Finite Group Databasebeta

← C3×#25534 #10644141

Subgroups — C3×#25534 #10644141

Order 768.

1212 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#553C211yesmaximal, characteristic, complemented
2C2×C3×#482C211yesmaximal, characteristic, complemented
3C2×C3×#466C211yesmaximal, characteristic, complemented
4C3×#2414C211yesmaximal, characteristic, complemented
5C3×#2059C211yesmaximal, characteristic, complemented
6C3×#2034C211yesmaximal, characteristic, complemented
7C3×#2025C211yesmaximal, characteristic, complemented
8C3×#1999C211yesmaximal, characteristic, complemented
9C3×#1879C211yesmaximal, characteristic, complemented
10C3×#1875C211yesmaximal, characteristic, complemented
11C3×#1874C211yesmaximal, characteristic, complemented
12C3×#1869C211yesmaximal, characteristic, complemented
13C3×#1862C211yesmaximal, characteristic, complemented
14C3×#1852C211yesmaximal, characteristic, complemented
15C3×#1735C211yesmaximal, characteristic, complemented
16#25534C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×D8C2211yescharacteristic
18C23×C3×C8C2211yescharacteristic
19C3×#553—24no—
20C3×#553—24no—
21C2×C3×#126—21no—
22C2×C3×#125C2211yescharacteristic
23C2×C3×#123—21no—
24C2×C3×#121—21no—
25C2×C3×#121C2211yescharacteristic
26C2×C3×#121C2211yescharacteristic
27C2×C3×#121C2211yescharacteristic
28C2×C3×#121C2211yescharacteristic
29C2×C3×C4×D4—21no—
30C2×C3×C4×D4C2211yescharacteristic
31C2×C3×C4×D4C2211yescharacteristic
32C2×C3×#117C2211yescharacteristic
33C2×C3×#117C2211yescharacteristic
34C22×C3×C4⋊C4C2211yescharacteristic
35C3×#482—24no—
36C3×#466—24no—
37C2×C3×#107C2211yescharacteristic
38C2×C3×#107C2211yescharacteristic
39C2×C3×#106C2211yescharacteristic
40C2×C3×#102C2211yescharacteristic
41C2×C3×#102C2211yescharacteristic
42C2×C3×#102C2211yescharacteristic
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×#553C2×C311yescharacteristic, complemented
65C2×#482C2×C311yescharacteristic, complemented
66C2×#466C2×C311yescharacteristic, complemented
67#2414C2×C311yescharacteristic, complemented
68#2059C2×C311yescharacteristic, complemented
69#2034C2×C311yescharacteristic, complemented
70#2025C2×C311yescharacteristic, complemented
71#1999C2×C311yescharacteristic, complemented
72#1879C2×C311yescharacteristic, complemented
73#1875C2×C311yescharacteristic, complemented
74#1874C2×C311yescharacteristic, complemented
75#1869C2×C311yescharacteristic, complemented
76#1862C2×C311yescharacteristic, complemented
77#1852C2×C311yescharacteristic, complemented
78#1735C2×C311yescharacteristic, complemented
79C22×C3×D4—21no—
80C22×C3×D4—21no—
81C22×C3×D4—21no—
82C22×C3×D4—21no—
83C22×C3×D4D411yescharacteristic
84C22×C3×D4C2311yescharacteristic
85C22×C3×D4C2311yescharacteristic
86C23×C3×C4—21no—
87C23×C3×C4—21no—
88C23×C3×C4C2311yescharacteristic
89C23×C3×C4C2311yescharacteristic
90C2×C3×D8—22no—
91C2×C3×D8—22no—
92C2×C3×D8—41no—
93C22×C3×C8—22no—
94C22×C3×C8—22no—
95C22×C3×C8—41no—
96C22×C3×C8C2311yescharacteristic
97C22×C3×C8C2311yescharacteristic
98C22×C3×C8C2311yescharacteristic
99C22×C3×C8C2311yescharacteristic
100C3×#126—28no—
101C3×#125—22no—
102C3×#125—22no—
103C3×#123—28no—
104C3×#121—28no—
105C3×#121—22no—
106C3×#121—22no—
107C3×#121—22no—
108C3×#121—22no—
109C3×#121—22no—
110C3×#121—22no—
111C3×#121—41no—
112C3×#121D414yescomplemented
113C3×C4×D4—28no—
114C3×C4×D4—22no—
115C3×C4×D4—22no—
116C3×C4×D4—22no—
117C3×C4×D4—22no—
118C3×#117—22no—
119C3×#117—22no—
120C3×#117—41no—
121C3×#117D414yescomplemented
122C2×C3×C4⋊C4—21no—
123C2×C3×C4⋊C4—21no—
124C2×C3×C4⋊C4—21no—
125C2×C3×C4⋊C4—22no—
126C2×C3×C4⋊C4—22no—
127C2×C3×C4⋊C4—21no—
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⋊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×#106—22no—
153C3×#102—22no—
154C3×#102—22no—
155C3×#102—22no—
156C3×#102—22no—
157C3×#102—22no—
158C3×#102—41no—
159C3×C22⋊C8—22no—
160C3×C22⋊C8—22no—
161C3×C22⋊C8—41no—
162C3×#95—21no—
163C3×#95—21no—
164C22×D8C22×C311yescharacteristic
165C23×C8C22×C311yescharacteristic
166#553—24no—
167#553—24no—
168C2×#126—21no—
169C2×#125C22×C311yescharacteristic
170C2×#123—21no—
171C2×#121—21no—
172C2×#121C22×C311yescharacteristic
173C2×#121C22×C311yescharacteristic
174C2×#121C22×C311yescharacteristic
175C2×#121C22×C311yescharacteristic
176C2×C4×D4—21no—
177C2×C4×D4C22×C311yescharacteristic
178C2×C4×D4C22×C311yescharacteristic
179C2×#117C22×C311yescharacteristic
180C2×#117C22×C311yescharacteristic
181C22×C4⋊C4C22×C311yescharacteristic
182#482—24no—
183#466—24no—
184C2×#107C22×C311yescharacteristic
185C2×#107C22×C311yescharacteristic
186C2×#106C22×C311yescharacteristic
187C2×#102C22×C311yescharacteristic
188C2×#102C22×C311yescharacteristic
189C2×#102C22×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×C3—21no—
213C24×C3C2×D411yescharacteristic
214C24×C3C2×D411yescharacteristic
215C2×C3×D4—24no—
216C2×C3×D4—22no—
217C2×C3×D4—22no—
218C2×C3×D4—24no—
219C2×C3×D4—21no—
220C2×C3×D4—21no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—41no—
231C2×C3×D4—42no—
232C2×C3×D4—42no—
233C2×C3×D4—42no—
234C2×C3×D4—42no—
235C2×C3×D4—42no—
236C2×C3×D4—81no—
237C2×C3×D4—81no—
238C2×C3×D4—81no—
239C2×C3×D4—81no—
240C2×C3×D4—81no—
241C2×C3×D4C2×D412yes—
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—24no—
251C22×C3×C4—24no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—81no—
261C22×C3×C4—81no—
262C22×C3×C4—81no—
263C22×C3×C4—81no—
264C22×C3×C4C2×D411yescharacteristic
265C22×C3×C4C2×D411yescharacteristic
266C22×C3×C4C2×D411yescharacteristic
267C22×C3×C4C2×D411yescharacteristic
268C22×C3×C4C2×D412yes—
269C22×C3×C4C2×D412yes—
270C22×C3×C4C2411yescharacteristic
271C3×D8—44no—
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—21no—
282C2×C3×C8—21no—
283C2×C3×C8—44no—
284C2×C3×C8#4112yes—
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—24no—
305C3×C22⋊C4—22no—
306C3×C22⋊C4—24no—
307C3×C22⋊C4—22no—
308C3×C22⋊C4—42no—
309C3×C22⋊C4—42no—
310C3×C22⋊C4—42no—
311C3×C22⋊C4—42no—
312C3×C22⋊C4—81no—
313C3×C22⋊C4—81no—
314C3×C42—24no—
315C3×C42—21no—
316C3×C42—21no—
317C3×C42—42no—
318C22×D4—21no—
319C22×D4—21no—
320C22×D4—21no—
321C22×D4—21no—
322C22×D4C3×D411yescharacteristic
323C22×D4C23×C311yescharacteristic
324C22×D4C23×C311yescharacteristic
325C23×C4—21no—
326C23×C4—21no—
327C23×C4C23×C311yescharacteristic
328C23×C4C23×C311yescharacteristic
329C2×D8—22no—
330C2×D8—22no—
331C2×D8—41no—
332C22×C8—22no—
333C22×C8—22no—
334C22×C8—41no—
335C22×C8C23×C311yescharacteristic
336C22×C8C23×C311yescharacteristic
337C22×C8C23×C311yescharacteristic
338C22×C8C23×C311yescharacteristic
339#126—28no—
340#125—22no—
341#125—22no—
342#123—28no—
343#121—28no—
344#121—22no—
345#121—22no—
346#121—22no—
347#121—22no—
348#121—22no—
349#121—22no—
350#121—41no—
351#121C3×D414yescomplemented
352C4×D4—28no—
353C4×D4—22no—
354C4×D4—22no—
355C4×D4—22no—
356C4×D4—22no—
357#117—22no—
358#117—22no—
359#117—41no—
360#117C3×D414yescomplemented
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4C3×D411yescharacteristic
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⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4C3×D411yescharacteristic
385C2×C22⋊C4C3×D411yescharacteristic
386C2×C42—21no—
387C2×C42—21no—
388C2×C42C23×C311yescharacteristic
389#107—22no—
390#107—22no—
391#106—22no—
392#102—22no—
393#102—22no—
394#102—22no—
395#102—22no—
396#102—22no—
397#102—41no—
398C22⋊C8—22no—
399C22⋊C8—22no—
400C22⋊C8—41no—
401#95—21no—
402#95—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—21no—
414C23×C3—21no—
415C23×C3—22no—
416C23×C3—41no—
417C23×C3—41no—
418C23×C3—41no—
419C23×C3—41no—
420C23×C3—41no—
421C23×C3—41no—
422C23×C3—41no—
423C23×C3—41no—
424C23×C3—41no—
425C23×C3—41no—
426C23×C3—41no—
427C23×C3—41no—
428C23×C3—41no—
429C23×C3#12012yes—
430C23×C3#13512yes—
431C23×C3C22×D411yescharacteristic
432C3×D4—22no—
433C3×D4—22no—
434C3×D4—44no—
435C3×D4—48no—
436C3×D4—41no—
437C3×D4—41no—
438C3×D4—41no—
439C3×D4—41no—
440C3×D4—41no—
441C3×D4—41no—
442C3×D4—84no—
443C3×D4—84no—
444C3×D4—84no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—22no—
448C2×C3×C4—22no—
449C2×C3×C4—22no—
450C2×C3×C4—22no—
451C2×C3×C4—21no—
452C2×C3×C4—22no—
453C2×C3×C4—21no—
454C2×C3×C4—22no—
455C2×C3×C4—21no—
456C2×C3×C4—22no—
457C2×C3×C4—22no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
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—41no—
475C2×C3×C4—41no—
476C2×C3×C4—41no—
477C2×C3×C4—41no—
478C2×C3×C4—41no—
479C2×C3×C4—41no—
480C2×C3×C4—41no—
481C2×C3×C4—41no—
482C2×C3×C4—84no—
483C2×C3×C4—84no—
484C2×C3×C4#12012yes—
485C2×C3×C4C22×D411yescharacteristic
486C2×C3×C4C22×D411yescharacteristic
487C2×C3×C4C2×#4111yescharacteristic
488C2×C3×C4C2×#4111yescharacteristic
489C2×C3×C4H(5,𝔽2)11yescharacteristic
490C2×C3×C42−1+411yescharacteristic
491C3×C8—22no—
492C3×C8—41no—
493C3×C8—41no—
494C3×C8—41no—
495C24—21no—
496C24—21no—
497C24C2×C3×D411yescharacteristic
498C24C2×C3×D411yescharacteristic
499C2×D4—24no—
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—24no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—41no—
515C2×D4—42no—
516C2×D4—42no—
517C2×D4—42no—
518C2×D4—42no—
519C2×D4—42no—
520C2×D4—81no—
521C2×D4—81no—
522C2×D4—81no—
523C2×D4—81no—
524C2×D4—81no—
525C2×D4C2×C3×D412yes—
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—24no—
535C22×C4—24no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—81no—
545C22×C4—81no—
546C22×C4—81no—
547C22×C4—81no—
548C22×C4C2×C3×D411yescharacteristic
549C22×C4C2×C3×D411yescharacteristic
550C22×C4C2×C3×D411yescharacteristic
551C22×C4C2×C3×D411yescharacteristic
552C22×C4C2×C3×D412yes—
553C22×C4C2×C3×D412yes—
554C22×C4C24×C311yescharacteristic
555D8—44no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—44no—
568C2×C8C3×#4112yes—
569C4⋊C4—24no—
570C4⋊C4—24no—
571C4⋊C4—24no—
572C4⋊C4—22no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—81no—
582C4⋊C4C2×C3×D412yes—
583C4⋊C4C2×C3×D412yes—
584C4⋊C4C2×C3×D412yes—
585C4⋊C4C3×#4112yes—
586C22⋊C4—24no—
587C22⋊C4—24no—
588C22⋊C4—24no—
589C22⋊C4—22no—
590C22⋊C4—24no—
591C22⋊C4—22no—
592C22⋊C4—42no—
593C22⋊C4—42no—
594C22⋊C4—42no—
595C22⋊C4—42no—
596C22⋊C4—81no—
597C22⋊C4—81no—
598C42—24no—
599C42—21no—
600C42—21no—
601C42—42no—
602C22×C3—22no—
603C22×C3—22no—
604C22×C3—22no—
605C22×C3—22no—
606C22×C3—22no—
607C22×C3—22no—
608C22×C3—41no—
609C22×C3—41no—
610C22×C3—41no—
611C22×C3—41no—
612C22×C3—41no—
613C22×C3—41no—
614C22×C3—41no—
615C22×C3—41no—
616C22×C3—42no—
617C22×C3—42no—
618C22×C3—42no—
619C22×C3—81no—
620C22×C3—81no—
621C22×C3—81no—
622C22×C3—81no—
623C22×C3—81no—
624C22×C3—81no—
625C22×C3—81no—
626C22×C3—81no—
627C22×C3—81no—
628C22×C3—81no—
629C22×C3—81no—
630C22×C3C2×#12011yescharacteristic
631C22×C3#54611yescharacteristic
632C22×C3#54711yescharacteristic
633C22×C3C2×#13511yescharacteristic
634C22×C3#57511yescharacteristic
635C22×C3#57611yescharacteristic
636C22×C3#57611yescharacteristic
637C3×C4—22no—
638C3×C4—41no—
639C3×C4—41no—
640C3×C4—42no—
641C3×C4—41no—
642C3×C4—42no—
643C3×C4—42no—
644C3×C4—42no—
645C3×C4—81no—
646C3×C4—81no—
647C3×C4#53211yescharacteristic
648C3×C4#53711yescharacteristic
649C3×C4#54611yescharacteristic
650C3×C4#54711yescharacteristic
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—22no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23C3×#12012yes—
678C23C3×#13512yes—
679C23C22×C3×D411yescharacteristic
680D4—22no—
681D4—22no—
682D4—44no—
683D4—48no—
684D4—41no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—41no—
690D4—84no—
691D4—84no—
692D4—84no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—22no—
705C2×C4—21no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—84no—
731C2×C4—84no—
732C2×C4C3×#12012yes—
733C2×C4C22×C3×D411yescharacteristic
734C2×C4C22×C3×D411yescharacteristic
735C2×C4C2×C3×#4111yescharacteristic
736C2×C4C2×C3×#4111yescharacteristic
737C2×C4C3×H(5,𝔽2)11yescharacteristic
738C2×C4C3×2−1+411yescharacteristic
739C8—22no—
740C8—41no—
741C8—41no—
742C8—41no—
743C2×C3—42no—
744C2×C3—42no—
745C2×C3—82no—
746C2×C3—161no—
747C2×C3#243011yescharacteristic
748C2×C3#300211yescharacteristic
749C2×C3#300811yescharacteristic
750C2×C3#329711yescharacteristic
751C2×C3#330911yescharacteristic
752C2×C3#333911yescharacteristic
753C2×C3#334711yescharacteristic
754C22—22no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—22no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22C2×C3×#12011yescharacteristic
783C22C3×#54611yescharacteristic
784C22C3×#54711yescharacteristic
785C22C2×C3×#13511yescharacteristic
786C22C3×#57511yescharacteristic
787C22C3×#57611yescharacteristic
788C22C3×#57611yescharacteristic
789C4—22no—
790C4—41no—
791C4—41no—
792C4—42no—
793C4—41no—
794C4—42no—
795C4—42no—
796C4—42no—
797C4—81no—
798C4—81no—
799C4C3×#53211yescharacteristic
800C4C3×#53711yescharacteristic
801C4C3×#54611yescharacteristic
802C4C3×#54711yescharacteristic
803C3#2553411yescharacteristic, direct product factor, Sylow
804C2—42no—
805C2—42no—
806C2—82no—
807C2—161no—
808C2C3×#243011yescharacteristic
809C2C3×#300211yescharacteristic
810C2C3×#300811yescharacteristic
811C2C3×#329711yescharacteristic
812C2C3×#330911yescharacteristic
813C2C3×#333911yescharacteristic
814C2C3×#334711yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
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×#553C2semidirect
2. C2×C3×#482C2semidirect
3. C2×C3×#466C2semidirect
4. C3×#2414C2semidirect
5. C3×#2059C2semidirect
6. C3×#2034C2semidirect
7. C3×#2025C2semidirect
8. C3×#1999C2semidirect
9. C3×#1879C2semidirect
10. C3×#1875C2semidirect
11. C3×#1874C2semidirect
12. C3×#1869C2semidirect
13. C3×#1862C2semidirect
14. C3×#1852C2semidirect
15. C3×#1735C2semidirect
16. #25534C3direct (N × H)
64. C2×#553C2×C3semidirect
65. C2×#482C2×C3semidirect
66. C2×#466C2×C3semidirect
67. #2414C2×C3semidirect
68. #2059C2×C3semidirect
69. #2034C2×C3semidirect
70. #2025C2×C3semidirect
71. #1999C2×C3semidirect
72. #1879C2×C3semidirect
73. #1875C2×C3semidirect
74. #1874C2×C3semidirect
75. #1869C2×C3semidirect
76. #1862C2×C3semidirect
77. #1852C2×C3semidirect
78. #1735C2×C3semidirect
112. C3×#121D4semidirect
121. C3×#117D4semidirect
351. #121C3×D4semidirect
360. #117C3×D4semidirect
803. C3#25534direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5532
C2×C3×#4822
C2×C3×#4662
C3×#24142
C3×#20592
C3×#20342
C3×#20252
C3×#19992
C3×#18792
C3×#18752
C3×#18742
C3×#18692
C3×#18622
C3×#18522
C3×#17352
#255343