Finite Group Databasebeta

← C3×#25576 #10644183

Subgroups — C3×#25576 #10644183

Order 768.

1174 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#552C211yesmaximal, characteristic, complemented
2C2×C3×#488C211yesmaximal, characteristic, complemented
3C2×C3×#464C211yesmaximal, characteristic, complemented
4C3×#2540C211yesmaximal, characteristic
5C3×#2001C211yesmaximal, characteristic, complemented
6C3×#2001C211yesmaximal, characteristic, complemented
7C3×#2000C211yesmaximal, characteristic, complemented
8C3×#2000C211yesmaximal, characteristic, complemented
9C3×#1989C211yesmaximal, characteristic, complemented
10C3×#1954C211yesmaximal, characteristic, complemented
11C3×#1875C211yesmaximal, characteristic, complemented
12C3×#1874C211yesmaximal, characteristic, complemented
13C3×#1873C211yesmaximal, characteristic, complemented
14C3×#1872C211yesmaximal, characteristic, complemented
15C3×C4×#103C211yesmaximal, characteristic, complemented
16#25576C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×Q16C2211yescharacteristic
18C22×C3×SD16C2211yescharacteristic
19C3×#552—24no—
20C3×#552—24no—
21C2×C3×#126—21no—
22C2×C3×#125—21no—
23C2×C3×#125C2211yescharacteristic
24C2×C3×#124C2211yescharacteristic
25C2×C3×#123—21no—
26C2×C3×C22⋊Q8C2211yescharacteristic
27C2×C3×C22⋊Q8C2211yescharacteristic
28C2×C3×C22⋊Q8C2211yescharacteristic
29C2×C3×C22⋊Q8C2211yescharacteristic
30C2×C3×#121C2211yescharacteristic
31C2×C3×#121C2211yescharacteristic
32C2×C3×C4×Q8C2211yescharacteristic
33C2×C3×C4×D4C2211yescharacteristic
34C2×C3×#117—21no—
35C2×C3×#117C2211yescharacteristic
36C22×C3×C4⋊C4C2211yescharacteristic
37C3×#488—24no—
38C3×#464—24no—
39C2×C3×C4⋊C8C2211yescharacteristic
40C2×C3×#103C2211yescharacteristic
41C2×C3×#103C2211yescharacteristic
42C2×C3×#103C2211yescharacteristic
43C2×C3×#103C2211yescharacteristic
44C2×C3×#103C2211yescharacteristic
45C2×C3×#102C2211yescharacteristic
46C2×C3×#102C2211yescharacteristic
47C2×C3×#102C2211yescharacteristic
48C2×C3×C22⋊C8C2211yescharacteristic
49C2×C3×C22⋊C8C2211yescharacteristic
50C2×C3×C22⋊C8C2211yescharacteristic
51C2×C3×C22⋊C8C2211yescharacteristic
52C2×C3×C4×C8C2211yescharacteristic
53C3×#399—21no—
54C3×#392—21no—
55C3×#390—21no—
56C3×#390—21no—
57C3×C4×C4⋊C4C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#340C2211yescharacteristic
61C3×#340C2211yescharacteristic
62C3×#340C2211yescharacteristic
63C3×#340C2211yescharacteristic
64C2×#552C2×C311yescharacteristic, complemented
65C2×#488C2×C311yescharacteristic, complemented
66C2×#464C2×C311yescharacteristic, complemented
67#2540C2×C311yescharacteristic
68#2001C2×C311yescharacteristic, complemented
69#2001C2×C311yescharacteristic, complemented
70#2000C2×C311yescharacteristic, complemented
71#2000C2×C311yescharacteristic, complemented
72#1989C2×C311yescharacteristic, complemented
73#1954C2×C311yescharacteristic, complemented
74#1875C2×C311yescharacteristic, complemented
75#1874C2×C311yescharacteristic, complemented
76#1873C2×C311yescharacteristic, complemented
77#1872C2×C311yescharacteristic, complemented
78C4×#103C2×C311yescharacteristic, complemented
79C22×C3×Q8C2311yescharacteristic
80C22×C3×Q8C2311yescharacteristic
81C22×C3×D4—21no—
82C22×C3×D4—21no—
83C22×C3×D4D411yescharacteristic
84C22×C3×D4C2311yescharacteristic
85C23×C3×C4—21no—
86C23×C3×C4C2311yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C2×C3×Q16—22no—
89C2×C3×Q16—41no—
90C2×C3×Q16—41no—
91C2×C3×SD16—22no—
92C2×C3×SD16—41no—
93C2×C3×SD16—41no—
94C22×C3×C8C2311yescharacteristic
95C22×C3×C8C2311yescharacteristic
96C22×C3×C8C2311yescharacteristic
97C22×C3×C8C2311yescharacteristic
98C3×#126—28no—
99C3×#125—28no—
100C3×#125—22no—
101C3×#125D414yescomplemented
102C3×#124—22no—
103C3×#124—22no—
104C3×#123—28no—
105C3×C22⋊Q8—22no—
106C3×C22⋊Q8—22no—
107C3×C22⋊Q8—22no—
108C3×C22⋊Q8—22no—
109C3×C22⋊Q8—22no—
110C3×C22⋊Q8—22no—
111C3×C22⋊Q8—41no—
112C3×C22⋊Q8—41no—
113C3×#121—22no—
114C3×#121—22no—
115C3×#121—41no—
116C3×#121—41no—
117C3×C4×Q8—22no—
118C3×C4×Q8D414yescomplemented
119C3×C4×D4—22no—
120C3×C4×D4—22no—
121C3×#117—28no—
122C3×#117—22no—
123C3×#117—22no—
124C2×C3×C4⋊C4—21no—
125C2×C3×C4⋊C4—21no—
126C2×C3×C4⋊C4—21no—
127C2×C3×C4⋊C4—21no—
128C2×C3×C4⋊C4—21no—
129C2×C3×C4⋊C4—21no—
130C2×C3×C4⋊C4—22no—
131C2×C3×C4⋊C4—22no—
132C2×C3×C4⋊C4—21no—
133C2×C3×C4⋊C4—21no—
134C2×C3×C4⋊C4D411yescharacteristic
135C2×C3×C4⋊C4C2311yescharacteristic
136C2×C3×C4⋊C4C2311yescharacteristic
137C2×C3×C4⋊C4C2311yescharacteristic
138C2×C3×C4⋊C4C2311yescharacteristic
139C2×C3×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
146C2×C3×C22⋊C4—21no—
147C2×C3×C22⋊C4—21no—
148C2×C3×C22⋊C4—21no—
149C2×C3×C22⋊C4D411yescharacteristic
150C2×C3×C22⋊C4D411yescharacteristic
151C2×C3×C42—21no—
152C2×C3×C42—21no—
153C2×C3×C42—21no—
154C2×C3×C42C2311yescharacteristic
155C3×C4⋊C8—22no—
156C3×#103—22no—
157C3×#103—22no—
158C3×#103—22no—
159C3×#103—22no—
160C3×#103—22no—
161C3×#102—22no—
162C3×#102—22no—
163C3×#102—22no—
164C3×C22⋊C8—41no—
165C3×C22⋊C8—41no—
166C3×C22⋊C8—41no—
167C3×C22⋊C8—41no—
168C3×C4×C8—22no—
169C3×#95—21no—
170C22×Q16C22×C311yescharacteristic
171C22×SD16C22×C311yescharacteristic
172#552—24no—
173#552—24no—
174C2×#126—21no—
175C2×#125—21no—
176C2×#125C22×C311yescharacteristic
177C2×#124C22×C311yescharacteristic
178C2×#123—21no—
179C2×C22⋊Q8C22×C311yescharacteristic
180C2×C22⋊Q8C22×C311yescharacteristic
181C2×C22⋊Q8C22×C311yescharacteristic
182C2×C22⋊Q8C22×C311yescharacteristic
183C2×#121C22×C311yescharacteristic
184C2×#121C22×C311yescharacteristic
185C2×C4×Q8C22×C311yescharacteristic
186C2×C4×D4C22×C311yescharacteristic
187C2×#117—21no—
188C2×#117C22×C311yescharacteristic
189C22×C4⋊C4C22×C311yescharacteristic
190#488—24no—
191#464—24no—
192C2×C4⋊C8C22×C311yescharacteristic
193C2×#103C22×C311yescharacteristic
194C2×#103C22×C311yescharacteristic
195C2×#103C22×C311yescharacteristic
196C2×#103C22×C311yescharacteristic
197C2×#103C22×C311yescharacteristic
198C2×#102C22×C311yescharacteristic
199C2×#102C22×C311yescharacteristic
200C2×#102C22×C311yescharacteristic
201C2×C22⋊C8C22×C311yescharacteristic
202C2×C22⋊C8C22×C311yescharacteristic
203C2×C22⋊C8C22×C311yescharacteristic
204C2×C22⋊C8C22×C311yescharacteristic
205C2×C4×C8C22×C311yescharacteristic
206#399—21no—
207#392—21no—
208#390—21no—
209#390—21no—
210C4×C4⋊C4C22×C311yescharacteristic
211#340C22×C311yescharacteristic
212#340C22×C311yescharacteristic
213#340C22×C311yescharacteristic
214#340C22×C311yescharacteristic
215#340C22×C311yescharacteristic
216#340C22×C311yescharacteristic
217C24×C3—21no—
218C24×C3C2×D411yescharacteristic
219C24×C3C2×D411yescharacteristic
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8—21no—
224C2×C3×Q8—21no—
225C2×C3×Q8—21no—
226C2×C3×Q8—21no—
227C2×C3×Q8—21no—
228C2×C3×Q8—21no—
229C2×C3×Q8—21no—
230C2×C3×Q8—21no—
231C2×C3×Q8C2×D412yes—
232C2×C3×D4—22no—
233C2×C3×D4—22no—
234C2×C3×D4—21no—
235C2×C3×D4—21no—
236C2×C3×D4—21no—
237C2×C3×D4—21no—
238C2×C3×D4—21no—
239C2×C3×D4—21no—
240C2×C3×D4—41no—
241C2×C3×D4—42no—
242C2×C3×D4—42no—
243C2×C3×D4—42no—
244C2×C3×D4—42no—
245C2×C3×D4—81no—
246C2×C3×D4—81no—
247C22×C3×C4—24no—
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—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—42no—
268C22×C3×C4—42no—
269C22×C3×C4C2×D411yescharacteristic
270C22×C3×C4C2×D411yescharacteristic
271C22×C3×C4C2×D411yescharacteristic
272C22×C3×C4C2×D411yescharacteristic
273C22×C3×C4C2411yescharacteristic
274C3×Q16—44no—
275C3×SD16—44no—
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—21no—
284C2×C3×C8—21no—
285C2×C3×C8—21no—
286C2×C3×C8—21no—
287C2×C3×C8—21no—
288C3×C4⋊C4—24no—
289C3×C4⋊C4—24no—
290C3×C4⋊C4—24no—
291C3×C4⋊C4—24no—
292C3×C4⋊C4—24no—
293C3×C4⋊C4—24no—
294C3×C4⋊C4—22no—
295C3×C4⋊C4—21no—
296C3×C4⋊C4—21no—
297C3×C4⋊C4—21no—
298C3×C4⋊C4—21no—
299C3×C4⋊C4—21no—
300C3×C4⋊C4—42no—
301C3×C4⋊C4—42no—
302C3×C4⋊C4C2×D412yes—
303C3×C4⋊C4C2×D412yes—
304C3×C4⋊C4C2×D412yes—
305C3×C4⋊C4#4112yes—
306C3×C4⋊C4#4112yes—
307C3×C22⋊C4—24no—
308C3×C22⋊C4—24no—
309C3×C22⋊C4—24no—
310C3×C22⋊C4—22no—
311C3×C22⋊C4—22no—
312C3×C22⋊C4—42no—
313C3×C22⋊C4—42no—
314C3×C22⋊C4—42no—
315C3×C22⋊C4—42no—
316C3×C22⋊C4—42no—
317C3×C22⋊C4—42no—
318C3×C42—24no—
319C3×C42—24no—
320C3×C42—81no—
321C3×C42C2×D412yes—
322C3×C42C2×D412yes—
323C22×Q8C23×C311yescharacteristic
324C22×Q8C23×C311yescharacteristic
325C22×D4—21no—
326C22×D4—21no—
327C22×D4C3×D411yescharacteristic
328C22×D4C23×C311yescharacteristic
329C23×C4—21no—
330C23×C4C23×C311yescharacteristic
331C23×C4C23×C311yescharacteristic
332C2×Q16—22no—
333C2×Q16—41no—
334C2×Q16—41no—
335C2×SD16—22no—
336C2×SD16—41no—
337C2×SD16—41no—
338C22×C8C23×C311yescharacteristic
339C22×C8C23×C311yescharacteristic
340C22×C8C23×C311yescharacteristic
341C22×C8C23×C311yescharacteristic
342#126—28no—
343#125—28no—
344#125—22no—
345#125C3×D414yescomplemented
346#124—22no—
347#124—22no—
348#123—28no—
349C22⋊Q8—22no—
350C22⋊Q8—22no—
351C22⋊Q8—22no—
352C22⋊Q8—22no—
353C22⋊Q8—22no—
354C22⋊Q8—22no—
355C22⋊Q8—41no—
356C22⋊Q8—41no—
357#121—22no—
358#121—22no—
359#121—41no—
360#121—41no—
361C4×Q8—22no—
362C4×Q8C3×D414yescomplemented
363C4×D4—22no—
364C4×D4—22no—
365#117—28no—
366#117—22no—
367#117—22no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4C3×D411yescharacteristic
379C2×C4⋊C4C23×C311yescharacteristic
380C2×C4⋊C4C23×C311yescharacteristic
381C2×C4⋊C4C23×C311yescharacteristic
382C2×C4⋊C4C23×C311yescharacteristic
383C2×C4⋊C4C23×C311yescharacteristic
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4C3×D411yescharacteristic
394C2×C22⋊C4C3×D411yescharacteristic
395C2×C42—21no—
396C2×C42—21no—
397C2×C42—21no—
398C2×C42C23×C311yescharacteristic
399C4⋊C8—22no—
400#103—22no—
401#103—22no—
402#103—22no—
403#103—22no—
404#103—22no—
405#102—22no—
406#102—22no—
407#102—22no—
408C22⋊C8—41no—
409C22⋊C8—41no—
410C22⋊C8—41no—
411C22⋊C8—41no—
412C4×C8—22no—
413#95—21no—
414C23×C3—21no—
415C23×C3—21no—
416C23×C3—21no—
417C23×C3—21no—
418C23×C3—21no—
419C23×C3—21no—
420C23×C3—21no—
421C23×C3—21no—
422C23×C3—21no—
423C23×C3—21no—
424C23×C3—21no—
425C23×C3—21no—
426C23×C3—21no—
427C23×C3—41no—
428C23×C3—41no—
429C23×C3—41no—
430C23×C3—41no—
431C23×C3—41no—
432C23×C3—41no—
433C23×C3—41no—
434C23×C3#13512yes—
435C23×C3C22×D411yescharacteristic
436C3×Q8—22no—
437C3×Q8—22no—
438C3×Q8—41no—
439C3×Q8—41no—
440C3×Q8—41no—
441C3×Q8—41no—
442C3×Q8—41no—
443C3×Q8—41no—
444C3×D4—44no—
445C3×D4—41no—
446C3×D4—41no—
447C3×D4—41no—
448C3×D4—41no—
449C3×D4—84no—
450C3×D4—84no—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—22no—
457C2×C3×C4—22no—
458C2×C3×C4—22no—
459C2×C3×C4—21no—
460C2×C3×C4—22no—
461C2×C3×C4—22no—
462C2×C3×C4—22no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—48no—
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—41no—
483C2×C3×C4—41no—
484C2×C3×C4—41no—
485C2×C3×C4—41no—
486C2×C3×C4—41no—
487C2×C3×C4—41no—
488C2×C3×C4—41no—
489C2×C3×C4—41no—
490C2×C3×C4—41no—
491C2×C3×C4#12012yes—
492C2×C3×C4#12012yes—
493C2×C3×C4C22×D411yescharacteristic
494C2×C3×C4C22×D411yescharacteristic
495C2×C3×C4C2×#4111yescharacteristic
496C2×C3×C4C2×#4111yescharacteristic
497C2×C3×C4H(5,𝔽2)11yescharacteristic
498C2×C3×C4H(5,𝔽2)11yescharacteristic
499C3×C8—41no—
500C3×C8—41no—
501C3×C8—41no—
502C3×C8—41no—
503C24—21no—
504C24C2×C3×D411yescharacteristic
505C24C2×C3×D411yescharacteristic
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8C2×C3×D412yes—
518C2×D4—22no—
519C2×D4—22no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—41no—
527C2×D4—42no—
528C2×D4—42no—
529C2×D4—42no—
530C2×D4—42no—
531C2×D4—81no—
532C2×D4—81no—
533C22×C4—24no—
534C22×C4—21no—
535C22×C4—21no—
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—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4C2×C3×D411yescharacteristic
556C22×C4C2×C3×D411yescharacteristic
557C22×C4C2×C3×D411yescharacteristic
558C22×C4C2×C3×D411yescharacteristic
559C22×C4C24×C311yescharacteristic
560Q16—44no—
561SD16—44no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C4⋊C4—24no—
575C4⋊C4—24no—
576C4⋊C4—24no—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—24no—
580C4⋊C4—22no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—42no—
587C4⋊C4—42no—
588C4⋊C4C2×C3×D412yes—
589C4⋊C4C2×C3×D412yes—
590C4⋊C4C2×C3×D412yes—
591C4⋊C4C3×#4112yes—
592C4⋊C4C3×#4112yes—
593C22⋊C4—24no—
594C22⋊C4—24no—
595C22⋊C4—24no—
596C22⋊C4—22no—
597C22⋊C4—22no—
598C22⋊C4—42no—
599C22⋊C4—42no—
600C22⋊C4—42no—
601C22⋊C4—42no—
602C22⋊C4—42no—
603C22⋊C4—42no—
604C42—24no—
605C42—24no—
606C42—81no—
607C42C2×C3×D412yes—
608C42C2×C3×D412yes—
609C22×C3—22no—
610C22×C3—22no—
611C22×C3—22no—
612C22×C3—41no—
613C22×C3—41no—
614C22×C3—41no—
615C22×C3—41no—
616C22×C3—41no—
617C22×C3—41no—
618C22×C3—41no—
619C22×C3—41no—
620C22×C3—41no—
621C22×C3—41no—
622C22×C3—41no—
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#54611yescharacteristic
633C22×C3C2×#13511yescharacteristic
634C22×C3#57511yescharacteristic
635C22×C3#57711yescharacteristic
636C22×C3#57811yescharacteristic
637C3×C4—22no—
638C3×C4—22no—
639C3×C4—41no—
640C3×C4—41no—
641C3×C4—42no—
642C3×C4—42no—
643C3×C4—42no—
644C3×C4—42no—
645C3×C4—42no—
646C3×C4—42no—
647C3×C4—81no—
648C3×C4#53211yescharacteristic
649C3×C4#53511yescharacteristic
650C3×C4#55011yescharacteristic
651C3×C4#55011yescharacteristic
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23C3×#13512yes—
673C23C22×C3×D411yescharacteristic
674Q8—22no—
675Q8—22no—
676Q8—41no—
677Q8—41no—
678Q8—41no—
679Q8—41no—
680Q8—41no—
681Q8—41no—
682D4—44no—
683D4—41no—
684D4—41no—
685D4—41no—
686D4—41no—
687D4—84no—
688D4—84no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—21no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—48no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
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×C4C3×#12012yes—
730C2×C4C3×#12012yes—
731C2×C4C22×C3×D411yescharacteristic
732C2×C4C22×C3×D411yescharacteristic
733C2×C4C2×C3×#4111yescharacteristic
734C2×C4C2×C3×#4111yescharacteristic
735C2×C4C3×H(5,𝔽2)11yescharacteristic
736C2×C4C3×H(5,𝔽2)11yescharacteristic
737C8—41no—
738C8—41no—
739C8—41no—
740C8—41no—
741C2×C3—42no—
742C2×C3—81no—
743C2×C3—161no—
744C2×C3#243111yescharacteristic
745C2×C3#300211yescharacteristic
746C2×C3#301311yescharacteristic
747C2×C3#329611yescharacteristic
748C2×C3#330011yescharacteristic
749C2×C3#332311yescharacteristic
750C2×C3#332711yescharacteristic
751C22—22no—
752C22—22no—
753C22—22no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—81no—
766C22—81no—
767C22—81no—
768C22—81no—
769C22—81no—
770C22—81no—
771C22—81no—
772C22C2×C3×#12011yescharacteristic
773C22C3×#54611yescharacteristic
774C22C3×#54611yescharacteristic
775C22C2×C3×#13511yescharacteristic
776C22C3×#57511yescharacteristic
777C22C3×#57711yescharacteristic
778C22C3×#57811yescharacteristic
779C4—22no—
780C4—22no—
781C4—41no—
782C4—41no—
783C4—42no—
784C4—42no—
785C4—42no—
786C4—42no—
787C4—42no—
788C4—42no—
789C4—81no—
790C4C3×#53211yescharacteristic
791C4C3×#53511yescharacteristic
792C4C3×#55011yescharacteristic
793C4C3×#55011yescharacteristic
794C3#2557611yescharacteristic, direct product factor, Sylow
795C2—42no—
796C2—81no—
797C2—161no—
798C2C3×#243111yescharacteristic
799C2C3×#300211yescharacteristic
800C2C3×#301311yescharacteristic
801C2C3×#329611yescharacteristic
802C2C3×#330011yescharacteristic
803C2C3×#332311yescharacteristic
804C2C3×#332711yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC3×#2540C2
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×#552C2semidirect
2. C2×C3×#488C2semidirect
3. C2×C3×#464C2semidirect
5. C3×#2001C2semidirect
6. C3×#2001C2semidirect
7. C3×#2000C2semidirect
8. C3×#2000C2semidirect
9. C3×#1989C2semidirect
10. C3×#1954C2semidirect
11. C3×#1875C2semidirect
12. C3×#1874C2semidirect
13. C3×#1873C2semidirect
14. C3×#1872C2semidirect
15. C3×C4×#103C2semidirect
16. #25576C3direct (N × H)
64. C2×#552C2×C3semidirect
65. C2×#488C2×C3semidirect
66. C2×#464C2×C3semidirect
68. #2001C2×C3semidirect
69. #2001C2×C3semidirect
70. #2000C2×C3semidirect
71. #2000C2×C3semidirect
72. #1989C2×C3semidirect
73. #1954C2×C3semidirect
74. #1875C2×C3semidirect
75. #1874C2×C3semidirect
76. #1873C2×C3semidirect
77. #1872C2×C3semidirect
78. C4×#103C2×C3semidirect
101. C3×#125D4semidirect
118. C3×C4×Q8D4semidirect
345. #125C3×D4semidirect
362. C4×Q8C3×D4semidirect
794. C3#25576direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5522
C2×C3×#4882
C2×C3×#4642
C3×#25402
C3×#20012
C3×#20002
C3×#19892
C3×#19542
C3×#18752
C3×#18742
C3×#18732
C3×#18722
C3×C4×#1032
#255763