Finite Group Databasebeta

← C3×#25546 #10644153

Subgroups — C3×#25546 #10644153

Order 768.

1098 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×#552C211yesmaximal, characteristic
2C2×C3×#485C211yesmaximal, characteristic, complemented
3C2×C3×#467C211yesmaximal, characteristic, complemented
4C3×#2415C211yesmaximal, characteristic
5C3×#2059C211yesmaximal, characteristic, complemented
6C3×#2035C211yesmaximal, characteristic, complemented
7C3×#2026C211yesmaximal, characteristic, complemented
8C3×#2001C211yesmaximal, characteristic, complemented
9C3×#1878C211yesmaximal, characteristic, complemented
10C3×#1873C211yesmaximal, characteristic, complemented
11C3×#1872C211yesmaximal, characteristic, complemented
12C3×#1869C211yesmaximal, characteristic
13C3×#1863C211yesmaximal, characteristic, complemented
14C3×#1852C211yesmaximal, characteristic, complemented
15C3×#1735C211yesmaximal, characteristic, complemented
16#25546C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×Q16C2211yescharacteristic
18C23×C3×C8C2211yescharacteristic
19C3×#552—24no—
20C3×#552—24no—
21C2×C3×#126—21no—
22C2×C3×#125—21no—
23C2×C3×#125C2211yescharacteristic
24C2×C3×#123—21no—
25C2×C3×C22⋊Q8C2211yescharacteristic
26C2×C3×C22⋊Q8C2211yescharacteristic
27C2×C3×C22⋊Q8C2211yescharacteristic
28C2×C3×C22⋊Q8C2211yescharacteristic
29C2×C3×C4×Q8C2211yescharacteristic
30C2×C3×C4×D4C2211yescharacteristic
31C2×C3×#117—21no—
32C2×C3×#117C2211yescharacteristic
33C2×C3×#117C2211yescharacteristic
34C22×C3×C4⋊C4C2211yescharacteristic
35C3×#485—24no—
36C3×#467—24no—
37C2×C3×#107C2211yescharacteristic
38C2×C3×#107C2211yescharacteristic
39C2×C3×#106C2211yescharacteristic
40C2×C3×#103C2211yescharacteristic
41C2×C3×#103C2211yescharacteristic
42C2×C3×#103C2211yescharacteristic
43C2×C3×#103C2211yescharacteristic
44C2×C3×#103C2211yescharacteristic
45C2×C3×#103C2211yescharacteristic
46C2×C3×C22⋊C8C2211yescharacteristic
47C2×C3×C22⋊C8C2211yescharacteristic
48C2×C3×C22⋊C8C2211yescharacteristic
49C3×#397—21no—
50C3×#394—21no—
51C3×#391C2211yescharacteristic
52C3×#389—21no—
53C3×#389C2211yescharacteristic
54C3×#388—21no—
55C3×#380C2211yescharacteristic
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#340C2211yescharacteristic
61C3×#340C2211yescharacteristic
62C3×#336C2211yescharacteristic
63C3×#336C2211yescharacteristic
64C2×#552C2×C311yescharacteristic
65C2×#485C2×C311yescharacteristic, complemented
66C2×#467C2×C311yescharacteristic, complemented
67#2415C2×C311yescharacteristic
68#2059C2×C311yescharacteristic, complemented
69#2035C2×C311yescharacteristic, complemented
70#2026C2×C311yescharacteristic, complemented
71#2001C2×C311yescharacteristic, complemented
72#1878C2×C311yescharacteristic, complemented
73#1873C2×C311yescharacteristic, complemented
74#1872C2×C311yescharacteristic, complemented
75#1869C2×C311yescharacteristic
76#1863C2×C311yescharacteristic, complemented
77#1852C2×C311yescharacteristic, complemented
78#1735C2×C311yescharacteristic, complemented
79C22×C3×Q8C2311yescharacteristic
80C22×C3×Q8C2311yescharacteristic
81C22×C3×D4D411yescharacteristic
82C23×C3×C4—21no—
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C2×C3×Q16—22no—
86C2×C3×Q16—22no—
87C2×C3×Q16—41no—
88C22×C3×C8—22no—
89C22×C3×C8—22no—
90C22×C3×C8—41no—
91C22×C3×C8C2311yescharacteristic
92C22×C3×C8C2311yescharacteristic
93C22×C3×C8C2311yescharacteristic
94C22×C3×C8C2311yescharacteristic
95C3×#126—28no—
96C3×#125—28no—
97C3×#125—22no—
98C3×#125—22no—
99C3×#123—28no—
100C3×C22⋊Q8—22no—
101C3×C22⋊Q8—22no—
102C3×C22⋊Q8—22no—
103C3×C22⋊Q8—22no—
104C3×C22⋊Q8—22no—
105C3×C22⋊Q8—22no—
106C3×C22⋊Q8—41no—
107C3×C22⋊Q8D414yes—
108C3×C4×Q8—22no—
109C3×C4×Q8—22no—
110C3×C4×D4—22no—
111C3×C4×D4—22no—
112C3×#117—28no—
113C3×#117—22no—
114C3×#117—22no—
115C3×#117—41no—
116C3×#117D414yes—
117C2×C3×C4⋊C4—21no—
118C2×C3×C4⋊C4—21no—
119C2×C3×C4⋊C4—21no—
120C2×C3×C4⋊C4—21no—
121C2×C3×C4⋊C4—21no—
122C2×C3×C4⋊C4—21no—
123C2×C3×C4⋊C4—22no—
124C2×C3×C4⋊C4—22no—
125C2×C3×C4⋊C4—21no—
126C2×C3×C4⋊C4—21no—
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⋊C4D411yescharacteristic
143C2×C3×C22⋊C4D411yescharacteristic
144C2×C3×C42—21no—
145C2×C3×C42—21no—
146C2×C3×C42—21no—
147C2×C3×C42C2311yescharacteristic
148C3×#107—22no—
149C3×#107—22no—
150C3×#106—22no—
151C3×#103—22no—
152C3×#103—22no—
153C3×#103—22no—
154C3×#103—22no—
155C3×#103—22no—
156C3×#103—41no—
157C3×C22⋊C8—22no—
158C3×C22⋊C8—22no—
159C3×C22⋊C8—41no—
160C3×#95—21no—
161C3×#95—21no—
162C3×#95—21no—
163C3×#95—21no—
164C22×Q16C22×C311yescharacteristic
165C23×C8C22×C311yescharacteristic
166#552—24no—
167#552—24no—
168C2×#126—21no—
169C2×#125—21no—
170C2×#125C22×C311yescharacteristic
171C2×#123—21no—
172C2×C22⋊Q8C22×C311yescharacteristic
173C2×C22⋊Q8C22×C311yescharacteristic
174C2×C22⋊Q8C22×C311yescharacteristic
175C2×C22⋊Q8C22×C311yescharacteristic
176C2×C4×Q8C22×C311yescharacteristic
177C2×C4×D4C22×C311yescharacteristic
178C2×#117—21no—
179C2×#117C22×C311yescharacteristic
180C2×#117C22×C311yescharacteristic
181C22×C4⋊C4C22×C311yescharacteristic
182#485—24no—
183#467—24no—
184C2×#107C22×C311yescharacteristic
185C2×#107C22×C311yescharacteristic
186C2×#106C22×C311yescharacteristic
187C2×#103C22×C311yescharacteristic
188C2×#103C22×C311yescharacteristic
189C2×#103C22×C311yescharacteristic
190C2×#103C22×C311yescharacteristic
191C2×#103C22×C311yescharacteristic
192C2×#103C22×C311yescharacteristic
193C2×C22⋊C8C22×C311yescharacteristic
194C2×C22⋊C8C22×C311yescharacteristic
195C2×C22⋊C8C22×C311yescharacteristic
196#397—21no—
197#394—21no—
198#391C22×C311yescharacteristic
199#389—21no—
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×C3C2×D411yescharacteristic
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×Q8—21no—
224C2×C3×Q8C2×D412yes—
225C2×C3×D4—22no—
226C2×C3×D4—22no—
227C2×C3×D4—41no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—24no—
233C22×C3×C4—21no—
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×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—42no—
248C22×C3×C4—42no—
249C22×C3×C4C2×D411yescharacteristic
250C22×C3×C4C2×D411yescharacteristic
251C22×C3×C4C2×D411yescharacteristic
252C22×C3×C4C2×D411yescharacteristic
253C22×C3×C4C2×D412yes—
254C22×C3×C4C2×D412yes—
255C22×C3×C4C2411yescharacteristic
256C3×Q16—44no—
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—21no—
267C2×C3×C8—21no—
268C2×C3×C8—44no—
269C2×C3×C8#4112yes—
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—22no—
277C3×C4⋊C4—21no—
278C3×C4⋊C4—21no—
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—42no—
286C3×C4⋊C4—42no—
287C3×C4⋊C4—42no—
288C3×C4⋊C4C2×D412yes—
289C3×C4⋊C4C2×D412yes—
290C3×C4⋊C4C2×D412yes—
291C3×C4⋊C4#4112yes—
292C3×C22⋊C4—24no—
293C3×C22⋊C4—24no—
294C3×C22⋊C4—24no—
295C3×C22⋊C4—22no—
296C3×C22⋊C4—22no—
297C3×C22⋊C4—42no—
298C3×C22⋊C4—42no—
299C3×C22⋊C4—42no—
300C3×C22⋊C4—42no—
301C3×C42—24no—
302C3×C42—24no—
303C3×C42—21no—
304C3×C42—21no—
305C3×C42—42no—
306C22×Q8C23×C311yescharacteristic
307C22×Q8C23×C311yescharacteristic
308C22×D4C3×D411yescharacteristic
309C23×C4—21no—
310C23×C4C23×C311yescharacteristic
311C23×C4C23×C311yescharacteristic
312C2×Q16—22no—
313C2×Q16—22no—
314C2×Q16—41no—
315C22×C8—22no—
316C22×C8—22no—
317C22×C8—41no—
318C22×C8C23×C311yescharacteristic
319C22×C8C23×C311yescharacteristic
320C22×C8C23×C311yescharacteristic
321C22×C8C23×C311yescharacteristic
322#126—28no—
323#125—28no—
324#125—22no—
325#125—22no—
326#123—28no—
327C22⋊Q8—22no—
328C22⋊Q8—22no—
329C22⋊Q8—22no—
330C22⋊Q8—22no—
331C22⋊Q8—22no—
332C22⋊Q8—22no—
333C22⋊Q8—41no—
334C22⋊Q8C3×D414yes—
335C4×Q8—22no—
336C4×Q8—22no—
337C4×D4—22no—
338C4×D4—22no—
339#117—28no—
340#117—22no—
341#117—22no—
342#117—41no—
343#117C3×D414yes—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4C3×D411yescharacteristic
356C2×C4⋊C4C23×C311yescharacteristic
357C2×C4⋊C4C23×C311yescharacteristic
358C2×C4⋊C4C23×C311yescharacteristic
359C2×C4⋊C4C23×C311yescharacteristic
360C2×C4⋊C4C23×C311yescharacteristic
361C2×C4⋊C4C23×C311yescharacteristic
362C2×C22⋊C4—21no—
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⋊C4C3×D411yescharacteristic
370C2×C22⋊C4C3×D411yescharacteristic
371C2×C42—21no—
372C2×C42—21no—
373C2×C42—21no—
374C2×C42C23×C311yescharacteristic
375#107—22no—
376#107—22no—
377#106—22no—
378#103—22no—
379#103—22no—
380#103—22no—
381#103—22no—
382#103—22no—
383#103—41no—
384C22⋊C8—22no—
385C22⋊C8—22no—
386C22⋊C8—41no—
387#95—21no—
388#95—21no—
389#95—21no—
390#95—21no—
391C23×C3—21no—
392C23×C3—21no—
393C23×C3—21no—
394C23×C3—21no—
395C23×C3—21no—
396C23×C3—21no—
397C23×C3—21no—
398C23×C3—21no—
399C23×C3—21no—
400C23×C3—21no—
401C23×C3—21no—
402C23×C3—21no—
403C23×C3#12012yes—
404C23×C3#13512yes—
405C23×C3C22×D411yescharacteristic
406C3×Q8—22no—
407C3×Q8—22no—
408C3×Q8—41no—
409C3×Q8—41no—
410C3×Q8—41no—
411C3×Q8—41no—
412C3×Q8—41no—
413C3×Q8—41no—
414C3×D4—44no—
415C2×C3×C4—21no—
416C2×C3×C4—21no—
417C2×C3×C4—22no—
418C2×C3×C4—22no—
419C2×C3×C4—22no—
420C2×C3×C4—22no—
421C2×C3×C4—21no—
422C2×C3×C4—22no—
423C2×C3×C4—22no—
424C2×C3×C4—22no—
425C2×C3×C4—21no—
426C2×C3×C4—21no—
427C2×C3×C4—22no—
428C2×C3×C4—22no—
429C2×C3×C4—21no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
432C2×C3×C4—21no—
433C2×C3×C4—21no—
434C2×C3×C4—21no—
435C2×C3×C4—48no—
436C2×C3×C4—41no—
437C2×C3×C4—41no—
438C2×C3×C4—41no—
439C2×C3×C4—41no—
440C2×C3×C4—41no—
441C2×C3×C4—41no—
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—41no—
468C3×C8—41no—
469C3×C8—41no—
470C24C2×C3×D411yescharacteristic
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×Q8—21no—
483C2×Q8C2×C3×D412yes—
484C2×D4—22no—
485C2×D4—22no—
486C2×D4—41no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—24no—
492C22×C4—21no—
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×C4—21no—
505C22×C4—21no—
506C22×C4—42no—
507C22×C4—42no—
508C22×C4C2×C3×D411yescharacteristic
509C22×C4C2×C3×D411yescharacteristic
510C22×C4C2×C3×D411yescharacteristic
511C22×C4C2×C3×D411yescharacteristic
512C22×C4C2×C3×D412yes—
513C22×C4C2×C3×D412yes—
514C22×C4C24×C311yescharacteristic
515Q16—44no—
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—21no—
526C2×C8—21no—
527C2×C8—44no—
528C2×C8C3×#4112yes—
529C4⋊C4—24no—
530C4⋊C4—24no—
531C4⋊C4—24no—
532C4⋊C4—24no—
533C4⋊C4—24no—
534C4⋊C4—24no—
535C4⋊C4—22no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—42no—
545C4⋊C4—42no—
546C4⋊C4—42no—
547C4⋊C4C2×C3×D412yes—
548C4⋊C4C2×C3×D412yes—
549C4⋊C4C2×C3×D412yes—
550C4⋊C4C3×#4112yes—
551C22⋊C4—24no—
552C22⋊C4—24no—
553C22⋊C4—24no—
554C22⋊C4—22no—
555C22⋊C4—22no—
556C22⋊C4—42no—
557C22⋊C4—42no—
558C22⋊C4—42no—
559C22⋊C4—42no—
560C42—24no—
561C42—24no—
562C42—21no—
563C42—21no—
564C42—42no—
565C22×C3—22no—
566C22×C3—22no—
567C22×C3—22no—
568C22×C3—22no—
569C22×C3—22no—
570C22×C3—22no—
571C22×C3—41no—
572C22×C3—41no—
573C22×C3—41no—
574C22×C3—41no—
575C22×C3—41no—
576C22×C3—41no—
577C22×C3—41no—
578C22×C3—41no—
579C22×C3C2×#12011yescharacteristic
580C22×C3#54611yescharacteristic
581C22×C3#54711yescharacteristic
582C22×C3C2×#13511yescharacteristic
583C22×C3#57511yescharacteristic
584C22×C3#57811yescharacteristic
585C22×C3#57811yescharacteristic
586C3×C4—22no—
587C3×C4—41no—
588C3×C4—42no—
589C3×C4—41no—
590C3×C4—42no—
591C3×C4—42no—
592C3×C4—41no—
593C3×C4—42no—
594C3×C4—42no—
595C3×C4—81no—
596C3×C4—81no—
597C3×C4—81no—
598C3×C4#53211yescharacteristic
599C3×C4#53711yescharacteristic
600C3×C4#54611yescharacteristic
601C3×C4#54711yescharacteristic
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23C3×#12012yes—
615C23C3×#13512yes—
616C23C22×C3×D411yescharacteristic
617Q8—22no—
618Q8—22no—
619Q8—41no—
620Q8—41no—
621Q8—41no—
622Q8—41no—
623Q8—41no—
624Q8—41no—
625D4—44no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—48no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
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—41no—
679C8—41no—
680C8—41no—
681C2×C3—42no—
682C2×C3—42no—
683C2×C3#243011yescharacteristic
684C2×C3#300211yescharacteristic
685C2×C3#301111yescharacteristic
686C2×C3#330011yescharacteristic
687C2×C3#331511yescharacteristic
688C2×C3#333611yescharacteristic
689C2×C3#334911yescharacteristic
690C22—22no—
691C22—22no—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22C2×C3×#12011yescharacteristic
705C22C3×#54611yescharacteristic
706C22C3×#54711yescharacteristic
707C22C2×C3×#13511yescharacteristic
708C22C3×#57511yescharacteristic
709C22C3×#57811yescharacteristic
710C22C3×#57811yescharacteristic
711C4—22no—
712C4—41no—
713C4—42no—
714C4—41no—
715C4—42no—
716C4—42no—
717C4—41no—
718C4—42no—
719C4—42no—
720C4—81no—
721C4—81no—
722C4—81no—
723C4C3×#53211yescharacteristic
724C4C3×#53711yescharacteristic
725C4C3×#54611yescharacteristic
726C4C3×#54711yescharacteristic
727C3#2554611yescharacteristic, direct product factor, Sylow
728C2—42no—
729C2—42no—
730C2C3×#243011yescharacteristic
731C2C3×#300211yescharacteristic
732C2C3×#301111yescharacteristic
733C2C3×#330011yescharacteristic
734C2C3×#331511yescharacteristic
735C2C3×#333611yescharacteristic
736C2C3×#334911yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC22×C3×D4D4
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
2. C2×C3×#485C2semidirect
3. C2×C3×#467C2semidirect
5. C3×#2059C2semidirect
6. C3×#2035C2semidirect
7. C3×#2026C2semidirect
8. C3×#2001C2semidirect
9. C3×#1878C2semidirect
10. C3×#1873C2semidirect
11. C3×#1872C2semidirect
13. C3×#1863C2semidirect
14. C3×#1852C2semidirect
15. C3×#1735C2semidirect
16. #25546C3direct (N × H)
65. C2×#485C2×C3semidirect
66. C2×#467C2×C3semidirect
68. #2059C2×C3semidirect
69. #2035C2×C3semidirect
70. #2026C2×C3semidirect
71. #2001C2×C3semidirect
72. #1878C2×C3semidirect
73. #1873C2×C3semidirect
74. #1872C2×C3semidirect
76. #1863C2×C3semidirect
77. #1852C2×C3semidirect
78. #1735C2×C3semidirect
727. C3#25546direct (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×#4852
C2×C3×#4672
C3×#24152
C3×#20592
C3×#20352
C3×#20262
C3×#20012
C3×#18782
C3×#18732
C3×#18722
C3×#18692
C3×#18632
C3×#18522
C3×#17352
#255463