Finite Group Databasebeta

← C3×#25575 #10644182

Subgroups — C3×#25575 #10644182

Order 768.

1238 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#553C211yesmaximal, characteristic, complemented
2C2×C3×#488C211yesmaximal, characteristic, complemented
3C2×C3×#463C211yesmaximal, characteristic, complemented
4C3×#2540C211yesmaximal, characteristic, complemented
5C3×#2000C211yesmaximal, characteristic, complemented
6C3×#2000C211yesmaximal, characteristic, complemented
7C3×#1999C211yesmaximal, characteristic, complemented
8C3×#1999C211yesmaximal, 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×#102C211yesmaximal, characteristic, complemented
16#25575C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×SD16C2211yescharacteristic
18C22×C3×D8C2211yescharacteristic
19C3×#553—24no—
20C3×#553—24no—
21C2×C3×#126—21no—
22C2×C3×#125C2211yescharacteristic
23C2×C3×#124C2211yescharacteristic
24C2×C3×#123—21no—
25C2×C3×C22⋊Q8C2211yescharacteristic
26C2×C3×C22⋊Q8C2211yescharacteristic
27C2×C3×#121—21no—
28C2×C3×#121C2211yescharacteristic
29C2×C3×#121C2211yescharacteristic
30C2×C3×#121C2211yescharacteristic
31C2×C3×#121C2211yescharacteristic
32C2×C3×C4×D4—21no—
33C2×C3×C4×D4C2211yescharacteristic
34C2×C3×C4×D4C2211yescharacteristic
35C2×C3×#117C2211yescharacteristic
36C22×C3×C4⋊C4C2211yescharacteristic
37C3×#488—24no—
38C3×#463—24no—
39C2×C3×C4⋊C8C2211yescharacteristic
40C2×C3×#103C2211yescharacteristic
41C2×C3×#103C2211yescharacteristic
42C2×C3×#103C2211yescharacteristic
43C2×C3×#102C2211yescharacteristic
44C2×C3×#102C2211yescharacteristic
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×#553C2×C311yescharacteristic, complemented
65C2×#488C2×C311yescharacteristic, complemented
66C2×#463C2×C311yescharacteristic, complemented
67#2540C2×C311yescharacteristic, complemented
68#2000C2×C311yescharacteristic, complemented
69#2000C2×C311yescharacteristic, complemented
70#1999C2×C311yescharacteristic, complemented
71#1999C2×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×#102C2×C311yescharacteristic, complemented
79C22×C3×Q8C2311yescharacteristic
80C22×C3×D4—21no—
81C22×C3×D4—21no—
82C22×C3×D4—21no—
83C22×C3×D4—21no—
84C22×C3×D4D411yescharacteristic
85C22×C3×D4C2311yescharacteristic
86C22×C3×D4C2311yescharacteristic
87C23×C3×C4—21no—
88C23×C3×C4—21no—
89C23×C3×C4C2311yescharacteristic
90C23×C3×C4C2311yescharacteristic
91C2×C3×SD16—22no—
92C2×C3×SD16—41no—
93C2×C3×SD16—41no—
94C2×C3×D8—22no—
95C2×C3×D8—41no—
96C2×C3×D8—41no—
97C22×C3×C8C2311yescharacteristic
98C22×C3×C8C2311yescharacteristic
99C22×C3×C8C2311yescharacteristic
100C22×C3×C8C2311yescharacteristic
101C3×#126—28no—
102C3×#125—22no—
103C3×#125D414yescomplemented
104C3×#124—22no—
105C3×#124—22no—
106C3×#123—28no—
107C3×C22⋊Q8—22no—
108C3×C22⋊Q8—22no—
109C3×C22⋊Q8—41no—
110C3×C22⋊Q8—41no—
111C3×#121—28no—
112C3×#121—22no—
113C3×#121—22no—
114C3×#121—22no—
115C3×#121—22no—
116C3×#121—22no—
117C3×#121—22no—
118C3×#121—41no—
119C3×#121—41no—
120C3×C4×D4—28no—
121C3×C4×D4—22no—
122C3×C4×D4—22no—
123C3×C4×D4—22no—
124C3×C4×D4D414yescomplemented
125C3×#117—22no—
126C3×#117—22no—
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⋊C4—21no—
150C2×C3×C22⋊C4D411yescharacteristic
151C2×C3×C22⋊C4D411yescharacteristic
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×#102—22no—
160C3×#102—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×SD16C22×C311yescharacteristic
171C22×D8C22×C311yescharacteristic
172#553—24no—
173#553—24no—
174C2×#126—21no—
175C2×#125C22×C311yescharacteristic
176C2×#124C22×C311yescharacteristic
177C2×#123—21no—
178C2×C22⋊Q8C22×C311yescharacteristic
179C2×C22⋊Q8C22×C311yescharacteristic
180C2×#121—21no—
181C2×#121C22×C311yescharacteristic
182C2×#121C22×C311yescharacteristic
183C2×#121C22×C311yescharacteristic
184C2×#121C22×C311yescharacteristic
185C2×C4×D4—21no—
186C2×C4×D4C22×C311yescharacteristic
187C2×C4×D4C22×C311yescharacteristic
188C2×#117C22×C311yescharacteristic
189C22×C4⋊C4C22×C311yescharacteristic
190#488—24no—
191#463—24no—
192C2×C4⋊C8C22×C311yescharacteristic
193C2×#103C22×C311yescharacteristic
194C2×#103C22×C311yescharacteristic
195C2×#103C22×C311yescharacteristic
196C2×#102C22×C311yescharacteristic
197C2×#102C22×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×C3—21no—
219C24×C3C2×D411yescharacteristic
220C24×C3C2×D411yescharacteristic
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×D4—24no—
228C2×C3×D4—22no—
229C2×C3×D4—24no—
230C2×C3×D4—22no—
231C2×C3×D4—21no—
232C2×C3×D4—21no—
233C2×C3×D4—21no—
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—21no—
241C2×C3×D4—21no—
242C2×C3×D4—41no—
243C2×C3×D4—42no—
244C2×C3×D4—42no—
245C2×C3×D4—42no—
246C2×C3×D4—42no—
247C2×C3×D4—42no—
248C2×C3×D4—42no—
249C2×C3×D4—81no—
250C2×C3×D4—81no—
251C2×C3×D4—81no—
252C2×C3×D4—81no—
253C2×C3×D4C2×D412yes—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—24no—
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—21no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—24no—
273C22×C3×C4—21no—
274C22×C3×C4—81no—
275C22×C3×C4—81no—
276C22×C3×C4—81no—
277C22×C3×C4—81no—
278C22×C3×C4C2×D411yescharacteristic
279C22×C3×C4C2×D411yescharacteristic
280C22×C3×C4C2×D411yescharacteristic
281C22×C3×C4C2×D411yescharacteristic
282C22×C3×C4C2411yescharacteristic
283C3×SD16—44no—
284C3×D8—44no—
285C2×C3×C8—21no—
286C2×C3×C8—21no—
287C2×C3×C8—21no—
288C2×C3×C8—21no—
289C2×C3×C8—21no—
290C2×C3×C8—21no—
291C2×C3×C8—21no—
292C2×C3×C8—21no—
293C2×C3×C8—21no—
294C2×C3×C8—21no—
295C2×C3×C8—21no—
296C2×C3×C8—21no—
297C3×C4⋊C4—24no—
298C3×C4⋊C4—24no—
299C3×C4⋊C4—24no—
300C3×C4⋊C4—22no—
301C3×C4⋊C4—21no—
302C3×C4⋊C4—21no—
303C3×C4⋊C4—21no—
304C3×C4⋊C4—21no—
305C3×C4⋊C4—21no—
306C3×C4⋊C4—42no—
307C3×C4⋊C4—42no—
308C3×C4⋊C4C2×D412yes—
309C3×C4⋊C4C2×D412yes—
310C3×C4⋊C4C2×D412yes—
311C3×C4⋊C4#4112yes—
312C3×C4⋊C4#4112yes—
313C3×C22⋊C4—24no—
314C3×C22⋊C4—24no—
315C3×C22⋊C4—24no—
316C3×C22⋊C4—24no—
317C3×C22⋊C4—22no—
318C3×C22⋊C4—22no—
319C3×C22⋊C4—42no—
320C3×C22⋊C4—42no—
321C3×C22⋊C4—42no—
322C3×C22⋊C4—42no—
323C3×C22⋊C4—42no—
324C3×C22⋊C4—42no—
325C3×C42—24no—
326C3×C42—81no—
327C3×C42C2×D412yes—
328C3×C42C2×D412yes—
329C22×Q8C23×C311yescharacteristic
330C22×D4—21no—
331C22×D4—21no—
332C22×D4—21no—
333C22×D4—21no—
334C22×D4C3×D411yescharacteristic
335C22×D4C23×C311yescharacteristic
336C22×D4C23×C311yescharacteristic
337C23×C4—21no—
338C23×C4—21no—
339C23×C4C23×C311yescharacteristic
340C23×C4C23×C311yescharacteristic
341C2×SD16—22no—
342C2×SD16—41no—
343C2×SD16—41no—
344C2×D8—22no—
345C2×D8—41no—
346C2×D8—41no—
347C22×C8C23×C311yescharacteristic
348C22×C8C23×C311yescharacteristic
349C22×C8C23×C311yescharacteristic
350C22×C8C23×C311yescharacteristic
351#126—28no—
352#125—22no—
353#125C3×D414yescomplemented
354#124—22no—
355#124—22no—
356#123—28no—
357C22⋊Q8—22no—
358C22⋊Q8—22no—
359C22⋊Q8—41no—
360C22⋊Q8—41no—
361#121—28no—
362#121—22no—
363#121—22no—
364#121—22no—
365#121—22no—
366#121—22no—
367#121—22no—
368#121—41no—
369#121—41no—
370C4×D4—28no—
371C4×D4—22no—
372C4×D4—22no—
373C4×D4—22no—
374C4×D4C3×D414yescomplemented
375#117—22no—
376#117—22no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4C3×D411yescharacteristic
385C2×C4⋊C4C23×C311yescharacteristic
386C2×C4⋊C4C23×C311yescharacteristic
387C2×C4⋊C4C23×C311yescharacteristic
388C2×C4⋊C4C23×C311yescharacteristic
389C2×C4⋊C4C23×C311yescharacteristic
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4C3×D411yescharacteristic
401C2×C22⋊C4C3×D411yescharacteristic
402C2×C42—21no—
403C2×C42—21no—
404C2×C42C23×C311yescharacteristic
405C4⋊C8—22no—
406#103—22no—
407#103—22no—
408#103—22no—
409#102—22no—
410#102—22no—
411#102—22no—
412#102—22no—
413#102—22no—
414C22⋊C8—41no—
415C22⋊C8—41no—
416C22⋊C8—41no—
417C22⋊C8—41no—
418C4×C8—22no—
419#95—21no—
420C23×C3—21no—
421C23×C3—21no—
422C23×C3—21no—
423C23×C3—21no—
424C23×C3—21no—
425C23×C3—21no—
426C23×C3—21no—
427C23×C3—22no—
428C23×C3—21no—
429C23×C3—21no—
430C23×C3—21no—
431C23×C3—21no—
432C23×C3—21no—
433C23×C3—21no—
434C23×C3—41no—
435C23×C3—41no—
436C23×C3—41no—
437C23×C3—41no—
438C23×C3—41no—
439C23×C3—41no—
440C23×C3—41no—
441C23×C3—41no—
442C23×C3—41no—
443C23×C3—41no—
444C23×C3—41no—
445C23×C3—41no—
446C23×C3—41no—
447C23×C3#13512yes—
448C23×C3C22×D411yescharacteristic
449C3×Q8—41no—
450C3×Q8—41no—
451C3×Q8—41no—
452C3×Q8—41no—
453C3×D4—22no—
454C3×D4—22no—
455C3×D4—44no—
456C3×D4—48no—
457C3×D4—41no—
458C3×D4—41no—
459C3×D4—41no—
460C3×D4—41no—
461C3×D4—41no—
462C3×D4—41no—
463C3×D4—84no—
464C3×D4—84no—
465C3×D4—84no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—22no—
472C2×C3×C4—22no—
473C2×C3×C4—21no—
474C2×C3×C4—22no—
475C2×C3×C4—22no—
476C2×C3×C4—22no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
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—41no—
492C2×C3×C4—41no—
493C2×C3×C4—41no—
494C2×C3×C4—41no—
495C2×C3×C4—41no—
496C2×C3×C4—41no—
497C2×C3×C4—41no—
498C2×C3×C4—41no—
499C2×C3×C4—41no—
500C2×C3×C4—41no—
501C2×C3×C4—41no—
502C2×C3×C4—84no—
503C2×C3×C4—84no—
504C2×C3×C4#12012yes—
505C2×C3×C4#12012yes—
506C2×C3×C4C22×D411yescharacteristic
507C2×C3×C4C22×D411yescharacteristic
508C2×C3×C4C2×#4111yescharacteristic
509C2×C3×C4C2×#4111yescharacteristic
510C2×C3×C4H(5,𝔽2)11yescharacteristic
511C2×C3×C4H(5,𝔽2)11yescharacteristic
512C3×C8—41no—
513C3×C8—41no—
514C3×C8—41no—
515C3×C8—41no—
516C24—21no—
517C24—21no—
518C24C2×C3×D411yescharacteristic
519C24C2×C3×D411yescharacteristic
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×D4—24no—
527C2×D4—22no—
528C2×D4—24no—
529C2×D4—22no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—41no—
542C2×D4—42no—
543C2×D4—42no—
544C2×D4—42no—
545C2×D4—42no—
546C2×D4—42no—
547C2×D4—42no—
548C2×D4—81no—
549C2×D4—81no—
550C2×D4—81no—
551C2×D4—81no—
552C2×D4C2×C3×D412yes—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—24no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—24no—
572C22×C4—21no—
573C22×C4—81no—
574C22×C4—81no—
575C22×C4—81no—
576C22×C4—81no—
577C22×C4C2×C3×D411yescharacteristic
578C22×C4C2×C3×D411yescharacteristic
579C22×C4C2×C3×D411yescharacteristic
580C22×C4C2×C3×D411yescharacteristic
581C22×C4C24×C311yescharacteristic
582SD16—44no—
583D8—44no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—24no—
599C4⋊C4—22no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—42no—
606C4⋊C4—42no—
607C4⋊C4C2×C3×D412yes—
608C4⋊C4C2×C3×D412yes—
609C4⋊C4C2×C3×D412yes—
610C4⋊C4C3×#4112yes—
611C4⋊C4C3×#4112yes—
612C22⋊C4—24no—
613C22⋊C4—24no—
614C22⋊C4—24no—
615C22⋊C4—24no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—42no—
622C22⋊C4—42no—
623C22⋊C4—42no—
624C42—24no—
625C42—81no—
626C42C2×C3×D412yes—
627C42C2×C3×D412yes—
628C22×C3—22no—
629C22×C3—22no—
630C22×C3—22no—
631C22×C3—41no—
632C22×C3—41no—
633C22×C3—41no—
634C22×C3—41no—
635C22×C3—41no—
636C22×C3—42no—
637C22×C3—41no—
638C22×C3—42no—
639C22×C3—42no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3—41no—
645C22×C3—81no—
646C22×C3—81no—
647C22×C3—81no—
648C22×C3—81no—
649C22×C3—81no—
650C22×C3—81no—
651C22×C3—81no—
652C22×C3—81no—
653C22×C3—81no—
654C22×C3—81no—
655C22×C3—81no—
656C22×C3C2×#12011yescharacteristic
657C22×C3#54611yescharacteristic
658C22×C3#54611yescharacteristic
659C22×C3C2×#13511yescharacteristic
660C22×C3#57511yescharacteristic
661C22×C3#57611yescharacteristic
662C22×C3#57711yescharacteristic
663C3×C4—22no—
664C3×C4—22no—
665C3×C4—41no—
666C3×C4—41no—
667C3×C4—42no—
668C3×C4—42no—
669C3×C4—42no—
670C3×C4—42no—
671C3×C4—42no—
672C3×C4—81no—
673C3×C4#53211yescharacteristic
674C3×C4#53511yescharacteristic
675C3×C4#55011yescharacteristic
676C3×C4#55011yescharacteristic
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—22no—
689C23—21no—
690C23—21no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23C3×#13512yes—
705C23C22×C3×D411yescharacteristic
706Q8—41no—
707Q8—41no—
708Q8—41no—
709Q8—41no—
710D4—22no—
711D4—22no—
712D4—44no—
713D4—48no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—41no—
718D4—41no—
719D4—41no—
720D4—84no—
721D4—84no—
722D4—84no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—21no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—84no—
760C2×C4—84no—
761C2×C4C3×#12012yes—
762C2×C4C3×#12012yes—
763C2×C4C22×C3×D411yescharacteristic
764C2×C4C22×C3×D411yescharacteristic
765C2×C4C2×C3×#4111yescharacteristic
766C2×C4C2×C3×#4111yescharacteristic
767C2×C4C3×H(5,𝔽2)11yescharacteristic
768C2×C4C3×H(5,𝔽2)11yescharacteristic
769C8—41no—
770C8—41no—
771C8—41no—
772C8—41no—
773C2×C3—42no—
774C2×C3—81no—
775C2×C3—82no—
776C2×C3—161no—
777C2×C3#243111yescharacteristic
778C2×C3#300211yescharacteristic
779C2×C3#301211yescharacteristic
780C2×C3#329711yescharacteristic
781C2×C3#330111yescharacteristic
782C2×C3#332211yescharacteristic
783C2×C3#332611yescharacteristic
784C22—22no—
785C22—22no—
786C22—22no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—42no—
793C22—41no—
794C22—42no—
795C22—42no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22C2×C3×#12011yescharacteristic
813C22C3×#54611yescharacteristic
814C22C3×#54611yescharacteristic
815C22C2×C3×#13511yescharacteristic
816C22C3×#57511yescharacteristic
817C22C3×#57611yescharacteristic
818C22C3×#57711yescharacteristic
819C4—22no—
820C4—22no—
821C4—41no—
822C4—41no—
823C4—42no—
824C4—42no—
825C4—42no—
826C4—42no—
827C4—42no—
828C4—81no—
829C4C3×#53211yescharacteristic
830C4C3×#53511yescharacteristic
831C4C3×#55011yescharacteristic
832C4C3×#55011yescharacteristic
833C3#2557511yescharacteristic, direct product factor, Sylow
834C2—42no—
835C2—81no—
836C2—82no—
837C2—161no—
838C2C3×#243111yescharacteristic
839C2C3×#300211yescharacteristic
840C2C3×#301211yescharacteristic
841C2C3×#329711yescharacteristic
842C2C3×#330111yescharacteristic
843C2C3×#332211yescharacteristic
844C2C3×#332611yescharacteristic
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×#488C2semidirect
3. C2×C3×#463C2semidirect
4. C3×#2540C2semidirect
5. C3×#2000C2semidirect
6. C3×#2000C2semidirect
7. C3×#1999C2semidirect
8. C3×#1999C2semidirect
9. C3×#1989C2semidirect
10. C3×#1954C2semidirect
11. C3×#1875C2semidirect
12. C3×#1874C2semidirect
13. C3×#1873C2semidirect
14. C3×#1872C2semidirect
15. C3×C4×#102C2semidirect
16. #25575C3direct (N × H)
64. C2×#553C2×C3semidirect
65. C2×#488C2×C3semidirect
66. C2×#463C2×C3semidirect
67. #2540C2×C3semidirect
68. #2000C2×C3semidirect
69. #2000C2×C3semidirect
70. #1999C2×C3semidirect
71. #1999C2×C3semidirect
72. #1989C2×C3semidirect
73. #1954C2×C3semidirect
74. #1875C2×C3semidirect
75. #1874C2×C3semidirect
76. #1873C2×C3semidirect
77. #1872C2×C3semidirect
78. C4×#102C2×C3semidirect
103. C3×#125D4semidirect
124. C3×C4×D4D4semidirect
353. #125C3×D4semidirect
374. C4×D4C3×D4semidirect
833. C3#25575direct (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×#4882
C2×C3×#4632
C3×#25402
C3×#20002
C3×#19992
C3×#19892
C3×#19542
C3×#18752
C3×#18742
C3×#18732
C3×#18722
C3×C4×#1022
#255753