Finite Group Databasebeta

← C3×#26798 #10645405

Subgroups — C3×#26798 #10645405

Order 768.

880 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#482C211yesmaximal, characteristic, complemented
2C2×C3×#478C211yesmaximal, characteristic, complemented
3C3×#2490C211yesmaximal, characteristic, complemented
4C3×#2363C211yesmaximal, characteristic, complemented
5C3×#2067C211yesmaximal, characteristic, complemented
6C3×#2059C211yesmaximal, characteristic, complemented
7C3×#2033C211yesmaximal, characteristic, complemented
8C3×#1999C211yesmaximal, characteristic
9C3×#1970C211yesmaximal, characteristic, complemented
10C3×#1926C211yesmaximal, characteristic, complemented
11C3×#1926C211yesmaximal, characteristic, complemented
12C3×#1923C211yesmaximal, characteristic, complemented
13C3×#1879C211yesmaximal, characteristic, complemented
14C3×#1854C211yesmaximal, characteristic, complemented
15C3×C4×#107C211yesmaximal, characteristic, complemented
16#26798C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×D8C2211yescharacteristic
18C2×C3×#125C2211yescharacteristic
19C2×C3×#121C2211yescharacteristic
20C2×C3×#121C2211yescharacteristic
21C2×C3×C4×D4C2211yescharacteristic
22C2×C3×#117C2211yescharacteristic
23C3×#482—24no—
24C3×#478—24no—
25C2×C3×#107C2211yescharacteristic
26C2×C3×#107C2211yescharacteristic
27C2×C3×#107C2211yescharacteristic
28C2×C3×#106C2211yescharacteristic
29C2×C3×#106C2211yescharacteristic
30C2×C3×C4⋊C8C2211yescharacteristic
31C2×C3×#102C2211yescharacteristic
32C2×C3×#102C2211yescharacteristic
33C2×C3×#102C2211yescharacteristic
34C2×C3×#102C2211yescharacteristic
35C2×C3×#102C2211yescharacteristic
36C2×C3×#102C2211yescharacteristic
37C2×C3×C22⋊C8C2211yescharacteristic
38C2×C3×C22⋊C8C2211yescharacteristic
39C2×C3×C4×C8C2211yescharacteristic
40C3×#397—21no—
41C3×#394—21no—
42C3×#390—21no—
43C3×#390—21no—
44C3×#390C2211yescharacteristic
45C3×#390C2211yescharacteristic
46C3×#390C2211yescharacteristic
47C3×#389C2211yescharacteristic
48C3×#388—21no—
49C3×#388—21no—
50C3×#386—21no—
51C3×#380C2211yescharacteristic
52C3×C4×C4⋊C4C2211yescharacteristic
53C3×C4×C4⋊C4C2211yescharacteristic
54C3×C4×C22⋊C4—21no—
55C3×C4×C22⋊C4C2211yescharacteristic
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#336C2211yescharacteristic
61C3×#336C2211yescharacteristic
62C2×#482C2×C311yescharacteristic, complemented
63C2×#478C2×C311yescharacteristic, complemented
64#2490C2×C311yescharacteristic, complemented
65#2363C2×C311yescharacteristic, complemented
66#2067C2×C311yescharacteristic, complemented
67#2059C2×C311yescharacteristic, complemented
68#2033C2×C311yescharacteristic, complemented
69#1999C2×C311yescharacteristic
70#1970C2×C311yescharacteristic, complemented
71#1926C2×C311yescharacteristic, complemented
72#1926C2×C311yescharacteristic, complemented
73#1923C2×C311yescharacteristic, complemented
74#1879C2×C311yescharacteristic, complemented
75#1854C2×C311yescharacteristic, complemented
76C4×#107C2×C311yescharacteristic, complemented
77C22×C3×D4—21no—
78C22×C3×D4—21no—
79C22×C3×D4C2311yescharacteristic
80C22×C3×D4C2311yescharacteristic
81C23×C3×C4—21no—
82C23×C3×C4C2311yescharacteristic
83C2×C3×D8—22no—
84C2×C3×D8—22no—
85C2×C3×D8—41no—
86C22×C3×C8C2311yescharacteristic
87C22×C3×C8C2311yescharacteristic
88C22×C3×C8C2311yescharacteristic
89C22×C3×C8C2311yescharacteristic
90C3×#125—22no—
91C3×#125—41no—
92C3×#121—22no—
93C3×#121—22no—
94C3×#121—22no—
95C3×#121—41no—
96C3×C4×D4—22no—
97C3×C4×D4—41no—
98C3×#117—22no—
99C3×#117—41no—
100C2×C3×C4⋊C4—21no—
101C2×C3×C4⋊C4—21no—
102C2×C3×C4⋊C4—21no—
103C2×C3×C4⋊C4C2311yescharacteristic
104C2×C3×C4⋊C4C2311yescharacteristic
105C2×C3×C4⋊C4C2311yescharacteristic
106C2×C3×C4⋊C4C2311yescharacteristic
107C2×C3×C4⋊C4C2311yescharacteristic
108C2×C3×C4⋊C4C2311yescharacteristic
109C2×C3×C22⋊C4—21no—
110C2×C3×C22⋊C4—21no—
111C2×C3×C22⋊C4—21no—
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⋊C4D411yescharacteristic
121C2×C3×C22⋊C4D411yescharacteristic
122C2×C3×C42—21no—
123C2×C3×C42—21no—
124C2×C3×C42—21no—
125C2×C3×C42C2311yescharacteristic
126C2×C3×C42C2311yescharacteristic
127C3×#107—22no—
128C3×#107—41no—
129C3×#107D414yescomplemented
130C3×#106—22no—
131C3×#106—22no—
132C3×C4⋊C8—22no—
133C3×#102—22no—
134C3×#102—22no—
135C3×#102—22no—
136C3×#102—22no—
137C3×#102—22no—
138C3×#102—22no—
139C3×C22⋊C8—22no—
140C3×C22⋊C8—22no—
141C3×C4×C8—22no—
142C3×#95—21no—
143C3×#95—21no—
144C3×#95—21no—
145C3×#95—21no—
146C3×#95D411yescharacteristic
147C3×#95D411yescharacteristic
148C22×D8C22×C311yescharacteristic
149C2×#125C22×C311yescharacteristic
150C2×#121C22×C311yescharacteristic
151C2×#121C22×C311yescharacteristic
152C2×C4×D4C22×C311yescharacteristic
153C2×#117C22×C311yescharacteristic
154#482—24no—
155#478—24no—
156C2×#107C22×C311yescharacteristic
157C2×#107C22×C311yescharacteristic
158C2×#107C22×C311yescharacteristic
159C2×#106C22×C311yescharacteristic
160C2×#106C22×C311yescharacteristic
161C2×C4⋊C8C22×C311yescharacteristic
162C2×#102C22×C311yescharacteristic
163C2×#102C22×C311yescharacteristic
164C2×#102C22×C311yescharacteristic
165C2×#102C22×C311yescharacteristic
166C2×#102C22×C311yescharacteristic
167C2×#102C22×C311yescharacteristic
168C2×C22⋊C8C22×C311yescharacteristic
169C2×C22⋊C8C22×C311yescharacteristic
170C2×C4×C8C22×C311yescharacteristic
171#397—21no—
172#394—21no—
173#390—21no—
174#390—21no—
175#390C22×C311yescharacteristic
176#390C22×C311yescharacteristic
177#390C22×C311yescharacteristic
178#389C22×C311yescharacteristic
179#388—21no—
180#388—21no—
181#386—21no—
182#380C22×C311yescharacteristic
183C4×C4⋊C4C22×C311yescharacteristic
184C4×C4⋊C4C22×C311yescharacteristic
185C4×C22⋊C4—21no—
186C4×C22⋊C4C22×C311yescharacteristic
187#340C22×C311yescharacteristic
188#340C22×C311yescharacteristic
189#340C22×C311yescharacteristic
190#340C22×C311yescharacteristic
191#336C22×C311yescharacteristic
192#336C22×C311yescharacteristic
193C24×C3—21no—
194C24×C3—21no—
195C24×C3C2×D411yescharacteristic
196C2×C3×D4—24no—
197C2×C3×D4—21no—
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—42no—
209C2×C3×D4—42no—
210C2×C3×D4—81no—
211C2×C3×D4—81no—
212C2×C3×D4—81no—
213C2×C3×D4#4112yes—
214C22×C3×C4—21no—
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—42no—
227C22×C3×C4—42no—
228C22×C3×C4—81no—
229C22×C3×C4C2×D411yescharacteristic
230C22×C3×C4C2×D411yescharacteristic
231C22×C3×C4C2×D411yescharacteristic
232C22×C3×C4C2×D411yescharacteristic
233C22×C3×C4C2×D411yescharacteristic
234C22×C3×C4C2411yescharacteristic
235C3×D8—44no—
236C2×C3×C8—21no—
237C2×C3×C8—21no—
238C2×C3×C8—21no—
239C2×C3×C8—21no—
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×C8C2×D412yes—
247C2×C3×C8#4112yes—
248C3×C4⋊C4—21no—
249C3×C4⋊C4—21no—
250C3×C4⋊C4—21no—
251C3×C4⋊C4—21no—
252C3×C4⋊C4—21no—
253C3×C4⋊C4—21no—
254C3×C4⋊C4—21no—
255C3×C4⋊C4—21no—
256C3×C4⋊C4—21no—
257C3×C4⋊C4—42no—
258C3×C4⋊C4—42no—
259C3×C4⋊C4—81no—
260C3×C4⋊C4C2×D412yes—
261C3×C4⋊C4C2×D412yes—
262C3×C4⋊C4#4112yes—
263C3×C22⋊C4—24no—
264C3×C22⋊C4—22no—
265C3×C22⋊C4—41no—
266C3×C22⋊C4—42no—
267C3×C22⋊C4—42no—
268C3×C22⋊C4—42no—
269C3×C22⋊C4—42no—
270C3×C22⋊C4—42no—
271C3×C22⋊C4—81no—
272C3×C22⋊C4—81no—
273C3×C22⋊C4—81no—
274C3×C22⋊C4—81no—
275C3×C22⋊C4—81no—
276C3×C42—21no—
277C3×C42—21no—
278C3×C42—21no—
279C3×C42—21no—
280C3×C42—42no—
281C3×C42—81no—
282C3×C42—81no—
283C22×D4—21no—
284C22×D4—21no—
285C22×D4C23×C311yescharacteristic
286C22×D4C23×C311yescharacteristic
287C23×C4—21no—
288C23×C4C23×C311yescharacteristic
289C2×D8—22no—
290C2×D8—22no—
291C2×D8—41no—
292C22×C8C23×C311yescharacteristic
293C22×C8C23×C311yescharacteristic
294C22×C8C23×C311yescharacteristic
295C22×C8C23×C311yescharacteristic
296#125—22no—
297#125—41no—
298#121—22no—
299#121—22no—
300#121—22no—
301#121—41no—
302C4×D4—22no—
303C4×D4—41no—
304#117—22no—
305#117—41no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4C23×C311yescharacteristic
310C2×C4⋊C4C23×C311yescharacteristic
311C2×C4⋊C4C23×C311yescharacteristic
312C2×C4⋊C4C23×C311yescharacteristic
313C2×C4⋊C4C23×C311yescharacteristic
314C2×C4⋊C4C23×C311yescharacteristic
315C2×C22⋊C4—21no—
316C2×C22⋊C4—21no—
317C2×C22⋊C4—21no—
318C2×C22⋊C4—21no—
319C2×C22⋊C4—21no—
320C2×C22⋊C4—21no—
321C2×C22⋊C4—21no—
322C2×C22⋊C4—21no—
323C2×C22⋊C4—21no—
324C2×C22⋊C4—21no—
325C2×C22⋊C4—21no—
326C2×C22⋊C4C3×D411yescharacteristic
327C2×C22⋊C4C3×D411yescharacteristic
328C2×C42—21no—
329C2×C42—21no—
330C2×C42—21no—
331C2×C42C23×C311yescharacteristic
332C2×C42C23×C311yescharacteristic
333#107—22no—
334#107—41no—
335#107C3×D414yescomplemented
336#106—22no—
337#106—22no—
338C4⋊C8—22no—
339#102—22no—
340#102—22no—
341#102—22no—
342#102—22no—
343#102—22no—
344#102—22no—
345C22⋊C8—22no—
346C22⋊C8—22no—
347C4×C8—22no—
348#95—21no—
349#95—21no—
350#95—21no—
351#95—21no—
352#95C3×D411yescharacteristic
353#95C3×D411yescharacteristic
354C23×C3—22no—
355C23×C3—21no—
356C23×C3—21no—
357C23×C3—21no—
358C23×C3—21no—
359C23×C3—21no—
360C23×C3—21no—
361C23×C3—21no—
362C23×C3—41no—
363C23×C3—41no—
364C23×C3—41no—
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×C3C22×D411yescharacteristic
376C3×D4—22no—
377C3×D4—22no—
378C3×D4—41no—
379C3×D4—41no—
380C3×D4—41no—
381C3×D4—41no—
382C3×D4—41no—
383C3×D4—41no—
384C3×D4—84no—
385C3×D4—84no—
386C2×C3×C4—21no—
387C2×C3×C4—21no—
388C2×C3×C4—21no—
389C2×C3×C4—22no—
390C2×C3×C4—21no—
391C2×C3×C4—21no—
392C2×C3×C4—21no—
393C2×C3×C4—22no—
394C2×C3×C4—22no—
395C2×C3×C4—21no—
396C2×C3×C4—21no—
397C2×C3×C4—21no—
398C2×C3×C4—21no—
399C2×C3×C4—21no—
400C2×C3×C4—21no—
401C2×C3×C4—21no—
402C2×C3×C4—21no—
403C2×C3×C4—41no—
404C2×C3×C4—41no—
405C2×C3×C4—41no—
406C2×C3×C4—41no—
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—84no—
423C2×C3×C4#13512yes—
424C2×C3×C4C22×D411yescharacteristic
425C2×C3×C4C2×#4111yescharacteristic
426C2×C3×C4C2×#4111yescharacteristic
427C2×C3×C4C2×#4111yescharacteristic
428C2×C3×C4H(5,𝔽2)11yescharacteristic
429C2×C3×C42−1+411yescharacteristic
430C3×C8—22no—
431C3×C8—22no—
432C3×C8—41no—
433C3×C8—41no—
434C24—21no—
435C24—21no—
436C24C2×C3×D411yescharacteristic
437C2×D4—24no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—42no—
450C2×D4—42no—
451C2×D4—81no—
452C2×D4—81no—
453C2×D4—81no—
454C2×D4C3×#4112yes—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—42no—
468C22×C4—42no—
469C22×C4—81no—
470C22×C4C2×C3×D411yescharacteristic
471C22×C4C2×C3×D411yescharacteristic
472C22×C4C2×C3×D411yescharacteristic
473C22×C4C2×C3×D411yescharacteristic
474C22×C4C2×C3×D411yescharacteristic
475C22×C4C24×C311yescharacteristic
476D8—44no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8C2×C3×D412yes—
488C2×C8C3×#4112yes—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—42no—
499C4⋊C4—42no—
500C4⋊C4—81no—
501C4⋊C4C2×C3×D412yes—
502C4⋊C4C2×C3×D412yes—
503C4⋊C4C3×#4112yes—
504C22⋊C4—24no—
505C22⋊C4—22no—
506C22⋊C4—41no—
507C22⋊C4—42no—
508C22⋊C4—42no—
509C22⋊C4—42no—
510C22⋊C4—42no—
511C22⋊C4—42no—
512C22⋊C4—81no—
513C22⋊C4—81no—
514C22⋊C4—81no—
515C22⋊C4—81no—
516C22⋊C4—81no—
517C42—21no—
518C42—21no—
519C42—21no—
520C42—21no—
521C42—42no—
522C42—81no—
523C42—81no—
524C22×C3—41no—
525C22×C3—41no—
526C22×C3—41no—
527C22×C3—42no—
528C22×C3—41no—
529C22×C3—42no—
530C22×C3—41no—
531C22×C3—42no—
532C22×C3—41no—
533C22×C3—41no—
534C22×C3—81no—
535C22×C3—81no—
536C22×C3—81no—
537C22×C3—81no—
538C22×C3—81no—
539C22×C3—81no—
540C22×C3—81no—
541C22×C3—81no—
542C22×C3—81no—
543C22×C3—81no—
544C22×C3—81no—
545C22×C3#52511yescharacteristic
546C22×C3D4211yescharacteristic
547C22×C3#54711yescharacteristic
548C22×C3C2×#13511yescharacteristic
549C22×C3#57511yescharacteristic
550C22×C3#57611yescharacteristic
551C22×C3#57611yescharacteristic
552C3×C4—22no—
553C3×C4—41no—
554C3×C4—42no—
555C3×C4—41no—
556C3×C4—41no—
557C3×C4—42no—
558C3×C4—42no—
559C3×C4—41no—
560C3×C4—81no—
561C3×C4—81no—
562C3×C4—81no—
563C3×C4#53211yescharacteristic
564C3×C4#54211yescharacteristic
565C3×C4#54811yescharacteristic
566C3×C4#55111yescharacteristic
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—22no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23C22×C3×D411yescharacteristic
589D4—22no—
590D4—22no—
591D4—41no—
592D4—41no—
593D4—41no—
594D4—41no—
595D4—41no—
596D4—41no—
597D4—84no—
598D4—84no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—22no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
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—84no—
636C2×C4C3×#13512yes—
637C2×C4C22×C3×D411yescharacteristic
638C2×C4C2×C3×#4111yescharacteristic
639C2×C4C2×C3×#4111yescharacteristic
640C2×C4C2×C3×#4111yescharacteristic
641C2×C4C3×H(5,𝔽2)11yescharacteristic
642C2×C4C3×2−1+411yescharacteristic
643C8—22no—
644C8—22no—
645C8—41no—
646C8—41no—
647C2×C3—81no—
648C2×C3—82no—
649C2×C3—161no—
650C2×C3#246111yescharacteristic
651C2×C3#310211yescharacteristic
652C2×C3#312211yescharacteristic
653C2×C3#327311yescharacteristic
654C2×C3#328711yescharacteristic
655C2×C3#333911yescharacteristic
656C2×C3#334711yescharacteristic
657C22—41no—
658C22—42no—
659C22—41no—
660C22—41no—
661C22—41no—
662C22—41no—
663C22—41no—
664C22—42no—
665C22—41no—
666C22—42no—
667C22—81no—
668C22—81no—
669C22—81no—
670C22—81no—
671C22—81no—
672C22—81no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22C3×#52511yescharacteristic
679C22C3×D4211yescharacteristic
680C22C3×#54711yescharacteristic
681C22C2×C3×#13511yescharacteristic
682C22C3×#57511yescharacteristic
683C22C3×#57611yescharacteristic
684C22C3×#57611yescharacteristic
685C4—22no—
686C4—41no—
687C4—41no—
688C4—42no—
689C4—42no—
690C4—41no—
691C4—41no—
692C4—42no—
693C4—81no—
694C4—81no—
695C4—81no—
696C4C3×#53211yescharacteristic
697C4C3×#54211yescharacteristic
698C4C3×#54811yescharacteristic
699C4C3×#55111yescharacteristic
700C3#2679811yescharacteristic, direct product factor, Sylow
701C2—81no—
702C2—82no—
703C2—161no—
704C2C3×#246111yescharacteristic
705C2C3×#310211yescharacteristic
706C2C3×#312211yescharacteristic
707C2C3×#327311yescharacteristic
708C2C3×#328711yescharacteristic
709C2C3×#333911yescharacteristic
710C2C3×#334711yescharacteristic
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×#482C2semidirect
2. C2×C3×#478C2semidirect
3. C3×#2490C2semidirect
4. C3×#2363C2semidirect
5. C3×#2067C2semidirect
6. C3×#2059C2semidirect
7. C3×#2033C2semidirect
9. C3×#1970C2semidirect
10. C3×#1926C2semidirect
11. C3×#1926C2semidirect
12. C3×#1923C2semidirect
13. C3×#1879C2semidirect
14. C3×#1854C2semidirect
15. C3×C4×#107C2semidirect
16. #26798C3direct (N × H)
62. C2×#482C2×C3semidirect
63. C2×#478C2×C3semidirect
64. #2490C2×C3semidirect
65. #2363C2×C3semidirect
66. #2067C2×C3semidirect
67. #2059C2×C3semidirect
68. #2033C2×C3semidirect
70. #1970C2×C3semidirect
71. #1926C2×C3semidirect
72. #1926C2×C3semidirect
73. #1923C2×C3semidirect
74. #1879C2×C3semidirect
75. #1854C2×C3semidirect
76. C4×#107C2×C3semidirect
129. C3×#107D4semidirect
335. #107C3×D4semidirect
700. C3#26798direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#4822
C2×C3×#4782
C3×#24902
C3×#23632
C3×#20672
C3×#20592
C3×#20332
C3×#19992
C3×#19702
C3×#19262
C3×#19232
C3×#18792
C3×#18542
C3×C4×#1072
#267983