Finite Group Databasebeta

← C3×#26787 #10645394

Subgroups — C3×#26787 #10645394

Order 768.

930 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#481C211yesmaximal, characteristic, complemented
2C2×C3×#478C211yesmaximal, characteristic, complemented
3C3×#2490C211yesmaximal, characteristic, complemented
4C3×#2361C211yesmaximal, characteristic, complemented
5C3×#2065C211yesmaximal, characteristic, complemented
6C3×#2059C211yesmaximal, characteristic, complemented
7C3×#2034C211yesmaximal, characteristic, complemented
8C3×#1999C211yesmaximal, characteristic
9C3×#1970C211yesmaximal, characteristic, complemented
10C3×#1926C211yesmaximal, characteristic, complemented
11C3×#1925C211yesmaximal, characteristic, complemented
12C3×#1923C211yesmaximal, characteristic, complemented
13C3×#1879C211yesmaximal, characteristic, complemented
14C3×#1852C211yesmaximal, characteristic, complemented
15C3×C4×#106C211yesmaximal, characteristic, complemented
16#26787C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×D8C2211yescharacteristic
18C2×C3×#125C2211yescharacteristic
19C2×C3×#121C2211yescharacteristic
20C2×C3×#121C2211yescharacteristic
21C2×C3×C4×D4—21no—
22C2×C3×C4×D4C2211yescharacteristic
23C22×C3×C4⋊C4C2211yescharacteristic
24C3×#481—24no—
25C3×#478—24no—
26C2×C3×#107C2211yescharacteristic
27C2×C3×#107C2211yescharacteristic
28C2×C3×#106C2211yescharacteristic
29C2×C3×#106C2211yescharacteristic
30C2×C3×#106C2211yescharacteristic
31C2×C3×C4⋊C8C2211yescharacteristic
32C2×C3×#102C2211yescharacteristic
33C2×C3×#102C2211yescharacteristic
34C2×C3×#102C2211yescharacteristic
35C2×C3×#102C2211yescharacteristic
36C2×C3×#102C2211yescharacteristic
37C2×C3×#102C2211yescharacteristic
38C2×C3×C22⋊C8C2211yescharacteristic
39C2×C3×C22⋊C8C2211yescharacteristic
40C2×C3×C4×C8C2211yescharacteristic
41C3×#397—21no—
42C3×#394—21no—
43C3×#390—21no—
44C3×#390C2211yescharacteristic
45C3×#390C2211yescharacteristic
46C3×#390C2211yescharacteristic
47C3×#389C2211yescharacteristic
48C3×#388—21no—
49C3×#388—21no—
50C3×#386—21no—
51C3×#385—21no—
52C3×#380C2211yescharacteristic
53C3×C4×C4⋊C4C2211yescharacteristic
54C3×C4×C4⋊C4C2211yescharacteristic
55C3×C4×C22⋊C4C2211yescharacteristic
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#336C2211yescharacteristic
61C3×#336C2211yescharacteristic
62C2×#481C2×C311yescharacteristic, complemented
63C2×#478C2×C311yescharacteristic, complemented
64#2490C2×C311yescharacteristic, complemented
65#2361C2×C311yescharacteristic, complemented
66#2065C2×C311yescharacteristic, complemented
67#2059C2×C311yescharacteristic, complemented
68#2034C2×C311yescharacteristic, complemented
69#1999C2×C311yescharacteristic
70#1970C2×C311yescharacteristic, complemented
71#1926C2×C311yescharacteristic, complemented
72#1925C2×C311yescharacteristic, complemented
73#1923C2×C311yescharacteristic, complemented
74#1879C2×C311yescharacteristic, complemented
75#1852C2×C311yescharacteristic, complemented
76C4×#106C2×C311yescharacteristic, complemented
77C22×C3×D4—21no—
78C22×C3×D4—21no—
79C22×C3×D4C2311yescharacteristic
80C22×C3×D4C2311yescharacteristic
81C23×C3×C4—21no—
82C23×C3×C4—21no—
83C23×C3×C4C2311yescharacteristic
84C2×C3×D8—22no—
85C2×C3×D8—22no—
86C2×C3×D8—41no—
87C22×C3×C8C2311yescharacteristic
88C22×C3×C8C2311yescharacteristic
89C22×C3×C8C2311yescharacteristic
90C22×C3×C8C2311yescharacteristic
91C3×#125—22no—
92C3×#125—41no—
93C3×#121—22no—
94C3×#121—22no—
95C3×#121—22no—
96C3×#121—41no—
97C3×C4×D4—22no—
98C3×C4×D4—41no—
99C3×C4×D4—44no—
100C2×C3×C4⋊C4—22no—
101C2×C3×C4⋊C4—21no—
102C2×C3×C4⋊C4—21no—
103C2×C3×C4⋊C4—21no—
104C2×C3×C4⋊C4—21no—
105C2×C3×C4⋊C4—41no—
106C2×C3×C4⋊C4C2311yescharacteristic
107C2×C3×C4⋊C4C2311yescharacteristic
108C2×C3×C4⋊C4C2311yescharacteristic
109C2×C3×C4⋊C4C2311yescharacteristic
110C2×C3×C4⋊C4C2311yescharacteristic
111C2×C3×C4⋊C4C2311yescharacteristic
112C2×C3×C22⋊C4—21no—
113C2×C3×C22⋊C4—21no—
114C2×C3×C22⋊C4—21no—
115C2×C3×C22⋊C4—21no—
116C2×C3×C22⋊C4—21no—
117C2×C3×C22⋊C4—21no—
118C2×C3×C22⋊C4—21no—
119C2×C3×C22⋊C4—21no—
120C2×C3×C22⋊C4—21no—
121C2×C3×C22⋊C4—21no—
122C2×C3×C22⋊C4D411yescharacteristic
123C2×C3×C22⋊C4D411yescharacteristic
124C2×C3×C42—21no—
125C2×C3×C42—21no—
126C2×C3×C42C2311yescharacteristic
127C2×C3×C42C2311yescharacteristic
128C3×#107—22no—
129C3×#107—41no—
130C3×#106—22no—
131C3×#106—22no—
132C3×#106D414yescomplemented
133C3×C4⋊C8—22no—
134C3×#102—22no—
135C3×#102—22no—
136C3×#102—22no—
137C3×#102—22no—
138C3×#102—22no—
139C3×#102—22no—
140C3×C22⋊C8—22no—
141C3×C22⋊C8—22no—
142C3×C4×C8—22no—
143C3×#95—21no—
144C3×#95—21no—
145C3×#95—21no—
146C3×#95—21no—
147C3×#95D411yescharacteristic
148C3×#95D411yescharacteristic
149C22×D8C22×C311yescharacteristic
150C2×#125C22×C311yescharacteristic
151C2×#121C22×C311yescharacteristic
152C2×#121C22×C311yescharacteristic
153C2×C4×D4—21no—
154C2×C4×D4C22×C311yescharacteristic
155C22×C4⋊C4C22×C311yescharacteristic
156#481—24no—
157#478—24no—
158C2×#107C22×C311yescharacteristic
159C2×#107C22×C311yescharacteristic
160C2×#106C22×C311yescharacteristic
161C2×#106C22×C311yescharacteristic
162C2×#106C22×C311yescharacteristic
163C2×C4⋊C8C22×C311yescharacteristic
164C2×#102C22×C311yescharacteristic
165C2×#102C22×C311yescharacteristic
166C2×#102C22×C311yescharacteristic
167C2×#102C22×C311yescharacteristic
168C2×#102C22×C311yescharacteristic
169C2×#102C22×C311yescharacteristic
170C2×C22⋊C8C22×C311yescharacteristic
171C2×C22⋊C8C22×C311yescharacteristic
172C2×C4×C8C22×C311yescharacteristic
173#397—21no—
174#394—21no—
175#390—21no—
176#390C22×C311yescharacteristic
177#390C22×C311yescharacteristic
178#390C22×C311yescharacteristic
179#389C22×C311yescharacteristic
180#388—21no—
181#388—21no—
182#386—21no—
183#385—21no—
184#380C22×C311yescharacteristic
185C4×C4⋊C4C22×C311yescharacteristic
186C4×C4⋊C4C22×C311yescharacteristic
187C4×C22⋊C4C22×C311yescharacteristic
188#340C22×C311yescharacteristic
189#340C22×C311yescharacteristic
190#340C22×C311yescharacteristic
191#340C22×C311yescharacteristic
192#336C22×C311yescharacteristic
193#336C22×C311yescharacteristic
194C24×C3—21no—
195C24×C3—21no—
196C24×C3C2×D411yescharacteristic
197C2×C3×D4—24no—
198C2×C3×D4—21no—
199C2×C3×D4—21no—
200C2×C3×D4—21no—
201C2×C3×D4—21no—
202C2×C3×D4—21no—
203C2×C3×D4—21no—
204C2×C3×D4—21no—
205C2×C3×D4—21no—
206C2×C3×D4—21no—
207C2×C3×D4—21no—
208C2×C3×D4—21no—
209C2×C3×D4—42no—
210C2×C3×D4—42no—
211C2×C3×D4—42no—
212C2×C3×D4—42no—
213C2×C3×D4—81no—
214C2×C3×D4#4112yes—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—21no—
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—42no—
228C22×C3×C4—42no—
229C22×C3×C4—42no—
230C22×C3×C4—42no—
231C22×C3×C4—81no—
232C22×C3×C4—81no—
233C22×C3×C4C2×D411yescharacteristic
234C22×C3×C4C2×D411yescharacteristic
235C22×C3×C4C2×D411yescharacteristic
236C22×C3×C4C2×D411yescharacteristic
237C22×C3×C4C2×D411yescharacteristic
238C22×C3×C4C2411yescharacteristic
239C3×D8—44no—
240C2×C3×C8—21no—
241C2×C3×C8—21no—
242C2×C3×C8—21no—
243C2×C3×C8—21no—
244C2×C3×C8—21no—
245C2×C3×C8—21no—
246C2×C3×C8—21no—
247C2×C3×C8—21no—
248C2×C3×C8—21no—
249C2×C3×C8—21no—
250C2×C3×C8C2×D412yes—
251C2×C3×C8#4112yes—
252C3×C4⋊C4—21no—
253C3×C4⋊C4—21no—
254C3×C4⋊C4—21no—
255C3×C4⋊C4—21no—
256C3×C4⋊C4—21no—
257C3×C4⋊C4—21no—
258C3×C4⋊C4—21no—
259C3×C4⋊C4—21no—
260C3×C4⋊C4—21no—
261C3×C4⋊C4—42no—
262C3×C4⋊C4—42no—
263C3×C4⋊C4—42no—
264C3×C4⋊C4—42no—
265C3×C4⋊C4C2×D412yes—
266C3×C4⋊C4C2×D412yes—
267C3×C4⋊C4#4112yes—
268C3×C22⋊C4—24no—
269C3×C22⋊C4—22no—
270C3×C22⋊C4—22no—
271C3×C22⋊C4—42no—
272C3×C22⋊C4—42no—
273C3×C22⋊C4—42no—
274C3×C22⋊C4—42no—
275C3×C22⋊C4—81no—
276C3×C22⋊C4—81no—
277C3×C22⋊C4—81no—
278C3×C22⋊C4—81no—
279C3×C22⋊C4—81no—
280C3×C42—21no—
281C3×C42—21no—
282C3×C42—21no—
283C3×C42—21no—
284C3×C42—42no—
285C3×C42—81no—
286C22×D4—21no—
287C22×D4—21no—
288C22×D4C23×C311yescharacteristic
289C22×D4C23×C311yescharacteristic
290C23×C4—21no—
291C23×C4—21no—
292C23×C4C23×C311yescharacteristic
293C2×D8—22no—
294C2×D8—22no—
295C2×D8—41no—
296C22×C8C23×C311yescharacteristic
297C22×C8C23×C311yescharacteristic
298C22×C8C23×C311yescharacteristic
299C22×C8C23×C311yescharacteristic
300#125—22no—
301#125—41no—
302#121—22no—
303#121—22no—
304#121—22no—
305#121—41no—
306C4×D4—22no—
307C4×D4—41no—
308C4×D4—44no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—41no—
315C2×C4⋊C4C23×C311yescharacteristic
316C2×C4⋊C4C23×C311yescharacteristic
317C2×C4⋊C4C23×C311yescharacteristic
318C2×C4⋊C4C23×C311yescharacteristic
319C2×C4⋊C4C23×C311yescharacteristic
320C2×C4⋊C4C23×C311yescharacteristic
321C2×C22⋊C4—21no—
322C2×C22⋊C4—21no—
323C2×C22⋊C4—21no—
324C2×C22⋊C4—21no—
325C2×C22⋊C4—21no—
326C2×C22⋊C4—21no—
327C2×C22⋊C4—21no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4C3×D411yescharacteristic
332C2×C22⋊C4C3×D411yescharacteristic
333C2×C42—21no—
334C2×C42—21no—
335C2×C42C23×C311yescharacteristic
336C2×C42C23×C311yescharacteristic
337#107—22no—
338#107—41no—
339#106—22no—
340#106—22no—
341#106C3×D414yescomplemented
342C4⋊C8—22no—
343#102—22no—
344#102—22no—
345#102—22no—
346#102—22no—
347#102—22no—
348#102—22no—
349C22⋊C8—22no—
350C22⋊C8—22no—
351C4×C8—22no—
352#95—21no—
353#95—21no—
354#95—21no—
355#95—21no—
356#95C3×D411yescharacteristic
357#95C3×D411yescharacteristic
358C23×C3—21no—
359C23×C3—21no—
360C23×C3—21no—
361C23×C3—21no—
362C23×C3—21no—
363C23×C3—21no—
364C23×C3—22no—
365C23×C3—41no—
366C23×C3—41no—
367C23×C3—41no—
368C23×C3—41no—
369C23×C3—41no—
370C23×C3—41no—
371C23×C3—41no—
372C23×C3—41no—
373C23×C3—41no—
374C23×C3—41no—
375C23×C3—41no—
376C23×C3—41no—
377C23×C3—41no—
378C23×C3#13512yes—
379C23×C3C22×D411yescharacteristic
380C3×D4—22no—
381C3×D4—22no—
382C3×D4—48no—
383C3×D4—41no—
384C3×D4—41no—
385C3×D4—41no—
386C3×D4—41no—
387C3×D4—41no—
388C3×D4—41no—
389C3×D4—84no—
390C2×C3×C4—21no—
391C2×C3×C4—21no—
392C2×C3×C4—21no—
393C2×C3×C4—22no—
394C2×C3×C4—21no—
395C2×C3×C4—21no—
396C2×C3×C4—21no—
397C2×C3×C4—22no—
398C2×C3×C4—22no—
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—21no—
407C2×C3×C4—41no—
408C2×C3×C4—41no—
409C2×C3×C4—41no—
410C2×C3×C4—41no—
411C2×C3×C4—41no—
412C2×C3×C4—41no—
413C2×C3×C4—41no—
414C2×C3×C4—41no—
415C2×C3×C4—41no—
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—84no—
427C2×C3×C4—84no—
428C2×C3×C4AGL(1,ℤ/8)12yes—
429C2×C3×C4C22×D411yescharacteristic
430C2×C3×C4C2×#4111yescharacteristic
431C2×C3×C4C2×#4111yescharacteristic
432C2×C3×C4C2×#4111yescharacteristic
433C2×C3×C4H(5,𝔽2)11yescharacteristic
434C2×C3×C42−1+411yescharacteristic
435C3×C8—22no—
436C3×C8—22no—
437C3×C8—41no—
438C3×C8—41no—
439C24—21no—
440C24—21no—
441C24C2×C3×D411yescharacteristic
442C2×D4—24no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—42no—
455C2×D4—42no—
456C2×D4—42no—
457C2×D4—42no—
458C2×D4—81no—
459C2×D4C3×#4112yes—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—42no—
473C22×C4—42no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4—81no—
477C22×C4—81no—
478C22×C4C2×C3×D411yescharacteristic
479C22×C4C2×C3×D411yescharacteristic
480C22×C4C2×C3×D411yescharacteristic
481C22×C4C2×C3×D411yescharacteristic
482C22×C4C2×C3×D411yescharacteristic
483C22×C4C24×C311yescharacteristic
484D8—44no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8C2×C3×D412yes—
496C2×C8C3×#4112yes—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—42no—
507C4⋊C4—42no—
508C4⋊C4—42no—
509C4⋊C4—42no—
510C4⋊C4C2×C3×D412yes—
511C4⋊C4C2×C3×D412yes—
512C4⋊C4C3×#4112yes—
513C22⋊C4—24no—
514C22⋊C4—22no—
515C22⋊C4—22no—
516C22⋊C4—42no—
517C22⋊C4—42no—
518C22⋊C4—42no—
519C22⋊C4—42no—
520C22⋊C4—81no—
521C22⋊C4—81no—
522C22⋊C4—81no—
523C22⋊C4—81no—
524C22⋊C4—81no—
525C42—21no—
526C42—21no—
527C42—21no—
528C42—21no—
529C42—42no—
530C42—81no—
531C22×C3—22no—
532C22×C3—22no—
533C22×C3—22no—
534C22×C3—41no—
535C22×C3—41no—
536C22×C3—41no—
537C22×C3—41no—
538C22×C3—42no—
539C22×C3—42no—
540C22×C3—42no—
541C22×C3—81no—
542C22×C3—81no—
543C22×C3—81no—
544C22×C3—81no—
545C22×C3—81no—
546C22×C3—81no—
547C22×C3—81no—
548C22×C3—81no—
549C22×C3—81no—
550C22×C3—81no—
551C22×C3—81no—
552C22×C3#52511yescharacteristic
553C22×C3D4211yescharacteristic
554C22×C3#54711yescharacteristic
555C22×C3C2×#13511yescharacteristic
556C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
557C22×C3#57611yescharacteristic
558C22×C3#57711yescharacteristic
559C3×C4—22no—
560C3×C4—41no—
561C3×C4—42no—
562C3×C4—41no—
563C3×C4—41no—
564C3×C4—42no—
565C3×C4—41no—
566C3×C4—42no—
567C3×C4—81no—
568C3×C4—81no—
569C3×C4—81no—
570C3×C4#53211yescharacteristic
571C3×C4#54211yescharacteristic
572C3×C4#54811yescharacteristic
573C3×C4#55111yescharacteristic
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—22no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23C3×#13512yes—
595C23C22×C3×D411yescharacteristic
596D4—22no—
597D4—22no—
598D4—48no—
599D4—41no—
600D4—41no—
601D4—41no—
602D4—41no—
603D4—41no—
604D4—41no—
605D4—84no—
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—21no—
617C2×C4—21no—
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—84no—
643C2×C4—84no—
644C2×C4C3×AGL(1,ℤ/8)12yes—
645C2×C4C22×C3×D411yescharacteristic
646C2×C4C2×C3×#4111yescharacteristic
647C2×C4C2×C3×#4111yescharacteristic
648C2×C4C2×C3×#4111yescharacteristic
649C2×C4C3×H(5,𝔽2)11yescharacteristic
650C2×C4C3×2−1+411yescharacteristic
651C8—22no—
652C8—22no—
653C8—41no—
654C8—41no—
655C2×C3—42no—
656C2×C3—82no—
657C2×C3—161no—
658C2×C3#246111yescharacteristic
659C2×C3#310511yescharacteristic
660C2×C3#311911yescharacteristic
661C2×C3#327411yescharacteristic
662C2×C3#328211yescharacteristic
663C2×C3#333911yescharacteristic
664C2×C3#334511yescharacteristic
665C22—22no—
666C22—22no—
667C22—22no—
668C22—41no—
669C22—41no—
670C22—41no—
671C22—41no—
672C22—42no—
673C22—42no—
674C22—42no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22—81no—
684C22—81no—
685C22—81no—
686C22C3×#52511yescharacteristic
687C22C3×D4211yescharacteristic
688C22C3×#54711yescharacteristic
689C22C2×C3×#13511yescharacteristic
690C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
691C22C3×#57611yescharacteristic
692C22C3×#57711yescharacteristic
693C4—22no—
694C4—41no—
695C4—41no—
696C4—42no—
697C4—41no—
698C4—42no—
699C4—41no—
700C4—42no—
701C4—81no—
702C4—81no—
703C4—81no—
704C4C3×#53211yescharacteristic
705C4C3×#54211yescharacteristic
706C4C3×#54811yescharacteristic
707C4C3×#55111yescharacteristic
708C3#2678711yescharacteristic, direct product factor, Sylow
709C2—42no—
710C2—82no—
711C2—161no—
712C2C3×#246111yescharacteristic
713C2C3×#310511yescharacteristic
714C2C3×#311911yescharacteristic
715C2C3×#327411yescharacteristic
716C2C3×#328211yescharacteristic
717C2C3×#333911yescharacteristic
718C2C3×#334511yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC3×#1999C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C3×C4×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#481C2semidirect
2. C2×C3×#478C2semidirect
3. C3×#2490C2semidirect
4. C3×#2361C2semidirect
5. C3×#2065C2semidirect
6. C3×#2059C2semidirect
7. C3×#2034C2semidirect
9. C3×#1970C2semidirect
10. C3×#1926C2semidirect
11. C3×#1925C2semidirect
12. C3×#1923C2semidirect
13. C3×#1879C2semidirect
14. C3×#1852C2semidirect
15. C3×C4×#106C2semidirect
16. #26787C3direct (N × H)
62. C2×#481C2×C3semidirect
63. C2×#478C2×C3semidirect
64. #2490C2×C3semidirect
65. #2361C2×C3semidirect
66. #2065C2×C3semidirect
67. #2059C2×C3semidirect
68. #2034C2×C3semidirect
70. #1970C2×C3semidirect
71. #1926C2×C3semidirect
72. #1925C2×C3semidirect
73. #1923C2×C3semidirect
74. #1879C2×C3semidirect
75. #1852C2×C3semidirect
76. C4×#106C2×C3semidirect
132. C3×#106D4semidirect
341. #106C3×D4semidirect
708. C3#26787direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#4812
C2×C3×#4782
C3×#24902
C3×#23612
C3×#20652
C3×#20592
C3×#20342
C3×#19992
C3×#19702
C3×#19262
C3×#19252
C3×#19232
C3×#18792
C3×#18522
C3×C4×#1062
#267873