Finite Group Databasebeta

← C3×#32675 #10651282

Subgroups — C3×#32675 #10651282

Order 768.

836 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2592C211yesmaximal, characteristic, complemented
2C3×#2548C211yesmaximal, characteristic, complemented
3C3×#2055C211yesmaximal, characteristic, complemented
4C3×#2054C211yesmaximal, characteristic, complemented
5C3×#2014C211yesmaximal, characteristic, complemented
6C3×#2012C211yesmaximal, characteristic, complemented
7C3×#2012C211yesmaximal, characteristic, complemented
8C3×#2011C211yesmaximal, characteristic
9C3×#1985C211yesmaximal, characteristic, complemented
10C3×#1973C211yesmaximal, characteristic, complemented
11C3×#1972C211yesmaximal, characteristic, complemented
12C3×#1927C211yesmaximal, characteristic, complemented
13C3×#1926C211yesmaximal, characteristic, complemented
14C3×#1925C211yesmaximal, characteristic, complemented
15C3×#1925C211yesmaximal, characteristic, complemented
16#32675C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×SD16C2211yescharacteristic
18C22×C3×SD16C2211yescharacteristic
19C22×C3×D8C2211yescharacteristic
20C22×C3×D8C2211yescharacteristic
21C2×C3×#127C2211yescharacteristic
22C2×C3×#124—21no—
23C2×C3×#124C2211yescharacteristic
24C2×C3×C4×Q8C2211yescharacteristic
25C2×C3×#107C2211yescharacteristic
26C2×C3×#106C2211yescharacteristic
27C2×C3×C4⋊C8C2211yescharacteristic
28C2×C3×#103C2211yescharacteristic
29C2×C3×#103C2211yescharacteristic
30C2×C3×#102C2211yescharacteristic
31C2×C3×#102C2211yescharacteristic
32C2×C3×#102C2211yescharacteristic
33C2×C3×#102C2211yescharacteristic
34C2×C3×#102C2211yescharacteristic
35C2×C3×#102C2211yescharacteristic
36C2×C3×#97C2211yescharacteristic
37C3×#397—21no—
38C3×#394—21no—
39C3×#394—21no—
40C3×#393—21no—
41C3×#391C2211yescharacteristic
42C3×#391C2211yescharacteristic
43C3×#390—21no—
44C3×#390C2211yescharacteristic
45C3×#390C2211yescharacteristic
46C3×#390C2211yescharacteristic
47C3×#390C2211yescharacteristic
48C3×#390C2211yescharacteristic
49C3×#390C2211yescharacteristic
50C3×#388—21no—
51C3×#388—21no—
52C3×C4×C4⋊C4C2211yescharacteristic
53C3×C4×C4⋊C4C2211yescharacteristic
54C3×#340C2211yescharacteristic
55C3×#340C2211yescharacteristic
56C3×#336C2211yescharacteristic
57C3×#336C2211yescharacteristic
58C3×#336C2211yescharacteristic
59C3×#336C2211yescharacteristic
60#2592C2×C311yescharacteristic, complemented
61#2548C2×C311yescharacteristic, complemented
62#2055C2×C311yescharacteristic, complemented
63#2054C2×C311yescharacteristic, complemented
64#2014C2×C311yescharacteristic, complemented
65#2012C2×C311yescharacteristic, complemented
66#2012C2×C311yescharacteristic, complemented
67#2011C2×C311yescharacteristic
68#1985C2×C311yescharacteristic, complemented
69#1973C2×C311yescharacteristic, complemented
70#1972C2×C311yescharacteristic, complemented
71#1927C2×C311yescharacteristic, complemented
72#1926C2×C311yescharacteristic, complemented
73#1925C2×C311yescharacteristic, complemented
74#1925C2×C311yescharacteristic, complemented
75C22×C3×Q8D411yescharacteristic
76C22×C3×Q8C2311yescharacteristic
77C22×C3×D4—21no—
78C22×C3×D4—21no—
79C22×C3×D4C2311yescharacteristic
80C22×C3×D4C2311yescharacteristic
81C22×C3×D4C2311yescharacteristic
82C2×C3×SD16—22no—
83C2×C3×SD16—41no—
84C2×C3×SD16—41no—
85C2×C3×SD16—41no—
86C2×C3×SD16—41no—
87C2×C3×SD16—41no—
88C2×C3×D8—22no—
89C2×C3×D8—41no—
90C2×C3×D8—41no—
91C2×C3×D8—41no—
92C2×C3×D8—41no—
93C2×C3×D8—41no—
94C22×C3×C8C2311yescharacteristic
95C22×C3×C8C2311yescharacteristic
96C22×C3×C8C2311yescharacteristic
97C22×C3×C8C2311yescharacteristic
98C3×#127—41no—
99C3×#127—41no—
100C3×#124—41no—
101C3×#124—41no—
102C3×#124—44no—
103C3×C4×Q8—41no—
104C3×C4×Q8—41no—
105C2×C3×C4⋊C4D411yescharacteristic
106C2×C3×C4⋊C4D411yescharacteristic
107C2×C3×C4⋊C4D411yescharacteristic
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⋊C4—21no—
123C2×C3×C22⋊C4—21no—
124C2×C3×C22⋊C4—21no—
125C2×C3×C22⋊C4—21no—
126C2×C3×C42—21no—
127C2×C3×C42—21no—
128C2×C3×C42C2311yescharacteristic
129C2×C3×C42C2311yescharacteristic
130C2×C3×C42C2311yescharacteristic
131C3×#107—41no—
132C3×#106—41no—
133C3×C4⋊C8—41no—
134C3×#103—22no—
135C3×#103—41no—
136C3×#102—22no—
137C3×#102—22no—
138C3×#102—22no—
139C3×#102—41no—
140C3×#102—41no—
141C3×#102—41no—
142C3×#97—41no—
143C3×#95—21no—
144C3×#95—21no—
145C3×#95—21no—
146C3×#95—21no—
147C3×#95—21no—
148C3×#95—21no—
149C22×SD16C22×C311yescharacteristic
150C22×SD16C22×C311yescharacteristic
151C22×D8C22×C311yescharacteristic
152C22×D8C22×C311yescharacteristic
153C2×#127C22×C311yescharacteristic
154C2×#124—21no—
155C2×#124C22×C311yescharacteristic
156C2×C4×Q8C22×C311yescharacteristic
157C2×#107C22×C311yescharacteristic
158C2×#106C22×C311yescharacteristic
159C2×C4⋊C8C22×C311yescharacteristic
160C2×#103C22×C311yescharacteristic
161C2×#103C22×C311yescharacteristic
162C2×#102C22×C311yescharacteristic
163C2×#102C22×C311yescharacteristic
164C2×#102C22×C311yescharacteristic
165C2×#102C22×C311yescharacteristic
166C2×#102C22×C311yescharacteristic
167C2×#102C22×C311yescharacteristic
168C2×#97C22×C311yescharacteristic
169#397—21no—
170#394—21no—
171#394—21no—
172#393—21no—
173#391C22×C311yescharacteristic
174#391C22×C311yescharacteristic
175#390—21no—
176#390C22×C311yescharacteristic
177#390C22×C311yescharacteristic
178#390C22×C311yescharacteristic
179#390C22×C311yescharacteristic
180#390C22×C311yescharacteristic
181#390C22×C311yescharacteristic
182#388—21no—
183#388—21no—
184C4×C4⋊C4C22×C311yescharacteristic
185C4×C4⋊C4C22×C311yescharacteristic
186#340C22×C311yescharacteristic
187#340C22×C311yescharacteristic
188#336C22×C311yescharacteristic
189#336C22×C311yescharacteristic
190#336C22×C311yescharacteristic
191#336C22×C311yescharacteristic
192C24×C3—21no—
193C24×C3—21no—
194C24×C3—21no—
195C2×C3×Q8—22no—
196C2×C3×Q8—21no—
197C2×C3×Q8—21no—
198C2×C3×Q8—21no—
199C2×C3×Q8—21no—
200C2×C3×Q8—21no—
201C2×C3×Q8—21no—
202C2×C3×Q8—41no—
203C2×C3×Q8—41no—
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—21no—
214C2×C3×D4—21no—
215C2×C3×D4—21no—
216C2×C3×D4—21no—
217C2×C3×D4—21no—
218C2×C3×D4—21no—
219C2×C3×D4—21no—
220C2×C3×D4—21no—
221C2×C3×D4—21no—
222C2×C3×D4—42no—
223C2×C3×D4—42no—
224C2×C3×D4—42no—
225C2×C3×D4—42no—
226C2×C3×D4—81no—
227C2×C3×D4—81no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4C2×D411yescharacteristic
234C22×C3×C4C2×D411yescharacteristic
235C22×C3×C4C2×D411yescharacteristic
236C22×C3×C4C2×D411yescharacteristic
237C22×C3×C4C2×D411yescharacteristic
238C22×C3×C4C2×D411yescharacteristic
239C22×C3×C4C2411yescharacteristic
240C3×SD16—44no—
241C3×SD16—44no—
242C3×D8—44no—
243C3×D8—44no—
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×C8—21no—
251C2×C3×C8—21no—
252C2×C3×C8—21no—
253C2×C3×C8—21no—
254C2×C3×C8#4112yes—
255C2×C3×C8#4112yes—
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—21no—
264C3×C4⋊C4—41no—
265C3×C4⋊C4—41no—
266C3×C4⋊C4—41no—
267C3×C22⋊C4—42no—
268C3×C22⋊C4—42no—
269C3×C22⋊C4—42no—
270C3×C22⋊C4—42no—
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×C22⋊C4—81no—
281C3×C42—21no—
282C3×C42—21no—
283C3×C42—21no—
284C3×C42—21no—
285C3×C42—21no—
286C3×C42—21no—
287C3×C42—42no—
288C3×C42—81no—
289C22×Q8C3×D411yescharacteristic
290C22×Q8C23×C311yescharacteristic
291C22×D4—21no—
292C22×D4—21no—
293C22×D4C23×C311yescharacteristic
294C22×D4C23×C311yescharacteristic
295C22×D4C23×C311yescharacteristic
296C2×SD16—22no—
297C2×SD16—41no—
298C2×SD16—41no—
299C2×SD16—41no—
300C2×SD16—41no—
301C2×SD16—41no—
302C2×D8—22no—
303C2×D8—41no—
304C2×D8—41no—
305C2×D8—41no—
306C2×D8—41no—
307C2×D8—41no—
308C22×C8C23×C311yescharacteristic
309C22×C8C23×C311yescharacteristic
310C22×C8C23×C311yescharacteristic
311C22×C8C23×C311yescharacteristic
312#127—41no—
313#127—41no—
314#124—41no—
315#124—41no—
316#124—44no—
317C4×Q8—41no—
318C4×Q8—41no—
319C2×C4⋊C4C3×D411yescharacteristic
320C2×C4⋊C4C3×D411yescharacteristic
321C2×C4⋊C4C3×D411yescharacteristic
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×C22⋊C4—21no—
339C2×C22⋊C4—21no—
340C2×C42—21no—
341C2×C42—21no—
342C2×C42C23×C311yescharacteristic
343C2×C42C23×C311yescharacteristic
344C2×C42C23×C311yescharacteristic
345#107—41no—
346#106—41no—
347C4⋊C8—41no—
348#103—22no—
349#103—41no—
350#102—22no—
351#102—22no—
352#102—22no—
353#102—41no—
354#102—41no—
355#102—41no—
356#97—41no—
357#95—21no—
358#95—21no—
359#95—21no—
360#95—21no—
361#95—21no—
362#95—21no—
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×C3—41no—
382C23×C3—41no—
383C23×C3—41no—
384C23×C3C22×D411yescharacteristic
385C3×Q8—44no—
386C3×Q8—41no—
387C3×Q8—41no—
388C3×Q8—41no—
389C3×Q8—41no—
390C3×D4—41no—
391C3×D4—41no—
392C3×D4—41no—
393C3×D4—41no—
394C3×D4—41no—
395C3×D4—41no—
396C3×D4—41no—
397C3×D4—41no—
398C3×D4—41no—
399C3×D4—41no—
400C3×D4—41no—
401C3×D4—41no—
402C3×D4—84no—
403C3×D4—84no—
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—21no—
415C2×C3×C4—21no—
416C2×C3×C4—21no—
417C2×C3×C4—21no—
418C2×C3×C4—21no—
419C2×C3×C4—21no—
420C2×C3×C4—21no—
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×C4AGL(1,ℤ/8)12yes—
437C2×C3×C4C2×#4111yescharacteristic
438C2×C3×C4C2×#4111yescharacteristic
439C2×C3×C4H(5,𝔽2)11yescharacteristic
440C2×C3×C4H(5,𝔽2)11yescharacteristic
441C2×C3×C4H(5,𝔽2)11yescharacteristic
442C2×C3×C4H(5,𝔽2)11yescharacteristic
443C3×C8—22no—
444C3×C8—22no—
445C3×C8—41no—
446C3×C8—41no—
447C24—21no—
448C24—21no—
449C24—21no—
450C2×Q8—22no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—41no—
458C2×Q8—41no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—42no—
478C2×D4—42no—
479C2×D4—42no—
480C2×D4—42no—
481C2×D4—81no—
482C2×D4—81no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4C2×C3×D411yescharacteristic
489C22×C4C2×C3×D411yescharacteristic
490C22×C4C2×C3×D411yescharacteristic
491C22×C4C2×C3×D411yescharacteristic
492C22×C4C2×C3×D411yescharacteristic
493C22×C4C2×C3×D411yescharacteristic
494C22×C4C24×C311yescharacteristic
495SD16—44no—
496SD16—44no—
497D8—44no—
498D8—44no—
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—
509C2×C8C3×#4112yes—
510C2×C8C3×#4112yes—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—41no—
520C4⋊C4—41no—
521C4⋊C4—41no—
522C22⋊C4—42no—
523C22⋊C4—42no—
524C22⋊C4—42no—
525C22⋊C4—42no—
526C22⋊C4—42no—
527C22⋊C4—42no—
528C22⋊C4—42no—
529C22⋊C4—42no—
530C22⋊C4—81no—
531C22⋊C4—81no—
532C22⋊C4—81no—
533C22⋊C4—81no—
534C22⋊C4—81no—
535C22⋊C4—81no—
536C42—21no—
537C42—21no—
538C42—21no—
539C42—21no—
540C42—21no—
541C42—21no—
542C42—42no—
543C42—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—81no—
557C22×C3—81no—
558C22×C3—81no—
559C22×C3—81no—
560C22×C3—81no—
561C22×C3—81no—
562C22×C3—81no—
563C22×C3—81no—
564C22×C3—81no—
565C22×C3#53411yescharacteristic
566C22×C3#55011yescharacteristic
567C22×C3#55011yescharacteristic
568C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
569C22×C3#57511yescharacteristic
570C22×C3#57611yescharacteristic
571C22×C3#57711yescharacteristic
572C3×C4—22no—
573C3×C4—41no—
574C3×C4—41no—
575C3×C4—41no—
576C3×C4—41no—
577C3×C4—41no—
578C3×C4—81no—
579C3×C4—81no—
580C3×C4—81no—
581C3×C4—81no—
582C3×C4—81no—
583C3×C4#53811yescharacteristic
584C3×C4#53811yescharacteristic
585C3×C4#55511yescharacteristic
586C3×C4H(3,𝔽4)11yescharacteristic
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23C22×C3×D411yescharacteristic
609Q8—44no—
610Q8—41no—
611Q8—41no—
612Q8—41no—
613Q8—41no—
614D4—41no—
615D4—41no—
616D4—41no—
617D4—41no—
618D4—41no—
619D4—41no—
620D4—41no—
621D4—41no—
622D4—41no—
623D4—41no—
624D4—41no—
625D4—41no—
626D4—84no—
627D4—84no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4C3×AGL(1,ℤ/8)12yes—
661C2×C4C2×C3×#4111yescharacteristic
662C2×C4C2×C3×#4111yescharacteristic
663C2×C4C3×H(5,𝔽2)11yescharacteristic
664C2×C4C3×H(5,𝔽2)11yescharacteristic
665C2×C4C3×H(5,𝔽2)11yescharacteristic
666C2×C4C3×H(5,𝔽2)11yescharacteristic
667C8—22no—
668C8—22no—
669C8—41no—
670C8—41no—
671C2×C3—161no—
672C2×C3—161no—
673C2×C3—161no—
674C2×C3#273311yescharacteristic
675C2×C3#319411yescharacteristic
676C2×C3#319811yescharacteristic
677C2×C3#339711yescharacteristic
678C2×C3#339911yescharacteristic
679C2×C3#340111yescharacteristic
680C2×C3#340311yescharacteristic
681C22—81no—
682C22—81no—
683C22—81no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22—81no—
690C22—81no—
691C22—81no—
692C22—81no—
693C22—81no—
694C22—81no—
695C22—81no—
696C22—81no—
697C22—81no—
698C22—81no—
699C22—81no—
700C22—81no—
701C22—81no—
702C22C3×#53411yescharacteristic
703C22C3×#55011yescharacteristic
704C22C3×#55011yescharacteristic
705C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
706C22C3×#57511yescharacteristic
707C22C3×#57611yescharacteristic
708C22C3×#57711yescharacteristic
709C4—22no—
710C4—41no—
711C4—41no—
712C4—41no—
713C4—41no—
714C4—41no—
715C4—81no—
716C4—81no—
717C4—81no—
718C4—81no—
719C4—81no—
720C4C3×#53811yescharacteristic
721C4C3×#53811yescharacteristic
722C4C3×#55511yescharacteristic
723C4C3×H(3,𝔽4)11yescharacteristic
724C3#3267511yescharacteristic, direct product factor, Sylow
725C2—161no—
726C2—161no—
727C2—161no—
728C2C3×#273311yescharacteristic
729C2C3×#319411yescharacteristic
730C2C3×#319811yescharacteristic
731C2C3×#339711yescharacteristic
732C2C3×#339911yescharacteristic
733C2C3×#340111yescharacteristic
734C2C3×#340311yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC3×#2011C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C2×C3×C4×Q8 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×#2592C2semidirect
2. C3×#2548C2semidirect
3. C3×#2055C2semidirect
4. C3×#2054C2semidirect
5. C3×#2014C2semidirect
6. C3×#2012C2semidirect
7. C3×#2012C2semidirect
9. C3×#1985C2semidirect
10. C3×#1973C2semidirect
11. C3×#1972C2semidirect
12. C3×#1927C2semidirect
13. C3×#1926C2semidirect
14. C3×#1925C2semidirect
15. C3×#1925C2semidirect
16. #32675C3direct (N × H)
60. #2592C2×C3semidirect
61. #2548C2×C3semidirect
62. #2055C2×C3semidirect
63. #2054C2×C3semidirect
64. #2014C2×C3semidirect
65. #2012C2×C3semidirect
66. #2012C2×C3semidirect
68. #1985C2×C3semidirect
69. #1973C2×C3semidirect
70. #1972C2×C3semidirect
71. #1927C2×C3semidirect
72. #1926C2×C3semidirect
73. #1925C2×C3semidirect
74. #1925C2×C3semidirect
724. C3#32675direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#25922
C3×#25482
C3×#20552
C3×#20542
C3×#20142
C3×#20122
C3×#20112
C3×#19852
C3×#19732
C3×#19722
C3×#19272
C3×#19262
C3×#19252
#326753