Finite Group Databasebeta

← C3×#25559 #10644166

Subgroups — C3×#25559 #10644166

Order 768.

1174 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#554C211yesmaximal, characteristic, complemented
2C2×C3×#480C211yesmaximal, characteristic, complemented
3C2×C3×#468C211yesmaximal, characteristic, complemented
4C3×#2414C211yesmaximal, characteristic
5C3×#2057C211yesmaximal, characteristic, complemented
6C3×#2036C211yesmaximal, characteristic, complemented
7C3×#2023C211yesmaximal, characteristic, complemented
8C3×#2000C211yesmaximal, characteristic, complemented
9C3×#1880C211yesmaximal, characteristic, complemented
10C3×#1874C211yesmaximal, characteristic, complemented
11C3×#1873C211yesmaximal, characteristic, complemented
12C3×#1870C211yesmaximal, characteristic, complemented
13C3×#1863C211yesmaximal, characteristic, complemented
14C3×#1852C211yesmaximal, characteristic, complemented
15C3×#1736C211yesmaximal, characteristic, complemented
16#25559C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×SD16C2211yescharacteristic
18C22×C3×M16C2211yescharacteristic
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×#121C2211yescharacteristic
28C2×C3×#121C2211yescharacteristic
29C2×C3×C4×Q8C2211yescharacteristic
30C2×C3×C4×D4—21no—
31C2×C3×C4×D4C2211yescharacteristic
32C2×C3×#117C2211yescharacteristic
33C22×C3×C4⋊C4C2211yescharacteristic
34C22×C3×C4⋊C4C2211yescharacteristic
35C3×#480—24no—
36C3×#468—24no—
37C2×C3×#107C2211yescharacteristic
38C2×C3×#107C2211yescharacteristic
39C2×C3×#107C2211yescharacteristic
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×#394—21no—
50C3×#392—21no—
51C3×#390—21no—
52C3×#390C2211yescharacteristic
53C3×#389C2211yescharacteristic
54C3×#388—21no—
55C3×#380C2211yescharacteristic
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#340C2211yescharacteristic
61C3×#340C2211yescharacteristic
62C3×#336C2211yescharacteristic
63C3×#336C2211yescharacteristic
64C2×#554C2×C311yescharacteristic, complemented
65C2×#480C2×C311yescharacteristic, complemented
66C2×#468C2×C311yescharacteristic, complemented
67#2414C2×C311yescharacteristic
68#2057C2×C311yescharacteristic, complemented
69#2036C2×C311yescharacteristic, complemented
70#2023C2×C311yescharacteristic, complemented
71#2000C2×C311yescharacteristic, complemented
72#1880C2×C311yescharacteristic, complemented
73#1874C2×C311yescharacteristic, complemented
74#1873C2×C311yescharacteristic, complemented
75#1870C2×C311yescharacteristic, complemented
76#1863C2×C311yescharacteristic, complemented
77#1852C2×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×#125—28no—
102C3×C22⋊Q8—28no—
103C3×C22⋊Q8—28no—
104C3×C22⋊Q8—22no—
105C3×C22⋊Q8—22no—
106C3×C22⋊Q8—22no—
107C3×C22⋊Q8D414yescomplemented
108C3×#121—22no—
109C3×#121—22no—
110C3×#121—22no—
111C3×#121—41no—
112C3×C4×Q8—22no—
113C3×C4×Q8—22no—
114C3×C4×D4—28no—
115C3×C4×D4—22no—
116C3×C4×D4—22no—
117C3×#117—22no—
118C3×#117—41no—
119C2×C3×C4⋊C4—21no—
120C2×C3×C4⋊C4—21no—
121C2×C3×C4⋊C4—22no—
122C2×C3×C4⋊C4—21no—
123C2×C3×C4⋊C4—21no—
124C2×C3×C4⋊C4—21no—
125C2×C3×C4⋊C4—21no—
126C2×C3×C4⋊C4—22no—
127C2×C3×C4⋊C4—22no—
128C2×C3×C4⋊C4—21no—
129C2×C3×C4⋊C4D411yescharacteristic
130C2×C3×C4⋊C4D414yescomplemented
131C2×C3×C4⋊C4C2311yescharacteristic
132C2×C3×C4⋊C4C2311yescharacteristic
133C2×C3×C4⋊C4C2311yescharacteristic
134C2×C3×C4⋊C4C2311yescharacteristic
135C2×C3×C4⋊C4C2311yescharacteristic
136C2×C3×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
144C2×C3×C22⋊C4—21no—
145C2×C3×C22⋊C4D411yescharacteristic
146C2×C3×C22⋊C4D411yescharacteristic
147C2×C3×C42—21no—
148C2×C3×C42—21no—
149C2×C3×C42C2311yescharacteristic
150C3×#107—22no—
151C3×#107—22no—
152C3×#107—22no—
153C3×#103—22no—
154C3×#103—22no—
155C3×#103—41no—
156C3×#102—22no—
157C3×#102—22no—
158C3×#102—22no—
159C3×C22⋊C8—22no—
160C3×C22⋊C8—22no—
161C3×C22⋊C8—41no—
162C3×#95—21no—
163C3×#95—21no—
164C22×SD16C22×C311yescharacteristic
165C22×M16C22×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×#121C22×C311yescharacteristic
175C2×#121C22×C311yescharacteristic
176C2×C4×Q8C22×C311yescharacteristic
177C2×C4×D4—21no—
178C2×C4×D4C22×C311yescharacteristic
179C2×#117C22×C311yescharacteristic
180C22×C4⋊C4C22×C311yescharacteristic
181C22×C4⋊C4C22×C311yescharacteristic
182#480—24no—
183#468—24no—
184C2×#107C22×C311yescharacteristic
185C2×#107C22×C311yescharacteristic
186C2×#107C22×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#394—21no—
197#392—21no—
198#390—21no—
199#390C22×C311yescharacteristic
200#389C22×C311yescharacteristic
201#388—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—81no—
221C2×C3×Q8—81no—
222C2×C3×Q8C2×D412yes—
223C2×C3×D4—22no—
224C2×C3×D4—22no—
225C2×C3×D4—22no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4—21no—
232C2×C3×D4—42no—
233C2×C3×D4—42no—
234C2×C3×D4—42no—
235C2×C3×D4—81no—
236C2×C3×D4—81no—
237C2×C3×D4—81no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—24no—
248C22×C3×C4—24no—
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—21no—
257C22×C3×C4—81no—
258C22×C3×C4—81no—
259C22×C3×C4—81no—
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—24no—
284C3×C4⋊C4—24no—
285C3×C4⋊C4—24no—
286C3×C4⋊C4—24no—
287C3×C4⋊C4—24no—
288C3×C4⋊C4—22no—
289C3×C4⋊C4—21no—
290C3×C4⋊C4—21no—
291C3×C4⋊C4—21no—
292C3×C4⋊C4—21no—
293C3×C4⋊C4—21no—
294C3×C4⋊C4—21no—
295C3×C4⋊C4—21no—
296C3×C4⋊C4—21no—
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—42no—
309C3×C22⋊C4—42no—
310C3×C22⋊C4—81no—
311C3×C22⋊C4—81no—
312C3×C42—24no—
313C3×C42—21no—
314C3×C42—21no—
315C3×C42—42no—
316C22×Q8—21no—
317C22×Q8C23×C311yescharacteristic
318C22×D4—21no—
319C22×D4—21no—
320C22×D4C3×D411yescharacteristic
321C22×D4C23×C311yescharacteristic
322C23×C4—21no—
323C23×C4—21no—
324C23×C4C23×C311yescharacteristic
325C23×C4C23×C311yescharacteristic
326C2×SD16—22no—
327C2×SD16—22no—
328C2×SD16—41no—
329C2×M16—22no—
330C2×M16—22no—
331C2×M16—41no—
332C22×C8C23×C311yescharacteristic
333C22×C8C23×C311yescharacteristic
334C22×C8C23×C311yescharacteristic
335C22×C8C23×C311yescharacteristic
336C4⋊Q8—22no—
337C4⋊Q8—22no—
338#125—28no—
339C22⋊Q8—28no—
340C22⋊Q8—28no—
341C22⋊Q8—22no—
342C22⋊Q8—22no—
343C22⋊Q8—22no—
344C22⋊Q8C3×D414yescomplemented
345#121—22no—
346#121—22no—
347#121—22no—
348#121—41no—
349C4×Q8—22no—
350C4×Q8—22no—
351C4×D4—28no—
352C4×D4—22no—
353C4×D4—22no—
354#117—22no—
355#117—41no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4C3×D411yescharacteristic
367C2×C4⋊C4C3×D414yescomplemented
368C2×C4⋊C4C23×C311yescharacteristic
369C2×C4⋊C4C23×C311yescharacteristic
370C2×C4⋊C4C23×C311yescharacteristic
371C2×C4⋊C4C23×C311yescharacteristic
372C2×C4⋊C4C23×C311yescharacteristic
373C2×C4⋊C4C23×C311yescharacteristic
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4C3×D411yescharacteristic
383C2×C22⋊C4C3×D411yescharacteristic
384C2×C42—21no—
385C2×C42—21no—
386C2×C42C23×C311yescharacteristic
387#107—22no—
388#107—22no—
389#107—22no—
390#103—22no—
391#103—22no—
392#103—41no—
393#102—22no—
394#102—22no—
395#102—22no—
396C22⋊C8—22no—
397C22⋊C8—22no—
398C22⋊C8—41no—
399#95—21no—
400#95—21no—
401C23×C3—21no—
402C23×C3—21no—
403C23×C3—21no—
404C23×C3—21no—
405C23×C3—21no—
406C23×C3—21no—
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—41no—
420C23×C3#12012yes—
421C23×C3#13712yes—
422C23×C3C22×D411yescharacteristic
423C3×Q8—22no—
424C3×Q8—22no—
425C3×Q8—41no—
426C3×Q8—41no—
427C3×Q8—84no—
428C3×D4—28no—
429C3×D4—41no—
430C3×D4—41no—
431C3×D4—41no—
432C3×D4—41no—
433C3×D4—84no—
434C3×D4—84no—
435C2×C3×C4—21no—
436C2×C3×C4—21no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—22no—
440C2×C3×C4—22no—
441C2×C3×C4—22no—
442C2×C3×C4—22no—
443C2×C3×C4—22no—
444C2×C3×C4—21no—
445C2×C3×C4—22no—
446C2×C3×C4—21no—
447C2×C3×C4—22no—
448C2×C3×C4—22no—
449C2×C3×C4—22no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
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—41no—
474C2×C3×C4—84no—
475C2×C3×C4—84no—
476C2×C3×C4#12012yes—
477C2×C3×C4#13712yes—
478C2×C3×C4C22×D411yescharacteristic
479C2×C3×C4C22×D411yescharacteristic
480C2×C3×C4C2×#4111yescharacteristic
481C2×C3×C4C2×#4111yescharacteristic
482C2×C3×C4H(5,𝔽2)11yescharacteristic
483C2×C3×C42−1+411yescharacteristic
484C3×C8—22no—
485C3×C8—41no—
486C3×C8—41no—
487C3×C8—41no—
488C24—21no—
489C24C2×C3×D411yescharacteristic
490C24C2×C3×D411yescharacteristic
491C2×Q8—24no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—81no—
498C2×Q8—81no—
499C2×Q8C2×C3×D412yes—
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—42no—
510C2×D4—42no—
511C2×D4—42no—
512C2×D4—81no—
513C2×D4—81no—
514C2×D4—81no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—81no—
535C22×C4—81no—
536C22×C4—81no—
537C22×C4—81no—
538C22×C4C2×C3×D411yescharacteristic
539C22×C4C2×C3×D411yescharacteristic
540C22×C4C2×C3×D411yescharacteristic
541C22×C4C2×C3×D412yes—
542C22×C4C2×C3×D412yes—
543C22×C4C2×C3×D411yescharacteristic
544C22×C4C24×C311yescharacteristic
545SD16—44no—
546M16—44no—
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×C8—21no—
557C2×C8—21no—
558C2×C8C3×#4112yes—
559C4⋊C4—24no—
560C4⋊C4—24no—
561C4⋊C4—24no—
562C4⋊C4—24no—
563C4⋊C4—24no—
564C4⋊C4—24no—
565C4⋊C4—22no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—81no—
575C4⋊C4C2×C3×D412yes—
576C4⋊C4C2×C3×D412yes—
577C4⋊C4C2×C3×D412yes—
578C4⋊C4C3×#4112yes—
579C22⋊C4—24no—
580C22⋊C4—24no—
581C22⋊C4—22no—
582C22⋊C4—22no—
583C22⋊C4—42no—
584C22⋊C4—42no—
585C22⋊C4—42no—
586C22⋊C4—42no—
587C22⋊C4—81no—
588C22⋊C4—81no—
589C42—24no—
590C42—21no—
591C42—21no—
592C42—42no—
593C22×C3—22no—
594C22×C3—22no—
595C22×C3—22no—
596C22×C3—22no—
597C22×C3—22no—
598C22×C3—22no—
599C22×C3—41no—
600C22×C3—41no—
601C22×C3—41no—
602C22×C3—41no—
603C22×C3—41no—
604C22×C3—41no—
605C22×C3—41no—
606C22×C3—41no—
607C22×C3—81no—
608C22×C3—81no—
609C22×C3—81no—
610C22×C3—81no—
611C22×C3—81no—
612C22×C3—81no—
613C22×C3—81no—
614C22×C3C2×#12011yescharacteristic
615C22×C3#54611yescharacteristic
616C22×C3#54711yescharacteristic
617C22×C3C2×#13711yescharacteristic
618C22×C3C2×#13711yescharacteristic
619C22×C3#57611yescharacteristic
620C22×C3#57611yescharacteristic
621C3×C4—22no—
622C3×C4—22no—
623C3×C4—41no—
624C3×C4—42no—
625C3×C4—41no—
626C3×C4—42no—
627C3×C4—42no—
628C3×C4—42no—
629C3×C4—42no—
630C3×C4—81no—
631C3×C4—81no—
632C3×C4#53211yescharacteristic
633C3×C4#53711yescharacteristic
634C3×C4#54611yescharacteristic
635C3×C4#54711yescharacteristic
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23C3×#12012yes—
656C23C3×#13712yes—
657C23C22×C3×D411yescharacteristic
658Q8—22no—
659Q8—22no—
660Q8—41no—
661Q8—41no—
662Q8—84no—
663D4—28no—
664D4—41no—
665D4—41no—
666D4—41no—
667D4—41no—
668D4—84no—
669D4—84no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—22no—
681C2×C4—21no—
682C2×C4—22no—
683C2×C4—21no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—21no—
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—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—84no—
710C2×C4—84no—
711C2×C4C3×#12012yes—
712C2×C4C3×#13712yes—
713C2×C4C22×C3×D411yescharacteristic
714C2×C4C22×C3×D411yescharacteristic
715C2×C4C2×C3×#4111yescharacteristic
716C2×C4C2×C3×#4111yescharacteristic
717C2×C4C3×H(5,𝔽2)11yescharacteristic
718C2×C4C3×2−1+411yescharacteristic
719C8—22no—
720C8—41no—
721C8—41no—
722C8—41no—
723C2×C3—42no—
724C2×C3—42no—
725C2×C3—161no—
726C2×C3#243011yescharacteristic
727C2×C3#300411yescharacteristic
728C2×C3#300811yescharacteristic
729C2×C3#331411yescharacteristic
730C2×C3#333311yescharacteristic
731C2×C3#334611yescharacteristic
732C2×C3#335711yescharacteristic
733C22—22no—
734C22—22no—
735C22—22no—
736C22—22no—
737C22—22no—
738C22—22no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22C2×C3×#12011yescharacteristic
755C22C3×#54611yescharacteristic
756C22C3×#54711yescharacteristic
757C22C2×C3×#13711yescharacteristic
758C22C2×C3×#13711yescharacteristic
759C22C3×#57611yescharacteristic
760C22C3×#57611yescharacteristic
761C4—22no—
762C4—22no—
763C4—41no—
764C4—42no—
765C4—41no—
766C4—42no—
767C4—42no—
768C4—42no—
769C4—42no—
770C4—81no—
771C4—81no—
772C4C3×#53211yescharacteristic
773C4C3×#53711yescharacteristic
774C4C3×#54611yescharacteristic
775C4C3×#54711yescharacteristic
776C3#2555911yescharacteristic, direct product factor, Sylow
777C2—42no—
778C2—42no—
779C2—161no—
780C2C3×#243011yescharacteristic
781C2C3×#300411yescharacteristic
782C2C3×#300811yescharacteristic
783C2C3×#331411yescharacteristic
784C2C3×#333311yescharacteristic
785C2C3×#334611yescharacteristic
786C2C3×#335711yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC3×#2414C2
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
1. C2×C3×#554C2semidirect
2. C2×C3×#480C2semidirect
3. C2×C3×#468C2semidirect
5. C3×#2057C2semidirect
6. C3×#2036C2semidirect
7. C3×#2023C2semidirect
8. C3×#2000C2semidirect
9. C3×#1880C2semidirect
10. C3×#1874C2semidirect
11. C3×#1873C2semidirect
12. C3×#1870C2semidirect
13. C3×#1863C2semidirect
14. C3×#1852C2semidirect
15. C3×#1736C2semidirect
16. #25559C3direct (N × H)
64. C2×#554C2×C3semidirect
65. C2×#480C2×C3semidirect
66. C2×#468C2×C3semidirect
68. #2057C2×C3semidirect
69. #2036C2×C3semidirect
70. #2023C2×C3semidirect
71. #2000C2×C3semidirect
72. #1880C2×C3semidirect
73. #1874C2×C3semidirect
74. #1873C2×C3semidirect
75. #1870C2×C3semidirect
76. #1863C2×C3semidirect
77. #1852C2×C3semidirect
78. #1736C2×C3semidirect
107. C3×C22⋊Q8D4semidirect
130. C2×C3×C4⋊C4D4semidirect
344. C22⋊Q8C3×D4semidirect
367. C2×C4⋊C4C3×D4semidirect
776. C3#25559direct (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×#4802
C2×C3×#4682
C3×#24142
C3×#20572
C3×#20362
C3×#20232
C3×#20002
C3×#18802
C3×#18742
C3×#18732
C3×#18702
C3×#18632
C3×#18522
C3×#17362
#255593