Finite Group Databasebeta

← C3×#25545 #10644152

Subgroups — C3×#25545 #10644152

Order 768.

1158 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#554C211yesmaximal, characteristic
2C2×C3×#484C211yesmaximal, characteristic, complemented
3C2×C3×#467C211yesmaximal, characteristic, complemented
4C3×#2417C211yesmaximal, characteristic
5C3×#2057C211yesmaximal, characteristic, complemented
6C3×#2036C211yesmaximal, characteristic, complemented
7C3×#2024C211yesmaximal, characteristic, complemented
8C3×#2001C211yesmaximal, characteristic, complemented
9C3×#1878C211yesmaximal, characteristic, complemented
10C3×#1872C211yesmaximal, characteristic, complemented
11C3×#1872C211yesmaximal, characteristic, complemented
12C3×#1869C211yesmaximal, characteristic
13C3×#1863C211yesmaximal, characteristic, complemented
14C3×#1852C211yesmaximal, characteristic, complemented
15C2×C3×#340C211yesmaximal, characteristic, complemented
16#25545C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×Q16C2211yescharacteristic
18C23×C3×C8C2211yescharacteristic
19C3×#554—24no—
20C3×#554—24no—
21C2×C3×C4⋊Q8C2211yescharacteristic
22C2×C3×#125—21no—
23C2×C3×C22⋊Q8—21no—
24C2×C3×C22⋊Q8—21no—
25C2×C3×C22⋊Q8C2211yescharacteristic
26C2×C3×C22⋊Q8C2211yescharacteristic
27C2×C3×C22⋊Q8C2211yescharacteristic
28C2×C3×C22⋊Q8C2211yescharacteristic
29C2×C3×C4×Q8C2211yescharacteristic
30C2×C3×C4×D4—21no—
31C2×C3×C4×D4C2211yescharacteristic
32C22×C3×C4⋊C4C2211yescharacteristic
33C22×C3×C4⋊C4C2211yescharacteristic
34C22×C3×C4⋊C4C2211yescharacteristic
35C3×#484—24no—
36C3×#467—24no—
37C2×C3×#107C2211yescharacteristic
38C2×C3×#107C2211yescharacteristic
39C2×C3×#107C2211yescharacteristic
40C2×C3×#103C2211yescharacteristic
41C2×C3×#103C2211yescharacteristic
42C2×C3×#103C2211yescharacteristic
43C2×C3×#103C2211yescharacteristic
44C2×C3×#103C2211yescharacteristic
45C2×C3×#103C2211yescharacteristic
46C2×C3×C22⋊C8C2211yescharacteristic
47C2×C3×C22⋊C8C2211yescharacteristic
48C2×C3×C22⋊C8C2211yescharacteristic
49C3×#398—21no—
50C3×#396—21no—
51C3×#391C2211yescharacteristic
52C3×#389C2211yescharacteristic
53C3×#386—21no—
54C3×#380—21no—
55C3×#380C2211yescharacteristic
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#340C2211yescharacteristic
61C3×#340C2211yescharacteristic
62C3×#336C2211yescharacteristic
63C3×#336C2211yescharacteristic
64C2×#554C2×C311yescharacteristic
65C2×#484C2×C311yescharacteristic, complemented
66C2×#467C2×C311yescharacteristic, complemented
67#2417C2×C311yescharacteristic
68#2057C2×C311yescharacteristic, complemented
69#2036C2×C311yescharacteristic, complemented
70#2024C2×C311yescharacteristic, complemented
71#2001C2×C311yescharacteristic, complemented
72#1878C2×C311yescharacteristic, complemented
73#1872C2×C311yescharacteristic, complemented
74#1872C2×C311yescharacteristic, complemented
75#1869C2×C311yescharacteristic
76#1863C2×C311yescharacteristic, complemented
77#1852C2×C311yescharacteristic, complemented
78C2×#340C2×C311yescharacteristic, complemented
79C22×C3×Q8—21no—
80C22×C3×Q8C2311yescharacteristic
81C22×C3×Q8C2311yescharacteristic
82C22×C3×D4D411yescharacteristic
83C23×C3×C4—21no—
84C23×C3×C4—21no—
85C23×C3×C4—21no—
86C23×C3×C4C2311yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C2×C3×Q16—22no—
89C2×C3×Q16—22no—
90C2×C3×Q16—41no—
91C22×C3×C8—22no—
92C22×C3×C8—22no—
93C22×C3×C8—41no—
94C22×C3×C8C2311yescharacteristic
95C22×C3×C8C2311yescharacteristic
96C22×C3×C8C2311yescharacteristic
97C22×C3×C8C2311yescharacteristic
98C3×C4⋊Q8—22no—
99C3×C4⋊Q8—22no—
100C3×#125—28no—
101C3×C22⋊Q8—28no—
102C3×C22⋊Q8—28no—
103C3×C22⋊Q8—22no—
104C3×C22⋊Q8—22no—
105C3×C22⋊Q8—22no—
106C3×C22⋊Q8—22no—
107C3×C22⋊Q8—22no—
108C3×C22⋊Q8—22no—
109C3×C22⋊Q8—41no—
110C3×C22⋊Q8D414yes—
111C3×C4×Q8—22no—
112C3×C4×Q8—22no—
113C3×C4×D4—28no—
114C3×C4×D4—22no—
115C3×C4×D4—22no—
116C2×C3×C4⋊C4—21no—
117C2×C3×C4⋊C4—21no—
118C2×C3×C4⋊C4—22no—
119C2×C3×C4⋊C4—21no—
120C2×C3×C4⋊C4—21no—
121C2×C3×C4⋊C4—21no—
122C2×C3×C4⋊C4—21no—
123C2×C3×C4⋊C4—22no—
124C2×C3×C4⋊C4—22no—
125C2×C3×C4⋊C4—22no—
126C2×C3×C4⋊C4—21no—
127C2×C3×C4⋊C4—21no—
128C2×C3×C4⋊C4—21no—
129C2×C3×C4⋊C4—21no—
130C2×C3×C4⋊C4—41no—
131C2×C3×C4⋊C4D411yescharacteristic
132C2×C3×C4⋊C4D414yes—
133C2×C3×C4⋊C4C2311yescharacteristic
134C2×C3×C4⋊C4C2311yescharacteristic
135C2×C3×C4⋊C4C2311yescharacteristic
136C2×C3×C4⋊C4C2311yescharacteristic
137C2×C3×C4⋊C4C2311yescharacteristic
138C2×C3×C4⋊C4C2311yescharacteristic
139C2×C3×C22⋊C4—21no—
140C2×C3×C22⋊C4—21no—
141C2×C3×C22⋊C4—21no—
142C2×C3×C22⋊C4—21no—
143C2×C3×C22⋊C4—21no—
144C2×C3×C22⋊C4D411yescharacteristic
145C2×C3×C22⋊C4D411yescharacteristic
146C2×C3×C42—21no—
147C2×C3×C42C2311yescharacteristic
148C3×#107—22no—
149C3×#107—22no—
150C3×#107—22no—
151C3×#103—22no—
152C3×#103—22no—
153C3×#103—22no—
154C3×#103—22no—
155C3×#103—22no—
156C3×#103—41no—
157C3×C22⋊C8—22no—
158C3×C22⋊C8—22no—
159C3×C22⋊C8—41no—
160C3×#95—21no—
161C3×#95—21no—
162C3×#95—21no—
163C3×#95—21no—
164C22×Q16C22×C311yescharacteristic
165C23×C8C22×C311yescharacteristic
166#554—24no—
167#554—24no—
168C2×C4⋊Q8C22×C311yescharacteristic
169C2×#125—21no—
170C2×C22⋊Q8—21no—
171C2×C22⋊Q8—21no—
172C2×C22⋊Q8C22×C311yescharacteristic
173C2×C22⋊Q8C22×C311yescharacteristic
174C2×C22⋊Q8C22×C311yescharacteristic
175C2×C22⋊Q8C22×C311yescharacteristic
176C2×C4×Q8C22×C311yescharacteristic
177C2×C4×D4—21no—
178C2×C4×D4C22×C311yescharacteristic
179C22×C4⋊C4C22×C311yescharacteristic
180C22×C4⋊C4C22×C311yescharacteristic
181C22×C4⋊C4C22×C311yescharacteristic
182#484—24no—
183#467—24no—
184C2×#107C22×C311yescharacteristic
185C2×#107C22×C311yescharacteristic
186C2×#107C22×C311yescharacteristic
187C2×#103C22×C311yescharacteristic
188C2×#103C22×C311yescharacteristic
189C2×#103C22×C311yescharacteristic
190C2×#103C22×C311yescharacteristic
191C2×#103C22×C311yescharacteristic
192C2×#103C22×C311yescharacteristic
193C2×C22⋊C8C22×C311yescharacteristic
194C2×C22⋊C8C22×C311yescharacteristic
195C2×C22⋊C8C22×C311yescharacteristic
196#398—21no—
197#396—21no—
198#391C22×C311yescharacteristic
199#389C22×C311yescharacteristic
200#386—21no—
201#380—21no—
202#380C22×C311yescharacteristic
203#340C22×C311yescharacteristic
204#340C22×C311yescharacteristic
205#340C22×C311yescharacteristic
206#340C22×C311yescharacteristic
207#340C22×C311yescharacteristic
208#340C22×C311yescharacteristic
209#336C22×C311yescharacteristic
210#336C22×C311yescharacteristic
211C24×C3C2×D411yescharacteristic
212C24×C3C2×D411yescharacteristic
213C2×C3×Q8—24no—
214C2×C3×Q8—21no—
215C2×C3×Q8—21no—
216C2×C3×Q8—21no—
217C2×C3×Q8—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8—21no—
224C2×C3×Q8—21no—
225C2×C3×Q8—81no—
226C2×C3×Q8—81no—
227C2×C3×Q8C2×D412yes—
228C2×C3×D4—22no—
229C2×C3×D4—22no—
230C2×C3×D4Q1614yescomplemented
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—24no—
241C22×C3×C4—24no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—42no—
252C22×C3×C4—42no—
253C22×C3×C4—81no—
254C22×C3×C4—81no—
255C22×C3×C4—81no—
256C22×C3×C4—81no—
257C22×C3×C4—81no—
258C22×C3×C4C2×D411yescharacteristic
259C22×C3×C4C2×D411yescharacteristic
260C22×C3×C4C2×D411yescharacteristic
261C22×C3×C4C2×D412yes—
262C22×C3×C4C2×D412yes—
263C22×C3×C4C2×D411yescharacteristic
264C22×C3×C4C2411yescharacteristic
265C3×Q16—44no—
266C2×C3×C8—21no—
267C2×C3×C8—21no—
268C2×C3×C8—21no—
269C2×C3×C8—21no—
270C2×C3×C8—21no—
271C2×C3×C8—21no—
272C2×C3×C8—21no—
273C2×C3×C8—21no—
274C2×C3×C8—21no—
275C2×C3×C8—21no—
276C2×C3×C8—21no—
277C2×C3×C8—44no—
278C2×C3×C8#4112yes—
279C3×C4⋊C4—24no—
280C3×C4⋊C4—24no—
281C3×C4⋊C4—24no—
282C3×C4⋊C4—24no—
283C3×C4⋊C4—24no—
284C3×C4⋊C4—24no—
285C3×C4⋊C4—22no—
286C3×C4⋊C4—21no—
287C3×C4⋊C4—21no—
288C3×C4⋊C4—21no—
289C3×C4⋊C4—21no—
290C3×C4⋊C4—21no—
291C3×C4⋊C4—21no—
292C3×C4⋊C4—21no—
293C3×C4⋊C4—21no—
294C3×C4⋊C4—42no—
295C3×C4⋊C4—42no—
296C3×C4⋊C4—42no—
297C3×C4⋊C4—81no—
298C3×C4⋊C4C2×D412yes—
299C3×C4⋊C4C2×D412yes—
300C3×C4⋊C4C2×D412yes—
301C3×C4⋊C4#4112yes—
302C3×C22⋊C4—24no—
303C3×C22⋊C4—24no—
304C3×C22⋊C4—22no—
305C3×C22⋊C4—22no—
306C3×C22⋊C4—42no—
307C3×C22⋊C4—42no—
308C3×C22⋊C4—81no—
309C3×C42—24no—
310C3×C42—21no—
311C3×C42—21no—
312C22×Q8—21no—
313C22×Q8C23×C311yescharacteristic
314C22×Q8C23×C311yescharacteristic
315C22×D4C3×D411yescharacteristic
316C23×C4—21no—
317C23×C4—21no—
318C23×C4—21no—
319C23×C4C23×C311yescharacteristic
320C23×C4C23×C311yescharacteristic
321C2×Q16—22no—
322C2×Q16—22no—
323C2×Q16—41no—
324C22×C8—22no—
325C22×C8—22no—
326C22×C8—41no—
327C22×C8C23×C311yescharacteristic
328C22×C8C23×C311yescharacteristic
329C22×C8C23×C311yescharacteristic
330C22×C8C23×C311yescharacteristic
331C4⋊Q8—22no—
332C4⋊Q8—22no—
333#125—28no—
334C22⋊Q8—28no—
335C22⋊Q8—28no—
336C22⋊Q8—22no—
337C22⋊Q8—22no—
338C22⋊Q8—22no—
339C22⋊Q8—22no—
340C22⋊Q8—22no—
341C22⋊Q8—22no—
342C22⋊Q8—41no—
343C22⋊Q8C3×D414yes—
344C4×Q8—22no—
345C4×Q8—22no—
346C4×D4—28no—
347C4×D4—22no—
348C4×D4—22no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—41no—
364C2×C4⋊C4C3×D411yescharacteristic
365C2×C4⋊C4C3×D414yes—
366C2×C4⋊C4C23×C311yescharacteristic
367C2×C4⋊C4C23×C311yescharacteristic
368C2×C4⋊C4C23×C311yescharacteristic
369C2×C4⋊C4C23×C311yescharacteristic
370C2×C4⋊C4C23×C311yescharacteristic
371C2×C4⋊C4C23×C311yescharacteristic
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4C3×D411yescharacteristic
378C2×C22⋊C4C3×D411yescharacteristic
379C2×C42—21no—
380C2×C42C23×C311yescharacteristic
381#107—22no—
382#107—22no—
383#107—22no—
384#103—22no—
385#103—22no—
386#103—22no—
387#103—22no—
388#103—22no—
389#103—41no—
390C22⋊C8—22no—
391C22⋊C8—22no—
392C22⋊C8—41no—
393#95—21no—
394#95—21no—
395#95—21no—
396#95—21no—
397C23×C3—21no—
398C23×C3—21no—
399C23×C3—21no—
400C23×C3—21no—
401C23×C3—21no—
402C23×C3—21no—
403C23×C3—21no—
404C23×C3—21no—
405C23×C3—21no—
406C23×C3—21no—
407C23×C3#12012yes—
408C23×C3C2×Q1612yes—
409C23×C3C2×Q1612yes—
410C23×C3#13712yes—
411C23×C3C22×D411yescharacteristic
412C3×Q8—22no—
413C3×Q8—22no—
414C3×Q8—41no—
415C3×Q8—41no—
416C3×Q8—41no—
417C3×Q8—41no—
418C3×Q8—41no—
419C3×Q8—41no—
420C3×Q8—84no—
421C3×D4—28no—
422C2×C3×C4—21no—
423C2×C3×C4—21no—
424C2×C3×C4—21no—
425C2×C3×C4—21no—
426C2×C3×C4—22no—
427C2×C3×C4—22no—
428C2×C3×C4—22no—
429C2×C3×C4—22no—
430C2×C3×C4—22no—
431C2×C3×C4—21no—
432C2×C3×C4—22no—
433C2×C3×C4—21no—
434C2×C3×C4—22no—
435C2×C3×C4—22no—
436C2×C3×C4—22no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—41no—
442C2×C3×C4—41no—
443C2×C3×C4—41no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4—41no—
447C2×C3×C4—41no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4—41no—
457C2×C3×C4—41no—
458C2×C3×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4—41no—
461C2×C3×C4—41no—
462C2×C3×C4—41no—
463C2×C3×C4—41no—
464C2×C3×C4—84no—
465C2×C3×C4—84no—
466C2×C3×C4—84no—
467C2×C3×C4#12012yes—
468C2×C3×C4C2×Q1612yes—
469C2×C3×C4C22×D411yescharacteristic
470C2×C3×C4C22×D411yescharacteristic
471C2×C3×C4C2×#4111yescharacteristic
472C2×C3×C4C2×#4111yescharacteristic
473C2×C3×C4H(5,𝔽2)11yescharacteristic
474C2×C3×C42−1+411yescharacteristic
475C3×C8—22no—
476C3×C8—41no—
477C3×C8—41no—
478C3×C8—41no—
479C24C2×C3×D411yescharacteristic
480C24C2×C3×D411yescharacteristic
481C2×Q8—24no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—81no—
494C2×Q8—81no—
495C2×Q8C2×C3×D412yes—
496C2×D4—22no—
497C2×D4—22no—
498C2×D4C3×Q1614yescomplemented
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—24no—
509C22×C4—24no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—81no—
522C22×C4—81no—
523C22×C4—81no—
524C22×C4—81no—
525C22×C4—81no—
526C22×C4C2×C3×D411yescharacteristic
527C22×C4C2×C3×D411yescharacteristic
528C22×C4C2×C3×D411yescharacteristic
529C22×C4C2×C3×D412yes—
530C22×C4C2×C3×D412yes—
531C22×C4C2×C3×D411yescharacteristic
532C22×C4C24×C311yescharacteristic
533Q16—44no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—44no—
546C2×C8C3×#4112yes—
547C4⋊C4—24no—
548C4⋊C4—24no—
549C4⋊C4—24no—
550C4⋊C4—24no—
551C4⋊C4—24no—
552C4⋊C4—24no—
553C4⋊C4—22no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—42no—
563C4⋊C4—42no—
564C4⋊C4—42no—
565C4⋊C4—81no—
566C4⋊C4C2×C3×D412yes—
567C4⋊C4C2×C3×D412yes—
568C4⋊C4C2×C3×D412yes—
569C4⋊C4C3×#4112yes—
570C22⋊C4—24no—
571C22⋊C4—24no—
572C22⋊C4—22no—
573C22⋊C4—22no—
574C22⋊C4—42no—
575C22⋊C4—42no—
576C22⋊C4—81no—
577C42—24no—
578C42—21no—
579C42—21no—
580C22×C3—22no—
581C22×C3—22no—
582C22×C3—22no—
583C22×C3—22no—
584C22×C3—22no—
585C22×C3—22no—
586C22×C3—22no—
587C22×C3—22no—
588C22×C3—22no—
589C22×C3—41no—
590C22×C3—41no—
591C22×C3—41no—
592C22×C3—41no—
593C22×C3#45114yes—
594C22×C3C2×#12011yescharacteristic
595C22×C3#54611yescharacteristic
596C22×C3#54711yescharacteristic
597C22×C3C22×Q1611yescharacteristic
598C22×C3C2×#13711yescharacteristic
599C22×C3#57611yescharacteristic
600C22×C3#57711yescharacteristic
601C3×C4—22no—
602C3×C4—22no—
603C3×C4—41no—
604C3×C4—42no—
605C3×C4—41no—
606C3×C4—42no—
607C3×C4—42no—
608C3×C4—42no—
609C3×C4—42no—
610C3×C4—81no—
611C3×C4—81no—
612C3×C4—81no—
613C3×C4#53211yescharacteristic
614C3×C4#53711yescharacteristic
615C3×C4#54611yescharacteristic
616C3×C4#54711yescharacteristic
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23C3×#12012yes—
628C23C2×C3×Q1612yes—
629C23C2×C3×Q1612yes—
630C23C3×#13712yes—
631C23C22×C3×D411yescharacteristic
632Q8—22no—
633Q8—22no—
634Q8—41no—
635Q8—41no—
636Q8—41no—
637Q8—41no—
638Q8—41no—
639Q8—41no—
640Q8—84no—
641D4—28no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—22no—
653C2×C4—21no—
654C2×C4—22no—
655C2×C4—21no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—84no—
685C2×C4—84no—
686C2×C4—84no—
687C2×C4C3×#12012yes—
688C2×C4C2×C3×Q1612yes—
689C2×C4C22×C3×D411yescharacteristic
690C2×C4C22×C3×D411yescharacteristic
691C2×C4C2×C3×#4111yescharacteristic
692C2×C4C2×C3×#4111yescharacteristic
693C2×C4C3×H(5,𝔽2)11yescharacteristic
694C2×C4C3×2−1+411yescharacteristic
695C8—22no—
696C8—41no—
697C8—41no—
698C8—41no—
699C2×C3—24no—
700C2×C3—42no—
701C2×C3#243011yescharacteristic
702C2×C3C2×#45111yescharacteristic
703C2×C3#301211yescharacteristic
704C2×C3#329911yescharacteristic
705C2×C3#331411yescharacteristic
706C2×C3#333811yescharacteristic
707C2×C3#334411yescharacteristic
708C22—22no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—22no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22C3×#45114yes—
722C22C2×C3×#12011yescharacteristic
723C22C3×#54611yescharacteristic
724C22C3×#54711yescharacteristic
725C22C22×C3×Q1611yescharacteristic
726C22C2×C3×#13711yescharacteristic
727C22C3×#57611yescharacteristic
728C22C3×#57711yescharacteristic
729C4—22no—
730C4—22no—
731C4—41no—
732C4—42no—
733C4—41no—
734C4—42no—
735C4—42no—
736C4—42no—
737C4—42no—
738C4—81no—
739C4—81no—
740C4—81no—
741C4C3×#53211yescharacteristic
742C4C3×#53711yescharacteristic
743C4C3×#54611yescharacteristic
744C4C3×#54711yescharacteristic
745C3#2554511yescharacteristic, direct product factor, Sylow
746C2—24no—
747C2—42no—
748C2C3×#243011yescharacteristic
749C2C2×C3×#45111yescharacteristic
750C2C3×#301211yescharacteristic
751C2C3×#329911yescharacteristic
752C2C3×#331411yescharacteristic
753C2C3×#333811yescharacteristic
754C2C3×#334411yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC22×C3×D4D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C2×C3×C4×D4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×#484C2semidirect
3. C2×C3×#467C2semidirect
5. C3×#2057C2semidirect
6. C3×#2036C2semidirect
7. C3×#2024C2semidirect
8. C3×#2001C2semidirect
9. C3×#1878C2semidirect
10. C3×#1872C2semidirect
11. C3×#1872C2semidirect
13. C3×#1863C2semidirect
14. C3×#1852C2semidirect
15. C2×C3×#340C2semidirect
16. #25545C3direct (N × H)
65. C2×#484C2×C3semidirect
66. C2×#467C2×C3semidirect
68. #2057C2×C3semidirect
69. #2036C2×C3semidirect
70. #2024C2×C3semidirect
71. #2001C2×C3semidirect
72. #1878C2×C3semidirect
73. #1872C2×C3semidirect
74. #1872C2×C3semidirect
76. #1863C2×C3semidirect
77. #1852C2×C3semidirect
78. C2×#340C2×C3semidirect
230. C2×C3×D4Q16semidirect
498. C2×D4C3×Q16semidirect
745. C3#25545direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5542
C2×C3×#4842
C2×C3×#4672
C3×#24172
C3×#20572
C3×#20362
C3×#20242
C3×#20012
C3×#18782
C3×#18722
C3×#18692
C3×#18632
C3×#18522
C2×C3×#3402
#255453