Finite Group Databasebeta

← C3×#26392 #10644999

Subgroups — C3×#26392 #10644999

Order 768.

962 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#476C211yesmaximal, characteristic, complemented
2C2×C3×#442C211yesmaximal, characteristic
3C3×#2452C211yesmaximal, characteristic, complemented
4C3×D4×C4⋊C4C211yesmaximal, characteristic, complemented
5C3×#2094C211yesmaximal, characteristic, complemented
6C3×#2084C211yesmaximal, characteristic, complemented
7C3×#2067C211yesmaximal, characteristic, complemented
8C3×#2058C211yesmaximal, characteristic, complemented
9C3×#1943C211yesmaximal, characteristic, complemented
10C3×#1917C211yesmaximal, characteristic, complemented
11C3×#1879C211yesmaximal, characteristic
12C3×#1879C211yesmaximal, characteristic
13C3×#1864C211yesmaximal, characteristic, complemented
14C3×#1864C211yesmaximal, characteristic, complemented
15C3×#1862C211yesmaximal, characteristic, complemented
16#26392C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×D8C2211yescharacteristic
18C2×C3×C4⋊Q8C2211yescharacteristic
19C2×C3×C22⋊Q8—21no—
20C2×C3×C4×D4C2211yescharacteristic
21C2×C3×C4×D4C2211yescharacteristic
22C2×C3×C4×D4C2211yescharacteristic
23C2×C3×C4×D4C2211yescharacteristic
24C22×C3×C4⋊C4—21no—
25C3×#476—24no—
26C3×#442—24no—
27C2×C3×#107C2211yescharacteristic
28C2×C3×#106C2211yescharacteristic
29C2×C3×#106C2211yescharacteristic
30C2×C3×#106C2211yescharacteristic
31C2×C3×#106C2211yescharacteristic
32C2×C3×C4⋊C8C2211yescharacteristic
33C2×C3×#102C2211yescharacteristic
34C2×C3×#102C2211yescharacteristic
35C2×C3×#102C2211yescharacteristic
36C2×C3×#102C2211yescharacteristic
37C2×C3×#102C2211yescharacteristic
38C2×C3×#102C2211yescharacteristic
39C2×C3×#97C2211yescharacteristic
40C3×#396—21no—
41C3×#393—21no—
42C3×#390C2211yescharacteristic
43C3×#390C2211yescharacteristic
44C3×#389C2211yescharacteristic
45C3×#389C2211yescharacteristic
46C3×#389C2211yescharacteristic
47C3×#389C2211yescharacteristic
48C3×#385—21no—
49C3×#385—21no—
50C3×#385—21no—
51C3×#384C2211yescharacteristic
52C3×#380—21no—
53C3×C4×C4⋊C4C2211yescharacteristic
54C3×#340C2211yescharacteristic
55C3×#340C2211yescharacteristic
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58C3×#336C2211yescharacteristic
59C3×#336C2211yescharacteristic
60C3×#336C2211yescharacteristic
61C3×#336C2211yescharacteristic
62C2×#476C2×C311yescharacteristic, complemented
63C2×#442C2×C311yescharacteristic
64#2452C2×C311yescharacteristic, complemented
65D4×C4⋊C4C2×C311yescharacteristic, complemented
66#2094C2×C311yescharacteristic, complemented
67#2084C2×C311yescharacteristic, complemented
68#2067C2×C311yescharacteristic, complemented
69#2058C2×C311yescharacteristic, complemented
70#1943C2×C311yescharacteristic, complemented
71#1917C2×C311yescharacteristic, complemented
72#1879C2×C311yescharacteristic
73#1879C2×C311yescharacteristic
74#1864C2×C311yescharacteristic, complemented
75#1864C2×C311yescharacteristic, complemented
76#1862C2×C311yescharacteristic, complemented
77C22×C3×Q8—21no—
78C22×C3×D4C2311yescharacteristic
79C22×C3×D4C2311yescharacteristic
80C23×C3×C4—21no—
81C23×C3×C4—21no—
82C23×C3×C4—21no—
83C23×C3×C4—21no—
84C2×C3×D8—22no—
85C2×C3×D8—22no—
86C2×C3×D8Q814yescomplemented
87C22×C3×C8C2311yescharacteristic
88C22×C3×C8C2311yescharacteristic
89C22×C3×C8C2311yescharacteristic
90C22×C3×C8C2311yescharacteristic
91C3×C4⋊Q8—22no—
92C3×C4⋊Q8—41no—
93C3×C22⋊Q8—44no—
94C3×C4×D4—22no—
95C3×C4×D4—22no—
96C3×C4×D4—22no—
97C3×C4×D4—22no—
98C3×C4×D4—22no—
99C3×C4×D4—41no—
100C3×C4×D4—41no—
101C3×C4×D4—41no—
102C2×C3×C4⋊C4—21no—
103C2×C3×C4⋊C4—21no—
104C2×C3×C4⋊C4—21no—
105C2×C3×C4⋊C4—21no—
106C2×C3×C4⋊C4—21no—
107C2×C3×C4⋊C4—21no—
108C2×C3×C4⋊C4—21no—
109C2×C3×C4⋊C4—44no—
110C2×C3×C4⋊C4D411yescharacteristic
111C2×C3×C4⋊C4D411yescharacteristic
112C2×C3×C4⋊C4C2311yescharacteristic
113C2×C3×C4⋊C4C2311yescharacteristic
114C2×C3×C4⋊C4C2311yescharacteristic
115C2×C3×C4⋊C4C2311yescharacteristic
116C2×C3×C4⋊C4C2311yescharacteristic
117C2×C3×C4⋊C4C2311yescharacteristic
118C2×C3×C22⋊C4—21no—
119C2×C3×C22⋊C4—21no—
120C2×C3×C22⋊C4—21no—
121C2×C3×C22⋊C4—21no—
122C2×C3×C22⋊C4—21no—
123C2×C3×C22⋊C4—21no—
124C2×C3×C22⋊C4—21no—
125C2×C3×C22⋊C4—21no—
126C2×C3×C42C2311yescharacteristic
127C2×C3×C42C2311yescharacteristic
128C2×C3×C42C2311yescharacteristic
129C3×#107—22no—
130C3×#106—22no—
131C3×#106—22no—
132C3×#106—22no—
133C3×#106—41no—
134C3×C4⋊C8—22no—
135C3×#102—22no—
136C3×#102—22no—
137C3×#102—22no—
138C3×#102—22no—
139C3×#102—41no—
140C3×#102D414yes—
141C3×#97—22no—
142C3×#95—21no—
143C3×#95—21no—
144C3×#95—21no—
145C3×#95—21no—
146C3×#95D411yescharacteristic
147C3×#95D411yescharacteristic
148C22×D8C22×C311yescharacteristic
149C2×C4⋊Q8C22×C311yescharacteristic
150C2×C22⋊Q8—21no—
151C2×C4×D4C22×C311yescharacteristic
152C2×C4×D4C22×C311yescharacteristic
153C2×C4×D4C22×C311yescharacteristic
154C2×C4×D4C22×C311yescharacteristic
155C22×C4⋊C4—21no—
156#476—24no—
157#442—24no—
158C2×#107C22×C311yescharacteristic
159C2×#106C22×C311yescharacteristic
160C2×#106C22×C311yescharacteristic
161C2×#106C22×C311yescharacteristic
162C2×#106C22×C311yescharacteristic
163C2×C4⋊C8C22×C311yescharacteristic
164C2×#102C22×C311yescharacteristic
165C2×#102C22×C311yescharacteristic
166C2×#102C22×C311yescharacteristic
167C2×#102C22×C311yescharacteristic
168C2×#102C22×C311yescharacteristic
169C2×#102C22×C311yescharacteristic
170C2×#97C22×C311yescharacteristic
171#396—21no—
172#393—21no—
173#390C22×C311yescharacteristic
174#390C22×C311yescharacteristic
175#389C22×C311yescharacteristic
176#389C22×C311yescharacteristic
177#389C22×C311yescharacteristic
178#389C22×C311yescharacteristic
179#385—21no—
180#385—21no—
181#385—21no—
182#384C22×C311yescharacteristic
183#380—21no—
184C4×C4⋊C4C22×C311yescharacteristic
185#340C22×C311yescharacteristic
186#340C22×C311yescharacteristic
187#340C22×C311yescharacteristic
188#340C22×C311yescharacteristic
189#336C22×C311yescharacteristic
190#336C22×C311yescharacteristic
191#336C22×C311yescharacteristic
192#336C22×C311yescharacteristic
193C24×C3—21no—
194C24×C3—21no—
195C2×C3×Q8—42no—
196C2×C3×Q8—42no—
197C2×C3×Q8—81no—
198C2×C3×D4—21no—
199C2×C3×D4—21no—
200C2×C3×D4—21no—
201C2×C3×D4—21no—
202C2×C3×D4—21no—
203C2×C3×D4—21no—
204C2×C3×D4—21no—
205C2×C3×D4—21no—
206C2×C3×D4C2×D412yes—
207C2×C3×D4C2×Q812yes—
208C2×C3×D4C2×Q812yes—
209C2×C3×D4#4112yes—
210C22×C3×C4—24no—
211C22×C3×C4—21no—
212C22×C3×C4—21no—
213C22×C3×C4—21no—
214C22×C3×C4—21no—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—42no—
218C22×C3×C4—42no—
219C22×C3×C4—42no—
220C22×C3×C4—42no—
221C22×C3×C4—42no—
222C22×C3×C4—42no—
223C22×C3×C4—42no—
224C22×C3×C4—42no—
225C22×C3×C4—81no—
226C22×C3×C4—81no—
227C22×C3×C4—81no—
228C22×C3×C4C2×D411yescharacteristic
229C22×C3×C4C2×D411yescharacteristic
230C22×C3×C4C2×D411yescharacteristic
231C22×C3×C4C2×D411yescharacteristic
232C22×C3×C4C2×D411yescharacteristic
233C22×C3×C4C2×D411yescharacteristic
234C22×C3×C4C2411yescharacteristic
235C3×D8—28no—
236C2×C3×C8—21no—
237C2×C3×C8—21no—
238C2×C3×C8—21no—
239C2×C3×C8—21no—
240C2×C3×C8—21no—
241C2×C3×C8—21no—
242C2×C3×C8—21no—
243C2×C3×C8—21no—
244C2×C3×C8—21no—
245C2×C3×C8—21no—
246C2×C3×C8C2×D412yes—
247C2×C3×C8C2×Q812yes—
248C3×C4⋊C4—22no—
249C3×C4⋊C4—22no—
250C3×C4⋊C4—21no—
251C3×C4⋊C4—21no—
252C3×C4⋊C4—21no—
253C3×C4⋊C4—21no—
254C3×C4⋊C4—21no—
255C3×C4⋊C4—21no—
256C3×C4⋊C4—21no—
257C3×C4⋊C4—21no—
258C3×C4⋊C4—21no—
259C3×C4⋊C4—21no—
260C3×C4⋊C4—42no—
261C3×C4⋊C4—42no—
262C3×C4⋊C4—42no—
263C3×C4⋊C4—42no—
264C3×C4⋊C4—42no—
265C3×C4⋊C4—42no—
266C3×C4⋊C4—81no—
267C3×C4⋊C4C2×D412yes—
268C3×C4⋊C4#4112yes—
269C3×C22⋊C4—24no—
270C3×C22⋊C4—42no—
271C3×C22⋊C4—42no—
272C3×C22⋊C4—42no—
273C3×C22⋊C4—42no—
274C3×C22⋊C4—42no—
275C3×C22⋊C4—42no—
276C3×C22⋊C4—81no—
277C3×C42—21no—
278C3×C42—21no—
279C3×C42—21no—
280C3×C42—21no—
281C3×C42—21no—
282C3×C42—21no—
283C22×Q8—21no—
284C22×D4C23×C311yescharacteristic
285C22×D4C23×C311yescharacteristic
286C23×C4—21no—
287C23×C4—21no—
288C23×C4—21no—
289C23×C4—21no—
290C2×D8—22no—
291C2×D8—22no—
292C2×D8C3×Q814yescomplemented
293C22×C8C23×C311yescharacteristic
294C22×C8C23×C311yescharacteristic
295C22×C8C23×C311yescharacteristic
296C22×C8C23×C311yescharacteristic
297C4⋊Q8—22no—
298C4⋊Q8—41no—
299C22⋊Q8—44no—
300C4×D4—22no—
301C4×D4—22no—
302C4×D4—22no—
303C4×D4—22no—
304C4×D4—22no—
305C4×D4—41no—
306C4×D4—41no—
307C4×D4—41no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—44no—
316C2×C4⋊C4C3×D411yescharacteristic
317C2×C4⋊C4C3×D411yescharacteristic
318C2×C4⋊C4C23×C311yescharacteristic
319C2×C4⋊C4C23×C311yescharacteristic
320C2×C4⋊C4C23×C311yescharacteristic
321C2×C4⋊C4C23×C311yescharacteristic
322C2×C4⋊C4C23×C311yescharacteristic
323C2×C4⋊C4C23×C311yescharacteristic
324C2×C22⋊C4—21no—
325C2×C22⋊C4—21no—
326C2×C22⋊C4—21no—
327C2×C22⋊C4—21no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C42C23×C311yescharacteristic
333C2×C42C23×C311yescharacteristic
334C2×C42C23×C311yescharacteristic
335#107—22no—
336#106—22no—
337#106—22no—
338#106—22no—
339#106—41no—
340C4⋊C8—22no—
341#102—22no—
342#102—22no—
343#102—22no—
344#102—22no—
345#102—41no—
346#102C3×D414yes—
347#97—22no—
348#95—21no—
349#95—21no—
350#95—21no—
351#95—21no—
352#95C3×D411yescharacteristic
353#95C3×D411yescharacteristic
354C23×C3—22no—
355C23×C3—22no—
356C23×C3—22no—
357C23×C3—22no—
358C23×C3—41no—
359C23×C3—41no—
360C23×C3—41no—
361C23×C3—41no—
362C23×C3—41no—
363C23×C3—41no—
364C23×C3—41no—
365C23×C3—41no—
366C23×C3—41no—
367C23×C3—41no—
368C23×C3C22×D411yescharacteristic
369C3×Q8—84no—
370C3×D4—22no—
371C3×D4—22no—
372C3×D4—22no—
373C3×D4—22no—
374C3×D4—22no—
375C3×D4—41no—
376C3×D4—41no—
377C3×D4C22⋊Q814yescomplemented
378C2×C3×C4—21no—
379C2×C3×C4—21no—
380C2×C3×C4—21no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—22no—
384C2×C3×C4—21no—
385C2×C3×C4—21no—
386C2×C3×C4—21no—
387C2×C3×C4—22no—
388C2×C3×C4—21no—
389C2×C3×C4—21no—
390C2×C3×C4—21no—
391C2×C3×C4—21no—
392C2×C3×C4—21no—
393C2×C3×C4—21no—
394C2×C3×C4—21no—
395C2×C3×C4—21no—
396C2×C3×C4—48no—
397C2×C3×C4—41no—
398C2×C3×C4—41no—
399C2×C3×C4—41no—
400C2×C3×C4—41no—
401C2×C3×C4—41no—
402C2×C3×C4—41no—
403C2×C3×C4—41no—
404C2×C3×C4—41no—
405C2×C3×C4—41no—
406C2×C3×C4—41no—
407C2×C3×C4—41no—
408C2×C3×C4—41no—
409C2×C3×C4—41no—
410C2×C3×C4—41no—
411C2×C3×C4—41no—
412C2×C3×C4—41no—
413C2×C3×C4—84no—
414C2×C3×C4—84no—
415C2×C3×C4—84no—
416C2×C3×C4AGL(1,ℤ/8)12yes—
417C2×C3×C4AGL(1,ℤ/8)12yes—
418C2×C3×C4C22×D411yescharacteristic
419C2×C3×C4C22×Q811yescharacteristic
420C2×C3×C4C2×#4111yescharacteristic
421C2×C3×C4C2×#4111yescharacteristic
422C2×C3×C4H(5,𝔽2)11yescharacteristic
423C2×C3×C42−1+411yescharacteristic
424C3×C8—22no—
425C3×C8—22no—
426C3×C8—41no—
427C3×C8—41no—
428C24—21no—
429C24—21no—
430C2×Q8—42no—
431C2×Q8—42no—
432C2×Q8—81no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4C2×C3×D412yes—
442C2×D4C2×C3×Q812yes—
443C2×D4C2×C3×Q812yes—
444C2×D4C3×#4112yes—
445C22×C4—24no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—42no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—42no—
456C22×C4—42no—
457C22×C4—42no—
458C22×C4—42no—
459C22×C4—42no—
460C22×C4—81no—
461C22×C4—81no—
462C22×C4—81no—
463C22×C4C2×C3×D411yescharacteristic
464C22×C4C2×C3×D411yescharacteristic
465C22×C4C2×C3×D411yescharacteristic
466C22×C4C2×C3×D411yescharacteristic
467C22×C4C2×C3×D411yescharacteristic
468C22×C4C2×C3×D411yescharacteristic
469C22×C4C24×C311yescharacteristic
470D8—28no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8C2×C3×D412yes—
482C2×C8C2×C3×Q812yes—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—42no—
496C4⋊C4—42no—
497C4⋊C4—42no—
498C4⋊C4—42no—
499C4⋊C4—42no—
500C4⋊C4—42no—
501C4⋊C4—81no—
502C4⋊C4C2×C3×D412yes—
503C4⋊C4C3×#4112yes—
504C22⋊C4—24no—
505C22⋊C4—42no—
506C22⋊C4—42no—
507C22⋊C4—42no—
508C22⋊C4—42no—
509C22⋊C4—42no—
510C22⋊C4—42no—
511C22⋊C4—81no—
512C42—21no—
513C42—21no—
514C42—21no—
515C42—21no—
516C42—21no—
517C42—21no—
518C22×C3—24no—
519C22×C3—42no—
520C22×C3—42no—
521C22×C3—42no—
522C22×C3—42no—
523C22×C3—42no—
524C22×C3—42no—
525C22×C3—42no—
526C22×C3—42no—
527C22×C3—42no—
528C22×C3—81no—
529C22×C3—81no—
530C22×C3—81no—
531C22×C3—81no—
532C22×C3#52511yescharacteristic
533C22×C3D4211yescharacteristic
534C22×C3D4×Q811yescharacteristic
535C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
536C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
537C22×C3#57711yescharacteristic
538C22×C3#57711yescharacteristic
539C3×C4—22no—
540C3×C4—22no—
541C3×C4—42no—
542C3×C4—41no—
543C3×C4—41no—
544C3×C4—41no—
545C3×C4—41no—
546C3×C4—42no—
547C3×C4—81no—
548C3×C4—81no—
549C3×C4—81no—
550C3×C4—81no—
551C3×C4C2×C22⋊Q811yescharacteristic
552C3×C4#53911yescharacteristic
553C3×C4#54711yescharacteristic
554C3×C4#55411yescharacteristic
555C23—22no—
556C23—22no—
557C23—22no—
558C23—22no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23C22×C3×D411yescharacteristic
570Q8—84no—
571D4—22no—
572D4—22no—
573D4—22no—
574D4—22no—
575D4—22no—
576D4—41no—
577D4—41no—
578D4C3×C22⋊Q814yescomplemented
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—22no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—22no—
597C2×C4—48no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—84no—
615C2×C4—84no—
616C2×C4—84no—
617C2×C4C3×AGL(1,ℤ/8)12yes—
618C2×C4C3×AGL(1,ℤ/8)12yes—
619C2×C4C22×C3×D411yescharacteristic
620C2×C4C22×C3×Q811yescharacteristic
621C2×C4C2×C3×#4111yescharacteristic
622C2×C4C2×C3×#4111yescharacteristic
623C2×C4C3×H(5,𝔽2)11yescharacteristic
624C2×C4C3×2−1+411yescharacteristic
625C8—22no—
626C8—22no—
627C8—41no—
628C8—41no—
629C2×C3—44no—
630C2×C3—82no—
631C2×C3#244911yescharacteristic
632C2×C3#310911yescharacteristic
633C2×C3#312511yescharacteristic
634C2×C3#326511yescharacteristic
635C2×C3#327211yescharacteristic
636C2×C3#338411yescharacteristic
637C2×C3#338411yescharacteristic
638C22—24no—
639C22—42no—
640C22—42no—
641C22—42no—
642C22—42no—
643C22—42no—
644C22—42no—
645C22—42no—
646C22—42no—
647C22—42no—
648C22—81no—
649C22—81no—
650C22—81no—
651C22—81no—
652C22C3×#52511yescharacteristic
653C22C3×D4211yescharacteristic
654C22C3×D4×Q811yescharacteristic
655C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
656C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
657C22C3×#57711yescharacteristic
658C22C3×#57711yescharacteristic
659C4—22no—
660C4—22no—
661C4—41no—
662C4—41no—
663C4—41no—
664C4—42no—
665C4—42no—
666C4—41no—
667C4—81no—
668C4—81no—
669C4—81no—
670C4—81no—
671C4C2×C3×C22⋊Q811yescharacteristic
672C4C3×#53911yescharacteristic
673C4C3×#54711yescharacteristic
674C4C3×#55411yescharacteristic
675C3#2639211yescharacteristic, direct product factor, Sylow
676C2—44no—
677C2—82no—
678C2C3×#244911yescharacteristic
679C2C3×#310911yescharacteristic
680C2C3×#312511yescharacteristic
681C2C3×#326511yescharacteristic
682C2C3×#327211yescharacteristic
683C2C3×#338411yescharacteristic
684C2C3×#338411yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC22×C3×D8C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C3×C4×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#476C2semidirect
3. C3×#2452C2semidirect
4. C3×D4×C4⋊C4C2semidirect
5. C3×#2094C2semidirect
6. C3×#2084C2semidirect
7. C3×#2067C2semidirect
8. C3×#2058C2semidirect
9. C3×#1943C2semidirect
10. C3×#1917C2semidirect
13. C3×#1864C2semidirect
14. C3×#1864C2semidirect
15. C3×#1862C2semidirect
16. #26392C3direct (N × H)
62. C2×#476C2×C3semidirect
64. #2452C2×C3semidirect
65. D4×C4⋊C4C2×C3semidirect
66. #2094C2×C3semidirect
67. #2084C2×C3semidirect
68. #2067C2×C3semidirect
69. #2058C2×C3semidirect
70. #1943C2×C3semidirect
71. #1917C2×C3semidirect
74. #1864C2×C3semidirect
75. #1864C2×C3semidirect
76. #1862C2×C3semidirect
86. C2×C3×D8Q8semidirect
292. C2×D8C3×Q8semidirect
377. C3×D4C22⋊Q8semidirect
578. D4C3×C22⋊Q8semidirect
675. C3#26392direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#4762
C2×C3×#4422
C3×#24522
C3×D4×C4⋊C42
C3×#20942
C3×#20842
C3×#20672
C3×#20582
C3×#19432
C3×#19172
C3×#18792
C3×#18642
C3×#18622
#263923