C22—22no—
946C22—22no—
947C22—22no—
948C22—22no—
949C22—22no—
950C22—22no—
951C22—41no—
952C22—41no—
953C22—41no—
954C22—41no—
955C22—41no—
956C22—41no—
957C22—41no—
958C22—41no—
959C22—41no—
960C22—41no—
961C22—41no—
962C22C3×#93514yes—
963C22C2×C3×#23711yescharacteristic
964C22C2×C3×#23711yescharacteristic
965C22C2×C3×#23711yescharacteristic
966C22C3×#100411yescharacteristic
967C22C3×D3×#4111yescharacteristic
968C22C3×#100911yescharacteristic
969C22C22×C3×#6711yescharacteristic
970C4—22no—
971C4—22no—
972C4—41no—
973C4—41no—
974C4—62no—
975C4—121no—
976C4—121no—
977C4—121no—
978C4—121no—
979C4—121no—
980C4—121no—
981C4—121no—
982C3—21no—
983C3#8265611yescharacteristic, direct product factor
984C3C3×#244411yescharacteristic, complemented
985C2—24no—
986C2—42no—
987C2—81no—
988C2C3×#560011yescharacteristic
989C2C3×#560111yescharacteristic
990C2C3×#561711yescharacteristic
991C2C3×#561811yescharacteristic
992C2C2×C3×#93511yescharacteristic
993C2C3×#580611yescharacteristic
994C2C3×#582911yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
Fitting, prime radicalC2×C32×#121C2
socleC23×C32C24
hypercenterC2×C3×#121D3
hypocenterC3C3×#2444
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×#121

Complements

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

NH ≅ G/Ntype
2. C2×C3×D4×Dic3C2semidirect
3. C3×#5222C2semidirect
4. C3×#5220C2semidirect
5. C3×#5220C2semidirect
6. C3×#5220C2semidirect
7. C3×#5220C2semidirect
8. C3×#5210C2semidirect
9. C2×C3×C3⋊#95C2semidirect
10. C3×#4986C2semidirect
11. C3×#4978C2semidirect
12. C3×#4953C2semidirect
13. C3×#4952C2semidirect
14. C3×#4944C2semidirect
15. C3×#4943C2semidirect
17. #82656C3direct (N × H)
59. C2×D4×Dic3C2×C3semidirect
73. #5222C2×C3semidirect
74. #5220C2×C3semidirect
75. #5220C2×C3semidirect
76. #5220C2×C3semidirect
77. #5220C2×C3semidirect
78. #5210C2×C3semidirect
79. C2×C3⋊#95C2×C3semidirect
80. #4986C2×C3semidirect
81. #4978C2×C3semidirect
82. #4953C2×C3semidirect
83. #4952C2×C3semidirect
84. #4944C2×C3semidirect
85. #4943C2×C3semidirect
846. C32#2444semidirect
983. C3#82656direct (N × H)
984. C3C3×#2444semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1212
C2×C3×D4×Dic32
C3×#52222
C3×#52202
C3×#52102
C2×C3×C3⋊#952
C3×#49862
C3×#49782
C3×#49532
C3×#49522
C3×#49442
C3×#49432
C3×#24443
#826563