Finite Group Databasebeta

← C3×#30422 #10649029

Subgroups — C3×#30422 #10649029

Order 768.

994 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#468C211yesmaximal, characteristic, complemented
2C2×C3×#452C211yesmaximal, characteristic, complemented
3C3×#2536C211yesmaximal, characteristic, complemented
4C3×#2407C211yesmaximal, characteristic
5C3×#2097C211yesmaximal, characteristic, complemented
6C3×#2076C211yesmaximal, characteristic, complemented
7C3×#2073C211yesmaximal, characteristic, complemented
8C3×#2035C211yesmaximal, characteristic, complemented
9C3×#2034C211yesmaximal, characteristic, complemented
10C3×#2001C211yesmaximal, characteristic, complemented
11C3×#1894C211yesmaximal, characteristic, complemented
12C3×#1880C211yesmaximal, characteristic, complemented
13C3×#1878C211yesmaximal, characteristic, complemented
14C3×#1870C211yesmaximal, characteristic, complemented
15C3×#1788C211yesmaximal, characteristic, complemented
16#30422C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×#41C2211yescharacteristic
18C22×C3×Q16C2211yescharacteristic
19C22×C3×SD16C2211yescharacteristic
20C22×C3×M16C2211yescharacteristic
21C2×C3×C22⋊Q8C2211yescharacteristic
22C2×C3×C22⋊Q8C2211yescharacteristic
23C2×C3×C22⋊Q8C2211yescharacteristic
24C2×C3×#121C2211yescharacteristic
25C2×C3×C4×Q8C2211yescharacteristic
26C2×C3×C4×D4C2211yescharacteristic
27C3×#468—24no—
28C3×#452—24no—
29C2×C3×#107C2211yescharacteristic
30C2×C3×#106C2211yescharacteristic
31C2×C3×#103C2211yescharacteristic
32C2×C3×#103C2211yescharacteristic
33C2×C3×#103C2211yescharacteristic
34C2×C3×#103C2211yescharacteristic
35C2×C3×#103C2211yescharacteristic
36C2×C3×#102C2211yescharacteristic
37C2×C3×#102C2211yescharacteristic
38C2×C3×#102C2211yescharacteristic
39C2×C3×C22⋊C8C2211yescharacteristic
40C2×C3×C22⋊C8C2211yescharacteristic
41C2×C3×C22⋊C8C2211yescharacteristic
42C3×#398—21no—
43C3×#394—21no—
44C3×#394—21no—
45C3×#392—21no—
46C3×#391C2211yescharacteristic
47C3×#390C2211yescharacteristic
48C3×#388—21no—
49C3×#388—21no—
50C3×#386—21no—
51C3×#385—21no—
52C3×#382C2211yescharacteristic
53C3×#380C2211yescharacteristic
54C3×#380C2211yescharacteristic
55C3×#380C2211yescharacteristic
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#336C2211yescharacteristic
61C3×#336C2211yescharacteristic
62C2×#468C2×C311yescharacteristic, complemented
63C2×#452C2×C311yescharacteristic, complemented
64#2536C2×C311yescharacteristic, complemented
65#2407C2×C311yescharacteristic
66#2097C2×C311yescharacteristic, complemented
67#2076C2×C311yescharacteristic, complemented
68#2073C2×C311yescharacteristic, complemented
69#2035C2×C311yescharacteristic, complemented
70#2034C2×C311yescharacteristic, complemented
71#2001C2×C311yescharacteristic, complemented
72#1894C2×C311yescharacteristic, complemented
73#1880C2×C311yescharacteristic, complemented
74#1878C2×C311yescharacteristic, complemented
75#1870C2×C311yescharacteristic, complemented
76#1788C2×C311yescharacteristic, complemented
77C2×C3×#41—22no—
78C2×C3×#41—22no—
79C2×C3×#41—41no—
80C2×C3×#41—41no—
81C2×C3×#41—41no—
82C2×C3×#41—41no—
83C22×C3×Q8C2311yescharacteristic
84C22×C3×Q8C2311yescharacteristic
85C22×C3×D4—21no—
86C22×C3×D4—21no—
87C22×C3×D4D411yescharacteristic
88C22×C3×D4C2311yescharacteristic
89C23×C3×C4—21no—
90C23×C3×C4C2311yescharacteristic
91C23×C3×C4C2311yescharacteristic
92C2×C3×Q16—22no—
93C2×C3×Q16—22no—
94C2×C3×Q16—41no—
95C2×C3×SD16—41no—
96C2×C3×SD16—41no—
97C2×C3×SD16D414yescomplemented
98C2×C3×M16—22no—
99C2×C3×M16—41no—
100C2×C3×M16—41no—
101C22×C3×C8C2311yescharacteristic
102C22×C3×C8C2311yescharacteristic
103C22×C3×C8C2311yescharacteristic
104C22×C3×C8C2311yescharacteristic
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×#121—22no—
112C3×#121—41no—
113C3×C4×Q8—41no—
114C3×C4×Q8—41no—
115C3×C4×D4—41no—
116C3×C4×D4—41no—
117C2×C3×C4⋊C4—21no—
118C2×C3×C4⋊C4—21no—
119C2×C3×C4⋊C4—21no—
120C2×C3×C4⋊C4—21no—
121C2×C3×C4⋊C4D411yescharacteristic
122C2×C3×C4⋊C4C2311yescharacteristic
123C2×C3×C4⋊C4C2311yescharacteristic
124C2×C3×C4⋊C4C2311yescharacteristic
125C2×C3×C4⋊C4C2311yescharacteristic
126C2×C3×C4⋊C4C2311yescharacteristic
127C2×C3×C22⋊C4—21no—
128C2×C3×C22⋊C4—21no—
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×#107—22no—
141C3×#106—41no—
142C3×#103—22no—
143C3×#103—22no—
144C3×#103—41no—
145C3×#103—41no—
146C3×#103—41no—
147C3×#102—22no—
148C3×#102—22no—
149C3×#102—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—
160C22×#41C22×C311yescharacteristic
161C22×Q16C22×C311yescharacteristic
162C22×SD16C22×C311yescharacteristic
163C22×M16C22×C311yescharacteristic
164C2×C22⋊Q8C22×C311yescharacteristic
165C2×C22⋊Q8C22×C311yescharacteristic
166C2×C22⋊Q8C22×C311yescharacteristic
167C2×#121C22×C311yescharacteristic
168C2×C4×Q8C22×C311yescharacteristic
169C2×C4×D4C22×C311yescharacteristic
170#468—24no—
171#452—24no—
172C2×#107C22×C311yescharacteristic
173C2×#106C22×C311yescharacteristic
174C2×#103C22×C311yescharacteristic
175C2×#103C22×C311yescharacteristic
176C2×#103C22×C311yescharacteristic
177C2×#103C22×C311yescharacteristic
178C2×#103C22×C311yescharacteristic
179C2×#102C22×C311yescharacteristic
180C2×#102C22×C311yescharacteristic
181C2×#102C22×C311yescharacteristic
182C2×C22⋊C8C22×C311yescharacteristic
183C2×C22⋊C8C22×C311yescharacteristic
184C2×C22⋊C8C22×C311yescharacteristic
185#398—21no—
186#394—21no—
187#394—21no—
188#392—21no—
189#391C22×C311yescharacteristic
190#390C22×C311yescharacteristic
191#388—21no—
192#388—21no—
193#386—21no—
194#385—21no—
195#382C22×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×C3—21no—
206C24×C3C2×D411yescharacteristic
207C24×C3C2×D411yescharacteristic
208C3×#41—44no—
209C3×#41—44no—
210C3×#41—44no—
211C3×#41—44no—
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×Q8C2×D412yes—
223C2×C3×Q8#4112yes—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—41no—
230C2×C3×D4—41no—
231C2×C3×D4—41no—
232C2×C3×D4—42no—
233C2×C3×D4—42no—
234C2×C3×D4—42no—
235C2×C3×D4—42no—
236C2×C3×D4—42no—
237C2×C3×D4—81no—
238C2×C3×D4C2×D412yes—
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—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—42no—
259C22×C3×C4—42no—
260C22×C3×C4—42no—
261C22×C3×C4C2×D411yescharacteristic
262C22×C3×C4C2×D411yescharacteristic
263C22×C3×C4C2×D411yescharacteristic
264C22×C3×C4C2×D411yescharacteristic
265C22×C3×C4C2411yescharacteristic
266C3×Q16—44no—
267C3×SD16—44no—
268C3×M16—44no—
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×C8—21no—
278C2×C3×C8—21no—
279C2×C3×C8—21no—
280C2×C3×C8C2×D412yes—
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—21no—
289C3×C4⋊C4—21no—
290C3×C4⋊C4—21no—
291C3×C4⋊C4—41no—
292C3×C4⋊C4—42no—
293C3×C4⋊C4—42no—
294C3×C4⋊C4—42no—
295C3×C4⋊C4—42no—
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—42no—
304C3×C22⋊C4—42no—
305C3×C22⋊C4—81no—
306C3×C22⋊C4—81no—
307C3×C42—21no—
308C3×C42—21no—
309C3×C42—42no—
310C2×#41—22no—
311C2×#41—22no—
312C2×#41—41no—
313C2×#41—41no—
314C2×#41—41no—
315C2×#41—41no—
316C22×Q8C23×C311yescharacteristic
317C22×Q8C23×C311yescharacteristic
318C22×D4—21no—
319C22×D4—21no—
320C22×D4C3×D411yescharacteristic
321C22×D4C23×C311yescharacteristic
322C23×C4—21no—
323C23×C4C23×C311yescharacteristic
324C23×C4C23×C311yescharacteristic
325C2×Q16—22no—
326C2×Q16—22no—
327C2×Q16—41no—
328C2×SD16—41no—
329C2×SD16—41no—
330C2×SD16C3×D414yescomplemented
331C2×M16—22no—
332C2×M16—41no—
333C2×M16—41no—
334C22×C8C23×C311yescharacteristic
335C22×C8C23×C311yescharacteristic
336C22×C8C23×C311yescharacteristic
337C22×C8C23×C311yescharacteristic
338C22⋊Q8—22no—
339C22⋊Q8—22no—
340C22⋊Q8—22no—
341C22⋊Q8—41no—
342C22⋊Q8—41no—
343C22⋊Q8—41no—
344#121—22no—
345#121—41no—
346C4×Q8—41no—
347C4×Q8—41no—
348C4×D4—41no—
349C4×D4—41no—
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⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4C3×D411yescharacteristic
370C2×C22⋊C4C3×D411yescharacteristic
371C2×C42—21no—
372C2×C42C23×C311yescharacteristic
373#107—22no—
374#106—41no—
375#103—22no—
376#103—22no—
377#103—41no—
378#103—41no—
379#103—41no—
380#102—22no—
381#102—22no—
382#102—41no—
383C22⋊C8—22no—
384C22⋊C8—41no—
385C22⋊C8—41no—
386#95—21no—
387#95—21no—
388#95—21no—
389#95—21no—
390#95—21no—
391#95—21no—
392#95—21no—
393C23×C3—21no—
394C23×C3—21no—
395C23×C3—21no—
396C23×C3—21no—
397C23×C3—22no—
398C23×C3—21no—
399C23×C3—21no—
400C23×C3—21no—
401C23×C3—21no—
402C23×C3—21no—
403C23×C3—21no—
404C23×C3—21no—
405C23×C3—21no—
406C23×C3—21no—
407C23×C3—21no—
408C23×C3—41no—
409C23×C3—41no—
410C23×C3—41no—
411C23×C3—41no—
412C23×C3—41no—
413C23×C3—41no—
414C23×C3C22×D411yescharacteristic
415C3×Q8—22no—
416C3×Q8—22no—
417C3×Q8—22no—
418C3×Q8—22no—
419C3×Q8—41no—
420C3×Q8—41no—
421C3×Q8—41no—
422C3×Q8—41no—
423C3×D4—22no—
424C3×D4—22no—
425C3×D4—44no—
426C3×D4—48no—
427C3×D4—41no—
428C3×D4—41no—
429C3×D4—84no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
432C2×C3×C4—21no—
433C2×C3×C4—21no—
434C2×C3×C4—21no—
435C2×C3×C4—22no—
436C2×C3×C4—21no—
437C2×C3×C4—22no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—48no—
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—41no—
465C2×C3×C4—41no—
466C2×C3×C4—41no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
470C2×C3×C4—41no—
471C2×C3×C4—41no—
472C2×C3×C4C22×D411yescharacteristic
473C2×C3×C4C2×#4111yescharacteristic
474C2×C3×C4H(5,𝔽2)11yescharacteristic
475C2×C3×C4H(5,𝔽2)11yescharacteristic
476C2×C3×C4H(5,𝔽2)11yescharacteristic
477C2×C3×C4H(5,𝔽2)11yescharacteristic
478C3×C8—22no—
479C3×C8—41no—
480C3×C8—41no—
481C3×C8—41no—
482C24—21no—
483C24C2×C3×D411yescharacteristic
484C24C2×C3×D411yescharacteristic
485#41—44no—
486#41—44no—
487#41—44no—
488#41—44no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8C2×C3×D412yes—
500C2×Q8C3×#4112yes—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—41no—
507C2×D4—41no—
508C2×D4—41no—
509C2×D4—42no—
510C2×D4—42no—
511C2×D4—42no—
512C2×D4—42no—
513C2×D4—42no—
514C2×D4—81no—
515C2×D4C2×C3×D412yes—
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—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4C2×C3×D411yescharacteristic
539C22×C4C2×C3×D411yescharacteristic
540C22×C4C2×C3×D411yescharacteristic
541C22×C4C2×C3×D411yescharacteristic
542C22×C4C24×C311yescharacteristic
543Q16—44no—
544SD16—44no—
545M16—44no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8C2×C3×D412yes—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—41no—
569C4⋊C4—42no—
570C4⋊C4—42no—
571C4⋊C4—42no—
572C4⋊C4—42no—
573C22⋊C4—41no—
574C22⋊C4—41no—
575C22⋊C4—42no—
576C22⋊C4—42no—
577C22⋊C4—42no—
578C22⋊C4—42no—
579C22⋊C4—42no—
580C22⋊C4—42no—
581C22⋊C4—42no—
582C22⋊C4—81no—
583C22⋊C4—81no—
584C42—21no—
585C42—21no—
586C42—42no—
587C22×C3—42no—
588C22×C3—41no—
589C22×C3—41no—
590C22×C3—41no—
591C22×C3—41no—
592C22×C3—41no—
593C22×C3—41no—
594C22×C3—41no—
595C22×C3—41no—
596C22×C3—42no—
597C22×C3—41no—
598C22×C3—42no—
599C22×C3—41no—
600C22×C3—41no—
601C22×C3—41no—
602C22×C3—41no—
603C22×C3—41no—
604C22×C3—81no—
605C22×C3—81no—
606C22×C3—81no—
607C22×C3—81no—
608C22×C3#53411yescharacteristic
609C22×C3D4211yescharacteristic
610C22×C3#54611yescharacteristic
611C22×C3#57511yescharacteristic
612C22×C3#57511yescharacteristic
613C22×C3#57711yescharacteristic
614C22×C3#57811yescharacteristic
615C3×C4—41no—
616C3×C4—41no—
617C3×C4—42no—
618C3×C4—42no—
619C3×C4—41no—
620C3×C4—41no—
621C3×C4—81no—
622C3×C4—81no—
623C3×C4—81no—
624C3×C4—81no—
625C3×C4—81no—
626C3×C4#53411yescharacteristic
627C3×C4#53811yescharacteristic
628C3×C4#54611yescharacteristic
629C3×C4#56011yescharacteristic
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—22no—
643C23—21no—
644C23—21no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23C22×C3×D411yescharacteristic
652Q8—22no—
653Q8—22no—
654Q8—22no—
655Q8—22no—
656Q8—41no—
657Q8—41no—
658Q8—41no—
659Q8—41no—
660D4—22no—
661D4—22no—
662D4—48no—
663D4—44no—
664D4—41no—
665D4—41no—
666D4—84no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—22no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—48no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4C22×C3×D411yescharacteristic
710C2×C4C2×C3×#4111yescharacteristic
711C2×C4C3×H(5,𝔽2)11yescharacteristic
712C2×C4C3×H(5,𝔽2)11yescharacteristic
713C2×C4C3×H(5,𝔽2)11yescharacteristic
714C2×C4C3×H(5,𝔽2)11yescharacteristic
715C8—22no—
716C8—41no—
717C8—41no—
718C8—41no—
719C2×C3—81no—
720C2×C3—81no—
721C2×C3—82no—
722C2×C3#266811yescharacteristic
723C2×C3#319711yescharacteristic
724C2×C3#320111yescharacteristic
725C2×C3#326911yescharacteristic
726C2×C3#327511yescharacteristic
727C2×C3#331711yescharacteristic
728C2×C3#332711yescharacteristic
729C22—42no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—42no—
739C22—41no—
740C22—42no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22C3×#53411yescharacteristic
751C22C3×D4211yescharacteristic
752C22C3×#54611yescharacteristic
753C22C3×#57511yescharacteristic
754C22C3×#57511yescharacteristic
755C22C3×#57711yescharacteristic
756C22C3×#57811yescharacteristic
757C4—41no—
758C4—41no—
759C4—42no—
760C4—42no—
761C4—41no—
762C4—41no—
763C4—81no—
764C4—81no—
765C4—81no—
766C4—81no—
767C4—81no—
768C4C3×#53411yescharacteristic
769C4C3×#53811yescharacteristic
770C4C3×#54611yescharacteristic
771C4C3×#56011yescharacteristic
772C3#3042211yescharacteristic, direct product factor, Sylow
773C2—81no—
774C2—81no—
775C2—82no—
776C2C3×#266811yescharacteristic
777C2C3×#319711yescharacteristic
778C2C3×#320111yescharacteristic
779C2C3×#326911yescharacteristic
780C2C3×#327511yescharacteristic
781C2C3×#331711yescharacteristic
782C2C3×#332711yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC3×#2407C2
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×#468C2semidirect
2. C2×C3×#452C2semidirect
3. C3×#2536C2semidirect
5. C3×#2097C2semidirect
6. C3×#2076C2semidirect
7. C3×#2073C2semidirect
8. C3×#2035C2semidirect
9. C3×#2034C2semidirect
10. C3×#2001C2semidirect
11. C3×#1894C2semidirect
12. C3×#1880C2semidirect
13. C3×#1878C2semidirect
14. C3×#1870C2semidirect
15. C3×#1788C2semidirect
16. #30422C3direct (N × H)
62. C2×#468C2×C3semidirect
63. C2×#452C2×C3semidirect
64. #2536C2×C3semidirect
66. #2097C2×C3semidirect
67. #2076C2×C3semidirect
68. #2073C2×C3semidirect
69. #2035C2×C3semidirect
70. #2034C2×C3semidirect
71. #2001C2×C3semidirect
72. #1894C2×C3semidirect
73. #1880C2×C3semidirect
74. #1878C2×C3semidirect
75. #1870C2×C3semidirect
76. #1788C2×C3semidirect
97. C2×C3×SD16D4semidirect
330. C2×SD16C3×D4semidirect
772. C3#30422direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#4682
C2×C3×#4522
C3×#25362
C3×#24072
C3×#20972
C3×#20762
C3×#20732
C3×#20352
C3×#20342
C3×#20012
C3×#18942
C3×#18802
C3×#18782
C3×#18702
C3×#17882
#304223