Finite Group Databasebeta

← C3×#29693 #10648300

Subgroups — C3×#29693 #10648300

Order 768.

1056 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#529C211yesmaximal, characteristic
2C2×C3×#479C211yesmaximal, characteristic, complemented
3C2×C3×#478C211yesmaximal, characteristic, complemented
4C3×#2851C211yesmaximal, characteristic, complemented
5C3×#2059C211yesmaximal, characteristic, complemented
6C3×#2059C211yesmaximal, characteristic, complemented
7C3×#2042C211yesmaximal, characteristic, complemented
8C3×#2042C211yesmaximal, characteristic, complemented
9C3×#2036C211yesmaximal, characteristic, complemented
10C3×#2035C211yesmaximal, characteristic, complemented
11C3×#2034C211yesmaximal, characteristic
12C3×#2033C211yesmaximal, characteristic
13C3×#1805C211yesmaximal, characteristic, complemented
14C3×#1804C211yesmaximal, characteristic, complemented
15C3×#1797C211yesmaximal, characteristic, complemented
16#29693C311yesmaximal, characteristic, direct product factor, Sylow
17C3×#529—24no—
18C3×#529—24no—
19C2×C3×#126—21no—
20C2×C3×#125C2211yescharacteristic
21C2×C3×#125C2211yescharacteristic
22C2×C3×#124C2211yescharacteristic
23C2×C3×#123—21no—
24C2×C3×C22⋊Q8C2211yescharacteristic
25C2×C3×#121C2211yescharacteristic
26C2×C3×C4×Q8C2211yescharacteristic
27C2×C3×C4×D4—21no—
28C2×C3×C4×D4C2211yescharacteristic
29C2×C3×#117—21no—
30C22×C3×C42C2211yescharacteristic
31C3×#479—24no—
32C3×#478—24no—
33C2×C3×#107C2211yescharacteristic
34C2×C3×#107C2211yescharacteristic
35C2×C3×#106C2211yescharacteristic
36C2×C3×#106C2211yescharacteristic
37C2×C3×C4⋊C8C2211yescharacteristic
38C2×C3×C4⋊C8C2211yescharacteristic
39C2×C3×#103C2211yescharacteristic
40C2×C3×#103C2211yescharacteristic
41C2×C3×#103C2211yescharacteristic
42C2×C3×#103C2211yescharacteristic
43C2×C3×#102C2211yescharacteristic
44C2×C3×#102C2211yescharacteristic
45C2×C3×#102C2211yescharacteristic
46C2×C3×#102C2211yescharacteristic
47C2×C3×C22⋊C8C2211yescharacteristic
48C2×C3×C22⋊C8C2211yescharacteristic
49C3×#389C2211yescharacteristic
50C3×#389C2211yescharacteristic
51C3×#387—21no—
52C3×#387—21no—
53C3×#385—21no—
54C3×#385—21no—
55C3×#382C2211yescharacteristic
56C3×#380C2211yescharacteristic
57C3×#380C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#340C2211yescharacteristic
61C3×#340C2211yescharacteristic
62C3×#336C2211yescharacteristic
63C3×#336C2211yescharacteristic
64C2×#529C2×C311yescharacteristic
65C2×#479C2×C311yescharacteristic, complemented
66C2×#478C2×C311yescharacteristic, complemented
67#2851C2×C311yescharacteristic, complemented
68#2059C2×C311yescharacteristic, complemented
69#2059C2×C311yescharacteristic, complemented
70#2042C2×C311yescharacteristic, complemented
71#2042C2×C311yescharacteristic, complemented
72#2036C2×C311yescharacteristic, complemented
73#2035C2×C311yescharacteristic, complemented
74#2034C2×C311yescharacteristic
75#2033C2×C311yescharacteristic
76#1805C2×C311yescharacteristic, complemented
77#1804C2×C311yescharacteristic, complemented
78#1797C2×C311yescharacteristic, complemented
79C22×C3×Q8C2311yescharacteristic
80C22×C3×D4—21no—
81C22×C3×D4C2311yescharacteristic
82C23×C3×C4—21no—
83C23×C3×C4D411yescharacteristic
84C23×C3×C4D411yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C22×C3×C8C2311yescharacteristic
87C22×C3×C8C2311yescharacteristic
88C22×C3×C8C2311yescharacteristic
89C22×C3×C8C2311yescharacteristic
90C3×#126—28no—
91C3×#125—22no—
92C3×#125—22no—
93C3×#125—22no—
94C3×#125—22no—
95C3×#124—22no—
96C3×#124—22no—
97C3×#123—28no—
98C3×C22⋊Q8—22no—
99C3×C22⋊Q8—22no—
100C3×#121—22no—
101C3×#121—22no—
102C3×C4×Q8—22no—
103C3×C4×Q8D414yes—
104C3×C4×D4—28no—
105C3×C4×D4—22no—
106C3×C4×D4D414yes—
107C3×#117—28no—
108C2×C3×C4⋊C4—21no—
109C2×C3×C4⋊C4—21no—
110C2×C3×C4⋊C4—21no—
111C2×C3×C4⋊C4—21no—
112C2×C3×C4⋊C4—21no—
113C2×C3×C4⋊C4—21no—
114C2×C3×C4⋊C4—21no—
115C2×C3×C4⋊C4—21no—
116C2×C3×C4⋊C4C2311yescharacteristic
117C2×C3×C4⋊C4C2311yescharacteristic
118C2×C3×C4⋊C4C2311yescharacteristic
119C2×C3×C4⋊C4C2311yescharacteristic
120C2×C3×C4⋊C4C2311yescharacteristic
121C2×C3×C4⋊C4C2311yescharacteristic
122C2×C3×C22⋊C4—21no—
123C2×C3×C22⋊C4—21no—
124C2×C3×C22⋊C4—21no—
125C2×C3×C22⋊C4—21no—
126C2×C3×C22⋊C4—21no—
127C2×C3×C22⋊C4—21no—
128C2×C3×C22⋊C4—21no—
129C2×C3×C42—21no—
130C2×C3×C42—22no—
131C2×C3×C42—22no—
132C2×C3×C42D411yescharacteristic
133C2×C3×C42D411yescharacteristic
134C2×C3×C42C2311yescharacteristic
135C2×C3×C42C2311yescharacteristic
136C3×#107—22no—
137C3×#107—22no—
138C3×#106—22no—
139C3×#106—22no—
140C3×C4⋊C8—22no—
141C3×C4⋊C8—22no—
142C3×#103—22no—
143C3×#103—22no—
144C3×#103—41no—
145C3×#103—41no—
146C3×#102—22no—
147C3×#102—22no—
148C3×#102—41no—
149C3×#102—41no—
150C3×C22⋊C8—41no—
151C3×C22⋊C8—41no—
152C3×#95—21no—
153C3×#95—21no—
154C3×#95—21no—
155C3×#95—21no—
156C3×#95—21no—
157C3×#95—21no—
158#529—24no—
159#529—24no—
160C2×#126—21no—
161C2×#125C22×C311yescharacteristic
162C2×#125C22×C311yescharacteristic
163C2×#124C22×C311yescharacteristic
164C2×#123—21no—
165C2×C22⋊Q8C22×C311yescharacteristic
166C2×#121C22×C311yescharacteristic
167C2×C4×Q8C22×C311yescharacteristic
168C2×C4×D4—21no—
169C2×C4×D4C22×C311yescharacteristic
170C2×#117—21no—
171C22×C42C22×C311yescharacteristic
172#479—24no—
173#478—24no—
174C2×#107C22×C311yescharacteristic
175C2×#107C22×C311yescharacteristic
176C2×#106C22×C311yescharacteristic
177C2×#106C22×C311yescharacteristic
178C2×C4⋊C8C22×C311yescharacteristic
179C2×C4⋊C8C22×C311yescharacteristic
180C2×#103C22×C311yescharacteristic
181C2×#103C22×C311yescharacteristic
182C2×#103C22×C311yescharacteristic
183C2×#103C22×C311yescharacteristic
184C2×#102C22×C311yescharacteristic
185C2×#102C22×C311yescharacteristic
186C2×#102C22×C311yescharacteristic
187C2×#102C22×C311yescharacteristic
188C2×C22⋊C8C22×C311yescharacteristic
189C2×C22⋊C8C22×C311yescharacteristic
190#389C22×C311yescharacteristic
191#389C22×C311yescharacteristic
192#387—21no—
193#387—21no—
194#385—21no—
195#385—21no—
196#382C22×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
207C2×C3×Q8—21no—
208C2×C3×Q8—21no—
209C2×C3×Q8—21no—
210C2×C3×Q8—21no—
211C2×C3×Q8—21no—
212C2×C3×Q8C2×D412yes—
213C2×C3×D4—24no—
214C2×C3×D4—21no—
215C2×C3×D4—21no—
216C2×C3×D4—21no—
217C2×C3×D4—21no—
218C2×C3×D4—21no—
219C2×C3×D4—42no—
220C2×C3×D4—42no—
221C2×C3×D4C2×D412yes—
222C22×C3×C4—22no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—22no—
227C22×C3×C4—22no—
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—41no—
240C22×C3×C4—41no—
241C22×C3×C4—41no—
242C22×C3×C4—42no—
243C22×C3×C4—42no—
244C22×C3×C4C2×D411yescharacteristic
245C22×C3×C4C2×D411yescharacteristic
246C22×C3×C4C2×D411yescharacteristic
247C22×C3×C4C2×D411yescharacteristic
248C22×C3×C4C2×D411yescharacteristic
249C22×C3×C4C2411yescharacteristic
250C2×C3×C8—21no—
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—21no—
262C3×C4⋊C4—24no—
263C3×C4⋊C4—24no—
264C3×C4⋊C4—24no—
265C3×C4⋊C4—24no—
266C3×C4⋊C4—21no—
267C3×C4⋊C4—21no—
268C3×C4⋊C4—21no—
269C3×C4⋊C4—21no—
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—42no—
277C3×C4⋊C4—42no—
278C3×C4⋊C4—42no—
279C3×C4⋊C4—42no—
280C3×C4⋊C4C2×D412yes—
281C3×C4⋊C4C2×D412yes—
282C3×C22⋊C4—24no—
283C3×C22⋊C4—24no—
284C3×C22⋊C4—24no—
285C3×C22⋊C4—24no—
286C3×C22⋊C4—24no—
287C3×C22⋊C4—42no—
288C3×C22⋊C4—42no—
289C3×C42—22no—
290C3×C42—22no—
291C3×C42—24no—
292C3×C42—21no—
293C3×C42—21no—
294C3×C42C2×D412yes—
295C3×C42C2×D412yes—
296C22×Q8C23×C311yescharacteristic
297C22×D4—21no—
298C22×D4C23×C311yescharacteristic
299C23×C4—21no—
300C23×C4C3×D411yescharacteristic
301C23×C4C3×D411yescharacteristic
302C23×C4C23×C311yescharacteristic
303C22×C8C23×C311yescharacteristic
304C22×C8C23×C311yescharacteristic
305C22×C8C23×C311yescharacteristic
306C22×C8C23×C311yescharacteristic
307#126—28no—
308#125—22no—
309#125—22no—
310#125—22no—
311#125—22no—
312#124—22no—
313#124—22no—
314#123—28no—
315C22⋊Q8—22no—
316C22⋊Q8—22no—
317#121—22no—
318#121—22no—
319C4×Q8—22no—
320C4×Q8C3×D414yes—
321C4×D4—28no—
322C4×D4—22no—
323C4×D4C3×D414yes—
324#117—28no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4C23×C311yescharacteristic
334C2×C4⋊C4C23×C311yescharacteristic
335C2×C4⋊C4C23×C311yescharacteristic
336C2×C4⋊C4C23×C311yescharacteristic
337C2×C4⋊C4C23×C311yescharacteristic
338C2×C4⋊C4C23×C311yescharacteristic
339C2×C22⋊C4—21no—
340C2×C22⋊C4—21no—
341C2×C22⋊C4—21no—
342C2×C22⋊C4—21no—
343C2×C22⋊C4—21no—
344C2×C22⋊C4—21no—
345C2×C22⋊C4—21no—
346C2×C42—21no—
347C2×C42—22no—
348C2×C42—22no—
349C2×C42C3×D411yescharacteristic
350C2×C42C3×D411yescharacteristic
351C2×C42C23×C311yescharacteristic
352C2×C42C23×C311yescharacteristic
353#107—22no—
354#107—22no—
355#106—22no—
356#106—22no—
357C4⋊C8—22no—
358C4⋊C8—22no—
359#103—22no—
360#103—22no—
361#103—41no—
362#103—41no—
363#102—22no—
364#102—22no—
365#102—41no—
366#102—41no—
367C22⋊C8—41no—
368C22⋊C8—41no—
369#95—21no—
370#95—21no—
371#95—21no—
372#95—21no—
373#95—21no—
374#95—21no—
375C23×C3—21no—
376C23×C3—21no—
377C23×C3—21no—
378C23×C3—21no—
379C23×C3—21no—
380C23×C3—21no—
381C23×C3—22no—
382C23×C3—41no—
383C23×C3—41no—
384C23×C3—41no—
385C23×C3—41no—
386C23×C3—41no—
387C23×C3—41no—
388C23×C3#13512yes—
389C23×C3C22×D411yescharacteristic
390C3×Q8—22no—
391C3×Q8—22no—
392C3×Q8—41no—
393C3×Q8—41no—
394C3×D4—22no—
395C3×D4—22no—
396C3×D4—48no—
397C3×D4—41no—
398C3×D4—41no—
399C2×C3×C4—21no—
400C2×C3×C4—21no—
401C2×C3×C4—21no—
402C2×C3×C4—21no—
403C2×C3×C4—21no—
404C2×C3×C4—21no—
405C2×C3×C4—21no—
406C2×C3×C4—22no—
407C2×C3×C4—22no—
408C2×C3×C4—22no—
409C2×C3×C4—21no—
410C2×C3×C4—21no—
411C2×C3×C4—21no—
412C2×C3×C4—21no—
413C2×C3×C4—21no—
414C2×C3×C4—21no—
415C2×C3×C4—44no—
416C2×C3×C4—44no—
417C2×C3×C4—48no—
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#12012yes—
441C2×C3×C4#12012yes—
442C2×C3×C4C22×D411yescharacteristic
443C2×C3×C4C22×D411yescharacteristic
444C2×C3×C4H(5,𝔽2)11yescharacteristic
445C2×C3×C42−1+411yescharacteristic
446C2×C3×C42−1+411yescharacteristic
447C2×C3×C42−1+411yescharacteristic
448C3×C8—41no—
449C3×C8—41no—
450C3×C8—41no—
451C3×C8—41no—
452C24—21no—
453C24C2×C3×D411yescharacteristic
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8C2×C3×D412yes—
460C2×D4—24no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—42no—
467C2×D4—42no—
468C2×D4C2×C3×D412yes—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—24no—
476C22×C4—21no—
477C22×C4—21no—
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—41no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4C2×C3×D411yescharacteristic
492C22×C4C2×C3×D411yescharacteristic
493C22×C4C2×C3×D411yescharacteristic
494C22×C4C2×C3×D411yescharacteristic
495C22×C4C2×C3×D411yescharacteristic
496C22×C4C24×C311yescharacteristic
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
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—
509C4⋊C4—24no—
510C4⋊C4—24no—
511C4⋊C4—24no—
512C4⋊C4—24no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—42no—
524C4⋊C4—42no—
525C4⋊C4—42no—
526C4⋊C4—42no—
527C4⋊C4C2×C3×D412yes—
528C4⋊C4C2×C3×D412yes—
529C22⋊C4—24no—
530C22⋊C4—24no—
531C22⋊C4—24no—
532C22⋊C4—24no—
533C22⋊C4—24no—
534C22⋊C4—42no—
535C22⋊C4—42no—
536C42—22no—
537C42—22no—
538C42—24no—
539C42—21no—
540C42—21no—
541C42C2×C3×D412yes—
542C42C2×C3×D412yes—
543C22×C3—22no—
544C22×C3—22no—
545C22×C3—22no—
546C22×C3—41no—
547C22×C3—41no—
548C22×C3—41no—
549C22×C3—41no—
550C22×C3—42no—
551C22×C3—42no—
552C22×C3—42no—
553C22×C3—81no—
554C22×C3—81no—
555C22×C3—81no—
556C22×C3—81no—
557C22×C3C2×#12011yescharacteristic
558C22×C3#53611yescharacteristic
559C22×C3#53711yescharacteristic
560C22×C3C2×#13511yescharacteristic
561C22×C3#57511yescharacteristic
562C22×C3#57511yescharacteristic
563C22×C3#57511yescharacteristic
564C3×C4—22no—
565C3×C4—22no—
566C3×C4—41no—
567C3×C4—42no—
568C3×C4—41no—
569C3×C4—42no—
570C3×C4—41no—
571C3×C4—42no—
572C3×C4—81no—
573C3×C4—81no—
574C3×C4—81no—
575C3×C4—81no—
576C3×C4#53611yescharacteristic
577C3×C4#53611yescharacteristic
578C3×C4#53711yescharacteristic
579C3×C4#53711yescharacteristic
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—22no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23C3×#13512yes—
594C23C22×C3×D411yescharacteristic
595Q8—22no—
596Q8—22no—
597Q8—41no—
598Q8—41no—
599D4—22no—
600D4—22no—
601D4—48no—
602D4—41no—
603D4—41no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—44no—
621C2×C4—44no—
622C2×C4—48no—
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×C4C3×#12012yes—
646C2×C4C3×#12012yes—
647C2×C4C22×C3×D411yescharacteristic
648C2×C4C22×C3×D411yescharacteristic
649C2×C4C3×H(5,𝔽2)11yescharacteristic
650C2×C4C3×2−1+411yescharacteristic
651C2×C4C3×2−1+411yescharacteristic
652C2×C4C3×2−1+411yescharacteristic
653C8—41no—
654C8—41no—
655C8—41no—
656C8—41no—
657C2×C3—42no—
658C2×C3—82no—
659C2×C3#261611yescharacteristic
660C2×C3#300211yescharacteristic
661C2×C3#300511yescharacteristic
662C2×C3#323211yescharacteristic
663C2×C3#324011yescharacteristic
664C2×C3#325011yescharacteristic
665C2×C3#325611yescharacteristic
666C22—22no—
667C22—22no—
668C22—22no—
669C22—41no—
670C22—41no—
671C22—41no—
672C22—41no—
673C22—42no—
674C22—42no—
675C22—42no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22—81no—
680C22C2×C3×#12011yescharacteristic
681C22C3×#53611yescharacteristic
682C22C3×#53711yescharacteristic
683C22C2×C3×#13511yescharacteristic
684C22C3×#57511yescharacteristic
685C22C3×#57511yescharacteristic
686C22C3×#57511yescharacteristic
687C4—22no—
688C4—22no—
689C4—41no—
690C4—42no—
691C4—41no—
692C4—42no—
693C4—41no—
694C4—42no—
695C4—81no—
696C4—81no—
697C4—81no—
698C4—81no—
699C4C3×#53611yescharacteristic
700C4C3×#53611yescharacteristic
701C4C3×#53711yescharacteristic
702C4C3×#53711yescharacteristic
703C3#2969311yescharacteristic, direct product factor, Sylow
704C2—42no—
705C2—82no—
706C2C3×#261611yescharacteristic
707C2C3×#300211yescharacteristic
708C2C3×#300511yescharacteristic
709C2C3×#323211yescharacteristic
710C2C3×#324011yescharacteristic
711C2C3×#325011yescharacteristic
712C2C3×#325611yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC2×C3×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C22×C3×C42 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×C3×#479C2semidirect
3. C2×C3×#478C2semidirect
4. C3×#2851C2semidirect
5. C3×#2059C2semidirect
6. C3×#2059C2semidirect
7. C3×#2042C2semidirect
8. C3×#2042C2semidirect
9. C3×#2036C2semidirect
10. C3×#2035C2semidirect
13. C3×#1805C2semidirect
14. C3×#1804C2semidirect
15. C3×#1797C2semidirect
16. #29693C3direct (N × H)
65. C2×#479C2×C3semidirect
66. C2×#478C2×C3semidirect
67. #2851C2×C3semidirect
68. #2059C2×C3semidirect
69. #2059C2×C3semidirect
70. #2042C2×C3semidirect
71. #2042C2×C3semidirect
72. #2036C2×C3semidirect
73. #2035C2×C3semidirect
76. #1805C2×C3semidirect
77. #1804C2×C3semidirect
78. #1797C2×C3semidirect
703. C3#29693direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5292
C2×C3×#4792
C2×C3×#4782
C3×#28512
C3×#20592
C3×#20422
C3×#20362
C3×#20352
C3×#20342
C3×#20332
C3×#18052
C3×#18042
C3×#17972
#296933