Finite Group Databasebeta

← C3×#25514 #10644121

Subgroups — C3×#25514 #10644121

Order 768.

1092 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#542C211yesmaximal, characteristic
2C2×C3×#468C211yesmaximal, characteristic
3C2×C3×#467C211yesmaximal, characteristic, complemented
4C3×#2625C211yesmaximal, characteristic, complemented
5C3×#2057C211yesmaximal, characteristic, complemented
6C3×#2042C211yesmaximal, characteristic, complemented
7C3×#2024C211yesmaximal, characteristic, complemented
8C3×#2015C211yesmaximal, characteristic, complemented
9C3×#1894C211yesmaximal, characteristic, complemented
10C3×#1893C211yesmaximal, characteristic
11C3×#1878C211yesmaximal, characteristic, complemented
12C3×#1877C211yesmaximal, characteristic, complemented
13C3×#1863C211yesmaximal, characteristic, complemented
14C3×#1862C211yesmaximal, characteristic, complemented
15C3×#1729C211yesmaximal, characteristic, complemented
16#25514C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×Q16C2211yescharacteristic
18C22×C3×SD16C2211yescharacteristic
19C22×C3×M16C2211yescharacteristic
20C23×C3×C8C2211yescharacteristic
21C3×#542—24no—
22C3×#542—24no—
23C2×C3×C4⋊Q8C2211yescharacteristic
24C2×C3×#126—21no—
25C2×C3×#124—21no—
26C2×C3×#124C2211yescharacteristic
27C2×C3×#123—21no—
28C2×C3×C22⋊Q8—21no—
29C2×C3×C22⋊Q8C2211yescharacteristic
30C2×C3×C22⋊Q8C2211yescharacteristic
31C2×C3×#121C2211yescharacteristic
32C2×C3×C4×Q8C2211yescharacteristic
33C2×C3×C4×D4C2211yescharacteristic
34C2×C3×#117C2211yescharacteristic
35C3×#468—24no—
36C3×#467—24no—
37C2×C3×#107C2211yescharacteristic
38C2×C3×#107C2211yescharacteristic
39C2×C3×#103C2211yescharacteristic
40C2×C3×#103C2211yescharacteristic
41C2×C3×#103C2211yescharacteristic
42C2×C3×#103C2211yescharacteristic
43C2×C3×#103C2211yescharacteristic
44C2×C3×#102C2211yescharacteristic
45C2×C3×#102C2211yescharacteristic
46C2×C3×#102C2211yescharacteristic
47C3×#400—21no—
48C3×#398—21no—
49C3×#397—21no—
50C3×#397—21no—
51C3×#391C2211yescharacteristic
52C3×#391C2211yescharacteristic
53C3×#389C2211yescharacteristic
54C3×#389C2211yescharacteristic
55C3×#380C2211yescharacteristic
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#336C2211yescharacteristic
61C3×#336C2211yescharacteristic
62C3×#336C2211yescharacteristic
63C3×#336C2211yescharacteristic
64C2×#542C2×C311yescharacteristic
65C2×#468C2×C311yescharacteristic
66C2×#467C2×C311yescharacteristic, complemented
67#2625C2×C311yescharacteristic, complemented
68#2057C2×C311yescharacteristic, complemented
69#2042C2×C311yescharacteristic, complemented
70#2024C2×C311yescharacteristic, complemented
71#2015C2×C311yescharacteristic, complemented
72#1894C2×C311yescharacteristic, complemented
73#1893C2×C311yescharacteristic
74#1878C2×C311yescharacteristic, complemented
75#1877C2×C311yescharacteristic, complemented
76#1863C2×C311yescharacteristic, complemented
77#1862C2×C311yescharacteristic, complemented
78#1729C2×C311yescharacteristic, complemented
79C22×C3×Q8—21no—
80C22×C3×Q8C2311yescharacteristic
81C22×C3×Q8C2311yescharacteristic
82C22×C3×D4—21no—
83C22×C3×D4C2311yescharacteristic
84C23×C3×C4—21no—
85C23×C3×C4C2311yescharacteristic
86C2×C3×Q16—22no—
87C2×C3×Q16—22no—
88C2×C3×Q16—41no—
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×C8—22no—
96C22×C3×C8—22no—
97C22×C3×C8—41no—
98C22×C3×C8C2311yescharacteristic
99C22×C3×C8C2311yescharacteristic
100C22×C3×C8C2311yescharacteristic
101C22×C3×C8C2311yescharacteristic
102C3×C4⋊Q8—22no—
103C3×C4⋊Q8—22no—
104C3×#126—28no—
105C3×#124—28no—
106C3×#124—22no—
107C3×#124—22no—
108C3×#123—28no—
109C3×C22⋊Q8—28no—
110C3×C22⋊Q8—22no—
111C3×C22⋊Q8—22no—
112C3×C22⋊Q8—22no—
113C3×C22⋊Q8D414yes—
114C3×#121—22no—
115C3×#121D414yes—
116C3×C4×Q8—22no—
117C3×C4×Q8—22no—
118C3×C4×D4—22no—
119C3×C4×D4—22no—
120C3×#117—22no—
121C3×#117—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—21no—
127C2×C3×C4⋊C4—21no—
128C2×C3×C4⋊C4D411yescharacteristic
129C2×C3×C4⋊C4D411yescharacteristic
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⋊C4D411yescharacteristic
143C2×C3×C22⋊C4D411yescharacteristic
144C2×C3×C42—21no—
145C2×C3×C42C2311yescharacteristic
146C2×C3×C42C2311yescharacteristic
147C3×#107—22no—
148C3×#107—22no—
149C3×#103—22no—
150C3×#103—22no—
151C3×#103—22no—
152C3×#103—22no—
153C3×#103—41no—
154C3×#102—22no—
155C3×#102—22no—
156C3×#102—41no—
157C3×#95—21no—
158C3×#95—21no—
159C3×#95—21no—
160C3×#95—21no—
161C3×#95—21no—
162C3×#95—21no—
163C3×#95—21no—
164C22×Q16C22×C311yescharacteristic
165C22×SD16C22×C311yescharacteristic
166C22×M16C22×C311yescharacteristic
167C23×C8C22×C311yescharacteristic
168#542—24no—
169#542—24no—
170C2×C4⋊Q8C22×C311yescharacteristic
171C2×#126—21no—
172C2×#124—21no—
173C2×#124C22×C311yescharacteristic
174C2×#123—21no—
175C2×C22⋊Q8—21no—
176C2×C22⋊Q8C22×C311yescharacteristic
177C2×C22⋊Q8C22×C311yescharacteristic
178C2×#121C22×C311yescharacteristic
179C2×C4×Q8C22×C311yescharacteristic
180C2×C4×D4C22×C311yescharacteristic
181C2×#117C22×C311yescharacteristic
182#468—24no—
183#467—24no—
184C2×#107C22×C311yescharacteristic
185C2×#107C22×C311yescharacteristic
186C2×#103C22×C311yescharacteristic
187C2×#103C22×C311yescharacteristic
188C2×#103C22×C311yescharacteristic
189C2×#103C22×C311yescharacteristic
190C2×#103C22×C311yescharacteristic
191C2×#102C22×C311yescharacteristic
192C2×#102C22×C311yescharacteristic
193C2×#102C22×C311yescharacteristic
194#400—21no—
195#398—21no—
196#397—21no—
197#397—21no—
198#391C22×C311yescharacteristic
199#391C22×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—24no—
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×Q8—21no—
224C2×C3×Q8—21no—
225C2×C3×Q8—81no—
226C2×C3×Q8—81no—
227C2×C3×Q8C2×D412yes—
228C2×C3×D4—24no—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4—21no—
232C2×C3×D4—21no—
233C2×C3×D4—21no—
234C2×C3×D4—81no—
235C2×C3×D4—81no—
236C2×C3×D4C2×D412yes—
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—24no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—81no—
250C22×C3×C4—81no—
251C22×C3×C4C2×D411yescharacteristic
252C22×C3×C4C2×D411yescharacteristic
253C22×C3×C4C2×D411yescharacteristic
254C22×C3×C4C2×D411yescharacteristic
255C22×C3×C4C2×D411yescharacteristic
256C22×C3×C4C2×D412yes—
257C22×C3×C4C2×D412yes—
258C22×C3×C4C2411yescharacteristic
259C3×Q16—44no—
260C3×SD16—44no—
261C3×M16—44no—
262C2×C3×C8—21no—
263C2×C3×C8—21no—
264C2×C3×C8—21no—
265C2×C3×C8—21no—
266C2×C3×C8—21no—
267C2×C3×C8—21no—
268C2×C3×C8—21no—
269C2×C3×C8—21no—
270C2×C3×C8—21no—
271C2×C3×C8—21no—
272C2×C3×C8—44no—
273C2×C3×C8#4112yes—
274C2×C3×C8#4112yes—
275C3×C4⋊C4—24no—
276C3×C4⋊C4—24no—
277C3×C4⋊C4—24no—
278C3×C4⋊C4—22no—
279C3×C4⋊C4—22no—
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—21no—
288C3×C4⋊C4—42no—
289C3×C4⋊C4—81no—
290C3×C4⋊C4—81no—
291C3×C4⋊C4C2×D412yes—
292C3×C4⋊C4C2×D412yes—
293C3×C22⋊C4—24no—
294C3×C22⋊C4—24no—
295C3×C22⋊C4—24no—
296C3×C22⋊C4—24no—
297C3×C22⋊C4—22no—
298C3×C22⋊C4—22no—
299C3×C22⋊C4—24no—
300C3×C22⋊C4—42no—
301C3×C22⋊C4—81no—
302C3×C42—24no—
303C3×C42—21no—
304C3×C42—21no—
305C3×C42—21no—
306C3×C42—21no—
307C22×Q8—21no—
308C22×Q8C23×C311yescharacteristic
309C22×Q8C23×C311yescharacteristic
310C22×D4—21no—
311C22×D4C23×C311yescharacteristic
312C23×C4—21no—
313C23×C4C23×C311yescharacteristic
314C2×Q16—22no—
315C2×Q16—22no—
316C2×Q16—41no—
317C2×SD16—22no—
318C2×SD16—22no—
319C2×SD16—41no—
320C2×M16—22no—
321C2×M16—22no—
322C2×M16—41no—
323C22×C8—22no—
324C22×C8—22no—
325C22×C8—41no—
326C22×C8C23×C311yescharacteristic
327C22×C8C23×C311yescharacteristic
328C22×C8C23×C311yescharacteristic
329C22×C8C23×C311yescharacteristic
330C4⋊Q8—22no—
331C4⋊Q8—22no—
332#126—28no—
333#124—28no—
334#124—22no—
335#124—22no—
336#123—28no—
337C22⋊Q8—28no—
338C22⋊Q8—22no—
339C22⋊Q8—22no—
340C22⋊Q8—22no—
341C22⋊Q8C3×D414yes—
342#121—22no—
343#121C3×D414yes—
344C4×Q8—22no—
345C4×Q8—22no—
346C4×D4—22no—
347C4×D4—22no—
348#117—22no—
349#117—22no—
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⋊C4C3×D411yescharacteristic
357C2×C4⋊C4C3×D411yescharacteristic
358C2×C4⋊C4C23×C311yescharacteristic
359C2×C4⋊C4C23×C311yescharacteristic
360C2×C4⋊C4C23×C311yescharacteristic
361C2×C4⋊C4C23×C311yescharacteristic
362C2×C4⋊C4C23×C311yescharacteristic
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4C3×D411yescharacteristic
371C2×C22⋊C4C3×D411yescharacteristic
372C2×C42—21no—
373C2×C42C23×C311yescharacteristic
374C2×C42C23×C311yescharacteristic
375#107—22no—
376#107—22no—
377#103—22no—
378#103—22no—
379#103—22no—
380#103—22no—
381#103—41no—
382#102—22no—
383#102—22no—
384#102—41no—
385#95—21no—
386#95—21no—
387#95—21no—
388#95—21no—
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—22no—
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—41no—
410C3×Q8—41no—
411C3×Q8—41no—
412C3×Q8—41no—
413C3×Q8—41no—
414C3×Q8—41no—
415C3×Q8—84no—
416C3×D4—22no—
417C3×D4—22no—
418C3×D4—41no—
419C3×D4—41no—
420C3×D4—84no—
421C2×C3×C4—21no—
422C2×C3×C4—21no—
423C2×C3×C4—22no—
424C2×C3×C4—22no—
425C2×C3×C4—22no—
426C2×C3×C4—22no—
427C2×C3×C4—21no—
428C2×C3×C4—21no—
429C2×C3×C4—22no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
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—41no—
460C2×C3×C4—84no—
461C2×C3×C4#12012yes—
462C2×C3×C4C22×D411yescharacteristic
463C2×C3×C4C22×D411yescharacteristic
464C2×C3×C4C2×#4111yescharacteristic
465C2×C3×C4C2×#4111yescharacteristic
466C2×C3×C4H(5,𝔽2)11yescharacteristic
467C2×C3×C42−1+411yescharacteristic
468C3×C8—22no—
469C3×C8—22no—
470C3×C8—41no—
471C3×C8—41no—
472C24—21no—
473C24C2×C3×D411yescharacteristic
474C2×Q8—24no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—81no—
487C2×Q8—81no—
488C2×Q8C2×C3×D412yes—
489C2×D4—24no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—81no—
496C2×D4—81no—
497C2×D4C2×C3×D412yes—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—24no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—81no—
511C22×C4—81no—
512C22×C4C2×C3×D411yescharacteristic
513C22×C4C2×C3×D411yescharacteristic
514C22×C4C2×C3×D411yescharacteristic
515C22×C4C2×C3×D411yescharacteristic
516C22×C4C2×C3×D411yescharacteristic
517C22×C4C2×C3×D412yes—
518C22×C4C2×C3×D412yes—
519C22×C4C24×C311yescharacteristic
520Q16—44no—
521SD16—44no—
522M16—44no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—44no—
534C2×C8C3×#4112yes—
535C2×C8C3×#4112yes—
536C4⋊C4—24no—
537C4⋊C4—24no—
538C4⋊C4—24no—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—42no—
550C4⋊C4—81no—
551C4⋊C4—81no—
552C4⋊C4C2×C3×D412yes—
553C4⋊C4C2×C3×D412yes—
554C22⋊C4—24no—
555C22⋊C4—24no—
556C22⋊C4—24no—
557C22⋊C4—24no—
558C22⋊C4—22no—
559C22⋊C4—22no—
560C22⋊C4—24no—
561C22⋊C4—42no—
562C22⋊C4—81no—
563C42—24no—
564C42—21no—
565C42—21no—
566C42—21no—
567C42—21no—
568C22×C3—22no—
569C22×C3—22no—
570C22×C3—22no—
571C22×C3—41no—
572C22×C3—41no—
573C22×C3—41no—
574C22×C3—41no—
575C22×C3—42no—
576C22×C3—42no—
577C22×C3—42no—
578C22×C3—81no—
579C22×C3—81no—
580C22×C3—81no—
581C22×C3—81no—
582C22×C3C2×#12011yescharacteristic
583C22×C3#53211yescharacteristic
584C22×C3#53711yescharacteristic
585C22×C3#57611yescharacteristic
586C22×C3#57711yescharacteristic
587C22×C3#57811yescharacteristic
588C22×C3#57811yescharacteristic
589C3×C4—22no—
590C3×C4—42no—
591C3×C4—41no—
592C3×C4—41no—
593C3×C4—41no—
594C3×C4—41no—
595C3×C4—42no—
596C3×C4—42no—
597C3×C4—81no—
598C3×C4—81no—
599C3×C4—81no—
600C3×C4—81no—
601C3×C4#54611yescharacteristic
602C3×C4#54611yescharacteristic
603C3×C4#54711yescharacteristic
604C3×C4#54711yescharacteristic
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—22no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23C3×#12012yes—
619C23C22×C3×D411yescharacteristic
620Q8—22no—
621Q8—22no—
622Q8—41no—
623Q8—41no—
624Q8—41no—
625Q8—41no—
626Q8—41no—
627Q8—41no—
628Q8—84no—
629D4—22no—
630D4—22no—
631D4—41no—
632D4—41no—
633D4—84no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
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—21no—
650C2×C4—22no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
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×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—84no—
674C2×C4C3×#12012yes—
675C2×C4C22×C3×D411yescharacteristic
676C2×C4C22×C3×D411yescharacteristic
677C2×C4C2×C3×#4111yescharacteristic
678C2×C4C2×C3×#4111yescharacteristic
679C2×C4C3×H(5,𝔽2)11yescharacteristic
680C2×C4C3×2−1+411yescharacteristic
681C8—22no—
682C8—22no—
683C8—41no—
684C8—41no—
685C2×C3—42no—
686C2×C3—82no—
687C2×C3#243011yescharacteristic
688C2×C3#301111yescharacteristic
689C2×C3#301211yescharacteristic
690C2×C3#317511yescharacteristic
691C2×C3#317811yescharacteristic
692C2×C3#325811yescharacteristic
693C2×C3#326211yescharacteristic
694C22—22no—
695C22—22no—
696C22—22no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—42no—
702C22—42no—
703C22—42no—
704C22—81no—
705C22—81no—
706C22—81no—
707C22—81no—
708C22C2×C3×#12011yescharacteristic
709C22C3×#53211yescharacteristic
710C22C3×#53711yescharacteristic
711C22C3×#57611yescharacteristic
712C22C3×#57711yescharacteristic
713C22C3×#57811yescharacteristic
714C22C3×#57811yescharacteristic
715C4—22no—
716C4—42no—
717C4—41no—
718C4—41no—
719C4—41no—
720C4—41no—
721C4—42no—
722C4—42no—
723C4—81no—
724C4—81no—
725C4—81no—
726C4—81no—
727C4C3×#54611yescharacteristic
728C4C3×#54611yescharacteristic
729C4C3×#54711yescharacteristic
730C4C3×#54711yescharacteristic
731C3#2551411yescharacteristic, direct product factor, Sylow
732C2—42no—
733C2—82no—
734C2C3×#243011yescharacteristic
735C2C3×#301111yescharacteristic
736C2C3×#301211yescharacteristic
737C2C3×#317511yescharacteristic
738C2C3×#317811yescharacteristic
739C2C3×#325811yescharacteristic
740C2C3×#326211yescharacteristic
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
3. C2×C3×#467C2semidirect
4. C3×#2625C2semidirect
5. C3×#2057C2semidirect
6. C3×#2042C2semidirect
7. C3×#2024C2semidirect
8. C3×#2015C2semidirect
9. C3×#1894C2semidirect
11. C3×#1878C2semidirect
12. C3×#1877C2semidirect
13. C3×#1863C2semidirect
14. C3×#1862C2semidirect
15. C3×#1729C2semidirect
16. #25514C3direct (N × H)
66. C2×#467C2×C3semidirect
67. #2625C2×C3semidirect
68. #2057C2×C3semidirect
69. #2042C2×C3semidirect
70. #2024C2×C3semidirect
71. #2015C2×C3semidirect
72. #1894C2×C3semidirect
74. #1878C2×C3semidirect
75. #1877C2×C3semidirect
76. #1863C2×C3semidirect
77. #1862C2×C3semidirect
78. #1729C2×C3semidirect
731. C3#25514direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5422
C2×C3×#4682
C2×C3×#4672
C3×#26252
C3×#20572
C3×#20422
C3×#20242
C3×#20152
C3×#18942
C3×#18932
C3×#18782
C3×#18772
C3×#18632
C3×#18622
C3×#17292
#255143