Finite Group Databasebeta

← C3×#26827 #10645434

Subgroups — C3×#26827 #10645434

Order 768.

924 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#490C211yesmaximal, characteristic, complemented
2C2×C3×C4×D8C211yesmaximal, characteristic, complemented
3C3×#2454C211yesmaximal, characteristic, complemented
4C3×#2445C211yesmaximal, characteristic, complemented
5C3×#2067C211yesmaximal, characteristic, complemented
6C3×#2059C211yesmaximal, characteristic, complemented
7C3×#2054C211yesmaximal, characteristic, complemented
8C3×#2011C211yesmaximal, characteristic
9C3×#1972C211yesmaximal, characteristic, complemented
10C3×#1936C211yesmaximal, characteristic, complemented
11C3×#1936C211yesmaximal, characteristic, complemented
12C3×#1934C211yesmaximal, characteristic, complemented
13C3×#1879C211yesmaximal, characteristic, complemented
14C3×#1864C211yesmaximal, characteristic, complemented
15C3×#1771C211yesmaximal, characteristic, complemented
16#26827C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×D8C2211yescharacteristic
18C22×C3×D8C2211yescharacteristic
19C2×C3×#127C2211yescharacteristic
20C2×C3×#125C2211yescharacteristic
21C2×C3×#123—21no—
22C2×C3×C4×D4C2211yescharacteristic
23C2×C3×C4×D4C2211yescharacteristic
24C3×#490—24no—
25C3×C4×D8—24no—
26C2×C3×#107C2211yescharacteristic
27C2×C3×#106C2211yescharacteristic
28C2×C3×C4⋊C8C2211yescharacteristic
29C2×C3×#102C2211yescharacteristic
30C2×C3×#102C2211yescharacteristic
31C2×C3×#102C2211yescharacteristic
32C2×C3×#102C2211yescharacteristic
33C2×C3×#102C2211yescharacteristic
34C2×C3×#102C2211yescharacteristic
35C2×C3×#102C2211yescharacteristic
36C2×C3×#102C2211yescharacteristic
37C2×C3×#97C2211yescharacteristic
38C2×C3×#97C2211yescharacteristic
39C2×C3×C4×C8C2211yescharacteristic
40C3×#399—21no—
41C3×#396—21no—
42C3×#394—21no—
43C3×#394—21no—
44C3×#390C2211yescharacteristic
45C3×#390C2211yescharacteristic
46C3×#390C2211yescharacteristic
47C3×#390C2211yescharacteristic
48C3×#390C2211yescharacteristic
49C3×#389C2211yescharacteristic
50C3×#389C2211yescharacteristic
51C3×#389C2211yescharacteristic
52C3×#386—21no—
53C3×#385—21no—
54C3×#380—21no—
55C3×C4×C4⋊C4C2211yescharacteristic
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#336C2211yescharacteristic
61C3×#336C2211yescharacteristic
62C2×#490C2×C311yescharacteristic, complemented
63C2×C4×D8C2×C311yescharacteristic, complemented
64#2454C2×C311yescharacteristic, complemented
65#2445C2×C311yescharacteristic, complemented
66#2067C2×C311yescharacteristic, complemented
67#2059C2×C311yescharacteristic, complemented
68#2054C2×C311yescharacteristic, complemented
69#2011C2×C311yescharacteristic
70#1972C2×C311yescharacteristic, complemented
71#1936C2×C311yescharacteristic, complemented
72#1936C2×C311yescharacteristic, complemented
73#1934C2×C311yescharacteristic, complemented
74#1879C2×C311yescharacteristic, complemented
75#1864C2×C311yescharacteristic, complemented
76#1771C2×C311yescharacteristic, complemented
77C22×C3×D4—21no—
78C22×C3×D4—21no—
79C22×C3×D4C2311yescharacteristic
80C22×C3×D4C2311yescharacteristic
81C22×C3×D4C2311yescharacteristic
82C23×C3×C4—21no—
83C23×C3×C4—21no—
84C2×C3×D8—22no—
85C2×C3×D8—22no—
86C2×C3×D8—22no—
87C2×C3×D8—22no—
88C2×C3×D8—22no—
89C2×C3×D8—41no—
90C22×C3×C8C2311yescharacteristic
91C22×C3×C8C2311yescharacteristic
92C22×C3×C8C2311yescharacteristic
93C22×C3×C8C2311yescharacteristic
94C3×#127—22no—
95C3×#127—41no—
96C3×#125—22no—
97C3×#125—41no—
98C3×#123—44no—
99C3×C4×D4—22no—
100C3×C4×D4—22no—
101C3×C4×D4—41no—
102C3×C4×D4—41no—
103C2×C3×C4⋊C4—21no—
104C2×C3×C4⋊C4—21no—
105C2×C3×C4⋊C4—21no—
106C2×C3×C4⋊C4—21no—
107C2×C3×C4⋊C4—21no—
108C2×C3×C4⋊C4D411yescharacteristic
109C2×C3×C4⋊C4D411yescharacteristic
110C2×C3×C4⋊C4C2311yescharacteristic
111C2×C3×C4⋊C4C2311yescharacteristic
112C2×C3×C4⋊C4C2311yescharacteristic
113C2×C3×C4⋊C4C2311yescharacteristic
114C2×C3×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
123C2×C3×C22⋊C4—21no—
124C2×C3×C22⋊C4—21no—
125C2×C3×C22⋊C4—21no—
126C2×C3×C22⋊C4—21no—
127C2×C3×C42C2311yescharacteristic
128C2×C3×C42C2311yescharacteristic
129C2×C3×C42C2311yescharacteristic
130C3×#107—22no—
131C3×#106—41no—
132C3×C4⋊C8—22no—
133C3×#102—22no—
134C3×#102—22no—
135C3×#102—22no—
136C3×#102—22no—
137C3×#102—22no—
138C3×#102—22no—
139C3×#102—22no—
140C3×#102D414yes—
141C3×#97—22no—
142C3×#97—22no—
143C3×C4×C8—22no—
144C3×#95—21no—
145C3×#95—21no—
146C3×#95—21no—
147C3×#95D411yescharacteristic
148C3×#95D411yescharacteristic
149C22×D8C22×C311yescharacteristic
150C22×D8C22×C311yescharacteristic
151C2×#127C22×C311yescharacteristic
152C2×#125C22×C311yescharacteristic
153C2×#123—21no—
154C2×C4×D4C22×C311yescharacteristic
155C2×C4×D4C22×C311yescharacteristic
156#490—24no—
157C4×D8—24no—
158C2×#107C22×C311yescharacteristic
159C2×#106C22×C311yescharacteristic
160C2×C4⋊C8C22×C311yescharacteristic
161C2×#102C22×C311yescharacteristic
162C2×#102C22×C311yescharacteristic
163C2×#102C22×C311yescharacteristic
164C2×#102C22×C311yescharacteristic
165C2×#102C22×C311yescharacteristic
166C2×#102C22×C311yescharacteristic
167C2×#102C22×C311yescharacteristic
168C2×#102C22×C311yescharacteristic
169C2×#97C22×C311yescharacteristic
170C2×#97C22×C311yescharacteristic
171C2×C4×C8C22×C311yescharacteristic
172#399—21no—
173#396—21no—
174#394—21no—
175#394—21no—
176#390C22×C311yescharacteristic
177#390C22×C311yescharacteristic
178#390C22×C311yescharacteristic
179#390C22×C311yescharacteristic
180#390C22×C311yescharacteristic
181#389C22×C311yescharacteristic
182#389C22×C311yescharacteristic
183#389C22×C311yescharacteristic
184#386—21no—
185#385—21no—
186#380—21no—
187C4×C4⋊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×C3—21no—
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—21no—
209C2×C3×D4—21no—
210C2×C3×D4—21no—
211C2×C3×D4—21no—
212C2×C3×D4—21no—
213C2×C3×D4—42no—
214C2×C3×D4—42no—
215C2×C3×D4—42no—
216C2×C3×D4—42no—
217C2×C3×D4—81no—
218C2×C3×D4—81no—
219C2×C3×D4C2×D412yes—
220C2×C3×D4#4112yes—
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—42no—
229C22×C3×C4—42no—
230C22×C3×C4—81no—
231C22×C3×C4—81no—
232C22×C3×C4C2×D411yescharacteristic
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—28no—
240C3×D8—44no—
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—
252C2×C3×C8#4112yes—
253C3×C4⋊C4—22no—
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—21no—
262C3×C4⋊C4—21no—
263C3×C4⋊C4—41no—
264C3×C4⋊C4—42no—
265C3×C4⋊C4—42no—
266C3×C4⋊C4—42no—
267C3×C4⋊C4—81no—
268C3×C4⋊C4—81no—
269C3×C4⋊C4C2×D412yes—
270C3×C22⋊C4—42no—
271C3×C22⋊C4—42no—
272C3×C22⋊C4—42no—
273C3×C22⋊C4—42no—
274C3×C22⋊C4—42no—
275C3×C22⋊C4—42no—
276C3×C22⋊C4—81no—
277C3×C22⋊C4—81no—
278C3×C22⋊C4—81no—
279C3×C22⋊C4—81no—
280C3×C22⋊C4—81no—
281C3×C22⋊C4—81no—
282C3×C42—21no—
283C3×C42—21no—
284C3×C42—21no—
285C3×C42—21no—
286C3×C42—21no—
287C3×C42—21no—
288C22×D4—21no—
289C22×D4—21no—
290C22×D4C23×C311yescharacteristic
291C22×D4C23×C311yescharacteristic
292C22×D4C23×C311yescharacteristic
293C23×C4—21no—
294C23×C4—21no—
295C2×D8—22no—
296C2×D8—22no—
297C2×D8—22no—
298C2×D8—22no—
299C2×D8—22no—
300C2×D8—41no—
301C22×C8C23×C311yescharacteristic
302C22×C8C23×C311yescharacteristic
303C22×C8C23×C311yescharacteristic
304C22×C8C23×C311yescharacteristic
305#127—22no—
306#127—41no—
307#125—22no—
308#125—41no—
309#123—44no—
310C4×D4—22no—
311C4×D4—22no—
312C4×D4—41no—
313C4×D4—41no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4C3×D411yescharacteristic
320C2×C4⋊C4C3×D411yescharacteristic
321C2×C4⋊C4C23×C311yescharacteristic
322C2×C4⋊C4C23×C311yescharacteristic
323C2×C4⋊C4C23×C311yescharacteristic
324C2×C4⋊C4C23×C311yescharacteristic
325C2×C4⋊C4C23×C311yescharacteristic
326C2×C22⋊C4—21no—
327C2×C22⋊C4—21no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—21no—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—21no—
336C2×C22⋊C4—21no—
337C2×C22⋊C4—21no—
338C2×C42C23×C311yescharacteristic
339C2×C42C23×C311yescharacteristic
340C2×C42C23×C311yescharacteristic
341#107—22no—
342#106—41no—
343C4⋊C8—22no—
344#102—22no—
345#102—22no—
346#102—22no—
347#102—22no—
348#102—22no—
349#102—22no—
350#102—22no—
351#102C3×D414yes—
352#97—22no—
353#97—22no—
354C4×C8—22no—
355#95—21no—
356#95—21no—
357#95—21no—
358#95C3×D411yescharacteristic
359#95C3×D411yescharacteristic
360C23×C3—22no—
361C23×C3—22no—
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×C3—41no—
376C23×C3—41no—
377C23×C3—41no—
378C23×C3—41no—
379C23×C3—41no—
380C23×C3—41no—
381C23×C3C22×D411yescharacteristic
382C3×D4—22no—
383C3×D4—22no—
384C3×D4—22no—
385C3×D4—22no—
386C3×D4—41no—
387C3×D4—41no—
388C3×D4—41no—
389C3×D4—41no—
390C3×D4—41no—
391C3×D4—41no—
392C3×D4—41no—
393C3×D4—41no—
394C3×D4—84no—
395C3×D4—84no—
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—22no—
404C2×C3×C4—21no—
405C2×C3×C4—21no—
406C2×C3×C4—21no—
407C2×C3×C4—21no—
408C2×C3×C4—21no—
409C2×C3×C4—21no—
410C2×C3×C4—21no—
411C2×C3×C4—21no—
412C2×C3×C4—21no—
413C2×C3×C4—21no—
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—41no—
427C2×C3×C4—41no—
428C2×C3×C4—84no—
429C2×C3×C4—84no—
430C2×C3×C4AGL(1,ℤ/8)12yes—
431C2×C3×C4C22×D411yescharacteristic
432C2×C3×C4C2×#4111yescharacteristic
433C2×C3×C4C2×#4111yescharacteristic
434C2×C3×C4C2×#4111yescharacteristic
435C2×C3×C4H(5,𝔽2)11yescharacteristic
436C2×C3×C42−1+411yescharacteristic
437C3×C8—22no—
438C3×C8—22no—
439C3×C8—22no—
440C3×C8—41no—
441C24—21no—
442C24—21no—
443C24—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—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—42no—
461C2×D4—42no—
462C2×D4—42no—
463C2×D4—42no—
464C2×D4—81no—
465C2×D4—81no—
466C2×D4C2×C3×D412yes—
467C2×D4C3×#4112yes—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—42no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4—42no—
477C22×C4—81no—
478C22×C4—81no—
479C22×C4C2×C3×D411yescharacteristic
480C22×C4C2×C3×D411yescharacteristic
481C22×C4C2×C3×D411yescharacteristic
482C22×C4C2×C3×D411yescharacteristic
483C22×C4C2×C3×D411yescharacteristic
484C22×C4C2×C3×D411yescharacteristic
485C22×C4C24×C311yescharacteristic
486D8—28no—
487D8—44no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8C2×C3×D412yes—
498C2×C8C3×#4112yes—
499C2×C8C3×#4112yes—
500C4⋊C4—22no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—41no—
511C4⋊C4—42no—
512C4⋊C4—42no—
513C4⋊C4—42no—
514C4⋊C4—81no—
515C4⋊C4—81no—
516C4⋊C4C2×C3×D412yes—
517C22⋊C4—42no—
518C22⋊C4—42no—
519C22⋊C4—42no—
520C22⋊C4—42no—
521C22⋊C4—42no—
522C22⋊C4—42no—
523C22⋊C4—81no—
524C22⋊C4—81no—
525C22⋊C4—81no—
526C22⋊C4—81no—
527C22⋊C4—81no—
528C22⋊C4—81no—
529C42—21no—
530C42—21no—
531C42—21no—
532C42—21no—
533C42—21no—
534C42—21no—
535C22×C3—42no—
536C22×C3—42no—
537C22×C3—42no—
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—81no—
553C22×C3—81no—
554C22×C3—81no—
555C22×C3—81no—
556C22×C3#53211yescharacteristic
557C22×C3D4211yescharacteristic
558C22×C3#54811yescharacteristic
559C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
560C22×C3#57511yescharacteristic
561C22×C3#57611yescharacteristic
562C22×C3#57611yescharacteristic
563C3×C4—22no—
564C3×C4—41no—
565C3×C4—41no—
566C3×C4—41no—
567C3×C4—42no—
568C3×C4—41no—
569C3×C4—41no—
570C3×C4—81no—
571C3×C4—81no—
572C3×C4—81no—
573C3×C4—81no—
574C3×C4#52511yescharacteristic
575C3×C4#54211yescharacteristic
576C3×C4#54711yescharacteristic
577C3×C4#55111yescharacteristic
578C23—22no—
579C23—22no—
580C23—41no—
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—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23C22×C3×D411yescharacteristic
600D4—22no—
601D4—22no—
602D4—22no—
603D4—22no—
604D4—41no—
605D4—41no—
606D4—41no—
607D4—41no—
608D4—41no—
609D4—41no—
610D4—41no—
611D4—41no—
612D4—84no—
613D4—84no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—22no—
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×C4—41no—
646C2×C4—84no—
647C2×C4—84no—
648C2×C4C3×AGL(1,ℤ/8)12yes—
649C2×C4C22×C3×D411yescharacteristic
650C2×C4C2×C3×#4111yescharacteristic
651C2×C4C2×C3×#4111yescharacteristic
652C2×C4C2×C3×#4111yescharacteristic
653C2×C4C3×H(5,𝔽2)11yescharacteristic
654C2×C4C3×2−1+411yescharacteristic
655C8—22no—
656C8—22no—
657C8—22no—
658C8—41no—
659C2×C3—82no—
660C2×C3—82no—
661C2×C3—161no—
662C2×C3#246111yescharacteristic
663C2×C3#317111yescharacteristic
664C2×C3#317611yescharacteristic
665C2×C3#326411yescharacteristic
666C2×C3#326811yescharacteristic
667C2×C3#336611yescharacteristic
668C2×C3#337011yescharacteristic
669C22—42no—
670C22—42no—
671C22—42no—
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—
686C22—81no—
687C22—81no—
688C22—81no—
689C22—81no—
690C22C3×#53211yescharacteristic
691C22C3×D4211yescharacteristic
692C22C3×#54811yescharacteristic
693C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
694C22C3×#57511yescharacteristic
695C22C3×#57611yescharacteristic
696C22C3×#57611yescharacteristic
697C4—22no—
698C4—41no—
699C4—41no—
700C4—41no—
701C4—42no—
702C4—41no—
703C4—41no—
704C4—81no—
705C4—81no—
706C4—81no—
707C4—81no—
708C4C3×#52511yescharacteristic
709C4C3×#54211yescharacteristic
710C4C3×#54711yescharacteristic
711C4C3×#55111yescharacteristic
712C3#2682711yescharacteristic, direct product factor, Sylow
713C2—82no—
714C2—82no—
715C2—161no—
716C2C3×#246111yescharacteristic
717C2C3×#317111yescharacteristic
718C2C3×#317611yescharacteristic
719C2C3×#326411yescharacteristic
720C2C3×#326811yescharacteristic
721C2C3×#336611yescharacteristic
722C2C3×#337011yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC3×#2011C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C3×C4×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#490C2semidirect
2. C2×C3×C4×D8C2semidirect
3. C3×#2454C2semidirect
4. C3×#2445C2semidirect
5. C3×#2067C2semidirect
6. C3×#2059C2semidirect
7. C3×#2054C2semidirect
9. C3×#1972C2semidirect
10. C3×#1936C2semidirect
11. C3×#1936C2semidirect
12. C3×#1934C2semidirect
13. C3×#1879C2semidirect
14. C3×#1864C2semidirect
15. C3×#1771C2semidirect
16. #26827C3direct (N × H)
62. C2×#490C2×C3semidirect
63. C2×C4×D8C2×C3semidirect
64. #2454C2×C3semidirect
65. #2445C2×C3semidirect
66. #2067C2×C3semidirect
67. #2059C2×C3semidirect
68. #2054C2×C3semidirect
70. #1972C2×C3semidirect
71. #1936C2×C3semidirect
72. #1936C2×C3semidirect
73. #1934C2×C3semidirect
74. #1879C2×C3semidirect
75. #1864C2×C3semidirect
76. #1771C2×C3semidirect
712. C3#26827direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#4902
C2×C3×C4×D82
C3×#24542
C3×#24452
C3×#20672
C3×#20592
C3×#20542
C3×#20112
C3×#19722
C3×#19362
C3×#19342
C3×#18792
C3×#18642
C3×#17712
#268273