Finite Group Databasebeta

← C3×#25511 #10644118

Subgroups — C3×#25511 #10644118

Order 768.

1070 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#541C211yesmaximal, characteristic, complemented
2C2×C3×#468C211yesmaximal, characteristic
3C2×C3×#465C211yesmaximal, characteristic
4C3×#2624C211yesmaximal, characteristic
5C3×#2059C211yesmaximal, characteristic, complemented
6C3×#2043C211yesmaximal, characteristic, complemented
7C3×#2025C211yesmaximal, characteristic, complemented
8C3×#2013C211yesmaximal, characteristic, complemented
9C3×#1894C211yesmaximal, characteristic, complemented
10C3×#1892C211yesmaximal, characteristic, complemented
11C3×#1880C211yesmaximal, characteristic, complemented
12C3×#1880C211yesmaximal, characteristic, complemented
13C3×#1865C211yesmaximal, characteristic, complemented
14C3×#1863C211yesmaximal, characteristic, complemented
15C3×#1729C211yesmaximal, characteristic, complemented
16#25511C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×SD16C2211yescharacteristic
18C22×C3×SD16C2211yescharacteristic
19C22×C3×M16C2211yescharacteristic
20C23×C3×C8C2211yescharacteristic
21C3×#541—24no—
22C3×#541—24no—
23C2×C3×C4⋊Q8C2211yescharacteristic
24C2×C3×#126—21no—
25C2×C3×#126—21no—
26C2×C3×#125—21no—
27C2×C3×#125—21no—
28C2×C3×#125C2211yescharacteristic
29C2×C3×C22⋊Q8C2211yescharacteristic
30C2×C3×C22⋊Q8C2211yescharacteristic
31C2×C3×#121C2211yescharacteristic
32C2×C3×C4×Q8C2211yescharacteristic
33C2×C3×C4×Q8C2211yescharacteristic
34C2×C3×#117C2211yescharacteristic
35C3×#468—24no—
36C3×#465—24no—
37C2×C3×#107C2211yescharacteristic
38C2×C3×#106C2211yescharacteristic
39C2×C3×#103C2211yescharacteristic
40C2×C3×#103C2211yescharacteristic
41C2×C3×#103C2211yescharacteristic
42C2×C3×#103C2211yescharacteristic
43C2×C3×#103C2211yescharacteristic
44C2×C3×#103C2211yescharacteristic
45C2×C3×#102C2211yescharacteristic
46C2×C3×#102C2211yescharacteristic
47C3×#399—21no—
48C3×#397—21no—
49C3×#394—21no—
50C3×#394—21no—
51C3×#390C2211yescharacteristic
52C3×#390C2211yescharacteristic
53C3×#389C2211yescharacteristic
54C3×#389C2211yescharacteristic
55C3×#380C2211yescharacteristic
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#336C2211yescharacteristic
61C3×#336C2211yescharacteristic
62C3×#336C2211yescharacteristic
63C3×#336C2211yescharacteristic
64C2×#541C2×C311yescharacteristic, complemented
65C2×#468C2×C311yescharacteristic
66C2×#465C2×C311yescharacteristic
67#2624C2×C311yescharacteristic
68#2059C2×C311yescharacteristic, complemented
69#2043C2×C311yescharacteristic, complemented
70#2025C2×C311yescharacteristic, complemented
71#2013C2×C311yescharacteristic, complemented
72#1894C2×C311yescharacteristic, complemented
73#1892C2×C311yescharacteristic, complemented
74#1880C2×C311yescharacteristic, complemented
75#1880C2×C311yescharacteristic, complemented
76#1865C2×C311yescharacteristic, complemented
77#1863C2×C311yescharacteristic, complemented
78#1729C2×C311yescharacteristic, complemented
79C22×C3×Q8C2311yescharacteristic
80C22×C3×Q8C2311yescharacteristic
81C22×C3×D4—21no—
82C22×C3×D4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C2×C3×SD16—22no—
85C2×C3×SD16—22no—
86C2×C3×SD16—22no—
87C2×C3×SD16—22no—
88C2×C3×SD16—41no—
89C2×C3×SD16—41no—
90C2×C3×M16—22no—
91C2×C3×M16—22no—
92C2×C3×M16—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×C4⋊Q8—22no—
101C3×C4⋊Q8—22no—
102C3×#126—28no—
103C3×#126—28no—
104C3×#125—28no—
105C3×#125—28no—
106C3×#125—22no—
107C3×#125—22no—
108C3×C22⋊Q8—22no—
109C3×C22⋊Q8—22no—
110C3×C22⋊Q8D414yes—
111C3×C22⋊Q8D414yes—
112C3×#121—22no—
113C3×#121—22no—
114C3×C4×Q8—22no—
115C3×C4×Q8—22no—
116C3×C4×Q8—22no—
117C3×C4×Q8—22no—
118C3×#117—22no—
119C3×#117—22no—
120C2×C3×C4⋊C4—21no—
121C2×C3×C4⋊C4—21no—
122C2×C3×C4⋊C4—21no—
123C2×C3×C4⋊C4—21no—
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⋊C4D411yescharacteristic
131C2×C3×C4⋊C4D411yescharacteristic
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
150C2×C3×C42C2311yescharacteristic
151C3×#107—22no—
152C3×#106—22no—
153C3×#103—22no—
154C3×#103—22no—
155C3×#103—22no—
156C3×#103—22no—
157C3×#103—41no—
158C3×#103—41no—
159C3×#102—22no—
160C3×#102—22no—
161C3×#95—21no—
162C3×#95—21no—
163C3×#95—21no—
164C22×SD16C22×C311yescharacteristic
165C22×SD16C22×C311yescharacteristic
166C22×M16C22×C311yescharacteristic
167C23×C8C22×C311yescharacteristic
168#541—24no—
169#541—24no—
170C2×C4⋊Q8C22×C311yescharacteristic
171C2×#126—21no—
172C2×#126—21no—
173C2×#125—21no—
174C2×#125—21no—
175C2×#125C22×C311yescharacteristic
176C2×C22⋊Q8C22×C311yescharacteristic
177C2×C22⋊Q8C22×C311yescharacteristic
178C2×#121C22×C311yescharacteristic
179C2×C4×Q8C22×C311yescharacteristic
180C2×C4×Q8C22×C311yescharacteristic
181C2×#117C22×C311yescharacteristic
182#468—24no—
183#465—24no—
184C2×#107C22×C311yescharacteristic
185C2×#106C22×C311yescharacteristic
186C2×#103C22×C311yescharacteristic
187C2×#103C22×C311yescharacteristic
188C2×#103C22×C311yescharacteristic
189C2×#103C22×C311yescharacteristic
190C2×#103C22×C311yescharacteristic
191C2×#103C22×C311yescharacteristic
192C2×#102C22×C311yescharacteristic
193C2×#102C22×C311yescharacteristic
194#399—21no—
195#397—21no—
196#394—21no—
197#394—21no—
198#390C22×C311yescharacteristic
199#390C22×C311yescharacteristic
200#389C22×C311yescharacteristic
201#389C22×C311yescharacteristic
202#380C22×C311yescharacteristic
203#340C22×C311yescharacteristic
204#340C22×C311yescharacteristic
205#340C22×C311yescharacteristic
206#340C22×C311yescharacteristic
207#336C22×C311yescharacteristic
208#336C22×C311yescharacteristic
209#336C22×C311yescharacteristic
210#336C22×C311yescharacteristic
211C24×C3—21no—
212C24×C3C2×D411yescharacteristic
213C2×C3×Q8—21no—
214C2×C3×Q8—21no—
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—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8C2×D412yes—
224C2×C3×Q8C2×D412yes—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4—42no—
232C2×C3×D4—81no—
233C2×C3×D4—81no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
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×C4C2×D411yescharacteristic
246C22×C3×C4C2×D411yescharacteristic
247C22×C3×C4C2×D411yescharacteristic
248C22×C3×C4C2×D411yescharacteristic
249C22×C3×C4C2×D411yescharacteristic
250C22×C3×C4C2×D412yes—
251C22×C3×C4C2×D412yes—
252C22×C3×C4C2411yescharacteristic
253C3×SD16—44no—
254C3×SD16—44no—
255C3×M16—44no—
256C2×C3×C8—21no—
257C2×C3×C8—21no—
258C2×C3×C8—21no—
259C2×C3×C8—21no—
260C2×C3×C8—21no—
261C2×C3×C8—21no—
262C2×C3×C8—21no—
263C2×C3×C8—21no—
264C2×C3×C8—21no—
265C2×C3×C8—21no—
266C2×C3×C8—44no—
267C2×C3×C8#4112yes—
268C2×C3×C8#4112yes—
269C3×C4⋊C4—24no—
270C3×C4⋊C4—24no—
271C3×C4⋊C4—24no—
272C3×C4⋊C4—24no—
273C3×C4⋊C4—24no—
274C3×C4⋊C4—24no—
275C3×C4⋊C4—24no—
276C3×C4⋊C4—24no—
277C3×C4⋊C4—22no—
278C3×C4⋊C4—22no—
279C3×C4⋊C4—21no—
280C3×C4⋊C4—21no—
281C3×C4⋊C4—21no—
282C3×C4⋊C4—21no—
283C3×C4⋊C4—21no—
284C3×C4⋊C4—21no—
285C3×C4⋊C4—21no—
286C3×C4⋊C4—21no—
287C3×C4⋊C4—81no—
288C3×C4⋊C4—81no—
289C3×C4⋊C4C2×D412yes—
290C3×C4⋊C4C2×D412yes—
291C3×C22⋊C4—24no—
292C3×C22⋊C4—24no—
293C3×C22⋊C4—22no—
294C3×C22⋊C4—22no—
295C3×C22⋊C4—42no—
296C3×C22⋊C4—81no—
297C3×C22⋊C4—81no—
298C3×C22⋊C4—81no—
299C3×C22⋊C4—81no—
300C3×C22⋊C4—81no—
301C3×C42—24no—
302C3×C42—24no—
303C3×C42—21no—
304C3×C42—21no—
305C3×C42—21no—
306C3×C42—21no—
307C22×Q8C23×C311yescharacteristic
308C22×Q8C23×C311yescharacteristic
309C22×D4—21no—
310C22×D4C23×C311yescharacteristic
311C23×C4C23×C311yescharacteristic
312C2×SD16—22no—
313C2×SD16—22no—
314C2×SD16—22no—
315C2×SD16—22no—
316C2×SD16—41no—
317C2×SD16—41no—
318C2×M16—22no—
319C2×M16—22no—
320C2×M16—41no—
321C22×C8—22no—
322C22×C8—22no—
323C22×C8—41no—
324C22×C8C23×C311yescharacteristic
325C22×C8C23×C311yescharacteristic
326C22×C8C23×C311yescharacteristic
327C22×C8C23×C311yescharacteristic
328C4⋊Q8—22no—
329C4⋊Q8—22no—
330#126—28no—
331#126—28no—
332#125—28no—
333#125—28no—
334#125—22no—
335#125—22no—
336C22⋊Q8—22no—
337C22⋊Q8—22no—
338C22⋊Q8C3×D414yes—
339C22⋊Q8C3×D414yes—
340#121—22no—
341#121—22no—
342C4×Q8—22no—
343C4×Q8—22no—
344C4×Q8—22no—
345C4×Q8—22no—
346#117—22no—
347#117—22no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4C3×D411yescharacteristic
359C2×C4⋊C4C3×D411yescharacteristic
360C2×C4⋊C4C23×C311yescharacteristic
361C2×C4⋊C4C23×C311yescharacteristic
362C2×C4⋊C4C23×C311yescharacteristic
363C2×C4⋊C4C23×C311yescharacteristic
364C2×C4⋊C4C23×C311yescharacteristic
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4C3×D411yescharacteristic
374C2×C22⋊C4C3×D411yescharacteristic
375C2×C42—21no—
376C2×C42—21no—
377C2×C42C23×C311yescharacteristic
378C2×C42C23×C311yescharacteristic
379#107—22no—
380#106—22no—
381#103—22no—
382#103—22no—
383#103—22no—
384#103—22no—
385#103—41no—
386#103—41no—
387#102—22no—
388#102—22no—
389#95—21no—
390#95—21no—
391#95—21no—
392C23×C3—21no—
393C23×C3—21no—
394C23×C3—21no—
395C23×C3—21no—
396C23×C3—21no—
397C23×C3—21no—
398C23×C3—41no—
399C23×C3—41no—
400C23×C3—41no—
401C23×C3—41no—
402C23×C3—41no—
403C23×C3—41no—
404C23×C3—41no—
405C23×C3#12012yes—
406C23×C3C22×D411yescharacteristic
407C3×Q8—22no—
408C3×Q8—22no—
409C3×Q8—22no—
410C3×Q8—22no—
411C3×Q8—41no—
412C3×Q8—41no—
413C3×Q8—41no—
414C3×Q8—41no—
415C3×D4—41no—
416C3×D4—41no—
417C3×D4—41no—
418C3×D4—41no—
419C3×D4—84no—
420C2×C3×C4—21no—
421C2×C3×C4—21no—
422C2×C3×C4—22no—
423C2×C3×C4—22no—
424C2×C3×C4—22no—
425C2×C3×C4—22no—
426C2×C3×C4—21no—
427C2×C3×C4—21no—
428C2×C3×C4—21no—
429C2×C3×C4—21no—
430C2×C3×C4—22no—
431C2×C3×C4—22no—
432C2×C3×C4—22no—
433C2×C3×C4—22no—
434C2×C3×C4—21no—
435C2×C3×C4—21no—
436C2×C3×C4—21no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—21no—
442C2×C3×C4—41no—
443C2×C3×C4—41no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4—41no—
447C2×C3×C4—41no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
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#12012yes—
460C2×C3×C4C22×D411yescharacteristic
461C2×C3×C4C22×D411yescharacteristic
462C2×C3×C4C2×#4111yescharacteristic
463C2×C3×C4C2×#4111yescharacteristic
464C2×C3×C4H(5,𝔽2)11yescharacteristic
465C2×C3×C42−1+411yescharacteristic
466C3×C8—22no—
467C3×C8—22no—
468C3×C8—41no—
469C3×C8—41no—
470C24—21no—
471C24C2×C3×D411yescharacteristic
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8C2×C3×D412yes—
483C2×Q8C2×C3×D412yes—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—42no—
491C2×D4—81no—
492C2×D4—81no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4C2×C3×D411yescharacteristic
505C22×C4C2×C3×D411yescharacteristic
506C22×C4C2×C3×D411yescharacteristic
507C22×C4C2×C3×D411yescharacteristic
508C22×C4C2×C3×D411yescharacteristic
509C22×C4C2×C3×D412yes—
510C22×C4C2×C3×D412yes—
511C22×C4C24×C311yescharacteristic
512SD16—44no—
513SD16—44no—
514M16—44no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—44no—
526C2×C8C3×#4112yes—
527C2×C8C3×#4112yes—
528C4⋊C4—24no—
529C4⋊C4—24no—
530C4⋊C4—24no—
531C4⋊C4—24no—
532C4⋊C4—24no—
533C4⋊C4—24no—
534C4⋊C4—24no—
535C4⋊C4—24no—
536C4⋊C4—22no—
537C4⋊C4—22no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—81no—
547C4⋊C4—81no—
548C4⋊C4C2×C3×D412yes—
549C4⋊C4C2×C3×D412yes—
550C22⋊C4—24no—
551C22⋊C4—24no—
552C22⋊C4—22no—
553C22⋊C4—22no—
554C22⋊C4—42no—
555C22⋊C4—81no—
556C22⋊C4—81no—
557C22⋊C4—81no—
558C22⋊C4—81no—
559C22⋊C4—81no—
560C42—24no—
561C42—24no—
562C42—21no—
563C42—21no—
564C42—21no—
565C42—21no—
566C22×C3—22no—
567C22×C3—22no—
568C22×C3—22no—
569C22×C3—41no—
570C22×C3—41no—
571C22×C3—41no—
572C22×C3—41no—
573C22×C3—81no—
574C22×C3—81no—
575C22×C3—81no—
576C22×C3—81no—
577C22×C3—81no—
578C22×C3—81no—
579C22×C3—81no—
580C22×C3C2×#12011yescharacteristic
581C22×C3#53211yescharacteristic
582C22×C3#53711yescharacteristic
583C22×C3#57711yescharacteristic
584C22×C3#57711yescharacteristic
585C22×C3#57711yescharacteristic
586C22×C3#57811yescharacteristic
587C3×C4—22no—
588C3×C4—42no—
589C3×C4—42no—
590C3×C4—41no—
591C3×C4—41no—
592C3×C4—42no—
593C3×C4—41no—
594C3×C4—41no—
595C3×C4—42no—
596C3×C4—81no—
597C3×C4—81no—
598C3×C4—81no—
599C3×C4#54611yescharacteristic
600C3×C4#54611yescharacteristic
601C3×C4#54711yescharacteristic
602C3×C4#54711yescharacteristic
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23C3×#12012yes—
617C23C22×C3×D411yescharacteristic
618Q8—22no—
619Q8—22no—
620Q8—22no—
621Q8—22no—
622Q8—41no—
623Q8—41no—
624Q8—41no—
625Q8—41no—
626D4—41no—
627D4—41no—
628D4—41no—
629D4—41no—
630D4—84no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4C3×#12012yes—
671C2×C4C22×C3×D411yescharacteristic
672C2×C4C22×C3×D411yescharacteristic
673C2×C4C2×C3×#4111yescharacteristic
674C2×C4C2×C3×#4111yescharacteristic
675C2×C4C3×H(5,𝔽2)11yescharacteristic
676C2×C4C3×2−1+411yescharacteristic
677C8—22no—
678C8—22no—
679C8—41no—
680C8—41no—
681C2×C3—42no—
682C2×C3—161no—
683C2×C3#243011yescharacteristic
684C2×C3#301011yescharacteristic
685C2×C3#301311yescharacteristic
686C2×C3#317411yescharacteristic
687C2×C3#317811yescharacteristic
688C2×C3#325811yescharacteristic
689C2×C3#326011yescharacteristic
690C22—22no—
691C22—22no—
692C22—22no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—81no—
698C22—81no—
699C22—81no—
700C22—81no—
701C22—81no—
702C22—81no—
703C22—81no—
704C22C2×C3×#12011yescharacteristic
705C22C3×#53211yescharacteristic
706C22C3×#53711yescharacteristic
707C22C3×#57711yescharacteristic
708C22C3×#57711yescharacteristic
709C22C3×#57711yescharacteristic
710C22C3×#57811yescharacteristic
711C4—22no—
712C4—42no—
713C4—42no—
714C4—41no—
715C4—41no—
716C4—42no—
717C4—41no—
718C4—41no—
719C4—42no—
720C4—81no—
721C4—81no—
722C4—81no—
723C4C3×#54611yescharacteristic
724C4C3×#54611yescharacteristic
725C4C3×#54711yescharacteristic
726C4C3×#54711yescharacteristic
727C3#2551111yescharacteristic, direct product factor, Sylow
728C2—42no—
729C2—161no—
730C2C3×#243011yescharacteristic
731C2C3×#301011yescharacteristic
732C2C3×#301311yescharacteristic
733C2C3×#317411yescharacteristic
734C2C3×#317811yescharacteristic
735C2C3×#325811yescharacteristic
736C2C3×#326011yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC2×C3×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C2×C3×#117 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C3×#541C2semidirect
5. C3×#2059C2semidirect
6. C3×#2043C2semidirect
7. C3×#2025C2semidirect
8. C3×#2013C2semidirect
9. C3×#1894C2semidirect
10. C3×#1892C2semidirect
11. C3×#1880C2semidirect
12. C3×#1880C2semidirect
13. C3×#1865C2semidirect
14. C3×#1863C2semidirect
15. C3×#1729C2semidirect
16. #25511C3direct (N × H)
64. C2×#541C2×C3semidirect
68. #2059C2×C3semidirect
69. #2043C2×C3semidirect
70. #2025C2×C3semidirect
71. #2013C2×C3semidirect
72. #1894C2×C3semidirect
73. #1892C2×C3semidirect
74. #1880C2×C3semidirect
75. #1880C2×C3semidirect
76. #1865C2×C3semidirect
77. #1863C2×C3semidirect
78. #1729C2×C3semidirect
727. C3#25511direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5412
C2×C3×#4682
C2×C3×#4652
C3×#26242
C3×#20592
C3×#20432
C3×#20252
C3×#20132
C3×#18942
C3×#18922
C3×#18802
C3×#18652
C3×#18632
C3×#17292
#255113