Finite Group Databasebeta

← C3×#25552 #10644159

Subgroups — C3×#25552 #10644159

Order 768.

1166 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#555C211yesmaximal, characteristic
2C2×C3×#485C211yesmaximal, characteristic, complemented
3C2×C3×#468C211yesmaximal, characteristic, complemented
4C3×#2417C211yesmaximal, characteristic, complemented
5C3×#2057C211yesmaximal, characteristic, complemented
6C3×#2033C211yesmaximal, characteristic, complemented
7C3×#2024C211yesmaximal, characteristic, complemented
8C3×#2000C211yesmaximal, characteristic, complemented
9C3×#1877C211yesmaximal, characteristic, complemented
10C3×#1874C211yesmaximal, characteristic, complemented
11C3×#1873C211yesmaximal, characteristic, complemented
12C3×#1870C211yesmaximal, characteristic, complemented
13C3×#1864C211yesmaximal, characteristic, complemented
14C3×#1854C211yesmaximal, characteristic, complemented
15C3×#1736C211yesmaximal, characteristic, complemented
16#25552C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×SD16C2211yescharacteristic
18C22×C3×M16C2211yescharacteristic
19C3×#555—24no—
20C3×#555—24no—
21C2×C3×C4⋊Q8C2211yescharacteristic
22C2×C3×#124—21no—
23C2×C3×#124—21no—
24C2×C3×C22⋊Q8C2211yescharacteristic
25C2×C3×C22⋊Q8C2211yescharacteristic
26C2×C3×#121—21no—
27C2×C3×#121C2211yescharacteristic
28C2×C3×#121C2211yescharacteristic
29C2×C3×C4×D4C2211yescharacteristic
30C2×C3×C4×D4C2211yescharacteristic
31C2×C3×#117—21no—
32C2×C3×#117C2211yescharacteristic
33C2×C3×#117C2211yescharacteristic
34C22×C3×C4⋊C4C2211yescharacteristic
35C3×#485—24no—
36C3×#468—24no—
37C2×C3×#107C2211yescharacteristic
38C2×C3×#107C2211yescharacteristic
39C2×C3×#106C2211yescharacteristic
40C2×C3×#103C2211yescharacteristic
41C2×C3×#103C2211yescharacteristic
42C2×C3×#103C2211yescharacteristic
43C2×C3×#102C2211yescharacteristic
44C2×C3×#102C2211yescharacteristic
45C2×C3×#102C2211yescharacteristic
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×#555C2×C311yescharacteristic
65C2×#485C2×C311yescharacteristic, complemented
66C2×#468C2×C311yescharacteristic, complemented
67#2417C2×C311yescharacteristic, complemented
68#2057C2×C311yescharacteristic, complemented
69#2033C2×C311yescharacteristic, complemented
70#2024C2×C311yescharacteristic, complemented
71#2000C2×C311yescharacteristic, complemented
72#1877C2×C311yescharacteristic, complemented
73#1874C2×C311yescharacteristic, complemented
74#1873C2×C311yescharacteristic, complemented
75#1870C2×C311yescharacteristic, complemented
76#1864C2×C311yescharacteristic, complemented
77#1854C2×C311yescharacteristic, complemented
78#1736C2×C311yescharacteristic, complemented
79C22×C3×Q8—21no—
80C22×C3×Q8C2311yescharacteristic
81C22×C3×D4—21no—
82C22×C3×D4—21no—
83C22×C3×D4D411yescharacteristic
84C22×C3×D4C2311yescharacteristic
85C23×C3×C4—21no—
86C23×C3×C4—21no—
87C23×C3×C4C2311yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C2×C3×SD16—22no—
90C2×C3×SD16—22no—
91C2×C3×SD16—41no—
92C2×C3×M16—22no—
93C2×C3×M16—22no—
94C2×C3×M16—41no—
95C22×C3×C8C2311yescharacteristic
96C22×C3×C8C2311yescharacteristic
97C22×C3×C8C2311yescharacteristic
98C22×C3×C8C2311yescharacteristic
99C3×C4⋊Q8—22no—
100C3×C4⋊Q8—22no—
101C3×#124—28no—
102C3×#124—28no—
103C3×C22⋊Q8—22no—
104C3×C22⋊Q8—22no—
105C3×C22⋊Q8—22no—
106C3×C22⋊Q8—41no—
107C3×#121—28no—
108C3×#121—22no—
109C3×#121—22no—
110C3×#121—22no—
111C3×#121D414yes—
112C3×C4×D4—22no—
113C3×C4×D4—22no—
114C3×C4×D4—22no—
115C3×C4×D4—22no—
116C3×#117—28no—
117C3×#117—22no—
118C3×#117—22no—
119C3×#117—22no—
120C3×#117D414yes—
121C2×C3×C4⋊C4—21no—
122C2×C3×C4⋊C4—22no—
123C2×C3×C4⋊C4—21no—
124C2×C3×C4⋊C4—21no—
125C2×C3×C4⋊C4—21no—
126C2×C3×C4⋊C4—21no—
127C2×C3×C4⋊C4—41no—
128C2×C3×C4⋊C4D411yescharacteristic
129C2×C3×C4⋊C4C2311yescharacteristic
130C2×C3×C4⋊C4C2311yescharacteristic
131C2×C3×C4⋊C4C2311yescharacteristic
132C2×C3×C4⋊C4C2311yescharacteristic
133C2×C3×C4⋊C4C2311yescharacteristic
134C2×C3×C4⋊C4C2311yescharacteristic
135C2×C3×C22⋊C4—21no—
136C2×C3×C22⋊C4—21no—
137C2×C3×C22⋊C4—21no—
138C2×C3×C22⋊C4—21no—
139C2×C3×C22⋊C4—21no—
140C2×C3×C22⋊C4—21no—
141C2×C3×C22⋊C4—21no—
142C2×C3×C22⋊C4—21no—
143C2×C3×C22⋊C4D411yescharacteristic
144C2×C3×C22⋊C4D411yescharacteristic
145C2×C3×C42—21no—
146C2×C3×C42—21no—
147C2×C3×C42C2311yescharacteristic
148C3×#107—22no—
149C3×#107—22no—
150C3×#106—22no—
151C3×#103—22no—
152C3×#103—22no—
153C3×#103—22no—
154C3×#102—22no—
155C3×#102—22no—
156C3×#102—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×SD16C22×C311yescharacteristic
165C22×M16C22×C311yescharacteristic
166#555—24no—
167#555—24no—
168C2×C4⋊Q8C22×C311yescharacteristic
169C2×#124—21no—
170C2×#124—21no—
171C2×C22⋊Q8C22×C311yescharacteristic
172C2×C22⋊Q8C22×C311yescharacteristic
173C2×#121—21no—
174C2×#121C22×C311yescharacteristic
175C2×#121C22×C311yescharacteristic
176C2×C4×D4C22×C311yescharacteristic
177C2×C4×D4C22×C311yescharacteristic
178C2×#117—21no—
179C2×#117C22×C311yescharacteristic
180C2×#117C22×C311yescharacteristic
181C22×C4⋊C4C22×C311yescharacteristic
182#485—24no—
183#468—24no—
184C2×#107C22×C311yescharacteristic
185C2×#107C22×C311yescharacteristic
186C2×#106C22×C311yescharacteristic
187C2×#103C22×C311yescharacteristic
188C2×#103C22×C311yescharacteristic
189C2×#103C22×C311yescharacteristic
190C2×#102C22×C311yescharacteristic
191C2×#102C22×C311yescharacteristic
192C2×#102C22×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×C3—21no—
212C24×C3C2×D411yescharacteristic
213C24×C3C2×D411yescharacteristic
214C2×C3×Q8—24no—
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—81no—
222C2×C3×Q8—81no—
223C2×C3×D4—22no—
224C2×C3×D4—24no—
225C2×C3×D4—24no—
226C2×C3×D4—22no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4—21no—
232C2×C3×D4—41no—
233C2×C3×D4—81no—
234C2×C3×D4—81no—
235C2×C3×D4—81no—
236C2×C3×D4—81no—
237C2×C3×D4C2×D412yes—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—24no—
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—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—42no—
257C22×C3×C4—42no—
258C22×C3×C4—42no—
259C22×C3×C4—42no—
260C22×C3×C4—81no—
261C22×C3×C4C2×D411yescharacteristic
262C22×C3×C4C2×D411yescharacteristic
263C22×C3×C4C2×D411yescharacteristic
264C22×C3×C4C2×D412yes—
265C22×C3×C4C2×D412yes—
266C22×C3×C4C2×D411yescharacteristic
267C22×C3×C4C2411yescharacteristic
268C3×SD16—44no—
269C3×M16—44no—
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—21no—
278C2×C3×C8—21no—
279C2×C3×C8—21no—
280C2×C3×C8—21no—
281C2×C3×C8#4112yes—
282C3×C4⋊C4—24no—
283C3×C4⋊C4—22no—
284C3×C4⋊C4—21no—
285C3×C4⋊C4—21no—
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—42no—
293C3×C4⋊C4—42no—
294C3×C4⋊C4—42no—
295C3×C4⋊C4—81no—
296C3×C4⋊C4C2×D412yes—
297C3×C4⋊C4C2×D412yes—
298C3×C4⋊C4C2×D412yes—
299C3×C4⋊C4#4112yes—
300C3×C22⋊C4—24no—
301C3×C22⋊C4—24no—
302C3×C22⋊C4—24no—
303C3×C22⋊C4—24no—
304C3×C22⋊C4—22no—
305C3×C22⋊C4—24no—
306C3×C22⋊C4—22no—
307C3×C22⋊C4—42no—
308C3×C22⋊C4—42no—
309C3×C22⋊C4—81no—
310C3×C42—24no—
311C3×C42—24no—
312C3×C42—21no—
313C3×C42—21no—
314C22×Q8—21no—
315C22×Q8C23×C311yescharacteristic
316C22×D4—21no—
317C22×D4—21no—
318C22×D4C3×D411yescharacteristic
319C22×D4C23×C311yescharacteristic
320C23×C4—21no—
321C23×C4—21no—
322C23×C4C23×C311yescharacteristic
323C23×C4C23×C311yescharacteristic
324C2×SD16—22no—
325C2×SD16—22no—
326C2×SD16—41no—
327C2×M16—22no—
328C2×M16—22no—
329C2×M16—41no—
330C22×C8C23×C311yescharacteristic
331C22×C8C23×C311yescharacteristic
332C22×C8C23×C311yescharacteristic
333C22×C8C23×C311yescharacteristic
334C4⋊Q8—22no—
335C4⋊Q8—22no—
336#124—28no—
337#124—28no—
338C22⋊Q8—22no—
339C22⋊Q8—22no—
340C22⋊Q8—22no—
341C22⋊Q8—41no—
342#121—28no—
343#121—22no—
344#121—22no—
345#121—22no—
346#121C3×D414yes—
347C4×D4—22no—
348C4×D4—22no—
349C4×D4—22no—
350C4×D4—22no—
351#117—28no—
352#117—22no—
353#117—22no—
354#117—22no—
355#117C3×D414yes—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—41no—
363C2×C4⋊C4C3×D411yescharacteristic
364C2×C4⋊C4C23×C311yescharacteristic
365C2×C4⋊C4C23×C311yescharacteristic
366C2×C4⋊C4C23×C311yescharacteristic
367C2×C4⋊C4C23×C311yescharacteristic
368C2×C4⋊C4C23×C311yescharacteristic
369C2×C4⋊C4C23×C311yescharacteristic
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4C3×D411yescharacteristic
379C2×C22⋊C4C3×D411yescharacteristic
380C2×C42—21no—
381C2×C42—21no—
382C2×C42C23×C311yescharacteristic
383#107—22no—
384#107—22no—
385#106—22no—
386#103—22no—
387#103—22no—
388#103—22no—
389#102—22no—
390#102—22no—
391#102—41no—
392C22⋊C8—22no—
393C22⋊C8—22no—
394C22⋊C8—41no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95—21no—
399C23×C3—21no—
400C23×C3—21no—
401C23×C3—21no—
402C23×C3—21no—
403C23×C3—21no—
404C23×C3—21no—
405C23×C3—21no—
406C23×C3—22no—
407C23×C3—21no—
408C23×C3—21no—
409C23×C3—21no—
410C23×C3—21no—
411C23×C3—21no—
412C23×C3—21no—
413C23×C3—41no—
414C23×C3—41no—
415C23×C3—41no—
416C23×C3—41no—
417C23×C3—41no—
418C23×C3—41no—
419C23×C3#12012yes—
420C23×C3C22×D411yescharacteristic
421C3×Q8—41no—
422C3×Q8—41no—
423C3×Q8—41no—
424C3×Q8—41no—
425C3×Q8—84no—
426C3×D4—22no—
427C3×D4—22no—
428C3×D4—44no—
429C3×D4—41no—
430C3×D4—41no—
431C3×D4—84no—
432C3×D4—84no—
433C2×C3×C4—21no—
434C2×C3×C4—21no—
435C2×C3×C4—21no—
436C2×C3×C4—21no—
437C2×C3×C4—22no—
438C2×C3×C4—22no—
439C2×C3×C4—22no—
440C2×C3×C4—22no—
441C2×C3×C4—21no—
442C2×C3×C4—22no—
443C2×C3×C4—21no—
444C2×C3×C4—22no—
445C2×C3×C4—22no—
446C2×C3×C4—22no—
447C2×C3×C4—21no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
450C2×C3×C4—21no—
451C2×C3×C4—48no—
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—41no—
465C2×C3×C4—41no—
466C2×C3×C4—41no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
470C2×C3×C4—41no—
471C2×C3×C4—41no—
472C2×C3×C4—41no—
473C2×C3×C4—84no—
474C2×C3×C4#12012yes—
475C2×C3×C4#13712yes—
476C2×C3×C4C22×D411yescharacteristic
477C2×C3×C4C22×D411yescharacteristic
478C2×C3×C4C2×#4111yescharacteristic
479C2×C3×C4C2×#4111yescharacteristic
480C2×C3×C4H(5,𝔽2)11yescharacteristic
481C2×C3×C42−1+411yescharacteristic
482C3×C8—22no—
483C3×C8—41no—
484C3×C8—41no—
485C3×C8—41no—
486C24—21no—
487C24C2×C3×D411yescharacteristic
488C24C2×C3×D411yescharacteristic
489C2×Q8—24no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—81no—
497C2×Q8—81no—
498C2×D4—22no—
499C2×D4—24no—
500C2×D4—24no—
501C2×D4—22no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—41no—
508C2×D4—81no—
509C2×D4—81no—
510C2×D4—81no—
511C2×D4—81no—
512C2×D4C2×C3×D412yes—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—24no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—81no—
536C22×C4C2×C3×D411yescharacteristic
537C22×C4C2×C3×D411yescharacteristic
538C22×C4C2×C3×D411yescharacteristic
539C22×C4C2×C3×D412yes—
540C22×C4C2×C3×D412yes—
541C22×C4C2×C3×D411yescharacteristic
542C22×C4C24×C311yescharacteristic
543SD16—44no—
544M16—44no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8C3×#4112yes—
557C4⋊C4—24no—
558C4⋊C4—22no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—42no—
568C4⋊C4—42no—
569C4⋊C4—42no—
570C4⋊C4—81no—
571C4⋊C4C2×C3×D412yes—
572C4⋊C4C2×C3×D412yes—
573C4⋊C4C2×C3×D412yes—
574C4⋊C4C3×#4112yes—
575C22⋊C4—24no—
576C22⋊C4—24no—
577C22⋊C4—24no—
578C22⋊C4—24no—
579C22⋊C4—22no—
580C22⋊C4—24no—
581C22⋊C4—22no—
582C22⋊C4—42no—
583C22⋊C4—42no—
584C22⋊C4—81no—
585C42—24no—
586C42—24no—
587C42—21no—
588C42—21no—
589C22×C3—22no—
590C22×C3—22no—
591C22×C3—22no—
592C22×C3—41no—
593C22×C3—41no—
594C22×C3—41no—
595C22×C3—41no—
596C22×C3—41no—
597C22×C3—41no—
598C22×C3—41no—
599C22×C3—41no—
600C22×C3—42no—
601C22×C3—42no—
602C22×C3—41no—
603C22×C3—41no—
604C22×C3—42no—
605C22×C3—41no—
606C22×C3—81no—
607C22×C3—81no—
608C22×C3—81no—
609C22×C3—81no—
610C22×C3C2×#12011yescharacteristic
611C22×C3#54611yescharacteristic
612C22×C3#54711yescharacteristic
613C22×C3C2×#13711yescharacteristic
614C22×C3#57511yescharacteristic
615C22×C3#57611yescharacteristic
616C22×C3#57711yescharacteristic
617C3×C4—22no—
618C3×C4—22no—
619C3×C4—41no—
620C3×C4—42no—
621C3×C4—41no—
622C3×C4—42no—
623C3×C4—42no—
624C3×C4—42no—
625C3×C4—81no—
626C3×C4—81no—
627C3×C4—81no—
628C3×C4#53211yescharacteristic
629C3×C4#53711yescharacteristic
630C3×C4#54611yescharacteristic
631C3×C4#54711yescharacteristic
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—22no—
644C23—21no—
645C23—21no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23C3×#12012yes—
653C23C22×C3×D411yescharacteristic
654Q8—41no—
655Q8—41no—
656Q8—41no—
657Q8—41no—
658Q8—84no—
659D4—22no—
660D4—22no—
661D4—44no—
662D4—41no—
663D4—41no—
664D4—84no—
665D4—84no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—22no—
678C2×C4—21no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—48no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—84no—
707C2×C4C3×#12012yes—
708C2×C4C3×#13712yes—
709C2×C4C22×C3×D411yescharacteristic
710C2×C4C22×C3×D411yescharacteristic
711C2×C4C2×C3×#4111yescharacteristic
712C2×C4C2×C3×#4111yescharacteristic
713C2×C4C3×H(5,𝔽2)11yescharacteristic
714C2×C4C3×2−1+411yescharacteristic
715C8—22no—
716C8—41no—
717C8—41no—
718C8—41no—
719C2×C3—42no—
720C2×C3—81no—
721C2×C3—82no—
722C2×C3#243011yescharacteristic
723C2×C3#300711yescharacteristic
724C2×C3#301211yescharacteristic
725C2×C3#331911yescharacteristic
726C2×C3#332911yescharacteristic
727C2×C3#334811yescharacteristic
728C2×C3#335711yescharacteristic
729C22—22no—
730C22—22no—
731C22—22no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—42no—
738C22—42no—
739C22—41no—
740C22—41no—
741C22—42no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22C2×C3×#12011yescharacteristic
751C22C3×#54611yescharacteristic
752C22C3×#54711yescharacteristic
753C22C2×C3×#13711yescharacteristic
754C22C3×#57511yescharacteristic
755C22C3×#57611yescharacteristic
756C22C3×#57711yescharacteristic
757C4—22no—
758C4—22no—
759C4—41no—
760C4—42no—
761C4—41no—
762C4—42no—
763C4—42no—
764C4—42no—
765C4—81no—
766C4—81no—
767C4—81no—
768C4C3×#53211yescharacteristic
769C4C3×#53711yescharacteristic
770C4C3×#54611yescharacteristic
771C4C3×#54711yescharacteristic
772C3#2555211yescharacteristic, direct product factor, Sylow
773C2—42no—
774C2—81no—
775C2—82no—
776C2C3×#243011yescharacteristic
777C2C3×#300711yescharacteristic
778C2C3×#301211yescharacteristic
779C2C3×#331911yescharacteristic
780C2C3×#332911yescharacteristic
781C2C3×#334811yescharacteristic
782C2C3×#335711yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC2×C3×#555C2
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×#485C2semidirect
3. C2×C3×#468C2semidirect
4. C3×#2417C2semidirect
5. C3×#2057C2semidirect
6. C3×#2033C2semidirect
7. C3×#2024C2semidirect
8. C3×#2000C2semidirect
9. C3×#1877C2semidirect
10. C3×#1874C2semidirect
11. C3×#1873C2semidirect
12. C3×#1870C2semidirect
13. C3×#1864C2semidirect
14. C3×#1854C2semidirect
15. C3×#1736C2semidirect
16. #25552C3direct (N × H)
65. C2×#485C2×C3semidirect
66. C2×#468C2×C3semidirect
67. #2417C2×C3semidirect
68. #2057C2×C3semidirect
69. #2033C2×C3semidirect
70. #2024C2×C3semidirect
71. #2000C2×C3semidirect
72. #1877C2×C3semidirect
73. #1874C2×C3semidirect
74. #1873C2×C3semidirect
75. #1870C2×C3semidirect
76. #1864C2×C3semidirect
77. #1854C2×C3semidirect
78. #1736C2×C3semidirect
772. C3#25552direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5552
C2×C3×#4852
C2×C3×#4682
C3×#24172
C3×#20572
C3×#20332
C3×#20242
C3×#20002
C3×#18772
C3×#18742
C3×#18732
C3×#18702
C3×#18642
C3×#18542
C3×#17362
#255523