Finite Group Databasebeta

← C3×#30423 #10649030

Subgroups — C3×#30423 #10649030

Order 768.

968 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#470C211yesmaximal, characteristic, complemented
2C2×C3×#451C211yesmaximal, characteristic, complemented
3C3×#2538C211yesmaximal, characteristic
4C3×#2409C211yesmaximal, characteristic
5C3×#2096C211yesmaximal, characteristic, complemented
6C3×#2077C211yesmaximal, characteristic, complemented
7C3×#2072C211yesmaximal, characteristic, complemented
8C3×#2035C211yesmaximal, characteristic, complemented
9C3×#2035C211yesmaximal, characteristic, complemented
10C3×#2001C211yesmaximal, characteristic, complemented
11C3×#1894C211yesmaximal, characteristic, complemented
12C3×#1878C211yesmaximal, characteristic, complemented
13C3×#1878C211yesmaximal, characteristic, complemented
14C3×#1870C211yesmaximal, characteristic
15C3×#1787C211yesmaximal, characteristic, complemented
16#30423C311yesmaximal, characteristic, direct product factor, Sylow
17C23×C3×Q8C2211yescharacteristic
18C22×C3×Q16C2211yescharacteristic
19C22×C3×Q16C2211yescharacteristic
20C22×C3×M16C2211yescharacteristic
21C2×C3×C22⋊Q8C2211yescharacteristic
22C2×C3×C22⋊Q8C2211yescharacteristic
23C2×C3×C22⋊Q8C2211yescharacteristic
24C2×C3×C22⋊Q8C2211yescharacteristic
25C2×C3×C4×Q8C2211yescharacteristic
26C2×C3×C4×D4C2211yescharacteristic
27C3×#470—24no—
28C3×#451—24no—
29C2×C3×#106C2211yescharacteristic
30C2×C3×#106C2211yescharacteristic
31C2×C3×#103C2211yescharacteristic
32C2×C3×#103C2211yescharacteristic
33C2×C3×#103C2211yescharacteristic
34C2×C3×#103C2211yescharacteristic
35C2×C3×#103C2211yescharacteristic
36C2×C3×#103C2211yescharacteristic
37C2×C3×#103C2211yescharacteristic
38C2×C3×#103C2211yescharacteristic
39C2×C3×C22⋊C8C2211yescharacteristic
40C2×C3×C22⋊C8C2211yescharacteristic
41C2×C3×C22⋊C8C2211yescharacteristic
42C3×#396—21no—
43C3×#396—21no—
44C3×#395—21no—
45C3×#393—21no—
46C3×#391C2211yescharacteristic
47C3×#391C2211yescharacteristic
48C3×#390—21no—
49C3×#389—21no—
50C3×#386—21no—
51C3×#385—21no—
52C3×#384C2211yescharacteristic
53C3×#380C2211yescharacteristic
54C3×#380C2211yescharacteristic
55C3×#380C2211yescharacteristic
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#336C2211yescharacteristic
61C3×#336C2211yescharacteristic
62C2×#470C2×C311yescharacteristic, complemented
63C2×#451C2×C311yescharacteristic, complemented
64#2538C2×C311yescharacteristic
65#2409C2×C311yescharacteristic
66#2096C2×C311yescharacteristic, complemented
67#2077C2×C311yescharacteristic, complemented
68#2072C2×C311yescharacteristic, complemented
69#2035C2×C311yescharacteristic, complemented
70#2035C2×C311yescharacteristic, complemented
71#2001C2×C311yescharacteristic, complemented
72#1894C2×C311yescharacteristic, complemented
73#1878C2×C311yescharacteristic, complemented
74#1878C2×C311yescharacteristic, complemented
75#1870C2×C311yescharacteristic
76#1787C2×C311yescharacteristic, complemented
77C22×C3×Q8—21no—
78C22×C3×Q8—22no—
79C22×C3×Q8—22no—
80C22×C3×Q8—41no—
81C22×C3×Q8—41no—
82C22×C3×Q8—41no—
83C22×C3×Q8—41no—
84C22×C3×Q8C2311yescharacteristic
85C22×C3×Q8C2311yescharacteristic
86C22×C3×Q8C2311yescharacteristic
87C22×C3×D4D411yescharacteristic
88C23×C3×C4—21no—
89C23×C3×C4C2311yescharacteristic
90C23×C3×C4C2311yescharacteristic
91C2×C3×Q16—22no—
92C2×C3×Q16—22no—
93C2×C3×Q16—41no—
94C2×C3×Q16—41no—
95C2×C3×Q16—41no—
96C2×C3×Q16D414yescomplemented
97C2×C3×M16—22no—
98C2×C3×M16—41no—
99C2×C3×M16—41no—
100C22×C3×C8C2311yescharacteristic
101C22×C3×C8C2311yescharacteristic
102C22×C3×C8C2311yescharacteristic
103C22×C3×C8C2311yescharacteristic
104C3×C22⋊Q8—22no—
105C3×C22⋊Q8—22no—
106C3×C22⋊Q8—22no—
107C3×C22⋊Q8—22no—
108C3×C22⋊Q8—41no—
109C3×C22⋊Q8—41no—
110C3×C22⋊Q8—41no—
111C3×C22⋊Q8—41no—
112C3×C4×Q8—41no—
113C3×C4×Q8—41no—
114C3×C4×D4—41no—
115C3×C4×D4—41no—
116C2×C3×C4⋊C4—21no—
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⋊C4D411yescharacteristic
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⋊C4—21no—
136C2×C3×C22⋊C4D411yescharacteristic
137C2×C3×C22⋊C4D411yescharacteristic
138C2×C3×C42—21no—
139C2×C3×C42C2311yescharacteristic
140C3×#106—22no—
141C3×#106—41no—
142C3×#103—22no—
143C3×#103—22no—
144C3×#103—22no—
145C3×#103—22no—
146C3×#103—41no—
147C3×#103—41no—
148C3×#103—41no—
149C3×#103—41no—
150C3×C22⋊C8—22no—
151C3×C22⋊C8—41no—
152C3×C22⋊C8—41no—
153C3×#95—21no—
154C3×#95—21no—
155C3×#95—21no—
156C3×#95—21no—
157C3×#95—21no—
158C3×#95—21no—
159C3×#95—21no—
160C23×Q8C22×C311yescharacteristic
161C22×Q16C22×C311yescharacteristic
162C22×Q16C22×C311yescharacteristic
163C22×M16C22×C311yescharacteristic
164C2×C22⋊Q8C22×C311yescharacteristic
165C2×C22⋊Q8C22×C311yescharacteristic
166C2×C22⋊Q8C22×C311yescharacteristic
167C2×C22⋊Q8C22×C311yescharacteristic
168C2×C4×Q8C22×C311yescharacteristic
169C2×C4×D4C22×C311yescharacteristic
170#470—24no—
171#451—24no—
172C2×#106C22×C311yescharacteristic
173C2×#106C22×C311yescharacteristic
174C2×#103C22×C311yescharacteristic
175C2×#103C22×C311yescharacteristic
176C2×#103C22×C311yescharacteristic
177C2×#103C22×C311yescharacteristic
178C2×#103C22×C311yescharacteristic
179C2×#103C22×C311yescharacteristic
180C2×#103C22×C311yescharacteristic
181C2×#103C22×C311yescharacteristic
182C2×C22⋊C8C22×C311yescharacteristic
183C2×C22⋊C8C22×C311yescharacteristic
184C2×C22⋊C8C22×C311yescharacteristic
185#396—21no—
186#396—21no—
187#395—21no—
188#393—21no—
189#391C22×C311yescharacteristic
190#391C22×C311yescharacteristic
191#390—21no—
192#389—21no—
193#386—21no—
194#385—21no—
195#384C22×C311yescharacteristic
196#380C22×C311yescharacteristic
197#380C22×C311yescharacteristic
198#380C22×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—21no—
208C2×C3×Q8—21no—
209C2×C3×Q8—21no—
210C2×C3×Q8—21no—
211C2×C3×Q8—21no—
212C2×C3×Q8—21no—
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—42no—
223C2×C3×Q8—42no—
224C2×C3×Q8—42no—
225C2×C3×Q8—44no—
226C2×C3×Q8—44no—
227C2×C3×Q8—44no—
228C2×C3×Q8—44no—
229C2×C3×Q8C2×D412yes—
230C2×C3×Q8C2×D412yes—
231C2×C3×Q8#4112yes—
232C2×C3×D4—22no—
233C2×C3×D4—22no—
234C2×C3×D4—41no—
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—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—42no—
256C22×C3×C4—42no—
257C22×C3×C4—42no—
258C22×C3×C4C2×D411yescharacteristic
259C22×C3×C4C2×D411yescharacteristic
260C22×C3×C4C2×D411yescharacteristic
261C22×C3×C4C2×D411yescharacteristic
262C22×C3×C4C2411yescharacteristic
263C3×Q16—44no—
264C3×Q16—44no—
265C3×M16—44no—
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—21no—
273C2×C3×C8—21no—
274C2×C3×C8—21no—
275C2×C3×C8—21no—
276C2×C3×C8—21no—
277C2×C3×C8C2×D412yes—
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—21no—
286C3×C4⋊C4—21no—
287C3×C4⋊C4—21no—
288C3×C4⋊C4—41no—
289C3×C4⋊C4—42no—
290C3×C4⋊C4—42no—
291C3×C4⋊C4—42no—
292C3×C4⋊C4—42no—
293C3×C4⋊C4—42no—
294C3×C4⋊C4—42no—
295C3×C4⋊C4—81no—
296C3×C22⋊C4—41no—
297C3×C22⋊C4—41no—
298C3×C22⋊C4—42no—
299C3×C22⋊C4—42no—
300C3×C22⋊C4—42no—
301C3×C22⋊C4—42no—
302C3×C22⋊C4—42no—
303C3×C22⋊C4—81no—
304C3×C22⋊C4—81no—
305C3×C42—21no—
306C3×C42—21no—
307C3×C42—42no—
308C22×Q8—21no—
309C22×Q8—22no—
310C22×Q8—22no—
311C22×Q8—41no—
312C22×Q8—41no—
313C22×Q8—41no—
314C22×Q8—41no—
315C22×Q8C23×C311yescharacteristic
316C22×Q8C23×C311yescharacteristic
317C22×Q8C23×C311yescharacteristic
318C22×D4C3×D411yescharacteristic
319C23×C4—21no—
320C23×C4C23×C311yescharacteristic
321C23×C4C23×C311yescharacteristic
322C2×Q16—22no—
323C2×Q16—22no—
324C2×Q16—41no—
325C2×Q16—41no—
326C2×Q16—41no—
327C2×Q16C3×D414yescomplemented
328C2×M16—22no—
329C2×M16—41no—
330C2×M16—41no—
331C22×C8C23×C311yescharacteristic
332C22×C8C23×C311yescharacteristic
333C22×C8C23×C311yescharacteristic
334C22×C8C23×C311yescharacteristic
335C22⋊Q8—22no—
336C22⋊Q8—22no—
337C22⋊Q8—22no—
338C22⋊Q8—22no—
339C22⋊Q8—41no—
340C22⋊Q8—41no—
341C22⋊Q8—41no—
342C22⋊Q8—41no—
343C4×Q8—41no—
344C4×Q8—41no—
345C4×D4—41no—
346C4×D4—41no—
347C2×C4⋊C4—21no—
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⋊C4C3×D411yescharacteristic
355C2×C4⋊C4C23×C311yescharacteristic
356C2×C4⋊C4C23×C311yescharacteristic
357C2×C4⋊C4C23×C311yescharacteristic
358C2×C4⋊C4C23×C311yescharacteristic
359C2×C4⋊C4C23×C311yescharacteristic
360C2×C22⋊C4—21no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4C3×D411yescharacteristic
368C2×C22⋊C4C3×D411yescharacteristic
369C2×C42—21no—
370C2×C42C23×C311yescharacteristic
371#106—22no—
372#106—41no—
373#103—22no—
374#103—22no—
375#103—22no—
376#103—22no—
377#103—41no—
378#103—41no—
379#103—41no—
380#103—41no—
381C22⋊C8—22no—
382C22⋊C8—41no—
383C22⋊C8—41no—
384#95—21no—
385#95—21no—
386#95—21no—
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—21no—
404C23×C3#13712yes—
405C23×C3C22×D411yescharacteristic
406C3×Q8—22no—
407C3×Q8—22no—
408C3×Q8—22no—
409C3×Q8—22no—
410C3×Q8—22no—
411C3×Q8—22no—
412C3×Q8—48no—
413C3×Q8—41no—
414C3×Q8—41no—
415C3×Q8—41no—
416C3×Q8—41no—
417C3×Q8—41no—
418C3×Q8—41no—
419C3×D4—44no—
420C2×C3×C4—21no—
421C2×C3×C4—21no—
422C2×C3×C4—21no—
423C2×C3×C4—21no—
424C2×C3×C4—21no—
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—21no—
433C2×C3×C4—21no—
434C2×C3×C4—48no—
435C2×C3×C4—41no—
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—41no—
460C2×C3×C4—41no—
461C2×C3×C4—41no—
462C2×C3×C4—41no—
463C2×C3×C4—41no—
464C2×C3×C4#13712yes—
465C2×C3×C4C22×D411yescharacteristic
466C2×C3×C4C2×#4111yescharacteristic
467C2×C3×C4H(5,𝔽2)11yescharacteristic
468C2×C3×C4H(5,𝔽2)11yescharacteristic
469C2×C3×C4H(5,𝔽2)11yescharacteristic
470C2×C3×C4H(5,𝔽2)11yescharacteristic
471C3×C8—22no—
472C3×C8—41no—
473C3×C8—41no—
474C3×C8—41no—
475C24C2×C3×D411yescharacteristic
476C24C2×C3×D411yescharacteristic
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—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—42no—
493C2×Q8—42no—
494C2×Q8—42no—
495C2×Q8—44no—
496C2×Q8—44no—
497C2×Q8—44no—
498C2×Q8—44no—
499C2×Q8C2×C3×D412yes—
500C2×Q8C2×C3×D412yes—
501C2×Q8C3×#4112yes—
502C2×D4—22no—
503C2×D4—22no—
504C2×D4—41no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4C2×C3×D411yescharacteristic
529C22×C4C2×C3×D411yescharacteristic
530C22×C4C2×C3×D411yescharacteristic
531C22×C4C2×C3×D411yescharacteristic
532C22×C4C24×C311yescharacteristic
533Q16—44no—
534Q16—44no—
535M16—44no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8C2×C3×D412yes—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—41no—
559C4⋊C4—42no—
560C4⋊C4—42no—
561C4⋊C4—42no—
562C4⋊C4—42no—
563C4⋊C4—42no—
564C4⋊C4—42no—
565C4⋊C4—81no—
566C22⋊C4—41no—
567C22⋊C4—41no—
568C22⋊C4—42no—
569C22⋊C4—42no—
570C22⋊C4—42no—
571C22⋊C4—42no—
572C22⋊C4—42no—
573C22⋊C4—81no—
574C22⋊C4—81no—
575C42—21no—
576C42—21no—
577C42—42no—
578C22×C3—22no—
579C22×C3—22no—
580C22×C3—22no—
581C22×C3—41no—
582C22×C3—41no—
583C22×C3—41no—
584C22×C3—41no—
585C22×C3—41no—
586C22×C3—41no—
587C22×C3—41no—
588C22×C3—41no—
589C22×C3—41no—
590C22×C3—41no—
591C22×C3—41no—
592C22×C3#53411yescharacteristic
593C22×C3D4211yescharacteristic
594C22×C3#54611yescharacteristic
595C22×C3C2×#13711yescharacteristic
596C22×C3C2×#13711yescharacteristic
597C22×C3#57711yescharacteristic
598C22×C3#57811yescharacteristic
599C3×C4—22no—
600C3×C4—41no—
601C3×C4—41no—
602C3×C4—42no—
603C3×C4—42no—
604C3×C4—42no—
605C3×C4—41no—
606C3×C4—81no—
607C3×C4—81no—
608C3×C4—81no—
609C3×C4—81no—
610C3×C4—81no—
611C3×C4#53411yescharacteristic
612C3×C4#53811yescharacteristic
613C3×C4#54611yescharacteristic
614C3×C4#56011yescharacteristic
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23C3×#13712yes—
629C23C22×C3×D411yescharacteristic
630Q8—22no—
631Q8—22no—
632Q8—22no—
633Q8—22no—
634Q8—22no—
635Q8—22no—
636Q8—48no—
637Q8—41no—
638Q8—41no—
639Q8—41no—
640Q8—41no—
641Q8—41no—
642Q8—41no—
643D4—44no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—22no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—48no—
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—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4C3×#13712yes—
689C2×C4C22×C3×D411yescharacteristic
690C2×C4C2×C3×#4111yescharacteristic
691C2×C4C3×H(5,𝔽2)11yescharacteristic
692C2×C4C3×H(5,𝔽2)11yescharacteristic
693C2×C4C3×H(5,𝔽2)11yescharacteristic
694C2×C4C3×H(5,𝔽2)11yescharacteristic
695C8—22no—
696C8—41no—
697C8—41no—
698C8—41no—
699C2×C3—42no—
700C2×C3—81no—
701C2×C3#266811yescharacteristic
702C2×C3#319511yescharacteristic
703C2×C3#320111yescharacteristic
704C2×C3#327011yescharacteristic
705C2×C3#327811yescharacteristic
706C2×C3#331611yescharacteristic
707C2×C3#332811yescharacteristic
708C22—22no—
709C22—22no—
710C22—22no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22C3×#53411yescharacteristic
723C22C3×D4211yescharacteristic
724C22C3×#54611yescharacteristic
725C22C2×C3×#13711yescharacteristic
726C22C2×C3×#13711yescharacteristic
727C22C3×#57711yescharacteristic
728C22C3×#57811yescharacteristic
729C4—22no—
730C4—41no—
731C4—41no—
732C4—42no—
733C4—42no—
734C4—42no—
735C4—41no—
736C4—81no—
737C4—81no—
738C4—81no—
739C4—81no—
740C4—81no—
741C4C3×#53411yescharacteristic
742C4C3×#53811yescharacteristic
743C4C3×#54611yescharacteristic
744C4C3×#56011yescharacteristic
745C3#3042311yescharacteristic, direct product factor, Sylow
746C2—42no—
747C2—81no—
748C2C3×#266811yescharacteristic
749C2C3×#319511yescharacteristic
750C2C3×#320111yescharacteristic
751C2C3×#327011yescharacteristic
752C2C3×#327811yescharacteristic
753C2C3×#331611yescharacteristic
754C2C3×#332811yescharacteristic
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
1. C2×C3×#470C2semidirect
2. C2×C3×#451C2semidirect
5. C3×#2096C2semidirect
6. C3×#2077C2semidirect
7. C3×#2072C2semidirect
8. C3×#2035C2semidirect
9. C3×#2035C2semidirect
10. C3×#2001C2semidirect
11. C3×#1894C2semidirect
12. C3×#1878C2semidirect
13. C3×#1878C2semidirect
15. C3×#1787C2semidirect
16. #30423C3direct (N × H)
62. C2×#470C2×C3semidirect
63. C2×#451C2×C3semidirect
66. #2096C2×C3semidirect
67. #2077C2×C3semidirect
68. #2072C2×C3semidirect
69. #2035C2×C3semidirect
70. #2035C2×C3semidirect
71. #2001C2×C3semidirect
72. #1894C2×C3semidirect
73. #1878C2×C3semidirect
74. #1878C2×C3semidirect
76. #1787C2×C3semidirect
96. C2×C3×Q16D4semidirect
327. C2×Q16C3×D4semidirect
745. C3#30423direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#4702
C2×C3×#4512
C3×#25382
C3×#24092
C3×#20962
C3×#20772
C3×#20722
C3×#20352
C3×#20012
C3×#18942
C3×#18782
C3×#18702
C3×#17872
#304233