Finite Group Databasebeta

← C3×#24109 #10642716

Subgroups — C3×#24109 #10642716

Order 768.

1084 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#554C211yesmaximal, characteristic
2C2×C3×#485C211yesmaximal, characteristic, complemented
3C2×C3×#428C211yesmaximal, characteristic, complemented
4C3×#2485C211yesmaximal, characteristic
5C3×#2058C211yesmaximal, characteristic, complemented
6C3×#2057C211yesmaximal, characteristic, complemented
7C3×#2036C211yesmaximal, characteristic, complemented
8C3×#2035C211yesmaximal, characteristic, complemented
9C3×#1894C211yesmaximal, characteristic, complemented
10C3×#1870C211yesmaximal, characteristic
11C3×#1865C211yesmaximal, characteristic, complemented
12C3×#1863C211yesmaximal, characteristic, complemented
13C3×#1853C211yesmaximal, characteristic, complemented
14C3×#1852C211yesmaximal, characteristic, complemented
15C3×#1823C211yesmaximal, characteristic, complemented
16#24109C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×M16C2211yescharacteristic
18C3×#554—24no—
19C3×#554—24no—
20C2×C3×C4⋊Q8C2211yescharacteristic
21C2×C3×#125—21no—
22C2×C3×C22⋊Q8—21no—
23C2×C3×C22⋊Q8—21no—
24C2×C3×C22⋊Q8C2211yescharacteristic
25C2×C3×C22⋊Q8C2211yescharacteristic
26C2×C3×C4×Q8C2211yescharacteristic
27C2×C3×C4×D4—21no—
28C2×C3×C4×D4C2211yescharacteristic
29C2×C3×#117C2211yescharacteristic
30C22×C3×C4⋊C4C2211yescharacteristic
31C22×C3×C4⋊C4C2211yescharacteristic
32C3×#485—24no—
33C3×#428—24no—
34C2×C3×#107C2211yescharacteristic
35C2×C3×#107C2211yescharacteristic
36C2×C3×#107C2211yescharacteristic
37C2×C3×#106C2211yescharacteristic
38C2×C3×#106C2211yescharacteristic
39C2×C3×#106C2211yescharacteristic
40C2×C3×#103C2211yescharacteristic
41C2×C3×#103C2211yescharacteristic
42C2×C3×#103C2211yescharacteristic
43C2×C3×#103C2211yescharacteristic
44C2×C3×C22⋊C8C2211yescharacteristic
45C2×C3×C22⋊C8C2211yescharacteristic
46C2×C3×C22⋊C8C2211yescharacteristic
47C3×#397—21no—
48C3×#394—21no—
49C3×#389C2211yescharacteristic
50C3×#389C2211yescharacteristic
51C3×#388—21no—
52C3×#387—21no—
53C3×#380C2211yescharacteristic
54C3×#380C2211yescharacteristic
55C3×#380C2211yescharacteristic
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#340C2211yescharacteristic
61C3×#340C2211yescharacteristic
62C3×#336C2211yescharacteristic
63C3×#336C2211yescharacteristic
64C2×#554C2×C311yescharacteristic
65C2×#485C2×C311yescharacteristic, complemented
66C2×#428C2×C311yescharacteristic, complemented
67#2485C2×C311yescharacteristic
68#2058C2×C311yescharacteristic, complemented
69#2057C2×C311yescharacteristic, complemented
70#2036C2×C311yescharacteristic, complemented
71#2035C2×C311yescharacteristic, complemented
72#1894C2×C311yescharacteristic, complemented
73#1870C2×C311yescharacteristic
74#1865C2×C311yescharacteristic, complemented
75#1863C2×C311yescharacteristic, complemented
76#1853C2×C311yescharacteristic, complemented
77#1852C2×C311yescharacteristic, complemented
78#1823C2×C311yescharacteristic, complemented
79C22×C3×Q8—21no—
80C22×C3×Q8C2311yescharacteristic
81C22×C3×D4D411yescharacteristic
82C23×C3×C4—21no—
83C23×C3×C4—21no—
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C2×C3×M16—22no—
87C2×C3×M16—22no—
88C2×C3×M16—22no—
89C22×C3×C8C2311yescharacteristic
90C22×C3×C8C2311yescharacteristic
91C22×C3×C8C2311yescharacteristic
92C22×C3×C8C2311yescharacteristic
93C3×C4⋊Q8—22no—
94C3×C4⋊Q8—22no—
95C3×#125—28no—
96C3×C22⋊Q8—28no—
97C3×C22⋊Q8—28no—
98C3×C22⋊Q8—22no—
99C3×C22⋊Q8—22no—
100C3×C22⋊Q8—22no—
101C3×C22⋊Q8D414yes—
102C3×C4×Q8—22no—
103C3×C4×Q8—22no—
104C3×C4×D4—28no—
105C3×C4×D4—22no—
106C3×C4×D4—22no—
107C3×#117—22no—
108C3×#117—22no—
109C2×C3×C4⋊C4—21no—
110C2×C3×C4⋊C4—21no—
111C2×C3×C4⋊C4—22no—
112C2×C3×C4⋊C4—21no—
113C2×C3×C4⋊C4—21no—
114C2×C3×C4⋊C4—21no—
115C2×C3×C4⋊C4—21no—
116C2×C3×C4⋊C4—22no—
117C2×C3×C4⋊C4—22no—
118C2×C3×C4⋊C4—21no—
119C2×C3×C4⋊C4—21no—
120C2×C3×C4⋊C4D411yescharacteristic
121C2×C3×C4⋊C4D414yes—
122C2×C3×C4⋊C4C2311yescharacteristic
123C2×C3×C4⋊C4C2311yescharacteristic
124C2×C3×C4⋊C4C2311yescharacteristic
125C2×C3×C4⋊C4C2311yescharacteristic
126C2×C3×C4⋊C4C2311yescharacteristic
127C2×C3×C4⋊C4C2311yescharacteristic
128C2×C3×C4⋊C4C2311yescharacteristic
129C2×C3×C22⋊C4—21no—
130C2×C3×C22⋊C4—21no—
131C2×C3×C22⋊C4—21no—
132C2×C3×C22⋊C4—21no—
133C2×C3×C22⋊C4—21no—
134C2×C3×C22⋊C4—21no—
135C2×C3×C22⋊C4D411yescharacteristic
136C2×C3×C22⋊C4D411yescharacteristic
137C2×C3×C42—21no—
138C2×C3×C42—21no—
139C2×C3×C42C2311yescharacteristic
140C3×#107—22no—
141C3×#107—22no—
142C3×#107—22no—
143C3×#106—22no—
144C3×#106—22no—
145C3×#106—22no—
146C3×#103—22no—
147C3×#103—22no—
148C3×#103—22no—
149C3×#103—22no—
150C3×C22⋊C8—22no—
151C3×C22⋊C8—22no—
152C3×C22⋊C8—22no—
153C3×#95—21no—
154C3×#95—21no—
155C3×#95—21no—
156C3×#95—21no—
157C3×#95—21no—
158C22×M16C22×C311yescharacteristic
159#554—24no—
160#554—24no—
161C2×C4⋊Q8C22×C311yescharacteristic
162C2×#125—21no—
163C2×C22⋊Q8—21no—
164C2×C22⋊Q8—21no—
165C2×C22⋊Q8C22×C311yescharacteristic
166C2×C22⋊Q8C22×C311yescharacteristic
167C2×C4×Q8C22×C311yescharacteristic
168C2×C4×D4—21no—
169C2×C4×D4C22×C311yescharacteristic
170C2×#117C22×C311yescharacteristic
171C22×C4⋊C4C22×C311yescharacteristic
172C22×C4⋊C4C22×C311yescharacteristic
173#485—24no—
174#428—24no—
175C2×#107C22×C311yescharacteristic
176C2×#107C22×C311yescharacteristic
177C2×#107C22×C311yescharacteristic
178C2×#106C22×C311yescharacteristic
179C2×#106C22×C311yescharacteristic
180C2×#106C22×C311yescharacteristic
181C2×#103C22×C311yescharacteristic
182C2×#103C22×C311yescharacteristic
183C2×#103C22×C311yescharacteristic
184C2×#103C22×C311yescharacteristic
185C2×C22⋊C8C22×C311yescharacteristic
186C2×C22⋊C8C22×C311yescharacteristic
187C2×C22⋊C8C22×C311yescharacteristic
188#397—21no—
189#394—21no—
190#389C22×C311yescharacteristic
191#389C22×C311yescharacteristic
192#388—21no—
193#387—21no—
194#380C22×C311yescharacteristic
195#380C22×C311yescharacteristic
196#380C22×C311yescharacteristic
197#340C22×C311yescharacteristic
198#340C22×C311yescharacteristic
199#340C22×C311yescharacteristic
200#340C22×C311yescharacteristic
201#340C22×C311yescharacteristic
202#340C22×C311yescharacteristic
203#336C22×C311yescharacteristic
204#336C22×C311yescharacteristic
205C24×C3C2×D411yescharacteristic
206C24×C3C2×D411yescharacteristic
207C2×C3×Q8—24no—
208C2×C3×Q8—21no—
209C2×C3×Q8—21no—
210C2×C3×Q8—21no—
211C2×C3×Q8—21no—
212C2×C3×Q8—21no—
213C2×C3×Q8—81no—
214C2×C3×Q8—81no—
215C2×C3×Q8C2×D412yes—
216C2×C3×D4—22no—
217C2×C3×D4—22no—
218C2×C3×D4—22no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—24no—
228C22×C3×C4—24no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
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—81no—
240C22×C3×C4—81no—
241C22×C3×C4—81no—
242C22×C3×C4—81no—
243C22×C3×C4C2×D411yescharacteristic
244C22×C3×C4C2×D411yescharacteristic
245C22×C3×C4C2×D411yescharacteristic
246C22×C3×C4C2×D412yes—
247C22×C3×C4C2×D412yes—
248C22×C3×C4C2×D411yescharacteristic
249C22×C3×C4C2411yescharacteristic
250C3×M16—28no—
251C2×C3×C8—21no—
252C2×C3×C8—21no—
253C2×C3×C8—21no—
254C2×C3×C8—21no—
255C2×C3×C8—21no—
256C2×C3×C8—21no—
257C2×C3×C8—21no—
258C2×C3×C8—21no—
259C2×C3×C8—21no—
260C2×C3×C8—21no—
261C2×C3×C8#4112yes—
262C2×C3×C8#4112yes—
263C3×C4⋊C4—24no—
264C3×C4⋊C4—24no—
265C3×C4⋊C4—24no—
266C3×C4⋊C4—24no—
267C3×C4⋊C4—24no—
268C3×C4⋊C4—24no—
269C3×C4⋊C4—22no—
270C3×C4⋊C4—21no—
271C3×C4⋊C4—21no—
272C3×C4⋊C4—21no—
273C3×C4⋊C4—21no—
274C3×C4⋊C4—21no—
275C3×C4⋊C4—21no—
276C3×C4⋊C4—21no—
277C3×C4⋊C4—21no—
278C3×C4⋊C4—21no—
279C3×C4⋊C4—21no—
280C3×C4⋊C4—21no—
281C3×C4⋊C4—42no—
282C3×C4⋊C4—81no—
283C3×C4⋊C4C2×D412yes—
284C3×C4⋊C4C2×D412yes—
285C3×C4⋊C4C2×D412yes—
286C3×C22⋊C4—24no—
287C3×C22⋊C4—24no—
288C3×C22⋊C4—22no—
289C3×C22⋊C4—22no—
290C3×C22⋊C4—42no—
291C3×C22⋊C4—42no—
292C3×C22⋊C4—81no—
293C3×C22⋊C4—81no—
294C3×C42—24no—
295C3×C42—21no—
296C3×C42—21no—
297C3×C42—42no—
298C22×Q8—21no—
299C22×Q8C23×C311yescharacteristic
300C22×D4C3×D411yescharacteristic
301C23×C4—21no—
302C23×C4—21no—
303C23×C4C23×C311yescharacteristic
304C23×C4C23×C311yescharacteristic
305C2×M16—22no—
306C2×M16—22no—
307C2×M16—22no—
308C22×C8C23×C311yescharacteristic
309C22×C8C23×C311yescharacteristic
310C22×C8C23×C311yescharacteristic
311C22×C8C23×C311yescharacteristic
312C4⋊Q8—22no—
313C4⋊Q8—22no—
314#125—28no—
315C22⋊Q8—28no—
316C22⋊Q8—28no—
317C22⋊Q8—22no—
318C22⋊Q8—22no—
319C22⋊Q8—22no—
320C22⋊Q8C3×D414yes—
321C4×Q8—22no—
322C4×Q8—22no—
323C4×D4—28no—
324C4×D4—22no—
325C4×D4—22no—
326#117—22no—
327#117—22no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4C3×D411yescharacteristic
340C2×C4⋊C4C3×D414yes—
341C2×C4⋊C4C23×C311yescharacteristic
342C2×C4⋊C4C23×C311yescharacteristic
343C2×C4⋊C4C23×C311yescharacteristic
344C2×C4⋊C4C23×C311yescharacteristic
345C2×C4⋊C4C23×C311yescharacteristic
346C2×C4⋊C4C23×C311yescharacteristic
347C2×C4⋊C4C23×C311yescharacteristic
348C2×C22⋊C4—21no—
349C2×C22⋊C4—21no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—21no—
354C2×C22⋊C4C3×D411yescharacteristic
355C2×C22⋊C4C3×D411yescharacteristic
356C2×C42—21no—
357C2×C42—21no—
358C2×C42C23×C311yescharacteristic
359#107—22no—
360#107—22no—
361#107—22no—
362#106—22no—
363#106—22no—
364#106—22no—
365#103—22no—
366#103—22no—
367#103—22no—
368#103—22no—
369C22⋊C8—22no—
370C22⋊C8—22no—
371C22⋊C8—22no—
372#95—21no—
373#95—21no—
374#95—21no—
375#95—21no—
376#95—21no—
377C23×C3—21no—
378C23×C3—21no—
379C23×C3—21no—
380C23×C3—21no—
381C23×C3—21no—
382C23×C3—21no—
383C23×C3—21no—
384C23×C3—21no—
385C23×C3—21no—
386C23×C3—21no—
387C23×C3—21no—
388C23×C3—21no—
389C23×C3#12012yes—
390C23×C3#13712yes—
391C23×C3C22×D411yescharacteristic
392C3×Q8—22no—
393C3×Q8—22no—
394C3×Q8—41no—
395C3×Q8—41no—
396C3×Q8—84no—
397C3×D4—28no—
398C2×C3×C4—21no—
399C2×C3×C4—21no—
400C2×C3×C4—21no—
401C2×C3×C4—21no—
402C2×C3×C4—22no—
403C2×C3×C4—22no—
404C2×C3×C4—22no—
405C2×C3×C4—22no—
406C2×C3×C4—22no—
407C2×C3×C4—21no—
408C2×C3×C4—22no—
409C2×C3×C4—21no—
410C2×C3×C4—22no—
411C2×C3×C4—22no—
412C2×C3×C4—21no—
413C2×C3×C4—21no—
414C2×C3×C4—21no—
415C2×C3×C4—21no—
416C2×C3×C4—41no—
417C2×C3×C4—41no—
418C2×C3×C4—41no—
419C2×C3×C4—41no—
420C2×C3×C4—41no—
421C2×C3×C4—41no—
422C2×C3×C4—41no—
423C2×C3×C4—41no—
424C2×C3×C4—41no—
425C2×C3×C4—41no—
426C2×C3×C4—41no—
427C2×C3×C4—41no—
428C2×C3×C4—41no—
429C2×C3×C4—41no—
430C2×C3×C4—41no—
431C2×C3×C4—41no—
432C2×C3×C4—41no—
433C2×C3×C4—41no—
434C2×C3×C4—41no—
435C2×C3×C4—41no—
436C2×C3×C4—41no—
437C2×C3×C4—41no—
438C2×C3×C4—41no—
439C2×C3×C4—41no—
440C2×C3×C4—84no—
441C2×C3×C4—84no—
442C2×C3×C4#12012yes—
443C2×C3×C4#13712yes—
444C2×C3×C4C22×D411yescharacteristic
445C2×C3×C4C22×D411yescharacteristic
446C2×C3×C4C2×#4111yescharacteristic
447C2×C3×C4C2×#4111yescharacteristic
448C2×C3×C42−1+411yescharacteristic
449C2×C3×C42−1+411yescharacteristic
450C3×C8—22no—
451C3×C8—22no—
452C3×C8—41no—
453C3×C8—41no—
454C24C2×C3×D411yescharacteristic
455C24C2×C3×D411yescharacteristic
456C2×Q8—24no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—81no—
463C2×Q8—81no—
464C2×Q8C2×C3×D412yes—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—81no—
489C22×C4—81no—
490C22×C4—81no—
491C22×C4—81no—
492C22×C4C2×C3×D411yescharacteristic
493C22×C4C2×C3×D411yescharacteristic
494C22×C4C2×C3×D411yescharacteristic
495C22×C4C2×C3×D412yes—
496C22×C4C2×C3×D412yes—
497C22×C4C2×C3×D411yescharacteristic
498C22×C4C24×C311yescharacteristic
499M16—28no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8C3×#4112yes—
511C2×C8C3×#4112yes—
512C4⋊C4—24no—
513C4⋊C4—24no—
514C4⋊C4—24no—
515C4⋊C4—24no—
516C4⋊C4—24no—
517C4⋊C4—24no—
518C4⋊C4—22no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—42no—
531C4⋊C4—81no—
532C4⋊C4C2×C3×D412yes—
533C4⋊C4C2×C3×D412yes—
534C4⋊C4C2×C3×D412yes—
535C22⋊C4—24no—
536C22⋊C4—24no—
537C22⋊C4—22no—
538C22⋊C4—22no—
539C22⋊C4—42no—
540C22⋊C4—42no—
541C22⋊C4—81no—
542C22⋊C4—81no—
543C42—24no—
544C42—21no—
545C42—21no—
546C42—42no—
547C22×C3—22no—
548C22×C3—22no—
549C22×C3—22no—
550C22×C3—22no—
551C22×C3—22no—
552C22×C3—22no—
553C22×C3—41no—
554C22×C3—41no—
555C22×C3—41no—
556C22×C3—41no—
557C22×C3—41no—
558C22×C3—41no—
559C22×C3—41no—
560C22×C3—41no—
561C22×C3C2×#12011yescharacteristic
562C22×C3#54711yescharacteristic
563C22×C3#54711yescharacteristic
564C22×C3C2×#13711yescharacteristic
565C22×C3C2×#13711yescharacteristic
566C22×C3#57611yescharacteristic
567C22×C3#57711yescharacteristic
568C3×C4—22no—
569C3×C4—22no—
570C3×C4—41no—
571C3×C4—42no—
572C3×C4—41no—
573C3×C4—42no—
574C3×C4—42no—
575C3×C4—42no—
576C3×C4—81no—
577C3×C4—81no—
578C3×C4—81no—
579C3×C4—81no—
580C3×C4#52511yescharacteristic
581C3×C4#53611yescharacteristic
582C3×C4#54711yescharacteristic
583C3×C4#54711yescharacteristic
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23C3×#12012yes—
597C23C3×#13712yes—
598C23C22×C3×D411yescharacteristic
599Q8—22no—
600Q8—22no—
601Q8—41no—
602Q8—41no—
603Q8—84no—
604D4—28no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—22no—
616C2×C4—21no—
617C2×C4—22no—
618C2×C4—21no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—84no—
648C2×C4—84no—
649C2×C4C3×#12012yes—
650C2×C4C3×#13712yes—
651C2×C4C22×C3×D411yescharacteristic
652C2×C4C22×C3×D411yescharacteristic
653C2×C4C2×C3×#4111yescharacteristic
654C2×C4C2×C3×#4111yescharacteristic
655C2×C4C3×2−1+411yescharacteristic
656C2×C4C3×2−1+411yescharacteristic
657C8—22no—
658C8—22no—
659C8—41no—
660C8—41no—
661C2×C3—42no—
662C2×C3—42no—
663C2×C3#240611yescharacteristic
664C2×C3#300411yescharacteristic
665C2×C3#301211yescharacteristic
666C2×C3#334411yescharacteristic
667C2×C3#334611yescharacteristic
668C2×C3#335611yescharacteristic
669C2×C3#335711yescharacteristic
670C22—22no—
671C22—22no—
672C22—22no—
673C22—22no—
674C22—22no—
675C22—22no—
676C22—41no—
677C22—41no—
678C22—41no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22C2×C3×#12011yescharacteristic
685C22C3×#54711yescharacteristic
686C22C3×#54711yescharacteristic
687C22C2×C3×#13711yescharacteristic
688C22C2×C3×#13711yescharacteristic
689C22C3×#57611yescharacteristic
690C22C3×#57711yescharacteristic
691C4—22no—
692C4—22no—
693C4—41no—
694C4—42no—
695C4—41no—
696C4—42no—
697C4—42no—
698C4—42no—
699C4—81no—
700C4—81no—
701C4—81no—
702C4—81no—
703C4C3×#52511yescharacteristic
704C4C3×#53611yescharacteristic
705C4C3×#54711yescharacteristic
706C4C3×#54711yescharacteristic
707C3#2410911yescharacteristic, direct product factor, Sylow
708C2—42no—
709C2—42no—
710C2C3×#240611yescharacteristic
711C2C3×#300411yescharacteristic
712C2C3×#301211yescharacteristic
713C2C3×#334411yescharacteristic
714C2C3×#334611yescharacteristic
715C2C3×#335611yescharacteristic
716C2C3×#335711yescharacteristic
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×#428C2semidirect
5. C3×#2058C2semidirect
6. C3×#2057C2semidirect
7. C3×#2036C2semidirect
8. C3×#2035C2semidirect
9. C3×#1894C2semidirect
11. C3×#1865C2semidirect
12. C3×#1863C2semidirect
13. C3×#1853C2semidirect
14. C3×#1852C2semidirect
15. C3×#1823C2semidirect
16. #24109C3direct (N × H)
65. C2×#485C2×C3semidirect
66. C2×#428C2×C3semidirect
68. #2058C2×C3semidirect
69. #2057C2×C3semidirect
70. #2036C2×C3semidirect
71. #2035C2×C3semidirect
72. #1894C2×C3semidirect
74. #1865C2×C3semidirect
75. #1863C2×C3semidirect
76. #1853C2×C3semidirect
77. #1852C2×C3semidirect
78. #1823C2×C3semidirect
707. C3#24109direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5542
C2×C3×#4852
C2×C3×#4282
C3×#24852
C3×#20582
C3×#20572
C3×#20362
C3×#20352
C3×#18942
C3×#18702
C3×#18652
C3×#18632
C3×#18532
C3×#18522
C3×#18232
#241093