Finite Group Databasebeta

← C3×#25524 #10644131

Subgroups — C3×#25524 #10644131

Order 768.

1246 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3494C211yesmaximal, characteristic, complemented
2C3×#3094C211yesmaximal, characteristic, complemented
3C3×#3055C211yesmaximal, characteristic, complemented
4C3×#2856C211yesmaximal, characteristic, complemented
5C3×#2060C211yesmaximal, characteristic, complemented
6C3×#2037C211yesmaximal, characteristic, complemented
7C3×#2027C211yesmaximal, characteristic, complemented
8C3×#2002C211yesmaximal, characteristic, complemented
9C3×#1900C211yesmaximal, characteristic, complemented
10C3×#1896C211yesmaximal, characteristic, complemented
11C3×#1887C211yesmaximal, characteristic, complemented
12C3×#1883C211yesmaximal, characteristic, complemented
13C3×#1859C211yesmaximal, characteristic, complemented
14C3×#1856C211yesmaximal, characteristic, complemented
15C2×C3×#339C211yesmaximal, characteristic, complemented
16#25524C311yesmaximal, characteristic, direct product factor, Sylow
17C2×C3×AGL(1,ℤ/8)C2211yescharacteristic
18C22×C3×M16C2211yescharacteristic
19C3×#555—21no—
20C3×#553—21no—
21C3×#553—21no—
22C3×#551—22no—
23C3×#547—21no—
24C3×#546—22no—
25C3×#544C2211yescharacteristic
26C3×#542—21no—
27C3×#540—21no—
28C3×#535C2211yescharacteristic
29C3×#532—21no—
30C2×C3×#127C2211yescharacteristic
31C3×#529—21no—
32C3×#525C2211yescharacteristic
33C2×C3×#121—22no—
34C2×C3×#121C2211yescharacteristic
35C2×C3×#121C2211yescharacteristic
36C3×#520C2211yescharacteristic
37C3×#518C2211yescharacteristic
38C2×C3×#117C2211yescharacteristic
39C22×C3×C42C2211yescharacteristic
40C3×#482—21no—
41C3×#482—21no—
42C3×#481—21no—
43C3×#480—21no—
44C3×#469—21no—
45C3×#468—21no—
46C3×#466—21no—
47C3×#465—21no—
48C3×#428C2211yescharacteristic
49C3×#428C2211yescharacteristic
50C3×#428C2211yescharacteristic
51C2×C3×#104C2211yescharacteristic
52C2×C3×#104C2211yescharacteristic
53C3×#418C2211yescharacteristic
54C3×#418C2211yescharacteristic
55C3×#418C2211yescharacteristic
56C3×#417C2211yescharacteristic
57C2×C3×#100C2211yescharacteristic
58C2×C3×#100C2211yescharacteristic
59C3×#407C2211yescharacteristic
60C3×#390—22no—
61C3×#390C2211yescharacteristic
62C3×#390C2211yescharacteristic
63C3×#384C2211yescharacteristic
64C3×#343C2211yescharacteristic
65C3×#343C2211yescharacteristic
66C3×#339C2211yescharacteristic
67C3×#339C2211yescharacteristic
68C3×#339C2211yescharacteristic
69C3×#339C2211yescharacteristic
70C3×#339C2211yescharacteristic
71C3×#339C2211yescharacteristic
72#3494C2×C311yescharacteristic, complemented
73#3094C2×C311yescharacteristic, complemented
74#3055C2×C311yescharacteristic, complemented
75#2856C2×C311yescharacteristic, complemented
76#2060C2×C311yescharacteristic, complemented
77#2037C2×C311yescharacteristic, complemented
78#2027C2×C311yescharacteristic, complemented
79#2002C2×C311yescharacteristic, complemented
80#1900C2×C311yescharacteristic, complemented
81#1896C2×C311yescharacteristic, complemented
82#1887C2×C311yescharacteristic, complemented
83#1883C2×C311yescharacteristic, complemented
84#1859C2×C311yescharacteristic, complemented
85#1856C2×C311yescharacteristic, complemented
86C2×#339C2×C311yescharacteristic, complemented
87C2×C3×#41—22no—
88C2×C3×#41C2311yescharacteristic
89C22×C3×D4—22no—
90C22×C3×D4—21no—
91C22×C3×D4D412yes—
92C22×C3×D4C2311yescharacteristic
93C22×C3×D4C2311yescharacteristic
94C23×C3×C4—21no—
95C23×C3×C4C2311yescharacteristic
96C3×AGL(1,ℤ/8)—22no—
97C3×AGL(1,ℤ/8)—41no—
98C2×C3×SD16—21no—
99C2×C3×D8—21no—
100C2×C3×M16—21no—
101C2×C3×M16—22no—
102C2×C3×M16—41no—
103C2×C3×M16C2311yescharacteristic
104C2×C3×M16C2311yescharacteristic
105C2×C3×M16C2311yescharacteristic
106C2×C3×M16C2311yescharacteristic
107C22×C3×C8—21no—
108C3×C4⋊Q8—21no—
109C3×C4⋊Q8—21no—
110C3×#127—21no—
111C3×#127—22no—
112C3×#127—41no—
113C3×#126—22no—
114C3×#126—22no—
115C3×#125—21no—
116C3×#125—21no—
117C3×#124—22no—
118C3×#124—22no—
119C3×#124—21no—
120C3×#123—22no—
121C3×#123—22no—
122C3×#123—22no—
123C3×#123—22no—
124C3×#123—21no—
125C3×C22⋊Q8—22no—
126C3×C22⋊Q8—22no—
127C3×C22⋊Q8D411yescharacteristic, complemented
128C3×C22⋊Q8D411yescharacteristic, complemented
129C3×#121—22no—
130C3×#121—22no—
131C3×#121—22no—
132C3×#121—21no—
133C3×#121—21no—
134C3×#121—21no—
135C3×#121—21no—
136C3×#121—21no—
137C3×#121—21no—
138C3×#121—21no—
139C3×#121—21no—
140C3×#121—21no—
141C3×#121—21no—
142C3×#121—48no—
143C3×#121D411yescharacteristic, complemented
144C3×#121D411yescharacteristic, complemented
145C3×#120—21no—
146C3×#120—22no—
147C3×C4×Q8—21no—
148C3×C4×D4—22no—
149C3×C4×D4—22no—
150C3×C4×D4—21no—
151C3×C4×D4—22no—
152C3×C4×D4—21no—
153C3×C4×D4—21no—
154C3×C4×D4—21no—
155C3×C4×D4—21no—
156C3×C4×D4—21no—
157C3×C4×D4—21no—
158C3×#117—22no—
159C3×#117—21no—
160C3×#117—21no—
161C3×#117—21no—
162C3×#117D411yescharacteristic, complemented
163C3×#117D411yescharacteristic, complemented
164C3×#117C2311yescharacteristic
165C3×#117C2311yescharacteristic
166C3×#117C2311yescharacteristic
167C2×C3×C4⋊C4—21no—
168C2×C3×C4⋊C4—22no—
169C2×C3×C4⋊C4D411yescharacteristic, complemented
170C2×C3×C4⋊C4D411yescharacteristic, complemented
171C2×C3×C4⋊C4C2311yescharacteristic
172C2×C3×C4⋊C4C2311yescharacteristic
173C2×C3×C22⋊C4—21no—
174C2×C3×C22⋊C4—22no—
175C2×C3×C22⋊C4—22no—
176C2×C3×C22⋊C4—21no—
177C2×C3×C22⋊C4—22no—
178C2×C3×C22⋊C4D412yes—
179C2×C3×C42—21no—
180C2×C3×C42—22no—
181C2×C3×C42—21no—
182C2×C3×C42—41no—
183C2×C3×C42C2311yescharacteristic
184C2×C3×C42C2311yescharacteristic
185C3×#107—21no—
186C3×#107—21no—
187C3×#107—21no—
188C3×#106—21no—
189C3×#106—21no—
190C3×#106—21no—
191C3×#104—22no—
192C3×#104—41no—
193C3×#103—21no—
194C3×#102—21no—
195C3×#102—21no—
196C3×#102—21no—
197C3×#102—21no—
198C3×#102—21no—
199C3×#102—21no—
200C3×#102—21no—
201C3×#100—22no—
202C3×#100—41no—
203C3×C22⋊C8—21no—
204C3×C22⋊C8—21no—
205C2×AGL(1,ℤ/8)C22×C311yescharacteristic
206C22×M16C22×C311yescharacteristic
207#555—21no—
208#553—21no—
209#553—21no—
210#551—22no—
211#547—21no—
212#546—22no—
213#544C22×C311yescharacteristic
214#542—21no—
215#540—21no—
216#535C22×C311yescharacteristic
217#532—21no—
218C2×#127C22×C311yescharacteristic
219#529—21no—
220#525C22×C311yescharacteristic
221C2×#121—22no—
222C2×#121C22×C311yescharacteristic
223C2×#121C22×C311yescharacteristic
224#520C22×C311yescharacteristic
225#518C22×C311yescharacteristic
226C2×#117C22×C311yescharacteristic
227C22×C42C22×C311yescharacteristic
228#482—21no—
229#482—21no—
230#481—21no—
231#480—21no—
232#469—21no—
233#468—21no—
234#466—21no—
235#465—21no—
236#428C22×C311yescharacteristic
237#428C22×C311yescharacteristic
238#428C22×C311yescharacteristic
239C2×#104C22×C311yescharacteristic
240C2×#104C22×C311yescharacteristic
241#418C22×C311yescharacteristic
242#418C22×C311yescharacteristic
243#418C22×C311yescharacteristic
244#417C22×C311yescharacteristic
245C2×#100C22×C311yescharacteristic
246C2×#100C22×C311yescharacteristic
247#407C22×C311yescharacteristic
248#390—22no—
249#390C22×C311yescharacteristic
250#390C22×C311yescharacteristic
251#384C22×C311yescharacteristic
252#343C22×C311yescharacteristic
253#343C22×C311yescharacteristic
254#339C22×C311yescharacteristic
255#339C22×C311yescharacteristic
256#339C22×C311yescharacteristic
257#339C22×C311yescharacteristic
258#339C22×C311yescharacteristic
259#339C22×C311yescharacteristic
260C24×C3—21no—
261C24×C3C2×D411yescharacteristic
262C24×C3C2×D412yes—
263C3×#41—21no—
264C3×#41—21no—
265C3×#41—21no—
266C3×#41—21no—
267C3×#41—84no—
268C2×C3×Q8—22no—
269C2×C3×Q8C2×D411yescharacteristic
270C2×C3×D4—21no—
271C2×C3×D4—22no—
272C2×C3×D4—21no—
273C2×C3×D4—22no—
274C2×C3×D4—22no—
275C2×C3×D4—21no—
276C2×C3×D4—22no—
277C2×C3×D4—21no—
278C2×C3×D4—21no—
279C2×C3×D4—21no—
280C2×C3×D4—21no—
281C2×C3×D4—21no—
282C2×C3×D4—21no—
283C2×C3×D4—21no—
284C2×C3×D4—21no—
285C2×C3×D4—21no—
286C2×C3×D4—21no—
287C2×C3×D4—21no—
288C2×C3×D4—21no—
289C2×C3×D4—44no—
290C2×C3×D4—44no—
291C2×C3×D4—44no—
292C2×C3×D4—44no—
293C2×C3×D4—44no—
294C2×C3×D4—41no—
295C2×C3×D4—41no—
296C2×C3×D4C2×D411yescharacteristic
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—24no—
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4—22no—
306C22×C3×C4—22no—
307C22×C3×C4—22no—
308C22×C3×C4—21no—
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—42no—
312C22×C3×C4—42no—
313C22×C3×C4C2×D411yescharacteristic
314C22×C3×C4C2×D411yescharacteristic
315C22×C3×C4C2×D411yescharacteristic
316C22×C3×C4C2×D411yescharacteristic
317C22×C3×C4C2×D411yescharacteristic
318C22×C3×C4C2×D412yes—
319C22×C3×C4C2411yescharacteristic
320C3×SD16—42no—
321C3×D8—42no—
322C3×M16—21no—
323C3×M16—21no—
324C3×M16—21no—
325C3×M16—21no—
326C3×M16—21no—
327C3×M16—21no—
328C3×M16—21no—
329C3×M16—42no—
330C3×M16#4112yescomplemented
331C2×C3×C8—21no—
332C2×C3×C8—21no—
333C2×C3×C8—21no—
334C2×C3×C8—21no—
335C2×C3×C8—42no—
336C3×C4⋊C4—22no—
337C3×C4⋊C4—22no—
338C3×C4⋊C4—22no—
339C3×C4⋊C4—22no—
340C3×C4⋊C4—21no—
341C3×C4⋊C4—21no—
342C3×C4⋊C4—21no—
343C3×C4⋊C4—21no—
344C3×C4⋊C4—21no—
345C3×C4⋊C4—21no—
346C3×C4⋊C4—21no—
347C3×C4⋊C4—21no—
348C3×C4⋊C4—44no—
349C3×C4⋊C4C2×D411yescharacteristic
350C3×C4⋊C4C2×D411yescharacteristic
351C3×C4⋊C4C2×D411yescharacteristic
352C3×C4⋊C4C2×D411yescharacteristic
353C3×C4⋊C4C2×D411yescharacteristic
354C3×C4⋊C4C2×D411yescharacteristic
355C3×C22⋊C4—22no—
356C3×C22⋊C4—22no—
357C3×C22⋊C4—22no—
358C3×C22⋊C4—22no—
359C3×C22⋊C4—22no—
360C3×C22⋊C4—21no—
361C3×C22⋊C4—21no—
362C3×C22⋊C4—21no—
363C3×C22⋊C4—21no—
364C3×C22⋊C4—21no—
365C3×C22⋊C4—21no—
366C3×C22⋊C4—21no—
367C3×C22⋊C4—22no—
368C3×C22⋊C4—22no—
369C3×C22⋊C4—21no—
370C3×C22⋊C4—21no—
371C3×C22⋊C4—44no—
372C3×C22⋊C4—44no—
373C3×C22⋊C4—41no—
374C3×C22⋊C4—41no—
375C3×C42—22no—
376C3×C42—21no—
377C3×C42—21no—
378C3×C42—21no—
379C3×C42—21no—
380C3×C42—21no—
381C3×C42—21no—
382C3×C42—21no—
383C3×C42—21no—
384C3×C42—42no—
385C3×C42#4112yescomplemented
386C2×#41—22no—
387C2×#41C23×C311yescharacteristic
388C22×D4—21no—
389C22×D4—22no—
390C22×D4C3×D412yes—
391C22×D4C23×C311yescharacteristic
392C22×D4C23×C311yescharacteristic
393C23×C4—21no—
394C23×C4C23×C311yescharacteristic
395AGL(1,ℤ/8)—22no—
396AGL(1,ℤ/8)—41no—
397C2×SD16—21no—
398C2×D8—21no—
399C2×M16—21no—
400C2×M16—22no—
401C2×M16—41no—
402C2×M16C23×C311yescharacteristic
403C2×M16C23×C311yescharacteristic
404C2×M16C23×C311yescharacteristic
405C2×M16C23×C311yescharacteristic
406C22×C8—21no—
407C4⋊Q8—21no—
408C4⋊Q8—21no—
409#127—21no—
410#127—22no—
411#127—41no—
412#126—22no—
413#126—22no—
414#125—21no—
415#125—21no—
416#124—22no—
417#124—22no—
418#124—21no—
419#123—22no—
420#123—22no—
421#123—22no—
422#123—22no—
423#123—21no—
424C22⋊Q8—22no—
425C22⋊Q8—22no—
426C22⋊Q8C3×D411yescharacteristic, complemented
427C22⋊Q8C3×D411yescharacteristic, complemented
428#121—22no—
429#121—22no—
430#121—22no—
431#121—21no—
432#121—21no—
433#121—21no—
434#121—21no—
435#121—21no—
436#121—21no—
437#121—21no—
438#121—21no—
439#121—21no—
440#121—21no—
441#121—48no—
442#121C3×D411yescharacteristic, complemented
443#121C3×D411yescharacteristic, complemented
444#120—21no—
445#120—22no—
446C4×Q8—21no—
447C4×D4—22no—
448C4×D4—22no—
449C4×D4—21no—
450C4×D4—22no—
451C4×D4—21no—
452C4×D4—21no—
453C4×D4—21no—
454C4×D4—21no—
455C4×D4—21no—
456C4×D4—21no—
457#117—22no—
458#117—21no—
459#117—21no—
460#117—21no—
461#117C3×D411yescharacteristic, complemented
462#117C3×D411yescharacteristic, complemented
463#117C23×C311yescharacteristic
464#117C23×C311yescharacteristic
465#117C23×C311yescharacteristic
466C2×C4⋊C4—21no—
467C2×C4⋊C4—22no—
468C2×C4⋊C4C3×D411yescharacteristic, complemented
469C2×C4⋊C4C3×D411yescharacteristic, complemented
470C2×C4⋊C4C23×C311yescharacteristic
471C2×C4⋊C4C23×C311yescharacteristic
472C2×C22⋊C4—21no—
473C2×C22⋊C4—22no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4C3×D412yes—
478C2×C42—21no—
479C2×C42—22no—
480C2×C42—21no—
481C2×C42—41no—
482C2×C42C23×C311yescharacteristic
483C2×C42C23×C311yescharacteristic
484#107—21no—
485#107—21no—
486#107—21no—
487#106—21no—
488#106—21no—
489#106—21no—
490#104—22no—
491#104—41no—
492#103—21no—
493#102—21no—
494#102—21no—
495#102—21no—
496#102—21no—
497#102—21no—
498#102—21no—
499#102—21no—
500#100—22no—
501#100—41no—
502C22⋊C8—21no—
503C22⋊C8—21no—
504C23×C3—21no—
505C23×C3—21no—
506C23×C3—22no—
507C23×C3—22no—
508C23×C3—21no—
509C23×C3—22no—
510C23×C3—22no—
511C23×C3—41no—
512C23×C3—42no—
513C23×C3—42no—
514C23×C3—42no—
515C23×C3—42no—
516C23×C3—41no—
517C23×C3—41no—
518C23×C3—41no—
519C23×C3#12011yescharacteristic
520C23×C3#12011yescharacteristic
521C23×C3C22×D411yescharacteristic
522C3×Q8—21no—
523C3×Q8—21no—
524C3×Q8—82no—
525C3×D4—21no—
526C3×D4—21no—
527C3×D4—41no—
528C3×D4—41no—
529C3×D4—44no—
530C3×D4—42no—
531C3×D4—41no—
532C3×D4—41no—
533C3×D4—41no—
534C3×D4—41no—
535C3×D4—41no—
536C3×D4—41no—
537C3×D4—41no—
538C3×D4—41no—
539C3×D4—88no—
540C3×D4—81no—
541C3×D4—82no—
542C3×D4—82no—
543C3×D4—82no—
544C3×D4—82no—
545C3×D4—82no—
546C2×C3×C4—22no—
547C2×C3×C4—22no—
548C2×C3×C4—22no—
549C2×C3×C4—21no—
550C2×C3×C4—21no—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—22no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
567C2×C3×C4—22no—
568C2×C3×C4—48no—
569C2×C3×C4—41no—
570C2×C3×C4—41no—
571C2×C3×C4—42no—
572C2×C3×C4—41no—
573C2×C3×C4—41no—
574C2×C3×C4—42no—
575C2×C3×C4—42no—
576C2×C3×C4—41no—
577C2×C3×C4—81no—
578C2×C3×C4—82no—
579C2×C3×C4—82no—
580C2×C3×C4—82no—
581C2×C3×C4#12011yescharacteristic
582C2×C3×C4#12011yescharacteristic
583C2×C3×C4C22×D411yescharacteristic
584C2×C3×C4C22×D411yescharacteristic
585C2×C3×C4C2×#4111yescharacteristic
586C2×C3×C4C2×#4111yescharacteristic
587C2×C3×C4H(5,𝔽2)11yescharacteristic
588C2×C3×C42−1+411yescharacteristic
589C3×C8—22no—
590C3×C8—41no—
591C3×C8—41no—
592C3×C8—41no—
593C24—21no—
594C24C2×C3×D411yescharacteristic
595C24C2×C3×D412yes—
596#41—21no—
597#41—21no—
598#41—21no—
599#41—21no—
600#41—84no—
601C2×Q8—22no—
602C2×Q8C2×C3×D411yescharacteristic
603C2×D4—21no—
604C2×D4—22no—
605C2×D4—21no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—21no—
609C2×D4—22no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—44no—
623C2×D4—44no—
624C2×D4—44no—
625C2×D4—44no—
626C2×D4—44no—
627C2×D4—41no—
628C2×D4—41no—
629C2×D4C2×C3×D411yescharacteristic
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—24no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—42no—
645C22×C4—42no—
646C22×C4C2×C3×D411yescharacteristic
647C22×C4C2×C3×D411yescharacteristic
648C22×C4C2×C3×D411yescharacteristic
649C22×C4C2×C3×D411yescharacteristic
650C22×C4C2×C3×D411yescharacteristic
651C22×C4C2×C3×D412yes—
652C22×C4C24×C311yescharacteristic
653SD16—42no—
654D8—42no—
655M16—21no—
656M16—21no—
657M16—21no—
658M16—21no—
659M16—21no—
660M16—21no—
661M16—21no—
662M16—42no—
663M16C3×#4112yescomplemented
664C2×C8—21no—
665C2×C8—21no—
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—42no—
669C4⋊C4—22no—
670C4⋊C4—22no—
671C4⋊C4—22no—
672C4⋊C4—22no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—44no—
682C4⋊C4C2×C3×D411yescharacteristic
683C4⋊C4C2×C3×D411yescharacteristic
684C4⋊C4C2×C3×D411yescharacteristic
685C4⋊C4C2×C3×D411yescharacteristic
686C4⋊C4C2×C3×D411yescharacteristic
687C4⋊C4C2×C3×D411yescharacteristic
688C22⋊C4—22no—
689C22⋊C4—22no—
690C22⋊C4—22no—
691C22⋊C4—22no—
692C22⋊C4—22no—
693C22⋊C4—21no—
694C22⋊C4—21no—
695C22⋊C4—21no—
696C22⋊C4—21no—
697C22⋊C4—21no—
698C22⋊C4—21no—
699C22⋊C4—21no—
700C22⋊C4—22no—
701C22⋊C4—22no—
702C22⋊C4—21no—
703C22⋊C4—21no—
704C22⋊C4—44no—
705C22⋊C4—44no—
706C22⋊C4—41no—
707C22⋊C4—41no—
708C42—22no—
709C42—21no—
710C42—21no—
711C42—21no—
712C42—21no—
713C42—21no—
714C42—21no—
715C42—21no—
716C42—21no—
717C42—42no—
718C42C3×#4112yescomplemented
719C22×C3—21no—
720C22×C3—21no—
721C22×C3—21no—
722C22×C3—21no—
723C22×C3—21no—
724C22×C3—21no—
725C22×C3—21no—
726C22×C3—42no—
727C22×C3—42no—
728C22×C3—41no—
729C22×C3—42no—
730C22×C3—41no—
731C22×C3—42no—
732C22×C3—42no—
733C22×C3—41no—
734C22×C3—82no—
735C22×C3—82no—
736C22×C3—82no—
737C22×C3—82no—
738C22×C3—81no—
739C22×C3—81no—
740C22×C3—81no—
741C22×C3#45312yes—
742C22×C3C2×#12011yescharacteristic
743C22×C3#54611yescharacteristic
744C22×C3#54711yescharacteristic
745C3×C4—24no—
746C3×C4—21no—
747C3×C4—21no—
748C3×C4—42no—
749C3×C4—41no—
750C3×C4—41no—
751C3×C4—41no—
752C3×C4—42no—
753C3×C4—41no—
754C3×C4—41no—
755C3×C4—41no—
756C3×C4—41no—
757C3×C4—81no—
758C3×C4#53211yescharacteristic
759C3×C4#53711yescharacteristic
760C3×C4#54611yescharacteristic
761C3×C4#54711yescharacteristic
762C23—22no—
763C23—21no—
764C23—21no—
765C23—22no—
766C23—21no—
767C23—22no—
768C23—22no—
769C23—41no—
770C23—42no—
771C23—42no—
772C23—42no—
773C23—42no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23C3×#12011yescharacteristic
778C23C3×#12011yescharacteristic
779C23C22×C3×D411yescharacteristic
780Q8—21no—
781Q8—21no—
782Q8—82no—
783D4—21no—
784D4—21no—
785D4—44no—
786D4—42no—
787D4—41no—
788D4—41no—
789D4—41no—
790D4—41no—
791D4—41no—
792D4—41no—
793D4—41no—
794D4—41no—
795D4—41no—
796D4—41no—
797D4—88no—
798D4—82no—
799D4—81no—
800D4—82no—
801D4—82no—
802D4—82no—
803D4—82no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—22no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—22no—
826C2×C4—48no—
827C2×C4—41no—
828C2×C4—42no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—41no—
835C2×C4—81no—
836C2×C4—82no—
837C2×C4—82no—
838C2×C4—82no—
839C2×C4C3×#12011yescharacteristic
840C2×C4C3×#12011yescharacteristic
841C2×C4C22×C3×D411yescharacteristic
842C2×C4C22×C3×D411yescharacteristic
843C2×C4C2×C3×#4111yescharacteristic
844C2×C4C2×C3×#4111yescharacteristic
845C2×C4C3×H(5,𝔽2)11yescharacteristic
846C2×C4C3×2−1+411yescharacteristic
847C8—22no—
848C8—41no—
849C8—41no—
850C8—41no—
851C2×C3—21no—
852C2×C3—21no—
853C2×C3—22no—
854C2×C3—41no—
855C2×C3—81no—
856C2×C3—82no—
857C2×C3—161no—
858C2×C3#243011yescharacteristic
859C2×C3C2×#45311yescharacteristic
860C2×C3#301811yescharacteristic
861C22—21no—
862C22—21no—
863C22—21no—
864C22—21no—
865C22—21no—
866C22—21no—
867C22—21no—
868C22—42no—
869C22—42no—
870C22—41no—
871C22—42no—
872C22—41no—
873C22—42no—
874C22—42no—
875C22—41no—
876C22—82no—
877C22—82no—
878C22—82no—
879C22—82no—
880C22—81no—
881C22—81no—
882C22—81no—
883C22C3×#45312yes—
884C22C2×C3×#12011yescharacteristic
885C22C3×#54611yescharacteristic
886C22C3×#54711yescharacteristic
887C4—24no—
888C4—21no—
889C4—21no—
890C4—42no—
891C4—41no—
892C4—41no—
893C4—41no—
894C4—42no—
895C4—41no—
896C4—41no—
897C4—41no—
898C4—41no—
899C4—81no—
900C4C3×#53211yescharacteristic
901C4C3×#53711yescharacteristic
902C4C3×#54611yescharacteristic
903C4C3×#54711yescharacteristic
904C3#2552411yescharacteristic, direct product factor, Sylow
905C2—21no—
906C2—21no—
907C2—22no—
908C2—41no—
909C2—82no—
910C2—81no—
911C2—161no—
912C2C3×#243011yescharacteristic
913C2C2×C3×#45311yescharacteristic
914C2C3×#301811yescharacteristic
subgroupG/H
center, socleC22×C3C2×#120
commutator, Frattini, cosocleC22×C4C24×C3
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×#3494C2semidirect
2. C3×#3094C2semidirect
3. C3×#3055C2semidirect
4. C3×#2856C2semidirect
5. C3×#2060C2semidirect
6. C3×#2037C2semidirect
7. C3×#2027C2semidirect
8. C3×#2002C2semidirect
9. C3×#1900C2semidirect
10. C3×#1896C2semidirect
11. C3×#1887C2semidirect
12. C3×#1883C2semidirect
13. C3×#1859C2semidirect
14. C3×#1856C2semidirect
15. C2×C3×#339C2semidirect
16. #25524C3direct (N × H)
72. #3494C2×C3semidirect
73. #3094C2×C3semidirect
74. #3055C2×C3semidirect
75. #2856C2×C3semidirect
76. #2060C2×C3semidirect
77. #2037C2×C3semidirect
78. #2027C2×C3semidirect
79. #2002C2×C3semidirect
80. #1900C2×C3semidirect
81. #1896C2×C3semidirect
82. #1887C2×C3semidirect
83. #1883C2×C3semidirect
84. #1859C2×C3semidirect
85. #1856C2×C3semidirect
86. C2×#339C2×C3semidirect
127. C3×C22⋊Q8D4semidirect
128. C3×C22⋊Q8D4semidirect
143. C3×#121D4semidirect
144. C3×#121D4semidirect
162. C3×#117D4semidirect
163. C3×#117D4semidirect
169. C2×C3×C4⋊C4D4semidirect
170. C2×C3×C4⋊C4D4semidirect
330. C3×M16#41semidirect
385. C3×C42#41semidirect
426. C22⋊Q8C3×D4semidirect
427. C22⋊Q8C3×D4semidirect
442. #121C3×D4semidirect
443. #121C3×D4semidirect
461. #117C3×D4semidirect
462. #117C3×D4semidirect
468. C2×C4⋊C4C3×D4semidirect
469. C2×C4⋊C4C3×D4semidirect
663. M16C3×#41semidirect
718. C42C3×#41semidirect
904. C3#25524direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#34942
C3×#30942
C3×#30552
C3×#28562
C3×#20602
C3×#20372
C3×#20272
C3×#20022
C3×#19002
C3×#18962
C3×#18872
C3×#18832
C3×#18592
C3×#18562
C2×C3×#3392
#255243