Finite Group Databasebeta

← C3×#29729 #10648336

Subgroups — C3×#29729 #10648336

Order 768.

1012 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#452C211yesmaximal, characteristic, complemented
2C2×C3×#449C211yesmaximal, characteristic
3C3×#2620C211yesmaximal, characteristic, complemented
4C3×#2311C211yesmaximal, characteristic, complemented
5C3×#2072C211yesmaximal, characteristic, complemented
6C3×#2071C211yesmaximal, characteristic, complemented
7C3×#2056C211yesmaximal, characteristic, complemented
8C3×#2055C211yesmaximal, characteristic, complemented
9C3×#2055C211yesmaximal, characteristic, complemented
10C3×#2054C211yesmaximal, characteristic, complemented
11C3×#2015C211yesmaximal, characteristic, complemented
12C3×#2012C211yesmaximal, characteristic, complemented
13C3×#1874C211yesmaximal, characteristic, complemented
14C3×#1872C211yesmaximal, characteristic, complemented
15C3×#1798C211yesmaximal, characteristic, complemented
16#29729C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×#41C2211yescharacteristic
18C22×C3×Q16C2211yescharacteristic
19C22×C3×SD16C2211yescharacteristic
20C22×C3×SD16C2211yescharacteristic
21C22×C3×D8C2211yescharacteristic
22C2×C3×#124C2211yescharacteristic
23C2×C3×C22⋊Q8C2211yescharacteristic
24C2×C3×#121C2211yescharacteristic
25C2×C3×#117C2211yescharacteristic
26C22×C3×C4⋊C4C2211yescharacteristic
27C3×#452—24no—
28C3×#449—24no—
29C2×C3×C4⋊C8C2211yescharacteristic
30C2×C3×C4⋊C8C2211yescharacteristic
31C2×C3×#103C2211yescharacteristic
32C2×C3×#103C2211yescharacteristic
33C2×C3×#103C2211yescharacteristic
34C2×C3×#103C2211yescharacteristic
35C2×C3×#102C2211yescharacteristic
36C2×C3×#102C2211yescharacteristic
37C2×C3×#102C2211yescharacteristic
38C2×C3×#102C2211yescharacteristic
39C2×C3×C22⋊C8C2211yescharacteristic
40C2×C3×C22⋊C8C2211yescharacteristic
41C3×#396—21no—
42C3×#396—21no—
43C3×#394—21no—
44C3×#394—21no—
45C3×#391C2211yescharacteristic
46C3×#391C2211yescharacteristic
47C3×#391C2211yescharacteristic
48C3×#390C2211yescharacteristic
49C3×#390C2211yescharacteristic
50C3×#390C2211yescharacteristic
51C3×#386—21no—
52C3×#386—21no—
53C3×#384C2211yescharacteristic
54C3×#380—21no—
55C3×#380—21no—
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#336C2211yescharacteristic
61C3×#336C2211yescharacteristic
62C2×#452C2×C311yescharacteristic, complemented
63C2×#449C2×C311yescharacteristic
64#2620C2×C311yescharacteristic, complemented
65#2311C2×C311yescharacteristic, complemented
66#2072C2×C311yescharacteristic, complemented
67#2071C2×C311yescharacteristic, complemented
68#2056C2×C311yescharacteristic, complemented
69#2055C2×C311yescharacteristic, complemented
70#2055C2×C311yescharacteristic, complemented
71#2054C2×C311yescharacteristic, complemented
72#2015C2×C311yescharacteristic, complemented
73#2012C2×C311yescharacteristic, complemented
74#1874C2×C311yescharacteristic, complemented
75#1872C2×C311yescharacteristic, complemented
76#1798C2×C311yescharacteristic, complemented
77C2×C3×#41—22no—
78C2×C3×#41—41no—
79C2×C3×#41—41no—
80C2×C3×#41—41no—
81C2×C3×#41—41no—
82C2×C3×#41D414yes—
83C22×C3×Q8C2311yescharacteristic
84C22×C3×Q8C2311yescharacteristic
85C22×C3×D4—21no—
86C22×C3×D4—21no—
87C22×C3×D4C2311yescharacteristic
88C22×C3×D4C2311yescharacteristic
89C23×C3×C4—21no—
90C23×C3×C4—21no—
91C23×C3×C4C2311yescharacteristic
92C2×C3×Q16—22no—
93C2×C3×Q16—41no—
94C2×C3×Q16—41no—
95C2×C3×SD16—22no—
96C2×C3×SD16—22no—
97C2×C3×SD16—41no—
98C2×C3×SD16—41no—
99C2×C3×SD16—41no—
100C2×C3×SD16—41no—
101C2×C3×D8—22no—
102C2×C3×D8—41no—
103C2×C3×D8—41no—
104C22×C3×C8C2311yescharacteristic
105C22×C3×C8C2311yescharacteristic
106C22×C3×C8C2311yescharacteristic
107C22×C3×C8C2311yescharacteristic
108C3×#124—41no—
109C3×#124—41no—
110C3×C22⋊Q8—22no—
111C3×C22⋊Q8—22no—
112C3×#121—22no—
113C3×#121—22no—
114C3×#117—41no—
115C3×#117—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—41no—
121C2×C3×C4⋊C4—41no—
122C2×C3×C4⋊C4D411yescharacteristic
123C2×C3×C4⋊C4D411yescharacteristic
124C2×C3×C4⋊C4C2311yescharacteristic
125C2×C3×C4⋊C4C2311yescharacteristic
126C2×C3×C4⋊C4C2311yescharacteristic
127C2×C3×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
137C2×C3×C22⋊C4—21no—
138C2×C3×C22⋊C4D411yescharacteristic
139C2×C3×C22⋊C4D411yescharacteristic
140C2×C3×C42C2311yescharacteristic
141C2×C3×C42C2311yescharacteristic
142C3×C4⋊C8—41no—
143C3×C4⋊C8—41no—
144C3×#103—22no—
145C3×#103—22no—
146C3×#103—41no—
147C3×#103—41no—
148C3×#102—22no—
149C3×#102—22no—
150C3×#102—41no—
151C3×#102—41no—
152C3×C22⋊C8—22no—
153C3×C22⋊C8—22no—
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×SD16C22×C311yescharacteristic
164C22×D8C22×C311yescharacteristic
165C2×#124C22×C311yescharacteristic
166C2×C22⋊Q8C22×C311yescharacteristic
167C2×#121C22×C311yescharacteristic
168C2×#117C22×C311yescharacteristic
169C22×C4⋊C4C22×C311yescharacteristic
170#452—24no—
171#449—24no—
172C2×C4⋊C8C22×C311yescharacteristic
173C2×C4⋊C8C22×C311yescharacteristic
174C2×#103C22×C311yescharacteristic
175C2×#103C22×C311yescharacteristic
176C2×#103C22×C311yescharacteristic
177C2×#103C22×C311yescharacteristic
178C2×#102C22×C311yescharacteristic
179C2×#102C22×C311yescharacteristic
180C2×#102C22×C311yescharacteristic
181C2×#102C22×C311yescharacteristic
182C2×C22⋊C8C22×C311yescharacteristic
183C2×C22⋊C8C22×C311yescharacteristic
184#396—21no—
185#396—21no—
186#394—21no—
187#394—21no—
188#391C22×C311yescharacteristic
189#391C22×C311yescharacteristic
190#391C22×C311yescharacteristic
191#390C22×C311yescharacteristic
192#390C22×C311yescharacteristic
193#390C22×C311yescharacteristic
194#386—21no—
195#386—21no—
196#384C22×C311yescharacteristic
197#380—21no—
198#380—21no—
199#340C22×C311yescharacteristic
200#340C22×C311yescharacteristic
201#340C22×C311yescharacteristic
202#340C22×C311yescharacteristic
203#336C22×C311yescharacteristic
204#336C22×C311yescharacteristic
205C24×C3—21no—
206C24×C3—21no—
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×Q8—21no—
223C2×C3×Q8C2×D412yes—
224C2×C3×D4—24no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4—21no—
232C2×C3×D4—21no—
233C2×C3×D4—21no—
234C2×C3×D4—21no—
235C2×C3×D4—21no—
236C2×C3×D4—42no—
237C2×C3×D4—42no—
238C2×C3×D4—42no—
239C2×C3×D4—81no—
240C2×C3×D4—81no—
241C2×C3×D4C2×D412yes—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—24no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—42no—
254C22×C3×C4—42no—
255C22×C3×C4—42no—
256C22×C3×C4—81no—
257C22×C3×C4—81no—
258C22×C3×C4C2×D411yescharacteristic
259C22×C3×C4C2×D411yescharacteristic
260C22×C3×C4C2×D411yescharacteristic
261C22×C3×C4C2×D411yescharacteristic
262C22×C3×C4C2×D411yescharacteristic
263C22×C3×C4C2×D412yes—
264C22×C3×C4#4112yes—
265C22×C3×C4C2411yescharacteristic
266C3×Q16—44no—
267C3×SD16—44no—
268C3×SD16—44no—
269C3×D8—44no—
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×C8—21no—
281C2×C3×C8—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—41no—
291C3×C4⋊C4—41no—
292C3×C4⋊C4—42no—
293C3×C4⋊C4—42no—
294C3×C4⋊C4—81no—
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—81no—
303C3×C22⋊C4—81no—
304C3×C22⋊C4—81no—
305C3×C22⋊C4—81no—
306C3×C22⋊C4—81no—
307C3×C22⋊C4—81no—
308C3×C42—21no—
309C3×C42—21no—
310C3×C42—21no—
311C3×C42—21no—
312C2×#41—22no—
313C2×#41—41no—
314C2×#41—41no—
315C2×#41—41no—
316C2×#41—41no—
317C2×#41C3×D414yes—
318C22×Q8C23×C311yescharacteristic
319C22×Q8C23×C311yescharacteristic
320C22×D4—21no—
321C22×D4—21no—
322C22×D4C23×C311yescharacteristic
323C22×D4C23×C311yescharacteristic
324C23×C4—21no—
325C23×C4—21no—
326C23×C4C23×C311yescharacteristic
327C2×Q16—22no—
328C2×Q16—41no—
329C2×Q16—41no—
330C2×SD16—22no—
331C2×SD16—22no—
332C2×SD16—41no—
333C2×SD16—41no—
334C2×SD16—41no—
335C2×SD16—41no—
336C2×D8—22no—
337C2×D8—41no—
338C2×D8—41no—
339C22×C8C23×C311yescharacteristic
340C22×C8C23×C311yescharacteristic
341C22×C8C23×C311yescharacteristic
342C22×C8C23×C311yescharacteristic
343#124—41no—
344#124—41no—
345C22⋊Q8—22no—
346C22⋊Q8—22no—
347#121—22no—
348#121—22no—
349#117—41no—
350#117—41no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—41no—
356C2×C4⋊C4—41no—
357C2×C4⋊C4C3×D411yescharacteristic
358C2×C4⋊C4C3×D411yescharacteristic
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⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4C3×D411yescharacteristic
374C2×C22⋊C4C3×D411yescharacteristic
375C2×C42C23×C311yescharacteristic
376C2×C42C23×C311yescharacteristic
377C4⋊C8—41no—
378C4⋊C8—41no—
379#103—22no—
380#103—22no—
381#103—41no—
382#103—41no—
383#102—22no—
384#102—22no—
385#102—41no—
386#102—41no—
387C22⋊C8—22no—
388C22⋊C8—22no—
389#95—21no—
390#95—21no—
391#95—21no—
392#95—21no—
393#95—21no—
394#95—21no—
395C23×C3—21no—
396C23×C3—21no—
397C23×C3—21no—
398C23×C3—21no—
399C23×C3—21no—
400C23×C3—21no—
401C23×C3—22no—
402C23×C3—41no—
403C23×C3—41no—
404C23×C3—41no—
405C23×C3—41no—
406C23×C3—41no—
407C23×C3—41no—
408C23×C3—41no—
409C23×C3—41no—
410C23×C3—41no—
411C23×C3—41no—
412C23×C3—41no—
413C23×C3—41no—
414C23×C3—41no—
415C23×C3#12112yes—
416C23×C3C22×D411yescharacteristic
417C3×Q8—22no—
418C3×Q8—22no—
419C3×Q8—41no—
420C3×Q8—41no—
421C3×Q8—41no—
422C3×Q8—41no—
423C3×Q8—41no—
424C3×Q8—41no—
425C3×D4—22no—
426C3×D4—22no—
427C3×D4—48no—
428C3×D4—41no—
429C3×D4—41no—
430C3×D4—41no—
431C3×D4—41no—
432C3×D4—41no—
433C3×D4—41no—
434C3×D4—84no—
435C2×C3×C4—21no—
436C2×C3×C4—21no—
437C2×C3×C4—22no—
438C2×C3×C4—22no—
439C2×C3×C4—22no—
440C2×C3×C4—22no—
441C2×C3×C4—22no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—21no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—48no—
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×C4—84no—
473C2×C3×C4#12112yes—
474C2×C3×C4C22×D411yescharacteristic
475C2×C3×C4C2×#4111yescharacteristic
476C2×C3×C4H(5,𝔽2)11yescharacteristic
477C2×C3×C4H(5,𝔽2)11yescharacteristic
478C2×C3×C4H(5,𝔽2)11yescharacteristic
479C2×C3×C4H(5,𝔽2)11yescharacteristic
480C3×C8—41no—
481C3×C8—41no—
482C3×C8—41no—
483C3×C8—41no—
484C24—21no—
485C24—21no—
486C24C2×C3×D411yescharacteristic
487#41—44no—
488#41—44no—
489#41—44no—
490#41—44no—
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×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8C2×C3×D412yes—
503C2×D4—24no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—42no—
516C2×D4—42no—
517C2×D4—42no—
518C2×D4—81no—
519C2×D4—81no—
520C2×D4C2×C3×D412yes—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—24no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—81no—
536C22×C4—81no—
537C22×C4C2×C3×D411yescharacteristic
538C22×C4C2×C3×D411yescharacteristic
539C22×C4C2×C3×D411yescharacteristic
540C22×C4C2×C3×D411yescharacteristic
541C22×C4C2×C3×D411yescharacteristic
542C22×C4C2×C3×D412yes—
543C22×C4C3×#4112yes—
544C22×C4C24×C311yescharacteristic
545Q16—44no—
546SD16—44no—
547SD16—44no—
548D8—44no—
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×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—41no—
570C4⋊C4—41no—
571C4⋊C4—42no—
572C4⋊C4—42no—
573C4⋊C4—81no—
574C4⋊C4—81no—
575C22⋊C4—41no—
576C22⋊C4—41no—
577C22⋊C4—42no—
578C22⋊C4—42no—
579C22⋊C4—42no—
580C22⋊C4—42no—
581C22⋊C4—81no—
582C22⋊C4—81no—
583C22⋊C4—81no—
584C22⋊C4—81no—
585C22⋊C4—81no—
586C22⋊C4—81no—
587C42—21no—
588C42—21no—
589C42—21no—
590C42—21no—
591C22×C3—22no—
592C22×C3—22no—
593C22×C3—22no—
594C22×C3—41no—
595C22×C3—41no—
596C22×C3—41no—
597C22×C3—41no—
598C22×C3—42no—
599C22×C3—42no—
600C22×C3—42no—
601C22×C3—81no—
602C22×C3—81no—
603C22×C3—81no—
604C22×C3—81no—
605C22×C3—81no—
606C22×C3—81no—
607C22×C3—81no—
608C22×C3—81no—
609C22×C3—81no—
610C22×C3—81no—
611C22×C3—81no—
612C22×C3C2×#12111yescharacteristic
613C22×C3#53411yescharacteristic
614C22×C3#53511yescharacteristic
615C22×C3#57611yescharacteristic
616C22×C3#57711yescharacteristic
617C22×C3#57711yescharacteristic
618C22×C3#57811yescharacteristic
619C3×C4—22no—
620C3×C4—42no—
621C3×C4—41no—
622C3×C4—41no—
623C3×C4—41no—
624C3×C4—41no—
625C3×C4—81no—
626C3×C4—81no—
627C3×C4—81no—
628C3×C4—81no—
629C3×C4—81no—
630C3×C4#53411yescharacteristic
631C3×C4#53411yescharacteristic
632C3×C4#53811yescharacteristic
633C3×C4#53811yescharacteristic
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—22no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23C3×#12112yes—
655C23C22×C3×D411yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—41no—
659Q8—41no—
660Q8—41no—
661Q8—41no—
662Q8—41no—
663Q8—41no—
664D4—22no—
665D4—22no—
666D4—48no—
667D4—41no—
668D4—41no—
669D4—41no—
670D4—41no—
671D4—41no—
672D4—41no—
673D4—84no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—22no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—48no—
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×C4—41no—
710C2×C4—41no—
711C2×C4—84no—
712C2×C4C3×#12112yes—
713C2×C4C22×C3×D411yescharacteristic
714C2×C4C2×C3×#4111yescharacteristic
715C2×C4C3×H(5,𝔽2)11yescharacteristic
716C2×C4C3×H(5,𝔽2)11yescharacteristic
717C2×C4C3×H(5,𝔽2)11yescharacteristic
718C2×C4C3×H(5,𝔽2)11yescharacteristic
719C8—41no—
720C8—41no—
721C8—41no—
722C8—41no—
723C2×C3—42no—
724C2×C3—82no—
725C2×C3—161no—
726C2×C3#261711yescharacteristic
727C2×C3#304511yescharacteristic
728C2×C3#304611yescharacteristic
729C2×C3#320311yescharacteristic
730C2×C3#320411yescharacteristic
731C2×C3#322411yescharacteristic
732C2×C3#322511yescharacteristic
733C22—22no—
734C22—22no—
735C22—22no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—81no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22C2×C3×#12111yescharacteristic
755C22C3×#53411yescharacteristic
756C22C3×#53511yescharacteristic
757C22C3×#57611yescharacteristic
758C22C3×#57711yescharacteristic
759C22C3×#57711yescharacteristic
760C22C3×#57811yescharacteristic
761C4—22no—
762C4—42no—
763C4—41no—
764C4—41no—
765C4—41no—
766C4—41no—
767C4—81no—
768C4—81no—
769C4—81no—
770C4—81no—
771C4—81no—
772C4C3×#53411yescharacteristic
773C4C3×#53411yescharacteristic
774C4C3×#53811yescharacteristic
775C4C3×#53811yescharacteristic
776C3#2972911yescharacteristic, direct product factor, Sylow
777C2—42no—
778C2—82no—
779C2—161no—
780C2C3×#261711yescharacteristic
781C2C3×#304511yescharacteristic
782C2C3×#304611yescharacteristic
783C2C3×#320311yescharacteristic
784C2C3×#320411yescharacteristic
785C2C3×#322411yescharacteristic
786C2C3×#322511yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC2×C3×#449C2
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
1. C2×C3×#452C2semidirect
3. C3×#2620C2semidirect
4. C3×#2311C2semidirect
5. C3×#2072C2semidirect
6. C3×#2071C2semidirect
7. C3×#2056C2semidirect
8. C3×#2055C2semidirect
9. C3×#2055C2semidirect
10. C3×#2054C2semidirect
11. C3×#2015C2semidirect
12. C3×#2012C2semidirect
13. C3×#1874C2semidirect
14. C3×#1872C2semidirect
15. C3×#1798C2semidirect
16. #29729C3direct (N × H)
62. C2×#452C2×C3semidirect
64. #2620C2×C3semidirect
65. #2311C2×C3semidirect
66. #2072C2×C3semidirect
67. #2071C2×C3semidirect
68. #2056C2×C3semidirect
69. #2055C2×C3semidirect
70. #2055C2×C3semidirect
71. #2054C2×C3semidirect
72. #2015C2×C3semidirect
73. #2012C2×C3semidirect
74. #1874C2×C3semidirect
75. #1872C2×C3semidirect
76. #1798C2×C3semidirect
776. C3#29729direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#4522
C2×C3×#4492
C3×#26202
C3×#23112
C3×#20722
C3×#20712
C3×#20562
C3×#20552
C3×#20542
C3×#20152
C3×#20122
C3×#18742
C3×#18722
C3×#17982
#297293